LMFDB - Embedded newform 966.2.s.a.727.2

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			727.2
Character	$\chi$	$=$	966.727
Dual form			966.2.s.a.97.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.959493 + 0.281733i) q^{2} +(-0.755750 + 0.654861i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.341716 - 2.37669i) q^{5} +(0.540641 - 0.841254i) q^{6} +(-0.0945662 + 2.64406i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(-0.959493 + 0.281733i) q^{2} +(-0.755750 + 0.654861i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.341716 - 2.37669i) q^{5} +(0.540641 - 0.841254i) q^{6} +(-0.0945662 + 2.64406i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(0.142315 - 0.989821i) q^{9} +(0.997464 + 2.18414i) q^{10} +(0.692982 - 2.36008i) q^{11} +(-0.281733 + 0.959493i) q^{12} +(-3.28973 + 1.50237i) q^{13} +(-0.654182 - 2.56360i) q^{14} +(1.81465 + 1.57240i) q^{15} +(0.415415 - 0.909632i) q^{16} +(5.60723 + 3.60355i) q^{17} +(0.142315 + 0.989821i) q^{18} +(-1.18505 + 0.761584i) q^{19} +(-1.57240 - 1.81465i) q^{20} +(-1.66002 - 2.06018i) q^{21} +2.45972i q^{22} +(-2.49619 - 4.09500i) q^{23} -1.00000i q^{24} +(-0.734408 + 0.215642i) q^{25} +(2.73321 - 2.36834i) q^{26} +(0.540641 + 0.841254i) q^{27} +(1.34993 + 2.27545i) q^{28} +(4.18123 + 2.68711i) q^{29} +(-2.18414 - 0.997464i) q^{30} +(-2.24033 - 1.94126i) q^{31} +(-0.142315 + 0.989821i) q^{32} +(1.02180 + 2.23744i) q^{33} +(-6.39533 - 1.87784i) q^{34} +(6.31642 - 0.678764i) q^{35} +(-0.415415 - 0.909632i) q^{36} +(3.08660 + 0.443787i) q^{37} +(0.922482 - 1.06460i) q^{38} +(1.50237 - 3.28973i) q^{39} +(2.01996 + 1.29815i) q^{40} +(8.12767 - 1.16858i) q^{41} +(2.17320 + 1.50904i) q^{42} +(4.24949 - 3.68220i) q^{43} +(-0.692982 - 2.36008i) q^{44} -2.40113 q^{45} +(3.54877 + 3.22586i) q^{46} -4.45289i q^{47} +(0.281733 + 0.959493i) q^{48} +(-6.98211 - 0.500077i) q^{49} +(0.643906 - 0.413814i) q^{50} +(-6.59748 + 0.948574i) q^{51} +(-1.95526 + 3.04244i) q^{52} +(7.96008 + 3.63525i) q^{53} +(-0.755750 - 0.654861i) q^{54} +(-5.84598 - 0.840525i) q^{55} +(-1.93632 - 1.80296i) q^{56} +(0.396868 - 1.35161i) q^{57} +(-4.76891 - 1.40028i) q^{58} +(-5.00403 + 2.28526i) q^{59} +(2.37669 + 0.341716i) q^{60} +(8.37626 - 9.66672i) q^{61} +(2.69650 + 1.23145i) q^{62} +(2.60369 + 0.469893i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(4.69482 + 7.30528i) q^{65} +(-1.61077 - 1.85893i) q^{66} +(0.857529 + 2.92048i) q^{67} +6.66532 q^{68} +(4.56815 + 1.46014i) q^{69} +(-5.86933 + 2.43081i) q^{70} +(14.8816 - 4.36963i) q^{71} +(0.654861 + 0.755750i) q^{72} +(7.27883 + 11.3261i) q^{73} +(-3.08660 + 0.443787i) q^{74} +(0.413814 - 0.643906i) q^{75} +(-0.585182 + 1.28137i) q^{76} +(6.17466 + 2.05547i) q^{77} +(-0.514689 + 3.57974i) q^{78} +(-0.459240 + 0.209728i) q^{79} +(-2.30386 - 0.676476i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-7.46921 + 3.41107i) q^{82} +(0.0423414 - 0.294491i) q^{83} +(-2.51032 - 0.835654i) q^{84} +(6.64842 - 14.5580i) q^{85} +(-3.03996 + 4.73027i) q^{86} +(-4.91965 + 0.707339i) q^{87} +(1.32982 + 2.06925i) q^{88} +(2.92830 + 3.37944i) q^{89} +(2.30386 - 0.676476i) q^{90} +(-3.66126 - 8.84032i) q^{91} +(-4.31385 - 2.09539i) q^{92} +2.96439 q^{93} +(1.25452 + 4.27251i) q^{94} +(2.21500 + 2.55624i) q^{95} +(-0.540641 - 0.841254i) q^{96} +(1.66184 + 11.5584i) q^{97} +(6.84018 - 1.48727i) q^{98} +(-2.23744 - 1.02180i) 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 $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$-1$	$e\left(\frac{21}{22}\right)$

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 $

$2$	−0.959493	+	0.281733i	−0.678464	+	0.199215i
$2$	−0.959493	+	0.281733i	−0.678464	+	0.199215i
$3$	−0.755750	+	0.654861i	−0.436332	+	0.378084i
$3$	−0.755750	+	0.654861i	−0.436332	+	0.378084i
$4$	0.841254	−	0.540641i	0.420627	−	0.270320i
$5$	−0.341716	−	2.37669i	−0.152820	−	1.06289i	−0.911464	−	0.411381i	$-0.865047\pi$
$5$	−0.341716	−	2.37669i	−0.152820	−	1.06289i	0.758643	−	0.651506i	$-0.225862\pi$
$6$	0.540641	−	0.841254i	0.220716	−	0.343440i
$7$	−0.0945662	+	2.64406i	−0.0357427	+	0.999361i
$7$	−0.0945662	+	2.64406i	−0.0357427	+	0.999361i
$8$	−0.654861	+	0.755750i	−0.231528	+	0.267198i
$9$	0.142315	−	0.989821i	0.0474383	−	0.329940i
$10$	0.997464	+	2.18414i	0.315426	+	0.690686i
$11$	0.692982	−	2.36008i	0.208942	−	0.711591i	−0.786616	−	0.617442i	$-0.788169\pi$
$11$	0.692982	−	2.36008i	0.208942	−	0.711591i	0.995558	−	0.0941488i	$-0.0300129\pi$
$12$	−0.281733	+	0.959493i	−0.0813292	+	0.276982i
$13$	−3.28973	+	1.50237i	−0.912407	+	0.416682i	−0.815597	−	0.578620i	$-0.803591\pi$
$13$	−3.28973	+	1.50237i	−0.912407	+	0.416682i	−0.0968103	+	0.995303i	$0.530864\pi$
$14$	−0.654182	−	2.56360i	−0.174838	−	0.685151i
$15$	1.81465	+	1.57240i	0.468541	+	0.405993i
$16$	0.415415	−	0.909632i	0.103854	−	0.227408i
$17$	5.60723	+	3.60355i	1.35995	+	0.873988i	0.998298	−	0.0583239i	$-0.0185756\pi$
$17$	5.60723	+	3.60355i	1.35995	+	0.873988i	0.361655	+	0.932312i	$0.382212\pi$
$18$	0.142315	+	0.989821i	0.0335439	+	0.233303i
$19$	−1.18505	+	0.761584i	−0.271869	+	0.174719i	−0.669470	−	0.742839i	$-0.733479\pi$
$19$	−1.18505	+	0.761584i	−0.271869	+	0.174719i	0.397602	+	0.917558i	$0.369843\pi$
$20$	−1.57240	−	1.81465i	−0.351600	−	0.405768i
$21$	−1.66002	−	2.06018i	−0.362247	−	0.449567i
$22$			2.45972i			0.524413i
$23$	−2.49619	−	4.09500i	−0.520492	−	0.853866i
$23$	−2.49619	−	4.09500i	−0.520492	−	0.853866i
$24$		−	1.00000i		−	0.204124i
$25$	−0.734408	+	0.215642i	−0.146882	+	0.0431284i
$26$	2.73321	−	2.36834i	0.536026	−	0.464469i
$27$	0.540641	+	0.841254i	0.104046	+	0.161899i
$28$	1.34993	+	2.27545i	0.255113	+	0.430020i
$29$	4.18123	+	2.68711i	0.776435	+	0.498984i	0.867849	−	0.496829i	$-0.165502\pi$
$29$	4.18123	+	2.68711i	0.776435	+	0.498984i	−0.0914137	+	0.995813i	$0.529139\pi$
$30$	−2.18414	−	0.997464i	−0.398768	−	0.182111i
$31$	−2.24033	−	1.94126i	−0.402376	−	0.348661i	0.430042	−	0.902809i	$-0.358499\pi$
$31$	−2.24033	−	1.94126i	−0.402376	−	0.348661i	−0.832418	+	0.554148i	$0.813044\pi$
$32$	−0.142315	+	0.989821i	−0.0251579	+	0.174977i
$33$	1.02180	+	2.23744i	0.177873	+	0.389488i
$34$	−6.39533	−	1.87784i	−1.09679	−	0.322047i
$35$	6.31642	−	0.678764i	1.06767	−	0.114732i
$36$	−0.415415	−	0.909632i	−0.0692358	−	0.151605i
$37$	3.08660	+	0.443787i	0.507435	+	0.0729581i	0.391278	−	0.920273i	$-0.372033\pi$
$37$	3.08660	+	0.443787i	0.507435	+	0.0729581i	0.116157	+	0.993231i	$0.462942\pi$
$38$	0.922482	−	1.06460i	0.149646	−	0.172701i
$39$	1.50237	−	3.28973i	0.240572	−	0.526779i
$40$	2.01996	+	1.29815i	0.319383	+	0.205255i
$41$	8.12767	−	1.16858i	1.26933	−	0.182502i	0.525454	−	0.850822i	$-0.323895\pi$
$41$	8.12767	−	1.16858i	1.26933	−	0.182502i	0.743874	+	0.668320i	$0.232986\pi$
$42$	2.17320	+	1.50904i	0.335332	+	0.232850i
$43$	4.24949	−	3.68220i	0.648041	−	0.561531i	−0.267599	−	0.963530i	$-0.586230\pi$
$43$	4.24949	−	3.68220i	0.648041	−	0.561531i	0.915640	+	0.402000i	$0.131685\pi$
$44$	−0.692982	−	2.36008i	−0.104471	−	0.355796i
$45$	−2.40113			−0.357939
$46$	3.54877	+	3.22586i	0.523238	+	0.475628i
$47$		−	4.45289i		−	0.649520i	−0.945796	−	0.324760i	$-0.894716\pi$
$47$		−	4.45289i		−	0.649520i	0.945796	−	0.324760i	$-0.105284\pi$
$48$	0.281733	+	0.959493i	0.0406646	+	0.138491i
$49$	−6.98211	−	0.500077i	−0.997445	−	0.0714396i
$50$	0.643906	−	0.413814i	0.0910621	−	0.0585221i
$51$	−6.59748	+	0.948574i	−0.923832	+	0.132827i
$52$	−1.95526	+	3.04244i	−0.271145	+	0.421910i
$53$	7.96008	+	3.63525i	1.09340	+	0.499340i	0.878717	−	0.477344i	$-0.158400\pi$
$53$	7.96008	+	3.63525i	1.09340	+	0.499340i	0.214685	+	0.976683i	$0.431128\pi$
$54$	−0.755750	−	0.654861i	−0.102844	−	0.0891153i
$55$	−5.84598	−	0.840525i	−0.788272	−	0.113336i
$56$	−1.93632	−	1.80296i	−0.258752	−	0.240931i
$57$	0.396868	−	1.35161i	0.0525664	−	0.179025i
$58$	−4.76891	−	1.40028i	−0.626188	−	0.183866i
$59$	−5.00403	+	2.28526i	−0.651469	+	0.297516i	−0.713602	−	0.700552i	$-0.752937\pi$
$59$	−5.00403	+	2.28526i	−0.651469	+	0.297516i	0.0621321	+	0.998068i	$0.480210\pi$
$60$	2.37669	+	0.341716i	0.306829	+	0.0441154i
$61$	8.37626	−	9.66672i	1.07247	−	1.23770i	0.102433	−	0.994740i	$-0.467337\pi$
$61$	8.37626	−	9.66672i	1.07247	−	1.23770i	0.970037	−	0.242957i	$-0.0781173\pi$
$62$	2.69650	+	1.23145i	0.342456	+	0.156394i
$63$	2.60369	+	0.469893i	0.328034	+	0.0592009i
$64$	−0.142315	−	0.989821i	−0.0177894	−	0.123728i
$65$	4.69482	+	7.30528i	0.582320	+	0.906108i
$66$	−1.61077	−	1.85893i	−0.198272	−	0.228818i
$67$	0.857529	+	2.92048i	0.104764	+	0.356793i	0.995145	−	0.0984236i	$-0.0313800\pi$
$67$	0.857529	+	2.92048i	0.104764	+	0.356793i	−0.890381	+	0.455217i	$0.849562\pi$
$68$	6.66532			0.808289
$69$	4.56815	+	1.46014i	0.549941	+	0.175780i
$70$	−5.86933	+	2.43081i	−0.701519	+	0.290537i
$71$	14.8816	−	4.36963i	1.76612	−	0.518580i	0.772869	−	0.634566i	$-0.218821\pi$
$71$	14.8816	−	4.36963i	1.76612	−	0.518580i	0.993251	+	0.115986i	$0.0370027\pi$
$72$	0.654861	+	0.755750i	0.0771761	+	0.0890659i
$73$	7.27883	+	11.3261i	0.851923	+	1.32562i	0.944027	+	0.329868i	$0.107004\pi$
$73$	7.27883	+	11.3261i	0.851923	+	1.32562i	−0.0921041	+	0.995749i	$0.529359\pi$
$74$	−3.08660	+	0.443787i	−0.358811	+	0.0515892i
$75$	0.413814	−	0.643906i	0.0477831	−	0.0743519i
$76$	−0.585182	+	1.28137i	−0.0671250	+	0.146983i
$77$	6.17466	+	2.05547i	0.703668	+	0.234243i
$78$	−0.514689	+	3.57974i	−0.0582770	+	0.405326i
$79$	−0.459240	+	0.209728i	−0.0516685	+	0.0235962i	−0.441082	−	0.897467i	$-0.645405\pi$
$79$	−0.459240	+	0.209728i	−0.0516685	+	0.0235962i	0.389413	+	0.921063i	$0.372678\pi$
$80$	−2.30386	−	0.676476i	−0.257580	−	0.0756323i
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$	−7.46921	+	3.41107i	−0.824836	+	0.376690i
$83$	0.0423414	−	0.294491i	0.00464757	−	0.0323246i	−0.987366	−	0.158458i	$-0.949348\pi$
$83$	0.0423414	−	0.294491i	0.00464757	−	0.0323246i	0.992013	+	0.126134i	$0.0402568\pi$
$84$	−2.51032	−	0.835654i	−0.273898	−	0.0911773i
$85$	6.64842	−	14.5580i	0.721123	−	1.57904i
$86$	−3.03996	+	4.73027i	−0.327807	+	0.510078i
$87$	−4.91965	+	0.707339i	−0.527442	+	0.0758347i
$88$	1.32982	+	2.06925i	0.141760	+	0.220582i
$89$	2.92830	+	3.37944i	0.310399	+	0.358220i	0.889418	−	0.457094i	$-0.151110\pi$
$89$	2.92830	+	3.37944i	0.310399	+	0.358220i	−0.579019	+	0.815314i	$0.696564\pi$
$90$	2.30386	−	0.676476i	0.242849	−	0.0713068i
$91$	−3.66126	−	8.84032i	−0.383804	−	0.926718i
$92$	−4.31385	−	2.09539i	−0.449750	−	0.218459i
$93$	2.96439			0.307393
$94$	1.25452	+	4.27251i	0.129394	+	0.440676i
$95$	2.21500	+	2.55624i	0.227254	+	0.262265i
$96$	−0.540641	−	0.841254i	−0.0551789	−	0.0858601i
$97$	1.66184	+	11.5584i	0.168735	+	1.17357i	0.881504	+	0.472176i	$0.156531\pi$
$97$	1.66184	+	11.5584i	0.168735	+	1.17357i	−0.712770	+	0.701398i	$0.752560\pi$
$98$	6.84018	−	1.48727i	0.690962	−	0.150237i
$99$	−2.23744	−	1.02180i	−0.224871	−	0.102695i
$100$	−0.501239	+	0.578461i	−0.0501239	+	0.0578461i
$101$	2.26081	+	0.325056i	0.224959	+	0.0323443i	0.253873	−	0.967238i	$-0.418296\pi$
$101$	2.26081	+	0.325056i	0.224959	+	0.0323443i	−0.0289133	+	0.999582i	$0.509205\pi$
$102$	6.06299	−	2.76888i	0.600326	−	0.274160i
$103$	6.13142	+	1.80035i	0.604146	+	0.177393i	0.569479	−	0.822006i	$-0.307145\pi$
$103$	6.13142	+	1.80035i	0.604146	+	0.177393i	0.0346668	+	0.999399i	$0.488963\pi$
$104$	1.01890	−	3.47006i	0.0999114	−	0.340267i
$105$	−4.32914	+	4.64935i	−0.422480	+	0.453730i
$106$	−8.66181	−	1.24538i	−0.841309	−	0.120962i
$107$	8.63552	+	7.48272i	0.834827	+	0.723382i	0.963328	−	0.268328i	$-0.0864710\pi$
$107$	8.63552	+	7.48272i	0.834827	+	0.723382i	−0.128501	+	0.991709i	$0.541016\pi$
$108$	0.909632	+	0.415415i	0.0875294	+	0.0399733i
$109$	−2.29125	+	3.56525i	−0.219462	+	0.341489i	−0.933475	−	0.358643i	$-0.883239\pi$
$109$	−2.29125	+	3.56525i	−0.219462	+	0.341489i	0.714013	+	0.700133i	$0.246876\pi$
$110$	5.84598	−	0.840525i	0.557392	−	0.0801409i
$111$	−2.62332	+	1.68590i	−0.248994	+	0.160019i
$112$	2.36584	+	1.18440i	0.223551	+	0.111916i
$113$	0.0553548	+	0.188521i	0.00520735	+	0.0177346i	0.962056	−	0.272853i	$-0.0879673\pi$
$113$	0.0553548	+	0.188521i	0.00520735	+	0.0177346i	−0.956848	+	0.290588i	$0.906149\pi$
$114$			1.40867i			0.131934i
$115$	−8.87955	+	7.33200i	−0.828022	+	0.683712i
$116$	4.97024			0.461475
$117$	1.01890	+	3.47006i	0.0941974	+	0.320807i
$118$	4.15750	−	3.60249i	0.382729	−	0.331636i
$119$	−10.0582	+	14.4851i	−0.922038	+	1.32784i
$120$	−2.37669	+	0.341716i	−0.216961	+	0.0311943i
$121$	4.16403	+	2.67606i	0.378548	+	0.243278i
$122$	−5.31353	+	11.6350i	−0.481065	+	1.05338i
$123$	−5.37722	+	6.20564i	−0.484848	+	0.559544i
$124$	−2.93421	−	0.421876i	−0.263500	−	0.0378856i
$125$	−4.22385	−	9.24894i	−0.377793	−	0.827250i
$126$	−2.63061	+	0.282685i	−0.234353	+	0.0251836i
$127$	10.3171	+	3.02939i	0.915499	+	0.268815i	0.705354	−	0.708855i	$-0.250788\pi$
$127$	10.3171	+	3.02939i	0.915499	+	0.268815i	0.210145	+	0.977670i	$0.432606\pi$
$128$	0.415415	+	0.909632i	0.0367178	+	0.0804009i
$129$	−0.800219	+	5.56565i	−0.0704554	+	0.490028i
$130$	−6.56278	−	5.68668i	−0.575594	−	0.498755i
$131$	−13.7001	−	6.25662i	−1.19698	−	0.546644i	−0.285658	−	0.958332i	$-0.592212\pi$
$131$	−13.7001	−	6.25662i	−1.19698	−	0.546644i	−0.911325	+	0.411688i	$0.864939\pi$
$132$	2.06925	+	1.32982i	0.180105	+	0.115746i
$133$	−1.90161	−	3.20536i	−0.164890	−	0.277940i
$134$	−1.64559	−	2.56058i	−0.142157	−	0.221201i
$135$	1.81465	−	1.57240i	0.156180	−	0.135331i
$136$	−6.39533	+	1.87784i	−0.548395	+	0.161023i
$137$			3.81617i			0.326038i	0.986623	+	0.163019i	$0.0521231\pi$
$137$			3.81617i			0.326038i	−0.986623	+	0.163019i	$0.947877\pi$
$138$	−4.79448	−	0.113993i	−0.408133	−	0.00970376i
$139$		−	17.9397i		−	1.52162i	−0.648972	−	0.760812i	$-0.724801\pi$
$139$		−	17.9397i		−	1.52162i	0.648972	−	0.760812i	$-0.275199\pi$
$140$	4.94674	−	3.98593i	0.418076	−	0.336872i
$141$	2.91602	+	3.36527i	0.245573	+	0.283407i
$142$	−13.0477	+	8.38526i	−1.09494	+	0.703675i
$143$	1.26599	+	8.80515i	0.105867	+	0.736323i
$144$	−0.841254	−	0.540641i	−0.0701045	−	0.0450534i
$145$	4.95764	−	10.8557i	0.411709	−	0.901517i
$146$	−10.1749	−	8.81661i	−0.842082	−	0.729668i
$147$	5.60421	−	4.19438i	0.462228	−	0.345947i
$148$	2.83655	−	1.29541i	0.233163	−	0.106482i
$149$	3.48036	−	11.8530i	0.285123	−	0.971038i	−0.685024	−	0.728520i	$-0.740208\pi$
$149$	3.48036	−	11.8530i	0.285123	−	0.971038i	0.970147	−	0.242518i	$-0.0779733\pi$
$150$	−0.215642	+	0.734408i	−0.0176071	+	0.0599642i
$151$	2.96277	+	6.48756i	0.241107	+	0.527950i	0.991040	−	0.133563i	$-0.0426419\pi$
$151$	2.96277	+	6.48756i	0.241107	+	0.527950i	−0.749934	+	0.661513i	$0.769915\pi$
$152$	0.200474	−	1.39433i	0.0162606	−	0.113095i
$153$	4.36486	−	5.03732i	0.352878	−	0.407243i
$154$	−6.50364	−	0.232606i	−0.524078	−	0.0187439i
$155$	−3.84821	+	5.98793i	−0.309096	+	0.480962i
$156$	−0.514689	−	3.57974i	−0.0412081	−	0.286609i
$157$	−3.91836	+	2.51818i	−0.312719	+	0.200973i	−0.687580	−	0.726109i	$-0.741327\pi$
$157$	−3.91836	+	2.51818i	−0.312719	+	0.200973i	0.374861	+	0.927081i	$0.377691\pi$
$158$	0.381550	−	0.330615i	0.0303545	−	0.0263023i
$159$	−8.39641	+	2.46541i	−0.665879	+	0.195520i
$160$	2.40113			0.189826
$161$	11.0635	−	6.21284i	0.871925	−	0.489640i
$162$	1.00000			0.0785674
$163$	−13.6295	+	4.00198i	−1.06754	+	0.313459i	−0.767885	−	0.640588i	$-0.778691\pi$
$163$	−13.6295	+	4.00198i	−1.06754	+	0.313459i	−0.299658	+	0.954047i	$0.596873\pi$
$164$	6.20564	−	5.37722i	0.484579	−	0.419890i
$165$	4.96852	−	3.19308i	0.386799	−	0.248581i
$166$	0.0423414	+	0.294491i	0.00328633	+	0.0228569i
$167$	6.68111	−	10.3960i	0.517000	−	0.804468i	−0.480361	−	0.877071i	$-0.659494\pi$
$167$	6.68111	−	10.3960i	0.517000	−	0.804468i	0.997361	+	0.0726033i	$0.0231307\pi$
$168$	2.64406	+	0.0945662i	0.203994	+	0.00729594i
$169$	0.0520260	−	0.0600412i	0.00400200	−	0.00461855i
$170$	−2.27765	+	15.8414i	−0.174688	+	1.21498i
$171$	0.585182	+	1.28137i	0.0447500	+	0.0979888i
$172$	1.58415	−	5.39511i	0.120790	−	0.411373i
$173$	6.74082	−	22.9571i	0.512495	−	1.74540i	−0.142531	−	0.989790i	$-0.545524\pi$
$173$	6.74082	−	22.9571i	0.512495	−	1.74540i	0.655025	−	0.755607i	$-0.272658\pi$
$174$	4.52109	−	2.06471i	0.342743	−	0.156525i
$175$	−0.500720	−	1.96221i	−0.0378509	−	0.148329i
$176$	−1.85893	−	1.61077i	−0.140122	−	0.121417i
$177$	2.28526	−	5.00403i	0.171771	−	0.376126i
$178$	−3.76178	−	2.41755i	−0.281958	−	0.181203i
$179$	−3.08460	−	21.4538i	−0.230554	−	1.60354i	−0.695721	−	0.718312i	$-0.744915\pi$
$179$	−3.08460	−	21.4538i	−0.230554	−	1.60354i	0.465167	−	0.885223i	$-0.345994\pi$
$180$	−2.01996	+	1.29815i	−0.150559	+	0.0967582i
$181$	3.96422	+	4.57495i	0.294658	+	0.340054i	0.883704	−	0.468046i	$-0.155042\pi$
$181$	3.96422	+	4.57495i	0.294658	+	0.340054i	−0.589046	+	0.808100i	$0.700496\pi$
$182$	6.00356	+	7.45073i	0.445013	+	0.552285i
$183$			12.7909i			0.945531i
$184$	4.72945	+	0.795158i	0.348660	+	0.0586198i
$185$		−	7.48754i		−	0.550495i
$186$	−2.84431	+	0.835164i	−0.208555	+	0.0612372i
$187$	12.3904	−	10.7363i	0.906074	−	0.785117i
$188$	−2.40741	−	3.74601i	−0.175579	−	0.273206i
$189$	−2.27545	+	1.34993i	−0.165515	+	0.0981932i
$190$	−2.84545	−	1.82866i	−0.206431	−	0.132665i
$191$	−12.8357	−	5.86189i	−0.928762	−	0.424151i	−0.107178	−	0.994240i	$-0.534182\pi$
$191$	−12.8357	−	5.86189i	−0.928762	−	0.424151i	−0.821583	+	0.570089i	$0.806909\pi$
$192$	0.755750	+	0.654861i	0.0545415	+	0.0472605i
$193$	−2.11111	+	14.6831i	−0.151961	+	1.05691i	0.760967	+	0.648791i	$0.224725\pi$
$193$	−2.11111	+	14.6831i	−0.151961	+	1.05691i	−0.912928	+	0.408121i	$0.866184\pi$
$194$	−4.85089	−	10.6220i	−0.348274	−	0.762613i
$195$	−8.33205	−	2.44651i	−0.596670	−	0.175198i
$196$	−6.14409	+	3.35412i	−0.438864	+	0.239580i
$197$	−11.3539	−	24.8616i	−0.808932	−	1.77131i	−0.611931	−	0.790911i	$-0.709607\pi$
$197$	−11.3539	−	24.8616i	−0.808932	−	1.77131i	−0.197001	−	0.980403i	$-0.563120\pi$
$198$	2.43468	+	0.350054i	0.173025	+	0.0248773i
$199$	−3.22577	+	3.72274i	−0.228669	+	0.263898i	−0.858476	−	0.512853i	$-0.828588\pi$
$199$	−3.22577	+	3.72274i	−0.228669	+	0.263898i	0.629807	+	0.776752i	$0.283134\pi$
$200$	0.317964	−	0.696244i	0.0224835	−	0.0492319i
$201$	−2.56058	−	1.64559i	−0.180610	−	0.116071i
$202$	−2.26081	+	0.325056i	−0.159070	+	0.0228708i
$203$	−7.50029	+	10.8013i	−0.526417	+	0.758104i
$204$	−5.03732	+	4.36486i	−0.352683	+	0.305601i
$205$	−5.55471	−	18.9176i	−0.387958	−	1.32126i
$206$	−6.39027			−0.445231
$207$	−4.40856	+	1.88801i	−0.306416	+	0.131225i
$208$			3.61655i			0.250763i
$209$	0.976183	+	3.32457i	0.0675240	+	0.229965i
$210$	2.84390	−	5.68068i	0.196248	−	0.392004i
$211$	−19.2657	+	12.3813i	−1.32630	+	0.852364i	−0.995810	−	0.0914441i	$-0.970852\pi$
$211$	−19.2657	+	12.3813i	−1.32630	+	0.852364i	−0.330494	+	0.943808i	$0.607215\pi$
$212$	8.66181	−	1.24538i	0.594896	−	0.0855331i
$213$	−8.38526	+	13.0477i	−0.574548	+	0.894015i
$214$	−10.3938	−	4.74671i	−0.710509	−	0.324478i
$215$	−10.2036	−	8.84144i	−0.695877	−	0.602981i
$216$	−0.989821	−	0.142315i	−0.0673488	−	0.00968330i
$217$	5.34467	−	5.74000i	0.362820	−	0.389657i
$218$	1.19399	−	4.06635i	0.0808671	−	0.275408i
$219$	−12.9180	−	3.79306i	−0.872916	−	0.256311i
$220$	−5.37237	+	2.45348i	−0.362205	+	0.165414i
$221$	−23.8601	−	3.43057i	−1.60501	−	0.230765i
$222$	2.04208	−	2.35669i	0.137056	−	0.158171i
$223$	−7.09139	−	3.23853i	−0.474875	−	0.216868i	0.163576	−	0.986531i	$-0.447697\pi$
$223$	−7.09139	−	3.23853i	−0.474875	−	0.216868i	−0.638451	+	0.769663i	$0.720424\pi$
$224$	−2.60369	−	0.469893i	−0.173966	−	0.0313960i
$225$	0.108930	+	0.757622i	0.00726198	+	0.0505082i
$226$	−0.106225	−	0.165290i	−0.00706599	−	0.0109949i
$227$	6.79740	+	7.84461i	0.451159	+	0.520665i	0.935075	−	0.354449i	$-0.115332\pi$
$227$	6.79740	+	7.84461i	0.451159	+	0.520665i	−0.483916	+	0.875114i	$0.660786\pi$
$228$	−0.396868	−	1.35161i	−0.0262832	−	0.0895124i
$229$	0.560336			0.0370280			0.0185140	−	0.999829i	$-0.494106\pi$
$229$	0.560336			0.0370280			0.0185140	+	0.999829i	$0.494106\pi$
$230$	6.45420	−	9.53666i	0.425577	−	0.628828i
$231$	−6.01255	+	2.49012i	−0.395597	+	0.163838i
$232$	−4.76891	+	1.40028i	−0.313094	+	0.0919328i
$233$	0.955398	+	1.10259i	0.0625902	+	0.0722330i	0.786181	−	0.617996i	$-0.212055\pi$
$233$	0.955398	+	1.10259i	0.0625902	+	0.0722330i	−0.723591	+	0.690229i	$0.757510\pi$
$234$	−1.95526	−	3.04244i	−0.127819	−	0.198890i
$235$	−10.5831	+	1.52162i	−0.690367	+	0.0992597i
$236$	−2.97415	+	4.62787i	−0.193601	+	0.301249i
$237$	0.209728	−	0.459240i	0.0136233	−	0.0298308i
$238$	5.56990	−	16.7321i	0.361043	−	1.08458i
$239$	−3.99347	+	27.7752i	−0.258316	+	1.79663i	0.286506	+	0.958078i	$0.407506\pi$
$239$	−3.99347	+	27.7752i	−0.258316	+	1.79663i	−0.544823	+	0.838551i	$0.683403\pi$
$240$	2.18414	−	0.997464i	0.140986	−	0.0643860i
$241$	−17.5219	−	5.14489i	−1.12868	−	0.331412i	−0.336494	−	0.941686i	$-0.609241\pi$
$241$	−17.5219	−	5.14489i	−1.12868	−	0.331412i	−0.792191	+	0.610274i	$0.791059\pi$
$242$	−4.74929	−	1.39452i	−0.305296	−	0.0896430i
$243$	0.909632	−	0.415415i	0.0583529	−	0.0266489i
$244$	1.82034	−	12.6607i	0.116535	−	0.810519i
$245$	1.19737	+	16.7652i	0.0764974	+	1.07109i
$246$	3.41107	−	7.46921i	0.217482	−	0.476219i
$247$	2.75431	−	4.28579i	0.175252	−	0.272698i
$248$	2.93421	−	0.421876i	0.186323	−	0.0267892i
$249$	0.160851	+	0.250289i	0.0101935	+	0.0158614i
$250$	6.65848	+	7.68430i	0.421119	+	0.485998i
$251$	24.7585	−	7.26974i	1.56274	−	0.458862i	0.617863	−	0.786286i	$-0.287999\pi$
$251$	24.7585	−	7.26974i	1.56274	−	0.458862i	0.944878	+	0.327424i	$0.106180\pi$
$252$	2.44441	−	1.01236i	0.153983	−	0.0637728i
$253$	−11.3943	+	3.05345i	−0.716357	+	0.191969i
$254$	−10.7527			−0.674685
$255$	4.50893	+	15.3560i	0.282360	+	0.961630i
$256$	−0.654861	−	0.755750i	−0.0409288	−	0.0472343i
$257$	−0.161494	−	0.251289i	−0.0100737	−	0.0156750i	0.836180	−	0.548455i	$-0.184784\pi$
$257$	−0.161494	−	0.251289i	−0.0100737	−	0.0156750i	−0.846254	+	0.532780i	$0.821147\pi$
$258$	−0.800219	−	5.56565i	−0.0498195	−	0.346502i
$259$	−1.46529	+	8.11920i	−0.0910485	+	0.504503i
$260$	7.89906	+	3.60738i	0.489879	+	0.223720i
$261$	3.25481	−	3.75626i	0.201468	−	0.232506i
$262$	14.9078	+	2.14342i	0.921009	+	0.132421i
$263$	−23.6803	+	10.8144i	−1.46019	+	0.666847i	−0.977883	−	0.209154i	$-0.932929\pi$
$263$	−23.6803	+	10.8144i	−1.46019	+	0.666847i	−0.482309	+	0.876001i	$0.660202\pi$
$264$	−2.36008	−	0.692982i	−0.145253	−	0.0426501i
$265$	5.91976	−	20.1608i	0.363648	−	1.23847i
$266$	2.72763	+	2.53977i	0.167242	+	0.155723i
$267$	−4.42613	−	0.636381i	−0.270875	−	0.0389459i
$268$	2.30033	+	1.99325i	0.140515	+	0.121757i
$269$	−10.5770	−	4.83034i	−0.644889	−	0.294511i	0.0659953	−	0.997820i	$-0.478978\pi$
$269$	−10.5770	−	4.83034i	−0.644889	−	0.294511i	−0.710884	+	0.703309i	$0.751705\pi$
$270$	−1.29815	+	2.01996i	−0.0790027	+	0.122931i
$271$	21.2607	−	3.05682i	1.29149	−	0.185689i	0.537888	−	0.843016i	$-0.319222\pi$
$271$	21.2607	−	3.05682i	1.29149	−	0.185689i	0.753605	+	0.657328i	$0.228313\pi$
$272$	5.60723	−	3.60355i	0.339988	−	0.218497i
$273$	8.55618	+	4.28345i	0.517843	+	0.259246i
$274$	−1.07514	−	3.66159i	−0.0649516	−	0.221205i
$275$			1.88270i			0.113531i
$276$	4.63238	−	1.24138i	0.278837	−	0.0747226i
$277$	9.02419			0.542211			0.271106	−	0.962550i	$-0.412611\pi$
$277$	9.02419			0.542211			0.271106	+	0.962550i	$0.412611\pi$
$278$	5.05419	+	17.2130i	0.303130	+	1.03237i
$279$	−2.24033	+	1.94126i	−0.134125	+	0.116220i
$280$	−3.62340	+	5.21813i	−0.216540	+	0.311843i
$281$	−20.9356	+	3.01009i	−1.24892	+	0.179567i	−0.734877	−	0.678200i	$-0.762760\pi$
$281$	−20.9356	+	3.01009i	−1.24892	+	0.179567i	−0.514038	+	0.857767i	$0.671851\pi$
$282$	−3.74601	−	2.40741i	−0.223071	−	0.143359i
$283$	0.997361	−	2.18392i	0.0592870	−	0.129820i	−0.877670	−	0.479266i	$-0.840903\pi$
$283$	0.997361	−	2.18392i	0.0592870	−	0.129820i	0.936957	+	0.349446i	$0.113630\pi$
$284$	10.1568	−	11.7216i	0.602695	−	0.695547i
$285$	−3.34797	−	0.481365i	−0.198316	−	0.0285136i
$286$	−3.69540	−	8.09181i	−0.218514	−	0.478479i
$287$	2.32120	+	21.6006i	0.137016	+	1.27504i
$288$	0.959493	+	0.281733i	0.0565387	+	0.0166013i
$289$	11.3934	+	24.9481i	0.670200	+	1.46753i
$290$	−1.69841	+	11.8127i	−0.0997341	+	0.693666i
$291$	−8.82506	−	7.64696i	−0.517334	−	0.448272i
$292$	12.2467	+	5.59287i	0.716683	+	0.327298i
$293$	−13.2389	−	8.50811i	−0.773424	−	0.497049i	0.0934214	−	0.995627i	$-0.470220\pi$
$293$	−13.2389	−	8.50811i	−0.773424	−	0.497049i	−0.866845	+	0.498577i	$0.833856\pi$
$294$	−4.19551	+	5.60337i	−0.244687	+	0.326795i
$295$	7.14132	+	11.1121i	0.415784	+	0.646972i
$296$	−2.35669	+	2.04208i	−0.136980	+	0.118694i
$297$	2.36008	−	0.692982i	0.136946	−	0.0402109i
$298$			12.3534i			0.715615i
$299$	14.3640	+	9.72124i	0.830692	+	0.562194i
$300$		−	0.765413i		−	0.0441911i
$301$	9.33411	+	11.5841i	0.538009	+	0.667697i
$302$	−4.67051	−	5.39006i	−0.268758	−	0.310163i
$303$	−1.92147	+	1.23486i	−0.110386	+	0.0709407i
$304$	0.200474	+	1.39433i	0.0114980	+	0.0799703i
$305$	−25.8371	−	16.6045i	−1.47943	−	0.950770i
$306$	−2.76888	+	6.06299i	−0.158286	+	0.346598i
$307$	6.78321	+	5.87768i	0.387138	+	0.335457i	0.826585	−	0.562811i	$-0.190280\pi$
$307$	6.78321	+	5.87768i	0.387138	+	0.335457i	−0.439447	+	0.898268i	$0.644826\pi$
$308$	6.30573	−	1.60910i	0.359302	−	0.0916872i
$309$	−5.81279	+	2.65461i	−0.330678	+	0.151016i
$310$	2.00534	−	6.82955i	0.113895	−	0.387892i
$311$	−3.10003	+	10.5577i	−0.175786	+	0.598673i	0.823712	+	0.567008i	$0.191899\pi$
$311$	−3.10003	+	10.5577i	−0.175786	+	0.598673i	−0.999499	+	0.0316651i	$0.989919\pi$
$312$	1.50237	+	3.28973i	0.0850549	+	0.186244i
$313$	0.772281	−	5.37133i	0.0436519	−	0.303606i	−0.956286	−	0.292434i	$-0.905535\pi$
$313$	0.772281	−	5.37133i	0.0436519	−	0.303606i	0.999938	−	0.0111716i	$-0.00355611\pi$
$314$	3.05019	−	3.52011i	0.172132	−	0.198651i
$315$	0.227065	−	6.34873i	0.0127937	−	0.357710i
$316$	−0.272950	+	0.424718i	−0.0153546	+	0.0238923i
$317$	0.740816	+	5.15249i	0.0416084	+	0.289393i	0.999992	+	0.00391028i	$0.00124468\pi$
$317$	0.740816	+	5.15249i	0.0416084	+	0.289393i	−0.958384	+	0.285482i	$0.907846\pi$
$318$	7.36171	−	4.73108i	0.412824	−	0.265306i
$319$	9.23932	−	8.00592i	0.517303	−	0.448245i
$320$	−2.30386	+	0.676476i	−0.128790	+	0.0378161i
$321$	−11.4264			−0.637761
$322$	−8.86498	+	9.07812i	−0.494026	+	0.505904i
$323$	−9.38923			−0.522431
$324$	−0.959493	+	0.281733i	−0.0533052	+	0.0156518i
$325$	2.09203	−	1.81276i	0.116045	−	0.100554i
$326$	11.9499	−	7.67974i	0.661844	−	0.425341i
$327$	−0.603134	−	4.19489i	−0.0333534	−	0.231978i
$328$	−4.43933	+	6.90774i	−0.245121	+	0.381416i
$329$	11.7737	+	0.421092i	0.649105	+	0.0232156i
$330$	−3.86767	+	4.46353i	−0.212908	+	0.245709i
$331$	−4.64984	+	32.3404i	−0.255579	+	1.77759i	0.307861	+	0.951431i	$0.400387\pi$
$331$	−4.64984	+	32.3404i	−0.255579	+	1.77759i	−0.563440	+	0.826157i	$0.690522\pi$
$332$	−0.123594	−	0.270633i	−0.00678310	−	0.0148529i
$333$	0.878539	−	2.99203i	0.0481437	−	0.163962i
$334$	−3.48158	+	11.8572i	−0.190504	+	0.648796i
$335$	6.64803	−	3.03605i	0.363221	−	0.165877i
$336$	−2.56360	+	0.654182i	−0.139856	+	0.0356886i
$337$	−16.9206	−	14.6618i	−0.921724	−	0.798678i	0.0581474	−	0.998308i	$-0.481481\pi$
$337$	−16.9206	−	14.6618i	−0.921724	−	0.798678i	−0.979871	+	0.199630i	$0.936026\pi$
$338$	−0.0330030	+	0.0722665i	−0.00179513	+	0.00393078i
$339$	−0.165290	−	0.106225i	−0.00897730	−	0.00576936i
$340$	−2.27765	−	15.8414i	−0.123523	−	0.859120i
$341$	−6.13404	+	3.94211i	−0.332177	+	0.213477i
$342$	−0.922482	−	1.06460i	−0.0498821	−	0.0575670i
$343$	1.98251	−	18.4138i	0.107045	−	0.994254i
$344$			5.62288i			0.303165i
$345$	1.90928	−	11.3560i	0.102792	−	0.611388i
$346$			23.9263i			1.28629i
$347$	22.1621	−	6.50738i	1.18972	−	0.349334i	0.373809	−	0.927506i	$-0.378052\pi$
$347$	22.1621	−	6.50738i	1.18972	−	0.349334i	0.815915	+	0.578171i	$0.196233\pi$
$348$	−3.75626	+	3.25481i	−0.201356	+	0.174476i
$349$	10.6148	+	16.5170i	0.568200	+	0.884136i	0.999840	−	0.0179101i	$-0.00570126\pi$
$349$	10.6148	+	16.5170i	0.568200	+	0.884136i	−0.431640	+	0.902046i	$0.642065\pi$
$350$	1.03326	+	1.74166i	0.0552299	+	0.0930957i
$351$	−3.04244	−	1.95526i	−0.162393	−	0.104364i
$352$	2.23744	+	1.02180i	0.119256	+	0.0544623i
$353$	−1.20343	−	1.04278i	−0.0640522	−	0.0555015i	0.622246	−	0.782821i	$-0.286220\pi$
$353$	−1.20343	−	1.04278i	−0.0640522	−	0.0555015i	−0.686299	+	0.727320i	$0.740766\pi$
$354$	−0.782897	+	5.44517i	−0.0416105	+	0.289407i
$355$	−15.4705	−	33.8757i	−0.821090	−	1.79794i
$356$	4.29051	+	1.25981i	0.227397	+	0.0667696i
$357$	−1.88419	−	17.5338i	−0.0997219	−	0.927989i
$358$	9.00389	+	19.7158i	0.475871	+	1.04201i
$359$	4.29578	+	0.617639i	0.226722	+	0.0325978i	0.254740	−	0.967010i	$-0.418010\pi$
$359$	4.29578	+	0.617639i	0.226722	+	0.0325978i	−0.0280172	+	0.999607i	$0.508919\pi$
$360$	1.57240	−	1.81465i	0.0828730	−	0.0956405i
$361$	−7.06856	+	15.4780i	−0.372029	+	0.814631i
$362$	−5.09256	−	3.27279i	−0.267659	−	0.172014i
$363$	−4.89941	+	0.704429i	−0.257152	+	0.0369729i
$364$	−7.85949	−	5.45753i	−0.411949	−	0.286052i
$365$	24.4313	−	21.1698i	1.27879	−	1.10808i
$366$	−3.60361	−	12.2728i	−0.188364	−	0.641509i
$367$	−3.15505			−0.164692			−0.0823462	−	0.996604i	$-0.526241\pi$
$367$	−3.15505			−0.164692			−0.0823462	+	0.996604i	$0.526241\pi$
$368$	−4.76190	+	0.569492i	−0.248231	+	0.0296868i
$369$		−	8.21124i		−	0.427460i
$370$	2.10949	+	7.18425i	0.109667	+	0.373491i
$371$	−10.3646	+	20.7032i	−0.538102	+	1.07485i
$372$	2.49380	−	1.60267i	0.129298	−	0.0830945i
$373$	22.1710	−	3.18771i	1.14797	−	0.165054i	0.458043	−	0.888930i	$-0.348550\pi$
$373$	22.1710	−	3.18771i	1.14797	−	0.165054i	0.689930	+	0.723876i	$0.257641\pi$
$374$	−8.86370	+	13.7922i	−0.458331	+	0.713177i
$375$	9.24894	+	4.22385i	0.477613	+	0.218119i
$376$	3.36527	+	2.91602i	0.173550	+	0.150382i
$377$	−17.7922	−	2.55813i	−0.916343	−	0.131750i
$378$	1.80296	−	1.93632i	0.0927343	−	0.0995936i
$379$	−0.880012	+	2.99705i	−0.0452032	+	0.153948i	−0.979002	−	0.203851i	$-0.934654\pi$
$379$	−0.880012	+	2.99705i	−0.0452032	+	0.153948i	0.933799	+	0.357798i	$0.116473\pi$
$380$	3.24538	+	0.952930i	0.166485	+	0.0488843i
$381$	−9.78101	+	4.46684i	−0.501096	+	0.228843i
$382$	13.9673	+	2.00819i	0.714629	+	0.102748i
$383$	−10.6892	+	12.3359i	−0.546191	+	0.630338i	−0.959991	−	0.280030i	$-0.909656\pi$
$383$	−10.6892	+	12.3359i	−0.546191	+	0.630338i	0.413801	+	0.910368i	$0.364201\pi$
$384$	−0.909632	−	0.415415i	−0.0464195	−	0.0211991i
$385$	2.77523	−	15.3776i	0.141439	−	0.783717i
$386$	−2.11111	−	14.6831i	−0.107453	−	0.747349i
$387$	−3.03996	−	4.73027i	−0.154530	−	0.240453i
$388$	7.64696	+	8.82506i	0.388215	+	0.448024i
$389$	−6.19999	−	21.1152i	−0.314352	−	1.07058i	−0.953473	−	0.301478i	$-0.902520\pi$
$389$	−6.19999	−	21.1152i	−0.314352	−	1.07058i	0.639121	−	0.769106i	$-0.279298\pi$
$390$	8.68380			0.439721
$391$	0.759803	−	31.9567i	0.0384249	−	1.61612i
$392$	4.95025	−	4.94925i	0.250025	−	0.249975i
$393$	14.4511	−	4.24321i	0.728959	−	0.214042i
$394$	17.8983	+	20.6557i	0.901704	+	1.04062i
$395$	0.655387	+	1.01980i	0.0329761	+	0.0513118i
$396$	−2.43468	+	0.350054i	−0.122347	+	0.0175909i
$397$	1.13341	−	1.76362i	0.0568843	−	0.0885137i	−0.811646	−	0.584149i	$-0.801428\pi$
$397$	1.13341	−	1.76362i	0.0568843	−	0.0885137i	0.868531	+	0.495635i	$0.165065\pi$
$398$	2.04629	−	4.48075i	0.102571	−	0.224600i
$399$	3.53620	+	1.17716i	0.177032	+	0.0589317i
$400$	−0.108930	+	0.757622i	−0.00544648	+	0.0378811i
$401$	3.74378	−	1.70973i	0.186956	−	0.0853798i	−0.319738	−	0.947506i	$-0.603595\pi$
$401$	3.74378	−	1.70973i	0.186956	−	0.0853798i	0.506694	+	0.862126i	$0.330868\pi$
$402$	2.92048	+	0.857529i	0.145660	+	0.0427697i
$403$	10.2866	+	3.02041i	0.512411	+	0.150458i
$404$	2.07766	−	0.948833i	0.103367	−	0.0472062i
$405$	−0.341716	+	2.37669i	−0.0169800	+	0.118099i
$406$	4.15340	−	12.4769i	0.206130	−	0.619216i
$407$	3.18634	−	6.97710i	0.157941	−	0.345842i
$408$	3.60355	−	5.60723i	0.178402	−	0.277599i
$409$	6.44905	−	0.927233i	0.318885	−	0.0458487i	0.0189861	−	0.999820i	$-0.493956\pi$
$409$	6.44905	−	0.927233i	0.318885	−	0.0458487i	0.299899	+	0.953971i	$0.403047\pi$
$410$	10.6594	+	16.5864i	0.526431	+	0.819142i
$411$	−2.49906	−	2.88407i	−0.123270	−	0.142261i
$412$	6.13142	−	1.80035i	0.302073	−	0.0886967i
$413$	−5.56917	−	13.4471i	−0.274041	−	0.661687i
$414$	3.69807	−	3.05356i	0.181750	−	0.150074i
$415$	−0.714381			−0.0350676
$416$	−1.01890	−	3.47006i	−0.0499557	−	0.170133i
$417$	11.7480	+	13.5579i	0.575302	+	0.663934i
$418$	−1.87328	−	2.91488i	−0.0916251	−	0.142572i
$419$	−3.13665	−	21.8159i	−0.153236	−	1.06578i	−0.910750	−	0.412958i	$-0.864496\pi$
$419$	−3.13665	−	21.8159i	−0.153236	−	1.06578i	0.757514	−	0.652818i	$-0.226414\pi$
$420$	−1.12827	+	6.25179i	−0.0550540	+	0.305056i
$421$	−0.222993	−	0.101837i	−0.0108680	−	0.00496325i	0.409974	−	0.912097i	$-0.365538\pi$
$421$	−0.222993	−	0.101837i	−0.0108680	−	0.00496325i	−0.420842	+	0.907134i	$0.638265\pi$
$422$	14.9971	−	17.3075i	0.730046	−	0.842518i
$423$	−4.40756	−	0.633712i	−0.214303	−	0.0308121i
$424$	−7.96008	+	3.63525i	−0.386576	+	0.176543i
$425$	−4.89507	−	1.43732i	−0.237446	−	0.0697204i
$426$	4.36963	−	14.8816i	0.211709	−	0.721015i
$427$	24.7673	+	23.0615i	1.19857	+	1.11602i
$428$	11.3101	+	1.62615i	0.546695	+	0.0786029i
$429$	−6.72292	−	5.82544i	−0.324585	−	0.281255i
$430$	12.2812	+	5.60862i	0.592250	+	0.270472i
$431$	−11.5985	+	18.0476i	−0.558678	+	0.869321i	−0.999602	−	0.0282243i	$-0.991015\pi$
$431$	−11.5985	+	18.0476i	−0.558678	+	0.869321i	0.440923	+	0.897545i	$0.354651\pi$
$432$	0.989821	−	0.142315i	0.0476228	−	0.00684713i
$433$	6.16783	−	3.96382i	0.296407	−	0.190489i	−0.383982	−	0.923341i	$-0.625447\pi$
$433$	6.16783	−	3.96382i	0.296407	−	0.190489i	0.680389	+	0.732852i	$0.261811\pi$
$434$	−3.51103	+	7.01326i	−0.168535	+	0.336647i
$435$	3.36225	+	11.4508i	0.161207	+	0.549022i
$436$			4.23802i			0.202965i
$437$	6.07679	+	2.95171i	0.290692	+	0.141199i
$438$	13.4633			0.643303
$439$	−8.17284	−	27.8341i	−0.390068	−	1.32845i	−0.887444	−	0.460915i	$-0.847521\pi$
$439$	−8.17284	−	27.8341i	−0.390068	−	1.32845i	0.497376	−	0.867535i	$-0.334297\pi$
$440$	4.46353	−	3.86767i	0.212790	−	0.184384i
$441$	−1.48865	+	6.83988i	−0.0708879	+	0.325708i
$442$	23.8601	−	3.43057i	1.13491	−	0.163175i
$443$	20.7664	+	13.3458i	0.986641	+	0.634076i	0.931247	−	0.364389i	$-0.118722\pi$
$443$	20.7664	+	13.3458i	0.986641	+	0.634076i	0.0553945	+	0.998465i	$0.482358\pi$
$444$	−1.29541	+	2.83655i	−0.0614773	+	0.134617i
$445$	7.03123	−	8.11447i	0.333312	−	0.384663i
$446$	7.71654	+	1.10947i	0.365389	+	0.0525350i
$447$	5.13180	+	11.2371i	0.242726	+	0.531495i
$448$	2.63061	−	0.282685i	0.124284	−	0.0133556i
$449$	22.3002	+	6.54792i	1.05241	+	0.309016i	0.761791	−	0.647823i	$-0.224320\pi$
$449$	22.3002	+	6.54792i	1.05241	+	0.309016i	0.290619	+	0.956839i	$0.406139\pi$
$450$	−0.317964	−	0.696244i	−0.0149890	−	0.0328213i
$451$	2.87438	−	19.9918i	0.135349	−	0.941375i
$452$	0.148490	+	0.128667i	0.00698437	+	0.00605199i
$453$	−6.48756	−	2.96277i	−0.304812	−	0.139203i
$454$	−8.73214	−	5.61180i	−0.409820	−	0.263375i
$455$	−19.7596	+	11.7226i	−0.926343	+	0.549562i
$456$	0.761584	+	1.18505i	0.0356644	+	0.0554949i
$457$	13.1550	−	11.3989i	0.615364	−	0.533216i	−0.290451	−	0.956890i	$-0.593805\pi$
$457$	13.1550	−	11.3989i	0.615364	−	0.533216i	0.905815	+	0.423674i	$0.139260\pi$
$458$	−0.537638	+	0.157865i	−0.0251222	+	0.00737654i
$459$			6.66532i			0.311111i
$460$	−3.50597	+	10.9687i	−0.163467	+	0.511419i
$461$			32.4450i			1.51111i	0.655084	+	0.755556i	$0.272633\pi$
$461$			32.4450i			1.51111i	−0.655084	+	0.755556i	$0.727367\pi$
$462$	5.06745	−	4.08319i	0.235759	−	0.189967i
$463$	−16.4059	−	18.9334i	−0.762446	−	0.879910i	0.233266	−	0.972413i	$-0.425059\pi$
$463$	−16.4059	−	18.9334i	−0.762446	−	0.879910i	−0.995712	+	0.0925030i	$0.970513\pi$
$464$	4.18123	−	2.68711i	0.194109	−	0.124746i
$465$	−1.01298	−	7.04542i	−0.0469757	−	0.326724i
$466$	−1.22733	−	0.788759i	−0.0568551	−	0.0365386i
$467$	−14.5759	+	31.9168i	−0.674493	+	1.47693i	0.193881	+	0.981025i	$0.437892\pi$
$467$	−14.5759	+	31.9168i	−0.674493	+	1.47693i	−0.868375	+	0.495909i	$0.834835\pi$
$468$	2.73321	+	2.36834i	0.126343	+	0.109476i
$469$	−7.80301	+	1.99118i	−0.360310	+	0.0919442i
$470$	9.72574	−	4.44160i	0.448615	−	0.204876i
$471$	1.31224	−	4.46909i	0.0604650	−	0.205925i
$472$	1.54986	−	5.27832i	0.0713379	−	0.242955i
$473$	−5.74548	−	12.5808i	−0.264177	−	0.578467i
$474$	−0.0718495	+	0.499725i	−0.00330016	+	0.0229531i
$475$	0.706080	−	0.814859i	0.0323972	−	0.0373883i
$476$	−0.630314	+	17.6235i	−0.0288904	+	0.807773i
$477$	4.73108	−	7.36171i	0.216621	−	0.337070i
$478$	−3.99347	−	27.7752i	−0.182657	−	1.27041i
$479$	1.47546	−	0.948219i	0.0674154	−	0.0433252i	−0.506499	−	0.862241i	$-0.669061\pi$
$479$	1.47546	−	0.948219i	0.0674154	−	0.0433252i	0.573914	+	0.818915i	$0.305424\pi$
$480$	−1.81465	+	1.57240i	−0.0828271	+	0.0717701i
$481$	−10.8208	+	3.17728i	−0.493387	+	0.144872i
$482$	18.2616			0.831794
$483$	−4.29268	+	11.9404i	−0.195324	+	0.543307i
$484$	4.94979			0.224991
$485$	26.9027	−	7.89936i	1.22159	−	0.358691i
$486$	−0.755750	+	0.654861i	−0.0342815	+	0.0297051i
$487$	35.9674	−	23.1148i	1.62984	−	1.04743i	0.680703	−	0.732560i	$-0.261675\pi$
$487$	35.9674	−	23.1148i	1.62984	−	1.04743i	0.949134	−	0.314873i	$-0.101962\pi$
$488$	1.82034	+	12.6607i	0.0824027	+	0.573123i
$489$	7.67974	−	11.9499i	0.347290	−	0.540393i
$490$	−5.87217	−	15.7487i	−0.265278	−	0.711456i
$491$	2.57962	−	2.97704i	0.116417	−	0.134352i	−0.694550	−	0.719445i	$-0.744396\pi$
$491$	2.57962	−	2.97704i	0.116417	−	0.134352i	0.810966	+	0.585093i	$0.198942\pi$
$492$	−1.16858	+	8.12767i	−0.0526837	+	0.366423i
$493$	13.7620	+	30.1345i	0.619808	+	1.35719i
$494$	−1.43529	+	4.88816i	−0.0645769	+	0.219929i
$495$	−1.66394	+	5.66686i	−0.0747885	+	0.254706i
$496$	−2.69650	+	1.23145i	−0.121076	+	0.0552938i
$497$	10.1463	+	39.7611i	0.455122	+	1.78353i
$498$	−0.224850	−	0.194834i	−0.0100758	−	0.00873070i
$499$	−4.83554	+	10.5884i	−0.216469	+	0.474000i	−0.986449	−	0.164067i	$-0.947539\pi$
$499$	−4.83554	+	10.5884i	−0.216469	+	0.474000i	0.769981	+	0.638067i	$0.220266\pi$
$500$	−8.55368	−	5.49712i	−0.382532	−	0.245839i
$501$	1.75869	+	12.2320i	0.0785726	+	0.546485i
$502$	−21.7075	+	13.9505i	−0.968851	+	0.622643i
$503$	3.36926	+	3.88834i	0.150228	+	0.173372i	0.825876	−	0.563852i	$-0.190681\pi$
$503$	3.36926	+	3.88834i	0.150228	+	0.173372i	−0.675648	+	0.737225i	$0.736136\pi$
$504$	−2.06018	+	1.66002i	−0.0917675	+	0.0739433i
$505$		−	5.48432i		−	0.244049i
$506$	10.0725	−	6.13993i	0.447779	−	0.272953i
$507$			0.0794458i			0.00352831i
$508$	10.3171	−	3.02939i	0.457749	−	0.134407i
$509$	16.1130	−	13.9620i	0.714196	−	0.618855i	−0.220048	−	0.975489i	$-0.570621\pi$
$509$	16.1130	−	13.9620i	0.714196	−	0.618855i	0.934244	+	0.356634i	$0.116076\pi$
$510$	−8.65257	−	13.4637i	−0.383142	−	0.596181i
$511$	−30.6352	+	18.1746i	−1.35522	+	0.803997i
$512$	0.841254	+	0.540641i	0.0371785	+	0.0238932i
$513$	−1.28137	−	0.585182i	−0.0565739	−	0.0258364i
$514$	0.225748	+	0.195612i	0.00995733	+	0.00862807i
$515$	2.18366	−	15.1877i	0.0962234	−	0.669248i
$516$	2.33583	+	5.11475i	0.102829	+	0.225164i
$517$	−10.5092	−	3.08577i	−0.462193	−	0.135712i
$518$	−0.881511	−	8.20314i	−0.0387314	−	0.360425i
$519$	9.93934	+	21.7641i	0.436289	+	0.955339i
$520$	−8.59541	−	1.23583i	−0.376934	−	0.0541949i
$521$	2.48517	−	2.86804i	0.108877	−	0.125651i	−0.698695	−	0.715420i	$-0.746236\pi$
$521$	2.48517	−	2.86804i	0.108877	−	0.125651i	0.807572	+	0.589768i	$0.200781\pi$
$522$	−2.06471	+	4.52109i	−0.0903700	+	0.197883i
$523$	8.77507	+	5.63939i	0.383707	+	0.246594i	0.718247	−	0.695788i	$-0.244945\pi$
$523$	8.77507	+	5.63939i	0.383707	+	0.246594i	−0.334540	+	0.942381i	$0.608581\pi$
$524$	−14.9078	+	2.14342i	−0.651252	+	0.0936359i
$525$	1.66339	+	1.15504i	0.0725965	+	0.0504101i
$526$	19.6743	−	17.0479i	0.857842	−	0.743324i
$527$	−5.56664	−	18.9582i	−0.242487	−	0.825833i
$528$	2.45972			0.107045
$529$	−10.5380	+	20.4438i	−0.458176	+	0.888862i
$530$			21.0120i			0.912702i
$531$	1.54986	+	5.27832i	0.0672580	+	0.229060i
$532$	−3.33268	−	1.66843i	−0.144490	−	0.0723357i
$533$	−24.9822	+	16.0551i	−1.08210	+	0.695423i
$534$	4.42613	−	0.636381i	0.191537	−	0.0275389i
$535$	14.8332	−	23.0809i	0.641295	−	0.997874i
$536$	−2.76871	−	1.26443i	−0.119590	−	0.0546150i
$537$	16.3805	+	14.1937i	0.706869	+	0.612505i
$538$	11.5094	+	1.65480i	0.496205	+	0.0713435i
$539$	−6.01870	+	16.1318i	−0.259244	+	0.694846i
$540$	0.676476	−	2.30386i	0.0291109	−	0.0991426i
$541$	−24.4289	−	7.17298i	−1.05028	−	0.308391i	−0.289351	−	0.957223i	$-0.593439\pi$
$541$	−24.4289	−	7.17298i	−1.05028	−	0.308391i	−0.760931	+	0.648833i	$0.775257\pi$
$542$	−19.5382	+	8.92282i	−0.839240	+	0.383268i
$543$	−5.99192	−	0.861507i	−0.257138	−	0.0369708i
$544$	−4.36486	+	5.03732i	−0.187142	+	0.215973i
$545$	9.25645	+	4.22728i	0.396503	+	0.181077i
$546$	−9.41638	−	1.69939i	−0.402984	−	0.0727272i
$547$	−3.77858	−	26.2806i	−0.161560	−	1.12368i	−0.895694	−	0.444671i	$-0.853320\pi$
$547$	−3.77858	−	26.2806i	−0.161560	−	1.12368i	0.734133	−	0.679005i	$-0.237589\pi$
$548$	2.06318	+	3.21037i	0.0881347	+	0.137140i
$549$	−8.37626	−	9.66672i	−0.357490	−	0.412566i
$550$	−0.530418	−	1.80644i	−0.0226171	−	0.0770267i
$551$	−7.00142			−0.298270
$552$	−4.09500	+	2.49619i	−0.174295	+	0.106245i
$553$	−0.511105	−	1.23409i	−0.0217344	−	0.0524789i
$554$	−8.65865	+	2.54241i	−0.367871	+	0.108017i
$555$	4.90330	+	5.65871i	0.208133	+	0.240199i
$556$	−9.69893	−	15.0918i	−0.411326	−	0.640036i
$557$	−22.9139	+	3.29453i	−0.970895	+	0.139594i	−0.609471	−	0.792808i	$-0.708618\pi$
$557$	−22.9139	+	3.29453i	−0.970895	+	0.139594i	−0.361423	+	0.932402i	$0.617709\pi$
$558$	1.60267	−	2.49380i	0.0678464	−	0.105571i
$559$	−8.44764	+	18.4978i	−0.357297	+	0.782372i
$560$	2.00651	−	6.02759i	0.0847906	−	0.254712i
$561$	−2.33322	+	16.2279i	−0.0985088	+	0.685144i
$562$	19.2396	−	8.78641i	0.811571	−	0.370632i
$563$	−4.06533	−	1.19369i	−0.171333	−	0.0503080i	0.194941	−	0.980815i	$-0.437549\pi$
$563$	−4.06533	−	1.19369i	−0.171333	−	0.0503080i	−0.366274	+	0.930507i	$0.619367\pi$
$564$	4.27251	+	1.25452i	0.179905	+	0.0528250i
$565$	0.429141	−	0.195982i	0.0180541	−	0.00824502i
$566$	−0.341681	+	2.37644i	−0.0143619	+	0.0998893i
$567$	0.835654	−	2.51032i	0.0350942	−	0.105423i
$568$	−6.44302	+	14.1083i	−0.270343	+	0.591969i
$569$	−6.11422	+	9.51392i	−0.256322	+	0.398844i	−0.945436	−	0.325809i	$-0.894363\pi$
$569$	−6.11422	+	9.51392i	−0.256322	+	0.398844i	0.689114	+	0.724653i	$0.258000\pi$
$570$	3.34797	−	0.481365i	0.140231	−	0.0201622i
$571$	12.0242	+	18.7101i	0.503199	+	0.782993i	0.996205	−	0.0870327i	$-0.0277385\pi$
$571$	12.0242	+	18.7101i	0.503199	+	0.782993i	−0.493006	+	0.870026i	$0.664102\pi$
$572$	5.82544	+	6.72292i	0.243574	+	0.281099i
$573$	13.5393	−	3.97550i	0.565613	−	0.166079i
$574$	−8.31275	−	20.0716i	−0.346968	−	0.837773i
$575$	2.71628	+	2.46912i	0.113277	+	0.102969i
$576$	−1.00000			−0.0416667
$577$	7.52646	+	25.6328i	0.313330	+	1.06711i	0.954129	+	0.299396i	$0.0967852\pi$
$577$	7.52646	+	25.6328i	0.313330	+	1.06711i	−0.640798	+	0.767709i	$0.721397\pi$
$578$	−17.9606	−	20.7276i	−0.747061	−	0.862154i
$579$	−8.01991	−	12.4792i	−0.333296	−	0.518619i
$580$	−1.69841	−	11.8127i	−0.0705226	−	0.490496i
$581$	0.774647	+	0.139802i	0.0321378	+	0.00579997i
$582$	10.6220	+	4.85089i	0.440295	+	0.201076i
$583$	14.0957	−	16.2673i	0.583783	−	0.673722i
$584$	−13.3263	−	1.91603i	−0.551446	−	0.0792860i
$585$	7.89906	−	3.60738i	0.326586	−	0.149147i
$586$	15.0996	+	4.43365i	0.623760	+	0.183152i
$587$	−4.97897	+	16.9568i	−0.205504	+	0.699882i	0.790651	+	0.612268i	$0.209743\pi$
$587$	−4.97897	+	16.9568i	−0.205504	+	0.699882i	−0.996154	+	0.0876144i	$0.972076\pi$
$588$	2.44691	−	6.55840i	0.100909	−	0.270464i
$589$	4.13333	+	0.594284i	0.170311	+	0.0244870i
$590$	−9.98269	−	8.65005i	−0.410981	−	0.356117i
$591$	24.8616	+	11.3539i	1.02267	+	0.467037i
$592$	1.68590	−	2.62332i	0.0692903	−	0.107818i
$593$	−10.4697	+	1.50532i	−0.429941	+	0.0618161i	−0.353888	−	0.935288i	$-0.615141\pi$
$593$	−10.4697	+	1.50532i	−0.429941	+	0.0618161i	−0.0760524	+	0.997104i	$0.524232\pi$
$594$	−2.06925	+	1.32982i	−0.0849022	+	0.0545633i
$595$	37.8636	+	18.9555i	1.55225	+	0.777101i
$596$	−3.48036	−	11.8530i	−0.142561	−	0.485519i
$597$		−	4.92589i		−	0.201603i
$598$	−16.5210	−	5.28066i	−0.675592	−	0.215942i
$599$	8.53087			0.348562			0.174281	−	0.984696i	$-0.444240\pi$
$599$	8.53087			0.348562			0.174281	+	0.984696i	$0.444240\pi$
$600$	0.215642	+	0.734408i	0.00880354	+	0.0299821i
$601$	28.9879	−	25.1181i	1.18244	−	1.02459i	0.183303	−	0.983056i	$-0.441321\pi$
$601$	28.9879	−	25.1181i	1.18244	−	1.02459i	0.999137	−	0.0415336i	$-0.0132243\pi$
$602$	−12.2196	−	8.48516i	−0.498035	−	0.345829i
$603$	3.01279	−	0.433174i	0.122690	−	0.0176402i
$604$	5.99988	+	3.85589i	0.244132	+	0.156894i
$605$	4.93724	−	10.8111i	0.200727	−	0.439532i
$606$	1.49574	−	1.72618i	0.0607604	−	0.0701212i
$607$	−45.4487	−	6.53454i	−1.84471	−	0.265229i	−0.870710	−	0.491796i	$-0.836340\pi$
$607$	−45.4487	−	6.53454i	−1.84471	−	0.265229i	−0.973995	+	0.226568i	$0.927250\pi$
$608$	−0.585182	−	1.28137i	−0.0237323	−	0.0519664i
$609$	−1.40501	−	13.0747i	−0.0569340	−	0.529815i
$610$	29.4685	+	8.65274i	1.19315	+	0.350339i
$611$	6.68988	+	14.6488i	0.270644	+	0.592627i
$612$	0.948574	−	6.59748i	0.0383438	−	0.266687i
$613$	3.45400	+	2.99291i	0.139506	+	0.120882i	0.721818	−	0.692082i	$-0.243307\pi$
$613$	3.45400	+	2.99291i	0.139506	+	0.120882i	−0.582313	+	0.812965i	$0.697852\pi$
$614$	−8.16437	−	3.72854i	−0.329487	−	0.150472i
$615$	16.5864	+	10.6594i	0.668827	+	0.429829i
$616$	−5.59697	+	3.32045i	−0.225508	+	0.133785i
$617$	20.9525	+	32.6028i	0.843517	+	1.31254i	0.948084	+	0.318020i	$0.103018\pi$
$617$	20.9525	+	32.6028i	0.843517	+	1.31254i	−0.104567	+	0.994518i	$0.533346\pi$
$618$	4.82944	−	4.18473i	0.194269	−	0.168335i
$619$	13.8717	−	4.07309i	0.557549	−	0.163711i	0.00919539	−	0.999958i	$-0.497073\pi$
$619$	13.8717	−	4.07309i	0.557549	−	0.163711i	0.548354	+	0.836247i	$0.315255\pi$
$620$			7.11787i			0.285861i
$621$	2.09539	−	4.31385i	0.0840851	−	0.173109i
$622$		−	11.0034i		−	0.441197i
$623$	−9.21237	+	7.42303i	−0.369086	+	0.297397i
$624$	−2.36834	−	2.73321i	−0.0948094	−	0.109416i
$625$	−23.7580	+	15.2683i	−0.950321	+	0.610734i
$626$	0.772281	+	5.37133i	0.0308666	+	0.214682i
$627$	−2.91488	−	1.87328i	−0.116409	−	0.0748116i
$628$	−1.93491	+	4.23685i	−0.0772112	+	0.169069i
$629$	15.7081	+	13.6111i	0.626322	+	0.542712i
$630$	1.57078	+	6.15553i	0.0625812	+	0.245242i
$631$	−37.4023	+	17.0810i	−1.48896	+	0.679986i	−0.983174	−	0.182673i	$-0.941525\pi$
$631$	−37.4023	+	17.0810i	−1.48896	+	0.679986i	−0.505787	+	0.862658i	$0.668798\pi$
$632$	0.142236	−	0.484413i	0.00565786	−	0.0192689i
$633$	6.45200	−	21.9735i	0.256444	−	0.873368i
$634$	−2.16243	−	4.73506i	−0.0858811	−	0.188053i
$635$	3.67437	−	25.5558i	0.145813	−	1.01415i
$636$	−5.73061	+	6.61347i	−0.227233	+	0.262241i
$637$	23.7206	−	8.84460i	0.939844	−	0.350436i
$638$	−6.60954	+	10.2846i	−0.261674	+	0.407173i
$639$	−2.20728	−	15.3520i	−0.0873187	−	0.607315i
$640$	2.01996	−	1.29815i	0.0798458	−	0.0513138i
$641$	24.4216	−	21.1615i	0.964596	−	0.835827i	−0.0218753	−	0.999761i	$-0.506964\pi$
$641$	24.4216	−	21.1615i	0.964596	−	0.835827i	0.986471	+	0.163933i	$0.0524182\pi$
$642$	10.9636	−	3.21920i	0.432698	−	0.127052i
$643$	−40.2738			−1.58825			−0.794123	−	0.607758i	$-0.792069\pi$
$643$	−40.2738			−1.58825			−0.794123	+	0.607758i	$0.792069\pi$
$644$	5.94828	−	11.2079i	0.234395	−	0.441655i
$645$	13.5012			0.531611
$646$	9.00890	−	2.64525i	0.354451	−	0.104076i
$647$	−23.5367	+	20.3946i	−0.925322	+	0.801796i	−0.980467	−	0.196682i	$-0.936983\pi$
$647$	−23.5367	+	20.3946i	−0.925322	+	0.801796i	0.0551454	+	0.998478i	$0.482438\pi$
$648$	0.841254	−	0.540641i	0.0330476	−	0.0212384i
$649$	1.92570	+	13.3936i	0.0755905	+	0.525743i
$650$	−1.49658	+	2.32872i	−0.0587006	+	0.0913399i
$651$	−0.280331	+	7.83802i	−0.0109870	+	0.307196i
$652$	−9.30221	+	10.7353i	−0.364303	+	0.420428i
$653$	−2.80403	+	19.5025i	−0.109730	+	0.763190i	0.858443	+	0.512909i	$0.171432\pi$
$653$	−2.80403	+	19.5025i	−0.109730	+	0.763190i	−0.968173	+	0.250281i	$0.919477\pi$
$654$	1.76054	+	3.85504i	0.0688425	+	0.150744i
$655$	−10.1885	+	34.6988i	−0.398097	+	1.35580i
$656$	2.31337	−	7.87863i	0.0903221	−	0.307609i
$657$	12.2467	−	5.59287i	0.477789	−	0.218199i
$658$	−11.4154	+	2.91300i	−0.445019	+	0.113561i
$659$	−30.6043	−	26.5188i	−1.19217	−	1.03303i	−0.998651	−	0.0519294i	$-0.983463\pi$
$659$	−30.6043	−	26.5188i	−1.19217	−	1.03303i	−0.193524	−	0.981096i	$-0.561992\pi$
$660$	2.45348	−	5.37237i	0.0955016	−	0.209119i
$661$	14.9433	+	9.60346i	0.581226	+	0.373531i	0.797970	−	0.602697i	$-0.205907\pi$
$661$	14.9433	+	9.60346i	0.581226	+	0.373531i	−0.216744	+	0.976229i	$0.569544\pi$
$662$	−4.64984	−	32.3404i	−0.180721	−	1.25694i
$663$	20.2788	−	13.0324i	0.787564	−	0.506137i
$664$	0.194834	+	0.224850i	0.00756101	+	0.00872587i
$665$	−6.96832	+	5.61485i	−0.270220	+	0.217735i
$666$			3.11835i			0.120833i
$667$	0.566574	−	23.8297i	0.0219378	−	0.922689i
$668$		−	12.3578i		−	0.478136i
$669$	7.48011	−	2.19636i	0.289198	−	0.0849161i
$670$	−5.52338	+	4.78604i	−0.213387	+	0.184901i
$671$	−17.0096	−	26.4675i	−0.656650	−	1.02177i
$672$	2.27545	−	1.34993i	0.0877775	−	0.0520748i
$673$	10.9866	+	7.06065i	0.423501	+	0.272168i	0.734985	−	0.678084i	$-0.237189\pi$
$673$	10.9866	+	7.06065i	0.423501	+	0.272168i	−0.311483	+	0.950252i	$0.600826\pi$
$674$	20.3659	+	9.30080i	0.784465	+	0.358253i
$675$	−0.578461	−	0.501239i	−0.0222650	−	0.0192927i
$676$	0.0113063	−	0.0786372i	0.000434859	−	0.00302451i
$677$	14.3865	+	31.5020i	0.552917	+	1.21072i	0.955406	+	0.295295i	$0.0954179\pi$
$677$	14.3865	+	31.5020i	0.552917	+	1.21072i	−0.402489	+	0.915425i	$0.631855\pi$
$678$	0.188521	+	0.0553548i	0.00724012	+	0.00212589i
$679$	−30.7182	+	3.30098i	−1.17886	+	0.126680i
$680$	6.64842	+	14.5580i	0.254955	+	0.558274i
$681$	−10.2743	−	1.47722i	−0.393710	−	0.0566070i
$682$	4.77495	−	5.51059i	0.182842	−	0.211011i
$683$	7.59330	−	16.6270i	0.290550	−	0.636215i	−0.706921	−	0.707292i	$-0.749916\pi$
$683$	7.59330	−	16.6270i	0.290550	−	0.636215i	0.997471	+	0.0710774i	$0.0226437\pi$
$684$	1.18505	+	0.761584i	0.0453114	+	0.0291199i
$685$	9.06985	−	1.30405i	0.346541	−	0.0498251i
$686$	3.28558	+	18.2265i	0.125444	+	0.695891i
$687$	−0.423473	+	0.366942i	−0.0161565	+	0.0139997i
$688$	−1.58415	−	5.39511i	−0.0603951	−	0.205687i
$689$	−31.6480			−1.20569
$690$	1.36742	+	11.4339i	0.0520569	+	0.435282i
$691$			4.11954i			0.156715i	0.996925	+	0.0783574i	$0.0249675\pi$
$691$			4.11954i			0.156715i	−0.996925	+	0.0783574i	$0.975032\pi$
$692$	−6.74082	−	22.9571i	−0.256247	−	0.872699i
$693$	2.91330	−	5.81929i	0.110667	−	0.221057i
$694$	−19.4310	+	12.4876i	−0.737592	+	0.474022i
$695$	−42.6370	+	6.13028i	−1.61731	+	0.232535i
$696$	2.68711	−	4.18123i	0.101855	−	0.158489i
$697$	49.7847	+	22.7359i	1.88573	+	0.861184i
$698$	−14.8383	−	12.8574i	−0.561636	−	0.486660i
$699$	−1.44408	−	0.207628i	−0.0546203	−	0.00785321i
$700$	−1.48208	−	1.38001i	−0.0560175	−	0.0521594i
$701$	2.86883	−	9.77032i	0.108354	−	0.369020i	−0.887408	−	0.460984i	$-0.847496\pi$
$701$	2.86883	−	9.77032i	0.108354	−	0.369020i	0.995762	+	0.0919644i	$0.0293146\pi$
$702$	3.47006	+	1.01890i	0.130969	+	0.0384559i
$703$	−3.99575	+	1.82480i	−0.150703	+	0.0688236i
$704$	−2.43468	−	0.350054i	−0.0917605	−	0.0131932i
$705$	7.00174	−	8.08044i	0.263701	−	0.304327i
$706$	1.44847	+	0.661493i	0.0545138	+	0.0248956i
$707$	−1.07326	+	5.94699i	−0.0403642	+	0.223659i
$708$	−0.782897	−	5.44517i	−0.0294231	−	0.204642i
$709$	−17.9631	−	27.9511i	−0.674618	−	1.04973i	−0.994748	−	0.102352i	$-0.967363\pi$
$709$	−17.9631	−	27.9511i	−0.674618	−	1.04973i	0.320130	−	0.947373i	$-0.396273\pi$
$710$	24.3877	+	28.1450i	0.915256	+	1.05626i
$711$	0.142236	+	0.484413i	0.00533428	+	0.0181669i
$712$	−4.47164			−0.167582
$713$	−2.35716	+	14.0199i	−0.0882762	+	0.525050i
$714$	6.74772	+	16.2928i	0.252527	+	0.609741i
$715$	20.4945	−	6.01772i	0.766450	−	0.225050i
$716$	−14.1937	−	16.3805i	−0.530445	−	0.612167i
$717$	−15.1708	−	23.6063i	−0.566565	−	0.881593i
$718$	−4.29578	+	0.617639i	−0.160317	+	0.0230501i
$719$	−10.6523	+	16.5752i	−0.397262	+	0.618152i	−0.981050	−	0.193754i	$-0.937934\pi$
$719$	−10.6523	+	16.5752i	−0.397262	+	0.618152i	0.583788	+	0.811906i	$0.301570\pi$
$720$	−0.997464	+	2.18414i	−0.0371733	+	0.0813982i
$721$	−5.34005	+	16.0416i	−0.198874	+	0.597420i
$722$	2.42158	−	16.8425i	0.0901219	−	0.626811i
$723$	16.6114	−	7.58615i	0.617783	−	0.282132i
$724$	5.80832	+	1.70548i	0.215865	+	0.0633836i
$725$	−3.65019	−	1.07179i	−0.135564	−	0.0398053i
$726$	4.50249	−	2.05622i	0.167103	−	0.0763134i
$727$	6.30408	−	43.8459i	0.233806	−	1.62615i	−0.447591	−	0.894239i	$-0.647718\pi$
$727$	6.30408	−	43.8459i	0.233806	−	1.62615i	0.681396	−	0.731915i	$-0.261373\pi$
$728$	9.07869	+	3.02218i	0.336478	+	0.112010i
$729$	−0.415415	+	0.909632i	−0.0153857	+	0.0336901i
$730$	−17.4774	+	27.1954i	−0.646868	+	1.00655i
$731$	37.0968	−	5.33372i	1.37208	−	0.197275i
$732$	6.91528	+	10.7604i	0.255596	+	0.397716i
$733$	−5.38369	−	6.21311i	−0.198851	−	0.229486i	0.647563	−	0.762012i	$-0.275788\pi$
$733$	−5.38369	−	6.21311i	−0.198851	−	0.229486i	−0.846414	+	0.532526i	$0.821243\pi$
$734$	3.02725	−	0.888881i	0.111738	−	0.0328092i
$735$	−11.8838	−	11.8862i	−0.438340	−	0.438428i
$736$	4.40856	−	1.88801i	0.162502	−	0.0695928i
$737$	7.48681			0.275780
$738$	2.31337	+	7.87863i	0.0851565	+	0.290016i
$739$	30.7215	+	35.4546i	1.13011	+	1.30422i	0.947039	+	0.321117i	$0.104058\pi$
$739$	30.7215	+	35.4546i	1.13011	+	1.30422i	0.183071	+	0.983100i	$0.441396\pi$
$740$	−4.04807	−	6.29892i	−0.148810	−	0.231553i
$741$	0.725026	+	5.04267i	0.0266345	+	0.185247i
$742$	4.11198	−	22.7846i	0.150955	−	0.836448i
$743$	−40.3843	−	18.4429i	−1.48156	−	0.676604i	−0.499694	−	0.866202i	$-0.666554\pi$
$743$	−40.3843	−	18.4429i	−1.48156	−	0.676604i	−0.981862	+	0.189598i	$0.939281\pi$
$744$	−1.94126	+	2.24033i	−0.0711701	+	0.0821346i
$745$	−29.3602	−	4.22137i	−1.07568	−	0.154659i
$746$	−20.3749	+	9.30489i	−0.745977	+	0.340676i
$747$	−0.285467	−	0.0838208i	−0.0104447	−	0.00306684i
$748$	4.61895	−	15.7307i	0.168886	−	0.575171i
$749$	−20.6014	+	22.1252i	−0.752758	+	0.808438i
$750$	−10.0643	−	1.44703i	−0.367496	−	0.0528379i
$751$	15.9106	+	13.7866i	0.580587	+	0.503081i	0.894917	−	0.446232i	$-0.147235\pi$
$751$	15.9106	+	13.7866i	0.580587	+	0.503081i	−0.314330	+	0.949314i	$0.601780\pi$
$752$	−4.05049	−	1.84980i	−0.147706	−	0.0674551i
$753$	−13.9505	+	21.7075i	−0.508386	+	0.791064i
$754$	17.7922	−	2.55813i	0.647952	−	0.0931615i
$755$	14.4065	−	9.25848i	0.524305	−	0.336951i
$756$	−1.18440	+	2.36584i	−0.0430763	+	0.0860447i
$757$	−13.6941	−	46.6379i	−0.497721	−	1.69508i	−0.698639	−	0.715474i	$-0.746211\pi$
$757$	−13.6941	−	46.6379i	−0.497721	−	1.69508i	0.200918	−	0.979608i	$-0.435607\pi$
$758$		−	3.12357i		−	0.113453i
$759$	6.61169	−	9.76936i	0.239989	−	0.354605i
$760$	−3.38239			−0.122692
$761$	−12.5617	−	42.7812i	−0.455361	−	1.55082i	−0.792807	−	0.609473i	$-0.791381\pi$
$761$	−12.5617	−	42.7812i	−0.455361	−	1.55082i	0.337445	−	0.941345i	$-0.390437\pi$
$762$	8.12635	−	7.04153i	0.294387	−	0.255088i
$763$	−9.21007	−	6.39535i	−0.333427	−	0.231527i
$764$	−13.9673	+	2.00819i	−0.505319	+	0.0726539i
$765$	−13.4637	−	8.65257i	−0.486780	−	0.312834i
$766$	6.78074	−	14.8477i	0.244998	−	0.536471i
$767$	13.0286	−	15.0358i	0.470436	−	0.542912i
$768$	0.989821	+	0.142315i	0.0357171	+	0.00513534i
$769$	10.1720	+	22.2736i	0.366811	+	0.803205i	0.999583	+	0.0288666i	$0.00918980\pi$
$769$	10.1720	+	22.2736i	0.366811	+	0.803205i	−0.632772	+	0.774338i	$0.718083\pi$
$770$	1.66957	+	15.5366i	0.0601670	+	0.559900i
$771$	0.286608	+	0.0841557i	0.0103219	+	0.00303079i
$772$	6.16230	+	13.4936i	0.221786	+	0.485643i
$773$	5.94387	−	41.3405i	0.213786	−	1.48691i	−0.546573	−	0.837411i	$-0.684068\pi$
$773$	5.94387	−	41.3405i	0.213786	−	1.48691i	0.760359	−	0.649503i	$-0.225023\pi$
$774$	4.24949	+	3.68220i	0.152745	+	0.132354i
$775$	2.06394	+	0.942568i	0.0741388	+	0.0338581i
$776$	−9.82351	−	6.31318i	−0.352643	−	0.226630i
$777$	−4.20956	−	7.09564i	−0.151017	−	0.254555i
$778$	11.8977	+	18.5132i	0.426553	+	0.663730i
$779$	−8.74170	+	7.57472i	−0.313204	+	0.271393i
$780$	−8.33205	+	2.44651i	−0.298335	+	0.0875991i
$781$		−	38.1498i		−	1.36511i
$782$	8.27423	+	30.8763i	0.295886	+	1.10414i
$783$			4.97024i			0.177622i
$784$	−3.35536	+	6.14342i	−0.119834	+	0.219408i
$785$	7.32389	+	8.45222i	0.261401	+	0.301673i
$786$	−12.6702	+	8.14266i	−0.451932	+	0.290439i
$787$	−5.08479	−	35.3655i	−0.181253	−	1.26064i	−0.853804	−	0.520594i	$-0.825711\pi$
$787$	−5.08479	−	35.3655i	−0.181253	−	1.26064i	0.672551	−	0.740051i	$-0.265199\pi$
$788$	−22.9927	−	14.7765i	−0.819081	−	0.526391i
$789$	10.8144	−	23.6803i	0.385005	−	0.843042i
$790$	−0.916151	−	0.793849i	−0.0325952	−	0.0282439i
$791$	−0.503696	+	0.128534i	−0.0179094	+	0.00457014i
$792$	2.23744	−	1.02180i	0.0795039	−	0.0363082i
$793$	−13.0327	+	44.3851i	−0.462803	+	1.57616i
$794$	−0.590630	+	2.01150i	−0.0209607	+	0.0713856i
$795$	8.72869	+	19.1132i	0.309575	+	0.677874i
$796$	−0.701028	+	4.87576i	−0.0248473	+	0.172817i
$797$	−22.7591	+	26.2654i	−0.806168	+	0.930368i	−0.998703	−	0.0509223i	$-0.983784\pi$
$797$	−22.7591	+	26.2654i	−0.806168	+	0.930368i	0.192534	+	0.981290i	$0.438329\pi$
$798$	−3.72461	−	0.133212i	−0.131850	−	0.00471567i
$799$	16.0462	−	24.9683i	0.567673	−	0.883317i
$800$	−0.108930	−	0.757622i	−0.00385124	−	0.0267860i
$801$	3.76178	−	2.41755i	0.132916	−	0.0854200i
$802$	−3.11045	+	2.69522i	−0.109834	+	0.0951715i
$803$	31.7746	−	9.32986i	1.12130	−	0.329244i
$804$	−3.04377			−0.107346
$805$	−18.5465	−	24.1714i	−0.653680	−	0.851931i
$806$	−10.7209			−0.377626
$807$	11.1567	−	3.27591i	0.392736	−	0.115318i
$808$	−1.72618	+	1.49574i	−0.0607267	+	0.0526200i
$809$	30.1380	−	19.3685i	1.05959	−	0.680960i	0.109838	−	0.993950i	$-0.464967\pi$
$809$	30.1380	−	19.3685i	1.05959	−	0.680960i	0.949756	+	0.312990i	$0.101331\pi$
$810$	−0.341716	−	2.37669i	−0.0120067	−	0.0835083i
$811$	17.0137	−	26.4739i	0.597433	−	0.929624i	−0.402466	−	0.915435i	$-0.631847\pi$
$811$	17.0137	−	26.4739i	0.597433	−	0.929624i	0.999899	−	0.0141894i	$-0.00451678\pi$
$812$	−0.470016	+	13.1416i	−0.0164943	+	0.461180i
$813$	−14.0659	+	16.2330i	−0.493314	+	0.569315i
$814$	−1.09159	+	7.59217i	−0.0382602	+	0.266106i
$815$	14.1689	+	31.0255i	0.496313	+	1.08677i
$816$	−1.87784	+	6.39533i	−0.0657375	+	0.223881i
$817$	−2.23154	+	7.59993i	−0.0780717	+	0.265888i
$818$	−5.92658	+	2.70658i	−0.207218	+	0.0946334i
$819$	−9.27139	+	2.36588i	−0.323969	+	0.0826707i
$820$	−14.9005	−	12.9114i	−0.520350	−	0.450885i
$821$	−13.7547	+	30.1186i	−0.480042	+	1.05115i	0.502410	+	0.864630i	$0.332447\pi$
$821$	−13.7547	+	30.1186i	−0.480042	+	1.05115i	−0.982452	+	0.186516i	$0.940280\pi$
$822$	3.21037	+	2.06318i	0.111975	+	0.0719617i
$823$	4.03659	+	28.0751i	0.140707	+	0.978637i	0.930768	+	0.365609i	$0.119139\pi$
$823$	4.03659	+	28.0751i	0.140707	+	0.978637i	−0.790062	+	0.613027i	$0.789952\pi$
$824$	−5.37583	+	3.45484i	−0.187276	+	0.120355i
$825$	−1.23291	−	1.42285i	−0.0429243	−	0.0495373i
$826$	9.13205	+	11.3334i	0.317745	+	0.394338i
$827$			6.50099i			0.226062i	0.993591	+	0.113031i	$0.0360559\pi$
$827$			6.50099i			0.226062i	−0.993591	+	0.113031i	$0.963944\pi$
$828$	−2.68799	+	3.97174i	−0.0934140	+	0.138028i
$829$		−	20.6491i		−	0.717174i	−0.933496	−	0.358587i	$-0.883259\pi$
$829$		−	20.6491i		−	0.717174i	0.933496	−	0.358587i	$-0.116741\pi$
$830$	0.685444	−	0.201264i	0.0237921	−	0.00698599i
$831$	−6.82003	+	5.90959i	−0.236584	+	0.205001i
$832$	1.95526	+	3.04244i	0.0677863	+	0.105478i
$833$	−37.3482	−	27.9644i	−1.29404	−	0.968910i
$834$	−15.0918	−	9.69893i	−0.522587	−	0.335846i
$835$	−26.9911	−	12.3264i	−0.934066	−	0.426574i
$836$	2.61862	+	2.26904i	0.0905667	+	0.0784765i
$837$	0.421876	−	2.93421i	0.0145822	−	0.101421i
$838$	9.15585	+	20.0485i	0.316284	+	0.692564i
$839$	5.27928	+	1.55014i	0.182261	+	0.0535166i	0.371589	−	0.928397i	$-0.378813\pi$
$839$	5.27928	+	1.55014i	0.182261	+	0.0535166i	−0.189329	+	0.981914i	$0.560631\pi$
$840$	−0.678764	−	6.31642i	−0.0234196	−	0.217937i
$841$	−1.78493	−	3.90844i	−0.0615492	−	0.134774i
$842$	0.242651	+	0.0348880i	0.00836231	+	0.00120232i
$843$	13.8509	−	15.9848i	0.477051	−	0.550546i
$844$	−9.51349	+	20.8316i	−0.327468	+	0.717054i
$845$	−0.160477	−	0.103132i	−0.00552058	−	0.00354786i
$846$	4.40756	−	0.633712i	0.151535	−	0.0217875i
$847$	−7.46944	+	10.7569i	−0.256653	+	0.369611i
$848$	6.61347	−	5.73061i	0.227108	−	0.196790i
$849$	0.676406	+	2.30363i	0.0232142	+	0.0790603i
$850$	5.10173			0.174988
$851$	−5.88745	−	13.7474i	−0.201819	−	0.471256i
$852$			15.5098i			0.531359i
$853$	13.5683	+	46.2095i	0.464571	+	1.58218i	0.775241	+	0.631666i	$0.217629\pi$
$853$	13.5683	+	46.2095i	0.464571	+	1.58218i	−0.310669	+	0.950518i	$0.600553\pi$
$854$	−30.2612	−	15.1496i	−1.03552	−	0.518408i
$855$	2.84545	−	1.82866i	0.0973123	−	0.0625388i
$856$	−11.3101	+	1.62615i	−0.386572	+	0.0555807i
$857$	3.39135	−	5.27704i	0.115846	−	0.180260i	−0.778488	−	0.627659i	$-0.784013\pi$
$857$	3.39135	−	5.27704i	0.115846	−	0.180260i	0.894334	+	0.447399i	$0.147650\pi$
$858$	8.09181	+	3.69540i	0.276250	+	0.126159i
$859$	−3.39223	−	2.93938i	−0.115741	−	0.100290i	0.595067	−	0.803676i	$-0.297125\pi$
$859$	−3.39223	−	2.93938i	−0.115741	−	0.100290i	−0.710809	+	0.703385i	$0.751671\pi$
$860$	−13.3638	−	1.92143i	−0.455703	−	0.0655201i
$861$	−15.8996	−	14.8045i	−0.541857	−	0.504538i
$862$	6.04406	−	20.5842i	0.205861	−	0.701100i
$863$	0.321975	+	0.0945405i	0.0109602	+	0.00321820i	0.287208	−	0.957868i	$-0.407273\pi$
$863$	0.321975	+	0.0945405i	0.0109602	+	0.00321820i	−0.276248	+	0.961086i	$0.589091\pi$
$864$	−0.909632	+	0.415415i	−0.0309463	+	0.0141327i
$865$	−56.8653	−	8.17600i	−1.93348	−	0.277992i
$866$	−4.80125	+	5.54094i	−0.163153	+	0.188289i
$867$	−24.9481	−	11.3934i	−0.847280	−	0.386940i
$868$	1.39294	−	7.71834i	0.0472796	−	0.261978i
$869$	0.176730	+	1.22918i	0.00599514	+	0.0416971i
$870$	−6.45210	−	10.0397i	−0.218747	−	0.340377i
$871$	−7.20868	−	8.31926i	−0.244257	−	0.281887i
$872$	−1.19399	−	4.06635i	−0.0404336	−	0.137704i
$873$	11.6772			0.395214
$874$	−6.66223	−	1.12011i	−0.225353	−	0.0378884i
$875$	24.8542	−	10.2935i	0.840225	−	0.347983i
$876$	−12.9180	+	3.79306i	−0.436458	+	0.128156i
$877$	12.5415	+	14.4737i	0.423498	+	0.488742i	0.926899	−	0.375310i	$-0.122464\pi$
$877$	12.5415	+	14.4737i	0.423498	+	0.488742i	−0.503402	+	0.864053i	$0.667918\pi$
$878$	15.6836	+	24.4041i	0.529294	+	0.823598i
$879$	15.5769	−	2.23962i	0.525396	−	0.0755406i
$880$	−3.19308	+	4.96852i	−0.107639	+	0.167489i
$881$	−14.6211	+	32.0157i	−0.492596	+	1.07864i	0.486209	+	0.873842i	$0.338379\pi$
$881$	−14.6211	+	32.0157i	−0.492596	+	1.07864i	−0.978805	+	0.204793i	$0.934348\pi$
$882$	−0.498671	−	6.98222i	−0.0167911	−	0.235103i
$883$	−7.11509	+	49.4865i	−0.239442	+	1.66535i	0.415438	+	0.909621i	$0.363628\pi$
$883$	−7.11509	+	49.4865i	−0.239442	+	1.66535i	−0.654880	+	0.755733i	$0.727281\pi$
$884$	−21.9271	+	10.0138i	−0.737489	+	0.336800i
$885$	−12.6739	−	3.72140i	−0.426029	−	0.125094i
$886$	−23.6851	−	6.95459i	−0.795718	−	0.233644i
$887$	9.25810	−	4.22803i	0.310857	−	0.141963i	−0.253877	−	0.967236i	$-0.581706\pi$
$887$	9.25810	−	4.22803i	0.310857	−	0.141963i	0.564734	+	0.825273i	$0.308979\pi$
$888$	0.443787	−	3.08660i	0.0148925	−	0.103580i
$889$	−8.98554	+	26.9927i	−0.301365	+	0.905306i
$890$	−4.46030	+	9.76670i	−0.149510	+	0.327381i
$891$	−1.32982	+	2.06925i	−0.0445508	+	0.0693223i
$892$	−7.71654	+	1.10947i	−0.258369	+	0.0371479i
$893$	3.39125	+	5.27688i	0.113484	+	0.176584i
$894$	−8.08978	−	9.33610i	−0.270563	−	0.312246i
$895$	−49.9350	+	14.6622i	−1.66914	+	0.490105i
$896$	−2.44441	+	1.01236i	−0.0816619	+	0.0338206i
$897$	−17.2217	+	2.05960i	−0.575014	+	0.0687680i
$898$	−23.2416			−0.775583
$899$	−4.15096	−	14.1369i	−0.138442	−	0.471492i
$900$	0.501239	+	0.578461i	0.0167080	+	0.0192820i
$901$	31.5342	+	49.0682i	1.05056	+	1.63470i
$902$	2.87438	+	19.9918i	0.0957064	+	0.665653i
$903$	−14.6402	−	2.64215i	−0.487196	−	0.0879252i
$904$	−0.178725	−	0.0816208i	−0.00594429	−	0.00271467i
$905$	9.51860	−	10.9850i	0.316409	−	0.365155i
$906$	7.05948	+	1.01500i	0.234535	+	0.0337211i
$907$	13.3030	−	6.07526i	0.441718	−	0.201726i	−0.182125	−	0.983275i	$-0.558298\pi$
$907$	13.3030	−	6.07526i	0.441718	−	0.201726i	0.623843	+	0.781550i	$0.285570\pi$
$908$	9.95945	+	2.92436i	0.330516	+	0.0970483i
$909$	0.643494	−	2.19154i	0.0213434	−	0.0726888i
$910$	15.6565	−	16.8146i	0.519009	−	0.557399i
$911$	5.16583	+	0.742734i	0.171152	+	0.0246079i	0.227358	−	0.973811i	$-0.426991\pi$
$911$	5.16583	+	0.742734i	0.171152	+	0.0246079i	−0.0562062	+	0.998419i	$0.517900\pi$
$912$	−1.06460	−	0.922482i	−0.0352525	−	0.0305464i
$913$	−0.665680	−	0.304006i	−0.0220308	−	0.0100611i
$914$	−9.41068	+	14.6433i	−0.311278	+	0.484357i
$915$	30.4000	−	4.37086i	1.00499	−	0.144496i
$916$	0.471384	−	0.302940i	0.0155750	−	0.0100094i
$917$	17.8385	−	35.6322i	0.589078	−	1.17668i
$918$	−1.87784	−	6.39533i	−0.0619779	−	0.211077i
$919$		−	29.5946i		−	0.976237i	−0.872777	−	0.488118i	$-0.837683\pi$
$919$		−	29.5946i		−	0.976237i	0.872777	−	0.488118i	$-0.162317\pi$
$920$	0.273713	−	11.5121i	0.00902404	−	0.379544i
$921$	−8.97547			−0.295752
$922$	−9.14080	−	31.1307i	−0.301036	−	1.02524i
$923$	−42.3916	+	36.7326i	−1.39534	+	1.20907i
$924$	−3.71181	+	5.34545i	−0.122110	+	0.175853i
$925$	−2.36253	+	0.339680i	−0.0776794	+	0.0111686i
$926$	21.0755	+	13.5444i	0.692584	+	0.445096i
$927$	2.65461	−	5.81279i	0.0871889	−	0.190917i
$928$	−3.25481	+	3.75626i	−0.106845	+	0.123305i
$929$	9.15093	+	1.31570i	0.300232	+	0.0431669i	0.290785	−	0.956788i	$-0.406084\pi$
$929$	9.15093	+	1.31570i	0.300232	+	0.0431669i	0.00944746	+	0.999955i	$0.496993\pi$
$930$	2.95687	+	6.47464i	0.0969596	+	0.212312i
$931$	8.65499	−	4.72485i	0.283656	−	0.154851i
$932$	1.39984	+	0.411029i	0.0458532	+	0.0134637i
$933$	−4.57099	−	10.0091i	−0.149648	−	0.327682i
$934$	4.99349	−	34.7305i	0.163392	−	1.13642i
$935$	−29.7509	−	25.7793i	−0.972957	−	0.843072i
$936$	−3.28973	−	1.50237i	−0.107528	−	0.0491065i
$937$	36.7655	+	23.6277i	1.20108	+	0.771884i	0.979142	−	0.203177i	$-0.0651268\pi$
$937$	36.7655	+	23.6277i	1.20108	+	0.771884i	0.221934	+	0.975062i	$0.428763\pi$
$938$	6.92595	−	4.10889i	0.226140	−	0.134160i
$939$	2.93382	+	4.56512i	0.0957417	+	0.148977i
$940$	−8.08044	+	7.00174i	−0.263555	+	0.228371i
$941$	26.7261	−	7.84750i	0.871247	−	0.255821i	0.184601	−	0.982813i	$-0.440901\pi$
$941$	26.7261	−	7.84750i	0.871247	−	0.255821i	0.686646	+	0.726992i	$0.259082\pi$
$942$			4.65777i			0.151758i
$943$	−25.0736	−	30.3658i	−0.816507	−	0.988846i
$944$			5.50116i			0.179048i
$945$	3.98593	+	4.94674i	0.129662	+	0.160918i
$946$	9.05717	+	10.4525i	0.294474	+	0.339841i
$947$	22.7703	−	14.6336i	0.739935	−	0.475527i	−0.115585	−	0.993298i	$-0.536874\pi$
$947$	22.7703	−	14.6336i	0.739935	−	0.475527i	0.855520	+	0.517770i	$0.173238\pi$
$948$	−0.0718495	−	0.499725i	−0.00233356	−	0.0162303i
$949$	−40.9614	−	26.3243i	−1.32966	−	0.854522i
$950$	−0.447906	+	0.980777i	−0.0145320	+	0.0318206i
$951$	−3.93403	−	3.40886i	−0.127570	−	0.110540i
$952$	−4.36034	−	17.0872i	−0.141319	−	0.553800i
$953$	−41.4223	+	18.9169i	−1.34180	+	0.612780i	−0.951426	−	0.307876i	$-0.900382\pi$
$953$	−41.4223	+	18.9169i	−1.34180	+	0.612780i	−0.390375	+	0.920656i	$0.627654\pi$
$954$	−2.46541	+	8.39641i	−0.0798205	+	0.271844i
$955$	−9.54569	+	32.5096i	−0.308891	+	1.05199i
$956$	11.6569	+	25.5250i	0.377011	+	0.825539i
$957$	−1.73985	+	12.1009i	−0.0562415	+	0.391168i
$958$	−1.14855	+	1.32549i	−0.0371079	+	0.0428248i
$959$	−10.0902	−	0.360881i	−0.325829	−	0.0116535i
$960$	1.29815	−	2.01996i	0.0418975	−	0.0651938i
$961$	−3.16116	−	21.9863i	−0.101973	−	0.709236i
$962$	9.48737	−	6.09716i	0.305885	−	0.196580i
$963$	8.63552	−	7.48272i	0.278276	−	0.241127i
$964$	−17.5219	+	5.14489i	−0.564342	+	0.165706i
$965$	35.6185			1.14660
$966$	0.754801	−	12.6661i	0.0242853	−	0.407525i
$967$	42.1518			1.35551			0.677756	−	0.735287i	$-0.262953\pi$
$967$	42.1518			1.35551			0.677756	+	0.735287i	$0.262953\pi$
$968$	−4.74929	+	1.39452i	−0.152648	+	0.0448215i
$969$	7.09591	−	6.14864i	0.227953	−	0.197523i
$970$	−23.5875	+	15.1588i	−0.757349	+	0.486718i
$971$	−6.74819	−	46.9347i	−0.216560	−	1.50621i	−0.750605	−	0.660751i	$-0.770238\pi$
$971$	−6.74819	−	46.9347i	−0.216560	−	1.50621i	0.534046	−	0.845456i	$-0.320671\pi$
$972$	0.540641	−	0.841254i	0.0173411	−	0.0269832i
$973$	47.4336	+	1.69649i	1.52065	+	0.0543869i
$974$	−27.9982	+	32.3117i	−0.897121	+	1.03533i
$975$	−0.393950	+	2.73998i	−0.0126165	+	0.0877496i
$976$	−5.31353	−	11.6350i	−0.170082	−	0.372428i
$977$	3.80492	−	12.9584i	0.121730	−	0.414575i	−0.875969	−	0.482367i	$-0.839777\pi$
$977$	3.80492	−	12.9584i	0.121730	−	0.414575i	0.997699	+	0.0677921i	$0.0215955\pi$
$978$	−4.00198	+	13.6295i	−0.127969	+	0.435823i
$979$	10.0050	−	4.56914i	0.319762	−	0.146030i
$980$	10.0712	+	13.4564i	0.321714	+	0.429850i
$981$	3.20288	+	2.77531i	0.102260	+	0.0886090i
$982$	−1.63640	+	3.58321i	−0.0522196	+	0.114345i
$983$	0.0919855	+	0.0591155i	0.00293388	+	0.00188549i	0.542107	−	0.840310i	$-0.317627\pi$
$983$	0.0919855	+	0.0591155i	0.00293388	+	0.00188549i	−0.539173	+	0.842195i	$0.681263\pi$
$984$	−1.16858	−	8.12767i	−0.0372530	−	0.259101i
$985$	−55.2084	+	35.4803i	−1.75909	+	1.13050i
$986$	−21.6944	−	25.0367i	−0.690890	−	0.797330i
$987$	−9.17373	+	7.39190i	−0.292003	+	0.235287i
$988$		−	5.09452i		−	0.162078i
$989$	−25.6862	−	8.21017i	−0.816772	−	0.261068i
$990$		−	5.90609i		−	0.187708i
$991$	43.7183	−	12.8369i	1.38876	−	0.407776i	0.499950	−	0.866055i	$-0.333352\pi$
$991$	43.7183	−	12.8369i	1.38876	−	0.407776i	0.888809	+	0.458278i	$0.151534\pi$
$992$	2.24033	−	1.94126i	0.0711307	−	0.0616351i
$993$	−17.6643	−	27.4862i	−0.560560	−	0.872249i
$994$	−20.9373	−	35.2919i	−0.664089	−	1.11939i
$995$	9.95009	+	6.39454i	0.315439	+	0.202720i
$996$	0.270633	+	0.123594i	0.00857533	+	0.00391622i
$997$	−12.1046	−	10.4887i	−0.383355	−	0.332179i	0.441771	−	0.897128i	$-0.354350\pi$
$997$	−12.1046	−	10.4887i	−0.383355	−	0.332179i	−0.825126	+	0.564949i	$0.808896\pi$
$998$	1.65658	−	11.5218i	0.0524382	−	0.364716i
$999$	1.29541	+	2.83655i	0.0409849	+	0.0897444i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.s.a.727.2	yes	160
7.6	odd	2	inner	966.2.s.a.727.15	yes	160
23.5	odd	22	inner	966.2.s.a.97.15	yes	160
161.97	even	22	inner	966.2.s.a.97.2	✓	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.s.a.97.2	✓	160	161.97	even	22	inner
966.2.s.a.97.15	yes	160	23.5	odd	22	inner
966.2.s.a.727.2	yes	160	1.1	even	1	trivial
966.2.s.a.727.15	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)

\(f(q)\)	\(=\)	\(q+(-0.959493 + 0.281733i) q^{2} +(-0.755750 + 0.654861i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.341716 - 2.37669i) q^{5} +(0.540641 - 0.841254i) q^{6} +(-0.0945662 + 2.64406i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(-0.959493 + 0.281733i) q^{2} +(-0.755750 + 0.654861i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.341716 - 2.37669i) q^{5} +(0.540641 - 0.841254i) q^{6} +(-0.0945662 + 2.64406i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(0.142315 - 0.989821i) q^{9} +(0.997464 + 2.18414i) q^{10} +(0.692982 - 2.36008i) q^{11} +(-0.281733 + 0.959493i) q^{12} +(-3.28973 + 1.50237i) q^{13} +(-0.654182 - 2.56360i) q^{14} +(1.81465 + 1.57240i) q^{15} +(0.415415 - 0.909632i) q^{16} +(5.60723 + 3.60355i) q^{17} +(0.142315 + 0.989821i) q^{18} +(-1.18505 + 0.761584i) q^{19} +(-1.57240 - 1.81465i) q^{20} +(-1.66002 - 2.06018i) q^{21} +2.45972i q^{22} +(-2.49619 - 4.09500i) q^{23} -1.00000i q^{24} +(-0.734408 + 0.215642i) q^{25} +(2.73321 - 2.36834i) q^{26} +(0.540641 + 0.841254i) q^{27} +(1.34993 + 2.27545i) q^{28} +(4.18123 + 2.68711i) q^{29} +(-2.18414 - 0.997464i) q^{30} +(-2.24033 - 1.94126i) q^{31} +(-0.142315 + 0.989821i) q^{32} +(1.02180 + 2.23744i) q^{33} +(-6.39533 - 1.87784i) q^{34} +(6.31642 - 0.678764i) q^{35} +(-0.415415 - 0.909632i) q^{36} +(3.08660 + 0.443787i) q^{37} +(0.922482 - 1.06460i) q^{38} +(1.50237 - 3.28973i) q^{39} +(2.01996 + 1.29815i) q^{40} +(8.12767 - 1.16858i) q^{41} +(2.17320 + 1.50904i) q^{42} +(4.24949 - 3.68220i) q^{43} +(-0.692982 - 2.36008i) q^{44} -2.40113 q^{45} +(3.54877 + 3.22586i) q^{46} -4.45289i q^{47} +(0.281733 + 0.959493i) q^{48} +(-6.98211 - 0.500077i) q^{49} +(0.643906 - 0.413814i) q^{50} +(-6.59748 + 0.948574i) q^{51} +(-1.95526 + 3.04244i) q^{52} +(7.96008 + 3.63525i) q^{53} +(-0.755750 - 0.654861i) q^{54} +(-5.84598 - 0.840525i) q^{55} +(-1.93632 - 1.80296i) q^{56} +(0.396868 - 1.35161i) q^{57} +(-4.76891 - 1.40028i) q^{58} +(-5.00403 + 2.28526i) q^{59} +(2.37669 + 0.341716i) q^{60} +(8.37626 - 9.66672i) q^{61} +(2.69650 + 1.23145i) q^{62} +(2.60369 + 0.469893i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(4.69482 + 7.30528i) q^{65} +(-1.61077 - 1.85893i) q^{66} +(0.857529 + 2.92048i) q^{67} +6.66532 q^{68} +(4.56815 + 1.46014i) q^{69} +(-5.86933 + 2.43081i) q^{70} +(14.8816 - 4.36963i) q^{71} +(0.654861 + 0.755750i) q^{72} +(7.27883 + 11.3261i) q^{73} +(-3.08660 + 0.443787i) q^{74} +(0.413814 - 0.643906i) q^{75} +(-0.585182 + 1.28137i) q^{76} +(6.17466 + 2.05547i) q^{77} +(-0.514689 + 3.57974i) q^{78} +(-0.459240 + 0.209728i) q^{79} +(-2.30386 - 0.676476i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-7.46921 + 3.41107i) q^{82} +(0.0423414 - 0.294491i) q^{83} +(-2.51032 - 0.835654i) q^{84} +(6.64842 - 14.5580i) q^{85} +(-3.03996 + 4.73027i) q^{86} +(-4.91965 + 0.707339i) q^{87} +(1.32982 + 2.06925i) q^{88} +(2.92830 + 3.37944i) q^{89} +(2.30386 - 0.676476i) q^{90} +(-3.66126 - 8.84032i) q^{91} +(-4.31385 - 2.09539i) q^{92} +2.96439 q^{93} +(1.25452 + 4.27251i) q^{94} +(2.21500 + 2.55624i) q^{95} +(-0.540641 - 0.841254i) q^{96} +(1.66184 + 11.5584i) q^{97} +(6.84018 - 1.48727i) q^{98} +(-2.23744 - 1.02180i) 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

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