LMFDB - Embedded newform 639.2.z.a.53.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [639,2,Mod(35,639)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(639, base_ring=CyclotomicField(70))

chi = DirichletCharacter(H, H._module([35, 29]))

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

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

chi := DirichletCharacter("639.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 639 = 3^{2} \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	639.z (of order $70$, degree $24$, 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:	$5.10244068916$
Analytic rank:	$0$
Dimension:	$576$
Relative dimension:	$24$ over $\Q(\zeta_{70})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{70}]$

Embedding invariants

Embedding label			53.15
Character	$\chi$	$=$	639.53
Dual form			639.2.z.a.422.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0602976 + 0.669962i) q^{2} +(1.52265 - 0.276320i) q^{4} +(2.37308 - 3.26627i) q^{5} +(-2.27890 - 3.81424i) q^{7} +(0.634845 + 2.30031i) q^{8} +O(q^{10})$	\(q+(0.0602976 + 0.669962i) q^{2} +(1.52265 - 0.276320i) q^{4} +(2.37308 - 3.26627i) q^{5} +(-2.27890 - 3.81424i) q^{7} +(0.634845 + 2.30031i) q^{8} +(2.33137 + 1.39293i) q^{10} +(-1.61425 + 2.44549i) q^{11} +(0.650605 - 0.429461i) q^{13} +(2.41798 - 1.75677i) q^{14} +(1.39484 - 0.523491i) q^{16} +(0.299273 - 0.921067i) q^{17} +(-2.84712 - 2.97785i) q^{19} +(2.71083 - 5.62910i) q^{20} +(-1.73572 - 0.934031i) q^{22} +(1.15669 + 5.06778i) q^{23} +(-3.49191 - 10.7470i) q^{25} +(0.326952 + 0.409985i) q^{26} +(-4.52392 - 5.17804i) q^{28} +(-3.39402 + 1.82640i) q^{29} +(-0.455852 + 1.21461i) q^{31} +(2.50558 + 5.20290i) q^{32} +(0.635125 + 0.144963i) q^{34} +(-17.8664 - 1.60800i) q^{35} +(-0.180026 + 0.788747i) q^{37} +(1.82337 - 2.08702i) q^{38} +(9.01997 + 3.38525i) q^{40} +(4.41208 - 5.53257i) q^{41} +(9.31912 - 8.14187i) q^{43} +(-1.78220 + 4.16966i) q^{44} +(-3.32547 + 1.08051i) q^{46} +(1.27122 + 9.38455i) q^{47} +(-6.03797 + 11.2204i) q^{49} +(6.98951 - 2.98746i) q^{50} +(0.871973 - 0.833692i) q^{52} +(7.74032 + 1.40466i) q^{53} +(4.15687 + 11.0759i) q^{55} +(7.32719 - 7.66364i) q^{56} +(-1.42827 - 2.16374i) q^{58} +(-0.0589308 - 1.31220i) q^{59} +(1.09992 - 1.84096i) q^{61} +(-0.841231 - 0.232165i) q^{62} +(-0.776765 + 0.464096i) q^{64} +(0.141206 - 3.14420i) q^{65} +(2.90803 + 16.0246i) q^{67} +(0.201178 - 1.48515i) q^{68} -12.0667i q^{70} +(5.91886 + 5.99726i) q^{71} +(12.9928 - 1.16937i) q^{73} +(-0.539286 - 0.0730512i) q^{74} +(-5.15799 - 3.74750i) q^{76} +(13.0064 + 0.584119i) q^{77} +(-8.89736 + 2.45552i) q^{79} +(1.60020 - 5.79820i) q^{80} +(3.97265 + 2.62232i) q^{82} +(-1.99877 + 0.0897650i) q^{83} +(-2.29825 - 3.16328i) q^{85} +(6.01666 + 5.75252i) q^{86} +(-6.65018 - 2.16078i) q^{88} +(2.46092 - 13.5608i) q^{89} +(-3.12074 - 1.50287i) q^{91} +(3.16155 + 7.39682i) q^{92} +(-6.21064 + 1.41754i) q^{94} +(-16.4829 + 2.23276i) q^{95} +(-11.4671 + 9.14467i) q^{97} +(-7.88133 - 3.36864i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 576 q - 24 q^{4}+O(q^{10}) $ 576 * q - 24 * q^4	$ 576 q - 24 q^{4} - 16 q^{10} + 76 q^{16} - 8 q^{19} + 20 q^{22} + 168 q^{25} - 20 q^{28} - 28 q^{31} + 40 q^{37} + 32 q^{40} + 52 q^{43} - 20 q^{46} - 208 q^{52} - 92 q^{55} + 56 q^{58} + 56 q^{61} - 144 q^{64} - 16 q^{67} - 44 q^{73} - 336 q^{76} + 88 q^{79} - 124 q^{82} + 60 q^{85} - 260 q^{88} + 80 q^{91} + 56 q^{94} - 56 q^{97}+O(q^{100}) $ 576 * q - 24 * q^4 - 16 * q^10 + 76 * q^16 - 8 * q^19 + 20 * q^22 + 168 * q^25 - 20 * q^28 - 28 * q^31 + 40 * q^37 + 32 * q^40 + 52 * q^43 - 20 * q^46 - 208 * q^52 - 92 * q^55 + 56 * q^58 + 56 * q^61 - 144 * q^64 - 16 * q^67 - 44 * q^73 - 336 * q^76 + 88 * q^79 - 124 * q^82 + 60 * q^85 - 260 * q^88 + 80 * q^91 + 56 * q^94 - 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/639\mathbb{Z}\right)^\times$.

$n$	$433$	$569$
$\chi(n)$	$e\left(\frac{23}{70}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.0602976	+	0.669962i	0.0426369	+	0.473734i	0.988716	+	0.149800i	$0.0478629\pi$
$2$	0.0602976	+	0.669962i	0.0426369	+	0.473734i	−0.946079	+	0.323935i	$0.894994\pi$
$3$		0			0
$3$		0			0
$4$	1.52265	−	0.276320i	0.761323	−	0.138160i
$5$	2.37308	−	3.26627i	1.06128	−	1.46072i	0.182668	−	0.983175i	$-0.441527\pi$
$5$	2.37308	−	3.26627i	1.06128	−	1.46072i	0.878607	−	0.477545i	$-0.158473\pi$
$6$		0			0
$7$	−2.27890	−	3.81424i	−0.861345	−	1.44165i	−0.896877	−	0.442280i	$-0.854170\pi$
$7$	−2.27890	−	3.81424i	−0.861345	−	1.44165i	0.0355322	−	0.999369i	$-0.488687\pi$
$8$	0.634845	+	2.30031i	0.224452	+	0.813283i
$9$		0			0
$10$	2.33137	+	1.39293i	0.737243	+	0.440482i
$11$	−1.61425	+	2.44549i	−0.486716	+	0.737343i	−0.992086	−	0.125560i	$-0.959927\pi$
$11$	−1.61425	+	2.44549i	−0.486716	+	0.737343i	0.505370	+	0.862903i	$0.331356\pi$
$12$		0			0
$13$	0.650605	−	0.429461i	0.180445	−	0.119111i	−0.457446	−	0.889238i	$-0.651236\pi$
$13$	0.650605	−	0.429461i	0.180445	−	0.119111i	0.637891	+	0.770127i	$0.279807\pi$
$14$	2.41798	−	1.75677i	0.646233	−	0.469516i
$15$		0			0
$16$	1.39484	−	0.523491i	0.348709	−	0.130873i
$17$	0.299273	−	0.921067i	0.0725843	−	0.223392i	−0.908183	−	0.418574i	$-0.862530\pi$
$17$	0.299273	−	0.921067i	0.0725843	−	0.223392i	0.980767	+	0.195183i	$0.0625300\pi$
$18$		0			0
$19$	−2.84712	−	2.97785i	−0.653173	−	0.683166i	0.310401	−	0.950606i	$-0.399537\pi$
$19$	−2.84712	−	2.97785i	−0.653173	−	0.683166i	−0.963575	+	0.267440i	$0.913822\pi$
$20$	2.71083	−	5.62910i	0.606161	−	1.25871i
$21$		0			0
$22$	−1.73572	−	0.934031i	−0.370057	−	0.199136i
$23$	1.15669	+	5.06778i	0.241186	+	1.05671i	0.939939	+	0.341342i	$0.110882\pi$
$23$	1.15669	+	5.06778i	0.241186	+	1.05671i	−0.698753	+	0.715363i	$0.746261\pi$
$24$		0			0
$25$	−3.49191	−	10.7470i	−0.698381	−	2.14940i
$26$	0.326952	+	0.409985i	0.0641206	+	0.0804047i
$27$		0			0
$28$	−4.52392	−	5.17804i	−0.854940	−	0.978557i
$29$	−3.39402	+	1.82640i	−0.630254	+	0.339154i	−0.757615	−	0.652702i	$-0.773635\pi$
$29$	−3.39402	+	1.82640i	−0.630254	+	0.339154i	0.127360	+	0.991857i	$0.459350\pi$
$30$		0			0
$31$	−0.455852	+	1.21461i	−0.0818735	+	0.218151i	−0.970796	−	0.239906i	$-0.922883\pi$
$31$	−0.455852	+	1.21461i	−0.0818735	+	0.218151i	0.888923	+	0.458058i	$0.151455\pi$
$32$	2.50558	+	5.20290i	0.442929	+	0.919751i
$33$		0			0
$34$	0.635125	+	0.144963i	0.108923	+	0.0248610i
$35$	−17.8664	−	1.60800i	−3.01997	−	0.271802i
$36$		0			0
$37$	−0.180026	+	0.788747i	−0.0295962	+	0.129669i	−0.987568	−	0.157194i	$-0.949755\pi$
$37$	−0.180026	+	0.788747i	−0.0295962	+	0.129669i	0.957972	+	0.286863i	$0.0926124\pi$
$38$	1.82337	−	2.08702i	0.295790	−	0.338559i
$39$		0			0
$40$	9.01997	+	3.38525i	1.42618	+	0.535256i
$41$	4.41208	−	5.53257i	0.689050	−	0.864042i	−0.307102	−	0.951677i	$-0.599359\pi$
$41$	4.41208	−	5.53257i	0.689050	−	0.864042i	0.996153	+	0.0876346i	$0.0279308\pi$
$42$		0			0
$43$	9.31912	−	8.14187i	1.42115	−	1.24162i	0.492686	−	0.870207i	$-0.336015\pi$
$43$	9.31912	−	8.14187i	1.42115	−	1.24162i	0.928466	−	0.371417i	$-0.121128\pi$
$44$	−1.78220	+	4.16966i	−0.268677	+	0.628601i
$45$		0			0
$46$	−3.32547	+	1.08051i	−0.490314	+	0.159313i
$47$	1.27122	+	9.38455i	0.185427	+	1.36888i	0.809320	+	0.587368i	$0.199836\pi$
$47$	1.27122	+	9.38455i	0.185427	+	1.36888i	−0.623893	+	0.781510i	$0.714450\pi$
$48$		0			0
$49$	−6.03797	+	11.2204i	−0.862567	+	1.60292i
$50$	6.98951	−	2.98746i	0.988466	−	0.422491i
$51$		0			0
$52$	0.871973	−	0.833692i	0.120921	−	0.115612i
$53$	7.74032	+	1.40466i	1.06321	+	0.192945i	0.681859	−	0.731483i	$-0.261172\pi$
$53$	7.74032	+	1.40466i	1.06321	+	0.192945i	0.381355	+	0.924428i	$0.375457\pi$
$54$		0			0
$55$	4.15687	+	11.0759i	0.560512	+	1.49348i
$56$	7.32719	−	7.66364i	0.979137	−	1.02410i
$57$		0			0
$58$	−1.42827	−	2.16374i	−0.187541	−	0.284113i
$59$	−0.0589308	−	1.31220i	−0.00767213	−	0.170833i	−0.999171	−	0.0407161i	$-0.987036\pi$
$59$	−0.0589308	−	1.31220i	−0.00767213	−	0.170833i	0.991499	−	0.130117i	$-0.0415354\pi$
$60$		0			0
$61$	1.09992	−	1.84096i	0.140831	−	0.235711i	−0.779905	−	0.625898i	$-0.784733\pi$
$61$	1.09992	−	1.84096i	0.140831	−	0.235711i	0.920736	+	0.390187i	$0.127590\pi$
$62$	−0.841231	−	0.232165i	−0.106837	−	0.0294850i
$63$		0			0
$64$	−0.776765	+	0.464096i	−0.0970957	+	0.0580120i
$65$	0.141206	−	3.14420i	0.0175145	−	0.389990i
$66$		0			0
$67$	2.90803	+	16.0246i	0.355272	+	1.95771i	0.277428	+	0.960746i	$0.410518\pi$
$67$	2.90803	+	16.0246i	0.355272	+	1.95771i	0.0778443	+	0.996966i	$0.475196\pi$
$68$	0.201178	−	1.48515i	0.0243964	−	0.180101i
$69$		0			0
$70$		−	12.0667i		−	1.44225i
$71$	5.91886	+	5.99726i	0.702439	+	0.711744i
$71$	5.91886	+	5.99726i	0.702439	+	0.711744i
$72$		0			0
$73$	12.9928	−	1.16937i	1.52069	−	0.136864i	0.702445	−	0.711738i	$-0.252092\pi$
$73$	12.9928	−	1.16937i	1.52069	−	0.136864i	0.818242	+	0.574874i	$0.194949\pi$
$74$	−0.539286	−	0.0730512i	−0.0626907	−	0.00849203i
$75$		0			0
$76$	−5.15799	−	3.74750i	−0.591662	−	0.429868i
$77$	13.0064	+	0.584119i	1.48222	+	0.0665665i
$78$		0			0
$79$	−8.89736	+	2.45552i	−1.00103	+	0.276267i	−0.727881	−	0.685704i	$-0.759494\pi$
$79$	−8.89736	+	2.45552i	−1.00103	+	0.276267i	−0.273151	+	0.961971i	$0.588066\pi$
$80$	1.60020	−	5.79820i	0.178908	−	0.648258i
$81$		0			0
$82$	3.97265	+	2.62232i	0.438705	+	0.289587i
$83$	−1.99877	+	0.0897650i	−0.219394	+	0.00985299i	−0.154290	−	0.988026i	$-0.549309\pi$
$83$	−1.99877	+	0.0897650i	−0.219394	+	0.00985299i	−0.0651034	+	0.997879i	$0.520738\pi$
$84$		0			0
$85$	−2.29825	−	3.16328i	−0.249281	−	0.343105i
$86$	6.01666	+	5.75252i	0.648793	+	0.620310i
$87$		0			0
$88$	−6.65018	−	2.16078i	−0.708912	−	0.230339i
$89$	2.46092	−	13.5608i	0.260857	−	1.43744i	−0.541554	−	0.840666i	$-0.682164\pi$
$89$	2.46092	−	13.5608i	0.260857	−	1.43744i	0.802411	−	0.596772i	$-0.203550\pi$
$90$		0			0
$91$	−3.12074	−	1.50287i	−0.327142	−	0.157543i
$92$	3.16155	+	7.39682i	0.329615	+	0.771172i
$93$		0			0
$94$	−6.21064	+	1.41754i	−0.640579	+	0.146208i
$95$	−16.4829	+	2.23276i	−1.69111	+	0.229076i
$96$		0			0
$97$	−11.4671	+	9.14467i	−1.16430	+	0.928501i	−0.998338	−	0.0576311i	$-0.981645\pi$
$97$	−11.4671	+	9.14467i	−1.16430	+	0.928501i	−0.165965	+	0.986132i	$0.553074\pi$
$98$	−7.88133	−	3.36864i	−0.796134	−	0.340284i
$99$		0			0
$100$	−8.28654	−	15.3990i	−0.828654	−	1.53990i
$101$	−7.39974	−	5.90110i	−0.736302	−	0.587181i	0.181889	−	0.983319i	$-0.441779\pi$
$101$	−7.39974	−	5.90110i	−0.736302	−	0.587181i	−0.918191	+	0.396138i	$0.870350\pi$
$102$		0			0
$103$	7.89546	−	3.80225i	0.777963	−	0.374647i	−0.00238158	−	0.999997i	$-0.500758\pi$
$103$	7.89546	−	3.80225i	0.777963	−	0.374647i	0.780344	+	0.625350i	$0.215044\pi$
$104$	1.40093	+	1.22395i	0.137372	+	0.120018i
$105$		0			0
$106$	−0.474346	+	5.27042i	−0.0460726	+	0.511908i
$107$	−0.657737	+	7.30806i	−0.0635858	+	0.706497i	0.899432	+	0.437060i	$0.143980\pi$
$107$	−0.657737	+	7.30806i	−0.0635858	+	0.706497i	−0.963018	+	0.269436i	$0.913163\pi$
$108$		0			0
$109$	6.96411	+	6.08436i	0.667041	+	0.582776i	0.923416	−	0.383801i	$-0.125385\pi$
$109$	6.96411	+	6.08436i	0.667041	+	0.582776i	−0.256375	+	0.966577i	$0.582528\pi$
$110$	−7.16980	+	3.45280i	−0.683614	+	0.329211i
$111$		0			0
$112$	−5.17542	−	4.12726i	−0.489031	−	0.389989i
$113$	0.822070	+	1.52766i	0.0773338	+	0.143710i	0.916326	−	0.400433i	$-0.131140\pi$
$113$	0.822070	+	1.52766i	0.0773338	+	0.143710i	−0.838992	+	0.544144i	$0.816855\pi$
$114$		0			0
$115$	19.2977	+	8.24821i	1.79952	+	0.769150i
$116$	−4.66323	+	3.71880i	−0.432970	+	0.345282i
$117$		0			0
$118$	0.875568	−	0.118604i	0.0806025	−	0.0109184i
$119$	−4.19519	+	0.957525i	−0.384572	+	0.0877761i
$120$		0			0
$121$	0.948672	+	2.21953i	0.0862429	+	0.201775i
$122$	1.29970	+	0.625901i	0.117669	+	0.0566664i
$123$		0			0
$124$	−0.358480	+	1.97539i	−0.0321925	+	0.177395i
$125$	−24.1905	−	7.85996i	−2.16366	−	0.703016i
$126$		0			0
$127$	−0.749883	−	0.716961i	−0.0665413	−	0.0636200i	0.657059	−	0.753839i	$-0.271800\pi$
$127$	−0.749883	−	0.716961i	−0.0665413	−	0.0636200i	−0.723601	+	0.690219i	$0.757514\pi$
$128$	6.43090	+	8.85137i	0.568416	+	0.782358i
$129$		0			0
$130$	2.11501	−	0.0949851i	0.185498	−	0.00833074i
$131$	1.21112	+	0.799453i	0.105816	+	0.0698485i	0.602697	−	0.797970i	$-0.294093\pi$
$131$	1.21112	+	0.799453i	0.105816	+	0.0698485i	−0.496881	+	0.867819i	$0.665521\pi$
$132$		0			0
$133$	−4.86994	+	17.6458i	−0.422277	+	1.53009i
$134$	−10.5605	+	2.91451i	−0.912288	+	0.251775i
$135$		0			0
$136$	2.30873	+	0.103685i	0.197972	+	0.00889094i
$137$	−11.0096	−	7.99894i	−0.940613	−	0.683395i	0.00795500	−	0.999968i	$-0.497468\pi$
$137$	−11.0096	−	7.99894i	−0.940613	−	0.683395i	−0.948568	+	0.316573i	$0.897468\pi$
$138$		0			0
$139$	0.465643	+	0.0630756i	0.0394953	+	0.00535000i	0.153954	−	0.988078i	$-0.450799\pi$
$139$	0.465643	+	0.0630756i	0.0394953	+	0.00535000i	−0.114459	+	0.993428i	$0.536513\pi$
$140$	−27.6485	+	2.48841i	−2.33672	+	0.210309i
$141$		0			0
$142$	−3.66104	+	4.32703i	−0.307228	+	0.363116i
$143$			2.28431i			0.191023i
$144$		0			0
$145$	−2.08878	+	15.4200i	−0.173464	+	1.28056i
$146$	1.56687	+	8.63414i	0.129675	+	0.714567i
$147$		0			0
$148$	−0.0561703	+	1.25073i	−0.00461717	+	0.102809i
$149$	−8.41789	+	5.02945i	−0.689620	+	0.412029i	−0.814516	−	0.580141i	$-0.802997\pi$
$149$	−8.41789	+	5.02945i	−0.689620	+	0.412029i	0.124896	+	0.992170i	$0.460140\pi$
$150$		0			0
$151$	−1.19156	−	0.328849i	−0.0969675	−	0.0267613i	0.217216	−	0.976123i	$-0.430302\pi$
$151$	−1.19156	−	0.328849i	−0.0969675	−	0.0267613i	−0.314184	+	0.949362i	$0.601731\pi$
$152$	5.04250	−	8.43973i	0.409001	−	0.684552i
$153$		0			0
$154$	0.392919	+	8.74902i	0.0316623	+	0.705016i
$155$	2.88548	+	4.37132i	0.231767	+	0.351113i
$156$		0			0
$157$	12.4260	−	12.9966i	0.991703	−	1.03724i	−0.00760251	−	0.999971i	$-0.502420\pi$
$157$	12.4260	−	12.9966i	0.991703	−	1.03724i	0.999305	−	0.0372687i	$-0.0118657\pi$
$158$	−2.18159	−	5.81283i	−0.173558	−	0.462444i
$159$		0			0
$160$	22.9400	+	4.16300i	1.81357	+	0.329114i
$161$	16.6938	−	15.9609i	1.31565	−	1.25789i
$162$		0			0
$163$	−19.3538	+	8.27223i	−1.51591	+	0.647931i	−0.980475	−	0.196645i	$-0.936995\pi$
$163$	−19.3538	+	8.27223i	−1.51591	+	0.647931i	−0.535436	+	0.844576i	$0.679853\pi$
$164$	5.18927	−	9.64329i	0.405214	−	0.753014i
$165$		0			0
$166$	−0.180660	−	1.33369i	−0.0140220	−	0.103514i
$167$	−8.89683	+	2.89076i	−0.688458	+	0.223693i	−0.632294	−	0.774728i	$-0.717887\pi$
$167$	−8.89683	+	2.89076i	−0.688458	+	0.223693i	−0.0561631	+	0.998422i	$0.517887\pi$
$168$		0			0
$169$	−4.87047	+	11.3950i	−0.374652	+	0.876542i
$170$	1.98069	−	1.73048i	0.151912	−	0.132722i
$171$		0			0
$172$	11.9400	−	14.9722i	0.910414	−	1.14162i
$173$	18.3627	+	6.89164i	1.39609	+	0.523961i	0.932204	−	0.361933i	$-0.117883\pi$
$173$	18.3627	+	6.89164i	1.39609	+	0.523961i	0.463886	+	0.885895i	$0.346455\pi$
$174$		0			0
$175$	−33.0339	+	37.8103i	−2.49713	+	2.85819i
$176$	−0.971428	+	4.25610i	−0.0732241	+	0.320816i
$177$		0			0
$178$	9.23358	+	0.831037i	0.692086	+	0.0622889i
$179$	−10.0219	−	2.28743i	−0.749071	−	0.170971i	−0.169090	−	0.985601i	$-0.554083\pi$
$179$	−10.0219	−	2.28743i	−0.749071	−	0.170971i	−0.579981	+	0.814630i	$0.696940\pi$
$180$		0			0
$181$	−6.05105	−	12.5651i	−0.449771	−	0.933960i	−0.995389	−	0.0959253i	$-0.969419\pi$
$181$	−6.05105	−	12.5651i	−0.449771	−	0.933960i	0.545617	−	0.838035i	$-0.316295\pi$
$182$	0.818690	−	2.18139i	0.0606854	−	0.161696i
$183$		0			0
$184$	−10.9232	+	5.87800i	−0.805265	+	0.433332i
$185$	2.14904	+	2.45978i	0.158001	+	0.180847i
$186$		0			0
$187$	1.76936	+	2.21870i	0.129388	+	0.162248i
$188$	4.52876	+	13.9381i	0.330294	+	1.01654i
$189$		0			0
$190$	−2.48974	−	10.9083i	−0.180625	−	0.791370i
$191$	−13.6574	−	7.34937i	−0.988216	−	0.531782i	−0.101867	−	0.994798i	$-0.532481\pi$
$191$	−13.6574	−	7.34937i	−0.988216	−	0.531782i	−0.886350	+	0.463016i	$0.846767\pi$
$192$		0			0
$193$	10.8050	−	22.4368i	0.777762	−	1.61504i	−0.0106904	−	0.999943i	$-0.503403\pi$
$193$	10.8050	−	22.4368i	0.777762	−	1.61504i	0.788452	−	0.615096i	$-0.210883\pi$
$194$	−6.81801	−	7.13108i	−0.489505	−	0.511982i
$195$		0			0
$196$	−6.09327	+	18.7531i	−0.435233	+	1.33951i
$197$	−9.39679	+	3.52667i	−0.669493	+	0.251265i	−0.662894	−	0.748713i	$-0.730672\pi$
$197$	−9.39679	+	3.52667i	−0.669493	+	0.251265i	−0.00659924	+	0.999978i	$0.502101\pi$
$198$		0			0
$199$	11.6703	−	8.47894i	0.827283	−	0.601056i	−0.0915063	−	0.995805i	$-0.529168\pi$
$199$	11.6703	−	8.47894i	0.827283	−	0.601056i	0.918789	+	0.394748i	$0.129168\pi$
$200$	22.5046	−	14.8551i	1.59131	−	1.05042i
$201$		0			0
$202$	3.50732	−	5.31337i	0.246774	−	0.373847i
$203$	14.7010	+	8.78344i	1.03181	+	0.616476i
$204$		0			0
$205$	−7.60063	−	27.5403i	−0.530851	−	1.92350i
$206$	3.02344	+	5.06039i	0.210653	+	0.352574i
$207$		0			0
$208$	0.682669	−	0.939613i	0.0473346	−	0.0651504i
$209$	11.8783	−	2.15559i	0.821637	−	0.149105i
$210$		0			0
$211$	−0.241273	−	2.68076i	−0.0166099	−	0.184551i	−0.999995	−	0.00302171i	$-0.999038\pi$
$211$	−0.241273	−	2.68076i	−0.0166099	−	0.184551i	0.983386	−	0.181529i	$-0.0581047\pi$
$212$	12.1739			0.836107
$213$		0			0
$214$	−4.93578			−0.337403
$215$	−4.47849	−	49.7601i	−0.305431	−	3.39361i
$216$		0			0
$217$	5.67168	−	1.02926i	0.385018	−	0.0698705i
$218$	−3.65637	+	5.03256i	−0.247641	+	0.340848i
$219$		0			0
$220$	9.38994	+	15.7161i	0.633069	+	1.05958i
$221$	−0.200854	−	0.727777i	−0.0135109	−	0.0489556i
$222$		0			0
$223$	−15.7629	−	9.41789i	−1.05556	−	0.630668i	−0.123268	−	0.992373i	$-0.539338\pi$
$223$	−15.7629	−	9.41789i	−1.05556	−	0.630668i	−0.932293	+	0.361705i	$0.882195\pi$
$224$	14.1351	−	21.4138i	0.944443	−	1.43077i
$225$		0			0
$226$	−0.973906	+	0.642870i	−0.0647832	+	0.0427630i
$227$	11.2173	−	8.14984i	0.744518	−	0.540924i	−0.149605	−	0.988746i	$-0.547800\pi$
$227$	11.2173	−	8.14984i	0.744518	−	0.540924i	0.894123	+	0.447822i	$0.147800\pi$
$228$		0			0
$229$	−6.85867	+	2.57410i	−0.453234	+	0.170102i	−0.567543	−	0.823344i	$-0.692106\pi$
$229$	−6.85867	+	2.57410i	−0.453234	+	0.170102i	0.114309	+	0.993445i	$0.463535\pi$
$230$	−4.36238	+	13.4260i	−0.287647	+	0.885287i
$231$		0			0
$232$	−6.35597	−	6.64782i	−0.417290	−	0.436451i
$233$	−10.0325	+	20.8328i	−0.657254	+	1.36480i	0.259653	+	0.965702i	$0.416392\pi$
$233$	−10.0325	+	20.8328i	−0.657254	+	1.36480i	−0.916907	+	0.399100i	$0.869323\pi$
$234$		0			0
$235$	33.6692	+	18.1182i	2.19634	+	1.18190i
$236$	−0.452316	−	1.98173i	−0.0294433	−	0.128999i
$237$		0			0
$238$	−0.894465	−	2.75288i	−0.0579795	−	0.178443i
$239$	−11.2457	−	14.1017i	−0.727425	−	0.912162i	0.271308	−	0.962493i	$-0.412544\pi$
$239$	−11.2457	−	14.1017i	−0.727425	−	0.912162i	−0.998733	+	0.0503306i	$0.983972\pi$
$240$		0			0
$241$	12.9185	+	14.7864i	0.832156	+	0.952479i	0.999441	−	0.0334297i	$-0.0106430\pi$
$241$	12.9185	+	14.7864i	0.832156	+	0.952479i	−0.167285	+	0.985909i	$0.553500\pi$
$242$	−1.42980	+	0.769406i	−0.0919108	+	0.0494593i
$243$		0			0
$244$	1.16610	−	3.10707i	0.0746520	−	0.198910i
$245$	22.3203	+	46.3486i	1.42599	+	2.96111i
$246$		0			0
$247$	−3.13122	−	0.714680i	−0.199235	−	0.0454740i
$248$	−3.08338	−	0.277510i	−0.195795	−	0.0176219i
$249$		0			0
$250$	3.80724	−	16.6806i	0.240791	−	1.05497i
$251$	−17.1981	+	19.6848i	−1.08554	+	1.24250i	−0.117129	+	0.993117i	$0.537369\pi$
$251$	−17.1981	+	19.6848i	−1.08554	+	1.24250i	−0.968406	+	0.249378i	$0.919774\pi$
$252$		0			0
$253$	−14.2604	−	5.35201i	−0.896543	−	0.336478i
$254$	0.435121	−	0.545624i	0.0273019	−	0.0342355i
$255$		0			0
$256$	−6.90514	+	6.03284i	−0.431571	+	0.377052i
$257$	−7.35777	+	17.2144i	−0.458965	+	1.07380i	0.517022	+	0.855972i	$0.327041\pi$
$257$	−7.35777	+	17.2144i	−0.458965	+	1.07380i	−0.975987	+	0.217830i	$0.930102\pi$
$258$		0			0
$259$	3.41874	−	1.11082i	0.212430	−	0.0690227i
$260$	−0.653797	−	4.82652i	−0.0405467	−	0.299328i
$261$		0			0
$262$	−0.462575	+	0.859609i	−0.0285780	+	0.0531068i
$263$	−4.78714	+	2.04612i	−0.295188	+	0.126169i	−0.535523	−	0.844521i	$-0.679885\pi$
$263$	−4.78714	+	2.04612i	−0.295188	+	0.126169i	0.240335	+	0.970690i	$0.422743\pi$
$264$		0			0
$265$	22.9564	−	21.9486i	1.41020	−	1.34829i
$266$	−12.1157	−	2.19867i	−0.742860	−	0.134809i
$267$		0			0
$268$	8.85580	+	23.5962i	0.540954	+	1.44137i
$269$	−11.2302	+	11.7458i	−0.684714	+	0.716155i	−0.970221	−	0.242222i	$-0.922124\pi$
$269$	−11.2302	+	11.7458i	−0.684714	+	0.716155i	0.285506	+	0.958377i	$0.407838\pi$
$270$		0			0
$271$	−10.0185	−	15.1774i	−0.608582	−	0.921962i	−0.999998	−	0.00174819i	$-0.999444\pi$
$271$	−10.0185	−	15.1774i	−0.608582	−	0.921962i	0.391417	−	0.920213i	$-0.371985\pi$
$272$	−0.0647335	−	1.44140i	−0.00392505	−	0.0873980i
$273$		0			0
$274$	4.69513	−	7.85832i	0.283643	−	0.474739i
$275$	31.9184	+	8.80893i	1.92475	+	0.531198i
$276$		0			0
$277$	4.22077	−	2.52180i	0.253602	−	0.151520i	−0.380472	−	0.924792i	$-0.624239\pi$
$277$	4.22077	−	2.52180i	0.253602	−	0.151520i	0.634074	+	0.773272i	$0.281381\pi$
$278$	−0.0141811	+	0.315766i	−0.000850524	+	0.0189384i
$279$		0			0
$280$	−7.64348	−	42.1190i	−0.456785	−	2.51709i
$281$	1.40905	−	10.4020i	0.0840566	−	0.620531i	−0.899097	−	0.437750i	$-0.855776\pi$
$281$	1.40905	−	10.4020i	0.0840566	−	0.620531i	0.983154	−	0.182781i	$-0.0585101\pi$
$282$		0			0
$283$			1.54467i			0.0918213i	0.998946	+	0.0459106i	$0.0146189\pi$
$283$			1.54467i			0.0918213i	−0.998946	+	0.0459106i	$0.985381\pi$
$284$	10.6695	+	7.49621i	0.633117	+	0.444818i
$285$		0			0
$286$	−1.53040	+	0.137738i	−0.0904943	+	0.00814464i
$287$	−31.1573	−	4.22054i	−1.83915	−	0.249130i
$288$		0			0
$289$	12.9945	+	9.44105i	0.764382	+	0.555356i
$290$	−10.4568	−	0.469613i	−0.614042	−	0.0275767i
$291$		0			0
$292$	19.4603	−	5.37069i	1.13883	−	0.314296i
$293$	−0.173785	+	0.629695i	−0.0101526	+	0.0367872i	−0.968864	−	0.247595i	$-0.920360\pi$
$293$	−0.173785	+	0.629695i	−0.0101526	+	0.0367872i	0.958711	+	0.284382i	$0.0917884\pi$
$294$		0			0
$295$	−4.42583	−	2.92147i	−0.257682	−	0.170094i
$296$	−1.92865	+	0.0866159i	−0.112101	+	0.00503445i
$297$		0			0
$298$	−3.87712	−	5.33640i	−0.224596	−	0.309129i
$299$	2.92896	+	2.80037i	0.169386	+	0.161950i
$300$		0			0
$301$	−52.2925	−	16.9909i	−3.01409	−	0.979336i
$302$	0.148468	−	0.818126i	0.00854337	−	0.0470779i
$303$		0			0
$304$	−5.53014	−	2.66317i	−0.317175	−	0.152743i
$305$	−3.40287	−	7.96141i	−0.194848	−	0.455869i
$306$		0			0
$307$	−21.4536	+	4.89664i	−1.22442	+	0.279466i	−0.785388	−	0.619004i	$-0.787536\pi$
$307$	−21.4536	+	4.89664i	−1.22442	+	0.279466i	−0.439034	+	0.898471i	$0.644679\pi$
$308$	19.9656	−	2.70452i	1.13764	−	0.154104i
$309$		0			0
$310$	−2.75463	+	2.19674i	−0.156452	+	0.124767i
$311$	10.1917	+	4.35613i	0.577917	+	0.247014i	0.662073	−	0.749439i	$-0.269677\pi$
$311$	10.1917	+	4.35613i	0.577917	+	0.247014i	−0.0841565	+	0.996453i	$0.526820\pi$
$312$		0			0
$313$	5.90585	+	10.9749i	0.333819	+	0.620339i	0.991072	−	0.133331i	$-0.0425674\pi$
$313$	5.90585	+	10.9749i	0.333819	+	0.620339i	−0.657253	+	0.753670i	$0.728282\pi$
$314$	9.45647	+	7.54128i	0.533659	+	0.425579i
$315$		0			0
$316$	−12.8690	+	6.19740i	−0.723940	+	0.348631i
$317$	10.5238	+	9.19433i	0.591073	+	0.516405i	0.900693	−	0.434455i	$-0.143059\pi$
$317$	10.5238	+	9.19433i	0.591073	+	0.516405i	−0.309620	+	0.950860i	$0.600202\pi$
$318$		0			0
$319$	1.01237	−	11.2483i	0.0566817	−	0.629785i
$320$	−0.327468	+	3.63846i	−0.0183060	+	0.203396i
$321$		0			0
$322$	11.6998	+	10.2218i	0.652003	+	0.569638i
$323$	−3.59487	+	1.73120i	−0.200024	+	0.0963263i
$324$		0			0
$325$	−6.88726	−	5.49240i	−0.382036	−	0.304664i
$326$	−6.70907	−	12.4675i	−0.371581	−	0.690513i
$327$		0			0
$328$	15.5276	+	6.63682i	0.857369	+	0.366457i
$329$	32.8980	−	26.2353i	1.81372	−	1.44640i
$330$		0			0
$331$	13.2800	−	1.79890i	0.729935	−	0.0988764i	0.240170	−	0.970731i	$-0.422797\pi$
$331$	13.2800	−	1.79890i	0.729935	−	0.0988764i	0.489765	+	0.871854i	$0.337083\pi$
$332$	−3.01862	+	0.688981i	−0.165668	+	0.0378127i
$333$		0			0
$334$	−2.47315	−	5.78623i	−0.135325	−	0.316608i
$335$	59.2415	+	28.5292i	3.23671	+	1.55872i
$336$		0			0
$337$	−1.96560	+	10.8314i	−0.107073	+	0.590023i	0.885125	+	0.465353i	$0.154073\pi$
$337$	−1.96560	+	10.8314i	−0.107073	+	0.590023i	−0.992198	+	0.124669i	$0.960213\pi$
$338$	−7.92792	−	2.57594i	−0.431222	−	0.140113i
$339$		0			0
$340$	−4.37350	−	4.18150i	−0.237187	−	0.226774i
$341$	−2.23446	−	3.07548i	−0.121003	−	0.166546i
$342$		0			0
$343$	25.4864	−	1.14460i	1.37614	−	0.0618024i
$344$	24.6450	+	16.2680i	1.32877	+	0.877114i
$345$		0			0
$346$	−3.50991	+	12.7179i	−0.188694	+	0.683716i
$347$	11.9408	−	3.29546i	0.641018	−	0.176910i	0.0696077	−	0.997574i	$-0.477825\pi$
$347$	11.9408	−	3.29546i	0.641018	−	0.176910i	0.571410	+	0.820665i	$0.306397\pi$
$348$		0			0
$349$	−11.4655	−	0.514915i	−0.613733	−	0.0275628i	−0.264171	−	0.964476i	$-0.585098\pi$
$349$	−11.4655	−	0.514915i	−0.613733	−	0.0275628i	−0.349562	+	0.936913i	$0.613670\pi$
$350$	−27.3233	−	19.8516i	−1.46049	−	1.06111i
$351$		0			0
$352$	−16.7683	−	2.27142i	−0.893752	−	0.121067i
$353$	−0.809596	+	0.0728650i	−0.0430905	+	0.00387821i	−0.111164	−	0.993802i	$-0.535458\pi$
$353$	−0.809596	+	0.0728650i	−0.0430905	+	0.00387821i	0.0680731	+	0.997680i	$0.478315\pi$
$354$		0			0
$355$	33.6346	−	5.10057i	1.78514	−	0.270710i
$356$		−	21.3282i		−	1.13039i
$357$		0			0
$358$	0.928195	−	6.85221i	0.0490566	−	0.362151i
$359$	−1.07794	−	5.93992i	−0.0568914	−	0.313497i	0.942918	−	0.333025i	$-0.108069\pi$
$359$	−1.07794	−	5.93992i	−0.0568914	−	0.313497i	−0.999809	+	0.0195279i	$0.993784\pi$
$360$		0			0
$361$	0.0909112	−	2.02430i	0.00478480	−	0.106542i
$362$	8.05330	−	4.81162i	0.423272	−	0.252893i
$363$		0			0
$364$	−5.16705	−	1.42601i	−0.270827	−	0.0747435i
$365$	27.0134	−	45.2129i	1.41395	−	2.36655i
$366$		0			0
$367$	1.23800	+	27.5661i	0.0646229	+	1.43894i	0.725384	+	0.688344i	$0.241662\pi$
$367$	1.23800	+	27.5661i	0.0646229	+	1.43894i	−0.660761	+	0.750596i	$0.729767\pi$
$368$	4.26633	+	6.46321i	0.222398	+	0.336918i
$369$		0			0
$370$	−1.51838	+	1.58810i	−0.0789366	+	0.0825612i
$371$	−12.2817	−	32.7245i	−0.637636	−	1.69897i
$372$		0			0
$373$	−0.985511	−	0.178844i	−0.0510279	−	0.00926019i	0.152983	−	0.988229i	$-0.451112\pi$
$373$	−0.985511	−	0.178844i	−0.0510279	−	0.00926019i	−0.204011	+	0.978969i	$0.565398\pi$
$374$	−1.37976	+	1.31918i	−0.0713456	+	0.0682134i
$375$		0			0
$376$	−20.7804	+	8.88195i	−1.07166	+	0.458052i
$377$	−1.42380	+	2.64587i	−0.0733295	+	0.136269i
$378$		0			0
$379$	−0.861486	−	6.35975i	−0.0442516	−	0.326678i	−0.999521	−	0.0309419i	$-0.990149\pi$
$379$	−0.861486	−	6.35975i	−0.0442516	−	0.326678i	0.955270	−	0.295736i	$-0.0955650\pi$
$380$	−24.4807	+	7.95426i	−1.25583	+	0.408045i
$381$		0			0
$382$	4.10029	−	9.59310i	0.209789	−	0.490826i
$383$	8.64502	−	7.55292i	0.441740	−	0.385936i	−0.408135	−	0.912922i	$-0.633821\pi$
$383$	8.64502	−	7.55292i	0.441740	−	0.385936i	0.849874	+	0.526985i	$0.176678\pi$
$384$		0			0
$385$	32.7732	−	41.0963i	1.67028	−	2.09446i
$386$	15.6833	+	5.88606i	0.798261	+	0.299592i
$387$		0			0
$388$	−14.9334	+	17.0927i	−0.758129	+	0.867749i
$389$	−3.71933	+	16.2954i	−0.188577	+	0.826211i	0.788790	+	0.614663i	$0.210708\pi$
$389$	−3.71933	+	16.2954i	−0.188577	+	0.826211i	−0.977367	+	0.211549i	$0.932149\pi$
$390$		0			0
$391$	5.01393	+	0.451262i	0.253565	+	0.0228213i
$392$	−29.6436	−	6.76596i	−1.49723	−	0.341733i
$393$		0			0
$394$	−2.92934	−	6.08284i	−0.147578	−	0.306449i
$395$	−13.0938	+	34.8883i	−0.658821	+	1.75542i
$396$		0			0
$397$	−14.6272	+	7.87123i	−0.734118	+	0.395046i	−0.797798	−	0.602925i	$-0.794002\pi$
$397$	−14.6272	+	7.87123i	−0.734118	+	0.395046i	0.0636802	+	0.997970i	$0.479716\pi$
$398$	6.38426	+	7.30737i	0.320014	+	0.366285i
$399$		0			0
$400$	−10.4966	−	13.1623i	−0.524829	−	0.658115i
$401$	9.28528	+	28.5772i	0.463685	+	1.42708i	0.860629	+	0.509233i	$0.170071\pi$
$401$	9.28528	+	28.5772i	0.463685	+	1.42708i	−0.396944	+	0.917843i	$0.629929\pi$
$402$		0			0
$403$	0.225049	+	0.986005i	0.0112105	+	0.0491164i
$404$	−12.8978	−	6.94059i	−0.641688	−	0.345307i
$405$		0			0
$406$	−4.99813	+	10.3787i	−0.248053	+	0.515087i
$407$	−1.63826	−	1.71349i	−0.0812058	−	0.0849346i
$408$		0			0
$409$	11.5886	−	35.6662i	0.573021	−	1.76358i	−0.0697995	−	0.997561i	$-0.522236\pi$
$409$	11.5886	−	35.6662i	0.573021	−	1.76358i	0.642821	−	0.766017i	$-0.277764\pi$
$410$	17.9926	−	6.75275i	0.888593	−	0.333494i
$411$		0			0
$412$	10.9714	−	7.97116i	0.540520	−	0.392711i
$413$	−4.87074	+	3.21515i	−0.239673	+	0.158207i
$414$		0			0
$415$	−4.45006	+	6.74155i	−0.218445	+	0.330930i
$416$	3.86459	+	2.30898i	0.189477	+	0.113207i
$417$		0			0
$418$	2.16039	+	7.82801i	0.105668	+	0.382880i
$419$	−1.51953	−	2.54327i	−0.0742341	−	0.124247i	0.819081	−	0.573678i	$-0.194484\pi$
$419$	−1.51953	−	2.54327i	−0.0742341	−	0.124247i	−0.893315	+	0.449431i	$0.851627\pi$
$420$		0			0
$421$	2.66176	−	3.66360i	0.129726	−	0.178553i	−0.739213	−	0.673472i	$-0.764802\pi$
$421$	2.66176	−	3.66360i	0.129726	−	0.178553i	0.868939	+	0.494919i	$0.164802\pi$
$422$	1.78146	−	0.323287i	0.0867199	−	0.0157374i
$423$		0			0
$424$	1.68275	+	18.6969i	0.0817215	+	0.908001i
$425$	−10.9437			−0.530849
$426$		0			0
$427$	−9.52850			−0.461117
$428$	1.01786	+	11.3093i	0.0492000	+	0.546657i
$429$		0			0
$430$	33.0673	−	6.00083i	1.59465	−	0.289386i
$431$	20.2093	−	27.8157i	0.973447	−	1.33983i	0.0331603	−	0.999450i	$-0.489443\pi$
$431$	20.2093	−	27.8157i	0.973447	−	1.33983i	0.940286	−	0.340384i	$-0.110557\pi$
$432$		0			0
$433$	12.9856	+	21.7343i	0.624050	+	1.04448i	0.993346	+	0.115172i	$0.0367420\pi$
$433$	12.9856	+	21.7343i	0.624050	+	1.04448i	−0.369295	+	0.929312i	$0.620401\pi$
$434$	1.03155	+	3.73774i	0.0495161	+	0.179417i
$435$		0			0
$436$	12.2851	+	7.34001i	0.588350	+	0.351523i
$437$	11.7979	−	17.8730i	0.564368	−	0.854982i
$438$		0			0
$439$	−20.6921	+	13.6587i	−0.987581	+	0.651897i	−0.937913	−	0.346869i	$-0.887245\pi$
$439$	−20.6921	+	13.6587i	−0.987581	+	0.651897i	−0.0496676	+	0.998766i	$0.515816\pi$
$440$	−22.8391	+	16.5936i	−1.08881	+	0.791069i
$441$		0			0
$442$	0.475472	−	0.178448i	0.0226159	−	0.00848789i
$443$	−6.71458	+	20.6654i	−0.319019	+	0.981841i	0.655049	+	0.755587i	$0.272648\pi$
$443$	−6.71458	+	20.6654i	−0.319019	+	0.981841i	−0.974068	+	0.226254i	$0.927352\pi$
$444$		0			0
$445$	−38.4532	−	40.2188i	−1.82285	−	1.90656i
$446$	5.35916	−	11.1284i	0.253763	−	0.526945i
$447$		0			0
$448$	3.54035	+	1.90514i	0.167266	+	0.0900095i
$449$	−5.43997	−	23.8340i	−0.256728	−	1.12480i	−0.924725	−	0.380635i	$-0.875706\pi$
$449$	−5.43997	−	23.8340i	−0.256728	−	1.12480i	0.667998	−	0.744163i	$-0.267152\pi$
$450$		0			0
$451$	6.40763	+	19.7206i	0.301723	+	0.928609i
$452$	1.67384	+	2.09893i	0.0787310	+	0.0987256i
$453$		0			0
$454$	6.13646	+	7.02374i	0.287998	+	0.329641i
$455$	−12.3145	+	6.62673i	−0.577314	+	0.310666i
$456$		0			0
$457$	5.38103	−	14.3377i	0.251714	−	0.670689i	−0.748259	−	0.663406i	$-0.769110\pi$
$457$	5.38103	−	14.3377i	0.251714	−	0.670689i	0.999973	−	0.00728334i	$-0.00231838\pi$
$458$	−2.13811	−	4.43984i	−0.0999074	−	0.207460i
$459$		0			0
$460$	31.6626	+	7.22679i	1.47628	+	0.336951i
$461$	−32.7583	−	2.94830i	−1.52571	−	0.137316i	−0.705223	−	0.708985i	$-0.749153\pi$
$461$	−32.7583	−	2.94830i	−1.52571	−	0.137316i	−0.820484	+	0.571669i	$0.806296\pi$
$462$		0			0
$463$	6.63165	−	29.0552i	0.308199	−	1.35031i	−0.549215	−	0.835681i	$-0.685073\pi$
$463$	6.63165	−	29.0552i	0.308199	−	1.35031i	0.857414	−	0.514627i	$-0.172070\pi$
$464$	−3.77800	+	4.32427i	−0.175389	+	0.200749i
$465$		0			0
$466$	−14.5621	−	5.46525i	−0.674577	−	0.253173i
$467$	17.4424	−	21.8721i	0.807139	−	1.01212i	−0.192387	−	0.981319i	$-0.561623\pi$
$467$	17.4424	−	21.8721i	0.807139	−	1.01212i	0.999526	−	0.0308009i	$-0.00980579\pi$
$468$		0			0
$469$	54.4945	−	47.6104i	2.51632	−	2.19844i
$470$	−10.1083	+	23.6496i	−0.466261	+	1.09087i
$471$		0			0
$472$	2.98105	−	0.968600i	0.137214	−	0.0445834i
$473$	4.86744	+	35.9328i	0.223805	+	1.65219i
$474$		0			0
$475$	−22.0610	+	40.9963i	−1.01223	+	1.88104i
$476$	−6.12321	+	2.61718i	−0.280657	+	0.119958i
$477$		0			0
$478$	8.76950	−	8.38450i	0.401107	−	0.383498i
$479$	−7.86018	−	1.42641i	−0.359141	−	0.0651745i	−0.00401235	−	0.999992i	$-0.501277\pi$
$479$	−7.86018	−	1.42641i	−0.359141	−	0.0651745i	−0.355129	+	0.934817i	$0.615563\pi$
$480$		0			0
$481$	0.221610	+	0.590478i	0.0101045	+	0.0269235i
$482$	−9.12740	+	9.54651i	−0.415742	+	0.434832i
$483$		0			0
$484$	2.05779	+	3.11742i	0.0935360	+	0.141701i
$485$	2.65668	+	59.1556i	0.120634	+	2.68612i
$486$		0			0
$487$	−15.0927	+	25.2609i	−0.683915	+	1.14468i	0.297856	+	0.954611i	$0.403729\pi$
$487$	−15.0927	+	25.2609i	−0.683915	+	1.14468i	−0.981771	+	0.190070i	$0.939129\pi$
$488$	4.93307	+	1.36144i	0.223310	+	0.0616295i
$489$		0			0
$490$	−29.7059	+	17.7485i	−1.34198	+	0.801794i
$491$	−0.429146	+	9.55569i	−0.0193671	+	0.431242i	0.965762	+	0.259428i	$0.0835342\pi$
$491$	−0.429146	+	9.55569i	−0.0193671	+	0.431242i	−0.985129	+	0.171814i	$0.945037\pi$
$492$		0			0
$493$	0.666500	+	3.67272i	0.0300176	+	0.165411i
$494$	0.290003	−	2.14089i	0.0130479	−	0.0963232i
$495$		0			0
$496$			1.93282i			0.0867862i
$497$	9.38651	−	36.2431i	0.421043	−	1.62573i
$498$		0			0
$499$	24.0347	−	2.16316i	1.07594	−	0.0968366i	0.462533	−	0.886602i	$-0.346941\pi$
$499$	24.0347	−	2.16316i	1.07594	−	0.0968366i	0.613409	+	0.789765i	$0.289798\pi$
$500$	−39.0054	−	5.28364i	−1.74437	−	0.236291i
$501$		0			0
$502$	−14.2251	−	10.3351i	−0.634897	−	0.461279i
$503$	−10.0728	−	0.452372i	−0.449126	−	0.0201703i	−0.180846	−	0.983511i	$-0.557884\pi$
$503$	−10.0728	−	0.452372i	−0.449126	−	0.0201703i	−0.268280	+	0.963341i	$0.586455\pi$
$504$		0			0
$505$	−36.8348	+	10.1658i	−1.63913	+	0.452370i
$506$	2.72578	−	9.87663i	0.121176	−	0.439070i
$507$		0			0
$508$	−1.33992	−	0.884471i	−0.0594492	−	0.0392421i
$509$	−0.874052	+	0.0392537i	−0.0387417	+	0.00173989i	−0.0642272	−	0.997935i	$-0.520458\pi$
$509$	−0.874052	+	0.0392537i	−0.0387417	+	0.00173989i	0.0254856	+	0.999675i	$0.491887\pi$
$510$		0			0
$511$	−34.0695	−	46.8927i	−1.50715	−	2.07441i
$512$	11.3579	+	10.8593i	0.501953	+	0.479917i
$513$		0			0
$514$	−11.9766	−	3.89144i	−0.528266	−	0.171644i
$515$	6.31740	−	34.8118i	0.278378	−	1.53399i
$516$		0			0
$517$	−25.0019	−	12.0403i	−1.09958	−	0.529531i
$518$	0.950345	+	2.22344i	0.0417558	+	0.0976925i
$519$		0			0
$520$	7.32228	−	1.67126i	0.321103	−	0.0732897i
$521$	−17.2786	+	2.34055i	−0.756989	+	0.102541i	−0.502551	−	0.864548i	$-0.667605\pi$
$521$	−17.2786	+	2.34055i	−0.756989	+	0.102541i	−0.254439	+	0.967089i	$0.581891\pi$
$522$		0			0
$523$	24.5990	−	19.6170i	1.07564	−	0.857793i	0.0852846	−	0.996357i	$-0.472820\pi$
$523$	24.5990	−	19.6170i	1.07564	−	0.857793i	0.990354	+	0.138564i	$0.0442486\pi$
$524$	2.06501	+	0.882628i	0.0902104	+	0.0385578i
$525$		0			0
$526$	−1.65948	−	3.08383i	−0.0723566	−	0.134461i
$527$	0.982317	+	0.783372i	0.0427904	+	0.0341242i
$528$		0			0
$529$	−3.62219	+	1.74435i	−0.157486	+	0.0758415i
$530$	16.0889	+	14.0565i	0.698859	+	0.610574i
$531$		0			0
$532$	−2.53931	+	28.2140i	−0.110093	+	1.22323i
$533$	0.494499	−	5.49433i	0.0214191	−	0.237986i
$534$		0			0
$535$	22.3092	+	19.4910i	0.964512	+	0.842668i
$536$	−35.0153	+	16.8625i	−1.51243	+	0.728349i
$537$		0			0
$538$	−8.54640	−	6.81553i	−0.368461	−	0.293838i
$539$	−17.6926	−	32.8784i	−0.762075	−	1.41617i
$540$		0			0
$541$	−6.27302	−	2.68122i	−0.269698	−	0.115274i	0.253927	−	0.967223i	$-0.418278\pi$
$541$	−6.27302	−	2.68122i	−0.269698	−	0.115274i	−0.523625	+	0.851949i	$0.675421\pi$
$542$	9.56419	−	7.62718i	0.410817	−	0.327616i
$543$		0			0
$544$	5.54207	−	0.750725i	0.237614	−	0.0321870i
$545$	36.3996	−	8.30797i	1.55919	−	0.355874i
$546$		0			0
$547$	−3.79161	−	8.87092i	−0.162118	−	0.379293i	0.818700	−	0.574222i	$-0.194695\pi$
$547$	−3.79161	−	8.87092i	−0.162118	−	0.379293i	−0.980817	+	0.194929i	$0.937552\pi$
$548$	−18.9740	−	9.13739i	−0.810528	−	0.390330i
$549$		0			0
$550$	−3.97704	+	21.9153i	−0.169581	+	0.934471i
$551$	15.1019	+	4.90691i	0.643364	+	0.209042i
$552$		0			0
$553$	29.6422	+	28.3408i	1.26051	+	1.20517i
$554$	1.94401	+	2.67570i	0.0825930	+	0.113680i
$555$		0			0
$556$	0.726438	−	0.0326244i	0.0308078	−	0.00138358i
$557$	−33.4268	−	22.0648i	−1.41634	−	0.934917i	−0.999666	−	0.0258606i	$-0.991767\pi$
$557$	−33.4268	−	22.0648i	−1.41634	−	0.934917i	−0.416673	−	0.909056i	$-0.636804\pi$
$558$		0			0
$559$	2.56646	−	9.29934i	0.108549	−	0.393320i
$560$	−25.7624	+	7.10998i	−1.08866	+	0.300452i
$561$		0			0
$562$	7.05390	+	0.316791i	0.297551	+	0.0133630i
$563$	−21.9306	−	15.9335i	−0.924264	−	0.671517i	0.0203178	−	0.999794i	$-0.493532\pi$
$563$	−21.9306	−	15.9335i	−0.924264	−	0.671517i	−0.944582	+	0.328277i	$0.893532\pi$
$564$		0			0
$565$	6.94059	+	0.940167i	0.291993	+	0.0395531i
$566$	−1.03487	+	0.0931401i	−0.0434989	+	0.00391497i
$567$		0			0
$568$	−10.0380	+	17.4225i	−0.421185	+	0.731033i
$569$			18.6653i			0.782490i	0.920287	+	0.391245i	$0.127955\pi$
$569$			18.6653i			0.782490i	−0.920287	+	0.391245i	$0.872045\pi$
$570$		0			0
$571$	−4.04403	+	29.8542i	−0.169237	+	1.24936i	0.684638	+	0.728883i	$0.259960\pi$
$571$	−4.04403	+	29.8542i	−0.169237	+	1.24936i	−0.853876	+	0.520477i	$0.825754\pi$
$572$	0.631199	+	3.47819i	0.0263917	+	0.145430i
$573$		0			0
$574$	0.948889	−	21.1287i	0.0396059	−	0.881893i
$575$	50.4243	−	30.1271i	2.10284	−	1.25639i
$576$		0			0
$577$	−25.7832	−	7.11572i	−1.07337	−	0.296231i	−0.315693	−	0.948861i	$-0.602237\pi$
$577$	−25.7832	−	7.11572i	−1.07337	−	0.296231i	−0.757676	+	0.652630i	$0.773665\pi$
$578$	−5.54160	+	9.27508i	−0.230500	+	0.385793i
$579$		0			0
$580$	1.08037	+	24.0564i	0.0448600	+	0.998887i
$581$	4.89740	+	7.41924i	0.203178	+	0.307802i
$582$		0			0
$583$	−15.9299	+	16.6614i	−0.659750	+	0.690044i
$584$	10.9383	+	29.1450i	0.452630	+	1.20603i
$585$		0			0
$586$	−0.432350	−	0.0784600i	−0.0178602	−	0.00324115i
$587$	−24.6582	+	23.5756i	−1.01775	+	0.973071i	−0.999642	−	0.0267648i	$-0.991479\pi$
$587$	−24.6582	+	23.5756i	−1.01775	+	0.973071i	−0.0181109	+	0.999836i	$0.505765\pi$
$588$		0			0
$589$	4.91480	−	2.10069i	0.202511	−	0.0865573i
$590$	1.69040	−	3.14130i	0.0695928	−	0.129325i
$591$		0			0
$592$	0.161795	+	1.19442i	0.00664972	+	0.0490902i
$593$	−3.72796	+	1.21129i	−0.153089	+	0.0497416i	−0.384559	−	0.923100i	$-0.625646\pi$
$593$	−3.72796	+	1.21129i	−0.153089	+	0.0497416i	0.231470	+	0.972842i	$0.425646\pi$
$594$		0			0
$595$	−6.82800	+	15.9749i	−0.279921	+	0.654907i
$596$	−11.4277	+	9.98411i	−0.468098	+	0.408965i
$597$		0			0
$598$	−1.69953	+	2.13115i	−0.0694991	+	0.0871491i
$599$	−6.84938	−	2.57061i	−0.279858	−	0.105032i	0.207499	−	0.978235i	$-0.433468\pi$
$599$	−6.84938	−	2.57061i	−0.279858	−	0.105032i	−0.487357	+	0.873203i	$0.662039\pi$
$600$		0			0
$601$	−1.87289	+	2.14370i	−0.0763969	+	0.0874432i	−0.790000	−	0.613107i	$-0.789919\pi$
$601$	−1.87289	+	2.14370i	−0.0763969	+	0.0874432i	0.713603	+	0.700551i	$0.247062\pi$
$602$	8.23011	−	36.0585i	0.335434	−	1.46963i
$603$		0			0
$604$	−1.90519	−	0.171470i	−0.0775209	−	0.00697701i
$605$	9.50086	+	2.16851i	0.386265	+	0.0881624i
$606$		0			0
$607$	16.3345	+	33.9189i	0.662997	+	1.37673i	0.912790	+	0.408428i	$0.133923\pi$
$607$	16.3345	+	33.9189i	0.662997	+	1.37673i	−0.249794	+	0.968299i	$0.580363\pi$
$608$	8.35976	−	22.2745i	0.339033	−	0.903350i
$609$		0			0
$610$	5.12865	−	2.75985i	0.207653	−	0.111743i
$611$	4.85736	+	5.55970i	0.196508	+	0.224921i
$612$		0			0
$613$	−2.57249	−	3.22580i	−0.103902	−	0.130289i	0.727162	−	0.686466i	$-0.240839\pi$
$613$	−2.57249	−	3.22580i	−0.103902	−	0.130289i	−0.831064	+	0.556177i	$0.812268\pi$
$614$	−4.57416	−	14.0778i	−0.184598	−	0.568135i
$615$		0			0
$616$	6.91341	+	30.2896i	0.278549	+	1.22040i
$617$	−21.4523	−	11.5440i	−0.863638	−	0.464743i	−0.0188358	−	0.999823i	$-0.505996\pi$
$617$	−21.4523	−	11.5440i	−0.863638	−	0.464743i	−0.844802	+	0.535079i	$0.820282\pi$
$618$		0			0
$619$	−4.55107	+	9.45039i	−0.182923	+	0.379843i	−0.972185	−	0.234213i	$-0.924749\pi$
$619$	−4.55107	+	9.45039i	−0.182923	+	0.379843i	0.789263	+	0.614056i	$0.210463\pi$
$620$	5.60145	+	5.85865i	0.224959	+	0.235289i
$621$		0			0
$622$	−2.30391	+	7.09070i	−0.0923782	+	0.284311i
$623$	−57.3323	+	21.5172i	−2.29697	+	0.862067i
$624$		0			0
$625$	−37.3691	+	27.1502i	−1.49476	+	1.08601i
$626$	−6.99666	+	4.61846i	−0.279643	+	0.184591i
$627$		0			0
$628$	15.3292	−	23.2227i	0.611701	−	0.926688i
$629$	0.672612	+	0.401867i	0.0268188	+	0.0160235i
$630$		0			0
$631$	−1.66783	−	6.04323i	−0.0663951	−	0.240577i	0.923231	−	0.384246i	$-0.125539\pi$
$631$	−1.66783	−	6.04323i	−0.0663951	−	0.240577i	−0.989626	+	0.143669i	$0.954110\pi$
$632$	−11.2969	−	18.9078i	−0.449367	−	0.752113i
$633$		0			0
$634$	−5.52529	+	7.60491i	−0.219437	+	0.302029i
$635$	−4.12132	+	0.747910i	−0.163550	+	0.0296799i
$636$		0			0
$637$	0.890398	+	9.89314i	0.0352789	+	0.391980i
$638$	7.59699			0.300768
$639$		0			0
$640$	44.1720			1.74605
$641$	−1.37652	−	15.2944i	−0.0543695	−	0.604094i	−0.976254	−	0.216629i	$-0.930494\pi$
$641$	−1.37652	−	15.2944i	−0.0543695	−	0.604094i	0.921884	−	0.387465i	$-0.126649\pi$
$642$		0			0
$643$	23.5319	−	4.27041i	0.928008	−	0.168409i	0.306549	−	0.951855i	$-0.400826\pi$
$643$	23.5319	−	4.27041i	0.928008	−	0.168409i	0.621459	+	0.783446i	$0.286540\pi$
$644$	21.0084	−	28.9156i	0.827847	−	1.13943i
$645$		0			0
$646$	−1.37660	−	2.30404i	−0.0541615	−	0.0906510i
$647$	−2.40099	−	8.69980i	−0.0943927	−	0.342024i	0.901476	−	0.432829i	$-0.142485\pi$
$647$	−2.40099	−	8.69980i	−0.0943927	−	0.342024i	−0.995869	+	0.0908048i	$0.971056\pi$
$648$		0			0
$649$	3.30409	+	1.97410i	0.129697	+	0.0774903i
$650$	3.26442	−	4.94538i	0.128041	−	0.193974i
$651$		0			0
$652$	−27.1833	+	17.9435i	−1.06458	+	0.702723i
$653$	11.8979	−	8.64433i	0.465601	−	0.338279i	−0.330124	−	0.943938i	$-0.607090\pi$
$653$	11.8979	−	8.64433i	0.465601	−	0.338279i	0.795724	+	0.605659i	$0.207090\pi$
$654$		0			0
$655$	5.48532	−	2.05867i	0.214329	−	0.0804390i
$656$	3.25787	−	10.0267i	0.127199	−	0.391477i
$657$		0			0
$658$	19.5603	+	20.4585i	0.762539	+	0.797554i
$659$	7.77769	−	16.1505i	0.302976	−	0.629135i	−0.692782	−	0.721147i	$-0.743615\pi$
$659$	7.77769	−	16.1505i	0.302976	−	0.629135i	0.995758	+	0.0920114i	$0.0293296\pi$
$660$		0			0
$661$	8.57574	+	4.61480i	0.333558	+	0.179495i	0.632071	−	0.774910i	$-0.282205\pi$
$661$	8.57574	+	4.61480i	0.333558	+	0.179495i	−0.298513	+	0.954405i	$0.596491\pi$
$662$	2.00595	+	8.78862i	0.0779633	+	0.341580i
$663$		0			0
$664$	−1.47540	−	4.54081i	−0.0572566	−	0.176218i
$665$	46.0793	+	57.7816i	1.78688	+	2.24067i
$666$		0			0
$667$	−13.1816	−	15.0876i	−0.510395	−	0.584194i
$668$	−12.7480	+	6.85997i	−0.493233	+	0.265420i
$669$		0			0
$670$	−15.5414	+	41.4098i	−0.600415	+	1.59980i
$671$	2.72650	+	5.66163i	0.105255	+	0.218565i
$672$		0			0
$673$	24.8895	+	5.68087i	0.959421	+	0.218982i	0.673430	−	0.739251i	$-0.264820\pi$
$673$	24.8895	+	5.68087i	0.959421	+	0.218982i	0.285991	+	0.958232i	$0.407677\pi$
$674$	−7.37513	−	0.663773i	−0.284079	−	0.0255676i
$675$		0			0
$676$	−4.26734	+	18.6964i	−0.164128	+	0.719093i
$677$	24.4191	−	27.9499i	0.938503	−	1.07420i	−0.0586111	−	0.998281i	$-0.518667\pi$
$677$	24.4191	−	27.9499i	0.938503	−	1.07420i	0.997114	−	0.0759219i	$-0.0241900\pi$
$678$		0			0
$679$	61.0123	+	22.8983i	2.34144	+	0.878756i
$680$	5.81748	−	7.29489i	0.223090	−	0.279746i
$681$		0			0
$682$	1.92572	−	1.68245i	0.0737395	−	0.0644243i
$683$	−2.42780	+	5.68012i	−0.0928972	+	0.217344i	−0.959532	−	0.281599i	$-0.909135\pi$
$683$	−2.42780	+	5.68012i	−0.0928972	+	0.217344i	0.866635	+	0.498943i	$0.166278\pi$
$684$		0			0
$685$	−52.2534	+	16.9782i	−1.99650	+	0.648702i
$686$	2.30361	+	17.0059i	0.0879521	+	0.649289i
$687$		0			0
$688$	8.73645	−	16.2350i	0.333074	−	0.618955i
$689$	5.63914	−	2.41028i	0.214834	−	0.0918245i
$690$		0			0
$691$	6.86889	−	6.56734i	0.261305	−	0.249833i	−0.549026	−	0.835805i	$-0.685001\pi$
$691$	6.86889	−	6.56734i	0.261305	−	0.249833i	0.810331	+	0.585972i	$0.199287\pi$
$692$	29.8642	+	5.41955i	1.13527	+	0.206020i
$693$		0			0
$694$	2.92784	+	7.80119i	0.111139	+	0.296129i
$695$	1.31103	−	1.37123i	0.0497302	−	0.0520137i
$696$		0			0
$697$	−3.77545	−	5.71957i	−0.143005	−	0.216644i
$698$	−0.346368	−	7.71248i	−0.0131102	−	0.291922i
$699$		0			0
$700$	−39.8512	+	66.6996i	−1.50623	+	2.52101i
$701$	13.9610	+	3.85299i	0.527299	+	0.145525i	0.519542	−	0.854445i	$-0.326102\pi$
$701$	13.9610	+	3.85299i	0.527299	+	0.145525i	0.00775654	+	0.999970i	$0.497531\pi$
$702$		0			0
$703$	2.86133	−	1.70956i	0.107917	−	0.0644774i
$704$	0.118955	−	2.64874i	0.00448329	−	0.0998281i
$705$		0			0
$706$	−0.0976335	−	0.538005i	−0.00367448	−	0.0202481i
$707$	−5.64492	+	41.6725i	−0.212299	+	1.56725i
$708$		0			0
$709$		−	42.8908i		−	1.61080i	−0.592734	−	0.805398i	$-0.701951\pi$
$709$		−	42.8908i		−	1.61080i	0.592734	−	0.805398i	$-0.298049\pi$
$710$	5.44528	+	22.2263i	0.204358	+	0.834140i
$711$		0			0
$712$	32.7563	−	2.94812i	1.22759	−	0.110485i
$713$	−6.68267	−	0.905230i	−0.250268	−	0.0339011i
$714$		0			0
$715$	7.46116	+	5.42085i	0.279032	+	0.202728i
$716$	−15.8919	−	0.713704i	−0.593907	−	0.0266724i
$717$		0			0
$718$	3.91452	−	1.08034i	0.146089	−	0.0403179i
$719$	−10.4196	+	37.7544i	−0.388584	+	1.40800i	0.464196	+	0.885733i	$0.346343\pi$
$719$	−10.4196	+	37.7544i	−0.388584	+	1.40800i	−0.852780	+	0.522270i	$0.825085\pi$
$720$		0			0
$721$	−32.4957	−	21.4502i	−1.21020	−	0.798848i
$722$	1.36168	−	0.0611532i	0.0506766	−	0.00227589i
$723$		0			0
$724$	−12.6856	−	17.4602i	−0.471457	−	0.648905i
$725$	31.4799	+	30.0979i	1.16913	+	1.11781i
$726$		0			0
$727$	−1.52398	−	0.495171i	−0.0565213	−	0.0183649i	0.280620	−	0.959819i	$-0.409460\pi$
$727$	−1.52398	−	0.495171i	−0.0565213	−	0.0183649i	−0.337141	+	0.941454i	$0.609460\pi$
$728$	1.47588	−	8.13275i	0.0546996	−	0.301420i
$729$		0			0
$730$	31.9197	+	15.3717i	1.18140	+	0.568933i
$731$	−4.71025	−	11.0202i	−0.174215	−	0.407596i
$732$		0			0
$733$	2.04643	−	0.467083i	0.0755865	−	0.0172521i	−0.184560	−	0.982821i	$-0.559086\pi$
$733$	2.04643	−	0.467083i	0.0755865	−	0.0172521i	0.260147	+	0.965569i	$0.416229\pi$
$734$	−18.3936	+	2.49158i	−0.678920	+	0.0919660i
$735$		0			0
$736$	−23.4690	+	18.7159i	−0.865077	+	0.689876i
$737$	−43.8822	−	18.7561i	−1.61642	−	0.690892i
$738$		0			0
$739$	−10.6422	−	19.7764i	−0.391478	−	0.727488i	0.606220	−	0.795297i	$-0.292685\pi$
$739$	−10.6422	−	19.7764i	−0.391478	−	0.727488i	−0.997698	+	0.0678086i	$0.978399\pi$
$740$	3.95192	+	3.15155i	0.145275	+	0.115853i
$741$		0			0
$742$	21.1836	−	10.2015i	0.777676	−	0.374509i
$743$	10.8920	+	9.51608i	0.399590	+	0.349111i	0.834156	−	0.551529i	$-0.185955\pi$
$743$	10.8920	+	9.51608i	0.399590	+	0.349111i	−0.434566	+	0.900640i	$0.643098\pi$
$744$		0			0
$745$	−3.54880	+	39.4304i	−0.130018	+	1.44462i
$746$	0.0603946	−	0.671039i	0.00221120	−	0.0245685i
$747$		0			0
$748$	3.30718	+	2.88939i	0.120922	+	0.105647i
$749$	29.3736	−	14.1456i	1.07329	−	0.516869i
$750$		0			0
$751$	−23.6951	−	18.8962i	−0.864647	−	0.689533i	0.0871723	−	0.996193i	$-0.472217\pi$
$751$	−23.6951	−	18.8962i	−0.864647	−	0.689533i	−0.951819	+	0.306661i	$0.900788\pi$
$752$	6.68588	+	12.4244i	0.243809	+	0.453073i
$753$		0			0
$754$	−1.85848	−	0.794353i	−0.0676819	−	0.0289286i
$755$	−3.90177	+	3.11156i	−0.142000	+	0.113241i
$756$		0			0
$757$	26.8496	−	3.63702i	0.975864	−	0.132190i	0.371099	−	0.928593i	$-0.378981\pi$
$757$	26.8496	−	3.63702i	0.975864	−	0.132190i	0.604765	+	0.796404i	$0.293267\pi$
$758$	4.20884	−	0.960641i	0.152872	−	0.0348920i
$759$		0			0
$760$	−15.6001	−	36.4983i	−0.565877	−	1.32393i
$761$	−31.7459	−	15.2880i	−1.15079	−	0.554190i	−0.241517	−	0.970397i	$-0.577645\pi$
$761$	−31.7459	−	15.2880i	−1.15079	−	0.554190i	−0.909270	+	0.416207i	$0.863359\pi$
$762$		0			0
$763$	7.33669	−	40.4285i	0.265606	−	1.46361i
$764$	−22.8262	−	7.41668i	−0.825823	−	0.268326i
$765$		0			0
$766$	5.58144	+	5.33641i	0.201666	+	0.192812i
$767$	−0.601877	−	0.828413i	−0.0217325	−	0.0299123i
$768$		0			0
$769$	−10.7782	+	0.484050i	−0.388672	+	0.0174553i	−0.238344	−	0.971181i	$-0.576604\pi$
$769$	−10.7782	+	0.484050i	−0.388672	+	0.0174553i	−0.150328	+	0.988636i	$0.548033\pi$
$770$	29.5091	+	19.4788i	1.06343	+	0.701967i
$771$		0			0
$772$	10.2525	−	37.1490i	0.368995	−	1.33702i
$773$	−29.9086	+	8.25426i	−1.07574	+	0.296885i	−0.758642	−	0.651508i	$-0.774137\pi$
$773$	−29.9086	+	8.25426i	−1.07574	+	0.296885i	−0.317097	+	0.948393i	$0.602708\pi$
$774$		0			0
$775$	14.6452	+	0.657718i	0.526072	+	0.0236259i
$776$	−28.3154	−	20.5723i	−1.01646	−	0.738504i
$777$		0			0
$778$	−11.1416	−	1.50923i	−0.399445	−	0.0541085i
$779$	−29.0369	+	2.61336i	−1.04035	+	0.0936335i
$780$		0			0
$781$	−24.2208	+	4.79340i	−0.866687	+	0.171521i
$782$			3.38635i			0.121096i
$783$		0			0
$784$	−2.54819	+	18.8115i	−0.0910067	+	0.671838i
$785$	−12.9624	−	71.4286i	−0.462647	−	2.54940i
$786$		0			0
$787$	0.389882	−	8.68141i	0.0138978	−	0.309459i	−0.979989	−	0.199053i	$-0.936213\pi$
$787$	0.389882	−	8.68141i	0.0138978	−	0.309459i	0.993887	−	0.110406i	$-0.0352151\pi$
$788$	−13.3335	+	7.96639i	−0.474986	+	0.283791i
$789$		0			0
$790$	−24.1634	−	6.66867i	−0.859694	−	0.237261i
$791$	3.95345	−	6.61697i	0.140569	−	0.235272i
$792$		0			0
$793$	−0.0750049	−	1.67011i	−0.00266350	−	0.0593075i
$794$	−6.15541	−	9.32504i	−0.218447	−	0.330933i
$795$		0			0
$796$	15.4268	−	16.1352i	0.546788	−	0.571895i
$797$	3.47981	+	9.27191i	0.123261	+	0.328428i	0.983351	−	0.181714i	$-0.0581644\pi$
$797$	3.47981	+	9.27191i	0.123261	+	0.328428i	−0.860090	+	0.510142i	$0.829593\pi$
$798$		0			0
$799$	9.02425	+	1.63766i	0.319255	+	0.0579362i
$800$	47.1662	−	45.0955i	1.66758	−	1.59437i
$801$		0			0
$802$	−18.5857	+	7.94392i	−0.656285	+	0.280510i
$803$	−18.1139	+	33.6613i	−0.639226	+	1.18788i
$804$		0			0
$805$	−12.5168	−	92.4028i	−0.441160	−	3.25677i
$806$	−0.647015	+	0.210228i	−0.0227901	+	0.00740497i
$807$		0			0
$808$	8.87666	−	20.7680i	0.312280	−	0.730615i
$809$	−16.5817	+	14.4870i	−0.582980	+	0.509334i	−0.898143	−	0.439703i	$-0.855084\pi$
$809$	−16.5817	+	14.4870i	−0.582980	+	0.509334i	0.315163	+	0.949037i	$0.397941\pi$
$810$		0			0
$811$	−0.368622	+	0.462237i	−0.0129441	+	0.0162313i	−0.788261	−	0.615341i	$-0.789019\pi$
$811$	−0.368622	+	0.462237i	−0.0129441	+	0.0162313i	0.775317	+	0.631572i	$0.217590\pi$
$812$	24.8115	+	9.31189i	0.870711	+	0.326783i
$813$		0			0
$814$	1.04919	−	1.20089i	0.0367741	−	0.0420913i
$815$	−18.9090	+	82.8456i	−0.662352	+	2.90195i
$816$		0			0
$817$	−50.7779	−	4.57009i	−1.77649	−	0.159887i
$818$	24.5937	+	5.61336i	0.859899	+	0.196266i
$819$		0			0
$820$	−19.1830	−	39.8339i	−0.669899	−	1.39106i
$821$	6.38496	−	17.0127i	0.222837	−	0.593746i	−0.776502	−	0.630115i	$-0.783008\pi$
$821$	6.38496	−	17.0127i	0.222837	−	0.593746i	0.999338	+	0.0363690i	$0.0115792\pi$
$822$		0			0
$823$	1.29928	−	0.699175i	0.0452902	−	0.0243717i	−0.451067	−	0.892490i	$-0.648956\pi$
$823$	1.29928	−	0.699175i	0.0452902	−	0.0243717i	0.496357	+	0.868118i	$0.334671\pi$
$824$	13.7588	+	15.7482i	0.479309	+	0.548613i
$825$		0			0
$826$	−2.44772	−	3.06934i	−0.0851670	−	0.106796i
$827$	−11.0220	−	33.9223i	−0.383274	−	1.17960i	−0.937725	−	0.347379i	$-0.887072\pi$
$827$	−11.0220	−	33.9223i	−0.383274	−	1.17960i	0.554451	−	0.832216i	$-0.312928\pi$
$828$		0			0
$829$	−6.34144	−	27.7837i	−0.220247	−	0.964967i	−0.957292	−	0.289123i	$-0.906636\pi$
$829$	−6.34144	−	27.7837i	−0.220247	−	0.964967i	0.737045	−	0.675844i	$-0.236221\pi$
$830$	−4.78491	−	2.57487i	−0.166087	−	0.0893750i
$831$		0			0
$832$	−0.306057	+	0.635533i	−0.0106106	+	0.0220332i
$833$	8.52776	+	8.91934i	0.295470	+	0.309037i
$834$		0			0
$835$	−11.6709	+	35.9195i	−0.403889	+	1.24304i
$836$	17.4908	−	6.56440i	0.604931	−	0.227034i
$837$		0			0
$838$	1.61227	−	1.17138i	0.0556949	−	0.0404647i
$839$	15.9110	−	10.5028i	0.549310	−	0.362596i	−0.245555	−	0.969383i	$-0.578970\pi$
$839$	15.9110	−	10.5028i	0.549310	−	0.362596i	0.794865	+	0.606786i	$0.207542\pi$
$840$		0			0
$841$	−7.79236	+	11.8049i	−0.268702	+	0.407066i
$842$	2.61497	+	1.56237i	0.0901177	+	0.0538428i
$843$		0			0
$844$	−1.10812	−	4.01518i	−0.0381430	−	0.138208i
$845$	25.6612	+	42.9497i	0.882773	+	1.47751i
$846$		0			0
$847$	6.30389	−	8.67656i	0.216604	−	0.298130i
$848$	11.5318	−	2.09271i	0.396004	−	0.0718641i
$849$		0			0
$850$	−0.659881	−	7.33188i	−0.0226337	−	0.251481i
$851$	−4.20543			−0.144160
$852$		0			0
$853$	44.9615			1.53945			0.769726	−	0.638375i	$-0.220393\pi$
$853$	44.9615			1.53945			0.769726	+	0.638375i	$0.220393\pi$
$854$	−0.574546	−	6.38373i	−0.0196606	−	0.218447i
$855$		0			0
$856$	−17.2284	+	3.12649i	−0.588853	+	0.106861i
$857$	−0.857286	+	1.17995i	−0.0292843	+	0.0403064i	−0.823408	−	0.567450i	$-0.807930\pi$
$857$	−0.857286	+	1.17995i	−0.0292843	+	0.0403064i	0.794124	+	0.607756i	$0.207930\pi$
$858$		0			0
$859$	−5.07583	−	8.49551i	−0.173185	−	0.289863i	0.759533	−	0.650468i	$-0.225427\pi$
$859$	−5.07583	−	8.49551i	−0.173185	−	0.289863i	−0.932719	+	0.360605i	$0.882570\pi$
$860$	−20.5688	−	74.5295i	−0.701392	−	2.54144i
$861$		0			0
$862$	19.8540	+	11.8622i	0.676230	+	0.404029i
$863$	2.31116	−	3.50126i	0.0786729	−	0.119184i	−0.793106	−	0.609083i	$-0.791538\pi$
$863$	2.31116	−	3.50126i	0.0786729	−	0.119184i	0.871779	+	0.489899i	$0.162966\pi$
$864$		0			0
$865$	66.0862	−	43.6231i	2.24700	−	1.48323i
$866$	−13.7781	+	10.0104i	−0.468201	+	0.340168i
$867$		0			0
$868$	8.35155	−	3.13439i	0.283470	−	0.106388i
$869$	8.35766	−	25.7222i	0.283514	−	0.872567i
$870$		0			0
$871$	8.77390	+	9.17678i	0.297292	+	0.310943i
$872$	−9.57479	+	19.8822i	−0.324243	+	0.673298i
$873$		0			0
$874$	12.6856	+	6.82642i	0.429097	+	0.230907i
$875$	25.1480	+	110.180i	0.850156	+	3.72478i
$876$		0			0
$877$	−3.13833	−	9.65877i	−0.105974	−	0.326154i	0.883984	−	0.467517i	$-0.154851\pi$
$877$	−3.13833	−	9.65877i	−0.105974	−	0.326154i	−0.989958	+	0.141363i	$0.954851\pi$
$878$	−10.3985	−	13.0393i	−0.350933	−	0.440056i
$879$		0			0
$880$	11.5963	+	13.2730i	0.390911	+	0.447434i
$881$	46.2065	−	24.8648i	1.55674	−	0.837715i	0.556761	−	0.830673i	$-0.312044\pi$
$881$	46.2065	−	24.8648i	1.55674	−	0.837715i	0.999975	−	0.00704271i	$-0.00224178\pi$
$882$		0			0
$883$	12.9587	−	34.5284i	0.436096	−	1.16197i	−0.516112	−	0.856521i	$-0.672621\pi$
$883$	12.9587	−	34.5284i	0.436096	−	1.16197i	0.952207	−	0.305452i	$-0.0988076\pi$
$884$	−0.506928	−	1.05265i	−0.0170498	−	0.0354044i
$885$		0			0
$886$	−14.2499	−	3.25244i	−0.478734	−	0.109268i
$887$	1.24249	+	0.111826i	0.0417187	+	0.00375475i	0.110479	−	0.993878i	$-0.464762\pi$
$887$	1.24249	+	0.111826i	0.0417187	+	0.00375475i	−0.0687603	+	0.997633i	$0.521904\pi$
$888$		0			0
$889$	−1.02575	+	4.49412i	−0.0344027	+	0.150728i
$890$	24.6265	−	28.1872i	0.825481	−	0.944838i
$891$		0			0
$892$	−26.6036	−	9.98452i	−0.890756	−	0.334306i
$893$	24.3265	−	30.5044i	0.814054	−	1.02079i
$894$		0			0
$895$	−31.2542	+	27.3059i	−1.04471	+	0.912737i
$896$	19.1059	−	44.7004i	0.638283	−	1.49334i
$897$		0			0
$898$	15.6399	−	5.08171i	0.521910	−	0.169579i
$899$	−0.671200	−	4.95500i	−0.0223858	−	0.165258i
$900$		0			0
$901$	3.61026	−	6.70898i	0.120275	−	0.223508i
$902$	−12.8257	+	5.48197i	−0.427050	+	0.182530i
$903$		0			0
$904$	−2.99221	+	2.86084i	−0.0995194	+	0.0951503i
$905$	−55.4008	−	10.0538i	−1.84158	−	0.334198i
$906$		0			0
$907$	−6.37926	−	16.9975i	−0.211820	−	0.564392i	0.786783	−	0.617229i	$-0.211745\pi$
$907$	−6.37926	−	16.9975i	−0.211820	−	0.564392i	−0.998603	+	0.0528372i	$0.983174\pi$
$908$	14.8280	−	15.5089i	0.492085	−	0.514681i
$909$		0			0
$910$	−5.18219	−	7.85069i	−0.171788	−	0.260248i
$911$	−2.19672	−	48.9139i	−0.0727807	−	1.62059i	−0.620693	−	0.784053i	$-0.713149\pi$
$911$	−2.19672	−	48.9139i	−0.0727807	−	1.62059i	0.547913	−	0.836535i	$-0.315423\pi$
$912$		0			0
$913$	3.00701	−	5.03288i	0.0995174	−	0.166564i
$914$	9.93018	+	2.74055i	0.328461	+	0.0906495i
$915$		0			0
$916$	−9.73206	+	5.81464i	−0.321556	+	0.192121i
$917$	0.289283	−	6.44138i	0.00955296	−	0.212713i
$918$		0			0
$919$	9.78832	+	53.9381i	0.322887	+	1.77925i	0.581780	+	0.813347i	$0.302357\pi$
$919$	9.78832	+	53.9381i	0.322887	+	1.77925i	−0.258893	+	0.965906i	$0.583358\pi$
$920$	−6.72242	+	49.6269i	−0.221632	+	1.63615i
$921$		0			0
$922$		−	22.1246i		−	0.728635i
$923$	6.42643	+	1.35993i	0.211528	+	0.0447628i
$924$		0			0
$925$	9.10529	−	0.819491i	0.299380	−	0.0269447i
$926$	19.8657	+	2.69100i	0.652828	+	0.0884316i
$927$		0			0
$928$	−18.0066	−	13.0825i	−0.591095	−	0.429456i
$929$	−23.8782	−	1.07237i	−0.783418	−	0.0351833i	−0.350437	−	0.936586i	$-0.613967\pi$
$929$	−23.8782	−	1.07237i	−0.783418	−	0.0351833i	−0.432981	+	0.901403i	$0.642538\pi$
$930$		0			0
$931$	50.6035	−	13.9657i	1.65846	−	0.457707i
$932$	−9.51951	+	34.4932i	−0.311822	+	1.12986i
$933$		0			0
$934$	15.7052	+	10.3669i	0.513890	+	0.339216i
$935$	11.4457	−	0.514028i	0.374315	−	0.0168105i
$936$		0			0
$937$	0.467214	+	0.643064i	0.0152632	+	0.0210080i	0.816580	−	0.577232i	$-0.195867\pi$
$937$	0.467214	+	0.643064i	0.0152632	+	0.0210080i	−0.801317	+	0.598240i	$0.795867\pi$
$938$	35.1830	+	33.6384i	1.14877	+	1.09833i
$939$		0			0
$940$	56.2727	+	18.2841i	1.83541	+	0.596362i
$941$	−5.53351	+	30.4921i	−0.180387	+	0.994016i	0.758983	+	0.651111i	$0.225697\pi$
$941$	−5.53351	+	30.4921i	−0.180387	+	0.994016i	−0.939370	+	0.342905i	$0.888589\pi$
$942$		0			0
$943$	33.1412	+	15.9600i	1.07923	+	0.519728i
$944$	−0.769121	−	1.79945i	−0.0250328	−	0.0585670i
$945$		0			0
$946$	−23.7801	+	5.42766i	−0.773159	+	0.176468i
$947$	23.5925	−	3.19582i	0.766654	−	0.103850i	0.259543	−	0.965731i	$-0.416428\pi$
$947$	23.5925	−	3.19582i	0.766654	−	0.103850i	0.507110	+	0.861881i	$0.330714\pi$
$948$		0			0
$949$	7.95096	−	6.34068i	0.258099	−	0.205827i
$950$	−28.7962	−	12.3081i	−0.934271	−	0.399326i
$951$		0			0
$952$	−4.86590	−	9.04236i	−0.157705	−	0.293064i
$953$	6.10562	+	4.86907i	0.197780	+	0.157725i	0.717372	−	0.696690i	$-0.245345\pi$
$953$	6.10562	+	4.86907i	0.197780	+	0.157725i	−0.519592	+	0.854414i	$0.673916\pi$
$954$		0			0
$955$	−56.4152	+	27.1681i	−1.82555	+	0.879141i
$956$	−21.0198	−	18.3645i	−0.679830	−	0.593949i
$957$		0			0
$958$	0.481691	−	5.35203i	0.0155627	−	0.172916i
$959$	−5.42009	+	60.2221i	−0.175024	+	1.94467i
$960$		0			0
$961$	22.0777	+	19.2887i	0.712185	+	0.622217i
$962$	−0.382235	+	0.184075i	−0.0123237	+	0.00593480i
$963$		0			0
$964$	23.7561	+	18.9449i	0.765134	+	0.610174i
$965$	−47.6436	−	88.5366i	−1.53370	−	2.85009i
$966$		0			0
$967$	−41.4023	−	17.6962i	−1.33141	−	0.569071i	−0.394579	−	0.918862i	$-0.629110\pi$
$967$	−41.4023	−	17.6962i	−1.33141	−	0.569071i	−0.936828	+	0.349791i	$0.886253\pi$
$968$	−4.50335	+	3.59130i	−0.144743	+	0.115429i
$969$		0			0
$970$	−39.4718	+	5.34681i	−1.26736	+	0.171676i
$971$	42.0637	−	9.60077i	1.34989	−	0.308103i	0.514372	−	0.857567i	$-0.328025\pi$
$971$	42.0637	−	9.60077i	1.34989	−	0.308103i	0.835517	+	0.549464i	$0.185168\pi$
$972$		0			0
$973$	−0.820569	−	1.91982i	−0.0263062	−	0.0615465i
$974$	−17.8339	−	8.58835i	−0.571435	−	0.275188i
$975$		0			0
$976$	0.570487	−	3.14364i	0.0182608	−	0.100626i
$977$	53.1630	+	17.2737i	1.70084	+	0.552635i	0.988766	−	0.149473i	$-0.0477578\pi$
$977$	53.1630	+	17.2737i	1.70084	+	0.552635i	0.712070	+	0.702108i	$0.247758\pi$
$978$		0			0
$979$	29.1902	+	27.9087i	0.932922	+	0.891964i
$980$	46.7930	+	64.4050i	1.49475	+	2.05734i
$981$		0			0
$982$	−6.42782	+	0.288674i	−0.205120	+	0.00921195i
$983$	5.08662	+	3.35765i	0.162238	+	0.107092i	0.629408	−	0.777075i	$-0.283298\pi$
$983$	5.08662	+	3.35765i	0.162238	+	0.107092i	−0.467169	+	0.884168i	$0.654726\pi$
$984$		0			0
$985$	−10.7803	+	39.0615i	−0.343489	+	1.24460i
$986$	−2.42039	+	0.667985i	−0.0770810	+	0.0212730i
$987$		0			0
$988$	−4.96522	−	0.222988i	−0.157965	−	0.00709420i
$989$	52.0405	+	37.8097i	1.65479	+	1.20228i
$990$		0			0
$991$	24.3516	+	3.29865i	0.773553	+	0.104785i	0.510363	−	0.859959i	$-0.329511\pi$
$991$	24.3516	+	3.29865i	0.773553	+	0.104785i	0.263190	+	0.964744i	$0.415225\pi$
$992$	−7.46168	+	0.671564i	−0.236909	+	0.0213222i
$993$		0			0
$994$	24.8475	+	4.10323i	0.788115	+	0.130146i
$995$		−	58.2395i		−	1.84632i
$996$		0			0
$997$	−0.729393	+	5.38459i	−0.0231001	+	0.170532i	−0.998825	−	0.0484695i	$-0.984566\pi$
$997$	−0.729393	+	5.38459i	−0.0231001	+	0.170532i	0.975725	+	0.219001i	$0.0702799\pi$
$998$	2.89848	+	15.9719i	0.0917496	+	0.505582i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	639.2.z.a.53.15	yes	576
3.2	odd	2	inner	639.2.z.a.53.10	✓	576
71.67	odd	70	inner	639.2.z.a.422.10	yes	576
213.209	even	70	inner	639.2.z.a.422.15	yes	576

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
639.2.z.a.53.10	✓	576	3.2	odd	2	inner
639.2.z.a.53.15	yes	576	1.1	even	1	trivial
639.2.z.a.422.10	yes	576	71.67	odd	70	inner
639.2.z.a.422.15	yes	576	213.209	even	70	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:	\( N \)	\(=\)	\( 639 = 3^{2} \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	639.z (of order \(70\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0602976 + 0.669962i) q^{2} +(1.52265 - 0.276320i) q^{4} +(2.37308 - 3.26627i) q^{5} +(-2.27890 - 3.81424i) q^{7} +(0.634845 + 2.30031i) q^{8} +O(q^{10})\)	\(q+(0.0602976 + 0.669962i) q^{2} +(1.52265 - 0.276320i) q^{4} +(2.37308 - 3.26627i) q^{5} +(-2.27890 - 3.81424i) q^{7} +(0.634845 + 2.30031i) q^{8} +(2.33137 + 1.39293i) q^{10} +(-1.61425 + 2.44549i) q^{11} +(0.650605 - 0.429461i) q^{13} +(2.41798 - 1.75677i) q^{14} +(1.39484 - 0.523491i) q^{16} +(0.299273 - 0.921067i) q^{17} +(-2.84712 - 2.97785i) q^{19} +(2.71083 - 5.62910i) q^{20} +(-1.73572 - 0.934031i) q^{22} +(1.15669 + 5.06778i) q^{23} +(-3.49191 - 10.7470i) q^{25} +(0.326952 + 0.409985i) q^{26} +(-4.52392 - 5.17804i) q^{28} +(-3.39402 + 1.82640i) q^{29} +(-0.455852 + 1.21461i) q^{31} +(2.50558 + 5.20290i) q^{32} +(0.635125 + 0.144963i) q^{34} +(-17.8664 - 1.60800i) q^{35} +(-0.180026 + 0.788747i) q^{37} +(1.82337 - 2.08702i) q^{38} +(9.01997 + 3.38525i) q^{40} +(4.41208 - 5.53257i) q^{41} +(9.31912 - 8.14187i) q^{43} +(-1.78220 + 4.16966i) q^{44} +(-3.32547 + 1.08051i) q^{46} +(1.27122 + 9.38455i) q^{47} +(-6.03797 + 11.2204i) q^{49} +(6.98951 - 2.98746i) q^{50} +(0.871973 - 0.833692i) q^{52} +(7.74032 + 1.40466i) q^{53} +(4.15687 + 11.0759i) q^{55} +(7.32719 - 7.66364i) q^{56} +(-1.42827 - 2.16374i) q^{58} +(-0.0589308 - 1.31220i) q^{59} +(1.09992 - 1.84096i) q^{61} +(-0.841231 - 0.232165i) q^{62} +(-0.776765 + 0.464096i) q^{64} +(0.141206 - 3.14420i) q^{65} +(2.90803 + 16.0246i) q^{67} +(0.201178 - 1.48515i) q^{68} -12.0667i q^{70} +(5.91886 + 5.99726i) q^{71} +(12.9928 - 1.16937i) q^{73} +(-0.539286 - 0.0730512i) q^{74} +(-5.15799 - 3.74750i) q^{76} +(13.0064 + 0.584119i) q^{77} +(-8.89736 + 2.45552i) q^{79} +(1.60020 - 5.79820i) q^{80} +(3.97265 + 2.62232i) q^{82} +(-1.99877 + 0.0897650i) q^{83} +(-2.29825 - 3.16328i) q^{85} +(6.01666 + 5.75252i) q^{86} +(-6.65018 - 2.16078i) q^{88} +(2.46092 - 13.5608i) q^{89} +(-3.12074 - 1.50287i) q^{91} +(3.16155 + 7.39682i) q^{92} +(-6.21064 + 1.41754i) q^{94} +(-16.4829 + 2.23276i) q^{95} +(-11.4671 + 9.14467i) q^{97} +(-7.88133 - 3.36864i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 576 q - 24 q^{4}+O(q^{10}) \) 576 * q - 24 * q^4	\( 576 q - 24 q^{4} - 16 q^{10} + 76 q^{16} - 8 q^{19} + 20 q^{22} + 168 q^{25} - 20 q^{28} - 28 q^{31} + 40 q^{37} + 32 q^{40} + 52 q^{43} - 20 q^{46} - 208 q^{52} - 92 q^{55} + 56 q^{58} + 56 q^{61} - 144 q^{64} - 16 q^{67} - 44 q^{73} - 336 q^{76} + 88 q^{79} - 124 q^{82} + 60 q^{85} - 260 q^{88} + 80 q^{91} + 56 q^{94} - 56 q^{97}+O(q^{100}) \) 576 * q - 24 * q^4 - 16 * q^10 + 76 * q^16 - 8 * q^19 + 20 * q^22 + 168 * q^25 - 20 * q^28 - 28 * q^31 + 40 * q^37 + 32 * q^40 + 52 * q^43 - 20 * q^46 - 208 * q^52 - 92 * q^55 + 56 * q^58 + 56 * q^61 - 144 * q^64 - 16 * q^67 - 44 * q^73 - 336 * q^76 + 88 * q^79 - 124 * q^82 + 60 * q^85 - 260 * q^88 + 80 * q^91 + 56 * q^94 - 56 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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