LMFDB - Embedded newform 558.2.q.a.185.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [558,2,Mod(185,558)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(558, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("558.185"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 558 = 2 \cdot 3^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	558.q (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.45565243279$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			185.9
Character	$\chi$	$=$	558.185
Dual form			558.2.q.a.371.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.217529 - 1.71834i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.11157 - 0.641767i) q^{5} +(0.670782 + 1.59689i) q^{6} +(0.353559 + 0.612382i) q^{7} +1.00000i q^{8} +(-2.90536 - 0.747578i) q^{9} +1.28353 q^{10} +(-2.81024 - 4.86747i) q^{11} +(-1.37936 - 1.04755i) q^{12} +(4.52776 + 2.61411i) q^{13} +(-0.612382 - 0.353559i) q^{14} +(-1.34457 + 1.77045i) q^{15} +(-0.500000 - 0.866025i) q^{16} -2.24216 q^{17} +(2.88991 - 0.805260i) q^{18} -7.50145 q^{19} +(-1.11157 + 0.641767i) q^{20} +(1.12919 - 0.474322i) q^{21} +(4.86747 + 2.81024i) q^{22} +(3.07487 - 5.32583i) q^{23} +(1.71834 + 0.217529i) q^{24} +(-1.67627 - 2.90338i) q^{25} -5.22821 q^{26} +(-1.91659 + 4.82977i) q^{27} +0.707117 q^{28} +(1.11816 + 1.93671i) q^{29} +(0.279207 - 2.20554i) q^{30} +(-3.48473 + 4.34243i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-8.97527 + 3.77011i) q^{33} +(1.94177 - 1.12108i) q^{34} -0.907610i q^{35} +(-2.10010 + 2.14233i) q^{36} +4.38424i q^{37} +(6.49644 - 3.75072i) q^{38} +(5.47684 - 7.21158i) q^{39} +(0.641767 - 1.11157i) q^{40} +(-5.25780 - 3.03559i) q^{41} +(-0.740744 + 0.975368i) q^{42} +(-6.72000 + 3.87979i) q^{43} -5.62047 q^{44} +(2.74975 + 2.69555i) q^{45} +6.14974i q^{46} +(-8.40445 + 4.85231i) q^{47} +(-1.59689 + 0.670782i) q^{48} +(3.24999 - 5.62915i) q^{49} +(2.90338 + 1.67627i) q^{50} +(-0.487736 + 3.85279i) q^{51} +(4.52776 - 2.61411i) q^{52} -1.21418 q^{53} +(-0.755068 - 5.14100i) q^{54} +7.21407i q^{55} +(-0.612382 + 0.353559i) q^{56} +(-1.63179 + 12.8900i) q^{57} +(-1.93671 - 1.11816i) q^{58} +(-4.10979 - 2.37279i) q^{59} +(0.860972 + 2.04966i) q^{60} +(5.11078 - 2.95071i) q^{61} +(0.846651 - 5.50302i) q^{62} +(-0.569413 - 2.04350i) q^{63} -1.00000 q^{64} +(-3.35530 - 5.81154i) q^{65} +(5.88775 - 7.75265i) q^{66} +(4.93759 - 8.55215i) q^{67} +(-1.12108 + 1.94177i) q^{68} +(-8.48270 - 6.44219i) q^{69} +(0.453805 + 0.786013i) q^{70} +1.16581i q^{71} +(0.747578 - 2.90536i) q^{72} -16.1091i q^{73} +(-2.19212 - 3.79686i) q^{74} +(-5.35363 + 2.24882i) q^{75} +(-3.75072 + 6.49644i) q^{76} +(1.98717 - 3.44187i) q^{77} +(-1.13729 + 8.98383i) q^{78} +(11.7293 - 6.77189i) q^{79} +1.28353i q^{80} +(7.88226 + 4.34397i) q^{81} +6.07118 q^{82} +(-4.57381 - 7.92206i) q^{83} +(0.153819 - 1.21507i) q^{84} +(2.49233 + 1.43895i) q^{85} +(3.87979 - 6.72000i) q^{86} +(3.57114 - 1.50008i) q^{87} +(4.86747 - 2.81024i) q^{88} +8.17378 q^{89} +(-3.72913 - 0.959542i) q^{90} +3.69696i q^{91} +(-3.07487 - 5.32583i) q^{92} +(6.70372 + 6.93254i) q^{93} +(4.85231 - 8.40445i) q^{94} +(8.33841 + 4.81418i) q^{95} +(1.04755 - 1.37936i) q^{96} +(8.14690 + 14.1108i) q^{97} +6.49998i q^{98} +(4.52594 + 16.2426i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 32 q^{4} + 12 q^{5} - 4 q^{7} - 4 q^{9} - 32 q^{16} + 8 q^{18} - 8 q^{19} + 12 q^{20} + 44 q^{25} - 8 q^{28} + 8 q^{31} - 36 q^{33} - 8 q^{36} + 36 q^{38} - 8 q^{39} + 24 q^{41} - 8 q^{45} - 48 q^{47}+ \cdots - 16 q^{97}+O(q^{100}) $ 64 * q + 32 * q^4 + 12 * q^5 - 4 * q^7 - 4 * q^9 - 32 * q^16 + 8 * q^18 - 8 * q^19 + 12 * q^20 + 44 * q^25 - 8 * q^28 + 8 * q^31 - 36 * q^33 - 8 * q^36 + 36 * q^38 - 8 * q^39 + 24 * q^41 - 8 * q^45 - 48 * q^47 - 36 * q^49 - 32 * q^51 - 12 * q^59 - 52 * q^63 - 64 * q^64 - 16 * q^66 + 16 * q^67 + 112 * q^69 - 12 * q^70 - 8 * q^72 - 4 * q^76 - 28 * q^78 + 60 * q^81 + 44 * q^87 + 56 * q^90 - 64 * q^93 - 180 * q^95 - 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/558\mathbb{Z}\right)^\times$.

$n$	$127$	$497$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	0.217529	−	1.71834i	0.125591	−	0.992082i
$3$	0.217529	−	1.71834i	0.125591	−	0.992082i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.11157	−	0.641767i	−0.497111	−	0.287007i	0.230409	−	0.973094i	$-0.425994\pi$
$5$	−1.11157	−	0.641767i	−0.497111	−	0.287007i	−0.727520	+	0.686087i	$0.759327\pi$
$6$	0.670782	+	1.59689i	0.273846	+	0.651927i
$7$	0.353559	+	0.612382i	0.133633	+	0.231459i	0.925074	−	0.379786i	$-0.124002\pi$
$7$	0.353559	+	0.612382i	0.133633	+	0.231459i	−0.791442	+	0.611245i	$0.790669\pi$
$8$			1.00000i			0.353553i
$9$	−2.90536	−	0.747578i	−0.968454	−	0.249193i
$10$	1.28353			0.405889
$11$	−2.81024	−	4.86747i	−0.847318	−	1.46760i	−0.883593	−	0.468256i	$-0.844882\pi$
$11$	−2.81024	−	4.86747i	−0.847318	−	1.46760i	0.0362745	−	0.999342i	$-0.488451\pi$
$12$	−1.37936	−	1.04755i	−0.398186	−	0.302403i
$13$	4.52776	+	2.61411i	1.25578	+	0.725023i	0.972250	−	0.233942i	$-0.0751627\pi$
$13$	4.52776	+	2.61411i	1.25578	+	0.725023i	0.283525	+	0.958965i	$0.408496\pi$
$14$	−0.612382	−	0.353559i	−0.163666	−	0.0944925i
$15$	−1.34457	+	1.77045i	−0.347167	+	0.457129i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.24216			−0.543804			−0.271902	−	0.962325i	$-0.587653\pi$
$17$	−2.24216			−0.543804			−0.271902	+	0.962325i	$0.587653\pi$
$18$	2.88991	−	0.805260i	0.681157	−	0.189802i
$19$	−7.50145			−1.72095			−0.860475	−	0.509492i	$-0.829833\pi$
$19$	−7.50145			−1.72095			−0.860475	+	0.509492i	$0.829833\pi$
$20$	−1.11157	+	0.641767i	−0.248555	+	0.143504i
$21$	1.12919	−	0.474322i	0.246409	−	0.103506i
$22$	4.86747	+	2.81024i	1.03775	+	0.599144i
$23$	3.07487	−	5.32583i	0.641155	−	1.11051i	−0.344020	−	0.938962i	$-0.611789\pi$
$23$	3.07487	−	5.32583i	0.641155	−	1.11051i	0.985175	−	0.171551i	$-0.0548778\pi$
$24$	1.71834	+	0.217529i	0.350754	+	0.0444030i
$25$	−1.67627	−	2.90338i	−0.335254	−	0.580677i
$26$	−5.22821			−1.02534
$27$	−1.91659	+	4.82977i	−0.368848	+	0.929490i
$28$	0.707117			0.133633
$29$	1.11816	+	1.93671i	0.207637	+	0.359637i	0.950970	−	0.309284i	$-0.100090\pi$
$29$	1.11816	+	1.93671i	0.207637	+	0.359637i	−0.743333	+	0.668922i	$0.766756\pi$
$30$	0.279207	−	2.20554i	0.0509759	−	0.402676i
$31$	−3.48473	+	4.34243i	−0.625876	+	0.779923i
$31$	−3.48473	+	4.34243i	−0.625876	+	0.779923i
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−8.97527	+	3.77011i	−1.56239	+	0.656293i
$34$	1.94177	−	1.12108i	0.333011	−	0.192264i
$35$		−	0.907610i		−	0.153414i
$36$	−2.10010	+	2.14233i	−0.350017	+	0.357055i
$37$			4.38424i			0.720765i	0.932805	+	0.360382i	$0.117354\pi$
$37$			4.38424i			0.720765i	−0.932805	+	0.360382i	$0.882646\pi$
$38$	6.49644	−	3.75072i	1.05386	−	0.608448i
$39$	5.47684	−	7.21158i	0.876996	−	1.15478i
$40$	0.641767	−	1.11157i	0.101472	−	0.175755i
$41$	−5.25780	−	3.03559i	−0.821130	−	0.474079i	0.0296762	−	0.999560i	$-0.490552\pi$
$41$	−5.25780	−	3.03559i	−0.821130	−	0.474079i	−0.850806	+	0.525480i	$0.823886\pi$
$42$	−0.740744	+	0.975368i	−0.114299	+	0.150503i
$43$	−6.72000	+	3.87979i	−1.02479	+	0.591663i	−0.915488	−	0.402346i	$-0.868195\pi$
$43$	−6.72000	+	3.87979i	−1.02479	+	0.591663i	−0.109302	+	0.994009i	$0.534862\pi$
$44$	−5.62047			−0.847318
$45$	2.74975	+	2.69555i	0.409909	+	0.401829i
$46$			6.14974i			0.906730i
$47$	−8.40445	+	4.85231i	−1.22591	+	0.707782i	−0.966173	−	0.257896i	$-0.916971\pi$
$47$	−8.40445	+	4.85231i	−1.22591	+	0.707782i	−0.259742	+	0.965678i	$0.583637\pi$
$48$	−1.59689	+	0.670782i	−0.230491	+	0.0968191i
$49$	3.24999	−	5.62915i	0.464285	−	0.804165i
$50$	2.90338	+	1.67627i	0.410600	+	0.237060i
$51$	−0.487736	+	3.85279i	−0.0682967	+	0.539498i
$52$	4.52776	−	2.61411i	0.627888	−	0.362511i
$53$	−1.21418			−0.166780			−0.0833901	−	0.996517i	$-0.526575\pi$
$53$	−1.21418			−0.166780			−0.0833901	+	0.996517i	$0.526575\pi$
$54$	−0.755068	−	5.14100i	−0.102752	−	0.699601i
$55$			7.21407i			0.972745i
$56$	−0.612382	+	0.353559i	−0.0818329	+	0.0472463i
$57$	−1.63179	+	12.8900i	−0.216135	+	1.70732i
$58$	−1.93671	−	1.11816i	−0.254302	−	0.146821i
$59$	−4.10979	−	2.37279i	−0.535049	−	0.308910i	0.208021	−	0.978124i	$-0.433298\pi$
$59$	−4.10979	−	2.37279i	−0.535049	−	0.308910i	−0.743070	+	0.669214i	$0.766631\pi$
$60$	0.860972	+	2.04966i	0.111151	+	0.264610i
$61$	5.11078	−	2.95071i	0.654369	−	0.377800i	−0.135759	−	0.990742i	$-0.543347\pi$
$61$	5.11078	−	2.95071i	0.654369	−	0.377800i	0.790128	+	0.612942i	$0.210014\pi$
$62$	0.846651	−	5.50302i	0.107525	−	0.698884i
$63$	−0.569413	−	2.04350i	−0.0717393	−	0.257457i
$64$	−1.00000			−0.125000
$65$	−3.35530	−	5.81154i	−0.416173	−	0.720833i
$66$	5.88775	−	7.75265i	0.724732	−	0.954285i
$67$	4.93759	−	8.55215i	0.603222	−	1.04481i	−0.389107	−	0.921192i	$-0.627216\pi$
$67$	4.93759	−	8.55215i	0.603222	−	1.04481i	0.992330	−	0.123620i	$-0.0394502\pi$
$68$	−1.12108	+	1.94177i	−0.135951	+	0.235474i
$69$	−8.48270	−	6.44219i	−1.02120	−	0.775549i
$70$	0.453805	+	0.786013i	0.0542401	+	0.0939465i
$71$			1.16581i			0.138357i	0.997604	+	0.0691783i	$0.0220378\pi$
$71$			1.16581i			0.138357i	−0.997604	+	0.0691783i	$0.977962\pi$
$72$	0.747578	−	2.90536i	0.0881029	−	0.342400i
$73$		−	16.1091i		−	1.88543i	−0.333598	−	0.942715i	$-0.608263\pi$
$73$		−	16.1091i		−	1.88543i	0.333598	−	0.942715i	$-0.391737\pi$
$74$	−2.19212	−	3.79686i	−0.254829	−	0.441376i
$75$	−5.35363	+	2.24882i	−0.618184	+	0.259672i
$76$	−3.75072	+	6.49644i	−0.430238	+	0.745193i
$77$	1.98717	−	3.44187i	0.226459	−	0.392238i
$78$	−1.13729	+	8.98383i	−0.128773	+	1.01722i
$79$	11.7293	−	6.77189i	1.31964	−	0.761897i	0.335973	−	0.941872i	$-0.390935\pi$
$79$	11.7293	−	6.77189i	1.31964	−	0.761897i	0.983671	+	0.179975i	$0.0576016\pi$
$80$			1.28353i			0.143504i
$81$	7.88226	+	4.34397i	0.875806	+	0.482663i
$82$	6.07118			0.670450
$83$	−4.57381	−	7.92206i	−0.502040	−	0.869559i	−0.999997	−	0.00235757i	$-0.999250\pi$
$83$	−4.57381	−	7.92206i	−0.502040	−	0.869559i	0.497957	−	0.867202i	$-0.334084\pi$
$84$	0.153819	−	1.21507i	0.0167830	−	0.132575i
$85$	2.49233	+	1.43895i	0.270331	+	0.156076i
$86$	3.87979	−	6.72000i	0.418369	−	0.724636i
$87$	3.57114	−	1.50008i	0.382867	−	0.160825i
$88$	4.86747	−	2.81024i	0.518874	−	0.299572i
$89$	8.17378			0.866419			0.433209	−	0.901293i	$-0.357381\pi$
$89$	8.17378			0.866419			0.433209	+	0.901293i	$0.357381\pi$
$90$	−3.72913	−	0.959542i	−0.393085	−	0.101145i
$91$			3.69696i			0.387547i
$92$	−3.07487	−	5.32583i	−0.320578	−	0.555257i
$93$	6.70372	+	6.93254i	0.695143	+	0.718871i
$94$	4.85231	−	8.40445i	0.500477	−	0.866852i
$95$	8.33841	+	4.81418i	0.855503	+	0.493925i
$96$	1.04755	−	1.37936i	0.106916	−	0.140780i
$97$	8.14690	+	14.1108i	0.827192	+	1.43274i	0.900232	+	0.435410i	$0.143396\pi$
$97$	8.14690	+	14.1108i	0.827192	+	1.43274i	−0.0730404	+	0.997329i	$0.523270\pi$
$98$			6.49998i			0.656598i
$99$	4.52594	+	16.2426i	0.454874	+	1.63245i
$100$	−3.35254			−0.335254
$101$	−8.12855	+	4.69302i	−0.808821	+	0.466973i	−0.846546	−	0.532315i	$-0.821322\pi$
$101$	−8.12855	+	4.69302i	−0.808821	+	0.466973i	0.0377253	+	0.999288i	$0.487989\pi$
$102$	−1.50400	−	3.58048i	−0.148918	−	0.354520i
$103$	5.56547	−	9.63968i	0.548382	−	0.949826i	−0.450004	−	0.893027i	$-0.648577\pi$
$103$	5.56547	−	9.63968i	0.548382	−	0.949826i	0.998386	−	0.0567989i	$-0.0180894\pi$
$104$	−2.61411	+	4.52776i	−0.256334	+	0.443984i
$105$	−1.55958	−	0.197432i	−0.152199	−	0.0192674i
$106$	1.05151	−	0.607089i	0.102132	−	0.0589657i
$107$		−	9.53282i		−	0.921572i	−0.887511	−	0.460786i	$-0.847568\pi$
$107$		−	9.53282i		−	0.921572i	0.887511	−	0.460786i	$-0.152432\pi$
$108$	3.22441	+	4.07470i	0.310269	+	0.392088i
$109$	−9.41960			−0.902234			−0.451117	−	0.892465i	$-0.648974\pi$
$109$	−9.41960			−0.902234			−0.451117	+	0.892465i	$0.648974\pi$
$110$	−3.60704	−	6.24757i	−0.343917	−	0.595682i
$111$	7.53360	+	0.953701i	0.715058	+	0.0905213i
$112$	0.353559	−	0.612382i	0.0334082	−	0.0578646i
$113$	9.47514	+	5.47047i	0.891346	+	0.514619i	0.874382	−	0.485237i	$-0.161267\pi$
$113$	9.47514	+	5.47047i	0.891346	+	0.514619i	0.0169633	+	0.999856i	$0.494600\pi$
$114$	−5.03184	−	11.9790i	−0.471275	−	1.12193i
$115$	−6.83589	+	3.94670i	−0.637450	+	0.368032i
$116$	2.23631			0.207637
$117$	−11.2005	−	10.9798i	−1.03549	−	1.01508i
$118$	4.74557			0.436865
$119$	−0.792736	−	1.37306i	−0.0726700	−	0.125868i
$120$	−1.77045	−	1.34457i	−0.161620	−	0.122742i
$121$	−10.2949	+	17.8312i	−0.935896	+	1.62102i
$122$	−2.95071	+	5.11078i	−0.267145	+	0.462709i
$123$	−6.35989	+	8.37433i	−0.573452	+	0.755088i
$124$	2.01829	+	5.18908i	0.181247	+	0.465993i
$125$			10.7208i			0.958895i
$126$	1.51488	+	1.48502i	0.134956	+	0.132296i
$127$		−	9.40116i		−	0.834218i	−0.908857	−	0.417109i	$-0.863043\pi$
$127$		−	9.40116i		−	0.834218i	0.908857	−	0.417109i	$-0.136957\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	5.20499	+	12.3912i	0.458274	+	1.09098i
$130$	5.81154	+	3.35530i	0.509706	+	0.294279i
$131$	14.5333	+	8.39082i	1.26978	+	0.733109i	0.974947	−	0.222439i	$-0.0714019\pi$
$131$	14.5333	+	8.39082i	1.26978	+	0.733109i	0.294835	+	0.955548i	$0.404735\pi$
$132$	−1.22262	+	9.65787i	−0.106415	+	0.840609i
$133$	−2.65220	−	4.59375i	−0.229975	−	0.398329i
$134$			9.87518i			0.853085i
$135$	5.23002	−	4.13864i	0.450129	−	0.356197i
$136$		−	2.24216i		−	0.192264i
$137$	1.01033	+	1.74994i	0.0863183	+	0.149508i	0.905952	−	0.423380i	$-0.139156\pi$
$137$	1.01033	+	1.74994i	0.0863183	+	0.149508i	−0.819634	+	0.572888i	$0.805823\pi$
$138$	10.5673	+	1.33775i	0.899551	+	0.113877i
$139$	−10.9271	−	6.30879i	−0.926829	−	0.535105i	−0.0410215	−	0.999158i	$-0.513061\pi$
$139$	−10.9271	−	6.30879i	−0.926829	−	0.535105i	−0.885807	+	0.464053i	$0.846395\pi$
$140$	−0.786013	−	0.453805i	−0.0664302	−	0.0383535i
$141$	6.50969	+	15.4972i	0.548214	+	1.30510i
$142$	−0.582907	−	1.00962i	−0.0489165	−	0.0847258i
$143$		−	29.3850i		−	2.45730i
$144$	0.805260	+	2.88991i	0.0671050	+	0.240826i
$145$		−	2.87039i		−	0.238373i
$146$	8.05456	+	13.9509i	0.666600	+	1.15459i
$147$	−8.96581	−	6.80909i	−0.739487	−	0.561604i
$148$	3.79686	+	2.19212i	0.312100	+	0.180191i
$149$	9.54696	+	5.51194i	0.782117	+	0.451556i	0.837180	−	0.546927i	$-0.184203\pi$
$149$	9.54696	+	5.51194i	0.782117	+	0.451556i	−0.0550627	+	0.998483i	$0.517536\pi$
$150$	3.51197	−	4.62435i	0.286751	−	0.377577i
$151$	10.6702	−	6.16045i	0.868330	−	0.501331i	0.00153714	−	0.999999i	$-0.499511\pi$
$151$	10.6702	−	6.16045i	0.868330	−	0.501331i	0.866793	+	0.498668i	$0.166177\pi$
$152$		−	7.50145i		−	0.608448i
$153$	6.51429	+	1.67619i	0.526649	+	0.135512i
$154$			3.97433i			0.320261i
$155$	6.66036	−	2.59054i	0.534973	−	0.208077i
$156$	−3.50699	−	8.34887i	−0.280784	−	0.668444i
$157$	−2.73647	+	4.73970i	−0.218394	+	0.378269i	−0.954317	−	0.298796i	$-0.903415\pi$
$157$	−2.73647	+	4.73970i	−0.218394	+	0.378269i	0.735923	+	0.677065i	$0.236748\pi$
$158$	−6.77189	+	11.7293i	−0.538742	+	0.933129i
$159$	−0.264120	+	2.08637i	−0.0209461	+	0.165460i
$160$	−0.641767	−	1.11157i	−0.0507362	−	0.0878776i
$161$	4.34859			0.342717
$162$	−8.99822	+	0.179141i	−0.706967	+	0.0140747i
$163$	0.342362			0.0268159			0.0134079	−	0.999910i	$-0.495732\pi$
$163$	0.342362			0.0268159			0.0134079	+	0.999910i	$0.495732\pi$
$164$	−5.25780	+	3.03559i	−0.410565	+	0.237040i
$165$	12.3962	+	1.56927i	0.965043	+	0.122168i
$166$	7.92206	+	4.57381i	0.614871	+	0.354996i
$167$	8.65410	−	14.9893i	0.669675	−	1.15991i	−0.308320	−	0.951283i	$-0.599767\pi$
$167$	8.65410	−	14.9893i	0.669675	−	1.15991i	0.977995	−	0.208628i	$-0.0668998\pi$
$168$	0.474322	+	1.12919i	0.0365947	+	0.0871187i
$169$	7.16710	+	12.4138i	0.551315	+	0.954906i
$170$	−2.87789			−0.220724
$171$	21.7944	+	5.60792i	1.66666	+	0.428848i
$172$			7.75958i			0.591663i
$173$	10.8981	−	6.29201i	0.828565	−	0.478372i	−0.0247959	−	0.999693i	$-0.507894\pi$
$173$	10.8981	−	6.29201i	0.828565	−	0.478372i	0.853361	+	0.521320i	$0.174560\pi$
$174$	−2.34266	+	3.08468i	−0.177597	+	0.233849i
$175$	1.18532	−	2.05303i	0.0896017	−	0.155195i
$176$	−2.81024	+	4.86747i	−0.211830	+	0.366900i
$177$	−4.97124	+	6.54584i	−0.373662	+	0.492016i
$178$	−7.07870	+	4.08689i	−0.530571	+	0.306325i
$179$	1.02900			0.0769110			0.0384555	−	0.999260i	$-0.487756\pi$
$179$	1.02900			0.0769110			0.0384555	+	0.999260i	$0.487756\pi$
$180$	3.70929	−	1.03358i	0.276475	−	0.0770384i
$181$		−	2.71575i		−	0.201860i	−0.994894	−	0.100930i	$-0.967818\pi$
$181$		−	2.71575i		−	0.201860i	0.994894	−	0.100930i	$-0.0321819\pi$
$182$	−1.84848	−	3.20166i	−0.137018	−	0.237323i
$183$	−3.95857	−	9.42392i	−0.292626	−	0.696636i
$184$	5.32583	+	3.07487i	0.392626	+	0.226683i
$185$	2.81366	−	4.87341i	0.206865	−	0.358300i
$186$	−9.27186	−	2.65190i	−0.679846	−	0.194447i
$187$	6.30101	+	10.9137i	0.460775	+	0.798086i
$188$			9.70462i			0.707782i
$189$	−3.63529	+	0.533921i	−0.264428	+	0.0388371i
$190$	−9.62837			−0.698515
$191$	−15.7481	+	9.09220i	−1.13950	+	0.657888i	−0.946306	−	0.323273i	$-0.895217\pi$
$191$	−15.7481	+	9.09220i	−1.13950	+	0.657888i	−0.193190	+	0.981161i	$0.561883\pi$
$192$	−0.217529	+	1.71834i	−0.0156988	+	0.124010i
$193$	13.0144	−	22.5415i	0.936795	−	1.62258i	0.165393	−	0.986228i	$-0.447111\pi$
$193$	13.0144	−	22.5415i	0.936795	−	1.62258i	0.771402	−	0.636348i	$-0.219556\pi$
$194$	−14.1108	−	8.14690i	−1.01310	−	0.584913i
$195$	−10.7161	+	4.50135i	−0.767393	+	0.322348i
$196$	−3.24999	−	5.62915i	−0.232142	−	0.402082i
$197$	−20.0578			−1.42906			−0.714531	−	0.699604i	$-0.753360\pi$
$197$	−20.0578			−1.42906			−0.714531	+	0.699604i	$0.753360\pi$
$198$	−12.0409	−	11.8036i	−0.855709	−	0.838843i
$199$		−	0.719173i		−	0.0509808i	−0.999675	−	0.0254904i	$-0.991885\pi$
$199$		−	0.719173i		−	0.0509808i	0.999675	−	0.0254904i	$-0.00811473\pi$
$200$	2.90338	−	1.67627i	0.205300	−	0.118530i
$201$	−13.6214	−	10.3448i	−0.960780	−	0.729665i
$202$	4.69302	−	8.12855i	0.330200	−	0.571923i
$203$	−0.790669	+	1.36948i	−0.0554941	+	0.0961185i
$204$	3.09274	+	2.34879i	0.216535	+	0.164448i
$205$	3.89628	+	6.74856i	0.272128	+	0.471340i
$206$			11.1309i			0.775529i
$207$	−12.9151	+	13.1748i	−0.897661	+	0.915710i
$208$		−	5.22821i		−	0.362511i
$209$	21.0808	+	36.5131i	1.45819	+	2.52566i
$210$	1.44935	−	0.608809i	0.100015	−	0.0420118i
$211$	12.0380	−	20.8504i	0.828730	−	1.43540i	−0.0703055	−	0.997526i	$-0.522397\pi$
$211$	12.0380	−	20.8504i	0.828730	−	1.43540i	0.899035	−	0.437876i	$-0.144269\pi$
$212$	−0.607089	+	1.05151i	−0.0416951	+	0.0722180i
$213$	2.00326	+	0.253599i	0.137261	+	0.0173763i
$214$	4.76641	+	8.25566i	0.325825	+	0.564345i
$215$	9.95969			0.679245
$216$	−4.82977	−	1.91659i	−0.328624	−	0.130408i
$217$	−3.89128	−	0.598682i	−0.264157	−	0.0406412i
$218$	8.15762	−	4.70980i	0.552503	−	0.318988i
$219$	−27.6809	−	3.50421i	−1.87050	−	0.236793i
$220$	6.24757	+	3.60704i	0.421211	+	0.243186i
$221$	−10.1520	−	5.86125i	−0.682896	−	0.394270i
$222$	−7.00114	+	2.94087i	−0.469886	+	0.197378i
$223$	−1.83957	+	1.06208i	−0.123187	+	0.0711219i	−0.560327	−	0.828271i	$-0.689325\pi$
$223$	−1.83957	+	1.06208i	−0.123187	+	0.0711219i	0.437140	+	0.899393i	$0.355991\pi$
$224$			0.707117i			0.0472463i
$225$	2.69966	+	9.68852i	0.179978	+	0.645901i
$226$	−10.9409			−0.727781
$227$	−9.18335	+	5.30201i	−0.609520	+	0.351907i	−0.772778	−	0.634677i	$-0.781133\pi$
$227$	−9.18335	+	5.30201i	−0.609520	+	0.351907i	0.163257	+	0.986583i	$0.447800\pi$
$228$	10.3472	+	7.85818i	0.685259	+	0.520420i
$229$	−5.44856	−	3.14573i	−0.360051	−	0.207876i	0.309052	−	0.951045i	$-0.399988\pi$
$229$	−5.44856	−	3.14573i	−0.360051	−	0.207876i	−0.669103	+	0.743169i	$0.733322\pi$
$230$	3.94670	−	6.83589i	0.260238	−	0.450745i
$231$	−5.48203	−	4.16333i	−0.360691	−	0.273927i
$232$	−1.93671	+	1.11816i	−0.127151	+	0.0734106i
$233$		−	2.77743i		−	0.181955i	−0.995853	−	0.0909777i	$-0.971001\pi$
$233$		−	2.77743i		−	0.181955i	0.995853	−	0.0909777i	$-0.0289992\pi$
$234$	15.1898	+	3.90849i	0.992991	+	0.255506i
$235$	12.4562			0.812554
$236$	−4.10979	+	2.37279i	−0.267524	+	0.154455i
$237$	−9.08493	−	21.6279i	−0.590129	−	1.40488i
$238$	1.37306	+	0.792736i	0.0890022	+	0.0513854i
$239$	11.1973	−	19.3943i	0.724293	−	1.25451i	−0.234971	−	0.972002i	$-0.575500\pi$
$239$	11.1973	−	19.3943i	0.724293	−	1.25451i	0.959264	−	0.282510i	$-0.0911671\pi$
$240$	2.20554	+	0.279207i	0.142367	+	0.0180227i
$241$	11.1238	−	6.42233i	0.716547	−	0.413699i	−0.0969333	−	0.995291i	$-0.530903\pi$
$241$	11.1238	−	6.42233i	0.716547	−	0.413699i	0.813481	+	0.581592i	$0.197570\pi$
$242$		−	20.5897i		−	1.32356i
$243$	9.17902	−	12.5994i	0.588834	−	0.808254i
$244$		−	5.90143i		−	0.377800i
$245$	−7.22521	+	4.17148i	−0.461602	+	0.266506i
$246$	1.32066	−	10.4323i	0.0842022	−	0.665141i
$247$	−33.9648	−	19.6096i	−2.16113	−	1.24773i
$248$	−4.34243	−	3.48473i	−0.275744	−	0.221281i
$249$	−14.6077	+	6.13605i	−0.925726	+	0.388857i
$250$	−5.36039	−	9.28446i	−0.339021	−	0.587201i
$251$	12.6675			0.799563			0.399782	−	0.916610i	$-0.369086\pi$
$251$	12.6675			0.799563			0.399782	+	0.916610i	$0.369086\pi$
$252$	−2.05443	−	0.528625i	−0.129417	−	0.0333003i
$253$	−34.5645			−2.17305
$254$	4.70058	+	8.14164i	0.294940	+	0.510852i
$255$	3.01475	−	3.96965i	0.188791	−	0.248589i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−5.56219	−	3.21133i	−0.346960	−	0.200317i	0.316386	−	0.948631i	$-0.397531\pi$
$257$	−5.56219	−	3.21133i	−0.346960	−	0.200317i	−0.663345	+	0.748313i	$0.730864\pi$
$258$	−10.7032	−	8.12858i	−0.666355	−	0.506064i
$259$	−2.68483	+	1.55009i	−0.166827	+	0.0963177i
$260$	−6.71059			−0.416173
$261$	−1.80081	−	6.46274i	−0.111468	−	0.400034i
$262$	−16.7816			−1.03677
$263$	−0.734546	−	1.27227i	−0.0452941	−	0.0784516i	0.842490	−	0.538713i	$-0.181089\pi$
$263$	−0.734546	−	1.27227i	−0.0452941	−	0.0784516i	−0.887784	+	0.460261i	$0.847756\pi$
$264$	−3.77011	−	8.97527i	−0.232034	−	0.552389i
$265$	1.34965	+	0.779220i	0.0829083	+	0.0478671i
$266$	4.59375	+	2.65220i	0.281661	+	0.162617i
$267$	1.77804	−	14.0453i	0.108814	−	0.859559i
$268$	−4.93759	−	8.55215i	−0.301611	−	0.522406i
$269$	−0.890223			−0.0542779			−0.0271389	−	0.999632i	$-0.508640\pi$
$269$	−0.890223			−0.0542779			−0.0271389	+	0.999632i	$0.508640\pi$
$270$	−2.46001	+	6.19918i	−0.149712	+	0.377270i
$271$			26.0532i			1.58262i	0.611417	+	0.791309i	$0.290600\pi$
$271$			26.0532i			1.58262i	−0.611417	+	0.791309i	$0.709400\pi$
$272$	1.12108	+	1.94177i	0.0679755	+	0.117737i
$273$	6.35262	+	0.804198i	0.384478	+	0.0486723i
$274$	−1.74994	−	1.01033i	−0.105718	−	0.0610363i
$275$	−9.42143	+	16.3184i	−0.568133	+	0.984036i
$276$	−9.82045	+	4.12514i	−0.591122	+	0.248304i
$277$	−14.3378	+	8.27793i	−0.861474	+	0.497372i	−0.864506	−	0.502623i	$-0.832368\pi$
$277$	−14.3378	+	8.27793i	−0.861474	+	0.497372i	0.00303145	+	0.999995i	$0.499035\pi$
$278$	12.6176			0.756752
$279$	13.3707	−	10.0112i	0.800483	−	0.599356i
$280$	0.907610			0.0542401
$281$	−14.6269	+	8.44483i	−0.872566	+	0.503776i	−0.868200	−	0.496214i	$-0.834723\pi$
$281$	−14.6269	+	8.44483i	−0.872566	+	0.503776i	−0.00436577	+	0.999990i	$0.501390\pi$
$282$	−13.3861	−	10.1661i	−0.797133	−	0.605383i
$283$	−2.97360	+	5.15043i	−0.176762	+	0.306161i	−0.940770	−	0.339046i	$-0.889896\pi$
$283$	−2.97360	+	5.15043i	−0.176762	+	0.306161i	0.764008	+	0.645207i	$0.223229\pi$
$284$	1.00962	+	0.582907i	0.0599102	+	0.0345892i
$285$	10.0862	−	13.2810i	0.597457	−	0.786697i
$286$	14.6925	+	25.4482i	0.868786	+	1.50478i
$287$		−	4.29304i		−	0.253410i
$288$	−2.14233	−	2.10010i	−0.126238	−	0.123750i
$289$	−11.9727			−0.704277
$290$	1.43519	+	2.48583i	0.0842775	+	0.145973i
$291$	26.0194	−	10.9296i	1.52528	−	0.640704i
$292$	−13.9509	−	8.05456i	−0.816416	−	0.471358i
$293$	2.50710	+	1.44747i	0.146466	+	0.0845624i	0.571442	−	0.820642i	$-0.306384\pi$
$293$	2.50710	+	1.44747i	0.146466	+	0.0845624i	−0.424976	+	0.905205i	$0.639717\pi$
$294$	11.1692	+	1.41394i	0.651399	+	0.0824626i
$295$	3.04555	+	5.27505i	0.177319	+	0.307125i
$296$	−4.38424			−0.254829
$297$	28.8948	−	4.24384i	1.67665	−	0.246252i
$298$	−11.0239			−0.638596
$299$	27.8446	−	16.0761i	1.61029	−	0.929704i
$300$	−0.729276	+	5.76079i	−0.0421048	+	0.332599i
$301$	−4.75183	−	2.74347i	−0.273891	−	0.158131i
$302$	−6.16045	+	10.6702i	−0.354494	+	0.614002i
$303$	6.29599	+	14.9885i	0.361695	+	0.861064i
$304$	3.75072	+	6.49644i	0.215119	+	0.372597i
$305$	−7.57468			−0.433725
$306$	−6.47964	+	1.80552i	−0.370416	+	0.103215i
$307$	−25.9885			−1.48324			−0.741622	−	0.670818i	$-0.765943\pi$
$307$	−25.9885			−1.48324			−0.741622	+	0.670818i	$0.765943\pi$
$308$	−1.98717	−	3.44187i	−0.113229	−	0.196119i
$309$	−15.3536	−	11.6603i	−0.873433	−	0.663329i
$310$	−4.47277	+	5.57365i	−0.254036	+	0.316562i
$311$	7.22219	+	4.16974i	0.409533	+	0.236444i	0.690589	−	0.723247i	$-0.257351\pi$
$311$	7.22219	+	4.16974i	0.409533	+	0.236444i	−0.281056	+	0.959691i	$0.590685\pi$
$312$	7.21158	+	5.47684i	0.408275	+	0.310065i
$313$	−0.192119	+	0.110920i	−0.0108592	+	0.00626955i	−0.505420	−	0.862874i	$-0.668662\pi$
$313$	−0.192119	+	0.110920i	−0.0108592	+	0.00626955i	0.494561	+	0.869143i	$0.335329\pi$
$314$		−	5.47293i		−	0.308855i
$315$	−0.678509	+	2.63693i	−0.0382296	+	0.148574i
$316$		−	13.5438i		−	0.761897i
$317$	5.84368	−	3.37385i	0.328214	−	0.189494i	−0.326834	−	0.945082i	$-0.605982\pi$
$317$	5.84368	−	3.37385i	0.328214	−	0.189494i	0.655048	+	0.755587i	$0.272648\pi$
$318$	−0.814450	−	1.93891i	−0.0456721	−	0.108729i
$319$	6.28457	−	10.8852i	0.351869	−	0.609454i
$320$	1.11157	+	0.641767i	0.0621389	+	0.0358759i
$321$	−16.3806	−	2.07367i	−0.914275	−	0.115741i
$322$	−3.76599	+	2.17430i	−0.209870	+	0.121169i
$323$	16.8195			0.935860
$324$	7.70311	−	4.65425i	0.427951	−	0.258569i
$325$		−	17.5278i		−	0.972266i
$326$	−0.296494	+	0.171181i	−0.0164213	+	0.00948084i
$327$	−2.04904	+	16.1860i	−0.113312	+	0.895091i
$328$	3.03559	−	5.25780i	0.167612	−	0.290313i
$329$	−5.94293	−	3.43115i	−0.327644	−	0.189166i
$330$	−11.5201	+	4.83907i	−0.634159	+	0.266382i
$331$	−27.5134	+	15.8849i	−1.51228	+	0.873113i	−0.512379	+	0.858759i	$0.671236\pi$
$331$	−27.5134	+	15.8849i	−1.51228	+	0.873113i	−0.999897	+	0.0143535i	$0.995431\pi$
$332$	−9.14761			−0.502040
$333$	3.27756	−	12.7378i	0.179609	−	0.698027i
$334$			17.3082i			0.947063i
$335$	−10.9770	+	6.33757i	−0.599737	+	0.346258i
$336$	−0.975368	−	0.740744i	−0.0532107	−	0.0404109i
$337$	−0.805514	−	0.465064i	−0.0438792	−	0.0253336i	0.477900	−	0.878414i	$-0.341398\pi$
$337$	−0.805514	−	0.465064i	−0.0438792	−	0.0253336i	−0.521779	+	0.853081i	$0.674731\pi$
$338$	−12.4138	−	7.16710i	−0.675221	−	0.389839i
$339$	11.4612	−	15.0915i	0.622489	−	0.819657i
$340$	2.49233	−	1.43895i	0.135165	−	0.0780378i
$341$	30.9296	+	4.75858i	1.67493	+	0.257692i
$342$	−21.6785	+	6.04061i	−1.17224	+	0.326639i
$343$	9.54607			0.515440
$344$	−3.87979	−	6.72000i	−0.209184	−	0.362318i
$345$	5.29476	+	12.6049i	0.285060	+	0.678624i
$346$	−6.29201	+	10.8981i	−0.338260	+	0.585884i
$347$	3.19676	−	5.53695i	0.171611	−	0.297239i	−0.767372	−	0.641202i	$-0.778436\pi$
$347$	3.19676	−	5.53695i	0.171611	−	0.297239i	0.938983	+	0.343963i	$0.111769\pi$
$348$	0.486464	−	3.84274i	0.0260772	−	0.205993i
$349$	−13.9063	−	24.0864i	−0.744387	−	1.28932i	−0.950481	−	0.310784i	$-0.899408\pi$
$349$	−13.9063	−	24.0864i	−0.744387	−	1.28932i	0.206093	−	0.978532i	$-0.433925\pi$
$350$			2.37064i			0.126716i
$351$	−21.3034	+	16.8579i	−1.13709	+	0.899807i
$352$		−	5.62047i		−	0.299572i
$353$	−2.21177	−	3.83090i	−0.117721	−	0.203898i	0.801143	−	0.598473i	$-0.204225\pi$
$353$	−2.21177	−	3.83090i	−0.117721	−	0.203898i	−0.918864	+	0.394574i	$0.870892\pi$
$354$	1.03230	−	8.15449i	0.0548662	−	0.433406i
$355$	0.748181	−	1.29589i	0.0397093	−	0.0687786i
$356$	4.08689	−	7.07870i	0.216605	−	0.375170i
$357$	−2.53182	+	1.06351i	−0.133998	+	0.0562867i
$358$	−0.891140	+	0.514500i	−0.0470982	+	0.0271922i
$359$		−	29.5785i		−	1.56109i	−0.625098	−	0.780547i	$-0.714941\pi$
$359$		−	29.5785i		−	1.56109i	0.625098	−	0.780547i	$-0.285059\pi$
$360$	−2.69555	+	2.74975i	−0.142068	+	0.144925i
$361$	37.2717			1.96167
$362$	1.35788	+	2.35191i	0.0713684	+	0.123614i
$363$	28.4006	+	21.5689i	1.49065	+	1.13207i
$364$	3.20166	+	1.84848i	0.167813	+	0.0968867i
$365$	−10.3383	+	17.9065i	−0.541132	+	0.937268i
$366$	8.14018	+	6.18206i	0.425494	+	0.323142i
$367$	−0.892986	+	0.515566i	−0.0466135	+	0.0269123i	−0.523126	−	0.852256i	$-0.675234\pi$
$367$	−0.892986	+	0.515566i	−0.0466135	+	0.0269123i	0.476512	+	0.879168i	$0.341901\pi$
$368$	−6.14974			−0.320578
$369$	13.0065	+	12.7501i	0.677089	+	0.663744i
$370$			5.62733i			0.292551i
$371$	−0.429283	−	0.743541i	−0.0222873	−	0.0386027i
$372$	9.35562	−	2.33932i	0.485066	−	0.121288i
$373$	−3.44710	+	5.97055i	−0.178484	+	0.309143i	−0.941361	−	0.337400i	$-0.890453\pi$
$373$	−3.44710	+	5.97055i	−0.178484	+	0.309143i	0.762877	+	0.646543i	$0.223786\pi$
$374$	−10.9137	−	6.30101i	−0.564332	−	0.325817i
$375$	18.4219	+	2.33208i	0.951303	+	0.120428i
$376$	−4.85231	−	8.40445i	−0.250239	−	0.433426i
$377$			11.6919i			0.602165i
$378$	2.88129	−	2.28003i	0.148198	−	0.117272i
$379$	4.71688			0.242290			0.121145	−	0.992635i	$-0.461343\pi$
$379$	4.71688			0.242290			0.121145	+	0.992635i	$0.461343\pi$
$380$	8.33841	−	4.81418i	0.427752	−	0.246962i
$381$	−16.1544	−	2.04503i	−0.827612	−	0.104770i
$382$	9.09220	−	15.7481i	0.465197	−	0.805745i
$383$	−13.7048	+	23.7375i	−0.700284	+	1.21293i	0.268083	+	0.963396i	$0.413610\pi$
$383$	−13.7048	+	23.7375i	−0.700284	+	1.21293i	−0.968367	+	0.249531i	$0.919723\pi$
$384$	−0.670782	−	1.59689i	−0.0342307	−	0.0814908i
$385$	−4.41777	+	2.55060i	−0.225150	+	0.129991i
$386$			26.0287i			1.32483i
$387$	22.4245	−	6.24848i	1.13990	−	0.317628i
$388$	16.2938			0.827192
$389$	9.35379	+	16.2012i	0.474256	+	0.821435i	0.999565	−	0.0294759i	$-0.00938382\pi$
$389$	9.35379	+	16.2012i	0.474256	+	0.821435i	−0.525310	+	0.850911i	$0.676050\pi$
$390$	7.02971	−	9.25631i	0.355963	−	0.468712i
$391$	−6.89436	+	11.9414i	−0.348663	+	0.603902i
$392$	5.62915	+	3.24999i	0.284315	+	0.164149i
$393$	17.5797	−	23.1479i	0.886777	−	1.16766i
$394$	17.3706	−	10.0289i	0.875118	−	0.505250i
$395$	−17.3839			−0.874679
$396$	16.3295	+	4.20174i	0.820589	+	0.211145i
$397$	−9.67823			−0.485736			−0.242868	−	0.970059i	$-0.578088\pi$
$397$	−9.67823			−0.485736			−0.242868	+	0.970059i	$0.578088\pi$
$398$	0.359586	+	0.622822i	0.0180244	+	0.0312192i
$399$	−8.47054	+	3.55810i	−0.424057	+	0.178128i
$400$	−1.67627	+	2.90338i	−0.0838135	+	0.145169i
$401$	−5.49997	+	9.52623i	−0.274656	+	0.475717i	−0.970048	−	0.242913i	$-0.921897\pi$
$401$	−5.49997	+	9.52623i	−0.274656	+	0.475717i	0.695393	+	0.718630i	$0.255230\pi$
$402$	16.9689	+	2.14814i	0.846331	+	0.107140i
$403$	−27.1296	+	10.5520i	−1.35142	+	0.525634i
$404$			9.38604i			0.466973i
$405$	−5.97389	−	9.88721i	−0.296845	−	0.491300i
$406$		−	1.58134i		−	0.0784804i
$407$	21.3402	−	12.3208i	1.05779	−	0.610717i
$408$	−3.85279	−	0.487736i	−0.190741	−	0.0241465i
$409$	−5.54067	−	3.19891i	−0.273969	−	0.158176i	0.356721	−	0.934211i	$-0.383895\pi$
$409$	−5.54067	−	3.19891i	−0.273969	−	0.158176i	−0.630690	+	0.776035i	$0.717228\pi$
$410$	−6.74856	−	3.89628i	−0.333288	−	0.192424i
$411$	3.22677	−	1.35542i	0.159165	−	0.0668581i
$412$	−5.56547	−	9.63968i	−0.274191	−	0.474913i
$413$		−	3.35568i		−	0.165122i
$414$	4.59741	−	17.8672i	0.225950	−	0.878126i
$415$			11.7413i			0.576357i
$416$	2.61411	+	4.52776i	0.128167	+	0.221992i
$417$	−13.2176	+	17.4042i	−0.647269	+	0.852286i
$418$	−36.5131	−	21.0808i	−1.78591	−	1.03110i
$419$	−2.55729	−	1.47645i	−0.124932	−	0.0721294i	0.436232	−	0.899834i	$-0.356313\pi$
$419$	−2.55729	−	1.47645i	−0.124932	−	0.0721294i	−0.561164	+	0.827705i	$0.689646\pi$
$420$	−0.950771	+	1.25192i	−0.0463929	+	0.0610874i
$421$	10.3560	+	17.9370i	0.504718	+	0.874198i	0.999985	+	0.00545676i	$0.00173695\pi$
$421$	10.3560	+	17.9370i	0.504718	+	0.874198i	−0.495267	+	0.868741i	$0.664930\pi$
$422$			24.0760i			1.17200i
$423$	28.0454	−	7.81474i	1.36362	−	0.379966i
$424$		−	1.21418i		−	0.0589657i
$425$	3.75847	+	6.50986i	0.182312	+	0.315774i
$426$	−1.86167	+	0.782008i	−0.0901984	+	0.0378884i
$427$	3.61392	+	2.08650i	0.174890	+	0.100973i
$428$	−8.25566	−	4.76641i	−0.399052	−	0.230393i
$429$	−50.4934	−	6.39211i	−2.43784	−	0.308614i
$430$	−8.62535	+	4.97985i	−0.415951	+	0.240150i
$431$			9.04220i			0.435548i	0.975999	+	0.217774i	$0.0698795\pi$
$431$			9.04220i			0.435548i	−0.975999	+	0.217774i	$0.930121\pi$
$432$	5.14100	−	0.755068i	0.247346	−	0.0363282i
$433$			5.45888i			0.262337i	0.991360	+	0.131169i	$0.0418729\pi$
$433$			5.45888i			0.262337i	−0.991360	+	0.131169i	$0.958127\pi$
$434$	3.66929	−	1.42717i	0.176131	−	0.0685061i
$435$	−4.93229	−	0.624394i	−0.236485	−	0.0299374i
$436$	−4.70980	+	8.15762i	−0.225559	+	0.390679i
$437$	−23.0660	+	39.9515i	−1.10340	+	1.91114i
$438$	25.7245	−	10.8057i	1.22916	−	0.516317i
$439$	12.7365	+	22.0602i	0.607878	+	1.05288i	0.991590	+	0.129422i	$0.0413123\pi$
$439$	12.7365	+	22.0602i	0.607878	+	1.05288i	−0.383712	+	0.923453i	$0.625354\pi$
$440$	−7.21407			−0.343917
$441$	−13.6506	+	13.9251i	−0.650030	+	0.663100i
$442$	11.7225			0.557582
$443$	−0.430684	+	0.248656i	−0.0204624	+	0.0118140i	−0.510196	−	0.860058i	$-0.670427\pi$
$443$	−0.430684	+	0.248656i	−0.0204624	+	0.0118140i	0.489734	+	0.871872i	$0.337094\pi$
$444$	4.59273	−	6.04744i	0.217961	−	0.286999i
$445$	−9.08576	−	5.24566i	−0.430706	−	0.248668i
$446$	1.06208	−	1.83957i	0.0502908	−	0.0871061i
$447$	11.5481	−	15.2059i	0.546207	−	0.719214i
$448$	−0.353559	−	0.612382i	−0.0167041	−	0.0289323i
$449$	−9.00131			−0.424798			−0.212399	−	0.977183i	$-0.568128\pi$
$449$	−9.00131			−0.424798			−0.212399	+	0.977183i	$0.568128\pi$
$450$	−7.18224	−	7.04067i	−0.338574	−	0.331901i
$451$			34.1229i			1.60678i
$452$	9.47514	−	5.47047i	0.445673	−	0.257309i
$453$	−8.26465	−	19.6751i	−0.388307	−	0.924417i
$454$	5.30201	−	9.18335i	0.248836	−	0.430996i
$455$	2.37259	−	4.10944i	0.111229	−	0.192654i
$456$	−12.8900	−	1.63179i	−0.603630	−	0.0764154i
$457$	15.0777	−	8.70512i	0.705306	−	0.407208i	−0.104015	−	0.994576i	$-0.533169\pi$
$457$	15.0777	−	8.70512i	0.705306	−	0.407208i	0.809320	+	0.587367i	$0.199836\pi$
$458$	6.29146			0.293981
$459$	4.29731	−	10.8291i	0.200581	−	0.505460i
$460$			7.89341i			0.368032i
$461$	−4.59254	−	7.95451i	−0.213896	−	0.370478i	0.739035	−	0.673667i	$-0.235282\pi$
$461$	−4.59254	−	7.95451i	−0.213896	−	0.370478i	−0.952930	+	0.303189i	$0.901949\pi$
$462$	6.82924	+	0.864535i	0.317725	+	0.0402218i
$463$	−9.79654	−	5.65603i	−0.455284	−	0.262858i	0.254775	−	0.967000i	$-0.417998\pi$
$463$	−9.79654	−	5.65603i	−0.455284	−	0.262858i	−0.710059	+	0.704142i	$0.751332\pi$
$464$	1.11816	−	1.93671i	0.0519092	−	0.0899093i
$465$	−3.00260	−	12.0083i	−0.139242	−	0.556870i
$466$	1.38871	+	2.40532i	0.0643309	+	0.111424i
$467$			9.06505i			0.419480i	0.977757	+	0.209740i	$0.0672618\pi$
$467$			9.06505i			0.419480i	−0.977757	+	0.209740i	$0.932738\pi$
$468$	−15.1090	+	4.21007i	−0.698416	+	0.194610i
$469$	6.98291			0.322441
$470$	−10.7874	+	6.22811i	−0.497586	+	0.287281i
$471$	7.54913	+	5.73319i	0.347846	+	0.264172i
$472$	2.37279	−	4.10979i	0.109216	−	0.189168i
$473$	37.7696	+	21.8063i	1.73665	+	1.00265i
$474$	18.6817	+	14.1878i	0.858080	+	0.651669i
$475$	12.5744	+	21.7796i	0.576955	+	0.999316i
$476$	−1.58547			−0.0726700
$477$	3.52763	+	0.907693i	0.161519	+	0.0415604i
$478$			22.3946i			1.02431i
$479$	−20.5716	+	11.8770i	−0.939939	+	0.542674i	−0.889941	−	0.456075i	$-0.849255\pi$
$479$	−20.5716	+	11.8770i	−0.939939	+	0.542674i	−0.0499981	+	0.998749i	$0.515922\pi$
$480$	−2.04966	+	0.860972i	−0.0935538	+	0.0392978i
$481$	−11.4609	+	19.8508i	−0.522571	+	0.905119i
$482$	−6.42233	+	11.1238i	−0.292529	+	0.506675i
$483$	0.945947	−	7.47234i	0.0430421	−	0.340003i
$484$	10.2949	+	17.8312i	0.467948	+	0.810510i
$485$		−	20.9136i		−	0.949640i
$486$	−1.64955	+	15.5009i	−0.0748252	+	0.703137i
$487$		−	24.6747i		−	1.11812i	−0.829129	−	0.559058i	$-0.811163\pi$
$487$		−	24.6747i		−	1.11812i	0.829129	−	0.559058i	$-0.188837\pi$
$488$	2.95071	+	5.11078i	0.133572	+	0.231354i
$489$	0.0744738	−	0.588293i	0.00336782	−	0.0266035i
$490$	4.17148	−	7.22521i	0.188448	−	0.326402i
$491$	19.7051	−	34.1302i	0.889277	−	1.54027i	0.0485460	−	0.998821i	$-0.484541\pi$
$491$	19.7051	−	34.1302i	0.889277	−	1.54027i	0.840731	−	0.541453i	$-0.182125\pi$
$492$	4.07244	+	9.69499i	0.183600	+	0.437084i
$493$	−2.50709	−	4.34241i	−0.112914	−	0.195572i
$494$	39.2192			1.76455
$495$	5.39308	−	20.9595i	0.242401	−	0.942059i
$496$	5.50302	+	0.846651i	0.247093	+	0.0380158i
$497$	−0.713923	+	0.412184i	−0.0320238	+	0.0184890i
$498$	9.58262	−	12.6178i	0.429407	−	0.565419i
$499$	24.6558	+	14.2350i	1.10375	+	0.637247i	0.937202	−	0.348787i	$-0.113406\pi$
$499$	24.6558	+	14.2350i	1.10375	+	0.637247i	0.166543	+	0.986034i	$0.446740\pi$
$500$	9.28446	+	5.36039i	0.415214	+	0.239724i
$501$	−23.8742	−	18.1313i	−1.06662	−	0.810046i
$502$	−10.9703	+	6.33373i	−0.489631	+	0.282688i
$503$			19.7297i			0.879706i	0.898070	+	0.439853i	$0.144969\pi$
$503$			19.7297i			0.879706i	−0.898070	+	0.439853i	$0.855031\pi$
$504$	2.04350	−	0.569413i	0.0910249	−	0.0253637i
$505$	12.0473			0.536098
$506$	29.9337	−	17.2822i	1.33072	−	0.768289i
$507$	22.8901	−	9.61513i	1.01659	−	0.427023i
$508$	−8.14164	−	4.70058i	−0.361227	−	0.208554i
$509$	−6.17585	+	10.6969i	−0.273740	+	0.474131i	−0.969816	−	0.243836i	$-0.921594\pi$
$509$	−6.17585	+	10.6969i	−0.273740	+	0.474131i	0.696077	+	0.717968i	$0.254927\pi$
$510$	−0.626026	+	4.94519i	−0.0277209	+	0.218977i
$511$	9.86493	−	5.69552i	0.436399	−	0.251955i
$512$		−	1.00000i		−	0.0441942i
$513$	14.3772	−	36.2303i	0.634770	−	1.59961i
$514$	6.42266			0.283291
$515$	−12.3729	+	7.14347i	−0.545213	+	0.314779i
$516$	13.3336	+	1.68794i	0.586978	+	0.0743073i
$517$	47.2370	+	27.2723i	2.07748	+	1.19943i
$518$	1.55009	−	2.68483i	0.0681069	−	0.117965i
$519$	−8.44113	−	20.0953i	−0.370525	−	0.882084i
$520$	5.81154	−	3.35530i	0.254853	−	0.147139i
$521$			29.3472i			1.28572i	0.765982	+	0.642862i	$0.222253\pi$
$521$			29.3472i			1.28572i	−0.765982	+	0.642862i	$0.777747\pi$
$522$	4.79092	+	4.69649i	0.209693	+	0.205560i
$523$		−	24.8762i		−	1.08776i	−0.839163	−	0.543880i	$-0.816955\pi$
$523$		−	24.8762i		−	1.08776i	0.839163	−	0.543880i	$-0.183045\pi$
$524$	14.5333	−	8.39082i	0.634891	−	0.366554i
$525$	−3.26996	−	2.48337i	−0.142713	−	0.108383i
$526$	1.27227	+	0.734546i	0.0554737	+	0.0320277i
$527$	7.81333	−	9.73642i	0.340354	−	0.424125i
$528$	7.75265	+	5.88775i	0.337391	+	0.256231i
$529$	−7.40967	−	12.8339i	−0.322160	−	0.557997i
$530$	−1.55844			−0.0676943
$531$	10.1666	+	9.96619i	0.441192	+	0.432496i
$532$	−5.30440			−0.229975
$533$	−15.8707	−	27.4889i	−0.687437	−	1.19068i
$534$	5.48283	+	13.0526i	0.237265	+	0.564842i
$535$	−6.11785	+	10.5964i	−0.264498	+	0.458123i
$536$	8.55215	+	4.93759i	0.369397	+	0.213271i
$537$	0.223838	−	1.76817i	0.00965931	−	0.0763021i
$538$	0.770956	−	0.445112i	0.0332383	−	0.0191901i
$539$	−36.5330			−1.57359
$540$	−0.969155	−	6.59865i	−0.0417058	−	0.283961i
$541$	16.8232			0.723285			0.361642	−	0.932317i	$-0.382216\pi$
$541$	16.8232			0.723285			0.361642	+	0.932317i	$0.382216\pi$
$542$	−13.0266	−	22.5627i	−0.559540	−	0.969151i
$543$	−4.66658	−	0.590756i	−0.200262	−	0.0253518i
$544$	−1.94177	−	1.12108i	−0.0832527	−	0.0480659i
$545$	10.4706	+	6.04519i	0.448511	+	0.258948i
$546$	−5.90363	+	2.47986i	−0.252652	+	0.106128i
$547$	−8.62009	−	14.9304i	−0.368569	−	0.638379i	0.620773	−	0.783990i	$-0.286819\pi$
$547$	−8.62009	−	14.9304i	−0.368569	−	0.638379i	−0.989342	+	0.145611i	$0.953485\pi$
$548$	2.02066			0.0863183
$549$	−17.0546	+	4.75218i	−0.727871	+	0.202818i
$550$		−	18.8429i		−	0.803462i
$551$	−8.38780	−	14.5281i	−0.357332	−	0.618918i
$552$	6.44219	−	8.48270i	0.274198	−	0.361048i
$553$	8.29396	+	4.78852i	0.352695	+	0.203629i
$554$	8.27793	−	14.3378i	0.351695	−	0.609154i
$555$	−7.76210	−	5.89493i	−0.329483	−	0.250226i
$556$	−10.9271	+	6.30879i	−0.463414	+	0.267552i
$557$	34.2080			1.44944			0.724719	−	0.689044i	$-0.241969\pi$
$557$	34.2080			1.44944			0.724719	+	0.689044i	$0.241969\pi$
$558$	−6.57376	+	15.3553i	−0.278289	+	0.650042i
$559$	−40.5687			−1.71587
$560$	−0.786013	+	0.453805i	−0.0332151	+	0.0191768i
$561$	20.1240	−	8.45321i	0.849636	−	0.356895i
$562$	8.44483	−	14.6269i	0.356223	−	0.616997i
$563$	−26.0864	−	15.0610i	−1.09941	−	0.634745i	−0.163345	−	0.986569i	$-0.552228\pi$
$563$	−26.0864	−	15.0610i	−1.09941	−	0.634745i	−0.936066	+	0.351824i	$0.885562\pi$
$564$	16.6758	+	2.11104i	0.702178	+	0.0888908i
$565$	−7.02154	−	12.1617i	−0.295398	−	0.511645i
$566$		−	5.94720i		−	0.249979i
$567$	0.126674	+	6.36280i	0.00531981	+	0.267212i
$568$	−1.16581			−0.0489165
$569$	10.9340	+	18.9382i	0.458375	+	0.793929i	0.998875	−	0.0474147i	$-0.0150982\pi$
$569$	10.9340	+	18.9382i	0.458375	+	0.793929i	−0.540500	+	0.841344i	$0.681765\pi$
$570$	−2.09445	+	16.5448i	−0.0877270	+	0.692985i
$571$	1.76321	+	1.01799i	0.0737879	+	0.0426015i	0.536440	−	0.843938i	$-0.319769\pi$
$571$	1.76321	+	1.01799i	0.0737879	+	0.0426015i	−0.462652	+	0.886540i	$0.653102\pi$
$572$	−25.4482	−	14.6925i	−1.06404	−	0.614325i
$573$	12.1978	+	29.0384i	0.509569	+	1.21310i
$574$	2.14652	+	3.71788i	0.0895939	+	0.155181i
$575$	−20.6173			−0.859799
$576$	2.90536	+	0.747578i	0.121057	+	0.0311491i
$577$	4.33070			0.180289			0.0901447	−	0.995929i	$-0.471267\pi$
$577$	4.33070			0.180289			0.0901447	+	0.995929i	$0.471267\pi$
$578$	10.3687	−	5.98636i	0.431280	−	0.249000i
$579$	−35.9030	−	27.2665i	−1.49208	−	1.13316i
$580$	−2.48583	−	1.43519i	−0.103218	−	0.0595932i
$581$	3.23422	−	5.60183i	0.134178	−	0.232403i
$582$	−17.0686	+	22.4750i	−0.707518	+	0.931618i
$583$	3.41213	+	5.90998i	0.141316	+	0.244766i
$584$	16.1091			0.666600
$585$	5.40377	+	19.3930i	0.223418	+	0.801801i
$586$	−2.89495			−0.119589
$587$	2.48794	+	4.30924i	0.102688	+	0.177861i	0.912791	−	0.408426i	$-0.133922\pi$
$587$	2.48794	+	4.30924i	0.102688	+	0.177861i	−0.810103	+	0.586287i	$0.800589\pi$
$588$	−10.3797	+	4.36007i	−0.428054	+	0.179806i
$589$	26.1405	−	32.5745i	1.07710	−	1.34221i
$590$	−5.27505	−	3.04555i	−0.217170	−	0.125383i
$591$	−4.36317	+	34.4661i	−0.179477	+	1.41775i
$592$	3.79686	−	2.19212i	0.156050	−	0.0900956i
$593$		−	22.5240i		−	0.924952i	−0.886632	−	0.462476i	$-0.846961\pi$
$593$		−	22.5240i		−	0.924952i	0.886632	−	0.462476i	$-0.153039\pi$
$594$	−22.9018	+	18.1227i	−0.939670	+	0.743583i
$595$			2.03501i			0.0834272i
$596$	9.54696	−	5.51194i	0.391059	−	0.225778i
$597$	−1.23578	−	0.156441i	−0.0505772	−	0.00640272i
$598$	−16.0761	+	27.8446i	−0.657400	+	1.13865i
$599$	15.7974	+	9.12061i	0.645463	+	0.372658i	0.786716	−	0.617316i	$-0.211780\pi$
$599$	15.7974	+	9.12061i	0.645463	+	0.372658i	−0.141253	+	0.989974i	$0.545113\pi$
$600$	−2.24882	−	5.35363i	−0.0918078	−	0.218561i
$601$	−4.15025	+	2.39615i	−0.169292	+	0.0977409i	−0.582252	−	0.813008i	$-0.697828\pi$
$601$	−4.15025	+	2.39615i	−0.169292	+	0.0977409i	0.412960	+	0.910749i	$0.364495\pi$
$602$	5.48694			0.223631
$603$	−20.7389	+	21.1559i	−0.844553	+	0.861534i
$604$		−	12.3209i		−	0.501331i
$605$	22.8870	−	13.2138i	0.930488	−	0.537218i
$606$	−12.9467	−	9.83239i	−0.525924	−	0.399413i
$607$	8.42581	−	14.5939i	0.341993	−	0.592349i	−0.642810	−	0.766026i	$-0.722231\pi$
$607$	8.42581	−	14.5939i	0.341993	−	0.592349i	0.984803	+	0.173676i	$0.0555647\pi$
$608$	−6.49644	−	3.75072i	−0.263466	−	0.152112i
$609$	2.18123	+	1.65654i	0.0883879	+	0.0671262i
$610$	6.55987	−	3.78734i	0.265601	−	0.153345i
$611$	−50.7378			−2.05263
$612$	4.70877	−	4.80345i	0.190341	−	0.194168i
$613$		−	14.7800i		−	0.596958i	−0.954416	−	0.298479i	$-0.903521\pi$
$613$		−	14.7800i		−	0.596958i	0.954416	−	0.298479i	$-0.0964794\pi$
$614$	22.5067	−	12.9943i	0.908297	−	0.524406i
$615$	12.4439	−	5.22712i	0.501785	−	0.210778i
$616$	3.44187	+	1.98717i	0.138677	+	0.0800652i
$617$	−1.12883	−	0.651729i	−0.0454449	−	0.0262376i	0.477105	−	0.878846i	$-0.341686\pi$
$617$	−1.12883	−	0.651729i	−0.0454449	−	0.0262376i	−0.522550	+	0.852608i	$0.675019\pi$
$618$	19.1267	+	2.42131i	0.769389	+	0.0973993i
$619$	−33.5003	+	19.3414i	−1.34649	+	0.777398i	−0.987751	−	0.156039i	$-0.950127\pi$
$619$	−33.5003	+	19.3414i	−1.34649	+	0.777398i	−0.358741	+	0.933437i	$0.616794\pi$
$620$	1.08671	−	7.06331i	0.0436432	−	0.283669i
$621$	19.8293	+	25.0584i	0.795721	+	1.00556i
$622$	−8.33947			−0.334382
$623$	2.88991	+	5.00547i	0.115782	+	0.200540i
$624$	−8.98383	−	1.13729i	−0.359641	−	0.0455280i
$625$	−1.50110	+	2.59999i	−0.0600442	+	0.104000i
$626$	0.110920	−	0.192119i	0.00443324	−	0.00767860i
$627$	67.3275	−	28.2813i	2.68880	−	1.12945i
$628$	2.73647	+	4.73970i	0.109197	+	0.189135i
$629$		−	9.83018i		−	0.391955i
$630$	−0.730862	−	2.62291i	−0.0291182	−	0.104499i
$631$			11.1713i			0.444723i	0.974964	+	0.222362i	$0.0713766\pi$
$631$			11.1713i			0.444723i	−0.974964	+	0.222362i	$0.928623\pi$
$632$	6.77189	+	11.7293i	0.269371	+	0.466565i
$633$	−33.2094	−	25.2209i	−1.31996	−	1.00244i
$634$	−3.37385	+	5.84368i	−0.133993	+	0.232082i
$635$	−6.03335	+	10.4501i	−0.239426	+	0.414699i
$636$	1.67479	+	1.27192i	0.0664097	+	0.0504348i
$637$	29.4304	−	16.9916i	1.16607	−	0.673234i
$638$			12.5691i			0.497617i
$639$	0.871537	−	3.38711i	0.0344775	−	0.133992i
$640$	−1.28353			−0.0507362
$641$	−23.6029	−	40.8814i	−0.932257	−	1.61472i	−0.779454	−	0.626460i	$-0.784503\pi$
$641$	−23.6029	−	40.8814i	−0.932257	−	1.61472i	−0.152803	−	0.988257i	$-0.548830\pi$
$642$	15.2228	−	6.39444i	0.600798	−	0.252369i
$643$	−13.7356	−	7.93026i	−0.541680	−	0.312739i	0.204080	−	0.978954i	$-0.434580\pi$
$643$	−13.7356	−	7.93026i	−0.541680	−	0.312739i	−0.745759	+	0.666215i	$0.767913\pi$
$644$	2.17430	−	3.76599i	0.0856792	−	0.148401i
$645$	2.16653	−	17.1141i	0.0853069	−	0.673867i
$646$	−14.5661	+	8.40973i	−0.573095	+	0.330876i
$647$	38.0085			1.49427			0.747133	−	0.664674i	$-0.231430\pi$
$647$	38.0085			1.49427			0.747133	+	0.664674i	$0.231430\pi$
$648$	−4.34397	+	7.88226i	−0.170647	+	0.309644i
$649$			26.6724i			1.04698i
$650$	8.76389	+	15.1795i	0.343748	+	0.595389i
$651$	−1.87520	+	6.55630i	−0.0734951	+	0.256961i
$652$	0.171181	−	0.296494i	0.00670397	−	0.0116116i
$653$	−38.8816	−	22.4483i	−1.52156	−	0.878471i	−0.999676	−	0.0254521i	$-0.991897\pi$
$653$	−38.8816	−	22.4483i	−1.52156	−	0.878471i	−0.521880	−	0.853019i	$-0.674769\pi$
$654$	−6.31850	−	15.0421i	−0.247073	−	0.588191i
$655$	−10.7699	−	18.6540i	−0.420815	−	0.728873i
$656$			6.07118i			0.237040i
$657$	−12.0428	+	46.8028i	−0.469835	+	1.82595i
$658$	6.86230			0.267520
$659$	−18.4570	+	10.6561i	−0.718982	+	0.415105i	−0.814378	−	0.580335i	$-0.802922\pi$
$659$	−18.4570	+	10.6561i	−0.718982	+	0.415105i	0.0953957	+	0.995439i	$0.469588\pi$
$660$	7.55713	−	9.95079i	0.294161	−	0.387334i
$661$	−7.05163	+	12.2138i	−0.274277	+	0.475061i	−0.969952	−	0.243295i	$-0.921772\pi$
$661$	−7.05163	+	12.2138i	−0.274277	+	0.475061i	0.695676	+	0.718356i	$0.255105\pi$
$662$	15.8849	−	27.5134i	0.617384	−	1.06934i
$663$	−12.2800	+	16.1695i	−0.476914	+	0.627972i
$664$	7.92206	−	4.57381i	0.307436	−	0.177498i
$665$			6.80839i			0.264018i
$666$	3.53045	+	12.6700i	0.136802	+	0.490954i
$667$	13.7528			0.532509
$668$	−8.65410	−	14.9893i	−0.334837	−	0.579955i
$669$	1.42484	+	3.39203i	0.0550876	+	0.131144i
$670$	6.33757	−	10.9770i	0.244842	−	0.424078i
$671$	−28.7250	−	16.5844i	−1.10892	−	0.640234i
$672$	1.21507	+	0.153819i	0.0468722	+	0.00593369i
$673$	3.53768	−	2.04248i	0.136368	−	0.0787318i	−0.430264	−	0.902703i	$-0.641580\pi$
$673$	3.53768	−	2.04248i	0.136368	−	0.0787318i	0.566632	+	0.823971i	$0.308246\pi$
$674$	0.930128			0.0358272
$675$	17.2354	−	2.53139i	0.663391	−	0.0974334i
$676$	14.3342			0.551315
$677$	14.8321	+	25.6899i	0.570042	+	0.987342i	0.996561	+	0.0828635i	$0.0264065\pi$
$677$	14.8321	+	25.6899i	0.570042	+	0.987342i	−0.426519	+	0.904479i	$0.640260\pi$
$678$	−2.37998	+	18.8002i	−0.0914025	+	0.722018i
$679$	−5.76081	+	9.97802i	−0.221080	+	0.382921i
$680$	−1.43895	+	2.49233i	−0.0551811	+	0.0955764i
$681$	7.11299	+	16.9334i	0.272570	+	0.648890i
$682$	−29.1651	+	11.3437i	−1.11679	+	0.434374i
$683$			24.2666i			0.928534i	0.885695	+	0.464267i	$0.153682\pi$
$683$			24.2666i			0.928534i	−0.885695	+	0.464267i	$0.846318\pi$
$684$	15.7538	−	16.0706i	0.602362	−	0.614473i
$685$		−	2.59359i		−	0.0990959i
$686$	−8.26714	+	4.77304i	−0.315641	+	0.182235i
$687$	−6.59065	+	8.67818i	−0.251449	+	0.331093i
$688$	6.72000	+	3.87979i	0.256197	+	0.147916i
$689$	−5.49752	−	3.17399i	−0.209439	−	0.120919i
$690$	−10.8878	−	8.26877i	−0.414493	−	0.314787i
$691$	−1.38475	−	2.39847i	−0.0526786	−	0.0912419i	0.838484	−	0.544927i	$-0.183443\pi$
$691$	−1.38475	−	2.39847i	−0.0526786	−	0.0912419i	−0.891162	+	0.453685i	$0.850109\pi$
$692$		−	12.5840i		−	0.478372i
$693$	−8.34651	+	8.51433i	−0.317058	+	0.323433i
$694$			6.39352i			0.242695i
$695$	8.09755	+	14.0254i	0.307158	+	0.532013i
$696$	1.50008	+	3.57114i	0.0568604	+	0.135364i
$697$	11.7888	+	6.80628i	0.446534	+	0.257806i
$698$	24.0864	+	13.9063i	0.911684	+	0.526361i
$699$	−4.77256	−	0.604173i	−0.180515	−	0.0228519i
$700$	−1.18532	−	2.05303i	−0.0448009	−	0.0775974i
$701$		−	4.72636i		−	0.178512i	−0.996009	−	0.0892560i	$-0.971551\pi$
$701$		−	4.72636i		−	0.178512i	0.996009	−	0.0892560i	$-0.0284489\pi$
$702$	10.0203	−	25.2511i	0.378194	−	0.953040i
$703$		−	32.8882i		−	1.24040i
$704$	2.81024	+	4.86747i	0.105915	+	0.183450i
$705$	2.70959	−	21.4040i	0.102049	−	0.806120i
$706$	3.83090	+	2.21177i	0.144178	+	0.0832411i
$707$	−5.74784	−	3.31852i	−0.216170	−	0.124806i
$708$	3.18325	+	7.57815i	0.119634	+	0.284804i
$709$	33.9498	−	19.6009i	1.27501	−	0.736129i	0.299085	−	0.954226i	$-0.403319\pi$
$709$	33.9498	−	19.6009i	1.27501	−	0.736129i	0.975927	+	0.218098i	$0.0699852\pi$
$710$			1.49636i			0.0561575i
$711$	−39.1402	+	10.9063i	−1.46787	+	0.409017i
$712$			8.17378i			0.306325i
$713$	12.4119	+	31.9115i	0.464831	+	1.19509i
$714$	1.66087	−	2.18693i	0.0621564	−	0.0818439i
$715$	−18.8583	+	32.6636i	−0.705262	+	1.22155i
$716$	0.514500	−	0.891140i	0.0192278	−	0.0333034i
$717$	−30.8902	−	23.4596i	−1.15361	−	0.876113i
$718$	14.7892	+	25.6157i	0.551930	+	0.955970i
$719$	19.5792			0.730182			0.365091	−	0.930972i	$-0.381038\pi$
$719$	19.5792			0.730182			0.365091	+	0.930972i	$0.381038\pi$
$720$	0.959542	−	3.72913i	0.0357600	−	0.138977i
$721$	7.87088			0.293127
$722$	−32.2783	+	18.6359i	−1.20127	+	0.693555i
$723$	−8.61597	−	20.5115i	−0.320431	−	0.762830i
$724$	−2.35191	−	1.35788i	−0.0874081	−	0.0504651i
$725$	3.74867	−	6.49288i	0.139222	−	0.241139i
$726$	−35.3801	−	4.47887i	−1.31308	−	0.166226i
$727$	−21.2122	−	36.7406i	−0.786717	−	1.36263i	−0.927968	−	0.372660i	$-0.878446\pi$
$727$	−21.2122	−	36.7406i	−0.786717	−	1.36263i	0.141251	−	0.989974i	$-0.454888\pi$
$728$	−3.69696			−0.137018
$729$	−19.6534	−	18.5134i	−0.727902	−	0.685681i
$730$		−	20.6766i		−	0.765276i
$731$	15.0673	−	8.69912i	0.557285	−	0.321749i
$732$	−10.1406	−	1.28373i	−0.374809	−	0.0474482i
$733$	4.57574	−	7.92542i	0.169009	−	0.292732i	−0.769063	−	0.639173i	$-0.779277\pi$
$733$	4.57574	−	7.92542i	0.169009	−	0.292732i	0.938072	+	0.346441i	$0.112610\pi$
$734$	0.515566	−	0.892986i	0.0190299	−	0.0329607i
$735$	5.59631	+	13.3228i	0.206423	+	0.491418i
$736$	5.32583	−	3.07487i	0.196313	−	0.113341i
$737$	−55.5032			−2.04449
$738$	−17.6390	−	4.53868i	−0.649300	−	0.167071i
$739$		−	6.54708i		−	0.240838i	−0.992723	−	0.120419i	$-0.961576\pi$
$739$		−	6.54708i		−	0.240838i	0.992723	−	0.120419i	$-0.0384238\pi$
$740$	−2.81366	−	4.87341i	−0.103432	−	0.179150i
$741$	−41.0842	+	54.0973i	−1.50927	+	1.98731i
$742$	0.743541	+	0.429283i	0.0272962	+	0.0157595i
$743$	6.37755	−	11.0462i	0.233970	−	0.405247i	−0.725003	−	0.688746i	$-0.758162\pi$
$743$	6.37755	−	11.0462i	0.233970	−	0.405247i	0.958973	+	0.283498i	$0.0914951\pi$
$744$	−6.93254	+	6.70372i	−0.254159	+	0.245770i
$745$	−7.07477	−	12.2539i	−0.259199	−	0.448947i
$746$		−	6.89420i		−	0.252414i
$747$	7.36620	+	26.4357i	0.269515	+	0.967233i
$748$	12.6020			0.460775
$749$	5.83772	−	3.37041i	0.213306	−	0.123152i
$750$	−17.1199	+	7.19131i	−0.625129	+	0.262589i
$751$	0.312036	−	0.540463i	0.0113864	−	0.0197218i	−0.860276	−	0.509828i	$-0.829709\pi$
$751$	0.312036	−	0.540463i	0.0113864	−	0.0197218i	0.871662	+	0.490107i	$0.163042\pi$
$752$	8.40445	+	4.85231i	0.306479	+	0.176946i
$753$	2.75555	−	21.7670i	0.100418	−	0.793233i
$754$	−5.84596	−	10.1255i	−0.212897	−	0.368749i
$755$	−15.8143			−0.575542
$756$	−1.35526	+	3.41521i	−0.0492902	+	0.124210i
$757$			29.9996i			1.09035i	0.838321	+	0.545176i	$0.183537\pi$
$757$			29.9996i			1.09035i	−0.838321	+	0.545176i	$0.816463\pi$
$758$	−4.08494	+	2.35844i	−0.148372	+	0.0856624i
$759$	−7.51879	+	59.3934i	−0.272915	+	2.15584i
$760$	−4.81418	+	8.33841i	−0.174629	+	0.302466i
$761$	14.3806	−	24.9079i	0.521295	−	0.902909i	−0.478399	−	0.878143i	$-0.658783\pi$
$761$	14.3806	−	24.9079i	0.521295	−	0.902909i	0.999693	−	0.0247661i	$-0.00788411\pi$
$762$	15.0126	−	6.30613i	0.543849	−	0.228447i
$763$	−3.33038	−	5.76839i	−0.120568	−	0.208830i
$764$			18.1844i			0.657888i
$765$	−6.16539	−	6.04387i	−0.222910	−	0.218517i
$766$		−	27.4097i		−	0.990351i
$767$	−12.4054	−	21.4868i	−0.447934	−	0.775844i
$768$	1.37936	+	1.04755i	0.0497733	+	0.0378004i
$769$	−9.19116	+	15.9196i	−0.331442	+	0.574074i	−0.982795	−	0.184701i	$-0.940868\pi$
$769$	−9.19116	+	15.9196i	−0.331442	+	0.574074i	0.651353	+	0.758775i	$0.274202\pi$
$770$	2.55060	−	4.41777i	0.0919172	−	0.159205i
$771$	−6.72808	+	8.85915i	−0.242306	+	0.319054i
$772$	−13.0144	−	22.5415i	−0.468397	−	0.811288i
$773$	17.1154			0.615596			0.307798	−	0.951452i	$-0.400408\pi$
$773$	17.1154			0.615596			0.307798	+	0.951452i	$0.400408\pi$
$774$	−16.2959	+	16.6236i	−0.585745	+	0.597522i
$775$	18.4491	+	2.83843i	0.662710	+	0.101959i
$776$	−14.1108	+	8.14690i	−0.506550	+	0.292457i
$777$	2.07954	+	4.95063i	0.0746031	+	0.177603i
$778$	−16.2012	−	9.35379i	−0.580842	−	0.335350i
$779$	39.4411	+	22.7713i	1.41312	+	0.815867i
$780$	−1.45975	+	11.5311i	−0.0522675	+	0.412878i
$781$	5.67457	−	3.27621i	0.203052	−	0.117232i
$782$		−	13.7887i		−	0.493084i
$783$	−11.4969	+	1.68857i	−0.410865	+	0.0603445i
$784$	−6.49998			−0.232142
$785$	6.08357	−	3.51235i	0.217132	−	0.125361i
$786$	−3.65050	+	28.8365i	−0.130209	+	1.02856i
$787$	29.0478	+	16.7708i	1.03544	+	0.597813i	0.918539	−	0.395330i	$-0.129370\pi$
$787$	29.0478	+	16.7708i	1.03544	+	0.597813i	0.116903	+	0.993143i	$0.462703\pi$
$788$	−10.0289	+	17.3706i	−0.357266	+	0.618802i
$789$	−2.34598	+	0.985441i	−0.0835190	+	0.0350826i
$790$	15.0549	−	8.69195i	0.535629	−	0.309246i
$791$			7.73653i			0.275079i
$792$	−16.2426	+	4.52594i	−0.577157	+	0.160822i
$793$	30.8539			1.09565
$794$	8.38159	−	4.83911i	0.297452	−	0.171734i
$795$	1.63255	−	2.14965i	0.0579006	−	0.0762402i
$796$	−0.622822	−	0.359586i	−0.0220753	−	0.0127452i
$797$	1.23838	−	2.14494i	0.0438656	−	0.0759775i	−0.843259	−	0.537507i	$-0.819366\pi$
$797$	1.23838	−	2.14494i	0.0438656	−	0.0759775i	0.887125	+	0.461530i	$0.152699\pi$
$798$	5.55665	−	7.31668i	0.196703	−	0.259008i
$799$	18.8441	−	10.8797i	0.666657	−	0.384895i
$800$		−	3.35254i		−	0.118530i
$801$	−23.7478	−	6.11054i	−0.839087	−	0.215905i
$802$		−	10.9999i		−	0.388422i
$803$	−78.4107	+	45.2705i	−2.76705	+	1.59756i
$804$	−15.7696	+	6.62409i	−0.556149	+	0.233614i
$805$	−4.83378	−	2.79078i	−0.170368	−	0.0983622i
$806$	18.2189	−	22.7031i	0.641734	−	0.799683i
$807$	−0.193650	+	1.52970i	−0.00681679	+	0.0538481i
$808$	−4.69302	−	8.12855i	−0.165100	−	0.285961i
$809$	−50.5194			−1.77617			−0.888083	−	0.459682i	$-0.847963\pi$
$809$	−50.5194			−1.77617			−0.888083	+	0.459682i	$0.847963\pi$
$810$	10.1171	+	5.57563i	0.355480	+	0.195908i
$811$	−23.6098			−0.829050			−0.414525	−	0.910038i	$-0.636052\pi$
$811$	−23.6098			−0.829050			−0.414525	+	0.910038i	$0.636052\pi$
$812$	0.790669	+	1.36948i	0.0277470	+	0.0480593i
$813$	44.7681	+	5.66733i	1.57009	+	0.198762i
$814$	−12.3208	+	21.3402i	−0.431842	+	0.747973i
$815$	−0.380561	−	0.219717i	−0.0133305	−	0.00769634i
$816$	3.58048	−	1.50400i	0.125342	−	0.0526506i
$817$	50.4097	−	29.1041i	1.76361	−	1.01822i
$818$	6.39782			0.223694
$819$	2.76376	−	10.7410i	0.0965737	−	0.375321i
$820$	7.79257			0.272128
$821$	−5.96385	−	10.3297i	−0.208140	−	0.360508i	0.742989	−	0.669304i	$-0.233408\pi$
$821$	−5.96385	−	10.3297i	−0.208140	−	0.360508i	−0.951129	+	0.308795i	$0.900074\pi$
$822$	−2.11675	+	2.78722i	−0.0738302	+	0.0972153i
$823$	11.1337	+	6.42806i	0.388097	+	0.224068i	0.681335	−	0.731971i	$-0.261400\pi$
$823$	11.1337	+	6.42806i	0.388097	+	0.224068i	−0.293238	+	0.956039i	$0.594733\pi$
$824$	9.63968	+	5.56547i	0.335814	+	0.193882i
$825$	25.9910	+	19.7389i	0.904892	+	0.687221i
$826$	1.67784	+	2.90610i	0.0583795	+	0.101116i
$827$	14.0893			0.489934			0.244967	−	0.969531i	$-0.421223\pi$
$827$	14.0893			0.489934			0.244967	+	0.969531i	$0.421223\pi$
$828$	4.95214	+	17.7722i	0.172099	+	0.617626i
$829$			23.6184i			0.820301i	0.912018	+	0.410150i	$0.134524\pi$
$829$			23.6184i			0.820301i	−0.912018	+	0.410150i	$0.865476\pi$
$830$	−5.87064	−	10.1682i	−0.203773	−	0.352945i
$831$	11.1054	+	26.4378i	0.385241	+	0.917119i
$832$	−4.52776	−	2.61411i	−0.156972	−	0.0906278i
$833$	−7.28701	+	12.6215i	−0.252480	+	0.437308i
$834$	2.74470	−	21.6813i	0.0950411	−	0.750761i
$835$	−19.2393	+	11.1078i	−0.665805	+	0.384403i
$836$	42.1617			1.45819
$837$	−14.2941	−	25.1531i	−0.494077	−	0.869418i
$838$	2.95290			0.102006
$839$	11.0886	−	6.40200i	0.382821	−	0.221022i	−0.296224	−	0.955119i	$-0.595727\pi$
$839$	11.0886	−	6.40200i	0.382821	−	0.221022i	0.679045	+	0.734097i	$0.262394\pi$
$840$	0.197432	−	1.55958i	0.00681205	−	0.0538106i
$841$	11.9994	−	20.7837i	0.413774	−	0.716678i
$842$	−17.9370	−	10.3560i	−0.618151	−	0.356890i
$843$	11.3293	+	26.9709i	0.390201	+	0.928927i
$844$	−12.0380	−	20.8504i	−0.414365	−	0.717701i
$845$		−	18.3984i		−	0.632926i
$846$	−20.3807	+	20.7905i	−0.700703	+	0.714791i
$847$	−14.5593			−0.500265
$848$	0.607089	+	1.05151i	0.0208475	+	0.0361090i
$849$	8.20332	+	6.23001i	0.281537	+	0.213814i
$850$	−6.50986	−	3.75847i	−0.223286	−	0.128914i
$851$	23.3497	+	13.4810i	0.800419	+	0.462122i
$852$	1.22125	−	1.60808i	0.0418395	−	0.0550918i
$853$	−0.257032	−	0.445192i	−0.00880061	−	0.0152431i	0.861592	−	0.507602i	$-0.169468\pi$
$853$	−0.257032	−	0.445192i	−0.00880061	−	0.0152431i	−0.870392	+	0.492359i	$0.836135\pi$
$854$	−4.17300			−0.142797
$855$	−20.6271	−	20.2206i	−0.705433	−	0.691529i
$856$	9.53282			0.325825
$857$	17.8657	−	10.3148i	0.610281	−	0.352346i	−0.162794	−	0.986660i	$-0.552051\pi$
$857$	17.8657	−	10.3148i	0.610281	−	0.352346i	0.773075	+	0.634314i	$0.218717\pi$
$858$	46.9246	−	19.7110i	1.60198	−	0.672921i
$859$	18.7672	+	10.8353i	0.640329	+	0.369694i	0.784741	−	0.619823i	$-0.212796\pi$
$859$	18.7672	+	10.8353i	0.640329	+	0.369694i	−0.144412	+	0.989518i	$0.546129\pi$
$860$	4.97985	−	8.62535i	0.169811	−	0.294122i
$861$	−7.37688	−	0.933862i	−0.251403	−	0.0318259i
$862$	−4.52110	−	7.83078i	−0.153989	−	0.266717i
$863$	−25.5663			−0.870286			−0.435143	−	0.900361i	$-0.643302\pi$
$863$	−25.5663			−0.870286			−0.435143	+	0.900361i	$0.643302\pi$
$864$	−4.07470	+	3.22441i	−0.138624	+	0.109697i
$865$	−16.1520			−0.549185
$866$	−2.72944	−	4.72753i	−0.0927502	−	0.160648i
$867$	−2.60442	+	20.5731i	−0.0884506	+	0.698701i
$868$	−2.46411	+	3.07060i	−0.0836374	+	0.104223i
$869$	−65.9240	−	38.0612i	−2.23632	−	1.29114i
$870$	4.58369	−	1.92541i	0.155402	−	0.0652773i
$871$	44.7125	−	25.8148i	1.51502	−	0.874700i
$872$		−	9.41960i		−	0.318988i
$873$	−13.1207	−	47.0875i	−0.444070	−	1.59367i
$874$		−	46.1320i		−	1.56044i
$875$	−6.56520	+	3.79042i	−0.221944	+	0.128140i
$876$	−16.8752	+	22.2203i	−0.570160	+	0.750753i
$877$	−13.5726	+	23.5085i	−0.458316	+	0.793826i	−0.998872	−	0.0474817i	$-0.984880\pi$
$877$	−13.5726	+	23.5085i	−0.458316	+	0.793826i	0.540556	+	0.841308i	$0.318214\pi$
$878$	−22.0602	−	12.7365i	−0.744495	−	0.429834i
$879$	3.03262	−	3.99317i	0.102288	−	0.134686i
$880$	6.24757	−	3.60704i	0.210606	−	0.121593i
$881$	35.6092			1.19970			0.599852	−	0.800111i	$-0.295226\pi$
$881$	35.6092			1.19970			0.599852	+	0.800111i	$0.295226\pi$
$882$	4.85924	−	18.8848i	0.163619	−	0.635885i
$883$			14.1721i			0.476929i	0.971151	+	0.238464i	$0.0766440\pi$
$883$			14.1721i			0.476929i	−0.971151	+	0.238464i	$0.923356\pi$
$884$	−10.1520	+	5.86125i	−0.341448	+	0.197135i
$885$	9.72681	−	4.08581i	0.326963	−	0.137343i
$886$	0.248656	−	0.430684i	0.00835375	−	0.0144691i
$887$	49.1586	+	28.3818i	1.65059	+	0.952966i	0.976831	+	0.214010i	$0.0686526\pi$
$887$	49.1586	+	28.3818i	1.65059	+	0.952966i	0.673754	+	0.738956i	$0.264681\pi$
$888$	−0.953701	+	7.53360i	−0.0320041	+	0.252811i
$889$	5.75709	−	3.32386i	0.193087	−	0.111479i
$890$	10.4913			0.351670
$891$	−1.00686	−	50.5742i	−0.0337311	−	1.69430i
$892$			2.12415i			0.0711219i
$893$	63.0455	−	36.3993i	2.10974	−	1.21806i
$894$	−2.39802	+	18.9427i	−0.0802017	+	0.633540i
$895$	−1.14381	−	0.660378i	−0.0382333	−	0.0220740i
$896$	0.612382	+	0.353559i	0.0204582	+	0.0118116i
$897$	−21.5671	−	51.3434i	−0.720104	−	1.71431i
$898$	7.79536	−	4.50066i	0.260135	−	0.150189i
$899$	−12.3065	−	1.89338i	−0.410444	−	0.0631477i
$900$	9.74034	+	2.50628i	0.324678	+	0.0835428i
$901$	2.72239			0.0906958
$902$	−17.0615	−	29.5513i	−0.568084	−	0.983951i
$903$	−5.74786	+	7.56845i	−0.191277	+	0.251862i
$904$	−5.47047	+	9.47514i	−0.181945	+	0.315138i
$905$	−1.74288	+	3.01876i	−0.0579354	+	0.100347i
$906$	16.9949	+	12.9068i	0.564619	+	0.428800i
$907$	16.5888	+	28.7327i	0.550823	+	0.954054i	0.998215	+	0.0597158i	$0.0190194\pi$
$907$	16.5888	+	28.7327i	0.550823	+	0.954054i	−0.447392	+	0.894338i	$0.647647\pi$
$908$			10.6040i			0.351907i
$909$	27.1248	−	7.55820i	0.899672	−	0.250690i
$910$			4.74518i			0.157301i
$911$	11.0952	+	19.2174i	0.367599	+	0.636701i	0.989190	−	0.146642i	$-0.0468465\pi$
$911$	11.0952	+	19.2174i	0.367599	+	0.636701i	−0.621590	+	0.783342i	$0.713513\pi$
$912$	11.9790	−	5.03184i	0.396663	−	0.166621i
$913$	−25.7069	+	44.5257i	−0.850776	+	1.47359i
$914$	−8.70512	+	15.0777i	−0.287940	+	0.498726i
$915$	−1.64772	+	13.0159i	−0.0544718	+	0.430291i
$916$	−5.44856	+	3.14573i	−0.180026	+	0.103938i
$917$			11.8666i			0.391869i
$918$	1.69298	+	11.5270i	0.0558768	+	0.380446i
$919$	−4.38591			−0.144678			−0.0723388	−	0.997380i	$-0.523046\pi$
$919$	−4.38591			−0.144678			−0.0723388	+	0.997380i	$0.523046\pi$
$920$	−3.94670	−	6.83589i	−0.130119	−	0.225373i
$921$	−5.65327	+	44.6570i	−0.186282	+	1.47150i
$922$	7.95451	+	4.59254i	0.261968	+	0.151247i
$923$	−3.04756	+	5.27853i	−0.100312	+	0.173745i
$924$	−6.34657	+	2.66591i	−0.208787	+	0.0877021i
$925$	12.7291	−	7.34917i	0.418531	−	0.241639i
$926$	11.3121			0.371738
$927$	−23.3761	+	23.8461i	−0.767772	+	0.783210i
$928$			2.23631i			0.0734106i
$929$	−9.13034	−	15.8142i	−0.299557	−	0.518848i	0.676478	−	0.736463i	$-0.263505\pi$
$929$	−9.13034	−	15.8142i	−0.299557	−	0.518848i	−0.976035	+	0.217615i	$0.930172\pi$
$930$	8.60445	+	8.89816i	0.282151	+	0.291782i
$931$	−24.3797	+	42.2268i	−0.799011	+	1.38393i
$932$	−2.40532	−	1.38871i	−0.0787890	−	0.0454888i
$933$	8.73605	−	11.5031i	0.286005	−	0.376595i
$934$	−4.53252	−	7.85056i	−0.148309	−	0.256878i
$935$		−	16.1751i		−	0.528983i
$936$	10.9798	−	11.2005i	0.358885	−	0.366101i
$937$	−8.19235			−0.267632			−0.133816	−	0.991006i	$-0.542723\pi$
$937$	−8.19235			−0.267632			−0.133816	+	0.991006i	$0.542723\pi$
$938$	−6.04738	+	3.49146i	−0.197454	+	0.114000i
$939$	0.148806	+	0.354253i	0.00485610	+	0.0115606i
$940$	6.22811	−	10.7874i	0.203138	−	0.351846i
$941$	−16.5708	+	28.7015i	−0.540193	+	0.935642i	0.458700	+	0.888591i	$0.348315\pi$
$941$	−16.5708	+	28.7015i	−0.540193	+	0.935642i	−0.998893	+	0.0470503i	$0.985018\pi$
$942$	−9.40434	−	1.19052i	−0.306410	−	0.0387894i
$943$	−32.3341	+	18.6681i	−1.05294	+	0.607917i
$944$			4.74557i			0.154455i
$945$	4.38355	+	1.73952i	0.142597	+	0.0565865i
$946$	−43.6125			−1.41797
$947$	−23.0321	−	39.8929i	−0.748444	−	1.29634i	−0.948568	−	0.316573i	$-0.897468\pi$
$947$	−23.0321	−	39.8929i	−0.748444	−	1.29634i	0.200124	−	0.979771i	$-0.435866\pi$
$948$	−23.2728	−	2.94617i	−0.755864	−	0.0956872i
$949$	42.1110	−	72.9383i	1.36698	−	2.36768i
$950$	−21.7796	−	12.5744i	−0.706623	−	0.407969i
$951$	−4.52624	−	10.7753i	−0.146773	−	0.349414i
$952$	1.37306	−	0.792736i	0.0445011	−	0.0256927i
$953$	11.0984			0.359511			0.179756	−	0.983711i	$-0.442469\pi$
$953$	11.0984			0.359511			0.179756	+	0.983711i	$0.442469\pi$
$954$	−3.50886	+	0.977729i	−0.113604	+	0.0316552i
$955$	23.3403			0.755274
$956$	−11.1973	−	19.3943i	−0.362147	−	0.627256i
$957$	−17.3374	−	13.1669i	−0.560437	−	0.425624i
$958$	11.8770	−	20.5716i	0.383729	−	0.664638i
$959$	−0.714422	+	1.23742i	−0.0230699	+	0.0399582i
$960$	1.34457	−	1.77045i	0.0433959	−	0.0571412i
$961$	−6.71332	−	30.2644i	−0.216559	−	0.976270i
$962$		−	22.9217i		−	0.739027i
$963$	−7.12652	+	27.6963i	−0.229649	+	0.892500i
$964$		−	12.8447i		−	0.413699i
$965$	−28.9329	+	16.7044i	−0.931382	+	0.537733i
$966$	2.91696	+	6.94421i	0.0938516	+	0.223426i
$967$	−32.1260	−	18.5480i	−1.03310	−	0.596463i	−0.115232	−	0.993339i	$-0.536761\pi$
$967$	−32.1260	−	18.5480i	−1.03310	−	0.596463i	−0.917872	+	0.396876i	$0.870094\pi$
$968$	−17.8312	−	10.2949i	−0.573117	−	0.330889i
$969$	3.65873	−	28.9015i	0.117535	−	0.928450i
$970$	10.4568	+	18.1118i	0.335748	+	0.581533i
$971$		−	58.8967i		−	1.89009i	−0.326947	−	0.945043i	$-0.606020\pi$
$971$		−	58.8967i		−	1.89009i	0.326947	−	0.945043i	$-0.393980\pi$
$972$	−6.32191	−	14.2490i	−0.202775	−	0.457036i
$973$		−	8.92211i		−	0.286030i
$974$	12.3373	+	21.3689i	0.395314	+	0.684703i
$975$	−30.1186	−	3.81281i	−0.964568	−	0.122108i
$976$	−5.11078	−	2.95071i	−0.163592	−	0.0944500i
$977$	2.81723	+	1.62653i	0.0901311	+	0.0520372i	0.544388	−	0.838833i	$-0.316762\pi$
$977$	2.81723	+	1.62653i	0.0901311	+	0.0520372i	−0.454257	+	0.890871i	$0.650095\pi$
$978$	0.229650	+	0.546714i	0.00734341	+	0.0174820i
$979$	−22.9703	−	39.7856i	−0.734132	−	1.27155i
$980$			8.34296i			0.266506i
$981$	27.3674	+	7.04189i	0.873772	+	0.224830i
$982$			39.4101i			1.25763i
$983$	−1.81578	−	3.14502i	−0.0579143	−	0.100311i	0.835615	−	0.549316i	$-0.185112\pi$
$983$	−1.81578	−	3.14502i	−0.0579143	−	0.100311i	−0.893529	+	0.449005i	$0.851778\pi$
$984$	−8.37433	−	6.35989i	−0.266964	−	0.202746i
$985$	22.2958	+	12.8725i	0.710402	+	0.410151i
$986$	4.34241	+	2.50709i	0.138290	+	0.0798420i
$987$	−7.18864	+	9.46558i	−0.228817	+	0.301293i
$988$	−33.9648	+	19.6096i	−1.08056	+	0.623864i
$989$			47.7194i			1.51739i
$990$	5.80920	+	20.8480i	0.184629	+	0.662593i
$991$			16.3924i			0.520723i	0.965511	+	0.260361i	$0.0838417\pi$
$991$			16.3924i			0.520723i	−0.965511	+	0.260361i	$0.916158\pi$
$992$	−5.18908	+	2.01829i	−0.164753	+	0.0640807i
$993$	21.3106	+	50.7328i	0.676272	+	1.60996i
$994$	0.412184	−	0.713923i	0.0130737	−	0.0226443i
$995$	−0.461542	+	0.799414i	−0.0146319	+	0.0253431i
$996$	−1.98987	+	15.7187i	−0.0630516	+	0.498065i
$997$	−16.5514	−	28.6678i	−0.524187	−	0.907918i	−0.999604	−	0.0281575i	$-0.991036\pi$
$997$	−16.5514	−	28.6678i	−0.524187	−	0.907918i	0.475417	−	0.879761i	$-0.342297\pi$
$998$	−28.4701			−0.901204
$999$	−21.1749	−	8.40280i	−0.669943	−	0.265853i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	558.2.q.a.185.9	yes	64
3.2	odd	2		1674.2.q.a.557.18		64
9.2	odd	6	inner	558.2.q.a.371.8	yes	64
9.7	even	3		1674.2.q.a.1115.28		64
31.30	odd	2	inner	558.2.q.a.185.8	✓	64
93.92	even	2		1674.2.q.a.557.28		64
279.61	odd	6		1674.2.q.a.1115.18		64
279.92	even	6	inner	558.2.q.a.371.9	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
558.2.q.a.185.8	✓	64	31.30	odd	2	inner
558.2.q.a.185.9	yes	64	1.1	even	1	trivial
558.2.q.a.371.8	yes	64	9.2	odd	6	inner
558.2.q.a.371.9	yes	64	279.92	even	6	inner
1674.2.q.a.557.18		64	3.2	odd	2
1674.2.q.a.557.28		64	93.92	even	2
1674.2.q.a.1115.18		64	279.61	odd	6
1674.2.q.a.1115.28		64	9.7	even	3

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:	\( N \)	\(=\)	\( 558 = 2 \cdot 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	558.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.217529 - 1.71834i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.11157 - 0.641767i) q^{5} +(0.670782 + 1.59689i) q^{6} +(0.353559 + 0.612382i) q^{7} +1.00000i q^{8} +(-2.90536 - 0.747578i) q^{9} +1.28353 q^{10} +(-2.81024 - 4.86747i) q^{11} +(-1.37936 - 1.04755i) q^{12} +(4.52776 + 2.61411i) q^{13} +(-0.612382 - 0.353559i) q^{14} +(-1.34457 + 1.77045i) q^{15} +(-0.500000 - 0.866025i) q^{16} -2.24216 q^{17} +(2.88991 - 0.805260i) q^{18} -7.50145 q^{19} +(-1.11157 + 0.641767i) q^{20} +(1.12919 - 0.474322i) q^{21} +(4.86747 + 2.81024i) q^{22} +(3.07487 - 5.32583i) q^{23} +(1.71834 + 0.217529i) q^{24} +(-1.67627 - 2.90338i) q^{25} -5.22821 q^{26} +(-1.91659 + 4.82977i) q^{27} +0.707117 q^{28} +(1.11816 + 1.93671i) q^{29} +(0.279207 - 2.20554i) q^{30} +(-3.48473 + 4.34243i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-8.97527 + 3.77011i) q^{33} +(1.94177 - 1.12108i) q^{34} -0.907610i q^{35} +(-2.10010 + 2.14233i) q^{36} +4.38424i q^{37} +(6.49644 - 3.75072i) q^{38} +(5.47684 - 7.21158i) q^{39} +(0.641767 - 1.11157i) q^{40} +(-5.25780 - 3.03559i) q^{41} +(-0.740744 + 0.975368i) q^{42} +(-6.72000 + 3.87979i) q^{43} -5.62047 q^{44} +(2.74975 + 2.69555i) q^{45} +6.14974i q^{46} +(-8.40445 + 4.85231i) q^{47} +(-1.59689 + 0.670782i) q^{48} +(3.24999 - 5.62915i) q^{49} +(2.90338 + 1.67627i) q^{50} +(-0.487736 + 3.85279i) q^{51} +(4.52776 - 2.61411i) q^{52} -1.21418 q^{53} +(-0.755068 - 5.14100i) q^{54} +7.21407i q^{55} +(-0.612382 + 0.353559i) q^{56} +(-1.63179 + 12.8900i) q^{57} +(-1.93671 - 1.11816i) q^{58} +(-4.10979 - 2.37279i) q^{59} +(0.860972 + 2.04966i) q^{60} +(5.11078 - 2.95071i) q^{61} +(0.846651 - 5.50302i) q^{62} +(-0.569413 - 2.04350i) q^{63} -1.00000 q^{64} +(-3.35530 - 5.81154i) q^{65} +(5.88775 - 7.75265i) q^{66} +(4.93759 - 8.55215i) q^{67} +(-1.12108 + 1.94177i) q^{68} +(-8.48270 - 6.44219i) q^{69} +(0.453805 + 0.786013i) q^{70} +1.16581i q^{71} +(0.747578 - 2.90536i) q^{72} -16.1091i q^{73} +(-2.19212 - 3.79686i) q^{74} +(-5.35363 + 2.24882i) q^{75} +(-3.75072 + 6.49644i) q^{76} +(1.98717 - 3.44187i) q^{77} +(-1.13729 + 8.98383i) q^{78} +(11.7293 - 6.77189i) q^{79} +1.28353i q^{80} +(7.88226 + 4.34397i) q^{81} +6.07118 q^{82} +(-4.57381 - 7.92206i) q^{83} +(0.153819 - 1.21507i) q^{84} +(2.49233 + 1.43895i) q^{85} +(3.87979 - 6.72000i) q^{86} +(3.57114 - 1.50008i) q^{87} +(4.86747 - 2.81024i) q^{88} +8.17378 q^{89} +(-3.72913 - 0.959542i) q^{90} +3.69696i q^{91} +(-3.07487 - 5.32583i) q^{92} +(6.70372 + 6.93254i) q^{93} +(4.85231 - 8.40445i) q^{94} +(8.33841 + 4.81418i) q^{95} +(1.04755 - 1.37936i) q^{96} +(8.14690 + 14.1108i) q^{97} +6.49998i q^{98} +(4.52594 + 16.2426i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 32 q^{4} + 12 q^{5} - 4 q^{7} - 4 q^{9} - 32 q^{16} + 8 q^{18} - 8 q^{19} + 12 q^{20} + 44 q^{25} - 8 q^{28} + 8 q^{31} - 36 q^{33} - 8 q^{36} + 36 q^{38} - 8 q^{39} + 24 q^{41} - 8 q^{45} - 48 q^{47}+ \cdots - 16 q^{97}+O(q^{100}) \) 64 * q + 32 * q^4 + 12 * q^5 - 4 * q^7 - 4 * q^9 - 32 * q^16 + 8 * q^18 - 8 * q^19 + 12 * q^20 + 44 * q^25 - 8 * q^28 + 8 * q^31 - 36 * q^33 - 8 * q^36 + 36 * q^38 - 8 * q^39 + 24 * q^41 - 8 * q^45 - 48 * q^47 - 36 * q^49 - 32 * q^51 - 12 * q^59 - 52 * q^63 - 64 * q^64 - 16 * q^66 + 16 * q^67 + 112 * q^69 - 12 * q^70 - 8 * q^72 - 4 * q^76 - 28 * q^78 + 60 * q^81 + 44 * q^87 + 56 * q^90 - 64 * q^93 - 180 * q^95 - 16 * q^97

Introduction

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