LMFDB - Embedded newform 756.2.cf.a.659.66

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [756,2,Mod(155,756)] 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("756.155"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(756, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 7, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.cf (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$648$
Relative dimension:	$108$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			659.66
Character	$\chi$	$=$	756.659
Dual form			756.2.cf.a.491.66

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.407683 - 1.35418i) q^{2} +(-0.577007 + 1.63311i) q^{3} +(-1.66759 - 1.10415i) q^{4} +(-0.161050 + 0.442481i) q^{5} +(1.97629 + 1.44716i) q^{6} +(-0.984808 - 0.173648i) q^{7} +(-2.17506 + 1.80807i) q^{8} +(-2.33413 - 1.88464i) q^{9} +(0.533540 + 0.398482i) q^{10} +(2.51159 - 0.914144i) q^{11} +(2.76541 - 2.08626i) q^{12} +(0.804920 - 0.675408i) q^{13} +(-0.636640 + 1.26281i) q^{14} +(-0.629696 - 0.518328i) q^{15} +(1.56171 + 3.68254i) q^{16} +(5.28454 - 3.05103i) q^{17} +(-3.50371 + 2.39249i) q^{18} +(1.94202 + 1.12122i) q^{19} +(0.757131 - 0.560054i) q^{20} +(0.851828 - 1.50811i) q^{21} +(-0.213980 - 3.77382i) q^{22} +(1.02538 + 5.81520i) q^{23} +(-1.69776 - 4.59539i) q^{24} +(3.66037 + 3.07141i) q^{25} +(-0.586470 - 1.36536i) q^{26} +(4.42463 - 2.72445i) q^{27} +(1.45052 + 1.37695i) q^{28} +(0.485627 - 0.578747i) q^{29} +(-0.958624 + 0.641406i) q^{30} +(5.63024 - 0.992764i) q^{31} +(5.62349 - 0.613522i) q^{32} +(0.0436973 + 4.62918i) q^{33} +(-1.97722 - 8.40006i) q^{34} +(0.235439 - 0.407793i) q^{35} +(1.81144 + 5.72002i) q^{36} +(5.10756 + 8.84655i) q^{37} +(2.31006 - 2.17273i) q^{38} +(0.638575 + 1.70424i) q^{39} +(-0.449743 - 1.25361i) q^{40} +(0.917066 + 1.09292i) q^{41} +(-1.69497 - 1.76836i) q^{42} +(-4.06992 - 11.1820i) q^{43} +(-5.19765 - 1.24875i) q^{44} +(1.20983 - 0.729286i) q^{45} +(8.29284 + 0.982217i) q^{46} +(-0.0862600 + 0.489205i) q^{47} +(-6.91512 + 0.425600i) q^{48} +(0.939693 + 0.342020i) q^{49} +(5.65151 - 3.70462i) q^{50} +(1.93347 + 10.3907i) q^{51} +(-2.08803 + 0.237551i) q^{52} +9.90231i q^{53} +(-1.88554 - 7.10245i) q^{54} +1.25855i q^{55} +(2.45598 - 1.40290i) q^{56} +(-2.95164 + 2.52458i) q^{57} +(-0.585745 - 0.893570i) q^{58} +(-9.24315 - 3.36423i) q^{59} +(0.477762 + 1.55964i) q^{60} +(1.06739 - 6.05349i) q^{61} +(0.950976 - 8.02908i) q^{62} +(1.97140 + 2.26132i) q^{63} +(1.46178 - 7.86532i) q^{64} +(0.169223 + 0.464937i) q^{65} +(6.28654 + 1.82806i) q^{66} +(-5.34665 - 6.37189i) q^{67} +(-12.1812 - 0.747056i) q^{68} +(-10.0885 - 1.68085i) q^{69} +(-0.456239 - 0.485077i) q^{70} +(2.25782 + 3.91065i) q^{71} +(8.48442 - 0.121059i) q^{72} +(7.88731 - 13.6612i) q^{73} +(14.0621 - 3.30995i) q^{74} +(-7.12803 + 4.20558i) q^{75} +(-2.00049 - 4.01402i) q^{76} +(-2.63217 + 0.464123i) q^{77} +(2.56818 - 0.169953i) q^{78} +(3.32939 - 3.96782i) q^{79} +(-1.88097 + 0.0979543i) q^{80} +(1.89629 + 8.79796i) q^{81} +(1.85388 - 0.796306i) q^{82} +(10.1246 + 8.49558i) q^{83} +(-3.08568 + 1.57436i) q^{84} +(0.498949 + 2.82968i) q^{85} +(-16.8016 + 0.952675i) q^{86} +(0.664951 + 1.12703i) q^{87} +(-3.81003 + 6.52944i) q^{88} +(-2.16596 - 1.25052i) q^{89} +(-0.494357 - 1.93564i) q^{90} +(-0.909975 + 0.525374i) q^{91} +(4.71095 - 10.8295i) q^{92} +(-1.62739 + 9.76767i) q^{93} +(0.627303 + 0.316252i) q^{94} +(-0.808883 + 0.678733i) q^{95} +(-2.24284 + 9.53780i) q^{96} +(-3.27748 + 1.19291i) q^{97} +(0.846252 - 1.13307i) q^{98} +(-7.58519 - 2.59971i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q + 18 q^{12} + 42 q^{18} + 42 q^{20} - 48 q^{30} - 30 q^{32} + 60 q^{33} + 60 q^{41} - 30 q^{42} - 144 q^{44} - 18 q^{48} - 156 q^{50} + 54 q^{52} - 12 q^{57} + 54 q^{58} - 186 q^{60} - 24 q^{65} - 186 q^{66}+ \cdots + 36 q^{97}+O(q^{100}) $ 648 * q + 18 * q^12 + 42 * q^18 + 42 * q^20 - 48 * q^30 - 30 * q^32 + 60 * q^33 + 60 * q^41 - 30 * q^42 - 144 * q^44 - 18 * q^48 - 156 * q^50 + 54 * q^52 - 12 * q^57 + 54 * q^58 - 186 * q^60 - 24 * q^65 - 186 * q^66 - 78 * q^68 - 42 * q^72 - 24 * q^81 - 30 * q^86 - 36 * q^89 + 198 * q^90 + 114 * q^92 - 144 * q^93 - 54 * q^94 + 156 * q^96 + 36 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	0.407683	−	1.35418i	0.288275	−	0.957548i
$2$	0.407683	−	1.35418i	0.288275	−	0.957548i
$3$	−0.577007	+	1.63311i	−0.333135	+	0.942879i
$3$	−0.577007	+	1.63311i	−0.333135	+	0.942879i
$4$	−1.66759	−	1.10415i	−0.833795	−	0.552075i
$5$	−0.161050	+	0.442481i	−0.0720238	+	0.197884i	−0.970481	−	0.241177i	$-0.922467\pi$
$5$	−0.161050	+	0.442481i	−0.0720238	+	0.197884i	0.898457	+	0.439061i	$0.144689\pi$
$6$	1.97629	+	1.44716i	0.806817	+	0.590801i
$7$	−0.984808	−	0.173648i	−0.372222	−	0.0656328i
$7$	−0.984808	−	0.173648i	−0.372222	−	0.0656328i
$8$	−2.17506	+	1.80807i	−0.769000	+	0.639249i
$9$	−2.33413	−	1.88464i	−0.778042	−	0.628212i
$10$	0.533540	+	0.398482i	0.168720	+	0.126011i
$11$	2.51159	−	0.914144i	0.757273	−	0.275625i	0.0656099	−	0.997845i	$-0.479101\pi$
$11$	2.51159	−	0.914144i	0.757273	−	0.275625i	0.691663	+	0.722221i	$0.256878\pi$
$12$	2.76541	−	2.08626i	0.798306	−	0.602252i
$13$	0.804920	−	0.675408i	0.223245	−	0.187325i	−0.524305	−	0.851531i	$-0.675675\pi$
$13$	0.804920	−	0.675408i	0.223245	−	0.187325i	0.747549	+	0.664206i	$0.231230\pi$
$14$	−0.636640	+	1.26281i	−0.170149	+	0.337500i
$15$	−0.629696	−	0.518328i	−0.162587	−	0.133832i
$16$	1.56171	+	3.68254i	0.390427	+	0.920634i
$17$	5.28454	−	3.05103i	1.28169	−	0.739984i	0.304533	−	0.952502i	$-0.401500\pi$
$17$	5.28454	−	3.05103i	1.28169	−	0.739984i	0.977157	+	0.212518i	$0.0681664\pi$
$18$	−3.50371	+	2.39249i	−0.825833	+	0.563914i
$19$	1.94202	+	1.12122i	0.445529	+	0.257226i	0.705940	−	0.708271i	$-0.250525\pi$
$19$	1.94202	+	1.12122i	0.445529	+	0.257226i	−0.260411	+	0.965498i	$0.583858\pi$
$20$	0.757131	−	0.560054i	0.169300	−	0.125232i
$21$	0.851828	−	1.50811i	0.185884	−	0.329096i
$22$	−0.213980	−	3.77382i	−0.0456207	−	0.804580i
$23$	1.02538	+	5.81520i	0.213806	+	1.21255i	0.882966	+	0.469436i	$0.155543\pi$
$23$	1.02538	+	5.81520i	0.213806	+	1.21255i	−0.669161	+	0.743118i	$0.733346\pi$
$24$	−1.69776	−	4.59539i	−0.346553	−	0.938030i
$25$	3.66037	+	3.07141i	0.732074	+	0.614283i
$26$	−0.586470	−	1.36536i	−0.115016	−	0.267768i
$27$	4.42463	−	2.72445i	0.851521	−	0.524320i
$28$	1.45052	+	1.37695i	0.274123	+	0.260219i
$29$	0.485627	−	0.578747i	0.0901786	−	0.107471i	−0.719068	−	0.694940i	$-0.755431\pi$
$29$	0.485627	−	0.578747i	0.0901786	−	0.107471i	0.809247	+	0.587469i	$0.199876\pi$
$30$	−0.958624	+	0.641406i	−0.175020	+	0.117104i
$31$	5.63024	−	0.992764i	1.01122	−	0.178306i	0.356596	−	0.934259i	$-0.383937\pi$
$31$	5.63024	−	0.992764i	1.01122	−	0.178306i	0.654626	+	0.755953i	$0.272826\pi$
$32$	5.62349	−	0.613522i	0.994101	−	0.108456i
$33$	0.0436973	+	4.62918i	0.00760673	+	0.805837i
$34$	−1.97722	−	8.40006i	−0.339090	−	1.44060i
$35$	0.235439	−	0.407793i	0.0397965	−	0.0689296i
$36$	1.81144	+	5.72002i	0.301907	+	0.953337i
$37$	5.10756	+	8.84655i	0.839678	+	1.45436i	0.890164	+	0.455640i	$0.150589\pi$
$37$	5.10756	+	8.84655i	0.839678	+	1.45436i	−0.0504865	+	0.998725i	$0.516077\pi$
$38$	2.31006	−	2.17273i	0.374742	−	0.352463i
$39$	0.638575	+	1.70424i	0.102254	+	0.272897i
$40$	−0.449743	−	1.25361i	−0.0711105	−	0.198214i
$41$	0.917066	+	1.09292i	0.143222	+	0.170685i	0.832887	−	0.553444i	$-0.186687\pi$
$41$	0.917066	+	1.09292i	0.143222	+	0.170685i	−0.689665	+	0.724129i	$0.742242\pi$
$42$	−1.69497	−	1.76836i	−0.261539	−	0.272863i
$43$	−4.06992	−	11.1820i	−0.620657	−	1.70524i	−0.705374	−	0.708835i	$-0.749221\pi$
$43$	−4.06992	−	11.1820i	−0.620657	−	1.70524i	0.0847177	−	0.996405i	$-0.473001\pi$
$44$	−5.19765	−	1.24875i	−0.783575	−	0.188257i
$45$	1.20983	−	0.729286i	0.180350	−	0.108716i
$46$	8.29284	+	0.982217i	1.22271	+	0.144820i
$47$	−0.0862600	+	0.489205i	−0.0125823	+	0.0713578i	−0.990452	−	0.137855i	$-0.955979\pi$
$47$	−0.0862600	+	0.489205i	−0.0125823	+	0.0713578i	0.977870	+	0.209213i	$0.0670902\pi$
$48$	−6.91512	+	0.425600i	−0.998111	+	0.0614301i
$49$	0.939693	+	0.342020i	0.134242	+	0.0488600i
$50$	5.65151	−	3.70462i	0.799244	−	0.523913i
$51$	1.93347	+	10.3907i	0.270740	+	1.45499i
$52$	−2.08803	+	0.237551i	−0.289557	+	0.0329425i
$53$			9.90231i			1.36019i	0.733126	+	0.680093i	$0.238061\pi$
$53$			9.90231i			1.36019i	−0.733126	+	0.680093i	$0.761939\pi$
$54$	−1.88554	−	7.10245i	−0.256589	−	0.966521i
$55$			1.25855i			0.169703i
$56$	2.45598	−	1.40290i	0.328195	−	0.187471i
$57$	−2.95164	+	2.52458i	−0.390955	+	0.334389i
$58$	−0.585745	−	0.893570i	−0.0769120	−	0.117331i
$59$	−9.24315	−	3.36423i	−1.20336	−	0.437986i	−0.338961	−	0.940800i	$-0.610076\pi$
$59$	−9.24315	−	3.36423i	−1.20336	−	0.437986i	−0.864394	+	0.502815i	$0.832298\pi$
$60$	0.477762	+	1.55964i	0.0616789	+	0.201348i
$61$	1.06739	−	6.05349i	0.136666	−	0.775069i	−0.837020	−	0.547173i	$-0.815704\pi$
$61$	1.06739	−	6.05349i	0.136666	−	0.775069i	0.973685	−	0.227897i	$-0.0731848\pi$
$62$	0.950976	−	8.02908i	0.120774	−	1.01969i
$63$	1.97140	+	2.26132i	0.248373	+	0.284900i
$64$	1.46178	−	7.86532i	0.182723	−	0.983164i
$65$	0.169223	+	0.464937i	0.0209895	+	0.0576683i
$66$	6.28654	+	1.82806i	0.773820	+	0.225019i
$67$	−5.34665	−	6.37189i	−0.653197	−	0.778450i	0.333195	−	0.942858i	$-0.391873\pi$
$67$	−5.34665	−	6.37189i	−0.653197	−	0.778450i	−0.986392	+	0.164408i	$0.947429\pi$
$68$	−12.1812	−	0.747056i	−1.47719	−	0.0905938i
$69$	−10.0885	−	1.68085i	−1.21452	−	0.202351i
$70$	−0.456239	−	0.485077i	−0.0545310	−	0.0579778i
$71$	2.25782	+	3.91065i	0.267954	+	0.464109i	0.968333	−	0.249661i	$-0.0803193\pi$
$71$	2.25782	+	3.91065i	0.267954	+	0.464109i	−0.700380	+	0.713771i	$0.746986\pi$
$72$	8.48442	−	0.121059i	0.999898	−	0.0142670i
$73$	7.88731	−	13.6612i	0.923140	−	1.59893i	0.128614	−	0.991695i	$-0.458947\pi$
$73$	7.88731	−	13.6612i	0.923140	−	1.59893i	0.794526	−	0.607231i	$-0.207720\pi$
$74$	14.0621	−	3.30995i	1.63468	−	0.384774i
$75$	−7.12803	+	4.20558i	−0.823074	+	0.485618i
$76$	−2.00049	−	4.01402i	−0.229472	−	0.460440i
$77$	−2.63217	+	0.464123i	−0.299964	+	0.0528917i
$78$	2.56818	−	0.169953i	0.290789	−	0.0192433i
$79$	3.32939	−	3.96782i	0.374586	−	0.446414i	−0.545512	−	0.838103i	$-0.683665\pi$
$79$	3.32939	−	3.96782i	0.374586	−	0.446414i	0.920098	+	0.391689i	$0.128109\pi$
$80$	−1.88097	+	0.0979543i	−0.210298	+	0.0109516i
$81$	1.89629	+	8.79796i	0.210699	+	0.977551i
$82$	1.85388	−	0.796306i	0.204726	−	0.0879373i
$83$	10.1246	+	8.49558i	1.11132	+	0.932511i	0.998134	−	0.0610626i	$-0.0194489\pi$
$83$	10.1246	+	8.49558i	1.11132	+	0.932511i	0.113189	+	0.993573i	$0.463893\pi$
$84$	−3.08568	+	1.57436i	−0.336675	+	0.171777i
$85$	0.498949	+	2.82968i	0.0541186	+	0.306922i
$86$	−16.8016	+	0.952675i	−1.81177	+	0.102730i
$87$	0.664951	+	1.12703i	0.0712902	+	0.120830i
$88$	−3.81003	+	6.52944i	−0.406150	+	0.696041i
$89$	−2.16596	−	1.25052i	−0.229591	−	0.132555i	0.380792	−	0.924661i	$-0.375651\pi$
$89$	−2.16596	−	1.25052i	−0.229591	−	0.132555i	−0.610384	+	0.792106i	$0.708985\pi$
$90$	−0.494357	−	1.93564i	−0.0521098	−	0.204034i
$91$	−0.909975	+	0.525374i	−0.0953913	+	0.0550742i
$92$	4.71095	−	10.8295i	0.491150	−	1.12906i
$93$	−1.62739	+	9.76767i	−0.168753	+	1.01286i
$94$	0.627303	+	0.316252i	0.0647014	+	0.0326189i
$95$	−0.808883	+	0.678733i	−0.0829896	+	0.0696365i
$96$	−2.24284	+	9.53780i	−0.228909	+	0.973448i
$97$	−3.27748	+	1.19291i	−0.332778	+	0.121121i	−0.503005	−	0.864284i	$-0.667772\pi$
$97$	−3.27748	+	1.19291i	−0.332778	+	0.121121i	0.170227	+	0.985405i	$0.445550\pi$
$98$	0.846252	−	1.13307i	0.0854844	−	0.114458i
$99$	−7.58519	−	2.59971i	−0.762341	−	0.261280i
$100$	−2.71269	−	9.16345i	−0.271269	−	0.916345i
$101$	−5.74502	−	1.01300i	−0.571651	−	0.100797i	−0.119652	−	0.992816i	$-0.538178\pi$
$101$	−5.74502	−	1.01300i	−0.571651	−	0.100797i	−0.451999	+	0.892018i	$0.649289\pi$
$102$	14.8591	+	1.61787i	1.47127	+	0.160193i
$103$	5.06450	−	13.9146i	0.499020	−	1.37105i	−0.393203	−	0.919452i	$-0.628633\pi$
$103$	5.06450	−	13.9146i	0.499020	−	1.37105i	0.892223	−	0.451595i	$-0.149145\pi$
$104$	−0.529567	+	2.92440i	−0.0519283	+	0.286761i
$105$	0.530122	+	0.619799i	0.0517347	+	0.0604862i
$106$	13.4095	+	4.03700i	1.30244	+	0.392108i
$107$	−13.9666			−1.35020			−0.675101	−	0.737725i	$-0.735900\pi$
$107$	−13.9666			−1.35020			−0.675101	+	0.737725i	$0.735900\pi$
$108$	−10.3867	−	0.342197i	−0.999458	−	0.0329279i
$109$	10.6848			1.02342			0.511710	−	0.859158i	$-0.329012\pi$
$109$	10.6848			1.02342			0.511710	+	0.859158i	$0.329012\pi$
$110$	1.70430	+	0.513091i	0.162499	+	0.0489213i
$111$	−17.3945	+	3.23671i	−1.65102	+	0.307215i
$112$	−0.898517	−	3.89778i	−0.0849019	−	0.368305i
$113$	−2.24677	+	6.17296i	−0.211359	+	0.580703i	−0.999390	−	0.0349323i	$-0.988878\pi$
$113$	−2.24677	+	6.17296i	−0.211359	+	0.580703i	0.788031	+	0.615636i	$0.211101\pi$
$114$	2.21540	+	5.02628i	0.207491	+	0.470754i
$115$	−2.73826	−	0.482828i	−0.255344	−	0.0450240i
$116$	−1.44885	+	0.428909i	−0.134522	+	0.0398232i
$117$	−3.15168	+	0.0595062i	−0.291373	+	0.00550135i
$118$	−8.32404	+	11.1453i	−0.766290	+	1.02601i
$119$	−5.73406	+	2.08703i	−0.525641	+	0.191318i
$120$	2.30680	−	0.0111378i	0.210581	−	0.00101674i
$121$	−2.95407	+	2.47876i	−0.268552	+	0.225342i
$122$	−7.76233	−	3.91334i	−0.702769	−	0.354297i
$123$	−2.31401	+	0.867054i	−0.208647	+	0.0781796i
$124$	−10.4851	−	4.56111i	−0.941589	−	0.409600i
$125$	−3.98751	+	2.30219i	−0.356654	+	0.205914i
$126$	3.86594	−	1.74772i	0.344405	−	0.155700i
$127$	5.36639	+	3.09828i	0.476190	+	0.274928i	0.718827	−	0.695189i	$-0.244679\pi$
$127$	5.36639	+	3.09828i	0.476190	+	0.274928i	−0.242637	+	0.970117i	$0.578013\pi$
$128$	−10.0551	−	5.18607i	−0.888752	−	0.458388i
$129$	20.6099	−	0.194548i	1.81460	−	0.0171290i
$130$	0.698596	−	0.0396113i	0.0612709	−	0.00347414i
$131$	1.22436	+	6.94371i	0.106973	+	0.606674i	0.990414	+	0.138132i	$0.0441097\pi$
$131$	1.22436	+	6.94371i	0.106973	+	0.606674i	−0.883441	+	0.468543i	$0.844779\pi$
$132$	5.03844	−	7.76782i	0.438540	−	0.676102i
$133$	−1.71782	−	1.44142i	−0.148953	−	0.124987i
$134$	−10.8084	+	4.64260i	−0.933704	+	0.401059i
$135$	0.492930	+	2.39659i	0.0424246	+	0.206266i
$136$	−5.97773	+	16.1910i	−0.512586	+	1.38837i
$137$	−2.41231	+	2.87488i	−0.206098	+	0.245617i	−0.859185	−	0.511665i	$-0.829029\pi$
$137$	−2.41231	+	2.87488i	−0.206098	+	0.245617i	0.653088	+	0.757282i	$0.273473\pi$
$138$	−6.38910	+	12.9764i	−0.543876	+	1.10463i
$139$	−17.1554	+	3.02496i	−1.45510	+	0.256574i	−0.844582	−	0.535426i	$-0.820151\pi$
$139$	−17.1554	+	3.02496i	−1.45510	+	0.256574i	−0.610522	+	0.792000i	$0.709040\pi$
$140$	−0.842880	+	0.420071i	−0.0712364	+	0.0355025i
$141$	−0.749155	−	0.423147i	−0.0630902	−	0.0356354i
$142$	6.21619	−	1.46318i	0.521651	−	0.122787i
$143$	1.40421	−	2.43216i	0.117426	−	0.203387i
$144$	3.29502	−	11.5388i	0.274585	−	0.961563i
$145$	0.177875	+	0.308088i	0.0147717	+	0.0255853i
$146$	−15.2842	−	16.2503i	−1.26493	−	1.34488i
$147$	−1.10077	+	1.33728i	−0.0907897	+	0.110297i
$148$	1.25060	−	20.3919i	0.102799	−	1.67621i
$149$	−10.9018	−	12.9923i	−0.893112	−	1.06437i	−0.997558	−	0.0698393i	$-0.977751\pi$
$149$	−10.9018	−	12.9923i	−0.893112	−	1.06437i	0.104446	−	0.994531i	$-0.466693\pi$
$150$	2.78912	+	11.3672i	0.227730	+	0.928124i
$151$	−1.20886	−	3.32131i	−0.0983754	−	0.270284i	0.880736	−	0.473607i	$-0.157048\pi$
$151$	−1.20886	−	3.32131i	−0.0983754	−	0.270284i	−0.979112	+	0.203323i	$0.934826\pi$
$152$	−6.25126	+	1.07257i	−0.507044	+	0.0869968i
$153$	−18.0849	−	2.83795i	−1.46208	−	0.229434i
$154$	−0.444587	+	3.75364i	−0.0358258	+	0.302477i
$155$	−0.467471	+	2.65116i	−0.0375482	+	0.212946i
$156$	0.816858	−	3.54706i	0.0654010	−	0.283992i
$157$	21.3781	+	7.78100i	1.70616	+	0.620991i	0.996503	−	0.0835569i	$-0.0266280\pi$
$157$	21.3781	+	7.78100i	1.70616	+	0.620991i	0.709656	+	0.704548i	$0.248850\pi$
$158$	−4.01579	−	6.12620i	−0.319479	−	0.487374i
$159$	−16.1716	−	5.71370i	−1.28249	−	0.453126i
$160$	−0.634190	+	2.58709i	−0.0501371	+	0.204528i
$161$		−	5.90491i		−	0.465372i
$162$	12.6871	+	1.01886i	0.996791	+	0.0800495i
$163$			14.8827i			1.16570i	0.812579	+	0.582851i	$0.198063\pi$
$163$			14.8827i			1.16570i	−0.812579	+	0.582851i	$0.801937\pi$
$164$	−0.322546	−	2.83512i	−0.0251866	−	0.221385i
$165$	−2.05536	−	0.726194i	−0.160010	−	0.0565341i
$166$	15.6322	−	10.2470i	1.21329	−	0.795325i
$167$	6.67079	+	2.42797i	0.516201	+	0.187882i	0.586967	−	0.809611i	$-0.300322\pi$
$167$	6.67079	+	2.42797i	0.516201	+	0.187882i	−0.0707653	+	0.997493i	$0.522544\pi$
$168$	0.873983	+	4.82039i	0.0674292	+	0.371901i
$169$	−2.06571	+	11.7152i	−0.158900	+	0.901169i
$170$	4.03530	+	0.477947i	0.309493	+	0.0366569i
$171$	−2.41981	−	6.27708i	−0.185048	−	0.480020i
$172$	−5.55965	+	23.1408i	−0.423920	+	1.76447i
$173$	2.35218	+	6.46257i	0.178833	+	0.491340i	0.996427	−	0.0844550i	$-0.0269149\pi$
$173$	2.35218	+	6.46257i	0.178833	+	0.491340i	−0.817594	+	0.575795i	$0.804693\pi$
$174$	1.79728	−	0.440992i	0.136251	−	0.0334315i
$175$	−3.07141	−	3.66037i	−0.232177	−	0.276698i
$176$	7.28874	+	7.82139i	0.549409	+	0.589559i
$177$	10.8275	−	13.1539i	0.813847	−	0.988710i
$178$	−2.57645	+	2.42328i	−0.193113	+	0.181632i
$179$	3.25123	+	5.63130i	0.243009	+	0.420903i	0.961570	−	0.274560i	$-0.0885323\pi$
$179$	3.25123	+	5.63130i	0.243009	+	0.420903i	−0.718561	+	0.695464i	$0.755199\pi$
$180$	−2.82274	−	0.119680i	−0.210394	−	0.00892041i
$181$	0.957837	−	1.65902i	0.0711954	−	0.123314i	−0.828230	−	0.560388i	$-0.810652\pi$
$181$	0.957837	−	1.65902i	0.0711954	−	0.123314i	0.899425	+	0.437074i	$0.143985\pi$
$182$	0.340468	+	1.44645i	0.0252372	+	0.107218i
$183$	9.27014	+	5.23608i	0.685269	+	0.387062i
$184$	−12.7445	−	10.7945i	−0.939540	−	0.795779i
$185$	−4.73701	+	0.835262i	−0.348272	+	0.0614097i
$186$	12.5637	+	6.18589i	0.921214	+	0.453571i
$187$	10.4835	−	12.4938i	0.766631	−	0.913635i
$188$	0.684001	−	0.720549i	0.0498859	−	0.0525514i
$189$	−4.83051	+	1.91473i	−0.351368	+	0.139276i
$190$	0.589357	+	1.37208i	0.0427565	+	0.0995410i
$191$	8.39772	+	7.04653i	0.607638	+	0.509869i	0.893890	−	0.448285i	$-0.147965\pi$
$191$	8.39772	+	7.04653i	0.607638	+	0.509869i	−0.286252	+	0.958154i	$0.592410\pi$
$192$	12.0015	+	6.92560i	0.866134	+	0.499812i
$193$	−0.0995968	−	0.564842i	−0.00716913	−	0.0406582i	0.981013	−	0.193940i	$-0.0621268\pi$
$193$	−0.0995968	−	0.564842i	−0.00716913	−	0.0406582i	−0.988182	+	0.153282i	$0.951016\pi$
$194$	0.279232	+	4.92462i	0.0200477	+	0.353567i
$195$	−0.856938	+	0.00808910i	−0.0613666	+	0.000579272i
$196$	−1.18938	−	1.60791i	−0.0849557	−	0.114851i
$197$	15.6298	+	9.02390i	1.11358	+	0.642926i	0.939754	−	0.341850i	$-0.111054\pi$
$197$	15.6298	+	9.02390i	1.11358	+	0.642926i	0.173826	+	0.984776i	$0.444387\pi$
$198$	−6.61281	+	9.21184i	−0.469952	+	0.654657i
$199$	10.1861	−	5.88093i	0.722072	−	0.416888i	−0.0934430	−	0.995625i	$-0.529787\pi$
$199$	10.1861	−	5.88093i	0.722072	−	0.416888i	0.815515	+	0.578736i	$0.196454\pi$
$200$	−13.5149	−	0.0623181i	−0.955644	−	0.00440656i
$201$	13.4911	−	5.05507i	0.951587	−	0.356557i
$202$	−3.71393	+	7.36679i	−0.261311	+	0.518325i
$203$	−0.578747	+	0.485627i	−0.0406201	+	0.0340843i
$204$	8.24869	−	19.4623i	0.577524	−	1.36263i
$205$	−0.631289	+	0.229770i	−0.0440911	+	0.0160479i
$206$	−16.7781	−	12.5310i	−1.16899	−	0.873074i
$207$	8.56619	−	15.5059i	0.595391	−	1.07773i
$208$	3.74427	+	1.90936i	0.259618	+	0.132390i
$209$	5.90251	+	1.04077i	0.408285	+	0.0719917i
$210$	1.05544	−	0.465198i	0.0728322	−	0.0321017i
$211$	6.89956	−	18.9564i	0.474985	−	1.30501i	−0.438716	−	0.898626i	$-0.644567\pi$
$211$	6.89956	−	18.9564i	0.474985	−	1.30501i	0.913702	−	0.406386i	$-0.133211\pi$
$212$	10.9336	−	16.5130i	0.750924	−	1.13412i
$213$	−7.68932	+	1.43080i	−0.526864	+	0.0980368i
$214$	−5.69394	+	18.9132i	−0.389230	+	1.29288i
$215$	5.60329			0.382141
$216$	−4.69786	+	13.9259i	−0.319649	+	0.947536i
$217$	−5.71710			−0.388102
$218$	4.35602	−	14.4691i	0.295027	−	0.979973i
$219$	17.7593	+	20.7635i	1.20006	+	1.40307i
$220$	1.38963	−	2.09875i	0.0936889	−	0.141498i
$221$	2.19294	−	6.02506i	0.147513	−	0.405289i
$222$	−2.70838	+	24.8748i	−0.181774	+	1.66949i
$223$	9.39719	+	1.65698i	0.629283	+	0.110960i	0.479188	−	0.877712i	$-0.340931\pi$
$223$	9.39719	+	1.65698i	0.629283	+	0.110960i	0.150094	+	0.988672i	$0.452042\pi$
$224$	−5.64459	−	0.372307i	−0.377145	−	0.0248758i
$225$	−2.75526	−	14.0675i	−0.183684	−	0.937836i
$226$	7.44331	+	5.55914i	0.495121	+	0.369788i
$227$	3.61570	−	1.31601i	0.239982	−	0.0873464i	−0.219229	−	0.975673i	$-0.570354\pi$
$227$	3.61570	−	1.31601i	0.239982	−	0.0873464i	0.459211	+	0.888327i	$0.348132\pi$
$228$	7.70965	−	0.950910i	0.510584	−	0.0629756i
$229$	−14.3091	+	12.0068i	−0.945575	+	0.793431i	−0.978547	−	0.206025i	$-0.933947\pi$
$229$	−14.3091	+	12.0068i	−0.945575	+	0.793431i	0.0329722	+	0.999456i	$0.489503\pi$
$230$	−1.77018	+	3.51124i	−0.116722	+	0.231524i
$231$	0.760815	−	4.56644i	0.0500580	−	0.300450i
$232$	−0.00985323	+	2.13686i	−0.000646896	+	0.140292i
$233$	−6.65635	+	3.84305i	−0.436072	+	0.251766i	−0.701930	−	0.712246i	$-0.747678\pi$
$233$	−6.65635	+	3.84305i	−0.436072	+	0.251766i	0.265858	+	0.964012i	$0.414345\pi$
$234$	−1.20431	+	4.29220i	−0.0787279	+	0.280590i
$235$	−0.202572	−	0.116955i	−0.0132143	−	0.00762929i
$236$	11.6992	+	15.8160i	0.761551	+	1.02953i
$237$	4.55882	+	7.72674i	0.296127	+	0.501906i
$238$	0.488526	+	8.61578i	0.0316664	+	0.558478i
$239$	−0.588763	−	3.33904i	−0.0380839	−	0.215985i	0.959827	−	0.280593i	$-0.0905312\pi$
$239$	−0.588763	−	3.33904i	−0.0380839	−	0.215985i	−0.997911	+	0.0646086i	$0.979420\pi$
$240$	0.925360	−	3.12835i	0.0597317	−	0.201934i
$241$	−8.83173	−	7.41070i	−0.568901	−	0.477365i	0.312380	−	0.949957i	$-0.398874\pi$
$241$	−8.83173	−	7.41070i	−0.568901	−	0.477365i	−0.881281	+	0.472592i	$0.843318\pi$
$242$	2.15235	+	5.01088i	0.138358	+	0.322111i
$243$	−15.4622	−	1.97962i	−0.991904	−	0.126993i
$244$	−8.46393	+	8.91617i	−0.541847	+	0.570799i
$245$	−0.302675	+	0.360714i	−0.0193372	+	0.0230452i
$246$	0.230761	+	3.48707i	0.0147128	+	0.222327i
$247$	2.32045	−	0.409158i	0.147647	−	0.0260341i
$248$	−10.4511	+	12.3392i	−0.663648	+	0.783539i
$249$	−19.7162	+	11.6327i	−1.24947	+	0.737191i
$250$	1.49193	+	6.33836i	0.0943581	+	0.400873i
$251$	−12.8812	+	22.3110i	−0.813057	+	1.40826i	0.0976575	+	0.995220i	$0.468865\pi$
$251$	−12.8812	+	22.3110i	−0.813057	+	1.40826i	−0.910715	+	0.413036i	$0.864468\pi$
$252$	−0.790652	−	5.94768i	−0.0498064	−	0.374668i
$253$	7.89126	+	13.6681i	0.496119	+	0.859304i
$254$	6.38341	−	6.00392i	0.400531	−	0.376719i
$255$	−4.90909	−	0.817904i	−0.307419	−	0.0512191i
$256$	−11.1221	+	11.5021i	−0.695133	+	0.718881i
$257$	−19.6764	−	23.4495i	−1.22738	−	1.46274i	−0.841559	−	0.540166i	$-0.818361\pi$
$257$	−19.6764	−	23.4495i	−1.22738	−	1.46274i	−0.385825	−	0.922572i	$-0.626083\pi$
$258$	8.13884	−	27.9887i	0.506702	−	1.74250i
$259$	−3.49378	−	9.59907i	−0.217093	−	0.596457i
$260$	0.231165	−	0.962171i	0.0143362	−	0.0596713i
$261$	−2.22424	+	0.435640i	−0.137677	+	0.0269654i
$262$	9.90216	+	1.17283i	0.611757	+	0.0724575i
$263$	0.405523	−	2.29984i	0.0250056	−	0.141814i	−0.969749	−	0.244104i	$-0.921506\pi$
$263$	0.405523	−	2.29984i	0.0250056	−	0.141814i	0.994755	+	0.102291i	$0.0326171\pi$
$264$	−8.46492	−	9.98974i	−0.520980	−	0.614826i
$265$	−4.38158	−	1.59477i	−0.269159	−	0.0979657i
$266$	−2.65226	+	1.73858i	−0.162620	+	0.106599i
$267$	3.29201	−	2.81570i	0.201468	−	0.172318i
$268$	1.88050	+	16.5292i	0.114870	+	1.00968i
$269$			5.77551i			0.352139i	0.984378	+	0.176069i	$0.0563383\pi$
$269$			5.77551i			0.352139i	−0.984378	+	0.176069i	$0.943662\pi$
$270$	3.44637	+	0.309535i	0.209739	+	0.0188377i
$271$			3.58119i			0.217542i	0.994067	+	0.108771i	$0.0346915\pi$
$271$			3.58119i			0.217542i	−0.994067	+	0.108771i	$0.965309\pi$
$272$	19.4884	+	14.6957i	1.18166	+	0.891057i
$273$	−0.332935	−	1.78924i	−0.0201501	−	0.108290i
$274$	2.90964	+	4.43873i	0.175778	+	0.268154i
$275$	12.0011	+	4.36803i	0.723691	+	0.263402i
$276$	14.9676	+	13.9422i	0.900946	+	0.839224i
$277$	−3.01732	+	17.1121i	−0.181293	+	1.02817i	0.749333	+	0.662194i	$0.230374\pi$
$277$	−3.01732	+	17.1121i	−0.181293	+	1.02817i	−0.930626	+	0.365972i	$0.880737\pi$
$278$	−2.89764	+	24.4647i	−0.173789	+	1.46730i
$279$	−15.0127	−	8.29373i	−0.898787	−	0.496532i
$280$	0.225222	+	1.31266i	0.0134596	+	0.0784467i
$281$	−10.1374	−	27.8523i	−0.604746	−	1.66153i	−0.741525	−	0.670925i	$-0.765897\pi$
$281$	−10.1374	−	27.8523i	−0.604746	−	1.66153i	0.136779	−	0.990602i	$-0.456325\pi$
$282$	−0.878433	+	0.841978i	−0.0523099	+	0.0501391i
$283$	−1.70135	−	2.02759i	−0.101135	−	0.120528i	0.713103	−	0.701059i	$-0.247289\pi$
$283$	−1.70135	−	2.02759i	−0.101135	−	0.120528i	−0.814238	+	0.580532i	$0.802845\pi$
$284$	0.552835	−	9.01433i	0.0328047	−	0.534902i
$285$	−0.641718	−	1.71263i	−0.0380121	−	0.101448i
$286$	−2.72110	−	2.89310i	−0.160902	−	0.171072i
$287$	−0.713351	−	1.23556i	−0.0421078	−	0.0729328i
$288$	−14.2822	−	9.16619i	−0.841586	−	0.540123i
$289$	10.1176	−	17.5242i	0.595153	−	1.03083i
$290$	0.489722	−	0.115272i	0.0287575	−	0.00676898i
$291$	−0.0570226	−	6.04082i	−0.00334272	−	0.354119i
$292$	−28.2368	+	14.0725i	−1.65244	+	0.823533i
$293$	3.17003	−	0.558961i	0.185195	−	0.0326549i	−0.0802814	−	0.996772i	$-0.525582\pi$
$293$	3.17003	−	0.558961i	0.185195	−	0.0326549i	0.265476	+	0.964117i	$0.414471\pi$
$294$	1.36215	+	2.03582i	0.0794420	+	0.118731i
$295$	2.97722	−	3.54811i	0.173340	−	0.206579i
$296$	−27.1044	−	10.0070i	−1.57541	−	0.581644i
$297$	8.62233	−	10.8874i	0.500318	−	0.631754i
$298$	−22.0383	+	9.46626i	−1.27665	+	0.548366i
$299$	4.75298	+	3.98823i	0.274872	+	0.230645i
$300$	16.5302	+	0.857237i	0.954372	+	0.0494926i
$301$	2.06635	+	11.7189i	0.119103	+	0.675464i
$302$	−4.99047	+	0.282966i	−0.287169	+	0.0162829i
$303$	4.96926	−	8.79777i	0.285477	−	0.505418i
$304$	−1.09608	+	8.90257i	−0.0628647	+	0.510598i
$305$	2.50665	+	1.44722i	0.143530	+	0.0828673i
$306$	−11.2160	+	23.3331i	−0.641175	+	1.33387i
$307$	9.16501	−	5.29142i	0.523075	−	0.301997i	−0.215117	−	0.976588i	$-0.569013\pi$
$307$	9.16501	−	5.29142i	0.523075	−	0.301997i	0.738192	+	0.674591i	$0.235680\pi$
$308$	4.90184	+	2.13234i	0.279308	+	0.121502i
$309$	19.8019	+	16.2997i	1.12649	+	0.927259i
$310$	3.39956	+	1.71387i	0.193082	+	0.0973414i
$311$	17.3662	−	14.5720i	0.984746	−	0.826300i	−5.21925e−5	−	1.00000i	$-0.500017\pi$
$311$	17.3662	−	14.5720i	0.984746	−	0.826300i	0.984799	+	0.173700i	$0.0555722\pi$
$312$	−4.47032	−	2.55224i	−0.253082	−	0.144492i
$313$	−2.22583	+	0.810135i	−0.125811	+	0.0457915i	−0.404159	−	0.914689i	$-0.632436\pi$
$313$	−2.22583	+	0.810135i	−0.125811	+	0.0457915i	0.278347	+	0.960480i	$0.410213\pi$
$314$	19.2523	−	25.7776i	1.08647	−	1.45471i
$315$	−1.31809	+	0.508123i	−0.0742658	+	0.0286295i
$316$	−9.93312	+	2.94054i	−0.558782	+	0.165418i
$317$	−14.5937	−	2.57326i	−0.819663	−	0.144529i	−0.251934	−	0.967744i	$-0.581067\pi$
$317$	−14.5937	−	2.57326i	−0.819663	−	0.144529i	−0.567729	+	0.823216i	$0.692178\pi$
$318$	−14.3302	+	19.5698i	−0.803600	+	1.09742i
$319$	0.690636	−	1.89751i	0.0386682	−	0.106240i
$320$	3.24483	+	1.91352i	0.181392	+	0.106969i
$321$	8.05882	−	22.8091i	0.449800	−	1.27308i
$322$	−7.99630	−	2.40733i	−0.445616	−	0.134155i
$323$	13.6836			0.761374
$324$	6.55203	−	16.7652i	0.364001	−	0.931398i
$325$	5.02076			0.278502
$326$	20.1538	+	6.06742i	1.11622	+	0.336043i
$327$	−6.16521	+	17.4495i	−0.340937	+	0.964961i
$328$	−3.97074	−	0.719043i	−0.219248	−	0.0397025i
$329$	0.169899	−	0.466794i	0.00936684	−	0.0257352i
$330$	−1.82133	+	2.48727i	−0.100261	+	0.136920i
$331$	0.695252	+	0.122592i	0.0382145	+	0.00673825i	0.192723	−	0.981253i	$-0.438268\pi$
$331$	0.695252	+	0.122592i	0.0382145	+	0.00673825i	−0.154508	+	0.987992i	$0.549379\pi$
$332$	−7.50335	−	25.3462i	−0.411800	−	1.39106i
$333$	4.75085	−	30.2749i	0.260345	−	1.65905i
$334$	6.00747	−	8.04359i	0.328714	−	0.440126i
$335$	3.68052	−	1.33960i	0.201088	−	0.0731901i
$336$	6.88397	+	0.781663i	0.375551	+	0.0426432i
$337$	1.65716	−	1.39052i	0.0902710	−	0.0757464i	−0.596535	−	0.802587i	$-0.703456\pi$
$337$	1.65716	−	1.39052i	0.0902710	−	0.0757464i	0.686806	+	0.726840i	$0.259012\pi$
$338$	15.0223	+	7.57342i	0.817105	+	0.411940i
$339$	−8.78475	−	7.23108i	−0.477122	−	0.392738i
$340$	2.29235	−	5.26966i	0.124320	−	0.285787i
$341$	13.2333	−	7.64027i	0.716625	−	0.413744i
$342$	−9.48679	+	0.717799i	−0.512987	+	0.0388141i
$343$	−0.866025	−	0.500000i	−0.0467610	−	0.0269975i
$344$	29.0701	+	16.9629i	1.56736	+	0.914576i
$345$	2.36851	−	4.19329i	0.127516	−	0.225759i
$346$	9.71040	−	0.550592i	0.522034	−	0.0296000i
$347$	−3.33498	−	18.9136i	−0.179031	−	1.01534i	−0.933387	−	0.358870i	$-0.883162\pi$
$347$	−3.33498	−	18.9136i	−0.179031	−	1.01534i	0.754356	−	0.656465i	$-0.227949\pi$
$348$	0.135539	−	2.61362i	0.00726567	−	0.140105i
$349$	−18.1275	−	15.2108i	−0.970343	−	0.814214i	0.0122615	−	0.999925i	$-0.496097\pi$
$349$	−18.1275	−	15.2108i	−0.970343	−	0.814214i	−0.982605	+	0.185710i	$0.940541\pi$
$350$	−6.20895	+	2.66697i	−0.331882	+	0.142555i
$351$	1.72136	−	5.18140i	0.0918795	−	0.276563i
$352$	13.5630	−	6.68159i	0.722912	−	0.356130i
$353$	0.121244	−	0.144493i	0.00645316	−	0.00769058i	−0.762808	−	0.646625i	$-0.776180\pi$
$353$	0.121244	−	0.144493i	0.00645316	−	0.00769058i	0.769261	+	0.638934i	$0.220624\pi$
$354$	−13.3986	−	20.0250i	−0.712125	−	1.06432i
$355$	−2.09401	+	0.369231i	−0.111139	+	0.0195967i
$356$	2.23117	+	4.47689i	0.118252	+	0.237275i
$357$	−0.0997629	−	10.5686i	−0.00528001	−	0.559350i
$358$	8.95125	−	2.10696i	0.473088	−	0.111356i
$359$	6.24530	−	10.8172i	0.329614	−	0.570909i	−0.652821	−	0.757512i	$-0.726415\pi$
$359$	6.24530	−	10.8172i	0.329614	−	0.570909i	0.982435	+	0.186603i	$0.0597479\pi$
$360$	−1.31285	+	3.77369i	−0.0691932	+	0.198891i
$361$	−6.98571	−	12.0996i	−0.367669	−	0.636822i
$362$	−1.85611	−	1.97343i	−0.0975552	−	0.103721i
$363$	−2.34358	−	6.25459i	−0.123006	−	0.328281i
$364$	2.09756	+	0.128640i	0.109942	+	0.00674256i
$365$	4.77458	+	5.69013i	0.249913	+	0.297835i
$366$	10.8699	−	10.4188i	0.568176	−	0.544597i
$367$	−1.37803	−	3.78609i	−0.0719324	−	0.197633i	0.898516	−	0.438940i	$-0.144646\pi$
$367$	−1.37803	−	3.78609i	−0.0719324	−	0.197633i	−0.970449	+	0.241308i	$0.922424\pi$
$368$	−19.8134	+	12.8576i	−1.03284	+	0.670251i
$369$	−0.0807973	−	4.27934i	−0.00420614	−	0.222774i
$370$	−0.800104	+	6.75527i	−0.0415954	+	0.351190i
$371$	1.71952	−	9.75187i	0.0892729	−	0.506292i
$372$	13.4988	−	14.4916i	0.699879	−	0.751353i
$373$	−28.9104	−	10.5225i	−1.49692	−	0.544835i	−0.541661	−	0.840597i	$-0.682204\pi$
$373$	−28.9104	−	10.5225i	−1.49692	−	0.544835i	−0.955262	+	0.295762i	$0.904426\pi$
$374$	−12.6448	−	19.2900i	−0.653848	−	0.997464i
$375$	−1.45892	−	7.84044i	−0.0753383	−	0.404879i
$376$	−0.696895	−	1.22001i	−0.0359396	−	0.0629174i
$377$		−	0.793842i		−	0.0408849i
$378$	0.623563	+	7.32196i	0.0320726	+	0.376601i
$379$		−	6.13531i		−	0.315150i	−0.987507	−	0.157575i	$-0.949632\pi$
$379$		−	6.13531i		−	0.315150i	0.987507	−	0.157575i	$-0.0503676\pi$
$380$	2.09831	−	0.238721i	0.107641	−	0.0122461i
$381$	−8.15629	+	6.97619i	−0.417860	+	0.357401i
$382$	12.9659	−	8.49925i	0.663391	−	0.434860i
$383$	3.13700	+	1.14178i	0.160293	+	0.0583420i	0.420921	−	0.907097i	$-0.361707\pi$
$383$	3.13700	+	1.14178i	0.160293	+	0.0583420i	−0.260627	+	0.965440i	$0.583929\pi$
$384$	14.2713	−	13.4287i	0.728279	−	0.685281i
$385$	0.218546	−	1.23943i	0.0111381	−	0.0631674i
$386$	−0.805499	−	0.0954046i	−0.0409988	−	0.00485596i
$387$	−11.5743	+	33.7705i	−0.588356	+	1.71665i
$388$	6.78264	+	1.62955i	0.344336	+	0.0827280i
$389$	6.78688	+	18.6468i	0.344109	+	0.945430i	0.984189	+	0.177122i	$0.0566789\pi$
$389$	6.78688	+	18.6468i	0.344109	+	0.945430i	−0.640080	+	0.768308i	$0.721099\pi$
$390$	−0.338405	+	1.16374i	−0.0171358	+	0.0589284i
$391$	23.1610	+	27.6022i	1.17130	+	1.39591i
$392$	−2.66228	+	0.955113i	−0.134466	+	0.0482405i
$393$	−12.0463	−	2.00704i	−0.607657	−	0.101242i
$394$	18.5920	−	17.4867i	0.936650	−	0.880966i
$395$	1.21949	+	2.11221i	0.0613590	+	0.106277i
$396$	9.77853	+	12.7104i	0.491389	+	0.638723i
$397$	14.4654	−	25.0548i	0.725997	−	1.25746i	−0.232566	−	0.972581i	$-0.574712\pi$
$397$	14.4654	−	25.0548i	0.725997	−	1.25746i	0.958562	−	0.284883i	$-0.0919546\pi$
$398$	−3.81113	−	16.1913i	−0.191035	−	0.811597i
$399$	3.34519	−	1.97368i	0.167469	−	0.0988076i
$400$	−5.59416	+	18.2761i	−0.279708	+	0.913805i
$401$	−14.0949	+	2.48530i	−0.703863	+	0.124110i	−0.514113	−	0.857722i	$-0.671879\pi$
$401$	−14.0949	+	2.48530i	−0.703863	+	0.124110i	−0.189750	+	0.981832i	$0.560768\pi$
$402$	−1.34537	−	20.3302i	−0.0671012	−	1.01398i
$403$	3.86138	−	4.60181i	0.192349	−	0.229232i
$404$	8.46183	+	8.03263i	0.420992	+	0.399638i
$405$	−4.19833	−	0.577838i	−0.208617	−	0.0287130i
$406$	0.421679	+	0.981708i	0.0209276	+	0.0487213i
$407$	20.9151	+	17.5499i	1.03672	+	0.869914i
$408$	−22.9926	−	19.1046i	−1.13830	−	0.945820i
$409$	−3.18176	−	18.0447i	−0.157328	−	0.892252i	−0.956626	−	0.291318i	$-0.905906\pi$
$409$	−3.18176	−	18.0447i	−0.157328	−	0.892252i	0.799298	−	0.600934i	$-0.205205\pi$
$410$	0.0537840	+	0.948550i	0.00265620	+	0.0468456i
$411$	−3.30309	−	5.59840i	−0.162929	−	0.276149i
$412$	−23.8093	+	17.6119i	−1.17300	+	0.867675i
$413$	8.51853	+	4.91818i	0.419170	+	0.242008i
$414$	−17.5054	−	17.9216i	−0.860345	−	0.880799i
$415$	−5.38971	+	3.11175i	−0.264570	+	0.152750i
$416$	4.11208	−	4.29198i	0.201611	−	0.210432i
$417$	4.95868	−	29.7622i	0.242828	−	1.45746i
$418$	3.81574	−	7.56874i	0.186634	−	0.370199i
$419$	−2.94909	+	2.47458i	−0.144073	+	0.120891i	−0.711976	−	0.702204i	$-0.752199\pi$
$419$	−2.94909	+	2.47458i	−0.144073	+	0.120891i	0.567903	+	0.823096i	$0.307755\pi$
$420$	−0.199676	−	1.61890i	−0.00974320	−	0.0789944i
$421$	−31.9607	+	11.6327i	−1.55767	+	0.566945i	−0.970201	−	0.242301i	$-0.922098\pi$
$421$	−31.9607	+	11.6327i	−1.55767	+	0.566945i	−0.587469	+	0.809247i	$0.699876\pi$
$422$	−22.8575	−	17.0714i	−1.11268	−	0.831024i
$423$	1.12331	−	0.979297i	0.0546174	−	0.0476150i
$424$	−17.9040	−	21.5381i	−0.869497	−	1.04598i
$425$	28.7144	+	5.06312i	1.39285	+	0.245597i
$426$	−1.19725	+	10.9960i	−0.0580069	+	0.532759i
$427$	−2.10235	+	5.77617i	−0.101740	+	0.279528i
$428$	23.2906	+	15.4212i	1.12579	+	0.745413i
$429$	3.16176	+	3.69661i	0.152651	+	0.178474i
$430$	2.28436	−	7.58784i	0.110162	−	0.365918i
$431$	−21.1265			−1.01763			−0.508814	−	0.860876i	$-0.669916\pi$
$431$	−21.1265			−1.01763			−0.508814	+	0.860876i	$0.669916\pi$
$432$	16.9429	+	12.0391i	0.815164	+	0.579230i
$433$	28.9623			1.39184			0.695920	−	0.718119i	$-0.254997\pi$
$433$	28.9623			1.39184			0.695920	+	0.718119i	$0.254997\pi$
$434$	−2.33076	+	7.74196i	−0.111880	+	0.371626i
$435$	−0.605778	+	0.112721i	−0.0290448	+	0.00540455i
$436$	−17.8179	−	11.7976i	−0.853322	−	0.565004i
$437$	−4.52885	+	12.4429i	−0.216644	+	0.595225i
$438$	35.3576	−	15.5843i	1.68945	−	0.744648i
$439$	−26.5419	−	4.68005i	−1.26678	−	0.223367i	−0.500420	−	0.865783i	$-0.666821\pi$
$439$	−26.5419	−	4.68005i	−1.26678	−	0.223367i	−0.766356	+	0.642416i	$0.777932\pi$
$440$	−2.27555	−	2.73743i	−0.108483	−	0.130502i
$441$	−1.54878	−	2.56930i	−0.0737513	−	0.122347i
$442$	−7.26497	−	5.42595i	−0.345559	−	0.258086i
$443$	−12.7896	+	4.65504i	−0.607653	+	0.221168i	−0.627476	−	0.778636i	$-0.715912\pi$
$443$	−12.7896	+	4.65504i	−0.607653	+	0.221168i	0.0198230	+	0.999804i	$0.493690\pi$
$444$	32.5807	+	13.8087i	1.54621	+	0.655330i
$445$	0.902159	−	0.757001i	0.0427664	−	0.0358853i
$446$	6.07492	−	12.0499i	0.287656	−	0.570581i
$447$	27.5083	−	10.3073i	1.30110	−	0.487518i
$448$	−2.80537	+	7.49199i	−0.132541	+	0.353963i
$449$	0.0153268	−	0.00884891i	0.000723315	−	0.000417606i	−0.499638	−	0.866234i	$-0.666534\pi$
$449$	0.0153268	−	0.00884891i	0.000723315	−	0.000417606i	0.500362	+	0.865817i	$0.333200\pi$
$450$	−20.1732	−	2.00398i	−0.950974	−	0.0944684i
$451$	3.30238	+	1.90663i	0.155503	+	0.0897796i
$452$	10.5626	−	7.81319i	0.496821	−	0.367501i
$453$	6.12160	−	0.0577851i	0.287618	−	0.00271498i
$454$	−0.308047	−	5.43280i	−0.0144574	−	0.254974i
$455$	−0.0859168	−	0.487258i	−0.00402784	−	0.0228430i
$456$	1.85539	−	10.8279i	0.0868866	−	0.507063i
$457$	−6.21760	−	5.21719i	−0.290847	−	0.244050i	0.485675	−	0.874139i	$-0.338574\pi$
$457$	−6.21760	−	5.21719i	−0.290847	−	0.244050i	−0.776522	+	0.630090i	$0.783018\pi$
$458$	10.4257	+	24.2721i	0.487162	+	1.13416i
$459$	15.0698	−	27.8972i	0.703398	−	1.30213i
$460$	4.03317	+	3.82860i	0.188048	+	0.178510i
$461$	−18.4570	+	21.9962i	−0.859627	+	1.02446i	0.139785	+	0.990182i	$0.455359\pi$
$461$	−18.4570	+	21.9962i	−0.859627	+	1.02446i	−0.999412	+	0.0342819i	$0.989086\pi$
$462$	−5.87360	−	2.89194i	−0.273264	−	0.134545i
$463$	−6.01770	+	1.06108i	−0.279666	+	0.0493127i	−0.311722	−	0.950173i	$-0.600906\pi$
$463$	−6.01770	+	1.06108i	−0.279666	+	0.0493127i	0.0320557	+	0.999486i	$0.489795\pi$
$464$	2.88967	+	0.884503i	0.134149	+	0.0410620i
$465$	−4.05992	−	2.29317i	−0.188274	−	0.106343i
$466$	2.49048	+	10.5806i	0.115369	+	0.490138i
$467$	−8.80710	+	15.2544i	−0.407544	+	0.705887i	−0.994614	−	0.103649i	$-0.966948\pi$
$467$	−8.80710	+	15.2544i	−0.407544	+	0.705887i	0.587070	+	0.809536i	$0.300281\pi$
$468$	5.32142	+	3.38070i	0.245983	+	0.156273i
$469$	4.15896	+	7.20352i	0.192043	+	0.332628i
$470$	−0.240963	+	0.226637i	−0.0111148	+	0.0104540i
$471$	−25.0426	+	30.4232i	−1.15390	+	1.40183i
$472$	26.1872	−	9.39483i	1.20536	−	0.432432i
$473$	−20.4439	−	24.3641i	−0.940012	−	1.12026i
$474$	12.3219	−	3.02338i	0.565965	−	0.138869i
$475$	3.66476	+	10.0688i	0.168151	+	0.461990i
$476$	11.8665	+	2.85096i	0.543898	+	0.130673i
$477$	18.6622	−	23.1132i	0.854486	−	1.05828i
$478$	−4.76168	−	0.563981i	−0.217794	−	0.0257959i
$479$	5.32769	−	30.2148i	0.243428	−	1.38055i	−0.580686	−	0.814127i	$-0.697216\pi$
$479$	5.32769	−	30.2148i	0.243428	−	1.38055i	0.824115	−	0.566423i	$-0.191673\pi$
$480$	−3.85909	−	2.52848i	−0.176143	−	0.115409i
$481$	10.0862	+	3.67108i	0.459892	+	0.167387i
$482$	−13.6359	+	8.93850i	−0.621100	+	0.407138i
$483$	9.64340	+	3.40718i	0.438790	+	0.155032i
$484$	7.66309	−	0.871817i	0.348322	−	0.0396280i
$485$		−	1.64234i		−	0.0745749i
$486$	−8.98445	+	20.1316i	−0.407543	+	0.913186i
$487$			23.9287i			1.08431i	0.840278	+	0.542156i	$0.182392\pi$
$487$			23.9287i			1.08431i	−0.840278	+	0.542156i	$0.817608\pi$
$488$	8.62347	+	15.0966i	0.390366	+	0.683392i
$489$	−24.3051	−	8.58741i	−1.09912	−	0.388336i
$490$	0.365075	+	0.556932i	0.0164924	+	0.0251596i
$491$	16.3342	+	5.94516i	0.737152	+	0.268302i	0.683189	−	0.730241i	$-0.260592\pi$
$491$	16.3342	+	5.94516i	0.737152	+	0.268302i	0.0539631	+	0.998543i	$0.482815\pi$
$492$	4.81618	+	1.10913i	0.217130	+	0.0500033i
$493$	0.800538	−	4.54008i	0.0360544	−	0.204475i
$494$	0.391936	−	3.30911i	0.0176340	−	0.148884i
$495$	2.37192	−	2.93762i	0.106610	−	0.132036i
$496$	12.4487	+	19.1832i	0.558963	+	0.861350i
$497$	−1.54444	−	4.24331i	−0.0692775	−	0.190338i
$498$	7.71474	+	31.4417i	0.345706	+	1.40894i
$499$	16.5673	+	19.7441i	0.741653	+	0.883867i	0.996541	−	0.0831031i	$-0.0264831\pi$
$499$	16.5673	+	19.7441i	0.741653	+	0.883867i	−0.254888	+	0.966971i	$0.582039\pi$
$500$	9.19149	+	0.563699i	0.411056	+	0.0252094i
$501$	−7.81425	+	9.49321i	−0.349115	+	0.424125i
$502$	24.9615	+	26.5393i	1.11409	+	1.18451i
$503$	8.23724	+	14.2673i	0.367280	+	0.636148i	0.989139	−	0.146981i	$-0.0469556\pi$
$503$	8.23724	+	14.2673i	0.367280	+	0.636148i	−0.621859	+	0.783129i	$0.713622\pi$
$504$	−8.37654	−	1.35408i	−0.373121	−	0.0603157i
$505$	1.37347	−	2.37892i	0.0611186	−	0.105861i
$506$	21.7261	−	5.11392i	0.965843	−	0.227342i
$507$	−17.9403	−	10.1333i	−0.796758	−	0.450035i
$508$	−5.52796	−	11.0920i	−0.245264	−	0.492126i
$509$	−21.4855	+	3.78847i	−0.952327	+	0.167921i	−0.628165	−	0.778080i	$-0.716194\pi$
$509$	−21.4855	+	3.78847i	−0.952327	+	0.167921i	−0.324163	+	0.946001i	$0.605082\pi$
$510$	−3.10894	+	6.31433i	−0.137666	+	0.279603i
$511$	−10.1397	+	12.0841i	−0.448555	+	0.534567i
$512$	11.0416	+	19.7505i	0.487973	+	0.872859i
$513$	11.6474	−	0.329918i	0.514247	−	0.0145662i
$514$	−39.7765	+	17.0854i	−1.75447	+	0.753606i
$515$	5.34131	+	4.48189i	0.235366	+	0.197496i
$516$	−34.5836	−	22.4319i	−1.52246	−	0.987511i
$517$	0.230554	+	1.30754i	0.0101397	+	0.0575053i
$518$	−14.4232	+	0.817814i	−0.633719	+	0.0359327i
$519$	−11.9113	+	0.112438i	−0.522850	+	0.00493546i
$520$	−1.20871	−	0.705299i	−0.0530053	−	0.0309294i
$521$	16.0760	+	9.28151i	0.704304	+	0.406630i	0.808948	−	0.587880i	$-0.200037\pi$
$521$	16.0760	+	9.28151i	0.704304	+	0.406630i	−0.104644	+	0.994510i	$0.533370\pi$
$522$	−0.316852	+	3.18962i	−0.0138683	+	0.139606i
$523$	21.7870	−	12.5787i	0.952679	−	0.550029i	0.0587666	−	0.998272i	$-0.481283\pi$
$523$	21.7870	−	12.5787i	0.952679	−	0.550029i	0.893912	+	0.448243i	$0.147950\pi$
$524$	5.62515	−	12.9311i	0.245736	−	0.564899i
$525$	7.75003	−	2.90391i	0.338239	−	0.126737i
$526$	−2.94906	−	1.48675i	−0.128585	−	0.0648255i
$527$	26.7243	−	22.4244i	1.16413	−	0.976821i
$528$	−16.9789	+	7.39034i	−0.738911	+	0.321623i
$529$	−11.1523	+	4.05909i	−0.484881	+	0.176482i
$530$	−3.94589	+	5.28328i	−0.171399	+	0.229491i
$531$	15.2343	+	25.2725i	0.661113	+	1.09673i
$532$	1.27307	+	4.30042i	0.0551946	+	0.186447i
$533$	1.47633	+	0.260317i	0.0639470	+	0.0112756i
$534$	−2.47086	−	5.60588i	−0.106925	−	0.242590i
$535$	2.24932	−	6.17996i	0.0972466	−	0.267183i
$536$	23.1501	+	4.19214i	0.999932	+	0.181073i
$537$	−11.0725	+	2.06034i	−0.477816	+	0.0889101i
$538$	7.82106	+	2.35458i	0.337190	+	0.101513i
$539$	2.67278			0.115125
$540$	1.82419	−	4.54080i	0.0785006	−	0.195405i
$541$	−1.54918			−0.0666044			−0.0333022	−	0.999445i	$-0.510602\pi$
$541$	−1.54918			−0.0666044			−0.0333022	+	0.999445i	$0.510602\pi$
$542$	4.84956	+	1.45999i	0.208307	+	0.0627119i
$543$	2.15669	+	2.52152i	0.0925526	+	0.108209i
$544$	27.8457	−	20.3996i	1.19387	−	0.874627i
$545$	−1.72079	+	4.72783i	−0.0737105	+	0.202518i
$546$	−2.55868	−	0.278589i	−0.109501	−	0.0119225i
$547$	−3.29683	−	0.581320i	−0.140962	−	0.0248555i	0.102722	−	0.994710i	$-0.467245\pi$
$547$	−3.29683	−	0.581320i	−0.140962	−	0.0248555i	−0.243684	+	0.969855i	$0.578356\pi$
$548$	7.19704	−	2.13057i	0.307442	−	0.0910133i
$549$	−13.9001	+	12.1180i	−0.593240	+	0.517182i
$550$	10.8077	−	14.4708i	0.460842	−	0.617036i
$551$	1.59200	−	0.579441i	0.0678215	−	0.0246850i
$552$	24.9823	−	14.5848i	1.06332	−	0.620771i
$553$	−3.96782	+	3.32939i	−0.168729	+	0.141580i
$554$	21.9427	+	11.0623i	0.932255	+	0.469992i
$555$	1.36921	−	8.21803i	0.0581196	−	0.348836i
$556$	31.9482	+	13.8978i	1.35491	+	0.589396i
$557$	26.1656	−	15.1067i	1.10867	−	0.640091i	0.170186	−	0.985412i	$-0.445563\pi$
$557$	26.1656	−	15.1067i	1.10867	−	0.640091i	0.938485	+	0.345321i	$0.112230\pi$
$558$	−17.3516	+	16.9486i	−0.734552	+	0.717493i
$559$	−10.8284	−	6.25177i	−0.457992	−	0.264422i
$560$	1.86940	+	0.230160i	0.0789965	+	0.00972604i
$561$	14.3547	+	24.3298i	0.606056	+	1.02720i
$562$	−41.8497	+	2.37293i	−1.76532	+	0.100096i
$563$	−5.48753	−	31.1213i	−0.231272	−	1.31161i	−0.850325	−	0.526258i	$-0.823595\pi$
$563$	−5.48753	−	31.1213i	−0.231272	−	1.31161i	0.619053	−	0.785349i	$-0.287516\pi$
$564$	0.782065	+	1.53281i	0.0329309	+	0.0645431i
$565$	−2.36958	−	1.98831i	−0.0996888	−	0.0836489i
$566$	−3.43933	+	1.47732i	−0.144566	+	0.0620963i
$567$	−0.339733	−	8.99359i	−0.0142674	−	0.377695i
$568$	−11.9816	−	4.42362i	−0.502738	−	0.185611i
$569$	−28.4392	+	33.8925i	−1.19223	+	1.42085i	−0.309547	+	0.950884i	$0.600177\pi$
$569$	−28.4392	+	33.8925i	−1.19223	+	1.42085i	−0.882686	+	0.469964i	$0.844267\pi$
$570$	−2.58082	+	0.170789i	−0.108099	+	0.00715357i
$571$	−33.1640	+	5.84771i	−1.38787	+	0.244719i	−0.817150	−	0.576425i	$-0.804447\pi$
$571$	−33.1640	+	5.84771i	−1.38787	+	0.244719i	−0.570721	+	0.821144i	$0.693336\pi$
$572$	−5.02711	+	2.50539i	−0.210194	+	0.104756i
$573$	−16.3533	+	9.64855i	−0.683170	+	0.403074i
$574$	−1.96399	+	0.462287i	−0.0819753	+	0.0192955i
$575$	−14.1076	+	24.4352i	−0.588329	+	1.01902i
$576$	−18.2352	+	15.6037i	−0.759802	+	0.650155i
$577$	−2.45243	−	4.24773i	−0.102096	−	0.176835i	0.810452	−	0.585805i	$-0.199222\pi$
$577$	−2.45243	−	4.24773i	−0.102096	−	0.176835i	−0.912548	+	0.408970i	$0.865888\pi$
$578$	−19.6061	−	20.8453i	−0.815505	−	0.867051i
$579$	0.979919	+	0.163264i	0.0407240	+	0.00678504i
$580$	0.0435532	−	0.710164i	0.00180845	−	0.0294880i
$581$	−8.49558	−	10.1246i	−0.352456	−	0.420041i
$582$	−8.20358	−	2.38552i	−0.340050	−	0.0988830i
$583$	9.05213	+	24.8705i	0.374901	+	1.03003i
$584$	7.54504	+	43.9748i	0.312216	+	1.81969i
$585$	0.481248	−	1.40414i	0.0198972	−	0.0580542i
$586$	0.535433	−	4.52066i	0.0221186	−	0.186747i
$587$	−7.67807	+	43.5445i	−0.316908	+	1.79727i	0.244409	+	0.969672i	$0.421406\pi$
$587$	−7.67807	+	43.5445i	−0.316908	+	1.79727i	−0.561317	+	0.827601i	$0.689705\pi$
$588$	3.31218	−	1.01462i	0.136592	−	0.0418422i
$589$	12.0471	+	4.38480i	0.496394	+	0.180673i
$590$	−3.59101	−	5.47818i	−0.147839	−	0.225533i
$591$	−23.7556	+	20.3185i	−0.977174	+	0.835791i
$592$	−24.6012	+	32.6245i	−1.01110	+	1.34086i
$593$			2.78045i			0.114180i	0.998369	+	0.0570898i	$0.0181821\pi$
$593$			2.78045i			0.114180i	−0.998369	+	0.0570898i	$0.981818\pi$
$594$	−11.2283	−	16.1148i	−0.460705	−	0.661197i
$595$		−	2.87333i		−	0.117795i
$596$	3.83434	+	33.7030i	0.157061	+	1.38053i
$597$	3.72680	+	20.0284i	0.152528	+	0.819706i
$598$	7.33847	−	4.81045i	0.300093	−	0.196714i
$599$	7.56649	+	2.75398i	0.309158	+	0.112524i	0.491940	−	0.870629i	$-0.336288\pi$
$599$	7.56649	+	2.75398i	0.309158	+	0.112524i	−0.182782	+	0.983154i	$0.558510\pi$
$600$	7.89994	−	22.0353i	0.322514	−	0.899589i
$601$	4.83845	−	27.4402i	0.197364	−	1.11931i	−0.711647	−	0.702537i	$-0.752050\pi$
$601$	4.83845	−	27.4402i	0.197364	−	1.11931i	0.909011	−	0.416772i	$-0.136839\pi$
$602$	16.7118	+	1.97937i	0.681123	+	0.0806733i
$603$	0.471062	+	24.9493i	0.0191831	+	1.01601i
$604$	−1.65134	+	6.87334i	−0.0671922	+	0.279672i
$605$	−0.621051	−	1.70632i	−0.0252493	−	0.0693719i
$606$	−9.88785	−	10.3160i	−0.401666	−	0.419057i
$607$	−10.1898	−	12.1437i	−0.413592	−	0.492900i	0.518522	−	0.855064i	$-0.326482\pi$
$607$	−10.1898	−	12.1437i	−0.413592	−	0.492900i	−0.932114	+	0.362165i	$0.882038\pi$
$608$	11.6088	+	5.11372i	0.470799	+	0.207389i
$609$	−0.459143	−	1.22537i	−0.0186054	−	0.0496545i
$610$	2.98170	−	2.80444i	0.120726	−	0.113549i
$611$	0.260981	+	0.452031i	0.0105581	+	0.0182872i
$612$	27.0246	+	24.7009i	1.09241	+	0.998476i
$613$	21.3795	−	37.0304i	0.863510	−	1.49564i	−0.00500949	−	0.999987i	$-0.501595\pi$
$613$	21.3795	−	37.0304i	0.863510	−	1.49564i	0.868519	−	0.495655i	$-0.165072\pi$
$614$	−3.42910	−	14.5683i	−0.138387	−	0.587927i
$615$	−0.0109833	−	1.16355i	−0.000442891	−	0.0469187i
$616$	4.88597	−	5.76864i	0.196861	−	0.232425i
$617$	31.4956	−	5.55353i	1.26797	−	0.223577i	0.501103	−	0.865387i	$-0.332928\pi$
$617$	31.4956	−	5.55353i	1.26797	−	0.223577i	0.766863	+	0.641811i	$0.221817\pi$
$618$	30.1456	−	20.1701i	1.21263	−	0.811362i
$619$	6.44188	−	7.67713i	0.258921	−	0.308570i	−0.620886	−	0.783901i	$-0.713227\pi$
$619$	6.44188	−	7.67713i	0.258921	−	0.308570i	0.879807	+	0.475331i	$0.157672\pi$
$620$	3.70683	−	3.90489i	0.148870	−	0.156824i
$621$	20.3801	+	22.9366i	0.817827	+	0.920413i
$622$	−12.6531	−	29.4576i	−0.507344	−	1.18114i
$623$	1.91590	+	1.60763i	0.0767591	+	0.0644085i
$624$	−5.27866	+	5.01310i	−0.211316	+	0.200685i
$625$	3.77220	+	21.3932i	0.150888	+	0.855729i
$626$	0.189634	+	3.34444i	0.00757930	+	0.133671i
$627$	−5.10549	+	9.03894i	−0.203894	+	0.360981i
$628$	−27.0585	−	36.5801i	−1.07975	−	1.45971i
$629$	53.9822	+	31.1667i	2.15241	+	1.24270i
$630$	0.150726	+	1.99208i	0.00600509	+	0.0793662i
$631$	−30.0452	+	17.3466i	−1.19608	+	0.690557i	−0.959679	−	0.281099i	$-0.909301\pi$
$631$	−30.0452	+	17.3466i	−1.19608	+	0.690557i	−0.236400	+	0.971656i	$0.575968\pi$
$632$	−0.0675524	+	14.6500i	−0.00268709	+	0.582746i
$633$	26.9769	+	22.2057i	1.07223	+	0.882599i
$634$	−9.43424	+	18.7133i	−0.374682	+	0.743202i
$635$	−2.23519	+	1.87555i	−0.0887008	+	0.0744288i
$636$	20.6588	+	27.3840i	0.819175	+	1.08584i
$637$	0.987381	−	0.359377i	0.0391215	−	0.0142390i
$638$	−2.28800	−	1.70883i	−0.0905828	−	0.0676530i
$639$	2.10013	−	13.3831i	0.0830799	−	0.529428i
$640$	3.91411	−	3.61397i	0.154719	−	0.142855i
$641$	42.8217	+	7.55062i	1.69136	+	0.298232i	0.934662	−	0.355537i	$-0.115702\pi$
$641$	42.8217	+	7.55062i	1.69136	+	0.298232i	0.756694	+	0.653769i	$0.226813\pi$
$642$	−27.6021	−	20.2119i	−1.08937	−	0.797701i
$643$	12.1941	−	33.5031i	0.480890	−	1.32124i	−0.427841	−	0.903854i	$-0.640726\pi$
$643$	12.1941	−	33.5031i	0.480890	−	1.32124i	0.908731	−	0.417381i	$-0.137052\pi$
$644$	−6.51991	+	9.84697i	−0.256920	+	0.388025i
$645$	−3.23314	+	9.15081i	−0.127305	+	0.360313i
$646$	5.57856	−	18.5300i	0.219485	−	0.729052i
$647$	−6.78859			−0.266887			−0.133444	−	0.991056i	$-0.542603\pi$
$647$	−6.78859			−0.266887			−0.133444	+	0.991056i	$0.542603\pi$
$648$	−20.0319	−	15.7075i	−0.786926	−	0.617048i
$649$	−26.2904			−1.03199
$650$	2.04688	−	6.79900i	0.0802852	−	0.266679i
$651$	3.29881	−	9.33668i	0.129290	−	0.365933i
$652$	16.4327	−	24.8182i	0.643555	−	0.971956i
$653$	0.0978719	−	0.268901i	0.00383002	−	0.0105229i	−0.937763	−	0.347276i	$-0.887107\pi$
$653$	0.0978719	−	0.268901i	0.00383002	−	0.0105229i	0.941593	+	0.336753i	$0.109329\pi$
$654$	21.1163	+	15.4627i	0.825712	+	0.604638i
$655$	−3.26964	−	0.576526i	−0.127756	−	0.0225267i
$656$	−2.59252	+	5.08395i	−0.101221	+	0.198495i
$657$	−44.1564	+	17.0223i	−1.72271	+	0.664103i
$658$	−0.562856	−	0.420377i	−0.0219424	−	0.0163880i
$659$	−38.7500	+	14.1038i	−1.50948	+	0.549407i	−0.958496	−	0.285106i	$-0.907971\pi$
$659$	−38.7500	+	14.1038i	−1.50948	+	0.549407i	−0.550988	+	0.834513i	$0.685749\pi$
$660$	2.62567	+	3.48042i	0.102204	+	0.135475i
$661$	8.42220	−	7.06707i	0.327586	−	0.274877i	−0.464130	−	0.885767i	$-0.653633\pi$
$661$	8.42220	−	7.06707i	0.327586	−	0.274877i	0.791715	+	0.610890i	$0.209188\pi$
$662$	0.449453	−	0.891516i	0.0174685	−	0.0346497i
$663$	8.57427	+	7.05783i	0.332997	+	0.274103i
$664$	−37.3823	−	0.172373i	−1.45071	−	0.00668936i
$665$	0.914455	−	0.527961i	0.0354610	−	0.0204734i
$666$	−39.0607	−	18.7760i	−1.51357	−	0.727556i
$667$	3.86348	+	2.23058i	0.149595	+	0.0863686i
$668$	−8.44330	−	11.4144i	−0.326681	−	0.441637i
$669$	−8.12828	+	14.3906i	−0.314258	+	0.556373i
$670$	−0.313570	−	5.53021i	−0.0121143	−	0.213650i
$671$	−2.85290	−	16.1796i	−0.110135	−	0.624607i
$672$	3.86499	−	9.00344i	0.149095	−	0.347315i
$673$	1.36315	+	1.14382i	0.0525454	+	0.0440908i	0.668682	−	0.743548i	$-0.266859\pi$
$673$	1.36315	+	1.14382i	0.0525454	+	0.0440908i	−0.616137	+	0.787639i	$0.711303\pi$
$674$	−1.20741	−	2.81097i	−0.0465078	−	0.108275i
$675$	24.5637	+	3.61740i	0.945457	+	0.139234i
$676$	16.3801	−	17.2553i	0.630003	−	0.663665i
$677$	−18.0052	+	21.4577i	−0.691995	+	0.824687i	−0.991595	−	0.129377i	$-0.958702\pi$
$677$	−18.0052	+	21.4577i	−0.691995	+	0.824687i	0.299601	+	0.954065i	$0.403147\pi$
$678$	−13.3736	+	8.94811i	−0.513608	+	0.343650i
$679$	3.43484	−	0.605654i	0.131817	−	0.0232429i
$680$	−6.20150	−	5.25259i	−0.237817	−	0.201428i
$681$	0.0629069	+	6.66419i	0.00241060	+	0.255372i
$682$	−4.95127	−	21.0351i	−0.189594	−	0.805475i
$683$	16.2144	−	28.0842i	0.620428	−	1.07461i	−0.368978	−	0.929438i	$-0.620292\pi$
$683$	16.2144	−	28.0842i	0.620428	−	1.07461i	0.989406	−	0.145174i	$-0.0463743\pi$
$684$	−2.89557	+	13.1394i	−0.110715	+	0.502398i
$685$	−0.883578	−	1.53040i	−0.0337598	−	0.0584736i
$686$	−1.03015	+	0.968910i	−0.0393314	+	0.0369932i
$687$	−11.3520	−	30.2965i	−0.433106	−	1.15588i
$688$	34.8221	−	32.4506i	1.32758	−	1.23717i
$689$	6.68810	+	7.97057i	0.254796	+	0.303654i
$690$	−4.71286	−	4.91691i	−0.179415	−	0.187184i
$691$	−5.11925	−	14.0650i	−0.194745	−	0.535058i	0.803433	−	0.595396i	$-0.203005\pi$
$691$	−5.11925	−	14.0650i	−0.194745	−	0.535058i	−0.998178	+	0.0603371i	$0.980782\pi$
$692$	3.21317	−	13.3741i	0.122146	−	0.508406i
$693$	7.01852	+	3.87737i	0.266612	+	0.147289i
$694$	−26.9720	−	3.19460i	−1.02384	−	0.121265i
$695$	1.42439	−	8.07812i	0.0540302	−	0.306421i
$696$	−3.48405	−	1.24907i	−0.132062	−	0.0473460i
$697$	8.18080	+	2.97757i	0.309870	+	0.112783i
$698$	−27.9884	+	18.3467i	−1.05938	+	0.694432i
$699$	−2.43537	−	13.0880i	−0.0921143	−	0.495035i
$700$	1.08026	+	9.49529i	0.0408301	+	0.358888i
$701$		−	16.5651i		−	0.625655i	−0.949810	−	0.312827i	$-0.898724\pi$
$701$		−	16.5651i		−	0.625655i	0.949810	−	0.312827i	$-0.101276\pi$
$702$	−6.31476	−	4.44340i	−0.238335	−	0.167705i
$703$			22.9069i			0.863949i
$704$	−3.51863	−	21.0907i	−0.132614	−	0.794886i
$705$	0.307886	−	0.263339i	0.0115957	−	0.00991793i
$706$	−0.146240	−	0.223093i	−0.00550381	−	0.00839621i
$707$	5.48183	+	1.99522i	0.206166	+	0.0750381i
$708$	−32.5798	+	9.98015i	−1.22442	+	0.375077i
$709$	−8.57277	+	48.6186i	−0.321957	+	1.82591i	0.208291	+	0.978067i	$0.433210\pi$
$709$	−8.57277	+	48.6186i	−0.321957	+	1.82591i	−0.530249	+	0.847842i	$0.677901\pi$
$710$	−0.353689	+	2.98619i	−0.0132737	+	0.112070i
$711$	−15.2491	+	2.98669i	−0.571887	+	0.112010i
$712$	6.97212	−	1.19625i	0.261291	−	0.0448314i
$713$	11.5463	+	31.7231i	0.432411	+	1.18804i
$714$	−14.3524	−	4.17355i	−0.537127	−	0.156191i
$715$	0.850038	+	1.01304i	0.0317896	+	0.0378854i
$716$	0.796076	−	12.9805i	0.0297508	−	0.485106i
$717$	5.79276	+	0.965132i	0.216335	+	0.0360435i
$718$	−12.1023	−	12.8672i	−0.451653	−	0.480200i
$719$	−11.8686	−	20.5570i	−0.442624	−	0.766647i	0.555259	−	0.831677i	$-0.312619\pi$
$719$	−11.8686	−	20.5570i	−0.442624	−	0.766647i	−0.997883	+	0.0650301i	$0.979286\pi$
$720$	4.57502	+	3.31630i	0.170501	+	0.123591i
$721$	−7.40380	+	12.8238i	−0.275732	+	0.477582i
$722$	−19.2330	+	4.52709i	−0.715777	+	0.168481i
$723$	17.1985	−	10.1472i	0.639618	−	0.377378i
$724$	−3.42909	+	1.70897i	−0.127441	+	0.0635134i
$725$	3.55515	−	0.626868i	0.132035	−	0.0232813i
$726$	−9.42526	+	0.623728i	−0.349804	+	0.0231487i
$727$	−18.2525	+	21.7524i	−0.676946	+	0.806753i	−0.989711	−	0.143078i	$-0.954300\pi$
$727$	−18.2525	+	21.7524i	−0.676946	+	0.806753i	0.312766	+	0.949830i	$0.398745\pi$
$728$	1.02934	−	2.78802i	0.0381498	−	0.103331i
$729$	12.1548	−	24.1094i	0.450177	−	0.892939i
$730$	9.65195	−	4.14586i	0.357235	−	0.153445i
$731$	−55.6243	−	46.6743i	−2.05734	−	1.72631i
$732$	−9.67738	−	18.9673i	−0.357686	−	0.701050i
$733$	−0.226595	−	1.28509i	−0.00836949	−	0.0474657i	0.980337	−	0.197331i	$-0.0632272\pi$
$733$	−0.226595	−	1.28509i	−0.00836949	−	0.0474657i	−0.988706	+	0.149865i	$0.952116\pi$
$734$	−5.68884	+	0.322564i	−0.209979	+	0.0119061i
$735$	−0.414442	−	0.702437i	−0.0152869	−	0.0259098i
$736$	9.33395	+	32.0726i	0.344054	+	1.18221i
$737$	−19.2534	−	11.1160i	−0.709208	−	0.409462i
$738$	−5.82793	−	1.63520i	−0.214529	−	0.0601926i
$739$	−22.2536	+	12.8481i	−0.818611	+	0.472625i	−0.849937	−	0.526884i	$-0.823360\pi$
$739$	−22.2536	+	12.8481i	−0.818611	+	0.472625i	0.0313261	+	0.999509i	$0.490027\pi$
$740$	8.82164	+	3.83749i	0.324290	+	0.141069i
$741$	−0.670715	+	4.02565i	−0.0246393	+	0.147886i
$742$	−12.5047	−	6.30420i	−0.459063	−	0.231434i
$743$	23.0100	−	19.3077i	0.844156	−	0.708331i	−0.114338	−	0.993442i	$-0.536475\pi$
$743$	23.0100	−	19.3077i	0.844156	−	0.708331i	0.958495	+	0.285110i	$0.0920303\pi$
$744$	−14.1209	−	24.1877i	−0.517698	−	0.886764i
$745$	7.50458	−	2.73145i	0.274947	−	0.100072i
$746$	−26.0356	+	34.8599i	−0.953231	+	1.27631i
$747$	−7.62110	−	38.9110i	−0.278842	−	1.42368i
$748$	−31.2772	+	9.25911i	−1.14361	+	0.338546i
$749$	13.7544	+	2.42527i	0.502575	+	0.0886176i
$750$	−11.2121	−	1.22078i	−0.409409	−	0.0445765i
$751$	−13.6836	+	37.5954i	−0.499321	+	1.37187i	0.392611	+	0.919705i	$0.371572\pi$
$751$	−13.6836	+	37.5954i	−0.499321	+	1.37187i	−0.891932	+	0.452169i	$0.850650\pi$
$752$	−1.93623	+	0.446340i	−0.0706069	+	0.0162763i
$753$	−29.0038	−	33.9101i	−1.05696	−	1.23575i
$754$	−1.07500	−	0.323636i	−0.0391493	−	0.0117861i
$755$	1.66430			0.0605702
$756$	10.1695	+	2.14062i	0.369859	+	0.0778538i
$757$	−33.5330			−1.21878			−0.609389	−	0.792871i	$-0.708585\pi$
$757$	−33.5330			−1.21878			−0.609389	+	0.792871i	$0.708585\pi$
$758$	−8.30829	−	2.50126i	−0.301771	−	0.0908499i
$759$	−26.8748	+	5.00077i	−0.975494	+	0.181516i
$760$	0.532174	−	2.93880i	0.0193040	−	0.106602i
$761$	15.0499	−	41.3492i	0.545558	−	1.49891i	−0.294091	−	0.955777i	$-0.595017\pi$
$761$	15.0499	−	41.3492i	0.545558	−	1.49891i	0.839649	−	0.543130i	$-0.182761\pi$
$762$	6.12182	+	13.8891i	0.221770	+	0.503150i
$763$	−10.5225	−	1.85540i	−0.380940	−	0.0671699i
$764$	−6.22354	−	21.0231i	−0.225160	−	0.760587i
$765$	4.16831	−	7.54517i	0.150705	−	0.272796i
$766$	2.82507	−	3.78258i	0.102074	−	0.136670i
$767$	−9.71223	+	3.53496i	−0.350688	+	0.127640i
$768$	−12.3667	−	24.8005i	−0.446244	−	0.894911i
$769$	−23.4311	+	19.6610i	−0.844945	+	0.708993i	−0.958670	−	0.284519i	$-0.908166\pi$
$769$	−23.4311	+	19.6610i	−0.844945	+	0.708993i	0.113725	+	0.993512i	$0.463722\pi$
$770$	−1.58931	−	0.801245i	−0.0572749	−	0.0288749i
$771$	49.6491	−	18.6034i	1.78807	−	0.669985i
$772$	−0.457583	+	1.05189i	−0.0164688	+	0.0378585i
$773$	−42.3062	+	24.4255i	−1.52165	+	0.878524i	−0.521976	+	0.852960i	$0.674805\pi$
$773$	−42.3062	+	24.4255i	−1.52165	+	0.878524i	−0.999673	+	0.0255641i	$0.991862\pi$
$774$	41.0126	+	29.4413i	1.47417	+	1.05825i
$775$	23.6580	+	13.6589i	0.849819	+	0.490643i
$776$	4.97187	−	8.52056i	0.178480	−	0.305870i
$777$	17.6923	−	0.167007i	0.634708	−	0.00599136i
$778$	28.0180	−	1.58865i	1.00449	−	0.0569560i
$779$	0.555554	+	3.15070i	0.0199048	+	0.112886i
$780$	1.43795	+	0.932698i	0.0514869	+	0.0333959i
$781$	9.24561	+	7.75799i	0.330834	+	0.277603i
$782$	46.8207	−	20.1112i	1.67430	−	0.719174i
$783$	0.571954	−	3.88381i	0.0204400	−	0.138796i
$784$	0.208024	+	3.99459i	0.00742944	+	0.142664i
$785$	−6.88589	+	8.20629i	−0.245768	+	0.292895i
$786$	−7.62897	+	15.4946i	−0.272116	+	0.552675i
$787$	15.4776	−	2.72911i	0.551716	−	0.0972824i	0.109162	−	0.994024i	$-0.465183\pi$
$787$	15.4776	−	2.72911i	0.551716	−	0.0972824i	0.442555	+	0.896742i	$0.354072\pi$
$788$	−16.1004	−	32.3058i	−0.573554	−	1.15085i
$789$	3.52190	+	1.98929i	0.125383	+	0.0708205i
$790$	3.35747	−	0.790287i	0.119453	−	0.0281171i
$791$	3.28456	−	5.68903i	0.116786	−	0.202279i
$792$	21.1987	−	8.06003i	0.753263	−	0.286401i
$793$	−3.22941	−	5.59350i	−0.114680	−	0.198631i
$794$	−28.0313	−	29.8031i	−0.994794	−	1.05767i
$795$	5.13264	−	6.23544i	0.182036	−	0.221148i
$796$	−23.4796	−	1.43997i	−0.832213	−	0.0510383i
$797$	21.9695	+	26.1822i	0.778200	+	0.927423i	0.998851	−	0.0479301i	$-0.0152625\pi$
$797$	21.9695	+	26.1822i	0.778200	+	0.927423i	−0.220651	+	0.975353i	$0.570818\pi$
$798$	−1.30894	−	5.33462i	−0.0463358	−	0.188843i
$799$	1.03673	+	2.84841i	0.0366770	+	0.100769i
$800$	22.4684	+	15.0263i	0.794379	+	0.531261i
$801$	2.69885	+	7.00091i	0.0953593	+	0.247365i
$802$	−2.38069	+	20.1001i	−0.0840651	+	0.709761i
$803$	7.32136	−	41.5215i	0.258365	−	1.46526i
$804$	−28.0791	−	6.46639i	−0.990274	−	0.228052i
$805$	2.61281	+	0.950986i	0.0920896	+	0.0335179i
$806$	−4.65745	−	7.10507i	−0.164052	−	0.250265i
$807$	−9.43206	−	3.33251i	−0.332024	−	0.117310i
$808$	14.3273	−	8.18404i	0.504034	−	0.287914i
$809$			50.5950i			1.77883i	0.457104	+	0.889413i	$0.348887\pi$
$809$			50.5950i			1.77883i	−0.457104	+	0.889413i	$0.651113\pi$
$810$	−2.49408	+	5.44971i	−0.0876331	+	0.191483i
$811$		−	1.23357i		−	0.0433165i	−0.999765	−	0.0216582i	$-0.993105\pi$
$811$		−	1.23357i		−	0.0433165i	0.999765	−	0.0216582i	$-0.00689457\pi$
$812$	1.50132	−	0.170802i	0.0526859	−	0.00599399i
$813$	−5.84849	−	2.06637i	−0.205116	−	0.0724708i
$814$	32.2924	−	21.1680i	1.13185	−	0.741937i
$815$	−6.58531	−	2.39686i	−0.230673	−	0.0839582i
$816$	−35.2447	+	23.3474i	−1.23381	+	0.817321i
$817$	4.63369	−	26.2789i	0.162112	−	0.919384i
$818$	−25.7328	−	3.04784i	−0.899728	−	0.106565i
$819$	3.11414	+	0.488682i	0.108817	+	0.0170759i
$820$	1.30643	+	0.313875i	0.0456226	+	0.0109610i
$821$	−9.67725	−	26.5880i	−0.337738	−	0.927928i	−0.986035	−	0.166540i	$-0.946740\pi$
$821$	−9.67725	−	26.5880i	−0.337738	−	0.927928i	0.648296	−	0.761388i	$-0.275482\pi$
$822$	−8.92784	+	2.19059i	−0.311394	+	0.0764056i
$823$	7.19437	+	8.57391i	0.250780	+	0.298868i	0.876718	−	0.481005i	$-0.159728\pi$
$823$	7.19437	+	8.57391i	0.250780	+	0.298868i	−0.625938	+	0.779873i	$0.715284\pi$
$824$	14.1429	+	39.4221i	0.492693	+	1.37333i
$825$	−14.0582	+	17.0787i	−0.489443	+	0.594605i
$826$	10.1329	−	9.53054i	0.352570	−	0.331610i
$827$	15.3984	+	26.6709i	0.535456	+	0.927437i	0.999141	+	0.0414371i	$0.0131936\pi$
$827$	15.3984	+	26.6709i	0.535456	+	0.927437i	−0.463685	+	0.886000i	$0.653473\pi$
$828$	−31.4057	+	16.3991i	−1.09142	+	0.569908i
$829$	−9.57396	+	16.5826i	−0.332518	+	0.575937i	−0.983005	−	0.183580i	$-0.941231\pi$
$829$	−9.57396	+	16.5826i	−0.332518	+	0.575937i	0.650487	+	0.759517i	$0.274565\pi$
$830$	2.01657	+	8.56722i	0.0699960	+	0.297373i
$831$	−26.2050	−	14.8014i	−0.909040	−	0.513455i
$832$	−4.13568	−	7.31825i	−0.143379	−	0.253715i
$833$	6.00936	−	1.05961i	0.208212	−	0.0367134i
$834$	−38.2817	−	18.8485i	−1.32559	−	0.652669i
$835$	−2.14866	+	2.56068i	−0.0743575	+	0.0886158i
$836$	−8.69379	−	8.25283i	−0.300681	−	0.285430i
$837$	22.2070	−	19.7319i	0.767588	−	0.682035i
$838$	2.14873	+	5.00244i	0.0742265	+	0.172806i
$839$	−36.4274	−	30.5662i	−1.25761	−	1.05526i	−0.995932	−	0.0901075i	$-0.971279\pi$
$839$	−36.4274	−	30.5662i	−1.25761	−	1.05526i	−0.261680	−	0.965155i	$-0.584277\pi$
$840$	−2.27369	−	0.389603i	−0.0784497	−	0.0134426i
$841$	4.93668	+	27.9973i	0.170230	+	0.965425i
$842$	2.72296	+	48.0229i	0.0938394	+	1.65498i
$843$	51.3353	−	0.484582i	1.76808	−	0.0166899i
$844$	−32.4363	+	23.9933i	−1.11650	+	0.825884i
$845$	−4.85108	−	2.80077i	−0.166882	−	0.0963494i
$846$	−0.868185	−	1.92041i	−0.0298488	−	0.0660250i
$847$	3.33962	−	1.92813i	0.114751	−	0.0662514i
$848$	−36.4656	+	15.4645i	−1.25223	+	0.531054i
$849$	4.29299	−	1.60857i	0.147335	−	0.0552060i
$850$	18.5627	−	36.8202i	0.636696	−	1.26292i
$851$	−46.2073	+	38.7726i	−1.58397	+	1.32911i
$852$	14.4024	+	6.10417i	0.493420	+	0.209126i
$853$	22.9454	−	8.35144i	0.785635	−	0.285948i	0.0821149	−	0.996623i	$-0.473833\pi$
$853$	22.9454	−	8.35144i	0.785635	−	0.285948i	0.703520	+	0.710675i	$0.251610\pi$
$854$	6.96486	+	5.20180i	0.238333	+	0.178002i
$855$	3.16720	−	0.0597992i	0.108316	−	0.00204509i
$856$	30.3782	−	25.2526i	1.03831	−	0.863115i
$857$	−10.2967	−	1.81559i	−0.351729	−	0.0620193i	−0.00500765	−	0.999987i	$-0.501594\pi$
$857$	−10.2967	−	1.81559i	−0.351729	−	0.0620193i	−0.346722	+	0.937968i	$0.612705\pi$
$858$	6.29485	−	2.77454i	0.214903	−	0.0947211i
$859$	0.624836	−	1.71672i	0.0213191	−	0.0585738i	−0.928577	−	0.371141i	$-0.878967\pi$
$859$	0.624836	−	1.71672i	0.0213191	−	0.0585738i	0.949896	+	0.312567i	$0.101189\pi$
$860$	−9.34398	−	6.18687i	−0.318627	−	0.210970i
$861$	2.42942	−	0.452057i	0.0827944	−	0.0154061i
$862$	−8.61292	+	28.6090i	−0.293357	+	0.974427i
$863$	−0.790030			−0.0268929			−0.0134465	−	0.999910i	$-0.504280\pi$
$863$	−0.790030			−0.0268929			−0.0134465	+	0.999910i	$0.504280\pi$
$864$	23.2104	−	18.0355i	0.789632	−	0.613580i
$865$	−3.23838			−0.110108
$866$	11.8074	−	39.2201i	0.401233	−	1.33275i
$867$	22.7811	+	26.6348i	0.773686	+	0.904564i
$868$	9.53378	+	6.31253i	0.323597	+	0.214261i
$869$	4.73491	−	13.0091i	0.160621	−	0.441302i
$870$	−0.0943213	+	0.866285i	−0.00319779	+	0.0293698i
$871$	−8.60725	−	1.51769i	−0.291646	−	0.0514250i
$872$	−23.2401	+	19.3189i	−0.787010	+	0.654220i
$873$	9.89825	+	3.39247i	0.335005	+	0.114818i
$874$	15.0036	+	11.2056i	0.507503	+	0.379036i
$875$	4.32670	−	1.57479i	0.146269	−	0.0532377i
$876$	−6.68923	−	54.2339i	−0.226008	−	1.83239i
$877$	−37.8072	+	31.7240i	−1.27666	+	1.07125i	−0.282965	+	0.959130i	$0.591318\pi$
$877$	−37.8072	+	31.7240i	−1.27666	+	1.07125i	−0.993695	+	0.112115i	$0.964238\pi$
$878$	−17.1583	+	34.0344i	−0.579065	+	1.14861i
$879$	−0.916279	+	5.49954i	−0.0309053	+	0.185495i
$880$	−4.63467	+	1.96549i	−0.156235	+	0.0662568i
$881$	50.1762	−	28.9692i	1.69048	−	0.975998i	0.736349	−	0.676602i	$-0.236548\pi$
$881$	50.1762	−	28.9692i	1.69048	−	0.975998i	0.954129	−	0.299395i	$-0.0967849\pi$
$882$	−4.11069	+	1.04986i	−0.138414	+	0.0353506i
$883$	−14.2351	−	8.21864i	−0.479049	−	0.276579i	0.240971	−	0.970532i	$-0.422534\pi$
$883$	−14.2351	−	8.21864i	−0.479049	−	0.276579i	−0.720020	+	0.693953i	$0.755867\pi$
$884$	−10.3095	+	7.62599i	−0.346746	+	0.256490i
$885$	4.07660	+	6.90942i	0.137033	+	0.232258i
$886$	1.08964	+	19.2172i	0.0366071	+	0.645614i
$887$	−2.17633	−	12.3426i	−0.0730740	−	0.414423i	−0.999298	−	0.0374507i	$-0.988076\pi$
$887$	−2.17633	−	12.3426i	−0.0730740	−	0.414423i	0.926224	−	0.376972i	$-0.123035\pi$
$888$	31.9820	−	38.4905i	1.07325	−	1.29166i
$889$	−4.74685	−	3.98308i	−0.159204	−	0.133588i
$890$	−0.657318	−	1.53030i	−0.0220334	−	0.0512957i
$891$	12.8053	+	20.3634i	0.428994	+	0.682199i
$892$	−13.8411	−	13.1391i	−0.463435	−	0.439929i
$893$	−0.716027	+	0.853327i	−0.0239609	+	0.0285555i
$894$	−2.74322	−	41.4532i	−0.0917470	−	1.38640i
$895$	−3.01536	+	0.531689i	−0.100792	+	0.0177724i
$896$	9.00177	+	6.85332i	0.300728	+	0.228953i
$897$	−9.25574	+	5.46093i	−0.309040	+	0.182335i
$898$	−0.00573453	−	0.0243627i	−0.000191364	−	0.000812994i
$899$	2.15964	−	3.74060i	0.0720279	−	0.124756i
$900$	−10.9380	+	26.5011i	−0.364600	+	0.883370i
$901$	30.2123	+	52.3292i	1.00652	+	1.74334i
$902$	3.92823	−	3.69470i	0.130796	−	0.123020i
$903$	−20.3305	−	3.38727i	−0.676558	−	0.112721i
$904$	−6.27426	−	17.4889i	−0.208679	−	0.581672i
$905$	0.579826	+	0.691010i	0.0192741	+	0.0229700i
$906$	2.41742	−	8.31328i	0.0803134	−	0.276190i
$907$	−9.23120	−	25.3625i	−0.306517	−	0.842148i	−0.993329	−	0.115313i	$-0.963213\pi$
$907$	−9.23120	−	25.3625i	−0.306517	−	0.842148i	0.686812	−	0.726835i	$-0.259009\pi$
$908$	−7.48256	−	1.79771i	−0.248318	−	0.0596592i
$909$	11.5005	+	13.1917i	0.381446	+	0.437543i
$910$	−0.694861	−	0.0823004i	−0.0230344	−	0.00272823i
$911$	6.43933	−	36.5192i	0.213344	−	1.20994i	−0.670412	−	0.741989i	$-0.733883\pi$
$911$	6.43933	−	36.5192i	0.213344	−	1.20994i	0.883756	−	0.467947i	$-0.155006\pi$
$912$	−13.9065	−	6.92688i	−0.460489	−	0.229372i
$913$	33.1951	+	12.0820i	1.09860	+	0.399857i
$914$	−9.59980	+	6.29277i	−0.317533	+	0.208146i
$915$	−3.80982	+	3.25859i	−0.125949	+	0.107726i
$916$	37.1191	−	4.22297i	1.22645	−	0.139531i
$917$		−	7.05082i		−	0.232839i
$918$	−31.6340	−	31.7804i	−1.04408	−	1.04891i
$919$		−	22.2999i		−	0.735606i	−0.929904	−	0.367803i	$-0.880110\pi$
$919$		−	22.2999i		−	0.735606i	0.929904	−	0.367803i	$-0.119890\pi$
$920$	6.82886	−	3.90077i	0.225141	−	0.128605i
$921$	3.35322	+	18.0207i	0.110492	+	0.593802i
$922$	22.2621	+	33.9615i	0.733163	+	1.11846i
$923$	4.45865	+	1.62282i	0.146758	+	0.0534156i
$924$	−6.31076	+	6.77489i	−0.207609	+	0.222878i
$925$	−8.47588	+	48.0691i	−0.278685	+	1.58050i
$926$	−1.01642	+	8.58161i	−0.0334016	+	0.282009i
$927$	−38.0451	+	22.9337i	−1.24957	+	0.753241i
$928$	2.37584	−	3.55252i	0.0779908	−	0.116617i
$929$	0.852504	+	2.34224i	0.0279698	+	0.0768463i	0.952892	−	0.303311i	$-0.0980921\pi$
$929$	0.852504	+	2.34224i	0.0279698	+	0.0768463i	−0.924922	+	0.380157i	$0.875870\pi$
$930$	−4.76052	+	4.56296i	−0.156104	+	0.149625i
$931$	1.44142	+	1.71782i	0.0472406	+	0.0562991i
$932$	15.3434	+	0.940983i	0.502588	+	0.0308229i
$933$	13.7773	+	36.7691i	0.451048	+	1.20377i
$934$	17.0666	+	18.1453i	0.558436	+	0.593733i
$935$	3.83989	+	6.65088i	0.125578	+	0.217507i
$936$	6.74751	−	5.82789i	0.220549	−	0.190490i
$937$	22.3529	−	38.7164i	0.730239	−	1.26481i	−0.226542	−	0.974001i	$-0.572742\pi$
$937$	22.3529	−	38.7164i	0.730239	−	1.26481i	0.956781	−	0.290809i	$-0.0939246\pi$
$938$	11.4504	−	2.69521i	0.373868	−	0.0880017i
$939$	−0.0387256	−	4.10248i	−0.00126376	−	0.133879i
$940$	0.208671	+	0.418702i	0.00680609	+	0.0136566i
$941$	−49.4973	+	8.72771i	−1.61357	+	0.284515i	−0.906364	−	0.422497i	$-0.861154\pi$
$941$	−49.4973	+	8.72771i	−1.61357	+	0.284515i	−0.707201	+	0.707012i	$0.750043\pi$
$942$	30.9890	+	46.3151i	1.00968	+	1.50903i
$943$	−5.41520	+	6.45358i	−0.176343	+	0.210158i
$944$	−2.04620	−	39.2922i	−0.0665982	−	1.27885i
$945$	−0.0692775	−	2.44578i	−0.00225360	−	0.0795611i
$946$	−41.3280	+	17.7518i	−1.34369	+	0.577162i
$947$	28.6871	+	24.0713i	0.932204	+	0.782212i	0.976212	−	0.216819i	$-0.0695682\pi$
$947$	28.6871	+	24.0713i	0.932204	+	0.782212i	−0.0440078	+	0.999031i	$0.514013\pi$
$948$	0.929240	−	17.9186i	0.0301803	−	0.581970i
$949$	−2.87825	−	16.3233i	−0.0934318	−	0.529878i
$950$	15.1290	−	0.857836i	0.490851	−	0.0278319i
$951$	12.6231	−	22.3484i	0.409331	−	0.724695i
$952$	8.69845	−	14.9070i	0.281918	−	0.483138i
$953$	−23.1974	−	13.3930i	−0.751436	−	0.433842i	0.0747763	−	0.997200i	$-0.476176\pi$
$953$	−23.1974	−	13.3930i	−0.751436	−	0.433842i	−0.826213	+	0.563358i	$0.809509\pi$
$954$	−23.6911	−	34.6948i	−0.767028	−	1.12329i
$955$	−4.47041	+	2.58099i	−0.144659	+	0.0835190i
$956$	−2.70499	+	6.21823i	−0.0874855	+	0.201112i
$957$	2.70035	+	2.22276i	0.0872898	+	0.0718517i
$958$	−38.7442	−	19.5327i	−1.25177	−	0.631073i
$959$	2.87488	−	2.41231i	0.0928347	−	0.0778975i
$960$	−4.99729	+	4.19507i	−0.161287	+	0.135395i
$961$	1.58360	−	0.576384i	0.0510839	−	0.0185930i
$962$	9.08327	−	12.1619i	0.292856	−	0.392115i
$963$	32.5998	+	26.3220i	1.05051	+	0.848213i
$964$	6.54517	+	22.1095i	0.210806	+	0.712100i
$965$	0.265972	+	0.0468980i	0.00856194	+	0.00150970i
$966$	8.54537	−	11.6698i	0.274943	−	0.375470i
$967$	−11.9219	+	32.7550i	−0.383381	+	1.05333i	0.586542	+	0.809919i	$0.300489\pi$
$967$	−11.9219	+	32.7550i	−0.383381	+	1.05333i	−0.969923	+	0.243412i	$0.921733\pi$
$968$	1.94352	−	10.7326i	0.0624670	−	0.344959i
$969$	−7.89551	+	22.3468i	−0.253640	+	0.717884i
$970$	−2.22402	−	0.669555i	−0.0714090	−	0.0214981i
$971$	14.3193			0.459528			0.229764	−	0.973246i	$-0.426205\pi$
$971$	14.3193			0.459528			0.229764	+	0.973246i	$0.426205\pi$
$972$	23.5989	+	20.3738i	0.756934	+	0.653491i
$973$	17.4201			0.558462
$974$	32.4036	+	9.75531i	1.03828	+	0.312580i
$975$	−2.89702	+	8.19948i	−0.0927787	+	0.262594i
$976$	23.9591	−	5.52307i	0.766913	−	0.176789i
$977$	11.1889	−	30.7411i	0.357963	−	0.983496i	−0.621772	−	0.783199i	$-0.713587\pi$
$977$	11.1889	−	30.7411i	0.357963	−	0.983496i	0.979735	−	0.200298i	$-0.0641909\pi$
$978$	−21.5377	+	29.4125i	−0.688698	+	0.940508i
$979$	−6.58315	−	1.16079i	−0.210399	−	0.0370989i
$980$	0.903020	−	0.267324i	0.0288459	−	0.00853937i
$981$	−24.9397	−	20.1370i	−0.796264	−	0.642925i
$982$	14.7100	−	19.6957i	0.469414	−	0.628514i
$983$	−50.2537	+	18.2908i	−1.60284	+	0.583387i	−0.980007	−	0.198964i	$-0.936242\pi$
$983$	−50.2537	+	18.2908i	−1.60284	+	0.583387i	−0.622837	+	0.782352i	$0.714020\pi$
$984$	3.46543	−	6.06979i	0.110474	−	0.193498i
$985$	−6.51009	+	5.46262i	−0.207429	+	0.174053i
$986$	−5.82170	−	2.93498i	−0.185401	−	0.0934689i
$987$	0.664295	+	0.546808i	0.0211447	+	0.0174051i
$988$	−4.32133	−	1.87982i	−0.137480	−	0.0598050i
$989$	60.8525	−	35.1332i	1.93500	−	1.11717i
$990$	−3.01107	−	4.40961i	−0.0956981	−	0.140147i
$991$	29.3765	+	16.9605i	0.933174	+	0.538768i	0.887814	−	0.460202i	$-0.152223\pi$
$991$	29.3765	+	16.9605i	0.933174	+	0.538768i	0.0453602	+	0.998971i	$0.485556\pi$
$992$	31.0525	−	9.03707i	0.985918	−	0.286927i
$993$	−0.601372	+	1.06469i	−0.0190839	+	0.0337869i
$994$	−6.37583	+	0.361518i	−0.202229	+	0.0114666i
$995$	0.961735	+	5.45427i	0.0304891	+	0.172912i
$996$	45.7228	+	2.37113i	1.44878	+	0.0751322i
$997$	−39.7403	−	33.3460i	−1.25859	−	1.05608i	−0.995831	−	0.0912170i	$-0.970924\pi$
$997$	−39.7403	−	33.3460i	−1.25859	−	1.05608i	−0.262755	−	0.964862i	$-0.584631\pi$
$998$	33.4912	−	14.3857i	1.06015	−	0.455371i
$999$	46.7011	+	25.2275i	1.47756	+	0.798162i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.cf.a.659.66	yes	648
4.3	odd	2	inner	756.2.cf.a.659.92	yes	648
27.5	odd	18	inner	756.2.cf.a.491.92	yes	648
108.59	even	18	inner	756.2.cf.a.491.66	✓	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.cf.a.491.66	✓	648	108.59	even	18	inner
756.2.cf.a.491.92	yes	648	27.5	odd	18	inner
756.2.cf.a.659.66	yes	648	1.1	even	1	trivial
756.2.cf.a.659.92	yes	648	4.3	odd	2	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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.cf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.407683 - 1.35418i) q^{2} +(-0.577007 + 1.63311i) q^{3} +(-1.66759 - 1.10415i) q^{4} +(-0.161050 + 0.442481i) q^{5} +(1.97629 + 1.44716i) q^{6} +(-0.984808 - 0.173648i) q^{7} +(-2.17506 + 1.80807i) q^{8} +(-2.33413 - 1.88464i) q^{9} +(0.533540 + 0.398482i) q^{10} +(2.51159 - 0.914144i) q^{11} +(2.76541 - 2.08626i) q^{12} +(0.804920 - 0.675408i) q^{13} +(-0.636640 + 1.26281i) q^{14} +(-0.629696 - 0.518328i) q^{15} +(1.56171 + 3.68254i) q^{16} +(5.28454 - 3.05103i) q^{17} +(-3.50371 + 2.39249i) q^{18} +(1.94202 + 1.12122i) q^{19} +(0.757131 - 0.560054i) q^{20} +(0.851828 - 1.50811i) q^{21} +(-0.213980 - 3.77382i) q^{22} +(1.02538 + 5.81520i) q^{23} +(-1.69776 - 4.59539i) q^{24} +(3.66037 + 3.07141i) q^{25} +(-0.586470 - 1.36536i) q^{26} +(4.42463 - 2.72445i) q^{27} +(1.45052 + 1.37695i) q^{28} +(0.485627 - 0.578747i) q^{29} +(-0.958624 + 0.641406i) q^{30} +(5.63024 - 0.992764i) q^{31} +(5.62349 - 0.613522i) q^{32} +(0.0436973 + 4.62918i) q^{33} +(-1.97722 - 8.40006i) q^{34} +(0.235439 - 0.407793i) q^{35} +(1.81144 + 5.72002i) q^{36} +(5.10756 + 8.84655i) q^{37} +(2.31006 - 2.17273i) q^{38} +(0.638575 + 1.70424i) q^{39} +(-0.449743 - 1.25361i) q^{40} +(0.917066 + 1.09292i) q^{41} +(-1.69497 - 1.76836i) q^{42} +(-4.06992 - 11.1820i) q^{43} +(-5.19765 - 1.24875i) q^{44} +(1.20983 - 0.729286i) q^{45} +(8.29284 + 0.982217i) q^{46} +(-0.0862600 + 0.489205i) q^{47} +(-6.91512 + 0.425600i) q^{48} +(0.939693 + 0.342020i) q^{49} +(5.65151 - 3.70462i) q^{50} +(1.93347 + 10.3907i) q^{51} +(-2.08803 + 0.237551i) q^{52} +9.90231i q^{53} +(-1.88554 - 7.10245i) q^{54} +1.25855i q^{55} +(2.45598 - 1.40290i) q^{56} +(-2.95164 + 2.52458i) q^{57} +(-0.585745 - 0.893570i) q^{58} +(-9.24315 - 3.36423i) q^{59} +(0.477762 + 1.55964i) q^{60} +(1.06739 - 6.05349i) q^{61} +(0.950976 - 8.02908i) q^{62} +(1.97140 + 2.26132i) q^{63} +(1.46178 - 7.86532i) q^{64} +(0.169223 + 0.464937i) q^{65} +(6.28654 + 1.82806i) q^{66} +(-5.34665 - 6.37189i) q^{67} +(-12.1812 - 0.747056i) q^{68} +(-10.0885 - 1.68085i) q^{69} +(-0.456239 - 0.485077i) q^{70} +(2.25782 + 3.91065i) q^{71} +(8.48442 - 0.121059i) q^{72} +(7.88731 - 13.6612i) q^{73} +(14.0621 - 3.30995i) q^{74} +(-7.12803 + 4.20558i) q^{75} +(-2.00049 - 4.01402i) q^{76} +(-2.63217 + 0.464123i) q^{77} +(2.56818 - 0.169953i) q^{78} +(3.32939 - 3.96782i) q^{79} +(-1.88097 + 0.0979543i) q^{80} +(1.89629 + 8.79796i) q^{81} +(1.85388 - 0.796306i) q^{82} +(10.1246 + 8.49558i) q^{83} +(-3.08568 + 1.57436i) q^{84} +(0.498949 + 2.82968i) q^{85} +(-16.8016 + 0.952675i) q^{86} +(0.664951 + 1.12703i) q^{87} +(-3.81003 + 6.52944i) q^{88} +(-2.16596 - 1.25052i) q^{89} +(-0.494357 - 1.93564i) q^{90} +(-0.909975 + 0.525374i) q^{91} +(4.71095 - 10.8295i) q^{92} +(-1.62739 + 9.76767i) q^{93} +(0.627303 + 0.316252i) q^{94} +(-0.808883 + 0.678733i) q^{95} +(-2.24284 + 9.53780i) q^{96} +(-3.27748 + 1.19291i) q^{97} +(0.846252 - 1.13307i) q^{98} +(-7.58519 - 2.59971i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 648 q + 18 q^{12} + 42 q^{18} + 42 q^{20} - 48 q^{30} - 30 q^{32} + 60 q^{33} + 60 q^{41} - 30 q^{42} - 144 q^{44} - 18 q^{48} - 156 q^{50} + 54 q^{52} - 12 q^{57} + 54 q^{58} - 186 q^{60} - 24 q^{65} - 186 q^{66}+ \cdots + 36 q^{97}+O(q^{100}) \) 648 * q + 18 * q^12 + 42 * q^18 + 42 * q^20 - 48 * q^30 - 30 * q^32 + 60 * q^33 + 60 * q^41 - 30 * q^42 - 144 * q^44 - 18 * q^48 - 156 * q^50 + 54 * q^52 - 12 * q^57 + 54 * q^58 - 186 * q^60 - 24 * q^65 - 186 * q^66 - 78 * q^68 - 42 * q^72 - 24 * q^81 - 30 * q^86 - 36 * q^89 + 198 * q^90 + 114 * q^92 - 144 * q^93 - 54 * q^94 + 156 * q^96 + 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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