LMFDB - Embedded newform 966.2.s.a.475.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(97,966)]

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([0, 11, 1]))

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

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

chi := DirichletCharacter("966.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.s (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:	$160$
Relative dimension:	$16$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			475.3
Character	$\chi$	$=$	966.475
Dual form			966.2.s.a.181.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 + 0.989821i) q^{2} +(-0.909632 + 0.415415i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-1.30557 - 1.50670i) q^{5} +(-0.281733 - 0.959493i) q^{6} +(2.10508 + 1.60270i) q^{7} +(0.415415 - 0.909632i) q^{8} +(0.654861 - 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.142315 + 0.989821i) q^{2} +(-0.909632 + 0.415415i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-1.30557 - 1.50670i) q^{5} +(-0.281733 - 0.959493i) q^{6} +(2.10508 + 1.60270i) q^{7} +(0.415415 - 0.909632i) q^{8} +(0.654861 - 0.755750i) q^{9} +(1.67717 - 1.07785i) q^{10} +(-5.59475 + 0.804403i) q^{11} +(0.989821 - 0.142315i) q^{12} +(2.36808 + 3.68480i) q^{13} +(-1.88597 + 1.85556i) q^{14} +(1.81349 + 0.828195i) q^{15} +(0.841254 + 0.540641i) q^{16} +(6.51798 - 1.91385i) q^{17} +(0.654861 + 0.755750i) q^{18} +(-0.721432 - 0.211831i) q^{19} +(0.828195 + 1.81349i) q^{20} +(-2.58063 - 0.583386i) q^{21} -5.65228i q^{22} +(-4.47709 + 1.71920i) q^{23} +1.00000i q^{24} +(0.145921 - 1.01490i) q^{25} +(-3.98430 + 1.81957i) q^{26} +(-0.281733 + 0.959493i) q^{27} +(-1.56827 - 2.13085i) q^{28} +(-8.03505 + 2.35930i) q^{29} +(-1.07785 + 1.67717i) q^{30} +(-6.73834 - 3.07730i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(4.75500 - 3.05585i) q^{33} +(0.966766 + 6.72401i) q^{34} +(-0.333525 - 5.26416i) q^{35} +(-0.841254 + 0.540641i) q^{36} +(1.80754 + 1.56625i) q^{37} +(0.312346 - 0.683942i) q^{38} +(-3.68480 - 2.36808i) q^{39} +(-1.91290 + 0.561678i) q^{40} +(-8.72376 + 7.55918i) q^{41} +(0.944710 - 2.47134i) q^{42} +(-8.11086 + 3.70410i) q^{43} +(5.59475 + 0.804403i) q^{44} -1.99366 q^{45} +(-1.06454 - 4.67619i) q^{46} -8.92364i q^{47} +(-0.989821 - 0.142315i) q^{48} +(1.86271 + 6.74762i) q^{49} +(0.983803 + 0.288871i) q^{50} +(-5.13392 + 4.44857i) q^{51} +(-1.23402 - 4.20270i) q^{52} +(2.91021 - 4.52838i) q^{53} +(-0.909632 - 0.415415i) q^{54} +(8.51632 + 7.37943i) q^{55} +(2.33235 - 1.24906i) q^{56} +(0.744235 - 0.107005i) q^{57} +(-1.19178 - 8.28903i) q^{58} +(-5.04989 - 7.85779i) q^{59} +(-1.50670 - 1.30557i) q^{60} +(-2.86290 + 6.26888i) q^{61} +(4.00494 - 6.23181i) q^{62} +(2.58977 - 0.541367i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(2.46022 - 8.37874i) q^{65} +(2.34804 + 5.14150i) q^{66} +(-6.35909 - 0.914298i) q^{67} -6.79315 q^{68} +(3.35833 - 3.42369i) q^{69} +(5.25805 + 0.419038i) q^{70} +(-0.385612 + 2.68199i) q^{71} +(-0.415415 - 0.909632i) q^{72} +(-0.959829 + 3.26888i) q^{73} +(-1.80754 + 1.56625i) q^{74} +(0.288871 + 0.983803i) q^{75} +(0.632529 + 0.406502i) q^{76} +(-13.0666 - 7.27337i) q^{77} +(2.86837 - 3.31028i) q^{78} +(-9.34521 - 14.5414i) q^{79} +(-0.283727 - 1.97336i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(-6.24072 - 9.71075i) q^{82} +(2.98441 - 3.44419i) q^{83} +(2.31174 + 1.28680i) q^{84} +(-11.3933 - 7.32201i) q^{85} +(-2.51211 - 8.55545i) q^{86} +(6.32885 - 5.48398i) q^{87} +(-1.59243 + 5.42332i) q^{88} +(2.71978 + 5.95548i) q^{89} +(0.283727 - 1.97336i) q^{90} +(-0.920640 + 11.5521i) q^{91} +(4.78009 - 0.388216i) q^{92} +7.40777 q^{93} +(8.83281 + 1.26997i) q^{94} +(0.622710 + 1.36354i) q^{95} +(0.281733 - 0.959493i) q^{96} +(2.35988 + 2.72345i) q^{97} +(-6.94403 + 0.883461i) q^{98} +(-3.05585 + 4.75500i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 16 q^{2} - 16 q^{4} - 16 q^{8} + 16 q^{9}+O(q^{10}) $ 160 * q - 16 * q^2 - 16 * q^4 - 16 * q^8 + 16 * q^9	$ 160 q - 16 q^{2} - 16 q^{4} - 16 q^{8} + 16 q^{9} - 22 q^{14} - 16 q^{16} + 16 q^{18} - 36 q^{23} + 96 q^{25} + 22 q^{28} - 20 q^{29} - 16 q^{32} - 50 q^{35} + 16 q^{36} + 22 q^{37} + 4 q^{39} - 110 q^{43} + 8 q^{46} - 36 q^{50} + 22 q^{51} - 88 q^{53} + 22 q^{57} + 24 q^{58} - 16 q^{64} - 72 q^{70} + 48 q^{71} + 16 q^{72} - 22 q^{74} + 24 q^{77} + 4 q^{78} + 88 q^{79} - 16 q^{81} + 22 q^{84} + 76 q^{85} + 44 q^{86} - 44 q^{88} + 8 q^{92} - 14 q^{95} + 22 q^{98} - 22 q^{99}+O(q^{100}) $ 160 * q - 16 * q^2 - 16 * q^4 - 16 * q^8 + 16 * q^9 - 22 * q^14 - 16 * q^16 + 16 * q^18 - 36 * q^23 + 96 * q^25 + 22 * q^28 - 20 * q^29 - 16 * q^32 - 50 * q^35 + 16 * q^36 + 22 * q^37 + 4 * q^39 - 110 * q^43 + 8 * q^46 - 36 * q^50 + 22 * q^51 - 88 * q^53 + 22 * q^57 + 24 * q^58 - 16 * q^64 - 72 * q^70 + 48 * q^71 + 16 * q^72 - 22 * q^74 + 24 * q^77 + 4 * q^78 + 88 * q^79 - 16 * q^81 + 22 * q^84 + 76 * q^85 + 44 * q^86 - 44 * q^88 + 8 * q^92 - 14 * q^95 + 22 * q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$-1$	$e\left(\frac{17}{22}\right)$

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 $

$2$	−0.142315	+	0.989821i	−0.100632	+	0.699909i
$2$	−0.142315	+	0.989821i	−0.100632	+	0.699909i
$3$	−0.909632	+	0.415415i	−0.525176	+	0.239840i
$3$	−0.909632	+	0.415415i	−0.525176	+	0.239840i
$4$	−0.959493	−	0.281733i	−0.479746	−	0.140866i
$5$	−1.30557	−	1.50670i	−0.583867	−	0.673819i	0.384564	−	0.923098i	$-0.374352\pi$
$5$	−1.30557	−	1.50670i	−0.583867	−	0.673819i	−0.968432	+	0.249279i	$0.919806\pi$
$6$	−0.281733	−	0.959493i	−0.115017	−	0.391711i
$7$	2.10508	+	1.60270i	0.795645	+	0.605764i
$7$	2.10508	+	1.60270i	0.795645	+	0.605764i
$8$	0.415415	−	0.909632i	0.146871	−	0.321603i
$9$	0.654861	−	0.755750i	0.218287	−	0.251917i
$10$	1.67717	−	1.07785i	0.530368	−	0.340847i
$11$	−5.59475	+	0.804403i	−1.68688	+	0.242537i	−0.917922	−	0.396762i	$-0.870134\pi$
$11$	−5.59475	+	0.804403i	−1.68688	+	0.242537i	−0.768959	+	0.639299i	$0.779225\pi$
$12$	0.989821	−	0.142315i	0.285737	−	0.0410828i
$13$	2.36808	+	3.68480i	0.656786	+	1.02198i	0.996672	+	0.0815125i	$0.0259751\pi$
$13$	2.36808	+	3.68480i	0.656786	+	1.02198i	−0.339886	+	0.940467i	$0.610389\pi$
$14$	−1.88597	+	1.85556i	−0.504047	+	0.495920i
$15$	1.81349	+	0.828195i	0.468242	+	0.213839i
$16$	0.841254	+	0.540641i	0.210313	+	0.135160i
$17$	6.51798	−	1.91385i	1.58084	−	0.464177i	0.630709	−	0.776019i	$-0.282764\pi$
$17$	6.51798	−	1.91385i	1.58084	−	0.464177i	0.950134	+	0.311842i	$0.100946\pi$
$18$	0.654861	+	0.755750i	0.154352	+	0.178132i
$19$	−0.721432	−	0.211831i	−0.165508	−	0.0485975i	0.197929	−	0.980216i	$-0.436579\pi$
$19$	−0.721432	−	0.211831i	−0.165508	−	0.0485975i	−0.363437	+	0.931619i	$0.618397\pi$
$20$	0.828195	+	1.81349i	0.185190	+	0.405509i
$21$	−2.58063	−	0.583386i	−0.563140	−	0.127305i
$22$		−	5.65228i		−	1.20507i
$23$	−4.47709	+	1.71920i	−0.933538	+	0.358478i
$23$	−4.47709	+	1.71920i	−0.933538	+	0.358478i
$24$			1.00000i			0.204124i
$25$	0.145921	−	1.01490i	0.0291841	−	0.202980i
$26$	−3.98430	+	1.81957i	−0.781386	+	0.356847i
$27$	−0.281733	+	0.959493i	−0.0542195	+	0.184655i
$28$	−1.56827	−	2.13085i	−0.296376	−	0.402692i
$29$	−8.03505	+	2.35930i	−1.49207	+	0.438112i	−0.923202	−	0.384316i	$-0.874437\pi$
$29$	−8.03505	+	2.35930i	−1.49207	+	0.438112i	−0.568870	+	0.822428i	$0.692619\pi$
$30$	−1.07785	+	1.67717i	−0.196788	+	0.306208i
$31$	−6.73834	−	3.07730i	−1.21024	−	0.552699i	−0.294959	−	0.955510i	$-0.595306\pi$
$31$	−6.73834	−	3.07730i	−1.21024	−	0.552699i	−0.915283	+	0.402811i	$0.868033\pi$
$32$	−0.654861	+	0.755750i	−0.115764	+	0.133599i
$33$	4.75500	−	3.05585i	0.827739	−	0.531956i
$34$	0.966766	+	6.72401i	0.165799	+	1.15316i
$35$	−0.333525	−	5.26416i	−0.0563760	−	0.889806i
$36$	−0.841254	+	0.540641i	−0.140209	+	0.0901068i
$37$	1.80754	+	1.56625i	0.297158	+	0.257489i	0.790660	−	0.612256i	$-0.209738\pi$
$37$	1.80754	+	1.56625i	0.297158	+	0.257489i	−0.493501	+	0.869745i	$0.664283\pi$
$38$	0.312346	−	0.683942i	0.0506692	−	0.110950i
$39$	−3.68480	−	2.36808i	−0.590040	−	0.379196i
$40$	−1.91290	+	0.561678i	−0.302456	+	0.0888091i
$41$	−8.72376	+	7.55918i	−1.36242	+	1.18055i	−0.397626	+	0.917548i	$0.630166\pi$
$41$	−8.72376	+	7.55918i	−1.36242	+	1.18055i	−0.964796	+	0.262998i	$0.915289\pi$
$42$	0.944710	−	2.47134i	0.145772	−	0.381336i
$43$	−8.11086	+	3.70410i	−1.23689	+	0.564871i	−0.923078	−	0.384613i	$-0.874335\pi$
$43$	−8.11086	+	3.70410i	−1.23689	+	0.564871i	−0.313816	+	0.949484i	$0.601608\pi$
$44$	5.59475	+	0.804403i	0.843440	+	0.121268i
$45$	−1.99366			−0.297197
$46$	−1.06454	−	4.67619i	−0.156958	−	0.689467i
$47$		−	8.92364i		−	1.30165i	−0.759229	−	0.650823i	$-0.774424\pi$
$47$		−	8.92364i		−	1.30165i	0.759229	−	0.650823i	$-0.225576\pi$
$48$	−0.989821	−	0.142315i	−0.142868	−	0.0205414i
$49$	1.86271	+	6.74762i	0.266101	+	0.963945i
$50$	0.983803	+	0.288871i	0.139131	+	0.0408525i
$51$	−5.13392	+	4.44857i	−0.718893	+	0.622924i
$52$	−1.23402	−	4.20270i	−0.171128	−	0.582810i
$53$	2.91021	−	4.52838i	0.399748	−	0.622020i	−0.581778	−	0.813348i	$-0.697643\pi$
$53$	2.91021	−	4.52838i	0.399748	−	0.622020i	0.981526	+	0.191327i	$0.0612791\pi$
$54$	−0.909632	−	0.415415i	−0.123785	−	0.0565308i
$55$	8.51632	+	7.37943i	1.14834	+	0.995042i
$56$	2.33235	−	1.24906i	0.311673	−	0.166913i
$57$	0.744235	−	0.107005i	0.0985764	−	0.0141731i
$58$	−1.19178	−	8.28903i	−0.156489	−	1.08840i
$59$	−5.04989	−	7.85779i	−0.657440	−	1.02300i	−0.996610	−	0.0822715i	$-0.973783\pi$
$59$	−5.04989	−	7.85779i	−0.657440	−	1.02300i	0.339170	−	0.940725i	$-0.389854\pi$
$60$	−1.50670	−	1.30557i	−0.194515	−	0.168548i
$61$	−2.86290	+	6.26888i	−0.366557	+	0.802648i	0.633036	+	0.774122i	$0.281808\pi$
$61$	−2.86290	+	6.26888i	−0.366557	+	0.802648i	−0.999593	+	0.0285256i	$0.990919\pi$
$62$	4.00494	−	6.23181i	0.508628	−	0.791441i
$63$	2.58977	−	0.541367i	0.326281	−	0.0682058i
$64$	−0.654861	−	0.755750i	−0.0818576	−	0.0944687i
$65$	2.46022	−	8.37874i	0.305153	−	1.03925i
$66$	2.34804	+	5.14150i	0.289024	+	0.632874i
$67$	−6.35909	−	0.914298i	−0.776886	−	0.111699i	−0.257545	−	0.966266i	$-0.582913\pi$
$67$	−6.35909	−	0.914298i	−0.776886	−	0.111699i	−0.519341	+	0.854567i	$0.673823\pi$
$68$	−6.79315			−0.823791
$69$	3.35833	−	3.42369i	0.404295	−	0.412164i
$70$	5.25805	+	0.419038i	0.628457	+	0.0500846i
$71$	−0.385612	+	2.68199i	−0.0457638	+	0.318294i	0.954062	+	0.299610i	$0.0968566\pi$
$71$	−0.385612	+	2.68199i	−0.0457638	+	0.318294i	−0.999825	+	0.0186837i	$0.994052\pi$
$72$	−0.415415	−	0.909632i	−0.0489571	−	0.107201i
$73$	−0.959829	+	3.26888i	−0.112339	+	0.382593i	−0.996400	−	0.0847798i	$-0.972981\pi$
$73$	−0.959829	+	3.26888i	−0.112339	+	0.382593i	0.884060	+	0.467373i	$0.154799\pi$
$74$	−1.80754	+	1.56625i	−0.210123	+	0.182072i
$75$	0.288871	+	0.983803i	0.0333559	+	0.113600i
$76$	0.632529	+	0.406502i	0.0725560	+	0.0466289i
$77$	−13.0666	−	7.27337i	−1.48908	−	0.828877i
$78$	2.86837	−	3.31028i	0.324779	−	0.374815i
$79$	−9.34521	−	14.5414i	−1.05142	−	1.63604i	−0.722056	−	0.691835i	$-0.756803\pi$
$79$	−9.34521	−	14.5414i	−1.05142	−	1.63604i	−0.329362	−	0.944204i	$-0.606834\pi$
$80$	−0.283727	−	1.97336i	−0.0317216	−	0.220629i
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$	−6.24072	−	9.71075i	−0.689172	−	1.07237i
$83$	2.98441	−	3.44419i	0.327581	−	0.378049i	−0.567938	−	0.823071i	$-0.692259\pi$
$83$	2.98441	−	3.44419i	0.327581	−	0.378049i	0.895520	+	0.445022i	$0.146804\pi$
$84$	2.31174	+	1.28680i	0.252231	+	0.140402i
$85$	−11.3933	−	7.32201i	−1.23577	−	0.794184i
$86$	−2.51211	−	8.55545i	−0.270887	−	0.922558i
$87$	6.32885	−	5.48398i	0.678524	−	0.587944i
$88$	−1.59243	+	5.42332i	−0.169754	+	0.578128i
$89$	2.71978	+	5.95548i	0.288296	+	0.631279i	0.997261	−	0.0739639i	$-0.0235650\pi$
$89$	2.71978	+	5.95548i	0.288296	+	0.631279i	−0.708965	+	0.705243i	$0.750838\pi$
$90$	0.283727	−	1.97336i	0.0299074	−	0.208011i
$91$	−0.920640	+	11.5521i	−0.0965093	+	1.21099i
$92$	4.78009	−	0.388216i	0.498359	−	0.0404743i
$93$	7.40777			0.768150
$94$	8.83281	+	1.26997i	0.911035	+	0.130987i
$95$	0.622710	+	1.36354i	0.0638887	+	0.139897i
$96$	0.281733	−	0.959493i	0.0287542	−	0.0979278i
$97$	2.35988	+	2.72345i	0.239610	+	0.276524i	0.862799	−	0.505546i	$-0.168709\pi$
$97$	2.35988	+	2.72345i	0.239610	+	0.276524i	−0.623190	+	0.782071i	$0.714164\pi$
$98$	−6.94403	+	0.883461i	−0.701453	+	0.0892431i
$99$	−3.05585	+	4.75500i	−0.307125	+	0.477896i
$100$	−0.425940	+	0.932679i	−0.0425940	+	0.0932679i
$101$	2.44827	+	2.12144i	0.243612	+	0.211091i	0.768105	−	0.640323i	$-0.221200\pi$
$101$	2.44827	+	2.12144i	0.243612	+	0.211091i	−0.524493	+	0.851415i	$0.675745\pi$
$102$	−3.67266	−	5.71476i	−0.363647	−	0.565846i
$103$	0.524155	+	3.64558i	0.0516465	+	0.359210i	0.999214	+	0.0396524i	$0.0126251\pi$
$103$	0.524155	+	3.64558i	0.0516465	+	0.359210i	−0.947567	+	0.319557i	$0.896466\pi$
$104$	4.33554	−	0.623357i	0.425135	−	0.0611252i
$105$	2.49020	+	4.64990i	0.243018	+	0.453784i
$106$	4.06812	+	3.52504i	0.395131	+	0.342383i
$107$	2.72713	+	1.24544i	0.263642	+	0.120401i	0.542851	−	0.839829i	$-0.317345\pi$
$107$	2.72713	+	1.24544i	0.263642	+	0.120401i	−0.279209	+	0.960230i	$0.590072\pi$
$108$	0.540641	−	0.841254i	0.0520232	−	0.0809497i
$109$	0.481994	+	1.64152i	0.0461667	+	0.157229i	0.979350	−	0.202171i	$-0.0647996\pi$
$109$	0.481994	+	1.64152i	0.0461667	+	0.157229i	−0.933184	+	0.359400i	$0.882981\pi$
$110$	−8.51632	+	7.37943i	−0.811999	+	0.703601i
$111$	−2.29484	−	0.673826i	−0.217817	−	0.0639567i
$112$	0.904419	+	2.48637i	0.0854596	+	0.234940i
$113$	−1.53569	−	0.220799i	−0.144466	−	0.0207711i	0.0697025	−	0.997568i	$-0.477795\pi$
$113$	−1.53569	−	0.220799i	−0.144466	−	0.0207711i	−0.214168	+	0.976797i	$0.568704\pi$
$114$			0.751889i			0.0704208i
$115$	8.43547	+	4.50113i	0.786611	+	0.419732i
$116$	8.37427			0.777531
$117$	4.33554	+	0.623357i	0.400821	+	0.0576294i
$118$	8.49648	−	3.88021i	0.782164	−	0.357202i
$119$	16.7882	+	6.41756i	1.53897	+	0.588297i
$120$	1.50670	−	1.30557i	0.137543	−	0.119181i
$121$	20.0997	−	5.90181i	1.82725	−	0.536528i
$122$	−5.79764	−	3.72592i	−0.524894	−	0.337329i
$123$	4.79521	−	10.5001i	0.432370	−	0.946758i
$124$	5.59842	+	4.85106i	0.502753	+	0.435638i
$125$	−10.1055	+	6.49442i	−0.903865	+	0.580879i
$126$	0.167293	+	2.64046i	0.0149037	+	0.235231i
$127$	1.51306	+	10.5236i	0.134262	+	0.933816i	0.939910	+	0.341421i	$0.110908\pi$
$127$	1.51306	+	10.5236i	0.134262	+	0.933816i	−0.805648	+	0.592395i	$0.798183\pi$
$128$	0.841254	−	0.540641i	0.0743570	−	0.0477863i
$129$	5.83916	−	6.73874i	0.514109	−	0.593313i
$130$	7.94333	+	3.62760i	0.696676	+	0.318161i
$131$	−2.43810	+	3.79376i	−0.213018	+	0.331463i	−0.931276	−	0.364314i	$-0.881303\pi$
$131$	−2.43810	+	3.79376i	−0.213018	+	0.331463i	0.718258	+	0.695777i	$0.244940\pi$
$132$	−5.42332	+	1.59243i	−0.472040	+	0.138603i
$133$	−1.17917	−	1.60216i	−0.102247	−	0.138925i
$134$	1.80998	−	6.16424i	0.156359	−	0.532509i
$135$	1.81349	−	0.828195i	0.156081	−	0.0712796i
$136$	0.966766	−	6.72401i	0.0828995	−	0.576579i
$137$			6.63603i			0.566954i	0.958979	+	0.283477i	$0.0914880\pi$
$137$			6.63603i			0.566954i	−0.958979	+	0.283477i	$0.908512\pi$
$138$	2.91090	+	3.81138i	0.247792	+	0.324447i
$139$		−	0.321449i		−	0.0272649i	−0.999907	−	0.0136325i	$-0.995661\pi$
$139$		−	0.321449i		−	0.0272649i	0.999907	−	0.0136325i	$-0.00433948\pi$
$140$	−1.16307	+	5.14489i	−0.0982974	+	0.434823i
$141$	3.70701	+	8.11723i	0.312187	+	0.683594i
$142$	−2.59982	−	0.763375i	−0.218172	−	0.0640610i
$143$	−16.2129	−	18.7106i	−1.35579	−	1.56466i
$144$	0.959493	−	0.281733i	0.0799577	−	0.0234777i
$145$	14.0451	+	9.02622i	1.16638	+	0.749587i
$146$	−3.09901	−	1.41527i	−0.256476	−	0.117129i
$147$	−4.49744	−	5.36405i	−0.370942	−	0.442419i
$148$	−1.29306	−	2.01205i	−0.106289	−	0.165389i
$149$	−17.3867	+	2.49983i	−1.42437	+	0.204794i	−0.811022	−	0.585015i	$-0.801089\pi$
$149$	−17.3867	+	2.49983i	−1.42437	+	0.204794i	−0.613353	+	0.789809i	$0.710179\pi$
$150$	−1.01490	+	0.145921i	−0.0828662	+	0.0119144i
$151$	8.49205	−	5.45751i	0.691073	−	0.444126i	−0.147394	−	0.989078i	$-0.547089\pi$
$151$	8.49205	−	5.45751i	0.691073	−	0.444126i	0.838467	+	0.544952i	$0.183452\pi$
$152$	−0.492382	+	0.568239i	−0.0399375	+	0.0460903i
$153$	2.82198	−	6.17927i	0.228143	−	0.499564i
$154$	9.05891	−	11.8985i	0.729988	−	0.958808i
$155$	4.16078	+	14.1703i	0.334202	+	1.13819i
$156$	2.86837	+	3.31028i	0.229654	+	0.265034i
$157$	9.19179	+	2.69895i	0.733585	+	0.215400i	0.627127	−	0.778917i	$-0.284231\pi$
$157$	9.19179	+	2.69895i	0.733585	+	0.215400i	0.106458	+	0.994317i	$0.466049\pi$
$158$	15.7234	−	7.18063i	1.25088	−	0.571260i
$159$	−0.766065	+	5.32810i	−0.0607529	+	0.422546i
$160$	1.99366			0.157612
$161$	−12.1800	−	3.55639i	−0.959917	−	0.280283i
$162$	1.00000			0.0785674
$163$	−1.52676	+	10.6188i	−0.119585	+	0.831732i	0.838429	+	0.545011i	$0.183474\pi$
$163$	−1.52676	+	10.6188i	−0.119585	+	0.831732i	−0.958014	+	0.286721i	$0.907435\pi$
$164$	10.5001	−	4.79521i	0.819916	−	0.374443i
$165$	−10.8122	−	3.17476i	−0.841732	−	0.247155i
$166$	2.98441	+	3.44419i	0.231635	+	0.267321i
$167$	3.30370	+	11.2514i	0.255648	+	0.870658i	0.982877	+	0.184263i	$0.0589897\pi$
$167$	3.30370	+	11.2514i	0.255648	+	0.870658i	−0.727229	+	0.686395i	$0.759192\pi$
$168$	−1.60270	+	2.10508i	−0.123651	+	0.162410i
$169$	−2.56956	+	5.62655i	−0.197658	+	0.432811i
$170$	8.86892	−	10.2353i	0.680215	−	0.785010i
$171$	−0.632529	+	0.406502i	−0.0483707	+	0.0310860i
$172$	8.82588	−	1.26897i	0.672967	−	0.0967580i
$173$	−7.56161	+	1.08719i	−0.574898	+	0.0826579i	−0.423631	−	0.905835i	$-0.639245\pi$
$173$	−7.56161	+	1.08719i	−0.574898	+	0.0826579i	−0.151268	+	0.988493i	$0.548336\pi$
$174$	4.52747	+	7.04488i	0.343227	+	0.534071i
$175$	1.93375	−	1.90258i	0.146178	−	0.143821i
$176$	−5.14150	−	2.34804i	−0.387555	−	0.176990i
$177$	7.85779	+	5.04989i	0.590627	+	0.379573i
$178$	−6.28193	+	1.84454i	−0.470850	+	0.138254i
$179$	−12.6908	−	14.6459i	−0.948553	−	1.09469i	−0.995402	−	0.0957866i	$-0.969463\pi$
$179$	−12.6908	−	14.6459i	−0.948553	−	1.09469i	0.0468488	−	0.998902i	$-0.485082\pi$
$180$	1.91290	+	0.561678i	0.142579	+	0.0418650i
$181$	1.79138	+	3.92257i	0.133152	+	0.291562i	0.964450	−	0.264264i	$-0.0851292\pi$
$181$	1.79138	+	3.92257i	0.133152	+	0.291562i	−0.831298	+	0.555826i	$0.812402\pi$
$182$	−11.3035	−	2.55531i	−0.837871	−	0.189412i
$183$		−	6.89167i		−	0.509447i
$184$	−0.296014	+	4.78669i	−0.0218224	+	0.352879i
$185$		−	4.76827i		−	0.350570i
$186$	−1.05424	+	7.33237i	−0.0773003	+	0.537635i
$187$	−34.9270	+	15.9506i	−2.55411	+	1.16642i
$188$	−2.51408	+	8.56217i	−0.183358	+	0.624460i
$189$	−2.13085	+	1.56827i	−0.154996	+	0.114075i
$190$	−1.43829	+	0.422319i	−0.104344	+	0.0306382i
$191$	−11.8527	+	18.4432i	−0.857635	+	1.33451i	0.0835119	+	0.996507i	$0.473386\pi$
$191$	−11.8527	+	18.4432i	−0.857635	+	1.33451i	−0.941147	+	0.337999i	$0.890250\pi$
$192$	0.909632	+	0.415415i	0.0656470	+	0.0299800i
$193$	−7.87126	+	9.08392i	−0.566586	+	0.653875i	−0.964666	−	0.263476i	$-0.915131\pi$
$193$	−7.87126	+	9.08392i	−0.566586	+	0.653875i	0.398080	+	0.917351i	$0.369677\pi$
$194$	−3.03158	+	1.94828i	−0.217654	+	0.139878i
$195$	1.24276	+	8.64358i	0.0889959	+	0.618980i
$196$	0.113769	−	6.99908i	0.00812636	−	0.499934i
$197$	11.3599	−	7.30059i	0.809363	−	0.520146i	−0.0692962	−	0.997596i	$-0.522075\pi$
$197$	11.3599	−	7.30059i	0.809363	−	0.520146i	0.878659	+	0.477450i	$0.158439\pi$
$198$	−4.27171	−	3.70146i	−0.303577	−	0.263051i
$199$	3.32999	−	7.29166i	0.236057	−	0.516892i	−0.754116	−	0.656741i	$-0.771934\pi$
$199$	3.32999	−	7.29166i	0.236057	−	0.516892i	0.990173	+	0.139849i	$0.0446617\pi$
$200$	−0.862568	−	0.554339i	−0.0609928	−	0.0391977i
$201$	6.16424	−	1.80998i	0.434792	−	0.127666i
$202$	−2.44827	+	2.12144i	−0.172260	+	0.149264i
$203$	−20.6957	−	7.91126i	−1.45255	−	0.555261i
$204$	6.17927	−	2.82198i	0.432635	−	0.197578i
$205$	22.7789	+	3.27511i	1.59095	+	0.228744i
$206$	−3.68307			−0.256611
$207$	−1.63259	+	4.50940i	−0.113473	+	0.313425i
$208$			4.38013i			0.303707i
$209$	4.20663	+	0.604822i	0.290978	+	0.0418364i
$210$	−4.95696	+	1.80310i	−0.342063	+	0.124426i
$211$	6.99203	+	2.05305i	0.481351	+	0.141337i	0.513401	−	0.858149i	$-0.328385\pi$
$211$	6.99203	+	2.05305i	0.481351	+	0.141337i	−0.0320498	+	0.999486i	$0.510204\pi$
$212$	−4.06812	+	3.52504i	−0.279400	+	0.242101i
$213$	−0.763375	−	2.59982i	−0.0523056	−	0.178136i
$214$	−1.62087	+	2.52213i	−0.110801	+	0.172409i
$215$	16.1703	+	7.38471i	1.10280	+	0.503633i
$216$	0.755750	+	0.654861i	0.0514222	+	0.0445576i
$217$	−9.25275	−	17.2775i	−0.628118	−	1.17287i
$218$	−1.69341	+	0.243475i	−0.114692	+	0.0164902i
$219$	−0.484850	−	3.37220i	−0.0327631	−	0.227872i
$220$	−6.09232	−	9.47984i	−0.410744	−	0.639130i
$221$	22.4872	+	19.4853i	1.51266	+	1.31072i
$222$	0.993557	−	2.17559i	0.0666832	−	0.146016i
$223$	7.29450	−	11.3505i	0.488476	−	0.760083i	−0.506279	−	0.862370i	$-0.668979\pi$
$223$	7.29450	−	11.3505i	0.488476	−	0.760083i	0.994755	+	0.102286i	$0.0326158\pi$
$224$	−2.58977	+	0.541367i	−0.173036	+	0.0361716i
$225$	−0.671453	−	0.774898i	−0.0447635	−	0.0516598i
$226$	0.437104	−	1.48864i	0.0290757	−	0.0990228i
$227$	4.39638	+	9.62674i	0.291798	+	0.638949i	0.997584	−	0.0694766i	$-0.0221329\pi$
$227$	4.39638	+	9.62674i	0.291798	+	0.638949i	−0.705785	+	0.708426i	$0.749406\pi$
$228$	−0.744235	−	0.107005i	−0.0492882	−	0.00708657i
$229$	−11.3543			−0.750312			−0.375156	−	0.926962i	$-0.622411\pi$
$229$	−11.3543			−0.750312			−0.375156	+	0.926962i	$0.622411\pi$
$230$	−5.65580	+	7.70903i	−0.372933	+	0.508318i
$231$	14.9073	+	1.18803i	0.980826	+	0.0781666i
$232$	−1.19178	+	8.28903i	−0.0782444	+	0.544201i
$233$	5.70870	+	12.5003i	0.373989	+	0.818922i	0.999258	+	0.0385128i	$0.0122620\pi$
$233$	5.70870	+	12.5003i	0.373989	+	0.818922i	−0.625269	+	0.780409i	$0.715011\pi$
$234$	−1.23402	+	4.20270i	−0.0806707	+	0.274739i
$235$	−13.4453	+	11.6504i	−0.877074	+	0.759989i
$236$	2.63154	+	8.96221i	0.171299	+	0.583390i
$237$	14.5414	+	9.34521i	0.944567	+	0.607036i
$238$	−8.74145	+	15.7040i	−0.566624	+	1.01794i
$239$	−0.227837	+	0.262937i	−0.0147375	+	0.0170080i	−0.763070	−	0.646315i	$-0.776309\pi$
$239$	−0.227837	+	0.262937i	−0.0147375	+	0.0170080i	0.748333	+	0.663323i	$0.230855\pi$
$240$	1.07785	+	1.67717i	0.0695750	+	0.108261i
$241$	−2.14494	−	14.9184i	−0.138168	−	0.960978i	−0.934461	−	0.356067i	$-0.884118\pi$
$241$	−2.14494	−	14.9184i	−0.138168	−	0.960978i	0.796293	−	0.604912i	$-0.206792\pi$
$242$	2.98125	+	20.7351i	0.191642	+	1.33290i
$243$	0.540641	+	0.841254i	0.0346821	+	0.0539664i
$244$	4.51308	−	5.20837i	0.288920	−	0.333432i
$245$	7.73478	−	11.6160i	0.494157	−	0.742120i
$246$	9.71075	+	6.24072i	0.619135	+	0.397894i
$247$	−0.927849	−	3.15996i	−0.0590376	−	0.201064i
$248$	−5.59842	+	4.85106i	−0.355500	+	0.308042i
$249$	−1.28394	+	4.37271i	−0.0813667	+	0.277110i
$250$	−4.99015	−	10.9269i	−0.315605	−	0.691078i
$251$	−3.24222	+	22.5501i	−0.204647	+	1.42335i	0.585619	+	0.810587i	$0.300852\pi$
$251$	−3.24222	+	22.5501i	−0.204647	+	1.42335i	−0.790266	+	0.612764i	$0.790057\pi$
$252$	−2.63739	−	0.210186i	−0.166140	−	0.0132405i
$253$	23.6653	−	13.2199i	1.48782	−	0.831126i
$254$	−10.6318			−0.667098
$255$	13.4054	+	1.92740i	0.839476	+	0.120698i
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	8.21357	−	27.9728i	0.512348	−	1.74490i	−0.143149	−	0.989701i	$-0.545723\pi$
$257$	8.21357	−	27.9728i	0.512348	−	1.74490i	0.655498	−	0.755197i	$-0.272459\pi$
$258$	5.83916	+	6.73874i	0.363530	+	0.419536i
$259$	1.29480	+	6.19402i	0.0804549	+	0.384878i
$260$	−4.72113	+	7.34622i	−0.292792	+	0.455593i
$261$	−3.47880	+	7.61750i	−0.215332	+	0.471512i
$262$	−3.40817	−	2.95320i	−0.210558	−	0.182449i
$263$	13.6196	+	21.1926i	0.839823	+	1.30679i	0.949800	+	0.312856i	$0.101286\pi$
$263$	13.6196	+	21.1926i	0.839823	+	1.30679i	−0.109977	+	0.993934i	$0.535078\pi$
$264$	−0.804403	−	5.59475i	−0.0495076	−	0.344333i
$265$	−10.6224	+	1.52727i	−0.652529	+	0.0938195i
$266$	1.75367	−	0.939154i	0.107524	−	0.0575833i
$267$	−4.94799	−	4.28746i	−0.302812	−	0.262388i
$268$	5.84391	+	2.66882i	0.356974	+	0.163024i
$269$	14.7559	−	22.9606i	0.899681	−	1.39993i	−0.0168023	−	0.999859i	$-0.505349\pi$
$269$	14.7559	−	22.9606i	0.899681	−	1.39993i	0.916483	−	0.400072i	$-0.131015\pi$
$270$	0.561678	+	1.91290i	0.0341826	+	0.116415i
$271$	22.1386	−	19.1832i	1.34482	−	1.16529i	0.373471	−	0.927642i	$-0.378167\pi$
$271$	22.1386	−	19.1832i	1.34482	−	1.16529i	0.971350	−	0.237653i	$-0.0763780\pi$
$272$	6.51798	+	1.91385i	0.395211	+	0.116044i
$273$	−3.96147	−	10.8906i	−0.239759	−	0.659130i
$274$	−6.56848	−	0.944405i	−0.396816	−	0.0570536i
$275$			5.79549i			0.349481i
$276$	−4.18685	+	2.33886i	−0.252019	+	0.140783i
$277$	−26.5187			−1.59336			−0.796678	−	0.604404i	$-0.793411\pi$
$277$	−26.5187			−1.59336			−0.796678	+	0.604404i	$0.793411\pi$
$278$	0.318177	+	0.0457469i	0.0190830	+	0.00274372i
$279$	−6.73834	+	3.07730i	−0.403414	+	0.184233i
$280$	−4.92700	−	1.88343i	−0.294445	−	0.112556i
$281$	16.4393	−	14.2447i	0.980686	−	0.849770i	−0.00796935	−	0.999968i	$-0.502537\pi$
$281$	16.4393	−	14.2447i	0.980686	−	0.849770i	0.988656	+	0.150199i	$0.0479913\pi$
$282$	−8.56217	+	2.51408i	−0.509870	+	0.149711i
$283$	−1.68007	−	1.07972i	−0.0998698	−	0.0641824i	0.489753	−	0.871861i	$-0.337087\pi$
$283$	−1.68007	−	1.07972i	−0.0998698	−	0.0641824i	−0.589622	+	0.807679i	$0.700723\pi$
$284$	1.12560	−	2.46471i	0.0667919	−	0.146254i
$285$	−1.13287	−	0.981641i	−0.0671057	−	0.0581474i
$286$	20.8275	−	13.3850i	1.23156	−	0.791473i
$287$	−30.4793	+	1.93110i	−1.79914	+	0.113989i
$288$	0.142315	+	0.989821i	0.00838598	+	0.0583258i
$289$	24.5200	−	15.7580i	1.44235	−	0.926942i
$290$	−10.9332	+	12.6175i	−0.642018	+	0.740928i
$291$	−3.27799	−	1.49701i	−0.192159	−	0.0877561i
$292$	1.84190	−	2.86605i	0.107789	−	0.167723i
$293$	18.7140	−	5.49492i	1.09328	−	0.321017i	0.315102	−	0.949058i	$-0.397961\pi$
$293$	18.7140	−	5.49492i	1.09328	−	0.321017i	0.778180	+	0.628041i	$0.216143\pi$
$294$	5.94951	−	3.68828i	0.346982	−	0.215105i
$295$	−5.24639	+	17.8676i	−0.305457	+	1.04029i
$296$	2.17559	−	0.993557i	0.126453	−	0.0577494i
$297$	0.804403	−	5.59475i	0.0466762	−	0.324640i
$298$		−	17.5655i		−	1.01754i
$299$	−16.9370	−	12.4260i	−0.979492	−	0.718614i
$300$		−	1.02534i		−	0.0591978i
$301$	−23.0106	−	5.20184i	−1.32631	−	0.299829i
$302$	4.19341	+	9.18230i	0.241304	+	0.528382i
$303$	−3.10831	−	0.912682i	−0.178568	−	0.0524322i
$304$	−0.492382	−	0.568239i	−0.0282401	−	0.0325908i
$305$	13.1831	−	3.87090i	0.754860	−	0.221647i
$306$	5.71476	+	3.67266i	0.326691	+	0.209952i
$307$	13.5705	+	6.19744i	0.774510	+	0.353707i	0.763144	−	0.646229i	$-0.223655\pi$
$307$	13.5705	+	6.19744i	0.774510	+	0.353707i	0.0113660	+	0.999935i	$0.496382\pi$
$308$	10.4882	+	10.6600i	0.597619	+	0.607412i
$309$	−1.99122	−	3.09839i	−0.113276	−	0.176261i
$310$	−14.6182	+	2.10178i	−0.830259	+	0.119373i
$311$	−2.61272	+	0.375653i	−0.148154	+	0.0213013i	−0.215993	−	0.976395i	$-0.569299\pi$
$311$	−2.61272	+	0.375653i	−0.148154	+	0.0213013i	0.0678388	+	0.997696i	$0.478390\pi$
$312$	−3.68480	+	2.36808i	−0.208611	+	0.134066i
$313$	3.10213	−	3.58005i	0.175343	−	0.202356i	−0.661275	−	0.750144i	$-0.729984\pi$
$313$	3.10213	−	3.58005i	0.175343	−	0.202356i	0.836618	+	0.547787i	$0.184530\pi$
$314$	−3.97961	+	8.71413i	−0.224582	+	0.491767i
$315$	−4.19680	−	3.19523i	−0.236463	−	0.180031i
$316$	4.86987	+	16.5852i	0.273951	+	0.932993i
$317$	−12.4747	−	14.3966i	−0.700648	−	0.808591i	0.288192	−	0.957573i	$-0.406946\pi$
$317$	−12.4747	−	14.3966i	−0.700648	−	0.808591i	−0.988840	+	0.148982i	$0.952400\pi$
$318$	−5.16485	−	1.51654i	−0.289630	−	0.0850431i
$319$	43.0563	−	19.6631i	2.41069	−	1.10092i
$320$	−0.283727	+	1.97336i	−0.0158608	+	0.110314i
$321$	−2.99806			−0.167335
$322$	5.25358	−	11.5499i	0.292771	−	0.643650i
$323$	−5.10769			−0.284200
$324$	−0.142315	+	0.989821i	−0.00790638	+	0.0549901i
$325$	4.08525	−	1.86567i	0.226609	−	0.103489i
$326$	−10.2935	−	3.02244i	−0.570103	−	0.167397i
$327$	−1.12035	−	1.29295i	−0.0619555	−	0.0715005i
$328$	3.25209	+	11.0756i	0.179567	+	0.611548i
$329$	14.3019	−	18.7850i	0.788490	−	1.03565i
$330$	4.68119	−	10.2504i	0.257691	−	0.564264i
$331$	−10.9301	+	12.6140i	−0.600774	+	0.693330i	−0.971938	−	0.235237i	$-0.924413\pi$
$331$	−10.9301	+	12.6140i	−0.600774	+	0.693330i	0.371164	+	0.928567i	$0.378959\pi$
$332$	−3.83386	+	2.46387i	−0.210410	+	0.135223i
$333$	2.36738	−	0.340378i	0.129732	−	0.0186526i
$334$	−11.6070	+	1.66884i	−0.635108	+	0.0913147i
$335$	6.92463	+	10.7749i	0.378333	+	0.588698i
$336$	−1.85556	−	1.88597i	−0.101229	−	0.102888i
$337$	12.3146	+	5.62390i	0.670820	+	0.306353i	0.721553	−	0.692359i	$-0.243428\pi$
$337$	12.3146	+	5.62390i	0.670820	+	0.306353i	−0.0507331	+	0.998712i	$0.516156\pi$
$338$	−5.20359	−	3.34414i	−0.283038	−	0.181897i
$339$	1.48864	−	0.437104i	0.0808518	−	0.0237402i
$340$	8.86892	+	10.2353i	0.480984	+	0.555086i
$341$	40.1747	+	11.7964i	2.17558	+	0.638809i
$342$	−0.312346	−	0.683942i	−0.0168897	−	0.0369833i
$343$	−6.89326	+	17.1896i	−0.372201	+	0.928152i
$344$			8.91664i			0.480753i
$345$	−9.54301	−	0.590150i	−0.513778	−	0.0317726i
$346$		−	7.63936i		−	0.410695i
$347$	−1.82270	+	12.6771i	−0.0978475	+	0.680544i	0.880571	+	0.473913i	$0.157159\pi$
$347$	−1.82270	+	12.6771i	−0.0978475	+	0.680544i	−0.978419	+	0.206631i	$0.933750\pi$
$348$	−7.61750	+	3.47880i	−0.408341	+	0.186483i
$349$	−6.32581	+	21.5437i	−0.338613	+	1.15321i	0.597605	+	0.801791i	$0.296119\pi$
$349$	−6.32581	+	21.5437i	−0.338613	+	1.15321i	−0.936218	+	0.351420i	$0.885699\pi$
$350$	1.60801	+	2.18484i	0.0859517	+	0.116784i
$351$	−4.20270	+	1.23402i	−0.224324	+	0.0658674i
$352$	3.05585	−	4.75500i	0.162878	−	0.253442i
$353$	1.98431	+	0.906206i	0.105614	+	0.0482325i	0.467522	−	0.883982i	$-0.345147\pi$
$353$	1.98431	+	0.906206i	0.105614	+	0.0482325i	−0.361907	+	0.932214i	$0.617874\pi$
$354$	−6.11677	+	7.05913i	−0.325103	+	0.375189i
$355$	4.54441	−	2.92052i	0.241192	−	0.155005i
$356$	−0.931754	−	6.48049i	−0.0493828	−	0.343465i
$357$	−17.9370	+	1.13645i	−0.949328	+	0.0601472i
$358$	16.3029	−	10.4773i	0.861637	−	0.553741i
$359$	−23.7178	−	20.5516i	−1.25178	−	1.08467i	−0.992923	−	0.118757i	$-0.962109\pi$
$359$	−23.7178	−	20.5516i	−1.25178	−	1.08467i	−0.258856	−	0.965916i	$-0.583345\pi$
$360$	−0.828195	+	1.81349i	−0.0436497	+	0.0955795i
$361$	−15.5082	−	9.96653i	−0.816222	−	0.524554i
$362$	−4.13758	+	1.21490i	−0.217466	+	0.0638539i
$363$	−15.8317	+	13.7182i	−0.830946	+	0.720019i
$364$	4.13795	−	10.8248i	0.216888	−	0.567373i
$365$	6.17835	−	2.82156i	0.323390	−	0.147687i
$366$	6.82152	+	0.980786i	0.356567	+	0.0512665i
$367$	−0.544838			−0.0284403			−0.0142201	−	0.999899i	$-0.504527\pi$
$367$	−0.544838			−0.0284403			−0.0142201	+	0.999899i	$0.504527\pi$
$368$	−4.69584	−	0.974218i	−0.244788	−	0.0507846i
$369$			11.5432i			0.600914i
$370$	4.71974	+	0.678596i	0.245367	+	0.0352785i
$371$	13.3839	−	4.86839i	0.694855	−	0.252754i
$372$	−7.10770	−	2.08701i	−0.368517	−	0.108206i
$373$	3.78615	−	3.28072i	0.196039	−	0.169869i	−0.551310	−	0.834301i	$-0.685872\pi$
$373$	3.78615	−	3.28072i	0.196039	−	0.169869i	0.747349	+	0.664432i	$0.231326\pi$
$374$	−10.8176	−	36.8415i	−0.559366	−	1.90503i
$375$	6.49442	−	10.1055i	0.335370	−	0.521846i
$376$	−8.11723	−	3.70701i	−0.418614	−	0.191175i
$377$	−27.7212	−	24.0205i	−1.42771	−	1.23712i
$378$	−1.24906	−	2.33235i	−0.0642448	−	0.119963i
$379$	7.31040	−	1.05108i	0.375510	−	0.0539902i	0.0480238	−	0.998846i	$-0.484708\pi$
$379$	7.31040	−	1.05108i	0.375510	−	0.0539902i	0.327486	+	0.944856i	$0.393799\pi$
$380$	−0.213331	−	1.48375i	−0.0109436	−	0.0761147i
$381$	−5.74798	−	8.94403i	−0.294478	−	0.458217i
$382$	−16.5687	−	14.3568i	−0.847728	−	0.734560i
$383$	−12.7245	+	27.8628i	−0.650193	+	1.42372i	0.241192	+	0.970477i	$0.422462\pi$
$383$	−12.7245	+	27.8628i	−0.650193	+	1.42372i	−0.891385	+	0.453247i	$0.850266\pi$
$384$	−0.540641	+	0.841254i	−0.0275895	+	0.0429300i
$385$	6.10050	+	29.1834i	0.310910	+	1.48732i
$386$	−7.87126	−	9.08392i	−0.400637	−	0.462360i
$387$	−2.51211	+	8.55545i	−0.127698	+	0.434898i
$388$	−1.49701	−	3.27799i	−0.0759990	−	0.166415i
$389$	15.7904	+	2.27032i	0.800606	+	0.115110i	0.530461	−	0.847710i	$-0.322019\pi$
$389$	15.7904	+	2.27032i	0.800606	+	0.115110i	0.270146	+	0.962819i	$0.412928\pi$
$390$	−8.73247			−0.442186
$391$	−25.8913	+	19.7742i	−1.30938	+	1.00002i
$392$	6.91164	+	1.10868i	0.349091	+	0.0559970i
$393$	0.641791	−	4.46375i	0.0323741	−	0.225167i
$394$	5.60959	+	12.2833i	0.282607	+	0.618824i
$395$	−9.70884	+	33.0653i	−0.488505	+	1.66369i
$396$	4.27171	−	3.70146i	0.214661	−	0.186005i
$397$	−0.569560	−	1.93974i	−0.0285854	−	0.0973529i	0.943965	−	0.330046i	$-0.107064\pi$
$397$	−0.569560	−	1.93974i	−0.0285854	−	0.0973529i	−0.972550	+	0.232693i	$0.925246\pi$
$398$	6.74353	+	4.33381i	0.338023	+	0.217234i
$399$	1.73817	+	0.967532i	0.0870174	+	0.0484372i
$400$	0.671453	−	0.774898i	0.0335726	−	0.0387449i
$401$	−7.74744	−	12.0553i	−0.386889	−	0.602011i	0.592115	−	0.805854i	$-0.298293\pi$
$401$	−7.74744	−	12.0553i	−0.386889	−	0.602011i	−0.979004	+	0.203843i	$0.934657\pi$
$402$	0.914298	+	6.35909i	0.0456011	+	0.317162i
$403$	−4.61768	−	32.1167i	−0.230023	−	1.59985i
$404$	−1.75142	−	2.72527i	−0.0871366	−	0.135587i
$405$	−1.30557	+	1.50670i	−0.0648741	+	0.0748688i
$406$	10.7760	−	19.3591i	0.534805	−	0.960777i
$407$	−11.3726	−	7.30875i	−0.563721	−	0.362281i
$408$	1.91385	+	6.51798i	0.0947498	+	0.322688i
$409$	−5.02564	+	4.35474i	−0.248502	+	0.215328i	−0.770201	−	0.637802i	$-0.779844\pi$
$409$	−5.02564	+	4.35474i	−0.248502	+	0.215328i	0.521699	+	0.853130i	$0.325299\pi$
$410$	−6.48355	+	22.0809i	−0.320200	+	1.09050i
$411$	−2.75670	−	6.03634i	−0.135978	−	0.297751i
$412$	0.524155	−	3.64558i	0.0258233	−	0.179605i
$413$	1.96325	−	24.6347i	0.0966054	−	1.21220i
$414$	−4.23116	−	2.25773i	−0.207950	−	0.110961i
$415$	−9.08572			−0.446001
$416$	−4.33554	−	0.623357i	−0.212568	−	0.0305626i
$417$	0.133535	+	0.292400i	0.00653922	+	0.0143189i
$418$	−1.19733	+	4.07773i	−0.0585634	+	0.199449i
$419$	−17.7800	−	20.5193i	−0.868612	−	1.00243i	−0.999938	−	0.0110928i	$-0.996469\pi$
$419$	−17.7800	−	20.5193i	−0.868612	−	1.00243i	0.131326	−	0.991339i	$-0.458076\pi$
$420$	−1.07930	−	5.16312i	−0.0526644	−	0.251934i
$421$	−6.05626	+	9.42373i	−0.295164	+	0.459284i	−0.956885	−	0.290465i	$-0.906190\pi$
$421$	−6.05626	+	9.42373i	−0.295164	+	0.459284i	0.661721	+	0.749750i	$0.269826\pi$
$422$	−3.02722	+	6.62868i	−0.147363	+	0.322679i
$423$	−6.74404	−	5.84374i	−0.327906	−	0.284132i
$424$	−2.91021	−	4.52838i	−0.141332	−	0.219917i
$425$	−0.991261	−	6.89437i	−0.0480832	−	0.334426i
$426$	2.68199	−	0.385612i	0.129943	−	0.0186830i
$427$	−16.0738	+	8.60811i	−0.777864	+	0.416576i
$428$	−2.26578	−	1.96331i	−0.109521	−	0.0949002i
$429$	22.5204	+	10.2847i	1.08730	+	0.496551i
$430$	−9.61081	+	14.9547i	−0.463475	+	0.721180i
$431$	10.5237	+	35.8406i	0.506911	+	1.72638i	0.672418	+	0.740171i	$0.265256\pi$
$431$	10.5237	+	35.8406i	0.506911	+	1.72638i	−0.165508	+	0.986209i	$0.552926\pi$
$432$	−0.755750	+	0.654861i	−0.0363610	+	0.0315070i
$433$	−0.717927	−	0.210803i	−0.0345014	−	0.0101305i	0.264436	−	0.964403i	$-0.414814\pi$
$433$	−0.717927	−	0.210803i	−0.0345014	−	0.0101305i	−0.298938	+	0.954273i	$0.596632\pi$
$434$	18.4184	−	6.69973i	0.884113	−	0.321597i
$435$	−16.5255	−	2.37600i	−0.792336	−	0.113921i
$436$		−	1.71082i		−	0.0819335i
$437$	3.59410	−	0.291895i	0.171929	−	0.0139632i
$438$	3.40688			0.162787
$439$	13.0120	+	1.87085i	0.621031	+	0.0892908i	0.445646	−	0.895209i	$-0.352974\pi$
$439$	13.0120	+	1.87085i	0.621031	+	0.0892908i	0.175385	+	0.984500i	$0.443883\pi$
$440$	10.2504	−	4.68119i	0.488667	−	0.223167i
$441$	6.31932	+	3.01101i	0.300920	+	0.143381i
$442$	−22.4872	+	19.4853i	−1.06961	+	0.926821i
$443$	30.9200	−	9.07893i	1.46905	−	0.431353i	0.553262	−	0.833007i	$-0.313383\pi$
$443$	30.9200	−	9.07893i	1.46905	−	0.431353i	0.915791	+	0.401654i	$0.131565\pi$
$444$	2.01205	+	1.29306i	0.0954874	+	0.0613660i
$445$	5.42230	−	11.8732i	0.257042	−	0.562842i
$446$	10.1968	+	8.83559i	0.482833	+	0.418377i
$447$	14.7770	−	9.49663i	0.698930	−	0.449175i
$448$	−0.167293	−	2.64046i	−0.00790386	−	0.124750i
$449$	−1.06903	−	7.43528i	−0.0504507	−	0.350892i	−0.999374	−	0.0353848i	$-0.988734\pi$
$449$	−1.06903	−	7.43528i	−0.0504507	−	0.350892i	0.948923	−	0.315508i	$-0.102175\pi$
$450$	0.862568	−	0.554339i	0.0406618	−	0.0261318i
$451$	42.7266	−	49.3091i	2.01192	−	2.32188i
$452$	1.41128	+	0.644510i	0.0663810	+	0.0303152i
$453$	−5.45751	+	8.49205i	−0.256416	+	0.398991i
$454$	−10.1544	+	2.98161i	−0.476571	+	0.139934i
$455$	18.6076	−	13.6949i	0.872336	−	0.642027i
$456$	0.211831	−	0.721432i	0.00991992	−	0.0337841i
$457$	3.87620	−	1.77020i	0.181321	−	0.0828066i	−0.322686	−	0.946506i	$-0.604586\pi$
$457$	3.87620	−	1.77020i	0.181321	−	0.0828066i	0.504007	+	0.863699i	$0.331859\pi$
$458$	1.61588	−	11.2387i	0.0755052	−	0.525150i
$459$			6.79315i			0.317077i
$460$	−6.82566	−	6.69535i	−0.318248	−	0.312172i
$461$			35.2401i			1.64129i	0.571436	+	0.820646i	$0.306386\pi$
$461$			35.2401i			1.64129i	−0.571436	+	0.820646i	$0.693614\pi$
$462$	−3.29746	+	14.5865i	−0.153412	+	0.678623i
$463$	−15.6832	−	34.3413i	−0.728859	−	1.59598i	−0.801058	−	0.598587i	$-0.795729\pi$
$463$	−15.6832	−	34.3413i	−0.728859	−	1.59598i	0.0721989	−	0.997390i	$-0.476998\pi$
$464$	−8.03505	−	2.35930i	−0.373018	−	0.109528i
$465$	−9.67133	−	11.1613i	−0.448497	−	0.517594i
$466$	−13.1855	+	3.87161i	−0.610807	+	0.179349i
$467$	16.0445	+	10.3112i	0.742450	+	0.477144i	0.856381	−	0.516345i	$-0.172708\pi$
$467$	16.0445	+	10.3112i	0.742450	+	0.477144i	−0.113931	+	0.993489i	$0.536344\pi$
$468$	−3.98430	−	1.81957i	−0.184175	−	0.0841097i
$469$	−11.9210	−	12.1164i	−0.550462	−	0.559482i
$470$	−9.61836	−	14.9665i	−0.443662	−	0.690351i
$471$	−9.48233	+	1.36335i	−0.436923	+	0.0628200i
$472$	−9.24549	+	1.32930i	−0.425558	+	0.0611861i
$473$	42.3986	−	27.2479i	1.94949	−	1.25286i
$474$	−11.3195	+	13.0635i	−0.519924	+	0.600024i
$475$	−0.320259	+	0.701270i	−0.0146945	+	0.0321765i
$476$	−14.3001	−	10.8874i	−0.655445	−	0.499022i
$477$	−1.51654	−	5.16485i	−0.0694374	−	0.236482i
$478$	−0.227837	−	0.262937i	−0.0104210	−	0.0120265i
$479$	20.4435	+	6.00277i	0.934089	+	0.274273i	0.713148	−	0.701014i	$-0.247269\pi$
$479$	20.4435	+	6.00277i	0.934089	+	0.274273i	0.220942	+	0.975287i	$0.429087\pi$
$480$	−1.81349	+	0.828195i	−0.0827743	+	0.0378017i
$481$	−1.49090	+	10.3694i	−0.0679791	+	0.472805i
$482$	15.0718			0.686502
$483$	12.5567	−	1.82474i	0.571349	−	0.0830287i
$484$	−20.9483			−0.952194
$485$	1.02245	−	7.11129i	0.0464270	−	0.322907i
$486$	−0.909632	+	0.415415i	−0.0412617	+	0.0188436i
$487$	−38.4126	−	11.2790i	−1.74064	−	0.511098i	−0.751713	−	0.659491i	$-0.770772\pi$
$487$	−38.4126	−	11.2790i	−1.74064	−	0.511098i	−0.988929	+	0.148392i	$0.952590\pi$
$488$	4.51308	+	5.20837i	0.204298	+	0.235772i
$489$	−3.02244	−	10.2935i	−0.136679	−	0.465487i
$490$	10.3970	+	9.30918i	0.469689	+	0.420546i
$491$	16.7438	−	36.6637i	0.755635	−	1.65461i	−0.000331542	−	1.00000i	$-0.500106\pi$
$491$	16.7438	−	36.6637i	0.755635	−	1.65461i	0.755967	−	0.654610i	$-0.227167\pi$
$492$	−7.55918	+	8.72376i	−0.340794	+	0.393297i
$493$	−47.8570	+	30.7558i	−2.15537	+	1.38517i
$494$	3.25985	−	0.468695i	0.146667	−	0.0210876i
$495$	11.1540	−	1.60370i	0.501335	−	0.0720811i
$496$	−4.00494	−	6.23181i	−0.179827	−	0.279817i
$497$	−5.11017	+	5.02778i	−0.229223	+	0.225527i
$498$	−4.14548	−	1.89318i	−0.185764	−	0.0848354i
$499$	−1.16810	−	0.750690i	−0.0522912	−	0.0336055i	0.514234	−	0.857650i	$-0.328076\pi$
$499$	−1.16810	−	0.750690i	−0.0522912	−	0.0336055i	−0.566525	+	0.824044i	$0.691713\pi$
$500$	11.5259	−	3.38430i	0.515452	−	0.151350i
$501$	−7.67914	−	8.86220i	−0.343079	−	0.395934i
$502$	−21.8592	−	6.41843i	−0.975623	−	0.286469i
$503$	7.44550	+	16.3034i	0.331978	+	0.726931i	0.999850	−	0.0173458i	$-0.00552163\pi$
$503$	7.44550	+	16.3034i	0.331978	+	0.726931i	−0.667871	+	0.744277i	$0.732794\pi$
$504$	0.583386	−	2.58063i	0.0259861	−	0.114950i
$505$		−	6.45851i		−	0.287400i
$506$	9.71739	+	25.3058i	0.431991	+	1.12498i
$507$		−	6.18552i		−	0.274709i
$508$	1.51306	−	10.5236i	0.0671312	−	0.466908i
$509$	25.8685	−	11.8137i	1.14660	−	0.523635i	0.250777	−	0.968045i	$-0.419314\pi$
$509$	25.8685	−	11.8137i	1.14660	−	0.523635i	0.895824	+	0.444410i	$0.146587\pi$
$510$	−3.81556	+	12.9946i	−0.168956	+	0.575411i
$511$	−7.25954	+	5.34292i	−0.321143	+	0.236357i
$512$	−0.959493	+	0.281733i	−0.0424040	+	0.0124509i
$513$	0.406502	−	0.632529i	0.0179475	−	0.0279268i
$514$	26.5192	+	12.1109i	1.16971	+	0.534190i
$515$	4.80849	−	5.54930i	0.211887	−	0.244531i
$516$	−7.50115	+	4.82070i	−0.330220	+	0.212219i
$517$	7.17821	+	49.9255i	0.315697	+	2.19572i
$518$	−6.31524	+	0.400119i	−0.277476	+	0.0175802i
$519$	6.42664	−	4.13015i	0.282098	−	0.181294i
$520$	−6.59956	−	5.71855i	−0.289410	−	0.250775i
$521$	−8.94027	+	19.5765i	−0.391680	+	0.857661i	0.606366	+	0.795186i	$0.292627\pi$
$521$	−8.94027	+	19.5765i	−0.391680	+	0.857661i	−0.998047	+	0.0624749i	$0.980101\pi$
$522$	−7.04488	−	4.52747i	−0.308346	−	0.198162i
$523$	20.3267	−	5.96846i	0.888825	−	0.260982i	0.194722	−	0.980858i	$-0.437620\pi$
$523$	20.3267	−	5.96846i	0.888825	−	0.260982i	0.694103	+	0.719876i	$0.255801\pi$
$524$	3.40817	−	2.95320i	0.148887	−	0.129011i
$525$	−0.968646	+	2.53396i	−0.0422752	+	0.110591i
$526$	−22.9151	+	10.4650i	−0.999148	+	0.456296i
$527$	−49.8099	−	7.16158i	−2.16975	−	0.311963i
$528$	5.65228			0.245984
$529$	17.0887	−	15.3940i	0.742988	−	0.669305i
$530$		−	10.7316i		−	0.466152i
$531$	−9.24549	−	1.32930i	−0.401220	−	0.0576868i
$532$	0.680023	+	1.86947i	0.0294827	+	0.0810519i
$533$	−48.5126	−	14.2446i	−2.10131	−	0.617001i
$534$	4.94799	−	4.28746i	0.214120	−	0.185536i
$535$	−1.68394	−	5.73498i	−0.0728032	−	0.247945i
$536$	−3.47333	+	5.40461i	−0.150025	+	0.233444i
$537$	17.6281	+	8.05047i	0.760708	+	0.347404i
$538$	20.6269	+	17.8733i	0.889289	+	0.770573i
$539$	−15.8492	−	36.2528i	−0.682673	−	1.56152i
$540$	−1.97336	+	0.283727i	−0.0849200	+	0.0122097i
$541$	−2.61040	−	18.1557i	−0.112230	−	0.780574i	−0.965742	−	0.259502i	$-0.916441\pi$
$541$	−2.61040	−	18.1557i	−0.112230	−	0.780574i	0.853513	−	0.521072i	$-0.174468\pi$
$542$	15.8373	+	24.6433i	0.680269	+	1.05852i
$543$	−3.25899	−	2.82393i	−0.139856	−	0.121186i
$544$	−2.82198	+	6.17927i	−0.120991	+	0.264934i
$545$	1.84401	−	2.86934i	0.0789888	−	0.122909i
$546$	11.3435	−	2.37126i	0.485458	−	0.101480i
$547$	8.71991	+	10.0633i	0.372837	+	0.430276i	0.910899	−	0.412628i	$-0.135389\pi$
$547$	8.71991	+	10.0633i	0.372837	+	0.430276i	−0.538063	+	0.842905i	$0.680844\pi$
$548$	1.86958	−	6.36722i	0.0798647	−	0.271994i
$549$	2.86290	+	6.26888i	0.122186	+	0.267549i
$550$	−5.73650	−	0.824784i	−0.244605	−	0.0351689i
$551$	6.29652			0.268241
$552$	−1.71920	−	4.47709i	−0.0731739	−	0.190558i
$553$	3.63315	−	45.5884i	0.154497	−	1.93862i
$554$	3.77401	−	26.2488i	0.160342	−	1.11520i
$555$	1.98081	+	4.33737i	0.0840808	+	0.184111i
$556$	−0.0905626	+	0.308428i	−0.00384071	+	0.0130803i
$557$	−25.7160	+	22.2830i	−1.08962	+	0.944163i	−0.998663	−	0.0516916i	$-0.983539\pi$
$557$	−25.7160	+	22.2830i	−1.08962	+	0.944163i	−0.0909591	+	0.995855i	$0.528993\pi$
$558$	−2.08701	−	7.10770i	−0.0883501	−	0.300893i
$559$	−32.8560	−	21.1153i	−1.38966	−	0.893081i
$560$	2.56544	−	4.60881i	0.108410	−	0.194758i
$561$	25.1446	−	29.0184i	1.06160	−	1.22516i
$562$	11.7602	+	18.2992i	0.496074	+	0.771906i
$563$	1.19638	+	8.32100i	0.0504214	+	0.350688i	0.999377	+	0.0352801i	$0.0112323\pi$
$563$	1.19638	+	8.32100i	0.0504214	+	0.350688i	−0.948956	+	0.315408i	$0.897859\pi$
$564$	−1.26997	−	8.83281i	−0.0534752	−	0.371928i
$565$	1.67227	+	2.60210i	0.0703530	+	0.109471i
$566$	1.30782	−	1.50931i	0.0549720	−	0.0634410i
$567$	1.28680	−	2.31174i	0.0540406	−	0.0970839i
$568$	2.27944	+	1.46491i	0.0956430	+	0.0614661i
$569$	1.85007	+	6.30076i	0.0775590	+	0.264142i	0.989139	−	0.146980i	$-0.0469553\pi$
$569$	1.85007	+	6.30076i	0.0775590	+	0.264142i	−0.911580	+	0.411122i	$0.865137\pi$
$570$	1.13287	−	0.981641i	0.0474509	−	0.0411164i
$571$	−4.40069	+	14.9874i	−0.184163	+	0.627202i	0.814716	+	0.579861i	$0.196893\pi$
$571$	−4.40069	+	14.9874i	−0.184163	+	0.627202i	−0.998879	+	0.0473414i	$0.984925\pi$
$572$	10.2847	+	22.5204i	0.430026	+	0.941625i
$573$	3.12004	−	21.7004i	0.130342	−	0.906546i
$574$	2.42621	−	30.4439i	0.101268	−	1.27070i
$575$	1.09151	+	4.79467i	0.0455193	+	0.199951i
$576$	−1.00000			−0.0416667
$577$	−40.7399	−	5.85751i	−1.69602	−	0.243851i	−0.774612	−	0.632437i	$-0.782055\pi$
$577$	−40.7399	−	5.85751i	−1.69602	−	0.243851i	−0.921413	+	0.388586i	$0.872964\pi$
$578$	12.1081	+	26.5130i	0.503629	+	1.10279i
$579$	3.38636	−	11.5329i	0.140732	−	0.479290i
$580$	−10.9332	−	12.6175i	−0.453975	−	0.523915i
$581$	11.8024	−	2.46718i	0.489647	−	0.102356i
$582$	1.94828	−	3.03158i	0.0807586	−	0.125663i
$583$	−12.6393	+	27.6761i	−0.523465	+	1.14623i
$584$	2.57475	+	2.23103i	0.106544	+	0.0923208i
$585$	−4.72113	−	7.34622i	−0.195195	−	0.303729i
$586$	2.77571	+	19.3055i	0.114664	+	0.797503i
$587$	6.19017	−	0.890012i	0.255496	−	0.0367347i	−0.0133768	−	0.999911i	$-0.504258\pi$
$587$	6.19017	−	0.890012i	0.255496	−	0.0367347i	0.268872	+	0.963176i	$0.413349\pi$
$588$	2.80403	+	6.41384i	0.115636	+	0.264502i
$589$	4.20938	+	3.64745i	0.173445	+	0.150291i
$590$	−16.9391	−	7.73581i	−0.697370	−	0.318478i
$591$	−7.30059	+	11.3599i	−0.300306	+	0.467286i
$592$	0.673826	+	2.29484i	0.0276941	+	0.0943174i
$593$	4.37623	−	3.79203i	0.179710	−	0.155720i	−0.560361	−	0.828249i	$-0.689337\pi$
$593$	4.37623	−	3.79203i	0.179710	−	0.155720i	0.740071	+	0.672529i	$0.234792\pi$
$594$	5.42332	+	1.59243i	0.222522	+	0.0653383i
$595$	−12.2487	−	33.6734i	−0.502149	−	1.38047i
$596$	17.3867	+	2.49983i	0.712187	+	0.102397i
$597$			8.01605i			0.328075i
$598$	14.7099	−	14.9962i	0.601532	−	0.613240i
$599$	−20.4023			−0.833616			−0.416808	−	0.908994i	$-0.636851\pi$
$599$	−20.4023			−0.833616			−0.416808	+	0.908994i	$0.636851\pi$
$600$	1.01490	+	0.145921i	0.0414331	+	0.00595718i
$601$	13.7990	−	6.30177i	0.562871	−	0.257055i	−0.113597	−	0.993527i	$-0.536237\pi$
$601$	13.7990	−	6.30177i	0.562871	−	0.257055i	0.676468	+	0.736472i	$0.263510\pi$
$602$	8.42364	−	22.0360i	0.343322	−	0.898122i
$603$	−4.85530	+	4.20714i	−0.197723	+	0.171328i
$604$	−9.68562	+	2.84395i	−0.394102	+	0.115719i
$605$	−35.1338	−	22.5791i	−1.42839	−	0.917972i
$606$	1.34575	−	2.94678i	0.0546674	−	0.119705i
$607$	14.9240	+	12.9317i	0.605747	+	0.524883i	0.902846	−	0.429964i	$-0.141474\pi$
$607$	14.9240	+	12.9317i	0.605747	+	0.524883i	−0.297099	+	0.954847i	$0.596019\pi$
$608$	0.632529	−	0.406502i	0.0256524	−	0.0164858i
$609$	22.1119	−	1.40096i	0.896019	−	0.0567697i
$610$	1.95535	+	13.5998i	0.0791698	+	0.550638i
$611$	32.8818	−	21.1319i	1.33026	−	0.854903i
$612$	−4.44857	+	5.13392i	−0.179823	+	0.207527i
$613$	−11.8467	−	5.41020i	−0.478483	−	0.218516i	0.161548	−	0.986865i	$-0.448351\pi$
$613$	−11.8467	−	5.41020i	−0.478483	−	0.218516i	−0.640031	+	0.768349i	$0.721079\pi$
$614$	−8.06565	+	12.5504i	−0.325503	+	0.506493i
$615$	−22.0809	+	6.48355i	−0.890390	+	0.261442i
$616$	−12.0442	+	8.86433i	−0.485273	+	0.357154i
$617$	−9.42261	+	32.0904i	−0.379340	+	1.29191i	0.519814	+	0.854280i	$0.326001\pi$
$617$	−9.42261	+	32.0904i	−0.379340	+	1.29191i	−0.899154	+	0.437633i	$0.855817\pi$
$618$	3.35024	−	1.53000i	0.134766	−	0.0615457i
$619$	3.85551	−	26.8157i	0.154966	−	1.07781i	−0.752774	−	0.658279i	$-0.771285\pi$
$619$	3.85551	−	26.8157i	0.154966	−	1.07781i	0.907740	−	0.419533i	$-0.137806\pi$
$620$		−	14.7685i		−	0.593119i
$621$	−0.388216	−	4.78009i	−0.0155786	−	0.191819i
$622$		−	2.63959i		−	0.105838i
$623$	−3.81950	+	16.8957i	−0.153025	+	0.676913i
$624$	−1.81957	−	3.98430i	−0.0728411	−	0.159500i
$625$	18.0596	+	5.30277i	0.722383	+	0.212111i
$626$	3.10213	+	3.58005i	0.123986	+	0.143088i
$627$	−4.07773	+	1.19733i	−0.162849	+	0.0478168i
$628$	−8.05908	−	5.17925i	−0.321592	−	0.206675i
$629$	14.7791	+	6.74939i	0.589281	+	0.269116i
$630$	3.75998	−	3.69935i	0.149801	−	0.147386i
$631$	−7.18378	−	11.1782i	−0.285982	−	0.444996i	0.668306	−	0.743887i	$-0.267020\pi$
$631$	−7.18378	−	11.1782i	−0.285982	−	0.444996i	−0.954287	+	0.298890i	$0.903383\pi$
$632$	−17.1095	+	2.45997i	−0.680579	+	0.0978525i
$633$	−7.21304	+	1.03708i	−0.286693	+	0.0412202i
$634$	16.0254	−	10.2989i	0.636448	−	0.409020i
$635$	13.8805	−	16.0190i	0.550831	−	0.635693i
$636$	2.23613	−	4.89645i	0.0886685	−	0.194157i
$637$	−20.4526	+	22.8426i	−0.810360	+	0.905055i
$638$	13.3354	+	45.4164i	0.527955	+	1.79805i
$639$	1.77439	+	2.04776i	0.0701939	+	0.0810080i
$640$	−1.91290	−	0.561678i	−0.0756140	−	0.0222023i
$641$	−19.2953	+	8.81189i	−0.762120	+	0.348049i	−0.758267	−	0.651944i	$-0.773954\pi$
$641$	−19.2953	+	8.81189i	−0.762120	+	0.348049i	−0.00385305	+	0.999993i	$0.501226\pi$
$642$	0.426668	−	2.96754i	0.0168393	−	0.117120i
$643$	−12.4208			−0.489829			−0.244915	−	0.969545i	$-0.578760\pi$
$643$	−12.4208			−0.489829			−0.244915	+	0.969545i	$0.578760\pi$
$644$	10.6847	+	6.84383i	0.421035	+	0.269685i
$645$	−17.7767			−0.699957
$646$	0.726901	−	5.05570i	0.0285995	−	0.198914i
$647$	14.7287	−	6.72639i	0.579046	−	0.264442i	−0.104288	−	0.994547i	$-0.533256\pi$
$647$	14.7287	−	6.72639i	0.579046	−	0.264442i	0.683334	+	0.730106i	$0.260529\pi$
$648$	−0.959493	−	0.281733i	−0.0376924	−	0.0110675i
$649$	34.5737	+	39.9002i	1.35714	+	1.56622i
$650$	1.26529	+	4.30918i	0.0496288	+	0.169020i
$651$	15.5939	+	11.8724i	0.611174	+	0.465317i
$652$	4.45659	−	9.75857i	0.174533	−	0.382175i
$653$	−17.5737	+	20.2811i	−0.687711	+	0.793660i	−0.987037	−	0.160490i	$-0.948692\pi$
$653$	−17.5737	+	20.2811i	−0.687711	+	0.793660i	0.299327	+	0.954151i	$0.403238\pi$
$654$	1.43924	−	0.924940i	0.0562785	−	0.0361680i
$655$	8.89919	−	1.27951i	0.347720	−	0.0499946i
$656$	−11.4257	+	1.64277i	−0.446098	+	0.0641393i
$657$	1.84190	+	2.86605i	0.0718593	+	0.111815i
$658$	16.5584	+	16.8297i	0.645513	+	0.656091i
$659$	31.1005	+	14.2031i	1.21150	+	0.553274i	0.915657	−	0.401961i	$-0.131671\pi$
$659$	31.1005	+	14.2031i	1.21150	+	0.553274i	0.295845	+	0.955236i	$0.404399\pi$
$660$	9.47984	+	6.09232i	0.369002	+	0.237143i
$661$	−31.4742	+	9.24166i	−1.22421	+	0.359459i	−0.829060	−	0.559160i	$-0.811124\pi$
$661$	−31.4742	+	9.24166i	−1.22421	+	0.359459i	−0.395145	+	0.918619i	$0.629306\pi$
$662$	−10.9301	−	12.6140i	−0.424811	−	0.490258i
$663$	−28.5496	−	8.38292i	−1.10877	−	0.325566i
$664$	−1.89318	−	4.14548i	−0.0734696	−	0.160876i
$665$	−0.874500	+	3.86839i	−0.0339116	+	0.150010i
$666$			2.39172i			0.0926774i
$667$	31.9176	−	24.3767i	1.23585	−	0.943868i
$668$		−	11.7264i		−	0.453707i
$669$	−1.92016	+	13.3550i	−0.0742376	+	0.516334i
$670$	−11.6507	+	5.32072i	−0.450108	+	0.205557i
$671$	10.9745	−	37.3757i	0.423666	−	1.44287i
$672$	2.13085	−	1.56827i	0.0821993	−	0.0604975i
$673$	22.9538	−	6.73984i	0.884803	−	0.259802i	0.192404	−	0.981316i	$-0.438372\pi$
$673$	22.9538	−	6.73984i	0.884803	−	0.259802i	0.692400	+	0.721514i	$0.256554\pi$
$674$	−7.31921	+	11.3889i	−0.281925	+	0.438685i
$675$	0.932679	+	0.425940i	0.0358988	+	0.0163944i
$676$	4.05065	−	4.67470i	0.155794	−	0.179796i
$677$	10.8159	−	6.95092i	0.415687	−	0.267146i	−0.316037	−	0.948747i	$-0.602352\pi$
$677$	10.8159	−	6.95092i	0.415687	−	0.267146i	0.731724	+	0.681601i	$0.238716\pi$
$678$	0.220799	+	1.53569i	0.00847975	+	0.0589779i
$679$	0.602865	+	9.51526i	0.0231358	+	0.365162i
$680$	−11.3933	+	7.32201i	−0.436912	+	0.280786i
$681$	−7.99818	−	6.93047i	−0.306491	−	0.265576i
$682$	−17.3937	+	38.0870i	−0.666041	+	1.45843i
$683$	−8.09085	−	5.19968i	−0.309588	−	0.198960i	0.376616	−	0.926370i	$-0.377088\pi$
$683$	−8.09085	−	5.19968i	−0.309588	−	0.198960i	−0.686204	+	0.727410i	$0.740724\pi$
$684$	0.721432	−	0.211831i	0.0275846	−	0.00809958i
$685$	9.99853	−	8.66378i	0.382024	−	0.331026i
$686$	−16.0336	−	9.26943i	−0.612167	−	0.353909i
$687$	10.3282	−	4.71674i	0.394046	−	0.179955i
$688$	−8.82588	−	1.26897i	−0.336483	−	0.0483790i
$689$	23.5778			0.898241
$690$	1.94225	−	9.36189i	0.0739404	−	0.356401i
$691$			6.61531i			0.251658i	0.992052	+	0.125829i	$0.0401591\pi$
$691$			6.61531i			0.251658i	−0.992052	+	0.125829i	$0.959841\pi$
$692$	7.56161	+	1.08719i	0.287449	+	0.0413290i
$693$	−14.0536	+	5.11203i	−0.533854	+	0.194190i
$694$	−12.2887	−	3.60829i	−0.466473	−	0.136969i
$695$	−0.484328	+	0.419673i	−0.0183716	+	0.0159191i
$696$	−2.35930	−	8.03505i	−0.0894292	−	0.304568i
$697$	−42.3941	+	65.9666i	−1.60579	+	2.49866i
$698$	−20.4242	−	9.32742i	−0.773068	−	0.353048i
$699$	−10.3856	−	8.99920i	−0.392821	−	0.340381i
$700$	−2.39144	+	1.28071i	−0.0903880	+	0.0484062i
$701$	−42.7656	+	6.14877i	−1.61523	+	0.232236i	−0.889898	−	0.456159i	$-0.849225\pi$
$701$	−42.7656	+	6.14877i	−1.61523	+	0.232236i	−0.725337	+	0.688394i	$0.758316\pi$
$702$	−0.623357	−	4.33554i	−0.0235271	−	0.163635i
$703$	−0.972239	−	1.51283i	−0.0366687	−	0.0570576i
$704$	4.27171	+	3.70146i	0.160996	+	0.139504i
$705$	7.39051	−	16.1830i	0.278343	−	0.609485i
$706$	−1.17938	+	1.83515i	−0.0443865	+	0.0690668i
$707$	1.75377	+	8.38965i	0.0659575	+	0.315525i
$708$	−6.11677	−	7.05913i	−0.229882	−	0.265298i
$709$	2.40707	−	8.19774i	0.0903995	−	0.307873i	−0.901864	−	0.432019i	$-0.857801\pi$
$709$	2.40707	−	8.19774i	0.0903995	−	0.307873i	0.992264	+	0.124147i	$0.0396194\pi$
$710$	2.24405	+	4.91379i	0.0842178	+	0.184411i
$711$	−17.1095	−	2.45997i	−0.641656	−	0.0922562i
$712$	6.54713			0.245364
$713$	35.4587	+	2.19280i	1.32794	+	0.0821211i
$714$	1.42782	−	17.9162i	0.0534350	−	0.670496i
$715$	−7.02443	+	48.8560i	−0.262699	+	1.82711i
$716$	8.05047	+	17.6281i	0.300860	+	0.658792i
$717$	0.0980193	−	0.333823i	0.00366060	−	0.0124669i
$718$	23.7178	−	20.5516i	0.885142	−	0.766980i
$719$	−2.03363	−	6.92590i	−0.0758415	−	0.258293i	0.912841	−	0.408315i	$-0.133884\pi$
$719$	−2.03363	−	6.92590i	−0.0758415	−	0.258293i	−0.988683	+	0.150023i	$0.952065\pi$
$720$	−1.67717	−	1.07785i	−0.0625044	−	0.0401692i
$721$	−4.73938	+	8.51429i	−0.176504	+	0.317089i
$722$	12.0721	−	13.9320i	0.449278	−	0.518495i
$723$	8.14843	+	12.6792i	0.303043	+	0.471545i
$724$	−0.613698	−	4.26836i	−0.0228079	−	0.158632i
$725$	1.22198	+	8.49904i	0.0453831	+	0.315647i
$726$	−11.3255	−	17.6228i	−0.420328	−	0.654044i
$727$	−10.2211	+	11.7958i	−0.379081	+	0.437483i	−0.912942	−	0.408089i	$-0.866195\pi$
$727$	−10.2211	+	11.7958i	−0.379081	+	0.437483i	0.533861	+	0.845572i	$0.320741\pi$
$728$	10.1257	+	5.63636i	0.375284	+	0.208897i
$729$	−0.841254	−	0.540641i	−0.0311575	−	0.0200237i
$730$	1.91357	+	6.51702i	0.0708244	+	0.241206i
$731$	−45.7773	+	39.6663i	−1.69314	+	1.46711i
$732$	−1.94161	+	6.61251i	−0.0717639	+	0.244405i
$733$	−6.07735	−	13.3075i	−0.224472	−	0.491526i	0.763567	−	0.645729i	$-0.223446\pi$
$733$	−6.07735	−	13.3075i	−0.224472	−	0.491526i	−0.988039	+	0.154203i	$0.950719\pi$
$734$	0.0775385	−	0.539292i	0.00286200	−	0.0199056i
$735$	−2.21033	+	13.7794i	−0.0815294	+	0.508262i
$736$	1.63259	−	4.50940i	0.0601780	−	0.166219i
$737$	36.3129			1.33760
$738$	−11.4257	−	1.64277i	−0.420586	−	0.0604711i
$739$	19.4734	+	42.6408i	0.716340	+	1.56857i	0.818964	+	0.573846i	$0.194549\pi$
$739$	19.4734	+	42.6408i	0.716340	+	1.56857i	−0.102624	+	0.994720i	$0.532724\pi$
$740$	−1.34338	+	4.57512i	−0.0493835	+	0.168185i
$741$	2.15670	+	2.48896i	0.0792283	+	0.0914343i
$742$	2.91412	+	13.9405i	0.106981	+	0.511771i
$743$	3.71784	−	5.78507i	0.136394	−	0.212234i	−0.766337	−	0.642439i	$-0.777923\pi$
$743$	3.71784	−	5.78507i	0.136394	−	0.212234i	0.902731	+	0.430206i	$0.141559\pi$
$744$	3.07730	−	6.73834i	0.112819	−	0.247040i
$745$	26.4660	+	22.9329i	0.969640	+	0.840198i
$746$	2.70850	+	4.21451i	0.0991652	+	0.154304i
$747$	−0.648574	−	4.51093i	−0.0237301	−	0.165046i
$748$	38.0060	−	5.46444i	1.38964	−	0.199800i
$749$	3.74476	+	6.99252i	0.136830	+	0.255501i
$750$	9.07840	+	7.86648i	0.331496	+	0.287243i
$751$	34.2356	+	15.6349i	1.24927	+	0.570525i	0.926622	−	0.375993i	$-0.122698\pi$
$751$	34.2356	+	15.6349i	1.24927	+	0.570525i	0.322652	+	0.946518i	$0.395426\pi$
$752$	4.82448	−	7.50704i	0.175931	−	0.273754i
$753$	−6.41843	−	21.8592i	−0.233901	−	0.796593i
$754$	27.7212	−	24.0205i	1.00955	−	0.874776i
$755$	−19.3098	−	5.66987i	−0.702755	−	0.206348i
$756$	2.48637	−	0.904419i	0.0904283	−	0.0328934i
$757$	−25.1172	−	3.61131i	−0.912901	−	0.131255i	−0.330171	−	0.943921i	$-0.607106\pi$
$757$	−25.1172	−	3.61131i	−0.912901	−	0.131255i	−0.582730	+	0.812666i	$0.698016\pi$
$758$			7.38557i			0.268256i
$759$	−16.0350	+	21.8561i	−0.582032	+	0.793327i
$760$	1.49901			0.0543747
$761$	−45.2021	−	6.49908i	−1.63857	−	0.235591i	−0.739427	−	0.673237i	$-0.764903\pi$
$761$	−45.2021	−	6.49908i	−1.63857	−	0.235591i	−0.899147	+	0.437646i	$0.855812\pi$
$762$	9.67101	−	4.41660i	0.350344	−	0.159997i
$763$	−1.61623	+	4.22802i	−0.0585115	+	0.153065i
$764$	16.5687	−	14.3568i	0.599434	−	0.519413i
$765$	−12.9946	+	3.81556i	−0.469821	+	0.137952i
$766$	−25.7683	−	16.5603i	−0.931048	−	0.598348i
$767$	16.9958	−	37.2157i	0.613684	−	1.34378i
$768$	−0.755750	−	0.654861i	−0.0272708	−	0.0236303i
$769$	−27.2302	+	17.4998i	−0.981947	+	0.631059i	−0.929988	−	0.367591i	$-0.880183\pi$
$769$	−27.2302	+	17.4998i	−0.981947	+	0.631059i	−0.0519588	+	0.998649i	$0.516546\pi$
$770$	−29.7545	+	1.88518i	−1.07228	+	0.0679371i
$771$	4.14902	+	28.8570i	0.149423	+	1.03926i
$772$	10.1117	−	6.49837i	0.363927	−	0.233881i
$773$	−9.25044	+	10.6756i	−0.332715	+	0.383974i	−0.897315	−	0.441391i	$-0.854485\pi$
$773$	−9.25044	+	10.6756i	−0.332715	+	0.383974i	0.564600	+	0.825365i	$0.309031\pi$
$774$	−8.11086	−	3.70410i	−0.291539	−	0.133141i
$775$	−4.10641	+	6.38970i	−0.147507	+	0.229525i
$776$	3.45767	−	1.01526i	0.124123	−	0.0364458i
$777$	−3.75088	−	5.09640i	−0.134562	−	0.182832i
$778$	−4.49442	+	15.3066i	−0.161133	+	0.548768i
$779$	7.89487	−	3.60547i	0.282863	−	0.129179i
$780$	1.24276	−	8.64358i	0.0444979	−	0.309490i
$781$		−	15.3153i		−	0.548023i
$782$	−15.8882	−	28.4419i	−0.568161	−	1.01708i
$783$		−	8.37427i		−	0.299272i
$784$	−2.08103	+	6.68351i	−0.0743224	+	0.238697i
$785$	−7.93397	−	17.3730i	−0.283176	−	0.620068i
$786$	4.32698	+	1.27052i	0.154338	+	0.0453178i
$787$	−2.09324	−	2.41573i	−0.0746159	−	0.0861114i	0.717214	−	0.696853i	$-0.245417\pi$
$787$	−2.09324	−	2.41573i	−0.0746159	−	0.0861114i	−0.791830	+	0.610741i	$0.790871\pi$
$788$	−12.9566	+	3.80440i	−0.461560	+	0.135526i
$789$	−21.1926	−	13.6196i	−0.754476	−	0.484872i
$790$	−31.3470	−	14.3157i	−1.11528	−	0.509330i
$791$	−2.87888	−	2.92605i	−0.102361	−	0.104039i
$792$	3.05585	+	4.75500i	0.108585	+	0.168962i
$793$	−29.8791	+	4.29597i	−1.06104	+	0.152554i
$794$	2.00106	−	0.287708i	0.0710148	−	0.0102104i
$795$	9.02803	−	5.80196i	0.320191	−	0.205774i
$796$	−5.24940	+	6.05813i	−0.186060	+	0.214725i
$797$	0.858162	−	1.87911i	0.0303977	−	0.0665616i	−0.893824	−	0.448418i	$-0.851988\pi$
$797$	0.858162	−	1.87911i	0.0303977	−	0.0665616i	0.924222	+	0.381856i	$0.124715\pi$
$798$	−1.20505	+	1.58278i	−0.0426584	+	0.0560299i
$799$	−17.0785	−	58.1641i	−0.604195	−	2.05770i
$800$	0.671453	+	0.774898i	0.0237394	+	0.0273968i
$801$	6.28193	+	1.84454i	0.221961	+	0.0651736i
$802$	13.0351	−	5.95294i	0.460286	−	0.210206i
$803$	2.74051	−	19.0606i	0.0967104	−	0.672635i
$804$	−6.42448			−0.226574
$805$	10.5434	+	22.9947i	0.371605	+	0.810458i
$806$	32.4470			1.14290
$807$	−3.88424	+	27.0155i	−0.136732	+	0.950990i
$808$	2.94678	−	1.34575i	0.103667	−	0.0473433i
$809$	53.8131	+	15.8010i	1.89197	+	0.555532i	0.993093	+	0.117328i	$0.0374328\pi$
$809$	53.8131	+	15.8010i	1.89197	+	0.555532i	0.898875	+	0.438204i	$0.144385\pi$
$810$	−1.30557	−	1.50670i	−0.0458729	−	0.0529402i
$811$	0.453665	+	1.54504i	0.0159303	+	0.0542537i	0.967075	−	0.254493i	$-0.0819086\pi$
$811$	0.453665	+	1.54504i	0.0159303	+	0.0542537i	−0.951144	+	0.308747i	$0.900090\pi$
$812$	17.6285	+	13.4214i	0.618639	+	0.471000i
$813$	−12.1690	+	26.6463i	−0.426784	+	0.934527i
$814$	8.85286	−	10.2167i	0.310292	−	0.358097i
$815$	17.9927	−	11.5632i	0.630258	−	0.405042i
$816$	−6.72401	+	0.966766i	−0.235387	+	0.0338436i
$817$	6.63608	−	0.954124i	0.232167	−	0.0333806i
$818$	−3.59519	−	5.59423i	−0.125703	−	0.195598i
$819$	8.12760	+	8.26079i	0.284001	+	0.288655i
$820$	−20.9335	−	9.56000i	−0.731029	−	0.333850i
$821$	−29.4354	−	18.9170i	−1.02730	−	0.660207i	−0.0854873	−	0.996339i	$-0.527245\pi$
$821$	−29.4354	−	18.9170i	−1.02730	−	0.660207i	−0.941815	+	0.336132i	$0.890881\pi$
$822$	6.36722	−	1.86958i	0.222082	−	0.0652092i
$823$	−30.1374	−	34.7805i	−1.05053	−	1.21237i	−0.976590	−	0.215107i	$-0.930990\pi$
$823$	−30.1374	−	34.7805i	−1.05053	−	1.21237i	−0.0739347	−	0.997263i	$-0.523556\pi$
$824$	3.53388	+	1.03764i	0.123108	+	0.0361479i
$825$	−2.40753	−	5.27176i	−0.0838195	−	0.183539i
$826$	24.1046	+	5.44916i	0.838705	+	0.189600i
$827$			30.0747i			1.04580i	0.852394	+	0.522899i	$0.175150\pi$
$827$			30.0747i			1.04580i	−0.852394	+	0.522899i	$0.824850\pi$
$828$	2.83690	−	3.86678i	0.0985891	−	0.134380i
$829$			6.98616i			0.242640i	0.992613	+	0.121320i	$0.0387126\pi$
$829$			6.98616i			0.242640i	−0.992613	+	0.121320i	$0.961287\pi$
$830$	1.29303	−	8.99324i	0.0448818	−	0.312160i
$831$	24.1223	−	11.0163i	0.836793	−	0.382150i
$832$	1.23402	−	4.20270i	0.0427821	−	0.145702i
$833$	25.0550	+	40.4159i	0.868105	+	1.40033i
$834$	−0.308428	+	0.0905626i	−0.0106800	+	0.00313593i
$835$	12.6393	−	19.6671i	0.437401	−	0.680609i
$836$	−3.86583	−	1.76547i	−0.133703	−	0.0610599i
$837$	4.85106	−	5.59842i	0.167677	−	0.193510i
$838$	22.8408	−	14.6789i	0.789022	−	0.507073i
$839$	2.24230	+	15.5955i	0.0774127	+	0.538417i	0.991215	+	0.132259i	$0.0422229\pi$
$839$	2.24230	+	15.5955i	0.0774127	+	0.538417i	−0.913803	+	0.406159i	$0.866868\pi$
$840$	5.26416	−	0.333525i	0.181631	−	0.0115077i
$841$	34.5994	−	22.2357i	1.19308	−	0.766747i
$842$	−8.46591	−	7.33576i	−0.291755	−	0.252807i
$843$	−9.03624	+	19.7866i	−0.311225	+	0.681487i
$844$	−6.13040	−	3.93977i	−0.211017	−	0.135612i
$845$	11.8323	−	3.47427i	0.407043	−	0.119518i
$846$	6.74404	−	5.84374i	0.231865	−	0.200912i
$847$	51.7703	+	19.7900i	1.77885	+	0.679994i
$848$	4.89645	−	2.23613i	0.168145	−	0.0767892i
$849$	1.97678	+	0.284218i	0.0678428	+	0.00975432i
$850$	6.96527			0.238907
$851$	−10.7852	−	3.90470i	−0.369713	−	0.133851i
$852$			2.70957i			0.0928284i
$853$	21.0167	+	3.02175i	0.719599	+	0.103463i	0.492379	−	0.870381i	$-0.336127\pi$
$853$	21.0167	+	3.02175i	0.719599	+	0.103463i	0.227220	+	0.973844i	$0.427036\pi$
$854$	−6.23296	−	17.1352i	−0.213287	−	0.586355i
$855$	1.43829	+	0.422319i	0.0491884	+	0.0144430i
$856$	2.26578	−	1.96331i	0.0774428	−	0.0671046i
$857$	−6.76447	−	23.0377i	−0.231070	−	0.786952i	−0.990637	−	0.136523i	$-0.956407\pi$
$857$	−6.76447	−	23.0377i	−0.231070	−	0.786952i	0.759567	−	0.650429i	$-0.225411\pi$
$858$	−13.3850	+	20.8275i	−0.456957	+	0.711040i
$859$	20.6848	+	9.44642i	0.705756	+	0.322308i	0.735760	−	0.677242i	$-0.236825\pi$
$859$	20.6848	+	9.44642i	0.705756	+	0.322308i	−0.0300047	+	0.999550i	$0.509552\pi$
$860$	−13.4347	−	11.6413i	−0.458121	−	0.396964i
$861$	26.9227	−	14.4181i	0.917524	−	0.491369i
$862$	−36.9735	+	5.31598i	−1.25932	+	0.181063i
$863$	3.44788	+	23.9805i	0.117367	+	0.816306i	0.960436	+	0.278501i	$0.0898374\pi$
$863$	3.44788	+	23.9805i	0.117367	+	0.816306i	−0.843069	+	0.537805i	$0.819253\pi$
$864$	−0.540641	−	0.841254i	−0.0183930	−	0.0286200i
$865$	11.5103	+	9.97370i	0.391361	+	0.339116i
$866$	0.310829	−	0.680620i	0.0105624	−	0.0231284i
$867$	−15.7580	+	24.5200i	−0.535170	+	0.832741i
$868$	4.01032	+	19.1844i	0.136119	+	0.651162i
$869$	63.9813	+	73.8383i	2.17042	+	2.50479i
$870$	4.70364	−	16.0191i	0.159468	−	0.543099i
$871$	−11.6898	−	25.5971i	−0.396093	−	0.867324i
$872$	1.69341	+	0.243475i	0.0573460	+	0.00824512i
$873$	3.60364			0.121965
$874$	−0.222569	+	3.59906i	−0.00752853	+	0.121740i
$875$	−31.6815	−	2.52485i	−1.07103	−	0.0853554i
$876$	−0.484850	+	3.37220i	−0.0163816	+	0.113936i
$877$	14.3014	+	31.3158i	0.482926	+	1.05746i	0.981649	+	0.190698i	$0.0610752\pi$
$877$	14.3014	+	31.3158i	0.482926	+	1.05746i	−0.498723	+	0.866761i	$0.666198\pi$
$878$	−3.70362	+	12.6134i	−0.124991	+	0.425680i
$879$	−14.7402	+	12.7724i	−0.497173	+	0.430803i
$880$	3.17476	+	10.8122i	0.107021	+	0.364481i
$881$	−2.57499	−	1.65485i	−0.0867538	−	0.0557533i	0.496545	−	0.868011i	$-0.334602\pi$
$881$	−2.57499	−	1.65485i	−0.0867538	−	0.0557533i	−0.583299	+	0.812258i	$0.698238\pi$
$882$	−3.87969	+	5.82649i	−0.130636	+	0.196188i
$883$	34.6779	−	40.0205i	1.16701	−	1.34680i	0.240439	−	0.970664i	$-0.422708\pi$
$883$	34.6779	−	40.0205i	1.16701	−	1.34680i	0.926566	−	0.376132i	$-0.122746\pi$
$884$	−16.0867	−	25.0314i	−0.541054	−	0.841897i
$885$	−2.65017	−	18.4323i	−0.0890845	−	0.619596i
$886$	4.58614	+	31.8973i	0.154075	+	1.07161i
$887$	9.10555	+	14.1685i	0.305735	+	0.475732i	0.959792	−	0.280713i	$-0.0905708\pi$
$887$	9.10555	+	14.1685i	0.305735	+	0.475732i	−0.654057	+	0.756445i	$0.726934\pi$
$888$	−1.56625	+	1.80754i	−0.0525597	+	0.0606572i
$889$	−13.6810	+	24.5779i	−0.458847	+	0.824317i
$890$	10.9806	+	7.05684i	0.368072	+	0.236546i
$891$	1.59243	+	5.42332i	0.0533485	+	0.181688i
$892$	−10.1968	+	8.83559i	−0.341415	+	0.295838i
$893$	−1.89031	+	6.43780i	−0.0632567	+	0.215433i
$894$	7.29697	+	15.9781i	0.244047	+	0.534389i
$895$	−5.49844	+	38.2425i	−0.183793	+	1.27831i
$896$	2.63739	+	0.210186i	0.0881090	+	0.00702181i
$897$	20.5684	+	4.26720i	0.686758	+	0.142478i
$898$	7.51174			0.250670
$899$	61.4032	+	8.82845i	2.04791	+	0.294445i
$900$	0.425940	+	0.932679i	0.0141980	+	0.0310893i
$901$	10.3021	−	35.0856i	0.343211	−	1.16887i
$902$	42.7266	+	49.3091i	1.42264	+	1.64181i
$903$	23.0921	−	4.82717i	0.768456	−	0.160638i
$904$	−0.838796	+	1.30519i	−0.0278979	+	0.0434100i
$905$	3.57139	−	7.82025i	0.118717	−	0.259954i
$906$	−7.62893	−	6.61050i	−0.253454	−	0.219619i
$907$	−20.5736	−	32.0131i	−0.683134	−	1.06298i	−0.993662	−	0.112413i	$-0.964142\pi$
$907$	−20.5736	−	32.0131i	−0.683134	−	1.06298i	0.310528	−	0.950564i	$-0.399494\pi$
$908$	−1.50613	−	10.4754i	−0.0499828	−	0.347638i
$909$	3.20656	−	0.461033i	0.106355	−	0.0152915i
$910$	10.9074	+	20.3672i	0.361576	+	0.675165i
$911$	23.0741	+	19.9938i	0.764479	+	0.662425i	0.947165	−	0.320746i	$-0.103934\pi$
$911$	23.0741	+	19.9938i	0.764479	+	0.662425i	−0.182686	+	0.983171i	$0.558479\pi$
$912$	0.683942	+	0.312346i	0.0226476	+	0.0103428i
$913$	−13.9265	+	21.6701i	−0.460900	+	0.717174i
$914$	1.20054	+	4.08867i	0.0397104	+	0.135241i
$915$	−10.3837	+	8.99753i	−0.343275	+	0.297449i
$916$	10.8943	+	3.19887i	0.359959	+	0.105694i
$917$	−11.2127	+	4.07862i	−0.370275	+	0.134688i
$918$	−6.72401	−	0.966766i	−0.221925	−	0.0319080i
$919$			22.7415i			0.750174i	0.926990	+	0.375087i	$0.122387\pi$
$919$			22.7415i			0.750174i	−0.926990	+	0.375087i	$0.877613\pi$
$920$	7.59859	−	5.80334i	0.250518	−	0.191330i
$921$	−14.9187			−0.491587
$922$	−34.8814	−	5.01518i	−1.14876	−	0.165166i
$923$	−10.7958	+	4.93026i	−0.355347	+	0.162281i
$924$	−13.9687	−	5.33977i	−0.459537	−	0.175665i
$925$	1.85334	−	1.60593i	0.0609374	−	0.0528026i
$926$	36.2237	−	10.6363i	1.19039	−	0.349529i
$927$	3.09839	+	1.99122i	0.101765	+	0.0654001i
$928$	3.47880	−	7.61750i	0.114197	−	0.250057i
$929$	−15.3065	−	13.2632i	−0.502190	−	0.435150i	0.366565	−	0.930393i	$-0.380534\pi$
$929$	−15.3065	−	13.2632i	−0.502190	−	0.435150i	−0.868755	+	0.495242i	$0.835079\pi$
$930$	12.4241	−	7.98447i	0.407402	−	0.261821i
$931$	0.0855416	−	5.26252i	0.00280351	−	0.172472i
$932$	−1.95571	−	13.6023i	−0.0640615	−	0.445557i
$933$	2.22056	−	1.42707i	0.0726980	−	0.0467201i
$934$	−12.4896	+	14.4137i	−0.408671	+	0.471632i
$935$	69.6323	+	31.8000i	2.27722	+	1.03997i
$936$	2.36808	−	3.68480i	0.0774030	−	0.120441i
$937$	−24.0126	+	7.05075i	−0.784459	+	0.230338i	−0.649347	−	0.760493i	$-0.724958\pi$
$937$	−24.0126	+	7.05075i	−0.784459	+	0.230338i	−0.135112	+	0.990830i	$0.543139\pi$
$938$	13.6896	−	10.0753i	0.446981	−	0.328972i
$939$	−1.33459	+	4.54520i	−0.0435527	+	0.148327i
$940$	16.1830	−	7.39051i	0.527830	−	0.241052i
$941$	6.01892	−	41.8625i	0.196211	−	1.36468i	−0.618943	−	0.785436i	$-0.712439\pi$
$941$	6.01892	−	41.8625i	0.196211	−	1.36468i	0.815155	−	0.579244i	$-0.196652\pi$
$942$		−	9.57984i		−	0.312128i
$943$	26.0613	−	48.8410i	0.848674	−	1.59048i
$944$		−	9.34057i		−	0.304010i
$945$	5.14489	+	1.16307i	0.167363	+	0.0378347i
$946$	20.9366	+	45.8448i	0.680709	+	1.49054i
$947$	−36.5109	−	10.7206i	−1.18644	−	0.348372i	−0.371790	−	0.928317i	$-0.621256\pi$
$947$	−36.5109	−	10.7206i	−1.18644	−	0.348372i	−0.814655	+	0.579945i	$0.803074\pi$
$948$	−11.3195	−	13.0635i	−0.367642	−	0.424281i
$949$	−14.3181	+	4.20417i	−0.464785	+	0.136473i
$950$	−0.648555	−	0.416801i	−0.0210419	−	0.0135228i
$951$	17.3279	+	7.91339i	0.561896	+	0.256609i
$952$	12.8117	−	12.6051i	0.415229	−	0.408534i
$953$	−12.6411	−	19.6699i	−0.409485	−	0.637171i	0.573853	−	0.818958i	$-0.305448\pi$
$953$	−12.6411	−	19.6699i	−0.409485	−	0.637171i	−0.983338	+	0.181787i	$0.941812\pi$
$954$	5.32810	−	0.766065i	0.172504	−	0.0248023i
$955$	43.2631	−	6.22029i	1.39996	−	0.201284i
$956$	0.292686	−	0.188098i	0.00946613	−	0.00608351i
$957$	−30.9970	+	35.7724i	−1.00199	+	1.15636i
$958$	−8.85109	+	19.3812i	−0.285966	+	0.626177i
$959$	−10.6356	+	13.9694i	−0.343440	+	0.451094i
$960$	−0.561678	−	1.91290i	−0.0181281	−	0.0617385i
$961$	15.6348	+	18.0435i	0.504348	+	0.582049i
$962$	−10.0517	−	2.95144i	−0.324080	−	0.0951584i
$963$	2.72713	−	1.24544i	0.0878806	−	0.0401337i
$964$	−2.14494	+	14.9184i	−0.0690839	+	0.480489i
$965$	23.9633			0.771404
$966$	0.0191684	+	12.6886i	0.000616733	+	0.408248i
$967$	27.1601			0.873409			0.436705	−	0.899605i	$-0.356146\pi$
$967$	27.1601			0.873409			0.436705	+	0.899605i	$0.356146\pi$
$968$	2.98125	−	20.7351i	0.0958210	−	0.666450i
$969$	4.64612	−	2.12181i	0.149255	−	0.0681624i
$970$	6.89340	+	2.02408i	0.221334	+	0.0649894i
$971$	28.1224	+	32.4550i	0.902491	+	1.04153i	0.998933	+	0.0461911i	$0.0147083\pi$
$971$	28.1224	+	32.4550i	0.902491	+	1.04153i	−0.0964420	+	0.995339i	$0.530746\pi$
$972$	−0.281733	−	0.959493i	−0.00903658	−	0.0307758i
$973$	0.515186	−	0.676675i	0.0165161	−	0.0216932i
$974$	16.6308	−	36.4165i	0.532886	−	1.16686i
$975$	−2.94105	+	3.39415i	−0.0941889	+	0.108700i
$976$	−5.79764	+	3.72592i	−0.185578	+	0.119264i
$977$	4.71152	−	0.677414i	0.150735	−	0.0216724i	−0.0665343	−	0.997784i	$-0.521194\pi$
$977$	4.71152	−	0.677414i	0.150735	−	0.0216724i	0.217269	+	0.976112i	$0.430285\pi$
$978$	10.6188	−	1.52676i	0.339553	−	0.0488204i
$979$	−20.0071	−	31.1316i	−0.639429	−	0.994971i
$980$	−10.6941	+	8.96635i	−0.341610	+	0.286419i
$981$	1.55622	+	0.710701i	0.0496862	+	0.0226909i
$982$	33.9076	+	21.7911i	1.08204	+	0.695383i
$983$	17.2412	−	5.06246i	0.549908	−	0.161467i	0.00503657	−	0.999987i	$-0.498397\pi$
$983$	17.2412	−	5.06246i	0.549908	−	0.161467i	0.544871	+	0.838520i	$0.316579\pi$
$984$	−7.55918	−	8.72376i	−0.240978	−	0.278103i
$985$	−25.8310	−	7.58467i	−0.823044	−	0.241668i
$986$	−23.6320	−	51.7469i	−0.752596	−	1.64796i
$987$	−5.20593	+	23.0286i	−0.165706	+	0.733009i
$988$			3.29337i			0.104776i
$989$	29.9450	−	30.5278i	0.952195	−	0.970727i
$990$			11.2687i			0.358143i
$991$	−4.94785	+	34.4130i	−0.157174	+	1.09317i	0.746637	+	0.665232i	$0.231667\pi$
$991$	−4.94785	+	34.4130i	−0.157174	+	1.09317i	−0.903810	+	0.427934i	$0.859242\pi$
$992$	6.73834	−	3.07730i	0.213943	−	0.0977043i
$993$	4.70233	−	16.0147i	0.149224	−	0.508210i
$994$	−4.24935	−	5.77369i	−0.134781	−	0.183130i
$995$	−15.3339	+	4.50244i	−0.486117	+	0.142737i
$996$	2.46387	−	3.83386i	0.0780708	−	0.121481i
$997$	−17.8789	−	8.16504i	−0.566232	−	0.258589i	0.111666	−	0.993746i	$-0.464381\pi$
$997$	−17.8789	−	8.16504i	−0.566232	−	0.258589i	−0.677897	+	0.735156i	$0.737109\pi$
$998$	0.909286	−	1.04937i	0.0287830	−	0.0332173i
$999$	−2.01205	+	1.29306i	−0.0636583	+	0.0409107i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.s.a.475.3	yes	160
7.6	odd	2	inner	966.2.s.a.475.14	yes	160
23.20	odd	22	inner	966.2.s.a.181.14	yes	160
161.20	even	22	inner	966.2.s.a.181.3	✓	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.s.a.181.3	✓	160	161.20	even	22	inner
966.2.s.a.181.14	yes	160	23.20	odd	22	inner
966.2.s.a.475.3	yes	160	1.1	even	1	trivial
966.2.s.a.475.14	yes	160	7.6	odd	2	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.s (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142315 + 0.989821i) q^{2} +(-0.909632 + 0.415415i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-1.30557 - 1.50670i) q^{5} +(-0.281733 - 0.959493i) q^{6} +(2.10508 + 1.60270i) q^{7} +(0.415415 - 0.909632i) q^{8} +(0.654861 - 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.142315 + 0.989821i) q^{2} +(-0.909632 + 0.415415i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-1.30557 - 1.50670i) q^{5} +(-0.281733 - 0.959493i) q^{6} +(2.10508 + 1.60270i) q^{7} +(0.415415 - 0.909632i) q^{8} +(0.654861 - 0.755750i) q^{9} +(1.67717 - 1.07785i) q^{10} +(-5.59475 + 0.804403i) q^{11} +(0.989821 - 0.142315i) q^{12} +(2.36808 + 3.68480i) q^{13} +(-1.88597 + 1.85556i) q^{14} +(1.81349 + 0.828195i) q^{15} +(0.841254 + 0.540641i) q^{16} +(6.51798 - 1.91385i) q^{17} +(0.654861 + 0.755750i) q^{18} +(-0.721432 - 0.211831i) q^{19} +(0.828195 + 1.81349i) q^{20} +(-2.58063 - 0.583386i) q^{21} -5.65228i q^{22} +(-4.47709 + 1.71920i) q^{23} +1.00000i q^{24} +(0.145921 - 1.01490i) q^{25} +(-3.98430 + 1.81957i) q^{26} +(-0.281733 + 0.959493i) q^{27} +(-1.56827 - 2.13085i) q^{28} +(-8.03505 + 2.35930i) q^{29} +(-1.07785 + 1.67717i) q^{30} +(-6.73834 - 3.07730i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(4.75500 - 3.05585i) q^{33} +(0.966766 + 6.72401i) q^{34} +(-0.333525 - 5.26416i) q^{35} +(-0.841254 + 0.540641i) q^{36} +(1.80754 + 1.56625i) q^{37} +(0.312346 - 0.683942i) q^{38} +(-3.68480 - 2.36808i) q^{39} +(-1.91290 + 0.561678i) q^{40} +(-8.72376 + 7.55918i) q^{41} +(0.944710 - 2.47134i) q^{42} +(-8.11086 + 3.70410i) q^{43} +(5.59475 + 0.804403i) q^{44} -1.99366 q^{45} +(-1.06454 - 4.67619i) q^{46} -8.92364i q^{47} +(-0.989821 - 0.142315i) q^{48} +(1.86271 + 6.74762i) q^{49} +(0.983803 + 0.288871i) q^{50} +(-5.13392 + 4.44857i) q^{51} +(-1.23402 - 4.20270i) q^{52} +(2.91021 - 4.52838i) q^{53} +(-0.909632 - 0.415415i) q^{54} +(8.51632 + 7.37943i) q^{55} +(2.33235 - 1.24906i) q^{56} +(0.744235 - 0.107005i) q^{57} +(-1.19178 - 8.28903i) q^{58} +(-5.04989 - 7.85779i) q^{59} +(-1.50670 - 1.30557i) q^{60} +(-2.86290 + 6.26888i) q^{61} +(4.00494 - 6.23181i) q^{62} +(2.58977 - 0.541367i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(2.46022 - 8.37874i) q^{65} +(2.34804 + 5.14150i) q^{66} +(-6.35909 - 0.914298i) q^{67} -6.79315 q^{68} +(3.35833 - 3.42369i) q^{69} +(5.25805 + 0.419038i) q^{70} +(-0.385612 + 2.68199i) q^{71} +(-0.415415 - 0.909632i) q^{72} +(-0.959829 + 3.26888i) q^{73} +(-1.80754 + 1.56625i) q^{74} +(0.288871 + 0.983803i) q^{75} +(0.632529 + 0.406502i) q^{76} +(-13.0666 - 7.27337i) q^{77} +(2.86837 - 3.31028i) q^{78} +(-9.34521 - 14.5414i) q^{79} +(-0.283727 - 1.97336i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(-6.24072 - 9.71075i) q^{82} +(2.98441 - 3.44419i) q^{83} +(2.31174 + 1.28680i) q^{84} +(-11.3933 - 7.32201i) q^{85} +(-2.51211 - 8.55545i) q^{86} +(6.32885 - 5.48398i) q^{87} +(-1.59243 + 5.42332i) q^{88} +(2.71978 + 5.95548i) q^{89} +(0.283727 - 1.97336i) q^{90} +(-0.920640 + 11.5521i) q^{91} +(4.78009 - 0.388216i) q^{92} +7.40777 q^{93} +(8.83281 + 1.26997i) q^{94} +(0.622710 + 1.36354i) q^{95} +(0.281733 - 0.959493i) q^{96} +(2.35988 + 2.72345i) q^{97} +(-6.94403 + 0.883461i) q^{98} +(-3.05585 + 4.75500i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 16 q^{2} - 16 q^{4} - 16 q^{8} + 16 q^{9}+O(q^{10}) \) 160 * q - 16 * q^2 - 16 * q^4 - 16 * q^8 + 16 * q^9	\( 160 q - 16 q^{2} - 16 q^{4} - 16 q^{8} + 16 q^{9} - 22 q^{14} - 16 q^{16} + 16 q^{18} - 36 q^{23} + 96 q^{25} + 22 q^{28} - 20 q^{29} - 16 q^{32} - 50 q^{35} + 16 q^{36} + 22 q^{37} + 4 q^{39} - 110 q^{43} + 8 q^{46} - 36 q^{50} + 22 q^{51} - 88 q^{53} + 22 q^{57} + 24 q^{58} - 16 q^{64} - 72 q^{70} + 48 q^{71} + 16 q^{72} - 22 q^{74} + 24 q^{77} + 4 q^{78} + 88 q^{79} - 16 q^{81} + 22 q^{84} + 76 q^{85} + 44 q^{86} - 44 q^{88} + 8 q^{92} - 14 q^{95} + 22 q^{98} - 22 q^{99}+O(q^{100}) \) 160 * q - 16 * q^2 - 16 * q^4 - 16 * q^8 + 16 * q^9 - 22 * q^14 - 16 * q^16 + 16 * q^18 - 36 * q^23 + 96 * q^25 + 22 * q^28 - 20 * q^29 - 16 * q^32 - 50 * q^35 + 16 * q^36 + 22 * q^37 + 4 * q^39 - 110 * q^43 + 8 * q^46 - 36 * q^50 + 22 * q^51 - 88 * q^53 + 22 * q^57 + 24 * q^58 - 16 * q^64 - 72 * q^70 + 48 * q^71 + 16 * q^72 - 22 * q^74 + 24 * q^77 + 4 * q^78 + 88 * q^79 - 16 * q^81 + 22 * q^84 + 76 * q^85 + 44 * q^86 - 44 * q^88 + 8 * q^92 - 14 * q^95 + 22 * q^98 - 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more