LMFDB - Embedded newform 507.2.k.k.80.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(80,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 1]))

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

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

chi := DirichletCharacter("507.80");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.k (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			80.3
Character	$\chi$	$=$	507.80
Dual form			507.2.k.k.488.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.522394 + 1.94960i) q^{2} +(0.152679 + 1.72531i) q^{3} +(-1.79600 - 1.03692i) q^{4} +(1.72251 + 1.72251i) q^{5} +(-3.44342 - 0.603628i) q^{6} +(3.00582 - 0.805406i) q^{7} +(0.105393 - 0.105393i) q^{8} +(-2.95338 + 0.526837i) q^{9} +(-4.25804 + 2.45838i) q^{10} +(2.67329 + 0.716305i) q^{11} +(1.51480 - 3.25697i) q^{12} +6.28089i q^{14} +(-2.70887 + 3.23485i) q^{15} +(-1.92343 - 3.33148i) q^{16} +(-2.89422 + 5.01294i) q^{17} +(0.515706 - 6.03313i) q^{18} +(0.388120 + 1.44849i) q^{19} +(-1.30752 - 4.87975i) q^{20} +(1.84850 + 5.06299i) q^{21} +(-2.79302 + 4.83765i) q^{22} +(-1.93268 - 3.34750i) q^{23} +(0.197926 + 0.165743i) q^{24} +0.934091i q^{25} +(-1.35988 - 5.01505i) q^{27} +(-6.23360 - 1.67029i) q^{28} +(2.53139 - 1.46150i) q^{29} +(-4.89158 - 6.97109i) q^{30} +(3.56552 - 3.56552i) q^{31} +(7.78778 - 2.08673i) q^{32} +(-0.827693 + 4.72161i) q^{33} +(-8.26131 - 8.26131i) q^{34} +(6.56488 + 3.79023i) q^{35} +(5.85056 + 2.11622i) q^{36} +(-1.03921 + 3.87837i) q^{37} -3.02672 q^{38} +0.363080 q^{40} +(1.75678 - 6.55640i) q^{41} +(-10.8365 + 0.958960i) q^{42} +(1.59566 + 0.921257i) q^{43} +(-4.05848 - 4.05848i) q^{44} +(-5.99471 - 4.17974i) q^{45} +(7.53592 - 2.01924i) q^{46} +(0.115676 - 0.115676i) q^{47} +(5.45416 - 3.82715i) q^{48} +(2.32408 - 1.34181i) q^{49} +(-1.82111 - 0.487964i) q^{50} +(-9.09075 - 4.22805i) q^{51} -10.0745i q^{53} +(10.4877 - 0.0313815i) q^{54} +(3.37093 + 5.83861i) q^{55} +(0.231907 - 0.401675i) q^{56} +(-2.43983 + 0.890781i) q^{57} +(1.52696 + 5.69869i) q^{58} +(-0.446576 - 1.66664i) q^{59} +(8.21944 - 3.00092i) q^{60} +(2.69796 - 4.67300i) q^{61} +(5.08874 + 8.81396i) q^{62} +(-8.45300 + 3.96225i) q^{63} +8.57945i q^{64} +(-8.77288 - 4.08021i) q^{66} +(-13.1928 - 3.53501i) q^{67} +(10.3961 - 6.00217i) q^{68} +(5.48039 - 3.84556i) q^{69} +(-10.8189 + 10.8189i) q^{70} +(0.326665 - 0.0875296i) q^{71} +(-0.255739 + 0.366789i) q^{72} +(8.54904 + 8.54904i) q^{73} +(-7.01840 - 4.05207i) q^{74} +(-1.61160 + 0.142616i) q^{75} +(0.804902 - 3.00393i) q^{76} +8.61233 q^{77} +10.4089 q^{79} +(2.42538 - 9.05163i) q^{80} +(8.44489 - 3.11190i) q^{81} +(11.8646 + 6.85005i) q^{82} +(2.83841 + 2.83841i) q^{83} +(1.93002 - 11.0099i) q^{84} +(-13.6202 + 3.64951i) q^{85} +(-2.62965 + 2.62965i) q^{86} +(2.90803 + 4.14429i) q^{87} +(0.357238 - 0.206251i) q^{88} +(-4.10839 - 1.10084i) q^{89} +(11.2804 - 9.50383i) q^{90} +8.01616i q^{92} +(6.69601 + 5.60725i) q^{93} +(0.165094 + 0.285951i) q^{94} +(-1.82649 + 3.16357i) q^{95} +(4.78928 + 13.1177i) q^{96} +(2.56119 + 9.55851i) q^{97} +(1.40191 + 5.23199i) q^{98} +(-8.27261 - 0.707134i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 24 q^{9} + 8 q^{16} - 112 q^{22} - 168 q^{27} + 256 q^{40} + 56 q^{42} + 188 q^{48} - 8 q^{55} - 56 q^{61} - 184 q^{66} + 72 q^{81} + 112 q^{87} - 296 q^{94}+O(q^{100}) $ 96 * q + 24 * q^9 + 8 * q^16 - 112 * q^22 - 168 * q^27 + 256 * q^40 + 56 * q^42 + 188 * q^48 - 8 * q^55 - 56 * q^61 - 184 * q^66 + 72 * q^81 + 112 * q^87 - 296 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$-1$	$e\left(\frac{1}{12}\right)$

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 $

$2$	−0.522394	+	1.94960i	−0.369389	+	1.37858i	0.491984	+	0.870604i	$0.336272\pi$
$2$	−0.522394	+	1.94960i	−0.369389	+	1.37858i	−0.861373	+	0.507973i	$0.830395\pi$
$3$	0.152679	+	1.72531i	0.0881493	+	0.996107i
$3$	0.152679	+	1.72531i	0.0881493	+	0.996107i
$4$	−1.79600	−	1.03692i	−0.898001	−	0.518461i
$5$	1.72251	+	1.72251i	0.770331	+	0.770331i	0.978164	−	0.207834i	$-0.0666413\pi$
$5$	1.72251	+	1.72251i	0.770331	+	0.770331i	−0.207834	+	0.978164i	$0.566641\pi$
$6$	−3.44342	−	0.603628i	−1.40577	−	0.246430i
$7$	3.00582	−	0.805406i	1.13609	−	0.304415i	0.358713	−	0.933448i	$-0.383216\pi$
$7$	3.00582	−	0.805406i	1.13609	−	0.304415i	0.777379	+	0.629033i	$0.216549\pi$
$8$	0.105393	−	0.105393i	0.0372619	−	0.0372619i
$9$	−2.95338	+	0.526837i	−0.984459	+	0.175612i
$10$	−4.25804	+	2.45838i	−1.34651	+	0.777409i
$11$	2.67329	+	0.716305i	0.806027	+	0.215974i	0.638228	−	0.769847i	$-0.279668\pi$
$11$	2.67329	+	0.716305i	0.806027	+	0.215974i	0.167798	+	0.985821i	$0.446334\pi$
$12$	1.51480	−	3.25697i	0.437285	−	0.940208i
$13$		0			0
$13$		0			0
$14$			6.28089i			1.67864i
$15$	−2.70887	+	3.23485i	−0.699428	+	0.835236i
$16$	−1.92343	−	3.33148i	−0.480857	−	0.832869i
$17$	−2.89422	+	5.01294i	−0.701952	+	1.21582i	0.265829	+	0.964020i	$0.414354\pi$
$17$	−2.89422	+	5.01294i	−0.701952	+	1.21582i	−0.967780	+	0.251796i	$0.918979\pi$
$18$	0.515706	−	6.03313i	0.121553	−	1.42202i
$19$	0.388120	+	1.44849i	0.0890409	+	0.332305i	0.996049	−	0.0888086i	$-0.0283059\pi$
$19$	0.388120	+	1.44849i	0.0890409	+	0.332305i	−0.907008	+	0.421114i	$0.861639\pi$
$20$	−1.30752	−	4.87975i	−0.292371	−	1.09114i
$21$	1.84850	+	5.06299i	0.403376	+	1.10484i
$22$	−2.79302	+	4.83765i	−0.595474	+	1.03139i
$23$	−1.93268	−	3.34750i	−0.402992	−	0.698002i	0.591094	−	0.806603i	$-0.298696\pi$
$23$	−1.93268	−	3.34750i	−0.402992	−	0.698002i	−0.994085	+	0.108601i	$0.965363\pi$
$24$	0.197926	+	0.165743i	0.0404015	+	0.0338322i
$25$			0.934091i			0.186818i
$26$		0			0
$27$	−1.35988	−	5.01505i	−0.261708	−	0.965147i
$28$	−6.23360	−	1.67029i	−1.17804	−	0.315655i
$29$	2.53139	−	1.46150i	0.470068	−	0.271394i	−0.246200	−	0.969219i	$-0.579182\pi$
$29$	2.53139	−	1.46150i	0.470068	−	0.271394i	0.716268	+	0.697825i	$0.245849\pi$
$30$	−4.89158	−	6.97109i	−0.893076	−	1.27274i
$31$	3.56552	−	3.56552i	0.640387	−	0.640387i	−0.310264	−	0.950651i	$-0.600417\pi$
$31$	3.56552	−	3.56552i	0.640387	−	0.640387i	0.950651	+	0.310264i	$0.100417\pi$
$32$	7.78778	−	2.08673i	1.37670	−	0.368885i
$33$	−0.827693	+	4.72161i	−0.144083	+	0.821927i
$34$	−8.26131	−	8.26131i	−1.41680	−	1.41680i
$35$	6.56488	+	3.79023i	1.10967	+	0.640666i
$36$	5.85056	+	2.11622i	0.975094	+	0.352704i
$37$	−1.03921	+	3.87837i	−0.170844	+	0.637600i	0.826378	+	0.563116i	$0.190398\pi$
$37$	−1.03921	+	3.87837i	−0.170844	+	0.637600i	−0.997222	+	0.0744837i	$0.976269\pi$
$38$	−3.02672			−0.490999
$39$		0			0
$40$	0.363080			0.0574080
$41$	1.75678	−	6.55640i	0.274363	−	1.02394i	−0.681904	−	0.731442i	$-0.738848\pi$
$41$	1.75678	−	6.55640i	0.274363	−	1.02394i	0.956267	−	0.292496i	$-0.0944857\pi$
$42$	−10.8365	+	0.958960i	−1.67210	+	0.147971i
$43$	1.59566	+	0.921257i	0.243336	+	0.140490i	0.616709	−	0.787191i	$-0.288465\pi$
$43$	1.59566	+	0.921257i	0.243336	+	0.140490i	−0.373373	+	0.927681i	$0.621799\pi$
$44$	−4.05848	−	4.05848i	−0.611839	−	0.611839i
$45$	−5.99471	−	4.17974i	−0.893639	−	0.623080i
$46$	7.53592	−	2.01924i	1.11111	−	0.297721i
$47$	0.115676	−	0.115676i	0.0168731	−	0.0168731i	−0.698620	−	0.715493i	$-0.746202\pi$
$47$	0.115676	−	0.115676i	0.0168731	−	0.0168731i	0.715493	+	0.698620i	$0.246202\pi$
$48$	5.45416	−	3.82715i	0.787239	−	0.552402i
$49$	2.32408	−	1.34181i	0.332012	−	0.191687i
$50$	−1.82111	−	0.487964i	−0.257543	−	0.0690085i
$51$	−9.09075	−	4.22805i	−1.27296	−	0.592046i
$52$		0			0
$53$		−	10.0745i		−	1.38384i	−0.721976	−	0.691918i	$-0.756766\pi$
$53$		−	10.0745i		−	1.38384i	0.721976	−	0.691918i	$-0.243234\pi$
$54$	10.4877	−	0.0313815i	1.42720	−	0.00427048i
$55$	3.37093	+	5.83861i	0.454535	+	0.787278i
$56$	0.231907	−	0.401675i	0.0309899	−	0.0536760i
$57$	−2.43983	+	0.890781i	−0.323163	+	0.117987i
$58$	1.52696	+	5.69869i	0.200500	+	0.748275i
$59$	−0.446576	−	1.66664i	−0.0581392	−	0.216978i	0.930744	−	0.365671i	$-0.119160\pi$
$59$	−0.446576	−	1.66664i	−0.0581392	−	0.216978i	−0.988884	+	0.148692i	$0.952494\pi$
$60$	8.21944	−	3.00092i	1.06112	−	0.387417i
$61$	2.69796	−	4.67300i	0.345438	−	0.598316i	−0.639995	−	0.768379i	$-0.721064\pi$
$61$	2.69796	−	4.67300i	0.345438	−	0.598316i	0.985433	+	0.170063i	$0.0543970\pi$
$62$	5.08874	+	8.81396i	0.646271	+	1.11937i
$63$	−8.45300	+	3.96225i	−1.06498	+	0.499196i
$64$			8.57945i			1.07243i
$65$		0			0
$66$	−8.77288	−	4.08021i	−1.07987	−	0.502240i
$67$	−13.1928	−	3.53501i	−1.61176	−	0.431870i	−0.663193	−	0.748448i	$-0.730799\pi$
$67$	−13.1928	−	3.53501i	−1.61176	−	0.431870i	−0.948566	+	0.316579i	$0.897466\pi$
$68$	10.3961	−	6.00217i	1.26071	−	0.727869i
$69$	5.48039	−	3.84556i	0.659762	−	0.462952i
$70$	−10.8189	+	10.8189i	−1.29311	+	1.29311i
$71$	0.326665	−	0.0875296i	0.0387680	−	0.0103879i	−0.239383	−	0.970925i	$-0.576945\pi$
$71$	0.326665	−	0.0875296i	0.0387680	−	0.0103879i	0.278151	+	0.960537i	$0.410278\pi$
$72$	−0.255739	+	0.366789i	−0.0301392	+	0.0432265i
$73$	8.54904	+	8.54904i	1.00059	+	1.00059i	1.00000		0.000589733i	$0.000187718\pi$
$73$	8.54904	+	8.54904i	1.00059	+	1.00059i	0.000589733		1.00000i	$0.499812\pi$
$74$	−7.01840	−	4.05207i	−0.815872	−	0.471044i
$75$	−1.61160	+	0.142616i	−0.186091	+	0.0164679i
$76$	0.804902	−	3.00393i	0.0923286	−	0.344575i
$77$	8.61233			0.981466
$78$		0			0
$79$	10.4089			1.17110			0.585549	−	0.810637i	$-0.300879\pi$
$79$	10.4089			1.17110			0.585549	+	0.810637i	$0.300879\pi$
$80$	2.42538	−	9.05163i	0.271165	−	1.01200i
$81$	8.44489	−	3.11190i	0.938321	−	0.345766i
$82$	11.8646	+	6.85005i	1.31023	+	0.756462i
$83$	2.83841	+	2.83841i	0.311556	+	0.311556i	0.845512	−	0.533956i	$-0.179295\pi$
$83$	2.83841	+	2.83841i	0.311556	+	0.311556i	−0.533956	+	0.845512i	$0.679295\pi$
$84$	1.93002	−	11.0099i	0.210583	−	1.20128i
$85$	−13.6202	+	3.64951i	−1.47731	+	0.395845i
$86$	−2.62965	+	2.62965i	−0.283562	+	0.283562i
$87$	2.90803	+	4.14429i	0.311774	+	0.444315i
$88$	0.357238	−	0.206251i	0.0380817	−	0.0219865i
$89$	−4.10839	−	1.10084i	−0.435488	−	0.116689i	0.0344130	−	0.999408i	$-0.489044\pi$
$89$	−4.10839	−	1.10084i	−0.435488	−	0.116689i	−0.469901	+	0.882719i	$0.655711\pi$
$90$	11.2804	−	9.50383i	1.18906	−	1.00179i
$91$		0			0
$92$			8.01616i			0.835743i
$93$	6.69601	+	5.60725i	0.694344	+	0.581444i
$94$	0.165094	+	0.285951i	0.0170282	+	0.0294936i
$95$	−1.82649	+	3.16357i	−0.187394	+	0.324576i
$96$	4.78928	+	13.1177i	0.488804	+	1.33882i
$97$	2.56119	+	9.55851i	0.260050	+	0.970520i	0.965211	+	0.261472i	$0.0842080\pi$
$97$	2.56119	+	9.55851i	0.260050	+	0.970520i	−0.705161	+	0.709047i	$0.749125\pi$
$98$	1.40191	+	5.23199i	0.141614	+	0.528511i
$99$	−8.27261	−	0.707134i	−0.831428	−	0.0710696i
$100$	0.968580	−	1.67763i	0.0968580	−	0.167763i
$101$	−4.61612	−	7.99536i	−0.459321	−	0.795568i	0.539604	−	0.841919i	$-0.318574\pi$
$101$	−4.61612	−	7.99536i	−0.459321	−	0.795568i	−0.998925	+	0.0463510i	$0.985241\pi$
$102$	12.9920	−	15.5146i	1.28640	−	1.53618i
$103$			17.2662i			1.70129i	0.525737	+	0.850647i	$0.323789\pi$
$103$			17.2662i			1.70129i	−0.525737	+	0.850647i	$0.676211\pi$
$104$		0			0
$105$	−5.53700	+	11.9051i	−0.540356	+	1.16182i
$106$	19.6412	+	5.26285i	1.90772	+	0.511173i
$107$	−9.20781	+	5.31613i	−0.890153	+	0.513930i	−0.873992	−	0.485939i	$-0.838478\pi$
$107$	−9.20781	+	5.31613i	−0.890153	+	0.513930i	−0.0161603	+	0.999869i	$0.505144\pi$
$108$	−2.75788	+	10.4171i	−0.265377	+	1.00239i
$109$	−0.625106	+	0.625106i	−0.0598743	+	0.0598743i	−0.736410	−	0.676536i	$-0.763480\pi$
$109$	−0.625106	+	0.625106i	−0.0598743	+	0.0598743i	0.676536	+	0.736410i	$0.263480\pi$
$110$	−13.1439	+	3.52190i	−1.25322	+	0.335800i
$111$	−6.85004	−	1.20080i	−0.650177	−	0.113975i
$112$	−8.46467	−	8.46467i	−0.799836	−	0.799836i
$113$	−5.88672	−	3.39870i	−0.553776	−	0.319723i	0.196868	−	0.980430i	$-0.436923\pi$
$113$	−5.88672	−	3.39870i	−0.553776	−	0.319723i	−0.750644	+	0.660707i	$0.770256\pi$
$114$	−0.462117	−	5.22203i	−0.0432812	−	0.489088i
$115$	2.43705	−	9.09518i	0.227256	−	0.848130i
$116$	−6.06185			−0.562829
$117$		0			0
$118$	3.48258			0.320597
$119$	−4.66205	+	17.3990i	−0.427369	+	1.59496i
$120$	0.0554347	+	0.626425i	0.00506047	+	0.0571845i
$121$	−2.89290	−	1.67022i	−0.262991	−	0.151838i
$122$	7.70110	+	7.70110i	0.697224	+	0.697224i
$123$	11.5800	+	2.02997i	1.04414	+	0.183036i
$124$	−10.1009	+	2.70652i	−0.907084	+	0.243052i
$125$	7.00357	−	7.00357i	0.626419	−	0.626419i
$126$	−3.30900	−	18.5498i	−0.294790	−	1.65255i
$127$	0.351315	−	0.202832i	0.0311742	−	0.0179984i	−0.484332	−	0.874884i	$-0.660937\pi$
$127$	0.351315	−	0.202832i	0.0311742	−	0.0179984i	0.515506	+	0.856886i	$0.327604\pi$
$128$	−1.15097	−	0.308400i	−0.101732	−	0.0272590i
$129$	−1.34583	+	2.89367i	−0.118493	+	0.254773i
$130$		0			0
$131$			7.22040i			0.630850i	0.948951	+	0.315425i	$0.102147\pi$
$131$			7.22040i			0.630850i	−0.948951	+	0.315425i	$0.897853\pi$
$132$	6.38248	−	7.62177i	0.555524	−	0.663390i
$133$	2.33324	+	4.04129i	0.202317	+	0.350424i
$134$	13.7837	−	23.8741i	1.19073	−	2.06241i
$135$	6.29608	−	10.9809i	0.541880	−	0.945084i
$136$	0.223297	+	0.833356i	0.0191476	+	0.0714597i
$137$	5.10426	+	19.0493i	0.436086	+	1.62750i	0.738454	+	0.674304i	$0.235556\pi$
$137$	5.10426	+	19.0493i	0.436086	+	1.62750i	−0.302368	+	0.953191i	$0.597777\pi$
$138$	4.63440	+	12.6935i	0.394506	+	1.08054i
$139$	−5.17924	+	8.97070i	−0.439297	+	0.760885i	−0.997635	−	0.0687285i	$-0.978106\pi$
$139$	−5.17924	+	8.97070i	−0.439297	+	0.760885i	0.558338	+	0.829613i	$0.311439\pi$
$140$	−7.86036	−	13.6145i	−0.664321	−	1.15064i
$141$	0.217239	+	0.181916i	0.0182948	+	0.0153201i
$142$			0.682592i			0.0572818i
$143$		0			0
$144$	7.43576	+	8.82577i	0.619646	+	0.735481i
$145$	6.87780	+	1.84290i	0.571171	+	0.153045i
$146$	−21.1332	+	12.2013i	−1.74900	+	1.00978i
$147$	2.66987	+	3.80489i	0.220207	+	0.313822i
$148$	5.88798	−	5.88798i	0.483989	−	0.483989i
$149$	−4.70169	+	1.25981i	−0.385177	+	0.103208i	−0.446211	−	0.894928i	$-0.647227\pi$
$149$	−4.70169	+	1.25981i	−0.385177	+	0.103208i	0.0610337	+	0.998136i	$0.480560\pi$
$150$	0.563843	−	3.21647i	0.0460376	−	0.262624i
$151$	3.11666	+	3.11666i	0.253630	+	0.253630i	0.822457	−	0.568827i	$-0.192603\pi$
$151$	3.11666	+	3.11666i	0.253630	+	0.253630i	−0.568827	+	0.822457i	$0.692603\pi$
$152$	0.193565	+	0.111755i	0.0157002	+	0.00906449i
$153$	5.90673	−	16.3299i	0.477531	−	1.32019i
$154$	−4.49903	+	16.7906i	−0.362543	+	1.35303i
$155$	12.2833			0.986619
$156$		0			0
$157$	−5.43153			−0.433483			−0.216741	−	0.976229i	$-0.569543\pi$
$157$	−5.43153			−0.433483			−0.216741	+	0.976229i	$0.569543\pi$
$158$	−5.43757	+	20.2933i	−0.432590	+	1.61445i
$159$	17.3816	−	1.53816i	1.37845	−	0.121984i
$160$	17.0090	+	9.82012i	1.34468	+	0.776349i
$161$	−8.50539	−	8.50539i	−0.670318	−	0.670318i
$162$	1.65540	+	18.0898i	0.130061	+	1.42127i
$163$	11.9029	−	3.18936i	0.932304	−	0.249810i	0.239467	−	0.970904i	$-0.423027\pi$
$163$	11.9029	−	3.18936i	0.932304	−	0.249810i	0.692837	+	0.721094i	$0.256361\pi$
$164$	−9.95367	+	9.95367i	−0.777251	+	0.777251i
$165$	−9.55874	+	6.70732i	−0.744147	+	0.522164i
$166$	−7.01655	+	4.05100i	−0.544590	+	0.314419i
$167$	21.3775	+	5.72807i	1.65424	+	0.443252i	0.960795	−	0.277260i	$-0.0894263\pi$
$167$	21.3775	+	5.72807i	1.65424	+	0.443252i	0.693443	+	0.720512i	$0.256093\pi$
$168$	0.728420	+	0.338784i	0.0561988	+	0.0261377i
$169$		0			0
$170$		−	28.4604i		−	2.18281i
$171$	−1.90938	−	4.07345i	−0.146014	−	0.311504i
$172$	−1.91054	−	3.30916i	−0.145678	−	0.252321i
$173$	4.66570	−	8.08124i	0.354727	−	0.614405i	−0.632344	−	0.774687i	$-0.717907\pi$
$173$	4.66570	−	8.08124i	0.354727	−	0.614405i	0.987071	+	0.160282i	$0.0512405\pi$
$174$	−9.59886	+	3.50455i	−0.727688	+	0.265679i
$175$	0.752323	+	2.80771i	0.0568703	+	0.212243i
$176$	−2.75552	−	10.2838i	−0.207705	−	0.775167i
$177$	2.80729	−	1.02494i	0.211009	−	0.0770394i
$178$	4.29240	−	7.43465i	0.321729	−	0.557251i
$179$	13.3578	+	23.1364i	0.998409	+	1.72929i	0.548044	+	0.836449i	$0.315373\pi$
$179$	13.3578	+	23.1364i	0.998409	+	1.72929i	0.450364	+	0.892845i	$0.351294\pi$
$180$	6.43244	+	13.7229i	0.479446	+	1.02284i
$181$		−	26.2746i		−	1.95297i	−0.215577	−	0.976487i	$-0.569163\pi$
$181$		−	26.2746i		−	1.95297i	0.215577	−	0.976487i	$-0.430837\pi$
$182$		0			0
$183$	8.47429	+	3.94134i	0.626438	+	0.291352i
$184$	−0.556492	−	0.149112i	−0.0410251	−	0.0109927i
$185$	−8.47057	+	4.89049i	−0.622769	+	0.359556i
$186$	−14.4299	+	10.1254i	−1.05805	+	0.742427i
$187$	−11.3279	+	11.3279i	−0.828377	+	0.828377i
$188$	−0.327702	+	0.0878076i	−0.0239002	+	0.00640403i
$189$	−8.12669	−	13.9791i	−0.591130	−	1.01683i
$190$	−5.21356	−	5.21356i	−0.378232	−	0.378232i
$191$	−6.67034	−	3.85112i	−0.482649	−	0.278657i	0.238871	−	0.971051i	$-0.423223\pi$
$191$	−6.67034	−	3.85112i	−0.482649	−	0.278657i	−0.721520	+	0.692394i	$0.756556\pi$
$192$	−14.8022	+	1.30990i	−1.06826	+	0.0945341i
$193$	4.03302	−	15.0515i	0.290303	−	1.08343i	−0.654573	−	0.755999i	$-0.727151\pi$
$193$	4.03302	−	15.0515i	0.290303	−	1.08343i	0.944876	−	0.327428i	$-0.106182\pi$
$194$	−19.9732			−1.43400
$195$		0			0
$196$	−5.56541			−0.397529
$197$	6.80534	−	25.3979i	0.484860	−	1.80952i	−0.0958291	−	0.995398i	$-0.530550\pi$
$197$	6.80534	−	25.3979i	0.484860	−	1.80952i	0.580689	−	0.814125i	$-0.302783\pi$
$198$	5.70019	−	15.7589i	0.405095	−	1.11994i
$199$	−11.8805	−	6.85923i	−0.842188	−	0.486238i	0.0158190	−	0.999875i	$-0.494964\pi$
$199$	−11.8805	−	6.85923i	−0.842188	−	0.486238i	−0.858008	+	0.513637i	$0.828298\pi$
$200$	0.0984463	+	0.0984463i	0.00696120	+	0.00696120i
$201$	4.08471	−	23.3014i	0.288113	−	1.64355i
$202$	17.9992	−	4.82287i	1.26642	−	0.339336i
$203$	6.43180	−	6.43180i	0.451424	−	0.451424i
$204$	11.9428	+	17.0200i	0.836167	+	1.19164i
$205$	14.3196	−	8.26740i	1.00012	−	0.577420i
$206$	−33.6623	−	9.01979i	−2.34536	−	0.628439i
$207$	7.47153	+	8.86823i	0.519307	+	0.616385i
$208$		0			0
$209$			4.15023i			0.287078i
$210$	−20.3178	−	17.0141i	−1.40206	−	1.17409i
$211$	−10.7717	−	18.6571i	−0.741555	−	1.28441i	−0.951787	−	0.306759i	$-0.900756\pi$
$211$	−10.7717	−	18.6571i	−0.741555	−	1.28441i	0.210233	−	0.977651i	$-0.432578\pi$
$212$	−10.4464	+	18.0938i	−0.717465	+	1.24269i
$213$	0.200890	+	0.550234i	0.0137648	+	0.0377014i
$214$	−5.55424	−	20.7287i	−0.379680	−	1.41698i
$215$	1.16167	+	4.33542i	0.0792254	+	0.295673i
$216$	−0.671870	−	0.385228i	−0.0457150	−	0.0262115i
$217$	7.84562	−	13.5890i	0.532595	−	0.922482i
$218$	−0.892156	−	1.54526i	−0.0604244	−	0.104658i
$219$	−13.4445	+	16.0550i	−0.908493	+	1.08490i
$220$		−	13.9816i		−	0.942636i
$221$		0			0
$222$	5.91951	−	12.7276i	0.397292	−	0.854218i
$223$	−14.3363	−	3.84141i	−0.960032	−	0.257240i	−0.255418	−	0.966831i	$-0.582213\pi$
$223$	−14.3363	−	3.84141i	−0.960032	−	0.257240i	−0.704614	+	0.709591i	$0.748880\pi$
$224$	21.7280	−	12.5447i	1.45176	−	0.838175i
$225$	−0.492114	−	2.75872i	−0.0328076	−	0.183915i
$226$	9.70130	−	9.70130i	0.645321	−	0.645321i
$227$	−2.20400	+	0.590561i	−0.146285	+	0.0391969i	−0.331218	−	0.943554i	$-0.607460\pi$
$227$	−2.20400	+	0.590561i	−0.146285	+	0.0391969i	0.184934	+	0.982751i	$0.440793\pi$
$228$	5.30561	+	0.930066i	0.351372	+	0.0615951i
$229$	−1.83952	−	1.83952i	−0.121559	−	0.121559i	0.643711	−	0.765269i	$-0.277394\pi$
$229$	−1.83952	−	1.83952i	−0.121559	−	0.121559i	−0.765269	+	0.643711i	$0.777394\pi$
$230$	16.4589	+	9.50254i	1.08527	+	0.626579i
$231$	1.31492	+	14.8589i	0.0865156	+	0.977646i
$232$	0.112759	−	0.420821i	0.00740297	−	0.0276283i
$233$	−16.4441			−1.07729			−0.538645	−	0.842533i	$-0.681064\pi$
$233$	−16.4441			−1.07729			−0.538645	+	0.842533i	$0.681064\pi$
$234$		0			0
$235$	0.398508			0.0259958
$236$	−0.926129	+	3.45636i	−0.0602858	+	0.224990i
$237$	1.58923	+	17.9586i	0.103231	+	1.16654i
$238$	−31.4857	−	18.1783i	−2.04091	−	1.17832i
$239$	−7.33986	−	7.33986i	−0.474776	−	0.474776i	0.428680	−	0.903456i	$-0.358979\pi$
$239$	−7.33986	−	7.33986i	−0.474776	−	0.474776i	−0.903456	+	0.428680i	$0.858979\pi$
$240$	15.9872	+	2.80253i	1.03197	+	0.180902i
$241$	−5.68906	+	1.52438i	−0.366465	+	0.0981939i	−0.437352	−	0.899290i	$-0.644084\pi$
$241$	−5.68906	+	1.52438i	−0.366465	+	0.0981939i	0.0708874	+	0.997484i	$0.477417\pi$
$242$	4.76750	−	4.76750i	0.306466	−	0.306466i
$243$	6.65834	+	14.0949i	0.427133	+	0.904189i
$244$	−9.69108	+	5.59515i	−0.620408	+	0.358193i
$245$	6.31454	+	1.69198i	0.403421	+	0.108096i
$246$	−10.0070	+	21.5160i	−0.638021	+	1.37181i
$247$		0			0
$248$		−	0.751559i		−	0.0477241i
$249$	−4.46377	+	5.33050i	−0.282880	+	0.337807i
$250$	9.99556	+	17.3128i	0.632175	+	1.09496i
$251$	−0.111077	+	0.192391i	−0.00701111	+	0.0121436i	−0.869510	−	0.493916i	$-0.835565\pi$
$251$	−0.111077	+	0.192391i	−0.00701111	+	0.0121436i	0.862499	+	0.506060i	$0.168898\pi$
$252$	19.2901	+	1.64890i	1.21517	+	0.103871i
$253$	−2.76878	−	10.3332i	−0.174072	−	0.649644i
$254$	0.211917	+	0.790883i	0.0132968	+	0.0496244i
$255$	−8.37605	−	22.9418i	−0.524529	−	1.43667i
$256$	−7.37694	+	12.7772i	−0.461059	+	0.798577i
$257$	12.6431	+	21.8986i	0.788658	+	1.36600i	0.926789	+	0.375582i	$0.122557\pi$
$257$	12.6431	+	21.8986i	0.788658	+	1.36600i	−0.138132	+	0.990414i	$0.544110\pi$
$258$	−4.93845	−	4.13546i	−0.307454	−	0.257463i
$259$			12.4946i			0.776379i
$260$		0			0
$261$	−6.70619	+	5.65000i	−0.415103	+	0.349726i
$262$	−14.0769	−	3.77190i	−0.869675	−	0.233029i
$263$	4.23596	−	2.44563i	0.261200	−	0.150804i	−0.363682	−	0.931523i	$-0.618480\pi$
$263$	4.23596	−	2.44563i	0.261200	−	0.150804i	0.624882	+	0.780719i	$0.285147\pi$
$264$	0.410390	+	0.584855i	0.0252578	+	0.0359954i
$265$	17.3534	−	17.3534i	1.06601	−	1.06601i
$266$	−9.09778	+	2.43774i	−0.557820	+	0.149468i
$267$	1.27202	−	7.25631i	0.0778465	−	0.444079i
$268$	20.0288	+	20.0288i	1.22345	+	1.22345i
$269$	18.3121	+	10.5725i	1.11651	+	0.644616i	0.940507	−	0.339774i	$-0.110350\pi$
$269$	18.3121	+	10.5725i	1.11651	+	0.644616i	0.176001	+	0.984390i	$0.443684\pi$
$270$	18.1193	+	18.0112i	1.10271	+	1.09613i
$271$	0.492584	−	1.83835i	0.0299224	−	0.111672i	−0.949349	−	0.314222i	$-0.898256\pi$
$271$	0.492584	−	1.83835i	0.0299224	−	0.111672i	0.979272	+	0.202550i	$0.0649230\pi$
$272$	22.2673			1.35015
$273$		0			0
$274$	−39.8051			−2.40471
$275$	−0.669094	+	2.49709i	−0.0403479	+	0.150580i
$276$	−13.8304	+	1.22390i	−0.832490	+	0.0736701i
$277$	−3.42082	−	1.97501i	−0.205537	−	0.118667i	0.393698	−	0.919240i	$-0.371195\pi$
$277$	−3.42082	−	1.97501i	−0.205537	−	0.118667i	−0.599236	+	0.800573i	$0.704529\pi$
$278$	−14.7837	−	14.7837i	−0.886667	−	0.886667i
$279$	−8.65189	+	12.4088i	−0.517975	+	0.742895i
$280$	1.09135	−	0.292427i	0.0652207	−	0.0174758i
$281$	3.08435	−	3.08435i	0.183997	−	0.183997i	−0.609098	−	0.793095i	$-0.708468\pi$
$281$	3.08435	−	3.08435i	0.183997	−	0.183997i	0.793095	+	0.609098i	$0.208468\pi$
$282$	−0.468148	+	0.328497i	−0.0278778	+	0.0195617i
$283$	−15.9660	+	9.21796i	−0.949079	+	0.547951i	−0.892795	−	0.450464i	$-0.851259\pi$
$283$	−15.9660	+	9.21796i	−0.949079	+	0.547951i	−0.0562842	+	0.998415i	$0.517925\pi$
$284$	−0.677453	−	0.181523i	−0.0401994	−	0.0107714i
$285$	−5.73701	−	2.66825i	−0.339831	−	0.158053i
$286$		0			0
$287$		−	21.1223i		−	1.24681i
$288$	−21.9009	+	10.2658i	−1.29052	+	0.604917i
$289$	−8.25302	−	14.2947i	−0.485472	−	0.840862i
$290$	−7.18585	+	12.4463i	−0.421968	+	0.730870i
$291$	−16.1003	+	5.87824i	−0.943818	+	0.344588i
$292$	−6.48941	−	24.2188i	−0.379764	−	1.41730i
$293$	−4.05197	−	15.1222i	−0.236719	−	0.883447i	−0.977366	−	0.211553i	$-0.932148\pi$
$293$	−4.05197	−	15.1222i	−0.236719	−	0.883447i	0.740648	−	0.671894i	$-0.234519\pi$
$294$	−8.81275	+	3.21754i	−0.513970	+	0.187651i
$295$	2.10158	−	3.64004i	0.122359	−	0.211931i
$296$	0.299227	+	0.518276i	0.0173922	+	0.0301242i
$297$	−0.0430302	−	14.3808i	−0.00249687	−	0.834457i
$298$		−	9.82454i		−	0.569121i
$299$		0			0
$300$	3.04231	+	1.41496i	0.175648	+	0.0816928i
$301$	5.53826	+	1.48397i	0.319220	+	0.0855347i
$302$	−7.70438	+	4.44813i	−0.443337	+	0.255961i
$303$	13.0897	−	9.18496i	0.751982	−	0.527662i
$304$	4.07907	−	4.07907i	0.233951	−	0.233951i
$305$	12.6966	−	3.40203i	0.727003	−	0.194800i
$306$	28.7511	+	20.0464i	1.64359	+	1.14598i
$307$	−4.22784	−	4.22784i	−0.241295	−	0.241295i	0.576090	−	0.817386i	$-0.304578\pi$
$307$	−4.22784	−	4.22784i	−0.241295	−	0.241295i	−0.817386	+	0.576090i	$0.804578\pi$
$308$	−15.4678	−	8.93032i	−0.881358	−	0.508852i
$309$	−29.7896	+	2.63619i	−1.69467	+	0.149968i
$310$	−6.41673	+	23.9476i	−0.364446	+	1.36013i
$311$	20.8485			1.18221			0.591106	−	0.806594i	$-0.298692\pi$
$311$	20.8485			1.18221			0.591106	+	0.806594i	$0.298692\pi$
$312$		0			0
$313$	6.93682			0.392092			0.196046	−	0.980595i	$-0.437190\pi$
$313$	6.93682			0.392092			0.196046	+	0.980595i	$0.437190\pi$
$314$	2.83740	−	10.5893i	0.160124	−	0.597590i
$315$	−21.3854	−	7.73537i	−1.20493	−	0.435839i
$316$	−18.6945	−	10.7933i	−1.05165	−	0.607169i
$317$	7.43185	+	7.43185i	0.417414	+	0.417414i	0.884311	−	0.466897i	$-0.154628\pi$
$317$	7.43185	+	7.43185i	0.417414	+	0.417414i	−0.466897	+	0.884311i	$0.654628\pi$
$318$	−6.08123	+	34.6907i	−0.341019	+	1.94536i
$319$	7.81402	−	2.09376i	0.437501	−	0.117228i
$320$	−14.7782	+	14.7782i	−0.826127	+	0.826127i
$321$	−10.5778	−	15.0747i	−0.590396	−	0.841385i
$322$	21.0253	−	12.1390i	1.17169	−	0.676478i
$323$	−8.38447	−	2.24661i	−0.466525	−	0.125005i
$324$	−18.3938	−	3.16772i	−1.02188	−	0.175984i
$325$		0			0
$326$			24.8719i			1.37753i
$327$	−1.17394	−	0.983060i	−0.0649191	−	0.0543633i
$328$	−0.505844	−	0.876148i	−0.0279306	−	0.0483772i
$329$	0.254535	−	0.440868i	0.0140330	−	0.0243059i
$330$	−8.08317	−	22.1396i	−0.444964	−	1.21875i
$331$	5.62946	+	21.0094i	0.309423	+	1.15478i	0.929070	+	0.369903i	$0.120609\pi$
$331$	5.62946	+	21.0094i	0.309423	+	1.15478i	−0.619647	+	0.784881i	$0.712724\pi$
$332$	−2.15458	−	8.04101i	−0.118248	−	0.441308i
$333$	1.02590	−	12.0018i	0.0562189	−	0.657693i
$334$	−22.3349	+	38.6852i	−1.22211	+	2.11676i
$335$	−16.6357	−	28.8139i	−0.908905	−	1.57427i
$336$	13.3118	−	15.8965i	0.726217	−	0.867227i
$337$		−	33.1734i		−	1.80707i	−0.428512	−	0.903536i	$-0.640962\pi$
$337$		−	33.1734i		−	1.80707i	0.428512	−	0.903536i	$-0.359038\pi$
$338$		0			0
$339$	4.96502	−	10.6753i	0.269663	−	0.579804i
$340$	28.2461	+	7.56853i	1.53186	+	0.410461i
$341$	12.0857	−	6.97767i	0.654476	−	0.377862i
$342$	8.93906	−	1.59459i	0.483369	−	0.0862255i
$343$	−9.49781	+	9.49781i	−0.512834	+	0.512834i
$344$	0.265265	−	0.0710774i	0.0143021	−	0.00383224i
$345$	16.0641	+	2.81601i	0.864860	+	0.151609i
$346$	13.3179	+	13.3179i	0.715973	+	0.715973i
$347$	−29.1720	−	16.8424i	−1.56603	−	0.904150i	−0.996624	−	0.0820954i	$-0.973839\pi$
$347$	−29.1720	−	16.8424i	−1.56603	−	0.904150i	−0.569409	−	0.822054i	$-0.692828\pi$
$348$	−0.925518	−	10.4586i	−0.0496130	−	0.560638i
$349$	−5.22478	+	19.4991i	−0.279676	+	1.04376i	0.672967	+	0.739673i	$0.265020\pi$
$349$	−5.22478	+	19.4991i	−0.279676	+	1.04376i	−0.952643	+	0.304092i	$0.901647\pi$
$350$	−5.86692			−0.313600
$351$		0			0
$352$	22.3137			1.18932
$353$	−4.66368	+	17.4051i	−0.248223	+	0.926380i	0.723513	+	0.690310i	$0.242526\pi$
$353$	−4.66368	+	17.4051i	−0.248223	+	0.926380i	−0.971736	+	0.236070i	$0.924141\pi$
$354$	0.531717	+	6.00852i	0.0282604	+	0.319349i
$355$	0.713455	+	0.411913i	0.0378663	+	0.0218621i
$356$	6.23719	+	6.23719i	0.330570	+	0.330570i
$357$	−30.7304	−	5.38701i	−1.62643	−	0.285111i
$358$	−52.0848	+	13.9561i	−2.75277	+	0.737601i
$359$	−17.0308	+	17.0308i	−0.898849	+	0.898849i	−0.995334	−	0.0964857i	$-0.969240\pi$
$359$	−17.0308	+	17.0308i	−0.898849	+	0.898849i	0.0964857	+	0.995334i	$0.469240\pi$
$360$	−1.07231	+	0.191284i	−0.0565158	+	0.0100815i
$361$	14.5070	−	8.37563i	0.763527	−	0.440822i
$362$	51.2250	+	13.7257i	2.69232	+	0.721406i
$363$	2.43996	−	5.24616i	0.128064	−	0.275352i
$364$		0			0
$365$			29.4516i			1.54157i
$366$	−12.1110	+	14.4626i	−0.633050	+	0.755970i
$367$	9.42059	+	16.3169i	0.491751	+	0.851738i	0.999955	−	0.00949906i	$-0.00302369\pi$
$367$	9.42059	+	16.3169i	0.491751	+	0.851738i	−0.508204	+	0.861237i	$0.669690\pi$
$368$	−7.43475	+	12.8774i	−0.387563	+	0.671279i
$369$	−1.73429	+	20.2891i	−0.0902834	+	1.05621i
$370$	−5.10953	−	19.0690i	−0.265632	−	0.991351i
$371$	−8.11405	−	30.2820i	−0.421260	−	1.57216i
$372$	−6.21177	−	17.0139i	−0.322065	−	0.882128i
$373$	8.98511	−	15.5627i	0.465231	−	0.805804i	−0.533981	−	0.845497i	$-0.679304\pi$
$373$	8.98511	−	15.5627i	0.465231	−	0.805804i	0.999212	+	0.0396925i	$0.0126378\pi$
$374$	−16.1672	−	28.0025i	−0.835988	−	1.44797i
$375$	13.1526	+	11.0140i	0.679199	+	0.568762i
$376$		−	0.0243828i		−	0.00125745i
$377$		0			0
$378$	31.4990	−	8.54123i	1.62013	−	0.439313i
$379$	15.6235	+	4.18632i	0.802528	+	0.215037i	0.636693	−	0.771117i	$-0.280302\pi$
$379$	15.6235	+	4.18632i	0.802528	+	0.215037i	0.165834	+	0.986154i	$0.446968\pi$
$380$	6.56076	−	3.78786i	0.336560	−	0.194313i
$381$	0.403586	+	0.575159i	0.0206763	+	0.0294663i
$382$	10.9927	−	10.9927i	0.562436	−	0.562436i
$383$	16.3191	−	4.37268i	0.833865	−	0.223433i	0.183466	−	0.983026i	$-0.441268\pi$
$383$	16.3191	−	4.37268i	0.833865	−	0.223433i	0.650399	+	0.759593i	$0.274602\pi$
$384$	0.356357	−	2.03286i	0.0181853	−	0.103739i
$385$	14.8348	+	14.8348i	0.756054	+	0.756054i
$386$	27.2375	+	15.7256i	1.38635	+	0.800411i
$387$	−5.19795	−	1.88016i	−0.264227	−	0.0955741i
$388$	5.31152	−	19.8229i	0.269652	−	1.00635i
$389$	−29.3747			−1.48936			−0.744678	−	0.667424i	$-0.767397\pi$
$389$	−29.3747			−1.48936			−0.744678	+	0.667424i	$0.767397\pi$
$390$		0			0
$391$	22.3744			1.13152
$392$	0.103524	−	0.386358i	0.00522876	−	0.0195140i
$393$	−12.4574	+	1.10240i	−0.628394	+	0.0556089i
$394$	45.9607	+	26.5354i	2.31547	+	1.33683i
$395$	17.9295	+	17.9295i	0.902132	+	0.902132i
$396$	14.1244	+	9.84807i	0.709777	+	0.494884i
$397$	15.6987	−	4.20647i	0.787898	−	0.211117i	0.157634	−	0.987498i	$-0.449613\pi$
$397$	15.6987	−	4.20647i	0.787898	−	0.211117i	0.630264	+	0.776381i	$0.282947\pi$
$398$	19.5791	−	19.5791i	0.981411	−	0.981411i
$399$	−6.61623	+	4.64258i	−0.331226	+	0.232420i
$400$	3.11190	−	1.79666i	0.155595	−	0.0898328i
$401$	1.99788	+	0.535331i	0.0997695	+	0.0267331i	0.308358	−	0.951270i	$-0.400220\pi$
$401$	1.99788	+	0.535331i	0.0997695	+	0.0267331i	−0.208589	+	0.978003i	$0.566887\pi$
$402$	43.2946	+	20.1361i	2.15934	+	1.00430i
$403$		0			0
$404$			19.1463i			0.952562i
$405$	19.9067	+	9.18613i	0.989171	+	0.456463i
$406$	9.17952	+	15.8994i	0.455572	+	0.789074i
$407$	−5.55619	+	9.62360i	−0.275410	+	0.477024i
$408$	−1.40370	+	0.512492i	−0.0694936	+	0.0253721i
$409$	−2.11287	−	7.88532i	−0.104474	−	0.389904i	0.893811	−	0.448445i	$-0.148022\pi$
$409$	−2.11287	−	7.88532i	−0.104474	−	0.389904i	−0.998285	+	0.0585408i	$0.981355\pi$
$410$	8.63768	+	32.2363i	0.426585	+	1.59204i
$411$	−32.0867	+	11.7149i	−1.58272	+	0.577851i
$412$	17.9038	−	31.0102i	0.882055	−	1.52776i
$413$	−2.68465	−	4.64995i	−0.132103	−	0.228809i
$414$	−21.1926	+	9.93379i	−1.04156	+	0.488219i
$415$			9.77840i			0.480003i
$416$		0			0
$417$	−16.2680	−	7.56614i	−0.796647	−	0.370516i
$418$	−8.09130	−	2.16806i	−0.395758	−	0.106043i
$419$	4.13398	−	2.38676i	0.201958	−	0.116601i	−0.395610	−	0.918418i	$-0.629467\pi$
$419$	4.13398	−	2.38676i	0.201958	−	0.116601i	0.597569	+	0.801818i	$0.296134\pi$
$420$	22.2892	−	15.6402i	1.08760	−	0.763163i
$421$	6.32386	−	6.32386i	0.308206	−	0.308206i	−0.536007	−	0.844213i	$-0.680068\pi$
$421$	6.32386	−	6.32386i	0.308206	−	0.308206i	0.844213	+	0.536007i	$0.180068\pi$
$422$	42.0011	−	11.2542i	2.04458	−	0.547844i
$423$	−0.280693	+	0.402578i	−0.0136478	+	0.0195740i
$424$	−1.06177	−	1.06177i	−0.0515643	−	0.0515643i
$425$	−4.68254	−	2.70347i	−0.227137	−	0.131137i
$426$	−1.17768	+	0.104217i	−0.0570589	+	0.00504935i
$427$	4.34591	−	16.2191i	0.210313	−	0.784899i
$428$	22.0497			1.06581
$429$		0			0
$430$	−9.05920			−0.436874
$431$	4.68871	−	17.4985i	0.225847	−	0.842873i	−0.756216	−	0.654322i	$-0.772954\pi$
$431$	4.68871	−	17.4985i	0.225847	−	0.842873i	0.982063	−	0.188551i	$-0.0603792\pi$
$432$	−14.0919	+	14.1765i	−0.677997	+	0.682066i
$433$	−22.0869	−	12.7519i	−1.06143	−	0.612816i	−0.135602	−	0.990763i	$-0.543297\pi$
$433$	−22.0869	−	12.7519i	−1.06143	−	0.612816i	−0.925827	+	0.377947i	$0.876630\pi$
$434$	22.3947	+	22.3947i	1.07498	+	1.07498i
$435$	−2.12948	+	12.1477i	−0.102101	+	0.582438i
$436$	1.77088	−	0.474505i	0.0848097	−	0.0227247i
$437$	4.09869	−	4.09869i	0.196067	−	0.196067i
$438$	−24.2775	−	34.5984i	−1.16003	−	1.65318i
$439$	−8.73521	+	5.04327i	−0.416909	+	0.240702i	−0.693754	−	0.720212i	$-0.744044\pi$
$439$	−8.73521	+	5.04327i	−0.416909	+	0.240702i	0.276845	+	0.960915i	$0.410711\pi$
$440$	0.970617	+	0.260076i	0.0462723	+	0.0123986i
$441$	−6.15698	+	5.18728i	−0.293189	+	0.247013i
$442$		0			0
$443$			19.3012i			0.917028i	0.888687	+	0.458514i	$0.151618\pi$
$443$			19.3012i			0.917028i	−0.888687	+	0.458514i	$0.848382\pi$
$444$	11.0576	+	9.25961i	0.524768	+	0.439442i
$445$	−5.18054	−	8.97295i	−0.245581	−	0.425359i
$446$	14.9784	−	25.9434i	0.709250	−	1.22846i
$447$	−2.89142	−	7.91952i	−0.136759	−	0.374580i
$448$	6.90995	+	25.7883i	0.326464	+	1.21838i
$449$	0.493905	+	1.84328i	0.0233088	+	0.0869898i	0.976600	−	0.215062i	$-0.0689952\pi$
$449$	0.493905	+	1.84328i	0.0233088	+	0.0869898i	−0.953292	+	0.302051i	$0.902329\pi$
$450$	5.63549	+	0.481716i	0.265660	+	0.0227083i
$451$	9.39277	−	16.2688i	0.442288	−	0.766066i
$452$	7.04838	+	12.2081i	0.331528	+	0.574223i
$453$	−4.90135	+	5.85305i	−0.230286	+	0.275000i
$454$		−	4.60544i		−	0.216144i
$455$		0			0
$456$	−0.163258	+	0.351021i	−0.00764525	+	0.0164381i
$457$	36.6573	+	9.82230i	1.71476	+	0.459468i	0.976583	−	0.215143i	$-0.0690216\pi$
$457$	36.6573	+	9.82230i	1.71476	+	0.459468i	0.738174	+	0.674610i	$0.235688\pi$
$458$	4.54728	−	2.62537i	0.212480	−	0.122676i
$459$	29.0759	+	7.69769i	1.35715	+	0.359298i
$460$	−13.8079	+	13.8079i	−0.643798	+	0.643798i
$461$	−14.0541	+	3.76579i	−0.654566	+	0.175390i	−0.570792	−	0.821094i	$-0.693364\pi$
$461$	−14.0541	+	3.76579i	−0.654566	+	0.175390i	−0.0837736	+	0.996485i	$0.526697\pi$
$462$	−29.6559	−	5.19864i	−1.37972	−	0.241863i
$463$	−0.201603	−	0.201603i	−0.00936928	−	0.00936928i	0.702407	−	0.711776i	$-0.252109\pi$
$463$	−0.201603	−	0.201603i	−0.00936928	−	0.00936928i	−0.711776	+	0.702407i	$0.752109\pi$
$464$	−9.73791	−	5.62218i	−0.452071	−	0.261003i
$465$	1.87540	+	21.1925i	0.0869698	+	0.982778i
$466$	8.59032	−	32.0595i	0.397939	−	1.48513i
$467$	−13.1442			−0.608242			−0.304121	−	0.952633i	$-0.598363\pi$
$467$	−13.1442			−0.608242			−0.304121	+	0.952633i	$0.598363\pi$
$468$		0			0
$469$	−42.5023			−1.96258
$470$	−0.208178	+	0.776931i	−0.00960254	+	0.0358372i
$471$	−0.829280	−	9.37106i	−0.0382112	−	0.431795i
$472$	−0.222717	−	0.128586i	−0.0102514	−	0.00591865i
$473$	3.60577	+	3.60577i	0.165793	+	0.165793i
$474$	−35.8424	−	6.28313i	−1.64630	−	0.288594i
$475$	−1.35302	+	0.362540i	−0.0620807	+	0.0166345i
$476$	26.4145	−	26.4145i	1.21070	−	1.21070i
$477$	5.30761	+	29.7537i	0.243019	+	1.36233i
$478$	18.1441	−	10.4755i	0.829892	−	0.479139i
$479$	−29.6166	−	7.93575i	−1.35322	−	0.362594i	−0.491896	−	0.870654i	$-0.663696\pi$
$479$	−29.6166	−	7.93575i	−1.35322	−	0.362594i	−0.861321	+	0.508060i	$0.830363\pi$
$480$	−14.3458	+	30.8450i	−0.654794	+	1.40788i
$481$		0			0
$482$		−	11.8877i		−	0.541471i
$483$	13.3758	−	15.9730i	0.608621	−	0.726797i
$484$	3.46377	+	5.99943i	0.157444	+	0.272702i
$485$	−12.0530	+	20.8763i	−0.547296	+	0.947945i
$486$	−30.9578	+	5.61801i	−1.40427	+	0.254838i
$487$	−0.268324	−	1.00140i	−0.0121589	−	0.0453777i	0.959580	−	0.281436i	$-0.0908109\pi$
$487$	−0.268324	−	1.00140i	−0.0121589	−	0.0453777i	−0.971739	+	0.236059i	$0.924144\pi$
$488$	−0.208155	−	0.776844i	−0.00942273	−	0.0351661i
$489$	7.31995	+	20.0492i	0.331020	+	0.906654i
$490$	−6.59736	+	11.4270i	−0.298038	+	0.516217i
$491$	−2.92987	−	5.07469i	−0.132223	−	0.229018i	0.792310	−	0.610119i	$-0.208878\pi$
$491$	−2.92987	−	5.07469i	−0.132223	−	0.229018i	−0.924533	+	0.381101i	$0.875545\pi$
$492$	−18.6929	−	15.6534i	−0.842739	−	0.705711i
$493$			16.9196i			0.762021i
$494$		0			0
$495$	−13.0316	−	15.4677i	−0.585727	−	0.695222i
$496$	−18.7365	−	5.02042i	−0.841293	−	0.225424i
$497$	0.911398	−	0.526196i	0.0408818	−	0.0236031i
$498$	−8.06051	−	11.4872i	−0.361200	−	0.514754i
$499$	−14.2320	+	14.2320i	−0.637111	+	0.637111i	−0.949842	−	0.312731i	$-0.898756\pi$
$499$	−14.2320	+	14.2320i	−0.637111	+	0.637111i	0.312731	+	0.949842i	$0.398756\pi$
$500$	−19.8406	+	5.31627i	−0.887299	+	0.237751i
$501$	−6.61880	+	37.7573i	−0.295706	+	1.68687i
$502$	−0.317060	−	0.317060i	−0.0141511	−	0.0141511i
$503$	26.1462	+	15.0955i	1.16580	+	0.673075i	0.952687	−	0.303952i	$-0.0983063\pi$
$503$	26.1462	+	15.0955i	1.16580	+	0.673075i	0.213113	+	0.977027i	$0.431640\pi$
$504$	−0.473292	+	1.30847i	−0.0210821	+	0.0582841i
$505$	5.82077	−	21.7234i	0.259021	−	0.966680i
$506$	21.5921			0.959885
$507$		0			0
$508$	−0.841284			−0.0373260
$509$	1.03366	−	3.85768i	0.0458163	−	0.170989i	−0.939227	−	0.343298i	$-0.888456\pi$
$509$	1.03366	−	3.85768i	0.0458163	−	0.170989i	0.985043	+	0.172309i	$0.0551227\pi$
$510$	49.1030	−	4.34531i	2.17432	−	0.192413i
$511$	32.5823	+	18.8114i	1.44136	+	0.832168i
$512$	−22.7420	−	22.7420i	−1.00506	−	1.00506i
$513$	6.73643	−	3.91620i	0.297421	−	0.172905i
$514$	−49.2982	+	13.2094i	−2.17445	+	0.582642i
$515$	−29.7413	+	29.7413i	−1.31056	+	1.31056i
$516$	5.41762	−	3.80152i	0.238497	−	0.167352i
$517$	0.392096	−	0.226377i	0.0172443	−	0.00995603i
$518$	−24.3596	−	6.52713i	−1.07030	−	0.286786i
$519$	14.6550	+	6.81594i	0.643282	+	0.299187i
$520$		0			0
$521$		−	30.7954i		−	1.34917i	−0.738197	−	0.674585i	$-0.764322\pi$
$521$		−	30.7954i		−	1.34917i	0.738197	−	0.674585i	$-0.235678\pi$
$522$	−7.51197	−	16.0259i	−0.328790	−	0.701436i
$523$	−6.77410	−	11.7331i	−0.296211	−	0.513052i	0.679055	−	0.734087i	$-0.262390\pi$
$523$	−6.77410	−	11.7331i	−0.296211	−	0.513052i	−0.975266	+	0.221035i	$0.929056\pi$
$524$	7.48700	−	12.9679i	0.327071	−	0.566504i
$525$	−4.72930	+	1.72667i	−0.206403	+	0.0753579i
$526$	2.55517	+	9.53602i	0.111411	+	0.415790i
$527$	7.55433	+	28.1931i	0.329072	+	1.22811i
$528$	17.3219	−	6.32424i	0.753841	−	0.275227i
$529$	4.02949	−	6.97928i	0.175195	−	0.303447i
$530$	24.7669	+	42.8975i	1.07581	+	1.86335i
$531$	2.19696	+	4.68695i	0.0953397	+	0.203396i
$532$		−	9.67755i		−	0.419575i
$533$		0			0
$534$	13.4824	+	6.27059i	0.583442	+	0.271355i
$535$	−25.0177	−	6.70346i	−1.08161	−	0.289816i
$536$	−1.76299	+	1.01786i	−0.0761495	+	0.0439649i
$537$	−37.8779	+	26.5788i	−1.63455	+	1.14696i
$538$	−30.1783	+	30.1783i	−1.30108	+	1.30108i
$539$	7.17409	−	1.92229i	0.309010	−	0.0827989i
$540$	−22.6941	+	13.1931i	−0.976599	+	0.567743i
$541$	−17.8219	−	17.8219i	−0.766224	−	0.766224i	0.211216	−	0.977439i	$-0.432258\pi$
$541$	−17.8219	−	17.8219i	−0.766224	−	0.766224i	−0.977439	+	0.211216i	$0.932258\pi$
$542$	3.32673	+	1.92069i	0.142895	+	0.0825006i
$543$	45.3317	−	4.01158i	1.94537	−	0.172153i
$544$	−12.0789	+	45.0791i	−0.517879	+	1.93275i
$545$	−2.15350			−0.0922459
$546$		0			0
$547$	−27.9877			−1.19667			−0.598333	−	0.801248i	$-0.704170\pi$
$547$	−27.9877			−1.19667			−0.598333	+	0.801248i	$0.704170\pi$
$548$	10.5854	−	39.5054i	0.452188	−	1.68759i
$549$	−5.50618	+	15.2225i	−0.234998	+	0.649681i
$550$	−4.51881	−	2.60894i	−0.192683	−	0.111245i
$551$	3.09945	+	3.09945i	0.132041	+	0.132041i
$552$	0.172299	−	0.982887i	0.00733352	−	0.0418344i
$553$	31.2874	−	8.38343i	1.33047	−	0.356500i
$554$	5.63751	−	5.63751i	0.239515	−	0.239515i
$555$	−9.73088	−	13.8677i	−0.413053	−	0.588650i
$556$	18.6038	−	10.7409i	0.788979	−	0.455517i
$557$	−18.8545	−	5.05204i	−0.798890	−	0.214062i	−0.163793	−	0.986495i	$-0.552373\pi$
$557$	−18.8545	−	5.05204i	−0.798890	−	0.214062i	−0.635096	+	0.772433i	$0.719040\pi$
$558$	−19.6725	−	23.3500i	−0.832803	−	0.988485i
$559$		0			0
$560$		−	29.1610i		−	1.23228i
$561$	−21.2736	−	17.8146i	−0.898173	−	0.752131i
$562$	4.40201	+	7.62451i	0.185688	+	0.321621i
$563$	16.9776	−	29.4060i	0.715519	−	1.23932i	−0.247240	−	0.968954i	$-0.579524\pi$
$563$	16.9776	−	29.4060i	0.715519	−	1.23932i	0.962759	−	0.270361i	$-0.0871431\pi$
$564$	−0.201528	−	0.551981i	−0.00848588	−	0.0232426i
$565$	−4.28564	−	15.9942i	−0.180298	−	0.672883i
$566$	−9.63082	−	35.9427i	−0.404814	−	1.51079i
$567$	22.8774	−	16.1554i	0.960762	−	0.678461i
$568$	0.0252031	−	0.0436530i	0.00105750	−	0.00183164i
$569$	−4.08073	−	7.06804i	−0.171073	−	0.296308i	0.767722	−	0.640783i	$-0.221390\pi$
$569$	−4.08073	−	7.06804i	−0.171073	−	0.296308i	−0.938795	+	0.344475i	$0.888057\pi$
$570$	8.19900	−	9.79101i	0.343418	−	0.410100i
$571$			19.3616i			0.810257i	0.914260	+	0.405128i	$0.132773\pi$
$571$			19.3616i			0.810257i	−0.914260	+	0.405128i	$0.867227\pi$
$572$		0			0
$573$	5.62595	−	12.0964i	0.235028	−	0.505333i
$574$	41.1800	+	11.0342i	1.71882	+	0.460557i
$575$	3.12687	−	1.80530i	0.130400	−	0.0752862i
$576$	−4.51997	−	25.3384i	−0.188332	−	1.05577i
$577$	10.9086	−	10.9086i	0.454132	−	0.454132i	−0.442592	−	0.896723i	$-0.645941\pi$
$577$	10.9086	−	10.9086i	0.454132	−	0.454132i	0.896723	+	0.442592i	$0.145941\pi$
$578$	32.1802	−	8.62267i	1.33852	−	0.358656i
$579$	26.5842	+	4.66017i	1.10480	+	0.193670i
$580$	−10.4416	−	10.4416i	−0.433564	−	0.433564i
$581$	10.8178	+	6.24567i	0.448799	+	0.259114i
$582$	−3.04950	−	34.4600i	−0.126406	−	1.42841i
$583$	7.21640	−	26.9320i	0.298873	−	1.11541i
$584$	1.80201			0.0745677
$585$		0			0
$586$	31.5990			1.30534
$587$	0.400823	−	1.49589i	0.0165437	−	0.0617420i	−0.957161	−	0.289558i	$-0.906492\pi$
$587$	0.400823	−	1.49589i	0.0165437	−	0.0617420i	0.973704	+	0.227816i	$0.0731584\pi$
$588$	−0.849722	−	9.60205i	−0.0350419	−	0.395982i
$589$	6.54846	+	3.78076i	0.269825	+	0.155783i
$590$	5.99878	+	5.99878i	0.246966	+	0.246966i
$591$	44.8582	+	7.86358i	1.84522	+	0.323465i
$592$	14.9195	−	3.99767i	0.613188	−	0.164303i
$593$	−3.02210	+	3.02210i	−0.124103	+	0.124103i	−0.766430	−	0.642327i	$-0.777969\pi$
$593$	−3.02210	+	3.02210i	−0.124103	+	0.124103i	0.642327	+	0.766430i	$0.277969\pi$
$594$	28.0592	+	7.42854i	1.15128	+	0.304797i
$595$	−38.0004	+	21.9395i	−1.55786	+	0.899433i
$596$	9.75058	+	2.61266i	0.399399	+	0.107019i
$597$	10.0204	−	21.5448i	0.410107	−	0.881772i
$598$		0			0
$599$		−	16.9927i		−	0.694302i	−0.937809	−	0.347151i	$-0.887149\pi$
$599$		−	16.9927i		−	0.694302i	0.937809	−	0.347151i	$-0.112851\pi$
$600$	−0.154819	+	0.184881i	−0.00632048	+	0.00754773i
$601$	−16.2819	−	28.2011i	−0.664154	−	1.15035i	−0.979514	−	0.201376i	$-0.935459\pi$
$601$	−16.2819	−	28.2011i	−0.664154	−	1.15035i	0.315360	−	0.948972i	$-0.397875\pi$
$602$	−5.78631	+	10.0222i	−0.235832	+	0.408474i
$603$	40.8258	+	3.48974i	1.66255	+	0.142113i
$604$	−2.36580	−	8.82927i	−0.0962629	−	0.359258i
$605$	−2.10609	−	7.86003i	−0.0856247	−	0.319556i
$606$	11.0690	+	30.3178i	0.449649	+	1.23158i
$607$	6.51258	−	11.2801i	0.264338	−	0.457846i	−0.703052	−	0.711138i	$-0.748180\pi$
$607$	6.51258	−	11.2801i	0.264338	−	0.457846i	0.967390	+	0.253292i	$0.0815133\pi$
$608$	6.04519	+	10.4706i	0.245165	+	0.424638i
$609$	12.0788	+	10.1148i	0.489460	+	0.409874i
$610$			26.5304i			1.07419i
$611$		0			0
$612$	−27.5413	+	23.2037i	−1.11329	+	0.937954i
$613$	5.10239	+	1.36718i	0.206084	+	0.0552199i	0.360384	−	0.932804i	$-0.382646\pi$
$613$	5.10239	+	1.36718i	0.206084	+	0.0552199i	−0.154300	+	0.988024i	$0.549312\pi$
$614$	10.4512	−	6.03400i	0.421776	−	0.243513i
$615$	16.4501	+	23.4434i	0.663332	+	0.945328i
$616$	0.907676	−	0.907676i	0.0365713	−	0.0365713i
$617$	−26.0891	+	6.99055i	−1.05031	+	0.281429i	−0.742379	−	0.669980i	$-0.766303\pi$
$617$	−26.0891	+	6.99055i	−1.05031	+	0.281429i	−0.307929	+	0.951409i	$0.599636\pi$
$618$	10.4224	−	59.4550i	0.419250	−	2.39163i
$619$	−21.7905	−	21.7905i	−0.875835	−	0.875835i	0.117266	−	0.993101i	$-0.462587\pi$
$619$	−21.7905	−	21.7905i	−0.875835	−	0.875835i	−0.993101	+	0.117266i	$0.962587\pi$
$620$	−22.0609	−	12.7368i	−0.885985	−	0.511524i
$621$	−14.1597	+	14.2447i	−0.568209	+	0.571619i
$622$	−10.8912	+	40.6463i	−0.436695	+	1.62977i
$623$	−13.2357			−0.530277
$624$		0			0
$625$	28.7979			1.15192
$626$	−3.62376	+	13.5240i	−0.144834	+	0.540529i
$627$	−7.16043	+	0.633654i	−0.285960	+	0.0253057i
$628$	9.75503	+	5.63207i	0.389268	+	0.224744i
$629$	−16.4343	−	16.4343i	−0.655279	−	0.655279i
$630$	26.2525	−	37.6521i	1.04593	−	1.50010i
$631$	−3.51195	+	0.941025i	−0.139809	+	0.0374616i	−0.328045	−	0.944662i	$-0.606390\pi$
$631$	−3.51195	+	0.941025i	−0.139809	+	0.0374616i	0.188236	+	0.982124i	$0.439723\pi$
$632$	1.09703	−	1.09703i	0.0436373	−	0.0436373i
$633$	30.5447	−	21.4331i	1.21404	−	0.851888i
$634$	−18.3715	+	10.6068i	−0.729625	+	0.421249i
$635$	0.954525	+	0.255764i	0.0378792	+	0.0101497i
$636$	−32.8123	−	15.2608i	−1.30109	−	0.605130i
$637$		0			0
$638$			16.3280i			0.646432i
$639$	−0.918651	+	0.430607i	−0.0363413	+	0.0170346i
$640$	−1.45133	−	2.51378i	−0.0573688	−	0.0993657i
$641$	−2.44180	+	4.22932i	−0.0964452	+	0.167048i	−0.910211	−	0.414145i	$-0.864081\pi$
$641$	−2.44180	+	4.22932i	−0.0964452	+	0.167048i	0.813766	+	0.581193i	$0.197414\pi$
$642$	34.9154	−	12.7476i	1.37800	−	0.503108i
$643$	−0.734494	−	2.74117i	−0.0289656	−	0.108101i	0.949930	−	0.312464i	$-0.101154\pi$
$643$	−0.734494	−	2.74117i	−0.0289656	−	0.108101i	−0.978895	+	0.204363i	$0.934488\pi$
$644$	6.45627	+	24.0951i	0.254413	+	0.949481i
$645$	−7.30258	+	2.66617i	−0.287539	+	0.104980i
$646$	8.76000	−	15.1728i	0.344658	−	0.596965i
$647$	−7.83061	−	13.5630i	−0.307853	−	0.533217i	0.670039	−	0.742326i	$-0.266277\pi$
$647$	−7.83061	−	13.5630i	−0.307853	−	0.533217i	−0.977892	+	0.209108i	$0.932944\pi$
$648$	0.562057	−	1.21800i	0.0220797	−	0.0478475i
$649$		−	4.77530i		−	0.187447i
$650$		0			0
$651$	24.6431	+	11.4614i	0.965839	+	0.449206i
$652$	−24.6847	−	6.61424i	−0.966727	−	0.259034i
$653$	−26.4569	+	15.2749i	−1.03534	+	0.597753i	−0.918510	−	0.395398i	$-0.870607\pi$
$653$	−26.4569	+	15.2749i	−1.03534	+	0.597753i	−0.116830	+	0.993152i	$0.537273\pi$
$654$	2.52984	−	1.77517i	0.0989244	−	0.0694147i
$655$	−12.4372	+	12.4372i	−0.485963	+	0.485963i
$656$	−25.2215	+	6.75809i	−0.984735	+	0.263859i
$657$	−29.7525	−	20.7446i	−1.16076	−	0.809324i
$658$	0.726550	+	0.726550i	0.0283239	+	0.0283239i
$659$	4.19022	+	2.41923i	0.163228	+	0.0942397i	0.579389	−	0.815051i	$-0.303291\pi$
$659$	4.19022	+	2.41923i	0.163228	+	0.0942397i	−0.416161	+	0.909291i	$0.636625\pi$
$660$	24.1225	−	2.13469i	0.938967	−	0.0830927i
$661$	−12.7370	+	47.5350i	−0.495410	+	1.84890i	0.0323096	+	0.999478i	$0.489714\pi$
$661$	−12.7370	+	47.5350i	−0.495410	+	1.84890i	−0.527720	+	0.849418i	$0.676953\pi$
$662$	−43.9009			−1.70626
$663$		0			0
$664$	0.598295			0.0232184
$665$	−2.94213	+	10.9802i	−0.114091	+	0.425794i
$666$	22.8628	+	8.26976i	0.885914	+	0.320447i
$667$	−9.78475	−	5.64923i	−0.378867	−	0.218739i
$668$	−32.4544	−	32.4544i	−1.25570	−	1.25570i
$669$	4.43876	−	25.3211i	0.171612	−	0.978971i
$670$	64.8660	−	17.3808i	2.50599	−	0.671478i
$671$	10.5597	−	10.5597i	0.407653	−	0.407653i
$672$	24.9608	+	35.5722i	0.962884	+	1.37223i
$673$	4.88266	−	2.81901i	0.188213	−	0.108665i	−0.402933	−	0.915230i	$-0.632009\pi$
$673$	4.88266	−	2.81901i	0.188213	−	0.108665i	0.591146	+	0.806565i	$0.298676\pi$
$674$	64.6750	+	17.3296i	2.49119	+	0.667512i
$675$	4.68451	−	1.27025i	0.180307	−	0.0488918i
$676$		0			0
$677$			20.0063i			0.768905i	0.923145	+	0.384452i	$0.125610\pi$
$677$			20.0063i			0.768905i	−0.923145	+	0.384452i	$0.874390\pi$
$678$	18.2189	+	15.2565i	0.699693	+	0.585924i
$679$	15.3970	+	26.6683i	0.590881	+	1.02344i
$680$	−1.05083	+	1.82010i	−0.0402976	+	0.0697975i
$681$	−1.35540	−	3.71242i	−0.0519392	−	0.142260i
$682$	7.29019	+	27.2073i	0.279156	+	1.04182i
$683$	3.70630	+	13.8321i	0.141818	+	0.529271i	0.999876	+	0.0157195i	$0.00500386\pi$
$683$	3.70630	+	13.8321i	0.141818	+	0.529271i	−0.858059	+	0.513552i	$0.828329\pi$
$684$	−0.794596	+	9.29581i	−0.0303821	+	0.355434i
$685$	−24.0206	+	41.6049i	−0.917779	+	1.58964i
$686$	−13.5554	−	23.4786i	−0.517546	−	0.896416i
$687$	2.89288	−	3.45459i	0.110370	−	0.131801i
$688$		−	7.08788i		−	0.270223i
$689$		0			0
$690$	−13.8819	+	29.8475i	−0.528474	+	1.13627i
$691$	−10.2181	−	2.73794i	−0.388716	−	0.104156i	0.0591676	−	0.998248i	$-0.481155\pi$
$691$	−10.2181	−	2.73794i	−0.388716	−	0.104156i	−0.447883	+	0.894092i	$0.647822\pi$
$692$	−16.7592	+	9.67595i	−0.637090	+	0.367824i
$693$	−25.4355	+	4.53730i	−0.966214	+	0.172358i
$694$	48.0753	−	48.0753i	1.82492	−	1.82492i
$695$	−24.3734	+	6.53084i	−0.924537	+	0.247729i
$696$	0.743262	+	0.130293i	0.0281733	+	0.00493874i
$697$	27.7823	+	27.7823i	1.05233	+	1.05233i
$698$	−35.2862	−	20.3725i	−1.33560	−	0.771109i
$699$	−2.51067	−	28.3712i	−0.0949624	−	1.07310i
$700$	1.56020	−	5.82275i	0.0589701	−	0.220079i
$701$	34.6355			1.30816			0.654082	−	0.756423i	$-0.273055\pi$
$701$	34.6355			1.30816			0.654082	+	0.756423i	$0.273055\pi$
$702$		0			0
$703$	−6.02109			−0.227090
$704$	−6.14551	+	22.9354i	−0.231618	+	0.864409i
$705$	0.0608438	+	0.687548i	0.00229151	+	0.0258946i
$706$	−31.4967	−	18.1847i	−1.18540	−	0.684389i
$707$	−20.3147	−	20.3147i	−0.764014	−	0.764014i
$708$	−6.10469	−	1.07014i	−0.229428	−	0.0402185i
$709$	−33.9830	+	9.10572i	−1.27626	+	0.341973i	−0.832426	−	0.554137i	$-0.813048\pi$
$709$	−33.9830	+	9.10572i	−1.27626	+	0.341973i	−0.443833	+	0.896109i	$0.646382\pi$
$710$	−1.17577	+	1.17577i	−0.0441259	+	0.0441259i
$711$	−30.7415	+	5.48382i	−1.15290	+	0.205659i
$712$	−0.549014	+	0.316973i	−0.0205752	+	0.0118791i
$713$	−18.8266	−	5.04458i	−0.705062	−	0.188921i
$714$	26.5559	−	57.0980i	0.993831	−	2.13684i
$715$		0			0
$716$		−	55.4040i		−	2.07054i
$717$	11.5429	−	13.7842i	0.431077	−	0.514779i
$718$	−24.3064	−	42.1000i	−0.907108	−	1.57116i
$719$	9.63051	−	16.6805i	0.359157	−	0.622079i	−0.628663	−	0.777678i	$-0.716397\pi$
$719$	9.63051	−	16.6805i	0.359157	−	0.622079i	0.987820	+	0.155599i	$0.0497308\pi$
$720$	−2.39432	+	28.0107i	−0.0892311	+	1.04390i
$721$	13.9063	+	51.8992i	0.517899	+	1.93283i
$722$	8.75076	+	32.6583i	0.325670	+	1.21542i
$723$	−3.49862	−	9.58264i	−0.130115	−	0.356382i
$724$	−27.2447	+	47.1892i	−1.01254	+	1.75377i
$725$	1.36517	+	2.36455i	0.0507013	+	0.0878172i
$726$	8.95330	+	7.49751i	0.332288	+	0.278259i
$727$		−	9.68612i		−	0.359238i	−0.983736	−	0.179619i	$-0.942513\pi$
$727$		−	9.68612i		−	0.359238i	0.983736	−	0.179619i	$-0.0574865\pi$
$728$		0			0
$729$	−23.3015	+	13.6397i	−0.863018	+	0.505174i
$730$	−57.4190	−	15.3854i	−2.12517	−	0.569438i
$731$	−9.23640	+	5.33264i	−0.341621	+	0.197235i
$732$	−11.1330	−	15.8658i	−0.411487	−	0.586418i
$733$	14.7153	−	14.7153i	0.543522	−	0.543522i	−0.381038	−	0.924559i	$-0.624433\pi$
$733$	14.7153	−	14.7153i	0.543522	−	0.543522i	0.924559	+	0.381038i	$0.124433\pi$
$734$	−36.7328	+	9.84253i	−1.35583	+	0.363294i
$735$	−1.95508	+	11.1529i	−0.0721143	+	0.411379i
$736$	−22.0366	−	22.0366i	−0.812281	−	0.812281i
$737$	−32.7361	−	18.9002i	−1.20585	−	0.696197i
$738$	−38.6496	−	13.9801i	−1.42271	−	0.514613i
$739$	5.47886	−	20.4474i	0.201543	−	0.752169i	−0.788932	−	0.614480i	$-0.789366\pi$
$739$	5.47886	−	20.4474i	0.201543	−	0.752169i	0.990475	−	0.137689i	$-0.0439675\pi$
$740$	20.2842			0.745663
$741$		0			0
$742$	63.2766			2.32296
$743$	−10.7330	+	40.0562i	−0.393756	+	1.46952i	0.430132	+	0.902766i	$0.358467\pi$
$743$	−10.7330	+	40.0562i	−0.393756	+	1.46952i	−0.823888	+	0.566752i	$0.808200\pi$
$744$	1.29667	−	0.114747i	0.0475383	−	0.00420684i
$745$	−10.2688	−	5.92867i	−0.376218	−	0.217210i
$746$	25.6472	+	25.6472i	0.939012	+	0.939012i
$747$	−9.87829	−	6.88752i	−0.361428	−	0.252001i
$748$	32.0910	−	8.59877i	1.17336	−	0.314402i
$749$	−23.3954	+	23.3954i	−0.854848	+	0.854848i
$750$	−28.3438	+	19.8887i	−1.03497	+	0.726234i
$751$	−4.81013	+	2.77713i	−0.175524	+	0.101339i	−0.585188	−	0.810898i	$-0.698979\pi$
$751$	−4.81013	+	2.77713i	−0.175524	+	0.101339i	0.409664	+	0.912237i	$0.365646\pi$
$752$	−0.607868	−	0.162878i	−0.0221667	−	0.00593954i
$753$	−0.348893	−	0.162268i	−0.0127144	−	0.00591337i
$754$		0			0
$755$			10.7370i			0.390758i
$756$	0.100338	+	33.5332i	0.00364927	+	1.21959i
$757$	−5.99015	−	10.3752i	−0.217716	−	0.377094i	0.736394	−	0.676553i	$-0.236527\pi$
$757$	−5.99015	−	10.3752i	−0.217716	−	0.377094i	−0.954109	+	0.299459i	$0.903194\pi$
$758$	−16.3233	+	28.2728i	−0.592889	+	1.02691i
$759$	17.4053	−	6.35467i	0.631771	−	0.230660i
$760$	0.140919	+	0.525916i	0.00511166	+	0.0190770i
$761$	−10.7421	−	40.0899i	−0.389400	−	1.45326i	−0.831113	−	0.556103i	$-0.812296\pi$
$761$	−10.7421	−	40.0899i	−0.389400	−	1.45326i	0.441714	−	0.897156i	$-0.354371\pi$
$762$	−1.33216	+	0.486373i	−0.0482592	+	0.0176194i
$763$	−1.37549	+	2.38242i	−0.0497961	+	0.0862493i
$764$	7.98663	+	13.8333i	0.288946	+	0.500469i
$765$	38.3028	−	17.9540i	1.38484	−	0.649128i
$766$			34.0999i			1.23208i
$767$		0			0
$768$	−23.1710	−	10.7767i	−0.836110	−	0.388870i
$769$	−28.9081	−	7.74591i	−1.04245	−	0.279325i	−0.303324	−	0.952887i	$-0.598096\pi$
$769$	−28.9081	−	7.74591i	−1.04245	−	0.279325i	−0.739130	+	0.673563i	$0.764763\pi$
$770$	−36.6717	+	21.1724i	−1.32156	+	0.763001i
$771$	−35.8514	+	25.1568i	−1.29116	+	0.905999i
$772$	−22.8505	+	22.8505i	−0.822408	+	0.822408i
$773$	−18.4571	+	4.94556i	−0.663855	+	0.177879i	−0.574985	−	0.818164i	$-0.694992\pi$
$773$	−18.4571	+	4.94556i	−0.663855	+	0.177879i	−0.0888698	+	0.996043i	$0.528326\pi$

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.k (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.522394 + 1.94960i) q^{2} +(0.152679 + 1.72531i) q^{3} +(-1.79600 - 1.03692i) q^{4} +(1.72251 + 1.72251i) q^{5} +(-3.44342 - 0.603628i) q^{6} +(3.00582 - 0.805406i) q^{7} +(0.105393 - 0.105393i) q^{8} +(-2.95338 + 0.526837i) q^{9} +(-4.25804 + 2.45838i) q^{10} +(2.67329 + 0.716305i) q^{11} +(1.51480 - 3.25697i) q^{12} +6.28089i q^{14} +(-2.70887 + 3.23485i) q^{15} +(-1.92343 - 3.33148i) q^{16} +(-2.89422 + 5.01294i) q^{17} +(0.515706 - 6.03313i) q^{18} +(0.388120 + 1.44849i) q^{19} +(-1.30752 - 4.87975i) q^{20} +(1.84850 + 5.06299i) q^{21} +(-2.79302 + 4.83765i) q^{22} +(-1.93268 - 3.34750i) q^{23} +(0.197926 + 0.165743i) q^{24} +0.934091i q^{25} +(-1.35988 - 5.01505i) q^{27} +(-6.23360 - 1.67029i) q^{28} +(2.53139 - 1.46150i) q^{29} +(-4.89158 - 6.97109i) q^{30} +(3.56552 - 3.56552i) q^{31} +(7.78778 - 2.08673i) q^{32} +(-0.827693 + 4.72161i) q^{33} +(-8.26131 - 8.26131i) q^{34} +(6.56488 + 3.79023i) q^{35} +(5.85056 + 2.11622i) q^{36} +(-1.03921 + 3.87837i) q^{37} -3.02672 q^{38} +0.363080 q^{40} +(1.75678 - 6.55640i) q^{41} +(-10.8365 + 0.958960i) q^{42} +(1.59566 + 0.921257i) q^{43} +(-4.05848 - 4.05848i) q^{44} +(-5.99471 - 4.17974i) q^{45} +(7.53592 - 2.01924i) q^{46} +(0.115676 - 0.115676i) q^{47} +(5.45416 - 3.82715i) q^{48} +(2.32408 - 1.34181i) q^{49} +(-1.82111 - 0.487964i) q^{50} +(-9.09075 - 4.22805i) q^{51} -10.0745i q^{53} +(10.4877 - 0.0313815i) q^{54} +(3.37093 + 5.83861i) q^{55} +(0.231907 - 0.401675i) q^{56} +(-2.43983 + 0.890781i) q^{57} +(1.52696 + 5.69869i) q^{58} +(-0.446576 - 1.66664i) q^{59} +(8.21944 - 3.00092i) q^{60} +(2.69796 - 4.67300i) q^{61} +(5.08874 + 8.81396i) q^{62} +(-8.45300 + 3.96225i) q^{63} +8.57945i q^{64} +(-8.77288 - 4.08021i) q^{66} +(-13.1928 - 3.53501i) q^{67} +(10.3961 - 6.00217i) q^{68} +(5.48039 - 3.84556i) q^{69} +(-10.8189 + 10.8189i) q^{70} +(0.326665 - 0.0875296i) q^{71} +(-0.255739 + 0.366789i) q^{72} +(8.54904 + 8.54904i) q^{73} +(-7.01840 - 4.05207i) q^{74} +(-1.61160 + 0.142616i) q^{75} +(0.804902 - 3.00393i) q^{76} +8.61233 q^{77} +10.4089 q^{79} +(2.42538 - 9.05163i) q^{80} +(8.44489 - 3.11190i) q^{81} +(11.8646 + 6.85005i) q^{82} +(2.83841 + 2.83841i) q^{83} +(1.93002 - 11.0099i) q^{84} +(-13.6202 + 3.64951i) q^{85} +(-2.62965 + 2.62965i) q^{86} +(2.90803 + 4.14429i) q^{87} +(0.357238 - 0.206251i) q^{88} +(-4.10839 - 1.10084i) q^{89} +(11.2804 - 9.50383i) q^{90} +8.01616i q^{92} +(6.69601 + 5.60725i) q^{93} +(0.165094 + 0.285951i) q^{94} +(-1.82649 + 3.16357i) q^{95} +(4.78928 + 13.1177i) q^{96} +(2.56119 + 9.55851i) q^{97} +(1.40191 + 5.23199i) q^{98} +(-8.27261 - 0.707134i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 24 q^{9} + 8 q^{16} - 112 q^{22} - 168 q^{27} + 256 q^{40} + 56 q^{42} + 188 q^{48} - 8 q^{55} - 56 q^{61} - 184 q^{66} + 72 q^{81} + 112 q^{87} - 296 q^{94}+O(q^{100}) \) 96 * q + 24 * q^9 + 8 * q^16 - 112 * q^22 - 168 * q^27 + 256 * q^40 + 56 * q^42 + 188 * q^48 - 8 * q^55 - 56 * q^61 - 184 * q^66 + 72 * q^81 + 112 * q^87 - 296 * q^94

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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