LMFDB - Embedded newform 455.2.cl.a.54.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [455,2,Mod(54,455)] 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("455.54"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(455, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 10, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 455 = 5 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	455.cl (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.63319329197$
Analytic rank:	$0$
Dimension:	$208$
Relative dimension:	$52$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			54.5
Character	$\chi$	$=$	455.54
Dual form			455.2.cl.a.59.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.67761 - 1.67761i) q^{2} +(-0.0710893 + 0.123130i) q^{3} +3.62875i q^{4} +(1.78039 + 1.35286i) q^{5} +(0.325824 - 0.0873044i) q^{6} +(0.569797 - 2.58367i) q^{7} +(2.73241 - 2.73241i) q^{8} +(1.48989 + 2.58057i) q^{9} +(-0.717231 - 5.25636i) q^{10} +(-1.27877 + 0.342645i) q^{11} +(-0.446809 - 0.257965i) q^{12} +(-3.31679 + 1.41383i) q^{13} +(-5.29028 + 3.37849i) q^{14} +(-0.293144 + 0.123046i) q^{15} -1.91033 q^{16} +3.94567i q^{17} +(1.82973 - 6.82865i) q^{18} +(-1.38911 + 5.18423i) q^{19} +(-4.90918 + 6.46058i) q^{20} +(0.277621 + 0.253830i) q^{21} +(2.72010 + 1.57045i) q^{22} +7.87791 q^{23} +(0.142197 + 0.530687i) q^{24} +(1.33956 + 4.81722i) q^{25} +(7.93613 + 3.19242i) q^{26} -0.850197 q^{27} +(9.37548 + 2.06765i) q^{28} +(0.969679 + 1.67953i) q^{29} +(0.698204 + 0.285358i) q^{30} +(1.53075 - 5.71283i) q^{31} +(-2.26003 - 2.26003i) q^{32} +(0.0487167 - 0.181813i) q^{33} +(6.61929 - 6.61929i) q^{34} +(4.50979 - 3.82907i) q^{35} +(-9.36424 + 5.40645i) q^{36} +(-6.97436 + 6.97436i) q^{37} +(11.0275 - 6.36673i) q^{38} +(0.0617027 - 0.508905i) q^{39} +(8.56130 - 1.16819i) q^{40} +(1.25511 - 4.68412i) q^{41} +(-0.0399118 - 0.891568i) q^{42} +(-5.68359 + 9.84426i) q^{43} +(-1.24337 - 4.64033i) q^{44} +(-0.838554 + 6.61002i) q^{45} +(-13.2161 - 13.2161i) q^{46} +(11.6183 - 3.11312i) q^{47} +(0.135804 - 0.235219i) q^{48} +(-6.35066 - 2.94433i) q^{49} +(5.83415 - 10.3287i) q^{50} +(-0.485831 - 0.280494i) q^{51} +(-5.13044 - 12.0358i) q^{52} +(9.08405 - 5.24468i) q^{53} +(1.42630 + 1.42630i) q^{54} +(-2.74025 - 1.11995i) q^{55} +(-5.50271 - 8.61654i) q^{56} +(-0.539584 - 0.539584i) q^{57} +(1.19086 - 4.44435i) q^{58} +(2.31495 - 2.31495i) q^{59} +(-0.446503 - 1.06375i) q^{60} +(6.96922 - 4.02368i) q^{61} +(-12.1519 + 7.01590i) q^{62} +(7.51627 - 2.37899i) q^{63} +11.4036i q^{64} +(-7.81788 - 1.96997i) q^{65} +(-0.386739 + 0.223284i) q^{66} +(7.71449 - 2.06709i) q^{67} -14.3178 q^{68} +(-0.560035 + 0.970009i) q^{69} +(-13.9894 - 1.14197i) q^{70} +(0.817561 + 3.05118i) q^{71} +(11.1222 + 2.98017i) q^{72} +(-1.62140 + 6.05114i) q^{73} +23.4005 q^{74} +(-0.688373 - 0.177512i) q^{75} +(-18.8123 - 5.04073i) q^{76} +(0.156642 + 3.49915i) q^{77} +(-0.957257 + 0.750231i) q^{78} +(3.91758 - 6.78544i) q^{79} +(-3.40112 - 2.58440i) q^{80} +(-4.40924 + 7.63702i) q^{81} +(-9.96370 + 5.75255i) q^{82} +(-4.27763 + 4.27763i) q^{83} +(-0.921086 + 1.00742i) q^{84} +(-5.33792 + 7.02481i) q^{85} +(26.0497 - 6.97999i) q^{86} -0.275735 q^{87} +(-2.55787 + 4.43036i) q^{88} +(4.22472 - 4.22472i) q^{89} +(12.4958 - 9.68228i) q^{90} +(1.76297 + 9.37507i) q^{91} +28.5870i q^{92} +(0.594602 + 0.594602i) q^{93} +(-24.7136 - 14.2684i) q^{94} +(-9.48666 + 7.35067i) q^{95} +(0.438942 - 0.117614i) q^{96} +(-3.32657 - 12.4149i) q^{97} +(5.71450 + 15.5934i) q^{98} +(-2.78944 - 2.78944i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 208 q - 6 q^{5} + 24 q^{6} - 84 q^{9} - 6 q^{10} - 22 q^{15} - 168 q^{16} - 24 q^{19} + 12 q^{20} + 12 q^{21} + 36 q^{24} - 12 q^{26} - 20 q^{29} + 18 q^{30} - 12 q^{31} + 24 q^{34} - 4 q^{35} - 12 q^{36}+ \cdots - 48 q^{99}+O(q^{100}) $ 208 * q - 6 * q^5 + 24 * q^6 - 84 * q^9 - 6 * q^10 - 22 * q^15 - 168 * q^16 - 24 * q^19 + 12 * q^20 + 12 * q^21 + 36 * q^24 - 12 * q^26 - 20 * q^29 + 18 * q^30 - 12 * q^31 + 24 * q^34 - 4 * q^35 - 12 * q^36 - 4 * q^39 + 48 * q^40 - 72 * q^41 + 88 * q^44 - 6 * q^45 - 84 * q^46 - 12 * q^49 + 36 * q^50 + 72 * q^51 - 36 * q^54 - 18 * q^55 + 72 * q^56 - 60 * q^59 + 74 * q^60 - 12 * q^61 + 44 * q^65 - 60 * q^66 - 84 * q^69 - 84 * q^70 - 64 * q^74 - 12 * q^75 - 48 * q^76 - 4 * q^79 - 150 * q^80 + 12 * q^81 + 252 * q^84 + 22 * q^85 + 80 * q^86 + 72 * q^89 + 144 * q^90 - 48 * q^91 + 48 * q^94 - 180 * q^96 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/455\mathbb{Z}\right)^\times$.

$n$	$66$	$92$	$106$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{12}\right)$

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 $

$2$	−1.67761	−	1.67761i	−1.18625	−	1.18625i	−0.978096	−	0.208153i	$-0.933255\pi$
$2$	−1.67761	−	1.67761i	−1.18625	−	1.18625i	−0.208153	−	0.978096i	$-0.566745\pi$
$3$	−0.0710893	+	0.123130i	−0.0410434	+	0.0710893i	−0.885817	−	0.464034i	$-0.846402\pi$
$3$	−0.0710893	+	0.123130i	−0.0410434	+	0.0710893i	0.844774	+	0.535123i	$0.179735\pi$
$4$			3.62875i			1.81438i
$5$	1.78039	+	1.35286i	0.796214	+	0.605016i
$5$	1.78039	+	1.35286i	0.796214	+	0.605016i
$6$	0.325824	−	0.0873044i	0.133017	−	0.0356419i
$7$	0.569797	−	2.58367i	0.215363	−	0.976534i
$7$	0.569797	−	2.58367i	0.215363	−	0.976534i
$8$	2.73241	−	2.73241i	0.966052	−	0.966052i
$9$	1.48989	+	2.58057i	0.496631	+	0.860190i
$10$	−0.717231	−	5.25636i	−0.226808	−	1.66221i
$11$	−1.27877	+	0.342645i	−0.385563	+	0.103311i	−0.446393	−	0.894837i	$-0.647292\pi$
$11$	−1.27877	+	0.342645i	−0.385563	+	0.103311i	0.0608305	+	0.998148i	$0.480625\pi$
$12$	−0.446809	−	0.257965i	−0.128983	−	0.0744681i
$13$	−3.31679	+	1.41383i	−0.919911	+	0.392126i
$13$	−3.31679	+	1.41383i	−0.919911	+	0.392126i
$14$	−5.29028	+	3.37849i	−1.41389	+	0.902939i
$15$	−0.293144	+	0.123046i	−0.0756894	+	0.0317703i
$16$	−1.91033			−0.477582
$17$			3.94567i			0.956965i	0.878097	+	0.478482i	$0.158813\pi$
$17$			3.94567i			0.956965i	−0.878097	+	0.478482i	$0.841187\pi$
$18$	1.82973	−	6.82865i	0.431272	−	1.60953i
$19$	−1.38911	+	5.18423i	−0.318683	+	1.18934i	0.601827	+	0.798626i	$0.294439\pi$
$19$	−1.38911	+	5.18423i	−0.318683	+	1.18934i	−0.920511	+	0.390717i	$0.872227\pi$
$20$	−4.90918	+	6.46058i	−1.09773	+	1.44463i
$21$	0.277621	+	0.253830i	0.0605819	+	0.0553903i
$22$	2.72010	+	1.57045i	0.579927	+	0.334821i
$23$	7.87791			1.64266			0.821329	−	0.570454i	$-0.193233\pi$
$23$	7.87791			1.64266			0.821329	+	0.570454i	$0.193233\pi$
$24$	0.142197	+	0.530687i	0.0290259	+	0.108326i
$25$	1.33956	+	4.81722i	0.267912	+	0.963443i
$26$	7.93613	+	3.19242i	1.55640	+	0.626085i
$27$	−0.850197			−0.163620
$28$	9.37548	+	2.06765i	1.77180	+	0.390749i
$29$	0.969679	+	1.67953i	0.180065	+	0.311882i	0.941902	−	0.335887i	$-0.109036\pi$
$29$	0.969679	+	1.67953i	0.180065	+	0.311882i	−0.761838	+	0.647768i	$0.775703\pi$
$30$	0.698204	+	0.285358i	0.127474	+	0.0520990i
$31$	1.53075	−	5.71283i	0.274930	−	1.02605i	−0.680958	−	0.732323i	$-0.738436\pi$
$31$	1.53075	−	5.71283i	0.274930	−	1.02605i	0.955888	−	0.293732i	$-0.0948972\pi$
$32$	−2.26003	−	2.26003i	−0.399521	−	0.399521i
$33$	0.0487167	−	0.181813i	0.00848049	−	0.0316496i
$34$	6.61929	−	6.61929i	1.13520	−	1.13520i
$35$	4.50979	−	3.82907i	0.762293	−	0.647232i
$36$	−9.36424	+	5.40645i	−1.56071	+	0.901075i
$37$	−6.97436	+	6.97436i	−1.14658	+	1.14658i	−0.159357	+	0.987221i	$0.550942\pi$
$37$	−6.97436	+	6.97436i	−1.14658	+	1.14658i	−0.987221	+	0.159357i	$0.949058\pi$
$38$	11.0275	−	6.36673i	1.78890	−	1.03282i
$39$	0.0617027	−	0.508905i	0.00988034	−	0.0814900i
$40$	8.56130	−	1.16819i	1.35366	−	0.184707i
$41$	1.25511	−	4.68412i	0.196015	−	0.731536i	−0.795987	−	0.605313i	$-0.793048\pi$
$41$	1.25511	−	4.68412i	0.196015	−	0.731536i	0.992002	−	0.126223i	$-0.0402855\pi$
$42$	−0.0399118	−	0.891568i	−0.00615852	−	0.137572i
$43$	−5.68359	+	9.84426i	−0.866739	+	1.50124i	−0.00142898	+	0.999999i	$0.500455\pi$
$43$	−5.68359	+	9.84426i	−0.866739	+	1.50124i	−0.865310	+	0.501237i	$0.832878\pi$
$44$	−1.24337	−	4.64033i	−0.187445	−	0.699556i
$45$	−0.838554	+	6.61002i	−0.125004	+	0.985364i
$46$	−13.2161	−	13.2161i	−1.94860	−	1.94860i
$47$	11.6183	−	3.11312i	1.69471	−	0.454096i	0.723110	−	0.690732i	$-0.242712\pi$
$47$	11.6183	−	3.11312i	1.69471	−	0.454096i	0.971598	+	0.236637i	$0.0760451\pi$
$48$	0.135804	−	0.235219i	0.0196016	−	0.0339509i
$49$	−6.35066	−	2.94433i	−0.907238	−	0.420618i
$50$	5.83415	−	10.3287i	0.825074	−	1.46069i
$51$	−0.485831	−	0.280494i	−0.0680299	−	0.0392771i
$52$	−5.13044	−	12.0358i	−0.711464	−	1.66906i
$53$	9.08405	−	5.24468i	1.24779	−	0.720412i	0.277122	−	0.960835i	$-0.410619\pi$
$53$	9.08405	−	5.24468i	1.24779	−	0.720412i	0.970668	+	0.240422i	$0.0772860\pi$
$54$	1.42630	+	1.42630i	0.194095	+	0.194095i
$55$	−2.74025	−	1.11995i	−0.369495	−	0.151014i
$56$	−5.50271	−	8.61654i	−0.735331	−	1.15143i
$57$	−0.539584	−	0.539584i	−0.0714696	−	0.0714696i
$58$	1.19086	−	4.44435i	0.156367	−	0.583571i
$59$	2.31495	−	2.31495i	0.301381	−	0.301381i	−0.540173	−	0.841554i	$-0.681641\pi$
$59$	2.31495	−	2.31495i	0.301381	−	0.301381i	0.841554	+	0.540173i	$0.181641\pi$
$60$	−0.446503	−	1.06375i	−0.0576433	−	0.137329i
$61$	6.96922	−	4.02368i	0.892317	−	0.515179i	0.0176171	−	0.999845i	$-0.494392\pi$
$61$	6.96922	−	4.02368i	0.892317	−	0.515179i	0.874700	+	0.484666i	$0.161059\pi$
$62$	−12.1519	+	7.01590i	−1.54329	+	0.891020i
$63$	7.51627	−	2.37899i	0.946961	−	0.299724i
$64$			11.4036i			1.42544i
$65$	−7.81788	−	1.96997i	−0.969688	−	0.244345i
$66$	−0.386739	+	0.223284i	−0.0476043	+	0.0274844i
$67$	7.71449	−	2.06709i	0.942474	−	0.252535i	0.245309	−	0.969445i	$-0.421111\pi$
$67$	7.71449	−	2.06709i	0.942474	−	0.252535i	0.697166	+	0.716910i	$0.254444\pi$
$68$	−14.3178			−1.73629
$69$	−0.560035	+	0.970009i	−0.0674203	+	0.116775i
$70$	−13.9894	−	1.14197i	−1.67205	−	0.136492i
$71$	0.817561	+	3.05118i	0.0970266	+	0.362108i	0.997319	−	0.0731776i	$-0.0233140\pi$
$71$	0.817561	+	3.05118i	0.0970266	+	0.362108i	−0.900292	+	0.435286i	$0.856647\pi$
$72$	11.1222	+	2.98017i	1.31076	+	0.351217i
$73$	−1.62140	+	6.05114i	−0.189770	+	0.708233i	0.803788	+	0.594915i	$0.202814\pi$
$73$	−1.62140	+	6.05114i	−0.189770	+	0.708233i	−0.993559	+	0.113317i	$0.963852\pi$
$74$	23.4005			2.72025
$75$	−0.688373	−	0.177512i	−0.0794865	−	0.0204973i
$76$	−18.8123	−	5.04073i	−2.15791	−	0.578211i
$77$	0.156642	+	3.49915i	0.0178510	+	0.398765i
$78$	−0.957257	+	0.750231i	−0.108388	+	0.0849469i
$79$	3.91758	−	6.78544i	0.440762	−	0.763422i	−0.556984	−	0.830523i	$-0.688042\pi$
$79$	3.91758	−	6.78544i	0.440762	−	0.763422i	0.997746	+	0.0671012i	$0.0213750\pi$
$80$	−3.40112	−	2.58440i	−0.380257	−	0.288944i
$81$	−4.40924	+	7.63702i	−0.489915	+	0.848558i
$82$	−9.96370	+	5.75255i	−1.10031	+	0.635262i
$83$	−4.27763	+	4.27763i	−0.469531	+	0.469531i	−0.901763	−	0.432232i	$-0.857726\pi$
$83$	−4.27763	+	4.27763i	−0.469531	+	0.469531i	0.432232	+	0.901763i	$0.357726\pi$
$84$	−0.921086	+	1.00742i	−0.100499	+	0.109918i
$85$	−5.33792	+	7.02481i	−0.578979	+	0.761948i
$86$	26.0497	−	6.97999i	2.80901	−	0.752672i
$87$	−0.275735			−0.0295619
$88$	−2.55787	+	4.43036i	−0.272670	+	0.472278i
$89$	4.22472	−	4.22472i	0.447820	−	0.447820i	−0.446809	−	0.894629i	$-0.647440\pi$
$89$	4.22472	−	4.22472i	0.447820	−	0.447820i	0.894629	+	0.446809i	$0.147440\pi$
$90$	12.4958	−	9.68228i	1.31717	−	1.02060i
$91$	1.76297	+	9.37507i	0.184810	+	0.982774i
$92$			28.5870i			2.98040i
$93$	0.594602	+	0.594602i	0.0616574	+	0.0616574i
$94$	−24.7136	−	14.2684i	−2.54902	−	1.47168i
$95$	−9.48666	+	7.35067i	−0.973311	+	0.754162i
$96$	0.438942	−	0.117614i	0.0447993	−	0.0120039i
$97$	−3.32657	−	12.4149i	−0.337762	−	1.26054i	−0.900844	−	0.434144i	$-0.857051\pi$
$97$	−3.32657	−	12.4149i	−0.337762	−	1.26054i	0.563082	−	0.826401i	$-0.309616\pi$
$98$	5.71450	+	15.5934i	0.577252	+	1.57517i
$99$	−2.78944	−	2.78944i	−0.280350	−	0.280350i
$100$	−17.4805	+	4.86093i	−1.74805	+	0.486093i
$101$	−8.04553	+	13.9353i	−0.800560	+	1.38661i	0.118688	+	0.992932i	$0.462131\pi$
$101$	−8.04553	+	13.9353i	−0.800560	+	1.38661i	−0.919248	+	0.393679i	$0.871202\pi$
$102$	0.344474	+	1.28559i	0.0341080	+	0.127293i
$103$	−1.65717	−	0.956766i	−0.163286	−	0.0942730i	0.416130	−	0.909305i	$-0.363386\pi$
$103$	−1.65717	−	0.956766i	−0.163286	−	0.0942730i	−0.579416	+	0.815032i	$0.696719\pi$
$104$	−5.19965	+	12.9260i	−0.509868	+	1.26750i
$105$	0.150877	+	0.827497i	0.0147241	+	0.0807555i
$106$	−24.0380	−	6.44097i	−2.33478	−	0.625602i
$107$		−	0.689874i		−	0.0666926i	−0.999444	−	0.0333463i	$-0.989384\pi$
$107$		−	0.689874i		−	0.0666926i	0.999444	−	0.0333463i	$-0.0106164\pi$
$108$		−	3.08515i		−	0.296869i
$109$	7.25262	+	1.94333i	0.694675	+	0.186138i	0.588844	−	0.808247i	$-0.299583\pi$
$109$	7.25262	+	1.94333i	0.694675	+	0.186138i	0.105831	+	0.994384i	$0.466250\pi$
$110$	2.71824	+	6.47591i	0.259174	+	0.617454i
$111$	−0.362952	−	1.35456i	−0.0344499	−	0.128569i
$112$	−1.08850	+	4.93565i	−0.102853	+	0.466375i
$113$	−0.974496	−	0.562626i	−0.0916729	−	0.0529274i	0.453463	−	0.891275i	$-0.350189\pi$
$113$	−0.974496	−	0.562626i	−0.0916729	−	0.0529274i	−0.545136	+	0.838348i	$0.683522\pi$
$114$			1.81042i			0.169562i
$115$	14.0257	+	10.6577i	1.30791	+	0.993834i
$116$	−6.09461	+	3.51872i	−0.565870	+	0.326705i
$117$	−8.59015	−	6.45275i	−0.794159	−	0.596557i
$118$	−7.76717			−0.715026
$119$	10.1943	+	2.24823i	0.934509	+	0.206095i
$120$	−0.464777	+	1.13720i	−0.0424281	+	0.103812i
$121$	−8.00844	+	4.62367i	−0.728040	+	0.420334i
$122$	−18.4418	−	4.94146i	−1.66964	−	0.447379i
$123$	0.487532	+	0.487532i	0.0439593	+	0.0439593i
$124$	20.7304	+	5.55470i	1.86165	+	0.498827i
$125$	−4.13207	+	10.3887i	−0.369583	+	0.929198i
$126$	−16.6004	−	8.61835i	−1.47888	−	0.767784i
$127$	−0.793923	−	1.37512i	−0.0704493	−	0.122022i	0.828649	−	0.559769i	$-0.189110\pi$
$127$	−0.793923	−	1.37512i	−0.0704493	−	0.122022i	−0.899098	+	0.437747i	$0.855777\pi$
$128$	14.6107	−	14.6107i	1.29141	−	1.29141i
$129$	−0.808084	−	1.39964i	−0.0711478	−	0.123232i
$130$	9.81051	+	16.4202i	0.860438	+	1.44015i
$131$	−9.67416	−	5.58538i	−0.845235	−	0.487997i	0.0138051	−	0.999905i	$-0.495606\pi$
$131$	−9.67416	−	5.58538i	−0.845235	−	0.487997i	−0.859040	+	0.511908i	$0.828939\pi$
$132$	0.659755	+	0.176781i	0.0574243	+	0.0153868i
$133$	12.6028	+	6.54295i	1.09280	+	0.567346i
$134$	−16.4097	−	9.47413i	−1.41758	−	0.818440i
$135$	−1.51368	−	1.15019i	−0.130277	−	0.0989930i
$136$	10.7812	+	10.7812i	0.924477	+	0.924477i
$137$	1.05958	−	1.05958i	0.0905264	−	0.0905264i	−0.660393	−	0.750920i	$-0.729610\pi$
$137$	1.05958	−	1.05958i	0.0905264	−	0.0905264i	0.750920	+	0.660393i	$0.229610\pi$
$138$	2.56682	−	0.687777i	0.218502	−	0.0585474i
$139$	−9.14340	−	5.27894i	−0.775533	−	0.447754i	0.0593118	−	0.998240i	$-0.481109\pi$
$139$	−9.14340	−	5.27894i	−0.775533	−	0.447754i	−0.834845	+	0.550485i	$0.814443\pi$
$140$	13.8948	+	16.3649i	1.17432	+	1.38309i
$141$	−0.442619	+	1.65188i	−0.0372753	+	0.139113i
$142$	3.74714	−	6.49023i	0.314453	−	0.544648i
$143$	3.75696	−	2.94444i	0.314173	−	0.246226i
$144$	−2.84618	−	4.92973i	−0.237182	−	0.410811i
$145$	−0.545763	+	4.30206i	−0.0453232	+	0.357266i
$146$	12.8715	−	7.43138i	1.06526	−	0.615025i
$147$	0.814000	−	0.572648i	0.0671376	−	0.0472312i
$148$	−25.3082	−	25.3082i	−2.08032	−	2.08032i
$149$	−6.15251	−	1.64856i	−0.504034	−	0.135055i	−0.00216223	−	0.999998i	$-0.500688\pi$
$149$	−6.15251	−	1.64856i	−0.504034	−	0.135055i	−0.501871	+	0.864942i	$0.667355\pi$
$150$	0.857026	+	1.45262i	0.0699758	+	0.118606i
$151$	−2.11155	+	7.88041i	−0.171835	+	0.641299i	0.825234	+	0.564792i	$0.191043\pi$
$151$	−2.11155	+	7.88041i	−0.171835	+	0.641299i	−0.997069	+	0.0765070i	$0.975623\pi$
$152$	10.3698	+	17.9610i	0.841102	+	1.45683i
$153$	−10.1821	+	5.87862i	−0.823171	+	0.475258i
$154$	5.60742	−	6.13299i	0.451859	−	0.494210i
$155$	10.4540	−	8.10017i	0.839682	−	0.650621i
$156$	1.84669	+	0.223904i	0.147853	+	0.0179266i
$157$	−8.02109	−	13.8929i	−0.640153	−	1.10878i	−0.985398	−	0.170264i	$-0.945538\pi$
$157$	−8.02109	−	13.8929i	−0.640153	−	1.10878i	0.345246	−	0.938512i	$-0.387796\pi$
$158$	−17.9555	+	4.81116i	−1.42846	+	0.382755i
$159$			1.49136i			0.118273i
$160$	−0.966234	−	7.08123i	−0.0763875	−	0.559820i
$161$	4.48881	−	20.3539i	0.353768	−	1.60411i
$162$	20.2089	−	5.41497i	1.58776	−	0.425440i
$163$	−10.0166	−	2.68393i	−0.784559	−	0.210222i	−0.155765	−	0.987794i	$-0.549784\pi$
$163$	−10.0166	−	2.68393i	−0.784559	−	0.210222i	−0.628794	+	0.777572i	$0.716451\pi$
$164$	16.9975	+	4.55446i	1.32728	+	0.355644i
$165$	0.332702	−	0.257791i	0.0259008	−	0.0200690i
$166$	14.3524			1.11396
$167$	0.581091	−	2.16866i	0.0449661	−	0.167816i	−0.939791	−	0.341749i	$-0.888981\pi$
$167$	0.581091	−	2.16866i	0.0449661	−	0.167816i	0.984758	+	0.173933i	$0.0556475\pi$
$168$	1.45214	−	0.0650063i	0.112035	−	0.00501535i
$169$	9.00216	−	9.37875i	0.692474	−	0.721443i
$170$	20.7398	−	2.82995i	1.59067	−	0.217047i
$171$	−15.4479	+	4.13925i	−1.18133	+	0.316536i
$172$	−35.7224	−	20.6243i	−2.72381	−	1.57259i
$173$	4.04026	−	2.33265i	0.307175	−	0.177348i	−0.338486	−	0.940971i	$-0.609915\pi$
$173$	4.04026	−	2.33265i	0.307175	−	0.177348i	0.645662	+	0.763624i	$0.276582\pi$
$174$	0.462576	+	0.462576i	0.0350678	+	0.0350678i
$175$	13.2094	−	0.716141i	0.998534	−	0.0541352i
$176$	2.44286	−	0.654563i	0.184138	−	0.0493396i
$177$	0.120472	+	0.449609i	0.00905525	+	0.0337947i
$178$	−14.1749			−1.06245
$179$	0.870258	+	0.502444i	0.0650462	+	0.0375544i	0.532170	−	0.846637i	$-0.321377\pi$
$179$	0.870258	+	0.502444i	0.0650462	+	0.0375544i	−0.467124	+	0.884192i	$0.654710\pi$
$180$	−23.9861	−	3.04290i	−1.78782	−	0.226805i
$181$	−8.31035			−0.617704			−0.308852	−	0.951110i	$-0.599945\pi$
$181$	−8.31035			−0.617704			−0.308852	+	0.951110i	$0.599945\pi$
$182$	12.7701	−	18.6853i	0.946585	−	1.38505i
$183$			1.14416i			0.0845788i
$184$	21.5257	−	21.5257i	1.58689	−	1.58689i
$185$	−21.8524	+	2.98176i	−1.60662	+	0.219223i
$186$		−	1.99502i		−	0.146282i
$187$	−1.35196	−	5.04559i	−0.0988652	−	0.368970i
$188$	11.2967	+	42.1600i	0.823900	+	3.07484i
$189$	−0.484439	+	2.19663i	−0.0352378	+	0.159781i
$190$	28.2465	+	3.58337i	2.04921	+	0.259965i
$191$	6.04233	+	10.4656i	0.437208	+	0.757266i	0.997473	−	0.0710475i	$-0.0226342\pi$
$191$	6.04233	+	10.4656i	0.437208	+	0.757266i	−0.560265	+	0.828313i	$0.689301\pi$
$192$	−1.40412	−	0.810670i	−0.101334	−	0.0585051i
$193$	0.405389	+	1.51293i	0.0291805	+	0.108903i	0.978980	−	0.203956i	$-0.0653799\pi$
$193$	0.405389	+	1.51293i	0.0291805	+	0.108903i	−0.949800	+	0.312859i	$0.898713\pi$
$194$	−15.2467	+	26.4081i	−1.09465	+	1.89599i
$195$	0.798330	−	0.822573i	0.0571696	−	0.0589057i
$196$	10.6842	−	23.0450i	0.763159	−	1.64607i
$197$	3.84559	−	14.3519i	0.273987	−	1.02253i	−0.682530	−	0.730857i	$-0.739120\pi$
$197$	3.84559	−	14.3519i	0.273987	−	1.02253i	0.956517	−	0.291676i	$-0.0942128\pi$
$198$			9.35920i			0.665129i
$199$	−6.20500			−0.439860			−0.219930	−	0.975516i	$-0.570583\pi$
$199$	−6.20500			−0.439860			−0.219930	+	0.975516i	$0.570583\pi$
$200$	16.8228	+	9.50238i	1.18955	+	0.671919i
$201$	−0.293896	+	1.09683i	−0.0207298	+	0.0773647i
$202$	36.8752	−	9.88068i	2.59453	−	0.695202i
$203$	4.89187	−	1.54834i	0.343342	−	0.108672i
$204$	1.01784	−	1.76296i	0.0712634	−	0.123432i
$205$	8.57151	−	6.64157i	0.598660	−	0.463867i
$206$	1.17500	+	4.38516i	0.0818662	+	0.305529i
$207$	11.7372	+	20.3295i	0.815795	+	1.41300i
$208$	6.33615	−	2.70088i	0.439333	−	0.187272i
$209$		−	7.10539i		−	0.491490i
$210$	1.13510	−	1.64133i	0.0783296	−	0.113263i
$211$	2.40233	+	4.16095i	0.165383	+	0.286452i	0.936791	−	0.349889i	$-0.113781\pi$
$211$	2.40233	+	4.16095i	0.165383	+	0.286452i	−0.771408	+	0.636341i	$0.780447\pi$
$212$	19.0316	+	32.9638i	1.30710	+	2.26396i
$213$	−0.433812	−	0.116240i	−0.0297243	−	0.00796460i
$214$	−1.15734	+	1.15734i	−0.0791141	+	0.0791141i
$215$	−23.4369	+	9.83752i	−1.59838	+	0.670914i
$216$	−2.32308	+	2.32308i	−0.158066	+	0.158066i
$217$	−13.8878	−	7.21009i	−0.942767	−	0.489453i
$218$	−8.90691	−	15.4272i	−0.603252	−	1.04486i
$219$	−0.629814	−	0.629814i	−0.0425589	−	0.0425589i
$220$	4.06401	−	9.94368i	0.273996	−	0.670403i
$221$	−5.57850	−	13.0869i	−0.375251	−	0.880323i
$222$	−1.66352	+	2.88131i	−0.111648	+	0.193381i
$223$	−0.523927	−	0.140386i	−0.0350847	−	0.00940092i	0.241234	−	0.970467i	$-0.422448\pi$
$223$	−0.523927	−	0.140386i	−0.0350847	−	0.00940092i	−0.276319	+	0.961066i	$0.589115\pi$
$224$	−7.12693	+	4.55141i	−0.476188	+	0.304104i
$225$	−10.4354	+	10.6340i	−0.695691	+	0.708931i
$226$	0.690958	+	2.57869i	0.0459619	+	0.171532i
$227$	3.47290	−	3.47290i	0.230504	−	0.230504i	−0.582399	−	0.812903i	$-0.697886\pi$
$227$	3.47290	−	3.47290i	0.230504	−	0.230504i	0.812903	+	0.582399i	$0.197886\pi$
$228$	1.95802	−	1.95802i	0.129673	−	0.129673i
$229$	−5.28304	−	19.7166i	−0.349113	−	1.30291i	−0.887733	−	0.460359i	$-0.847721\pi$
$229$	−5.28304	−	19.7166i	−0.349113	−	1.30291i	0.538619	−	0.842549i	$-0.318946\pi$
$230$	−5.65028	−	41.4092i	−0.372568	−	2.73044i
$231$	−0.441986	−	0.229464i	−0.0290806	−	0.0150976i
$232$	7.23873	+	1.93961i	0.475246	+	0.127342i
$233$	10.8887	−	18.8598i	0.713342	−	1.23555i	−0.250253	−	0.968181i	$-0.580514\pi$
$233$	10.8887	−	18.8598i	0.713342	−	1.23555i	0.963595	−	0.267365i	$-0.0861529\pi$
$234$	3.58573	+	25.2361i	0.234406	+	1.64974i
$235$	24.8968	+	10.1754i	1.62409	+	0.663768i
$236$	8.40038	+	8.40038i	0.546818	+	0.546818i
$237$	0.556995	+	0.964744i	0.0361807	+	0.0626669i
$238$	−13.3304	−	20.8737i	−0.864081	−	1.35304i
$239$	−2.96286	+	2.96286i	−0.191652	+	0.191652i	−0.796409	−	0.604758i	$-0.793270\pi$
$239$	−2.96286	+	2.96286i	−0.191652	+	0.191652i	0.604758	+	0.796409i	$0.293270\pi$
$240$	0.560001	−	0.235058i	0.0361479	−	0.0151729i
$241$	−1.59282	+	1.59282i	−0.102602	+	0.102602i	−0.756544	−	0.653942i	$-0.773114\pi$
$241$	−1.59282	+	1.59282i	−0.102602	+	0.102602i	0.653942	+	0.756544i	$0.273114\pi$
$242$	21.1918	+	5.67831i	1.36226	+	0.365016i
$243$	−1.90219	−	3.29470i	−0.122026	−	0.211355i
$244$	14.6009	+	25.2895i	0.934728	+	1.61900i
$245$	−7.32339	−	13.8336i	−0.467874	−	0.883795i
$246$		−	1.63578i		−	0.104293i
$247$	−2.72224	−	19.1589i	−0.173212	−	1.21905i
$248$	−11.4271	−	19.7924i	−0.725625	−	1.25682i
$249$	−0.222612	−	0.830799i	−0.0141075	−	0.0526497i
$250$	24.3603	−	10.4963i	1.54068	−	0.663842i
$251$	3.49611	−	6.05545i	0.220673	−	0.382216i	−0.734340	−	0.678782i	$-0.762508\pi$
$251$	3.49611	−	6.05545i	0.220673	−	0.382216i	0.955012	+	0.296566i	$0.0958414\pi$
$252$	8.63274	+	27.2747i	0.543812	+	1.71814i
$253$	−10.0740	+	2.69933i	−0.633348	+	0.169705i
$254$	−0.975014	+	3.63880i	−0.0611778	+	0.228319i
$255$	−0.485498	−	1.15665i	−0.0304031	−	0.0724321i
$256$	−26.2148			−1.63843
$257$			14.3839i			0.897245i	0.893721	+	0.448622i	$0.148085\pi$
$257$			14.3839i			0.897245i	−0.893721	+	0.448622i	$0.851915\pi$
$258$	−0.992405	+	3.70370i	−0.0617844	+	0.230583i
$259$	14.0455	+	21.9934i	0.872742	+	1.36660i
$260$	7.14853	−	28.3691i	0.443333	−	1.75938i
$261$	−2.88944	+	5.00465i	−0.178852	+	0.309780i
$262$	6.85938	+	25.5996i	0.423774	+	1.58155i
$263$	1.18425	+	0.683726i	0.0730239	+	0.0421603i	0.536067	−	0.844175i	$-0.319909\pi$
$263$	1.18425	+	0.683726i	0.0730239	+	0.0421603i	−0.463044	+	0.886336i	$0.653243\pi$
$264$	−0.363674	−	0.629902i	−0.0223826	−	0.0387678i
$265$	23.2684	+	2.95185i	1.42937	+	0.181331i
$266$	−10.1661	−	32.1191i	−0.623322	−	1.96935i
$267$	0.219859	+	0.820524i	0.0134551	+	0.0502152i
$268$	7.50095	+	27.9939i	0.458194	+	1.71000i
$269$		−	4.05887i		−	0.247474i	−0.992315	−	0.123737i	$-0.960512\pi$
$269$		−	4.05887i		−	0.247474i	0.992315	−	0.123737i	$-0.0394879\pi$
$270$	0.609787	+	4.46894i	0.0371105	+	0.271971i
$271$	15.1860	−	15.1860i	0.922484	−	0.922484i	−0.0747203	−	0.997205i	$-0.523806\pi$
$271$	15.1860	−	15.1860i	0.922484	−	0.922484i	0.997205	+	0.0747203i	$0.0238064\pi$
$272$		−	7.53751i		−	0.457029i
$273$	−1.27968	−	0.449391i	−0.0774499	−	0.0271984i
$274$	−3.55514			−0.214774
$275$	−3.36358	−	5.70111i	−0.202831	−	0.343790i
$276$	−3.51992	−	2.03223i	−0.211874	−	0.122326i
$277$	21.7236			1.30525			0.652624	−	0.757682i	$-0.273668\pi$
$277$	21.7236			1.30525			0.652624	+	0.757682i	$0.273668\pi$
$278$	6.48305	+	24.1951i	0.388827	+	1.45112i
$279$	17.0230	−	4.56130i	1.01914	−	0.273078i
$280$	1.85999	−	22.7852i	0.111155	−	1.36167i
$281$	9.21813	+	9.21813i	0.549908	+	0.549908i	0.926414	−	0.376506i	$-0.122875\pi$
$281$	9.21813	+	9.21813i	0.549908	+	0.549908i	−0.376506	+	0.926414i	$0.622875\pi$
$282$	3.51375	−	2.02866i	0.209241	−	0.120805i
$283$	7.41216	+	4.27941i	0.440607	+	0.254385i	0.703855	−	0.710344i	$-0.251460\pi$
$283$	7.41216	+	4.27941i	0.440607	+	0.254385i	−0.263248	+	0.964728i	$0.584794\pi$
$284$	−11.0720	+	2.96672i	−0.657000	+	0.176043i
$285$	−0.230689	−	1.69065i	−0.0136648	−	0.100145i
$286$	−11.2423	−	1.36309i	−0.664773	−	0.0806011i
$287$	−11.3870	−	5.91177i	−0.672156	−	0.348961i
$288$	2.46496	−	9.19937i	0.145249	−	0.542078i
$289$	1.43172			0.0842188
$290$	8.13275	−	6.30160i	0.477572	−	0.370043i
$291$	1.76514	+	0.472967i	0.103474	+	0.0277258i
$292$	−21.9581	−	5.88365i	−1.28500	−	0.344315i
$293$	−21.0442	+	5.63878i	−1.22942	+	0.329421i	−0.814352	−	0.580371i	$-0.802907\pi$
$293$	−21.0442	+	5.63878i	−1.22942	+	0.329421i	−0.415064	+	0.909792i	$0.636241\pi$
$294$	−2.32625	−	0.404893i	−0.135670	−	0.0236139i
$295$	7.25331	−	0.989714i	0.422304	−	0.0576234i
$296$			38.1136i			2.21531i
$297$	1.08720	−	0.291315i	0.0630860	−	0.0169038i
$298$	7.55588	+	13.0872i	0.437700	+	0.758119i
$299$	−26.1294	+	11.1380i	−1.51110	+	0.644129i
$300$	0.644147	−	2.49793i	0.0371899	−	0.144218i
$301$	22.1958	+	20.2937i	1.27934	+	1.16971i
$302$	16.7626	−	9.67790i	0.964580	−	0.556900i
$303$	−1.14390	−	1.98129i	−0.0657154	−	0.113822i
$304$	2.65365	−	9.90356i	0.152197	−	0.568008i
$305$	17.8514	+	2.26464i	1.02217	+	0.129673i
$306$	26.9436	+	7.21951i	1.54026	+	0.412712i
$307$	−19.9482	−	19.9482i	−1.13850	−	1.13850i	−0.988719	−	0.149784i	$-0.952142\pi$
$307$	−19.9482	−	19.9482i	−1.13850	−	1.13850i	−0.149784	−	0.988719i	$-0.547858\pi$
$308$	−12.6975	+	0.568416i	−0.723509	+	0.0323885i
$309$	0.235614	−	0.136032i	0.0134036	−	0.00773857i
$310$	−31.1266	−	3.94875i	−1.76787	−	0.224274i
$311$	−6.08371	−	10.5373i	−0.344976	−	0.597515i	0.640374	−	0.768063i	$-0.278779\pi$
$311$	−6.08371	−	10.5373i	−0.344976	−	0.597515i	−0.985349	+	0.170548i	$0.945446\pi$
$312$	−1.22194	−	1.55913i	−0.0691787	−	0.0882685i
$313$	−0.771888	+	1.33695i	−0.0436297	+	0.0755688i	−0.887016	−	0.461739i	$-0.847225\pi$
$313$	−0.771888	+	1.33695i	−0.0436297	+	0.0755688i	0.843386	+	0.537308i	$0.180559\pi$
$314$	−9.85066	+	36.7632i	−0.555905	+	2.07467i
$315$	16.6003	+	5.93291i	0.935321	+	0.334282i
$316$	24.6227	+	14.2159i	1.38513	+	0.799707i
$317$	7.29647	−	1.95508i	0.409811	−	0.109808i	−0.0480231	−	0.998846i	$-0.515292\pi$
$317$	7.29647	−	1.95508i	0.409811	−	0.109808i	0.457834	+	0.889038i	$0.348625\pi$
$318$	2.50192	−	2.50192i	0.140301	−	0.140301i
$319$	−1.81548	−	1.81548i	−0.101647	−	0.101647i
$320$	−15.4274	+	20.3027i	−0.862416	+	1.13496i
$321$	0.0849443	+	0.0490426i	0.00474113	+	0.00273729i
$322$	−41.6764	+	26.6154i	−2.32253	+	1.48322i
$323$	−20.4552	−	5.48096i	−1.13816	−	0.304969i
$324$	−27.7129	−	16.0000i	−1.53960	−	0.888890i
$325$	−11.2538	−	14.0838i	−0.624247	−	0.781227i
$326$	12.3013	+	21.3065i	0.681307	+	1.18006i
$327$	−0.754866	+	0.754866i	−0.0417442	+	0.0417442i
$328$	−9.36946	−	16.2284i	−0.517342	−	0.896062i
$329$	−1.42319	−	31.7918i	−0.0784627	−	1.75274i
$330$	−0.990617	−	0.125671i	−0.0545317	−	0.00691794i
$331$	8.94160	+	2.39589i	0.491475	+	0.131690i	0.496041	−	0.868299i	$-0.334787\pi$
$331$	8.94160	+	2.39589i	0.491475	+	0.131690i	−0.00456592	+	0.999990i	$0.501453\pi$
$332$	−15.5224	−	15.5224i	−0.851905	−	0.851905i
$333$	−28.3889	−	7.60678i	−1.55570	−	0.416849i
$334$	−4.61301	+	2.66332i	−0.252413	+	0.145730i
$335$	16.5313	+	6.75637i	0.903199	+	0.369140i
$336$	−0.530347	−	0.484898i	−0.0289328	−	0.0264534i
$337$	−14.2062			−0.773861			−0.386931	−	0.922109i	$-0.626465\pi$
$337$	−14.2062			−0.773861			−0.386931	+	0.922109i	$0.626465\pi$
$338$	−30.8360	+	0.631772i	−1.67726	+	0.0343639i
$339$	0.138552	−	0.0799933i	0.00752514	−	0.00434464i
$340$	−25.4913	−	19.3700i	−1.38246	−	1.05048i
$341$			7.82988i			0.424012i
$342$	32.8596	+	18.9715i	1.77684	+	1.02586i
$343$	−11.2257	+	14.7303i	−0.606133	+	0.795363i
$344$	11.3687	+	42.4284i	0.612957	+	2.28759i
$345$	−2.30936	+	0.969345i	−0.124332	+	0.0521878i
$346$	−10.6912	−	2.86471i	−0.574765	−	0.154008i
$347$		−	32.5405i		−	1.74686i	−0.486947	−	0.873432i	$-0.661889\pi$
$347$		−	32.5405i		−	1.74686i	0.486947	−	0.873432i	$-0.338111\pi$
$348$		−	1.00057i		−	0.0536364i
$349$	−15.6128	−	4.18344i	−0.835735	−	0.223934i	−0.184521	−	0.982829i	$-0.559073\pi$
$349$	−15.6128	−	4.18344i	−0.835735	−	0.223934i	−0.651214	+	0.758894i	$0.725740\pi$
$350$	−23.3616	−	20.9587i	−1.24873	−	1.12029i
$351$	2.81992	−	1.20203i	0.150516	−	0.0641599i
$352$	3.66444	+	2.11567i	0.195315	+	0.112765i
$353$	4.93232	+	18.4077i	0.262521	+	0.979742i	0.963750	+	0.266806i	$0.0859683\pi$
$353$	4.93232	+	18.4077i	0.262521	+	0.979742i	−0.701229	+	0.712936i	$0.747365\pi$
$354$	0.552162	−	0.956373i	0.0293471	−	0.0508307i
$355$	−2.67223	+	6.53832i	−0.141827	+	0.347018i
$356$	15.3305	+	15.3305i	0.812513	+	0.812513i
$357$	−1.00153	+	1.09540i	−0.0530065	+	0.0579747i
$358$	−0.617049	−	2.30286i	−0.0326121	−	0.121710i
$359$	10.4153	−	2.79078i	0.549700	−	0.147292i	0.0267301	−	0.999643i	$-0.491491\pi$
$359$	10.4153	−	2.79078i	0.549700	−	0.147292i	0.522970	+	0.852351i	$0.324824\pi$
$360$	15.7700	+	20.3525i	0.831152	+	1.07267i
$361$	−8.49209	−	4.90291i	−0.446952	−	0.258048i
$362$	13.9415	+	13.9415i	0.732751	+	0.732751i
$363$		−	1.31477i		−	0.0690078i
$364$	−34.0198	+	6.39739i	−1.78312	+	0.335314i
$365$	−11.0730	+	8.57986i	−0.579590	+	0.449090i
$366$	1.91946	−	1.91946i	0.100332	−	0.100332i
$367$	3.49665	−	6.05637i	0.182523	−	0.316140i	−0.760216	−	0.649671i	$-0.774907\pi$
$367$	3.49665	−	6.05637i	0.182523	−	0.316140i	0.942739	+	0.333531i	$0.108240\pi$
$368$	−15.0494			−0.784504
$369$	13.9577	−	3.73995i	0.726607	−	0.194694i
$370$	41.6620	+	31.6575i	2.16590	+	1.64580i
$371$	−8.37444	−	26.4586i	−0.434779	−	1.37366i
$372$	−2.15766	+	2.15766i	−0.111870	+	0.111870i
$373$	0.249644	−	0.144132i	0.0129261	−	0.00746288i	−0.493523	−	0.869733i	$-0.664291\pi$
$373$	0.249644	−	0.144132i	0.0129261	−	0.00746288i	0.506449	+	0.862270i	$0.330958\pi$
$374$	−6.19647	+	10.7326i	−0.320412	+	0.554969i
$375$	−0.985423	−	1.24731i	−0.0508870	−	0.0644108i
$376$	23.2397	−	40.2523i	1.19850	−	2.07586i
$377$	−5.59080	−	4.19969i	−0.287941	−	0.216295i
$378$	4.49778	−	2.87238i	0.231341	−	0.147739i
$379$	33.6199	+	9.00843i	1.72694	+	0.462732i	0.979474	−	0.201570i	$-0.0646045\pi$
$379$	33.6199	+	9.00843i	1.72694	+	0.462732i	0.747464	+	0.664302i	$0.231271\pi$
$380$	−26.6737	−	34.4247i	−1.36833	−	1.76595i
$381$	0.225758			0.0115659
$382$	7.42056	−	27.6939i	0.379669	−	1.41694i
$383$	−20.3678	−	5.45752i	−1.04074	−	0.278866i	−0.302322	−	0.953206i	$-0.597762\pi$
$383$	−20.3678	−	5.45752i	−1.04074	−	0.278866i	−0.738422	+	0.674339i	$0.764429\pi$
$384$	0.760352	+	2.83767i	0.0388016	+	0.144809i
$385$	−4.45496	+	6.44175i	−0.227046	+	0.328302i
$386$	1.85802	−	3.21819i	0.0945710	−	0.163802i
$387$	−33.8717			−1.72180
$388$	45.0507	−	12.0713i	2.28710	−	0.612827i
$389$	−28.2809	+	16.3280i	−1.43390	+	0.827861i	−0.997415	−	0.0718525i	$-0.977109\pi$
$389$	−28.2809	+	16.3280i	−1.43390	+	0.827861i	−0.436482	+	0.899713i	$0.643776\pi$
$390$	−2.71924	+	0.0406706i	−0.137694	+	0.00205943i
$391$			31.0836i			1.57197i
$392$	−25.3977	+	9.30750i	−1.28278	+	0.470099i
$393$	1.37546	−	0.794121i	0.0693827	−	0.0400581i
$394$	−30.5284	+	17.6256i	−1.53800	+	0.887962i
$395$	16.1545	−	6.78080i	0.812823	−	0.341179i
$396$	10.1222	−	10.1222i	0.508660	−	0.508660i
$397$	−0.692844	+	2.58573i	−0.0347729	+	0.129774i	−0.981130	−	0.193347i	$-0.938066\pi$
$397$	−0.692844	+	2.58573i	−0.0347729	+	0.129774i	0.946358	+	0.323121i	$0.104732\pi$
$398$	10.4096	+	10.4096i	0.521784	+	0.521784i
$399$	−1.70156	+	1.08665i	−0.0851845	+	0.0544006i
$400$	−2.55900	−	9.20246i	−0.127950	−	0.460123i
$401$	12.8634	+	12.8634i	0.642367	+	0.642367i	0.951137	−	0.308770i	$-0.0999173\pi$
$401$	12.8634	+	12.8634i	0.642367	+	0.642367i	−0.308770	+	0.951137i	$0.599917\pi$
$402$	2.33310	−	1.34702i	0.116365	−	0.0671831i
$403$	2.99981	+	21.1125i	0.149431	+	1.05169i
$404$	−50.5676	−	29.1952i	−2.51583	−	1.45252i
$405$	−18.1819	+	7.63180i	−0.903468	+	0.379227i
$406$	−10.8042	−	5.60916i	−0.536201	−	0.278378i
$407$	6.52886	−	11.3083i	0.323623	−	0.560532i
$408$	−2.09391	+	0.561062i	−0.103664	+	0.0277767i
$409$	−4.78480	−	4.78480i	−0.236593	−	0.236593i	0.578845	−	0.815438i	$-0.303504\pi$
$409$	−4.78480	−	4.78480i	−0.236593	−	0.236593i	−0.815438	+	0.578845i	$0.803504\pi$
$410$	−25.5216	−	3.23770i	−1.26042	−	0.159898i
$411$	0.0551418	+	0.205792i	0.00271994	+	0.0101510i
$412$	3.47187	−	6.01345i	0.171047	−	0.296261i
$413$	−4.66201	−	7.30011i	−0.229403	−	0.359215i
$414$	14.4145	−	53.7955i	0.708432	−	2.64390i
$415$	−13.4029	+	1.82882i	−0.657920	+	0.0897732i
$416$	10.6913	+	4.30074i	0.524186	+	0.210861i
$417$	1.29999	−	0.750552i	0.0636610	−	0.0367547i
$418$	−11.9201	+	11.9201i	−0.583030	+	0.583030i
$419$	13.1110	−	7.56962i	0.640512	−	0.369800i	−0.144299	−	0.989534i	$-0.546093\pi$
$419$	13.1110	−	7.56962i	0.640512	−	0.369800i	0.784812	+	0.619734i	$0.212760\pi$
$420$	−3.00278	+	0.547496i	−0.146521	+	0.0267151i
$421$	−14.9807	+	14.9807i	−0.730117	+	0.730117i	−0.970643	−	0.240526i	$-0.922680\pi$
$421$	−14.9807	+	14.9807i	−0.730117	+	0.730117i	0.240526	+	0.970643i	$0.422680\pi$
$422$	2.95029	−	11.0106i	0.143618	−	0.535989i
$423$	25.3437	+	25.3437i	1.23225	+	1.23225i
$424$	10.4907	−	39.1519i	0.509475	−	1.90139i
$425$	−19.0071	+	5.28545i	−0.921981	+	0.256382i
$426$	0.532763	+	0.922772i	0.0258124	+	0.0447084i
$427$	−6.42481	−	20.2988i	−0.310918	−	0.982328i
$428$	2.50338			0.121005
$429$	0.0954702	+	0.671913i	0.00460934	+	0.0324403i
$430$	55.8214	+	22.8144i	2.69195	+	1.10021i
$431$	−6.19117	−	23.1058i	−0.298218	−	1.11296i	−0.938628	−	0.344931i	$-0.887902\pi$
$431$	−6.19117	−	23.1058i	−0.298218	−	1.11296i	0.640410	−	0.768033i	$-0.278765\pi$
$432$	1.62415			0.0781421
$433$	12.2230	+	7.05694i	0.587399	+	0.339135i	0.764068	−	0.645135i	$-0.223199\pi$
$433$	12.2230	+	7.05694i	0.587399	+	0.339135i	−0.176669	+	0.984270i	$0.556532\pi$
$434$	11.2026	+	35.3941i	0.537744	+	1.69897i
$435$	−0.490915	−	0.373030i	−0.0235376	−	0.0178854i
$436$	−7.05187	+	26.3179i	−0.337723	+	1.26040i
$437$	−10.9433	+	40.8409i	−0.523488	+	1.95368i
$438$			2.11317i			0.100971i
$439$	17.0543			0.813956			0.406978	−	0.913438i	$-0.366583\pi$
$439$	17.0543			0.813956			0.406978	+	0.913438i	$0.366583\pi$
$440$	−10.5476	+	4.42733i	−0.502839	+	0.211064i
$441$	−1.86376	−	20.7751i	−0.0887506	−	0.989289i
$442$	−12.5962	+	31.3133i	−0.599141	+	1.48942i
$443$	18.5627	+	10.7172i	0.881943	+	0.509190i	0.871298	−	0.490754i	$-0.163278\pi$
$443$	18.5627	+	10.7172i	0.881943	+	0.509190i	0.0106442	+	0.999943i	$0.496612\pi$
$444$	4.91535	−	1.31706i	0.233272	−	0.0625051i
$445$	13.2371	−	1.80620i	0.627498	−	0.0856222i
$446$	0.643432	+	1.11446i	0.0304674	+	0.0527711i
$447$	0.640365	−	0.640365i	0.0302882	−	0.0302882i
$448$	29.4630	+	6.49771i	1.39200	+	0.306988i
$449$	29.5420	−	7.91576i	1.39417	−	0.373568i	0.517925	−	0.855426i	$-0.326705\pi$
$449$	29.5420	−	7.91576i	1.39417	−	0.373568i	0.876249	+	0.481858i	$0.160038\pi$
$450$	35.3461	−	0.333170i	1.66623	−	0.0157058i
$451$			6.41995i			0.302304i
$452$	2.04163	−	3.53620i	0.0960301	−	0.166329i
$453$	−0.820208	−	0.820208i	−0.0385367	−	0.0385367i
$454$	−11.6523			−0.546871
$455$	−9.54435	+	19.0763i	−0.447446	+	0.894311i
$456$	−2.94873			−0.138087
$457$	7.89270	+	7.89270i	0.369205	+	0.369205i	0.867187	−	0.497982i	$-0.165926\pi$
$457$	7.89270	+	7.89270i	0.369205	+	0.369205i	−0.497982	+	0.867187i	$0.665926\pi$
$458$	−24.2139	+	41.9396i	−1.13144	+	1.95971i
$459$		−	3.35459i		−	0.156579i
$460$	−38.6741	+	50.8959i	−1.80319	+	2.37303i
$461$	5.42151	−	1.45269i	0.252505	−	0.0676585i	−0.130346	−	0.991469i	$-0.541609\pi$
$461$	5.42151	−	1.45269i	0.252505	−	0.0676585i	0.382851	+	0.923810i	$0.374942\pi$
$462$	0.356529	+	1.12643i	0.0165872	+	0.0524064i
$463$	17.2134	−	17.2134i	0.799973	−	0.799973i	−0.183118	−	0.983091i	$-0.558619\pi$
$463$	17.2134	−	17.2134i	0.799973	−	0.799973i	0.983091	+	0.183118i	$0.0586192\pi$
$464$	−1.85240	−	3.20846i	−0.0859957	−	0.148949i
$465$	0.254211	+	1.86303i	0.0117888	+	0.0863961i
$466$	−49.9064	+	13.3724i	−2.31187	+	0.619463i
$467$	12.4376	+	7.18085i	0.575544	+	0.332290i	0.759360	−	0.650670i	$-0.225512\pi$
$467$	12.4376	+	7.18085i	0.575544	+	0.332290i	−0.183817	+	0.982961i	$0.558845\pi$
$468$	23.4154	−	31.1715i	1.08238	−	1.44090i
$469$	−0.944984	−	21.1095i	−0.0436353	−	0.974745i
$470$	−24.6967	−	58.8373i	−1.13918	−	2.71396i
$471$	2.28085			0.105096
$472$		−	12.6508i		−	0.582299i
$473$	3.89490	−	14.5360i	0.179088	−	0.668365i
$474$	0.684043	−	2.55288i	0.0314192	−	0.117258i
$475$	−26.8343	+	0.252939i	−1.23124	+	0.0116056i
$476$	−8.15825	+	36.9925i	−0.373933	+	1.69555i
$477$	27.0685	+	15.6280i	1.23938	+	0.715558i
$478$	9.94106			0.454694
$479$	1.59640	+	5.95784i	0.0729413	+	0.272221i	0.992759	−	0.120126i	$-0.0383300\pi$
$479$	1.59640	+	5.95784i	0.0729413	+	0.272221i	−0.919817	+	0.392347i	$0.871663\pi$
$480$	0.940602	+	0.384427i	0.0429324	+	0.0175466i
$481$	13.2719	−	32.9930i	0.605147	−	1.50435i
$482$	5.34424			0.243424
$483$	2.18707	+	1.99965i	0.0995153	+	0.0909873i
$484$	−16.7782	−	29.0606i	−0.762644	−	1.32094i
$485$	10.8730	−	26.6038i	0.493719	−	1.20801i
$486$	−2.33608	+	8.71836i	−0.105967	+	0.395473i
$487$	−25.7987	−	25.7987i	−1.16905	−	1.16905i	−0.982433	−	0.186616i	$-0.940248\pi$
$487$	−25.7987	−	25.7987i	−1.16905	−	1.16905i	−0.186616	−	0.982433i	$-0.559752\pi$
$488$	8.04841	−	30.0371i	0.364334	−	1.35971i
$489$	1.04254	−	1.04254i	0.0471455	−	0.0471455i
$490$	−10.9216	+	35.4931i	−0.493386	+	1.60342i
$491$	−1.47362	+	0.850792i	−0.0665033	+	0.0383957i	−0.532883	−	0.846189i	$-0.678891\pi$
$491$	−1.47362	+	0.850792i	−0.0665033	+	0.0383957i	0.466380	+	0.884585i	$0.345558\pi$
$492$	−1.76913	+	1.76913i	−0.0797586	+	0.0797586i
$493$	−6.62688	+	3.82603i	−0.298460	+	0.172316i
$494$	−27.5744	+	36.7081i	−1.24063	+	1.65157i
$495$	−1.19257	−	8.74001i	−0.0536022	−	0.392834i
$496$	−2.92423	+	10.9134i	−0.131302	+	0.490025i
$497$	8.34907	−	0.373753i	0.374507	−	0.0167651i
$498$	−1.02030	+	1.76721i	−0.0457208	+	0.0791907i
$499$	−1.19067	−	4.44363i	−0.0533016	−	0.198924i	0.934141	−	0.356905i	$-0.116168\pi$
$499$	−1.19067	−	4.44363i	−0.0533016	−	0.198924i	−0.987442	+	0.157981i	$0.949501\pi$
$500$	−37.6982	−	14.9942i	−1.68591	−	0.670563i
$501$	0.225718	+	0.225718i	0.0100843	+	0.0100843i
$502$	−16.0238	+	4.29356i	−0.715177	+	0.191631i
$503$	16.5218	−	28.6166i	0.736669	−	1.27595i	−0.217318	−	0.976101i	$-0.569731\pi$
$503$	16.5218	−	28.6166i	0.736669	−	1.27595i	0.953987	−	0.299848i	$-0.0969360\pi$
$504$	14.0371	−	27.0379i	0.625264	−	1.20436i
$505$	−33.1766	+	13.9257i	−1.47634	+	0.619687i
$506$	21.4287	+	12.3719i	0.952622	+	0.549996i
$507$	0.514851	+	1.77517i	0.0228653	+	0.0788379i
$508$	4.98995	−	2.88095i	0.221393	−	0.127821i
$509$	−12.7856	−	12.7856i	−0.566712	−	0.566712i	0.364494	−	0.931206i	$-0.381242\pi$
$509$	−12.7856	−	12.7856i	−0.566712	−	0.566712i	−0.931206	+	0.364494i	$0.881242\pi$
$510$	−1.12593	+	2.75488i	−0.0498569	+	0.121988i
$511$	14.7103	+	7.63707i	0.650744	+	0.337844i
$512$	14.7570	+	14.7570i	0.652172	+	0.652172i
$513$	1.18102	−	4.40761i	0.0521431	−	0.194601i
$514$	24.1306	−	24.1306i	1.06436	−	1.06436i
$515$	−1.65603	−	3.94532i	−0.0729736	−	0.173852i
$516$	5.07895	−	2.93234i	0.223588	−	0.129089i
$517$	−13.7905	+	7.96192i	−0.606504	+	0.350165i
$518$	13.3335	−	60.4591i	0.585842	−	2.65642i
$519$			0.663304i			0.0291158i
$520$	−26.7444	+	15.9789i	−1.17282	+	0.700720i
$521$	24.9926	−	14.4295i	1.09495	−	0.632167i	0.160057	−	0.987108i	$-0.448832\pi$
$521$	24.9926	−	14.4295i	1.09495	−	0.632167i	0.934889	+	0.354941i	$0.115499\pi$
$522$	13.2432	−	3.54850i	0.579639	−	0.155314i
$523$	34.1834			1.49474			0.747368	−	0.664411i	$-0.231317\pi$
$523$	34.1834			1.49474			0.747368	+	0.664411i	$0.231317\pi$
$524$	20.2679	−	35.1051i	0.885409	−	1.53357i
$525$	−0.850865	+	1.67738i	−0.0371348	+	0.0732069i
$526$	−0.839681	−	3.13373i	−0.0366118	−	0.136637i
$527$	22.5409	+	6.03982i	0.981898	+	0.263099i
$528$	−0.0930648	+	0.347323i	−0.00405013	+	0.0151153i
$529$	39.0615			1.69833
$530$	−34.0833	−	43.9874i	−1.48048	−	1.91069i
$531$	9.42292	+	2.52486i	0.408920	+	0.109570i
$532$	−23.7427	+	45.7324i	−1.02938	+	1.98275i
$533$	2.45963	+	17.3107i	0.106538	+	0.749811i
$534$	1.00768	−	1.74536i	0.0436067	−	0.0755289i
$535$	0.933300	−	1.22824i	0.0403501	−	0.0531016i
$536$	15.4310	−	26.7272i	0.666517	−	1.15444i
$537$	−0.123732	+	0.0714367i	−0.00533943	+	0.00308272i
$538$	−6.80920	+	6.80920i	−0.293566	+	0.293566i
$539$	9.12988	+	1.58909i	0.393252	+	0.0684470i
$540$	4.17377	−	5.49277i	0.179610	−	0.236371i
$541$	13.2816	−	3.55879i	0.571020	−	0.153004i	0.0382555	−	0.999268i	$-0.487820\pi$
$541$	13.2816	−	3.55879i	0.571020	−	0.153004i	0.532764	+	0.846264i	$0.321153\pi$
$542$	−50.9524			−2.18859
$543$	0.590777	−	1.02326i	0.0253527	−	0.0439121i
$544$	8.91733	−	8.91733i	0.382327	−	0.382327i
$545$	10.2834	+	13.2716i	0.440493	+	0.568494i
$546$	1.39290	+	2.90071i	0.0596108	+	0.124139i
$547$			11.6333i			0.497405i	0.968580	+	0.248703i	$0.0800042\pi$
$547$			11.6333i			0.497405i	−0.968580	+	0.248703i	$0.919996\pi$
$548$	3.84497	+	3.84497i	0.164249	+	0.164249i
$549$	20.7668	+	11.9897i	0.886304	+	0.511708i
$550$	−3.92146	+	15.2070i	−0.167212	+	0.648429i
$551$	−10.0541	+	2.69398i	−0.428318	+	0.114767i
$552$	1.12022	+	4.18070i	0.0476796	+	0.177943i
$553$	−15.2991	−	13.9880i	−0.650584	−	0.594832i
$554$	−36.4438	−	36.4438i	−1.54835	−	1.54835i
$555$	1.18632	−	2.90266i	0.0503567	−	0.123211i
$556$	19.1560	−	33.1791i	0.812394	−	1.40711i
$557$	8.01072	+	29.8964i	0.339425	+	1.26675i	0.898992	+	0.437966i	$0.144301\pi$
$557$	8.01072	+	29.8964i	0.339425	+	1.26675i	−0.559567	+	0.828785i	$0.689032\pi$
$558$	−36.2100	−	20.9059i	−1.53289	−	0.885016i
$559$	4.93313	−	40.6870i	0.208649	−	1.72088i
$560$	−8.61517	+	7.31478i	−0.364057	+	0.309106i
$561$	0.717374	+	0.192220i	0.0302876	+	0.00811553i
$562$		−	30.9289i		−	1.30466i
$563$		−	34.4967i		−	1.45386i	−0.686710	−	0.726932i	$-0.740946\pi$
$563$		−	34.4967i		−	1.45386i	0.686710	−	0.726932i	$-0.259054\pi$
$564$	−5.99425	−	1.60615i	−0.252404	−	0.0676313i
$565$	−0.973829	−	2.32005i	−0.0409693	−	0.0976050i
$566$	−5.25553	−	19.6139i	−0.220906	−	0.824433i
$567$	17.2192	+	15.7436i	0.723137	+	0.661167i
$568$	10.5710	+	6.10315i	0.443548	+	0.256083i
$569$		−	11.6109i		−	0.486755i	−0.969932	−	0.243377i	$-0.921745\pi$
$569$		−	11.6109i		−	0.486755i	0.969932	−	0.243377i	$-0.0782554\pi$
$570$	−2.44924	+	3.22325i	−0.102587	+	0.135007i
$571$	14.6159	−	8.43850i	0.611657	−	0.353140i	−0.161957	−	0.986798i	$-0.551781\pi$
$571$	14.6159	−	8.43850i	0.611657	−	0.353140i	0.773614	+	0.633658i	$0.218447\pi$
$572$	10.6846	+	13.6331i	0.446747	+	0.570027i
$573$	−1.71818			−0.0717779
$574$	9.18537	+	29.0207i	0.383390	+	1.21130i
$575$	10.5529	+	37.9496i	0.440088	+	1.58261i
$576$	−29.4277	+	16.9901i	−1.22615	+	0.707920i
$577$	−23.8297	−	6.38515i	−0.992043	−	0.265817i	−0.273935	−	0.961748i	$-0.588325\pi$
$577$	−23.8297	−	6.38515i	−0.992043	−	0.265817i	−0.718109	+	0.695931i	$0.754992\pi$
$578$	−2.40187	−	2.40187i	−0.0999045	−	0.0999045i
$579$	−0.215106	−	0.0576376i	−0.00893951	−	0.00239534i
$580$	−15.6111	−	1.98044i	−0.648215	−	0.0822332i
$581$	8.61459	+	13.4893i	0.357393	+	0.559632i
$582$	−2.16776	−	3.75466i	−0.0898564	−	0.155636i
$583$	−9.81933	+	9.81933i	−0.406675	+	0.406675i
$584$	12.1039	+	20.9645i	0.500861	+	0.867517i
$585$	−6.56415	−	23.1096i	−0.271394	−	0.955465i
$586$	44.7636	+	25.8443i	1.84917	+	1.06762i
$587$	1.42738	+	0.382466i	0.0589144	+	0.0157861i	0.288156	−	0.957584i	$-0.406958\pi$
$587$	1.42738	+	0.382466i	0.0589144	+	0.0157861i	−0.229241	+	0.973370i	$0.573625\pi$
$588$	2.07800	+	2.95380i	0.0856952	+	0.121813i
$589$	27.4902	+	15.8715i	1.13271	+	0.653973i
$590$	−13.8286	−	10.5079i	−0.569313	−	0.432602i
$591$	1.49378	+	1.49378i	0.0614458	+	0.0614458i
$592$	13.3233	−	13.3233i	0.547585	−	0.547585i
$593$	−6.23671	+	1.67112i	−0.256111	+	0.0686247i	−0.384590	−	0.923087i	$-0.625657\pi$
$593$	−6.23671	+	1.67112i	−0.256111	+	0.0686247i	0.128479	+	0.991712i	$0.458991\pi$
$594$	−2.31262	−	1.33519i	−0.0948879	−	0.0547835i
$595$	15.1082	+	17.7941i	0.619378	+	0.729488i
$596$	5.98222	−	22.3259i	0.245041	−	0.914506i
$597$	0.441109	−	0.764022i	0.0180534	−	0.0312694i
$598$	62.5202	+	25.1496i	2.55664	+	1.02844i
$599$	1.86703	+	3.23379i	0.0762847	+	0.132129i	0.901644	−	0.432479i	$-0.142361\pi$
$599$	1.86703	+	3.23379i	0.0762847	+	0.132129i	−0.825359	+	0.564608i	$0.809028\pi$
$600$	−2.36595	+	1.39588i	−0.0965896	+	0.0569866i
$601$	−33.9624	+	19.6082i	−1.38536	+	0.799836i	−0.992788	−	0.119887i	$-0.961747\pi$
$601$	−33.9624	+	19.6082i	−1.38536	+	0.799836i	−0.392569	+	0.919723i	$0.628413\pi$
$602$	−3.19095	−	71.2808i	−0.130053	−	2.90519i
$603$	16.8280	+	16.8280i	0.685290	+	0.685290i
$604$	−28.5960	−	7.66228i	−1.16356	−	0.311774i
$605$	−20.5133	−	2.60234i	−0.833984	−	0.105800i
$606$	−1.40482	+	5.24286i	−0.0570669	+	0.212977i
$607$	15.6134	+	27.0432i	0.633728	+	1.09765i	0.986783	+	0.162046i	$0.0518094\pi$
$607$	15.6134	+	27.0432i	0.633728	+	1.09765i	−0.353055	+	0.935602i	$0.614857\pi$
$608$	14.8559	−	8.57708i	0.602488	−	0.347847i
$609$	−0.157113	+	0.712408i	−0.00636654	+	0.0288682i
$610$	−26.1484	−	33.7468i	−1.05872	−	1.36637i
$611$	−34.1341	+	26.7519i	−1.38092	+	1.08227i
$612$	−21.3320	−	36.9482i	−0.862297	−	1.49354i
$613$	22.8357	−	6.11880i	0.922325	−	0.247136i	0.233746	−	0.972298i	$-0.424902\pi$
$613$	22.8357	−	6.11880i	0.922325	−	0.247136i	0.688579	+	0.725162i	$0.258235\pi$
$614$			66.9306i			2.70110i
$615$	0.208435	+	1.52756i	0.00840491	+	0.0615970i
$616$	9.98910	+	9.13308i	0.402472	+	0.367982i
$617$	−40.8523	+	10.9463i	−1.64465	+	0.440683i	−0.958108	−	0.286407i	$-0.907539\pi$
$617$	−40.8523	+	10.9463i	−1.64465	+	0.440683i	−0.686543	+	0.727089i	$0.740873\pi$
$618$	−0.623476	−	0.167060i	−0.0250799	−	0.00672013i
$619$	−18.2759	−	4.89702i	−0.734572	−	0.196828i	−0.127907	−	0.991786i	$-0.540826\pi$
$619$	−18.2759	−	4.89702i	−0.734572	−	0.196828i	−0.606664	+	0.794958i	$0.707493\pi$
$620$	29.3935	+	37.9348i	1.18047	+	1.52350i
$621$	−6.69778			−0.268773
$622$	−7.47138	+	27.8836i	−0.299575	+	1.11803i
$623$	−8.50805	−	13.3225i	−0.340868	−	0.533755i
$624$	−0.117872	+	0.972175i	−0.00471867	+	0.0389181i
$625$	−21.4112	+	12.9059i	−0.856446	+	0.516236i
$626$	3.53780	−	0.947952i	0.141399	−	0.0378878i
$627$	0.874888	+	0.505117i	0.0349397	+	0.0201724i
$628$	50.4140	−	29.1065i	2.01174	−	1.16148i
$629$	−27.5185	−	27.5185i	−1.09723	−	1.09723i
$630$	−17.8957	−	37.8019i	−0.712982	−	1.50606i
$631$	−42.7554	+	11.4563i	−1.70207	+	0.456068i	−0.973459	−	0.228863i	$-0.926499\pi$
$631$	−42.7554	+	11.4563i	−1.70207	+	0.456068i	−0.728609	+	0.684930i	$0.759833\pi$
$632$	−7.83617	−	29.2450i	−0.311706	−	1.16330i
$633$	−0.683119			−0.0271515
$634$	−15.5205	−	8.96077i	−0.616398	−	0.355878i
$635$	0.446842	−	3.52230i	0.0177324	−	0.139778i
$636$	−5.41178			−0.214591
$637$	25.2266	+	0.786948i	0.999514	+	0.0311800i
$638$			6.09133i			0.241158i
$639$	−6.65570	+	6.65570i	−0.263295	+	0.263295i
$640$	45.7787	−	6.24651i	1.80956	−	0.246915i
$641$			34.0975i			1.34677i	0.739291	+	0.673386i	$0.235161\pi$
$641$			34.0975i			1.34677i	−0.739291	+	0.673386i	$0.764839\pi$
$642$	−0.0602290	−	0.224778i	−0.00237705	−	0.00887127i
$643$	−1.10015	−	4.10581i	−0.0433856	−	0.161917i	0.940834	−	0.338867i	$-0.110044\pi$
$643$	−1.10015	−	4.10581i	−0.0433856	−	0.161917i	−0.984220	+	0.176950i	$0.943377\pi$
$644$	73.8592	+	16.2888i	2.91046	+	0.641867i
$645$	0.454813	−	3.58513i	0.0179082	−	0.141164i
$646$	25.1210	+	43.5108i	0.988371	+	1.71191i
$647$	5.65801	+	3.26665i	0.222439	+	0.128425i	0.607079	−	0.794641i	$-0.292341\pi$
$647$	5.65801	+	3.26665i	0.222439	+	0.128425i	−0.384640	+	0.923067i	$0.625674\pi$
$648$	8.81963	+	32.9153i	0.346468	+	1.29303i
$649$	−2.16708	+	3.75349i	−0.0850653	+	0.147337i
$650$	−4.74766	+	42.5065i	−0.186218	+	1.66724i
$651$	1.87506	−	1.19745i	0.0734892	−	0.0469318i
$652$	9.73932	−	36.3477i	0.381421	−	1.42348i
$653$			13.7278i			0.537211i	0.963250	+	0.268605i	$0.0865628\pi$
$653$			13.7278i			0.537211i	−0.963250	+	0.268605i	$0.913437\pi$
$654$	2.53274			0.0990380
$655$	−9.66754	−	23.0319i	−0.377742	−	0.899930i
$656$	−2.39766	+	8.94820i	−0.0936130	+	0.349368i
$657$	−18.0311	+	4.83142i	−0.703460	+	0.188492i
$658$	−50.9466	+	55.7217i	−1.98611	+	2.17226i
$659$	23.4244	−	40.5722i	0.912485	−	1.58047i	0.101943	−	0.994790i	$-0.467494\pi$
$659$	23.4244	−	40.5722i	0.912485	−	1.58047i	0.810542	−	0.585680i	$-0.199173\pi$
$660$	0.935460	+	1.20729i	0.0364127	+	0.0469938i
$661$	1.06879	+	3.98880i	0.0415713	+	0.155146i	0.983592	−	0.180410i	$-0.0577424\pi$
$661$	1.06879	+	3.98880i	0.0415713	+	0.155146i	−0.942020	+	0.335556i	$0.891076\pi$
$662$	−10.9811	−	19.0199i	−0.426794	−	0.739229i
$663$	2.00797	+	0.243458i	0.0779831	+	0.00945513i
$664$			23.3764i			0.907182i
$665$	13.5862	+	28.6988i	0.526850	+	1.11289i
$666$	34.8643	+	60.3867i	1.35096	+	2.33994i
$667$	7.63905	+	13.2312i	0.295785	+	0.512315i
$668$	7.86952	+	2.10863i	0.304481	+	0.0815855i
$669$	0.0545313	−	0.0545313i	0.00210830	−	0.00210830i
$670$	−16.3984	−	39.0675i	−0.633527	−	1.50931i
$671$	−7.53331	+	7.53331i	−0.290820	+	0.290820i
$672$	−0.0537681	−	1.20110i	−0.00207415	−	0.0463333i
$673$	9.04689	+	15.6697i	0.348732	+	0.604022i	0.986024	−	0.166600i	$-0.0532790\pi$
$673$	9.04689	+	15.6697i	0.348732	+	0.604022i	−0.637292	+	0.770622i	$0.719946\pi$
$674$	23.8325	+	23.8325i	0.917992	+	0.917992i
$675$	−1.13889	−	4.09558i	−0.0438359	−	0.157639i
$676$	34.0332	+	32.6666i	1.30897	+	1.25641i
$677$	13.1510	−	22.7782i	0.505435	−	0.875438i	−0.494546	−	0.869152i	$-0.664666\pi$
$677$	13.1510	−	22.7782i	0.505435	−	0.875438i	0.999980	−	0.00628666i	$-0.00200112\pi$
$678$	−0.366634	−	0.0982394i	−0.0140805	−	0.00377286i
$679$	−33.9715	+	1.52076i	−1.30371	+	0.0583615i
$680$	4.60928	+	33.7800i	0.176758	+	1.29540i
$681$	0.180733	+	0.674504i	0.00692570	+	0.0258471i
$682$	13.1355	−	13.1355i	0.502984	−	0.502984i
$683$	−3.80304	+	3.80304i	−0.145519	+	0.145519i	−0.776113	−	0.630594i	$-0.782811\pi$
$683$	−3.80304	+	3.80304i	−0.145519	+	0.145519i	0.630594	+	0.776113i	$0.282811\pi$
$684$	−15.0203	−	56.0565i	−0.574315	−	2.14337i
$685$	3.31994	−	0.453005i	0.126848	−	0.0173084i
$686$	43.5442	−	5.87932i	1.66252	−	0.224473i
$687$	2.80327	+	0.751135i	0.106952	+	0.0286576i
$688$	10.8575	−	18.8058i	0.413939	−	0.716963i
$689$	−22.7148	+	30.2388i	−0.865364	+	1.15201i
$690$	5.50039	+	2.24803i	0.209396	+	0.0855809i
$691$	−9.44363	−	9.44363i	−0.359253	−	0.359253i	0.504285	−	0.863537i	$-0.331756\pi$
$691$	−9.44363	−	9.44363i	−0.359253	−	0.359253i	−0.863537	+	0.504285i	$0.831756\pi$
$692$	8.46459	+	14.6611i	0.321775	+	0.557331i
$693$	−8.79641	+	5.61758i	−0.334148	+	0.213394i
$694$	−54.5902	+	54.5902i	−2.07222	+	2.07222i
$695$	−9.13714	−	21.7683i	−0.346592	−	0.825718i
$696$	−0.753421	+	0.753421i	−0.0285583	+	0.0285583i
$697$	18.4820	+	4.95223i	0.700054	+	0.187579i
$698$	19.1740	+	33.2104i	0.725748	+	1.25703i
$699$	1.54814	+	2.68146i	0.0585560	+	0.101422i
$700$	2.59870	+	47.9335i	0.0982215	+	1.81171i
$701$		−	2.32063i		−	0.0876491i	−0.999039	−	0.0438246i	$-0.986046\pi$
$701$		−	2.32063i		−	0.0876491i	0.999039	−	0.0438246i	$-0.0139543\pi$
$702$	−6.74728	−	2.71419i	−0.254660	−	0.102440i
$703$	−26.4685	−	45.8448i	−0.998279	−	1.72907i
$704$	−3.90737	−	14.5825i	−0.147264	−	0.549598i
$705$	−3.02279	+	2.34218i	−0.113845	+	0.0882117i
$706$	22.6064	−	39.1554i	0.850803	−	1.47363i
$707$	31.4198	+	28.7272i	1.18166	+	1.08040i
$708$	−1.63152	+	0.437164i	−0.0613162	+	0.0164296i
$709$	1.13231	−	4.22584i	0.0425248	−	0.158705i	−0.941398	−	0.337297i	$-0.890487\pi$
$709$	1.13231	−	4.22584i	0.0425248	−	0.158705i	0.983923	+	0.178592i	$0.0571542\pi$
$710$	15.4517	−	6.48579i	0.579893	−	0.243407i
$711$	23.3471			0.875584
$712$		−	23.0873i		−	0.865234i
$713$	12.0591	−	45.0052i	0.451617	−	1.68546i
$714$	3.51783	−	0.157479i	0.131651	−	0.00589349i
$715$	10.6722	−	0.159620i	0.399119	−	0.00596946i
$716$	−1.82324	+	3.15795i	−0.0681378	+	0.118018i
$717$	−0.154190	−	0.575446i	−0.00575834	−	0.0214904i
$718$	−22.1547	−	12.7910i	−0.826807	−	0.477357i
$719$	7.04187	+	12.1969i	0.262617	+	0.454867i	0.966937	−	0.255017i	$-0.0820810\pi$
$719$	7.04187	+	12.1969i	0.262617	+	0.454867i	−0.704319	+	0.709883i	$0.748748\pi$
$720$	1.60191	−	12.6273i	0.0596997	−	0.470592i
$721$	−3.41621	+	3.73641i	−0.127226	+	0.139151i
$722$	6.02124	+	22.4716i	0.224087	+	0.836306i
$723$	−0.0828916	−	0.309356i	−0.00308277	−	0.0115051i
$724$		−	30.1562i		−	1.12075i
$725$	−6.79174	+	6.92099i	−0.252239	+	0.257039i
$726$	−2.20568	+	2.20568i	−0.0818604	+	0.0818604i
$727$			1.30833i			0.0485232i	0.999706	+	0.0242616i	$0.00772346\pi$
$727$			1.30833i			0.0485232i	−0.999706	+	0.0242616i	$0.992277\pi$
$728$	30.4337	+	20.7993i	1.12795	+	0.770875i
$729$	−25.9145			−0.959797
$730$	32.9699	+	4.18259i	1.22027	+	0.154805i
$731$	−38.8422	−	22.4255i	−1.43663	−	0.829439i
$732$	−4.15188			−0.153458
$733$	1.74119	+	6.49822i	0.0643124	+	0.240017i	0.990598	−	0.136805i	$-0.0436834\pi$
$733$	1.74119	+	6.49822i	0.0643124	+	0.240017i	−0.926286	+	0.376822i	$0.877017\pi$
$734$	−16.0262	+	4.29422i	−0.591539	+	0.158502i
$735$	2.22395	+	0.0816886i	0.0820315	+	0.00301313i
$736$	−17.8043	−	17.8043i	−0.656276	−	0.656276i
$737$	−9.15676	+	5.28666i	−0.337293	+	0.194736i
$738$	−29.6897	−	17.1413i	−1.09289	−	0.630982i
$739$	15.7387	−	4.21716i	0.578956	−	0.155131i	0.0425551	−	0.999094i	$-0.486450\pi$
$739$	15.7387	−	4.21716i	0.578956	−	0.155131i	0.536401	+	0.843963i	$0.319784\pi$
$740$	−10.8200	−	79.2968i	−0.397753	−	2.91501i
$741$	2.55257	+	1.02681i	0.0937709	+	0.0377206i
$742$	−30.3381	+	58.4362i	−1.11375	+	2.14526i
$743$	−2.61079	+	9.74360i	−0.0957806	+	0.357458i	−0.997137	−	0.0756208i	$-0.975906\pi$
$743$	−2.61079	+	9.74360i	−0.0957806	+	0.357458i	0.901356	+	0.433079i	$0.142573\pi$
$744$	3.24939			0.119128
$745$	−8.72359	−	11.2585i	−0.319608	−	0.412481i
$746$	−0.660603	−	0.177008i	−0.0241864	−	0.00648072i
$747$	−17.4119	−	4.66551i	−0.637069	−	0.170702i
$748$	18.3092	−	4.90593i	0.669450	−	0.179379i
$749$	−1.78240	−	0.393088i	−0.0651276	−	0.0143631i
$750$	−0.439346	+	3.74566i	−0.0160426	+	0.136772i
$751$		−	49.1157i		−	1.79226i	−0.443793	−	0.896129i	$-0.646367\pi$
$751$		−	49.1157i		−	1.79226i	0.443793	−	0.896129i	$-0.353633\pi$
$752$	−22.1948	+	5.94708i	−0.809362	+	0.216868i
$753$	0.497072	+	0.860955i	0.0181143	+	0.0313749i
$754$	2.33373	+	16.4246i	0.0849893	+	0.598150i
$755$	−14.4204	+	11.1736i	−0.524813	+	0.406647i
$756$	−7.97100	−	1.75791i	−0.289903	−	0.0639345i
$757$	4.17448	−	2.41014i	0.151724	−	0.0875979i	−0.422216	−	0.906495i	$-0.638748\pi$
$757$	4.17448	−	2.41014i	0.151724	−	0.0875979i	0.573940	+	0.818897i	$0.305414\pi$
$758$	−41.2885	−	71.5137i	−1.49966	−	2.59749i
$759$	0.383786	−	1.43231i	0.0139306	−	0.0519895i
$760$	−5.83642	+	46.0064i	−0.211709	+	1.66883i
$761$	−5.77748	−	1.54807i	−0.209433	−	0.0561175i	0.152577	−	0.988292i	$-0.451243\pi$
$761$	−5.77748	−	1.54807i	−0.209433	−	0.0561175i	−0.362010	+	0.932174i	$0.617909\pi$
$762$	−0.378733	−	0.378733i	−0.0137201	−	0.0137201i
$763$	9.15344	−	17.6310i	0.331377	−	0.638286i
$764$	−37.9771	+	21.9261i	−1.37396	+	0.793258i
$765$	−26.0810	−	3.30865i	−0.942959	−	0.119625i
$766$	25.0136	+	43.3247i	0.903776	+	1.56539i
$767$	−4.40525	+	10.9512i	−0.159064	+	0.395423i
$768$	1.86359	−	3.22784i	0.0672467	−	0.116475i
$769$	−11.1220	+	41.5080i	−0.401071	+	1.49682i	0.410117	+	0.912033i	$0.365488\pi$
$769$	−11.1220	+	41.5080i	−0.401071	+	1.49682i	−0.811188	+	0.584785i	$0.801179\pi$
$770$	18.2804	−	3.33306i	0.658781	−	0.120115i
$771$	−1.77110	−	1.02254i	−0.0637845	−	0.0368260i
$772$	−5.49005	+	1.47105i	−0.197591	+	0.0529444i
$773$	−17.6026	+	17.6026i	−0.633122	+	0.633122i	−0.948850	−	0.315728i	$-0.897751\pi$
$773$	−17.6026	+	17.6026i	−0.633122	+	0.633122i	0.315728	+	0.948850i	$0.397751\pi$
$774$	56.8236	+	56.8236i	2.04248	+	2.04248i
$775$	29.5705	−	0.278729i	1.06220	−	0.0100123i
$776$	−43.0122	−	24.8331i	−1.54405	−	0.891456i
$777$	−3.70653	+	0.165926i	−0.132971	+	0.00595256i
$778$	74.8362	+	20.0523i	2.68301	+	0.718910i
$779$	22.5400	+	13.0135i	0.807581	+	0.466257i
$780$	2.98491	+	2.89694i	0.106877	+	0.103727i
$781$	−2.09094	−	3.62161i	−0.0748197	−	0.129592i
$782$	52.1462	−	52.1462i	1.86474	−	1.86474i
$783$	−0.824418	−	1.42793i	−0.0294623	−	0.0510302i
$784$	12.1318	+	5.62463i	0.433280	+	0.200880i
$785$	4.51450	−	35.5862i	0.161129	−	1.27013i
$786$	−3.63971	−	0.975256i	−0.129824	−	0.0347862i
$787$	−8.80517	−	8.80517i	−0.313870	−	0.313870i	0.532537	−	0.846407i	$-0.321239\pi$
$787$	−8.80517	−	8.80517i	−0.313870	−	0.313870i	−0.846407	+	0.532537i	$0.821239\pi$
$788$	52.0796	+	13.9547i	1.85526	+	0.497115i
$789$	−0.168375	+	0.0972111i	−0.00599429	+	0.00346081i
$790$	−38.4765	−	15.7255i	−1.36893	−	0.559487i
$791$	−2.00890	+	2.19719i	−0.0714283	+	0.0781231i
$792$	−15.2438			−0.541665
$793$	−17.4266	+	23.1990i	−0.618837	+	0.823820i
$794$	5.50017	−	3.17552i	0.195194	−	0.112695i
$795$	−2.01760	+	2.65520i	−0.0715568	+	0.0941703i
$796$		−	22.5164i		−	0.798072i
$797$	−1.85270	−	1.06966i	−0.0656262	−	0.0378893i	0.466828	−	0.884348i	$-0.345397\pi$
$797$	−1.85270	−	1.06966i	−0.0656262	−	0.0378893i	−0.532454	+	0.846459i	$0.678730\pi$
$798$	4.67753	+	1.03157i	0.165583	+	0.0365173i
$799$	12.2833	+	45.8421i	0.434554	+	1.62178i
$800$	7.85962	−	13.9145i	0.277879	−	0.491952i
$801$	17.1966	+	4.60781i	0.607611	+	0.162809i
$802$		−	43.1595i		−	1.52401i
$803$		−	8.29357i		−	0.292674i
$804$	−3.98014	−	1.06647i	−0.140369	−	0.0376117i
$805$	35.5277	−	30.1651i	1.25219	−	1.06318i
$806$	30.3860	−	40.4510i	1.07030	−	1.42483i
$807$	0.499770	+	0.288542i	0.0175927	+	0.0101572i
$808$	16.0932	+	60.0605i	0.566155	+	2.11292i
$809$	10.7646	−	18.6449i	0.378464	−	0.655519i	−0.612375	−	0.790567i	$-0.709786\pi$
$809$	10.7646	−	18.6449i	0.378464	−	0.655519i	0.990839	+	0.135049i	$0.0431191\pi$
$810$	43.3054	+	17.6990i	1.52160	+	0.621881i
$811$	13.1617	+	13.1617i	0.462171	+	0.462171i	0.899366	−	0.437196i	$-0.144028\pi$
$811$	13.1617	+	13.1617i	0.462171	+	0.462171i	−0.437196	+	0.899366i	$0.644028\pi$
$812$	5.61852	+	17.7514i	0.197171	+	0.622952i
$813$	0.790294	+	2.94942i	0.0277168	+	0.103441i
$814$	−29.9238	+	8.01806i	−1.04883	+	0.281033i
$815$	−14.2024	−	18.3294i	−0.497489	−	0.642052i
$816$	0.928095	+	0.535836i	0.0324898	+	0.0187580i
$817$	−43.1398	−	43.1398i	−1.50927	−	1.50927i
$818$			16.0540i			0.561317i
$819$	−21.5664	+	18.5173i	−0.753590	+	0.647048i
$820$	24.1006	+	31.1039i	0.841629	+	1.08619i
$821$	16.0814	−	16.0814i	0.561246	−	0.561246i	−0.368415	−	0.929661i	$-0.620100\pi$
$821$	16.0814	−	16.0814i	0.561246	−	0.561246i	0.929661	+	0.368415i	$0.120100\pi$
$822$	0.252732	−	0.437745i	0.00881504	−	0.0152681i
$823$	−18.4924			−0.644604			−0.322302	−	0.946637i	$-0.604457\pi$
$823$	−18.4924			−0.644604			−0.322302	+	0.946637i	$0.604457\pi$
$824$	−7.14233	+	1.91378i	−0.248815	+	0.0666698i
$825$	0.941093	−	0.00887068i	0.0327646	−	0.000308837i
$826$	−4.42571	+	20.0678i	−0.153990	+	0.698247i
$827$	−11.6185	+	11.6185i	−0.404017	+	0.404017i	−0.879646	−	0.475629i	$-0.842220\pi$
$827$	−11.6185	+	11.6185i	−0.404017	+	0.404017i	0.475629	+	0.879646i	$0.342220\pi$
$828$	−73.7707	+	42.5915i	−2.56371	+	1.48016i
$829$	−6.29543	+	10.9040i	−0.218649	+	0.378712i	−0.954395	−	0.298546i	$-0.903498\pi$
$829$	−6.29543	+	10.9040i	−0.218649	+	0.378712i	0.735746	+	0.677258i	$0.236832\pi$
$830$	25.5528	+	19.4167i	0.886951	+	0.673964i
$831$	−1.54432	+	2.67484i	−0.0535718	+	0.0927891i
$832$	−16.1227	−	37.8232i	−0.558954	−	1.31128i
$833$	11.6173	−	25.0576i	0.402517	−	0.868194i
$834$	−3.44002	−	0.921750i	−0.119118	−	0.0319176i
$835$	3.96845	−	3.07492i	0.137334	−	0.106412i
$836$	25.7837			0.891747
$837$	−1.30144	+	4.85703i	−0.0449843	+	0.167884i
$838$	−34.6939	−	9.29621i	−1.19848	−	0.321132i
$839$	−9.60515	−	35.8469i	−0.331606	−	1.23757i	−0.907502	−	0.420049i	$-0.862013\pi$
$839$	−9.60515	−	35.8469i	−0.331606	−	1.23757i	0.575895	−	0.817524i	$-0.304654\pi$
$840$	2.67332	+	1.84880i	0.0922382	+	0.0637897i
$841$	12.6194	−	21.8575i	0.435153	−	0.753708i
$842$	50.2637			1.73220
$843$	−1.79034	+	0.479720i	−0.0616626	+	0.0165224i
$844$	−15.0991	+	8.71745i	−0.519731	+	0.300067i
$845$	28.7154	−	4.51918i	0.987841	−	0.155465i
$846$		−	85.0337i		−	2.92352i
$847$	7.38285	+	23.3257i	0.253678	+	0.801480i
$848$	−17.3535	+	10.0191i	−0.595922	+	0.344056i
$849$	−1.05385	+	0.608440i	−0.0361680	+	0.0208816i
$850$	40.7535	+	23.0196i	1.39783	+	0.789566i
$851$	−54.9434	+	54.9434i	−1.88344	+	1.88344i
$852$	0.421804	−	1.57420i	0.0144508	−	0.0539310i
$853$	−6.99837	−	6.99837i	−0.239620	−	0.239620i	0.577073	−	0.816693i	$-0.304195\pi$
$853$	−6.99837	−	6.99837i	−0.239620	−	0.239620i	−0.816693	+	0.577073i	$0.804195\pi$
$854$	−23.2752	+	44.8318i	−0.796459	+	1.53411i
$855$	−33.1030	−	13.5293i	−1.13210	−	0.462692i
$856$	−1.88502	−	1.88502i	−0.0644285	−	0.0644285i
$857$	19.5178	−	11.2686i	0.666715	−	0.384928i	−0.128116	−	0.991759i	$-0.540893\pi$
$857$	19.5178	−	11.2686i	0.666715	−	0.384928i	0.794831	+	0.606831i	$0.207560\pi$
$858$	0.967046	−	1.28737i	0.0330144	−	0.0439501i
$859$	−36.0935	−	20.8386i	−1.23150	−	0.711004i	−0.264154	−	0.964481i	$-0.585093\pi$
$859$	−36.0935	−	20.8386i	−1.23150	−	0.711004i	−0.967342	+	0.253476i	$0.918426\pi$
$860$	−35.6979	−	85.0465i	−1.21729	−	2.90006i
$861$	1.53741	−	0.981826i	0.0523949	−	0.0334605i
$862$	−28.3761	+	49.1488i	−0.966493	+	1.67401i
$863$	14.2161	−	3.80919i	0.483922	−	0.129666i	−0.00860634	−	0.999963i	$-0.502740\pi$
$863$	14.2161	−	3.80919i	0.483922	−	0.129666i	0.492528	+	0.870297i	$0.336073\pi$
$864$	1.92147	+	1.92147i	0.0653698	+	0.0653698i
$865$	10.3490	+	1.31288i	0.351875	+	0.0446392i
$866$	−8.66660	−	32.3442i	−0.294503	−	1.09910i
$867$	−0.101780	+	0.176288i	−0.00345663	+	0.00598705i
$868$	26.1636	−	50.3955i	0.888051	−	1.71053i
$869$	−2.68467	+	10.0193i	−0.0910713	+	0.339883i
$870$	0.197766	+	1.44936i	0.00670488	+	0.0491380i
$871$	−22.6648	+	17.7631i	−0.767967	+	0.601879i
$872$	25.1271	−	14.5071i	0.850910	−	0.491273i
$873$	27.0814	−	27.0814i	0.916565	−	0.916565i
$874$	86.8736	−	50.1565i	2.93854	−	1.69657i
$875$	24.4866	+	16.5954i	0.827799	+	0.561025i
$876$	2.28544	−	2.28544i	0.0772178	−	0.0772178i
$877$	7.75725	−	28.9505i	0.261944	−	0.977588i	−0.702151	−	0.712028i	$-0.747777\pi$
$877$	7.75725	−	28.9505i	0.261944	−	0.977588i	0.964095	−	0.265559i	$-0.0855566\pi$
$878$	−28.6104	−	28.6104i	−0.965555	−	0.965555i
$879$	0.801713	−	2.99203i	0.0270411	−	0.100919i
$880$	5.23477	+	2.13947i	0.176464	+	0.0721214i
$881$	−3.17014	−	5.49085i	−0.106805	−	0.184991i	0.807669	−	0.589636i	$-0.200729\pi$
$881$	−3.17014	−	5.49085i	−0.106805	−	0.184991i	−0.914474	+	0.404644i	$0.867395\pi$
$882$	−31.7258	+	37.9791i	−1.06826	+	1.27882i
$883$	−6.13201			−0.206359			−0.103179	−	0.994663i	$-0.532902\pi$
$883$	−6.13201			−0.206359			−0.103179	+	0.994663i	$0.532902\pi$
$884$	47.4892	−	20.2430i	1.59724	−	0.680846i
$885$	−0.393769	+	0.963459i	−0.0132364	+	0.0323863i
$886$	−13.1618	−	49.1203i	−0.442178	−	1.65023i
$887$	18.7791			0.630539			0.315270	−	0.949002i	$-0.397905\pi$
$887$	18.7791			0.630539			0.315270	+	0.949002i	$0.397905\pi$
$888$	−4.69293	−	2.70947i	−0.157485	−	0.0909237i
$889$	−4.00521	+	1.26770i	−0.134331	+	0.0425172i
$890$	−25.2368	−	19.1766i	−0.845939	−	0.642800i
$891$	3.02160	−	11.2768i	0.101228	−	0.377786i
$892$	0.509425	−	1.90120i	0.0170568	−	0.0636568i
$893$			64.5565i			2.16030i
$894$	−2.14857			−0.0718588
$895$	0.869663	+	2.07188i	0.0290696	+	0.0692553i
$896$	−29.4240	−	46.0742i	−0.982985	−	1.53923i
$897$	0.486089	−	4.00911i	0.0162300	−	0.133860i
$898$	−62.8396	−	36.2804i	−2.09698	−	1.21069i
$899$	11.0792	−	2.96867i	0.369513	−	0.0990107i
$900$	−38.5880	−	37.8673i	−1.28627	−	1.26224i
$901$	20.6938	+	35.8426i	0.689409	+	1.19409i
$902$	10.7702	−	10.7702i	0.358608	−	0.358608i
$903$	−4.07665	+	1.29031i	−0.135663	+	0.0429388i
$904$	−4.20004	+	1.12540i	−0.139691	+	0.0374302i
$905$	−14.7956	−	11.2427i	−0.491824	−	0.373720i
$906$			2.75198i			0.0914283i
$907$	23.1567	−	40.1086i	0.768906	−	1.33178i	−0.169251	−	0.985573i	$-0.554135\pi$
$907$	23.1567	−	40.1086i	0.768906	−	1.33178i	0.938157	−	0.346211i	$-0.112532\pi$
$908$	12.6023	+	12.6023i	0.418221	+	0.418221i
$909$	−47.9479			−1.59033
$910$	48.0143	−	15.9909i	1.59166	−	0.530093i
$911$	−27.6521			−0.916156			−0.458078	−	0.888912i	$-0.651462\pi$
$911$	−27.6521			−0.916156			−0.458078	+	0.888912i	$0.651462\pi$
$912$	1.03078	+	1.03078i	0.0341326	+	0.0341326i
$913$	4.00439	−	6.93580i	0.132526	−	0.229541i
$914$		−	26.4817i		−	0.875938i
$915$	−1.54789	+	2.03705i	−0.0511715	+	0.0673428i
$916$	71.5466	−	19.1708i	2.36396	−	0.633422i
$917$	−19.9431	+	21.8123i	−0.658578	+	0.720305i
$918$	−5.62770	+	5.62770i	−0.185742	+	0.185742i
$919$	13.9880	+	24.2279i	0.461420	+	0.799203i	0.999032	−	0.0439893i	$-0.0140067\pi$
$919$	13.9880	+	24.2279i	0.461420	+	0.799203i	−0.537612	+	0.843192i	$0.680673\pi$
$920$	67.4452	−	9.20290i	2.22360	−	0.303410i
$921$	3.87433	−	1.03812i	0.127663	−	0.0342073i
$922$	−11.5322	−	6.65814i	−0.379794	−	0.219274i
$923$	−7.02553	−	8.96422i	−0.231248	−	0.295061i
$924$	0.832669	−	1.60386i	0.0273928	−	0.0527630i
$925$	−42.9396	−	24.2544i	−1.41184	−	0.797481i
$926$	−57.7546			−1.89793
$927$		−	5.70192i		−	0.187275i
$928$	1.60429	−	5.98730i	0.0526635	−	0.196543i
$929$	8.49877	−	31.7178i	0.278836	−	1.04063i	−0.674392	−	0.738374i	$-0.735594\pi$
$929$	8.49877	−	31.7178i	0.278836	−	1.04063i	0.953227	−	0.302255i	$-0.0977394\pi$
$930$	2.69898	−	3.55191i	0.0885029	−	0.116472i
$931$	24.0858	−	28.8333i	0.789381	−	0.944973i
$932$	68.4374	+	39.5124i	2.24174	+	1.29427i
$933$	1.72995			0.0566359
$934$	−8.81877	−	32.9121i	−0.288559	−	1.07692i
$935$	4.41894	−	10.8121i	0.144515	−	0.353594i
$936$	−41.1033	+	5.84025i	−1.34350	+	0.190895i
$937$	43.5318			1.42212			0.711061	−	0.703130i	$-0.248215\pi$
$937$	43.5318			1.42212			0.711061	+	0.703130i	$0.248215\pi$
$938$	−33.8282	+	36.9988i	−1.10453	+	1.20805i
$939$	−0.109746	−	0.190085i	−0.00358142	−	0.00620320i
$940$	−36.9239	+	90.3441i	−1.20432	+	2.94670i
$941$	1.68501	−	6.28854i	0.0549297	−	0.205001i	−0.933007	−	0.359858i	$-0.882825\pi$
$941$	1.68501	−	6.28854i	0.0549297	−	0.205001i	0.987937	+	0.154857i	$0.0494918\pi$
$942$	−3.82638	−	3.82638i	−0.124670	−	0.124670i
$943$	9.88761	−	36.9011i	0.321985	−	1.20166i
$944$	−4.42231	+	4.42231i	−0.143934	+	0.143934i
$945$	−3.83421	+	3.25547i	−0.124727	+	0.105900i
$946$	−30.9198	+	17.8516i	−1.00529	+	0.580404i
$947$	−8.77955	+	8.77955i	−0.285297	+	0.285297i	−0.835217	−	0.549920i	$-0.814658\pi$
$947$	−8.77955	+	8.77955i	−0.285297	+	0.285297i	0.549920	+	0.835217i	$0.314658\pi$
$948$	−3.50081	+	2.02120i	−0.113701	+	0.0656454i
$949$	−3.17746	−	22.3627i	−0.103145	−	0.725925i
$950$	45.4419	+	44.5932i	1.47433	+	1.44679i
$951$	−0.277971	+	1.03740i	−0.00901383	+	0.0336401i
$952$	33.9980	−	21.7119i	1.10188	−	0.703686i
$953$	−6.00632	+	10.4033i	−0.194564	+	0.336994i	−0.946757	−	0.321948i	$-0.895662\pi$
$953$	−6.00632	+	10.4033i	−0.194564	+	0.336994i	0.752194	+	0.658942i	$0.228996\pi$
$954$	−19.1927	−	71.6281i	−0.621387	−	2.31905i
$955$	−3.40079	+	26.8073i	−0.110047	+	0.867463i
$956$	−10.7515	−	10.7515i	−0.347728	−	0.347728i
$957$	0.352601	−	0.0944792i	0.0113980	−	0.00305408i
$958$	7.31680	−	12.6731i	0.236395	−	0.409448i
$959$	−2.13386	−	3.34136i	−0.0689061	−	0.107898i
$960$	−1.40316	−	3.34288i	−0.0452868	−	0.107891i
$961$	−3.44644	−	1.98980i	−0.111176	−	0.0641872i
$962$	−77.6145	+	33.0844i	−2.50239	+	1.06668i
$963$	1.78027	−	1.02784i	0.0573683	−	0.0331216i
$964$	−5.77993	−	5.77993i	−0.186159	−	0.186159i
$965$	−1.32503	+	3.24204i	−0.0426542	+	0.104365i
$966$	−0.314422	−	7.02369i	−0.0101164	−	0.225984i
$967$	30.9319	+	30.9319i	0.994703	+	0.994703i	0.999986	−	0.00528347i	$-0.00168179\pi$
$967$	30.9319	+	30.9319i	0.994703	+	0.994703i	−0.00528347	+	0.999986i	$0.501682\pi$
$968$	−9.24855	+	34.5161i	−0.297260	+	1.10939i
$969$	2.12902	−	2.12902i	0.0683939	−	0.0683939i
$970$	−62.8714	+	26.3900i	−2.01868	+	0.847332i
$971$	15.9007	−	9.18028i	0.510278	−	0.294609i	−0.222670	−	0.974894i	$-0.571477\pi$
$971$	15.9007	−	9.18028i	0.510278	−	0.294609i	0.732948	+	0.680285i	$0.238144\pi$
$972$	11.9556	−	6.90259i	0.383477	−	0.221401i
$973$	−18.8489	+	20.6156i	−0.604268	+	0.660905i
$974$			86.5602i			2.77357i
$975$	2.53416	−	0.384473i	0.0811581	−	0.0123130i
$976$	−13.3135	+	7.68654i	−0.426154	+	0.246040i
$977$	−26.1360	+	7.00312i	−0.836164	+	0.224050i	−0.651401	−	0.758733i	$-0.725819\pi$
$977$	−26.1360	+	7.00312i	−0.836164	+	0.224050i	−0.184763	+	0.982783i	$0.559152\pi$
$978$	−3.49797			−0.111853
$979$	−3.95486	+	6.85002i	−0.126398	+	0.218928i
$980$	50.1986	−	26.5747i	1.60354	−	0.848899i
$981$	5.79071	+	21.6112i	0.184883	+	0.689994i
$982$	3.89945	+	1.04485i	0.124436	+	0.0333426i
$983$	−6.32370	+	23.6004i	−0.201695	+	0.752735i	0.788737	+	0.614731i	$0.210735\pi$
$983$	−6.32370	+	23.6004i	−0.201695	+	0.752735i	−0.990432	+	0.138004i	$0.955931\pi$
$984$	2.66427			0.0849339
$985$	26.2627	−	20.3495i	0.836801	−	0.648388i
$986$	17.5359	+	4.69873i	0.558457	+	0.149638i
$987$	4.01570	+	2.08482i	0.127821	+	0.0663604i
$988$	69.5230	−	9.87832i	2.21182	−	0.314271i
$989$	−44.7748	+	77.5523i	−1.42376	+	2.46602i
$990$	−12.6617	+	16.6630i	−0.402414	+	0.529585i
$991$	3.35636	−	5.81338i	0.106618	−	0.184668i	−0.807780	−	0.589484i	$-0.799331\pi$
$991$	3.35636	−	5.81338i	0.106618	−	0.184668i	0.914398	+	0.404816i	$0.132664\pi$
$992$	−16.3707	+	9.45164i	−0.519771	+	0.300090i
$993$	−0.930658	+	0.930658i	−0.0295336	+	0.0295336i
$994$	−14.6335	−	13.3795i	−0.464146	−	0.424371i
$995$	−11.0473	−	8.39447i	−0.350223	−	0.266123i
$996$	3.01476	−	0.807803i	0.0955264	−	0.0255962i
$997$	59.4026			1.88130			0.940650	−	0.339378i	$-0.110217\pi$
$997$	59.4026			1.88130			0.940650	+	0.339378i	$0.110217\pi$
$998$	−5.45721	+	9.45216i	−0.172745	+	0.299203i
$999$	5.92958	−	5.92958i	0.187604	−	0.187604i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	455.2.cl.a.54.5	✓	208
5.4	even	2	inner	455.2.cl.a.54.48	yes	208
7.3	odd	6		455.2.dn.a.444.48	yes	208
13.7	odd	12		455.2.dn.a.124.5	yes	208
35.24	odd	6		455.2.dn.a.444.5	yes	208
65.59	odd	12		455.2.dn.a.124.48	yes	208
91.59	even	12	inner	455.2.cl.a.59.48	yes	208
455.59	even	12	inner	455.2.cl.a.59.5	yes	208

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
455.2.cl.a.54.5	✓	208	1.1	even	1	trivial
455.2.cl.a.54.48	yes	208	5.4	even	2	inner
455.2.cl.a.59.5	yes	208	455.59	even	12	inner
455.2.cl.a.59.48	yes	208	91.59	even	12	inner
455.2.dn.a.124.5	yes	208	13.7	odd	12
455.2.dn.a.124.48	yes	208	65.59	odd	12
455.2.dn.a.444.5	yes	208	35.24	odd	6
455.2.dn.a.444.48	yes	208	7.3	odd	6

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:	\( N \)	\(=\)	\( 455 = 5 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	455.cl (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.67761 - 1.67761i) q^{2} +(-0.0710893 + 0.123130i) q^{3} +3.62875i q^{4} +(1.78039 + 1.35286i) q^{5} +(0.325824 - 0.0873044i) q^{6} +(0.569797 - 2.58367i) q^{7} +(2.73241 - 2.73241i) q^{8} +(1.48989 + 2.58057i) q^{9} +(-0.717231 - 5.25636i) q^{10} +(-1.27877 + 0.342645i) q^{11} +(-0.446809 - 0.257965i) q^{12} +(-3.31679 + 1.41383i) q^{13} +(-5.29028 + 3.37849i) q^{14} +(-0.293144 + 0.123046i) q^{15} -1.91033 q^{16} +3.94567i q^{17} +(1.82973 - 6.82865i) q^{18} +(-1.38911 + 5.18423i) q^{19} +(-4.90918 + 6.46058i) q^{20} +(0.277621 + 0.253830i) q^{21} +(2.72010 + 1.57045i) q^{22} +7.87791 q^{23} +(0.142197 + 0.530687i) q^{24} +(1.33956 + 4.81722i) q^{25} +(7.93613 + 3.19242i) q^{26} -0.850197 q^{27} +(9.37548 + 2.06765i) q^{28} +(0.969679 + 1.67953i) q^{29} +(0.698204 + 0.285358i) q^{30} +(1.53075 - 5.71283i) q^{31} +(-2.26003 - 2.26003i) q^{32} +(0.0487167 - 0.181813i) q^{33} +(6.61929 - 6.61929i) q^{34} +(4.50979 - 3.82907i) q^{35} +(-9.36424 + 5.40645i) q^{36} +(-6.97436 + 6.97436i) q^{37} +(11.0275 - 6.36673i) q^{38} +(0.0617027 - 0.508905i) q^{39} +(8.56130 - 1.16819i) q^{40} +(1.25511 - 4.68412i) q^{41} +(-0.0399118 - 0.891568i) q^{42} +(-5.68359 + 9.84426i) q^{43} +(-1.24337 - 4.64033i) q^{44} +(-0.838554 + 6.61002i) q^{45} +(-13.2161 - 13.2161i) q^{46} +(11.6183 - 3.11312i) q^{47} +(0.135804 - 0.235219i) q^{48} +(-6.35066 - 2.94433i) q^{49} +(5.83415 - 10.3287i) q^{50} +(-0.485831 - 0.280494i) q^{51} +(-5.13044 - 12.0358i) q^{52} +(9.08405 - 5.24468i) q^{53} +(1.42630 + 1.42630i) q^{54} +(-2.74025 - 1.11995i) q^{55} +(-5.50271 - 8.61654i) q^{56} +(-0.539584 - 0.539584i) q^{57} +(1.19086 - 4.44435i) q^{58} +(2.31495 - 2.31495i) q^{59} +(-0.446503 - 1.06375i) q^{60} +(6.96922 - 4.02368i) q^{61} +(-12.1519 + 7.01590i) q^{62} +(7.51627 - 2.37899i) q^{63} +11.4036i q^{64} +(-7.81788 - 1.96997i) q^{65} +(-0.386739 + 0.223284i) q^{66} +(7.71449 - 2.06709i) q^{67} -14.3178 q^{68} +(-0.560035 + 0.970009i) q^{69} +(-13.9894 - 1.14197i) q^{70} +(0.817561 + 3.05118i) q^{71} +(11.1222 + 2.98017i) q^{72} +(-1.62140 + 6.05114i) q^{73} +23.4005 q^{74} +(-0.688373 - 0.177512i) q^{75} +(-18.8123 - 5.04073i) q^{76} +(0.156642 + 3.49915i) q^{77} +(-0.957257 + 0.750231i) q^{78} +(3.91758 - 6.78544i) q^{79} +(-3.40112 - 2.58440i) q^{80} +(-4.40924 + 7.63702i) q^{81} +(-9.96370 + 5.75255i) q^{82} +(-4.27763 + 4.27763i) q^{83} +(-0.921086 + 1.00742i) q^{84} +(-5.33792 + 7.02481i) q^{85} +(26.0497 - 6.97999i) q^{86} -0.275735 q^{87} +(-2.55787 + 4.43036i) q^{88} +(4.22472 - 4.22472i) q^{89} +(12.4958 - 9.68228i) q^{90} +(1.76297 + 9.37507i) q^{91} +28.5870i q^{92} +(0.594602 + 0.594602i) q^{93} +(-24.7136 - 14.2684i) q^{94} +(-9.48666 + 7.35067i) q^{95} +(0.438942 - 0.117614i) q^{96} +(-3.32657 - 12.4149i) q^{97} +(5.71450 + 15.5934i) q^{98} +(-2.78944 - 2.78944i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 208 q - 6 q^{5} + 24 q^{6} - 84 q^{9} - 6 q^{10} - 22 q^{15} - 168 q^{16} - 24 q^{19} + 12 q^{20} + 12 q^{21} + 36 q^{24} - 12 q^{26} - 20 q^{29} + 18 q^{30} - 12 q^{31} + 24 q^{34} - 4 q^{35} - 12 q^{36}+ \cdots - 48 q^{99}+O(q^{100}) \) 208 * q - 6 * q^5 + 24 * q^6 - 84 * q^9 - 6 * q^10 - 22 * q^15 - 168 * q^16 - 24 * q^19 + 12 * q^20 + 12 * q^21 + 36 * q^24 - 12 * q^26 - 20 * q^29 + 18 * q^30 - 12 * q^31 + 24 * q^34 - 4 * q^35 - 12 * q^36 - 4 * q^39 + 48 * q^40 - 72 * q^41 + 88 * q^44 - 6 * q^45 - 84 * q^46 - 12 * q^49 + 36 * q^50 + 72 * q^51 - 36 * q^54 - 18 * q^55 + 72 * q^56 - 60 * q^59 + 74 * q^60 - 12 * q^61 + 44 * q^65 - 60 * q^66 - 84 * q^69 - 84 * q^70 - 64 * q^74 - 12 * q^75 - 48 * q^76 - 4 * q^79 - 150 * q^80 + 12 * q^81 + 252 * q^84 + 22 * q^85 + 80 * q^86 + 72 * q^89 + 144 * q^90 - 48 * q^91 + 48 * q^94 - 180 * q^96 - 48 * q^99

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