LMFDB - Embedded newform 920.2.bv.a.17.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [920,2,Mod(17,920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(920, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 0, 11, 14]))

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

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

chi := DirichletCharacter("920.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 920 = 2^{3} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	920.bv (of order $44$, degree $20$, 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:	$7.34623698596$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$36$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			17.6
Character	$\chi$	$=$	920.17
Dual form			920.2.bv.a.433.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.01190 + 1.09858i) q^{3} +(0.842192 + 2.07140i) q^{5} +(-0.883794 - 1.18061i) q^{7} +(1.21895 - 1.89673i) q^{9} +(-1.98634 + 0.907130i) q^{11} +(0.198154 + 0.148336i) q^{13} +(-3.97002 - 3.24225i) q^{15} +(0.428234 + 5.98749i) q^{17} +(-4.04133 - 4.66394i) q^{19} +(3.07511 + 1.40435i) q^{21} +(0.803484 + 4.72805i) q^{23} +(-3.58143 + 3.48904i) q^{25} +(0.121889 - 1.70423i) q^{27} +(-6.18882 - 5.36265i) q^{29} +(3.84624 - 1.12936i) q^{31} +(2.99976 - 4.00721i) q^{33} +(1.70120 - 2.82500i) q^{35} +(-0.158968 + 0.0345815i) q^{37} +(-0.561627 - 0.0807498i) q^{39} +(0.671458 - 0.431520i) q^{41} +(-3.66249 - 6.70736i) q^{43} +(4.95548 + 0.927535i) q^{45} +(-0.703539 - 0.703539i) q^{47} +(1.35938 - 4.62962i) q^{49} +(-7.43933 - 11.5758i) q^{51} +(2.68173 - 2.00752i) q^{53} +(-3.55191 - 3.35053i) q^{55} +(13.2545 + 4.94367i) q^{57} +(-9.94388 + 1.42971i) q^{59} +(-3.21033 - 10.9334i) q^{61} +(-3.31660 + 0.237208i) q^{63} +(-0.140381 + 0.535385i) q^{65} +(2.23540 + 5.99335i) q^{67} +(-6.81068 - 8.62968i) q^{69} +(-2.70281 + 5.91832i) q^{71} +(-7.94370 - 0.568145i) q^{73} +(3.37249 - 10.9541i) q^{75} +(2.82648 + 1.54337i) q^{77} +(-1.89883 - 13.2066i) q^{79} +(4.43685 + 9.71534i) q^{81} +(-2.54996 - 11.7220i) q^{83} +(-12.0419 + 5.92966i) q^{85} +(18.3426 + 3.99020i) q^{87} +(1.66699 + 0.489473i) q^{89} -0.365042i q^{91} +(-6.49758 + 6.49758i) q^{93} +(6.25734 - 12.2992i) q^{95} +(0.258745 - 1.18943i) q^{97} +(-0.700673 + 4.87329i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) $ 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$1$	$e\left(\frac{7}{22}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	−2.01190	+	1.09858i	−1.16157	+	0.634267i	−0.940100	−	0.340899i	$-0.889269\pi$
$3$	−2.01190	+	1.09858i	−1.16157	+	0.634267i	−0.221474	+	0.975166i	$0.571087\pi$
$4$		0			0
$5$	0.842192	+	2.07140i	0.376640	+	0.926360i
$5$	0.842192	+	2.07140i	0.376640	+	0.926360i
$6$		0			0
$7$	−0.883794	−	1.18061i	−0.334043	−	0.446229i	0.601800	−	0.798647i	$-0.294450\pi$
$7$	−0.883794	−	1.18061i	−0.334043	−	0.446229i	−0.935843	+	0.352418i	$0.885360\pi$
$8$		0			0
$9$	1.21895	−	1.89673i	0.406318	−	0.632242i
$10$		0			0
$11$	−1.98634	+	0.907130i	−0.598903	+	0.273510i	−0.691711	−	0.722174i	$-0.743143\pi$
$11$	−1.98634	+	0.907130i	−0.598903	+	0.273510i	0.0928082	+	0.995684i	$0.470416\pi$
$12$		0			0
$13$	0.198154	+	0.148336i	0.0549581	+	0.0411411i	0.626404	−	0.779499i	$-0.284526\pi$
$13$	0.198154	+	0.148336i	0.0549581	+	0.0411411i	−0.571445	+	0.820640i	$0.693617\pi$
$14$		0			0
$15$	−3.97002	−	3.24225i	−1.02505	−	0.837145i
$16$		0			0
$17$	0.428234	+	5.98749i	0.103862	+	1.45218i	0.735820	+	0.677178i	$0.236797\pi$
$17$	0.428234	+	5.98749i	0.103862	+	1.45218i	−0.631958	+	0.775003i	$0.717748\pi$
$18$		0			0
$19$	−4.04133	−	4.66394i	−0.927145	−	1.06998i	−0.997372	−	0.0724512i	$-0.976918\pi$
$19$	−4.04133	−	4.66394i	−0.927145	−	1.06998i	0.0702271	−	0.997531i	$-0.477628\pi$
$20$		0			0
$21$	3.07511	+	1.40435i	0.671044	+	0.306455i
$22$		0			0
$23$	0.803484	+	4.72805i	0.167538	+	0.985866i
$23$	0.803484	+	4.72805i	0.167538	+	0.985866i
$24$		0			0
$25$	−3.58143	+	3.48904i	−0.716285	+	0.697808i
$26$		0			0
$27$	0.121889	−	1.70423i	0.0234575	−	0.327979i
$28$		0			0
$29$	−6.18882	−	5.36265i	−1.14924	−	0.995819i	−0.999975	−	0.00702060i	$-0.997765\pi$
$29$	−6.18882	−	5.36265i	−1.14924	−	0.995819i	−0.149260	−	0.988798i	$-0.547689\pi$
$30$		0			0
$31$	3.84624	−	1.12936i	0.690805	−	0.202839i	0.0825580	−	0.996586i	$-0.473691\pi$
$31$	3.84624	−	1.12936i	0.690805	−	0.202839i	0.608247	+	0.793748i	$0.291873\pi$
$32$		0			0
$33$	2.99976	−	4.00721i	0.522192	−	0.697566i
$34$		0			0
$35$	1.70120	−	2.82500i	0.287555	−	0.477511i
$36$		0			0
$37$	−0.158968	+	0.0345815i	−0.0261342	+	0.00568516i	−0.225613	−	0.974217i	$-0.572439\pi$
$37$	−0.158968	+	0.0345815i	−0.0261342	+	0.00568516i	0.199479	+	0.979902i	$0.436075\pi$
$38$		0			0
$39$	−0.561627	−	0.0807498i	−0.0899324	−	0.0129303i
$40$		0			0
$41$	0.671458	−	0.431520i	0.104864	−	0.0673921i	−0.487158	−	0.873314i	$-0.661966\pi$
$41$	0.671458	−	0.431520i	0.104864	−	0.0673921i	0.592022	+	0.805922i	$0.298330\pi$
$42$		0			0
$43$	−3.66249	−	6.70736i	−0.558525	−	1.02286i	−0.992536	−	0.121955i	$-0.961084\pi$
$43$	−3.66249	−	6.70736i	−0.558525	−	1.02286i	0.434010	−	0.900908i	$-0.357098\pi$
$44$		0			0
$45$	4.95548	+	0.927535i	0.738719	+	0.138269i
$46$		0			0
$47$	−0.703539	−	0.703539i	−0.102622	−	0.102622i	0.653932	−	0.756554i	$-0.273118\pi$
$47$	−0.703539	−	0.703539i	−0.102622	−	0.102622i	−0.756554	+	0.653932i	$0.773118\pi$
$48$		0			0
$49$	1.35938	−	4.62962i	0.194197	−	0.661374i
$50$		0			0
$51$	−7.43933	−	11.5758i	−1.04171	−	1.62094i
$52$		0			0
$53$	2.68173	−	2.00752i	0.368364	−	0.275754i	−0.399019	−	0.916943i	$-0.630649\pi$
$53$	2.68173	−	2.00752i	0.368364	−	0.275754i	0.767383	+	0.641189i	$0.221558\pi$
$54$		0			0
$55$	−3.55191	−	3.35053i	−0.478939	−	0.451785i
$56$		0			0
$57$	13.2545	+	4.94367i	1.75560	+	0.654806i
$58$		0			0
$59$	−9.94388	+	1.42971i	−1.29458	+	0.186133i	−0.754958	−	0.655773i	$-0.772343\pi$
$59$	−9.94388	+	1.42971i	−1.29458	+	0.186133i	−0.539625	+	0.841906i	$0.681434\pi$
$60$		0			0
$61$	−3.21033	−	10.9334i	−0.411041	−	1.39988i	−0.861808	−	0.507234i	$-0.830668\pi$
$61$	−3.21033	−	10.9334i	−0.411041	−	1.39988i	0.450768	−	0.892641i	$-0.351150\pi$
$62$		0			0
$63$	−3.31660	+	0.237208i	−0.417852	+	0.0298854i
$64$		0			0
$65$	−0.140381	+	0.535385i	−0.0174121	+	0.0664064i
$66$		0			0
$67$	2.23540	+	5.99335i	0.273098	+	0.732204i	0.999013	+	0.0444195i	$0.0141438\pi$
$67$	2.23540	+	5.99335i	0.273098	+	0.732204i	−0.725915	+	0.687784i	$0.758583\pi$
$68$		0			0
$69$	−6.81068	−	8.62968i	−0.819910	−	1.03889i
$70$		0			0
$71$	−2.70281	+	5.91832i	−0.320764	+	0.702376i	−0.999487	−	0.0320187i	$-0.989806\pi$
$71$	−2.70281	+	5.91832i	−0.320764	+	0.702376i	0.678723	+	0.734394i	$0.262534\pi$
$72$		0			0
$73$	−7.94370	−	0.568145i	−0.929740	−	0.0664963i	−0.401752	−	0.915748i	$-0.631599\pi$
$73$	−7.94370	−	0.568145i	−0.929740	−	0.0664963i	−0.527988	+	0.849252i	$0.677053\pi$
$74$		0			0
$75$	3.37249	−	10.9541i	0.389422	−	1.26487i
$76$		0			0
$77$	2.82648	+	1.54337i	0.322107	+	0.175884i
$78$		0			0
$79$	−1.89883	−	13.2066i	−0.213635	−	1.48586i	−0.760881	−	0.648891i	$-0.775233\pi$
$79$	−1.89883	−	13.2066i	−0.213635	−	1.48586i	0.547246	−	0.836972i	$-0.315676\pi$
$80$		0			0
$81$	4.43685	+	9.71534i	0.492983	+	1.07948i
$82$		0			0
$83$	−2.54996	−	11.7220i	−0.279894	−	1.28665i	−0.875438	−	0.483330i	$-0.839427\pi$
$83$	−2.54996	−	11.7220i	−0.279894	−	1.28665i	0.595544	−	0.803323i	$-0.296936\pi$
$84$		0			0
$85$	−12.0419	+	5.92966i	−1.30612	+	0.643162i
$86$		0			0
$87$	18.3426	+	3.99020i	1.96654	+	0.427794i
$88$		0			0
$89$	1.66699	+	0.489473i	0.176701	+	0.0518840i	0.368886	−	0.929475i	$-0.379739\pi$
$89$	1.66699	+	0.489473i	0.176701	+	0.0518840i	−0.192185	+	0.981359i	$0.561557\pi$
$90$		0			0
$91$		−	0.365042i		−	0.0382668i
$92$		0			0
$93$	−6.49758	+	6.49758i	−0.673767	+	0.673767i
$94$		0			0
$95$	6.25734	−	12.2992i	0.641989	−	1.26187i
$96$		0			0
$97$	0.258745	−	1.18943i	0.0262716	−	0.120769i	−0.962144	−	0.272543i	$-0.912135\pi$
$97$	0.258745	−	1.18943i	0.0262716	−	0.120769i	0.988415	+	0.151775i	$0.0484988\pi$
$98$		0			0
$99$	−0.700673	+	4.87329i	−0.0704203	+	0.489784i
$100$		0			0
$101$	0.462483	+	0.297220i	0.0460188	+	0.0295745i	0.563448	−	0.826152i	$-0.309475\pi$
$101$	0.462483	+	0.297220i	0.0460188	+	0.0295745i	−0.517429	+	0.855726i	$0.673111\pi$
$102$		0			0
$103$	−6.54740	+	17.5542i	−0.645134	+	1.72967i	0.0378966	+	0.999282i	$0.487934\pi$
$103$	−6.54740	+	17.5542i	−0.645134	+	1.72967i	−0.683031	+	0.730390i	$0.739338\pi$
$104$		0			0
$105$	−0.319155	+	7.55253i	−0.0311464	+	0.737051i
$106$		0			0
$107$	−6.49817	+	11.9005i	−0.628202	+	1.15047i	0.348792	+	0.937200i	$0.386592\pi$
$107$	−6.49817	+	11.9005i	−0.628202	+	1.15047i	−0.976994	+	0.213266i	$0.931590\pi$
$108$		0			0
$109$	6.62457	−	7.64517i	0.634519	−	0.732274i	−0.343877	−	0.939015i	$-0.611740\pi$
$109$	6.62457	−	7.64517i	0.634519	−	0.732274i	0.978396	+	0.206741i	$0.0662857\pi$
$110$		0			0
$111$	0.281839	−	0.244215i	0.0267509	−	0.0231798i
$112$		0			0
$113$	−8.20614	+	3.06073i	−0.771969	+	0.287929i	−0.704417	−	0.709786i	$-0.748791\pi$
$113$	−8.20614	+	3.06073i	−0.771969	+	0.287929i	−0.0675517	+	0.997716i	$0.521519\pi$
$114$		0			0
$115$	−9.11700	+	5.64626i	−0.850165	+	0.526517i
$116$		0			0
$117$	0.522894	−	0.195030i	0.0483416	−	0.0180305i
$118$		0			0
$119$	6.69043	−	5.79729i	0.613311	−	0.531437i
$120$		0			0
$121$	−4.08082	+	4.70951i	−0.370983	+	0.428138i
$122$		0			0
$123$	−0.876849	+	1.60583i	−0.0790628	+	0.144793i
$124$		0			0
$125$	−10.2435	−	4.48014i	−0.916202	−	0.400716i
$126$		0			0
$127$	−3.05818	+	8.19930i	−0.271370	+	0.727571i	0.727759	+	0.685833i	$0.240562\pi$
$127$	−3.05818	+	8.19930i	−0.271370	+	0.727571i	−0.999129	+	0.0417374i	$0.986711\pi$
$128$		0			0
$129$	14.7372	+	9.47101i	1.29754	+	0.833876i
$130$		0			0
$131$	0.908481	−	6.31862i	0.0793743	−	0.552061i	−0.910867	−	0.412699i	$-0.864586\pi$
$131$	0.908481	−	6.31862i	0.0793743	−	0.552061i	0.990242	−	0.139361i	$-0.0445049\pi$
$132$		0			0
$133$	−1.93460	+	8.89321i	−0.167751	+	0.771139i
$134$		0			0
$135$	3.63280	−	1.18281i	0.312661	−	0.101800i
$136$		0			0
$137$	8.93288	−	8.93288i	0.763187	−	0.763187i	−0.213710	−	0.976897i	$-0.568555\pi$
$137$	8.93288	−	8.93288i	0.763187	−	0.763187i	0.976897	+	0.213710i	$0.0685548\pi$
$138$		0			0
$139$			0.841079i			0.0713394i	0.999364	+	0.0356697i	$0.0113564\pi$
$139$			0.841079i			0.0713394i	−0.999364	+	0.0356697i	$0.988644\pi$
$140$		0			0
$141$	2.18835	+	0.642558i	0.184292	+	0.0541131i
$142$		0			0
$143$	−0.528162	−	0.114895i	−0.0441671	−	0.00960796i
$144$		0			0
$145$	5.89603	−	17.3359i	0.489639	−	1.43967i
$146$		0			0
$147$	2.35108	+	10.8077i	0.193914	+	0.891407i
$148$		0			0
$149$	2.91795	+	6.38942i	0.239048	+	0.523441i	0.990691	−	0.136128i	$-0.0434659\pi$
$149$	2.91795	+	6.38942i	0.239048	+	0.523441i	−0.751644	+	0.659570i	$0.770739\pi$
$150$		0			0
$151$	0.937136	+	6.51793i	0.0762631	+	0.530421i	0.991761	+	0.128099i	$0.0408876\pi$
$151$	0.937136	+	6.51793i	0.0762631	+	0.530421i	−0.915498	+	0.402322i	$0.868203\pi$
$152$		0			0
$153$	11.8786	+	6.48623i	0.960331	+	0.524380i
$154$		0			0
$155$	5.57863	+	7.01598i	0.448086	+	0.563537i
$156$		0			0
$157$	5.06230	+	0.362063i	0.404015	+	0.0288957i	0.271869	−	0.962334i	$-0.412358\pi$
$157$	5.06230	+	0.362063i	0.404015	+	0.0288957i	0.132147	+	0.991230i	$0.457813\pi$
$158$		0			0
$159$	−3.18996	+	6.98504i	−0.252980	+	0.553949i
$160$		0			0
$161$	4.87187	−	5.12722i	0.383957	−	0.404082i
$162$		0			0
$163$	7.07496	+	18.9687i	0.554154	+	1.48574i	0.848055	+	0.529908i	$0.177773\pi$
$163$	7.07496	+	18.9687i	0.554154	+	1.48574i	−0.293902	+	0.955836i	$0.594954\pi$
$164$		0			0
$165$	10.8269	+	2.83888i	0.842876	+	0.221006i
$166$		0			0
$167$	−5.84948	+	0.418363i	−0.452646	+	0.0323739i	−0.295802	−	0.955249i	$-0.595587\pi$
$167$	−5.84948	+	0.418363i	−0.452646	+	0.0323739i	−0.156845	+	0.987623i	$0.550132\pi$
$168$		0			0
$169$	−3.64526	−	12.4146i	−0.280405	−	0.954971i
$170$		0			0
$171$	−13.7724	+	1.98018i	−1.05320	+	0.151428i
$172$		0			0
$173$	16.1109	+	6.00904i	1.22489	+	0.456859i	0.876915	−	0.480646i	$-0.159598\pi$
$173$	16.1109	+	6.00904i	1.22489	+	0.456859i	0.347971	+	0.937505i	$0.386871\pi$
$174$		0			0
$175$	7.28444	+	1.14468i	0.550652	+	0.0865296i
$176$		0			0
$177$	18.4355	−	13.8006i	1.38570	−	1.03732i
$178$		0			0
$179$	9.16948	+	14.2680i	0.685359	+	1.06644i	0.993359	+	0.115053i	$0.0367039\pi$
$179$	9.16948	+	14.2680i	0.685359	+	1.06644i	−0.308000	+	0.951386i	$0.599660\pi$
$180$		0			0
$181$	−6.39709	+	21.7865i	−0.475492	+	1.61938i	0.277065	+	0.960851i	$0.410638\pi$
$181$	−6.39709	+	21.7865i	−0.475492	+	1.61938i	−0.752557	+	0.658527i	$0.771180\pi$
$182$		0			0
$183$	18.4701	+	18.4701i	1.36535	+	1.36535i
$184$		0			0
$185$	−0.205514	−	0.300164i	−0.0151097	−	0.0220685i
$186$		0			0
$187$	−6.28205	−	11.5047i	−0.459389	−	0.841308i
$188$		0			0
$189$	−2.11975	+	1.36228i	−0.154189	+	0.0990915i
$190$		0			0
$191$	−7.86954	−	1.13147i	−0.569420	−	0.0818703i	−0.148410	−	0.988926i	$-0.547415\pi$
$191$	−7.86954	−	1.13147i	−0.569420	−	0.0818703i	−0.421011	+	0.907056i	$0.638324\pi$
$192$		0			0
$193$	−13.7074	+	2.98186i	−0.986681	+	0.214639i	−0.676825	−	0.736144i	$-0.736644\pi$
$193$	−13.7074	+	2.98186i	−0.986681	+	0.214639i	−0.309856	+	0.950783i	$0.600281\pi$
$194$		0			0
$195$	−0.305732	−	1.23136i	−0.0218940	−	0.0881798i
$196$		0			0
$197$	−3.67760	+	4.91270i	−0.262018	+	0.350015i	−0.912187	−	0.409775i	$-0.865607\pi$
$197$	−3.67760	+	4.91270i	−0.262018	+	0.350015i	0.650169	+	0.759790i	$0.274698\pi$
$198$		0			0
$199$	13.2337	−	3.88576i	0.938112	−	0.275455i	0.223283	−	0.974754i	$-0.428323\pi$
$199$	13.2337	−	3.88576i	0.938112	−	0.275455i	0.714829	+	0.699299i	$0.246504\pi$
$200$		0			0
$201$	−11.0816	−	9.60227i	−0.781636	−	0.677292i
$202$		0			0
$203$	−0.861552	+	12.0461i	−0.0604691	+	0.845468i
$204$		0			0
$205$	1.45935	+	1.02744i	0.101925	+	0.0717594i
$206$		0			0
$207$	9.94722	+	4.23927i	0.691380	+	0.294650i
$208$		0			0
$209$	12.2582	+	5.59815i	0.847921	+	0.387232i
$210$		0			0
$211$	4.01927	+	4.63848i	0.276698	+	0.319326i	0.877040	−	0.480417i	$-0.159515\pi$
$211$	4.01927	+	4.63848i	0.276698	+	0.319326i	−0.600343	+	0.799743i	$0.704969\pi$
$212$		0			0
$213$	−1.06398	−	14.8764i	−0.0729026	−	1.01931i
$214$		0			0
$215$	10.8091	−	13.2354i	0.737176	−	0.902646i
$216$		0			0
$217$	−4.73262	−	3.54279i	−0.321271	−	0.240501i
$218$		0			0
$219$	16.6061	−	7.58376i	1.12214	−	0.512463i
$220$		0			0
$221$	−0.803307	+	1.24997i	−0.0540363	+	0.0840821i
$222$		0			0
$223$	−5.43753	−	7.26369i	−0.364124	−	0.486413i	0.580642	−	0.814159i	$-0.302802\pi$
$223$	−5.43753	−	7.26369i	−0.364124	−	0.486413i	−0.944766	+	0.327746i	$0.893711\pi$
$224$		0			0
$225$	2.25216	+	11.0460i	0.150144	+	0.736397i
$226$		0			0
$227$	−8.22203	+	4.48957i	−0.545715	+	0.297983i	−0.728359	−	0.685196i	$-0.759716\pi$
$227$	−8.22203	+	4.48957i	−0.545715	+	0.297983i	0.182643	+	0.983179i	$0.441535\pi$
$228$		0			0
$229$	−19.4102			−1.28266			−0.641330	−	0.767265i	$-0.721617\pi$
$229$	−19.4102			−1.28266			−0.641330	+	0.767265i	$0.721617\pi$
$230$		0			0
$231$	−7.38213			−0.485709
$232$		0			0
$233$	2.28393	−	1.24712i	0.149625	−	0.0817016i	−0.402692	−	0.915335i	$-0.631925\pi$
$233$	2.28393	−	1.24712i	0.149625	−	0.0817016i	0.552317	+	0.833634i	$0.313744\pi$
$234$		0			0
$235$	0.864799	−	2.04983i	0.0564133	−	0.133716i
$236$		0			0
$237$	18.3289	+	24.4845i	1.19059	+	1.59044i
$238$		0			0
$239$	−10.3795	+	16.1508i	−0.671395	+	1.04471i	0.323735	+	0.946148i	$0.395061\pi$
$239$	−10.3795	+	16.1508i	−0.671395	+	1.04471i	−0.995131	+	0.0985639i	$0.968575\pi$
$240$		0			0
$241$	−0.282296	+	0.128920i	−0.0181843	+	0.00830448i	−0.424486	−	0.905434i	$-0.639545\pi$
$241$	−0.282296	+	0.128920i	−0.0181843	+	0.00830448i	0.406302	+	0.913739i	$0.366818\pi$
$242$		0			0
$243$	−15.4962	−	11.6003i	−0.994084	−	0.744162i
$244$		0			0
$245$	10.7347	−	1.08320i	0.685812	−	0.0692034i
$246$		0			0
$247$	−0.108974	−	1.52366i	−0.00693386	−	0.0969480i
$248$		0			0
$249$	18.0078	+	20.7821i	1.14120	+	1.31701i
$250$		0			0
$251$	9.60342	+	4.38573i	0.606162	+	0.276825i	0.694759	−	0.719243i	$-0.255511\pi$
$251$	9.60342	+	4.38573i	0.606162	+	0.276825i	−0.0885968	+	0.996068i	$0.528238\pi$
$252$		0			0
$253$	−5.88494	−	8.66263i	−0.369983	−	0.544615i
$254$		0			0
$255$	17.7128	−	25.1589i	1.10922	−	1.57551i
$256$		0			0
$257$	0.124781	−	1.74466i	0.00778362	−	0.108829i	−0.992075	−	0.125648i	$-0.959899\pi$
$257$	0.124781	−	1.74466i	0.00778362	−	0.108829i	0.999859	+	0.0168183i	$0.00535370\pi$
$258$		0			0
$259$	0.181323	+	0.157117i	0.0112668	+	0.00976277i
$260$		0			0
$261$	−17.7154	+	5.20170i	−1.09655	+	0.321977i
$262$		0			0
$263$	−6.61177	+	8.83229i	−0.407699	+	0.544623i	−0.956653	−	0.291230i	$-0.905935\pi$
$263$	−6.61177	+	8.83229i	−0.407699	+	0.544623i	0.548954	+	0.835853i	$0.315026\pi$
$264$		0			0
$265$	6.41691	+	3.86423i	0.394188	+	0.237378i
$266$		0			0
$267$	−3.89156	+	0.846556i	−0.238159	+	0.0518084i
$268$		0			0
$269$	−27.0923	−	3.89529i	−1.65185	−	0.237500i	−0.747490	−	0.664273i	$-0.768741\pi$
$269$	−27.0923	−	3.89529i	−1.65185	−	0.237500i	−0.904359	+	0.426773i	$0.859650\pi$
$270$		0			0
$271$	−14.4170	+	9.26523i	−0.875769	+	0.562822i	−0.899512	−	0.436896i	$-0.856078\pi$
$271$	−14.4170	+	9.26523i	−0.875769	+	0.562822i	0.0237434	+	0.999718i	$0.492442\pi$
$272$		0			0
$273$	0.401029	+	0.734430i	0.0242714	+	0.0444497i
$274$		0			0
$275$	3.94891	−	10.1792i	0.238128	−	0.613830i
$276$		0			0
$277$	−9.13896	−	9.13896i	−0.549107	−	0.549107i	0.377076	−	0.926183i	$-0.376930\pi$
$277$	−9.13896	−	9.13896i	−0.549107	−	0.549107i	−0.926183	+	0.377076i	$0.876930\pi$
$278$		0			0
$279$	2.54630	−	8.67190i	0.152443	−	0.519173i
$280$		0			0
$281$	−10.5007	−	16.3395i	−0.626422	−	0.974732i	−0.998909	−	0.0466944i	$-0.985131\pi$
$281$	−10.5007	−	16.3395i	−0.626422	−	0.974732i	0.372487	−	0.928037i	$-0.378505\pi$
$282$		0			0
$283$	10.2167	−	7.64815i	0.607322	−	0.454635i	−0.250830	−	0.968031i	$-0.580704\pi$
$283$	10.2167	−	7.64815i	0.607322	−	0.454635i	0.858152	+	0.513396i	$0.171613\pi$
$284$		0			0
$285$	0.922488	+	31.6189i	0.0546435	+	1.87294i
$286$		0			0
$287$	−1.10289	−	0.411356i	−0.0651014	−	0.0242816i
$288$		0			0
$289$	−18.8397	+	2.70875i	−1.10822	+	0.159338i
$290$		0			0
$291$	0.786119	+	2.67728i	0.0460831	+	0.156945i
$292$		0			0
$293$	−24.1439	+	1.72680i	−1.41050	+	0.100881i	−0.755699	−	0.654919i	$-0.772703\pi$
$293$	−24.1439	+	1.72680i	−1.41050	+	0.100881i	−0.654802	+	0.755800i	$0.727248\pi$
$294$		0			0
$295$	−11.3362	−	19.3937i	−0.660017	−	1.12914i
$296$		0			0
$297$	1.30384	+	3.49574i	0.0756566	+	0.202843i
$298$		0			0
$299$	−0.542128	+	1.05607i	−0.0313521	+	0.0610740i
$300$		0			0
$301$	−4.68189	+	10.2519i	−0.269860	+	0.590910i
$302$		0			0
$303$	−1.25699	−	0.0899018i	−0.0722123	−	0.00516472i
$304$		0			0
$305$	19.9437	−	15.8579i	1.14197	−	0.908020i
$306$		0			0
$307$	−17.2883	−	9.44013i	−0.986696	−	0.538777i	−0.0969775	−	0.995287i	$-0.530917\pi$
$307$	−17.2883	−	9.44013i	−0.986696	−	0.538777i	−0.889718	+	0.456510i	$0.849099\pi$
$308$		0			0
$309$	−6.11206	−	42.5103i	−0.347703	−	2.41833i
$310$		0			0
$311$	−6.33828	−	13.8789i	−0.359411	−	0.787000i	−0.999820	−	0.0189663i	$-0.993962\pi$
$311$	−6.33828	−	13.8789i	−0.359411	−	0.787000i	0.640409	−	0.768034i	$-0.278765\pi$
$312$		0			0
$313$	4.16273	+	19.1358i	0.235292	+	1.08162i	0.931489	+	0.363768i	$0.118510\pi$
$313$	4.16273	+	19.1358i	0.235292	+	1.08162i	−0.696198	+	0.717850i	$0.745126\pi$
$314$		0			0
$315$	−3.28457	−	6.67024i	−0.185064	−	0.375826i
$316$		0			0
$317$	32.6430	+	7.10105i	1.83341	+	0.398835i	0.990305	−	0.138909i	$-0.0443595\pi$
$317$	32.6430	+	7.10105i	1.83341	+	0.398835i	0.843108	+	0.537744i	$0.180723\pi$
$318$		0			0
$319$	17.1577	+	5.03796i	0.960647	+	0.282071i
$320$		0			0
$321$		−	31.0815i		−	1.73480i
$322$		0			0
$323$	26.1947	−	26.1947i	1.45751	−	1.45751i
$324$		0			0
$325$	−1.22723	+	0.160112i	−0.0680743	+	0.00888141i
$326$		0			0
$327$	−4.92916	+	22.6590i	−0.272583	+	1.25304i
$328$		0			0
$329$	−0.208822	+	1.45239i	−0.0115127	+	0.0800729i
$330$		0			0
$331$	6.64717	+	4.27188i	0.365361	+	0.234804i	0.710421	−	0.703777i	$-0.248505\pi$
$331$	6.64717	+	4.27188i	0.365361	+	0.234804i	−0.345059	+	0.938581i	$0.612141\pi$
$332$		0			0
$333$	−0.128183	+	0.343673i	−0.00702441	+	0.0188332i
$334$		0			0
$335$	−10.5320	+	9.67797i	−0.575425	+	0.528764i
$336$		0			0
$337$	10.6518	−	19.5072i	0.580238	−	1.06263i	−0.408470	−	0.912772i	$-0.633938\pi$
$337$	10.6518	−	19.5072i	0.580238	−	1.06263i	0.988708	−	0.149855i	$-0.0478806\pi$
$338$		0			0
$339$	13.1475	−	15.1730i	0.714074	−	0.824086i
$340$		0			0
$341$	−6.61546	+	5.73233i	−0.358247	+	0.310423i
$342$		0			0
$343$	−16.3397	+	6.09438i	−0.882259	+	0.329065i
$344$		0			0
$345$	12.1397	−	21.3755i	0.653577	−	1.15082i
$346$		0			0
$347$	12.2823	−	4.58106i	0.659349	−	0.245924i	0.00255740	−	0.999997i	$-0.499186\pi$
$347$	12.2823	−	4.58106i	0.659349	−	0.245924i	0.656791	+	0.754072i	$0.271913\pi$
$348$		0			0
$349$	−17.2634	+	14.9588i	−0.924089	+	0.800727i	−0.980264	−	0.197694i	$-0.936655\pi$
$349$	−17.2634	+	14.9588i	−0.924089	+	0.800727i	0.0561753	+	0.998421i	$0.482109\pi$
$350$		0			0
$351$	0.276952	−	0.319619i	0.0147826	−	0.0170600i
$352$		0			0
$353$	5.87818	−	10.7651i	0.312864	−	0.572967i	−0.673175	−	0.739483i	$-0.735070\pi$
$353$	5.87818	−	10.7651i	0.312864	−	0.572967i	0.986039	+	0.166516i	$0.0532517\pi$
$354$		0			0
$355$	−14.5355	−	0.614243i	−0.771465	−	0.0326006i
$356$		0			0
$357$	−7.09170	+	19.0136i	−0.375333	+	1.00631i
$358$		0			0
$359$	17.4334	+	11.2038i	0.920101	+	0.591313i	0.912687	−	0.408660i	$-0.134004\pi$
$359$	17.4334	+	11.2038i	0.920101	+	0.591313i	0.00741398	+	0.999973i	$0.497640\pi$
$360$		0			0
$361$	−2.71604	+	18.8905i	−0.142949	+	0.994236i
$362$		0			0
$363$	3.03642	−	13.9582i	0.159371	−	0.732616i
$364$		0			0
$365$	−5.51326	−	16.9331i	−0.288577	−	0.886319i
$366$		0			0
$367$	6.60439	−	6.60439i	0.344747	−	0.344747i	−0.513402	−	0.858148i	$-0.671615\pi$
$367$	6.60439	−	6.60439i	0.344747	−	0.344747i	0.858148	+	0.513402i	$0.171615\pi$
$368$		0			0
$369$		−	1.79957i		−	0.0936821i
$370$		0			0
$371$	−4.74019	−	1.39185i	−0.246099	−	0.0722611i
$372$		0			0
$373$	−28.7399	−	6.25198i	−1.48809	−	0.323715i	−0.606257	−	0.795269i	$-0.707330\pi$
$373$	−28.7399	−	6.25198i	−1.48809	−	0.323715i	−0.881837	+	0.471554i	$0.843693\pi$
$374$		0			0
$375$	25.5307	−	2.23967i	1.31840	−	0.115656i
$376$		0			0
$377$	−0.430866	−	1.98066i	−0.0221907	−	0.102009i
$378$		0			0
$379$	13.0305	+	28.5327i	0.669330	+	1.46563i	0.873566	+	0.486706i	$0.161802\pi$
$379$	13.0305	+	28.5327i	0.669330	+	1.46563i	−0.204236	+	0.978922i	$0.565471\pi$
$380$		0			0
$381$	−2.85484	−	19.8559i	−0.146258	−	1.01725i
$382$		0			0
$383$	5.24589	+	2.86447i	0.268053	+	0.146368i	0.607654	−	0.794201i	$-0.292111\pi$
$383$	5.24589	+	2.86447i	0.268053	+	0.146368i	−0.339602	+	0.940569i	$0.610292\pi$
$384$		0			0
$385$	−0.816514	+	7.15460i	−0.0416134	+	0.364632i
$386$		0			0
$387$	−17.1864	−	1.22920i	−0.873636	−	0.0624837i
$388$		0			0
$389$	−3.35266	+	7.34129i	−0.169986	+	0.372218i	−0.975383	−	0.220518i	$-0.929225\pi$
$389$	−3.35266	+	7.34129i	−0.169986	+	0.372218i	0.805396	+	0.592737i	$0.201952\pi$
$390$		0			0
$391$	−27.9651	+	6.83557i	−1.41425	+	0.345690i
$392$		0			0
$393$	5.11375	+	13.7105i	0.257955	+	0.691603i
$394$		0			0
$395$	25.7571	−	15.0558i	1.29598	−	0.757538i
$396$		0			0
$397$	−34.0952	+	2.43854i	−1.71119	+	0.122387i	−0.892264	−	0.451513i	$-0.850884\pi$
$397$	−34.0952	+	2.43854i	−1.71119	+	0.122387i	−0.818925	+	0.573900i	$0.805430\pi$
$398$		0			0
$399$	−5.87770	−	20.0176i	−0.294253	−	1.00213i
$400$		0			0
$401$	34.8432	−	5.00969i	1.73998	−	0.250172i	0.802117	−	0.597167i	$-0.203707\pi$
$401$	34.8432	−	5.00969i	1.73998	−	0.250172i	0.937867	+	0.346995i	$0.112798\pi$
$402$		0			0
$403$	0.929674	+	0.346751i	0.0463104	+	0.0172729i
$404$		0			0
$405$	−16.3877	+	17.3727i	−0.814312	+	0.863255i
$406$		0			0
$407$	0.284395	−	0.212895i	0.0140969	−	0.0105528i
$408$		0			0
$409$	14.2159	+	22.1204i	0.702933	+	1.09379i	0.990697	+	0.136084i	$0.0434516\pi$
$409$	14.2159	+	22.1204i	0.702933	+	1.09379i	−0.287764	+	0.957701i	$0.592912\pi$
$410$		0			0
$411$	−8.15859	+	27.7856i	−0.402433	+	1.37056i
$412$		0			0
$413$	10.4763	+	10.4763i	0.515504	+	0.515504i
$414$		0			0
$415$	22.1334	−	15.1541i	1.08648	−	0.743887i
$416$		0			0
$417$	−0.923995	−	1.69217i	−0.0452482	−	0.0828660i
$418$		0			0
$419$	−12.6403	+	8.12344i	−0.617520	+	0.396856i	−0.811670	−	0.584116i	$-0.801441\pi$
$419$	−12.6403	+	8.12344i	−0.617520	+	0.396856i	0.194150	+	0.980972i	$0.437805\pi$
$420$		0			0
$421$	−14.1128	−	2.02912i	−0.687818	−	0.0988932i	−0.210460	−	0.977602i	$-0.567496\pi$
$421$	−14.1128	−	2.02912i	−0.687818	−	0.0988932i	−0.477357	+	0.878709i	$0.658405\pi$
$422$		0			0
$423$	−2.19200	+	0.476841i	−0.106579	+	0.0231848i
$424$		0			0
$425$	−22.4243	−	19.9496i	−1.08774	−	0.967700i
$426$		0			0
$427$	−10.0708	+	13.4530i	−0.487360	+	0.651036i
$428$		0			0
$429$	1.18883	−	0.349073i	0.0573973	−	0.0168534i
$430$		0			0
$431$	9.84043	+	8.52678i	0.473997	+	0.410721i	0.858826	−	0.512267i	$-0.171194\pi$
$431$	9.84043	+	8.52678i	0.473997	+	0.410721i	−0.384829	+	0.922988i	$0.625740\pi$
$432$		0			0
$433$	−1.52747	+	21.3568i	−0.0734054	+	1.02634i	0.818614	+	0.574344i	$0.194743\pi$
$433$	−1.52747	+	21.3568i	−0.0734054	+	1.02634i	−0.892019	+	0.451997i	$0.850712\pi$
$434$		0			0
$435$	7.18271	+	41.3555i	0.344385	+	1.98285i
$436$		0			0
$437$	18.8042	−	22.8550i	0.899527	−	1.09330i
$438$		0			0
$439$	−11.3485	−	5.18269i	−0.541635	−	0.247356i	0.125759	−	0.992061i	$-0.459863\pi$
$439$	−11.3485	−	5.18269i	−0.541635	−	0.247356i	−0.667395	+	0.744704i	$0.732591\pi$
$440$		0			0
$441$	−7.12410	−	8.22165i	−0.339243	−	0.391507i
$442$		0			0
$443$	−2.05323	−	28.7079i	−0.0975519	−	1.36395i	−0.776662	−	0.629918i	$-0.783089\pi$
$443$	−2.05323	−	28.7079i	−0.0975519	−	1.36395i	0.679110	−	0.734037i	$-0.262366\pi$
$444$		0			0
$445$	0.390031	+	3.86524i	0.0184892	+	0.183230i
$446$		0			0
$447$	−12.8899	−	9.64929i	−0.609673	−	0.456396i
$448$		0			0
$449$	19.4816	−	8.89695i	0.919394	−	0.419873i	0.101233	−	0.994863i	$-0.467721\pi$
$449$	19.4816	−	8.89695i	0.919394	−	0.419873i	0.818161	+	0.574990i	$0.194994\pi$
$450$		0			0
$451$	−0.942297	+	1.46624i	−0.0443710	+	0.0690427i
$452$		0			0
$453$	−9.04591	−	12.0839i	−0.425014	−	0.567752i
$454$		0			0
$455$	0.756149	−	0.307435i	0.0354488	−	0.0144128i
$456$		0			0
$457$	−24.2815	+	13.2587i	−1.13584	+	0.620215i	−0.933314	−	0.359062i	$-0.883097\pi$
$457$	−24.2815	+	13.2587i	−1.13584	+	0.620215i	−0.202525	+	0.979277i	$0.564915\pi$
$458$		0			0
$459$	10.2562			0.478721
$460$		0			0
$461$	0.663206			0.0308886			0.0154443	−	0.999881i	$-0.495084\pi$
$461$	0.663206			0.0308886			0.0154443	+	0.999881i	$0.495084\pi$
$462$		0			0
$463$	21.4407	−	11.7075i	0.996432	−	0.544093i	0.103665	−	0.994612i	$-0.466943\pi$
$463$	21.4407	−	11.7075i	0.996432	−	0.544093i	0.892767	+	0.450519i	$0.148761\pi$
$464$		0			0
$465$	−18.9313	−	7.98690i	−0.877918	−	0.370384i
$466$		0			0
$467$	−2.32328	−	3.10354i	−0.107509	−	0.143615i	0.743560	−	0.668669i	$-0.233136\pi$
$467$	−2.32328	−	3.10354i	−0.107509	−	0.143615i	−0.851069	+	0.525055i	$0.824045\pi$
$468$		0			0
$469$	5.10017	−	7.93603i	0.235504	−	0.366452i
$470$		0			0
$471$	−10.5826	+	4.83292i	−0.487621	+	0.222689i
$472$		0			0
$473$	13.3594	+	10.0007i	0.614266	+	0.459833i
$474$		0			0
$475$	30.7464	+	2.60322i	1.41074	+	0.119444i
$476$		0			0
$477$	−0.538812	−	7.53358i	−0.0246705	−	0.344939i
$478$		0			0
$479$	−6.96317	−	8.03592i	−0.318155	−	0.367171i	0.574035	−	0.818831i	$-0.305377\pi$
$479$	−6.96317	−	8.03592i	−0.318155	−	0.367171i	−0.892190	+	0.451660i	$0.850832\pi$
$480$		0			0
$481$	−0.0366300	−	0.0167283i	−0.00167018	−	0.000762747i
$482$		0			0
$483$	−4.16905	+	15.6676i	−0.189698	+	0.712902i
$484$		0			0
$485$	2.68171	−	0.465764i	0.121770	−	0.0211493i
$486$		0			0
$487$	−0.873464	+	12.2126i	−0.0395804	+	0.553407i	0.938514	+	0.345243i	$0.112203\pi$
$487$	−0.873464	+	12.2126i	−0.0395804	+	0.553407i	−0.978094	+	0.208164i	$0.933251\pi$
$488$		0			0
$489$	−35.0728	−	30.3908i	−1.58605	−	1.37432i
$490$		0			0
$491$	22.3820	−	6.57195i	1.01009	−	0.296588i	0.265498	−	0.964112i	$-0.414464\pi$
$491$	22.3820	−	6.57195i	1.01009	−	0.296588i	0.744589	+	0.667523i	$0.232646\pi$
$492$		0			0
$493$	29.4586	−	39.3520i	1.32675	−	1.77233i
$494$		0			0
$495$	−10.6846	+	2.65287i	−0.480239	+	0.119237i
$496$		0			0
$497$	9.37596	−	2.03962i	0.420569	−	0.0914893i
$498$		0			0
$499$	37.2405	+	5.35438i	1.66711	+	0.239695i	0.910304	−	0.413939i	$-0.135847\pi$
$499$	37.2405	+	5.35438i	1.66711	+	0.239695i	0.756810	+	0.653634i	$0.226757\pi$
$500$		0			0
$501$	11.3090	−	7.26784i	0.505248	−	0.324703i
$502$		0			0
$503$	−10.4543	−	19.1456i	−0.466134	−	0.853661i	−0.999967	−	0.00807128i	$-0.997431\pi$
$503$	−10.4543	−	19.1456i	−0.466134	−	0.853661i	0.533833	−	0.845590i	$-0.320751\pi$
$504$		0			0
$505$	−0.226163	+	1.20830i	−0.0100641	+	0.0537688i
$506$		0			0
$507$	20.9724	+	20.9724i	0.931417	+	0.931417i
$508$		0			0
$509$	−5.59523	+	19.0556i	−0.248004	+	0.844625i	0.737554	+	0.675288i	$0.235981\pi$
$509$	−5.59523	+	19.0556i	−0.248004	+	0.844625i	−0.985558	+	0.169337i	$0.945838\pi$
$510$		0			0
$511$	6.34984	+	9.88054i	0.280900	+	0.437089i
$512$		0			0
$513$	−8.44101	+	6.31886i	−0.372680	+	0.278985i
$514$		0			0
$515$	−41.8761	+	1.22174i	−1.84528	+	0.0538364i
$516$		0			0
$517$	2.03567	+	0.759265i	0.0895286	+	0.0333924i
$518$		0			0
$519$	−39.0149	+	5.60950i	−1.71257	+	0.246230i
$520$		0			0
$521$	−12.1777	−	41.4734i	−0.533514	−	1.81698i	−0.575418	−	0.817860i	$-0.695161\pi$
$521$	−12.1777	−	41.4734i	−0.533514	−	1.81698i	0.0419039	−	0.999122i	$-0.486658\pi$
$522$		0			0
$523$	−18.6687	+	1.33521i	−0.816323	+	0.0583846i	−0.473255	−	0.880926i	$-0.656921\pi$
$523$	−18.6687	+	1.33521i	−0.816323	+	0.0583846i	−0.343069	+	0.939310i	$0.611466\pi$
$524$		0			0
$525$	−15.9131	+	5.69958i	−0.694506	+	0.248750i
$526$		0			0
$527$	8.40912	+	22.5457i	0.366307	+	0.982107i
$528$		0			0
$529$	−21.7088	+	7.59782i	−0.943862	+	0.330340i
$530$		0			0
$531$	−9.40934	+	20.6036i	−0.408331	+	0.894119i
$532$		0			0
$533$	0.197062	+	0.0140942i	0.00853572	+	0.000610487i
$534$		0			0
$535$	−30.1235	−	3.43783i	−1.30235	−	0.148630i
$536$		0			0
$537$	−34.1227	−	18.6324i	−1.47250	−	0.804047i
$538$		0			0
$539$	1.49948	+	10.4291i	0.0645872	+	0.449214i
$540$		0			0
$541$	−15.8456	−	34.6971i	−0.681256	−	1.49174i	−0.861307	−	0.508085i	$-0.830353\pi$
$541$	−15.8456	−	34.6971i	−0.681256	−	1.49174i	0.180051	−	0.983657i	$-0.442374\pi$
$542$		0			0
$543$	−11.0639	−	50.8601i	−0.474799	−	2.18262i
$544$		0			0
$545$	21.4154	+	7.28347i	0.917334	+	0.311990i
$546$		0			0
$547$	−18.6365	−	4.05412i	−0.796838	−	0.173341i	−0.204326	−	0.978903i	$-0.565500\pi$
$547$	−18.6365	−	4.05412i	−0.796838	−	0.173341i	−0.592512	+	0.805561i	$0.701864\pi$
$548$		0			0
$549$	−24.6509	−	7.23815i	−1.05207	−	0.308917i
$550$		0			0
$551$			50.5366i			2.15293i
$552$		0			0
$553$	−13.9137	+	13.9137i	−0.591672	+	0.591672i
$554$		0			0
$555$	0.743229	+	0.378126i	0.0315483	+	0.0160506i
$556$		0			0
$557$	0.118984	−	0.546959i	0.00504150	−	0.0231754i	−0.974557	−	0.224138i	$-0.928043\pi$
$557$	0.118984	−	0.546959i	0.00504150	−	0.0231754i	0.979599	+	0.200963i	$0.0644070\pi$
$558$		0			0
$559$	0.269207	−	1.87237i	0.0113862	−	0.0791930i
$560$		0			0
$561$	25.2778	+	16.2450i	1.06723	+	0.685866i
$562$		0			0
$563$	−2.29958	+	6.16541i	−0.0969158	+	0.259841i	−0.976356	−	0.216168i	$-0.930644\pi$
$563$	−2.29958	+	6.16541i	−0.0969158	+	0.259841i	0.879441	+	0.476009i	$0.157917\pi$
$564$		0			0
$565$	−13.2512	−	14.4205i	−0.557480	−	0.606675i
$566$		0			0
$567$	7.54877	−	13.8245i	0.317019	−	0.580576i
$568$		0			0
$569$	−27.7985	+	32.0812i	−1.16537	+	1.34491i	−0.237783	+	0.971318i	$0.576421\pi$
$569$	−27.7985	+	32.0812i	−1.16537	+	1.34491i	−0.927592	+	0.373596i	$0.878125\pi$
$570$		0			0
$571$	13.8599	−	12.0097i	0.580018	−	0.502589i	−0.314717	−	0.949186i	$-0.601910\pi$
$571$	13.8599	−	12.0097i	0.580018	−	0.502589i	0.894735	+	0.446597i	$0.147364\pi$
$572$		0			0
$573$	17.0758	−	6.36894i	0.713351	−	0.266066i
$574$		0			0
$575$	−19.3739	−	14.1298i	−0.807950	−	0.589252i
$576$		0			0
$577$	35.0224	−	13.0627i	1.45800	−	0.543807i	0.509470	−	0.860488i	$-0.329841\pi$
$577$	35.0224	−	13.0627i	1.45800	−	0.543807i	0.948532	+	0.316682i	$0.102569\pi$
$578$		0			0
$579$	24.3022	−	21.0579i	1.00996	−	0.875138i
$580$		0			0
$581$	−11.5854	+	13.3703i	−0.480645	+	0.554694i
$582$		0			0
$583$	−3.50574	+	6.42028i	−0.145193	+	0.265901i
$584$		0			0
$585$	0.844362	+	0.918873i	0.0349101	+	0.0379907i
$586$		0			0
$587$	−1.75806	+	4.71355i	−0.0725631	+	0.194549i	−0.968168	−	0.250301i	$-0.919470\pi$
$587$	−1.75806	+	4.71355i	−0.0725631	+	0.194549i	0.895605	+	0.444850i	$0.146743\pi$
$588$		0			0
$589$	−20.8112	−	13.3745i	−0.857510	−	0.551089i
$590$		0			0
$591$	2.00197	−	13.9240i	0.0823502	−	0.572758i
$592$		0			0
$593$	2.03087	−	9.33575i	0.0833978	−	0.383373i	−0.916462	−	0.400122i	$-0.868968\pi$
$593$	2.03087	−	9.33575i	0.0833978	−	0.383373i	0.999860	+	0.0167485i	$0.00533145\pi$
$594$		0			0
$595$	17.6432	+	8.97615i	0.723299	+	0.367986i
$596$		0			0
$597$	−22.3561	+	22.3561i	−0.914974	+	0.914974i
$598$		0			0
$599$			29.3946i			1.20103i	0.799613	+	0.600516i	$0.205038\pi$
$599$			29.3946i			1.20103i	−0.799613	+	0.600516i	$0.794962\pi$
$600$		0			0
$601$	21.5470	+	6.32678i	0.878922	+	0.258075i	0.689906	−	0.723899i	$-0.257652\pi$
$601$	21.5470	+	6.32678i	0.878922	+	0.258075i	0.189016	+	0.981974i	$0.439470\pi$
$602$		0			0
$603$	14.0926	+	3.06566i	0.573895	+	0.124843i
$604$		0			0
$605$	−13.1921	−	4.48671i	−0.536337	−	0.182411i
$606$		0			0
$607$	−1.23951	−	5.69792i	−0.0503100	−	0.231271i	0.945126	−	0.326707i	$-0.105939\pi$
$607$	−1.23951	−	5.69792i	−0.0503100	−	0.231271i	−0.995436	+	0.0954359i	$0.969575\pi$
$608$		0			0
$609$	−11.5002	−	25.1820i	−0.466013	−	1.02043i
$610$		0			0
$611$	−0.0350488	−	0.243770i	−0.00141792	−	0.00986187i
$612$		0			0
$613$	−1.30867	−	0.714588i	−0.0528567	−	0.0288619i	0.452603	−	0.891712i	$-0.350495\pi$
$613$	−1.30867	−	0.714588i	−0.0528567	−	0.0288619i	−0.505460	+	0.862850i	$0.668677\pi$
$614$		0			0
$615$	−4.06479	−	0.463892i	−0.163908	−	0.0187059i
$616$		0			0
$617$	33.3847	+	2.38772i	1.34402	+	0.0961259i	0.724726	−	0.689037i	$-0.241966\pi$
$617$	33.3847	+	2.38772i	1.34402	+	0.0961259i	0.619289	+	0.785163i	$0.287421\pi$
$618$		0			0
$619$	10.7610	−	23.5633i	0.432522	−	0.947091i	−0.560389	−	0.828230i	$-0.689348\pi$
$619$	10.7610	−	23.5633i	0.432522	−	0.947091i	0.992911	−	0.118861i	$-0.0379244\pi$
$620$		0			0
$621$	8.15560	−	0.793024i	0.327273	−	0.0318230i
$622$		0			0
$623$	−0.895401	−	2.40066i	−0.0358735	−	0.0961805i
$624$		0			0
$625$	0.653228	−	24.9915i	0.0261291	−	0.999659i
$626$		0			0
$627$	−30.8125	+	2.20375i	−1.23053	+	0.0880093i
$628$		0			0
$629$	−0.275132	−	0.937014i	−0.0109702	−	0.0373612i
$630$		0			0
$631$	11.9278	−	1.71496i	0.474840	−	0.0682717i	0.0992597	−	0.995062i	$-0.468353\pi$
$631$	11.9278	−	1.71496i	0.474840	−	0.0682717i	0.375580	+	0.926790i	$0.377443\pi$
$632$		0			0
$633$	−13.1821	−	4.91669i	−0.523943	−	0.195421i
$634$		0			0
$635$	−19.5596	+	0.570656i	−0.776201	+	0.0226458i
$636$		0			0
$637$	0.956108	−	0.715733i	0.0378824	−	0.0283584i
$638$		0			0
$639$	7.93085	+	12.3406i	0.313740	+	0.488188i
$640$		0			0
$641$	11.0107	−	37.4991i	0.434898	−	1.48113i	−0.392628	−	0.919697i	$-0.628434\pi$
$641$	11.0107	−	37.4991i	0.434898	−	1.48113i	0.827526	−	0.561428i	$-0.189748\pi$
$642$		0			0
$643$	−15.0031	−	15.0031i	−0.591664	−	0.591664i	0.346416	−	0.938081i	$-0.387398\pi$
$643$	−15.0031	−	15.0031i	−0.591664	−	0.591664i	−0.938081	+	0.346416i	$0.887398\pi$
$644$		0			0
$645$	−7.20675	+	38.5031i	−0.283766	+	1.51606i
$646$		0			0
$647$	0.0313600	+	0.0574315i	0.00123289	+	0.00225787i	0.878295	−	0.478120i	$-0.158681\pi$
$647$	0.0313600	+	0.0574315i	0.00123289	+	0.00225787i	−0.877062	+	0.480378i	$0.840500\pi$
$648$		0			0
$649$	18.4550	−	11.8603i	0.724421	−	0.465557i
$650$		0			0
$651$	13.4136	+	1.92859i	0.525722	+	0.0755873i
$652$		0			0
$653$	28.4019	−	6.17846i	1.11145	−	0.241782i	0.380886	−	0.924622i	$-0.375619\pi$
$653$	28.4019	−	6.17846i	1.11145	−	0.241782i	0.730568	+	0.682840i	$0.239255\pi$
$654$		0			0
$655$	13.8535	−	3.43966i	0.541302	−	0.134399i
$656$		0			0
$657$	−10.7606	+	14.3745i	−0.419811	+	0.560802i
$658$		0			0
$659$	24.6663	−	7.24269i	0.960864	−	0.282135i	0.236561	−	0.971617i	$-0.423980\pi$
$659$	24.6663	−	7.24269i	0.960864	−	0.282135i	0.724303	+	0.689482i	$0.242162\pi$
$660$		0			0
$661$	−0.891819	−	0.772765i	−0.0346877	−	0.0300571i	0.637344	−	0.770579i	$-0.280033\pi$
$661$	−0.891819	−	0.772765i	−0.0346877	−	0.0300571i	−0.672032	+	0.740522i	$0.734578\pi$
$662$		0			0
$663$	0.242981	−	3.39732i	0.00943661	−	0.131941i
$664$		0			0
$665$	−20.0507	+	3.48245i	−0.777534	+	0.135044i
$666$		0			0
$667$	20.3822	−	33.5698i	0.789203	−	1.29983i
$668$		0			0
$669$	18.9196	+	8.64027i	0.731472	+	0.334052i
$670$		0			0
$671$	16.2948	+	18.8052i	0.629053	+	0.725966i
$672$		0			0
$673$	3.12678	+	43.7181i	0.120529	+	1.68521i	0.594050	+	0.804428i	$0.297528\pi$
$673$	3.12678	+	43.7181i	0.120529	+	1.68521i	−0.473522	+	0.880782i	$0.657017\pi$
$674$		0			0
$675$	5.50958	+	6.52884i	0.212064	+	0.251295i
$676$		0			0
$677$	−7.00991	−	5.24755i	−0.269413	−	0.201680i	0.456026	−	0.889966i	$-0.349272\pi$
$677$	−7.00991	−	5.24755i	−0.269413	−	0.201680i	−0.725439	+	0.688287i	$0.758363\pi$
$678$		0			0
$679$	−1.63293	+	0.745736i	−0.0626662	+	0.0286187i
$680$		0			0
$681$	11.6098	−	18.0652i	0.444888	−	0.692259i
$682$		0			0
$683$	7.18275	+	9.59503i	0.274840	+	0.367144i	0.916630	−	0.399737i	$-0.130899\pi$
$683$	7.18275	+	9.59503i	0.274840	+	0.367144i	−0.641790	+	0.766881i	$0.721808\pi$
$684$		0			0
$685$	26.0268	+	10.9804i	0.994432	+	0.419539i
$686$		0			0
$687$	39.0514	−	21.3237i	1.48990	−	0.813550i
$688$		0			0
$689$	0.829184			0.0315894
$690$		0			0
$691$	32.7965			1.24764			0.623819	−	0.781569i	$-0.285580\pi$
$691$	32.7965			1.24764			0.623819	+	0.781569i	$0.285580\pi$
$692$		0			0
$693$	6.37271	−	3.47976i	0.242079	−	0.132185i
$694$		0			0
$695$	−1.74221	+	0.708350i	−0.0660859	+	0.0268692i
$696$		0			0
$697$	2.87126	+	3.83556i	0.108757	+	0.145282i
$698$		0			0
$699$	−3.22499	+	5.01818i	−0.121980	+	0.189805i
$700$		0			0
$701$	−18.6167	+	8.50198i	−0.703145	+	0.321116i	−0.734705	−	0.678386i	$-0.762680\pi$
$701$	−18.6167	+	8.50198i	−0.703145	+	0.321116i	0.0315605	+	0.999502i	$0.489952\pi$
$702$		0			0
$703$	0.803730	+	0.601665i	0.0303133	+	0.0226922i
$704$		0			0
$705$	0.512014	+	5.07411i	0.0192836	+	0.191102i
$706$		0			0
$707$	−0.0578389	−	0.808693i	−0.00217525	−	0.0304140i
$708$		0			0
$709$	−20.2557	−	23.3763i	−0.760719	−	0.877917i	0.234842	−	0.972034i	$-0.424543\pi$
$709$	−20.2557	−	23.3763i	−0.760719	−	0.877917i	−0.995561	+	0.0941170i	$0.969997\pi$
$710$		0			0
$711$	−27.3640	−	12.4967i	−1.02623	−	0.468663i
$712$		0			0
$713$	8.43005	+	17.2778i	0.315708	+	0.647058i
$714$		0			0
$715$	−0.206820	−	1.19080i	−0.00773464	−	0.0445334i
$716$		0			0
$717$	3.13956	−	43.8967i	0.117249	−	1.63935i
$718$		0			0
$719$	−30.0590	−	26.0463i	−1.12101	−	0.971364i	−0.121239	−	0.992623i	$-0.538687\pi$
$719$	−30.0590	−	26.0463i	−1.12101	−	0.971364i	−0.999774	+	0.0212598i	$0.993232\pi$
$720$		0			0
$721$	26.5113	−	7.78442i	0.987332	−	0.289907i
$722$		0			0
$723$	0.426323	−	0.569500i	0.0158551	−	0.0211800i
$724$		0			0
$725$	40.8753	−	2.38712i	1.51807	−	0.0886554i
$726$		0			0
$727$	−28.9452	+	6.29665i	−1.07352	+	0.233530i	−0.714383	−	0.699755i	$-0.753292\pi$
$727$	−28.9452	+	6.29665i	−1.07352	+	0.233530i	−0.359137	+	0.933285i	$0.616929\pi$
$728$		0			0
$729$	12.2055	+	1.75489i	0.452055	+	0.0649958i
$730$		0			0
$731$	38.5919	−	24.8015i	1.42737	−	0.917316i
$732$		0			0
$733$	−10.4175	−	19.0782i	−0.384779	−	0.704669i	0.611464	−	0.791272i	$-0.290581\pi$
$733$	−10.4175	−	19.0782i	−0.384779	−	0.704669i	−0.996243	+	0.0866026i	$0.972399\pi$
$734$		0			0
$735$	−20.4071	+	13.9722i	−0.752728	+	0.515373i
$736$		0			0
$737$	−9.87701	−	9.87701i	−0.363824	−	0.363824i
$738$		0			0
$739$	−9.31537	+	31.7252i	−0.342671	+	1.16703i	0.590331	+	0.807161i	$0.298997\pi$
$739$	−9.31537	+	31.7252i	−0.342671	+	1.16703i	−0.933002	+	0.359870i	$0.882821\pi$
$740$		0			0
$741$	1.89311	+	2.94574i	0.0695451	+	0.108214i
$742$		0			0
$743$	−38.2630	+	28.6433i	−1.40373	+	1.05082i	−0.413636	+	0.910443i	$0.635741\pi$
$743$	−38.2630	+	28.6433i	−1.40373	+	1.05082i	−0.990098	+	0.140379i	$0.955168\pi$
$744$		0			0
$745$	−10.7776	+	11.4254i	−0.394860	+	0.418593i
$746$		0			0
$747$	−25.3416	−	9.45194i	−0.927202	−	0.345828i
$748$		0			0
$749$	19.7929	−	2.84579i	0.723218	−	0.103983i
$750$		0			0
$751$	−9.37652	−	31.9335i	−0.342154	−	1.16527i	−0.933418	−	0.358792i	$-0.883189\pi$
$751$	−9.37652	−	31.9335i	−0.342154	−	1.16527i	0.591264	−	0.806478i	$-0.298629\pi$
$752$		0			0
$753$	−24.1392	+	1.72647i	−0.879683	+	0.0629162i
$754$		0			0
$755$	−12.7120	+	7.43053i	−0.462637	+	0.270425i
$756$		0			0
$757$	0.803043	+	2.15304i	0.0291871	+	0.0782537i	0.950726	−	0.310032i	$-0.100340\pi$
$757$	0.803043	+	2.15304i	0.0291871	+	0.0782537i	−0.921539	+	0.388286i	$0.873067\pi$
$758$		0			0
$759$	21.3566	+	10.9633i	0.775194	+	0.397942i
$760$		0			0
$761$	−3.90978	+	8.56122i	−0.141729	+	0.310344i	−0.967164	−	0.254154i	$-0.918203\pi$
$761$	−3.90978	+	8.56122i	−0.141729	+	0.310344i	0.825434	+	0.564498i	$0.190930\pi$
$762$		0			0
$763$	−14.8807	−	1.06429i	−0.538718	−	0.0385299i
$764$		0			0
$765$	−3.43150	+	30.0681i	−0.124066	+	1.08711i
$766$		0			0
$767$	−2.18250	−	1.19174i	−0.0788056	−	0.0430311i
$768$		0			0
$769$	−5.38385	−	37.4455i	−0.194147	−	1.35032i	−0.820887	−	0.571091i	$-0.806520\pi$
$769$	−5.38385	−	37.4455i	−0.194147	−	1.35032i	0.626740	−	0.779228i	$-0.284389\pi$
$770$		0			0
$771$	1.66561	+	3.64718i	0.0599855	+	0.131350i
$772$		0			0
$773$	11.4931	+	52.8327i	0.413377	+	1.90026i	0.434871	+	0.900493i	$0.356794\pi$
$773$	11.4931	+	52.8327i	0.413377	+	1.90026i	−0.0214939	+	0.999769i	$0.506842\pi$
$774$		0			0
$775$	−9.83466	+	17.4644i	−0.353271	+	0.627340i
$776$		0			0
$777$	−0.537410	−	0.116906i	−0.0192795	−	0.00419399i
$778$		0			0
$779$	−4.72617	−	1.38773i	−0.169332	−	0.0497205i
$780$		0			0
$781$		−	14.2076i		−	0.508387i
$782$		0			0
$783$	−9.89352	+	9.89352i	−0.353565	+	0.353565i
$784$		0			0
$785$	3.51345	+	10.7910i	0.125400	+	0.385147i
$786$		0			0
$787$	7.21883	−	33.1844i	0.257324	−	1.18290i	−0.649159	−	0.760653i	$-0.724879\pi$
$787$	7.21883	−	33.1844i	0.257324	−	1.18290i	0.906482	−	0.422244i	$-0.138758\pi$
$788$		0			0
$789$	3.59925	−	25.0333i	0.128137	−	0.891209i
$790$		0			0
$791$	10.8661	+	6.98320i	0.386353	+	0.248294i
$792$		0			0
$793$	0.985678	−	2.64270i	0.0350024	−	0.0938452i
$794$		0			0
$795$	−17.1554	−	0.724953i	−0.608439	−	0.0257114i
$796$		0			0
$797$	−8.02442	+	14.6956i	−0.284239	+	0.520546i	−0.980319	−	0.197419i	$-0.936744\pi$
$797$	−8.02442	+	14.6956i	−0.284239	+	0.520546i	0.696080	+	0.717964i	$0.254926\pi$
$798$		0			0
$799$	3.91116	−	4.51372i	0.138367	−	0.159684i
$800$		0			0
$801$	2.96038	−	2.56518i	0.104600	−	0.0906363i
$802$		0			0
$803$	16.2942	−	6.07744i	0.575011	−	0.214468i
$804$		0			0
$805$	14.7236	+	5.77350i	0.518938	+	0.203489i
$806$		0			0
$807$	58.7865	−	21.9262i	2.06938	−	0.771840i
$808$		0			0
$809$	9.98746	−	8.65419i	0.351141	−	0.304265i	−0.461374	−	0.887206i	$-0.652643\pi$
$809$	9.98746	−	8.65419i	0.351141	−	0.304265i	0.812515	+	0.582941i	$0.198098\pi$
$810$		0			0
$811$	10.7303	−	12.3834i	0.376791	−	0.434840i	−0.535404	−	0.844596i	$-0.679841\pi$
$811$	10.7303	−	12.3834i	0.376791	−	0.434840i	0.912195	+	0.409756i	$0.134386\pi$
$812$		0			0
$813$	18.8270	−	34.4790i	0.660290	−	1.20923i
$814$		0			0
$815$	−33.3334	+	30.6304i	−1.16762	+	1.07294i
$816$		0			0
$817$	−16.4814	+	44.1883i	−0.576611	+	1.54595i
$818$		0			0
$819$	−0.692385	−	0.444969i	−0.0241939	−	0.0155485i
$820$		0			0
$821$	−5.44827	+	37.8935i	−0.190146	+	1.32249i	0.641473	+	0.767146i	$0.278324\pi$
$821$	−5.44827	+	37.8935i	−0.190146	+	1.32249i	−0.831618	+	0.555347i	$0.812585\pi$
$822$		0			0
$823$	−5.56427	+	25.5785i	−0.193958	+	0.891611i	0.772546	+	0.634959i	$0.218983\pi$
$823$	−5.56427	+	25.5785i	−0.193958	+	0.891611i	−0.966504	+	0.256652i	$0.917381\pi$
$824$		0			0
$825$	3.23789	+	24.8178i	0.112729	+	0.864046i
$826$		0			0
$827$	−5.47033	+	5.47033i	−0.190222	+	0.190222i	−0.795792	−	0.605570i	$-0.792945\pi$
$827$	−5.47033	+	5.47033i	−0.190222	+	0.190222i	0.605570	+	0.795792i	$0.292945\pi$
$828$		0			0
$829$			41.0401i			1.42538i	0.701478	+	0.712691i	$0.252524\pi$
$829$			41.0401i			1.42538i	−0.701478	+	0.712691i	$0.747476\pi$
$830$		0			0
$831$	28.4266	+	8.34681i	0.986109	+	0.289548i
$832$		0			0
$833$	28.3019	+	6.15671i	0.980604	+	0.213317i
$834$		0			0
$835$	−5.79298	−	11.7643i	−0.200474	−	0.407120i
$836$		0			0
$837$	−1.45587	−	6.69253i	−0.0503222	−	0.231328i
$838$		0			0
$839$	−5.73657	−	12.5613i	−0.198048	−	0.433665i	0.784386	−	0.620273i	$-0.212978\pi$
$839$	−5.73657	−	12.5613i	−0.198048	−	0.433665i	−0.982435	+	0.186607i	$0.940251\pi$
$840$		0			0
$841$	5.41644	+	37.6721i	0.186774	+	1.29904i
$842$		0			0
$843$	39.0768	+	21.3375i	1.34588	+	0.734904i
$844$		0			0
$845$	22.6457	−	18.0063i	0.779035	−	0.619436i
$846$		0			0
$847$	9.16671	+	0.655616i	0.314972	+	0.0225272i
$848$		0			0
$849$	−12.1530	+	26.6113i	−0.417089	+	0.913297i
$850$		0			0
$851$	−0.291231	−	0.723824i	−0.00998328	−	0.0248124i
$852$		0			0
$853$	14.3439	+	38.4575i	0.491126	+	1.31676i	0.912204	+	0.409736i	$0.134379\pi$
$853$	14.3439	+	38.4575i	0.491126	+	1.31676i	−0.421078	+	0.907025i	$0.638348\pi$
$854$		0			0
$855$	−15.7008	−	26.8606i	−0.536955	−	0.918612i
$856$		0			0
$857$	−18.3066	+	1.30932i	−0.625342	+	0.0447254i	−0.380415	−	0.924816i	$-0.624219\pi$
$857$	−18.3066	+	1.30932i	−0.625342	+	0.0447254i	−0.244928	+	0.969541i	$0.578764\pi$
$858$		0			0
$859$	12.3679	+	42.1211i	0.421987	+	1.43715i	0.846818	+	0.531882i	$0.178515\pi$
$859$	12.3679	+	42.1211i	0.421987	+	1.43715i	−0.424832	+	0.905272i	$0.639667\pi$
$860$		0			0
$861$	2.67081	−	0.384005i	0.0910210	−	0.0130868i
$862$		0			0
$863$	7.52030	+	2.80493i	0.255994	+	0.0954808i	0.474185	−	0.880425i	$-0.342743\pi$
$863$	7.52030	+	2.80493i	0.255994	+	0.0954808i	−0.218191	+	0.975906i	$0.570016\pi$
$864$		0			0
$865$	1.12128	+	38.4329i	0.0381248	+	1.30676i
$866$		0			0
$867$	34.9280	−	26.1468i	1.18622	−	0.887990i
$868$		0			0
$869$	15.7518	+	24.5104i	0.534345	+	0.831457i
$870$		0			0
$871$	−0.446077	+	1.51920i	−0.0151147	+	0.0514761i
$872$		0			0
$873$	−1.94063	−	1.94063i	−0.0656804	−	0.0656804i
$874$		0			0
$875$	3.76380	+	16.0531i	0.127240	+	0.542692i
$876$		0			0
$877$	1.85138	+	3.39055i	0.0625167	+	0.114491i	0.907068	−	0.420983i	$-0.138315\pi$
$877$	1.85138	+	3.39055i	0.0625167	+	0.114491i	−0.844552	+	0.535474i	$0.820133\pi$
$878$		0			0
$879$	46.6782	−	29.9982i	1.57442	−	1.01182i
$880$		0			0
$881$	41.9629	+	6.03336i	1.41377	+	0.203269i	0.806502	−	0.591231i	$-0.201358\pi$
$881$	41.9629	+	6.03336i	1.41377	+	0.203269i	0.607264	+	0.794500i	$0.292267\pi$
$882$		0			0
$883$	−39.5988	+	8.61419i	−1.33261	+	0.289891i	−0.821785	−	0.569797i	$-0.807022\pi$
$883$	−39.5988	+	8.61419i	−1.33261	+	0.289891i	−0.510820	+	0.859688i	$0.670658\pi$
$884$		0			0
$885$	44.1129	+	26.5645i	1.48284	+	0.892957i
$886$		0			0
$887$	−18.4009	+	24.5808i	−0.617843	+	0.825342i	−0.994902	−	0.100848i	$-0.967845\pi$
$887$	−18.4009	+	24.5808i	−0.617843	+	0.825342i	0.377059	+	0.926189i	$0.376935\pi$
$888$		0			0
$889$	12.3830	−	3.63597i	0.415312	−	0.121947i
$890$		0			0
$891$	−17.6261	−	15.2731i	−0.590498	−	0.511669i
$892$		0			0
$893$	−0.438033	+	6.12450i	−0.0146582	+	0.204949i
$894$		0			0
$895$	−21.8323	+	31.0101i	−0.729774	+	1.03655i
$896$		0			0
$897$	−0.0694699	−	2.72028i	−0.00231953	−	0.0908275i
$898$		0			0
$899$	−29.8601	−	13.6366i	−0.995889	−	0.454807i
$900$		0			0
$901$	13.1684	+	15.1972i	0.438703	+	0.506291i
$902$		0			0
$903$	−1.84306	−	25.7693i	−0.0613331	−	0.857548i
$904$		0			0
$905$	−50.5162	+	5.09745i	−1.67922	+	0.169445i
$906$		0			0
$907$	−44.0916	−	33.0066i	−1.46404	−	1.09597i	−0.974607	−	0.223924i	$-0.928113\pi$
$907$	−44.0916	−	33.0066i	−1.46404	−	1.09597i	−0.489432	−	0.872042i	$-0.662796\pi$
$908$		0			0
$909$	1.12749	−	0.514907i	0.0373965	−	0.0170784i
$910$		0			0
$911$	−2.81195	+	4.37548i	−0.0931641	+	0.144966i	−0.884707	−	0.466147i	$-0.845642\pi$
$911$	−2.81195	+	4.37548i	−0.0931641	+	0.144966i	0.791543	+	0.611113i	$0.209278\pi$
$912$		0			0
$913$	15.6984	+	20.9706i	0.519542	+	0.694026i
$914$		0			0
$915$	−22.7037	+	53.8144i	−0.750560	+	1.77905i
$916$		0			0
$917$	−8.26274	+	4.51180i	−0.272860	+	0.148993i
$918$		0			0
$919$	35.0195			1.15519			0.577594	−	0.816324i	$-0.303992\pi$
$919$	35.0195			1.15519			0.577594	+	0.816324i	$0.303992\pi$
$920$		0			0
$921$	45.1532			1.48785
$922$		0			0
$923$	−1.41348	+	0.771816i	−0.0465251	+	0.0254046i
$924$		0			0
$925$	0.448678	−	0.678498i	0.0147524	−	0.0223089i
$926$		0			0
$927$	25.3147	+	33.8164i	0.831442	+	1.11068i
$928$		0			0
$929$	−10.5682	+	16.4445i	−0.346732	+	0.539525i	−0.970194	−	0.242328i	$-0.922089\pi$
$929$	−10.5682	+	16.4445i	−0.346732	+	0.539525i	0.623462	+	0.781853i	$0.285725\pi$
$930$		0			0
$931$	−27.0860	+	12.3697i	−0.887707	+	0.405402i
$932$		0			0
$933$	27.9991	+	20.9599i	0.916651	+	0.686196i
$934$		0			0
$935$	18.5402	−	22.7018i	0.606330	−	0.742430i
$936$		0			0
$937$	2.18999	+	30.6201i	0.0715439	+	1.00031i	0.898763	+	0.438435i	$0.144467\pi$
$937$	2.18999	+	30.6201i	0.0715439	+	1.00031i	−0.827219	+	0.561879i	$0.810079\pi$
$938$		0			0
$939$	−29.3973	−	33.9262i	−0.959343	−	1.10714i
$940$		0			0
$941$	8.72687	+	3.98543i	0.284488	+	0.129921i	0.552548	−	0.833481i	$-0.313655\pi$
$941$	8.72687	+	3.98543i	0.284488	+	0.129921i	−0.268061	+	0.963402i	$0.586383\pi$
$942$		0			0
$943$	2.57975	+	2.82796i	0.0840082	+	0.0920912i
$944$		0			0
$945$	−4.60708	−	3.24356i	−0.149868	−	0.105513i
$946$		0			0
$947$	−3.14952	+	44.0360i	−0.102345	+	1.43098i	0.643800	+	0.765194i	$0.277357\pi$
$947$	−3.14952	+	44.0360i	−0.102345	+	1.43098i	−0.746145	+	0.665783i	$0.768098\pi$
$948$		0			0
$949$	−1.48980	−	1.29092i	−0.0483610	−	0.0419051i
$950$		0			0
$951$	−73.4757	+	21.5744i	−2.38261	+	0.699598i
$952$		0			0
$953$	28.3936	−	37.9294i	0.919760	−	1.22866i	−0.0534115	−	0.998573i	$-0.517009\pi$
$953$	28.3936	−	37.9294i	0.919760	−	1.22866i	0.973171	−	0.230082i	$-0.0738996\pi$
$954$		0			0
$955$	−4.28393	−	17.2539i	−0.138625	−	0.558324i
$956$		0			0
$957$	−40.0543	+	8.71328i	−1.29477	+	0.281660i
$958$		0			0
$959$	−18.4411	−	2.65143i	−0.595493	−	0.0856190i
$960$		0			0
$961$	−12.5607	+	8.07230i	−0.405185	+	0.260397i
$962$		0			0
$963$	14.6511	+	26.8314i	0.472124	+	0.864631i
$964$		0			0
$965$	−17.7209	−	25.8823i	−0.570456	−	0.833180i
$966$		0			0
$967$	−29.6971	−	29.6971i	−0.954993	−	0.954993i	0.0440368	−	0.999030i	$-0.485978\pi$
$967$	−29.6971	−	29.6971i	−0.954993	−	0.954993i	−0.999030	+	0.0440368i	$0.985978\pi$
$968$		0			0
$969$	−23.9242	+	81.4783i	−0.768556	+	2.61746i
$970$		0			0
$971$	−22.8501	−	35.5555i	−0.733295	−	1.14103i	−0.984887	−	0.173196i	$-0.944591\pi$
$971$	−22.8501	−	35.5555i	−0.733295	−	1.14103i	0.251592	−	0.967833i	$-0.419046\pi$
$972$		0			0
$973$	0.992987	−	0.743341i	0.0318337	−	0.0238304i
$974$		0			0
$975$	2.29317	−	1.67034i	0.0734401	−	0.0534937i
$976$		0			0
$977$	−18.2796	−	6.81792i	−0.584815	−	0.218125i	0.0396025	−	0.999216i	$-0.487391\pi$
$977$	−18.2796	−	6.81792i	−0.584815	−	0.218125i	−0.624417	+	0.781091i	$0.714664\pi$
$978$		0			0
$979$	−3.75522	+	0.539920i	−0.120017	+	0.0172559i
$980$		0			0
$981$	−6.42575	−	21.8841i	−0.205158	−	0.698706i
$982$		0			0
$983$	30.0743	−	2.15096i	0.959222	−	0.0686049i	0.417060	−	0.908879i	$-0.363060\pi$
$983$	30.0743	−	2.15096i	0.959222	−	0.0686049i	0.542162	+	0.840274i	$0.317606\pi$
$984$		0			0
$985$	−13.2734	−	3.48036i	−0.422927	−	0.110894i
$986$		0			0
$987$	−1.17544	−	3.15148i	−0.0374147	−	0.100313i
$988$		0			0
$989$	28.7699	−	22.7057i	0.914831	−	0.721999i
$990$		0			0
$991$	6.48741	−	14.2054i	0.206079	−	0.451251i	−0.778166	−	0.628059i	$-0.783850\pi$
$991$	6.48741	−	14.2054i	0.206079	−	0.451251i	0.984245	+	0.176808i	$0.0565771\pi$
$992$		0			0
$993$	−18.0665	−	1.29214i	−0.573322	−	0.0410048i
$994$		0			0
$995$	19.1943	+	24.1398i	0.608500	+	0.765282i
$996$		0			0
$997$	51.0557	+	27.8785i	1.61695	+	0.882922i	0.995001	+	0.0998661i	$0.0318415\pi$
$997$	51.0557	+	27.8785i	1.61695	+	0.882922i	0.621951	+	0.783056i	$0.286340\pi$
$998$		0			0
$999$	0.0395582	+	0.275133i	0.00125157	+	0.00870484i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bv.a.17.6	✓	720
5.3	odd	4	inner	920.2.bv.a.753.6	yes	720
23.19	odd	22	inner	920.2.bv.a.617.6	yes	720
115.88	even	44	inner	920.2.bv.a.433.6	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.17.6	✓	720	1.1	even	1	trivial
920.2.bv.a.433.6	yes	720	115.88	even	44	inner
920.2.bv.a.617.6	yes	720	23.19	odd	22	inner
920.2.bv.a.753.6	yes	720	5.3	odd	4	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:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bv (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.01190 + 1.09858i) q^{3} +(0.842192 + 2.07140i) q^{5} +(-0.883794 - 1.18061i) q^{7} +(1.21895 - 1.89673i) q^{9} +(-1.98634 + 0.907130i) q^{11} +(0.198154 + 0.148336i) q^{13} +(-3.97002 - 3.24225i) q^{15} +(0.428234 + 5.98749i) q^{17} +(-4.04133 - 4.66394i) q^{19} +(3.07511 + 1.40435i) q^{21} +(0.803484 + 4.72805i) q^{23} +(-3.58143 + 3.48904i) q^{25} +(0.121889 - 1.70423i) q^{27} +(-6.18882 - 5.36265i) q^{29} +(3.84624 - 1.12936i) q^{31} +(2.99976 - 4.00721i) q^{33} +(1.70120 - 2.82500i) q^{35} +(-0.158968 + 0.0345815i) q^{37} +(-0.561627 - 0.0807498i) q^{39} +(0.671458 - 0.431520i) q^{41} +(-3.66249 - 6.70736i) q^{43} +(4.95548 + 0.927535i) q^{45} +(-0.703539 - 0.703539i) q^{47} +(1.35938 - 4.62962i) q^{49} +(-7.43933 - 11.5758i) q^{51} +(2.68173 - 2.00752i) q^{53} +(-3.55191 - 3.35053i) q^{55} +(13.2545 + 4.94367i) q^{57} +(-9.94388 + 1.42971i) q^{59} +(-3.21033 - 10.9334i) q^{61} +(-3.31660 + 0.237208i) q^{63} +(-0.140381 + 0.535385i) q^{65} +(2.23540 + 5.99335i) q^{67} +(-6.81068 - 8.62968i) q^{69} +(-2.70281 + 5.91832i) q^{71} +(-7.94370 - 0.568145i) q^{73} +(3.37249 - 10.9541i) q^{75} +(2.82648 + 1.54337i) q^{77} +(-1.89883 - 13.2066i) q^{79} +(4.43685 + 9.71534i) q^{81} +(-2.54996 - 11.7220i) q^{83} +(-12.0419 + 5.92966i) q^{85} +(18.3426 + 3.99020i) q^{87} +(1.66699 + 0.489473i) q^{89} -0.365042i q^{91} +(-6.49758 + 6.49758i) q^{93} +(6.25734 - 12.2992i) q^{95} +(0.258745 - 1.18943i) q^{97} +(-0.700673 + 4.87329i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) \) 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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