LMFDB - Embedded newform 48.9.l.a.43.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,9,Mod(19,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("48.19");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	48.l (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:	$19.5541732829$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.22
Character	$\chi$	$=$	48.43
Dual form			48.9.l.a.19.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(8.00822 + 13.8517i) q^{2} +(-33.0681 - 33.0681i) q^{3} +(-127.737 + 221.854i) q^{4} +(318.765 + 318.765i) q^{5} +(193.231 - 722.865i) q^{6} -621.384 q^{7} +(-4095.99 + 7.29198i) q^{8} +2187.00i q^{9} +O(q^{10})$	\(q+(8.00822 + 13.8517i) q^{2} +(-33.0681 - 33.0681i) q^{3} +(-127.737 + 221.854i) q^{4} +(318.765 + 318.765i) q^{5} +(193.231 - 722.865i) q^{6} -621.384 q^{7} +(-4095.99 + 7.29198i) q^{8} +2187.00i q^{9} +(-1862.68 + 6968.17i) q^{10} +(-4413.00 + 4413.00i) q^{11} +(11560.3 - 3112.29i) q^{12} +(-772.862 + 772.862i) q^{13} +(-4976.18 - 8607.19i) q^{14} -21081.9i q^{15} +(-32902.6 - 56677.9i) q^{16} -39806.2 q^{17} +(-30293.6 + 17514.0i) q^{18} +(-134962. - 134962. i) q^{19} +(-111437. + 30001.4i) q^{20} +(20548.0 + 20548.0i) q^{21} +(-96467.7 - 25787.1i) q^{22} -287703. q^{23} +(135688. + 135206. i) q^{24} -187402. i q^{25} +(-16894.7 - 4516.17i) q^{26} +(72320.0 - 72320.0i) q^{27} +(79373.6 - 137857. i) q^{28} +(-20613.9 + 20613.9i) q^{29} +(292020. - 168829. i) q^{30} -826064. i q^{31} +(521591. - 909645. i) q^{32} +291859. q^{33} +(-318777. - 551382. i) q^{34} +(-198076. - 198076. i) q^{35} +(-485195. - 279360. i) q^{36} +(463796. + 463796. i) q^{37} +(788644. - 2.95026e6i) q^{38} +51114.2 q^{39} +(-1.30798e6 - 1.30334e6i) q^{40} +2.66585e6i q^{41} +(-120071. + 449177. i) q^{42} +(-3.62915e6 + 3.62915e6i) q^{43} +(-415341. - 1.54275e6i) q^{44} +(-697140. + 697140. i) q^{45} +(-2.30399e6 - 3.98516e6i) q^{46} +855972. i q^{47} +(-786203. + 2.96226e6i) q^{48} -5.37868e6 q^{49} +(2.59583e6 - 1.50076e6i) q^{50} +(1.31632e6 + 1.31632e6i) q^{51} +(-72739.9 - 270186. i) q^{52} +(3.79242e6 + 3.79242e6i) q^{53} +(1.58091e6 + 422597. i) q^{54} -2.81342e6 q^{55} +(2.54518e6 - 4531.12i) q^{56} +8.92591e6i q^{57} +(-450617. - 120456. i) q^{58} +(-2.22470e6 + 2.22470e6i) q^{59} +(4.67712e6 + 2.69294e6i) q^{60} +(-3.05565e6 + 3.05565e6i) q^{61} +(1.14424e7 - 6.61531e6i) q^{62} -1.35897e6i q^{63} +(1.67771e7 - 59735.8i) q^{64} -492723. q^{65} +(2.33727e6 + 4.04274e6i) q^{66} +(7.26153e6 + 7.26153e6i) q^{67} +(5.08472e6 - 8.83118e6i) q^{68} +(9.51378e6 + 9.51378e6i) q^{69} +(1.15744e6 - 4.32991e6i) q^{70} +1.90275e7 q^{71} +(-15947.6 - 8.95794e6i) q^{72} +4.82517e7i q^{73} +(-2.71016e6 + 1.01385e7i) q^{74} +(-6.19704e6 + 6.19704e6i) q^{75} +(4.71817e7 - 1.27023e7i) q^{76} +(2.74217e6 - 2.74217e6i) q^{77} +(409334. + 708016. i) q^{78} +3.72507e7i q^{79} +(7.57873e6 - 2.85552e7i) q^{80} -4.78297e6 q^{81} +(-3.69264e7 + 2.13487e7i) q^{82} +(-5.70604e7 - 5.70604e7i) q^{83} +(-7.18339e6 + 1.93392e6i) q^{84} +(-1.26888e7 - 1.26888e7i) q^{85} +(-7.93328e7 - 2.12067e7i) q^{86} +1.36333e6 q^{87} +(1.80435e7 - 1.81078e7i) q^{88} +2.95501e7i q^{89} +(-1.52394e7 - 4.07369e6i) q^{90} +(480244. - 480244. i) q^{91} +(3.67502e7 - 6.38280e7i) q^{92} +(-2.73164e7 + 2.73164e7i) q^{93} +(-1.18566e7 + 6.85481e6i) q^{94} -8.60427e7i q^{95} +(-4.73283e7 + 1.28322e7i) q^{96} +2.58703e7 q^{97} +(-4.30737e7 - 7.45037e7i) q^{98} +(-9.65124e6 - 9.65124e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 372 q^{4} + 17460 q^{8}+O(q^{10}) $ 64 * q - 372 * q^4 + 17460 * q^8	\( 64 q - 372 q^{4} + 17460 q^{8} - 13784 q^{10} + 39552 q^{11} - 22680 q^{12} + 116772 q^{14} - 161824 q^{16} - 26244 q^{18} - 167552 q^{19} + 690000 q^{20} - 1252768 q^{22} + 1691136 q^{23} - 74844 q^{24} - 1682100 q^{26} + 678600 q^{28} - 2132352 q^{29} - 2054808 q^{30} + 1407840 q^{32} - 3704544 q^{34} - 2415744 q^{35} - 1041012 q^{36} - 4720512 q^{37} + 2413320 q^{38} - 3544848 q^{40} + 9436500 q^{42} - 7244672 q^{43} - 3982056 q^{44} + 11165992 q^{46} - 9467280 q^{48} + 52706752 q^{49} + 17072676 q^{50} + 13862016 q^{51} - 22890864 q^{52} - 5358720 q^{53} - 4960116 q^{54} - 46326784 q^{55} - 9637152 q^{56} + 25732944 q^{58} + 44938752 q^{59} + 40927032 q^{60} + 24476032 q^{61} - 17024868 q^{62} - 116303448 q^{64} + 29941632 q^{65} - 56828952 q^{66} - 44244736 q^{67} - 12614400 q^{68} - 8636544 q^{69} - 60922560 q^{70} + 159664128 q^{71} - 18502020 q^{72} + 140654028 q^{74} + 12918528 q^{75} + 204842760 q^{76} - 94964352 q^{77} + 14001660 q^{78} + 38076648 q^{80} - 306110016 q^{81} - 260917000 q^{82} + 209328000 q^{83} - 127862712 q^{84} + 106960000 q^{85} - 123451824 q^{86} + 104240736 q^{88} + 53520264 q^{90} - 45401472 q^{91} + 351567216 q^{92} + 208488216 q^{94} + 49597920 q^{96} - 681890712 q^{98} + 86500224 q^{99}+O(q^{100}) \) 64 * q - 372 * q^4 + 17460 * q^8 - 13784 * q^10 + 39552 * q^11 - 22680 * q^12 + 116772 * q^14 - 161824 * q^16 - 26244 * q^18 - 167552 * q^19 + 690000 * q^20 - 1252768 * q^22 + 1691136 * q^23 - 74844 * q^24 - 1682100 * q^26 + 678600 * q^28 - 2132352 * q^29 - 2054808 * q^30 + 1407840 * q^32 - 3704544 * q^34 - 2415744 * q^35 - 1041012 * q^36 - 4720512 * q^37 + 2413320 * q^38 - 3544848 * q^40 + 9436500 * q^42 - 7244672 * q^43 - 3982056 * q^44 + 11165992 * q^46 - 9467280 * q^48 + 52706752 * q^49 + 17072676 * q^50 + 13862016 * q^51 - 22890864 * q^52 - 5358720 * q^53 - 4960116 * q^54 - 46326784 * q^55 - 9637152 * q^56 + 25732944 * q^58 + 44938752 * q^59 + 40927032 * q^60 + 24476032 * q^61 - 17024868 * q^62 - 116303448 * q^64 + 29941632 * q^65 - 56828952 * q^66 - 44244736 * q^67 - 12614400 * q^68 - 8636544 * q^69 - 60922560 * q^70 + 159664128 * q^71 - 18502020 * q^72 + 140654028 * q^74 + 12918528 * q^75 + 204842760 * q^76 - 94964352 * q^77 + 14001660 * q^78 + 38076648 * q^80 - 306110016 * q^81 - 260917000 * q^82 + 209328000 * q^83 - 127862712 * q^84 + 106960000 * q^85 - 123451824 * q^86 + 104240736 * q^88 + 53520264 * q^90 - 45401472 * q^91 + 351567216 * q^92 + 208488216 * q^94 + 49597920 * q^96 - 681890712 * q^98 + 86500224 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	8.00822	+	13.8517i	0.500514	+	0.865729i
$2$	8.00822	+	13.8517i	0.500514	+	0.865729i
$3$	−33.0681	−	33.0681i	−0.408248	−	0.408248i
$3$	−33.0681	−	33.0681i	−0.408248	−	0.408248i
$4$	−127.737	+	221.854i	−0.498972	+	0.866618i
$5$	318.765	+	318.765i	0.510024	+	0.510024i	0.914534	−	0.404509i	$-0.132558\pi$
$5$	318.765	+	318.765i	0.510024	+	0.510024i	−0.404509	+	0.914534i	$0.632558\pi$
$6$	193.231	−	722.865i	0.149098	−	0.557766i
$7$	−621.384			−0.258802			−0.129401	−	0.991592i	$-0.541305\pi$
$7$	−621.384			−0.258802			−0.129401	+	0.991592i	$0.541305\pi$
$8$	−4095.99	+	7.29198i	−0.999998	+	0.00178027i
$9$			2187.00i			0.333333i
$10$	−1862.68	+	6968.17i	−0.186268	+	0.696817i
$11$	−4413.00	+	4413.00i	−0.301414	+	0.301414i	−0.841567	−	0.540153i	$-0.818366\pi$
$11$	−4413.00	+	4413.00i	−0.301414	+	0.301414i	0.540153	+	0.841567i	$0.318366\pi$
$12$	11560.3	−	3112.29i	0.557500	−	0.150091i
$13$	−772.862	+	772.862i	−0.0270601	+	0.0270601i	−0.720507	−	0.693447i	$-0.756091\pi$
$13$	−772.862	+	772.862i	−0.0270601	+	0.0270601i	0.693447	+	0.720507i	$0.256091\pi$
$14$	−4976.18	−	8607.19i	−0.129534	−	0.224052i
$15$		−	21081.9i		−	0.416433i
$16$	−32902.6	−	56677.9i	−0.502054	−	0.864836i
$17$	−39806.2			−0.476601			−0.238301	−	0.971191i	$-0.576590\pi$
$17$	−39806.2			−0.476601			−0.238301	+	0.971191i	$0.576590\pi$
$18$	−30293.6	+	17514.0i	−0.288576	+	0.166838i
$19$	−134962.	−	134962.i	−1.03562	−	1.03562i	−0.999342	−	0.0362737i	$-0.988451\pi$
$19$	−134962.	−	134962.i	−1.03562	−	1.03562i	−0.0362737	−	0.999342i	$-0.511549\pi$
$20$	−111437.	+	30001.4i	−0.696484	+	0.187509i
$21$	20548.0	+	20548.0i	0.105656	+	0.105656i
$22$	−96467.7	−	25787.1i	−0.411805	−	0.110081i
$23$	−287703.			−1.02809			−0.514047	−	0.857762i	$-0.671854\pi$
$23$	−287703.			−1.02809			−0.514047	+	0.857762i	$0.671854\pi$
$24$	135688.	+	135206.i	0.408974	+	0.407521i
$25$		−	187402.i		−	0.479750i
$26$	−16894.7	−	4516.17i	−0.0369706	−	0.00988273i
$27$	72320.0	−	72320.0i	0.136083	−	0.136083i
$28$	79373.6	−	137857.i	0.129135	−	0.224283i
$29$	−20613.9	+	20613.9i	−0.0291453	+	0.0291453i	−0.721529	−	0.692384i	$-0.756560\pi$
$29$	−20613.9	+	20613.9i	−0.0291453	+	0.0291453i	0.692384	+	0.721529i	$0.256560\pi$
$30$	292020.	−	168829.i	0.360518	−	0.208431i
$31$		−	826064.i		−	0.894473i	−0.894416	−	0.447236i	$-0.852408\pi$
$31$		−	826064.i		−	0.894473i	0.894416	−	0.447236i	$-0.147592\pi$
$32$	521591.	−	909645.i	0.497428	−	0.867505i
$33$	291859.			0.246104
$34$	−318777.	−	551382.i	−0.238546	−	0.412607i
$35$	−198076.	−	198076.i	−0.131995	−	0.131995i
$36$	−485195.	−	279360.i	−0.288873	−	0.166324i
$37$	463796.	+	463796.i	0.247469	+	0.247469i	0.819931	−	0.572462i	$-0.194012\pi$
$37$	463796.	+	463796.i	0.247469	+	0.247469i	−0.572462	+	0.819931i	$0.694012\pi$
$38$	788644.	−	2.95026e6i	0.378222	−	1.41490i
$39$	51114.2			0.0220944
$40$	−1.30798e6	−	1.30334e6i	−0.510932	−	0.509116i
$41$			2.66585e6i			0.943408i	0.881757	+	0.471704i	$0.156361\pi$
$41$			2.66585e6i			0.943408i	−0.881757	+	0.471704i	$0.843639\pi$
$42$	−120071.	+	449177.i	−0.0385869	+	0.144351i
$43$	−3.62915e6	+	3.62915e6i	−1.06153	+	1.06153i	−0.0635491	+	0.997979i	$0.520242\pi$
$43$	−3.62915e6	+	3.62915e6i	−1.06153	+	1.06153i	−0.997979	+	0.0635491i	$0.979758\pi$
$44$	−415341.	−	1.54275e6i	−0.110814	−	0.411608i
$45$	−697140.	+	697140.i	−0.170008	+	0.170008i
$46$	−2.30399e6	−	3.98516e6i	−0.514575	−	0.890049i
$47$			855972.i			0.175416i	0.996146	+	0.0877078i	$0.0279542\pi$
$47$			855972.i			0.175416i	−0.996146	+	0.0877078i	$0.972046\pi$
$48$	−786203.	+	2.96226e6i	−0.148105	+	0.558031i
$49$	−5.37868e6			−0.933021
$50$	2.59583e6	−	1.50076e6i	0.415333	−	0.240122i
$51$	1.31632e6	+	1.31632e6i	0.194572	+	0.194572i
$52$	−72739.9	−	270186.i	−0.00994854	−	0.0369530i
$53$	3.79242e6	+	3.79242e6i	0.480632	+	0.480632i	0.905334	−	0.424701i	$-0.139621\pi$
$53$	3.79242e6	+	3.79242e6i	0.480632	+	0.480632i	−0.424701	+	0.905334i	$0.639621\pi$
$54$	1.58091e6	+	422597.i	0.185922	+	0.0496994i
$55$	−2.81342e6			−0.307457
$56$	2.54518e6	−	4531.12i	0.258802	−	0.000460737i
$57$			8.92591e6i			0.845577i
$58$	−450617.	−	120456.i	−0.0398195	−	0.0106443i
$59$	−2.22470e6	+	2.22470e6i	−0.183596	+	0.183596i	−0.792921	−	0.609325i	$-0.791441\pi$
$59$	−2.22470e6	+	2.22470e6i	−0.183596	+	0.183596i	0.609325	+	0.792921i	$0.291441\pi$
$60$	4.67712e6	+	2.69294e6i	0.360889	+	0.207788i
$61$	−3.05565e6	+	3.05565e6i	−0.220691	+	0.220691i	−0.808789	−	0.588099i	$-0.799877\pi$
$61$	−3.05565e6	+	3.05565e6i	−0.220691	+	0.220691i	0.588099	+	0.808789i	$0.299877\pi$
$62$	1.14424e7	−	6.61531e6i	0.774370	−	0.447696i
$63$		−	1.35897e6i		−	0.0862674i
$64$	1.67771e7	−	59735.8i	0.999994	−	0.00356053i
$65$	−492723.			−0.0276026
$66$	2.33727e6	+	4.04274e6i	0.123178	+	0.213059i
$67$	7.26153e6	+	7.26153e6i	0.360354	+	0.360354i	0.863943	−	0.503589i	$-0.167988\pi$
$67$	7.26153e6	+	7.26153e6i	0.360354	+	0.360354i	−0.503589	+	0.863943i	$0.667988\pi$
$68$	5.08472e6	−	8.83118e6i	0.237811	−	0.413031i
$69$	9.51378e6	+	9.51378e6i	0.419717	+	0.419717i
$70$	1.15744e6	−	4.32991e6i	0.0482067	−	0.180338i
$71$	1.90275e7			0.748770			0.374385	−	0.927273i	$-0.377854\pi$
$71$	1.90275e7			0.748770			0.374385	+	0.927273i	$0.377854\pi$
$72$	−15947.6	−	8.95794e6i	−0.000593423	−	0.333333i
$73$			4.82517e7i			1.69911i	0.527500	+	0.849555i	$0.323130\pi$
$73$			4.82517e7i			1.69911i	−0.527500	+	0.849555i	$0.676870\pi$
$74$	−2.71016e6	+	1.01385e7i	−0.0903792	+	0.338102i
$75$	−6.19704e6	+	6.19704e6i	−0.195857	+	0.195857i
$76$	4.71817e7	−	1.27023e7i	1.41423	−	0.380740i
$77$	2.74217e6	−	2.74217e6i	0.0780066	−	0.0780066i
$78$	409334.	+	708016.i	0.0110586	+	0.0191278i
$79$			3.72507e7i			0.956370i	0.878259	+	0.478185i	$0.158705\pi$
$79$			3.72507e7i			0.956370i	−0.878259	+	0.478185i	$0.841295\pi$
$80$	7.57873e6	−	2.85552e7i	0.185028	−	0.697148i
$81$	−4.78297e6			−0.111111
$82$	−3.69264e7	+	2.13487e7i	−0.816736	+	0.472189i
$83$	−5.70604e7	−	5.70604e7i	−1.20233	−	1.20233i	−0.973457	−	0.228868i	$-0.926498\pi$
$83$	−5.70604e7	−	5.70604e7i	−1.20233	−	1.20233i	−0.228868	−	0.973457i	$-0.573502\pi$
$84$	−7.18339e6	+	1.93392e6i	−0.144282	+	0.0388439i
$85$	−1.26888e7	−	1.26888e7i	−0.243078	−	0.243078i
$86$	−7.93328e7	−	2.12067e7i	−1.45030	−	0.387686i
$87$	1.36333e6			0.0237970
$88$	1.80435e7	−	1.81078e7i	0.300877	−	0.301950i
$89$			2.95501e7i			0.470976i	0.971877	+	0.235488i	$0.0756689\pi$
$89$			2.95501e7i			0.470976i	−0.971877	+	0.235488i	$0.924331\pi$
$90$	−1.52394e7	−	4.07369e6i	−0.232272	−	0.0620895i
$91$	480244.	−	480244.i	0.00700320	−	0.00700320i
$92$	3.67502e7	−	6.38280e7i	0.512989	−	0.890964i
$93$	−2.73164e7	+	2.73164e7i	−0.365167	+	0.365167i
$94$	−1.18566e7	+	6.85481e6i	−0.151862	+	0.0877979i
$95$		−	8.60427e7i		−	1.05638i
$96$	−4.73283e7	+	1.28322e7i	−0.557232	+	0.151083i
$97$	2.58703e7			0.292223			0.146112	−	0.989268i	$-0.453324\pi$
$97$	2.58703e7			0.292223			0.146112	+	0.989268i	$0.453324\pi$
$98$	−4.30737e7	−	7.45037e7i	−0.466990	−	0.807743i
$99$	−9.65124e6	−	9.65124e6i	−0.100471	−	0.100471i
$100$	4.15760e7	+	2.39382e7i	0.415760	+	0.239382i
$101$	−4.52115e7	−	4.52115e7i	−0.434474	−	0.434474i	0.455673	−	0.890147i	$-0.349399\pi$
$101$	−4.52115e7	−	4.52115e7i	−0.434474	−	0.434474i	−0.890147	+	0.455673i	$0.849399\pi$
$102$	−7.69181e6	+	2.87745e7i	−0.0710604	+	0.265832i
$103$	−4.49951e7			−0.399775			−0.199888	−	0.979819i	$-0.564058\pi$
$103$	−4.49951e7			−0.399775			−0.199888	+	0.979819i	$0.564058\pi$
$104$	3.16000e6	−	3.17128e6i	0.0270118	−	0.0271082i
$105$			1.31000e7i			0.107774i
$106$	−2.21608e7	+	8.29019e7i	−0.175534	+	0.656660i
$107$	1.58071e8	−	1.58071e8i	1.20592	−	1.20592i	0.233583	−	0.972337i	$-0.424955\pi$
$107$	1.58071e8	−	1.58071e8i	1.20592	−	1.20592i	0.972337	−	0.233583i	$-0.0750450\pi$
$108$	6.80657e6	+	2.52824e7i	0.0500303	+	0.185833i
$109$	−7.19658e7	+	7.19658e7i	−0.509824	+	0.509824i	−0.914472	−	0.404649i	$-0.867394\pi$
$109$	−7.19658e7	+	7.19658e7i	−0.509824	+	0.509824i	0.404649	+	0.914472i	$0.367394\pi$
$110$	−2.25305e7	−	3.89706e7i	−0.153887	−	0.266174i
$111$		−	3.06737e7i		−	0.202057i
$112$	2.04452e7	+	3.52187e7i	0.129933	+	0.223821i
$113$	6.72550e7			0.412488			0.206244	−	0.978501i	$-0.433876\pi$
$113$	6.72550e7			0.412488			0.206244	+	0.978501i	$0.433876\pi$
$114$	−1.23639e8	+	7.14806e7i	−0.732040	+	0.423223i
$115$	−9.17096e7	−	9.17096e7i	−0.524353	−	0.524353i
$116$	−1.94013e6	−	7.20644e6i	−0.0107152	−	0.0398005i
$117$	−1.69025e6	−	1.69025e6i	−0.00902002	−	0.00902002i
$118$	−4.86316e7	−	1.29999e7i	−0.250837	−	0.0670520i
$119$	2.47349e7			0.123345
$120$	153729.	+	8.63515e7i	0.000741363	+	0.416433i
$121$			1.75410e8i			0.818299i
$122$	−6.67961e7	−	1.78555e7i	−0.301517	−	0.0805995i
$123$	8.81545e7	−	8.81545e7i	0.385145	−	0.385145i
$124$	1.83266e8	+	1.05519e8i	0.775166	+	0.446317i
$125$	1.84255e8	−	1.84255e8i	0.754709	−	0.754709i
$126$	1.88239e7	−	1.08829e7i	0.0746841	−	0.0431780i
$127$		−	3.67547e8i		−	1.41286i	−0.707785	−	0.706428i	$-0.750305\pi$
$127$		−	3.67547e8i		−	1.41286i	0.707785	−	0.706428i	$-0.249695\pi$
$128$	1.35182e8	+	2.31912e8i	0.503593	+	0.863941i
$129$	2.40018e8			0.866734
$130$	−3.94584e6	−	6.82504e6i	−0.0138155	−	0.0238963i
$131$	−1.84850e8	−	1.84850e8i	−0.627674	−	0.627674i	0.319809	−	0.947482i	$-0.396381\pi$
$131$	−1.84850e8	−	1.84850e8i	−0.627674	−	0.627674i	−0.947482	+	0.319809i	$0.896381\pi$
$132$	−3.72812e7	+	6.47503e7i	−0.122799	+	0.213278i
$133$	8.38635e7	+	8.38635e7i	0.268019	+	0.268019i
$134$	−4.24323e7	+	1.58736e8i	−0.131606	+	0.492331i
$135$	4.61062e7			0.138811
$136$	1.63046e8	−	290266.i	0.476601	−	0.000848478i
$137$			2.90047e8i			0.823352i	0.911330	+	0.411676i	$0.135057\pi$
$137$			2.90047e8i			0.823352i	−0.911330	+	0.411676i	$0.864943\pi$
$138$	−5.55932e7	+	2.07970e8i	−0.153287	+	0.573435i
$139$	2.03632e8	−	2.03632e8i	0.545489	−	0.545489i	−0.379644	−	0.925133i	$-0.623953\pi$
$139$	2.03632e8	−	2.03632e8i	0.545489	−	0.545489i	0.925133	+	0.379644i	$0.123953\pi$
$140$	6.92454e7	−	1.86424e7i	0.180252	−	0.0485276i
$141$	2.83054e7	−	2.83054e7i	0.0716131	−	0.0716131i
$142$	1.52376e8	+	2.63562e8i	0.374770	+	0.648231i
$143$		−	6.82129e6i		−	0.0163126i
$144$	1.23955e8	−	7.19580e7i	0.288279	−	0.167351i
$145$	−1.31420e7			−0.0297296
$146$	−6.68367e8	+	3.86411e8i	−1.47097	+	0.850428i
$147$	1.77863e8	+	1.77863e8i	0.380904	+	0.380904i
$148$	−1.62139e8	+	4.36513e7i	−0.337941	+	0.0909810i
$149$	3.68052e8	+	3.68052e8i	0.746732	+	0.746732i	0.973864	−	0.227132i	$-0.0729350\pi$
$149$	3.68052e8	+	3.68052e8i	0.746732	+	0.746732i	−0.227132	+	0.973864i	$0.572935\pi$
$150$	−1.35467e8	−	3.62120e7i	−0.267588	−	0.0715299i
$151$	−8.19817e8			−1.57692			−0.788459	−	0.615087i	$-0.789121\pi$
$151$	−8.19817e8			−1.57692			−0.788459	+	0.615087i	$0.789121\pi$
$152$	5.53789e8	+	5.51821e8i	1.03746	+	1.03377i
$153$		−	8.70562e7i		−	0.158867i
$154$	5.99435e7	+	1.60237e7i	0.106576	+	0.0284892i
$155$	2.63321e8	−	2.63321e8i	0.456203	−	0.456203i
$156$	−6.52916e6	+	1.13399e7i	−0.0110245	+	0.0191475i
$157$	−6.08729e8	+	6.08729e8i	−1.00190	+	1.00190i	−0.00190456	+	0.999998i	$0.500606\pi$
$157$	−6.08729e8	+	6.08729e8i	−1.00190	+	1.00190i	−0.999998	+	0.00190456i	$0.999394\pi$
$158$	−5.15984e8	+	2.98312e8i	−0.827956	+	0.478676i
$159$		−	2.50816e8i		−	0.392435i
$160$	4.56228e8	−	1.23698e8i	0.696149	−	0.188748i
$161$	1.78774e8			0.266073
$162$	−3.83031e7	−	6.62520e7i	−0.0556126	−	0.0961921i
$163$	−1.84283e8	−	1.84283e8i	−0.261056	−	0.261056i	0.564427	−	0.825483i	$-0.309097\pi$
$163$	−1.84283e8	−	1.84283e8i	−0.261056	−	0.261056i	−0.825483	+	0.564427i	$0.809097\pi$
$164$	−5.91429e8	−	3.40527e8i	−0.817575	−	0.470734i
$165$	9.30346e7	+	9.30346e7i	0.125519	+	0.125519i
$166$	3.33428e8	−	1.24733e9i	0.439107	−	1.64267i
$167$	−1.60877e8			−0.206836			−0.103418	−	0.994638i	$-0.532978\pi$
$167$	−1.60877e8			−0.206836			−0.103418	+	0.994638i	$0.532978\pi$
$168$	−8.43143e7	−	8.40146e7i	−0.105843	−	0.105467i
$169$			8.14536e8i			0.998536i
$170$	7.41464e7	−	2.77377e8i	0.0887758	−	0.332104i
$171$	2.95163e8	−	2.95163e8i	0.345205	−	0.345205i
$172$	−3.41567e8	−	1.26872e9i	−0.390267	−	1.44961i
$173$	3.26527e8	−	3.26527e8i	0.364531	−	0.364531i	−0.500947	−	0.865478i	$-0.667015\pi$
$173$	3.26527e8	−	3.26527e8i	0.364531	−	0.364531i	0.865478	+	0.500947i	$0.167015\pi$
$174$	1.09178e7	+	1.88843e7i	0.0119107	+	0.0206018i
$175$			1.16449e8i			0.124160i
$176$	3.95319e8	+	1.04920e8i	0.412000	+	0.109348i
$177$	1.47133e8			0.149906
$178$	−4.09318e8	+	2.36644e8i	−0.407738	+	0.235730i
$179$	5.94844e8	+	5.94844e8i	0.579417	+	0.579417i	0.934743	−	0.355326i	$-0.115630\pi$
$179$	5.94844e8	+	5.94844e8i	0.579417	+	0.579417i	−0.355326	+	0.934743i	$0.615630\pi$
$180$	−6.56130e7	−	2.43714e8i	−0.0625029	−	0.232161i
$181$	−9.60431e8	−	9.60431e8i	−0.894853	−	0.894853i	0.100122	−	0.994975i	$-0.468077\pi$
$181$	−9.60431e8	−	9.60431e8i	−0.894853	−	0.894853i	−0.994975	+	0.100122i	$0.968077\pi$
$182$	1.04981e7	+	2.80628e6i	0.00956807	+	0.00255767i
$183$	2.02089e8			0.180193
$184$	1.17843e9	−	2.09792e6i	1.02809	−	0.00183028i
$185$			2.95684e8i			0.252430i
$186$	−5.97133e8	−	1.59622e8i	−0.498907	−	0.133364i
$187$	1.75665e8	−	1.75665e8i	0.143654	−	0.143654i
$188$	−1.89901e8	−	1.09339e8i	−0.152018	−	0.0875274i
$189$	−4.49385e7	+	4.49385e7i	−0.0352185	+	0.0352185i
$190$	1.19183e9	−	6.89049e8i	0.914537	−	0.528732i
$191$			2.10463e9i			1.58141i	0.612200	+	0.790703i	$0.290285\pi$
$191$			2.10463e9i			1.58141i	−0.612200	+	0.790703i	$0.709715\pi$
$192$	−5.56763e8	−	5.52812e8i	−0.409699	−	0.406792i
$193$	−6.39400e8			−0.460833			−0.230417	−	0.973092i	$-0.574009\pi$
$193$	−6.39400e8			−0.460833			−0.230417	+	0.973092i	$0.574009\pi$
$194$	2.07175e8	+	3.58347e8i	0.146262	+	0.252986i
$195$	1.62934e7	+	1.62934e7i	0.0112687	+	0.0112687i
$196$	6.87056e8	−	1.19328e9i	0.465551	−	0.808573i
$197$	−1.33538e9	−	1.33538e9i	−0.886622	−	0.886622i	0.107575	−	0.994197i	$-0.465691\pi$
$197$	−1.33538e9	−	1.33538e9i	−0.886622	−	0.886622i	−0.994197	+	0.107575i	$0.965691\pi$
$198$	5.63964e7	−	2.10975e8i	0.0366936	−	0.137268i
$199$	−1.72977e9			−1.10300			−0.551502	−	0.834174i	$-0.685945\pi$
$199$	−1.72977e9			−1.10300			−0.551502	+	0.834174i	$0.685945\pi$
$200$	1.36653e6	+	7.67599e8i	0.000854084	+	0.479749i
$201$		−	4.80250e8i		−	0.294228i
$202$	2.64190e8	−	9.88318e8i	0.158676	−	0.593596i
$203$	1.28091e7	−	1.28091e7i	0.00754286	−	0.00754286i
$204$	−4.60173e8	+	1.23888e8i	−0.265705	+	0.0715336i
$205$	−8.49779e8	+	8.49779e8i	−0.481161	+	0.481161i
$206$	−3.60330e8	−	6.23256e8i	−0.200093	−	0.346097i
$207$		−	6.29206e8i		−	0.342698i
$208$	6.92334e7	+	1.83750e7i	0.0369881	+	0.00981690i
$209$	1.19118e9			0.624298
$210$	−1.81456e8	+	1.04907e8i	−0.0933028	+	0.0539423i
$211$	9.52545e8	+	9.52545e8i	0.480569	+	0.480569i	0.905313	−	0.424744i	$-0.139636\pi$
$211$	9.52545e8	+	9.52545e8i	0.480569	+	0.480569i	−0.424744	+	0.905313i	$0.639636\pi$
$212$	−1.32580e9	+	3.56933e8i	−0.656347	+	0.176703i
$213$	−6.29203e8	−	6.29203e8i	−0.305684	−	0.305684i
$214$	3.45542e9	+	9.23681e8i	1.64758	+	0.440420i
$215$	−2.31370e9			−1.08281
$216$	−2.95695e8	+	2.96749e8i	−0.135840	+	0.136325i
$217$			5.13303e8i			0.231491i
$218$	−1.57316e9	−	4.20527e8i	−0.696543	−	0.186195i
$219$	1.59559e9	−	1.59559e9i	0.693659	−	0.693659i
$220$	3.59378e8	−	6.24170e8i	0.153412	−	0.266448i
$221$	3.07647e7	−	3.07647e7i	0.0128969	−	0.0128969i
$222$	4.24882e8	−	2.45642e8i	0.174927	−	0.101132i
$223$			4.18527e9i			1.69240i	0.532862	+	0.846202i	$0.321117\pi$
$223$			4.18527e9i			1.69240i	−0.532862	+	0.846202i	$0.678883\pi$
$224$	−3.24108e8	+	5.65239e8i	−0.128735	+	0.224512i
$225$	4.09849e8			0.159917
$226$	5.38593e8	+	9.31594e8i	0.206456	+	0.357102i
$227$	4.06778e8	+	4.06778e8i	0.153198	+	0.153198i	0.779545	−	0.626347i	$-0.215450\pi$
$227$	4.06778e8	+	4.06778e8i	0.153198	+	0.153198i	−0.626347	+	0.779545i	$0.715450\pi$
$228$	−1.98025e9	−	1.14017e9i	−0.732792	−	0.421919i
$229$	−1.68702e9	−	1.68702e9i	−0.613448	−	0.613448i	0.330395	−	0.943843i	$-0.392818\pi$
$229$	−1.68702e9	−	1.68702e9i	−0.613448	−	0.613448i	−0.943843	+	0.330395i	$0.892818\pi$
$230$	5.35899e8	−	2.00476e9i	0.191501	−	0.716393i
$231$	−1.81357e8			−0.0636921
$232$	8.42841e7	−	8.45847e7i	0.0290933	−	0.0291971i
$233$			2.52831e9i			0.857842i	0.903342	+	0.428921i	$0.141106\pi$
$233$			2.52831e9i			0.857842i	−0.903342	+	0.428921i	$0.858894\pi$
$234$	9.87687e6	−	3.69487e7i	0.00329424	−	0.0123235i
$235$	−2.72854e8	+	2.72854e8i	−0.0894662	+	0.0894662i
$236$	−2.09383e8	−	7.77735e8i	−0.0674984	−	0.250717i
$237$	1.23181e9	−	1.23181e9i	0.390436	−	0.390436i
$238$	1.98083e8	+	3.42620e8i	0.0617361	+	0.106784i
$239$			5.08623e9i			1.55885i	0.626495	+	0.779426i	$0.284489\pi$
$239$			5.08623e9i			1.55885i	−0.626495	+	0.779426i	$0.715511\pi$
$240$	−1.19488e9	+	6.93651e8i	−0.360146	+	0.209072i
$241$	2.44542e9			0.724913			0.362457	−	0.932001i	$-0.381938\pi$
$241$	2.44542e9			0.724913			0.362457	+	0.932001i	$0.381938\pi$
$242$	−2.42971e9	+	1.40472e9i	−0.708425	+	0.409570i
$243$	1.58164e8	+	1.58164e8i	0.0453609	+	0.0453609i
$244$	−2.87590e8	−	1.06823e9i	−0.0811361	−	0.301373i
$245$	−1.71454e9	−	1.71454e9i	−0.475864	−	0.475864i
$246$	1.92705e9	+	5.15125e8i	0.526201	+	0.140661i
$247$	2.08615e8			0.0560476
$248$	6.02364e6	+	3.38355e9i	0.00159240	+	0.894471i
$249$			3.77376e9i			0.981695i
$250$	4.02779e9	+	1.07668e9i	1.03112	+	0.275631i
$251$	1.33899e9	−	1.33899e9i	0.337351	−	0.337351i	−0.518018	−	0.855369i	$-0.673330\pi$
$251$	1.33899e9	−	1.33899e9i	0.337351	−	0.337351i	0.855369	+	0.518018i	$0.173330\pi$
$252$	3.01492e8	+	1.73590e8i	0.0747609	+	0.0430450i
$253$	1.26963e9	−	1.26963e9i	0.309882	−	0.309882i
$254$	5.09113e9	−	2.94340e9i	1.22315	−	0.707154i
$255$			8.39192e8i			0.198473i
$256$	−2.12980e9	+	3.72970e9i	−0.495883	+	0.868389i
$257$	7.28950e9			1.67096			0.835479	−	0.549523i	$-0.185190\pi$
$257$	7.28950e9			1.67096			0.835479	+	0.549523i	$0.185190\pi$
$258$	1.92212e9	+	3.32465e9i	0.433812	+	0.750356i
$259$	−2.88195e8	−	2.88195e8i	−0.0640454	−	0.0640454i
$260$	6.29389e7	−	1.09313e8i	0.0137729	−	0.0239209i
$261$	−4.50826e7	−	4.50826e7i	−0.00971509	−	0.00971509i
$262$	1.08016e9	−	4.04080e9i	0.229236	−	0.857554i
$263$	−8.88932e8			−0.185800			−0.0929000	−	0.995675i	$-0.529614\pi$
$263$	−8.88932e8			−0.185800			−0.0929000	+	0.995675i	$0.529614\pi$
$264$	−1.19545e9	+	2.12823e6i	−0.246103	+	0.000438130i
$265$			2.41778e9i			0.490269i
$266$	−4.90051e8	+	1.83325e9i	−0.0978847	+	0.366180i
$267$	9.77166e8	−	9.77166e8i	0.192275	−	0.192275i
$268$	−2.53857e9	+	6.83437e8i	−0.492095	+	0.132483i
$269$	7.14145e9	−	7.14145e9i	1.36388	−	1.36388i	0.494976	−	0.868907i	$-0.335177\pi$
$269$	7.14145e9	−	7.14145e9i	1.36388	−	1.36388i	0.868907	−	0.494976i	$-0.164823\pi$
$270$	3.69229e8	+	6.38647e8i	0.0694769	+	0.120173i
$271$		−	3.44515e8i		−	0.0638751i	−0.999490	−	0.0319376i	$-0.989832\pi$
$271$		−	3.44515e8i		−	0.0638751i	0.999490	−	0.0319376i	$-0.0101678\pi$
$272$	1.30973e9	+	2.25613e9i	0.239280	+	0.412182i
$273$	−3.17615e7			−0.00571809
$274$	−4.01763e9	+	2.32276e9i	−0.712800	+	0.412099i
$275$	8.27007e8	+	8.27007e8i	0.144603	+	0.144603i
$276$	−3.32593e9	+	8.95413e8i	−0.573162	+	0.154308i
$277$	−7.54714e9	−	7.54714e9i	−1.28193	−	1.28193i	−0.939570	−	0.342358i	$-0.888774\pi$
$277$	−7.54714e9	−	7.54714e9i	−1.28193	−	1.28193i	−0.342358	−	0.939570i	$-0.611226\pi$
$278$	4.45136e9	+	1.18991e9i	0.745270	+	0.199221i
$279$	1.80660e9			0.298158
$280$	8.12761e8	+	8.09872e8i	0.132230	+	0.131760i
$281$		−	1.23093e10i		−	1.97428i	−0.159848	−	0.987142i	$-0.551100\pi$
$281$		−	1.23093e10i		−	1.97428i	0.159848	−	0.987142i	$-0.448900\pi$
$282$	6.18752e8	+	1.65401e8i	0.0978409	+	0.0261542i
$283$	3.03852e9	−	3.03852e9i	0.473714	−	0.473714i	−0.429400	−	0.903114i	$-0.641275\pi$
$283$	3.03852e9	−	3.03852e9i	0.473714	−	0.473714i	0.903114	+	0.429400i	$0.141275\pi$
$284$	−2.43051e9	+	4.22133e9i	−0.373615	+	0.648897i
$285$	−2.84527e9	+	2.84527e9i	−0.431265	+	0.431265i
$286$	9.44862e7	−	5.46264e7i	0.0141223	−	0.00816467i
$287$		−	1.65651e9i		−	0.244156i
$288$	1.98939e9	+	1.14072e9i	0.289168	+	0.165809i
$289$	−5.39122e9			−0.772851
$290$	−1.05244e8	−	1.82038e8i	−0.0148801	−	0.0257378i
$291$	−8.55483e8	−	8.55483e8i	−0.119300	−	0.119300i
$292$	−1.07049e10	−	6.16352e9i	−1.47248	−	0.847808i
$293$	−8.95371e9	−	8.95371e9i	−1.21488	−	1.21488i	−0.969403	−	0.245474i	$-0.921056\pi$
$293$	−8.95371e9	−	8.95371e9i	−1.21488	−	1.21488i	−0.245474	−	0.969403i	$-0.578944\pi$
$294$	−1.03933e9	+	3.88806e9i	−0.139112	+	0.520408i
$295$	−1.41831e9			−0.187277
$296$	−1.90309e9	−	1.89632e9i	−0.247909	−	0.247028i
$297$			6.38296e8i			0.0820345i
$298$	−2.15069e9	+	8.04558e9i	−0.272717	+	1.02022i
$299$	2.22355e8	−	2.22355e8i	0.0278203	−	0.0278203i
$300$	−5.83250e8	−	2.16643e9i	−0.0720062	−	0.267461i
$301$	2.25510e9	−	2.25510e9i	0.274726	−	0.274726i
$302$	−6.56528e9	−	1.13558e10i	−0.789270	−	1.36518i
$303$			2.99012e9i			0.354746i
$304$	−3.20877e9	+	1.20900e10i	−0.375703	+	1.41557i
$305$	−1.94807e9			−0.225115
$306$	1.20587e9	−	6.97165e8i	0.137536	−	0.0795152i
$307$	−1.10912e8	−	1.10912e8i	−0.0124861	−	0.0124861i	0.700836	−	0.713322i	$-0.252810\pi$
$307$	−1.10912e8	−	1.10912e8i	−0.0124861	−	0.0124861i	−0.713322	+	0.700836i	$0.752810\pi$
$308$	2.58086e8	+	9.58638e8i	0.0286788	+	0.106525i
$309$	1.48790e9	+	1.48790e9i	0.163208	+	0.163208i
$310$	5.75616e9	+	1.53870e9i	0.623284	+	0.166612i
$311$	−1.06330e10			−1.13661			−0.568306	−	0.822817i	$-0.692401\pi$
$311$	−1.06330e10			−1.13661			−0.568306	+	0.822817i	$0.692401\pi$
$312$	−2.09363e8	+	372724.i	−0.0220944	+	3.93340e-5i
$313$			6.90929e9i			0.719873i	0.932977	+	0.359937i	$0.117202\pi$
$313$			6.90929e9i			0.719873i	−0.932977	+	0.359937i	$0.882798\pi$
$314$	−1.33067e10	−	3.55707e9i	−1.36884	−	0.365910i
$315$	4.33191e8	−	4.33191e8i	0.0439985	−	0.0439985i
$316$	−8.26422e9	−	4.75828e9i	−0.828807	−	0.477201i
$317$	7.11296e9	−	7.11296e9i	0.704390	−	0.704390i	−0.260960	−	0.965350i	$-0.584039\pi$
$317$	7.11296e9	−	7.11296e9i	0.704390	−	0.704390i	0.965350	+	0.260960i	$0.0840389\pi$
$318$	3.47422e9	−	2.00859e9i	0.339742	−	0.196419i
$319$		−	1.81938e8i		−	0.0175696i
$320$	5.36700e9	+	5.32892e9i	0.511837	+	0.508205i
$321$	−1.04543e10			−0.984629
$322$	1.43166e9	+	2.47631e9i	0.133173	+	0.230347i
$323$	5.37235e9	+	5.37235e9i	0.493576	+	0.493576i
$324$	6.10961e8	−	1.06112e9i	0.0554413	−	0.0962909i
$325$	1.44836e8	+	1.44836e8i	0.0129821	+	0.0129821i
$326$	1.07684e9	−	4.02840e9i	0.0953417	−	0.356666i
$327$	4.75954e9			0.416269
$328$	−1.94393e7	−	1.09193e10i	−0.00167952	−	0.943407i
$329$		−	5.31887e8i		−	0.0453979i
$330$	−5.43642e8	+	2.03373e9i	−0.0458413	+	0.171489i
$331$	1.19997e10	−	1.19997e10i	0.999676	−	0.999676i	−0.000324380	−	1.00000i	$-0.500103\pi$
$331$	1.19997e10	−	1.19997e10i	0.999676	−	0.999676i	1.00000		0.000324380i	$0.000103253\pi$
$332$	1.99478e10	−	5.37038e9i	1.64188	−	0.442031i
$333$	−1.01432e9	+	1.01432e9i	−0.0824896	+	0.0824896i
$334$	−1.28834e9	−	2.22841e9i	−0.103524	−	0.179064i
$335$			4.62945e9i			0.367578i
$336$	4.88534e8	−	1.84070e9i	0.0383299	−	0.144419i
$337$	1.86179e10			1.44348			0.721742	−	0.692162i	$-0.243342\pi$
$337$	1.86179e10			1.44348			0.721742	+	0.692162i	$0.243342\pi$
$338$	−1.12827e10	+	6.52299e9i	−0.864461	+	0.499781i
$339$	−2.22400e9	−	2.22400e9i	−0.168397	−	0.168397i
$340$	4.43591e9	−	1.19424e9i	0.331945	−	0.0893669i
$341$	3.64542e9	+	3.64542e9i	0.269607	+	0.269607i
$342$	6.45222e9	+	1.72477e9i	0.471634	+	0.126074i
$343$	6.92438e9			0.500270
$344$	1.48385e10	−	1.48914e10i	1.05964	−	1.06342i
$345$			6.06533e9i			0.428132i
$346$	7.13783e9	+	1.90804e9i	0.498037	+	0.133132i
$347$	−1.02474e10	+	1.02474e10i	−0.706798	+	0.706798i	−0.965861	−	0.259062i	$-0.916587\pi$
$347$	−1.02474e10	+	1.02474e10i	−0.706798	+	0.706798i	0.259062	+	0.965861i	$0.416587\pi$
$348$	−1.74147e8	+	3.02460e8i	−0.0118740	+	0.0206229i
$349$	−1.00807e10	+	1.00807e10i	−0.679496	+	0.679496i	−0.959886	−	0.280390i	$-0.909536\pi$
$349$	−1.00807e10	+	1.00807e10i	−0.679496	+	0.679496i	0.280390	+	0.959886i	$0.409536\pi$
$350$	−1.61301e9	+	9.32548e8i	−0.107489	+	0.0621440i
$351$			1.11787e8i			0.00736482i
$352$	1.71248e9	+	6.31605e9i	0.111546	+	0.411410i
$353$	1.24001e10			0.798595			0.399298	−	0.916821i	$-0.369254\pi$
$353$	1.24001e10			0.798595			0.399298	+	0.916821i	$0.369254\pi$
$354$	1.17828e9	+	2.03804e9i	0.0750298	+	0.129777i
$355$	6.06530e9	+	6.06530e9i	0.381891	+	0.381891i
$356$	−6.55582e9	−	3.77464e9i	−0.408157	−	0.235004i
$357$	−8.17938e8	−	8.17938e8i	−0.0503556	−	0.0503556i
$358$	−3.47593e9	+	1.30032e10i	−0.211612	+	0.791624i
$359$	−2.12712e10			−1.28060			−0.640301	−	0.768124i	$-0.721190\pi$
$359$	−2.12712e10			−1.28060			−0.640301	+	0.768124i	$0.721190\pi$
$360$	2.85040e9	−	2.86056e9i	0.169705	−	0.170311i
$361$			1.94462e10i			1.14500i
$362$	5.61222e9	−	2.09949e10i	0.326814	−	1.22259i
$363$	5.80047e9	−	5.80047e9i	0.334069	−	0.334069i
$364$	4.51994e7	+	1.67889e8i	0.00257470	+	0.00956350i
$365$	−1.53810e10	+	1.53810e10i	−0.866588	+	0.866588i
$366$	1.61837e9	+	2.79927e9i	0.0901892	+	0.155998i
$367$		−	2.26089e10i		−	1.24628i	−0.782112	−	0.623138i	$-0.785857\pi$
$367$		−	2.26089e10i		−	1.24628i	0.782112	−	0.623138i	$-0.214143\pi$
$368$	9.46617e9	+	1.63064e10i	0.516158	+	0.889132i
$369$	−5.83021e9			−0.314469
$370$	−4.09572e9	+	2.36790e9i	−0.218536	+	0.126345i
$371$	−2.35655e9	−	2.35655e9i	−0.124389	−	0.124389i
$372$	−2.57095e9	−	9.54956e9i	−0.134252	−	0.498668i
$373$	2.29312e10	+	2.29312e10i	1.18465	+	1.18465i	0.978525	+	0.206128i	$0.0660862\pi$
$373$	2.29312e10	+	2.29312e10i	1.18465	+	1.18465i	0.206128	+	0.978525i	$0.433914\pi$
$374$	3.84002e9	+	1.02649e9i	0.196267	+	0.0524647i
$375$	−1.21859e10			−0.616217
$376$	−6.24173e6	−	3.50606e9i	−0.000312287	−	0.175415i
$377$		−	3.18634e7i		−	0.00157735i
$378$	−9.82349e8	−	2.62595e8i	−0.0481170	−	0.0128623i
$379$	5.04981e9	−	5.04981e9i	0.244747	−	0.244747i	−0.574063	−	0.818811i	$-0.694634\pi$
$379$	5.04981e9	−	5.04981e9i	0.244747	−	0.244747i	0.818811	+	0.574063i	$0.194634\pi$
$380$	1.90889e10	+	1.09908e10i	0.915477	+	0.527103i
$381$	−1.21541e10	+	1.21541e10i	−0.576796	+	0.576796i
$382$	−2.91527e10	+	1.68544e10i	−1.36907	+	0.791515i
$383$			3.56199e10i			1.65538i	0.561187	+	0.827689i	$0.310345\pi$
$383$			3.56199e10i			1.65538i	−0.561187	+	0.827689i	$0.689655\pi$
$384$	3.19868e9	−	1.21391e10i	0.147111	−	0.558293i
$385$	1.74822e9			0.0795705
$386$	−5.12046e9	−	8.85676e9i	−0.230653	−	0.398956i
$387$	−7.93696e9	−	7.93696e9i	−0.353843	−	0.353843i
$388$	−3.30459e9	+	5.73944e9i	−0.145811	+	0.253246i
$389$	6.66491e9	+	6.66491e9i	0.291069	+	0.291069i	0.837502	−	0.546434i	$-0.184015\pi$
$389$	6.66491e9	+	6.66491e9i	0.291069	+	0.291069i	−0.546434	+	0.837502i	$0.684015\pi$
$390$	−9.52096e7	+	3.56172e8i	−0.00411550	+	0.0153958i
$391$	1.14524e10			0.489991
$392$	2.20311e10	−	3.92212e7i	0.933020	−	0.00166103i
$393$			1.22253e10i			0.512493i
$394$	7.80318e9	−	2.91911e10i	0.323807	−	1.21134i
$395$	−1.18742e10	+	1.18742e10i	−0.487772	+	0.487772i
$396$	3.37399e9	−	9.08350e8i	0.137203	−	0.0369379i
$397$	−7.50641e9	+	7.50641e9i	−0.302183	+	0.302183i	−0.841868	−	0.539684i	$-0.818544\pi$
$397$	−7.50641e9	+	7.50641e9i	−0.302183	+	0.302183i	0.539684	+	0.841868i	$0.318544\pi$
$398$	−1.38524e10	−	2.39602e10i	−0.552069	−	0.954902i
$399$		−	5.54641e9i		−	0.218837i
$400$	−1.06216e10	+	6.16603e9i	−0.414905	+	0.240861i
$401$	1.04685e9			0.0404862			0.0202431	−	0.999795i	$-0.493556\pi$
$401$	1.04685e9			0.0404862			0.0202431	+	0.999795i	$0.493556\pi$
$402$	6.65226e9	−	3.84595e9i	0.254721	−	0.147265i
$403$	6.38434e8	+	6.38434e8i	0.0242045	+	0.0242045i
$404$	1.58055e10	−	4.25519e9i	0.593313	−	0.159733i
$405$	−1.52464e9	−	1.52464e9i	−0.0566694	−	0.0566694i
$406$	2.80006e8	+	7.48494e7i	0.0103054	+	0.00275476i
$407$	−4.09347e9			−0.149181
$408$	−5.40122e9	−	5.38203e9i	−0.194918	−	0.194225i
$409$		−	6.36239e9i		−	0.227367i	−0.993517	−	0.113683i	$-0.963735\pi$
$409$		−	6.36239e9i		−	0.227367i	0.993517	−	0.113683i	$-0.0362649\pi$
$410$	−1.85761e10	−	4.96563e9i	−0.657383	−	0.175727i
$411$	9.59130e9	−	9.59130e9i	0.336132	−	0.336132i
$412$	5.74752e9	−	9.98234e9i	0.199477	−	0.346453i
$413$	1.38239e9	−	1.38239e9i	0.0475150	−	0.0475150i
$414$	8.71554e9	−	5.03882e9i	0.296683	−	0.171525i
$415$		−	3.63777e10i		−	1.22643i
$416$	2.99912e8	+	1.10615e9i	0.0100143	+	0.0369352i
$417$	−1.34674e10			−0.445390
$418$	9.53923e9	+	1.64998e10i	0.312470	+	0.540473i
$419$	−2.86956e10	−	2.86956e10i	−0.931020	−	0.931020i	0.0667493	−	0.997770i	$-0.478737\pi$
$419$	−2.86956e10	−	2.86956e10i	−0.931020	−	0.931020i	−0.997770	+	0.0667493i	$0.978737\pi$
$420$	−2.90628e9	−	1.67335e9i	−0.0933987	−	0.0537761i
$421$	−1.53566e10	−	1.53566e10i	−0.488841	−	0.488841i	0.419100	−	0.907940i	$-0.362346\pi$
$421$	−1.53566e10	−	1.53566e10i	−0.488841	−	0.488841i	−0.907940	+	0.419100i	$0.862346\pi$
$422$	−5.56614e9	+	2.08225e10i	−0.175511	+	0.656574i
$423$	−1.87201e9			−0.0584719
$424$	−1.55614e10	−	1.55061e10i	−0.481487	−	0.479776i
$425$			7.45978e9i			0.228650i
$426$	3.67671e9	−	1.37543e10i	0.111640	−	0.417638i
$427$	1.89873e9	−	1.89873e9i	0.0571152	−	0.0571152i
$428$	1.48773e10	+	5.52604e10i	0.443352	+	1.64679i
$429$	−2.25567e8	+	2.25567e8i	−0.00665958	+	0.00665958i
$430$	−1.85286e10	−	3.20485e10i	−0.541962	−	0.937420i
$431$		−	4.03961e9i		−	0.117066i	−0.998285	−	0.0585329i	$-0.981358\pi$
$431$		−	4.03961e9i		−	0.117066i	0.998285	−	0.0585329i	$-0.0186423\pi$
$432$	−6.47846e9	−	1.71943e9i	−0.186010	−	0.0493684i
$433$	1.50341e10			0.427688			0.213844	−	0.976868i	$-0.431402\pi$
$433$	1.50341e10			0.427688			0.213844	+	0.976868i	$0.431402\pi$
$434$	−7.11010e9	+	4.11064e9i	−0.200409	+	0.115865i
$435$	4.34581e8	+	4.34581e8i	0.0121371	+	0.0121371i
$436$	−6.77324e9	−	2.51586e10i	−0.187435	−	0.696210i
$437$	3.88290e10	+	3.88290e10i	1.06471	+	1.06471i
$438$	3.48795e10	+	9.32375e9i	0.947706	+	0.253334i
$439$	2.52445e10			0.679687			0.339843	−	0.940482i	$-0.389626\pi$
$439$	2.52445e10			0.679687			0.339843	+	0.940482i	$0.389626\pi$
$440$	1.15238e10	−	2.05154e7i	0.307457	−	0.000547356i
$441$		−	1.17632e10i		−	0.311007i
$442$	6.72513e8	+	1.79772e8i	0.0176202	+	0.00471012i
$443$	−4.35983e9	+	4.35983e9i	−0.113202	+	0.113202i	−0.761439	−	0.648237i	$-0.775507\pi$
$443$	−4.35983e9	+	4.35983e9i	−0.113202	+	0.113202i	0.648237	+	0.761439i	$0.275507\pi$
$444$	6.80510e9	+	3.91816e9i	0.175107	+	0.100821i
$445$	−9.41955e9	+	9.41955e9i	−0.240209	+	0.240209i
$446$	−5.79730e10	+	3.35166e10i	−1.46516	+	0.847072i
$447$		−	2.43416e10i		−	0.609704i
$448$	−1.04250e10	+	3.71189e7i	−0.258800	+	0.000921473i
$449$	−4.90162e10			−1.20602			−0.603009	−	0.797734i	$-0.706032\pi$
$449$	−4.90162e10			−1.20602			−0.603009	+	0.797734i	$0.706032\pi$
$450$	3.28216e9	+	5.67709e9i	0.0800405	+	0.138444i
$451$	−1.17644e10	−	1.17644e10i	−0.284357	−	0.284357i
$452$	−8.59094e9	+	1.49208e10i	−0.205820	+	0.357469i
$453$	2.71098e10	+	2.71098e10i	0.643774	+	0.643774i
$454$	−2.37698e9	+	8.89211e9i	−0.0559502	+	0.209306i
$455$	3.06170e8			0.00714361
$456$	−6.50875e7	−	3.65605e10i	−0.00150535	−	0.845575i
$457$		−	3.71830e10i		−	0.852470i	−0.904612	−	0.426235i	$-0.859840\pi$
$457$		−	3.71830e10i		−	0.852470i	0.904612	−	0.426235i	$-0.140160\pi$
$458$	9.85798e9	−	3.68780e10i	0.224040	−	0.838119i
$459$	−2.87878e9	+	2.87878e9i	−0.0648572	+	0.0648572i
$460$	3.20609e10	−	8.63148e9i	0.716051	−	0.192776i
$461$	4.57317e10	−	4.57317e10i	1.01254	−	1.01254i	0.0126233	−	0.999920i	$-0.495982\pi$
$461$	4.57317e10	−	4.57317e10i	1.01254	−	1.01254i	0.999920	−	0.0126233i	$-0.00401823\pi$
$462$	−1.45234e9	−	2.51209e9i	−0.0318788	−	0.0551401i
$463$		−	7.12209e10i		−	1.54983i	−0.632066	−	0.774914i	$-0.717793\pi$
$463$		−	7.12209e10i		−	1.54983i	0.632066	−	0.774914i	$-0.282207\pi$
$464$	1.84660e9	+	4.90101e8i	0.0398384	+	0.0105734i
$465$	−1.74150e10			−0.372488
$466$	−3.50213e10	+	2.02473e10i	−0.742658	+	0.429362i
$467$	8.51196e9	+	8.51196e9i	0.178962	+	0.178962i	0.790903	−	0.611941i	$-0.209611\pi$
$467$	8.51196e9	+	8.51196e9i	0.178962	+	0.178962i	−0.611941	+	0.790903i	$0.709611\pi$
$468$	5.90896e8	−	1.59082e8i	0.0123177	−	0.00331618i
$469$	−4.51220e9	−	4.51220e9i	−0.0932603	−	0.0932603i
$470$	−5.96456e9	−	1.59441e9i	−0.122233	−	0.0326744i
$471$	4.02591e10			0.818050
$472$	9.09613e9	−	9.12857e9i	0.183269	−	0.183923i
$473$		−	3.20309e10i		−	0.639919i
$474$	2.69272e10	+	7.19800e9i	0.533431	+	0.142593i
$475$	−2.52923e10	+	2.52923e10i	−0.496837	+	0.496837i
$476$	−3.15956e9	+	5.48755e9i	−0.0615459	+	0.106893i
$477$	−8.29402e9	+	8.29402e9i	−0.160211	+	0.160211i
$478$	−7.04528e10	+	4.07317e10i	−1.34954	+	0.780227i
$479$		−	1.33207e9i		−	0.0253038i	−0.999920	−	0.0126519i	$-0.995973\pi$
$479$		−	1.33207e9i		−	0.0253038i	0.999920	−	0.0126519i	$-0.00402733\pi$
$480$	−1.91771e10	−	1.09962e10i	−0.361258	−	0.207146i
$481$	−7.16901e8			−0.0133930
$482$	1.95835e10	+	3.38732e10i	0.362829	+	0.627578i
$483$	−5.91171e9	−	5.91171e9i	−0.108624	−	0.108624i
$484$	−3.89154e10	−	2.24063e10i	−0.709153	−	0.408308i
$485$	8.24656e9	+	8.24656e9i	0.149041	+	0.149041i
$486$	−9.24220e8	+	3.45744e9i	−0.0165665	+	0.0619740i
$487$	2.18424e10			0.388316			0.194158	−	0.980970i	$-0.437803\pi$
$487$	2.18424e10			0.388316			0.194158	+	0.980970i	$0.437803\pi$
$488$	1.24936e10	−	1.25382e10i	0.220297	−	0.221083i
$489$			1.21878e10i			0.213152i
$490$	1.00188e10	−	3.74796e10i	0.173792	−	0.650145i
$491$	−6.18919e10	+	6.18919e10i	−1.06490	+	1.06490i	−0.0671558	+	0.997743i	$0.521392\pi$
$491$	−6.18919e10	+	6.18919e10i	−1.06490	+	1.06490i	−0.997743	+	0.0671558i	$0.978608\pi$
$492$	8.29688e9	+	3.08180e10i	0.141597	+	0.525950i
$493$	8.20562e8	−	8.20562e8i	0.0138907	−	0.0138907i
$494$	1.67063e9	+	2.88966e9i	0.0280526	+	0.0485220i
$495$		−	6.15296e9i		−	0.102486i
$496$	−4.68196e10	+	2.71797e10i	−0.773572	+	0.449074i
$497$	−1.18234e10			−0.193783
$498$	−5.22728e10	+	3.02211e10i	−0.849881	+	0.491352i
$499$	3.96547e10	+	3.96547e10i	0.639576	+	0.639576i	0.950451	−	0.310875i	$-0.100622\pi$
$499$	3.96547e10	+	3.96547e10i	0.639576	+	0.639576i	−0.310875	+	0.950451i	$0.600622\pi$
$500$	1.73416e10	+	6.44139e10i	0.277466	+	1.03062i
$501$	5.31988e9	+	5.31988e9i	0.0844406	+	0.0844406i
$502$	2.92701e10	+	7.82430e9i	0.460903	+	0.123206i
$503$	9.90111e10			1.54672			0.773360	−	0.633967i	$-0.218574\pi$
$503$	9.90111e10			1.54672			0.773360	+	0.633967i	$0.218574\pi$
$504$	9.90955e6	+	5.56632e9i	0.000153579	+	0.0862672i
$505$		−	2.88237e10i		−	0.443184i
$506$	2.77540e10	+	7.41902e9i	0.423374	+	0.113173i
$507$	2.69352e10	−	2.69352e10i	0.407650	−	0.407650i
$508$	8.15418e10	+	4.69493e10i	1.22441	+	0.704975i
$509$	4.78060e10	−	4.78060e10i	0.712216	−	0.712216i	−0.254782	−	0.966998i	$-0.582004\pi$
$509$	4.78060e10	−	4.78060e10i	0.712216	−	0.712216i	0.966998	+	0.254782i	$0.0820039\pi$
$510$	−1.16242e10	+	6.72044e9i	−0.171823	+	0.0993383i
$511$		−	2.99829e10i		−	0.439733i
$512$	−6.87185e10	+	3.67016e8i	−0.999986	+	0.00534078i
$513$	−1.95210e10			−0.281859
$514$	5.83760e10	+	1.00972e11i	0.836337	+	1.44660i
$515$	−1.43429e10	−	1.43429e10i	−0.203895	−	0.203895i
$516$	−3.06592e10	+	5.32491e10i	−0.432476	+	0.751127i
$517$	−3.77741e9	−	3.77741e9i	−0.0528727	−	0.0528727i
$518$	1.68405e9	−	6.29992e9i	0.0233903	−	0.0875016i
$519$	−2.15952e10			−0.297638
$520$	2.01819e9	−	3.59293e6i	0.0276025	−	4.91400e-5i
$521$		−	7.55247e10i		−	1.02503i	−0.858677	−	0.512517i	$-0.828713\pi$
$521$		−	7.55247e10i		−	1.02503i	0.858677	−	0.512517i	$-0.171287\pi$
$522$	2.63437e8	−	9.85500e8i	0.00354809	−	0.0132732i
$523$	−9.47605e10	+	9.47605e10i	−1.26654	+	1.26654i	−0.318683	+	0.947861i	$0.603241\pi$
$523$	−9.47605e10	+	9.47605e10i	−1.26654	+	1.26654i	−0.947861	+	0.318683i	$0.896759\pi$
$524$	6.46219e10	−	1.73976e10i	0.857145	−	0.230762i
$525$	3.85074e9	−	3.85074e9i	0.0506882	−	0.0506882i
$526$	−7.11876e9	−	1.23132e10i	−0.0929954	−	0.160852i
$527$			3.28825e10i			0.426307i
$528$	−9.60294e9	−	1.65420e10i	−0.123557	−	0.212839i
$529$	4.46179e9			0.0569753
$530$	−3.34903e10	+	1.93622e10i	−0.424439	+	0.245386i
$531$	−4.86542e9	−	4.86542e9i	−0.0611987	−	0.0611987i
$532$	−2.93179e10	+	7.89302e9i	−0.366005	+	0.0985364i
$533$	−2.06033e9	−	2.06033e9i	−0.0255287	−	0.0255287i
$534$	2.13607e10	+	5.71001e9i	0.262695	+	0.0702217i
$535$	1.00775e11			1.23010
$536$	−2.97961e10	−	2.96902e10i	−0.360995	−	0.359712i
$537$		−	3.93408e10i		−	0.473092i
$538$	1.56111e11	+	4.17306e10i	1.86339	+	0.498110i
$539$	2.37361e10	−	2.37361e10i	0.281226	−	0.281226i
$540$	−5.88946e9	+	1.02289e10i	−0.0692628	+	0.120296i
$541$	−5.88403e10	+	5.88403e10i	−0.686888	+	0.686888i	−0.961543	−	0.274655i	$-0.911436\pi$
$541$	−5.88403e10	+	5.88403e10i	−0.686888	+	0.686888i	0.274655	+	0.961543i	$0.411436\pi$
$542$	4.77211e9	−	2.75896e9i	0.0552985	−	0.0319704i
$543$			6.35193e10i			0.730645i
$544$	−2.07626e10	+	3.62095e10i	−0.237075	+	0.413454i
$545$	−4.58804e10			−0.520045
$546$	−2.54353e8	−	4.39950e8i	−0.00286198	−	0.00495031i
$547$	3.03779e10	+	3.03779e10i	0.339319	+	0.339319i	0.856111	−	0.516792i	$-0.172874\pi$
$547$	3.03779e10	+	3.03779e10i	0.339319	+	0.339319i	−0.516792	+	0.856111i	$0.672874\pi$
$548$	−6.43481e10	−	3.70496e10i	−0.713532	−	0.410830i
$549$	−6.68270e9	−	6.68270e9i	−0.0735636	−	0.0735636i
$550$	−4.83256e9	+	1.80783e10i	−0.0528113	+	0.197563i
$551$	5.56421e9			0.0603666
$552$	−3.90378e10	−	3.88990e10i	−0.420464	−	0.418969i
$553$		−	2.31470e10i		−	0.247510i
$554$	4.41012e10	−	1.64980e11i	0.468179	−	1.75142i
$555$	9.77772e9	−	9.77772e9i	0.103054	−	0.103054i
$556$	1.91653e10	+	7.11878e10i	0.200547	+	0.744915i
$557$	5.87145e10	−	5.87145e10i	0.609993	−	0.609993i	−0.332951	−	0.942944i	$-0.608044\pi$
$557$	5.87145e10	−	5.87145e10i	0.609993	−	0.609993i	0.942944	+	0.332951i	$0.108044\pi$
$558$	1.44677e10	+	2.50244e10i	0.149232	+	0.258123i
$559$		−	5.60967e9i		−	0.0574500i
$560$	−4.70930e9	+	1.77437e10i	−0.0478855	+	0.180423i
$561$	−1.16178e10			−0.117293
$562$	1.70505e11	−	9.85759e10i	1.70919	−	0.988156i
$563$	−1.43143e10	−	1.43143e10i	−0.142474	−	0.142474i	0.632272	−	0.774746i	$-0.282122\pi$
$563$	−1.43143e10	−	1.43143e10i	−0.142474	−	0.142474i	−0.774746	+	0.632272i	$0.782122\pi$
$564$	2.66403e9	+	9.89531e9i	0.0263283	+	0.0977941i
$565$	2.14386e10	+	2.14386e10i	0.210379	+	0.210379i
$566$	6.64217e10	+	1.77554e10i	0.647208	+	0.173007i
$567$	2.97206e9			0.0287558
$568$	−7.79365e10	+	1.38748e8i	−0.748768	+	0.00133301i
$569$		−	9.55666e10i		−	0.911711i	−0.890054	−	0.455855i	$-0.849333\pi$
$569$		−	9.55666e10i		−	0.911711i	0.890054	−	0.455855i	$-0.150667\pi$
$570$	−6.21972e10	−	1.66261e10i	−0.589212	−	0.157504i
$571$	−1.02300e11	+	1.02300e11i	−0.962346	+	0.962346i	−0.999316	−	0.0369701i	$-0.988229\pi$
$571$	−1.02300e11	+	1.02300e11i	−0.962346	+	0.962346i	0.0369701	+	0.999316i	$0.488229\pi$
$572$	1.51333e9	+	8.71330e8i	0.0141368	+	0.00813951i
$573$	6.95963e10	−	6.95963e10i	0.645606	−	0.645606i
$574$	2.29455e10	−	1.32657e10i	0.211373	−	0.122203i
$575$			5.39162e10i			0.493228i
$576$	1.30642e8	+	3.66915e10i	0.00118684	+	0.333331i
$577$	2.54448e9			0.0229560			0.0114780	−	0.999934i	$-0.496346\pi$
$577$	2.54448e9			0.0229560			0.0114780	+	0.999934i	$0.496346\pi$
$578$	−4.31741e10	−	7.46774e10i	−0.386823	−	0.669079i
$579$	2.11438e10	+	2.11438e10i	0.188134	+	0.188134i
$580$	1.67872e9	−	2.91561e9i	0.0148342	−	0.0257642i
$581$	3.54564e10	+	3.54564e10i	0.311164	+	0.311164i
$582$	4.99896e9	−	1.87008e10i	0.0435700	−	0.162992i
$583$	−3.34719e10			−0.289739
$584$	−3.51851e8	−	1.97639e11i	−0.00302487	−	1.69911i
$585$		−	1.07759e9i		−	0.00920086i
$586$	5.23204e10	−	1.95727e11i	0.443691	−	1.65982i
$587$	−1.17516e8	+	1.17516e8i	−0.000989796	+	0.000989796i	−0.707602	−	0.706612i	$-0.750223\pi$
$587$	−1.17516e8	+	1.17516e8i	−0.000989796	+	0.000989796i	0.706612	+	0.707602i	$0.250223\pi$
$588$	−6.21793e10	+	1.67400e10i	−0.520159	+	0.140038i
$589$	−1.11488e11	+	1.11488e11i	−0.926330	+	0.926330i
$590$	−1.13582e10	−	1.96460e10i	−0.0937347	−	0.162131i
$591$			8.83167e10i			0.723924i
$592$	1.10269e10	−	4.15471e10i	0.0897771	−	0.338263i
$593$	−4.29057e10			−0.346974			−0.173487	−	0.984836i	$-0.555503\pi$
$593$	−4.29057e10			−0.346974			−0.173487	+	0.984836i	$0.555503\pi$
$594$	−8.84146e9	+	5.11162e9i	−0.0710196	+	0.0410594i
$595$	7.88464e9	+	7.88464e9i	0.0629092	+	0.0629092i
$596$	−1.28668e11	+	3.46402e10i	−1.01973	+	0.274533i
$597$	5.72003e10	+	5.72003e10i	0.450299	+	0.450299i
$598$	4.86064e9	+	1.29931e9i	0.0380092	+	0.0101604i
$599$	−4.47946e10			−0.347951			−0.173976	−	0.984750i	$-0.555661\pi$
$599$	−4.47946e10			−0.347951			−0.173976	+	0.984750i	$0.555661\pi$
$600$	2.53379e10	−	2.54282e10i	0.195508	−	0.196206i
$601$			1.03608e11i			0.794134i	0.917790	+	0.397067i	$0.129972\pi$
$601$			1.03608e11i			0.794134i	−0.917790	+	0.397067i	$0.870028\pi$
$602$	4.92961e10	+	1.31775e10i	0.375342	+	0.100334i
$603$	−1.58810e10	+	1.58810e10i	−0.120118	+	0.120118i
$604$	1.04721e11	−	1.81880e11i	0.786838	−	1.36659i
$605$	−5.59145e10	+	5.59145e10i	−0.417353	+	0.417353i
$606$	−4.14181e10	+	2.39455e10i	−0.307114	+	0.177555i
$607$			2.43626e10i			0.179461i	0.995966	+	0.0897303i	$0.0286005\pi$
$607$			2.43626e10i			0.179461i	−0.995966	+	0.0897303i	$0.971399\pi$
$608$	−1.93163e11	+	5.23727e10i	−1.41355	+	0.383257i
$609$	−8.47148e8			−0.00615872
$610$	−1.56006e10	−	2.69840e10i	−0.112673	−	0.194889i
$611$	−6.61549e8	−	6.61549e8i	−0.00474676	−	0.00474676i
$612$	1.93138e10	+	1.11203e10i	0.137677	+	0.0792702i
$613$	−1.34916e11	−	1.34916e11i	−0.955477	−	0.955477i	0.0435728	−	0.999050i	$-0.486126\pi$
$613$	−1.34916e11	−	1.34916e11i	−0.955477	−	0.955477i	−0.999050	+	0.0435728i	$0.986126\pi$
$614$	6.48107e8	−	2.42452e9i	0.00456009	−	0.0170590i
$615$	5.62012e10			0.392867
$616$	−1.12119e10	+	1.12519e10i	−0.0778676	+	0.0781453i
$617$		−	3.73734e10i		−	0.257883i	−0.991652	−	0.128941i	$-0.958842\pi$
$617$		−	3.73734e10i		−	0.257883i	0.991652	−	0.128941i	$-0.0411579\pi$
$618$	−8.69446e9	+	3.25253e10i	−0.0596058	+	0.222981i
$619$	−1.52844e11	+	1.52844e11i	−1.04108	+	1.04108i	−0.0419626	+	0.999119i	$0.513361\pi$
$619$	−1.52844e11	+	1.52844e11i	−1.04108	+	1.04108i	−0.999119	+	0.0419626i	$0.986639\pi$
$620$	2.47831e10	+	9.20545e10i	0.167721	+	0.622986i
$621$	−2.08066e10	+	2.08066e10i	−0.139906	+	0.139906i
$622$	−8.51510e10	−	1.47284e11i	−0.568890	−	0.983998i
$623$		−	1.83620e10i		−	0.121890i
$624$	−1.68179e9	−	2.89705e9i	−0.0110926	−	0.0191081i
$625$	4.42642e10			0.290090
$626$	−9.57051e10	+	5.53311e10i	−0.623215	+	0.360307i
$627$	−3.93901e10	−	3.93901e10i	−0.254869	−	0.254869i
$628$	−5.72921e10	−	2.12806e11i	−0.368346	−	1.36819i
$629$	−1.84620e10	−	1.84620e10i	−0.117944	−	0.117944i
$630$	9.46951e9	+	2.53133e9i	0.0601126	+	0.0160689i
$631$	−2.90522e11			−1.83257			−0.916287	−	0.400521i	$-0.868829\pi$
$631$	−2.90522e11			−1.83257			−0.916287	+	0.400521i	$0.868829\pi$
$632$	−2.71631e8	−	1.52579e11i	−0.00170259	−	0.956368i
$633$		−	6.29977e10i		−	0.392383i
$634$	1.55488e11	+	4.15641e10i	0.962368	+	0.257254i
$635$	1.17161e11	−	1.17161e11i	0.720591	−	0.720591i
$636$	5.56447e10	+	3.20385e10i	0.340091	+	0.195814i
$637$	4.15698e9	−	4.15698e9i	0.0252476	−	0.0252476i
$638$	2.52015e9	−	1.45700e9i	0.0152105	−	0.00879383i
$639$			4.16131e10i			0.249590i
$640$	−3.08342e10	+	1.17017e11i	−0.183786	+	0.697476i
$641$	−3.64351e10			−0.215818			−0.107909	−	0.994161i	$-0.534416\pi$
$641$	−3.64351e10			−0.215818			−0.107909	+	0.994161i	$0.534416\pi$
$642$	−8.37200e10	−	1.44809e11i	−0.492821	−	0.852422i
$643$	1.60028e10	+	1.60028e10i	0.0936165	+	0.0936165i	0.752364	−	0.658748i	$-0.228913\pi$
$643$	1.60028e10	+	1.60028e10i	0.0936165	+	0.0936165i	−0.658748	+	0.752364i	$0.728913\pi$
$644$	−2.28360e10	+	3.96617e10i	−0.132763	+	0.230583i
$645$	7.65095e10	+	7.65095e10i	0.442055	+	0.442055i
$646$	−3.13930e10	+	1.17439e11i	−0.180261	+	0.674344i
$647$	8.16595e10			0.466004			0.233002	−	0.972476i	$-0.425145\pi$
$647$	8.16595e10			0.466004			0.233002	+	0.972476i	$0.425145\pi$
$648$	1.95910e10	−	3.48773e7i	0.111111	−	0.000197808i
$649$		−	1.96352e10i		−	0.110677i
$650$	−8.46341e8	+	3.16610e9i	−0.00474124	+	0.0177367i
$651$	1.69740e10	−	1.69740e10i	0.0945060	−	0.0945060i
$652$	6.44236e10	−	1.73442e10i	0.356496	−	0.0959765i
$653$	1.24004e10	−	1.24004e10i	0.0681997	−	0.0681997i	−0.672184	−	0.740384i	$-0.734644\pi$
$653$	1.24004e10	−	1.24004e10i	0.0681997	−	0.0681997i	0.740384	+	0.672184i	$0.234644\pi$
$654$	3.81155e10	+	6.59276e10i	0.208349	+	0.360376i
$655$		−	1.17847e11i		−	0.640258i
$656$	1.51095e11	−	8.77134e10i	0.815894	−	0.473642i
$657$	−1.05527e11			−0.566370
$658$	7.36752e9	−	4.25947e9i	0.0393023	−	0.0227223i
$659$	7.14903e10	+	7.14903e10i	0.379058	+	0.379058i	0.870762	−	0.491704i	$-0.163626\pi$
$659$	7.14903e10	+	7.14903e10i	0.379058	+	0.379058i	−0.491704	+	0.870762i	$0.663626\pi$
$660$	−3.25241e10	+	8.75619e9i	−0.171407	+	0.0461466i
$661$	−8.83121e10	−	8.83121e10i	−0.462609	−	0.462609i	0.436900	−	0.899510i	$-0.356076\pi$
$661$	−8.83121e10	−	8.83121e10i	−0.462609	−	0.462609i	−0.899510	+	0.436900i	$0.856076\pi$
$662$	2.62312e11	+	7.01196e10i	1.36580	+	0.365096i
$663$	−2.03466e9			−0.0105302
$664$	2.34135e11	+	2.33303e11i	1.20446	+	1.20018i
$665$			5.34655e10i			0.273393i
$666$	−2.21730e10	−	5.92713e9i	−0.112701	−	0.0301264i
$667$	5.93067e9	−	5.93067e9i	0.0299641	−	0.0299641i
$668$	2.05499e10	−	3.56911e10i	0.103206	−	0.179248i
$669$	1.38399e11	−	1.38399e11i	0.690921	−	0.690921i
$670$	−6.41255e10	+	3.70736e10i	−0.318223	+	0.183978i
$671$		−	2.69692e10i		−	0.133039i
$672$	2.94090e10	−	7.97373e9i	0.144213	−	0.0391007i
$673$	2.35677e11			1.14883			0.574415	−	0.818564i	$-0.305229\pi$
$673$	2.35677e11			1.14883			0.574415	+	0.818564i	$0.305229\pi$
$674$	1.49097e11	+	2.57889e11i	0.722484	+	1.24967i
$675$	−1.35529e10	−	1.35529e10i	−0.0652857	−	0.0652857i
$676$	−1.80708e11	−	1.04046e11i	−0.865349	−	0.498241i
$677$	2.23573e11	+	2.23573e11i	1.06430	+	1.06430i	0.997785	+	0.0665155i	$0.0211882\pi$
$677$	2.23573e11	+	2.23573e11i	1.06430	+	1.06430i	0.0665155	+	0.997785i	$0.478812\pi$
$678$	1.29958e10	−	4.86163e10i	0.0615012	−	0.230072i
$679$	−1.60754e10			−0.0756280
$680$	5.20659e10	+	5.18809e10i	0.243511	+	0.242645i
$681$		−	2.69027e10i		−	0.125086i
$682$	−2.13018e10	+	7.96885e10i	−0.0984643	+	0.368348i
$683$	1.67100e11	−	1.67100e11i	0.767879	−	0.767879i	−0.209854	−	0.977733i	$-0.567299\pi$
$683$	1.67100e11	−	1.67100e11i	0.767879	−	0.767879i	0.977733	+	0.209854i	$0.0672989\pi$
$684$	2.77800e10	+	1.03186e11i	0.126913	+	0.471409i
$685$	−9.24568e10	+	9.24568e10i	−0.419930	+	0.419930i
$686$	5.54520e10	+	9.59141e10i	0.250392	+	0.433098i
$687$			1.11573e11i			0.500878i
$688$	3.25101e11	+	8.62841e10i	1.45099	+	0.385103i
$689$	−5.86204e9			−0.0260119
$690$	−8.40148e10	+	4.85725e10i	−0.370646	+	0.214286i
$691$	2.44135e11	+	2.44135e11i	1.07082	+	1.07082i	0.997293	+	0.0735320i	$0.0234271\pi$
$691$	2.44135e11	+	2.44135e11i	1.07082	+	1.07082i	0.0735320	+	0.997293i	$0.476573\pi$
$692$	3.07319e10	+	1.14151e11i	0.134018	+	0.497800i
$693$	5.99712e9	+	5.99712e9i	0.0260022	+	0.0260022i
$694$	−2.24007e11	−	5.98800e10i	−0.965658	−	0.258133i
$695$	1.29821e11			0.556426
$696$	−5.58417e9	+	9.94134e6i	−0.0237970	+	4.23651e-5i
$697$		−	1.06117e11i		−	0.449630i
$698$	−2.20362e11	−	5.89056e10i	−0.928356	−	0.248162i
$699$	8.36066e10	−	8.36066e10i	0.350213	−	0.350213i
$700$	−2.58347e10	−	1.48748e10i	−0.107600	−	0.0619525i
$701$	−3.11942e11	+	3.11942e11i	−1.29182	+	1.29182i	−0.358156	+	0.933662i	$0.616594\pi$
$701$	−3.11942e11	+	3.11942e11i	−1.29182	+	1.29182i	−0.933662	+	0.358156i	$0.883406\pi$
$702$	−1.54843e9	+	8.95213e8i	−0.00637593	+	0.00368619i
$703$		−	1.25190e11i		−	0.512565i
$704$	−7.37738e10	+	7.43011e10i	−0.300339	+	0.302485i
$705$	1.80455e10			0.0730489
$706$	9.93028e10	+	1.71762e11i	0.399708	+	0.691367i
$707$	2.80937e10	+	2.80937e10i	0.112443	+	0.112443i
$708$	−1.87943e10	+	3.26421e10i	−0.0747986	+	0.129911i
$709$	−1.56809e11	−	1.56809e11i	−0.620562	−	0.620562i	0.325113	−	0.945675i	$-0.394598\pi$
$709$	−1.56809e11	−	1.56809e11i	−0.620562	−	0.620562i	−0.945675	+	0.325113i	$0.894598\pi$
$710$	−3.54422e10	+	1.32587e11i	−0.139472	+	0.521755i
$711$	−8.14672e10			−0.318790
$712$	−2.15479e8	−	1.21037e11i	−0.000838464	−	0.470975i
$713$			2.37661e11i			0.919601i
$714$	4.77957e9	−	1.78800e10i	0.0183906	−	0.0687979i
$715$	2.17439e9	−	2.17439e9i	0.00831981	−	0.00831981i
$716$	−2.07952e11	+	5.59853e10i	−0.791246	+	0.213021i
$717$	1.68192e11	−	1.68192e11i	0.636398	−	0.636398i
$718$	−1.70345e11	−	2.94641e11i	−0.640959	−	1.10865i
$719$		−	6.88638e10i		−	0.257677i	−0.991666	−	0.128838i	$-0.958875\pi$
$719$		−	6.88638e10i		−	0.257677i	0.991666	−	0.128838i	$-0.0411249\pi$
$720$	6.24501e10	+	1.65747e10i	0.232383	+	0.0616759i
$721$	2.79592e10			0.103463
$722$	−2.69362e11	+	1.55729e11i	−0.991259	+	0.573088i
$723$	−8.08656e10	−	8.08656e10i	−0.295945	−	0.295945i
$724$	3.35758e11	−	9.03934e10i	1.22200	−	0.328990i
$725$	3.86309e9	+	3.86309e9i	0.0139825	+	0.0139825i
$726$	1.26797e11	+	3.38947e10i	0.456420	+	0.122007i
$727$	2.39781e11			0.858375			0.429187	−	0.903215i	$-0.358800\pi$
$727$	2.39781e11			0.858375			0.429187	+	0.903215i	$0.358800\pi$
$728$	−1.96358e9	+	1.97058e9i	−0.00699072	+	0.00701566i
$729$		−	1.04604e10i		−	0.0370370i
$730$	−3.36226e11	−	8.98778e10i	−1.18397	−	0.316491i
$731$	1.44463e11	−	1.44463e11i	0.505926	−	0.505926i
$732$	−2.58142e10	+	4.48343e10i	−0.0899113	+	0.156159i
$733$	2.95068e11	−	2.95068e11i	1.02213	−	1.02213i	0.0223799	−	0.999750i	$-0.492876\pi$
$733$	2.95068e11	−	2.95068e11i	1.02213	−	1.02213i	0.999750	−	0.0223799i	$-0.00712433\pi$
$734$	3.13170e11	−	1.81057e11i	1.07894	−	0.623778i
$735$			1.13393e11i			0.388541i
$736$	−1.50063e11	+	2.61707e11i	−0.511402	+	0.891876i
$737$	−6.40903e10			−0.217231
$738$	−4.66896e10	−	8.07580e10i	−0.157396	−	0.272245i
$739$	−1.75675e11	−	1.75675e11i	−0.589021	−	0.589021i	0.348345	−	0.937366i	$-0.386744\pi$
$739$	−1.75675e11	−	1.75675e11i	−0.589021	−	0.589021i	−0.937366	+	0.348345i	$0.886744\pi$
$740$	−6.55988e10	−	3.77698e10i	−0.218761	−	0.125956i
$741$	−6.89850e9	−	6.89850e9i	−0.0228814	−	0.0228814i
$742$	1.37703e10	−	5.15139e10i	0.0454286	−	0.169945i
$743$	−3.77030e11			−1.23715			−0.618573	−	0.785727i	$-0.712289\pi$
$743$	−3.77030e11			−1.23715			−0.618573	+	0.785727i	$0.712289\pi$
$744$	1.11689e11	−	1.12087e11i	0.364516	−	0.365816i
$745$			2.34645e11i			0.761703i
$746$	−1.33997e11	+	5.01273e11i	−0.432653	+	1.61852i
$747$	1.24791e11	−	1.24791e11i	0.400775	−	0.400775i
$748$	1.65331e10	+	6.14109e10i	0.0528140	+	0.196173i
$749$	−9.82231e10	+	9.82231e10i	−0.312095	+	0.312095i
$750$	−9.75877e10	−	1.68795e11i	−0.308425	−	0.533477i
$751$		−	4.09569e11i		−	1.28756i	−0.765211	−	0.643779i	$-0.777366\pi$
$751$		−	4.09569e11i		−	1.28756i	0.765211	−	0.643779i	$-0.222634\pi$
$752$	4.85147e10	−	2.81637e10i	0.151706	−	0.0880681i
$753$	−8.85557e10			−0.275446
$754$	4.41361e8	−	2.55169e8i	0.00136555	−	0.000789484i
$755$	−2.61329e11	−	2.61329e11i	−0.804267	−	0.804267i
$756$	−4.22949e9	−	1.57101e10i	−0.0129480	−	0.0480940i
$757$	−2.11515e11	−	2.11515e11i	−0.644106	−	0.644106i	0.307456	−	0.951562i	$-0.400522\pi$
$757$	−2.11515e11	−	2.11515e11i	−0.644106	−	0.644106i	−0.951562	+	0.307456i	$0.900522\pi$
$758$	1.10388e11	+	2.95082e10i	0.334384	+	0.0893853i
$759$	−8.39687e10			−0.253017
$760$	6.27421e8	+	3.52430e11i	0.00188064	+	1.05638i
$761$			6.04891e11i			1.80359i	0.432160	+	0.901797i	$0.357752\pi$
$761$			6.04891e11i			1.80359i	−0.432160	+	0.901797i	$0.642248\pi$
$762$	−2.65687e11	−	7.10216e10i	−0.788043	−	0.210654i
$763$	4.47184e10	−	4.47184e10i	0.131943	−	0.131943i
$764$	−4.66922e11	−	2.68839e11i	−1.37047	−	0.789077i
$765$	2.77505e10	−	2.77505e10i	0.0810261	−	0.0810261i
$766$	−4.93394e11	+	2.85252e11i	−1.43311	+	0.828540i
$767$		−	3.43877e9i		−	0.00993624i
$768$	1.93763e11	−	5.29058e10i	0.556962	−	0.152075i
$769$	6.91263e11			1.97669			0.988343	−	0.152241i	$-0.0486491\pi$
$769$	6.91263e11			1.97669			0.988343	+	0.152241i	$0.0486491\pi$
$770$	1.40001e10	+	2.42157e10i	0.0398262	+	0.0688865i
$771$	−2.41050e11	−	2.41050e11i	−0.682166	−	0.682166i
$772$	8.16750e10	−	1.41854e11i	0.229943	−	0.399366i
$773$	−2.00523e11	−	2.00523e11i	−0.561625	−	0.561625i	0.368144	−	0.929769i	$-0.379993\pi$
$773$	−2.00523e11	−	2.00523e11i	−0.561625	−	0.561625i	−0.929769	+	0.368144i	$0.879993\pi$
$774$	4.63791e10	−	1.73501e11i	0.129229	−	0.483435i
$775$	−1.54806e11			−0.429123
$776$	−1.05965e11	+	1.88646e8i	−0.292223	+	0.000520236i
$777$			1.90602e10i			0.0522929i
$778$	−3.89460e10	+	1.45694e11i	−0.106303	+	0.397671i
$779$	3.59789e11	−	3.59789e11i	0.977008	−	0.977008i
$780$	−5.69604e9	+	1.53350e9i	−0.0153884	+	0.00414290i
$781$	−8.39684e10	+	8.39684e10i	−0.225690	+	0.225690i
$782$	9.17130e10	+	1.58634e11i	0.245247	+	0.424199i
$783$			2.98159e9i			0.00793234i
$784$	1.76973e11	+	3.04852e11i	0.468427	+	0.806911i
$785$	−3.88084e11			−1.02199
$786$	−1.69340e11	+	9.79027e10i	−0.443680	+	0.256510i
$787$	9.69348e10	+	9.69348e10i	0.252686	+	0.252686i	0.822071	−	0.569385i	$-0.192819\pi$
$787$	9.69348e10	+	9.69348e10i	0.252686	+	0.252686i	−0.569385	+	0.822071i	$0.692819\pi$
$788$	4.66835e11	−	1.25682e11i	1.21076	−	0.325963i
$789$	2.93953e10	+	2.93953e10i	0.0758525	+	0.0758525i
$790$	−2.59569e11	−	6.93862e10i	−0.666415	−	0.178141i
$791$	−4.17912e10			−0.106753
$792$	3.96018e10	+	3.94610e10i	0.100650	+	0.100292i
$793$		−	4.72319e9i		−	0.0119438i
$794$	−1.64089e11	−	4.38632e10i	−0.412856	−	0.110362i
$795$	7.99516e10	−	7.99516e10i	0.200151	−	0.200151i
$796$	2.20956e11	−	3.83758e11i	0.550368	−	0.955883i
$797$	3.07150e11	−	3.07150e11i	0.761233	−	0.761233i	−0.215312	−	0.976545i	$-0.569077\pi$
$797$	3.07150e11	−	3.07150e11i	0.761233	−	0.761233i	0.976545	+	0.215312i	$0.0690768\pi$
$798$	7.68270e10	−	4.44169e10i	0.189453	−	0.109531i
$799$		−	3.40730e10i		−	0.0836033i
$800$	−1.70470e11	−	9.77475e10i	−0.416186	−	0.238641i
$801$	−6.46261e10			−0.156992
$802$	8.38341e9	+	1.45006e10i	0.0202639	+	0.0350501i
$803$	−2.12935e11	−	2.12935e11i	−0.512136	−	0.512136i
$804$	1.06546e11	+	6.13456e10i	0.254983	+	0.146811i
$805$	5.69869e10	+	5.69869e10i	0.135704	+	0.135704i
$806$	−3.73065e9	+	1.39561e10i	−0.00883983	+	0.0330692i
$807$	−4.72308e11			−1.11361
$808$	1.85516e11	+	1.84856e11i	0.435246	+	0.433699i
$809$			2.59226e11i			0.605181i	0.953121	+	0.302590i	$0.0978514\pi$
$809$			2.59226e11i			0.605181i	−0.953121	+	0.302590i	$0.902149\pi$
$810$	8.90916e9	−	3.33285e10i	0.0206965	−	0.0774241i
$811$	−1.25823e10	+	1.25823e10i	−0.0290854	+	0.0290854i	−0.721500	−	0.692415i	$-0.756547\pi$
$811$	−1.25823e10	+	1.25823e10i	−0.0290854	+	0.0290854i	0.692415	+	0.721500i	$0.256547\pi$
$812$	1.20556e9	+	4.47796e9i	0.00277310	+	0.0103005i
$813$	−1.13925e10	+	1.13925e10i	−0.0260769	+	0.0260769i
$814$	−3.27814e10	−	5.67013e10i	−0.0746672	−	0.129150i
$815$		−	1.17486e11i		−	0.266290i
$816$	3.12958e10	−	1.17916e11i	0.0705871	−	0.265958i
$817$	9.79599e11			2.19867
$818$	8.81296e10	−	5.09514e10i	0.196838	−	0.113800i
$819$	1.05029e9	+	1.05029e9i	0.00233440	+	0.00233440i
$820$	−7.99791e10	−	2.97075e11i	−0.176897	−	0.657069i
$821$	6.06554e10	+	6.06554e10i	0.133505	+	0.133505i	0.770701	−	0.637197i	$-0.219906\pi$
$821$	6.06554e10	+	6.06554e10i	0.133505	+	0.133505i	−0.637197	+	0.770701i	$0.719906\pi$
$822$	2.09665e11	+	5.60461e10i	0.459238	+	0.122760i
$823$	7.66725e10			0.167125			0.0835623	−	0.996503i	$-0.473370\pi$
$823$	7.66725e10			0.167125			0.0835623	+	0.996503i	$0.473370\pi$
$824$	1.84299e11	−	3.28103e8i	0.399775	−	0.000711707i
$825$		−	5.46951e10i		−	0.118068i
$826$	3.02189e10	+	8.07792e9i	0.0649170	+	0.0173532i
$827$	5.28707e11	−	5.28707e11i	1.13030	−	1.13030i	0.140172	−	0.990127i	$-0.455235\pi$
$827$	5.28707e11	−	5.28707e11i	1.13030	−	1.13030i	0.990127	−	0.140172i	$-0.0447654\pi$
$828$	1.39592e11	+	8.03727e10i	0.296988	+	0.170996i
$829$	−2.11019e11	+	2.11019e11i	−0.446790	+	0.446790i	−0.894286	−	0.447496i	$-0.852316\pi$
$829$	−2.11019e11	+	2.11019e11i	−0.446790	+	0.446790i	0.447496	+	0.894286i	$0.352316\pi$
$830$	5.03892e11	−	2.91321e11i	1.06176	−	0.613846i
$831$			4.99139e11i			1.04669i
$832$	−1.29202e10	+	1.30126e10i	−0.0269635	+	0.0271562i
$833$	2.14105e11			0.444679
$834$	−1.07850e11	−	1.86546e11i	−0.222924	−	0.385587i
$835$	−5.12819e10	−	5.12819e10i	−0.105492	−	0.105492i
$836$	−1.52157e11	+	2.64268e11i	−0.311507	+	0.541028i
$837$	−5.97409e10	−	5.97409e10i	−0.121722	−	0.121722i
$838$	1.67681e11	−	6.27282e11i	0.340022	−	1.27200i
$839$	−2.43038e11			−0.490486			−0.245243	−	0.969462i	$-0.578868\pi$
$839$	−2.43038e11			−0.490486			−0.245243	+	0.969462i	$0.578868\pi$
$840$	−9.55247e7	−	5.36574e10i	−0.000191866	−	0.107774i
$841$			4.99397e11i			0.998301i
$842$	8.97354e10	−	3.35694e11i	0.178532	−	0.667875i
$843$	−4.07047e11	+	4.07047e11i	−0.805998	+	0.805998i
$844$	−3.33001e11	+	8.96512e10i	−0.656260	+	0.176679i
$845$	−2.59646e11	+	2.59646e11i	−0.509278	+	0.509278i
$846$	−1.49915e10	−	2.59304e10i	−0.0292660	−	0.0506208i
$847$		−	1.08997e11i		−	0.211778i
$848$	9.01658e10	−	3.39727e11i	0.174365	−	0.656972i
$849$	−2.00956e11			−0.386786
$850$	−1.03330e11	+	5.97396e10i	−0.197948	+	0.114442i
$851$	−1.33435e11	−	1.33435e11i	−0.254421	−	0.254421i
$852$	2.19964e11	−	5.92190e10i	0.417439	−	0.112384i
$853$	−5.61796e11	−	5.61796e11i	−1.06116	−	1.06116i	−0.998003	−	0.0631599i	$-0.979882\pi$
$853$	−5.61796e11	−	5.61796e11i	−1.06116	−	1.06116i	−0.0631599	−	0.998003i	$-0.520118\pi$
$854$	4.15060e10	+	1.10951e10i	0.0780332	+	0.0208593i
$855$	1.88175e11			0.352126
$856$	−6.46307e11	+	6.48612e11i	−1.20377	+	1.20806i
$857$			7.68673e11i			1.42501i	0.701666	+	0.712506i	$0.252440\pi$
$857$			7.68673e11i			1.42501i	−0.701666	+	0.712506i	$0.747560\pi$
$858$	−4.93087e9	−	1.31809e9i	−0.00909860	−	0.00243218i
$859$	−8.28793e10	+	8.28793e10i	−0.152221	+	0.152221i	−0.779109	−	0.626888i	$-0.784328\pi$
$859$	−8.28793e10	+	8.28793e10i	−0.152221	+	0.152221i	0.626888	+	0.779109i	$0.284328\pi$
$860$	2.95544e11	−	5.13303e11i	0.540292	−	0.938383i
$861$	−5.47778e10	+	5.47778e10i	−0.0996763	+	0.0996763i
$862$	5.59553e10	−	3.23501e10i	0.101347	−	0.0585931i
$863$			5.83323e11i			1.05164i	0.850597	+	0.525819i	$0.176241\pi$
$863$			5.83323e11i			1.05164i	−0.850597	+	0.525819i	$0.823759\pi$
$864$	−2.80640e10	−	1.03507e11i	−0.0503611	−	0.185744i
$865$	2.08171e11			0.371839
$866$	1.20397e11	+	2.08248e11i	0.214064	+	0.370262i
$867$	1.78278e11	+	1.78278e11i	0.315515	+	0.315515i
$868$	−1.13878e11	−	6.55677e10i	−0.200615	−	0.115508i
$869$	−1.64387e11	−	1.64387e11i	−0.288263	−	0.288263i
$870$	−2.53945e9	+	9.49988e9i	−0.00443263	+	0.0165822i
$871$	−1.12243e10			−0.0195024
$872$	2.94247e11	−	2.95296e11i	0.508915	−	0.510730i
$873$			5.65784e10i			0.0974078i
$874$	−2.26895e11	+	8.48798e11i	−0.388847	+	1.45465i
$875$	−1.14493e11	+	1.14493e11i	−0.195320	+	0.195320i
$876$	1.50173e11	+	5.57805e11i	0.255021	+	0.947254i
$877$	−1.21676e11	+	1.21676e11i	−0.205686	+	0.205686i	−0.802431	−	0.596745i	$-0.796460\pi$
$877$	−1.21676e11	+	1.21676e11i	−0.205686	+	0.205686i	0.596745	+	0.802431i	$0.296460\pi$
$878$	2.02164e11	+	3.49678e11i	0.340193	+	0.588424i
$879$			5.92164e11i			0.991943i
$880$	9.25691e10	+	1.59459e11i	0.154360	+	0.265900i
$881$	−9.90255e11			−1.64378			−0.821890	−	0.569647i	$-0.807080\pi$
$881$	−9.90255e11			−1.64378			−0.821890	+	0.569647i	$0.807080\pi$
$882$	1.62940e11	−	9.42021e10i	0.269248	−	0.155663i
$883$	5.85135e11	+	5.85135e11i	0.962527	+	0.962527i	0.999323	−	0.0367957i	$-0.0117151\pi$
$883$	5.85135e11	+	5.85135e11i	0.962527	+	0.962527i	−0.0367957	+	0.999323i	$0.511715\pi$
$884$	2.89550e9	+	1.07551e10i	0.00474149	+	0.0176118i
$885$	4.69010e10	+	4.69010e10i	0.0764555	+	0.0764555i
$886$	−9.53053e10	−	2.54764e10i	−0.154661	−	0.0413431i
$887$	5.23134e11			0.845121			0.422560	−	0.906335i	$-0.361131\pi$
$887$	5.23134e11			0.845121			0.422560	+	0.906335i	$0.361131\pi$
$888$	2.23672e8	+	1.25639e11i	0.000359716	+	0.202057i
$889$			2.28388e11i			0.365650i
$890$	−2.05910e11	−	5.50425e10i	−0.328184	−	0.0877280i
$891$	2.11073e10	−	2.11073e10i	0.0334905	−	0.0334905i
$892$	−9.28521e11	−	5.34613e11i	−1.46667	−	0.844462i
$893$	1.15524e11	−	1.15524e11i	0.181663	−	0.181663i
$894$	3.37171e11	−	1.94933e11i	0.527838	−	0.305165i
$895$			3.79231e11i			0.591034i
$896$	−8.40001e10	−	1.44107e11i	−0.130331	−	0.223590i
$897$	−1.47057e10			−0.0227152
$898$	−3.92532e11	−	6.78955e11i	−0.603629	−	1.04408i
$899$	1.70284e10	+	1.70284e10i	0.0260697	+	0.0260697i
$900$	−5.23528e10	+	9.09268e10i	−0.0797939	+	0.138587i
$901$	−1.50962e11	−	1.50962e11i	−0.229070	−	0.229070i
$902$	6.87445e10	−	2.57168e11i	0.103851	−	0.388500i
$903$	−1.49144e11			−0.224313
$904$	−2.75476e11	+	4.90422e8i	−0.412487	+	0.000734339i
$905$		−	6.12304e11i		−	0.912794i
$906$	−1.58414e11	+	5.92617e11i	−0.235116	+	0.879552i
$907$	−6.89993e9	+	6.89993e9i	−0.0101957	+	0.0101957i	−0.712186	−	0.701991i	$-0.752295\pi$
$907$	−6.89993e9	+	6.89993e9i	−0.0101957	+	0.0101957i	0.701991	+	0.712186i	$0.252295\pi$
$908$	−1.42206e11	+	3.82849e10i	−0.209206	+	0.0563228i
$909$	9.88776e10	−	9.88776e10i	0.144825	−	0.144825i
$910$	2.45188e9	+	4.24097e9i	0.00357547	+	0.00618442i
$911$			1.09472e12i			1.58938i	0.607015	+	0.794691i	$0.292367\pi$
$911$			1.09472e12i			1.58938i	−0.607015	+	0.794691i	$0.707633\pi$
$912$	5.05902e11	−	2.93686e11i	0.731285	−	0.424525i
$913$	5.03615e11			0.724796
$914$	5.15045e11	−	2.97769e11i	0.738008	−	0.426673i
$915$	6.44190e10	+	6.44190e10i	0.0919029	+	0.0919029i
$916$	5.89766e11	−	1.58778e11i	0.837718	−	0.225532i
$917$	1.14863e11	+	1.14863e11i	0.162443	+	0.162443i
$918$	−6.29299e10	−	1.68220e10i	−0.0886107	−	0.0236868i
$919$	−7.73899e11			−1.08498			−0.542490	−	0.840062i	$-0.682519\pi$
$919$	−7.73899e11			−1.08498			−0.542490	+	0.840062i	$0.682519\pi$
$920$	3.76311e11	+	3.74973e11i	0.525285	+	0.523418i
$921$			7.33530e9i			0.0101948i
$922$	9.99690e11	+	2.67230e11i	1.38338	+	0.369796i
$923$	−1.47056e10	+	1.47056e10i	−0.0202618	+	0.0202618i
$924$	2.31659e10	−	4.02348e10i	0.0317806	−	0.0551967i
$925$	8.69165e10	−	8.69165e10i	0.118723	−	0.118723i
$926$	9.86528e11	−	5.70353e11i	1.34173	−	0.775711i
$927$		−	9.84042e10i		−	0.133258i
$928$	7.99930e9	+	2.95034e10i	0.0107860	+	0.0397814i
$929$	−1.24950e11			−0.167754			−0.0838770	−	0.996476i	$-0.526730\pi$
$929$	−1.24950e11			−0.167754			−0.0838770	+	0.996476i	$0.526730\pi$
$930$	−1.39463e11	−	2.41227e11i	−0.186435	−	0.322474i
$931$	7.25920e11	+	7.25920e11i	0.966252	+	0.966252i
$932$	−5.60917e11	−	3.22959e11i	−0.743421	−	0.428039i
$933$	3.51612e11	+	3.51612e11i	0.464020	+	0.464020i
$934$	−4.97391e10	+	1.86070e11i	−0.0653597	+	0.244506i
$935$	1.11992e11			0.146534
$936$	6.93558e9	+	6.91093e9i	0.00903607	+	0.00900395i
$937$		−	7.27224e11i		−	0.943430i	−0.881751	−	0.471715i	$-0.843635\pi$
$937$		−	7.27224e11i		−	0.943430i	0.881751	−	0.471715i	$-0.156365\pi$
$938$	2.63667e10	−	9.86361e10i	0.0340600	−	0.127416i
$939$	2.28477e11	−	2.28477e11i	0.293887	−	0.293887i
$940$	−2.56803e10	−	9.53874e10i	−0.0328919	−	0.122174i
$941$	−1.05516e11	+	1.05516e11i	−0.134574	+	0.134574i	−0.771185	−	0.636611i	$-0.780336\pi$
$941$	−1.05516e11	+	1.05516e11i	−0.134574	+	0.134574i	0.636611	+	0.771185i	$0.280336\pi$
$942$	3.22403e11	+	5.57655e11i	0.409445	+	0.708209i
$943$		−	7.66971e11i		−	0.969912i
$944$	1.99290e11	+	5.28928e10i	0.250956	+	0.0666053i
$945$	−2.86496e10			−0.0359246
$946$	4.43681e11	−	2.56511e11i	0.553996	−	0.320288i
$947$	3.92589e11	+	3.92589e11i	0.488133	+	0.488133i	0.907717	−	0.419584i	$-0.137824\pi$
$947$	3.92589e11	+	3.92589e11i	0.488133	+	0.488133i	−0.419584	+	0.907717i	$0.637824\pi$
$948$	1.15935e11	+	4.30630e11i	0.143542	+	0.533176i
$949$	−3.72920e10	−	3.72920e10i	−0.0459780	−	0.0459780i
$950$	−5.52886e11	−	1.47794e11i	−0.678799	−	0.181452i
$951$	−4.70424e11			−0.575132
$952$	−1.01314e11	+	1.80367e8i	−0.123345	+	0.000219588i
$953$		−	9.87035e11i		−	1.19663i	−0.801260	−	0.598317i	$-0.795837\pi$
$953$		−	9.87035e11i		−	1.19663i	0.801260	−	0.598317i	$-0.204163\pi$
$954$	−1.81306e11	−	4.84656e10i	−0.218887	−	0.0585113i
$955$	−6.70884e11	+	6.70884e11i	−0.806555	+	0.806555i
$956$	−1.12840e12	−	6.49699e11i	−1.35093	−	0.777823i
$957$	−6.01636e9	+	6.01636e9i	−0.00717276	+	0.00717276i
$958$	1.84514e10	−	1.06675e10i	0.0219062	−	0.0126649i
$959$		−	1.80230e11i		−	0.213085i
$960$	−1.25935e9	−	3.53694e11i	−0.00148272	−	0.416431i
$961$	1.70509e11			0.199919
$962$	−5.74110e9	−	9.93027e9i	−0.00670340	−	0.0115947i
$963$	3.45702e11	+	3.45702e11i	0.401973	+	0.401973i
$964$	−3.12371e11	+	5.42528e11i	−0.361711	+	0.628223i
$965$	−2.03819e11	−	2.03819e11i	−0.235036	−	0.235036i
$966$	3.45447e10	−	1.29229e11i	0.0396710	−	0.148406i
$967$	1.08595e12			1.24194			0.620972	−	0.783832i	$-0.286738\pi$
$967$	1.08595e12			1.24194			0.620972	+	0.783832i	$0.286738\pi$
$968$	−1.27908e9	−	7.18477e11i	−0.00145679	−	0.818298i
$969$		−	3.55307e11i		−	0.403003i
$970$	−4.81883e10	+	1.80269e11i	−0.0544320	+	0.203626i
$971$	−1.48411e11	+	1.48411e11i	−0.166951	+	0.166951i	−0.785638	−	0.618687i	$-0.787665\pi$
$971$	−1.48411e11	+	1.48411e11i	−0.166951	+	0.166951i	0.618687	+	0.785638i	$0.287665\pi$
$972$	−5.52926e10	+	1.48860e10i	−0.0619444	+	0.0166768i
$973$	−1.26533e11	+	1.26533e11i	−0.141174	+	0.141174i
$974$	1.74919e11	+	3.02554e11i	0.194357	+	0.336176i
$975$		−	9.57892e9i		−	0.0105998i
$976$	2.73727e11	+	7.26489e10i	0.301660	+	0.0800626i
$977$	−1.49627e11			−0.164222			−0.0821109	−	0.996623i	$-0.526166\pi$
$977$	−1.49627e11			−0.164222			−0.0821109	+	0.996623i	$0.526166\pi$
$978$	−1.68821e11	+	9.76024e10i	−0.184532	+	0.106685i
$979$	−1.30405e11	−	1.30405e11i	−0.141959	−	0.141959i
$980$	5.99387e11	−	1.61368e11i	0.649835	−	0.174950i
$981$	−1.57389e11	−	1.57389e11i	−0.169941	−	0.169941i
$982$	−1.35295e12	−	3.61662e11i	−1.45491	−	0.388917i
$983$	−6.11162e11			−0.654549			−0.327274	−	0.944929i	$-0.606130\pi$
$983$	−6.11162e11			−0.654549			−0.327274	+	0.944929i	$0.606130\pi$
$984$	−3.60437e11	+	3.61723e11i	−0.384459	+	0.385830i
$985$		−	8.51343e11i		−	0.904398i
$986$	1.79374e10	+	4.79490e9i	0.0189780	+	0.00507308i
$987$	−1.75885e10	+	1.75885e10i	−0.0185336	+	0.0185336i
$988$	−2.66478e10	+	4.62821e10i	−0.0279662	+	0.0485719i
$989$	1.04412e12	−	1.04412e12i	1.09135	−	1.09135i
$990$	8.52287e10	−	4.92743e10i	0.0887248	−	0.0512955i
$991$		−	4.84001e11i		−	0.501824i	−0.968010	−	0.250912i	$-0.919269\pi$
$991$		−	4.84001e11i		−	0.501824i	0.968010	−	0.250912i	$-0.0807305\pi$
$992$	−7.51425e11	−	4.30868e11i	−0.775960	−	0.444936i
$993$	−7.93616e11			−0.816232
$994$	−9.46842e10	−	1.63773e11i	−0.0969911	−	0.167764i
$995$	−5.51392e11	−	5.51392e11i	−0.562559	−	0.562559i
$996$	−8.37224e11	−	4.82047e11i	−0.850755	−	0.489838i
$997$	−1.86143e11	−	1.86143e11i	−0.188393	−	0.188393i	0.606608	−	0.795001i	$-0.292530\pi$
$997$	−1.86143e11	−	1.86143e11i	−0.188393	−	0.188393i	−0.795001	+	0.606608i	$0.792530\pi$
$998$	−2.31720e11	+	8.66846e11i	−0.233583	+	0.873816i
$999$	6.70834e10			0.0673524

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.9.l.a.43.22	yes	64
4.3	odd	2		192.9.l.a.79.29		64
16.3	odd	4	inner	48.9.l.a.19.22	✓	64
16.13	even	4		192.9.l.a.175.29		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.9.l.a.19.22	✓	64	16.3	odd	4	inner
48.9.l.a.43.22	yes	64	1.1	even	1	trivial
192.9.l.a.79.29		64	4.3	odd	2
192.9.l.a.175.29		64	16.13	even	4

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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	48.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(8.00822 + 13.8517i) q^{2} +(-33.0681 - 33.0681i) q^{3} +(-127.737 + 221.854i) q^{4} +(318.765 + 318.765i) q^{5} +(193.231 - 722.865i) q^{6} -621.384 q^{7} +(-4095.99 + 7.29198i) q^{8} +2187.00i q^{9} +O(q^{10})\)	\(q+(8.00822 + 13.8517i) q^{2} +(-33.0681 - 33.0681i) q^{3} +(-127.737 + 221.854i) q^{4} +(318.765 + 318.765i) q^{5} +(193.231 - 722.865i) q^{6} -621.384 q^{7} +(-4095.99 + 7.29198i) q^{8} +2187.00i q^{9} +(-1862.68 + 6968.17i) q^{10} +(-4413.00 + 4413.00i) q^{11} +(11560.3 - 3112.29i) q^{12} +(-772.862 + 772.862i) q^{13} +(-4976.18 - 8607.19i) q^{14} -21081.9i q^{15} +(-32902.6 - 56677.9i) q^{16} -39806.2 q^{17} +(-30293.6 + 17514.0i) q^{18} +(-134962. - 134962. i) q^{19} +(-111437. + 30001.4i) q^{20} +(20548.0 + 20548.0i) q^{21} +(-96467.7 - 25787.1i) q^{22} -287703. q^{23} +(135688. + 135206. i) q^{24} -187402. i q^{25} +(-16894.7 - 4516.17i) q^{26} +(72320.0 - 72320.0i) q^{27} +(79373.6 - 137857. i) q^{28} +(-20613.9 + 20613.9i) q^{29} +(292020. - 168829. i) q^{30} -826064. i q^{31} +(521591. - 909645. i) q^{32} +291859. q^{33} +(-318777. - 551382. i) q^{34} +(-198076. - 198076. i) q^{35} +(-485195. - 279360. i) q^{36} +(463796. + 463796. i) q^{37} +(788644. - 2.95026e6i) q^{38} +51114.2 q^{39} +(-1.30798e6 - 1.30334e6i) q^{40} +2.66585e6i q^{41} +(-120071. + 449177. i) q^{42} +(-3.62915e6 + 3.62915e6i) q^{43} +(-415341. - 1.54275e6i) q^{44} +(-697140. + 697140. i) q^{45} +(-2.30399e6 - 3.98516e6i) q^{46} +855972. i q^{47} +(-786203. + 2.96226e6i) q^{48} -5.37868e6 q^{49} +(2.59583e6 - 1.50076e6i) q^{50} +(1.31632e6 + 1.31632e6i) q^{51} +(-72739.9 - 270186. i) q^{52} +(3.79242e6 + 3.79242e6i) q^{53} +(1.58091e6 + 422597. i) q^{54} -2.81342e6 q^{55} +(2.54518e6 - 4531.12i) q^{56} +8.92591e6i q^{57} +(-450617. - 120456. i) q^{58} +(-2.22470e6 + 2.22470e6i) q^{59} +(4.67712e6 + 2.69294e6i) q^{60} +(-3.05565e6 + 3.05565e6i) q^{61} +(1.14424e7 - 6.61531e6i) q^{62} -1.35897e6i q^{63} +(1.67771e7 - 59735.8i) q^{64} -492723. q^{65} +(2.33727e6 + 4.04274e6i) q^{66} +(7.26153e6 + 7.26153e6i) q^{67} +(5.08472e6 - 8.83118e6i) q^{68} +(9.51378e6 + 9.51378e6i) q^{69} +(1.15744e6 - 4.32991e6i) q^{70} +1.90275e7 q^{71} +(-15947.6 - 8.95794e6i) q^{72} +4.82517e7i q^{73} +(-2.71016e6 + 1.01385e7i) q^{74} +(-6.19704e6 + 6.19704e6i) q^{75} +(4.71817e7 - 1.27023e7i) q^{76} +(2.74217e6 - 2.74217e6i) q^{77} +(409334. + 708016. i) q^{78} +3.72507e7i q^{79} +(7.57873e6 - 2.85552e7i) q^{80} -4.78297e6 q^{81} +(-3.69264e7 + 2.13487e7i) q^{82} +(-5.70604e7 - 5.70604e7i) q^{83} +(-7.18339e6 + 1.93392e6i) q^{84} +(-1.26888e7 - 1.26888e7i) q^{85} +(-7.93328e7 - 2.12067e7i) q^{86} +1.36333e6 q^{87} +(1.80435e7 - 1.81078e7i) q^{88} +2.95501e7i q^{89} +(-1.52394e7 - 4.07369e6i) q^{90} +(480244. - 480244. i) q^{91} +(3.67502e7 - 6.38280e7i) q^{92} +(-2.73164e7 + 2.73164e7i) q^{93} +(-1.18566e7 + 6.85481e6i) q^{94} -8.60427e7i q^{95} +(-4.73283e7 + 1.28322e7i) q^{96} +2.58703e7 q^{97} +(-4.30737e7 - 7.45037e7i) q^{98} +(-9.65124e6 - 9.65124e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 372 q^{4} + 17460 q^{8}+O(q^{10}) \) 64 * q - 372 * q^4 + 17460 * q^8	\( 64 q - 372 q^{4} + 17460 q^{8} - 13784 q^{10} + 39552 q^{11} - 22680 q^{12} + 116772 q^{14} - 161824 q^{16} - 26244 q^{18} - 167552 q^{19} + 690000 q^{20} - 1252768 q^{22} + 1691136 q^{23} - 74844 q^{24} - 1682100 q^{26} + 678600 q^{28} - 2132352 q^{29} - 2054808 q^{30} + 1407840 q^{32} - 3704544 q^{34} - 2415744 q^{35} - 1041012 q^{36} - 4720512 q^{37} + 2413320 q^{38} - 3544848 q^{40} + 9436500 q^{42} - 7244672 q^{43} - 3982056 q^{44} + 11165992 q^{46} - 9467280 q^{48} + 52706752 q^{49} + 17072676 q^{50} + 13862016 q^{51} - 22890864 q^{52} - 5358720 q^{53} - 4960116 q^{54} - 46326784 q^{55} - 9637152 q^{56} + 25732944 q^{58} + 44938752 q^{59} + 40927032 q^{60} + 24476032 q^{61} - 17024868 q^{62} - 116303448 q^{64} + 29941632 q^{65} - 56828952 q^{66} - 44244736 q^{67} - 12614400 q^{68} - 8636544 q^{69} - 60922560 q^{70} + 159664128 q^{71} - 18502020 q^{72} + 140654028 q^{74} + 12918528 q^{75} + 204842760 q^{76} - 94964352 q^{77} + 14001660 q^{78} + 38076648 q^{80} - 306110016 q^{81} - 260917000 q^{82} + 209328000 q^{83} - 127862712 q^{84} + 106960000 q^{85} - 123451824 q^{86} + 104240736 q^{88} + 53520264 q^{90} - 45401472 q^{91} + 351567216 q^{92} + 208488216 q^{94} + 49597920 q^{96} - 681890712 q^{98} + 86500224 q^{99}+O(q^{100}) \) 64 * q - 372 * q^4 + 17460 * q^8 - 13784 * q^10 + 39552 * q^11 - 22680 * q^12 + 116772 * q^14 - 161824 * q^16 - 26244 * q^18 - 167552 * q^19 + 690000 * q^20 - 1252768 * q^22 + 1691136 * q^23 - 74844 * q^24 - 1682100 * q^26 + 678600 * q^28 - 2132352 * q^29 - 2054808 * q^30 + 1407840 * q^32 - 3704544 * q^34 - 2415744 * q^35 - 1041012 * q^36 - 4720512 * q^37 + 2413320 * q^38 - 3544848 * q^40 + 9436500 * q^42 - 7244672 * q^43 - 3982056 * q^44 + 11165992 * q^46 - 9467280 * q^48 + 52706752 * q^49 + 17072676 * q^50 + 13862016 * q^51 - 22890864 * q^52 - 5358720 * q^53 - 4960116 * q^54 - 46326784 * q^55 - 9637152 * q^56 + 25732944 * q^58 + 44938752 * q^59 + 40927032 * q^60 + 24476032 * q^61 - 17024868 * q^62 - 116303448 * q^64 + 29941632 * q^65 - 56828952 * q^66 - 44244736 * q^67 - 12614400 * q^68 - 8636544 * q^69 - 60922560 * q^70 + 159664128 * q^71 - 18502020 * q^72 + 140654028 * q^74 + 12918528 * q^75 + 204842760 * q^76 - 94964352 * q^77 + 14001660 * q^78 + 38076648 * q^80 - 306110016 * q^81 - 260917000 * q^82 + 209328000 * q^83 - 127862712 * q^84 + 106960000 * q^85 - 123451824 * q^86 + 104240736 * q^88 + 53520264 * q^90 - 45401472 * q^91 + 351567216 * q^92 + 208488216 * q^94 + 49597920 * q^96 - 681890712 * q^98 + 86500224 * q^99

Introduction

L-functions

Modular forms

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