LMFDB - Embedded newform 507.2.k.k.80.4

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			80.4
Character	$\chi$	$=$	507.80
Dual form			507.2.k.k.488.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.522394 + 1.94960i) q^{2} +(1.41782 + 0.994878i) q^{3} +(-1.79600 - 1.03692i) q^{4} +(1.72251 + 1.72251i) q^{5} +(-2.68028 + 2.24447i) q^{6} +(-3.00582 + 0.805406i) q^{7} +(0.105393 - 0.105393i) q^{8} +(1.02043 + 2.82112i) q^{9} +O(q^{10})$	\(q+(-0.522394 + 1.94960i) q^{2} +(1.41782 + 0.994878i) q^{3} +(-1.79600 - 1.03692i) q^{4} +(1.72251 + 1.72251i) q^{5} +(-2.68028 + 2.24447i) q^{6} +(-3.00582 + 0.805406i) q^{7} +(0.105393 - 0.105393i) q^{8} +(1.02043 + 2.82112i) q^{9} +(-4.25804 + 2.45838i) q^{10} +(2.67329 + 0.716305i) q^{11} +(-1.51480 - 3.25697i) q^{12} -6.28089i q^{14} +(0.728525 + 4.15590i) q^{15} +(-1.92343 - 3.33148i) q^{16} +(2.89422 - 5.01294i) q^{17} +(-6.03313 + 0.515706i) q^{18} +(-0.388120 - 1.44849i) q^{19} +(-1.30752 - 4.87975i) q^{20} +(-5.06299 - 1.84850i) q^{21} +(-2.79302 + 4.83765i) q^{22} +(1.93268 + 3.34750i) q^{23} +(0.254281 - 0.0445751i) q^{24} +0.934091i q^{25} +(-1.35988 + 5.01505i) q^{27} +(6.23360 + 1.67029i) q^{28} +(-2.53139 + 1.46150i) q^{29} +(-8.48293 - 0.750687i) q^{30} +(-3.56552 + 3.56552i) q^{31} +(7.78778 - 2.08673i) q^{32} +(3.07761 + 3.67519i) q^{33} +(8.26131 + 8.26131i) q^{34} +(-6.56488 - 3.79023i) q^{35} +(1.09258 - 6.12485i) q^{36} +(1.03921 - 3.87837i) q^{37} +3.02672 q^{38} +0.363080 q^{40} +(1.75678 - 6.55640i) q^{41} +(6.24872 - 8.90518i) q^{42} +(1.59566 + 0.921257i) q^{43} +(-4.05848 - 4.05848i) q^{44} +(-3.10170 + 6.61712i) q^{45} +(-7.53592 + 2.01924i) q^{46} +(0.115676 - 0.115676i) q^{47} +(0.587334 - 6.63701i) q^{48} +(2.32408 - 1.34181i) q^{49} +(-1.82111 - 0.487964i) q^{50} +(9.09075 - 4.22805i) q^{51} +10.0745i q^{53} +(-9.06696 - 5.27105i) q^{54} +(3.37093 + 5.83861i) q^{55} +(-0.231907 + 0.401675i) q^{56} +(0.890781 - 2.43983i) q^{57} +(-1.52696 - 5.69869i) q^{58} +(-0.446576 - 1.66664i) q^{59} +(3.00092 - 8.21944i) q^{60} +(2.69796 - 4.67300i) q^{61} +(-5.08874 - 8.81396i) q^{62} +(-5.33939 - 7.65790i) q^{63} +8.57945i q^{64} +(-8.77288 + 4.08021i) q^{66} +(13.1928 + 3.53501i) q^{67} +(-10.3961 + 6.00217i) q^{68} +(-0.590160 + 6.66894i) q^{69} +(10.8189 - 10.8189i) q^{70} +(0.326665 - 0.0875296i) q^{71} +(0.404871 + 0.189779i) q^{72} +(-8.54904 - 8.54904i) q^{73} +(7.01840 + 4.05207i) q^{74} +(-0.929307 + 1.32437i) q^{75} +(-0.804902 + 3.00393i) q^{76} -8.61233 q^{77} +10.4089 q^{79} +(2.42538 - 9.05163i) q^{80} +(-6.91743 + 5.75754i) q^{81} +(11.8646 + 6.85005i) q^{82} +(2.83841 + 2.83841i) q^{83} +(7.17640 + 8.56984i) q^{84} +(13.6202 - 3.64951i) q^{85} +(-2.62965 + 2.62965i) q^{86} +(-5.04308 - 0.446281i) q^{87} +(0.357238 - 0.206251i) q^{88} +(-4.10839 - 1.10084i) q^{89} +(-11.2804 - 9.50383i) q^{90} -8.01616i q^{92} +(-8.60253 + 1.50801i) q^{93} +(0.165094 + 0.285951i) q^{94} +(1.82649 - 3.16357i) q^{95} +(13.1177 + 4.78928i) q^{96} +(-2.56119 - 9.55851i) q^{97} +(1.40191 + 5.23199i) q^{98} +(0.707134 + 8.27261i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 24 q^{9}+O(q^{10}) $ 96 * q + 24 * q^9	$ 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

Display 100 coefficients 10 coefficients

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	$0.830395\pi$
$3$	1.41782	+	0.994878i	0.818580	+	0.574393i
$3$	1.41782	+	0.994878i	0.818580	+	0.574393i
$4$	−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	$0.566641\pi$
$6$	−2.68028	+	2.24447i	−1.09422	+	0.916301i
$7$	−3.00582	+	0.805406i	−1.13609	+	0.304415i	−0.777379	−	0.629033i	$-0.783451\pi$
$7$	−3.00582	+	0.805406i	−1.13609	+	0.304415i	−0.358713	+	0.933448i	$0.616784\pi$
$8$	0.105393	−	0.105393i	0.0372619	−	0.0372619i
$9$	1.02043	+	2.82112i	0.340145	+	0.940373i
$10$	−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
$15$	0.728525	+	4.15590i	0.188104	+	1.07305i
$16$	−1.92343	−	3.33148i	−0.480857	−	0.832869i
$17$	2.89422	−	5.01294i	0.701952	−	1.21582i	−0.265829	−	0.964020i	$-0.585646\pi$
$17$	2.89422	−	5.01294i	0.701952	−	1.21582i	0.967780	−	0.251796i	$-0.0810210\pi$
$18$	−6.03313	+	0.515706i	−1.42202	+	0.121553i
$19$	−0.388120	−	1.44849i	−0.0890409	−	0.332305i	0.907008	−	0.421114i	$-0.138361\pi$
$19$	−0.388120	−	1.44849i	−0.0890409	−	0.332305i	−0.996049	+	0.0888086i	$0.971694\pi$
$20$	−1.30752	−	4.87975i	−0.292371	−	1.09114i
$21$	−5.06299	−	1.84850i	−1.10484	−	0.403376i
$22$	−2.79302	+	4.83765i	−0.595474	+	1.03139i
$23$	1.93268	+	3.34750i	0.402992	+	0.698002i	0.994085	−	0.108601i	$-0.0346369\pi$
$23$	1.93268	+	3.34750i	0.402992	+	0.698002i	−0.591094	+	0.806603i	$0.701304\pi$
$24$	0.254281	−	0.0445751i	0.0519048	−	0.00909885i
$25$			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	−0.716268	−	0.697825i	$-0.754151\pi$
$29$	−2.53139	+	1.46150i	−0.470068	+	0.271394i	0.246200	+	0.969219i	$0.420818\pi$
$30$	−8.48293	−	0.750687i	−1.54876	−	0.137056i
$31$	−3.56552	+	3.56552i	−0.640387	+	0.640387i	−0.950651	−	0.310264i	$-0.899583\pi$
$31$	−3.56552	+	3.56552i	−0.640387	+	0.640387i	0.310264	+	0.950651i	$0.399583\pi$
$32$	7.78778	−	2.08673i	1.37670	−	0.368885i
$33$	3.07761	+	3.67519i	0.535743	+	0.639768i
$34$	8.26131	+	8.26131i	1.41680	+	1.41680i
$35$	−6.56488	−	3.79023i	−1.10967	−	0.640666i
$36$	1.09258	−	6.12485i	0.182096	−	1.02081i
$37$	1.03921	−	3.87837i	0.170844	−	0.637600i	−0.826378	−	0.563116i	$-0.809602\pi$
$37$	1.03921	−	3.87837i	0.170844	−	0.637600i	0.997222	−	0.0744837i	$-0.0237309\pi$
$38$	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	$-0.0944857\pi$
$42$	6.24872	−	8.90518i	0.964198	−	1.37410i
$43$	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
$45$	−3.10170	+	6.61712i	−0.462374	+	0.986422i
$46$	−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	$0.246202\pi$
$48$	0.587334	−	6.63701i	0.0847744	−	0.957970i
$49$	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	$0.243234\pi$
$53$			10.0745i			1.38384i	−0.721976	+	0.691918i	$0.756766\pi$
$54$	−9.06696	−	5.27105i	−1.23386	−	0.717299i
$55$	3.37093	+	5.83861i	0.454535	+	0.787278i
$56$	−0.231907	+	0.401675i	−0.0309899	+	0.0536760i
$57$	0.890781	−	2.43983i	0.117987	−	0.323163i
$58$	−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	$0.952494\pi$
$60$	3.00092	−	8.21944i	0.387417	−	1.06112i
$61$	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
$63$	−5.33939	−	7.65790i	−0.672700	−	0.964805i
$64$			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	0.948566	−	0.316579i	$-0.102534\pi$
$67$	13.1928	+	3.53501i	1.61176	+	0.431870i	0.663193	+	0.748448i	$0.269201\pi$
$68$	−10.3961	+	6.00217i	−1.26071	+	0.727869i
$69$	−0.590160	+	6.66894i	−0.0710469	+	0.802846i
$70$	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	$0.410278\pi$
$72$	0.404871	+	0.189779i	0.0477145	+	0.0223656i
$73$	−8.54904	−	8.54904i	−1.00059	−	1.00059i	−1.00000		0.000589733i	$-0.999812\pi$
$73$	−8.54904	−	8.54904i	−1.00059	−	1.00059i	−0.000589733	−	1.00000i	$-0.500188\pi$
$74$	7.01840	+	4.05207i	0.815872	+	0.471044i
$75$	−0.929307	+	1.32437i	−0.107307	+	0.152926i
$76$	−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
$81$	−6.91743	+	5.75754i	−0.768603	+	0.639726i
$82$	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	$0.679295\pi$
$84$	7.17640	+	8.56984i	0.783009	+	0.935047i
$85$	13.6202	−	3.64951i	1.47731	−	0.395845i
$86$	−2.62965	+	2.62965i	−0.283562	+	0.283562i
$87$	−5.04308	−	0.446281i	−0.540675	−	0.0478464i
$88$	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
$93$	−8.60253	+	1.50801i	−0.892041	+	0.156374i
$94$	0.165094	+	0.285951i	0.0170282	+	0.0294936i
$95$	1.82649	−	3.16357i	0.187394	−	0.324576i
$96$	13.1177	+	4.78928i	1.33882	+	0.488804i
$97$	−2.56119	−	9.55851i	−0.260050	−	0.970520i	−0.965211	−	0.261472i	$-0.915792\pi$
$97$	−2.56119	−	9.55851i	−0.260050	−	0.970520i	0.705161	−	0.709047i	$-0.250875\pi$
$98$	1.40191	+	5.23199i	0.141614	+	0.528511i
$99$	0.707134	+	8.27261i	0.0710696	+	0.831428i
$100$	0.968580	−	1.67763i	0.0968580	−	0.167763i
$101$	4.61612	+	7.99536i	0.459321	+	0.795568i	0.998925	−	0.0463510i	$-0.0147593\pi$
$101$	4.61612	+	7.99536i	0.459321	+	0.795568i	−0.539604	+	0.841919i	$0.681426\pi$
$102$	3.49406	+	19.9321i	0.345964	+	1.97357i
$103$			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	0.0161603	−	0.999869i	$-0.494856\pi$
$107$	9.20781	−	5.31613i	0.890153	−	0.513930i	0.873992	+	0.485939i	$0.161522\pi$
$108$	7.64256	−	7.59696i	0.735406	−	0.731018i
$109$	0.625106	−	0.625106i	0.0598743	−	0.0598743i	−0.676536	−	0.736410i	$-0.736520\pi$
$109$	0.625106	−	0.625106i	0.0598743	−	0.0598743i	0.736410	+	0.676536i	$0.236520\pi$
$110$	−13.1439	+	3.52190i	−1.25322	+	0.335800i
$111$	5.33191	−	4.46495i	0.506082	−	0.423794i
$112$	8.46467	+	8.46467i	0.799836	+	0.799836i
$113$	5.88672	+	3.39870i	0.553776	+	0.319723i	0.750644	−	0.660707i	$-0.229744\pi$
$113$	5.88672	+	3.39870i	0.553776	+	0.319723i	−0.196868	+	0.980430i	$0.563077\pi$
$114$	4.29135	+	3.01122i	0.401922	+	0.282027i
$115$	−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
$120$	0.514782	+	0.361220i	0.0469930	+	0.0329747i
$121$	−2.89290	−	1.67022i	−0.262991	−	0.151838i
$122$	7.70110	+	7.70110i	0.697224	+	0.697224i
$123$	9.01362	−	7.54802i	0.812731	−	0.680582i
$124$	10.1009	−	2.70652i	0.907084	−	0.243052i
$125$	7.00357	−	7.00357i	0.626419	−	0.626419i
$126$	17.7191	−	6.40924i	1.57855	−	0.570980i
$127$	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	$-0.897853\pi$
$131$		−	7.22040i		−	0.630850i	0.948951	−	0.315425i	$-0.102147\pi$
$132$	−1.71651	−	9.79189i	−0.149403	−	0.852275i
$133$	2.33324	+	4.04129i	0.202317	+	0.350424i
$134$	−13.7837	+	23.8741i	−1.19073	+	2.06241i
$135$	−10.9809	+	6.29608i	−0.945084	+	0.541880i
$136$	−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	$0.597777\pi$
$138$	−12.6935	−	4.63440i	−1.08054	−	0.394506i
$139$	−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
$141$	0.279092	−	0.0489245i	0.0235038	−	0.00412019i
$142$			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
$147$	4.63007	+	0.409732i	0.381882	+	0.0337942i
$148$	−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	$0.480560\pi$
$150$	−2.09654	−	2.50362i	−0.171182	−	0.204420i
$151$	−3.11666	−	3.11666i	−0.253630	−	0.253630i	0.568827	−	0.822457i	$-0.307397\pi$
$151$	−3.11666	−	3.11666i	−0.253630	−	0.253630i	−0.822457	+	0.568827i	$0.807397\pi$
$152$	−0.193565	−	0.111755i	−0.0157002	−	0.00906449i
$153$	17.0955	+	3.04956i	1.38209	+	0.246543i
$154$	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
$159$	−10.0229	+	14.2838i	−0.794866	+	1.13278i
$160$	17.0090	+	9.82012i	1.34468	+	0.776349i
$161$	−8.50539	−	8.50539i	−0.670318	−	0.670318i
$162$	−7.61128	−	16.4939i	−0.597999	−	1.29589i
$163$	−11.9029	+	3.18936i	−0.932304	+	0.249810i	−0.692837	−	0.721094i	$-0.743639\pi$
$163$	−11.9029	+	3.18936i	−0.932304	+	0.249810i	−0.239467	+	0.970904i	$0.576973\pi$
$164$	−9.95367	+	9.95367i	−0.777251	+	0.777251i
$165$	−1.02934	+	11.6318i	−0.0801340	+	0.905532i
$166$	−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
$171$	3.69030	−	2.57302i	0.282204	−	0.196764i
$172$	−1.91054	−	3.30916i	−0.145678	−	0.252321i
$173$	−4.66570	+	8.08124i	−0.354727	+	0.614405i	−0.987071	−	0.160282i	$-0.948759\pi$
$173$	−4.66570	+	8.08124i	−0.354727	+	0.614405i	0.632344	+	0.774687i	$0.282093\pi$
$174$	3.50455	−	9.59886i	0.265679	−	0.727688i
$175$	−0.752323	−	2.80771i	−0.0568703	−	0.212243i
$176$	−2.75552	−	10.2838i	−0.207705	−	0.775167i
$177$	1.02494	−	2.80729i	0.0770394	−	0.211009i
$178$	4.29240	−	7.43465i	0.321729	−	0.557251i
$179$	−13.3578	−	23.1364i	−0.998409	−	1.72929i	−0.548044	−	0.836449i	$-0.684627\pi$
$179$	−13.3578	−	23.1364i	−0.998409	−	1.72929i	−0.450364	−	0.892845i	$-0.648706\pi$
$180$	12.4321	−	8.66814i	0.926634	−	0.646085i
$181$		−	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
$186$	1.55389	−	17.5593i	0.113937	−	1.28751i
$187$	11.3279	−	11.3279i	0.828377	−	0.828377i
$188$	−0.327702	+	0.0878076i	−0.0239002	+	0.00640403i
$189$	0.0483827	−	16.1696i	0.00351933	−	1.17616i
$190$	5.21356	+	5.21356i	0.378232	+	0.378232i
$191$	6.67034	+	3.85112i	0.482649	+	0.278657i	0.721520	−	0.692394i	$-0.243444\pi$
$191$	6.67034	+	3.85112i	0.482649	+	0.278657i	−0.238871	+	0.971051i	$0.576777\pi$
$192$	−8.53551	+	12.1641i	−0.615997	+	0.877871i
$193$	−4.03302	+	15.0515i	−0.290303	+	1.08343i	0.654573	+	0.755999i	$0.272849\pi$
$193$	−4.03302	+	15.0515i	−0.290303	+	1.08343i	−0.944876	+	0.327428i	$0.893818\pi$
$194$	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	$-0.302783\pi$
$198$	−16.4977	−	2.94293i	−1.17244	−	0.209145i
$199$	−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
$201$	15.1882	+	18.1373i	1.07129	+	1.27930i
$202$	−17.9992	+	4.82287i	−1.26642	+	0.339336i
$203$	6.43180	−	6.43180i	0.451424	−	0.451424i
$204$	−20.7112	−	1.83281i	−1.45007	−	0.128322i
$205$	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
$210$	26.1028	−	4.57578i	1.80126	−	0.315759i
$211$	−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
$213$	0.550234	+	0.200890i	0.0377014	+	0.0137648i
$214$	5.55424	+	20.7287i	0.379680	+	1.41698i
$215$	1.16167	+	4.33542i	0.0792254	+	0.295673i
$216$	0.385228	+	0.671870i	0.0262115	+	0.0457150i
$217$	7.84562	−	13.5890i	0.532595	−	0.922482i
$218$	0.892156	+	1.54526i	0.0604244	+	0.104658i
$219$	−3.61576	−	20.6263i	−0.244330	−	1.39379i
$220$		−	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	0.704614	−	0.709591i	$-0.251120\pi$
$223$	14.3363	+	3.84141i	0.960032	+	0.257240i	0.255418	+	0.966831i	$0.417787\pi$
$224$	−21.7280	+	12.5447i	−1.45176	+	0.838175i
$225$	−2.63518	+	0.953179i	−0.175679	+	0.0635453i
$226$	−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	$0.440793\pi$
$228$	−4.12976	+	3.45826i	−0.273500	+	0.229029i
$229$	1.83952	+	1.83952i	0.121559	+	0.121559i	0.765269	−	0.643711i	$-0.222606\pi$
$229$	1.83952	+	1.83952i	0.121559	+	0.121559i	−0.643711	+	0.765269i	$0.722606\pi$
$230$	−16.4589	−	9.50254i	−1.08527	−	0.626579i
$231$	−12.2108	−	8.56822i	−0.803408	−	0.563748i
$232$	−0.112759	+	0.420821i	−0.00740297	+	0.0276283i
$233$	16.4441			1.07729			0.538645	−	0.842533i	$-0.318936\pi$
$233$	16.4441			1.07729			0.538645	+	0.842533i	$0.318936\pi$
$234$		0			0
$235$	0.398508			0.0259958
$236$	−0.926129	+	3.45636i	−0.0602858	+	0.224990i
$237$	14.7580	+	10.3556i	0.958637	+	0.672670i
$238$	−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	$0.858979\pi$
$240$	12.4440	−	10.4206i	0.803258	−	0.672649i
$241$	5.68906	−	1.52438i	0.366465	−	0.0981939i	−0.0708874	−	0.997484i	$-0.522583\pi$
$241$	5.68906	−	1.52438i	0.366465	−	0.0981939i	0.437352	+	0.899290i	$0.355916\pi$
$242$	4.76750	−	4.76750i	0.306466	−	0.306466i
$243$	−15.5357	+	1.28116i	−0.996617	+	0.0821867i
$244$	−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
$249$	1.20049	+	6.84824i	0.0760778	+	0.433989i
$250$	9.99556	+	17.3128i	0.632175	+	1.09496i
$251$	0.111077	−	0.192391i	0.00701111	−	0.0121436i	−0.862499	−	0.506060i	$-0.831102\pi$
$251$	0.111077	−	0.192391i	0.00701111	−	0.0121436i	0.869510	+	0.493916i	$0.164435\pi$
$252$	1.64890	+	19.2901i	0.103871	+	1.21517i
$253$	2.76878	+	10.3332i	0.174072	+	0.649644i
$254$	0.211917	+	0.790883i	0.0132968	+	0.0496244i
$255$	22.9418	+	8.37605i	1.43667	+	0.524529i
$256$	−7.37694	+	12.7772i	−0.461059	+	0.798577i
$257$	−12.6431	−	21.8986i	−0.788658	−	1.36600i	−0.926789	−	0.375582i	$-0.877443\pi$
$257$	−12.6431	−	21.8986i	−0.788658	−	1.36600i	0.138132	−	0.990414i	$-0.455890\pi$
$258$	−6.34455	+	1.11219i	−0.394995	+	0.0692421i
$259$			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	−0.624882	−	0.780719i	$-0.714853\pi$
$263$	−4.23596	+	2.44563i	−0.261200	+	0.150804i	0.363682	+	0.931523i	$0.381520\pi$
$264$	0.711695	+	0.0629806i	0.0438018	+	0.00387619i
$265$	−17.3534	+	17.3534i	−1.06601	+	1.06601i
$266$	−9.09778	+	2.43774i	−0.557820	+	0.149468i
$267$	−4.72976	−	5.64814i	−0.289457	−	0.345661i
$268$	−20.0288	−	20.0288i	−1.22345	−	1.22345i
$269$	−18.3121	−	10.5725i	−1.11651	−	0.644616i	−0.176001	−	0.984390i	$-0.556316\pi$
$269$	−18.3121	−	10.5725i	−1.11651	−	0.644616i	−0.940507	+	0.339774i	$0.889650\pi$
$270$	−6.53850	−	24.6974i	−0.397921	−	1.50304i
$271$	−0.492584	+	1.83835i	−0.0299224	+	0.111672i	−0.979272	−	0.202550i	$-0.935077\pi$
$271$	−0.492584	+	1.83835i	−0.0299224	+	0.111672i	0.949349	+	0.314222i	$0.101744\pi$
$272$	−22.2673			−1.35015
$273$		0			0
$274$	−39.8051			−2.40471
$275$	−0.669094	+	2.49709i	−0.0403479	+	0.150580i
$276$	7.97511	−	11.3655i	0.480045	−	0.684122i
$277$	−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
$279$	−13.6971	−	6.42038i	−0.820027	−	0.384378i
$280$	−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	$0.208468\pi$
$282$	−0.0504128	+	0.569677i	−0.00300204	+	0.0339238i
$283$	−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
$288$	13.8338	+	19.8409i	0.815166	+	1.16913i
$289$	−8.25302	−	14.2947i	−0.485472	−	0.840862i
$290$	7.18585	−	12.4463i	0.421968	−	0.730870i
$291$	5.87824	−	16.1003i	0.344588	−	0.943818i
$292$	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	$-0.234519\pi$
$294$	−3.21754	+	8.81275i	−0.187651	+	0.513970i
$295$	2.10158	−	3.64004i	0.122359	−	0.211931i
$296$	−0.299227	−	0.518276i	−0.0173922	−	0.0301242i
$297$	−7.22765	+	12.4326i	−0.419391	+	0.721412i
$298$		−	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
$303$	−1.40957	+	15.9285i	−0.0809777	+	0.915067i
$304$	−4.07907	+	4.07907i	−0.233951	+	0.233951i
$305$	12.6966	−	3.40203i	0.727003	−	0.194800i
$306$	−14.8760	+	31.7363i	−0.850405	+	1.81424i
$307$	4.22784	+	4.22784i	0.241295	+	0.241295i	0.817386	−	0.576090i	$-0.195422\pi$
$307$	4.22784	+	4.22784i	0.241295	+	0.241295i	−0.576090	+	0.817386i	$0.695422\pi$
$308$	15.4678	+	8.93032i	0.881358	+	0.508852i
$309$	−17.1778	+	24.4805i	−0.977212	+	1.39264i
$310$	6.41673	−	23.9476i	0.364446	−	1.36013i
$311$	−20.8485			−1.18221			−0.591106	−	0.806594i	$-0.701308\pi$
$311$	−20.8485			−1.18221			−0.591106	+	0.806594i	$0.701308\pi$
$312$		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
$315$	3.99367	−	22.3880i	0.225018	−	1.26142i
$316$	−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	$0.654628\pi$
$318$	−22.6118	−	27.0024i	−1.26801	−	1.51422i
$319$	−7.81402	+	2.09376i	−0.437501	+	0.117228i
$320$	−14.7782	+	14.7782i	−0.826127	+	0.826127i
$321$	18.3439	+	1.62332i	1.02386	+	0.0906051i
$322$	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
$327$	1.50819	−	0.264384i	0.0834032	−	0.0146205i
$328$	−0.505844	−	0.876148i	−0.0279306	−	0.0483772i
$329$	−0.254535	+	0.440868i	−0.0140330	+	0.0243059i
$330$	−22.1396	−	8.08317i	−1.21875	−	0.444964i
$331$	−5.62946	−	21.0094i	−0.309423	−	1.15478i	−0.929070	−	0.369903i	$-0.879391\pi$
$331$	−5.62946	−	21.0094i	−0.309423	−	1.15478i	0.619647	−	0.784881i	$-0.287276\pi$
$332$	−2.15458	−	8.04101i	−0.118248	−	0.441308i
$333$	12.0018	−	1.02590i	0.657693	−	0.0562189i
$334$	−22.3349	+	38.6852i	−1.22211	+	2.11676i
$335$	16.6357	+	28.8139i	0.908905	+	1.57427i
$336$	3.58007	+	20.4227i	0.195309	+	1.11415i
$337$		−	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
$342$	3.08857	+	8.53874i	0.167011	+	0.461722i
$343$	9.49781	−	9.49781i	0.512834	−	0.512834i
$344$	0.265265	−	0.0710774i	0.0143021	−	0.00383224i
$345$	−12.5039	+	10.4708i	−0.673187	+	0.563727i
$346$	−13.3179	−	13.3179i	−0.715973	−	0.715973i
$347$	29.1720	+	16.8424i	1.56603	+	0.904150i	0.996624	+	0.0820954i	$0.0261612\pi$
$347$	29.1720	+	16.8424i	1.56603	+	0.904150i	0.569409	+	0.822054i	$0.307172\pi$
$348$	8.59462	+	6.03080i	0.460720	+	0.323285i
$349$	5.22478	−	19.4991i	0.279676	−	1.04376i	−0.672967	−	0.739673i	$-0.734980\pi$
$349$	5.22478	−	19.4991i	0.279676	−	1.04376i	0.952643	−	0.304092i	$-0.0983530\pi$
$350$	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	$0.924141\pi$
$354$	4.93767	+	3.46474i	0.262434	+	0.184149i
$355$	0.713455	+	0.411913i	0.0378663	+	0.0218621i
$356$	6.23719	+	6.23719i	0.330570	+	0.330570i
$357$	−23.9198	+	20.0305i	−1.26597	+	1.06013i
$358$	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	$0.469240\pi$
$360$	0.370499	+	1.02429i	0.0195270	+	0.0539849i
$361$	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
$366$	3.25713	+	18.5804i	0.170253	+	0.971215i
$367$	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
$369$	20.2891	−	1.73429i	1.05621	−	0.0902834i
$370$	5.10953	+	19.0690i	0.265632	+	0.991351i
$371$	−8.11405	−	30.2820i	−0.421260	−	1.57216i
$372$	17.0139	+	6.21177i	0.882128	+	0.322065i
$373$	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
$375$	16.8975	−	2.96211i	0.872584	−	0.152963i
$376$		−	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	−0.165834	−	0.986154i	$-0.553032\pi$
$379$	−15.6235	−	4.18632i	−0.802528	−	0.215037i	−0.636693	+	0.771117i	$0.719698\pi$
$380$	−6.56076	+	3.78786i	−0.336560	+	0.194313i
$381$	0.699895	+	0.0619364i	0.0358567	+	0.00317310i
$382$	−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	$0.274602\pi$
$384$	−1.32504	−	1.58233i	−0.0676184	−	0.0807478i
$385$	−14.8348	−	14.8348i	−0.756054	−	0.756054i
$386$	−27.2375	−	15.7256i	−1.38635	−	0.800411i
$387$	−0.970704	+	5.44164i	−0.0493437	+	0.276614i
$388$	−5.31152	+	19.8229i	−0.269652	+	1.00635i
$389$	29.3747			1.48936			0.744678	−	0.667424i	$-0.232603\pi$
$389$	29.3747			1.48936			0.744678	+	0.667424i	$0.232603\pi$
$390$		0			0
$391$	22.3744			1.13152
$392$	0.103524	−	0.386358i	0.00522876	−	0.0195140i
$393$	7.18342	−	10.2372i	0.362356	−	0.516401i
$394$	45.9607	+	26.5354i	2.31547	+	1.33683i
$395$	17.9295	+	17.9295i	0.902132	+	0.902132i
$396$	7.30804	−	15.5909i	0.367243	−	0.783471i
$397$	−15.6987	+	4.20647i	−0.787898	+	0.211117i	−0.630264	−	0.776381i	$-0.717053\pi$
$397$	−15.6987	+	4.20647i	−0.787898	+	0.211117i	−0.157634	+	0.987498i	$0.550387\pi$
$398$	19.5791	−	19.5791i	0.981411	−	0.981411i
$399$	−0.712473	+	8.05111i	−0.0356683	+	0.403060i
$400$	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
$405$	−21.8328	−	1.99792i	−1.08488	−	0.0992775i
$406$	9.17952	+	15.8994i	0.455572	+	0.789074i
$407$	5.55619	−	9.62360i	0.275410	−	0.477024i
$408$	0.512492	−	1.40370i	0.0253721	−	0.0694936i
$409$	2.11287	+	7.88532i	0.104474	+	0.389904i	0.998285	−	0.0585408i	$-0.0186448\pi$
$409$	2.11287	+	7.88532i	0.104474	+	0.389904i	−0.893811	+	0.448445i	$0.851978\pi$
$410$	8.63768	+	32.2363i	0.426585	+	1.59204i
$411$	−11.7149	+	32.0867i	−0.577851	+	1.58272i
$412$	17.9038	−	31.0102i	0.882055	−	1.52776i
$413$	2.68465	+	4.64995i	0.132103	+	0.228809i
$414$	−13.3864	−	19.1992i	−0.657908	−	0.943590i
$415$			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	−0.597569	−	0.801818i	$-0.703866\pi$
$419$	−4.13398	+	2.38676i	−0.201958	+	0.116601i	0.395610	+	0.918418i	$0.370533\pi$
$420$	−2.40022	+	27.1231i	−0.117119	+	1.32347i
$421$	−6.32386	+	6.32386i	−0.308206	+	0.308206i	−0.844213	−	0.536007i	$-0.819932\pi$
$421$	−6.32386	+	6.32386i	−0.308206	+	0.308206i	0.536007	+	0.844213i	$0.319932\pi$
$422$	42.0011	−	11.2542i	2.04458	−	0.547844i
$423$	0.444377	+	0.208297i	0.0216063	+	0.0101277i
$424$	1.06177	+	1.06177i	0.0515643	+	0.0515643i
$425$	4.68254	+	2.70347i	0.227137	+	0.131137i
$426$	−0.679096	+	0.967793i	−0.0329023	+	0.0468897i
$427$	−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	$-0.0603792\pi$
$432$	19.3231	−	5.11570i	0.929685	−	0.246129i
$433$	−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
$435$	−7.91804	−	9.45548i	−0.379641	−	0.453356i
$436$	−1.77088	+	0.474505i	−0.0848097	+	0.0227247i
$437$	4.09869	−	4.09869i	0.196067	−	0.196067i
$438$	42.1019	+	3.72575i	2.01171	+	0.178023i
$439$	−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	$-0.848382\pi$
$443$		−	19.3012i		−	0.917028i	0.888687	−	0.458514i	$-0.151618\pi$
$444$	−14.2059	+	2.49028i	−0.674184	+	0.118184i
$445$	−5.18054	−	8.97295i	−0.245581	−	0.425359i
$446$	−14.9784	+	25.9434i	−0.709250	+	1.22846i
$447$	−7.91952	−	2.89142i	−0.374580	−	0.136759i
$448$	−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	$0.902329\pi$
$450$	−0.481716	−	5.63549i	−0.0227083	−	0.265660i
$451$	9.39277	−	16.2688i	0.442288	−	0.766066i
$452$	−7.04838	−	12.2081i	−0.331528	−	0.574223i
$453$	−1.31817	−	7.51957i	−0.0619331	−	0.353300i
$454$		−	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	−0.738174	−	0.674610i	$-0.764312\pi$
$457$	−36.6573	−	9.82230i	−1.71476	−	0.459468i	−0.976583	+	0.215143i	$0.930978\pi$
$458$	−4.54728	+	2.62537i	−0.212480	+	0.122676i
$459$	21.2044	+	21.3316i	0.989735	+	0.995675i
$460$	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	$0.526697\pi$
$462$	23.0835	−	19.3301i	1.07394	−	0.899318i
$463$	0.201603	+	0.201603i	0.00936928	+	0.00936928i	0.711776	−	0.702407i	$-0.247891\pi$
$463$	0.201603	+	0.201603i	0.00936928	+	0.00936928i	−0.702407	+	0.711776i	$0.747891\pi$
$464$	9.73791	+	5.62218i	0.452071	+	0.261003i
$465$	−17.4155	−	12.2204i	−0.807626	−	0.566707i
$466$	−8.59032	+	32.0595i	−0.397939	+	1.48513i
$467$	13.1442			0.608242			0.304121	−	0.952633i	$-0.401637\pi$
$467$	13.1442			0.608242			0.304121	+	0.952633i	$0.401637\pi$
$468$		0			0
$469$	−42.5023			−1.96258
$470$	−0.208178	+	0.776931i	−0.00960254	+	0.0358372i
$471$	−7.70093	−	5.40371i	−0.354840	−	0.248990i
$472$	−0.222717	−	0.128586i	−0.0102514	−	0.00591865i
$473$	3.60577	+	3.60577i	0.165793	+	0.165793i
$474$	−27.8989	+	23.3626i	−1.28144	+	1.07308i
$475$	1.35302	−	0.362540i	0.0620807	−	0.0166345i
$476$	26.4145	−	26.4145i	1.21070	−	1.21070i
$477$	−28.4213	+	10.2803i	−1.30132	+	0.470705i
$478$	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
$483$	−3.59730	−	20.5209i	−0.163683	−	0.933735i
$484$	3.46377	+	5.99943i	0.157444	+	0.272702i
$485$	12.0530	−	20.8763i	0.547296	−	0.947945i
$486$	5.61801	−	30.9578i	0.254838	−	1.40427i
$487$	0.268324	+	1.00140i	0.0121589	+	0.0453777i	0.971739	−	0.236059i	$-0.0758558\pi$
$487$	0.268324	+	1.00140i	0.0121589	+	0.0453777i	−0.959580	+	0.281436i	$0.909189\pi$
$488$	−0.208155	−	0.776844i	−0.00942273	−	0.0351661i
$489$	−20.0492	−	7.31995i	−0.906654	−	0.331020i
$490$	−6.59736	+	11.4270i	−0.298038	+	0.516217i
$491$	2.92987	+	5.07469i	0.132223	+	0.229018i	0.924533	−	0.381101i	$-0.124455\pi$
$491$	2.92987	+	5.07469i	0.132223	+	0.229018i	−0.792310	+	0.610119i	$0.791122\pi$
$492$	−24.0152	+	4.20984i	−1.08269	+	0.189794i
$493$			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
$498$	−13.9785	−	1.23701i	−0.626390	−	0.0554316i
$499$	14.2320	−	14.2320i	0.637111	−	0.637111i	−0.312731	−	0.949842i	$-0.601244\pi$
$499$	14.2320	−	14.2320i	0.637111	−	0.637111i	0.949842	+	0.312731i	$0.101244\pi$
$500$	−19.8406	+	5.31627i	−0.887299	+	0.237751i
$501$	24.6107	+	29.3894i	1.09952	+	1.31302i
$502$	0.317060	+	0.317060i	0.0141511	+	0.0141511i
$503$	−26.1462	−	15.0955i	−1.16580	−	0.673075i	−0.213113	−	0.977027i	$-0.568360\pi$
$503$	−26.1462	−	15.0955i	−1.16580	−	0.673075i	−0.952687	+	0.303952i	$0.901694\pi$
$504$	−1.36982	−	0.244354i	−0.0610165	−	0.0108844i
$505$	−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	$0.0551227\pi$
$510$	−28.3146	+	40.3518i	−1.25379	+	1.78681i
$511$	32.5823	+	18.8114i	1.44136	+	0.832168i
$512$	−22.7420	−	22.7420i	−1.00506	−	1.00506i
$513$	7.79202	+	0.0233153i	0.344026	+	0.00102940i
$514$	49.2982	−	13.2094i	2.17445	−	0.582642i
$515$	−29.7413	+	29.7413i	−1.31056	+	1.31056i
$516$	0.583400	−	6.59255i	0.0256828	−	0.290221i
$517$	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	$0.235678\pi$
$521$			30.7954i			1.34917i	−0.738197	+	0.674585i	$0.764322\pi$
$522$	14.5185	−	10.1229i	0.635458	−	0.443066i
$523$	−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
$525$	1.72667	−	4.72930i	0.0753579	−	0.206403i
$526$	−2.55517	−	9.53602i	−0.111411	−	0.415790i
$527$	7.55433	+	28.1931i	0.329072	+	1.22811i
$528$	6.32424	−	17.3219i	0.275227	−	0.753841i
$529$	4.02949	−	6.97928i	0.175195	−	0.303447i
$530$	−24.7669	−	42.8975i	−1.07581	−	1.86335i
$531$	4.24610	−	2.96054i	0.184265	−	0.128477i
$532$		−	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
$537$	4.07891	−	46.0926i	0.176018	−	1.98904i
$538$	30.1783	−	30.1783i	1.30108	−	1.30108i
$539$	7.17409	−	1.92229i	0.309010	−	0.0827989i
$540$	26.2502	+	0.0785461i	1.12963	+	0.00338009i
$541$	17.8219	+	17.8219i	0.766224	+	0.766224i	0.977439	−	0.211216i	$-0.0677422\pi$
$541$	17.8219	+	17.8219i	0.766224	+	0.766224i	−0.211216	+	0.977439i	$0.567742\pi$
$542$	−3.32673	−	1.92069i	−0.142895	−	0.0825006i
$543$	26.1400	−	37.2527i	1.12177	−	1.59866i
$544$	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
$549$	15.9362	+	2.84277i	0.680140	+	0.121326i
$550$	−4.51881	−	2.60894i	−0.192683	−	0.111245i
$551$	3.09945	+	3.09945i	0.132041	+	0.132041i
$552$	0.640658	+	0.765055i	0.0272682	+	0.0325629i
$553$	−31.2874	+	8.38343i	−1.33047	+	0.356500i
$554$	5.63751	−	5.63751i	0.239515	−	0.239515i
$555$	16.8752	+	1.49335i	0.716312	+	0.0633892i
$556$	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
$561$	27.3308	−	4.79105i	1.15391	−	0.202278i
$562$	4.40201	+	7.62451i	0.185688	+	0.321621i
$563$	−16.9776	+	29.4060i	−0.715519	+	1.23932i	0.247240	+	0.968954i	$0.420476\pi$
$563$	−16.9776	+	29.4060i	−0.715519	+	1.23932i	−0.962759	+	0.270361i	$0.912857\pi$
$564$	−0.551981	−	0.201528i	−0.0232426	−	0.00848588i
$565$	4.28564	+	15.9942i	0.180298	+	0.672883i
$566$	−9.63082	−	35.9427i	−0.404814	−	1.51079i
$567$	16.1554	−	22.8774i	0.678461	−	0.960762i
$568$	0.0252031	−	0.0436530i	0.00105750	−	0.00183164i
$569$	4.08073	+	7.06804i	0.171073	+	0.296308i	0.938795	−	0.344475i	$-0.111943\pi$
$569$	4.08073	+	7.06804i	0.171073	+	0.296308i	−0.767722	+	0.640783i	$0.778610\pi$
$570$	2.20504	+	12.5788i	0.0923590	+	0.526866i
$571$			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
$576$	−24.2037	+	8.75477i	−1.00849	+	0.364782i
$577$	−10.9086	+	10.9086i	−0.454132	+	0.454132i	−0.896723	−	0.442592i	$-0.854059\pi$
$577$	−10.9086	+	10.9086i	−0.454132	+	0.454132i	0.442592	+	0.896723i	$0.354059\pi$
$578$	32.1802	−	8.62267i	1.33852	−	0.358656i
$579$	−20.6925	+	17.3279i	−0.859950	+	0.720123i
$580$	10.4416	+	10.4416i	0.433564	+	0.433564i
$581$	−10.8178	−	6.24567i	−0.448799	−	0.259114i
$582$	28.3185	+	19.8709i	1.17384	+	0.823677i
$583$	−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	$0.0731584\pi$
$588$	−7.89076	−	5.53690i	−0.325409	−	0.228338i
$589$	6.54846	+	3.78076i	0.269825	+	0.155783i
$590$	5.99878	+	5.99878i	0.246966	+	0.246966i
$591$	34.9165	−	29.2392i	1.43627	−	1.20274i
$592$	−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	$0.277969\pi$
$594$	−20.4629	−	20.5858i	−0.839604	−	0.844644i
$595$	−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	$0.112851\pi$
$599$			16.9927i			0.694302i	−0.937809	+	0.347151i	$0.887149\pi$
$600$	0.0416372	+	0.237521i	0.00169983	+	0.00969676i
$601$	−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
$603$	3.48974	+	40.8258i	0.142113	+	1.66255i
$604$	2.36580	+	8.82927i	0.0962629	+	0.359258i
$605$	−2.10609	−	7.86003i	−0.0856247	−	0.319556i
$606$	−30.3178	−	11.0690i	−1.23158	−	0.449649i
$607$	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
$609$	15.5180	−	2.72029i	0.628822	−	0.110232i
$610$			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	0.154300	−	0.988024i	$-0.450688\pi$
$613$	−5.10239	−	1.36718i	−0.206084	−	0.0552199i	−0.360384	+	0.932804i	$0.617354\pi$
$614$	−10.4512	+	6.03400i	−0.421776	+	0.243513i
$615$	28.5276	+	2.52452i	1.15034	+	0.101798i
$616$	−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	$0.599636\pi$
$618$	−38.7536	−	46.2784i	−1.55890	−	1.86159i
$619$	21.7905	+	21.7905i	0.875835	+	0.875835i	0.993101	−	0.117266i	$-0.0374129\pi$
$619$	21.7905	+	21.7905i	0.875835	+	0.875835i	−0.117266	+	0.993101i	$0.537413\pi$
$620$	22.0609	+	12.7368i	0.885985	+	0.511524i
$621$	−19.4161	+	5.14031i	−0.779141	+	0.206274i
$622$	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
$627$	4.12897	−	5.88429i	0.164895	−	0.234996i
$628$	9.75503	+	5.63207i	0.389268	+	0.224744i
$629$	−16.4343	−	16.4343i	−0.655279	−	0.655279i
$630$	41.5614	+	19.4814i	1.65585	+	0.776159i
$631$	3.51195	−	0.941025i	0.139809	−	0.0374616i	−0.188236	−	0.982124i	$-0.560277\pi$
$631$	3.51195	−	0.941025i	0.139809	−	0.0374616i	0.328045	+	0.944662i	$0.393610\pi$
$632$	1.09703	−	1.09703i	0.0436373	−	0.0436373i
$633$	3.28923	−	37.1690i	0.130735	−	1.47734i
$634$	−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
$639$	0.580272	+	0.832243i	0.0229552	+	0.0329230i
$640$	−1.45133	−	2.51378i	−0.0573688	−	0.0993657i
$641$	2.44180	−	4.22932i	0.0964452	−	0.167048i	−0.813766	−	0.581193i	$-0.802586\pi$
$641$	2.44180	−	4.22932i	0.0964452	−	0.167048i	0.910211	+	0.414145i	$0.135919\pi$
$642$	−12.7476	+	34.9154i	−0.503108	+	1.37800i
$643$	0.734494	+	2.74117i	0.0289656	+	0.108101i	0.978895	−	0.204363i	$-0.0655123\pi$
$643$	0.734494	+	2.74117i	0.0289656	+	0.108101i	−0.949930	+	0.312464i	$0.898846\pi$
$644$	6.45627	+	24.0951i	0.254413	+	0.949481i
$645$	−2.66617	+	7.30258i	−0.104980	+	0.287539i
$646$	8.76000	−	15.1728i	0.344658	−	0.596965i
$647$	7.83061	+	13.5630i	0.307853	+	0.533217i	0.977892	−	0.209108i	$-0.0670561\pi$
$647$	7.83061	+	13.5630i	0.307853	+	0.533217i	−0.670039	+	0.742326i	$0.733723\pi$
$648$	−0.122244	+	1.33585i	−0.00480218	+	0.0524770i
$649$		−	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	0.116830	−	0.993152i	$-0.462727\pi$
$653$	26.4569	−	15.2749i	1.03534	−	0.597753i	0.918510	+	0.395398i	$0.129393\pi$
$654$	−0.272427	+	3.07849i	−0.0106527	+	0.120378i
$655$	12.4372	−	12.4372i	0.485963	−	0.485963i
$656$	−25.2215	+	6.75809i	−0.984735	+	0.263859i
$657$	15.3941	−	32.8416i	0.600582	−	1.28127i
$658$	−0.726550	−	0.726550i	−0.0283239	−	0.0283239i
$659$	−4.19022	−	2.41923i	−0.163228	−	0.0942397i	0.416161	−	0.909291i	$-0.363375\pi$
$659$	−4.19022	−	2.41923i	−0.163228	−	0.0942397i	−0.579389	+	0.815051i	$0.696709\pi$
$660$	13.9099	−	19.8233i	0.541444	−	0.771623i
$661$	12.7370	−	47.5350i	0.495410	−	1.84890i	−0.0323096	−	0.999478i	$-0.510286\pi$
$661$	12.7370	−	47.5350i	0.495410	−	1.84890i	0.527720	−	0.849418i	$-0.323047\pi$
$662$	43.9009			1.70626
$663$		0			0
$664$	0.598295			0.0232184
$665$	−2.94213	+	10.9802i	−0.114091	+	0.425794i
$666$	−4.26956	+	23.9346i	−0.165442	+	0.927447i
$667$	−9.78475	−	5.64923i	−0.378867	−	0.218739i
$668$	−32.4544	−	32.4544i	−1.25570	−	1.25570i
$669$	16.5046	+	19.7093i	0.638106	+	0.762007i
$670$	−64.8660	+	17.3808i	−2.50599	+	0.671478i
$671$	10.5597	−	10.5597i	0.407653	−	0.407653i
$672$	−43.2868	−	3.83061i	−1.66982	−	0.147769i
$673$	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	$-0.874390\pi$
$677$		−	20.0063i		−	0.768905i	0.923145	−	0.384452i	$-0.125610\pi$
$678$	−23.4063	+	4.10310i	−0.898914	+	0.157579i
$679$	15.3970	+	26.6683i	0.590881	+	1.02344i
$680$	1.05083	−	1.82010i	0.0402976	−	0.0697975i
$681$	−3.71242	−	1.35540i	−0.142260	−	0.0519392i
$682$	−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	$0.828329\pi$
$684$	−9.29581	+	0.794596i	−0.355434	+	0.0303821i
$685$	−24.0206	+	41.6049i	−0.917779	+	1.58964i
$686$	13.5554	+	23.4786i	0.517546	+	0.896416i
$687$	0.778010	+	4.43820i	0.0296829	+	0.169328i
$688$		−	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	0.447883	−	0.894092i	$-0.352178\pi$
$691$	10.2181	+	2.73794i	0.388716	+	0.104156i	−0.0591676	+	0.998248i	$0.518845\pi$
$692$	16.7592	−	9.67595i	0.637090	−	0.367824i
$693$	−8.78833	−	24.2964i	−0.333841	−	0.922945i
$694$	−48.0753	+	48.0753i	−1.82492	+	1.82492i
$695$	−24.3734	+	6.53084i	−0.924537	+	0.247729i
$696$	−0.578538	+	0.484468i	−0.0219294	+	0.0183637i
$697$	−27.7823	−	27.7823i	−1.05233	−	1.05233i
$698$	35.2862	+	20.3725i	1.33560	+	0.771109i
$699$	23.3148	+	16.3599i	0.881848	+	0.618788i
$700$	−1.56020	+	5.82275i	−0.0589701	+	0.220079i
$701$	−34.6355			−1.30816			−0.654082	−	0.756423i	$-0.726945\pi$
$701$	−34.6355			−1.30816			−0.654082	+	0.756423i	$0.726945\pi$
$702$		0			0
$703$	−6.02109			−0.227090
$704$	−6.14551	+	22.9354i	−0.231618	+	0.864409i
$705$	0.565013	+	0.396466i	0.0212796	+	0.0149318i
$706$	−31.4967	−	18.1847i	−1.18540	−	0.684389i
$707$	−20.3147	−	20.3147i	−0.764014	−	0.764014i
$708$	−4.75174	+	3.97911i	−0.178581	+	0.149544i
$709$	33.9830	−	9.10572i	1.27626	−	0.341973i	0.443833	−	0.896109i	$-0.353618\pi$
$709$	33.9830	−	9.10572i	1.27626	−	0.341973i	0.832426	+	0.554137i	$0.186952\pi$
$710$	−1.17577	+	1.17577i	−0.0441259	+	0.0441259i
$711$	10.6216	+	29.3649i	0.398343	+	1.10127i
$712$	−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
$717$	−3.10434	−	17.7089i	−0.115934	−	0.661350i
$718$	−24.3064	−	42.1000i	−0.907108	−	1.57116i
$719$	−9.63051	+	16.6805i	−0.359157	+	0.622079i	−0.987820	−	0.155599i	$-0.950269\pi$
$719$	−9.63051	+	16.6805i	−0.359157	+	0.622079i	0.628663	+	0.777678i	$0.283603\pi$
$720$	28.0107	−	2.39432i	1.04390	−	0.0892311i
$721$	−13.9063	−	51.8992i	−0.517899	−	1.93283i
$722$	8.75076	+	32.6583i	0.325670	+	1.21542i
$723$	9.58264	+	3.49862i	0.356382	+	0.130115i
$724$	−27.2447	+	47.1892i	−1.01254	+	1.75377i
$725$	−1.36517	−	2.36455i	−0.0507013	−	0.0878172i
$726$	11.5025	−	2.01638i	0.426899	−	0.0748349i
$727$		−	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
$732$	−19.3067	−	1.70852i	−0.713597	−	0.0631489i
$733$	−14.7153	+	14.7153i	−0.543522	+	0.543522i	−0.924559	−	0.381038i	$-0.875567\pi$
$733$	−14.7153	+	14.7153i	−0.543522	+	0.543522i	0.381038	+	0.924559i	$0.375567\pi$
$734$	−36.7328	+	9.84253i	−1.35583	+	0.363294i
$735$	7.26958	+	8.68112i	0.268142	+	0.320208i
$736$	22.0366	+	22.0366i	0.812281	+	0.812281i
$737$	32.7361	+	18.9002i	1.20585	+	0.696197i
$738$	−7.21772	+	40.4616i	−0.265688	+	1.48941i
$739$	−5.47886	+	20.4474i	−0.201543	+	0.752169i	0.788932	+	0.614480i	$0.210634\pi$
$739$	−5.47886	+	20.4474i	−0.201543	+	0.752169i	−0.990475	+	0.137689i	$0.956033\pi$
$740$	−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	$0.808200\pi$
$744$	−0.747710	+	1.06558i	−0.0274124	+	0.0390659i
$745$	−10.2688	−	5.92867i	−0.376218	−	0.217210i
$746$	25.6472	+	25.6472i	0.939012	+	0.939012i
$747$	−5.11108	+	10.9039i	−0.187005	+	0.398953i
$748$	−32.0910	+	8.59877i	−1.17336	+	0.314402i
$749$	−23.3954	+	23.3954i	−0.854848	+	0.854848i
$750$	−3.05222	+	34.4908i	−0.111451	+	1.25943i
$751$	−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
$756$	−16.8535	+	28.9904i	−0.612956	+	1.05437i
$757$	−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
$759$	−6.35467	+	17.4053i	−0.230660	+	0.631771i
$760$	−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	$-0.354371\pi$
$762$	−0.486373	+	1.33216i	−0.0176194	+	0.0482592i
$763$	−1.37549	+	2.38242i	−0.0497961	+	0.0862493i
$764$	−7.98663	−	13.8333i	−0.288946	−	0.500469i
$765$	24.1942	+	34.7000i	0.874743	+	1.25458i
$766$			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	0.739130	−	0.673563i	$-0.235237\pi$
$769$	28.9081	+	7.74591i	1.04245	+	0.279325i	0.303324	+	0.952887i	$0.401904\pi$
$770$	36.6717	−	21.1724i	1.32156	−	0.763001i
$771$	3.86069	−	43.6267i	0.139039	−	1.57118i
$772$	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	$0.528326\pi$
$774$	−10.1019	−	4.73517i	−0.363107	−	0.170202i
$775$	−3.33052	−	3.33052i	−0.119636	−	0.119636i
$776$	−1.27733	−	0.737465i	−0.0458534	−	0.0264734i
$777$	−12.4306	+	17.7152i	−0.445947	+	0.635528i
$778$	−15.3452	+	57.2690i	−0.550151	+	2.05319i
$779$	−10.1787			−0.364690
$780$		0			0
$781$	0.935968			0.0334916
$782$	−11.6883	+	43.6212i	−0.417972	+	1.55989i
$783$	−3.88712	−	14.6825i	−0.138914	−	0.524711i
$784$	−8.94041	−	5.16175i	−0.319300	−	0.184348i
$785$	−9.35586	−	9.35586i	−0.333925	−	0.333925i
$786$	16.2060	+	19.3527i	0.578048	+	0.690288i
$787$	16.9411	−	4.53936i	0.603886	−	0.161811i	0.0560940	−	0.998425i	$-0.482135\pi$
$787$	16.9411	−	4.53936i	0.603886	−	0.161811i	0.547792	+	0.836615i	$0.315469\pi$
$788$	−38.5580	+	38.5580i	−1.37357	+	1.37357i
$789$	−8.43894	−	0.746794i	−0.300434	−	0.0265866i
$790$	−44.3217	+	25.5892i	−1.57690	+	0.910421i
$791$	−20.4317	−	5.47467i	−0.726469	−	0.194657i
$792$	0.946398	+	0.797345i	0.0336288	+	0.0283324i
$793$		0			0
$794$		−	32.8038i		−	1.16416i
$795$	−41.8685	+	7.33950i	−1.48492	+	0.260305i
$796$	14.2250	+	24.6384i	0.504191	+	0.873284i
$797$	−16.0954	+	27.8780i	−0.570128	+	0.987491i	0.426424	+	0.904523i	$0.359773\pi$
$797$	−16.0954	+	27.8780i	−0.570128	+	0.987491i	−0.996552	+	0.0829676i	$0.973560\pi$
$798$	−15.3243	−	5.59490i	−0.542474	−	0.198057i
$799$	−0.245085	−	0.914671i	−0.00867049	−	0.0323587i
$800$	1.94919	+	7.27449i	0.0689144	+	0.257192i
$801$	−1.08674	−	12.7136i	−0.0383982	−	0.449213i
$802$	−2.08736	+	3.61542i	−0.0737074	+	0.127665i
$803$	−16.7303	−	28.9778i	−0.590400	−	1.02260i
$804$	−8.47105	−	48.3235i	−0.298751	−	1.70424i
$805$		−	29.3013i		−	1.03273i
$806$		0			0
$807$	−15.4449	−	33.2082i	−0.543688	−	1.16898i
$808$	1.32916	+	0.356146i	0.0467596	+	0.0125292i
$809$	−10.5726	+	6.10408i	−0.371712	+	0.214608i	−0.674206	−	0.738543i	$-0.735514\pi$
$809$	−10.5726	+	6.10408i	−0.371712	+	0.214608i	0.302494	+	0.953151i	$0.402181\pi$
$810$	15.3005	−	41.5215i	0.537604	−	1.45892i
$811$	−6.35825	+	6.35825i	−0.223268	+	0.223268i	−0.809873	−	0.586605i	$-0.800464\pi$
$811$	−6.35825	+	6.35825i	−0.223268	+	0.223268i	0.586605	+	0.809873i	$0.300464\pi$
$812$	−18.2208	+	4.88225i	−0.639425	+	0.171334i
$813$	−2.52733	+	2.11639i	−0.0886373	+	0.0742250i
$814$	15.8597	+	15.8597i	0.555881	+	0.555881i
$815$	−25.9965	−	15.0091i	−0.910619	−	0.525746i
$816$	−31.5711	−	22.1533i	−1.10521	−	0.775519i
$817$	0.715117	−	2.66885i	0.0250188	−	0.0933714i
$818$	−16.4770			−0.576104
$819$		0			0
$820$	−34.2906			−1.19748
$821$	−5.63170	+	21.0178i	−0.196548	+	0.733525i	0.795313	+	0.606199i	$0.207306\pi$
$821$	−5.63170	+	21.0178i	−0.196548	+	0.733525i	−0.991861	+	0.127327i	$0.959360\pi$
$822$	−56.4365	−	39.6012i	−1.96845	−	1.38125i
$823$	−16.9466	−	9.78414i	−0.590722	−	0.341054i	0.174661	−	0.984629i	$-0.444117\pi$
$823$	−16.9466	−	9.78414i	−0.590722	−	0.341054i	−0.765383	+	0.643575i	$0.777450\pi$
$824$	1.81973	+	1.81973i	0.0633934	+	0.0633934i
$825$	−3.43296	+	2.87477i	−0.119520	+	0.100087i
$826$	−10.4680	+	2.80489i	−0.364228	+	0.0975947i
$827$	11.8247	−	11.8247i	0.411186	−	0.411186i	−0.470966	−	0.882152i	$-0.656094\pi$
$827$	11.8247	−	11.8247i	0.411186	−	0.411186i	0.882152	+	0.470966i	$0.156094\pi$
$828$	22.6146	−	8.17997i	0.785910	−	0.284274i
$829$	17.0184	−	9.82557i	0.591073	−	0.341256i	−0.174449	−	0.984666i	$-0.555814\pi$
$829$	17.0184	−	9.82557i	0.591073	−	0.341256i	0.765522	+	0.643410i	$0.222481\pi$
$830$	−19.0640	−	5.10818i	−0.661720	−	0.177307i
$831$	−2.88522	−	6.20352i	−0.100087	−	0.215198i
$832$		0			0
$833$		−	15.5340i		−	0.538220i
$834$	−6.25266	−	35.6686i	−0.216512	−	1.23510i
$835$	26.9563	+	46.6896i	0.932860	+	1.61576i
$836$	−4.30347	+	7.45383i	−0.148839	+	0.257796i
$837$	−13.0326	−	22.7299i	−0.450473	−	0.785662i
$838$	−2.49366	−	9.30645i	−0.0861419	−	0.321486i
$839$	−0.976003	−	3.64249i	−0.0336954	−	0.125753i	0.947030	−	0.321147i	$-0.104068\pi$
$839$	−0.976003	−	3.64249i	−0.0336954	−	0.125753i	−0.980725	+	0.195394i	$0.937402\pi$
$840$	−1.83827	−	0.671153i	−0.0634264	−	0.0231570i
$841$	−10.2280	+	17.7155i	−0.352691	+	0.610878i
$842$	−9.02546	−	15.6326i	−0.311038	−	0.538734i
$843$	7.44162	−	1.30451i	0.256303	−	0.0449296i
$844$			44.6777i			1.53787i
$845$		0			0
$846$	−0.638235	+	0.757545i	−0.0219430	+	0.0260449i
$847$	10.0407	+	2.69041i	0.345004	+	0.0924436i
$848$	33.5629	−	19.3775i	1.15255	−	0.665427i
$849$	−31.8077	−	2.81478i	−1.09164	−	0.0966030i
$850$	−7.71681	+	7.71681i	−0.264685	+	0.264685i
$851$	14.9913	−	4.01691i	0.513895	−	0.137698i
$852$	−0.779914	−	0.931350i	−0.0267194	−	0.0319075i
$853$	4.56091	+	4.56091i	0.156162	+	0.156162i	0.780864	−	0.624701i	$-0.214779\pi$
$853$	4.56091	+	4.56091i	0.156162	+	0.156162i	−0.624701	+	0.780864i	$0.714779\pi$
$854$	−29.3506	−	16.9456i	−1.00436	−	0.579866i
$855$	10.7886	+	1.92453i	0.368964	+	0.0658174i
$856$	0.410154	−	1.53072i	0.0140188	−	0.0523188i
$857$	31.9796			1.09240			0.546201	−	0.837654i	$-0.316073\pi$
$857$	31.9796			1.09240			0.546201	+	0.837654i	$0.316073\pi$
$858$		0			0
$859$	18.1029			0.617664			0.308832	−	0.951117i	$-0.400062\pi$
$859$	18.1029			0.617664			0.308832	+	0.951117i	$0.400062\pi$
$860$	2.40913	−	8.99100i	0.0821507	−	0.306590i
$861$	−21.0141	+	29.9476i	−0.716158	+	1.02061i
$862$	31.6658	+	18.2822i	1.07854	+	0.622695i
$863$	33.7030	+	33.7030i	1.14726	+	1.14726i	0.987089	+	0.160173i	$0.0512051\pi$
$863$	33.7030	+	33.7030i	1.14726	+	1.14726i	0.160173	+	0.987089i	$0.448795\pi$
$864$	−0.125355	+	41.8938i	−0.00426466	+	1.42526i
$865$	−21.9567	+	5.88329i	−0.746552	+	0.200038i
$866$	36.3992	−	36.3992i	1.23689	−	1.23689i
$867$	2.52013	−	28.4780i	0.0855880	−	0.967164i
$868$	−28.1815	+	16.2706i	−0.956542	+	0.552260i
$869$	27.8261	+	7.45598i	0.943936	+	0.252927i
$870$	22.5708	−	10.4975i	0.765221	−	0.355900i
$871$		0			0
$872$		−	0.131763i		−	0.00446206i
$873$	24.3522	−	16.9793i	0.824196	−	0.574661i
$874$	5.84969	+	10.1320i	0.197869	+	0.342719i
$875$	−15.4107	+	26.6922i	−0.520978	+	0.902361i
$876$	−14.8939	+	40.7941i	−0.503219	+	1.37830i
$877$	8.57211	+	31.9915i	0.289460	+	1.08028i	0.945519	+	0.325568i	$0.105556\pi$
$877$	8.57211	+	31.9915i	0.289460	+	1.08028i	−0.656059	+	0.754710i	$0.727778\pi$
$878$	−5.26916	−	19.6648i	−0.177825	−	0.663653i
$879$	9.29975	−	25.4718i	0.313673	−	0.859141i
$880$	12.9675	−	22.4603i	0.437133	−	0.757137i
$881$	25.8329	+	44.7438i	0.870331	+	1.50746i	0.861654	+	0.507495i	$0.169429\pi$
$881$	25.8329	+	44.7438i	0.870331	+	1.50746i	0.00867661	+	0.999962i	$0.497238\pi$
$882$	−13.3295	+	9.29385i	−0.448828	+	0.312940i
$883$			29.2334i			0.983782i	0.870657	+	0.491891i	$0.163694\pi$
$883$			29.2334i			0.983782i	−0.870657	+	0.491891i	$0.836306\pi$
$884$		0			0
$885$	6.60106	−	3.07011i	0.221892	−	0.103201i
$886$	37.6297	+	10.0828i	1.26419	+	0.338740i
$887$	−41.5069	+	23.9640i	−1.39367	+	0.804634i	−0.993719	−	0.111904i	$-0.964305\pi$
$887$	−41.5069	+	23.9640i	−1.39367	+	0.804634i	−0.399948	+	0.916538i	$0.630972\pi$
$888$	0.0913713	−	1.03252i	0.00306622	−	0.0346490i
$889$	−0.892628	+	0.892628i	−0.0299378	+	0.0299378i
$890$	20.2000	−	5.41257i	0.677105	−	0.181430i
$891$	−22.6164	+	10.4366i	−0.757679	+	0.349638i
$892$	−21.7649	−	21.7649i	−0.728741	−	0.728741i
$893$	−0.212452	−	0.122659i	−0.00710943	−	0.00410463i
$894$	9.77422	−	13.9294i	0.326899	−	0.465870i
$895$	16.8437	−	62.8616i	0.563024	−	2.10123i
$896$	3.70798			0.123875
$897$		0			0
$898$	−3.85168			−0.128532
$899$	3.81473	−	14.2368i	0.127228	−	0.474822i
$900$	5.72117	+	1.02057i	0.190706	+	0.0340189i
$901$	50.5027	+	29.1577i	1.68249	+	0.971385i
$902$	26.8109	+	26.8109i	0.892704	+	0.892704i
$903$	−6.37589	−	7.61390i	−0.212176	−	0.253375i
$904$	0.978614	−	0.262219i	0.0325482	−	0.00872127i
$905$	45.2583	−	45.2583i	1.50444	−	1.50444i
$906$	15.3488	+	1.35827i	0.509929	+	0.0451255i
$907$	20.2327	−	11.6814i	0.671816	−	0.387873i	−0.124949	−	0.992163i	$-0.539877\pi$
$907$	20.2327	−	11.6814i	0.671816	−	0.387873i	0.796764	+	0.604290i	$0.206543\pi$
$908$	4.57076	+	1.22473i	0.151686	+	0.0406442i
$909$	−17.8454	+	21.1814i	−0.591895	+	0.702542i
$910$		0			0
$911$			27.4965i			0.910999i	0.890236	+	0.455500i	$0.150539\pi$
$911$			27.4965i			0.910999i	−0.890236	+	0.455500i	$0.849461\pi$
$912$	−9.84157	+	1.72522i	−0.325887	+	0.0571276i
$913$	5.55472	+	9.62106i	0.183835	+	0.318411i
$914$	38.2991	−	66.3361i	1.26682	−	2.19420i
$915$	21.3861	+	7.80806i	0.707002	+	0.258126i
$916$	−1.39634	−	5.21121i	−0.0461363	−	0.172183i
$917$	5.81536	+	21.7032i	0.192040	+	0.716703i
$918$	−52.6652	+	30.1965i	−1.73821	+	0.996634i
$919$	−11.3910	+	19.7298i	−0.375754	+	0.650825i	−0.990440	−	0.137947i	$-0.955950\pi$
$919$	−11.3910	+	19.7298i	−0.375754	+	0.650825i	0.614686	+	0.788772i	$0.289283\pi$
$920$	0.701718	+	1.21541i	0.0231349	+	0.0400709i
$921$	1.78814	+	10.2005i	0.0589211	+	0.336118i
$922$		−	29.3672i		−	0.967157i
$923$		0			0
$924$	13.0460	+	28.0502i	0.429180	+	0.922782i
$925$	3.62275	+	0.970712i	0.119115	+	0.0319168i
$926$	−0.498362	+	0.287729i	−0.0163772	+	0.00945537i
$927$	−48.7101	+	17.6191i	−1.59985	+	0.578687i
$928$	−16.6642	+	16.6642i	−0.547028	+	0.547028i
$929$	44.7156	−	11.9815i	1.46707	−	0.393100i	0.565145	−	0.824992i	$-0.308820\pi$
$929$	44.7156	−	11.9815i	1.46707	−	0.393100i	0.901926	+	0.431891i	$0.142154\pi$
$930$	32.9227	−	27.5695i	1.07958	−	0.904040i
$931$	−2.84561	−	2.84561i	−0.0932613	−	0.0932613i
$932$	−29.5337	−	17.0513i	−0.967408	−	0.558534i
$933$	−29.5595	−	20.7417i	−0.967734	−	0.679054i
$934$	−6.86647	+	25.6260i	−0.224678	+	0.838509i
$935$	39.0248			1.27625
$936$		0			0
$937$	37.0828			1.21144			0.605722	−	0.795677i	$-0.292885\pi$
$937$	37.0828			1.21144			0.605722	+	0.795677i	$0.292885\pi$
$938$	22.2030	−	82.8626i	0.724953	−	2.70556i
$939$	9.83517	+	6.90129i	0.320959	+	0.225215i
$940$	−0.715721	−	0.413221i	−0.0233442	−	0.0134778i
$941$	−28.3019	−	28.3019i	−0.922617	−	0.922617i	0.0745966	−	0.997214i	$-0.476233\pi$
$941$	−28.3019	−	28.3019i	−0.922617	−	0.922617i	−0.997214	+	0.0745966i	$0.976233\pi$
$942$	14.5580	−	12.1909i	0.474325	−	0.397201i
$943$	25.3429	−	6.79060i	0.825277	−	0.221132i
$944$	−4.69342	+	4.69342i	−0.152758	+	0.152758i
$945$	27.9356	−	27.7689i	0.908746	−	0.903324i
$946$	−8.91344	+	5.14618i	−0.289801	+	0.167317i
$947$	−8.45116	−	2.26448i	−0.274626	−	0.0735858i	0.118878	−	0.992909i	$-0.462070\pi$
$947$	−8.45116	−	2.26448i	−0.274626	−	0.0735858i	−0.393503	+	0.919323i	$0.628737\pi$
$948$	−15.7675	−	33.9017i	−0.512103	−	1.10108i
$949$		0			0
$950$			2.82723i			0.0917276i
$951$	3.14325	+	17.9308i	0.101927	+	0.581446i
$952$	1.34238	+	2.32507i	0.0435068	+	0.0753560i
$953$	7.07695	−	12.2576i	0.229245	−	0.397064i	−0.728340	−	0.685216i	$-0.759708\pi$
$953$	7.07695	−	12.2576i	0.229245	−	0.397064i	0.957585	+	0.288152i	$0.0930410\pi$
$954$	−5.19546	−	60.7806i	−0.168209	−	1.96784i
$955$	4.85613	+	18.1233i	0.157141	+	0.586457i
$956$	5.57154	+	20.7933i	0.180197	+	0.672503i
$957$	−13.1619	−	4.80542i	−0.425465	−	0.155337i
$958$	30.9431	−	53.5950i	0.999726	−	1.73158i
$959$	−30.6849	−	53.1479i	−0.990868	−	1.71623i
$960$	−35.6554	+	6.25034i	−1.15077	+	0.201729i
$961$			5.57410i			0.179810i
$962$		0			0
$963$	24.3934	+	20.5516i	0.786067	+	0.662265i
$964$	−11.7982	−	3.16133i	−0.379995	−	0.101819i
$965$	−32.8732	+	18.9794i	−1.05823	+	0.610967i
$966$	41.8869	+	3.70673i	1.34769	+	0.119262i
$967$	38.9465	−	38.9465i	1.25244	−	1.25244i	0.297811	−	0.954625i	$-0.403744\pi$
$967$	38.9465	−	38.9465i	1.25244	−	1.25244i	0.954625	−	0.297811i	$-0.0962564\pi$
$968$	−0.480919	+	0.128862i	−0.0154573	+	0.00414178i
$969$	−9.65258	−	11.5268i	−0.310085	−	0.370295i
$970$	34.4041	+	34.4041i	1.10465	+	1.10465i
$971$	13.4552	+	7.76839i	0.431799	+	0.249300i	0.700113	−	0.714032i	$-0.253133\pi$
$971$	13.4552	+	7.76839i	0.431799	+	0.249300i	−0.268314	+	0.963332i	$0.586466\pi$
$972$	29.2307	+	13.8084i	0.937574	+	0.442904i
$973$	8.34278	−	31.1357i	0.267457	−	0.998164i
$974$	−2.09250			−0.0670480
$975$		0			0
$976$	−20.7573			−0.664426
$977$	0.257788	−	0.962077i	0.00824736	−	0.0307796i	−0.961680	−	0.274176i	$-0.911595\pi$
$977$	0.257788	−	0.962077i	0.00824736	−	0.0307796i	0.969927	+	0.243396i	$0.0782616\pi$
$978$	24.7446	−	35.2640i	0.791244	−	1.12762i
$979$	−10.1944	−	5.88572i	−0.325813	−	0.188108i
$980$	−9.58648	−	9.58648i	−0.306229	−	0.306229i
$981$	2.40138	+	1.12562i	0.0766701	+	0.0359382i
$982$	−11.4242	+	3.06110i	−0.364560	+	0.0976836i
$983$	15.8405	−	15.8405i	0.505234	−	0.505234i	−0.407826	−	0.913060i	$-0.633713\pi$
$983$	15.8405	−	15.8405i	0.505234	−	0.505234i	0.913060	+	0.407826i	$0.133713\pi$
$984$	0.154464	−	1.74547i	0.00492412	−	0.0556437i
$985$	55.4704	−	32.0258i	1.76743	−	1.02043i
$986$	−32.9865	−	8.83871i	−1.05051	−	0.281482i
$987$	−0.799496	+	0.371841i	−0.0254482	+	0.0118358i
$988$		0			0
$989$			7.12198i			0.226466i
$990$	−23.3482	−	33.4867i	−0.742056	−	1.06428i
$991$	−13.6723	−	23.6811i	−0.434315	−	0.752255i	0.562925	−	0.826508i	$-0.309676\pi$
$991$	−13.6723	−	23.6811i	−0.434315	−	0.752255i	−0.997239	+	0.0742528i	$0.976343\pi$
$992$	−20.3272	+	35.2078i	−0.645390	+	1.11785i
$993$	12.9203	−	35.3883i	0.410012	−	1.12301i
$994$	−0.549764	−	2.05175i	−0.0174374	−	0.0650774i
$995$	−8.64925	−	32.2794i	−0.274200	−	1.02333i
$996$	4.94501	−	13.5443i	0.156689	−	0.429166i
$997$	−18.6448	+	32.2937i	−0.590486	+	1.02275i	0.403681	+	0.914900i	$0.367731\pi$
$997$	−18.6448	+	32.2937i	−0.590486	+	1.02275i	−0.994167	+	0.107852i	$0.965603\pi$
$998$	20.3120	+	35.1814i	0.642965	+	1.11365i
$999$	18.0370	+	10.4858i	0.570666	+	0.331755i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.k.k.80.4		96
3.2	odd	2	inner	507.2.k.k.80.21		96
13.2	odd	12		507.2.f.g.437.4	yes	48
13.3	even	3		507.2.f.g.239.4	yes	48
13.4	even	6	inner	507.2.k.k.188.3		96
13.5	odd	4	inner	507.2.k.k.89.22		96
13.6	odd	12	inner	507.2.k.k.488.3		96
13.7	odd	12	inner	507.2.k.k.488.21		96
13.8	odd	4	inner	507.2.k.k.89.4		96
13.9	even	3	inner	507.2.k.k.188.21		96
13.10	even	6		507.2.f.g.239.22	yes	48
13.11	odd	12		507.2.f.g.437.22	yes	48
13.12	even	2	inner	507.2.k.k.80.22		96
39.2	even	12		507.2.f.g.437.21	yes	48
39.5	even	4	inner	507.2.k.k.89.3		96
39.8	even	4	inner	507.2.k.k.89.21		96
39.11	even	12		507.2.f.g.437.3	yes	48
39.17	odd	6	inner	507.2.k.k.188.22		96
39.20	even	12	inner	507.2.k.k.488.4		96
39.23	odd	6		507.2.f.g.239.3	✓	48
39.29	odd	6		507.2.f.g.239.21	yes	48
39.32	even	12	inner	507.2.k.k.488.22		96
39.35	odd	6	inner	507.2.k.k.188.4		96
39.38	odd	2	inner	507.2.k.k.80.3		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.f.g.239.3	✓	48	39.23	odd	6
507.2.f.g.239.4	yes	48	13.3	even	3
507.2.f.g.239.21	yes	48	39.29	odd	6
507.2.f.g.239.22	yes	48	13.10	even	6
507.2.f.g.437.3	yes	48	39.11	even	12
507.2.f.g.437.4	yes	48	13.2	odd	12
507.2.f.g.437.21	yes	48	39.2	even	12
507.2.f.g.437.22	yes	48	13.11	odd	12
507.2.k.k.80.3		96	39.38	odd	2	inner
507.2.k.k.80.4		96	1.1	even	1	trivial
507.2.k.k.80.21		96	3.2	odd	2	inner
507.2.k.k.80.22		96	13.12	even	2	inner
507.2.k.k.89.3		96	39.5	even	4	inner
507.2.k.k.89.4		96	13.8	odd	4	inner
507.2.k.k.89.21		96	39.8	even	4	inner
507.2.k.k.89.22		96	13.5	odd	4	inner
507.2.k.k.188.3		96	13.4	even	6	inner
507.2.k.k.188.4		96	39.35	odd	6	inner
507.2.k.k.188.21		96	13.9	even	3	inner
507.2.k.k.188.22		96	39.17	odd	6	inner
507.2.k.k.488.3		96	13.6	odd	12	inner
507.2.k.k.488.4		96	39.20	even	12	inner
507.2.k.k.488.21		96	13.7	odd	12	inner
507.2.k.k.488.22		96	39.32	even	12	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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.k (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.522394 + 1.94960i) q^{2} +(1.41782 + 0.994878i) q^{3} +(-1.79600 - 1.03692i) q^{4} +(1.72251 + 1.72251i) q^{5} +(-2.68028 + 2.24447i) q^{6} +(-3.00582 + 0.805406i) q^{7} +(0.105393 - 0.105393i) q^{8} +(1.02043 + 2.82112i) q^{9} +O(q^{10})\)	\(q+(-0.522394 + 1.94960i) q^{2} +(1.41782 + 0.994878i) q^{3} +(-1.79600 - 1.03692i) q^{4} +(1.72251 + 1.72251i) q^{5} +(-2.68028 + 2.24447i) q^{6} +(-3.00582 + 0.805406i) q^{7} +(0.105393 - 0.105393i) q^{8} +(1.02043 + 2.82112i) q^{9} +(-4.25804 + 2.45838i) q^{10} +(2.67329 + 0.716305i) q^{11} +(-1.51480 - 3.25697i) q^{12} -6.28089i q^{14} +(0.728525 + 4.15590i) q^{15} +(-1.92343 - 3.33148i) q^{16} +(2.89422 - 5.01294i) q^{17} +(-6.03313 + 0.515706i) q^{18} +(-0.388120 - 1.44849i) q^{19} +(-1.30752 - 4.87975i) q^{20} +(-5.06299 - 1.84850i) q^{21} +(-2.79302 + 4.83765i) q^{22} +(1.93268 + 3.34750i) q^{23} +(0.254281 - 0.0445751i) q^{24} +0.934091i q^{25} +(-1.35988 + 5.01505i) q^{27} +(6.23360 + 1.67029i) q^{28} +(-2.53139 + 1.46150i) q^{29} +(-8.48293 - 0.750687i) q^{30} +(-3.56552 + 3.56552i) q^{31} +(7.78778 - 2.08673i) q^{32} +(3.07761 + 3.67519i) q^{33} +(8.26131 + 8.26131i) q^{34} +(-6.56488 - 3.79023i) q^{35} +(1.09258 - 6.12485i) q^{36} +(1.03921 - 3.87837i) q^{37} +3.02672 q^{38} +0.363080 q^{40} +(1.75678 - 6.55640i) q^{41} +(6.24872 - 8.90518i) q^{42} +(1.59566 + 0.921257i) q^{43} +(-4.05848 - 4.05848i) q^{44} +(-3.10170 + 6.61712i) q^{45} +(-7.53592 + 2.01924i) q^{46} +(0.115676 - 0.115676i) q^{47} +(0.587334 - 6.63701i) q^{48} +(2.32408 - 1.34181i) q^{49} +(-1.82111 - 0.487964i) q^{50} +(9.09075 - 4.22805i) q^{51} +10.0745i q^{53} +(-9.06696 - 5.27105i) q^{54} +(3.37093 + 5.83861i) q^{55} +(-0.231907 + 0.401675i) q^{56} +(0.890781 - 2.43983i) q^{57} +(-1.52696 - 5.69869i) q^{58} +(-0.446576 - 1.66664i) q^{59} +(3.00092 - 8.21944i) q^{60} +(2.69796 - 4.67300i) q^{61} +(-5.08874 - 8.81396i) q^{62} +(-5.33939 - 7.65790i) q^{63} +8.57945i q^{64} +(-8.77288 + 4.08021i) q^{66} +(13.1928 + 3.53501i) q^{67} +(-10.3961 + 6.00217i) q^{68} +(-0.590160 + 6.66894i) q^{69} +(10.8189 - 10.8189i) q^{70} +(0.326665 - 0.0875296i) q^{71} +(0.404871 + 0.189779i) q^{72} +(-8.54904 - 8.54904i) q^{73} +(7.01840 + 4.05207i) q^{74} +(-0.929307 + 1.32437i) q^{75} +(-0.804902 + 3.00393i) q^{76} -8.61233 q^{77} +10.4089 q^{79} +(2.42538 - 9.05163i) q^{80} +(-6.91743 + 5.75754i) q^{81} +(11.8646 + 6.85005i) q^{82} +(2.83841 + 2.83841i) q^{83} +(7.17640 + 8.56984i) q^{84} +(13.6202 - 3.64951i) q^{85} +(-2.62965 + 2.62965i) q^{86} +(-5.04308 - 0.446281i) q^{87} +(0.357238 - 0.206251i) q^{88} +(-4.10839 - 1.10084i) q^{89} +(-11.2804 - 9.50383i) q^{90} -8.01616i q^{92} +(-8.60253 + 1.50801i) q^{93} +(0.165094 + 0.285951i) q^{94} +(1.82649 - 3.16357i) q^{95} +(13.1177 + 4.78928i) q^{96} +(-2.56119 - 9.55851i) q^{97} +(1.40191 + 5.23199i) q^{98} +(0.707134 + 8.27261i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 24 q^{9}+O(q^{10}) \) 96 * q + 24 * q^9	\( 96 q + 24 q^{9} + 8 q^{16} - 112 q^{22} - 168 q^{27} + 256 q^{40} + 56 q^{42} + 188 q^{48} - 8 q^{55} - 56 q^{61} - 184 q^{66} + 72 q^{81} + 112 q^{87} - 296 q^{94}+O(q^{100}) \) 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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more