LMFDB - Embedded newform 91.8.r.a.25.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,8,Mod(25,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 3]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("91.25");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	91.r (of order $6$, 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:	$28.4270373191$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$64$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			25.2
Character	$\chi$	$=$	91.25
Dual form			91.8.r.a.51.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-18.4363 + 10.6442i) q^{2} +(-3.90686 + 6.76688i) q^{3} +(162.597 - 281.627i) q^{4} +(454.211 - 262.239i) q^{5} -166.341i q^{6} +(-231.201 - 877.547i) q^{7} +4197.94i q^{8} +(1062.97 + 1841.12i) q^{9} +O(q^{10})$	\(q+(-18.4363 + 10.6442i) q^{2} +(-3.90686 + 6.76688i) q^{3} +(162.597 - 281.627i) q^{4} +(454.211 - 262.239i) q^{5} -166.341i q^{6} +(-231.201 - 877.547i) q^{7} +4197.94i q^{8} +(1062.97 + 1841.12i) q^{9} +(-5582.63 + 9669.41i) q^{10} +(5052.11 + 2916.84i) q^{11} +(1270.49 + 2200.55i) q^{12} +(3083.75 - 7296.51i) q^{13} +(13603.3 + 13717.7i) q^{14} +4098.12i q^{15} +(-23871.2 - 41346.2i) q^{16} +(-8861.49 + 15348.5i) q^{17} +(-39194.5 - 22629.0i) q^{18} +(19720.3 - 11385.5i) q^{19} -170557. i q^{20} +(6841.53 + 1863.94i) q^{21} -124189. q^{22} +(39927.3 + 69156.1i) q^{23} +(-28407.0 - 16400.8i) q^{24} +(98475.9 - 170565. i) q^{25} +(20812.6 + 167344. i) q^{26} -33700.2 q^{27} +(-284733. - 77574.2i) q^{28} +40348.1 q^{29} +(-43621.2 - 75554.1i) q^{30} +(25269.6 + 14589.4i) q^{31} +(414845. + 239511. i) q^{32} +(-39475.8 + 22791.4i) q^{33} -377293. i q^{34} +(-335141. - 337961. i) q^{35} +691345. q^{36} +(182330. - 105268. i) q^{37} +(-242379. + 419813. i) q^{38} +(37326.8 + 49373.8i) q^{39} +(1.10086e6 + 1.90675e6i) q^{40} +420095. i q^{41} +(-145972. + 38458.4i) q^{42} -611293. q^{43} +(1.64292e6 - 948539. i) q^{44} +(965628. + 557505. i) q^{45} +(-1.47222e6 - 849986. i) q^{46} +(31895.3 - 18414.7i) q^{47} +373046. q^{48} +(-716635. + 405780. i) q^{49} +4.19278e6i q^{50} +(-69241.2 - 119929. i) q^{51} +(-1.55348e6 - 2.05486e6i) q^{52} +(328129. - 568336. i) q^{53} +(621305. - 358711. i) q^{54} +3.05963e6 q^{55} +(3.68389e6 - 970570. i) q^{56} +177927. i q^{57} +(-743868. + 429472. i) q^{58} +(-151043. - 87204.7i) q^{59} +(1.15414e6 + 666343. i) q^{60} +(92112.7 + 159544. i) q^{61} -621169. q^{62} +(1.36991e6 - 1.35848e6i) q^{63} -4.08656e6 q^{64} +(-512755. - 4.12283e6i) q^{65} +(485191. - 840375. i) q^{66} +(-148899. - 85967.1i) q^{67} +(2.88170e6 + 4.99126e6i) q^{68} -623961. q^{69} +(9.77607e6 + 2.66344e6i) q^{70} -2.58438e6i q^{71} +(-7.72893e6 + 4.46230e6i) q^{72} +(-157127. - 90717.0i) q^{73} +(-2.24099e6 + 3.88152e6i) q^{74} +(769463. + 1.33275e6i) q^{75} -7.40502e6i q^{76} +(1.39161e6 - 5.10784e6i) q^{77} +(-1.21371e6 - 512955. i) q^{78} +(3.26117e6 + 5.64851e6i) q^{79} +(-2.16852e7 - 1.25199e7i) q^{80} +(-2.19306e6 + 3.79849e6i) q^{81} +(-4.47156e6 - 7.74497e6i) q^{82} +4.76102e6i q^{83} +(1.63735e6 - 1.62368e6i) q^{84} +9.29530e6i q^{85} +(1.12700e7 - 6.50671e6i) q^{86} +(-157634. + 273031. i) q^{87} +(-1.22447e7 + 2.12085e7i) q^{88} +(3.55800e6 - 2.05421e6i) q^{89} -2.37368e7 q^{90} +(-7.11600e6 - 1.01917e6i) q^{91} +2.59683e7 q^{92} +(-197449. + 113997. i) q^{93} +(-392020. + 678998. i) q^{94} +(5.97145e6 - 1.03429e7i) q^{95} +(-3.24149e6 + 1.87147e6i) q^{96} -1.45822e7i q^{97} +(8.89287e6 - 1.51091e7i) q^{98} +1.24021e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 52 q^{3} + 4094 q^{4} - 44052 q^{9}+O(q^{10}) $ 128 * q + 52 * q^3 + 4094 * q^4 - 44052 * q^9	$ 128 q + 52 q^{3} + 4094 q^{4} - 44052 q^{9} - 4514 q^{10} + 2090 q^{12} + 11132 q^{13} + 18748 q^{14} - 230074 q^{16} - 28972 q^{17} + 179920 q^{22} + 20508 q^{23} + 920040 q^{25} + 144684 q^{26} - 357584 q^{27} + 44600 q^{29} + 46580 q^{30} - 1216824 q^{35} - 4529248 q^{36} - 129032 q^{38} + 104546 q^{39} + 2082020 q^{40} + 2426496 q^{42} - 1434416 q^{43} - 3783940 q^{48} - 34428 q^{49} - 756008 q^{51} - 2348612 q^{52} + 1103824 q^{53} - 4216216 q^{55} + 8135574 q^{56} + 531568 q^{61} + 26627120 q^{62} - 27402496 q^{64} - 7495542 q^{65} + 2808402 q^{66} + 531760 q^{68} + 24238760 q^{69} - 7462590 q^{74} - 1547944 q^{75} - 1811116 q^{77} - 31233508 q^{78} + 2961020 q^{79} - 34639872 q^{81} - 10292872 q^{82} + 43455484 q^{87} + 21936790 q^{88} - 58442348 q^{90} + 16479848 q^{91} + 24834900 q^{92} + 26036992 q^{94} + 89048 q^{95}+O(q^{100}) $ 128 * q + 52 * q^3 + 4094 * q^4 - 44052 * q^9 - 4514 * q^10 + 2090 * q^12 + 11132 * q^13 + 18748 * q^14 - 230074 * q^16 - 28972 * q^17 + 179920 * q^22 + 20508 * q^23 + 920040 * q^25 + 144684 * q^26 - 357584 * q^27 + 44600 * q^29 + 46580 * q^30 - 1216824 * q^35 - 4529248 * q^36 - 129032 * q^38 + 104546 * q^39 + 2082020 * q^40 + 2426496 * q^42 - 1434416 * q^43 - 3783940 * q^48 - 34428 * q^49 - 756008 * q^51 - 2348612 * q^52 + 1103824 * q^53 - 4216216 * q^55 + 8135574 * q^56 + 531568 * q^61 + 26627120 * q^62 - 27402496 * q^64 - 7495542 * q^65 + 2808402 * q^66 + 531760 * q^68 + 24238760 * q^69 - 7462590 * q^74 - 1547944 * q^75 - 1811116 * q^77 - 31233508 * q^78 + 2961020 * q^79 - 34639872 * q^81 - 10292872 * q^82 + 43455484 * q^87 + 21936790 * q^88 - 58442348 * q^90 + 16479848 * q^91 + 24834900 * q^92 + 26036992 * q^94 + 89048 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−18.4363	+	10.6442i	−1.62955	+	0.940822i	−0.645324	+	0.763909i	$0.723278\pi$
$2$	−18.4363	+	10.6442i	−1.62955	+	0.940822i	−0.984227	+	0.176913i	$0.943389\pi$
$3$	−3.90686	+	6.76688i	−0.0835418	+	0.144699i	−0.904769	−	0.425903i	$-0.859957\pi$
$3$	−3.90686	+	6.76688i	−0.0835418	+	0.144699i	0.821227	+	0.570601i	$0.193290\pi$
$4$	162.597	−	281.627i	1.27029	−	2.20021i
$5$	454.211	−	262.239i	1.62503	−	0.938214i	0.639489	−	0.768800i	$-0.279146\pi$
$5$	454.211	−	262.239i	1.62503	−	0.938214i	0.985545	−	0.169414i	$-0.0541875\pi$
$6$		−	166.341i		−	0.314392i
$7$	−231.201	−	877.547i	−0.254769	−	0.967002i
$7$	−231.201	−	877.547i	−0.254769	−	0.967002i
$8$			4197.94i			2.89882i
$9$	1062.97	+	1841.12i	0.486042	+	0.841849i
$10$	−5582.63	+	9669.41i	−1.76538	+	3.05773i
$11$	5052.11	+	2916.84i	1.14445	+	0.660751i	0.947530	−	0.319668i	$-0.103571\pi$
$11$	5052.11	+	2916.84i	1.14445	+	0.660751i	0.196924	+	0.980419i	$0.436905\pi$
$12$	1270.49	+	2200.55i	0.212245	+	0.367618i
$13$	3083.75	−	7296.51i	0.389294	−	0.921114i
$13$	3083.75	−	7296.51i	0.389294	−	0.921114i
$14$	13603.3	+	13717.7i	1.32494	+	1.33609i
$15$			4098.12i			0.313520i
$16$	−23871.2	−	41346.2i	−1.45698	−	2.52357i
$17$	−8861.49	+	15348.5i	−0.437457	+	0.757698i	−0.997493	−	0.0707709i	$-0.977454\pi$
$17$	−8861.49	+	15348.5i	−0.437457	+	0.757698i	0.560036	+	0.828468i	$0.310787\pi$
$18$	−39194.5	−	22629.0i	−1.58406	−	0.914557i
$19$	19720.3	−	11385.5i	0.659593	−	0.380816i	−0.132529	−	0.991179i	$-0.542310\pi$
$19$	19720.3	−	11385.5i	0.659593	−	0.380816i	0.792122	+	0.610363i	$0.208976\pi$
$20$		−	170557.i		−	4.76722i
$21$	6841.53	+	1863.94i	0.161208	+	0.0439203i
$22$	−124189.			−2.48659
$23$	39927.3	+	69156.1i	0.684262	+	1.18518i	0.973668	+	0.227970i	$0.0732088\pi$
$23$	39927.3	+	69156.1i	0.684262	+	1.18518i	−0.289406	+	0.957206i	$0.593458\pi$
$24$	−28407.0	−	16400.8i	−0.419456	−	0.242173i
$25$	98475.9	−	170565.i	1.26049	−	2.18323i
$26$	20812.6	+	167344.i	0.232230	+	1.86726i
$27$	−33700.2			−0.329503
$28$	−284733.	−	77574.2i	−2.45124	−	0.667828i
$29$	40348.1			0.307206			0.153603	−	0.988133i	$-0.450912\pi$
$29$	40348.1			0.307206			0.153603	+	0.988133i	$0.450912\pi$
$30$	−43621.2	−	75554.1i	−0.294967	−	0.510897i
$31$	25269.6	+	14589.4i	0.152346	+	0.0879572i	0.574235	−	0.818690i	$-0.305299\pi$
$31$	25269.6	+	14589.4i	0.152346	+	0.0879572i	−0.421889	+	0.906648i	$0.638633\pi$
$32$	414845.	+	239511.i	2.23801	+	1.29211i
$33$	−39475.8	+	22791.4i	−0.191219	+	0.110401i
$34$		−	377293.i		−	1.64628i
$35$	−335141.	−	337961.i	−1.32126	−	1.33238i
$36$	691345.			2.46966
$37$	182330.	−	105268.i	0.591770	−	0.341659i	−0.174027	−	0.984741i	$-0.555678\pi$
$37$	182330.	−	105268.i	0.591770	−	0.341659i	0.765797	+	0.643082i	$0.222345\pi$
$38$	−242379.	+	419813.i	−0.716560	+	1.24112i
$39$	37326.8	+	49373.8i	0.100762	+	0.133282i
$40$	1.10086e6	+	1.90675e6i	2.71972	+	4.71069i
$41$			420095.i			0.951927i	0.879465	+	0.475963i	$0.157901\pi$
$41$			420095.i			0.951927i	−0.879465	+	0.475963i	$0.842099\pi$
$42$	−145972.	+	38458.4i	−0.304017	+	0.0800974i
$43$	−611293.			−1.17249			−0.586246	−	0.810133i	$-0.699395\pi$
$43$	−611293.			−1.17249			−0.586246	+	0.810133i	$0.699395\pi$
$44$	1.64292e6	−	948539.i	2.90758	−	1.67869i
$45$	965628.	+	557505.i	1.57967	+	0.912022i
$46$	−1.47222e6	−	849986.i	−2.23008	−	1.28754i
$47$	31895.3	−	18414.7i	0.0448109	−	0.0258716i	−0.477427	−	0.878671i	$-0.658431\pi$
$47$	31895.3	−	18414.7i	0.0448109	−	0.0258716i	0.522238	+	0.852800i	$0.325097\pi$
$48$	373046.			0.486876
$49$	−716635.	+	405780.i	−0.870185	+	0.492725i
$50$			4.19278e6i			4.74359i
$51$	−69241.2	−	119929.i	−0.0730918	−	0.126599i
$52$	−1.55348e6	−	2.05486e6i	−1.53213	−	2.02661i
$53$	328129.	−	568336.i	0.302746	−	0.524372i	−0.674011	−	0.738722i	$-0.735430\pi$
$53$	328129.	−	568336.i	0.302746	−	0.524372i	0.976757	+	0.214349i	$0.0687631\pi$
$54$	621305.	−	358711.i	0.536941	−	0.310003i
$55$	3.05963e6			2.47970
$56$	3.68389e6	−	970570.i	2.80317	−	0.738531i
$57$			177927.i			0.127256i
$58$	−743868.	+	429472.i	−0.500608	+	0.289026i
$59$	−151043.	−	87204.7i	−0.0957455	−	0.0552787i	0.451363	−	0.892341i	$-0.350938\pi$
$59$	−151043.	−	87204.7i	−0.0957455	−	0.0552787i	−0.547108	+	0.837062i	$0.684271\pi$
$60$	1.15414e6	+	666343.i	0.689809	+	0.398262i
$61$	92112.7	+	159544.i	0.0519595	+	0.0899965i	0.890835	−	0.454326i	$-0.150120\pi$
$61$	92112.7	+	159544.i	0.0519595	+	0.0899965i	−0.838876	+	0.544323i	$0.816787\pi$
$62$	−621169.			−0.331008
$63$	1.36991e6	−	1.35848e6i	0.690241	−	0.684480i
$64$	−4.08656e6			−1.94862
$65$	−512755.	−	4.12283e6i	−0.231586	−	1.86208i
$66$	485191.	−	840375.i	0.207734	−	0.359807i
$67$	−148899.	−	85967.1i	−0.0604827	−	0.0349197i	0.469454	−	0.882957i	$-0.344451\pi$
$67$	−148899.	−	85967.1i	−0.0604827	−	0.0349197i	−0.529936	+	0.848037i	$0.677784\pi$
$68$	2.88170e6	+	4.99126e6i	1.11139	+	1.92499i
$69$	−623961.			−0.228658
$70$	9.77607e6	+	2.66344e6i	3.40660	+	0.928112i
$71$		−	2.58438e6i		−	0.856943i	−0.903555	−	0.428472i	$-0.859052\pi$
$71$		−	2.58438e6i		−	0.856943i	0.903555	−	0.428472i	$-0.140948\pi$
$72$	−7.72893e6	+	4.46230e6i	−2.44037	+	1.40895i
$73$	−157127.	−	90717.0i	−0.0472737	−	0.0272935i	0.476177	−	0.879350i	$-0.342022\pi$
$73$	−157127.	−	90717.0i	−0.0472737	−	0.0272935i	−0.523451	+	0.852056i	$0.675356\pi$
$74$	−2.24099e6	+	3.88152e6i	−0.642880	+	1.11350i
$75$	769463.	+	1.33275e6i	0.210607	+	0.364783i
$76$		−	7.40502e6i		−	1.93499i
$77$	1.39161e6	−	5.10784e6i	0.347375	−	1.27503i
$78$	−1.21371e6	−	512955.i	−0.289590	−	0.122391i
$79$	3.26117e6	+	5.64851e6i	0.744180	+	1.28896i	0.950577	+	0.310490i	$0.100493\pi$
$79$	3.26117e6	+	5.64851e6i	0.744180	+	1.28896i	−0.206396	+	0.978468i	$0.566174\pi$
$80$	−2.16852e7	−	1.25199e7i	−4.73530	−	2.73393i
$81$	−2.19306e6	+	3.79849e6i	−0.458514	+	0.794170i
$82$	−4.47156e6	−	7.74497e6i	−0.895593	−	1.55121i
$83$			4.76102e6i			0.913959i	0.889477	+	0.456979i	$0.151069\pi$
$83$			4.76102e6i			0.913959i	−0.889477	+	0.456979i	$0.848931\pi$
$84$	1.63735e6	−	1.62368e6i	0.301414	−	0.298899i
$85$			9.29530e6i			1.64171i
$86$	1.12700e7	−	6.50671e6i	1.91063	−	1.10311i
$87$	−157634.	+	273031.i	−0.0256645	+	0.0444523i
$88$	−1.22447e7	+	2.12085e7i	−1.91540	+	3.31757i
$89$	3.55800e6	−	2.05421e6i	0.534984	−	0.308873i	−0.208060	−	0.978116i	$-0.566715\pi$
$89$	3.55800e6	−	2.05421e6i	0.534984	−	0.308873i	0.743044	+	0.669243i	$0.233382\pi$
$90$	−2.37368e7			−3.43220
$91$	−7.11600e6	−	1.01917e6i	−0.989899	−	0.141776i
$92$	2.59683e7			3.47685
$93$	−197449.	+	113997.i	−0.0254546	+	0.0146962i
$94$	−392020.	+	678998.i	−0.0486811	+	0.0843181i
$95$	5.97145e6	−	1.03429e7i	0.714574	−	1.23768i
$96$	−3.24149e6	+	1.87147e6i	−0.373934	+	0.215891i
$97$		−	1.45822e7i		−	1.62227i	−0.584860	−	0.811134i	$-0.698851\pi$
$97$		−	1.45822e7i		−	1.62227i	0.584860	−	0.811134i	$-0.301149\pi$
$98$	8.89287e6	−	1.51091e7i	0.954444	−	1.62161i
$99$			1.24021e7i			1.28461i
$100$	−3.20238e7	−	5.54668e7i	−3.20238	−	5.54668i
$101$	6.34466e6	−	1.09893e7i	0.612751	−	1.06132i	−0.378024	−	0.925796i	$-0.623396\pi$
$101$	6.34466e6	−	1.09893e7i	0.612751	−	1.06132i	0.990775	−	0.135519i	$-0.0432703\pi$
$102$	2.55310e6	+	1.47403e6i	0.238214	+	0.137533i
$103$	714415.	+	1.23740e6i	0.0644199	+	0.111579i	0.896437	−	0.443172i	$-0.146147\pi$
$103$	714415.	+	1.23740e6i	0.0644199	+	0.111579i	−0.832017	+	0.554751i	$0.812814\pi$
$104$	3.06303e7	+	1.29454e7i	2.67015	+	1.12849i
$105$	3.59630e6	−	947492.i	0.303175	−	0.0798754i
$106$			1.39707e7i			1.13932i
$107$	−4.63241e6	−	8.02356e6i	−0.365564	−	0.633176i	0.623302	−	0.781981i	$-0.285791\pi$
$107$	−4.63241e6	−	8.02356e6i	−0.365564	−	0.633176i	−0.988867	+	0.148805i	$0.952457\pi$
$108$	−5.47955e6	+	9.49086e6i	−0.418564	+	0.724974i
$109$	3.49461e6	+	2.01761e6i	0.258467	+	0.149226i	0.623635	−	0.781715i	$-0.285655\pi$
$109$	3.49461e6	+	2.01761e6i	0.258467	+	0.149226i	−0.365168	+	0.930942i	$0.618988\pi$
$110$	−5.64081e7	+	3.25673e7i	−4.04080	+	2.33296i
$111$			1.64508e6i			0.114171i
$112$	−3.07642e7	+	3.05074e7i	−2.06910	+	2.05184i
$113$	2.58758e6			0.168702			0.0843509	−	0.996436i	$-0.473118\pi$
$113$	2.58758e6			0.168702			0.0843509	+	0.996436i	$0.473118\pi$
$114$	−1.89388e6	−	3.28030e6i	−0.119725	−	0.207371i
$115$	3.62708e7	+	2.09410e7i	2.22390	+	1.28397i
$116$	6.56048e6	−	1.13631e7i	0.390241	−	0.675917i
$117$	1.67117e7	−	2.07843e6i	0.964651	−	0.119973i
$118$	3.71289e6			0.208030
$119$	1.55179e7	+	4.22777e6i	0.844146	+	0.229983i
$120$	−1.72037e7			−0.908840
$121$	7.27228e6	+	1.25960e7i	0.373183	+	0.646372i
$122$	−3.39643e6	−	1.96093e6i	−0.169341	−	0.0977692i
$123$	−2.84273e6	−	1.64125e6i	−0.137742	−	0.0795256i
$124$	8.21752e6	−	4.74439e6i	0.387048	−	0.223462i
$125$		−	6.23219e7i		−	2.85401i
$126$	−1.07961e7	+	3.96269e7i	−0.480808	+	1.76479i
$127$	1.80341e7			0.781234			0.390617	−	0.920553i	$-0.372262\pi$
$127$	1.80341e7			0.781234			0.390617	+	0.920553i	$0.372262\pi$
$128$	2.22407e7	−	1.28407e7i	0.937376	−	0.541194i
$129$	2.38824e6	−	4.13655e6i	0.0979520	−	0.169658i
$130$	5.33374e7	+	7.05517e7i	2.12927	+	2.81648i
$131$	5.09483e6	+	8.82450e6i	0.198007	+	0.342958i	0.947882	−	0.318622i	$-0.103220\pi$
$131$	5.09483e6	+	8.82450e6i	0.198007	+	0.342958i	−0.749875	+	0.661579i	$0.769887\pi$
$132$			1.48232e7i			0.560963i
$133$	−1.45507e7	−	1.46732e7i	−0.536294	−	0.540808i
$134$	3.66020e6			0.131413
$135$	−1.53070e7	+	8.83749e6i	−0.535453	+	0.309144i
$136$	−6.44323e7	−	3.72000e7i	−2.19643	−	1.26811i
$137$	1.78225e7	+	1.02898e7i	0.592171	+	0.341890i	0.765956	−	0.642894i	$-0.222266\pi$
$137$	1.78225e7	+	1.02898e7i	0.592171	+	0.341890i	−0.173784	+	0.984784i	$0.555600\pi$
$138$	1.15035e7	−	6.64156e6i	0.372609	−	0.215126i
$139$	4.89886e7			1.54719			0.773593	−	0.633682i	$-0.218457\pi$
$139$	4.89886e7			1.54719			0.773593	+	0.633682i	$0.218457\pi$
$140$	−1.49672e8	+	3.94330e7i	−4.60991	+	1.21454i
$141$			287775.i			0.00864543i
$142$	2.75086e7	+	4.76463e7i	0.806231	+	1.39643i
$143$	3.68621e7	−	2.78680e7i	1.05416	−	0.796946i
$144$	5.07490e7	−	8.78998e7i	1.41631	−	2.45312i
$145$	1.83265e7	−	1.05808e7i	0.499221	−	0.288225i
$146$	3.86243e6			0.102713
$147$	53926.0	−	6.43471e6i	0.00140019	−	0.167078i
$148$		−	6.84654e7i		−	1.73602i
$149$	−5.75431e7	+	3.32225e7i	−1.42509	+	0.822774i	−0.996728	−	0.0808345i	$-0.974241\pi$
$149$	−5.75431e7	+	3.32225e7i	−1.42509	+	0.822774i	−0.428359	+	0.903609i	$0.640908\pi$
$150$	−2.83720e7	−	1.63806e7i	−0.686390	−	0.396288i
$151$	−3.11294e7	−	1.79726e7i	−0.735786	−	0.424806i	0.0847491	−	0.996402i	$-0.472991\pi$
$151$	−3.11294e7	−	1.79726e7i	−0.735786	−	0.424806i	−0.820535	+	0.571596i	$0.806324\pi$
$152$	4.77958e7	+	8.27848e7i	1.10392	+	1.91204i
$153$	−3.76781e7			−0.850489
$154$	2.87127e7	+	1.08982e8i	0.633508	+	2.40454i
$155$	1.53036e7			0.330091
$156$	1.99742e7	−	2.48419e6i	0.421244	−	0.0523899i
$157$	−5.92379e6	+	1.02603e7i	−0.122166	+	0.211598i	−0.920622	−	0.390456i	$-0.872317\pi$
$157$	−5.92379e6	+	1.02603e7i	−0.122166	+	0.211598i	0.798456	+	0.602054i	$0.205651\pi$
$158$	−1.20247e8	−	6.94249e7i	−2.42536	−	1.40028i
$159$	2.56391e6	+	4.44082e6i	0.0505839	+	0.0876140i
$160$	2.51236e8			4.84912
$161$	5.14565e7	−	5.10271e7i	0.971739	−	0.963629i
$162$		−	9.33733e7i		−	1.72552i
$163$	−4.52615e7	+	2.61318e7i	−0.818602	+	0.472620i	−0.849934	−	0.526889i	$-0.823358\pi$
$163$	−4.52615e7	+	2.61318e7i	−0.818602	+	0.472620i	0.0313323	+	0.999509i	$0.490025\pi$
$164$	1.18310e8	+	6.83062e7i	2.09444	+	1.20922i
$165$	−1.19536e7	+	2.07042e7i	−0.207159	+	0.358809i
$166$	−5.06772e7	−	8.77754e7i	−0.859872	−	1.48934i
$167$			4.97136e7i			0.825976i	0.910736	+	0.412988i	$0.135515\pi$
$167$			4.97136e7i			0.825976i	−0.910736	+	0.412988i	$0.864485\pi$
$168$	−7.82473e6	+	2.87204e7i	−0.127317	+	0.467313i
$169$	−4.37295e7	−	4.50012e7i	−0.696901	−	0.717167i
$170$	−9.89409e7	−	1.71371e8i	−1.54456	−	2.67525i
$171$	4.19243e7	+	2.42050e7i	0.641179	+	0.370185i
$172$	−9.93945e7	+	1.72156e8i	−1.48940	+	2.57972i
$173$	−3.54218e7	−	6.13524e7i	−0.520127	−	0.900887i	−0.999726	−	0.0233989i	$-0.992551\pi$
$173$	−3.54218e7	−	6.13524e7i	−0.520127	−	0.900887i	0.479599	−	0.877488i	$-0.340782\pi$
$174$		−	6.71155e6i		−	0.0965830i
$175$	−1.72447e8	−	4.69823e7i	−2.43233	−	0.662676i
$176$		−	2.78514e8i		−	3.85082i
$177$	1.18021e6	−	681394.i	0.0159975	−	0.00923616i
$178$	−4.37308e7	+	7.57439e7i	−0.581189	+	1.00665i
$179$	1.50011e6	−	2.59827e6i	0.0195496	−	0.0338609i	−0.856085	−	0.516835i	$-0.827110\pi$
$179$	1.50011e6	−	2.59827e6i	0.0195496	−	0.0338609i	0.875635	+	0.482974i	$0.160443\pi$
$180$	3.14017e8	−	1.81298e8i	4.01328	−	2.31707i
$181$	1.16034e8			1.45449			0.727244	−	0.686379i	$-0.240801\pi$
$181$	1.16034e8			1.45449			0.727244	+	0.686379i	$0.240801\pi$
$182$	1.42041e8	−	5.69542e7i	1.74648	−	0.700287i
$183$	−1.43949e6			−0.0173631
$184$	−2.90313e8	+	1.67613e8i	−3.43562	+	1.98355i
$185$	5.52110e7	−	9.56282e7i	0.641098	−	1.11041i
$186$	2.42682e6	−	4.20338e6i	0.0276530	−	0.0478964i
$187$	−8.95384e7	+	5.16950e7i	−1.00130	+	0.578100i
$188$		−	1.19767e7i		−	0.131458i
$189$	7.79152e6	+	2.95735e7i	0.0839472	+	0.318630i
$190$			2.54245e8i			2.68915i
$191$	3.37228e7	+	5.84097e7i	0.350193	+	0.606552i	0.986283	−	0.165063i	$-0.0527827\pi$
$191$	3.37228e7	+	5.84097e7i	0.350193	+	0.606552i	−0.636090	+	0.771615i	$0.719449\pi$
$192$	1.59656e7	−	2.76533e7i	0.162792	−	0.281963i
$193$	−1.28256e8	−	7.40486e7i	−1.28418	−	0.741423i	−0.306572	−	0.951847i	$-0.599182\pi$
$193$	−1.28256e8	−	7.40486e7i	−1.28418	−	0.741423i	−0.977610	+	0.210424i	$0.932515\pi$
$194$	1.55216e8	+	2.68842e8i	1.52627	+	2.64357i
$195$	2.99020e7	+	1.26376e7i	0.288788	+	0.122051i
$196$	−2.24431e6	+	2.67802e8i	−0.0212906	+	2.54049i
$197$		−	1.70269e8i		−	1.58673i	−0.608744	−	0.793366i	$-0.708327\pi$
$197$		−	1.70269e8i		−	1.58673i	0.608744	−	0.793366i	$-0.291673\pi$
$198$	−1.32010e8	−	2.28648e8i	−1.20859	−	2.09334i
$199$	−5.11101e7	+	8.85252e7i	−0.459749	+	0.796308i	−0.998947	−	0.0458703i	$-0.985394\pi$
$199$	−5.11101e7	+	8.85252e7i	−0.459749	+	0.796308i	0.539199	+	0.842179i	$0.318727\pi$
$200$	7.16023e8	+	4.13396e8i	6.32881	+	3.65394i
$201$	1.16346e6	−	671723.i	0.0101057	−	0.00583451i
$202$			2.70135e8i			2.30596i
$203$	−9.32853e6	−	3.54073e7i	−0.0782667	−	0.297069i
$204$	−4.50337e7			−0.371391
$205$	1.10165e8	+	1.90812e8i	0.893111	+	1.54691i
$206$	−2.63423e7	−	1.52087e7i	−0.209951	−	0.121215i
$207$	−8.48832e7	+	1.47022e8i	−0.665159	+	1.15209i
$208$	−3.75296e8	+	4.66754e7i	−2.89169	+	0.359639i
$209$	1.32839e8			1.00650
$210$	−5.62170e7	+	5.57478e7i	−0.418890	+	0.415394i
$211$	−7.17778e7			−0.526019			−0.263010	−	0.964793i	$-0.584715\pi$
$211$	−7.17778e7			−0.526019			−0.263010	+	0.964793i	$0.584715\pi$
$212$	−1.06706e8	−	1.84820e8i	−0.769152	−	1.33221i
$213$	1.74882e7	+	1.00968e7i	0.123998	+	0.0715906i
$214$	1.70809e8	+	9.86164e7i	1.19141	+	0.687861i
$215$	−2.77656e8	+	1.60305e8i	−1.90534	+	1.10005i
$216$		−	1.41471e8i		−	0.955170i
$217$	6.96052e6	−	2.55483e7i	0.0462416	−	0.169728i
$218$	−8.59034e7			−0.561581
$219$	1.22774e6	−	708838.i	0.00789866	−	0.00456029i
$220$	4.97487e8	−	8.61673e8i	3.14994	−	5.45586i
$221$	8.46642e7	+	1.11989e8i	0.527627	+	0.697914i
$222$	−1.75105e7	−	3.03291e7i	−0.107415	−	0.186048i
$223$		−	2.04830e8i		−	1.23687i	−0.785834	−	0.618437i	$-0.787766\pi$
$223$		−	2.04830e8i		−	1.23687i	0.785834	−	0.618437i	$-0.212234\pi$
$224$	1.14269e8	−	4.19422e8i	0.679301	−	2.49335i
$225$	4.18709e8			2.45060
$226$	−4.77054e7	+	2.75427e7i	−0.274908	+	0.158718i
$227$	−1.04770e8	−	6.04891e7i	−0.594494	−	0.343231i	0.172379	−	0.985031i	$-0.444855\pi$
$227$	−1.04770e8	−	6.04891e7i	−0.594494	−	0.343231i	−0.766872	+	0.641800i	$0.778188\pi$
$228$	5.01089e7	+	2.89304e7i	0.279990	+	0.161652i
$229$	2.62984e8	−	1.51834e8i	1.44712	−	0.835495i	0.448811	−	0.893627i	$-0.351848\pi$
$229$	2.62984e8	−	1.51834e8i	1.44712	−	0.835495i	0.998309	+	0.0581316i	$0.0185143\pi$
$230$	−8.91598e8			−4.83194
$231$	2.91273e7	+	2.93725e7i	0.155474	+	0.156783i
$232$			1.69379e8i			0.890536i
$233$	−1.63216e8	−	2.82698e8i	−0.845311	−	1.46412i	−0.885351	−	0.464924i	$-0.846082\pi$
$233$	−1.63216e8	−	2.82698e8i	−0.845311	−	1.46412i	0.0400395	−	0.999198i	$-0.487252\pi$
$234$	−2.85978e8	+	2.16201e8i	−1.45907	+	1.10307i
$235$	9.65812e6	−	1.67284e7i	0.0485462	−	0.0840844i
$236$	−4.91183e7	+	2.83585e7i	−0.243249	+	0.140440i
$237$	−5.09637e7			−0.248681
$238$	−3.31092e8	+	8.72307e7i	−1.59195	+	0.419421i
$239$		−	1.95160e8i		−	0.924694i	−0.886699	−	0.462347i	$-0.847007\pi$
$239$		−	1.95160e8i		−	0.924694i	0.886699	−	0.462347i	$-0.152993\pi$
$240$	1.69442e8	−	9.78273e7i	0.791191	−	0.456794i
$241$	−1.13411e8	−	6.54778e7i	−0.521909	−	0.301324i	0.215806	−	0.976436i	$-0.430762\pi$
$241$	−1.13411e8	−	6.54778e7i	−0.521909	−	0.301324i	−0.737715	+	0.675112i	$0.764095\pi$
$242$	−2.68147e8	−	1.54815e8i	−1.21624	−	0.702197i
$243$	−5.39871e7	−	9.35084e7i	−0.241361	−	0.418050i
$244$	5.99090e7			0.264015
$245$	−2.19092e8	+	3.72239e8i	−0.951799	+	1.61711i
$246$	6.98791e7			0.299278
$247$	−2.22621e7	−	1.79000e8i	−0.0939998	−	0.755810i
$248$	−6.12455e7	+	1.06080e8i	−0.254972	+	0.441625i
$249$	−3.22173e7	−	1.86006e7i	−0.132249	−	0.0763537i
$250$	6.63366e8	+	1.14898e9i	2.68512	+	4.65076i
$251$	4.19404e8			1.67407			0.837037	−	0.547146i	$-0.184286\pi$
$251$	4.19404e8			1.67407			0.837037	+	0.547146i	$0.184286\pi$
$252$	−1.59840e8	−	6.06688e8i	−0.629193	−	2.38816i
$253$			4.65845e8i			1.80851i
$254$	−3.32481e8	+	1.91958e8i	−1.27306	+	0.735001i
$255$	−6.29002e7	−	3.63155e7i	−0.237554	−	0.137152i
$256$	−1.18170e7	+	2.04677e7i	−0.0440219	+	0.0762482i
$257$	−2.38561e8	−	4.13200e8i	−0.876666	−	1.51843i	−0.854977	−	0.518665i	$-0.826429\pi$
$257$	−2.38561e8	−	4.13200e8i	−0.876666	−	1.51843i	−0.0216885	−	0.999765i	$-0.506904\pi$
$258$			1.01683e8i			0.368621i
$259$	−1.34533e8	−	1.35665e8i	−0.481149	−	0.485199i
$260$	−1.24447e9	−	5.25955e8i	−4.39115	−	1.85585i
$261$	4.28889e7	+	7.42858e7i	0.149315	+	0.258621i
$262$	−1.87859e8	−	1.08460e8i	−0.645324	−	0.372578i
$263$	−3.55339e7	+	6.15466e7i	−0.120448	+	0.208621i	−0.919944	−	0.392049i	$-0.871766\pi$
$263$	−3.55339e7	+	6.15466e7i	−0.120448	+	0.208621i	0.799497	+	0.600671i	$0.205100\pi$
$264$	−9.56768e7	−	1.65717e8i	−0.320032	−	0.554311i
$265$		−	3.44193e8i		−	1.13616i
$266$	4.24444e8	+	1.15638e8i	1.38272	+	0.376716i
$267$			3.21021e7i			0.103215i
$268$	−4.84212e7	+	2.79560e7i	−0.153661	+	0.0887163i
$269$	−2.35432e8	+	4.07780e8i	−0.737450	+	1.27730i	0.216190	+	0.976351i	$0.430637\pi$
$269$	−2.35432e8	+	4.07780e8i	−0.737450	+	1.27730i	−0.953640	+	0.300950i	$0.902696\pi$
$270$	1.88136e8	−	3.25861e8i	0.581699	−	1.00753i
$271$	−7.15523e7	+	4.13108e7i	−0.218389	+	0.126087i	−0.605204	−	0.796070i	$-0.706909\pi$
$271$	−7.15523e7	+	4.13108e7i	−0.218389	+	0.126087i	0.386815	+	0.922157i	$0.373575\pi$
$272$	8.46139e8			2.54947
$273$	3.46978e7	−	4.41713e7i	0.103213	−	0.131393i
$274$	−4.38108e8			−1.28663
$275$	9.95022e8	−	5.74476e8i	2.88515	−	1.66574i
$276$	−1.01454e8	+	1.75724e8i	−0.290462	+	0.503095i
$277$	8.96512e7	−	1.55280e8i	0.253441	−	0.438973i	−0.711030	−	0.703162i	$-0.751771\pi$
$277$	8.96512e7	−	1.55280e8i	0.253441	−	0.438973i	0.964471	+	0.264189i	$0.0851043\pi$
$278$	−9.03166e8	+	5.21443e8i	−2.52122	+	1.45563i
$279$			6.20325e7i			0.171003i
$280$	1.41874e9	−	1.40690e9i	3.86234	−	3.83011i
$281$		−	2.24670e7i		−	0.0604051i	−0.999544	−	0.0302026i	$-0.990385\pi$
$281$		−	2.24670e7i		−	0.0604051i	0.999544	−	0.0302026i	$-0.00961523\pi$
$282$	−3.06313e6	−	5.30550e6i	−0.00813381	−	0.0140882i
$283$	−1.67332e8	+	2.89828e8i	−0.438861	+	0.760130i	−0.997602	−	0.0692123i	$-0.977951\pi$
$283$	−1.67332e8	+	2.89828e8i	−0.438861	+	0.760130i	0.558741	+	0.829343i	$0.311285\pi$
$284$	−7.27830e8	−	4.20213e8i	−1.88545	−	1.08857i
$285$	4.66593e7	+	8.08163e7i	0.119394	+	0.206796i
$286$	−3.82969e8	+	9.06148e8i	−0.968015	+	2.29044i
$287$	3.68653e8	−	9.71264e7i	0.920515	−	0.242522i
$288$			1.01838e9i			2.51208i
$289$	4.81175e7	+	8.33419e7i	0.117263	+	0.203105i
$290$	−2.25249e8	+	3.90142e8i	−0.542337	+	0.939355i
$291$	9.86762e7	+	5.69707e7i	0.234740	+	0.135527i
$292$	−5.10967e7	+	2.95007e7i	−0.120103	+	0.0693413i
$293$			5.97303e8i			1.38726i	0.720332	+	0.693630i	$0.243990\pi$
$293$			5.97303e8i			1.38726i	−0.720332	+	0.693630i	$0.756010\pi$
$294$	6.74980e7	+	1.19206e8i	0.154909	+	0.273579i
$295$	−9.14738e7			−0.207453
$296$	4.41911e8	+	7.65413e8i	0.990408	+	1.71544i
$297$	−1.70257e8	−	9.82979e7i	−0.377101	−	0.217719i
$298$	7.07253e8	−	1.22500e9i	1.54817	−	2.68150i
$299$	6.27724e8	−	7.80698e7i	1.35806	−	0.168902i
$300$	5.00450e8			1.07013
$301$	1.41332e8	+	5.36438e8i	0.298715	+	1.13380i
$302$	7.65213e8			1.59867
$303$	4.95754e7	+	8.58672e7i	0.102381	+	0.177328i
$304$	−9.41497e8	−	5.43573e8i	−1.92203	−	1.10969i
$305$	8.36771e7	+	4.83110e7i	0.168872	+	0.0974982i
$306$	6.94643e8	−	4.01052e8i	1.38591	−	0.800158i
$307$			1.59632e8i			0.314873i	0.987529	+	0.157437i	$0.0503230\pi$
$307$			1.59632e8i			0.314873i	−0.987529	+	0.157437i	$0.949677\pi$
$308$	−1.21223e9	−	1.22243e9i	−2.36406	−	2.38395i
$309$	−1.11645e7			−0.0215270
$310$	−2.82142e8	+	1.62895e8i	−0.537900	+	0.310556i
$311$	−1.37013e8	+	2.37314e8i	−0.258286	+	0.447365i	−0.965783	−	0.259352i	$-0.916491\pi$
$311$	−1.37013e8	+	2.37314e8i	−0.258286	+	0.447365i	0.707497	+	0.706717i	$0.249824\pi$
$312$	−2.07268e8	+	1.56696e8i	−0.386360	+	0.292090i
$313$	7.99039e7	+	1.38398e8i	0.147287	+	0.255108i	0.930224	−	0.366993i	$-0.119613\pi$
$313$	7.99039e7	+	1.38398e8i	0.147287	+	0.255108i	−0.782937	+	0.622101i	$0.786279\pi$
$314$		−	2.52215e8i		−	0.459746i
$315$	2.65983e8	−	9.76280e8i	0.479476	−	1.75990i
$316$	2.12103e9			3.78130
$317$	−1.15359e8	+	6.66027e7i	−0.203397	+	0.117431i	−0.598239	−	0.801318i	$-0.704133\pi$
$317$	−1.15359e8	+	6.66027e7i	−0.203397	+	0.117431i	0.394842	+	0.918749i	$0.370799\pi$
$318$	−9.45378e7	−	5.45814e7i	−0.164858	−	0.0951809i
$319$	2.03843e8	+	1.17689e8i	0.351583	+	0.202987i
$320$	−1.85616e9	+	1.07166e9i	−3.16658	+	1.82823i
$321$	7.23927e7			0.122159
$322$	−4.05524e8	+	1.48846e9i	−0.676894	+	2.48452i
$323$			4.03571e8i			0.666363i
$324$	7.13171e8	+	1.23525e9i	1.16489	+	2.01765i
$325$	−9.40855e8	−	1.24451e9i	−1.52031	−	2.01097i
$326$	5.56302e8	−	9.63544e8i	0.889302	−	1.54032i
$327$	−2.73059e7	+	1.57651e7i	−0.0431856	+	0.0249332i
$328$	−1.76353e9			−2.75947
$329$	−2.35340e7	−	2.37321e7i	−0.0364343	−	0.0367409i
$330$		−	5.08943e8i		−	0.779598i
$331$	7.51687e8	−	4.33987e8i	1.13930	−	0.657777i	0.193045	−	0.981190i	$-0.438164\pi$
$331$	7.51687e8	−	4.33987e8i	1.13930	−	0.657777i	0.946258	+	0.323413i	$0.104830\pi$
$332$	1.34083e9	+	7.74128e8i	2.01090	+	1.16099i
$333$	3.87624e8	+	2.23795e8i	0.575250	+	0.332121i
$334$	−5.29161e8	−	9.16533e8i	−0.777096	−	1.34597i
$335$	−9.01756e7			−0.131049
$336$	−8.62489e7	−	3.27366e8i	−0.124041	−	0.470810i
$337$	−1.07865e8			−0.153525			−0.0767623	−	0.997049i	$-0.524458\pi$
$337$	−1.07865e8			−0.153525			−0.0767623	+	0.997049i	$0.524458\pi$
$338$	1.28521e9	+	3.64189e8i	1.81036	+	0.513001i
$339$	−1.01093e7	+	1.75099e7i	−0.0140937	+	0.0244109i
$340$	2.61780e9	+	1.51139e9i	3.61211	+	2.08545i
$341$	8.51098e7	+	1.47414e8i	0.116236	+	0.201326i
$342$	−1.03057e9			−1.39311
$343$	5.21778e8	+	5.35064e8i	0.698163	+	0.715939i
$344$		−	2.56617e9i		−	3.39885i
$345$	−2.83410e8	+	1.63627e8i	−0.371577	+	0.214530i
$346$	1.30609e9	+	7.54073e8i	1.69515	+	0.978694i
$347$	−7.13706e8	+	1.23618e9i	−0.916993	+	1.58828i	−0.113037	+	0.993591i	$0.536058\pi$
$347$	−7.13706e8	+	1.23618e9i	−0.916993	+	1.58828i	−0.803956	+	0.594688i	$0.797275\pi$
$348$	5.12618e7	+	8.87880e7i	0.0652028	+	0.112935i
$349$		−	3.44751e8i		−	0.434126i	−0.976158	−	0.217063i	$-0.930352\pi$
$349$		−	3.44751e8i		−	0.434126i	0.976158	−	0.217063i	$-0.0696477\pi$
$350$	3.67936e9	−	9.69376e8i	4.58706	−	1.20852i
$351$	−1.03923e8	+	2.45893e8i	−0.128273	+	0.303509i
$352$	1.39723e9	+	2.42007e9i	1.70753	+	2.95753i
$353$	7.95594e8	+	4.59336e8i	0.962675	+	0.555801i	0.896995	−	0.442040i	$-0.145745\pi$
$353$	7.95594e8	+	4.59336e8i	0.962675	+	0.555801i	0.0656799	+	0.997841i	$0.479078\pi$
$354$	−1.45058e7	+	2.51247e7i	−0.0173792	+	0.0301016i
$355$	−6.77725e8	−	1.17385e9i	−0.803996	−	1.39256i
$356$		−	1.33604e9i		−	1.56943i
$357$	−8.92349e7	+	8.84902e7i	−0.103800	+	0.102933i
$358$			6.38698e7i			0.0735707i
$359$	−9.44769e8	+	5.45462e8i	−1.07769	+	0.622206i	−0.930273	−	0.366868i	$-0.880430\pi$
$359$	−9.44769e8	+	5.45462e8i	−1.07769	+	0.622206i	−0.147420	+	0.989074i	$0.547097\pi$
$360$	−2.34038e9	+	4.05365e9i	−2.64379	+	4.57918i
$361$	−1.87675e8	+	3.25063e8i	−0.209958	+	0.363658i
$362$	−2.13923e9	+	1.23509e9i	−2.37016	+	1.36841i
$363$	−1.13647e8			−0.124706
$364$	−1.44407e9	+	1.83834e9i	−1.56940	+	1.99789i
$365$	−9.51581e7			−0.102428
$366$	2.65387e7	−	1.53221e7i	0.0282941	−	0.0163356i
$367$	−3.78972e8	+	6.56398e8i	−0.400199	+	0.693164i	−0.993750	−	0.111632i	$-0.964392\pi$
$367$	−3.78972e8	+	6.56398e8i	−0.400199	+	0.693164i	0.593551	+	0.804796i	$0.297726\pi$
$368$	1.90623e9	−	3.30168e9i	1.99392	−	3.45357i
$369$	−7.73446e8	+	4.46549e8i	−0.801378	+	0.462676i
$370$			2.35070e9i			2.41263i
$371$	−5.74606e8	−	1.56549e8i	−0.584199	−	0.159162i
$372$			7.41427e7i			0.0746738i
$373$	−8.39837e8	−	1.45464e9i	−0.837942	−	1.45136i	−0.891612	−	0.452799i	$-0.850425\pi$
$373$	−8.39837e8	−	1.45464e9i	−0.837942	−	1.45136i	0.0536706	−	0.998559i	$-0.482908\pi$
$374$	1.10050e9	−	1.90613e9i	1.08778	−	1.88409i
$375$	4.21725e8	+	2.43483e8i	0.412972	+	0.238429i
$376$	7.73041e7	+	1.33895e8i	0.0749972	+	0.129899i
$377$	1.24423e8	−	2.94400e8i	0.119593	−	0.282972i
$378$	−4.58432e8	−	4.62290e8i	−0.436570	−	0.440244i
$379$		−	1.36762e9i		−	1.29041i	−0.764008	−	0.645207i	$-0.776771\pi$
$379$		−	1.36762e9i		−	1.29041i	0.764008	−	0.645207i	$-0.223229\pi$
$380$	−1.94188e9	−	3.36344e9i	−1.81543	−	3.14442i
$381$	−7.04566e7	+	1.22034e8i	−0.0652656	+	0.113043i
$382$	−1.24345e9	−	7.17904e8i	−1.14131	−	0.658938i
$383$	9.13798e8	−	5.27581e8i	0.831102	−	0.479837i	−0.0231277	−	0.999733i	$-0.507362\pi$
$383$	9.13798e8	−	5.27581e8i	0.831102	−	0.479837i	0.854230	+	0.519895i	$0.174029\pi$
$384$			2.00667e8i			0.180849i
$385$	−7.07391e8	−	2.68497e9i	−0.631752	−	2.39788i
$386$	3.15275e9			2.79019
$387$	−6.49788e8	−	1.12547e9i	−0.569880	−	0.987060i
$388$	−4.10674e9	−	2.37103e9i	−3.56933	−	2.06075i
$389$	−1.94434e8	+	3.36770e8i	−0.167475	+	0.290074i	−0.937531	−	0.347901i	$-0.886895\pi$
$389$	−1.94434e8	+	3.36770e8i	−0.167475	+	0.290074i	0.770057	+	0.637975i	$0.220228\pi$
$390$	−6.85797e8	+	8.52924e7i	−0.585423	+	0.0728088i
$391$	−1.41526e9			−1.19734
$392$	−1.70344e9	−	3.00839e9i	−1.42832	−	2.52251i
$393$	−7.96191e7			−0.0661673
$394$	1.81237e9	+	3.13912e9i	1.49283	+	2.58566i
$395$	2.96252e9	+	1.71041e9i	2.41864	+	1.39640i
$396$	3.49275e9	+	2.01654e9i	2.82641	+	1.63183i
$397$	4.06387e8	−	2.34628e8i	0.325967	−	0.188197i	−0.328082	−	0.944649i	$-0.606402\pi$
$397$	4.06387e8	−	2.34628e8i	0.325967	−	0.188197i	0.654049	+	0.756452i	$0.273069\pi$
$398$		−	2.17610e9i		−	1.73017i
$399$	1.56139e8	−	4.11369e7i	0.123057	−	0.0324210i
$400$	−9.40296e9			−7.34606
$401$	1.93705e8	−	1.11836e8i	0.150016	−	0.0866115i	−0.423113	−	0.906077i	$-0.639063\pi$
$401$	1.93705e8	−	1.11836e8i	0.150016	−	0.0866115i	0.573129	+	0.819465i	$0.305729\pi$
$402$	−1.42999e7	+	2.47681e7i	−0.0109785	+	0.0190152i
$403$	1.84377e8	−	1.39390e8i	0.140326	−	0.106087i
$404$	−2.06325e9	−	3.57365e9i	−1.55674	−	2.69636i
$405$			2.30042e9i			1.72074i
$406$	5.48865e8	+	5.53484e8i	0.407028	+	0.410454i
$407$	1.22820e9			0.903005
$408$	5.03456e8	−	2.90671e8i	0.366987	−	0.211880i
$409$	4.10663e8	+	2.37096e8i	0.296793	+	0.171354i	0.641001	−	0.767540i	$-0.278519\pi$
$409$	4.10663e8	+	2.37096e8i	0.296793	+	0.171354i	−0.344208	+	0.938893i	$0.611853\pi$
$410$	−4.06206e9	−	2.34523e9i	−2.91074	−	1.68052i
$411$	−1.39260e8	+	8.04020e7i	−0.0989421	+	0.0571242i
$412$	4.64647e8			0.327328
$413$	−4.16049e7	+	1.52709e8i	−0.0290616	+	0.106669i
$414$		−	3.61405e9i		−	2.50319i
$415$	1.24852e9	+	2.16251e9i	0.857489	+	1.48521i
$416$	3.02687e9	−	2.28833e9i	2.06143	−	1.55845i
$417$	−1.91391e8	+	3.31500e8i	−0.129255	+	0.223876i
$418$	−2.44905e9	+	1.41396e9i	−1.64014	+	0.946936i
$419$	−1.18249e9			−0.785324			−0.392662	−	0.919683i	$-0.628446\pi$
$419$	−1.18249e9			−0.785324			−0.392662	+	0.919683i	$0.628446\pi$
$420$	3.17909e8	−	1.16687e9i	0.209377	−	0.768512i
$421$			4.19131e8i			0.273755i	0.990588	+	0.136878i	$0.0437067\pi$
$421$			4.19131e8i			0.273755i	−0.990588	+	0.136878i	$0.956293\pi$
$422$	1.32331e9	−	7.64016e8i	0.857175	−	0.494890i
$423$	6.78076e7	+	3.91487e7i	0.0435599	+	0.0251493i
$424$	2.38584e9	+	1.37747e9i	1.52006	+	0.877608i
$425$	1.74528e9	+	3.02292e9i	1.10282	+	1.91014i
$426$	−4.29889e8			−0.269416
$427$	1.18711e8	−	1.17720e8i	0.0737891	−	0.0731733i
$428$	−3.01286e9			−1.85749
$429$	4.45639e7	+	3.58318e8i	0.0272510	+	0.219113i
$430$	3.41262e9	−	5.91084e9i	2.06990	−	3.58517i
$431$	−2.06583e9	−	1.19271e9i	−1.24287	−	0.717569i	−0.273189	−	0.961960i	$-0.588078\pi$
$431$	−2.06583e9	−	1.19271e9i	−1.24287	−	0.717569i	−0.969677	+	0.244392i	$0.921412\pi$
$432$	8.04465e8	+	1.39337e9i	0.480080	+	0.831523i
$433$	2.72465e8			0.161289			0.0806443	−	0.996743i	$-0.474302\pi$
$433$	2.72465e8			0.161289			0.0806443	+	0.996743i	$0.474302\pi$
$434$	1.43615e8	+	5.45105e8i	0.0843307	+	0.320085i
$435$			1.65351e8i			0.0963153i
$436$	1.13643e9	−	6.56116e8i	0.656657	−	0.379121i
$437$	1.57476e9	+	9.09186e8i	0.902669	+	0.521156i
$438$	−1.50900e7	+	2.61366e7i	−0.00858084	+	0.0148624i
$439$	−5.09188e8	−	8.81939e8i	−0.287245	−	0.497523i	0.685906	−	0.727690i	$-0.259406\pi$
$439$	−5.09188e8	−	8.81939e8i	−0.287245	−	0.497523i	−0.973151	+	0.230167i	$0.926073\pi$
$440$			1.28442e10i			7.18822i
$441$	−1.50885e9	−	8.88080e8i	−0.837746	−	0.493079i
$442$	−2.75292e9	−	1.16348e9i	−1.51641	−	0.640884i
$443$	1.61900e9	+	2.80419e9i	0.884775	+	1.53248i	0.845971	+	0.533229i	$0.179022\pi$
$443$	1.61900e9	+	2.80419e9i	0.884775	+	1.53248i	0.0388045	+	0.999247i	$0.487645\pi$
$444$	4.63298e8	+	2.67485e8i	0.251200	+	0.145030i
$445$	1.07739e9	−	1.86609e9i	0.579578	−	1.00386i
$446$	2.18024e9	+	3.77629e9i	1.16368	+	2.01555i
$447$		−	5.19183e8i		−	0.274944i
$448$	9.44819e8	+	3.58615e9i	0.496450	+	1.88432i
$449$			5.47325e8i			0.285354i	0.989769	+	0.142677i	$0.0455709\pi$
$449$			5.47325e8i			0.285354i	−0.989769	+	0.142677i	$0.954429\pi$
$450$	−7.71942e9	+	4.45681e9i	−3.99338	+	2.30558i
$451$	−1.22535e9	+	2.12236e9i	−0.628986	+	1.08944i
$452$	4.20734e8	−	7.28732e8i	0.214300	−	0.371179i
$453$	2.43237e8	−	1.40433e8i	0.122938	−	0.0709781i
$454$	2.57543e9			1.29168
$455$	−3.49943e9	+	1.40317e9i	−1.74164	+	0.698346i
$456$	−7.46926e8			−0.368893
$457$	−1.89107e9	+	1.09181e9i	−0.926831	+	0.535106i	−0.885808	−	0.464052i	$-0.846395\pi$
$457$	−1.89107e9	+	1.09181e9i	−0.926831	+	0.535106i	−0.0410233	+	0.999158i	$0.513062\pi$
$458$	−3.23229e9	+	5.59849e9i	−1.57210	+	2.72296i
$459$	2.98634e8	−	5.17248e8i	0.144143	−	0.249663i
$460$	1.17951e10	−	6.80988e9i	5.64999	−	3.26202i
$461$			1.00784e9i			0.479114i	0.970882	+	0.239557i	$0.0770022\pi$
$461$			1.00784e9i			0.479114i	−0.970882	+	0.239557i	$0.922998\pi$
$462$	−8.49645e8	−	2.31482e8i	−0.400858	−	0.109212i
$463$			2.39301e9i			1.12050i	0.828324	+	0.560249i	$0.189295\pi$
$463$			2.39301e9i			1.12050i	−0.828324	+	0.560249i	$0.810705\pi$
$464$	−9.63159e8	−	1.66824e9i	−0.447595	−	0.775257i
$465$	−5.97891e7	+	1.03558e8i	−0.0275764	+	0.0477637i
$466$	6.01818e9	+	3.47460e9i	2.75495	+	1.59057i
$467$	−2.98244e8	−	5.16574e8i	−0.135507	−	0.234705i	0.790284	−	0.612741i	$-0.209933\pi$
$467$	−2.98244e8	−	5.16574e8i	−0.135507	−	0.234705i	−0.925791	+	0.378035i	$0.876600\pi$
$468$	2.13194e9	−	5.04441e9i	0.961421	−	2.27483i
$469$	−4.10144e7	+	1.50542e8i	−0.0183583	+	0.0673833i
$470$			4.11211e8i			0.182693i
$471$	−4.62868e7	−	8.01711e7i	−0.0204119	−	0.0353545i
$472$	3.66081e8	−	6.34070e8i	0.160243	−	0.277549i
$473$	−3.08832e9	−	1.78304e9i	−1.34186	−	0.774725i
$474$	9.39580e8	−	5.42467e8i	0.405238	−	0.233964i
$475$		−	4.48480e9i		−	1.92006i
$476$	3.71381e9	−	3.68282e9i	1.57832	−	1.56515i
$477$	1.39517e9			0.588589
$478$	2.07732e9	+	3.59802e9i	0.869972	+	1.50684i
$479$	8.41682e8	+	4.85945e8i	0.349924	+	0.202029i	0.664652	−	0.747153i	$-0.268580\pi$
$479$	8.41682e8	+	4.85945e8i	0.349924	+	0.202029i	−0.314728	+	0.949182i	$0.601913\pi$
$480$	−9.81546e8	+	1.70009e9i	−0.405104	+	0.701660i
$481$	−2.05831e8	−	1.65500e9i	−0.0843342	−	0.678093i
$482$	2.78783e9			1.13397
$483$	1.44261e8	+	5.47556e8i	0.0582550	+	0.221112i
$484$	4.72981e9			1.89620
$485$	−3.82402e9	−	6.62341e9i	−1.52203	−	2.63624i
$486$	1.99064e9	+	1.14930e9i	0.786622	+	0.454156i
$487$	−1.65000e9	−	9.52627e8i	−0.647339	−	0.373742i	0.140097	−	0.990138i	$-0.455259\pi$
$487$	−1.65000e9	−	9.52627e8i	−0.647339	−	0.373742i	−0.787436	+	0.616396i	$0.788592\pi$
$488$	−6.69756e8	+	3.86684e8i	−0.260884	+	0.150621i
$489$		−	4.08373e8i		−	0.157934i
$490$	7.70566e7	−	9.19476e9i	0.0295885	−	3.53064i
$491$	−1.50041e9			−0.572038			−0.286019	−	0.958224i	$-0.592332\pi$
$491$	−1.50041e9			−0.572038			−0.286019	+	0.958224i	$0.592332\pi$
$492$	−9.24440e8	+	5.33726e8i	−0.349946	+	0.202041i
$493$	−3.57544e8	+	6.19284e8i	−0.134389	+	0.232769i
$494$	2.31573e9	+	3.06312e9i	0.864260	+	1.14319i
$495$	3.25230e9	+	5.63316e9i	1.20524	+	2.08753i
$496$		−	1.39307e9i		−	0.512609i
$497$	−2.26791e9	+	5.97512e8i	−0.828666	+	0.218323i
$498$	7.91954e8			0.287341
$499$	−4.17864e9	+	2.41254e9i	−1.50551	+	0.869205i	−0.505528	+	0.862810i	$0.668702\pi$
$499$	−4.17864e9	+	2.41254e9i	−1.50551	+	0.869205i	−0.999980	+	0.00639532i	$0.997964\pi$
$500$	−1.75515e10	−	1.01334e10i	−6.27942	−	3.62543i
$501$	−3.36406e8	−	1.94224e8i	−0.119518	−	0.0690035i
$502$	−7.73225e9	+	4.46421e9i	−2.72799	+	1.57501i
$503$	−5.30861e9			−1.85991			−0.929957	−	0.367667i	$-0.880157\pi$
$503$	−5.30861e9			−1.85991			−0.929957	+	0.367667i	$0.880157\pi$
$504$	5.70282e9	+	5.75081e9i	1.98419	+	2.00089i
$505$		−	6.65527e9i		−	2.29956i
$506$	−4.95854e9	−	8.58845e9i	−1.70148	−	2.94705i
$507$	4.75363e8	−	1.20099e8i	0.161993	−	0.0409272i
$508$	2.93229e9	−	5.07888e9i	0.992393	−	1.71888i
$509$	−2.04547e9	+	1.18095e9i	−0.687512	+	0.396935i	−0.802679	−	0.596411i	$-0.796593\pi$
$509$	−2.04547e9	+	1.18095e9i	−0.687512	+	0.396935i	0.115167	+	0.993346i	$0.463260\pi$
$510$	1.54619e9			0.516141
$511$	−4.32806e7	+	1.58860e8i	−0.0143490	+	0.0526673i
$512$			2.78408e9i			0.916721i
$513$	−6.64578e8	+	3.83694e8i	−0.217338	+	0.125480i
$514$	8.79636e9	+	5.07858e9i	2.85714	+	1.64957i
$515$	6.48990e8	+	3.74694e8i	0.209369	+	0.120879i
$516$	−7.76641e8	−	1.34518e9i	−0.248855	−	0.431029i
$517$	2.14851e8			0.0683787
$518$	3.92433e9	+	1.06917e9i	1.24054	+	0.337980i
$519$	5.53553e8			0.173809
$520$	1.73074e10	−	2.15252e9i	5.39785	−	0.671328i
$521$	−4.60592e8	+	7.97769e8i	−0.142687	+	0.247141i	−0.928508	−	0.371313i	$-0.878908\pi$
$521$	−4.60592e8	+	7.97769e8i	−0.142687	+	0.247141i	0.785821	+	0.618454i	$0.212241\pi$
$522$	−1.58142e9	−	9.13035e8i	−0.486633	−	0.280957i
$523$	8.38423e8	+	1.45219e9i	0.256276	+	0.443882i	0.965241	−	0.261361i	$-0.0841712\pi$
$523$	8.38423e8	+	1.45219e9i	0.256276	+	0.443882i	−0.708966	+	0.705243i	$0.750838\pi$
$524$	3.31362e9			1.00610
$525$	9.91649e8	−	9.83374e8i	0.299089	−	0.296593i
$526$		−	1.51292e9i		−	0.453279i
$527$	−4.47852e8	+	2.58567e8i	−0.133290	+	0.0769550i
$528$	1.88467e9	+	1.08812e9i	0.557207	+	0.321704i
$529$	−1.48596e9	+	2.57376e9i	−0.436429	+	0.755917i
$530$	3.66365e9	+	6.34563e9i	1.06893	+	1.85144i
$531$		−	3.70785e8i		−	0.107471i
$532$	−6.49825e9	+	1.71205e9i	−1.87114	+	0.492976i
$533$	3.06522e9	+	1.29547e9i	0.876833	+	0.370579i
$534$	−3.41700e8	−	5.91842e8i	−0.0971071	−	0.168194i
$535$	−4.20818e9	−	2.42959e9i	−1.18811	−	0.685955i
$536$	3.60885e8	−	6.25071e8i	0.101226	−	0.175329i
$537$	1.17214e7	+	2.03021e7i	0.00326641	+	0.00565759i
$538$		−	1.00239e10i		−	2.77524i
$539$	−4.80411e9	−	4.02608e7i	−1.32146	−	0.0110744i
$540$			5.74780e9i			1.57081i
$541$	5.56426e8	−	3.21253e8i	0.151084	−	0.0872281i	−0.422552	−	0.906338i	$-0.638866\pi$
$541$	5.56426e8	−	3.21253e8i	0.151084	−	0.0872281i	0.573636	+	0.819110i	$0.305532\pi$
$542$	8.79438e8	−	1.52323e9i	0.237251	−	0.410931i
$543$	−4.53329e8	+	7.85188e8i	−0.121510	+	0.210462i
$544$	−7.35229e9	+	4.24485e9i	−1.95806	+	1.13049i
$545$	2.11639e9			0.560025
$546$	−1.69530e8	+	1.18368e9i	−0.0445732	+	0.311216i
$547$	3.65266e8			0.0954232			0.0477116	−	0.998861i	$-0.484807\pi$
$547$	3.65266e8			0.0954232			0.0477116	+	0.998861i	$0.484807\pi$
$548$	5.79578e9	−	3.34620e9i	1.50446	−	0.868600i
$549$	−1.95827e8	+	3.39181e8i	−0.0505089	+	0.0874841i
$550$	−1.22297e10	+	2.11824e10i	−3.13433	+	5.42882i
$551$	7.95677e8	−	4.59384e8i	0.202631	−	0.116989i
$552$		−	2.61936e9i		−	0.662838i
$553$	4.20285e9	−	4.16777e9i	1.05683	−	1.04801i
$554$			3.81705e9i			0.953771i
$555$	4.31403e8	+	7.47212e8i	0.107117	+	0.185532i
$556$	7.96540e9	−	1.37965e10i	1.96538	−	3.40413i
$557$	2.92875e9	+	1.69092e9i	0.718107	+	0.414599i	0.814056	−	0.580787i	$-0.197255\pi$
$557$	2.92875e9	+	1.69092e9i	0.718107	+	0.414599i	−0.0959483	+	0.995386i	$0.530588\pi$
$558$	−6.60285e8	−	1.14365e9i	−0.160884	−	0.278659i
$559$	−1.88507e9	+	4.46030e9i	−0.456443	+	1.08000i
$560$	−5.97319e9	+	2.19244e10i	−1.43730	+	5.27557i
$561$		−	8.07861e8i		−	0.193182i
$562$	2.39143e8	+	4.14208e8i	0.0568304	+	0.0984332i
$563$	−1.24352e9	+	2.15385e9i	−0.293680	+	0.508669i	−0.974677	−	0.223617i	$-0.928213\pi$
$563$	−1.24352e9	+	2.15385e9i	−0.293680	+	0.508669i	0.680997	+	0.732287i	$0.261547\pi$
$564$	8.10452e7	+	4.67915e7i	0.0190217	+	0.0109822i
$565$	1.17531e9	−	6.78565e8i	0.274146	−	0.158278i
$566$		−	7.12446e9i		−	1.65156i
$567$	3.84039e9	+	1.04630e9i	0.884779	+	0.241054i
$568$	1.08491e10			2.48413
$569$	−2.54514e9	−	4.40831e9i	−0.579187	−	1.00318i	−0.995573	−	0.0939929i	$-0.970037\pi$
$569$	−2.54514e9	−	4.40831e9i	−0.579187	−	1.00318i	0.416386	−	0.909188i	$-0.363296\pi$
$570$	−1.72045e9	−	9.93300e8i	−0.389116	−	0.224656i
$571$	−2.51842e9	+	4.36203e9i	−0.566111	+	0.980533i	0.430835	+	0.902431i	$0.358219\pi$
$571$	−2.51842e9	+	4.36203e9i	−0.566111	+	0.980533i	−0.996945	+	0.0781017i	$0.975114\pi$
$572$	−1.85468e9	−	1.49126e10i	−0.414364	−	3.33171i
$573$	−5.27002e8			−0.117023
$574$	−5.76275e9	+	5.71466e9i	−1.27186	+	1.26124i
$575$	1.57275e10			3.45002
$576$	−4.34390e9	−	7.52386e9i	−0.947113	−	1.64045i
$577$	−4.30717e9	−	2.48675e9i	−0.933419	−	0.538910i	−0.0455276	−	0.998963i	$-0.514497\pi$
$577$	−4.30717e9	−	2.48675e9i	−0.933419	−	0.538910i	−0.887891	+	0.460053i	$0.847830\pi$
$578$	−1.77421e9	−	1.02434e9i	−0.382172	−	0.220647i
$579$	1.00216e9	−	5.78595e8i	0.214566	−	0.123880i
$580$		−	6.88165e9i		−	1.46452i
$581$	4.17802e9	−	1.10075e9i	0.883800	−	0.232849i
$582$	−2.42563e9			−0.510027
$583$	3.31549e9	−	1.91420e9i	0.692959	−	0.400080i
$584$	3.80825e8	−	6.59608e8i	0.0791190	−	0.137038i
$585$	7.04559e9	−	5.32650e9i	1.45503	−	1.10001i
$586$	−6.35780e9	−	1.10120e10i	−1.30516	−	2.26061i
$587$			4.70185e9i			0.959479i	0.877411	+	0.479740i	$0.159269\pi$
$587$			4.70185e9i			0.959479i	−0.877411	+	0.479740i	$0.840731\pi$
$588$	−1.80342e9	−	1.06145e9i	−0.365827	−	0.215318i
$589$	6.64432e8			0.133982
$590$	1.68644e9	−	9.73664e8i	0.338055	−	0.195176i
$591$	1.15219e9	+	6.65217e8i	0.229598	+	0.132558i
$592$	−8.70490e9	−	5.02578e9i	−1.72440	−	0.995583i
$593$	−3.42520e9	+	1.97754e9i	−0.674519	+	0.389434i	−0.797787	−	0.602940i	$-0.793996\pi$
$593$	−3.42520e9	+	1.97754e9i	−0.674519	+	0.389434i	0.123268	+	0.992373i	$0.460663\pi$
$594$	4.18520e9			0.819339
$595$	8.15706e9	−	2.14909e9i	1.58754	−	0.418258i
$596$			2.16076e10i			4.18065i
$597$	−3.99360e8	−	6.91712e8i	−0.0768165	−	0.133050i
$598$	−1.07419e10	+	8.12092e9i	−2.05412	+	1.55293i
$599$	−3.26512e8	+	5.65536e8i	−0.0620734	+	0.107514i	−0.895392	−	0.445279i	$-0.853105\pi$
$599$	−3.26512e8	+	5.65536e8i	−0.0620734	+	0.107514i	0.833319	+	0.552793i	$0.186438\pi$
$600$	−5.59481e9	+	3.23016e9i	−1.05744	+	0.610513i
$601$	−2.86037e9			−0.537478			−0.268739	−	0.963213i	$-0.586607\pi$
$601$	−2.86037e9			−0.537478			−0.268739	+	0.963213i	$0.586607\pi$
$602$	−8.31557e9	−	8.38556e9i	−1.55348	−	1.56655i
$603$		−	3.65523e8i		−	0.0678897i
$604$	−1.01231e10	+	5.84458e9i	−1.86932	+	1.07925i
$605$	6.60630e9	+	3.81415e9i	1.21287	+	0.700251i
$606$	−1.82797e9	−	1.05538e9i	−0.333669	−	0.192644i
$607$	3.17846e9	+	5.50526e9i	0.576842	+	0.999119i	0.995839	+	0.0911314i	$0.0290483\pi$
$607$	3.17846e9	+	5.50526e9i	0.576842	+	0.999119i	−0.418997	+	0.907987i	$0.637618\pi$
$608$	1.09078e10			1.96823
$609$	2.76043e8	+	7.52065e7i	0.0495240	+	0.0134926i
$610$	−2.05692e9			−0.366914
$611$	−3.60063e7	−	2.89510e8i	−0.00638608	−	0.0513476i
$612$	−6.12635e9	+	1.06111e10i	−1.08037	+	1.87125i
$613$	3.42722e9	+	1.97871e9i	0.600940	+	0.346953i	0.769411	−	0.638754i	$-0.220550\pi$
$613$	3.42722e9	+	1.97871e9i	0.600940	+	0.346953i	−0.168472	+	0.985707i	$0.553883\pi$
$614$	−1.69915e9	−	2.94302e9i	−0.296240	−	0.513102i
$615$	−1.72160e9			−0.298448
$616$	2.14424e10	+	5.84189e9i	3.69608	+	1.00698i
$617$		−	1.10549e10i		−	1.89477i	−0.320090	−	0.947387i	$-0.603713\pi$
$617$		−	1.10549e10i		−	1.89477i	0.320090	−	0.947387i	$-0.396287\pi$
$618$	2.05831e8	−	1.18837e8i	0.0350793	−	0.0202531i
$619$	8.25033e8	+	4.76333e8i	0.139815	+	0.0807223i	0.568276	−	0.822838i	$-0.307611\pi$
$619$	8.25033e8	+	4.76333e8i	0.139815	+	0.0807223i	−0.428461	+	0.903560i	$0.640944\pi$
$620$	2.48833e9	−	4.30991e9i	0.419311	−	0.726268i
$621$	−1.34556e9	−	2.33057e9i	−0.225466	−	0.390519i
$622$		−	5.83358e9i		−	0.972005i
$623$	−2.62528e9	−	2.64737e9i	−0.434978	−	0.438639i
$624$	1.15038e9	−	2.72194e9i	0.189538	−	0.448468i
$625$	−8.64981e9	−	1.49819e10i	−1.41718	−	2.45463i
$626$	−2.94626e9	−	1.70102e9i	−0.480022	−	0.277141i
$627$	−5.18983e8	+	8.98905e8i	−0.0840847	+	0.145639i
$628$	1.92638e9	+	3.33659e9i	0.310373	+	0.537581i
$629$			3.73134e9i			0.597844i
$630$	5.48797e9	+	2.08301e10i	0.874419	+	3.31894i
$631$			1.18761e9i			0.188178i	0.995564	+	0.0940892i	$0.0299939\pi$
$631$			1.18761e9i			0.188178i	−0.995564	+	0.0940892i	$0.970006\pi$
$632$	−2.37121e10	+	1.36902e10i	−3.73646	+	2.15725i
$633$	2.80426e8	−	4.85712e8i	0.0439446	−	0.0761143i
$634$	1.41786e9	−	2.45581e9i	0.220964	−	0.382721i
$635$	8.19127e9	−	4.72923e9i	1.26953	−	0.732964i
$636$	1.66754e9			0.257025
$637$	7.50857e8	+	6.48026e9i	0.115098	+	0.993354i
$638$	−5.01080e9			−0.763897
$639$	4.75816e9	−	2.74713e9i	0.721417	−	0.416510i
$640$	6.73465e9	−	1.16648e10i	1.01551	−	1.75892i
$641$	5.34605e9	−	9.25963e9i	0.801733	−	1.38864i	−0.116741	−	0.993162i	$-0.537245\pi$
$641$	5.34605e9	−	9.25963e9i	0.801733	−	1.38864i	0.918474	−	0.395481i	$-0.129422\pi$
$642$	−1.33465e9	+	7.70561e8i	−0.199065	+	0.114930i
$643$			1.12897e10i			1.67473i	0.546644	+	0.837365i	$0.315905\pi$
$643$			1.12897e10i			1.67473i	−0.546644	+	0.837365i	$0.684095\pi$
$644$	−6.00390e9	−	2.27884e10i	−0.885794	−	3.36212i
$645$		−	2.50515e9i		−	0.367600i
$646$	−4.29568e9	−	7.44034e9i	−0.626929	−	1.08587i
$647$	5.73849e8	−	9.93936e8i	0.0832977	−	0.144276i	−0.821367	−	0.570400i	$-0.806788\pi$
$647$	5.73849e8	−	9.93936e8i	0.0832977	−	0.144276i	0.904665	+	0.426124i	$0.140121\pi$
$648$	−1.59459e10	−	9.20634e9i	−2.30216	−	1.32915i
$649$	−5.08724e8	−	8.81136e8i	−0.0730509	−	0.126528i
$650$	3.05926e10	+	1.29295e10i	4.36938	+	1.84665i
$651$	1.45689e8	+	1.46915e8i	0.0206963	+	0.0208705i
$652$			1.69958e10i			2.40146i
$653$	−3.48161e9	−	6.03033e9i	−0.489311	−	0.847511i	0.510614	−	0.859810i	$-0.329418\pi$
$653$	−3.48161e9	−	6.03033e9i	−0.489311	−	0.847511i	−0.999924	+	0.0122995i	$0.996085\pi$
$654$	3.35612e8	−	5.81298e8i	0.0469155	−	0.0812600i
$655$	4.62825e9	+	2.67212e9i	0.643535	+	0.371545i
$656$	1.73693e10	−	1.00282e10i	2.40226	−	1.38694i
$657$		−	3.85719e8i		−	0.0530631i
$658$	6.86488e8	+	1.87030e8i	0.0939383	+	0.0255930i
$659$	6.76386e7			0.00920652			0.00460326	−	0.999989i	$-0.498535\pi$
$659$	6.76386e7			0.00920652			0.00460326	+	0.999989i	$0.498535\pi$
$660$	3.88723e9	+	6.73288e9i	0.526303	+	0.911584i
$661$	−1.22721e9	−	7.08531e8i	−0.165278	−	0.0954231i	0.415080	−	0.909785i	$-0.363754\pi$
$661$	−1.22721e9	−	7.08531e8i	−0.165278	−	0.0954231i	−0.580357	+	0.814362i	$0.697087\pi$
$662$	−9.23887e9	+	1.60022e10i	−1.23770	+	2.14376i
$663$	−1.08859e9	+	1.35387e8i	−0.145066	+	0.0180418i
$664$	−1.99865e10			−2.64940
$665$	−1.04570e10	−	2.84895e9i	−1.37889	−	0.375672i
$666$	−9.52846e9			−1.24986
$667$	1.61099e9	+	2.79032e9i	0.210209	+	0.364093i
$668$	1.40007e10	+	8.08329e9i	1.81732	+	1.04923i
$669$	1.38606e9	+	8.00241e8i	0.178974	+	0.103331i
$670$	1.66250e9	−	9.59846e8i	0.213550	−	0.123293i
$671$			1.07471e9i			0.137329i
$672$	2.39174e9	+	2.41187e9i	0.304034	+	0.306593i
$673$	1.18108e10			1.49358			0.746789	−	0.665061i	$-0.231594\pi$
$673$	1.18108e10			1.49358			0.746789	+	0.665061i	$0.231594\pi$
$674$	1.98864e9	−	1.14814e9i	0.250176	−	0.144439i
$675$	−3.31865e9	+	5.74807e9i	−0.415335	+	0.719381i
$676$	−1.97838e10	+	4.99833e9i	−2.46318	+	0.622316i
$677$	6.24522e9	+	1.08170e10i	0.773548	+	1.33982i	0.935607	+	0.353044i	$0.114853\pi$
$677$	6.24522e9	+	1.08170e10i	0.773548	+	1.33982i	−0.162059	+	0.986781i	$0.551813\pi$
$678$		−	4.30422e8i		−	0.0530384i
$679$	−1.27966e10	+	3.37143e9i	−1.56874	+	0.413304i
$680$	−3.90212e10			−4.75904
$681$	8.18646e8	−	4.72645e8i	0.0993301	−	0.0573483i
$682$	−3.13821e9	−	1.81185e9i	−0.378824	−	0.218714i
$683$	1.58665e9	+	9.16054e8i	0.190550	+	0.110014i	0.592240	−	0.805762i	$-0.298244\pi$
$683$	1.58665e9	+	9.16054e8i	0.190550	+	0.110014i	−0.401690	+	0.915776i	$0.631577\pi$
$684$	1.36335e10	−	7.87133e9i	1.62897	−	0.940485i
$685$	1.07936e10			1.28306
$686$	−1.53150e10	−	4.31068e9i	−1.81126	−	0.509813i
$687$			2.37277e9i			0.279195i
$688$	1.45923e10	+	2.52746e10i	1.70830	+	2.95887i
$689$	−3.13500e9	−	4.14680e9i	−0.365149	−	0.482999i
$690$	3.48335e9	−	6.03334e9i	0.403669	−	0.699175i
$691$	1.02249e10	−	5.90336e9i	1.17893	−	0.680653i	0.223160	−	0.974782i	$-0.428363\pi$
$691$	1.02249e10	−	5.90336e9i	1.17893	−	0.680653i	0.955766	+	0.294129i	$0.0950294\pi$
$692$	−2.30380e10			−2.64285
$693$	1.08834e10	−	2.86738e9i	1.24222	−	0.327279i
$694$		−	3.03873e10i		−	3.45091i
$695$	2.22511e10	−	1.28467e10i	2.51423	−	1.45159i
$696$	−1.14617e9	−	6.61740e8i	−0.128859	−	0.0743970i
$697$	−6.44784e9	−	3.72266e9i	−0.721273	−	0.416427i
$698$	3.66959e9	+	6.35591e9i	0.408435	+	0.707431i
$699$	2.55065e9			0.282475
$700$	−4.12708e10	+	4.09264e10i	−4.54778	+	4.50983i
$701$	8.34094e9			0.914539			0.457269	−	0.889328i	$-0.348828\pi$
$701$	8.34094e9			0.914539			0.457269	+	0.889328i	$0.348828\pi$
$702$	−7.01386e8	−	5.63953e9i	−0.0765204	−	0.615266i
$703$	2.39707e9	−	4.15186e9i	0.260218	−	0.450711i
$704$	−2.06458e10	−	1.19198e10i	−2.23011	−	1.28756i
$705$	7.54659e7	+	1.30711e8i	0.00811127	+	0.0140491i
$706$	−1.95570e10			−2.09164
$707$	−1.11105e10	−	3.02700e9i	−1.18240	−	0.322140i
$708$		−	4.43171e8i		−	0.0469304i
$709$	−8.95865e9	+	5.17228e9i	−0.944019	+	0.545029i	−0.891218	−	0.453576i	$-0.850148\pi$
$709$	−8.95865e9	+	5.17228e9i	−0.944019	+	0.545029i	−0.0528008	+	0.998605i	$0.516815\pi$
$710$	2.49894e10	+	1.44276e10i	2.62031	+	1.51283i
$711$	−6.93306e9	+	1.20084e10i	−0.723405	+	1.25297i
$712$	8.62346e9	+	1.49363e10i	0.895368	+	1.55082i
$713$			2.33006e9i			0.240743i
$714$	7.03252e8	−	2.58126e9i	0.0723049	−	0.265392i
$715$	9.43513e9	−	2.23246e10i	0.965332	−	2.28409i
$716$	−4.87827e8	−	8.44942e8i	−0.0496673	−	0.0860263i
$717$	1.32062e9	+	7.62463e8i	0.133802	+	0.0772506i
$718$	1.16120e10	−	2.01126e10i	1.17077	−	2.02783i
$719$	2.93496e8	+	5.08351e8i	0.0294477	+	0.0510049i	0.880374	−	0.474281i	$-0.157292\pi$
$719$	2.93496e8	+	5.08351e8i	0.0294477	+	0.0510049i	−0.850926	+	0.525286i	$0.823958\pi$
$720$		−	5.32334e10i		−	5.31521i
$721$	9.20705e8	−	9.13021e8i	0.0914844	−	0.0907209i
$722$		−	7.99060e9i		−	0.790131i
$723$	8.86161e8	−	5.11625e8i	0.0872024	−	0.0503463i
$724$	1.88668e10	−	3.26782e10i	1.84762	−	3.20018i
$725$	3.97331e9	−	6.88198e9i	0.387231	−	0.670703i
$726$	2.09523e9	−	1.20968e9i	0.203214	−	0.117326i
$727$	−2.24475e9			−0.216669			−0.108335	−	0.994114i	$-0.534552\pi$
$727$	−2.24475e9			−0.216669			−0.108335	+	0.994114i	$0.534552\pi$
$728$	4.27843e9	−	2.98726e10i	0.410983	−	2.86954i
$729$	−8.74876e9			−0.836374
$730$	1.75436e9	−	1.01288e9i	0.166912	−	0.0963669i
$731$	5.41696e9	−	9.38245e9i	0.512915	−	0.888394i
$732$	−2.34056e8	+	4.05397e8i	−0.0220562	+	0.0382025i
$733$	−6.28363e8	+	3.62786e8i	−0.0589314	+	0.0340241i	−0.529176	−	0.848512i	$-0.677499\pi$
$733$	−6.28363e8	+	3.62786e8i	−0.0589314	+	0.0340241i	0.470245	+	0.882536i	$0.344166\pi$
$734$		−	1.61354e10i		−	1.50606i
$735$	−1.66294e9	−	2.93686e9i	−0.154479	−	0.272821i
$736$			3.82521e10i			3.53658i
$737$	−5.01504e8	−	8.68630e8i	−0.0461464	−	0.0799280i
$738$	9.50630e9	−	1.64654e10i	0.870591	−	1.50791i
$739$	−1.03478e10	−	5.97433e9i	−0.943180	−	0.544545i	−0.0522243	−	0.998635i	$-0.516631\pi$
$739$	−1.03478e10	−	5.97433e9i	−0.943180	−	0.544545i	−0.890956	+	0.454090i	$0.849964\pi$
$740$	−1.79543e10	−	3.10977e10i	−1.62876	−	2.82110i
$741$	1.29824e9	+	5.48681e8i	0.117218	+	0.0495400i
$742$	1.22599e10	−	3.23004e9i	1.10173	−	0.290264i
$743$			1.53209e10i			1.37033i	0.728390	+	0.685163i	$0.240269\pi$
$743$			1.53209e10i			1.37033i	−0.728390	+	0.685163i	$0.759731\pi$
$744$	−4.78555e8	−	8.28882e8i	−0.0426017	−	0.0737883i
$745$	−1.74245e10	+	3.01801e10i	−1.54388	+	2.67407i
$746$	3.09669e10	+	1.78787e10i	2.73094	+	1.57671i
$747$	−8.76562e9	+	5.06083e9i	−0.769415	+	0.444222i
$748$			3.36218e10i			2.93742i
$749$	−5.97004e9	+	5.92021e9i	−0.519147	+	0.514815i
$750$	−1.03667e10			−0.897278
$751$	−6.29236e9	−	1.08987e10i	−0.542093	−	0.938933i	−0.998784	−	0.0493073i	$-0.984299\pi$
$751$	−6.29236e9	−	1.08987e10i	−0.542093	−	0.938933i	0.456690	−	0.889626i	$-0.349035\pi$
$752$	−1.52276e9	−	8.79165e8i	−0.130578	−	0.0753890i
$753$	−1.63855e9	+	2.83806e9i	−0.139855	+	0.242236i
$754$	8.39746e8	+	6.75202e9i	0.0713425	+	0.573633i
$755$	−1.88524e10			−1.59424
$756$	9.59556e9	+	2.61426e9i	0.807689	+	0.220051i
$757$	3.08931e9			0.258837			0.129418	−	0.991590i	$-0.458689\pi$
$757$	3.08931e9			0.258837			0.129418	+	0.991590i	$0.458689\pi$
$758$	1.45572e10	+	2.52138e10i	1.21405	+	2.10279i
$759$	−3.15232e9	−	1.81999e9i	−0.261688	−	0.151086i
$760$	4.34188e10	+	2.50678e10i	3.58781	+	2.07142i
$761$	−1.01761e10	+	5.87519e9i	−0.837021	+	0.483254i	−0.856250	−	0.516561i	$-0.827212\pi$
$761$	−1.01761e10	+	5.87519e9i	−0.837021	+	0.483254i	0.0192298	+	0.999815i	$0.493879\pi$
$762$		−	2.99981e9i		−	0.245613i
$763$	9.62592e8	−	3.53316e9i	0.0784524	−	0.287957i
$764$	2.19330e10			1.77939
$765$	−1.71138e10	+	9.88065e9i	−1.38207	+	0.797941i
$766$	−1.12313e10	+	1.94533e10i	−0.902882	+	1.56384i
$767$	−1.10207e9	+	8.33169e8i	−0.0881911	+	0.0666729i
$768$	−9.23351e7	−	1.59929e8i	−0.00735534	−	0.0127398i
$769$		−	1.43511e10i		−	1.13800i	−0.822338	−	0.569000i	$-0.807331\pi$
$769$		−	1.43511e10i		−	1.13800i	0.822338	−	0.569000i	$-0.192669\pi$
$770$	4.16209e10	+	4.19712e10i	3.28545	+	3.31310i
$771$	3.72810e9			0.292953
$772$	−4.17081e10	+	2.40802e10i	−3.26257	+	1.88365i
$773$	−5.34701e9	−	3.08710e9i	−0.416373	−	0.240393i	0.277151	−	0.960826i	$-0.410610\pi$
$773$	−5.34701e9	−	3.08710e9i	−0.416373	−	0.240393i	−0.693524	+	0.720433i	$0.743943\pi$
$774$	2.39593e10	+	1.38329e10i	1.85730	+	1.07231i
$775$	4.97689e9	−	2.87341e9i	0.384062	−	0.221739i
$776$	6.12154e10			4.70267
$777$	1.44363e9	−	3.80344e8i	0.110404	−	0.0290873i
$778$		−	8.27836e9i		−	0.630255i
$779$	4.78300e9	+	8.28440e9i	0.362509	+	0.627884i
$780$	8.42105e9	−	6.36636e9i	0.635383	−	0.480352i
$781$	7.53821e9	−	1.30566e10i	0.566226	−	0.980732i
$782$	2.60921e10	−	1.50643e10i	1.95113	−	1.12648i
$783$	−1.35974e9			−0.101225
$784$	3.38844e10	+	1.99437e10i	2.51127	+	1.47808i
$785$			6.21379e9i			0.458472i
$786$	1.46788e9	−	8.47480e8i	0.107823	−	0.0622516i
$787$	1.49540e10	+	8.63367e9i	1.09357	+	0.631370i	0.934523	−	0.355902i	$-0.115826\pi$
$787$	1.49540e10	+	8.63367e9i	1.09357	+	0.631370i	0.159042	+	0.987272i	$0.449160\pi$
$788$	−4.79523e10	−	2.76853e10i	−3.49114	−	2.01561i
$789$	−2.77652e8	−	4.80908e8i	−0.0201248	−	0.0348572i
$790$	−7.28236e10			−5.25506
$791$	−5.98253e8	−	2.27073e9i	−0.0429801	−	0.163135i
$792$	−5.20632e10			−3.72385
$793$	1.44816e9	−	1.80108e8i	0.103124	−	0.0128256i
$794$	−4.99484e9	+	8.65132e9i	−0.354120	+	0.613353i
$795$	2.32911e9	+	1.34471e9i	0.164401	+	0.0949171i
$796$	1.66207e10	+	2.87879e10i	1.16803	+	2.02309i
$797$	9.91405e9			0.693661			0.346830	−	0.937928i	$-0.387258\pi$
$797$	9.91405e9			0.693661			0.346830	+	0.937928i	$0.387258\pi$
$798$	−2.44075e9	+	2.42038e9i	−0.170025	+	0.168606i
$799$			6.52728e8i			0.0452708i
$800$	8.17045e10	−	4.71721e10i	5.64198	−	3.25740i
$801$	7.56411e9	+	4.36714e9i	0.520049	+	0.300250i
$802$	−2.38080e9	+	4.12367e9i	−0.162972	+	0.282276i
$803$	−5.29214e8	−	9.16625e8i	−0.0360684	−	0.0624723i
$804$		−	4.36881e8i		−	0.0296461i
$805$	9.99082e9	−	3.66709e10i	0.675018	−	2.47763i
$806$	−1.91553e9	+	4.53236e9i	−0.128859	+	0.304896i
$807$	−1.83960e9	−	3.18628e9i	−0.123216	−	0.213416i
$808$	4.61324e10	+	2.66345e10i	3.07656	+	1.77626i
$809$	−9.31202e9	+	1.61289e10i	−0.618335	+	1.07099i	0.371454	+	0.928451i	$0.378859\pi$
$809$	−9.31202e9	+	1.61289e10i	−0.618335	+	1.07099i	−0.989790	+	0.142537i	$0.954474\pi$
$810$	−2.44861e10	−	4.24112e10i	−1.61891	−	2.80403i
$811$			1.89557e10i			1.24786i	0.781480	+	0.623930i	$0.214465\pi$
$811$			1.89557e10i			1.24786i	−0.781480	+	0.623930i	$0.785535\pi$
$812$	−1.14884e10	−	3.12997e9i	−0.753035	−	0.205161i
$813$		−	6.45582e8i		−	0.0421342i
$814$	−2.26435e10	+	1.30732e10i	−1.47149	+	0.849566i
$815$	−1.37055e10	+	2.37387e10i	−0.886837	+	1.53605i
$816$	−3.30575e9	+	5.72572e9i	−0.212987	+	0.368905i
$817$	−1.20549e10	+	6.95989e9i	−0.773367	+	0.446504i
$818$	−1.00948e10			−0.644853
$819$	−5.68769e9	−	1.41848e10i	−0.361778	−	0.902254i
$820$	7.16501e10			4.53804
$821$	−2.09523e9	+	1.20968e9i	−0.132139	+	0.0762905i	−0.564612	−	0.825356i	$-0.690974\pi$
$821$	−2.09523e9	+	1.20968e9i	−0.132139	+	0.0762905i	0.432473	+	0.901647i	$0.357641\pi$
$822$	1.71163e9	−	2.96462e9i	0.107487	−	0.186174i
$823$	6.95528e8	−	1.20469e9i	0.0434926	−	0.0753314i	−0.843460	−	0.537193i	$-0.819485\pi$
$823$	6.95528e8	−	1.20469e9i	0.0434926	−	0.0753314i	0.886952	+	0.461861i	$0.152818\pi$
$824$	−5.19455e9	+	2.99907e9i	−0.323446	+	0.186742i
$825$			8.97759e9i			0.556636i
$826$	−8.58426e8	−	3.25824e9i	−0.0529996	−	0.201165i
$827$		−	2.12990e10i		−	1.30945i	−0.755866	−	0.654726i	$-0.772784\pi$
$827$		−	2.12990e10i		−	1.30945i	0.755866	−	0.654726i	$-0.227216\pi$
$828$	2.76035e10	+	4.78107e10i	1.68989	+	2.92698i
$829$	−4.52517e9	+	7.83782e9i	−0.275863	+	0.477809i	−0.970353	−	0.241694i	$-0.922297\pi$
$829$	−4.52517e9	+	7.83782e9i	−0.275863	+	0.477809i	0.694489	+	0.719503i	$0.255630\pi$
$830$	−4.60362e10	−	2.65790e10i	−2.79464	−	1.61349i
$831$	7.00510e8	+	1.21332e9i	0.0423458	+	0.0733451i
$832$	−1.26019e10	+	2.98176e10i	−0.758587	+	1.79490i
$833$	1.22314e8	−	1.45951e10i	0.00733195	−	0.874883i
$834$		−	8.14882e9i		−	0.486423i
$835$	1.30368e10	+	2.25805e10i	0.774943	+	1.34224i
$836$	2.15992e10	−	3.74110e10i	1.27855	−	2.21451i
$837$	−8.51589e8	−	4.91665e8i	−0.0501985	−	0.0289821i
$838$	2.18007e10	−	1.25867e10i	1.27973	−	0.738850i
$839$		−	6.03916e9i		−	0.353029i	−0.984298	−	0.176514i	$-0.943518\pi$
$839$		−	6.03916e9i		−	0.353029i	0.984298	−	0.176514i	$-0.0564822\pi$
$840$	3.97752e9	+	1.50970e10i	0.231545	+	0.878850i
$841$	−1.56219e10			−0.905624
$842$	−4.46131e9	−	7.72721e9i	−0.257555	−	0.446098i
$843$	1.52032e8	+	8.77756e7i	0.00874053	+	0.00504635i
$844$	−1.16709e10	+	2.02145e10i	−0.668197	+	1.15735i
$845$	−3.16635e10	−	8.97245e9i	−1.80534	−	0.511579i
$846$	−1.66683e9			−0.0946441
$847$	9.37219e9	−	9.29398e9i	0.529967	−	0.525545i
$848$	−3.13314e10			−1.76439
$849$	−1.30749e9	−	2.26464e9i	−0.0733265	−	0.127005i
$850$	−6.43531e10	−	3.71543e10i	−3.59421	−	2.07512i
$851$	1.45599e10	+	8.40617e9i	0.809851	+	0.467568i
$852$	5.68706e9	−	3.28343e9i	0.315028	−	0.181882i
$853$		−	1.55970e10i		−	0.860439i	−0.902724	−	0.430219i	$-0.858436\pi$
$853$		−	1.55970e10i		−	0.860439i	0.902724	−	0.430219i	$-0.141564\pi$
$854$	−9.35548e8	+	3.43389e9i	−0.0514000	+	0.188662i
$855$	2.53900e10			1.38925
$856$	3.36825e10	−	1.94466e10i	1.83546	−	1.05971i
$857$	8.56957e9	−	1.48429e10i	0.465078	−	0.805539i	−0.534127	−	0.845404i	$-0.679359\pi$
$857$	8.56957e9	−	1.48429e10i	0.465078	−	0.805539i	0.999205	+	0.0398651i	$0.0126928\pi$
$858$	−4.63559e9	−	6.13170e9i	−0.250553	−	0.331417i
$859$	1.34030e10	+	2.32146e10i	0.721482	+	1.24964i	0.960406	+	0.278605i	$0.0898719\pi$
$859$	1.34030e10	+	2.32146e10i	0.721482	+	1.24964i	−0.238924	+	0.971038i	$0.576795\pi$
$860$			1.04260e11i			5.58952i
$861$	−7.83032e8	+	2.87409e9i	−0.0418089	+	0.153458i
$862$	5.07816e10			2.70042
$863$	1.57963e10	−	9.12000e9i	0.836600	−	0.483011i	−0.0195071	−	0.999810i	$-0.506210\pi$
$863$	1.57963e10	−	9.12000e9i	0.836600	−	0.483011i	0.856107	+	0.516798i	$0.172876\pi$
$864$	−1.39804e10	−	8.07156e9i	−0.737429	−	0.425755i
$865$	−3.21780e10	−	1.85780e10i	−1.69045	−	0.975981i
$866$	−5.02324e9	+	2.90017e9i	−0.262828	+	0.151744i
$867$	−7.51953e8			−0.0391854
$868$	−6.06333e9	−	6.11435e9i	−0.314697	−	0.317345i
$869$			3.80492e10i			1.96687i
$870$	−1.76003e9	−	3.04846e9i	−0.0906155	−	0.156951i
$871$	−1.08643e9	+	8.21345e8i	−0.0557105	+	0.0421174i
$872$	−8.46983e9	+	1.46702e10i	−0.432580	+	0.749251i
$873$	2.68477e10	−	1.55005e10i	1.36570	−	0.788490i
$874$	−3.87102e10			−1.96126
$875$	−5.46904e10	+	1.44089e10i	−2.75984	+	0.727115i
$876$		−	4.61020e8i		−	0.0231716i
$877$	−3.24828e10	+	1.87540e10i	−1.62613	+	0.938847i	−0.640898	+	0.767626i	$0.721438\pi$
$877$	−3.24828e10	+	1.87540e10i	−1.62613	+	0.938847i	−0.985233	+	0.171221i	$0.945229\pi$
$878$	1.87750e10	+	1.08398e10i	0.936160	+	0.540492i
$879$	−4.04188e9	−	2.33358e9i	−0.200734	−	0.115894i
$880$	−7.30372e10	−	1.26504e11i	−3.61289	−	6.25771i
$881$	2.45804e10			1.21108			0.605540	−	0.795815i	$-0.292957\pi$
$881$	2.45804e10			1.21108			0.605540	+	0.795815i	$0.292957\pi$
$882$	3.72705e10	+	3.12345e8i	1.82905	+	0.0153283i
$883$	−1.68538e10			−0.823826			−0.411913	−	0.911223i	$-0.635139\pi$
$883$	−1.68538e10			−0.823826			−0.411913	+	0.911223i	$0.635139\pi$
$884$	4.53052e10	−	5.63459e9i	2.20580	−	0.274334i
$885$	3.57376e8	−	6.18993e8i	0.0173310	−	0.0300182i
$886$	−5.96965e10	−	3.44658e10i	−2.88357	−	1.66483i
$887$	9.07294e9	+	1.57148e10i	0.436531	+	0.756094i	0.997419	−	0.0717973i	$-0.0228735\pi$
$887$	9.07294e9	+	1.57148e10i	0.436531	+	0.756094i	−0.560888	+	0.827892i	$0.689540\pi$
$888$	−6.90594e9			−0.330962
$889$	−4.16950e9	−	1.58258e10i	−0.199034	−	0.755454i
$890$			4.58716e10i			2.18112i
$891$	−2.21592e10	+	1.27936e10i	−1.04950	+	0.605927i
$892$	−5.76855e10	−	3.33047e10i	−2.72138	−	1.57119i
$893$	4.19323e8	−	7.26289e8i	0.0197046	−	0.0341295i
$894$	5.52628e9	+	9.57180e9i	0.258673	+	0.448035i
$895$		−	1.57355e9i		−	0.0733668i
$896$	−1.64104e10	−	1.65485e10i	−0.762150	−	0.768564i
$897$	−1.92414e9	+	4.55274e9i	−0.0890150	+	0.210620i
$898$	−5.82583e9	−	1.00906e10i	−0.268467	−	0.464998i
$899$	1.01958e9	+	5.88654e8i	0.0468017	+	0.0270210i
$900$	6.80808e10	−	1.17919e11i	3.11298	−	5.39184i
$901$	5.81542e9	+	1.00726e10i	0.264877	+	0.458781i
$902$		−	5.21713e10i		−	2.36706i
$903$	−4.18218e9	−	1.13941e9i	−0.189015	−	0.0514961i
$904$			1.08625e10i			0.489037i
$905$	5.27039e10	−	3.04286e10i	2.36359	−	1.36462i
$906$	−2.98958e9	+	5.17811e9i	−0.133555	+	0.231325i
$907$	−2.93366e9	+	5.08125e9i	−0.130552	+	0.226123i	−0.923890	−	0.382659i	$-0.875008\pi$
$907$	−2.93366e9	+	5.08125e9i	−0.130552	+	0.226123i	0.793337	+	0.608782i	$0.208342\pi$
$908$	−3.40707e10	+	1.96707e10i	−1.51036	+	0.872007i
$909$	2.69768e10			1.19129
$910$	4.95808e10	−	6.31178e10i	2.18106	−	2.77656i
$911$	5.82715e9			0.255353			0.127677	−	0.991816i	$-0.459248\pi$
$911$	5.82715e9			0.255353			0.127677	+	0.991816i	$0.459248\pi$
$912$	7.35659e9	−	4.24733e9i	0.321140	−	0.185410i
$913$	−1.38871e10	+	2.40532e10i	−0.603899	+	1.04598i
$914$	2.32428e10	−	4.02578e10i	1.00688	−	1.74397i
$915$	−6.53830e8	+	3.77489e8i	−0.0282157	+	0.0162903i
$916$		−	9.87509e10i		−	4.24529i
$917$	6.56598e9	−	6.51119e9i	0.281195	−	0.278848i
$918$			1.27148e10i			0.542452i
$919$	6.73152e9	+	1.16593e10i	0.286094	+	0.495529i	0.972874	−	0.231336i	$-0.0743097\pi$
$919$	6.73152e9	+	1.16593e10i	0.286094	+	0.495529i	−0.686780	+	0.726865i	$0.740976\pi$
$920$	−8.79090e10	+	1.52263e11i	−3.72200	+	6.44669i
$921$	−1.08021e9	−	6.23660e8i	−0.0455617	−	0.0263051i
$922$	−1.07276e10	−	1.85808e10i	−0.450761	−	0.780740i
$923$	−1.88569e10	−	7.96958e9i	−0.789342	−	0.333602i
$924$	1.30081e10	−	3.42715e9i	0.542452	−	0.142916i
$925$		−	4.14656e10i		−	1.72263i
$926$	−2.54716e10	−	4.41182e10i	−1.05419	−	1.82591i
$927$	−1.51881e9	+	2.63065e9i	−0.0626215	+	0.108464i
$928$	1.67382e10	+	9.66381e9i	0.687529	+	0.396945i
$929$	−1.43877e10	+	8.30673e9i	−0.588757	+	0.339919i	−0.764606	−	0.644498i	$-0.777066\pi$
$929$	−1.43877e10	+	8.30673e9i	−0.588757	+	0.339919i	0.175849	+	0.984417i	$0.443733\pi$
$930$		−	2.54563e9i		−	0.103778i
$931$	−9.51224e9	+	1.61614e10i	−0.386330	+	0.656379i
$932$	−1.06154e11			−4.29516
$933$	−1.07058e9	−	1.85431e9i	−0.0431554	−	0.0747473i
$934$	1.09970e10	+	6.34913e9i	0.441632	+	0.254976i
$935$	−2.71129e10	+	4.69609e10i	−1.08476	+	1.87886i
$936$	8.72513e9	+	7.01548e10i	0.347781	+	2.79635i
$937$	4.95017e9			0.196576			0.0982882	−	0.995158i	$-0.468663\pi$
$937$	4.95017e9			0.196576			0.0982882	+	0.995158i	$0.468663\pi$
$938$	−8.46243e8	−	3.21200e9i	−0.0334800	−	0.127076i
$939$	−1.24869e9			−0.0492183
$940$	−3.14077e9	−	5.43997e9i	−0.123335	−	0.213623i
$941$	4.21382e10	+	2.43285e10i	1.64859	+	0.951812i	0.977634	+	0.210312i	$0.0674481\pi$
$941$	4.21382e10	+	2.43285e10i	1.64859	+	0.951812i	0.670953	+	0.741500i	$0.265885\pi$
$942$	1.70671e9	+	9.85371e8i	0.0665246	+	0.0384080i
$943$	−2.90521e10	+	1.67732e10i	−1.12820	+	0.651367i
$944$			8.32674e9i			0.322161i
$945$	1.12943e10	+	1.13894e10i	0.435360	+	0.439024i
$946$	7.59160e10			2.91551
$947$	−1.63873e10	+	9.46124e9i	−0.627023	+	0.362012i	−0.779598	−	0.626280i	$-0.784577\pi$
$947$	−1.63873e10	+	9.46124e9i	−0.627023	+	0.362012i	0.152575	+	0.988292i	$0.451243\pi$
$948$	−8.28656e9	+	1.43527e10i	−0.315897	+	0.547149i
$949$	−1.14646e9	+	8.66726e8i	−0.0435437	+	0.0329193i
$950$	4.77370e10	+	8.26829e10i	1.80644	+	3.12884i
$951$		−	1.04083e9i		−	0.0392417i
$952$	−1.77479e10	+	6.51431e10i	−0.666681	+	2.44703i
$953$	4.20228e9			0.157275			0.0786375	−	0.996903i	$-0.474943\pi$
$953$	4.20228e9			0.157275			0.0786375	+	0.996903i	$0.474943\pi$
$954$	−2.57217e10	+	1.48504e10i	−0.959136	+	0.553758i
$955$	3.06346e10	+	1.76869e10i	1.13815	+	0.657112i
$956$	−5.49622e10	−	3.17325e10i	−2.03452	−	1.17463i
$957$	−1.59277e9	+	9.19587e8i	−0.0587438	+	0.0339157i
$958$	−2.06899e10			−0.760291
$959$	4.90923e9	−	1.80191e10i	0.179741	−	0.659734i
$960$		−	1.67472e10i		−	0.610933i
$961$	−1.33306e10	−	2.30893e10i	−0.484527	−	0.839225i
$962$	2.14108e10	+	2.83210e10i	0.775391	+	1.02564i
$963$	9.84825e9	−	1.70577e10i	0.355359	−	0.615499i
$964$	−3.68806e10	+	2.12930e10i	−1.32595	+	0.765539i
$965$	−7.76736e10			−2.78245
$966$	−8.48791e9	−	8.55934e9i	−0.302957	−	0.305506i
$967$			1.30291e10i			0.463365i	0.972791	+	0.231683i	$0.0744231\pi$
$967$			1.30291e10i			0.463365i	−0.972791	+	0.231683i	$0.925577\pi$
$968$	−5.28772e10	+	3.05286e10i	−1.87372	+	1.08179i
$969$	−2.73092e9	−	1.57670e9i	−0.0964218	−	0.0556691i
$970$	1.41001e11	+	8.14072e10i	4.96047	+	2.86393i
$971$	4.49751e9	+	7.78991e9i	0.157654	+	0.273064i	0.934022	−	0.357215i	$-0.116274\pi$
$971$	4.49751e9	+	7.78991e9i	0.157654	+	0.273064i	−0.776368	+	0.630279i	$0.782940\pi$
$972$	−3.51126e10			−1.22640
$973$	−1.13262e10	−	4.29898e10i	−0.394176	−	1.49613i
$974$	4.05597e10			1.40650
$975$	1.20972e10	−	1.50453e9i	0.417994	−	0.0519858i
$976$	4.39769e9	−	7.61702e9i	0.151408	−	0.262247i
$977$	1.60900e10	+	9.28954e9i	0.551981	+	0.318686i	0.749920	−	0.661528i	$-0.230092\pi$
$977$	1.60900e10	+	9.28954e9i	0.551981	+	0.318686i	−0.197940	+	0.980214i	$0.563425\pi$
$978$	4.34679e9	+	7.52887e9i	0.148588	+	0.257361i
$979$	2.39672e10			0.816352
$980$	6.92087e10	+	1.22227e11i	2.34893	+	4.14836i
$981$			8.57867e9i			0.290121i
$982$	2.76620e10	−	1.59706e10i	0.932165	−	0.538186i
$983$	−2.51168e10	−	1.45012e10i	−0.843387	−	0.486930i	0.0150272	−	0.999887i	$-0.495217\pi$
$983$	−2.51168e10	−	1.45012e10i	−0.843387	−	0.486930i	−0.858414	+	0.512958i	$0.828550\pi$
$984$	6.88988e9	−	1.19336e10i	0.230531	−	0.399291i
$985$	−4.46511e10	−	7.73380e10i	−1.48869	−	2.57850i
$986$		−	1.52230e10i		−	0.505746i
$987$	2.52536e8	−	6.65341e7i	0.00836015	−	0.00220259i
$988$	−5.40308e10	−	2.28352e10i	−1.78235	−	0.753279i
$989$	−2.44073e10	−	4.22746e10i	−0.802291	−	1.38961i
$990$	−1.19921e11	−	6.92362e10i	−3.92799	−	2.26783i
$991$	−1.30344e10	+	2.25763e10i	−0.425435	+	0.736876i	−0.996461	−	0.0840566i	$-0.973212\pi$
$991$	−1.30344e10	+	2.25763e10i	−0.425435	+	0.736876i	0.571026	+	0.820932i	$0.306546\pi$
$992$	6.98865e9	+	1.21047e10i	0.227301	+	0.393698i
$993$			6.78210e9i			0.219807i
$994$	3.54518e10	−	3.51560e10i	1.14495	−	1.13539i
$995$			5.36122e10i			1.72537i
$996$	−1.04769e10	+	6.04882e9i	−0.335988	+	0.193983i
$997$	9.49518e9	−	1.64461e10i	0.303438	−	0.525571i	−0.673474	−	0.739211i	$-0.735199\pi$
$997$	9.49518e9	−	1.64461e10i	0.303438	−	0.525571i	0.976912	+	0.213640i	$0.0685320\pi$
$998$	5.13590e10	−	8.89564e10i	1.63553	−	2.83283i
$999$	−6.14456e9	+	3.54757e9i	−0.194990	+	0.112577i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.r.a.25.2	✓	128
7.2	even	3	inner	91.8.r.a.51.63	yes	128
13.12	even	2	inner	91.8.r.a.25.63	yes	128
91.51	even	6	inner	91.8.r.a.51.2	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.r.a.25.2	✓	128	1.1	even	1	trivial
91.8.r.a.25.63	yes	128	13.12	even	2	inner
91.8.r.a.51.2	yes	128	91.51	even	6	inner
91.8.r.a.51.63	yes	128	7.2	even	3	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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	91.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-18.4363 + 10.6442i) q^{2} +(-3.90686 + 6.76688i) q^{3} +(162.597 - 281.627i) q^{4} +(454.211 - 262.239i) q^{5} -166.341i q^{6} +(-231.201 - 877.547i) q^{7} +4197.94i q^{8} +(1062.97 + 1841.12i) q^{9} +O(q^{10})\)	\(q+(-18.4363 + 10.6442i) q^{2} +(-3.90686 + 6.76688i) q^{3} +(162.597 - 281.627i) q^{4} +(454.211 - 262.239i) q^{5} -166.341i q^{6} +(-231.201 - 877.547i) q^{7} +4197.94i q^{8} +(1062.97 + 1841.12i) q^{9} +(-5582.63 + 9669.41i) q^{10} +(5052.11 + 2916.84i) q^{11} +(1270.49 + 2200.55i) q^{12} +(3083.75 - 7296.51i) q^{13} +(13603.3 + 13717.7i) q^{14} +4098.12i q^{15} +(-23871.2 - 41346.2i) q^{16} +(-8861.49 + 15348.5i) q^{17} +(-39194.5 - 22629.0i) q^{18} +(19720.3 - 11385.5i) q^{19} -170557. i q^{20} +(6841.53 + 1863.94i) q^{21} -124189. q^{22} +(39927.3 + 69156.1i) q^{23} +(-28407.0 - 16400.8i) q^{24} +(98475.9 - 170565. i) q^{25} +(20812.6 + 167344. i) q^{26} -33700.2 q^{27} +(-284733. - 77574.2i) q^{28} +40348.1 q^{29} +(-43621.2 - 75554.1i) q^{30} +(25269.6 + 14589.4i) q^{31} +(414845. + 239511. i) q^{32} +(-39475.8 + 22791.4i) q^{33} -377293. i q^{34} +(-335141. - 337961. i) q^{35} +691345. q^{36} +(182330. - 105268. i) q^{37} +(-242379. + 419813. i) q^{38} +(37326.8 + 49373.8i) q^{39} +(1.10086e6 + 1.90675e6i) q^{40} +420095. i q^{41} +(-145972. + 38458.4i) q^{42} -611293. q^{43} +(1.64292e6 - 948539. i) q^{44} +(965628. + 557505. i) q^{45} +(-1.47222e6 - 849986. i) q^{46} +(31895.3 - 18414.7i) q^{47} +373046. q^{48} +(-716635. + 405780. i) q^{49} +4.19278e6i q^{50} +(-69241.2 - 119929. i) q^{51} +(-1.55348e6 - 2.05486e6i) q^{52} +(328129. - 568336. i) q^{53} +(621305. - 358711. i) q^{54} +3.05963e6 q^{55} +(3.68389e6 - 970570. i) q^{56} +177927. i q^{57} +(-743868. + 429472. i) q^{58} +(-151043. - 87204.7i) q^{59} +(1.15414e6 + 666343. i) q^{60} +(92112.7 + 159544. i) q^{61} -621169. q^{62} +(1.36991e6 - 1.35848e6i) q^{63} -4.08656e6 q^{64} +(-512755. - 4.12283e6i) q^{65} +(485191. - 840375. i) q^{66} +(-148899. - 85967.1i) q^{67} +(2.88170e6 + 4.99126e6i) q^{68} -623961. q^{69} +(9.77607e6 + 2.66344e6i) q^{70} -2.58438e6i q^{71} +(-7.72893e6 + 4.46230e6i) q^{72} +(-157127. - 90717.0i) q^{73} +(-2.24099e6 + 3.88152e6i) q^{74} +(769463. + 1.33275e6i) q^{75} -7.40502e6i q^{76} +(1.39161e6 - 5.10784e6i) q^{77} +(-1.21371e6 - 512955. i) q^{78} +(3.26117e6 + 5.64851e6i) q^{79} +(-2.16852e7 - 1.25199e7i) q^{80} +(-2.19306e6 + 3.79849e6i) q^{81} +(-4.47156e6 - 7.74497e6i) q^{82} +4.76102e6i q^{83} +(1.63735e6 - 1.62368e6i) q^{84} +9.29530e6i q^{85} +(1.12700e7 - 6.50671e6i) q^{86} +(-157634. + 273031. i) q^{87} +(-1.22447e7 + 2.12085e7i) q^{88} +(3.55800e6 - 2.05421e6i) q^{89} -2.37368e7 q^{90} +(-7.11600e6 - 1.01917e6i) q^{91} +2.59683e7 q^{92} +(-197449. + 113997. i) q^{93} +(-392020. + 678998. i) q^{94} +(5.97145e6 - 1.03429e7i) q^{95} +(-3.24149e6 + 1.87147e6i) q^{96} -1.45822e7i q^{97} +(8.89287e6 - 1.51091e7i) q^{98} +1.24021e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 52 q^{3} + 4094 q^{4} - 44052 q^{9}+O(q^{10}) \) 128 * q + 52 * q^3 + 4094 * q^4 - 44052 * q^9	\( 128 q + 52 q^{3} + 4094 q^{4} - 44052 q^{9} - 4514 q^{10} + 2090 q^{12} + 11132 q^{13} + 18748 q^{14} - 230074 q^{16} - 28972 q^{17} + 179920 q^{22} + 20508 q^{23} + 920040 q^{25} + 144684 q^{26} - 357584 q^{27} + 44600 q^{29} + 46580 q^{30} - 1216824 q^{35} - 4529248 q^{36} - 129032 q^{38} + 104546 q^{39} + 2082020 q^{40} + 2426496 q^{42} - 1434416 q^{43} - 3783940 q^{48} - 34428 q^{49} - 756008 q^{51} - 2348612 q^{52} + 1103824 q^{53} - 4216216 q^{55} + 8135574 q^{56} + 531568 q^{61} + 26627120 q^{62} - 27402496 q^{64} - 7495542 q^{65} + 2808402 q^{66} + 531760 q^{68} + 24238760 q^{69} - 7462590 q^{74} - 1547944 q^{75} - 1811116 q^{77} - 31233508 q^{78} + 2961020 q^{79} - 34639872 q^{81} - 10292872 q^{82} + 43455484 q^{87} + 21936790 q^{88} - 58442348 q^{90} + 16479848 q^{91} + 24834900 q^{92} + 26036992 q^{94} + 89048 q^{95}+O(q^{100}) \) 128 * q + 52 * q^3 + 4094 * q^4 - 44052 * q^9 - 4514 * q^10 + 2090 * q^12 + 11132 * q^13 + 18748 * q^14 - 230074 * q^16 - 28972 * q^17 + 179920 * q^22 + 20508 * q^23 + 920040 * q^25 + 144684 * q^26 - 357584 * q^27 + 44600 * q^29 + 46580 * q^30 - 1216824 * q^35 - 4529248 * q^36 - 129032 * q^38 + 104546 * q^39 + 2082020 * q^40 + 2426496 * q^42 - 1434416 * q^43 - 3783940 * q^48 - 34428 * q^49 - 756008 * q^51 - 2348612 * q^52 + 1103824 * q^53 - 4216216 * q^55 + 8135574 * q^56 + 531568 * q^61 + 26627120 * q^62 - 27402496 * q^64 - 7495542 * q^65 + 2808402 * q^66 + 531760 * q^68 + 24238760 * q^69 - 7462590 * q^74 - 1547944 * q^75 - 1811116 * q^77 - 31233508 * q^78 + 2961020 * q^79 - 34639872 * q^81 - 10292872 * q^82 + 43455484 * q^87 + 21936790 * q^88 - 58442348 * q^90 + 16479848 * q^91 + 24834900 * q^92 + 26036992 * q^94 + 89048 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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