LMFDB - Embedded newform 185.2.u.a.177.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [185,2,Mod(8,185)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(185, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 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("185.8"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 185 = 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	185.u (of order $12$, degree $4$, 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:	$1.47723243739$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			177.5
Character	$\chi$	$=$	185.177
Dual form			185.2.u.a.23.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.14153 + 0.659061i) q^{2} +(-1.18821 + 0.318379i) q^{3} +(-0.131277 + 0.227378i) q^{4} +(0.817423 - 2.08130i) q^{5} +(1.14654 - 1.14654i) q^{6} +(4.13076 - 1.10683i) q^{7} -2.98232i q^{8} +(-1.28760 + 0.743399i) q^{9} +(0.438595 + 2.91460i) q^{10} +4.89589i q^{11} +(0.0835914 - 0.311968i) q^{12} +(2.57679 + 1.48771i) q^{13} +(-3.98591 + 3.98591i) q^{14} +(-0.308624 + 2.73327i) q^{15} +(1.70298 + 2.94965i) q^{16} +(2.10881 + 3.65256i) q^{17} +(0.979891 - 1.69722i) q^{18} +(4.90693 - 1.31481i) q^{19} +(0.365933 + 0.459090i) q^{20} +(-4.55581 + 2.63030i) q^{21} +(-3.22669 - 5.58880i) q^{22} -6.57051i q^{23} +(0.949509 + 3.54362i) q^{24} +(-3.66364 - 3.40261i) q^{25} -3.92197 q^{26} +(3.90274 - 3.90274i) q^{27} +(-0.290603 + 1.08454i) q^{28} +(-0.417950 + 0.417950i) q^{29} +(-1.44909 - 3.32351i) q^{30} +(3.03803 + 3.03803i) q^{31} +(1.27754 + 0.737586i) q^{32} +(-1.55875 - 5.81734i) q^{33} +(-4.81453 - 2.77967i) q^{34} +(1.07292 - 9.50212i) q^{35} -0.390363i q^{36} +(0.219784 + 6.07879i) q^{37} +(-4.73486 + 4.73486i) q^{38} +(-3.53541 - 0.947311i) q^{39} +(-6.20711 - 2.43782i) q^{40} +(-0.897477 - 0.518158i) q^{41} +(3.46706 - 6.00512i) q^{42} +3.17618i q^{43} +(-1.11322 - 0.642716i) q^{44} +(0.494720 + 3.28757i) q^{45} +(4.33037 + 7.50041i) q^{46} +(-4.44958 - 4.44958i) q^{47} +(-2.96260 - 2.96260i) q^{48} +(9.77595 - 5.64415i) q^{49} +(6.42467 + 1.46961i) q^{50} +(-3.66860 - 3.66860i) q^{51} +(-0.676543 + 0.390602i) q^{52} +(-6.40827 - 1.71709i) q^{53} +(-1.88294 + 7.02724i) q^{54} +(10.1898 + 4.00202i) q^{55} +(-3.30094 - 12.3193i) q^{56} +(-5.41184 + 3.12453i) q^{57} +(0.201647 - 0.752555i) q^{58} +(1.57132 - 5.86425i) q^{59} +(-0.580969 - 0.428988i) q^{60} +(1.68182 - 0.450642i) q^{61} +(-5.47024 - 1.46575i) q^{62} +(-4.49597 + 4.49597i) q^{63} -8.75638 q^{64} +(5.20270 - 4.14699i) q^{65} +(5.61334 + 5.61334i) q^{66} +(-3.09017 - 11.5327i) q^{67} -1.10735 q^{68} +(2.09191 + 7.80712i) q^{69} +(5.03771 + 11.5541i) q^{70} +(-1.78413 + 3.09021i) q^{71} +(2.21705 + 3.84005i) q^{72} +(2.50291 + 2.50291i) q^{73} +(-4.25718 - 6.79426i) q^{74} +(5.43648 + 2.87658i) q^{75} +(-0.345207 + 1.28833i) q^{76} +(5.41895 + 20.2238i) q^{77} +(4.66011 - 1.24867i) q^{78} +(-3.97409 + 1.06485i) q^{79} +(7.53116 - 1.13331i) q^{80} +(-1.16452 + 2.01701i) q^{81} +1.36599 q^{82} +(2.57020 + 0.688684i) q^{83} -1.38119i q^{84} +(9.32588 - 1.40338i) q^{85} +(-2.09329 - 3.62569i) q^{86} +(0.363544 - 0.629677i) q^{87} +14.6011 q^{88} +(-11.4703 - 3.07346i) q^{89} +(-2.73144 - 3.42680i) q^{90} +(12.2907 + 3.29330i) q^{91} +(1.49399 + 0.862553i) q^{92} +(-4.57706 - 2.64257i) q^{93} +(8.01187 + 2.14677i) q^{94} +(1.27452 - 11.2876i) q^{95} +(-1.75281 - 0.469664i) q^{96} -10.2570 q^{97} +(-7.43968 + 12.8859i) q^{98} +(-3.63960 - 6.30397i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 6 q^{2} - 4 q^{3} + 30 q^{4} - 8 q^{6} - 2 q^{7} - 6 q^{10} - 10 q^{12} - 6 q^{13} - 16 q^{15} - 26 q^{16} - 10 q^{17} - 8 q^{18} - 4 q^{19} - 28 q^{20} - 12 q^{21} - 14 q^{22} + 20 q^{25} - 24 q^{26}+ \cdots - 32 q^{99}+O(q^{100}) $ 68 * q - 6 * q^2 - 4 * q^3 + 30 * q^4 - 8 * q^6 - 2 * q^7 - 6 * q^10 - 10 * q^12 - 6 * q^13 - 16 * q^15 - 26 * q^16 - 10 * q^17 - 8 * q^18 - 4 * q^19 - 28 * q^20 - 12 * q^21 - 14 * q^22 + 20 * q^25 - 24 * q^26 + 68 * q^27 + 14 * q^28 - 14 * q^29 + 26 * q^30 - 24 * q^31 + 18 * q^32 + 10 * q^33 - 22 * q^35 - 18 * q^37 - 36 * q^38 - 52 * q^39 + 84 * q^40 - 18 * q^41 - 40 * q^42 + 36 * q^44 - 66 * q^45 - 52 * q^46 - 24 * q^47 + 60 * q^48 + 36 * q^49 - 12 * q^50 - 8 * q^51 - 78 * q^52 - 38 * q^53 - 40 * q^54 + 6 * q^55 + 16 * q^56 + 90 * q^57 + 16 * q^58 + 8 * q^59 - 52 * q^60 + 4 * q^61 - 22 * q^62 - 48 * q^63 + 20 * q^64 - 20 * q^65 + 80 * q^66 - 56 * q^67 - 20 * q^68 - 8 * q^69 + 62 * q^70 + 4 * q^71 + 32 * q^72 + 60 * q^73 + 44 * q^74 + 64 * q^75 + 72 * q^76 + 6 * q^77 - 24 * q^78 - 56 * q^79 - 76 * q^80 - 6 * q^81 - 8 * q^82 + 12 * q^83 + 20 * q^85 - 4 * q^86 - 32 * q^87 - 36 * q^88 + 22 * q^89 - 74 * q^90 + 44 * q^91 + 156 * q^92 - 30 * q^93 + 20 * q^94 + 28 * q^95 - 8 * q^96 + 16 * q^97 + 48 * q^98 - 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/185\mathbb{Z}\right)^\times$.

$n$	$76$	$112$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.14153	+	0.659061i	−0.807182	+	0.466027i	−0.845976	−	0.533221i	$-0.820982\pi$
$2$	−1.14153	+	0.659061i	−0.807182	+	0.466027i	0.0387944	+	0.999247i	$0.487648\pi$
$3$	−1.18821	+	0.318379i	−0.686012	+	0.183816i	−0.584957	−	0.811064i	$-0.698889\pi$
$3$	−1.18821	+	0.318379i	−0.686012	+	0.183816i	−0.101055	+	0.994881i	$0.532222\pi$
$4$	−0.131277	+	0.227378i	−0.0656383	+	0.113689i
$5$	0.817423	−	2.08130i	0.365563	−	0.930787i
$5$	0.817423	−	2.08130i	0.365563	−	0.930787i
$6$	1.14654	−	1.14654i	0.468073	−	0.468073i
$7$	4.13076	−	1.10683i	1.56128	−	0.418344i	0.628213	−	0.778041i	$-0.283787\pi$
$7$	4.13076	−	1.10683i	1.56128	−	0.418344i	0.933069	+	0.359697i	$0.117120\pi$
$8$		−	2.98232i		−	1.05441i
$9$	−1.28760	+	0.743399i	−0.429201	+	0.247800i
$10$	0.438595	+	2.91460i	0.138696	+	0.921676i
$11$			4.89589i			1.47617i	0.674709	+	0.738084i	$0.264269\pi$
$11$			4.89589i			1.47617i	−0.674709	+	0.738084i	$0.735731\pi$
$12$	0.0835914	−	0.311968i	0.0241308	−	0.0900573i
$13$	2.57679	+	1.48771i	0.714672	+	0.412616i	0.812789	−	0.582559i	$-0.197948\pi$
$13$	2.57679	+	1.48771i	0.714672	+	0.412616i	−0.0981164	+	0.995175i	$0.531282\pi$
$14$	−3.98591	+	3.98591i	−1.06528	+	1.06528i
$15$	−0.308624	+	2.73327i	−0.0796865	+	0.705727i
$16$	1.70298	+	2.94965i	0.425745	+	0.737412i
$17$	2.10881	+	3.65256i	0.511461	+	0.885877i	0.999912	+	0.0132853i	$0.00422898\pi$
$17$	2.10881	+	3.65256i	0.511461	+	0.885877i	−0.488450	+	0.872592i	$0.662438\pi$
$18$	0.979891	−	1.69722i	0.230962	−	0.400039i
$19$	4.90693	−	1.31481i	1.12573	−	0.301638i	0.352528	−	0.935801i	$-0.385322\pi$
$19$	4.90693	−	1.31481i	1.12573	−	0.301638i	0.773199	+	0.634164i	$0.218655\pi$
$20$	0.365933	+	0.459090i	0.0818251	+	0.102656i
$21$	−4.55581	+	2.63030i	−0.994160	+	0.573978i
$22$	−3.22669	−	5.58880i	−0.687933	−	1.19154i
$23$		−	6.57051i		−	1.37005i	−0.728522	−	0.685023i	$-0.759792\pi$
$23$		−	6.57051i		−	1.37005i	0.728522	−	0.685023i	$-0.240208\pi$
$24$	0.949509	+	3.54362i	0.193818	+	0.723338i
$25$	−3.66364	−	3.40261i	−0.732728	−	0.680522i
$26$	−3.92197			−0.769161
$27$	3.90274	−	3.90274i	0.751083	−	0.751083i
$28$	−0.290603	+	1.08454i	−0.0549188	+	0.204960i
$29$	−0.417950	+	0.417950i	−0.0776113	+	0.0776113i	−0.744847	−	0.667236i	$-0.767477\pi$
$29$	−0.417950	+	0.417950i	−0.0776113	+	0.0776113i	0.667236	+	0.744847i	$0.267477\pi$
$30$	−1.44909	−	3.32351i	−0.264566	−	0.606786i
$31$	3.03803	+	3.03803i	0.545646	+	0.545646i	0.925179	−	0.379532i	$-0.123915\pi$
$31$	3.03803	+	3.03803i	0.545646	+	0.545646i	−0.379532	+	0.925179i	$0.623915\pi$
$32$	1.27754	+	0.737586i	0.225839	+	0.130388i
$33$	−1.55875	−	5.81734i	−0.271344	−	1.01267i
$34$	−4.81453	−	2.77967i	−0.825685	−	0.476709i
$35$	1.07292	−	9.50212i	0.181357	−	1.60615i
$36$		−	0.390363i		−	0.0650605i
$37$	0.219784	+	6.07879i	0.0361323	+	0.999347i
$37$	0.219784	+	6.07879i	0.0361323	+	0.999347i
$38$	−4.73486	+	4.73486i	−0.768095	+	0.768095i
$39$	−3.53541	−	0.947311i	−0.566119	−	0.151691i
$40$	−6.20711	−	2.43782i	−0.981431	−	0.385453i
$41$	−0.897477	−	0.518158i	−0.140162	−	0.0809228i	0.428279	−	0.903647i	$-0.359120\pi$
$41$	−0.897477	−	0.518158i	−0.140162	−	0.0809228i	−0.568441	+	0.822724i	$0.692453\pi$
$42$	3.46706	−	6.00512i	0.534978	−	0.926610i
$43$			3.17618i			0.484362i	0.970231	+	0.242181i	$0.0778628\pi$
$43$			3.17618i			0.484362i	−0.970231	+	0.242181i	$0.922137\pi$
$44$	−1.11322	−	0.642716i	−0.167824	−	0.0968931i
$45$	0.494720	+	3.28757i	0.0737486	+	0.490081i
$46$	4.33037	+	7.50041i	0.638478	+	1.10588i
$47$	−4.44958	−	4.44958i	−0.649038	−	0.649038i	0.303722	−	0.952761i	$-0.401770\pi$
$47$	−4.44958	−	4.44958i	−0.649038	−	0.649038i	−0.952761	+	0.303722i	$0.901770\pi$
$48$	−2.96260	−	2.96260i	−0.427615	−	0.427615i
$49$	9.77595	−	5.64415i	1.39656	−	0.806307i
$50$	6.42467	+	1.46961i	0.908586	+	0.207834i
$51$	−3.66860	−	3.66860i	−0.513707	−	0.513707i
$52$	−0.676543	+	0.390602i	−0.0938197	+	0.0541668i
$53$	−6.40827	−	1.71709i	−0.880243	−	0.235861i	−0.209731	−	0.977759i	$-0.567259\pi$
$53$	−6.40827	−	1.71709i	−0.880243	−	0.235861i	−0.670512	+	0.741899i	$0.733926\pi$
$54$	−1.88294	+	7.02724i	−0.256236	+	0.956286i
$55$	10.1898	+	4.00202i	1.37400	+	0.539632i
$56$	−3.30094	−	12.3193i	−0.441106	−	1.64623i
$57$	−5.41184	+	3.12453i	−0.716816	+	0.413854i
$58$	0.201647	−	0.752555i	0.0264775	−	0.0988154i
$59$	1.57132	−	5.86425i	0.204568	−	0.763460i	−0.785012	−	0.619480i	$-0.787343\pi$
$59$	1.57132	−	5.86425i	0.204568	−	0.763460i	0.989581	−	0.143979i	$-0.0459899\pi$
$60$	−0.580969	−	0.428988i	−0.0750028	−	0.0553822i
$61$	1.68182	−	0.450642i	0.215335	−	0.0576988i	−0.149539	−	0.988756i	$-0.547779\pi$
$61$	1.68182	−	0.450642i	0.215335	−	0.0576988i	0.364874	+	0.931057i	$0.381112\pi$
$62$	−5.47024	−	1.46575i	−0.694722	−	0.186150i
$63$	−4.49597	+	4.49597i	−0.566439	+	0.566439i
$64$	−8.75638			−1.09455
$65$	5.20270	−	4.14699i	0.645315	−	0.514370i
$66$	5.61334	+	5.61334i	0.690954	+	0.690954i
$67$	−3.09017	−	11.5327i	−0.377524	−	1.40894i	−0.849621	−	0.527394i	$-0.823169\pi$
$67$	−3.09017	−	11.5327i	−0.377524	−	1.40894i	0.472097	−	0.881547i	$-0.343497\pi$
$68$	−1.10735			−0.134286
$69$	2.09191	+	7.80712i	0.251837	+	0.939867i
$70$	5.03771	+	11.5541i	0.602121	+	1.38097i
$71$	−1.78413	+	3.09021i	−0.211738	+	0.366741i	−0.952258	−	0.305293i	$-0.901246\pi$
$71$	−1.78413	+	3.09021i	−0.211738	+	0.366741i	0.740521	+	0.672034i	$0.234579\pi$
$72$	2.21705	+	3.84005i	0.261282	+	0.452554i
$73$	2.50291	+	2.50291i	0.292943	+	0.292943i	0.838242	−	0.545298i	$-0.183584\pi$
$73$	2.50291	+	2.50291i	0.292943	+	0.292943i	−0.545298	+	0.838242i	$0.683584\pi$
$74$	−4.25718	−	6.79426i	−0.494888	−	0.789816i
$75$	5.43648	+	2.87658i	0.627751	+	0.332159i
$76$	−0.345207	+	1.28833i	−0.0395979	+	0.147781i
$77$	5.41895	+	20.2238i	0.617546	+	2.30471i
$78$	4.66011	−	1.24867i	0.527653	−	0.141384i
$79$	−3.97409	+	1.06485i	−0.447120	+	0.119805i	−0.475351	−	0.879796i	$-0.657679\pi$
$79$	−3.97409	+	1.06485i	−0.447120	+	0.119805i	0.0282316	+	0.999601i	$0.491012\pi$
$80$	7.53116	−	1.13331i	0.842010	−	0.126708i
$81$	−1.16452	+	2.01701i	−0.129391	+	0.224112i
$82$	1.36599			0.150849
$83$	2.57020	+	0.688684i	0.282117	+	0.0755929i	0.397103	−	0.917774i	$-0.370016\pi$
$83$	2.57020	+	0.688684i	0.282117	+	0.0755929i	−0.114986	+	0.993367i	$0.536682\pi$
$84$		−	1.38119i		−	0.150700i
$85$	9.32588	−	1.40338i	1.01153	−	0.152218i
$86$	−2.09329	−	3.62569i	−0.225726	−	0.390968i
$87$	0.363544	−	0.629677i	0.0389760	−	0.0675085i
$88$	14.6011			1.55649
$89$	−11.4703	−	3.07346i	−1.21585	−	0.325786i	−0.406795	−	0.913519i	$-0.633354\pi$
$89$	−11.4703	−	3.07346i	−1.21585	−	0.325786i	−0.809055	+	0.587734i	$0.800020\pi$
$90$	−2.73144	−	3.42680i	−0.287919	−	0.361216i
$91$	12.2907	+	3.29330i	1.28842	+	0.345231i
$92$	1.49399	+	0.862553i	0.155759	+	0.0899274i
$93$	−4.57706	−	2.64257i	−0.474619	−	0.274021i
$94$	8.01187	+	2.14677i	0.826361	+	0.221423i
$95$	1.27452	−	11.2876i	0.130763	−	1.15808i
$96$	−1.75281	−	0.469664i	−0.178895	−	0.0479349i
$97$	−10.2570			−1.04144			−0.520719	−	0.853728i	$-0.674336\pi$
$97$	−10.2570			−1.04144			−0.520719	+	0.853728i	$0.674336\pi$
$98$	−7.43968	+	12.8859i	−0.751521	+	1.30167i
$99$	−3.63960	−	6.30397i	−0.365794	−	0.633573i
$100$	1.25463	−	0.386347i	0.125463	−	0.0386347i
$101$			19.0134i			1.89190i	0.324311	+	0.945951i	$0.394868\pi$
$101$			19.0134i			1.89190i	−0.324311	+	0.945951i	$0.605132\pi$
$102$	6.60565	+	1.76998i	0.654056	+	0.175254i
$103$	−18.1801			−1.79133			−0.895667	−	0.444724i	$-0.853302\pi$
$103$	−18.1801			−1.79133			−0.895667	+	0.444724i	$0.853302\pi$
$104$	4.43683	−	7.68481i	0.435067	−	0.753558i
$105$	1.75042	+	11.6321i	0.170824	+	1.13518i
$106$	8.44688	−	2.26334i	0.820434	−	0.219835i
$107$	6.32701	−	1.69532i	0.611656	−	0.163893i	0.0603240	−	0.998179i	$-0.480787\pi$
$107$	6.32701	−	1.69532i	0.611656	−	0.163893i	0.551332	+	0.834286i	$0.314120\pi$
$108$	0.375058	+	1.39974i	0.0360900	+	0.134690i
$109$	−1.79221	+	6.68861i	−0.171662	+	0.640652i	0.825434	+	0.564499i	$0.190931\pi$
$109$	−1.79221	+	6.68861i	−0.171662	+	0.640652i	−0.997096	+	0.0761534i	$0.975736\pi$
$110$	−14.2696	+	2.14731i	−1.36055	+	0.204738i
$111$	−2.19651	−	7.15289i	−0.208483	−	0.678922i
$112$	10.2994	+	10.2994i	0.973200	+	0.973200i
$113$	0.777094	+	1.34597i	0.0731029	+	0.126618i	0.900260	−	0.435353i	$-0.143377\pi$
$113$	0.777094	+	1.34597i	0.0731029	+	0.126618i	−0.827157	+	0.561971i	$0.810043\pi$
$114$	4.11851	−	7.13347i	0.385734	−	0.668111i
$115$	−13.6752	−	5.37088i	−1.27522	−	0.500837i
$116$	−0.0401654	−	0.149899i	−0.00372926	−	0.0139178i
$117$	−4.42384			−0.408984
$118$	2.07119	+	7.72979i	0.190669	+	0.711585i
$119$	12.7538	+	12.7538i	1.16914	+	1.16914i
$120$	8.15149	+	0.920418i	0.744126	+	0.0840222i
$121$	−12.9698			−1.17907
$122$	−1.62284	+	1.62284i	−0.146925	+	0.146925i
$123$	1.23136	+	0.329942i	0.111028	+	0.0297498i
$124$	−1.08960	+	0.291958i	−0.0978492	+	0.0262186i
$125$	−10.0766	+	4.84377i	−0.901278	+	0.433240i
$126$	2.16915	−	8.09539i	0.193244	−	0.721195i
$127$	4.21459	−	15.7291i	0.373984	−	1.39573i	−0.480839	−	0.876809i	$-0.659668\pi$
$127$	4.21459	−	15.7291i	0.373984	−	1.39573i	0.854823	−	0.518920i	$-0.173666\pi$
$128$	7.44057	−	4.29582i	0.657660	−	0.379700i
$129$	−1.01123	−	3.77396i	−0.0890337	−	0.332278i
$130$	−3.20590	+	8.16280i	−0.281176	+	0.715925i
$131$	3.68624	−	13.7572i	0.322068	−	1.20197i	−0.595158	−	0.803608i	$-0.702911\pi$
$131$	3.68624	−	13.7572i	0.322068	−	1.20197i	0.917227	−	0.398366i	$-0.130423\pi$
$132$	1.52736	+	0.409255i	0.132940	+	0.0356211i
$133$	18.8141	−	10.8623i	1.63139	−	0.941883i
$134$	11.1283	+	11.1283i	0.961335	+	0.961335i
$135$	−4.93260	−	11.3130i	−0.424530	−	0.973666i
$136$	10.8931	−	6.28915i	0.934078	−	0.539290i
$137$	−7.34260	−	7.34260i	−0.627321	−	0.627321i	0.320072	−	0.947393i	$-0.396293\pi$
$137$	−7.34260	−	7.34260i	−0.627321	−	0.627321i	−0.947393	+	0.320072i	$0.896293\pi$
$138$	−7.53335	−	7.53335i	−0.641281	−	0.641281i
$139$	4.37561	+	7.57878i	0.371135	+	0.642824i	0.989740	−	0.142877i	$-0.0456355\pi$
$139$	4.37561	+	7.57878i	0.371135	+	0.642824i	−0.618606	+	0.785702i	$0.712302\pi$
$140$	2.01972	+	1.49136i	0.170698	+	0.126043i
$141$	6.70368	+	3.87037i	0.564552	+	0.325944i
$142$		−	4.70341i		−	0.394702i
$143$	−7.28366	+	12.6157i	−0.609091	+	1.05498i
$144$	−4.38553	−	2.53199i	−0.365461	−	0.210999i
$145$	0.528238	+	1.21152i	0.0438678	+	0.100611i
$146$	−4.50671	−	1.20757i	−0.372978	−	0.0999392i
$147$	−9.81888	+	9.81888i	−0.809848	+	0.809848i
$148$	−1.41103	−	0.748029i	−0.115986	−	0.0614876i
$149$			16.7086i			1.36883i	0.729095	+	0.684413i	$0.239941\pi$
$149$			16.7086i			1.36883i	−0.729095	+	0.684413i	$0.760059\pi$
$150$	−8.10174	+	0.299283i	−0.661504	+	0.0244364i
$151$	−3.85044	−	2.22305i	−0.313344	−	0.180909i	0.335078	−	0.942190i	$-0.391237\pi$
$151$	−3.85044	−	2.22305i	−0.313344	−	0.180909i	−0.648422	+	0.761281i	$0.724571\pi$
$152$	−3.92118	−	14.6340i	−0.318050	−	1.18698i
$153$	−5.43062	−	3.13537i	−0.439040	−	0.253480i
$154$	−19.5146	−	19.5146i	−1.57253	−	1.57253i
$155$	8.80642	−	3.83971i	0.707348	−	0.308413i
$156$	0.679514	−	0.679514i	0.0544047	−	0.0544047i
$157$	2.50499	−	9.34877i	0.199920	−	0.746113i	−0.791018	−	0.611793i	$-0.790448\pi$
$157$	2.50499	−	9.34877i	0.199920	−	0.746113i	0.990938	−	0.134320i	$-0.0428849\pi$
$158$	3.83473	−	3.83473i	0.305075	−	0.305075i
$159$	8.16104			0.647213
$160$	2.57943	−	2.05602i	0.203922	−	0.162543i
$161$	−7.27247	−	27.1412i	−0.573151	−	2.13903i
$162$		−	3.06996i		−	0.241199i
$163$	8.18322	+	14.1737i	0.640959	+	1.11017i	0.985219	+	0.171299i	$0.0547965\pi$
$163$	8.18322	+	14.1737i	0.640959	+	1.11017i	−0.344260	+	0.938874i	$0.611870\pi$
$164$	0.235635	−	0.136044i	0.0184000	−	0.0106233i
$165$	−13.3818	−	1.51099i	−1.04177	−	0.117631i
$166$	−3.38784	+	0.907770i	−0.262948	+	0.0704566i
$167$	−4.92891	+	8.53712i	−0.381411	+	0.660623i	−0.991264	−	0.131892i	$-0.957895\pi$
$167$	−4.92891	+	8.53712i	−0.381411	+	0.660623i	0.609854	+	0.792514i	$0.291228\pi$
$168$	7.84440	+	13.5869i	0.605209	+	1.04825i
$169$	−2.07344	−	3.59131i	−0.159496	−	0.276255i
$170$	−9.72084	+	7.74832i	−0.745554	+	0.594269i
$171$	−5.34076	+	5.34076i	−0.408418	+	0.408418i
$172$	−0.722191	−	0.416957i	−0.0550666	−	0.0317927i
$173$	1.95280	−	7.28794i	0.148468	−	0.554092i	−0.851108	−	0.524991i	$-0.824069\pi$
$173$	1.95280	−	7.28794i	0.148468	−	0.554092i	0.999576	−	0.0291012i	$-0.00926452\pi$
$174$			0.958392i			0.0726555i
$175$	−18.8998	−	10.0003i	−1.42869	−	0.755954i
$176$	−14.4412	+	8.33761i	−1.08854	+	0.628471i
$177$			7.46822i			0.561346i
$178$	15.1193	−	4.05119i	1.13324	−	0.303650i
$179$	15.1099	−	15.1099i	1.12937	−	1.12937i	0.139089	−	0.990280i	$-0.455583\pi$
$179$	15.1099	−	15.1099i	1.12937	−	1.12937i	0.990280	−	0.139089i	$-0.0444174\pi$
$180$	−0.812464	−	0.319092i	−0.0605575	−	0.0237837i
$181$	−0.167025	+	0.289295i	−0.0124148	+	0.0215032i	−0.872166	−	0.489210i	$-0.837285\pi$
$181$	−0.167025	+	0.289295i	−0.0124148	+	0.0215032i	0.859751	+	0.510713i	$0.170619\pi$
$182$	−16.2007	+	4.34097i	−1.20088	+	0.321774i
$183$	−1.85487	+	1.07091i	−0.137116	+	0.0791641i
$184$	−19.5954			−1.44459
$185$	12.8315	+	4.51151i	0.943388	+	0.331692i
$186$	6.96645			0.510805
$187$	−17.8826	+	10.3245i	−1.30770	+	0.755003i
$188$	1.59586	−	0.427610i	0.116390	−	0.0311866i
$189$	11.8016	−	20.4410i	0.858442	−	1.48686i
$190$	5.98429	+	13.7250i	0.434146	+	0.995720i
$191$	−2.98486	+	2.98486i	−0.215977	+	0.215977i	−0.806801	−	0.590824i	$-0.798803\pi$
$191$	−2.98486	+	2.98486i	−0.215977	+	0.215977i	0.590824	+	0.806801i	$0.298803\pi$
$192$	10.4044	−	2.78785i	0.750872	−	0.201196i
$193$		−	7.99715i		−	0.575648i	−0.957683	−	0.287824i	$-0.907068\pi$
$193$		−	7.99715i		−	0.575648i	0.957683	−	0.287824i	$-0.0929318\pi$
$194$	11.7086	−	6.75997i	0.840629	−	0.485338i
$195$	−4.86157	+	6.58391i	−0.348144	+	0.471484i
$196$			2.96378i			0.211698i
$197$	−1.27223	+	4.74803i	−0.0906426	+	0.338283i	−0.996323	−	0.0856786i	$-0.972694\pi$
$197$	−1.27223	+	4.74803i	−0.0906426	+	0.338283i	0.905680	+	0.423962i	$0.139361\pi$
$198$	8.30941	+	4.79744i	0.590524	+	0.340939i
$199$	7.98996	−	7.98996i	0.566393	−	0.566393i	−0.364723	−	0.931116i	$-0.618836\pi$
$199$	7.98996	−	7.98996i	0.566393	−	0.566393i	0.931116	+	0.364723i	$0.118836\pi$
$200$	−10.1477	+	10.9262i	−0.717549	+	0.772596i
$201$	7.34353	+	12.7194i	0.517973	+	0.897155i
$202$	−12.5310	−	21.7043i	−0.881676	−	1.52711i
$203$	−1.26385	+	2.18905i	−0.0887049	+	0.153641i
$204$	1.31576	−	0.352557i	0.0921216	−	0.0246839i
$205$	−1.81206	+	1.44437i	−0.126560	+	0.100879i
$206$	20.7530	−	11.9818i	1.44593	−	0.834810i
$207$	4.88451	+	8.46021i	0.339497	+	0.588025i
$208$			10.1342i			0.702677i
$209$	6.43716	+	24.0238i	0.445268	+	1.66176i
$210$	−9.66442	−	12.1247i	−0.666908	−	0.836685i
$211$	−16.1514			−1.11191			−0.555955	−	0.831213i	$-0.687647\pi$
$211$	−16.1514			−1.11191			−0.555955	+	0.831213i	$0.687647\pi$
$212$	1.23168	−	1.23168i	0.0845923	−	0.0845923i
$213$	1.13606	−	4.23984i	0.0778417	−	0.290509i
$214$	−6.10514	+	6.10514i	−0.417339	+	0.417339i
$215$	6.61058	+	2.59628i	0.450838	+	0.177065i
$216$	−11.6392	−	11.6392i	−0.791950	−	0.791950i
$217$	15.9120	+	9.18679i	1.08018	+	0.623640i
$218$	−2.36235	−	8.81640i	−0.159998	−	0.597122i
$219$	−3.77085	−	2.17710i	−0.254811	−	0.147115i
$220$	−2.24765	+	1.79157i	−0.151537	+	0.120788i
$221$			12.5492i			0.844149i
$222$	7.22157	+	6.71759i	0.484680	+	0.450855i
$223$	−2.37166	+	2.37166i	−0.158818	+	0.158818i	−0.782043	−	0.623225i	$-0.785822\pi$
$223$	−2.37166	+	2.37166i	−0.158818	+	0.158818i	0.623225	+	0.782043i	$0.285822\pi$
$224$	6.09359	+	1.63277i	0.407145	+	0.109094i
$225$	7.24681	+	1.65767i	0.483121	+	0.110511i
$226$	−1.77415	−	1.02431i	−0.118015	−	0.0681358i
$227$	−2.15053	+	3.72482i	−0.142735	+	0.247225i	−0.928526	−	0.371268i	$-0.878923\pi$
$227$	−2.15053	+	3.72482i	−0.142735	+	0.247225i	0.785790	+	0.618493i	$0.212256\pi$
$228$		−	1.64071i		−	0.108659i
$229$	−6.37880	−	3.68280i	−0.421523	−	0.243366i	0.274206	−	0.961671i	$-0.411585\pi$
$229$	−6.37880	−	3.68280i	−0.421523	−	0.243366i	−0.695729	+	0.718305i	$0.744918\pi$
$230$	19.1504	−	2.88179i	1.26274	−	0.190020i
$231$	−12.8777	−	22.3048i	−0.847288	−	1.46755i
$232$	1.24646	+	1.24646i	0.0818341	+	0.0818341i
$233$	2.31125	+	2.31125i	0.151415	+	0.151415i	0.778750	−	0.627335i	$-0.215854\pi$
$233$	2.31125	+	2.31125i	0.151415	+	0.151415i	−0.627335	+	0.778750i	$0.715854\pi$
$234$	5.04994	−	2.91558i	0.330125	−	0.190598i
$235$	−12.8981	+	5.62374i	−0.841380	+	0.366852i
$236$	1.12712	+	1.12712i	0.0733693	+	0.0733693i
$237$	4.38301	−	2.53053i	0.284707	−	0.164376i
$238$	−22.9643	−	6.15327i	−1.48856	−	0.398857i
$239$	−4.53201	+	16.9137i	−0.293151	+	1.09406i	0.649523	+	0.760342i	$0.274968\pi$
$239$	−4.53201	+	16.9137i	−0.293151	+	1.09406i	−0.942675	+	0.333713i	$0.891698\pi$
$240$	−8.58776	+	3.74437i	−0.554338	+	0.241698i
$241$	−5.49887	−	20.5221i	−0.354213	−	1.32194i	−0.881472	−	0.472237i	$-0.843447\pi$
$241$	−5.49887	−	20.5221i	−0.354213	−	1.32194i	0.527258	−	0.849705i	$-0.323220\pi$
$242$	14.8054	−	8.54788i	0.951724	−	0.549478i
$243$	−3.54399	+	13.2264i	−0.227347	+	0.848471i
$244$	−0.118317	+	0.441567i	−0.00757450	+	0.0282684i
$245$	−3.75609	−	24.9604i	−0.239968	−	1.59466i
$246$	−1.62308	+	0.434904i	−0.103484	+	0.0277284i
$247$	14.6002	+	3.91210i	0.928986	+	0.248921i
$248$	9.06039	−	9.06039i	0.575335	−	0.575335i
$249$	−3.27320			−0.207431
$250$	8.31037	−	12.1704i	0.525594	−	0.769723i
$251$	17.7562	+	17.7562i	1.12076	+	1.12076i	0.991627	+	0.129136i	$0.0412203\pi$
$251$	17.7562	+	17.7562i	1.12076	+	1.12076i	0.129136	+	0.991627i	$0.458780\pi$
$252$	−0.432068	−	1.61250i	−0.0272177	−	0.101578i
$253$	32.1685			2.02242
$254$	5.55535	+	20.7328i	0.348573	+	1.30089i
$255$	−10.6343	+	4.63667i	−0.665944	+	0.290360i
$256$	3.09396	−	5.35890i	0.193373	−	0.334931i
$257$	−2.64029	−	4.57311i	−0.164696	−	0.285263i	0.771851	−	0.635803i	$-0.219331\pi$
$257$	−2.64029	−	4.57311i	−0.164696	−	0.285263i	−0.936547	+	0.350541i	$0.885998\pi$
$258$	3.64161	+	3.64161i	0.226717	+	0.226717i
$259$	7.63609	+	24.8668i	0.474484	+	1.54515i
$260$	0.259940	+	1.72738i	0.0161208	+	0.107127i
$261$	0.227451	−	0.848857i	0.0140788	−	0.0525429i
$262$	4.85891	+	18.1337i	0.300185	+	1.12030i
$263$	16.7100	−	4.47743i	1.03038	−	0.276090i	0.296261	−	0.955107i	$-0.404260\pi$
$263$	16.7100	−	4.47743i	1.03038	−	0.276090i	0.734123	+	0.679017i	$0.237594\pi$
$264$	−17.3492	+	4.64870i	−1.06777	+	0.286108i
$265$	−8.81205	+	11.9340i	−0.541320	+	0.733097i
$266$	−14.3179	+	24.7993i	−0.877885	+	1.52054i
$267$	14.6076			0.893972
$268$	3.02794	+	0.811334i	0.184961	+	0.0495601i
$269$			0.173030i			0.0105498i	0.999986	+	0.00527492i	$0.00167907\pi$
$269$			0.173030i			0.0105498i	−0.999986	+	0.00527492i	$0.998321\pi$
$270$	13.0866	+	9.66320i	0.796428	+	0.588083i
$271$	−9.17400	−	15.8898i	−0.557281	−	0.965239i	−0.997722	−	0.0674574i	$-0.978511\pi$
$271$	−9.17400	−	15.8898i	−0.557281	−	0.965239i	0.440441	−	0.897781i	$-0.354822\pi$
$272$	−7.18252	+	12.4405i	−0.435504	+	0.754315i
$273$	−15.6525			−0.947331
$274$	13.2210	+	3.54256i	0.798710	+	0.214014i
$275$	16.6588	−	17.9368i	1.00456	−	1.08163i
$276$	−2.04978	−	0.549238i	−0.123383	−	0.0330602i
$277$	−1.59242	−	0.919384i	−0.0956793	−	0.0552405i	0.451397	−	0.892323i	$-0.350926\pi$
$277$	−1.59242	−	0.919384i	−0.0956793	−	0.0552405i	−0.547076	+	0.837083i	$0.684259\pi$
$278$	−9.98977	−	5.76759i	−0.599146	−	0.345917i
$279$	−6.17025	−	1.65331i	−0.369403	−	0.0989813i
$280$	−28.3384	−	3.19980i	−1.69354	−	0.191225i
$281$	3.28246	+	0.879533i	0.195815	+	0.0524686i	0.355394	−	0.934717i	$-0.384347\pi$
$281$	3.28246	+	0.879533i	0.195815	+	0.0524686i	−0.159578	+	0.987185i	$0.551013\pi$
$282$	−10.2032			−0.607595
$283$	6.28759	−	10.8904i	0.373758	−	0.647369i	−0.616382	−	0.787447i	$-0.711402\pi$
$283$	6.28759	−	10.8904i	0.373758	−	0.647369i	0.990140	+	0.140079i	$0.0447356\pi$
$284$	−0.468430	−	0.811344i	−0.0277962	−	0.0481444i
$285$	2.07933	+	13.8177i	0.123169	+	0.818492i
$286$		−	19.2015i		−	1.13541i
$287$	−4.28078	−	1.14703i	−0.252686	−	0.0677071i
$288$	−2.19328			−0.129240
$289$	−0.394151	+	0.682690i	−0.0231854	+	0.0401582i
$290$	−1.40146	−	1.03484i	−0.0822968	−	0.0607681i
$291$	12.1874	−	3.26561i	0.714438	−	0.191433i
$292$	−0.897679	+	0.240532i	−0.0525327	+	0.0140761i
$293$	−2.72847	−	10.1828i	−0.159399	−	0.594885i	−0.998688	−	0.0512000i	$-0.983695\pi$
$293$	−2.72847	−	10.1828i	−0.159399	−	0.594885i	0.839290	−	0.543685i	$-0.182971\pi$
$294$	4.73728	−	17.6798i	0.276284	−	1.03110i
$295$	−10.9208	−	8.06396i	−0.635836	−	0.469502i
$296$	18.1289	−	0.655467i	1.05372	−	0.0380982i
$297$	19.1074	+	19.1074i	1.10872	+	1.10872i
$298$	−11.0120	−	19.0734i	−0.637909	−	1.10489i
$299$	9.77500	−	16.9308i	0.565303	−	0.979133i
$300$	−1.36775	+	0.858508i	−0.0789672	+	0.0495660i
$301$	3.51550	+	13.1200i	0.202630	+	0.756226i
$302$	5.86051			0.337234
$303$	−6.05346	−	22.5918i	−0.347762	−	1.29787i
$304$	12.2346	+	12.2346i	0.701704	+	0.701704i
$305$	0.436835	−	3.86874i	0.0250131	−	0.221523i
$306$	8.26561			0.472513
$307$	7.96428	−	7.96428i	0.454546	−	0.454546i	−0.442314	−	0.896860i	$-0.645842\pi$
$307$	7.96428	−	7.96428i	0.454546	−	0.454546i	0.896860	+	0.442314i	$0.145842\pi$
$308$	−5.30982	−	1.42276i	−0.302555	−	0.0810693i
$309$	21.6017	−	5.78816i	1.22888	−	0.329277i
$310$	−7.52217	+	10.1871i	−0.427230	+	0.578588i
$311$	0.179038	−	0.668180i	0.0101523	−	0.0378890i	−0.960664	−	0.277714i	$-0.910423\pi$
$311$	0.179038	−	0.668180i	0.0101523	−	0.0378890i	0.970816	+	0.239825i	$0.0770900\pi$
$312$	−2.82519	+	10.5437i	−0.159945	+	0.596922i
$313$	−20.1350	+	11.6249i	−1.13810	+	0.657081i	−0.945959	−	0.324287i	$-0.894876\pi$
$313$	−20.1350	+	11.6249i	−1.13810	+	0.657081i	−0.192139	+	0.981368i	$0.561542\pi$
$314$	3.30189	+	12.3228i	0.186336	+	0.695417i
$315$	5.68237	+	13.0326i	0.320165	+	0.734303i
$316$	0.279581	−	1.04341i	0.0157276	−	0.0586963i
$317$	−31.3969	−	8.41276i	−1.76342	−	0.472508i	−0.776017	−	0.630713i	$-0.782763\pi$
$317$	−31.3969	−	8.41276i	−1.76342	−	0.472508i	−0.987406	+	0.158205i	$0.949429\pi$
$318$	−9.31605	+	5.37862i	−0.522418	+	0.301618i
$319$	−2.04624	−	2.04624i	−0.114567	−	0.114567i
$320$	−7.15766	+	18.2247i	−0.400126	+	1.01879i
$321$	−6.97805	+	4.02878i	−0.389477	+	0.224865i
$322$	26.1894	+	26.1894i	1.45948	+	1.45948i
$323$	15.1502	+	15.1502i	0.842979	+	0.842979i
$324$	−0.305748	−	0.529572i	−0.0169860	−	0.0294207i
$325$	−4.37833	−	14.2182i	−0.242866	−	0.788685i
$326$	−18.6827	−	10.7865i	−1.03474	−	0.597408i
$327$		−	8.51805i		−	0.471049i
$328$	−1.54532	+	2.67656i	−0.0853258	+	0.147789i
$329$	−23.3051	−	13.4552i	−1.28485	−	0.741810i
$330$	16.2715	−	7.09459i	0.895718	−	0.390544i
$331$	20.5568	+	5.50817i	1.12990	+	0.302757i	0.774885	−	0.632103i	$-0.217808\pi$
$331$	20.5568	+	5.50817i	1.12990	+	0.302757i	0.355018	+	0.934859i	$0.384475\pi$
$332$	−0.493999	+	0.493999i	−0.0271117	+	0.0271117i
$333$	−4.80196	−	7.66369i	−0.263146	−	0.419968i
$334$		−	12.9938i		−	0.710990i
$335$	−26.5290	−	2.99549i	−1.44943	−	0.163661i
$336$	−15.5169	−	8.95869i	−0.846517	−	0.488737i
$337$	−0.488128	−	1.82172i	−0.0265900	−	0.0992352i	0.951356	−	0.308095i	$-0.0996915\pi$
$337$	−0.488128	−	1.82172i	−0.0265900	−	0.0992352i	−0.977946	+	0.208860i	$0.933025\pi$
$338$	4.73379	+	2.73305i	0.257484	+	0.148659i
$339$	−1.35188	−	1.35188i	−0.0734239	−	0.0734239i
$340$	−0.905172	+	2.30473i	−0.0490898	+	0.124991i
$341$	−14.8739	+	14.8739i	−0.805466	+	0.805466i
$342$	2.57674	−	9.61651i	0.139334	−	0.520001i
$343$	12.9675	−	12.9675i	0.700179	−	0.700179i
$344$	9.47238			0.510716
$345$	17.9590	+	2.02782i	0.966878	+	0.109174i
$346$	2.57403	+	9.60640i	0.138381	+	0.516443i
$347$			6.76364i			0.363091i	0.983383	+	0.181546i	$0.0581100\pi$
$347$			6.76364i			0.363091i	−0.983383	+	0.181546i	$0.941890\pi$
$348$	0.0954497	+	0.165324i	0.00511664	+	0.00886228i
$349$	−12.1596	+	7.02035i	−0.650888	+	0.375790i	−0.788796	−	0.614655i	$-0.789295\pi$
$349$	−12.1596	+	7.02035i	−0.650888	+	0.375790i	0.137908	+	0.990445i	$0.455962\pi$
$350$	28.1654	−	1.04045i	1.50551	−	0.0556143i
$351$	15.8627	−	4.25039i	0.846688	−	0.226869i
$352$	−3.61114	+	6.25468i	−0.192475	+	0.333376i
$353$	7.21056	+	12.4891i	0.383779	+	0.664725i	0.991599	−	0.129350i	$-0.0412890\pi$
$353$	7.21056	+	12.4891i	0.383779	+	0.664725i	−0.607820	+	0.794075i	$0.707956\pi$
$354$	−4.92201	−	8.52517i	−0.261602	−	0.453108i
$355$	4.97327	+	6.23933i	0.263954	+	0.331149i
$356$	2.20462	−	2.20462i	0.116844	−	0.116844i
$357$	−19.2147	−	11.0936i	−1.01695	−	0.587135i
$358$	−7.29003	+	27.2068i	−0.385290	+	1.43792i
$359$		−	2.87625i		−	0.151803i	−0.997115	−	0.0759013i	$-0.975817\pi$
$359$		−	2.87625i		−	0.151803i	0.997115	−	0.0759013i	$-0.0241834\pi$
$360$	9.80458	−	1.47542i	0.516747	−	0.0777612i
$361$	5.89475	−	3.40334i	0.310250	−	0.179123i
$362$		−	0.440318i		−	0.0231426i
$363$	15.4108	−	4.12931i	0.808856	−	0.216732i
$364$	−2.36231	+	2.36231i	−0.123819	+	0.123819i
$365$	7.25525	−	3.16338i	0.379757	−	0.165579i
$366$	1.41159	−	2.44495i	0.0737852	−	0.127800i
$367$	−25.2940	+	6.77750i	−1.32033	+	0.353783i	−0.849103	−	0.528227i	$-0.822857\pi$
$367$	−25.2940	+	6.77750i	−1.32033	+	0.353783i	−0.471231	+	0.882010i	$0.656190\pi$
$368$	19.3807	−	11.1894i	1.01029	−	0.583290i
$369$	1.54079			0.0802105
$370$	−17.6208	+	3.30671i	−0.916063	+	0.171908i
$371$	−28.3716			−1.47298
$372$	1.20172	−	0.693814i	0.0623063	−	0.0359726i
$373$	−33.2235	+	8.90222i	−1.72025	+	0.460939i	−0.977900	−	0.209074i	$-0.932955\pi$
$373$	−33.2235	+	8.90222i	−1.72025	+	0.460939i	−0.742349	+	0.670013i	$0.766288\pi$
$374$	13.6090	−	23.5714i	0.703703	−	1.21885i
$375$	10.4309	−	8.96359i	0.538651	−	0.462878i
$376$	−13.2701	+	13.2701i	−0.684352	+	0.684352i
$377$	−1.69875	+	0.455180i	−0.0874903	+	0.0234430i
$378$			31.1120i			1.60023i
$379$	1.99724	−	1.15311i	0.102591	−	0.0592312i	−0.447826	−	0.894121i	$-0.647802\pi$
$379$	1.99724	−	1.15311i	0.102591	−	0.0592312i	0.550418	+	0.834889i	$0.314468\pi$
$380$	2.39922	+	1.77159i	0.123078	+	0.0908806i
$381$			20.0312i			1.02623i
$382$	1.44009	−	5.37450i	0.0736816	−	0.274983i
$383$	0.121710	+	0.0702694i	0.00621910	+	0.00359060i	0.503106	−	0.864225i	$-0.332190\pi$
$383$	0.121710	+	0.0702694i	0.00621910	+	0.00359060i	−0.496887	+	0.867815i	$0.665524\pi$
$384$	−7.47325	+	7.47325i	−0.381367	+	0.381367i
$385$	46.5214	+	5.25292i	2.37095	+	0.267713i
$386$	5.27061	+	9.12897i	0.268267	+	0.464652i
$387$	−2.36116	−	4.08966i	−0.120025	−	0.207889i
$388$	1.34650	−	2.33220i	0.0683581	−	0.118400i
$389$	−5.08702	+	1.36306i	−0.257922	+	0.0691101i	−0.385463	−	0.922723i	$-0.625958\pi$
$389$	−5.08702	+	1.36306i	−0.257922	+	0.0691101i	0.127541	+	0.991833i	$0.459292\pi$
$390$	1.21041	−	10.7198i	0.0612917	−	0.542818i
$391$	23.9992	−	13.8559i	1.21369	−	0.700725i
$392$	−16.8327	−	29.1550i	−0.850178	−	1.47255i
$393$			17.5201i			0.883770i
$394$	−1.67696	−	6.25848i	−0.0844838	−	0.315298i
$395$	−1.03223	+	9.14172i	−0.0519370	+	0.459970i
$396$	1.91118			0.0960402
$397$	3.01599	−	3.01599i	0.151368	−	0.151368i	−0.627361	−	0.778729i	$-0.715865\pi$
$397$	3.01599	−	3.01599i	0.151368	−	0.151368i	0.778729	+	0.627361i	$0.215865\pi$
$398$	−3.85489	+	14.3866i	−0.193228	+	0.721137i
$399$	−18.8967	+	18.8967i	−0.946019	+	0.946019i
$400$	3.79739	−	16.6010i	0.189870	−	0.830051i
$401$	−6.97260	−	6.97260i	−0.348195	−	0.348195i	0.511242	−	0.859437i	$-0.329186\pi$
$401$	−6.97260	−	6.97260i	−0.348195	−	0.348195i	−0.859437	+	0.511242i	$0.829186\pi$
$402$	−16.7657	−	9.67967i	−0.836196	−	0.482778i
$403$	3.30865	+	12.3481i	0.164816	+	0.615101i
$404$	−4.32321	−	2.49601i	−0.215088	−	0.124181i
$405$	3.24610	+	4.07247i	0.161300	+	0.202363i
$406$		−	3.33182i		−	0.165355i
$407$	−29.7611	+	1.07604i	−1.47520	+	0.0533373i
$408$	−10.9410	+	10.9410i	−0.541658	+	0.541658i
$409$	−8.95729	−	2.40010i	−0.442910	−	0.118677i	0.0304703	−	0.999536i	$-0.490300\pi$
$409$	−8.95729	−	2.40010i	−0.442910	−	0.118677i	−0.473380	+	0.880858i	$0.656966\pi$
$410$	1.11659	−	2.84304i	0.0551446	−	0.140408i
$411$	11.0623	+	6.38680i	0.545661	+	0.315038i
$412$	2.38662	−	4.13374i	0.117580	−	0.203655i
$413$		−	25.9630i		−	1.27756i
$414$	−11.1516	−	6.43838i	−0.548071	−	0.316429i
$415$	3.53430	−	4.78643i	0.173492	−	0.234956i
$416$	2.19463	+	3.80120i	0.107600	+	0.186369i
$417$	−7.61206	−	7.61206i	−0.372764	−	0.372764i
$418$	−23.1814	−	23.1814i	−1.13384	−	1.13384i
$419$	−29.2106	+	16.8648i	−1.42703	+	0.823898i	−0.996886	−	0.0788607i	$-0.974872\pi$
$419$	−29.2106	+	16.8648i	−1.42703	+	0.823898i	−0.430147	+	0.902759i	$0.641538\pi$
$420$	−2.87467	−	1.12901i	−0.140269	−	0.0550902i
$421$	6.17988	+	6.17988i	0.301189	+	0.301189i	0.841479	−	0.540290i	$-0.181685\pi$
$421$	6.17988	+	6.17988i	0.301189	+	0.301189i	−0.540290	+	0.841479i	$0.681685\pi$
$422$	18.4373	−	10.6448i	0.897513	−	0.518179i
$423$	9.03711	+	2.42149i	0.439400	+	0.117737i
$424$	−5.12092	+	19.1115i	−0.248694	+	0.928138i
$425$	4.70233	−	20.5571i	0.228096	−	0.997167i
$426$	1.49747	+	5.58863i	0.0725526	+	0.270770i
$427$	6.44841	−	3.72299i	0.312060	−	0.180168i
$428$	−0.445111	+	1.66118i	−0.0215153	+	0.0802960i
$429$	4.63794	−	17.3090i	0.223922	−	0.835687i
$430$	−9.25727	+	1.39305i	−0.446425	+	0.0671791i
$431$	3.98861	−	1.06874i	0.192124	−	0.0514796i	−0.161474	−	0.986877i	$-0.551625\pi$
$431$	3.98861	−	1.06874i	0.192124	−	0.0514796i	0.353598	+	0.935397i	$0.384958\pi$
$432$	18.1580	+	4.86542i	0.873628	+	0.234088i
$433$	−2.42155	+	2.42155i	−0.116372	+	0.116372i	−0.762895	−	0.646523i	$-0.776223\pi$
$433$	−2.42155	+	2.42155i	−0.116372	+	0.116372i	0.646523	+	0.762895i	$0.276223\pi$
$434$	−24.2186			−1.16253
$435$	−1.01338	−	1.27136i	−0.0485878	−	0.0609570i
$436$	−1.28556	−	1.28556i	−0.0615674	−	0.0615674i
$437$	−8.63895	−	32.2410i	−0.413257	−	1.54230i
$438$	5.73937			0.274238
$439$	−2.19354	−	8.18640i	−0.104692	−	0.390716i	0.893618	−	0.448828i	$-0.148158\pi$
$439$	−2.19354	−	8.18640i	−0.104692	−	0.390716i	−0.998310	+	0.0581125i	$0.981492\pi$
$440$	11.9353	−	30.3894i	0.568993	−	1.44876i
$441$	−8.39170	+	14.5349i	−0.399605	+	0.692136i
$442$	−8.27068	−	14.3252i	−0.393396	−	0.681382i
$443$	−21.9112	−	21.9112i	−1.04103	−	1.04103i	−0.999121	−	0.0419105i	$-0.986656\pi$
$443$	−21.9112	−	21.9112i	−1.04103	−	1.04103i	−0.0419105	−	0.999121i	$-0.513344\pi$
$444$	1.91476	+	0.439569i	0.0908704	+	0.0208610i
$445$	−15.7729	+	21.3609i	−0.747706	+	1.01260i
$446$	1.14425	−	4.27038i	0.0541816	−	0.202209i
$447$	−5.31969	−	19.8533i	−0.251613	−	0.939031i
$448$	−36.1705	+	9.69186i	−1.70890	+	0.457898i
$449$	24.7248	−	6.62498i	1.16683	−	0.312652i	0.377142	−	0.926155i	$-0.376907\pi$
$449$	24.7248	−	6.62498i	1.16683	−	0.312652i	0.789692	+	0.613503i	$0.210240\pi$
$450$	−9.36494	+	2.88382i	−0.441468	+	0.135945i
$451$	2.53685	−	4.39395i	0.119456	−	0.206903i
$452$	−0.408057			−0.0191934
$453$	5.28289	+	1.41555i	0.248212	+	0.0665082i
$454$		−	5.66931i		−	0.266074i
$455$	16.9011	−	22.8888i	0.792335	−	1.07304i
$456$	9.31835	+	16.1399i	0.436372	+	0.755818i
$457$	13.3314	−	23.0907i	0.623617	−	1.08014i	−0.365190	−	0.930933i	$-0.618996\pi$
$457$	13.3314	−	23.0907i	0.623617	−	1.08014i	0.988807	−	0.149203i	$-0.0476708\pi$
$458$	9.70877			0.453661
$459$	22.4852	+	6.02488i	1.04952	+	0.281217i
$460$	3.01645	−	2.40437i	0.140643	−	0.112104i
$461$	28.6141	+	7.66712i	1.33269	+	0.357094i	0.853718	−	0.520736i	$-0.174342\pi$
$461$	28.6141	+	7.66712i	1.33269	+	0.357094i	0.478973	+	0.877829i	$0.341009\pi$
$462$	29.4004	+	16.9743i	1.36783	+	0.789718i
$463$	16.3053	+	9.41385i	0.757770	+	0.437499i	0.828495	−	0.559997i	$-0.189198\pi$
$463$	16.3053	+	9.41385i	0.757770	+	0.437499i	−0.0707245	+	0.997496i	$0.522531\pi$
$464$	−1.94456	−	0.521044i	−0.0902741	−	0.0241889i
$465$	−9.24137	+	7.36615i	−0.428558	+	0.341597i
$466$	−4.16161	−	1.11510i	−0.192783	−	0.0516560i
$467$	22.1604			1.02546			0.512731	−	0.858549i	$-0.328634\pi$
$467$	22.1604			1.02546			0.512731	+	0.858549i	$0.328634\pi$
$468$	0.580747	−	1.00588i	0.0268450	−	0.0464970i
$469$	−25.5295	−	44.2185i	−1.17884	−	2.04182i
$470$	11.0172	−	14.9203i	0.508184	−	0.688222i
$471$			11.9058i			0.548591i
$472$	−17.4891	−	4.68618i	−0.805000	−	0.215699i
$473$	−15.5502			−0.715000
$474$	−3.33555	+	5.77735i	−0.153207	+	0.265362i
$475$	−22.4510	−	11.8794i	−1.03012	−	0.545063i
$476$	−4.57420	+	1.22565i	−0.209658	+	0.0561777i
$477$	9.52780	−	2.55297i	0.436248	−	0.116892i
$478$	−5.97374	−	22.2943i	−0.273233	−	1.01972i
$479$	1.61172	−	6.01501i	0.0736412	−	0.274833i	−0.919281	−	0.393603i	$-0.871228\pi$
$479$	1.61172	−	6.01501i	0.0736412	−	0.274833i	0.992922	+	0.118770i	$0.0378952\pi$
$480$	−2.41030	+	3.26421i	−0.110015	+	0.148990i
$481$	−8.47713	+	15.9907i	−0.386524	+	0.729114i
$482$	19.8024	+	19.8024i	0.901975	+	0.901975i
$483$	17.2824	+	29.9340i	0.786376	+	1.36204i
$484$	1.70263	−	2.94904i	0.0773921	−	0.134047i
$485$	−8.38428	+	21.3479i	−0.380711	+	0.969356i
$486$	−4.67141	−	17.4340i	−0.211900	−	0.790820i
$487$	13.1383			0.595352			0.297676	−	0.954667i	$-0.403788\pi$
$487$	13.1383			0.595352			0.297676	+	0.954667i	$0.403788\pi$
$488$	−1.34396	−	5.01572i	−0.0608382	−	0.227051i
$489$	−14.2360	−	14.2360i	−0.643774	−	0.643774i
$490$	20.7381	+	26.0175i	0.936852	+	1.17535i
$491$	−1.90585			−0.0860099			−0.0430050	−	0.999075i	$-0.513693\pi$
$491$	−1.90585			−0.0860099			−0.0430050	+	0.999075i	$0.513693\pi$
$492$	−0.236670	+	0.236670i	−0.0106699	+	0.0106699i
$493$	−2.40796	−	0.645212i	−0.108449	−	0.0290589i
$494$	−19.2448	+	5.15663i	−0.865865	+	0.232008i
$495$	−16.0956	+	2.42210i	−0.723442	+	0.108865i
$496$	−3.78742	+	14.1348i	−0.170060	+	0.634672i
$497$	−3.94948	+	14.7397i	−0.177159	+	0.661165i
$498$	3.73645	−	2.15724i	0.167434	−	0.0966682i
$499$	−5.11290	−	19.0816i	−0.228885	−	0.854210i	−0.980811	−	0.194962i	$-0.937542\pi$
$499$	−5.11290	−	19.0816i	−0.228885	−	0.854210i	0.751926	−	0.659248i	$-0.229125\pi$
$500$	0.221456	−	2.92707i	0.00990379	−	0.130902i
$501$	3.13853	−	11.7131i	0.140219	−	0.523304i
$502$	−31.9717	−	8.56678i	−1.42696	−	0.382354i
$503$	11.0969	−	6.40682i	0.494788	−	0.285666i	−0.231770	−	0.972770i	$-0.574452\pi$
$503$	11.0969	−	6.40682i	0.494788	−	0.285666i	0.726559	+	0.687104i	$0.241118\pi$
$504$	13.4084	+	13.4084i	0.597259	+	0.597259i
$505$	39.5726	+	15.5420i	1.76096	+	0.691608i
$506$	−36.7212	+	21.2010i	−1.63246	+	0.942500i
$507$	3.60708	+	3.60708i	0.160196	+	0.160196i
$508$	3.02316	+	3.02316i	0.134131	+	0.134131i
$509$	16.2560	+	28.1562i	0.720534	+	1.24800i	0.960786	+	0.277291i	$0.0894366\pi$
$509$	16.2560	+	28.1562i	0.720534	+	1.24800i	−0.240252	+	0.970711i	$0.577230\pi$
$510$	9.08347	−	12.3015i	0.402223	−	0.544721i
$511$	13.1092	+	7.56862i	0.579919	+	0.334816i
$512$			25.3397i			1.11987i
$513$	14.0191	−	24.2818i	0.618960	−	1.07207i
$514$	6.02792	+	3.48022i	0.265880	+	0.153506i
$515$	−14.8608	+	37.8382i	−0.654845	+	1.66735i
$516$	0.990864	+	0.265501i	0.0436203	+	0.0116880i
$517$	21.7847	−	21.7847i	0.958089	−	0.958089i
$518$	−25.1055	−	23.3535i	−1.10307	−	1.02609i
$519$			9.28132i			0.407405i
$520$	−12.3677	−	15.5161i	−0.542357	−	0.680427i
$521$	24.6860	+	14.2524i	1.08151	+	0.624411i	0.931304	−	0.364244i	$-0.118672\pi$
$521$	24.6860	+	14.2524i	1.08151	+	0.624411i	0.150208	+	0.988654i	$0.452006\pi$
$522$	0.299808	+	1.11890i	0.0131222	+	0.0489728i
$523$	−23.1609	−	13.3720i	−1.01276	−	0.584716i	−0.100760	−	0.994911i	$-0.532127\pi$
$523$	−23.1609	−	13.3720i	−1.01276	−	0.584716i	−0.911998	+	0.410195i	$0.865461\pi$
$524$	2.64417	+	2.64417i	0.115511	+	0.115511i
$525$	25.6407	+	5.86517i	1.11905	+	0.255977i
$526$	−16.1240	+	16.1240i	−0.703041	+	0.703041i
$527$	−4.68998	+	17.5032i	−0.204299	+	0.762453i
$528$	14.5046	−	14.5046i	0.631231	−	0.631231i
$529$	−20.1715			−0.877024
$530$	2.19399	−	19.4306i	0.0953008	−	0.844012i
$531$	2.33623	+	8.71894i	0.101384	+	0.378370i
$532$			5.70387i			0.247294i
$533$	−1.54174	−	2.67037i	−0.0667801	−	0.115666i
$534$	−16.6750	+	9.62732i	−0.721598	+	0.416615i
$535$	1.64338	−	14.5542i	0.0710493	−	0.629234i
$536$	−34.3942	+	9.21589i	−1.48560	+	0.398066i
$537$	−13.1430	+	22.7644i	−0.567164	+	0.982357i
$538$	−0.114037	−	0.197519i	−0.00491650	−	0.00851563i
$539$	27.6331	+	47.8620i	1.19024	+	2.06156i
$540$	3.21985	+	0.363567i	0.138560	+	0.0156454i
$541$	17.2856	−	17.2856i	0.743165	−	0.743165i	−0.230021	−	0.973186i	$-0.573879\pi$
$541$	17.2856	−	17.2856i	0.743165	−	0.743165i	0.973186	+	0.230021i	$0.0738794\pi$
$542$	20.9448	+	12.0925i	0.899654	+	0.519416i
$543$	0.106354	−	0.396920i	0.00456410	−	0.0170335i
$544$			6.22171i			0.266754i
$545$	12.4560	+	9.19754i	0.533557	+	0.393979i
$546$	17.8677	−	10.3159i	0.764669	−	0.441482i
$547$			13.5842i			0.580818i	0.956903	+	0.290409i	$0.0937913\pi$
$547$			13.5842i			0.580818i	−0.956903	+	0.290409i	$0.906209\pi$
$548$	2.63345	−	0.705632i	0.112496	−	0.0301431i
$549$	−1.83051	+	1.83051i	−0.0781243	+	0.0781243i
$550$	−7.19505	+	31.4545i	−0.306798	+	1.34123i
$551$	−1.50133	+	2.60037i	−0.0639586	+	0.110780i
$552$	23.2834	−	6.23876i	0.991006	−	0.265539i
$553$	−15.2374	+	8.79732i	−0.647960	+	0.374100i
$554$	2.42372			0.102974
$555$	−16.6828	−	1.27533i	−0.708146	−	0.0541349i
$556$	−2.29766			−0.0974425
$557$	35.3898	−	20.4323i	1.49951	−	0.865744i	0.499513	−	0.866307i	$-0.333512\pi$
$557$	35.3898	−	20.4323i	1.49951	−	0.865744i	1.00000		0.000562636i	$0.000179093\pi$
$558$	8.13315	−	2.17927i	0.344303	−	0.0922558i
$559$	−4.72522	+	8.18433i	−0.199856	+	0.346160i
$560$	29.8551	−	13.0172i	1.26161	−	0.550076i
$561$	17.9611	−	17.9611i	0.758318	−	0.758318i
$562$	−4.32669	+	1.15933i	−0.182510	+	0.0489035i
$563$			27.8829i			1.17512i	0.809180	+	0.587561i	$0.199912\pi$
$563$			27.8829i			1.17512i	−0.809180	+	0.587561i	$0.800088\pi$
$564$	−1.76007	+	1.01618i	−0.0741124	+	0.0427888i
$565$	3.43658	−	0.517144i	0.144578	−	0.0217564i
$566$			16.5756i			0.696726i
$567$	−2.57786	+	9.62072i	−0.108260	+	0.404032i
$568$	9.21600	+	5.32086i	0.386695	+	0.223258i
$569$	10.7860	−	10.7860i	0.452173	−	0.452173i	−0.443902	−	0.896075i	$-0.646406\pi$
$569$	10.7860	−	10.7860i	0.452173	−	0.452173i	0.896075	+	0.443902i	$0.146406\pi$
$570$	−11.4803	−	14.4029i	−0.480859	−	0.603272i
$571$	16.7650	+	29.0378i	0.701594	+	1.21520i	0.967907	+	0.251310i	$0.0808612\pi$
$571$	16.7650	+	29.0378i	0.701594	+	1.21520i	−0.266313	+	0.963887i	$0.585805\pi$
$572$	−1.91235	−	3.31228i	−0.0799593	−	0.138494i
$573$	2.59631	−	4.49695i	0.108463	−	0.187863i
$574$	5.64259	−	1.51193i	0.235517	−	0.0631067i
$575$	−22.3569	+	24.0720i	−0.932345	+	1.00387i
$576$	11.2747	−	6.50948i	0.469781	−	0.271228i
$577$	8.95508	+	15.5106i	0.372805	+	0.645717i	0.989996	−	0.141097i	$-0.0450628\pi$
$577$	8.95508	+	15.5106i	0.372805	+	0.645717i	−0.617191	+	0.786813i	$0.711729\pi$
$578$		−	1.03908i		−	0.0432200i
$579$	2.54613	+	9.50228i	0.105813	+	0.394901i
$580$	−0.344818	−	0.0389348i	−0.0143178	−	0.00161668i
$581$	11.3792			0.472087
$582$	−11.7600	+	11.7600i	−0.487469	+	0.487469i
$583$	8.40669	−	31.3742i	0.348170	−	1.29939i
$584$	7.46448	−	7.46448i	0.308883	−	0.308883i
$585$	−3.61615	+	9.20736i	−0.149509	+	0.380677i
$586$	9.82570	+	9.82570i	0.405896	+	0.405896i
$587$	−32.4251	−	18.7207i	−1.33833	−	0.772684i	−0.351769	−	0.936087i	$-0.614420\pi$
$587$	−32.4251	−	18.7207i	−1.33833	−	0.772684i	−0.986560	+	0.163402i	$0.947753\pi$
$588$	−0.943605	−	3.52158i	−0.0389136	−	0.145228i
$589$	18.9018	+	10.9130i	0.778836	+	0.449661i
$590$	17.7811	+	2.00773i	0.732035	+	0.0826571i
$591$		−	6.04669i		−	0.248728i
$592$	−17.5560	+	11.0003i	−0.721547	+	0.452111i
$593$	8.22207	−	8.22207i	0.337640	−	0.337640i	−0.517839	−	0.855478i	$-0.673263\pi$
$593$	8.22207	−	8.22207i	0.337640	−	0.337640i	0.855478	+	0.517839i	$0.173263\pi$
$594$	−34.4046	−	9.21869i	−1.41164	−	0.378247i
$595$	36.9697	−	16.1192i	1.51561	−	0.660824i
$596$	−3.79917	−	2.19345i	−0.155620	−	0.0898473i
$597$	−6.94990	+	12.0376i	−0.284440	+	0.492665i
$598$			25.7693i			1.05378i
$599$	15.7152	+	9.07320i	0.642107	+	0.370721i	0.785426	−	0.618956i	$-0.212444\pi$
$599$	15.7152	+	9.07320i	0.642107	+	0.370721i	−0.143318	+	0.989677i	$0.545777\pi$
$600$	8.57888	−	16.2133i	0.350231	−	0.661907i
$601$	−21.7617	−	37.6924i	−0.887679	−	1.53751i	−0.842612	−	0.538521i	$-0.818983\pi$
$601$	−21.7617	−	37.6924i	−0.887679	−	1.53751i	−0.0450671	−	0.998984i	$-0.514350\pi$
$602$	−12.6599	−	12.6599i	−0.515981	−	0.515981i
$603$	12.5523	+	12.5523i	0.511169	+	0.511169i
$604$	1.01094	−	0.583669i	0.0411347	−	0.0237492i
$605$	−10.6018	+	26.9940i	−0.431024	+	1.09746i
$606$	21.7996	+	21.7996i	0.885548	+	0.885548i
$607$	12.4039	−	7.16138i	0.503458	−	0.290671i	−0.226683	−	0.973969i	$-0.572788\pi$
$607$	12.4039	−	7.16138i	0.503458	−	0.290671i	0.730140	+	0.683297i	$0.239455\pi$
$608$	7.23856	+	1.93957i	0.293563	+	0.0786598i
$609$	0.804767	−	3.00343i	0.0326108	−	0.121705i
$610$	2.05108	+	4.70417i	0.0830457	+	0.190466i
$611$	−4.84594	−	18.0853i	−0.196046	−	0.731653i
$612$	1.42583	−	0.823201i	0.0576356	−	0.0332759i
$613$	0.0869843	−	0.324630i	0.00351326	−	0.0131117i	−0.964147	−	0.265369i	$-0.914506\pi$
$613$	0.0869843	−	0.324630i	0.00351326	−	0.0131117i	0.967660	+	0.252257i	$0.0811729\pi$
$614$	−3.84250	+	14.3404i	−0.155071	+	0.578731i
$615$	1.69325	−	2.29313i	0.0682784	−	0.0924679i
$616$	60.3138	−	16.1610i	2.43011	−	0.651147i
$617$	−25.9211	−	6.94555i	−1.04355	−	0.279617i	−0.303964	−	0.952684i	$-0.598310\pi$
$617$	−25.9211	−	6.94555i	−1.04355	−	0.279617i	−0.739582	+	0.673066i	$0.764977\pi$
$618$	−20.8442	+	20.8442i	−0.838476	+	0.838476i
$619$	−45.2493			−1.81872			−0.909361	−	0.416008i	$-0.863429\pi$
$619$	−45.2493			−1.81872			−0.909361	+	0.416008i	$0.863429\pi$
$620$	−0.283013	+	2.50645i	−0.0113661	+	0.100661i
$621$	−25.6430	−	25.6430i	−1.02902	−	1.02902i
$622$	0.235995	+	0.880744i	0.00946252	+	0.0353146i
$623$	−50.7829			−2.03457
$624$	−3.22650	−	12.0415i	−0.129164	−	0.482045i
$625$	1.84451	+	24.9319i	0.0737805	+	0.997275i
$626$	15.3231	−	26.5404i	0.612434	−	1.06077i
$627$	−15.2974	−	26.4958i	−0.610918	−	1.05814i
$628$	1.79685	+	1.79685i	0.0717023	+	0.0717023i
$629$	−21.7397	+	13.6218i	−0.866818	+	0.543136i
$630$	−15.0758	−	11.1320i	−0.600636	−	0.443511i
$631$	−8.96677	+	33.4644i	−0.356961	+	1.33220i	0.521037	+	0.853534i	$0.325545\pi$
$631$	−8.96677	+	33.4644i	−0.356961	+	1.33220i	−0.877998	+	0.478664i	$0.841121\pi$
$632$	3.17574	+	11.8520i	0.126324	+	0.471448i
$633$	19.1912	−	5.14227i	0.762783	−	0.204387i
$634$	41.3849	−	11.0890i	1.64360	−	0.440402i
$635$	−29.2918	−	21.6291i	−1.16241	−	0.858326i
$636$	−1.07135	+	1.85564i	−0.0424819	+	0.0735808i
$637$	33.5874			1.33078
$638$	3.68443	+	0.987240i	0.145868	+	0.0390852i
$639$		−	5.30529i		−	0.209874i
$640$	−2.85880	−	18.9976i	−0.113004	−	0.750945i
$641$	−5.16086	−	8.93888i	−0.203842	−	0.353065i	0.745921	−	0.666034i	$-0.232010\pi$
$641$	−5.16086	−	8.93888i	−0.203842	−	0.353065i	−0.949763	+	0.312970i	$0.898676\pi$
$642$	5.31043	−	9.19793i	0.209586	−	0.363013i
$643$	−9.55874			−0.376960			−0.188480	−	0.982077i	$-0.560356\pi$
$643$	−9.55874			−0.376960			−0.188480	+	0.982077i	$0.560356\pi$
$644$	7.12601	+	1.90941i	0.280804	+	0.0752412i
$645$	−8.68134	−	0.980245i	−0.341828	−	0.0385971i
$646$	−27.2793	−	7.30946i	−1.07329	−	0.287587i
$647$	1.47670	+	0.852572i	0.0580550	+	0.0335181i	0.528747	−	0.848780i	$-0.322662\pi$
$647$	1.47670	+	0.852572i	0.0580550	+	0.0335181i	−0.470692	+	0.882298i	$0.655996\pi$
$648$	6.01537	+	3.47298i	0.236306	+	0.136431i
$649$	28.7107	+	7.69301i	1.12699	+	0.301977i
$650$	14.3687	+	13.3449i	0.563586	+	0.523430i
$651$	−21.8316	−	5.84977i	−0.855649	−	0.229270i
$652$	−4.29706			−0.168286
$653$	−14.4314	+	24.9960i	−0.564746	+	0.978168i	0.432328	+	0.901717i	$0.357692\pi$
$653$	−14.4314	+	24.9960i	−0.564746	+	0.978168i	−0.997073	+	0.0764516i	$0.975641\pi$
$654$	5.61392	+	9.72359i	0.219522	+	0.380223i
$655$	−25.6197	−	18.9176i	−1.00105	−	0.739174i
$656$		−	3.52965i		−	0.137810i
$657$	−5.08342	−	1.36210i	−0.198323	−	0.0531405i
$658$	35.4713			1.38281
$659$	11.5673	−	20.0352i	0.450598	−	0.780459i	−0.547825	−	0.836593i	$-0.684544\pi$
$659$	11.5673	−	20.0352i	0.450598	−	0.780459i	0.998423	+	0.0561341i	$0.0178774\pi$
$660$	2.10028	−	2.84436i	0.0817534	−	0.110717i
$661$	−32.1200	+	8.60652i	−1.24932	+	0.334755i	−0.822074	−	0.569380i	$-0.807183\pi$
$661$	−32.1200	+	8.60652i	−1.24932	+	0.334755i	−0.427247	+	0.904135i	$0.640517\pi$
$662$	−27.0964	+	7.26045i	−1.05313	+	0.282185i
$663$	−3.99540	−	14.9110i	−0.155168	−	0.579096i
$664$	2.05388	−	7.66518i	0.0797059	−	0.297466i
$665$	−7.22871	−	48.0369i	−0.280317	−	1.86279i
$666$	10.5324	+	5.58353i	0.408123	+	0.216357i
$667$	2.74614	+	2.74614i	0.106331	+	0.106331i
$668$	−1.29410	−	2.24145i	−0.0500703	−	0.0867242i
$669$	2.06294	−	3.57311i	0.0797577	−	0.138144i
$670$	32.2578	−	14.0648i	1.24623	−	0.543370i
$671$	2.20629	+	8.23400i	0.0851731	+	0.317870i
$672$	−7.76029			−0.299360
$673$	−9.06446	−	33.8290i	−0.349409	−	1.30401i	−0.887376	−	0.461047i	$-0.847474\pi$
$673$	−9.06446	−	33.8290i	−0.349409	−	1.30401i	0.537966	−	0.842966i	$-0.319193\pi$
$674$	1.75783	+	1.75783i	0.0677092	+	0.0677092i
$675$	−27.5778	+	1.01874i	−1.06147	+	0.0392113i
$676$	1.08878			0.0418761
$677$	9.71006	−	9.71006i	0.373188	−	0.373188i	−0.495449	−	0.868637i	$-0.664996\pi$
$677$	9.71006	−	9.71006i	0.373188	−	0.373188i	0.868637	+	0.495449i	$0.164996\pi$
$678$	2.43418	+	0.652235i	0.0934839	+	0.0250489i
$679$	−42.3691	+	11.3528i	−1.62598	+	0.435679i
$680$	−4.18533	−	27.8128i	−0.160500	−	1.06657i
$681$	1.36937	−	5.11054i	0.0524742	−	0.195836i
$682$	7.17614	−	26.7817i	0.274789	−	1.02553i
$683$	−4.90289	+	2.83069i	−0.187604	+	0.108313i	−0.590860	−	0.806774i	$-0.701212\pi$
$683$	−4.90289	+	2.83069i	−0.187604	+	0.108313i	0.403256	+	0.915087i	$0.367878\pi$
$684$	−0.513253	−	1.91548i	−0.0196247	−	0.0732404i
$685$	−21.2842	+	9.28016i	−0.813227	+	0.354577i
$686$	−6.25638	+	23.3491i	−0.238870	+	0.891474i
$687$	8.75186	+	2.34506i	0.333904	+	0.0894694i
$688$	−9.36860	+	5.40896i	−0.357174	+	0.206215i
$689$	−13.9582	−	13.9582i	−0.531766	−	0.531766i
$690$	−21.8371	+	9.52125i	−0.831325	+	0.362468i
$691$	27.9652	−	16.1457i	1.06385	−	0.614212i	0.137353	−	0.990522i	$-0.456141\pi$
$691$	27.9652	−	16.1457i	1.06385	−	0.614212i	0.926494	+	0.376310i	$0.122807\pi$
$692$	1.40076	+	1.40076i	0.0532488	+	0.0532488i
$693$	−22.0118	−	22.0118i	−0.836159	−	0.836159i
$694$	−4.45765	−	7.72088i	−0.169210	−	0.293081i
$695$	19.3505	−	2.91190i	0.734005	−	0.110455i
$696$	−1.87790	−	1.08421i	−0.0711816	−	0.0410967i
$697$		−	4.37079i		−	0.165555i
$698$	9.25368	−	16.0278i	0.350257	−	0.606663i
$699$	−3.48210	−	2.01039i	−0.131705	−	0.0760399i
$700$	4.75495	−	2.98457i	0.179720	−	0.112806i
$701$	−45.2722	−	12.1306i	−1.70991	−	0.458168i	−0.734505	−	0.678603i	$-0.762586\pi$
$701$	−45.2722	−	12.1306i	−1.70991	−	0.458168i	−0.975402	+	0.220435i	$0.929252\pi$
$702$	−15.3064	+	15.3064i	−0.577704	+	0.577704i
$703$	9.07091	+	29.5392i	0.342116	+	1.11409i
$704$		−	42.8703i		−	1.61573i
$705$	13.5352	−	10.7887i	0.509764	−	0.406324i
$706$	−16.4621	−	9.50440i	−0.619559	−	0.357703i
$707$	21.0447	+	78.5397i	0.791466	+	2.95379i
$708$	−1.69811	−	0.980401i	−0.0638187	−	0.0368457i
$709$	21.6799	+	21.6799i	0.814204	+	0.814204i	0.985261	−	0.171057i	$-0.0547181\pi$
$709$	21.6799	+	21.6799i	0.814204	+	0.814204i	−0.171057	+	0.985261i	$0.554718\pi$
$710$	−9.78923	−	3.84468i	−0.367383	−	0.144288i
$711$	4.32544	−	4.32544i	0.162217	−	0.162217i
$712$	−9.16604	+	34.2081i	−0.343512	+	1.28200i
$713$	19.9614	−	19.9614i	0.747560	−	0.747560i
$714$	29.2454			1.09448
$715$	20.3032	+	25.4719i	0.759297	+	0.952593i
$716$	1.45208	+	5.41924i	0.0542668	+	0.202526i
$717$		−	21.5399i		−	0.804421i
$718$	1.89562	+	3.28332i	0.0707440	+	0.122532i
$719$	4.69821	−	2.71251i	0.175214	−	0.101160i	−0.409828	−	0.912163i	$-0.634411\pi$
$719$	4.69821	−	2.71251i	0.175214	−	0.101160i	0.585042	+	0.811003i	$0.301078\pi$
$720$	−8.85466	+	7.05791i	−0.329994	+	0.263033i
$721$	−75.0976	+	20.1223i	−2.79678	+	0.749395i
$722$	−4.48602	+	7.77001i	−0.166952	+	0.289170i
$723$	13.0676	+	22.6337i	0.485989	+	0.841758i
$724$	−0.0438528	−	0.0759554i	−0.00162978	−	0.00282286i
$725$	2.95334	−	0.109098i	0.109684	−	0.00405180i
$726$	−14.8704	+	14.8704i	−0.551891	+	0.551891i
$727$	−22.1381	−	12.7814i	−0.821057	−	0.474037i	0.0297241	−	0.999558i	$-0.490537\pi$
$727$	−22.1381	−	12.7814i	−0.821057	−	0.474037i	−0.850781	+	0.525521i	$0.823870\pi$
$728$	9.82167	−	36.6550i	0.364015	−	1.35852i
$729$		−	23.8311i		−	0.882634i
$730$	−6.19721	+	8.39274i	−0.229369	+	0.310629i
$731$	−11.6012	+	6.69795i	−0.429085	+	0.247733i
$732$		−	0.562343i		−	0.0207848i
$733$	20.1942	−	5.41101i	0.745889	−	0.199860i	0.134195	−	0.990955i	$-0.457155\pi$
$733$	20.1942	−	5.41101i	0.745889	−	0.199860i	0.611694	+	0.791095i	$0.290489\pi$
$734$	24.4070	−	24.4070i	0.900878	−	0.900878i
$735$	12.4099	+	28.4622i	0.457745	+	1.04985i
$736$	4.84631	−	8.39406i	0.178637	−	0.309409i
$737$	56.4628	−	15.1291i	2.07983	−	0.557289i
$738$	−1.75886	+	1.01548i	−0.0647445	+	0.0373802i
$739$	23.1549			0.851767			0.425884	−	0.904778i	$-0.359963\pi$
$739$	23.1549			0.851767			0.425884	+	0.904778i	$0.359963\pi$
$740$	−2.71028	+	2.32533i	−0.0996320	+	0.0854809i
$741$	−18.5936			−0.683051
$742$	32.3869	−	18.6986i	1.18896	−	0.686448i
$743$	−24.2877	+	6.50787i	−0.891029	+	0.238750i	−0.675159	−	0.737672i	$-0.735925\pi$
$743$	−24.2877	+	6.50787i	−0.891029	+	0.238750i	−0.215869	+	0.976422i	$0.569259\pi$
$744$	−7.88098	+	13.6503i	−0.288931	+	0.500443i
$745$	34.7757	+	13.6580i	1.27408	+	0.500391i
$746$	32.0585	−	32.0585i	1.17374	−	1.17374i
$747$	−3.82137	+	1.02393i	−0.139817	+	0.0374638i
$748$		−	5.42146i		−	0.198228i
$749$	24.2590	−	14.0059i	0.886403	−	0.511765i
$750$	−5.99965	+	17.1068i	−0.219076	+	0.624652i
$751$		−	49.5019i		−	1.80635i	−0.429272	−	0.903175i	$-0.641230\pi$
$751$		−	49.5019i		−	1.80635i	0.429272	−	0.903175i	$-0.358770\pi$
$752$	5.54715	−	20.7022i	0.202284	−	0.754933i
$753$	−26.7513	−	15.4449i	−0.974871	−	0.562842i
$754$	1.63918	−	1.63918i	0.0596955	−	0.0596955i
$755$	−7.77428	+	6.19675i	−0.282935	+	0.225523i
$756$	3.09855	+	5.36685i	0.112693	+	0.195190i
$757$	17.8035	+	30.8365i	0.647078	+	1.12077i	0.983817	+	0.179174i	$0.0573425\pi$
$757$	17.8035	+	30.8365i	0.647078	+	1.12077i	−0.336740	+	0.941598i	$0.609324\pi$
$758$	−1.51994	+	2.63261i	−0.0552067	+	0.0956207i
$759$	−38.2229	+	10.2418i	−1.38740	+	0.371753i
$760$	−33.6631	−	3.80104i	−1.22109	−	0.137878i
$761$	9.14549	−	5.28015i	0.331524	−	0.191405i	−0.324994	−	0.945716i	$-0.605362\pi$
$761$	9.14549	−	5.28015i	0.331524	−	0.191405i	0.656517	+	0.754311i	$0.272029\pi$
$762$	−13.2018	−	22.8662i	−0.478251	−	0.828355i
$763$			29.6127i			1.07205i
$764$	−0.286848	−	1.07053i	−0.0103778	−	0.0387305i
$765$	−10.9648	+	8.73985i	−0.396432	+	0.315990i
$766$	−0.185247			−0.00669326
$767$	12.7732	−	12.7732i	0.461215	−	0.461215i
$768$	−1.97011	+	7.35254i	−0.0710901	+	0.265312i
$769$	−10.0805	+	10.0805i	−0.363511	+	0.363511i	−0.865104	−	0.501593i	$-0.832748\pi$
$769$	−10.0805	+	10.0805i	−0.363511	+	0.363511i	0.501593	+	0.865104i	$0.332748\pi$
$770$	−56.5674	+	24.6641i	−2.03855	+	0.888832i
$771$	4.59319	+	4.59319i	0.165420	+	0.165420i
$772$	1.81837	+	1.04984i	0.0654447	+	0.0377845i
$773$	−0.806988	−	3.01172i	−0.0290253	−	0.108324i	0.949893	−	0.312574i	$-0.101191\pi$
$773$	−0.806988	−	3.01172i	−0.0290253	−	0.108324i	−0.978919	+	0.204250i	$0.934525\pi$
$774$	5.39067	+	3.11230i	0.193764	+	0.111869i
$775$	−0.793022	−	21.4675i	−0.0284862	−	0.771135i
$776$			30.5896i			1.09810i
$777$	−16.9903	−	27.1157i	−0.609525	−	0.972771i
$778$	4.90864	−	4.90864i	0.175983	−	0.175983i
$779$	−5.08513	−	1.36256i	−0.182194	−	0.0488187i
$780$	−0.858824	−	1.96973i	−0.0307508	−	0.0705275i
$781$	−15.1293	−	8.73493i	−0.541370	−	0.312560i
$782$	−18.2638	+	31.6339i	−0.653113	+	1.13123i
$783$			3.26230i			0.116585i
$784$	33.2965	+	19.2237i	1.18916	+	0.686562i
$785$	−17.4100	−	12.8555i	−0.621389	−	0.458834i
$786$	−11.5468	−	19.9996i	−0.411861	−	0.713363i
$787$	14.6240	+	14.6240i	0.521288	+	0.521288i	0.917960	−	0.396673i	$-0.129835\pi$
$787$	14.6240	+	14.6240i	0.521288	+	0.521288i	−0.396673	+	0.917960i	$0.629835\pi$
$788$	−0.912581	−	0.912581i	−0.0325094	−	0.0325094i
$789$	−18.4294	+	10.6402i	−0.656105	+	0.378803i
$790$	−4.84663	−	11.1158i	−0.172435	−	0.395483i
$791$	4.69976	+	4.69976i	0.167104	+	0.167104i
$792$	−18.8005	+	10.8545i	−0.668046	+	0.385697i
$793$	5.00411	+	1.34085i	0.177701	+	0.0476149i
$794$	−1.45512	+	5.43057i	−0.0516401	+	0.192724i
$795$	6.67102	−	16.9856i	0.236597	−	0.602417i
$796$	0.767844	+	2.86563i	0.0272155	+	0.101570i
$797$	−8.17798	+	4.72156i	−0.289679	+	0.167246i	−0.637797	−	0.770204i	$-0.720154\pi$
$797$	−8.17798	+	4.72156i	−0.289679	+	0.167246i	0.348118	+	0.937451i	$0.386821\pi$
$798$	9.11703	−	34.0252i	0.322739	−	1.20448i
$799$	6.86907	−	25.6357i	0.243010	−	0.906926i
$800$	−2.17072	−	7.04921i	−0.0767464	−	0.249227i
$801$	17.0540	−	4.56961i	0.602574	−	0.161459i
$802$	12.5548	+	3.36405i	0.443325	+	0.118789i
$803$	−12.2540	+	12.2540i	−0.432434	+	0.432434i
$804$	−3.85613			−0.135995
$805$	−62.4337	−	7.04965i	−2.20050	−	0.248467i
$806$	−11.9151	−	11.9151i	−0.419690	−	0.419690i
$807$	−0.0550892	−	0.205596i	−0.00193923	−	0.00723731i
$808$	56.7040			1.99484
$809$	0.700060	+	2.61266i	0.0246128	+	0.0918562i	0.977140	−	0.212598i	$-0.0681925\pi$
$809$	0.700060	+	2.61266i	0.0246128	+	0.0918562i	−0.952527	+	0.304454i	$0.901526\pi$
$810$	−6.38952	−	2.50946i	−0.224505	−	0.0881733i
$811$	−6.24691	+	10.8200i	−0.219359	+	0.379940i	−0.954612	−	0.297852i	$-0.903730\pi$
$811$	−6.24691	+	10.8200i	−0.219359	+	0.379940i	0.735253	+	0.677792i	$0.237063\pi$
$812$	−0.331828	−	0.574742i	−0.0116449	−	0.0201695i
$813$	15.9596	+	15.9596i	0.559728	+	0.559728i
$814$	33.2640	−	20.8427i	1.16590	−	0.730537i
$815$	36.1890	−	5.44580i	1.26765	−	0.190758i
$816$	4.57353	−	17.0686i	0.160106	−	0.597522i
$817$	4.17606	+	15.5853i	0.146102	+	0.545260i
$818$	11.8068	−	3.16362i	0.412815	−	0.110614i
$819$	−18.2739	+	4.89646i	−0.638540	+	0.171096i
$820$	−0.0905352	−	0.601634i	−0.00316163	−	0.0210100i
$821$	−12.5053	+	21.6598i	−0.436438	+	0.755932i	−0.997412	−	0.0719010i	$-0.977093\pi$
$821$	−12.5053	+	21.6598i	−0.436438	+	0.755932i	0.560974	+	0.827833i	$0.310427\pi$
$822$	−16.8372			−0.587264
$823$	1.31661	+	0.352784i	0.0458940	+	0.0122973i	0.281693	−	0.959505i	$-0.409104\pi$
$823$	1.31661	+	0.352784i	0.0458940	+	0.0122973i	−0.235799	+	0.971802i	$0.575771\pi$
$824$			54.2188i			1.88880i
$825$	−14.0834	+	26.6164i	−0.490322	+	0.926666i
$826$	17.1112	+	29.6375i	0.595375	+	1.03122i
$827$	16.4986	−	28.5764i	0.573712	−	0.993698i	−0.422469	−	0.906378i	$-0.638836\pi$
$827$	16.4986	−	28.5764i	0.573712	−	0.993698i	0.996180	−	0.0873203i	$-0.0278304\pi$
$828$	−2.56488			−0.0891359
$829$	−37.2077	−	9.96978i	−1.29228	−	0.346265i	−0.453752	−	0.891128i	$-0.649915\pi$
$829$	−37.2077	−	9.96978i	−1.29228	−	0.346265i	−0.838525	+	0.544863i	$0.816582\pi$
$830$	−0.879957	+	7.79316i	−0.0305437	+	0.270504i
$831$	2.18484	+	0.585426i	0.0757912	+	0.0203082i
$832$	−22.5633	−	13.0269i	−0.782242	−	0.451628i
$833$	41.2312	+	23.8049i	1.42858	+	0.824790i
$834$	13.7062	+	3.67256i	0.474607	+	0.127171i
$835$	13.7393	+	17.2370i	0.475469	+	0.596511i
$836$	−6.30752	−	1.69010i	−0.218150	−	0.0584532i
$837$	23.7133			0.819652
$838$	22.2298	−	38.5032i	0.767917	−	1.33007i
$839$	21.2111	+	36.7387i	0.732288	+	1.26836i	0.955903	+	0.293683i	$0.0948810\pi$
$839$	21.2111	+	36.7387i	0.732288	+	1.26836i	−0.223614	+	0.974678i	$0.571786\pi$
$840$	34.6906	−	5.22033i	1.19694	−	0.180118i
$841$			28.6506i			0.987953i
$842$	−11.1274	−	2.98158i	−0.383476	−	0.102752i
$843$	−4.18027			−0.143976
$844$	2.12030	−	3.67247i	0.0729838	−	0.126412i
$845$	−9.16949	+	1.37985i	−0.315440	+	0.0474681i
$846$	−11.9120	+	3.19182i	−0.409544	+	0.109737i
$847$	−53.5751	+	14.3554i	−1.84086	+	0.493257i
$848$	−5.84834	−	21.8263i	−0.200833	−	0.749518i
$849$	−4.00368	+	14.9419i	−0.137406	+	0.512806i
$850$	8.18057	+	26.5657i	0.280591	+	0.911194i
$851$	39.9407	−	1.44409i	1.36915	−	0.0495028i
$852$	0.814907	+	0.814907i	0.0279183	+	0.0279183i
$853$	20.9962	+	36.3664i	0.718895	+	1.24516i	0.961438	+	0.275022i	$0.0886852\pi$
$853$	20.9962	+	36.3664i	0.718895	+	1.24516i	−0.242543	+	0.970141i	$0.577981\pi$
$854$	−4.90736	+	8.49979i	−0.167926	+	0.290857i
$855$	6.75007	+	15.4814i	0.230848	+	0.529452i
$856$	−5.05599	−	18.8692i	−0.172810	−	0.644936i
$857$	−26.5861			−0.908164			−0.454082	−	0.890960i	$-0.650033\pi$
$857$	−26.5861			−0.908164			−0.454082	+	0.890960i	$0.650033\pi$
$858$	6.11337	+	22.8154i	0.208707	+	0.778905i
$859$	8.37407	+	8.37407i	0.285720	+	0.285720i	0.835385	−	0.549665i	$-0.185245\pi$
$859$	8.37407	+	8.37407i	0.285720	+	0.285720i	−0.549665	+	0.835385i	$0.685245\pi$
$860$	−1.45815	+	1.16227i	−0.0497225	+	0.0396330i
$861$	5.45165			0.185792
$862$	−3.84874	+	3.84874i	−0.131089	+	0.131089i
$863$	−29.3868	−	7.87417i	−1.00034	−	0.268040i	−0.278751	−	0.960363i	$-0.589920\pi$
$863$	−29.3868	−	7.87417i	−1.00034	−	0.268040i	−0.721587	+	0.692324i	$0.756587\pi$
$864$	7.86451	−	2.10729i	0.267556	−	0.0716914i
$865$	−13.5721	−	10.0217i	−0.461467	−	0.340748i
$866$	1.16831	−	4.36021i	0.0397009	−	0.148166i
$867$	0.250979	−	0.936666i	0.00852369	−	0.0318109i
$868$	−4.17774	+	2.41202i	−0.141802	+	0.0818693i
$869$	−5.21341	−	19.4567i	−0.176853	−	0.660024i
$870$	1.99470	+	0.783412i	0.0676268	+	0.0265601i
$871$	9.19455	−	34.3145i	0.311545	−	1.16270i
$872$	19.9476	+	5.34494i	0.675510	+	0.181002i
$873$	13.2069	−	7.62502i	0.446986	−	0.258068i
$874$	31.1104	+	31.1104i	1.05233	+	1.05233i
$875$	−36.2628	+	31.1616i	−1.22591	+	1.05345i
$876$	0.990049	−	0.571605i	0.0334506	−	0.0193127i
$877$	29.7086	+	29.7086i	1.00319	+	1.00319i	0.999995	+	0.00319179i	$0.00101598\pi$
$877$	29.7086	+	29.7086i	1.00319	+	1.00319i	0.00319179	+	0.999995i	$0.498984\pi$
$878$	7.89932	+	7.89932i	0.266589	+	0.266589i
$879$	6.48398	+	11.2306i	0.218699	+	0.378798i
$880$	5.54855	+	36.8718i	0.187042	+	1.24295i
$881$	32.3408	+	18.6720i	1.08959	+	0.629074i	0.933467	−	0.358664i	$-0.116767\pi$
$881$	32.3408	+	18.6720i	1.08959	+	0.629074i	0.156122	+	0.987738i	$0.450101\pi$
$882$		−	22.1226i		−	0.744906i
$883$	22.4292	−	38.8484i	0.754801	−	1.30735i	−0.190672	−	0.981654i	$-0.561067\pi$
$883$	22.4292	−	38.8484i	0.754801	−	1.30735i	0.945473	−	0.325700i	$-0.105600\pi$
$884$	−2.85340	−	1.64741i	−0.0959703	−	0.0554085i
$885$	15.5436	+	6.10469i	0.522493	+	0.205207i
$886$	39.4530	+	10.5714i	1.32545	+	0.355153i
$887$	−24.0980	+	24.0980i	−0.809132	+	0.809132i	−0.984503	−	0.175370i	$-0.943888\pi$
$887$	−24.0980	+	24.0980i	−0.809132	+	0.809132i	0.175370	+	0.984503i	$0.443888\pi$
$888$	−21.3322	+	6.55070i	−0.715863	+	0.219827i
$889$		−	69.6379i		−	2.33558i
$890$	3.92707	−	34.7793i	0.131636	−	1.16580i
$891$	−9.87506	−	5.70137i	−0.330827	−	0.191003i
$892$	−0.227919	−	0.850605i	−0.00763129	−	0.0284804i
$893$	−27.6841	−	15.9834i	−0.926414	−	0.534865i
$894$	19.1571	+	19.1571i	0.640710	+	0.640710i
$895$	−19.0971	−	43.7995i	−0.638347	−	1.46406i
$896$	25.9805	−	25.9805i	0.867947	−	0.867947i
$897$	−6.22431	+	23.2295i	−0.207824	+	0.775609i
$898$	−23.8577	+	23.8577i	−0.796143	+	0.796143i
$899$	−2.53949			−0.0846966
$900$	−1.32825	+	1.43015i	−0.0442751	+	0.0476717i
$901$	−7.24203	−	27.0276i	−0.241267	−	0.900421i
$902$			6.68775i			0.222678i
$903$	−8.35429	−	14.4701i	−0.278013	−	0.481533i
$904$	4.01411	−	2.31755i	0.133507	−	0.0770804i
$905$	0.465581	+	0.584106i	0.0154764	+	0.0194163i
$906$	−6.96350	+	1.86586i	−0.231347	+	0.0619892i
$907$	3.65102	−	6.32376i	0.121230	−	0.209977i	−0.799023	−	0.601301i	$-0.794649\pi$
$907$	3.65102	−	6.32376i	0.121230	−	0.209977i	0.920253	+	0.391324i	$0.127983\pi$
$908$	−0.564627	−	0.977963i	−0.0187378	−	0.0324548i
$909$	−14.1345	−	24.4817i	−0.468812	−	0.812007i
$910$	−4.20797	+	37.2670i	−0.139493	+	1.23539i
$911$	38.5071	−	38.5071i	1.27580	−	1.27580i	0.332797	−	0.942998i	$-0.392008\pi$
$911$	38.5071	−	38.5071i	1.27580	−	1.27580i	0.942998	−	0.332797i	$-0.107992\pi$
$912$	−18.4325	−	10.6420i	−0.610362	−	0.352392i
$913$	−3.37172	+	12.5834i	−0.111588	+	0.416451i
$914$			35.1449i			1.16249i
$915$	0.712676	+	4.73594i	0.0235603	+	0.156565i
$916$	1.67477	−	0.966931i	0.0553361	−	0.0319483i
$917$		−	60.9079i		−	2.01136i
$918$	−29.6382	+	7.94153i	−0.978206	+	0.262110i
$919$	−9.38503	+	9.38503i	−0.309583	+	0.309583i	−0.844748	−	0.535164i	$-0.820250\pi$
$919$	−9.38503	+	9.38503i	−0.309583	+	0.309583i	0.535164	+	0.844748i	$0.320250\pi$
$920$	−16.0177	+	40.7839i	−0.528088	+	1.34460i
$921$	−6.92756	+	11.9989i	−0.228271	+	0.395377i
$922$	−37.7169	+	10.1062i	−1.24214	+	0.332830i
$923$	−9.19467	+	5.30854i	−0.302646	+	0.174733i
$924$	6.76214			0.222458
$925$	19.8785	−	23.0183i	0.653602	−	0.756838i
$926$	−24.8172			−0.815544
$927$	23.4087	−	13.5150i	0.768844	−	0.443892i
$928$	−0.842219	+	0.225672i	−0.0276472	+	0.00740805i
$929$	3.03772	−	5.26148i	0.0996643	−	0.172624i	−0.811881	−	0.583822i	$-0.801556\pi$
$929$	3.03772	−	5.26148i	0.0996643	−	0.172624i	0.911546	+	0.411199i	$0.134890\pi$
$930$	5.69453	−	14.4993i	0.186731	−	0.475450i
$931$	40.5489	−	40.5489i	1.32894	−	1.32894i
$932$	−0.828939	+	0.222113i	−0.0271528	+	0.00727557i
$933$			0.850939i			0.0278585i
$934$	−25.2967	+	14.6051i	−0.827734	+	0.477892i
$935$	6.87080	+	45.6585i	0.224699	+	1.49319i
$936$			13.1933i			0.431237i
$937$	−8.90460	+	33.2324i	−0.290901	+	1.08566i	0.653518	+	0.756911i	$0.273292\pi$
$937$	−8.90460	+	33.2324i	−0.290901	+	1.08566i	−0.944419	+	0.328745i	$0.893374\pi$
$938$	58.2853	+	33.6511i	1.90308	+	1.09875i
$939$	20.2234	−	20.2234i	0.659966	−	0.659966i
$940$	0.414508	−	3.67101i	0.0135198	−	0.119735i
$941$	−27.4941	−	47.6211i	−0.896281	−	1.55240i	−0.832211	−	0.554459i	$-0.812925\pi$
$941$	−27.4941	−	47.6211i	−0.896281	−	1.55240i	−0.0640700	−	0.997945i	$-0.520408\pi$
$942$	−7.84666	−	13.5908i	−0.255658	−	0.442813i
$943$	−3.40456	+	5.89688i	−0.110868	+	0.192029i
$944$	19.9734	−	5.35185i	0.650078	−	0.174188i
$945$	−32.8970	−	41.2717i	−1.07014	−	1.34257i
$946$	17.7510	−	10.2485i	0.577135	−	0.333209i
$947$	19.3878	+	33.5806i	0.630018	+	1.09122i	0.987548	+	0.157321i	$0.0502856\pi$
$947$	19.3878	+	33.5806i	0.630018	+	1.09122i	−0.357530	+	0.933902i	$0.616381\pi$
$948$			1.32880i			0.0431574i
$949$	2.72587	+	10.1731i	0.0884853	+	0.330232i
$950$	33.4577	−	1.23595i	1.08551	−	0.0400994i
$951$	39.9844			1.29658
$952$	38.0359	−	38.0359i	1.23275	−	1.23275i
$953$	−10.5419	+	39.3428i	−0.341485	+	1.27444i	0.555181	+	0.831729i	$0.312649\pi$
$953$	−10.5419	+	39.3428i	−0.341485	+	1.27444i	−0.896666	+	0.442708i	$0.854018\pi$
$954$	−9.19368	+	9.19368i	−0.297656	+	0.297656i
$955$	3.77250	+	8.65228i	0.122075	+	0.279981i
$956$	−3.25085	−	3.25085i	−0.105140	−	0.105140i
$957$	3.08283	+	1.77987i	0.0996538	+	0.0575352i
$958$	2.12444	+	7.92852i	0.0686375	+	0.256159i
$959$	−38.4576	−	22.2035i	−1.24186	−	0.716988i
$960$	2.70243	−	23.9335i	0.0872206	−	0.772452i
$961$		−	12.5407i		−	0.404540i
$962$	−0.861985	−	23.8408i	−0.0277915	−	0.768658i
$963$	−6.88639	+	6.88639i	−0.221911	+	0.221911i
$964$	5.38813	+	1.44374i	0.173540	+	0.0464999i
$965$	−16.6445	−	6.53706i	−0.535805	−	0.210435i
$966$	−39.4567	−	22.7803i	−1.26950	−	0.732945i
$967$	−23.0800	+	39.9757i	−0.742202	+	1.28553i	0.209288	+	0.977854i	$0.432885\pi$
$967$	−23.0800	+	39.9757i	−0.742202	+	1.28553i	−0.951491	+	0.307678i	$0.900448\pi$
$968$			38.6800i			1.24322i
$969$	−22.8251	−	13.1781i	−0.733247	−	0.423341i
$970$	−4.49866	−	29.8949i	−0.144443	−	0.959868i
$971$	−2.87600	−	4.98139i	−0.0922954	−	0.159860i	0.816181	−	0.577796i	$-0.196087\pi$
$971$	−2.87600	−	4.98139i	−0.0922954	−	0.159860i	−0.908477	+	0.417936i	$0.862754\pi$
$972$	−2.54213	−	2.54213i	−0.0815390	−	0.0815390i
$973$	26.4631	+	26.4631i	0.848368	+	0.848368i
$974$	−14.9977	+	8.65893i	−0.480557	+	0.277450i
$975$	9.72915	+	15.5002i	0.311582	+	0.496405i
$976$	4.19334	+	4.19334i	0.134225	+	0.134225i
$977$	41.8050	−	24.1361i	1.33746	−	0.772184i	0.351031	−	0.936364i	$-0.385831\pi$
$977$	41.8050	−	24.1361i	1.33746	−	0.772184i	0.986430	+	0.164180i	$0.0524979\pi$
$978$	25.6332	+	6.86838i	0.819658	+	0.219627i
$979$	15.0473	−	56.1574i	0.480915	−	1.79480i
$980$	6.16852	+	2.42266i	0.197046	+	0.0773890i
$981$	−2.66465	−	9.94460i	−0.0850757	−	0.317507i
$982$	2.17558	−	1.25607i	0.0694257	−	0.0400829i
$983$	−7.98131	+	29.7867i	−0.254564	+	0.950047i	0.713768	+	0.700382i	$0.246987\pi$
$983$	−7.98131	+	29.7867i	−0.254564	+	0.950047i	−0.968332	+	0.249665i	$0.919680\pi$
$984$	0.983993	−	3.67231i	0.0313685	−	0.117069i
$985$	8.84213	+	6.52904i	0.281734	+	0.208033i
$986$	3.17399	−	0.850468i	0.101080	−	0.0270844i
$987$	31.9752	+	8.56773i	1.01778	+	0.272714i
$988$	−2.80618	+	2.80618i	−0.0892766	+	0.0892766i
$989$	20.8691			0.663598
$990$	16.7772	−	13.3729i	0.533215	−	0.425017i
$991$	−18.7066	−	18.7066i	−0.594235	−	0.594235i	0.344537	−	0.938773i	$-0.388036\pi$
$991$	−18.7066	−	18.7066i	−0.594235	−	0.594235i	−0.938773	+	0.344537i	$0.888036\pi$
$992$	1.64039	+	6.12200i	0.0520823	+	0.194374i
$993$	−26.1794			−0.830778
$994$	−5.20590	−	19.4287i	−0.165121	−	0.616241i
$995$	−10.0984	−	23.1607i	−0.320139	−	0.734244i
$996$	0.429694	−	0.744252i	0.0136154	−	0.0235825i
$997$	16.0200	+	27.7475i	0.507359	+	0.878771i	0.999964	+	0.00851805i	$0.00271141\pi$
$997$	16.0200	+	27.7475i	0.507359	+	0.878771i	−0.492605	+	0.870253i	$0.663955\pi$
$998$	18.4125	+	18.4125i	0.582836	+	0.582836i
$999$	24.5817	+	22.8662i	0.777731	+	0.723455i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	185.2.u.a.177.5	yes	68
5.2	odd	4		925.2.t.b.843.5		68
5.3	odd	4		185.2.p.a.103.13	yes	68
5.4	even	2		925.2.y.b.732.13		68
37.23	odd	12		185.2.p.a.97.13	✓	68
185.23	even	12	inner	185.2.u.a.23.5	yes	68
185.97	even	12		925.2.y.b.393.13		68
185.134	odd	12		925.2.t.b.282.5		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.p.a.97.13	✓	68	37.23	odd	12
185.2.p.a.103.13	yes	68	5.3	odd	4
185.2.u.a.23.5	yes	68	185.23	even	12	inner
185.2.u.a.177.5	yes	68	1.1	even	1	trivial
925.2.t.b.282.5		68	185.134	odd	12
925.2.t.b.843.5		68	5.2	odd	4
925.2.y.b.393.13		68	185.97	even	12
925.2.y.b.732.13		68	5.4	even	2

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:	\( N \)	\(=\)	\( 185 = 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	185.u (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.14153 + 0.659061i) q^{2} +(-1.18821 + 0.318379i) q^{3} +(-0.131277 + 0.227378i) q^{4} +(0.817423 - 2.08130i) q^{5} +(1.14654 - 1.14654i) q^{6} +(4.13076 - 1.10683i) q^{7} -2.98232i q^{8} +(-1.28760 + 0.743399i) q^{9} +(0.438595 + 2.91460i) q^{10} +4.89589i q^{11} +(0.0835914 - 0.311968i) q^{12} +(2.57679 + 1.48771i) q^{13} +(-3.98591 + 3.98591i) q^{14} +(-0.308624 + 2.73327i) q^{15} +(1.70298 + 2.94965i) q^{16} +(2.10881 + 3.65256i) q^{17} +(0.979891 - 1.69722i) q^{18} +(4.90693 - 1.31481i) q^{19} +(0.365933 + 0.459090i) q^{20} +(-4.55581 + 2.63030i) q^{21} +(-3.22669 - 5.58880i) q^{22} -6.57051i q^{23} +(0.949509 + 3.54362i) q^{24} +(-3.66364 - 3.40261i) q^{25} -3.92197 q^{26} +(3.90274 - 3.90274i) q^{27} +(-0.290603 + 1.08454i) q^{28} +(-0.417950 + 0.417950i) q^{29} +(-1.44909 - 3.32351i) q^{30} +(3.03803 + 3.03803i) q^{31} +(1.27754 + 0.737586i) q^{32} +(-1.55875 - 5.81734i) q^{33} +(-4.81453 - 2.77967i) q^{34} +(1.07292 - 9.50212i) q^{35} -0.390363i q^{36} +(0.219784 + 6.07879i) q^{37} +(-4.73486 + 4.73486i) q^{38} +(-3.53541 - 0.947311i) q^{39} +(-6.20711 - 2.43782i) q^{40} +(-0.897477 - 0.518158i) q^{41} +(3.46706 - 6.00512i) q^{42} +3.17618i q^{43} +(-1.11322 - 0.642716i) q^{44} +(0.494720 + 3.28757i) q^{45} +(4.33037 + 7.50041i) q^{46} +(-4.44958 - 4.44958i) q^{47} +(-2.96260 - 2.96260i) q^{48} +(9.77595 - 5.64415i) q^{49} +(6.42467 + 1.46961i) q^{50} +(-3.66860 - 3.66860i) q^{51} +(-0.676543 + 0.390602i) q^{52} +(-6.40827 - 1.71709i) q^{53} +(-1.88294 + 7.02724i) q^{54} +(10.1898 + 4.00202i) q^{55} +(-3.30094 - 12.3193i) q^{56} +(-5.41184 + 3.12453i) q^{57} +(0.201647 - 0.752555i) q^{58} +(1.57132 - 5.86425i) q^{59} +(-0.580969 - 0.428988i) q^{60} +(1.68182 - 0.450642i) q^{61} +(-5.47024 - 1.46575i) q^{62} +(-4.49597 + 4.49597i) q^{63} -8.75638 q^{64} +(5.20270 - 4.14699i) q^{65} +(5.61334 + 5.61334i) q^{66} +(-3.09017 - 11.5327i) q^{67} -1.10735 q^{68} +(2.09191 + 7.80712i) q^{69} +(5.03771 + 11.5541i) q^{70} +(-1.78413 + 3.09021i) q^{71} +(2.21705 + 3.84005i) q^{72} +(2.50291 + 2.50291i) q^{73} +(-4.25718 - 6.79426i) q^{74} +(5.43648 + 2.87658i) q^{75} +(-0.345207 + 1.28833i) q^{76} +(5.41895 + 20.2238i) q^{77} +(4.66011 - 1.24867i) q^{78} +(-3.97409 + 1.06485i) q^{79} +(7.53116 - 1.13331i) q^{80} +(-1.16452 + 2.01701i) q^{81} +1.36599 q^{82} +(2.57020 + 0.688684i) q^{83} -1.38119i q^{84} +(9.32588 - 1.40338i) q^{85} +(-2.09329 - 3.62569i) q^{86} +(0.363544 - 0.629677i) q^{87} +14.6011 q^{88} +(-11.4703 - 3.07346i) q^{89} +(-2.73144 - 3.42680i) q^{90} +(12.2907 + 3.29330i) q^{91} +(1.49399 + 0.862553i) q^{92} +(-4.57706 - 2.64257i) q^{93} +(8.01187 + 2.14677i) q^{94} +(1.27452 - 11.2876i) q^{95} +(-1.75281 - 0.469664i) q^{96} -10.2570 q^{97} +(-7.43968 + 12.8859i) q^{98} +(-3.63960 - 6.30397i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 6 q^{2} - 4 q^{3} + 30 q^{4} - 8 q^{6} - 2 q^{7} - 6 q^{10} - 10 q^{12} - 6 q^{13} - 16 q^{15} - 26 q^{16} - 10 q^{17} - 8 q^{18} - 4 q^{19} - 28 q^{20} - 12 q^{21} - 14 q^{22} + 20 q^{25} - 24 q^{26}+ \cdots - 32 q^{99}+O(q^{100}) \) 68 * q - 6 * q^2 - 4 * q^3 + 30 * q^4 - 8 * q^6 - 2 * q^7 - 6 * q^10 - 10 * q^12 - 6 * q^13 - 16 * q^15 - 26 * q^16 - 10 * q^17 - 8 * q^18 - 4 * q^19 - 28 * q^20 - 12 * q^21 - 14 * q^22 + 20 * q^25 - 24 * q^26 + 68 * q^27 + 14 * q^28 - 14 * q^29 + 26 * q^30 - 24 * q^31 + 18 * q^32 + 10 * q^33 - 22 * q^35 - 18 * q^37 - 36 * q^38 - 52 * q^39 + 84 * q^40 - 18 * q^41 - 40 * q^42 + 36 * q^44 - 66 * q^45 - 52 * q^46 - 24 * q^47 + 60 * q^48 + 36 * q^49 - 12 * q^50 - 8 * q^51 - 78 * q^52 - 38 * q^53 - 40 * q^54 + 6 * q^55 + 16 * q^56 + 90 * q^57 + 16 * q^58 + 8 * q^59 - 52 * q^60 + 4 * q^61 - 22 * q^62 - 48 * q^63 + 20 * q^64 - 20 * q^65 + 80 * q^66 - 56 * q^67 - 20 * q^68 - 8 * q^69 + 62 * q^70 + 4 * q^71 + 32 * q^72 + 60 * q^73 + 44 * q^74 + 64 * q^75 + 72 * q^76 + 6 * q^77 - 24 * q^78 - 56 * q^79 - 76 * q^80 - 6 * q^81 - 8 * q^82 + 12 * q^83 + 20 * q^85 - 4 * q^86 - 32 * q^87 - 36 * q^88 + 22 * q^89 - 74 * q^90 + 44 * q^91 + 156 * q^92 - 30 * q^93 + 20 * q^94 + 28 * q^95 - 8 * q^96 + 16 * q^97 + 48 * q^98 - 32 * q^99

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