LMFDB - Embedded newform 966.2.t.a.41.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(41,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 12]))

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

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

chi := DirichletCharacter("966.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.t (of order $22$, degree $10$, 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:	$640$
Relative dimension:	$64$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			41.20
Character	$\chi$	$=$	966.41
Dual form			966.2.t.a.377.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.281733 + 0.959493i) q^{2} +(0.543127 + 1.64469i) q^{3} +(-0.841254 - 0.540641i) q^{4} +(-0.342096 + 2.37933i) q^{5} +(-1.73109 + 0.0577632i) q^{6} +(0.513888 + 2.59537i) q^{7} +(0.755750 - 0.654861i) q^{8} +(-2.41003 + 1.78655i) q^{9} +O(q^{10})$	\(q+(-0.281733 + 0.959493i) q^{2} +(0.543127 + 1.64469i) q^{3} +(-0.841254 - 0.540641i) q^{4} +(-0.342096 + 2.37933i) q^{5} +(-1.73109 + 0.0577632i) q^{6} +(0.513888 + 2.59537i) q^{7} +(0.755750 - 0.654861i) q^{8} +(-2.41003 + 1.78655i) q^{9} +(-2.18657 - 0.998573i) q^{10} +(1.81320 + 6.17519i) q^{11} +(0.432280 - 1.67724i) q^{12} +(0.243328 + 0.111124i) q^{13} +(-2.63501 - 0.238127i) q^{14} +(-4.09906 + 0.729635i) q^{15} +(0.415415 + 0.909632i) q^{16} +(0.0293727 - 0.0188767i) q^{17} +(-1.03520 - 2.81573i) q^{18} +(3.31713 - 5.16155i) q^{19} +(1.57415 - 1.81667i) q^{20} +(-3.98947 + 2.25480i) q^{21} -6.43589 q^{22} +(4.39654 - 1.91583i) q^{23} +(1.48751 + 0.887303i) q^{24} +(-0.746708 - 0.219253i) q^{25} +(-0.175176 + 0.202164i) q^{26} +(-4.24728 - 2.99343i) q^{27} +(0.970851 - 2.46119i) q^{28} +(0.282799 + 0.440045i) q^{29} +(0.454760 - 4.13859i) q^{30} +(4.67543 - 4.05128i) q^{31} +(-0.989821 + 0.142315i) q^{32} +(-9.17149 + 6.33607i) q^{33} +(0.00983680 + 0.0335010i) q^{34} +(-6.35102 + 0.334844i) q^{35} +(2.99333 - 0.199986i) q^{36} +(0.107765 + 0.749525i) q^{37} +(4.01793 + 4.63694i) q^{38} +(-0.0506071 + 0.460554i) q^{39} +(1.29959 + 2.02220i) q^{40} +(-0.254767 + 1.77194i) q^{41} +(-1.03950 - 4.46312i) q^{42} +(0.762510 - 0.879984i) q^{43} +(1.81320 - 6.17519i) q^{44} +(-3.42634 - 6.34542i) q^{45} +(0.599579 + 4.75820i) q^{46} -11.8177 q^{47} +(-1.27044 + 1.17728i) q^{48} +(-6.47184 + 2.66745i) q^{49} +(0.420744 - 0.654690i) q^{50} +(0.0469994 + 0.0380566i) q^{51} +(-0.144622 - 0.225037i) q^{52} +(7.88029 - 3.59881i) q^{53} +(4.06877 - 3.23189i) q^{54} +(-15.3131 + 2.20169i) q^{55} +(2.08797 + 1.62492i) q^{56} +(10.2908 + 2.65228i) q^{57} +(-0.501894 + 0.147369i) q^{58} +(3.27192 - 7.16449i) q^{59} +(3.84282 + 1.60231i) q^{60} +(-5.39038 + 4.67079i) q^{61} +(2.56996 + 5.62742i) q^{62} +(-5.87524 - 5.33681i) q^{63} +(0.142315 - 0.989821i) q^{64} +(-0.347642 + 0.540942i) q^{65} +(-3.49551 - 10.5851i) q^{66} +(-0.154784 - 0.0454486i) q^{67} -0.0349154 q^{68} +(5.53884 + 6.19042i) q^{69} +(1.46801 - 6.18810i) q^{70} +(3.11564 - 10.6109i) q^{71} +(-0.651432 + 2.92842i) q^{72} +(7.50519 - 11.6783i) q^{73} +(-0.749525 - 0.107765i) q^{74} +(-0.0449532 - 1.34719i) q^{75} +(-5.58109 + 2.54880i) q^{76} +(-15.0951 + 7.87927i) q^{77} +(-0.427641 - 0.178310i) q^{78} +(-4.00236 + 8.76394i) q^{79} +(-2.30642 + 0.677227i) q^{80} +(2.61645 - 8.61128i) q^{81} +(-1.62839 - 0.743661i) q^{82} +(0.465212 + 3.23562i) q^{83} +(4.57519 + 0.260012i) q^{84} +(0.0348655 + 0.0763449i) q^{85} +(0.629514 + 0.979544i) q^{86} +(-0.570142 + 0.704118i) q^{87} +(5.41422 + 3.47950i) q^{88} +(3.04562 - 3.51483i) q^{89} +(7.05369 - 1.49984i) q^{90} +(-0.163365 + 0.688631i) q^{91} +(-4.73438 - 0.765249i) q^{92} +(9.20246 + 5.48928i) q^{93} +(3.32942 - 11.3390i) q^{94} +(11.1462 + 9.65828i) q^{95} +(-0.771663 - 1.55066i) q^{96} +(3.78819 + 0.544659i) q^{97} +(-0.736073 - 6.96119i) q^{98} +(-15.4022 - 11.6430i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 640 q + 64 q^{4} + 8 q^{9}+O(q^{10}) $ 640 * q + 64 * q^4 + 8 * q^9	$ 640 q + 64 q^{4} + 8 q^{9} + 8 q^{15} - 64 q^{16} + 20 q^{18} + 54 q^{21} - 8 q^{22} - 56 q^{25} - 44 q^{30} - 8 q^{36} + 20 q^{37} - 16 q^{39} - 4 q^{42} - 28 q^{43} + 24 q^{46} - 68 q^{49} - 40 q^{51} + 32 q^{57} - 80 q^{58} - 8 q^{60} + 86 q^{63} + 64 q^{64} + 24 q^{67} + 72 q^{70} - 64 q^{72} - 8 q^{78} - 144 q^{79} + 20 q^{81} + 34 q^{84} + 32 q^{85} + 8 q^{88} - 40 q^{91} + 16 q^{93} + 68 q^{99}+O(q^{100}) $ 640 * q + 64 * q^4 + 8 * q^9 + 8 * q^15 - 64 * q^16 + 20 * q^18 + 54 * q^21 - 8 * q^22 - 56 * q^25 - 44 * q^30 - 8 * q^36 + 20 * q^37 - 16 * q^39 - 4 * q^42 - 28 * q^43 + 24 * q^46 - 68 * q^49 - 40 * q^51 + 32 * q^57 - 80 * q^58 - 8 * q^60 + 86 * q^63 + 64 * q^64 + 24 * q^67 + 72 * q^70 - 64 * q^72 - 8 * q^78 - 144 * q^79 + 20 * q^81 + 34 * q^84 + 32 * q^85 + 8 * q^88 - 40 * q^91 + 16 * q^93 + 68 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{6}{11}\right)$

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 $

$2$	−0.281733	+	0.959493i	−0.199215	+	0.678464i
$2$	−0.281733	+	0.959493i	−0.199215	+	0.678464i
$3$	0.543127	+	1.64469i	0.313575	+	0.949564i
$3$	0.543127	+	1.64469i	0.313575	+	0.949564i
$4$	−0.841254	−	0.540641i	−0.420627	−	0.270320i
$5$	−0.342096	+	2.37933i	−0.152990	+	1.06407i	0.758182	+	0.652042i	$0.226088\pi$
$5$	−0.342096	+	2.37933i	−0.152990	+	1.06407i	−0.911172	+	0.412025i	$0.864821\pi$
$6$	−1.73109	+	0.0577632i	−0.706713	+	0.0235817i
$7$	0.513888	+	2.59537i	0.194231	+	0.980956i
$7$	0.513888	+	2.59537i	0.194231	+	0.980956i
$8$	0.755750	−	0.654861i	0.267198	−	0.231528i
$9$	−2.41003	+	1.78655i	−0.803342	+	0.595518i
$10$	−2.18657	−	0.998573i	−0.691454	−	0.315776i
$11$	1.81320	+	6.17519i	0.546700	+	1.86189i	0.505660	+	0.862733i	$0.331249\pi$
$11$	1.81320	+	6.17519i	0.546700	+	1.86189i	0.0410401	+	0.999157i	$0.486933\pi$
$12$	0.432280	−	1.67724i	0.124789	−	0.484177i
$13$	0.243328	+	0.111124i	0.0674871	+	0.0308203i	0.448873	−	0.893596i	$-0.351826\pi$
$13$	0.243328	+	0.111124i	0.0674871	+	0.0308203i	−0.381386	+	0.924416i	$0.624553\pi$
$14$	−2.63501	−	0.238127i	−0.704237	−	0.0636422i
$15$	−4.09906	+	0.729635i	−1.05837	+	0.188391i
$16$	0.415415	+	0.909632i	0.103854	+	0.227408i
$17$	0.0293727	−	0.0188767i	0.00712392	−	0.00457827i	−0.537074	−	0.843535i	$-0.680470\pi$
$17$	0.0293727	−	0.0188767i	0.00712392	−	0.00457827i	0.544198	+	0.838957i	$0.316834\pi$
$18$	−1.03520	−	2.81573i	−0.244000	−	0.663675i
$19$	3.31713	−	5.16155i	0.761001	−	1.18414i	−0.217128	−	0.976143i	$-0.569669\pi$
$19$	3.31713	−	5.16155i	0.761001	−	1.18414i	0.978129	−	0.207997i	$-0.0666946\pi$
$20$	1.57415	−	1.81667i	0.351991	−	0.406219i
$21$	−3.98947	+	2.25480i	−0.870574	+	0.492038i
$22$	−6.43589			−1.37214
$23$	4.39654	−	1.91583i	0.916742	−	0.399479i
$23$	4.39654	−	1.91583i	0.916742	−	0.399479i
$24$	1.48751	+	0.887303i	0.303637	+	0.181120i
$25$	−0.746708	−	0.219253i	−0.149342	−	0.0438507i
$26$	−0.175176	+	0.202164i	−0.0343549	+	0.0396477i
$27$	−4.24728	−	2.99343i	−0.817390	−	0.576085i
$28$	0.970851	−	2.46119i	0.183474	−	0.465121i
$29$	0.282799	+	0.440045i	0.0525145	+	0.0817142i	0.866518	−	0.499146i	$-0.166353\pi$
$29$	0.282799	+	0.440045i	0.0525145	+	0.0817142i	−0.814004	+	0.580860i	$0.802716\pi$
$30$	0.454760	−	4.13859i	0.0830274	−	0.755599i
$31$	4.67543	−	4.05128i	0.839732	−	0.727632i	−0.124635	−	0.992203i	$-0.539776\pi$
$31$	4.67543	−	4.05128i	0.839732	−	0.727632i	0.964366	+	0.264571i	$0.0852304\pi$
$32$	−0.989821	+	0.142315i	−0.174977	+	0.0251579i
$33$	−9.17149	+	6.33607i	−1.59655	+	1.10297i
$34$	0.00983680	+	0.0335010i	0.00168700	+	0.00574538i
$35$	−6.35102	+	0.334844i	−1.07352	+	0.0565989i
$36$	2.99333	−	0.199986i	0.498888	−	0.0333310i
$37$	0.107765	+	0.749525i	0.0177165	+	0.123221i	0.996760	−	0.0804283i	$-0.0256288\pi$
$37$	0.107765	+	0.749525i	0.0177165	+	0.123221i	−0.979044	+	0.203649i	$0.934720\pi$
$38$	4.01793	+	4.63694i	0.651794	+	0.752210i
$39$	−0.0506071	+	0.460554i	−0.00810362	+	0.0737477i
$40$	1.29959	+	2.02220i	0.205483	+	0.319738i
$41$	−0.254767	+	1.77194i	−0.0397879	+	0.276731i	−0.999997	−	0.00255210i	$-0.999188\pi$
$41$	−0.254767	+	1.77194i	−0.0397879	+	0.276731i	0.960209	+	0.279283i	$0.0900967\pi$
$42$	−1.03950	−	4.46312i	−0.160398	−	0.688674i
$43$	0.762510	−	0.879984i	0.116282	−	0.134196i	−0.694624	−	0.719373i	$-0.744429\pi$
$43$	0.762510	−	0.879984i	0.116282	−	0.134196i	0.810906	+	0.585177i	$0.198975\pi$
$44$	1.81320	−	6.17519i	0.273350	−	0.930945i
$45$	−3.42634	−	6.34542i	−0.510768	−	0.945919i
$46$	0.599579	+	4.75820i	0.0884031	+	0.701559i
$47$	−11.8177			−1.72378			−0.861891	−	0.507093i	$-0.830720\pi$
$47$	−11.8177			−1.72378			−0.861891	+	0.507093i	$0.830720\pi$
$48$	−1.27044	+	1.17728i	−0.183372	+	0.169925i
$49$	−6.47184	+	2.66745i	−0.924548	+	0.381065i
$50$	0.420744	−	0.654690i	0.0595022	−	0.0925872i
$51$	0.0469994	+	0.0380566i	0.00658123	+	0.00532899i
$52$	−0.144622	−	0.225037i	−0.0200555	−	0.0312070i
$53$	7.88029	−	3.59881i	1.08244	−	0.494334i	0.207337	−	0.978270i	$-0.433520\pi$
$53$	7.88029	−	3.59881i	1.08244	−	0.494334i	0.875104	+	0.483935i	$0.160793\pi$
$54$	4.06877	−	3.23189i	0.553689	−	0.439805i
$55$	−15.3131	+	2.20169i	−2.06482	+	0.296876i
$56$	2.08797	+	1.62492i	0.279017	+	0.217139i
$57$	10.2908	+	2.65228i	1.36305	+	0.351302i
$58$	−0.501894	+	0.147369i	−0.0659018	+	0.0193505i
$59$	3.27192	−	7.16449i	0.425967	−	0.932738i	−0.567997	−	0.823031i	$-0.692281\pi$
$59$	3.27192	−	7.16449i	0.425967	−	0.932738i	0.993964	−	0.109707i	$-0.0349913\pi$
$60$	3.84282	+	1.60231i	0.496106	+	0.206858i
$61$	−5.39038	+	4.67079i	−0.690168	+	0.598034i	−0.927691	−	0.373348i	$-0.878210\pi$
$61$	−5.39038	+	4.67079i	−0.690168	+	0.598034i	0.237523	+	0.971382i	$0.423664\pi$
$62$	2.56996	+	5.62742i	0.326385	+	0.714683i
$63$	−5.87524	−	5.33681i	−0.740211	−	0.672375i
$64$	0.142315	−	0.989821i	0.0177894	−	0.123728i
$65$	−0.347642	+	0.540942i	−0.0431197	+	0.0670956i
$66$	−3.49551	−	10.5851i	−0.430267	−	1.30293i
$67$	−0.154784	−	0.0454486i	−0.0189098	−	0.00555243i	0.272264	−	0.962223i	$-0.412228\pi$
$67$	−0.154784	−	0.0454486i	−0.0189098	−	0.00555243i	−0.291174	+	0.956670i	$0.594046\pi$
$68$	−0.0349154			−0.00423411
$69$	5.53884	+	6.19042i	0.666798	+	0.745239i
$70$	1.46801	−	6.18810i	0.175461	−	0.739619i
$71$	3.11564	−	10.6109i	0.369759	−	1.25928i	−0.539123	−	0.842227i	$-0.681244\pi$
$71$	3.11564	−	10.6109i	0.369759	−	1.25928i	0.908881	−	0.417055i	$-0.136938\pi$
$72$	−0.651432	+	2.92842i	−0.0767720	+	0.345117i
$73$	7.50519	−	11.6783i	0.878416	−	1.36684i	−0.0513458	−	0.998681i	$-0.516351\pi$
$73$	7.50519	−	11.6783i	0.878416	−	1.36684i	0.929762	−	0.368161i	$-0.120013\pi$
$74$	−0.749525	−	0.107765i	−0.0871305	−	0.0125275i
$75$	−0.0449532	−	1.34719i	−0.00519074	−	0.155560i
$76$	−5.58109	+	2.54880i	−0.640195	+	0.292367i
$77$	−15.0951	+	7.87927i	−1.72025	+	0.897926i
$78$	−0.427641	−	0.178310i	−0.0484208	−	0.0201897i
$79$	−4.00236	+	8.76394i	−0.450300	+	0.986020i	0.539292	+	0.842119i	$0.318692\pi$
$79$	−4.00236	+	8.76394i	−0.450300	+	0.986020i	−0.989592	+	0.143901i	$0.954035\pi$
$80$	−2.30642	+	0.677227i	−0.257866	+	0.0757163i
$81$	2.61645	−	8.61128i	0.290717	−	0.956809i
$82$	−1.62839	−	0.743661i	−0.179826	−	0.0821236i
$83$	0.465212	+	3.23562i	0.0510636	+	0.355155i	0.999294	+	0.0375719i	$0.0119623\pi$
$83$	0.465212	+	3.23562i	0.0510636	+	0.355155i	−0.948230	+	0.317584i	$0.897129\pi$
$84$	4.57519	+	0.260012i	0.499195	+	0.0283697i
$85$	0.0348655	+	0.0763449i	0.00378170	+	0.00828076i
$86$	0.629514	+	0.979544i	0.0678823	+	0.105627i
$87$	−0.570142	+	0.704118i	−0.0611256	+	0.0754894i
$88$	5.41422	+	3.47950i	0.577157	+	0.370916i
$89$	3.04562	−	3.51483i	0.322835	−	0.372571i	−0.571013	−	0.820941i	$-0.693450\pi$
$89$	3.04562	−	3.51483i	0.322835	−	0.372571i	0.893848	+	0.448369i	$0.147995\pi$
$90$	7.05369	−	1.49984i	0.743524	−	0.158097i
$91$	−0.163365	+	0.688631i	−0.0171253	+	0.0721881i
$92$	−4.73438	−	0.765249i	−0.493594	−	0.0797827i
$93$	9.20246	+	5.48928i	0.954251	+	0.569212i
$94$	3.32942	−	11.3390i	0.343403	−	1.16952i
$95$	11.1462	+	9.65828i	1.14358	+	0.990918i
$96$	−0.771663	−	1.55066i	−0.0787575	−	0.158263i
$97$	3.78819	+	0.544659i	0.384632	+	0.0553018i	0.331919	−	0.943308i	$-0.392304\pi$
$97$	3.78819	+	0.544659i	0.384632	+	0.0553018i	0.0527134	+	0.998610i	$0.483213\pi$
$98$	−0.736073	−	6.96119i	−0.0743546	−	0.703187i
$99$	−15.4022	−	11.6430i	−1.54798	−	1.17016i
$100$	0.509634	+	0.588148i	0.0509634	+	0.0588148i
$101$	0.166657	+	1.15912i	0.0165830	+	0.115337i	0.996432	−	0.0844045i	$-0.0268988\pi$
$101$	0.166657	+	1.15912i	0.0165830	+	0.115337i	−0.979849	+	0.199742i	$0.935990\pi$
$102$	−0.0497563	+	0.0343738i	−0.00492661	+	0.00340352i
$103$	2.04986	+	6.98119i	0.201979	+	0.687877i	0.996720	+	0.0809281i	$0.0257884\pi$
$103$	2.04986	+	6.98119i	0.201979	+	0.687877i	−0.794741	+	0.606949i	$0.792393\pi$
$104$	0.256666	−	0.0753639i	0.0251682	−	0.00739004i
$105$	−4.00013	−	10.2636i	−0.390372	−	1.00163i
$106$	1.23290	+	8.57498i	0.119749	+	0.832876i
$107$	7.10831	−	6.15938i	0.687186	−	0.595450i	−0.239676	−	0.970853i	$-0.577041\pi$
$107$	7.10831	−	6.15938i	0.687186	−	0.595450i	0.926862	+	0.375403i	$0.122496\pi$
$108$	1.95467	+	4.81448i	0.188088	+	0.463274i
$109$	9.74351	−	6.26177i	0.933259	−	0.599769i	0.0167829	−	0.999859i	$-0.494658\pi$
$109$	9.74351	−	6.26177i	0.933259	−	0.599769i	0.916476	+	0.400090i	$0.131021\pi$
$110$	2.20169	−	15.3131i	0.209923	−	1.46005i
$111$	−1.17421	+	0.584328i	−0.111451	+	0.0554620i
$112$	−2.14735	+	1.54560i	−0.202906	+	0.146046i
$113$	0.711434	−	2.42292i	0.0669261	−	0.227929i	−0.919238	−	0.393703i	$-0.871194\pi$
$113$	0.711434	−	2.42292i	0.0669261	−	0.227929i	0.986164	+	0.165774i	$0.0530121\pi$
$114$	−5.44409	+	9.12670i	−0.509886	+	0.854794i
$115$	3.05436	+	11.1162i	0.284820	+	1.03659i
$116$		−	0.523082i		−	0.0485669i
$117$	−0.784956	+	0.166906i	−0.0725692	+	0.0154305i
$118$	5.95248	+	5.15785i	0.547970	+	0.474819i
$119$	0.0640861	+	0.0665323i	0.00587476	+	0.00609901i
$120$	−2.62006	+	3.23574i	−0.239177	+	0.295381i
$121$	−25.5915	+	16.4467i	−2.32650	+	1.49515i
$122$	−2.96295	−	6.48795i	−0.268253	−	0.587391i
$123$	−3.05267	+	0.543377i	−0.275250	+	0.0489946i
$124$	−6.12351	+	0.880427i	−0.549907	+	0.0790647i
$125$	−4.21574	+	9.23119i	−0.377067	+	0.825663i
$126$	6.77588	−	4.13370i	0.603643	−	0.368259i
$127$	0.517545	−	0.151965i	0.0459247	−	0.0134847i	−0.258689	−	0.965961i	$-0.583291\pi$
$127$	0.517545	−	0.151965i	0.0459247	−	0.0134847i	0.304614	+	0.952476i	$0.401472\pi$
$128$	0.909632	+	0.415415i	0.0804009	+	0.0367178i
$129$	1.86144	+	0.776152i	0.163891	+	0.0683364i
$130$	−0.421088	−	0.485962i	−0.0369319	−	0.0426216i
$131$	−7.87468	−	17.2431i	−0.688014	−	1.50654i	−0.853923	−	0.520399i	$-0.825783\pi$
$131$	−7.87468	−	17.2431i	−0.688014	−	1.50654i	0.165909	−	0.986141i	$-0.446944\pi$
$132$	11.1411	−	0.371758i	0.969707	−	0.0323573i
$133$	15.1007	+	5.95670i	1.30940	+	0.516511i
$134$	0.0872152	−	0.135710i	0.00753425	−	0.0117235i
$135$	8.57532	−	9.08164i	0.738046	−	0.781623i
$136$	0.00983680	−	0.0335010i	0.000843498	−	0.00287269i
$137$			14.0968i			1.20437i	0.798356	+	0.602186i	$0.205704\pi$
$137$			14.0968i			1.20437i	−0.798356	+	0.602186i	$0.794296\pi$
$138$	−7.50013	+	3.57043i	−0.638454	+	0.303935i
$139$			15.3521i			1.30215i	0.759015	+	0.651073i	$0.225681\pi$
$139$			15.3521i			1.30215i	−0.759015	+	0.651073i	$0.774319\pi$
$140$	5.52385	+	3.15193i	0.466851	+	0.266387i
$141$	−6.41849	−	19.4364i	−0.540534	−	1.63684i
$142$	9.30330	+	5.97887i	0.780716	+	0.501736i
$143$	−0.245011	+	1.70409i	−0.0204888	+	0.142503i
$144$	−2.62627	−	1.45008i	−0.218856	−	0.120840i
$145$	−1.14375	+	0.522335i	−0.0949837	+	0.0433776i
$146$	9.09079	+	10.4913i	0.752360	+	0.868269i
$147$	−7.90217	−	9.19542i	−0.651760	−	0.758425i
$148$	0.314566	−	0.688803i	0.0258571	−	0.0566193i
$149$	−2.37712	−	8.09573i	−0.194741	−	0.663228i	−0.997737	−	0.0672428i	$-0.978580\pi$
$149$	−2.37712	−	8.09573i	−0.194741	−	0.663228i	0.802995	−	0.595985i	$-0.203238\pi$
$150$	1.30528	+	0.336414i	0.106576	+	0.0274681i
$151$	−3.19743	+	7.00140i	−0.260203	+	0.569766i	−0.993972	−	0.109634i	$-0.965032\pi$
$151$	−3.19743	+	7.00140i	−0.260203	+	0.569766i	0.733769	+	0.679399i	$0.237760\pi$
$152$	−0.873179	−	6.07309i	−0.0708242	−	0.492593i
$153$	−0.0370647	+	0.0979691i	−0.00299651	+	0.00792034i
$154$	−3.30732	−	16.7035i	−0.266512	−	1.34601i
$155$	8.03988	+	12.5103i	0.645779	+	1.00485i
$156$	0.291568	−	0.360083i	0.0233441	−	0.0288297i
$157$	10.0280	−	15.6039i	0.800325	−	1.24533i	−0.165519	−	0.986207i	$-0.552930\pi$
$157$	10.0280	−	15.6039i	0.800325	−	1.24533i	0.965844	−	0.259123i	$-0.0834336\pi$
$158$	−7.28134	−	6.30932i	−0.579273	−	0.501943i
$159$	10.1989	+	11.0060i	0.808828	+	0.872836i
$160$		−	2.40380i		−	0.190037i
$161$	7.23161	+	10.4261i	0.569931	+	0.821693i
$162$	7.52533	+	4.93655i	0.591245	+	0.387852i
$163$	5.17357	+	1.51910i	0.405225	+	0.118985i	0.477992	−	0.878364i	$-0.341365\pi$
$163$	5.17357	+	1.51910i	0.405225	+	0.118985i	−0.0727670	+	0.997349i	$0.523183\pi$
$164$	1.17231	−	1.35292i	0.0915418	−	0.105645i
$165$	−11.9381	−	23.9895i	−0.929377	−	1.86758i
$166$	−3.23562	−	0.465212i	−0.251133	−	0.0361075i
$167$	6.76647	−	4.34855i	0.523605	−	0.336501i	−0.251991	−	0.967729i	$-0.581085\pi$
$167$	6.76647	−	4.34855i	0.523605	−	0.336501i	0.775597	+	0.631229i	$0.217449\pi$
$168$	−1.53846	+	4.31661i	−0.118695	+	0.333034i
$169$	−8.46633	−	9.77067i	−0.651256	−	0.751590i
$170$	−0.0830751	+	0.0119444i	−0.00637157	+	0.000916094i
$171$	1.22702	+	18.3657i	0.0938329	+	1.40446i
$172$	−1.11722	+	0.328045i	−0.0851872	+	0.0250132i
$173$	−0.403020	+	0.118337i	−0.0306411	+	0.00899703i	−0.297017	−	0.954872i	$-0.595992\pi$
$173$	−0.403020	+	0.118337i	−0.0306411	+	0.00899703i	0.266376	+	0.963869i	$0.414174\pi$
$174$	−0.514969	−	0.745420i	−0.0390397	−	0.0565102i
$175$	0.185318	−	2.05065i	0.0140087	−	0.155015i
$176$	−4.86392	+	4.21461i	−0.366632	+	0.317688i
$177$	13.5605	+	1.49006i	1.01927	+	0.112000i
$178$	2.51441	+	3.91249i	0.188463	+	0.293254i
$179$	1.73768	+	0.249841i	0.129881	+	0.0186740i	0.206949	−	0.978352i	$-0.433647\pi$
$179$	1.73768	+	0.249841i	0.129881	+	0.0186740i	−0.0770679	+	0.997026i	$0.524556\pi$
$180$	−0.548171	+	7.19052i	−0.0408583	+	0.535950i
$181$	0.920876	+	0.797943i	0.0684481	+	0.0593107i	0.688413	−	0.725319i	$-0.258308\pi$
$181$	0.920876	+	0.797943i	0.0684481	+	0.0593107i	−0.619965	+	0.784630i	$0.712853\pi$
$182$	−0.614711	−	0.350757i	−0.0455654	−	0.0259998i
$183$	−10.6097	−	6.32869i	−0.784290	−	0.467830i
$184$	2.06808	−	4.32701i	0.152461	−	0.318992i
$185$	−1.82023			−0.133826
$186$	−7.85956	+	7.28319i	−0.576291	+	0.534029i
$187$	0.169826	+	0.147155i	0.0124189	+	0.0107610i
$188$	9.94164	+	6.38911i	0.725069	+	0.465974i
$189$	5.58641	−	12.5615i	0.406351	−	0.913717i
$190$	−12.4073	+	7.97369i	−0.900121	+	0.578472i
$191$	−4.04296	+	1.84636i	−0.292539	+	0.133598i	−0.556278	−	0.830996i	$-0.687771\pi$
$191$	−4.04296	+	1.84636i	−0.292539	+	0.133598i	0.263740	+	0.964594i	$0.415044\pi$
$192$	1.70525	−	0.303535i	0.123066	−	0.0219057i
$193$	2.21377	+	15.3971i	0.159351	+	1.10831i	0.899833	+	0.436234i	$0.143688\pi$
$193$	2.21377	+	15.3971i	0.159351	+	1.10831i	−0.740483	+	0.672075i	$0.765403\pi$
$194$	−1.58985	+	3.48129i	−0.114145	+	0.249942i
$195$	−1.07850	−	0.277965i	−0.0772328	−	0.0199055i
$196$	6.88659	+	1.25494i	0.491899	+	0.0896384i
$197$	−11.4932	−	5.24876i	−0.818855	−	0.373959i	−0.0384717	−	0.999260i	$-0.512249\pi$
$197$	−11.4932	−	5.24876i	−0.818855	−	0.373959i	−0.780384	+	0.625301i	$0.784976\pi$
$198$	15.5107	−	11.4981i	1.10229	−	0.817132i
$199$	−18.4001	+	15.9438i	−1.30435	+	1.13022i	−0.321279	+	0.946985i	$0.604113\pi$
$199$	−18.4001	+	15.9438i	−1.30435	+	1.13022i	−0.983069	+	0.183238i	$0.941342\pi$
$200$	−0.707905	+	0.323289i	−0.0500564	+	0.0228600i
$201$	−0.00931825	−	0.279256i	−0.000657259	−	0.0196972i
$202$	−1.15912	−	0.166657i	−0.0815557	−	0.0117259i
$203$	−0.996749	+	0.960101i	−0.0699581	+	0.0673859i
$204$	−0.0189635	−	0.0574250i	−0.00132771	−	0.00402056i
$205$	−4.12888	−	1.21235i	−0.288373	−	0.0846740i
$206$	−7.27591			−0.506937
$207$	−7.17304	+	12.4719i	−0.498561	+	0.866855i
$208$			0.267502i			0.0185479i
$209$	37.8882	+	11.1250i	2.62078	+	0.769530i
$210$	10.9748	−	0.946499i	0.757336	−	0.0653146i
$211$	16.8407	+	10.8229i	1.15936	+	0.745079i	0.971482	−	0.237113i	$-0.0762011\pi$
$211$	16.8407	+	10.8229i	1.15936	+	0.745079i	0.187883	+	0.982191i	$0.439837\pi$
$212$	−8.57498	−	1.23290i	−0.588932	−	0.0846757i
$213$	19.1439	−	0.638795i	1.31172	−	0.0437695i
$214$	3.90724	+	8.55567i	0.267094	+	0.584853i
$215$	1.83292	+	2.11530i	0.125004	+	0.144262i
$216$	−5.17016	+	0.519098i	−0.351785	+	0.0353201i
$217$	12.9172	+	10.0525i	0.876876	+	0.682411i
$218$	3.26306	+	11.1130i	0.221002	+	0.752665i
$219$	23.2835	+	6.00093i	1.57335	+	0.405505i
$220$	14.0725	+	6.42670i	0.948769	+	0.433288i
$221$	0.00924485	−	0.00132921i	0.000621876	−	8.94123e-5i
$222$	−0.229846	−	1.29127i	−0.0154263	−	0.0866643i
$223$	−18.4436	+	8.42291i	−1.23507	+	0.564040i	−0.922553	−	0.385871i	$-0.873901\pi$
$223$	−18.4436	+	8.42291i	−1.23507	+	0.564040i	−0.312522	+	0.949911i	$0.601174\pi$
$224$	−0.878016	−	2.49581i	−0.0586649	−	0.166759i
$225$	2.19129	−	0.805628i	0.146086	−	0.0537085i
$226$	2.12434	+	1.36523i	0.141309	+	0.0908139i
$227$	−5.57171	+	6.43009i	−0.369807	+	0.426780i	−0.909902	−	0.414824i	$-0.863843\pi$
$227$	−5.57171	+	6.43009i	−0.369807	+	0.426780i	0.540094	+	0.841604i	$0.318389\pi$
$228$	−7.22323	−	7.79485i	−0.478370	−	0.516227i
$229$			12.9466i			0.855536i	0.903888	+	0.427768i	$0.140700\pi$
$229$			12.9466i			0.855536i	−0.903888	+	0.427768i	$0.859300\pi$
$230$	−11.5264	−	0.201166i	−0.760031	−	0.0132645i
$231$	−21.1575	−	20.5473i	−1.39206	−	1.35192i
$232$	0.501894	+	0.147369i	0.0329509	+	0.00967526i
$233$	6.83284	+	5.92069i	0.447634	+	0.387877i	0.849301	−	0.527909i	$-0.177024\pi$
$233$	6.83284	+	5.92069i	0.447634	+	0.387877i	−0.401667	+	0.915786i	$0.631569\pi$
$234$	0.0610022	−	0.800183i	0.00398784	−	0.0523096i
$235$	4.04277	−	28.1181i	0.263721	−	1.83422i
$236$	−6.62593	+	4.25823i	−0.431311	+	0.277187i
$237$	−16.5878	−	1.82271i	−1.07749	−	0.118398i
$238$	−0.0818924	+	0.0427458i	−0.00530830	+	0.00277080i
$239$	−17.0465	+	2.45092i	−1.10265	+	0.158537i	−0.669519	−	0.742795i	$-0.733500\pi$
$239$	−17.0465	+	2.45092i	−1.10265	+	0.158537i	−0.433129	+	0.901332i	$0.642591\pi$
$240$	−2.36651	−	3.42554i	−0.152758	−	0.221118i
$241$	−3.04252	−	10.3619i	−0.195986	−	0.667468i	−0.997575	−	0.0695927i	$-0.977830\pi$
$241$	−3.04252	−	10.3619i	−0.195986	−	0.667468i	0.801589	−	0.597875i	$-0.203988\pi$
$242$	−8.57050	−	29.1884i	−0.550932	−	1.87630i
$243$	15.5840	−	0.373763i	0.999713	−	0.0239769i
$244$	7.05990	−	1.01506i	0.451964	−	0.0649826i
$245$	−4.13275	−	16.3112i	−0.264032	−	1.04208i
$246$	0.338671	−	3.08210i	0.0215928	−	0.196508i
$247$	1.38072	−	0.887337i	0.0878533	−	0.0564599i
$248$	0.880427	−	6.12351i	0.0559072	−	0.388843i
$249$	−5.06893	+	2.52248i	−0.321230	+	0.159856i
$250$	−7.66955	−	6.64570i	−0.485065	−	0.420311i
$251$	−22.5876	−	6.63231i	−1.42572	−	0.418628i	−0.524282	−	0.851545i	$-0.675666\pi$
$251$	−22.5876	−	6.63231i	−1.42572	−	0.418628i	−0.901434	+	0.432917i	$0.857484\pi$
$252$	2.05727	+	7.66601i	0.129596	+	0.482913i
$253$	19.8024	+	23.6757i	1.24497	+	1.48848i
$254$			0.539395i			0.0338446i
$255$	−0.106627	+	0.0988080i	−0.00667727	+	0.00618760i
$256$	−0.654861	+	0.755750i	−0.0409288	+	0.0472343i
$257$	22.8854	+	14.7076i	1.42755	+	0.917434i	0.999909	+	0.0134873i	$0.00429329\pi$
$257$	22.8854	+	14.7076i	1.42755	+	0.917434i	0.427646	+	0.903946i	$0.359343\pi$
$258$	−1.26914	+	1.56737i	−0.0790133	+	0.0975805i
$259$	−1.88991	+	0.664862i	−0.117433	+	0.0413125i
$260$	0.584911	−	0.267120i	0.0362746	−	0.0165661i
$261$	−1.46772	−	0.555282i	−0.0908494	−	0.0343711i
$262$	18.7632	−	2.69774i	1.15920	−	0.166667i
$263$	−15.4063	−	7.03584i	−0.949996	−	0.433849i	−0.120719	−	0.992687i	$-0.538520\pi$
$263$	−15.4063	−	7.03584i	−0.949996	−	0.433849i	−0.829277	+	0.558838i	$0.811247\pi$
$264$	−2.78211	+	10.7945i	−0.171227	+	0.664358i
$265$	5.86693	+	19.9809i	0.360403	+	1.22742i
$266$	−9.96978	+	12.8109i	−0.611286	+	0.785484i
$267$	7.43497	+	3.10011i	0.455013	+	0.189723i
$268$	0.105641	+	0.121916i	0.00645305	+	0.00744722i
$269$	−0.117456	−	0.257194i	−0.00716144	−	0.0156814i	0.906017	−	0.423240i	$-0.139107\pi$
$269$	−0.117456	−	0.257194i	−0.00716144	−	0.0156814i	−0.913179	+	0.407559i	$0.866380\pi$
$270$	6.29782	+	10.7866i	0.383273	+	0.656449i
$271$	4.28396	+	0.615941i	0.260232	+	0.0374158i	0.271196	−	0.962524i	$-0.412581\pi$
$271$	4.28396	+	0.615941i	0.260232	+	0.0374158i	−0.0109637	+	0.999940i	$0.503490\pi$
$272$	0.0293727	+	0.0188767i	0.00178098	+	0.00114457i
$273$	−1.22131	+	0.105329i	−0.0739172	+	0.00637482i
$274$	−13.5258	−	3.97153i	−0.817124	−	0.239929i
$275$		−	5.00862i		−	0.302031i
$276$	−1.31277	−	8.20223i	−0.0790197	−	0.493716i
$277$	29.8724			1.79486			0.897429	−	0.441159i	$-0.145432\pi$
$277$	29.8724			1.79486			0.897429	+	0.441159i	$0.145432\pi$
$278$	−14.7302	−	4.32518i	−0.883460	−	0.259407i
$279$	−4.03007	+	18.1166i	−0.241274	+	1.08461i
$280$	−4.58051	+	4.41209i	−0.273738	+	0.263673i
$281$	14.8446	+	2.13434i	0.885556	+	0.127324i	0.570060	−	0.821603i	$-0.306920\pi$
$281$	14.8446	+	2.13434i	0.885556	+	0.127324i	0.315496	+	0.948927i	$0.397829\pi$
$282$	20.4574	−	0.682625i	1.21822	−	0.0406498i
$283$	13.6290	−	6.22416i	0.810161	−	0.369988i	0.0331304	−	0.999451i	$-0.489452\pi$
$283$	13.6290	−	6.22416i	0.810161	−	0.369988i	0.777030	+	0.629463i	$0.216725\pi$
$284$	−8.35773	+	7.24201i	−0.495940	+	0.429734i
$285$	−9.83107	+	23.5778i	−0.582342	+	1.39663i
$286$	−1.56603	−	0.715183i	−0.0926015	−	0.0422897i
$287$	−4.72976	+	0.249366i	−0.279189	+	0.0147196i
$288$	2.13124	−	2.11135i	0.125585	−	0.124413i
$289$	−7.06155	+	15.4626i	−0.415385	+	0.909567i
$290$	−0.178944	−	1.24458i	−0.0105080	−	0.0730845i
$291$	1.16167	+	6.52623i	0.0680984	+	0.382574i
$292$	−12.6275	+	5.76680i	−0.738971	+	0.337477i
$293$	14.0837	−	9.05105i	0.822779	−	0.528768i	−0.0601969	−	0.998187i	$-0.519173\pi$
$293$	14.0837	−	9.05105i	0.822779	−	0.528768i	0.882976	+	0.469419i	$0.155537\pi$
$294$	11.0492	−	4.99143i	0.644405	−	0.291106i
$295$	15.9274	+	10.2359i	0.927328	+	0.595957i
$296$	0.572278	+	0.495882i	0.0332630	+	0.0288226i
$297$	10.7838	−	31.6555i	0.625740	−	1.83684i
$298$	8.43751			0.488772
$299$	1.28270	+	0.0223863i	0.0741803	+	0.00129463i
$300$	−0.690528	+	1.15763i	−0.0398676	+	0.0668358i
$301$	2.67572	+	1.52678i	0.154226	+	0.0880021i
$302$	−5.81697	−	5.04044i	−0.334729	−	0.290044i
$303$	−1.81589	+	0.903651i	−0.104320	+	0.0519134i
$304$	6.07309	+	0.873179i	0.348316	+	0.0500803i
$305$	−9.26933	−	14.4234i	−0.530760	−	0.825879i
$306$	−0.0835584	−	0.0631644i	−0.00477671	−	0.00361087i
$307$	−15.7931	+	13.6848i	−0.901357	+	0.781030i	−0.976359	−	0.216153i	$-0.930649\pi$
$307$	−15.7931	+	13.6848i	−0.901357	+	0.781030i	0.0750025	+	0.997183i	$0.476104\pi$
$308$	16.9587	+	1.53256i	0.966309	+	0.0873258i
$309$	−10.3686	+	7.16306i	−0.589847	+	0.407492i
$310$	−14.2686	+	4.18965i	−0.810405	+	0.237956i
$311$	18.1336	−	5.32451i	1.02826	−	0.301925i	0.276259	−	0.961083i	$-0.410905\pi$
$311$	18.1336	−	5.32451i	1.02826	−	0.301925i	0.752005	+	0.659158i	$0.229087\pi$
$312$	0.263353	+	0.381204i	0.0149094	+	0.0215814i
$313$	27.6879	−	3.98092i	1.56501	−	0.225015i	0.695354	−	0.718667i	$-0.255248\pi$
$313$	27.6879	−	3.98092i	1.56501	−	0.225015i	0.869659	+	0.493652i	$0.164339\pi$
$314$	12.1466	+	14.0180i	0.685475	+	0.791080i
$315$	14.7079	−	12.1534i	0.828697	−	0.684768i
$316$	8.10514	−	5.20886i	0.455950	−	0.293021i
$317$	−22.7420	−	3.26980i	−1.27732	−	0.183650i	−0.529931	−	0.848041i	$-0.677782\pi$
$317$	−22.7420	−	3.26980i	−1.27732	−	0.183650i	−0.747385	+	0.664391i	$0.768691\pi$
$318$	−13.4336	+	6.68504i	−0.753318	+	0.374878i
$319$	−2.20459	+	2.54423i	−0.123433	+	0.142450i
$320$	2.30642	+	0.677227i	0.128933	+	0.0378582i
$321$	13.9910	+	8.34565i	0.780902	+	0.465809i
$322$	−12.0412	+	4.00131i	−0.671028	+	0.222984i
$323$		−	0.214225i		−	0.0119198i
$324$	−6.85671	+	5.82971i	−0.380928	+	0.323873i
$325$	−0.157331	−	0.136328i	−0.00872714	−	0.00756211i
$326$	−2.91512	+	4.53602i	−0.161454	+	0.251227i
$327$	15.5907	+	12.6241i	0.862165	+	0.698116i
$328$	0.967835	+	1.50598i	0.0534398	+	0.0831539i
$329$	−6.07295	−	30.6711i	−0.334812	−	1.69095i
$330$	26.3811	−	4.69585i	1.45223	−	0.258498i
$331$	−3.42284	−	23.8063i	−0.188136	−	1.30851i	−0.836829	−	0.547465i	$-0.815593\pi$
$331$	−3.42284	−	23.8063i	−0.188136	−	1.30851i	0.648693	−	0.761050i	$-0.275316\pi$
$332$	1.35795	−	2.97349i	0.0745270	−	0.163191i
$333$	−1.59878	−	1.61385i	−0.0876128	−	0.0884382i
$334$	2.26606	+	7.71751i	0.123994	+	0.422283i
$335$	0.161088	−	0.352733i	0.00880118	−	0.0192719i
$336$	−3.70832	−	2.69227i	−0.202306	−	0.146876i
$337$	−18.4587	−	21.3024i	−1.00551	−	1.16042i	−0.987021	−	0.160588i	$-0.948661\pi$
$337$	−18.4587	−	21.3024i	−1.00551	−	1.16042i	−0.0184861	−	0.999829i	$-0.505885\pi$
$338$	11.7601	−	5.37067i	0.639666	−	0.292126i
$339$	4.37136	−	0.145864i	0.237420	−	0.00792226i
$340$	0.0119444	−	0.0830751i	0.000647776	−	0.00450538i
$341$	33.4949	+	21.5259i	1.81385	+	1.16569i
$342$	−17.9674	−	3.99689i	−0.971568	−	0.216127i
$343$	−10.2488	−	15.4260i	−0.553384	−	0.832927i
$344$		−	1.16439i		−	0.0627795i
$345$	−16.6239	+	11.0610i	−0.894998	+	0.595504i
$346$		−	0.420035i		−	0.0225812i
$347$	6.69570	−	22.8035i	0.359444	−	1.22415i	−0.559188	−	0.829041i	$-0.688887\pi$
$347$	6.69570	−	22.8035i	0.359444	−	1.22415i	0.918632	−	0.395114i	$-0.129295\pi$
$348$	0.860309	−	0.284100i	0.0461174	−	0.0152294i
$349$	−3.93867	+	6.12869i	−0.210832	+	0.328061i	−0.930523	−	0.366233i	$-0.880647\pi$
$349$	−3.93867	+	6.12869i	−0.210832	+	0.328061i	0.719691	+	0.694295i	$0.244284\pi$
$350$	1.91538	+	0.755547i	0.102381	+	0.0403857i
$351$	−0.700841	−	1.20036i	−0.0374081	−	0.0640705i
$352$	−2.67357	−	5.85429i	−0.142502	−	0.312035i
$353$	14.7426	+	17.0139i	0.784671	+	0.905559i	0.997437	−	0.0715442i	$-0.0227927\pi$
$353$	14.7426	+	17.0139i	0.784671	+	0.905559i	−0.212766	+	0.977103i	$0.568247\pi$
$354$	−5.25013	+	12.5914i	−0.279041	+	0.669223i
$355$	24.1810	+	11.0431i	1.28339	+	0.586106i
$356$	−4.46240	+	1.31028i	−0.236507	+	0.0694446i
$357$	−0.0746183	+	0.141537i	−0.00394922	+	0.00749096i
$358$	−0.729283	+	1.59691i	−0.0385438	+	0.0843992i
$359$	−11.8822	+	1.70840i	−0.627116	+	0.0901657i	−0.448544	−	0.893761i	$-0.648057\pi$
$359$	−11.8822	+	1.70840i	−0.627116	+	0.0901657i	−0.178573	+	0.983927i	$0.557148\pi$
$360$	−6.74482	−	2.55177i	−0.355483	−	0.134490i
$361$	−7.74538	−	16.9600i	−0.407651	−	0.892632i
$362$	−1.02506	+	0.658767i	−0.0538760	+	0.0346240i
$363$	−40.9491	−	33.1575i	−2.14927	−	1.74032i
$364$	0.509733	−	0.490991i	0.0267173	−	0.0257349i
$365$	25.2190	+	21.8524i	1.32002	+	1.14381i
$366$	9.06143	−	8.39692i	0.473648	−	0.438914i
$367$		−	32.7795i		−	1.71108i	−0.517741	−	0.855538i	$-0.673227\pi$
$367$		−	32.7795i		−	1.71108i	0.517741	−	0.855538i	$-0.326773\pi$
$368$	3.56909	+	3.20337i	0.186052	+	0.166987i
$369$	−2.55167	−	4.72558i	−0.132835	−	0.246004i
$370$	0.512819	−	1.74650i	0.0266602	−	0.0907962i
$371$	13.3898	+	18.6028i	0.695164	+	0.965811i
$372$	−4.77387	−	9.59310i	−0.247514	−	0.497379i
$373$	3.41608	−	23.7594i	0.176878	−	1.23021i	−0.687054	−	0.726606i	$-0.741096\pi$
$373$	3.41608	−	23.7594i	0.176878	−	1.23021i	0.863932	−	0.503608i	$-0.167994\pi$
$374$	−0.189039	+	0.121488i	−0.00977499	+	0.00628200i
$375$	−17.4721	−	1.91989i	−0.902258	−	0.0991428i
$376$	−8.93119	+	7.73892i	−0.460591	+	0.399104i
$377$	0.0199134	+	0.138501i	0.00102559	+	0.00713317i
$378$	10.4788	+	8.89911i	0.538973	+	0.457721i
$379$	−16.2169	+	4.76172i	−0.833008	+	0.244593i	−0.670309	−	0.742082i	$-0.733838\pi$
$379$	−16.2169	+	4.76172i	−0.833008	+	0.244593i	−0.162700	+	0.986676i	$0.552020\pi$
$380$	−4.15516	−	14.1512i	−0.213155	−	0.725940i
$381$	0.531029	+	0.768667i	0.0272054	+	0.0393800i
$382$	−0.632534	−	4.39937i	−0.0323633	−	0.225092i
$383$	−9.86828	−	11.3886i	−0.504246	−	0.581931i	0.445370	−	0.895347i	$-0.353072\pi$
$383$	−9.86828	−	11.3886i	−0.504246	−	0.581931i	−0.949616	+	0.313416i	$0.898527\pi$
$384$	−0.189184	+	1.72169i	−0.00965426	+	0.0878595i
$385$	−13.5834	−	38.6116i	−0.692274	−	1.96783i
$386$	−15.3971	−	2.21377i	−0.783693	−	0.112678i
$387$	−0.265531	+	3.48305i	−0.0134977	+	0.177053i
$388$	−2.89236	−	2.50625i	−0.146837	−	0.127235i
$389$	−0.00954892	+	0.0325206i	−0.000484149	+	0.00164886i	−0.959735	−	0.280908i	$-0.909364\pi$
$389$	−0.00954892	+	0.0325206i	−0.000484149	+	0.00164886i	0.959251	+	0.282557i	$0.0911826\pi$
$390$	0.570553	−	0.956499i	0.0288911	−	0.0484342i
$391$	0.0929737	−	0.139265i	0.00470188	−	0.00704295i
$392$	−3.14428	+	6.25408i	−0.158810	+	0.315879i
$393$	24.0827	−	22.3166i	1.21481	−	1.12573i
$394$	8.27415	−	9.54888i	0.416846	−	0.481066i
$395$	−19.4831	−	12.5210i	−0.980301	−	0.630001i
$396$	6.66245	+	18.1218i	0.334801	+	0.910652i
$397$	−20.6045	−	32.0612i	−1.03411	−	1.60911i	−0.762822	−	0.646608i	$-0.776187\pi$
$397$	−20.6045	−	32.0612i	−1.03411	−	1.60911i	−0.271288	−	0.962498i	$-0.587449\pi$
$398$	−10.1140	−	22.1466i	−0.506970	−	1.11011i
$399$	−1.59532	+	28.0713i	−0.0798658	+	1.40532i
$400$	−0.110754	−	0.770311i	−0.00553770	−	0.0385155i
$401$	14.8071	+	6.76216i	0.739430	+	0.337686i	0.749269	−	0.662265i	$-0.230405\pi$
$401$	14.8071	+	6.76216i	0.739430	+	0.337686i	−0.00983977	+	0.999952i	$0.503132\pi$
$402$	0.270569	+	0.0697347i	0.0134948	+	0.00347805i
$403$	1.58786	−	0.466237i	0.0790969	−	0.0232249i
$404$	0.486469	−	1.06522i	0.0242028	−	0.0529966i
$405$	19.5940	+	9.17128i	0.973633	+	0.455725i
$406$	−0.640394	−	1.22687i	−0.0317822	−	0.0608883i
$407$	−4.43306	+	2.02451i	−0.219739	+	0.100351i
$408$	0.0604416	−	0.00201682i	0.00299230	−	9.98476e-5i
$409$	−29.2196	−	4.20114i	−1.44481	−	0.207733i	−0.625118	−	0.780530i	$-0.714949\pi$
$409$	−29.2196	−	4.20114i	−1.44481	−	0.207733i	−0.819697	+	0.572797i	$0.805858\pi$
$410$	2.32648	−	3.62007i	0.114897	−	0.178783i
$411$	−23.1849	+	7.65636i	−1.14363	+	0.377661i
$412$	2.04986	−	6.98119i	0.100989	−	0.343938i
$413$	20.2759	+	4.81007i	0.997711	+	0.236688i
$414$	−9.94579	−	10.3962i	−0.488809	−	0.510946i
$415$	−7.85775			−0.385722
$416$	−0.256666	−	0.0753639i	−0.0125841	−	0.00369502i
$417$	−25.2495	+	8.33813i	−1.23647	+	0.408320i
$418$	−21.3487	+	33.2192i	−1.04420	+	1.62480i
$419$	−1.46865	+	10.2147i	−0.0717483	+	0.499020i	0.921983	+	0.387229i	$0.126568\pi$
$419$	−1.46865	+	10.2147i	−0.0717483	+	0.499020i	−0.993732	+	0.111791i	$0.964341\pi$
$420$	−2.18381	+	10.7969i	−0.106559	+	0.526837i
$421$	−4.29554	−	9.40592i	−0.209352	−	0.458416i	0.775605	−	0.631219i	$-0.217445\pi$
$421$	−4.29554	−	9.40592i	−0.209352	−	0.458416i	−0.984956	+	0.172803i	$0.944718\pi$
$422$	−15.1291	+	13.1094i	−0.736472	+	0.638157i
$423$	28.4809	−	21.1129i	1.38479	−	1.02654i
$424$	3.59881	−	7.88029i	0.174774	−	0.382701i
$425$	−0.0260716	+	0.00765531i	−0.00126466	+	0.000371337i
$426$	−4.78053	+	18.5484i	−0.231617	+	0.898671i
$427$	−14.8925	−	11.5898i	−0.720697	−	0.560867i
$428$	−9.30990	+	1.33856i	−0.450011	+	0.0647018i
$429$	−2.93577	+	0.522569i	−0.141740	+	0.0252299i
$430$	−2.54601	+	1.16272i	−0.122779	+	0.0560715i
$431$	−1.58328	−	2.46364i	−0.0762641	−	0.118669i	0.801026	−	0.598629i	$-0.204288\pi$
$431$	−1.58328	−	2.46364i	−0.0762641	−	0.118669i	−0.877290	+	0.479960i	$0.840651\pi$
$432$	0.958531	−	5.10698i	0.0461174	−	0.245710i
$433$	−7.73034	+	12.0286i	−0.371497	+	0.578060i	−0.975792	−	0.218700i	$-0.929818\pi$
$433$	−7.73034	+	12.0286i	−0.371497	+	0.578060i	0.604296	+	0.796760i	$0.293455\pi$
$434$	−13.2845	+	9.56183i	−0.637678	+	0.458983i
$435$	−1.48029	−	1.59743i	−0.0709742	−	0.0765909i
$436$	−11.5821			−0.554683
$437$	4.69522	−	29.0480i	0.224603	−	1.38956i
$438$	−12.3176	+	20.6497i	−0.588556	+	0.986680i
$439$	−1.36820	+	4.65965i	−0.0653004	+	0.222393i	−0.985678	−	0.168638i	$-0.946063\pi$
$439$	−1.36820	+	4.65965i	−0.0653004	+	0.222393i	0.920378	+	0.391031i	$0.127881\pi$
$440$	−10.1311	+	11.6919i	−0.482980	+	0.557388i
$441$	10.8318	−	17.9909i	0.515798	−	0.856710i
$442$	−0.00132921	+	0.00924485i	−6.32240e−5	+	0.000439733i
$443$	−7.96019	−	12.3863i	−0.378200	−	0.588491i	0.599016	−	0.800737i	$-0.295558\pi$
$443$	−7.96019	−	12.3863i	−0.378200	−	0.588491i	−0.977216	+	0.212246i	$0.931922\pi$
$444$	1.30372	+	0.143256i	0.0618717	+	0.00679865i
$445$	7.32104	+	8.44893i	0.347051	+	0.400518i
$446$	−2.88556	−	20.0695i	−0.136635	−	0.950319i
$447$	12.0239	−	8.30664i	0.568711	−	0.392891i
$448$	2.64208	−	0.139298i	0.124827	−	0.00658121i
$449$	10.6371	+	36.2267i	0.501997	+	1.70965i	0.686780	+	0.726866i	$0.259024\pi$
$449$	10.6371	+	36.2267i	0.501997	+	1.70965i	−0.184782	+	0.982779i	$0.559158\pi$
$450$	0.155636	+	2.32950i	0.00733674	+	0.109814i
$451$	−11.4040	+	1.63965i	−0.536994	+	0.0772081i
$452$	−1.90843	+	1.65366i	−0.0897648	+	0.0777817i
$453$	−13.2518	−	1.45614i	−0.622622	−	0.0684156i
$454$	−4.59990	−	7.15758i	−0.215884	−	0.335922i
$455$	−1.58259	−	0.624276i	−0.0741930	−	0.0292665i
$456$	9.51412	−	4.73457i	0.445540	−	0.221717i
$457$	5.60839	−	6.47243i	0.262349	−	0.302767i	−0.609258	−	0.792972i	$-0.708533\pi$
$457$	5.60839	−	6.47243i	0.262349	−	0.302767i	0.871607	+	0.490205i	$0.163078\pi$
$458$	−12.4222	−	3.64748i	−0.580451	−	0.170436i
$459$	−0.181260	−	0.00775038i	−0.00846049	−	0.000361757i
$460$	3.44039	−	11.0029i	0.160409	−	0.513011i
$461$	−38.7934			−1.80679			−0.903394	−	0.428811i	$-0.858933\pi$
$461$	−38.7934			−1.80679			−0.903394	+	0.428811i	$0.858933\pi$
$462$	25.6758	−	14.5116i	1.19455	−	0.675143i
$463$	−26.2042	+	30.2412i	−1.21781	+	1.40543i	−0.330789	+	0.943705i	$0.607315\pi$
$463$	−26.2042	+	30.2412i	−1.21781	+	1.40543i	−0.887023	+	0.461725i	$0.847231\pi$
$464$	−0.282799	+	0.440045i	−0.0131286	+	0.0204286i
$465$	−16.2089	+	20.0178i	−0.751671	+	0.928304i
$466$	−7.60589	+	4.88801i	−0.352336	+	0.226433i
$467$	8.55814	+	18.7397i	0.396024	+	0.867171i	0.997658	+	0.0683990i	$0.0217891\pi$
$467$	8.55814	+	18.7397i	0.396024	+	0.867171i	−0.601635	+	0.798771i	$0.705484\pi$
$468$	0.750584	+	0.283969i	0.0346957	+	0.0131265i
$469$	0.0384143	−	0.425076i	0.00177381	−	0.0196282i
$470$	25.8401	+	11.8008i	1.19192	+	0.544330i
$471$	31.1102	+	8.01812i	1.43348	+	0.369456i
$472$	−2.21900	−	7.55721i	−0.102138	−	0.347849i
$473$	6.81665	+	3.11306i	0.313430	+	0.143139i
$474$	6.42220	−	15.4023i	0.294981	−	0.707453i
$475$	−3.60861	+	3.12688i	−0.165574	+	0.143471i
$476$	−0.0179426	−	0.0906181i	−0.000822396	−	0.00415347i
$477$	−12.5622	+	22.7518i	−0.575185	+	1.04173i
$478$	2.45092	−	17.0465i	0.112102	−	0.779690i
$479$	0.414117	+	0.266137i	0.0189215	+	0.0121601i	0.550067	−	0.835120i	$-0.314602\pi$
$479$	0.414117	+	0.266137i	0.0189215	+	0.0121601i	−0.531146	+	0.847280i	$0.678238\pi$
$480$	3.95350	−	1.30557i	0.180452	−	0.0595907i
$481$	−0.0570680	+	0.194356i	−0.00260208	+	0.00886186i
$482$	10.7993			0.491896
$483$	−13.2201	+	17.5565i	−0.601533	+	0.798848i
$484$	30.4207			1.38276
$485$	−2.59185	+	8.82702i	−0.117690	+	0.400814i
$486$	−4.03189	+	15.0580i	−0.182890	+	0.683045i
$487$	−5.62548	−	3.61528i	−0.254915	−	0.163824i	0.406942	−	0.913454i	$-0.366595\pi$
$487$	−5.62548	−	3.61528i	−0.254915	−	0.163824i	−0.661857	+	0.749630i	$0.730231\pi$
$488$	−1.01506	+	7.05990i	−0.0459496	+	0.319587i
$489$	0.311458	+	9.33399i	0.0140846	+	0.422098i
$490$	16.8148	+	0.630035i	0.759614	+	0.0284621i
$491$	0.725658	−	0.628787i	0.0327485	−	0.0283767i	−0.638333	−	0.769761i	$-0.720376\pi$
$491$	0.725658	−	0.628787i	0.0327485	−	0.0283767i	0.671081	+	0.741384i	$0.265830\pi$
$492$	2.86184	+	1.19328i	0.129022	+	0.0537972i
$493$	0.0166132	+	0.00758697i	0.000748219	+	0.000341700i
$494$	0.462399	+	1.57479i	0.0208043	+	0.0708530i
$495$	32.9715	−	32.6638i	1.48196	−	1.46813i
$496$	5.62742	+	2.56996i	0.252679	+	0.115394i
$497$	29.1402	+	2.63342i	1.30712	+	0.118125i
$498$	−0.992222	−	5.57427i	−0.0444625	−	0.249789i
$499$	−6.88320	−	15.0721i	−0.308134	−	0.674720i	0.690692	−	0.723149i	$-0.257306\pi$
$499$	−6.88320	−	15.0721i	−0.308134	−	0.674720i	−0.998827	+	0.0484287i	$0.984579\pi$
$500$	8.53726	−	5.48657i	0.381798	−	0.245367i
$501$	10.8271	+	8.76695i	0.483718	+	0.391678i
$502$	12.7273	−	19.8041i	0.568048	−	0.883900i
$503$	9.46620	−	10.9246i	0.422077	−	0.487103i	−0.504392	−	0.863475i	$-0.668283\pi$
$503$	9.46620	−	10.9246i	0.422077	−	0.487103i	0.926468	+	0.376372i	$0.122829\pi$
$504$	−7.93508	−	0.185827i	−0.353456	−	0.00827737i
$505$	−2.81495			−0.125264
$506$	−28.2957	+	12.3301i	−1.25790	+	0.548139i
$507$	11.4714	−	19.2312i	0.509465	−	0.854088i
$508$	−0.517545	−	0.151965i	−0.0229624	−	0.00674236i
$509$	−13.9179	+	16.0621i	−0.616900	+	0.711941i	−0.975115	−	0.221698i	$-0.928840\pi$
$509$	−13.9179	+	16.0621i	−0.616900	+	0.711941i	0.358215	+	0.933639i	$0.383385\pi$
$510$	−0.0647652	−	0.130146i	−0.00286785	−	0.00576295i
$511$	34.1663	+	13.4774i	1.51143	+	0.596204i
$512$	−0.540641	−	0.841254i	−0.0238932	−	0.0371785i
$513$	−29.5395	+	11.9930i	−1.30420	+	0.529503i
$514$	−20.5594	+	17.8148i	−0.906836	+	0.785778i
$515$	−17.3118	+	2.48906i	−0.762848	+	0.109681i
$516$	−1.14633	−	1.65931i	−0.0504642	−	0.0730472i
$517$	−21.4278	−	72.9763i	−0.942392	−	3.20949i
$518$	−0.105481	−	2.00067i	−0.00463457	−	0.0879044i
$519$	−0.413520	−	0.598572i	−0.0181515	−	0.0262744i
$520$	0.0915112	+	0.636474i	0.00401303	+	0.0279112i
$521$	19.8679	+	22.9288i	0.870429	+	1.00453i	0.999916	+	0.0129475i	$0.00412143\pi$
$521$	19.8679	+	22.9288i	0.870429	+	1.00453i	−0.129487	+	0.991581i	$0.541333\pi$
$522$	0.946293	−	1.25182i	0.0414181	−	0.0547908i
$523$	−18.0616	−	28.1044i	−0.789780	−	1.22892i	−0.969473	−	0.245199i	$-0.921147\pi$
$523$	−18.0616	−	28.1044i	−0.789780	−	1.22892i	0.179693	−	0.983723i	$-0.442490\pi$
$524$	−2.69774	+	18.7632i	−0.117852	+	0.819675i
$525$	3.47334	−	0.808973i	0.151589	−	0.0353065i
$526$	11.0913	−	12.8001i	0.483604	−	0.558109i
$527$	0.0608551	−	0.207253i	0.00265089	−	0.00902810i
$528$	−9.57347	−	5.71058i	−0.416632	−	0.248521i
$529$	15.6592	−	16.8461i	0.680833	−	0.732438i
$530$	−20.8245			−0.904557
$531$	4.91435	+	23.1121i	0.213265	+	1.00298i
$532$	−9.48311	−	13.1752i	−0.411145	−	0.571216i
$533$	−0.258898	+	0.402852i	−0.0112141	+	0.0174495i
$534$	−5.06920	+	6.26040i	−0.219366	+	0.270914i
$535$	12.2235	+	19.0201i	0.528467	+	0.822310i
$536$	−0.146740	+	0.0670140i	−0.00633821	+	0.00289456i
$537$	0.532871	+	2.99365i	0.0229951	+	0.129186i
$538$	0.279867	−	0.0402388i	0.0120659	−	0.00173482i
$539$	−28.2068	−	35.1282i	−1.21495	−	1.51308i
$540$	−12.1239	+	3.00379i	−0.521731	+	0.129263i
$541$	−15.1841	+	4.45845i	−0.652815	+	0.191684i	−0.591337	−	0.806425i	$-0.701400\pi$
$541$	−15.1841	+	4.45845i	−0.652815	+	0.191684i	−0.0614781	+	0.998108i	$0.519581\pi$
$542$	−1.79792	+	3.93690i	−0.0772274	+	0.169104i
$543$	−0.812219	+	1.94794i	−0.0348556	+	0.0835942i
$544$	−0.0263873	+	0.0228647i	−0.00113135	+	0.000980316i
$545$	11.5656	+	25.3251i	0.495416	+	1.08481i
$546$	0.243021	−	1.20152i	0.0104003	−	0.0514201i
$547$	0.970798	−	6.75205i	0.0415083	−	0.288697i	−0.958485	−	0.285142i	$-0.907959\pi$
$547$	0.970798	−	6.75205i	0.0415083	−	0.288697i	0.999994	−	0.00355497i	$-0.00113158\pi$
$548$	7.62132	−	11.8590i	0.325567	−	0.506591i
$549$	4.64634	−	20.8869i	0.198301	−	0.891433i
$550$	4.80573	+	1.41109i	0.204917	+	0.0601691i
$551$	3.20939			0.136725
$552$	8.23984	+	1.05124i	0.350711	+	0.0447437i
$553$	−24.8024	−	5.88390i	−1.05470	−	0.250209i
$554$	−8.41603	+	28.6624i	−0.357563	+	1.21775i
$555$	−0.988617	−	2.99372i	−0.0419645	−	0.127076i
$556$	8.29996	−	12.9150i	0.351997	−	0.547718i
$557$	−1.74647	−	0.251104i	−0.0740001	−	0.0106396i	0.105215	−	0.994449i	$-0.466447\pi$
$557$	−1.74647	−	0.251104i	−0.0740001	−	0.0106396i	−0.179215	+	0.983810i	$0.557356\pi$
$558$	−16.2473	−	8.97086i	−0.687805	−	0.379767i
$559$	0.283328	−	0.129391i	0.0119835	−	0.00547267i
$560$	−2.94290	−	5.63800i	−0.124360	−	0.238249i
$561$	−0.149787	+	0.359235i	−0.00632403	+	0.0151669i
$562$	−6.23010	+	13.6420i	−0.262801	+	0.575453i
$563$	−39.2830	+	11.5345i	−1.65558	+	0.486122i	−0.970249	−	0.242110i	$-0.922160\pi$
$563$	−39.2830	+	11.5345i	−1.65558	+	0.486122i	−0.685330	+	0.728232i	$0.740342\pi$
$564$	−5.10854	+	19.8210i	−0.215108	+	0.834617i
$565$	5.52155	+	2.52161i	0.232293	+	0.106085i
$566$	2.13230	+	14.8305i	0.0896274	+	0.623372i
$567$	23.6940	+	2.36541i	0.995054	+	0.0993381i
$568$	−4.59402	−	10.0595i	−0.192761	−	0.422087i
$569$	−18.7696	−	29.2060i	−0.786861	−	1.22438i	−0.970433	−	0.241373i	$-0.922402\pi$
$569$	−18.7696	−	29.2060i	−0.786861	−	1.22438i	0.183572	−	0.983006i	$-0.441234\pi$
$570$	−19.8530	−	16.0755i	−0.831551	−	0.673328i
$571$	−8.38126	−	5.38631i	−0.350745	−	0.225410i	0.353390	−	0.935476i	$-0.385029\pi$
$571$	−8.38126	−	5.38631i	−0.350745	−	0.225410i	−0.704135	+	0.710066i	$0.748665\pi$
$572$	1.12742	−	1.30111i	0.0471396	−	0.0544020i
$573$	−5.23254	−	5.64662i	−0.218592	−	0.235891i
$574$	1.09326	−	4.60842i	0.0456319	−	0.192352i
$575$	−3.70299	+	0.466612i	−0.154425	+	0.0194591i
$576$	1.42539	+	2.63975i	0.0593911	+	0.109990i
$577$	8.06669	−	27.4726i	0.335821	−	1.14370i	−0.602553	−	0.798079i	$-0.705850\pi$
$577$	8.06669	−	27.4726i	0.335821	−	1.14370i	0.938374	−	0.345622i	$-0.112332\pi$
$578$	−12.8468	−	11.1318i	−0.534357	−	0.463023i
$579$	−24.1212	+	12.0036i	−1.00244	+	0.498851i
$580$	1.24458	+	0.178944i	0.0516785	+	0.00743025i
$581$	−8.15855	+	2.87014i	−0.338474	+	0.119073i
$582$	−6.58915	−	0.724035i	−0.273129	−	0.0300122i
$583$	36.5119	+	42.1369i	1.51217	+	1.74513i
$584$	−1.97562	−	13.7407i	−0.0817517	−	0.568595i
$585$	−0.128595	−	1.92477i	−0.00531675	−	0.0795793i
$586$	4.71658	+	16.0632i	0.194840	+	0.663564i
$587$	27.1080	−	7.95963i	1.11887	−	0.328529i	0.330544	−	0.943791i	$-0.392768\pi$
$587$	27.1080	−	7.95963i	1.11887	−	0.328529i	0.788323	+	0.615262i	$0.210950\pi$
$588$	1.67631	+	12.0079i	0.0691298	+	0.495198i
$589$	−5.40190	−	37.5711i	−0.222582	−	1.54809i
$590$	−14.3085	+	12.3984i	−0.589073	+	0.510435i
$591$	2.39034	−	21.7535i	0.0983254	−	0.894819i
$592$	−0.637025	+	0.409391i	−0.0261816	+	0.0168259i
$593$	3.32972	−	23.1587i	0.136735	−	0.951013i	−0.799757	−	0.600324i	$-0.795038\pi$
$593$	3.32972	−	23.1587i	0.136735	−	0.951013i	0.936492	−	0.350689i	$-0.114053\pi$
$594$	27.3350	+	19.2654i	1.12157	+	0.790467i
$595$	−0.180226	+	0.129721i	−0.00738854	+	0.00531806i
$596$	−2.37712	+	8.09573i	−0.0973707	+	0.331614i
$597$	−36.2162	−	21.6030i	−1.48223	−	0.884151i
$598$	−0.382857	+	1.22443i	−0.0156562	+	0.0500708i
$599$			26.2101i			1.07092i	0.844561	+	0.535459i	$0.179861\pi$
$599$			26.2101i			1.07092i	−0.844561	+	0.535459i	$0.820139\pi$
$600$	−0.916194	−	0.988698i	−0.0374034	−	0.0403634i
$601$	13.8461	+	11.9977i	0.564795	+	0.489398i	0.889822	−	0.456307i	$-0.150828\pi$
$601$	13.8461	+	11.9977i	0.564795	+	0.489398i	−0.325027	+	0.945705i	$0.605374\pi$
$602$	−2.21877	+	2.13719i	−0.0904305	+	0.0871056i
$603$	0.454229	−	0.166997i	0.0184976	−	0.00680065i
$604$	6.47509	−	4.16129i	0.263468	−	0.169320i
$605$	−30.3773	−	66.5169i	−1.23501	−	2.70430i
$606$	−0.355452	−	1.99692i	−0.0144393	−	0.0811193i
$607$	−40.4268	+	5.81249i	−1.64087	+	0.235922i	−0.900052	−	0.435783i	$-0.856472\pi$
$607$	−40.4268	+	5.81249i	−1.64087	+	0.235922i	−0.740819	+	0.671704i	$0.765563\pi$
$608$	−2.54880	+	5.58109i	−0.103367	+	0.226343i
$609$	−2.12043	−	1.11789i	−0.0859243	−	0.0452991i
$610$	16.4506	−	4.83032i	0.666064	−	0.195574i
$611$	−2.87557	−	1.31323i	−0.116333	−	0.0531275i
$612$	0.0841469	−	0.0623782i	0.00340144	−	0.00252149i
$613$	17.1994	+	19.8492i	0.694678	+	0.801702i	0.988023	−	0.154305i	$-0.0493139\pi$
$613$	17.1994	+	19.8492i	0.694678	+	0.801702i	−0.293345	+	0.956007i	$0.594768\pi$
$614$	−8.68101	−	19.0088i	−0.350337	−	0.767131i
$615$	−0.248566	−	7.44919i	−0.0100231	−	0.300380i
$616$	−6.24829	+	15.8399i	−0.251751	+	0.638209i
$617$	13.9452	−	21.6992i	0.561413	−	0.873576i	−0.438267	−	0.898845i	$-0.644408\pi$
$617$	13.9452	−	21.6992i	0.561413	−	0.873576i	0.999681	+	0.0252685i	$0.00804405\pi$
$618$	−3.95174	−	11.9666i	−0.158962	−	0.481369i
$619$	0.415241	−	1.41418i	0.0166899	−	0.0568407i	−0.950727	−	0.310029i	$-0.899661\pi$
$619$	0.415241	−	1.41418i	0.0166899	−	0.0568407i	0.967417	+	0.253189i	$0.0814793\pi$
$620$		−	14.8710i		−	0.597235i
$621$	−24.4083	−	5.02364i	−0.979470	−	0.201592i
$622$			18.8992i			0.757788i
$623$	10.6874	+	6.09826i	0.428181	+	0.244322i
$624$	−0.439958	+	0.145287i	−0.0176124	+	0.00581615i
$625$	−23.7953	−	15.2923i	−0.951812	−	0.611692i
$626$	−3.98092	+	27.6879i	−0.159110	+	1.10663i
$627$	2.28093	+	68.3566i	0.0910918	+	2.72990i
$628$	−16.8723	+	7.70530i	−0.673276	+	0.307475i
$629$	0.0173139	+	0.0199813i	0.000690350	+	0.000796707i
$630$	7.51743	+	17.5362i	0.299502	+	0.698657i
$631$	−3.01033	+	6.59169i	−0.119839	+	0.262411i	−0.960039	−	0.279865i	$-0.909710\pi$
$631$	−3.01033	+	6.59169i	−0.119839	+	0.262411i	0.840200	+	0.542276i	$0.182437\pi$
$632$	2.71438	+	9.24433i	0.107972	+	0.367720i
$633$	−8.65366	+	33.5761i	−0.343952	+	1.33453i
$634$	9.54450	−	20.8995i	0.379061	−	0.830027i
$635$	0.184525	+	1.28340i	0.00732264	+	0.0509301i
$636$	−2.62957	−	14.7728i	−0.104269	−	0.585781i
$637$	−1.87120	−	0.0701122i	−0.0741396	−	0.00277795i
$638$	−1.82007	−	2.83208i	−0.0720571	−	0.112123i
$639$	11.4482	+	31.1388i	0.452882	+	1.23183i
$640$	−1.29959	+	2.02220i	−0.0513708	+	0.0799345i
$641$	8.10965	+	7.02706i	0.320312	+	0.277552i	0.800143	−	0.599809i	$-0.204757\pi$
$641$	8.10965	+	7.02706i	0.320312	+	0.277552i	−0.479831	+	0.877361i	$0.659302\pi$
$642$	−11.9493	+	11.0730i	−0.471602	+	0.437018i
$643$		−	6.24021i		−	0.246090i	−0.992401	−	0.123045i	$-0.960734\pi$
$643$		−	6.24021i		−	0.246090i	0.992401	−	0.123045i	$-0.0392659\pi$
$644$	−0.446841	−	12.6807i	−0.0176080	−	0.499690i
$645$	−2.48351	+	4.16347i	−0.0977882	+	0.163936i
$646$	0.205547	+	0.0603541i	0.00808715	+	0.00237460i
$647$	−29.0819	+	33.5623i	−1.14333	+	1.31947i	−0.203007	+	0.979177i	$0.565072\pi$
$647$	−29.0819	+	33.5623i	−1.14333	+	1.31947i	−0.940320	+	0.340293i	$0.889474\pi$
$648$	−3.66181	−	8.22138i	−0.143849	−	0.322966i
$649$	50.1748	+	7.21404i	1.96953	+	0.283176i
$650$	0.175131	−	0.112550i	0.00686919	−	0.00441456i
$651$	−9.51765	+	26.7046i	−0.373026	+	1.04664i
$652$	−3.53100	−	4.07499i	−0.138284	−	0.159589i
$653$	35.9769	−	5.17270i	1.40789	−	0.202423i	0.603894	−	0.797064i	$-0.293615\pi$
$653$	35.9769	−	5.17270i	1.40789	−	0.202423i	0.803991	+	0.594641i	$0.202706\pi$
$654$	−16.5052	+	11.4025i	−0.645403	+	0.445873i
$655$	43.7210	−	12.8376i	1.70832	−	0.501608i
$656$	−1.71765	+	0.504347i	−0.0670629	+	0.0196915i
$657$	2.77621	+	41.5534i	0.108310	+	1.62115i
$658$	31.1397	+	2.81411i	1.21395	+	0.109705i
$659$	36.1120	−	31.2912i	1.40672	−	1.21893i	0.463793	−	0.885944i	$-0.346488\pi$
$659$	36.1120	−	31.2912i	1.40672	−	1.21893i	0.942931	−	0.332989i	$-0.108057\pi$
$660$	−2.92679	+	26.6355i	−0.113925	+	1.03678i
$661$	16.2959	+	25.3569i	0.633837	+	0.986270i	0.998480	+	0.0551222i	$0.0175548\pi$
$661$	16.2959	+	25.3569i	0.633837	+	0.986270i	−0.364643	+	0.931148i	$0.618809\pi$
$662$	23.8063	+	3.42284i	0.925260	+	0.133032i
$663$	0.00720727	+	0.0144830i	0.000279907	+	0.000562473i
$664$	2.47046	+	2.14067i	0.0958726	+	0.0830741i
$665$	−19.3388	+	33.8918i	−0.749928	+	1.31427i
$666$	1.99890	−	1.07935i	0.0774559	−	0.0418239i
$667$	2.08639	+	1.39288i	0.0807854	+	0.0539325i
$668$	−8.04332			−0.311205
$669$	−23.8703	−	25.7593i	−0.922880	−	0.995913i
$670$	0.293062	+	0.253939i	0.0113220	+	0.00981053i
$671$	−38.6169	−	24.8176i	−1.49079	−	0.958072i
$672$	3.62797	−	2.79961i	0.139952	−	0.107997i
$673$	41.6146	−	26.7441i	1.60413	−	1.03091i	0.638971	−	0.769231i	$-0.279360\pi$
$673$	41.6146	−	26.7441i	1.60413	−	1.03091i	0.965155	−	0.261678i	$-0.0842759\pi$
$674$	25.6399	−	11.7094i	0.987614	−	0.451028i
$675$	2.51516	+	3.16645i	0.0968086	+	0.121877i
$676$	1.83991	+	12.7968i	0.0707657	+	0.492187i
$677$	−12.8318	+	28.0978i	−0.493168	+	1.07989i	0.485462	+	0.874258i	$0.338651\pi$
$677$	−12.8318	+	28.0978i	−0.493168	+	1.07989i	−0.978630	+	0.205629i	$0.934076\pi$
$678$	−1.09160	+	4.23538i	−0.0419226	+	0.162659i
$679$	0.533113	+	10.1116i	0.0204590	+	0.388049i
$680$	0.0763449	+	0.0348655i	0.00292769	+	0.00133703i
$681$	−13.6017	−	5.67139i	−0.521217	−	0.217328i
$682$	−30.0905	+	26.0736i	−1.15223	+	0.998410i
$683$	11.2085	−	5.11873i	0.428880	−	0.195863i	−0.189267	−	0.981926i	$-0.560611\pi$
$683$	11.2085	−	5.11873i	0.428880	−	0.195863i	0.618146	+	0.786063i	$0.287884\pi$
$684$	8.89700	−	16.1136i	0.340185	−	0.616118i
$685$	−33.5410	−	4.82246i	−1.28153	−	0.184257i
$686$	17.6886	−	5.48765i	0.675353	−	0.209519i
$687$	−21.2932	+	7.03166i	−0.812386	+	0.268274i
$688$	1.11722	+	0.328045i	0.0425936	+	0.0125066i
$689$	2.31741			0.0882863
$690$	−5.92947	−	19.0667i	−0.225731	−	0.725857i
$691$		−	21.0578i		−	0.801078i	−0.916280	−	0.400539i	$-0.868823\pi$
$691$		−	21.0578i		−	0.801078i	0.916280	−	0.400539i	$-0.131177\pi$
$692$	0.403020	+	0.118337i	0.0153205	+	0.00449852i
$693$	22.3028	−	45.9574i	0.847215	−	1.74578i
$694$	19.9934	+	12.8490i	0.758938	+	0.487740i
$695$	−36.5276	−	5.25188i	−1.38557	−	0.199215i
$696$	0.0302149	+	0.905501i	0.00114529	+	0.0343229i
$697$	0.0259652	+	0.0568558i	0.000983501	+	0.00215357i
$698$	−4.77078	−	5.50578i	−0.180577	−	0.208397i
$699$	−6.02661	+	14.4536i	−0.227947	+	0.546685i
$700$	−1.26457	+	1.62493i	−0.0477961	+	0.0614165i
$701$	−8.40910	−	28.6388i	−0.317607	−	1.08167i	−0.951346	−	0.308124i	$-0.900299\pi$
$701$	−8.40910	−	28.6388i	−0.317607	−	1.08167i	0.633739	−	0.773547i	$-0.281519\pi$
$702$	1.34919	−	0.334271i	0.0509218	−	0.0126163i
$703$	4.22618	+	1.93003i	0.159393	+	0.0727926i
$704$	6.37038	−	0.915923i	0.240093	−	0.0345201i
$705$	48.4413	−	8.62258i	1.82441	−	0.324745i
$706$	−20.4782	+	9.35208i	−0.770707	+	0.351970i
$707$	−2.92271	+	1.02820i	−0.109920	+	0.0386693i
$708$	−10.6022	−	8.58486i	−0.398455	−	0.322639i
$709$	−26.5383	−	17.0551i	−0.996665	−	0.640518i	−0.0627563	−	0.998029i	$-0.519989\pi$
$709$	−26.5383	−	17.0551i	−0.996665	−	0.640518i	−0.933909	+	0.357511i	$0.883625\pi$
$710$	−17.4083	+	20.0903i	−0.653322	+	0.753974i
$711$	−6.01147	−	28.2718i	−0.225448	−	1.06027i
$712$		−	4.65079i		−	0.174296i
$713$	12.7941	−	26.7690i	0.479144	−	1.00251i
$714$	−0.114782	−	0.111471i	−0.00429560	−	0.00417171i
$715$	−3.97077	−	1.16592i	−0.148498	−	0.0436030i
$716$	−1.32676	−	1.14964i	−0.0495833	−	0.0429642i
$717$	−13.2894	−	26.7051i	−0.496303	−	0.997321i
$718$	1.70840	−	11.8822i	0.0637568	−	0.443438i
$719$	−9.86036	+	6.33687i	−0.367729	+	0.236325i	−0.711435	−	0.702752i	$-0.751954\pi$
$719$	−9.86036	+	6.33687i	−0.367729	+	0.236325i	0.343705	+	0.939078i	$0.388318\pi$
$720$	4.34864	−	5.75269i	0.162064	−	0.214390i
$721$	−17.0653	+	8.90768i	−0.635546	+	0.331739i
$722$	18.4551	−	2.65345i	0.686829	−	0.0987511i
$723$	15.3896	−	10.6318i	0.572347	−	0.395402i
$724$	−0.343289	−	1.16914i	−0.0127582	−	0.0434506i
$725$	−0.114687	−	0.390590i	−0.00425938	−	0.0145061i
$726$	43.3511	−	29.9489i	1.60891	−	1.11151i
$727$	3.79797	−	0.546066i	0.140859	−	0.0202525i	−0.0715246	−	0.997439i	$-0.522786\pi$
$727$	3.79797	−	0.546066i	0.140859	−	0.0202525i	0.212384	+	0.977186i	$0.431877\pi$
$728$	0.327494	+	0.627413i	0.0121377	+	0.0232535i
$729$	9.07880	+	25.4278i	0.336252	+	0.941772i
$730$	−28.0723	+	18.0409i	−1.03900	+	0.667725i
$731$	0.00578580	−	0.0402411i	0.000213996	−	0.00148837i
$732$	5.50389	+	11.0601i	0.203429	+	0.408792i
$733$	16.5929	+	14.3778i	0.612872	+	0.531057i	0.905049	−	0.425307i	$-0.139834\pi$
$733$	16.5929	+	14.3778i	0.612872	+	0.531057i	−0.292177	+	0.956364i	$0.594379\pi$
$734$	31.4517	+	9.23505i	1.16090	+	0.340872i
$735$	24.5822	−	15.6561i	0.906729	−	0.577485i
$736$	−4.07914	+	2.52203i	−0.150359	+	0.0929631i
$737$		−	1.03823i		−	0.0382436i
$738$	5.25305	−	1.11696i	0.193367	−	0.0411160i
$739$	12.5247	−	14.4542i	0.460728	−	0.531708i	−0.477082	−	0.878859i	$-0.658305\pi$
$739$	12.5247	−	14.4542i	0.460728	−	0.531708i	0.937809	+	0.347151i	$0.112851\pi$
$740$	1.53128	+	0.984092i	0.0562909	+	0.0361759i
$741$	2.20930	+	1.78893i	0.0811608	+	0.0657179i
$742$	−21.6216	+	7.60639i	−0.793755	+	0.279239i
$743$	31.5835	−	14.4237i	1.15869	−	0.529155i	0.259080	−	0.965856i	$-0.416581\pi$
$743$	31.5835	−	14.4237i	1.15869	−	0.529155i	0.899607	+	0.436701i	$0.143853\pi$
$744$	10.5495	−	1.87781i	0.386762	−	0.0688439i
$745$	20.0756	−	2.88644i	0.735513	−	0.105751i
$746$	21.8345	+	9.97150i	0.799420	+	0.365083i
$747$	−6.90178	−	6.96680i	−0.252523	−	0.254902i
$748$	−0.0633085	−	0.215609i	−0.00231479	−	0.00788345i
$749$	19.6387	+	15.2834i	0.717583	+	0.558444i
$750$	6.76460	−	16.2235i	0.247008	−	0.592399i
$751$	−21.3535	−	24.6432i	−0.779200	−	0.899245i	0.217851	−	0.975982i	$-0.430095\pi$
$751$	−21.3535	−	24.6432i	−0.779200	−	0.899245i	−0.997051	+	0.0767372i	$0.975550\pi$
$752$	−4.90923	−	10.7497i	−0.179021	−	0.392002i
$753$	−1.35981	−	40.7518i	−0.0495543	−	1.48508i
$754$	−0.138501	−	0.0199134i	−0.00504391	−	0.000725205i
$755$	−15.5648	−	10.0029i	−0.566461	−	0.364042i
$756$	−11.4909	+	7.54719i	−0.417919	+	0.274489i
$757$	−5.25855	−	1.54405i	−0.191125	−	0.0561194i	0.184769	−	0.982782i	$-0.440846\pi$
$757$	−5.25855	−	1.54405i	−0.191125	−	0.0561194i	−0.375894	+	0.926663i	$0.622664\pi$
$758$		−	16.9016i		−	0.613893i
$759$	−28.1840	+	45.4278i	−1.02301	+	1.64893i
$760$	14.7486			0.534988
$761$	38.2766	+	11.2390i	1.38753	+	0.407414i	0.888382	−	0.459105i	$-0.151830\pi$
$761$	38.2766	+	11.2390i	1.38753	+	0.407414i	0.499143	+	0.866519i	$0.333648\pi$
$762$	−0.887138	+	0.292960i	−0.0321376	+	0.0106128i
$763$	21.2586	+	22.0701i	0.769615	+	0.798992i
$764$	4.39937	+	0.632534i	0.159164	+	0.0228843i
$765$	−0.220421	−	0.121704i	−0.00796934	−	0.00440022i
$766$	13.7075	−	6.26001i	0.495272	−	0.226183i
$767$	1.59230	−	1.37973i	0.0574945	−	0.0498193i
$768$	−1.59865	−	0.666576i	−0.0576862	−	0.0240530i
$769$	5.41561	+	2.47323i	0.195292	+	0.0891868i	0.510661	−	0.859782i	$-0.329401\pi$
$769$	5.41561	+	2.47323i	0.195292	+	0.0891868i	−0.315369	+	0.948969i	$0.602128\pi$
$770$	40.8745	−	2.15502i	1.47301	−	0.0776614i
$771$	−11.7597	+	45.6276i	−0.423517	+	1.64324i
$772$	6.46197	−	14.1497i	0.232571	−	0.509260i
$773$	3.25633	+	22.6483i	0.117122	+	0.814601i	0.960699	+	0.277593i	$0.0895366\pi$
$773$	3.25633	+	22.6483i	0.117122	+	0.814601i	−0.843577	+	0.537008i	$0.819554\pi$
$774$	−3.26715	−	1.23606i	−0.117435	−	0.0444294i
$775$	−4.37944	+	2.00002i	−0.157314	+	0.0718429i
$776$	3.21960	−	2.06911i	0.115577	−	0.0742767i
$777$	−2.11996	−	2.74722i	−0.0760530	−	0.0985559i
$778$	−0.0285131	−	0.0183242i	−0.00102224	−	0.000656956i
$779$	8.30087	+	7.19275i	0.297410	+	0.257707i
$780$	0.757011	+	0.816919i	0.0271053	+	0.0292504i
$781$	71.1736			2.54679
$782$	0.107430	+	0.128443i	0.00384170	+	0.00459312i
$783$	0.116112	−	2.71553i	0.00414950	−	0.0970452i
$784$	−5.11490	−	4.77889i	−0.182675	−	0.170675i
$785$	33.6963	+	29.1980i	1.20267	+	1.04212i
$786$	14.6278	+	29.3945i	0.521756	+	1.04847i
$787$	0.491881	+	0.0707219i	0.0175337	+	0.00252096i	0.151076	−	0.988522i	$-0.451726\pi$
$787$	0.491881	+	0.0707219i	0.0175337	+	0.00252096i	−0.133542	+	0.991043i	$0.542635\pi$
$788$	6.83099	+	10.6292i	0.243344	+	0.378650i
$789$	3.20419	−	29.1601i	0.114072	−	1.03813i
$790$	17.5029	−	15.1663i	0.622724	−	0.539593i
$791$	6.65396	+	0.601322i	0.236588	+	0.0213805i
$792$	−19.2647	+	1.28709i	−0.684542	+	0.0457347i
$793$	−1.83067	+	0.537533i	−0.0650090	+	0.0190884i
$794$	36.5675	−	10.7372i	1.29773	−	0.381048i
$795$	−29.6760	+	20.5015i	−1.05250	+	0.727112i
$796$	24.0990	−	3.46491i	0.854166	−	0.122810i
$797$	−8.94183	−	10.3194i	−0.316736	−	0.365533i	0.574949	−	0.818189i	$-0.305022\pi$
$797$	−8.94183	−	10.3194i	−0.316736	−	0.365533i	−0.891685	+	0.452656i	$0.850476\pi$
$798$	−26.4848	−	9.43930i	−0.937551	−	0.334147i
$799$	−0.347116	+	0.223078i	−0.0122801	+	0.00789193i
$800$	0.770311	+	0.110754i	0.0272346	+	0.00391574i
$801$	−1.06059	+	13.9120i	−0.0374739	+	0.491556i
$802$	−10.6599	+	12.3022i	−0.376413	+	0.434404i
$803$	85.7242	+	25.1709i	3.02514	+	0.888261i
$804$	−0.143138	+	0.239963i	−0.00504809	+	0.00846284i
$805$	−27.2810	+	13.6397i	−0.961530	+	0.480735i
$806$			1.65489i			0.0582911i
$807$	0.359211	−	0.332868i	0.0126448	−	0.0117175i
$808$	0.885016	+	0.766871i	0.0311348	+	0.0269784i
$809$	−1.93579	+	3.01214i	−0.0680586	+	0.105901i	−0.873615	−	0.486618i	$-0.838230\pi$
$809$	−1.93579	+	3.01214i	−0.0680586	+	0.105901i	0.805556	+	0.592519i	$0.201867\pi$
$810$	−14.3200	+	16.2164i	−0.503155	+	0.569788i
$811$	6.45463	+	10.0436i	0.226653	+	0.352679i	0.935891	−	0.352291i	$-0.114597\pi$
$811$	6.45463	+	10.0436i	0.226653	+	0.352679i	−0.709238	+	0.704969i	$0.750961\pi$
$812$	1.35759	−	0.268805i	0.0476420	−	0.00943322i
$813$	1.31370	+	7.38034i	0.0460736	+	0.258840i
$814$	−0.693567	−	4.82386i	−0.0243095	−	0.169076i
$815$	−5.38428	+	11.7899i	−0.188603	+	0.412984i
$816$	−0.0150932	+	0.0585614i	−0.000528369	+	0.00205006i
$817$	−2.01274	−	6.85475i	−0.0704168	−	0.239817i
$818$	12.2631	−	26.8524i	0.428768	−	0.938871i
$819$	−0.836563	−	1.95148i	−0.0292319	−	0.0681901i
$820$	2.81799	+	3.25213i	0.0984084	+	0.113569i
$821$	19.8994	−	9.08775i	0.694494	−	0.317165i	−0.0367077	−	0.999326i	$-0.511687\pi$
$821$	19.8994	−	9.08775i	0.694494	−	0.317165i	0.731202	+	0.682161i	$0.238960\pi$
$822$	−0.814277	−	24.4028i	−0.0284012	−	0.851146i
$823$	−3.32625	+	23.1346i	−0.115946	+	0.806420i	0.846001	+	0.533182i	$0.179004\pi$
$823$	−3.32625	+	23.1346i	−0.115946	+	0.806420i	−0.961946	+	0.273238i	$0.911905\pi$
$824$	6.12089	+	3.93365i	0.213231	+	0.137035i
$825$	8.23763	−	2.72031i	0.286798	−	0.0947092i
$826$	−10.3276	+	18.0994i	−0.359343	+	0.629759i
$827$		−	3.45092i		−	0.120000i	−0.998198	−	0.0600001i	$-0.980890\pi$
$827$		−	3.45092i		−	0.120000i	0.998198	−	0.0600001i	$-0.0191101\pi$
$828$	12.7771	−	6.61396i	0.444037	−	0.229851i
$829$			47.8850i			1.66311i	0.555440	+	0.831557i	$0.312550\pi$
$829$			47.8850i			1.66311i	−0.555440	+	0.831557i	$0.687450\pi$
$830$	2.21378	−	7.53946i	0.0768416	−	0.261698i
$831$	16.2245	+	49.1309i	0.562822	+	1.70433i
$832$	0.144622	−	0.225037i	0.00501388	−	0.00780175i
$833$	−0.139743	+	0.200517i	−0.00484180	+	0.00694750i
$834$	−0.886785	−	26.5758i	−0.0307069	−	0.920245i
$835$	8.03184	+	17.5873i	0.277953	+	0.608633i
$836$	−25.8589	−	29.8428i	−0.894350	−	1.03214i
$837$	−31.9851	+	3.21139i	−1.10557	+	0.111002i
$838$	−9.38716	−	4.28697i	−0.324274	−	0.148091i
$839$	−6.93293	+	2.03569i	−0.239351	+	0.0702799i	−0.399208	−	0.916860i	$-0.630715\pi$
$839$	−6.93293	+	2.03569i	−0.239351	+	0.0702799i	0.159857	+	0.987140i	$0.448897\pi$
$840$	−9.74434	−	5.13720i	−0.336212	−	0.177250i
$841$	11.9334	−	26.1304i	0.411496	−	0.901050i
$842$	10.2351	−	1.47159i	0.352725	−	0.0507142i
$843$	4.55219	+	25.5741i	0.156786	+	0.880818i
$844$	−8.31604	−	18.2096i	−0.286250	−	0.626800i
$845$	26.1439	−	16.8017i	0.899378	−	0.577995i
$846$	12.2337	+	33.2754i	0.420602	+	1.14403i
$847$	−55.8362	−	57.9676i	−1.91856	−	1.99179i
$848$	6.54718	+	5.67316i	0.224831	+	0.194817i
$849$	17.6391	+	19.0350i	0.605373	+	0.653280i
$850$		−	0.0271723i		−	0.000932001i
$851$	1.90976	+	3.08886i	0.0654657	+	0.105885i
$852$	−16.4502	−	9.81256i	−0.563574	−	0.336173i
$853$	−7.26594	+	24.7455i	−0.248781	+	0.847270i	0.736516	+	0.676420i	$0.236470\pi$
$853$	−7.26594	+	24.7455i	−0.248781	+	0.847270i	−0.985297	+	0.170850i	$0.945349\pi$
$854$	15.3160	−	11.0240i	0.524102	−	0.377234i
$855$	−44.1178	−	3.36333i	−1.50880	−	0.115023i
$856$	1.33856	−	9.30990i	0.0457511	−	0.318206i
$857$	−15.7240	+	10.1052i	−0.537122	+	0.345187i	−0.780912	−	0.624641i	$-0.785245\pi$
$857$	−15.7240	+	10.1052i	−0.537122	+	0.345187i	0.243791	+	0.969828i	$0.421609\pi$
$858$	0.325702	−	2.96408i	0.0111193	−	0.101192i
$859$	8.65795	−	7.50216i	0.295405	−	0.255970i	−0.494530	−	0.869161i	$-0.664660\pi$
$859$	8.65795	−	7.50216i	0.295405	−	0.255970i	0.789935	+	0.613190i	$0.210114\pi$
$860$	−0.398331	−	2.77046i	−0.0135830	−	0.0944718i
$861$	−2.97899	−	7.64356i	−0.101524	−	0.260492i
$862$	2.80990	−	0.825062i	0.0957057	−	0.0281017i
$863$	−7.03319	−	23.9528i	−0.239412	−	0.815364i	−0.988281	−	0.152645i	$-0.951221\pi$
$863$	−7.03319	−	23.9528i	−0.239412	−	0.815364i	0.748869	−	0.662718i	$-0.230597\pi$
$864$	4.63006	+	2.35851i	0.157518	+	0.0802380i
$865$	−0.143692	−	0.999400i	−0.00488568	−	0.0339806i
$866$	−9.36351	−	10.8061i	−0.318185	−	0.367205i
$867$	−29.2666	−	3.21590i	−0.993946	−	0.109218i
$868$	−5.43182	−	15.4403i	−0.184368	−	0.524078i
$869$	−61.3761	−	8.82455i	−2.08204	−	0.299352i
$870$	1.94977	−	0.970275i	0.0661033	−	0.0328954i
$871$	−0.0326128	−	0.0282591i	−0.00110504	−	0.000957524i
$872$	3.26306	−	11.1130i	0.110501	−	0.376333i
$873$	−10.1027	+	5.45516i	−0.341925	+	0.184629i
$874$	26.5486	+	12.6888i	0.898019	+	0.429205i
$875$	−26.1247	−	6.19760i	−0.883177	−	0.209517i
$876$	−16.3430	−	17.6363i	−0.552178	−	0.595876i
$877$	2.78955	−	3.21931i	0.0941964	−	0.108708i	−0.706694	−	0.707519i	$-0.749814\pi$
$877$	2.78955	−	3.21931i	0.0941964	−	0.108708i	0.800891	+	0.598811i	$0.204360\pi$
$878$	−4.08543	−	2.62555i	−0.137877	−	0.0886080i
$879$	22.5354	+	18.2475i	0.760101	+	0.615473i
$880$	−8.36402	−	13.0147i	−0.281951	−	0.438724i
$881$	−9.23619	−	20.2244i	−0.311175	−	0.681379i	0.687835	−	0.725867i	$-0.258561\pi$
$881$	−9.23619	−	20.2244i	−0.311175	−	0.681379i	−0.999010	+	0.0444888i	$0.985834\pi$
$882$	14.2105	+	15.4616i	0.478492	+	0.520620i
$883$	1.42844	+	9.93502i	0.0480709	+	0.334340i	0.999638	+	0.0268996i	$0.00856343\pi$
$883$	1.42844	+	9.93502i	0.0480709	+	0.334340i	−0.951567	+	0.307441i	$0.900527\pi$
$884$	−0.00849589	−	0.00387994i	−0.000285748	−	0.000130497i
$885$	−8.18432	+	31.7550i	−0.275113	+	1.06743i
$886$	14.1272	−	4.14812i	0.474613	−	0.139359i
$887$	−13.5216	+	29.6082i	−0.454011	+	0.994145i	0.534801	+	0.844978i	$0.320387\pi$
$887$	−13.5216	+	29.6082i	−0.454011	+	0.994145i	−0.988812	+	0.149167i	$0.952341\pi$
$888$	−0.504753	+	1.21055i	−0.0169384	+	0.0406233i
$889$	0.660365	+	1.26513i	0.0221479	+	0.0424310i
$890$	−10.1693	+	4.64415i	−0.340875	+	0.155672i
$891$	57.9205	+	0.543111i	1.94041	+	0.0181949i
$892$	20.0695	+	2.88556i	0.671977	+	0.0966157i
$893$	−39.2007	+	60.9974i	−1.31180	+	2.04120i
$894$	4.58264	+	13.8771i	0.153266	+	0.464120i
$895$	−1.18891	+	4.04905i	−0.0397408	+	0.135345i
$896$	−0.610705	+	2.57430i	−0.0204022	+	0.0860014i
$897$	0.659849	+	2.12180i	0.0220317	+	0.0708449i
$898$	−37.7561			−1.25994
$899$	3.10495	+	0.911696i	0.103556	+	0.0304068i
$900$	−2.27899	−	0.506965i	−0.0759663	−	0.0168988i
$901$	0.163532	−	0.254460i	0.00544803	−	0.00847730i
$902$	1.63965	−	11.4040i	0.0545944	−	0.379712i
$903$	−1.05783	+	5.22998i	−0.0352022	+	0.174043i
$904$	−1.04901	−	2.29701i	−0.0348896	−	0.0763975i
$905$	−2.21360	+	1.91809i	−0.0735824	+	0.0637595i
$906$	5.13061	−	12.3047i	0.170453	−	0.408797i
$907$	15.9787	−	34.9885i	0.530564	−	1.16177i	−0.434718	−	0.900567i	$-0.643152\pi$
$907$	15.9787	−	34.9885i	0.530564	−	1.16177i	0.965283	−	0.261208i	$-0.0841207\pi$
$908$	8.16359	−	2.39705i	0.270918	−	0.0795487i
$909$	−2.47249	−	2.49578i	−0.0820072	−	0.0827798i
$910$	1.04486	−	1.34261i	0.0346366	−	0.0445070i
$911$	−46.4294	+	6.67555i	−1.53828	+	0.221171i	−0.858717	−	0.512450i	$-0.828738\pi$
$911$	−46.4294	+	6.67555i	−1.53828	+	0.221171i	−0.679559	+	0.733621i	$0.737829\pi$
$912$	1.86235	+	10.4626i	0.0616686	+	0.346452i
$913$	−19.1371	+	8.73960i	−0.633344	+	0.289239i
$914$	4.63018	+	7.20470i	0.153153	+	0.238310i
$915$	18.6876	−	23.0789i	0.617792	−	0.762965i
$916$	6.99947	−	10.8914i	0.231269	−	0.359861i
$917$	40.7056	−	29.2987i	1.34422	−	0.967528i
$918$	0.0585033	−	0.171734i	0.00193090	−	0.00566807i
$919$	38.3531			1.26515			0.632575	−	0.774499i	$-0.281998\pi$
$919$	38.3531			1.26515			0.632575	+	0.774499i	$0.281998\pi$
$920$	9.58790	+	6.40090i	0.316104	+	0.211031i
$921$	−31.0848	−	18.5421i	−1.02428	−	0.610985i
$922$	10.9294	−	37.2220i	0.359939	−	1.22584i
$923$	1.93725	−	2.23571i	0.0637654	−	0.0735892i
$924$	6.69011	+	28.7241i	0.220089	+	0.944955i
$925$	0.0838665	−	0.583304i	0.00275751	−	0.0191789i
$926$	−21.6337	−	33.6627i	−0.710927	−	1.10622i
$927$	−17.4125	−	13.1627i	−0.571901	−	0.432318i
$928$	−0.342546	−	0.395319i	−0.0112446	−	0.0129770i
$929$	5.80532	+	40.3769i	0.190466	+	1.32472i	0.830776	+	0.556607i	$0.187897\pi$
$929$	5.80532	+	40.3769i	0.190466	+	1.32472i	−0.640310	+	0.768117i	$0.721194\pi$
$930$	−14.6404	−	21.1920i	−0.480077	−	0.694914i
$931$	−7.69972	+	42.2530i	−0.252348	+	1.38479i
$932$	−2.54718	−	8.67491i	−0.0834358	−	0.284156i
$933$	18.6060	+	26.9323i	0.609135	+	0.881725i
$934$	−20.3917	+	2.93189i	−0.667238	+	0.0959343i
$935$	−0.408226	+	0.353730i	−0.0133504	+	0.0115682i
$936$	−0.483930	+	0.640177i	−0.0158177	+	0.0209248i
$937$	20.9647	+	32.6218i	0.684888	+	1.06571i	0.993424	+	0.114494i	$0.0365246\pi$
$937$	20.9647	+	32.6218i	0.684888	+	1.06571i	−0.308536	+	0.951213i	$0.599839\pi$
$938$	0.397035	+	0.156616i	0.0129636	+	0.00511369i
$939$	21.5854	+	43.3759i	0.704414	+	1.41552i
$940$	−18.6028	+	21.4687i	−0.606756	+	0.700233i
$941$	36.0953	+	10.5985i	1.17667	+	0.345503i	0.810891	−	0.585198i	$-0.198983\pi$
$941$	36.0953	+	10.5985i	1.17667	+	0.345503i	0.365783	+	0.930700i	$0.380801\pi$
$942$	−16.4581	+	27.5910i	−0.536233	+	0.898964i
$943$	2.27465	+	8.27851i	0.0740729	+	0.269585i
$944$	7.87626			0.256350
$945$	27.9769	+	17.5891i	0.910089	+	0.572175i
$946$	−4.90743	+	5.66348i	−0.159554	+	0.184136i
$947$	−26.0953	+	40.6051i	−0.847984	+	1.31949i	0.0979705	+	0.995189i	$0.468765\pi$
$947$	−26.0953	+	40.6051i	−0.847984	+	1.31949i	−0.945954	+	0.324299i	$0.894871\pi$
$948$	12.9691	+	10.5014i	0.421216	+	0.341069i
$949$	3.12397	−	2.00765i	0.101408	−	0.0651711i
$950$	−1.98356	−	4.34338i	−0.0643550	−	0.140918i
$951$	−6.97396	−	39.1795i	−0.226146	−	1.27048i
$952$	0.0920025	+	0.00831430i	0.00298182	+	0.000269468i
$953$	21.2732	+	9.71515i	0.689107	+	0.314705i	0.729014	−	0.684499i	$-0.239979\pi$
$953$	21.2732	+	9.71515i	0.689107	+	0.314705i	−0.0399070	+	0.999203i	$0.512706\pi$
$954$	−18.2910	−	18.4633i	−0.592192	−	0.597771i
$955$	−3.01001	−	10.2512i	−0.0974018	−	0.331720i
$956$	15.6655	+	7.15420i	0.506659	+	0.231383i
$957$	−5.38185	−	2.24403i	−0.173970	−	0.0725391i
$958$	−0.372027	+	0.322363i	−0.0120196	+	0.0104151i
$959$	−36.5864	+	7.24418i	−1.18144	+	0.233927i
$960$	0.138851	+	4.16118i	0.00448139	+	0.134301i
$961$	1.03498	−	7.19847i	0.0333866	−	0.232209i
$962$	−0.170405	−	0.109513i	−0.00549408	−	0.00353083i
$963$	−6.12714	+	27.5436i	−0.197444	+	0.887581i
$964$	−3.04252	+	10.3619i	−0.0979931	+	0.333734i
$965$	−37.3921			−1.20370
$966$	−13.1208	−	17.6308i	−0.422155	−	0.567261i
$967$	16.7570			0.538868			0.269434	−	0.963019i	$-0.413163\pi$
$967$	16.7570			0.538868			0.269434	+	0.963019i	$0.413163\pi$
$968$	−8.57050	+	29.1884i	−0.275466	+	0.938152i
$969$	0.352334	−	0.116351i	0.0113186	−	0.00373774i
$970$	−7.73926	−	4.97372i	−0.248493	−	0.159696i
$971$	−2.76263	+	19.2145i	−0.0886570	+	0.616623i	0.896251	+	0.443546i	$0.146280\pi$
$971$	−2.76263	+	19.2145i	−0.0886570	+	0.616623i	−0.984908	+	0.173077i	$0.944629\pi$
$972$	−13.3121	−	8.11090i	−0.426987	−	0.260157i
$973$	−39.8443	+	7.88924i	−1.27735	+	0.252918i
$974$	5.05372	−	4.37907i	0.161932	−	0.140314i
$975$	0.138767	−	0.332804i	0.00444409	−	0.0106583i
$976$	−6.48795	−	2.96295i	−0.207674	−	0.0948416i
$977$	0.673326	+	2.29314i	0.0215416	+	0.0733640i	0.969562	−	0.244845i	$-0.0787369\pi$
$977$	0.673326	+	2.29314i	0.0215416	+	0.0733640i	−0.948021	+	0.318209i	$0.896919\pi$
$978$	−9.04365	−	2.33085i	−0.289184	−	0.0745323i
$979$	27.2271	+	12.4342i	0.870181	+	0.397398i
$980$	−5.34178	+	15.9562i	−0.170637	+	0.509701i
$981$	−12.2951	+	32.4983i	−0.392553	+	1.03759i
$982$	0.398875	+	0.873414i	0.0127286	+	0.0278718i
$983$	46.4091	−	29.8253i	1.48022	−	0.951281i	0.483092	−	0.875570i	$-0.339514\pi$
$983$	46.4091	−	29.8253i	1.48022	−	0.951281i	0.997130	−	0.0757108i	$-0.0241226\pi$
$984$	−1.95122	+	2.40973i	−0.0622026	+	0.0768194i
$985$	16.4203	−	25.5505i	0.523194	−	0.814106i
$986$	−0.0119601	+	0.0138027i	−0.000380888	+	0.000439568i
$987$	47.1462	−	26.6464i	1.50068	−	0.848166i
$988$	−1.64127			−0.0522157
$989$	1.66651	−	5.32973i	0.0529918	−	0.169476i
$990$	22.0515	+	40.8384i	0.700844	+	1.29793i
$991$	−37.0904	−	10.8907i	−1.17822	−	0.345956i	−0.366731	−	0.930327i	$-0.619523\pi$
$991$	−37.0904	−	10.8907i	−1.17822	−	0.345956i	−0.811486	+	0.584371i	$0.801341\pi$
$992$	−4.05128	+	4.67543i	−0.128628	+	0.148445i
$993$	37.2951	−	18.5594i	1.18352	−	0.588964i
$994$	−10.7365	+	27.2179i	−0.340541	+	0.863301i
$995$	−31.6408	−	49.2341i	−1.00308	−	1.56083i
$996$	5.62801	+	0.618423i	0.178330	+	0.0195955i
$997$	−12.0680	+	10.4570i	−0.382197	+	0.331176i	−0.824678	−	0.565602i	$-0.808644\pi$
$997$	−12.0680	+	10.4570i	−0.382197	+	0.331176i	0.442481	+	0.896778i	$0.354098\pi$
$998$	16.4008	−	2.35808i	0.519158	−	0.0746437i
$999$	1.78594	−	3.50603i	0.0565046	−	0.110926i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.t.a.41.20	yes	640
3.2	odd	2	inner	966.2.t.a.41.62	yes	640
7.6	odd	2	inner	966.2.t.a.41.13	✓	640
21.20	even	2	inner	966.2.t.a.41.35	yes	640
23.9	even	11	inner	966.2.t.a.377.35	yes	640
69.32	odd	22	inner	966.2.t.a.377.13	yes	640
161.55	odd	22	inner	966.2.t.a.377.62	yes	640
483.377	even	22	inner	966.2.t.a.377.20	yes	640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.t.a.41.13	✓	640	7.6	odd	2	inner
966.2.t.a.41.20	yes	640	1.1	even	1	trivial
966.2.t.a.41.35	yes	640	21.20	even	2	inner
966.2.t.a.41.62	yes	640	3.2	odd	2	inner
966.2.t.a.377.13	yes	640	69.32	odd	22	inner
966.2.t.a.377.20	yes	640	483.377	even	22	inner
966.2.t.a.377.35	yes	640	23.9	even	11	inner
966.2.t.a.377.62	yes	640	161.55	odd	22	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.t (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.281733 + 0.959493i) q^{2} +(0.543127 + 1.64469i) q^{3} +(-0.841254 - 0.540641i) q^{4} +(-0.342096 + 2.37933i) q^{5} +(-1.73109 + 0.0577632i) q^{6} +(0.513888 + 2.59537i) q^{7} +(0.755750 - 0.654861i) q^{8} +(-2.41003 + 1.78655i) q^{9} +O(q^{10})\)	\(q+(-0.281733 + 0.959493i) q^{2} +(0.543127 + 1.64469i) q^{3} +(-0.841254 - 0.540641i) q^{4} +(-0.342096 + 2.37933i) q^{5} +(-1.73109 + 0.0577632i) q^{6} +(0.513888 + 2.59537i) q^{7} +(0.755750 - 0.654861i) q^{8} +(-2.41003 + 1.78655i) q^{9} +(-2.18657 - 0.998573i) q^{10} +(1.81320 + 6.17519i) q^{11} +(0.432280 - 1.67724i) q^{12} +(0.243328 + 0.111124i) q^{13} +(-2.63501 - 0.238127i) q^{14} +(-4.09906 + 0.729635i) q^{15} +(0.415415 + 0.909632i) q^{16} +(0.0293727 - 0.0188767i) q^{17} +(-1.03520 - 2.81573i) q^{18} +(3.31713 - 5.16155i) q^{19} +(1.57415 - 1.81667i) q^{20} +(-3.98947 + 2.25480i) q^{21} -6.43589 q^{22} +(4.39654 - 1.91583i) q^{23} +(1.48751 + 0.887303i) q^{24} +(-0.746708 - 0.219253i) q^{25} +(-0.175176 + 0.202164i) q^{26} +(-4.24728 - 2.99343i) q^{27} +(0.970851 - 2.46119i) q^{28} +(0.282799 + 0.440045i) q^{29} +(0.454760 - 4.13859i) q^{30} +(4.67543 - 4.05128i) q^{31} +(-0.989821 + 0.142315i) q^{32} +(-9.17149 + 6.33607i) q^{33} +(0.00983680 + 0.0335010i) q^{34} +(-6.35102 + 0.334844i) q^{35} +(2.99333 - 0.199986i) q^{36} +(0.107765 + 0.749525i) q^{37} +(4.01793 + 4.63694i) q^{38} +(-0.0506071 + 0.460554i) q^{39} +(1.29959 + 2.02220i) q^{40} +(-0.254767 + 1.77194i) q^{41} +(-1.03950 - 4.46312i) q^{42} +(0.762510 - 0.879984i) q^{43} +(1.81320 - 6.17519i) q^{44} +(-3.42634 - 6.34542i) q^{45} +(0.599579 + 4.75820i) q^{46} -11.8177 q^{47} +(-1.27044 + 1.17728i) q^{48} +(-6.47184 + 2.66745i) q^{49} +(0.420744 - 0.654690i) q^{50} +(0.0469994 + 0.0380566i) q^{51} +(-0.144622 - 0.225037i) q^{52} +(7.88029 - 3.59881i) q^{53} +(4.06877 - 3.23189i) q^{54} +(-15.3131 + 2.20169i) q^{55} +(2.08797 + 1.62492i) q^{56} +(10.2908 + 2.65228i) q^{57} +(-0.501894 + 0.147369i) q^{58} +(3.27192 - 7.16449i) q^{59} +(3.84282 + 1.60231i) q^{60} +(-5.39038 + 4.67079i) q^{61} +(2.56996 + 5.62742i) q^{62} +(-5.87524 - 5.33681i) q^{63} +(0.142315 - 0.989821i) q^{64} +(-0.347642 + 0.540942i) q^{65} +(-3.49551 - 10.5851i) q^{66} +(-0.154784 - 0.0454486i) q^{67} -0.0349154 q^{68} +(5.53884 + 6.19042i) q^{69} +(1.46801 - 6.18810i) q^{70} +(3.11564 - 10.6109i) q^{71} +(-0.651432 + 2.92842i) q^{72} +(7.50519 - 11.6783i) q^{73} +(-0.749525 - 0.107765i) q^{74} +(-0.0449532 - 1.34719i) q^{75} +(-5.58109 + 2.54880i) q^{76} +(-15.0951 + 7.87927i) q^{77} +(-0.427641 - 0.178310i) q^{78} +(-4.00236 + 8.76394i) q^{79} +(-2.30642 + 0.677227i) q^{80} +(2.61645 - 8.61128i) q^{81} +(-1.62839 - 0.743661i) q^{82} +(0.465212 + 3.23562i) q^{83} +(4.57519 + 0.260012i) q^{84} +(0.0348655 + 0.0763449i) q^{85} +(0.629514 + 0.979544i) q^{86} +(-0.570142 + 0.704118i) q^{87} +(5.41422 + 3.47950i) q^{88} +(3.04562 - 3.51483i) q^{89} +(7.05369 - 1.49984i) q^{90} +(-0.163365 + 0.688631i) q^{91} +(-4.73438 - 0.765249i) q^{92} +(9.20246 + 5.48928i) q^{93} +(3.32942 - 11.3390i) q^{94} +(11.1462 + 9.65828i) q^{95} +(-0.771663 - 1.55066i) q^{96} +(3.78819 + 0.544659i) q^{97} +(-0.736073 - 6.96119i) q^{98} +(-15.4022 - 11.6430i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q + 64 q^{4} + 8 q^{9}+O(q^{10}) \) 640 * q + 64 * q^4 + 8 * q^9	\( 640 q + 64 q^{4} + 8 q^{9} + 8 q^{15} - 64 q^{16} + 20 q^{18} + 54 q^{21} - 8 q^{22} - 56 q^{25} - 44 q^{30} - 8 q^{36} + 20 q^{37} - 16 q^{39} - 4 q^{42} - 28 q^{43} + 24 q^{46} - 68 q^{49} - 40 q^{51} + 32 q^{57} - 80 q^{58} - 8 q^{60} + 86 q^{63} + 64 q^{64} + 24 q^{67} + 72 q^{70} - 64 q^{72} - 8 q^{78} - 144 q^{79} + 20 q^{81} + 34 q^{84} + 32 q^{85} + 8 q^{88} - 40 q^{91} + 16 q^{93} + 68 q^{99}+O(q^{100}) \) 640 * q + 64 * q^4 + 8 * q^9 + 8 * q^15 - 64 * q^16 + 20 * q^18 + 54 * q^21 - 8 * q^22 - 56 * q^25 - 44 * q^30 - 8 * q^36 + 20 * q^37 - 16 * q^39 - 4 * q^42 - 28 * q^43 + 24 * q^46 - 68 * q^49 - 40 * q^51 + 32 * q^57 - 80 * q^58 - 8 * q^60 + 86 * q^63 + 64 * q^64 + 24 * q^67 + 72 * q^70 - 64 * q^72 - 8 * q^78 - 144 * q^79 + 20 * q^81 + 34 * q^84 + 32 * q^85 + 8 * q^88 - 40 * q^91 + 16 * q^93 + 68 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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