LMFDB - Embedded newform 1860.2.s.a.1177.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1860,2,Mod(433,1860)] 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("1860.433"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1860, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1860 = 2^{2} \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1860.s (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$14.8521747760$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1177.1
Character	$\chi$	$=$	1860.1177
Dual form			1860.2.s.a.433.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 - 0.707107i) q^{3} +(1.97917 + 1.04062i) q^{5} +(-0.798115 - 0.798115i) q^{7} +1.00000i q^{9} +5.73785i q^{11} +(-1.95385 - 1.95385i) q^{13} +(-0.663658 - 2.13531i) q^{15} +(-3.32507 + 3.32507i) q^{17} -6.00031i q^{19} +1.12871i q^{21} +(5.81565 + 5.81565i) q^{23} +(2.83424 + 4.11912i) q^{25} +(0.707107 - 0.707107i) q^{27} -9.28455 q^{29} +(-5.26962 - 1.79752i) q^{31} +(4.05727 - 4.05727i) q^{33} +(-0.749075 - 2.41014i) q^{35} +(-6.10518 + 6.10518i) q^{37} +2.76317i q^{39} -9.94893 q^{41} +(-0.0243918 - 0.0243918i) q^{43} +(-1.04062 + 1.97917i) q^{45} +(8.37241 + 8.37241i) q^{47} -5.72602i q^{49} +4.70235 q^{51} +(-3.37690 - 3.37690i) q^{53} +(-5.97090 + 11.3562i) q^{55} +(-4.24286 + 4.24286i) q^{57} +0.400120i q^{59} -8.24999i q^{61} +(0.798115 - 0.798115i) q^{63} +(-1.83380 - 5.90022i) q^{65} +(5.55356 + 5.55356i) q^{67} -8.22458i q^{69} -6.44096 q^{71} +(6.75269 + 6.75269i) q^{73} +(0.908548 - 4.91676i) q^{75} +(4.57947 - 4.57947i) q^{77} +0.429917 q^{79} -1.00000 q^{81} +(-1.28389 - 1.28389i) q^{83} +(-10.0410 + 3.12076i) q^{85} +(6.56517 + 6.56517i) q^{87} -3.49070 q^{89} +3.11880i q^{91} +(2.45515 + 4.99722i) q^{93} +(6.24403 - 11.8756i) q^{95} +(-0.568489 - 0.568489i) q^{97} -5.73785 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{7} + 16 q^{25} + 8 q^{31} - 8 q^{33} + 24 q^{35} + 16 q^{41} + 56 q^{47} + 8 q^{63} - 32 q^{67} - 16 q^{71} - 64 q^{81} - 32 q^{87} - 32 q^{95} + 64 q^{97}+O(q^{100}) $ 64 * q - 8 * q^7 + 16 * q^25 + 8 * q^31 - 8 * q^33 + 24 * q^35 + 16 * q^41 + 56 * q^47 + 8 * q^63 - 32 * q^67 - 16 * q^71 - 64 * q^81 - 32 * q^87 - 32 * q^95 + 64 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1860\mathbb{Z}\right)^\times$.

$n$	$931$	$1117$	$1241$	$1801$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

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			0
$2$		0			0
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$		0			0
$5$	1.97917	+	1.04062i	0.885112	+	0.465378i
$5$	1.97917	+	1.04062i	0.885112	+	0.465378i
$6$		0			0
$7$	−0.798115	−	0.798115i	−0.301659	−	0.301659i	0.540004	−	0.841663i	$-0.318423\pi$
$7$	−0.798115	−	0.798115i	−0.301659	−	0.301659i	−0.841663	+	0.540004i	$0.818423\pi$
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$			5.73785i			1.73003i	0.501748	+	0.865014i	$0.332690\pi$
$11$			5.73785i			1.73003i	−0.501748	+	0.865014i	$0.667310\pi$
$12$		0			0
$13$	−1.95385	−	1.95385i	−0.541902	−	0.541902i	0.382184	−	0.924086i	$-0.375172\pi$
$13$	−1.95385	−	1.95385i	−0.541902	−	0.541902i	−0.924086	+	0.382184i	$0.875172\pi$
$14$		0			0
$15$	−0.663658	−	2.13531i	−0.171356	−	0.551335i
$16$		0			0
$17$	−3.32507	+	3.32507i	−0.806447	+	0.806447i	−0.984094	−	0.177647i	$-0.943151\pi$
$17$	−3.32507	+	3.32507i	−0.806447	+	0.806447i	0.177647	+	0.984094i	$0.443151\pi$
$18$		0			0
$19$		−	6.00031i		−	1.37657i	−0.725442	−	0.688283i	$-0.758365\pi$
$19$		−	6.00031i		−	1.37657i	0.725442	−	0.688283i	$-0.241635\pi$
$20$		0			0
$21$			1.12871i			0.246304i
$22$		0			0
$23$	5.81565	+	5.81565i	1.21265	+	1.21265i	0.970153	+	0.242495i	$0.0779658\pi$
$23$	5.81565	+	5.81565i	1.21265	+	1.21265i	0.242495	+	0.970153i	$0.422034\pi$
$24$		0			0
$25$	2.83424	+	4.11912i	0.566847	+	0.823823i
$26$		0			0
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$		0			0
$29$	−9.28455			−1.72410			−0.862049	−	0.506825i	$-0.830819\pi$
$29$	−9.28455			−1.72410			−0.862049	+	0.506825i	$0.830819\pi$
$30$		0			0
$31$	−5.26962	−	1.79752i	−0.946452	−	0.322844i
$31$	−5.26962	−	1.79752i	−0.946452	−	0.322844i
$32$		0			0
$33$	4.05727	−	4.05727i	0.706281	−	0.706281i
$34$		0			0
$35$	−0.749075	−	2.41014i	−0.126617	−	0.407388i
$36$		0			0
$37$	−6.10518	+	6.10518i	−1.00369	+	1.00369i	−0.00369215	+	0.999993i	$0.501175\pi$
$37$	−6.10518	+	6.10518i	−1.00369	+	1.00369i	−0.999993	+	0.00369215i	$0.998825\pi$
$38$		0			0
$39$			2.76317i			0.442461i
$40$		0			0
$41$	−9.94893			−1.55376			−0.776881	−	0.629648i	$-0.783199\pi$
$41$	−9.94893			−1.55376			−0.776881	+	0.629648i	$0.783199\pi$
$42$		0			0
$43$	−0.0243918	−	0.0243918i	−0.00371971	−	0.00371971i	0.705244	−	0.708964i	$-0.250837\pi$
$43$	−0.0243918	−	0.0243918i	−0.00371971	−	0.00371971i	−0.708964	+	0.705244i	$0.750837\pi$
$44$		0			0
$45$	−1.04062	+	1.97917i	−0.155126	+	0.295037i
$46$		0			0
$47$	8.37241	+	8.37241i	1.22124	+	1.22124i	0.967191	+	0.254051i	$0.0817631\pi$
$47$	8.37241	+	8.37241i	1.22124	+	1.22124i	0.254051	+	0.967191i	$0.418237\pi$
$48$		0			0
$49$		−	5.72602i		−	0.818003i
$50$		0			0
$51$	4.70235			0.658461
$52$		0			0
$53$	−3.37690	−	3.37690i	−0.463853	−	0.463853i	0.436063	−	0.899916i	$-0.356372\pi$
$53$	−3.37690	−	3.37690i	−0.463853	−	0.463853i	−0.899916	+	0.436063i	$0.856372\pi$
$54$		0			0
$55$	−5.97090	+	11.3562i	−0.805116	+	1.53127i
$56$		0			0
$57$	−4.24286	+	4.24286i	−0.561981	+	0.561981i
$58$		0			0
$59$			0.400120i			0.0520912i	0.999661	+	0.0260456i	$0.00829151\pi$
$59$			0.400120i			0.0520912i	−0.999661	+	0.0260456i	$0.991708\pi$
$60$		0			0
$61$		−	8.24999i		−	1.05630i	−0.849150	−	0.528152i	$-0.822885\pi$
$61$		−	8.24999i		−	1.05630i	0.849150	−	0.528152i	$-0.177115\pi$
$62$		0			0
$63$	0.798115	−	0.798115i	0.100553	−	0.100553i
$64$		0			0
$65$	−1.83380	−	5.90022i	−0.227455	−	0.731833i
$66$		0			0
$67$	5.55356	+	5.55356i	0.678475	+	0.678475i	0.959655	−	0.281180i	$-0.0907258\pi$
$67$	5.55356	+	5.55356i	0.678475	+	0.678475i	−0.281180	+	0.959655i	$0.590726\pi$
$68$		0			0
$69$		−	8.22458i		−	0.990123i
$70$		0			0
$71$	−6.44096			−0.764402			−0.382201	−	0.924079i	$-0.624834\pi$
$71$	−6.44096			−0.764402			−0.382201	+	0.924079i	$0.624834\pi$
$72$		0			0
$73$	6.75269	+	6.75269i	0.790342	+	0.790342i	0.981550	−	0.191208i	$-0.0612404\pi$
$73$	6.75269	+	6.75269i	0.790342	+	0.790342i	−0.191208	+	0.981550i	$0.561240\pi$
$74$		0			0
$75$	0.908548	−	4.91676i	0.104910	−	0.567739i
$76$		0			0
$77$	4.57947	−	4.57947i	0.521879	−	0.521879i
$78$		0			0
$79$	0.429917			0.0483695			0.0241847	−	0.999708i	$-0.492301\pi$
$79$	0.429917			0.0483695			0.0241847	+	0.999708i	$0.492301\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−1.28389	−	1.28389i	−0.140925	−	0.140925i	0.633125	−	0.774050i	$-0.281772\pi$
$83$	−1.28389	−	1.28389i	−0.140925	−	0.140925i	−0.774050	+	0.633125i	$0.781772\pi$
$84$		0			0
$85$	−10.0410	+	3.12076i	−1.08910	+	0.338493i
$86$		0			0
$87$	6.56517	+	6.56517i	0.703860	+	0.703860i
$88$		0			0
$89$	−3.49070			−0.370014			−0.185007	−	0.982737i	$-0.559231\pi$
$89$	−3.49070			−0.370014			−0.185007	+	0.982737i	$0.559231\pi$
$90$		0			0
$91$			3.11880i			0.326939i
$92$		0			0
$93$	2.45515	+	4.99722i	0.254587	+	0.518188i
$94$		0			0
$95$	6.24403	−	11.8756i	0.640624	−	1.21842i
$96$		0			0
$97$	−0.568489	−	0.568489i	−0.0577213	−	0.0577213i	0.677657	−	0.735378i	$-0.262995\pi$
$97$	−0.568489	−	0.568489i	−0.0577213	−	0.0577213i	−0.735378	+	0.677657i	$0.762995\pi$
$98$		0			0
$99$	−5.73785			−0.576676
$100$		0			0
$101$	10.0681			1.00181			0.500907	−	0.865501i	$-0.333000\pi$
$101$	10.0681			1.00181			0.500907	+	0.865501i	$0.333000\pi$
$102$		0			0
$103$	−4.06232	+	4.06232i	−0.400273	+	0.400273i	−0.878329	−	0.478057i	$-0.841341\pi$
$103$	−4.06232	+	4.06232i	−0.400273	+	0.400273i	0.478057	+	0.878329i	$0.341341\pi$
$104$		0			0
$105$	−1.17455	+	2.23390i	−0.114624	+	0.218006i
$106$		0			0
$107$	4.36960	+	4.36960i	0.422425	+	0.422425i	0.886038	−	0.463613i	$-0.153447\pi$
$107$	4.36960	+	4.36960i	0.422425	+	0.422425i	−0.463613	+	0.886038i	$0.653447\pi$
$108$		0			0
$109$			17.8625i			1.71091i	0.517873	+	0.855457i	$0.326724\pi$
$109$			17.8625i			1.71091i	−0.517873	+	0.855457i	$0.673276\pi$
$110$		0			0
$111$	8.63403			0.819506
$112$		0			0
$113$	−11.1366	+	11.1366i	−1.04764	+	1.04764i	−0.0488350	+	0.998807i	$0.515551\pi$
$113$	−11.1366	+	11.1366i	−1.04764	+	1.04764i	−0.998807	+	0.0488350i	$0.984449\pi$
$114$		0			0
$115$	5.45831	+	17.5620i	0.508990	+	1.63767i
$116$		0			0
$117$	1.95385	−	1.95385i	0.180634	−	0.180634i
$118$		0			0
$119$	5.30757			0.486544
$120$		0			0
$121$	−21.9230			−1.99300
$122$		0			0
$123$	7.03496	+	7.03496i	0.634321	+	0.634321i
$124$		0			0
$125$	1.32302	+	11.1018i	0.118334	+	0.992974i
$126$		0			0
$127$	1.93317	−	1.93317i	0.171541	−	0.171541i	−0.616115	−	0.787656i	$-0.711294\pi$
$127$	1.93317	−	1.93317i	0.171541	−	0.171541i	0.787656	+	0.616115i	$0.211294\pi$
$128$		0			0
$129$			0.0344952i			0.00303713i
$130$		0			0
$131$	1.51559			0.132418			0.0662090	−	0.997806i	$-0.478910\pi$
$131$	1.51559			0.132418			0.0662090	+	0.997806i	$0.478910\pi$
$132$		0			0
$133$	−4.78894	+	4.78894i	−0.415254	+	0.415254i
$134$		0			0
$135$	2.13531	−	0.663658i	0.183778	−	0.0571186i
$136$		0			0
$137$	−5.95493	+	5.95493i	−0.508764	+	0.508764i	−0.914147	−	0.405383i	$-0.867138\pi$
$137$	−5.95493	+	5.95493i	−0.508764	+	0.508764i	0.405383	+	0.914147i	$0.367138\pi$
$138$		0			0
$139$	−2.65283			−0.225010			−0.112505	−	0.993651i	$-0.535887\pi$
$139$	−2.65283			−0.225010			−0.112505	+	0.993651i	$0.535887\pi$
$140$		0			0
$141$		−	11.8404i		−	0.997140i
$142$		0			0
$143$	11.2109	−	11.2109i	0.937505	−	0.937505i
$144$		0			0
$145$	−18.3757	−	9.66166i	−1.52602	−	0.802357i
$146$		0			0
$147$	−4.04891	+	4.04891i	−0.333948	+	0.333948i
$148$		0			0
$149$			20.9921i			1.71974i	0.510516	+	0.859868i	$0.329454\pi$
$149$			20.9921i			1.71974i	−0.510516	+	0.859868i	$0.670546\pi$
$150$		0			0
$151$			2.48405i			0.202149i	0.994879	+	0.101075i	$0.0322281\pi$
$151$			2.48405i			0.202149i	−0.994879	+	0.101075i	$0.967772\pi$
$152$		0			0
$153$	−3.32507	−	3.32507i	−0.268816	−	0.268816i
$154$		0			0
$155$	−8.55895	−	9.04126i	−0.687472	−	0.726211i
$156$		0			0
$157$	−9.03382	−	9.03382i	−0.720977	−	0.720977i	0.247827	−	0.968804i	$-0.420284\pi$
$157$	−9.03382	−	9.03382i	−0.720977	−	0.720977i	−0.968804	+	0.247827i	$0.920284\pi$
$158$		0			0
$159$			4.77566i			0.378735i
$160$		0			0
$161$		−	9.28312i		−	0.731613i
$162$		0			0
$163$	1.80357	−	1.80357i	0.141266	−	0.141266i	−0.632937	−	0.774203i	$-0.718151\pi$
$163$	1.80357	−	1.80357i	0.141266	−	0.141266i	0.774203	+	0.632937i	$0.218151\pi$
$164$		0			0
$165$	12.2521	−	3.80797i	0.953825	−	0.296450i
$166$		0			0
$167$	−1.90436	+	1.90436i	−0.147363	+	0.147363i	−0.776939	−	0.629576i	$-0.783229\pi$
$167$	−1.90436	+	1.90436i	−0.147363	+	0.147363i	0.629576	+	0.776939i	$0.283229\pi$
$168$		0			0
$169$		−	5.36491i		−	0.412685i
$170$		0			0
$171$	6.00031			0.458856
$172$		0			0
$173$	14.9456	−	14.9456i	1.13629	−	1.13629i	0.147182	−	0.989109i	$-0.452980\pi$
$173$	14.9456	−	14.9456i	1.13629	−	1.13629i	0.989109	−	0.147182i	$-0.0470203\pi$
$174$		0			0
$175$	1.02548	−	5.54958i	0.0775192	−	0.419508i
$176$		0			0
$177$	0.282928	−	0.282928i	0.0212661	−	0.0212661i
$178$		0			0
$179$	−8.99820			−0.672557			−0.336278	−	0.941763i	$-0.609168\pi$
$179$	−8.99820			−0.672557			−0.336278	+	0.941763i	$0.609168\pi$
$180$		0			0
$181$			17.9811i			1.33653i	0.743925	+	0.668264i	$0.232962\pi$
$181$			17.9811i			1.33653i	−0.743925	+	0.668264i	$0.767038\pi$
$182$		0			0
$183$	−5.83363	+	5.83363i	−0.431234	+	0.431234i
$184$		0			0
$185$	−18.4363	+	5.73004i	−1.35547	+	0.421281i
$186$		0			0
$187$	−19.0787	−	19.0787i	−1.39518	−	1.39518i
$188$		0			0
$189$	−1.12871			−0.0821012
$190$		0			0
$191$	14.9908			1.08470			0.542348	−	0.840154i	$-0.317536\pi$
$191$	14.9908			1.08470			0.542348	+	0.840154i	$0.317536\pi$
$192$		0			0
$193$	−4.18430	+	4.18430i	−0.301193	+	0.301193i	−0.841480	−	0.540288i	$-0.818315\pi$
$193$	−4.18430	+	4.18430i	−0.301193	+	0.301193i	0.540288	+	0.841480i	$0.318315\pi$
$194$		0			0
$195$	−2.87540	+	5.46878i	−0.205911	+	0.391627i
$196$		0			0
$197$	−14.9983	+	14.9983i	−1.06858	+	1.06858i	−0.0711143	+	0.997468i	$0.522656\pi$
$197$	−14.9983	+	14.9983i	−1.06858	+	1.06858i	−0.997468	+	0.0711143i	$0.977344\pi$
$198$		0			0
$199$	4.19851			0.297625			0.148812	−	0.988865i	$-0.452455\pi$
$199$	4.19851			0.297625			0.148812	+	0.988865i	$0.452455\pi$
$200$		0			0
$201$		−	7.85392i		−	0.553973i
$202$		0			0
$203$	7.41014	+	7.41014i	0.520090	+	0.520090i
$204$		0			0
$205$	−19.6906	−	10.3530i	−1.37525	−	0.723086i
$206$		0			0
$207$	−5.81565	+	5.81565i	−0.404216	+	0.404216i
$208$		0			0
$209$	34.4289			2.38150
$210$		0			0
$211$	3.74541			0.257845			0.128922	−	0.991655i	$-0.458848\pi$
$211$	3.74541			0.257845			0.128922	+	0.991655i	$0.458848\pi$
$212$		0			0
$213$	4.55445	+	4.55445i	0.312066	+	0.312066i
$214$		0			0
$215$	−0.0228930	−	0.0736580i	−0.00156129	−	0.00502343i
$216$		0			0
$217$	2.77114	+	5.64039i	0.188117	+	0.382895i
$218$		0			0
$219$		−	9.54974i		−	0.645312i
$220$		0			0
$221$	12.9934			0.874030
$222$		0			0
$223$	6.66838	+	6.66838i	0.446547	+	0.446547i	0.894205	−	0.447658i	$-0.147742\pi$
$223$	6.66838	+	6.66838i	0.446547	+	0.446547i	−0.447658	+	0.894205i	$0.647742\pi$
$224$		0			0
$225$	−4.11912	+	2.83424i	−0.274608	+	0.188949i
$226$		0			0
$227$	7.28192	+	7.28192i	0.483318	+	0.483318i	0.906190	−	0.422872i	$-0.138978\pi$
$227$	7.28192	+	7.28192i	0.483318	+	0.483318i	−0.422872	+	0.906190i	$0.638978\pi$
$228$		0			0
$229$	17.0953			1.12969			0.564844	−	0.825198i	$-0.308936\pi$
$229$	17.0953			1.12969			0.564844	+	0.825198i	$0.308936\pi$
$230$		0			0
$231$	−6.47635			−0.426112
$232$		0			0
$233$	13.1640	−	13.1640i	0.862402	−	0.862402i	−0.129215	−	0.991617i	$-0.541246\pi$
$233$	13.1640	−	13.1640i	0.862402	−	0.862402i	0.991617	+	0.129215i	$0.0412457\pi$
$234$		0			0
$235$	7.85797	+	25.2829i	0.512597	+	1.64927i
$236$		0			0
$237$	−0.303998	−	0.303998i	−0.0197468	−	0.0197468i
$238$		0			0
$239$	7.48050			0.483873			0.241937	−	0.970292i	$-0.422217\pi$
$239$	7.48050			0.483873			0.241937	+	0.970292i	$0.422217\pi$
$240$		0			0
$241$			7.22271i			0.465256i	0.972566	+	0.232628i	$0.0747324\pi$
$241$			7.22271i			0.465256i	−0.972566	+	0.232628i	$0.925268\pi$
$242$		0			0
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$		0			0
$245$	5.95859	−	11.3328i	0.380681	−	0.724025i
$246$		0			0
$247$	−11.7237	+	11.7237i	−0.745964	+	0.745964i
$248$		0			0
$249$			1.81569i			0.115065i
$250$		0			0
$251$		−	27.3980i		−	1.72935i	−0.502335	−	0.864673i	$-0.667525\pi$
$251$		−	27.3980i		−	1.72935i	0.502335	−	0.864673i	$-0.332475\pi$
$252$		0			0
$253$	−33.3694	+	33.3694i	−2.09791	+	2.09791i
$254$		0			0
$255$	9.30676	+	4.89335i	0.582812	+	0.306433i
$256$		0			0
$257$	15.0381	+	15.0381i	0.938054	+	0.938054i	0.998190	−	0.0601363i	$-0.0191535\pi$
$257$	15.0381	+	15.0381i	0.938054	+	0.938054i	−0.0601363	+	0.998190i	$0.519154\pi$
$258$		0			0
$259$	9.74527			0.605542
$260$		0			0
$261$		−	9.28455i		−	0.574699i
$262$		0			0
$263$	−3.17111	−	3.17111i	−0.195539	−	0.195539i	0.602546	−	0.798084i	$-0.294153\pi$
$263$	−3.17111	−	3.17111i	−0.195539	−	0.195539i	−0.798084	+	0.602546i	$0.794153\pi$
$264$		0			0
$265$	−3.16941	−	10.1975i	−0.194695	−	0.626429i
$266$		0			0
$267$	2.46830	+	2.46830i	0.151057	+	0.151057i
$268$		0			0
$269$	14.8820			0.907375			0.453687	−	0.891161i	$-0.350108\pi$
$269$	14.8820			0.907375			0.453687	+	0.891161i	$0.350108\pi$
$270$		0			0
$271$		−	32.1810i		−	1.95485i	−0.211272	−	0.977427i	$-0.567761\pi$
$271$		−	32.1810i		−	1.95485i	0.211272	−	0.977427i	$-0.432239\pi$
$272$		0			0
$273$	2.20533	−	2.20533i	0.133472	−	0.133472i
$274$		0			0
$275$	−23.6349	+	16.2624i	−1.42524	+	0.980661i
$276$		0			0
$277$	13.4665	−	13.4665i	0.809124	−	0.809124i	−0.175377	−	0.984501i	$-0.556114\pi$
$277$	13.4665	−	13.4665i	0.809124	−	0.809124i	0.984501	+	0.175377i	$0.0561145\pi$
$278$		0			0
$279$	1.79752	−	5.26962i	0.107615	−	0.315484i
$280$		0			0
$281$	−22.2715			−1.32861			−0.664303	−	0.747464i	$-0.731271\pi$
$281$	−22.2715			−1.32861			−0.664303	+	0.747464i	$0.731271\pi$
$282$		0			0
$283$	−5.66049	+	5.66049i	−0.336481	+	0.336481i	−0.855041	−	0.518560i	$-0.826468\pi$
$283$	−5.66049	+	5.66049i	−0.336481	+	0.336481i	0.518560	+	0.855041i	$0.326468\pi$
$284$		0			0
$285$	−12.8125	+	3.98216i	−0.758950	+	0.235883i
$286$		0			0
$287$	7.94039	+	7.94039i	0.468707	+	0.468707i
$288$		0			0
$289$		−	5.11213i		−	0.300713i
$290$		0			0
$291$			0.803964i			0.0471292i
$292$		0			0
$293$	16.5839	−	16.5839i	0.968844	−	0.968844i	−0.0306851	−	0.999529i	$-0.509769\pi$
$293$	16.5839	−	16.5839i	0.968844	−	0.968844i	0.999529	+	0.0306851i	$0.00976889\pi$
$294$		0			0
$295$	−0.416372	+	0.791906i	−0.0242421	+	0.0461066i
$296$		0			0
$297$	4.05727	+	4.05727i	0.235427	+	0.235427i
$298$		0			0
$299$		−	22.7259i		−	1.31427i
$300$		0			0
$301$			0.0389349i			0.00224417i
$302$		0			0
$303$	−7.11922	−	7.11922i	−0.408989	−	0.408989i
$304$		0			0
$305$	8.58508	−	16.3281i	0.491580	−	0.934947i
$306$		0			0
$307$	−2.42293	−	2.42293i	−0.138284	−	0.138284i	0.634576	−	0.772860i	$-0.281175\pi$
$307$	−2.42293	−	2.42293i	−0.138284	−	0.138284i	−0.772860	+	0.634576i	$0.781175\pi$
$308$		0			0
$309$	5.74499			0.326821
$310$		0			0
$311$	−9.71622			−0.550957			−0.275478	−	0.961307i	$-0.588836\pi$
$311$	−9.71622			−0.550957			−0.275478	+	0.961307i	$0.588836\pi$
$312$		0			0
$313$	1.40470	+	1.40470i	0.0793984	+	0.0793984i	0.745691	−	0.666292i	$-0.232120\pi$
$313$	1.40470	+	1.40470i	0.0793984	+	0.0793984i	−0.666292	+	0.745691i	$0.732120\pi$
$314$		0			0
$315$	2.41014	−	0.749075i	0.135796	−	0.0422056i
$316$		0			0
$317$	−22.5469	−	22.5469i	−1.26636	−	1.26636i	−0.947955	−	0.318404i	$-0.896853\pi$
$317$	−22.5469	−	22.5469i	−1.26636	−	1.26636i	−0.318404	−	0.947955i	$-0.603147\pi$
$318$		0			0
$319$		−	53.2734i		−	2.98274i
$320$		0			0
$321$		−	6.17955i		−	0.344909i
$322$		0			0
$323$	19.9514	+	19.9514i	1.11013	+	1.11013i
$324$		0			0
$325$	2.51047	−	13.5858i	0.139256	−	0.753606i
$326$		0			0
$327$	12.6307	−	12.6307i	0.698478	−	0.698478i
$328$		0			0
$329$		−	13.3643i		−	0.736798i
$330$		0			0
$331$			16.9639i			0.932419i	0.884674	+	0.466209i	$0.154381\pi$
$331$			16.9639i			0.932419i	−0.884674	+	0.466209i	$0.845619\pi$
$332$		0			0
$333$	−6.10518	−	6.10518i	−0.334562	−	0.334562i
$334$		0			0
$335$	5.21232	+	16.7706i	0.284779	+	0.916274i
$336$		0			0
$337$	18.0862	−	18.0862i	0.985218	−	0.985218i	−0.0146743	−	0.999892i	$-0.504671\pi$
$337$	18.0862	−	18.0862i	0.985218	−	0.985218i	0.999892	+	0.0146743i	$0.00467114\pi$
$338$		0			0
$339$	15.7495			0.855396
$340$		0			0
$341$	10.3139	−	30.2363i	0.558529	−	1.63739i
$342$		0			0
$343$	−10.1568	+	10.1568i	−0.548418	+	0.548418i
$344$		0			0
$345$	8.55863	−	16.2778i	0.460781	−	0.876370i
$346$		0			0
$347$	20.8608	−	20.8608i	1.11986	−	1.11986i	0.128104	−	0.991761i	$-0.459111\pi$
$347$	20.8608	−	20.8608i	1.11986	−	1.11986i	0.991761	−	0.128104i	$-0.0408891\pi$
$348$		0			0
$349$		−	4.35902i		−	0.233333i	−0.993171	−	0.116667i	$-0.962779\pi$
$349$		−	4.35902i		−	0.233333i	0.993171	−	0.116667i	$-0.0372209\pi$
$350$		0			0
$351$	−2.76317			−0.147487
$352$		0			0
$353$	−24.8795	−	24.8795i	−1.32420	−	1.32420i	−0.910340	−	0.413860i	$-0.864180\pi$
$353$	−24.8795	−	24.8795i	−1.32420	−	1.32420i	−0.413860	−	0.910340i	$-0.635820\pi$
$354$		0			0
$355$	−12.7478	−	6.70257i	−0.676581	−	0.355735i
$356$		0			0
$357$	−3.75302	−	3.75302i	−0.198631	−	0.198631i
$358$		0			0
$359$			18.7264i			0.988341i	0.869365	+	0.494170i	$0.164528\pi$
$359$			18.7264i			0.988341i	−0.869365	+	0.494170i	$0.835472\pi$
$360$		0			0
$361$	−17.0038			−0.894936
$362$		0			0
$363$	15.5019	+	15.5019i	0.813637	+	0.813637i
$364$		0			0
$365$	6.33776	+	20.3917i	0.331734	+	1.06735i
$366$		0			0
$367$	−13.4958	+	13.4958i	−0.704477	+	0.704477i	−0.965368	−	0.260892i	$-0.915984\pi$
$367$	−13.4958	+	13.4958i	−0.704477	+	0.704477i	0.260892	+	0.965368i	$0.415984\pi$
$368$		0			0
$369$		−	9.94893i		−	0.517921i
$370$		0			0
$371$			5.39031i			0.279851i
$372$		0			0
$373$	18.2475	−	18.2475i	0.944818	−	0.944818i	−0.0537370	−	0.998555i	$-0.517113\pi$
$373$	18.2475	−	18.2475i	0.944818	−	0.944818i	0.998555	+	0.0537370i	$0.0171133\pi$
$374$		0			0
$375$	6.91463	−	8.78566i	0.357070	−	0.453690i
$376$		0			0
$377$	18.1407	+	18.1407i	0.934292	+	0.934292i
$378$		0			0
$379$		−	12.3391i		−	0.633816i	−0.948456	−	0.316908i	$-0.897355\pi$
$379$		−	12.3391i		−	0.633816i	0.948456	−	0.316908i	$-0.102645\pi$
$380$		0			0
$381$	−2.73391			−0.140063
$382$		0			0
$383$	5.02993	+	5.02993i	0.257018	+	0.257018i	0.823840	−	0.566822i	$-0.191827\pi$
$383$	5.02993	+	5.02993i	0.257018	+	0.257018i	−0.566822	+	0.823840i	$0.691827\pi$
$384$		0			0
$385$	13.8290	−	4.29808i	0.704792	−	0.219050i
$386$		0			0
$387$	0.0243918	−	0.0243918i	0.00123990	−	0.00123990i
$388$		0			0
$389$	−14.2705			−0.723543			−0.361772	−	0.932267i	$-0.617828\pi$
$389$	−14.2705			−0.723543			−0.361772	+	0.932267i	$0.617828\pi$
$390$		0			0
$391$	−38.6749			−1.95587
$392$		0			0
$393$	−1.07169	−	1.07169i	−0.0540595	−	0.0540595i
$394$		0			0
$395$	0.850880	+	0.447379i	0.0428124	+	0.0225101i
$396$		0			0
$397$	3.00360	+	3.00360i	0.150747	+	0.150747i	0.778451	−	0.627705i	$-0.216006\pi$
$397$	3.00360	+	3.00360i	0.150747	+	0.150747i	−0.627705	+	0.778451i	$0.716006\pi$
$398$		0			0
$399$	6.77259			0.339053
$400$		0			0
$401$		−	7.37276i		−	0.368178i	−0.982910	−	0.184089i	$-0.941067\pi$
$401$		−	7.37276i		−	0.368178i	0.982910	−	0.184089i	$-0.0589335\pi$
$402$		0			0
$403$	6.78398	+	13.8082i	0.337934	+	0.687834i
$404$		0			0
$405$	−1.97917	−	1.04062i	−0.0983458	−	0.0517086i
$406$		0			0
$407$	−35.0306	−	35.0306i	−1.73640	−	1.73640i
$408$		0			0
$409$	−7.79882			−0.385627			−0.192813	−	0.981235i	$-0.561761\pi$
$409$	−7.79882			−0.385627			−0.192813	+	0.981235i	$0.561761\pi$
$410$		0			0
$411$	8.42154			0.415404
$412$		0			0
$413$	0.319342	−	0.319342i	0.0157138	−	0.0157138i
$414$		0			0
$415$	−1.20500	−	3.87707i	−0.0591510	−	0.190318i
$416$		0			0
$417$	1.87583	+	1.87583i	0.0918600	+	0.0918600i
$418$		0			0
$419$			12.9455i			0.632429i	0.948688	+	0.316215i	$0.102412\pi$
$419$			12.9455i			0.632429i	−0.948688	+	0.316215i	$0.897588\pi$
$420$		0			0
$421$	−21.8822			−1.06647			−0.533237	−	0.845966i	$-0.679025\pi$
$421$	−21.8822			−1.06647			−0.533237	+	0.845966i	$0.679025\pi$
$422$		0			0
$423$	−8.37241	+	8.37241i	−0.407081	+	0.407081i
$424$		0			0
$425$	−23.1203	−	4.27231i	−1.12150	−	0.207238i
$426$		0			0
$427$	−6.58445	+	6.58445i	−0.318644	+	0.318644i
$428$		0			0
$429$	−15.8546			−0.765469
$430$		0			0
$431$	−33.9068			−1.63323			−0.816615	−	0.577182i	$-0.804152\pi$
$431$	−33.9068			−1.63323			−0.816615	+	0.577182i	$0.804152\pi$
$432$		0			0
$433$	7.38568	+	7.38568i	0.354933	+	0.354933i	0.861941	−	0.507008i	$-0.169249\pi$
$433$	7.38568	+	7.38568i	0.354933	+	0.354933i	−0.507008	+	0.861941i	$0.669249\pi$
$434$		0			0
$435$	6.16177	+	19.8254i	0.295434	+	0.950556i
$436$		0			0
$437$	34.8958	−	34.8958i	1.66929	−	1.66929i
$438$		0			0
$439$			1.36569i			0.0651809i	0.999469	+	0.0325904i	$0.0103757\pi$
$439$			1.36569i			0.0651809i	−0.999469	+	0.0325904i	$0.989624\pi$
$440$		0			0
$441$	5.72602			0.272668
$442$		0			0
$443$	15.8303	−	15.8303i	0.752121	−	0.752121i	−0.222754	−	0.974875i	$-0.571505\pi$
$443$	15.8303	−	15.8303i	0.752121	−	0.752121i	0.974875	+	0.222754i	$0.0715046\pi$
$444$		0			0
$445$	−6.90870	−	3.63248i	−0.327504	−	0.172196i
$446$		0			0
$447$	14.8436	−	14.8436i	0.702080	−	0.702080i
$448$		0			0
$449$	26.3420			1.24315			0.621577	−	0.783353i	$-0.286492\pi$
$449$	26.3420			1.24315			0.621577	+	0.783353i	$0.286492\pi$
$450$		0			0
$451$		−	57.0855i		−	2.68805i
$452$		0			0
$453$	1.75649	−	1.75649i	0.0825270	−	0.0825270i
$454$		0			0
$455$	−3.24548	+	6.17264i	−0.152150	+	0.289378i
$456$		0			0
$457$	6.97668	−	6.97668i	0.326355	−	0.326355i	−0.524844	−	0.851199i	$-0.675876\pi$
$457$	6.97668	−	6.97668i	0.326355	−	0.326355i	0.851199	+	0.524844i	$0.175876\pi$
$458$		0			0
$459$			4.70235i			0.219487i
$460$		0			0
$461$		−	30.7574i		−	1.43251i	−0.697837	−	0.716257i	$-0.745854\pi$
$461$		−	30.7574i		−	1.43251i	0.697837	−	0.716257i	$-0.254146\pi$
$462$		0			0
$463$	18.2805	+	18.2805i	0.849568	+	0.849568i	0.990079	−	0.140512i	$-0.0448747\pi$
$463$	18.2805	+	18.2805i	0.849568	+	0.849568i	−0.140512	+	0.990079i	$0.544875\pi$
$464$		0			0
$465$	−0.341039	+	12.4452i	−0.0158153	+	0.577134i
$466$		0			0
$467$	12.9675	+	12.9675i	0.600064	+	0.600064i	0.940330	−	0.340265i	$-0.110517\pi$
$467$	12.9675	+	12.9675i	0.600064	+	0.600064i	−0.340265	+	0.940330i	$0.610517\pi$
$468$		0			0
$469$		−	8.86476i		−	0.409337i
$470$		0			0
$471$			12.7758i			0.588676i
$472$		0			0
$473$	0.139956	−	0.139956i	0.00643520	−	0.00643520i
$474$		0			0
$475$	24.7160	−	17.0063i	1.13405	−	0.780303i
$476$		0			0
$477$	3.37690	−	3.37690i	0.154618	−	0.154618i
$478$		0			0
$479$			27.2131i			1.24340i	0.783256	+	0.621699i	$0.213557\pi$
$479$			27.2131i			1.24340i	−0.783256	+	0.621699i	$0.786443\pi$
$480$		0			0
$481$	23.8573			1.08780
$482$		0			0
$483$	−6.56416	+	6.56416i	−0.298680	+	0.298680i
$484$		0			0
$485$	−0.533558	−	1.71671i	−0.0242276	−	0.0779520i
$486$		0			0
$487$	−10.7772	+	10.7772i	−0.488361	+	0.488361i	−0.907789	−	0.419428i	$-0.862231\pi$
$487$	−10.7772	+	10.7772i	−0.488361	+	0.488361i	0.419428	+	0.907789i	$0.362231\pi$
$488$		0			0
$489$	−2.55063			−0.115343
$490$		0			0
$491$		−	32.2194i		−	1.45404i	−0.686616	−	0.727021i	$-0.740904\pi$
$491$		−	32.2194i		−	1.45404i	0.686616	−	0.727021i	$-0.259096\pi$
$492$		0			0
$493$	30.8718	−	30.8718i	1.39039	−	1.39039i
$494$		0			0
$495$	−11.3562	−	5.97090i	−0.510423	−	0.268372i
$496$		0			0
$497$	5.14063	+	5.14063i	0.230589	+	0.230589i
$498$		0			0
$499$	26.9926			1.20835			0.604177	−	0.796850i	$-0.293502\pi$
$499$	26.9926			1.20835			0.604177	+	0.796850i	$0.293502\pi$
$500$		0			0
$501$	2.69316			0.120322
$502$		0			0
$503$	12.6291	−	12.6291i	0.563105	−	0.563105i	−0.367083	−	0.930188i	$-0.619643\pi$
$503$	12.6291	−	12.6291i	0.563105	−	0.563105i	0.930188	+	0.367083i	$0.119643\pi$
$504$		0			0
$505$	19.9265	+	10.4770i	0.886717	+	0.466222i
$506$		0			0
$507$	−3.79356	+	3.79356i	−0.168478	+	0.168478i
$508$		0			0
$509$	−2.67880			−0.118736			−0.0593680	−	0.998236i	$-0.518909\pi$
$509$	−2.67880			−0.118736			−0.0593680	+	0.998236i	$0.518909\pi$
$510$		0			0
$511$		−	10.7788i		−	0.476828i
$512$		0			0
$513$	−4.24286	−	4.24286i	−0.187327	−	0.187327i
$514$		0			0
$515$	−12.2674	+	3.81271i	−0.540564	+	0.168008i
$516$		0			0
$517$	−48.0397	+	48.0397i	−2.11278	+	2.11278i
$518$		0			0
$519$	−21.1362			−0.927778
$520$		0			0
$521$	−40.2355			−1.76275			−0.881374	−	0.472419i	$-0.843381\pi$
$521$	−40.2355			−1.76275			−0.881374	+	0.472419i	$0.843381\pi$
$522$		0			0
$523$	−2.85134	−	2.85134i	−0.124680	−	0.124680i	0.642013	−	0.766694i	$-0.278099\pi$
$523$	−2.85134	−	2.85134i	−0.124680	−	0.124680i	−0.766694	+	0.642013i	$0.778099\pi$
$524$		0			0
$525$	−4.64927	+	3.19902i	−0.202911	+	0.139617i
$526$		0			0
$527$	23.4987	−	11.5450i	1.02362	−	0.502907i
$528$		0			0
$529$			44.6437i			1.94103i
$530$		0			0
$531$	−0.400120			−0.0173637
$532$		0			0
$533$	19.4388	+	19.4388i	0.841986	+	0.841986i
$534$		0			0
$535$	4.10111	+	13.1953i	0.177306	+	0.570481i
$536$		0			0
$537$	6.36269	+	6.36269i	0.274570	+	0.274570i
$538$		0			0
$539$	32.8551			1.41517
$540$		0			0
$541$	14.7352			0.633516			0.316758	−	0.948506i	$-0.397406\pi$
$541$	14.7352			0.633516			0.316758	+	0.948506i	$0.397406\pi$
$542$		0			0
$543$	12.7146	−	12.7146i	0.545635	−	0.545635i
$544$		0			0
$545$	−18.5880	+	35.3529i	−0.796222	+	1.51435i
$546$		0			0
$547$	1.15252	+	1.15252i	0.0492780	+	0.0492780i	0.731316	−	0.682038i	$-0.238906\pi$
$547$	1.15252	+	1.15252i	0.0492780	+	0.0492780i	−0.682038	+	0.731316i	$0.738906\pi$
$548$		0			0
$549$	8.24999			0.352101
$550$		0			0
$551$			55.7102i			2.37334i
$552$		0			0
$553$	−0.343124	−	0.343124i	−0.0145911	−	0.0145911i
$554$		0			0
$555$	17.0882	+	8.98471i	0.725354	+	0.381380i
$556$		0			0
$557$	−8.04562	+	8.04562i	−0.340904	+	0.340904i	−0.856707	−	0.515803i	$-0.827494\pi$
$557$	−8.04562	+	8.04562i	−0.340904	+	0.340904i	0.515803	+	0.856707i	$0.327494\pi$
$558$		0			0
$559$			0.0953159i			0.00403143i
$560$		0			0
$561$			26.9814i			1.13916i
$562$		0			0
$563$	5.47387	−	5.47387i	0.230696	−	0.230696i	−0.582287	−	0.812983i	$-0.697842\pi$
$563$	5.47387	−	5.47387i	0.230696	−	0.230696i	0.812983	+	0.582287i	$0.197842\pi$
$564$		0			0
$565$	−33.6301	+	10.4523i	−1.41483	+	0.439731i
$566$		0			0
$567$	0.798115	+	0.798115i	0.0335177	+	0.0335177i
$568$		0			0
$569$	22.0428			0.924082			0.462041	−	0.886858i	$-0.347117\pi$
$569$	22.0428			0.924082			0.462041	+	0.886858i	$0.347117\pi$
$570$		0			0
$571$			9.66898i			0.404634i	0.979320	+	0.202317i	$0.0648472\pi$
$571$			9.66898i			0.404634i	−0.979320	+	0.202317i	$0.935153\pi$
$572$		0			0
$573$	−10.6001	−	10.6001i	−0.442825	−	0.442825i
$574$		0			0
$575$	−7.47242	+	40.4383i	−0.311621	+	1.68639i
$576$		0			0
$577$	20.2758	+	20.2758i	0.844093	+	0.844093i	0.989388	−	0.145295i	$-0.0464132\pi$
$577$	20.2758	+	20.2758i	0.844093	+	0.844093i	−0.145295	+	0.989388i	$0.546413\pi$
$578$		0			0
$579$	5.91750			0.245923
$580$		0			0
$581$			2.04938i			0.0850226i
$582$		0			0
$583$	19.3762	−	19.3762i	0.802479	−	0.802479i
$584$		0			0
$585$	5.90022	−	1.83380i	0.243944	−	0.0758182i
$586$		0			0
$587$	7.41783	−	7.41783i	0.306167	−	0.306167i	−0.537254	−	0.843421i	$-0.680538\pi$
$587$	7.41783	−	7.41783i	0.306167	−	0.306167i	0.843421	+	0.537254i	$0.180538\pi$
$588$		0			0
$589$	−10.7857	+	31.6194i	−0.444417	+	1.30285i
$590$		0			0
$591$	21.2108			0.872494
$592$		0			0
$593$	1.57463	−	1.57463i	0.0646625	−	0.0646625i	−0.674036	−	0.738698i	$-0.735441\pi$
$593$	1.57463	−	1.57463i	0.0646625	−	0.0646625i	0.738698	+	0.674036i	$0.235441\pi$
$594$		0			0
$595$	10.5046	+	5.52315i	0.430646	+	0.226427i
$596$		0			0
$597$	−2.96880	−	2.96880i	−0.121505	−	0.121505i
$598$		0			0
$599$			28.2074i			1.15252i	0.817266	+	0.576261i	$0.195489\pi$
$599$			28.2074i			1.15252i	−0.817266	+	0.576261i	$0.804511\pi$
$600$		0			0
$601$		−	28.2152i		−	1.15092i	−0.817830	−	0.575460i	$-0.804823\pi$
$601$		−	28.2152i		−	1.15092i	0.817830	−	0.575460i	$-0.195177\pi$
$602$		0			0
$603$	−5.55356	+	5.55356i	−0.226158	+	0.226158i
$604$		0			0
$605$	−43.3893	−	22.8134i	−1.76402	−	0.927496i
$606$		0			0
$607$	−19.0668	−	19.0668i	−0.773897	−	0.773897i	0.204889	−	0.978785i	$-0.434317\pi$
$607$	−19.0668	−	19.0668i	−0.773897	−	0.773897i	−0.978785	+	0.204889i	$0.934317\pi$
$608$		0			0
$609$		−	10.4795i		−	0.424652i
$610$		0			0
$611$		−	32.7169i		−	1.32359i
$612$		0			0
$613$	6.07282	+	6.07282i	0.245279	+	0.245279i	0.819030	−	0.573751i	$-0.194512\pi$
$613$	6.07282	+	6.07282i	0.245279	+	0.245279i	−0.573751	+	0.819030i	$0.694512\pi$
$614$		0			0
$615$	6.60269	+	21.2441i	0.266246	+	0.856644i
$616$		0			0
$617$	14.5580	+	14.5580i	0.586082	+	0.586082i	0.936568	−	0.350486i	$-0.113984\pi$
$617$	14.5580	+	14.5580i	0.586082	+	0.586082i	−0.350486	+	0.936568i	$0.613984\pi$
$618$		0			0
$619$	23.6069			0.948841			0.474420	−	0.880298i	$-0.342658\pi$
$619$	23.6069			0.948841			0.474420	+	0.880298i	$0.342658\pi$
$620$		0			0
$621$	8.22458			0.330041
$622$		0			0
$623$	2.78598	+	2.78598i	0.111618	+	0.111618i
$624$		0			0
$625$	−8.93422	+	23.3491i	−0.357369	+	0.933963i
$626$		0			0
$627$	−24.3449	−	24.3449i	−0.972243	−	0.972243i
$628$		0			0
$629$		−	40.6002i		−	1.61884i
$630$		0			0
$631$		−	34.5225i		−	1.37432i	−0.726506	−	0.687160i	$-0.758857\pi$
$631$		−	34.5225i		−	1.37432i	0.726506	−	0.687160i	$-0.241143\pi$
$632$		0			0
$633$	−2.64841	−	2.64841i	−0.105265	−	0.105265i
$634$		0			0
$635$	5.83775	−	1.81438i	0.231664	−	0.0720016i
$636$		0			0
$637$	−11.1878	+	11.1878i	−0.443277	+	0.443277i
$638$		0			0
$639$		−	6.44096i		−	0.254801i
$640$		0			0
$641$			20.5657i			0.812297i	0.913807	+	0.406149i	$0.133128\pi$
$641$			20.5657i			0.812297i	−0.913807	+	0.406149i	$0.866872\pi$
$642$		0			0
$643$	8.40875	+	8.40875i	0.331609	+	0.331609i	0.853197	−	0.521588i	$-0.174660\pi$
$643$	8.40875	+	8.40875i	0.331609	+	0.331609i	−0.521588	+	0.853197i	$0.674660\pi$
$644$		0			0
$645$	−0.0358962	+	0.0682718i	−0.00141341	+	0.00268820i
$646$		0			0
$647$	−34.5054	+	34.5054i	−1.35655	+	1.35655i	−0.478415	+	0.878134i	$0.658789\pi$
$647$	−34.5054	+	34.5054i	−1.35655	+	1.35655i	−0.878134	+	0.478415i	$0.841211\pi$
$648$		0			0
$649$	−2.29583			−0.0901192
$650$		0			0
$651$	2.02887	−	5.94785i	0.0795177	−	0.233115i
$652$		0			0
$653$	−10.1277	+	10.1277i	−0.396326	+	0.396326i	−0.876935	−	0.480609i	$-0.840416\pi$
$653$	−10.1277	+	10.1277i	−0.396326	+	0.396326i	0.480609	+	0.876935i	$0.340416\pi$
$654$		0			0
$655$	2.99962	+	1.57715i	0.117205	+	0.0616244i
$656$		0			0
$657$	−6.75269	+	6.75269i	−0.263447	+	0.263447i
$658$		0			0
$659$		−	27.0689i		−	1.05445i	−0.849725	−	0.527226i	$-0.823232\pi$
$659$		−	27.0689i		−	1.05445i	0.849725	−	0.527226i	$-0.176768\pi$
$660$		0			0
$661$	−19.4726			−0.757397			−0.378698	−	0.925520i	$-0.623628\pi$
$661$	−19.4726			−0.757397			−0.378698	+	0.925520i	$0.623628\pi$
$662$		0			0
$663$	−9.18771	−	9.18771i	−0.356821	−	0.356821i
$664$		0			0
$665$	−14.4616	+	4.49468i	−0.560796	+	0.174296i
$666$		0			0
$667$	−53.9957	−	53.9957i	−2.09072	−	2.09072i
$668$		0			0
$669$		−	9.43051i		−	0.364604i
$670$		0			0
$671$	47.3372			1.82743
$672$		0			0
$673$	−3.13560	−	3.13560i	−0.120869	−	0.120869i	0.644085	−	0.764954i	$-0.277238\pi$
$673$	−3.13560	−	3.13560i	−0.120869	−	0.120869i	−0.764954	+	0.644085i	$0.777238\pi$
$674$		0			0
$675$	4.91676	+	0.908548i	0.189246	+	0.0349700i
$676$		0			0
$677$	−29.7476	+	29.7476i	−1.14329	+	1.14329i	−0.155448	+	0.987844i	$0.549682\pi$
$677$	−29.7476	+	29.7476i	−1.14329	+	1.14329i	−0.987844	+	0.155448i	$0.950318\pi$
$678$		0			0
$679$			0.907439i			0.0348243i
$680$		0			0
$681$		−	10.2982i		−	0.394627i
$682$		0			0
$683$	−2.34143	+	2.34143i	−0.0895924	+	0.0895924i	−0.750483	−	0.660890i	$-0.770179\pi$
$683$	−2.34143	+	2.34143i	−0.0895924	+	0.0895924i	0.660890	+	0.750483i	$0.270179\pi$
$684$		0			0
$685$	−17.9826	+	5.58903i	−0.687081	+	0.213546i
$686$		0			0
$687$	−12.0882	−	12.0882i	−0.461193	−	0.461193i
$688$		0			0
$689$			13.1959i			0.502726i
$690$		0			0
$691$	−8.70214			−0.331045			−0.165523	−	0.986206i	$-0.552931\pi$
$691$	−8.70214			−0.331045			−0.165523	+	0.986206i	$0.552931\pi$
$692$		0			0
$693$	4.57947	+	4.57947i	0.173960	+	0.173960i
$694$		0			0
$695$	−5.25040	−	2.76058i	−0.199159	−	0.104715i
$696$		0			0
$697$	33.0808	−	33.0808i	1.25303	−	1.25303i
$698$		0			0
$699$	−18.6167			−0.704148
$700$		0			0
$701$	13.7719			0.520159			0.260079	−	0.965587i	$-0.416251\pi$
$701$	13.7719			0.520159			0.260079	+	0.965587i	$0.416251\pi$
$702$		0			0
$703$	36.6330	+	36.6330i	1.38164	+	1.38164i
$704$		0			0
$705$	12.3213	−	23.4341i	0.464047	−	0.882581i
$706$		0			0
$707$	−8.03551	−	8.03551i	−0.302206	−	0.302206i
$708$		0			0
$709$	6.99441			0.262681			0.131340	−	0.991337i	$-0.458072\pi$
$709$	6.99441			0.262681			0.131340	+	0.991337i	$0.458072\pi$
$710$		0			0
$711$			0.429917i			0.0161232i
$712$		0			0
$713$	−20.1925	−	41.1001i	−0.756217	−	1.53921i
$714$		0			0
$715$	33.8546	−	10.5221i	1.26609	−	0.393503i
$716$		0			0
$717$	−5.28951	−	5.28951i	−0.197540	−	0.197540i
$718$		0			0
$719$	−46.4889			−1.73374			−0.866871	−	0.498532i	$-0.833873\pi$
$719$	−46.4889			−1.73374			−0.866871	+	0.498532i	$0.833873\pi$
$720$		0			0
$721$	6.48440			0.241492
$722$		0			0
$723$	5.10723	−	5.10723i	0.189940	−	0.189940i
$724$		0			0
$725$	−26.3146	−	38.2441i	−0.977300	−	1.42035i
$726$		0			0
$727$	28.5539	+	28.5539i	1.05901	+	1.05901i	0.998146	+	0.0608593i	$0.0193841\pi$
$727$	28.5539	+	28.5539i	1.05901	+	1.05901i	0.0608593	+	0.998146i	$0.480616\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	0.162208			0.00599950
$732$		0			0
$733$	−22.3309	+	22.3309i	−0.824809	+	0.824809i	−0.986793	−	0.161984i	$-0.948211\pi$
$733$	−22.3309	+	22.3309i	−0.824809	+	0.824809i	0.161984	+	0.986793i	$0.448211\pi$
$734$		0			0
$735$	−12.2268	+	3.80012i	−0.450994	+	0.140170i
$736$		0			0
$737$	−31.8655	+	31.8655i	−1.17378	+	1.17378i
$738$		0			0
$739$	−12.7951			−0.470677			−0.235338	−	0.971913i	$-0.575620\pi$
$739$	−12.7951			−0.470677			−0.235338	+	0.971913i	$0.575620\pi$
$740$		0			0
$741$	16.5799			0.609077
$742$		0			0
$743$	−2.80467	−	2.80467i	−0.102894	−	0.102894i	0.653786	−	0.756680i	$-0.273180\pi$
$743$	−2.80467	−	2.80467i	−0.102894	−	0.102894i	−0.756680	+	0.653786i	$0.773180\pi$
$744$		0			0
$745$	−21.8447	+	41.5469i	−0.800327	+	1.52216i
$746$		0			0
$747$	1.28389	−	1.28389i	0.0469750	−	0.0469750i
$748$		0			0
$749$		−	6.97489i		−	0.254857i
$750$		0			0
$751$	40.5377			1.47924			0.739621	−	0.673024i	$-0.235005\pi$
$751$	40.5377			1.47924			0.739621	+	0.673024i	$0.235005\pi$
$752$		0			0
$753$	−19.3733	+	19.3733i	−0.706003	+	0.706003i
$754$		0			0
$755$	−2.58494	+	4.91636i	−0.0940757	+	0.178925i
$756$		0			0
$757$	5.08917	−	5.08917i	0.184969	−	0.184969i	−0.608548	−	0.793517i	$-0.708248\pi$
$757$	5.08917	−	5.08917i	0.184969	−	0.184969i	0.793517	+	0.608548i	$0.208248\pi$
$758$		0			0
$759$	47.1914			1.71294
$760$		0			0
$761$			35.4461i			1.28492i	0.766320	+	0.642459i	$0.222086\pi$
$761$			35.4461i			1.28492i	−0.766320	+	0.642459i	$0.777914\pi$
$762$		0			0
$763$	14.2563	−	14.2563i	0.516113	−	0.516113i
$764$		0			0
$765$	−3.12076	−	10.0410i	−0.112831	−	0.363033i
$766$		0			0
$767$	0.781776	−	0.781776i	0.0282283	−	0.0282283i
$768$		0			0
$769$		−	34.0144i		−	1.22659i	−0.789854	−	0.613295i	$-0.789844\pi$
$769$		−	34.0144i		−	1.22659i	0.789854	−	0.613295i	$-0.210156\pi$
$770$		0			0
$771$		−	21.2672i		−	0.765918i
$772$		0			0
$773$	−1.22760	−	1.22760i	−0.0441537	−	0.0441537i	0.684685	−	0.728839i	$-0.259940\pi$
$773$	−1.22760	−	1.22760i	−0.0441537	−	0.0441537i	−0.728839	+	0.684685i	$0.759940\pi$
$774$		0			0
$775$	−7.53115	−	26.8008i	−0.270527	−	0.962712i
$776$		0			0
$777$	−6.89095	−	6.89095i	−0.247211	−	0.247211i
$778$		0			0
$779$			59.6967i			2.13886i
$780$		0			0
$781$		−	36.9573i		−	1.32244i
$782$		0			0
$783$	−6.56517	+	6.56517i	−0.234620	+	0.234620i
$784$		0			0
$785$	−8.47873	−	27.2802i	−0.302619	−	0.973673i
$786$		0			0
$787$	−18.3484	+	18.3484i	−0.654050	+	0.654050i	−0.953966	−	0.299915i	$-0.903042\pi$
$787$	−18.3484	+	18.3484i	−0.654050	+	0.654050i	0.299915	+	0.953966i	$0.403042\pi$
$788$		0			0
$789$			4.48462i			0.159657i
$790$		0			0
$791$	17.7766			0.632062
$792$		0			0
$793$	−16.1193	+	16.1193i	−0.572412	+	0.572412i
$794$		0			0
$795$	−4.96963	+	9.45185i	−0.176255	+	0.335223i
$796$		0			0
$797$	2.73726	−	2.73726i	0.0969587	−	0.0969587i	−0.656964	−	0.753922i	$-0.728159\pi$
$797$	2.73726	−	2.73726i	0.0969587	−	0.0969587i	0.753922	+	0.656964i	$0.228159\pi$
$798$		0			0
$799$	−55.6776			−1.96973
$800$		0			0
$801$		−	3.49070i		−	0.123338i
$802$		0			0
$803$	−38.7459	+	38.7459i	−1.36731	+	1.36731i
$804$		0			0
$805$	9.66017	−	18.3729i	0.340476	−	0.647559i
$806$		0			0
$807$	−10.5232	−	10.5232i	−0.370434	−	0.370434i
$808$		0			0
$809$	21.6698			0.761871			0.380935	−	0.924602i	$-0.375602\pi$
$809$	21.6698			0.761871			0.380935	+	0.924602i	$0.375602\pi$
$810$		0			0
$811$	35.6735			1.25267			0.626333	−	0.779556i	$-0.284555\pi$
$811$	35.6735			1.25267			0.626333	+	0.779556i	$0.284555\pi$
$812$		0			0
$813$	−22.7554	+	22.7554i	−0.798066	+	0.798066i
$814$		0			0
$815$	5.44638	−	1.69274i	0.190779	−	0.0592943i
$816$		0			0
$817$	−0.146358	+	0.146358i	−0.00512043	+	0.00512043i
$818$		0			0
$819$	−3.11880			−0.108980
$820$		0			0
$821$		−	5.77012i		−	0.201378i	−0.994918	−	0.100689i	$-0.967895\pi$
$821$		−	5.77012i		−	0.201378i	0.994918	−	0.100689i	$-0.0321048\pi$
$822$		0			0
$823$	12.4190	+	12.4190i	0.432898	+	0.432898i	0.889613	−	0.456715i	$-0.150974\pi$
$823$	12.4190	+	12.4190i	0.432898	+	0.432898i	−0.456715	+	0.889613i	$0.650974\pi$
$824$		0			0
$825$	28.2117	+	5.21311i	0.982204	+	0.181497i
$826$		0			0
$827$	23.1939	−	23.1939i	0.806530	−	0.806530i	−0.177577	−	0.984107i	$-0.556826\pi$
$827$	23.1939	−	23.1939i	0.806530	−	0.806530i	0.984107	+	0.177577i	$0.0568259\pi$
$828$		0			0
$829$	26.2577			0.911967			0.455984	−	0.889988i	$-0.349288\pi$
$829$	26.2577			0.911967			0.455984	+	0.889988i	$0.349288\pi$
$830$		0			0
$831$	−19.0445			−0.660647
$832$		0			0
$833$	19.0394	+	19.0394i	0.659676	+	0.659676i
$834$		0			0
$835$	−5.75075	+	1.78734i	−0.199013	+	0.0618535i
$836$		0			0
$837$	−4.99722	+	2.45515i	−0.172729	+	0.0848623i
$838$		0			0
$839$		−	6.03760i		−	0.208441i	−0.994554	−	0.104221i	$-0.966765\pi$
$839$		−	6.03760i		−	0.208441i	0.994554	−	0.104221i	$-0.0332348\pi$
$840$		0			0
$841$	57.2029			1.97251
$842$		0			0
$843$	15.7483	+	15.7483i	0.542401	+	0.542401i
$844$		0			0
$845$	5.58281	−	10.6181i	0.192055	−	0.365273i
$846$		0			0
$847$	17.4970	+	17.4970i	0.601206	+	0.601206i
$848$		0			0
$849$	8.00514			0.274736
$850$		0			0
$851$	−71.0112			−2.43423
$852$		0			0
$853$	−1.27800	+	1.27800i	−0.0437579	+	0.0437579i	−0.728647	−	0.684889i	$-0.759851\pi$
$853$	−1.27800	+	1.27800i	−0.0437579	+	0.0437579i	0.684889	+	0.728647i	$0.259851\pi$
$854$		0			0
$855$	11.8756	+	6.24403i	0.406139	+	0.213541i
$856$		0			0
$857$	31.5215	+	31.5215i	1.07675	+	1.07675i	0.996799	+	0.0799545i	$0.0254775\pi$
$857$	31.5215	+	31.5215i	1.07675	+	1.07675i	0.0799545	+	0.996799i	$0.474523\pi$
$858$		0			0
$859$	−50.1532			−1.71121			−0.855603	−	0.517632i	$-0.826814\pi$
$859$	−50.1532			−1.71121			−0.855603	+	0.517632i	$0.826814\pi$
$860$		0			0
$861$		−	11.2294i		−	0.382697i
$862$		0			0
$863$	−10.0497	−	10.0497i	−0.342097	−	0.342097i	0.515058	−	0.857155i	$-0.327770\pi$
$863$	−10.0497	−	10.0497i	−0.342097	−	0.342097i	−0.857155	+	0.515058i	$0.827770\pi$
$864$		0			0
$865$	45.1325	−	14.0272i	1.53455	−	0.476941i
$866$		0			0
$867$	−3.61482	+	3.61482i	−0.122766	+	0.122766i
$868$		0			0
$869$			2.46680i			0.0836806i
$870$		0			0
$871$		−	21.7017i		−	0.735333i
$872$		0			0
$873$	0.568489	−	0.568489i	0.0192404	−	0.0192404i
$874$		0			0
$875$	7.80458	−	9.91642i	0.263843	−	0.335236i
$876$		0			0
$877$	−2.60917	−	2.60917i	−0.0881054	−	0.0881054i	0.661680	−	0.749786i	$-0.269844\pi$
$877$	−2.60917	−	2.60917i	−0.0881054	−	0.0881054i	−0.749786	+	0.661680i	$0.769844\pi$
$878$		0			0
$879$	−23.4532			−0.791058
$880$		0			0
$881$			12.9131i			0.435055i	0.976054	+	0.217527i	$0.0697991\pi$
$881$			12.9131i			0.435055i	−0.976054	+	0.217527i	$0.930201\pi$
$882$		0			0
$883$	17.6294	+	17.6294i	0.593277	+	0.593277i	0.938515	−	0.345238i	$-0.112202\pi$
$883$	17.6294	+	17.6294i	0.593277	+	0.593277i	−0.345238	+	0.938515i	$0.612202\pi$
$884$		0			0
$885$	0.854381	−	0.265543i	0.0287197	−	0.00892613i
$886$		0			0
$887$	38.4411	+	38.4411i	1.29072	+	1.29072i	0.934339	+	0.356385i	$0.115991\pi$
$887$	38.4411	+	38.4411i	1.29072	+	1.29072i	0.356385	+	0.934339i	$0.384009\pi$
$888$		0			0
$889$	−3.08578			−0.103494
$890$		0			0
$891$		−	5.73785i		−	0.192225i
$892$		0			0
$893$	50.2371	−	50.2371i	1.68112	−	1.68112i
$894$		0			0
$895$	−17.8090	−	9.36367i	−0.595288	−	0.312993i
$896$		0			0
$897$	−16.0696	+	16.0696i	−0.536549	+	0.536549i
$898$		0			0
$899$	48.9261	+	16.6892i	1.63178	+	0.556615i
$900$		0			0
$901$	22.4568			0.748146
$902$		0			0
$903$	0.0275311	−	0.0275311i	0.000916179	−	0.000916179i
$904$		0			0
$905$	−18.7115	+	35.5877i	−0.621990	+	1.18298i
$906$		0			0
$907$	−30.1617	−	30.1617i	−1.00150	−	1.00150i	−0.999999	−	0.00150265i	$-0.999522\pi$
$907$	−30.1617	−	30.1617i	−1.00150	−	1.00150i	−0.00150265	−	0.999999i	$-0.500478\pi$
$908$		0			0
$909$			10.0681i			0.333938i
$910$		0			0
$911$			25.9969i			0.861315i	0.902515	+	0.430658i	$0.141718\pi$
$911$			25.9969i			0.861315i	−0.902515	+	0.430658i	$0.858282\pi$
$912$		0			0
$913$	7.36675	−	7.36675i	0.243804	−	0.243804i
$914$		0			0
$915$	−17.6163	+	5.47518i	−0.582377	+	0.181004i
$916$		0			0
$917$	−1.20962	−	1.20962i	−0.0399451	−	0.0399451i
$918$		0			0
$919$			39.0347i			1.28764i	0.765178	+	0.643819i	$0.222651\pi$
$919$			39.0347i			1.28764i	−0.765178	+	0.643819i	$0.777349\pi$
$920$		0			0
$921$			3.42655i			0.112908i
$922$		0			0
$923$	12.5847	+	12.5847i	0.414230	+	0.414230i
$924$		0			0
$925$	−42.4515	−	7.84442i	−1.39580	−	0.257923i
$926$		0			0
$927$	−4.06232	−	4.06232i	−0.133424	−	0.133424i
$928$		0			0
$929$	0.768095			0.0252004			0.0126002	−	0.999921i	$-0.495989\pi$
$929$	0.768095			0.0252004			0.0126002	+	0.999921i	$0.495989\pi$
$930$		0			0
$931$	−34.3579			−1.12604
$932$		0			0
$933$	6.87041	+	6.87041i	0.224927	+	0.224927i
$934$		0			0
$935$	−17.9064	−	57.6137i	−0.585603	−	1.88417i
$936$		0			0
$937$	9.88502	+	9.88502i	0.322930	+	0.322930i	0.849890	−	0.526960i	$-0.176668\pi$
$937$	9.88502	+	9.88502i	0.322930	+	0.322930i	−0.526960	+	0.849890i	$0.676668\pi$
$938$		0			0
$939$		−	1.98655i		−	0.0648285i
$940$		0			0
$941$			17.7260i			0.577851i	0.957352	+	0.288926i	$0.0932981\pi$
$941$			17.7260i			0.577851i	−0.957352	+	0.288926i	$0.906702\pi$
$942$		0			0
$943$	−57.8595	−	57.8595i	−1.88417	−	1.88417i
$944$		0			0
$945$	−2.23390	−	1.17455i	−0.0726688	−	0.0382081i
$946$		0			0
$947$	14.3854	−	14.3854i	0.467464	−	0.467464i	−0.433628	−	0.901092i	$-0.642767\pi$
$947$	14.3854	−	14.3854i	0.467464	−	0.467464i	0.901092	+	0.433628i	$0.142767\pi$
$948$		0			0
$949$		−	26.3875i		−	0.856575i
$950$		0			0
$951$			31.8861i			1.03398i
$952$		0			0
$953$	−1.80350	−	1.80350i	−0.0584211	−	0.0584211i	0.677293	−	0.735714i	$-0.263153\pi$
$953$	−1.80350	−	1.80350i	−0.0584211	−	0.0584211i	−0.735714	+	0.677293i	$0.763153\pi$
$954$		0			0
$955$	29.6693	+	15.5997i	0.960077	+	0.504793i
$956$		0			0
$957$	−37.6700	+	37.6700i	−1.21770	+	1.21770i
$958$		0			0
$959$	9.50544			0.306947
$960$		0			0
$961$	24.5378	+	18.9445i	0.791543	+	0.611113i
$962$		0			0
$963$	−4.36960	+	4.36960i	−0.140808	+	0.140808i
$964$		0			0
$965$	−12.6357	+	3.92720i	−0.406758	+	0.126421i
$966$		0			0
$967$	−20.4392	+	20.4392i	−0.657279	+	0.657279i	−0.954736	−	0.297456i	$-0.903862\pi$
$967$	−20.4392	+	20.4392i	−0.657279	+	0.657279i	0.297456	+	0.954736i	$0.403862\pi$
$968$		0			0
$969$		−	28.2156i		−	0.906416i
$970$		0			0
$971$	−17.6698			−0.567051			−0.283525	−	0.958965i	$-0.591504\pi$
$971$	−17.6698			−0.567051			−0.283525	+	0.958965i	$0.591504\pi$
$972$		0			0
$973$	2.11726	+	2.11726i	0.0678764	+	0.0678764i
$974$		0			0
$975$	−11.3818	+	7.83146i	−0.364509	+	0.250808i
$976$		0			0
$977$	−35.2566	−	35.2566i	−1.12796	−	1.12796i	−0.990509	−	0.137451i	$-0.956109\pi$
$977$	−35.2566	−	35.2566i	−1.12796	−	1.12796i	−0.137451	−	0.990509i	$-0.543891\pi$
$978$		0			0
$979$		−	20.0291i		−	0.640134i
$980$		0			0
$981$	−17.8625			−0.570305
$982$		0			0
$983$	−15.3153	−	15.3153i	−0.488481	−	0.488481i	0.419346	−	0.907827i	$-0.362260\pi$
$983$	−15.3153	−	15.3153i	−0.488481	−	0.488481i	−0.907827	+	0.419346i	$0.862260\pi$
$984$		0			0
$985$	−45.2916	+	14.0767i	−1.44311	+	0.448521i
$986$		0			0
$987$	−9.44999	+	9.44999i	−0.300796	+	0.300796i
$988$		0			0
$989$		−	0.283708i		−	0.00902140i
$990$		0			0
$991$			62.0161i			1.97001i	0.172536	+	0.985003i	$0.444804\pi$
$991$			62.0161i			1.97001i	−0.172536	+	0.985003i	$0.555196\pi$
$992$		0			0
$993$	11.9953	−	11.9953i	0.380658	−	0.380658i
$994$		0			0
$995$	8.30958	+	4.36904i	0.263431	+	0.138508i
$996$		0			0
$997$	−27.2478	−	27.2478i	−0.862948	−	0.862948i	0.128732	−	0.991679i	$-0.458909\pi$
$997$	−27.2478	−	27.2478i	−0.862948	−	0.862948i	−0.991679	+	0.128732i	$0.958909\pi$
$998$		0			0
$999$			8.63403i			0.273169i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1860.2.s.a.1177.1	yes	64
5.3	odd	4	inner	1860.2.s.a.433.19	yes	64
31.30	odd	2	inner	1860.2.s.a.1177.19	yes	64
155.123	even	4	inner	1860.2.s.a.433.1	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1860.2.s.a.433.1	✓	64	155.123	even	4	inner
1860.2.s.a.433.19	yes	64	5.3	odd	4	inner
1860.2.s.a.1177.1	yes	64	1.1	even	1	trivial
1860.2.s.a.1177.19	yes	64	31.30	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:	\( N \)	\(=\)	\( 1860 = 2^{2} \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1860.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{3} +(1.97917 + 1.04062i) q^{5} +(-0.798115 - 0.798115i) q^{7} +1.00000i q^{9} +5.73785i q^{11} +(-1.95385 - 1.95385i) q^{13} +(-0.663658 - 2.13531i) q^{15} +(-3.32507 + 3.32507i) q^{17} -6.00031i q^{19} +1.12871i q^{21} +(5.81565 + 5.81565i) q^{23} +(2.83424 + 4.11912i) q^{25} +(0.707107 - 0.707107i) q^{27} -9.28455 q^{29} +(-5.26962 - 1.79752i) q^{31} +(4.05727 - 4.05727i) q^{33} +(-0.749075 - 2.41014i) q^{35} +(-6.10518 + 6.10518i) q^{37} +2.76317i q^{39} -9.94893 q^{41} +(-0.0243918 - 0.0243918i) q^{43} +(-1.04062 + 1.97917i) q^{45} +(8.37241 + 8.37241i) q^{47} -5.72602i q^{49} +4.70235 q^{51} +(-3.37690 - 3.37690i) q^{53} +(-5.97090 + 11.3562i) q^{55} +(-4.24286 + 4.24286i) q^{57} +0.400120i q^{59} -8.24999i q^{61} +(0.798115 - 0.798115i) q^{63} +(-1.83380 - 5.90022i) q^{65} +(5.55356 + 5.55356i) q^{67} -8.22458i q^{69} -6.44096 q^{71} +(6.75269 + 6.75269i) q^{73} +(0.908548 - 4.91676i) q^{75} +(4.57947 - 4.57947i) q^{77} +0.429917 q^{79} -1.00000 q^{81} +(-1.28389 - 1.28389i) q^{83} +(-10.0410 + 3.12076i) q^{85} +(6.56517 + 6.56517i) q^{87} -3.49070 q^{89} +3.11880i q^{91} +(2.45515 + 4.99722i) q^{93} +(6.24403 - 11.8756i) q^{95} +(-0.568489 - 0.568489i) q^{97} -5.73785 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{7} + 16 q^{25} + 8 q^{31} - 8 q^{33} + 24 q^{35} + 16 q^{41} + 56 q^{47} + 8 q^{63} - 32 q^{67} - 16 q^{71} - 64 q^{81} - 32 q^{87} - 32 q^{95} + 64 q^{97}+O(q^{100}) \) 64 * q - 8 * q^7 + 16 * q^25 + 8 * q^31 - 8 * q^33 + 24 * q^35 + 16 * q^41 + 56 * q^47 + 8 * q^63 - 32 * q^67 - 16 * q^71 - 64 * q^81 - 32 * q^87 - 32 * q^95 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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