LMFDB - Embedded newform 840.2.cf.a.101.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(101,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 3, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.101"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.cf (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$128$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.13
Character	$\chi$	$=$	840.101
Dual form			840.2.cf.a.341.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.35626 - 0.400715i) q^{2} +(-1.62841 + 0.590144i) q^{3} +(1.67886 + 1.08694i) q^{4} +(0.866025 - 0.500000i) q^{5} +(2.44502 - 0.147856i) q^{6} +(-2.64480 + 0.0708975i) q^{7} +(-1.84140 - 2.14691i) q^{8} +(2.30346 - 1.92200i) q^{9} +(-1.37491 + 0.331098i) q^{10} +(-0.735536 + 1.27399i) q^{11} +(-3.37532 - 0.779227i) q^{12} -1.58306 q^{13} +(3.61543 + 0.963656i) q^{14} +(-1.11518 + 1.32529i) q^{15} +(1.63711 + 3.64964i) q^{16} +(2.77818 - 4.81195i) q^{17} +(-3.89425 + 1.68369i) q^{18} +(2.80571 + 4.85963i) q^{19} +(1.99740 + 0.101893i) q^{20} +(4.26499 - 1.67626i) q^{21} +(1.50808 - 1.43311i) q^{22} +(1.32154 - 0.762994i) q^{23} +(4.26555 + 2.40937i) q^{24} +(0.500000 - 0.866025i) q^{25} +(2.14703 + 0.634356i) q^{26} +(-2.61673 + 4.48918i) q^{27} +(-4.51730 - 2.75572i) q^{28} -5.28450 q^{29} +(2.04352 - 1.35056i) q^{30} +(0.436649 + 0.252099i) q^{31} +(-0.757874 - 5.60586i) q^{32} +(0.445922 - 2.50865i) q^{33} +(-5.69614 + 5.41297i) q^{34} +(-2.25502 + 1.38380i) q^{35} +(5.95628 - 0.723022i) q^{36} +(0.430562 - 0.248585i) q^{37} +(-1.85793 - 7.71519i) q^{38} +(2.57788 - 0.934233i) q^{39} +(-2.66816 - 0.938581i) q^{40} -2.40233 q^{41} +(-6.45612 + 0.564395i) q^{42} -0.257653i q^{43} +(-2.61961 + 1.33935i) q^{44} +(1.03386 - 2.81623i) q^{45} +(-2.09809 + 0.505252i) q^{46} +(5.41938 + 9.38664i) q^{47} +(-4.81970 - 4.97699i) q^{48} +(6.98995 - 0.375020i) q^{49} +(-1.02516 + 0.974194i) q^{50} +(-1.68429 + 9.47537i) q^{51} +(-2.65773 - 1.72070i) q^{52} +(-5.79342 + 10.0345i) q^{53} +(5.34784 - 5.03990i) q^{54} +1.47107i q^{55} +(5.02235 + 5.54761i) q^{56} +(-7.43674 - 6.25772i) q^{57} +(7.16713 + 2.11758i) q^{58} +(-3.84363 - 2.21912i) q^{59} +(-3.31273 + 1.01283i) q^{60} +(7.65781 + 13.2637i) q^{61} +(-0.491187 - 0.516882i) q^{62} +(-5.95593 + 5.24661i) q^{63} +(-1.21848 + 7.90666i) q^{64} +(-1.37097 + 0.791530i) q^{65} +(-1.61004 + 3.22368i) q^{66} +(6.84692 + 3.95307i) q^{67} +(9.89448 - 5.05884i) q^{68} +(-1.70175 + 2.02237i) q^{69} +(3.61289 - 0.973167i) q^{70} +3.60793i q^{71} +(-8.36796 - 1.40617i) q^{72} +(8.97713 + 5.18295i) q^{73} +(-0.683564 + 0.164612i) q^{74} +(-0.303127 + 1.70532i) q^{75} +(-0.571762 + 11.2083i) q^{76} +(1.85502 - 3.42158i) q^{77} +(-3.87062 + 0.234065i) q^{78} +(-3.01199 - 5.21691i) q^{79} +(3.24260 + 2.34213i) q^{80} +(1.61187 - 8.85448i) q^{81} +(3.25817 + 0.962648i) q^{82} +13.3919i q^{83} +(8.98230 + 1.82160i) q^{84} -5.55636i q^{85} +(-0.103246 + 0.349444i) q^{86} +(8.60535 - 3.11861i) q^{87} +(4.08955 - 0.766786i) q^{88} +(-3.02937 - 5.24701i) q^{89} +(-2.53068 + 3.40524i) q^{90} +(4.18688 - 0.112235i) q^{91} +(3.04801 + 0.155487i) q^{92} +(-0.859819 - 0.152836i) q^{93} +(-3.58869 - 14.9023i) q^{94} +(4.85963 + 2.80571i) q^{95} +(4.54239 + 8.68140i) q^{96} +16.9823i q^{97} +(-9.63043 - 2.29235i) q^{98} +(0.754316 + 4.34827i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + 30 q^{12} + 16 q^{16} - 10 q^{18} + 8 q^{22} + 128 q^{25} + 12 q^{28} - 40 q^{36} - 54 q^{42} + 16 q^{46} + 16 q^{49} + 36 q^{52} - 72 q^{54} - 16 q^{58} - 14 q^{60} + 80 q^{63} - 48 q^{64} - 60 q^{66}+ \cdots - 144 q^{96}+O(q^{100}) $ 256 * q + 30 * q^12 + 16 * q^16 - 10 * q^18 + 8 * q^22 + 128 * q^25 + 12 * q^28 - 40 * q^36 - 54 * q^42 + 16 * q^46 + 16 * q^49 + 36 * q^52 - 72 * q^54 - 16 * q^58 - 14 * q^60 + 80 * q^63 - 48 * q^64 - 60 * q^66 - 12 * q^70 - 50 * q^72 + 48 * q^73 - 16 * q^78 + 64 * q^79 - 8 * q^81 - 72 * q^82 - 56 * q^84 - 8 * q^88 - 72 * q^94 - 144 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$	$-1$	$1$

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 $

$2$	−1.35626	−	0.400715i	−0.959017	−	0.283348i
$2$	−1.35626	−	0.400715i	−0.959017	−	0.283348i
$3$	−1.62841	+	0.590144i	−0.940165	+	0.340720i
$3$	−1.62841	+	0.590144i	−0.940165	+	0.340720i
$4$	1.67886	+	1.08694i	0.839428	+	0.543471i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$6$	2.44502	−	0.147856i	0.998177	−	0.0603619i
$7$	−2.64480	+	0.0708975i	−0.999641	+	0.0267967i
$7$	−2.64480	+	0.0708975i	−0.999641	+	0.0267967i
$8$	−1.84140	−	2.14691i	−0.651034	−	0.759049i
$9$	2.30346	−	1.92200i	0.767820	−	0.640665i
$10$	−1.37491	+	0.331098i	−0.434784	+	0.104702i
$11$	−0.735536	+	1.27399i	−0.221772	+	0.384121i	−0.955346	−	0.295489i	$-0.904518\pi$
$11$	−0.735536	+	1.27399i	−0.221772	+	0.384121i	0.733574	+	0.679610i	$0.237851\pi$
$12$	−3.37532	−	0.779227i	−0.974372	−	0.224943i
$13$	−1.58306			−0.439062			−0.219531	−	0.975606i	$-0.570453\pi$
$13$	−1.58306			−0.439062			−0.219531	+	0.975606i	$0.570453\pi$
$14$	3.61543	+	0.963656i	0.966266	+	0.257548i
$15$	−1.11518	+	1.32529i	−0.287937	+	0.342187i
$16$	1.63711	+	3.64964i	0.409277	+	0.912410i
$17$	2.77818	−	4.81195i	0.673808	−	1.16707i	−0.303008	−	0.952988i	$-0.597991\pi$
$17$	2.77818	−	4.81195i	0.673808	−	1.16707i	0.976816	−	0.214081i	$-0.0686758\pi$
$18$	−3.89425	+	1.68369i	−0.917884	+	0.396848i
$19$	2.80571	+	4.85963i	0.643674	+	1.11488i	0.984606	+	0.174788i	$0.0559241\pi$
$19$	2.80571	+	4.85963i	0.643674	+	1.11488i	−0.340932	+	0.940088i	$0.610743\pi$
$20$	1.99740	+	0.101893i	0.446633	+	0.0227839i
$21$	4.26499	−	1.67626i	0.930697	−	0.365791i
$22$	1.50808	−	1.43311i	0.321523	−	0.305540i
$23$	1.32154	−	0.762994i	0.275561	−	0.159095i	−0.355851	−	0.934543i	$-0.615809\pi$
$23$	1.32154	−	0.762994i	0.275561	−	0.159095i	0.631412	+	0.775447i	$0.282476\pi$
$24$	4.26555	+	2.40937i	0.870702	+	0.491811i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	2.14703	+	0.634356i	0.421068	+	0.124407i
$27$	−2.61673	+	4.48918i	−0.503591	+	0.863942i
$28$	−4.51730	−	2.75572i	−0.853689	−	0.520782i
$29$	−5.28450			−0.981306			−0.490653	−	0.871355i	$-0.663242\pi$
$29$	−5.28450			−0.981306			−0.490653	+	0.871355i	$0.663242\pi$
$30$	2.04352	−	1.35056i	0.373095	−	0.246577i
$31$	0.436649	+	0.252099i	0.0784244	+	0.0452783i	0.538699	−	0.842498i	$-0.318916\pi$
$31$	0.436649	+	0.252099i	0.0784244	+	0.0452783i	−0.460275	+	0.887776i	$0.652249\pi$
$32$	−0.757874	−	5.60586i	−0.133974	−	0.990985i
$33$	0.445922	−	2.50865i	0.0776250	−	0.436699i
$34$	−5.69614	+	5.41297i	−0.976880	+	0.928317i
$35$	−2.25502	+	1.38380i	−0.381167	+	0.233905i
$36$	5.95628	−	0.723022i	0.992713	−	0.120504i
$37$	0.430562	−	0.248585i	0.0707840	−	0.0408672i	−0.464190	−	0.885735i	$-0.653655\pi$
$37$	0.430562	−	0.248585i	0.0707840	−	0.0408672i	0.534974	+	0.844868i	$0.320321\pi$
$38$	−1.85793	−	7.71519i	−0.301396	−	1.25157i
$39$	2.57788	−	0.934233i	0.412791	−	0.149597i
$40$	−2.66816	−	0.938581i	−0.421873	−	0.148403i
$41$	−2.40233			−0.375181			−0.187590	−	0.982247i	$-0.560068\pi$
$41$	−2.40233			−0.375181			−0.187590	+	0.982247i	$0.560068\pi$
$42$	−6.45612	+	0.564395i	−0.996201	+	0.0870881i
$43$		−	0.257653i		−	0.0392918i	−0.999807	−	0.0196459i	$-0.993746\pi$
$43$		−	0.257653i		−	0.0392918i	0.999807	−	0.0196459i	$-0.00625388\pi$
$44$	−2.61961	+	1.33935i	−0.394921	+	0.201915i
$45$	1.03386	−	2.81623i	0.154118	−	0.419818i
$46$	−2.09809	+	0.505252i	−0.309347	+	0.0744954i
$47$	5.41938	+	9.38664i	0.790498	+	1.36918i	0.925659	+	0.378358i	$0.123511\pi$
$47$	5.41938	+	9.38664i	0.790498	+	1.36918i	−0.135162	+	0.990824i	$0.543155\pi$
$48$	−4.81970	−	4.97699i	−0.695664	−	0.718367i
$49$	6.98995	−	0.375020i	0.998564	−	0.0535742i
$50$	−1.02516	+	0.974194i	−0.144979	+	0.137772i
$51$	−1.68429	+	9.47537i	−0.235847	+	1.32682i
$52$	−2.65773	−	1.72070i	−0.368561	−	0.238618i
$53$	−5.79342	+	10.0345i	−0.795788	+	1.37835i	0.126550	+	0.991960i	$0.459610\pi$
$53$	−5.79342	+	10.0345i	−0.795788	+	1.37835i	−0.922338	+	0.386385i	$0.873724\pi$
$54$	5.34784	−	5.03990i	0.727748	−	0.685844i
$55$			1.47107i			0.198359i
$56$	5.02235	+	5.54761i	0.671140	+	0.741331i
$57$	−7.43674	−	6.25772i	−0.985020	−	0.828855i
$58$	7.16713	+	2.11758i	0.941090	+	0.278051i
$59$	−3.84363	−	2.21912i	−0.500397	−	0.288905i	0.228480	−	0.973549i	$-0.426624\pi$
$59$	−3.84363	−	2.21912i	−0.500397	−	0.288905i	−0.728878	+	0.684644i	$0.759958\pi$
$60$	−3.31273	+	1.01283i	−0.427671	+	0.130756i
$61$	7.65781	+	13.2637i	0.980482	+	1.69824i	0.660510	+	0.750817i	$0.270340\pi$
$61$	7.65781	+	13.2637i	0.980482	+	1.69824i	0.319971	+	0.947427i	$0.396327\pi$
$62$	−0.491187	−	0.516882i	−0.0623808	−	0.0656441i
$63$	−5.95593	+	5.24661i	−0.750377	+	0.661010i
$64$	−1.21848	+	7.90666i	−0.152310	+	0.988333i
$65$	−1.37097	+	0.791530i	−0.170048	+	0.0981772i
$66$	−1.61004	+	3.22368i	−0.198182	+	0.396807i
$67$	6.84692	+	3.95307i	0.836484	+	0.482945i	0.856068	−	0.516864i	$-0.172901\pi$
$67$	6.84692	+	3.95307i	0.836484	+	0.482945i	−0.0195833	+	0.999808i	$0.506234\pi$
$68$	9.89448	−	5.05884i	1.19988	−	0.613475i
$69$	−1.70175	+	2.02237i	−0.204866	+	0.243465i
$70$	3.61289	−	0.973167i	0.431822	−	0.116316i
$71$			3.60793i			0.428182i	0.976814	+	0.214091i	$0.0686790\pi$
$71$			3.60793i			0.428182i	−0.976814	+	0.214091i	$0.931321\pi$
$72$	−8.36796	−	1.40617i	−0.986173	−	0.165718i
$73$	8.97713	+	5.18295i	1.05069	+	0.606618i	0.922843	−	0.385175i	$-0.125859\pi$
$73$	8.97713	+	5.18295i	1.05069	+	0.606618i	0.127850	+	0.991794i	$0.459192\pi$
$74$	−0.683564	+	0.164612i	−0.0794627	+	0.0191358i
$75$	−0.303127	+	1.70532i	−0.0350021	+	0.196913i
$76$	−0.571762	+	11.2083i	−0.0655856	+	1.28568i
$77$	1.85502	−	3.42158i	0.211399	−	0.389926i
$78$	−3.87062	+	0.234065i	−0.438261	+	0.0265026i
$79$	−3.01199	−	5.21691i	−0.338875	−	0.586949i	0.645346	−	0.763890i	$-0.276713\pi$
$79$	−3.01199	−	5.21691i	−0.338875	−	0.586949i	−0.984221	+	0.176941i	$0.943380\pi$
$80$	3.24260	+	2.34213i	0.362534	+	0.261858i
$81$	1.61187	−	8.85448i	0.179096	−	0.983832i
$82$	3.25817	+	0.962648i	0.359805	+	0.106307i
$83$			13.3919i			1.46995i	0.678092	+	0.734977i	$0.262807\pi$
$83$			13.3919i			1.46995i	−0.678092	+	0.734977i	$0.737193\pi$
$84$	8.98230	+	1.82160i	0.980050	+	0.198753i
$85$		−	5.55636i		−	0.602672i
$86$	−0.103246	+	0.349444i	−0.0111332	+	0.0376815i
$87$	8.60535	−	3.11861i	0.922590	−	0.334350i
$88$	4.08955	−	0.766786i	0.435948	−	0.0817397i
$89$	−3.02937	−	5.24701i	−0.321112	−	0.556182i	0.659606	−	0.751612i	$-0.270723\pi$
$89$	−3.02937	−	5.24701i	−0.321112	−	0.556182i	−0.980718	+	0.195429i	$0.937390\pi$
$90$	−2.53068	+	3.40524i	−0.266757	+	0.358944i
$91$	4.18688	−	0.112235i	0.438904	−	0.0117654i
$92$	3.04801	+	0.155487i	0.317777	+	0.0162106i
$93$	−0.859819	−	0.152836i	−0.0891591	−	0.0158484i
$94$	−3.58869	−	14.9023i	−0.370145	−	1.53705i
$95$	4.85963	+	2.80571i	0.498588	+	0.287860i
$96$	4.54239	+	8.68140i	0.463606	+	0.886041i
$97$			16.9823i			1.72429i	0.506661	+	0.862145i	$0.330879\pi$
$97$			16.9823i			1.72429i	−0.506661	+	0.862145i	$0.669121\pi$
$98$	−9.63043	−	2.29235i	−0.972820	−	0.231563i
$99$	0.754316	+	4.34827i	0.0758116	+	0.437018i
$100$	1.78075	−	0.910460i	0.178075	−	0.0910460i
$101$	7.67901	+	4.43348i	0.764090	+	0.441148i	0.830762	−	0.556627i	$-0.187905\pi$
$101$	7.67901	+	4.43348i	0.764090	+	0.441148i	−0.0666722	+	0.997775i	$0.521238\pi$
$102$	6.08124	−	12.1761i	0.602133	−	1.20561i
$103$	−10.1609	+	5.86637i	−1.00118	+	0.578031i	−0.908597	−	0.417674i	$-0.862845\pi$
$103$	−10.1609	+	5.86637i	−1.00118	+	0.578031i	−0.0925817	+	0.995705i	$0.529512\pi$
$104$	2.91505	+	3.39869i	0.285844	+	0.333269i
$105$	2.85546	−	3.58418i	0.278664	−	0.349780i
$106$	11.8783	−	11.2878i	1.15373	−	1.09637i
$107$	−4.55994	−	7.89804i	−0.440826	−	0.763533i	0.556925	−	0.830563i	$-0.311981\pi$
$107$	−4.55994	−	7.89804i	−0.440826	−	0.763533i	−0.997751	+	0.0670301i	$0.978648\pi$
$108$	−9.27260	+	4.69244i	−0.892256	+	0.451530i
$109$	5.48653	+	3.16765i	0.525514	+	0.303406i	0.739188	−	0.673499i	$-0.235210\pi$
$109$	5.48653	+	3.16765i	0.525514	+	0.303406i	−0.213674	+	0.976905i	$0.568543\pi$
$110$	0.589480	−	1.99515i	0.0562047	−	0.190230i
$111$	−0.554432	+	0.658893i	−0.0526244	+	0.0625394i
$112$	−4.58858	−	9.53650i	−0.433580	−	0.901115i
$113$			11.0625i			1.04068i	0.853960	+	0.520338i	$0.174194\pi$
$113$			11.0625i			1.04068i	−0.853960	+	0.520338i	$0.825806\pi$
$114$	7.57855	+	11.4671i	0.709796	+	1.07399i
$115$	0.762994	−	1.32154i	0.0711496	−	0.123235i
$116$	−8.87191	−	5.74395i	−0.823736	−	0.533312i
$117$	−3.64652	+	3.04264i	−0.337121	+	0.281292i
$118$	4.32370	+	4.54989i	0.398029	+	0.418851i
$119$	−7.00658	+	12.9236i	−0.642292	+	1.18471i
$120$	4.89876	−	0.0461979i	0.447194	−	0.00421727i
$121$	4.41797	+	7.65216i	0.401634	+	0.695651i
$122$	−5.07097	−	21.0576i	−0.459104	−	1.90646i
$123$	3.91198	−	1.41772i	0.352732	−	0.127831i
$124$	0.459052	+	0.897850i	0.0412241	+	0.0806293i
$125$		−	1.00000i		−	0.0894427i
$126$	10.1802	−	4.72911i	0.906920	−	0.421302i
$127$	−10.6377			−0.943945			−0.471972	−	0.881613i	$-0.656458\pi$
$127$	−10.6377			−0.943945			−0.471972	+	0.881613i	$0.656458\pi$
$128$	4.82089	−	10.2352i	0.426110	−	0.904671i
$129$	0.152052	+	0.419566i	0.0133875	+	0.0369407i
$130$	2.17656	−	0.524149i	0.190897	−	0.0459709i
$131$	8.76573	−	5.06090i	0.765865	−	0.442173i	−0.0655323	−	0.997850i	$-0.520875\pi$
$131$	8.76573	−	5.06090i	0.765865	−	0.442173i	0.831398	+	0.555678i	$0.187541\pi$
$132$	3.47539	−	3.72696i	0.302494	−	0.324390i
$133$	−7.76508	−	12.6538i	−0.673318	−	1.09723i
$134$	−7.70212	−	8.10504i	−0.665361	−	0.700168i
$135$	−0.0215693	+	5.19611i	−0.00185639	+	0.447210i
$136$	−15.4466	+	2.89622i	−1.32453	+	0.248349i
$137$	10.1637	+	5.86801i	0.868343	+	0.501338i	0.866797	−	0.498661i	$-0.166175\pi$
$137$	10.1637	+	5.86801i	0.868343	+	0.501338i	0.00154582	+	0.999999i	$0.499508\pi$
$138$	3.11839	−	2.06094i	0.265455	−	0.175439i
$139$	0.697482			0.0591597			0.0295798	−	0.999562i	$-0.490583\pi$
$139$	0.697482			0.0591597			0.0295798	+	0.999562i	$0.490583\pi$
$140$	−5.28996	−	0.127875i	−0.447083	−	0.0108074i
$141$	−14.3645	−	12.0871i	−1.20971	−	1.01792i
$142$	1.44575	−	4.89327i	0.121325	−	0.410634i
$143$	1.16440	−	2.01680i	0.0973718	−	0.168653i
$144$	10.7856	+	5.26028i	0.898801	+	0.438357i
$145$	−4.57651	+	2.64225i	−0.380058	+	0.219427i
$146$	−10.0984	−	10.6267i	−0.835749	−	0.879469i
$147$	−11.1612	+	4.73576i	−0.920561	+	0.390599i
$148$	0.993049	+	0.0506580i	0.0816282	+	0.00416406i
$149$	−10.3136	−	17.8637i	−0.844922	−	1.46345i	−0.885689	−	0.464279i	$-0.846314\pi$
$149$	−10.3136	−	17.8637i	−0.844922	−	1.46345i	0.0407675	−	0.999169i	$-0.487020\pi$
$150$	1.09446	−	2.19138i	0.0893627	−	0.178925i
$151$	1.06809	−	1.84999i	0.0869203	−	0.150550i	−0.819288	−	0.573383i	$-0.805631\pi$
$151$	1.06809	−	1.84999i	0.0869203	−	0.150550i	0.906208	+	0.422832i	$0.138964\pi$
$152$	5.26677	−	14.9722i	0.427192	−	1.21440i
$153$	−2.84912	−	16.4238i	−0.230337	−	1.32778i
$154$	−3.88696	+	3.89721i	−0.313220	+	0.314046i
$155$	0.504198			0.0404982
$156$	5.34334	+	1.23356i	0.427810	+	0.0987641i
$157$	−1.38285	+	2.39516i	−0.110363	+	0.191155i	−0.915917	−	0.401368i	$-0.868535\pi$
$157$	−1.38285	+	2.39516i	−0.110363	+	0.191155i	0.805553	+	0.592523i	$0.201868\pi$
$158$	1.99453	+	8.28241i	0.158676	+	0.658913i
$159$	3.51229	−	19.7593i	0.278543	−	1.56701i
$160$	−3.45927	−	4.47588i	−0.273479	−	0.353849i
$161$	−3.44113	+	2.11166i	−0.271199	+	0.166422i
$162$	−5.73422	+	11.3630i	−0.450523	+	0.892765i
$163$	3.88843	−	2.24499i	0.304566	−	0.175841i	−0.339926	−	0.940452i	$-0.610402\pi$
$163$	3.88843	−	2.24499i	0.304566	−	0.175841i	0.644492	+	0.764611i	$0.277069\pi$
$164$	−4.03316	−	2.61119i	−0.314937	−	0.203900i
$165$	−0.868143	−	2.39551i	−0.0675849	−	0.186490i
$166$	5.36634	−	18.1629i	0.416509	−	1.40971i
$167$	6.10705			0.472578			0.236289	−	0.971683i	$-0.424069\pi$
$167$	6.10705			0.472578			0.236289	+	0.971683i	$0.424069\pi$
$168$	−11.4524	−	6.06989i	−0.883568	−	0.468302i
$169$	−10.4939			−0.807225
$170$	−2.22652	+	7.53584i	−0.170766	+	0.577973i
$171$	15.8030	+	5.80141i	1.20849	+	0.443645i
$172$	0.280054	−	0.432563i	0.0213540	−	0.0329826i
$173$	−11.2340	+	6.48593i	−0.854103	+	0.493116i	−0.862033	−	0.506852i	$-0.830809\pi$
$173$	−11.2340	+	6.48593i	−0.854103	+	0.493116i	0.00793028	+	0.999969i	$0.497476\pi$
$174$	−12.9207	+	0.781344i	−0.979517	+	0.0592335i
$175$	−1.26100	+	2.32591i	−0.0953228	+	0.175823i
$176$	−5.85374	−	0.598786i	−0.441242	−	0.0451352i
$177$	7.56861	+	1.34535i	0.568892	+	0.101123i
$178$	2.00604	+	8.33020i	0.150359	+	0.624375i
$179$	2.81245	−	4.87131i	0.210213	−	0.364099i	−0.741568	−	0.670877i	$-0.765918\pi$
$179$	2.81245	−	4.87131i	0.210213	−	0.364099i	0.951781	+	0.306778i	$0.0992511\pi$
$180$	4.79678	−	3.60429i	0.357531	−	0.268648i
$181$	21.6254			1.60740			0.803700	−	0.595034i	$-0.202862\pi$
$181$	21.6254			1.60740			0.803700	+	0.595034i	$0.202862\pi$
$182$	−5.72345	−	1.52553i	−0.424250	−	0.113079i
$183$	−20.2976	−	17.0796i	−1.50044	−	1.26256i
$184$	−4.07158	−	1.43226i	−0.300161	−	0.105588i
$185$	0.248585	−	0.430562i	0.0182763	−	0.0316556i
$186$	1.10489	+	0.551827i	0.0810145	+	0.0404619i
$187$	4.08690	+	7.07872i	0.298864	+	0.517647i
$188$	−1.10439	+	21.6494i	−0.0805458	+	1.57894i
$189$	6.60247	−	12.0585i	0.480259	−	0.877127i
$190$	−5.46661	−	5.75259i	−0.396590	−	0.417336i
$191$	−15.8732	+	9.16437i	−1.14854	+	0.663110i	−0.948531	−	0.316683i	$-0.897431\pi$
$191$	−15.8732	+	9.16437i	−1.14854	+	0.663110i	−0.200010	+	0.979794i	$0.564097\pi$
$192$	−2.68188	−	13.5944i	−0.193548	−	0.981091i
$193$	12.9693	−	22.4634i	0.933547	−	1.61695i	0.156343	−	0.987703i	$-0.450029\pi$
$193$	12.9693	−	22.4634i	0.933547	−	1.61695i	0.777204	−	0.629249i	$-0.216637\pi$
$194$	6.80506	−	23.0323i	0.488574	−	1.65362i
$195$	1.76539	−	2.09801i	0.126422	−	0.150241i
$196$	12.1427	+	6.96807i	0.867338	+	0.497719i
$197$	−9.99529			−0.712135			−0.356068	−	0.934460i	$-0.615883\pi$
$197$	−9.99529			−0.712135			−0.356068	+	0.934460i	$0.615883\pi$
$198$	0.719372	−	6.19963i	0.0511235	−	0.440589i
$199$	−18.0771	−	10.4368i	−1.28145	−	0.739847i	−0.304339	−	0.952564i	$-0.598436\pi$
$199$	−18.0771	−	10.4368i	−1.28145	−	0.739847i	−0.977114	+	0.212716i	$0.931769\pi$
$200$	−2.77998	+	0.521244i	−0.196574	+	0.0368575i
$201$	−13.4825	−	2.39657i	−0.950982	−	0.169041i
$202$	−8.63814	−	9.09002i	−0.607777	−	0.639572i
$203$	13.9764	−	0.374658i	0.980954	−	0.0262958i
$204$	−13.1269	+	14.0771i	−0.919064	+	0.985591i
$205$	−2.08048	+	1.20116i	−0.145307	+	0.0838929i
$206$	16.1314	−	3.88469i	1.12393	−	0.270659i
$207$	1.57766	−	4.29753i	0.109655	−	0.298699i
$208$	−2.59164	−	5.77760i	−0.179698	−	0.400605i
$209$	−8.25480			−0.570996
$210$	−5.30896	+	3.71684i	−0.366353	+	0.256486i
$211$		−	10.3677i		−	0.713744i	−0.934153	−	0.356872i	$-0.883843\pi$
$211$		−	10.3677i		−	0.713744i	0.934153	−	0.356872i	$-0.116157\pi$
$212$	−20.6333	+	10.5494i	−1.41710	+	0.724533i
$213$	−2.12920	−	5.87520i	−0.145890	−	0.402562i
$214$	3.01957	+	12.5390i	0.206414	+	0.857148i
$215$	−0.128827	−	0.223134i	−0.00878591	−	0.0152176i
$216$	14.4563	−	2.64848i	0.983629	−	0.180206i
$217$	−1.17272	−	0.635795i	−0.0796095	−	0.0431606i
$218$	−6.17181	−	6.49467i	−0.418007	−	0.439875i
$219$	−17.6772	−	3.14219i	−1.19451	−	0.212329i
$220$	−1.59897	+	2.46972i	−0.107803	+	0.166508i
$221$	−4.39803	+	7.61761i	−0.295843	+	0.512416i
$222$	1.01598	−	0.671458i	0.0681881	−	0.0450653i
$223$		−	2.40508i		−	0.161056i	−0.996752	−	0.0805281i	$-0.974339\pi$
$223$		−	2.40508i		−	0.161056i	0.996752	−	0.0805281i	$-0.0256607\pi$
$224$	2.40187	+	14.7726i	0.160481	+	0.987039i
$225$	−0.512767	−	2.95585i	−0.0341844	−	0.197057i
$226$	4.43292	−	15.0036i	0.294874	−	0.998026i
$227$	8.39441	+	4.84652i	0.557157	+	0.321675i	0.752004	−	0.659159i	$-0.229088\pi$
$227$	8.39441	+	4.84652i	0.557157	+	0.321675i	−0.194847	+	0.980834i	$0.562421\pi$
$228$	−5.68342	−	18.5891i	−0.376394	−	1.23109i
$229$	−8.99570	−	15.5810i	−0.594452	−	1.02962i	−0.993624	−	0.112746i	$-0.964035\pi$
$229$	−8.99570	−	15.5810i	−0.594452	−	1.02962i	0.399171	−	0.916876i	$-0.369298\pi$
$230$	−1.56438	+	1.48661i	−0.103152	+	0.0980241i
$231$	−1.00152	+	6.66648i	−0.0658951	+	0.438623i
$232$	9.73088	+	11.3454i	0.638864	+	0.744859i
$233$	21.6500	−	12.4996i	1.41834	−	0.818877i	0.422184	−	0.906510i	$-0.361264\pi$
$233$	21.6500	−	12.4996i	1.41834	−	0.818877i	0.996153	+	0.0876331i	$0.0279303\pi$
$234$	6.16484	−	2.66538i	0.403008	−	0.174241i
$235$	9.38664	+	5.41938i	0.612317	+	0.353521i
$236$	−4.04084	−	7.90338i	−0.263036	−	0.514466i
$237$	7.98349	+	6.71779i	0.518583	+	0.436367i
$238$	14.6814	−	14.7201i	0.951653	−	0.954161i
$239$			7.80454i			0.504834i	0.967619	+	0.252417i	$0.0812254\pi$
$239$			7.80454i			0.504834i	−0.967619	+	0.252417i	$0.918775\pi$
$240$	−6.66248	−	1.90035i	−0.430061	−	0.122667i
$241$	13.1988	+	7.62031i	0.850207	+	0.490867i	0.860721	−	0.509077i	$-0.170013\pi$
$241$	13.1988	+	7.62031i	0.850207	+	0.490867i	−0.0105136	+	0.999945i	$0.503347\pi$
$242$	−2.92557	−	12.1486i	−0.188063	−	0.780943i
$243$	2.60063	+	15.3700i	0.166831	+	0.985986i
$244$	−1.56055	+	30.5914i	−0.0999038	+	1.95842i
$245$	5.86596	−	3.81975i	0.374763	−	0.244035i
$246$	−5.87375	+	0.355198i	−0.374496	+	0.0226466i
$247$	−4.44161	−	7.69309i	−0.282613	−	0.489500i
$248$	−0.262810	−	1.40166i	−0.0166885	−	0.0890057i
$249$	−7.90316	−	21.8076i	−0.500842	−	1.38200i
$250$	−0.400715	+	1.35626i	−0.0253434	+	0.0857771i
$251$			13.8272i			0.872763i	0.899762	+	0.436382i	$0.143740\pi$
$251$			13.8272i			0.872763i	−0.899762	+	0.436382i	$0.856260\pi$
$252$	−15.7019	+	2.33453i	−0.989127	+	0.147062i
$253$			2.24484i			0.141132i
$254$	14.4275	+	4.26269i	0.905259	+	0.267465i
$255$	3.27905	+	9.04805i	0.205342	+	0.566611i
$256$	−10.6397	+	11.9497i	−0.664984	+	0.746858i
$257$	4.26584	+	7.38865i	0.266096	+	0.460891i	0.967850	−	0.251528i	$-0.0809330\pi$
$257$	4.26584	+	7.38865i	0.266096	+	0.460891i	−0.701755	+	0.712419i	$0.747600\pi$
$258$	−0.0380955	−	0.629968i	−0.00237173	−	0.0392201i
$259$	−1.12113	+	0.687984i	−0.0696635	+	0.0427493i
$260$	−3.16201	−	0.161302i	−0.196100	−	0.0100035i
$261$	−12.1726	+	10.1568i	−0.753467	+	0.628689i
$262$	−13.9165	+	3.35131i	−0.859767	+	0.207045i
$263$	−4.70164	−	2.71449i	−0.289915	−	0.167383i	0.347988	−	0.937499i	$-0.386865\pi$
$263$	−4.70164	−	2.71449i	−0.289915	−	0.167383i	−0.637904	+	0.770116i	$0.720198\pi$
$264$	−6.20697	+	3.66207i	−0.382013	+	0.225385i
$265$			11.5868i			0.711774i
$266$	5.46085	+	20.2734i	0.334826	+	1.24304i
$267$	8.02955	+	6.75655i	0.491401	+	0.413494i
$268$	7.19823	+	14.0788i	0.439702	+	0.860002i
$269$	15.0753	+	8.70371i	0.919156	+	0.530675i	0.883366	−	0.468684i	$-0.155272\pi$
$269$	15.0753	+	8.70371i	0.919156	+	0.530675i	0.0357901	+	0.999359i	$0.488605\pi$
$270$	2.11141	−	7.03860i	0.128496	−	0.428356i
$271$	11.9864	−	6.92036i	0.728122	−	0.420382i	−0.0896124	−	0.995977i	$-0.528563\pi$
$271$	11.9864	−	6.92036i	0.728122	−	0.420382i	0.817735	+	0.575595i	$0.195230\pi$
$272$	22.1101	+	2.26167i	1.34062	+	0.137134i
$273$	−6.75174	+	2.65363i	−0.408634	+	0.160605i
$274$	−11.4332	−	12.0313i	−0.690703	−	0.726835i
$275$	0.735536	+	1.27399i	0.0443545	+	0.0768242i
$276$	−5.05519	+	1.54557i	−0.304286	+	0.0930323i
$277$	−20.9220	−	12.0793i	−1.25708	−	0.725775i	−0.284573	−	0.958654i	$-0.591852\pi$
$277$	−20.9220	−	12.0793i	−1.25708	−	0.725775i	−0.972506	+	0.232879i	$0.925185\pi$
$278$	−0.945964	−	0.279491i	−0.0567351	−	0.0167628i
$279$	1.49034	−	0.258536i	0.0892241	−	0.0154781i
$280$	7.12329	+	2.29320i	0.425698	+	0.137045i
$281$			32.8316i			1.95857i	0.202491	+	0.979284i	$0.435096\pi$
$281$			32.8316i			1.95857i	−0.202491	+	0.979284i	$0.564904\pi$
$282$	14.6384	+	22.1493i	0.871703	+	1.31897i
$283$	0.974962	−	1.68868i	0.0579555	−	0.100382i	−0.835592	−	0.549351i	$-0.814875\pi$
$283$	0.974962	−	1.68868i	0.0579555	−	0.100382i	0.893548	+	0.448969i	$0.148209\pi$
$284$	−3.92161	+	6.05719i	−0.232705	+	0.359428i
$285$	−9.56926	−	1.70098i	−0.566834	−	0.100757i
$286$	−2.38738	+	2.26870i	−0.141169	+	0.134151i
$287$	6.35368	−	0.170319i	0.375046	−	0.0100536i
$288$	−12.5202	−	11.4562i	−0.737758	−	0.675066i
$289$	−6.93658	−	12.0145i	−0.408034	−	0.706735i
$290$	7.26570	−	1.74969i	0.426657	−	0.102745i
$291$	−10.0220	−	27.6542i	−0.587499	−	1.62112i
$292$	9.43773	+	18.4590i	0.552301	+	1.08023i
$293$		−	14.7459i		−	0.861467i	−0.902479	−	0.430733i	$-0.858255\pi$
$293$		−	14.7459i		−	0.861467i	0.902479	−	0.430733i	$-0.141745\pi$
$294$	17.0351	−	1.95044i	0.993509	−	0.113752i
$295$	−4.43824			−0.258404
$296$	−1.32653	−	0.466635i	−0.0771029	−	0.0271226i
$297$	−3.79444	−	6.63563i	−0.220176	−	0.385038i
$298$	6.82962	+	28.3605i	0.395629	+	1.64288i
$299$	−2.09209	+	1.20787i	−0.120988	+	0.0698527i
$300$	−2.36249	+	2.53350i	−0.136399	+	0.146272i
$301$	0.0182670	+	0.681442i	0.00105289	+	0.0392777i
$302$	−2.18993	+	2.08106i	−0.126016	+	0.119752i
$303$	−15.1210	−	2.68782i	−0.868678	−	0.154411i
$304$	−13.1427	+	18.1956i	−0.753783	+	1.04359i
$305$	13.2637	+	7.65781i	0.759478	+	0.438485i
$306$	−2.71713	+	23.4165i	−0.155328	+	1.33863i
$307$	−24.9046			−1.42138			−0.710691	−	0.703504i	$-0.751618\pi$
$307$	−24.9046			−1.42138			−0.710691	+	0.703504i	$0.751618\pi$
$308$	6.83338	−	3.72804i	0.389368	−	0.212425i
$309$	13.0841	−	15.5492i	0.744327	−	0.884565i
$310$	−0.683822	−	0.202040i	−0.0388385	−	0.0114751i
$311$	3.98354	−	6.89970i	0.225886	−	0.391246i	−0.730699	−	0.682700i	$-0.760806\pi$
$311$	3.98354	−	6.89970i	0.225886	−	0.391246i	0.956585	+	0.291454i	$0.0941390\pi$
$312$	−6.75263	−	3.81418i	−0.382292	−	0.215936i
$313$	24.7452	−	14.2866i	1.39868	−	0.807528i	0.404425	−	0.914571i	$-0.367472\pi$
$313$	24.7452	−	14.2866i	1.39868	−	0.807528i	0.994254	+	0.107043i	$0.0341382\pi$
$314$	2.83527	−	2.69432i	0.160004	−	0.152050i
$315$	−2.53469	+	7.52166i	−0.142813	+	0.423798i
$316$	0.613798	−	12.0323i	0.0345288	−	0.676870i
$317$	−5.89293	−	10.2069i	−0.330980	−	0.573274i	0.651724	−	0.758456i	$-0.274046\pi$
$317$	−5.89293	−	10.2069i	−0.330980	−	0.573274i	−0.982704	+	0.185182i	$0.940713\pi$
$318$	−12.6814	+	25.3912i	−0.711137	+	1.42387i
$319$	3.88694	−	6.73237i	0.217627	−	0.376940i
$320$	2.89810	+	7.45661i	0.162009	+	0.416837i
$321$	12.0864	+	10.1703i	0.674599	+	0.567649i
$322$	5.51322	−	1.48504i	0.307240	−	0.0827581i
$323$	31.1791			1.73485
$324$	12.3304	−	13.1134i	0.685023	−	0.728522i
$325$	−0.791530	+	1.37097i	−0.0439062	+	0.0760478i
$326$	−6.17331	+	1.48662i	−0.341908	+	0.0823365i
$327$	−10.8037	−	1.92040i	−0.597446	−	0.106198i
$328$	4.42365	+	5.15759i	0.244255	+	0.284780i
$329$	−14.9987	−	24.4416i	−0.826903	−	1.34751i
$330$	0.217506	+	3.59680i	0.0119733	+	0.197998i
$331$	5.08881	−	2.93803i	0.279706	−	0.161489i	−0.353584	−	0.935403i	$-0.615037\pi$
$331$	5.08881	−	2.93803i	0.279706	−	0.161489i	0.633290	+	0.773914i	$0.281704\pi$
$332$	−14.5563	+	22.4831i	−0.798878	+	1.23392i
$333$	0.514003	−	1.40014i	0.0281672	−	0.0767275i
$334$	−8.28271	−	2.44718i	−0.453210	−	0.133904i
$335$	7.90614			0.431959
$336$	13.1000	+	12.8215i	0.714664	+	0.699468i
$337$	8.48352			0.462127			0.231063	−	0.972939i	$-0.425780\pi$
$337$	8.48352			0.462127			0.231063	+	0.972939i	$0.425780\pi$
$338$	14.2324	+	4.20507i	0.774142	+	0.228726i
$339$	−6.52849	−	18.0144i	−0.354579	−	0.978407i
$340$	6.03945	−	9.32833i	0.327535	−	0.505900i
$341$	−0.642341	+	0.370856i	−0.0347847	+	0.0200830i
$342$	−19.1082	−	14.2007i	−1.03326	−	0.767886i
$343$	−18.4604	+	1.48742i	−0.996770	+	0.0803133i
$344$	−0.553160	+	0.474443i	−0.0298244	+	0.0255803i
$345$	−0.462569	+	2.60230i	−0.0249039	+	0.140103i
$346$	17.8351	−	4.29496i	0.958823	−	0.230899i
$347$	13.0330	−	22.5738i	0.699649	−	1.21183i	−0.268939	−	0.963157i	$-0.586673\pi$
$347$	13.0330	−	22.5738i	0.699649	−	1.21183i	0.968588	−	0.248670i	$-0.0799935\pi$
$348$	17.8369	+	4.11782i	0.956157	+	0.220738i
$349$	−14.2563			−0.763123			−0.381562	−	0.924343i	$-0.624614\pi$
$349$	−14.2563			−0.763123			−0.381562	+	0.924343i	$0.624614\pi$
$350$	2.64227	−	2.64923i	0.141235	−	0.141607i
$351$	4.14245	−	7.10664i	0.221107	−	0.379324i
$352$	7.69922	+	3.15779i	0.410370	+	0.168311i
$353$	−6.08482	+	10.5392i	−0.323862	+	0.560946i	−0.981281	−	0.192579i	$-0.938315\pi$
$353$	−6.08482	+	10.5392i	−0.323862	+	0.560946i	0.657419	+	0.753525i	$0.271648\pi$
$354$	−9.72586	−	4.85749i	−0.516924	−	0.258173i
$355$	1.80396	+	3.12456i	0.0957445	+	0.165834i
$356$	0.617340	−	12.1017i	0.0327189	−	0.641390i
$357$	3.78282	−	25.1799i	0.200208	−	1.33266i
$358$	−5.76641	+	5.47975i	−0.304764	+	0.289614i
$359$	7.41150	−	4.27903i	0.391164	−	0.225839i	−0.291500	−	0.956571i	$-0.594154\pi$
$359$	7.41150	−	4.27903i	0.391164	−	0.225839i	0.682664	+	0.730732i	$0.260821\pi$
$360$	−7.94995	+	2.96620i	−0.418999	+	0.156333i
$361$	−6.24402	+	10.8150i	−0.328633	+	0.569209i
$362$	−29.3295	−	8.66560i	−1.54152	−	0.455454i
$363$	−11.7102	−	9.85364i	−0.614624	−	0.517182i
$364$	7.15116	+	4.36247i	0.374823	+	0.228656i
$365$	10.3659			0.542576
$366$	20.6846	+	31.2978i	1.08120	+	1.63596i
$367$	25.2674	+	14.5881i	1.31895	+	0.761494i	0.983559	−	0.180587i	$-0.0577997\pi$
$367$	25.2674	+	14.5881i	1.31895	+	0.761494i	0.335387	+	0.942081i	$0.391133\pi$
$368$	4.94817	+	3.57406i	0.257941	+	0.186311i
$369$	−5.53367	+	4.61726i	−0.288071	+	0.240365i
$370$	−0.509678	+	0.484340i	−0.0264969	+	0.0251797i
$371$	14.6110	−	26.9500i	0.758567	−	1.39917i
$372$	−1.27739	−	1.19116i	−0.0662295	−	0.0617590i
$373$	−11.1475	+	6.43599i	−0.577193	+	0.333243i	−0.760017	−	0.649903i	$-0.774810\pi$
$373$	−11.1475	+	6.43599i	−0.577193	+	0.333243i	0.182824	+	0.983146i	$0.441476\pi$
$374$	−2.70633	−	11.2382i	−0.139941	−	0.581115i
$375$	0.590144	+	1.62841i	0.0304749	+	0.0840909i
$376$	10.1731	−	28.9195i	0.524635	−	1.49141i
$377$	8.36568			0.430854
$378$	−13.7867	+	13.7087i	−0.709109	+	0.705099i
$379$		−	1.38872i		−	0.0713338i	−0.999364	−	0.0356669i	$-0.988644\pi$
$379$		−	1.38872i		−	0.0713338i	0.999364	−	0.0356669i	$-0.0113555\pi$
$380$	5.10897	+	9.99253i	0.262085	+	0.512606i
$381$	17.3226	−	6.27778i	0.887464	−	0.321620i
$382$	25.2003	−	6.06861i	1.28936	−	0.310497i
$383$	−4.01414	−	6.95269i	−0.205113	−	0.355266i	0.745056	−	0.667002i	$-0.232423\pi$
$383$	−4.01414	−	6.95269i	−0.205113	−	0.355266i	−0.950169	+	0.311736i	$0.899089\pi$
$384$	−1.81016	+	19.5121i	−0.0923746	+	0.995724i
$385$	−0.104295	−	3.89069i	−0.00531538	−	0.198288i
$386$	−26.5910	+	25.2691i	−1.35345	+	1.28617i
$387$	−0.495209	−	0.593494i	−0.0251729	−	0.0301690i
$388$	−18.4588	+	28.5108i	−0.937103	+	1.44742i
$389$	−3.02937	+	5.24702i	−0.153595	+	0.266034i	−0.932547	−	0.361050i	$-0.882418\pi$
$389$	−3.02937	+	5.24702i	−0.153595	+	0.266034i	0.778952	+	0.627084i	$0.215752\pi$
$390$	−3.23502	+	2.13802i	−0.163812	+	0.108263i
$391$		−	8.47894i		−	0.428799i
$392$	−13.6764	−	14.3163i	−0.690764	−	0.723080i
$393$	−11.2876	+	13.4143i	−0.569383	+	0.676661i
$394$	13.5562	+	4.00526i	0.682950	+	0.201782i
$395$	−5.21691	−	3.01199i	−0.262491	−	0.151550i
$396$	−3.45993	+	8.12002i	−0.173868	+	0.408046i
$397$	16.3278	+	28.2806i	0.819469	+	1.41936i	0.906074	+	0.423119i	$0.139065\pi$
$397$	16.3278	+	28.2806i	0.819469	+	1.41936i	−0.0866048	+	0.996243i	$0.527602\pi$
$398$	20.3350	+	21.3988i	1.01930	+	1.07262i
$399$	20.1124	+	16.0232i	1.00688	+	0.802162i
$400$	3.97924	+	0.407041i	0.198962	+	0.0203521i
$401$	−0.464438	+	0.268144i	−0.0231929	+	0.0133905i	−0.511552	−	0.859253i	$-0.670929\pi$
$401$	−0.464438	+	0.268144i	−0.0231929	+	0.0133905i	0.488359	+	0.872643i	$0.337596\pi$
$402$	17.3254	+	8.65299i	0.864111	+	0.431572i
$403$	−0.691241	−	0.399088i	−0.0344332	−	0.0198800i
$404$	8.07301	+	15.7898i	0.401647	+	0.785573i
$405$	−3.03133	−	8.47414i	−0.150628	−	0.421083i
$406$	−19.1058	−	5.09244i	−0.948203	−	0.252733i
$407$			0.731373i			0.0362528i
$408$	23.4442	−	13.8319i	1.16066	−	0.684783i
$409$	−25.6969	−	14.8361i	−1.27063	−	0.733598i	−0.295523	−	0.955336i	$-0.595494\pi$
$409$	−25.6969	−	14.8361i	−1.27063	−	0.733598i	−0.975106	+	0.221737i	$0.928827\pi$
$410$	3.30298	−	0.795406i	0.163123	−	0.0392823i
$411$	−20.0137	−	3.55751i	−0.987201	−	0.175479i
$412$	−23.4350	−	1.19548i	−1.15456	−	0.0588970i
$413$	10.3230	+	5.59662i	0.507959	+	0.275392i
$414$	−3.86179	+	5.19636i	−0.189796	+	0.255387i
$415$	6.69596	+	11.5977i	0.328692	+	0.569311i
$416$	1.19976	+	8.87441i	0.0588231	+	0.435104i
$417$	−1.13579	+	0.411615i	−0.0556199	+	0.0201569i
$418$	11.1956	+	3.30782i	0.547595	+	0.161791i
$419$			28.9694i			1.41525i	0.706589	+	0.707624i	$0.250233\pi$
$419$			28.9694i			1.41525i	−0.706589	+	0.707624i	$0.749767\pi$
$420$	8.68970	−	2.91360i	0.424014	−	0.142169i
$421$		−	6.53258i		−	0.318379i	−0.987248	−	0.159189i	$-0.949112\pi$
$421$		−	6.53258i		−	0.318379i	0.987248	−	0.159189i	$-0.0508880\pi$
$422$	−4.15450	+	14.0613i	−0.202238	+	0.684493i
$423$	30.5244	+	11.2057i	1.48415	+	0.544841i
$424$	32.2112	−	6.03957i	1.56432	−	0.293307i
$425$	−2.77818	−	4.81195i	−0.134762	−	0.233414i
$426$	0.533453	+	8.82147i	0.0258459	+	0.427402i
$427$	−21.1937	−	34.5370i	−1.02564	−	1.67136i
$428$	0.929248	−	18.2161i	0.0449169	−	0.880507i
$429$	−0.705921	+	3.97134i	−0.0340822	+	0.191738i
$430$	0.0853086	+	0.354250i	0.00411394	+	0.0170834i
$431$	9.31568	+	5.37841i	0.448721	+	0.259069i	0.707290	−	0.706924i	$-0.249918\pi$
$431$	9.31568	+	5.37841i	0.448721	+	0.259069i	−0.258569	+	0.965993i	$0.583251\pi$
$432$	−20.6678	−	2.20086i	−0.994378	−	0.105889i
$433$			11.7672i			0.565497i	0.959194	+	0.282748i	$0.0912462\pi$
$433$			11.7672i			0.565497i	−0.959194	+	0.282748i	$0.908754\pi$
$434$	1.33574	+	1.33223i	0.0641175	+	0.0639489i
$435$	5.89314	−	7.00347i	0.282555	−	0.335791i
$436$	5.76803	+	11.2816i	0.276239	+	0.540289i
$437$	7.41574	+	4.28148i	0.354743	+	0.204811i
$438$	22.7156	+	11.3451i	1.08539	+	0.542090i
$439$	25.8121	−	14.9026i	1.23194	−	0.711262i	0.264507	−	0.964384i	$-0.414791\pi$
$439$	25.8121	−	14.9026i	1.23194	−	0.711262i	0.967434	+	0.253122i	$0.0814573\pi$
$440$	3.15826	−	2.70883i	0.150564	−	0.129139i
$441$	15.3803	−	14.2985i	0.732394	−	0.680881i
$442$	9.01734	−	8.56906i	0.428911	−	0.407589i
$443$	−14.3028	−	24.7731i	−0.679546	−	1.17701i	−0.975118	−	0.221687i	$-0.928844\pi$
$443$	−14.3028	−	24.7731i	−0.679546	−	1.17701i	0.295572	−	0.955320i	$-0.404490\pi$
$444$	−1.64699	+	0.503550i	−0.0781627	+	0.0238974i
$445$	−5.24701	−	3.02937i	−0.248732	−	0.143606i
$446$	−0.963752	+	3.26190i	−0.0456350	+	0.154456i
$447$	27.3369	+	23.0029i	1.29299	+	1.08800i
$448$	2.66207	−	20.9979i	0.125771	−	0.992059i
$449$		−	13.3090i		−	0.628089i	−0.949408	−	0.314045i	$-0.898316\pi$
$449$		−	13.3090i		−	0.628089i	0.949408	−	0.314045i	$-0.101684\pi$
$450$	−0.489012	+	4.21436i	−0.0230522	+	0.198667i
$451$	1.76700	−	3.06053i	0.0832047	−	0.144115i
$452$	−12.0243	+	18.5724i	−0.565578	+	0.873572i
$453$	−0.647537	+	3.64288i	−0.0304240	+	0.171158i
$454$	−9.44289	−	9.93688i	−0.443177	−	0.466361i
$455$	3.56983	−	2.19064i	0.167356	−	0.102699i
$456$	0.259236	+	27.4890i	0.0121398	+	1.28729i
$457$	20.7718	+	35.9778i	0.971662	+	1.68297i	0.690537	+	0.723297i	$0.257374\pi$
$457$	20.7718	+	35.9778i	0.971662	+	1.68297i	0.281125	+	0.959671i	$0.409292\pi$
$458$	5.95692	+	24.7365i	0.278349	+	1.15586i
$459$	14.3319	+	25.0633i	0.668957	+	1.16986i
$460$	2.71740	−	1.38935i	0.126699	−	0.0647788i
$461$		−	1.91633i		−	0.0892525i	−0.999004	−	0.0446262i	$-0.985790\pi$
$461$		−	1.91633i		−	0.0892525i	0.999004	−	0.0446262i	$-0.0142097\pi$
$462$	4.02967	−	8.64013i	0.187477	−	0.401975i
$463$	7.93638			0.368835			0.184417	−	0.982848i	$-0.440960\pi$
$463$	7.93638			0.368835			0.184417	+	0.982848i	$0.440960\pi$
$464$	−8.65130	−	19.2865i	−0.401627	−	0.895354i
$465$	−0.821043	+	0.297549i	−0.0380750	+	0.0137985i
$466$	−34.3717	+	8.27720i	−1.59224	+	0.383434i
$467$	−24.2364	+	13.9929i	−1.12153	+	0.647513i	−0.941790	−	0.336201i	$-0.890858\pi$
$467$	−24.2364	+	13.9929i	−1.12153	+	0.647513i	−0.179736	+	0.983715i	$0.557524\pi$
$468$	−9.42915	+	1.14459i	−0.435862	+	0.0529086i
$469$	−18.3890	−	9.96966i	−0.849125	−	0.460356i
$470$	−10.5591	−	11.1114i	−0.487053	−	0.512532i
$471$	0.838358	−	4.71640i	0.0386295	−	0.217320i
$472$	2.31340	+	12.3382i	0.106483	+	0.567913i
$473$	0.328246	+	0.189513i	0.0150928	+	0.00871383i
$474$	−8.13573	−	12.3101i	−0.373686	−	0.565423i
$475$	5.61142			0.257470
$476$	−25.8103	+	14.0811i	−1.18301	+	0.645408i
$477$	5.94135	+	34.2490i	0.272036	+	1.56816i
$478$	3.12739	−	10.5849i	0.143044	−	0.484144i
$479$	−16.4157	+	28.4329i	−0.750054	+	1.29913i	0.197743	+	0.980254i	$0.436639\pi$
$479$	−16.4157	+	28.4329i	−0.750054	+	1.29913i	−0.947796	+	0.318877i	$0.896694\pi$
$480$	8.27453	+	5.24711i	0.377679	+	0.239497i
$481$	−0.681606	+	0.393525i	−0.0310786	+	0.0179432i
$482$	−14.8473	−	15.6240i	−0.676277	−	0.711655i
$483$	4.35740	−	5.46942i	0.198268	−	0.248867i
$484$	−0.900318	+	17.6490i	−0.0409235	+	0.802225i
$485$	8.49114	+	14.7071i	0.385563	+	0.667815i
$486$	2.63186	−	21.8877i	0.119384	−	0.992848i
$487$	−17.4947	+	30.3017i	−0.792761	+	1.37310i	0.131491	+	0.991317i	$0.458024\pi$
$487$	−17.4947	+	30.3017i	−0.792761	+	1.37310i	−0.924251	+	0.381785i	$0.875310\pi$
$488$	14.3749	−	40.8645i	0.650723	−	1.84985i
$489$	−5.00711	+	5.95050i	−0.226429	+	0.269091i
$490$	−9.48637	+	2.82998i	−0.428551	+	0.127845i
$491$	−33.0134			−1.48987			−0.744937	−	0.667135i	$-0.767520\pi$
$491$	−33.0134			−1.48987			−0.744937	+	0.667135i	$0.767520\pi$
$492$	8.10863	+	1.87196i	0.365565	+	0.0843944i
$493$	−14.6813	+	25.4287i	−0.661212	+	1.14525i
$494$	2.94122	+	12.2136i	0.132332	+	0.549516i
$495$	2.82739	+	3.38856i	0.127082	+	0.152304i
$496$	−0.205229	+	2.00632i	−0.00921507	+	0.0900866i
$497$	−0.255793	−	9.54225i	−0.0114739	−	0.428029i
$498$	1.98007	+	32.7436i	0.0887292	+	1.46727i
$499$	−30.1483	+	17.4061i	−1.34962	+	0.779206i	−0.988196	−	0.153195i	$-0.951044\pi$
$499$	−30.1483	+	17.4061i	−1.34962	+	0.779206i	−0.361428	+	0.932400i	$0.617711\pi$
$500$	1.08694	−	1.67886i	0.0486096	−	0.0750807i
$501$	−9.94480	+	3.60404i	−0.444301	+	0.161016i
$502$	5.54075	−	18.7532i	0.247296	−	0.836995i
$503$	−7.82401			−0.348855			−0.174428	−	0.984670i	$-0.555807\pi$
$503$	−7.82401			−0.348855			−0.174428	+	0.984670i	$0.555807\pi$
$504$	22.2313	+	3.12576i	0.990260	+	0.139233i
$505$	8.86696			0.394574
$506$	0.899540	−	3.04457i	0.0399894	−	0.135348i
$507$	17.0884	−	6.19292i	0.758924	−	0.275037i
$508$	−17.8592	−	11.5626i	−0.792373	−	0.513007i
$509$	26.6916	−	15.4104i	1.18308	−	0.683054i	0.226359	−	0.974044i	$-0.427318\pi$
$509$	26.6916	−	15.4104i	1.18308	−	0.683054i	0.956726	+	0.290990i	$0.0939846\pi$
$510$	−0.821540	−	13.5854i	−0.0363784	−	0.601573i
$511$	−24.1102	−	13.0714i	−1.06657	−	0.578245i
$512$	19.2186	−	11.9434i	0.849352	−	0.527827i
$513$	−29.1575	−	0.121035i	−1.28734	−	0.00534381i
$514$	−2.82482	−	11.7303i	−0.124598	−	0.517400i
$515$	−5.86637	+	10.1609i	−0.258503	+	0.447741i
$516$	−0.200770	+	0.869663i	−0.00883842	+	0.0382848i
$517$	−15.9446			−0.701242
$518$	1.79622	−	0.483830i	0.0789214	−	0.0212583i
$519$	14.4659	−	17.1914i	0.634983	−	0.754620i
$520$	4.22386	+	1.48583i	0.185228	+	0.0651580i
$521$	−2.96129	+	5.12911i	−0.129737	+	0.224710i	−0.923574	−	0.383419i	$-0.874747\pi$
$521$	−2.96129	+	5.12911i	−0.129737	+	0.224710i	0.793838	+	0.608129i	$0.208080\pi$
$522$	20.5792	−	8.89743i	0.900726	−	0.389430i
$523$	−10.9378	−	18.9448i	−0.478275	−	0.828396i	0.521415	−	0.853303i	$-0.325404\pi$
$523$	−10.9378	−	18.9448i	−0.478275	−	0.828396i	−0.999690	+	0.0249070i	$0.992071\pi$
$524$	20.2173	+	1.03134i	0.883197	+	0.0450541i
$525$	0.680809	−	4.53172i	0.0297129	−	0.197781i
$526$	5.28888	+	5.56556i	0.230606	+	0.242670i
$527$	2.42618	−	1.40075i	0.105686	−	0.0610178i
$528$	9.88568	−	2.47948i	0.430219	−	0.107905i
$529$	−10.3357	+	17.9019i	−0.449377	+	0.778344i
$530$	4.64302	−	15.7147i	0.201680	−	0.682604i
$531$	−13.1188	+	2.27578i	−0.569307	+	0.0987604i
$532$	0.717559	−	29.6842i	0.0311101	−	1.28697i
$533$	3.80303			0.164727
$534$	−8.18267	−	12.3812i	−0.354099	−	0.535785i
$535$	−7.89804	−	4.55994i	−0.341462	−	0.197143i
$536$	−4.12103	−	21.9789i	−0.178001	−	0.949346i
$537$	−1.70506	+	9.59226i	−0.0735789	+	0.413936i
$538$	−16.9582	−	17.8453i	−0.731120	−	0.769367i
$539$	−4.66359	+	9.18093i	−0.200875	+	0.395451i
$540$	−5.68408	+	8.70007i	−0.244604	+	0.374391i
$541$	−18.9551	+	10.9437i	−0.814943	+	0.470508i	−0.848670	−	0.528923i	$-0.822596\pi$
$541$	−18.9551	+	10.9437i	−0.814943	+	0.470508i	0.0337264	+	0.999431i	$0.489263\pi$
$542$	−19.0297	+	4.58264i	−0.817396	+	0.196841i
$543$	−35.2150	+	12.7621i	−1.51122	+	0.547673i
$544$	−29.0806	−	11.9272i	−1.24682	−	0.511376i
$545$	6.33530			0.271374
$546$	10.2204	−	0.893472i	0.437394	−	0.0382371i
$547$		−	36.9373i		−	1.57933i	−0.613541	−	0.789663i	$-0.710255\pi$
$547$		−	36.9373i		−	1.57933i	0.613541	−	0.789663i	$-0.289745\pi$
$548$	10.6852	+	20.8989i	0.456448	+	0.892757i
$549$	43.1323	+	15.8342i	1.84084	+	0.675786i
$550$	−0.487069	−	2.02259i	−0.0207687	−	0.0862435i
$551$	−14.8268	−	25.6807i	−0.631642	−	1.09404i
$552$	7.47545	−	0.0704975i	0.318176	−	0.00300057i
$553$	8.33597	+	13.5842i	0.354482	+	0.577657i
$554$	23.5352	+	24.7664i	0.999913	+	1.05222i
$555$	−0.150706	+	0.847834i	−0.00639711	+	0.0359886i
$556$	1.17097	+	0.758123i	0.0496603	+	0.0321516i
$557$	2.68615	−	4.65254i	0.113816	−	0.197135i	−0.803490	−	0.595318i	$-0.797026\pi$
$557$	2.68615	−	4.65254i	0.113816	−	0.197135i	0.917306	+	0.398184i	$0.130359\pi$
$558$	−2.12488	−	0.246559i	−0.0899532	−	0.0104377i
$559$			0.407881i			0.0172515i
$560$	−8.74208	−	5.96457i	−0.369420	−	0.252049i
$561$	−10.8326	−	9.11523i	−0.457354	−	0.384845i
$562$	13.1561	−	44.5280i	0.554957	−	1.87830i
$563$	−0.425627	−	0.245736i	−0.0179380	−	0.0103565i	0.491004	−	0.871157i	$-0.336630\pi$
$563$	−0.425627	−	0.245736i	−0.0179380	−	0.0103565i	−0.508942	+	0.860801i	$0.669963\pi$
$564$	−10.9778	−	35.9059i	−0.462250	−	1.51191i
$565$	5.53127	+	9.58044i	0.232702	+	0.403052i
$566$	−1.99898	+	1.89960i	−0.0840233	+	0.0798463i
$567$	−3.63530	+	23.5326i	−0.152668	+	0.988277i
$568$	7.74591	−	6.64365i	0.325011	−	0.278761i
$569$	7.08363	−	4.08974i	0.296961	−	0.171451i	−0.344116	−	0.938927i	$-0.611821\pi$
$569$	7.08363	−	4.08974i	0.296961	−	0.171451i	0.641077	+	0.767477i	$0.278488\pi$
$570$	12.2968	+	6.14150i	0.515054	+	0.257239i
$571$	19.9812	+	11.5362i	0.836188	+	0.482773i	0.855967	−	0.517031i	$-0.172963\pi$
$571$	19.9812	+	11.5362i	0.836188	+	0.482773i	−0.0197790	+	0.999804i	$0.506296\pi$
$572$	4.14700	−	2.12027i	0.173395	−	0.0886531i
$573$	20.4398	−	24.2908i	0.853883	−	1.01476i
$574$	−8.68546	−	2.31502i	−0.362524	−	0.0966269i
$575$		−	1.52599i		−	0.0636381i
$576$	12.3899	+	20.5546i	0.516244	+	0.856442i
$577$	−24.5113	−	14.1516i	−1.02042	−	0.589138i	−0.106192	−	0.994346i	$-0.533866\pi$
$577$	−24.5113	−	14.1516i	−1.02042	−	0.589138i	−0.914225	+	0.405208i	$0.867199\pi$
$578$	4.59338	+	19.0743i	0.191059	+	0.793387i
$579$	−7.86267	+	44.2334i	−0.326761	+	1.83828i
$580$	−10.5553	−	0.538451i	−0.438284	−	0.0223580i
$581$	−0.949454	−	35.4190i	−0.0393900	−	1.46943i
$582$	2.51093	+	41.5221i	0.104081	+	1.72115i
$583$	−8.52254	−	14.7615i	−0.352967	−	0.611358i
$584$	−5.40316	−	28.8170i	−0.223584	−	1.19246i
$585$	−1.63666	+	4.45826i	−0.0676675	+	0.184326i
$586$	−5.90892	+	19.9993i	−0.244095	+	0.826162i
$587$			16.1519i			0.666662i	0.942810	+	0.333331i	$0.108173\pi$
$587$			16.1519i			0.666662i	−0.942810	+	0.333331i	$0.891827\pi$
$588$	−23.8856	−	4.18094i	−0.985024	−	0.172419i
$589$			2.82927i			0.116578i
$590$	6.01938	+	1.77847i	0.247814	+	0.0732183i
$591$	16.2765	−	5.89866i	0.669524	−	0.242638i
$592$	1.61212	+	1.16444i	0.0662579	+	0.0478580i
$593$	6.22547	+	10.7828i	0.255650	+	0.442798i	0.965072	−	0.261986i	$-0.0843773\pi$
$593$	6.22547	+	10.7828i	0.255650	+	0.442798i	−0.709422	+	0.704784i	$0.751044\pi$
$594$	2.48724	+	10.5201i	0.102053	+	0.431645i
$595$	0.393932	+	14.6955i	0.0161496	+	0.602456i
$596$	2.10176	−	41.2008i	0.0860913	−	1.68765i
$597$	35.5963	+	6.32738i	1.45686	+	0.258962i
$598$	3.32141	−	0.799845i	0.135823	−	0.0327081i
$599$	15.3718	+	8.87490i	0.628073	+	0.362618i	0.780006	−	0.625773i	$-0.215216\pi$
$599$	15.3718	+	8.87490i	0.628073	+	0.362618i	−0.151932	+	0.988391i	$0.548550\pi$
$600$	4.21935	−	2.48939i	0.172254	−	0.101629i
$601$		−	23.7047i		−	0.966933i	−0.875363	−	0.483466i	$-0.839378\pi$
$601$		−	23.7047i		−	0.966933i	0.875363	−	0.483466i	$-0.160622\pi$
$602$	0.248289	−	0.931529i	0.0101195	−	0.0379663i
$603$	23.3694	−	4.05401i	0.951676	−	0.165092i
$604$	3.80401	−	1.94491i	0.154783	−	0.0791374i
$605$	7.65216	+	4.41797i	0.311104	+	0.179616i
$606$	19.4309	+	9.70457i	0.789325	+	0.394221i
$607$	−18.4365	+	10.6443i	−0.748313	+	0.432039i	−0.825084	−	0.565010i	$-0.808872\pi$
$607$	−18.4365	+	10.6443i	−0.748313	+	0.432039i	0.0767711	+	0.997049i	$0.475539\pi$
$608$	25.1160	−	19.4114i	1.01859	−	0.787236i
$609$	−22.5383	+	8.85821i	−0.913299	+	0.358953i
$610$	−14.9204	−	15.7009i	−0.604108	−	0.635711i
$611$	−8.57920	−	14.8596i	−0.347077	−	0.601156i
$612$	13.0685	−	30.6700i	0.528262	−	1.23976i
$613$	12.7964	+	7.38799i	0.516841	+	0.298398i	0.735641	−	0.677372i	$-0.236881\pi$
$613$	12.7964	+	7.38799i	0.516841	+	0.298398i	−0.218801	+	0.975770i	$0.570214\pi$
$614$	33.7770	+	9.97966i	1.36313	+	0.402746i
$615$	2.67902	−	3.18377i	0.108028	−	0.128382i
$616$	−10.7617	+	2.31794i	−0.433601	+	0.0933923i
$617$			30.4468i			1.22574i	0.790183	+	0.612871i	$0.209985\pi$
$617$			30.4468i			1.22574i	−0.790183	+	0.612871i	$0.790015\pi$
$618$	−23.9761	+	15.8458i	−0.964462	+	0.637410i
$619$	16.2068	−	28.0710i	0.651407	−	1.12827i	−0.331374	−	0.943499i	$-0.607512\pi$
$619$	16.2068	−	28.0710i	0.651407	−	1.12827i	0.982782	−	0.184771i	$-0.0591544\pi$
$620$	0.846476	+	0.548035i	0.0339953	+	0.0220096i
$621$	−0.0329146	+	7.92920i	−0.00132082	+	0.318188i
$622$	−8.16751	+	7.76149i	−0.327487	+	0.311207i
$623$	8.38407	+	13.6625i	0.335901	+	0.547378i
$624$	7.62988	+	7.87888i	0.305440	+	0.315408i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−39.2856	+	9.46056i	−1.57017	+	0.378120i
$627$	13.4422	−	4.87152i	0.536831	−	0.194550i
$628$	−4.92501	+	2.51806i	−0.196529	+	0.100481i
$629$		−	2.76246i		−	0.110146i
$630$	6.45172	−	9.18560i	0.257043	−	0.365963i
$631$	−8.40055			−0.334421			−0.167210	−	0.985921i	$-0.553476\pi$
$631$	−8.40055			−0.334421			−0.167210	+	0.985921i	$0.553476\pi$
$632$	−5.65399	+	16.0729i	−0.224904	+	0.639346i
$633$	6.11845	+	16.8830i	0.243187	+	0.671037i
$634$	3.90228	+	16.2045i	0.154979	+	0.643562i
$635$	−9.21253	+	5.31886i	−0.365588	+	0.211072i
$636$	27.3738	−	29.3553i	1.08544	−	1.16401i
$637$	−11.0655	+	0.593679i	−0.438431	+	0.0235224i
$638$	−7.96944	+	7.57326i	−0.315513	+	0.299828i
$639$	6.93442	+	8.31072i	0.274322	+	0.328767i
$640$	−0.942584	−	11.2744i	−0.0372589	−	0.445659i
$641$	−30.8062	−	17.7860i	−1.21677	−	0.702504i	−0.252547	−	0.967585i	$-0.581268\pi$
$641$	−30.8062	−	17.7860i	−1.21677	−	0.702504i	−0.964226	+	0.265081i	$0.914601\pi$
$642$	−12.3169	−	18.6367i	−0.486110	−	0.735531i
$643$	35.4168			1.39670			0.698351	−	0.715756i	$-0.253918\pi$
$643$	35.4168			1.39670			0.698351	+	0.715756i	$0.253918\pi$
$644$	−8.07241	−	0.195135i	−0.318098	−	0.00768941i
$645$	0.341464	+	0.287329i	0.0134451	+	0.0113136i
$646$	−42.2868	−	12.4939i	−1.66375	−	0.491567i
$647$	18.0279	−	31.2253i	0.708750	−	1.22759i	−0.256570	−	0.966526i	$-0.582593\pi$
$647$	18.0279	−	31.2253i	0.708750	−	1.22759i	0.965321	−	0.261066i	$-0.0840741\pi$
$648$	−21.9779	+	12.8441i	−0.863374	+	0.504565i
$649$	5.65425	−	3.26448i	0.221949	−	0.128142i
$650$	1.62289	−	1.54221i	0.0636548	−	0.0604904i
$651$	2.28489	+	0.343263i	0.0895518	+	0.0134535i
$652$	8.96829	+	0.457495i	0.351225	+	0.0179169i
$653$	−6.06477	−	10.5045i	−0.237333	−	0.411073i	0.722615	−	0.691251i	$-0.242940\pi$
$653$	−6.06477	−	10.5045i	−0.237333	−	0.411073i	−0.959948	+	0.280178i	$0.909607\pi$
$654$	13.8830	+	6.93376i	0.542870	+	0.271131i
$655$	5.06090	−	8.76573i	0.197746	−	0.342505i
$656$	−3.93287	−	8.76763i	−0.153553	−	0.342318i
$657$	30.6401	−	5.31528i	1.19538	−	0.207369i
$658$	10.5479	+	39.1592i	0.411201	+	1.52658i
$659$	−6.15679			−0.239834			−0.119917	−	0.992784i	$-0.538263\pi$
$659$	−6.15679			−0.239834			−0.119917	+	0.992784i	$0.538263\pi$
$660$	1.14630	−	4.96534i	0.0446196	−	0.193276i
$661$	−18.7652	+	32.5024i	−0.729883	+	1.26420i	0.227049	+	0.973883i	$0.427092\pi$
$661$	−18.7652	+	32.5024i	−0.729883	+	1.26420i	−0.956932	+	0.290312i	$0.906241\pi$
$662$	−8.07904	+	1.94555i	−0.314001	+	0.0756160i
$663$	2.66633	−	15.0001i	0.103551	−	0.582555i
$664$	28.7513	−	24.6599i	1.11577	−	0.956990i
$665$	−13.0517	−	7.07601i	−0.506122	−	0.274396i
$666$	−1.25818	+	1.69298i	−0.0487534	+	0.0656018i
$667$	−6.98370	+	4.03204i	−0.270410	+	0.156121i
$668$	10.2528	+	6.63801i	0.396695	+	0.256832i
$669$	1.41934	+	3.91647i	0.0548750	+	0.151419i
$670$	−10.7227	−	3.16811i	−0.414256	−	0.122395i
$671$	−22.5304			−0.869775
$672$	−12.6292	−	22.6385i	−0.487183	−	0.873300i
$673$	7.24538			0.279289			0.139644	−	0.990202i	$-0.455404\pi$
$673$	7.24538			0.279289			0.139644	+	0.990202i	$0.455404\pi$
$674$	−11.5058	−	3.39947i	−0.443187	−	0.130943i
$675$	2.57937	+	4.51075i	0.0992802	+	0.173619i
$676$	−17.6178	−	11.4063i	−0.677607	−	0.438704i
$677$	5.99640	−	3.46202i	0.230460	−	0.133056i	−0.380324	−	0.924853i	$-0.624188\pi$
$677$	5.99640	−	3.46202i	0.230460	−	0.133056i	0.610784	+	0.791797i	$0.290854\pi$
$678$	1.63566	+	27.0482i	0.0628172	+	1.03878i
$679$	−1.20400	−	44.9148i	−0.0462054	−	1.72367i
$680$	−11.9290	+	10.2315i	−0.457457	+	0.392360i
$681$	−16.5297	−	2.93822i	−0.633420	−	0.112593i
$682$	1.01979	−	0.245579i	0.0390496	−	0.00940372i
$683$	0.187389	−	0.324567i	0.00717025	−	0.0124192i	−0.862418	−	0.506197i	$-0.831051\pi$
$683$	0.187389	−	0.324567i	0.00717025	−	0.0124192i	0.869588	+	0.493778i	$0.164384\pi$
$684$	20.2252	+	26.9167i	0.773330	+	1.02919i
$685$	11.7360			0.448410
$686$	25.6331	+	5.38004i	0.978676	+	0.205411i
$687$	23.8437	+	20.0636i	0.909696	+	0.765473i
$688$	0.940342	−	0.421807i	0.0358502	−	0.0160812i
$689$	9.17134	−	15.8852i	0.349400	−	0.605179i
$690$	1.67014	−	3.34402i	0.0635812	−	0.127305i
$691$	−12.7306	−	22.0500i	−0.484294	−	0.838821i	0.515544	−	0.856863i	$-0.327590\pi$
$691$	−12.7306	−	22.0500i	−0.484294	−	0.838821i	−0.999837	+	0.0180422i	$0.994257\pi$
$692$	−25.9100	−	1.32174i	−0.984952	−	0.0502449i
$693$	−2.30330	−	11.4468i	−0.0874951	−	0.434829i
$694$	−26.7218	+	25.3934i	−1.01434	+	0.963919i
$695$	0.604037	−	0.348741i	0.0229124	−	0.0132285i
$696$	−22.5413	−	12.7323i	−0.854425	−	0.482617i
$697$	−6.67410	+	11.5599i	−0.252800	+	0.437862i
$698$	19.3352	+	5.71272i	0.731848	+	0.216230i
$699$	−27.8785	+	33.1311i	−1.05446	+	1.25313i
$700$	−4.64517	+	2.53424i	−0.175571	+	0.0957851i
$701$	−36.9898			−1.39709			−0.698544	−	0.715568i	$-0.746168\pi$
$701$	−36.9898			−1.39709			−0.698544	+	0.715568i	$0.746168\pi$
$702$	−8.46595	+	7.97847i	−0.319527	+	0.301128i
$703$	2.41607	+	1.39492i	0.0911236	+	0.0526103i
$704$	−9.17673	−	7.36796i	−0.345861	−	0.277690i
$705$	−18.4835	−	3.28552i	−0.696130	−	0.123740i
$706$	12.4758	−	11.8556i	0.469532	−	0.446191i
$707$	−20.6238	−	11.1812i	−0.775637	−	0.420514i
$708$	11.2443	+	10.4853i	0.422586	+	0.394062i
$709$	10.7817	−	6.22482i	0.404916	−	0.233778i	−0.283687	−	0.958917i	$-0.591558\pi$
$709$	10.7817	−	6.22482i	0.404916	−	0.233778i	0.688603	+	0.725139i	$0.258224\pi$
$710$	−1.19458	−	4.96057i	−0.0448318	−	0.186167i
$711$	−16.9649	−	6.22793i	−0.636233	−	0.233566i
$712$	−5.68661	+	16.1656i	−0.213115	+	0.605833i
$713$	0.769401			0.0288143
$714$	−15.2204	+	32.6345i	−0.569610	+	1.22132i
$715$		−	2.32879i		−	0.0870920i
$716$	10.0165	−	5.12125i	0.374335	−	0.191390i
$717$	−4.60580	−	12.7090i	−0.172007	−	0.474627i
$718$	−11.7666	+	2.83356i	−0.439124	+	0.105748i
$719$	24.7488	+	42.8661i	0.922974	+	1.59864i	0.794788	+	0.606887i	$0.207582\pi$
$719$	24.7488	+	42.8661i	0.922974	+	1.59864i	0.128186	+	0.991750i	$0.459085\pi$
$720$	11.9708	−	0.837265i	0.446124	−	0.0312030i
$721$	26.4575	−	16.2358i	0.985330	−	0.604651i
$722$	12.8022	−	12.1658i	0.476449	−	0.452763i
$723$	−25.9901	−	4.61985i	−0.966583	−	0.171814i
$724$	36.3059	+	23.5055i	1.34930	+	0.873576i
$725$	−2.64225	+	4.57651i	−0.0981306	+	0.169967i
$726$	11.9335	+	18.0565i	0.442892	+	0.670139i
$727$		−	25.7928i		−	0.956601i	−0.878196	−	0.478300i	$-0.841253\pi$
$727$		−	25.7928i		−	0.956601i	0.878196	−	0.478300i	$-0.158747\pi$
$728$	−7.95069	−	8.78220i	−0.294672	−	0.325490i
$729$	−13.3054	−	23.4940i	−0.492793	−	0.870147i
$730$	−14.0588	−	4.15377i	−0.520339	−	0.153738i
$731$	−1.23981	−	0.715807i	−0.0458562	−	0.0264751i
$732$	−15.5121	−	50.7365i	−0.573345	−	1.87527i
$733$	16.5408	+	28.6495i	0.610949	+	1.05819i	0.991081	+	0.133262i	$0.0425451\pi$
$733$	16.5408	+	28.6495i	0.610949	+	1.05819i	−0.380132	+	0.924932i	$0.624122\pi$
$734$	−28.4233	−	29.9102i	−1.04912	−	1.10401i
$735$	−7.29801	+	9.68189i	−0.269191	+	0.357122i
$736$	−5.27880	−	6.83014i	−0.194579	−	0.251762i
$737$	−10.0723	+	5.81525i	−0.371018	+	0.214207i
$738$	9.35527	−	4.04476i	0.344372	−	0.148890i
$739$	34.5398	+	19.9416i	1.27057	+	0.733563i	0.975095	−	0.221788i	$-0.0711894\pi$
$739$	34.5398	+	19.9416i	1.27057	+	0.733563i	0.295473	+	0.955351i	$0.404523\pi$
$740$	0.885335	−	0.452654i	0.0325456	−	0.0166399i
$741$	11.7728	+	9.90635i	0.432485	+	0.363919i
$742$	−30.6156	+	30.6962i	−1.12393	+	1.12689i
$743$		−	28.6559i		−	1.05128i	−0.850706	−	0.525642i	$-0.823825\pi$
$743$		−	28.6559i		−	1.05128i	0.850706	−	0.525642i	$-0.176175\pi$
$744$	1.25515	+	2.12739i	0.0460159	+	0.0779939i
$745$	−17.8637	−	10.3136i	−0.654474	−	0.377860i
$746$	17.6978	−	4.26189i	0.647962	−	0.156039i
$747$	25.7392	+	30.8478i	0.941749	+	1.12866i
$748$	−0.832850	+	16.3264i	−0.0304520	+	0.596951i
$749$	12.6201	+	20.5655i	0.461128	+	0.751446i
$750$	−0.147856	−	2.44502i	−0.00539893	−	0.0892796i
$751$	6.99268	+	12.1117i	0.255166	+	0.441961i	0.964941	−	0.262468i	$-0.0845364\pi$
$751$	6.99268	+	12.1117i	0.255166	+	0.441961i	−0.709774	+	0.704429i	$0.751203\pi$
$752$	−25.3857	+	35.1457i	−0.925722	+	1.28163i
$753$	−8.16002	−	22.5164i	−0.297368	−	0.820541i
$754$	−11.3460	−	3.35225i	−0.413197	−	0.122082i
$755$		−	2.13619i		−	0.0777439i
$756$	24.1915	−	13.0680i	0.879836	−	0.475277i
$757$		−	20.8260i		−	0.756933i	−0.925615	−	0.378467i	$-0.876451\pi$
$757$		−	20.8260i		−	0.756933i	0.925615	−	0.378467i	$-0.123549\pi$
$758$	−0.556481	+	1.88346i	−0.0202123	+	0.0684104i
$759$	−1.32478	−	3.65552i	−0.0480863	−	0.132687i
$760$	−2.92492	−	15.5997i	−0.106098	−	0.565859i
$761$	10.6790	+	18.4965i	0.387112	+	0.670498i	0.992060	−	0.125767i	$-0.0401392\pi$
$761$	10.6790	+	18.4965i	0.387112	+	0.670498i	−0.604947	+	0.796265i	$0.706806\pi$
$762$	−26.0095	+	1.57285i	−0.942223	+	0.0569783i
$763$	−14.7354	−	7.98882i	−0.533456	−	0.289215i
$764$	−36.6099	−	1.86756i	−1.32450	−	0.0675660i
$765$	−10.6793	−	12.7989i	−0.386111	−	0.462744i
$766$	2.65815	+	11.0381i	0.0960428	+	0.398824i
$767$	6.08469	+	3.51300i	0.219706	+	0.126847i
$768$	10.2738	−	25.7381i	0.370725	−	0.928742i
$769$			20.6278i			0.743856i	0.928262	+	0.371928i	$0.121303\pi$
$769$			20.6278i			0.743856i	−0.928262	+	0.371928i	$0.878697\pi$
$770$	−1.41761	+	5.31856i	−0.0510870	+	0.191668i
$771$	−11.3069	−	9.51431i	−0.407208	−	0.342650i
$772$	46.1899	−	23.6160i	1.66241	−	0.849957i
$773$	7.19484	+	4.15394i	0.258780	+	0.149407i	0.623778	−	0.781602i	$-0.285597\pi$
$773$	7.19484	+	4.15394i	0.258780	+	0.149407i	−0.364998	+	0.931008i	$0.618930\pi$
$774$	0.433807	+	1.00337i	0.0155929	+	0.0360653i
$775$	0.436649	−	0.252099i	0.0156849	−	0.00905567i
$776$	36.4595	−	31.2712i	1.30882	−	1.12257i
$777$	1.41965	−	1.78195i	0.0509296	−	0.0639271i
$778$	6.21115	−	5.90238i	0.222681	−	0.211611i
$779$	−6.74023	−	11.6744i	−0.241494	−	0.418280i
$780$	5.24425	−	1.60337i	0.187774	−	0.0574100i
$781$	−4.59645	−	2.65376i	−0.164474	−	0.0949590i
$782$	−3.39764	+	11.4996i	−0.121499	+	0.411225i
$783$	13.8281	−	23.7230i	0.494177	−	0.847792i
$784$	12.8120	+	24.8968i	0.457571	+	0.889173i
$785$			2.76570i			0.0987119i
$786$	20.6841	−	13.6701i	0.737779	−	0.487595i
$787$	23.7585	−	41.1509i	0.846899	−	1.46687i	−0.0370629	−	0.999313i	$-0.511800\pi$
$787$	23.7585	−	41.1509i	0.846899	−	1.46687i	0.883962	−	0.467559i	$-0.154866\pi$
$788$	−16.7806	−	10.8643i	−0.597786	−	0.387025i
$789$	9.25815	+	1.64567i	0.329599	+	0.0585875i
$790$	5.86852	+	6.17552i	0.208793	+	0.219715i
$791$	−0.784307	−	29.2582i	−0.0278867	−	1.04030i
$792$	7.94637	−	9.62637i	0.282362	−	0.342058i
$793$	−12.1228	−	20.9973i	−0.430492	−	0.745634i
$794$	−10.8122	−	44.8985i	−0.383711	−	1.59339i
$795$	−6.83790	−	18.8682i	−0.242515	−	0.669185i
$796$	−19.0046	−	37.1707i	−0.673601	−	1.31748i
$797$			23.1123i			0.818681i	0.912382	+	0.409341i	$0.134241\pi$
$797$			23.1123i			0.818681i	−0.912382	+	0.409341i	$0.865759\pi$
$798$	−20.8568	−	29.7908i	−0.738321	−	1.05458i
$799$	60.2240			2.13057
$800$	−5.23375	−	2.14659i	−0.185041	−	0.0758934i
$801$	−17.0628	−	6.26387i	−0.602883	−	0.221323i
$802$	0.737346	−	0.177564i	0.0260366	−	0.00627000i
$803$	−13.2060	+	7.62449i	−0.466029	+	0.269062i
$804$	−20.0302	−	18.6782i	−0.706412	−	0.658729i
$805$	−1.92427	+	3.54932i	−0.0678217	+	0.125097i
$806$	0.777579	+	0.818256i	0.0273890	+	0.0288218i
$807$	−29.6852	−	5.27667i	−1.04497	−	0.185748i
$808$	−4.62184	−	24.6500i	−0.162596	−	0.867184i
$809$	−40.9428	−	23.6383i	−1.43947	−	0.831080i	−0.441660	−	0.897183i	$-0.645610\pi$
$809$	−40.9428	−	23.6383i	−1.43947	−	0.831080i	−0.997813	+	0.0661027i	$0.978943\pi$
$810$	0.715537	+	12.7078i	0.0251414	+	0.446506i
$811$	10.6244			0.373074			0.186537	−	0.982448i	$-0.440274\pi$
$811$	10.6244			0.373074			0.186537	+	0.982448i	$0.440274\pi$
$812$	23.8717	+	14.5626i	0.837731	+	0.511047i
$813$	−15.4348	+	18.3429i	−0.541323	+	0.643314i
$814$	0.293072	−	0.991928i	0.0102722	−	0.0347671i
$815$	2.24499	−	3.88843i	0.0786385	−	0.136206i
$816$	−37.3390	+	9.36519i	−1.30713	+	0.327847i
$817$	1.25210	−	0.722901i	0.0438055	−	0.0252911i
$818$	28.9065	+	30.4187i	1.01069	+	1.06356i
$819$	9.42860	−	8.30570i	0.329462	−	0.290224i
$820$	−4.79842	−	0.244779i	−0.167568	−	0.00854807i
$821$	−10.7148	−	18.5585i	−0.373948	−	0.647697i	0.616221	−	0.787573i	$-0.288663\pi$
$821$	−10.7148	−	18.5585i	−0.373948	−	0.647697i	−0.990169	+	0.139876i	$0.955329\pi$
$822$	25.7181	+	12.8447i	0.897021	+	0.448009i
$823$	0.539744	−	0.934864i	0.0188143	−	0.0325873i	−0.856465	−	0.516205i	$-0.827344\pi$
$823$	0.539744	−	0.934864i	0.0188143	−	0.0325873i	0.875279	+	0.483618i	$0.160678\pi$
$824$	31.3048	+	11.0121i	1.09055	+	0.383626i
$825$	−1.94959	−	1.64050i	−0.0678760	−	0.0571150i
$826$	−11.7579	−	11.7270i	−0.409110	−	0.408035i
$827$	0.330867			0.0115054			0.00575268	−	0.999983i	$-0.498169\pi$
$827$	0.330867			0.0115054			0.00575268	+	0.999983i	$0.498169\pi$
$828$	7.31983	−	5.50011i	0.254382	−	0.191142i
$829$	−12.3113	+	21.3239i	−0.427591	+	0.740609i	−0.996658	−	0.0816820i	$-0.973971\pi$
$829$	−12.3113	+	21.3239i	−0.427591	+	0.740609i	0.569068	+	0.822291i	$0.307304\pi$
$830$	−4.43404	−	18.4127i	−0.153908	−	0.639113i
$831$	41.1981	+	7.32313i	1.42915	+	0.254037i
$832$	1.92893	−	12.5167i	0.0668735	−	0.433939i
$833$	17.6148	−	34.6771i	0.610315	−	1.20149i
$834$	1.70536	−	0.103127i	0.0590518	−	0.00357099i
$835$	5.28886	−	3.05352i	0.183029	−	0.105672i
$836$	−13.8586	−	8.97250i	−0.479310	−	0.310320i
$837$	−2.27431	+	1.30052i	−0.0786117	+	0.0449524i
$838$	11.6085	−	39.2899i	0.401008	−	1.35725i
$839$	−31.3993			−1.08402			−0.542012	−	0.840371i	$-0.682337\pi$
$839$	−31.3993			−1.08402			−0.542012	+	0.840371i	$0.682337\pi$
$840$	−12.9530	+	0.469494i	−0.446920	+	0.0161991i
$841$	−1.07409			−0.0370376
$842$	−2.61770	+	8.85985i	−0.0902120	+	0.305330i
$843$	−19.3754	−	53.4634i	−0.667323	−	1.84138i
$844$	11.2691	−	17.4059i	0.387900	−	0.599137i
$845$	−9.08800	+	5.24696i	−0.312637	+	0.180501i
$846$	−36.9086	−	27.4294i	−1.26894	−	0.943043i
$847$	−12.2272	−	19.9252i	−0.420131	−	0.684638i
$848$	−46.1068	−	4.71632i	−1.58331	−	0.161959i
$849$	−0.591076	+	3.32524i	−0.0202857	+	0.114122i
$850$	1.83970	+	7.63949i	0.0631012	+	0.262032i
$851$	0.379338	−	0.657033i	0.0130035	−	0.0225228i
$852$	2.81139	−	12.1779i	0.0963168	−	0.417209i
$853$	18.6873			0.639841			0.319920	−	0.947444i	$-0.396344\pi$
$853$	18.6873			0.639841			0.319920	+	0.947444i	$0.396344\pi$
$854$	14.9046	+	55.3336i	0.510027	+	1.89348i
$855$	16.5865	−	2.87735i	0.567248	−	0.0984033i
$856$	−8.55974	+	24.3333i	−0.292566	+	0.831694i
$857$	−26.9989	+	46.7635i	−0.922266	+	1.59741i	−0.126367	+	0.991984i	$0.540332\pi$
$857$	−26.9989	+	46.7635i	−0.922266	+	1.59741i	−0.795900	+	0.605428i	$0.793002\pi$
$858$	2.54878	−	5.10327i	0.0870140	−	0.174223i
$859$	−10.5039	−	18.1932i	−0.358388	−	0.620745i	0.629304	−	0.777159i	$-0.283340\pi$
$859$	−10.5039	−	18.1932i	−0.358388	−	0.620745i	−0.987692	+	0.156414i	$0.950007\pi$
$860$	0.0262530	−	0.514637i	0.000895219	−	0.0175490i
$861$	−10.2459	+	4.02693i	−0.349179	+	0.137237i
$862$	−10.4792	−	11.0274i	−0.356924	−	0.375596i
$863$	6.39202	−	3.69044i	0.217587	−	0.125624i	−0.387245	−	0.921977i	$-0.626573\pi$
$863$	6.39202	−	3.69044i	0.217587	−	0.125624i	0.604832	+	0.796353i	$0.293240\pi$
$864$	27.1488	+	11.2668i	0.923622	+	0.383304i
$865$	−6.48593	+	11.2340i	−0.220528	+	0.381966i
$866$	4.71530	−	15.9594i	0.160233	−	0.542321i
$867$	18.3859	+	15.4710i	0.624418	+	0.525423i
$868$	−1.27776	−	2.34209i	−0.0433699	−	0.0794957i
$869$	8.86169			0.300612
$870$	−10.7990	+	7.13702i	−0.366120	+	0.241968i
$871$	−10.8391	−	6.25795i	−0.367269	−	0.212043i
$872$	−3.30223	−	17.6120i	−0.111828	−	0.596418i
$873$	32.6399	+	39.1180i	1.10469	+	1.32395i
$874$	−8.34199	−	8.77838i	−0.282172	−	0.296933i
$875$	0.0708975	+	2.64480i	0.00239677	+	0.0894106i
$876$	−26.2620	−	24.4893i	−0.887311	−	0.827418i
$877$	5.16655	−	2.98291i	0.174462	−	0.100726i	−0.410226	−	0.911984i	$-0.634550\pi$
$877$	5.16655	−	2.98291i	0.174462	−	0.100726i	0.584688	+	0.811258i	$0.301217\pi$
$878$	−40.9794	+	9.86845i	−1.38299	+	0.333044i
$879$	8.70222	+	24.0125i	0.293519	+	0.809921i
$880$	−5.36888	+	2.40831i	−0.180985	+	0.0811840i
$881$	6.16710			0.207775			0.103887	−	0.994589i	$-0.466872\pi$
$881$	6.16710			0.207775			0.103887	+	0.994589i	$0.466872\pi$
$882$	−26.5892	+	13.2293i	−0.895305	+	0.445453i
$883$		−	33.1527i		−	1.11568i	−0.829950	−	0.557839i	$-0.811631\pi$
$883$		−	33.1527i		−	1.11568i	0.829950	−	0.557839i	$-0.188369\pi$
$884$	−15.6636	+	8.00846i	−0.526822	+	0.269354i
$885$	7.22728	−	2.61920i	0.242943	−	0.0880434i
$886$	9.47125	+	39.3300i	0.318193	+	1.32132i
$887$	−27.6596	−	47.9079i	−0.928719	−	1.60859i	−0.785467	−	0.618903i	$-0.787577\pi$
$887$	−27.6596	−	47.9079i	−0.928719	−	1.60859i	−0.143252	−	0.989686i	$-0.545756\pi$
$888$	2.43552	−	0.0229682i	0.0817307	−	0.000770763i
$889$	28.1346	−	0.754188i	0.943606	−	0.0252946i
$890$	5.90238	+	6.21115i	0.197848	+	0.208198i
$891$	10.0949	+	8.56628i	0.338192	+	0.286981i
$892$	2.61419	−	4.03778i	0.0875294	−	0.135195i
$893$	−30.4104	+	52.6724i	−1.01765	+	1.76261i
$894$	−27.8582	−	42.1521i	−0.931717	−	1.40978i
$895$		−	5.62490i		−	0.188020i
$896$	−12.0246	+	27.4118i	−0.401715	+	0.915765i
$897$	2.69397	−	3.20154i	0.0899489	−	0.106896i
$898$	−5.33310	+	18.0504i	−0.177968	+	0.602348i
$899$	−2.30747	−	1.33222i	−0.0769584	−	0.0444319i
$900$	2.35198	−	5.51980i	0.0783994	−	0.183993i
$901$	32.1904	+	55.7553i	1.07242	+	1.85748i
$902$	−3.62290	+	3.44280i	−0.120629	+	0.114633i
$903$	−0.431895	−	1.09889i	−0.0143726	−	0.0365687i
$904$	23.7503	−	20.3706i	0.789924	−	0.677515i
$905$	18.7281	−	10.8127i	0.622544	−	0.359426i
$906$	2.33798	−	4.68120i	0.0776743	−	0.155523i
$907$	26.3055	+	15.1875i	0.873460	+	0.504292i	0.868496	−	0.495695i	$-0.165087\pi$
$907$	26.3055	+	15.1875i	0.873460	+	0.504292i	0.00496351	+	0.999988i	$0.498420\pi$
$908$	8.82512	+	17.2608i	0.292872	+	0.572821i
$909$	26.2094	−	4.54668i	0.869312	−	0.150804i
$910$	−5.71942	+	1.54058i	−0.189597	+	0.0510698i
$911$			27.1919i			0.900908i	0.892800	+	0.450454i	$0.148738\pi$
$911$			27.1919i			0.900908i	−0.892800	+	0.450454i	$0.851262\pi$
$912$	10.6637	−	37.3860i	0.353109	−	1.23797i
$913$	−17.0611	−	9.85023i	−0.564640	−	0.325995i
$914$	−13.7550	−	57.1186i	−0.454975	−	1.88931i
$915$	−26.1180	−	4.64258i	−0.863435	−	0.153479i
$916$	1.83319	−	35.9361i	0.0605703	−	1.18736i
$917$	−22.8248	+	14.0065i	−0.753742	+	0.462537i
$918$	−9.39451	−	39.7353i	−0.310065	−	1.31146i
$919$	2.13532	+	3.69848i	0.0704376	+	0.122002i	0.899093	−	0.437757i	$-0.144227\pi$
$919$	2.13532	+	3.69848i	0.0704376	+	0.122002i	−0.828656	+	0.559759i	$0.810894\pi$
$920$	−4.24222	+	0.795412i	−0.139862	+	0.0262239i
$921$	40.5550	−	14.6973i	1.33633	−	0.484293i
$922$	−0.767903	+	2.59903i	−0.0252895	+	0.0855946i
$923$		−	5.71157i		−	0.187999i
$924$	−8.92749	+	10.1035i	−0.293693	+	0.332380i
$925$		−	0.497170i		−	0.0163469i
$926$	−10.7638	−	3.18022i	−0.353719	−	0.104509i
$927$	−12.1300	+	33.0421i	−0.398401	+	1.08524i
$928$	4.00498	+	29.6241i	0.131470	+	0.972460i
$929$	10.0716	+	17.4445i	0.330438	+	0.572335i	0.982598	−	0.185747i	$-0.0594704\pi$
$929$	10.0716	+	17.4445i	0.330438	+	0.572335i	−0.652160	+	0.758081i	$0.726137\pi$
$930$	1.23278	−	0.0745487i	0.0404243	−	0.00244455i
$931$	21.4342	+	32.9164i	0.702478	+	1.07879i
$932$	49.9335	+	2.54724i	1.63563	+	0.0834375i
$933$	−2.41504	+	13.5864i	−0.0790649	+	0.444800i
$934$	38.4779	−	9.26604i	1.25903	−	0.303194i
$935$	7.07872	+	4.08690i	0.231499	+	0.133656i
$936$	13.2470	+	2.22605i	0.432991	+	0.0727606i
$937$		−	16.7110i		−	0.545926i	−0.962025	−	0.272963i	$-0.911996\pi$
$937$		−	16.7110i		−	0.545926i	0.962025	−	0.272963i	$-0.0880036\pi$
$938$	20.9452	+	20.8901i	0.683885	+	0.682087i
$939$	−31.8642	+	37.8677i	−1.03985	+	1.23577i
$940$	9.86825	+	19.3011i	0.321867	+	0.629532i
$941$	16.1422	+	9.31972i	0.526221	+	0.303814i	0.739476	−	0.673183i	$-0.235073\pi$
$941$	16.1422	+	9.31972i	0.526221	+	0.303814i	−0.213255	+	0.976997i	$0.568407\pi$
$942$	−3.02696	+	6.06069i	−0.0986236	+	0.197468i
$943$	−3.17478	+	1.83296i	−0.103385	+	0.0596894i
$944$	1.80654	−	17.6608i	0.0587980	−	0.574810i
$945$	−0.311345	−	13.7442i	−0.0101280	−	0.447099i
$946$	−0.369245	−	0.388561i	−0.0120052	−	0.0126332i
$947$	0.965283	+	1.67192i	0.0313675	+	0.0543301i	0.881283	−	0.472589i	$-0.156680\pi$
$947$	0.965283	+	1.67192i	0.0313675	+	0.0543301i	−0.849916	+	0.526919i	$0.823347\pi$
$948$	6.10127	+	19.9558i	0.198160	+	0.648134i
$949$	−14.2113	−	8.20492i	−0.461320	−	0.266343i
$950$	−7.61052	−	2.24858i	−0.246918	−	0.0729536i
$951$	15.6196	+	13.1433i	0.506501	+	0.426201i
$952$	40.6478	−	8.75505i	1.31740	−	0.283753i
$953$			42.6606i			1.38191i	0.722897	+	0.690956i	$0.242810\pi$
$953$			42.6606i			1.38191i	−0.722897	+	0.690956i	$0.757190\pi$
$954$	5.66611	−	48.8312i	0.183447	−	1.58097i
$955$	−9.16437	+	15.8732i	−0.296552	+	0.513643i
$956$	−8.48309	+	13.1027i	−0.274363	+	0.423771i
$957$	−2.35647	+	13.2569i	−0.0761740	+	0.428536i
$958$	33.6574	−	31.9842i	1.08742	−	1.03336i
$959$	−27.2970	−	14.7991i	−0.881466	−	0.477889i
$960$	−9.11977	−	10.4322i	−0.294339	−	0.336696i
$961$	−15.3729	−	26.6266i	−0.495900	−	0.858924i
$962$	1.08212	−	0.260591i	0.0348890	−	0.00840180i
$963$	−25.6836	−	9.42865i	−0.827644	−	0.303834i
$964$	13.8760	+	27.1397i	0.446915	+	0.874111i
$965$		−	25.9385i		−	0.834990i
$966$	−8.10142	+	5.67185i	−0.260659	+	0.182489i
$967$	33.0187			1.06181			0.530905	−	0.847432i	$-0.321852\pi$
$967$	33.0187			1.06181			0.530905	+	0.847432i	$0.321852\pi$
$968$	8.29326	−	23.5757i	0.266555	−	0.757752i
$969$	−50.7724	+	18.4001i	−1.63105	+	0.591098i
$970$	−5.62281	−	23.3491i	−0.180537	−	0.749694i
$971$	13.4749	−	7.77976i	0.432431	−	0.249664i	−0.267951	−	0.963433i	$-0.586346\pi$
$971$	13.4749	−	7.77976i	0.432431	−	0.249664i	0.700382	+	0.713768i	$0.253013\pi$
$972$	−12.3402	+	28.6307i	−0.395813	+	0.918331i
$973$	−1.84470	+	0.0494498i	−0.0591384	+	0.00158529i
$974$	35.8696	−	34.0865i	1.14934	−	1.09220i
$975$	0.479869	−	2.69962i	0.0153681	−	0.0864571i
$976$	−35.8711	+	49.6624i	−1.14821	+	1.58965i
$977$	14.1606	+	8.17565i	0.453039	+	0.261562i	0.709113	−	0.705095i	$-0.249096\pi$
$977$	14.1606	+	8.17565i	0.453039	+	0.261562i	−0.256074	+	0.966657i	$0.582429\pi$
$978$	9.17538	−	6.06398i	0.293396	−	0.193905i
$979$	8.91282			0.284855
$980$	14.0000	−	0.0368416i	0.447212	−	0.00117686i
$981$	18.7262	−	3.24853i	0.597882	−	0.103718i
$982$	44.7746	+	13.2290i	1.42881	+	0.422153i
$983$	26.2863	−	45.5291i	0.838401	−	1.45215i	−0.0528295	−	0.998604i	$-0.516824\pi$
$983$	26.2863	−	45.5291i	0.838401	−	1.45215i	0.891231	−	0.453550i	$-0.149843\pi$
$984$	−10.2472	−	5.78810i	−0.326670	−	0.184518i
$985$	−8.65618	+	4.99765i	−0.275809	+	0.159238i
$986$	30.1012	−	28.6048i	0.958619	−	0.910964i
$987$	38.8481	+	30.9496i	1.23655	+	0.985137i
$988$	0.905134	−	17.7434i	0.0287962	−	0.564492i
$989$	−0.196588	−	0.340500i	−0.00625113	−	0.0108273i
$990$	−2.47682	−	5.72872i	−0.0787185	−	0.182071i
$991$	−22.9752	+	39.7941i	−0.729830	+	1.26410i	0.227125	+	0.973866i	$0.427067\pi$
$991$	−22.9752	+	39.7941i	−0.729830	+	1.26410i	−0.956955	+	0.290237i	$0.906266\pi$
$992$	1.08231	−	2.63885i	0.0343633	−	0.0837835i
$993$	−6.55283	+	7.78745i	−0.207948	+	0.247127i
$994$	−3.47680	+	13.0442i	−0.110277	+	0.413738i
$995$	−20.8737			−0.661740
$996$	10.4353	−	45.2021i	0.330657	−	1.43228i
$997$	−1.39446	+	2.41527i	−0.0441629	+	0.0764923i	−0.887262	−	0.461266i	$-0.847395\pi$
$997$	−1.39446	+	2.41527i	−0.0441629	+	0.0764923i	0.843099	+	0.537758i	$0.180729\pi$
$998$	47.8637	−	11.5263i	1.51510	−	0.364858i
$999$	−0.0107236	+	2.58335i	−0.000339281	+	0.0817336i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.cf.a.101.13	✓	256
3.2	odd	2	inner	840.2.cf.a.101.116	yes	256
7.5	odd	6	inner	840.2.cf.a.341.73	yes	256
8.5	even	2	inner	840.2.cf.a.101.56	yes	256
21.5	even	6	inner	840.2.cf.a.341.56	yes	256
24.5	odd	2	inner	840.2.cf.a.101.73	yes	256
56.5	odd	6	inner	840.2.cf.a.341.116	yes	256
168.5	even	6	inner	840.2.cf.a.341.13	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.cf.a.101.13	✓	256	1.1	even	1	trivial
840.2.cf.a.101.56	yes	256	8.5	even	2	inner
840.2.cf.a.101.73	yes	256	24.5	odd	2	inner
840.2.cf.a.101.116	yes	256	3.2	odd	2	inner
840.2.cf.a.341.13	yes	256	168.5	even	6	inner
840.2.cf.a.341.56	yes	256	21.5	even	6	inner
840.2.cf.a.341.73	yes	256	7.5	odd	6	inner
840.2.cf.a.341.116	yes	256	56.5	odd	6	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.cf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35626 - 0.400715i) q^{2} +(-1.62841 + 0.590144i) q^{3} +(1.67886 + 1.08694i) q^{4} +(0.866025 - 0.500000i) q^{5} +(2.44502 - 0.147856i) q^{6} +(-2.64480 + 0.0708975i) q^{7} +(-1.84140 - 2.14691i) q^{8} +(2.30346 - 1.92200i) q^{9} +(-1.37491 + 0.331098i) q^{10} +(-0.735536 + 1.27399i) q^{11} +(-3.37532 - 0.779227i) q^{12} -1.58306 q^{13} +(3.61543 + 0.963656i) q^{14} +(-1.11518 + 1.32529i) q^{15} +(1.63711 + 3.64964i) q^{16} +(2.77818 - 4.81195i) q^{17} +(-3.89425 + 1.68369i) q^{18} +(2.80571 + 4.85963i) q^{19} +(1.99740 + 0.101893i) q^{20} +(4.26499 - 1.67626i) q^{21} +(1.50808 - 1.43311i) q^{22} +(1.32154 - 0.762994i) q^{23} +(4.26555 + 2.40937i) q^{24} +(0.500000 - 0.866025i) q^{25} +(2.14703 + 0.634356i) q^{26} +(-2.61673 + 4.48918i) q^{27} +(-4.51730 - 2.75572i) q^{28} -5.28450 q^{29} +(2.04352 - 1.35056i) q^{30} +(0.436649 + 0.252099i) q^{31} +(-0.757874 - 5.60586i) q^{32} +(0.445922 - 2.50865i) q^{33} +(-5.69614 + 5.41297i) q^{34} +(-2.25502 + 1.38380i) q^{35} +(5.95628 - 0.723022i) q^{36} +(0.430562 - 0.248585i) q^{37} +(-1.85793 - 7.71519i) q^{38} +(2.57788 - 0.934233i) q^{39} +(-2.66816 - 0.938581i) q^{40} -2.40233 q^{41} +(-6.45612 + 0.564395i) q^{42} -0.257653i q^{43} +(-2.61961 + 1.33935i) q^{44} +(1.03386 - 2.81623i) q^{45} +(-2.09809 + 0.505252i) q^{46} +(5.41938 + 9.38664i) q^{47} +(-4.81970 - 4.97699i) q^{48} +(6.98995 - 0.375020i) q^{49} +(-1.02516 + 0.974194i) q^{50} +(-1.68429 + 9.47537i) q^{51} +(-2.65773 - 1.72070i) q^{52} +(-5.79342 + 10.0345i) q^{53} +(5.34784 - 5.03990i) q^{54} +1.47107i q^{55} +(5.02235 + 5.54761i) q^{56} +(-7.43674 - 6.25772i) q^{57} +(7.16713 + 2.11758i) q^{58} +(-3.84363 - 2.21912i) q^{59} +(-3.31273 + 1.01283i) q^{60} +(7.65781 + 13.2637i) q^{61} +(-0.491187 - 0.516882i) q^{62} +(-5.95593 + 5.24661i) q^{63} +(-1.21848 + 7.90666i) q^{64} +(-1.37097 + 0.791530i) q^{65} +(-1.61004 + 3.22368i) q^{66} +(6.84692 + 3.95307i) q^{67} +(9.89448 - 5.05884i) q^{68} +(-1.70175 + 2.02237i) q^{69} +(3.61289 - 0.973167i) q^{70} +3.60793i q^{71} +(-8.36796 - 1.40617i) q^{72} +(8.97713 + 5.18295i) q^{73} +(-0.683564 + 0.164612i) q^{74} +(-0.303127 + 1.70532i) q^{75} +(-0.571762 + 11.2083i) q^{76} +(1.85502 - 3.42158i) q^{77} +(-3.87062 + 0.234065i) q^{78} +(-3.01199 - 5.21691i) q^{79} +(3.24260 + 2.34213i) q^{80} +(1.61187 - 8.85448i) q^{81} +(3.25817 + 0.962648i) q^{82} +13.3919i q^{83} +(8.98230 + 1.82160i) q^{84} -5.55636i q^{85} +(-0.103246 + 0.349444i) q^{86} +(8.60535 - 3.11861i) q^{87} +(4.08955 - 0.766786i) q^{88} +(-3.02937 - 5.24701i) q^{89} +(-2.53068 + 3.40524i) q^{90} +(4.18688 - 0.112235i) q^{91} +(3.04801 + 0.155487i) q^{92} +(-0.859819 - 0.152836i) q^{93} +(-3.58869 - 14.9023i) q^{94} +(4.85963 + 2.80571i) q^{95} +(4.54239 + 8.68140i) q^{96} +16.9823i q^{97} +(-9.63043 - 2.29235i) q^{98} +(0.754316 + 4.34827i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 30 q^{12} + 16 q^{16} - 10 q^{18} + 8 q^{22} + 128 q^{25} + 12 q^{28} - 40 q^{36} - 54 q^{42} + 16 q^{46} + 16 q^{49} + 36 q^{52} - 72 q^{54} - 16 q^{58} - 14 q^{60} + 80 q^{63} - 48 q^{64} - 60 q^{66}+ \cdots - 144 q^{96}+O(q^{100}) \) 256 * q + 30 * q^12 + 16 * q^16 - 10 * q^18 + 8 * q^22 + 128 * q^25 + 12 * q^28 - 40 * q^36 - 54 * q^42 + 16 * q^46 + 16 * q^49 + 36 * q^52 - 72 * q^54 - 16 * q^58 - 14 * q^60 + 80 * q^63 - 48 * q^64 - 60 * q^66 - 12 * q^70 - 50 * q^72 + 48 * q^73 - 16 * q^78 + 64 * q^79 - 8 * q^81 - 72 * q^82 - 56 * q^84 - 8 * q^88 - 72 * q^94 - 144 * q^96

Introduction

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