LMFDB - Embedded newform 29.7.c.a.12.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,7,Mod(12,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("29.12");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	29.c (of order $4$, degree $2$, 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:	$6.67156842498$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			12.14
Character	$\chi$	$=$	29.12
Dual form			29.7.c.a.17.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(10.8910 + 10.8910i) q^{2} +(5.95173 + 5.95173i) q^{3} +173.227i q^{4} -50.8966i q^{5} +129.640i q^{6} +66.1657 q^{7} +(-1189.59 + 1189.59i) q^{8} -658.154i q^{9} +O(q^{10})$	\(q+(10.8910 + 10.8910i) q^{2} +(5.95173 + 5.95173i) q^{3} +173.227i q^{4} -50.8966i q^{5} +129.640i q^{6} +66.1657 q^{7} +(-1189.59 + 1189.59i) q^{8} -658.154i q^{9} +(554.314 - 554.314i) q^{10} +(1335.29 + 1335.29i) q^{11} +(-1031.00 + 1031.00i) q^{12} -2395.47i q^{13} +(720.610 + 720.610i) q^{14} +(302.923 - 302.923i) q^{15} -14825.1 q^{16} +(-2037.62 - 2037.62i) q^{17} +(7167.95 - 7167.95i) q^{18} +(5916.99 + 5916.99i) q^{19} +8816.67 q^{20} +(393.801 + 393.801i) q^{21} +29085.2i q^{22} +558.105 q^{23} -14160.3 q^{24} +13034.5 q^{25} +(26089.1 - 26089.1i) q^{26} +(8255.96 - 8255.96i) q^{27} +11461.7i q^{28} +(-10578.4 - 21975.5i) q^{29} +6598.25 q^{30} +(-4779.70 - 4779.70i) q^{31} +(-85326.4 - 85326.4i) q^{32} +15894.5i q^{33} -44383.3i q^{34} -3367.61i q^{35} +114010. q^{36} +(-40122.5 + 40122.5i) q^{37} +128884. i q^{38} +(14257.2 - 14257.2i) q^{39} +(60546.2 + 60546.2i) q^{40} +(90582.1 - 90582.1i) q^{41} +8577.75i q^{42} +(-62838.2 - 62838.2i) q^{43} +(-231308. + 231308. i) q^{44} -33497.8 q^{45} +(6078.32 + 6078.32i) q^{46} +(-100308. + 100308. i) q^{47} +(-88235.1 - 88235.1i) q^{48} -113271. q^{49} +(141959. + 141959. i) q^{50} -24254.7i q^{51} +414961. q^{52} -197633. q^{53} +179831. q^{54} +(67961.5 - 67961.5i) q^{55} +(-78710.3 + 78710.3i) q^{56} +70432.6i q^{57} +(124126. - 354543. i) q^{58} -178150. q^{59} +(52474.4 + 52474.4i) q^{60} +(-83104.8 - 83104.8i) q^{61} -104111. i q^{62} -43547.2i q^{63} -909769. i q^{64} -121921. q^{65} +(-173107. + 173107. i) q^{66} +214263. i q^{67} +(352971. - 352971. i) q^{68} +(3321.69 + 3321.69i) q^{69} +(36676.6 - 36676.6i) q^{70} -116516. i q^{71} +(782935. + 782935. i) q^{72} +(361698. - 361698. i) q^{73} -873948. q^{74} +(77578.0 + 77578.0i) q^{75} +(-1.02498e6 + 1.02498e6i) q^{76} +(88350.3 + 88350.3i) q^{77} +310550. q^{78} +(217064. + 217064. i) q^{79} +754548. i q^{80} -381520. q^{81} +1.97306e6 q^{82} +365549. q^{83} +(-68217.0 + 68217.0i) q^{84} +(-103708. + 103708. i) q^{85} -1.36874e6i q^{86} +(67832.5 - 193752. i) q^{87} -3.17690e6 q^{88} +(737861. + 737861. i) q^{89} +(-364824. - 364824. i) q^{90} -158498. i q^{91} +96679.0i q^{92} -56894.9i q^{93} -2.18491e6 q^{94} +(301154. - 301154. i) q^{95} -1.01568e6i q^{96} +(562245. - 562245. i) q^{97} +(-1.23363e6 - 1.23363e6i) q^{98} +(878825. - 878825. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{3} - 4 q^{7} + 354 q^{8}+O(q^{10}) $ 28 * q - 2 * q^3 - 4 * q^7 + 354 * q^8	\( 28 q - 2 q^{3} - 4 q^{7} + 354 q^{8} - 3714 q^{10} + 1934 q^{11} - 2706 q^{12} + 2648 q^{14} + 16280 q^{15} - 36632 q^{16} - 5236 q^{17} + 5258 q^{18} + 6718 q^{19} + 24828 q^{20} + 7380 q^{21} - 21524 q^{23} + 90648 q^{24} - 73196 q^{25} - 5394 q^{26} + 5824 q^{27} - 12510 q^{29} - 1780 q^{30} + 1150 q^{31} + 104646 q^{32} - 32904 q^{36} - 256832 q^{37} + 127752 q^{39} - 256374 q^{40} + 265716 q^{41} + 80590 q^{43} + 188482 q^{44} - 78008 q^{45} + 405572 q^{46} - 445250 q^{47} - 1016886 q^{48} + 532764 q^{49} - 80230 q^{50} + 619608 q^{52} + 143428 q^{53} + 373816 q^{54} - 533304 q^{55} - 619392 q^{56} + 326848 q^{58} - 957340 q^{59} + 1790622 q^{60} - 115640 q^{61} - 643584 q^{65} - 1821654 q^{66} + 1457028 q^{68} - 1049340 q^{69} + 3024084 q^{70} + 1480560 q^{72} - 627512 q^{73} - 3652060 q^{74} + 586518 q^{75} - 1343752 q^{76} - 115820 q^{77} + 1820304 q^{78} + 235966 q^{79} + 2710496 q^{81} + 796544 q^{82} + 3881892 q^{83} + 219332 q^{84} - 3064608 q^{85} + 900526 q^{87} - 9844332 q^{88} + 3821436 q^{89} - 4192912 q^{90} - 648556 q^{94} - 620200 q^{95} - 620288 q^{97} + 4735296 q^{98} + 4021770 q^{99}+O(q^{100}) \) 28 * q - 2 * q^3 - 4 * q^7 + 354 * q^8 - 3714 * q^10 + 1934 * q^11 - 2706 * q^12 + 2648 * q^14 + 16280 * q^15 - 36632 * q^16 - 5236 * q^17 + 5258 * q^18 + 6718 * q^19 + 24828 * q^20 + 7380 * q^21 - 21524 * q^23 + 90648 * q^24 - 73196 * q^25 - 5394 * q^26 + 5824 * q^27 - 12510 * q^29 - 1780 * q^30 + 1150 * q^31 + 104646 * q^32 - 32904 * q^36 - 256832 * q^37 + 127752 * q^39 - 256374 * q^40 + 265716 * q^41 + 80590 * q^43 + 188482 * q^44 - 78008 * q^45 + 405572 * q^46 - 445250 * q^47 - 1016886 * q^48 + 532764 * q^49 - 80230 * q^50 + 619608 * q^52 + 143428 * q^53 + 373816 * q^54 - 533304 * q^55 - 619392 * q^56 + 326848 * q^58 - 957340 * q^59 + 1790622 * q^60 - 115640 * q^61 - 643584 * q^65 - 1821654 * q^66 + 1457028 * q^68 - 1049340 * q^69 + 3024084 * q^70 + 1480560 * q^72 - 627512 * q^73 - 3652060 * q^74 + 586518 * q^75 - 1343752 * q^76 - 115820 * q^77 + 1820304 * q^78 + 235966 * q^79 + 2710496 * q^81 + 796544 * q^82 + 3881892 * q^83 + 219332 * q^84 - 3064608 * q^85 + 900526 * q^87 - 9844332 * q^88 + 3821436 * q^89 - 4192912 * q^90 - 648556 * q^94 - 620200 * q^95 - 620288 * q^97 + 4735296 * q^98 + 4021770 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	10.8910	+	10.8910i	1.36137	+	1.36137i	0.872169	+	0.489204i	$0.162713\pi$
$2$	10.8910	+	10.8910i	1.36137	+	1.36137i	0.489204	+	0.872169i	$0.337287\pi$
$3$	5.95173	+	5.95173i	0.220434	+	0.220434i	0.808681	−	0.588247i	$-0.200182\pi$
$3$	5.95173	+	5.95173i	0.220434	+	0.220434i	−0.588247	+	0.808681i	$0.700182\pi$
$4$			173.227i			2.70668i
$5$		−	50.8966i		−	0.407172i	−0.979057	−	0.203586i	$-0.934740\pi$
$5$		−	50.8966i		−	0.407172i	0.979057	−	0.203586i	$-0.0652597\pi$
$6$			129.640i			0.600187i
$7$	66.1657			0.192903			0.0964515	−	0.995338i	$-0.469251\pi$
$7$	66.1657			0.192903			0.0964515	+	0.995338i	$0.469251\pi$
$8$	−1189.59	+	1189.59i	−2.32342	+	2.32342i
$9$		−	658.154i		−	0.902817i
$10$	554.314	−	554.314i	0.554314	−	0.554314i
$11$	1335.29	+	1335.29i	1.00322	+	1.00322i	0.999995	+	0.00322656i	$0.00102705\pi$
$11$	1335.29	+	1335.29i	1.00322	+	1.00322i	0.00322656	+	0.999995i	$0.498973\pi$
$12$	−1031.00	+	1031.00i	−0.596644	+	0.596644i
$13$		−	2395.47i		−	1.09034i	−0.838326	−	0.545169i	$-0.816465\pi$
$13$		−	2395.47i		−	1.09034i	0.838326	−	0.545169i	$-0.183535\pi$
$14$	720.610	+	720.610i	0.262613	+	0.262613i
$15$	302.923	−	302.923i	0.0897548	−	0.0897548i
$16$	−14825.1			−3.61942
$17$	−2037.62	−	2037.62i	−0.414740	−	0.414740i	0.468646	−	0.883386i	$-0.344742\pi$
$17$	−2037.62	−	2037.62i	−0.414740	−	0.414740i	−0.883386	+	0.468646i	$0.844742\pi$
$18$	7167.95	−	7167.95i	1.22907	−	1.22907i
$19$	5916.99	+	5916.99i	0.862660	+	0.862660i	0.991646	−	0.128986i	$-0.0411722\pi$
$19$	5916.99	+	5916.99i	0.862660	+	0.862660i	−0.128986	+	0.991646i	$0.541172\pi$
$20$	8816.67			1.10208
$21$	393.801	+	393.801i	0.0425225	+	0.0425225i
$22$			29085.2i			2.73152i
$23$	558.105			0.0458704			0.0229352	−	0.999737i	$-0.492699\pi$
$23$	558.105			0.0458704			0.0229352	+	0.999737i	$0.492699\pi$
$24$	−14160.3			−1.02432
$25$	13034.5			0.834211
$26$	26089.1	−	26089.1i	1.48436	−	1.48436i
$27$	8255.96	−	8255.96i	0.419446	−	0.419446i
$28$			11461.7i			0.522126i
$29$	−10578.4	−	21975.5i	−0.433735	−	0.901040i
$29$	−10578.4	−	21975.5i	−0.433735	−	0.901040i
$30$	6598.25			0.244380
$31$	−4779.70	−	4779.70i	−0.160441	−	0.160441i	0.622321	−	0.782762i	$-0.286190\pi$
$31$	−4779.70	−	4779.70i	−0.160441	−	0.160441i	−0.782762	+	0.622321i	$0.786190\pi$
$32$	−85326.4	−	85326.4i	−2.60395	−	2.60395i
$33$			15894.5i			0.442289i
$34$		−	44383.3i		−	1.12923i
$35$		−	3367.61i		−	0.0785448i
$36$	114010.			2.44363
$37$	−40122.5	+	40122.5i	−0.792106	+	0.792106i	−0.981836	−	0.189731i	$-0.939239\pi$
$37$	−40122.5	+	40122.5i	−0.792106	+	0.792106i	0.189731	+	0.981836i	$0.439239\pi$
$38$			128884.i			2.34881i
$39$	14257.2	−	14257.2i	0.240348	−	0.240348i
$40$	60546.2	+	60546.2i	0.946034	+	0.946034i
$41$	90582.1	−	90582.1i	1.31429	−	1.31429i	0.396068	−	0.918221i	$-0.370374\pi$
$41$	90582.1	−	90582.1i	1.31429	−	1.31429i	0.918221	−	0.396068i	$-0.129626\pi$
$42$			8577.75i			0.115778i
$43$	−62838.2	−	62838.2i	−0.790349	−	0.790349i	0.191202	−	0.981551i	$-0.438761\pi$
$43$	−62838.2	−	62838.2i	−0.790349	−	0.790349i	−0.981551	+	0.191202i	$0.938761\pi$
$44$	−231308.	+	231308.i	−2.71539	+	2.71539i
$45$	−33497.8			−0.367602
$46$	6078.32	+	6078.32i	0.0624467	+	0.0624467i
$47$	−100308.	+	100308.i	−0.966146	+	0.966146i	−0.999445	−	0.0332994i	$-0.989399\pi$
$47$	−100308.	+	100308.i	−0.966146	+	0.966146i	0.0332994	+	0.999445i	$0.489399\pi$
$48$	−88235.1	−	88235.1i	−0.797844	−	0.797844i
$49$	−113271.			−0.962788
$50$	141959.	+	141959.i	1.13567	+	1.13567i
$51$		−	24254.7i		−	0.182846i
$52$	414961.			2.95119
$53$	−197633.			−1.32749			−0.663747	−	0.747958i	$-0.731035\pi$
$53$	−197633.			−1.32749			−0.663747	+	0.747958i	$0.731035\pi$
$54$	179831.			1.14205
$55$	67961.5	−	67961.5i	0.408484	−	0.408484i
$56$	−78710.3	+	78710.3i	−0.448195	+	0.448195i
$57$			70432.6i			0.380320i
$58$	124126.	−	354543.i	0.636177	−	1.81713i
$59$	−178150.			−0.867419			−0.433710	−	0.901053i	$-0.642796\pi$
$59$	−178150.			−0.867419			−0.433710	+	0.901053i	$0.642796\pi$
$60$	52474.4	+	52474.4i	0.242937	+	0.242937i
$61$	−83104.8	−	83104.8i	−0.366131	−	0.366131i	0.499933	−	0.866064i	$-0.333358\pi$
$61$	−83104.8	−	83104.8i	−0.366131	−	0.366131i	−0.866064	+	0.499933i	$0.833358\pi$
$62$		−	104111.i		−	0.436840i
$63$		−	43547.2i		−	0.174156i
$64$		−	909769.i		−	3.47049i
$65$	−121921.			−0.443956
$66$	−173107.	+	173107.i	−0.602120	+	0.602120i
$67$			214263.i			0.712397i	0.934410	+	0.356199i	$0.115927\pi$
$67$			214263.i			0.712397i	−0.934410	+	0.356199i	$0.884073\pi$
$68$	352971.	−	352971.i	1.12257	−	1.12257i
$69$	3321.69	+	3321.69i	0.0101114	+	0.0101114i
$70$	36676.6	−	36676.6i	0.106929	−	0.106929i
$71$		−	116516.i		−	0.325545i	−0.986664	−	0.162772i	$-0.947956\pi$
$71$		−	116516.i		−	0.325545i	0.986664	−	0.162772i	$-0.0520436\pi$
$72$	782935.	+	782935.i	2.09763	+	2.09763i
$73$	361698.	−	361698.i	0.929773	−	0.929773i	−0.0679179	−	0.997691i	$-0.521636\pi$
$73$	361698.	−	361698.i	0.929773	−	0.929773i	0.997691	+	0.0679179i	$0.0216356\pi$
$74$	−873948.			−2.15670
$75$	77578.0	+	77578.0i	0.183889	+	0.183889i
$76$	−1.02498e6	+	1.02498e6i	−2.33494	+	2.33494i
$77$	88350.3	+	88350.3i	0.193524	+	0.193524i
$78$	310550.			0.654407
$79$	217064.	+	217064.i	0.440256	+	0.440256i	0.892098	−	0.451842i	$-0.149233\pi$
$79$	217064.	+	217064.i	0.440256	+	0.440256i	−0.451842	+	0.892098i	$0.649233\pi$
$80$			754548.i			1.47373i
$81$	−381520.			−0.717897
$82$	1.97306e6			3.57848
$83$	365549.			0.639309			0.319655	−	0.947534i	$-0.396433\pi$
$83$	365549.			0.639309			0.319655	+	0.947534i	$0.396433\pi$
$84$	−68217.0	+	68217.0i	−0.115095	+	0.115095i
$85$	−103708.	+	103708.i	−0.168871	+	0.168871i
$86$		−	1.36874e6i		−	2.15192i
$87$	67832.5	−	193752.i	0.103010	−	0.294230i
$88$	−3.17690e6			−4.66181
$89$	737861.	+	737861.i	1.04666	+	1.04666i	0.998857	+	0.0478005i	$0.0152212\pi$
$89$	737861.	+	737861.i	1.04666	+	1.04666i	0.0478005	+	0.998857i	$0.484779\pi$
$90$	−364824.	−	364824.i	−0.500444	−	0.500444i
$91$		−	158498.i		−	0.210330i
$92$			96679.0i			0.124156i
$93$		−	56894.9i		−	0.0707334i
$94$	−2.18491e6			−2.63057
$95$	301154.	−	301154.i	0.351252	−	0.351252i
$96$		−	1.01568e6i		−	1.14800i
$97$	562245.	−	562245.i	0.616042	−	0.616042i	−0.328472	−	0.944514i	$-0.606534\pi$
$97$	562245.	−	562245.i	0.616042	−	0.616042i	0.944514	+	0.328472i	$0.106534\pi$
$98$	−1.23363e6	−	1.23363e6i	−1.31071	−	1.31071i
$99$	878825.	−	878825.i	0.905726	−	0.905726i
$100$			2.25794e6i			2.25794i
$101$	1.20066e6	+	1.20066e6i	1.16535	+	1.16535i	0.983287	+	0.182063i	$0.0582776\pi$
$101$	1.20066e6	+	1.20066e6i	1.16535	+	1.16535i	0.182063	+	0.983287i	$0.441722\pi$
$102$	264158.	−	264158.i	0.248922	−	0.248922i
$103$	4330.66			0.00396317			0.00198158	−	0.999998i	$-0.499369\pi$
$103$	4330.66			0.00396317			0.00198158	+	0.999998i	$0.499369\pi$
$104$	2.84964e6	+	2.84964e6i	2.53332	+	2.53332i
$105$	20043.1	−	20043.1i	0.0173140	−	0.0173140i
$106$	−2.15242e6	−	2.15242e6i	−1.80721	−	1.80721i
$107$	190718.			0.155683			0.0778413	−	0.996966i	$-0.475197\pi$
$107$	190718.			0.155683			0.0778413	+	0.996966i	$0.475197\pi$
$108$	1.43016e6	+	1.43016e6i	1.13531	+	1.13531i
$109$			122739.i			0.0947768i	0.998877	+	0.0473884i	$0.0150898\pi$
$109$			122739.i			0.0947768i	−0.998877	+	0.0473884i	$0.984910\pi$
$110$	1.48034e6			1.11220
$111$	−477597.			−0.349215
$112$	−980916.			−0.698196
$113$	−1.59076e6	+	1.59076e6i	−1.10248	+	1.10248i	−0.108369	+	0.994111i	$0.534563\pi$
$113$	−1.59076e6	+	1.59076e6i	−1.10248	+	1.10248i	−0.994111	+	0.108369i	$0.965437\pi$
$114$	−767081.	+	767081.i	−0.517758	+	0.517758i
$115$		−	28405.6i		−	0.0186772i
$116$	3.80675e6	−	1.83246e6i	2.43882	−	1.17398i
$117$	−1.57659e6			−0.984376
$118$	−1.94023e6	−	1.94023e6i	−1.18088	−	1.18088i
$119$	−134821.	−	134821.i	−0.0800046	−	0.0800046i
$120$			720709.i			0.417077i
$121$			1.79443e6i			1.01291i
$122$		−	1.81019e6i		−	0.996882i
$123$	1.07824e6			0.579429
$124$	827974.	−	827974.i	0.434262	−	0.434262i
$125$		−	1.45867e6i		−	0.746840i
$126$	474272.	−	474272.i	0.237092	−	0.237092i
$127$	675331.	+	675331.i	0.329690	+	0.329690i	0.852468	−	0.522779i	$-0.175105\pi$
$127$	675331.	+	675331.i	0.329690	+	0.329690i	−0.522779	+	0.852468i	$0.675105\pi$
$128$	4.44739e6	−	4.44739e6i	2.12068	−	2.12068i
$129$		−	747992.i		−	0.348440i
$130$	−1.32784e6	−	1.32784e6i	−0.604390	−	0.604390i
$131$	−2.37032e6	+	2.37032e6i	−1.05437	+	1.05437i	−0.0559365	+	0.998434i	$0.517814\pi$
$131$	−2.37032e6	+	2.37032e6i	−1.05437	+	1.05437i	−0.998434	+	0.0559365i	$0.982186\pi$
$132$	−2.75337e6			−1.19713
$133$	391502.	+	391502.i	0.166410	+	0.166410i
$134$	−2.33353e6	+	2.33353e6i	−0.969839	+	0.969839i
$135$	−420200.	−	420200.i	−0.170787	−	0.170787i
$136$	4.84787e6			1.92723
$137$	−1.43668e6	−	1.43668e6i	−0.558725	−	0.558725i	0.370219	−	0.928944i	$-0.379283\pi$
$137$	−1.43668e6	−	1.43668e6i	−0.558725	−	0.558725i	−0.928944	+	0.370219i	$0.879283\pi$
$138$			72353.0i			0.0275308i
$139$	−641724.			−0.238948			−0.119474	−	0.992837i	$-0.538121\pi$
$139$	−641724.			−0.238948			−0.119474	+	0.992837i	$0.538121\pi$
$140$	583362.			0.212595
$141$	−1.19401e6			−0.425944
$142$	1.26897e6	−	1.26897e6i	0.443188	−	0.443188i
$143$	3.19865e6	−	3.19865e6i	1.09385	−	1.09385i
$144$			9.75721e6i			3.26767i
$145$	−1.11848e6	+	538402.i	−0.366879	+	0.176605i
$146$	7.87849e6			2.53154
$147$	−674159.	−	674159.i	−0.212232	−	0.212232i
$148$	−6.95031e6	−	6.95031e6i	−2.14397	−	2.14397i
$149$			3.97624e6i			1.20203i	0.799239	+	0.601013i	$0.205236\pi$
$149$			3.97624e6i			1.20203i	−0.799239	+	0.601013i	$0.794764\pi$
$150$			1.68980e6i			0.500682i
$151$		−	3.80012e6i		−	1.10374i	−0.833930	−	0.551870i	$-0.813914\pi$
$151$		−	3.80012e6i		−	1.10374i	0.833930	−	0.551870i	$-0.186086\pi$
$152$	−1.40776e7			−4.00865
$153$	−1.34107e6	+	1.34107e6i	−0.374435	+	0.374435i
$154$			1.92444e6i			0.526918i
$155$	−243270.	+	243270.i	−0.0653271	+	0.0653271i
$156$	2.46974e6	+	2.46974e6i	0.650544	+	0.650544i
$157$	−1.22272e6	+	1.22272e6i	−0.315956	+	0.315956i	−0.847212	−	0.531255i	$-0.821720\pi$
$157$	−1.22272e6	+	1.22272e6i	−0.315956	+	0.315956i	0.531255	+	0.847212i	$0.321720\pi$
$158$			4.72807e6i			1.19871i
$159$	−1.17626e6	−	1.17626e6i	−0.292625	−	0.292625i
$160$	−4.34282e6	+	4.34282e6i	−1.06026	+	1.06026i
$161$	36927.4			0.00884854
$162$	−4.15513e6	−	4.15513e6i	−0.977325	−	0.977325i
$163$	4.97669e6	−	4.97669e6i	1.14915	−	1.14915i	0.162435	−	0.986719i	$-0.448065\pi$
$163$	4.97669e6	−	4.97669e6i	1.14915	−	1.14915i	0.986719	−	0.162435i	$-0.0519346\pi$
$164$	1.56913e7	+	1.56913e7i	3.55735	+	3.55735i
$165$	808977.			0.180088
$166$	3.98119e6	+	3.98119e6i	0.870339	+	0.870339i
$167$			5.20769e6i			1.11814i	0.829121	+	0.559070i	$0.188842\pi$
$167$			5.20769e6i			1.11814i	−0.829121	+	0.559070i	$0.811158\pi$
$168$	−936924.			−0.197595
$169$	−911482.			−0.188837
$170$	−2.25896e6			−0.459792
$171$	3.89429e6	−	3.89429e6i	0.778825	−	0.778825i
$172$	1.08853e7	−	1.08853e7i	2.13922	−	2.13922i
$173$			2.21856e6i			0.428483i	0.976781	+	0.214241i	$0.0687279\pi$
$173$			2.21856e6i			0.428483i	−0.976781	+	0.214241i	$0.931272\pi$
$174$	2.84891e6	−	1.37138e6i	0.540793	−	0.260322i
$175$	862440.			0.160922
$176$	−1.97958e7	−	1.97958e7i	−3.63108	−	3.63108i
$177$	−1.06030e6	−	1.06030e6i	−0.191209	−	0.191209i
$178$			1.60721e7i			2.84978i
$179$		−	2.82469e6i		−	0.492506i	−0.969206	−	0.246253i	$-0.920801\pi$
$179$		−	2.82469e6i		−	0.492506i	0.969206	−	0.246253i	$-0.0791994\pi$
$180$		−	5.80273e6i		−	0.994980i
$181$	−3.61722e6			−0.610013			−0.305007	−	0.952350i	$-0.598659\pi$
$181$	−3.61722e6			−0.610013			−0.305007	+	0.952350i	$0.598659\pi$
$182$	1.72620e6	−	1.72620e6i	0.286337	−	0.286337i
$183$		−	989234.i		−	0.161416i
$184$	−663918.	+	663918.i	−0.106576	+	0.106576i
$185$	2.04210e6	+	2.04210e6i	0.322524	+	0.322524i
$186$	619642.	−	619642.i	0.0962946	−	0.0962946i
$187$		−	5.44161e6i		−	0.832152i
$188$	−1.73761e7	−	1.73761e7i	−2.61504	−	2.61504i
$189$	546262.	−	546262.i	0.0809125	−	0.0809125i
$190$	6.55974e6			0.956369
$191$	2.10544e6	+	2.10544e6i	0.302164	+	0.302164i	0.841860	−	0.539696i	$-0.181461\pi$
$191$	2.10544e6	+	2.10544e6i	0.302164	+	0.302164i	−0.539696	+	0.841860i	$0.681461\pi$
$192$	5.41470e6	−	5.41470e6i	0.765016	−	0.765016i
$193$	−1.49379e6	−	1.49379e6i	−0.207786	−	0.207786i	0.595540	−	0.803326i	$-0.296938\pi$
$193$	−1.49379e6	−	1.49379e6i	−0.207786	−	0.207786i	−0.803326	+	0.595540i	$0.796938\pi$
$194$	1.22468e7			1.67733
$195$	−725643.	−	725643.i	−0.0978631	−	0.0978631i
$196$		−	1.96216e7i		−	2.60596i
$197$	1.71951e6			0.224909			0.112454	−	0.993657i	$-0.464129\pi$
$197$	1.71951e6			0.224909			0.112454	+	0.993657i	$0.464129\pi$
$198$	1.91425e7			2.46606
$199$	−1.44363e6			−0.183187			−0.0915937	−	0.995796i	$-0.529196\pi$
$199$	−1.44363e6			−0.183187			−0.0915937	+	0.995796i	$0.529196\pi$
$200$	−1.55058e7	+	1.55058e7i	−1.93822	+	1.93822i
$201$	−1.27523e6	+	1.27523e6i	−0.157037	+	0.157037i
$202$			2.61528e7i			3.17295i
$203$	−699925.	−	1.45402e6i	−0.0836688	−	0.173813i
$204$	4.20157e6			0.494905
$205$	−4.61032e6	−	4.61032e6i	−0.535142	−	0.535142i
$206$	47165.1	+	47165.1i	0.00539535	+	0.00539535i
$207$		−	367319.i		−	0.0414126i
$208$			3.55132e7i			3.94639i
$209$			1.58018e7i			1.73088i
$210$	436578.			0.0471416
$211$	7.48586e6	−	7.48586e6i	0.796882	−	0.796882i	−0.185720	−	0.982603i	$-0.559462\pi$
$211$	7.48586e6	−	7.48586e6i	0.796882	−	0.796882i	0.982603	+	0.185720i	$0.0594619\pi$
$212$		−	3.42354e7i		−	3.59309i
$213$	693471.	−	693471.i	0.0717612	−	0.0717612i
$214$	2.07711e6	+	2.07711e6i	0.211942	+	0.211942i
$215$	−3.19825e6	+	3.19825e6i	−0.321808	+	0.321808i
$216$			1.96425e7i			1.94910i
$217$	−316252.	−	316252.i	−0.0309496	−	0.0309496i
$218$	−1.33675e6	+	1.33675e6i	−0.129027	+	0.129027i
$219$	4.30545e6			0.409908
$220$	1.17728e7	+	1.17728e7i	1.10563	+	1.10563i
$221$	−4.88106e6	+	4.88106e6i	−0.452207	+	0.452207i
$222$	−5.20150e6	−	5.20150e6i	−0.475412	−	0.475412i
$223$	−9.65767e6			−0.870879			−0.435439	−	0.900218i	$-0.643407\pi$
$223$	−9.65767e6			−0.870879			−0.435439	+	0.900218i	$0.643407\pi$
$224$	−5.64568e6	−	5.64568e6i	−0.502311	−	0.502311i
$225$		−	8.57873e6i		−	0.753140i
$226$	−3.46500e7			−3.00177
$227$	2.47859e6			0.211898			0.105949	−	0.994372i	$-0.466212\pi$
$227$	2.47859e6			0.211898			0.105949	+	0.994372i	$0.466212\pi$
$228$	−1.22008e7			−1.02940
$229$	131274.	−	131274.i	0.0109313	−	0.0109313i	−0.701620	−	0.712551i	$-0.747540\pi$
$229$	131274.	−	131274.i	0.0109313	−	0.0109313i	0.712551	+	0.701620i	$0.247540\pi$
$230$	309365.	−	309365.i	0.0254266	−	0.0254266i
$231$			1.05167e6i			0.0853189i
$232$	3.87258e7	+	1.35579e7i	3.10125	+	1.08575i
$233$	1.02861e6			0.0813173			0.0406587	−	0.999173i	$-0.487054\pi$
$233$	1.02861e6			0.0813173			0.0406587	+	0.999173i	$0.487054\pi$
$234$	−1.71706e7	−	1.71706e7i	−1.34010	−	1.34010i
$235$	5.10534e6	+	5.10534e6i	0.393388	+	0.393388i
$236$		−	3.08604e7i		−	2.34782i
$237$			2.58381e6i			0.194095i
$238$		−	2.93666e6i		−	0.217832i
$239$	−2.20891e7			−1.61802			−0.809012	−	0.587792i	$-0.799997\pi$
$239$	−2.20891e7			−1.61802			−0.809012	+	0.587792i	$0.799997\pi$
$240$	−4.49086e6	+	4.49086e6i	−0.324860	+	0.324860i
$241$			428150.i			0.0305875i	0.999883	+	0.0152938i	$0.00486835\pi$
$241$			428150.i			0.0305875i	−0.999883	+	0.0152938i	$0.995132\pi$
$242$	−1.95431e7	+	1.95431e7i	−1.37894	+	1.37894i
$243$	−8.28930e6	−	8.28930e6i	−0.577695	−	0.577695i
$244$	1.43960e7	−	1.43960e7i	0.990998	−	0.990998i
$245$			5.76511e6i			0.392021i
$246$	1.17431e7	+	1.17431e7i	0.788819	+	0.788819i
$247$	1.41740e7	−	1.41740e7i	0.940592	−	0.940592i
$248$	1.13718e7			0.745544
$249$	2.17565e6	+	2.17565e6i	0.140926	+	0.140926i
$250$	1.58864e7	−	1.58864e7i	1.01673	−	1.01673i
$251$	8.84907e6	+	8.84907e6i	0.559599	+	0.559599i	0.929193	−	0.369595i	$-0.120503\pi$
$251$	8.84907e6	+	8.84907e6i	0.559599	+	0.559599i	−0.369595	+	0.929193i	$0.620503\pi$
$252$	7.54357e6			0.471384
$253$	745231.	+	745231.i	0.0460182	+	0.0460182i
$254$			1.47100e7i			0.897662i
$255$	−1.23448e6			−0.0744498
$256$	3.86478e7			2.30359
$257$	−3.76272e6			−0.221667			−0.110834	−	0.993839i	$-0.535352\pi$
$257$	−3.76272e6			−0.221667			−0.110834	+	0.993839i	$0.535352\pi$
$258$	8.14637e6	−	8.14637e6i	0.474357	−	0.474357i
$259$	−2.65474e6	+	2.65474e6i	−0.152800	+	0.152800i
$260$		−	2.11201e7i		−	1.20164i
$261$	−1.44632e7	+	6.96219e6i	−0.813475	+	0.391584i
$262$	−5.16303e7			−2.87078
$263$	9.45088e6	+	9.45088e6i	0.519523	+	0.519523i	0.917427	−	0.397904i	$-0.130262\pi$
$263$	9.45088e6	+	9.45088e6i	0.519523	+	0.519523i	−0.397904	+	0.917427i	$0.630262\pi$
$264$	−1.89080e7	−	1.89080e7i	−1.02762	−	1.02762i
$265$			1.00588e7i			0.540519i
$266$			8.52768e6i			0.453092i
$267$			8.78310e6i			0.461439i
$268$	−3.71161e7			−1.92823
$269$	−1.12204e7	+	1.12204e7i	−0.576438	+	0.576438i	−0.933920	−	0.357482i	$-0.883635\pi$
$269$	−1.12204e7	+	1.12204e7i	−0.576438	+	0.576438i	0.357482	+	0.933920i	$0.383635\pi$
$270$		−	9.15279e6i		−	0.465010i
$271$	2.57434e7	−	2.57434e7i	1.29348	−	1.29348i	0.360853	−	0.932623i	$-0.382486\pi$
$271$	2.57434e7	−	2.57434e7i	1.29348	−	1.29348i	0.932623	−	0.360853i	$-0.117514\pi$
$272$	3.02079e7	+	3.02079e7i	1.50112	+	1.50112i
$273$	943339.	−	943339.i	0.0463639	−	0.0463639i
$274$		−	3.12937e7i		−	1.52127i
$275$	1.74049e7	+	1.74049e7i	0.836898	+	0.836898i
$276$	−575407.	+	575407.i	−0.0273683	+	0.0273683i
$277$	−1.34120e7			−0.631038			−0.315519	−	0.948919i	$-0.602179\pi$
$277$	−1.34120e7			−0.631038			−0.315519	+	0.948919i	$0.602179\pi$
$278$	−6.98901e6	−	6.98901e6i	−0.325298	−	0.325298i
$279$	−3.14578e6	+	3.14578e6i	−0.144849	+	0.144849i
$280$	4.00608e6	+	4.00608e6i	0.182493	+	0.182493i
$281$	2.73534e7			1.23280			0.616400	−	0.787433i	$-0.288590\pi$
$281$	2.73534e7			1.23280			0.616400	+	0.787433i	$0.288590\pi$
$282$	−1.30040e7	−	1.30040e7i	−0.579868	−	0.579868i
$283$			1.31973e6i			0.0582274i	0.999576	+	0.0291137i	$0.00926849\pi$
$283$			1.31973e6i			0.0582274i	−0.999576	+	0.0291137i	$0.990732\pi$
$284$	2.01837e7			0.881143
$285$	3.58478e6			0.154856
$286$	6.96728e7			2.97828
$287$	5.99343e6	−	5.99343e6i	0.253530	−	0.253530i
$288$	−5.61579e7	+	5.61579e7i	−2.35089	+	2.35089i
$289$		−	1.58338e7i		−	0.655981i
$290$	−1.80450e7	−	6.31758e6i	−0.739884	−	0.259034i
$291$	6.69266e6			0.271594
$292$	6.26559e7	+	6.26559e7i	2.51659	+	2.51659i
$293$	−1.00866e7	−	1.00866e7i	−0.400999	−	0.400999i	0.477586	−	0.878585i	$-0.341512\pi$
$293$	−1.00866e7	−	1.00866e7i	−0.400999	−	0.400999i	−0.878585	+	0.477586i	$0.841512\pi$
$294$		−	1.46845e7i		−	0.577853i
$295$			9.06721e6i			0.353189i
$296$		−	9.54589e7i		−	3.68079i
$297$	2.20482e7			0.841595
$298$	−4.33052e7	+	4.33052e7i	−1.63641	+	1.63641i
$299$		−	1.33693e6i		−	0.0500142i
$300$	−1.34386e7	+	1.34386e7i	−0.497727	+	0.497727i
$301$	−4.15774e6	−	4.15774e6i	−0.152461	−	0.152461i
$302$	4.13871e7	−	4.13871e7i	1.50260	−	1.50260i
$303$			1.42920e7i			0.513766i
$304$	−8.77201e7	−	8.77201e7i	−3.12233	−	3.12233i
$305$	−4.22975e6	+	4.22975e6i	−0.149078	+	0.149078i
$306$	−2.92111e7			−1.01949
$307$	−1.14963e7	−	1.14963e7i	−0.397324	−	0.397324i	0.479964	−	0.877288i	$-0.340650\pi$
$307$	−1.14963e7	−	1.14963e7i	−0.397324	−	0.397324i	−0.877288	+	0.479964i	$0.840650\pi$
$308$	−1.53047e7	+	1.53047e7i	−0.523808	+	0.523808i
$309$	25774.9	+	25774.9i	0.000873618	+	0.000873618i
$310$	−5.29890e6			−0.177869
$311$	1.38574e7	+	1.38574e7i	0.460682	+	0.460682i	0.898879	−	0.438197i	$-0.144383\pi$
$311$	1.38574e7	+	1.38574e7i	0.460682	+	0.460682i	−0.438197	+	0.898879i	$0.644383\pi$
$312$			3.39205e7i			1.11686i
$313$	3.32694e7			1.08496			0.542478	−	0.840070i	$-0.317486\pi$
$313$	3.32694e7			1.08496			0.542478	+	0.840070i	$0.317486\pi$
$314$	−2.66332e7			−0.860269
$315$	−2.21640e6			−0.0709116
$316$	−3.76013e7	+	3.76013e7i	−1.19163	+	1.19163i
$317$	−569563.	+	569563.i	−0.0178799	+	0.0178799i	−0.715990	−	0.698110i	$-0.754024\pi$
$317$	−569563.	+	569563.i	−0.0178799	+	0.0178799i	0.698110	+	0.715990i	$0.254024\pi$
$318$		−	2.56212e7i		−	0.796744i
$319$	1.52184e7	−	4.34687e7i	0.468811	−	1.33908i
$320$	−4.63041e7			−1.41309
$321$	1.13510e6	+	1.13510e6i	0.0343178	+	0.0343178i
$322$	402176.	+	402176.i	0.0120462	+	0.0120462i
$323$		−	2.41131e7i		−	0.715560i
$324$		−	6.60896e7i		−	1.94311i
$325$		−	3.12239e7i		−	0.909572i
$326$	1.08402e8			3.12886
$327$	−730507.	+	730507.i	−0.0208921	+	0.0208921i
$328$			2.15512e8i			6.10730i
$329$	−6.63697e6	+	6.63697e6i	−0.186373	+	0.186373i
$330$	8.81056e6	+	8.81056e6i	0.245167	+	0.245167i
$331$	−3.89675e7	+	3.89675e7i	−1.07453	+	1.07453i	−0.0775419	+	0.996989i	$0.524707\pi$
$331$	−3.89675e7	+	3.89675e7i	−1.07453	+	1.07453i	−0.996989	+	0.0775419i	$0.975293\pi$
$332$			6.33230e7i			1.73040i
$333$	2.64068e7	+	2.64068e7i	0.715127	+	0.715127i
$334$	−5.67169e7	+	5.67169e7i	−1.52220	+	1.52220i
$335$	1.09052e7			0.290069
$336$	−5.83814e6	−	5.83814e6i	−0.153906	−	0.153906i
$337$	−1.53419e7	+	1.53419e7i	−0.400857	+	0.400857i	−0.878535	−	0.477678i	$-0.841479\pi$
$337$	−1.53419e7	+	1.53419e7i	−0.400857	+	0.400857i	0.477678	+	0.878535i	$0.341479\pi$
$338$	−9.92694e6	−	9.92694e6i	−0.257078	−	0.257078i
$339$	−1.89356e7			−0.486049
$340$	−1.79650e7	−	1.79650e7i	−0.457078	−	0.457078i
$341$		−	1.27645e7i		−	0.321916i
$342$	8.48253e7			2.12054
$343$	−1.52790e7			−0.378628
$344$	1.49504e8			3.67263
$345$	169063.	−	169063.i	0.00411709	−	0.00411709i
$346$	−2.41623e7	+	2.41623e7i	−0.583325	+	0.583325i
$347$			5.72698e7i			1.37068i	0.728221	+	0.685342i	$0.240347\pi$
$347$			5.72698e7i			1.37068i	−0.728221	+	0.685342i	$0.759653\pi$
$348$	3.35631e7	+	1.17504e7i	0.796386	+	0.278815i
$349$	3.57105e7			0.840078			0.420039	−	0.907506i	$-0.362016\pi$
$349$	3.57105e7			0.840078			0.420039	+	0.907506i	$0.362016\pi$
$350$	9.39282e6	+	9.39282e6i	0.219075	+	0.219075i
$351$	−1.97769e7	−	1.97769e7i	−0.457338	−	0.457338i
$352$		−	2.27870e8i		−	5.22468i
$353$		−	5.16103e7i		−	1.17331i	−0.809837	−	0.586654i	$-0.800445\pi$
$353$		−	5.16103e7i		−	1.17331i	0.809837	−	0.586654i	$-0.199555\pi$
$354$		−	2.30954e7i		−	0.520614i
$355$	−5.93026e6			−0.132553
$356$	−1.27818e8	+	1.27818e8i	−2.83296	+	2.83296i
$357$		−	1.60483e6i		−	0.0352715i
$358$	3.07637e7	−	3.07637e7i	0.670485	−	0.670485i
$359$	−3.14455e7	−	3.14455e7i	−0.679635	−	0.679635i	0.280282	−	0.959918i	$-0.409572\pi$
$359$	−3.14455e7	−	3.14455e7i	−0.679635	−	0.679635i	−0.959918	+	0.280282i	$0.909572\pi$
$360$	3.98487e7	−	3.98487e7i	0.854096	−	0.854096i
$361$			2.29756e7i			0.488366i
$362$	−3.93951e7	−	3.93951e7i	−0.830456	−	0.830456i
$363$	−1.06799e7	+	1.06799e7i	−0.223279	+	0.223279i
$364$	2.74562e7			0.569294
$365$	−1.84092e7	−	1.84092e7i	−0.378578	−	0.378578i
$366$	1.07737e7	−	1.07737e7i	0.219747	−	0.219747i
$367$	−6.95914e7	−	6.95914e7i	−1.40785	−	1.40785i	−0.770914	−	0.636940i	$-0.780200\pi$
$367$	−6.95914e7	−	6.95914e7i	−1.40785	−	1.40785i	−0.636940	−	0.770914i	$-0.719800\pi$
$368$	−8.27398e6			−0.166024
$369$	−5.96170e7	−	5.96170e7i	−1.18656	−	1.18656i
$370$			4.44809e7i			0.878150i
$371$	−1.30765e7			−0.256077
$372$	9.85575e6			0.191452
$373$	1.52530e7			0.293919			0.146960	−	0.989142i	$-0.453051\pi$
$373$	1.52530e7			0.293919			0.146960	+	0.989142i	$0.453051\pi$
$374$	5.92645e7	−	5.92645e7i	1.13287	−	1.13287i
$375$	8.68162e6	−	8.68162e6i	0.164629	−	0.164629i
$376$		−	2.38652e8i		−	4.48953i
$377$	−5.26417e7	+	2.53402e7i	−0.982439	+	0.472918i
$378$	1.18987e7			0.220304
$379$	5.76820e7	+	5.76820e7i	1.05955	+	1.05955i	0.998111	+	0.0614414i	$0.0195697\pi$
$379$	5.76820e7	+	5.76820e7i	1.05955	+	1.05955i	0.0614414	+	0.998111i	$0.480430\pi$
$380$	5.21681e7	+	5.21681e7i	0.950724	+	0.950724i
$381$			8.03877e6i			0.145350i
$382$			4.58607e7i			0.822717i
$383$			4.77029e7i			0.849080i	0.905409	+	0.424540i	$0.139564\pi$
$383$			4.77029e7i			0.849080i	−0.905409	+	0.424540i	$0.860436\pi$
$384$	5.29393e7			0.934942
$385$	4.49673e6	−	4.49673e6i	0.0787978	−	0.0787978i
$386$		−	3.25377e7i		−	0.565750i
$387$	−4.13572e7	+	4.13572e7i	−0.713540	+	0.713540i
$388$	9.73961e7	+	9.73961e7i	1.66743	+	1.66743i
$389$	−1.97653e6	+	1.97653e6i	−0.0335780	+	0.0335780i	−0.723696	−	0.690118i	$-0.757558\pi$
$389$	−1.97653e6	+	1.97653e6i	−0.0335780	+	0.0335780i	0.690118	+	0.723696i	$0.257558\pi$
$390$		−	1.58059e7i		−	0.266456i
$391$	−1.13721e6	−	1.13721e6i	−0.0190243	−	0.0190243i
$392$	1.34746e8	−	1.34746e8i	2.23696	−	2.23696i
$393$	−2.82150e7			−0.464839
$394$	1.87272e7	+	1.87272e7i	0.306185	+	0.306185i
$395$	1.10478e7	−	1.10478e7i	0.179260	−	0.179260i
$396$	1.52236e8	+	1.52236e8i	2.45151	+	2.45151i
$397$	3.50521e6			0.0560200			0.0280100	−	0.999608i	$-0.491083\pi$
$397$	3.50521e6			0.0560200			0.0280100	+	0.999608i	$0.491083\pi$
$398$	−1.57225e7	−	1.57225e7i	−0.249387	−	0.249387i
$399$			4.66023e6i			0.0733649i
$400$	−1.93239e8			−3.01935
$401$	3.63152e7			0.563191			0.281596	−	0.959533i	$-0.409136\pi$
$401$	3.63152e7			0.563191			0.281596	+	0.959533i	$0.409136\pi$
$402$	−2.77771e7			−0.427572
$403$	−1.14496e7	+	1.14496e7i	−0.174935	+	0.174935i
$404$	−2.07987e8	+	2.07987e8i	−3.15422	+	3.15422i
$405$			1.94180e7i			0.292308i
$406$	8.21288e6	−	2.34586e7i	0.122721	−	0.350530i
$407$	−1.07150e8			−1.58931
$408$	2.88532e7	+	2.88532e7i	0.424828	+	0.424828i
$409$	5.30243e6	+	5.30243e6i	0.0775005	+	0.0775005i	0.744794	−	0.667294i	$-0.232548\pi$
$409$	5.30243e6	+	5.30243e6i	0.0775005	+	0.0775005i	−0.667294	+	0.744794i	$0.732548\pi$
$410$		−	1.00422e8i		−	1.45706i
$411$		−	1.71015e7i		−	0.246325i
$412$			750188.i			0.0107270i
$413$	−1.17874e7			−0.167328
$414$	4.00047e6	−	4.00047e6i	0.0563780	−	0.0563780i
$415$		−	1.86052e7i		−	0.260309i
$416$	−2.04397e8	+	2.04397e8i	−2.83919	+	2.83919i
$417$	−3.81937e6	−	3.81937e6i	−0.0526724	−	0.0526724i
$418$	−1.72097e8	+	1.72097e8i	−2.35637	+	2.35637i
$419$		−	7.60205e7i		−	1.03345i	−0.856152	−	0.516724i	$-0.827151\pi$
$419$		−	7.60205e7i		−	1.03345i	0.856152	−	0.516724i	$-0.172849\pi$
$420$	3.47201e6	+	3.47201e6i	0.0468633	+	0.0468633i
$421$	8.93692e7	−	8.93692e7i	1.19768	−	1.19768i	0.222824	−	0.974859i	$-0.428472\pi$
$421$	8.93692e7	−	8.93692e7i	1.19768	−	1.19768i	0.974859	−	0.222824i	$-0.0715276\pi$
$422$	1.63057e8			2.16971
$423$	6.60182e7	+	6.60182e7i	0.872253	+	0.872253i
$424$	2.35103e8	−	2.35103e8i	3.08433	−	3.08433i
$425$	−2.65594e7	−	2.65594e7i	−0.345981	−	0.345981i
$426$	1.51052e7			0.195388
$427$	−5.49869e6	−	5.49869e6i	−0.0706278	−	0.0706278i
$428$			3.30375e7i			0.421382i
$429$	3.80749e7			0.482245
$430$	−6.96642e7			−0.876202
$431$	6.84334e6			0.0854745			0.0427372	−	0.999086i	$-0.486392\pi$
$431$	6.84334e6			0.0854745			0.0427372	+	0.999086i	$0.486392\pi$
$432$	−1.22396e8	+	1.22396e8i	−1.51815	+	1.51815i
$433$	2.41141e7	−	2.41141e7i	0.297034	−	0.297034i	−0.542817	−	0.839851i	$-0.682642\pi$
$433$	2.41141e7	−	2.41141e7i	0.297034	−	0.297034i	0.839851	+	0.542817i	$0.182642\pi$
$434$		−	6.88860e6i		−	0.0842678i
$435$	−9.86129e6	−	3.45244e6i	−0.119803	−	0.0419429i
$436$	−2.12617e7			−0.256530
$437$	3.30230e6	+	3.30230e6i	0.0395706	+	0.0395706i
$438$	4.68906e7	+	4.68906e7i	0.558038	+	0.558038i
$439$			7.23194e7i			0.854793i	0.904064	+	0.427397i	$0.140569\pi$
$439$			7.23194e7i			0.854793i	−0.904064	+	0.427397i	$0.859431\pi$
$440$			1.61693e8i			1.89816i
$441$			7.45498e7i			0.869222i
$442$	−1.06319e8			−1.23125
$443$	−1.62276e7	+	1.62276e7i	−0.186657	+	0.186657i	−0.794249	−	0.607592i	$-0.792136\pi$
$443$	−1.62276e7	+	1.62276e7i	−0.186657	+	0.186657i	0.607592	+	0.794249i	$0.292136\pi$
$444$		−	8.27328e7i		−	0.945211i
$445$	3.75546e7	−	3.75546e7i	0.426170	−	0.426170i
$446$	−1.05182e8	−	1.05182e8i	−1.18559	−	1.18559i
$447$	−2.36655e7	+	2.36655e7i	−0.264968	+	0.264968i
$448$		−	6.01955e7i		−	0.669469i
$449$	5.26924e7	+	5.26924e7i	0.582115	+	0.582115i	0.935484	−	0.353369i	$-0.114964\pi$
$449$	5.26924e7	+	5.26924e7i	0.582115	+	0.582115i	−0.353369	+	0.935484i	$0.614964\pi$
$450$	9.34309e7	−	9.34309e7i	1.02530	−	1.02530i
$451$	2.41906e8			2.63705
$452$	−2.75564e8	−	2.75564e8i	−2.98405	−	2.98405i
$453$	2.26173e7	−	2.26173e7i	0.243302	−	0.243302i
$454$	2.69943e7	+	2.69943e7i	0.288472	+	0.288472i
$455$	−8.06702e6			−0.0856404
$456$	−8.37861e7	−	8.37861e7i	−0.883644	−	0.883644i
$457$		−	1.40122e8i		−	1.46810i	−0.679093	−	0.734052i	$-0.737627\pi$
$457$		−	1.40122e8i		−	1.46810i	0.679093	−	0.734052i	$-0.262373\pi$
$458$	2.85941e6			0.0297632
$459$	−3.36450e7			−0.347922
$460$	4.92063e6			0.0505530
$461$	8.83018e7	−	8.83018e7i	0.901294	−	0.901294i	−0.0942540	−	0.995548i	$-0.530047\pi$
$461$	8.83018e7	−	8.83018e7i	0.901294	−	0.901294i	0.995548	+	0.0942540i	$0.0300466\pi$
$462$	−1.14538e7	+	1.14538e7i	−0.116151	+	0.116151i
$463$			6.59399e7i			0.664363i	0.943215	+	0.332182i	$0.107785\pi$
$463$			6.59399e7i			0.664363i	−0.943215	+	0.332182i	$0.892215\pi$
$464$	1.56826e8	+	3.25789e8i	1.56987	+	3.26124i
$465$	−2.89576e6			−0.0288007
$466$	1.12026e7	+	1.12026e7i	0.110703	+	0.110703i
$467$	4.72696e7	+	4.72696e7i	0.464121	+	0.464121i	0.900004	−	0.435882i	$-0.143564\pi$
$467$	4.72696e7	+	4.72696e7i	0.464121	+	0.464121i	−0.435882	+	0.900004i	$0.643564\pi$
$468$		−	2.73108e8i		−	2.66439i
$469$			1.41769e7i			0.137424i
$470$			1.11204e8i			1.07110i
$471$	−1.45546e7			−0.139295
$472$	2.11926e8	−	2.11926e8i	2.01538	−	2.01538i
$473$		−	1.67814e8i		−	1.58579i
$474$	−2.81402e7	+	2.81402e7i	−0.264236	+	0.264236i
$475$	7.71252e7	+	7.71252e7i	0.719640	+	0.719640i
$476$	2.33546e7	−	2.33546e7i	0.216547	−	0.216547i
$477$			1.30073e8i			1.19848i
$478$	−2.40572e8	−	2.40572e8i	−2.20274	−	2.20274i
$479$	−1.45433e8	+	1.45433e8i	−1.32329	+	1.32329i	−0.412201	+	0.911093i	$0.635240\pi$
$479$	−1.45433e8	+	1.45433e8i	−1.32329	+	1.32329i	−0.911093	+	0.412201i	$0.864760\pi$
$480$	−5.16946e7			−0.467435
$481$	9.61124e7	+	9.61124e7i	0.863663	+	0.863663i
$482$	−4.66297e6	+	4.66297e6i	−0.0416410	+	0.0416410i
$483$	219782.	+	219782.i	0.00195052	+	0.00195052i
$484$	−3.10843e8			−2.74161
$485$	−2.86163e7	−	2.86163e7i	−0.250835	−	0.250835i
$486$		−	1.80557e8i		−	1.57292i
$487$	−1.80778e8			−1.56516			−0.782581	−	0.622549i	$-0.786097\pi$
$487$	−1.80778e8			−1.56516			−0.782581	+	0.622549i	$0.786097\pi$
$488$	1.97722e8			1.70135
$489$	5.92399e7			0.506626
$490$	−6.27877e7	+	6.27877e7i	−0.533687	+	0.533687i
$491$	3.41055e7	−	3.41055e7i	0.288124	−	0.288124i	−0.548214	−	0.836338i	$-0.684692\pi$
$491$	3.41055e7	−	3.41055e7i	0.288124	−	0.288124i	0.836338	+	0.548214i	$0.184692\pi$
$492$			1.86781e8i			1.56833i
$493$	−2.32230e7	+	6.63323e7i	−0.193810	+	0.553585i
$494$	3.08737e8			2.56099
$495$	−4.47292e7	−	4.47292e7i	−0.368787	−	0.368787i
$496$	7.08596e7	+	7.08596e7i	0.580703	+	0.580703i
$497$		−	7.70937e6i		−	0.0627985i
$498$			4.73899e7i			0.383705i
$499$			1.16325e8i			0.936206i	0.883674	+	0.468103i	$0.155062\pi$
$499$			1.16325e8i			0.936206i	−0.883674	+	0.468103i	$0.844938\pi$
$500$	2.52682e8			2.02145
$501$	−3.09948e7	+	3.09948e7i	−0.246476	+	0.246476i
$502$			1.92750e8i			1.52365i
$503$	9.22800e7	−	9.22800e7i	0.725110	−	0.725110i	−0.244532	−	0.969641i	$-0.578634\pi$
$503$	9.22800e7	−	9.22800e7i	0.725110	−	0.725110i	0.969641	+	0.244532i	$0.0786342\pi$
$504$	5.18035e7	+	5.18035e7i	0.404638	+	0.404638i
$505$	6.11095e7	−	6.11095e7i	0.474498	−	0.474498i
$506$			1.62326e7i			0.125296i
$507$	−5.42489e6	−	5.42489e6i	−0.0416263	−	0.0416263i
$508$	−1.16986e8	+	1.16986e8i	−0.892363	+	0.892363i
$509$	1.67859e8			1.27289			0.636447	−	0.771321i	$-0.280404\pi$
$509$	1.67859e8			1.27289			0.636447	+	0.771321i	$0.280404\pi$
$510$	−1.34447e7	−	1.34447e7i	−0.101354	−	0.101354i
$511$	2.39320e7	−	2.39320e7i	0.179356	−	0.179356i
$512$	1.36279e8	+	1.36279e8i	1.01536	+	1.01536i
$513$	9.77009e7			0.723680
$514$	−4.09797e7	−	4.09797e7i	−0.301772	−	0.301772i
$515$		−	220416.i		−	0.00161369i
$516$	1.29573e8			0.943114
$517$	−2.67881e8			−1.93852
$518$	−5.78254e7			−0.416035
$519$	−1.32043e7	+	1.32043e7i	−0.0944523	+	0.0944523i
$520$	1.45037e8	−	1.45037e8i	1.03150	−	1.03150i
$521$			1.15597e8i			0.817395i	0.912670	+	0.408698i	$0.134017\pi$
$521$			1.15597e8i			0.817395i	−0.912670	+	0.408698i	$0.865983\pi$
$522$	−2.33344e8	−	8.16939e7i	−1.64053	−	0.574352i
$523$	1.19434e8			0.834878			0.417439	−	0.908705i	$-0.362928\pi$
$523$	1.19434e8			0.834878			0.417439	+	0.908705i	$0.362928\pi$
$524$	−4.10604e8	−	4.10604e8i	−2.85384	−	2.85384i
$525$	5.13301e6	+	5.13301e6i	0.0354727	+	0.0354727i
$526$			2.05859e8i			1.41453i
$527$			1.94784e7i			0.133083i
$528$		−	2.35639e8i		−	1.60083i
$529$	−1.47724e8			−0.997896
$530$	−1.09551e8	+	1.09551e8i	−0.735848	+	0.735848i
$531$			1.17250e8i			0.783121i
$532$	−6.78188e7	+	6.78188e7i	−0.450417	+	0.450417i
$533$	−2.16987e8	−	2.16987e8i	−1.43302	−	1.43302i
$534$	−9.56566e7	+	9.56566e7i	−0.628190	+	0.628190i
$535$		−	9.70689e6i		−	0.0633897i
$536$	−2.54885e8	−	2.54885e8i	−1.65520	−	1.65520i
$537$	1.68118e7	−	1.68118e7i	0.108565	−	0.108565i
$538$	−2.44403e8			−1.56949
$539$	−1.51249e8	−	1.51249e8i	−0.965890	−	0.965890i
$540$	7.27901e7	−	7.27901e7i	0.462265	−	0.462265i
$541$	−3.41759e7	−	3.41759e7i	−0.215838	−	0.215838i	0.590904	−	0.806742i	$-0.298771\pi$
$541$	−3.41759e7	−	3.41759e7i	−0.215838	−	0.215838i	−0.806742	+	0.590904i	$0.798771\pi$
$542$	5.60742e8			3.52181
$543$	−2.15287e7	−	2.15287e7i	−0.134468	−	0.134468i
$544$			3.47725e8i			2.15993i
$545$	6.24698e6			0.0385905
$546$	2.05478e7			0.126237
$547$	1.97515e8			1.20681			0.603405	−	0.797435i	$-0.293810\pi$
$547$	1.97515e8			1.20681			0.603405	+	0.797435i	$0.293810\pi$
$548$	2.48872e8	−	2.48872e8i	1.51229	−	1.51229i
$549$	−5.46957e7	+	5.46957e7i	−0.330549	+	0.330549i
$550$			3.79112e8i			2.27866i
$551$	6.74366e7	−	1.92621e8i	0.403126	−	1.15146i
$552$	−7.90291e6			−0.0469862
$553$	1.43622e7	+	1.43622e7i	0.0849268	+	0.0849268i
$554$	−1.46070e8	−	1.46070e8i	−0.859079	−	0.859079i
$555$			2.43080e7i			0.142191i
$556$		−	1.11164e8i		−	0.646756i
$557$		−	3.65214e7i		−	0.211340i	−0.994401	−	0.105670i	$-0.966301\pi$
$557$		−	3.65214e7i		−	0.211340i	0.994401	−	0.105670i	$-0.0336987\pi$
$558$	−6.85212e7			−0.394387
$559$	−1.50527e8	+	1.50527e8i	−0.861747	+	0.861747i
$560$			4.99252e7i			0.284286i
$561$	3.23870e7	−	3.23870e7i	0.183435	−	0.183435i
$562$	2.97906e8	+	2.97906e8i	1.67830	+	1.67830i
$563$	−1.79567e8	+	1.79567e8i	−1.00624	+	1.00624i	−0.00625953	+	0.999980i	$0.501992\pi$
$563$	−1.79567e8	+	1.79567e8i	−1.00624	+	1.00624i	−0.999980	+	0.00625953i	$0.998008\pi$
$564$		−	2.06836e8i		−	1.15289i
$565$	8.09645e7	+	8.09645e7i	0.448899	+	0.448899i
$566$	−1.43732e7	+	1.43732e7i	−0.0792692	+	0.0792692i
$567$	−2.52435e7			−0.138484
$568$	1.38606e8	+	1.38606e8i	0.756377	+	0.756377i
$569$	−3.21566e7	+	3.21566e7i	−0.174555	+	0.174555i	−0.788977	−	0.614422i	$-0.789389\pi$
$569$	−3.21566e7	+	3.21566e7i	−0.174555	+	0.174555i	0.614422	+	0.788977i	$0.289389\pi$
$570$	3.90418e7	+	3.90418e7i	0.210817	+	0.210817i
$571$	−1.11403e8			−0.598396			−0.299198	−	0.954191i	$-0.596719\pi$
$571$	−1.11403e8			−0.598396			−0.299198	+	0.954191i	$0.596719\pi$
$572$	5.54092e8	+	5.54092e8i	2.96070	+	2.96070i
$573$			2.50620e7i			0.133215i
$574$	1.30549e8			0.690299
$575$	7.27464e6			0.0382656
$576$	−5.98768e8			−3.13322
$577$	3.55344e7	−	3.55344e7i	0.184979	−	0.184979i	−0.608543	−	0.793521i	$-0.708246\pi$
$577$	3.55344e7	−	3.55344e7i	0.184979	−	0.184979i	0.793521	+	0.608543i	$0.208246\pi$
$578$	1.72446e8	−	1.72446e8i	0.893036	−	0.893036i
$579$		−	1.77812e7i		−	0.0916065i
$580$	−9.32659e7	−	1.93751e8i	−0.478012	−	0.993022i
$581$	2.41868e7			0.123325
$582$	7.28897e7	+	7.28897e7i	0.369740	+	0.369740i
$583$	−2.63897e8	−	2.63897e8i	−1.33177	−	1.33177i
$584$			8.60545e8i			4.32051i
$585$			8.02430e7i			0.400811i
$586$		−	2.19707e8i		−	1.09182i
$587$	−4.98963e7			−0.246691			−0.123346	−	0.992364i	$-0.539362\pi$
$587$	−4.98963e7			−0.246691			−0.123346	+	0.992364i	$0.539362\pi$
$588$	1.16783e8	−	1.16783e8i	0.574442	−	0.574442i
$589$		−	5.65628e7i		−	0.276812i
$590$	−9.87508e7	+	9.87508e7i	−0.480822	+	0.480822i
$591$	1.02341e7	+	1.02341e7i	0.0495777	+	0.0495777i
$592$	5.94822e8	−	5.94822e8i	2.86696	−	2.86696i
$593$			1.73461e8i			0.831836i	0.909402	+	0.415918i	$0.136540\pi$
$593$			1.73461e8i			0.831836i	−0.909402	+	0.415918i	$0.863460\pi$
$594$	2.40126e8	+	2.40126e8i	1.14573	+	1.14573i
$595$	−6.86190e6	+	6.86190e6i	−0.0325757	+	0.0325757i
$596$	−6.88793e8			−3.25349
$597$	−8.59208e6	−	8.59208e6i	−0.0403808	−	0.0403808i
$598$	1.45604e7	−	1.45604e7i	0.0680881	−	0.0680881i
$599$	−5.02617e7	−	5.02617e7i	−0.233860	−	0.233860i	0.580441	−	0.814302i	$-0.302880\pi$
$599$	−5.02617e7	−	5.02617e7i	−0.233860	−	0.233860i	−0.814302	+	0.580441i	$0.802880\pi$
$600$	−1.84572e8			−0.854502
$601$	−2.45882e8	−	2.45882e8i	−1.13267	−	1.13267i	−0.989731	−	0.142940i	$-0.954344\pi$
$601$	−2.45882e8	−	2.45882e8i	−1.13267	−	1.13267i	−0.142940	−	0.989731i	$-0.545656\pi$
$602$		−	9.05638e7i		−	0.415112i
$603$	1.41018e8			0.643165
$604$	6.58285e8			2.98747
$605$	9.13301e7			0.412428
$606$	−1.55654e8	+	1.55654e8i	−0.699428	+	0.699428i
$607$	1.42552e8	−	1.42552e8i	0.637391	−	0.637391i	−0.312520	−	0.949911i	$-0.601173\pi$
$607$	1.42552e8	−	1.42552e8i	0.637391	−	0.637391i	0.949911	+	0.312520i	$0.101173\pi$
$608$		−	1.00975e9i		−	4.49266i
$609$	4.48819e6	−	1.28197e7i	0.0198710	−	0.0567579i
$610$	−9.21323e7			−0.405903
$611$	2.40286e8	+	2.40286e8i	1.05343	+	1.05343i
$612$	−2.32309e8	−	2.32309e8i	−1.01347	−	1.01347i
$613$		−	3.23335e7i		−	0.140369i	−0.997534	−	0.0701844i	$-0.977641\pi$
$613$		−	3.23335e7i		−	0.140369i	0.997534	−	0.0701844i	$-0.0223588\pi$
$614$		−	2.50413e8i		−	1.08181i
$615$		−	5.48787e7i		−	0.235928i
$616$	−2.10202e8			−0.899278
$617$	−2.39199e8	+	2.39199e8i	−1.01837	+	1.01837i	−0.0185385	+	0.999828i	$0.505901\pi$
$617$	−2.39199e8	+	2.39199e8i	−1.01837	+	1.01837i	−0.999828	+	0.0185385i	$0.994099\pi$
$618$			561428.i			0.00237864i
$619$	2.71747e8	−	2.71747e8i	1.14576	−	1.14576i	0.158379	−	0.987378i	$-0.449373\pi$
$619$	2.71747e8	−	2.71747e8i	1.14576	−	1.14576i	0.987378	−	0.158379i	$-0.0506267\pi$
$620$	−4.21410e7	−	4.21410e7i	−0.176819	−	0.176819i
$621$	4.60770e6	−	4.60770e6i	0.0192402	−	0.0192402i
$622$			3.01842e8i			1.25432i
$623$	4.88211e7	+	4.88211e7i	0.201903	+	0.201903i
$624$	−2.11365e8	+	2.11365e8i	−0.869919	+	0.869919i
$625$	1.29423e8			0.530118
$626$	3.62337e8	+	3.62337e8i	1.47703	+	1.47703i
$627$	−9.40478e7	+	9.40478e7i	−0.381545	+	0.381545i
$628$	−2.11808e8	−	2.11808e8i	−0.855191	−	0.855191i
$629$	1.63509e8			0.657036
$630$	−2.41388e7	−	2.41388e7i	−0.0965372	−	0.0965372i
$631$		−	2.60009e8i		−	1.03491i	−0.855712	−	0.517453i	$-0.826880\pi$
$631$		−	2.60009e8i		−	1.03491i	0.855712	−	0.517453i	$-0.173120\pi$
$632$	−5.16434e8			−2.04580
$633$	8.91076e7			0.351320
$634$	−1.24062e7			−0.0486823
$635$	3.43720e7	−	3.43720e7i	0.134241	−	0.134241i
$636$	2.03760e8	−	2.03760e8i	0.792041	−	0.792041i
$637$			2.71338e8i			1.04976i
$638$	6.39161e8	−	3.07674e8i	2.46121	−	1.18476i
$639$	−7.66854e7			−0.293907
$640$	−2.26357e8	−	2.26357e8i	−0.863483	−	0.863483i
$641$	1.37650e8	+	1.37650e8i	0.522641	+	0.522641i	0.918368	−	0.395727i	$-0.129507\pi$
$641$	1.37650e8	+	1.37650e8i	0.522641	+	0.522641i	−0.395727	+	0.918368i	$0.629507\pi$
$642$			2.47248e7i			0.0934387i
$643$			3.04778e8i			1.14644i	0.819402	+	0.573220i	$0.194306\pi$
$643$			3.04778e8i			1.14644i	−0.819402	+	0.573220i	$0.805694\pi$
$644$			6.39684e6i			0.0239501i
$645$	−3.80702e7			−0.141875
$646$	2.62616e8	−	2.62616e8i	0.974144	−	0.974144i
$647$		−	4.70262e8i		−	1.73631i	−0.496295	−	0.868154i	$-0.665306\pi$
$647$		−	4.70262e8i		−	1.73631i	0.496295	−	0.868154i	$-0.334694\pi$
$648$	4.53853e8	−	4.53853e8i	1.66798	−	1.66798i
$649$	−2.37881e8	−	2.37881e8i	−0.870214	−	0.870214i
$650$	3.40059e8	−	3.40059e8i	1.23827	−	1.23827i
$651$		−	3.76449e6i		−	0.0136447i
$652$	8.62099e8	+	8.62099e8i	3.11039	+	3.11039i
$653$	−8.82066e7	+	8.82066e7i	−0.316783	+	0.316783i	−0.847530	−	0.530747i	$-0.821911\pi$
$653$	−8.82066e7	+	8.82066e7i	−0.316783	+	0.316783i	0.530747	+	0.847530i	$0.321911\pi$
$654$	−1.59119e7			−0.0568838
$655$	1.20641e8	+	1.20641e8i	0.429311	+	0.429311i
$656$	−1.34289e9	+	1.34289e9i	−4.75696	+	4.75696i
$657$	−2.38053e8	−	2.38053e8i	−0.839415	−	0.839415i
$658$	−1.44566e8			−0.507445
$659$	−1.80340e8	−	1.80340e8i	−0.630138	−	0.630138i	0.317964	−	0.948103i	$-0.397001\pi$
$659$	−1.80340e8	−	1.80340e8i	−0.630138	−	0.630138i	−0.948103	+	0.317964i	$0.897001\pi$
$660$			1.40137e8i			0.487439i
$661$	5.58214e8			1.93284			0.966421	−	0.256962i	$-0.0827217\pi$
$661$	5.58214e8			1.93284			0.966421	+	0.256962i	$0.0827217\pi$
$662$	−8.48790e8			−2.92568
$663$	−5.81015e7			−0.199364
$664$	−4.34854e8	+	4.34854e8i	−1.48539	+	1.48539i
$665$	1.99261e7	−	1.99261e7i	0.0677575	−	0.0677575i
$666$			5.75192e8i			1.94711i
$667$	−5.90384e6	−	1.22646e7i	−0.0198956	−	0.0413311i
$668$	−9.02114e8			−3.02644
$669$	−5.74798e7	−	5.74798e7i	−0.191972	−	0.191972i
$670$	1.18769e8	+	1.18769e8i	0.394892	+	0.394892i
$671$		−	2.21938e8i		−	0.734621i
$672$		−	6.72031e7i		−	0.221453i
$673$			1.19642e8i			0.392498i	0.980554	+	0.196249i	$0.0628760\pi$
$673$			1.19642e8i			0.392498i	−0.980554	+	0.196249i	$0.937124\pi$
$674$	−3.34177e8			−1.09143
$675$	1.07613e8	−	1.07613e8i	0.349907	−	0.349907i
$676$		−	1.57893e8i		−	0.511121i
$677$	−2.29742e7	+	2.29742e7i	−0.0740413	+	0.0740413i	−0.743158	−	0.669116i	$-0.766673\pi$
$677$	−2.29742e7	+	2.29742e7i	−0.0740413	+	0.0740413i	0.669116	+	0.743158i	$0.266673\pi$
$678$	−2.06227e8	−	2.06227e8i	−0.661694	−	0.661694i
$679$	3.72014e7	−	3.72014e7i	0.118836	−	0.118836i
$680$		−	2.46740e8i		−	0.784716i
$681$	1.47519e7	+	1.47519e7i	0.0467096	+	0.0467096i
$682$	1.39018e8	−	1.39018e8i	0.438247	−	0.438247i
$683$	4.86611e8			1.52728			0.763641	−	0.645641i	$-0.223410\pi$
$683$	4.86611e8			1.52728			0.763641	+	0.645641i	$0.223410\pi$
$684$	6.74597e8	+	6.74597e8i	2.10803	+	2.10803i
$685$	−7.31221e7	+	7.31221e7i	−0.227498	+	0.227498i
$686$	−1.66403e8	−	1.66403e8i	−0.515454	−	0.515454i
$687$	1.56261e6			0.00481927
$688$	9.31585e8	+	9.31585e8i	2.86060	+	2.86060i
$689$			4.73425e8i			1.44742i
$690$	3.68252e6			0.0112098
$691$	3.85661e8			1.16888			0.584441	−	0.811436i	$-0.301314\pi$
$691$	3.85661e8			1.16888			0.584441	+	0.811436i	$0.301314\pi$
$692$	−3.84315e8			−1.15976
$693$	5.81481e7	−	5.81481e7i	0.174717	−	0.174717i
$694$	−6.23725e8	+	6.23725e8i	−1.86601	+	1.86601i
$695$			3.26616e7i			0.0972932i
$696$	1.49792e8	+	3.11178e8i	0.444285	+	0.922958i
$697$	−3.69144e8			−1.09018
$698$	3.88923e8	+	3.88923e8i	1.14366	+	1.14366i
$699$	6.12201e6	+	6.12201e6i	0.0179251	+	0.0179251i
$700$			1.49398e8i			0.435563i
$701$		−	9.81695e7i		−	0.284985i	−0.989796	−	0.142493i	$-0.954488\pi$
$701$		−	9.81695e7i		−	0.284985i	0.989796	−	0.142493i	$-0.0455118\pi$
$702$		−	4.30781e8i		−	1.24522i
$703$	−4.74809e8			−1.36664
$704$	1.21480e9	−	1.21480e9i	3.48167	−	3.48167i
$705$			6.07712e7i			0.173433i
$706$	5.62087e8	−	5.62087e8i	1.59731	−	1.59731i
$707$	7.94427e7	+	7.94427e7i	0.224800	+	0.224800i
$708$	1.83673e8	−	1.83673e8i	0.517541	−	0.517541i
$709$			5.56332e8i			1.56097i	0.625174	+	0.780486i	$0.285028\pi$
$709$			5.56332e8i			1.56097i	−0.625174	+	0.780486i	$0.714972\pi$
$710$	−6.45864e7	−	6.45864e7i	−0.180454	−	0.180454i
$711$	1.42861e8	−	1.42861e8i	0.397471	−	0.397471i
$712$	−1.75551e9			−4.86365
$713$	−2.66757e6	−	2.66757e6i	−0.00735949	−	0.00735949i
$714$	1.74782e7	−	1.74782e7i	0.0480177	−	0.0480177i
$715$	−1.62800e8	−	1.62800e8i	−0.445386	−	0.445386i
$716$	4.89313e8			1.33305
$717$	−1.31469e8	−	1.31469e8i	−0.356668	−	0.356668i
$718$		−	6.84946e8i		−	1.85047i
$719$	−3.25700e8			−0.876255			−0.438128	−	0.898913i	$-0.644358\pi$
$719$	−3.25700e8			−0.876255			−0.438128	+	0.898913i	$0.644358\pi$
$720$	4.96609e8			1.33051
$721$	286541.			0.000764507
$722$	−2.50227e8	+	2.50227e8i	−0.664848	+	0.664848i
$723$	−2.54823e6	+	2.54823e6i	−0.00674254	+	0.00674254i
$724$		−	6.26601e8i		−	1.65111i
$725$	−1.37884e8	−	2.86440e8i	−0.361826	−	0.751657i
$726$	−2.32630e8			−0.607933
$727$	−9.24370e7	−	9.24370e7i	−0.240571	−	0.240571i	0.576516	−	0.817086i	$-0.304412\pi$
$727$	−9.24370e7	−	9.24370e7i	−0.240571	−	0.240571i	−0.817086	+	0.576516i	$0.804412\pi$
$728$	1.88548e8	+	1.88548e8i	0.488684	+	0.488684i
$729$			1.79457e8i			0.463209i
$730$		−	4.00988e8i		−	1.03077i
$731$			2.56081e8i			0.655578i
$732$	1.71362e8			0.436900
$733$	−4.72430e8	+	4.72430e8i	−1.19957	+	1.19957i	−0.225274	+	0.974295i	$0.572328\pi$
$733$	−4.72430e8	+	4.72430e8i	−1.19957	+	1.19957i	−0.974295	+	0.225274i	$0.927672\pi$
$734$		−	1.51584e9i		−	3.83323i
$735$	−3.43124e7	+	3.43124e7i	−0.0864149	+	0.0864149i
$736$	−4.76211e7	−	4.76211e7i	−0.119444	−	0.119444i
$737$	−2.86102e8	+	2.86102e8i	−0.714692	+	0.714692i
$738$		−	1.29858e9i		−	3.23071i
$739$	3.31055e8	+	3.31055e8i	0.820290	+	0.820290i	0.986149	−	0.165859i	$-0.0530398\pi$
$739$	3.31055e8	+	3.31055e8i	0.820290	+	0.820290i	−0.165859	+	0.986149i	$0.553040\pi$
$740$	−3.53747e8	+	3.53747e8i	−0.872967	+	0.872967i
$741$	1.68719e8			0.414677
$742$	−1.42417e8	−	1.42417e8i	−0.348617	−	0.348617i
$743$	−2.46015e8	+	2.46015e8i	−0.599785	+	0.599785i	−0.940255	−	0.340470i	$-0.889414\pi$
$743$	−2.46015e8	+	2.46015e8i	−0.599785	+	0.599785i	0.340470	+	0.940255i	$0.389414\pi$
$744$	6.76817e7	+	6.76817e7i	0.164344	+	0.164344i
$745$	2.02377e8			0.489432
$746$	1.66120e8	+	1.66120e8i	0.400134	+	0.400134i
$747$		−	2.40587e8i		−	0.577180i
$748$	9.42635e8			2.25237
$749$	1.26190e7			0.0300317
$750$	1.89103e8			0.448244
$751$	4.35108e8	−	4.35108e8i	1.02725	−	1.02725i	0.0276355	−	0.999618i	$-0.491202\pi$
$751$	4.35108e8	−	4.35108e8i	1.02725	−	1.02725i	0.999618	−	0.0276355i	$-0.00879777\pi$
$752$	1.48708e9	−	1.48708e9i	3.49688	−	3.49688i
$753$			1.05335e8i			0.246710i
$754$	−8.49299e8	−	2.97340e8i	−1.98128	−	0.693648i
$755$	−1.93413e8			−0.449413
$756$	9.46274e7	+	9.46274e7i	0.219004	+	0.219004i
$757$	−4.25874e8	−	4.25874e8i	−0.981732	−	0.981732i	0.0181038	−	0.999836i	$-0.494237\pi$
$757$	−4.25874e8	−	4.25874e8i	−0.981732	−	0.981732i	−0.999836	+	0.0181038i	$0.994237\pi$
$758$			1.25643e9i			2.88489i
$759$			8.87082e6i			0.0202880i
$760$			7.16502e8i			1.63221i
$761$	−2.13014e8			−0.483342			−0.241671	−	0.970358i	$-0.577696\pi$
$761$	−2.13014e8			−0.483342			−0.241671	+	0.970358i	$0.577696\pi$
$762$	−8.75502e7	+	8.75502e7i	−0.197876	+	0.197876i
$763$			8.12110e6i			0.0182827i
$764$	−3.64720e8	+	3.64720e8i	−0.817861	+	0.817861i
$765$	6.82557e7	+	6.82557e7i	0.152459	+	0.152459i
$766$	−5.19532e8	+	5.19532e8i	−1.15592	+	1.15592i
$767$			4.26753e8i			0.945780i
$768$	2.30021e8	+	2.30021e8i	0.507790	+	0.507790i
$769$	5.72051e7	−	5.72051e7i	0.125793	−	0.125793i	−0.641408	−	0.767200i	$-0.721649\pi$
$769$	5.72051e7	−	5.72051e7i	0.125793	−	0.125793i	0.767200	+	0.641408i	$0.221649\pi$
$770$	9.79476e7			0.214547
$771$	−2.23947e7	−	2.23947e7i	−0.0488631	−	0.0488631i
$772$	2.58765e8	−	2.58765e8i	0.562410	−	0.562410i
$773$	2.74277e8	+	2.74277e8i	0.593814	+	0.593814i	0.938659	−	0.344845i	$-0.112069\pi$
$773$	2.74277e8	+	2.74277e8i	0.593814	+	0.593814i	−0.344845	+	0.938659i	$0.612069\pi$
$774$	−9.00842e8			−1.94279
$775$	−6.23011e7	−	6.23011e7i	−0.133842	−	0.133842i
$776$			1.33768e9i			2.86265i
$777$	−3.16005e7			−0.0673646
$778$	−4.30527e7			−0.0914243
$779$	1.07195e9			2.26757
$780$	1.25701e8	−	1.25701e8i	0.264884	−	0.264884i
$781$	1.55582e8	−	1.55582e8i	0.326593	−	0.326593i
$782$		−	2.47706e7i		−	0.0517983i
$783$	−2.68763e8	−	9.40941e7i	−0.559867	−	0.196010i
$784$	1.67926e9			3.48473
$785$	6.22321e7	+	6.22321e7i	0.128649	+	0.128649i
$786$	−3.07289e8	−	3.07289e8i	−0.632820	−	0.632820i
$787$		−	1.35051e8i		−	0.277059i	−0.990358	−	0.138530i	$-0.955762\pi$
$787$		−	1.35051e8i		−	0.277059i	0.990358	−	0.138530i	$-0.0442376\pi$
$788$			2.97866e8i			0.608756i
$789$			1.12498e8i			0.229042i
$790$	2.40643e8			0.488080
$791$	−1.05254e8	+	1.05254e8i	−0.212672	+	0.212672i
$792$			2.09089e9i			4.20877i
$793$	−1.99075e8	+	1.99075e8i	−0.399207	+	0.399207i
$794$	3.81752e7	+	3.81752e7i	0.0762641	+	0.0762641i
$795$	−5.98675e7	+	5.98675e7i	−0.119149	+	0.119149i
$796$		−	2.50075e8i		−	0.495829i
$797$	−2.99864e8	−	2.99864e8i	−0.592310	−	0.592310i	0.345945	−	0.938255i	$-0.387558\pi$
$797$	−2.99864e8	−	2.99864e8i	−0.592310	−	0.592310i	−0.938255	+	0.345945i	$0.887558\pi$
$798$	−5.07545e7	+	5.07545e7i	−0.0998770	+	0.0998770i
$799$	4.08780e8			0.801399
$800$	−1.11219e9	−	1.11219e9i	−2.17225	−	2.17225i
$801$	4.85626e8	−	4.85626e8i	0.944940	−	0.944940i
$802$	3.95509e8	+	3.95509e8i	0.766714	+	0.766714i
$803$	9.65940e8			1.86554
$804$	−2.20905e8	−	2.20905e8i	−0.425048	−	0.425048i
$805$		−	1.87948e6i		−	0.00360288i
$806$	−2.49396e8			−0.476303
$807$	−1.33562e8			−0.254133
$808$	−2.85659e9			−5.41520
$809$	1.92832e8	−	1.92832e8i	0.364196	−	0.364196i	−0.501159	−	0.865355i	$-0.667093\pi$
$809$	1.92832e8	−	1.92832e8i	0.364196	−	0.364196i	0.865355	+	0.501159i	$0.167093\pi$
$810$	−2.11482e8	+	2.11482e8i	−0.397940	+	0.397940i
$811$			5.63247e8i			1.05593i	0.849265	+	0.527966i	$0.177045\pi$
$811$			5.63247e8i			1.05593i	−0.849265	+	0.527966i	$0.822955\pi$
$812$	2.51876e8	−	1.21246e8i	0.470457	−	0.226464i
$813$	3.06436e8			0.570253
$814$	−1.16697e9	−	1.16697e9i	−2.16365	−	2.16365i
$815$	−2.53297e8	−	2.53297e8i	−0.467904	−	0.467904i
$816$			3.59579e8i			0.661796i
$817$		−	7.43626e8i		−	1.36360i
$818$			1.15497e8i			0.211014i
$819$	−1.04316e8			−0.189889
$820$	7.98633e8	−	7.98633e8i	1.44846	−	1.44846i
$821$			5.23686e8i			0.946327i	0.880975	+	0.473164i	$0.156888\pi$
$821$			5.23686e8i			0.946327i	−0.880975	+	0.473164i	$0.843112\pi$
$822$	1.86252e8	−	1.86252e8i	0.335340	−	0.335340i
$823$	−2.40769e8	−	2.40769e8i	−0.431917	−	0.431917i	0.457363	−	0.889280i	$-0.348794\pi$
$823$	−2.40769e8	−	2.40769e8i	−0.431917	−	0.431917i	−0.889280	+	0.457363i	$0.848794\pi$
$824$	−5.15172e6	+	5.15172e6i	−0.00920811	+	0.00920811i
$825$			2.07178e8i			0.368962i
$826$	−1.28377e8	−	1.28377e8i	−0.227796	−	0.227796i
$827$	−2.75347e8	+	2.75347e8i	−0.486815	+	0.486815i	−0.907300	−	0.420485i	$-0.861860\pi$
$827$	−2.75347e8	+	2.75347e8i	−0.486815	+	0.486815i	0.420485	+	0.907300i	$0.361860\pi$
$828$	6.36297e7			0.112090
$829$	−2.21091e8	−	2.21091e8i	−0.388068	−	0.388068i	0.485930	−	0.873998i	$-0.338481\pi$
$829$	−2.21091e8	−	2.21091e8i	−0.388068	−	0.388068i	−0.873998	+	0.485930i	$0.838481\pi$
$830$	2.02629e8	−	2.02629e8i	0.354378	−	0.354378i
$831$	−7.98249e7	−	7.98249e7i	−0.139103	−	0.139103i
$832$	−2.17933e9			−3.78401
$833$	2.30803e8	+	2.30803e8i	0.399307	+	0.399307i
$834$		−	8.31934e7i		−	0.143414i
$835$	2.65054e8			0.455275
$836$	−2.73730e9			−4.68493
$837$	−7.89220e7			−0.134593
$838$	8.27938e8	−	8.27938e8i	1.40691	−	1.40691i
$839$	6.69181e7	−	6.69181e7i	0.113307	−	0.113307i	−0.648180	−	0.761487i	$-0.724470\pi$
$839$	6.69181e7	−	6.69181e7i	0.113307	−	0.113307i	0.761487	+	0.648180i	$0.224470\pi$
$840$			4.76862e7i			0.0804554i
$841$	−3.71020e8	+	4.64929e8i	−0.623748	+	0.781626i
$842$	1.94664e9			3.26099
$843$	1.62800e8	+	1.62800e8i	0.271752	+	0.271752i
$844$	1.29675e9	+	1.29675e9i	2.15690	+	2.15690i
$845$			4.63913e7i			0.0768894i
$846$			1.43801e9i			2.37493i
$847$			1.18729e8i			0.195393i
$848$	2.92994e9			4.80475
$849$	−7.85470e6	+	7.85470e6i	−0.0128353	+	0.0128353i
$850$		−	5.78516e8i		−	0.942017i
$851$	−2.23926e7	+	2.23926e7i	−0.0363342	+	0.0363342i
$852$	1.20128e8	+	1.20128e8i	0.194234	+	0.194234i
$853$	9.45098e7	−	9.45098e7i	0.152275	−	0.152275i	−0.626858	−	0.779134i	$-0.715659\pi$
$853$	9.45098e7	−	9.45098e7i	0.152275	−	0.152275i	0.779134	+	0.626858i	$0.215659\pi$
$854$		−	1.19772e8i		−	0.192302i
$855$	−1.98206e8	−	1.98206e8i	−0.317116	−	0.317116i
$856$	−2.26877e8	+	2.26877e8i	−0.361717	+	0.361717i
$857$	1.01813e9			1.61756			0.808778	−	0.588114i	$-0.200129\pi$
$857$	1.01813e9			1.61756			0.808778	+	0.588114i	$0.200129\pi$
$858$	4.14674e8	+	4.14674e8i	0.656515	+	0.656515i
$859$	2.27893e8	−	2.27893e8i	0.359543	−	0.359543i	−0.504101	−	0.863644i	$-0.668176\pi$
$859$	2.27893e8	−	2.27893e8i	0.359543	−	0.359543i	0.863644	+	0.504101i	$0.168176\pi$
$860$	−5.54024e8	−	5.54024e8i	−0.871030	−	0.871030i
$861$	7.13426e7			0.111774
$862$	7.45307e7	+	7.45307e7i	0.116363	+	0.116363i
$863$		−	1.22644e9i		−	1.90815i	−0.299570	−	0.954074i	$-0.596843\pi$
$863$		−	1.22644e9i		−	1.90815i	0.299570	−	0.954074i	$-0.403157\pi$
$864$	−1.40890e9			−2.18444
$865$	1.12917e8			0.174466
$866$	5.25252e8			0.808749
$867$	9.42384e7	−	9.42384e7i	0.144601	−	0.144601i
$868$	5.47835e7	−	5.47835e7i	0.0837704	−	0.0837704i
$869$			5.79685e8i			0.883349i
$870$	−6.97987e7	−	1.45000e8i	−0.105996	−	0.220196i
$871$	5.13261e8			0.776754
$872$	−1.46009e8	−	1.46009e8i	−0.220206	−	0.220206i
$873$	−3.70044e8	−	3.70044e8i	−0.556173	−	0.556173i
$874$			7.19306e7i			0.107741i
$875$		−	9.65141e7i		−	0.144068i
$876$			7.45821e8i			1.10949i
$877$	−1.89988e7			−0.0281662			−0.0140831	−	0.999901i	$-0.504483\pi$
$877$	−1.89988e7			−0.0281662			−0.0140831	+	0.999901i	$0.504483\pi$
$878$	−7.87630e8	+	7.87630e8i	−1.16369	+	1.16369i
$879$		−	1.20066e8i		−	0.176788i
$880$	−1.00754e9	+	1.00754e9i	−1.47847	+	1.47847i
$881$	−6.46980e6	−	6.46980e6i	−0.00946157	−	0.00946157i	0.702360	−	0.711822i	$-0.252130\pi$
$881$	−6.46980e6	−	6.46980e6i	−0.00946157	−	0.00946157i	−0.711822	+	0.702360i	$0.752130\pi$
$882$	−8.11921e8	+	8.11921e8i	−1.18334	+	1.18334i
$883$			2.71433e8i			0.394258i	0.980378	+	0.197129i	$0.0631617\pi$
$883$			2.71433e8i			0.394258i	−0.980378	+	0.197129i	$0.936838\pi$
$884$	−8.45532e8	−	8.45532e8i	−1.22398	−	1.22398i
$885$	−5.39656e7	+	5.39656e7i	−0.0778551	+	0.0778551i
$886$	−3.53470e8			−0.508219
$887$	−2.60950e8	−	2.60950e8i	−0.373926	−	0.373926i	0.494979	−	0.868905i	$-0.335176\pi$
$887$	−2.60950e8	−	2.60950e8i	−0.373926	−	0.373926i	−0.868905	+	0.494979i	$0.835176\pi$
$888$	5.68145e8	−	5.68145e8i	0.811373	−	0.811373i
$889$	4.46838e7	+	4.46838e7i	0.0635982	+	0.0635982i
$890$	8.18013e8			1.16035
$891$	−5.09438e8	−	5.09438e8i	−0.720209	−	0.720209i
$892$		−	1.67297e9i		−	2.35719i
$893$	−1.18704e9			−1.66691
$894$	−5.15481e8			−0.721440
$895$	−1.43767e8			−0.200535
$896$	2.94265e8	−	2.94265e8i	0.409086	−	0.409086i
$897$	7.95702e6	−	7.95702e6i	0.0110249	−	0.0110249i
$898$			1.14774e9i			1.58495i
$899$	−5.44747e7	+	1.55597e8i	−0.0749749	+	0.214153i
$900$	1.48607e9			2.03850
$901$	4.02701e8	+	4.02701e8i	0.550565	+	0.550565i
$902$	2.63460e9	+	2.63460e9i	3.59000	+	3.59000i
$903$		−	4.94915e7i		−	0.0672151i
$904$		−	3.78472e9i		−	5.12305i
$905$			1.84104e8i			0.248381i
$906$	4.92649e8			0.662450
$907$	−5.31964e8	+	5.31964e8i	−0.712953	+	0.712953i	−0.967152	−	0.254199i	$-0.918188\pi$
$907$	−5.31964e8	+	5.31964e8i	−0.712953	+	0.712953i	0.254199	+	0.967152i	$0.418188\pi$
$908$			4.29359e8i			0.573539i
$909$	7.90220e8	−	7.90220e8i	1.05210	−	1.05210i
$910$	−8.78578e7	−	8.78578e7i	−0.116589	−	0.116589i
$911$	−4.75774e8	+	4.75774e8i	−0.629282	+	0.629282i	−0.947887	−	0.318605i	$-0.896786\pi$
$911$	−4.75774e8	+	4.75774e8i	−0.629282	+	0.629282i	0.318605	+	0.947887i	$0.396786\pi$
$912$		−	1.04417e9i		−	1.37654i
$913$	4.88113e8	+	4.88113e8i	0.641369	+	0.641369i
$914$	1.52606e9	−	1.52606e9i	1.99864	−	1.99864i
$915$	−5.03486e7			−0.0657240
$916$	2.27402e7	+	2.27402e7i	0.0295875	+	0.0295875i
$917$	−1.56834e8	+	1.56834e8i	−0.203391	+	0.203391i
$918$	−3.66427e8	−	3.66427e8i	−0.473652	−	0.473652i
$919$	−8.65543e8			−1.11517			−0.557587	−	0.830119i	$-0.688273\pi$
$919$	−8.65543e8			−1.11517			−0.557587	+	0.830119i	$0.688273\pi$
$920$	3.37911e7	+	3.37911e7i	0.0433949	+	0.0433949i
$921$		−	1.36846e8i		−	0.175168i
$922$	1.92339e9			2.45400
$923$	−2.79111e8			−0.354954
$924$	−1.82179e8			−0.230931
$925$	−5.22979e8	+	5.22979e8i	−0.660783	+	0.660783i
$926$	−7.18151e8	+	7.18151e8i	−0.904446	+	0.904446i
$927$		−	2.85024e6i		−	0.00357801i
$928$	−9.72474e8	+	2.77770e9i	−1.21684	+	3.47569i
$929$	−3.25178e8			−0.405578			−0.202789	−	0.979222i	$-0.565001\pi$
$929$	−3.25178e8			−0.405578			−0.202789	+	0.979222i	$0.565001\pi$
$930$	−3.15376e7	−	3.15376e7i	−0.0392085	−	0.0392085i
$931$	−6.70224e8	−	6.70224e8i	−0.830559	−	0.830559i
$932$			1.78183e8i			0.220100i
$933$			1.64951e8i			0.203100i
$934$			1.02963e9i			1.26369i
$935$	−2.76959e8			−0.338829
$936$	1.87550e9	−	1.87550e9i	2.28712	−	2.28712i
$937$		−	7.69961e8i		−	0.935945i	−0.883743	−	0.467972i	$-0.844985\pi$
$937$		−	7.69961e8i		−	0.935945i	0.883743	−	0.467972i	$-0.155015\pi$
$938$	−1.54400e8	+	1.54400e8i	−0.187085	+	0.187085i
$939$	1.98010e8	+	1.98010e8i	0.239162	+	0.239162i
$940$	−8.84384e8	+	8.84384e8i	−1.06477	+	1.06477i
$941$		−	7.31594e8i		−	0.878014i	−0.898484	−	0.439007i	$-0.855330\pi$
$941$		−	7.31594e8i		−	0.878014i	0.898484	−	0.439007i	$-0.144670\pi$
$942$	−1.58514e8	−	1.58514e8i	−0.189633	−	0.189633i
$943$	5.05543e7	−	5.05543e7i	0.0602870	−	0.0602870i
$944$	2.64109e9			3.13955
$945$	−2.78029e7	−	2.78029e7i	−0.0329453	−	0.0329453i
$946$	1.82766e9	−	1.82766e9i	2.15885	−	2.15885i
$947$	1.89105e8	+	1.89105e8i	0.222666	+	0.222666i	0.809620	−	0.586954i	$-0.199673\pi$
$947$	1.89105e8	+	1.89105e8i	0.222666	+	0.222666i	−0.586954	+	0.809620i	$0.699673\pi$
$948$	−4.47586e8			−0.525353
$949$	−8.66437e8	−	8.66437e8i	−1.01377	−	1.01377i
$950$			1.67994e9i			1.95940i
$951$	−6.77977e6			−0.00788267
$952$	3.20763e8			0.371769
$953$	1.37594e8			0.158972			0.0794860	−	0.996836i	$-0.474672\pi$
$953$	1.37594e8			0.158972			0.0794860	+	0.996836i	$0.474672\pi$
$954$	−1.41662e9	+	1.41662e9i	−1.63158	+	1.63158i
$955$	1.07160e8	−	1.07160e8i	0.123033	−	0.123033i
$956$		−	3.82644e9i		−	4.37947i
$957$	3.49290e8	−	1.68138e8i	0.398520	−	0.191836i
$958$	−3.16782e9			−3.60299
$959$	−9.50590e7	−	9.50590e7i	−0.107780	−	0.107780i
$960$	−2.75589e8	−	2.75589e8i	−0.311493	−	0.311493i
$961$		−	8.41813e8i		−	0.948517i
$962$			2.09352e9i			2.35154i
$963$		−	1.25522e8i		−	0.140553i
$964$	−7.41671e7			−0.0827905
$965$	−7.60287e7	+	7.60287e7i	−0.0846049	+	0.0846049i
$966$			4.78729e6i			0.00531078i
$967$	−1.07636e9	+	1.07636e9i	−1.19036	+	1.19036i	−0.213391	+	0.976967i	$0.568451\pi$
$967$	−1.07636e9	+	1.07636e9i	−1.19036	+	1.19036i	−0.976967	+	0.213391i	$0.931549\pi$
$968$	−2.13463e9	−	2.13463e9i	−2.35341	−	2.35341i
$969$	1.43515e8	−	1.43515e8i	0.157734	−	0.157734i
$970$		−	6.23320e8i		−	0.682961i
$971$	9.55028e8	+	9.55028e8i	1.04318	+	1.04318i	0.999025	+	0.0441527i	$0.0140588\pi$
$971$	9.55028e8	+	9.55028e8i	1.04318	+	1.04318i	0.0441527	+	0.999025i	$0.485941\pi$
$972$	1.43593e9	−	1.43593e9i	1.56363	−	1.56363i
$973$	−4.24602e7			−0.0460939
$974$	−1.96885e9	−	1.96885e9i	−2.13077	−	2.13077i
$975$	1.85836e8	−	1.85836e8i	0.200501	−	0.200501i
$976$	1.23204e9	+	1.23204e9i	1.32518	+	1.32518i
$977$	−1.37731e9			−1.47689			−0.738445	−	0.674314i	$-0.764440\pi$
$977$	−1.37731e9			−1.47689			−0.738445	+	0.674314i	$0.764440\pi$
$978$	6.45181e8	+	6.45181e8i	0.689707	+	0.689707i
$979$			1.97051e9i			2.10006i
$980$	−9.98674e8			−1.06107
$981$	8.07809e7			0.0855661
$982$	7.42884e8			0.784489
$983$	8.91774e8	−	8.91774e8i	0.938846	−	0.938846i	−0.0593893	−	0.998235i	$-0.518915\pi$
$983$	8.91774e8	−	8.91774e8i	0.938846	−	0.938846i	0.998235	+	0.0593893i	$0.0189153\pi$
$984$	−1.28267e9	+	1.28267e9i	−1.34626	+	1.34626i
$985$		−	8.75173e7i		−	0.0915767i
$986$	−9.75345e8	+	4.69503e8i	−1.01748	+	0.489788i
$987$	−7.90028e7			−0.0821658
$988$	2.45532e9	+	2.45532e9i	2.54588	+	2.54588i
$989$	−3.50703e7	−	3.50703e7i	−0.0362536	−	0.0362536i
$990$		−	9.74289e8i		−	1.00411i
$991$			5.45563e8i			0.560562i	0.959918	+	0.280281i	$0.0904277\pi$
$991$			5.45563e8i			0.560562i	−0.959918	+	0.280281i	$0.909572\pi$
$992$			8.15668e8i			0.835562i
$993$	−4.63848e8			−0.473727
$994$	8.39626e7	−	8.39626e7i	0.0854922	−	0.0854922i
$995$			7.34756e7i			0.0745889i
$996$	−3.76881e8	+	3.76881e8i	−0.381440	+	0.381440i
$997$	−7.23560e8	−	7.23560e8i	−0.730111	−	0.730111i	0.240530	−	0.970642i	$-0.422679\pi$
$997$	−7.23560e8	−	7.23560e8i	−0.730111	−	0.730111i	−0.970642	+	0.240530i	$0.922679\pi$
$998$	−1.26689e9	+	1.26689e9i	−1.27453	+	1.27453i
$999$			6.62500e8i			0.664492i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.7.c.a.12.14	✓	28
29.17	odd	4	inner	29.7.c.a.17.14	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.7.c.a.12.14	✓	28	1.1	even	1	trivial
29.7.c.a.17.14	yes	28	29.17	odd	4	inner

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:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	29.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(10.8910 + 10.8910i) q^{2} +(5.95173 + 5.95173i) q^{3} +173.227i q^{4} -50.8966i q^{5} +129.640i q^{6} +66.1657 q^{7} +(-1189.59 + 1189.59i) q^{8} -658.154i q^{9} +O(q^{10})\)	\(q+(10.8910 + 10.8910i) q^{2} +(5.95173 + 5.95173i) q^{3} +173.227i q^{4} -50.8966i q^{5} +129.640i q^{6} +66.1657 q^{7} +(-1189.59 + 1189.59i) q^{8} -658.154i q^{9} +(554.314 - 554.314i) q^{10} +(1335.29 + 1335.29i) q^{11} +(-1031.00 + 1031.00i) q^{12} -2395.47i q^{13} +(720.610 + 720.610i) q^{14} +(302.923 - 302.923i) q^{15} -14825.1 q^{16} +(-2037.62 - 2037.62i) q^{17} +(7167.95 - 7167.95i) q^{18} +(5916.99 + 5916.99i) q^{19} +8816.67 q^{20} +(393.801 + 393.801i) q^{21} +29085.2i q^{22} +558.105 q^{23} -14160.3 q^{24} +13034.5 q^{25} +(26089.1 - 26089.1i) q^{26} +(8255.96 - 8255.96i) q^{27} +11461.7i q^{28} +(-10578.4 - 21975.5i) q^{29} +6598.25 q^{30} +(-4779.70 - 4779.70i) q^{31} +(-85326.4 - 85326.4i) q^{32} +15894.5i q^{33} -44383.3i q^{34} -3367.61i q^{35} +114010. q^{36} +(-40122.5 + 40122.5i) q^{37} +128884. i q^{38} +(14257.2 - 14257.2i) q^{39} +(60546.2 + 60546.2i) q^{40} +(90582.1 - 90582.1i) q^{41} +8577.75i q^{42} +(-62838.2 - 62838.2i) q^{43} +(-231308. + 231308. i) q^{44} -33497.8 q^{45} +(6078.32 + 6078.32i) q^{46} +(-100308. + 100308. i) q^{47} +(-88235.1 - 88235.1i) q^{48} -113271. q^{49} +(141959. + 141959. i) q^{50} -24254.7i q^{51} +414961. q^{52} -197633. q^{53} +179831. q^{54} +(67961.5 - 67961.5i) q^{55} +(-78710.3 + 78710.3i) q^{56} +70432.6i q^{57} +(124126. - 354543. i) q^{58} -178150. q^{59} +(52474.4 + 52474.4i) q^{60} +(-83104.8 - 83104.8i) q^{61} -104111. i q^{62} -43547.2i q^{63} -909769. i q^{64} -121921. q^{65} +(-173107. + 173107. i) q^{66} +214263. i q^{67} +(352971. - 352971. i) q^{68} +(3321.69 + 3321.69i) q^{69} +(36676.6 - 36676.6i) q^{70} -116516. i q^{71} +(782935. + 782935. i) q^{72} +(361698. - 361698. i) q^{73} -873948. q^{74} +(77578.0 + 77578.0i) q^{75} +(-1.02498e6 + 1.02498e6i) q^{76} +(88350.3 + 88350.3i) q^{77} +310550. q^{78} +(217064. + 217064. i) q^{79} +754548. i q^{80} -381520. q^{81} +1.97306e6 q^{82} +365549. q^{83} +(-68217.0 + 68217.0i) q^{84} +(-103708. + 103708. i) q^{85} -1.36874e6i q^{86} +(67832.5 - 193752. i) q^{87} -3.17690e6 q^{88} +(737861. + 737861. i) q^{89} +(-364824. - 364824. i) q^{90} -158498. i q^{91} +96679.0i q^{92} -56894.9i q^{93} -2.18491e6 q^{94} +(301154. - 301154. i) q^{95} -1.01568e6i q^{96} +(562245. - 562245. i) q^{97} +(-1.23363e6 - 1.23363e6i) q^{98} +(878825. - 878825. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{3} - 4 q^{7} + 354 q^{8}+O(q^{10}) \) 28 * q - 2 * q^3 - 4 * q^7 + 354 * q^8	\( 28 q - 2 q^{3} - 4 q^{7} + 354 q^{8} - 3714 q^{10} + 1934 q^{11} - 2706 q^{12} + 2648 q^{14} + 16280 q^{15} - 36632 q^{16} - 5236 q^{17} + 5258 q^{18} + 6718 q^{19} + 24828 q^{20} + 7380 q^{21} - 21524 q^{23} + 90648 q^{24} - 73196 q^{25} - 5394 q^{26} + 5824 q^{27} - 12510 q^{29} - 1780 q^{30} + 1150 q^{31} + 104646 q^{32} - 32904 q^{36} - 256832 q^{37} + 127752 q^{39} - 256374 q^{40} + 265716 q^{41} + 80590 q^{43} + 188482 q^{44} - 78008 q^{45} + 405572 q^{46} - 445250 q^{47} - 1016886 q^{48} + 532764 q^{49} - 80230 q^{50} + 619608 q^{52} + 143428 q^{53} + 373816 q^{54} - 533304 q^{55} - 619392 q^{56} + 326848 q^{58} - 957340 q^{59} + 1790622 q^{60} - 115640 q^{61} - 643584 q^{65} - 1821654 q^{66} + 1457028 q^{68} - 1049340 q^{69} + 3024084 q^{70} + 1480560 q^{72} - 627512 q^{73} - 3652060 q^{74} + 586518 q^{75} - 1343752 q^{76} - 115820 q^{77} + 1820304 q^{78} + 235966 q^{79} + 2710496 q^{81} + 796544 q^{82} + 3881892 q^{83} + 219332 q^{84} - 3064608 q^{85} + 900526 q^{87} - 9844332 q^{88} + 3821436 q^{89} - 4192912 q^{90} - 648556 q^{94} - 620200 q^{95} - 620288 q^{97} + 4735296 q^{98} + 4021770 q^{99}+O(q^{100}) \) 28 * q - 2 * q^3 - 4 * q^7 + 354 * q^8 - 3714 * q^10 + 1934 * q^11 - 2706 * q^12 + 2648 * q^14 + 16280 * q^15 - 36632 * q^16 - 5236 * q^17 + 5258 * q^18 + 6718 * q^19 + 24828 * q^20 + 7380 * q^21 - 21524 * q^23 + 90648 * q^24 - 73196 * q^25 - 5394 * q^26 + 5824 * q^27 - 12510 * q^29 - 1780 * q^30 + 1150 * q^31 + 104646 * q^32 - 32904 * q^36 - 256832 * q^37 + 127752 * q^39 - 256374 * q^40 + 265716 * q^41 + 80590 * q^43 + 188482 * q^44 - 78008 * q^45 + 405572 * q^46 - 445250 * q^47 - 1016886 * q^48 + 532764 * q^49 - 80230 * q^50 + 619608 * q^52 + 143428 * q^53 + 373816 * q^54 - 533304 * q^55 - 619392 * q^56 + 326848 * q^58 - 957340 * q^59 + 1790622 * q^60 - 115640 * q^61 - 643584 * q^65 - 1821654 * q^66 + 1457028 * q^68 - 1049340 * q^69 + 3024084 * q^70 + 1480560 * q^72 - 627512 * q^73 - 3652060 * q^74 + 586518 * q^75 - 1343752 * q^76 - 115820 * q^77 + 1820304 * q^78 + 235966 * q^79 + 2710496 * q^81 + 796544 * q^82 + 3881892 * q^83 + 219332 * q^84 - 3064608 * q^85 + 900526 * q^87 - 9844332 * q^88 + 3821436 * q^89 - 4192912 * q^90 - 648556 * q^94 - 620200 * q^95 - 620288 * q^97 + 4735296 * q^98 + 4021770 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more