LMFDB - Embedded newform 966.2.y.d.121.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(25,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 44, 6]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("966.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.y (of order $33$, degree $20$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$8$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			121.2
Character	$\chi$	$=$	966.121
Dual form			966.2.y.d.487.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.580057 + 0.814576i) q^{2} +(0.235759 + 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(-0.180250 - 3.78390i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(1.94204 + 1.79680i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +O(q^{10})$	\(q+(0.580057 + 0.814576i) q^{2} +(0.235759 + 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(-0.180250 - 3.78390i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(1.94204 + 1.79680i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +(2.97772 - 2.34171i) q^{10} +(2.56281 - 3.59896i) q^{11} +(-0.995472 - 0.0950560i) q^{12} +(0.0889206 + 0.618456i) q^{13} +(-0.337138 + 2.62418i) q^{14} +(3.63475 - 1.06726i) q^{15} +(-0.786053 - 0.618159i) q^{16} +(-4.85079 - 0.934912i) q^{17} +(-0.888835 - 0.458227i) q^{18} +(8.13612 - 1.56811i) q^{19} +(3.63475 + 1.06726i) q^{20} +(-1.28830 + 2.31091i) q^{21} +4.41820 q^{22} +(0.0745912 - 4.79525i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-9.30808 + 0.888814i) q^{25} +(-0.452201 + 0.431172i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(-2.33316 + 1.24755i) q^{28} +(2.11949 - 2.44602i) q^{29} +(2.97772 + 2.34171i) q^{30} +(4.88607 + 4.65886i) q^{31} +(0.0475819 - 0.998867i) q^{32} +(4.10172 + 1.64208i) q^{33} +(-2.05217 - 4.49364i) q^{34} +(6.44887 - 7.67235i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(9.05725 - 4.66934i) q^{37} +(5.99675 + 5.71789i) q^{38} +(-0.580059 + 0.232221i) q^{39} +(1.23900 + 3.57985i) q^{40} +(-6.70701 + 4.31034i) q^{41} +(-2.62969 + 0.291040i) q^{42} +(7.17990 + 2.10821i) q^{43} +(2.56281 + 3.59896i) q^{44} +(1.89410 + 3.28067i) q^{45} +(3.94936 - 2.72076i) q^{46} +(-4.96430 + 8.59843i) q^{47} +(0.415415 - 0.909632i) q^{48} +(0.543018 + 6.97891i) q^{49} +(-6.12322 - 7.06657i) q^{50} +(-0.235057 - 4.93446i) q^{51} +(-0.613525 - 0.118247i) q^{52} +(5.45842 - 2.18522i) q^{53} +(0.235759 - 0.971812i) q^{54} +(-14.0801 - 9.04872i) q^{55} +(-2.36959 - 1.17688i) q^{56} +(3.44207 + 7.53708i) q^{57} +(3.22189 + 0.307653i) q^{58} +(-1.98638 + 1.56211i) q^{59} +(-0.180250 + 3.78390i) q^{60} +(1.31409 - 5.41674i) q^{61} +(-0.960796 + 6.68248i) q^{62} +(-2.54949 - 0.707167i) q^{63} +(0.841254 - 0.540641i) q^{64} +(2.32415 - 0.447943i) q^{65} +(1.04163 + 4.29366i) q^{66} +(-3.21973 + 0.307447i) q^{67} +(2.47003 - 4.27822i) q^{68} +(4.67767 - 1.05803i) q^{69} +(9.99043 + 0.802690i) q^{70} +(0.276764 - 0.606029i) q^{71} +(0.723734 - 0.690079i) q^{72} +(-1.86059 + 5.37581i) q^{73} +(9.05725 + 4.66934i) q^{74} +(-3.05822 - 8.83615i) q^{75} +(-1.17920 + 8.20151i) q^{76} +(11.4437 - 2.38446i) q^{77} +(-0.525629 - 0.337801i) q^{78} +(-8.12499 - 3.25275i) q^{79} +(-2.19737 + 3.08577i) q^{80} +(0.580057 - 0.814576i) q^{81} +(-7.40155 - 2.96313i) q^{82} +(-3.31394 - 2.12974i) q^{83} +(-1.76245 - 1.97327i) q^{84} +(-2.66327 + 18.5234i) q^{85} +(2.44745 + 7.07146i) q^{86} +(2.87676 + 1.48307i) q^{87} +(-1.44505 + 4.17521i) q^{88} +(2.56278 - 2.44361i) q^{89} +(-1.57367 + 3.44586i) q^{90} +(-0.938555 + 1.36084i) q^{91} +(4.50712 + 1.63886i) q^{92} +(-3.37560 + 5.84671i) q^{93} +(-9.88365 + 0.943774i) q^{94} +(-7.40010 - 30.5036i) q^{95} +(0.981929 - 0.189251i) q^{96} +(-4.38893 + 2.82059i) q^{97} +(-5.36987 + 4.49049i) q^{98} +(-0.628776 + 4.37323i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) $ 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9} - 2 q^{10} - 4 q^{11} + 8 q^{12} - 4 q^{13} + 5 q^{14} + 26 q^{15} + 8 q^{16} - 13 q^{17} + 8 q^{18} + 4 q^{19} + 26 q^{20} + 11 q^{21} - 124 q^{22} + 26 q^{23} - 80 q^{24} + 14 q^{25} + 2 q^{26} - 16 q^{27} - 22 q^{28} + 54 q^{29} - 2 q^{30} + 15 q^{31} + 8 q^{32} - 4 q^{33} + 4 q^{34} - 2 q^{35} - 16 q^{36} + 7 q^{37} - 7 q^{38} + 2 q^{39} + 9 q^{40} - 30 q^{41} + 6 q^{42} + 36 q^{43} - 4 q^{44} + 20 q^{45} + 4 q^{46} - 6 q^{47} - 16 q^{48} + 14 q^{49} - 28 q^{50} + 9 q^{51} + 2 q^{52} - 24 q^{53} + 8 q^{54} - 14 q^{55} + 6 q^{56} - 30 q^{57} - 5 q^{58} + 4 q^{59} - 2 q^{60} + 32 q^{61} - 8 q^{62} - 6 q^{63} - 16 q^{64} + 38 q^{65} - 4 q^{66} + 6 q^{67} + 42 q^{68} - 30 q^{69} - 8 q^{70} - 180 q^{71} + 8 q^{72} - 32 q^{73} + 7 q^{74} + 14 q^{75} - 8 q^{76} + 61 q^{77} + 18 q^{78} - 66 q^{79} - 2 q^{80} + 8 q^{81} - 7 q^{82} + 130 q^{83} + 5 q^{84} - 70 q^{85} - 40 q^{86} + 6 q^{87} - 15 q^{88} - 4 q^{89} + 4 q^{90} - 6 q^{91} + 58 q^{92} - 18 q^{93} + 16 q^{94} + 19 q^{95} + 8 q^{96} + 40 q^{97} + 43 q^{98} + 8 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9 - 2 * q^10 - 4 * q^11 + 8 * q^12 - 4 * q^13 + 5 * q^14 + 26 * q^15 + 8 * q^16 - 13 * q^17 + 8 * q^18 + 4 * q^19 + 26 * q^20 + 11 * q^21 - 124 * q^22 + 26 * q^23 - 80 * q^24 + 14 * q^25 + 2 * q^26 - 16 * q^27 - 22 * q^28 + 54 * q^29 - 2 * q^30 + 15 * q^31 + 8 * q^32 - 4 * q^33 + 4 * q^34 - 2 * q^35 - 16 * q^36 + 7 * q^37 - 7 * q^38 + 2 * q^39 + 9 * q^40 - 30 * q^41 + 6 * q^42 + 36 * q^43 - 4 * q^44 + 20 * q^45 + 4 * q^46 - 6 * q^47 - 16 * q^48 + 14 * q^49 - 28 * q^50 + 9 * q^51 + 2 * q^52 - 24 * q^53 + 8 * q^54 - 14 * q^55 + 6 * q^56 - 30 * q^57 - 5 * q^58 + 4 * q^59 - 2 * q^60 + 32 * q^61 - 8 * q^62 - 6 * q^63 - 16 * q^64 + 38 * q^65 - 4 * q^66 + 6 * q^67 + 42 * q^68 - 30 * q^69 - 8 * q^70 - 180 * q^71 + 8 * q^72 - 32 * q^73 + 7 * q^74 + 14 * q^75 - 8 * q^76 + 61 * q^77 + 18 * q^78 - 66 * q^79 - 2 * q^80 + 8 * q^81 - 7 * q^82 + 130 * q^83 + 5 * q^84 - 70 * q^85 - 40 * q^86 + 6 * q^87 - 15 * q^88 - 4 * q^89 + 4 * q^90 - 6 * q^91 + 58 * q^92 - 18 * q^93 + 16 * q^94 + 19 * q^95 + 8 * q^96 + 40 * q^97 + 43 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{9}{11}\right)$

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 $

$2$	0.580057	+	0.814576i	0.410162	+	0.575992i
$2$	0.580057	+	0.814576i	0.410162	+	0.575992i
$3$	0.235759	+	0.971812i	0.136115	+	0.561076i
$3$	0.235759	+	0.971812i	0.136115	+	0.561076i
$4$	−0.327068	+	0.945001i	−0.163534	+	0.472500i
$5$	−0.180250	−	3.78390i	−0.0806101	−	1.69221i	−0.571191	−	0.820817i	$-0.693518\pi$
$5$	−0.180250	−	3.78390i	−0.0806101	−	1.69221i	0.490581	−	0.871396i	$-0.336785\pi$
$6$	−0.654861	+	0.755750i	−0.267346	+	0.308533i
$7$	1.94204	+	1.79680i	0.734021	+	0.679127i
$7$	1.94204	+	1.79680i	0.734021	+	0.679127i
$8$	−0.959493	+	0.281733i	−0.339232	+	0.0996075i
$9$	−0.888835	+	0.458227i	−0.296278	+	0.152742i
$10$	2.97772	−	2.34171i	0.941638	−	0.740513i
$11$	2.56281	−	3.59896i	0.772716	−	1.08513i	−0.221226	−	0.975223i	$-0.571006\pi$
$11$	2.56281	−	3.59896i	0.772716	−	1.08513i	0.993942	−	0.109906i	$-0.0350549\pi$
$12$	−0.995472	−	0.0950560i	−0.287368	−	0.0274403i
$13$	0.0889206	+	0.618456i	0.0246621	+	0.171529i	0.998430	−	0.0560152i	$-0.0178395\pi$
$13$	0.0889206	+	0.618456i	0.0246621	+	0.171529i	−0.973768	+	0.227544i	$0.926930\pi$
$14$	−0.337138	+	2.62418i	−0.0901040	+	0.701342i
$15$	3.63475	−	1.06726i	0.938487	−	0.275565i
$16$	−0.786053	−	0.618159i	−0.196513	−	0.154540i
$17$	−4.85079	−	0.934912i	−1.17649	−	0.226750i	−0.436711	−	0.899602i	$-0.643857\pi$
$17$	−4.85079	−	0.934912i	−1.17649	−	0.226750i	−0.739777	+	0.672852i	$0.765069\pi$
$18$	−0.888835	−	0.458227i	−0.209501	−	0.108005i
$19$	8.13612	−	1.56811i	1.86655	−	0.359749i	0.874444	−	0.485127i	$-0.161226\pi$
$19$	8.13612	−	1.56811i	1.86655	−	0.359749i	0.992109	+	0.125378i	$0.0400144\pi$
$20$	3.63475	+	1.06726i	0.812754	+	0.238646i
$21$	−1.28830	+	2.31091i	−0.281130	+	0.504281i
$22$	4.41820			0.941964
$23$	0.0745912	−	4.79525i	0.0155533	−	0.999879i
$23$	0.0745912	−	4.79525i	0.0155533	−	0.999879i
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−9.30808	+	0.888814i	−1.86162	+	0.177763i
$26$	−0.452201	+	0.431172i	−0.0886838	+	0.0845599i
$27$	−0.654861	−	0.755750i	−0.126028	−	0.145444i
$28$	−2.33316	+	1.24755i	−0.440925	+	0.235765i
$29$	2.11949	−	2.44602i	0.393579	−	0.454214i	−0.524029	−	0.851700i	$-0.675572\pi$
$29$	2.11949	−	2.44602i	0.393579	−	0.454214i	0.917608	+	0.397486i	$0.130117\pi$
$30$	2.97772	+	2.34171i	0.543655	+	0.427535i
$31$	4.88607	+	4.65886i	0.877565	+	0.836756i	0.987571	−	0.157175i	$-0.0502385\pi$
$31$	4.88607	+	4.65886i	0.877565	+	0.836756i	−0.110006	+	0.993931i	$0.535087\pi$
$32$	0.0475819	−	0.998867i	0.00841137	−	0.176576i
$33$	4.10172	+	1.64208i	0.714018	+	0.285850i
$34$	−2.05217	−	4.49364i	−0.351945	−	0.770652i
$35$	6.44887	−	7.67235i	1.09006	−	1.29686i
$36$	−0.142315	−	0.989821i	−0.0237191	−	0.164970i
$37$	9.05725	−	4.66934i	1.48900	−	0.767634i	0.494190	−	0.869354i	$-0.335465\pi$
$37$	9.05725	−	4.66934i	1.48900	−	0.767634i	0.994813	+	0.101720i	$0.0324346\pi$
$38$	5.99675	+	5.71789i	0.972802	+	0.927565i
$39$	−0.580059	+	0.232221i	−0.0928838	+	0.0371851i
$40$	1.23900	+	3.57985i	0.195903	+	0.566024i
$41$	−6.70701	+	4.31034i	−1.04746	+	0.673161i	−0.946821	−	0.321762i	$-0.895725\pi$
$41$	−6.70701	+	4.31034i	−1.04746	+	0.673161i	−0.100639	+	0.994923i	$0.532089\pi$
$42$	−2.62969	+	0.291040i	−0.405771	+	0.0449084i
$43$	7.17990	+	2.10821i	1.09492	+	0.321499i	0.778834	−	0.627230i	$-0.215811\pi$
$43$	7.17990	+	2.10821i	1.09492	+	0.321499i	0.316091	+	0.948729i	$0.397630\pi$
$44$	2.56281	+	3.59896i	0.386358	+	0.542564i
$45$	1.89410	+	3.28067i	0.282355	+	0.489054i
$46$	3.94936	−	2.72076i	0.582302	−	0.401154i
$47$	−4.96430	+	8.59843i	−0.724118	+	1.25421i	0.235218	+	0.971943i	$0.424420\pi$
$47$	−4.96430	+	8.59843i	−0.724118	+	1.25421i	−0.959336	+	0.282267i	$0.908914\pi$
$48$	0.415415	−	0.909632i	0.0599600	−	0.131294i
$49$	0.543018	+	6.97891i	0.0775740	+	0.996987i
$50$	−6.12322	−	7.06657i	−0.865954	−	0.999365i
$51$	−0.235057	−	4.93446i	−0.0329146	−	0.690963i
$52$	−0.613525	−	0.118247i	−0.0850806	−	0.0163979i
$53$	5.45842	−	2.18522i	0.749772	−	0.300163i	0.0348733	−	0.999392i	$-0.488897\pi$
$53$	5.45842	−	2.18522i	0.749772	−	0.300163i	0.714898	+	0.699228i	$0.246473\pi$
$54$	0.235759	−	0.971812i	0.0320827	−	0.132247i
$55$	−14.0801	−	9.04872i	−1.89856	−	1.22013i
$56$	−2.36959	−	1.17688i	−0.316650	−	0.157267i
$57$	3.44207	+	7.53708i	0.455913	+	0.998310i
$58$	3.22189	+	0.307653i	0.423055	+	0.0403969i
$59$	−1.98638	+	1.56211i	−0.258605	+	0.203369i	−0.739041	−	0.673661i	$-0.764721\pi$
$59$	−1.98638	+	1.56211i	−0.258605	+	0.203369i	0.480436	+	0.877030i	$0.340479\pi$
$60$	−0.180250	+	3.78390i	−0.0232701	+	0.488500i
$61$	1.31409	−	5.41674i	0.168252	−	0.693543i	−0.823711	−	0.567010i	$-0.808100\pi$
$61$	1.31409	−	5.41674i	0.168252	−	0.693543i	0.991962	−	0.126533i	$-0.0403849\pi$
$62$	−0.960796	+	6.68248i	−0.122021	+	0.848676i
$63$	−2.54949	−	0.707167i	−0.321206	−	0.0890946i
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	2.32415	−	0.447943i	0.288275	−	0.0555605i
$66$	1.04163	+	4.29366i	0.128216	+	0.528513i
$67$	−3.21973	+	0.307447i	−0.393353	+	0.0375606i	−0.289859	−	0.957069i	$-0.593608\pi$
$67$	−3.21973	+	0.307447i	−0.393353	+	0.0375606i	−0.103494	+	0.994630i	$0.533002\pi$
$68$	2.47003	−	4.27822i	0.299535	−	0.518810i
$69$	4.67767	−	1.05803i	0.563125	−	0.127372i
$70$	9.99043	+	0.802690i	1.19408	+	0.0959398i
$71$	0.276764	−	0.606029i	0.0328459	−	0.0719224i	−0.892498	−	0.451051i	$-0.851049\pi$
$71$	0.276764	−	0.606029i	0.0328459	−	0.0719224i	0.925344	+	0.379129i	$0.123776\pi$
$72$	0.723734	−	0.690079i	0.0852929	−	0.0813266i
$73$	−1.86059	+	5.37581i	−0.217765	+	0.629191i	0.782216	+	0.623008i	$0.214089\pi$
$73$	−1.86059	+	5.37581i	−0.217765	+	0.629191i	−0.999981	+	0.00618341i	$0.998032\pi$
$74$	9.05725	+	4.66934i	1.05288	+	0.542799i
$75$	−3.05822	−	8.83615i	−0.353133	−	1.02031i
$76$	−1.17920	+	8.20151i	−0.135263	+	0.940778i
$77$	11.4437	−	2.38446i	1.30413	−	0.271735i
$78$	−0.525629	−	0.337801i	−0.0595157	−	0.0382484i
$79$	−8.12499	−	3.25275i	−0.914132	−	0.365963i	−0.133569	−	0.991040i	$-0.542644\pi$
$79$	−8.12499	−	3.25275i	−0.914132	−	0.365963i	−0.780564	+	0.625076i	$0.785068\pi$
$80$	−2.19737	+	3.08577i	−0.245673	+	0.345000i
$81$	0.580057	−	0.814576i	0.0644508	−	0.0905084i
$82$	−7.40155	−	2.96313i	−0.817364	−	0.327223i
$83$	−3.31394	−	2.12974i	−0.363752	−	0.233769i	0.345979	−	0.938242i	$-0.387547\pi$
$83$	−3.31394	−	2.12974i	−0.363752	−	0.233769i	−0.709730	+	0.704473i	$0.751183\pi$
$84$	−1.76245	−	1.97327i	−0.192299	−	0.215301i
$85$	−2.66327	+	18.5234i	−0.288872	+	2.00915i
$86$	2.44745	+	7.07146i	0.263916	+	0.762535i
$87$	2.87676	+	1.48307i	0.308421	+	0.159002i
$88$	−1.44505	+	4.17521i	−0.154043	+	0.445079i
$89$	2.56278	−	2.44361i	0.271654	−	0.259022i	−0.541990	−	0.840385i	$-0.682329\pi$
$89$	2.56278	−	2.44361i	0.271654	−	0.259022i	0.813644	+	0.581363i	$0.197480\pi$
$90$	−1.57367	+	3.44586i	−0.165880	+	0.363226i
$91$	−0.938555	+	1.36084i	−0.0983873	+	0.142655i
$92$	4.50712	+	1.63886i	0.469900	+	0.170863i
$93$	−3.37560	+	5.84671i	−0.350033	+	0.606276i
$94$	−9.88365	+	0.943774i	−1.01942	+	0.0973429i
$95$	−7.40010	−	30.5036i	−0.759234	−	3.12961i
$96$	0.981929	−	0.189251i	0.100218	−	0.0193154i
$97$	−4.38893	+	2.82059i	−0.445628	+	0.286388i	−0.744147	−	0.668016i	$-0.767144\pi$
$97$	−4.38893	+	2.82059i	−0.445628	+	0.286388i	0.298519	+	0.954404i	$0.403507\pi$
$98$	−5.36987	+	4.49049i	−0.542439	+	0.453608i
$99$	−0.628776	+	4.37323i	−0.0631944	+	0.439527i
$100$	2.20444	−	9.08684i	0.220444	−	0.908684i
$101$	−0.159245	+	3.34296i	−0.0158455	+	0.332637i	0.977001	+	0.213236i	$0.0684004\pi$
$101$	−0.159245	+	3.34296i	−0.0158455	+	0.332637i	−0.992846	+	0.119401i	$0.961903\pi$
$102$	3.88315	−	3.05374i	0.384489	−	0.302366i
$103$	−8.79837	−	0.840143i	−0.866929	−	0.0827817i	−0.347893	−	0.937534i	$-0.613103\pi$
$103$	−8.79837	−	0.840143i	−0.866929	−	0.0827817i	−0.519036	+	0.854752i	$0.673709\pi$
$104$	−0.259558	−	0.568353i	−0.0254518	−	0.0557316i
$105$	8.97646	+	4.45826i	0.876013	+	0.435081i
$106$	4.94622	+	3.17874i	0.480420	+	0.308747i
$107$	−2.93206	+	12.0861i	−0.283453	+	1.16841i	0.634883	+	0.772609i	$0.281048\pi$
$107$	−2.93206	+	12.0861i	−0.283453	+	1.16841i	−0.918336	+	0.395802i	$0.870467\pi$
$108$	0.928368	−	0.371662i	0.0893322	−	0.0357632i
$109$	−18.9991	−	3.66177i	−1.81978	−	0.350734i	−0.838738	−	0.544535i	$-0.816706\pi$
$109$	−18.9991	−	3.66177i	−1.81978	−	0.350734i	−0.981041	+	0.193801i	$0.937918\pi$
$110$	−0.796379	−	16.7181i	−0.0759318	−	1.59400i
$111$	6.67304	+	7.70110i	0.633377	+	0.730956i
$112$	−0.415836	−	2.61287i	−0.0392928	−	0.246893i
$113$	3.21777	−	7.04593i	0.302702	−	0.662826i	−0.695759	−	0.718275i	$-0.744932\pi$
$113$	3.21777	−	7.04593i	0.302702	−	0.662826i	0.998461	+	0.0554495i	$0.0176592\pi$
$114$	−4.14293	+	7.17576i	−0.388021	+	0.672071i
$115$	−18.1582	+	0.582096i	−1.69326	+	0.0542807i
$116$	1.61827	+	2.80293i	0.150253	+	0.260246i
$117$	−0.362429	−	0.508960i	−0.0335066	−	0.0470534i
$118$	−2.42467	−	0.711948i	−0.223209	−	0.0655401i
$119$	−7.74056	−	10.5315i	−0.709576	−	0.965424i
$120$	−3.18683	+	2.04805i	−0.290917	+	0.186961i
$121$	−2.78679	−	8.05191i	−0.253345	−	0.731992i
$122$	5.17459	−	2.07160i	0.468486	−	0.187553i
$123$	−5.77007	−	5.50175i	−0.520270	−	0.496076i
$124$	−6.00071	+	3.09358i	−0.538879	+	0.277812i
$125$	2.34538	+	16.3125i	0.209777	+	1.45903i
$126$	−0.902810	−	2.48695i	−0.0804287	−	0.221555i
$127$	3.95121	+	8.65195i	0.350614	+	0.767737i	0.999974	+	0.00725560i	$0.00230955\pi$
$127$	3.95121	+	8.65195i	0.350614	+	0.767737i	−0.649360	+	0.760481i	$0.724963\pi$
$128$	0.928368	+	0.371662i	0.0820569	+	0.0328506i
$129$	−0.356056	+	7.47454i	−0.0313490	+	0.658097i
$130$	1.71302	+	1.63337i	0.150242	+	0.143256i
$131$	10.9230	+	8.58998i	0.954351	+	0.750510i	0.968403	−	0.249391i	$-0.0802306\pi$
$131$	10.9230	+	8.58998i	0.954351	+	0.750510i	−0.0140519	+	0.999901i	$0.504473\pi$
$132$	−2.89331	+	3.33906i	−0.251830	+	0.290628i
$133$	18.6182	+	11.5737i	1.61440	+	1.00356i
$134$	−2.11807	−	2.44438i	−0.182973	−	0.211162i
$135$	−2.74165	+	2.61415i	−0.235963	+	0.224991i
$136$	4.91769	−	0.469582i	0.421688	−	0.0402664i
$137$	7.35479	+	12.7389i	0.628362	+	1.08835i	0.987880	+	0.155217i	$0.0496076\pi$
$137$	7.35479	+	12.7389i	0.628362	+	1.08835i	−0.359519	+	0.933138i	$0.617059\pi$
$138$	3.57516	+	3.19659i	0.304338	+	0.272112i
$139$	−4.26944			−0.362129			−0.181065	−	0.983471i	$-0.557954\pi$
$139$	−4.26944			−0.362129			−0.181065	+	0.983471i	$0.557954\pi$
$140$	5.14116	+	8.60357i	0.434508	+	0.727134i
$141$	−9.52643	−	2.79721i	−0.802270	−	0.235568i
$142$	0.654196	−	0.126086i	0.0548989	−	0.0105809i
$143$	2.45369	+	1.26496i	0.205188	+	0.105782i
$144$	0.981929	+	0.189251i	0.0818274	+	0.0157709i
$145$	−9.63753	−	7.57904i	−0.800354	−	0.629405i
$146$	−5.45825	+	1.60269i	−0.451728	+	0.132639i
$147$	−6.65416	+	2.17305i	−0.548826	+	0.179230i
$148$	1.45019	+	10.0863i	0.119205	+	0.829089i
$149$	−10.9682	−	1.04734i	−0.898554	−	0.0858015i	−0.364452	−	0.931222i	$-0.618744\pi$
$149$	−10.9682	−	1.04734i	−0.898554	−	0.0858015i	−0.534101	+	0.845421i	$0.679350\pi$
$150$	5.42377	−	7.61663i	0.442849	−	0.621895i
$151$	9.38738	−	7.38231i	0.763934	−	0.600764i	−0.158303	−	0.987391i	$-0.550602\pi$
$151$	9.38738	−	7.38231i	0.763934	−	0.600764i	0.922236	+	0.386626i	$0.126360\pi$
$152$	−7.36476	+	3.79680i	−0.597361	+	0.307961i
$153$	4.73995	−	1.39178i	0.383202	−	0.112518i
$154$	8.58032	+	7.93863i	0.691422	+	0.639713i
$155$	16.7480	−	19.3282i	1.34523	−	1.55248i
$156$	−0.0297299	−	0.624108i	−0.00238030	−	0.0499687i
$157$	4.04317	−	11.6820i	0.322680	−	0.932324i	−0.660681	−	0.750666i	$-0.729733\pi$
$157$	4.04317	−	11.6820i	0.322680	−	0.932324i	0.983362	−	0.181658i	$-0.0581462\pi$
$158$	−2.06334	−	8.50520i	−0.164150	−	0.676637i
$159$	3.41049	+	4.78937i	0.270470	+	0.379822i
$160$	−3.78819			−0.299483
$161$	8.76097	−	9.17853i	0.690461	−	0.723370i
$162$	1.00000			0.0785674
$163$	−13.0990	−	18.3950i	−1.02600	−	1.44081i	−0.893197	−	0.449666i	$-0.851543\pi$
$163$	−13.0990	−	18.3950i	−1.02600	−	1.44081i	−0.132798	−	0.991143i	$-0.542396\pi$
$164$	−1.87962	−	7.74791i	−0.146774	−	0.605010i
$165$	5.47414	−	15.8165i	0.426161	−	1.23131i
$166$	−0.187439	−	3.93482i	−0.0145481	−	0.305401i
$167$	5.80802	−	6.70281i	0.449438	−	0.518679i	−0.485141	−	0.874436i	$-0.661232\pi$
$167$	5.80802	−	6.70281i	0.449438	−	0.518679i	0.934578	+	0.355757i	$0.115777\pi$
$168$	0.585056	−	2.58025i	0.0451381	−	0.199071i
$169$	12.0988	−	3.55254i	0.930679	−	0.273272i
$170$	−16.6336	+	8.57521i	−1.27574	+	0.657688i
$171$	−6.51312	+	5.12197i	−0.498071	+	0.391687i
$172$	−4.34058	+	6.09548i	−0.330966	+	0.464776i
$173$	−10.8227	−	1.03344i	−0.822835	−	0.0785713i	−0.324860	−	0.945762i	$-0.605317\pi$
$173$	−10.8227	−	1.03344i	−0.822835	−	0.0785713i	−0.497976	+	0.867191i	$0.665923\pi$
$174$	0.460609	+	3.20360i	0.0349186	+	0.242864i
$175$	−19.6737	−	14.9986i	−1.48719	−	1.13379i
$176$	−4.23924	+	1.24475i	−0.319544	+	0.0938267i
$177$	−1.98638	−	1.56211i	−0.149306	−	0.117415i
$178$	3.47706	+	0.670149i	0.260617	+	0.0502298i
$179$	−10.2029	−	5.25994i	−0.762598	−	0.393146i	0.0326220	−	0.999468i	$-0.489614\pi$
$179$	−10.2029	−	5.25994i	−0.762598	−	0.393146i	−0.795220	+	0.606321i	$0.792645\pi$
$180$	−3.71974	+	0.716921i	−0.277253	+	0.0534361i
$181$	3.03742	+	0.891867i	0.225770	+	0.0662920i	0.392661	−	0.919683i	$-0.371555\pi$
$181$	3.03742	+	0.891867i	0.225770	+	0.0662920i	−0.166891	+	0.985975i	$0.553373\pi$
$182$	−1.65292	+	0.0248387i	−0.122523	+	0.00184117i
$183$	5.57386			0.412032
$184$	1.27941	+	4.62202i	0.0943193	+	0.340740i
$185$	−19.3009	−	33.4301i	−1.41903	−	2.45783i
$186$	−6.72063	+	0.641742i	−0.492781	+	0.0470548i
$187$	−15.7964	+	15.0618i	−1.15514	+	1.10143i
$188$	−6.50186	−	7.50354i	−0.474197	−	0.547252i
$189$	0.0861671	−	2.64435i	0.00626773	−	0.192348i
$190$	20.5550	−	23.7218i	1.49122	−	1.72096i
$191$	13.5761	+	10.6764i	0.982332	+	0.772514i	0.973790	−	0.227449i	$-0.0730386\pi$
$191$	13.5761	+	10.6764i	0.982332	+	0.772514i	0.00854177	+	0.999964i	$0.497281\pi$
$192$	0.723734	+	0.690079i	0.0522310	+	0.0498022i
$193$	−0.415106	+	8.71414i	−0.0298800	+	0.627257i	0.933413	+	0.358804i	$0.116815\pi$
$193$	−0.415106	+	8.71414i	−0.0298800	+	0.627257i	−0.963293	+	0.268453i	$0.913488\pi$
$194$	−4.84341	−	1.93901i	−0.347737	−	0.139213i
$195$	0.983256	+	2.15303i	0.0704124	+	0.154182i
$196$	−6.77268	−	1.76942i	−0.483763	−	0.126387i
$197$	0.325417	+	2.26333i	0.0231850	+	0.161255i	0.998125	−	0.0612142i	$-0.0194973\pi$
$197$	0.325417	+	2.26333i	0.0231850	+	0.161255i	−0.974940	+	0.222470i	$0.928588\pi$
$198$	−3.92706	+	2.02454i	−0.279084	+	0.143878i
$199$	−11.4434	−	10.9113i	−0.811202	−	0.773480i	0.165924	−	0.986138i	$-0.446939\pi$
$199$	−11.4434	−	10.9113i	−0.811202	−	0.773480i	−0.977127	+	0.212659i	$0.931788\pi$
$200$	8.68063	−	3.47520i	0.613813	−	0.245734i
$201$	−1.05786	−	3.05649i	−0.0746158	−	0.215588i
$202$	−2.81547	+	1.80939i	−0.198096	+	0.127308i
$203$	8.51113	−	0.941964i	0.597364	−	0.0661129i
$204$	4.73995	+	1.39178i	0.331863	+	0.0974438i
$205$	17.5188	+	24.6018i	1.22357	+	1.71826i
$206$	−4.41920	−	7.65427i	−0.307900	−	0.533298i
$207$	2.13101	+	4.29637i	0.148116	+	0.298618i
$208$	0.312408	−	0.541107i	0.0216616	−	0.0375190i
$209$	15.2078	−	33.3003i	1.05194	−	2.30343i
$210$	1.57527	+	9.89805i	0.108704	+	0.683031i
$211$	−15.3558	−	17.7216i	−1.05714	−	1.22000i	−0.974726	−	0.223405i	$-0.928283\pi$
$211$	−15.3558	−	17.7216i	−1.05714	−	1.22000i	−0.0824133	−	0.996598i	$-0.526263\pi$
$212$	0.279762	+	5.87293i	0.0192141	+	0.403354i
$213$	0.654196	+	0.126086i	0.0448248	+	0.00863926i
$214$	−11.5458	+	4.62226i	−0.789257	+	0.315971i
$215$	6.68309	−	27.5481i	0.455783	−	1.87876i
$216$	0.841254	+	0.540641i	0.0572401	+	0.0367859i
$217$	1.11789	+	17.8270i	0.0758875	+	1.21017i
$218$	−8.03774	−	17.6002i	−0.544385	−	1.19204i
$219$	−5.66293	−	0.540744i	−0.382665	−	0.0365401i
$220$	13.1562	−	10.3461i	0.886990	−	0.697537i
$221$	0.146868	−	3.08313i	0.00987939	−	0.207394i
$222$	−2.40239	+	9.90278i	−0.161238	+	0.664631i
$223$	−1.72419	+	11.9920i	−0.115460	+	0.803044i	0.846995	+	0.531602i	$0.178410\pi$
$223$	−1.72419	+	11.9920i	−0.115460	+	0.803044i	−0.962455	+	0.271442i	$0.912499\pi$
$224$	1.88717	−	1.85434i	0.126092	−	0.123898i
$225$	7.86607	−	5.05522i	0.524405	−	0.337015i
$226$	7.60594	−	1.46592i	0.505939	−	0.0975118i
$227$	1.38380	+	5.70408i	0.0918457	+	0.378593i	0.999120	−	0.0419465i	$-0.0133559\pi$
$227$	1.38380	+	5.70408i	0.0918457	+	0.378593i	−0.907274	+	0.420540i	$0.861841\pi$
$228$	−8.24833	+	0.787620i	−0.546259	+	0.0521614i
$229$	−4.59394	+	7.95693i	−0.303576	+	0.525809i	−0.976943	−	0.213499i	$-0.931514\pi$
$229$	−4.59394	+	7.95693i	−0.303576	+	0.525809i	0.673367	+	0.739308i	$0.264847\pi$
$230$	−11.0070	−	14.4536i	−0.725777	−	0.953042i
$231$	5.01520	+	10.5590i	0.329976	+	0.694728i
$232$	−1.34451	+	2.94407i	−0.0882714	+	0.193287i
$233$	−2.42351	+	2.31081i	−0.158769	+	0.151386i	−0.765300	−	0.643674i	$-0.777409\pi$
$233$	−2.42351	+	2.31081i	−0.158769	+	0.151386i	0.606531	+	0.795060i	$0.292561\pi$
$234$	0.204357	−	0.590452i	0.0133593	−	0.0385990i
$235$	33.4304	+	17.2346i	2.18076	+	1.12426i
$236$	−0.826512	−	2.38805i	−0.0538014	−	0.155449i
$237$	1.24553	−	8.66282i	0.0809056	−	0.562711i
$238$	4.08877	−	12.4142i	0.265035	−	0.804690i
$239$	20.5759	+	13.2234i	1.33095	+	0.855348i	0.996211	−	0.0869640i	$-0.0277165\pi$
$239$	20.5759	+	13.2234i	1.33095	+	0.855348i	0.334736	+	0.942312i	$0.391353\pi$
$240$	−3.51684	−	1.40793i	−0.227011	−	0.0908815i
$241$	7.77498	−	10.9184i	0.500830	−	0.703318i	−0.484343	−	0.874878i	$-0.660941\pi$
$241$	7.77498	−	10.9184i	0.500830	−	0.703318i	0.985174	+	0.171560i	$0.0548808\pi$
$242$	4.94239	−	6.94062i	0.317709	−	0.446160i
$243$	0.928368	+	0.371662i	0.0595548	+	0.0238422i
$244$	4.68903	+	3.01346i	0.300184	+	0.192917i
$245$	26.3096	−	3.31267i	1.68086	−	0.211639i
$246$	1.13463	−	7.89149i	0.0723411	−	0.503143i
$247$	1.69327	+	4.89240i	0.107740	+	0.311296i
$248$	−6.00071	−	3.09358i	−0.381045	−	0.196442i
$249$	1.28841	−	3.72263i	0.0816499	−	0.235912i
$250$	−11.9273	+	11.3727i	−0.754349	+	0.719270i
$251$	−1.08822	+	2.38288i	−0.0686880	+	0.150406i	−0.940862	−	0.338790i	$-0.889982\pi$
$251$	−1.08822	+	2.38288i	−0.0686880	+	0.150406i	0.872174	+	0.489196i	$0.162710\pi$
$252$	1.50213	−	2.17798i	0.0946253	−	0.137200i
$253$	−17.0668	−	12.5578i	−1.07298	−	0.789500i
$254$	−4.75574	+	8.23719i	−0.298402	+	0.516847i
$255$	−18.6292	+	1.77887i	−1.16660	+	0.111397i
$256$	0.235759	+	0.971812i	0.0147349	+	0.0607382i
$257$	−27.3085	+	5.26327i	−1.70345	+	0.328314i	−0.945900	−	0.324458i	$-0.894818\pi$
$257$	−27.3085	+	5.26327i	−1.70345	+	0.328314i	−0.757554	+	0.652772i	$0.773606\pi$
$258$	−6.29511	+	4.04562i	−0.391917	+	0.251870i
$259$	25.9794	+	7.20604i	1.61428	+	0.447762i
$260$	−0.336849	+	2.34283i	−0.0208905	+	0.145296i
$261$	−0.763045	+	3.14531i	−0.0472313	+	0.194690i
$262$	−0.661201	+	13.8803i	−0.0408492	+	0.857529i
$263$	−22.0046	+	17.3046i	−1.35686	+	1.06705i	−0.366227	+	0.930526i	$0.619351\pi$
$263$	−22.0046	+	17.3046i	−1.35686	+	1.06705i	−0.990637	+	0.136524i	$0.956407\pi$
$264$	−4.39820	−	0.419977i	−0.270690	−	0.0258478i
$265$	−9.25255	−	20.2602i	−0.568379	−	1.24458i
$266$	1.37201	+	21.8793i	0.0841232	+	1.34151i
$267$	2.97893	+	1.91444i	0.182307	+	0.117162i
$268$	0.762533	−	3.14320i	0.0465791	−	0.192002i
$269$	−11.5127	+	4.60897i	−0.701939	+	0.281014i	−0.695049	−	0.718962i	$-0.744617\pi$
$269$	−11.5127	+	4.60897i	−0.701939	+	0.281014i	−0.00688992	+	0.999976i	$0.502193\pi$
$270$	−3.71974	−	0.716921i	−0.226376	−	0.0436304i
$271$	0.635210	+	13.3347i	0.0385863	+	0.810025i	0.932365	+	0.361518i	$0.117741\pi$
$271$	0.635210	+	13.3347i	0.0385863	+	0.810025i	−0.893779	+	0.448508i	$0.851956\pi$
$272$	3.23505	+	3.73345i	0.196154	+	0.226374i
$273$	−1.54375	−	0.591269i	−0.0934320	−	0.0357852i
$274$	−6.11058	+	13.3803i	−0.369154	+	0.808333i
$275$	−20.6560	+	35.7773i	−1.24561	+	2.15745i
$276$	−0.530071	+	4.76645i	−0.0319065	+	0.286906i
$277$	11.9119	+	20.6321i	0.715719	+	1.23966i	0.962681	+	0.270637i	$0.0872343\pi$
$277$	11.9119	+	20.6321i	0.715719	+	1.23966i	−0.246962	+	0.969025i	$0.579432\pi$
$278$	−2.47652	−	3.47778i	−0.148532	−	0.208584i
$279$	−6.47773	−	1.90203i	−0.387812	−	0.113872i
$280$	−4.02609	+	9.17843i	−0.240605	+	0.548516i
$281$	−4.43865	+	2.85255i	−0.264787	+	0.170169i	−0.666297	−	0.745686i	$-0.732122\pi$
$281$	−4.43865	+	2.85255i	−0.264787	+	0.170169i	0.401510	+	0.915855i	$0.368486\pi$
$282$	−3.24733	−	9.38254i	−0.193376	−	0.558722i
$283$	−10.0869	+	4.03820i	−0.599605	+	0.240046i	−0.651552	−	0.758604i	$-0.725882\pi$
$283$	−10.0869	+	4.03820i	−0.599605	+	0.240046i	0.0519465	+	0.998650i	$0.483457\pi$
$284$	0.482177	+	0.459755i	0.0286120	+	0.0272815i
$285$	27.8991	−	14.3830i	1.65260	−	0.851976i
$286$	0.392869	+	2.73247i	0.0232309	+	0.161574i
$287$	−20.7701	−	3.68033i	−1.22602	−	0.217243i
$288$	0.415415	+	0.909632i	0.0244786	+	0.0536006i
$289$	6.87381	+	2.75186i	0.404342	+	0.161874i
$290$	0.583386	−	12.2468i	0.0342576	−	0.719156i
$291$	−3.77581	−	3.60023i	−0.221342	−	0.211049i
$292$	−4.47161	−	3.51651i	−0.261681	−	0.205788i
$293$	−1.29386	+	1.49320i	−0.0755882	+	0.0872335i	−0.792284	−	0.610152i	$-0.791108\pi$
$293$	−1.29386	+	1.49320i	−0.0755882	+	0.0872335i	0.716696	+	0.697386i	$0.245654\pi$
$294$	−5.62991	−	4.15983i	−0.328343	−	0.242606i
$295$	6.26892	+	7.23472i	0.364991	+	0.421222i
$296$	−7.37486	+	7.03192i	−0.428655	+	0.408722i
$297$	−4.39820	+	0.419977i	−0.255209	+	0.0243695i
$298$	−5.50907	−	9.54199i	−0.319132	−	0.552752i
$299$	2.97229	−	0.380265i	0.171892	−	0.0219913i
$300$	9.35042			0.539847
$301$	10.1556	+	16.9951i	0.585359	+	0.979580i
$302$	11.4587	+	3.36457i	0.659372	+	0.193609i
$303$	−3.28627	+	0.633377i	−0.188791	+	0.0363865i
$304$	−7.36476	−	3.79680i	−0.422398	−	0.217761i
$305$	−20.7333	−	3.99602i	−1.18719	−	0.228811i
$306$	3.88315	+	3.05374i	0.221985	+	0.174571i
$307$	−10.8156	+	3.17575i	−0.617279	+	0.181250i	−0.575399	−	0.817873i	$-0.695153\pi$
$307$	−10.8156	+	3.17575i	−0.617279	+	0.181250i	−0.0418807	+	0.999123i	$0.513335\pi$
$308$	−1.48955	+	11.5942i	−0.0848747	+	0.660640i
$309$	−1.25783	−	8.74843i	−0.0715557	−	0.497681i
$310$	25.4591	+	2.43105i	1.44598	+	0.138074i
$311$	−4.41770	+	6.20379i	−0.250505	+	0.351785i	−0.920611	−	0.390480i	$-0.872309\pi$
$311$	−4.41770	+	6.20379i	−0.250505	+	0.351785i	0.670107	+	0.742265i	$0.266248\pi$
$312$	0.491139	−	0.386236i	0.0278052	−	0.0218663i
$313$	−10.2520	+	5.28526i	−0.579476	+	0.298741i	−0.722936	−	0.690915i	$-0.757208\pi$
$313$	−10.2520	+	5.28526i	−0.579476	+	0.298741i	0.143459	+	0.989656i	$0.454177\pi$
$314$	11.8611	−	3.48274i	0.669363	−	0.196543i
$315$	−2.21631	+	9.77450i	−0.124875	+	0.550731i
$316$	5.73128	−	6.61425i	0.322410	−	0.372080i
$317$	1.22357	+	25.6859i	0.0687226	+	1.44266i	0.725314	+	0.688418i	$0.241694\pi$
$317$	1.22357	+	25.6859i	0.0687226	+	1.44266i	−0.656592	+	0.754246i	$0.728003\pi$
$318$	−1.92302	+	5.55621i	−0.107838	+	0.311577i
$319$	−3.37129	−	13.8966i	−0.188756	−	0.778062i
$320$	−2.19737	−	3.08577i	−0.122837	−	0.172500i
$321$	−12.4367			−0.694149
$322$	12.5585	+	1.81240i	0.699856	+	0.101001i
$323$	−40.9326			−2.27755
$324$	0.580057	+	0.814576i	0.0322254	+	0.0452542i
$325$	−1.37737	−	5.67761i	−0.0764029	−	0.314937i
$326$	7.38595	−	21.3403i	0.409070	−	1.18193i
$327$	−0.920649	−	19.3268i	−0.0509120	−	1.06877i
$328$	5.22097	−	6.02532i	0.288280	−	0.332693i
$329$	−25.0905	+	7.77860i	−1.38329	+	0.428848i
$330$	16.0591	−	4.71536i	0.884022	−	0.259572i
$331$	16.5226	−	8.51802i	0.908167	−	0.468193i	0.0601665	−	0.998188i	$-0.480837\pi$
$331$	16.5226	−	8.51802i	0.908167	−	0.468193i	0.848000	+	0.529996i	$0.177807\pi$
$332$	3.09649	−	2.43510i	0.169942	−	0.133644i
$333$	−5.91079	+	8.30054i	−0.323909	+	0.454867i
$334$	8.82893	+	0.843060i	0.483097	+	0.0461302i
$335$	1.74370	+	12.1277i	0.0952688	+	0.662609i
$336$	2.44118	−	1.02012i	0.133177	−	0.0556522i
$337$	15.0829	−	4.42874i	0.821618	−	0.241249i	0.156206	−	0.987725i	$-0.450074\pi$
$337$	15.0829	−	4.42874i	0.821618	−	0.241249i	0.665413	+	0.746476i	$0.268256\pi$
$338$	9.91182	+	7.79474i	0.539132	+	0.423978i
$339$	7.60594	+	1.46592i	0.413098	+	0.0796181i
$340$	−16.6336	−	8.57521i	−0.902083	−	0.465056i
$341$	29.2892	−	5.64502i	1.58610	−	0.305695i
$342$	−7.95022	−	2.33439i	−0.429898	−	0.126230i
$343$	−11.4851	+	14.5290i	−0.620139	+	0.784492i
$344$	−7.48302			−0.403457
$345$	−4.84665	−	17.5091i	−0.260935	−	0.942660i
$346$	−5.43597	−	9.41538i	−0.292240	−	0.506174i
$347$	15.5647	−	1.48625i	0.835557	−	0.0797860i	0.331499	−	0.943456i	$-0.392446\pi$
$347$	15.5647	−	1.48625i	0.835557	−	0.0797860i	0.504058	+	0.863670i	$0.331840\pi$
$348$	−2.34240	+	2.23347i	−0.125566	+	0.119727i
$349$	12.7570	+	14.7223i	0.682865	+	0.788068i	0.986331	−	0.164774i	$-0.0526894\pi$
$349$	12.7570	+	14.7223i	0.682865	+	0.788068i	−0.303466	+	0.952842i	$0.598144\pi$
$350$	0.805698	−	24.7258i	0.0430664	−	1.32165i
$351$	0.409167	−	0.472204i	0.0218397	−	0.0252044i
$352$	−3.47294	−	2.73115i	−0.185109	−	0.145571i
$353$	1.95445	+	1.86357i	0.104025	+	0.0991877i	0.740307	−	0.672269i	$-0.234680\pi$
$353$	1.95445	+	1.86357i	0.104025	+	0.0991877i	−0.636282	+	0.771456i	$0.719529\pi$
$354$	0.120241	−	2.52417i	0.00639075	−	0.134158i
$355$	−2.34304	−	0.938013i	−0.124356	−	0.0497846i
$356$	1.47101	+	3.22106i	0.0779632	+	0.170716i
$357$	8.40976	−	10.0053i	0.445091	−	0.529535i
$358$	−1.63362	−	11.3621i	−0.0863395	−	0.600504i
$359$	−0.691175	+	0.356325i	−0.0364788	+	0.0188061i	−0.476369	−	0.879245i	$-0.658048\pi$
$359$	−0.691175	+	0.356325i	−0.0364788	+	0.0188061i	0.439891	+	0.898051i	$0.355017\pi$
$360$	−2.74165	−	2.61415i	−0.144497	−	0.137778i
$361$	46.0984	−	18.4550i	2.42623	−	0.971317i
$362$	1.03538	+	2.99154i	0.0544185	+	0.157232i
$363$	7.16793	−	4.60655i	0.376219	−	0.241781i
$364$	−0.979021	−	1.33202i	−0.0513147	−	0.0698169i
$365$	20.6769	+	6.07129i	1.08228	+	0.317786i
$366$	3.23316	+	4.54033i	0.169000	+	0.237327i
$367$	−4.51877	−	7.82674i	−0.235878	−	0.408552i	0.723650	−	0.690168i	$-0.242463\pi$
$367$	−4.51877	−	7.82674i	−0.235878	−	0.408552i	−0.959527	+	0.281615i	$0.909130\pi$
$368$	−3.02286	+	3.72321i	−0.157577	+	0.194086i
$369$	3.98632	−	6.90451i	0.207520	−	0.359434i
$370$	16.0358	−	35.1134i	0.833659	−	1.82546i
$371$	14.5269	+	5.56391i	0.754197	+	0.288864i
$372$	−4.42110	−	5.10222i	−0.229223	−	0.264538i
$373$	1.61539	+	33.9112i	0.0836417	+	1.75586i	0.518244	+	0.855233i	$0.326586\pi$
$373$	1.61539	+	33.9112i	0.0836417	+	1.75586i	−0.434602	+	0.900623i	$0.643111\pi$
$374$	−21.4318	−	4.13063i	−1.10821	−	0.213590i
$375$	−15.2997	+	6.12508i	−0.790074	+	0.316298i
$376$	2.34076	−	9.64874i	0.120715	−	0.497596i
$377$	1.70122	+	1.09331i	0.0876174	+	0.0563083i
$378$	2.20400	−	1.46368i	0.113362	−	0.0752837i
$379$	−14.9039	−	32.6350i	−0.765562	−	1.67635i	−0.736186	−	0.676779i	$-0.763375\pi$
$379$	−14.9039	−	32.6350i	−0.765562	−	1.67635i	−0.0293764	−	0.999568i	$-0.509352\pi$
$380$	31.2463	+	2.98366i	1.60290	+	0.153058i
$381$	−7.47653	+	5.87961i	−0.383034	+	0.301222i
$382$	−0.821798	+	17.2517i	−0.0420468	+	0.882671i
$383$	−7.95811	+	32.8038i	−0.406640	+	1.67619i	0.288626	+	0.957442i	$0.406802\pi$
$383$	−7.95811	+	32.8038i	−0.406640	+	1.67619i	−0.695266	+	0.718752i	$0.744714\pi$
$384$	−0.142315	+	0.989821i	−0.00726247	+	0.0505116i
$385$	−11.0853	−	42.8720i	−0.564959	−	2.18496i
$386$	−7.33911	+	4.71656i	−0.373551	+	0.240067i
$387$	−7.34779	+	1.41617i	−0.373509	+	0.0719880i
$388$	−1.22998	−	5.07007i	−0.0624430	−	0.257394i
$389$	13.2251	−	1.26284i	0.670537	−	0.0640286i	0.245766	−	0.969329i	$-0.420961\pi$
$389$	13.2251	−	1.26284i	0.670537	−	0.0640286i	0.424771	+	0.905301i	$0.360354\pi$
$390$	−1.18346	+	2.04982i	−0.0599269	+	0.103797i
$391$	−4.84497	+	23.1910i	−0.245020	+	1.17282i
$392$	−2.48721	−	6.54323i	−0.125623	−	0.330483i
$393$	−5.77263	+	12.6403i	−0.291191	+	0.637619i
$394$	−1.65489	+	1.57794i	−0.0833723	+	0.0794953i
$395$	−10.8436	+	31.3305i	−0.545600	+	1.57641i
$396$	−3.92706	−	2.02454i	−0.197342	−	0.101737i
$397$	−7.88279	−	22.7758i	−0.395626	−	1.14309i	−0.950385	−	0.311075i	$-0.899311\pi$
$397$	−7.88279	−	22.7758i	−0.395626	−	1.14309i	0.554759	−	0.832011i	$-0.312810\pi$
$398$	2.25023	−	15.6507i	0.112794	−	0.784498i
$399$	−6.85800	+	20.8220i	−0.343329	+	1.04240i
$400$	7.86607	+	5.05522i	0.393304	+	0.252761i
$401$	−21.9854	−	8.80163i	−1.09790	−	0.439533i	−0.249224	−	0.968446i	$-0.580175\pi$
$401$	−21.9854	−	8.80163i	−1.09790	−	0.439533i	−0.848676	+	0.528913i	$0.822600\pi$
$402$	1.87612	−	2.63465i	0.0935725	−	0.131404i
$403$	−2.44683	+	3.43609i	−0.121885	+	0.171164i
$404$	−3.10702	−	1.24386i	−0.154580	−	0.0618844i
$405$	−3.18683	−	2.04805i	−0.158355	−	0.101769i
$406$	5.70424	+	6.38657i	0.283097	+	0.316960i
$407$	6.40724	−	44.5633i	0.317595	−	2.20892i
$408$	1.61574	+	4.66836i	0.0799908	+	0.231118i
$409$	−12.0405	−	6.20729i	−0.595363	−	0.306931i	0.134082	−	0.990970i	$-0.457191\pi$
$409$	−12.0405	−	6.20729i	−0.595363	−	0.306931i	−0.729445	+	0.684039i	$0.760222\pi$
$410$	−9.87808	+	28.5408i	−0.487844	+	1.40953i
$411$	−10.6458	+	10.1508i	−0.525120	+	0.500700i
$412$	3.67160	−	8.03969i	0.180887	−	0.396087i
$413$	−6.66443	−	0.535460i	−0.327935	−	0.0263483i
$414$	−2.26361	+	4.22801i	−0.111250	+	0.207795i
$415$	−7.46139	+	12.9235i	−0.366265	+	0.634390i
$416$	0.621987	−	0.0593925i	0.0304954	−	0.00291196i
$417$	−1.00656	−	4.14909i	−0.0492914	−	0.203182i
$418$	35.9470	−	6.92822i	1.75823	−	0.338870i
$419$	−2.00298	+	1.28723i	−0.0978518	+	0.0628855i	−0.588652	−	0.808387i	$-0.700341\pi$
$419$	−2.00298	+	1.28723i	−0.0978518	+	0.0628855i	0.490800	+	0.871272i	$0.336705\pi$
$420$	−7.14897	+	7.02461i	−0.348834	+	0.342766i
$421$	−1.53430	+	10.6713i	−0.0747773	+	0.520087i	0.917663	+	0.397359i	$0.130073\pi$
$421$	−1.53430	+	10.6713i	−0.0747773	+	0.520087i	−0.992440	+	0.122728i	$0.960836\pi$
$422$	5.52831	−	22.7880i	0.269114	−	1.10930i
$423$	0.472422	−	9.91736i	0.0229700	−	0.482199i
$424$	−4.62167	+	3.63452i	−0.224448	+	0.176508i
$425$	45.9825	+	4.39079i	2.23048	+	0.212985i
$426$	0.276764	+	0.606029i	0.0134093	+	0.0293622i
$427$	12.2848	−	8.15837i	0.594504	−	0.394811i
$428$	−10.4624	−	6.72379i	−0.505720	−	0.325007i
$429$	−0.650828	+	2.68275i	−0.0314223	+	0.129524i
$430$	26.3166	−	10.5356i	1.26910	−	0.508070i
$431$	−6.10268	−	1.17619i	−0.293956	−	0.0566553i	0.0401414	−	0.999194i	$-0.487219\pi$
$431$	−6.10268	−	1.17619i	−0.293956	−	0.0566553i	−0.334097	+	0.942539i	$0.608431\pi$
$432$	0.0475819	+	0.998867i	0.00228929	+	0.0480580i
$433$	9.24442	+	10.6686i	0.444258	+	0.512701i	0.933073	−	0.359686i	$-0.117116\pi$
$433$	9.24442	+	10.6686i	0.444258	+	0.512701i	−0.488815	+	0.872387i	$0.662571\pi$
$434$	−13.8730	+	11.2513i	−0.665925	+	0.540078i
$435$	5.09326	−	11.1527i	0.244203	−	0.534731i
$436$	9.67435	−	16.7565i	0.463318	−	0.802489i
$437$	−6.91259	−	39.1317i	−0.330674	−	1.87192i
$438$	−2.84434	−	4.92654i	−0.135908	−	0.235399i
$439$	13.7481	+	19.3065i	0.656159	+	0.921447i	0.999844	−	0.0176383i	$-0.00561473\pi$
$439$	13.7481	+	19.3065i	0.656159	+	0.921447i	−0.343685	+	0.939085i	$0.611675\pi$
$440$	16.0591	+	4.71536i	0.765585	+	0.224796i
$441$	−3.68057	−	5.95427i	−0.175265	−	0.283537i
$442$	2.59664	−	1.66876i	0.123509	−	0.0793747i
$443$	−2.43779	−	7.04354i	−0.115823	−	0.334649i	0.872158	−	0.489224i	$-0.162720\pi$
$443$	−2.43779	−	7.04354i	−0.115823	−	0.334649i	−0.987981	+	0.154576i	$0.950599\pi$
$444$	−9.46009	+	3.78725i	−0.448956	+	0.179735i
$445$	−9.70832	−	9.25686i	−0.460218	−	0.438817i
$446$	−10.7685	+	5.55156i	−0.509904	+	0.262874i
$447$	−1.56804	−	10.9060i	−0.0741660	−	0.515836i
$448$	2.60517	+	0.461620i	0.123083	+	0.0218095i
$449$	5.69811	+	12.4771i	0.268911	+	0.588832i	0.995123	−	0.0986378i	$-0.0314485\pi$
$449$	5.69811	+	12.4771i	0.268911	+	0.588832i	−0.726213	+	0.687470i	$0.758721\pi$
$450$	8.68063	+	3.47520i	0.409209	+	0.163822i
$451$	−1.67606	+	35.1849i	−0.0789227	+	1.65679i
$452$	5.60598	+	5.34529i	0.263683	+	0.251421i
$453$	9.38738	+	7.38231i	0.441057	+	0.346851i
$454$	−3.84373	+	4.43590i	−0.180395	+	0.208187i
$455$	5.31845	+	3.30611i	0.249333	+	0.154993i
$456$	−5.42608	−	6.26203i	−0.254099	−	0.293246i
$457$	0.875920	−	0.835188i	0.0409738	−	0.0390684i	−0.669316	−	0.742978i	$-0.733413\pi$
$457$	0.875920	−	0.835188i	0.0409738	−	0.0390684i	0.710289	+	0.703910i	$0.248564\pi$
$458$	−9.14627	+	0.873363i	−0.427377	+	0.0408096i
$459$	2.47003	+	4.27822i	0.115291	+	0.199690i
$460$	5.38889	−	17.3499i	0.251258	−	0.808944i
$461$	27.7829			1.29398			0.646989	−	0.762499i	$-0.276028\pi$
$461$	27.7829			1.29398			0.646989	+	0.762499i	$0.276028\pi$
$462$	−5.69197	+	10.2101i	−0.264814	+	0.475015i
$463$	32.9577	+	9.67725i	1.53167	+	0.449740i	0.935562	−	0.353162i	$-0.114893\pi$
$463$	32.9577	+	9.67725i	1.53167	+	0.449740i	0.596111	+	0.802902i	$0.296712\pi$
$464$	−3.17806	+	0.612520i	−0.147538	+	0.0284355i
$465$	22.7318	+	11.7191i	1.05416	+	0.543459i
$466$	−3.28810	−	0.633730i	−0.152318	−	0.0293570i
$467$	6.10364	+	4.79996i	0.282443	+	0.222116i	0.749322	−	0.662205i	$-0.230379\pi$
$467$	6.10364	+	4.79996i	0.282443	+	0.222116i	−0.466879	+	0.884321i	$0.654622\pi$
$468$	0.599507	−	0.176031i	0.0277122	−	0.00813704i
$469$	−6.80526	−	5.18814i	−0.314238	−	0.239566i
$470$	5.35268	+	37.2287i	0.246900	+	1.71723i
$471$	12.3059	+	1.17507i	0.567026	+	0.0541444i
$472$	1.46582	−	2.05846i	0.0674700	−	0.0947484i
$473$	25.9881	−	20.4373i	1.19493	−	0.939706i
$474$	7.77900	−	4.01035i	0.357301	−	0.184202i
$475$	−74.3379	+	21.8276i	−3.41085	+	1.00152i
$476$	12.4840	−	3.87031i	0.572203	−	0.177395i
$477$	−3.85031	+	4.44349i	−0.176294	+	0.203454i
$478$	1.16379	+	24.4310i	0.0532305	+	1.11745i
$479$	9.00018	−	26.0043i	0.411229	−	1.18817i	−0.529294	−	0.848438i	$-0.677543\pi$
$479$	9.00018	−	26.0043i	0.411229	−	1.18817i	0.940523	−	0.339730i	$-0.110336\pi$
$480$	−0.893101	−	3.68141i	−0.0407643	−	0.168033i
$481$	3.69316	+	5.18631i	0.168393	+	0.236476i
$482$	13.4038			0.610527
$483$	10.9853	+	6.35009i	0.499848	+	0.288939i
$484$	8.52053			0.387297
$485$	11.4640	+	16.0989i	0.520551	+	0.731012i
$486$	0.235759	+	0.971812i	0.0106942	+	0.0440823i
$487$	−3.33518	+	9.63636i	−0.151131	+	0.436665i	−0.994999	−	0.0998865i	$-0.968152\pi$
$487$	−3.33518	+	9.63636i	−0.151131	+	0.436665i	0.843868	+	0.536551i	$0.180273\pi$
$488$	0.265215	+	5.56755i	0.0120057	+	0.252031i
$489$	14.7883	−	17.0666i	0.668749	−	0.771777i
$490$	17.9595	+	19.5097i	0.811328	+	0.881356i
$491$	12.7232	−	3.73588i	0.574192	−	0.168598i	0.0182708	−	0.999833i	$-0.494184\pi$
$491$	12.7232	−	3.73588i	0.574192	−	0.168598i	0.555921	+	0.831235i	$0.312366\pi$
$492$	7.08637	−	3.65328i	0.319478	−	0.164702i
$493$	−12.5680	+	9.88358i	−0.566034	+	0.445134i
$494$	−3.00303	+	4.21717i	−0.135113	+	0.189739i
$495$	16.6612	+	1.59095i	0.748867	+	0.0715081i
$496$	−0.960796	−	6.68248i	−0.0431410	−	0.300052i
$497$	1.62640	−	0.679641i	0.0729540	−	0.0304861i
$498$	3.77971	−	1.10982i	0.169373	−	0.0497324i
$499$	−16.3205	−	12.8345i	−0.730604	−	0.574553i	0.182049	−	0.983290i	$-0.441727\pi$
$499$	−16.3205	−	12.8345i	−0.730604	−	0.574553i	−0.912653	+	0.408736i	$0.865970\pi$
$500$	−16.1824	−	3.11890i	−0.723699	−	0.139482i
$501$	7.88316	+	4.06405i	0.352194	+	0.181568i
$502$	−2.57227	+	0.495764i	−0.114806	+	0.0221270i
$503$	37.4623	+	10.9999i	1.67036	+	0.490462i	0.973870	−	0.227105i	$-0.0729260\pi$
$503$	37.4623	+	10.9999i	1.67036	+	0.490462i	0.696490	+	0.717567i	$0.254744\pi$
$504$	2.64545	−	0.0397537i	0.117838	−	0.00177077i
$505$	12.6781			0.564170
$506$	0.329559	−	21.1864i	0.0146507	−	0.941850i
$507$	6.30480	+	10.9202i	0.280006	+	0.484985i
$508$	−9.46842	+	0.904124i	−0.420093	+	0.0401140i
$509$	−11.5565	+	11.0191i	−0.512233	+	0.488413i	−0.901540	−	0.432695i	$-0.857563\pi$
$509$	−11.5565	+	11.0191i	−0.512233	+	0.488413i	0.389308	+	0.921108i	$0.372714\pi$
$510$	−12.2550	−	14.1430i	−0.542661	−	0.626264i
$511$	−13.2726	+	7.09692i	−0.587145	+	0.313949i
$512$	−0.654861	+	0.755750i	−0.0289410	+	0.0333997i
$513$	−6.51312	−	5.12197i	−0.287561	−	0.226141i
$514$	−20.1278	−	19.1918i	−0.887799	−	0.846514i
$515$	−1.59312	+	33.4436i	−0.0702011	+	1.47370i
$516$	−6.94699	−	2.78116i	−0.305824	−	0.122434i
$517$	18.2229	+	39.9025i	0.801440	+	1.75491i
$518$	9.19965	+	25.3421i	0.404209	+	1.11347i
$519$	−1.54724	−	10.7613i	−0.0679162	−	0.472368i
$520$	−2.10381	+	1.08459i	−0.0922580	+	0.0475623i
$521$	−13.8712	−	13.2262i	−0.607708	−	0.579449i	0.322459	−	0.946583i	$-0.395490\pi$
$521$	−13.8712	−	13.2262i	−0.607708	−	0.579449i	−0.930168	+	0.367134i	$0.880339\pi$
$522$	−3.00471	+	1.20290i	−0.131512	+	0.0526496i
$523$	−12.2077	−	35.2718i	−0.533805	−	1.54233i	−0.813101	−	0.582122i	$-0.802223\pi$
$523$	−12.2077	−	35.2718i	−0.533805	−	1.54233i	0.279297	−	0.960205i	$-0.409899\pi$
$524$	−11.6901	+	7.51278i	−0.510685	+	0.328197i
$525$	9.93762	−	22.6552i	0.433713	−	0.988752i
$526$	−26.8599	−	7.88677i	−1.17115	−	0.343880i
$527$	−19.3457	−	27.1672i	−0.842711	−	1.18342i
$528$	−2.20910	−	3.82628i	−0.0961388	−	0.166517i
$529$	−22.9889	−	0.715368i	−0.999516	−	0.0311029i
$530$	11.1365	−	19.2890i	0.483739	−	0.837861i
$531$	1.04977	−	2.29867i	0.0455561	−	0.0997539i
$532$	−17.0265	+	13.8089i	−0.738194	+	0.598690i
$533$	−3.26215	−	3.76472i	−0.141299	−	0.163068i
$534$	0.168490	+	3.53704i	0.00729128	+	0.153063i
$535$	46.2613	+	8.91613i	2.00005	+	0.385478i
$536$	3.00269	−	1.20210i	0.129697	−	0.0519226i
$537$	2.70626	−	11.1553i	0.116784	−	0.481388i
$538$	−10.4324	−	6.70447i	−0.449771	−	0.289050i
$539$	26.5085	+	15.9313i	1.14180	+	0.686210i
$540$	−1.57367	−	3.44586i	−0.0677201	−	0.148286i
$541$	−2.48943	−	0.237712i	−0.107029	−	0.0102200i	0.0414040	−	0.999142i	$-0.486817\pi$
$541$	−2.48943	−	0.237712i	−0.107029	−	0.0102200i	−0.148433	+	0.988922i	$0.547423\pi$
$542$	−10.4937	+	8.25231i	−0.450742	+	0.354467i
$543$	−0.150628	+	3.16207i	−0.00646406	+	0.135697i
$544$	−1.16466	+	4.80081i	−0.0499345	+	0.205833i
$545$	−10.4312	+	72.5506i	−0.446824	+	3.10773i
$546$	−0.413830	−	1.60047i	−0.0177103	−	0.0684939i
$547$	30.3453	−	19.5017i	1.29747	−	0.833834i	0.304537	−	0.952501i	$-0.401498\pi$
$547$	30.3453	−	19.5017i	1.29747	−	0.833834i	0.992934	+	0.118667i	$0.0378621\pi$
$548$	−14.4438	+	2.78381i	−0.617007	+	0.118918i
$549$	1.31409	+	5.41674i	0.0560839	+	0.231181i
$550$	−41.1250	+	3.92696i	−1.75358	+	0.167446i
$551$	13.4088	−	23.2247i	0.571233	−	0.989404i
$552$	−4.19011	+	2.33303i	−0.178343	+	0.0993003i
$553$	−9.93448	−	20.9159i	−0.422457	−	0.889436i
$554$	−9.89680	+	21.6710i	−0.420475	+	0.920711i
$555$	27.9374	−	26.6383i	1.18588	−	1.13073i
$556$	1.39640	−	4.03463i	0.0592204	−	0.171106i
$557$	15.6099	+	8.04747i	0.661413	+	0.340982i	0.756035	−	0.654531i	$-0.227134\pi$
$557$	15.6099	+	8.04747i	0.661413	+	0.340982i	−0.0946218	+	0.995513i	$0.530164\pi$
$558$	−2.20810	−	6.37989i	−0.0934764	−	0.270082i
$559$	−0.665394	+	4.62792i	−0.0281432	+	0.195740i
$560$	−9.81189	+	2.04445i	−0.414628	+	0.0863939i
$561$	−18.3614	−	11.8001i	−0.775217	−	0.498202i
$562$	−4.89828	−	1.96098i	−0.206622	−	0.0827188i
$563$	3.54196	−	4.97399i	0.149276	−	0.209629i	−0.733166	−	0.680049i	$-0.761958\pi$
$563$	3.54196	−	4.97399i	0.149276	−	0.209629i	0.882442	+	0.470421i	$0.155898\pi$
$564$	5.75916	−	8.08761i	0.242504	−	0.340550i
$565$	−27.2411	−	10.9057i	−1.14604	−	0.458806i
$566$	−9.14041	−	5.87418i	−0.384200	−	0.246910i
$567$	2.59012	−	0.539690i	0.108775	−	0.0226649i
$568$	−0.0948152	+	0.659454i	−0.00397836	+	0.0276701i
$569$	−0.248801	−	0.718862i	−0.0104303	−	0.0301363i	0.939666	−	0.342095i	$-0.111136\pi$
$569$	−0.248801	−	0.718862i	−0.0104303	−	0.0301363i	−0.950096	+	0.311958i	$0.899015\pi$
$570$	27.8991	+	14.3830i	1.16857	+	0.602438i
$571$	2.05030	−	5.92396i	0.0858025	−	0.247910i	−0.893935	−	0.448197i	$-0.852066\pi$
$571$	2.05030	−	5.92396i	0.0858025	−	0.247910i	0.979737	+	0.200287i	$0.0641875\pi$
$572$	−1.99791	+	1.90501i	−0.0835370	+	0.0796524i
$573$	−7.17472	+	15.7105i	−0.299728	+	0.656314i
$574$	−9.04992	−	19.0536i	−0.377736	−	0.795282i
$575$	3.56778	+	44.7009i	0.148787	+	1.86416i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−10.0463	+	0.959304i	−0.418232	+	0.0399363i	−0.302051	−	0.953292i	$-0.597671\pi$
$577$	−10.0463	+	0.959304i	−0.418232	+	0.0399363i	−0.116181	+	0.993228i	$0.537065\pi$
$578$	1.74560	+	7.19547i	0.0726075	+	0.299292i
$579$	−8.56636	+	1.65103i	−0.356006	+	0.0686145i
$580$	10.3143	−	6.62862i	0.428279	−	0.275238i
$581$	−2.60907	−	10.0905i	−0.108243	−	0.418625i
$582$	0.742475	−	5.16402i	0.0307766	−	0.214056i
$583$	6.12436	−	25.2450i	0.253645	−	1.04554i
$584$	0.270678	−	5.68224i	0.0112008	−	0.235133i
$585$	−1.86053	+	1.46314i	−0.0769234	+	0.0604932i
$586$	−1.96684	−	0.187810i	−0.0812492	−	0.00775836i
$587$	5.81498	+	12.7330i	0.240010	+	0.525549i	0.990855	−	0.134930i	$-0.0430808\pi$
$587$	5.81498	+	12.7330i	0.240010	+	0.525549i	−0.750845	+	0.660478i	$0.770354\pi$
$588$	0.122828	−	6.99892i	0.00506535	−	0.288631i
$589$	47.0593	+	30.2432i	1.93904	+	1.24615i
$590$	−2.25690	+	9.30306i	−0.0929150	+	0.383001i
$591$	−2.12281	+	0.849844i	−0.0873207	+	0.0349579i
$592$	−10.0059	−	1.92847i	−0.411239	−	0.0792598i
$593$	2.10394	+	44.1672i	0.0863986	+	1.81373i	0.461926	+	0.886918i	$0.347159\pi$
$593$	2.10394	+	44.1672i	0.0863986	+	1.81373i	−0.375527	+	0.926811i	$0.622538\pi$
$594$	−2.89331	−	3.33906i	−0.118714	−	0.137003i
$595$	−38.4551	+	31.1878i	−1.57650	+	1.27858i
$596$	4.57710	−	10.0224i	0.187485	−	0.410536i
$597$	7.90582	−	13.6933i	0.323563	−	0.560428i
$598$	2.03385	+	2.20058i	0.0831703	+	0.0899883i
$599$	2.72650	+	4.72243i	0.111402	+	0.192953i	0.916336	−	0.400411i	$-0.131133\pi$
$599$	2.72650	+	4.72243i	0.111402	+	0.192953i	−0.804934	+	0.593364i	$0.797799\pi$
$600$	5.42377	+	7.61663i	0.221425	+	0.310947i
$601$	37.9040	+	11.1296i	1.54614	+	0.453987i	0.939943	−	0.341331i	$-0.110878\pi$
$601$	37.9040	+	11.1296i	1.54614	+	0.453987i	0.606193	+	0.795317i	$0.292696\pi$
$602$	−7.95295	+	18.1306i	−0.324138	+	0.738949i
$603$	2.72093	−	1.74864i	0.110805	−	0.0712100i
$604$	3.90598	+	11.2856i	0.158932	+	0.459204i
$605$	−29.9653	+	11.9963i	−1.21826	+	0.487719i
$606$	−2.42216	−	2.30952i	−0.0983934	−	0.0938180i
$607$	−29.7819	+	15.3537i	−1.20881	+	0.623185i	−0.940384	−	0.340115i	$-0.889534\pi$
$607$	−29.7819	+	15.3537i	−1.20881	+	0.623185i	−0.268427	+	0.963300i	$0.586504\pi$
$608$	−1.17920	−	8.20151i	−0.0478229	−	0.332615i
$609$	2.92199	+	8.04914i	0.118405	+	0.326168i
$610$	−8.77144	−	19.2068i	−0.355145	−	0.777659i
$611$	−5.75918	−	2.30563i	−0.232992	−	0.0932757i
$612$	−0.235057	+	4.93446i	−0.00950164	+	0.199464i
$613$	−2.75172	−	2.62376i	−0.111141	−	0.105973i	0.632471	−	0.774584i	$-0.282041\pi$
$613$	−2.75172	−	2.62376i	−0.111141	−	0.105973i	−0.743612	+	0.668611i	$0.766889\pi$
$614$	−8.86056	−	6.96802i	−0.357583	−	0.281206i
$615$	−19.7781	+	22.8251i	−0.797528	+	0.920396i
$616$	−10.3084	+	5.51194i	−0.415336	+	0.222082i
$617$	−2.22652	−	2.56954i	−0.0896363	−	0.103446i	0.709159	−	0.705048i	$-0.249075\pi$
$617$	−2.22652	−	2.56954i	−0.0896363	−	0.103446i	−0.798796	+	0.601602i	$0.794529\pi$
$618$	6.39665	−	6.09919i	0.257311	−	0.245345i
$619$	1.76422	−	0.168463i	0.0709101	−	0.00677110i	−0.0595407	−	0.998226i	$-0.518964\pi$
$619$	1.76422	−	0.168463i	0.0709101	−	0.00677110i	0.130451	+	0.991455i	$0.458358\pi$
$620$	12.7874	+	22.1485i	0.513556	+	0.889504i
$621$	−3.67286	+	3.08385i	−0.147387	+	0.123751i
$622$	−7.61598			−0.305373
$623$	9.36769	−	0.140770i	0.375309	−	0.00563983i
$624$	0.599507	+	0.176031i	0.0239995	+	0.00704688i
$625$	15.3949	−	2.96712i	0.615796	−	0.118685i
$626$	−10.2520	−	5.28526i	−0.409752	−	0.211242i
$627$	35.9470	+	6.92822i	1.43559	+	0.276686i
$628$	9.71709	+	7.64161i	0.387754	+	0.304933i
$629$	−48.3002	+	14.1822i	−1.92586	+	0.565482i
$630$	−9.24766	+	3.86442i	−0.368436	+	0.153962i
$631$	0.186757	+	1.29893i	0.00743470	+	0.0517095i	0.993201	−	0.116412i	$-0.0371392\pi$
$631$	0.186757	+	1.29893i	0.00743470	+	0.0517095i	−0.985766	+	0.168121i	$0.946230\pi$
$632$	8.71227	+	0.831921i	0.346556	+	0.0330920i
$633$	13.6018	−	19.1010i	0.540621	−	0.759196i
$634$	−20.2134	+	15.8960i	−0.802776	+	0.631310i
$635$	32.0260	−	16.5105i	1.27091	−	0.655200i
$636$	−5.64142	+	1.65647i	−0.223697	+	0.0656833i
$637$	−4.26786	+	0.956401i	−0.169099	+	0.0378940i
$638$	9.36433	−	10.8070i	0.370737	−	0.427854i
$639$	0.0317008	+	0.665481i	0.00125406	+	0.0263260i
$640$	1.23900	−	3.57985i	0.0489757	−	0.141506i
$641$	1.87783	+	7.74053i	0.0741700	+	0.305733i	0.996798	−	0.0799576i	$-0.0254785\pi$
$641$	1.87783	+	7.74053i	0.0741700	+	0.305733i	−0.922628	+	0.385690i	$0.873963\pi$
$642$	−7.21400	−	10.1306i	−0.284714	−	0.399825i
$643$	−23.6811			−0.933893			−0.466946	−	0.884286i	$-0.654646\pi$
$643$	−23.6811			−0.933893			−0.466946	+	0.884286i	$0.654646\pi$
$644$	5.80829	+	11.2811i	0.228879	+	0.444539i
$645$	28.3471			1.11617
$646$	−23.7432	−	33.3427i	−0.934165	−	1.31185i
$647$	6.22048	+	25.6412i	0.244552	+	1.00806i	0.953162	+	0.302459i	$0.0978074\pi$
$647$	6.22048	+	25.6412i	0.244552	+	1.00806i	−0.708610	+	0.705600i	$0.750677\pi$
$648$	−0.327068	+	0.945001i	−0.0128484	+	0.0371231i
$649$	0.531250	+	11.1523i	0.0208534	+	0.437767i
$650$	3.82589	−	4.41531i	0.150064	−	0.173183i
$651$	−17.0609	+	5.28925i	−0.668670	+	0.207302i
$652$	21.6676	−	6.36217i	0.848568	−	0.249162i
$653$	22.9420	−	11.8274i	0.897791	−	0.462843i	0.0534012	−	0.998573i	$-0.482994\pi$
$653$	22.9420	−	11.8274i	0.897791	−	0.462843i	0.844389	+	0.535730i	$0.179963\pi$
$654$	15.2091	−	11.9606i	0.594723	−	0.467696i
$655$	30.5348	−	42.8801i	1.19309	−	1.67546i
$656$	7.93654	+	0.757848i	0.309870	+	0.0295890i
$657$	−0.809584	−	5.63078i	−0.0315849	−	0.219678i
$658$	−20.8902	−	15.9261i	−0.814385	−	0.620864i
$659$	4.48183	−	1.31598i	0.174587	−	0.0512634i	−0.193271	−	0.981145i	$-0.561910\pi$
$659$	4.48183	−	1.31598i	0.174587	−	0.0512634i	0.367858	+	0.929882i	$0.380091\pi$
$660$	13.1562	+	10.3461i	0.512104	+	0.402723i
$661$	8.45587	+	1.62974i	0.328895	+	0.0633893i	0.351026	−	0.936366i	$-0.385833\pi$
$661$	8.45587	+	1.62974i	0.328895	+	0.0633893i	−0.0221308	+	0.999755i	$0.507045\pi$
$662$	16.5226	+	8.51802i	0.642171	+	0.331062i
$663$	3.03085	−	0.584148i	0.117708	−	0.0226864i
$664$	3.77971	+	1.10982i	0.146681	+	0.0430695i
$665$	40.4377	−	72.5357i	1.56811	−	2.81281i
$666$	−10.1900			−0.394855
$667$	−11.5712	−	10.3459i	−0.448038	−	0.400596i
$668$	4.43454	+	7.68085i	0.171578	+	0.297181i
$669$	−12.0605	+	1.15163i	−0.466284	+	0.0445247i
$670$	−8.86751	+	8.45516i	−0.342582	+	0.326651i
$671$	−16.1269	−	18.6114i	−0.622572	−	0.718487i
$672$	2.24699	+	1.39680i	0.0866795	+	0.0538826i
$673$	−29.1389	+	33.6281i	−1.12322	+	1.29627i	−0.172923	+	0.984935i	$0.555321\pi$
$673$	−29.1389	+	33.6281i	−1.12322	+	1.29627i	−0.950301	+	0.311333i	$0.899224\pi$
$674$	12.3565	+	9.71725i	0.475954	+	0.374295i
$675$	6.76722	+	6.45253i	0.260470	+	0.248358i
$676$	−0.599989	+	12.5953i	−0.0230765	+	0.484435i
$677$	9.66008	+	3.86731i	0.371267	+	0.148633i	0.549790	−	0.835303i	$-0.314708\pi$
$677$	9.66008	+	3.86731i	0.371267	+	0.148633i	−0.178523	+	0.983936i	$0.557132\pi$
$678$	3.21777	+	7.04593i	0.123578	+	0.270597i
$679$	−13.5915	−	2.40833i	−0.521594	−	0.0924232i
$680$	−2.66327	−	18.5234i	−0.102132	−	0.710341i
$681$	−5.21705	+	2.68958i	−0.199918	+	0.103065i
$682$	21.5877	+	20.5838i	0.826635	+	0.788195i
$683$	−14.1087	+	5.64827i	−0.539854	+	0.216125i	−0.625533	−	0.780198i	$-0.715118\pi$
$683$	−14.1087	+	5.64827i	−0.539854	+	0.216125i	0.0856788	+	0.996323i	$0.472694\pi$
$684$	−2.71004	−	7.83014i	−0.103621	−	0.299393i
$685$	46.8769	−	30.1260i	1.79108	−	1.15105i
$686$	−18.4970	−	0.927877i	−0.706219	−	0.0354265i
$687$	−8.81570	−	2.58852i	−0.336340	−	0.0987583i
$688$	−4.34058	−	6.09548i	−0.165483	−	0.232388i
$689$	1.83683	+	3.18148i	0.0699776	+	0.121205i
$690$	11.4512	−	14.1043i	0.435939	−	0.536940i
$691$	16.4206	−	28.4413i	0.624669	−	1.08196i	−0.363936	−	0.931424i	$-0.618567\pi$
$691$	16.4206	−	28.4413i	0.624669	−	1.08196i	0.988605	−	0.150534i	$-0.0480994\pi$
$692$	4.51637	−	9.88946i	0.171687	−	0.375941i
$693$	−9.07893	+	7.36320i	−0.344880	+	0.279705i
$694$	10.2391	+	11.8165i	0.388670	+	0.448549i
$695$	0.769565	+	16.1552i	0.0291913	+	0.612800i
$696$	−3.17806	−	0.612520i	−0.120464	−	0.0232175i
$697$	36.5641	−	14.6380i	1.38496	−	0.554456i
$698$	−4.59269	+	18.9313i	−0.173836	+	0.716561i
$699$	−2.81703	−	1.81040i	−0.106550	−	0.0684756i
$700$	20.6084	−	13.6860i	0.778923	−	0.517284i
$701$	11.5739	+	25.3433i	0.437140	+	0.957203i	0.992114	+	0.125335i	$0.0400007\pi$
$701$	11.5739	+	25.3433i	0.437140	+	0.957203i	−0.554975	+	0.831867i	$0.687272\pi$
$702$	0.621987	+	0.0593925i	0.0234754	+	0.00224163i
$703$	66.3688	−	52.1930i	2.50315	−	1.96850i
$704$	0.210227	−	4.41320i	0.00792321	−	0.166329i
$705$	−8.86725	+	36.5513i	−0.333960	+	1.37660i
$706$	−0.384323	+	2.67303i	−0.0144642	+	0.100601i
$707$	−6.31589	+	6.20602i	−0.237534	+	0.233402i
$708$	2.12588	−	1.36622i	0.0798954	−	0.0513456i
$709$	−11.2989	+	2.17769i	−0.424341	+	0.0817850i	−0.396951	−	0.917840i	$-0.629932\pi$
$709$	−11.2989	+	2.17769i	−0.424341	+	0.0817850i	−0.0273898	+	0.999625i	$0.508720\pi$
$710$	−0.595015	−	2.45269i	−0.0223305	−	0.0920477i
$711$	8.71227	−	0.831921i	0.326736	−	0.0311995i
$712$	−1.77053	+	3.06664i	−0.0663533	+	0.114927i
$713$	22.7049	−	23.0824i	0.850304	−	0.864444i
$714$	13.0282	+	1.04676i	0.487568	+	0.0391741i
$715$	4.34423	−	9.51253i	0.162465	−	0.355748i
$716$	8.30768	−	7.92136i	0.310473	−	0.296035i
$717$	−7.99965	+	23.1135i	−0.298752	+	0.863188i
$718$	−0.691175	−	0.356325i	−0.0257944	−	0.0132979i
$719$	−11.3492	−	32.7913i	−0.423254	−	1.22291i	−0.932147	−	0.362081i	$-0.882066\pi$
$719$	−11.3492	−	32.7913i	−0.423254	−	1.22291i	0.508893	−	0.860830i	$-0.330055\pi$
$720$	0.539116	−	3.74964i	0.0200917	−	0.139741i
$721$	−15.5772	−	17.4405i	−0.580125	−	0.649518i
$722$	41.7727	+	26.8457i	1.55462	+	0.999094i
$723$	12.4437	+	4.98170i	0.462785	+	0.185271i
$724$	−1.83626	+	2.57866i	−0.0682440	+	0.0958353i
$725$	−17.5543	+	24.6516i	−0.651950	+	0.915536i
$726$	7.91019	+	3.16676i	0.293575	+	0.117530i
$727$	15.0752	+	9.68825i	0.559109	+	0.359317i	0.789471	−	0.613788i	$-0.210355\pi$
$727$	15.0752	+	9.68825i	0.559109	+	0.359317i	−0.230363	+	0.973105i	$0.573991\pi$
$728$	0.517145	−	1.57014i	0.0191667	−	0.0581931i
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$	7.04826	+	20.3646i	0.260868	+	0.753728i
$731$	−32.8572	−	16.9390i	−1.21527	−	0.626513i
$732$	−1.82303	+	5.26730i	−0.0673812	+	0.194685i
$733$	9.49260	−	9.05118i	0.350617	−	0.334313i	−0.494219	−	0.869337i	$-0.664546\pi$
$733$	9.49260	−	9.05118i	0.350617	−	0.334313i	0.844837	+	0.535024i	$0.179698\pi$
$734$	3.75433	−	8.22083i	0.138575	−	0.303436i
$735$	9.42202	+	24.7870i	0.347537	+	0.914283i
$736$	−4.78627	−	0.302674i	−0.176424	−	0.0111567i
$737$	−7.14507	+	12.3756i	−0.263192	+	0.455862i
$738$	7.93654	−	0.757848i	0.292148	−	0.0278968i
$739$	−7.33242	−	30.2246i	−0.269727	−	1.11183i	−0.931968	−	0.362540i	$-0.881909\pi$
$739$	−7.33242	−	30.2246i	−0.269727	−	1.11183i	0.662241	−	0.749291i	$-0.269606\pi$
$740$	37.9042	−	7.30543i	1.39339	−	0.268553i
$741$	−4.35528	+	2.79897i	−0.159995	+	0.102823i
$742$	3.89418	+	15.0606i	0.142960	+	0.552893i
$743$	6.19449	−	43.0836i	0.227254	−	1.58058i	−0.482347	−	0.875980i	$-0.660215\pi$
$743$	6.19449	−	43.0836i	0.227254	−	1.58058i	0.709601	−	0.704604i	$-0.248875\pi$
$744$	1.59166	−	6.56090i	0.0583529	−	0.240534i
$745$	−1.98601	+	41.6916i	−0.0727619	+	1.52746i
$746$	−26.6862	+	20.9863i	−0.977053	+	0.768363i
$747$	3.92145	+	0.374453i	0.143478	+	0.0137005i
$748$	−9.06693	−	19.8538i	−0.331520	−	0.725927i
$749$	−27.4105	+	18.2034i	−1.00156	+	0.665137i
$750$	−13.8641	−	8.90989i	−0.506244	−	0.325343i
$751$	−10.3299	+	42.5803i	−0.376942	+	1.55378i	0.395362	+	0.918525i	$0.370619\pi$
$751$	−10.3299	+	42.5803i	−0.376942	+	1.55378i	−0.772305	+	0.635252i	$0.780896\pi$
$752$	9.21740	−	3.69009i	0.336124	−	0.134564i
$753$	−2.57227	−	0.495764i	−0.0937386	−	0.0180666i
$754$	0.0962223	+	2.01996i	0.00350421	+	0.0735624i
$755$	−29.6260	−	34.1903i	−1.07820	−	1.24431i
$756$	2.47073	+	0.946309i	0.0898595	+	0.0344169i
$757$	10.6852	−	23.3973i	0.388360	−	0.850390i	−0.609959	−	0.792433i	$-0.708814\pi$
$757$	10.6852	−	23.3973i	0.388360	−	0.850390i	0.998319	−	0.0579568i	$-0.0184586\pi$
$758$	17.9386	−	31.0705i	0.651558	−	1.12853i
$759$	8.18014	−	19.5463i	0.296920	−	0.709485i
$760$	15.6942	+	27.1832i	0.569289	+	0.986037i
$761$	1.90487	+	2.67501i	0.0690515	+	0.0969692i	0.847657	−	0.530544i	$-0.178012\pi$
$761$	1.90487	+	2.67501i	0.0690515	+	0.0969692i	−0.778606	+	0.627513i	$0.784073\pi$
$762$	−9.12621	−	2.67970i	−0.330608	−	0.0970751i
$763$	−30.3174	−	41.2488i	−1.09756	−	1.49331i
$764$	−14.5295	+	9.33753i	−0.525658	+	0.337820i
$765$	−6.12072	−	17.6847i	−0.221295	−	0.639390i
$766$	−31.3373	+	12.5456i	−1.13226	+	0.453290i
$767$	−1.14273	−	1.08959i	−0.0412615	−	0.0393427i
$768$	−0.888835	+	0.458227i	−0.0320731	+	0.0165348i
$769$	−5.21148	−	36.2467i	−0.187931	−	1.30709i	−0.837354	−	0.546661i	$-0.815899\pi$
$769$	−5.21148	−	36.2467i	−0.187931	−	1.30709i	0.649423	−	0.760427i	$-0.275010\pi$
$770$	28.4924	−	33.8980i	1.02680	−	1.22160i
$771$	−11.5531	−	25.2978i	−0.416075	−	0.911078i
$772$	−8.09910	−	3.24239i	−0.291493	−	0.116696i
$773$	−0.336537	+	7.06478i	−0.0121044	+	0.254102i	0.984702	+	0.174247i	$0.0557490\pi$
$773$	−0.336537	+	7.06478i	−0.0121044	+	0.254102i	−0.996806	+	0.0798558i	$0.974554\pi$
$774$	−5.41571	−	5.16387i	−0.194664	−	0.185612i
$775$	−49.6208	−	39.0222i	−1.78243	−	1.40172i
$776$	3.41649	−	3.94284i	0.122645	−	0.141540i
$777$	−0.878044	+	26.9460i	−0.0314996	+	0.966681i
$778$	8.69997	+	10.0403i	0.311909	+	0.359962i
$779$	−47.8100	+	45.5867i	−1.71297	+	1.63331i
$780$	−2.35621	+	0.224990i	−0.0843657	+	0.00805595i
$781$	−1.47178	−	2.54920i	−0.0526645	−	0.0912176i
$782$	−21.7012	+	9.50551i	−0.776033	+	0.339916i
$783$	−3.23655			−0.115665
$784$	3.88723	−	5.82146i	0.138830	−	0.207909i
$785$	−44.9323	−	13.1933i	−1.60370	−	0.470890i
$786$	−13.6449	+	2.62985i	−0.486699	+	0.0938036i
$787$	−47.5706	−	24.5244i	−1.69571	−	0.874199i	−0.985389	−	0.170321i	$-0.945520\pi$
$787$	−47.5706	−	24.5244i	−1.69571	−	0.874199i	−0.710321	−	0.703878i	$-0.751450\pi$
$788$	−2.24528	−	0.432742i	−0.0799848	−	0.0154158i
$789$	−22.0046	−	17.3046i	−0.783386	−	0.616061i
$790$	−31.8109	+	9.34054i	−1.13178	+	0.332321i
$791$	18.9092	−	7.90178i	0.672332	−	0.280955i
$792$	−0.628776	−	4.37323i	−0.0223426	−	0.155396i
$793$	3.46687	+	0.331046i	0.123112	+	0.0117558i
$794$	13.9802	−	19.6324i	0.496138	−	0.696728i
$795$	17.5078	−	13.7683i	0.620937	−	0.488310i
$796$	14.0539	−	7.24531i	0.498129	−	0.256803i
$797$	−6.46378	+	1.89794i	−0.228959	+	0.0672284i	−0.394200	−	0.919025i	$-0.628978\pi$
$797$	−6.46378	+	1.89794i	−0.228959	+	0.0672284i	0.165241	+	0.986253i	$0.447160\pi$
$798$	−20.9391	+	6.49158i	−0.741237	+	0.229799i
$799$	32.1196	−	37.0679i	1.13631	−	1.31137i
$800$	0.444911	+	9.33983i	0.0157300	+	0.330213i
$801$	−1.15817	+	3.34630i	−0.0409218	+	0.118236i
$802$	−5.58319	−	23.0142i	−0.197149	−	0.812661i
$803$	14.5790	+	20.4734i	0.514482	+	0.722489i
$804$	3.23438			0.114068
$805$	−36.3098	−	31.4962i	−1.27975	−	1.11010i
$806$	−4.21826			−0.148582
$807$	−7.19326	−	10.1015i	−0.253215	−	0.355591i
$808$	−0.789027	−	3.25241i	−0.0277579	−	0.114419i
$809$	14.8795	−	42.9915i	0.523135	−	1.51150i	−0.305767	−	0.952106i	$-0.598913\pi$
$809$	14.8795	−	42.9915i	0.523135	−	1.51150i	0.828902	−	0.559394i	$-0.188966\pi$
$810$	−0.180250	−	3.78390i	−0.00633332	−	0.132953i
$811$	3.21558	−	3.71097i	0.112914	−	0.130310i	−0.696479	−	0.717578i	$-0.745251\pi$
$811$	3.21558	−	3.71097i	0.112914	−	0.130310i	0.809393	+	0.587268i	$0.199796\pi$
$812$	−1.89356	+	8.35111i	−0.0664510	+	0.293067i
$813$	−12.8091	+	3.76108i	−0.449233	+	0.131907i
$814$	40.0168	−	20.6301i	1.40259	−	0.723084i
$815$	−67.2439	+	52.8812i	−2.35545	+	1.85235i
$816$	−2.86552	+	4.02405i	−0.100313	+	0.140870i
$817$	61.7224	+	5.89378i	2.15939	+	0.206197i
$818$	−1.92784	−	13.4085i	−0.0674055	−	0.468816i
$819$	0.210649	−	1.63963i	0.00736068	−	0.0572934i
$820$	−28.9785	+	8.50886i	−1.01197	+	0.297142i
$821$	−3.31350	−	2.60576i	−0.115642	−	0.0909417i	0.558663	−	0.829394i	$-0.311314\pi$
$821$	−3.31350	−	2.60576i	−0.115642	−	0.0909417i	−0.674305	+	0.738453i	$0.735557\pi$
$822$	−14.4438	−	2.78381i	−0.503784	−	0.0970964i
$823$	17.7243	+	9.13753i	0.617832	+	0.318514i	0.738577	−	0.674169i	$-0.235498\pi$
$823$	17.7243	+	9.13753i	0.617832	+	0.318514i	−0.120745	+	0.992684i	$0.538528\pi$
$824$	8.67867	−	1.67268i	0.302336	−	0.0582705i
$825$	−39.6386	−	11.6390i	−1.38004	−	0.405216i
$826$	−3.42958	−	5.73928i	−0.119330	−	0.199695i
$827$	7.90934			0.275035			0.137517	−	0.990499i	$-0.456088\pi$
$827$	7.90934			0.275035			0.137517	+	0.990499i	$0.456088\pi$
$828$	−4.75706	+	0.608603i	−0.165319	+	0.0211504i
$829$	8.55703	+	14.8212i	0.297198	+	0.514762i	0.975494	−	0.220027i	$-0.0706146\pi$
$829$	8.55703	+	14.8212i	0.297198	+	0.514762i	−0.678296	+	0.734789i	$0.737281\pi$
$830$	−14.8552	+	1.41850i	−0.515632	+	0.0492368i
$831$	−17.2422	+	16.4404i	−0.598124	+	0.570310i
$832$	0.409167	+	0.472204i	0.0141853	+	0.0163707i
$833$	3.89060	−	34.3609i	0.134801	−	1.19053i
$834$	2.79589	−	3.22663i	0.0968137	−	0.111729i
$835$	−26.4097	−	20.7688i	−0.913945	−	0.718734i
$836$	26.4949	+	25.2628i	0.916345	+	0.873733i
$837$	0.321235	−	6.74355i	0.0111035	−	0.233091i
$838$	−2.21039	−	0.884907i	−0.0763567	−	0.0305686i
$839$	16.5649	+	36.2720i	0.571883	+	1.25225i	0.945789	+	0.324783i	$0.105291\pi$
$839$	16.5649	+	36.2720i	0.571883	+	1.25225i	−0.373905	+	0.927467i	$0.621981\pi$
$840$	−9.86889	−	1.74871i	−0.340509	−	0.0603361i
$841$	2.63635	+	18.3362i	0.0909086	+	0.632283i
$842$	−9.58256	+	4.94016i	−0.330237	+	0.170249i
$843$	−3.81859	−	3.64102i	−0.131519	−	0.125403i
$844$	21.7693	−	8.71511i	0.749330	−	0.299987i
$845$	−15.6233	−	45.1405i	−0.537457	−	1.55288i
$846$	8.35248	−	5.36781i	0.287164	−	0.184549i
$847$	9.05562	−	20.6444i	0.311155	−	0.709351i
$848$	−5.64142	−	1.65647i	−0.193727	−	0.0568834i
$849$	−6.30245	−	8.85055i	−0.216299	−	0.303750i
$850$	23.0958	+	40.0031i	0.792180	+	1.37210i
$851$	−21.7151	−	43.7801i	−0.744382	−	1.50076i
$852$	−0.333118	+	0.576977i	−0.0114124	+	0.0197669i
$853$	−22.9108	+	50.1676i	−0.784450	+	1.71771i	−0.0925545	+	0.995708i	$0.529503\pi$
$853$	−22.9108	+	50.1676i	−0.784450	+	1.71771i	−0.691895	+	0.721998i	$0.743224\pi$
$854$	13.7715	+	5.27460i	0.471251	+	0.180493i
$855$	20.5550	+	23.7218i	0.702968	+	0.811268i
$856$	−0.591762	−	12.4226i	−0.0202260	−	0.424596i
$857$	16.3481	+	3.15084i	0.558441	+	0.107631i	0.460659	−	0.887577i	$-0.347613\pi$
$857$	16.3481	+	3.15084i	0.558441	+	0.107631i	0.0977818	+	0.995208i	$0.468825\pi$
$858$	−2.56282	+	1.02600i	−0.0874932	+	0.0350270i
$859$	10.2799	−	42.3742i	0.350745	−	1.44579i	−0.474120	−	0.880460i	$-0.657234\pi$
$859$	10.2799	−	42.3742i	0.350745	−	1.44579i	0.824865	−	0.565330i	$-0.191251\pi$
$860$	23.8471	+	15.3256i	0.813180	+	0.522599i
$861$	−1.32014	−	21.0523i	−0.0449904	−	0.717460i
$862$	−2.58180	−	5.65335i	−0.0879364	−	0.192554i
$863$	13.7342	+	1.31145i	0.467516	+	0.0446424i	0.326156	−	0.945316i	$-0.394246\pi$
$863$	13.7342	+	1.31145i	0.467516	+	0.0446424i	0.141360	+	0.989958i	$0.454852\pi$
$864$	−0.786053	+	0.618159i	−0.0267421	+	0.0210302i
$865$	−1.95966	+	41.1384i	−0.0666305	+	1.39875i
$866$	−3.32812	+	13.7187i	−0.113094	+	0.466180i
$867$	−1.05373	+	7.32882i	−0.0357864	+	0.248900i
$868$	−17.2121	−	4.77422i	−0.584218	−	0.162048i
$869$	−32.5293	+	20.9053i	−1.10348	+	0.709165i
$870$	12.0391	−	2.32035i	0.408164	−	0.0786671i
$871$	−0.476443	−	1.96392i	−0.0161437	−	0.0665450i
$872$	19.2611	−	1.83921i	0.652263	−	0.0622836i
$873$	2.60856	−	4.51817i	0.0882865	−	0.152917i
$874$	27.8660	−	28.3294i	0.942583	−	0.958257i
$875$	−24.7555	+	35.8936i	−0.836887	+	1.21343i
$876$	2.36316	−	5.17461i	0.0798439	−	0.174834i
$877$	7.54610	−	7.19519i	0.254814	−	0.242964i	−0.551895	−	0.833913i	$-0.686095\pi$
$877$	7.54610	−	7.19519i	0.254814	−	0.242964i	0.806709	+	0.590949i	$0.201247\pi$
$878$	−7.75191	+	22.3977i	−0.261614	+	0.755885i
$879$	−1.75615	−	0.905356i	−0.0592333	−	0.0305369i
$880$	5.47414	+	15.8165i	0.184533	+	0.533174i
$881$	4.91821	−	34.2069i	0.165699	−	1.15246i	−0.721953	−	0.691943i	$-0.756755\pi$
$881$	4.91821	−	34.2069i	0.165699	−	1.15246i	0.887651	−	0.460516i	$-0.152336\pi$
$882$	2.71527	−	6.45192i	0.0914278	−	0.217248i
$883$	−33.0682	−	21.2517i	−1.11283	−	0.715175i	−0.150925	−	0.988545i	$-0.548225\pi$
$883$	−33.0682	−	21.2517i	−1.11283	−	0.715175i	−0.961909	+	0.273370i	$0.911862\pi$
$884$	2.86553	+	1.14718i	0.0963781	+	0.0385840i
$885$	−5.55283	+	7.79786i	−0.186656	+	0.262122i
$886$	4.32344	−	6.07142i	0.145249	−	0.203973i
$887$	23.5375	+	9.42298i	0.790311	+	0.316393i	0.731469	−	0.681875i	$-0.238835\pi$
$887$	23.5375	+	9.42298i	0.790311	+	0.316393i	0.0588416	+	0.998267i	$0.481259\pi$
$888$	−8.57239	−	5.50914i	−0.287671	−	0.184875i
$889$	−7.87243	+	23.9020i	−0.264033	+	0.801646i
$890$	1.90904	−	13.2777i	0.0639912	−	0.445068i
$891$	−1.44505	−	4.17521i	−0.0484111	−	0.139875i
$892$	−10.7685	−	5.55156i	−0.360557	−	0.185880i
$893$	−26.9069	+	77.7424i	−0.900405	+	2.60155i
$894$	7.97420	−	7.60339i	0.266697	−	0.254295i
$895$	−18.0641	+	39.5548i	−0.603815	+	1.32217i
$896$	1.13512	+	2.38987i	0.0379218	+	0.0798401i
$897$	1.07029	+	2.79885i	0.0357359	+	0.0934509i
$898$	−6.85834	+	11.8790i	−0.228866	+	0.396407i
$899$	21.7516	−	2.07703i	0.725458	−	0.0692728i
$900$	2.20444	+	9.08684i	0.0734815	+	0.302895i
$901$	−28.5206	+	5.49690i	−0.950159	+	0.183128i
$902$	−29.6330	+	19.0439i	−0.986670	+	0.634094i
$903$	−14.1217	+	13.8761i	−0.469942	+	0.461767i
$904$	−1.10236	+	7.66707i	−0.0366639	+	0.255003i
$905$	2.82725	−	11.6541i	0.0939808	−	0.387394i
$906$	−0.568243	+	11.9289i	−0.0188786	+	0.396311i
$907$	9.76452	−	7.67891i	0.324226	−	0.254974i	−0.442757	−	0.896642i	$-0.646000\pi$
$907$	9.76452	−	7.67891i	0.324226	−	0.254974i	0.766983	+	0.641668i	$0.221757\pi$
$908$	−5.84296	−	0.557935i	−0.193905	−	0.0185157i
$909$	−1.39029	−	3.04431i	−0.0461130	−	0.100973i
$910$	0.391926	+	6.25002i	0.0129922	+	0.207186i
$911$	−47.3270	−	30.4152i	−1.56801	−	1.00770i	−0.980035	−	0.198825i	$-0.936287\pi$
$911$	−47.3270	−	30.4152i	−1.56801	−	1.00770i	−0.587979	−	0.808876i	$-0.700076\pi$
$912$	1.95346	−	8.05229i	0.0646856	−	0.266638i
$913$	−16.1578	+	6.46862i	−0.534746	+	0.214080i
$914$	1.18841	+	0.229047i	0.0393090	+	0.00757619i
$915$	−1.00469	−	21.0910i	−0.0332139	−	0.697246i
$916$	−6.01678	−	6.94373i	−0.198800	−	0.229427i
$917$	5.77849	+	36.3086i	0.190822	+	1.19902i
$918$	−2.05217	+	4.49364i	−0.0677319	+	0.148312i
$919$	24.0015	−	41.5718i	0.791736	−	1.37133i	−0.133155	−	0.991095i	$-0.542511\pi$
$919$	24.0015	−	41.5718i	0.791736	−	1.37133i	0.924891	−	0.380232i	$-0.124156\pi$
$920$	17.2587	−	5.67428i	0.569002	−	0.187075i
$921$	−5.63611	−	9.76202i	−0.185716	−	0.321670i
$922$	16.1157	+	22.6313i	0.530741	+	0.745321i
$923$	0.399413	+	0.117278i	0.0131468	+	0.00386026i
$924$	−11.6185	+	1.28587i	−0.382222	+	0.0423021i
$925$	−80.1554	+	51.5128i	−2.63549	+	1.69373i
$926$	11.2345	+	32.4599i	0.369188	+	1.06670i
$927$	8.20528	−	3.28490i	0.269497	−	0.107890i
$928$	−2.34240	−	2.23347i	−0.0768930	−	0.0733173i
$929$	−28.3242	+	14.6021i	−0.929286	+	0.479080i	−0.855273	−	0.518177i	$-0.826611\pi$
$929$	−28.3242	+	14.6021i	−0.929286	+	0.479080i	−0.0740126	+	0.997257i	$0.523580\pi$
$930$	3.63968	+	25.3145i	0.119350	+	0.830097i
$931$	15.3617	+	55.9297i	0.503460	+	1.83302i
$932$	−1.39107	−	3.04601i	−0.0455659	−	0.0997753i
$933$	−7.07043	−	2.83057i	−0.231475	−	0.0926688i
$934$	−0.369470	+	7.75613i	−0.0120894	+	0.253788i
$935$	59.8397	+	57.0570i	1.95697	+	1.86596i
$936$	0.491139	+	0.386236i	0.0160534	+	0.0126245i
$937$	26.9239	−	31.0718i	0.879565	−	1.01507i	−0.120186	−	0.992751i	$-0.538349\pi$
$937$	26.9239	−	31.0718i	0.879565	−	1.01507i	0.999751	−	0.0223210i	$-0.00710560\pi$
$938$	0.278697	−	8.55282i	0.00909977	−	0.279259i
$939$	−7.55328	−	8.71695i	−0.246492	−	0.284467i
$940$	−27.2207	+	25.9549i	−0.887842	+	0.846556i
$941$	39.1744	−	3.74070i	1.27705	−	0.121943i	0.565600	−	0.824680i	$-0.308645\pi$
$941$	39.1744	−	3.74070i	1.27705	−	0.121943i	0.711450	+	0.702736i	$0.248039\pi$
$942$	6.18094	+	10.7057i	0.201386	+	0.348811i
$943$	20.1689	+	32.4833i	0.656788	+	1.05780i
$944$	2.52704			0.0822480
$945$	−10.0215	+	0.150595i	−0.325999	+	0.00489884i
$946$	31.7223	+	9.31450i	1.03138	+	0.302841i
$947$	0.117222	−	0.0225927i	0.00380921	−	0.000734165i	−0.187346	−	0.982294i	$-0.559989\pi$
$947$	0.117222	−	0.0225927i	0.00380921	−	0.000734165i	0.191155	+	0.981560i	$0.438777\pi$
$948$	7.77900	+	4.01035i	0.252650	+	0.130250i
$949$	−3.49015	−	0.672671i	−0.113295	−	0.0218358i
$950$	−60.9004	−	47.8926i	−1.97587	−	1.55384i
$951$	−24.6734	+	7.24476i	−0.800090	+	0.234927i
$952$	10.3941	+	7.92416i	0.336874	+	0.256824i
$953$	−4.38378	−	30.4899i	−0.142005	−	0.987664i	−0.928835	−	0.370494i	$-0.879188\pi$
$953$	−4.38378	−	30.4899i	−0.142005	−	0.987664i	0.786830	−	0.617169i	$-0.211721\pi$
$954$	−5.85296	−	0.558890i	−0.189497	−	0.0180947i
$955$	37.9512	−	53.2950i	1.22807	−	1.72459i
$956$	−19.2258	+	15.1193i	−0.621807	+	0.488995i
$957$	12.7101	−	6.55251i	0.410859	−	0.211813i
$958$	26.4031	−	7.75265i	0.853046	−	0.250477i
$959$	−8.60592	+	37.9544i	−0.277900	+	1.22561i
$960$	2.48074	−	2.86293i	0.0800655	−	0.0924006i
$961$	0.693683	+	14.5622i	0.0223769	+	0.469748i
$962$	−2.08240	+	6.01671i	−0.0671394	+	0.193987i
$963$	−2.93206	−	12.0861i	−0.0944845	−	0.389470i
$964$	7.77498	+	10.9184i	0.250415	+	0.351659i
$965$	33.0483			1.06386
$966$	1.19946	+	12.6318i	0.0385919	+	0.406420i
$967$	−12.5542			−0.403717			−0.201858	−	0.979415i	$-0.564698\pi$
$967$	−12.5542			−0.403717			−0.201858	+	0.979415i	$0.564698\pi$
$968$	4.94239	+	6.94062i	0.158855	+	0.223080i
$969$	−9.65023	−	39.7788i	−0.310010	−	1.27788i
$970$	−6.46401	+	18.6765i	−0.207547	+	0.599667i
$971$	0.283430	+	5.94993i	0.00909570	+	0.190942i	0.998842	+	0.0481071i	$0.0153189\pi$
$971$	0.283430	+	5.94993i	0.00909570	+	0.190942i	−0.989746	+	0.142835i	$0.954378\pi$
$972$	−0.654861	+	0.755750i	−0.0210047	+	0.0242407i
$973$	−8.29141	−	7.67133i	−0.265811	−	0.245932i
$974$	−9.78413	+	2.87288i	−0.313504	+	0.0920531i
$975$	5.19284	−	2.67709i	0.166304	−	0.0857356i
$976$	−4.38135	+	3.44553i	−0.140244	+	0.110289i
$977$	5.23824	−	7.35608i	0.167586	−	0.235342i	−0.722239	−	0.691644i	$-0.756887\pi$
$977$	5.23824	−	7.35608i	0.167586	−	0.235342i	0.889825	+	0.456302i	$0.150826\pi$
$978$	22.4801	+	2.14659i	0.718833	+	0.0686403i
$979$	−2.22653	−	15.4859i	−0.0711602	−	0.494930i
$980$	−5.47456	+	25.9461i	−0.174878	+	0.828817i
$981$	18.5649	−	5.45116i	0.592733	−	0.174042i
$982$	10.4234	+	8.19702i	0.332623	+	0.261577i
$983$	−52.7374	−	10.1643i	−1.68206	−	0.324191i	−0.743353	−	0.668900i	$-0.766766\pi$
$983$	−52.7374	−	10.1643i	−1.68206	−	0.324191i	−0.938710	+	0.344709i	$0.887978\pi$
$984$	7.08637	+	3.65328i	0.225905	+	0.116462i
$985$	8.50556	−	1.63931i	0.271010	−	0.0522328i
$986$	−15.3411	−	4.50455i	−0.488559	−	0.143454i
$987$	−13.4747	−	22.5494i	−0.428903	−	0.717755i
$988$	−5.17713			−0.164707
$989$	10.6450	−	34.2722i	0.338490	−	1.08979i
$990$	8.36851	+	14.4947i	0.265969	+	0.460671i
$991$	−33.8577	+	3.23302i	−1.07552	+	0.102700i	−0.617755	−	0.786371i	$-0.711958\pi$
$991$	−33.8577	+	3.23302i	−1.07552	+	0.102700i	−0.457770	+	0.889071i	$0.651352\pi$
$992$	4.88607	−	4.65886i	0.155133	−	0.147919i
$993$	12.1733	+	14.0487i	0.386307	+	0.445822i
$994$	1.49702	+	0.930596i	0.0474827	+	0.0295167i
$995$	−39.2245	+	45.2675i	−1.24350	+	1.43508i
$996$	3.09649	+	2.43510i	0.0981159	+	0.0771592i
$997$	11.0934	+	10.5776i	0.351332	+	0.334994i	0.845109	−	0.534594i	$-0.179536\pi$
$997$	11.0934	+	10.5776i	0.351332	+	0.334994i	−0.493777	+	0.869589i	$0.664384\pi$
$998$	0.987921	−	20.7390i	0.0312721	−	0.656482i
$999$	−9.46009	−	3.78725i	−0.299304	−	0.119823i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.y.d.121.2	✓	160
7.4	even	3	inner	966.2.y.d.949.7	yes	160
23.4	even	11	inner	966.2.y.d.625.7	yes	160
161.4	even	33	inner	966.2.y.d.487.2	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.y.d.121.2	✓	160	1.1	even	1	trivial
966.2.y.d.487.2	yes	160	161.4	even	33	inner
966.2.y.d.625.7	yes	160	23.4	even	11	inner
966.2.y.d.949.7	yes	160	7.4	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.580057 + 0.814576i) q^{2} +(0.235759 + 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(-0.180250 - 3.78390i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(1.94204 + 1.79680i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +O(q^{10})\)	\(q+(0.580057 + 0.814576i) q^{2} +(0.235759 + 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(-0.180250 - 3.78390i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(1.94204 + 1.79680i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +(2.97772 - 2.34171i) q^{10} +(2.56281 - 3.59896i) q^{11} +(-0.995472 - 0.0950560i) q^{12} +(0.0889206 + 0.618456i) q^{13} +(-0.337138 + 2.62418i) q^{14} +(3.63475 - 1.06726i) q^{15} +(-0.786053 - 0.618159i) q^{16} +(-4.85079 - 0.934912i) q^{17} +(-0.888835 - 0.458227i) q^{18} +(8.13612 - 1.56811i) q^{19} +(3.63475 + 1.06726i) q^{20} +(-1.28830 + 2.31091i) q^{21} +4.41820 q^{22} +(0.0745912 - 4.79525i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-9.30808 + 0.888814i) q^{25} +(-0.452201 + 0.431172i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(-2.33316 + 1.24755i) q^{28} +(2.11949 - 2.44602i) q^{29} +(2.97772 + 2.34171i) q^{30} +(4.88607 + 4.65886i) q^{31} +(0.0475819 - 0.998867i) q^{32} +(4.10172 + 1.64208i) q^{33} +(-2.05217 - 4.49364i) q^{34} +(6.44887 - 7.67235i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(9.05725 - 4.66934i) q^{37} +(5.99675 + 5.71789i) q^{38} +(-0.580059 + 0.232221i) q^{39} +(1.23900 + 3.57985i) q^{40} +(-6.70701 + 4.31034i) q^{41} +(-2.62969 + 0.291040i) q^{42} +(7.17990 + 2.10821i) q^{43} +(2.56281 + 3.59896i) q^{44} +(1.89410 + 3.28067i) q^{45} +(3.94936 - 2.72076i) q^{46} +(-4.96430 + 8.59843i) q^{47} +(0.415415 - 0.909632i) q^{48} +(0.543018 + 6.97891i) q^{49} +(-6.12322 - 7.06657i) q^{50} +(-0.235057 - 4.93446i) q^{51} +(-0.613525 - 0.118247i) q^{52} +(5.45842 - 2.18522i) q^{53} +(0.235759 - 0.971812i) q^{54} +(-14.0801 - 9.04872i) q^{55} +(-2.36959 - 1.17688i) q^{56} +(3.44207 + 7.53708i) q^{57} +(3.22189 + 0.307653i) q^{58} +(-1.98638 + 1.56211i) q^{59} +(-0.180250 + 3.78390i) q^{60} +(1.31409 - 5.41674i) q^{61} +(-0.960796 + 6.68248i) q^{62} +(-2.54949 - 0.707167i) q^{63} +(0.841254 - 0.540641i) q^{64} +(2.32415 - 0.447943i) q^{65} +(1.04163 + 4.29366i) q^{66} +(-3.21973 + 0.307447i) q^{67} +(2.47003 - 4.27822i) q^{68} +(4.67767 - 1.05803i) q^{69} +(9.99043 + 0.802690i) q^{70} +(0.276764 - 0.606029i) q^{71} +(0.723734 - 0.690079i) q^{72} +(-1.86059 + 5.37581i) q^{73} +(9.05725 + 4.66934i) q^{74} +(-3.05822 - 8.83615i) q^{75} +(-1.17920 + 8.20151i) q^{76} +(11.4437 - 2.38446i) q^{77} +(-0.525629 - 0.337801i) q^{78} +(-8.12499 - 3.25275i) q^{79} +(-2.19737 + 3.08577i) q^{80} +(0.580057 - 0.814576i) q^{81} +(-7.40155 - 2.96313i) q^{82} +(-3.31394 - 2.12974i) q^{83} +(-1.76245 - 1.97327i) q^{84} +(-2.66327 + 18.5234i) q^{85} +(2.44745 + 7.07146i) q^{86} +(2.87676 + 1.48307i) q^{87} +(-1.44505 + 4.17521i) q^{88} +(2.56278 - 2.44361i) q^{89} +(-1.57367 + 3.44586i) q^{90} +(-0.938555 + 1.36084i) q^{91} +(4.50712 + 1.63886i) q^{92} +(-3.37560 + 5.84671i) q^{93} +(-9.88365 + 0.943774i) q^{94} +(-7.40010 - 30.5036i) q^{95} +(0.981929 - 0.189251i) q^{96} +(-4.38893 + 2.82059i) q^{97} +(-5.36987 + 4.49049i) q^{98} +(-0.628776 + 4.37323i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) \) 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9} - 2 q^{10} - 4 q^{11} + 8 q^{12} - 4 q^{13} + 5 q^{14} + 26 q^{15} + 8 q^{16} - 13 q^{17} + 8 q^{18} + 4 q^{19} + 26 q^{20} + 11 q^{21} - 124 q^{22} + 26 q^{23} - 80 q^{24} + 14 q^{25} + 2 q^{26} - 16 q^{27} - 22 q^{28} + 54 q^{29} - 2 q^{30} + 15 q^{31} + 8 q^{32} - 4 q^{33} + 4 q^{34} - 2 q^{35} - 16 q^{36} + 7 q^{37} - 7 q^{38} + 2 q^{39} + 9 q^{40} - 30 q^{41} + 6 q^{42} + 36 q^{43} - 4 q^{44} + 20 q^{45} + 4 q^{46} - 6 q^{47} - 16 q^{48} + 14 q^{49} - 28 q^{50} + 9 q^{51} + 2 q^{52} - 24 q^{53} + 8 q^{54} - 14 q^{55} + 6 q^{56} - 30 q^{57} - 5 q^{58} + 4 q^{59} - 2 q^{60} + 32 q^{61} - 8 q^{62} - 6 q^{63} - 16 q^{64} + 38 q^{65} - 4 q^{66} + 6 q^{67} + 42 q^{68} - 30 q^{69} - 8 q^{70} - 180 q^{71} + 8 q^{72} - 32 q^{73} + 7 q^{74} + 14 q^{75} - 8 q^{76} + 61 q^{77} + 18 q^{78} - 66 q^{79} - 2 q^{80} + 8 q^{81} - 7 q^{82} + 130 q^{83} + 5 q^{84} - 70 q^{85} - 40 q^{86} + 6 q^{87} - 15 q^{88} - 4 q^{89} + 4 q^{90} - 6 q^{91} + 58 q^{92} - 18 q^{93} + 16 q^{94} + 19 q^{95} + 8 q^{96} + 40 q^{97} + 43 q^{98} + 8 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9 - 2 * q^10 - 4 * q^11 + 8 * q^12 - 4 * q^13 + 5 * q^14 + 26 * q^15 + 8 * q^16 - 13 * q^17 + 8 * q^18 + 4 * q^19 + 26 * q^20 + 11 * q^21 - 124 * q^22 + 26 * q^23 - 80 * q^24 + 14 * q^25 + 2 * q^26 - 16 * q^27 - 22 * q^28 + 54 * q^29 - 2 * q^30 + 15 * q^31 + 8 * q^32 - 4 * q^33 + 4 * q^34 - 2 * q^35 - 16 * q^36 + 7 * q^37 - 7 * q^38 + 2 * q^39 + 9 * q^40 - 30 * q^41 + 6 * q^42 + 36 * q^43 - 4 * q^44 + 20 * q^45 + 4 * q^46 - 6 * q^47 - 16 * q^48 + 14 * q^49 - 28 * q^50 + 9 * q^51 + 2 * q^52 - 24 * q^53 + 8 * q^54 - 14 * q^55 + 6 * q^56 - 30 * q^57 - 5 * q^58 + 4 * q^59 - 2 * q^60 + 32 * q^61 - 8 * q^62 - 6 * q^63 - 16 * q^64 + 38 * q^65 - 4 * q^66 + 6 * q^67 + 42 * q^68 - 30 * q^69 - 8 * q^70 - 180 * q^71 + 8 * q^72 - 32 * q^73 + 7 * q^74 + 14 * q^75 - 8 * q^76 + 61 * q^77 + 18 * q^78 - 66 * q^79 - 2 * q^80 + 8 * q^81 - 7 * q^82 + 130 * q^83 + 5 * q^84 - 70 * q^85 - 40 * q^86 + 6 * q^87 - 15 * q^88 - 4 * q^89 + 4 * q^90 - 6 * q^91 + 58 * q^92 - 18 * q^93 + 16 * q^94 + 19 * q^95 + 8 * q^96 + 40 * q^97 + 43 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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