LMFDB - Embedded newform 504.2.bs.a.353.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,2,Mod(257,504)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("504.257"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bs (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			353.19
Character	$\chi$	$=$	504.353
Dual form			504.2.bs.a.257.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.10617 - 1.33281i) q^{3} +(-0.103514 + 0.179292i) q^{5} +(2.64517 + 0.0556151i) q^{7} +(-0.552770 - 2.94863i) q^{9} +(-1.31380 + 0.758523i) q^{11} +(3.39130 - 1.95797i) q^{13} +(0.124457 + 0.336292i) q^{15} +(0.873421 - 1.51281i) q^{17} +(-0.968573 + 0.559206i) q^{19} +(3.00013 - 3.46399i) q^{21} +(-1.25201 - 0.722851i) q^{23} +(2.47857 + 4.29301i) q^{25} +(-4.54143 - 2.52496i) q^{27} +(1.99711 + 1.15303i) q^{29} -5.95518i q^{31} +(-0.442321 + 2.59010i) q^{33} +(-0.283783 + 0.468499i) q^{35} +(-2.13573 - 3.69920i) q^{37} +(1.14176 - 6.68581i) q^{39} +(2.91134 + 5.04260i) q^{41} +(-0.213489 + 0.369774i) q^{43} +(0.585885 + 0.206118i) q^{45} -8.26814 q^{47} +(6.99381 + 0.294222i) q^{49} +(-1.05014 - 2.83753i) q^{51} +(-8.16638 - 4.71486i) q^{53} -0.314071i q^{55} +(-0.326092 + 1.90950i) q^{57} +3.26809 q^{59} +12.1526i q^{61} +(-1.29818 - 7.83037i) q^{63} +0.810709i q^{65} -6.48982 q^{67} +(-2.34837 + 0.869102i) q^{69} +7.10884i q^{71} +(10.6188 + 6.13075i) q^{73} +(8.46349 + 1.44534i) q^{75} +(-3.51741 + 1.93335i) q^{77} +5.15612 q^{79} +(-8.38889 + 3.25983i) q^{81} +(-8.36457 + 14.4879i) q^{83} +(0.180823 + 0.313194i) q^{85} +(3.74591 - 1.38632i) q^{87} +(-1.96290 - 3.39984i) q^{89} +(9.07945 - 4.99055i) q^{91} +(-7.93713 - 6.58745i) q^{93} -0.231543i q^{95} +(13.1184 + 7.57392i) q^{97} +(2.96284 + 3.45463i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{9} + 8 q^{15} + 8 q^{21} - 12 q^{23} - 24 q^{25} - 18 q^{27} + 18 q^{29} - 10 q^{39} + 6 q^{41} - 6 q^{43} + 6 q^{45} + 36 q^{47} + 6 q^{49} - 12 q^{51} + 12 q^{53} + 4 q^{57} + 46 q^{63} - 54 q^{75}+ \cdots - 64 q^{99}+O(q^{100}) $ 48 * q - 4 * q^9 + 8 * q^15 + 8 * q^21 - 12 * q^23 - 24 * q^25 - 18 * q^27 + 18 * q^29 - 10 * q^39 + 6 * q^41 - 6 * q^43 + 6 * q^45 + 36 * q^47 + 6 * q^49 - 12 * q^51 + 12 * q^53 + 4 * q^57 + 46 * q^63 - 54 * q^75 - 36 * q^77 - 12 * q^79 - 24 * q^87 + 18 * q^89 + 6 * q^91 + 16 * q^93 - 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

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
$3$	1.10617	−	1.33281i	0.638648	−	0.769499i
$3$	1.10617	−	1.33281i	0.638648	−	0.769499i
$4$		0			0
$5$	−0.103514	+	0.179292i	−0.0462929	+	0.0801816i	−0.888243	−	0.459373i	$-0.848074\pi$
$5$	−0.103514	+	0.179292i	−0.0462929	+	0.0801816i	0.841951	+	0.539555i	$0.181407\pi$
$6$		0			0
$7$	2.64517	+	0.0556151i	0.999779	+	0.0210205i
$7$	2.64517	+	0.0556151i	0.999779	+	0.0210205i
$8$		0			0
$9$	−0.552770	−	2.94863i	−0.184257	−	0.982878i
$10$		0			0
$11$	−1.31380	+	0.758523i	−0.396126	+	0.228703i	−0.684811	−	0.728721i	$-0.740115\pi$
$11$	−1.31380	+	0.758523i	−0.396126	+	0.228703i	0.288685	+	0.957424i	$0.406782\pi$
$12$		0			0
$13$	3.39130	−	1.95797i	0.940578	−	0.543043i	0.0504364	−	0.998727i	$-0.483939\pi$
$13$	3.39130	−	1.95797i	0.940578	−	0.543043i	0.890141	+	0.455684i	$0.150605\pi$
$14$		0			0
$15$	0.124457	+	0.336292i	0.0321348	+	0.0868302i
$16$		0			0
$17$	0.873421	−	1.51281i	0.211836	−	0.366910i	−0.740453	−	0.672108i	$-0.765389\pi$
$17$	0.873421	−	1.51281i	0.211836	−	0.366910i	0.952289	+	0.305198i	$0.0987225\pi$
$18$		0			0
$19$	−0.968573	+	0.559206i	−0.222206	+	0.128291i	−0.606971	−	0.794724i	$-0.707616\pi$
$19$	−0.968573	+	0.559206i	−0.222206	+	0.128291i	0.384765	+	0.923014i	$0.374282\pi$
$20$		0			0
$21$	3.00013	−	3.46399i	0.654682	−	0.755904i
$22$		0			0
$23$	−1.25201	−	0.722851i	−0.261063	−	0.150725i	0.363756	−	0.931494i	$-0.381494\pi$
$23$	−1.25201	−	0.722851i	−0.261063	−	0.150725i	−0.624819	+	0.780769i	$0.714827\pi$
$24$		0			0
$25$	2.47857	+	4.29301i	0.495714	+	0.858602i
$26$		0			0
$27$	−4.54143	−	2.52496i	−0.873999	−	0.485928i
$28$		0			0
$29$	1.99711	+	1.15303i	0.370853	+	0.214112i	0.673831	−	0.738885i	$-0.264648\pi$
$29$	1.99711	+	1.15303i	0.370853	+	0.214112i	−0.302978	+	0.952998i	$0.597981\pi$
$30$		0			0
$31$		−	5.95518i		−	1.06958i	−0.844985	−	0.534791i	$-0.820390\pi$
$31$		−	5.95518i		−	1.06958i	0.844985	−	0.534791i	$-0.179610\pi$
$32$		0			0
$33$	−0.442321	+	2.59010i	−0.0769982	+	0.450879i
$34$		0			0
$35$	−0.283783	+	0.468499i	−0.0479681	+	0.0791908i
$36$		0			0
$37$	−2.13573	−	3.69920i	−0.351113	−	0.608145i	0.635332	−	0.772239i	$-0.280863\pi$
$37$	−2.13573	−	3.69920i	−0.351113	−	0.608145i	−0.986445	+	0.164094i	$0.947530\pi$
$38$		0			0
$39$	1.14176	−	6.68581i	0.182828	−	1.07059i
$40$		0			0
$41$	2.91134	+	5.04260i	0.454676	+	0.787521i	0.998669	−	0.0515680i	$-0.0164219\pi$
$41$	2.91134	+	5.04260i	0.454676	+	0.787521i	−0.543994	+	0.839089i	$0.683089\pi$
$42$		0			0
$43$	−0.213489	+	0.369774i	−0.0325568	+	0.0563900i	−0.881845	−	0.471540i	$-0.843698\pi$
$43$	−0.213489	+	0.369774i	−0.0325568	+	0.0563900i	0.849288	+	0.527930i	$0.177032\pi$
$44$		0			0
$45$	0.585885	+	0.206118i	0.0873385	+	0.0307263i
$46$		0			0
$47$	−8.26814			−1.20603			−0.603016	−	0.797729i	$-0.706034\pi$
$47$	−8.26814			−1.20603			−0.603016	+	0.797729i	$0.706034\pi$
$48$		0			0
$49$	6.99381	+	0.294222i	0.999116	+	0.0420318i
$50$		0			0
$51$	−1.05014	−	2.83753i	−0.147048	−	0.397334i
$52$		0			0
$53$	−8.16638	−	4.71486i	−1.12174	−	0.647636i	−0.179894	−	0.983686i	$-0.557576\pi$
$53$	−8.16638	−	4.71486i	−1.12174	−	0.647636i	−0.941844	+	0.336050i	$0.890909\pi$
$54$		0			0
$55$		−	0.314071i		−	0.0423494i
$56$		0			0
$57$	−0.326092	+	1.90950i	−0.0431919	+	0.252920i
$58$		0			0
$59$	3.26809			0.425469			0.212735	−	0.977110i	$-0.431763\pi$
$59$	3.26809			0.425469			0.212735	+	0.977110i	$0.431763\pi$
$60$		0			0
$61$			12.1526i			1.55598i	0.628277	+	0.777990i	$0.283760\pi$
$61$			12.1526i			1.55598i	−0.628277	+	0.777990i	$0.716240\pi$
$62$		0			0
$63$	−1.29818	−	7.83037i	−0.163555	−	0.986534i
$64$		0			0
$65$			0.810709i			0.100556i
$66$		0			0
$67$	−6.48982			−0.792858			−0.396429	−	0.918065i	$-0.629751\pi$
$67$	−6.48982			−0.792858			−0.396429	+	0.918065i	$0.629751\pi$
$68$		0			0
$69$	−2.34837	+	0.869102i	−0.282710	+	0.104628i
$70$		0			0
$71$			7.10884i			0.843665i	0.906674	+	0.421832i	$0.138613\pi$
$71$			7.10884i			0.843665i	−0.906674	+	0.421832i	$0.861387\pi$
$72$		0			0
$73$	10.6188	+	6.13075i	1.24283	+	0.717549i	0.969670	−	0.244419i	$-0.0785971\pi$
$73$	10.6188	+	6.13075i	1.24283	+	0.717549i	0.273162	+	0.961968i	$0.411930\pi$
$74$		0			0
$75$	8.46349	+	1.44534i	0.977280	+	0.166893i
$76$		0			0
$77$	−3.51741	+	1.93335i	−0.400846	+	0.220326i
$78$		0			0
$79$	5.15612			0.580109			0.290054	−	0.957010i	$-0.406327\pi$
$79$	5.15612			0.580109			0.290054	+	0.957010i	$0.406327\pi$
$80$		0			0
$81$	−8.38889	+	3.25983i	−0.932099	+	0.362204i
$82$		0			0
$83$	−8.36457	+	14.4879i	−0.918131	+	1.59025i	−0.115879	+	0.993263i	$0.536969\pi$
$83$	−8.36457	+	14.4879i	−0.918131	+	1.59025i	−0.802252	+	0.596986i	$0.796365\pi$
$84$		0			0
$85$	0.180823	+	0.313194i	0.0196130	+	0.0339707i
$86$		0			0
$87$	3.74591	−	1.38632i	0.401604	−	0.148629i
$88$		0			0
$89$	−1.96290	−	3.39984i	−0.208067	−	0.360382i	0.743039	−	0.669248i	$-0.233384\pi$
$89$	−1.96290	−	3.39984i	−0.208067	−	0.360382i	−0.951105	+	0.308866i	$0.900050\pi$
$90$		0			0
$91$	9.07945	−	4.99055i	0.951785	−	0.523151i
$92$		0			0
$93$	−7.93713	−	6.58745i	−0.823042	−	0.683086i
$94$		0			0
$95$		−	0.231543i		−	0.0237558i
$96$		0			0
$97$	13.1184	+	7.57392i	1.33197	+	0.769016i	0.985602	−	0.169082i	$-0.0540802\pi$
$97$	13.1184	+	7.57392i	1.33197	+	0.769016i	0.346372	+	0.938097i	$0.387414\pi$
$98$		0			0
$99$	2.96284	+	3.45463i	0.297776	+	0.347203i
$100$		0			0
$101$	5.13315	+	8.89088i	0.510767	+	0.884675i	0.999922	+	0.0124781i	$0.00397201\pi$
$101$	5.13315	+	8.89088i	0.510767	+	0.884675i	−0.489155	+	0.872197i	$0.662695\pi$
$102$		0			0
$103$	−9.74935	−	5.62879i	−0.960632	−	0.554621i	−0.0642646	−	0.997933i	$-0.520470\pi$
$103$	−9.74935	−	5.62879i	−0.960632	−	0.554621i	−0.896368	+	0.443312i	$0.853804\pi$
$104$		0			0
$105$	0.310508	+	0.896470i	0.0303025	+	0.0874865i
$106$		0			0
$107$	−9.87450	+	5.70104i	−0.954604	+	0.551141i	−0.894508	−	0.447052i	$-0.852474\pi$
$107$	−9.87450	+	5.70104i	−0.954604	+	0.551141i	−0.0600957	+	0.998193i	$0.519141\pi$
$108$		0			0
$109$	1.50422	−	2.60538i	0.144078	−	0.249550i	−0.784951	−	0.619558i	$-0.787312\pi$
$109$	1.50422	−	2.60538i	0.144078	−	0.249550i	0.929029	+	0.370008i	$0.120645\pi$
$110$		0			0
$111$	−7.29282	−	1.24542i	−0.692204	−	0.118210i
$112$		0			0
$113$	14.2634	−	8.23500i	1.34179	−	0.774683i	0.354721	−	0.934972i	$-0.384576\pi$
$113$	14.2634	−	8.23500i	1.34179	−	0.774683i	0.987070	+	0.160289i	$0.0512426\pi$
$114$		0			0
$115$	0.259202	−	0.149650i	0.0241707	−	0.0139550i
$116$		0			0
$117$	−7.64794	−	8.91740i	−0.707053	−	0.824414i
$118$		0			0
$119$	2.39448	−	3.95306i	0.219502	−	0.362376i
$120$		0			0
$121$	−4.34928	+	7.53318i	−0.395390	+	0.684835i
$122$		0			0
$123$	9.94127	+	1.69770i	0.896374	+	0.153077i
$124$		0			0
$125$	−2.06141			−0.184378
$126$		0			0
$127$	−8.52680			−0.756631			−0.378316	−	0.925677i	$-0.623497\pi$
$127$	−8.52680			−0.756631			−0.378316	+	0.925677i	$0.623497\pi$
$128$		0			0
$129$	0.256683	+	0.693575i	0.0225997	+	0.0610658i
$130$		0			0
$131$	−7.27730	+	12.6047i	−0.635821	+	1.10127i	0.350520	+	0.936555i	$0.386005\pi$
$131$	−7.27730	+	12.6047i	−0.635821	+	1.10127i	−0.986341	+	0.164719i	$0.947328\pi$
$132$		0			0
$133$	−2.59314	+	1.42533i	−0.224853	+	0.123591i
$134$		0			0
$135$	0.922805	−	0.552872i	0.0794224	−	0.0475836i
$136$		0			0
$137$	−9.25263	+	5.34201i	−0.790505	+	0.456398i	−0.840140	−	0.542369i	$-0.817527\pi$
$137$	−9.25263	+	5.34201i	−0.790505	+	0.456398i	0.0496351	+	0.998767i	$0.484194\pi$
$138$		0			0
$139$	−7.46448	+	4.30962i	−0.633129	+	0.365537i	−0.781963	−	0.623325i	$-0.785781\pi$
$139$	−7.46448	+	4.30962i	−0.633129	+	0.365537i	0.148834	+	0.988862i	$0.452448\pi$
$140$		0			0
$141$	−9.14598	+	11.0199i	−0.770230	+	0.928040i
$142$		0			0
$143$	−2.97033	+	5.14476i	−0.248391	+	0.430227i
$144$		0			0
$145$	−0.413457	+	0.238709i	−0.0343357	+	0.0198237i
$146$		0			0
$147$	8.12850	−	8.99597i	0.670427	−	0.741975i
$148$		0			0
$149$	−19.0951	−	11.0245i	−1.56433	−	0.903166i	−0.996811	−	0.0798049i	$-0.974570\pi$
$149$	−19.0951	−	11.0245i	−1.56433	−	0.903166i	−0.567518	−	0.823361i	$-0.692096\pi$
$150$		0			0
$151$	4.40064	+	7.62212i	0.358119	+	0.620280i	0.987647	−	0.156698i	$-0.0500850\pi$
$151$	4.40064	+	7.62212i	0.358119	+	0.620280i	−0.629528	+	0.776978i	$0.716752\pi$
$152$		0			0
$153$	−4.94352	−	1.73916i	−0.399660	−	0.140603i
$154$		0			0
$155$	1.06771	+	0.616444i	0.0857608	+	0.0495140i
$156$		0			0
$157$			10.5531i			0.842228i	0.907008	+	0.421114i	$0.138361\pi$
$157$			10.5531i			0.842228i	−0.907008	+	0.421114i	$0.861639\pi$
$158$		0			0
$159$	−15.3174	+	5.66879i	−1.21475	+	0.449565i
$160$		0			0
$161$	−3.27159	−	1.98169i	−0.257837	−	0.156179i
$162$		0			0
$163$	−4.64731	−	8.04937i	−0.364005	−	0.630475i	0.624611	−	0.780936i	$-0.285258\pi$
$163$	−4.64731	−	8.04937i	−0.364005	−	0.630475i	−0.988616	+	0.150461i	$0.951924\pi$
$164$		0			0
$165$	−0.418598	−	0.347417i	−0.0325878	−	0.0270463i
$166$		0			0
$167$	4.44458	+	7.69824i	0.343932	+	0.595707i	0.985159	−	0.171644i	$-0.0549078\pi$
$167$	4.44458	+	7.69824i	0.343932	+	0.595707i	−0.641227	+	0.767351i	$0.721574\pi$
$168$		0			0
$169$	1.16728	−	2.02179i	0.0897910	−	0.155523i
$170$		0			0
$171$	2.18429	+	2.54685i	0.167037	+	0.194763i
$172$		0			0
$173$	9.79940			0.745034			0.372517	−	0.928025i	$-0.378495\pi$
$173$	9.79940			0.745034			0.372517	+	0.928025i	$0.378495\pi$
$174$		0			0
$175$	6.31747	+	11.4936i	0.477556	+	0.868832i
$176$		0			0
$177$	3.61507	−	4.35575i	0.271725	−	0.327398i
$178$		0			0
$179$	14.3141	+	8.26425i	1.06989	+	0.617699i	0.928150	−	0.372206i	$-0.121398\pi$
$179$	14.3141	+	8.26425i	1.06989	+	0.617699i	0.141735	+	0.989905i	$0.454732\pi$
$180$		0			0
$181$		−	23.8542i		−	1.77307i	−0.462664	−	0.886534i	$-0.653106\pi$
$181$		−	23.8542i		−	1.77307i	0.462664	−	0.886534i	$-0.346894\pi$
$182$		0			0
$183$	16.1971	+	13.4428i	1.19732	+	0.993723i
$184$		0			0
$185$	0.884314			0.0650161
$186$		0			0
$187$			2.65004i			0.193790i
$188$		0			0
$189$	−11.8724	−	6.93151i	−0.863591	−	0.504193i
$190$		0			0
$191$		−	22.3601i		−	1.61792i	−0.587864	−	0.808960i	$-0.700031\pi$
$191$		−	22.3601i		−	1.61792i	0.587864	−	0.808960i	$-0.299969\pi$
$192$		0			0
$193$	−8.65700			−0.623145			−0.311572	−	0.950222i	$-0.600856\pi$
$193$	−8.65700			−0.623145			−0.311572	+	0.950222i	$0.600856\pi$
$194$		0			0
$195$	1.08052	+	0.896783i	0.0773778	+	0.0642200i
$196$		0			0
$197$		−	23.2821i		−	1.65878i	−0.558668	−	0.829391i	$-0.688687\pi$
$197$		−	23.2821i		−	1.65878i	0.558668	−	0.829391i	$-0.311313\pi$
$198$		0			0
$199$	8.80893	+	5.08584i	0.624449	+	0.360526i	0.778599	−	0.627522i	$-0.215931\pi$
$199$	8.80893	+	5.08584i	0.624449	+	0.360526i	−0.154150	+	0.988047i	$0.549264\pi$
$200$		0			0
$201$	−7.17885	+	8.64970i	−0.506357	+	0.610103i
$202$		0			0
$203$	5.21855	+	3.16102i	0.366270	+	0.221860i
$204$		0			0
$205$	−1.20546			−0.0841930
$206$		0			0
$207$	−1.43935	+	4.09130i	−0.100042	+	0.284365i
$208$		0			0
$209$	0.848341	−	1.46937i	0.0586810	−	0.101638i
$210$		0			0
$211$	−13.2184	−	22.8949i	−0.909991	−	1.57615i	−0.814073	−	0.580762i	$-0.802755\pi$
$211$	−13.2184	−	22.8949i	−0.909991	−	1.57615i	−0.0959178	−	0.995389i	$-0.530579\pi$
$212$		0			0
$213$	9.47475	+	7.86360i	0.649199	+	0.538805i
$214$		0			0
$215$	−0.0441983	−	0.0765537i	−0.00301430	−	0.00522092i
$216$		0			0
$217$	0.331198	−	15.7524i	0.0224832	−	1.06935i
$218$		0			0
$219$	19.9173	−	7.37115i	1.34589	−	0.498096i
$220$		0			0
$221$		−	6.84052i		−	0.460143i
$222$		0			0
$223$	14.4887	+	8.36504i	0.970233	+	0.560164i	0.899307	−	0.437317i	$-0.144071\pi$
$223$	14.4887	+	8.36504i	0.970233	+	0.560164i	0.0709258	+	0.997482i	$0.477405\pi$
$224$		0			0
$225$	11.2884	−	9.68144i	0.752562	−	0.645429i
$226$		0			0
$227$	−4.44461	−	7.69828i	−0.294999	−	0.510953i	0.679986	−	0.733225i	$-0.261986\pi$
$227$	−4.44461	−	7.69828i	−0.294999	−	0.510953i	−0.974985	+	0.222272i	$0.928653\pi$
$228$		0			0
$229$	−14.6822	−	8.47679i	−0.970229	−	0.560162i	−0.0709229	−	0.997482i	$-0.522594\pi$
$229$	−14.6822	−	8.47679i	−0.970229	−	0.560162i	−0.899306	+	0.437320i	$0.855928\pi$
$230$		0			0
$231$	−1.31406	+	6.82666i	−0.0864589	+	0.449161i
$232$		0			0
$233$	17.3861	−	10.0379i	1.13900	−	0.657602i	0.192817	−	0.981235i	$-0.438238\pi$
$233$	17.3861	−	10.0379i	1.13900	−	0.657602i	0.946183	+	0.323633i	$0.104904\pi$
$234$		0			0
$235$	0.855868	−	1.48241i	0.0558307	−	0.0967016i
$236$		0			0
$237$	5.70355	−	6.87213i	0.370486	−	0.446393i
$238$		0			0
$239$	11.5629	−	6.67585i	0.747943	−	0.431825i	−0.0770074	−	0.997031i	$-0.524536\pi$
$239$	11.5629	−	6.67585i	0.747943	−	0.431825i	0.824950	+	0.565206i	$0.191203\pi$
$240$		0			0
$241$	−11.0568	+	6.38367i	−0.712234	+	0.411209i	−0.811888	−	0.583814i	$-0.801560\pi$
$241$	−11.0568	+	6.38367i	−0.712234	+	0.411209i	0.0996536	+	0.995022i	$0.468227\pi$
$242$		0			0
$243$	−4.93481	+	14.7867i	−0.316568	+	0.948570i
$244$		0			0
$245$	−0.776709	+	1.22348i	−0.0496221	+	0.0781650i
$246$		0			0
$247$	−2.18981	+	3.79287i	−0.139335	+	0.241335i
$248$		0			0
$249$	10.0569	+	27.1744i	0.637332	+	1.72211i
$250$		0			0
$251$	17.8367			1.12584			0.562921	−	0.826511i	$-0.309678\pi$
$251$	17.8367			1.12584			0.562921	+	0.826511i	$0.309678\pi$
$252$		0			0
$253$	2.19320			0.137885
$254$		0			0
$255$	0.617449	+	0.105444i	0.0386662	+	0.00660315i
$256$		0			0
$257$	0.818588	−	1.41784i	0.0510621	−	0.0884421i	−0.839365	−	0.543569i	$-0.817073\pi$
$257$	0.818588	−	1.41784i	0.0510621	−	0.0884421i	0.890427	+	0.455127i	$0.150406\pi$
$258$		0			0
$259$	−5.44364	−	9.90378i	−0.338251	−	0.615391i
$260$		0			0
$261$	2.29592	−	6.52609i	0.142114	−	0.403955i
$262$		0			0
$263$	26.6087	−	15.3626i	1.64077	−	0.947296i	0.660203	−	0.751087i	$-0.270470\pi$
$263$	26.6087	−	15.3626i	1.64077	−	0.947296i	0.980562	−	0.196210i	$-0.0628633\pi$
$264$		0			0
$265$	1.69067	−	0.976108i	0.103857	−	0.0599619i
$266$		0			0
$267$	−6.70264	−	1.14463i	−0.410195	−	0.0700503i
$268$		0			0
$269$	−0.491194	+	0.850773i	−0.0299486	+	0.0518726i	−0.880611	−	0.473839i	$-0.842868\pi$
$269$	−0.491194	+	0.850773i	−0.0299486	+	0.0518726i	0.850663	+	0.525712i	$0.176201\pi$
$270$		0			0
$271$	−0.707412	+	0.408425i	−0.0429722	+	0.0248100i	−0.521332	−	0.853354i	$-0.674565\pi$
$271$	−0.707412	+	0.408425i	−0.0429722	+	0.0248100i	0.478360	+	0.878164i	$0.341231\pi$
$272$		0			0
$273$	3.39197	−	17.6216i	0.205292	−	1.06651i
$274$		0			0
$275$	−6.51269	−	3.76011i	−0.392730	−	0.226743i
$276$		0			0
$277$	−5.30188	−	9.18313i	−0.318559	−	0.551761i	0.661629	−	0.749832i	$-0.269866\pi$
$277$	−5.30188	−	9.18313i	−0.318559	−	0.551761i	−0.980188	+	0.198071i	$0.936532\pi$
$278$		0			0
$279$	−17.5596	+	3.29184i	−1.05127	+	0.197077i
$280$		0			0
$281$	14.1764	+	8.18477i	0.845695	+	0.488262i	0.859196	−	0.511647i	$-0.170964\pi$
$281$	14.1764	+	8.18477i	0.845695	+	0.488262i	−0.0135009	+	0.999909i	$0.504298\pi$
$282$		0			0
$283$		−	6.55510i		−	0.389660i	−0.980837	−	0.194830i	$-0.937584\pi$
$283$		−	6.55510i		−	0.389660i	0.980837	−	0.194830i	$-0.0624156\pi$
$284$		0			0
$285$	−0.308602	−	0.256126i	−0.0182800	−	0.0151716i
$286$		0			0
$287$	7.42055	+	13.5004i	0.438021	+	0.796905i
$288$		0			0
$289$	6.97427	+	12.0798i	0.410251	+	0.710576i
$290$		0			0
$291$	24.6058	−	9.10632i	1.44242	−	0.533822i
$292$		0			0
$293$	7.02441	+	12.1666i	0.410370	+	0.710782i	0.994930	−	0.100568i	$-0.0320662\pi$
$293$	7.02441	+	12.1666i	0.410370	+	0.710782i	−0.584560	+	0.811351i	$0.698733\pi$
$294$		0			0
$295$	−0.338293	+	0.585941i	−0.0196962	+	0.0341148i
$296$		0			0
$297$	7.88177	−	0.127489i	0.457347	−	0.00739769i
$298$		0			0
$299$	−5.66128			−0.327400
$300$		0			0
$301$	−0.585280	+	0.966241i	−0.0337350	+	0.0556932i
$302$		0			0
$303$	17.5280	+	2.99331i	1.00696	+	0.171961i
$304$		0			0
$305$	−2.17886	−	1.25796i	−0.124761	−	0.0720308i
$306$		0			0
$307$		−	17.4335i		−	0.994982i	−0.867469	−	0.497491i	$-0.834255\pi$
$307$		−	17.4335i		−	0.994982i	0.867469	−	0.497491i	$-0.165745\pi$
$308$		0			0
$309$	−18.2866	+	6.76764i	−1.04029	+	0.384997i
$310$		0			0
$311$	−15.5963			−0.884382			−0.442191	−	0.896921i	$-0.645799\pi$
$311$	−15.5963			−0.884382			−0.442191	+	0.896921i	$0.645799\pi$
$312$		0			0
$313$			2.22985i			0.126039i	0.998012	+	0.0630193i	$0.0200730\pi$
$313$			2.22985i			0.126039i	−0.998012	+	0.0630193i	$0.979927\pi$
$314$		0			0
$315$	1.53830	+	0.577801i	0.0866734	+	0.0325554i
$316$		0			0
$317$		−	34.3250i		−	1.92789i	−0.266109	−	0.963943i	$-0.585738\pi$
$317$		−	34.3250i		−	1.92789i	0.266109	−	0.963943i	$-0.414262\pi$
$318$		0			0
$319$	−3.49840			−0.195873
$320$		0			0
$321$	−3.32447	+	19.4672i	−0.185554	+	1.08655i
$322$		0			0
$323$			1.95369i			0.108706i
$324$		0			0
$325$	16.8112	+	9.70592i	0.932515	+	0.538388i
$326$		0			0
$327$	−1.80856	−	4.88683i	−0.100013	−	0.270242i
$328$		0			0
$329$	−21.8706	−	0.459833i	−1.20577	−	0.0253514i
$330$		0			0
$331$	−22.5403			−1.23893			−0.619463	−	0.785026i	$-0.712650\pi$
$331$	−22.5403			−1.23893			−0.619463	+	0.785026i	$0.712650\pi$
$332$		0			0
$333$	−9.72702	+	8.34231i	−0.533037	+	0.457156i
$334$		0			0
$335$	0.671787	−	1.16357i	0.0367037	−	0.0635726i
$336$		0			0
$337$	−11.3776	−	19.7065i	−0.619776	−	1.07348i	−0.989526	−	0.144353i	$-0.953890\pi$
$337$	−11.3776	−	19.7065i	−0.619776	−	1.07348i	0.369750	−	0.929131i	$-0.379443\pi$
$338$		0			0
$339$	4.80211	−	28.1198i	0.260815	−	1.52726i
$340$		0			0
$341$	4.51714	+	7.82392i	0.244617	+	0.423689i
$342$		0			0
$343$	18.4834	+	1.16723i	0.998012	+	0.0630244i
$344$		0			0
$345$	0.0872663	−	0.511007i	0.00469826	−	0.0275117i
$346$		0			0
$347$		−	7.47007i		−	0.401015i	−0.979692	−	0.200507i	$-0.935741\pi$
$347$		−	7.47007i		−	0.401015i	0.979692	−	0.200507i	$-0.0642590\pi$
$348$		0			0
$349$	−7.60969	−	4.39346i	−0.407337	−	0.235176i	0.282308	−	0.959324i	$-0.408900\pi$
$349$	−7.60969	−	4.39346i	−0.407337	−	0.235176i	−0.689645	+	0.724148i	$0.742233\pi$
$350$		0			0
$351$	−20.3451	+	0.329087i	−1.08594	+	0.0175654i
$352$		0			0
$353$	3.66305	+	6.34459i	0.194965	+	0.337689i	0.946889	−	0.321561i	$-0.104207\pi$
$353$	3.66305	+	6.34459i	0.194965	+	0.337689i	−0.751924	+	0.659249i	$0.770874\pi$
$354$		0			0
$355$	−1.27456	−	0.735865i	−0.0676464	−	0.0390557i
$356$		0			0
$357$	−2.61997	−	7.56415i	−0.138664	−	0.400337i
$358$		0			0
$359$	−11.0036	+	6.35295i	−0.580749	+	0.335296i	−0.761431	−	0.648246i	$-0.775503\pi$
$359$	−11.0036	+	6.35295i	−0.580749	+	0.335296i	0.180682	+	0.983542i	$0.442170\pi$
$360$		0			0
$361$	−8.87458	+	15.3712i	−0.467083	+	0.809012i
$362$		0			0
$363$	5.22925	+	14.1298i	0.274465	+	0.741620i
$364$		0			0
$365$	−2.19838	+	1.26924i	−0.115069	+	0.0664349i
$366$		0			0
$367$	−14.0927	+	8.13641i	−0.735632	+	0.424717i	−0.820479	−	0.571677i	$-0.806293\pi$
$367$	−14.0927	+	8.13641i	−0.735632	+	0.424717i	0.0848471	+	0.996394i	$0.472960\pi$
$368$		0			0
$369$	13.2595	−	11.3719i	0.690260	−	0.591997i
$370$		0			0
$371$	−21.3392	−	12.9258i	−1.10788	−	0.671072i
$372$		0			0
$373$	−7.94015	+	13.7527i	−0.411126	+	0.712090i	−0.995013	−	0.0997442i	$-0.968198\pi$
$373$	−7.94015	+	13.7527i	−0.411126	+	0.712090i	0.583888	+	0.811835i	$0.301531\pi$
$374$		0			0
$375$	−2.28027	+	2.74747i	−0.117753	+	0.141879i
$376$		0			0
$377$	9.03038			0.465088
$378$		0			0
$379$	−0.0882488			−0.00453304			−0.00226652	−	0.999997i	$-0.500721\pi$
$379$	−0.0882488			−0.00453304			−0.00226652	+	0.999997i	$0.500721\pi$
$380$		0			0
$381$	−9.43211	+	11.3646i	−0.483221	+	0.582227i
$382$		0			0
$383$	16.9637	−	29.3819i	0.866802	−	1.50135i	0.00155547	−	0.999999i	$-0.499505\pi$
$383$	16.9637	−	29.3819i	0.866802	−	1.50135i	0.865247	−	0.501346i	$-0.167162\pi$
$384$		0			0
$385$	0.0174671	−	0.830771i	0.000890205	−	0.0423400i
$386$		0			0
$387$	1.20834	+	0.425102i	0.0614234	+	0.0216091i
$388$		0			0
$389$	9.87060	−	5.69879i	0.500459	−	0.288940i	−0.228444	−	0.973557i	$-0.573364\pi$
$389$	9.87060	−	5.69879i	0.500459	−	0.288940i	0.728903	+	0.684617i	$0.240030\pi$
$390$		0			0
$391$	−2.18707	+	1.26271i	−0.110605	+	0.0638578i
$392$		0			0
$393$	8.74968	+	23.6422i	0.441363	+	1.19259i
$394$		0			0
$395$	−0.533731	+	0.924449i	−0.0268549	+	0.0465141i
$396$		0			0
$397$	−3.81168	+	2.20068i	−0.191303	+	0.110449i	−0.592592	−	0.805503i	$-0.701895\pi$
$397$	−3.81168	+	2.20068i	−0.191303	+	0.110449i	0.401289	+	0.915951i	$0.368562\pi$
$398$		0			0
$399$	−0.968765	+	5.03281i	−0.0484989	+	0.251956i
$400$		0			0
$401$	−7.34606	−	4.24125i	−0.366845	−	0.211798i	0.305234	−	0.952277i	$-0.401265\pi$
$401$	−7.34606	−	4.24125i	−0.366845	−	0.211798i	−0.672079	+	0.740479i	$0.734599\pi$
$402$		0			0
$403$	−11.6601	−	20.1958i	−0.580828	−	1.00602i
$404$		0			0
$405$	0.283908	−	1.84150i	0.0141075	−	0.0915047i
$406$		0			0
$407$	5.61186	+	3.24001i	0.278170	+	0.160601i
$408$		0			0
$409$			11.5764i			0.572415i	0.958168	+	0.286207i	$0.0923946\pi$
$409$			11.5764i			0.572415i	−0.958168	+	0.286207i	$0.907605\pi$
$410$		0			0
$411$	−3.11511	+	18.2412i	−0.153657	+	0.899771i
$412$		0			0
$413$	8.64465	+	0.181755i	0.425375	+	0.00894359i
$414$		0			0
$415$	−1.73170	−	2.99939i	−0.0850059	−	0.147234i
$416$		0			0
$417$	−2.51309	+	14.7159i	−0.123066	+	0.720642i
$418$		0			0
$419$	11.3173	+	19.6021i	0.552885	+	0.957625i	0.998065	+	0.0621839i	$0.0198065\pi$
$419$	11.3173	+	19.6021i	0.552885	+	0.957625i	−0.445180	+	0.895441i	$0.646860\pi$
$420$		0			0
$421$	−3.51429	+	6.08693i	−0.171276	+	0.296659i	−0.938866	−	0.344282i	$-0.888122\pi$
$421$	−3.51429	+	6.08693i	−0.171276	+	0.296659i	0.767590	+	0.640941i	$0.221456\pi$
$422$		0			0
$423$	4.57038	+	24.3797i	0.222219	+	1.18538i
$424$		0			0
$425$	8.65934			0.420040
$426$		0			0
$427$	−0.675867	+	32.1456i	−0.0327075	+	1.55564i
$428$		0			0
$429$	3.57130	+	9.64988i	0.172424	+	0.465900i
$430$		0			0
$431$	−0.267173	−	0.154252i	−0.0128693	−	0.00743007i	0.493552	−	0.869717i	$-0.335698\pi$
$431$	−0.267173	−	0.154252i	−0.0128693	−	0.00743007i	−0.506421	+	0.862286i	$0.669032\pi$
$432$		0			0
$433$		−	32.8376i		−	1.57807i	−0.614347	−	0.789036i	$-0.710580\pi$
$433$		−	32.8376i		−	1.57807i	0.614347	−	0.789036i	$-0.289420\pi$
$434$		0			0
$435$	−0.139200	+	0.815113i	−0.00667411	+	0.0390817i
$436$		0			0
$437$	1.61689			0.0773463
$438$		0			0
$439$		−	3.36313i		−	0.160514i	−0.996774	−	0.0802568i	$-0.974426\pi$
$439$		−	3.36313i		−	0.160514i	0.996774	−	0.0802568i	$-0.0255740\pi$
$440$		0			0
$441$	−2.99842	−	20.7848i	−0.142782	−	0.989754i
$442$		0			0
$443$			35.9108i			1.70617i	0.521768	+	0.853087i	$0.325273\pi$
$443$			35.9108i			1.70617i	−0.521768	+	0.853087i	$0.674727\pi$
$444$		0			0
$445$	0.812749			0.0385280
$446$		0			0
$447$	−35.8160	+	13.2551i	−1.69404	+	0.626944i
$448$		0			0
$449$			13.9993i			0.660668i	0.943864	+	0.330334i	$0.107161\pi$
$449$			13.9993i			0.660668i	−0.943864	+	0.330334i	$0.892839\pi$
$450$		0			0
$451$	−7.64985	−	4.41664i	−0.360217	−	0.207972i
$452$		0			0
$453$	15.0267	+	2.56616i	0.706016	+	0.120569i
$454$		0			0
$455$	−0.0450876	+	2.14446i	−0.00211374	+	0.100534i
$456$		0			0
$457$	7.94102			0.371465			0.185733	−	0.982600i	$-0.440534\pi$
$457$	7.94102			0.371465			0.185733	+	0.982600i	$0.440534\pi$
$458$		0			0
$459$	−7.78636	+	4.66497i	−0.363436	+	0.217742i
$460$		0			0
$461$	−2.12627	+	3.68281i	−0.0990304	+	0.171526i	−0.911284	−	0.411779i	$-0.864907\pi$
$461$	−2.12627	+	3.68281i	−0.0990304	+	0.171526i	0.812253	+	0.583305i	$0.198241\pi$
$462$		0			0
$463$	−10.2557	−	17.7634i	−0.476622	−	0.825534i	0.523019	−	0.852321i	$-0.324806\pi$
$463$	−10.2557	−	17.7634i	−0.476622	−	0.825534i	−0.999641	+	0.0267869i	$0.991472\pi$
$464$		0			0
$465$	2.00268	−	0.741166i	0.0928719	−	0.0343708i
$466$		0			0
$467$	−13.8842	−	24.0481i	−0.642484	−	1.11281i	−0.984877	−	0.173257i	$-0.944571\pi$
$467$	−13.8842	−	24.0481i	−0.642484	−	1.11281i	0.342393	−	0.939557i	$-0.388763\pi$
$468$		0			0
$469$	−17.1667	−	0.360932i	−0.792682	−	0.0166663i
$470$		0			0
$471$	14.0653	+	11.6735i	0.648093	+	0.537887i
$472$		0			0
$473$		−	0.647746i		−	0.0297834i
$474$		0			0
$475$	−4.80135	−	2.77206i	−0.220301	−	0.127191i
$476$		0			0
$477$	−9.38827	+	26.6859i	−0.429860	+	1.22186i
$478$		0			0
$479$	−15.7064	−	27.2042i	−0.717643	−	1.24299i	−0.961931	−	0.273291i	$-0.911888\pi$
$479$	−15.7064	−	27.2042i	−0.717643	−	1.24299i	0.244289	−	0.969703i	$-0.421446\pi$
$480$		0			0
$481$	−14.4858	−	8.36340i	−0.660497	−	0.381338i
$482$		0			0
$483$	−6.26016	+	2.16831i	−0.284847	+	0.0986617i
$484$		0			0
$485$	−2.71588	+	1.56801i	−0.123322	+	0.0711999i
$486$		0			0
$487$	−16.1798	+	28.0242i	−0.733176	+	1.26990i	0.222343	+	0.974968i	$0.428629\pi$
$487$	−16.1798	+	28.0242i	−0.733176	+	1.26990i	−0.955519	+	0.294929i	$0.904704\pi$
$488$		0			0
$489$	−15.8690	−	2.71000i	−0.717621	−	0.122551i
$490$		0			0
$491$	33.6617	−	19.4346i	1.51913	−	0.877071i	0.519385	−	0.854540i	$-0.326161\pi$
$491$	33.6617	−	19.4346i	1.51913	−	0.877071i	0.999746	−	0.0225309i	$-0.00717243\pi$
$492$		0			0
$493$	3.48863	−	2.01416i	0.157120	−	0.0907132i
$494$		0			0
$495$	−0.926081	+	0.173609i	−0.0416243	+	0.00780315i
$496$		0			0
$497$	−0.395359	+	18.8041i	−0.0177343	+	0.843478i
$498$		0			0
$499$	−19.8770	+	34.4280i	−0.889816	+	1.54121i	−0.0497240	+	0.998763i	$0.515834\pi$
$499$	−19.8770	+	34.4280i	−0.889816	+	1.54121i	−0.840092	+	0.542444i	$0.817499\pi$
$500$		0			0
$501$	15.1768	+	2.59179i	0.678048	+	0.115792i
$502$		0			0
$503$	4.45463			0.198622			0.0993110	−	0.995056i	$-0.468336\pi$
$503$	4.45463			0.198622			0.0993110	+	0.995056i	$0.468336\pi$
$504$		0			0
$505$	−2.12541			−0.0945796
$506$		0			0
$507$	−1.40345	−	3.79222i	−0.0623296	−	0.168418i
$508$		0			0
$509$	−9.92165	+	17.1848i	−0.439769	+	0.761703i	−0.997671	−	0.0682040i	$-0.978273\pi$
$509$	−9.92165	+	17.1848i	−0.439769	+	0.761703i	0.557902	+	0.829907i	$0.311606\pi$
$510$		0			0
$511$	27.7474	+	16.8074i	1.22747	+	0.743516i
$512$		0			0
$513$	5.81068	−	0.0939890i	0.256548	−	0.00414971i
$514$		0			0
$515$	2.01839	−	1.16532i	0.0889409	−	0.0513500i
$516$		0			0
$517$	10.8627	−	6.27157i	0.477740	−	0.275824i
$518$		0			0
$519$	10.8398	−	13.0607i	0.475815	−	0.573303i
$520$		0			0
$521$	6.51527	−	11.2848i	0.285439	−	0.494395i	−0.687277	−	0.726396i	$-0.741194\pi$
$521$	6.51527	−	11.2848i	0.285439	−	0.494395i	0.972716	+	0.232001i	$0.0745273\pi$
$522$		0			0
$523$	28.6981	−	16.5688i	1.25488	−	0.724505i	0.282805	−	0.959177i	$-0.408735\pi$
$523$	28.6981	−	16.5688i	1.25488	−	0.724505i	0.972075	+	0.234672i	$0.0754017\pi$
$524$		0			0
$525$	22.3070	+	4.29386i	0.973556	+	0.187399i
$526$		0			0
$527$	−9.00905	−	5.20138i	−0.392440	−	0.226575i
$528$		0			0
$529$	−10.4550	−	18.1085i	−0.454564	−	0.787328i
$530$		0			0
$531$	−1.80650	−	9.63641i	−0.0783955	−	0.418185i
$532$		0			0
$533$	19.7465	+	11.4006i	0.855315	+	0.493817i
$534$		0			0
$535$		−	2.36055i		−	0.102056i
$536$		0			0
$537$	26.8485	−	9.93631i	1.15860	−	0.428783i
$538$		0			0
$539$	−9.41165	+	4.91842i	−0.405389	+	0.211851i
$540$		0			0
$541$	13.3022	+	23.0402i	0.571908	+	0.990574i	0.996370	+	0.0851281i	$0.0271300\pi$
$541$	13.3022	+	23.0402i	0.571908	+	0.990574i	−0.424462	+	0.905446i	$0.639537\pi$
$542$		0			0
$543$	−31.7931	−	26.3868i	−1.36437	−	1.13237i
$544$		0			0
$545$	0.311415	+	0.539387i	0.0133396	+	0.0231048i
$546$		0			0
$547$	−4.32361	+	7.48870i	−0.184864	+	0.320194i	−0.943531	−	0.331285i	$-0.892518\pi$
$547$	−4.32361	+	7.48870i	−0.184864	+	0.320194i	0.758667	+	0.651479i	$0.225851\pi$
$548$		0			0
$549$	35.8335	−	6.71758i	1.52934	−	0.286699i
$550$		0			0
$551$	−2.57912			−0.109874
$552$		0			0
$553$	13.6388	+	0.286758i	0.579981	+	0.0121942i
$554$		0			0
$555$	0.978203	−	1.17862i	0.0415224	−	0.0500298i
$556$		0			0
$557$	−19.1707	−	11.0682i	−0.812289	−	0.468975i	0.0354610	−	0.999371i	$-0.488710\pi$
$557$	−19.1707	−	11.0682i	−0.812289	−	0.468975i	−0.847750	+	0.530396i	$0.822043\pi$
$558$		0			0
$559$			1.67202i			0.0707190i
$560$		0			0
$561$	3.53200	+	2.93140i	0.149121	+	0.123764i
$562$		0			0
$563$	12.2055			0.514400			0.257200	−	0.966358i	$-0.417200\pi$
$563$	12.2055			0.514400			0.257200	+	0.966358i	$0.417200\pi$
$564$		0			0
$565$			3.40975i			0.143449i
$566$		0			0
$567$	−22.3713	+	8.15625i	−0.939507	+	0.342530i
$568$		0			0
$569$		−	9.42392i		−	0.395071i	−0.980296	−	0.197536i	$-0.936706\pi$
$569$		−	9.42392i		−	0.395071i	0.980296	−	0.197536i	$-0.0632938\pi$
$570$		0			0
$571$	15.4716			0.647465			0.323733	−	0.946149i	$-0.395062\pi$
$571$	15.4716			0.647465			0.323733	+	0.946149i	$0.395062\pi$
$572$		0			0
$573$	−29.8018	−	24.7341i	−1.24499	−	1.03328i
$574$		0			0
$575$		−	7.16655i		−	0.298866i
$576$		0			0
$577$	−8.48608	−	4.89944i	−0.353280	−	0.203966i	0.312849	−	0.949803i	$-0.398717\pi$
$577$	−8.48608	−	4.89944i	−0.353280	−	0.203966i	−0.666129	+	0.745836i	$0.732050\pi$
$578$		0			0
$579$	−9.57613	+	11.5381i	−0.397970	+	0.479509i
$580$		0			0
$581$	−22.9314	+	37.8576i	−0.951356	+	1.57060i
$582$		0			0
$583$	14.3053			0.592466
$584$		0			0
$585$	2.39048	−	0.448135i	0.0988344	−	0.0185281i
$586$		0			0
$587$	−12.4297	+	21.5289i	−0.513028	+	0.888591i	0.486858	+	0.873481i	$0.338143\pi$
$587$	−12.4297	+	21.5289i	−0.513028	+	0.888591i	−0.999886	+	0.0151097i	$0.995190\pi$
$588$		0			0
$589$	3.33017	+	5.76802i	0.137217	+	0.237667i
$590$		0			0
$591$	−31.0307	−	25.7540i	−1.27643	−	1.05938i
$592$		0			0
$593$	20.9831	+	36.3438i	0.861673	+	1.49246i	0.870313	+	0.492500i	$0.163917\pi$
$593$	20.9831	+	36.3438i	0.861673	+	1.49246i	−0.00863918	+	0.999963i	$0.502750\pi$
$594$		0			0
$595$	0.460888	+	0.838507i	0.0188946	+	0.0343754i
$596$		0			0
$597$	16.5226	−	6.11483i	0.676227	−	0.250263i
$598$		0			0
$599$		−	30.3196i		−	1.23882i	−0.785066	−	0.619412i	$-0.787371\pi$
$599$		−	30.3196i		−	1.23882i	0.785066	−	0.619412i	$-0.212629\pi$
$600$		0			0
$601$	2.71173	+	1.56562i	0.110614	+	0.0638628i	0.554286	−	0.832326i	$-0.312991\pi$
$601$	2.71173	+	1.56562i	0.110614	+	0.0638628i	−0.443673	+	0.896189i	$0.646325\pi$
$602$		0			0
$603$	3.58738	+	19.1361i	0.146089	+	0.779282i
$604$		0			0
$605$	−0.900424	−	1.55958i	−0.0366074	−	0.0634060i
$606$		0			0
$607$	12.4592	+	7.19329i	0.505701	+	0.291967i	0.731065	−	0.682308i	$-0.239024\pi$
$607$	12.4592	+	7.19329i	0.505701	+	0.291967i	−0.225364	+	0.974275i	$0.572357\pi$
$608$		0			0
$609$	9.98566	−	3.45871i	0.404639	−	0.140154i
$610$		0			0
$611$	−28.0397	+	16.1888i	−1.13437	+	0.654927i
$612$		0			0
$613$	−4.36863	+	7.56669i	−0.176447	+	0.305616i	−0.940661	−	0.339347i	$-0.889794\pi$
$613$	−4.36863	+	7.56669i	−0.176447	+	0.305616i	0.764214	+	0.644963i	$0.223127\pi$
$614$		0			0
$615$	−1.33345	+	1.60665i	−0.0537697	+	0.0647864i
$616$		0			0
$617$	−25.9444	+	14.9790i	−1.04448	+	0.603033i	−0.921100	−	0.389326i	$-0.872708\pi$
$617$	−25.9444	+	14.9790i	−1.04448	+	0.603033i	−0.123384	+	0.992359i	$0.539375\pi$
$618$		0			0
$619$	−2.27825	+	1.31535i	−0.0915706	+	0.0528683i	−0.545086	−	0.838380i	$-0.683503\pi$
$619$	−2.27825	+	1.31535i	−0.0915706	+	0.0528683i	0.453515	+	0.891248i	$0.350170\pi$
$620$		0			0
$621$	3.86077	+	6.44406i	0.154927	+	0.258591i
$622$		0			0
$623$	−5.00311	−	9.10230i	−0.200445	−	0.364676i
$624$		0			0
$625$	−12.1795	+	21.0955i	−0.487179	+	0.843818i
$626$		0			0
$627$	−1.01998	−	2.75605i	−0.0407341	−	0.110066i
$628$		0			0
$629$	−7.46158			−0.297513
$630$		0			0
$631$	−18.0872			−0.720039			−0.360019	−	0.932945i	$-0.617230\pi$
$631$	−18.0872			−0.720039			−0.360019	+	0.932945i	$0.617230\pi$
$632$		0			0
$633$	−45.1364	−	7.70809i	−1.79401	−	0.306369i
$634$		0			0
$635$	0.882644	−	1.52878i	0.0350266	−	0.0606679i
$636$		0			0
$637$	24.2942	−	12.6959i	0.962572	−	0.503029i
$638$		0			0
$639$	20.9614	−	3.92955i	0.829220	−	0.155451i
$640$		0			0
$641$	−35.6571	+	20.5867i	−1.40837	+	0.813124i	−0.995231	−	0.0975432i	$-0.968902\pi$
$641$	−35.6571	+	20.5867i	−1.40837	+	0.813124i	−0.413141	+	0.910667i	$0.635568\pi$
$642$		0			0
$643$	31.3046	−	18.0737i	1.23453	−	0.712758i	0.266561	−	0.963818i	$-0.414113\pi$
$643$	31.3046	−	18.0737i	1.23453	−	0.712758i	0.967971	+	0.251060i	$0.0807792\pi$
$644$		0			0
$645$	−0.150922	−	0.0257735i	−0.00594256	−	0.00101483i
$646$		0			0
$647$	−4.09812	+	7.09815i	−0.161114	+	0.279057i	−0.935268	−	0.353939i	$-0.884842\pi$
$647$	−4.09812	+	7.09815i	−0.161114	+	0.279057i	0.774155	+	0.632996i	$0.218175\pi$
$648$		0			0
$649$	−4.29362	+	2.47892i	−0.168539	+	0.0973063i
$650$		0			0
$651$	−20.6287	−	17.8663i	−0.808501	−	0.700236i
$652$		0			0
$653$	23.3611	+	13.4875i	0.914190	+	0.527808i	0.881777	−	0.471667i	$-0.156348\pi$
$653$	23.3611	+	13.4875i	0.914190	+	0.527808i	0.0324129	+	0.999475i	$0.489681\pi$
$654$		0			0
$655$	−1.50661	−	2.60952i	−0.0588680	−	0.101962i
$656$		0			0
$657$	12.2076	−	34.6997i	0.476264	−	1.35377i
$658$		0			0
$659$	−2.60125	−	1.50183i	−0.101330	−	0.0585032i	0.448478	−	0.893794i	$-0.351966\pi$
$659$	−2.60125	−	1.50183i	−0.101330	−	0.0585032i	−0.549809	+	0.835291i	$0.685299\pi$
$660$		0			0
$661$		−	36.0755i		−	1.40317i	−0.712585	−	0.701586i	$-0.752476\pi$
$661$		−	36.0755i		−	1.40317i	0.712585	−	0.701586i	$-0.247524\pi$
$662$		0			0
$663$	−9.11712	−	7.56679i	−0.354080	−	0.293870i
$664$		0			0
$665$	0.0128773	−	0.612469i	0.000499359	−	0.0237505i
$666$		0			0
$667$	−1.66694	−	2.88722i	−0.0645441	−	0.111794i
$668$		0			0
$669$	27.1760	−	10.0575i	1.05068	−	0.388845i
$670$		0			0
$671$	−9.21802	−	15.9661i	−0.355858	−	0.616364i
$672$		0			0
$673$	3.20540	−	5.55191i	0.123559	−	0.214010i	−0.797610	−	0.603174i	$-0.793903\pi$
$673$	3.20540	−	5.55191i	0.123559	−	0.214010i	0.921169	+	0.389163i	$0.127236\pi$
$674$		0			0
$675$	−0.416588	−	25.7547i	−0.0160345	−	0.991298i
$676$		0			0
$677$	34.4498			1.32401			0.662007	−	0.749498i	$-0.269705\pi$
$677$	34.4498			1.32401			0.662007	+	0.749498i	$0.269705\pi$
$678$		0			0
$679$	34.2792	+	20.7639i	1.31551	+	0.796844i
$680$		0			0
$681$	−15.1769	−	2.59180i	−0.581578	−	0.0993180i
$682$		0			0
$683$	−2.53802	−	1.46533i	−0.0971148	−	0.0560693i	0.450656	−	0.892698i	$-0.351190\pi$
$683$	−2.53802	−	1.46533i	−0.0971148	−	0.0560693i	−0.547771	+	0.836628i	$0.684523\pi$
$684$		0			0
$685$		−	2.21189i		−	0.0845120i
$686$		0			0
$687$	−27.5390	+	10.1919i	−1.05068	+	0.388843i
$688$		0			0
$689$	−36.9262			−1.40678
$690$		0			0
$691$			3.80337i			0.144687i	0.997380	+	0.0723434i	$0.0230478\pi$
$691$			3.80337i			0.144687i	−0.997380	+	0.0723434i	$0.976952\pi$
$692$		0			0
$693$	7.64507	+	9.30285i	0.290412	+	0.353386i
$694$		0			0
$695$		−	1.78443i		−	0.0676871i
$696$		0			0
$697$	10.1713			0.385266
$698$		0			0
$699$	5.85341	−	34.2759i	0.221396	−	1.29643i
$700$		0			0
$701$		−	36.7042i		−	1.38630i	−0.720795	−	0.693149i	$-0.756223\pi$
$701$		−	36.7042i		−	1.38630i	0.720795	−	0.693149i	$-0.243777\pi$
$702$		0			0
$703$	4.13723	+	2.38863i	0.156039	+	0.0900889i
$704$		0			0
$705$	−1.02903	−	2.78051i	−0.0387556	−	0.104720i
$706$		0			0
$707$	13.0836	+	23.8033i	0.492058	+	0.895216i
$708$		0			0
$709$	20.8080			0.781460			0.390730	−	0.920505i	$-0.372223\pi$
$709$	20.8080			0.781460			0.390730	+	0.920505i	$0.372223\pi$
$710$		0			0
$711$	−2.85015	−	15.2035i	−0.106889	−	0.570176i
$712$		0			0
$713$	−4.30471	+	7.45597i	−0.161213	+	0.279228i
$714$		0			0
$715$	−0.614942	−	1.06511i	−0.0229975	−	0.0398329i
$716$		0			0
$717$	3.89292	−	22.7958i	0.145384	−	0.851325i
$718$		0			0
$719$	−15.1577	−	26.2540i	−0.565288	−	0.979108i	−0.997023	−	0.0771074i	$-0.975432\pi$
$719$	−15.1577	−	26.2540i	−0.565288	−	0.979108i	0.431734	−	0.902001i	$-0.357902\pi$
$720$		0			0
$721$	−25.4756	−	15.4313i	−0.948761	−	0.574692i
$722$		0			0
$723$	−3.72254	+	21.7981i	−0.138443	+	0.810681i
$724$		0			0
$725$			11.4315i			0.424554i
$726$		0			0
$727$	29.7259	+	17.1622i	1.10247	+	0.636512i	0.936869	−	0.349680i	$-0.113710\pi$
$727$	29.7259	+	17.1622i	1.10247	+	0.636512i	0.165602	+	0.986193i	$0.447043\pi$
$728$		0			0
$729$	14.2492	+	22.9338i	0.527747	+	0.849401i
$730$		0			0
$731$	0.372932	+	0.645937i	0.0137934	+	0.0238908i
$732$		0			0
$733$	−5.35388	−	3.09106i	−0.197750	−	0.114171i	0.397855	−	0.917448i	$-0.369755\pi$
$733$	−5.35388	−	3.09106i	−0.197750	−	0.114171i	−0.595606	+	0.803277i	$0.703088\pi$
$734$		0			0
$735$	0.771488	+	2.38858i	0.0284568	+	0.0881041i
$736$		0			0
$737$	8.52633	−	4.92268i	0.314071	−	0.181329i
$738$		0			0
$739$	−13.5892	+	23.5372i	−0.499887	+	0.865829i	−1.00000		0.000131035i	$-0.999958\pi$
$739$	−13.5892	+	23.5372i	−0.499887	+	0.865829i	0.500113	+	0.865960i	$0.333292\pi$
$740$		0			0
$741$	2.63287	+	7.11417i	0.0967208	+	0.261346i
$742$		0			0
$743$	24.3213	−	14.0419i	0.892262	−	0.515148i	0.0175804	−	0.999845i	$-0.494404\pi$
$743$	24.3213	−	14.0419i	0.892262	−	0.515148i	0.874682	+	0.484698i	$0.161070\pi$
$744$		0			0
$745$	3.95321	−	2.28239i	0.144835	−	0.0836203i
$746$		0			0
$747$	47.3431	+	16.6556i	1.73219	+	0.609397i
$748$		0			0
$749$	−26.4368	+	14.5310i	−0.965978	+	0.530953i
$750$		0			0
$751$	21.0921	−	36.5326i	0.769661	−	1.33309i	−0.168086	−	0.985772i	$-0.553759\pi$
$751$	21.0921	−	36.5326i	0.769661	−	1.33309i	0.937747	−	0.347320i	$-0.112908\pi$
$752$		0			0
$753$	19.7304	−	23.7729i	0.719017	−	0.866334i
$754$		0			0
$755$	−1.82211			−0.0663134
$756$		0			0
$757$	−32.6771			−1.18767			−0.593835	−	0.804587i	$-0.702387\pi$
$757$	−32.6771			−1.18767			−0.593835	+	0.804587i	$0.702387\pi$
$758$		0			0
$759$	2.42605	−	2.92312i	0.0880601	−	0.106102i
$760$		0			0
$761$	15.8783	−	27.5021i	0.575589	−	0.996949i	−0.420388	−	0.907344i	$-0.638106\pi$
$761$	15.8783	−	27.5021i	0.575589	−	0.996949i	0.995977	−	0.0896051i	$-0.0285605\pi$
$762$		0			0
$763$	4.12380	−	6.80801i	0.149292	−	0.246466i
$764$		0			0
$765$	0.823541	−	0.706304i	0.0297752	−	0.0255365i
$766$		0			0
$767$	11.0831	−	6.39882i	0.400187	−	0.231048i
$768$		0			0
$769$	30.8593	−	17.8166i	1.11281	−	0.642484i	0.173258	−	0.984877i	$-0.444571\pi$
$769$	30.8593	−	17.8166i	1.11281	−	0.642484i	0.939557	+	0.342393i	$0.111237\pi$
$770$		0			0
$771$	−0.984208	−	2.65939i	−0.0354454	−	0.0957756i
$772$		0			0
$773$	−6.44721	+	11.1669i	−0.231890	+	0.401645i	−0.958364	−	0.285548i	$-0.907824\pi$
$773$	−6.44721	+	11.1669i	−0.231890	+	0.401645i	0.726474	+	0.687194i	$0.241158\pi$
$774$		0			0
$775$	25.5656	−	14.7603i	0.918344	−	0.530206i
$776$		0			0
$777$	−19.2215	−	3.69993i	−0.689566	−	0.132734i
$778$		0			0
$779$	−5.63970	−	3.25608i	−0.202063	−	0.116661i
$780$		0			0
$781$	−5.39222	−	9.33961i	−0.192949	−	0.334197i
$782$		0			0
$783$	−6.15837	−	10.2790i	−0.220082	−	0.367342i
$784$		0			0
$785$	−1.89208	−	1.09239i	−0.0675312	−	0.0389892i
$786$		0			0
$787$		−	17.6852i		−	0.630409i	−0.949024	−	0.315205i	$-0.897927\pi$
$787$		−	17.6852i		−	0.630409i	0.949024	−	0.315205i	$-0.102073\pi$
$788$		0			0
$789$	8.95844	−	52.4581i	0.318929	−	1.86756i
$790$		0			0
$791$	38.1871	−	20.9897i	1.35778	−	0.746307i
$792$		0			0
$793$	23.7944	+	41.2131i	0.844963	+	1.46352i
$794$		0			0
$795$	0.569202	−	3.33309i	0.0201875	−	0.118212i
$796$		0			0
$797$	22.8391	+	39.5585i	0.809003	+	1.40123i	0.913555	+	0.406714i	$0.133326\pi$
$797$	22.8391	+	39.5585i	0.809003	+	1.40123i	−0.104553	+	0.994519i	$0.533341\pi$
$798$		0			0
$799$	−7.22156	+	12.5081i	−0.255481	+	0.442505i
$800$		0			0
$801$	−8.93985	+	7.66719i	−0.315874	+	0.270907i
$802$		0			0
$803$	−18.6013			−0.656424
$804$		0			0
$805$	0.693956	−	0.381435i	0.0244587	−	0.0134438i
$806$		0			0
$807$	0.590575	+	1.59577i	0.0207892	+	0.0561738i
$808$		0			0
$809$	10.8291	+	6.25218i	0.380731	+	0.219815i	0.678136	−	0.734936i	$-0.262788\pi$
$809$	10.8291	+	6.25218i	0.380731	+	0.219815i	−0.297405	+	0.954751i	$0.596121\pi$
$810$		0			0
$811$		−	9.57778i		−	0.336322i	−0.985760	−	0.168161i	$-0.946217\pi$
$811$		−	9.57778i		−	0.336322i	0.985760	−	0.168161i	$-0.0537828\pi$
$812$		0			0
$813$	−0.238166	+	1.39463i	−0.00835286	+	0.0489119i
$814$		0			0
$815$	1.92425			0.0674034
$816$		0			0
$817$		−	0.477538i		−	0.0167069i
$818$		0			0
$819$	−19.7341	−	24.0134i	−0.689567	−	0.839095i
$820$		0			0
$821$			27.8721i			0.972742i	0.873752	+	0.486371i	$0.161680\pi$
$821$			27.8721i			0.972742i	−0.873752	+	0.486371i	$0.838320\pi$
$822$		0			0
$823$	47.2766			1.64796			0.823980	−	0.566619i	$-0.191749\pi$
$823$	47.2766			1.64796			0.823980	+	0.566619i	$0.191749\pi$
$824$		0			0
$825$	−12.2157	+	4.52087i	−0.425295	+	0.157396i
$826$		0			0
$827$			24.1672i			0.840377i	0.907437	+	0.420188i	$0.138036\pi$
$827$			24.1672i			0.840377i	−0.907437	+	0.420188i	$0.861964\pi$
$828$		0			0
$829$	23.0216	+	13.2915i	0.799572	+	0.461633i	0.843322	−	0.537409i	$-0.180597\pi$
$829$	23.0216	+	13.2915i	0.799572	+	0.461633i	−0.0437494	+	0.999043i	$0.513930\pi$
$830$		0			0
$831$	−18.1042	−	3.09171i	−0.628026	−	0.107250i
$832$		0			0
$833$	6.55365	−	10.3233i	0.227070	−	0.357682i
$834$		0			0
$835$	−1.84030			−0.0636864
$836$		0			0
$837$	−15.0366	+	27.0450i	−0.519740	+	0.934813i
$838$		0			0
$839$	−4.03255	+	6.98459i	−0.139219	+	0.241135i	−0.927201	−	0.374563i	$-0.877793\pi$
$839$	−4.03255	+	6.98459i	−0.139219	+	0.241135i	0.787982	+	0.615698i	$0.211126\pi$
$840$		0			0
$841$	−11.8410	−	20.5093i	−0.408312	−	0.707217i
$842$		0			0
$843$	26.5903	−	9.84075i	0.915819	−	0.338933i
$844$		0			0
$845$	0.241660	+	0.418568i	0.00831337	+	0.0143992i
$846$		0			0
$847$	−11.9235	+	19.6846i	−0.409698	+	0.676372i
$848$		0			0
$849$	−8.73671	−	7.25107i	−0.299843	−	0.248856i
$850$		0			0
$851$			6.17527i			0.211686i
$852$		0			0
$853$	11.6046	+	6.69994i	0.397335	+	0.229402i	0.685334	−	0.728229i	$-0.259656\pi$
$853$	11.6046	+	6.69994i	0.397335	+	0.229402i	−0.287998	+	0.957631i	$0.592990\pi$
$854$		0			0
$855$	−0.682734	+	0.127990i	−0.0233490	+	0.00437716i
$856$		0			0
$857$	−22.3340	−	38.6836i	−0.762914	−	1.32141i	−0.941343	−	0.337452i	$-0.890435\pi$
$857$	−22.3340	−	38.6836i	−0.762914	−	1.32141i	0.178429	−	0.983953i	$-0.442899\pi$
$858$		0			0
$859$	43.7433	+	25.2552i	1.49250	+	0.861696i	0.999963	−	0.00859547i	$-0.00273606\pi$
$859$	43.7433	+	25.2552i	1.49250	+	0.861696i	0.492538	+	0.870291i	$0.336069\pi$
$860$		0			0
$861$	26.2019	+	5.04359i	0.892958	+	0.171885i
$862$		0			0
$863$	−0.227203	+	0.131176i	−0.00773408	+	0.00446528i	−0.503862	−	0.863784i	$-0.668088\pi$
$863$	−0.227203	+	0.131176i	−0.00773408	+	0.00446528i	0.496128	+	0.868249i	$0.334755\pi$
$864$		0			0
$865$	−1.01438	+	1.75695i	−0.0344898	+	0.0597381i
$866$		0			0
$867$	23.8148	+	4.06694i	0.808794	+	0.138120i
$868$		0			0
$869$	−6.77412	+	3.91104i	−0.229796	+	0.132673i
$870$		0			0
$871$	−22.0089	+	12.7069i	−0.745744	+	0.430556i
$872$		0			0
$873$	15.0813	−	42.8681i	0.510424	−	1.45086i
$874$		0			0
$875$	−5.45277	−	0.114645i	−0.184337	−	0.00387572i
$876$		0			0
$877$	4.63303	−	8.02465i	0.156446	−	0.270973i	−0.777138	−	0.629330i	$-0.783329\pi$
$877$	4.63303	−	8.02465i	0.156446	−	0.270973i	0.933585	+	0.358357i	$0.116663\pi$
$878$		0			0
$879$	23.9860	+	4.09617i	0.809028	+	0.138160i
$880$		0			0
$881$	−41.5555			−1.40004			−0.700021	−	0.714122i	$-0.746826\pi$
$881$	−41.5555			−1.40004			−0.700021	+	0.714122i	$0.746826\pi$
$882$		0			0
$883$	−29.4547			−0.991231			−0.495615	−	0.868542i	$-0.665057\pi$
$883$	−29.4547			−0.991231			−0.495615	+	0.868542i	$0.665057\pi$
$884$		0			0
$885$	0.406739	+	1.09903i	0.0136724	+	0.0369436i
$886$		0			0
$887$	7.79122	−	13.4948i	0.261603	−	0.453111i	−0.705065	−	0.709143i	$-0.749082\pi$
$887$	7.79122	−	13.4948i	0.261603	−	0.453111i	0.966668	+	0.256032i	$0.0824154\pi$
$888$		0			0
$889$	−22.5548	−	0.474219i	−0.756464	−	0.0159048i
$890$		0			0
$891$	8.54867	−	10.6459i	0.286391	−	0.356652i
$892$		0			0
$893$	8.00829	−	4.62359i	0.267987	−	0.154723i
$894$		0			0
$895$	−2.96342	+	1.71093i	−0.0990562	+	0.0571901i
$896$		0			0
$897$	−6.26235	+	7.54542i	−0.209094	+	0.251934i
$898$		0			0
$899$	6.86649	−	11.8931i	0.229010	−	0.396658i
$900$		0			0
$901$	−14.2654	+	8.23612i	−0.475248	+	0.274385i
$902$		0			0
$903$	0.640397	+	1.84890i	0.0213111	+	0.0615274i
$904$		0			0
$905$	4.27685	+	2.46924i	0.142167	+	0.0820804i
$906$		0			0
$907$	−10.2604	−	17.7716i	−0.340692	−	0.590095i	0.643870	−	0.765135i	$-0.277328\pi$
$907$	−10.2604	−	17.7716i	−0.340692	−	0.590095i	−0.984561	+	0.175040i	$0.943995\pi$
$908$		0			0
$909$	23.3785	−	20.0504i	0.775416	−	0.665029i
$910$		0			0
$911$	−15.0554	−	8.69226i	−0.498809	−	0.287987i	0.229413	−	0.973329i	$-0.426319\pi$
$911$	−15.0554	−	8.69226i	−0.498809	−	0.287987i	−0.728222	+	0.685342i	$0.759653\pi$
$912$		0			0
$913$		−	25.3789i		−	0.839919i
$914$		0			0
$915$	−4.08682	+	1.51248i	−0.135106	+	0.0500011i
$916$		0			0
$917$	−19.9507	+	32.9367i	−0.658830	+	1.08767i
$918$		0			0
$919$	17.1002	+	29.6183i	0.564082	+	0.977019i	0.997134	+	0.0756501i	$0.0241032\pi$
$919$	17.1002	+	29.6183i	0.564082	+	0.977019i	−0.433052	+	0.901369i	$0.642563\pi$
$920$		0			0
$921$	−23.2355	−	19.2844i	−0.765637	−	0.635444i
$922$		0			0
$923$	13.9189	+	24.1082i	0.458146	+	0.793532i
$924$		0			0
$925$	10.5871	−	18.3375i	0.348103	−	0.602932i
$926$		0			0
$927$	−11.2081	+	31.8587i	−0.368122	+	1.04638i
$928$		0			0
$929$	−2.99192			−0.0981617			−0.0490808	−	0.998795i	$-0.515629\pi$
$929$	−2.99192			−0.0981617			−0.0490808	+	0.998795i	$0.515629\pi$
$930$		0			0
$931$	−6.93855	+	3.62600i	−0.227402	+	0.118838i
$932$		0			0
$933$	−17.2521	+	20.7869i	−0.564809	+	0.680531i
$934$		0			0
$935$	−0.475130	−	0.274316i	−0.0155384	−	0.00897110i
$936$		0			0
$937$		−	10.9928i		−	0.359120i	−0.983747	−	0.179560i	$-0.942533\pi$
$937$		−	10.9928i		−	0.359120i	0.983747	−	0.179560i	$-0.0574674\pi$
$938$		0			0
$939$	2.97197	+	2.46660i	0.0969865	+	0.0804943i
$940$		0			0
$941$	−9.90600			−0.322926			−0.161463	−	0.986879i	$-0.551621\pi$
$941$	−9.90600			−0.322926			−0.161463	+	0.986879i	$0.551621\pi$
$942$		0			0
$943$		−	8.41787i		−	0.274124i
$944$		0			0
$945$	2.47172	−	1.41112i	0.0804051	−	0.0459036i
$946$		0			0
$947$			27.0453i			0.878854i	0.898278	+	0.439427i	$0.144819\pi$
$947$			27.0453i			0.878854i	−0.898278	+	0.439427i	$0.855181\pi$
$948$		0			0
$949$	48.0152			1.55864
$950$		0			0
$951$	−45.7488	−	37.9694i	−1.48351	−	1.23124i
$952$		0			0
$953$		−	51.9958i		−	1.68431i	−0.539236	−	0.842155i	$-0.681287\pi$
$953$		−	51.9958i		−	1.68431i	0.539236	−	0.842155i	$-0.318713\pi$
$954$		0			0
$955$	4.00898	+	2.31458i	0.129727	+	0.0748982i
$956$		0			0
$957$	−3.86983	+	4.66270i	−0.125094	+	0.150724i
$958$		0			0
$959$	−24.7718	+	13.6159i	−0.799924	+	0.439681i
$960$		0			0
$961$	−4.46414			−0.144004
$962$		0			0
$963$	22.2686	+	25.9649i	0.717596	+	0.836708i
$964$		0			0
$965$	0.896121	−	1.55213i	0.0288472	−	0.0499648i
$966$		0			0
$967$	8.23005	+	14.2549i	0.264660	+	0.458405i	0.967475	−	0.252968i	$-0.0814068\pi$
$967$	8.23005	+	14.2549i	0.264660	+	0.458405i	−0.702814	+	0.711374i	$0.748073\pi$
$968$		0			0
$969$	2.60390	+	2.16111i	0.0836492	+	0.0694250i
$970$		0			0
$971$	6.09724	+	10.5607i	0.195670	+	0.338910i	0.947120	−	0.320880i	$-0.103979\pi$
$971$	6.09724	+	10.5607i	0.195670	+	0.338910i	−0.751450	+	0.659790i	$0.770645\pi$
$972$		0			0
$973$	−19.9845	+	10.9845i	−0.640673	+	0.352148i
$974$		0			0
$975$	31.5322	−	11.6697i	1.00984	−	0.373729i
$976$		0			0
$977$		−	21.7574i		−	0.696081i	−0.937480	−	0.348040i	$-0.886847\pi$
$977$		−	21.7574i		−	0.696081i	0.937480	−	0.348040i	$-0.113153\pi$
$978$		0			0
$979$	5.15771	+	2.97781i	0.164841	+	0.0951711i
$980$		0			0
$981$	−8.51380	−	2.99521i	−0.271825	−	0.0956297i
$982$		0			0
$983$	31.2373	+	54.1046i	0.996316	+	1.72567i	0.572430	+	0.819954i	$0.306001\pi$
$983$	31.2373	+	54.1046i	0.996316	+	1.72567i	0.423886	+	0.905716i	$0.360666\pi$
$984$		0			0
$985$	4.17429	+	2.41003i	0.133004	+	0.0767898i
$986$		0			0
$987$	−24.8055	+	28.6407i	−0.789568	+	0.911644i
$988$		0			0
$989$	0.534583	−	0.308642i	0.0169988	−	0.00981424i
$990$		0			0
$991$	−27.5362	+	47.6942i	−0.874717	+	1.51505i	−0.0176535	+	0.999844i	$0.505620\pi$
$991$	−27.5362	+	47.6942i	−0.874717	+	1.51505i	−0.857064	+	0.515210i	$0.827714\pi$
$992$		0			0
$993$	−24.9334	+	30.0419i	−0.791238	+	0.953352i
$994$		0			0
$995$	−1.82370	+	1.05291i	−0.0578151	+	0.0333795i
$996$		0			0
$997$	−20.6726	+	11.9353i	−0.654707	+	0.377995i	−0.790257	−	0.612775i	$-0.790053\pi$
$997$	−20.6726	+	11.9353i	−0.654707	+	0.377995i	0.135550	+	0.990770i	$0.456720\pi$
$998$		0			0
$999$	0.358965	+	22.1923i	0.0113572	+	0.702133i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bs.a.353.19	yes	48
3.2	odd	2		1512.2.bs.a.521.12		48
4.3	odd	2		1008.2.ca.e.353.6		48
7.5	odd	6		504.2.cx.a.425.10	yes	48
9.4	even	3		1512.2.cx.a.17.12		48
9.5	odd	6		504.2.cx.a.185.10	yes	48
12.11	even	2		3024.2.ca.e.2033.12		48
21.5	even	6		1512.2.cx.a.89.12		48
28.19	even	6		1008.2.df.e.929.15		48
36.23	even	6		1008.2.df.e.689.15		48
36.31	odd	6		3024.2.df.e.17.12		48
63.5	even	6	inner	504.2.bs.a.257.19	✓	48
63.40	odd	6		1512.2.bs.a.1097.12		48
84.47	odd	6		3024.2.df.e.1601.12		48
252.103	even	6		3024.2.ca.e.2609.12		48
252.131	odd	6		1008.2.ca.e.257.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.19	✓	48	63.5	even	6	inner
504.2.bs.a.353.19	yes	48	1.1	even	1	trivial
504.2.cx.a.185.10	yes	48	9.5	odd	6
504.2.cx.a.425.10	yes	48	7.5	odd	6
1008.2.ca.e.257.6		48	252.131	odd	6
1008.2.ca.e.353.6		48	4.3	odd	2
1008.2.df.e.689.15		48	36.23	even	6
1008.2.df.e.929.15		48	28.19	even	6
1512.2.bs.a.521.12		48	3.2	odd	2
1512.2.bs.a.1097.12		48	63.40	odd	6
1512.2.cx.a.17.12		48	9.4	even	3
1512.2.cx.a.89.12		48	21.5	even	6
3024.2.ca.e.2033.12		48	12.11	even	2
3024.2.ca.e.2609.12		48	252.103	even	6
3024.2.df.e.17.12		48	36.31	odd	6
3024.2.df.e.1601.12		48	84.47	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.10617 - 1.33281i) q^{3} +(-0.103514 + 0.179292i) q^{5} +(2.64517 + 0.0556151i) q^{7} +(-0.552770 - 2.94863i) q^{9} +(-1.31380 + 0.758523i) q^{11} +(3.39130 - 1.95797i) q^{13} +(0.124457 + 0.336292i) q^{15} +(0.873421 - 1.51281i) q^{17} +(-0.968573 + 0.559206i) q^{19} +(3.00013 - 3.46399i) q^{21} +(-1.25201 - 0.722851i) q^{23} +(2.47857 + 4.29301i) q^{25} +(-4.54143 - 2.52496i) q^{27} +(1.99711 + 1.15303i) q^{29} -5.95518i q^{31} +(-0.442321 + 2.59010i) q^{33} +(-0.283783 + 0.468499i) q^{35} +(-2.13573 - 3.69920i) q^{37} +(1.14176 - 6.68581i) q^{39} +(2.91134 + 5.04260i) q^{41} +(-0.213489 + 0.369774i) q^{43} +(0.585885 + 0.206118i) q^{45} -8.26814 q^{47} +(6.99381 + 0.294222i) q^{49} +(-1.05014 - 2.83753i) q^{51} +(-8.16638 - 4.71486i) q^{53} -0.314071i q^{55} +(-0.326092 + 1.90950i) q^{57} +3.26809 q^{59} +12.1526i q^{61} +(-1.29818 - 7.83037i) q^{63} +0.810709i q^{65} -6.48982 q^{67} +(-2.34837 + 0.869102i) q^{69} +7.10884i q^{71} +(10.6188 + 6.13075i) q^{73} +(8.46349 + 1.44534i) q^{75} +(-3.51741 + 1.93335i) q^{77} +5.15612 q^{79} +(-8.38889 + 3.25983i) q^{81} +(-8.36457 + 14.4879i) q^{83} +(0.180823 + 0.313194i) q^{85} +(3.74591 - 1.38632i) q^{87} +(-1.96290 - 3.39984i) q^{89} +(9.07945 - 4.99055i) q^{91} +(-7.93713 - 6.58745i) q^{93} -0.231543i q^{95} +(13.1184 + 7.57392i) q^{97} +(2.96284 + 3.45463i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{9} + 8 q^{15} + 8 q^{21} - 12 q^{23} - 24 q^{25} - 18 q^{27} + 18 q^{29} - 10 q^{39} + 6 q^{41} - 6 q^{43} + 6 q^{45} + 36 q^{47} + 6 q^{49} - 12 q^{51} + 12 q^{53} + 4 q^{57} + 46 q^{63} - 54 q^{75}+ \cdots - 64 q^{99}+O(q^{100}) \) 48 * q - 4 * q^9 + 8 * q^15 + 8 * q^21 - 12 * q^23 - 24 * q^25 - 18 * q^27 + 18 * q^29 - 10 * q^39 + 6 * q^41 - 6 * q^43 + 6 * q^45 + 36 * q^47 + 6 * q^49 - 12 * q^51 + 12 * q^53 + 4 * q^57 + 46 * q^63 - 54 * q^75 - 36 * q^77 - 12 * q^79 - 24 * q^87 + 18 * q^89 + 6 * q^91 + 16 * q^93 - 64 * q^99

Introduction

L-functions

Modular forms

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Database

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