LMFDB - Embedded newform 552.2.bb.a.133.32

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [552,2,Mod(13,552)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(552, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 11, 0, 14])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("552.13"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.bb (of order $22$, degree $10$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			133.32
Character	$\chi$	$=$	552.133
Dual form			552.2.bb.a.469.32

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.750277 - 1.19878i) q^{2} +(0.755750 + 0.654861i) q^{3} +(-0.874167 - 1.79884i) q^{4} +(4.14042 + 0.595303i) q^{5} +(1.35206 - 0.414653i) q^{6} +(-0.0911276 - 0.199542i) q^{7} +(-2.81229 - 0.301692i) q^{8} +(0.142315 + 0.989821i) q^{9} +(3.82011 - 4.51683i) q^{10} +(-1.00493 - 3.42246i) q^{11} +(0.517339 - 1.93193i) q^{12} +(-0.385957 - 0.176261i) q^{13} +(-0.307578 - 0.0404693i) q^{14} +(2.73928 + 3.16130i) q^{15} +(-2.47166 + 3.14498i) q^{16} +(1.76125 - 1.13188i) q^{17} +(1.29336 + 0.572036i) q^{18} +(-3.17850 + 4.94584i) q^{19} +(-2.54857 - 7.96836i) q^{20} +(0.0618023 - 0.210479i) q^{21} +(-4.85677 - 1.36311i) q^{22} +(4.45930 + 1.76485i) q^{23} +(-1.92782 - 2.06966i) q^{24} +(11.9912 + 3.52095i) q^{25} +(-0.500874 + 0.330435i) q^{26} +(-0.540641 + 0.841254i) q^{27} +(-0.279283 + 0.338357i) q^{28} +(-0.283534 - 0.441187i) q^{29} +(5.84494 - 0.911956i) q^{30} +(-3.25640 - 3.75808i) q^{31} +(1.91572 + 5.32260i) q^{32} +(1.48176 - 3.24461i) q^{33} +(-0.0354616 - 2.96058i) q^{34} +(-0.258519 - 0.880435i) q^{35} +(1.65613 - 1.12127i) q^{36} +(-3.88113 + 0.558022i) q^{37} +(3.54424 + 7.52109i) q^{38} +(-0.176261 - 0.385957i) q^{39} +(-11.4645 - 2.92330i) q^{40} +(-0.393302 + 2.73548i) q^{41} +(-0.205951 - 0.232006i) q^{42} +(-3.77564 - 3.27161i) q^{43} +(-5.27800 + 4.79951i) q^{44} +4.18300i q^{45} +(5.46138 - 4.02161i) q^{46} -12.1022 q^{47} +(-3.92748 + 0.758220i) q^{48} +(4.55251 - 5.25388i) q^{49} +(13.2176 - 11.7332i) q^{50} +(2.07229 + 0.297950i) q^{51} +(0.0203260 + 0.848357i) q^{52} +(-5.83907 + 2.66661i) q^{53} +(0.602851 + 1.27929i) q^{54} +(-2.12342 - 14.7687i) q^{55} +(0.196077 + 0.588662i) q^{56} +(-5.64099 + 1.65634i) q^{57} +(-0.741618 + 0.00888303i) q^{58} +(4.28842 + 1.95846i) q^{59} +(3.29209 - 7.69104i) q^{60} +(-1.70276 + 1.47545i) q^{61} +(-6.94833 + 1.08411i) q^{62} +(0.184542 - 0.118598i) q^{63} +(7.81796 + 1.69689i) q^{64} +(-1.49310 - 0.959555i) q^{65} +(-2.77786 - 4.21068i) q^{66} +(-1.22351 + 4.16688i) q^{67} +(-3.57570 - 2.17875i) q^{68} +(2.21438 + 4.25400i) q^{69} +(-1.24941 - 0.350662i) q^{70} +(1.36258 + 0.400090i) q^{71} +(-0.101609 - 2.82660i) q^{72} +(9.58497 + 6.15989i) q^{73} +(-2.24298 + 5.07131i) q^{74} +(6.75665 + 10.5136i) q^{75} +(11.6753 + 1.39412i) q^{76} +(-0.591348 + 0.512406i) q^{77} +(-0.594924 - 0.0782764i) q^{78} +(3.32782 - 7.28692i) q^{79} +(-12.1059 + 11.5501i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(2.98416 + 2.52385i) q^{82} +(1.57312 - 0.226180i) q^{83} +(-0.432645 + 0.0728216i) q^{84} +(7.96612 - 3.63800i) q^{85} +(-6.75473 + 2.07156i) q^{86} +(0.0746357 - 0.519102i) q^{87} +(1.79361 + 9.92814i) q^{88} +(-7.92669 + 9.14789i) q^{89} +(5.01451 + 3.13841i) q^{90} +0.0930768i q^{91} +(-0.723488 - 9.56434i) q^{92} -4.97265i q^{93} +(-9.08000 + 14.5079i) q^{94} +(-16.1046 + 18.5857i) q^{95} +(-2.03776 + 5.27708i) q^{96} +(-0.773454 + 5.37949i) q^{97} +(-2.88262 - 9.39935i) q^{98} +(3.24461 - 1.48176i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32}+ \cdots - 132 q^{98}+O(q^{100}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{6}{11}\right)$	$1$	$-1$	$1$

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 $

$2$	0.750277	−	1.19878i	0.530526	−	0.847668i
$2$	0.750277	−	1.19878i	0.530526	−	0.847668i
$3$	0.755750	+	0.654861i	0.436332	+	0.378084i
$3$	0.755750	+	0.654861i	0.436332	+	0.378084i
$4$	−0.874167	−	1.79884i	−0.437084	−	0.899421i
$5$	4.14042	+	0.595303i	1.85165	+	0.266228i	0.976168	−	0.217017i	$-0.0696327\pi$
$5$	4.14042	+	0.595303i	1.85165	+	0.266228i	0.875485	+	0.483245i	$0.160542\pi$
$6$	1.35206	−	0.414653i	0.551976	−	0.169282i
$7$	−0.0911276	−	0.199542i	−0.0344430	−	0.0754197i	0.891629	−	0.452768i	$-0.149563\pi$
$7$	−0.0911276	−	0.199542i	−0.0344430	−	0.0754197i	−0.926072	+	0.377348i	$0.876836\pi$
$8$	−2.81229	−	0.301692i	−0.994295	−	0.106664i
$9$	0.142315	+	0.989821i	0.0474383	+	0.329940i
$10$	3.82011	−	4.51683i	1.20802	−	1.42835i
$11$	−1.00493	−	3.42246i	−0.302997	−	1.03191i	−0.960458	−	0.278424i	$-0.910188\pi$
$11$	−1.00493	−	3.42246i	−0.302997	−	1.03191i	0.657462	−	0.753488i	$-0.271630\pi$
$12$	0.517339	−	1.93193i	0.149343	−	0.557701i
$13$	−0.385957	−	0.176261i	−0.107045	−	0.0488859i	0.361173	−	0.932499i	$-0.382377\pi$
$13$	−0.385957	−	0.176261i	−0.107045	−	0.0488859i	−0.468218	+	0.883613i	$0.655104\pi$
$14$	−0.307578	−	0.0404693i	−0.0822038	−	0.0108159i
$15$	2.73928	+	3.16130i	0.707280	+	0.816244i
$16$	−2.47166	+	3.14498i	−0.617916	+	0.786244i
$17$	1.76125	−	1.13188i	0.427165	−	0.274522i	−0.309344	−	0.950950i	$-0.600109\pi$
$17$	1.76125	−	1.13188i	0.427165	−	0.274522i	0.736509	+	0.676428i	$0.236473\pi$
$18$	1.29336	+	0.572036i	0.304847	+	0.134830i
$19$	−3.17850	+	4.94584i	−0.729198	+	1.13465i	0.256568	+	0.966526i	$0.417408\pi$
$19$	−3.17850	+	4.94584i	−0.729198	+	1.13465i	−0.985765	+	0.168127i	$0.946228\pi$
$20$	−2.54857	−	7.96836i	−0.569877	−	1.78178i
$21$	0.0618023	−	0.210479i	0.0134864	−	0.0459304i
$22$	−4.85677	−	1.36311i	−1.03547	−	0.290616i
$23$	4.45930	+	1.76485i	0.929827	+	0.367996i
$23$	4.45930	+	1.76485i	0.929827	+	0.367996i
$24$	−1.92782	−	2.06966i	−0.393515	−	0.422468i
$25$	11.9912	+	3.52095i	2.39825	+	0.704190i
$26$	−0.500874	+	0.330435i	−0.0982294	+	0.0648036i
$27$	−0.540641	+	0.841254i	−0.104046	+	0.161899i
$28$	−0.279283	+	0.338357i	−0.0527795	+	0.0639435i
$29$	−0.283534	−	0.441187i	−0.0526509	−	0.0819265i	0.813930	−	0.580963i	$-0.197324\pi$
$29$	−0.283534	−	0.441187i	−0.0526509	−	0.0819265i	−0.866581	+	0.499036i	$0.833687\pi$
$30$	5.84494	−	0.911956i	1.06713	−	0.166500i
$31$	−3.25640	−	3.75808i	−0.584866	−	0.674971i	0.383778	−	0.923426i	$-0.374623\pi$
$31$	−3.25640	−	3.75808i	−0.584866	−	0.674971i	−0.968644	+	0.248454i	$0.920077\pi$
$32$	1.91572	+	5.32260i	0.338654	+	0.940911i
$33$	1.48176	−	3.24461i	0.257942	−	0.564815i
$34$	−0.0354616	−	2.96058i	−0.00608161	−	0.507735i
$35$	−0.258519	−	0.880435i	−0.0436977	−	0.148821i
$36$	1.65613	−	1.12127i	0.276021	−	0.186879i
$37$	−3.88113	+	0.558022i	−0.638054	+	0.0917382i	−0.453747	−	0.891131i	$-0.649913\pi$
$37$	−3.88113	+	0.558022i	−0.638054	+	0.0917382i	−0.184307	+	0.982869i	$0.559004\pi$
$38$	3.54424	+	7.52109i	0.574952	+	1.22008i
$39$	−0.176261	−	0.385957i	−0.0282243	−	0.0618026i
$40$	−11.4645	−	2.92330i	−1.81269	−	0.462214i
$41$	−0.393302	+	2.73548i	−0.0614235	+	0.427210i	0.935787	+	0.352566i	$0.114691\pi$
$41$	−0.393302	+	2.73548i	−0.0614235	+	0.427210i	−0.997210	+	0.0746434i	$0.976218\pi$
$42$	−0.205951	−	0.232006i	−0.0317789	−	0.0357992i
$43$	−3.77564	−	3.27161i	−0.575779	−	0.498916i	0.317596	−	0.948226i	$-0.397124\pi$
$43$	−3.77564	−	3.27161i	−0.575779	−	0.498916i	−0.893376	+	0.449310i	$0.851670\pi$
$44$	−5.27800	+	4.79951i	−0.795688	+	0.723553i
$45$			4.18300i			0.623565i
$46$	5.46138	−	4.02161i	0.805237	−	0.592954i
$47$	−12.1022			−1.76529			−0.882643	−	0.470044i	$-0.844238\pi$
$47$	−12.1022			−1.76529			−0.882643	+	0.470044i	$0.844238\pi$
$48$	−3.92748	+	0.758220i	−0.566883	+	0.109440i
$49$	4.55251	−	5.25388i	0.650359	−	0.750554i
$50$	13.2176	−	11.7332i	1.86925	−	1.65933i
$51$	2.07229	+	0.297950i	0.290178	+	0.0417213i
$52$	0.0203260	+	0.848357i	0.00281871	+	0.117646i
$53$	−5.83907	+	2.66661i	−0.802058	+	0.366288i	−0.773894	−	0.633316i	$-0.781693\pi$
$53$	−5.83907	+	2.66661i	−0.802058	+	0.366288i	−0.0281644	+	0.999603i	$0.508966\pi$
$54$	0.602851	+	1.27929i	0.0820376	+	0.174089i
$55$	−2.12342	−	14.7687i	−0.286321	−	1.99141i
$56$	0.196077	+	0.588662i	0.0262019	+	0.0786632i
$57$	−5.64099	+	1.65634i	−0.747167	+	0.219388i
$58$	−0.741618	+	0.00888303i	−0.0973792	+	0.00116640i
$59$	4.28842	+	1.95846i	0.558305	+	0.254969i	0.674522	−	0.738254i	$-0.264350\pi$
$59$	4.28842	+	1.95846i	0.558305	+	0.254969i	−0.116217	+	0.993224i	$0.537077\pi$
$60$	3.29209	−	7.69104i	0.425007	−	0.992909i
$61$	−1.70276	+	1.47545i	−0.218016	+	0.188912i	−0.757021	−	0.653390i	$-0.773346\pi$
$61$	−1.70276	+	1.47545i	−0.218016	+	0.188912i	0.539005	+	0.842303i	$0.318801\pi$
$62$	−6.94833	+	1.08411i	−0.882439	+	0.137682i
$63$	0.184542	−	0.118598i	0.0232501	−	0.0149419i
$64$	7.81796	+	1.69689i	0.977245	+	0.212112i
$65$	−1.49310	−	0.959555i	−0.185196	−	0.119018i
$66$	−2.77786	−	4.21068i	−0.341930	−	0.518298i
$67$	−1.22351	+	4.16688i	−0.149475	+	0.509066i	−0.999854	−	0.0171057i	$-0.994555\pi$
$67$	−1.22351	+	4.16688i	−0.149475	+	0.509066i	0.850378	+	0.526171i	$0.176373\pi$
$68$	−3.57570	−	2.17875i	−0.433618	−	0.264212i
$69$	2.21438	+	4.25400i	0.266580	+	0.512121i
$70$	−1.24941	−	0.350662i	−0.149333	−	0.0419121i
$71$	1.36258	+	0.400090i	0.161709	+	0.0474819i	0.361585	−	0.932339i	$-0.382236\pi$
$71$	1.36258	+	0.400090i	0.161709	+	0.0474819i	−0.199876	+	0.979821i	$0.564054\pi$
$72$	−0.101609	−	2.82660i	−0.0119748	−	0.333118i
$73$	9.58497	+	6.15989i	1.12184	+	0.720960i	0.963841	−	0.266480i	$-0.0858605\pi$
$73$	9.58497	+	6.15989i	1.12184	+	0.720960i	0.157995	+	0.987440i	$0.449497\pi$
$74$	−2.24298	+	5.07131i	−0.260741	+	0.589527i
$75$	6.75665	+	10.5136i	0.780191	+	1.21400i
$76$	11.6753	+	1.39412i	1.33925	+	0.159917i
$77$	−0.591348	+	0.512406i	−0.0673903	+	0.0583940i
$78$	−0.594924	−	0.0782764i	−0.0673619	−	0.00886306i
$79$	3.32782	−	7.28692i	0.374409	−	0.819842i	−0.624827	−	0.780763i	$-0.714830\pi$
$79$	3.32782	−	7.28692i	0.374409	−	0.819842i	0.999236	−	0.0390788i	$-0.0124423\pi$
$80$	−12.1059	+	11.5501i	−1.35349	+	1.29135i
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$	2.98416	+	2.52385i	0.329546	+	0.278713i
$83$	1.57312	−	0.226180i	0.172672	−	0.0248265i	−0.0554365	−	0.998462i	$-0.517655\pi$
$83$	1.57312	−	0.226180i	0.172672	−	0.0248265i	0.228108	+	0.973636i	$0.426746\pi$
$84$	−0.432645	+	0.0728216i	−0.0472054	+	0.00794549i
$85$	7.96612	−	3.63800i	0.864047	−	0.394597i
$86$	−6.75473	+	2.07156i	−0.728381	+	0.223382i
$87$	0.0746357	−	0.519102i	0.00800178	−	0.0556536i
$88$	1.79361	+	9.92814i	0.191200	+	1.05834i
$89$	−7.92669	+	9.14789i	−0.840228	+	0.969674i	−0.999847	−	0.0175044i	$-0.994428\pi$
$89$	−7.92669	+	9.14789i	−0.840228	+	0.969674i	0.159619	+	0.987179i	$0.448973\pi$
$90$	5.01451	+	3.13841i	0.528576	+	0.330817i
$91$			0.0930768i			0.00975710i
$92$	−0.723488	−	9.56434i	−0.0754289	−	0.997151i
$93$		−	4.97265i		−	0.515640i
$94$	−9.08000	+	14.5079i	−0.936531	+	1.49638i
$95$	−16.1046	+	18.5857i	−1.65230	+	1.90685i
$96$	−2.03776	+	5.27708i	−0.207978	+	0.538589i
$97$	−0.773454	+	5.37949i	−0.0785324	+	0.546205i	0.912134	+	0.409893i	$0.134434\pi$
$97$	−0.773454	+	5.37949i	−0.0785324	+	0.546205i	−0.990666	+	0.136312i	$0.956475\pi$
$98$	−2.88262	−	9.39935i	−0.291189	−	0.949478i
$99$	3.24461	−	1.48176i	0.326096	−	0.148923i
$100$	−4.14873	−	24.6483i	−0.414873	−	2.46483i
$101$	−18.7060	+	2.68952i	−1.86132	+	0.267618i	−0.979124	−	0.203262i	$-0.934846\pi$
$101$	−18.7060	+	2.68952i	−1.86132	+	0.267618i	−0.882197	+	0.470880i	$0.843936\pi$
$102$	1.91197	−	2.26068i	0.189313	−	0.223841i
$103$	8.50963	−	2.49865i	0.838479	−	0.246200i	0.165823	−	0.986155i	$-0.446972\pi$
$103$	8.50963	−	2.49865i	0.838479	−	0.246200i	0.672655	+	0.739956i	$0.265154\pi$
$104$	1.03225	+	0.612137i	0.101220	+	0.0600250i
$105$	0.381187	−	0.834683i	0.0372000	−	0.0814567i
$106$	−1.18423	+	9.00049i	−0.115022	+	0.874204i
$107$	−10.7233	+	9.29181i	−1.03666	+	0.898273i	−0.994901	−	0.100855i	$-0.967842\pi$
$107$	−10.7233	+	9.29181i	−1.03666	+	0.898273i	−0.0417612	+	0.999128i	$0.513297\pi$
$108$	1.98589	+	0.237131i	0.191093	+	0.0228179i
$109$	−10.3561	−	16.1144i	−0.991933	−	1.54348i	−0.830820	−	0.556541i	$-0.812128\pi$
$109$	−10.3561	−	16.1144i	−0.991933	−	1.54348i	−0.161113	−	0.986936i	$-0.551508\pi$
$110$	−19.2976	−	8.53509i	−1.83996	−	0.813789i
$111$	−3.29859	−	2.11987i	−0.313088	−	0.201209i
$112$	0.852791	+	0.206605i	0.0805811	+	0.0195224i
$113$	11.8372	+	3.47573i	1.11355	+	0.326969i	0.786224	−	0.617941i	$-0.212033\pi$
$113$	11.8372	+	3.47573i	1.11355	+	0.326969i	0.327329	+	0.944910i	$0.393851\pi$
$114$	−2.24671	+	8.00504i	−0.210423	+	0.749741i
$115$	17.4127	+	9.96185i	1.62375	+	0.928947i
$116$	−0.545770	+	0.895704i	−0.0506735	+	0.0831641i
$117$	0.119539	−	0.407113i	0.0110514	−	0.0376376i
$118$	5.56528	−	3.67151i	0.512325	−	0.337990i
$119$	−0.386356	−	0.248296i	−0.0354172	−	0.0227613i
$120$	−6.74992	−	9.71692i	−0.616180	−	0.887029i
$121$	−1.44960	+	0.931599i	−0.131781	+	0.0846908i
$122$	0.491205	+	3.14824i	0.0444716	+	0.285029i
$123$	−2.08860	+	1.80978i	−0.188322	+	0.163182i
$124$	−3.91356	+	9.14293i	−0.351448	+	0.821060i
$125$	28.5278	+	13.0282i	2.55161	+	1.16528i
$126$	−0.00371563	−	0.310207i	−0.000331015	−	0.0276354i
$127$	−19.3735	+	5.68859i	−1.71912	+	0.504780i	−0.984752	−	0.173966i	$-0.944342\pi$
$127$	−19.3735	+	5.68859i	−1.71912	+	0.504780i	−0.734373	+	0.678746i	$0.762524\pi$
$128$	7.89985	−	8.09891i	0.698255	−	0.715849i
$129$	−0.710988	−	4.94503i	−0.0625990	−	0.435386i
$130$	−2.27054	+	1.06997i	−0.199139	+	0.0938425i
$131$	−2.55262	+	1.16574i	−0.223023	+	0.101851i	−0.523793	−	0.851845i	$-0.675484\pi$
$131$	−2.55262	+	1.16574i	−0.223023	+	0.101851i	0.300770	+	0.953697i	$0.402756\pi$
$132$	−7.13186	+	0.170874i	−0.620748	+	0.0148727i
$133$	1.27655	+	0.183540i	0.110691	+	0.0159150i
$134$	4.07722	+	4.59304i	0.352218	+	0.396778i
$135$	−2.73928	+	3.16130i	−0.235760	+	0.272081i
$136$	−5.29462	+	2.65183i	−0.454010	+	0.227393i
$137$	21.0275			1.79650			0.898252	−	0.439482i	$-0.144838\pi$
$137$	21.0275			1.79650			0.898252	+	0.439482i	$0.144838\pi$
$138$	6.76103	+	0.537116i	0.575537	+	0.0457223i
$139$			18.2457i			1.54758i	0.633444	+	0.773789i	$0.281641\pi$
$139$			18.2457i			1.54758i	−0.633444	+	0.773789i	$0.718359\pi$
$140$	−1.35777	+	1.23468i	−0.114753	+	0.104350i
$141$	−9.14623	−	7.92525i	−0.770251	−	0.667426i
$142$	1.50194	−	1.33326i	0.126040	−	0.111885i
$143$	−0.215388	+	1.49805i	−0.0180116	+	0.125274i
$144$	−3.46472	−	1.99893i	−0.288727	−	0.166577i
$145$	−0.911310	−	1.99549i	−0.0756802	−	0.165717i
$146$	14.5758	−	6.86869i	1.20630	−	0.568457i
$147$	6.88112	−	0.989356i	0.567545	−	0.0816007i
$148$	4.39655	+	6.49373i	0.361394	+	0.533781i
$149$	3.33962	+	11.3737i	0.273592	+	0.931770i	0.975592	+	0.219593i	$0.0704728\pi$
$149$	3.33962	+	11.3737i	0.273592	+	0.931770i	−0.701999	+	0.712178i	$0.747709\pi$
$150$	17.6728	−	0.211684i	1.44298	−	0.0172839i
$151$	4.59862	−	10.0696i	0.374230	−	0.819450i	−0.625015	−	0.780612i	$-0.714907\pi$
$151$	4.59862	−	10.0696i	0.374230	−	0.819450i	0.999246	−	0.0388372i	$-0.0123654\pi$
$152$	10.4310	−	12.9502i	0.846065	−	1.05040i
$153$	1.37101	+	1.58224i	0.110840	+	0.127916i
$154$	0.170589	+	1.09334i	0.0137465	+	0.0881042i
$155$	−11.2457	−	17.4986i	−0.903273	−	1.40552i
$156$	−0.540195	+	0.654456i	−0.0432502	+	0.0523984i
$157$	4.96388	−	7.72394i	0.396160	−	0.616438i	−0.584677	−	0.811266i	$-0.698779\pi$
$157$	4.96388	−	7.72394i	0.396160	−	0.616438i	0.980837	+	0.194829i	$0.0624150\pi$
$158$	−6.23865	−	9.45655i	−0.496320	−	0.752323i
$159$	−6.15914	−	1.80849i	−0.488451	−	0.143422i
$160$	4.76332	+	23.1782i	0.376573	+	1.83240i
$161$	−0.0542043	−	1.05064i	−0.00427190	−	0.0828021i
$162$	−0.382149	+	1.36160i	−0.0300245	+	0.106978i
$163$	5.90544	−	20.1121i	0.462550	−	1.57530i	−0.316662	−	0.948538i	$-0.602562\pi$
$163$	5.90544	−	20.1121i	0.462550	−	1.57530i	0.779212	−	0.626761i	$-0.215620\pi$
$164$	5.26450	−	1.68378i	0.411089	−	0.131481i
$165$	8.06666	−	12.5520i	0.627989	−	0.977169i
$166$	0.909132	−	2.05552i	0.0705624	−	0.159540i
$167$	4.75697	−	3.05712i	0.368105	−	0.236567i	−0.343490	−	0.939156i	$-0.611609\pi$
$167$	4.75697	−	3.05712i	0.368105	−	0.236567i	0.711596	+	0.702589i	$0.247973\pi$
$168$	−0.237306	+	0.573284i	−0.0183086	+	0.0442298i
$169$	−8.39529	−	9.68869i	−0.645792	−	0.745284i
$170$	1.61562	−	12.2792i	0.123912	−	0.941769i
$171$	−5.34785	−	2.44228i	−0.408960	−	0.186766i
$172$	−2.58457	+	9.65171i	−0.197071	+	0.735936i
$173$	0.754096	+	2.56821i	0.0573329	+	0.195258i	0.983180	−	0.182641i	$-0.0584648\pi$
$173$	0.754096	+	2.56821i	0.0573329	+	0.195258i	−0.925847	+	0.377899i	$0.876647\pi$
$174$	−0.566294	−	0.478943i	−0.0429307	−	0.0363086i
$175$	−0.390158	−	2.71361i	−0.0294932	−	0.205130i
$176$	13.2474	+	5.29871i	0.998561	+	0.399405i
$177$	1.95846	+	4.28842i	0.147207	+	0.322338i
$178$	5.01913	+	16.3658i	0.376199	+	1.22667i
$179$	−10.8041	−	1.55340i	−0.807537	−	0.116106i	−0.273833	−	0.961777i	$-0.588291\pi$
$179$	−10.8041	−	1.55340i	−0.807537	−	0.116106i	−0.533704	+	0.845671i	$0.679201\pi$
$180$	7.52455	−	3.65664i	0.560847	−	0.272550i
$181$	4.85288	+	4.20505i	0.360712	+	0.312559i	0.816296	−	0.577634i	$-0.196024\pi$
$181$	4.85288	+	4.20505i	0.360712	+	0.312559i	−0.455584	+	0.890193i	$0.650569\pi$
$182$	0.111579	+	0.0698334i	0.00827078	+	0.00517640i
$183$	−2.25308			−0.166552
$184$	−12.0084	−	6.30860i	−0.885271	−	0.465076i
$185$	−16.4017			−1.20588
$186$	−5.96114	−	3.73087i	−0.437092	−	0.273561i
$187$	−5.64375	−	4.89034i	−0.412712	−	0.357617i
$188$	10.5793	+	21.7699i	0.771578	+	1.58773i
$189$	0.217132	+	0.0312189i	0.0157941	+	0.00227084i
$190$	10.1973	+	33.2504i	0.739792	+	2.41224i
$191$	−2.18215	−	4.77824i	−0.157895	−	0.345741i	0.814107	−	0.580715i	$-0.197227\pi$
$191$	−2.18215	−	4.77824i	−0.157895	−	0.345741i	−0.972002	+	0.234974i	$0.924500\pi$
$192$	4.79719	+	6.40210i	0.346208	+	0.462032i
$193$	−2.51780	−	17.5117i	−0.181236	−	1.26052i	−0.853847	−	0.520525i	$-0.825736\pi$
$193$	−2.51780	−	17.5117i	−0.181236	−	1.26052i	0.672611	−	0.739996i	$-0.265173\pi$
$194$	5.86854	+	4.96332i	0.421337	+	0.356345i
$195$	−0.500033	−	1.70295i	−0.0358081	−	0.121951i
$196$	−13.4306	−	3.59648i	−0.959325	−	0.256891i
$197$	3.66287	+	1.67278i	0.260969	+	0.119180i	0.541603	−	0.840634i	$-0.317818\pi$
$197$	3.66287	+	1.67278i	0.260969	+	0.119180i	−0.280634	+	0.959815i	$0.590545\pi$
$198$	0.658043	−	5.00133i	0.0467651	−	0.355429i
$199$	10.0474	+	11.5953i	0.712242	+	0.821971i	0.990351	−	0.138578i	$-0.0442533\pi$
$199$	10.0474	+	11.5953i	0.712242	+	0.821971i	−0.278110	+	0.960549i	$0.589708\pi$
$200$	−32.6606	−	13.5196i	−2.30946	−	0.955980i
$201$	−3.65339	+	2.34789i	−0.257690	+	0.165608i
$202$	−10.8106	+	24.4424i	−0.760629	+	1.71976i
$203$	−0.0621975	+	0.0967812i	−0.00436541	+	0.00679271i
$204$	−1.27556	−	3.98817i	−0.0893071	−	0.279228i
$205$	−3.25688	+	11.0919i	−0.227470	+	0.774692i
$206$	3.38924	−	12.0759i	0.236139	−	0.841367i
$207$	−1.11226	+	4.66507i	−0.0773074	+	0.324245i
$208$	1.50829	−	0.778170i	0.104581	−	0.0539564i
$209$	20.1211	+	5.90809i	1.39181	+	0.408671i
$210$	−0.714608	−	1.08320i	−0.0493127	−	0.0747482i
$211$	4.94464	−	7.69401i	0.340403	−	0.529677i	−0.628277	−	0.777990i	$-0.716240\pi$
$211$	4.94464	−	7.69401i	0.340403	−	0.529677i	0.968680	+	0.248312i	$0.0798760\pi$
$212$	9.90114	+	8.17250i	0.680013	+	0.561289i
$213$	0.767767	+	1.19467i	0.0526065	+	0.0818574i
$214$	3.09341	+	19.8264i	0.211461	+	1.35530i
$215$	−13.6851	−	15.7935i	−0.933318	−	1.07711i
$216$	1.77424	−	2.20274i	0.120722	−	0.149878i
$217$	−0.453146	+	0.992252i	−0.0307616	+	0.0673584i
$218$	−27.0876	+	0.324453i	−1.83460	+	0.0219747i
$219$	3.20997	+	10.9322i	0.216910	+	0.738726i
$220$	−24.7103	+	16.7300i	−1.66597	+	1.12794i
$221$	−0.879272	+	0.126420i	−0.0591463	+	0.00850395i
$222$	−5.01613	+	2.36380i	−0.336660	+	0.158648i
$223$	3.12298	+	6.83836i	0.209130	+	0.457931i	0.984909	−	0.173074i	$-0.0553701\pi$
$223$	3.12298	+	6.83836i	0.209130	+	0.457931i	−0.775779	+	0.631005i	$0.782643\pi$
$224$	0.887505	−	0.867301i	0.0592989	−	0.0579490i
$225$	−1.77858	+	12.3703i	−0.118572	+	0.824685i
$226$	13.0479	−	11.5825i	0.867931	−	0.770459i
$227$	3.16819	+	2.74525i	0.210280	+	0.182209i	0.753633	−	0.657296i	$-0.228300\pi$
$227$	3.16819	+	2.74525i	0.210280	+	0.182209i	−0.543352	+	0.839505i	$0.682845\pi$
$228$	7.91066	+	8.69932i	0.523897	+	0.576127i
$229$		−	4.56557i		−	0.301701i	−0.988557	−	0.150851i	$-0.951799\pi$
$229$		−	4.56557i		−	0.301701i	0.988557	−	0.150851i	$-0.0482013\pi$
$230$	25.0065	−	13.4000i	1.64888	−	0.883568i
$231$	−0.782465			−0.0514824
$232$	0.664277	+	1.32629i	0.0436119	+	0.0870750i
$233$	−8.04701	+	9.28674i	−0.527177	+	0.608395i	−0.955413	−	0.295272i	$-0.904590\pi$
$233$	−8.04701	+	9.28674i	−0.527177	+	0.608395i	0.428236	+	0.903667i	$0.359135\pi$
$234$	−0.398353	−	0.448750i	−0.0260412	−	0.0293357i
$235$	−50.1082	−	7.20447i	−3.26870	−	0.469968i
$236$	−0.225845	−	9.42622i	−0.0147013	−	0.613594i
$237$	7.28692	−	3.32782i	0.473336	−	0.216165i
$238$	−0.587528	+	0.276867i	−0.0380838	+	0.0179466i
$239$	−1.92636	−	13.3981i	−0.124606	−	0.866651i	−0.952233	−	0.305373i	$-0.901219\pi$
$239$	−1.92636	−	13.3981i	−0.124606	−	0.866651i	0.827627	−	0.561278i	$-0.189690\pi$
$240$	−16.7128	+	0.801312i	−1.07881	+	0.0517245i
$241$	23.0331	−	6.76314i	1.48369	−	0.435652i	0.563171	−	0.826340i	$-0.309581\pi$
$241$	23.0331	−	6.76314i	1.48369	−	0.435652i	0.920523	+	0.390688i	$0.127763\pi$
$242$	0.0291867	+	2.43671i	0.00187619	+	0.156638i
$243$	−0.909632	−	0.415415i	−0.0583529	−	0.0266489i
$244$	4.14261	+	1.77321i	0.265203	+	0.113518i
$245$	21.9770	−	19.0432i	1.40406	−	1.21662i
$246$	0.602507	+	3.86161i	0.0384145	+	0.246207i
$247$	2.09852	−	1.34864i	0.133526	−	0.0858118i
$248$	8.02415	+	11.5513i	0.509534	+	0.733505i
$249$	1.33700	+	0.859236i	0.0847288	+	0.0544519i
$250$	37.0218	−	24.4239i	2.34147	−	1.54471i
$251$	2.49452	−	8.49557i	0.157453	−	0.536236i	−0.842544	−	0.538627i	$-0.818943\pi$
$251$	2.49452	−	8.49557i	0.157453	−	0.536236i	0.999997	+	0.00239171i	$0.000761305\pi$
$252$	−0.374659	−	0.228287i	−0.0236013	−	0.0143807i
$253$	1.55887	−	17.0353i	0.0980051	−	1.07100i
$254$	−7.71615	+	27.4927i	−0.484154	+	1.72505i
$255$	8.40277	+	2.46728i	0.526202	+	0.154507i
$256$	−3.78177	−	15.5466i	−0.236360	−	0.971665i
$257$	−19.9982	−	12.8521i	−1.24746	−	0.801691i	−0.260939	−	0.965355i	$-0.584032\pi$
$257$	−19.9982	−	12.8521i	−1.24746	−	0.801691i	−0.986516	+	0.163664i	$0.947669\pi$
$258$	−6.46147	−	2.85783i	−0.402273	−	0.177920i
$259$	0.465027	+	0.723596i	0.0288953	+	0.0449620i
$260$	−0.420871	+	3.52466i	−0.0261013	+	0.218590i
$261$	0.396346	−	0.343436i	0.0245332	−	0.0212581i
$262$	−0.517699	+	3.93467i	−0.0319836	+	0.243085i
$263$	−6.38503	+	13.9813i	−0.393718	+	0.862121i	0.604151	+	0.796870i	$0.293512\pi$
$263$	−6.38503	+	13.9813i	−0.393718	+	0.862121i	−0.997869	+	0.0652516i	$0.979215\pi$
$264$	−5.14603	+	8.67776i	−0.316716	+	0.534079i
$265$	−25.7637	+	7.56489i	−1.58265	+	0.464708i
$266$	1.17779	−	1.39260i	0.0722151	−	0.0853859i
$267$	−11.9812	+	1.72263i	−0.733237	+	0.105424i
$268$	8.56511	−	1.44166i	0.523198	−	0.0880632i
$269$	−6.84613	+	3.12652i	−0.417416	+	0.190627i	−0.613041	−	0.790051i	$-0.710054\pi$
$269$	−6.84613	+	3.12652i	−0.417416	+	0.190627i	0.195625	+	0.980679i	$0.437327\pi$
$270$	1.73449	+	5.65566i	0.105558	+	0.344193i
$271$	−3.08485	+	21.4556i	−0.187391	+	1.30333i	0.651340	+	0.758786i	$0.274207\pi$
$271$	−3.08485	+	21.4556i	−0.187391	+	1.30333i	−0.838731	+	0.544547i	$0.816702\pi$
$272$	−0.793457	+	8.33671i	−0.0481104	+	0.505488i
$273$	−0.0609523	+	0.0703427i	−0.00368900	+	0.00425734i
$274$	15.7765	−	25.2075i	0.953092	−	1.52284i
$275$		−	44.5779i		−	2.68815i
$276$	5.71653	−	7.70203i	0.344095	−	0.463608i
$277$		−	27.3752i		−	1.64482i	−0.568896	−	0.822409i	$-0.692629\pi$
$277$		−	27.3752i		−	1.64482i	0.568896	−	0.822409i	$-0.307371\pi$
$278$	21.8726	+	13.6893i	1.31183	+	0.821031i
$279$	3.25640	−	3.75808i	0.194955	−	0.224990i
$280$	0.461410	+	2.55403i	0.0275745	+	0.152633i
$281$	4.01441	−	27.9208i	0.239479	−	1.66562i	−0.415216	−	0.909723i	$-0.636294\pi$
$281$	4.01441	−	27.9208i	0.239479	−	1.66562i	0.654695	−	0.755893i	$-0.272797\pi$
$282$	−16.3629	+	5.01821i	−0.974395	+	0.298830i
$283$	26.5348	−	12.1180i	1.57733	−	0.720342i	0.581670	−	0.813425i	$-0.302399\pi$
$283$	26.5348	−	12.1180i	1.57733	−	0.720342i	0.995658	+	0.0930829i	$0.0296722\pi$
$284$	−0.471426	−	2.80081i	−0.0279740	−	0.166198i
$285$	−24.3421	+	3.49986i	−1.44190	+	0.207314i
$286$	1.63424	+	1.38216i	0.0966348	+	0.0817288i
$287$	0.581682	−	0.170797i	0.0343356	−	0.0100819i
$288$	−4.99579	+	2.65370i	−0.294379	+	0.156371i
$289$	−5.24123	+	11.4767i	−0.308308	+	0.675100i
$290$	−3.07590	−	0.404708i	−0.180623	−	0.0237653i
$291$	−4.10736	+	3.55904i	−0.240777	+	0.208635i
$292$	2.70179	−	22.6266i	0.158110	−	1.32412i
$293$	−14.1643	−	22.0401i	−0.827486	−	1.28759i	−0.955253	−	0.295789i	$-0.904417\pi$
$293$	−14.1643	−	22.0401i	−0.827486	−	1.28759i	0.127767	−	0.991804i	$-0.459219\pi$
$294$	3.97672	−	8.99127i	0.231927	−	0.524381i
$295$	16.5900	+	10.6618i	0.965908	+	0.620751i
$296$	11.0832	−	0.398413i	0.644199	−	0.0231573i
$297$	3.42246	+	1.00493i	0.198592	+	0.0583117i
$298$	16.1403	+	4.52995i	0.934980	+	0.262413i
$299$	−1.41002	−	1.46715i	−0.0815438	−	0.0848477i
$300$	13.0058	−	21.3447i	0.750889	−	1.23234i
$301$	−0.308757	+	1.05153i	−0.0177965	+	0.0606092i
$302$	−8.62100	−	13.0677i	−0.496083	−	0.751963i
$303$	−15.8984	−	10.2173i	−0.913336	−	0.586966i
$304$	−7.69838	−	22.2208i	−0.441532	−	1.27445i
$305$	−7.92850	+	5.09534i	−0.453985	+	0.291758i
$306$	2.92540	−	0.456435i	0.167234	−	0.0260927i
$307$	−1.52762	+	1.32369i	−0.0871859	+	0.0755470i	−0.697363	−	0.716718i	$-0.745644\pi$
$307$	−1.52762	+	1.32369i	−0.0871859	+	0.0755470i	0.610177	+	0.792265i	$0.291098\pi$
$308$	1.43867	+	0.615813i	0.0819760	+	0.0350892i
$309$	8.06742	+	3.68427i	0.458939	+	0.209591i
$310$	−29.4144	+	0.352323i	−1.67063	+	0.0200106i
$311$	11.4572	−	3.36413i	0.649676	−	0.190762i	0.0597423	−	0.998214i	$-0.480972\pi$
$311$	11.4572	−	3.36413i	0.649676	−	0.190762i	0.589934	+	0.807452i	$0.299154\pi$
$312$	0.379256	+	1.13860i	0.0214712	+	0.0644606i
$313$	−2.68627	−	18.6834i	−0.151837	−	1.05605i	−0.913138	−	0.407652i	$-0.866348\pi$
$313$	−2.68627	−	18.6834i	−0.151837	−	1.05605i	0.761300	−	0.648399i	$-0.224561\pi$
$314$	−5.53506	−	11.7457i	−0.312361	−	0.662849i
$315$	0.834683	−	0.381187i	0.0470290	−	0.0214774i
$316$	−16.0171	+	0.383757i	−0.901031	+	0.0215880i
$317$	28.6864	+	4.12448i	1.61119	+	0.231654i	0.888284	−	0.459294i	$-0.151898\pi$
$317$	28.6864	+	4.12448i	1.61119	+	0.231654i	0.722905	+	0.690948i	$0.242807\pi$
$318$	−6.78904	+	6.02661i	−0.380711	+	0.337955i
$319$	−1.22502	+	1.41375i	−0.0685878	+	0.0791546i
$320$	31.3595	+	11.6799i	1.75305	+	0.652927i
$321$	−14.1890			−0.791952
$322$	−1.30016	−	0.723293i	−0.0724551	−	0.0403076i
$323$			12.3085i			0.684865i
$324$	1.34555	+	1.47969i	0.0747528	+	0.0822053i
$325$	−4.00750	−	3.47252i	−0.222296	−	0.192621i
$326$	−19.6793	−	22.1690i	−1.08994	−	1.22783i
$327$	2.72607	−	18.9602i	0.150752	−	1.04850i
$328$	1.93135	−	7.57430i	0.106641	−	0.418221i
$329$	1.10284	+	2.41489i	0.0608017	+	0.133137i
$330$	−8.99487	−	19.0876i	−0.495151	−	1.05074i
$331$	24.1538	−	3.47279i	1.32761	−	0.190882i	0.558239	−	0.829680i	$-0.311477\pi$
$331$	24.1538	−	3.47279i	1.32761	−	0.190882i	0.769374	+	0.638798i	$0.220568\pi$
$332$	−1.78203	−	2.63207i	−0.0978015	−	0.144453i
$333$	−1.10468	−	3.76221i	−0.0605363	−	0.206168i
$334$	−0.0957785	−	7.99627i	−0.00524077	−	0.437536i
$335$	−7.54639	+	16.5243i	−0.412304	+	0.902819i
$336$	0.509198	+	0.714601i	0.0277791	+	0.0389847i
$337$	1.23243	+	1.42230i	0.0671350	+	0.0774779i	0.788324	−	0.615261i	$-0.210949\pi$
$337$	1.23243	+	1.42230i	0.0671350	+	0.0774779i	−0.721189	+	0.692739i	$0.756404\pi$
$338$	−17.9134	+	2.79494i	−0.974363	+	0.152025i
$339$	6.66987	+	10.3785i	0.362258	+	0.563684i
$340$	−13.5079	−	11.1496i	−0.732569	−	0.604670i
$341$	−9.58946	+	14.9215i	−0.519299	+	0.808044i
$342$	−6.94014	+	4.57853i	−0.375280	+	0.247578i
$343$	−2.93658	−	0.862259i	−0.158561	−	0.0465576i
$344$	9.63117	+	10.3398i	0.519278	+	0.557484i
$345$	6.63605	+	18.9316i	0.357273	+	1.01924i
$346$	3.64452	+	1.02288i	0.195930	+	0.0549901i
$347$	3.07269	−	10.4646i	0.164951	−	0.561770i	−0.834983	−	0.550275i	$-0.814523\pi$
$347$	3.07269	−	10.4646i	0.164951	−	0.561770i	0.999934	−	0.0114949i	$-0.00365902\pi$
$348$	−0.999027	+	0.319525i	−0.0535535	+	0.0171283i
$349$	−16.6696	+	25.9385i	−0.892305	+	1.38845i	0.0289857	+	0.999580i	$0.490772\pi$
$349$	−16.6696	+	25.9385i	−0.892305	+	1.38845i	−0.921291	+	0.388874i	$0.872864\pi$
$350$	−3.54576	−	1.56824i	−0.189529	−	0.0838262i
$351$	0.356944	−	0.229394i	0.0190523	−	0.0122442i
$352$	16.2912	−	11.9053i	0.868326	−	0.634554i
$353$	8.96925	+	10.3511i	0.477385	+	0.550932i	0.942451	−	0.334344i	$-0.108515\pi$
$353$	8.96925	+	10.3511i	0.477385	+	0.550932i	−0.465066	+	0.885276i	$0.653969\pi$
$354$	6.61028	+	0.869740i	0.351333	+	0.0462262i
$355$	5.40349	+	2.46769i	0.286787	+	0.130971i
$356$	23.3849	+	6.26208i	1.23939	+	0.331889i
$357$	−0.129389	−	0.440659i	−0.00684800	−	0.0233222i
$358$	−9.96827	+	11.7863i	−0.526839	+	0.622926i
$359$	−1.88427	−	13.1054i	−0.0994478	−	0.691674i	−0.977163	−	0.212492i	$-0.931842\pi$
$359$	−1.88427	−	13.1054i	−0.0994478	−	0.691674i	0.877715	−	0.479183i	$-0.159067\pi$
$360$	1.26198	−	11.7638i	0.0665121	−	0.620007i
$361$	−6.46560	−	14.1577i	−0.340295	−	0.745141i
$362$	8.68195	−	2.66261i	0.456313	−	0.139944i
$363$	−1.70560	−	0.245228i	−0.0895208	−	0.0128711i
$364$	0.167430	−	0.0813647i	0.00877574	−	0.00426467i
$365$	36.0188	+	31.2105i	1.88531	+	1.63363i
$366$	−1.69043	+	2.70096i	−0.0883604	+	0.141181i
$367$	27.6525			1.44345			0.721725	−	0.692180i	$-0.243349\pi$
$367$	27.6525			1.44345			0.721725	+	0.692180i	$0.243349\pi$
$368$	−16.5723	+	9.66227i	−0.863890	+	0.503681i
$369$	−2.76361			−0.143868
$370$	−12.3058	+	19.6621i	−0.639750	+	1.02218i
$371$	1.06420	+	0.922136i	0.0552506	+	0.0478749i
$372$	−8.94502	+	4.34693i	−0.463778	+	0.225378i
$373$	−15.3936	−	2.21327i	−0.797051	−	0.114599i	−0.268256	−	0.963348i	$-0.586447\pi$
$373$	−15.3936	−	2.21327i	−0.797051	−	0.114599i	−0.528796	+	0.848749i	$0.677356\pi$
$374$	−10.0968	+	3.09653i	−0.522095	+	0.160118i
$375$	13.0282	+	28.5278i	0.672775	+	1.47317i
$376$	34.0349	+	3.65114i	1.75522	+	0.188293i
$377$	0.0316679	+	0.220255i	0.00163098	+	0.0113437i
$378$	0.200334	−	0.236872i	0.0103041	−	0.0121834i
$379$	6.59480	+	22.4598i	0.338752	+	1.15368i	0.936109	+	0.351709i	$0.114399\pi$
$379$	6.59480	+	22.4598i	0.338752	+	1.15368i	−0.597357	+	0.801975i	$0.703783\pi$
$380$	47.5108	+	12.7226i	2.43726	+	0.652656i
$381$	−18.3668	−	8.38783i	−0.940959	−	0.429721i
$382$	−7.36529	−	0.969080i	−0.376841	−	0.0495824i
$383$	−4.32831	−	4.99514i	−0.221167	−	0.255240i	0.634313	−	0.773076i	$-0.281283\pi$
$383$	−4.32831	−	4.99514i	−0.221167	−	0.255240i	−0.855480	+	0.517836i	$0.826738\pi$
$384$	11.2740	−	0.947445i	0.575322	−	0.0483491i
$385$	−2.75347	+	1.76954i	−0.140330	+	0.0901844i
$386$	−22.8818	−	10.1203i	−1.16465	−	0.515112i
$387$	2.70098	−	4.20280i	0.137298	−	0.213641i
$388$	10.3530	−	3.31125i	0.525593	−	0.168103i
$389$	−3.49589	+	11.9059i	−0.177249	+	0.603654i	0.822159	+	0.569257i	$0.192769\pi$
$389$	−3.49589	+	11.9059i	−0.177249	+	0.603654i	−0.999408	+	0.0343968i	$0.989049\pi$
$390$	−2.41664	−	0.678257i	−0.122371	−	0.0343449i
$391$	9.85152	−	1.93907i	0.498213	−	0.0980632i
$392$	−14.3880	+	13.4020i	−0.726706	+	0.676902i
$393$	−2.69254	−	0.790600i	−0.135821	−	0.0398805i
$394$	4.75347	−	3.13594i	0.239476	−	0.157987i
$395$	18.1165	−	28.1899i	0.911541	−	1.41839i
$396$	−5.50179	−	4.54123i	−0.276476	−	0.228206i
$397$	−20.1829	−	31.4053i	−1.01295	−	1.57619i	−0.800785	−	0.598952i	$-0.795584\pi$
$397$	−20.1829	−	31.4053i	−1.01295	−	1.57619i	−0.212168	−	0.977233i	$-0.568052\pi$
$398$	21.4386	−	3.34496i	1.07462	−	0.167668i
$399$	0.844559	+	0.974673i	0.0422808	+	0.0487947i
$400$	−40.7116	+	29.0096i	−2.03558	+	1.45048i
$401$	9.37783	−	20.5346i	0.468307	−	1.02545i	−0.517208	−	0.855860i	$-0.673029\pi$
$401$	9.37783	−	20.5346i	0.468307	−	1.02545i	0.985515	−	0.169589i	$-0.0542440\pi$
$402$	0.0735587	+	6.14120i	0.00366878	+	0.306295i
$403$	0.594427	+	2.02443i	0.0296105	+	0.100844i
$404$	21.1902	+	31.2981i	1.05425	+	1.55714i
$405$	−4.14042	+	0.595303i	−0.205739	+	0.0295808i
$406$	0.0693544	+	0.147174i	0.00344200	+	0.00730413i
$407$	5.81006	+	12.7223i	0.287994	+	0.630619i
$408$	−5.73799	−	1.46312i	−0.284073	−	0.0724350i
$409$	−0.122094	+	0.849182i	−0.00603716	+	0.0419893i	−0.992617	−	0.121288i	$-0.961297\pi$
$409$	−0.122094	+	0.849182i	−0.00603716	+	0.0419893i	0.986580	+	0.163277i	$0.0522066\pi$
$410$	10.8532	+	12.2263i	0.536003	+	0.603814i
$411$	15.8915	+	13.7701i	0.783872	+	0.679229i
$412$	−11.9335	−	13.1232i	−0.587922	−	0.646535i
$413$		−	1.03419i		−	0.0508891i
$414$	4.75791	+	4.83346i	0.233838	+	0.237551i
$415$	6.64801			0.326338
$416$	0.198780	−	2.39196i	0.00974601	−	0.117275i
$417$	−11.9484	+	13.7892i	−0.585114	+	0.675258i
$418$	22.1790	−	19.6882i	1.08481	−	0.962980i
$419$	27.6349	+	3.97330i	1.35005	+	0.194108i	0.779113	−	0.626883i	$-0.215670\pi$
$419$	27.6349	+	3.97330i	1.35005	+	0.194108i	0.570940	+	0.820992i	$0.306579\pi$
$420$	−1.83468	+	0.0439576i	−0.0895234	+	0.00214491i
$421$	−10.8951	+	4.97564i	−0.530996	+	0.242498i	−0.662825	−	0.748775i	$-0.730642\pi$
$421$	−10.8951	+	4.97564i	−0.530996	+	0.242498i	0.131828	+	0.991273i	$0.457915\pi$
$422$	−5.51360	−	11.7002i	−0.268398	−	0.569556i
$423$	−1.72232	−	11.9790i	−0.0837421	−	0.582439i
$424$	17.2257	−	5.73769i	0.836552	−	0.278647i
$425$	25.1048	−	7.37145i	1.21776	−	0.357568i
$426$	2.00819	−	0.0240539i	0.0972971	−	0.00116541i
$427$	0.449583	+	0.205318i	0.0217568	+	0.00993602i
$428$	26.0885	+	11.1670i	1.26103	+	0.539775i
$429$	−1.14380	+	0.991105i	−0.0552230	+	0.0478510i
$430$	−29.2006	+	4.55603i	−1.40818	+	0.219711i
$431$	31.9957	−	20.5624i	1.54118	−	0.990454i	0.553695	−	0.832720i	$-0.313217\pi$
$431$	31.9957	−	20.5624i	1.54118	−	0.990454i	0.987482	−	0.157734i	$-0.0504190\pi$
$432$	−1.30944	−	3.77960i	−0.0630005	−	0.181846i
$433$	−3.62917	−	2.33232i	−0.174407	−	0.112084i	0.450525	−	0.892764i	$-0.351237\pi$
$433$	−3.62917	−	2.33232i	−0.174407	−	0.112084i	−0.624932	+	0.780679i	$0.714873\pi$
$434$	0.849510	+	1.28769i	0.0407778	+	0.0618110i
$435$	0.618046	−	2.10487i	0.0296331	−	0.100921i
$436$	−19.9343	+	32.7156i	−0.954678	+	1.56679i
$437$	−22.9025	+	16.4454i	−1.09558	+	0.786690i
$438$	15.5137	+	4.35409i	0.741271	+	0.208046i
$439$	−18.0713	−	5.30621i	−0.862496	−	0.253252i	−0.179575	−	0.983744i	$-0.557472\pi$
$439$	−18.0713	−	5.30621i	−0.862496	−	0.253252i	−0.682921	+	0.730493i	$0.739291\pi$
$440$	1.51606	+	42.1745i	0.0722756	+	2.01059i
$441$	5.84829	+	3.75847i	0.278490	+	0.178975i
$442$	−0.508148	+	1.14891i	−0.0241701	+	0.0546480i
$443$	4.36640	+	6.79426i	0.207454	+	0.322805i	0.929352	−	0.369195i	$-0.120366\pi$
$443$	4.36640	+	6.79426i	0.207454	+	0.322805i	−0.721898	+	0.691999i	$0.756730\pi$
$444$	−0.929799	+	7.78676i	−0.0441263	+	0.369543i
$445$	−38.2656	+	33.1573i	−1.81396	+	1.57181i
$446$	10.5408	+	1.38690i	0.499122	+	0.0656714i
$447$	−4.92428	+	10.7827i	−0.232910	+	0.510002i
$448$	−0.373831	−	1.71464i	−0.0176619	−	0.0810093i
$449$	−35.4833	+	10.4188i	−1.67456	+	0.491696i	−0.974875	−	0.222754i	$-0.928495\pi$
$449$	−35.4833	+	10.4188i	−1.67456	+	0.491696i	−0.699687	+	0.714450i	$0.746677\pi$
$450$	13.4949	+	11.4133i	0.636154	+	0.538027i
$451$	9.75732	−	1.40289i	0.459454	−	0.0660595i
$452$	−4.09544	−	24.3317i	−0.192634	−	1.14447i
$453$	10.0696	−	4.59862i	0.473109	−	0.216062i
$454$	5.66799	−	1.73828i	0.266012	−	0.0815813i
$455$	−0.0554089	+	0.385377i	−0.00259761	+	0.0180668i
$456$	16.3638	−	2.95628i	0.766305	−	0.138440i
$457$	−6.07736	+	7.01364i	−0.284287	+	0.328084i	−0.879875	−	0.475206i	$-0.842374\pi$
$457$	−6.07736	+	7.01364i	−0.284287	+	0.328084i	0.595588	+	0.803290i	$0.296919\pi$
$458$	−5.47313	−	3.42544i	−0.255743	−	0.160060i
$459$			2.09360i			0.0977207i
$460$	2.69813	−	40.0311i	0.125801	−	1.86646i
$461$			7.94036i			0.369819i	0.982756	+	0.184910i	$0.0591993\pi$
$461$			7.94036i			0.369819i	−0.982756	+	0.184910i	$0.940801\pi$
$462$	−0.587066	+	0.938007i	−0.0273128	+	0.0436400i
$463$	18.2666	−	21.0808i	0.848923	−	0.979709i	−0.151038	−	0.988528i	$-0.548262\pi$
$463$	18.2666	−	21.0808i	0.848923	−	0.979709i	0.999961	+	0.00881848i	$0.00280705\pi$
$464$	2.08832	+	0.198759i	0.0969481	+	0.00922714i
$465$	2.96024	−	20.5889i	0.137278	−	0.954787i
$466$	5.09531	+	16.6143i	0.236036	+	0.769640i
$467$	−7.72357	+	3.52723i	−0.357404	+	0.163221i	−0.586022	−	0.810295i	$-0.699307\pi$
$467$	−7.72357	+	3.52723i	−0.357404	+	0.163221i	0.228618	+	0.973516i	$0.426579\pi$
$468$	−0.836830	+	0.140853i	−0.0386825	+	0.00651093i
$469$	0.942962	−	0.135577i	0.0435419	−	0.00626039i
$470$	−46.2316	+	54.6635i	−2.13251	+	2.52144i
$471$	8.80955	−	2.58672i	0.405923	−	0.119190i
$472$	−11.4694	−	6.80154i	−0.527924	−	0.313066i
$473$	−7.40273	+	16.2097i	−0.340378	+	0.745323i
$474$	1.47787	−	11.2322i	0.0678807	−	0.515914i
$475$	−55.5282	+	48.1155i	−2.54781	+	2.20769i
$476$	−0.108905	+	0.912046i	−0.00499167	+	0.0418036i
$477$	−3.47046	−	5.40014i	−0.158901	−	0.247255i
$478$	−17.5067	−	7.74301i	−0.800739	−	0.354157i
$479$	5.77870	+	3.71374i	0.264035	+	0.169685i	0.665960	−	0.745988i	$-0.268022\pi$
$479$	5.77870	+	3.71374i	0.264035	+	0.169685i	−0.401924	+	0.915673i	$0.631659\pi$
$480$	−11.5786	+	20.6362i	−0.528490	+	0.941911i
$481$	1.59631	+	0.468718i	0.0727853	+	0.0213717i
$482$	9.17370	−	32.6860i	0.417850	−	1.48881i
$483$	0.647059	−	0.829518i	0.0294422	−	0.0377444i
$484$	2.94299	+	1.79322i	0.133772	+	0.0815100i
$485$	−6.40485	+	21.8129i	−0.290829	+	0.990474i
$486$	−1.18047	+	0.778776i	−0.0535472	+	0.0353260i
$487$	7.42887	+	4.77424i	0.336634	+	0.216342i	0.698026	−	0.716072i	$-0.254062\pi$
$487$	7.42887	+	4.77424i	0.336634	+	0.216342i	−0.361392	+	0.932414i	$0.617698\pi$
$488$	5.23380	−	3.63569i	0.236923	−	0.164580i
$489$	17.6336	−	11.3325i	0.797421	−	0.512471i
$490$	−6.33981	−	40.6333i	−0.286403	−	1.83563i
$491$	−26.8461	+	23.2623i	−1.21155	+	1.04981i	−0.214217	+	0.976786i	$0.568720\pi$
$491$	−26.8461	+	23.2623i	−1.21155	+	1.04981i	−0.997330	+	0.0730250i	$0.976735\pi$
$492$	5.08129	+	2.17500i	0.229082	+	0.0980567i
$493$	−0.998746	−	0.456112i	−0.0449813	−	0.0205423i
$494$	−0.0422524	−	3.52753i	−0.00190103	−	0.158711i
$495$	14.3162	−	4.20361i	0.643464	−	0.188938i
$496$	19.8678	−	0.952582i	0.892090	−	0.0427722i
$497$	−0.0443342	−	0.308351i	−0.00198866	−	0.0138314i
$498$	2.03316	−	0.958106i	0.0911080	−	0.0429338i
$499$	37.8851	−	17.3016i	1.69597	−	0.774524i	0.697660	−	0.716429i	$-0.254225\pi$
$499$	37.8851	−	17.3016i	1.69597	−	0.774524i	0.998311	−	0.0580953i	$-0.0185027\pi$
$500$	−1.50239	−	62.7059i	−0.0671888	−	2.80429i
$501$	5.59706	+	0.804736i	0.250058	+	0.0359530i
$502$	−8.31277	−	9.36443i	−0.371017	−	0.417955i
$503$	10.8259	−	12.4937i	0.482702	−	0.557068i	−0.461199	−	0.887297i	$-0.652580\pi$
$503$	10.8259	−	12.4937i	0.482702	−	0.557068i	0.943901	+	0.330229i	$0.107126\pi$
$504$	−0.554765	+	0.277857i	−0.0247112	+	0.0123767i
$505$	−79.0520			−3.51777
$506$	−19.2521	−	14.6500i	−0.855860	−	0.651270i
$507$		−	12.8200i		−	0.569355i
$508$	27.1686	+	29.8772i	1.20541	+	1.32558i
$509$	−16.9672	−	14.7022i	−0.752059	−	0.651663i	0.192017	−	0.981392i	$-0.438497\pi$
$509$	−16.9672	−	14.7022i	−0.752059	−	0.651663i	−0.944076	+	0.329729i	$0.893043\pi$
$510$	9.26214	−	8.22197i	0.410135	−	0.364075i
$511$	0.355698	−	2.47394i	0.0157352	−	0.109441i
$512$	−21.4744	−	7.13078i	−0.949046	−	0.315139i
$513$	−2.44228	−	5.34785i	−0.107829	−	0.236113i
$514$	−30.4111	+	14.3309i	−1.34138	+	0.632110i
$515$	36.7209	−	5.27967i	1.61812	−	0.232650i
$516$	−8.27381	+	5.60174i	−0.364234	+	0.246603i
$517$	12.1618	+	41.4193i	0.534876	+	1.82162i
$518$	1.21633	−	0.0145691i	0.0534426	−	0.000640131i
$519$	−1.11192	+	2.43476i	−0.0488077	+	0.106874i
$520$	3.90953	+	3.14901i	0.171444	+	0.138093i
$521$	12.2814	+	14.1735i	0.538058	+	0.620952i	0.958059	−	0.286572i	$-0.0925158\pi$
$521$	12.2814	+	14.1735i	0.538058	+	0.620952i	−0.420001	+	0.907524i	$0.637970\pi$
$522$	−0.114336	−	0.732805i	−0.00500434	−	0.0320740i
$523$	3.46903	+	5.39792i	0.151690	+	0.236034i	0.908779	−	0.417277i	$-0.137016\pi$
$523$	3.46903	+	5.39792i	0.151690	+	0.236034i	−0.757089	+	0.653312i	$0.773379\pi$
$524$	4.32840	+	3.57270i	0.189087	+	0.156074i
$525$	1.48217	−	2.30631i	0.0646874	−	0.100656i
$526$	11.9700	+	18.1441i	0.521916	+	0.791120i
$527$	−9.98903	−	2.93304i	−0.435129	−	0.127765i
$528$	6.54181	+	12.6797i	0.284696	+	0.551813i
$529$	16.7706	+	15.7400i	0.729158	+	0.684346i
$530$	−10.2612	+	36.5608i	−0.445719	+	1.58810i
$531$	−1.32822	+	4.52349i	−0.0576397	+	0.196303i
$532$	−0.785759	−	2.45676i	−0.0340670	−	0.106514i
$533$	0.633955	−	0.986454i	0.0274597	−	0.0427281i
$534$	−6.92415	+	15.6553i	−0.299637	+	0.677472i
$535$	−49.9305	+	32.0884i	−2.15868	+	1.38730i
$536$	4.69798	−	11.3494i	0.202922	−	0.490218i
$537$	−7.14794	−	8.24916i	−0.308456	−	0.355978i
$538$	−1.38847	+	10.5528i	−0.0598612	+	0.454963i
$539$	−22.5562	−	10.3011i	−0.971562	−	0.443698i
$540$	8.08127	+	2.16403i	0.347762	+	0.0931250i
$541$	−5.12532	−	17.4552i	−0.220355	−	0.750459i	−0.993257	−	0.115934i	$-0.963014\pi$
$541$	−5.12532	−	17.4552i	−0.220355	−	0.750459i	0.772902	−	0.634525i	$-0.218804\pi$
$542$	23.4061	+	19.7957i	1.00538	+	0.850298i
$543$	0.913844	+	6.35593i	0.0392168	+	0.272759i
$544$	9.39861	+	7.20603i	0.402962	+	0.308956i
$545$	−33.2856	−	72.8853i	−1.42580	−	3.12206i
$546$	0.0385946	+	0.125845i	0.00165170	+	0.00538568i
$547$	−7.68198	−	1.10450i	−0.328458	−	0.0472251i	−0.0238867	−	0.999715i	$-0.507604\pi$
$547$	−7.68198	−	1.10450i	−0.328458	−	0.0472251i	−0.304571	+	0.952490i	$0.598513\pi$
$548$	−18.3816	−	37.8252i	−0.785222	−	1.61581i
$549$	−1.70276	−	1.47545i	−0.0726722	−	0.0629708i
$550$	−53.4393	−	33.4458i	−2.27866	−	1.42613i
$551$	3.08326			0.131351
$552$	−4.94408	−	12.6315i	−0.210434	−	0.537634i
$553$	−1.75730			−0.0747280
$554$	−32.8170	−	20.5390i	−1.39426	−	0.872620i
$555$	−12.3956	−	10.7408i	−0.526163	−	0.455923i
$556$	32.8211	−	15.9498i	1.39192	−	0.676421i
$557$	38.3557	+	5.51472i	1.62518	+	0.233666i	0.893854	−	0.448359i	$-0.147991\pi$
$557$	38.3557	+	5.51472i	1.62518	+	0.233666i	0.731329	+	0.682025i	$0.238900\pi$
$558$	−2.06193	−	6.72332i	−0.0872884	−	0.284621i
$559$	0.880578	+	1.92820i	0.0372445	+	0.0815541i
$560$	3.40792	+	1.36310i	0.144011	+	0.0576016i
$561$	−1.06277	−	7.39175i	−0.0448703	−	0.312080i
$562$	−30.4591	−	25.7608i	−1.28484	−	1.08665i
$563$	−0.807531	−	2.75020i	−0.0340334	−	0.115907i	0.940724	−	0.339172i	$-0.110147\pi$
$563$	−0.807531	−	2.75020i	−0.0340334	−	0.115907i	−0.974758	+	0.223265i	$0.928329\pi$
$564$	−6.26094	+	23.3806i	−0.263633	+	0.984501i
$565$	46.9421	+	21.4377i	1.97487	+	0.901892i
$566$	5.38155	−	40.9014i	0.226203	−	1.71921i
$567$	0.143654	+	0.165785i	0.00603289	+	0.00696232i
$568$	−3.71127	−	1.53625i	−0.155721	−	0.0644596i
$569$	10.1861	−	6.54621i	0.427023	−	0.274431i	−0.309426	−	0.950923i	$-0.600137\pi$
$569$	10.1861	−	6.54621i	0.427023	−	0.274431i	0.736450	+	0.676492i	$0.236501\pi$
$570$	−14.0677	+	31.8068i	−0.589233	+	1.33224i
$571$	−1.38147	+	2.14961i	−0.0578127	+	0.0899583i	−0.868957	−	0.494888i	$-0.835209\pi$
$571$	−1.38147	+	2.14961i	−0.0578127	+	0.0899583i	0.811144	+	0.584847i	$0.198845\pi$
$572$	2.88305	−	0.922102i	0.120546	−	0.0385550i
$573$	1.47992	−	5.04015i	0.0618247	−	0.210555i
$574$	0.231674	−	0.825457i	0.00966989	−	0.0344539i
$575$	47.2586	+	36.8637i	1.97082	+	1.53732i
$576$	−0.567010	+	7.97988i	−0.0236254	+	0.332495i
$577$	−5.86008	−	1.72067i	−0.243958	−	0.0716326i	0.157468	−	0.987524i	$-0.449667\pi$
$577$	−5.86008	−	1.72067i	−0.243958	−	0.0716326i	−0.401426	+	0.915892i	$0.631485\pi$
$578$	9.82570	+	14.8938i	0.408695	+	0.619501i
$579$	9.56490	−	14.8833i	0.397504	−	0.618528i
$580$	−2.79293	+	3.38370i	−0.115970	+	0.140500i
$581$	−0.188487	−	0.293291i	−0.00781974	−	0.0121678i
$582$	1.18487	+	7.59410i	0.0491144	+	0.314786i
$583$	14.9942	+	17.3043i	0.620997	+	0.716669i
$584$	−25.0973	−	20.2151i	−1.03854	−	0.836507i
$585$	0.737299	−	1.61446i	0.0304835	−	0.0667497i
$586$	−37.0484	+	0.443762i	−1.53046	+	0.0183317i
$587$	7.72367	+	26.3044i	0.318790	+	1.08570i	0.950559	+	0.310543i	$0.100511\pi$
$587$	7.72367	+	26.3044i	0.318790	+	1.08570i	−0.631769	+	0.775156i	$0.717671\pi$
$588$	−7.79494	−	11.5132i	−0.321458	−	0.474796i
$589$	28.9373	−	4.16056i	1.19234	−	0.171433i
$590$	25.2283	−	11.8886i	1.03863	−	0.489445i
$591$	1.67278	+	3.66287i	0.0688089	+	0.150670i
$592$	7.83787	−	13.5853i	0.322135	−	0.558352i
$593$	−0.628062	+	4.36826i	−0.0257914	+	0.179383i	−0.998645	−	0.0520378i	$-0.983428\pi$
$593$	−0.628062	+	4.36826i	−0.0257914	+	0.179383i	0.972854	+	0.231421i	$0.0743375\pi$
$594$	3.77249	−	3.34882i	0.154787	−	0.137404i
$595$	−1.45187	−	1.25805i	−0.0595207	−	0.0515750i
$596$	17.5401	−	15.9500i	0.718471	−	0.653336i
$597$			15.3428i			0.627940i
$598$	−2.81671	+	0.589541i	−0.115184	+	0.0241081i
$599$	1.93249			0.0789592			0.0394796	−	0.999220i	$-0.487430\pi$
$599$	1.93249			0.0789592			0.0394796	+	0.999220i	$0.487430\pi$
$600$	−15.8298	−	31.6056i	−0.646249	−	1.29029i
$601$	−14.0388	+	16.2017i	−0.572656	+	0.660881i	−0.966009	−	0.258507i	$-0.916770\pi$
$601$	−14.0388	+	16.2017i	−0.572656	+	0.660881i	0.393353	+	0.919387i	$0.371315\pi$
$602$	1.02890	+	1.15907i	0.0419350	+	0.0472403i
$603$	−4.29859	−	0.618044i	−0.175052	−	0.0251687i
$604$	−22.1335	+	0.530302i	−0.900600	+	0.0215777i
$605$	−6.55652	+	2.99426i	−0.266561	+	0.121734i
$606$	−24.1765	+	11.3929i	−0.982101	+	0.462806i
$607$	−4.49715	−	31.2784i	−0.182534	−	1.26955i	−0.850745	−	0.525579i	$-0.823849\pi$
$607$	−4.49715	−	31.2784i	−0.182534	−	1.26955i	0.668211	−	0.743972i	$-0.267060\pi$
$608$	−32.4138	−	7.44304i	−1.31455	−	0.301855i
$609$	−0.110384	+	0.0324116i	−0.00447298	+	0.00131339i
$610$	0.159635	+	13.3275i	0.00646344	+	0.539614i
$611$	4.67093	+	2.13314i	0.188966	+	0.0862977i
$612$	1.64769	−	3.84938i	0.0666041	−	0.155602i
$613$	18.7906	−	16.2822i	0.758946	−	0.657631i	−0.186851	−	0.982388i	$-0.559828\pi$
$613$	18.7906	−	16.2822i	0.758946	−	0.657631i	0.945797	+	0.324758i	$0.105283\pi$
$614$	0.440680	+	2.82442i	0.0177844	+	0.113984i
$615$	−9.72503	+	6.24990i	−0.392151	+	0.252020i
$616$	1.81763	−	1.26263i	0.0732344	−	0.0508728i
$617$	33.0977	+	21.2706i	1.33246	+	0.856322i	0.996339	−	0.0854950i	$-0.0272472\pi$
$617$	33.0977	+	21.2706i	1.33246	+	0.856322i	0.336125	+	0.941817i	$0.390884\pi$
$618$	10.4694	−	6.90687i	0.421143	−	0.277835i
$619$	−1.40277	+	4.77738i	−0.0563819	+	0.192019i	−0.982868	−	0.184309i	$-0.940995\pi$
$619$	−1.40277	+	4.77738i	−0.0563819	+	0.192019i	0.926486	+	0.376328i	$0.122813\pi$
$620$	−21.6466	+	35.5259i	−0.869348	+	1.42675i
$621$	−3.89556	+	2.79725i	−0.156323	+	0.112250i
$622$	4.56319	−	16.2587i	0.182967	−	0.651914i
$623$	2.54773	+	0.748080i	0.102072	+	0.0299712i
$624$	1.64948	+	0.399620i	0.0660322	+	0.0159976i
$625$	57.7938	+	37.1418i	2.31175	+	1.48567i
$626$	−24.4129	−	10.7975i	−0.975735	−	0.431555i
$627$	11.3375	+	17.6416i	0.452778	+	0.704536i
$628$	−18.2334	−	2.17721i	−0.727592	−	0.0868801i
$629$	−6.20400	+	5.37580i	−0.247370	+	0.214347i
$630$	0.169283	−	1.28660i	0.00674439	−	0.0512594i
$631$	−7.58590	+	16.6108i	−0.301990	+	0.661266i	−0.998410	−	0.0563685i	$-0.982048\pi$
$631$	−7.58590	+	16.6108i	−0.301990	+	0.661266i	0.696420	+	0.717634i	$0.254775\pi$
$632$	−11.5572	+	19.4890i	−0.459721	+	0.775229i
$633$	8.77541	−	2.57669i	0.348791	−	0.102414i
$634$	26.4671	−	31.2943i	1.05114	−	1.24286i
$635$	−83.6011	+	12.0200i	−3.31761	+	0.477000i
$636$	2.13094	+	12.6602i	0.0844971	+	0.502011i
$637$	−2.68313	+	1.22534i	−0.106309	+	0.0485499i
$638$	0.775673	+	2.52923i	0.0307092	+	0.100133i
$639$	−0.202102	+	1.40565i	−0.00799504	+	0.0556067i
$640$	37.5300	−	28.8301i	1.48350	−	1.13961i
$641$	−19.8396	+	22.8962i	−0.783618	+	0.904344i	−0.997365	−	0.0725452i	$-0.976888\pi$
$641$	−19.8396	+	22.8962i	−0.783618	+	0.904344i	0.213747	+	0.976889i	$0.431433\pi$
$642$	−10.6457	+	17.0095i	−0.420151	+	0.671313i
$643$		−	31.1709i		−	1.22926i	−0.788815	−	0.614631i	$-0.789305\pi$
$643$		−	31.1709i		−	1.22926i	0.788815	−	0.614631i	$-0.210695\pi$
$644$	−1.84255	+	1.01594i	−0.0726068	+	0.0400337i
$645$		−	20.8978i		−	0.822849i
$646$	14.7553	+	9.23482i	0.580539	+	0.363339i
$647$	−3.76390	+	4.34378i	−0.147974	+	0.170771i	−0.824898	−	0.565282i	$-0.808767\pi$
$647$	−3.76390	+	4.34378i	−0.147974	+	0.170771i	0.676923	+	0.736053i	$0.263313\pi$
$648$	2.78337	−	0.502842i	0.109341	−	0.0197535i
$649$	2.39320	−	16.6451i	0.0939414	−	0.653377i
$650$	−7.16954	+	2.19878i	−0.281213	+	0.0862431i
$651$	−0.992252	+	0.453146i	−0.0388894	+	0.0177602i
$652$	−41.3408	+	6.95837i	−1.61903	+	0.272511i
$653$	4.63630	−	0.666599i	0.181432	−	0.0260860i	−0.0509997	−	0.998699i	$-0.516241\pi$
$653$	4.63630	−	0.666599i	0.181432	−	0.0260860i	0.232432	+	0.972613i	$0.425332\pi$
$654$	−20.6839	−	17.4934i	−0.808805	−	0.684046i
$655$	−11.2629	+	3.30708i	−0.440077	+	0.129218i
$656$	−7.63091	−	7.99811i	−0.297937	−	0.312274i
$657$	−4.73310	+	10.3641i	−0.184656	+	0.404340i
$658$	3.72237	+	0.489767i	0.145113	+	0.0190931i
$659$	−15.8866	+	13.7658i	−0.618852	+	0.536239i	−0.906883	−	0.421382i	$-0.861545\pi$
$659$	−15.8866	+	13.7658i	−0.618852	+	0.536239i	0.288031	+	0.957621i	$0.407000\pi$
$660$	−29.6306	−	3.53812i	−1.15337	−	0.137721i
$661$	6.86170	+	10.6770i	0.266889	+	0.415288i	0.948669	−	0.316269i	$-0.102430\pi$
$661$	6.86170	+	10.6770i	0.266889	+	0.415288i	−0.681780	+	0.731557i	$0.738794\pi$
$662$	13.9589	−	31.5608i	0.542529	−	1.22664i
$663$	−0.747297	−	0.480259i	−0.0290226	−	0.0186517i
$664$	−4.49230	+	0.161487i	−0.174335	+	0.00626690i
$665$	5.17620	+	1.51987i	0.200724	+	0.0589380i
$666$	−5.33890	−	1.49842i	−0.206878	−	0.0580627i
$667$	−0.485733	−	2.46778i	−0.0188077	−	0.0955528i
$668$	−9.65766	−	5.88460i	−0.373666	−	0.227682i
$669$	−2.11799	+	7.21320i	−0.0818861	+	0.278879i
$670$	14.1472	+	21.4443i	0.546553	+	0.828466i
$671$	6.76084	+	4.34493i	0.260999	+	0.167734i
$672$	1.23869	−	0.0742700i	0.0477836	−	0.00286503i
$673$	−15.8247	+	10.1699i	−0.609997	+	0.392021i	−0.808856	−	0.588007i	$-0.799913\pi$
$673$	−15.8247	+	10.1699i	−0.609997	+	0.392021i	0.198859	+	0.980028i	$0.436276\pi$
$674$	2.62970	−	0.410299i	0.101292	−	0.0158041i
$675$	−9.44497	+	8.18411i	−0.363537	+	0.315007i
$676$	−10.0895	+	23.5713i	−0.388058	+	0.906590i
$677$	−25.0723	−	11.4502i	−0.963608	−	0.440065i	−0.129447	−	0.991586i	$-0.541320\pi$
$677$	−25.0723	−	11.4502i	−0.963608	−	0.440065i	−0.834161	+	0.551521i	$0.814048\pi$
$678$	17.4459	−	0.208965i	0.670004	−	0.00802525i
$679$	1.14392	−	0.335884i	0.0438995	−	0.0128900i
$680$	−23.5006	+	7.82781i	−0.901207	+	0.300183i
$681$	0.596600	+	4.14945i	0.0228618	+	0.159007i
$682$	10.6929	+	22.6910i	0.409452	+	0.868882i
$683$	−9.27224	+	4.23449i	−0.354792	+	0.162028i	−0.584835	−	0.811152i	$-0.698841\pi$
$683$	−9.27224	+	4.23449i	−0.354792	+	0.162028i	0.230043	+	0.973181i	$0.426113\pi$
$684$	0.281638	+	11.7549i	0.0107687	+	0.449459i
$685$	87.0629	+	12.5177i	3.32650	+	0.478279i
$686$	−3.23691	+	2.87340i	−0.123586	+	0.109707i
$687$	2.98981	−	3.45043i	0.114068	−	0.131642i
$688$	19.6212	−	3.78798i	0.748053	−	0.144415i
$689$	2.72365			0.103763
$690$	27.6738	+	6.24875i	1.05352	+	0.237886i
$691$			26.9353i			1.02467i	0.858786	+	0.512334i	$0.171219\pi$
$691$			26.9353i			1.02467i	−0.858786	+	0.512334i	$0.828781\pi$
$692$	3.96061	−	3.60155i	0.150560	−	0.136910i
$693$	−0.591348	−	0.512406i	−0.0224634	−	0.0194647i
$694$	−10.2394	−	11.5349i	−0.388684	−	0.437857i
$695$	−10.8617	+	75.5448i	−0.412008	+	2.86558i
$696$	−0.366507	+	1.43735i	−0.0138924	+	0.0544826i
$697$	2.40354	+	5.26302i	0.0910406	+	0.199351i
$698$	18.5878	+	39.4443i	0.703557	+	1.49299i
$699$	−12.1630	+	1.74878i	−0.460048	+	0.0661450i
$700$	−4.54029	+	3.07398i	−0.171607	+	0.116186i
$701$	8.50475	+	28.9645i	0.321220	+	1.09397i	0.948919	+	0.315519i	$0.102179\pi$
$701$	8.50475	+	28.9645i	0.321220	+	1.09397i	−0.627699	+	0.778456i	$0.716003\pi$
$702$	−0.00718684	−	0.600008i	−0.000271250	−	0.0226459i
$703$	9.57627	−	20.9691i	0.361176	−	0.790865i
$704$	−2.04892	−	28.4620i	−0.0772215	−	1.07270i
$705$	−33.1513	−	38.2587i	−1.24855	−	1.44090i
$706$	19.1381	−	2.98602i	0.720273	−	0.112380i
$707$	2.24131	+	3.48755i	0.0842931	+	0.131163i
$708$	6.00218	−	7.27176i	0.225576	−	0.273289i
$709$	−11.0443	+	17.1852i	−0.414777	+	0.645405i	−0.984286	−	0.176579i	$-0.943497\pi$
$709$	−11.0443	+	17.1852i	−0.414777	+	0.645405i	0.569510	+	0.821985i	$0.307133\pi$
$710$	7.01234	−	4.62616i	0.263169	−	0.173617i
$711$	7.68635	+	2.25691i	0.288260	+	0.0846409i
$712$	25.0520	−	23.3351i	0.938864	−	0.874520i
$713$	−7.88879	−	22.5054i	−0.295437	−	0.842835i
$714$	−0.625333	−	0.175507i	−0.0234025	−	0.00656818i
$715$	−1.78359	+	6.07436i	−0.0667025	+	0.227168i
$716$	6.65028	+	20.7928i	0.248533	+	0.777064i
$717$	7.31805	−	11.3871i	0.273297	−	0.425259i
$718$	−17.1242	−	7.57383i	−0.639070	−	0.282653i
$719$	11.6629	−	7.49530i	0.434953	−	0.279528i	−0.304786	−	0.952421i	$-0.598585\pi$
$719$	11.6629	−	7.49530i	0.434953	−	0.279528i	0.739740	+	0.672893i	$0.234949\pi$
$720$	−13.1554	−	10.3390i	−0.490274	−	0.385310i
$721$	−1.27405	−	1.47033i	−0.0474480	−	0.0547579i
$722$	−21.8230	−	2.87134i	−0.812168	−	0.106860i
$723$	21.8362	+	9.97226i	0.812097	+	0.370872i
$724$	3.32198	−	12.4055i	0.123460	−	0.461046i
$725$	−1.84653	−	6.28870i	−0.0685783	−	0.233556i
$726$	−1.57365	+	1.86066i	−0.0584036	+	0.0690554i
$727$	2.58715	+	17.9941i	0.0959523	+	0.667363i	0.979858	+	0.199697i	$0.0639958\pi$
$727$	2.58715	+	17.9941i	0.0959523	+	0.667363i	−0.883905	+	0.467666i	$0.845095\pi$
$728$	0.0280806	−	0.261759i	0.00104073	−	0.00970143i
$729$	−0.415415	−	0.909632i	−0.0153857	−	0.0336901i
$730$	64.4388	−	19.7623i	2.38499	−	0.731435i
$731$	−10.3529	−	1.48852i	−0.382916	−	0.0550550i
$732$	1.96957	+	4.05293i	0.0727973	+	0.149801i
$733$	−16.6952	−	14.4665i	−0.616652	−	0.534332i	0.289558	−	0.957161i	$-0.406492\pi$
$733$	−16.6952	−	14.4665i	−0.616652	−	0.534332i	−0.906210	+	0.422829i	$0.861037\pi$
$734$	20.7471	−	33.1494i	0.765788	−	1.22357i
$735$	29.0797			1.07262
$736$	−0.850829	+	27.1160i	−0.0313620	+	0.999508i
$737$	15.4905			0.570601
$738$	−2.07347	+	3.31297i	−0.0763256	+	0.121952i
$739$	−1.14943	−	0.995984i	−0.0422823	−	0.0366379i	0.633463	−	0.773773i	$-0.281633\pi$
$739$	−1.14943	−	0.995984i	−0.0422823	−	0.0366379i	−0.675746	+	0.737135i	$0.736178\pi$
$740$	14.3378	+	29.5041i	0.527069	+	1.08459i
$741$	2.46913	+	0.355007i	0.0907057	+	0.0130415i
$742$	1.90389	−	0.583890i	0.0698939	−	0.0214353i
$743$	−5.89959	−	12.9183i	−0.216435	−	0.473926i	0.770007	−	0.638035i	$-0.220252\pi$
$743$	−5.89959	−	12.9183i	−0.216435	−	0.473926i	−0.986442	+	0.164109i	$0.947525\pi$
$744$	−1.50021	+	13.9846i	−0.0550004	+	0.512699i
$745$	7.05664	+	49.0800i	0.258535	+	1.79815i
$746$	−14.2027	+	16.7931i	−0.519998	+	0.614838i
$747$	0.447755	+	1.52491i	0.0163825	+	0.0557937i
$748$	−3.86336	+	14.4272i	−0.141259	+	0.527511i
$749$	2.83129	+	1.29301i	0.103453	+	0.0472455i
$750$	43.9735	+	5.78576i	1.60569	+	0.211266i
$751$	30.9257	+	35.6902i	1.12850	+	1.30235i	0.947818	+	0.318812i	$0.103284\pi$
$751$	30.9257	+	35.6902i	1.12850	+	1.30235i	0.180678	+	0.983542i	$0.442171\pi$
$752$	29.9125	−	38.0611i	1.09080	−	1.38795i
$753$	7.44865	−	4.78696i	0.271444	−	0.174446i
$754$	0.287798	+	0.127290i	0.0104810	+	0.00463562i
$755$	25.0347	−	38.9547i	0.911104	−	1.41771i
$756$	−0.133652	−	0.417877i	−0.00486088	−	0.0151981i
$757$	5.47853	−	18.6582i	0.199120	−	0.678142i	−0.798024	−	0.602626i	$-0.794121\pi$
$757$	5.47853	−	18.6582i	0.199120	−	0.678142i	0.997145	−	0.0755165i	$-0.0240606\pi$
$758$	31.8724	+	8.94536i	1.15766	+	0.324910i
$759$	12.3339	−	11.8536i	0.447691	−	0.430258i
$760$	50.8980	−	47.4098i	1.84626	−	1.71973i
$761$	−25.9982	−	7.63376i	−0.942434	−	0.276724i	−0.225800	−	0.974174i	$-0.572500\pi$
$761$	−25.9982	−	7.63376i	−0.942434	−	0.276724i	−0.716633	+	0.697450i	$0.754318\pi$
$762$	−23.8354	+	15.7246i	−0.863465	+	0.569643i
$763$	−2.27176	+	3.53493i	−0.0822434	+	0.127973i
$764$	−6.68773	+	8.10232i	−0.241954	+	0.293132i
$765$	4.73467	+	7.36729i	0.171182	+	0.266365i
$766$	−9.23553	+	1.44097i	−0.333693	+	0.0520645i
$767$	−1.30995	−	1.51176i	−0.0472995	−	0.0545866i
$768$	7.32282	−	14.2259i	0.264240	−	0.513333i
$769$	−0.762684	+	1.67004i	−0.0275031	+	0.0602233i	−0.922885	−	0.385076i	$-0.874175\pi$
$769$	−0.762684	+	1.67004i	−0.0275031	+	0.0602233i	0.895382	+	0.445299i	$0.146903\pi$
$770$	0.0554393	+	4.62846i	0.00199789	+	0.166798i
$771$	−6.69733	−	22.8090i	−0.241198	−	0.821446i
$772$	−29.2998	+	19.8373i	−1.05452	+	0.713960i
$773$	−17.3726	+	2.49780i	−0.624848	+	0.0898396i	−0.447464	−	0.894302i	$-0.647673\pi$
$773$	−17.3726	+	2.49780i	−0.624848	+	0.0898396i	−0.177384	+	0.984142i	$0.556764\pi$
$774$	−3.01177	−	6.39116i	−0.108256	−	0.229726i
$775$	−25.8162	−	56.5297i	−0.927347	−	2.03061i
$776$	3.79813	−	14.8954i	0.136345	−	0.534712i
$777$	−0.122411	+	0.851385i	−0.00439146	+	0.0305433i
$778$	11.6497	+	13.1236i	0.417663	+	0.470503i
$779$	−12.2791	−	10.6399i	−0.439945	−	0.381215i
$780$	−2.62623	+	2.38815i	−0.0940342	+	0.0855094i
$781$		−	5.06545i		−	0.181256i
$782$	5.06684	−	13.2647i	0.181190	−	0.474344i
$783$	0.524441			0.0187420
$784$	5.27106	+	27.3034i	0.188252	+	0.975120i
$785$	25.1506	−	29.0254i	0.897665	−	1.03596i
$786$	−2.96791	+	2.63460i	−0.105862	+	0.0939732i
$787$	6.58190	+	0.946334i	0.234619	+	0.0337332i	0.258621	−	0.965979i	$-0.416732\pi$
$787$	6.58190	+	0.946334i	0.234619	+	0.0337332i	−0.0240022	+	0.999712i	$0.507641\pi$
$788$	−0.192901	−	8.05121i	−0.00687181	−	0.286813i
$789$	−13.9813	+	6.38503i	−0.497746	+	0.227313i
$790$	−20.2011	−	42.8680i	−0.718724	−	1.52518i
$791$	−0.385147	−	2.67876i	−0.0136943	−	0.0952456i
$792$	−9.57183	+	3.18828i	−0.340120	+	0.113291i
$793$	0.917258	−	0.269331i	0.0325728	−	0.00956424i
$794$	−52.7909	+	0.632325i	−1.87348	+	0.0224404i
$795$	−24.4248	−	11.1544i	−0.866259	−	0.395607i
$796$	12.0750	−	28.2100i	0.427988	−	0.999875i
$797$	−8.03093	+	6.95884i	−0.284470	+	0.246495i	−0.785393	−	0.618997i	$-0.787539\pi$
$797$	−8.03093	+	6.95884i	−0.284470	+	0.246495i	0.500923	+	0.865492i	$0.332994\pi$
$798$	1.80208	−	0.281169i	0.0637928	−	0.00995327i
$799$	−21.3149	+	13.6983i	−0.754068	+	0.484610i
$800$	4.23124	+	70.5697i	0.149597	+	2.49502i
$801$	−10.1829	−	6.54413i	−0.359794	−	0.231225i
$802$	−17.5806	−	26.6486i	−0.620791	−	0.940996i
$803$	11.4498	−	38.9945i	0.404055	−	1.37608i
$804$	7.41717	+	4.51942i	0.261583	+	0.159388i
$805$	0.401021	−	4.38237i	0.0141341	−	0.154458i
$806$	2.87284	+	0.806297i	0.101192	+	0.0284006i
$807$	−7.22139	−	2.12039i	−0.254205	−	0.0746414i
$808$	53.4183	−	1.92025i	1.87925	−	0.0675542i
$809$	−36.0191	−	23.1481i	−1.26636	−	0.813843i	−0.277223	−	0.960806i	$-0.589414\pi$
$809$	−36.0191	−	23.1481i	−1.26636	−	0.813843i	−0.989142	+	0.146963i	$0.953050\pi$
$810$	−2.39283	+	5.41012i	−0.0840753	+	0.190092i
$811$	12.0579	+	18.7624i	0.423409	+	0.658837i	0.985779	−	0.168049i	$-0.0537466\pi$
$811$	12.0579	+	18.7624i	0.423409	+	0.658837i	−0.562370	+	0.826886i	$0.690110\pi$
$812$	0.228465	+	0.0272805i	0.00801755	+	0.000957358i
$813$	−16.3818	+	14.1949i	−0.574534	+	0.497837i
$814$	19.6104	+	2.58021i	0.687344	+	0.0904364i
$815$	36.4238	−	79.7570i	1.27587	−	2.79376i
$816$	−6.05904	+	5.78086i	−0.212109	+	0.202371i
$817$	28.1817	−	8.27490i	0.985953	−	0.289502i
$818$	0.926382	+	0.783486i	0.0323902	+	0.0273940i
$819$	−0.0921294	+	0.0132462i	−0.00321926	+	0.000462860i
$820$	22.7996	−	3.83757i	0.796198	−	0.134014i
$821$	−5.27194	+	2.40762i	−0.183992	+	0.0840264i	−0.505281	−	0.862955i	$-0.668611\pi$
$821$	−5.27194	+	2.40762i	−0.183992	+	0.0840264i	0.321289	+	0.946981i	$0.395884\pi$
$822$	28.4305	−	8.71914i	0.991626	−	0.304115i
$823$	5.52209	−	38.4070i	0.192488	−	1.33878i	−0.632907	−	0.774228i	$-0.718138\pi$
$823$	5.52209	−	38.4070i	0.192488	−	1.33878i	0.825395	−	0.564556i	$-0.190952\pi$
$824$	−24.6854	+	4.45965i	−0.859956	+	0.155359i
$825$	29.1923	−	33.6897i	1.01635	−	1.17293i
$826$	−1.23977	−	0.775929i	−0.0431371	−	0.0269980i
$827$			19.4206i			0.675322i	0.941268	+	0.337661i	$0.109636\pi$
$827$			19.4206i			0.675322i	−0.941268	+	0.337661i	$0.890364\pi$
$828$	9.36402	−	2.07727i	0.325422	−	0.0721902i
$829$			17.5507i			0.609563i	0.952422	+	0.304781i	$0.0985834\pi$
$829$			17.5507i			0.609563i	−0.952422	+	0.304781i	$0.901417\pi$
$830$	4.98785	−	7.96953i	0.173131	−	0.276626i
$831$	17.9270	−	20.6888i	0.621880	−	0.717687i
$832$	−2.71830	−	2.03293i	−0.0942402	−	0.0704791i
$833$	2.07131	−	14.4063i	0.0717667	−	0.499148i
$834$	7.56563	+	24.6692i	0.261976	+	0.854225i
$835$	21.5158	−	9.82593i	0.744584	−	0.340040i
$836$	−6.96150	−	41.3594i	−0.240769	−	1.43044i
$837$	4.92204	−	0.707683i	0.170131	−	0.0244611i
$838$	25.4970	−	30.1472i	0.880778	−	1.04142i
$839$	−30.3624	+	8.91520i	−1.04823	+	0.307787i	−0.760100	−	0.649806i	$-0.774850\pi$
$839$	−30.3624	+	8.91520i	−1.04823	+	0.307787i	−0.288126	+	0.957593i	$0.593032\pi$
$840$	−1.32383	+	2.23237i	−0.0456763	+	0.0770241i
$841$	11.9328	−	26.1291i	0.411475	−	0.901005i
$842$	−2.20965	+	16.7940i	−0.0761497	+	0.578760i
$843$	21.3181	−	18.4723i	0.734236	−	0.636219i
$844$	−18.1627	−	2.16877i	−0.625187	−	0.0746522i
$845$	−28.9924	−	45.1130i	−0.997368	−	1.55193i
$846$	−15.6525	−	6.92289i	−0.538143	−	0.238014i
$847$	0.317991	+	0.204360i	0.0109263	+	0.00702191i
$848$	6.04577	−	24.9547i	0.207613	−	0.856948i
$849$	27.9893	+	8.21839i	0.960589	+	0.282054i
$850$	9.99882	−	35.6259i	0.342957	−	1.22196i
$851$	−18.2919	−	4.36122i	−0.627039	−	0.149501i
$852$	1.47786	−	2.42543i	0.0506308	−	0.0830939i
$853$	5.62093	−	19.1431i	0.192457	−	0.655449i	−0.805561	−	0.592514i	$-0.798136\pi$
$853$	5.62093	−	19.1431i	0.192457	−	0.655449i	0.998018	−	0.0629352i	$-0.0200461\pi$
$854$	0.583444	−	0.384908i	0.0199650	−	0.0131713i
$855$	−20.6884	−	13.2957i	−0.707530	−	0.454702i
$856$	32.9604	−	22.8961i	1.12656	−	0.782574i
$857$	27.2665	−	17.5231i	0.931404	−	0.598577i	0.0154591	−	0.999881i	$-0.495079\pi$
$857$	27.2665	−	17.5231i	0.931404	−	0.598577i	0.915945	+	0.401303i	$0.131443\pi$
$858$	0.329956	+	2.11477i	0.0112645	+	0.0721970i
$859$	−0.733713	+	0.635766i	−0.0250340	+	0.0216921i	−0.667288	−	0.744800i	$-0.732545\pi$
$859$	−0.733713	+	0.635766i	−0.0250340	+	0.0216921i	0.642254	+	0.766492i	$0.277999\pi$
$860$	−16.4469	+	38.4235i	−0.560834	+	1.31023i
$861$	0.551455	+	0.251841i	0.0187935	+	0.00858272i
$862$	−0.644212	−	53.7834i	−0.0219419	−	1.83187i
$863$	−22.0918	+	6.48674i	−0.752014	+	0.220811i	−0.635205	−	0.772343i	$-0.719085\pi$
$863$	−22.0918	+	6.48674i	−0.752014	+	0.220811i	−0.116809	+	0.993154i	$0.537266\pi$
$864$	−5.51337	−	1.26601i	−0.187569	−	0.0430705i
$865$	1.59341	+	11.0824i	0.0541776	+	0.376813i
$866$	−5.51884	+	2.60070i	−0.187538	+	0.0883753i
$867$	−11.4767	+	5.24123i	−0.389769	+	0.178001i
$868$	2.18103	−	0.0522558i	0.0740290	−	0.00177368i
$869$	−28.2834	−	4.06654i	−0.959450	−	0.137948i
$870$	−2.05958	−	2.32014i	−0.0698264	−	0.0786602i
$871$	1.20668	−	1.39258i	0.0408868	−	0.0471859i
$872$	24.2627	+	48.4427i	0.821640	+	1.64048i
$873$	−5.43481			−0.183940
$874$	2.53124	+	39.7938i	0.0856203	+	1.34605i
$875$		−	6.87973i		−	0.232577i
$876$	16.8592	−	15.3308i	0.569618	−	0.517978i
$877$	−26.0713	−	22.5909i	−0.880367	−	0.762842i	0.0921328	−	0.995747i	$-0.470632\pi$
$877$	−26.0713	−	22.5909i	−0.880367	−	0.762842i	−0.972500	+	0.232905i	$0.925177\pi$
$878$	−19.9195	+	17.6825i	−0.672250	+	0.596754i
$879$	3.72852	−	25.9324i	0.125760	−	0.874678i
$880$	51.6955	+	29.8251i	1.74266	+	1.00540i
$881$	4.53411	+	9.92832i	0.152758	+	0.334494i	0.970504	−	0.241086i	$-0.0775037\pi$
$881$	4.53411	+	9.92832i	0.152758	+	0.334494i	−0.817746	+	0.575580i	$0.804776\pi$
$882$	8.89344	−	4.19095i	0.299458	−	0.141116i
$883$	6.15362	−	0.884758i	0.207086	−	0.0297745i	−0.0379911	−	0.999278i	$-0.512096\pi$
$883$	6.15362	−	0.884758i	0.207086	−	0.0297745i	0.245077	+	0.969504i	$0.421187\pi$
$884$	0.996041	+	1.47116i	0.0335005	+	0.0494804i
$885$	5.55593	+	18.9218i	0.186761	+	0.636048i
$886$	11.4209	−	0.136798i	0.383691	−	0.00459582i
$887$	−3.51755	+	7.70237i	−0.118108	+	0.258620i	−0.959448	−	0.281886i	$-0.909040\pi$
$887$	−3.51755	+	7.70237i	−0.118108	+	0.258620i	0.841340	+	0.540506i	$0.181767\pi$
$888$	8.63704	+	6.95686i	0.289840	+	0.233457i
$889$	2.90058	+	3.34744i	0.0972822	+	0.112270i
$890$	11.0387	+	70.7494i	0.370017	+	2.37153i
$891$	1.92844	+	3.00071i	0.0646051	+	0.100528i
$892$	9.57113	−	11.5956i	0.320465	−	0.388250i
$893$	38.4668	−	59.8555i	1.28724	−	2.00299i
$894$	9.23151	+	13.9931i	0.308748	+	0.468000i
$895$	−43.8088	−	12.8634i	−1.46437	−	0.429977i
$896$	−2.33596	−	0.838315i	−0.0780391	−	0.0280061i
$897$	−0.104843	−	2.03217i	−0.00350060	−	0.0678522i
$898$	−14.1324	+	50.3539i	−0.471604	+	1.68033i
$899$	−0.734720	+	2.50223i	−0.0245043	+	0.0834539i
$900$	23.8069	−	7.61431i	0.793565	−	0.253810i
$901$	−7.26574	+	11.3057i	−0.242057	+	0.376648i
$902$	5.63893	−	12.7495i	0.187756	−	0.424511i
$903$	−0.921949	+	0.592501i	−0.0306806	+	0.0197172i
$904$	−32.2412	−	13.3460i	−1.07232	−	0.443880i
$905$	17.5897	+	20.2996i	0.584702	+	0.674782i
$906$	2.04222	−	15.5215i	0.0678482	−	0.515666i
$907$	−20.8657	−	9.52906i	−0.692836	−	0.316407i	0.0376932	−	0.999289i	$-0.487999\pi$
$907$	−20.8657	−	9.52906i	−0.692836	−	0.316407i	−0.730529	+	0.682882i	$0.760726\pi$
$908$	2.16875	−	8.09888i	0.0719724	−	0.268771i
$909$	−5.32430	−	18.1329i	−0.176596	−	0.601430i
$910$	0.420412	+	0.355563i	0.0139365	+	0.0117868i
$911$	6.11432	+	42.5260i	0.202576	+	1.40895i	0.796602	+	0.604504i	$0.206629\pi$
$911$	6.11432	+	42.5260i	0.202576	+	1.40895i	−0.594026	+	0.804446i	$0.702462\pi$
$912$	8.73345	−	21.8347i	0.289194	−	0.723019i
$913$	−2.35496	−	5.15664i	−0.0779377	−	0.170660i
$914$	3.84814	+	12.5476i	0.127285	+	0.415038i
$915$	−9.32870	−	1.34126i	−0.308397	−	0.0443408i
$916$	−8.21274	+	3.99107i	−0.271356	+	0.131869i
$917$	0.465228	+	0.403122i	0.0153632	+	0.0133123i
$918$	2.50977	+	1.57078i	0.0828348	+	0.0518434i
$919$	−33.3342			−1.09959			−0.549797	−	0.835298i	$-0.685295\pi$
$919$	−33.3342			−1.09959			−0.549797	+	0.835298i	$0.685295\pi$
$920$	−45.9643	−	33.2689i	−1.51540	−	1.09684i
$921$	−2.02133			−0.0666051
$922$	9.51878	+	5.95747i	0.313484	+	0.196199i
$923$	−0.455378	−	0.394587i	−0.0149889	−	0.0129880i
$924$	0.684005	+	1.40753i	0.0225021	+	0.0463044i
$925$	−48.5043	−	6.97387i	−1.59481	−	0.229299i
$926$	−11.5663	−	37.7142i	−0.380093	−	1.23937i
$927$	3.68427	+	8.06742i	0.121007	+	0.264969i
$928$	1.80509	−	2.35433i	0.0592551	−	0.0772846i
$929$	6.93626	+	48.2427i	0.227571	+	1.58279i	0.708293	+	0.705919i	$0.249466\pi$
$929$	6.93626	+	48.2427i	0.227571	+	1.58279i	−0.480721	+	0.876873i	$0.659625\pi$
$930$	−22.4606	−	18.9961i	−0.736513	−	0.622906i
$931$	11.5147	+	39.2154i	0.377379	+	1.28523i
$932$	23.7398	+	6.35712i	0.777623	+	0.208235i
$933$	10.8618	+	4.96041i	0.355599	+	0.162396i
$934$	−1.56642	+	11.9053i	−0.0512550	+	0.389553i
$935$	−20.4563	−	23.6078i	−0.668992	−	0.772058i
$936$	−0.459002	+	1.10886i	−0.0150030	+	0.0362441i
$937$	20.4359	−	13.1334i	0.667612	−	0.429048i	−0.162452	−	0.986716i	$-0.551940\pi$
$937$	20.4359	−	13.1334i	0.667612	−	0.429048i	0.830064	+	0.557669i	$0.188304\pi$
$938$	0.544955	−	1.23213i	0.0177934	−	0.0402304i
$939$	10.2049	−	15.8791i	0.333025	−	0.518196i
$940$	30.8432	+	96.4346i	1.00600	+	3.14535i
$941$	−8.55367	+	29.1311i	−0.278842	+	0.949648i	0.694347	+	0.719640i	$0.255693\pi$
$941$	−8.55367	+	29.1311i	−0.278842	+	0.949648i	−0.973189	+	0.230008i	$0.926125\pi$
$942$	3.50869	−	12.5015i	0.114319	−	0.407321i
$943$	−6.58155	+	11.5042i	−0.214325	+	0.374628i
$944$	−16.7588	+	8.64635i	−0.545454	+	0.281415i
$945$	0.880435	+	0.258519i	0.0286406	+	0.00840963i
$946$	13.8778	+	21.0360i	0.451208	+	0.683941i
$947$	18.9337	−	29.4614i	0.615262	−	0.957367i	−0.384156	−	0.923268i	$-0.625508\pi$
$947$	18.9337	−	29.4614i	0.615262	−	0.957367i	0.999418	−	0.0340988i	$-0.0108561\pi$
$948$	−12.3562	−	10.1989i	−0.401311	−	0.331246i
$949$	−2.61364	−	4.06691i	−0.0848424	−	0.132017i
$950$	16.0185	+	102.666i	0.519709	+	3.33093i
$951$	18.9788	+	21.9027i	0.615429	+	0.710243i
$952$	1.01164	+	0.814841i	0.0327873	+	0.0264092i
$953$	−10.7854	+	23.6167i	−0.349373	+	0.765021i	0.650611	+	0.759411i	$0.274513\pi$
$953$	−10.7854	+	23.6167i	−0.349373	+	0.765021i	−0.999984	+	0.00560944i	$0.998214\pi$
$954$	−9.07741	+	0.108728i	−0.293892	+	0.00352021i
$955$	−6.19052	−	21.0830i	−0.200320	−	0.682229i
$956$	−22.4171	+	15.1774i	−0.725021	+	0.490872i
$957$	−1.85161	+	0.266222i	−0.0598542	+	0.00860573i
$958$	8.78760	−	4.14107i	0.283915	−	0.133792i
$959$	−1.91619	−	4.19587i	−0.0618770	−	0.135492i
$960$	16.0512	+	29.3632i	0.518051	+	0.947693i
$961$	0.892699	−	6.20886i	0.0287967	−	0.200286i
$962$	1.75956	−	1.56196i	0.0567306	−	0.0503596i
$963$	−10.7233	−	9.29181i	−0.345554	−	0.299424i
$964$	−32.3006	−	35.5208i	−1.04033	−	1.14405i
$965$		−	74.0047i		−	2.38230i
$966$	−0.508939	−	1.39805i	−0.0163749	−	0.0449816i
$967$	−45.9396			−1.47732			−0.738659	−	0.674079i	$-0.764541\pi$
$967$	−45.9396			−1.47732			−0.738659	+	0.674079i	$0.764541\pi$
$968$	4.35774	−	2.18260i	0.140063	−	0.0701513i
$969$	−8.06037	+	9.30217i	−0.258937	+	0.298829i
$970$	21.3436	+	24.0438i	0.685301	+	0.771999i
$971$	23.9688	+	3.44620i	0.769197	+	0.110594i	0.515731	−	0.856751i	$-0.327520\pi$
$971$	23.9688	+	3.44620i	0.769197	+	0.110594i	0.253466	+	0.967344i	$0.418429\pi$
$972$	0.0479047	+	1.99943i	0.00153655	+	0.0641316i
$973$	3.64077	−	1.66268i	0.116718	−	0.0533032i
$974$	11.2970	−	5.32360i	0.361979	−	0.170579i
$975$	−0.754651	−	5.24871i	−0.0241682	−	0.168093i
$976$	−0.431609	−	9.00197i	−0.0138155	−	0.288146i
$977$	−30.2206	+	8.87357i	−0.966843	+	0.283891i	−0.726783	−	0.686867i	$-0.758985\pi$
$977$	−30.2206	+	8.87357i	−0.966843	+	0.283891i	−0.240060	+	0.970758i	$0.577167\pi$
$978$	−0.355042	−	29.6414i	−0.0113530	−	0.947828i
$979$	39.2741	+	17.9359i	1.25520	+	0.573233i
$980$	−53.4672	−	22.8862i	−1.70795	−	0.731073i
$981$	14.4765	−	12.5440i	0.462200	−	0.400499i
$982$	7.74442	+	49.6358i	0.247134	+	1.58394i
$983$	−1.02169	+	0.656603i	−0.0325870	+	0.0209424i	−0.556833	−	0.830625i	$-0.687984\pi$
$983$	−1.02169	+	0.656603i	−0.0325870	+	0.0209424i	0.524246	+	0.851567i	$0.324347\pi$
$984$	6.41973	−	4.45951i	0.204654	−	0.142164i
$985$	14.1700	+	9.10652i	0.451494	+	0.290158i
$986$	−1.29612	+	0.855070i	−0.0412768	+	0.0272310i
$987$	−0.747944	+	2.54726i	−0.0238073	+	0.0810802i
$988$	−4.26045	−	2.59597i	−0.135543	−	0.0825889i
$989$	−11.0628	−	21.2525i	−0.351776	−	0.675790i
$990$	5.70188	−	20.3159i	0.181218	−	0.645681i
$991$	22.2694	+	6.53888i	0.707410	+	0.207714i	0.615596	−	0.788062i	$-0.288915\pi$
$991$	22.2694	+	6.53888i	0.707410	+	0.207714i	0.0918139	+	0.995776i	$0.470734\pi$
$992$	13.7644	−	24.5319i	0.437021	−	0.778889i
$993$	20.5284	+	13.1928i	0.651450	+	0.418661i
$994$	−0.402909	−	0.178202i	−0.0127795	−	0.00565221i
$995$	34.6978	+	53.9908i	1.09999	+	1.71162i
$996$	0.376870	−	3.15616i	0.0119416	−	0.100007i
$997$	−9.22150	+	7.99047i	−0.292048	+	0.253061i	−0.788544	−	0.614978i	$-0.789165\pi$
$997$	−9.22150	+	7.99047i	−0.292048	+	0.253061i	0.496497	+	0.868039i	$0.334619\pi$
$998$	7.68352	−	58.3971i	0.243218	−	1.84853i
$999$	1.62886	−	3.56670i	0.0515348	−	0.112845i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.bb.a.133.32	yes	480
8.5	even	2	inner	552.2.bb.a.133.22	✓	480
23.9	even	11	inner	552.2.bb.a.469.22	yes	480
184.101	even	22	inner	552.2.bb.a.469.32	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.bb.a.133.22	✓	480	8.5	even	2	inner
552.2.bb.a.133.32	yes	480	1.1	even	1	trivial
552.2.bb.a.469.22	yes	480	23.9	even	11	inner
552.2.bb.a.469.32	yes	480	184.101	even	22	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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.bb (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.750277 - 1.19878i) q^{2} +(0.755750 + 0.654861i) q^{3} +(-0.874167 - 1.79884i) q^{4} +(4.14042 + 0.595303i) q^{5} +(1.35206 - 0.414653i) q^{6} +(-0.0911276 - 0.199542i) q^{7} +(-2.81229 - 0.301692i) q^{8} +(0.142315 + 0.989821i) q^{9} +(3.82011 - 4.51683i) q^{10} +(-1.00493 - 3.42246i) q^{11} +(0.517339 - 1.93193i) q^{12} +(-0.385957 - 0.176261i) q^{13} +(-0.307578 - 0.0404693i) q^{14} +(2.73928 + 3.16130i) q^{15} +(-2.47166 + 3.14498i) q^{16} +(1.76125 - 1.13188i) q^{17} +(1.29336 + 0.572036i) q^{18} +(-3.17850 + 4.94584i) q^{19} +(-2.54857 - 7.96836i) q^{20} +(0.0618023 - 0.210479i) q^{21} +(-4.85677 - 1.36311i) q^{22} +(4.45930 + 1.76485i) q^{23} +(-1.92782 - 2.06966i) q^{24} +(11.9912 + 3.52095i) q^{25} +(-0.500874 + 0.330435i) q^{26} +(-0.540641 + 0.841254i) q^{27} +(-0.279283 + 0.338357i) q^{28} +(-0.283534 - 0.441187i) q^{29} +(5.84494 - 0.911956i) q^{30} +(-3.25640 - 3.75808i) q^{31} +(1.91572 + 5.32260i) q^{32} +(1.48176 - 3.24461i) q^{33} +(-0.0354616 - 2.96058i) q^{34} +(-0.258519 - 0.880435i) q^{35} +(1.65613 - 1.12127i) q^{36} +(-3.88113 + 0.558022i) q^{37} +(3.54424 + 7.52109i) q^{38} +(-0.176261 - 0.385957i) q^{39} +(-11.4645 - 2.92330i) q^{40} +(-0.393302 + 2.73548i) q^{41} +(-0.205951 - 0.232006i) q^{42} +(-3.77564 - 3.27161i) q^{43} +(-5.27800 + 4.79951i) q^{44} +4.18300i q^{45} +(5.46138 - 4.02161i) q^{46} -12.1022 q^{47} +(-3.92748 + 0.758220i) q^{48} +(4.55251 - 5.25388i) q^{49} +(13.2176 - 11.7332i) q^{50} +(2.07229 + 0.297950i) q^{51} +(0.0203260 + 0.848357i) q^{52} +(-5.83907 + 2.66661i) q^{53} +(0.602851 + 1.27929i) q^{54} +(-2.12342 - 14.7687i) q^{55} +(0.196077 + 0.588662i) q^{56} +(-5.64099 + 1.65634i) q^{57} +(-0.741618 + 0.00888303i) q^{58} +(4.28842 + 1.95846i) q^{59} +(3.29209 - 7.69104i) q^{60} +(-1.70276 + 1.47545i) q^{61} +(-6.94833 + 1.08411i) q^{62} +(0.184542 - 0.118598i) q^{63} +(7.81796 + 1.69689i) q^{64} +(-1.49310 - 0.959555i) q^{65} +(-2.77786 - 4.21068i) q^{66} +(-1.22351 + 4.16688i) q^{67} +(-3.57570 - 2.17875i) q^{68} +(2.21438 + 4.25400i) q^{69} +(-1.24941 - 0.350662i) q^{70} +(1.36258 + 0.400090i) q^{71} +(-0.101609 - 2.82660i) q^{72} +(9.58497 + 6.15989i) q^{73} +(-2.24298 + 5.07131i) q^{74} +(6.75665 + 10.5136i) q^{75} +(11.6753 + 1.39412i) q^{76} +(-0.591348 + 0.512406i) q^{77} +(-0.594924 - 0.0782764i) q^{78} +(3.32782 - 7.28692i) q^{79} +(-12.1059 + 11.5501i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(2.98416 + 2.52385i) q^{82} +(1.57312 - 0.226180i) q^{83} +(-0.432645 + 0.0728216i) q^{84} +(7.96612 - 3.63800i) q^{85} +(-6.75473 + 2.07156i) q^{86} +(0.0746357 - 0.519102i) q^{87} +(1.79361 + 9.92814i) q^{88} +(-7.92669 + 9.14789i) q^{89} +(5.01451 + 3.13841i) q^{90} +0.0930768i q^{91} +(-0.723488 - 9.56434i) q^{92} -4.97265i q^{93} +(-9.08000 + 14.5079i) q^{94} +(-16.1046 + 18.5857i) q^{95} +(-2.03776 + 5.27708i) q^{96} +(-0.773454 + 5.37949i) q^{97} +(-2.88262 - 9.39935i) q^{98} +(3.24461 - 1.48176i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32}+ \cdots - 132 q^{98}+O(q^{100}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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