LMFDB - Embedded newform 756.2.bi.c.307.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(307,756)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("756.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bi (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			307.12
Character	$\chi$	$=$	756.307
Dual form			756.2.bi.c.559.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.955367 + 1.04272i) q^{2} +(-0.174547 - 1.99237i) q^{4} +(1.82425 + 1.05323i) q^{5} +(-2.54762 - 0.713899i) q^{7} +(2.24425 + 1.72144i) q^{8} +O(q^{10})$	\(q+(-0.955367 + 1.04272i) q^{2} +(-0.174547 - 1.99237i) q^{4} +(1.82425 + 1.05323i) q^{5} +(-2.54762 - 0.713899i) q^{7} +(2.24425 + 1.72144i) q^{8} +(-2.84106 + 0.895969i) q^{10} +(1.99265 - 1.15046i) q^{11} +(-0.218388 - 0.126086i) q^{13} +(3.17831 - 1.97442i) q^{14} +(-3.93907 + 0.695524i) q^{16} +4.60054i q^{17} +4.87573 q^{19} +(1.78001 - 3.81843i) q^{20} +(-0.704104 + 3.17690i) q^{22} +(4.23165 + 2.44314i) q^{23} +(-0.281399 - 0.487397i) q^{25} +(0.340113 - 0.107259i) q^{26} +(-0.977672 + 5.20040i) q^{28} +(-1.08689 - 1.88255i) q^{29} +(-1.78200 + 3.08652i) q^{31} +(3.03802 - 4.77184i) q^{32} +(-4.79709 - 4.39520i) q^{34} +(-3.89560 - 3.98557i) q^{35} +10.5786 q^{37} +(-4.65811 + 5.08404i) q^{38} +(2.28100 + 5.50406i) q^{40} +(-1.15076 - 0.664389i) q^{41} +(8.60873 - 4.97025i) q^{43} +(-2.63995 - 3.76929i) q^{44} +(-6.59030 + 2.07834i) q^{46} +(5.43270 + 9.40970i) q^{47} +(5.98070 + 3.63748i) q^{49} +(0.777059 + 0.172222i) q^{50} +(-0.213091 + 0.457117i) q^{52} +7.98161 q^{53} +4.84680 q^{55} +(-4.48855 - 5.98773i) q^{56} +(3.00136 + 0.665200i) q^{58} +(-3.69586 + 6.40141i) q^{59} +(-12.5132 + 7.22449i) q^{61} +(-1.51592 - 4.80690i) q^{62} +(2.07329 + 7.72667i) q^{64} +(-0.265596 - 0.460026i) q^{65} +(-7.35240 - 4.24491i) q^{67} +(9.16597 - 0.803010i) q^{68} +(7.87757 - 0.254350i) q^{70} +6.14583i q^{71} -2.16000i q^{73} +(-10.1064 + 11.0305i) q^{74} +(-0.851044 - 9.71425i) q^{76} +(-5.89782 + 1.50837i) q^{77} +(2.84679 - 1.64360i) q^{79} +(-7.91841 - 2.87994i) q^{80} +(1.79217 - 0.565185i) q^{82} +(4.56438 + 7.90574i) q^{83} +(-4.84544 + 8.39255i) q^{85} +(-3.04190 + 13.7250i) q^{86} +(6.45245 + 0.848317i) q^{88} -4.62446i q^{89} +(0.466355 + 0.477126i) q^{91} +(4.12902 - 8.85744i) q^{92} +(-15.0019 - 3.32492i) q^{94} +(8.89457 + 5.13528i) q^{95} +(4.34667 - 2.50955i) q^{97} +(-9.50665 + 2.76108i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 6 q^{2} - 2 q^{4} + 24 q^{8}+O(q^{10}) $ 80 * q + 6 * q^2 - 2 * q^4 + 24 * q^8	$ 80 q + 6 q^{2} - 2 q^{4} + 24 q^{8} - 10 q^{14} - 18 q^{16} - 14 q^{22} + 32 q^{25} + 28 q^{28} - 8 q^{29} + 16 q^{32} - 16 q^{37} + 84 q^{44} + 24 q^{46} - 24 q^{49} + 12 q^{50} + 48 q^{53} - 32 q^{56} - 14 q^{58} - 8 q^{64} + 40 q^{65} - 22 q^{70} - 64 q^{74} + 12 q^{77} + 40 q^{85} + 52 q^{86} + 6 q^{88} - 30 q^{92} - 20 q^{98}+O(q^{100}) $ 80 * q + 6 * q^2 - 2 * q^4 + 24 * q^8 - 10 * q^14 - 18 * q^16 - 14 * q^22 + 32 * q^25 + 28 * q^28 - 8 * q^29 + 16 * q^32 - 16 * q^37 + 84 * q^44 + 24 * q^46 - 24 * q^49 + 12 * q^50 + 48 * q^53 - 32 * q^56 - 14 * q^58 - 8 * q^64 + 40 * q^65 - 22 * q^70 - 64 * q^74 + 12 * q^77 + 40 * q^85 + 52 * q^86 + 6 * q^88 - 30 * q^92 - 20 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$

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 $

$2$	−0.955367	+	1.04272i	−0.675547	+	0.737317i
$2$	−0.955367	+	1.04272i	−0.675547	+	0.737317i
$3$		0			0
$3$		0			0
$4$	−0.174547	−	1.99237i	−0.0872735	−	0.996184i
$5$	1.82425	+	1.05323i	0.815831	+	0.471020i	0.848977	−	0.528430i	$-0.177219\pi$
$5$	1.82425	+	1.05323i	0.815831	+	0.471020i	−0.0331456	+	0.999451i	$0.510553\pi$
$6$		0			0
$7$	−2.54762	−	0.713899i	−0.962908	−	0.269829i
$7$	−2.54762	−	0.713899i	−0.962908	−	0.269829i
$8$	2.24425	+	1.72144i	0.793461	+	0.608621i
$9$		0			0
$10$	−2.84106	+	0.895969i	−0.898423	+	0.283330i
$11$	1.99265	−	1.15046i	0.600807	−	0.346876i	−0.168552	−	0.985693i	$-0.553909\pi$
$11$	1.99265	−	1.15046i	0.600807	−	0.346876i	0.769359	+	0.638817i	$0.220576\pi$
$12$		0			0
$13$	−0.218388	−	0.126086i	−0.0605698	−	0.0349700i	0.469409	−	0.882981i	$-0.344467\pi$
$13$	−0.218388	−	0.126086i	−0.0605698	−	0.0349700i	−0.529979	+	0.848011i	$0.677800\pi$
$14$	3.17831	−	1.97442i	0.849439	−	0.527687i
$15$		0			0
$16$	−3.93907	+	0.695524i	−0.984767	+	0.173881i
$17$			4.60054i			1.11579i	0.829910	+	0.557897i	$0.188392\pi$
$17$			4.60054i			1.11579i	−0.829910	+	0.557897i	$0.811608\pi$
$18$		0			0
$19$	4.87573			1.11857			0.559285	−	0.828976i	$-0.311076\pi$
$19$	4.87573			1.11857			0.559285	+	0.828976i	$0.311076\pi$
$20$	1.78001	−	3.81843i	0.398023	−	0.853826i
$21$		0			0
$22$	−0.704104	+	3.17690i	−0.150115	+	0.677317i
$23$	4.23165	+	2.44314i	0.882359	+	0.509430i	0.871435	−	0.490510i	$-0.163190\pi$
$23$	4.23165	+	2.44314i	0.882359	+	0.509430i	0.0109235	+	0.999940i	$0.496523\pi$
$24$		0			0
$25$	−0.281399	−	0.487397i	−0.0562797	−	0.0974793i
$26$	0.340113	−	0.107259i	0.0667017	−	0.0210353i
$27$		0			0
$28$	−0.977672	+	5.20040i	−0.184763	+	0.982783i
$29$	−1.08689	−	1.88255i	−0.201831	−	0.349581i	0.747288	−	0.664501i	$-0.231356\pi$
$29$	−1.08689	−	1.88255i	−0.201831	−	0.349581i	−0.949118	+	0.314920i	$0.898022\pi$
$30$		0			0
$31$	−1.78200	+	3.08652i	−0.320057	+	0.554355i	−0.980500	−	0.196521i	$-0.937035\pi$
$31$	−1.78200	+	3.08652i	−0.320057	+	0.554355i	0.660442	+	0.750877i	$0.270369\pi$
$32$	3.03802	−	4.77184i	0.537050	−	0.843550i
$33$		0			0
$34$	−4.79709	−	4.39520i	−0.822694	−	0.753771i
$35$	−3.89560	−	3.98557i	−0.658476	−	0.673684i
$36$		0			0
$37$	10.5786			1.73911			0.869553	−	0.493839i	$-0.164407\pi$
$37$	10.5786			1.73911			0.869553	+	0.493839i	$0.164407\pi$
$38$	−4.65811	+	5.08404i	−0.755646	+	0.824740i
$39$		0			0
$40$	2.28100	+	5.50406i	0.360658	+	0.870268i
$41$	−1.15076	−	0.664389i	−0.179718	−	0.103760i	0.407442	−	0.913231i	$-0.366421\pi$
$41$	−1.15076	−	0.664389i	−0.179718	−	0.103760i	−0.587160	+	0.809471i	$0.699754\pi$
$42$		0			0
$43$	8.60873	−	4.97025i	1.31282	−	0.757957i	0.330257	−	0.943891i	$-0.392864\pi$
$43$	8.60873	−	4.97025i	1.31282	−	0.757957i	0.982562	+	0.185934i	$0.0595311\pi$
$44$	−2.63995	−	3.76929i	−0.397987	−	0.568242i
$45$		0			0
$46$	−6.59030	+	2.07834i	−0.971686	+	0.306435i
$47$	5.43270	+	9.40970i	0.792440	+	1.37255i	0.924452	+	0.381298i	$0.124523\pi$
$47$	5.43270	+	9.40970i	0.792440	+	1.37255i	−0.132012	+	0.991248i	$0.542144\pi$
$48$		0			0
$49$	5.98070	+	3.63748i	0.854385	+	0.519641i
$50$	0.777059	+	0.172222i	0.109893	+	0.0243558i
$51$		0			0
$52$	−0.213091	+	0.457117i	−0.0295504	+	0.0633907i
$53$	7.98161			1.09636			0.548179	−	0.836361i	$-0.315321\pi$
$53$	7.98161			1.09636			0.548179	+	0.836361i	$0.315321\pi$
$54$		0			0
$55$	4.84680			0.653543
$56$	−4.48855	−	5.98773i	−0.599807	−	0.800145i
$57$		0			0
$58$	3.00136	+	0.665200i	0.394098	+	0.0873450i
$59$	−3.69586	+	6.40141i	−0.481160	+	0.833393i	−0.999766	−	0.0216198i	$-0.993118\pi$
$59$	−3.69586	+	6.40141i	−0.481160	+	0.833393i	0.518606	+	0.855013i	$0.326451\pi$
$60$		0			0
$61$	−12.5132	+	7.22449i	−1.60215	+	0.925001i	−0.611092	+	0.791559i	$0.709270\pi$
$61$	−12.5132	+	7.22449i	−1.60215	+	0.925001i	−0.991057	+	0.133442i	$0.957397\pi$
$62$	−1.51592	−	4.80690i	−0.192522	−	0.610477i
$63$		0			0
$64$	2.07329	+	7.72667i	0.259162	+	0.965834i
$65$	−0.265596	−	0.460026i	−0.0329432	−	0.0570592i
$66$		0			0
$67$	−7.35240	−	4.24491i	−0.898239	−	0.518598i	−0.0216103	−	0.999766i	$-0.506879\pi$
$67$	−7.35240	−	4.24491i	−0.898239	−	0.518598i	−0.876628	+	0.481168i	$0.840213\pi$
$68$	9.16597	−	0.803010i	1.11154	−	0.0973793i
$69$		0			0
$70$	7.87757	−	0.254350i	0.941550	−	0.0304007i
$71$			6.14583i			0.729375i	0.931130	+	0.364688i	$0.118824\pi$
$71$			6.14583i			0.729375i	−0.931130	+	0.364688i	$0.881176\pi$
$72$		0			0
$73$		−	2.16000i		−	0.252809i	−0.991979	−	0.126404i	$-0.959656\pi$
$73$		−	2.16000i		−	0.252809i	0.991979	−	0.126404i	$-0.0403437\pi$
$74$	−10.1064	+	11.0305i	−1.17485	+	1.28227i
$75$		0			0
$76$	−0.851044	−	9.71425i	−0.0976215	−	1.11430i
$77$	−5.89782	+	1.50837i	−0.672119	+	0.171895i
$78$		0			0
$79$	2.84679	−	1.64360i	0.320289	−	0.184919i	−0.331232	−	0.943549i	$-0.607464\pi$
$79$	2.84679	−	1.64360i	0.320289	−	0.184919i	0.651522	+	0.758630i	$0.274131\pi$
$80$	−7.91841	−	2.87994i	−0.885305	−	0.321988i
$81$		0			0
$82$	1.79217	−	0.565185i	0.197912	−	0.0624143i
$83$	4.56438	+	7.90574i	0.501006	+	0.867768i	0.999999	+	0.00116189i	$0.000369841\pi$
$83$	4.56438	+	7.90574i	0.501006	+	0.867768i	−0.498993	+	0.866606i	$0.666297\pi$
$84$		0			0
$85$	−4.84544	+	8.39255i	−0.525562	+	0.910300i
$86$	−3.04190	+	13.7250i	−0.328016	+	1.48000i
$87$		0			0
$88$	6.45245	+	0.848317i	0.687833	+	0.0904309i
$89$		−	4.62446i		−	0.490191i	−0.969499	−	0.245096i	$-0.921181\pi$
$89$		−	4.62446i		−	0.490191i	0.969499	−	0.245096i	$-0.0788194\pi$
$90$		0			0
$91$	0.466355	+	0.477126i	0.0488873	+	0.0500164i
$92$	4.12902	−	8.85744i	0.430480	−	0.923452i
$93$		0			0
$94$	−15.0019	−	3.32492i	−1.54733	−	0.342939i
$95$	8.89457	+	5.13528i	0.912564	+	0.526869i
$96$		0			0
$97$	4.34667	−	2.50955i	0.441338	−	0.254807i	−0.262827	−	0.964843i	$-0.584655\pi$
$97$	4.34667	−	2.50955i	0.441338	−	0.254807i	0.704165	+	0.710036i	$0.251322\pi$
$98$	−9.50665	+	2.76108i	−0.960317	+	0.278911i
$99$		0			0
$100$	−0.921957	+	0.645724i	−0.0921957	+	0.0645724i
$101$	−4.75755	+	2.74677i	−0.473394	+	0.273314i	−0.717659	−	0.696394i	$-0.754787\pi$
$101$	−4.75755	+	2.74677i	−0.473394	+	0.273314i	0.244265	+	0.969708i	$0.421453\pi$
$102$		0			0
$103$	−2.95680	+	5.12133i	−0.291342	+	0.504619i	−0.974127	−	0.226000i	$-0.927435\pi$
$103$	−2.95680	+	5.12133i	−0.291342	+	0.504619i	0.682785	+	0.730619i	$0.260768\pi$
$104$	−0.273066	−	0.658909i	−0.0267763	−	0.0646114i
$105$		0			0
$106$	−7.62536	+	8.32261i	−0.740641	+	0.808364i
$107$		−	8.51213i		−	0.822899i	−0.911433	−	0.411450i	$-0.865023\pi$
$107$		−	8.51213i		−	0.822899i	0.911433	−	0.411450i	$-0.134977\pi$
$108$		0			0
$109$	−6.38002			−0.611095			−0.305548	−	0.952177i	$-0.598840\pi$
$109$	−6.38002			−0.611095			−0.305548	+	0.952177i	$0.598840\pi$
$110$	−4.63048	+	5.05388i	−0.441499	+	0.481869i
$111$		0			0
$112$	10.5318	+	1.04017i	0.995158	+	0.0982867i
$113$	−5.84315	+	10.1206i	−0.549677	+	0.952069i	0.448619	+	0.893723i	$0.351916\pi$
$113$	−5.84315	+	10.1206i	−0.549677	+	0.952069i	−0.998296	+	0.0583459i	$0.981417\pi$
$114$		0			0
$115$	5.14640	+	8.91382i	0.479904	+	0.831218i
$116$	−3.56102	+	2.49408i	−0.330633	+	0.231570i
$117$		0			0
$118$	−3.14401	−	9.96946i	−0.289429	−	0.917763i
$119$	3.28432	−	11.7204i	0.301073	−	1.07441i
$120$		0			0
$121$	−2.85289	+	4.94135i	−0.259354	+	0.449214i
$122$	4.42154	−	19.9498i	0.400307	−	1.80617i
$123$		0			0
$124$	6.46053	+	3.01166i	0.580173	+	0.270455i
$125$		−	11.7178i		−	1.04808i
$126$		0			0
$127$		−	13.8984i		−	1.23328i	−0.787244	−	0.616642i	$-0.788493\pi$
$127$		−	13.8984i		−	1.23328i	0.787244	−	0.616642i	$-0.211507\pi$
$128$	−10.0375	−	5.21994i	−0.887202	−	0.461382i
$129$		0			0
$130$	0.733422	+	0.162550i	0.0643254	+	0.0142566i
$131$	7.18258	−	12.4406i	0.627545	−	1.08694i	−0.360498	−	0.932760i	$-0.617393\pi$
$131$	7.18258	−	12.4406i	0.627545	−	1.08694i	0.988043	−	0.154180i	$-0.0492735\pi$
$132$		0			0
$133$	−12.4215	−	3.48078i	−1.07708	−	0.301822i
$134$	11.4505	−	3.61108i	0.989174	−	0.311950i
$135$		0			0
$136$	−7.91955	+	10.3247i	−0.679096	+	0.885340i
$137$	1.07629	+	1.86419i	0.0919538	+	0.159269i	0.908333	−	0.418247i	$-0.137355\pi$
$137$	1.07629	+	1.86419i	0.0919538	+	0.159269i	−0.816379	+	0.577516i	$0.804022\pi$
$138$		0			0
$139$	8.26506	−	14.3155i	0.701033	−	1.21423i	−0.267071	−	0.963677i	$-0.586056\pi$
$139$	8.26506	−	14.3155i	0.701033	−	1.21423i	0.968104	−	0.250549i	$-0.0806110\pi$
$140$	−7.26076	+	8.45713i	−0.613646	+	0.714758i
$141$		0			0
$142$	−6.40840	−	5.87152i	−0.537781	−	0.492727i
$143$	−0.580227			−0.0485210
$144$		0			0
$145$		−	4.57900i		−	0.380265i
$146$	2.25229	+	2.06359i	0.186400	+	0.170784i
$147$		0			0
$148$	−1.84646	−	21.0764i	−0.151778	−	1.73247i
$149$	4.33757	−	7.51290i	0.355348	−	0.615480i	−0.631830	−	0.775107i	$-0.717696\pi$
$149$	4.33757	−	7.51290i	0.355348	−	0.615480i	0.987177	+	0.159627i	$0.0510291\pi$
$150$		0			0
$151$	2.31838	−	1.33852i	0.188667	−	0.108927i	−0.402691	−	0.915336i	$-0.631925\pi$
$151$	2.31838	−	1.33852i	0.188667	−	0.108927i	0.591359	+	0.806409i	$0.298592\pi$
$152$	10.9423	+	8.39327i	0.887541	+	0.680784i
$153$		0			0
$154$	4.06177	−	7.59085i	0.327307	−	0.611688i
$155$	−6.50165	+	3.75373i	−0.522225	+	0.301507i
$156$		0			0
$157$	15.5179	+	8.95927i	1.23846	+	0.715028i	0.968780	−	0.247921i	$-0.0797474\pi$
$157$	15.5179	+	8.95927i	1.23846	+	0.715028i	0.269684	+	0.962949i	$0.413081\pi$
$158$	−1.00592	+	4.53866i	−0.0800263	+	0.361076i
$159$		0			0
$160$	10.5680	−	5.50531i	0.835472	−	0.435233i
$161$	−9.03645	−	9.24516i	−0.712172	−	0.728620i
$162$		0			0
$163$			2.86313i			0.224258i	0.993694	+	0.112129i	$0.0357669\pi$
$163$			2.86313i			0.224258i	−0.993694	+	0.112129i	$0.964233\pi$
$164$	−1.12285	+	2.40870i	−0.0876796	+	0.188088i
$165$		0			0
$166$	−12.6042	−	2.79349i	−0.978273	−	0.216817i
$167$	3.53318	−	6.11964i	0.273405	−	0.473552i	−0.696326	−	0.717725i	$-0.745183\pi$
$167$	3.53318	−	6.11964i	0.273405	−	0.473552i	0.969732	+	0.244174i	$0.0785167\pi$
$168$		0			0
$169$	−6.46820	−	11.2033i	−0.497554	−	0.861789i
$170$	−4.12194	−	13.0704i	−0.316138	−	1.00246i
$171$		0			0
$172$	−11.4052	−	16.2842i	−0.869639	−	1.24166i
$173$	−14.4716	+	8.35518i	−1.10025	+	0.635232i	−0.936288	−	0.351234i	$-0.885762\pi$
$173$	−14.4716	+	8.35518i	−1.10025	+	0.635232i	−0.163967	+	0.986466i	$0.552429\pi$
$174$		0			0
$175$	0.368943	+	1.44259i	0.0278895	+	0.109050i
$176$	−7.04902	+	5.91767i	−0.531340	+	0.446061i
$177$		0			0
$178$	4.82203	+	4.41805i	0.361427	+	0.331147i
$179$		−	13.2700i		−	0.991844i	−0.868367	−	0.495922i	$-0.834830\pi$
$179$		−	13.2700i		−	0.991844i	0.868367	−	0.495922i	$-0.165170\pi$
$180$		0			0
$181$		−	14.7060i		−	1.09309i	−0.837431	−	0.546543i	$-0.815943\pi$
$181$		−	14.7060i		−	1.09309i	0.837431	−	0.546543i	$-0.184057\pi$
$182$	−0.943051	+	0.0304491i	−0.0699036	+	0.00225704i
$183$		0			0
$184$	5.29114	+	12.7675i	0.390068	+	0.941235i
$185$	19.2980	+	11.1417i	1.41882	+	0.819155i
$186$		0			0
$187$	5.29273	+	9.16727i	0.387043	+	0.670377i
$188$	17.7993	−	12.4664i	1.29815	−	0.909203i
$189$		0			0
$190$	−13.8523	+	4.36850i	−1.00495	+	0.316924i
$191$	−13.5569	+	7.82708i	−0.980943	+	0.566348i	−0.902555	−	0.430575i	$-0.858311\pi$
$191$	−13.5569	+	7.82708i	−0.980943	+	0.566348i	−0.0783882	+	0.996923i	$0.524977\pi$
$192$		0			0
$193$	2.25489	−	3.90558i	0.162310	−	0.281130i	−0.773386	−	0.633935i	$-0.781439\pi$
$193$	2.25489	−	3.90558i	0.162310	−	0.281130i	0.935697	+	0.352805i	$0.114772\pi$
$194$	−1.53590	+	6.92993i	−0.110271	+	0.497540i
$195$		0			0
$196$	6.20330	−	12.5507i	0.443093	−	0.896476i
$197$	7.04052			0.501616			0.250808	−	0.968037i	$-0.419304\pi$
$197$	7.04052			0.501616			0.250808	+	0.968037i	$0.419304\pi$
$198$		0			0
$199$	−1.64695			−0.116749			−0.0583747	−	0.998295i	$-0.518592\pi$
$199$	−1.64695			−0.116749			−0.0583747	+	0.998295i	$0.518592\pi$
$200$	0.207496	−	1.57825i	0.0146722	−	0.111599i
$201$		0			0
$202$	1.68108	−	7.58499i	0.118280	−	0.533678i
$203$	1.42503	+	5.57195i	0.100017	+	0.391074i
$204$		0			0
$205$	−1.39951	−	2.42403i	−0.0977463	−	0.169302i
$206$	−2.51530	−	7.97587i	−0.175249	−	0.555705i
$207$		0			0
$208$	0.947939	+	0.344768i	0.0657278	+	0.0239053i
$209$	9.71563	−	5.60932i	0.672045	−	0.388005i
$210$		0			0
$211$	7.67682	+	4.43221i	0.528494	+	0.305126i	0.740403	−	0.672163i	$-0.234635\pi$
$211$	7.67682	+	4.43221i	0.528494	+	0.305126i	−0.211909	+	0.977289i	$0.567968\pi$
$212$	−1.39317	−	15.9023i	−0.0956830	−	1.09217i
$213$		0			0
$214$	8.87581	+	8.13221i	0.606738	+	0.555907i
$215$	20.9394			1.42805
$216$		0			0
$217$	6.74333	−	6.59110i	0.457767	−	0.447433i
$218$	6.09526	−	6.65260i	0.412823	−	0.450571i
$219$		0			0
$220$	−0.845995	−	9.65662i	−0.0570370	−	0.651049i
$221$	0.580064	−	1.00470i	0.0390193	−	0.0675835i
$222$		0			0
$223$	−8.51444	−	14.7474i	−0.570169	−	0.987561i	−0.996548	−	0.0830169i	$-0.973544\pi$
$223$	−8.51444	−	14.7474i	−0.570169	−	0.987561i	0.426379	−	0.904544i	$-0.359789\pi$
$224$	−11.1463	+	9.98798i	−0.744744	+	0.667350i
$225$		0			0
$226$	−4.97067	−	15.7617i	−0.330644	−	1.04845i
$227$	−3.29592	−	5.70870i	−0.218758	−	0.378900i	0.735671	−	0.677339i	$-0.236867\pi$
$227$	−3.29592	−	5.70870i	−0.218758	−	0.378900i	−0.954429	+	0.298440i	$0.903534\pi$
$228$		0			0
$229$	−15.0244	−	8.67434i	−0.992840	−	0.573217i	−0.0867182	−	0.996233i	$-0.527638\pi$
$229$	−15.0244	−	8.67434i	−0.992840	−	0.573217i	−0.906122	+	0.423016i	$0.860971\pi$
$230$	−14.2114	−	3.14970i	−0.937069	−	0.207685i
$231$		0			0
$232$	0.801445	−	6.09593i	0.0526174	−	0.400217i
$233$	−1.69802			−0.111241			−0.0556204	−	0.998452i	$-0.517714\pi$
$233$	−1.69802			−0.111241			−0.0556204	+	0.998452i	$0.517714\pi$
$234$		0			0
$235$			22.8876i			1.49302i
$236$	13.3991	+	6.24617i	0.872206	+	0.406591i
$237$		0			0
$238$	9.08342	+	14.6219i	0.588790	+	0.947799i
$239$	−24.4418	−	14.1115i	−1.58101	−	0.912795i	−0.994713	−	0.102698i	$-0.967252\pi$
$239$	−24.4418	−	14.1115i	−1.58101	−	0.912795i	−0.586295	−	0.810097i	$-0.699414\pi$
$240$		0			0
$241$	23.6006	−	13.6258i	1.52025	−	0.877717i	0.520535	−	0.853840i	$-0.325733\pi$
$241$	23.6006	−	13.6258i	1.52025	−	0.877717i	0.999715	−	0.0238762i	$-0.00760075\pi$
$242$	−2.42691	−	7.69559i	−0.156008	−	0.494691i
$243$		0			0
$244$	16.5780	+	23.6699i	1.06130	+	1.51531i
$245$	7.07919	+	12.9348i	0.452273	+	0.826372i
$246$		0			0
$247$	−1.06480	−	0.614762i	−0.0677515	−	0.0391164i
$248$	−9.31251	+	3.85930i	−0.591345	+	0.245066i
$249$		0			0
$250$	12.2185	+	11.1948i	0.772765	+	0.708024i
$251$	−29.8268			−1.88265			−0.941326	−	0.337498i	$-0.890419\pi$
$251$	−29.8268			−1.88265			−0.941326	+	0.337498i	$0.890419\pi$
$252$		0			0
$253$	11.2429			0.706837
$254$	14.4922	+	13.2781i	0.909322	+	0.833141i
$255$		0			0
$256$	15.0325	−	5.47943i	0.939531	−	0.342464i
$257$	−22.9770	−	13.2658i	−1.43326	−	0.827496i	−0.435896	−	0.899997i	$-0.643569\pi$
$257$	−22.9770	−	13.2658i	−1.43326	−	0.827496i	−0.997368	+	0.0725013i	$0.976902\pi$
$258$		0			0
$259$	−26.9501	−	7.55204i	−1.67460	−	0.469261i
$260$	−0.870183	+	0.609462i	−0.0539664	+	0.0377972i
$261$		0			0
$262$	6.11011	+	19.3748i	0.377484	+	1.19698i
$263$	−3.65334	+	2.10926i	−0.225274	+	0.130062i	−0.608390	−	0.793638i	$-0.708184\pi$
$263$	−3.65334	+	2.10926i	−0.225274	+	0.130062i	0.383116	+	0.923700i	$0.374851\pi$
$264$		0			0
$265$	14.5605	+	8.40649i	0.894443	+	0.516407i
$266$	15.4966	−	9.62676i	0.950156	−	0.590255i
$267$		0			0
$268$	−7.17409	+	15.3896i	−0.438227	+	0.940071i
$269$			28.6035i			1.74399i	0.489519	+	0.871993i	$0.337172\pi$
$269$			28.6035i			1.74399i	−0.489519	+	0.871993i	$0.662828\pi$
$270$		0			0
$271$	−1.52227			−0.0924715			−0.0462357	−	0.998931i	$-0.514723\pi$
$271$	−1.52227			−0.0924715			−0.0462357	+	0.998931i	$0.514723\pi$
$272$	−3.19979	−	18.1218i	−0.194015	−	1.09880i
$273$		0			0
$274$	−2.97209	−	0.658713i	−0.179551	−	0.0397943i
$275$	−1.12146	−	0.647475i	−0.0676265	−	0.0390442i
$276$		0			0
$277$	3.40358	+	5.89517i	0.204501	+	0.354206i	0.949974	−	0.312330i	$-0.101109\pi$
$277$	3.40358	+	5.89517i	0.204501	+	0.354206i	−0.745472	+	0.666536i	$0.767776\pi$
$278$	7.03096	+	22.2947i	0.421689	+	1.33715i
$279$		0			0
$280$	−1.88177	−	15.6506i	−0.112457	−	0.935304i
$281$	−13.4890	−	23.3636i	−0.804684	−	1.39375i	−0.916504	−	0.400025i	$-0.869002\pi$
$281$	−13.4890	−	23.3636i	−0.804684	−	1.39375i	0.111821	−	0.993728i	$-0.464332\pi$
$282$		0			0
$283$	−6.69636	+	11.5984i	−0.398057	+	0.689455i	−0.993486	−	0.113953i	$-0.963649\pi$
$283$	−6.69636	+	11.5984i	−0.398057	+	0.689455i	0.595429	+	0.803408i	$0.296982\pi$
$284$	12.2448	−	1.07274i	0.726592	−	0.0636552i
$285$		0			0
$286$	0.554330	−	0.605017i	0.0327782	−	0.0357754i
$287$	2.45738	+	2.51413i	0.145054	+	0.148405i
$288$		0			0
$289$	−4.16495			−0.244997
$290$	4.77464	+	4.37463i	0.280376	+	0.256887i
$291$		0			0
$292$	−4.30352	+	0.377022i	−0.251844	+	0.0220635i
$293$	20.0411	+	11.5707i	1.17081	+	0.675969i	0.953871	−	0.300215i	$-0.0970585\pi$
$293$	20.0411	+	11.5707i	1.17081	+	0.675969i	0.216942	+	0.976185i	$0.430392\pi$
$294$		0			0
$295$	−13.4844	+	7.78520i	−0.785090	+	0.453272i
$296$	23.7409	+	18.2104i	1.37991	+	1.05846i
$297$		0			0
$298$	3.68990	+	11.7005i	0.213750	+	0.677790i
$299$	−0.616092	−	1.06710i	−0.0356295	−	0.0617122i
$300$		0			0
$301$	−25.4800	+	6.51653i	−1.46864	+	0.375607i
$302$	−0.819201	+	3.69621i	−0.0471397	+	0.212693i
$303$		0			0
$304$	−19.2058	+	3.39119i	−1.10153	+	0.194498i
$305$	−30.4363			−1.74278
$306$		0			0
$307$	−10.2865			−0.587083			−0.293542	−	0.955946i	$-0.594834\pi$
$307$	−10.2865			−0.587083			−0.293542	+	0.955946i	$0.594834\pi$
$308$	4.03468	+	11.4874i	0.229897	+	0.654553i
$309$		0			0
$310$	2.29736	−	10.3656i	0.130481	−	0.588728i
$311$	−0.476652	+	0.825585i	−0.0270284	+	0.0468146i	−0.879223	−	0.476410i	$-0.841938\pi$
$311$	−0.476652	+	0.825585i	−0.0270284	+	0.0468146i	0.852195	+	0.523225i	$0.175271\pi$
$312$		0			0
$313$	−25.2144	+	14.5576i	−1.42520	+	0.822842i	−0.996737	−	0.0807151i	$-0.974280\pi$
$313$	−25.2144	+	14.5576i	−1.42520	+	0.822842i	−0.428467	+	0.903557i	$0.640946\pi$
$314$	−24.1674	+	7.62151i	−1.36384	+	0.430107i
$315$		0			0
$316$	−3.77155	−	5.38498i	−0.212166	−	0.302929i
$317$	−0.119800	−	0.207499i	−0.00672861	−	0.0116543i	0.862641	−	0.505816i	$-0.168808\pi$
$317$	−0.119800	−	0.207499i	−0.00672861	−	0.0116543i	−0.869370	+	0.494162i	$0.835475\pi$
$318$		0			0
$319$	−4.33159	−	2.50085i	−0.242523	−	0.140021i
$320$	−4.35578	+	16.2791i	−0.243495	+	0.910028i
$321$		0			0
$322$	18.2733	−	0.590005i	1.01833	−	0.0328797i
$323$			22.4310i			1.24809i
$324$		0			0
$325$			0.141922i			0.00787241i
$326$	−2.98546	−	2.73534i	−0.165349	−	0.151497i
$327$		0			0
$328$	−1.43888	−	3.47201i	−0.0794486	−	0.191710i
$329$	−7.12284	−	27.8507i	−0.392695	−	1.53546i
$330$		0			0
$331$	7.65430	−	4.41921i	0.420718	−	0.242902i	−0.274666	−	0.961540i	$-0.588567\pi$
$331$	7.65430	−	4.41921i	0.420718	−	0.242902i	0.695385	+	0.718638i	$0.255234\pi$
$332$	14.9544	−	10.4739i	0.820732	−	0.574827i
$333$		0			0
$334$	3.00562	+	9.53063i	0.164460	+	0.521493i
$335$	−8.94176	−	15.4876i	−0.488541	−	0.846177i
$336$		0			0
$337$	6.89773	−	11.9472i	0.375743	−	0.650806i	−0.614695	−	0.788765i	$-0.710721\pi$
$337$	6.89773	−	11.9472i	0.375743	−	0.650806i	0.990438	+	0.137959i	$0.0440541\pi$
$338$	17.8614	+	3.95867i	0.971533	+	0.215323i
$339$		0			0
$340$	17.5668	+	8.18901i	0.952694	+	0.444111i
$341$			8.20048i			0.444081i
$342$		0			0
$343$	−12.6397	−	13.5365i	−0.682481	−	0.730904i
$344$	27.8761	+	3.66493i	1.50298	+	0.197600i
$345$		0			0
$346$	5.11354	−	23.0721i	0.274906	−	1.24037i
$347$	−2.29653	−	1.32590i	−0.123284	−	0.0711782i	0.437090	−	0.899418i	$-0.356009\pi$
$347$	−2.29653	−	1.32590i	−0.123284	−	0.0711782i	−0.560374	+	0.828240i	$0.689343\pi$
$348$		0			0
$349$	−3.36079	+	1.94035i	−0.179899	+	0.103865i	−0.587245	−	0.809409i	$-0.699788\pi$
$349$	−3.36079	+	1.94035i	−0.179899	+	0.103865i	0.407346	+	0.913274i	$0.366454\pi$
$350$	−1.85670	−	0.993497i	−0.0992448	−	0.0531047i
$351$		0			0
$352$	0.563904	−	13.0037i	0.0300562	−	0.693101i
$353$	27.8946	−	16.1049i	1.48468	−	0.857180i	0.484831	−	0.874608i	$-0.338881\pi$
$353$	27.8946	−	16.1049i	1.48468	−	0.857180i	0.999848	+	0.0174283i	$0.00554789\pi$
$354$		0			0
$355$	−6.47299	+	11.2115i	−0.343551	+	0.595047i
$356$	−9.21362	+	0.807185i	−0.488321	+	0.0427807i
$357$		0			0
$358$	13.8369	+	12.6777i	0.731304	+	0.670037i
$359$			16.9972i			0.897079i	0.893763	+	0.448539i	$0.148056\pi$
$359$			16.9972i			0.897079i	−0.893763	+	0.448539i	$0.851944\pi$
$360$		0			0
$361$	4.77275			0.251197
$362$	15.3343	+	14.0496i	0.805952	+	0.738431i
$363$		0			0
$364$	0.869210	−	1.01243i	0.0455590	−	0.0530658i
$365$	2.27499	−	3.94039i	0.119078	−	0.206249i
$366$		0			0
$367$	0.947065	+	1.64036i	0.0494364	+	0.0856263i	0.889685	−	0.456575i	$-0.150924\pi$
$367$	0.947065	+	1.64036i	0.0494364	+	0.0856263i	−0.840248	+	0.542202i	$0.817591\pi$
$368$	−18.3680	−	6.68049i	−0.957498	−	0.348244i
$369$		0			0
$370$	−30.0544	+	9.47807i	−1.56245	+	0.492741i
$371$	−20.3341	−	5.69806i	−1.05569	−	0.295829i
$372$		0			0
$373$	−6.46642	+	11.2002i	−0.334818	+	0.579922i	−0.983450	−	0.181180i	$-0.942008\pi$
$373$	−6.46642	+	11.2002i	−0.334818	+	0.579922i	0.648632	+	0.761103i	$0.275342\pi$
$374$	−14.6154	−	3.23926i	−0.755746	−	0.167498i
$375$		0			0
$376$	−4.00592	+	30.4698i	−0.206590	+	1.57136i
$377$			0.548168i			0.0282321i
$378$		0			0
$379$			19.4116i			0.997106i	0.866859	+	0.498553i	$0.166135\pi$
$379$			19.4116i			0.997106i	−0.866859	+	0.498553i	$0.833865\pi$
$380$	8.67886	−	18.6176i	0.445216	−	0.955063i
$381$		0			0
$382$	4.79033	−	21.6138i	0.245095	−	1.10586i
$383$	−6.44294	+	11.1595i	−0.329219	+	0.570224i	−0.982357	−	0.187015i	$-0.940119\pi$
$383$	−6.44294	+	11.1595i	−0.329219	+	0.570224i	0.653138	+	0.757239i	$0.273452\pi$
$384$		0			0
$385$	−12.3478	−	3.46013i	−0.629302	−	0.176345i
$386$	1.91820	+	6.08249i	0.0976337	+	0.309591i
$387$		0			0
$388$	−5.75865	−	8.22214i	−0.292351	−	0.417416i
$389$	9.53163	+	16.5093i	0.483273	+	0.837053i	0.999816	−	0.0192083i	$-0.00611458\pi$
$389$	9.53163	+	16.5093i	0.483273	+	0.837053i	−0.516543	+	0.856261i	$0.672781\pi$
$390$		0			0
$391$	−11.2398	+	19.4678i	−0.568419	+	0.984531i
$392$	7.16045	+	18.4588i	0.361657	+	0.932311i
$393$		0			0
$394$	−6.72628	+	7.34132i	−0.338865	+	0.369850i
$395$	6.92437			0.348403
$396$		0			0
$397$			2.33175i			0.117027i	0.998287	+	0.0585135i	$0.0186361\pi$
$397$			2.33175i			0.117027i	−0.998287	+	0.0585135i	$0.981364\pi$
$398$	1.57344	−	1.71732i	0.0788697	−	0.0860814i
$399$		0			0
$400$	1.44744	+	1.72417i	0.0723722	+	0.0862084i
$401$	−8.17411	+	14.1580i	−0.408195	+	0.707015i	−0.994688	−	0.102940i	$-0.967175\pi$
$401$	−8.17411	+	14.1580i	−0.408195	+	0.707015i	0.586492	+	0.809955i	$0.300508\pi$
$402$		0			0
$403$	0.778335	−	0.449372i	0.0387716	−	0.0223848i
$404$	6.30300	+	8.99935i	0.313586	+	0.447735i
$405$		0			0
$406$	−7.17143	−	3.83734i	−0.355912	−	0.190444i
$407$	21.0794	−	12.1702i	1.04487	−	0.603255i
$408$		0			0
$409$	16.5082	+	9.53101i	0.816278	+	0.471278i	0.849131	−	0.528182i	$-0.177126\pi$
$409$	16.5082	+	9.53101i	0.816278	+	0.471278i	−0.0328535	+	0.999460i	$0.510459\pi$
$410$	3.86464	+	0.856531i	0.190861	+	0.0423011i
$411$		0			0
$412$	10.7197	+	4.99712i	0.528120	+	0.246190i
$413$	13.9856	−	13.6699i	0.688186	−	0.672651i
$414$		0			0
$415$			19.2294i			0.943936i
$416$	−1.26513	+	0.659059i	−0.0620280	+	0.0323130i
$417$		0			0
$418$	−3.43302	+	15.4897i	−0.167915	+	0.757626i
$419$	5.27532	−	9.13712i	0.257716	−	0.446377i	−0.707914	−	0.706299i	$-0.750363\pi$
$419$	5.27532	−	9.13712i	0.257716	−	0.446377i	0.965630	+	0.259922i	$0.0836968\pi$
$420$		0			0
$421$	17.6583	+	30.5850i	0.860611	+	1.49062i	0.871340	+	0.490679i	$0.163251\pi$
$421$	17.6583	+	30.5850i	0.860611	+	1.49062i	−0.0107298	+	0.999942i	$0.503415\pi$
$422$	−11.9558	+	3.77041i	−0.581997	+	0.183541i
$423$		0			0
$424$	17.9127	+	13.7398i	0.869917	+	0.667266i
$425$	2.24229	−	1.29459i	0.108767	−	0.0627966i
$426$		0			0
$427$	37.0363	−	9.47207i	1.79231	−	0.458386i
$428$	−16.9593	+	1.48577i	−0.819759	+	0.0718173i
$429$		0			0
$430$	−20.0048	+	21.8340i	−0.964716	+	1.05293i
$431$			1.78484i			0.0859726i	0.999076	+	0.0429863i	$0.0136872\pi$
$431$			1.78484i			0.0859726i	−0.999076	+	0.0429863i	$0.986313\pi$
$432$		0			0
$433$			6.52824i			0.313727i	0.987620	+	0.156864i	$0.0501383\pi$
$433$			6.52824i			0.313727i	−0.987620	+	0.156864i	$0.949862\pi$
$434$	0.430344	+	13.3283i	0.0206572	+	0.639781i
$435$		0			0
$436$	1.11361	+	12.7114i	0.0533324	+	0.608764i
$437$	20.6324	+	11.9121i	0.986980	+	0.569833i
$438$		0			0
$439$	−7.67744	−	13.2977i	−0.366424	−	0.634665i	0.622579	−	0.782557i	$-0.286085\pi$
$439$	−7.67744	−	13.2977i	−0.366424	−	0.634665i	−0.989004	+	0.147891i	$0.952751\pi$
$440$	10.8774	+	8.34348i	0.518561	+	0.397760i
$441$		0			0
$442$	0.493451	+	1.56470i	0.0234711	+	0.0744254i
$443$	11.2566	−	6.49898i	0.534816	−	0.308776i	−0.208160	−	0.978095i	$-0.566747\pi$
$443$	11.2566	−	6.49898i	0.534816	−	0.308776i	0.742975	+	0.669319i	$0.233414\pi$
$444$		0			0
$445$	4.87063	−	8.43618i	0.230890	−	0.399913i
$446$	23.5119	+	5.21101i	1.11332	+	0.246748i
$447$		0			0
$448$	0.234112	−	21.1647i	0.0110608	−	0.999939i
$449$	30.5126			1.43998			0.719989	−	0.693985i	$-0.244147\pi$
$449$	30.5126			1.43998			0.719989	+	0.693985i	$0.244147\pi$
$450$		0			0
$451$	−3.05741			−0.143968
$452$	21.1839	+	9.87518i	0.996408	+	0.464489i
$453$		0			0
$454$	9.10142	+	2.01717i	0.427151	+	0.0946705i
$455$	0.348225	+	1.36158i	0.0163250	+	0.0638318i
$456$		0			0
$457$	−16.7185	−	28.9573i	−0.782060	−	1.35457i	−0.930740	−	0.365682i	$-0.880836\pi$
$457$	−16.7185	−	28.9573i	−0.782060	−	1.35457i	0.148680	−	0.988885i	$-0.452498\pi$
$458$	23.3988	−	7.37912i	1.09335	−	0.344804i
$459$		0			0
$460$	16.8613	−	11.8094i	0.786164	−	0.550616i
$461$	−8.42658	+	4.86509i	−0.392465	+	0.226590i	−0.683228	−	0.730206i	$-0.739424\pi$
$461$	−8.42658	+	4.86509i	−0.392465	+	0.226590i	0.290763	+	0.956795i	$0.406091\pi$
$462$		0			0
$463$	7.80112	+	4.50398i	0.362549	+	0.209318i	0.670198	−	0.742182i	$-0.266209\pi$
$463$	7.80112	+	4.50398i	0.362549	+	0.209318i	−0.307650	+	0.951500i	$0.599542\pi$
$464$	5.59070	+	6.65954i	0.259542	+	0.309161i
$465$		0			0
$466$	1.62223	−	1.77056i	0.0751483	−	0.0820197i
$467$	6.77334			0.313433			0.156716	−	0.987644i	$-0.449909\pi$
$467$	6.77334			0.313433			0.156716	+	0.987644i	$0.449909\pi$
$468$		0			0
$469$	15.7007	+	16.0633i	0.724989	+	0.741733i
$470$	−23.8654	−	21.8660i	−1.10083	−	1.00861i
$471$		0			0
$472$	−19.3141	+	8.00416i	−0.889002	+	0.368421i
$473$	11.4361	−	19.8080i	0.525834	−	0.910772i
$474$		0			0
$475$	−1.37202	−	2.37642i	−0.0629528	−	0.109037i
$476$	−23.9246	−	4.49782i	−1.09658	−	0.206157i
$477$		0			0
$478$	38.0653	−	12.0044i	1.74106	−	0.549069i
$479$	−2.68770	−	4.65524i	−0.122804	−	0.212703i	0.798068	−	0.602567i	$-0.205855\pi$
$479$	−2.68770	−	4.65524i	−0.122804	−	0.212703i	−0.920873	+	0.389864i	$0.872522\pi$
$480$		0			0
$481$	−2.31023	−	1.33381i	−0.105337	−	0.0608166i
$482$	−8.33928	+	37.6266i	−0.379844	+	1.71384i
$483$		0			0
$484$	10.3430	+	4.82151i	0.470135	+	0.219160i
$485$	10.5726			0.480076
$486$		0			0
$487$			14.5792i			0.660648i	0.943868	+	0.330324i	$0.107158\pi$
$487$			14.5792i			0.660648i	−0.943868	+	0.330324i	$0.892842\pi$
$488$	−40.5192	−	5.32714i	−1.83422	−	0.241148i
$489$		0			0
$490$	−20.2506	−	4.97581i	−0.914829	−	0.224784i
$491$	7.49552	+	4.32754i	0.338268	+	0.195299i	0.659506	−	0.751699i	$-0.270766\pi$
$491$	7.49552	+	4.32754i	0.338268	+	0.195299i	−0.321238	+	0.946999i	$0.604099\pi$
$492$		0			0
$493$	8.66075	−	5.00029i	0.390061	−	0.225202i
$494$	1.65830	−	0.522968i	0.0746105	−	0.0235294i
$495$		0			0
$496$	4.87268	−	13.3974i	0.218790	−	0.601563i
$497$	4.38750	−	15.6572i	0.196806	−	0.702322i
$498$		0			0
$499$	−34.8419	−	20.1160i	−1.55974	−	0.900516i	−0.997281	−	0.0736908i	$-0.976522\pi$
$499$	−34.8419	−	20.1160i	−1.55974	−	0.900516i	−0.562459	−	0.826825i	$-0.690144\pi$
$500$	−23.3463	+	2.04532i	−1.04408	+	0.0914693i
$501$		0			0
$502$	28.4956	−	31.1011i	1.27182	−	1.38811i
$503$	−3.02477			−0.134868			−0.0674339	−	0.997724i	$-0.521481\pi$
$503$	−3.02477			−0.134868			−0.0674339	+	0.997724i	$0.521481\pi$
$504$		0			0
$505$	−11.5720			−0.514946
$506$	−10.7411	+	11.7233i	−0.477501	+	0.521163i
$507$		0			0
$508$	−27.6907	+	2.42593i	−1.22858	+	0.107633i
$509$	−8.81165	−	5.08741i	−0.390569	−	0.225495i	0.291837	−	0.956468i	$-0.405733\pi$
$509$	−8.81165	−	5.08741i	−0.390569	−	0.225495i	−0.682407	+	0.730973i	$0.739067\pi$
$510$		0			0
$511$	−1.54202	+	5.50285i	−0.0682151	+	0.243432i
$512$	−8.64801	+	20.9096i	−0.382192	+	0.924083i
$513$		0			0
$514$	35.7840	−	11.2850i	1.57836	−	0.497759i
$515$	−10.7879	+	6.22840i	−0.475372	+	0.274456i
$516$		0			0
$517$	21.6509	+	12.5002i	0.952207	+	0.549757i
$518$	33.6220	−	20.8866i	1.47726	−	0.917704i
$519$		0			0
$520$	0.195844	−	1.48962i	0.00858831	−	0.0653242i
$521$			6.75953i			0.296140i	0.988977	+	0.148070i	$0.0473061\pi$
$521$			6.75953i			0.296140i	−0.988977	+	0.148070i	$0.952694\pi$
$522$		0			0
$523$	−7.45208			−0.325857			−0.162928	−	0.986638i	$-0.552094\pi$
$523$	−7.45208			−0.325857			−0.162928	+	0.986638i	$0.552094\pi$
$524$	−26.0399	−	12.1389i	−1.13756	−	0.530289i
$525$		0			0
$526$	1.29091	−	5.82454i	0.0562862	−	0.253962i
$527$	−14.1997	−	8.19817i	−0.618547	−	0.357118i
$528$		0			0
$529$	0.437880	+	0.758431i	0.0190383	+	0.0329752i
$530$	−22.6763	+	7.15127i	−0.984993	+	0.310631i
$531$		0			0
$532$	−4.76687	+	25.3557i	−0.206670	+	1.09931i
$533$	0.167541	+	0.290189i	0.00725699	+	0.0125695i
$534$		0			0
$535$	8.96527	−	15.5283i	0.387602	−	0.671347i
$536$	−9.19325	−	22.1833i	−0.397088	−	0.958174i
$537$		0			0
$538$	−29.8255	−	27.3268i	−1.28587	−	1.17814i
$539$	16.1022	+	0.367699i	0.693572	+	0.0158379i
$540$		0			0
$541$	−23.2824			−1.00099			−0.500494	−	0.865740i	$-0.666848\pi$
$541$	−23.2824			−1.00099			−0.500494	+	0.865740i	$0.666848\pi$
$542$	1.45433	−	1.58731i	0.0624688	−	0.0681808i
$543$		0			0
$544$	21.9530	+	13.9765i	0.941229	+	0.599238i
$545$	−11.6388	−	6.71965i	−0.498551	−	0.287838i
$546$		0			0
$547$	−2.95053	+	1.70349i	−0.126155	+	0.0728358i	−0.561750	−	0.827307i	$-0.689872\pi$
$547$	−2.95053	+	1.70349i	−0.126155	+	0.0728358i	0.435594	+	0.900143i	$0.356538\pi$
$548$	3.52629	−	2.46976i	0.150636	−	0.105503i
$549$		0			0
$550$	1.74654	−	0.550796i	0.0744728	−	0.0234860i
$551$	−5.29939	−	9.17881i	−0.225762	−	0.391031i
$552$		0			0
$553$	−8.42590	+	2.15493i	−0.358306	+	0.0916369i
$554$	−9.39870	−	2.08306i	−0.399313	−	0.0885007i
$555$		0			0
$556$	−29.9644	−	13.9683i	−1.27077	−	0.592389i
$557$	−5.02799			−0.213043			−0.106521	−	0.994310i	$-0.533971\pi$
$557$	−5.02799			−0.213043			−0.106521	+	0.994310i	$0.533971\pi$
$558$		0			0
$559$	−2.50672			−0.106023
$560$	18.1171	+	12.9899i	0.765586	+	0.548925i
$561$		0			0
$562$	37.2487	+	8.25552i	1.57124	+	0.348238i
$563$	−11.5220	+	19.9567i	−0.485595	+	0.841076i	−0.999863	−	0.0165541i	$-0.994730\pi$
$563$	−11.5220	+	19.9567i	−0.485595	+	0.841076i	0.514268	+	0.857630i	$0.328064\pi$
$564$		0			0
$565$	−21.3188	+	12.3084i	−0.896888	+	0.517818i
$566$	−5.69649	−	18.0632i	−0.239441	−	0.759254i
$567$		0			0
$568$	−10.5797	+	13.7928i	−0.443913	+	0.578731i
$569$	0.515380	+	0.892665i	0.0216059	+	0.0374225i	0.876626	−	0.481172i	$-0.159789\pi$
$569$	0.515380	+	0.892665i	0.0216059	+	0.0374225i	−0.855020	+	0.518595i	$0.826455\pi$
$570$		0			0
$571$	−10.5140	−	6.07026i	−0.439997	−	0.254032i	0.263599	−	0.964632i	$-0.415090\pi$
$571$	−10.5140	−	6.07026i	−0.439997	−	0.254032i	−0.703596	+	0.710600i	$0.748424\pi$
$572$	0.101277	+	1.15603i	0.00423460	+	0.0483359i
$573$		0			0
$574$	−4.96924	+	0.160446i	−0.207412	+	0.00669690i
$575$		−	2.74999i		−	0.114682i
$576$		0			0
$577$		−	29.8675i		−	1.24340i	−0.783256	−	0.621699i	$-0.786443\pi$
$577$		−	29.8675i		−	1.24340i	0.783256	−	0.621699i	$-0.213557\pi$
$578$	3.97906	−	4.34290i	0.165507	−	0.180641i
$579$		0			0
$580$	−9.12306	+	0.799251i	−0.378814	+	0.0331871i
$581$	−5.98439	−	23.3993i	−0.248274	−	0.970766i
$582$		0			0
$583$	15.9046	−	9.18250i	0.658700	−	0.380300i
$584$	3.71831	−	4.84758i	0.153865	−	0.200594i
$585$		0			0
$586$	−31.2117	+	9.84303i	−1.28934	+	0.406612i
$587$	10.4711	+	18.1365i	0.432189	+	0.748573i	0.997062	−	0.0766048i	$-0.0244080\pi$
$587$	10.4711	+	18.1365i	0.432189	+	0.748573i	−0.564873	+	0.825178i	$0.691075\pi$
$588$		0			0
$589$	−8.68857	+	15.0490i	−0.358006	+	0.620085i
$590$	4.76470	−	21.4982i	0.196160	−	0.885067i
$591$		0			0
$592$	−41.6697	+	7.35765i	−1.71261	+	0.302398i
$593$		−	19.8667i		−	0.815828i	−0.913020	−	0.407914i	$-0.866256\pi$
$593$		−	19.8667i		−	0.815828i	0.913020	−	0.407914i	$-0.133744\pi$
$594$		0			0
$595$	18.3358	−	17.9218i	0.751693	−	0.734724i
$596$	−15.7256	−	7.33069i	−0.644144	−	0.300277i
$597$		0			0
$598$	1.70129	+	0.377061i	0.0695709	+	0.0154192i
$599$	−18.7134	−	10.8042i	−0.764610	−	0.441448i	0.0663385	−	0.997797i	$-0.478868\pi$
$599$	−18.7134	−	10.8042i	−0.764610	−	0.441448i	−0.830948	+	0.556349i	$0.812202\pi$
$600$		0			0
$601$	27.9379	−	16.1299i	1.13961	−	0.657954i	0.193276	−	0.981144i	$-0.438089\pi$
$601$	27.9379	−	16.1299i	1.13961	−	0.657954i	0.946334	+	0.323190i	$0.104755\pi$
$602$	17.5478	−	32.7943i	0.715196	−	1.33660i
$603$		0			0
$604$	−3.07149	−	4.38544i	−0.124977	−	0.178441i
$605$	−10.4088	+	6.00952i	−0.423178	+	0.244322i
$606$		0			0
$607$	7.23936	−	12.5389i	0.293837	−	0.508940i	−0.680877	−	0.732398i	$-0.738401\pi$
$607$	7.23936	−	12.5389i	0.293837	−	0.508940i	0.974714	+	0.223458i	$0.0717345\pi$
$608$	14.8125	−	23.2662i	0.600728	−	0.943569i
$609$		0			0
$610$	29.0778	−	31.7367i	1.17733	−	1.28498i
$611$		−	2.73995i		−	0.110847i
$612$		0			0
$613$	−5.59075			−0.225808			−0.112904	−	0.993606i	$-0.536015\pi$
$613$	−5.59075			−0.225808			−0.112904	+	0.993606i	$0.536015\pi$
$614$	9.82741	−	10.7260i	0.396602	−	0.432867i
$615$		0			0
$616$	−15.8327	−	6.76759i	−0.637920	−	0.272674i
$617$	−13.2535	+	22.9557i	−0.533564	+	0.924161i	0.465667	+	0.884960i	$0.345814\pi$
$617$	−13.2535	+	22.9557i	−0.533564	+	0.924161i	−0.999231	+	0.0392006i	$0.987519\pi$
$618$		0			0
$619$	0.214256	+	0.371103i	0.00861169	+	0.0149159i	0.870299	−	0.492524i	$-0.163925\pi$
$619$	0.214256	+	0.371103i	0.00861169	+	0.0149159i	−0.861687	+	0.507439i	$0.830592\pi$
$620$	8.61366	+	12.2985i	0.345933	+	0.493919i
$621$		0			0
$622$	−0.405480	−	1.28575i	−0.0162583	−	0.0515540i
$623$	−3.30140	+	11.7813i	−0.132268	+	0.472009i
$624$		0			0
$625$	10.9346	−	18.9393i	0.437385	−	0.757574i
$626$	8.90953	−	40.1995i	0.356096	−	1.60670i
$627$		0			0
$628$	15.1416	−	32.4812i	0.604214	−	1.29614i
$629$			48.6671i			1.94049i
$630$		0			0
$631$		−	23.4474i		−	0.933428i	−0.884408	−	0.466714i	$-0.845438\pi$
$631$		−	23.4474i		−	0.933428i	0.884408	−	0.466714i	$-0.154562\pi$
$632$	9.21826	+	1.21194i	0.366683	+	0.0482086i
$633$		0			0
$634$	0.330817	+	0.0733198i	0.0131384	+	0.00291190i
$635$	14.6383	−	25.3542i	0.580902	−	1.00615i
$636$		0			0
$637$	−0.847473	−	1.54846i	−0.0335781	−	0.0613524i
$638$	6.74596	−	2.12743i	0.267075	−	0.0842258i
$639$		0			0
$640$	−12.8132	−	20.0944i	−0.506487	−	0.794299i
$641$	−5.26351	−	9.11666i	−0.207896	−	0.360086i	0.743156	−	0.669119i	$-0.233328\pi$
$641$	−5.26351	−	9.11666i	−0.207896	−	0.360086i	−0.951052	+	0.309032i	$0.899995\pi$
$642$		0			0
$643$	−8.71937	+	15.1024i	−0.343858	+	0.595580i	−0.985146	−	0.171721i	$-0.945067\pi$
$643$	−8.71937	+	15.1024i	−0.343858	+	0.595580i	0.641287	+	0.767301i	$0.278401\pi$
$644$	−16.8425	+	19.6177i	−0.663686	+	0.773044i
$645$		0			0
$646$	−23.3893	−	21.4298i	−0.920241	−	0.843145i
$647$	−2.85701			−0.112321			−0.0561604	−	0.998422i	$-0.517886\pi$
$647$	−2.85701			−0.112321			−0.0561604	+	0.998422i	$0.517886\pi$
$648$		0			0
$649$			17.0077i			0.667612i
$650$	−0.147985	−	0.135587i	−0.00580446	−	0.00531818i
$651$		0			0
$652$	5.70441	−	0.499751i	0.223402	−	0.0195718i
$653$	−14.1498	+	24.5081i	−0.553724	+	0.959078i	0.444278	+	0.895889i	$0.353460\pi$
$653$	−14.1498	+	24.5081i	−0.553724	+	0.959078i	−0.998002	+	0.0631888i	$0.979873\pi$
$654$		0			0
$655$	26.2057	−	15.1299i	1.02394	−	0.591173i
$656$	4.99500	+	1.81669i	0.195022	+	0.0709300i
$657$		0			0
$658$	35.8455	+	19.1805i	1.39740	+	0.747734i
$659$	16.3336	−	9.43023i	0.636268	−	0.367350i	−0.146907	−	0.989150i	$-0.546932\pi$
$659$	16.3336	−	9.43023i	0.636268	−	0.367350i	0.783176	+	0.621801i	$0.213599\pi$
$660$		0			0
$661$	−5.06764	−	2.92580i	−0.197108	−	0.113801i	0.398198	−	0.917300i	$-0.369636\pi$
$661$	−5.06764	−	2.92580i	−0.197108	−	0.113801i	−0.595306	+	0.803499i	$0.702969\pi$
$662$	−2.70465	+	12.2033i	−0.105119	+	0.474294i
$663$		0			0
$664$	−3.36565	+	25.5997i	−0.130613	+	0.993463i
$665$	−18.9939	−	19.4326i	−0.736551	−	0.753562i
$666$		0			0
$667$		−	10.6217i		−	0.411275i
$668$	−12.8093	−	5.97122i	−0.495606	−	0.231034i
$669$		0			0
$670$	24.6919	+	5.47254i	0.953933	+	0.211423i
$671$	−16.6229	+	28.7918i	−0.641722	+	1.11149i
$672$		0			0
$673$	−17.5342	−	30.3701i	−0.675893	−	1.17068i	−0.976207	−	0.216841i	$-0.930425\pi$
$673$	−17.5342	−	30.3701i	−0.675893	−	1.17068i	0.300314	−	0.953840i	$-0.402909\pi$
$674$	5.86779	+	18.6064i	0.226019	+	0.716692i
$675$		0			0
$676$	−21.1920	+	14.8425i	−0.815078	+	0.570867i
$677$	16.9051	−	9.76017i	0.649716	−	0.375114i	−0.138631	−	0.990344i	$-0.544270\pi$
$677$	16.9051	−	9.76017i	0.649716	−	0.375114i	0.788347	+	0.615230i	$0.210937\pi$
$678$		0			0
$679$	−12.8652	+	3.29029i	−0.493722	+	0.126270i
$680$	−25.3216	+	10.4938i	−0.971040	+	0.402420i
$681$		0			0
$682$	−8.55084	−	7.83447i	−0.327429	−	0.299997i
$683$		−	2.90828i		−	0.111282i	−0.998451	−	0.0556411i	$-0.982280\pi$
$683$		−	2.90828i		−	0.111282i	0.998451	−	0.0556411i	$-0.0177203\pi$
$684$		0			0
$685$			4.53435i			0.173248i
$686$	26.1904	−	0.247384i	0.999955	−	0.00944516i
$687$		0			0
$688$	−30.4534	+	25.5657i	−1.16103	+	0.974685i
$689$	−1.74308	−	1.00637i	−0.0664062	−	0.0383396i
$690$		0			0
$691$	5.35077	+	9.26780i	0.203553	+	0.352564i	0.949671	−	0.313250i	$-0.101418\pi$
$691$	5.35077	+	9.26780i	0.203553	+	0.352564i	−0.746118	+	0.665814i	$0.768084\pi$
$692$	19.1726	+	27.3744i	0.728832	+	1.04062i
$693$		0			0
$694$	3.57658	−	1.12792i	0.135765	−	0.0428154i
$695$	30.1551	−	17.4101i	1.14385	−	0.660402i
$696$		0			0
$697$	3.05655	−	5.29410i	0.115775	−	0.200528i
$698$	1.18753	−	5.35812i	0.0449489	−	0.202808i
$699$		0			0
$700$	2.80977	−	0.986871i	0.106199	−	0.0373002i
$701$	−20.8466			−0.787365			−0.393682	−	0.919247i	$-0.628799\pi$
$701$	−20.8466			−0.787365			−0.393682	+	0.919247i	$0.628799\pi$
$702$		0			0
$703$	51.5783			1.94531
$704$	13.0206	+	13.0113i	0.490731	+	0.490383i
$705$		0			0
$706$	−9.85656	+	44.4725i	−0.370956	+	1.67374i
$707$	14.0813	−	3.60131i	0.529583	−	0.135441i
$708$		0			0
$709$	25.1621	+	43.5820i	0.944981	+	1.63676i	0.755789	+	0.654815i	$0.227254\pi$
$709$	25.1621	+	43.5820i	0.944981	+	1.63676i	0.189192	+	0.981940i	$0.439413\pi$
$710$	−5.50647	−	17.4607i	−0.206654	−	0.655288i
$711$		0			0
$712$	7.96072	−	10.3784i	0.298341	−	0.388948i
$713$	−15.0816	+	8.70737i	−0.564811	+	0.326094i
$714$		0			0
$715$	−1.05848	−	0.611115i	−0.0395850	−	0.0228544i
$716$	−26.4387	+	2.31623i	−0.988059	+	0.0865617i
$717$		0			0
$718$	−17.7234	−	16.2386i	−0.661432	−	0.606019i
$719$	−3.83545			−0.143038			−0.0715190	−	0.997439i	$-0.522785\pi$
$719$	−3.83545			−0.143038			−0.0715190	+	0.997439i	$0.522785\pi$
$720$		0			0
$721$	11.1889	−	10.9363i	0.416696	−	0.407290i
$722$	−4.55973	+	4.97666i	−0.169695	+	0.185212i
$723$		0			0
$724$	−29.2997	+	2.56689i	−1.08892	+	0.0953975i
$725$	−0.611700	+	1.05949i	−0.0227180	+	0.0393486i
$726$		0			0
$727$	26.0730	+	45.1597i	0.966993	+	1.67488i	0.704162	+	0.710039i	$0.251323\pi$
$727$	26.0730	+	45.1597i	0.966993	+	1.67488i	0.262831	+	0.964842i	$0.415344\pi$
$728$	0.225273	+	1.87359i	0.00834916	+	0.0694399i
$729$		0			0
$730$	1.93529	+	6.13670i	0.0716284	+	0.227130i
$731$	22.8658	+	39.6048i	0.845724	+	1.46484i
$732$		0			0
$733$	−31.3189	−	18.0820i	−1.15679	−	0.667874i	−0.206258	−	0.978498i	$-0.566129\pi$
$733$	−31.3189	−	18.0820i	−1.15679	−	0.667874i	−0.950533	+	0.310624i	$0.899462\pi$
$734$	−2.61524	−	0.579623i	−0.0965304	−	0.0213943i
$735$		0			0
$736$	24.5141	−	12.7704i	0.903601	−	0.470724i
$737$	−19.5344			−0.719558
$738$		0			0
$739$		−	41.8456i		−	1.53932i	−0.638456	−	0.769658i	$-0.720427\pi$
$739$		−	41.8456i		−	1.53932i	0.638456	−	0.769658i	$-0.279573\pi$
$740$	18.8300	−	40.3935i	0.692204	−	1.48489i
$741$		0			0
$742$	25.3680	−	15.7591i	0.931289	−	0.578534i
$743$	18.1807	+	10.4967i	0.666987	+	0.385085i	0.794934	−	0.606696i	$-0.207505\pi$
$743$	18.1807	+	10.4967i	0.666987	+	0.385085i	−0.127947	+	0.991781i	$0.540839\pi$
$744$		0			0
$745$	15.8257	−	9.13695i	0.579808	−	0.334752i
$746$	−5.50088	−	17.4430i	−0.201401	−	0.638632i
$747$		0			0
$748$	17.3408	−	12.1452i	0.634041	−	0.444072i
$749$	−6.07681	+	21.6857i	−0.222042	+	0.792376i
$750$		0			0
$751$	17.9902	+	10.3866i	0.656470	+	0.379013i	0.790931	−	0.611906i	$-0.209597\pi$
$751$	17.9902	+	10.3866i	0.656470	+	0.379013i	−0.134460	+	0.990919i	$0.542930\pi$
$752$	−27.9444	−	33.2869i	−1.01903	−	1.21385i
$753$		0			0
$754$	−0.571588	−	0.523702i	−0.0208160	−	0.0190721i
$755$	5.63910			0.205228
$756$		0			0
$757$	16.5395			0.601137			0.300568	−	0.953760i	$-0.402824\pi$
$757$	16.5395			0.601137			0.300568	+	0.953760i	$0.402824\pi$
$758$	−20.2409	−	18.5452i	−0.735183	−	0.673591i
$759$		0			0
$760$	11.1215	+	26.8363i	0.403421	+	0.973455i
$761$	6.77126	+	3.90939i	0.245458	+	0.141715i	0.617683	−	0.786427i	$-0.288072\pi$
$761$	6.77126	+	3.90939i	0.245458	+	0.141715i	−0.372225	+	0.928143i	$0.621405\pi$
$762$		0			0
$763$	16.2538	+	4.55469i	0.588429	+	0.164891i
$764$	17.9607	+	25.6442i	0.649797	+	0.927773i
$765$		0			0
$766$	−5.48090	−	17.3796i	−0.198033	−	0.627951i
$767$	1.61426	−	0.931993i	0.0582875	−	0.0336523i
$768$		0			0
$769$	−21.7560	−	12.5608i	−0.784542	−	0.452955i	0.0534956	−	0.998568i	$-0.482964\pi$
$769$	−21.7560	−	12.5608i	−0.784542	−	0.452955i	−0.838038	+	0.545613i	$0.816297\pi$
$770$	15.4046	−	9.56965i	0.555145	−	0.344866i
$771$		0			0
$772$	−8.17494	−	3.81086i	−0.294223	−	0.137156i
$773$			6.00293i			0.215910i	0.994156	+	0.107955i	$0.0344303\pi$
$773$			6.00293i			0.215910i	−0.994156	+	0.107955i	$0.965570\pi$
$774$		0			0
$775$	2.00581			0.0720509
$776$	14.0751	+	1.85048i	0.505265	+	0.0664282i
$777$		0			0
$778$	−26.3208	−	5.83355i	−0.943647	−	0.209143i
$779$	−5.61078	−	3.23938i	−0.201027	−	0.116063i
$780$		0			0
$781$	7.07052	+	12.2465i	0.253003	+	0.438214i
$782$	−9.56149	−	30.3189i	−0.341918	−	1.08420i
$783$		0			0
$784$	−26.0883	−	10.1686i	−0.931726	−	0.363163i
$785$	18.8724	+	32.6880i	0.673585	+	1.16668i
$786$		0			0
$787$	−14.5065	+	25.1260i	−0.517100	+	0.895644i	0.482703	+	0.875784i	$0.339655\pi$
$787$	−14.5065	+	25.1260i	−0.517100	+	0.895644i	−0.999803	+	0.0198595i	$0.993678\pi$
$788$	−1.22890	−	14.0273i	−0.0437778	−	0.499702i
$789$		0			0
$790$	−6.61531	+	7.22020i	−0.235362	+	0.256883i
$791$	22.1112	−	21.6121i	0.786184	−	0.768436i
$792$		0			0
$793$	3.64363			0.129389
$794$	−2.43137	−	2.22767i	−0.0862860	−	0.0790572i
$795$		0			0
$796$	0.287471	+	3.28134i	0.0101891	+	0.116304i
$797$	−13.1794	−	7.60913i	−0.466838	−	0.269529i	0.248077	−	0.968740i	$-0.420201\pi$
$797$	−13.1794	−	7.60913i	−0.466838	−	0.269529i	−0.714915	+	0.699211i	$0.753535\pi$
$798$		0			0
$799$	−43.2897	+	24.9933i	−1.53148	+	0.884200i
$800$	−3.18067	−	0.137929i	−0.112454	−	0.00487654i
$801$		0			0
$802$	−6.95358	−	22.0494i	−0.245539	−	0.778591i
$803$	−2.48499	−	4.30413i	−0.0876934	−	0.151889i
$804$		0			0
$805$	−6.74747	−	26.3830i	−0.237817	−	0.929879i
$806$	−0.275025	+	1.24090i	−0.00968733	+	0.0437090i
$807$		0			0
$808$	−15.4055	−	2.02540i	−0.541964	−	0.0712532i
$809$	−22.3835			−0.786960			−0.393480	−	0.919333i	$-0.628729\pi$
$809$	−22.3835			−0.786960			−0.393480	+	0.919333i	$0.628729\pi$
$810$		0			0
$811$	7.32710			0.257289			0.128645	−	0.991691i	$-0.458937\pi$
$811$	7.32710			0.257289			0.128645	+	0.991691i	$0.458937\pi$
$812$	10.8526	−	3.81175i	0.380853	−	0.133766i
$813$		0			0
$814$	−7.44842	+	33.6070i	−0.261067	+	1.17793i
$815$	−3.01555	+	5.22308i	−0.105630	+	0.182956i
$816$		0			0
$817$	41.9739	−	24.2336i	1.46848	−	0.847827i
$818$	−25.7096	+	8.10788i	−0.898915	+	0.283485i
$819$		0			0
$820$	−4.58528	+	3.21145i	−0.160125	+	0.112149i
$821$	−6.58917	−	11.4128i	−0.229964	−	0.398309i	0.727833	−	0.685754i	$-0.240527\pi$
$821$	−6.58917	−	11.4128i	−0.229964	−	0.398309i	−0.957797	+	0.287445i	$0.907194\pi$
$822$		0			0
$823$	6.62089	+	3.82257i	0.230790	+	0.133246i	0.610936	−	0.791680i	$-0.290793\pi$
$823$	6.62089	+	3.82257i	0.230790	+	0.133246i	−0.380147	+	0.924926i	$0.624126\pi$
$824$	−15.4518	+	6.40357i	−0.538290	+	0.223079i
$825$		0			0
$826$	0.892530	+	27.6429i	0.0310551	+	0.961818i
$827$		−	33.7614i		−	1.17400i	−0.809587	−	0.587000i	$-0.800309\pi$
$827$		−	33.7614i		−	1.17400i	0.809587	−	0.587000i	$-0.199691\pi$
$828$		0			0
$829$		−	16.4004i		−	0.569611i	−0.958585	−	0.284805i	$-0.908071\pi$
$829$		−	16.4004i		−	0.569611i	0.958585	−	0.284805i	$-0.0919290\pi$
$830$	−20.0510	−	18.3712i	−0.695980	−	0.637673i
$831$		0			0
$832$	0.521445	−	1.94882i	0.0180778	−	0.0675633i
$833$	−16.7344	+	27.5144i	−0.579812	+	0.953318i
$834$		0			0
$835$	12.8908	−	7.44252i	0.446105	−	0.257559i
$836$	−12.8717	−	18.3780i	−0.445176	−	0.635618i
$837$		0			0
$838$	4.48763	+	14.2300i	0.155022	+	0.491567i
$839$	−16.1916	−	28.0447i	−0.558996	−	0.968209i	−0.997581	−	0.0695192i	$-0.977854\pi$
$839$	−16.1916	−	28.0447i	−0.558996	−	0.968209i	0.438585	−	0.898690i	$-0.355480\pi$
$840$		0			0
$841$	12.1373	−	21.0225i	0.418529	−	0.724913i
$842$	−48.7618	−	10.8072i	−1.68044	−	0.372441i
$843$		0			0
$844$	7.49064	−	16.0687i	0.257838	−	0.553107i
$845$		−	27.2501i		−	0.937433i
$846$		0			0
$847$	10.7957	−	10.5520i	0.370945	−	0.362571i
$848$	−31.4401	+	5.55140i	−1.07966	+	0.190636i
$849$		0			0
$850$	−0.792313	+	3.57489i	−0.0271761	+	0.122618i
$851$	44.7648	+	25.8450i	1.53452	+	0.885953i
$852$		0			0
$853$	−12.4256	+	7.17395i	−0.425446	+	0.245631i	−0.697405	−	0.716678i	$-0.745662\pi$
$853$	−12.4256	+	7.17395i	−0.425446	+	0.245631i	0.271959	+	0.962309i	$0.412329\pi$
$854$	−25.5066	+	47.6680i	−0.872816	+	1.63117i
$855$		0			0
$856$	14.6531	−	19.1033i	0.500833	−	0.652939i
$857$	−15.0174	+	8.67031i	−0.512985	+	0.296172i	−0.734060	−	0.679085i	$-0.762377\pi$
$857$	−15.0174	+	8.67031i	−0.512985	+	0.296172i	0.221075	+	0.975257i	$0.429044\pi$
$858$		0			0
$859$	25.4872	−	44.1451i	0.869612	−	1.50621i	0.00721838	−	0.999974i	$-0.497702\pi$
$859$	25.4872	−	44.1451i	0.869612	−	1.50621i	0.862394	−	0.506238i	$-0.168964\pi$
$860$	−3.65490	−	41.7189i	−0.124631	−	1.42260i
$861$		0			0
$862$	−1.86109	−	1.70517i	−0.0633891	−	0.0580785i
$863$			19.5828i			0.666606i	0.942820	+	0.333303i	$0.108163\pi$
$863$			19.5828i			0.666606i	−0.942820	+	0.333303i	$0.891837\pi$
$864$		0			0
$865$	−35.1998			−1.19683
$866$	−6.80715	−	6.23686i	−0.231316	−	0.211937i
$867$		0			0
$868$	−14.3089	−	12.2847i	−0.485677	−	0.416971i
$869$	3.78178	−	6.55023i	0.128288	−	0.222201i
$870$		0			0
$871$	1.07045	+	1.85407i	0.0362708	+	0.0628228i
$872$	−14.3183	−	10.9828i	−0.484880	−	0.371925i
$873$		0			0
$874$	−32.1325	+	10.1334i	−1.08690	+	0.342768i
$875$	−8.36537	+	29.8526i	−0.282801	+	1.00920i
$876$		0			0
$877$	1.48110	−	2.56533i	0.0500130	−	0.0866251i	−0.839935	−	0.542687i	$-0.817407\pi$
$877$	1.48110	−	2.56533i	0.0500130	−	0.0866251i	0.889948	+	0.456062i	$0.150740\pi$
$878$	21.2006	+	4.69875i	0.715486	+	0.158575i
$879$		0			0
$880$	−19.0919	+	3.37107i	−0.643587	+	0.113639i
$881$		−	27.0811i		−	0.912384i	−0.889881	−	0.456192i	$-0.849213\pi$
$881$		−	27.0811i		−	0.912384i	0.889881	−	0.456192i	$-0.150787\pi$
$882$		0			0
$883$		−	24.9046i		−	0.838107i	−0.907962	−	0.419054i	$-0.862362\pi$
$883$		−	24.9046i		−	0.838107i	0.907962	−	0.419054i	$-0.137638\pi$
$884$	−2.10298	−	0.980334i	−0.0707309	−	0.0329722i
$885$		0			0
$886$	−3.97751	+	17.9464i	−0.133627	+	0.602921i
$887$	−22.4128	+	38.8200i	−0.752547	+	1.30345i	0.194038	+	0.980994i	$0.437841\pi$
$887$	−22.4128	+	38.8200i	−0.752547	+	1.30345i	−0.946585	+	0.322455i	$0.895492\pi$
$888$		0			0
$889$	−9.92206	+	35.4078i	−0.332775	+	1.18754i
$890$	4.14337	+	13.1384i	0.138886	+	0.440399i
$891$		0			0
$892$	−27.8962	+	19.5380i	−0.934033	+	0.654181i
$893$	26.4884	+	45.8792i	0.886399	+	1.53529i
$894$		0			0
$895$	13.9764	−	24.2078i	0.467179	−	0.809177i
$896$	21.8453	+	20.4642i	0.729800	+	0.683661i
$897$		0			0
$898$	−29.1507	+	31.8162i	−0.972772	+	1.06172i
$899$	7.74738			0.258390
$900$		0			0
$901$			36.7197i			1.22331i
$902$	2.92095	−	3.18803i	0.0972569	−	0.106150i
$903$		0			0
$904$	−30.5355	+	12.6546i	−1.01560	+	0.420885i
$905$	15.4888	−	26.8274i	0.514866	−	0.891774i
$906$		0			0
$907$	49.7076	−	28.6987i	1.65051	−	0.952924i	0.673651	−	0.739049i	$-0.264725\pi$
$907$	49.7076	−	28.6987i	1.65051	−	0.952924i	0.976861	−	0.213874i	$-0.0686083\pi$
$908$	−10.7985	+	7.56313i	−0.358362	+	0.250991i
$909$		0			0
$910$	−1.75243	−	0.937706i	−0.0580926	−	0.0310846i
$911$	41.7826	−	24.1232i	1.38432	−	0.799237i	0.391652	−	0.920113i	$-0.371904\pi$
$911$	41.7826	−	24.1232i	1.38432	−	0.799237i	0.992668	+	0.120876i	$0.0385703\pi$
$912$		0			0
$913$	18.1904	+	10.5023i	0.602016	+	0.347574i
$914$	46.1669	+	10.2321i	1.52706	+	0.338447i
$915$		0			0
$916$	−14.6600	+	31.4482i	−0.484381	+	1.03908i
$917$	−27.1798	+	26.5662i	−0.897556	+	0.877294i
$918$		0			0
$919$			50.4712i			1.66489i	0.554106	+	0.832446i	$0.313060\pi$
$919$			50.4712i			1.66489i	−0.554106	+	0.832446i	$0.686940\pi$
$920$	−3.79481	+	28.8640i	−0.125111	+	0.951619i
$921$		0			0
$922$	2.97753	−	13.4345i	0.0980598	−	0.442443i
$923$	0.774903	−	1.34217i	0.0255063	−	0.0441781i
$924$		0			0
$925$	−2.97680	−	5.15596i	−0.0978765	−	0.169527i
$926$	−12.1493	+	3.83146i	−0.399252	+	0.125910i
$927$		0			0
$928$	−12.2852	−	0.532747i	−0.403282	−	0.0174883i
$929$	−20.5217	+	11.8482i	−0.673295	+	0.388727i	−0.797324	−	0.603552i	$-0.793752\pi$
$929$	−20.5217	+	11.8482i	−0.673295	+	0.388727i	0.124029	+	0.992279i	$0.460418\pi$
$930$		0			0
$931$	29.1603	+	17.7354i	0.955689	+	0.581254i
$932$	0.296384	+	3.38307i	0.00970837	+	0.110816i
$933$		0			0
$934$	−6.47102	+	7.06272i	−0.211738	+	0.231099i
$935$			22.2979i			0.729220i
$936$		0			0
$937$			34.0220i			1.11145i	0.831366	+	0.555725i	$0.187559\pi$
$937$			34.0220i			1.11145i	−0.831366	+	0.555725i	$0.812441\pi$
$938$	−31.7495	+	1.02512i	−1.03666	+	0.0334714i
$939$		0			0
$940$	45.6005	−	3.99496i	1.48732	−	0.130301i
$941$	14.0890	+	8.13430i	0.459289	+	0.265171i	0.711745	−	0.702438i	$-0.247905\pi$
$941$	14.0890	+	8.13430i	0.459289	+	0.265171i	−0.252456	+	0.967608i	$0.581238\pi$
$942$		0			0
$943$	−3.24639	−	5.62292i	−0.105717	−	0.183107i
$944$	10.1059	−	27.7862i	0.328919	−	0.904362i
$945$		0			0
$946$	9.72854	+	30.8486i	0.316302	+	1.00298i
$947$	14.2574	−	8.23153i	0.463304	−	0.267489i	−0.250128	−	0.968213i	$-0.580473\pi$
$947$	14.2574	−	8.23153i	0.463304	−	0.267489i	0.713433	+	0.700724i	$0.247140\pi$
$948$		0			0
$949$	−0.272346	+	0.471717i	−0.00884073	+	0.0153126i
$950$	3.78873	+	0.839707i	0.122923	+	0.0272437i
$951$		0			0
$952$	27.5468	−	20.6497i	0.892797	−	0.669262i
$953$	20.7444			0.671977			0.335988	−	0.941866i	$-0.390930\pi$
$953$	20.7444			0.671977			0.335988	+	0.941866i	$0.390930\pi$
$954$		0			0
$955$	−32.9750			−1.06704
$956$	−23.8490	+	51.1602i	−0.771332	+	1.65464i
$957$		0			0
$958$	7.42187	+	1.64493i	0.239790	+	0.0531453i
$959$	−1.41113	−	5.51761i	−0.0455678	−	0.178173i
$960$		0			0
$961$	9.14893	+	15.8464i	0.295127	+	0.511174i
$962$	3.59791	−	1.13465i	0.116001	−	0.0365826i
$963$		0			0
$964$	−31.2671	−	44.6428i	−1.00705	−	1.43785i
$965$	8.22698	−	4.74985i	0.264836	−	0.152903i
$966$		0			0
$967$	6.47848	+	3.74035i	0.208334	+	0.120282i	0.600537	−	0.799597i	$-0.294954\pi$
$967$	6.47848	+	3.74035i	0.208334	+	0.120282i	−0.392203	+	0.919879i	$0.628287\pi$
$968$	−14.9088	+	6.17854i	−0.479188	+	0.198586i
$969$		0			0
$970$	−10.1007	+	11.0243i	−0.324314	+	0.353968i
$971$	−57.8577			−1.85674			−0.928371	−	0.371655i	$-0.878790\pi$
$971$	−57.8577			−1.85674			−0.928371	+	0.371655i	$0.878790\pi$
$972$		0			0
$973$	−31.2760	+	30.5700i	−1.00266	+	0.980029i
$974$	−15.2021	−	13.9285i	−0.487107	−	0.446298i
$975$		0			0
$976$	44.2655	−	37.1610i	1.41690	−	1.18949i
$977$	16.3314	−	28.2869i	0.522489	−	0.904977i	−0.477169	−	0.878812i	$-0.658337\pi$
$977$	16.3314	−	28.2869i	0.522489	−	0.904977i	0.999658	−	0.0261653i	$-0.00832964\pi$
$978$		0			0
$979$	−5.32024	−	9.21493i	−0.170036	−	0.294511i
$980$	24.5352	−	16.3621i	0.783747	−	0.522667i
$981$		0			0
$982$	−11.6734	+	3.68137i	−0.372513	+	0.117477i
$983$	−15.4395	−	26.7421i	−0.492445	−	0.852939i	0.507518	−	0.861641i	$-0.330563\pi$
$983$	−15.4395	−	26.7421i	−0.492445	−	0.852939i	−0.999962	+	0.00870241i	$0.997230\pi$
$984$		0			0
$985$	12.8437	+	7.41531i	0.409234	+	0.236271i
$986$	−3.06028	+	13.8079i	−0.0974591	+	0.439733i
$987$		0			0
$988$	−1.03898	+	2.22878i	−0.0330542	+	0.0709068i
$989$	48.5721			1.54450
$990$		0			0
$991$		−	8.94754i		−	0.284228i	−0.989850	−	0.142114i	$-0.954610\pi$
$991$		−	8.94754i		−	0.284228i	0.989850	−	0.142114i	$-0.0453900\pi$
$992$	9.31463	+	17.8803i	0.295740	+	0.567701i
$993$		0			0
$994$	12.1345	+	19.5333i	0.384882	+	0.619560i
$995$	−3.00446	−	1.73463i	−0.0952478	−	0.0549913i
$996$		0			0
$997$	−1.31627	+	0.759946i	−0.0416865	+	0.0240677i	−0.520698	−	0.853741i	$-0.674328\pi$
$997$	−1.31627	+	0.759946i	−0.0416865	+	0.0240677i	0.479012	+	0.877808i	$0.340995\pi$
$998$	54.2623	−	17.1124i	1.71764	−	0.541682i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bi.c.307.12		80
3.2	odd	2		252.2.bi.c.139.29	yes	80
4.3	odd	2	inner	756.2.bi.c.307.38		80
7.6	odd	2	inner	756.2.bi.c.307.11		80
9.2	odd	6		252.2.bi.c.223.3	yes	80
9.7	even	3	inner	756.2.bi.c.559.37		80
12.11	even	2		252.2.bi.c.139.4	yes	80
21.20	even	2		252.2.bi.c.139.30	yes	80
28.27	even	2	inner	756.2.bi.c.307.37		80
36.7	odd	6	inner	756.2.bi.c.559.11		80
36.11	even	6		252.2.bi.c.223.30	yes	80
63.20	even	6		252.2.bi.c.223.4	yes	80
63.34	odd	6	inner	756.2.bi.c.559.38		80
84.83	odd	2		252.2.bi.c.139.3	✓	80
252.83	odd	6		252.2.bi.c.223.29	yes	80
252.223	even	6	inner	756.2.bi.c.559.12		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.bi.c.139.3	✓	80	84.83	odd	2
252.2.bi.c.139.4	yes	80	12.11	even	2
252.2.bi.c.139.29	yes	80	3.2	odd	2
252.2.bi.c.139.30	yes	80	21.20	even	2
252.2.bi.c.223.3	yes	80	9.2	odd	6
252.2.bi.c.223.4	yes	80	63.20	even	6
252.2.bi.c.223.29	yes	80	252.83	odd	6
252.2.bi.c.223.30	yes	80	36.11	even	6
756.2.bi.c.307.11		80	7.6	odd	2	inner
756.2.bi.c.307.12		80	1.1	even	1	trivial
756.2.bi.c.307.37		80	28.27	even	2	inner
756.2.bi.c.307.38		80	4.3	odd	2	inner
756.2.bi.c.559.11		80	36.7	odd	6	inner
756.2.bi.c.559.12		80	252.223	even	6	inner
756.2.bi.c.559.37		80	9.7	even	3	inner
756.2.bi.c.559.38		80	63.34	odd	6	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bi (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.955367 + 1.04272i) q^{2} +(-0.174547 - 1.99237i) q^{4} +(1.82425 + 1.05323i) q^{5} +(-2.54762 - 0.713899i) q^{7} +(2.24425 + 1.72144i) q^{8} +O(q^{10})\)	\(q+(-0.955367 + 1.04272i) q^{2} +(-0.174547 - 1.99237i) q^{4} +(1.82425 + 1.05323i) q^{5} +(-2.54762 - 0.713899i) q^{7} +(2.24425 + 1.72144i) q^{8} +(-2.84106 + 0.895969i) q^{10} +(1.99265 - 1.15046i) q^{11} +(-0.218388 - 0.126086i) q^{13} +(3.17831 - 1.97442i) q^{14} +(-3.93907 + 0.695524i) q^{16} +4.60054i q^{17} +4.87573 q^{19} +(1.78001 - 3.81843i) q^{20} +(-0.704104 + 3.17690i) q^{22} +(4.23165 + 2.44314i) q^{23} +(-0.281399 - 0.487397i) q^{25} +(0.340113 - 0.107259i) q^{26} +(-0.977672 + 5.20040i) q^{28} +(-1.08689 - 1.88255i) q^{29} +(-1.78200 + 3.08652i) q^{31} +(3.03802 - 4.77184i) q^{32} +(-4.79709 - 4.39520i) q^{34} +(-3.89560 - 3.98557i) q^{35} +10.5786 q^{37} +(-4.65811 + 5.08404i) q^{38} +(2.28100 + 5.50406i) q^{40} +(-1.15076 - 0.664389i) q^{41} +(8.60873 - 4.97025i) q^{43} +(-2.63995 - 3.76929i) q^{44} +(-6.59030 + 2.07834i) q^{46} +(5.43270 + 9.40970i) q^{47} +(5.98070 + 3.63748i) q^{49} +(0.777059 + 0.172222i) q^{50} +(-0.213091 + 0.457117i) q^{52} +7.98161 q^{53} +4.84680 q^{55} +(-4.48855 - 5.98773i) q^{56} +(3.00136 + 0.665200i) q^{58} +(-3.69586 + 6.40141i) q^{59} +(-12.5132 + 7.22449i) q^{61} +(-1.51592 - 4.80690i) q^{62} +(2.07329 + 7.72667i) q^{64} +(-0.265596 - 0.460026i) q^{65} +(-7.35240 - 4.24491i) q^{67} +(9.16597 - 0.803010i) q^{68} +(7.87757 - 0.254350i) q^{70} +6.14583i q^{71} -2.16000i q^{73} +(-10.1064 + 11.0305i) q^{74} +(-0.851044 - 9.71425i) q^{76} +(-5.89782 + 1.50837i) q^{77} +(2.84679 - 1.64360i) q^{79} +(-7.91841 - 2.87994i) q^{80} +(1.79217 - 0.565185i) q^{82} +(4.56438 + 7.90574i) q^{83} +(-4.84544 + 8.39255i) q^{85} +(-3.04190 + 13.7250i) q^{86} +(6.45245 + 0.848317i) q^{88} -4.62446i q^{89} +(0.466355 + 0.477126i) q^{91} +(4.12902 - 8.85744i) q^{92} +(-15.0019 - 3.32492i) q^{94} +(8.89457 + 5.13528i) q^{95} +(4.34667 - 2.50955i) q^{97} +(-9.50665 + 2.76108i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 6 q^{2} - 2 q^{4} + 24 q^{8}+O(q^{10}) \) 80 * q + 6 * q^2 - 2 * q^4 + 24 * q^8	\( 80 q + 6 q^{2} - 2 q^{4} + 24 q^{8} - 10 q^{14} - 18 q^{16} - 14 q^{22} + 32 q^{25} + 28 q^{28} - 8 q^{29} + 16 q^{32} - 16 q^{37} + 84 q^{44} + 24 q^{46} - 24 q^{49} + 12 q^{50} + 48 q^{53} - 32 q^{56} - 14 q^{58} - 8 q^{64} + 40 q^{65} - 22 q^{70} - 64 q^{74} + 12 q^{77} + 40 q^{85} + 52 q^{86} + 6 q^{88} - 30 q^{92} - 20 q^{98}+O(q^{100}) \) 80 * q + 6 * q^2 - 2 * q^4 + 24 * q^8 - 10 * q^14 - 18 * q^16 - 14 * q^22 + 32 * q^25 + 28 * q^28 - 8 * q^29 + 16 * q^32 - 16 * q^37 + 84 * q^44 + 24 * q^46 - 24 * q^49 + 12 * q^50 + 48 * q^53 - 32 * q^56 - 14 * q^58 - 8 * q^64 + 40 * q^65 - 22 * q^70 - 64 * q^74 + 12 * q^77 + 40 * q^85 + 52 * q^86 + 6 * q^88 - 30 * q^92 - 20 * q^98

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