LMFDB - Embedded newform 29.9.f.a.15.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,9,Mod(2,29)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(28))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 9, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("29.2");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	29.f (of order $28$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.8139796918$
Analytic rank:	$0$
Dimension:	$228$
Relative dimension:	$19$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			15.5
Character	$\chi$	$=$	29.15
Dual form			29.9.f.a.2.5

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-21.4136 + 2.41273i) q^{2} +(91.7346 - 57.6407i) q^{3} +(203.138 - 46.3649i) q^{4} +(-731.114 - 583.044i) q^{5} +(-1825.29 + 1455.62i) q^{6} +(246.757 - 1081.11i) q^{7} +(968.946 - 339.049i) q^{8} +(2246.08 - 4664.03i) q^{9} +O(q^{10})$	\(q+(-21.4136 + 2.41273i) q^{2} +(91.7346 - 57.6407i) q^{3} +(203.138 - 46.3649i) q^{4} +(-731.114 - 583.044i) q^{5} +(-1825.29 + 1455.62i) q^{6} +(246.757 - 1081.11i) q^{7} +(968.946 - 339.049i) q^{8} +(2246.08 - 4664.03i) q^{9} +(17062.5 + 10721.1i) q^{10} +(1725.95 + 603.935i) q^{11} +(15962.3 - 15962.3i) q^{12} +(-2140.33 - 4444.45i) q^{13} +(-2675.52 + 23745.9i) q^{14} +(-100676. - 11343.4i) q^{15} +(-67988.9 + 32741.7i) q^{16} +(-11256.2 - 11256.2i) q^{17} +(-36843.5 + 105293. i) q^{18} +(-124871. + 198730. i) q^{19} +(-175550. - 84540.4i) q^{20} +(-39680.0 - 113399. i) q^{21} +(-38415.8 - 8768.16i) q^{22} +(-242749. - 304398. i) q^{23} +(69342.9 - 86953.2i) q^{24} +(107665. + 471713. i) q^{25} +(56555.5 + 90007.5i) q^{26} +(16792.2 + 149034. i) q^{27} -231056. i q^{28} +(-643056. + 294492. i) q^{29} +2.18319e6 q^{30} +(505726. - 56981.6i) q^{31} +(1.15437e6 - 725339. i) q^{32} +(193140. - 44083.0i) q^{33} +(268195. + 213878. i) q^{34} +(-810745. + 646548. i) q^{35} +(240017. - 1.05158e6i) q^{36} +(-2.15384e6 + 753660. i) q^{37} +(2.19444e6 - 4.55680e6i) q^{38} +(-452524. - 284340. i) q^{39} +(-906091. - 317055. i) q^{40} +(-1.56467e6 + 1.56467e6i) q^{41} +(1.12329e6 + 2.33254e6i) q^{42} +(110419. - 979994. i) q^{43} +(378607. + 42658.8i) q^{44} +(-4.36148e6 + 2.10038e6i) q^{45} +(5.93256e6 + 5.93256e6i) q^{46} +(1.52363e6 - 4.35427e6i) q^{47} +(-4.34968e6 + 6.92247e6i) q^{48} +(4.08599e6 + 1.96771e6i) q^{49} +(-3.44362e6 - 9.84129e6i) q^{50} +(-1.68140e6 - 383770. i) q^{51} +(-640850. - 803600. i) q^{52} +(8.59706e6 - 1.07804e7i) q^{53} +(-719160. - 3.15084e6i) q^{54} +(-909744. - 1.44785e6i) q^{55} +(-127456. - 1.13120e6i) q^{56} +2.54281e7i q^{57} +(1.30596e7 - 7.85765e6i) q^{58} +9.44114e6 q^{59} +(-2.09770e7 + 2.36354e6i) q^{60} +(-1.14038e7 + 7.16550e6i) q^{61} +(-1.06919e7 + 2.44036e6i) q^{62} +(-4.48812e6 - 3.57915e6i) q^{63} +(-7.86551e6 + 6.27253e6i) q^{64} +(-1.02648e6 + 4.49731e6i) q^{65} +(-4.02946e6 + 1.40997e6i) q^{66} +(210114. - 436306. i) q^{67} +(-2.80847e6 - 1.76468e6i) q^{68} +(-3.98142e7 - 1.39316e7i) q^{69} +(1.58010e7 - 1.58010e7i) q^{70} +(3.75374e6 + 7.79473e6i) q^{71} +(594995. - 5.28073e6i) q^{72} +(-3.47680e7 - 3.91741e6i) q^{73} +(4.43029e7 - 2.13352e7i) q^{74} +(3.70665e7 + 3.70665e7i) q^{75} +(-1.61518e7 + 4.61593e7i) q^{76} +(1.07881e6 - 1.71692e6i) q^{77} +(1.03762e7 + 4.99691e6i) q^{78} +(-1.28345e7 - 3.66789e7i) q^{79} +(6.87975e7 + 1.57026e7i) q^{80} +(3.13072e7 + 3.92580e7i) q^{81} +(2.97300e7 - 3.72802e7i) q^{82} +(-2.06941e7 - 9.06670e7i) q^{83} +(-1.33182e7 - 2.11959e7i) q^{84} +(1.66671e6 + 1.47925e7i) q^{85} +2.12516e7i q^{86} +(-4.20157e7 + 6.40813e7i) q^{87} +1.87711e6 q^{88} +(-1.02040e8 + 1.14971e7i) q^{89} +(8.83272e7 - 5.54996e7i) q^{90} +(-5.33310e6 + 1.21725e6i) q^{91} +(-6.34250e7 - 5.05798e7i) q^{92} +(4.31081e7 - 3.43776e7i) q^{93} +(-2.21206e7 + 9.69166e7i) q^{94} +(2.07163e8 - 7.24895e7i) q^{95} +(6.40867e7 - 1.33077e8i) q^{96} +(8.11144e7 + 5.09675e7i) q^{97} +(-9.22431e7 - 3.22773e7i) q^{98} +(6.69339e6 - 6.69339e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 228 q - 6 q^{2} - 12 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 10 q^{7} + 3664 q^{8} - 14 q^{9}+O(q^{10}) $ 228 * q - 6 * q^2 - 12 * q^3 - 14 * q^4 - 14 * q^5 - 14 * q^6 - 10 * q^7 + 3664 * q^8 - 14 * q^9	\( 228 q - 6 q^{2} - 12 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 10 q^{7} + 3664 q^{8} - 14 q^{9} - 15884 q^{10} + 8376 q^{11} - 5036 q^{12} - 14 q^{13} - 12742 q^{14} + 35516 q^{15} + 245898 q^{16} - 76248 q^{17} + 465008 q^{18} + 164474 q^{19} - 907274 q^{20} - 628270 q^{21} + 1214962 q^{22} + 173408 q^{23} + 1858618 q^{24} + 43976 q^{25} - 4604204 q^{26} - 1727586 q^{27} + 1079922 q^{29} + 8909208 q^{30} + 3657848 q^{31} + 1160364 q^{32} - 4279184 q^{33} - 8655374 q^{34} - 8269058 q^{35} - 3366854 q^{36} - 5622890 q^{37} + 15536626 q^{38} + 16110008 q^{39} - 23544696 q^{40} - 9561672 q^{41} - 14 q^{42} + 5181008 q^{43} + 51041750 q^{44} - 35245194 q^{45} - 43159224 q^{46} - 12806808 q^{47} + 83954488 q^{48} + 10429400 q^{49} + 80809398 q^{50} + 18760882 q^{51} - 93050550 q^{52} - 30960322 q^{53} - 106220916 q^{54} - 126174004 q^{55} - 40136268 q^{56} + 159368354 q^{58} + 11188020 q^{59} + 255893612 q^{60} + 139657128 q^{61} + 102501616 q^{62} + 9797746 q^{63} - 135941792 q^{64} - 14207858 q^{65} - 447597656 q^{66} - 148930894 q^{67} - 167094904 q^{68} + 66986722 q^{69} + 586255934 q^{70} - 15272096 q^{71} + 41230600 q^{72} - 219415072 q^{73} - 347464696 q^{74} + 391507416 q^{75} + 271512490 q^{76} + 240416780 q^{77} + 141747906 q^{78} + 112667220 q^{79} - 375642638 q^{80} - 358099268 q^{81} - 262154910 q^{82} - 109463350 q^{83} - 694921012 q^{84} - 356627386 q^{85} + 199703522 q^{87} + 251202768 q^{88} + 839849154 q^{89} + 675826020 q^{90} + 533256766 q^{91} + 742339570 q^{92} + 78998570 q^{93} - 209116610 q^{94} - 633414122 q^{95} - 431412576 q^{96} - 402046736 q^{97} - 2192087384 q^{98} - 1966368188 q^{99}+O(q^{100}) \) 228 * q - 6 * q^2 - 12 * q^3 - 14 * q^4 - 14 * q^5 - 14 * q^6 - 10 * q^7 + 3664 * q^8 - 14 * q^9 - 15884 * q^10 + 8376 * q^11 - 5036 * q^12 - 14 * q^13 - 12742 * q^14 + 35516 * q^15 + 245898 * q^16 - 76248 * q^17 + 465008 * q^18 + 164474 * q^19 - 907274 * q^20 - 628270 * q^21 + 1214962 * q^22 + 173408 * q^23 + 1858618 * q^24 + 43976 * q^25 - 4604204 * q^26 - 1727586 * q^27 + 1079922 * q^29 + 8909208 * q^30 + 3657848 * q^31 + 1160364 * q^32 - 4279184 * q^33 - 8655374 * q^34 - 8269058 * q^35 - 3366854 * q^36 - 5622890 * q^37 + 15536626 * q^38 + 16110008 * q^39 - 23544696 * q^40 - 9561672 * q^41 - 14 * q^42 + 5181008 * q^43 + 51041750 * q^44 - 35245194 * q^45 - 43159224 * q^46 - 12806808 * q^47 + 83954488 * q^48 + 10429400 * q^49 + 80809398 * q^50 + 18760882 * q^51 - 93050550 * q^52 - 30960322 * q^53 - 106220916 * q^54 - 126174004 * q^55 - 40136268 * q^56 + 159368354 * q^58 + 11188020 * q^59 + 255893612 * q^60 + 139657128 * q^61 + 102501616 * q^62 + 9797746 * q^63 - 135941792 * q^64 - 14207858 * q^65 - 447597656 * q^66 - 148930894 * q^67 - 167094904 * q^68 + 66986722 * q^69 + 586255934 * q^70 - 15272096 * q^71 + 41230600 * q^72 - 219415072 * q^73 - 347464696 * q^74 + 391507416 * q^75 + 271512490 * q^76 + 240416780 * q^77 + 141747906 * q^78 + 112667220 * q^79 - 375642638 * q^80 - 358099268 * q^81 - 262154910 * q^82 - 109463350 * q^83 - 694921012 * q^84 - 356627386 * q^85 + 199703522 * q^87 + 251202768 * q^88 + 839849154 * q^89 + 675826020 * q^90 + 533256766 * q^91 + 742339570 * q^92 + 78998570 * q^93 - 209116610 * q^94 - 633414122 * q^95 - 431412576 * q^96 - 402046736 * q^97 - 2192087384 * q^98 - 1966368188 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{27}{28}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−21.4136	+	2.41273i	−1.33835	+	0.150796i	−0.751946	−	0.659225i	$-0.770885\pi$
$2$	−21.4136	+	2.41273i	−1.33835	+	0.150796i	−0.586402	+	0.810020i	$0.699456\pi$
$3$	91.7346	−	57.6407i	1.13253	−	0.711613i	0.170713	−	0.985321i	$-0.445393\pi$
$3$	91.7346	−	57.6407i	1.13253	−	0.711613i	0.961813	+	0.273708i	$0.0882500\pi$
$4$	203.138	−	46.3649i	0.793508	−	0.181113i
$5$	−731.114	−	583.044i	−1.16978	−	0.932871i	−0.171155	−	0.985244i	$-0.554750\pi$
$5$	−731.114	−	583.044i	−1.16978	−	0.932871i	−0.998628	+	0.0523732i	$0.983321\pi$
$6$	−1825.29	+	1455.62i	−1.40841	+	1.12317i
$7$	246.757	−	1081.11i	0.102773	−	0.450277i	−0.897190	−	0.441645i	$-0.854395\pi$
$7$	246.757	−	1081.11i	0.102773	−	0.450277i	0.999963	−	0.00863196i	$-0.00274767\pi$
$8$	968.946	−	339.049i	0.236559	−	0.0827756i
$9$	2246.08	−	4664.03i	0.342338	−	0.710872i
$10$	17062.5	+	10721.1i	1.70625	+	1.07211i
$11$	1725.95	+	603.935i	0.117885	+	0.0412496i	0.388577	−	0.921416i	$-0.372967\pi$
$11$	1725.95	+	603.935i	0.117885	+	0.0412496i	−0.270692	+	0.962666i	$0.587253\pi$
$12$	15962.3	−	15962.3i	0.769786	−	0.769786i
$13$	−2140.33	−	4444.45i	−0.0749391	−	0.155613i	0.860133	−	0.510069i	$-0.170380\pi$
$13$	−2140.33	−	4444.45i	−0.0749391	−	0.155613i	−0.935073	+	0.354457i	$0.884666\pi$
$14$	−2675.52	+	23745.9i	−0.0696459	+	0.618124i
$15$	−100676.	−	11343.4i	−1.98865	−	0.224067i
$16$	−67988.9	+	32741.7i	−1.03743	+	0.499599i
$17$	−11256.2	−	11256.2i	−0.134771	−	0.134771i	0.636503	−	0.771274i	$-0.280380\pi$
$17$	−11256.2	−	11256.2i	−0.134771	−	0.134771i	−0.771274	+	0.636503i	$0.780380\pi$
$18$	−36843.5	+	105293.i	−0.350971	+	1.00302i
$19$	−124871.	+	198730.i	−0.958177	+	1.52493i	−0.110863	+	0.993836i	$0.535362\pi$
$19$	−124871.	+	198730.i	−0.958177	+	1.52493i	−0.847313	+	0.531094i	$0.821781\pi$
$20$	−175550.	−	84540.4i	−1.09719	−	0.528377i
$21$	−39680.0	−	113399.i	−0.204030	−	0.583084i
$22$	−38415.8	−	8768.16i	−0.163991	−	0.0374298i
$23$	−242749.	−	304398.i	−0.867455	−	1.08775i	−0.995384	−	0.0959707i	$-0.969404\pi$
$23$	−242749.	−	304398.i	−0.867455	−	1.08775i	0.127929	−	0.991783i	$-0.459167\pi$
$24$	69342.9	−	86953.2i	0.209005	−	0.262084i
$25$	107665.	+	471713.i	0.275623	+	1.20759i
$26$	56555.5	+	90007.5i	0.123760	+	0.196963i
$27$	16792.2	+	149034.i	0.0315974	+	0.280435i
$28$		−	231056.i		−	0.375911i
$29$	−643056.	+	294492.i	−0.909194	+	0.416373i
$29$	−643056.	+	294492.i	−0.909194	+	0.416373i
$30$	2.18319e6			2.69530
$31$	505726.	−	56981.6i	0.547606	−	0.0617004i	0.166173	−	0.986097i	$-0.446859\pi$
$31$	505726.	−	56981.6i	0.547606	−	0.0617004i	0.381433	+	0.924396i	$0.375431\pi$
$32$	1.15437e6	−	725339.i	1.10089	−	0.691737i
$33$	193140.	−	44083.0i	0.162861	−	0.0371720i
$34$	268195.	+	213878.i	0.200694	+	0.160048i
$35$	−810745.	+	646548.i	−0.540272	+	0.430852i
$36$	240017.	−	1.05158e6i	0.142900	−	0.626084i
$37$	−2.15384e6	+	753660.i	−1.14923	+	0.402132i	−0.836638	−	0.547757i	$-0.815482\pi$
$37$	−2.15384e6	+	753660.i	−1.14923	+	0.402132i	−0.312589	+	0.949889i	$0.601196\pi$
$38$	2.19444e6	−	4.55680e6i	1.05242	−	2.18537i
$39$	−452524.	−	284340.i	−0.195606	−	0.122908i
$40$	−906091.	−	317055.i	−0.353942	−	0.123850i
$41$	−1.56467e6	+	1.56467e6i	−0.553715	+	0.553715i	−0.927511	−	0.373796i	$-0.878056\pi$
$41$	−1.56467e6	+	1.56467e6i	−0.553715	+	0.553715i	0.373796	+	0.927511i	$0.378056\pi$
$42$	1.12329e6	+	2.33254e6i	0.360990	+	0.749603i
$43$	110419.	−	979994.i	0.0322975	−	0.286649i	−0.967173	−	0.254118i	$-0.918215\pi$
$43$	110419.	−	979994.i	0.0322975	−	0.286649i	0.999471	−	0.0325305i	$-0.0103566\pi$
$44$	378607.	+	42658.8i	0.101013	+	0.0113814i
$45$	−4.36148e6	+	2.10038e6i	−1.06361	+	0.512209i
$46$	5.93256e6	+	5.93256e6i	1.32498	+	1.32498i
$47$	1.52363e6	−	4.35427e6i	0.312239	−	0.892327i	−0.675658	−	0.737215i	$-0.736140\pi$
$47$	1.52363e6	−	4.35427e6i	0.312239	−	0.892327i	0.987897	−	0.155112i	$-0.0495739\pi$
$48$	−4.34968e6	+	6.92247e6i	−0.819393	+	1.30406i
$49$	4.08599e6	+	1.96771e6i	0.708782	+	0.341331i
$50$	−3.44362e6	−	9.84129e6i	−0.550979	−	1.57461i
$51$	−1.68140e6	−	383770.i	−0.248537	−	0.0567270i
$52$	−640850.	−	803600.i	−0.0876482	−	0.109907i
$53$	8.59706e6	−	1.07804e7i	1.08955	−	1.36625i	0.164511	−	0.986375i	$-0.447395\pi$
$53$	8.59706e6	−	1.07804e7i	1.08955	−	1.36625i	0.925038	−	0.379876i	$-0.124033\pi$
$54$	−719160.	−	3.15084e6i	−0.0845766	−	0.370554i
$55$	−909744.	−	1.44785e6i	−0.0994188	−	0.158224i
$56$	−127456.	−	1.13120e6i	−0.0129601	−	0.115024i
$57$			2.54281e7i			2.40887i
$58$	1.30596e7	−	7.85765e6i	1.15403	−	0.694354i
$59$	9.44114e6			0.779142			0.389571	−	0.920997i	$-0.372623\pi$
$59$	9.44114e6			0.779142			0.389571	+	0.920997i	$0.372623\pi$
$60$	−2.09770e7	+	2.36354e6i	−1.61859	+	0.182372i
$61$	−1.14038e7	+	7.16550e6i	−0.823628	+	0.517520i	−0.876681	−	0.481072i	$-0.840248\pi$
$61$	−1.14038e7	+	7.16550e6i	−0.823628	+	0.517520i	0.0530531	+	0.998592i	$0.483105\pi$
$62$	−1.06919e7	+	2.44036e6i	−0.723583	+	0.165153i
$63$	−4.48812e6	−	3.57915e6i	−0.284906	−	0.227205i
$64$	−7.86551e6	+	6.27253e6i	−0.468821	+	0.373872i
$65$	−1.02648e6	+	4.49731e6i	−0.0575040	+	0.251941i
$66$	−4.02946e6	+	1.40997e6i	−0.212359	+	0.0743078i
$67$	210114.	−	436306.i	0.0104269	−	0.0216517i	−0.895690	−	0.444678i	$-0.853318\pi$
$67$	210114.	−	436306.i	0.0104269	−	0.0216517i	0.906117	+	0.423027i	$0.139032\pi$
$68$	−2.80847e6	−	1.76468e6i	−0.131351	−	0.0825333i
$69$	−3.98142e7	−	1.39316e7i	−1.75648	−	0.614617i
$70$	1.58010e7	−	1.58010e7i	0.658101	−	0.658101i
$71$	3.75374e6	+	7.79473e6i	0.147717	+	0.306738i	0.961678	−	0.274182i	$-0.0884071\pi$
$71$	3.75374e6	+	7.79473e6i	0.147717	+	0.306738i	−0.813961	+	0.580920i	$0.802693\pi$
$72$	594995.	−	5.28073e6i	0.0221403	−	0.196501i
$73$	−3.47680e7	−	3.91741e6i	−1.22430	−	0.137946i	−0.523953	−	0.851747i	$-0.675543\pi$
$73$	−3.47680e7	−	3.91741e6i	−1.22430	−	0.137946i	−0.700348	+	0.713802i	$0.746972\pi$
$74$	4.43029e7	−	2.13352e7i	1.47743	−	0.711490i
$75$	3.70665e7	+	3.70665e7i	1.17148	+	1.17148i
$76$	−1.61518e7	+	4.61593e7i	−0.484136	+	1.38358i
$77$	1.07881e6	−	1.71692e6i	0.0306890	−	0.0488413i
$78$	1.03762e7	+	4.99691e6i	0.280323	+	0.134997i
$79$	−1.28345e7	−	3.66789e7i	−0.329511	−	0.941689i	−0.982815	−	0.184593i	$-0.940903\pi$
$79$	−1.28345e7	−	3.66789e7i	−0.329511	−	0.941689i	0.653304	−	0.757096i	$-0.273382\pi$
$80$	6.87975e7	+	1.57026e7i	1.67963	+	0.383364i
$81$	3.13072e7	+	3.92580e7i	0.727285	+	0.911986i
$82$	2.97300e7	−	3.72802e7i	0.657566	−	0.824561i
$83$	−2.06941e7	−	9.06670e7i	−0.436049	−	1.91046i	−0.413024	−	0.910720i	$-0.635527\pi$
$83$	−2.06941e7	−	9.06670e7i	−0.436049	−	1.91046i	−0.0230253	−	0.999735i	$-0.507330\pi$
$84$	−1.33182e7	−	2.11959e7i	−0.267504	−	0.425730i
$85$	1.66671e6	+	1.47925e7i	0.0319290	+	0.283378i
$86$			2.12516e7i			0.388506i
$87$	−4.20157e7	+	6.40813e7i	−0.733390	+	1.11855i
$88$	1.87711e6			0.0313011
$89$	−1.02040e8	+	1.14971e7i	−1.62633	+	0.183244i	−0.877521	−	0.479538i	$-0.840804\pi$
$89$	−1.02040e8	+	1.14971e7i	−1.62633	+	0.183244i	−0.748812	+	0.662782i	$0.769376\pi$
$90$	8.83272e7	−	5.54996e7i	1.34625	−	0.845902i
$91$	−5.33310e6	+	1.21725e6i	−0.0777704	+	0.0177506i
$92$	−6.34250e7	−	5.05798e7i	−0.885339	−	0.706034i
$93$	4.31081e7	−	3.43776e7i	0.576271	−	0.459561i
$94$	−2.21206e7	+	9.69166e7i	−0.283325	+	1.24133i
$95$	2.07163e8	−	7.24895e7i	2.54342	−	0.889981i
$96$	6.40867e7	−	1.33077e8i	0.754541	−	1.56682i
$97$	8.11144e7	+	5.09675e7i	0.916243	+	0.575714i	0.905555	−	0.424229i	$-0.139455\pi$
$97$	8.11144e7	+	5.09675e7i	0.916243	+	0.575714i	0.0106884	+	0.999943i	$0.496598\pi$
$98$	−9.22431e7	−	3.22773e7i	−1.00007	−	0.349939i
$99$	6.69339e6	−	6.69339e6i	0.0696796	−	0.0696796i
$100$	4.37419e7	+	9.08309e7i	0.437419	+	0.908309i
$101$	−2.37782e6	+	2.11037e7i	−0.0228504	+	0.202803i	−0.999950	−	0.00997872i	$-0.996824\pi$
$101$	−2.37782e6	+	2.11037e7i	−0.0228504	+	0.202803i	0.977100	+	0.212781i	$0.0682522\pi$
$102$	3.69308e7	+	4.16110e6i	0.341183	+	0.0384421i
$103$	9.42714e7	−	4.53987e7i	0.837589	−	0.403362i	0.0346331	−	0.999400i	$-0.488974\pi$
$103$	9.42714e7	−	4.53987e7i	0.837589	−	0.403362i	0.802956	+	0.596038i	$0.203259\pi$
$104$	−3.58076e6	−	3.58076e6i	−0.0306085	−	0.0306085i
$105$	−3.71059e7	+	1.06043e8i	−0.305272	+	0.872416i
$106$	−1.58084e8	+	2.51589e8i	−1.25217	+	1.99282i
$107$	−2.03209e8	−	9.78602e7i	−1.55027	−	0.746571i	−0.553972	−	0.832535i	$-0.686888\pi$
$107$	−2.03209e8	−	9.78602e7i	−1.55027	−	0.746571i	−0.996298	+	0.0859648i	$0.972603\pi$
$108$	1.03211e7	+	2.94960e7i	0.0758631	+	0.216804i
$109$	−8.75303e7	−	1.99782e7i	−0.620087	−	0.141531i	−0.0990748	−	0.995080i	$-0.531588\pi$
$109$	−8.75303e7	−	1.99782e7i	−0.620087	−	0.141531i	−0.521012	+	0.853549i	$0.674445\pi$
$110$	2.29741e7	+	2.88087e7i	0.156916	+	0.196767i
$111$	−1.54140e8	+	1.93285e8i	−1.01537	+	1.27323i
$112$	1.86208e7	+	8.15830e7i	0.118338	+	0.518475i
$113$	−1.29475e8	−	2.06058e8i	−0.794095	−	1.26380i	−0.960650	−	0.277763i	$-0.910407\pi$
$113$	−1.29475e8	−	2.06058e8i	−0.794095	−	1.26380i	0.166555	−	0.986032i	$-0.446736\pi$
$114$	−6.13510e7	−	5.44506e8i	−0.363247	−	3.22391i
$115$			3.64084e8i			2.08166i
$116$	−1.16975e8	+	8.96378e7i	−0.646042	+	0.495062i
$117$	−2.55364e7			−0.136275
$118$	−2.02168e8	+	2.27789e7i	−1.04276	+	0.117491i
$119$	−1.49468e7	+	9.39172e6i	−0.0745352	+	0.0468336i
$120$	−1.01395e8	+	2.31428e7i	−0.488981	+	0.111607i
$121$	−1.64978e8	−	1.31566e8i	−0.769636	−	0.613764i
$122$	2.26908e8	−	1.80953e8i	1.02426	−	0.816821i
$123$	−5.33456e7	+	2.33722e8i	−0.233066	+	1.02113i
$124$	1.00090e8	−	3.50231e7i	0.423355	−	0.148138i
$125$	3.78224e7	−	7.85391e7i	0.154921	−	0.321696i
$126$	1.04742e8	+	6.58138e7i	0.415565	+	0.261117i
$127$	1.95361e8	+	6.83599e7i	0.750973	+	0.262777i	0.678507	−	0.734594i	$-0.262627\pi$
$127$	1.95361e8	+	6.83599e7i	0.750973	+	0.262777i	0.0724659	+	0.997371i	$0.476913\pi$
$128$	−9.34956e7	+	9.34956e7i	−0.348298	+	0.348298i
$129$	−4.63583e7	−	9.62640e7i	−0.167405	−	0.347620i
$130$	1.11298e7	−	9.87801e7i	0.0389687	−	0.345857i
$131$	3.86813e8	+	4.35834e7i	1.31346	+	0.147991i	0.740756	−	0.671774i	$-0.234467\pi$
$131$	3.86813e8	+	4.35834e7i	1.31346	+	0.147991i	0.572700	+	0.819765i	$0.305896\pi$
$132$	3.71902e7	−	1.79099e7i	0.122499	−	0.0589925i
$133$	1.84037e8	+	1.84037e8i	0.588166	+	0.588166i
$134$	−3.44660e6	+	9.84982e6i	−0.0106899	+	0.0305499i
$135$	7.46167e7	−	1.18752e8i	0.224647	−	0.357524i
$136$	−1.47231e7	−	7.09028e6i	−0.0430372	−	0.0207256i
$137$	−7.13136e7	−	2.03803e8i	−0.202437	−	0.578532i	0.797247	−	0.603653i	$-0.206289\pi$
$137$	−7.13136e7	−	2.03803e8i	−0.202437	−	0.578532i	−0.999684	+	0.0251207i	$0.992003\pi$
$138$	8.86178e8	+	2.02264e8i	2.44346	+	0.557703i
$139$	−1.74155e8	−	2.18383e8i	−0.466527	−	0.585006i	0.491790	−	0.870714i	$-0.336343\pi$
$139$	−1.74155e8	−	2.18383e8i	−0.466527	−	0.585006i	−0.958317	+	0.285708i	$0.907771\pi$
$140$	−1.34716e8	+	1.68929e8i	−0.350677	+	0.439735i
$141$	−1.11214e8	−	4.87260e8i	−0.281373	−	1.23278i
$142$	−9.91876e7	−	1.57856e8i	−0.243952	−	0.388247i
$143$	−1.00995e6	−	8.96351e6i	−0.00241520	−	0.0214355i
$144$			3.90643e8i			0.908510i
$145$	6.41849e8	+	1.59622e8i	1.45198	+	0.361095i
$146$	7.53958e8			1.65934
$147$	4.88246e8	−	5.50122e7i	1.04561	−	0.117812i
$148$	−4.02582e8	+	2.52959e8i	−0.839089	+	0.527234i
$149$	1.64110e8	−	3.74571e7i	0.332959	−	0.0759958i	−0.0527731	−	0.998607i	$-0.516806\pi$
$149$	1.64110e8	−	3.74571e7i	0.332959	−	0.0759958i	0.385732	+	0.922611i	$0.373949\pi$
$150$	−8.83157e8	−	7.04294e8i	−1.74451	−	1.39120i
$151$	−5.16816e7	+	4.12147e7i	−0.0994096	+	0.0792765i	−0.671933	−	0.740612i	$-0.734536\pi$
$151$	−5.16816e7	+	4.12147e7i	−0.0994096	+	0.0792765i	0.572524	+	0.819888i	$0.305964\pi$
$152$	−5.36135e7	+	2.34896e8i	−0.100438	+	0.440050i
$153$	−7.77819e7	+	2.72171e7i	−0.141943	+	0.0496679i
$154$	−1.89588e7	+	3.93683e7i	−0.0337076	+	0.0699945i
$155$	−4.02966e8	−	2.53200e8i	−0.698139	−	0.438670i
$156$	−1.05108e8	−	3.67789e7i	−0.177475	−	0.0621013i
$157$	−1.36709e8	+	1.36709e8i	−0.225008	+	0.225008i	−0.810604	−	0.585595i	$-0.800861\pi$
$157$	−1.36709e8	+	1.36709e8i	−0.225008	+	0.225008i	0.585595	+	0.810604i	$0.300861\pi$
$158$	3.63328e8	+	7.54459e8i	0.583003	+	1.21062i
$159$	1.67260e8	−	1.48447e9i	0.261700	−	2.32265i
$160$	−1.26688e9	−	1.42743e8i	−1.93311	−	0.217809i
$161$	−3.88989e8	+	1.87327e8i	−0.578941	+	0.278803i
$162$	−7.65118e8	−	7.65118e8i	−1.11088	−	1.11088i
$163$	−3.18231e8	+	9.09451e8i	−0.450808	+	1.28833i	0.464498	+	0.885574i	$0.346235\pi$
$163$	−3.18231e8	+	9.09451e8i	−0.450808	+	1.28833i	−0.915305	+	0.402760i	$0.868051\pi$
$164$	−2.45298e8	+	3.90389e8i	−0.339092	+	0.539662i
$165$	−1.66910e8	−	8.03797e7i	−0.225189	−	0.108445i
$166$	6.61890e8	+	1.89157e9i	0.871673	+	2.49110i
$167$	−6.86376e7	−	1.56661e7i	−0.0882463	−	0.0201416i	0.178170	−	0.984000i	$-0.442982\pi$
$167$	−6.86376e7	−	1.56661e7i	−0.0882463	−	0.0201416i	−0.266416	+	0.963858i	$0.585840\pi$
$168$	−7.68955e7	−	9.64239e7i	−0.0965304	−	0.121045i
$169$	4.93428e8	−	6.18739e8i	0.604890	−	0.758509i
$170$	−7.13805e7	−	3.12739e8i	−0.0854642	−	0.374443i
$171$	6.46415e8	+	1.02876e9i	0.756010	+	1.20318i
$172$	−2.30071e7	−	2.04194e8i	−0.0262874	−	0.233307i
$173$			9.17622e8i			1.02442i	0.858859	+	0.512212i	$0.171174\pi$
$173$			9.17622e8i			1.02442i	−0.858859	+	0.512212i	$0.828826\pi$
$174$	7.45096e8	−	1.47358e9i	0.812859	−	1.60760i
$175$	5.36543e8			0.572074
$176$	−1.37119e8	+	1.54496e7i	−0.142905	+	0.0161015i
$177$	8.66079e8	−	5.44194e8i	0.882398	−	0.554448i
$178$	2.15730e9	−	4.92389e8i	2.14897	−	0.490488i
$179$	−1.03522e9	−	8.25563e8i	−1.00837	−	0.804152i	−0.0276643	−	0.999617i	$-0.508807\pi$
$179$	−1.03522e9	−	8.25563e8i	−1.00837	−	0.804152i	−0.980711	+	0.195465i	$0.937378\pi$
$180$	−7.88598e8	+	6.28886e8i	−0.751218	+	0.599076i
$181$	3.18897e8	−	1.39718e9i	0.297122	−	1.30178i	−0.577268	−	0.816555i	$-0.695881\pi$
$181$	3.18897e8	−	1.39718e9i	0.297122	−	1.30178i	0.874390	−	0.485224i	$-0.161262\pi$
$182$	1.11264e8	−	3.89329e7i	0.101407	−	0.0354839i
$183$	−6.33101e8	+	1.31465e9i	−0.564506	+	1.17221i
$184$	−3.38417e8	−	2.12642e8i	−0.295244	−	0.185514i
$185$	2.01412e9	+	7.04770e8i	1.71948	+	0.601673i
$186$	−8.40154e8	+	8.40154e8i	−0.701952	+	0.701952i
$187$	−1.26296e7	−	2.62257e7i	−0.0103282	−	0.0214467i
$188$	1.07621e8	−	9.55161e8i	0.0861519	−	0.764619i
$189$	1.65267e8	+	1.86211e7i	0.129521	+	0.0145935i
$190$	−4.26121e9	+	2.05209e9i	−3.26978	+	1.57464i
$191$	−3.27414e8	−	3.27414e8i	−0.246016	−	0.246016i	0.573317	−	0.819333i	$-0.305656\pi$
$191$	−3.27414e8	−	3.27414e8i	−0.246016	−	0.246016i	−0.819333	+	0.573317i	$0.805656\pi$
$192$	−3.59986e8	+	1.02878e9i	−0.264899	+	0.757039i
$193$	−2.20908e7	+	3.51572e7i	−0.0159214	+	0.0253388i	−0.854590	−	0.519303i	$-0.826192\pi$
$193$	−2.20908e7	+	3.51572e7i	−0.0159214	+	0.0253388i	0.838669	+	0.544642i	$0.183334\pi$
$194$	−1.85992e9	−	8.95690e8i	−1.31307	−	0.632340i
$195$	1.65064e8	+	4.71726e8i	0.114160	+	0.326251i
$196$	9.21252e8	+	2.10270e8i	0.624244	+	0.142480i
$197$	1.49913e8	+	1.87985e8i	0.0995348	+	0.124813i	0.829104	−	0.559094i	$-0.188851\pi$
$197$	1.49913e8	+	1.87985e8i	0.0995348	+	0.124813i	−0.729569	+	0.683907i	$0.760280\pi$
$198$	−1.27180e8	+	1.59479e8i	−0.0827481	+	0.103763i
$199$	−5.90253e8	−	2.58607e9i	−0.376380	−	1.64903i	−0.708442	−	0.705769i	$-0.750601\pi$
$199$	−5.90253e8	−	2.58607e9i	−0.376380	−	1.64903i	0.332062	−	0.943258i	$-0.392256\pi$
$200$	2.64256e8	+	4.20561e8i	0.165160	+	0.262850i
$201$	−5.87426e6	−	5.21355e7i	−0.00359889	−	0.0319411i
$202$		−	4.57643e8i		−	0.274866i
$203$	1.59701e8	+	7.67885e8i	0.0940425	+	0.452181i
$204$	−3.59351e8			−0.207490
$205$	2.05622e9	−	2.31680e8i	1.16427	−	0.131182i
$206$	−1.90915e9	+	1.19960e9i	−1.06016	+	0.666143i
$207$	−1.96496e9	+	4.48489e8i	−1.07022	+	0.244270i
$208$	2.91038e8	+	2.32095e8i	0.155488	+	0.123997i
$209$	−3.35540e8	+	2.67584e8i	−0.175857	+	0.140241i
$210$	5.38718e8	−	2.36028e9i	0.277003	−	1.21363i
$211$	−2.88675e8	+	1.01012e8i	−0.145640	+	0.0509616i	−0.402115	−	0.915589i	$-0.631725\pi$
$211$	−2.88675e8	+	1.01012e8i	−0.145640	+	0.0509616i	0.256475	+	0.966551i	$0.417439\pi$
$212$	1.24656e9	−	2.58851e9i	0.617120	−	1.28146i
$213$	7.93642e8	+	4.98678e8i	0.385573	+	0.242271i
$214$	4.58753e9	+	1.60525e9i	2.18738	+	0.765397i
$215$	−6.52109e8	+	6.52109e8i	−0.305187	+	0.305187i
$216$	6.68007e7	+	1.38713e8i	0.0306878	+	0.0637239i
$217$	6.31879e7	−	5.60808e8i	0.0284967	−	0.252915i
$218$	1.92254e9	+	2.16618e8i	0.851234	+	0.0959111i
$219$	−3.41523e9	+	1.64469e9i	−1.48472	+	0.715002i
$220$	−2.51933e8	−	2.51933e8i	−0.107546	−	0.107546i
$221$	−2.59357e7	+	7.41200e7i	−0.0108725	+	0.0310718i
$222$	2.83434e9	−	4.51082e9i	1.16692	−	1.85714i
$223$	−3.01789e9	−	1.45334e9i	−1.22035	−	0.587689i	−0.290940	−	0.956741i	$-0.593968\pi$
$223$	−3.01789e9	−	1.45334e9i	−1.22035	−	0.587689i	−0.929409	+	0.369052i	$0.879682\pi$
$224$	−4.99325e8	−	1.42699e9i	−0.198331	−	0.566798i
$225$	2.44191e9	+	5.57350e8i	0.952795	+	0.217469i
$226$	3.26969e9	+	4.10006e9i	1.25335	+	1.57165i
$227$	3.01448e8	−	3.78004e8i	0.113530	−	0.142362i	−0.721820	−	0.692081i	$-0.756694\pi$
$227$	3.01448e8	−	3.78004e8i	0.113530	−	0.142362i	0.835349	+	0.549720i	$0.185265\pi$
$228$	1.17897e9	+	5.16541e9i	0.436278	+	1.91146i
$229$	1.07064e9	+	1.70391e9i	0.389315	+	0.619591i	0.982673	−	0.185347i	$-0.0593411\pi$
$229$	1.07064e9	+	1.70391e9i	0.389315	+	0.619591i	−0.593358	+	0.804939i	$0.702198\pi$
$230$	−8.78435e8	−	7.79633e9i	−0.313905	−	2.78598i
$231$		−	2.19685e8i		−	0.0771528i
$232$	−5.23239e8	+	5.03375e8i	−0.180613	+	0.173756i
$233$	2.92256e9			0.991608			0.495804	−	0.868434i	$-0.334873\pi$
$233$	2.92256e9			0.991608			0.495804	+	0.868434i	$0.334873\pi$
$234$	5.46826e8	−	6.16125e7i	0.182384	−	0.0205497i
$235$	−3.65268e9	+	2.29513e9i	−1.19768	+	0.752551i
$236$	1.91785e9	−	4.37738e8i	0.618255	−	0.141113i
$237$	−3.29156e9	−	2.62493e9i	−1.04330	−	0.832003i
$238$	2.97406e8	−	2.37173e8i	0.0926918	−	0.0739192i
$239$	−5.34538e8	+	2.34197e9i	−0.163828	+	0.717776i	0.824554	+	0.565783i	$0.191426\pi$
$239$	−5.34538e8	+	2.34197e9i	−0.163828	+	0.717776i	−0.988382	+	0.151993i	$0.951431\pi$
$240$	7.21622e9	−	2.52506e9i	2.17503	−	0.761075i
$241$	−1.40013e9	+	2.90741e9i	−0.415051	+	0.861862i	0.583704	+	0.811967i	$0.301603\pi$
$241$	−1.40013e9	+	2.90741e9i	−0.415051	+	0.861862i	−0.998754	+	0.0498950i	$0.984111\pi$
$242$	3.85021e9	+	2.41925e9i	1.12259	+	0.705373i
$243$	4.20603e9	+	1.47175e9i	1.20628	+	0.422095i
$244$	−1.98432e9	+	1.98432e9i	−0.559826	+	0.559826i
$245$	−1.84006e9	−	3.82093e9i	−0.510703	−	1.06049i
$246$	5.78411e8	−	5.13354e9i	0.157941	−	1.40177i
$247$	1.15051e9	+	1.29632e8i	0.309103	+	0.0348276i
$248$	4.70701e8	−	2.26678e8i	0.124434	−	0.0599242i
$249$	−7.12448e9	−	7.12448e9i	−1.85334	−	1.85334i
$250$	−6.20420e8	+	1.77306e9i	−0.158827	+	0.453903i
$251$	−2.25443e9	+	3.58790e9i	−0.567991	+	0.903952i	0.432007	+	0.901870i	$0.357806\pi$
$251$	−2.25443e9	+	3.58790e9i	−0.567991	+	0.903952i	−0.999998	+	0.00208179i	$0.999337\pi$
$252$	−1.07765e9	−	5.18971e8i	−0.267225	−	0.128689i
$253$	−2.35136e8	−	6.71980e8i	−0.0573901	−	0.164012i
$254$	−4.34832e9	−	9.92476e8i	−1.04469	−	0.238443i
$255$	1.00554e9	+	1.26091e9i	0.237816	+	0.298211i
$256$	3.38226e9	−	4.24122e9i	0.787494	−	0.987487i
$257$	5.31442e8	+	2.32840e9i	0.121821	+	0.533734i	0.998603	+	0.0528448i	$0.0168289\pi$
$257$	5.31442e8	+	2.32840e9i	0.121821	+	0.533734i	−0.876781	+	0.480889i	$0.840314\pi$
$258$	1.22496e9	+	1.94951e9i	0.276466	+	0.439993i
$259$	2.83318e8	+	2.51451e9i	0.0629614	+	0.558798i
$260$			9.61168e8i			0.210332i
$261$	−7.08321e7	+	3.66069e9i	−0.0152640	+	0.788861i
$262$	−8.38820e9			−1.78018
$263$	−3.99939e9	+	4.50623e8i	−0.835931	+	0.0941868i	−0.519544	−	0.854444i	$-0.673898\pi$
$263$	−3.99939e9	+	4.50623e8i	−0.835931	+	0.0941868i	−0.316387	+	0.948630i	$0.602470\pi$
$264$	1.72196e8	−	1.08198e8i	0.0354493	−	0.0222743i
$265$	−1.25709e10	+	2.86922e9i	−2.54907	+	0.581809i
$266$	−4.38493e9	−	3.49687e9i	−0.875863	−	0.698477i
$267$	−8.69788e9	+	6.93633e9i	−1.71147	+	1.36485i
$268$	2.24528e7	−	9.83723e7i	0.00435243	−	0.0190693i
$269$	7.62086e9	−	2.66665e9i	1.45544	−	0.509281i	0.517382	−	0.855755i	$-0.326907\pi$
$269$	7.62086e9	−	2.66665e9i	1.45544	−	0.509281i	0.938060	+	0.346474i	$0.112621\pi$
$270$	−1.31129e9	+	2.72293e9i	−0.246743	+	0.512367i
$271$	1.67219e8	+	1.05071e8i	0.0310034	+	0.0194807i	0.547445	−	0.836842i	$-0.315601\pi$
$271$	1.67219e8	+	1.05071e8i	0.0310034	+	0.0194807i	−0.516441	+	0.856323i	$0.672744\pi$
$272$	1.13385e9	+	3.96750e8i	0.207147	+	0.0724839i
$273$	−4.19067e8	+	4.19067e8i	−0.0754455	+	0.0754455i
$274$	2.01880e9	+	4.19208e9i	0.358171	+	0.743751i
$275$	−9.90592e7	+	8.79175e8i	−0.0173206	+	0.153725i
$276$	−8.73372e9	−	9.84054e8i	−1.50509	−	0.169583i
$277$	7.47472e9	−	3.59964e9i	1.26963	−	0.611420i	0.326923	−	0.945051i	$-0.393988\pi$
$277$	7.47472e9	−	3.59964e9i	1.26963	−	0.611420i	0.942704	+	0.333631i	$0.108274\pi$
$278$	4.25618e9	+	4.25618e9i	0.712591	+	0.712591i
$279$	8.70136e8	−	2.48671e9i	0.143605	−	0.410400i
$280$	−5.66357e8	+	9.01352e8i	−0.0921422	+	0.146643i
$281$	1.82393e9	+	8.78359e8i	0.292539	+	0.140879i	0.574397	−	0.818577i	$-0.305237\pi$
$281$	1.82393e9	+	8.78359e8i	0.292539	+	0.140879i	−0.281858	+	0.959456i	$0.590951\pi$
$282$	3.55712e9	+	1.01657e10i	0.562473	+	1.60746i
$283$	9.30412e9	+	2.12360e9i	1.45054	+	0.331076i	0.873973	−	0.485974i	$-0.161535\pi$
$283$	9.30412e9	+	2.12360e9i	1.45054	+	0.331076i	0.576566	+	0.817050i	$0.304392\pi$
$284$	1.12393e9	+	1.40936e9i	0.172769	+	0.216646i
$285$	1.48257e10	−	1.85908e10i	2.24717	−	2.81786i
$286$	4.32531e7	+	1.89504e8i	0.00646477	+	0.0283240i
$287$	1.30549e9	+	2.07768e9i	0.192418	+	0.306232i
$288$	−7.90196e8	−	7.01319e9i	−0.114859	−	1.01940i
$289$		−	6.72235e9i		−	0.963673i
$290$	−1.41294e10	−	1.86947e9i	−1.99771	−	0.264318i
$291$	1.03788e10			1.44736
$292$	−7.24433e9	+	8.16240e8i	−0.996476	+	0.112276i
$293$	−1.27677e8	+	8.02247e7i	−0.0173237	+	0.0108852i	−0.540666	−	0.841237i	$-0.681828\pi$
$293$	−1.27677e8	+	8.02247e7i	−0.0173237	+	0.0108852i	0.523342	+	0.852123i	$0.324685\pi$
$294$	−1.03224e10	+	2.35601e9i	−1.38162	+	0.315347i
$295$	−6.90255e9	−	5.50460e9i	−0.911427	−	0.726839i
$296$	−1.83142e9	+	1.46051e9i	−0.238573	+	0.190256i
$297$	−6.10248e7	+	2.67367e8i	−0.00784297	+	0.0343623i
$298$	−3.42381e9	+	1.19804e9i	−0.434155	+	0.151918i
$299$	−8.33318e8	+	1.73040e9i	−0.104262	+	0.216502i
$300$	9.24820e9	+	5.81103e9i	1.14175	+	0.717411i
$301$	−1.03224e9	−	3.61196e8i	−0.125752	−	0.0440025i
$302$	1.00725e9	−	1.00725e9i	0.121090	−	0.121090i
$303$	9.98304e8	+	2.07300e9i	0.118438	+	0.245940i
$304$	1.98303e9	−	1.75999e10i	0.232186	−	2.06071i
$305$	1.25153e10	+	1.41014e9i	1.44625	+	0.162953i
$306$	1.59992e9	−	7.70481e8i	0.182479	−	0.0878772i
$307$	7.38884e9	+	7.38884e9i	0.831807	+	0.831807i	0.987764	−	0.155957i	$-0.0498461\pi$
$307$	7.38884e9	+	7.38884e9i	0.831807	+	0.831807i	−0.155957	+	0.987764i	$0.549846\pi$
$308$	1.39543e8	−	3.98791e8i	0.0155062	−	0.0443142i
$309$	6.03114e9	−	9.59850e9i	0.661554	−	1.05286i
$310$	9.23985e9	+	4.44968e9i	1.00050	+	0.481816i
$311$	−3.04845e9	−	8.71197e9i	−0.325865	−	0.931268i	−0.983969	−	0.178341i	$-0.942927\pi$
$311$	−3.04845e9	−	8.71197e9i	−0.325865	−	0.931268i	0.658104	−	0.752927i	$-0.271359\pi$
$312$	−5.34876e8	−	1.22082e8i	−0.0564463	−	0.0128835i
$313$	3.83088e9	+	4.80377e9i	0.399136	+	0.500501i	0.940267	−	0.340437i	$-0.110575\pi$
$313$	3.83088e9	+	4.80377e9i	0.399136	+	0.500501i	−0.541131	+	0.840938i	$0.682004\pi$
$314$	2.59759e9	−	3.25727e9i	0.267209	−	0.335070i
$315$	1.19452e9	+	5.23354e9i	0.121325	+	0.531561i
$316$	−4.30779e9	−	6.85580e9i	−0.432022	−	0.687559i
$317$	3.41064e8	+	3.02703e9i	0.0337753	+	0.299764i	0.999231	+	0.0391985i	$0.0124805\pi$
$317$	3.41064e8	+	3.02703e9i	0.0337753	+	0.299764i	−0.965456	+	0.260566i	$0.916091\pi$
$318$			3.21914e10i			3.14798i
$319$	−1.28773e9	+	1.19915e8i	−0.124355	+	0.0115800i
$320$	9.40775e9			0.897193
$321$	−2.42820e10	+	2.73592e9i	−2.28699	+	0.257682i
$322$	7.87768e9	−	4.94987e9i	0.732782	−	0.460437i
$323$	3.64253e9	−	8.31384e8i	0.334652	−	0.0763821i
$324$	8.17988e9	+	6.52324e9i	0.742279	+	0.591947i
$325$	1.86607e9	−	1.48814e9i	0.167260	−	0.133386i
$326$	4.62019e9	−	2.02424e10i	0.409063	−	1.79222i
$327$	−9.18112e9	+	3.21261e9i	−0.802980	+	0.280975i
$328$	−9.85579e8	+	2.04658e9i	−0.0851523	+	0.176820i
$329$	−4.33150e9	−	2.72166e9i	−0.369705	−	0.232301i
$330$	3.76807e9	+	1.31851e9i	0.317734	+	0.111180i
$331$	1.22073e10	−	1.22073e10i	1.01697	−	1.01697i	0.0171115	−	0.999854i	$-0.494553\pi$
$331$	1.22073e10	−	1.22073e10i	1.01697	−	1.01697i	0.999854	−	0.0171115i	$-0.00544702\pi$
$332$	−8.40754e9	−	1.74584e10i	−0.692016	−	1.43699i
$333$	−1.32259e9	+	1.17383e10i	−0.107560	+	0.954618i
$334$	1.50757e9	+	1.69863e8i	0.121142	+	0.0136494i
$335$	−4.08003e8	+	1.96484e8i	−0.0323955	+	0.0156008i
$336$	6.41067e9	+	6.41067e9i	0.502975	+	0.502975i
$337$	2.56462e9	−	7.32927e9i	0.198840	−	0.568252i	−0.800685	−	0.599086i	$-0.795531\pi$
$337$	2.56462e9	−	7.32927e9i	0.198840	−	0.568252i	0.999525	+	0.0308342i	$0.00981639\pi$
$338$	−9.07320e9	+	1.44399e10i	−0.695174	+	1.10636i
$339$	−2.37547e10	−	1.14397e10i	−1.79867	−	0.866192i
$340$	1.02443e9	+	2.92764e9i	0.0766593	+	0.219080i
$341$	9.07269e8	+	2.07078e8i	0.0670994	+	0.0153150i
$342$	−1.63242e10	−	2.04699e10i	−1.19324	−	1.49627i
$343$	7.12134e9	−	8.92988e9i	0.514500	−	0.645162i
$344$	−2.25276e8	−	9.86999e8i	−0.0160872	−	0.0704828i
$345$	2.09860e10	+	3.33991e10i	1.48134	+	2.35753i
$346$	−2.21397e9	−	1.96496e10i	−0.154479	−	1.37104i
$347$			2.82795e10i			1.95053i	0.221028	+	0.975267i	$0.429059\pi$
$347$			2.82795e10i			1.95053i	−0.221028	+	0.975267i	$0.570941\pi$
$348$	−5.56386e9	+	1.49654e10i	−0.379367	+	1.02040i
$349$	−1.03125e10			−0.695124			−0.347562	−	0.937657i	$-0.612990\pi$
$349$	−1.03125e10			−0.695124			−0.347562	+	0.937657i	$0.612990\pi$
$350$	−1.14893e10	+	1.29453e9i	−0.765634	+	0.0862662i
$351$	6.26436e8	−	3.93616e8i	0.0412713	−	0.0259325i
$352$	2.43044e9	−	5.54732e8i	0.158312	−	0.0361337i
$353$	−2.15415e10	−	1.71788e10i	−1.38732	−	1.10635i	−0.981298	−	0.192493i	$-0.938343\pi$
$353$	−2.15415e10	−	1.71788e10i	−1.38732	−	1.10635i	−0.406026	−	0.913861i	$-0.633086\pi$
$354$	−1.72329e10	+	1.37427e10i	−1.09735	+	0.875105i
$355$	1.80026e9	−	7.88744e9i	0.113350	−	0.496618i
$356$	−2.01951e10	+	7.06657e9i	−1.25732	+	0.439955i
$357$	−8.29798e8	+	1.72309e9i	−0.0510857	+	0.106081i
$358$	2.41597e10	+	1.51805e10i	1.47082	+	0.924177i
$359$	1.68278e10	+	5.88831e9i	1.01309	+	0.354497i	0.785236	−	0.619197i	$-0.212542\pi$
$359$	1.68278e10	+	5.88831e9i	1.01309	+	0.354497i	0.227859	+	0.973694i	$0.426828\pi$
$360$	−3.51391e9	+	3.51391e9i	−0.209209	+	0.209209i
$361$	−1.65322e10	−	3.43295e10i	−0.973423	−	2.02133i
$362$	−3.45770e9	+	3.06880e10i	−0.201351	+	1.78704i
$363$	−2.27178e10	−	2.55968e9i	−1.30840	−	0.147421i
$364$	−1.02692e9	+	4.94538e8i	−0.0584966	+	0.0281705i
$365$	2.31354e10	+	2.31354e10i	1.30348	+	1.30348i
$366$	1.03851e10	−	2.96788e10i	0.578742	−	1.65395i
$367$	2.83656e9	−	4.51436e9i	0.156361	−	0.248847i	−0.759352	−	0.650680i	$-0.774484\pi$
$367$	2.83656e9	−	4.51436e9i	0.156361	−	0.248847i	0.915713	+	0.401833i	$0.131627\pi$
$368$	2.64708e10	+	1.27477e10i	1.44336	+	0.695087i
$369$	3.78329e9	+	1.08120e10i	0.204063	+	0.583178i
$370$	−4.48298e10	−	1.02321e10i	−2.39200	−	0.545957i
$371$	−9.53343e9	−	1.19545e10i	−0.503215	−	0.631012i
$372$	7.16298e9	−	8.98209e9i	0.374043	−	0.469035i
$373$	−2.63206e9	−	1.15318e10i	−0.135976	−	0.595748i	−0.996296	−	0.0859936i	$-0.972594\pi$
$373$	−2.63206e9	−	1.15318e10i	−0.135976	−	0.595748i	0.860320	−	0.509754i	$-0.170264\pi$
$374$	3.33721e8	+	5.31114e8i	0.0170568	+	0.0271457i
$375$	−1.05742e9	−	9.38487e9i	−0.0534715	−	0.474573i
$376$		−	4.73564e9i		−	0.236934i
$377$	2.68521e9	+	2.22772e9i	0.132927	+	0.110279i
$378$	−3.58388e9			−0.175544
$379$	1.10992e10	−	1.25058e9i	0.537940	−	0.0606113i	0.161185	−	0.986924i	$-0.448468\pi$
$379$	1.10992e10	−	1.25058e9i	0.537940	−	0.0606113i	0.376755	+	0.926313i	$0.377040\pi$
$380$	3.87217e10	−	2.43305e10i	1.85704	−	1.16685i
$381$	2.18617e10	−	4.98980e9i	1.03749	−	0.236801i
$382$	7.80106e9	+	6.22113e9i	0.366353	+	0.292157i
$383$	−4.25423e9	+	3.39264e9i	−0.197709	+	0.157668i	−0.717340	−	0.696723i	$-0.754641\pi$
$383$	−4.25423e9	+	3.39264e9i	−0.197709	+	0.157668i	0.519631	+	0.854391i	$0.326069\pi$
$384$	−3.18763e9	+	1.39659e10i	−0.146603	+	0.642310i
$385$	−1.78978e9	+	6.26270e8i	−0.0814622	+	0.0285048i
$386$	3.88217e8	−	8.06141e8i	0.0174874	−	0.0363130i
$387$	−4.32272e9	−	2.71614e9i	−0.192714	−	0.121090i
$388$	1.88405e10	+	6.59258e9i	0.831315	+	0.290890i
$389$	−1.87688e10	+	1.87688e10i	−0.819668	+	0.819668i	−0.986060	−	0.166392i	$-0.946788\pi$
$389$	−1.87688e10	+	1.87688e10i	−0.819668	+	0.819668i	0.166392	+	0.986060i	$0.446788\pi$
$390$	−4.67276e9	−	9.70309e9i	−0.201983	−	0.419422i
$391$	−6.93933e8	+	6.15883e9i	−0.0296900	+	0.263506i
$392$	4.62625e9	+	5.21253e8i	0.195923	+	0.0220752i
$393$	3.79963e10	−	1.82981e10i	1.59284	−	0.767070i
$394$	−3.66373e9	−	3.66373e9i	−0.152033	−	0.152033i
$395$	−1.20019e10	+	3.42995e10i	−0.493018	+	1.40896i
$396$	1.04934e9	−	1.67002e9i	0.0426714	−	0.0679111i
$397$	−6.42381e9	−	3.09354e9i	−0.258601	−	0.124536i	0.300092	−	0.953910i	$-0.402983\pi$
$397$	−6.42381e9	−	3.09354e9i	−0.258601	−	0.124536i	−0.558693	+	0.829375i	$0.688697\pi$
$398$	1.88789e10	+	5.39528e10i	0.752393	+	2.15022i
$399$	2.74906e10	+	6.27456e9i	1.08466	+	0.247566i
$400$	−2.27647e10	−	2.85461e10i	−0.889247	−	1.11508i
$401$	−1.79436e10	+	2.25006e10i	−0.693957	+	0.870195i	−0.996556	−	0.0829230i	$-0.973574\pi$
$401$	−1.79436e10	+	2.25006e10i	−0.693957	+	0.870195i	0.302598	+	0.953118i	$0.402146\pi$
$402$	2.51578e8	+	1.10223e9i	0.00963314	+	0.0422056i
$403$	−1.33567e9	−	2.12571e9i	−0.0506384	−	0.0805906i
$404$	4.95447e8	+	4.39721e9i	0.0185982	+	0.165064i
$405$		−	4.69556e10i		−	1.74529i
$406$	−5.27247e9	−	1.60578e10i	−0.194048	−	0.590994i
$407$	−4.17257e9			−0.152064
$408$	−1.75931e9	+	1.98226e8i	−0.0634894	+	0.00715353i
$409$	−4.03209e9	+	2.53353e9i	−0.144091	+	0.0905383i	−0.602148	−	0.798384i	$-0.705688\pi$
$409$	−4.03209e9	+	2.53353e9i	−0.144091	+	0.0905383i	0.458057	+	0.888923i	$0.348545\pi$
$410$	−4.34720e10	+	9.92221e9i	−1.53842	+	0.351134i
$411$	−1.82892e10	−	1.45852e10i	−0.640957	−	0.511146i
$412$	1.70452e10	−	1.35931e10i	0.591579	−	0.471769i
$413$	2.32967e9	−	1.02070e10i	0.0800745	−	0.350829i
$414$	4.09947e10	−	1.43447e10i	1.39549	−	0.488302i
$415$	−3.77331e10	+	7.83536e10i	−1.27213	+	2.64160i
$416$	−5.69447e9	−	3.57807e9i	−0.190143	−	0.119475i
$417$	−2.85638e10	−	9.99491e9i	−0.944652	−	0.330548i
$418$	6.53950e9	−	6.53950e9i	0.214210	−	0.214210i
$419$	−1.80225e10	−	3.74240e10i	−0.584733	−	1.21421i	−0.958075	−	0.286518i	$-0.907502\pi$
$419$	−1.80225e10	−	3.74240e10i	−0.584733	−	1.21421i	0.373342	−	0.927694i	$-0.378212\pi$
$420$	−2.62097e9	+	2.32617e10i	−0.0842295	+	0.747557i
$421$	1.38732e10	+	1.56313e9i	0.441618	+	0.0497584i	0.329975	−	0.943990i	$-0.392960\pi$
$421$	1.38732e10	+	1.56313e9i	0.441618	+	0.0497584i	0.111644	+	0.993748i	$0.464388\pi$
$422$	5.93786e9	−	2.85952e9i	0.187232	−	0.0901661i
$423$	−1.68863e10	−	1.68863e10i	−0.527440	−	0.527440i
$424$	4.67502e9	−	1.33604e10i	0.144650	−	0.413387i
$425$	4.09781e9	−	6.52162e9i	0.125602	−	0.199894i
$426$	−1.81979e10	−	8.76363e9i	−0.552564	−	0.266101i
$427$	4.93274e9	+	1.40970e10i	0.148381	+	0.424047i
$428$	−4.58167e10	−	1.04574e10i	−1.36536	−	0.311636i
$429$	−6.09310e8	−	7.64051e8i	−0.0179891	−	0.0225576i
$430$	1.23906e10	−	1.55373e10i	0.362426	−	0.454467i
$431$	4.58017e9	+	2.00670e10i	0.132731	+	0.581532i	0.996924	+	0.0783721i	$0.0249722\pi$
$431$	4.58017e9	+	2.00670e10i	0.132731	+	0.581532i	−0.864193	+	0.503160i	$0.832171\pi$
$432$	−6.02132e9	−	9.58288e9i	−0.172885	−	0.275145i
$433$	−8.16114e7	−	7.24321e8i	−0.00232166	−	0.0206053i	0.992498	−	0.122261i	$-0.0390145\pi$
$433$	−8.16114e7	−	7.24321e8i	−0.00232166	−	0.0206053i	−0.994820	+	0.101656i	$0.967586\pi$
$434$			1.21614e10i			0.342786i
$435$	6.80805e10	−	2.23537e10i	1.90137	−	0.624300i
$436$	−1.87070e10			−0.517677
$437$	9.08054e10	−	1.02313e10i	2.48992	−	0.280547i
$438$	6.91641e10	−	4.34587e10i	1.87925	−	1.18081i
$439$	3.56224e10	−	8.13058e9i	0.959102	−	0.218909i	0.285811	−	0.958286i	$-0.407737\pi$
$439$	3.56224e10	−	8.13058e9i	0.959102	−	0.218909i	0.673291	+	0.739377i	$0.264880\pi$
$440$	−1.37239e9	−	1.09444e9i	−0.0366155	−	0.0291999i
$441$	1.83549e10	−	1.46375e10i	0.485286	−	0.387003i
$442$	3.76544e8	−	1.64975e9i	0.00986568	−	0.0432244i
$443$	−1.80362e9	+	6.31112e8i	−0.0468305	+	0.0163867i	−0.353593	−	0.935399i	$-0.615040\pi$
$443$	−1.80362e9	+	6.31112e8i	−0.0468305	+	0.0163867i	0.306762	+	0.951786i	$0.400754\pi$
$444$	−2.23500e10	+	4.64102e10i	−0.575103	+	1.19421i
$445$	8.13061e10	+	5.10880e10i	2.07340	+	1.30280i
$446$	6.81303e10	+	2.38398e10i	1.72187	+	0.602509i
$447$	1.28955e10	−	1.28955e10i	0.323005	−	0.323005i
$448$	4.84045e9	+	1.00513e10i	0.120164	+	0.249523i
$449$	−6.31108e9	+	5.60124e10i	−0.155281	+	1.37816i	0.638345	+	0.769750i	$0.279619\pi$
$449$	−6.31108e9	+	5.60124e10i	−0.155281	+	1.37816i	−0.793626	+	0.608406i	$0.791809\pi$
$450$	−5.36347e10	−	6.04318e9i	−1.30796	−	0.147372i
$451$	−3.64549e9	+	1.75558e9i	−0.0881150	+	0.0424339i
$452$	−3.58552e10	−	3.58552e10i	−0.859010	−	0.859010i
$453$	−2.36535e9	+	6.75978e9i	−0.0561698	+	0.160524i
$454$	−5.54306e9	+	8.82172e9i	−0.130475	+	0.207649i
$455$	4.60882e9	+	2.21949e9i	0.107534	+	0.0517854i
$456$	8.62136e9	+	2.46384e10i	0.199396	+	0.569841i
$457$	−6.07225e10	−	1.38595e10i	−1.39215	−	0.317748i	−0.540270	−	0.841492i	$-0.681678\pi$
$457$	−6.07225e10	−	1.38595e10i	−1.39215	−	0.317748i	−0.851876	+	0.523744i	$0.824535\pi$
$458$	−2.70373e10	−	3.39037e10i	−0.614470	−	0.770521i
$459$	1.48855e9	−	1.86658e9i	0.0335361	−	0.0420530i
$460$	1.68807e10	+	7.39592e10i	0.377016	+	1.65181i
$461$	−2.79867e10	−	4.45406e10i	−0.619652	−	0.986170i	−0.998164	−	0.0605738i	$-0.980707\pi$
$461$	−2.79867e10	−	4.45406e10i	−0.619652	−	0.986170i	0.378512	−	0.925596i	$-0.376436\pi$
$462$	5.30040e8	+	4.70423e9i	0.0116343	+	0.103257i
$463$			2.02649e10i			0.440981i	0.975389	+	0.220491i	$0.0707658\pi$
$463$			2.02649e10i			0.440981i	−0.975389	+	0.220491i	$0.929234\pi$
$464$	3.40784e10	−	4.10769e10i	0.735204	−	0.886189i
$465$	−5.15606e10			−1.10282
$466$	−6.25825e10	+	7.05135e9i	−1.32712	+	0.149530i
$467$	−6.44880e10	+	4.05205e10i	−1.35585	+	0.851936i	−0.996687	−	0.0813389i	$-0.974080\pi$
$467$	−6.44880e10	+	4.05205e10i	−1.35585	+	0.851936i	−0.359162	+	0.933275i	$0.616938\pi$
$468$	−5.18742e9	+	1.18399e9i	−0.108135	+	0.0246812i
$469$	−4.19850e8	−	3.34819e8i	−0.00867766	−	0.00692020i
$470$	7.26794e10	−	5.79599e10i	1.48943	−	1.18778i
$471$	−4.66095e9	+	2.04210e10i	−0.0947089	+	0.414947i
$472$	9.14796e9	−	3.20101e9i	0.184313	−	0.0644939i
$473$	7.82430e8	−	1.62473e9i	0.0156315	−	0.0324592i
$474$	7.68173e10	+	4.82675e10i	1.52176	+	0.956184i
$475$	−1.07188e11	−	3.75067e10i	−2.10558	−	0.736774i
$476$	−2.60083e9	+	2.60083e9i	−0.0506621	+	0.0506621i
$477$	−3.09703e10	−	6.43106e10i	−0.598236	−	1.24225i
$478$	5.79584e9	−	5.14395e10i	0.111021	−	0.985339i
$479$	−4.76793e10	−	5.37217e9i	−0.905708	−	0.102049i	−0.353192	−	0.935551i	$-0.614904\pi$
$479$	−4.76793e10	−	5.37217e9i	−0.905708	−	0.102049i	−0.552516	+	0.833502i	$0.686332\pi$
$480$	−1.24445e11	+	5.99294e10i	−2.34429	+	1.12895i
$481$	7.95953e9	+	7.95953e9i	0.148699	+	0.148699i
$482$	2.29671e10	−	6.56361e10i	0.425517	−	1.21606i
$483$	−2.48861e10	+	3.96060e10i	−0.457266	+	0.727734i
$484$	−3.96134e10	−	1.90768e10i	−0.721873	−	0.347636i
$485$	−2.95876e10	−	8.45564e10i	−0.534739	−	1.52820i
$486$	−9.36171e10	−	2.13675e10i	−1.67807	−	0.383008i
$487$	1.80271e10	+	2.26052e10i	0.320486	+	0.401877i	0.915812	−	0.401607i	$-0.131548\pi$
$487$	1.80271e10	+	2.26052e10i	0.320486	+	0.401877i	−0.595326	+	0.803485i	$0.702977\pi$
$488$	−8.62024e9	+	1.08094e10i	−0.151999	+	0.190600i
$489$	2.32286e10	+	1.01771e11i	0.406245	+	1.77987i
$490$	4.86212e10	+	7.73802e10i	0.843415	+	1.34229i
$491$	2.09071e9	+	1.85556e10i	0.0359723	+	0.319263i	0.998793	+	0.0491213i	$0.0156421\pi$
$491$	2.09071e9	+	1.85556e10i	0.0359723	+	0.319263i	−0.962820	+	0.270142i	$0.912929\pi$
$492$			4.99513e10i			0.852484i
$493$	1.05533e10	+	3.92351e9i	0.178648	+	0.0664182i
$494$	−2.49493e10			−0.418939
$495$	−8.79618e9	+	9.91091e8i	−0.146512	+	0.0165079i
$496$	−3.25180e10	+	2.04324e10i	−0.537276	+	0.337593i
$497$	9.35326e9	−	2.13482e9i	0.153298	−	0.0349893i
$498$	1.69750e11	+	1.35371e11i	2.75989	+	2.20094i
$499$	−2.94013e10	+	2.34468e10i	−0.474204	+	0.378165i	−0.831229	−	0.555930i	$-0.812362\pi$
$499$	−2.94013e10	+	2.34468e10i	−0.474204	+	0.378165i	0.357026	+	0.934095i	$0.383791\pi$
$500$	4.04172e9	−	1.77079e10i	0.0646674	−	0.283327i
$501$	−7.19945e9	+	2.51920e9i	−0.114274	+	0.0399863i
$502$	3.96187e10	−	8.22690e10i	0.623857	−	1.29545i
$503$	−6.48715e10	−	4.07615e10i	−1.01340	−	0.636763i	−0.0804485	−	0.996759i	$-0.525635\pi$
$503$	−6.48715e10	−	4.07615e10i	−1.01340	−	0.636763i	−0.932954	+	0.359996i	$0.882778\pi$
$504$	−5.56225e9	−	1.94632e9i	−0.0862042	−	0.0301642i
$505$	1.40429e10	−	1.40429e10i	0.215919	−	0.215919i
$506$	6.65641e9	+	1.38222e10i	0.101540	+	0.210850i
$507$	9.59988e9	−	8.52013e10i	0.145289	−	1.28948i
$508$	4.28548e10	+	4.82858e9i	0.643495	+	0.0725045i
$509$	8.10824e10	−	3.90472e10i	1.20797	−	0.581727i	0.282031	−	0.959405i	$-0.408992\pi$
$509$	8.10824e10	−	3.90472e10i	1.20797	−	0.581727i	0.925937	+	0.377678i	$0.123277\pi$
$510$	−2.45745e10	−	2.45745e10i	−0.363249	−	0.363249i
$511$	−1.28144e10	+	3.66215e10i	−0.187938	+	0.537097i
$512$	−4.41846e10	+	7.03194e10i	−0.642971	+	1.02328i
$513$	−3.17145e10	−	1.52729e10i	−0.457919	−	0.220522i
$514$	−1.69979e10	−	4.85771e10i	−0.243524	−	0.695951i
$515$	−9.53926e10	−	2.17727e10i	−1.35608	−	0.309517i
$516$	−1.38804e10	−	1.74055e10i	−0.195796	−	0.245520i
$517$	5.25940e9	−	6.59508e9i	0.0736163	−	0.0923119i
$518$	−1.21337e10	−	5.31611e10i	−0.168529	−	0.738372i
$519$	5.28924e10	+	8.41777e10i	0.728993	+	1.16019i
$520$	5.30203e8	+	4.70568e9i	0.00725152	+	0.0643590i
$521$			5.03959e10i			0.683981i	0.939703	+	0.341991i	$0.111101\pi$
$521$			5.03959e10i			0.683981i	−0.939703	+	0.341991i	$0.888899\pi$
$522$	−7.31548e9	−	7.85592e10i	−0.0985282	−	1.05807i
$523$	1.39207e11			1.86061			0.930305	−	0.366786i	$-0.119542\pi$
$523$	1.39207e11			1.86061			0.930305	+	0.366786i	$0.119542\pi$
$524$	8.05971e10	−	9.08112e9i	1.06904	−	0.120452i
$525$	4.92195e10	−	3.09267e10i	0.647889	−	0.407095i
$526$	8.45539e10	−	1.92989e10i	1.10456	−	0.252109i
$527$	−6.33397e9	−	5.05117e9i	−0.0821171	−	0.0654862i
$528$	−1.16880e10	+	9.32090e9i	−0.150386	+	0.119928i
$529$	−1.63051e10	+	7.14374e10i	−0.208210	+	0.912227i
$530$	2.62265e11	−	9.17703e10i	3.32381	−	1.16305i
$531$	2.12056e10	−	4.40338e10i	0.266730	−	0.553870i
$532$	4.59179e10	+	2.88521e10i	0.573238	+	0.360190i
$533$	1.03030e10	+	3.60517e9i	0.127660	+	0.0446701i
$534$	1.69517e11	−	1.69517e11i	2.08472	−	2.08472i
$535$	9.15120e10	+	1.90027e11i	1.11703	+	2.31953i
$536$	5.56600e7	−	4.93996e8i	0.000674348	−	0.00598501i
$537$	−1.42552e11	−	1.60617e10i	−1.71426	−	0.193150i
$538$	−1.56756e11	+	7.54896e10i	−1.87109	+	0.901069i
$539$	5.86383e9	+	5.86383e9i	0.0694747	+	0.0694747i
$540$	9.65157e9	−	2.75826e10i	0.113507	−	0.324385i
$541$	−2.32409e10	+	3.69877e10i	−0.271309	+	0.431786i	−0.954393	−	0.298554i	$-0.903496\pi$
$541$	−2.32409e10	+	3.69877e10i	−0.271309	+	0.431786i	0.683084	+	0.730340i	$0.260638\pi$
$542$	−3.83427e9	−	1.84649e9i	−0.0444309	−	0.0213968i
$543$	−5.12804e10	−	1.46551e11i	−0.589864	−	1.68573i
$544$	−2.11585e10	−	4.82928e9i	−0.241595	−	0.0551425i
$545$	5.23465e10	+	6.56404e10i	0.593337	+	0.744021i
$546$	7.96263e9	−	9.98482e9i	0.0895954	−	0.112349i
$547$	5.37104e9	+	2.35321e10i	0.0599942	+	0.262852i	0.996026	−	0.0890639i	$-0.0283875\pi$
$547$	5.37104e9	+	2.35321e10i	0.0599942	+	0.262852i	−0.936032	+	0.351916i	$0.885530\pi$
$548$	−2.39358e10	−	3.80936e10i	−0.265415	−	0.422406i
$549$	7.80622e9	+	6.92821e10i	0.0859313	+	0.762661i
$550$		−	1.90653e10i		−	0.208349i
$551$	2.17741e10	−	1.64568e11i	0.236230	−	1.78542i
$552$	−4.33014e10			−0.466386
$553$	−4.28211e10	+	4.82477e9i	−0.457885	+	0.0515913i
$554$	−1.51376e11	+	9.51156e10i	−1.60700	+	1.00975i
$555$	2.25388e11	−	5.14433e10i	2.37552	−	0.542196i
$556$	−4.55028e10	−	3.62873e10i	−0.476145	−	0.379713i
$557$	6.15322e9	−	4.90703e9i	0.0639266	−	0.0509797i	−0.591005	−	0.806668i	$-0.701269\pi$
$557$	6.15322e9	−	4.90703e9i	0.0639266	−	0.0509797i	0.654932	+	0.755688i	$0.272697\pi$
$558$	−1.26330e10	+	5.53486e10i	−0.130307	+	0.570913i
$559$	−4.59187e9	+	1.60676e9i	−0.0470265	+	0.0164553i
$560$	3.39526e10	−	7.05032e10i	0.345240	−	0.716897i
$561$	−2.67024e9	−	1.67783e9i	−0.0269587	−	0.0169393i
$562$	−4.11761e10	−	1.44081e10i	−0.412762	−	0.144432i
$563$	1.03593e11	−	1.03593e11i	1.03109	−	1.03109i	0.0315924	−	0.999501i	$-0.489942\pi$
$563$	1.03593e11	−	1.03593e11i	1.03109	−	1.03109i	0.999501	−	0.0315924i	$-0.0100579\pi$
$564$	−4.51836e10	−	9.38247e10i	−0.446544	−	0.927258i
$565$	−2.54801e10	+	2.26142e11i	−0.250039	+	2.21915i
$566$	−2.04358e11	−	2.30256e10i	−1.99125	−	0.224360i
$567$	5.01677e10	−	2.41595e10i	0.485391	−	0.233752i
$568$	6.27997e9	+	6.27997e9i	0.0603343	+	0.0603343i
$569$	−1.06807e10	+	3.05238e10i	−0.101895	+	0.291199i	−0.983533	−	0.180727i	$-0.942155\pi$
$569$	−1.06807e10	+	3.05238e10i	−0.101895	+	0.291199i	0.881638	+	0.471925i	$0.156441\pi$
$570$	−2.72616e11	+	4.33866e11i	−2.58257	+	4.11014i
$571$	−1.55543e10	−	7.49054e9i	−0.146320	−	0.0704642i	0.359291	−	0.933226i	$-0.383019\pi$
$571$	−1.55543e10	−	7.49054e9i	−0.146320	−	0.0704642i	−0.505611	+	0.862761i	$0.668733\pi$
$572$	−6.20751e8	−	1.77400e9i	−0.00579874	−	0.0165718i
$573$	−4.89075e10	−	1.11628e10i	−0.453688	−	0.103551i
$574$	−3.29681e10	−	4.13407e10i	−0.303701	−	0.380829i
$575$	1.17453e11	−	1.47281e11i	1.07446	−	1.34734i
$576$	1.15887e10	+	5.07736e10i	0.105280	+	0.461262i
$577$	−8.16362e10	−	1.29923e11i	−0.736511	−	1.17215i	−0.979367	−	0.202088i	$-0.935227\pi$
$577$	−8.16362e10	−	1.29923e11i	−0.736511	−	1.17215i	0.242856	−	0.970062i	$-0.421916\pi$
$578$	1.62192e10	+	1.43950e11i	0.145318	+	1.28973i
$579$			4.49846e9i			0.0400267i
$580$	1.37785e11	+	2.66606e9i	1.21756	+	0.0235590i
$581$	−1.03128e11			−0.905047
$582$	−2.22247e11	+	2.50412e10i	−1.93706	+	0.218255i
$583$	2.13487e10	−	1.34143e10i	0.184798	−	0.116116i
$584$	−3.50165e10	+	7.99229e9i	−0.301038	+	0.0687100i
$585$	1.86700e10	+	1.48889e10i	0.159412	+	0.127127i
$586$	2.54046e9	−	2.02595e9i	0.0215438	−	0.0171806i
$587$	2.56021e10	−	1.12170e11i	0.215637	−	0.944767i	−0.745023	−	0.667039i	$-0.767561\pi$
$587$	2.56021e10	−	1.12170e11i	0.215637	−	0.944767i	0.960660	−	0.277728i	$-0.0895814\pi$
$588$	9.66308e10	−	3.38126e10i	0.808362	−	0.282858i
$589$	−5.18263e10	+	1.07618e11i	−0.430615	+	0.894180i
$590$	1.61089e11	+	1.01219e11i	1.32941	+	0.835324i
$591$	2.45878e10	+	8.60365e9i	0.201544	+	0.0705234i
$592$	1.21761e11	−	1.21761e11i	0.991335	−	0.991335i
$593$	2.52976e10	+	5.25311e10i	0.204579	+	0.424813i	0.977863	−	0.209247i	$-0.0671014\pi$
$593$	2.52976e10	+	5.25311e10i	0.204579	+	0.424813i	−0.773284	+	0.634060i	$0.781387\pi$
$594$	6.61674e8	−	5.87252e9i	0.00531494	−	0.0471714i
$595$	1.64036e10	+	1.84825e9i	0.130880	+	0.0147466i
$596$	3.16004e10	−	1.52179e10i	0.250442	−	0.120606i
$597$	−2.03209e11	−	2.03209e11i	−1.59973	−	1.59973i
$598$	1.36693e10	−	3.90646e10i	0.106891	−	0.305477i
$599$	8.25461e9	−	1.31371e10i	0.0641193	−	0.102045i	−0.813126	−	0.582088i	$-0.802236\pi$
$599$	8.25461e9	−	1.31371e10i	0.0641193	−	0.102045i	0.877245	+	0.480043i	$0.159379\pi$
$600$	4.84828e10	+	2.33481e10i	0.374096	+	0.180155i
$601$	−1.61029e10	−	4.60196e10i	−0.123426	−	0.352732i	0.865547	−	0.500828i	$-0.166971\pi$
$601$	−1.61029e10	−	4.60196e10i	−0.123426	−	0.352732i	−0.988973	+	0.148096i	$0.952685\pi$
$602$	2.29754e10	+	5.24398e9i	0.174935	+	0.0399278i
$603$	−1.56301e9	−	1.95996e9i	−0.0118221	−	0.0148244i
$604$	−8.58759e9	+	1.07685e10i	−0.0645243	+	0.0809109i
$605$	4.39093e10	+	1.92379e11i	0.327744	+	1.43594i
$606$	−2.63788e10	−	4.19817e10i	−0.195598	−	0.311293i
$607$	−6.02170e9	−	5.34441e10i	−0.0443573	−	0.393682i	−0.996200	−	0.0870949i	$-0.972242\pi$
$607$	−6.02170e9	−	5.34441e10i	−0.0443573	−	0.393682i	0.951843	−	0.306587i	$-0.0991869\pi$
$608$			3.19982e11i			2.34159i
$609$	5.89115e10	+	6.12363e10i	0.428283	+	0.445184i
$610$	−2.71400e11			−1.96015
$611$	−2.26134e10	+	2.54792e9i	−0.162256	+	0.0182819i
$612$	−1.45385e10	+	9.13517e9i	−0.103637	+	0.0651195i
$613$	−1.85980e11	+	4.24487e10i	−1.31712	+	0.300623i	−0.822637	−	0.568567i	$-0.807498\pi$
$613$	−1.85980e11	+	4.24487e10i	−1.31712	+	0.300623i	−0.494478	+	0.869190i	$0.664641\pi$
$614$	−1.76049e11	−	1.40394e11i	−1.23868	−	0.987814i
$615$	1.75272e11	−	1.39775e11i	1.22522	−	0.977078i
$616$	4.63192e8	−	2.02938e9i	0.00321690	−	0.0140942i
$617$	1.10626e11	−	3.87096e10i	0.763335	−	0.267102i	0.0795940	−	0.996827i	$-0.474638\pi$
$617$	1.10626e11	−	3.87096e10i	0.763335	−	0.267102i	0.683741	+	0.729725i	$0.260352\pi$
$618$	−1.05990e11	+	2.20090e11i	−0.726623	+	1.50885i
$619$	−5.58131e10	−	3.50697e10i	−0.380166	−	0.238874i	0.328369	−	0.944549i	$-0.393501\pi$
$619$	−5.58131e10	−	3.50697e10i	−0.380166	−	0.238874i	−0.708536	+	0.705675i	$0.750644\pi$
$620$	−9.35973e10	−	3.27511e10i	−0.633427	−	0.221646i
$621$	4.12895e10	−	4.12895e10i	0.277635	−	0.277635i
$622$	8.62978e10	+	1.79199e11i	0.576552	+	1.19722i
$623$	−1.27494e10	+	1.13154e11i	−0.0846323	+	0.751132i
$624$	4.00764e10	+	4.51552e9i	0.264332	+	0.0297831i
$625$	9.68402e10	−	4.66358e10i	0.634652	−	0.305632i
$626$	−9.36229e10	−	9.36229e10i	−0.609656	−	0.609656i
$627$	−1.53569e10	+	4.38875e10i	−0.0993650	+	0.283969i
$628$	−2.14323e10	+	3.41093e10i	−0.137794	+	0.219298i
$629$	3.27275e10	+	1.57607e10i	0.209079	+	0.100687i
$630$	−3.82061e10	−	1.09187e11i	−0.242533	−	0.693119i
$631$	1.12550e11	+	2.56888e10i	0.709951	+	0.162042i	0.562222	−	0.826986i	$-0.309947\pi$
$631$	1.12550e11	+	2.56888e10i	0.709951	+	0.162042i	0.147729	+	0.989028i	$0.452804\pi$
$632$	−2.48719e10	−	3.11883e10i	−0.155898	−	0.195490i
$633$	−2.06591e10	+	2.59057e10i	−0.128676	+	0.161354i
$634$	−1.46068e10	−	6.39966e10i	−0.0904062	−	0.396096i
$635$	−1.02975e11	−	1.63883e11i	−0.633338	−	1.00795i
$636$	−3.48506e10	−	3.09308e11i	−0.213001	−	1.89044i
$637$		−	2.23715e10i		−	0.135874i
$638$	2.72857e10	−	5.67475e9i	0.164684	−	0.0342503i
$639$	4.47861e10			0.268621
$640$	1.22868e11	−	1.38439e10i	0.732351	−	0.0825161i
$641$	1.22030e11	−	7.66766e10i	0.722828	−	0.454183i	−0.119718	−	0.992808i	$-0.538199\pi$
$641$	1.22030e11	−	7.66766e10i	0.722828	−	0.454183i	0.842546	+	0.538625i	$0.181056\pi$
$642$	5.13363e11	−	1.17172e11i	3.02193	−	0.689736i
$643$	2.08764e11	+	1.66483e11i	1.22127	+	0.973928i	0.999999	−	0.00128448i	$-0.000408863\pi$
$643$	2.08764e11	+	1.66483e11i	1.22127	+	0.973928i	0.221268	+	0.975213i	$0.428980\pi$
$644$	−7.03331e10	+	5.60888e10i	−0.408899	+	0.326086i
$645$	−2.22330e10	+	9.74089e10i	−0.128457	+	0.562808i
$646$	−7.59936e10	+	2.65913e10i	−0.436362	+	0.152690i
$647$	4.48481e10	−	9.31280e10i	0.255933	−	0.531451i	−0.732925	−	0.680309i	$-0.761846\pi$
$647$	4.48481e10	−	9.31280e10i	0.255933	−	0.531451i	0.988859	+	0.148858i	$0.0475598\pi$
$648$	4.36454e10	+	2.74242e10i	0.247536	+	0.155537i
$649$	1.62949e10	+	5.70184e9i	0.0918488	+	0.0321393i
$650$	−3.63686e10	+	3.63686e10i	−0.203739	+	0.203739i
$651$	−2.65288e10	−	5.50877e10i	−0.147705	−	0.306712i
$652$	−2.24781e10	+	1.99499e11i	−0.124385	+	1.10395i
$653$	6.68911e10	+	7.53682e9i	0.367888	+	0.0414510i	0.293973	−	0.955814i	$-0.405022\pi$
$653$	6.68911e10	+	7.53682e9i	0.367888	+	0.0414510i	0.0739144	+	0.997265i	$0.476451\pi$
$654$	1.88849e11	−	9.09451e10i	1.03230	−	0.497128i
$655$	−2.57394e11	−	2.57394e11i	−1.39840	−	1.39840i
$656$	5.51500e10	−	1.57610e11i	0.297804	−	0.851075i
$657$	−9.63626e10	+	1.53360e11i	−0.517186	+	0.823097i
$658$	9.93195e10	+	4.78298e10i	0.529823	+	0.255149i
$659$	6.80230e10	+	1.94398e11i	0.360673	+	1.03074i	0.971100	+	0.238672i	$0.0767121\pi$
$659$	6.80230e10	+	1.94398e11i	0.360673	+	1.03074i	−0.610427	+	0.792073i	$0.709002\pi$
$660$	−3.76326e10	−	8.58939e9i	−0.198330	−	0.0452675i
$661$	7.95811e10	+	9.97915e10i	0.416873	+	0.522742i	0.945285	−	0.326246i	$-0.105784\pi$
$661$	7.95811e10	+	9.97915e10i	0.416873	+	0.522742i	−0.528412	+	0.848988i	$0.677212\pi$
$662$	−2.31948e11	+	2.90854e11i	−1.20770	+	1.51441i
$663$	1.89312e9	+	8.29432e9i	0.00979772	+	0.0429266i
$664$	−5.07921e10	−	8.08351e10i	−0.261290	−	0.415841i
$665$	−2.72504e10	−	2.41854e11i	−0.139344	−	1.23671i
$666$		−	2.54551e11i		−	1.29383i
$667$	2.45744e11	+	1.24257e11i	1.24160	+	0.627795i
$668$	−1.46693e10			−0.0736720
$669$	−3.60616e11	+	4.06317e10i	−1.80028	+	0.202843i
$670$	8.26275e9	−	5.19183e9i	0.0410039	−	0.0257645i
$671$	−2.40099e10	+	5.48010e9i	−0.118441	+	0.0270333i
$672$	−1.28058e11	−	1.02123e11i	−0.627956	−	0.500778i
$673$	2.80135e10	−	2.23400e10i	0.136555	−	0.108899i	−0.552830	−	0.833294i	$-0.686452\pi$
$673$	2.80135e10	−	2.23400e10i	0.136555	−	0.108899i	0.689385	+	0.724395i	$0.257881\pi$
$674$	−3.72342e10	+	1.63133e11i	−0.180427	+	0.790503i
$675$	−6.84935e10	+	2.39669e10i	−0.329940	+	0.115451i
$676$	7.15461e10	−	1.48567e11i	0.342609	−	0.711436i
$677$	−9.35932e10	−	5.88085e10i	−0.445543	−	0.279953i	0.290517	−	0.956870i	$-0.406173\pi$
$677$	−9.35932e10	−	5.88085e10i	−0.445543	−	0.279953i	−0.736060	+	0.676917i	$0.763316\pi$
$678$	5.36274e11	+	1.87650e11i	2.53786	+	0.888035i
$679$	7.51173e10	−	7.51173e10i	0.353395	−	0.353395i
$680$	6.63033e9	+	1.37680e10i	0.0310099	+	0.0643926i
$681$	5.86482e9	−	5.20517e10i	0.0272688	−	0.242017i
$682$	−1.99275e10	−	2.24529e9i	−0.0921118	−	0.0103785i
$683$	−2.62168e11	+	1.26253e11i	−1.20475	+	0.580176i	−0.925026	−	0.379905i	$-0.875957\pi$
$683$	−2.62168e11	+	1.26253e11i	−1.20475	+	0.580176i	−0.279722	+	0.960081i	$0.590242\pi$
$684$	1.79010e11	+	1.79010e11i	0.817811	+	0.817811i
$685$	−6.66875e10	+	1.90582e11i	−0.302888	+	0.865605i
$686$	−1.30948e11	+	2.08402e11i	−0.591292	+	0.941036i
$687$	1.96429e11	+	9.45953e10i	0.881818	+	0.424661i
$688$	2.45794e10	+	7.02440e10i	0.109703	+	0.313513i
$689$	−6.63134e10	−	1.51356e10i	−0.294256	−	0.0671619i
$690$	−5.29968e11	−	6.64559e11i	−2.33805	−	2.93182i
$691$	−5.72458e10	+	7.17839e10i	−0.251091	+	0.314858i	−0.891363	−	0.453290i	$-0.850250\pi$
$691$	−5.72458e10	+	7.17839e10i	−0.251091	+	0.314858i	0.640272	+	0.768148i	$0.278822\pi$
$692$	4.25455e10	+	1.86404e11i	0.185536	+	0.812888i
$693$	−5.58468e9	−	8.88796e9i	−0.0242139	−	0.0385362i
$694$	−6.82308e10	−	6.05565e11i	−0.294132	−	2.61049i
$695$			2.61203e11i			1.11954i
$696$	−1.89843e10	+	7.63367e10i	−0.0809016	+	0.325309i
$697$	3.52245e10			0.149250
$698$	2.20827e11	−	2.48813e10i	0.930318	−	0.104822i
$699$	2.68100e11	−	1.68458e11i	1.12302	−	0.705641i
$700$	1.08992e11	−	2.48768e10i	0.453945	−	0.103610i
$701$	2.05854e11	+	1.64163e11i	0.852486	+	0.679835i	0.948924	−	0.315504i	$-0.102174\pi$
$701$	2.05854e11	+	1.64163e11i	0.852486	+	0.679835i	−0.0964383	+	0.995339i	$0.530745\pi$
$702$	−1.24645e10	+	9.94013e9i	−0.0513248	+	0.0409302i
$703$	1.19176e11	−	5.22142e11i	0.487939	−	2.13780i
$704$	−1.73637e10	+	6.07581e9i	−0.0706888	+	0.0247351i
$705$	−2.02784e11	+	4.21086e11i	−0.820876	+	1.70457i
$706$	5.02729e11	+	3.15886e11i	2.02356	+	1.27148i
$707$	2.22288e10	+	7.77819e9i	0.0889689	+	0.0311316i
$708$	1.50702e11	−	1.50702e11i	0.599772	−	0.599772i
$709$	−1.43384e11	−	2.97740e11i	−0.567435	−	1.17829i	−0.965372	−	0.260879i	$-0.915988\pi$
$709$	−1.43384e11	−	2.97740e11i	−0.567435	−	1.17829i	0.397936	−	0.917413i	$-0.369727\pi$
$710$	−1.95197e10	+	1.73242e11i	−0.0768137	+	0.681740i
$711$	−1.99899e11	−	2.25232e10i	−0.782225	−	0.0881356i
$712$	−9.49730e10	+	4.57366e10i	−0.369556	+	0.177969i
$713$	−1.40110e11	−	1.40110e11i	−0.542138	−	0.542138i
$714$	1.36116e10	−	3.88996e10i	0.0523740	−	0.149676i
$715$	−4.48774e9	+	7.14220e9i	−0.0171713	+	0.0273280i
$716$	−2.48570e11	−	1.19705e11i	−0.945796	−	0.455471i
$717$	8.59568e10	+	2.45650e11i	0.325240	+	0.929482i
$718$	−3.74550e11	−	8.54887e10i	−1.40933	−	0.321670i
$719$	−7.08279e10	−	8.88153e10i	−0.265026	−	0.332332i	0.631456	−	0.775411i	$-0.282457\pi$
$719$	−7.08279e10	−	8.88153e10i	−0.265026	−	0.332332i	−0.896482	+	0.443079i	$0.853886\pi$
$720$	2.27762e11	−	2.85605e11i	0.847523	−	1.06276i
$721$	−2.58190e10	−	1.13121e11i	−0.0955430	−	0.418601i
$722$	4.36841e11	+	6.95228e11i	1.60759	+	2.55846i
$723$	3.91442e10	+	3.47414e11i	0.143256	+	1.27144i
$724$		−	2.98605e11i		−	1.08678i
$725$	−2.08151e11	−	2.71631e11i	−0.753401	−	0.983167i
$726$	4.92644e11			1.77332
$727$	−2.04842e11	+	2.30801e10i	−0.733299	+	0.0826230i	−0.470714	−	0.882286i	$-0.656004\pi$
$727$	−2.04842e11	+	2.30801e10i	−0.733299	+	0.0826230i	−0.262585	+	0.964909i	$0.584575\pi$
$728$	−4.75478e9	+	2.98763e9i	−0.0169280	+	0.0106366i
$729$	1.49485e11	−	3.41189e10i	0.529281	−	0.120805i
$730$	−5.51230e11	−	4.39591e11i	−1.94107	−	1.54795i
$731$	−1.22740e10	+	9.78815e9i	−0.0429848	+	0.0342792i
$732$	−6.76533e10	+	2.96409e11i	−0.235638	+	1.03240i
$733$	6.58819e10	−	2.30531e10i	0.228218	−	0.0798570i	−0.213748	−	0.976889i	$-0.568567\pi$
$733$	6.58819e10	−	2.30531e10i	0.228218	−	0.0798570i	0.441966	+	0.897032i	$0.354281\pi$
$734$	−4.98489e10	+	1.03512e11i	−0.171740	+	0.356622i
$735$	−3.89039e11	−	2.44449e11i	−1.33304	−	0.837605i
$736$	−5.01014e11	−	1.75313e11i	−1.70741	−	0.597450i
$737$	6.26147e8	−	6.26147e8i	0.00212230	−	0.00212230i
$738$	−1.07100e11	−	2.22396e11i	−0.361048	−	0.749724i
$739$	−4.43857e10	+	3.93934e11i	−0.148821	+	1.32083i	0.668098	+	0.744074i	$0.267109\pi$
$739$	−4.43857e10	+	3.93934e11i	−0.148821	+	1.32083i	−0.816919	+	0.576752i	$0.804320\pi$
$740$	4.41820e11	+	4.97812e10i	1.47339	+	0.166012i
$741$	1.13014e11	−	5.44246e10i	0.374851	−	0.180519i
$742$	2.32988e11	+	2.32988e11i	0.768630	+	0.768630i
$743$	−2.71919e10	+	7.77100e10i	−0.0892245	+	0.254989i	−0.979845	−	0.199758i	$-0.935985\pi$
$743$	−2.71919e10	+	7.77100e10i	−0.0892245	+	0.254989i	0.890621	+	0.454747i	$0.150270\pi$
$744$	3.01137e10	−	4.79258e10i	0.0982818	−	0.156415i
$745$	−1.41823e11	−	6.82982e10i	−0.460384	−	0.221709i
$746$	8.41850e10	+	2.40587e11i	0.271819	+	0.776813i
$747$	−4.69355e11	−	1.07127e11i	−1.50737	−	0.344046i
$748$	−3.78151e9	−	4.74187e9i	−0.0120798	−	0.0151476i
$749$	−1.55941e11	+	1.95544e11i	−0.495489	+	0.621323i
$750$	4.52863e10	+	1.98412e11i	0.143127	+	0.627080i
$751$	2.72292e11	+	4.33350e11i	0.856002	+	1.36232i	0.930956	+	0.365132i	$0.118976\pi$
$751$	2.72292e11	+	4.33350e11i	0.856002	+	1.36232i	−0.0749540	+	0.997187i	$0.523881\pi$
$752$	3.89767e10	+	3.45928e11i	0.121880	+	1.08172i
$753$			4.59081e11i			1.42794i
$754$	−6.28748e10	−	4.12247e10i	−0.194532	−	0.127547i
$755$	6.18152e10			0.190242
$756$	3.44353e10	−	3.87993e9i	0.105419	−	0.0118778i
$757$	1.17601e11	−	7.38935e10i	0.358119	−	0.225021i	−0.340940	−	0.940085i	$-0.610745\pi$
$757$	1.17601e11	−	7.38935e10i	0.358119	−	0.225021i	0.699059	+	0.715064i	$0.253603\pi$
$758$	−2.34656e11	+	5.35586e10i	−0.710811	+	0.162238i
$759$	−6.03035e10	−	4.80904e10i	−0.181709	−	0.144908i
$760$	1.76153e11	−	1.40477e11i	0.528001	−	0.421067i
$761$	6.93987e10	−	3.04056e11i	0.206925	−	0.906597i	−0.759674	−	0.650304i	$-0.774642\pi$
$761$	6.93987e10	−	3.04056e11i	0.206925	−	0.906597i	0.966599	−	0.256293i	$-0.0825013\pi$
$762$	−4.56098e11	+	1.59596e11i	−1.35282	+	0.473371i
$763$	−4.31975e10	+	8.97005e10i	−0.127456	+	0.264665i
$764$	−8.16907e10	−	5.13297e10i	−0.239772	−	0.150659i
$765$	7.27362e10	+	2.54515e10i	0.212376	+	0.0743135i
$766$	8.29128e10	−	8.29128e10i	0.240828	−	0.240828i
$767$	−2.02072e10	−	4.19607e10i	−0.0583882	−	0.121244i
$768$	6.58036e10	−	5.84023e11i	0.189149	−	1.67875i
$769$	1.64475e11	+	1.85318e10i	0.470320	+	0.0529924i	0.343944	−	0.938990i	$-0.388237\pi$
$769$	1.64475e11	+	1.85318e10i	0.470320	+	0.0529924i	0.126376	+	0.991982i	$0.459665\pi$
$770$	3.68145e10	−	1.77289e10i	0.104726	−	0.0504335i
$771$	1.82962e11	+	1.82962e11i	0.517778	+	0.517778i
$772$	−2.85741e9	+	8.16601e9i	−0.00804458	+	0.0229901i
$773$	3.24991e11	−	5.17221e11i	0.910236	−	1.44863i	0.0165885	−	0.999862i	$-0.494719\pi$
$773$	3.24991e11	−	5.17221e11i	0.910236	−	1.44863i	0.893647	−	0.448770i	$-0.148138\pi$
$774$	9.91181e10	+	4.77327e10i	0.276178	+	0.133000i
$775$	8.13281e10	+	2.32422e11i	0.225442	+	0.644275i
$776$	9.58760e10	+	2.18831e10i	0.264401	+	0.0603478i
$777$	1.70928e11	+	2.14337e11i	0.468954	+	0.588049i
$778$	3.56623e11	−	4.47191e11i	0.973399	−	1.22060i
$779$	−1.15566e11	−	5.06327e11i	−0.313820	−	1.37493i
$780$	5.54024e10	+	8.81723e10i	0.149675	+	0.238207i
$781$	1.77125e9	+	1.57203e10i	0.00476077	+	0.0422530i
$782$		−	1.33557e11i		−	0.357140i
$783$	−5.46878e10	−	9.08923e10i	−0.145493	−	0.241813i
$784$	−3.42228e11			−0.905839
$785$	1.79657e11	−	2.02425e10i	0.473115	−	0.0533073i
$786$	−7.69488e11	+	4.83501e11i	−2.01610	+	1.26680i
$787$	−5.40499e11	+	1.23365e11i	−1.40895	+	0.321584i	−0.858298	−	0.513151i	$-0.828478\pi$
$787$	−5.40499e11	+	1.23365e11i	−1.40895	+	0.321584i	−0.550652	+	0.834735i	$0.685621\pi$
$788$	3.91690e10	+	3.12362e10i	0.101587	+	0.0810128i
$789$	−3.40908e11	+	2.71865e11i	−0.879689	+	0.701528i
$790$	1.74248e11	−	7.63433e11i	0.447364	−	1.96003i
$791$	−2.54722e11	+	8.91310e10i	−0.650669	+	0.227679i
$792$	4.21615e9	−	8.75492e9i	0.0107156	−	0.0222511i
$793$	5.62547e10	+	3.53472e10i	0.142255	+	0.0893844i
$794$	1.45021e11	+	5.07449e10i	0.364878	+	0.127676i
$795$	−9.87800e11	+	9.87800e11i	−2.47287	+	2.47287i
$796$	−2.39806e11	−	4.97962e11i	−0.597320	−	1.24035i
$797$	4.67440e10	−	4.14864e11i	0.115849	−	1.02819i	−0.792470	−	0.609911i	$-0.791205\pi$
$797$	4.67440e10	−	4.14864e11i	0.115849	−	1.02819i	0.908319	−	0.418278i	$-0.137366\pi$
$798$	−6.03812e11	−	6.80332e10i	−1.48898	−	0.167768i
$799$	−6.61631e10	+	3.18625e10i	−0.162341	+	0.0781794i
$800$	4.66437e11	+	4.66437e11i	1.13876	+	1.13876i
$801$	−1.75567e11	+	5.01740e11i	−0.426493	+	1.21885i
$802$	3.29949e11	−	5.25111e11i	0.797535	−	1.26927i
$803$	−5.76419e10	−	2.77589e10i	−0.138636	−	0.0667636i
$804$	−3.61054e9	−	1.03183e10i	−0.00864069	−	0.0246937i
$805$	3.93616e11	+	8.98403e10i	0.937323	+	0.213938i
$806$	3.37303e10	+	4.22965e10i	0.0799246	+	0.100222i
$807$	5.45389e11	−	6.83896e11i	1.28591	−	1.61249i
$808$	4.85122e9	+	2.12546e10i	0.0113816	+	0.0498663i
$809$	−4.50146e11	−	7.16404e11i	−1.05090	−	1.67249i	−0.658245	−	0.752804i	$-0.728701\pi$
$809$	−4.50146e11	−	7.16404e11i	−1.05090	−	1.67249i	−0.392651	−	0.919688i	$-0.628442\pi$
$810$	1.13291e11	+	1.00549e12i	0.263182	+	2.33580i
$811$			4.91760e11i			1.13676i	0.822766	+	0.568381i	$0.192430\pi$
$811$			4.91760e11i			1.13676i	−0.822766	+	0.568381i	$0.807570\pi$
$812$	6.80443e10	+	1.48582e11i	0.156519	+	0.341776i
$813$	2.13961e10			0.0489749
$814$	8.93496e10	−	1.00673e10i	0.203514	−	0.0229306i
$815$	7.62913e11	−	4.79370e11i	1.72920	−	1.08653i
$816$	1.26882e11	−	2.89600e10i	0.286180	−	0.0653188i
$817$	1.80967e11	+	1.44316e11i	0.406172	+	0.323911i
$818$	8.02286e10	−	6.39802e10i	0.179191	−	0.142900i
$819$	−6.30130e9	+	2.76078e10i	−0.0140054	+	0.0613615i
$820$	4.06955e11	−	1.42400e11i	0.900099	−	0.314958i
$821$	1.16784e10	−	2.42505e10i	0.0257047	−	0.0533763i	−0.887721	−	0.460381i	$-0.847713\pi$
$821$	1.16784e10	−	2.42505e10i	0.0257047	−	0.0533763i	0.913426	+	0.407005i	$0.133427\pi$
$822$	4.26828e11	+	2.68194e11i	0.934901	+	0.587437i
$823$	1.18914e11	+	4.16096e10i	0.259198	+	0.0906974i	0.456750	−	0.889595i	$-0.349013\pi$
$823$	1.18914e11	+	4.16096e10i	0.259198	+	0.0906974i	−0.197552	+	0.980292i	$0.563299\pi$
$824$	7.59515e10	−	7.59515e10i	0.164751	−	0.164751i
$825$	4.15891e10	+	8.63606e10i	0.0897767	+	0.186423i
$826$	−2.52599e10	+	2.24188e11i	−0.0542640	+	0.481607i
$827$	1.10131e10	+	1.24088e9i	0.0235444	+	0.00265282i	0.123729	−	0.992316i	$-0.460515\pi$
$827$	1.10131e10	+	1.24088e9i	0.0235444	+	0.00265282i	−0.100184	+	0.994969i	$0.531943\pi$
$828$	−3.78363e11	+	1.82210e11i	−0.804985	+	0.387660i
$829$	2.34335e11	+	2.34335e11i	0.496158	+	0.496158i	0.910240	−	0.414082i	$-0.135897\pi$
$829$	2.34335e11	+	2.34335e11i	0.496158	+	0.496158i	−0.414082	+	0.910240i	$0.635897\pi$
$830$	6.18954e11	−	1.76887e12i	1.30421	−	3.72720i
$831$	4.78205e11	−	7.61059e11i	1.00279	−	1.59593i
$832$	4.47128e10	+	2.15325e10i	0.0933122	+	0.0449368i
$833$	−2.38439e10	−	6.81419e10i	−0.0495218	−	0.141525i
$834$	6.35768e11	+	1.45110e11i	1.31412	+	0.299939i
$835$	4.10479e10	+	5.14725e10i	0.0844395	+	0.105884i
$836$	−5.57544e10	+	6.99139e10i	−0.114144	+	0.143132i
$837$	1.69844e10	+	7.44137e10i	0.0346058	+	0.151618i
$838$	4.76219e11	+	7.57898e11i	0.965675	+	1.53686i
$839$	−8.36224e10	−	7.42170e11i	−0.168762	−	1.49781i	−0.737534	−	0.675310i	$-0.764010\pi$
$839$	−8.36224e10	−	7.42170e11i	−0.168762	−	1.49781i	0.568772	−	0.822495i	$-0.307419\pi$
$840$			1.15330e11i			0.231647i
$841$	3.26795e11	−	3.78750e11i	0.653268	−	0.757127i
$842$	−3.00845e11			−0.598542
$843$	2.17947e11	−	2.45567e10i	0.431559	−	0.0486250i
$844$	−5.39575e10	+	3.39038e10i	−0.106336	+	0.0668156i
$845$	−7.21504e11	+	1.64679e11i	−1.41518	+	0.323006i
$846$	4.02338e11	+	3.20854e11i	0.785433	+	0.626362i
$847$	−1.82947e11	+	1.45896e11i	−0.355461	+	0.283471i
$848$	−2.31537e11	+	1.01443e12i	−0.447751	+	1.96172i
$849$	9.75916e11	−	3.41488e11i	1.87837	−	0.657271i
$850$	−7.20138e10	+	1.49538e11i	−0.137956	+	0.286468i
$851$	7.52255e11	+	4.72673e11i	1.43432	+	0.901245i
$852$	1.84340e11	+	6.45033e10i	0.349833	+	0.122412i
$853$	−8.16202e10	+	8.16202e10i	−0.154171	+	0.154171i	−0.779978	−	0.625807i	$-0.784770\pi$
$853$	−8.16202e10	+	8.16202e10i	−0.154171	+	0.154171i	0.625807	+	0.779978i	$0.284770\pi$
$854$	−1.39640e11	−	2.89965e11i	−0.262529	−	0.545148i
$855$	1.27211e11	−	1.12903e12i	0.238047	−	2.11272i
$856$	−2.30078e11	−	2.59235e10i	−0.428528	−	0.0482836i
$857$	2.76253e11	−	1.33036e11i	0.512134	−	0.246631i	−0.159924	−	0.987129i	$-0.551125\pi$
$857$	2.76253e11	−	1.33036e11i	0.512134	−	0.246631i	0.672058	+	0.740498i	$0.265411\pi$
$858$	1.48909e10	+	1.48909e10i	0.0274772	+	0.0274772i
$859$	−1.93830e11	+	5.53935e11i	−0.355999	+	1.01739i	0.617077	+	0.786903i	$0.288317\pi$
$859$	−1.93830e11	+	5.53935e11i	−0.355999	+	1.01739i	−0.973076	+	0.230484i	$0.925969\pi$
$860$	−1.02233e11	+	1.62703e11i	−0.186895	+	0.297442i
$861$	2.39517e11	+	1.15345e11i	0.435837	+	0.209888i
$862$	−1.46494e11	−	4.18656e11i	−0.265333	−	0.758277i
$863$	−9.09531e11	−	2.07595e11i	−1.63974	−	0.374259i	−0.699461	−	0.714671i	$-0.746577\pi$
$863$	−9.09531e11	−	2.07595e11i	−1.63974	−	0.374259i	−0.940277	+	0.340411i	$0.889434\pi$
$864$	1.27485e11	+	1.59861e11i	0.228772	+	0.286871i
$865$	5.35014e11	−	6.70887e11i	0.955655	−	1.19835i
$866$	3.49518e9	+	1.53134e10i	0.00621438	+	0.0272270i
$867$	−3.87481e11	−	6.16672e11i	−0.685763	−	1.09139i
$868$	−1.31660e10	−	1.16851e11i	−0.0231939	−	0.205851i
$869$		−	7.10570e10i		−	0.124603i
$870$	−1.40391e12	+	6.42933e11i	−2.45055	+	1.12225i
$871$	−2.38886e9			−0.00415066
$872$	−9.15858e10	+	1.03192e10i	−0.158403	+	0.0178477i
$873$	4.19904e11	−	2.63843e11i	0.722924	−	0.454243i
$874$	−1.91978e12	+	4.38178e11i	−3.29008	+	0.750939i
$875$	−7.55768e10	−	6.02705e10i	−0.128931	−	0.102819i
$876$	−6.17507e11	+	4.92446e11i	−1.04864	+	0.836261i
$877$	−1.33271e11	+	5.83899e11i	−0.225288	+	0.987050i	0.728140	+	0.685428i	$0.240385\pi$
$877$	−1.33271e11	+	5.83899e11i	−0.225288	+	0.987050i	−0.953428	+	0.301622i	$0.902472\pi$
$878$	−7.43185e11	+	2.60052e11i	−1.25060	+	0.437605i
$879$	−7.08818e9	+	1.47188e10i	−0.0118735	+	0.0246556i
$880$	1.09258e11	+	6.86511e10i	0.182188	+	0.114477i
$881$	5.19932e11	+	1.81932e11i	0.863064	+	0.301999i	0.725272	−	0.688462i	$-0.241714\pi$
$881$	5.19932e11	+	1.81932e11i	0.863064	+	0.301999i	0.137792	+	0.990461i	$0.455999\pi$
$882$	−3.57728e11	+	3.57728e11i	−0.591123	+	0.591123i
$883$	−1.08037e11	−	2.24340e11i	−0.177717	−	0.369033i	0.793014	−	0.609204i	$-0.208511\pi$
$883$	−1.08037e11	−	2.24340e11i	−0.177717	−	0.369033i	−0.970731	+	0.240171i	$0.922796\pi$
$884$	−1.83196e9	+	1.62591e10i	−0.00299990	+	0.0266248i
$885$	−9.50492e11	−	1.07095e11i	−1.54944	−	0.174580i
$886$	3.70991e10	−	1.78660e10i	0.0602045	−	0.0289930i
$887$	4.32628e11	+	4.32628e11i	0.698908	+	0.698908i	0.964175	−	0.265267i	$-0.0854602\pi$
$887$	4.32628e11	+	4.32628e11i	0.698908	+	0.698908i	−0.265267	+	0.964175i	$0.585460\pi$
$888$	−8.38200e10	+	2.39544e11i	−0.134802	+	0.385242i
$889$	1.22112e11	−	1.94340e11i	0.195502	−	0.311139i
$890$	−1.86431e12	−	8.97807e11i	−2.97139	−	1.43094i
$891$	3.03253e10	+	8.66648e10i	0.0481166	+	0.137509i
$892$	−6.80432e11	−	1.55304e11i	−1.07479	−	0.245315i
$893$	6.75070e11	+	8.46511e11i	1.06156	+	1.33115i
$894$	−2.45026e11	+	3.07253e11i	−0.383586	+	0.481001i
$895$	2.75527e11	+	1.20716e12i	0.429410	+	1.88137i
$896$	7.80087e10	+	1.24150e11i	0.121035	+	0.192626i
$897$	2.32975e10	+	2.06771e11i	0.0359864	+	0.319389i
$898$		−	1.21465e12i		−	1.86787i
$899$	−3.08429e11	+	1.85575e11i	−0.472190	+	0.284106i
$900$	5.21886e11			0.795437
$901$	−2.18117e11	+	2.45759e10i	−0.330972	+	0.0372915i
$902$	7.38272e10	−	4.63887e10i	0.111530	−	0.0700787i
$903$	−1.15512e11	+	2.63648e10i	−0.173730	+	0.0396527i
$904$	−1.95318e11	−	1.55761e11i	−0.292462	−	0.233231i
$905$	−1.04777e12	+	8.35565e11i	−1.56196	+	1.24562i
$906$	3.43411e10	−	1.50458e11i	0.0509684	−	0.223307i
$907$	3.79197e10	−	1.32687e10i	0.0560320	−	0.0196064i	−0.302118	−	0.953271i	$-0.597694\pi$
$907$	3.79197e10	−	1.32687e10i	0.0560320	−	0.0196064i	0.358150	+	0.933664i	$0.383408\pi$
$908$	4.37094e10	−	9.07636e10i	0.0643031	−	0.133527i
$909$	9.30877e10	+	5.84909e10i	0.136344	+	0.0856707i
$910$	−1.04046e11	−	3.64073e10i	−0.151726	−	0.0530913i
$911$	−5.24001e11	+	5.24001e11i	−0.760780	+	0.760780i	−0.976463	−	0.215683i	$-0.930802\pi$
$911$	−5.24001e11	+	5.24001e11i	−0.760780	+	0.760780i	0.215683	+	0.976463i	$0.430802\pi$
$912$	−8.32558e11	−	1.72883e12i	−1.20347	−	2.49903i
$913$	1.90400e10	−	1.68984e11i	0.0274021	−	0.243200i
$914$	1.33372e12	+	1.50275e11i	1.91109	+	0.215328i
$915$	1.22937e12	−	5.92032e11i	1.75387	−	0.844619i
$916$	2.96489e11	+	2.96489e11i	0.421140	+	0.421140i
$917$	1.42567e11	−	4.07434e11i	0.201624	−	0.576210i
$918$	−2.73716e10	+	4.35617e10i	−0.0385416	+	0.0613386i
$919$	8.16867e10	+	3.93382e10i	0.114522	+	0.0551509i	0.490268	−	0.871572i	$-0.336899\pi$
$919$	8.16867e10	+	3.93382e10i	0.114522	+	0.0551509i	−0.375746	+	0.926723i	$0.622613\pi$
$920$	1.23442e11	+	3.52777e11i	0.172311	+	0.492436i
$921$	1.10371e12	+	2.51914e11i	1.53397	+	0.350118i
$922$	7.06759e11	+	8.86248e11i	0.978020	+	1.22640i
$923$	2.66090e10	−	3.33667e10i	0.0366625	−	0.0459733i
$924$	−1.01857e10	−	4.46263e10i	−0.0139734	−	0.0612214i
$925$	−5.87405e11	−	9.34849e11i	−0.802362	−	1.27695i
$926$	−4.88937e10	−	4.33943e11i	−0.0664980	−	0.590186i
$927$		−	5.41654e11i		−	0.733505i
$928$	−5.28717e11	+	8.06386e11i	−0.712905	+	1.08730i
$929$	−4.26516e11			−0.572627			−0.286314	−	0.958136i	$-0.592430\pi$
$929$	−4.26516e11			−0.572627			−0.286314	+	0.958136i	$0.592430\pi$
$930$	1.10410e12	−	1.24402e11i	1.47596	−	0.166301i
$931$	−9.01263e11	+	5.66301e11i	−1.19964	+	0.753787i
$932$	5.93683e11	−	1.35504e11i	0.786849	−	0.179593i
$933$	−7.81812e11	−	6.23475e11i	−1.03175	−	0.822796i
$934$	1.28315e12	−	1.02328e12i	1.68613	−	1.34464i
$935$	−6.05705e9	+	2.65377e10i	−0.00792528	+	0.0347229i
$936$	−2.47434e10	+	8.65810e9i	−0.0322371	+	0.0112803i
$937$	5.68698e11	−	1.18091e12i	0.737774	−	1.53200i	−0.105439	−	0.994426i	$-0.533625\pi$
$937$	5.68698e11	−	1.18091e12i	0.737774	−	1.53200i	0.843214	−	0.537579i	$-0.180661\pi$
$938$	9.79831e9	+	6.15669e9i	0.0126573	+	0.00795309i
$939$	6.28317e11	+	2.19857e11i	0.808195	+	0.282800i
$940$	−6.35584e11	+	6.35584e11i	−0.814070	+	0.814070i
$941$	5.69050e11	+	1.18164e12i	0.725758	+	1.50705i	0.856785	+	0.515673i	$0.172458\pi$
$941$	5.69050e11	+	1.18164e12i	0.725758	+	1.50705i	−0.131028	+	0.991379i	$0.541828\pi$
$942$	5.05373e10	−	4.48531e11i	0.0641813	−	0.569625i
$943$	8.56104e11	+	9.64597e10i	1.08263	+	0.121983i
$944$	−6.41892e11	+	3.09119e11i	−0.808303	+	0.389258i
$945$	−1.09972e11	−	1.09972e11i	−0.137897	−	0.137897i
$946$	−1.28346e10	+	3.66791e10i	−0.0160257	+	0.0457988i
$947$	1.48273e11	−	2.35975e11i	0.184358	−	0.293404i	−0.741740	−	0.670688i	$-0.765999\pi$
$947$	1.48273e11	−	2.35975e11i	0.184358	−	0.293404i	0.926098	+	0.377284i	$0.123142\pi$
$948$	−7.90346e11	−	3.80611e11i	−0.978552	−	0.471246i
$949$	5.70044e10	+	1.62909e11i	0.0702819	+	0.200854i
$950$	2.38577e12	+	5.44536e11i	2.92910	+	0.668547i
$951$	2.05768e11	+	2.58024e11i	0.251568	+	0.315456i
$952$	−1.12984e10	+	1.41678e10i	−0.0137553	+	0.0172486i
$953$	−3.36509e11	−	1.47434e12i	−0.407967	−	1.78742i	−0.593555	−	0.804793i	$-0.702276\pi$
$953$	−3.36509e11	−	1.47434e12i	−0.407967	−	1.78742i	0.185588	−	0.982628i	$-0.440581\pi$
$954$	8.18349e11	+	1.30240e12i	0.987973	+	1.57235i
$955$	4.84802e10	+	4.30274e11i	0.0582842	+	0.517287i
$956$			5.00526e11i			0.599232i
$957$	−1.11218e11	+	8.52262e10i	−0.132595	+	0.101607i
$958$	1.03395e12			1.22754
$959$	−2.37931e11	+	2.68084e10i	−0.281305	+	0.0316954i
$960$	8.63016e11	−	5.42269e11i	1.01609	−	0.638455i
$961$	−5.78996e11	+	1.32152e11i	−0.678862	+	0.154946i
$962$	−1.89646e11	−	1.51238e11i	−0.221434	−	0.176588i
$963$	−9.12846e11	+	7.27970e11i	−1.06143	+	0.846464i
$964$	−1.49619e11	+	6.55522e11i	−0.173252	+	0.759065i
$965$	3.66491e10	−	1.28241e10i	0.0422624	−	0.0147883i
$966$	4.37342e11	−	9.08150e11i	0.502241	−	1.04291i
$967$	−8.72391e11	−	5.48159e11i	−0.997712	−	0.626904i	−0.0689651	−	0.997619i	$-0.521970\pi$
$967$	−8.72391e11	−	5.48159e11i	−0.997712	−	0.626904i	−0.928747	+	0.370715i	$0.879113\pi$
$968$	−2.04462e11	−	7.15445e10i	−0.232869	−	0.0814845i
$969$	2.86225e11	−	2.86225e11i	0.324647	−	0.324647i
$970$	8.37587e11	+	1.73927e12i	0.946113	+	1.96462i
$971$	−1.02126e11	+	9.06389e11i	−0.114883	+	1.01962i	0.795529	+	0.605916i	$0.207193\pi$
$971$	−1.02126e11	+	9.06389e11i	−0.114883	+	1.01962i	−0.910412	+	0.413703i	$0.864235\pi$
$972$	9.22642e11	+	1.03957e11i	1.03364	+	0.116463i
$973$	−2.79071e11	+	1.34394e11i	−0.311361	+	0.149943i
$974$	−4.40564e11	−	4.40564e11i	−0.489523	−	0.489523i
$975$	8.54055e10	−	2.44075e11i	0.0945078	−	0.270088i
$976$	5.40722e11	−	8.60555e11i	0.595902	−	0.948373i
$977$	4.91733e11	+	2.36806e11i	0.539698	+	0.259905i	0.683815	−	0.729656i	$-0.260320\pi$
$977$	4.91733e11	+	2.36806e11i	0.539698	+	0.259905i	−0.144117	+	0.989561i	$0.546034\pi$
$978$	−7.42953e11	−	2.12324e12i	−0.812094	−	2.32083i
$979$	−1.83059e11	−	4.17820e10i	−0.199278	−	0.0454840i
$980$	−5.50944e11	−	6.90862e11i	−0.597315	−	0.749009i
$981$	−2.89779e11	+	3.63372e11i	−0.312890	+	0.392351i
$982$	−8.95393e10	−	3.92297e11i	−0.0962870	−	0.421861i
$983$	−2.05150e11	−	3.26495e11i	−0.219714	−	0.349673i	0.718620	−	0.695403i	$-0.244774\pi$
$983$	−2.05150e11	−	3.26495e11i	−0.219714	−	0.349673i	−0.938334	+	0.345730i	$0.887631\pi$
$984$	2.75543e10	+	2.44551e11i	0.0293907	+	0.260849i
$985$		−	2.24845e11i		−	0.238857i
$986$	−2.35450e11	−	5.85542e10i	−0.249109	−	0.0619513i
$987$	−5.54227e11			−0.584008
$988$	2.39723e11	−	2.70103e10i	0.251583	−	0.0283466i
$989$	−3.25113e11	+	2.04282e11i	−0.339820	+	0.213523i
$990$	1.85966e11	−	4.24456e10i	0.193595	−	0.0441867i
$991$	−6.92873e11	−	5.52548e11i	−0.718388	−	0.572896i	0.194599	−	0.980883i	$-0.437659\pi$
$991$	−6.92873e11	−	5.52548e11i	−0.718388	−	0.572896i	−0.912988	+	0.407987i	$0.866231\pi$
$992$	5.42464e11	−	4.32600e11i	0.560175	−	0.446725i
$993$	4.16193e11	−	1.82346e12i	0.428054	−	1.87543i
$994$	−1.95136e11	+	6.82810e10i	−0.199890	+	0.0699446i
$995$	−1.07625e12	+	2.23486e12i	−1.09805	+	2.28012i
$996$	−1.77758e12	−	1.11693e12i	−1.80631	−	1.13498i
$997$	−1.33011e12	−	4.65427e11i	−1.34620	−	0.471054i	−0.441556	−	0.897233i	$-0.645574\pi$
$997$	−1.33011e12	−	4.65427e11i	−1.34620	−	0.471054i	−0.904639	+	0.426179i	$0.859859\pi$
$998$	5.73017e11	−	5.73017e11i	0.577624	−	0.577624i
$999$	−1.48489e11	−	3.08340e11i	−0.149084	−	0.309577i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.9.f.a.15.5	yes	228
29.2	odd	28	inner	29.9.f.a.2.5	✓	228

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.9.f.a.2.5	✓	228	29.2	odd	28	inner
29.9.f.a.15.5	yes	228	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	29.f (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-21.4136 + 2.41273i) q^{2} +(91.7346 - 57.6407i) q^{3} +(203.138 - 46.3649i) q^{4} +(-731.114 - 583.044i) q^{5} +(-1825.29 + 1455.62i) q^{6} +(246.757 - 1081.11i) q^{7} +(968.946 - 339.049i) q^{8} +(2246.08 - 4664.03i) q^{9} +O(q^{10})\)	\(q+(-21.4136 + 2.41273i) q^{2} +(91.7346 - 57.6407i) q^{3} +(203.138 - 46.3649i) q^{4} +(-731.114 - 583.044i) q^{5} +(-1825.29 + 1455.62i) q^{6} +(246.757 - 1081.11i) q^{7} +(968.946 - 339.049i) q^{8} +(2246.08 - 4664.03i) q^{9} +(17062.5 + 10721.1i) q^{10} +(1725.95 + 603.935i) q^{11} +(15962.3 - 15962.3i) q^{12} +(-2140.33 - 4444.45i) q^{13} +(-2675.52 + 23745.9i) q^{14} +(-100676. - 11343.4i) q^{15} +(-67988.9 + 32741.7i) q^{16} +(-11256.2 - 11256.2i) q^{17} +(-36843.5 + 105293. i) q^{18} +(-124871. + 198730. i) q^{19} +(-175550. - 84540.4i) q^{20} +(-39680.0 - 113399. i) q^{21} +(-38415.8 - 8768.16i) q^{22} +(-242749. - 304398. i) q^{23} +(69342.9 - 86953.2i) q^{24} +(107665. + 471713. i) q^{25} +(56555.5 + 90007.5i) q^{26} +(16792.2 + 149034. i) q^{27} -231056. i q^{28} +(-643056. + 294492. i) q^{29} +2.18319e6 q^{30} +(505726. - 56981.6i) q^{31} +(1.15437e6 - 725339. i) q^{32} +(193140. - 44083.0i) q^{33} +(268195. + 213878. i) q^{34} +(-810745. + 646548. i) q^{35} +(240017. - 1.05158e6i) q^{36} +(-2.15384e6 + 753660. i) q^{37} +(2.19444e6 - 4.55680e6i) q^{38} +(-452524. - 284340. i) q^{39} +(-906091. - 317055. i) q^{40} +(-1.56467e6 + 1.56467e6i) q^{41} +(1.12329e6 + 2.33254e6i) q^{42} +(110419. - 979994. i) q^{43} +(378607. + 42658.8i) q^{44} +(-4.36148e6 + 2.10038e6i) q^{45} +(5.93256e6 + 5.93256e6i) q^{46} +(1.52363e6 - 4.35427e6i) q^{47} +(-4.34968e6 + 6.92247e6i) q^{48} +(4.08599e6 + 1.96771e6i) q^{49} +(-3.44362e6 - 9.84129e6i) q^{50} +(-1.68140e6 - 383770. i) q^{51} +(-640850. - 803600. i) q^{52} +(8.59706e6 - 1.07804e7i) q^{53} +(-719160. - 3.15084e6i) q^{54} +(-909744. - 1.44785e6i) q^{55} +(-127456. - 1.13120e6i) q^{56} +2.54281e7i q^{57} +(1.30596e7 - 7.85765e6i) q^{58} +9.44114e6 q^{59} +(-2.09770e7 + 2.36354e6i) q^{60} +(-1.14038e7 + 7.16550e6i) q^{61} +(-1.06919e7 + 2.44036e6i) q^{62} +(-4.48812e6 - 3.57915e6i) q^{63} +(-7.86551e6 + 6.27253e6i) q^{64} +(-1.02648e6 + 4.49731e6i) q^{65} +(-4.02946e6 + 1.40997e6i) q^{66} +(210114. - 436306. i) q^{67} +(-2.80847e6 - 1.76468e6i) q^{68} +(-3.98142e7 - 1.39316e7i) q^{69} +(1.58010e7 - 1.58010e7i) q^{70} +(3.75374e6 + 7.79473e6i) q^{71} +(594995. - 5.28073e6i) q^{72} +(-3.47680e7 - 3.91741e6i) q^{73} +(4.43029e7 - 2.13352e7i) q^{74} +(3.70665e7 + 3.70665e7i) q^{75} +(-1.61518e7 + 4.61593e7i) q^{76} +(1.07881e6 - 1.71692e6i) q^{77} +(1.03762e7 + 4.99691e6i) q^{78} +(-1.28345e7 - 3.66789e7i) q^{79} +(6.87975e7 + 1.57026e7i) q^{80} +(3.13072e7 + 3.92580e7i) q^{81} +(2.97300e7 - 3.72802e7i) q^{82} +(-2.06941e7 - 9.06670e7i) q^{83} +(-1.33182e7 - 2.11959e7i) q^{84} +(1.66671e6 + 1.47925e7i) q^{85} +2.12516e7i q^{86} +(-4.20157e7 + 6.40813e7i) q^{87} +1.87711e6 q^{88} +(-1.02040e8 + 1.14971e7i) q^{89} +(8.83272e7 - 5.54996e7i) q^{90} +(-5.33310e6 + 1.21725e6i) q^{91} +(-6.34250e7 - 5.05798e7i) q^{92} +(4.31081e7 - 3.43776e7i) q^{93} +(-2.21206e7 + 9.69166e7i) q^{94} +(2.07163e8 - 7.24895e7i) q^{95} +(6.40867e7 - 1.33077e8i) q^{96} +(8.11144e7 + 5.09675e7i) q^{97} +(-9.22431e7 - 3.22773e7i) q^{98} +(6.69339e6 - 6.69339e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 228 q - 6 q^{2} - 12 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 10 q^{7} + 3664 q^{8} - 14 q^{9}+O(q^{10}) \) 228 * q - 6 * q^2 - 12 * q^3 - 14 * q^4 - 14 * q^5 - 14 * q^6 - 10 * q^7 + 3664 * q^8 - 14 * q^9	\( 228 q - 6 q^{2} - 12 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 10 q^{7} + 3664 q^{8} - 14 q^{9} - 15884 q^{10} + 8376 q^{11} - 5036 q^{12} - 14 q^{13} - 12742 q^{14} + 35516 q^{15} + 245898 q^{16} - 76248 q^{17} + 465008 q^{18} + 164474 q^{19} - 907274 q^{20} - 628270 q^{21} + 1214962 q^{22} + 173408 q^{23} + 1858618 q^{24} + 43976 q^{25} - 4604204 q^{26} - 1727586 q^{27} + 1079922 q^{29} + 8909208 q^{30} + 3657848 q^{31} + 1160364 q^{32} - 4279184 q^{33} - 8655374 q^{34} - 8269058 q^{35} - 3366854 q^{36} - 5622890 q^{37} + 15536626 q^{38} + 16110008 q^{39} - 23544696 q^{40} - 9561672 q^{41} - 14 q^{42} + 5181008 q^{43} + 51041750 q^{44} - 35245194 q^{45} - 43159224 q^{46} - 12806808 q^{47} + 83954488 q^{48} + 10429400 q^{49} + 80809398 q^{50} + 18760882 q^{51} - 93050550 q^{52} - 30960322 q^{53} - 106220916 q^{54} - 126174004 q^{55} - 40136268 q^{56} + 159368354 q^{58} + 11188020 q^{59} + 255893612 q^{60} + 139657128 q^{61} + 102501616 q^{62} + 9797746 q^{63} - 135941792 q^{64} - 14207858 q^{65} - 447597656 q^{66} - 148930894 q^{67} - 167094904 q^{68} + 66986722 q^{69} + 586255934 q^{70} - 15272096 q^{71} + 41230600 q^{72} - 219415072 q^{73} - 347464696 q^{74} + 391507416 q^{75} + 271512490 q^{76} + 240416780 q^{77} + 141747906 q^{78} + 112667220 q^{79} - 375642638 q^{80} - 358099268 q^{81} - 262154910 q^{82} - 109463350 q^{83} - 694921012 q^{84} - 356627386 q^{85} + 199703522 q^{87} + 251202768 q^{88} + 839849154 q^{89} + 675826020 q^{90} + 533256766 q^{91} + 742339570 q^{92} + 78998570 q^{93} - 209116610 q^{94} - 633414122 q^{95} - 431412576 q^{96} - 402046736 q^{97} - 2192087384 q^{98} - 1966368188 q^{99}+O(q^{100}) \) 228 * q - 6 * q^2 - 12 * q^3 - 14 * q^4 - 14 * q^5 - 14 * q^6 - 10 * q^7 + 3664 * q^8 - 14 * q^9 - 15884 * q^10 + 8376 * q^11 - 5036 * q^12 - 14 * q^13 - 12742 * q^14 + 35516 * q^15 + 245898 * q^16 - 76248 * q^17 + 465008 * q^18 + 164474 * q^19 - 907274 * q^20 - 628270 * q^21 + 1214962 * q^22 + 173408 * q^23 + 1858618 * q^24 + 43976 * q^25 - 4604204 * q^26 - 1727586 * q^27 + 1079922 * q^29 + 8909208 * q^30 + 3657848 * q^31 + 1160364 * q^32 - 4279184 * q^33 - 8655374 * q^34 - 8269058 * q^35 - 3366854 * q^36 - 5622890 * q^37 + 15536626 * q^38 + 16110008 * q^39 - 23544696 * q^40 - 9561672 * q^41 - 14 * q^42 + 5181008 * q^43 + 51041750 * q^44 - 35245194 * q^45 - 43159224 * q^46 - 12806808 * q^47 + 83954488 * q^48 + 10429400 * q^49 + 80809398 * q^50 + 18760882 * q^51 - 93050550 * q^52 - 30960322 * q^53 - 106220916 * q^54 - 126174004 * q^55 - 40136268 * q^56 + 159368354 * q^58 + 11188020 * q^59 + 255893612 * q^60 + 139657128 * q^61 + 102501616 * q^62 + 9797746 * q^63 - 135941792 * q^64 - 14207858 * q^65 - 447597656 * q^66 - 148930894 * q^67 - 167094904 * q^68 + 66986722 * q^69 + 586255934 * q^70 - 15272096 * q^71 + 41230600 * q^72 - 219415072 * q^73 - 347464696 * q^74 + 391507416 * q^75 + 271512490 * q^76 + 240416780 * q^77 + 141747906 * q^78 + 112667220 * q^79 - 375642638 * q^80 - 358099268 * q^81 - 262154910 * q^82 - 109463350 * q^83 - 694921012 * q^84 - 356627386 * q^85 + 199703522 * q^87 + 251202768 * q^88 + 839849154 * q^89 + 675826020 * q^90 + 533256766 * q^91 + 742339570 * q^92 + 78998570 * q^93 - 209116610 * q^94 - 633414122 * q^95 - 431412576 * q^96 - 402046736 * q^97 - 2192087384 * q^98 - 1966368188 * q^99

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