LMFDB - Embedded newform 187.2.m.a.10.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [187,2,Mod(10,187)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("187.10"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(187, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.m (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.49320251780$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			10.12
Character	$\chi$	$=$	187.10
Dual form			187.2.m.a.131.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.30126 + 0.539000i) q^{2} +(-2.38581 - 1.59415i) q^{3} +(-0.0114548 - 0.0114548i) q^{4} +(-3.07041 + 0.610742i) q^{5} +(-2.24531 - 3.36035i) q^{6} +(-0.785949 + 3.95123i) q^{7} +(-1.08673 - 2.62360i) q^{8} +(2.00273 + 4.83502i) q^{9} +(-4.32459 - 0.860214i) q^{10} +(-0.367376 - 3.29622i) q^{11} +(0.00906833 + 0.0455896i) q^{12} +(-2.62889 - 2.62889i) q^{13} +(-3.15244 + 4.71796i) q^{14} +(8.29901 + 3.43756i) q^{15} -3.96734i q^{16} +(-3.70164 - 1.81600i) q^{17} +7.37109i q^{18} +(3.36364 + 1.39327i) q^{19} +(0.0421668 + 0.0281750i) q^{20} +(8.17397 - 8.17397i) q^{21} +(1.29861 - 4.48725i) q^{22} +(0.347005 - 0.231861i) q^{23} +(-1.58967 + 7.99182i) q^{24} +(4.43499 - 1.83703i) q^{25} +(-2.00390 - 4.83785i) q^{26} +(1.25022 - 6.28530i) q^{27} +(0.0542635 - 0.0362577i) q^{28} +(3.98923 - 0.793506i) q^{29} +(8.94633 + 8.94633i) q^{30} +(-4.24988 + 6.36039i) q^{31} +(-0.0350676 + 0.0846607i) q^{32} +(-4.37816 + 8.44979i) q^{33} +(-3.83797 - 4.35828i) q^{34} -12.6119i q^{35} +(0.0324433 - 0.0783250i) q^{36} +(-4.99821 - 3.33970i) q^{37} +(3.62601 + 3.62601i) q^{38} +(2.08120 + 10.4629i) q^{39} +(4.93905 + 7.39181i) q^{40} +(0.955894 - 4.80561i) q^{41} +(15.0422 - 6.23069i) q^{42} +(-4.62394 + 1.91530i) q^{43} +(-0.0335493 + 0.0419657i) q^{44} +(-9.10213 - 13.6223i) q^{45} +(0.576517 - 0.114676i) q^{46} +(0.913702 - 0.913702i) q^{47} +(-6.32452 + 9.46531i) q^{48} +(-8.52737 - 3.53215i) q^{49} +6.76123 q^{50} +(5.93643 + 10.2336i) q^{51} +0.0602269i q^{52} +(0.589271 - 1.42263i) q^{53} +(5.01465 - 7.50495i) q^{54} +(3.14113 + 9.89634i) q^{55} +(11.2206 - 2.23191i) q^{56} +(-5.80394 - 8.68621i) q^{57} +(5.61872 + 1.11763i) q^{58} +(-7.76265 + 3.21539i) q^{59} +(-0.0556869 - 0.134440i) q^{60} +(-10.3909 - 2.06688i) q^{61} +(-8.95845 + 5.98585i) q^{62} +(-20.6783 + 4.11317i) q^{63} +(-5.70193 + 5.70193i) q^{64} +(9.67734 + 6.46619i) q^{65} +(-10.2516 + 8.63555i) q^{66} +5.61756i q^{67} +(0.0215996 + 0.0632035i) q^{68} -1.19751 q^{69} +(6.79781 - 16.4114i) q^{70} +(4.07475 + 2.72266i) q^{71} +(10.5087 - 10.5087i) q^{72} +(-1.07863 - 5.42263i) q^{73} +(-4.70388 - 7.03986i) q^{74} +(-13.5095 - 2.68721i) q^{75} +(-0.0225703 - 0.0544895i) q^{76} +(13.3129 + 1.13907i) q^{77} +(-2.93131 + 14.7367i) q^{78} +(8.24845 - 5.51144i) q^{79} +(2.42302 + 12.1813i) q^{80} +(-1.90081 + 1.90081i) q^{81} +(3.83409 - 5.73812i) q^{82} +(2.46970 - 5.96239i) q^{83} -0.187262 q^{84} +(12.4746 + 3.31512i) q^{85} -7.04929 q^{86} +(-10.7825 - 4.46625i) q^{87} +(-8.24872 + 4.54595i) q^{88} +(-3.16348 - 3.16348i) q^{89} +(-4.50183 - 22.6322i) q^{90} +(12.4535 - 8.32119i) q^{91} +(-0.00663080 - 0.00131895i) q^{92} +(20.2788 - 8.39975i) q^{93} +(1.68145 - 0.696479i) q^{94} +(-11.1787 - 2.22358i) q^{95} +(0.218626 - 0.146081i) q^{96} +(0.954251 + 4.79734i) q^{97} +(-9.19250 - 9.19250i) q^{98} +(15.2015 - 8.37769i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{9} - 64 q^{12} + 16 q^{14} - 16 q^{15} - 16 q^{20} + 8 q^{22} - 32 q^{23} + 16 q^{26} + 32 q^{27} - 80 q^{31} - 16 q^{34} + 16 q^{36} + 16 q^{37} + 80 q^{38}+ \cdots - 112 q^{99}+O(q^{100}) $ 128 * q - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^9 - 64 * q^12 + 16 * q^14 - 16 * q^15 - 16 * q^20 + 8 * q^22 - 32 * q^23 + 16 * q^26 + 32 * q^27 - 80 * q^31 - 16 * q^34 + 16 * q^36 + 16 * q^37 + 80 * q^38 - 112 * q^42 - 72 * q^44 - 16 * q^45 - 16 * q^47 + 32 * q^48 + 48 * q^49 - 16 * q^53 - 8 * q^55 - 16 * q^56 - 128 * q^58 + 48 * q^59 + 112 * q^60 + 48 * q^64 + 72 * q^66 - 192 * q^69 + 128 * q^70 - 16 * q^71 + 48 * q^75 + 8 * q^77 - 16 * q^78 + 112 * q^80 - 16 * q^82 + 32 * q^86 - 168 * q^88 - 16 * q^89 + 144 * q^91 - 176 * q^92 + 48 * q^93 + 48 * q^97 - 112 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$-1$	$e\left(\frac{3}{16}\right)$

Coefficient data

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

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

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

$2$	1.30126	+	0.539000i	0.920130	+	0.381130i	0.791926	−	0.610617i	$-0.209079\pi$
$2$	1.30126	+	0.539000i	0.920130	+	0.381130i	0.128204	+	0.991748i	$0.459079\pi$
$3$	−2.38581	−	1.59415i	−1.37745	−	0.920381i	−0.377463	−	0.926025i	$-0.623203\pi$
$3$	−2.38581	−	1.59415i	−1.37745	−	0.920381i	−0.999984	+	0.00564401i	$0.998203\pi$
$4$	−0.0114548	−	0.0114548i	−0.00572740	−	0.00572740i
$5$	−3.07041	+	0.610742i	−1.37313	+	0.273132i	−0.825883	−	0.563841i	$-0.809323\pi$
$5$	−3.07041	+	0.610742i	−1.37313	+	0.273132i	−0.547244	+	0.836973i	$0.684323\pi$
$6$	−2.24531	−	3.36035i	−0.916646	−	1.37186i
$7$	−0.785949	+	3.95123i	−0.297061	+	1.49343i	0.487363	+	0.873200i	$0.337959\pi$
$7$	−0.785949	+	3.95123i	−0.297061	+	1.49343i	−0.784423	+	0.620226i	$0.787041\pi$
$8$	−1.08673	−	2.62360i	−0.384218	−	0.927583i
$9$	2.00273	+	4.83502i	0.667576	+	1.61167i
$10$	−4.32459	−	0.860214i	−1.36755	−	0.272024i
$11$	−0.367376	−	3.29622i	−0.110768	−	0.993846i
$11$	−0.367376	−	3.29622i	−0.110768	−	0.993846i
$12$	0.00906833	+	0.0455896i	0.00261780	+	0.0131606i
$13$	−2.62889	−	2.62889i	−0.729124	−	0.729124i	0.241321	−	0.970445i	$-0.422419\pi$
$13$	−2.62889	−	2.62889i	−0.729124	−	0.729124i	−0.970445	+	0.241321i	$0.922419\pi$
$14$	−3.15244	+	4.71796i	−0.842525	+	1.26093i
$15$	8.29901	+	3.43756i	2.14279	+	0.887575i
$16$		−	3.96734i		−	0.991835i
$17$	−3.70164	−	1.81600i	−0.897779	−	0.440445i
$17$	−3.70164	−	1.81600i	−0.897779	−	0.440445i
$18$			7.37109i			1.73738i
$19$	3.36364	+	1.39327i	0.771673	+	0.319637i	0.733550	−	0.679636i	$-0.237862\pi$
$19$	3.36364	+	1.39327i	0.771673	+	0.319637i	0.0381232	+	0.999273i	$0.487862\pi$
$20$	0.0421668	+	0.0281750i	0.00942878	+	0.00630011i
$21$	8.17397	−	8.17397i	1.78371	−	1.78371i
$22$	1.29861	−	4.48725i	0.276864	−	0.956685i
$23$	0.347005	−	0.231861i	0.0723556	−	0.0483464i	−0.518866	−	0.854855i	$-0.673646\pi$
$23$	0.347005	−	0.231861i	0.0723556	−	0.0483464i	0.591222	+	0.806509i	$0.298646\pi$
$24$	−1.58967	+	7.99182i	−0.324490	+	1.63132i
$25$	4.43499	−	1.83703i	0.886997	−	0.367406i
$26$	−2.00390	−	4.83785i	−0.392998	−	0.948780i
$27$	1.25022	−	6.28530i	0.240606	−	1.20961i
$28$	0.0542635	−	0.0362577i	0.0102548	−	0.00685206i
$29$	3.98923	−	0.793506i	0.740781	−	0.147350i	0.189746	−	0.981833i	$-0.439233\pi$
$29$	3.98923	−	0.793506i	0.740781	−	0.147350i	0.551034	+	0.834483i	$0.314233\pi$
$30$	8.94633	+	8.94633i	1.63337	+	1.63337i
$31$	−4.24988	+	6.36039i	−0.763301	+	1.14236i	0.222580	+	0.974914i	$0.428552\pi$
$31$	−4.24988	+	6.36039i	−0.763301	+	1.14236i	−0.985881	+	0.167446i	$0.946448\pi$
$32$	−0.0350676	+	0.0846607i	−0.00619914	+	0.0149660i
$33$	−4.37816	+	8.44979i	−0.762140	+	1.47092i
$34$	−3.83797	−	4.35828i	−0.658207	−	0.747438i
$35$		−	12.6119i		−	2.13180i
$36$	0.0324433	−	0.0783250i	0.00540721	−	0.0130542i
$37$	−4.99821	−	3.33970i	−0.821701	−	0.549043i	0.0721569	−	0.997393i	$-0.477012\pi$
$37$	−4.99821	−	3.33970i	−0.821701	−	0.549043i	−0.893858	+	0.448350i	$0.852012\pi$
$38$	3.62601	+	3.62601i	0.588216	+	0.588216i
$39$	2.08120	+	10.4629i	0.333258	+	1.67540i
$40$	4.93905	+	7.39181i	0.780932	+	1.16875i
$41$	0.955894	−	4.80561i	0.149286	−	0.750509i	−0.831516	−	0.555501i	$-0.812527\pi$
$41$	0.955894	−	4.80561i	0.149286	−	0.750509i	0.980802	−	0.195009i	$-0.0624735\pi$
$42$	15.0422	−	6.23069i	2.32107	−	0.961417i
$43$	−4.62394	+	1.91530i	−0.705144	+	0.292080i	−0.706293	−	0.707919i	$-0.749634\pi$
$43$	−4.62394	+	1.91530i	−0.705144	+	0.292080i	0.00114951	+	0.999999i	$0.499634\pi$
$44$	−0.0335493	+	0.0419657i	−0.00505774	+	0.00632657i
$45$	−9.10213	−	13.6223i	−1.35687	−	2.03069i
$46$	0.576517	−	0.114676i	0.0850028	−	0.0169081i
$47$	0.913702	−	0.913702i	0.133277	−	0.133277i	−0.637321	−	0.770598i	$-0.719958\pi$
$47$	0.913702	−	0.913702i	0.133277	−	0.133277i	0.770598	+	0.637321i	$0.219958\pi$
$48$	−6.32452	+	9.46531i	−0.912865	+	1.36620i
$49$	−8.52737	−	3.53215i	−1.21820	−	0.504593i
$50$	6.76123			0.956183
$51$	5.93643	+	10.2336i	0.831266	+	1.43299i
$52$			0.0602269i			0.00835197i
$53$	0.589271	−	1.42263i	0.0809426	−	0.195413i	−0.878227	−	0.478244i	$-0.841274\pi$
$53$	0.589271	−	1.42263i	0.0809426	−	0.195413i	0.959170	+	0.282831i	$0.0912736\pi$
$54$	5.01465	−	7.50495i	0.682407	−	1.02129i
$55$	3.14113	+	9.89634i	0.423550	+	1.33442i
$56$	11.2206	−	2.23191i	1.49941	−	0.298252i
$57$	−5.80394	−	8.68621i	−0.768751	−	1.15052i
$58$	5.61872	+	1.11763i	0.737774	+	0.146752i
$59$	−7.76265	+	3.21539i	−1.01061	+	0.418609i	−0.825677	−	0.564143i	$-0.809207\pi$
$59$	−7.76265	+	3.21539i	−1.01061	+	0.418609i	−0.184933	+	0.982751i	$0.559207\pi$
$60$	−0.0556869	−	0.134440i	−0.00718915	−	0.0173561i
$61$	−10.3909	−	2.06688i	−1.33042	−	0.264637i	−0.521849	−	0.853038i	$-0.674757\pi$
$61$	−10.3909	−	2.06688i	−1.33042	−	0.264637i	−0.808569	+	0.588401i	$0.799757\pi$
$62$	−8.95845	+	5.98585i	−1.13772	+	0.760203i
$63$	−20.6783	+	4.11317i	−2.60522	+	0.518211i
$64$	−5.70193	+	5.70193i	−0.712741	+	0.712741i
$65$	9.67734	+	6.46619i	1.20033	+	0.802033i
$66$	−10.2516	+	8.63555i	−1.26188	+	1.06296i
$67$			5.61756i			0.686295i	0.939282	+	0.343147i	$0.111493\pi$
$67$			5.61756i			0.686295i	−0.939282	+	0.343147i	$0.888507\pi$
$68$	0.0215996	+	0.0632035i	0.00261933	+	0.00766455i
$69$	−1.19751			−0.144163
$70$	6.79781	−	16.4114i	0.812494	−	1.96153i
$71$	4.07475	+	2.72266i	0.483584	+	0.323120i	0.773352	−	0.633976i	$-0.218578\pi$
$71$	4.07475	+	2.72266i	0.483584	+	0.323120i	−0.289769	+	0.957097i	$0.593578\pi$
$72$	10.5087	−	10.5087i	1.23847	−	1.23847i
$73$	−1.07863	−	5.42263i	−0.126244	−	0.634671i	−0.991151	−	0.132739i	$-0.957623\pi$
$73$	−1.07863	−	5.42263i	−0.126244	−	0.634671i	0.864907	−	0.501932i	$-0.167377\pi$
$74$	−4.70388	−	7.03986i	−0.546815	−	0.818367i
$75$	−13.5095	−	2.68721i	−1.55995	−	0.310292i
$76$	−0.0225703	−	0.0544895i	−0.00258899	−	0.00625037i
$77$	13.3129	+	1.13907i	1.51714	+	0.129809i
$78$	−2.93131	+	14.7367i	−0.331906	+	1.66860i
$79$	8.24845	−	5.51144i	0.928023	−	0.620085i	0.00299959	−	0.999996i	$-0.499045\pi$
$79$	8.24845	−	5.51144i	0.928023	−	0.620085i	0.925023	+	0.379910i	$0.124045\pi$
$80$	2.42302	+	12.1813i	0.270902	+	1.36191i
$81$	−1.90081	+	1.90081i	−0.211201	+	0.211201i
$82$	3.83409	−	5.73812i	0.423404	−	0.633669i
$83$	2.46970	−	5.96239i	0.271085	−	0.654458i	−0.728445	−	0.685104i	$-0.759757\pi$
$83$	2.46970	−	5.96239i	0.271085	−	0.654458i	0.999530	+	0.0306466i	$0.00975664\pi$
$84$	−0.187262			−0.0204320
$85$	12.4746	+	3.31512i	1.35306	+	0.359575i
$86$	−7.04929			−0.760145
$87$	−10.7825	−	4.46625i	−1.15600	−	0.478833i
$88$	−8.24872	+	4.54595i	−0.879316	+	0.484600i
$89$	−3.16348	−	3.16348i	−0.335329	−	0.335329i	0.519277	−	0.854606i	$-0.326201\pi$
$89$	−3.16348	−	3.16348i	−0.335329	−	0.335329i	−0.854606	+	0.519277i	$0.826201\pi$
$90$	−4.50183	−	22.6322i	−0.474534	−	2.38565i
$91$	12.4535	−	8.32119i	1.30549	−	0.872298i
$92$	−0.00663080	−	0.00131895i	−0.000691309	−	0.000137510i
$93$	20.2788	−	8.39975i	2.10281	−	0.871014i
$94$	1.68145	−	0.696479i	0.173428	−	0.0718363i
$95$	−11.1787	−	2.22358i	−1.14691	−	0.228134i
$96$	0.218626	−	0.146081i	0.0223134	−	0.0149094i
$97$	0.954251	+	4.79734i	0.0968895	+	0.487097i	0.998510	+	0.0545686i	$0.0173783\pi$
$97$	0.954251	+	4.79734i	0.0968895	+	0.487097i	−0.901620	+	0.432528i	$0.857622\pi$
$98$	−9.19250	−	9.19250i	−0.928583	−	0.928583i
$99$	15.2015	−	8.37769i	1.52781	−	0.841990i
$100$	−0.0718447	−	0.0297590i	−0.00718447	−	0.00297590i
$101$	12.3450			1.22837			0.614186	−	0.789161i	$-0.289485\pi$
$101$	12.3450			1.22837			0.614186	+	0.789161i	$0.289485\pi$
$102$	2.20894	+	16.5163i	0.218717	+	1.63536i
$103$	−0.115119			−0.0113430			−0.00567150	−	0.999984i	$-0.501805\pi$
$103$	−0.115119			−0.0113430			−0.00567150	+	0.999984i	$0.501805\pi$
$104$	−4.04027	+	9.75407i	−0.396181	+	0.956465i
$105$	−20.1052	+	30.0896i	−1.96207	+	2.93644i
$106$	1.53359	−	1.53359i	0.148956	−	0.148956i
$107$	−0.343870	−	1.72875i	−0.0332432	−	0.167125i	0.960597	−	0.277943i	$-0.0896528\pi$
$107$	−0.343870	−	1.72875i	−0.0332432	−	0.167125i	−0.993841	+	0.110819i	$0.964653\pi$
$108$	−0.0863180	+	0.0576758i	−0.00830595	+	0.00554986i
$109$	0.286262	−	1.43914i	0.0274189	−	0.137844i	−0.964651	−	0.263530i	$-0.915113\pi$
$109$	0.286262	−	1.43914i	0.0274189	−	0.137844i	0.992070	+	0.125686i	$0.0401131\pi$
$110$	−1.24670	+	14.5708i	−0.118868	+	1.38927i
$111$	6.60081	+	15.9358i	0.626521	+	1.51256i
$112$	15.6759	+	3.11813i	1.48123	+	0.294635i
$113$	−10.0715	−	15.0731i	−0.947448	−	1.41796i	−0.908111	−	0.418730i	$-0.862475\pi$
$113$	−10.0715	−	15.0731i	−0.947448	−	1.41796i	−0.0393374	−	0.999226i	$-0.512525\pi$
$114$	−2.87057	−	14.4313i	−0.268854	−	1.35162i
$115$	−0.923839	+	0.923839i	−0.0861484	+	0.0861484i
$116$	−0.0547852	−	0.0366063i	−0.00508668	−	0.00339881i
$117$	7.44578	−	17.9757i	0.688363	−	1.66185i
$118$	−11.8343			−1.08944
$119$	10.0848	−	13.1988i	0.924468	−	1.20993i
$120$		−	25.5090i		−	2.32864i
$121$	−10.7301	+	2.42190i	−0.975461	+	0.220173i
$122$	−12.4072	−	8.29024i	−1.12330	−	0.750563i
$123$	−9.94142	+	9.94142i	−0.896387	+	0.896387i
$124$	0.121539	−	0.0241755i	0.0109145	−	0.00217103i
$125$	0.519569	−	0.347165i	0.0464716	−	0.0310514i
$126$	−29.1249	−	5.79330i	−2.59465	−	0.516108i
$127$	4.62535	+	11.1666i	0.410434	+	0.990875i	0.985021	+	0.172432i	$0.0551624\pi$
$127$	4.62535	+	11.1666i	0.410434	+	0.990875i	−0.574588	+	0.818443i	$0.694838\pi$
$128$	−10.3237	+	4.27622i	−0.912496	+	0.377968i
$129$	14.0851	+	2.80170i	1.24012	+	0.246676i
$130$	9.10747	+	13.6303i	0.798778	+	1.19546i
$131$	−7.72466	+	1.53653i	−0.674907	+	0.134247i	−0.520633	−	0.853781i	$-0.674304\pi$
$131$	−7.72466	+	1.53653i	−0.674907	+	0.134247i	−0.154274	+	0.988028i	$0.549304\pi$
$132$	0.146942	−	0.0466397i	0.0127896	−	0.00405946i
$133$	−8.14878	+	12.1955i	−0.706589	+	1.05748i
$134$	−3.02787	+	7.30991i	−0.261568	+	0.631480i
$135$			20.0620i			1.72666i
$136$	−0.741782	+	11.6851i	−0.0636073	+	1.00199i
$137$	−21.2886			−1.81880			−0.909402	−	0.415918i	$-0.863460\pi$
$137$	−21.2886			−1.81880			−0.909402	+	0.415918i	$0.863460\pi$
$138$	−1.55827	−	0.645457i	−0.132649	−	0.0549449i
$139$	2.92332	−	4.37506i	0.247953	−	0.371087i	−0.686527	−	0.727105i	$-0.740866\pi$
$139$	2.92332	−	4.37506i	0.247953	−	0.371087i	0.934479	+	0.356017i	$0.115866\pi$
$140$	−0.144467	+	0.144467i	−0.0122097	+	0.0122097i
$141$	−3.63649	+	0.723343i	−0.306248	+	0.0609165i
$142$	3.83480	+	5.73918i	0.321809	+	0.481621i
$143$	−7.69961	+	9.63119i	−0.643874	+	0.805401i
$144$	19.1821	−	7.94550i	1.59851	−	0.662125i
$145$	−11.7639	+	4.87277i	−0.976940	+	0.404662i
$146$	1.51922	−	7.63764i	0.125732	−	0.632096i
$147$	14.7139	+	22.0209i	1.21358	+	1.81625i
$148$	0.0189979	+	0.0955091i	0.00156162	+	0.00785080i
$149$	3.37840	+	3.37840i	0.276770	+	0.276770i	0.831818	−	0.555048i	$-0.187300\pi$
$149$	3.37840	+	3.37840i	0.276770	+	0.276770i	−0.555048	+	0.831818i	$0.687300\pi$
$150$	−16.1310	−	10.7784i	−1.31709	−	0.880052i
$151$	2.40439	−	5.80470i	0.195666	−	0.472380i	−0.795345	−	0.606157i	$-0.792710\pi$
$151$	2.40439	−	5.80470i	0.195666	−	0.472380i	0.991012	+	0.133777i	$0.0427105\pi$
$152$		−	10.3390i		−	0.838601i
$153$	1.36702	−	21.5344i	0.110517	−	1.74096i
$154$	16.7095	+	8.65785i	1.34649	+	0.697670i
$155$	9.16429	−	22.1246i	0.736094	−	1.77709i
$156$	0.0960105	−	0.143690i	0.00768699	−	0.0115044i
$157$	−7.31284	−	7.31284i	−0.583628	−	0.583628i	0.352270	−	0.935898i	$-0.385410\pi$
$157$	−7.31284	−	7.31284i	−0.583628	−	0.583628i	−0.935898	+	0.352270i	$0.885410\pi$
$158$	13.7040	−	2.72590i	1.09024	−	0.216861i
$159$	−3.67376	+	2.45473i	−0.291348	+	0.194673i
$160$	0.0559660	−	0.281360i	0.00442450	−	0.0222435i
$161$	0.643410	+	1.55333i	0.0507078	+	0.122419i
$162$	−3.49798	+	1.44891i	−0.274827	+	0.113837i
$163$	−0.795935	+	4.00144i	−0.0623425	+	0.313417i	−0.999356	−	0.0358756i	$-0.988578\pi$
$163$	−0.795935	+	4.00144i	−0.0623425	+	0.313417i	0.937014	+	0.349292i	$0.113578\pi$
$164$	−0.0659968	+	0.0440977i	−0.00515349	+	0.00344345i
$165$	8.28209	−	28.6182i	0.644760	−	2.22792i
$166$	6.42746	−	6.42746i	0.498867	−	0.498867i
$167$	9.81399	+	6.55750i	0.759430	+	0.507435i	0.873968	−	0.485984i	$-0.161539\pi$
$167$	9.81399	+	6.55750i	0.759430	+	0.507435i	−0.114538	+	0.993419i	$0.536539\pi$
$168$	−30.3281	−	12.5623i	−2.33987	−	0.969204i
$169$			0.822165i			0.0632435i
$170$	14.4459	+	11.0377i	1.10795	+	0.846550i
$171$			19.0536i			1.45707i
$172$	0.0749056	+	0.0310269i	0.00571150	+	0.00236578i
$173$	7.58181	−	11.3470i	0.576435	−	0.862695i	−0.422614	−	0.906310i	$-0.638887\pi$
$173$	7.58181	−	11.3470i	0.576435	−	0.862695i	0.999048	+	0.0436145i	$0.0138873\pi$
$174$	−11.6235	−	11.6235i	−0.881177	−	0.881177i
$175$	3.77286	+	18.9675i	0.285202	+	1.43381i
$176$	−13.0772	+	1.45750i	−0.985731	+	0.109864i
$177$	23.6460	+	4.70348i	1.77734	+	0.353535i
$178$	−2.41140	−	5.82163i	−0.180742	−	0.436350i
$179$	−5.50626	−	13.2933i	−0.411557	−	0.993587i	−0.984720	−	0.174145i	$-0.944284\pi$
$179$	−5.50626	−	13.2933i	−0.411557	−	0.993587i	0.573163	−	0.819441i	$-0.305716\pi$
$180$	−0.0517777	+	0.260304i	−0.00385928	+	0.0194019i
$181$	8.08052	+	12.0934i	0.600620	+	0.898892i	0.999839	−	0.0179641i	$-0.00571845\pi$
$181$	8.08052	+	12.0934i	0.600620	+	0.898892i	−0.399218	+	0.916856i	$0.630718\pi$
$182$	20.6904	−	4.11558i	1.53368	−	0.305067i
$183$	21.4958	+	21.4958i	1.58901	+	1.58901i
$184$	−0.985413	−	0.658432i	−0.0726456	−	0.0485402i
$185$	17.3862	+	7.20161i	1.27826	+	0.529473i
$186$	30.9155			2.26683
$187$	−4.62604	+	12.8686i	−0.338290	+	0.941042i
$188$	−0.0209325			−0.00152666
$189$	23.8521	+	9.87986i	1.73498	+	0.718654i
$190$	−13.3479	−	8.91876i	−0.968356	−	0.647035i
$191$	1.54854	+	1.54854i	0.112049	+	0.112049i	0.760908	−	0.648860i	$-0.224754\pi$
$191$	1.54854	+	1.54854i	0.112049	+	0.112049i	−0.648860	+	0.760908i	$0.724754\pi$
$192$	22.6934	−	4.51400i	1.63776	−	0.325770i
$193$	11.1373	+	16.6682i	0.801683	+	1.19980i	0.976567	+	0.215214i	$0.0690449\pi$
$193$	11.1373	+	16.6682i	0.801683	+	1.19980i	−0.174884	+	0.984589i	$0.555955\pi$
$194$	−1.34404	+	6.75694i	−0.0964963	+	0.485120i
$195$	−12.7802	−	30.8542i	−0.915211	−	2.20952i
$196$	0.0572192	+	0.138139i	0.00408709	+	0.00986710i
$197$	−2.46684	−	0.490684i	−0.175755	−	0.0349598i	0.106428	−	0.994320i	$-0.466059\pi$
$197$	−2.46684	−	0.490684i	−0.175755	−	0.0349598i	−0.282183	+	0.959361i	$0.591059\pi$
$198$	24.2967	−	2.70796i	1.72669	−	0.192446i
$199$	−2.90465	−	14.6027i	−0.205905	−	1.03516i	−0.936051	−	0.351864i	$-0.885548\pi$
$199$	−2.90465	−	14.6027i	−0.205905	−	1.03516i	0.730146	−	0.683292i	$-0.239452\pi$
$200$	−9.63927	−	9.63927i	−0.681600	−	0.681600i
$201$	8.95522	−	13.4024i	0.631652	−	0.945334i
$202$	16.0640	+	6.65394i	1.13026	+	0.468170i
$203$			16.3860i			1.15007i
$204$	0.0492231	−	0.185224i	0.00344631	−	0.0129683i
$205$			15.3390i			1.07132i
$206$	−0.149800	−	0.0620490i	−0.0104370	−	0.00432316i
$207$	1.81601	+	1.21342i	0.126221	+	0.0843385i
$208$	−10.4297	+	10.4297i	−0.723170	+	0.723170i
$209$	3.35679	−	11.5992i	0.232194	−	0.802330i
$210$	−42.3804	+	28.3177i	−2.92452	+	1.95410i
$211$	0.385947	−	1.94029i	0.0265697	−	0.133575i	−0.965224	−	0.261425i	$-0.915808\pi$
$211$	0.385947	−	1.94029i	0.0265697	−	0.133575i	0.991794	+	0.127850i	$0.0408076\pi$
$212$	−0.0230459	+	0.00954592i	−0.00158280	+	0.000655616i
$213$	−5.38125	−	12.9915i	−0.368717	−	0.890162i
$214$	0.484332	−	2.43490i	0.0331083	−	0.166447i
$215$	13.0276	−	8.70477i	0.888476	−	0.593661i
$216$	−17.8488	+	3.55034i	−1.21446	+	0.241570i
$217$	−21.7912	−	21.7912i	−1.47928	−	1.47928i
$218$	1.14820	−	1.71840i	0.0777657	−	0.116385i
$219$	−6.07107	+	14.6569i	−0.410245	+	0.990418i
$220$	0.0773797	−	0.149342i	0.00521693	−	0.0100686i
$221$	4.95714	+	14.5053i	0.333453	+	0.975732i
$222$			24.2944i			1.63053i
$223$	−10.5369	+	25.4384i	−0.705604	+	1.70348i	0.00510044	+	0.999987i	$0.498376\pi$
$223$	−10.5369	+	25.4384i	−0.705604	+	1.70348i	−0.710704	+	0.703491i	$0.751624\pi$
$224$	−0.306953	−	0.205099i	−0.0205092	−	0.0137038i
$225$	17.7641	+	17.7641i	1.18428	+	1.18428i
$226$	−4.98127	−	25.0426i	−0.331349	−	1.66581i
$227$	−13.2731	−	19.8646i	−0.880967	−	1.31846i	−0.947196	−	0.320656i	$-0.896097\pi$
$227$	−13.2731	−	19.8646i	−0.880967	−	1.31846i	0.0662291	−	0.997804i	$-0.478903\pi$
$228$	−0.0330158	+	0.165982i	−0.00218653	+	0.0109924i
$229$	0.998409	−	0.413554i	0.0659767	−	0.0273284i	−0.349451	−	0.936955i	$-0.613632\pi$
$229$	0.998409	−	0.413554i	0.0659767	−	0.0273284i	0.415428	+	0.909626i	$0.363632\pi$
$230$	−1.70010	+	0.704206i	−0.112102	+	0.0464340i
$231$	−29.9461	−	23.9402i	−1.97031	−	1.57515i
$232$	−6.41706	−	9.60381i	−0.421301	−	0.630521i
$233$	−15.6479	+	3.11257i	−1.02513	+	0.203911i	−0.678894	−	0.734236i	$-0.737540\pi$
$233$	−15.6479	+	3.11257i	−1.02513	+	0.203911i	−0.346236	+	0.938147i	$0.612540\pi$
$234$	19.3778	−	19.3778i	1.26677	−	1.26677i
$235$	−2.24740	+	3.36347i	−0.146604	+	0.219409i
$236$	0.125751	+	0.0520879i	0.00818571	+	0.00339063i
$237$	−28.4652			−1.84902
$238$	20.2370	−	11.7393i	1.31177	−	0.760948i
$239$			7.44492i			0.481572i	0.970578	+	0.240786i	$0.0774051\pi$
$239$			7.44492i			0.481572i	−0.970578	+	0.240786i	$0.922595\pi$
$240$	13.6380	−	32.9250i	0.880327	−	2.12530i
$241$	13.0840	−	19.5815i	0.842812	−	1.26136i	−0.120430	−	0.992722i	$-0.538427\pi$
$241$	13.0840	−	19.5815i	0.842812	−	1.26136i	0.963242	−	0.268635i	$-0.0865726\pi$
$242$	−15.2680	−	2.63198i	−0.981466	−	0.169190i
$243$	−11.2908	+	2.24588i	−0.724304	+	0.144073i
$244$	0.0953499	+	0.142701i	0.00610415	+	0.00913551i
$245$	28.3397	+	5.63712i	1.81056	+	0.360142i
$246$	−18.2948	+	7.57795i	−1.16643	+	0.483153i
$247$	−5.17991	−	12.5054i	−0.329590	−	0.795701i
$248$	21.3056	+	4.23795i	1.35291	+	0.269110i
$249$	−15.3972	+	10.2881i	−0.975756	+	0.651979i
$250$	0.863216	−	0.171704i	0.0545946	−	0.0108595i
$251$	−7.88160	+	7.88160i	−0.497482	+	0.497482i	−0.910653	−	0.413171i	$-0.864421\pi$
$251$	−7.88160	+	7.88160i	−0.497482	+	0.497482i	0.413171	+	0.910653i	$0.364421\pi$
$252$	0.283981	+	0.189750i	0.0178892	+	0.0119531i
$253$	−0.891746	−	1.05862i	−0.0560636	−	0.0665551i
$254$			17.0237i			1.06816i
$255$	−24.4773	−	27.7956i	−1.53283	−	1.74063i
$256$	0.388763			0.0242977
$257$	−2.97567	+	7.18391i	−0.185617	+	0.448120i	−0.989107	−	0.147199i	$-0.952974\pi$
$257$	−2.97567	+	7.18391i	−0.185617	+	0.448120i	0.803490	+	0.595319i	$0.202974\pi$
$258$	16.8183	+	11.2376i	1.04706	+	0.699623i
$259$	17.1243	−	17.1243i	1.06405	−	1.06405i
$260$	−0.0367831	−	0.184921i	−0.00228119	−	0.0114683i
$261$	11.8260	+	17.6988i	0.732008	+	1.09553i
$262$	−10.8800	−	2.16416i	−0.672168	−	0.133703i
$263$	−5.92709	−	14.3092i	−0.365480	−	0.882346i	−0.994479	−	0.104940i	$-0.966535\pi$
$263$	−5.92709	−	14.3092i	−0.365480	−	0.882346i	0.628999	−	0.777406i	$-0.283465\pi$
$264$	26.9268	+	2.30390i	1.65723	+	0.141795i
$265$	−0.940444	+	4.72793i	−0.0577710	+	0.290435i
$266$	−17.1771	+	11.4773i	−1.05319	+	0.703721i
$267$	2.50441	+	12.5905i	0.153267	+	0.770527i
$268$	0.0643481	−	0.0643481i	0.00393068	−	0.00393068i
$269$	−4.89714	+	7.32909i	−0.298584	+	0.446862i	−0.950179	−	0.311704i	$-0.899100\pi$
$269$	−4.89714	+	7.32909i	−0.298584	+	0.446862i	0.651595	+	0.758567i	$0.274100\pi$
$270$	−10.8134	+	26.1059i	−0.658083	+	1.58875i
$271$	10.0401			0.609895			0.304947	−	0.952369i	$-0.401361\pi$
$271$	10.0401			0.609895			0.304947	+	0.952369i	$0.401361\pi$
$272$	−7.20470	+	14.6857i	−0.436849	+	0.890449i
$273$	−42.9770			−2.60108
$274$	−27.7020	−	11.4745i	−1.67354	−	0.693202i
$275$	−7.68456	−	13.9438i	−0.463396	−	0.840842i
$276$	0.0137172	+	0.0137172i	0.000825679	+	0.000825679i
$277$	4.02565	+	20.2383i	0.241878	+	1.21600i	0.890533	+	0.454919i	$0.150332\pi$
$277$	4.02565	+	20.2383i	0.241878	+	1.21600i	−0.648655	+	0.761083i	$0.724668\pi$
$278$	6.16215	−	4.11742i	0.369581	−	0.246946i
$279$	−39.2640	−	7.81009i	−2.35067	−	0.467578i
$280$	−33.0886	+	13.7057i	−1.97742	+	0.819075i
$281$	−10.4019	+	4.30861i	−0.620526	+	0.257030i	−0.670722	−	0.741709i	$-0.734015\pi$
$281$	−10.4019	+	4.30861i	−0.620526	+	0.257030i	0.0501959	+	0.998739i	$0.484015\pi$
$282$	−5.12190	−	1.01881i	−0.305005	−	0.0606693i
$283$	16.5354	−	11.0486i	0.982925	−	0.656770i	0.0433312	−	0.999061i	$-0.486203\pi$
$283$	16.5354	−	11.0486i	0.982925	−	0.656770i	0.939594	+	0.342291i	$0.111203\pi$
$284$	−0.0154879	−	0.0778629i	−0.000919038	−	0.00462031i
$285$	23.1255	+	23.1255i	1.36984	+	1.36984i
$286$	−15.2104	+	8.38260i	−0.899410	+	0.495674i
$287$	18.2368	+	7.55392i	1.07648	+	0.445894i
$288$	−0.479567			−0.0282588
$289$	10.4043	+	13.4444i	0.612016	+	0.790846i
$290$	−17.9343			−1.05314
$291$	5.37101	−	12.9668i	0.314854	−	0.760125i
$292$	−0.0497597	+	0.0744707i	−0.00291197	+	0.00435807i
$293$	−20.2811	+	20.2811i	−1.18484	+	1.18484i	−0.206360	+	0.978476i	$0.566162\pi$
$293$	−20.2811	+	20.2811i	−1.18484	+	1.18484i	−0.978476	+	0.206360i	$0.933838\pi$
$294$	7.27735	+	36.5857i	0.424424	+	2.13372i
$295$	21.8707	−	14.6135i	1.27336	−	0.850833i
$296$	−3.33032	+	16.7427i	−0.193571	+	0.973148i
$297$	−21.1770	−	1.81194i	−1.22882	−	0.105139i
$298$	2.57523	+	6.21714i	0.149179	+	0.360149i
$299$	−1.52178	−	0.302701i	−0.0880067	−	0.0175056i
$300$	0.123967	+	0.185530i	0.00715726	+	0.0107116i
$301$	−3.93361	−	19.7756i	−0.226729	−	1.13985i
$302$	6.25747	−	6.25747i	0.360077	−	0.360077i
$303$	−29.4528	−	19.6797i	−1.69202	−	1.13057i
$304$	5.52756	−	13.3447i	0.317027	−	0.765372i
$305$	33.1666			1.89911
$306$	13.3859	−	27.2851i	0.765222	−	1.55979i
$307$		−	3.80846i		−	0.217360i	−0.994077	−	0.108680i	$-0.965338\pi$
$307$		−	3.80846i		−	0.217360i	0.994077	−	0.108680i	$-0.0346624\pi$
$308$	−0.139448	−	0.165544i	−0.00794580	−	0.00943274i
$309$	0.274651	+	0.183516i	0.0156244	+	0.0104399i
$310$	23.8503	−	23.8503i	1.35460	−	1.35460i
$311$	−15.6392	+	3.11084i	−0.886819	+	0.176399i	−0.617424	−	0.786630i	$-0.711824\pi$
$311$	−15.6392	+	3.11084i	−0.886819	+	0.176399i	−0.269395	+	0.963030i	$0.586824\pi$
$312$	25.1887	−	16.8306i	1.42603	−	0.952843i
$313$	29.4139	+	5.85079i	1.66257	+	0.330706i	0.934817	−	0.355130i	$-0.115563\pi$
$313$	29.4139	+	5.85079i	1.66257	+	0.330706i	0.727756	+	0.685836i	$0.240563\pi$
$314$	−5.57429	−	13.4575i	−0.314575	−	0.759452i
$315$	60.9787	−	25.2582i	3.43576	−	1.42314i
$316$	−0.157617	−	0.0313519i	−0.00886663	−	0.00176368i
$317$	−2.20530	−	3.30046i	−0.123862	−	0.185373i	0.764356	−	0.644794i	$-0.223057\pi$
$317$	−2.20530	−	3.30046i	−0.123862	−	0.185373i	−0.888218	+	0.459421i	$0.848057\pi$
$318$	−6.10362	+	1.21409i	−0.342274	+	0.0680825i
$319$	−4.08111	−	12.8578i	−0.228498	−	0.719900i
$320$	14.0248	−	20.9896i	0.784012	−	1.17336i
$321$	−1.93548	+	4.67265i	−0.108028	+	0.260802i
$322$			2.36808i			0.131968i
$323$	−9.92082	−	11.2658i	−0.552009	−	0.626844i
$324$	0.0435467			0.00241926
$325$	−16.4885	−	6.82975i	−0.914615	−	0.378846i
$326$	−3.19249	+	4.77790i	−0.176816	+	0.264624i
$327$	−2.97716	+	2.97716i	−0.164637	+	0.164637i
$328$	−13.6468	+	2.71452i	−0.753518	+	0.149884i
$329$	2.89212	+	4.32837i	0.159448	+	0.238631i
$330$	26.2024	−	32.7757i	1.44239	−	1.80424i
$331$	−9.91169	+	4.10556i	−0.544796	+	0.225662i	−0.638070	−	0.769979i	$-0.720267\pi$
$331$	−9.91169	+	4.10556i	−0.544796	+	0.225662i	0.0932739	+	0.995640i	$0.470267\pi$
$332$	−0.0965880	+	0.0400081i	−0.00530095	+	0.00219573i
$333$	6.13743	−	30.8549i	0.336329	−	1.69084i
$334$	9.23607	+	13.8228i	0.505375	+	0.756348i
$335$	−3.43088	−	17.2482i	−0.187449	−	0.942369i
$336$	−32.4289	−	32.4289i	−1.76914	−	1.76914i
$337$	−18.9263	−	12.6462i	−1.03098	−	0.688881i	−0.0795798	−	0.996828i	$-0.525358\pi$
$337$	−18.9263	−	12.6462i	−1.03098	−	0.688881i	−0.951403	+	0.307948i	$0.900358\pi$
$338$	−0.443147	+	1.06985i	−0.0241040	+	0.0581922i
$339$			52.0169i			2.82517i
$340$	−0.104920	−	0.180869i	−0.00569011	−	0.00980897i
$341$	22.5265	+	11.6719i	1.21988	+	0.632067i
$342$	−10.2699	+	24.7937i	−0.555332	+	1.34069i
$343$	4.99107	−	7.46966i	0.269492	−	0.403324i
$344$	10.0500	+	10.0500i	0.541857	+	0.541857i
$345$	3.67684	−	0.731368i	0.197954	−	0.0393755i
$346$	15.9819	−	10.6788i	0.859194	−	0.574095i
$347$	0.0812614	−	0.408529i	0.00436234	−	0.0219310i	−0.978543	−	0.206044i	$-0.933941\pi$
$347$	0.0812614	−	0.408529i	0.00436234	−	0.0219310i	0.982905	+	0.184113i	$0.0589411\pi$
$348$	0.0723512	+	0.174671i	0.00387843	+	0.00936337i
$349$	−6.88195	+	2.85060i	−0.368382	+	0.152589i	−0.559192	−	0.829038i	$-0.688889\pi$
$349$	−6.88195	+	2.85060i	−0.368382	+	0.152589i	0.190810	+	0.981627i	$0.438889\pi$
$350$	−5.31398	+	26.7152i	−0.284044	+	1.42799i
$351$	−19.8101	+	13.2367i	−1.05739	+	0.706522i
$352$	0.291943	+	0.0844881i	0.0155606	+	0.00450323i
$353$	16.0357	−	16.0357i	0.853494	−	0.853494i	−0.137068	−	0.990562i	$-0.543768\pi$
$353$	16.0357	−	16.0357i	0.853494	−	0.853494i	0.990562	+	0.137068i	$0.0437678\pi$
$354$	28.2344	+	18.8656i	1.50064	+	1.00270i
$355$	−14.1740	−	5.87105i	−0.752276	−	0.311603i
$356$			0.0724741i			0.00384112i
$357$	−45.1010	+	15.4131i	−2.38700	+	0.815749i
$358$		−	20.2659i		−	1.07109i
$359$	10.0023	+	4.14309i	0.527901	+	0.218664i	0.630684	−	0.776040i	$-0.282775\pi$
$359$	10.0023	+	4.14309i	0.527901	+	0.218664i	−0.102782	+	0.994704i	$0.532775\pi$
$360$	−25.8479	+	38.6842i	−1.36231	+	2.03883i
$361$	−4.06212	−	4.06212i	−0.213796	−	0.213796i
$362$	3.99655	+	20.0920i	0.210054	+	1.05601i
$363$	29.4608	+	11.3271i	1.54629	+	0.594519i
$364$	−0.237970	−	0.0473353i	−0.0124730	−	0.00248104i
$365$	6.62366	+	15.9909i	0.346698	+	0.837003i
$366$	16.3854	+	39.5578i	0.856478	+	2.06772i
$367$	3.81640	−	19.1863i	0.199214	−	1.00152i	−0.743708	−	0.668505i	$-0.766935\pi$
$367$	3.81640	−	19.1863i	0.199214	−	1.00152i	0.942922	−	0.333013i	$-0.108065\pi$
$368$	−0.919872	−	1.37669i	−0.0479517	−	0.0717647i
$369$	25.1496	−	5.00256i	1.30923	−	0.260423i
$370$	18.7424	+	18.7424i	0.974369	+	0.974369i
$371$	5.15799	+	3.44646i	0.267790	+	0.178931i
$372$	−0.328507	−	0.136072i	−0.0170323	−	0.00705501i
$373$	−14.2538			−0.738034			−0.369017	−	0.929423i	$-0.620306\pi$
$373$	−14.2538			−0.738034			−0.369017	+	0.929423i	$0.620306\pi$
$374$	−12.9558	+	14.2519i	−0.669931	+	0.736949i
$375$	−1.79302			−0.0925913
$376$	−3.39014	−	1.40424i	−0.174833	−	0.0724182i
$377$	−12.5733	−	8.40121i	−0.647558	−	0.432684i
$378$	25.7125	+	25.7125i	1.32251	+	1.32251i
$379$	−22.0668	+	4.38935i	−1.13349	+	0.225466i	−0.725968	−	0.687728i	$-0.758608\pi$
$379$	−22.0668	+	4.38935i	−1.13349	+	0.225466i	−0.407525	+	0.913194i	$0.633608\pi$
$380$	0.102579	+	0.153520i	0.00526219	+	0.00787542i
$381$	6.76597	−	34.0148i	0.346631	−	1.74263i
$382$	1.18039	+	2.84972i	0.0603942	+	0.145805i
$383$	−6.98443	−	16.8619i	−0.356887	−	0.861603i	−0.995734	−	0.0922685i	$-0.970588\pi$
$383$	−6.98443	−	16.8619i	−0.356887	−	0.861603i	0.638847	−	0.769334i	$-0.279412\pi$
$384$	31.4473	+	6.25526i	1.60479	+	0.319212i
$385$	−41.5715	+	4.63331i	−2.11868	+	0.236135i
$386$	5.50842	+	27.6927i	0.280371	+	1.40952i
$387$	−18.5210	−	18.5210i	−0.941475	−	0.941475i
$388$	0.0440219	−	0.0658834i	0.00223487	−	0.00334472i
$389$	−0.199979	−	0.0828340i	−0.0101393	−	0.00419985i	0.377608	−	0.925966i	$-0.376747\pi$
$389$	−0.199979	−	0.0828340i	−0.0101393	−	0.00419985i	−0.387747	+	0.921766i	$0.626747\pi$
$390$		−	47.0379i		−	2.38186i
$391$	−1.70555	+	0.228105i	−0.0862533	+	0.0115358i
$392$			26.2109i			1.32385i
$393$	20.8790	+	8.64837i	1.05321	+	0.436253i
$394$	−2.94552	−	1.96813i	−0.148393	−	0.0991531i
$395$	−21.9600	+	21.9600i	−1.10493	+	1.10493i
$396$	−0.270095	−	0.0781653i	−0.0135728	−	0.00392795i
$397$	−13.7795	+	9.20716i	−0.691573	+	0.462094i	−0.851034	−	0.525110i	$-0.824024\pi$
$397$	−13.7795	+	9.20716i	−0.691573	+	0.462094i	0.159462	+	0.987204i	$0.449024\pi$
$398$	4.09113	−	20.5675i	0.205070	−	1.03096i
$399$	38.8828	−	16.1058i	1.94658	−	0.806298i
$400$	−7.28812	−	17.5951i	−0.364406	−	0.879754i
$401$	−2.56410	+	12.8906i	−0.128045	+	0.643726i	0.862446	+	0.506149i	$0.168931\pi$
$401$	−2.56410	+	12.8906i	−0.128045	+	0.643726i	−0.990491	+	0.137577i	$0.956069\pi$
$402$	18.8770	−	12.6132i	0.941498	−	0.629089i
$403$	27.8933	−	5.54832i	1.38946	−	0.276381i
$404$	−0.141409	−	0.141409i	−0.00703538	−	0.00703538i
$405$	4.67534	−	6.99715i	0.232320	−	0.347691i
$406$	−8.83206	+	21.3225i	−0.438328	+	1.05822i
$407$	−9.17214	+	17.7021i	−0.454646	+	0.877461i
$408$	20.3976	−	26.6960i	1.00983	−	1.32165i
$409$		−	22.4329i		−	1.10924i	−0.832105	−	0.554618i	$-0.812864\pi$
$409$		−	22.4329i		−	1.10924i	0.832105	−	0.554618i	$-0.187136\pi$
$410$	−8.26770	+	19.9600i	−0.408312	+	0.985753i
$411$	50.7904	+	33.9371i	2.50531	+	1.67399i
$412$	0.00131866	+	0.00131866i	6.49659e−5	+	6.49659e-5i
$413$	−6.60372	−	33.1992i	−0.324948	−	1.63362i
$414$	1.70907	+	2.55780i	0.0839962	+	0.125709i
$415$	−3.94151	+	19.8153i	−0.193481	+	0.972695i
$416$	0.314753	−	0.130375i	0.0154320	−	0.00639216i
$417$	−13.9490	+	5.77785i	−0.683083	+	0.282942i
$418$	10.6200	−	13.2842i	0.519441	−	0.649752i
$419$	−9.19057	−	13.7547i	−0.448989	−	0.671959i	0.536071	−	0.844173i	$-0.319908\pi$
$419$	−9.19057	−	13.7547i	−0.448989	−	0.671959i	−0.985060	+	0.172214i	$0.944908\pi$
$420$	0.574971	−	0.114369i	0.0280557	−	0.00558063i
$421$	−14.3431	+	14.3431i	−0.699042	+	0.699042i	−0.964204	−	0.265162i	$-0.914574\pi$
$421$	−14.3431	+	14.3431i	−0.699042	+	0.699042i	0.265162	+	0.964204i	$0.414574\pi$
$422$	1.54803	−	2.31680i	0.0753571	−	0.112780i
$423$	6.24766	+	2.58786i	0.303771	+	0.125826i
$424$	−4.37278			−0.212361
$425$	−19.7528	−	1.25392i	−0.958150	−	0.0608241i
$426$		−	19.8058i		−	0.959594i
$427$	16.3334	−	39.4324i	0.790430	−	1.90827i
$428$	−0.0158635	+	0.0237415i	−0.000766793	+	0.00114759i
$429$	33.7233	−	10.7039i	1.62818	−	0.516788i
$430$	21.6442	−	4.30530i	1.04378	−	0.207620i
$431$	16.0431	+	24.0102i	0.772771	+	1.15653i	0.983838	+	0.179061i	$0.0573061\pi$
$431$	16.0431	+	24.0102i	0.772771	+	1.15653i	−0.211067	+	0.977472i	$0.567694\pi$
$432$	−24.9359	−	4.96006i	−1.19973	−	0.238641i
$433$	3.18484	−	1.31920i	0.153054	−	0.0633969i	−0.304841	−	0.952403i	$-0.598603\pi$
$433$	3.18484	−	1.31920i	0.153054	−	0.0633969i	0.457895	+	0.889006i	$0.348603\pi$
$434$	−16.6106	−	40.1015i	−0.797334	−	1.92493i
$435$	35.8344	+	7.12790i	1.71813	+	0.341756i
$436$	−0.0197641	+	0.0132059i	−0.000946529	+	0.000632450i
$437$	1.49025	−	0.296428i	0.0712882	−	0.0141801i
$438$	−15.8001	+	15.8001i	−0.754957	+	0.754957i
$439$	21.5343	+	14.3887i	1.02777	+	0.686737i	0.950644	−	0.310284i	$-0.100424\pi$
$439$	21.5343	+	14.3887i	1.02777	+	0.686737i	0.0771310	+	0.997021i	$0.475424\pi$
$440$	22.5505	−	18.9957i	1.07505	−	0.905586i
$441$		−	48.3039i		−	2.30018i
$442$	−1.36783	+	21.5471i	−0.0650608	+	1.02489i
$443$	37.9397			1.80257			0.901284	−	0.433228i	$-0.142626\pi$
$443$	37.9397			1.80257			0.901284	+	0.433228i	$0.142626\pi$
$444$	0.106930	−	0.258152i	0.00507467	−	0.0122513i
$445$	11.6452	+	7.78110i	0.552038	+	0.368860i
$446$	−27.4225	+	27.4225i	−1.29849	+	1.29849i
$447$	−2.67455	−	13.4459i	−0.126502	−	0.635969i
$448$	−18.0482	−	27.0111i	−0.852698	−	1.27615i
$449$	7.81894	+	1.55528i	0.368999	+	0.0733984i	0.376107	−	0.926576i	$-0.377263\pi$
$449$	7.81894	+	1.55528i	0.368999	+	0.0733984i	−0.00710811	+	0.999975i	$0.502263\pi$
$450$	13.5409	+	32.6907i	0.638325	+	1.54105i
$451$	−16.1915	−	1.38537i	−0.762427	−	0.0652345i
$452$	−0.0572920	+	0.288026i	−0.00269479	+	0.0135476i
$453$	−14.9899	+	10.0160i	−0.704289	+	0.470591i
$454$	−6.56475	−	33.0032i	−0.308099	−	1.54892i
$455$	−33.1553	+	33.1553i	−1.55435	+	1.55435i
$456$	−16.4818	+	24.6668i	−0.771832	+	1.15513i
$457$	11.3326	−	27.3593i	0.530116	−	1.27981i	−0.401329	−	0.915934i	$-0.631452\pi$
$457$	11.3326	−	27.3593i	0.530116	−	1.27981i	0.931446	−	0.363880i	$-0.118548\pi$
$458$	1.52210			0.0711229
$459$	−16.0420	+	20.9955i	−0.748777	+	0.979987i
$460$	0.0211648			0.000986813
$461$	36.6312	+	15.1731i	1.70609	+	0.706684i	0.999999	−	0.00144206i	$-0.000459023\pi$
$461$	36.6312	+	15.1731i	1.70609	+	0.706684i	0.706086	+	0.708126i	$0.250459\pi$
$462$	−26.0639	−	47.2934i	−1.21260	−	2.20029i
$463$	−13.2732	−	13.2732i	−0.616858	−	0.616858i	0.327866	−	0.944724i	$-0.393670\pi$
$463$	−13.2732	−	13.2732i	−0.616858	−	0.616858i	−0.944724	+	0.327866i	$0.893670\pi$
$464$	−3.14811	−	15.8266i	−0.146147	−	0.734732i
$465$	−57.1340	+	38.1757i	−2.64953	+	1.77036i
$466$	−22.0397	−	4.38397i	−1.02097	−	0.203084i
$467$	5.90306	−	2.44513i	0.273161	−	0.113147i	−0.241898	−	0.970302i	$-0.577770\pi$
$467$	5.90306	−	2.44513i	0.273161	−	0.113147i	0.515059	+	0.857155i	$0.327770\pi$
$468$	−0.291198	+	0.120618i	−0.0134606	+	0.00557558i
$469$	−22.1963	−	4.41512i	−1.02493	−	0.203871i
$470$	−4.73736	+	3.16540i	−0.218518	+	0.146009i
$471$	5.78930	+	29.1048i	0.266757	+	1.34108i
$472$	16.8718	+	16.8718i	0.776588	+	0.776588i
$473$	8.01196	+	14.5379i	0.368390	+	0.668452i
$474$	−37.0407	−	15.3428i	−1.70134	−	0.704717i
$475$	17.4772			0.801908
$476$	−0.266708	+	0.0356702i	−0.0122245	+	0.00163494i
$477$	8.05857			0.368977
$478$	−4.01281	+	9.68778i	−0.183542	+	0.443109i
$479$	−9.91608	+	14.8405i	−0.453077	+	0.678078i	−0.985745	−	0.168246i	$-0.946190\pi$
$479$	−9.91608	+	14.8405i	−0.453077	+	0.678078i	0.532668	+	0.846324i	$0.321190\pi$
$480$	−0.582053	+	0.582053i	−0.0265670	+	0.0265670i
$481$	4.36006	+	21.9195i	0.198801	+	0.999442i
$482$	27.5801	−	18.4284i	1.25624	−	0.839392i
$483$	0.941180	−	4.73163i	0.0428252	−	0.215297i
$484$	0.150653	+	0.0951684i	0.00684787	+	0.00432584i
$485$	−5.85988	−	14.1470i	−0.266083	−	0.642382i
$486$	−15.9028	−	3.16326i	−0.721365	−	0.143488i
$487$	5.29670	+	7.92707i	0.240016	+	0.359210i	0.931848	−	0.362849i	$-0.118196\pi$
$487$	5.29670	+	7.92707i	0.240016	+	0.359210i	−0.691832	+	0.722059i	$0.743196\pi$
$488$	5.86945	+	29.5077i	0.265697	+	1.33575i
$489$	8.27782	−	8.27782i	0.374336	−	0.374336i
$490$	33.8389	+	22.6105i	1.52869	+	1.02144i
$491$	10.1853	−	24.5895i	0.459657	−	1.10971i	−0.508879	−	0.860838i	$-0.669940\pi$
$491$	10.1853	−	24.5895i	0.459657	−	1.10971i	0.968536	−	0.248872i	$-0.0800599\pi$
$492$	0.227754			0.0102679
$493$	−16.2077	−	4.30717i	−0.729957	−	0.193985i
$494$		−	19.0648i		−	0.857765i
$495$	−41.5581	+	35.0071i	−1.86790	+	1.57345i
$496$	25.2338	+	16.8607i	1.13303	+	0.757068i
$497$	−13.9604	+	13.9604i	−0.626210	+	0.626210i
$498$	−25.5810	+	5.08838i	−1.14631	+	0.228016i
$499$	9.26251	−	6.18901i	0.414647	−	0.277058i	−0.330699	−	0.943736i	$-0.607284\pi$
$499$	9.26251	−	6.18901i	0.414647	−	0.277058i	0.745346	+	0.666678i	$0.232284\pi$
$500$	−0.00992826	−	0.00197485i	−0.000444005	−	8.83181e-5i
$501$	−12.9607	−	31.2899i	−0.579041	−	1.39793i
$502$	−14.5042	+	6.00784i	−0.647354	+	0.268143i
$503$	26.5698	+	5.28506i	1.18469	+	0.235649i	0.747835	−	0.663884i	$-0.231093\pi$
$503$	26.5698	+	5.28506i	1.18469	+	0.235649i	0.436852	+	0.899533i	$0.356093\pi$
$504$	33.2631	+	49.7817i	1.48166	+	2.21745i
$505$	−37.9041	+	7.53959i	−1.68671	+	0.335508i
$506$	−0.589797	−	1.85820i	−0.0262197	−	0.0826069i
$507$	1.31065	−	1.96153i	0.0582081	−	0.0871145i
$508$	0.0749286	−	0.180894i	0.00332442	−	0.00802585i
$509$		−	38.9436i		−	1.72614i	−0.505082	−	0.863071i	$-0.668538\pi$
$509$		−	38.9436i		−	1.72614i	0.505082	−	0.863071i	$-0.331462\pi$
$510$	−16.8695	−	49.3626i	−0.746995	−	2.18581i
$511$	22.2738			0.985336
$512$	21.1533	+	8.76199i	0.934853	+	0.387229i
$513$	12.9624	−	19.3996i	0.572305	−	0.856515i
$514$	−7.74425	+	7.74425i	−0.341584	+	0.341584i
$515$	0.353461	−	0.0703078i	0.0155754	−	0.00309813i
$516$	−0.129249	−	0.193435i	−0.00568987	−	0.00851549i
$517$	−3.34743	−	2.67609i	−0.147220	−	0.117694i
$518$	31.5131	−	13.0532i	1.38461	−	0.573523i
$519$	−36.1775	+	14.9852i	−1.58802	+	0.657778i
$520$	6.44804	−	32.4165i	0.282765	−	1.42156i
$521$	−3.82365	−	5.72249i	−0.167517	−	0.250707i	0.738208	−	0.674574i	$-0.235673\pi$
$521$	−3.82365	−	5.72249i	−0.167517	−	0.250707i	−0.905725	+	0.423867i	$0.860673\pi$
$522$	5.84900	+	29.4049i	0.256004	+	1.28702i
$523$	8.19761	+	8.19761i	0.358457	+	0.358457i	0.863244	−	0.504787i	$-0.168429\pi$
$523$	8.19761	+	8.19761i	0.358457	+	0.358457i	−0.504787	+	0.863244i	$0.668429\pi$
$524$	0.106085	+	0.0708838i	0.00463435	+	0.00309657i
$525$	21.2356	−	51.2672i	0.926797	−	2.23749i
$526$		−	21.8148i		−	0.951169i
$527$	27.2820	−	15.8261i	1.18842	−	0.689395i
$528$	33.5232	+	17.3696i	1.45891	+	0.755917i
$529$	−8.73507	+	21.0883i	−0.379785	+	0.916883i
$530$	−3.77212	+	5.64537i	−0.163850	+	0.245219i
$531$	−31.0929	−	31.0929i	−1.34932	−	1.34932i
$532$	0.233040	−	0.0463545i	0.0101036	−	0.00200972i
$533$	−15.1464	+	10.1205i	−0.656062	+	0.438367i
$534$	−3.52740	+	17.7334i	−0.152645	+	0.767400i
$535$	2.11164	+	5.09795i	0.0912942	+	0.220404i
$536$	14.7382	−	6.10478i	0.636595	−	0.263686i
$537$	−8.05456	+	40.4930i	−0.347580	+	1.74740i
$538$	−10.3228	+	6.89750i	−0.445049	+	0.297372i
$539$	−8.50998	+	29.4057i	−0.366551	+	1.26659i
$540$	0.229806	−	0.229806i	0.00988928	−	0.00988928i
$541$	−7.09178	−	4.73858i	−0.304900	−	0.203727i	0.393702	−	0.919238i	$-0.371194\pi$
$541$	−7.09178	−	4.73858i	−0.304900	−	0.203727i	−0.698602	+	0.715511i	$0.746194\pi$
$542$	13.0648	+	5.41163i	0.561183	+	0.232449i
$543$		−	41.7339i		−	1.79098i
$544$	0.283552	−	0.249701i	0.0121572	−	0.0107058i
$545$			4.59357i			0.196767i
$546$	−55.9243	−	23.1646i	−2.39334	−	0.991353i
$547$	−21.5268	+	32.2172i	−0.920420	+	1.37751i	0.00558053	+	0.999984i	$0.498224\pi$
$547$	−21.5268	+	32.2172i	−0.920420	+	1.37751i	−0.926001	+	0.377522i	$0.876776\pi$
$548$	0.243856	+	0.243856i	0.0104170	+	0.0104170i
$549$	−10.8168	−	54.3795i	−0.461648	−	2.32086i
$550$	−2.48391	−	22.2865i	−0.105914	−	0.950299i
$551$	14.5239	+	2.88898i	0.618739	+	0.123075i
$552$	1.30137	+	3.14178i	0.0553900	+	0.133723i
$553$	15.2941	+	36.9232i	0.650372	+	1.57014i
$554$	−5.67003	+	28.5051i	−0.240896	+	1.21107i
$555$	−29.9998	−	44.8979i	−1.27342	−	1.90581i
$556$	−0.0836014	+	0.0166294i	−0.00354549	+	0.000705242i
$557$	6.07611	+	6.07611i	0.257453	+	0.257453i	0.824017	−	0.566564i	$-0.191728\pi$
$557$	6.07611	+	6.07611i	0.257453	+	0.257453i	−0.566564	+	0.824017i	$0.691728\pi$
$558$	−46.8830	−	31.3262i	−1.98472	−	1.32614i
$559$	17.1910	+	7.12073i	0.727100	+	0.301175i
$560$	−50.0357			−2.11439
$561$	31.5512	−	23.3273i	1.33209	−	0.984880i
$562$	−15.8579			−0.668926
$563$	−31.9075	−	13.2165i	−1.34474	−	0.557011i	−0.409919	−	0.912122i	$-0.634443\pi$
$563$	−31.9075	−	13.2165i	−1.34474	−	0.557011i	−0.934824	+	0.355111i	$0.884443\pi$
$564$	0.0499410	+	0.0333695i	0.00210290	+	0.00140511i
$565$	40.1294	+	40.1294i	1.68826	+	1.68826i
$566$	27.4720	−	5.46452i	1.15473	−	0.229691i
$567$	−6.01659	−	9.00446i	−0.252673	−	0.378152i
$568$	2.71502	−	13.6493i	0.113920	−	0.572712i
$569$	−7.52490	−	18.1667i	−0.315460	−	0.761589i	−0.999484	−	0.0321285i	$-0.989771\pi$
$569$	−7.52490	−	18.1667i	−0.315460	−	0.761589i	0.684023	−	0.729460i	$-0.260229\pi$
$570$	17.6276	+	42.5569i	0.738341	+	1.78251i
$571$	−25.2269	−	5.01795i	−1.05571	−	0.209995i	−0.363431	−	0.931621i	$-0.618395\pi$
$571$	−25.2269	−	5.01795i	−1.05571	−	0.209995i	−0.692283	+	0.721626i	$0.743395\pi$
$572$	0.198521	−	0.0221259i	0.00830057	−	0.000925131i
$573$	−1.22592	−	6.16313i	−0.0512137	−	0.257469i
$574$	19.6592	+	19.6592i	0.820561	+	0.820561i
$575$	1.11303	−	1.66576i	0.0464164	−	0.0694670i
$576$	−38.9883	−	16.1495i	−1.62451	−	0.672896i
$577$		−	41.9672i		−	1.74712i	−0.486717	−	0.873560i	$-0.661806\pi$
$577$		−	41.9672i		−	1.74712i	0.486717	−	0.873560i	$-0.338194\pi$
$578$	6.29214	+	23.1025i	0.261719	+	0.960939i
$579$		−	57.5217i		−	2.39052i
$580$	0.190570	+	0.0789366i	0.00791298	+	0.00327767i
$581$	21.6177	+	14.4445i	0.896855	+	0.599259i
$582$	13.9782	−	13.9782i	0.579414	−	0.579414i
$583$	−4.90577	−	1.41973i	−0.203176	−	0.0587990i
$584$	−13.0546	+	8.72284i	−0.540205	+	0.360954i
$585$	−11.8831	+	59.7401i	−0.491304	+	2.46995i
$586$	−37.3226	+	15.4595i	−1.54178	+	0.638627i
$587$	15.5903	+	37.6382i	0.643479	+	1.55350i	0.821955	+	0.569552i	$0.192883\pi$
$587$	15.5903	+	37.6382i	0.643479	+	1.55350i	−0.178476	+	0.983944i	$0.557117\pi$
$588$	0.0837003	−	0.420790i	0.00345174	−	0.0173531i
$589$	−23.1568	+	15.4729i	−0.954160	+	0.637549i
$590$	36.3362	−	7.22771i	1.49594	−	0.297560i
$591$	5.10318	+	5.10318i	0.209917	+	0.209917i
$592$	−13.2497	+	19.8296i	−0.544560	+	0.814992i
$593$	−10.9265	+	26.3788i	−0.448697	+	1.08325i	0.524114	+	0.851648i	$0.324397\pi$
$593$	−10.9265	+	26.3788i	−0.448697	+	1.08325i	−0.972811	+	0.231601i	$0.925603\pi$
$594$	−26.5802	−	13.7722i	−1.09060	−	0.565081i
$595$	−22.9032	+	46.6847i	−0.938942	+	1.91389i
$596$		−	0.0773979i		−	0.00317034i
$597$	−16.3489	+	39.4696i	−0.669114	+	1.61538i
$598$	−1.81707	−	1.21413i	−0.0743057	−	0.0496495i
$599$	−4.58304	−	4.58304i	−0.187258	−	0.187258i	0.607252	−	0.794510i	$-0.292272\pi$
$599$	−4.58304	−	4.58304i	−0.187258	−	0.187258i	−0.794510	+	0.607252i	$0.792272\pi$
$600$	7.63105	+	38.3639i	0.311536	+	1.56620i
$601$	−4.39138	−	6.57217i	−0.179128	−	0.268084i	0.731030	−	0.682345i	$-0.239040\pi$
$601$	−4.39138	−	6.57217i	−0.179128	−	0.268084i	−0.910158	+	0.414261i	$0.864040\pi$
$602$	5.54039	−	27.8534i	0.225809	−	1.13522i
$603$	−27.1610	+	11.2505i	−1.10608	+	0.458154i
$604$	−0.0940335	+	0.0389499i	−0.00382617	+	0.00158485i
$605$	31.4665	−	13.9895i	1.27930	−	0.568755i
$606$	−27.7184	−	41.4835i	−1.12598	−	1.68515i
$607$	41.4734	−	8.24957i	1.68335	−	0.334840i	0.741522	−	0.670928i	$-0.234104\pi$
$607$	41.4734	−	8.24957i	1.68335	−	0.334840i	0.941830	+	0.336089i	$0.109104\pi$
$608$	−0.235910	+	0.235910i	−0.00956742	+	0.00956742i
$609$	26.1217	−	39.0939i	1.05850	−	1.58416i
$610$	43.1584	+	17.8768i	1.74743	+	0.723810i
$611$	−4.80405			−0.194351
$612$	−0.262332	+	0.231014i	−0.0106041	+	0.00933818i
$613$		−	9.92999i		−	0.401069i	−0.979687	−	0.200534i	$-0.935732\pi$
$613$		−	9.92999i		−	0.401069i	0.979687	−	0.200534i	$-0.0642678\pi$
$614$	2.05276	−	4.95580i	0.0828427	−	0.200000i
$615$	24.4525	−	36.5958i	0.986022	−	1.47569i
$616$	−11.4790	−	36.1655i	−0.462503	−	1.45715i
$617$	−16.5025	+	3.28255i	−0.664365	+	0.132150i	−0.515743	−	0.856744i	$-0.672484\pi$
$617$	−16.5025	+	3.28255i	−0.664365	+	0.132150i	−0.148623	+	0.988894i	$0.547484\pi$
$618$	0.258478	+	0.386839i	0.0103975	+	0.0155610i
$619$	11.2658	+	2.24091i	0.452811	+	0.0900697i	0.416227	−	0.909261i	$-0.363352\pi$
$619$	11.2658	+	2.24091i	0.452811	+	0.0900697i	0.0365843	+	0.999331i	$0.488352\pi$
$620$	−0.358408	+	0.148457i	−0.0143940	+	0.00596219i
$621$	−1.02348	−	2.47091i	−0.0410710	−	0.0991542i
$622$	−22.0275	−	4.38153i	−0.883220	−	0.175683i
$623$	14.9860	−	10.0133i	0.600401	−	0.401175i
$624$	41.5098	−	8.25681i	1.66172	−	0.330537i
$625$	−18.3552	+	18.3552i	−0.734208	+	0.734208i
$626$	35.1216	+	23.4675i	1.40374	+	0.937950i
$627$	−26.4994	+	22.3221i	−1.05828	+	0.891460i
$628$			0.167534i			0.00668534i
$629$	12.4367	+	21.4391i	0.495883	+	0.854834i
$630$	92.9634			3.70375
$631$	13.4053	−	32.3631i	0.533655	−	1.28836i	−0.395432	−	0.918495i	$-0.629405\pi$
$631$	13.4053	−	32.3631i	0.533655	−	1.28836i	0.929087	−	0.369861i	$-0.120595\pi$
$632$	−23.4237	−	15.6512i	−0.931743	−	0.622571i
$633$	−4.01390	+	4.01390i	−0.159538	+	0.159538i
$634$	−1.09072	−	5.48342i	−0.0433180	−	0.217774i
$635$	−21.0216	−	31.4611i	−0.834217	−	1.24849i
$636$	0.0702006	+	0.0139638i	0.00278364	+	0.000553700i
$637$	13.1319	+	31.7032i	0.520304	+	1.25613i
$638$	1.61978	−	18.9311i	0.0641276	−	0.749490i
$639$	−5.00348	+	25.1542i	−0.197935	+	0.995085i
$640$	29.0863	−	19.4349i	1.14974	−	0.768230i
$641$	1.87885	+	9.44564i	0.0742103	+	0.373080i	0.999988	−	0.00498907i	$-0.00158808\pi$
$641$	1.87885	+	9.44564i	0.0742103	+	0.373080i	−0.925777	+	0.378069i	$0.876588\pi$
$642$	−5.03712	+	5.03712i	−0.198799	+	0.198799i
$643$	−0.814561	+	1.21908i	−0.0321232	+	0.0480757i	−0.847184	−	0.531300i	$-0.821704\pi$
$643$	−0.814561	+	1.21908i	−0.0321232	+	0.0480757i	0.815060	+	0.579376i	$0.196704\pi$
$644$	0.0104229	−	0.0251632i	0.000410721	−	0.000991569i
$645$	−44.9581			−1.77022
$646$	−6.83733	−	20.0070i	−0.269011	−	0.787166i
$647$	9.01370			0.354365			0.177183	−	0.984178i	$-0.443302\pi$
$647$	9.01370			0.354365			0.177183	+	0.984178i	$0.443302\pi$
$648$	7.05262	+	2.92129i	0.277053	+	0.114759i
$649$	13.4504	+	24.4061i	0.527976	+	0.958023i
$650$	−17.7746	−	17.7746i	−0.697176	−	0.697176i
$651$	17.2513	+	86.7280i	0.676131	+	3.39914i
$652$	0.0549529	−	0.0367184i	0.00215212	−	0.00143800i
$653$	−44.3071	−	8.81323i	−1.73387	−	0.344888i	−0.775704	−	0.631097i	$-0.782605\pi$
$653$	−44.3071	−	8.81323i	−1.73387	−	0.344888i	−0.958167	+	0.286209i	$0.907605\pi$
$654$	−5.47875	+	2.26937i	−0.214236	+	0.0887395i
$655$	22.7794	−	9.43554i	0.890066	−	0.368677i
$656$	−19.0655	−	3.79236i	−0.744381	−	0.148067i
$657$	24.0583	−	16.0753i	0.938604	−	0.627155i
$658$	1.43042	+	7.19119i	0.0557635	+	0.280342i
$659$	−17.0254	−	17.0254i	−0.663217	−	0.663217i	0.292920	−	0.956137i	$-0.405373\pi$
$659$	−17.0254	−	17.0254i	−0.663217	−	0.663217i	−0.956137	+	0.292920i	$0.905373\pi$
$660$	−0.422685	+	0.232946i	−0.0164530	+	0.00906741i
$661$	−6.92595	−	2.86882i	−0.269388	−	0.111584i	0.243900	−	0.969800i	$-0.421573\pi$
$661$	−6.92595	−	2.86882i	−0.269388	−	0.111584i	−0.513289	+	0.858216i	$0.671573\pi$
$662$	−15.1106			−0.587290
$663$	11.2968	−	42.5093i	0.438731	−	1.65092i
$664$	−18.3268			−0.711220
$665$	17.5717	−	42.4219i	0.681403	−	1.64505i
$666$	24.6172	−	36.8423i	0.953897	−	1.42761i
$667$	1.20030	−	1.20030i	0.0464757	−	0.0464757i
$668$	−0.0373025	−	0.187532i	−0.00144328	−	0.00725584i
$669$	65.6915	−	43.8937i	2.53978	−	1.69703i
$670$	4.83231	−	24.2936i	0.186688	−	0.938545i
$671$	−2.99551	+	35.0099i	−0.115640	+	1.35154i
$672$	0.405372	+	0.978656i	0.0156376	+	0.0377525i
$673$	20.4525	+	4.06826i	0.788387	+	0.156820i	0.572833	−	0.819672i	$-0.305844\pi$
$673$	20.4525	+	4.06826i	0.788387	+	0.156820i	0.215554	+	0.976492i	$0.430844\pi$
$674$	−17.8118	−	26.6573i	−0.686085	−	1.02680i
$675$	−6.00157	−	30.1719i	−0.231001	−	1.16132i
$676$	0.00941774	−	0.00941774i	0.000362221	−	0.000362221i
$677$	−32.6954	−	21.8464i	−1.25659	−	0.839625i	−0.264404	−	0.964412i	$-0.585175\pi$
$677$	−32.6954	−	21.8464i	−1.25659	−	0.839625i	−0.992184	+	0.124787i	$0.960175\pi$
$678$	−28.0371	+	67.6876i	−1.07676	+	2.59953i
$679$	−19.7054			−0.756225
$680$	−4.85903	−	36.3311i	−0.186335	−	1.39324i
$681$			68.5524i			2.62693i
$682$	23.0218	+	27.3299i	0.881549	+	1.04652i
$683$	−5.02407	−	3.35698i	−0.192241	−	0.128451i	0.455725	−	0.890121i	$-0.349380\pi$
$683$	−5.02407	−	3.35698i	−0.192241	−	0.128451i	−0.647966	+	0.761669i	$0.724380\pi$
$684$	0.218255	−	0.218255i	0.00834520	−	0.00834520i
$685$	65.3645	−	13.0018i	2.49745	−	0.496773i
$686$	10.5208	−	7.02979i	0.401687	−	0.268399i
$687$	−3.04128	−	0.604948i	−0.116032	−	0.0230802i
$688$	7.59864	+	18.3447i	0.289695	+	0.699386i
$689$	−5.28906	+	2.19080i	−0.201497	+	0.0834629i
$690$	5.17873	+	1.03011i	0.197151	+	0.0392157i
$691$	−3.72768	−	5.57886i	−0.141807	−	0.212230i	0.753767	−	0.657142i	$-0.228235\pi$
$691$	−3.72768	−	5.57886i	−0.141807	−	0.212230i	−0.895574	+	0.444912i	$0.853235\pi$
$692$	−0.216826	+	0.0431293i	−0.00824247	+	0.00163953i
$693$	21.1546	+	66.6491i	0.803597	+	2.53179i
$694$	0.325939	−	0.487802i	0.0123725	−	0.0185167i
$695$	−6.30374	+	15.2186i	−0.239115	+	0.577274i
$696$			33.1426i			1.25627i
$697$	−12.2654	+	16.0527i	−0.464584	+	0.608040i
$698$	−10.4917			−0.397116
$699$	42.2949	+	17.5191i	1.59974	+	0.662633i
$700$	0.174051	−	0.260486i	0.00657852	−	0.00984544i
$701$	12.7202	−	12.7202i	0.480436	−	0.480436i	−0.424835	−	0.905271i	$-0.639668\pi$
$701$	12.7202	−	12.7202i	0.480436	−	0.480436i	0.905271	+	0.424835i	$0.139668\pi$
$702$	−32.9127	+	6.54674i	−1.24221	+	0.247091i
$703$	−12.1591	−	18.1974i	−0.458590	−	0.686328i
$704$	20.8895	+	16.7000i	0.787304	+	0.629406i
$705$	10.7237	−	4.44191i	0.403879	−	0.167292i
$706$	29.5099	−	12.2234i	1.11062	−	0.460033i
$707$	−9.70253	+	48.7779i	−0.364901	+	1.83448i
$708$	−0.216983	−	0.324737i	−0.00815471	−	0.0122044i
$709$	−1.58705	−	7.97866i	−0.0596031	−	0.299645i	0.939473	−	0.342623i	$-0.111315\pi$
$709$	−1.58705	−	7.97866i	−0.0596031	−	0.299645i	−0.999076	+	0.0429782i	$0.986315\pi$
$710$	−15.2795	−	15.2795i	−0.573431	−	0.573431i
$711$	43.1673	+	28.8435i	1.61890	+	1.08171i
$712$	−4.86186	+	11.7376i	−0.182206	+	0.439884i
$713$			3.19247i			0.119559i
$714$	−66.9959	−	4.25295i	−2.50726	−	0.159163i
$715$	17.7587	−	34.2741i	0.664139	−	1.28178i
$716$	−0.0891988	+	0.215345i	−0.00333352	+	0.00804782i
$717$	11.8683	−	17.7621i	0.443229	−	0.663339i
$718$	10.7825	+	10.7825i	0.402398	+	0.402398i
$719$	−38.4081	+	7.63984i	−1.43238	+	0.284918i	−0.849477	−	0.527625i	$-0.823083\pi$
$719$	−38.4081	+	7.63984i	−1.43238	+	0.284918i	−0.582901	+	0.812543i	$0.698083\pi$
$720$	−54.0443	+	36.1112i	−2.01411	+	1.34579i
$721$	0.0904775	−	0.454861i	0.00336956	−	0.0169399i
$722$	−3.09639	−	7.47535i	−0.115236	−	0.278204i
$723$	−62.4316	+	25.8600i	−2.32186	+	0.961745i
$724$	0.0459662	−	0.231088i	0.00170832	−	0.00858831i
$725$	16.2345	−	10.8475i	0.602933	−	0.402867i
$726$	32.2308	+	30.6189i	1.19620	+	1.13637i
$727$	22.9557	−	22.9557i	0.851381	−	0.851381i	−0.138922	−	0.990303i	$-0.544364\pi$
$727$	22.9557	−	22.9557i	0.851381	−	0.851381i	0.990303	+	0.138922i	$0.0443638\pi$
$728$	−35.3652	−	23.6302i	−1.31072	−	0.875795i
$729$	37.9685	+	15.7271i	1.40624	+	0.582484i
$730$			24.3785i			0.902289i
$731$	20.5943	+	1.30735i	0.761709	+	0.0483539i
$732$		−	0.492460i		−	0.0182018i
$733$	41.1360	+	17.0391i	1.51939	+	0.629354i	0.977470	−	0.211074i	$-0.0676960\pi$
$733$	41.1360	+	17.0391i	1.51939	+	0.629354i	0.541924	+	0.840427i	$0.317696\pi$
$734$	15.3076	−	22.9094i	0.565012	−	0.845600i
$735$	−58.6267	−	58.6267i	−2.16248	−	2.16248i
$736$	0.00746091	+	0.0375085i	0.000275013	+	0.00138258i
$737$	18.5167	−	2.06376i	0.682071	−	0.0760195i
$738$	35.4225	+	7.04598i	1.30392	+	0.259366i
$739$	−5.27271	−	12.7295i	−0.193960	−	0.468261i	0.796741	−	0.604321i	$-0.206556\pi$
$739$	−5.27271	−	12.7295i	−0.193960	−	0.468261i	−0.990700	+	0.136061i	$0.956556\pi$
$740$	−0.116663	−	0.281649i	−0.00428861	−	0.0103536i
$741$	−7.57718	+	38.0931i	−0.278355	+	1.39938i
$742$	4.85425	+	7.26490i	0.178205	+	0.266703i
$743$	−37.4573	+	7.45071i	−1.37417	+	0.273340i	−0.826304	−	0.563224i	$-0.809561\pi$
$743$	−37.4573	+	7.45071i	−1.37417	+	0.273340i	−0.547869	+	0.836564i	$0.684561\pi$
$744$	−44.0752	−	44.0752i	−1.61588	−	1.61588i
$745$	−12.4364	−	8.30974i	−0.455634	−	0.304445i
$746$	−18.5479	−	7.68280i	−0.679088	−	0.281287i
$747$	33.7744			1.23574
$748$	0.200397	−	0.0944163i	0.00732724	−	0.00345220i
$749$	7.10097			0.259464
$750$	−2.33319	−	0.966439i	−0.0851961	−	0.0352894i
$751$	−39.8460	−	26.6242i	−1.45400	−	0.971532i	−0.996610	−	0.0822653i	$-0.973785\pi$
$751$	−39.8460	−	26.6242i	−1.45400	−	0.971532i	−0.457390	−	0.889266i	$-0.651215\pi$
$752$	−3.62496	−	3.62496i	−0.132189	−	0.132189i
$753$	31.3684	−	6.23957i	1.14313	−	0.227382i
$754$	−11.8329	−	17.7092i	−0.430928	−	0.644930i
$755$	−3.83727	+	19.2912i	−0.139652	+	0.702080i
$756$	−0.160049	−	0.386393i	−0.00582093	−	0.0140530i
$757$	−17.5626	−	42.4000i	−0.638325	−	1.54105i	−0.828910	−	0.559382i	$-0.811038\pi$
$757$	−17.5626	−	42.4000i	−0.638325	−	1.54105i	0.190585	−	0.981671i	$-0.438962\pi$
$758$	−31.0805	−	6.18229i	−1.12889	−	0.224551i
$759$	0.439936	+	3.94725i	0.0159687	+	0.143276i
$760$	6.31444	+	31.7448i	0.229049	+	1.15151i
$761$	15.9860	+	15.9860i	0.579491	+	0.579491i	0.934763	−	0.355272i	$-0.115612\pi$
$761$	15.9860	+	15.9860i	0.579491	+	0.579491i	−0.355272	+	0.934763i	$0.615612\pi$
$762$	27.1383	−	40.6153i	0.983116	−	1.47134i
$763$	5.46138	+	2.26218i	0.197715	+	0.0818963i
$764$		−	0.0354765i		−	0.00128350i
$765$	8.95466	+	66.9544i	0.323757	+	2.42074i
$766$		−	25.7063i		−	0.928807i
$767$	28.8601	+	11.9542i	1.04208	+	0.431643i
$768$	−0.927514	−	0.619745i	−0.0334688	−	0.0223631i
$769$	9.51372	−	9.51372i	0.343074	−	0.343074i	−0.514448	−	0.857522i	$-0.672003\pi$
$769$	9.51372	−	9.51372i	0.343074	−	0.343074i	0.857522	+	0.514448i	$0.172003\pi$
$770$	−56.5927	−	16.3779i	−2.03946	−	0.590219i
$771$	18.5516	−	12.3958i	0.668119	−	0.446423i
$772$	0.0633549	−	0.318507i	0.00228019	−	0.0114633i
$773$	−28.5270	+	11.8163i	−1.02604	+	0.425001i	−0.831283	−	0.555849i	$-0.812393\pi$
$773$	−28.5270	+	11.8163i	−1.02604	+	0.425001i	−0.194761	+	0.980851i	$0.562393\pi$
$774$	−14.1178	−	34.0834i	−0.507455	−	1.22510i
$775$	−7.16391	+	36.0154i	−0.257335	+	1.29371i
$776$	11.5493	−	7.71700i	0.414596	−	0.277024i
$777$	−68.1538	+	13.5566i	−2.44500	+	0.486342i
$778$	−0.215577	−	0.215577i	−0.00772882	−	0.00772882i
$779$	9.91078	−	14.8325i	0.355091	−	0.531431i
$780$	−0.207034	+	0.499824i	−0.00741300	+	0.0178966i
$781$	7.47751	−	14.4315i	0.267566	−	0.516399i
$782$	−2.34231	−	0.622467i	−0.0837609	−	0.0222594i
$783$		−	26.0656i		−	0.931507i
$784$	−14.0132	+	33.8309i	−0.500473	+	1.20825i
$785$	26.9196	+	17.9871i	0.960803	+	0.641988i
$786$	22.5076	+	22.5076i	0.802819	+	0.802819i
$787$	9.53502	+	47.9358i	0.339887	+	1.70873i	0.651611	+	0.758553i	$0.274093\pi$
$787$	9.53502	+	47.9358i	0.339887	+	1.70873i	−0.311724	+	0.950173i	$0.600907\pi$
$788$	0.0226364	+	0.0338778i	0.000806390	+	0.00120685i
$789$	−8.67015	+	43.5878i	−0.308665	+	1.55177i
$790$	−40.4121	+	16.7393i	−1.43780	+	0.595556i
$791$	67.4729	−	27.9482i	2.39906	−	0.993724i
$792$	−38.4997	−	30.7784i	−1.36803	−	1.09366i
$793$	21.8830	+	32.7502i	0.777087	+	1.16299i
$794$	−22.8934	+	4.55377i	−0.812455	+	0.161607i
$795$	9.78073	−	9.78073i	0.346887	−	0.346887i
$796$	−0.133998	+	0.200543i	−0.00474945	+	0.00710805i
$797$	−18.2842	−	7.57358i	−0.647661	−	0.268270i	0.0345749	−	0.999402i	$-0.488992\pi$
$797$	−18.2842	−	7.57358i	−0.647661	−	0.268270i	−0.682236	+	0.731132i	$0.738992\pi$
$798$	59.2777			2.09841
$799$	−5.04148	+	1.72291i	−0.178355	+	0.0609521i
$800$			0.439889i			0.0155524i
$801$	8.95989	−	21.6311i	0.316582	−	0.764297i
$802$	−10.2846	+	15.3920i	−0.363162	+	0.543510i
$803$	−17.4779	+	5.54754i	−0.616782	+	0.195768i
$804$	−0.256102	+	0.0509419i	−0.00903203	+	0.00179658i
$805$	−2.92421	−	4.37639i	−0.103065	−	0.154248i
$806$	39.2870	+	7.81466i	1.38382	+	0.275260i
$807$	23.3673	−	9.67904i	0.822567	−	0.340718i
$808$	−13.4157	−	32.3883i	−0.471962	−	1.13942i
$809$	−10.9926	−	2.18657i	−0.386480	−	0.0768756i	−0.00197376	−	0.999998i	$-0.500628\pi$
$809$	−10.9926	−	2.18657i	−0.386480	−	0.0768756i	−0.384506	+	0.923122i	$0.625628\pi$
$810$	9.85530	−	6.58510i	0.346280	−	0.231377i
$811$	−24.9074	+	4.95438i	−0.874616	+	0.173972i	−0.611932	−	0.790910i	$-0.709608\pi$
$811$	−24.9074	+	4.95438i	−0.874616	+	0.173972i	−0.262684	+	0.964882i	$0.584608\pi$
$812$	0.187699	−	0.187699i	0.00658693	−	0.00658693i
$813$	−23.9538	−	16.0054i	−0.840098	−	0.561335i
$814$	−21.4768	+	18.0913i	−0.752761	+	0.634099i
$815$		−	12.7721i		−	0.447389i
$816$	40.6001	−	23.5518i	1.42129	−	0.824478i
$817$	−18.2218			−0.637500
$818$	12.0913	−	29.1911i	0.422764	−	1.02064i
$819$	65.1742	+	43.5480i	2.27737	+	1.52169i
$820$	0.175705	−	0.175705i	0.00613587	−	0.00613587i
$821$	−3.80546	−	19.1313i	−0.132811	−	0.667688i	−0.988625	−	0.150403i	$-0.951943\pi$
$821$	−3.80546	−	19.1313i	−0.132811	−	0.667688i	0.855813	−	0.517285i	$-0.173057\pi$
$822$	47.7995	+	71.5370i	1.66720	+	2.49514i
$823$	25.2220	+	5.01698i	0.879185	+	0.174881i	0.613990	−	0.789314i	$-0.289564\pi$
$823$	25.2220	+	5.01698i	0.879185	+	0.174881i	0.265195	+	0.964195i	$0.414564\pi$
$824$	0.125103	+	0.302026i	0.00435818	+	0.0105216i
$825$	−3.89455	+	45.5175i	−0.135591	+	1.58472i
$826$	9.30117	−	46.7602i	0.323629	−	1.62699i
$827$	10.2419	−	6.84339i	0.356144	−	0.237968i	−0.364607	−	0.931161i	$-0.618797\pi$
$827$	10.2419	−	6.84339i	0.356144	−	0.237968i	0.720752	+	0.693193i	$0.243797\pi$
$828$	−0.00690256	−	0.0347015i	−0.000239880	−	0.00120596i
$829$	7.84159	−	7.84159i	0.272350	−	0.272350i	−0.557696	−	0.830046i	$-0.688314\pi$
$829$	7.84159	−	7.84159i	0.272350	−	0.272350i	0.830046	+	0.557696i	$0.188314\pi$
$830$	−15.8094	+	23.6604i	−0.548752	+	0.821265i
$831$	22.6584	−	54.7022i	0.786011	−	1.89760i
$832$	29.9795			1.03935
$833$	25.1508	+	28.5605i	0.871425	+	0.989562i
$834$	−21.2655			−0.736364
$835$	−34.1379	−	14.1404i	−1.18139	−	0.489348i
$836$	−0.171317	+	0.0944146i	−0.00592513	+	0.00326540i
$837$	34.6637	+	34.6637i	1.19815	+	1.19815i
$838$	−4.54557	−	22.8521i	−0.157024	−	0.789413i
$839$	−35.5055	+	23.7240i	−1.22579	+	0.819045i	−0.988326	−	0.152352i	$-0.951315\pi$
$839$	−35.5055	+	23.7240i	−1.22579	+	0.819045i	−0.237461	+	0.971397i	$0.576315\pi$
$840$	100.792	+	20.0488i	3.47765	+	0.691748i
$841$	−11.5082	+	4.76687i	−0.396836	+	0.164375i
$842$	−26.3951	+	10.9332i	−0.909635	+	0.376783i
$843$	31.6855	+	6.30264i	1.09131	+	0.217074i
$844$	−0.0266466	+	0.0178047i	−0.000917213	+	0.000612862i
$845$	−0.502130	−	2.52438i	−0.0172738	−	0.0868413i
$846$	6.73497	+	6.73497i	0.231553	+	0.231553i
$847$	−1.13620	−	44.3005i	−0.0390403	−	1.52218i
$848$	−5.64404	−	2.33784i	−0.193817	−	0.0802817i
$849$	−57.0632			−1.95841
$850$	−25.0276	−	12.2784i	−0.858441	−	0.421146i
$851$	−2.50875			−0.0859989
$852$	−0.0871737	+	0.210456i	−0.00298652	+	0.00721010i
$853$	−6.97827	+	10.4437i	−0.238932	+	0.357586i	−0.931485	−	0.363781i	$-0.881486\pi$
$853$	−6.97827	+	10.4437i	−0.238932	+	0.357586i	0.692553	+	0.721367i	$0.256486\pi$
$854$	42.5081	−	42.5081i	1.45460	−	1.45460i
$855$	−11.6368	−	58.5023i	−0.397971	−	2.00074i
$856$	−4.16186	+	2.78087i	−0.142250	+	0.0950481i
$857$	9.03714	−	45.4328i	0.308703	−	1.55195i	−0.445482	−	0.895291i	$-0.646968\pi$
$857$	9.03714	−	45.4328i	0.308703	−	1.55195i	0.754184	−	0.656663i	$-0.228032\pi$
$858$	49.6522	+	4.24833i	1.69510	+	0.145035i
$859$	−15.2858	−	36.9031i	−0.521543	−	1.25912i	−0.936944	−	0.349478i	$-0.886359\pi$
$859$	−15.2858	−	36.9031i	−0.521543	−	1.25912i	0.415401	−	0.909638i	$-0.363641\pi$
$860$	−0.248940	−	0.0495173i	−0.00848879	−	0.00168852i
$861$	−31.4674	−	47.0943i	−1.07241	−	1.60497i
$862$	7.93478	+	39.8908i	0.270260	+	1.35869i
$863$	−5.18306	+	5.18306i	−0.176434	+	0.176434i	−0.789799	−	0.613366i	$-0.789815\pi$
$863$	−5.18306	+	5.18306i	−0.176434	+	0.176434i	0.613366	+	0.789799i	$0.289815\pi$
$864$	0.488276	+	0.326256i	0.0166115	+	0.0110994i
$865$	−16.3492	+	39.4704i	−0.555888	+	1.34203i
$866$	4.85536			0.164992
$867$	−3.39028	−	48.6616i	−0.115140	−	1.65264i
$868$			0.499228i			0.0169449i
$869$	−21.1972	−	25.1639i	−0.719064	−	0.853627i
$870$	42.7879	+	28.5900i	1.45065	+	0.969290i
$871$	14.7680	−	14.7680i	0.500394	−	0.500394i
$872$	−4.08681	+	0.812917i	−0.138397	+	0.0275289i
$873$	−21.2841	+	14.2216i	−0.720359	+	0.481328i
$874$	2.09897	+	0.417512i	0.0709989	+	0.0141226i
$875$	0.963374	+	2.32579i	0.0325680	+	0.0786261i
$876$	0.237434	−	0.0983485i	0.00802216	−	0.00332289i
$877$	14.6691	+	2.91786i	0.495340	+	0.0985292i	0.436438	−	0.899735i	$-0.356240\pi$
$877$	14.6691	+	2.91786i	0.495340	+	0.0985292i	0.0589023	+	0.998264i	$0.481240\pi$
$878$	20.2662	+	30.3305i	0.683950	+	1.02360i
$879$	80.7180	−	16.0558i	2.72255	−	0.541549i
$880$	39.2621	−	12.4619i	1.32353	−	0.420091i
$881$	−17.0841	+	25.5682i	−0.575578	+	0.861414i	−0.999009	−	0.0445147i	$-0.985826\pi$
$881$	−17.0841	+	25.5682i	−0.575578	+	0.861414i	0.423430	+	0.905929i	$0.360826\pi$
$882$	26.0358	−	62.8559i	0.876671	−	2.11647i
$883$			36.5852i			1.23119i	0.788063	+	0.615594i	$0.211084\pi$
$883$			36.5852i			1.23119i	−0.788063	+	0.615594i	$0.788916\pi$
$884$	0.109372	−	0.222938i	0.00367859	−	0.00749823i
$885$	−75.4754			−2.53708
$886$	49.3694	+	20.4495i	1.65860	+	0.687014i
$887$	19.7979	−	29.6297i	0.664749	−	0.994867i	−0.333885	−	0.942614i	$-0.608360\pi$
$887$	19.7979	−	29.6297i	0.664749	−	0.994867i	0.998634	−	0.0522528i	$-0.0166402\pi$
$888$	34.6358	−	34.6358i	1.16230	−	1.16230i
$889$	−47.7571	+	9.49947i	−1.60172	+	0.318602i
$890$	10.9595	+	16.4020i	0.367363	+	0.549797i
$891$	6.96378	+	5.56716i	0.233295	+	0.186507i
$892$	0.412089	−	0.170693i	0.0137978	−	0.00571523i
$893$	4.34640	−	1.80034i	0.145447	−	0.0602460i
$894$	3.76704	−	18.9382i	0.125989	−	0.633388i
$895$	25.0252	+	37.4529i	0.836500	+	1.25191i
$896$	−8.78243	−	44.1523i	−0.293401	−	1.47502i
$897$	3.14812	+	3.14812i	0.105113	+	0.105113i
$898$	9.33618	+	6.23824i	0.311552	+	0.208173i
$899$	−11.9067	+	28.7454i	−0.397111	+	0.958711i
$900$		−	0.406969i		−	0.0135656i
$901$	−4.76476	+	4.19593i	−0.158737	+	0.139787i
$902$	−20.3226	−	10.5299i	−0.676669	−	0.350608i
$903$	−22.1403	+	53.4515i	−0.736784	+	1.77875i
$904$	−28.6007	+	42.8040i	−0.951246	+	1.42364i
$905$	−32.1964	−	32.1964i	−1.07024	−	1.07024i
$906$	−24.9044	+	4.95380i	−0.827394	+	0.164579i
$907$	−8.58614	+	5.73707i	−0.285098	+	0.190496i	−0.689894	−	0.723911i	$-0.742343\pi$
$907$	−8.58614	+	5.73707i	−0.285098	+	0.190496i	0.404796	+	0.914407i	$0.367343\pi$
$908$	−0.0755043	+	0.379586i	−0.00250570	+	0.0125970i
$909$	24.7237	+	59.6882i	0.820032	+	1.97973i
$910$	−61.0145	+	25.2730i	−2.02261	+	0.837792i
$911$	1.57081	−	7.89699i	0.0520432	−	0.261639i	−0.946000	−	0.324167i	$-0.894916\pi$
$911$	1.57081	−	7.89699i	0.0520432	−	0.261639i	0.998043	+	0.0625277i	$0.0199162\pi$
$912$	−34.4611	+	23.0262i	−1.14112	+	0.762473i
$913$	−20.5606	−	5.95024i	−0.680458	−	0.196924i
$914$	29.4933	−	29.4933i	0.975552	−	0.975552i
$915$	−79.1291	−	52.8724i	−2.61593	−	1.74791i
$916$	−0.0161738	−	0.00669939i	−0.000534396	−	0.000221354i
$917$		−	31.7296i		−	1.04780i
$918$	−32.1914	+	18.6740i	−1.06248	+	0.616334i
$919$		−	3.45703i		−	0.114037i	−0.998373	−	0.0570184i	$-0.981841\pi$
$919$		−	3.45703i		−	0.114037i	0.998373	−	0.0570184i	$-0.0181594\pi$
$920$	3.42775	+	1.41982i	0.113010	+	0.0468101i
$921$	−6.07124	+	9.08626i	−0.200054	+	0.299402i
$922$	39.4884	+	39.4884i	1.30048	+	1.30048i
$923$	−3.55450	−	17.8697i	−0.116998	−	0.588187i
$924$	0.0687956	+	0.617257i	0.00226321	+	0.0203063i
$925$	−28.3021	−	5.62964i	−0.930568	−	0.185102i
$926$	−10.1176	−	24.4261i	−0.332486	−	0.802693i
$927$	−0.230552	−	0.556601i	−0.00757231	−	0.0182812i
$928$	−0.0727139	+	0.365557i	−0.00238695	+	0.0120000i
$929$	5.41165	+	8.09911i	0.177551	+	0.265723i	0.909561	−	0.415570i	$-0.136418\pi$
$929$	5.41165	+	8.09911i	0.177551	+	0.265723i	−0.732011	+	0.681293i	$0.761418\pi$
$930$	−94.9230	+	18.8814i	−3.11265	+	0.619144i
$931$	−23.7618	−	23.7618i	−0.778762	−	0.778762i
$932$	0.214898	+	0.143590i	0.00703921	+	0.00470345i
$933$	42.2713	+	17.5094i	1.38390	+	0.573231i
$934$	8.99934			0.294467
$935$	6.34447	−	42.3370i	0.207486	−	1.38457i
$936$	−55.2526			−1.80599
$937$	−9.06268	−	3.75388i	−0.296065	−	0.122634i	0.229707	−	0.973260i	$-0.426223\pi$
$937$	−9.06268	−	3.75388i	−0.296065	−	0.122634i	−0.525771	+	0.850626i	$0.676223\pi$
$938$	−26.5034	−	17.7090i	−0.865367	−	0.578220i
$939$	−60.8490	−	60.8490i	−1.98573	−	1.98573i
$940$	0.0642714	−	0.0127844i	0.00209630	−	0.000416980i
$941$	−27.2665	−	40.8072i	−0.888863	−	1.33028i	−0.943363	−	0.331763i	$-0.892357\pi$
$941$	−27.2665	−	40.8072i	−0.888863	−	1.33028i	0.0545002	−	0.998514i	$-0.482643\pi$
$942$	−8.15408	+	40.9933i	−0.265674	+	1.33563i
$943$	−0.782534	−	1.88920i	−0.0254828	−	0.0615210i
$944$	12.7566	+	30.7970i	0.415190	+	1.00236i
$945$	−79.2696	−	15.7677i	−2.57864	−	0.512923i
$946$	2.58974	+	23.2360i	0.0841997	+	0.755467i
$947$	2.60185	+	13.0804i	0.0845487	+	0.425055i	0.999756	+	0.0220724i	$0.00702643\pi$
$947$	2.60185	+	13.0804i	0.0845487	+	0.425055i	−0.915208	+	0.402982i	$0.867974\pi$
$948$	0.326064	+	0.326064i	0.0105901	+	0.0105901i
$949$	−11.4199	+	17.0911i	−0.370706	+	0.554801i
$950$	22.7424	+	9.42020i	0.737860	+	0.305632i
$951$			11.3898i			0.369341i
$952$	−45.5877	−	12.1149i	−1.47751	−	0.392645i
$953$			59.5796i			1.92997i	0.262300	+	0.964986i	$0.415519\pi$
$953$			59.5796i			1.92997i	−0.262300	+	0.964986i	$0.584481\pi$
$954$	10.4863	+	4.34357i	0.339507	+	0.140628i
$955$	−5.70042	−	3.80890i	−0.184461	−	0.123253i
$956$	0.0852800	−	0.0852800i	0.00275815	−	0.00275815i
$957$	−10.7605	+	37.1822i	−0.347838	+	1.20193i
$958$	−20.9024	+	13.9665i	−0.675326	+	0.451239i
$959$	16.7317	−	84.1160i	0.540295	−	2.71625i
$960$	−66.9211	+	27.7196i	−2.15987	+	0.894647i
$961$	−10.5299	−	25.4215i	−0.339676	−	0.820050i
$962$	−6.14103	+	30.8730i	−0.197995	+	0.995387i
$963$	7.66986	−	5.12484i	0.247158	−	0.165146i
$964$	−0.374177	+	0.0744283i	−0.0120514	+	0.00239718i
$965$	−44.3761	−	44.3761i	−1.42852	−	1.42852i
$966$	3.77507	−	5.64979i	0.121461	−	0.181779i
$967$	14.8754	−	35.9124i	0.478361	−	1.15487i	−0.482016	−	0.876162i	$-0.660095\pi$
$967$	14.8754	−	35.9124i	0.478361	−	1.15487i	0.960377	−	0.278704i	$-0.0899047\pi$
$968$	18.0148	+	25.5195i	0.579018	+	0.820227i
$969$	5.70991	+	42.6932i	0.183429	+	1.37150i
$970$		−	21.5674i		−	0.692487i
$971$	14.6258	−	35.3098i	0.469364	−	1.13314i	−0.495078	−	0.868849i	$-0.664860\pi$
$971$	14.6258	−	35.3098i	0.469364	−	1.13314i	0.964442	−	0.264296i	$-0.0851396\pi$
$972$	0.155060	+	0.103608i	0.00497354	+	0.00332322i
$973$	14.9893	+	14.9893i	0.480534	+	0.480534i
$974$	2.61970	+	13.1701i	0.0839405	+	0.421997i
$975$	28.4507	+	42.5795i	0.911152	+	1.36363i
$976$	−8.20000	+	41.2242i	−0.262476	+	1.31955i
$977$	49.1692	−	20.3665i	1.57306	−	0.651583i	0.585766	−	0.810480i	$-0.300794\pi$
$977$	49.1692	−	20.3665i	1.57306	−	0.651583i	0.987295	+	0.158897i	$0.0507936\pi$
$978$	15.2334	−	6.30986i	0.487109	−	0.201767i
$979$	−9.26533	+	11.5897i	−0.296121	+	0.370409i
$980$	−0.260054	−	0.389198i	−0.00830711	−	0.0124325i
$981$	7.53155	−	1.49812i	0.240464	−	0.0478313i
$982$	26.5075	−	26.5075i	0.845888	−	0.845888i
$983$	−15.2361	+	22.8024i	−0.485956	+	0.727285i	−0.990712	−	0.135978i	$-0.956582\pi$
$983$	−15.2361	+	22.8024i	−0.485956	+	0.727285i	0.504756	+	0.863262i	$0.331582\pi$
$984$	36.8860	+	15.2787i	1.17588	+	0.487066i
$985$	7.87387			0.250882
$986$	−18.7689	−	14.3407i	−0.597722	−	0.456701i
$987$		−	14.9371i		−	0.475454i
$988$	−0.0839122	+	0.202582i	−0.00266960	+	0.00644499i
$989$	−1.16045	+	1.73673i	−0.0369000	+	0.0552248i
$990$	−72.9468	+	23.1535i	−2.31840	+	0.735867i
$991$	1.00605	−	0.200116i	0.0319582	−	0.00635689i	−0.179085	−	0.983834i	$-0.557314\pi$
$991$	1.00605	−	0.200116i	0.0319582	−	0.00635689i	0.211044	+	0.977477i	$0.432314\pi$
$992$	−0.389442	−	0.582842i	−0.0123648	−	0.0185052i
$993$	30.1922	+	6.00561i	0.958122	+	0.190582i
$994$	−25.6908	+	10.6415i	−0.814862	+	0.337527i
$995$	17.8369	+	43.0621i	0.565468	+	1.36516i
$996$	0.294219	+	0.0585238i	0.00932269	+	0.00185440i
$997$	30.7727	−	20.5616i	0.974581	−	0.651194i	0.0371293	−	0.999310i	$-0.488179\pi$
$997$	30.7727	−	20.5616i	0.974581	−	0.651194i	0.937451	+	0.348117i	$0.113179\pi$
$998$	15.3888	−	3.06103i	0.487125	−	0.0968951i
$999$	−27.2399	+	27.2399i	−0.861833	+	0.861833i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.m.a.10.12	yes	128
11.10	odd	2	inner	187.2.m.a.10.5	✓	128
17.12	odd	16	inner	187.2.m.a.131.5	yes	128
187.131	even	16	inner	187.2.m.a.131.12	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.m.a.10.5	✓	128	11.10	odd	2	inner
187.2.m.a.10.12	yes	128	1.1	even	1	trivial
187.2.m.a.131.5	yes	128	17.12	odd	16	inner
187.2.m.a.131.12	yes	128	187.131	even	16	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:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.m (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.30126 + 0.539000i) q^{2} +(-2.38581 - 1.59415i) q^{3} +(-0.0114548 - 0.0114548i) q^{4} +(-3.07041 + 0.610742i) q^{5} +(-2.24531 - 3.36035i) q^{6} +(-0.785949 + 3.95123i) q^{7} +(-1.08673 - 2.62360i) q^{8} +(2.00273 + 4.83502i) q^{9} +(-4.32459 - 0.860214i) q^{10} +(-0.367376 - 3.29622i) q^{11} +(0.00906833 + 0.0455896i) q^{12} +(-2.62889 - 2.62889i) q^{13} +(-3.15244 + 4.71796i) q^{14} +(8.29901 + 3.43756i) q^{15} -3.96734i q^{16} +(-3.70164 - 1.81600i) q^{17} +7.37109i q^{18} +(3.36364 + 1.39327i) q^{19} +(0.0421668 + 0.0281750i) q^{20} +(8.17397 - 8.17397i) q^{21} +(1.29861 - 4.48725i) q^{22} +(0.347005 - 0.231861i) q^{23} +(-1.58967 + 7.99182i) q^{24} +(4.43499 - 1.83703i) q^{25} +(-2.00390 - 4.83785i) q^{26} +(1.25022 - 6.28530i) q^{27} +(0.0542635 - 0.0362577i) q^{28} +(3.98923 - 0.793506i) q^{29} +(8.94633 + 8.94633i) q^{30} +(-4.24988 + 6.36039i) q^{31} +(-0.0350676 + 0.0846607i) q^{32} +(-4.37816 + 8.44979i) q^{33} +(-3.83797 - 4.35828i) q^{34} -12.6119i q^{35} +(0.0324433 - 0.0783250i) q^{36} +(-4.99821 - 3.33970i) q^{37} +(3.62601 + 3.62601i) q^{38} +(2.08120 + 10.4629i) q^{39} +(4.93905 + 7.39181i) q^{40} +(0.955894 - 4.80561i) q^{41} +(15.0422 - 6.23069i) q^{42} +(-4.62394 + 1.91530i) q^{43} +(-0.0335493 + 0.0419657i) q^{44} +(-9.10213 - 13.6223i) q^{45} +(0.576517 - 0.114676i) q^{46} +(0.913702 - 0.913702i) q^{47} +(-6.32452 + 9.46531i) q^{48} +(-8.52737 - 3.53215i) q^{49} +6.76123 q^{50} +(5.93643 + 10.2336i) q^{51} +0.0602269i q^{52} +(0.589271 - 1.42263i) q^{53} +(5.01465 - 7.50495i) q^{54} +(3.14113 + 9.89634i) q^{55} +(11.2206 - 2.23191i) q^{56} +(-5.80394 - 8.68621i) q^{57} +(5.61872 + 1.11763i) q^{58} +(-7.76265 + 3.21539i) q^{59} +(-0.0556869 - 0.134440i) q^{60} +(-10.3909 - 2.06688i) q^{61} +(-8.95845 + 5.98585i) q^{62} +(-20.6783 + 4.11317i) q^{63} +(-5.70193 + 5.70193i) q^{64} +(9.67734 + 6.46619i) q^{65} +(-10.2516 + 8.63555i) q^{66} +5.61756i q^{67} +(0.0215996 + 0.0632035i) q^{68} -1.19751 q^{69} +(6.79781 - 16.4114i) q^{70} +(4.07475 + 2.72266i) q^{71} +(10.5087 - 10.5087i) q^{72} +(-1.07863 - 5.42263i) q^{73} +(-4.70388 - 7.03986i) q^{74} +(-13.5095 - 2.68721i) q^{75} +(-0.0225703 - 0.0544895i) q^{76} +(13.3129 + 1.13907i) q^{77} +(-2.93131 + 14.7367i) q^{78} +(8.24845 - 5.51144i) q^{79} +(2.42302 + 12.1813i) q^{80} +(-1.90081 + 1.90081i) q^{81} +(3.83409 - 5.73812i) q^{82} +(2.46970 - 5.96239i) q^{83} -0.187262 q^{84} +(12.4746 + 3.31512i) q^{85} -7.04929 q^{86} +(-10.7825 - 4.46625i) q^{87} +(-8.24872 + 4.54595i) q^{88} +(-3.16348 - 3.16348i) q^{89} +(-4.50183 - 22.6322i) q^{90} +(12.4535 - 8.32119i) q^{91} +(-0.00663080 - 0.00131895i) q^{92} +(20.2788 - 8.39975i) q^{93} +(1.68145 - 0.696479i) q^{94} +(-11.1787 - 2.22358i) q^{95} +(0.218626 - 0.146081i) q^{96} +(0.954251 + 4.79734i) q^{97} +(-9.19250 - 9.19250i) q^{98} +(15.2015 - 8.37769i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{9} - 64 q^{12} + 16 q^{14} - 16 q^{15} - 16 q^{20} + 8 q^{22} - 32 q^{23} + 16 q^{26} + 32 q^{27} - 80 q^{31} - 16 q^{34} + 16 q^{36} + 16 q^{37} + 80 q^{38}+ \cdots - 112 q^{99}+O(q^{100}) \) 128 * q - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^9 - 64 * q^12 + 16 * q^14 - 16 * q^15 - 16 * q^20 + 8 * q^22 - 32 * q^23 + 16 * q^26 + 32 * q^27 - 80 * q^31 - 16 * q^34 + 16 * q^36 + 16 * q^37 + 80 * q^38 - 112 * q^42 - 72 * q^44 - 16 * q^45 - 16 * q^47 + 32 * q^48 + 48 * q^49 - 16 * q^53 - 8 * q^55 - 16 * q^56 - 128 * q^58 + 48 * q^59 + 112 * q^60 + 48 * q^64 + 72 * q^66 - 192 * q^69 + 128 * q^70 - 16 * q^71 + 48 * q^75 + 8 * q^77 - 16 * q^78 + 112 * q^80 - 16 * q^82 + 32 * q^86 - 168 * q^88 - 16 * q^89 + 144 * q^91 - 176 * q^92 + 48 * q^93 + 48 * q^97 - 112 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more