LMFDB - Embedded newform 490.2.p.a.239.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,2,Mod(29,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 6]))

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

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

chi := DirichletCharacter("490.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	490.p (of order $14$, degree $6$, 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:	$3.91266969904$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$28$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			239.7
Character	$\chi$	$=$	490.239
Dual form			490.2.p.a.449.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.781831 - 0.623490i) q^{2} +(-0.103853 + 0.215653i) q^{3} +(0.222521 + 0.974928i) q^{4} +(-1.67783 - 1.47813i) q^{5} +(0.215653 - 0.103853i) q^{6} +(-1.09132 + 2.41019i) q^{7} +(0.433884 - 0.900969i) q^{8} +(1.83475 + 2.30070i) q^{9} +O(q^{10})$	\(q+(-0.781831 - 0.623490i) q^{2} +(-0.103853 + 0.215653i) q^{3} +(0.222521 + 0.974928i) q^{4} +(-1.67783 - 1.47813i) q^{5} +(0.215653 - 0.103853i) q^{6} +(-1.09132 + 2.41019i) q^{7} +(0.433884 - 0.900969i) q^{8} +(1.83475 + 2.30070i) q^{9} +(0.390182 + 2.20176i) q^{10} +(2.57089 - 3.22379i) q^{11} +(-0.233356 - 0.0532620i) q^{12} +(-5.11802 - 4.08149i) q^{13} +(2.35596 - 1.20394i) q^{14} +(0.493013 - 0.208322i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(-3.47661 - 0.793513i) q^{17} -2.94271i q^{18} -3.34878 q^{19} +(1.06772 - 1.96468i) q^{20} +(-0.406429 - 0.485653i) q^{21} +(-4.02000 + 0.917539i) q^{22} +(-3.83716 + 0.875807i) q^{23} +(0.149237 + 0.187137i) q^{24} +(0.630247 + 4.96012i) q^{25} +(1.45667 + 6.38207i) q^{26} +(-1.38677 + 0.316520i) q^{27} +(-2.59260 - 0.527638i) q^{28} +(-0.0137595 + 0.0602842i) q^{29} +(-0.515339 - 0.144516i) q^{30} -7.12501 q^{31} +(0.974928 + 0.222521i) q^{32} +(0.428226 + 0.889221i) q^{33} +(2.22338 + 2.78802i) q^{34} +(5.39363 - 2.43079i) q^{35} +(-1.83475 + 2.30070i) q^{36} +(-0.607347 - 0.138623i) q^{37} +(2.61818 + 2.08793i) q^{38} +(1.41171 - 0.679844i) q^{39} +(-2.05974 + 0.870338i) q^{40} +(-9.16537 - 4.41381i) q^{41} +(0.0149597 + 0.633103i) q^{42} +(-0.738335 - 1.53317i) q^{43} +(3.71504 + 1.78907i) q^{44} +(0.322341 - 6.57220i) q^{45} +(3.54607 + 1.70770i) q^{46} +(8.91040 + 7.10581i) q^{47} -0.239357i q^{48} +(-4.61805 - 5.26057i) q^{49} +(2.59984 - 4.27093i) q^{50} +(0.532181 - 0.667334i) q^{51} +(2.84029 - 5.89792i) q^{52} +(-8.18697 + 1.86862i) q^{53} +(1.28156 + 0.617169i) q^{54} +(-9.07871 + 1.60887i) q^{55} +(1.69800 + 2.02899i) q^{56} +(0.347781 - 0.722175i) q^{57} +(0.0483442 - 0.0385532i) q^{58} +(11.3529 - 5.46727i) q^{59} +(0.312804 + 0.434296i) q^{60} +(-1.90248 + 8.33533i) q^{61} +(5.57056 + 4.44237i) q^{62} +(-7.54743 + 1.91130i) q^{63} +(-0.623490 - 0.781831i) q^{64} +(2.55421 + 14.4132i) q^{65} +(0.219619 - 0.962216i) q^{66} -11.8515i q^{67} -3.56602i q^{68} +(0.209631 - 0.918452i) q^{69} +(-5.73248 - 1.46241i) q^{70} +(-1.58243 - 6.93308i) q^{71} +(2.86893 - 0.654814i) q^{72} +(1.13206 - 0.902790i) q^{73} +(0.388413 + 0.487054i) q^{74} +(-1.13512 - 0.379209i) q^{75} +(-0.745173 - 3.26482i) q^{76} +(4.96430 + 9.71451i) q^{77} +(-1.52759 - 0.348663i) q^{78} -11.2657 q^{79} +(2.15301 + 0.603767i) q^{80} +(-1.88868 + 8.27485i) q^{81} +(4.41381 + 9.16537i) q^{82} +(2.98042 - 2.37680i) q^{83} +(0.383037 - 0.504307i) q^{84} +(4.66025 + 6.47027i) q^{85} +(-0.378661 + 1.65902i) q^{86} +(-0.0115715 - 0.00922798i) q^{87} +(-1.78907 - 3.71504i) q^{88} +(7.55418 + 9.47264i) q^{89} +(-4.34971 + 4.93737i) q^{90} +(15.4226 - 7.88122i) q^{91} +(-1.70770 - 3.54607i) q^{92} +(0.739955 - 1.53653i) q^{93} +(-2.53603 - 11.1111i) q^{94} +(5.61869 + 4.94994i) q^{95} +(-0.149237 + 0.187137i) q^{96} +2.68300i q^{97} +(0.330623 + 6.99219i) q^{98} +12.1339 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q + 28 q^{4} - 4 q^{5} + 14 q^{6} + 18 q^{9}+O(q^{10}) $ 168 * q + 28 * q^4 - 4 * q^5 + 14 * q^6 + 18 * q^9	$ 168 q + 28 q^{4} - 4 q^{5} + 14 q^{6} + 18 q^{9} - 4 q^{10} - 24 q^{11} + 4 q^{14} - 2 q^{15} - 28 q^{16} + 44 q^{19} - 10 q^{20} + 22 q^{26} - 2 q^{29} - 12 q^{30} - 16 q^{31} - 8 q^{34} - 4 q^{35} - 18 q^{36} - 80 q^{39} - 10 q^{40} + 52 q^{41} - 18 q^{44} - 72 q^{45} + 26 q^{46} - 52 q^{49} - 8 q^{50} + 64 q^{51} - 42 q^{54} - 60 q^{55} + 10 q^{56} - 58 q^{59} + 2 q^{60} + 32 q^{61} + 28 q^{64} + 4 q^{65} + 48 q^{66} - 48 q^{69} + 18 q^{70} - 68 q^{71} - 10 q^{74} - 16 q^{76} - 4 q^{80} + 34 q^{81} + 84 q^{84} - 48 q^{85} - 64 q^{86} + 100 q^{89} + 54 q^{90} + 78 q^{91} - 86 q^{94} - 64 q^{95} - 212 q^{99}+O(q^{100}) $ 168 * q + 28 * q^4 - 4 * q^5 + 14 * q^6 + 18 * q^9 - 4 * q^10 - 24 * q^11 + 4 * q^14 - 2 * q^15 - 28 * q^16 + 44 * q^19 - 10 * q^20 + 22 * q^26 - 2 * q^29 - 12 * q^30 - 16 * q^31 - 8 * q^34 - 4 * q^35 - 18 * q^36 - 80 * q^39 - 10 * q^40 + 52 * q^41 - 18 * q^44 - 72 * q^45 + 26 * q^46 - 52 * q^49 - 8 * q^50 + 64 * q^51 - 42 * q^54 - 60 * q^55 + 10 * q^56 - 58 * q^59 + 2 * q^60 + 32 * q^61 + 28 * q^64 + 4 * q^65 + 48 * q^66 - 48 * q^69 + 18 * q^70 - 68 * q^71 - 10 * q^74 - 16 * q^76 - 4 * q^80 + 34 * q^81 + 84 * q^84 - 48 * q^85 - 64 * q^86 + 100 * q^89 + 54 * q^90 + 78 * q^91 - 86 * q^94 - 64 * q^95 - 212 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{1}{7}\right)$	$-1$

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 $

$2$	−0.781831	−	0.623490i	−0.552838	−	0.440874i
$2$	−0.781831	−	0.623490i	−0.552838	−	0.440874i
$3$	−0.103853	+	0.215653i	−0.0599597	+	0.124508i	−0.928795	−	0.370593i	$-0.879154\pi$
$3$	−0.103853	+	0.215653i	−0.0599597	+	0.124508i	0.868836	+	0.495101i	$0.164869\pi$
$4$	0.222521	+	0.974928i	0.111260	+	0.487464i
$5$	−1.67783	−	1.47813i	−0.750350	−	0.661041i
$5$	−1.67783	−	1.47813i	−0.750350	−	0.661041i
$6$	0.215653	−	0.103853i	0.0880401	−	0.0423979i
$7$	−1.09132	+	2.41019i	−0.412480	+	0.910967i
$7$	−1.09132	+	2.41019i	−0.412480	+	0.910967i
$8$	0.433884	−	0.900969i	0.153401	−	0.318541i
$9$	1.83475	+	2.30070i	0.611583	+	0.766901i
$10$	0.390182	+	2.20176i	0.123386	+	0.696258i
$11$	2.57089	−	3.22379i	0.775151	−	0.972009i	−0.224846	−	0.974394i	$-0.572188\pi$
$11$	2.57089	−	3.22379i	0.775151	−	0.972009i	0.999997	+	0.00238541i	$0.000759299\pi$
$12$	−0.233356	−	0.0532620i	−0.0673641	−	0.0153754i
$13$	−5.11802	−	4.08149i	−1.41948	−	1.13200i	−0.971244	−	0.238088i	$-0.923479\pi$
$13$	−5.11802	−	4.08149i	−1.41948	−	1.13200i	−0.448241	−	0.893913i	$-0.647949\pi$
$14$	2.35596	−	1.20394i	0.629656	−	0.321766i
$15$	0.493013	−	0.208322i	0.127295	−	0.0537884i
$16$	−0.900969	+	0.433884i	−0.225242	+	0.108471i
$17$	−3.47661	−	0.793513i	−0.843202	−	0.192455i	−0.220962	−	0.975282i	$-0.570920\pi$
$17$	−3.47661	−	0.793513i	−0.843202	−	0.192455i	−0.622239	+	0.782827i	$0.713777\pi$
$18$		−	2.94271i		−	0.693603i
$19$	−3.34878			−0.768262			−0.384131	−	0.923279i	$-0.625499\pi$
$19$	−3.34878			−0.768262			−0.384131	+	0.923279i	$0.625499\pi$
$20$	1.06772	−	1.96468i	0.238749	−	0.439316i
$21$	−0.406429	−	0.485653i	−0.0886901	−	0.105978i
$22$	−4.02000	+	0.917539i	−0.857067	+	0.195620i
$23$	−3.83716	+	0.875807i	−0.800104	+	0.182618i	−0.602976	−	0.797759i	$-0.706019\pi$
$23$	−3.83716	+	0.875807i	−0.800104	+	0.182618i	−0.197128	+	0.980378i	$0.563161\pi$
$24$	0.149237	+	0.187137i	0.0304628	+	0.0381992i
$25$	0.630247	+	4.96012i	0.126049	+	0.992024i
$26$	1.45667	+	6.38207i	0.285676	+	1.25163i
$27$	−1.38677	+	0.316520i	−0.266883	+	0.0609144i
$28$	−2.59260	−	0.527638i	−0.489956	−	0.0997143i
$29$	−0.0137595	+	0.0602842i	−0.00255507	+	0.0111945i	−0.976189	−	0.216920i	$-0.930399\pi$
$29$	−0.0137595	+	0.0602842i	−0.00255507	+	0.0111945i	0.973634	+	0.228115i	$0.0732561\pi$
$30$	−0.515339	−	0.144516i	−0.0940876	−	0.0263849i
$31$	−7.12501			−1.27969			−0.639845	−	0.768504i	$-0.721001\pi$
$31$	−7.12501			−1.27969			−0.639845	+	0.768504i	$0.721001\pi$
$32$	0.974928	+	0.222521i	0.172345	+	0.0393365i
$33$	0.428226	+	0.889221i	0.0745446	+	0.154793i
$34$	2.22338	+	2.78802i	0.381306	+	0.478142i
$35$	5.39363	−	2.43079i	0.911690	−	0.410878i
$36$	−1.83475	+	2.30070i	−0.305791	+	0.383450i
$37$	−0.607347	−	0.138623i	−0.0998472	−	0.0227895i	0.172305	−	0.985044i	$-0.444878\pi$
$37$	−0.607347	−	0.138623i	−0.0998472	−	0.0227895i	−0.272153	+	0.962254i	$0.587736\pi$
$38$	2.61818	+	2.08793i	0.424725	+	0.338707i
$39$	1.41171	−	0.679844i	0.226054	−	0.108862i
$40$	−2.05974	+	0.870338i	−0.325673	+	0.137612i
$41$	−9.16537	−	4.41381i	−1.43139	−	0.689322i	−0.452135	−	0.891949i	$-0.649338\pi$
$41$	−9.16537	−	4.41381i	−1.43139	−	0.689322i	−0.979256	+	0.202628i	$0.935052\pi$
$42$	0.0149597	+	0.633103i	0.00230833	+	0.0976899i
$43$	−0.738335	−	1.53317i	−0.112595	−	0.233806i	0.837055	−	0.547119i	$-0.184275\pi$
$43$	−0.738335	−	1.53317i	−0.112595	−	0.233806i	−0.949650	+	0.313313i	$0.898561\pi$
$44$	3.71504	+	1.78907i	0.560063	+	0.269712i
$45$	0.322341	−	6.57220i	0.0480518	−	0.979725i
$46$	3.54607	+	1.70770i	0.522840	+	0.251786i
$47$	8.91040	+	7.10581i	1.29972	+	1.03649i	0.996502	+	0.0835660i	$0.0266309\pi$
$47$	8.91040	+	7.10581i	1.29972	+	1.03649i	0.303213	+	0.952923i	$0.401940\pi$
$48$		−	0.239357i		−	0.0345482i
$49$	−4.61805	−	5.26057i	−0.659721	−	0.751510i
$50$	2.59984	−	4.27093i	0.367672	−	0.604001i
$51$	0.532181	−	0.667334i	0.0745202	−	0.0934454i
$52$	2.84029	−	5.89792i	0.393877	−	0.817894i
$53$	−8.18697	+	1.86862i	−1.12457	+	0.256675i	−0.744066	−	0.668106i	$-0.767105\pi$
$53$	−8.18697	+	1.86862i	−1.12457	+	0.256675i	−0.380501	+	0.924781i	$0.624248\pi$
$54$	1.28156	+	0.617169i	0.174399	+	0.0839861i
$55$	−9.07871	+	1.60887i	−1.22417	+	0.216940i
$56$	1.69800	+	2.02899i	0.226905	+	0.271135i
$57$	0.347781	−	0.722175i	0.0460648	−	0.0956544i
$58$	0.0483442	−	0.0385532i	0.00634790	−	0.00506228i
$59$	11.3529	−	5.46727i	1.47802	−	0.711778i	0.490821	−	0.871260i	$-0.336697\pi$
$59$	11.3529	−	5.46727i	1.47802	−	0.711778i	0.987201	+	0.159482i	$0.0509825\pi$
$60$	0.312804	+	0.434296i	0.0403828	+	0.0560673i
$61$	−1.90248	+	8.33533i	−0.243588	+	1.06723i	0.694135	+	0.719845i	$0.255787\pi$
$61$	−1.90248	+	8.33533i	−0.243588	+	1.06723i	−0.937723	+	0.347385i	$0.887070\pi$
$62$	5.57056	+	4.44237i	0.707461	+	0.564182i
$63$	−7.54743	+	1.91130i	−0.950886	+	0.240801i
$64$	−0.623490	−	0.781831i	−0.0779362	−	0.0977289i
$65$	2.55421	+	14.4132i	0.316811	+	1.78773i
$66$	0.219619	−	0.962216i	0.0270333	−	0.118441i
$67$		−	11.8515i		−	1.44789i	−0.689857	−	0.723945i	$-0.742327\pi$
$67$		−	11.8515i		−	1.44789i	0.689857	−	0.723945i	$-0.257673\pi$
$68$		−	3.56602i		−	0.432443i
$69$	0.209631	−	0.918452i	0.0252366	−	0.110569i
$70$	−5.73248	−	1.46241i	−0.685163	−	0.174791i
$71$	−1.58243	−	6.93308i	−0.187800	−	0.822806i	−0.977773	−	0.209665i	$-0.932763\pi$
$71$	−1.58243	−	6.93308i	−0.187800	−	0.822806i	0.789973	−	0.613141i	$-0.210094\pi$
$72$	2.86893	−	0.654814i	0.338106	−	0.0771706i
$73$	1.13206	−	0.902790i	0.132498	−	0.105664i	−0.554998	−	0.831851i	$-0.687281\pi$
$73$	1.13206	−	0.902790i	0.132498	−	0.105664i	0.687496	+	0.726188i	$0.258710\pi$
$74$	0.388413	+	0.487054i	0.0451521	+	0.0566189i
$75$	−1.13512	−	0.379209i	−0.131072	−	0.0437873i
$76$	−0.745173	−	3.26482i	−0.0854772	−	0.374500i
$77$	4.96430	+	9.71451i	0.565734	+	1.10707i
$78$	−1.52759	−	0.348663i	−0.172966	−	0.0394784i
$79$	−11.2657			−1.26749			−0.633743	−	0.773544i	$-0.718482\pi$
$79$	−11.2657			−1.26749			−0.633743	+	0.773544i	$0.718482\pi$
$80$	2.15301	+	0.603767i	0.240714	+	0.0675032i
$81$	−1.88868	+	8.27485i	−0.209853	+	0.919428i
$82$	4.41381	+	9.16537i	0.487424	+	1.01215i
$83$	2.98042	−	2.37680i	0.327143	−	0.260888i	−0.446120	−	0.894973i	$-0.647195\pi$
$83$	2.98042	−	2.37680i	0.327143	−	0.260888i	0.773263	+	0.634085i	$0.218623\pi$
$84$	0.383037	−	0.504307i	0.0417928	−	0.0550244i
$85$	4.66025	+	6.47027i	0.505475	+	0.701800i
$86$	−0.378661	+	1.65902i	−0.0408321	+	0.178897i
$87$	−0.0115715	−	0.00922798i	−0.00124060	−	0.000989343i
$88$	−1.78907	−	3.71504i	−0.190715	−	0.396024i
$89$	7.55418	+	9.47264i	0.800742	+	1.00410i	0.999710	+	0.0240923i	$0.00766956\pi$
$89$	7.55418	+	9.47264i	0.800742	+	1.00410i	−0.198968	+	0.980006i	$0.563759\pi$
$90$	−4.34971	+	4.93737i	−0.458500	+	0.520445i
$91$	15.4226	−	7.88122i	1.61672	−	0.826176i
$92$	−1.70770	−	3.54607i	−0.178040	−	0.369704i
$93$	0.739955	−	1.53653i	0.0767297	−	0.159331i
$94$	−2.53603	−	11.1111i	−0.261572	−	1.14602i
$95$	5.61869	+	4.94994i	0.576465	+	0.507853i
$96$	−0.149237	+	0.187137i	−0.0152314	+	0.0190996i
$97$			2.68300i			0.272417i	0.990680	+	0.136209i	$0.0434917\pi$
$97$			2.68300i			0.272417i	−0.990680	+	0.136209i	$0.956508\pi$
$98$	0.330623	+	6.99219i	0.0333980	+	0.706318i
$99$	12.1339			1.21950
$100$	−4.69552	+	1.71818i	−0.469552	+	0.171818i
$101$	−6.43527	−	3.09906i	−0.640333	−	0.308368i	0.0853976	−	0.996347i	$-0.472784\pi$
$101$	−6.43527	−	3.09906i	−0.640333	−	0.308368i	−0.725731	+	0.687979i	$0.758498\pi$
$102$	−0.832151	+	0.189933i	−0.0823953	+	0.0188062i
$103$	2.76575	−	5.74314i	0.272517	−	0.565888i	−0.719129	−	0.694877i	$-0.755459\pi$
$103$	2.76575	−	5.74314i	0.272517	−	0.565888i	0.991646	+	0.128989i	$0.0411731\pi$
$104$	−5.89792	+	2.84029i	−0.578339	+	0.278513i
$105$	−0.0359388	+	1.41560i	−0.00350726	+	0.138148i
$106$	7.56590	+	3.64354i	0.734865	+	0.353892i
$107$	−3.05695	+	2.43784i	−0.295527	+	0.235675i	−0.760016	−	0.649904i	$-0.774809\pi$
$107$	−3.05695	+	2.43784i	−0.295527	+	0.235675i	0.464490	+	0.885578i	$0.346238\pi$
$108$	−0.617169	−	1.28156i	−0.0593871	−	0.123319i
$109$	4.33717	−	5.43863i	0.415425	−	0.520927i	−0.529457	−	0.848337i	$-0.677604\pi$
$109$	4.33717	−	5.43863i	0.415425	−	0.520927i	0.944882	+	0.327410i	$0.106176\pi$
$110$	8.10113	+	4.40262i	0.772413	+	0.419773i
$111$	0.0929694	−	0.116580i	0.00882426	−	0.0110653i
$112$	−0.0624993	−	2.64501i	−0.00590563	−	0.249930i
$113$	14.3749	−	11.4636i	1.35228	−	1.07841i	0.363089	−	0.931754i	$-0.381722\pi$
$113$	14.3749	−	11.4636i	1.35228	−	1.07841i	0.989188	−	0.146651i	$-0.0468494\pi$
$114$	−0.722175	+	0.347781i	−0.0676379	+	0.0325727i
$115$	7.73268	+	4.20238i	0.721076	+	0.391874i
$116$	−0.0618345			−0.00574119
$117$		−	19.2636i		−	1.78092i
$118$	−12.2848	−	2.80394i	−1.13091	−	0.258123i
$119$	5.70661	−	7.51332i	0.523124	−	0.688745i
$120$	0.0262189	−	0.534576i	0.00239345	−	0.0487999i
$121$	−1.33563	−	5.85178i	−0.121421	−	0.531980i
$122$	6.68442	−	5.33064i	0.605179	−	0.482614i
$123$	1.90371	−	1.51816i	0.171651	−	0.136887i
$124$	−1.58546	−	6.94637i	−0.142379	−	0.623802i
$125$	6.27427	−	9.25384i	0.561187	−	0.827689i
$126$	7.09249	+	3.21143i	0.631849	+	0.286097i
$127$	10.3518	+	2.36274i	0.918575	+	0.209659i	0.655569	−	0.755135i	$-0.272429\pi$
$127$	10.3518	+	2.36274i	0.918575	+	0.209659i	0.263006	+	0.964794i	$0.415286\pi$
$128$			1.00000i			0.0883883i
$129$	0.407311			0.0358617
$130$	6.98951	−	12.8612i	0.613020	−	1.12800i
$131$	5.10045	−	2.45625i	0.445628	−	0.214603i	−0.197592	−	0.980284i	$-0.563312\pi$
$131$	5.10045	−	2.45625i	0.445628	−	0.214603i	0.643220	+	0.765681i	$0.277598\pi$
$132$	−0.771637	+	0.615360i	−0.0671624	+	0.0535602i
$133$	3.65458	−	8.07120i	0.316892	−	0.699862i
$134$	−7.38929	+	9.26587i	−0.638337	+	0.800450i
$135$	2.79462	+	1.51876i	0.240523	+	0.130714i
$136$	−2.22338	+	2.78802i	−0.190653	+	0.239071i
$137$	4.14312	+	8.60327i	0.353970	+	0.735027i	0.999590	−	0.0286323i	$-0.00911519\pi$
$137$	4.14312	+	8.60327i	0.353970	+	0.735027i	−0.645620	+	0.763659i	$0.723401\pi$
$138$	−0.736542	+	0.587372i	−0.0626986	+	0.0500005i
$139$	−4.40397	−	2.12084i	−0.373540	−	0.179887i	0.237689	−	0.971341i	$-0.423610\pi$
$139$	−4.40397	−	2.12084i	−0.373540	−	0.179887i	−0.611229	+	0.791454i	$0.709324\pi$
$140$	3.57004	+	4.71750i	0.301723	+	0.398702i
$141$	−2.45776	+	1.18360i	−0.206981	+	0.0996769i
$142$	−3.08551	+	6.40713i	−0.258930	+	0.537675i
$143$	−26.3157	+	6.00639i	−2.20063	+	0.502280i
$144$	−2.65129	−	1.27679i	−0.220941	−	0.106399i
$145$	0.112194	−	0.0808085i	0.00931721	−	0.00671078i
$146$	−1.44796			−0.119834
$147$	1.61406	−	0.449571i	0.133125	−	0.0370800i
$148$		−	0.622966i		−	0.0512075i
$149$	−11.0935	+	13.9108i	−0.908813	+	1.13962i	0.0809249	+	0.996720i	$0.474213\pi$
$149$	−11.0935	+	13.9108i	−0.908813	+	1.13962i	−0.989738	+	0.142895i	$0.954359\pi$
$150$	0.651039	+	1.00421i	0.0531571	+	0.0819937i
$151$	−2.37946	−	10.4251i	−0.193637	−	0.848381i	−0.974627	−	0.223836i	$-0.928142\pi$
$151$	−2.37946	−	10.4251i	−0.193637	−	0.848381i	0.780989	−	0.624544i	$-0.214715\pi$
$152$	−1.45298	+	3.01714i	−0.117852	+	0.244723i
$153$	−4.55307	−	9.45454i	−0.368094	−	0.764354i
$154$	2.17565	−	10.6903i	0.175319	−	0.861449i
$155$	11.9546	+	10.5317i	0.960215	+	0.845927i
$156$	0.976933	+	1.22504i	0.0782173	+	0.0980814i
$157$	6.23871	+	12.9548i	0.497903	+	1.03391i	0.986857	+	0.161597i	$0.0516645\pi$
$157$	6.23871	+	12.9548i	0.497903	+	1.03391i	−0.488954	+	0.872310i	$0.662621\pi$
$158$	8.80785	+	7.02402i	0.700715	+	0.558801i
$159$	0.447268	−	1.95961i	0.0354707	−	0.155407i
$160$	−1.30685	−	1.81443i	−0.103316	−	0.143443i
$161$	2.07670	−	10.2041i	0.163667	−	0.804194i
$162$	6.63592	−	5.29197i	0.521367	−	0.415776i
$163$	−0.755903	−	1.56965i	−0.0592069	−	0.122944i	0.869266	−	0.494345i	$-0.164592\pi$
$163$	−0.755903	−	1.56965i	−0.0592069	−	0.122944i	−0.928473	+	0.371400i	$0.878878\pi$
$164$	2.26366	−	9.91774i	0.176762	−	0.774446i
$165$	0.595894	−	2.12494i	0.0463903	−	0.165426i
$166$	−3.81210			−0.295876
$167$	5.28031	+	1.20520i	0.408603	+	0.0932609i	0.421882	−	0.906651i	$-0.361370\pi$
$167$	5.28031	+	1.20520i	0.408603	+	0.0932609i	−0.0132788	+	0.999912i	$0.504227\pi$
$168$	−0.613901	+	0.155463i	−0.0473635	+	0.0119942i
$169$	6.64285	+	29.1042i	0.510989	+	2.23879i
$170$	0.390618	−	7.96428i	0.0299590	−	0.610833i
$171$	−6.14417	−	7.70454i	−0.469856	−	0.589181i
$172$	1.33043	−	1.06098i	0.101445	−	0.0808993i
$173$	5.05350	−	1.15343i	0.384210	−	0.0876935i	−0.0260532	−	0.999661i	$-0.508294\pi$
$173$	5.05350	−	1.15343i	0.384210	−	0.0876935i	0.410263	+	0.911967i	$0.365437\pi$
$174$	0.00329343	+	0.0144294i	0.000249674	+	0.00109389i
$175$	−12.6426	−	3.89405i	−0.955694	−	0.294363i
$176$	−0.917539	+	4.02000i	−0.0691621	+	0.303019i
$177$			3.01608i			0.226703i
$178$		−	12.1160i		−	0.908130i
$179$	−0.455728	+	1.99667i	−0.0340627	+	0.149238i	−0.989099	−	0.147249i	$-0.952958\pi$
$179$	−0.455728	+	1.99667i	−0.0340627	+	0.149238i	0.955037	+	0.296487i	$0.0958153\pi$
$180$	6.47914	−	1.14819i	0.482927	−	0.0855812i
$181$	4.26571	+	5.34903i	0.317068	+	0.397590i	0.914669	−	0.404203i	$-0.132451\pi$
$181$	4.26571	+	5.34903i	0.317068	+	0.397590i	−0.597602	+	0.801793i	$0.703880\pi$
$182$	−16.9717	−	3.45403i	−1.25803	−	0.256029i
$183$	−1.59996	−	1.27593i	−0.118273	−	0.0943193i
$184$	−0.875807	+	3.83716i	−0.0645654	+	0.282879i
$185$	0.814123	+	1.13033i	0.0598555	+	0.0831032i
$186$	−1.53653	+	0.739955i	−0.112664	+	0.0542561i
$187$	−11.4961	+	9.16782i	−0.840677	+	0.670418i
$188$	−4.94490	+	10.2682i	−0.360644	+	0.748885i
$189$	0.750529	−	3.68780i	0.0545929	−	0.268248i
$190$	−1.30663	−	7.37321i	−0.0947931	−	0.534909i
$191$	−15.7602	−	7.58969i	−1.14036	−	0.549171i	−0.234239	−	0.972179i	$-0.575260\pi$
$191$	−15.7602	−	7.58969i	−1.14036	−	0.549171i	−0.906126	+	0.423008i	$0.860974\pi$
$192$	0.233356	−	0.0532620i	0.0168410	−	0.00384385i
$193$	−9.54430	+	19.8189i	−0.687014	+	1.42660i	0.206901	+	0.978362i	$0.433662\pi$
$193$	−9.54430	+	19.8189i	−0.687014	+	1.42660i	−0.893915	+	0.448237i	$0.852052\pi$
$194$	1.67282	−	2.09765i	0.120102	−	0.150603i
$195$	−3.37351	−	0.946030i	−0.241582	−	0.0677466i
$196$	4.10107	−	5.67285i	0.292933	−	0.405204i
$197$		−	2.37700i		−	0.169354i	−0.996408	−	0.0846772i	$-0.973014\pi$
$197$		−	2.37700i		−	0.169354i	0.996408	−	0.0846772i	$-0.0269859\pi$
$198$	−9.48667	−	7.56537i	−0.674188	−	0.537647i
$199$	9.89821	+	4.76673i	0.701665	+	0.337904i	0.750470	−	0.660904i	$-0.229827\pi$
$199$	9.89821	+	4.76673i	0.701665	+	0.337904i	−0.0488051	+	0.998808i	$0.515541\pi$
$200$	4.74237	+	1.58428i	0.335336	+	0.112026i
$201$	2.55581	+	1.23082i	0.180273	+	0.0868150i
$202$	3.09906	+	6.43527i	0.218049	+	0.452784i
$203$	−0.130280	−	0.0989522i	−0.00914390	−	0.00694508i
$204$	0.769023	+	0.370342i	0.0538424	+	0.0259291i
$205$	8.85377	+	20.9533i	0.618374	+	1.46344i
$206$	−5.74314	+	2.76575i	−0.400143	+	0.192699i
$207$	−9.05520	−	7.22128i	−0.629380	−	0.501914i
$208$	6.38207	+	1.45667i	0.442517	+	0.101002i
$209$	−8.60933	+	10.7958i	−0.595520	+	0.746758i
$210$	0.910710	−	1.08435i	0.0628450	−	0.0748275i
$211$	2.51687	+	3.15605i	0.173268	+	0.217271i	0.860881	−	0.508806i	$-0.169913\pi$
$211$	2.51687	+	3.15605i	0.173268	+	0.217271i	−0.687613	+	0.726077i	$0.741341\pi$
$212$	−3.64354	−	7.56590i	−0.250240	−	0.519628i
$213$	1.65948	+	0.378766i	0.113706	+	0.0259526i
$214$	3.90999			0.267281
$215$	−1.02742	+	3.66376i	−0.0700697	+	0.249866i
$216$	−0.316520	+	1.38677i	−0.0215365	+	0.0943575i
$217$	7.77565	−	17.1726i	0.527846	−	1.16575i
$218$	−6.78187	+	1.54792i	−0.459326	+	0.104838i
$219$	0.0771214	+	0.337891i	0.00521138	+	0.0228326i
$220$	−3.58873	−	8.49308i	−0.241952	−	0.572603i
$221$	14.5547	+	18.2510i	0.979052	+	1.22769i
$222$	−0.145373	+	0.0331804i	−0.00975678	+	0.00222692i
$223$	6.25649	−	1.42800i	0.418966	−	0.0956262i	−0.00784057	−	0.999969i	$-0.502496\pi$
$223$	6.25649	−	1.42800i	0.418966	−	0.0956262i	0.426806	+	0.904343i	$0.359639\pi$
$224$	−1.60027	+	2.10692i	−0.106923	+	0.140775i
$225$	−10.2554	+	10.5506i	−0.683694	+	0.703372i
$226$	−18.3862			−1.22303
$227$			4.81766i			0.319759i	0.987137	+	0.159879i	$0.0511106\pi$
$227$			4.81766i			0.319759i	−0.987137	+	0.159879i	$0.948889\pi$
$228$	0.781457	+	0.178363i	0.0517533	+	0.0118123i
$229$	−26.2723	+	12.6521i	−1.73612	+	0.836072i	−0.751867	+	0.659315i	$0.770847\pi$
$229$	−26.2723	+	12.6521i	−1.73612	+	0.836072i	−0.984254	+	0.176757i	$0.943439\pi$
$230$	−3.42551	−	8.10680i	−0.225872	−	0.534546i
$231$	−2.61052	+	0.0616844i	−0.171760	+	0.00405853i
$232$	0.0483442	+	0.0385532i	0.00317395	+	0.00253114i
$233$	−6.58109	−	1.50209i	−0.431141	−	0.0984052i	0.00144240	−	0.999999i	$-0.499541\pi$
$233$	−6.58109	−	1.50209i	−0.431141	−	0.0984052i	−0.432584	+	0.901594i	$0.642398\pi$
$234$	−12.0106	+	15.0609i	−0.785159	+	0.984559i
$235$	−4.44684	−	25.0931i	−0.290080	−	1.63689i
$236$	7.85645	+	9.85168i	0.511412	+	0.641290i
$237$	1.16997	−	2.42948i	0.0759980	−	0.157812i
$238$	−9.14608	+	2.31614i	−0.592853	+	0.150133i
$239$	0.130811	−	0.0629951i	0.00846144	−	0.00407481i	−0.429648	−	0.902996i	$-0.641362\pi$
$239$	0.130811	−	0.0629951i	0.00846144	−	0.00407481i	0.438110	+	0.898922i	$0.355648\pi$
$240$	−0.353802	+	0.401601i	−0.0228378	+	0.0259233i
$241$	−0.636890	−	2.79040i	−0.0410257	−	0.179745i	0.950264	−	0.311446i	$-0.100813\pi$
$241$	−0.636890	−	2.79040i	−0.0410257	−	0.179745i	−0.991290	+	0.131701i	$0.957956\pi$
$242$	−2.60429	+	5.40786i	−0.167410	+	0.347630i
$243$	−4.92466	−	3.92728i	−0.315917	−	0.251935i
$244$	−8.54969			−0.547338
$245$	−0.0275087	+	15.6525i	−0.00175747	+	0.999998i
$246$	−2.43493			−0.155246
$247$	17.1391	+	13.6680i	1.09054	+	0.869674i
$248$	−3.09143	+	6.41941i	−0.196306	+	0.407633i
$249$	0.203040	+	0.889575i	0.0128671	+	0.0563745i
$250$	−10.6751	+	3.32300i	−0.675152	+	0.210165i
$251$	12.0356	−	5.79606i	0.759683	−	0.365844i	−0.0135979	−	0.999908i	$-0.504328\pi$
$251$	12.0356	−	5.79606i	0.759683	−	0.365844i	0.773281	+	0.634063i	$0.218614\pi$
$252$	−3.54284	−	6.93289i	−0.223178	−	0.436731i
$253$	−7.04149	+	14.6218i	−0.442695	+	0.919265i
$254$	−6.62024	−	8.30151i	−0.415391	−	0.520883i
$255$	−1.87932	+	0.333040i	−0.117687	+	0.0208558i
$256$	0.623490	−	0.781831i	0.0389681	−	0.0488645i
$257$	−22.4260	−	5.11858i	−1.39889	−	0.319288i	−0.544433	−	0.838804i	$-0.683255\pi$
$257$	−22.4260	−	5.11858i	−1.39889	−	0.319288i	−0.854461	+	0.519516i	$0.826112\pi$
$258$	−0.318449	−	0.253954i	−0.0198257	−	0.0158105i
$259$	0.996916	−	1.31254i	0.0619454	−	0.0815573i
$260$	−13.4834	+	5.69740i	−0.836207	+	0.353338i
$261$	−0.163941	+	0.0789499i	−0.0101477	+	0.00488687i
$262$	−5.51913	−	1.25971i	−0.340973	−	0.0778249i
$263$		−	17.1742i		−	1.05901i	−0.848308	−	0.529503i	$-0.822378\pi$
$263$		−	17.1742i		−	1.05901i	0.848308	−	0.529503i	$-0.177622\pi$
$264$	0.986961			0.0607432
$265$	16.4984	+	8.96619i	1.01349	+	0.550789i
$266$	−7.88958	+	4.03172i	−0.483741	+	0.247201i
$267$	−2.82733	+	0.645320i	−0.173030	+	0.0394930i
$268$	11.5544	−	2.63721i	0.705795	−	0.161093i
$269$	−12.7754	−	16.0199i	−0.778932	−	0.976750i	−0.999999	−	0.00149128i	$-0.999525\pi$
$269$	−12.7754	−	16.0199i	−0.778932	−	0.976750i	0.221067	−	0.975259i	$-0.429046\pi$
$270$	−1.23799	−	2.92983i	−0.0753419	−	0.178304i
$271$	2.31697	+	10.1513i	0.140746	+	0.616649i	0.995262	+	0.0972247i	$0.0309965\pi$
$271$	2.31697	+	10.1513i	0.140746	+	0.616649i	−0.854516	+	0.519425i	$0.826146\pi$
$272$	3.47661	−	0.793513i	0.210800	−	0.0481138i
$273$	0.0979289	+	4.14442i	0.00592693	+	0.250831i
$274$	2.12483	−	9.30949i	0.128366	−	0.562407i
$275$	17.6107	+	10.7201i	1.06196	+	0.646447i
$276$	0.942072			0.0567061
$277$	−16.0315	−	3.65908i	−0.963237	−	0.219853i	−0.288146	−	0.957587i	$-0.593039\pi$
$277$	−16.0315	−	3.65908i	−0.963237	−	0.219853i	−0.675092	+	0.737734i	$0.735896\pi$
$278$	2.12084	+	4.40397i	0.127199	+	0.264132i
$279$	−13.0726	−	16.3925i	−0.782636	−	0.981395i
$280$	0.150147	−	5.91417i	0.00897300	−	0.353440i
$281$	17.4338	−	21.8613i	1.04001	−	1.30413i	0.0886496	−	0.996063i	$-0.471745\pi$
$281$	17.4338	−	21.8613i	1.04001	−	1.30413i	0.951363	−	0.308072i	$-0.0996837\pi$
$282$	2.65952	+	0.607018i	0.158372	+	0.0361474i
$283$	−18.3558	−	14.6382i	−1.09114	−	0.870153i	−0.0989727	−	0.995090i	$-0.531556\pi$
$283$	−18.3558	−	14.6382i	−1.09114	−	0.870153i	−0.992165	+	0.124937i	$0.960127\pi$
$284$	6.40713	−	3.08551i	0.380193	−	0.183092i
$285$	−1.65099	+	0.697623i	−0.0977962	+	0.0413236i
$286$	24.3194	+	11.7116i	1.43803	+	0.692521i
$287$	20.6405	−	17.2734i	1.21837	−	1.01962i
$288$	1.27679	+	2.65129i	0.0752358	+	0.156229i
$289$	−3.85932	−	1.85855i	−0.227019	−	0.109327i
$290$	−0.138100	−	0.00677329i	−0.00810952	−	0.000397741i
$291$	−0.578598	−	0.278638i	−0.0339180	−	0.0163340i
$292$	1.13206	+	0.902790i	0.0662490	+	0.0528318i
$293$			15.3741i			0.898163i	0.893491	+	0.449081i	$0.148249\pi$
$293$			15.3741i			0.898163i	−0.893491	+	0.449081i	$0.851751\pi$
$294$	−1.54222	−	0.654861i	−0.0899444	−	0.0381923i
$295$	−27.1296	−	7.60793i	−1.57955	−	0.442951i
$296$	−0.388413	+	0.487054i	−0.0225760	+	0.0283095i
$297$	−2.54482	+	5.28438i	−0.147666	+	0.306631i
$298$	17.3465	−	3.95922i	1.00485	−	0.229351i
$299$	23.2133	+	11.1789i	1.34246	+	0.646494i
$300$	0.117114	−	1.19104i	0.00676157	−	0.0687648i
$301$	4.50099	−	0.106354i	0.259433	−	0.00613016i
$302$	−4.63960	+	9.63422i	−0.266979	+	0.554387i
$303$	1.33665	−	1.06594i	0.0767883	−	0.0612367i
$304$	3.01714	−	1.45298i	0.173045	−	0.0833341i
$305$	15.5128	−	11.1732i	0.888259	−	0.639774i
$306$	−2.33508	+	10.2306i	−0.133488	+	0.584847i
$307$	−23.9069	−	19.0651i	−1.36444	−	1.08810i	−0.986763	−	0.162166i	$-0.948152\pi$
$307$	−23.9069	−	19.0651i	−1.36444	−	1.08810i	−0.377676	−	0.925938i	$-0.623277\pi$
$308$	−8.36628	+	7.00151i	−0.476713	+	0.398948i
$309$	0.951295	+	1.19289i	0.0541173	+	0.0678609i
$310$	−2.78005	−	15.6876i	−0.157896	−	0.890995i
$311$	3.01277	−	13.1998i	0.170838	−	0.748492i	−0.814816	−	0.579719i	$-0.803162\pi$
$311$	3.01277	−	13.1998i	0.170838	−	0.748492i	0.985655	−	0.168773i	$-0.0539805\pi$
$312$		−	1.56688i		−	0.0887071i
$313$		−	17.6699i		−	0.998764i	−0.866382	−	0.499382i	$-0.833560\pi$
$313$		−	17.6699i		−	0.998764i	0.866382	−	0.499382i	$-0.166440\pi$
$314$	3.19958	−	14.0183i	0.180562	−	0.791096i
$315$	15.4885	+	7.94926i	0.872677	+	0.447890i
$316$	−2.50685	−	10.9832i	−0.141021	−	0.617854i
$317$	3.28476	−	0.749724i	0.184490	−	0.0421087i	−0.129277	−	0.991608i	$-0.541266\pi$
$317$	3.28476	−	0.749724i	0.184490	−	0.0421087i	0.313768	+	0.949500i	$0.398409\pi$
$318$	−1.57149	+	1.25322i	−0.0881245	+	0.0702770i
$319$	0.158969	+	0.199341i	0.00890058	+	0.0111610i
$320$	−0.109539	+	2.23338i	−0.00612341	+	0.124850i
$321$	−0.208254	−	0.912419i	−0.0116236	−	0.0509263i
$322$	−7.98577	+	6.68307i	−0.445030	+	0.372433i
$323$	11.6424	+	2.65730i	0.647800	+	0.147856i
$324$	−8.48766			−0.471536
$325$	17.0190	−	27.9584i	0.944047	−	1.55085i
$326$	−0.387671	+	1.69850i	−0.0214711	+	0.0940712i
$327$	0.722431	+	1.50014i	0.0399505	+	0.0829581i
$328$	−7.95341	+	6.34264i	−0.439154	+	0.350213i
$329$	−26.8504	+	13.7211i	−1.48031	+	0.756468i
$330$	−1.79077	+	1.28981i	−0.0985785	+	0.0710017i
$331$	−5.28175	+	23.1408i	−0.290311	+	1.27194i	0.593782	+	0.804626i	$0.297634\pi$
$331$	−5.28175	+	23.1408i	−0.290311	+	1.27194i	−0.884093	+	0.467310i	$0.845223\pi$
$332$	2.98042	+	2.37680i	0.163572	+	0.130444i
$333$	−0.795398	−	1.65166i	−0.0435876	−	0.0905105i
$334$	−3.37689	−	4.23448i	−0.184775	−	0.231701i
$335$	−17.5181	+	19.8848i	−0.957115	+	1.08642i
$336$	0.576897	+	0.261215i	0.0314723	+	0.0142504i
$337$	6.94944	+	14.4307i	0.378560	+	0.786088i	0.999997	+	0.00262346i	$0.000835075\pi$
$337$	6.94944	+	14.4307i	0.378560	+	0.786088i	−0.621437	+	0.783464i	$0.713451\pi$
$338$	12.9526	−	26.8964i	0.704529	−	1.46297i
$339$	0.979285	+	4.29053i	0.0531875	+	0.233030i
$340$	−5.27105	+	5.98318i	−0.285863	+	0.324484i
$341$	−18.3176	+	22.9695i	−0.991953	+	1.24387i
$342$			9.85448i			0.532869i
$343$	17.7187	−	5.38943i	0.956723	−	0.291002i
$344$	−1.70169			−0.0917489
$345$	−1.70932	+	1.23115i	−0.0920267	+	0.0662828i
$346$	−4.67013	−	2.24902i	−0.251068	−	0.120908i
$347$	3.25739	−	0.743477i	0.174866	−	0.0399119i	−0.134191	−	0.990955i	$-0.542844\pi$
$347$	3.25739	−	0.743477i	0.174866	−	0.0399119i	0.309057	+	0.951043i	$0.399987\pi$
$348$	0.00642171	−	0.0133348i	0.000344240	−	0.000714821i
$349$	−7.07205	+	3.40572i	−0.378558	+	0.182304i	−0.613480	−	0.789710i	$-0.710231\pi$
$349$	−7.07205	+	3.40572i	−0.378558	+	0.182304i	0.234922	+	0.972014i	$0.424517\pi$
$350$	7.45651	+	10.9271i	0.398567	+	0.584075i
$351$	8.38938	+	4.04011i	0.447792	+	0.215645i
$352$	3.22379	−	2.57089i	0.171829	−	0.137029i
$353$	3.03109	+	6.29413i	0.161329	+	0.335003i	0.965926	−	0.258818i	$-0.0833331\pi$
$353$	3.03109	+	6.29413i	0.161329	+	0.335003i	−0.804597	+	0.593821i	$0.797619\pi$
$354$	1.88050	−	2.35807i	0.0999474	−	0.125330i
$355$	−7.59296	+	13.9716i	−0.402993	+	0.741536i
$356$	−7.55418	+	9.47264i	−0.400371	+	0.502049i
$357$	1.02762	+	2.01093i	0.0543876	+	0.106430i
$358$	1.60121	−	1.27692i	0.0846265	−	0.0674874i
$359$	31.5049	−	15.1720i	1.66277	−	0.800746i	0.664181	−	0.747572i	$-0.268780\pi$
$359$	31.5049	−	15.1720i	1.66277	−	0.800746i	0.998585	−	0.0531746i	$-0.0169340\pi$
$360$	−5.78148	−	3.14199i	−0.304711	−	0.165597i
$361$	−7.78569			−0.409773
$362$		−	6.84167i		−	0.359590i
$363$	1.40067	+	0.319693i	0.0735159	+	0.0167795i
$364$	11.1155	+	13.2821i	0.582608	+	0.696174i
$365$	−3.23386	−	0.158608i	−0.169268	−	0.00830194i
$366$	0.455373	+	1.99512i	0.0238027	+	0.104287i
$367$	−26.7925	+	21.3663i	−1.39856	+	1.11531i	−0.420426	+	0.907327i	$0.638120\pi$
$367$	−26.7925	+	21.3663i	−1.39856	+	1.11531i	−0.978132	+	0.207986i	$0.933309\pi$
$368$	3.07717	−	2.45396i	0.160408	−	0.127921i
$369$	−6.66129	−	29.1850i	−0.346773	−	1.51931i
$370$	0.0682390	−	1.39132i	0.00354758	−	0.0723314i
$371$	4.43085	−	21.7714i	0.230038	−	1.13032i
$372$	1.66266	+	0.379492i	0.0862051	+	0.0196757i
$373$		−	3.83937i		−	0.198795i	−0.995048	−	0.0993975i	$-0.968308\pi$
$373$		−	3.83937i		−	0.198795i	0.995048	−	0.0993975i	$-0.0316915\pi$
$374$	14.7040			0.760328
$375$	1.34402	+	2.31411i	0.0694049	+	0.119500i
$376$	10.2682	−	4.94490i	0.529541	−	0.255014i
$377$	0.316470	−	0.252377i	0.0162991	−	0.0129981i
$378$	−2.88609	+	2.41529i	−0.148445	+	0.124229i
$379$	7.75416	−	9.72341i	0.398304	−	0.499458i	−0.541723	−	0.840557i	$-0.682228\pi$
$379$	7.75416	−	9.72341i	0.398304	−	0.499458i	0.940027	+	0.341099i	$0.110799\pi$
$380$	−3.57556	+	6.57928i	−0.183422	+	0.337510i
$381$	−1.58460	+	1.98703i	−0.0811816	+	0.101798i
$382$	7.58969	+	15.7602i	0.388322	+	0.806360i
$383$	5.45637	−	4.35131i	0.278808	−	0.222342i	−0.474095	−	0.880474i	$-0.657225\pi$
$383$	5.45637	−	4.35131i	0.278808	−	0.222342i	0.752902	+	0.658132i	$0.228653\pi$
$384$	−0.215653	−	0.103853i	−0.0110050	−	0.00529974i
$385$	6.03007	−	23.6372i	0.307321	−	1.20466i
$386$	19.8189	−	9.54430i	1.00876	−	0.485792i
$387$	2.17270	−	4.51166i	0.110445	−	0.229341i
$388$	−2.61573	+	0.597023i	−0.132794	+	0.0303093i
$389$	5.86300	+	2.82347i	0.297266	+	0.143156i	0.576572	−	0.817046i	$-0.304390\pi$
$389$	5.86300	+	2.82347i	0.297266	+	0.143156i	−0.279306	+	0.960202i	$0.590104\pi$
$390$	2.04768	+	2.84299i	0.103688	+	0.143960i
$391$	14.0353			0.709795
$392$	−6.74331	+	1.87824i	−0.340589	+	0.0948655i
$393$			1.35502i			0.0683516i
$394$	−1.48204	+	1.85841i	−0.0746639	+	0.0936256i
$395$	18.9019	+	16.6521i	0.951058	+	0.837860i
$396$	2.70005	+	11.8297i	0.135683	+	0.594464i
$397$	−7.48277	+	15.5381i	−0.375549	+	0.779836i	−0.999999	−	0.00122857i	$-0.999609\pi$
$397$	−7.48277	+	15.5381i	−0.375549	+	0.779836i	0.624450	+	0.781065i	$0.285323\pi$
$398$	−4.76673	−	9.89821i	−0.238934	−	0.496152i
$399$	1.36104	+	1.62634i	0.0681373	+	0.0814190i
$400$	−2.71995	−	4.19546i	−0.135997	−	0.209773i
$401$	−14.9414	−	18.7359i	−0.746138	−	0.935628i	0.253358	−	0.967373i	$-0.418465\pi$
$401$	−14.9414	−	18.7359i	−0.746138	−	0.935628i	−0.999496	+	0.0317449i	$0.989894\pi$
$402$	−1.23082	−	2.55581i	−0.0613875	−	0.127472i
$403$	36.4660	+	29.0806i	1.81650	+	1.44861i
$404$	1.58938	−	6.96353i	0.0790746	−	0.346449i
$405$	15.4002	−	11.0921i	0.765243	−	0.551171i
$406$	0.0401617	+	0.158592i	0.00199319	+	0.00787081i
$407$	−2.00831	+	1.60157i	−0.0995482	+	0.0793871i
$408$	−0.370342	−	0.769023i	−0.0183347	−	0.0380723i
$409$	−3.79417	+	16.6233i	−0.187610	+	0.821972i	0.790262	+	0.612768i	$0.209944\pi$
$409$	−3.79417	+	16.6233i	−0.187610	+	0.821972i	−0.977872	+	0.209203i	$0.932913\pi$
$410$	6.14200	−	21.9022i	0.303332	−	1.08167i
$411$	−2.28560			−0.112740
$412$	6.21458	+	1.41844i	0.306171	+	0.0698814i
$413$	0.787540	+	33.3292i	0.0387523	+	1.64002i
$414$	2.57725	+	11.2916i	0.126665	+	0.554954i
$415$	−8.51387	−	0.417573i	−0.417929	−	0.0204978i
$416$	−4.08149	−	5.11802i	−0.200111	−	0.250932i
$417$	0.914732	−	0.729474i	0.0447946	−	0.0357225i
$418$	13.4621	−	3.07263i	0.658452	−	0.150287i
$419$	0.992733	+	4.34945i	0.0484982	+	0.212484i	0.993371	−	0.114953i	$-0.0366719\pi$
$419$	0.992733	+	4.34945i	0.0484982	+	0.212484i	−0.944873	+	0.327438i	$0.893815\pi$
$420$	−1.38811	+	0.279963i	−0.0677326	+	0.0136608i
$421$	8.35052	−	36.5860i	0.406979	−	1.78309i	−0.191009	−	0.981588i	$-0.561176\pi$
$421$	8.35052	−	36.5860i	0.406979	−	1.78309i	0.597988	−	0.801505i	$-0.295967\pi$
$422$		−	4.03674i		−	0.196505i
$423$			33.5375i			1.63065i
$424$	−1.86862	+	8.18697i	−0.0907483	+	0.397594i
$425$	1.74480	−	17.7445i	0.0846351	−	0.860735i
$426$	−1.06128	−	1.33080i	−0.0514192	−	0.0644776i
$427$	−18.0135	−	13.6819i	−0.871736	−	0.662111i
$428$	−3.05695	−	2.43784i	−0.147763	−	0.117837i
$429$	1.43767	−	6.29885i	0.0694115	−	0.304112i
$430$	3.08759	−	2.22385i	0.148897	−	0.107244i
$431$	−33.5817	+	16.1721i	−1.61757	+	0.778981i	−0.999972	−	0.00751156i	$-0.997609\pi$
$431$	−33.5817	+	16.1721i	−1.61757	+	0.778981i	−0.617599	+	0.786493i	$0.711895\pi$
$432$	1.11210	−	0.886870i	0.0535060	−	0.0426696i
$433$	2.09832	−	4.35720i	0.100839	−	0.209394i	−0.844446	−	0.535641i	$-0.820070\pi$
$433$	2.09832	−	4.35720i	0.100839	−	0.209394i	0.945284	+	0.326247i	$0.105784\pi$
$434$	−16.7862	+	8.57807i	−0.805764	+	0.411761i
$435$	0.00577490	+	0.0325872i	0.000276885	+	0.00156244i
$436$	6.26739	+	3.01821i	0.300153	+	0.144546i
$437$	12.8498	−	2.93288i	0.614690	−	0.140299i
$438$	0.150376	−	0.312258i	0.00718522	−	0.0149203i
$439$	13.3816	−	16.7800i	0.638669	−	0.800866i	−0.352166	−	0.935937i	$-0.614555\pi$
$439$	13.3816	−	16.7800i	0.638669	−	0.800866i	0.990836	+	0.135071i	$0.0431263\pi$
$440$	−2.48956	+	8.87769i	−0.118685	+	0.423227i
$441$	3.63005	−	20.2766i	0.172860	−	0.965552i
$442$		−	23.3439i		−	1.11035i
$443$	15.9075	+	12.6858i	0.755787	+	0.602720i	0.923716	−	0.383079i	$-0.125136\pi$
$443$	15.9075	+	12.6858i	0.755787	+	0.602720i	−0.167928	+	0.985799i	$0.553708\pi$
$444$	0.134345	+	0.0646970i	0.00637572	+	0.00307038i
$445$	1.32717	−	27.0596i	0.0629139	−	1.28275i
$446$	−5.78187	−	2.78440i	−0.273779	−	0.131845i
$447$	−1.84781	−	3.83702i	−0.0873986	−	0.181485i
$448$	2.56479	−	0.649503i	0.121175	−	0.0306861i
$449$	−30.5039	−	14.6899i	−1.43957	−	0.693259i	−0.458817	−	0.888531i	$-0.651727\pi$
$449$	−30.5039	−	14.6899i	−1.43957	−	0.693259i	−0.980749	+	0.195272i	$0.937441\pi$
$450$	14.5962	−	1.85463i	0.688071	−	0.0874283i
$451$	−37.7923	+	18.1998i	−1.77957	+	0.856996i
$452$	14.3749	+	11.4636i	0.676139	+	0.539203i
$453$	2.49532	+	0.569540i	0.117240	+	0.0267593i
$454$	3.00376	−	3.76659i	0.140973	−	0.176775i
$455$	−37.5260	−	9.57323i	−1.75924	−	0.448800i
$456$	−0.499761	−	0.626680i	−0.0234034	−	0.0293470i
$457$	−5.15420	−	10.7028i	−0.241103	−	0.500656i	0.744943	−	0.667128i	$-0.232477\pi$
$457$	−5.15420	−	10.7028i	−0.241103	−	0.500656i	−0.986046	+	0.166472i	$0.946762\pi$
$458$	28.4289	+	6.48872i	1.32840	+	0.303198i
$459$	5.07241			0.236760
$460$	−2.37633	+	8.47392i	−0.110797	+	0.395099i
$461$	2.43904	−	10.6861i	0.113597	−	0.497703i	−0.885835	−	0.464001i	$-0.846413\pi$
$461$	2.43904	−	10.6861i	0.113597	−	0.497703i	0.999432	−	0.0337015i	$-0.0107295\pi$
$462$	2.07945	+	1.57941i	0.0967447	+	0.0734807i
$463$	23.7338	−	5.41709i	1.10300	−	0.251753i	0.368006	−	0.929823i	$-0.380041\pi$
$463$	23.7338	−	5.41709i	1.10300	−	0.251753i	0.734997	+	0.678070i	$0.237183\pi$
$464$	−0.0137595	−	0.0602842i	−0.000638767	−	0.00279862i
$465$	−3.51272	+	1.48429i	−0.162898	+	0.0688324i
$466$	4.20876	+	5.27762i	0.194967	+	0.244481i
$467$	23.8083	−	5.43410i	1.10172	−	0.251460i	0.367263	−	0.930117i	$-0.380295\pi$
$467$	23.8083	−	5.43410i	1.10172	−	0.251460i	0.734455	+	0.678657i	$0.237438\pi$
$468$	18.7806	−	4.28654i	0.868132	−	0.198146i
$469$	28.5644	+	12.9338i	1.31898	+	0.597225i
$470$	−12.1686	+	22.3911i	−0.561297	+	1.03283i
$471$	−3.44166			−0.158583
$472$		−	12.6008i		−	0.579998i
$473$	−6.84078	−	1.56136i	−0.314540	−	0.0717916i
$474$	−2.42948	+	1.16997i	−0.111590	+	0.0537387i
$475$	−2.11056	−	16.6103i	−0.0968390	−	0.762135i
$476$	8.59478	+	3.89166i	0.393941	+	0.178374i
$477$	−19.3202	−	15.4073i	−0.884610	−	0.705453i
$478$	−0.141549	−	0.0323076i	−0.00647429	−	0.00147771i
$479$	1.31505	−	1.64902i	0.0600862	−	0.0753457i	−0.750880	−	0.660438i	$-0.770370\pi$
$479$	1.31505	−	1.64902i	0.0600862	−	0.0753457i	0.810966	+	0.585093i	$0.198942\pi$
$480$	0.527008	−	0.0933928i	0.0240545	−	0.00426278i
$481$	2.54263	+	3.18835i	0.115934	+	0.145376i
$482$	−1.24184	+	2.57872i	−0.0565645	+	0.117457i
$483$	1.98487	+	1.50757i	0.0903148	+	0.0685970i
$484$	5.40786	−	2.60429i	0.245812	−	0.118377i
$485$	3.96583	−	4.50162i	0.180079	−	0.204408i
$486$	1.40163	+	6.14094i	0.0635793	+	0.278559i
$487$	7.01637	−	14.5696i	0.317942	−	0.660213i	−0.679345	−	0.733819i	$-0.737736\pi$
$487$	7.01637	−	14.5696i	0.317942	−	0.660213i	0.997287	+	0.0736053i	$0.0234505\pi$
$488$	6.68442	+	5.33064i	0.302589	+	0.241307i
$489$	0.417003			0.0188575
$490$	9.78065	−	12.2204i	0.441845	−	0.552063i
$491$	−28.8547			−1.30219			−0.651097	−	0.758995i	$-0.725691\pi$
$491$	−28.8547			−1.30219			−0.651097	+	0.758995i	$0.725691\pi$
$492$	1.90371	+	1.51816i	0.0858257	+	0.0684437i
$493$	0.0956726	−	0.198666i	0.00430888	−	0.00894748i
$494$	−4.87805	−	21.3721i	−0.219474	−	0.961578i
$495$	−20.3587	−	17.9355i	−0.915054	−	0.806142i
$496$	6.41941	−	3.09143i	0.288240	−	0.138809i
$497$	18.4370	+	3.75224i	0.827012	+	0.168311i
$498$	0.395898	−	0.822091i	0.0177406	−	0.0368388i
$499$	13.0632	+	16.3808i	0.584790	+	0.733303i	0.982922	−	0.184025i	$-0.0589128\pi$
$499$	13.0632	+	16.3808i	0.584790	+	0.733303i	−0.398132	+	0.917328i	$0.630341\pi$
$500$	10.4180	+	4.05778i	0.465906	+	0.181470i
$501$	−0.808282	+	1.01355i	−0.0361114	+	0.0452822i
$502$	−13.0236	−	2.97256i	−0.581273	−	0.132672i
$503$	−6.28039	−	5.00845i	−0.280029	−	0.223316i	0.473396	−	0.880850i	$-0.343028\pi$
$503$	−6.28039	−	5.00845i	−0.280029	−	0.223316i	−0.753425	+	0.657534i	$0.771599\pi$
$504$	−1.55269	+	7.62928i	−0.0691621	+	0.339835i
$505$	6.21648	+	14.7119i	0.276630	+	0.654671i
$506$	14.6218	−	7.04149i	0.650018	−	0.313032i
$507$	−6.96631	−	1.59001i	−0.309385	−	0.0706150i
$508$			10.6180i			0.471099i
$509$	−7.36219			−0.326323			−0.163162	−	0.986599i	$-0.552169\pi$
$509$	−7.36219			−0.326323			−0.163162	+	0.986599i	$0.552169\pi$
$510$	1.67696	+	0.911354i	0.0742569	+	0.0403554i
$511$	0.940457	+	3.71372i	0.0416034	+	0.164285i
$512$	−0.974928	+	0.222521i	−0.0430861	+	0.00983413i
$513$	4.64397	−	1.05996i	0.205036	−	0.0467982i
$514$	14.3419	+	17.9842i	0.632596	+	0.793250i
$515$	−13.1296	+	5.54788i	−0.578559	+	0.244469i
$516$	0.0906353	+	0.397099i	0.00398999	+	0.0174813i
$517$	45.8153	−	10.4570i	2.01495	−	0.459900i
$518$	−1.59778	+	0.404618i	−0.0702023	+	0.0177779i
$519$	−0.276081	+	1.20959i	−0.0121186	+	0.0530951i
$520$	14.0941	+	3.95238i	0.618065	+	0.173323i
$521$	15.4548			0.677085			0.338543	−	0.940951i	$-0.390066\pi$
$521$	15.4548			0.677085			0.338543	+	0.940951i	$0.390066\pi$
$522$	0.177399	+	0.0404901i	0.00776453	+	0.00177220i
$523$	1.56115	+	3.24176i	0.0682643	+	0.141752i	0.932309	−	0.361663i	$-0.117791\pi$
$523$	1.56115	+	3.24176i	0.0682643	+	0.141752i	−0.864045	+	0.503415i	$0.832077\pi$
$524$	3.52962	+	4.42600i	0.154192	+	0.193351i
$525$	2.15274	−	2.32202i	0.0939534	−	0.101341i
$526$	−10.7079	+	13.4273i	−0.466888	+	0.585459i
$527$	24.7709	+	5.65379i	1.07904	+	0.246283i
$528$	−0.771637	−	0.615360i	−0.0335812	−	0.0267801i
$529$	−6.76550	+	3.25810i	−0.294152	+	0.141656i
$530$	−7.30867	−	17.2967i	−0.317468	−	0.751319i
$531$	33.4083	+	16.0886i	1.44980	+	0.698185i
$532$	8.68206	+	1.76694i	0.376415	+	0.0766067i
$533$	28.8937	+	59.9984i	1.25152	+	2.59882i
$534$	2.61285	+	1.25828i	0.113069	+	0.0544512i
$535$	8.73250	+	0.428296i	0.377539	+	0.0185169i
$536$	−10.6778	−	5.14217i	−0.461212	−	0.222108i
$537$	−0.383261	−	0.305640i	−0.0165389	−	0.0131893i
$538$			20.4902i			0.883396i
$539$	−28.8315	+	1.36328i	−1.24186	+	0.0587208i
$540$	−0.858816	+	3.06251i	−0.0369576	+	0.131789i
$541$	12.0222	−	15.0754i	0.516875	−	0.648140i	−0.453067	−	0.891476i	$-0.649670\pi$
$541$	12.0222	−	15.0754i	0.516875	−	0.648140i	0.969942	+	0.243336i	$0.0782418\pi$
$542$	4.51777	−	9.38124i	0.194055	−	0.402959i
$543$	−1.59654	+	0.364401i	−0.0685143	+	0.0156379i
$544$	−3.21287	−	1.54724i	−0.137751	−	0.0663372i
$545$	−15.3161	+	2.71421i	−0.656068	+	0.116264i
$546$	2.50744	−	3.30129i	0.107308	−	0.141282i
$547$	−20.1777	+	41.8995i	−0.862737	+	1.79149i	−0.334501	+	0.942396i	$0.608568\pi$
$547$	−20.1777	+	41.8995i	−0.862737	+	1.79149i	−0.528237	+	0.849097i	$0.677147\pi$
$548$	−7.46564	+	5.95365i	−0.318916	+	0.254327i
$549$	−22.6677	+	10.9162i	−0.967434	+	0.465891i
$550$	−7.08469	−	19.3614i	−0.302092	−	0.825573i
$551$	0.0460774	−	0.201878i	0.00196296	−	0.00860031i
$552$	−0.736542	−	0.587372i	−0.0313493	−	0.0250002i
$553$	12.2944	−	27.1524i	0.522812	−	1.15464i
$554$	10.2525	+	12.8562i	0.435587	+	0.546209i
$555$	−0.328308	+	0.0581806i	−0.0139359	+	0.00246963i
$556$	1.08769	−	4.76548i	0.0461283	−	0.202101i
$557$		−	28.7199i		−	1.21690i	−0.793592	−	0.608450i	$-0.791791\pi$
$557$		−	28.7199i		−	1.21690i	0.793592	−	0.608450i	$-0.208209\pi$
$558$			20.9668i			0.887596i
$559$	−2.47879	+	10.8603i	−0.104842	+	0.459341i
$560$	−3.80482	+	4.53027i	−0.160783	+	0.191439i
$561$	−0.783167	−	3.43128i	−0.0330653	−	0.144869i
$562$	−27.2606	+	6.22205i	−1.14992	+	0.262461i
$563$	11.9291	−	9.51315i	0.502752	−	0.400931i	−0.339008	−	0.940784i	$-0.610091\pi$
$563$	11.9291	−	9.51315i	0.502752	−	0.400931i	0.841760	+	0.539852i	$0.181520\pi$
$564$	−1.70083	−	2.13277i	−0.0716177	−	0.0898058i
$565$	−41.0634	−	2.01400i	−1.72755	−	0.0847298i
$566$	5.22433	+	22.8893i	0.219595	+	0.962108i
$567$	−17.8828	−	13.5826i	−0.751008	−	0.570415i
$568$	−6.93308	−	1.58243i	−0.290906	−	0.0663973i
$569$	2.60688			0.109286			0.0546430	−	0.998506i	$-0.482598\pi$
$569$	2.60688			0.109286			0.0546430	+	0.998506i	$0.482598\pi$
$570$	1.72576	+	0.483952i	0.0722840	+	0.0202705i
$571$	−7.78208	+	34.0955i	−0.325670	+	1.42685i	0.501625	+	0.865085i	$0.332736\pi$
$571$	−7.78208	+	34.0955i	−0.325670	+	1.42685i	−0.827295	+	0.561768i	$0.810121\pi$
$572$	−11.7116	−	24.3194i	−0.489686	−	1.01684i
$573$	3.27348	−	2.61052i	0.136752	−	0.109056i
$574$	−26.9072	+	0.635793i	−1.12308	+	0.0265375i
$575$	−6.76247	−	18.4808i	−0.282015	−	0.770703i
$576$	0.654814	−	2.86893i	0.0272839	−	0.119539i
$577$	18.0533	+	14.3970i	0.751567	+	0.599354i	0.922531	−	0.385923i	$-0.126117\pi$
$577$	18.0533	+	14.3970i	0.751567	+	0.599354i	−0.170964	+	0.985277i	$0.554688\pi$
$578$	1.85855	+	3.85932i	0.0773055	+	0.160527i
$579$	−3.28282	−	4.11652i	−0.136429	−	0.171077i
$580$	0.103748	+	0.0913996i	0.00430790	+	0.00379516i
$581$	2.47597	+	9.77722i	0.102720	+	0.405628i
$582$	0.278638	+	0.578598i	0.0115499	+	0.0239836i
$583$	−15.0237	+	31.1971i	−0.622219	+	1.29205i
$584$	−0.322202	−	1.41166i	−0.0133328	−	0.0584149i
$585$	−28.4741	+	32.3210i	−1.17726	+	1.33631i
$586$	9.58558	−	12.0199i	0.395977	−	0.496539i
$587$		−	3.14259i		−	0.129708i	−0.997895	−	0.0648542i	$-0.979342\pi$
$587$		−	3.14259i		−	0.129708i	0.997895	−	0.0648542i	$-0.0206582\pi$
$588$	0.797461	+	1.47355i	0.0328867	+	0.0607683i
$589$	23.8601			0.983137
$590$	16.4673	+	22.8632i	0.677949	+	0.941262i
$591$	0.512608	+	0.246859i	0.0210859	+	0.0101544i
$592$	0.607347	−	0.138623i	0.0249618	−	0.00569737i
$593$	6.87848	−	14.2833i	0.282465	−	0.586545i	−0.710669	−	0.703527i	$-0.751608\pi$
$593$	6.87848	−	14.2833i	0.282465	−	0.586545i	0.993134	+	0.116982i	$0.0373219\pi$
$594$	5.28438	−	2.54482i	0.216821	−	0.104415i
$595$	−20.6804	+	4.17097i	−0.847814	+	0.170993i
$596$	−16.0305	−	7.71990i	−0.656636	−	0.316219i
$597$	−2.05592	+	1.63954i	−0.0841432	+	0.0671020i
$598$	−11.1789	−	23.2133i	−0.457140	−	0.949262i
$599$	5.85739	−	7.34494i	0.239327	−	0.300106i	−0.647634	−	0.761952i	$-0.724241\pi$
$599$	5.85739	−	7.34494i	0.239327	−	0.300106i	0.886960	+	0.461846i	$0.152813\pi$
$600$	−0.834166	+	0.858175i	−0.0340547	+	0.0350348i
$601$	0.509060	−	0.638341i	0.0207650	−	0.0260385i	−0.771341	−	0.636423i	$-0.780413\pi$
$601$	0.509060	−	0.638341i	0.0207650	−	0.0260385i	0.792106	+	0.610384i	$0.208985\pi$
$602$	−3.58532	−	2.72317i	−0.146127	−	0.110988i
$603$	27.2668	−	21.7445i	1.11039	−	0.885505i
$604$	9.63422	−	4.63960i	0.392011	−	0.188782i
$605$	−6.40874	+	11.7925i	−0.260552	+	0.479435i
$606$	−1.70964			−0.0694492
$607$			22.6310i			0.918566i	0.888290	+	0.459283i	$0.151894\pi$
$607$			22.6310i			0.918566i	−0.888290	+	0.459283i	$0.848106\pi$
$608$	−3.26482	−	0.745173i	−0.132406	−	0.0302208i
$609$	0.0348694	−	0.0178189i	0.00141298	−	0.000722059i
$610$	−19.0947	−	0.936524i	−0.773123	−	0.0379187i
$611$	−16.6014	−	72.7354i	−0.671620	−	2.94256i
$612$	8.20434	−	6.54274i	0.331641	−	0.264475i
$613$	6.17485	−	4.92428i	0.249400	−	0.198890i	−0.490808	−	0.871268i	$-0.663298\pi$
$613$	6.17485	−	4.92428i	0.249400	−	0.198890i	0.740208	+	0.672378i	$0.234727\pi$
$614$	6.80426	+	29.8114i	0.274598	+	1.20309i
$615$	−5.43814	−	0.266720i	−0.219287	−	0.0107552i
$616$	10.9064	−	0.257709i	0.439431	−	0.0103834i
$617$	−26.6860	−	6.09091i	−1.07434	−	0.245211i	−0.351472	−	0.936198i	$-0.614319\pi$
$617$	−26.6860	−	6.09091i	−1.07434	−	0.245211i	−0.722867	+	0.690988i	$0.757176\pi$
$618$		−	1.52576i		−	0.0613750i
$619$	12.7185			0.511199			0.255600	−	0.966783i	$-0.417727\pi$
$619$	12.7185			0.511199			0.255600	+	0.966783i	$0.417727\pi$
$620$	−7.60751	+	13.9984i	−0.305525	+	0.562188i
$621$	5.04404	−	2.42908i	0.202410	−	0.0974756i
$622$	−10.5854	+	8.44159i	−0.424437	+	0.338477i
$623$	−31.0749	+	7.86936i	−1.24499	+	0.315279i
$624$	−0.976933	+	1.22504i	−0.0391086	+	0.0490407i
$625$	−24.2056	+	6.25220i	−0.968223	+	0.250088i
$626$	−11.0170	+	13.8149i	−0.440329	+	0.552155i
$627$	−1.43403	−	2.97780i	−0.0572698	−	0.118922i
$628$	−11.2418	+	8.96501i	−0.448595	+	0.357743i
$629$	2.00151	+	0.963876i	0.0798054	+	0.0384322i
$630$	−7.15309	−	15.8719i	−0.284986	−	0.632351i
$631$	−12.3879	+	5.96570i	−0.493155	+	0.237491i	−0.663896	−	0.747825i	$-0.731098\pi$
$631$	−12.3879	+	5.96570i	−0.493155	+	0.237491i	0.170741	+	0.985316i	$0.445384\pi$
$632$	−4.88799	+	10.1500i	−0.194434	+	0.403746i
$633$	−0.941997	+	0.215005i	−0.0374410	+	0.00854567i
$634$	−3.03557	−	1.46185i	−0.120558	−	0.0580576i
$635$	−13.8762	−	19.2656i	−0.550660	−	0.764533i
$636$	2.01001			0.0797019
$637$	2.16432	+	45.7722i	0.0857537	+	1.81356i
$638$		−	0.254967i		−	0.0100942i
$639$	13.0476	−	16.3612i	0.516155	−	0.647238i
$640$	1.47813	−	1.67783i	0.0584283	−	0.0663222i
$641$	4.80638	+	21.0581i	0.189841	+	0.831747i	0.976699	+	0.214613i	$0.0688490\pi$
$641$	4.80638	+	21.0581i	0.189841	+	0.831747i	−0.786858	+	0.617134i	$0.788294\pi$
$642$	−0.406065	+	0.843202i	−0.0160261	+	0.0332785i
$643$	−11.6361	−	24.1627i	−0.458884	−	0.952883i	−0.994131	−	0.108187i	$-0.965496\pi$
$643$	−11.6361	−	24.1627i	−0.458884	−	0.952883i	0.535246	−	0.844696i	$-0.320219\pi$
$644$	10.4104	−	0.245988i	0.410225	−	0.00969327i
$645$	−0.683400	−	0.602060i	−0.0269089	−	0.0237061i
$646$	−7.44559	−	9.33647i	−0.292943	−	0.367339i
$647$	−18.4048	−	38.2180i	−0.723568	−	1.50250i	−0.859142	−	0.511738i	$-0.829002\pi$
$647$	−18.4048	−	38.2180i	−0.723568	−	1.50250i	0.135574	−	0.990767i	$-0.456712\pi$
$648$	6.63592	+	5.29197i	0.260683	+	0.207888i
$649$	11.5617	−	50.6551i	0.453836	−	1.98839i
$650$	−30.7378	+	11.2475i	−1.20563	+	0.441164i
$651$	2.89581	+	3.46028i	0.113496	+	0.135619i
$652$	1.36209	−	1.08623i	0.0533436	−	0.0425401i
$653$	−19.3525	−	40.1858i	−0.757321	−	1.57259i	−0.818527	−	0.574467i	$-0.805209\pi$
$653$	−19.3525	−	40.1858i	−0.757321	−	1.57259i	0.0612068	−	0.998125i	$-0.480505\pi$
$654$	0.370505	−	1.62329i	0.0144879	−	0.0634756i
$655$	−12.1884	−	3.41797i	−0.476238	−	0.133551i
$656$	10.1728			0.397181
$657$	4.15410	+	0.948147i	0.162067	+	0.0369907i
$658$	29.5475	+	6.01341i	1.15188	+	0.234427i
$659$	0.181882	+	0.796878i	0.00708512	+	0.0310420i	0.978347	−	0.206972i	$-0.0663608\pi$
$659$	0.181882	+	0.796878i	0.00708512	+	0.0310420i	−0.971262	+	0.238014i	$0.923504\pi$
$660$	2.20426	+	0.108111i	0.0858008	+	0.00420820i
$661$	3.84842	+	4.82576i	0.149686	+	0.187700i	0.851021	−	0.525131i	$-0.175984\pi$
$661$	3.84842	+	4.82576i	0.149686	+	0.187700i	−0.701335	+	0.712832i	$0.747412\pi$
$662$	18.5575	−	14.7991i	0.721258	−	0.575184i
$663$	−5.44743	+	1.24334i	−0.211561	+	0.0482873i
$664$	−0.848271	−	3.71652i	−0.0329193	−	0.144229i
$665$	−18.0621	+	8.14016i	−0.700417	+	0.315662i
$666$	−0.407927	+	1.78724i	−0.0158068	+	0.0692543i
$667$		−	0.243371i		−	0.00942336i
$668$			5.41611i			0.209555i
$669$	−0.341803	+	1.49754i	−0.0132149	+	0.0578981i
$670$	26.0942	−	4.62424i	1.00811	−	0.178650i
$671$	21.9803	+	27.5624i	0.848539	+	1.06403i
$672$	−0.288171	−	0.563915i	−0.0111164	−	0.0217535i
$673$	−12.6351	−	10.0761i	−0.487045	−	0.388406i	0.348951	−	0.937141i	$-0.386538\pi$
$673$	−12.6351	−	10.0761i	−0.487045	−	0.388406i	−0.835996	+	0.548735i	$0.815109\pi$
$674$	3.56408	−	15.6152i	0.137283	−	0.601477i
$675$	−2.44398	−	6.67904i	−0.0940690	−	0.257076i
$676$	−26.8964	+	12.9526i	−1.03448	+	0.498177i
$677$	7.10543	−	5.66639i	0.273084	−	0.217777i	−0.477366	−	0.878705i	$-0.658408\pi$
$677$	7.10543	−	5.66639i	0.273084	−	0.217777i	0.750450	+	0.660927i	$0.229837\pi$
$678$	1.90946	−	3.96504i	0.0733326	−	0.152277i
$679$	−6.46654	−	2.92800i	−0.248163	−	0.112367i
$680$	7.85152	−	1.39140i	0.301092	−	0.0533576i
$681$	−1.03894	−	0.500329i	−0.0398124	−	0.0191726i
$682$	28.6425	−	6.53747i	1.09678	−	0.250333i
$683$	−13.1286	+	27.2618i	−0.502351	+	1.04314i	0.483473	+	0.875359i	$0.339375\pi$
$683$	−13.1286	+	27.2618i	−0.502351	+	1.04314i	−0.985824	+	0.167783i	$0.946339\pi$
$684$	6.14417	−	7.70454i	0.234928	−	0.294590i
$685$	5.76532	−	20.5589i	0.220281	−	0.785516i
$686$	−17.2133	−	6.83384i	−0.657208	−	0.260917i
$687$		−	6.97966i		−	0.266291i
$688$	1.33043	+	1.06098i	0.0507223	+	0.0404497i
$689$	49.5279	+	23.8514i	1.88686	+	0.908665i
$690$	2.10401	+	0.103194i	0.0800982	+	0.00392851i
$691$	24.3782	+	11.7399i	0.927389	+	0.446607i	0.835704	−	0.549181i	$-0.185060\pi$
$691$	24.3782	+	11.7399i	0.927389	+	0.446607i	0.0916858	+	0.995788i	$0.470774\pi$
$692$	2.24902	+	4.67013i	0.0854948	+	0.177532i
$693$	−13.2420	+	29.2450i	−0.503020	+	1.11093i
$694$	−3.01028	−	1.44967i	−0.114269	−	0.0550288i
$695$	4.25424	+	10.0681i	0.161373	+	0.381903i
$696$	−0.0133348	+	0.00642171i	−0.000505455	+	0.000243414i
$697$	28.3620	+	22.6179i	1.07429	+	0.856716i
$698$	7.65258	+	1.74665i	0.289654	+	0.0661117i
$699$	1.00740	−	1.26324i	0.0381033	−	0.0477800i
$700$	0.983168	−	13.1922i	0.0371603	−	0.498617i
$701$	−27.7853	−	34.8416i	−1.04944	−	1.31595i	−0.947008	−	0.321210i	$-0.895910\pi$
$701$	−27.7853	−	34.8416i	−1.04944	−	1.31595i	−0.102427	−	0.994740i	$-0.532661\pi$
$702$	−4.04011	−	8.38938i	−0.152484	−	0.316637i
$703$	2.03387	+	0.464217i	0.0767088	+	0.0175083i
$704$	−4.12338			−0.155406
$705$	5.87323	+	1.64702i	0.221199	+	0.0620305i
$706$	1.55452	−	6.81080i	0.0585052	−	0.256328i
$707$	14.4923	−	12.1282i	0.545038	−	0.456127i
$708$	−2.94047	+	0.671142i	−0.110509	+	0.0252231i
$709$	4.12322	+	18.0650i	0.154851	+	0.678445i	0.991434	+	0.130606i	$0.0416922\pi$
$709$	4.12322	+	18.0650i	0.154851	+	0.678445i	−0.836584	+	0.547839i	$0.815451\pi$
$710$	14.6476	−	6.18930i	0.549713	−	0.232280i
$711$	−20.6697	−	25.9189i	−0.775173	−	0.972036i
$712$	11.8122	−	2.69606i	0.442681	−	0.101039i
$713$	27.3398	−	6.24014i	1.02388	−	0.233695i
$714$	0.450367	−	2.21292i	0.0168545	−	0.0828165i
$715$	53.0316	+	28.8204i	1.98327	+	1.07782i
$716$	−2.04802			−0.0765382
$717$			0.0347520i			0.00129784i
$718$	−34.0911	−	7.78107i	−1.27227	−	0.290387i
$719$	−6.18020	+	2.97623i	−0.230483	+	0.110995i	−0.545561	−	0.838071i	$-0.683683\pi$
$719$	−6.18020	+	2.97623i	−0.230483	+	0.110995i	0.315079	+	0.949066i	$0.397969\pi$
$720$	2.56115	+	6.06120i	0.0954484	+	0.225888i
$721$	10.8238	+	12.9336i	0.403098	+	0.481672i
$722$	6.08709	+	4.85430i	0.226538	+	0.180658i
$723$	0.667902	+	0.152444i	0.0248395	+	0.00566946i
$724$	−4.26571	+	5.34903i	−0.158534	+	0.198795i
$725$	−0.307689	−	0.0302547i	−0.0114273	−	0.00112363i
$726$	−0.895759	−	1.12325i	−0.0332447	−	0.0416876i
$727$	−20.9174	+	43.4354i	−0.775783	+	1.61093i	0.0158053	+	0.999875i	$0.494969\pi$
$727$	−20.9174	+	43.4354i	−0.775783	+	1.61093i	−0.791588	+	0.611055i	$0.790745\pi$
$728$	−0.409133	−	17.3148i	−0.0151635	−	0.641728i
$729$	−21.5830	+	10.3938i	−0.799369	+	0.384956i
$730$	2.42944	+	2.14028i	0.0899176	+	0.0792154i
$731$	1.35031	+	5.91610i	0.0499431	+	0.218815i
$732$	0.887912	−	1.84377i	0.0328182	−	0.0681477i
$733$	−22.1767	−	17.6853i	−0.819116	−	0.653223i	0.121539	−	0.992587i	$-0.461217\pi$
$733$	−22.1767	−	17.6853i	−0.819116	−	0.653223i	−0.940655	+	0.339364i	$0.889788\pi$
$734$	34.2689			1.26489
$735$	−3.37265	−	1.63149i	−0.124402	−	0.0601784i
$736$	−3.93584			−0.145077
$737$	−38.2067	−	30.4688i	−1.40736	−	1.12233i
$738$	−12.9886	+	26.9710i	−0.478115	+	0.992817i
$739$	−1.39148	−	6.09645i	−0.0511863	−	0.224262i	0.942865	−	0.333175i	$-0.108120\pi$
$739$	−1.39148	−	6.09645i	−0.0511863	−	0.224262i	−0.994051	+	0.108913i	$0.965263\pi$
$740$	−0.920826	+	1.04523i	−0.0338502	+	0.0384235i
$741$	−4.72750	+	2.27664i	−0.173669	+	0.0836346i
$742$	−17.0384	+	14.2590i	−0.625501	+	0.523464i
$743$	9.43193	−	19.5856i	0.346024	−	0.718526i	−0.653229	−	0.757160i	$-0.726586\pi$
$743$	9.43193	−	19.5856i	0.346024	−	0.718526i	0.999253	+	0.0386337i	$0.0123005\pi$
$744$	−1.06331	−	1.33335i	−0.0389830	−	0.0488831i
$745$	39.1750	−	6.94233i	1.43526	−	0.254347i
$746$	−2.39381	+	3.00174i	−0.0876435	+	0.109901i
$747$	10.9366	+	2.49621i	0.400150	+	0.0913317i
$748$	−11.4961	−	9.16782i	−0.420339	−	0.335209i
$749$	−2.53955	−	10.0283i	−0.0927931	−	0.366426i
$750$	0.392026	−	2.64722i	0.0143148	−	0.0966630i
$751$	−10.1305	+	4.87861i	−0.369669	+	0.178023i	−0.609490	−	0.792794i	$-0.708626\pi$
$751$	−10.1305	+	4.87861i	−0.369669	+	0.178023i	0.239821	+	0.970817i	$0.422911\pi$
$752$	−11.1111	−	2.53603i	−0.405180	−	0.0924796i
$753$			3.19747i			0.116522i
$754$	−0.404781			−0.0147412
$755$	−11.4173	+	21.0087i	−0.415519	+	0.764585i
$756$	3.76235	−	0.0889009i	0.136835	−	0.00323329i
$757$	−28.7090	+	6.55265i	−1.04345	+	0.238160i	−0.709701	−	0.704503i	$-0.751170\pi$
$757$	−28.7090	+	6.55265i	−1.04345	+	0.238160i	−0.333747	+	0.942663i	$0.608313\pi$
$758$	−12.1249	+	2.76743i	−0.440396	+	0.100517i
$759$	−2.42196	−	3.03704i	−0.0879116	−	0.110238i
$760$	6.89760	−	2.91457i	0.250202	−	0.105722i
$761$	6.08378	+	26.6548i	0.220537	+	0.966234i	0.957075	+	0.289839i	$0.0936018\pi$
$761$	6.08378	+	26.6548i	0.220537	+	0.966234i	−0.736539	+	0.676395i	$0.763541\pi$
$762$	2.47778	−	0.565538i	0.0897606	−	0.0204873i
$763$	8.37492	+	16.3887i	0.303193	+	0.593310i
$764$	3.89244	−	17.0539i	0.140823	−	0.616988i
$765$	−6.33578	+	22.5932i	−0.229071	+	0.816858i
$766$	−6.97896			−0.252160
$767$	−80.4190	−	18.3551i	−2.90376	−	0.662765i
$768$	0.103853	+	0.215653i	0.00374748	+	0.00778172i
$769$	2.01209	+	2.52308i	0.0725579	+	0.0909848i	0.816786	−	0.576941i	$-0.195754\pi$
$769$	2.01209	+	2.52308i	0.0725579	+	0.0909848i	−0.744228	+	0.667926i	$0.767182\pi$
$770$	−19.4521	+	14.7206i	−0.701004	+	0.530494i
$771$	3.43285	−	4.30465i	0.123631	−	0.155028i
$772$	−21.4458	−	4.89487i	−0.771853	−	0.176170i
$773$	12.1885	+	9.72001i	0.438390	+	0.349605i	0.817680	−	0.575674i	$-0.195260\pi$
$773$	12.1885	+	9.72001i	0.438390	+	0.349605i	−0.379289	+	0.925278i	$0.623832\pi$
$774$	−4.51166	+	2.17270i	−0.162168	+	0.0780962i
$775$	−4.49052	−	35.3409i	−0.161304	−	1.26948i
$776$	2.41730	+	1.16411i	0.0867759	+	0.0417891i
$777$	0.179521	+	0.351300i	0.00644027	+	0.0126028i
$778$	−2.82347	−	5.86300i	−0.101226	−	0.210199i
$779$	30.6928	+	14.7809i	1.09968	+	0.529580i
$780$	0.171634	−	3.49944i	0.00614549	−	0.125300i
$781$	−26.4191	−	12.7227i	−0.945348	−	0.455256i
$782$	−10.9732	−	8.75085i	−0.392402	−	0.312930i
$783$		−	0.0879552i		−	0.00314326i
$784$	6.44320	+	2.73592i	0.230114	+	0.0977113i
$785$	8.68142	−	30.9577i	0.309853	−	1.10493i
$786$	0.844840	−	1.05940i	0.0301344	−	0.0377874i
$787$	7.51905	−	15.6135i	0.268025	−	0.556560i	−0.722903	−	0.690949i	$-0.757193\pi$
$787$	7.51905	−	15.6135i	0.268025	−	0.556560i	0.990929	+	0.134389i	$0.0429072\pi$
$788$	2.31740	−	0.528933i	0.0825541	−	0.0188424i
$789$	3.70367	+	1.78359i	0.131854	+	0.0634977i
$790$	−4.39566	−	24.8043i	−0.156390	−	0.882498i
$791$	11.9419	+	47.1567i	0.424605	+	1.67670i
$792$	5.26470	−	10.9323i	0.187073	−	0.388461i
$793$	43.7575	−	34.8955i	1.55387	−	1.23917i
$794$	15.5381	−	7.48277i	0.551428	−	0.265554i
$795$	−3.64701	+	2.62678i	−0.129346	+	0.0931622i
$796$	−2.44466	+	10.7107i	−0.0866485	+	0.379632i
$797$	−37.2720	−	29.7235i	−1.32024	−	1.05286i	−0.994205	−	0.107502i	$-0.965715\pi$
$797$	−37.2720	−	29.7235i	−1.32024	−	1.05286i	−0.326038	−	0.945357i	$-0.605714\pi$
$798$	−0.0500966	−	2.12012i	−0.00177340	−	0.0750515i
$799$	−25.3394	−	31.7746i	−0.896445	−	1.12411i
$800$	−0.489285	+	4.97600i	−0.0172988	+	0.175928i
$801$	−7.93371	+	34.7598i	−0.280324	+	1.22818i
$802$			23.9642i			0.846204i
$803$		−	5.97050i		−	0.210695i
$804$	−0.631234	+	2.76562i	−0.0222619	+	0.0975358i
$805$	−18.5673	+	14.0511i	−0.654413	+	0.495236i
$806$	−10.3788	−	45.4723i	−0.365576	−	1.60169i
$807$	4.78151	−	1.09135i	0.168317	−	0.0384173i
$808$	−5.58432	+	4.45334i	−0.196456	+	0.156668i
$809$	−4.26048	−	5.34247i	−0.149790	−	0.187831i	0.701275	−	0.712891i	$-0.252614\pi$
$809$	−4.26048	−	5.34247i	−0.149790	−	0.187831i	−0.851066	+	0.525060i	$0.824043\pi$
$810$	−18.9562	−	0.929729i	−0.666053	−	0.0326673i
$811$	−0.0294920	−	0.129213i	−0.00103560	−	0.00453728i	0.974407	−	0.224789i	$-0.0721693\pi$
$811$	−0.0294920	−	0.129213i	−0.00103560	−	0.00453728i	−0.975443	+	0.220252i	$0.929312\pi$
$812$	0.0674811	−	0.149033i	0.00236812	−	0.00523003i
$813$	−2.42979	−	0.554584i	−0.0852166	−	0.0194501i
$814$	2.56873			0.0900338
$815$	−1.05187	+	3.75094i	−0.0368454	+	0.131390i
$816$	−0.189933	+	0.832151i	−0.00664899	+	0.0291311i
$817$	2.47252	+	5.13424i	0.0865025	+	0.179624i
$818$	13.3309	−	10.6310i	0.466104	−	0.371705i
$819$	46.4289	+	21.0227i	1.62236	+	0.734591i
$820$	−18.4578	+	13.2943i	−0.644574	+	0.464258i
$821$	3.47239	−	15.2135i	0.121187	−	0.530956i	−0.877493	−	0.479590i	$-0.840785\pi$
$821$	3.47239	−	15.2135i	0.121187	−	0.530956i	0.998680	−	0.0513662i	$-0.0163576\pi$
$822$	1.78695	+	1.42505i	0.0623272	+	0.0497042i
$823$	19.3059	+	40.0890i	0.672960	+	1.39742i	0.905297	+	0.424780i	$0.139649\pi$
$823$	19.3059	+	40.0890i	0.672960	+	1.39742i	−0.232337	+	0.972635i	$0.574637\pi$
$824$	−3.97438	−	4.98371i	−0.138454	−	0.173616i
$825$	−4.14075	+	2.68448i	−0.144163	+	0.0934617i
$826$	20.1647	−	26.5488i	0.701620	−	0.923752i
$827$	−10.1412	−	21.0584i	−0.352644	−	0.732273i	0.646896	−	0.762578i	$-0.276067\pi$
$827$	−10.1412	−	21.0584i	−0.352644	−	0.732273i	−0.999541	+	0.0303045i	$0.990352\pi$
$828$	5.02526	−	10.4351i	0.174640	−	0.362643i
$829$	−9.80423	−	42.9551i	−0.340515	−	1.49189i	−0.797990	−	0.602671i	$-0.794103\pi$
$829$	−9.80423	−	42.9551i	−0.340515	−	1.49189i	0.457475	−	0.889222i	$-0.348754\pi$
$830$	6.39606	+	5.63478i	0.222010	+	0.195586i
$831$	2.45401	−	3.07723i	0.0851287	−	0.106748i
$832$			6.54620i			0.226949i
$833$	11.8808	+	21.9534i	0.411646	+	0.760642i
$834$	−1.16999			−0.0405133
$835$	−7.07804	−	9.82712i	−0.244946	−	0.340082i
$836$	−12.4408	−	5.99119i	−0.430275	−	0.207210i
$837$	9.88072	−	2.25521i	0.341528	−	0.0779515i
$838$	1.93569	−	4.01950i	0.0668672	−	0.138851i
$839$	−7.49857	+	3.61112i	−0.258879	+	0.124670i	−0.558822	−	0.829287i	$-0.688747\pi$
$839$	−7.49857	+	3.61112i	−0.258879	+	0.124670i	0.299943	+	0.953957i	$0.403032\pi$
$840$	1.25982	+	0.646585i	0.0434679	+	0.0223093i
$841$	26.1247	+	12.5810i	0.900850	+	0.433827i
$842$	−29.3397	+	23.3976i	−1.01111	+	0.806336i
$843$	2.90390	+	6.03002i	0.100016	+	0.207685i
$844$	−2.51687	+	3.15605i	−0.0866341	+	0.108636i
$845$	31.8743	−	58.6511i	1.09651	−	2.01766i
$846$	20.9103	−	26.2207i	0.718912	−	0.901487i
$847$	15.5615	+	3.16703i	0.534700	+	0.108820i
$848$	6.56544	−	5.23576i	0.225458	−	0.179797i
$849$	5.06309	−	2.43826i	0.173765	−	0.0836807i
$850$	−12.4277	+	12.7854i	−0.426265	+	0.438534i
$851$	2.45190			0.0840499
$852$			1.70216i			0.0583150i
$853$	−23.5435	−	5.37365i	−0.806114	−	0.183990i	−0.200443	−	0.979705i	$-0.564238\pi$
$853$	−23.5435	−	5.37365i	−0.806114	−	0.183990i	−0.605671	+	0.795715i	$0.707095\pi$
$854$	5.55305	+	21.9282i	0.190021	+	0.750366i
$855$	−1.07945	+	22.0088i	−0.0369164	+	0.752686i
$856$	0.870054	+	3.81196i	0.0297378	+	0.130290i
$857$	−19.5533	+	15.5932i	−0.667928	+	0.532654i	−0.897710	−	0.440588i	$-0.854770\pi$
$857$	−19.5533	+	15.5932i	−0.667928	+	0.532654i	0.229782	+	0.973242i	$0.426199\pi$
$858$	−5.05129	+	4.02827i	−0.172448	+	0.137523i
$859$	−10.6370	−	46.6038i	−0.362930	−	1.59010i	−0.745715	−	0.666265i	$-0.767892\pi$
$859$	−10.6370	−	46.6038i	−0.362930	−	1.59010i	0.382785	−	0.923838i	$-0.374965\pi$
$860$	−3.80052	−	0.186401i	−0.129597	−	0.00635622i
$861$	1.58150	+	6.24509i	0.0538972	+	0.212832i
$862$	36.3383	+	8.29398i	1.23769	+	0.282494i
$863$			23.1181i			0.786948i	0.919336	+	0.393474i	$0.128727\pi$
$863$			23.1181i			0.786948i	−0.919336	+	0.393474i	$0.871273\pi$
$864$	−1.42243			−0.0483920
$865$	−10.1838	−	5.53448i	−0.346261	−	0.188178i
$866$	−4.35720	+	2.09832i	−0.148064	+	0.0713037i
$867$	0.801606	−	0.639259i	0.0272240	−	0.0217104i
$868$	18.4723	+	3.75943i	0.626992	+	0.127603i
$869$	−28.9627	+	36.3181i	−0.982493	+	1.23201i
$870$	0.0158028	−	0.0290783i	0.000535766	−	0.000985848i
$871$	−48.3717	+	60.6562i	−1.63901	+	2.05526i
$872$	−3.01821	−	6.26739i	−0.102210	−	0.212240i
$873$	−6.17278	+	4.92263i	−0.208917	+	0.166606i
$874$	−11.8750	−	5.71870i	−0.401678	−	0.193438i
$875$	15.4563	+	25.2211i	0.522519	+	0.852628i
$876$	−0.312258	+	0.150376i	−0.0105502	+	0.00508072i
$877$	−4.99522	+	10.3727i	−0.168676	+	0.350260i	−0.968122	−	0.250478i	$-0.919412\pi$
$877$	−4.99522	+	10.3727i	−0.168676	+	0.350260i	0.799446	+	0.600738i	$0.205127\pi$
$878$	−20.9243	+	4.77584i	−0.706162	+	0.161177i
$879$	−3.31547	−	1.59665i	−0.111828	−	0.0538535i
$880$	7.48157	−	5.38864i	0.252204	−	0.181651i
$881$	33.6949			1.13521			0.567604	−	0.823302i	$-0.307870\pi$
$881$	33.6949			1.13521			0.567604	+	0.823302i	$0.307870\pi$
$882$	−15.4803	+	13.5896i	−0.521250	+	0.457585i
$883$		−	4.10600i		−	0.138178i	−0.997611	−	0.0690889i	$-0.977991\pi$
$883$		−	4.10600i		−	0.138178i	0.997611	−	0.0690889i	$-0.0220092\pi$
$884$	−14.5547	+	18.2510i	−0.489526	+	0.613846i
$885$	4.45817	−	5.06049i	0.149860	−	0.170106i
$886$	−4.52751	−	19.8363i	−0.152105	−	0.666414i
$887$	0.350618	−	0.728066i	0.0117726	−	0.0244461i	−0.895000	−	0.446067i	$-0.852824\pi$
$887$	0.350618	−	0.728066i	0.0117726	−	0.0244461i	0.906772	+	0.421621i	$0.138539\pi$
$888$	−0.0646970	−	0.134345i	−0.00217109	−	0.00450831i
$889$	−16.9918	+	22.3714i	−0.569886	+	0.750312i
$890$	−17.9090	+	20.3286i	−0.600311	+	0.681415i
$891$	21.8208	+	27.3624i	0.731024	+	0.916675i
$892$	2.78440	+	5.78187i	0.0932286	+	0.193591i
$893$	−29.8390	−	23.7958i	−0.998523	−	0.796295i
$894$	−0.947667	+	4.15200i	−0.0316947	+	0.138864i
$895$	3.71598	−	2.67646i	0.124212	−	0.0894642i
$896$	−2.41019	−	1.09132i	−0.0805189	−	0.0364584i
$897$	−4.82155	+	3.84506i	−0.160987	+	0.128383i
$898$	14.6899	+	30.5039i	0.490208	+	1.01793i
$899$	0.0980363	−	0.429525i	0.00326970	−	0.0143255i
$900$	−12.5681	−	7.65056i	−0.418937	−	0.255019i
$901$	29.9457			0.997635
$902$	40.8946	+	9.33393i	1.36164	+	0.310786i
$903$	−0.444506	+	0.981698i	−0.0147922	+	0.0326689i
$904$	−4.09131	−	17.9252i	−0.136075	−	0.596184i
$905$	0.749429	−	15.2801i	0.0249119	−	0.507927i
$906$	−1.59582	−	2.00109i	−0.0530174	−	0.0664817i
$907$	24.4274	−	19.4802i	0.811099	−	0.646830i	−0.127501	−	0.991838i	$-0.540696\pi$
$907$	24.4274	−	19.4802i	0.811099	−	0.646830i	0.938599	+	0.345009i	$0.112124\pi$
$908$	−4.69687	+	1.07203i	−0.155871	+	0.0355765i
$909$	−4.67708	−	20.4916i	−0.155129	−	0.679665i
$910$	23.3702	+	30.8817i	0.774714	+	1.02372i
$911$	9.97010	−	43.6819i	0.330324	−	1.44724i	−0.488179	−	0.872743i	$-0.662339\pi$
$911$	9.97010	−	43.6819i	0.330324	−	1.44724i	0.818504	−	0.574501i	$-0.194804\pi$
$912$			0.801554i			0.0265421i
$913$		−	15.7187i		−	0.520214i
$914$	−2.64338	+	11.5814i	−0.0874351	+	0.383078i
$915$	0.798480	+	4.50575i	0.0263969	+	0.148956i
$916$	−18.1810	−	22.7982i	−0.600717	−	0.753275i
$917$	0.353813	+	14.9736i	0.0116839	+	0.494472i
$918$	−3.96577	−	3.16259i	−0.130890	−	0.104381i
$919$	−8.02609	+	35.1646i	−0.264756	+	1.15997i	0.651267	+	0.758848i	$0.274238\pi$
$919$	−8.02609	+	35.1646i	−0.264756	+	1.15997i	−0.916023	+	0.401125i	$0.868619\pi$
$920$	7.14129	−	5.14356i	0.235442	−	0.169578i
$921$	6.59427	−	3.17563i	0.217288	−	0.104641i
$922$	−8.56961	+	6.83404i	−0.282225	+	0.225067i
$923$	−20.1984	+	41.9424i	−0.664838	+	1.38055i
$924$	−0.641034	−	2.53135i	−0.0210885	−	0.0832752i
$925$	0.304808	−	3.09988i	0.0100220	−	0.101923i
$926$	−21.9333	−	10.5625i	−0.720774	−	0.347106i
$927$	18.2877	−	4.17405i	0.600647	−	0.137094i
$928$	−0.0268290	+	0.0557110i	−0.000880704	+	0.00182880i
$929$	−24.8438	+	31.1532i	−0.815100	+	1.02210i	0.184132	+	0.982902i	$0.441053\pi$
$929$	−24.8438	+	31.1532i	−0.815100	+	1.02210i	−0.999231	+	0.0392012i	$0.987519\pi$
$930$	3.67180	+	1.02968i	0.120403	+	0.0337645i
$931$	15.4648	+	17.6165i	0.506839	+	0.577357i
$932$		−	6.75033i		−	0.221114i
$933$	2.53370	+	2.02056i	0.0829495	+	0.0661500i
$934$	−22.0022	−	10.5957i	−0.719934	−	0.346702i
$935$	32.8398	+	1.61067i	1.07398	+	0.0526744i
$936$	−17.3559	−	8.35814i	−0.567294	−	0.273194i
$937$	−17.2482	−	35.8162i	−0.563474	−	1.17007i	−0.966924	−	0.255064i	$-0.917903\pi$
$937$	−17.2482	−	35.8162i	−0.563474	−	1.17007i	0.403450	−	0.915002i	$-0.367811\pi$
$938$	−14.2685	−	27.9216i	−0.465882	−	0.911673i
$939$	3.81058	+	1.83508i	0.124354	+	0.0598856i
$940$	23.4745	−	9.91909i	0.765653	−	0.323525i
$941$	4.05619	−	1.95336i	0.132228	−	0.0636777i	−0.366600	−	0.930379i	$-0.619478\pi$
$941$	4.05619	−	1.95336i	0.132228	−	0.0636777i	0.498828	+	0.866701i	$0.333764\pi$
$942$	2.69080	+	2.14584i	0.0876709	+	0.0699152i
$943$	39.0347	+	8.90941i	1.27114	+	0.290130i
$944$	−7.85645	+	9.85168i	−0.255706	+	0.320645i
$945$	−6.71032	+	5.07813i	−0.218287	+	0.165192i
$946$	4.37484	+	5.48588i	0.142238	+	0.178361i
$947$	1.29865	+	2.69668i	0.0422005	+	0.0876303i	0.921003	−	0.389555i	$-0.127371\pi$
$947$	1.29865	+	2.69668i	0.0422005	+	0.0876303i	−0.878803	+	0.477185i	$0.841657\pi$
$948$	2.62891	+	0.600031i	0.0853830	+	0.0194881i
$949$	−9.47866			−0.307690
$950$	−8.70628	+	14.3024i	−0.282469	+	0.464031i
$951$	−0.179452	+	0.786230i	−0.00581913	+	0.0254953i
$952$	−4.29326	−	8.40138i	−0.139145	−	0.272290i
$953$	−46.3406	+	10.5769i	−1.50112	+	0.342620i	−0.892575	−	0.450900i	$-0.851103\pi$
$953$	−46.3406	+	10.5769i	−1.50112	+	0.342620i	−0.608544	+	0.793520i	$0.708246\pi$
$954$	5.49881	+	24.0919i	0.178031	+	0.780003i
$955$	15.2243	+	36.0298i	0.492648	+	1.16590i
$956$	0.0905238	+	0.113513i	0.00292775	+	0.00367128i
$957$	−0.0594981	+	0.0135801i	−0.00192330	+	0.000438981i
$958$	−2.05630	+	0.469336i	−0.0664359	+	0.0151636i
$959$	−25.2570	+	0.596800i	−0.815590	+	0.0192717i
$960$	−0.470261	−	0.255566i	−0.0151776	−	0.00824837i
$961$	19.7658			0.637605
$962$		−	4.07806i		−	0.131482i
$963$	−11.2175	−	2.56032i	−0.361478	−	0.0825050i
$964$	2.57872	−	1.24184i	0.0830549	−	0.0399971i
$965$	45.3088	−	19.1451i	1.45854	−	0.616304i
$966$	−0.611879	−	2.41622i	−0.0196869	−	0.0777405i
$967$	23.1181	+	18.4361i	0.743429	+	0.592865i	0.920228	−	0.391382i	$-0.128003\pi$
$967$	23.1181	+	18.4361i	0.743429	+	0.592865i	−0.176799	+	0.984247i	$0.556574\pi$
$968$	−5.85178	−	1.33563i	−0.188083	−	0.0429288i
$969$	−1.78216	+	2.23475i	−0.0572511	+	0.0717906i
$970$	−5.90732	+	1.04686i	−0.189673	+	0.0336126i
$971$	−0.204476	−	0.256405i	−0.00656195	−	0.00822842i	0.778540	−	0.627595i	$-0.215961\pi$
$971$	−0.204476	−	0.256405i	−0.00656195	−	0.00822842i	−0.785102	+	0.619367i	$0.787389\pi$
$972$	2.73298	−	5.67509i	0.0876603	−	0.182028i
$973$	9.91776	−	8.29990i	0.317949	−	0.266082i
$974$	−14.5696	+	7.01637i	−0.466841	+	0.224819i
$975$	4.26183	+	6.57378i	0.136488	+	0.210529i
$976$	−1.90248	−	8.33533i	−0.0608971	−	0.266807i
$977$	−24.3768	+	50.6189i	−0.779882	+	1.61944i	0.00515052	+	0.999987i	$0.498361\pi$
$977$	−24.3768	+	50.6189i	−0.779882	+	1.61944i	−0.785032	+	0.619455i	$0.787354\pi$
$978$	−0.326026	−	0.259997i	−0.0104252	−	0.00831379i
$979$	49.9587			1.59669
$980$	−15.2661	+	3.45618i	−0.487659	+	0.110404i
$981$	20.4703			0.653566
$982$	22.5595	+	17.9906i	0.719903	+	0.574103i
$983$	20.8302	−	43.2543i	0.664380	−	1.37960i	−0.247397	−	0.968914i	$-0.579575\pi$
$983$	20.8302	−	43.2543i	0.664380	−	1.37960i	0.911777	−	0.410685i	$-0.134710\pi$
$984$	−0.541823	−	2.37388i	−0.0172727	−	0.0756766i
$985$	−3.51352	+	3.98821i	−0.111950	+	0.127075i
$986$	−0.198666	+	0.0956726i	−0.00632682	+	0.00304684i
$987$	−0.170493	−	7.21537i	−0.00542684	−	0.229668i
$988$	−9.51150	+	19.7508i	−0.302601	+	0.628358i
$989$	4.17587	+	5.23637i	0.132785	+	0.166507i
$990$	4.73443	+	26.7160i	0.150470	+	0.849090i
$991$	−26.5306	+	33.2683i	−0.842772	+	1.05680i	0.154854	+	0.987937i	$0.450509\pi$
$991$	−26.5306	+	33.2683i	−0.842772	+	1.05680i	−0.997626	+	0.0688656i	$0.978062\pi$
$992$	−6.94637	−	1.58546i	−0.220547	−	0.0503385i
$993$	−4.44188	−	3.54228i	−0.140959	−	0.112411i
$994$	−12.0751	−	14.4289i	−0.383000	−	0.457657i
$995$	−9.56169	−	22.6286i	−0.303126	−	0.717376i
$996$	−0.822091	+	0.395898i	−0.0260490	+	0.0125445i
$997$	33.0498	+	7.54340i	1.04670	+	0.238902i	0.711091	−	0.703100i	$-0.248202\pi$
$997$	33.0498	+	7.54340i	1.04670	+	0.238902i	0.335607	+	0.942002i	$0.391059\pi$
$998$		−	20.9518i		−	0.663217i
$999$	0.886125			0.0280358

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.2.p.a.239.7	✓	168
5.4	even	2	inner	490.2.p.a.239.22	yes	168
49.8	even	7	inner	490.2.p.a.449.22	yes	168
245.204	even	14	inner	490.2.p.a.449.7	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
490.2.p.a.239.7	✓	168	1.1	even	1	trivial
490.2.p.a.239.22	yes	168	5.4	even	2	inner
490.2.p.a.449.7	yes	168	245.204	even	14	inner
490.2.p.a.449.22	yes	168	49.8	even	7	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:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	490.p (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.781831 - 0.623490i) q^{2} +(-0.103853 + 0.215653i) q^{3} +(0.222521 + 0.974928i) q^{4} +(-1.67783 - 1.47813i) q^{5} +(0.215653 - 0.103853i) q^{6} +(-1.09132 + 2.41019i) q^{7} +(0.433884 - 0.900969i) q^{8} +(1.83475 + 2.30070i) q^{9} +O(q^{10})\)	\(q+(-0.781831 - 0.623490i) q^{2} +(-0.103853 + 0.215653i) q^{3} +(0.222521 + 0.974928i) q^{4} +(-1.67783 - 1.47813i) q^{5} +(0.215653 - 0.103853i) q^{6} +(-1.09132 + 2.41019i) q^{7} +(0.433884 - 0.900969i) q^{8} +(1.83475 + 2.30070i) q^{9} +(0.390182 + 2.20176i) q^{10} +(2.57089 - 3.22379i) q^{11} +(-0.233356 - 0.0532620i) q^{12} +(-5.11802 - 4.08149i) q^{13} +(2.35596 - 1.20394i) q^{14} +(0.493013 - 0.208322i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(-3.47661 - 0.793513i) q^{17} -2.94271i q^{18} -3.34878 q^{19} +(1.06772 - 1.96468i) q^{20} +(-0.406429 - 0.485653i) q^{21} +(-4.02000 + 0.917539i) q^{22} +(-3.83716 + 0.875807i) q^{23} +(0.149237 + 0.187137i) q^{24} +(0.630247 + 4.96012i) q^{25} +(1.45667 + 6.38207i) q^{26} +(-1.38677 + 0.316520i) q^{27} +(-2.59260 - 0.527638i) q^{28} +(-0.0137595 + 0.0602842i) q^{29} +(-0.515339 - 0.144516i) q^{30} -7.12501 q^{31} +(0.974928 + 0.222521i) q^{32} +(0.428226 + 0.889221i) q^{33} +(2.22338 + 2.78802i) q^{34} +(5.39363 - 2.43079i) q^{35} +(-1.83475 + 2.30070i) q^{36} +(-0.607347 - 0.138623i) q^{37} +(2.61818 + 2.08793i) q^{38} +(1.41171 - 0.679844i) q^{39} +(-2.05974 + 0.870338i) q^{40} +(-9.16537 - 4.41381i) q^{41} +(0.0149597 + 0.633103i) q^{42} +(-0.738335 - 1.53317i) q^{43} +(3.71504 + 1.78907i) q^{44} +(0.322341 - 6.57220i) q^{45} +(3.54607 + 1.70770i) q^{46} +(8.91040 + 7.10581i) q^{47} -0.239357i q^{48} +(-4.61805 - 5.26057i) q^{49} +(2.59984 - 4.27093i) q^{50} +(0.532181 - 0.667334i) q^{51} +(2.84029 - 5.89792i) q^{52} +(-8.18697 + 1.86862i) q^{53} +(1.28156 + 0.617169i) q^{54} +(-9.07871 + 1.60887i) q^{55} +(1.69800 + 2.02899i) q^{56} +(0.347781 - 0.722175i) q^{57} +(0.0483442 - 0.0385532i) q^{58} +(11.3529 - 5.46727i) q^{59} +(0.312804 + 0.434296i) q^{60} +(-1.90248 + 8.33533i) q^{61} +(5.57056 + 4.44237i) q^{62} +(-7.54743 + 1.91130i) q^{63} +(-0.623490 - 0.781831i) q^{64} +(2.55421 + 14.4132i) q^{65} +(0.219619 - 0.962216i) q^{66} -11.8515i q^{67} -3.56602i q^{68} +(0.209631 - 0.918452i) q^{69} +(-5.73248 - 1.46241i) q^{70} +(-1.58243 - 6.93308i) q^{71} +(2.86893 - 0.654814i) q^{72} +(1.13206 - 0.902790i) q^{73} +(0.388413 + 0.487054i) q^{74} +(-1.13512 - 0.379209i) q^{75} +(-0.745173 - 3.26482i) q^{76} +(4.96430 + 9.71451i) q^{77} +(-1.52759 - 0.348663i) q^{78} -11.2657 q^{79} +(2.15301 + 0.603767i) q^{80} +(-1.88868 + 8.27485i) q^{81} +(4.41381 + 9.16537i) q^{82} +(2.98042 - 2.37680i) q^{83} +(0.383037 - 0.504307i) q^{84} +(4.66025 + 6.47027i) q^{85} +(-0.378661 + 1.65902i) q^{86} +(-0.0115715 - 0.00922798i) q^{87} +(-1.78907 - 3.71504i) q^{88} +(7.55418 + 9.47264i) q^{89} +(-4.34971 + 4.93737i) q^{90} +(15.4226 - 7.88122i) q^{91} +(-1.70770 - 3.54607i) q^{92} +(0.739955 - 1.53653i) q^{93} +(-2.53603 - 11.1111i) q^{94} +(5.61869 + 4.94994i) q^{95} +(-0.149237 + 0.187137i) q^{96} +2.68300i q^{97} +(0.330623 + 6.99219i) q^{98} +12.1339 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q + 28 q^{4} - 4 q^{5} + 14 q^{6} + 18 q^{9}+O(q^{10}) \) 168 * q + 28 * q^4 - 4 * q^5 + 14 * q^6 + 18 * q^9	\( 168 q + 28 q^{4} - 4 q^{5} + 14 q^{6} + 18 q^{9} - 4 q^{10} - 24 q^{11} + 4 q^{14} - 2 q^{15} - 28 q^{16} + 44 q^{19} - 10 q^{20} + 22 q^{26} - 2 q^{29} - 12 q^{30} - 16 q^{31} - 8 q^{34} - 4 q^{35} - 18 q^{36} - 80 q^{39} - 10 q^{40} + 52 q^{41} - 18 q^{44} - 72 q^{45} + 26 q^{46} - 52 q^{49} - 8 q^{50} + 64 q^{51} - 42 q^{54} - 60 q^{55} + 10 q^{56} - 58 q^{59} + 2 q^{60} + 32 q^{61} + 28 q^{64} + 4 q^{65} + 48 q^{66} - 48 q^{69} + 18 q^{70} - 68 q^{71} - 10 q^{74} - 16 q^{76} - 4 q^{80} + 34 q^{81} + 84 q^{84} - 48 q^{85} - 64 q^{86} + 100 q^{89} + 54 q^{90} + 78 q^{91} - 86 q^{94} - 64 q^{95} - 212 q^{99}+O(q^{100}) \) 168 * q + 28 * q^4 - 4 * q^5 + 14 * q^6 + 18 * q^9 - 4 * q^10 - 24 * q^11 + 4 * q^14 - 2 * q^15 - 28 * q^16 + 44 * q^19 - 10 * q^20 + 22 * q^26 - 2 * q^29 - 12 * q^30 - 16 * q^31 - 8 * q^34 - 4 * q^35 - 18 * q^36 - 80 * q^39 - 10 * q^40 + 52 * q^41 - 18 * q^44 - 72 * q^45 + 26 * q^46 - 52 * q^49 - 8 * q^50 + 64 * q^51 - 42 * q^54 - 60 * q^55 + 10 * q^56 - 58 * q^59 + 2 * q^60 + 32 * q^61 + 28 * q^64 + 4 * q^65 + 48 * q^66 - 48 * q^69 + 18 * q^70 - 68 * q^71 - 10 * q^74 - 16 * q^76 - 4 * q^80 + 34 * q^81 + 84 * q^84 - 48 * q^85 - 64 * q^86 + 100 * q^89 + 54 * q^90 + 78 * q^91 - 86 * q^94 - 64 * q^95 - 212 * q^99

Introduction

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