LMFDB - Embedded newform 2380.2.cb.b.781.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2380,2,Mod(781,2380)] 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("2380.781"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2380, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2380 = 2^{2} \cdot 5 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2380.cb (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [92] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$19.0043956811$
Analytic rank:	$0$
Dimension:	$92$
Relative dimension:	$46$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			781.13
Character	$\chi$	$=$	2380.781
Dual form			2380.2.cb.b.1801.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.43555 - 0.828817i) q^{3} +(-0.866025 + 0.500000i) q^{5} +(-0.635268 + 2.56835i) q^{7} +(-0.126124 - 0.218454i) q^{9} +(-1.98492 - 1.14599i) q^{11} +1.85101 q^{13} +1.65763 q^{15} +(-3.96367 + 1.13549i) q^{17} +(2.04691 + 3.54536i) q^{19} +(3.04066 - 3.16049i) q^{21} +(2.98157 - 1.72141i) q^{23} +(0.500000 - 0.866025i) q^{25} +5.39104i q^{27} +3.58666i q^{29} +(-1.09474 - 0.632048i) q^{31} +(1.89964 + 3.29027i) q^{33} +(-0.734018 - 2.54189i) q^{35} +(-6.78481 + 3.91721i) q^{37} +(-2.65723 - 1.53415i) q^{39} -10.2832i q^{41} -1.10738 q^{43} +(0.218454 + 0.126124i) q^{45} +(3.34245 + 5.78929i) q^{47} +(-6.19287 - 3.26318i) q^{49} +(6.63117 + 1.65511i) q^{51} +(3.96203 - 6.86243i) q^{53} +2.29198 q^{55} -6.78607i q^{57} +(7.35612 - 12.7412i) q^{59} +(-4.03071 + 2.32713i) q^{61} +(0.641189 - 0.185155i) q^{63} +(-1.60303 + 0.925507i) q^{65} +(7.06075 - 12.2296i) q^{67} -5.70694 q^{69} +3.28416i q^{71} +(4.89356 + 2.82530i) q^{73} +(-1.43555 + 0.828817i) q^{75} +(4.20427 - 4.36996i) q^{77} +(-2.93011 + 1.69170i) q^{79} +(4.08981 - 7.08376i) q^{81} -2.06606 q^{83} +(2.86489 - 2.96519i) q^{85} +(2.97268 - 5.14884i) q^{87} +(0.339195 + 0.587503i) q^{89} +(-1.17589 + 4.75406i) q^{91} +(1.04771 + 1.81468i) q^{93} +(-3.54536 - 2.04691i) q^{95} +6.57359i q^{97} +0.578150i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q + 56 q^{9} - 24 q^{13} + 12 q^{15} + 4 q^{17} - 24 q^{21} + 46 q^{25} - 24 q^{33} + 14 q^{35} - 64 q^{43} + 16 q^{47} + 38 q^{49} - 22 q^{51} - 8 q^{53} + 18 q^{59} + 16 q^{67} - 36 q^{69} - 12 q^{77}+ \cdots + 44 q^{93}+O(q^{100}) $ 92 * q + 56 * q^9 - 24 * q^13 + 12 * q^15 + 4 * q^17 - 24 * q^21 + 46 * q^25 - 24 * q^33 + 14 * q^35 - 64 * q^43 + 16 * q^47 + 38 * q^49 - 22 * q^51 - 8 * q^53 + 18 * q^59 + 16 * q^67 - 36 * q^69 - 12 * q^77 - 86 * q^81 + 8 * q^83 - 20 * q^85 + 20 * q^87 + 2 * q^89 + 44 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2380\mathbb{Z}\right)^\times$.

$n$	$477$	$1191$	$1261$	$1361$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.43555	−	0.828817i	−0.828817	−	0.478518i	0.0246304	−	0.999697i	$-0.492159\pi$
$3$	−1.43555	−	0.828817i	−0.828817	−	0.478518i	−0.853447	+	0.521179i	$0.825492\pi$
$4$		0			0
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$		0			0
$7$	−0.635268	+	2.56835i	−0.240109	+	0.970746i
$7$	−0.635268	+	2.56835i	−0.240109	+	0.970746i
$8$		0			0
$9$	−0.126124	−	0.218454i	−0.0420415	−	0.0728180i
$10$		0			0
$11$	−1.98492	−	1.14599i	−0.598475	−	0.345530i	0.169966	−	0.985450i	$-0.445634\pi$
$11$	−1.98492	−	1.14599i	−0.598475	−	0.345530i	−0.768441	+	0.639920i	$0.778967\pi$
$12$		0			0
$13$	1.85101			0.513379			0.256690	−	0.966494i	$-0.417368\pi$
$13$	1.85101			0.513379			0.256690	+	0.966494i	$0.417368\pi$
$14$		0			0
$15$	1.65763			0.427999
$16$		0			0
$17$	−3.96367	+	1.13549i	−0.961331	+	0.275396i
$17$	−3.96367	+	1.13549i	−0.961331	+	0.275396i
$18$		0			0
$19$	2.04691	+	3.54536i	0.469594	+	0.813361i	0.999396	−	0.0347606i	$-0.0110669\pi$
$19$	2.04691	+	3.54536i	0.469594	+	0.813361i	−0.529801	+	0.848122i	$0.677734\pi$
$20$		0			0
$21$	3.04066	−	3.16049i	0.663525	−	0.689675i
$22$		0			0
$23$	2.98157	−	1.72141i	0.621701	−	0.358939i	−0.155830	−	0.987784i	$-0.549805\pi$
$23$	2.98157	−	1.72141i	0.621701	−	0.358939i	0.777531	+	0.628845i	$0.216472\pi$
$24$		0			0
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$		0			0
$27$			5.39104i			1.03751i
$28$		0			0
$29$			3.58666i			0.666025i	0.942922	+	0.333013i	$0.108065\pi$
$29$			3.58666i			0.666025i	−0.942922	+	0.333013i	$0.891935\pi$
$30$		0			0
$31$	−1.09474	−	0.632048i	−0.196621	−	0.113519i	0.398457	−	0.917187i	$-0.369546\pi$
$31$	−1.09474	−	0.632048i	−0.196621	−	0.113519i	−0.595078	+	0.803668i	$0.702879\pi$
$32$		0			0
$33$	1.89964	+	3.29027i	0.330684	+	0.572762i
$34$		0			0
$35$	−0.734018	−	2.54189i	−0.124072	−	0.429658i
$36$		0			0
$37$	−6.78481	+	3.91721i	−1.11542	+	0.643986i	−0.940227	−	0.340549i	$-0.889387\pi$
$37$	−6.78481	+	3.91721i	−1.11542	+	0.643986i	−0.175190	+	0.984535i	$0.556054\pi$
$38$		0			0
$39$	−2.65723	−	1.53415i	−0.425497	−	0.245661i
$40$		0			0
$41$		−	10.2832i		−	1.60597i	−0.596002	−	0.802983i	$-0.703245\pi$
$41$		−	10.2832i		−	1.60597i	0.596002	−	0.802983i	$-0.296755\pi$
$42$		0			0
$43$	−1.10738			−0.168874			−0.0844372	−	0.996429i	$-0.526909\pi$
$43$	−1.10738			−0.168874			−0.0844372	+	0.996429i	$0.526909\pi$
$44$		0			0
$45$	0.218454	+	0.126124i	0.0325652	+	0.0188015i
$46$		0			0
$47$	3.34245	+	5.78929i	0.487546	+	0.844455i	0.999897	−	0.0143210i	$-0.00455868\pi$
$47$	3.34245	+	5.78929i	0.487546	+	0.844455i	−0.512351	+	0.858776i	$0.671225\pi$
$48$		0			0
$49$	−6.19287	−	3.26318i	−0.884696	−	0.466169i
$50$		0			0
$51$	6.63117	+	1.65511i	0.928549	+	0.231761i
$52$		0			0
$53$	3.96203	−	6.86243i	0.544226	−	0.942628i	−0.454429	−	0.890783i	$-0.650157\pi$
$53$	3.96203	−	6.86243i	0.544226	−	0.942628i	0.998655	−	0.0518447i	$-0.0165101\pi$
$54$		0			0
$55$	2.29198			0.309051
$56$		0			0
$57$		−	6.78607i		−	0.898837i
$58$		0			0
$59$	7.35612	−	12.7412i	0.957685	−	1.65876i	0.229584	−	0.973289i	$-0.426263\pi$
$59$	7.35612	−	12.7412i	0.957685	−	1.65876i	0.728101	−	0.685470i	$-0.240403\pi$
$60$		0			0
$61$	−4.03071	+	2.32713i	−0.516079	+	0.297958i	−0.735329	−	0.677710i	$-0.762972\pi$
$61$	−4.03071	+	2.32713i	−0.516079	+	0.297958i	0.219250	+	0.975669i	$0.429639\pi$
$62$		0			0
$63$	0.641189	−	0.185155i	0.0807823	−	0.0233274i
$64$		0			0
$65$	−1.60303	+	0.925507i	−0.198831	+	0.114795i
$66$		0			0
$67$	7.06075	−	12.2296i	0.862607	−	1.49408i	−0.00679605	−	0.999977i	$-0.502163\pi$
$67$	7.06075	−	12.2296i	0.862607	−	1.49408i	0.869403	−	0.494103i	$-0.164503\pi$
$68$		0			0
$69$	−5.70694			−0.687035
$70$		0			0
$71$			3.28416i			0.389758i	0.980827	+	0.194879i	$0.0624314\pi$
$71$			3.28416i			0.389758i	−0.980827	+	0.194879i	$0.937569\pi$
$72$		0			0
$73$	4.89356	+	2.82530i	0.572747	+	0.330676i	0.758246	−	0.651969i	$-0.226057\pi$
$73$	4.89356	+	2.82530i	0.572747	+	0.330676i	−0.185499	+	0.982645i	$0.559390\pi$
$74$		0			0
$75$	−1.43555	+	0.828817i	−0.165763	+	0.0957036i
$76$		0			0
$77$	4.20427	−	4.36996i	0.479121	−	0.498003i
$78$		0			0
$79$	−2.93011	+	1.69170i	−0.329663	+	0.190331i	−0.655692	−	0.755029i	$-0.727623\pi$
$79$	−2.93011	+	1.69170i	−0.329663	+	0.190331i	0.326028	+	0.945360i	$0.394289\pi$
$80$		0			0
$81$	4.08981	−	7.08376i	0.454424	−	0.787085i
$82$		0			0
$83$	−2.06606			−0.226780			−0.113390	−	0.993551i	$-0.536171\pi$
$83$	−2.06606			−0.226780			−0.113390	+	0.993551i	$0.536171\pi$
$84$		0			0
$85$	2.86489	−	2.96519i	0.310741	−	0.321620i
$86$		0			0
$87$	2.97268	−	5.14884i	0.318705	−	0.552013i
$88$		0			0
$89$	0.339195	+	0.587503i	0.0359546	+	0.0622752i	0.883443	−	0.468539i	$-0.155219\pi$
$89$	0.339195	+	0.587503i	0.0359546	+	0.0622752i	−0.847488	+	0.530814i	$0.821886\pi$
$90$		0			0
$91$	−1.17589	+	4.75406i	−0.123267	+	0.498361i
$92$		0			0
$93$	1.04771	+	1.81468i	0.108642	+	0.188173i
$94$		0			0
$95$	−3.54536	−	2.04691i	−0.363746	−	0.210009i
$96$		0			0
$97$			6.57359i			0.667447i	0.942671	+	0.333723i	$0.108305\pi$
$97$			6.57359i			0.667447i	−0.942671	+	0.333723i	$0.891695\pi$
$98$		0			0
$99$			0.578150i			0.0581063i
$100$		0			0
$101$	−0.754844	+	1.30743i	−0.0751098	+	0.130094i	−0.901134	−	0.433541i	$-0.857264\pi$
$101$	−0.754844	+	1.30743i	−0.0751098	+	0.130094i	0.826024	+	0.563635i	$0.190597\pi$
$102$		0			0
$103$	−0.303984	−	0.526516i	−0.0299524	−	0.0518791i	0.850661	−	0.525715i	$-0.176202\pi$
$103$	−0.303984	−	0.526516i	−0.0299524	−	0.0518791i	−0.880613	+	0.473836i	$0.842869\pi$
$104$		0			0
$105$	−1.05304	+	4.25739i	−0.102766	+	0.415479i
$106$		0			0
$107$	8.10796	−	4.68113i	0.783826	−	0.452542i	−0.0539585	−	0.998543i	$-0.517184\pi$
$107$	8.10796	−	4.68113i	0.783826	−	0.452542i	0.837785	+	0.546001i	$0.183851\pi$
$108$		0			0
$109$	−13.6321	−	7.87051i	−1.30572	−	0.753858i	−0.324341	−	0.945940i	$-0.605143\pi$
$109$	−13.6321	−	7.87051i	−1.30572	−	0.753858i	−0.981379	+	0.192082i	$0.938476\pi$
$110$		0			0
$111$	12.9866			1.23263
$112$		0			0
$113$		−	19.5449i		−	1.83863i	−0.393528	−	0.919313i	$-0.628746\pi$
$113$		−	19.5449i		−	1.83863i	0.393528	−	0.919313i	$-0.371254\pi$
$114$		0			0
$115$	−1.72141	+	2.98157i	−0.160522	+	0.278033i
$116$		0			0
$117$	−0.233458	−	0.404361i	−0.0215832	−	0.0373832i
$118$		0			0
$119$	−0.398338	−	10.9014i	−0.0365156	−	0.999333i
$120$		0			0
$121$	−2.87340	−	4.97688i	−0.261218	−	0.452444i
$122$		0			0
$123$	−8.52289	+	14.7621i	−0.768484	+	1.33105i
$124$		0			0
$125$			1.00000i			0.0894427i
$126$		0			0
$127$	−6.24771			−0.554394			−0.277197	−	0.960813i	$-0.589406\pi$
$127$	−6.24771			−0.554394			−0.277197	+	0.960813i	$0.589406\pi$
$128$		0			0
$129$	1.58971	+	0.917818i	0.139966	+	0.0808094i
$130$		0			0
$131$	15.6383	−	9.02875i	1.36632	−	0.788846i	0.375865	−	0.926674i	$-0.377346\pi$
$131$	15.6383	−	9.02875i	1.36632	−	0.788846i	0.990456	+	0.137829i	$0.0440123\pi$
$132$		0			0
$133$	−10.4061	+	3.00494i	−0.902321	+	0.260562i
$134$		0			0
$135$	−2.69552	−	4.66878i	−0.231993	−	0.401824i
$136$		0			0
$137$	0.617232	−	1.06908i	0.0527337	−	0.0913374i	−0.838454	−	0.544973i	$-0.816540\pi$
$137$	0.617232	−	1.06908i	0.0527337	−	0.0913374i	0.891187	+	0.453636i	$0.149873\pi$
$138$		0			0
$139$		−	22.1090i		−	1.87526i	−0.347636	−	0.937630i	$-0.613015\pi$
$139$		−	22.1090i		−	1.87526i	0.347636	−	0.937630i	$-0.386985\pi$
$140$		0			0
$141$		−	11.0811i		−	0.933198i
$142$		0			0
$143$	−3.67411	−	2.12125i	−0.307245	−	0.177388i
$144$		0			0
$145$	−1.79333	−	3.10614i	−0.148928	−	0.257951i
$146$		0			0
$147$	6.18561	+	9.81723i	0.510181	+	0.809711i
$148$		0			0
$149$	−10.2472	−	17.7487i	−0.839485	−	1.45403i	−0.890325	−	0.455325i	$-0.849523\pi$
$149$	−10.2472	−	17.7487i	−0.839485	−	1.45403i	0.0508401	−	0.998707i	$-0.483810\pi$
$150$		0			0
$151$	−0.132394	+	0.229313i	−0.0107741	+	0.0186612i	−0.871362	−	0.490640i	$-0.836763\pi$
$151$	−0.132394	+	0.229313i	−0.0107741	+	0.0186612i	0.860588	+	0.509302i	$0.170096\pi$
$152$		0			0
$153$	0.747967	+	0.722666i	0.0604695	+	0.0584241i
$154$		0			0
$155$	1.26410			0.101535
$156$		0			0
$157$	−2.62348	+	4.54400i	−0.209376	+	0.362651i	−0.951518	−	0.307592i	$-0.900477\pi$
$157$	−2.62348	+	4.54400i	−0.209376	+	0.362651i	0.742142	+	0.670243i	$0.233810\pi$
$158$		0			0
$159$	−11.3754	+	6.56759i	−0.902128	+	0.520844i
$160$		0			0
$161$	2.52710	+	8.75129i	0.199163	+	0.689698i
$162$		0			0
$163$	11.3096	−	6.52958i	0.885834	−	0.511437i	0.0132565	−	0.999912i	$-0.495780\pi$
$163$	11.3096	−	6.52958i	0.885834	−	0.511437i	0.872578	+	0.488476i	$0.162447\pi$
$164$		0			0
$165$	−3.29027	−	1.89964i	−0.256147	−	0.147886i
$166$		0			0
$167$		−	5.07341i		−	0.392593i	−0.980545	−	0.196296i	$-0.937109\pi$
$167$		−	5.07341i		−	0.392593i	0.980545	−	0.196296i	$-0.0628914\pi$
$168$		0			0
$169$	−9.57375			−0.736442
$170$		0			0
$171$	0.516332	−	0.894313i	0.0394849	−	0.0683898i
$172$		0			0
$173$	10.4176	−	6.01459i	0.792034	−	0.457281i	−0.0486442	−	0.998816i	$-0.515490\pi$
$173$	10.4176	−	6.01459i	0.792034	−	0.457281i	0.840678	+	0.541535i	$0.182157\pi$
$174$		0			0
$175$	1.90662	+	1.83433i	0.144127	+	0.138663i
$176$		0			0
$177$	−21.1202	+	12.1938i	−1.58749	+	0.916539i
$178$		0			0
$179$	0.955505	−	1.65498i	0.0714178	−	0.123699i	−0.828105	−	0.560573i	$-0.810581\pi$
$179$	0.955505	−	1.65498i	0.0714178	−	0.123699i	0.899523	+	0.436874i	$0.143914\pi$
$180$		0			0
$181$		−	10.5375i		−	0.783244i	−0.920126	−	0.391622i	$-0.871914\pi$
$181$		−	10.5375i		−	0.783244i	0.920126	−	0.391622i	$-0.128086\pi$
$182$		0			0
$183$	7.71506			0.570313
$184$		0			0
$185$	3.91721	−	6.78481i	0.287999	−	0.498829i
$186$		0			0
$187$	9.16881	+	2.28849i	0.670490	+	0.167351i
$188$		0			0
$189$	−13.8461	−	3.42475i	−1.00715	−	0.249114i
$190$		0			0
$191$	4.14907	+	7.18640i	0.300216	+	0.519990i	0.976185	−	0.216941i	$-0.0696078\pi$
$191$	4.14907	+	7.18640i	0.300216	+	0.519990i	−0.675969	+	0.736930i	$0.736275\pi$
$192$		0			0
$193$	−10.9536	−	6.32407i	−0.788458	−	0.455217i	0.0509613	−	0.998701i	$-0.483771\pi$
$193$	−10.9536	−	6.32407i	−0.788458	−	0.455217i	−0.839419	+	0.543484i	$0.817105\pi$
$194$		0			0
$195$	3.06830			0.219726
$196$		0			0
$197$			9.76831i			0.695963i	0.937501	+	0.347982i	$0.113133\pi$
$197$			9.76831i			0.695963i	−0.937501	+	0.347982i	$0.886867\pi$
$198$		0			0
$199$	6.33846	+	3.65951i	0.449321	+	0.259416i	0.707543	−	0.706670i	$-0.249803\pi$
$199$	6.33846	+	3.65951i	0.449321	+	0.259416i	−0.258222	+	0.966086i	$0.583137\pi$
$200$		0			0
$201$	−20.2722	+	11.7041i	−1.42989	+	0.825546i
$202$		0			0
$203$	−9.21180	−	2.27849i	−0.646541	−	0.159918i
$204$		0			0
$205$	5.14160	+	8.90552i	0.359105	+	0.621988i
$206$		0			0
$207$	−0.752098	−	0.434224i	−0.0522744	−	0.0301807i
$208$		0			0
$209$		−	9.38299i		−	0.649035i
$210$		0			0
$211$		−	10.5952i		−	0.729405i	−0.931124	−	0.364702i	$-0.881171\pi$
$211$		−	10.5952i		−	0.729405i	0.931124	−	0.364702i	$-0.118829\pi$
$212$		0			0
$213$	2.72197	−	4.71459i	0.186506	−	0.323038i
$214$		0			0
$215$	0.959022	−	0.553692i	0.0654048	−	0.0377615i
$216$		0			0
$217$	2.31878	−	2.41016i	0.157409	−	0.163612i
$218$		0			0
$219$	−4.68331	−	8.11173i	−0.316469	−	0.548140i
$220$		0			0
$221$	−7.33681	+	2.10180i	−0.493527	+	0.141382i
$222$		0			0
$223$	1.26330			0.0845968			0.0422984	−	0.999105i	$-0.486532\pi$
$223$	1.26330			0.0845968			0.0422984	+	0.999105i	$0.486532\pi$
$224$		0			0
$225$	−0.252249			−0.0168166
$226$		0			0
$227$	−3.72983	−	2.15342i	−0.247558	−	0.142927i	0.371088	−	0.928598i	$-0.378985\pi$
$227$	−3.72983	−	2.15342i	−0.247558	−	0.142927i	−0.618645	+	0.785670i	$0.712318\pi$
$228$		0			0
$229$	−0.273482	−	0.473684i	−0.0180722	−	0.0313019i	0.856848	−	0.515569i	$-0.172420\pi$
$229$	−0.273482	−	0.473684i	−0.0180722	−	0.0313019i	−0.874920	+	0.484267i	$0.839086\pi$
$230$		0			0
$231$	−9.65734	+	2.78874i	−0.635406	+	0.183485i
$232$		0			0
$233$	−0.153735	+	0.0887591i	−0.0100715	+	0.00581480i	−0.505027	−	0.863103i	$-0.668518\pi$
$233$	−0.153735	+	0.0887591i	−0.0100715	+	0.00581480i	0.494956	+	0.868918i	$0.335184\pi$
$234$		0			0
$235$	−5.78929	−	3.34245i	−0.377652	−	0.218037i
$236$		0			0
$237$	5.60844			0.364307
$238$		0			0
$239$	−16.8293			−1.08859			−0.544297	−	0.838892i	$-0.683204\pi$
$239$	−16.8293			−1.08859			−0.544297	+	0.838892i	$0.683204\pi$
$240$		0			0
$241$	9.53024	+	5.50229i	0.613897	+	0.354434i	0.774489	−	0.632587i	$-0.218007\pi$
$241$	9.53024	+	5.50229i	0.613897	+	0.354434i	−0.160592	+	0.987021i	$0.551340\pi$
$242$		0			0
$243$	2.26404	−	1.30715i	0.145238	−	0.0838534i
$244$		0			0
$245$	6.99477	−	0.270436i	0.446880	−	0.0172775i
$246$		0			0
$247$	3.78887	+	6.56251i	0.241080	+	0.417563i
$248$		0			0
$249$	2.96594	+	1.71239i	0.187959	+	0.108518i
$250$		0			0
$251$	−28.1247			−1.77521			−0.887607	−	0.460602i	$-0.847634\pi$
$251$	−28.1247			−1.77521			−0.887607	+	0.460602i	$0.847634\pi$
$252$		0			0
$253$	−7.89090			−0.496097
$254$		0			0
$255$	−6.57031	+	1.88222i	−0.411449	+	0.117869i
$256$		0			0
$257$	4.36925	+	7.56776i	0.272546	+	0.472064i	0.969513	−	0.245039i	$-0.0788009\pi$
$257$	4.36925	+	7.56776i	0.272546	+	0.472064i	−0.696967	+	0.717103i	$0.745468\pi$
$258$		0			0
$259$	−5.75061	−	19.9143i	−0.357326	−	1.23741i
$260$		0			0
$261$	0.783519	−	0.452365i	0.0484986	−	0.0280007i
$262$		0			0
$263$	−7.63300	+	13.2207i	−0.470671	+	0.815226i	−0.999437	−	0.0335417i	$-0.989321\pi$
$263$	−7.63300	+	13.2207i	−0.470671	+	0.815226i	0.528767	+	0.848767i	$0.322655\pi$
$264$		0			0
$265$			7.92406i			0.486771i
$266$		0			0
$267$		−	1.12452i		−	0.0688197i
$268$		0			0
$269$	−13.2646	−	7.65830i	−0.808755	−	0.466935i	0.0377684	−	0.999287i	$-0.487975\pi$
$269$	−13.2646	−	7.65830i	−0.808755	−	0.466935i	−0.846523	+	0.532352i	$0.821308\pi$
$270$		0			0
$271$	8.12650	+	14.0755i	0.493650	+	0.855026i	0.999973	−	0.00731742i	$-0.00232923\pi$
$271$	8.12650	+	14.0755i	0.493650	+	0.855026i	−0.506324	+	0.862344i	$0.668996\pi$
$272$		0			0
$273$	5.62830	−	5.85011i	0.340640	−	0.354065i
$274$		0			0
$275$	−1.98492	+	1.14599i	−0.119695	+	0.0691059i
$276$		0			0
$277$	0.658799	+	0.380358i	0.0395834	+	0.0228535i	0.519661	−	0.854372i	$-0.326058\pi$
$277$	0.658799	+	0.380358i	0.0395834	+	0.0228535i	−0.480078	+	0.877226i	$0.659392\pi$
$278$		0			0
$279$			0.318867i			0.0190901i
$280$		0			0
$281$	−1.94519			−0.116040			−0.0580202	−	0.998315i	$-0.518479\pi$
$281$	−1.94519			−0.116040			−0.0580202	+	0.998315i	$0.518479\pi$
$282$		0			0
$283$	22.5131	+	12.9979i	1.33826	+	0.772648i	0.986550	−	0.163460i	$-0.0522653\pi$
$283$	22.5131	+	12.9979i	1.33826	+	0.772648i	0.351715	+	0.936107i	$0.385599\pi$
$284$		0			0
$285$	3.39303	+	5.87691i	0.200986	+	0.348118i
$286$		0			0
$287$	26.4109	+	6.53259i	1.55899	+	0.385606i
$288$		0			0
$289$	14.4213	−	9.00138i	0.848314	−	0.529493i
$290$		0			0
$291$	5.44830	−	9.43674i	0.319385	−	0.553191i
$292$		0			0
$293$	27.6570			1.61574			0.807870	−	0.589361i	$-0.200620\pi$
$293$	27.6570			1.61574			0.807870	+	0.589361i	$0.200620\pi$
$294$		0			0
$295$			14.7122i			0.856579i
$296$		0			0
$297$	6.17809	−	10.7008i	0.358489	−	0.620921i
$298$		0			0
$299$	5.51893	−	3.18636i	0.319168	−	0.184272i
$300$		0			0
$301$	0.703485	−	2.84415i	0.0405482	−	0.163934i
$302$		0			0
$303$	2.16724	−	1.25126i	0.124505	−	0.0718827i
$304$		0			0
$305$	2.32713	−	4.03071i	0.133251	−	0.230798i
$306$		0			0
$307$	31.5992			1.80346			0.901731	−	0.432298i	$-0.142297\pi$
$307$	31.5992			1.80346			0.901731	+	0.432298i	$0.142297\pi$
$308$		0			0
$309$			1.00779i			0.0573311i
$310$		0			0
$311$	27.9958	+	16.1634i	1.58750	+	0.916542i	0.993718	+	0.111915i	$0.0356983\pi$
$311$	27.9958	+	16.1634i	1.58750	+	0.916542i	0.593780	+	0.804628i	$0.297635\pi$
$312$		0			0
$313$	−11.1297	+	6.42576i	−0.629090	+	0.363205i	−0.780400	−	0.625281i	$-0.784984\pi$
$313$	−11.1297	+	6.42576i	−0.629090	+	0.363205i	0.151310	+	0.988486i	$0.451651\pi$
$314$		0			0
$315$	−0.462709	+	0.480944i	−0.0260707	+	0.0270981i
$316$		0			0
$317$	11.9496	−	6.89908i	0.671154	−	0.387491i	−0.125360	−	0.992111i	$-0.540009\pi$
$317$	11.9496	−	6.89908i	0.671154	−	0.387491i	0.796514	+	0.604621i	$0.206675\pi$
$318$		0			0
$319$	4.11028	−	7.11922i	0.230132	−	0.398600i
$320$		0			0
$321$	−15.5192			−0.866198
$322$		0			0
$323$	−12.1390	−	11.7284i	−0.675432	−	0.652585i
$324$		0			0
$325$	0.925507	−	1.60303i	0.0513379	−	0.0889199i
$326$		0			0
$327$	13.0464	+	22.5971i	0.721469	+	1.24962i
$328$		0			0
$329$	−16.9923	+	4.90684i	−0.936815	+	0.270523i
$330$		0			0
$331$	−14.6139	−	25.3120i	−0.803253	−	1.39128i	−0.917464	−	0.397819i	$-0.869767\pi$
$331$	−14.6139	−	25.3120i	−0.803253	−	1.39128i	0.114211	−	0.993457i	$-0.463566\pi$
$332$		0			0
$333$	1.71146	+	0.988112i	0.0937875	+	0.0541482i
$334$		0			0
$335$			14.1215i			0.771539i
$336$		0			0
$337$			25.2631i			1.37617i	0.725630	+	0.688085i	$0.241548\pi$
$337$			25.2631i			1.37617i	−0.725630	+	0.688085i	$0.758452\pi$
$338$		0			0
$339$	−16.1991	+	28.0577i	−0.879815	+	1.52388i
$340$		0			0
$341$	1.44865	+	2.50913i	0.0784486	+	0.135877i
$342$		0			0
$343$	12.3151	−	13.8325i	0.664955	−	0.746884i
$344$		0			0
$345$	4.94236	−	2.85347i	0.266088	−	0.153626i
$346$		0			0
$347$	−9.90901	−	5.72097i	−0.531943	−	0.307118i	0.209864	−	0.977731i	$-0.432698\pi$
$347$	−9.90901	−	5.72097i	−0.531943	−	0.307118i	−0.741807	+	0.670613i	$0.766031\pi$
$348$		0			0
$349$	−12.5080			−0.669536			−0.334768	−	0.942301i	$-0.608658\pi$
$349$	−12.5080			−0.669536			−0.334768	+	0.942301i	$0.608658\pi$
$350$		0			0
$351$			9.97889i			0.532634i
$352$		0			0
$353$	9.02968	−	15.6399i	0.480601	−	0.832426i	−0.519151	−	0.854682i	$-0.673752\pi$
$353$	9.02968	−	15.6399i	0.480601	−	0.832426i	0.999752	+	0.0222568i	$0.00708516\pi$
$354$		0			0
$355$	−1.64208	−	2.84417i	−0.0871526	−	0.150953i
$356$		0			0
$357$	−8.46346	+	15.9797i	−0.447934	+	0.845738i
$358$		0			0
$359$	4.98301	+	8.63083i	0.262993	+	0.455518i	0.967036	−	0.254640i	$-0.0819569\pi$
$359$	4.98301	+	8.63083i	0.262993	+	0.455518i	−0.704043	+	0.710158i	$0.748624\pi$
$360$		0			0
$361$	1.12029	−	1.94039i	0.0589624	−	0.102126i
$362$		0			0
$363$			9.52610i			0.499991i
$364$		0			0
$365$	−5.65059			−0.295765
$366$		0			0
$367$	19.5510	+	11.2878i	1.02055	+	0.589217i	0.914264	−	0.405118i	$-0.132770\pi$
$367$	19.5510	+	11.2878i	1.02055	+	0.589217i	0.106289	+	0.994335i	$0.466103\pi$
$368$		0			0
$369$	−2.24641	+	1.29696i	−0.116943	+	0.0675172i
$370$		0			0
$371$	15.1082	+	14.5354i	0.784379	+	0.754639i
$372$		0			0
$373$	−4.17546	−	7.23211i	−0.216197	−	0.374465i	0.737445	−	0.675407i	$-0.236032\pi$
$373$	−4.17546	−	7.23211i	−0.216197	−	0.374465i	−0.953642	+	0.300943i	$0.902699\pi$
$374$		0			0
$375$	0.828817	−	1.43555i	0.0427999	−	0.0741317i
$376$		0			0
$377$			6.63895i			0.341923i
$378$		0			0
$379$		−	5.68789i		−	0.292167i	−0.989272	−	0.146084i	$-0.953333\pi$
$379$		−	5.68789i		−	0.292167i	0.989272	−	0.146084i	$-0.0466669\pi$
$380$		0			0
$381$	8.96892	+	5.17821i	0.459492	+	0.265288i
$382$		0			0
$383$	6.92066	+	11.9869i	0.353629	+	0.612504i	0.986882	−	0.161441i	$-0.0516141\pi$
$383$	6.92066	+	11.9869i	0.353629	+	0.612504i	−0.633253	+	0.773945i	$0.718281\pi$
$384$		0			0
$385$	−1.45602	+	5.88663i	−0.0742059	+	0.300010i
$386$		0			0
$387$	0.139668	+	0.241912i	0.00709973	+	0.0122971i
$388$		0			0
$389$	11.7325	−	20.3213i	0.594861	−	1.03033i	−0.398706	−	0.917079i	$-0.630541\pi$
$389$	11.7325	−	20.3213i	0.594861	−	1.03033i	0.993567	−	0.113250i	$-0.0361261\pi$
$390$		0			0
$391$	−9.86333	+	10.2086i	−0.498810	+	0.516273i
$392$		0			0
$393$	−29.9327			−1.50991
$394$		0			0
$395$	1.69170	−	2.93011i	0.0851187	−	0.147430i
$396$		0			0
$397$	−19.3696	+	11.1830i	−0.972133	+	0.561261i	−0.899886	−	0.436126i	$-0.856350\pi$
$397$	−19.3696	+	11.1830i	−0.972133	+	0.561261i	−0.0722471	+	0.997387i	$0.523017\pi$
$398$		0			0
$399$	17.4290	+	4.31097i	0.872542	+	0.215818i
$400$		0			0
$401$	−10.3130	+	5.95423i	−0.515008	+	0.297340i	−0.734890	−	0.678187i	$-0.762766\pi$
$401$	−10.3130	+	5.95423i	−0.515008	+	0.297340i	0.219882	+	0.975527i	$0.429433\pi$
$402$		0			0
$403$	−2.02638	−	1.16993i	−0.100941	−	0.0582784i
$404$		0			0
$405$			8.17962i			0.406449i
$406$		0			0
$407$	17.9564			0.890065
$408$		0			0
$409$	−11.2006	+	19.4000i	−0.553834	+	0.959269i	0.444159	+	0.895948i	$0.353503\pi$
$409$	−11.2006	+	19.4000i	−0.553834	+	0.959269i	−0.997993	+	0.0633210i	$0.979831\pi$
$410$		0			0
$411$	−1.77214	+	1.02314i	−0.0874131	+	0.0504680i
$412$		0			0
$413$	28.0507	+	26.9872i	1.38029	+	1.32795i
$414$		0			0
$415$	1.78926	−	1.03303i	0.0878314	−	0.0507095i
$416$		0			0
$417$	−18.3243	+	31.7386i	−0.897345	+	1.55425i
$418$		0			0
$419$		−	21.2301i		−	1.03716i	−0.855029	−	0.518580i	$-0.826461\pi$
$419$		−	21.2301i		−	1.03716i	0.855029	−	0.518580i	$-0.173539\pi$
$420$		0			0
$421$	−4.03128			−0.196472			−0.0982362	−	0.995163i	$-0.531320\pi$
$421$	−4.03128			−0.196472			−0.0982362	+	0.995163i	$0.531320\pi$
$422$		0			0
$423$	0.843129	−	1.46034i	0.0409943	−	0.0710043i
$424$		0			0
$425$	−0.998475	+	4.00038i	−0.0484331	+	0.194047i
$426$		0			0
$427$	−3.41631	−	11.8306i	−0.165327	−	0.572524i
$428$		0			0
$429$	3.51625	+	6.09033i	0.169766	+	0.294044i
$430$		0			0
$431$	−13.7778	−	7.95462i	−0.663654	−	0.383161i	0.130014	−	0.991512i	$-0.458498\pi$
$431$	−13.7778	−	7.95462i	−0.663654	−	0.383161i	−0.793668	+	0.608351i	$0.791831\pi$
$432$		0			0
$433$	−32.0080			−1.53821			−0.769104	−	0.639124i	$-0.779297\pi$
$433$	−32.0080			−1.53821			−0.769104	+	0.639124i	$0.779297\pi$
$434$		0			0
$435$			5.94536i			0.285058i
$436$		0			0
$437$	12.2060	+	7.04716i	0.583894	+	0.337112i
$438$		0			0
$439$	16.0733	−	9.27994i	0.767138	−	0.442907i	−0.0647146	−	0.997904i	$-0.520614\pi$
$439$	16.0733	−	9.27994i	0.767138	−	0.442907i	0.831853	+	0.554996i	$0.187280\pi$
$440$		0			0
$441$	0.0682171	+	1.76442i	0.00324843	+	0.0840202i
$442$		0			0
$443$	15.7680	+	27.3110i	0.749160	+	1.29758i	0.948226	+	0.317597i	$0.102876\pi$
$443$	15.7680	+	27.3110i	0.749160	+	1.29758i	−0.199066	+	0.979986i	$0.563791\pi$
$444$		0			0
$445$	−0.587503	−	0.339195i	−0.0278503	−	0.0160794i
$446$		0			0
$447$			33.9723i			1.60683i
$448$		0			0
$449$		−	11.0589i		−	0.521901i	−0.965352	−	0.260950i	$-0.915964\pi$
$449$		−	11.0589i		−	0.521901i	0.965352	−	0.260950i	$-0.0840359\pi$
$450$		0			0
$451$	−11.7845	+	20.4113i	−0.554909	+	0.961131i
$452$		0			0
$453$	0.380117	−	0.219461i	0.0178595	−	0.0103112i
$454$		0			0
$455$	−1.35868	−	4.70508i	−0.0636958	−	0.220578i
$456$		0			0
$457$	−5.25676	−	9.10498i	−0.245901	−	0.425913i	0.716484	−	0.697604i	$-0.245750\pi$
$457$	−5.25676	−	9.10498i	−0.245901	−	0.425913i	−0.962385	+	0.271691i	$0.912417\pi$
$458$		0			0
$459$	−6.12145	−	21.3683i	−0.285725	−	0.997387i
$460$		0			0
$461$	15.3372			0.714327			0.357163	−	0.934042i	$-0.383744\pi$
$461$	15.3372			0.714327			0.357163	+	0.934042i	$0.383744\pi$
$462$		0			0
$463$	−11.6436			−0.541123			−0.270562	−	0.962703i	$-0.587209\pi$
$463$	−11.6436			−0.541123			−0.270562	+	0.962703i	$0.587209\pi$
$464$		0			0
$465$	−1.81468	−	1.04771i	−0.0841537	−	0.0485862i
$466$		0			0
$467$	13.9157	+	24.1027i	0.643942	+	1.11534i	0.984545	+	0.175133i	$0.0560357\pi$
$467$	13.9157	+	24.1027i	0.643942	+	1.11534i	−0.340602	+	0.940207i	$0.610631\pi$
$468$		0			0
$469$	26.9244	+	25.9035i	1.24325	+	1.19611i
$470$		0			0
$471$	7.53229	−	4.34877i	0.347070	−	0.200381i
$472$		0			0
$473$	2.19806	+	1.26905i	0.101067	+	0.0583511i
$474$		0			0
$475$	4.09383			0.187838
$476$		0			0
$477$	−1.99883			−0.0915203
$478$		0			0
$479$	6.64099	+	3.83418i	0.303434	+	0.175188i	0.643985	−	0.765038i	$-0.277280\pi$
$479$	6.64099	+	3.83418i	0.303434	+	0.175188i	−0.340550	+	0.940226i	$0.610613\pi$
$480$		0			0
$481$	−12.5588	+	7.25082i	−0.572631	+	0.330609i
$482$		0			0
$483$	3.62544	−	14.6574i	0.164963	−	0.666937i
$484$		0			0
$485$	−3.28679	−	5.69289i	−0.149246	−	0.258501i
$486$		0			0
$487$	−6.27188	−	3.62107i	−0.284206	−	0.164086i	0.351120	−	0.936330i	$-0.385801\pi$
$487$	−6.27188	−	3.62107i	−0.284206	−	0.164086i	−0.635326	+	0.772244i	$0.719134\pi$
$488$		0			0
$489$	−21.6473			−0.978926
$490$		0			0
$491$	−5.20382			−0.234845			−0.117423	−	0.993082i	$-0.537463\pi$
$491$	−5.20382			−0.234845			−0.117423	+	0.993082i	$0.537463\pi$
$492$		0			0
$493$	−4.07260	−	14.2163i	−0.183421	−	0.640271i
$494$		0			0
$495$	−0.289075	−	0.500693i	−0.0129930	−	0.0225045i
$496$		0			0
$497$	−8.43488	−	2.08632i	−0.378356	−	0.0935843i
$498$		0			0
$499$	31.5727	−	18.2285i	1.41339	−	0.816021i	0.417684	−	0.908592i	$-0.362842\pi$
$499$	31.5727	−	18.2285i	1.41339	−	0.816021i	0.995706	+	0.0925711i	$0.0295085\pi$
$500$		0			0
$501$	−4.20493	+	7.28316i	−0.187862	+	0.325387i
$502$		0			0
$503$		−	12.0546i		−	0.537489i	−0.963212	−	0.268744i	$-0.913391\pi$
$503$		−	12.0546i		−	0.537489i	0.963212	−	0.268744i	$-0.0866087\pi$
$504$		0			0
$505$		−	1.50969i		−	0.0671802i
$506$		0			0
$507$	13.7436	+	7.93488i	0.610376	+	0.352401i
$508$		0			0
$509$	14.0412	+	24.3200i	0.622364	+	1.07797i	0.989044	+	0.147619i	$0.0471610\pi$
$509$	14.0412	+	24.3200i	0.622364	+	1.07797i	−0.366680	+	0.930347i	$0.619506\pi$
$510$		0			0
$511$	−10.3651	+	10.7736i	−0.458524	+	0.476594i
$512$		0			0
$513$	−19.1132	+	11.0350i	−0.843867	+	0.487207i
$514$		0			0
$515$	0.526516	+	0.303984i	0.0232011	+	0.0133951i
$516$		0			0
$517$		−	15.3217i		−	0.673847i
$518$		0			0
$519$	−19.9400			−0.875268
$520$		0			0
$521$	−8.35689	−	4.82485i	−0.366122	−	0.211381i	0.305641	−	0.952147i	$-0.401129\pi$
$521$	−8.35689	−	4.82485i	−0.366122	−	0.211381i	−0.671763	+	0.740766i	$0.734463\pi$
$522$		0			0
$523$	1.06564	+	1.84575i	0.0465974	+	0.0807091i	0.888383	−	0.459102i	$-0.151829\pi$
$523$	1.06564	+	1.84575i	0.0465974	+	0.0807091i	−0.841786	+	0.539811i	$0.818496\pi$
$524$		0			0
$525$	−1.21673	−	4.21353i	−0.0531026	−	0.183893i
$526$		0			0
$527$	5.05687	+	1.26217i	0.220281	+	0.0549809i
$528$		0			0
$529$	−5.57348	+	9.65356i	−0.242325	+	0.419720i
$530$		0			0
$531$	−3.71114			−0.161050
$532$		0			0
$533$		−	19.0344i		−	0.824470i
$534$		0			0
$535$	−4.68113	+	8.10796i	−0.202383	+	0.350538i
$536$		0			0
$537$	−2.74336	+	1.58388i	−0.118385	+	0.0683493i
$538$		0			0
$539$	8.55275	+	13.5741i	0.368393	+	0.584679i
$540$		0			0
$541$	5.38035	−	3.10635i	0.231319	−	0.133552i	−0.379861	−	0.925044i	$-0.624028\pi$
$541$	5.38035	−	3.10635i	0.231319	−	0.133552i	0.611181	+	0.791491i	$0.290695\pi$
$542$		0			0
$543$	−8.73364	+	15.1271i	−0.374796	+	0.649166i
$544$		0			0
$545$	15.7410			0.674271
$546$		0			0
$547$		−	3.34325i		−	0.142947i	−0.997442	−	0.0714735i	$-0.977230\pi$
$547$		−	3.34325i		−	0.142947i	0.997442	−	0.0714735i	$-0.0227701\pi$
$548$		0			0
$549$	1.01674	+	0.587015i	0.0433934	+	0.0250532i
$550$		0			0
$551$	−12.7160	+	7.34158i	−0.541719	+	0.312762i
$552$		0			0
$553$	−2.48348	−	8.60024i	−0.105608	−	0.365719i
$554$		0			0
$555$	−11.2467	+	6.49331i	−0.477397	+	0.275626i
$556$		0			0
$557$	22.1183	−	38.3099i	0.937180	−	1.62324i	0.166481	−	0.986045i	$-0.446759\pi$
$557$	22.1183	−	38.3099i	0.937180	−	1.62324i	0.770699	−	0.637199i	$-0.219907\pi$
$558$		0			0
$559$	−2.04978			−0.0866966
$560$		0			0
$561$	−11.2656	−	10.8845i	−0.475633	−	0.459545i
$562$		0			0
$563$	−7.90031	+	13.6837i	−0.332958	+	0.576701i	−0.983090	−	0.183121i	$-0.941380\pi$
$563$	−7.90031	+	13.6837i	−0.332958	+	0.576701i	0.650132	+	0.759821i	$0.274713\pi$
$564$		0			0
$565$	9.77243	+	16.9263i	0.411129	+	0.712097i
$566$		0			0
$567$	15.5955	+	15.0042i	0.654948	+	0.630116i
$568$		0			0
$569$	−12.2131	−	21.1537i	−0.511999	−	0.886808i	−0.999903	−	0.0139112i	$-0.995572\pi$
$569$	−12.2131	−	21.1537i	−0.511999	−	0.886808i	0.487904	−	0.872897i	$-0.337762\pi$
$570$		0			0
$571$	34.9908	+	20.2019i	1.46432	+	0.845424i	0.999207	−	0.0398280i	$-0.0126810\pi$
$571$	34.9908	+	20.2019i	1.46432	+	0.845424i	0.465111	+	0.885252i	$0.346014\pi$
$572$		0			0
$573$		−	13.7553i		−	0.574635i
$574$		0			0
$575$		−	3.44282i		−	0.143576i
$576$		0			0
$577$	21.4661	−	37.1803i	0.893645	−	1.54784i	0.0581717	−	0.998307i	$-0.481473\pi$
$577$	21.4661	−	37.1803i	0.893645	−	1.54784i	0.835473	−	0.549531i	$-0.185194\pi$
$578$		0			0
$579$	10.4830	+	18.1571i	0.435658	+	0.754583i
$580$		0			0
$581$	1.31250	−	5.30637i	0.0544518	−	0.220145i
$582$		0			0
$583$	−15.7286	+	9.08091i	−0.651412	+	0.376093i
$584$		0			0
$585$	0.404361	+	0.233458i	0.0167183	+	0.00965230i
$586$		0			0
$587$	−0.876945			−0.0361954			−0.0180977	−	0.999836i	$-0.505761\pi$
$587$	−0.876945			−0.0361954			−0.0180977	+	0.999836i	$0.505761\pi$
$588$		0			0
$589$		−	5.17500i		−	0.213232i
$590$		0			0
$591$	8.09614	−	14.0229i	0.333031	−	0.576826i
$592$		0			0
$593$	−12.5372	−	21.7151i	−0.514842	−	0.891732i	−0.999852	−	0.0172232i	$-0.994517\pi$
$593$	−12.5372	−	21.7151i	−0.514842	−	0.891732i	0.485010	−	0.874509i	$-0.338816\pi$
$594$		0			0
$595$	5.79569	+	9.24175i	0.237600	+	0.378875i
$596$		0			0
$597$	−6.06613	−	10.5068i	−0.248270	−	0.430016i
$598$		0			0
$599$	−19.6809	+	34.0884i	−0.804141	+	1.39281i	0.112728	+	0.993626i	$0.464041\pi$
$599$	−19.6809	+	34.0884i	−0.804141	+	1.39281i	−0.916869	+	0.399187i	$0.869292\pi$
$600$		0			0
$601$		−	25.3186i		−	1.03277i	−0.856357	−	0.516384i	$-0.827278\pi$
$601$		−	25.3186i		−	1.03277i	0.856357	−	0.516384i	$-0.172722\pi$
$602$		0			0
$603$	−3.56213			−0.145061
$604$		0			0
$605$	4.97688	+	2.87340i	0.202339	+	0.116820i
$606$		0			0
$607$	−24.6593	+	14.2370i	−1.00089	+	0.577864i	−0.908511	−	0.417860i	$-0.862780\pi$
$607$	−24.6593	+	14.2370i	−1.00089	+	0.577864i	−0.0923782	+	0.995724i	$0.529447\pi$
$608$		0			0
$609$	11.3356	+	10.9058i	0.459341	+	0.441925i
$610$		0			0
$611$	6.18692	+	10.7161i	0.250296	+	0.433526i
$612$		0			0
$613$	−17.3975	+	30.1333i	−0.702676	+	1.21707i	0.264847	+	0.964290i	$0.414679\pi$
$613$	−17.3975	+	30.1333i	−0.702676	+	1.21707i	−0.967524	+	0.252781i	$0.918655\pi$
$614$		0			0
$615$		−	17.0458i		−	0.687353i
$616$		0			0
$617$			22.9421i			0.923613i	0.886981	+	0.461806i	$0.152798\pi$
$617$			22.9421i			0.923613i	−0.886981	+	0.461806i	$0.847202\pi$
$618$		0			0
$619$	−1.76637	−	1.01982i	−0.0709966	−	0.0409899i	0.464081	−	0.885793i	$-0.346384\pi$
$619$	−1.76637	−	1.01982i	−0.0709966	−	0.0409899i	−0.535078	+	0.844803i	$0.679718\pi$
$620$		0			0
$621$	9.28020	+	16.0738i	0.372401	+	0.645018i
$622$		0			0
$623$	−1.72439	+	0.497951i	−0.0690864	+	0.0199500i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−7.77678	+	13.4698i	−0.310575	+	0.537931i
$628$		0			0
$629$	22.4448	−	23.2306i	0.894933	−	0.926265i
$630$		0			0
$631$	−31.5409			−1.25563			−0.627813	−	0.778364i	$-0.716050\pi$
$631$	−31.5409			−1.25563			−0.627813	+	0.778364i	$0.716050\pi$
$632$		0			0
$633$	−8.78150	+	15.2100i	−0.349033	+	0.604543i
$634$		0			0
$635$	5.41067	−	3.12385i	0.214716	−	0.123966i
$636$		0			0
$637$	−11.4631	−	6.04020i	−0.454184	−	0.239321i
$638$		0			0
$639$	0.717438	−	0.414213i	0.0283814	−	0.0163860i
$640$		0			0
$641$	30.5828	+	17.6570i	1.20795	+	0.697408i	0.962310	−	0.271954i	$-0.0876699\pi$
$641$	30.5828	+	17.6570i	1.20795	+	0.697408i	0.245636	+	0.969362i	$0.421003\pi$
$642$		0			0
$643$			35.7989i			1.41177i	0.708327	+	0.705884i	$0.249450\pi$
$643$			35.7989i			1.41177i	−0.708327	+	0.705884i	$0.750550\pi$
$644$		0			0
$645$	−1.83564			−0.0722781
$646$		0			0
$647$	−2.45836	+	4.25800i	−0.0966481	+	0.167399i	−0.910295	−	0.413960i	$-0.864145\pi$
$647$	−2.45836	+	4.25800i	−0.0966481	+	0.167399i	0.813647	+	0.581359i	$0.197479\pi$
$648$		0			0
$649$	−29.2026	+	16.8601i	−1.14630	+	0.661817i
$650$		0			0
$651$	−5.32631	+	1.53807i	−0.208754	+	0.0602817i
$652$		0			0
$653$	20.8091	−	12.0141i	0.814323	−	0.470150i	−0.0341319	−	0.999417i	$-0.510867\pi$
$653$	20.8091	−	12.0141i	0.814323	−	0.470150i	0.848455	+	0.529268i	$0.177533\pi$
$654$		0			0
$655$	−9.02875	+	15.6383i	−0.352783	+	0.611037i
$656$		0			0
$657$		−	1.42535i		−	0.0556084i
$658$		0			0
$659$	−31.1409			−1.21308			−0.606539	−	0.795054i	$-0.707443\pi$
$659$	−31.1409			−1.21308			−0.606539	+	0.795054i	$0.707443\pi$
$660$		0			0
$661$	15.0092	−	25.9966i	0.583789	−	1.01115i	−0.411236	−	0.911529i	$-0.634903\pi$
$661$	15.0092	−	25.9966i	0.583789	−	1.01115i	0.995025	−	0.0996234i	$-0.0317638\pi$
$662$		0			0
$663$	12.2744	+	3.06362i	0.476698	+	0.118981i
$664$		0			0
$665$	7.50945	−	7.80539i	0.291204	−	0.302680i
$666$		0			0
$667$	6.17411	+	10.6939i	0.239063	+	0.414069i
$668$		0			0
$669$	−1.81353	−	1.04704i	−0.0701153	−	0.0404811i
$670$		0			0
$671$	10.6675			0.411814
$672$		0			0
$673$			14.9067i			0.574610i	0.957839	+	0.287305i	$0.0927593\pi$
$673$			14.9067i			0.574610i	−0.957839	+	0.287305i	$0.907241\pi$
$674$		0			0
$675$	4.66878	+	2.69552i	0.179701	+	0.103751i
$676$		0			0
$677$	−26.5469	+	15.3268i	−1.02028	+	0.589058i	−0.914185	−	0.405298i	$-0.867168\pi$
$677$	−26.5469	+	15.3268i	−1.02028	+	0.589058i	−0.106094	+	0.994356i	$0.533835\pi$
$678$		0			0
$679$	−16.8833	−	4.17599i	−0.647921	−	0.160260i
$680$		0			0
$681$	3.56958	+	6.18270i	0.136787	+	0.236921i
$682$		0			0
$683$	−16.3296	−	9.42791i	−0.624836	−	0.360749i	0.153914	−	0.988084i	$-0.450812\pi$
$683$	−16.3296	−	9.42791i	−0.624836	−	0.360749i	−0.778749	+	0.627335i	$0.784146\pi$
$684$		0			0
$685$			1.23446i			0.0471664i
$686$		0			0
$687$			0.906665i			0.0345914i
$688$		0			0
$689$	7.33377	−	12.7025i	0.279394	−	0.483925i
$690$		0			0
$691$	−32.0159	+	18.4844i	−1.21794	+	0.703180i	−0.964478	−	0.264165i	$-0.914904\pi$
$691$	−32.0159	+	18.4844i	−1.21794	+	0.703180i	−0.253466	+	0.967344i	$0.581570\pi$
$692$		0			0
$693$	−1.48489	−	0.367280i	−0.0564065	−	0.0139518i
$694$		0			0
$695$	11.0545	+	19.1469i	0.419321	+	0.726285i
$696$		0			0
$697$	11.6764	+	40.7592i	0.442277	+	1.54387i
$698$		0			0
$699$	0.294260			0.0111299
$700$		0			0
$701$	−14.2279			−0.537379			−0.268690	−	0.963227i	$-0.586591\pi$
$701$	−14.2279			−0.537379			−0.268690	+	0.963227i	$0.586591\pi$
$702$		0			0
$703$	−27.7759	−	16.0364i	−1.04759	−	0.604824i
$704$		0			0
$705$	5.54056	+	9.59653i	0.208670	+	0.361426i
$706$		0			0
$707$	−2.87841	−	2.76927i	−0.108254	−	0.104149i
$708$		0			0
$709$	18.5183	−	10.6916i	0.695470	−	0.401530i	−0.110188	−	0.993911i	$-0.535145\pi$
$709$	18.5183	−	10.6916i	0.695470	−	0.401530i	0.805658	+	0.592381i	$0.201812\pi$
$710$		0			0
$711$	0.739117	+	0.426729i	0.0277190	+	0.0160036i
$712$		0			0
$713$	−4.35206			−0.162986
$714$		0			0
$715$	4.24250			0.158660
$716$		0			0
$717$	24.1593	+	13.9484i	0.902246	+	0.520912i
$718$		0			0
$719$	31.2943	−	18.0678i	1.16708	−	0.673815i	0.214090	−	0.976814i	$-0.431321\pi$
$719$	31.2943	−	18.0678i	1.16708	−	0.673815i	0.952991	+	0.302999i	$0.0979880\pi$
$720$		0			0
$721$	1.54539	−	0.446260i	0.0575533	−	0.0166196i
$722$		0			0
$723$	−9.12078	−	15.7977i	−0.339206	−	0.587521i
$724$		0			0
$725$	3.10614	+	1.79333i	0.115359	+	0.0666025i
$726$		0			0
$727$	−21.7441			−0.806443			−0.403222	−	0.915102i	$-0.632110\pi$
$727$	−21.7441			−0.806443			−0.403222	+	0.915102i	$0.632110\pi$
$728$		0			0
$729$	−28.8724			−1.06935
$730$		0			0
$731$	4.38930	−	1.25742i	0.162344	−	0.0465073i
$732$		0			0
$733$	−21.2381	−	36.7854i	−0.784447	−	1.35870i	−0.929329	−	0.369252i	$-0.879614\pi$
$733$	−21.2381	−	36.7854i	−0.784447	−	1.35870i	0.144883	−	0.989449i	$-0.453720\pi$
$734$		0			0
$735$	−10.2655	−	5.40916i	−0.378649	−	0.199520i
$736$		0			0
$737$	−28.0300	+	16.1831i	−1.03250	+	0.596113i
$738$		0			0
$739$	−6.40704	+	11.0973i	−0.235687	+	0.408221i	−0.959472	−	0.281804i	$-0.909067\pi$
$739$	−6.40704	+	11.0973i	−0.235687	+	0.408221i	0.723785	+	0.690025i	$0.242401\pi$
$740$		0			0
$741$		−	12.5611i		−	0.461444i
$742$		0			0
$743$		−	40.3418i		−	1.48000i	−0.672608	−	0.739999i	$-0.734826\pi$
$743$		−	40.3418i		−	1.48000i	0.672608	−	0.739999i	$-0.265174\pi$
$744$		0			0
$745$	17.7487	+	10.2472i	0.650263	+	0.375429i
$746$		0			0
$747$	0.260581	+	0.451339i	0.00953415	+	0.0165136i
$748$		0			0
$749$	6.87207	+	23.7979i	0.251100	+	0.869555i
$750$		0			0
$751$	21.4119	−	12.3622i	0.781332	−	0.451102i	−0.0555700	−	0.998455i	$-0.517698\pi$
$751$	21.4119	−	12.3622i	0.781332	−	0.451102i	0.836902	+	0.547352i	$0.184364\pi$
$752$		0			0
$753$	40.3745	+	23.3102i	1.47133	+	0.849471i
$754$		0			0
$755$		−	0.264788i		−	0.00963662i
$756$		0			0
$757$	45.0684			1.63804			0.819019	−	0.573767i	$-0.194518\pi$
$757$	45.0684			1.63804			0.819019	+	0.573767i	$0.194518\pi$
$758$		0			0
$759$	11.3278	+	6.54011i	0.411173	+	0.237391i
$760$		0			0
$761$	−2.28549	−	3.95859i	−0.0828490	−	0.143499i	0.821624	−	0.570030i	$-0.193069\pi$
$761$	−2.28549	−	3.95859i	−0.0828490	−	0.143499i	−0.904473	+	0.426532i	$0.859735\pi$
$762$		0			0
$763$	28.8743	−	30.0122i	1.04532	−	1.08651i
$764$		0			0
$765$	−1.00909	−	0.251864i	−0.0364838	−	0.00910616i
$766$		0			0
$767$	13.6163	−	23.5841i	0.491655	−	0.851572i
$768$		0			0
$769$	−27.2297			−0.981927			−0.490964	−	0.871180i	$-0.663355\pi$
$769$	−27.2297			−0.981927			−0.490964	+	0.871180i	$0.663355\pi$
$770$		0			0
$771$		−	14.4852i		−	0.521673i
$772$		0			0
$773$	21.2672	−	36.8358i	0.764927	−	1.32489i	−0.175358	−	0.984505i	$-0.556108\pi$
$773$	21.2672	−	36.8358i	0.764927	−	1.32489i	0.940285	−	0.340388i	$-0.110558\pi$
$774$		0			0
$775$	−1.09474	+	0.632048i	−0.0393242	+	0.0227039i
$776$		0			0
$777$	−8.24998	+	33.3542i	−0.295966	+	1.19658i
$778$		0			0
$779$	36.4576	−	21.0488i	1.30623	−	0.754153i
$780$		0			0
$781$	3.76362	−	6.51879i	0.134673	−	0.233261i
$782$		0			0
$783$	−19.3358			−0.691005
$784$		0			0
$785$		−	5.24696i		−	0.187272i
$786$		0			0
$787$	−7.06643	−	4.07981i	−0.251891	−	0.145429i	0.368739	−	0.929533i	$-0.379790\pi$
$787$	−7.06643	−	4.07981i	−0.251891	−	0.145429i	−0.620630	+	0.784104i	$0.713123\pi$
$788$		0			0
$789$	21.9151	−	12.6527i	0.780200	−	0.450449i
$790$		0			0
$791$	50.1981	+	12.4162i	1.78484	+	0.441470i
$792$		0			0
$793$	−7.46089	+	4.30755i	−0.264944	+	0.152966i
$794$		0			0
$795$	6.56759	−	11.3754i	0.232929	−	0.403444i
$796$		0			0
$797$	−22.1034			−0.782943			−0.391471	−	0.920190i	$-0.628034\pi$
$797$	−22.1034			−0.782943			−0.391471	+	0.920190i	$0.628034\pi$
$798$		0			0
$799$	−19.8220	−	19.1515i	−0.701253	−	0.677533i
$800$		0			0
$801$	0.0855615	−	0.148197i	0.00302317	−	0.00523628i
$802$		0			0
$803$	−6.47554	−	11.2160i	−0.228517	−	0.395802i
$804$		0			0
$805$	−6.56417	−	6.31529i	−0.231357	−	0.222585i
$806$		0			0
$807$	12.6947	+	21.9878i	0.446873	+	0.774007i
$808$		0			0
$809$	−6.63543	−	3.83096i	−0.233289	−	0.134690i	0.378799	−	0.925479i	$-0.376337\pi$
$809$	−6.63543	−	3.83096i	−0.233289	−	0.134690i	−0.612088	+	0.790789i	$0.709670\pi$
$810$		0			0
$811$			21.4622i			0.753640i	0.926287	+	0.376820i	$0.122982\pi$
$811$			21.4622i			0.753640i	−0.926287	+	0.376820i	$0.877018\pi$
$812$		0			0
$813$		−	26.9415i		−	0.944880i
$814$		0			0
$815$	−6.52958	+	11.3096i	−0.228721	+	0.396157i
$816$		0			0
$817$	−2.26672	−	3.92607i	−0.0793024	−	0.137356i
$818$		0			0
$819$	1.18685	−	0.342725i	0.0414719	−	0.0119758i
$820$		0			0
$821$	26.8990	−	15.5302i	0.938782	−	0.542006i	0.0492038	−	0.998789i	$-0.484332\pi$
$821$	26.8990	−	15.5302i	0.938782	−	0.542006i	0.889578	+	0.456783i	$0.150998\pi$
$822$		0			0
$823$	−47.9515	−	27.6848i	−1.67148	−	0.965031i	−0.966809	−	0.255500i	$-0.917760\pi$
$823$	−47.9515	−	27.6848i	−1.67148	−	0.965031i	−0.704674	−	0.709531i	$-0.748907\pi$
$824$		0			0
$825$	3.79927			0.132274
$826$		0			0
$827$		−	23.8140i		−	0.828094i	−0.910256	−	0.414047i	$-0.864115\pi$
$827$		−	23.8140i		−	0.828094i	0.910256	−	0.414047i	$-0.135885\pi$
$828$		0			0
$829$	−1.81879	+	3.15023i	−0.0631691	+	0.109412i	−0.895880	−	0.444295i	$-0.853454\pi$
$829$	−1.81879	+	3.15023i	−0.0631691	+	0.109412i	0.832711	+	0.553707i	$0.186787\pi$
$830$		0			0
$831$	−0.630494	−	1.09205i	−0.0218716	−	0.0378827i
$832$		0			0
$833$	28.2518	+	5.90226i	0.978866	+	0.204501i
$834$		0			0
$835$	2.53671	+	4.39370i	0.0877864	+	0.152050i
$836$		0			0
$837$	3.40740	−	5.90179i	0.117777	−	0.203996i
$838$		0			0
$839$		−	14.7134i		−	0.507962i	−0.967209	−	0.253981i	$-0.918260\pi$
$839$		−	14.7134i		−	0.507962i	0.967209	−	0.253981i	$-0.0817401\pi$
$840$		0			0
$841$	16.1359			0.556410
$842$		0			0
$843$	2.79243	+	1.61221i	0.0961763	+	0.0555274i
$844$		0			0
$845$	8.29111	−	4.78687i	0.285223	−	0.164673i
$846$		0			0
$847$	14.6078	−	4.21826i	0.501929	−	0.144941i
$848$		0			0
$849$	−21.5458	−	37.3185i	−0.739451	−	1.28077i
$850$		0			0
$851$	−13.4863	+	23.3589i	−0.462304	+	0.800733i
$852$		0			0
$853$			31.3265i			1.07260i	0.844028	+	0.536299i	$0.180178\pi$
$853$			31.3265i			1.07260i	−0.844028	+	0.536299i	$0.819822\pi$
$854$		0			0
$855$			1.03266i			0.0353163i
$856$		0			0
$857$	−2.40326	−	1.38752i	−0.0820937	−	0.0473968i	0.458391	−	0.888751i	$-0.348426\pi$
$857$	−2.40326	−	1.38752i	−0.0820937	−	0.0473968i	−0.540485	+	0.841354i	$0.681759\pi$
$858$		0			0
$859$	4.86474	+	8.42597i	0.165983	+	0.287491i	0.937004	−	0.349319i	$-0.113587\pi$
$859$	4.86474	+	8.42597i	0.165983	+	0.287491i	−0.771021	+	0.636810i	$0.780254\pi$
$860$		0			0
$861$	−32.4999	−	31.2677i	−1.10759	−	1.06560i
$862$		0			0
$863$	4.11084	+	7.12018i	0.139935	+	0.242374i	0.927472	−	0.373893i	$-0.121977\pi$
$863$	4.11084	+	7.12018i	0.139935	+	0.242374i	−0.787537	+	0.616267i	$0.788644\pi$
$864$		0			0
$865$	−6.01459	+	10.4176i	−0.204502	+	0.354208i
$866$		0			0
$867$	−28.1631	+	0.969309i	−0.956469	+	0.0329195i
$868$		0			0
$869$	7.75470			0.263060
$870$		0			0
$871$	13.0695	−	22.6371i	0.442845	−	0.767029i
$872$		0			0
$873$	1.43603	−	0.829090i	0.0486021	−	0.0280604i
$874$		0			0
$875$	−2.56835	−	0.635268i	−0.0868262	−	0.0214760i
$876$		0			0
$877$	2.08816	−	1.20560i	0.0705121	−	0.0407102i	−0.464329	−	0.885663i	$-0.653705\pi$
$877$	2.08816	−	1.20560i	0.0705121	−	0.0407102i	0.534842	+	0.844952i	$0.320371\pi$
$878$		0			0
$879$	−39.7031	−	22.9226i	−1.33915	−	0.773160i
$880$		0			0
$881$		−	40.4257i		−	1.36198i	−0.732294	−	0.680988i	$-0.761550\pi$
$881$		−	40.4257i		−	1.36198i	0.732294	−	0.680988i	$-0.238450\pi$
$882$		0			0
$883$	−44.9234			−1.51179			−0.755897	−	0.654691i	$-0.772799\pi$
$883$	−44.9234			−1.51179			−0.755897	+	0.654691i	$0.772799\pi$
$884$		0			0
$885$	12.1938	−	21.1202i	0.409888	−	0.709948i
$886$		0			0
$887$	−39.4867	+	22.7976i	−1.32583	+	0.765470i	−0.984652	−	0.174528i	$-0.944160\pi$
$887$	−39.4867	+	22.7976i	−1.32583	+	0.765470i	−0.341181	+	0.939998i	$0.610827\pi$
$888$		0			0
$889$	3.96897	−	16.0463i	0.133115	−	0.538176i
$890$		0			0
$891$	−16.2359	+	9.37379i	−0.543922	+	0.314034i
$892$		0			0
$893$	−13.6834	+	23.7004i	−0.457898	+	0.793103i
$894$		0			0
$895$			1.91101i			0.0638780i
$896$		0			0
$897$	−10.5636			−0.352709
$898$		0			0
$899$	2.26694	−	3.92646i	0.0756067	−	0.130955i
$900$		0			0
$901$	−7.91197	+	31.6992i	−0.263586	+	1.05605i
$902$		0			0
$903$	−3.36717	+	3.49987i	−0.112052	+	0.116468i
$904$		0			0
$905$	5.26874	+	9.12572i	0.175139	+	0.303349i
$906$		0			0
$907$	−0.896334	−	0.517498i	−0.0297623	−	0.0171833i	0.485045	−	0.874489i	$-0.338803\pi$
$907$	−0.896334	−	0.517498i	−0.0297623	−	0.0171833i	−0.514807	+	0.857306i	$0.672137\pi$
$908$		0			0
$909$	0.380817			0.0126309
$910$		0			0
$911$		−	10.3487i		−	0.342866i	−0.985196	−	0.171433i	$-0.945160\pi$
$911$		−	10.3487i		−	0.342866i	0.985196	−	0.171433i	$-0.0548398\pi$
$912$		0			0
$913$	4.10096	+	2.36769i	0.135722	+	0.0783591i
$914$		0			0
$915$	−6.68143	+	3.85753i	−0.220881	+	0.127526i
$916$		0			0
$917$	13.2545	+	45.9002i	0.437703	+	1.51576i
$918$		0			0
$919$	23.4531	+	40.6220i	0.773646	+	1.33999i	0.935552	+	0.353188i	$0.114903\pi$
$919$	23.4531	+	40.6220i	0.773646	+	1.33999i	−0.161906	+	0.986806i	$0.551764\pi$
$920$		0			0
$921$	−45.3623	−	26.1900i	−1.49474	−	0.862988i
$922$		0			0
$923$			6.07903i			0.200094i
$924$		0			0
$925$			7.83443i			0.257594i
$926$		0			0
$927$	−0.0766796	+	0.132813i	−0.00251849	+	0.00436215i
$928$		0			0
$929$	31.4827	−	18.1766i	1.03291	−	0.596353i	0.115096	−	0.993354i	$-0.463282\pi$
$929$	31.4827	−	18.1766i	1.03291	−	0.596353i	0.917818	+	0.397001i	$0.129949\pi$
$930$		0			0
$931$	−1.10712	−	28.6354i	−0.0362843	−	0.938487i
$932$		0			0
$933$	−26.7930	−	46.4068i	−0.877163	−	1.51929i
$934$		0			0
$935$	−9.08467	+	2.60252i	−0.297100	+	0.0851114i
$936$		0			0
$937$	6.64333			0.217028			0.108514	−	0.994095i	$-0.465391\pi$
$937$	6.64333			0.217028			0.108514	+	0.994095i	$0.465391\pi$
$938$		0			0
$939$	21.3031			0.695201
$940$		0			0
$941$	−42.5638	−	24.5742i	−1.38754	−	0.801097i	−0.394502	−	0.918895i	$-0.629083\pi$
$941$	−42.5638	−	24.5742i	−1.38754	−	0.801097i	−0.993038	+	0.117798i	$0.962416\pi$
$942$		0			0
$943$	−17.7016	−	30.6601i	−0.576444	−	0.998431i
$944$		0			0
$945$	13.7034	−	3.95712i	0.445773	−	0.128725i
$946$		0			0
$947$	26.5242	−	15.3137i	0.861920	−	0.497630i	−0.00273456	−	0.999996i	$-0.500870\pi$
$947$	26.5242	−	15.3137i	0.861920	−	0.497630i	0.864655	+	0.502366i	$0.167537\pi$
$948$		0			0
$949$	9.05804	+	5.22966i	0.294036	+	0.169762i
$950$		0			0
$951$	−22.8723			−0.741685
$952$		0			0
$953$	43.3506			1.40426			0.702132	−	0.712047i	$-0.252232\pi$
$953$	43.3506			1.40426			0.702132	+	0.712047i	$0.252232\pi$
$954$		0			0
$955$	−7.18640	−	4.14907i	−0.232546	−	0.134261i
$956$		0			0
$957$	−11.8011	+	6.81334i	−0.381474	+	0.220244i
$958$		0			0
$959$	2.35366	+	2.26442i	0.0760036	+	0.0731219i
$960$		0			0
$961$	−14.7010	−	25.4629i	−0.474227	−	0.821385i
$962$		0			0
$963$	−2.04522	−	1.18081i	−0.0659064	−	0.0380511i
$964$		0			0
$965$	12.6481			0.407158
$966$		0			0
$967$	−32.3742			−1.04108			−0.520542	−	0.853836i	$-0.674270\pi$
$967$	−32.3742			−1.04108			−0.520542	+	0.853836i	$0.674270\pi$
$968$		0			0
$969$	7.70549	+	26.8977i	0.247536	+	0.864080i
$970$		0			0
$971$	−12.3766	−	21.4369i	−0.397184	−	0.687942i	0.596194	−	0.802841i	$-0.296679\pi$
$971$	−12.3766	−	21.4369i	−0.397184	−	0.687942i	−0.993377	+	0.114899i	$0.963346\pi$
$972$		0			0
$973$	56.7837	+	14.0451i	1.82040	+	0.450266i
$974$		0			0
$975$	−2.65723	+	1.53415i	−0.0850995	+	0.0491322i
$976$		0			0
$977$	−3.83328	+	6.63943i	−0.122637	+	0.212414i	−0.920807	−	0.390019i	$-0.872469\pi$
$977$	−3.83328	+	6.63943i	−0.122637	+	0.212414i	0.798170	+	0.602433i	$0.205802\pi$
$978$		0			0
$979$		−	1.55486i		−	0.0496935i
$980$		0			0
$981$			3.97065i			0.126773i
$982$		0			0
$983$	−20.0196	−	11.5583i	−0.638526	−	0.368653i	0.145520	−	0.989355i	$-0.453514\pi$
$983$	−20.0196	−	11.5583i	−0.638526	−	0.368653i	−0.784047	+	0.620702i	$0.786848\pi$
$984$		0			0
$985$	−4.88416	−	8.45961i	−0.155622	−	0.269545i
$986$		0			0
$987$	28.4602	+	7.03948i	0.905899	+	0.224069i
$988$		0			0
$989$	−3.30174	+	1.90626i	−0.104989	+	0.0606156i
$990$		0			0
$991$	15.6930	+	9.06034i	0.498504	+	0.287811i	0.728095	−	0.685476i	$-0.240406\pi$
$991$	15.6930	+	9.06034i	0.498504	+	0.287811i	−0.229592	+	0.973287i	$0.573739\pi$
$992$		0			0
$993$			48.4490i			1.53748i
$994$		0			0
$995$	−7.31902			−0.232028
$996$		0			0
$997$	12.8870	+	7.44029i	0.408134	+	0.235636i	0.689988	−	0.723821i	$-0.257616\pi$
$997$	12.8870	+	7.44029i	0.408134	+	0.235636i	−0.281854	+	0.959457i	$0.590949\pi$
$998$		0			0
$999$	−21.1179	−	36.5772i	−0.668139	−	1.15725i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2380.2.cb.b.781.13	✓	92
7.2	even	3	inner	2380.2.cb.b.1801.34	yes	92
17.16	even	2	inner	2380.2.cb.b.781.34	yes	92
119.16	even	6	inner	2380.2.cb.b.1801.13	yes	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2380.2.cb.b.781.13	✓	92	1.1	even	1	trivial
2380.2.cb.b.781.34	yes	92	17.16	even	2	inner
2380.2.cb.b.1801.13	yes	92	119.16	even	6	inner
2380.2.cb.b.1801.34	yes	92	7.2	even	3	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:	\( N \)	\(=\)	\( 2380 = 2^{2} \cdot 5 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2380.cb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.43555 - 0.828817i) q^{3} +(-0.866025 + 0.500000i) q^{5} +(-0.635268 + 2.56835i) q^{7} +(-0.126124 - 0.218454i) q^{9} +(-1.98492 - 1.14599i) q^{11} +1.85101 q^{13} +1.65763 q^{15} +(-3.96367 + 1.13549i) q^{17} +(2.04691 + 3.54536i) q^{19} +(3.04066 - 3.16049i) q^{21} +(2.98157 - 1.72141i) q^{23} +(0.500000 - 0.866025i) q^{25} +5.39104i q^{27} +3.58666i q^{29} +(-1.09474 - 0.632048i) q^{31} +(1.89964 + 3.29027i) q^{33} +(-0.734018 - 2.54189i) q^{35} +(-6.78481 + 3.91721i) q^{37} +(-2.65723 - 1.53415i) q^{39} -10.2832i q^{41} -1.10738 q^{43} +(0.218454 + 0.126124i) q^{45} +(3.34245 + 5.78929i) q^{47} +(-6.19287 - 3.26318i) q^{49} +(6.63117 + 1.65511i) q^{51} +(3.96203 - 6.86243i) q^{53} +2.29198 q^{55} -6.78607i q^{57} +(7.35612 - 12.7412i) q^{59} +(-4.03071 + 2.32713i) q^{61} +(0.641189 - 0.185155i) q^{63} +(-1.60303 + 0.925507i) q^{65} +(7.06075 - 12.2296i) q^{67} -5.70694 q^{69} +3.28416i q^{71} +(4.89356 + 2.82530i) q^{73} +(-1.43555 + 0.828817i) q^{75} +(4.20427 - 4.36996i) q^{77} +(-2.93011 + 1.69170i) q^{79} +(4.08981 - 7.08376i) q^{81} -2.06606 q^{83} +(2.86489 - 2.96519i) q^{85} +(2.97268 - 5.14884i) q^{87} +(0.339195 + 0.587503i) q^{89} +(-1.17589 + 4.75406i) q^{91} +(1.04771 + 1.81468i) q^{93} +(-3.54536 - 2.04691i) q^{95} +6.57359i q^{97} +0.578150i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q + 56 q^{9} - 24 q^{13} + 12 q^{15} + 4 q^{17} - 24 q^{21} + 46 q^{25} - 24 q^{33} + 14 q^{35} - 64 q^{43} + 16 q^{47} + 38 q^{49} - 22 q^{51} - 8 q^{53} + 18 q^{59} + 16 q^{67} - 36 q^{69} - 12 q^{77}+ \cdots + 44 q^{93}+O(q^{100}) \) 92 * q + 56 * q^9 - 24 * q^13 + 12 * q^15 + 4 * q^17 - 24 * q^21 + 46 * q^25 - 24 * q^33 + 14 * q^35 - 64 * q^43 + 16 * q^47 + 38 * q^49 - 22 * q^51 - 8 * q^53 + 18 * q^59 + 16 * q^67 - 36 * q^69 - 12 * q^77 - 86 * q^81 + 8 * q^83 - 20 * q^85 + 20 * q^87 + 2 * q^89 + 44 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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