LMFDB - Embedded newform 725.2.y.b.282.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [725,2,Mod(18,725)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("725.18"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(725, base_ring=CyclotomicField(28)) chi = DirichletCharacter(H, H._module([21, 11])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 725 = 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	725.y (of order $28$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [156] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.78915414654$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$13$ over $\Q(\zeta_{28})$
Twist minimal:	no (minimal twist has level 145)
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			282.5
Character	$\chi$	$=$	725.282
Dual form			725.2.y.b.18.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.871464 + 0.419675i) q^{2} +(-2.22031 + 1.77064i) q^{3} +(-0.663657 + 0.832199i) q^{4} +(1.19183 - 2.47485i) q^{6} +(-0.156487 + 1.38886i) q^{7} +(0.659568 - 2.88975i) q^{8} +(1.12705 - 4.93793i) q^{9} +(4.68013 + 2.94072i) q^{11} -3.02283i q^{12} +(2.43545 - 3.87599i) q^{13} +(-0.446497 - 1.27601i) q^{14} +(0.164256 + 0.719651i) q^{16} +5.34543 q^{17} +(1.09014 + 4.77622i) q^{18} +(3.75785 - 0.423408i) q^{19} +(-2.11171 - 3.36077i) q^{21} +(-5.31271 - 0.598599i) q^{22} +(2.32115 - 0.812207i) q^{23} +(3.65226 + 7.58400i) q^{24} +(-0.495748 + 4.39988i) q^{26} +(2.54434 + 5.28338i) q^{27} +(-1.05195 - 1.05195i) q^{28} +(-3.20546 - 4.32724i) q^{29} +(1.32279 - 3.78032i) q^{31} +(3.25097 + 4.07659i) q^{32} +(-15.5983 + 1.75750i) q^{33} +(-4.65835 + 2.24334i) q^{34} +(3.36136 + 4.21502i) q^{36} +(3.61961 + 0.826152i) q^{37} +(-3.09714 + 1.94606i) q^{38} +(1.45553 + 12.9182i) q^{39} +(-5.71038 - 5.71038i) q^{41} +(3.25072 + 2.04256i) q^{42} +(-0.322307 + 0.669277i) q^{43} +(-5.55327 + 1.94317i) q^{44} +(-1.68194 + 1.68194i) q^{46} +(-0.0268913 + 0.00613776i) q^{47} +(-1.63894 - 1.30701i) q^{48} +(4.92005 + 1.12297i) q^{49} +(-11.8685 + 9.46480i) q^{51} +(1.60930 + 4.59910i) q^{52} +(0.574381 - 1.64149i) q^{53} +(-4.43460 - 3.53648i) q^{54} +(3.91025 + 1.36826i) q^{56} +(-7.59388 + 7.59388i) q^{57} +(4.60948 + 2.42578i) q^{58} +4.00143i q^{59} +(3.92555 + 0.442303i) q^{61} +(0.433740 + 3.84955i) q^{62} +(6.68171 + 2.33803i) q^{63} +(-5.87407 - 2.82880i) q^{64} +(12.8558 - 8.07781i) q^{66} +(-3.79538 - 6.04031i) q^{67} +(-3.54753 + 4.44846i) q^{68} +(-3.71555 + 5.91327i) q^{69} +(3.42315 - 0.781312i) q^{71} +(-13.5260 - 6.51379i) q^{72} +(2.88745 + 1.39052i) q^{73} +(-3.50108 + 0.799098i) q^{74} +(-2.14156 + 3.40828i) q^{76} +(-4.81662 + 6.03986i) q^{77} +(-6.68988 - 10.6469i) q^{78} +(7.95966 - 5.00139i) q^{79} +(-1.31416 - 0.632868i) q^{81} +(7.37289 + 2.57989i) q^{82} +(1.66068 + 14.7389i) q^{83} +(4.19829 + 0.473033i) q^{84} -0.718515i q^{86} +(14.7791 + 3.93209i) q^{87} +(11.5848 - 11.5848i) q^{88} +(-12.9395 - 4.52773i) q^{89} +(5.00209 + 3.98903i) q^{91} +(-0.864532 + 2.47069i) q^{92} +(3.75656 + 10.7356i) q^{93} +(0.0208589 - 0.0166344i) q^{94} +(-14.4363 - 3.29499i) q^{96} +(-6.87837 - 5.48532i) q^{97} +(-4.75893 + 1.08620i) q^{98} +(19.7958 - 19.7958i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q + 8 q^{2} + 14 q^{3} - 22 q^{4} - 28 q^{6} + 10 q^{7} - 4 q^{8} + 10 q^{9} - 20 q^{11} + 4 q^{14} - 34 q^{16} + 48 q^{17} + 94 q^{18} - 16 q^{21} + 6 q^{22} + 10 q^{23} + 56 q^{24} + 36 q^{26} + 56 q^{27}+ \cdots + 76 q^{99}+O(q^{100}) $ 156 * q + 8 * q^2 + 14 * q^3 - 22 * q^4 - 28 * q^6 + 10 * q^7 - 4 * q^8 + 10 * q^9 - 20 * q^11 + 4 * q^14 - 34 * q^16 + 48 * q^17 + 94 * q^18 - 16 * q^21 + 6 * q^22 + 10 * q^23 + 56 * q^24 + 36 * q^26 + 56 * q^27 - 8 * q^28 - 8 * q^31 - 28 * q^32 + 14 * q^33 - 24 * q^34 + 78 * q^36 - 28 * q^37 - 92 * q^38 + 16 * q^39 - 22 * q^41 + 10 * q^42 + 42 * q^43 - 112 * q^44 + 4 * q^46 + 14 * q^47 - 154 * q^48 + 84 * q^49 - 28 * q^51 + 166 * q^52 - 14 * q^53 + 4 * q^56 - 12 * q^57 - 126 * q^58 - 46 * q^61 - 84 * q^62 - 38 * q^63 - 30 * q^64 - 48 * q^66 + 46 * q^67 + 44 * q^68 - 124 * q^69 - 28 * q^71 - 60 * q^72 - 130 * q^73 + 112 * q^74 - 48 * q^76 + 44 * q^77 + 210 * q^78 - 4 * q^79 + 58 * q^81 - 72 * q^82 - 46 * q^83 + 120 * q^84 + 144 * q^87 - 40 * q^88 + 46 * q^89 - 28 * q^91 + 14 * q^92 + 6 * q^93 - 84 * q^94 - 28 * q^96 - 154 * q^97 - 98 * q^98 + 76 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/725\mathbb{Z}\right)^\times$.

$n$	$176$	$552$
$\chi(n)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.871464	+	0.419675i	−0.616218	+	0.296755i	−0.715834	−	0.698271i	$-0.753953\pi$
$2$	−0.871464	+	0.419675i	−0.616218	+	0.296755i	0.0996153	+	0.995026i	$0.468239\pi$
$3$	−2.22031	+	1.77064i	−1.28189	+	1.02228i	−0.283908	+	0.958851i	$0.591631\pi$
$3$	−2.22031	+	1.77064i	−1.28189	+	1.02228i	−0.997987	+	0.0634256i	$0.979797\pi$
$4$	−0.663657	+	0.832199i	−0.331828	+	0.416100i
$5$		0			0
$5$		0			0
$6$	1.19183	−	2.47485i	0.486561	−	1.01035i
$7$	−0.156487	+	1.38886i	−0.0591465	+	0.524939i	0.928849	+	0.370458i	$0.120799\pi$
$7$	−0.156487	+	1.38886i	−0.0591465	+	0.524939i	−0.987996	+	0.154481i	$0.950629\pi$
$8$	0.659568	−	2.88975i	0.233192	−	1.02168i
$9$	1.12705	−	4.93793i	0.375683	−	1.64598i
$10$		0			0
$11$	4.68013	+	2.94072i	1.41111	+	0.886661i	0.999693	−	0.0247855i	$-0.00789028\pi$
$11$	4.68013	+	2.94072i	1.41111	+	0.886661i	0.411419	+	0.911446i	$0.365033\pi$
$12$		−	3.02283i		−	0.872617i
$13$	2.43545	−	3.87599i	0.675471	−	1.07501i	−0.316506	−	0.948590i	$-0.602510\pi$
$13$	2.43545	−	3.87599i	0.675471	−	1.07501i	0.991977	−	0.126416i	$-0.0403473\pi$
$14$	−0.446497	−	1.27601i	−0.119331	−	0.341029i
$15$		0			0
$16$	0.164256	+	0.719651i	0.0410639	+	0.179913i
$17$	5.34543			1.29646			0.648228	−	0.761446i	$-0.275510\pi$
$17$	5.34543			1.29646			0.648228	+	0.761446i	$0.275510\pi$
$18$	1.09014	+	4.77622i	0.256949	+	1.12577i
$19$	3.75785	−	0.423408i	0.862110	−	0.0971365i	0.330173	−	0.943920i	$-0.392893\pi$
$19$	3.75785	−	0.423408i	0.862110	−	0.0971365i	0.531937	+	0.846784i	$0.321464\pi$
$20$		0			0
$21$	−2.11171	−	3.36077i	−0.460814	−	0.733381i
$22$	−5.31271	−	0.598599i	−1.13267	−	0.127622i
$23$	2.32115	−	0.812207i	0.483994	−	0.169357i	−0.0772424	−	0.997012i	$-0.524612\pi$
$23$	2.32115	−	0.812207i	0.483994	−	0.169357i	0.561237	+	0.827655i	$0.310326\pi$
$24$	3.65226	+	7.58400i	0.745515	+	1.54808i
$25$		0			0
$26$	−0.495748	+	4.39988i	−0.0972241	+	0.862888i
$27$	2.54434	+	5.28338i	0.489659	+	1.01679i
$28$	−1.05195	−	1.05195i	−0.198801	−	0.198801i
$29$	−3.20546	−	4.32724i	−0.595240	−	0.803548i
$29$	−3.20546	−	4.32724i	−0.595240	−	0.803548i
$30$		0			0
$31$	1.32279	−	3.78032i	0.237580	−	0.678965i	−0.761930	−	0.647660i	$-0.775748\pi$
$31$	1.32279	−	3.78032i	0.237580	−	0.678965i	0.999510	−	0.0313051i	$-0.00996635\pi$
$32$	3.25097	+	4.07659i	0.574696	+	0.720646i
$33$	−15.5983	+	1.75750i	−2.71531	+	0.305942i
$34$	−4.65835	+	2.24334i	−0.798900	+	0.384730i
$35$		0			0
$36$	3.36136	+	4.21502i	0.560227	+	0.702503i
$37$	3.61961	+	0.826152i	0.595060	+	0.135819i	0.509436	−	0.860509i	$-0.329854\pi$
$37$	3.61961	+	0.826152i	0.595060	+	0.135819i	0.0856247	+	0.996327i	$0.472711\pi$
$38$	−3.09714	+	1.94606i	−0.502422	+	0.315693i
$39$	1.45553	+	12.9182i	0.233071	+	2.06856i
$40$		0			0
$41$	−5.71038	−	5.71038i	−0.891811	−	0.891811i	0.102882	−	0.994694i	$-0.467193\pi$
$41$	−5.71038	−	5.71038i	−0.891811	−	0.891811i	−0.994694	+	0.102882i	$0.967193\pi$
$42$	3.25072	+	2.04256i	0.501597	+	0.315174i
$43$	−0.322307	+	0.669277i	−0.0491513	+	0.102064i	−0.924098	−	0.382155i	$-0.875182\pi$
$43$	−0.322307	+	0.669277i	−0.0491513	+	0.102064i	0.874947	+	0.484219i	$0.160896\pi$
$44$	−5.55327	+	1.94317i	−0.837186	+	0.292944i
$45$		0			0
$46$	−1.68194	+	1.68194i	−0.247989	+	0.247989i
$47$	−0.0268913	+	0.00613776i	−0.00392249	+	0.000895284i	−0.224482	−	0.974478i	$-0.572069\pi$
$47$	−0.0268913	+	0.00613776i	−0.00392249	+	0.000895284i	0.220559	+	0.975374i	$0.429212\pi$
$48$	−1.63894	−	1.30701i	−0.236560	−	0.188651i
$49$	4.92005	+	1.12297i	0.702865	+	0.160424i
$50$		0			0
$51$	−11.8685	+	9.46480i	−1.66192	+	1.32534i
$52$	1.60930	+	4.59910i	0.223169	+	0.637781i
$53$	0.574381	−	1.64149i	0.0788973	−	0.225476i	−0.897678	−	0.440653i	$-0.854747\pi$
$53$	0.574381	−	1.64149i	0.0788973	−	0.225476i	0.976575	+	0.215177i	$0.0690328\pi$
$54$	−4.43460	−	3.53648i	−0.603473	−	0.481254i
$55$		0			0
$56$	3.91025	+	1.36826i	0.522529	+	0.182841i
$57$	−7.59388	+	7.59388i	−1.00583	+	1.00583i
$58$	4.60948	+	2.42578i	0.605255	+	0.318521i
$59$			4.00143i			0.520942i	0.965482	+	0.260471i	$0.0838778\pi$
$59$			4.00143i			0.520942i	−0.965482	+	0.260471i	$0.916122\pi$
$60$		0			0
$61$	3.92555	+	0.442303i	0.502615	+	0.0566311i	0.359632	−	0.933094i	$-0.382902\pi$
$61$	3.92555	+	0.442303i	0.502615	+	0.0566311i	0.142983	+	0.989725i	$0.454331\pi$
$62$	0.433740	+	3.84955i	0.0550851	+	0.488894i
$63$	6.68171	+	2.33803i	0.841817	+	0.294564i
$64$	−5.87407	−	2.82880i	−0.734258	−	0.353600i
$65$		0			0
$66$	12.8558	−	8.07781i	1.58243	−	0.994309i
$67$	−3.79538	−	6.04031i	−0.463679	−	0.737941i	0.530264	−	0.847832i	$-0.322093\pi$
$67$	−3.79538	−	6.04031i	−0.463679	−	0.737941i	−0.993944	+	0.109891i	$0.964950\pi$
$68$	−3.54753	+	4.44846i	−0.430201	+	0.539455i
$69$	−3.71555	+	5.91327i	−0.447300	+	0.711874i
$70$		0			0
$71$	3.42315	−	0.781312i	0.406253	−	0.0927247i	−0.0145109	−	0.999895i	$-0.504619\pi$
$71$	3.42315	−	0.781312i	0.406253	−	0.0927247i	0.420764	+	0.907170i	$0.361762\pi$
$72$	−13.5260	−	6.51379i	−1.59406	−	0.767658i
$73$	2.88745	+	1.39052i	0.337951	+	0.162748i	0.595160	−	0.803607i	$-0.297089\pi$
$73$	2.88745	+	1.39052i	0.337951	+	0.162748i	−0.257209	+	0.966356i	$0.582803\pi$
$74$	−3.50108	+	0.799098i	−0.406992	+	0.0928932i
$75$		0			0
$76$	−2.14156	+	3.40828i	−0.245654	+	0.390956i
$77$	−4.81662	+	6.03986i	−0.548905	+	0.688306i
$78$	−6.68988	−	10.6469i	−0.757479	−	1.20552i
$79$	7.95966	−	5.00139i	0.895532	−	0.562700i	−0.00378707	−	0.999993i	$-0.501205\pi$
$79$	7.95966	−	5.00139i	0.895532	−	0.562700i	0.899319	+	0.437293i	$0.144063\pi$
$80$		0			0
$81$	−1.31416	−	0.632868i	−0.146018	−	0.0703186i
$82$	7.37289	+	2.57989i	0.814200	+	0.284901i
$83$	1.66068	+	14.7389i	0.182283	+	1.61780i	0.668325	+	0.743869i	$0.267011\pi$
$83$	1.66068	+	14.7389i	0.182283	+	1.61780i	−0.486042	+	0.873935i	$0.661560\pi$
$84$	4.19829	+	0.473033i	0.458071	+	0.0516122i
$85$		0			0
$86$		−	0.718515i		−	0.0774795i
$87$	14.7791	+	3.93209i	1.58448	+	0.421565i
$88$	11.5848	−	11.5848i	1.23495	−	1.23495i
$89$	−12.9395	−	4.52773i	−1.37159	−	0.479939i	−0.458860	−	0.888509i	$-0.651742\pi$
$89$	−12.9395	−	4.52773i	−1.37159	−	0.479939i	−0.912727	+	0.408570i	$0.866028\pi$
$90$		0			0
$91$	5.00209	+	3.98903i	0.524361	+	0.418164i
$92$	−0.864532	+	2.47069i	−0.0901337	+	0.257587i
$93$	3.75656	+	10.7356i	0.389537	+	1.11323i
$94$	0.0208589	−	0.0166344i	0.00215143	−	0.00171571i
$95$		0			0
$96$	−14.4363	−	3.29499i	−1.47340	−	0.336294i
$97$	−6.87837	−	5.48532i	−0.698393	−	0.556950i	0.208649	−	0.977991i	$-0.433093\pi$
$97$	−6.87837	−	5.48532i	−0.698393	−	0.556950i	−0.907042	+	0.421041i	$0.861665\pi$
$98$	−4.75893	+	1.08620i	−0.480725	+	0.109722i
$99$	19.7958	−	19.7958i	1.98955	−	1.98955i
$100$		0			0
$101$	5.10791	−	1.78734i	0.508256	−	0.177847i	−0.0639551	−	0.997953i	$-0.520371\pi$
$101$	5.10791	−	1.78734i	0.508256	−	0.177847i	0.572211	+	0.820106i	$0.306086\pi$
$102$	6.37082	−	13.2291i	0.630805	−	1.30988i
$103$	6.73869	+	4.23420i	0.663983	+	0.417208i	0.821422	−	0.570321i	$-0.193181\pi$
$103$	6.73869	+	4.23420i	0.663983	+	0.417208i	−0.157439	+	0.987529i	$0.550324\pi$
$104$	−9.59432	−	9.59432i	−0.940800	−	0.940800i
$105$		0			0
$106$	0.188339	+	1.67155i	0.0182931	+	0.162355i
$107$	9.64143	−	6.05811i	0.932072	−	0.585660i	0.0218417	−	0.999761i	$-0.493047\pi$
$107$	9.64143	−	6.05811i	0.932072	−	0.585660i	0.910231	+	0.414102i	$0.135904\pi$
$108$	−6.08539	−	1.38895i	−0.585567	−	0.133652i
$109$	4.37246	+	5.48290i	0.418806	+	0.525166i	0.945820	−	0.324690i	$-0.105260\pi$
$109$	4.37246	+	5.48290i	0.418806	+	0.525166i	−0.527014	+	0.849856i	$0.676689\pi$
$110$		0			0
$111$	−9.49946	+	4.57470i	−0.901649	+	0.434211i
$112$	−1.02520	+	0.115512i	−0.0968721	+	0.0109149i
$113$	−9.20127	−	11.5380i	−0.865583	−	1.08541i	−0.995582	−	0.0938923i	$-0.970069\pi$
$113$	−9.20127	−	11.5380i	−0.865583	−	1.08541i	0.130000	−	0.991514i	$-0.458502\pi$
$114$	3.43083	−	9.80476i	0.321327	−	0.918300i
$115$		0			0
$116$	5.72845	+	0.204218i	0.531874	+	0.0189612i
$117$	−16.3945	−	16.3945i	−1.51567	−	1.51567i
$118$	−1.67930	−	3.48710i	−0.154592	−	0.321014i
$119$	−0.836489	+	7.42404i	−0.0766808	+	0.680561i
$120$		0			0
$121$	8.48306	+	17.6153i	0.771187	+	1.60139i
$122$	−3.60660	+	1.26200i	−0.326526	+	0.114256i
$123$	22.7898	+	2.56779i	2.05489	+	0.231530i
$124$	2.26810	+	3.60966i	0.203681	+	0.324157i
$125$		0			0
$126$	−6.80409	+	0.766637i	−0.606156	+	0.0682974i
$127$	0.164908	+	0.722509i	0.0146332	+	0.0641123i	0.981717	−	0.190344i	$-0.0609605\pi$
$127$	0.164908	+	0.722509i	0.0146332	+	0.0641123i	−0.967084	+	0.254457i	$0.918103\pi$
$128$	−4.12209			−0.364345
$129$	−0.469426	−	2.05669i	−0.0413306	−	0.181081i
$130$		0			0
$131$	−4.84709	−	13.8522i	−0.423493	−	1.21027i	−0.936126	−	0.351665i	$-0.885616\pi$
$131$	−4.84709	−	13.8522i	−0.423493	−	1.21027i	0.512633	−	0.858608i	$-0.328670\pi$
$132$	8.88930	−	14.1472i	0.773715	−	1.23136i
$133$			5.28538i			0.458301i
$134$	5.84251	+	3.67109i	0.504716	+	0.317134i
$135$		0			0
$136$	3.52567	−	15.4470i	0.302324	−	1.32457i
$137$	1.45940	−	6.39404i	0.124685	−	0.546280i	−0.873542	−	0.486749i	$-0.838183\pi$
$137$	1.45940	−	6.39404i	0.124685	−	0.546280i	0.998226	−	0.0595303i	$-0.0189603\pi$
$138$	0.756320	−	6.71253i	0.0643822	−	0.571408i
$139$	1.98467	−	4.12120i	0.168337	−	0.349556i	−0.799685	−	0.600420i	$-0.795000\pi$
$139$	1.98467	−	4.12120i	0.168337	−	0.349556i	0.968022	+	0.250864i	$0.0807146\pi$
$140$		0			0
$141$	0.0488391	−	0.0612423i	0.00411300	−	0.00515753i
$142$	−2.65526	+	2.11750i	−0.222824	+	0.177696i
$143$	22.7964	−	10.9782i	1.90633	−	0.918041i
$144$	3.73871			0.311559
$145$		0			0
$146$	−3.09988			−0.256548
$147$	−12.9124	+	6.21829i	−1.06500	+	0.512876i
$148$	−3.08970	+	2.46396i	−0.253972	+	0.202536i
$149$	−5.04369	+	6.32459i	−0.413195	+	0.518130i	−0.944260	−	0.329201i	$-0.893221\pi$
$149$	−5.04369	+	6.32459i	−0.413195	+	0.518130i	0.531065	+	0.847331i	$0.321792\pi$
$150$		0			0
$151$	−4.21845	+	8.75970i	−0.343292	+	0.712854i	−0.999115	−	0.0420610i	$-0.986608\pi$
$151$	−4.21845	+	8.75970i	−0.343292	+	0.712854i	0.655823	+	0.754915i	$0.272322\pi$
$152$	1.25501	−	11.1385i	0.101795	−	0.903454i
$153$	6.02456	−	26.3953i	0.487057	−	2.13393i
$154$	1.66274	−	7.28494i	0.133987	−	0.587037i
$155$		0			0
$156$	−11.7165	−	7.36194i	−0.938068	−	0.589427i
$157$			4.05125i			0.323325i	0.986846	+	0.161663i	$0.0516856\pi$
$157$			4.05125i			0.323325i	−0.986846	+	0.161663i	$0.948314\pi$
$158$	−4.83760	+	7.69900i	−0.384859	+	0.612500i
$159$	1.63117	+	4.66163i	0.129360	+	0.369691i
$160$		0			0
$161$	0.764811	+	3.35086i	0.0602755	+	0.264084i
$162$	1.41084			0.110846
$163$	−1.31164	−	5.74667i	−0.102736	−	0.450114i	−0.999963	−	0.00854627i	$-0.997280\pi$
$163$	−1.31164	−	5.74667i	−0.102736	−	0.450114i	0.897228	−	0.441568i	$-0.145578\pi$
$164$	8.54190	−	0.962441i	0.667011	−	0.0751540i
$165$		0			0
$166$	−7.63277	−	12.1475i	−0.592418	−	0.942827i
$167$	−13.9385	−	1.57049i	−1.07859	−	0.121528i	−0.445254	−	0.895404i	$-0.646887\pi$
$167$	−13.9385	−	1.57049i	−1.07859	−	0.121528i	−0.633336	+	0.773877i	$0.718315\pi$
$168$	−11.1046	+	3.88568i	−0.856741	+	0.299787i
$169$	−3.45141	−	7.16693i	−0.265493	−	0.551302i
$170$		0			0
$171$	2.14453	−	19.0332i	0.163996	−	1.45550i
$172$	−0.343071	−	0.712394i	−0.0261589	−	0.0543195i
$173$	−9.47799	−	9.47799i	−0.720598	−	0.720598i	0.248129	−	0.968727i	$-0.420184\pi$
$173$	−9.47799	−	9.47799i	−0.720598	−	0.720598i	−0.968727	+	0.248129i	$0.920184\pi$
$174$	−14.5296	+	2.77573i	−1.10149	+	0.210428i
$175$		0			0
$176$	−1.34756	+	3.85109i	−0.101576	+	0.290287i
$177$	−7.08507	−	8.88440i	−0.532547	−	0.667792i
$178$	13.1765	−	1.48464i	0.987621	−	0.111278i
$179$	3.08837	−	1.48728i	0.230836	−	0.111165i	−0.314891	−	0.949128i	$-0.601968\pi$
$179$	3.08837	−	1.48728i	0.230836	−	0.111165i	0.545727	+	0.837963i	$0.316254\pi$
$180$		0			0
$181$	11.0324	+	13.8343i	0.820036	+	1.02829i	0.999012	+	0.0444387i	$0.0141499\pi$
$181$	11.0324	+	13.8343i	0.820036	+	1.02829i	−0.178977	+	0.983853i	$0.557279\pi$
$182$	−6.03324	−	1.37705i	−0.447213	−	0.102074i
$183$	−9.49908	+	5.96867i	−0.702192	+	0.441217i
$184$	−0.816121	−	7.24327i	−0.0601652	−	0.533981i
$185$		0			0
$186$	−7.77919	−	7.77919i	−0.570398	−	0.570398i
$187$	25.0173	+	15.7194i	1.82945	+	1.14952i
$188$	0.0127387	−	0.0264523i	0.000929068	−	0.00192923i
$189$	−7.73602	+	2.70695i	−0.562713	+	0.196902i
$190$		0			0
$191$	−16.2424	+	16.2424i	−1.17526	+	1.17526i	−0.194321	+	0.980938i	$0.562250\pi$
$191$	−16.2424	+	16.2424i	−1.17526	+	1.17526i	−0.980938	+	0.194321i	$0.937750\pi$
$192$	18.0510	−	4.12002i	1.30272	−	0.297337i
$193$	10.6262	+	8.47412i	0.764891	+	0.609980i	0.926248	−	0.376916i	$-0.123015\pi$
$193$	10.6262	+	8.47412i	0.764891	+	0.609980i	−0.161356	+	0.986896i	$0.551587\pi$
$194$	8.29631	+	1.89358i	0.595640	+	0.135951i
$195$		0			0
$196$	−4.19976	+	3.34920i	−0.299983	+	0.239228i
$197$	3.53390	+	10.0993i	0.251780	+	0.719545i	0.998518	+	0.0544269i	$0.0173332\pi$
$197$	3.53390	+	10.0993i	0.251780	+	0.719545i	−0.746738	+	0.665118i	$0.768381\pi$
$198$	−8.94353	+	25.5591i	−0.635589	+	1.81641i
$199$	8.87767	+	7.07970i	0.629321	+	0.501867i	0.885425	−	0.464782i	$-0.153867\pi$
$199$	8.87767	+	7.07970i	0.629321	+	0.501867i	−0.256104	+	0.966649i	$0.582439\pi$
$200$		0			0
$201$	19.1221	+	6.69111i	1.34877	+	0.471955i
$202$	−3.70126	+	3.70126i	−0.260420	+	0.260420i
$203$	6.51154	−	3.77478i	0.457020	−	0.264938i
$204$		−	16.1583i		−	1.13131i
$205$		0			0
$206$	−7.64952	−	0.861893i	−0.532967	−	0.0600510i
$207$	−1.39456	−	12.3771i	−0.0969288	−	0.860267i
$208$	3.18940	+	1.11602i	0.221145	+	0.0773819i
$209$	18.8324	+	9.06918i	1.30266	+	0.627329i
$210$		0			0
$211$	1.27617	−	0.801873i	0.0878554	−	0.0552032i	−0.487388	−	0.873186i	$-0.662050\pi$
$211$	1.27617	−	0.801873i	0.0878554	−	0.0552032i	0.575243	+	0.817982i	$0.304907\pi$
$212$	0.984852	+	1.56738i	0.0676399	+	0.107648i
$213$	−6.21703	+	7.79591i	−0.425984	+	0.534167i
$214$	−5.85972	+	9.32570i	−0.400562	+	0.637492i
$215$		0			0
$216$	16.9458	−	3.86777i	1.15302	−	0.263169i
$217$	5.04333	+	2.42874i	0.342363	+	0.164873i
$218$	−6.11148	−	2.94313i	−0.413922	−	0.199334i
$219$	−8.87314	+	2.02524i	−0.599591	+	0.136853i
$220$		0			0
$221$	13.0185	−	20.7188i	0.875719	−	1.39370i
$222$	6.35855	−	7.97337i	0.426758	−	0.535138i
$223$	4.66654	+	7.42676i	0.312495	+	0.497333i	0.965634	−	0.259905i	$-0.0836913\pi$
$223$	4.66654	+	7.42676i	0.312495	+	0.497333i	−0.653139	+	0.757238i	$0.726548\pi$
$224$	−6.17054	+	3.87721i	−0.412287	+	0.259057i
$225$		0			0
$226$	12.8608	+	6.19344i	0.855488	+	0.411981i
$227$	−19.5884	−	6.85426i	−1.30013	−	0.454934i	−0.410598	−	0.911816i	$-0.634680\pi$
$227$	−19.5884	−	6.85426i	−1.30013	−	0.454934i	−0.889527	+	0.456883i	$0.848966\pi$
$228$	−1.27989	−	11.3594i	−0.0847629	−	0.752292i
$229$	5.35144	+	0.602962i	0.353633	+	0.0398449i	0.286994	−	0.957932i	$-0.407344\pi$
$229$	5.35144	+	0.602962i	0.353633	+	0.0398449i	0.0666386	+	0.997777i	$0.478773\pi$
$230$		0			0
$231$		−	21.9388i		−	1.44347i
$232$	−14.6189	+	6.40890i	−0.959777	+	0.420765i
$233$	−13.8913	+	13.8913i	−0.910051	+	0.910051i	−0.996276	−	0.0862245i	$-0.972520\pi$
$233$	−13.8913	+	13.8913i	−0.910051	+	0.910051i	0.0862245	+	0.996276i	$0.472520\pi$
$234$	21.1676	+	7.40685i	1.38377	+	0.484201i
$235$		0			0
$236$	−3.32999	−	2.65558i	−0.216764	−	0.172863i
$237$	−8.81726	+	25.1983i	−0.572743	+	1.63680i
$238$	−2.38672	−	6.82084i	−0.154708	−	0.442129i
$239$	−7.62904	+	6.08395i	−0.493481	+	0.393538i	−0.838367	−	0.545107i	$-0.816489\pi$
$239$	−7.62904	+	6.08395i	−0.493481	+	0.393538i	0.344885	+	0.938645i	$0.387918\pi$
$240$		0			0
$241$	−19.6440	−	4.48362i	−1.26538	−	0.288815i	−0.463392	−	0.886153i	$-0.653368\pi$
$241$	−19.6440	−	4.48362i	−1.26538	−	0.288815i	−0.801990	+	0.597338i	$0.796225\pi$
$242$	−14.7854	−	11.7909i	−0.950439	−	0.757950i
$243$	−13.1128	+	2.99292i	−0.841188	+	0.191996i
$244$	−2.97330	+	2.97330i	−0.190346	+	0.190346i
$245$		0			0
$246$	−20.9381	+	7.32657i	−1.33497	+	0.467125i
$247$	7.51092	−	15.5966i	0.477908	−	0.992386i
$248$	−10.0517	−	6.31591i	−0.638285	−	0.401061i
$249$	−29.7844	−	29.7844i	−1.88751	−	1.88751i
$250$		0			0
$251$	−2.78070	−	24.6794i	−0.175516	−	1.55775i	−0.704863	−	0.709344i	$-0.748991\pi$
$251$	−2.78070	−	24.6794i	−0.175516	−	1.55775i	0.529347	−	0.848406i	$-0.322437\pi$
$252$	−6.38007	+	4.00887i	−0.401907	+	0.252535i
$253$	13.2518	+	3.02463i	0.833132	+	0.190157i
$254$	−0.446930	−	0.560433i	−0.0280429	−	0.0351647i
$255$		0			0
$256$	15.3404	−	7.38754i	0.958774	−	0.461721i
$257$	−1.02264	+	0.115223i	−0.0637903	+	0.00718744i	−0.143802	−	0.989606i	$-0.545933\pi$
$257$	−1.02264	+	0.115223i	−0.0637903	+	0.00718744i	0.0800116	+	0.996794i	$0.474504\pi$
$258$	1.27223	+	1.59532i	0.0792055	+	0.0993206i
$259$	−1.71383	+	4.89785i	−0.106492	+	0.304337i
$260$		0			0
$261$	−24.9803	+	10.9513i	−1.54624	+	0.677870i
$262$	10.0375	+	10.0375i	0.620118	+	0.620118i
$263$	−1.72037	−	3.57239i	−0.106083	−	0.220283i	0.841170	−	0.540771i	$-0.181867\pi$
$263$	−1.72037	−	3.57239i	−0.106083	−	0.220283i	−0.947253	+	0.320488i	$0.896153\pi$
$264$	−5.20936	+	46.2344i	−0.320614	+	2.84553i
$265$		0			0
$266$	−2.21814	−	4.60602i	−0.136003	−	0.282413i
$267$	36.7467	−	12.8582i	2.24886	−	0.786910i
$268$	7.54557	+	0.850182i	0.460919	+	0.0519331i
$269$	3.84254	+	6.11537i	0.234284	+	0.372861i	0.943087	−	0.332546i	$-0.107908\pi$
$269$	3.84254	+	6.11537i	0.234284	+	0.372861i	−0.708803	+	0.705406i	$0.750765\pi$
$270$		0			0
$271$	1.02753	−	0.115774i	0.0624178	−	0.00703279i	−0.0807004	−	0.996738i	$-0.525716\pi$
$271$	1.02753	−	0.115774i	0.0624178	−	0.00703279i	0.143118	+	0.989706i	$0.454287\pi$
$272$	0.878017	+	3.84684i	0.0532376	+	0.233249i
$273$	−18.1693			−1.09966
$274$	1.41161	+	6.18465i	0.0852782	+	0.373628i
$275$		0			0
$276$	−2.45517	−	7.01646i	−0.147784	−	0.422341i
$277$	−8.85116	+	14.0865i	−0.531815	+	0.846378i	−0.999292	−	0.0376270i	$-0.988020\pi$
$277$	−8.85116	+	14.0865i	−0.531815	+	0.846378i	0.467477	+	0.884005i	$0.345163\pi$
$278$			4.42440i			0.265358i
$279$	−17.1761	−	10.7924i	−1.02830	−	0.646126i
$280$		0			0
$281$	−3.44157	+	15.0785i	−0.205307	+	0.899507i	0.762336	+	0.647182i	$0.224052\pi$
$281$	−3.44157	+	15.0785i	−0.205307	+	0.899507i	−0.967642	+	0.252325i	$0.918805\pi$
$282$	−0.0168597	+	0.0738671i	−0.00100398	+	0.00439872i
$283$	−0.425710	+	3.77828i	−0.0253059	+	0.224596i	0.974694	+	0.223545i	$0.0717630\pi$
$283$	−0.425710	+	3.77828i	−0.0253059	+	0.224596i	−0.999999	+	0.00105059i	$0.999666\pi$
$284$	−1.62159	+	3.36727i	−0.0962237	+	0.199811i
$285$		0			0
$286$	−15.2590	+	19.1342i	−0.902283	+	1.13143i
$287$	8.82451	−	7.03731i	0.520894	−	0.415399i
$288$	23.7939	−	11.4585i	1.40207	−	0.675201i
$289$	11.5736			0.680799
$290$		0			0
$291$	24.9846			1.46462
$292$	−3.07347	+	1.48011i	−0.179861	+	0.0866166i
$293$	19.6561	−	15.6752i	1.14832	−	0.915755i	0.150972	−	0.988538i	$-0.451760\pi$
$293$	19.6561	−	15.6752i	1.14832	−	0.915755i	0.997348	+	0.0727831i	$0.0231881\pi$
$294$	8.64304	−	10.8380i	0.504072	−	0.632087i
$295$		0			0
$296$	4.77476	−	9.91488i	0.277527	−	0.576291i
$297$	−3.62909	+	32.2091i	−0.210581	+	1.86896i
$298$	1.74112	−	7.62836i	0.100861	−	0.441899i
$299$	2.50494	−	10.9749i	0.144864	−	0.634692i
$300$		0			0
$301$	−0.879095	−	0.552372i	−0.0506702	−	0.0318382i
$302$		−	9.40414i		−	0.541147i
$303$	−8.17641	+	13.0127i	−0.469723	+	0.747559i
$304$	0.921955	+	2.63479i	0.0528777	+	0.151116i
$305$		0			0
$306$	5.82727	+	25.5309i	0.333123	+	1.45951i
$307$	22.4912			1.28364			0.641820	−	0.766855i	$-0.278180\pi$
$307$	22.4912			1.28364			0.641820	+	0.766855i	$0.278180\pi$
$308$	−1.82978	−	8.01678i	−0.104261	−	0.456799i
$309$	−22.4592	+	2.53054i	−1.27766	+	0.143958i
$310$		0			0
$311$	16.9687	+	27.0055i	0.962205	+	1.53134i	0.842615	+	0.538517i	$0.181015\pi$
$311$	16.9687	+	27.0055i	0.962205	+	1.53134i	0.119590	+	0.992823i	$0.461842\pi$
$312$	38.2904	+	4.31429i	2.16777	+	0.244249i
$313$	24.1206	−	8.44016i	1.36338	−	0.477066i	0.453245	−	0.891386i	$-0.350266\pi$
$313$	24.1206	−	8.44016i	1.36338	−	0.477066i	0.910131	+	0.414320i	$0.135981\pi$
$314$	−1.70021	−	3.53052i	−0.0959484	−	0.199239i
$315$		0			0
$316$	−1.12033	+	9.94323i	−0.0630237	+	0.559351i
$317$	10.3085	+	21.4059i	0.578985	+	1.20228i	0.960595	+	0.277952i	$0.0896555\pi$
$317$	10.3085	+	21.4059i	0.578985	+	1.20228i	−0.381610	+	0.924323i	$0.624630\pi$
$318$	−3.37788	−	3.37788i	−0.189422	−	0.189422i
$319$	−2.27678	−	29.6784i	−0.127475	−	1.66167i
$320$		0			0
$321$	−10.6802	+	30.5223i	−0.596112	+	1.70359i
$322$	−2.07278	−	2.59918i	−0.115511	−	0.144847i
$323$	20.0873	−	2.26330i	1.11769	−	0.125933i
$324$	1.39883	−	0.673639i	0.0777125	−	0.0374244i
$325$		0			0
$326$	3.55478	+	4.45756i	0.196881	+	0.246881i
$327$	−19.4164	−	4.43167i	−1.07373	−	0.245072i
$328$	−20.2680	+	12.7352i	−1.11911	+	0.703184i
$329$	−0.00431635	−	0.0383086i	−0.000237968	−	0.00211202i
$330$		0			0
$331$	0.695071	+	0.695071i	0.0382046	+	0.0382046i	0.725951	−	0.687746i	$-0.241400\pi$
$331$	0.695071	+	0.695071i	0.0382046	+	0.0382046i	−0.687746	+	0.725951i	$0.741400\pi$
$332$	−13.3678	−	8.39956i	−0.733654	−	0.460986i
$333$	8.15896	−	16.9423i	0.447108	−	0.928430i
$334$	12.8060	−	4.48100i	0.700711	−	0.245189i
$335$		0			0
$336$	2.07172	−	2.07172i	0.113022	−	0.113022i
$337$	−26.8681	+	6.13247i	−1.46360	+	0.334057i	−0.878827	−	0.477140i	$-0.841673\pi$
$337$	−26.8681	+	6.13247i	−1.46360	+	0.334057i	−0.584772	+	0.811197i	$0.698816\pi$
$338$	6.01556	+	4.79725i	0.327203	+	0.260936i
$339$	40.8593	+	9.32587i	2.21917	+	0.506512i
$340$		0			0
$341$	17.3077	−	13.8024i	0.937263	−	0.747443i
$342$	6.11888	+	17.4868i	0.330871	+	0.945575i
$343$	−5.56087	+	15.8920i	−0.300259	+	0.858090i
$344$	1.72146	+	1.37282i	0.0928151	+	0.0740176i
$345$		0			0
$346$	12.2374	+	4.28205i	0.657887	+	0.230205i
$347$	−0.132362	+	0.132362i	−0.00710559	+	0.00710559i	−0.710651	−	0.703545i	$-0.751599\pi$
$347$	−0.132362	+	0.132362i	−0.00710559	+	0.00710559i	0.703545	+	0.710651i	$0.251599\pi$
$348$	−13.0805	+	9.68958i	−0.701189	+	0.519416i
$349$		−	32.4359i		−	1.73625i	−0.496342	−	0.868127i	$-0.665324\pi$
$349$		−	32.4359i		−	1.73625i	0.496342	−	0.868127i	$-0.334676\pi$
$350$		0			0
$351$	26.6749	+	3.00554i	1.42380	+	0.160424i
$352$	3.22686	+	28.6392i	0.171992	+	1.52647i
$353$	−18.4750	−	6.46469i	−0.983326	−	0.344081i	−0.209730	−	0.977759i	$-0.567258\pi$
$353$	−18.4750	−	6.46469i	−0.983326	−	0.344081i	−0.773596	+	0.633679i	$0.781544\pi$
$354$	9.90295	+	4.76901i	0.526336	+	0.253470i
$355$		0			0
$356$	12.3554	−	7.76340i	0.654834	−	0.411459i
$357$	−11.2880	−	17.9648i	−0.597425	−	0.950796i
$358$	−2.06723	+	2.59223i	−0.109257	+	0.137003i
$359$	−8.60134	+	13.6890i	−0.453962	+	0.722476i	−0.992780	−	0.119946i	$-0.961728\pi$
$359$	−8.60134	+	13.6890i	−0.453962	+	0.722476i	0.538819	+	0.842422i	$0.318871\pi$
$360$		0			0
$361$	−4.58146	+	1.04569i	−0.241130	+	0.0550362i
$362$	−15.4203	−	7.42601i	−0.810472	−	0.390303i
$363$	−50.0252	−	24.0909i	−2.62564	−	1.26444i
$364$	−6.63934	+	1.51539i	−0.347996	+	0.0794278i
$365$		0			0
$366$	5.77321	−	9.18801i	0.301771	−	0.480265i
$367$	8.72758	−	10.9440i	0.455576	−	0.571274i	−0.499997	−	0.866027i	$-0.666666\pi$
$367$	8.72758	−	10.9440i	0.455576	−	0.571274i	0.955574	+	0.294752i	$0.0952372\pi$
$368$	0.965769	+	1.53701i	0.0503442	+	0.0801223i
$369$	−34.6333	+	21.7615i	−1.80294	+	1.13286i
$370$		0			0
$371$	2.18991	+	1.05461i	0.113695	+	0.0547524i
$372$	−11.4273	−	3.99857i	−0.592476	−	0.207316i
$373$	2.24082	+	19.8878i	0.116025	+	1.02975i	0.907934	+	0.419112i	$0.137659\pi$
$373$	2.24082	+	19.8878i	0.116025	+	1.02975i	−0.791909	+	0.610639i	$0.790913\pi$
$374$	−28.3987	−	3.19977i	−1.46846	−	0.165456i
$375$		0			0
$376$			0.0817574i			0.00421632i
$377$	−24.5791	+	1.88558i	−1.26589	+	0.0971125i
$378$	5.60563	−	5.60563i	0.288322	−	0.288322i
$379$	28.3344	+	9.91464i	1.45544	+	0.509281i	0.938060	−	0.346474i	$-0.112621\pi$
$379$	28.3344	+	9.91464i	1.45544	+	0.509281i	0.517382	+	0.855755i	$0.326907\pi$
$380$		0			0
$381$	−1.64545	−	1.31220i	−0.0842988	−	0.0672260i
$382$	7.33814	−	20.9712i	0.375452	−	1.07298i
$383$	1.57738	+	4.50789i	0.0806003	+	0.230342i	0.977131	−	0.212640i	$-0.0682062\pi$
$383$	1.57738	+	4.50789i	0.0806003	+	0.230342i	−0.896530	+	0.442982i	$0.853920\pi$
$384$	9.15232	−	7.29873i	0.467052	−	0.372462i
$385$		0			0
$386$	−12.8167	−	2.92534i	−0.652355	−	0.148896i
$387$	2.94159	+	2.34584i	0.149529	+	0.119246i
$388$	9.12976	−	2.08381i	0.463493	−	0.105789i
$389$	11.4859	−	11.4859i	0.582361	−	0.582361i	−0.353191	−	0.935551i	$-0.614903\pi$
$389$	11.4859	−	11.4859i	0.582361	−	0.582361i	0.935551	+	0.353191i	$0.114903\pi$
$390$		0			0
$391$	12.4076	−	4.34159i	0.627477	−	0.219564i
$392$	6.49022	−	13.4771i	0.327806	−	0.680695i
$393$	35.2892	+	22.1737i	1.78011	+	1.11852i
$394$	−7.31809	−	7.31809i	−0.368680	−	0.368680i
$395$		0			0
$396$	3.33643	+	29.6117i	0.167662	+	1.48804i
$397$	0.0511183	−	0.0321198i	0.00256555	−	0.00161204i	−0.530749	−	0.847529i	$-0.678089\pi$
$397$	0.0511183	−	0.0321198i	0.00256555	−	0.00161204i	0.533314	+	0.845917i	$0.320946\pi$
$398$	−10.7077	−	2.44397i	−0.536731	−	0.122505i
$399$	−9.35849	−	11.7352i	−0.468510	−	0.587493i
$400$		0			0
$401$	−31.3147	+	15.0804i	−1.56378	+	0.753078i	−0.997468	−	0.0711105i	$-0.977346\pi$
$401$	−31.3147	+	15.0804i	−1.56378	+	0.753078i	−0.566315	+	0.824189i	$0.691631\pi$
$402$	−19.4723	+	2.19400i	−0.971191	+	0.109427i
$403$	−11.4309	−	14.3339i	−0.569413	−	0.714021i
$404$	−1.90248	+	5.43698i	−0.0946520	+	0.270500i
$405$		0			0
$406$	−4.09039	+	6.02232i	−0.203003	+	0.298883i
$407$	14.5108	+	14.5108i	0.719272	+	0.719272i
$408$	19.5229	+	40.5397i	0.966527	+	2.00701i
$409$	3.06651	−	27.2160i	0.151629	−	1.34575i	−0.655421	−	0.755264i	$-0.727509\pi$
$409$	3.06651	−	27.2160i	0.151629	−	1.34575i	0.807050	−	0.590483i	$-0.201063\pi$
$410$		0			0
$411$	8.08120	+	16.7808i	0.398616	+	0.827735i
$412$	−7.99588	+	2.79788i	−0.393928	+	0.137842i
$413$	−5.55742	−	0.626171i	−0.273463	−	0.0308119i
$414$	6.40967	+	10.2009i	0.315018	+	0.501348i
$415$		0			0
$416$	23.7184	−	2.67242i	1.16289	−	0.131026i
$417$	2.89058	+	12.6645i	0.141552	+	0.620181i
$418$	−20.2178			−0.988887
$419$	−1.69231	−	7.41451i	−0.0826749	−	0.362222i	0.916620	−	0.399759i	$-0.130906\pi$
$419$	−1.69231	−	7.41451i	−0.0826749	−	0.362222i	−0.999295	+	0.0375364i	$0.988049\pi$
$420$		0			0
$421$	−7.52865	−	21.5156i	−0.366924	−	1.04861i	−0.968332	−	0.249666i	$-0.919679\pi$
$421$	−7.52865	−	21.5156i	−0.366924	−	1.04861i	0.601408	−	0.798942i	$-0.294607\pi$
$422$	−0.775613	+	1.23438i	−0.0377563	+	0.0600888i
$423$			0.139705i			0.00679267i
$424$	−4.36465	−	2.74249i	−0.211966	−	0.133187i
$425$		0			0
$426$	2.14617	−	9.40298i	0.103982	−	0.455576i
$427$	−1.22859	+	5.38282i	−0.0594558	+	0.260493i
$428$	−1.35704	+	12.0441i	−0.0655952	+	0.582174i
$429$	−31.1767	+	64.7390i	−1.50522	+	3.12563i
$430$		0			0
$431$	−20.2333	+	25.3717i	−0.974602	+	1.22211i	0.000418849		1.00000i	$0.499867\pi$
$431$	−20.2333	+	25.3717i	−0.974602	+	1.22211i	−0.975021	+	0.222113i	$0.928705\pi$
$432$	−3.38427	+	2.69886i	−0.162826	+	0.129849i
$433$	−29.1921	+	14.0582i	−1.40288	+	0.675592i	−0.973744	−	0.227646i	$-0.926897\pi$
$433$	−29.1921	+	14.0582i	−1.40288	+	0.675592i	−0.429138	+	0.903239i	$0.641183\pi$
$434$	−5.41436			−0.259898
$435$		0			0
$436$	−7.46468			−0.357493
$437$	8.37866	−	4.03495i	0.400806	−	0.193018i
$438$	6.88268	−	5.48876i	0.328867	−	0.262263i
$439$	−10.5436	+	13.2212i	−0.503218	+	0.631015i	−0.966952	−	0.254959i	$-0.917938\pi$
$439$	−10.5436	+	13.2212i	−0.503218	+	0.631015i	0.463734	+	0.885975i	$0.346509\pi$
$440$		0			0
$441$	11.0903	−	23.0292i	0.528109	−	1.09663i
$442$	−2.64998	+	23.5192i	−0.126047	+	1.11870i
$443$	−7.27982	+	31.8950i	−0.345875	+	1.51538i	0.440571	+	0.897718i	$0.354776\pi$
$443$	−7.27982	+	31.8950i	−0.345875	+	1.51538i	−0.786446	+	0.617659i	$0.788081\pi$
$444$	2.49732	−	10.9415i	0.118518	−	0.519259i
$445$		0			0
$446$	−7.18355	−	4.51373i	−0.340151	−	0.213731i
$447$		−	22.9731i		−	1.08659i
$448$	4.84802	−	7.71558i	0.229047	−	0.364527i
$449$	−1.53366	−	4.38294i	−0.0723777	−	0.206844i	0.902011	−	0.431712i	$-0.142090\pi$
$449$	−1.53366	−	4.38294i	−0.0723777	−	0.206844i	−0.974389	+	0.224869i	$0.927805\pi$
$450$		0			0
$451$	−9.93268	−	43.5179i	−0.467712	−	2.04918i
$452$	15.7084			0.738862
$453$	−6.14398	−	26.9185i	−0.288670	−	1.26474i
$454$	19.9471	−	2.24750i	0.936165	−	0.105480i
$455$		0			0
$456$	16.9358	+	26.9531i	0.793090	+	1.26220i
$457$	5.07881	+	0.572244i	0.237577	+	0.0267684i	0.229950	−	0.973202i	$-0.426144\pi$
$457$	5.07881	+	0.572244i	0.237577	+	0.0267684i	0.00762663	+	0.999971i	$0.497572\pi$
$458$	−4.91663	+	1.72040i	−0.229739	+	0.0803892i
$459$	13.6006	+	28.2419i	0.634821	+	1.31822i
$460$		0			0
$461$	1.19509	−	10.6068i	0.0556611	−	0.494006i	−0.934694	−	0.355453i	$-0.884326\pi$
$461$	1.19509	−	10.6068i	0.0556611	−	0.494006i	0.990355	−	0.138553i	$-0.0442450\pi$
$462$	9.20718	+	19.1189i	0.428357	+	0.889492i
$463$	3.63850	+	3.63850i	0.169096	+	0.169096i	0.786582	−	0.617486i	$-0.211849\pi$
$463$	3.63850	+	3.63850i	0.169096	+	0.169096i	−0.617486	+	0.786582i	$0.711849\pi$
$464$	2.58759	−	3.01759i	0.120126	−	0.140088i
$465$		0			0
$466$	6.27595	−	17.9356i	0.290728	−	0.830853i
$467$	−2.85976	−	3.58602i	−0.132334	−	0.165941i	0.711250	−	0.702940i	$-0.248130\pi$
$467$	−2.85976	−	3.58602i	−0.132334	−	0.165941i	−0.843583	+	0.536998i	$0.819558\pi$
$468$	24.5238	−	2.76317i	1.13361	−	0.127727i
$469$	8.98307	−	4.32602i	0.414799	−	0.199757i
$470$		0			0
$471$	−7.17330	−	8.99503i	−0.330528	−	0.414469i
$472$	11.5631	+	2.63921i	0.532237	+	0.121480i
$473$	−3.47660	+	2.18449i	−0.159854	+	0.100443i
$474$	−2.89116	−	25.6598i	−0.132796	−	1.17859i
$475$		0			0
$476$	−5.62314	−	5.62314i	−0.257736	−	0.257736i
$477$	−7.45819	−	4.68629i	−0.341487	−	0.214570i
$478$	4.09515	−	8.50367i	0.187308	−	0.388949i
$479$	−29.4941	+	10.3204i	−1.34762	+	0.471553i	−0.905097	−	0.425205i	$-0.860202\pi$
$479$	−29.4941	+	10.3204i	−1.34762	+	0.471553i	−0.442523	+	0.896757i	$0.645916\pi$
$480$		0			0
$481$	12.0175	−	12.0175i	0.547952	−	0.547952i
$482$	19.0007	−	4.33679i	0.865459	−	0.197535i
$483$	−7.63126	−	6.08573i	−0.347234	−	0.276910i
$484$	−20.2892	−	4.63089i	−0.922238	−	0.210495i
$485$		0			0
$486$	10.1713	−	8.11134i	0.461380	−	0.367938i
$487$	−1.72349	−	4.92544i	−0.0780986	−	0.223193i	0.898214	−	0.439559i	$-0.144865\pi$
$487$	−1.72349	−	4.92544i	−0.0780986	−	0.223193i	−0.976312	+	0.216366i	$0.930580\pi$
$488$	3.86731	−	11.0521i	0.175065	−	0.500307i
$489$	13.0875	+	10.4369i	0.591838	+	0.471975i
$490$		0			0
$491$	2.20709	+	0.772293i	0.0996044	+	0.0348531i	0.379621	−	0.925142i	$-0.376054\pi$
$491$	2.20709	+	0.772293i	0.0996044	+	0.0348531i	−0.280017	+	0.959995i	$0.590340\pi$
$492$	−17.2615	+	17.2615i	−0.778209	+	0.778209i
$493$	−17.1346	−	23.1309i	−0.771702	−	1.04177i
$494$			16.7440i			0.753348i
$495$		0			0
$496$	2.93778	+	0.331009i	0.131910	+	0.0148627i
$497$	0.549454	+	4.87654i	0.0246464	+	0.218743i
$498$	38.4558	+	13.4563i	1.72325	+	0.602990i
$499$	−20.3394	−	9.79495i	−0.910517	−	0.438482i	−0.0808412	−	0.996727i	$-0.525761\pi$
$499$	−20.3394	−	9.79495i	−0.910517	−	0.438482i	−0.829676	+	0.558245i	$0.811475\pi$
$500$		0			0
$501$	33.7284	−	21.1930i	1.50687	−	0.946832i
$502$	12.7806	+	20.3402i	0.570426	+	0.907828i
$503$	−7.03932	+	8.82703i	−0.313868	+	0.393578i	−0.913594	−	0.406627i	$-0.866705\pi$
$503$	−7.03932	+	8.82703i	−0.313868	+	0.393578i	0.599726	+	0.800205i	$0.295276\pi$
$504$	11.1634	−	17.7664i	0.497257	−	0.791379i
$505$		0			0
$506$	−12.8178	+	2.92558i	−0.569821	+	0.130058i
$507$	20.3532	+	9.80159i	0.903918	+	0.435304i
$508$	−0.710714	−	0.342262i	−0.0315328	−	0.0151854i
$509$	33.9185	−	7.74166i	1.50341	−	0.343143i	0.610005	−	0.792398i	$-0.291167\pi$
$509$	33.9185	−	7.74166i	1.50341	−	0.343143i	0.893404	+	0.449254i	$0.148310\pi$
$510$		0			0
$511$	−2.38309	+	3.79266i	−0.105422	+	0.167778i
$512$	−5.12807	+	6.43039i	−0.226631	+	0.284186i
$513$	11.7983	+	18.7768i	0.520907	+	0.829018i
$514$	0.842835	−	0.529588i	0.0371758	−	0.0233591i
$515$		0			0
$516$	2.02311	+	0.974280i	0.0890626	+	0.0428903i
$517$	−0.143904	−	0.0503542i	−0.00632889	−	0.00221458i
$518$	−0.561962	−	4.98755i	−0.0246912	−	0.219140i
$519$	37.8261	+	4.26198i	1.66038	+	0.187080i
$520$		0			0
$521$			7.44577i			0.326205i	0.986609	+	0.163102i	$0.0521501\pi$
$521$			7.44577i			0.326205i	−0.986609	+	0.163102i	$0.947850\pi$
$522$	17.1734	−	20.0273i	0.751661	−	0.876571i
$523$	27.9535	−	27.9535i	1.22232	−	1.22232i	0.255514	−	0.966805i	$-0.417755\pi$
$523$	27.9535	−	27.9535i	1.22232	−	1.22232i	0.966805	−	0.255514i	$-0.0822448\pi$
$524$	14.7446	+	5.15936i	0.644121	+	0.225388i
$525$		0			0
$526$	2.99848	+	2.39121i	0.130740	+	0.104262i
$527$	7.07087	−	20.2074i	0.308012	−	0.880248i
$528$	−3.82689	−	10.9366i	−0.166544	−	0.475956i
$529$	−13.2540	+	10.5697i	−0.576263	+	0.459554i
$530$		0			0
$531$	19.7588	+	4.50981i	0.857457	+	0.195709i
$532$	−4.39849	−	3.50768i	−0.190699	−	0.152077i
$533$	−36.0407	+	8.22605i	−1.56110	+	0.356310i
$534$	−26.6271	+	26.6271i	−1.15227	+	1.15227i
$535$		0			0
$536$	−19.9583	+	6.98372i	−0.862068	+	0.301651i
$537$	−4.22370	+	8.77060i	−0.182266	+	0.378480i
$538$	−5.91511	−	3.71671i	−0.255018	−	0.160239i
$539$	19.7242	+	19.7242i	0.849579	+	0.849579i
$540$		0			0
$541$	1.67468	+	14.8632i	0.0720000	+	0.639018i	0.976945	+	0.213490i	$0.0684830\pi$
$541$	1.67468	+	14.8632i	0.0720000	+	0.639018i	−0.904945	+	0.425528i	$0.860088\pi$
$542$	−0.846865	+	0.532120i	−0.0363760	+	0.0228565i
$543$	−48.9908	−	11.1818i	−2.10240	−	0.479859i
$544$	17.3778	+	21.7911i	0.745068	+	0.934286i
$545$		0			0
$546$	15.8339	−	7.62520i	0.677628	−	0.326328i
$547$	−20.2804	+	2.28505i	−0.867127	+	0.0977017i	−0.534309	−	0.845289i	$-0.679428\pi$
$547$	−20.2804	+	2.28505i	−0.867127	+	0.0977017i	−0.332818	+	0.942991i	$0.607999\pi$
$548$	4.35257	+	5.45796i	0.185933	+	0.233152i
$549$	6.60835	−	18.8856i	0.282037	−	0.806017i
$550$		0			0
$551$	−13.8778	−	14.9039i	−0.591216	−	0.634928i
$552$	14.6372	+	14.6372i	0.623002	+	0.623002i
$553$	5.70064	+	11.8375i	0.242416	+	0.503382i
$554$	1.80170	−	15.9905i	0.0765469	−	0.679372i
$555$		0			0
$556$	2.11253	+	4.38670i	0.0895910	+	0.186038i
$557$	29.0790	−	10.1752i	1.23212	−	0.431137i	0.365830	−	0.930682i	$-0.380785\pi$
$557$	29.0790	−	10.1752i	1.23212	−	0.431137i	0.866288	+	0.499545i	$0.166499\pi$
$558$	19.4976	+	2.19686i	0.825401	+	0.0930004i
$559$	1.80915	+	2.87925i	0.0765189	+	0.121779i
$560$		0			0
$561$	−83.3794	+	9.39460i	−3.52028	+	0.396640i
$562$	−3.32886	−	14.5847i	−0.140420	−	0.615219i
$563$	−12.4601			−0.525130			−0.262565	−	0.964914i	$-0.584568\pi$
$563$	−12.4601			−0.525130			−0.262565	+	0.964914i	$0.584568\pi$
$564$	0.0185534	+	0.0812878i	0.000781239	+	0.00342283i
$565$		0			0
$566$	−1.21466	−	3.47130i	−0.0510560	−	0.145910i
$567$	1.08461	−	1.72615i	0.0455495	−	0.0724915i
$568$		−	10.4074i		−	0.436685i
$569$	3.79658	+	2.38555i	0.159161	+	0.100007i	0.609258	−	0.792972i	$-0.291468\pi$
$569$	3.79658	+	2.38555i	0.159161	+	0.100007i	−0.450097	+	0.892980i	$0.648610\pi$
$570$		0			0
$571$	−1.25968	+	5.51903i	−0.0527160	+	0.230964i	−0.994422	−	0.105472i	$-0.966365\pi$
$571$	−1.25968	+	5.51903i	−0.0527160	+	0.230964i	0.941706	+	0.336436i	$0.109222\pi$
$572$	−5.99296	+	26.2569i	−0.250578	+	1.09786i
$573$	7.30374	−	64.8225i	0.305118	−	2.70800i
$574$	−4.73686	+	9.83619i	−0.197713	+	0.410555i
$575$		0			0
$576$	−20.5888	+	25.8175i	−0.857865	+	1.07573i
$577$	36.9281	−	29.4491i	1.53734	−	1.22598i	0.654736	−	0.755857i	$-0.272780\pi$
$577$	36.9281	−	29.4491i	1.53734	−	1.22598i	0.882599	−	0.470127i	$-0.155792\pi$
$578$	−10.0860	+	4.85714i	−0.419521	+	0.202030i
$579$	−38.5980			−1.60408
$580$		0			0
$581$	−20.7301			−0.860031
$582$	−21.7732	+	10.4854i	−0.902528	+	0.434634i
$583$	7.51533	−	5.99328i	0.311253	−	0.248216i
$584$	5.92274	−	7.42688i	0.245085	−	0.307327i
$585$		0			0
$586$	−10.5511	+	21.9095i	−0.435861	+	0.905075i
$587$	1.55975	−	13.8431i	0.0643776	−	0.571367i	−0.919572	−	0.392921i	$-0.871464\pi$
$587$	1.55975	−	13.8431i	0.0643776	−	0.571367i	0.983950	−	0.178446i	$-0.0571070\pi$
$588$	3.39455	−	14.8725i	0.139989	−	0.613332i
$589$	3.37023	−	14.7659i	0.138868	−	0.608420i
$590$		0			0
$591$	−25.7285	−	16.1663i	−1.05833	−	0.664993i
$592$			2.74056i			0.112636i
$593$	11.3359	−	18.0409i	0.465508	−	0.740852i	−0.528643	−	0.848844i	$-0.677299\pi$
$593$	11.3359	−	18.0409i	0.465508	−	0.740852i	0.994152	+	0.107992i	$0.0344420\pi$
$594$	−10.3547	−	29.5921i	−0.424860	−	1.21418i
$595$		0			0
$596$	−1.91604	−	8.39471i	−0.0784840	−	0.343861i
$597$	−32.2467			−1.31977
$598$	2.42291	+	10.6155i	0.0990801	+	0.434098i
$599$	9.52133	−	1.07280i	0.389031	−	0.0438332i	0.0847169	−	0.996405i	$-0.473001\pi$
$599$	9.52133	−	1.07280i	0.389031	−	0.0438332i	0.304314	+	0.952572i	$0.401573\pi$
$600$		0			0
$601$	−18.7867	−	29.8988i	−0.766324	−	1.21960i	−0.970603	−	0.240685i	$-0.922628\pi$
$601$	−18.7867	−	29.8988i	−0.766324	−	1.21960i	0.204279	−	0.978913i	$-0.434515\pi$
$602$	0.997916	+	0.112438i	0.0406720	+	0.00458264i
$603$	−34.1042	+	11.9336i	−1.38883	+	0.485973i
$604$	−4.49021	−	9.32402i	−0.182704	−	0.379389i
$605$		0			0
$606$	1.66435	−	14.7715i	0.0676096	−	0.600052i
$607$	−13.3355	−	27.6914i	−0.541270	−	1.12396i	−0.974854	−	0.222846i	$-0.928465\pi$
$607$	−13.3355	−	27.6914i	−0.541270	−	1.12396i	0.433583	−	0.901113i	$-0.357249\pi$
$608$	13.9427	+	13.9427i	0.565452	+	0.565452i
$609$	−7.77385	+	19.9107i	−0.315012	+	0.806824i
$610$		0			0
$611$	−0.0417023	+	0.119178i	−0.00168710	+	0.00482144i
$612$	17.9679	+	22.5311i	0.726310	+	0.910764i
$613$	5.43065	−	0.611887i	0.219342	−	0.0247139i	−0.00160954	−	0.999999i	$-0.500512\pi$
$613$	5.43065	−	0.611887i	0.219342	−	0.0247139i	0.220951	+	0.975285i	$0.429084\pi$
$614$	−19.6003	+	9.43899i	−0.791003	+	0.380927i
$615$		0			0
$616$	14.2768	+	17.9026i	0.575229	+	0.721315i
$617$	8.50028	+	1.94013i	0.342208	+	0.0781068i	0.390171	−	0.920742i	$-0.372416\pi$
$617$	8.50028	+	1.94013i	0.342208	+	0.0781068i	−0.0479630	+	0.998849i	$0.515273\pi$
$618$	18.5104	−	11.6308i	0.744596	−	0.467861i
$619$	0.314355	+	2.78998i	0.0126350	+	0.112139i	0.998447	−	0.0557167i	$-0.0177444\pi$
$619$	0.314355	+	2.78998i	0.0126350	+	0.112139i	−0.985812	+	0.167855i	$0.946316\pi$
$620$		0			0
$621$	10.1970	+	10.1970i	0.409192	+	0.409192i
$622$	−26.1211	−	16.4130i	−1.04736	−	0.658101i
$623$	8.31325	−	17.2626i	0.333063	−	0.691613i
$624$	−9.05750	+	3.16936i	−0.362590	+	0.126876i
$625$		0			0
$626$	−17.4781	+	17.4781i	−0.698566	+	0.698566i
$627$	−57.8718	+	13.2089i	−2.31118	+	0.527511i
$628$	−3.37145	−	2.68864i	−0.134536	−	0.107289i
$629$	19.3484	+	4.41614i	0.771470	+	0.176083i
$630$		0			0
$631$	34.6785	−	27.6552i	1.38053	−	1.10093i	0.397476	−	0.917613i	$-0.369886\pi$
$631$	34.6785	−	27.6552i	1.38053	−	1.10093i	0.983053	−	0.183322i	$-0.0586851\pi$
$632$	−9.20285	−	26.3002i	−0.366070	−	1.04617i
$633$	−1.41367	+	4.04004i	−0.0561884	+	0.160577i
$634$	−17.9670	−	14.3282i	−0.713563	−	0.569047i
$635$		0			0
$636$	−4.96194	−	1.73626i	−0.196754	−	0.0688471i
$637$	16.3351	−	16.3351i	0.647222	−	0.647222i
$638$	14.4394	+	24.9082i	0.571662	+	0.986124i
$639$		−	17.7838i		−	0.703518i
$640$		0			0
$641$	19.6936	+	2.21894i	0.777852	+	0.0876428i	0.491959	−	0.870619i	$-0.336281\pi$
$641$	19.6936	+	2.21894i	0.777852	+	0.0876428i	0.285893	+	0.958261i	$0.407710\pi$
$642$	−3.50203	−	31.0813i	−0.138214	−	1.22668i
$643$	28.6585	+	10.0280i	1.13018	+	0.395467i	0.829638	−	0.558302i	$-0.188547\pi$
$643$	28.6585	+	10.0280i	1.13018	+	0.395467i	0.300542	+	0.953769i	$0.402833\pi$
$644$	−3.29615	−	1.58734i	−0.129887	−	0.0625501i
$645$		0			0
$646$	−16.5555	+	10.4025i	−0.651368	+	0.409282i
$647$	2.55620	+	4.06817i	0.100495	+	0.159936i	0.893187	−	0.449686i	$-0.148464\pi$
$647$	2.55620	+	4.06817i	0.100495	+	0.159936i	−0.792692	+	0.609622i	$0.791321\pi$
$648$	−2.69561	+	3.38019i	−0.105894	+	0.132786i
$649$	−11.7671	+	18.7272i	−0.461898	+	0.735107i
$650$		0			0
$651$	−15.4981	+	3.53735i	−0.607420	+	0.138640i
$652$	5.65286	+	2.72227i	0.221383	+	0.106612i
$653$	−28.0887	−	13.5268i	−1.09920	−	0.529345i	−0.205791	−	0.978596i	$-0.565977\pi$
$653$	−28.0887	−	13.5268i	−1.09920	−	0.529345i	−0.893406	+	0.449251i	$0.851691\pi$
$654$	18.7806	−	4.28655i	0.734379	−	0.167617i
$655$		0			0
$656$	3.17152	−	5.04744i	0.123827	−	0.197070i
$657$	10.1206	−	12.6908i	0.394842	−	0.495117i
$658$	0.0198387	+	0.0315732i	0.000773394	+	0.00123085i
$659$	−11.5058	+	7.22958i	−0.448203	+	0.281624i	−0.737161	−	0.675717i	$-0.763834\pi$
$659$	−11.5058	+	7.22958i	−0.448203	+	0.281624i	0.288958	+	0.957342i	$0.406691\pi$
$660$		0			0
$661$	−20.4402	−	9.84350i	−0.795033	−	0.382868i	−0.00814767	−	0.999967i	$-0.502594\pi$
$661$	−20.4402	−	9.84350i	−0.795033	−	0.382868i	−0.786886	+	0.617099i	$0.788308\pi$
$662$	−0.897434	−	0.314026i	−0.0348797	−	0.0122050i
$663$	7.78042	+	69.0531i	0.302166	+	2.68180i
$664$	43.6871	+	4.92236i	1.69539	+	0.191025i
$665$		0			0
$666$			18.1887i			0.704797i
$667$	−10.9550	−	7.44069i	−0.424179	−	0.288105i
$668$	10.5573	−	10.5573i	0.408475	−	0.408475i
$669$	−23.5113	−	8.22694i	−0.908997	−	0.318072i
$670$		0			0
$671$	17.0714	+	13.6140i	0.659034	+	0.525562i
$672$	6.83538	−	19.5344i	0.263680	−	0.753555i
$673$	−3.92195	−	11.2083i	−0.151180	−	0.432048i	0.843240	−	0.537537i	$-0.180645\pi$
$673$	−3.92195	−	11.2083i	−0.151180	−	0.432048i	−0.994421	+	0.105489i	$0.966359\pi$
$674$	20.8410	−	16.6201i	0.802764	−	0.640183i
$675$		0			0
$676$	8.25486	+	1.88412i	0.317495	+	0.0724661i
$677$	0.860917	+	0.686559i	0.0330877	+	0.0263866i	0.639894	−	0.768463i	$-0.278978\pi$
$677$	0.860917	+	0.686559i	0.0330877	+	0.0263866i	−0.606806	+	0.794850i	$0.707550\pi$
$678$	−39.5212	+	9.02047i	−1.51780	+	0.346429i
$679$	8.69471	−	8.69471i	0.333672	−	0.333672i
$680$		0			0
$681$	55.6286	−	19.4653i	2.13169	−	0.745911i
$682$	−9.29049	+	19.2919i	−0.355751	+	0.738725i
$683$	0.322462	+	0.202616i	0.0123387	+	0.00775289i	0.538187	−	0.842825i	$-0.319109\pi$
$683$	0.322462	+	0.202616i	0.0123387	+	0.00775289i	−0.525849	+	0.850578i	$0.676252\pi$
$684$	14.4162	+	14.4162i	0.551216	+	0.551216i
$685$		0			0
$686$	−1.82340	−	16.1831i	−0.0696177	−	0.617874i
$687$	−12.9495	+	8.13668i	−0.494053	+	0.310434i
$688$	−0.534587	−	0.122016i	−0.0203809	−	0.00465182i
$689$	−4.96351	−	6.22405i	−0.189095	−	0.237117i
$690$		0			0
$691$	−9.56118	+	4.60442i	−0.363724	+	0.175160i	−0.606815	−	0.794843i	$-0.707553\pi$
$691$	−9.56118	+	4.60442i	−0.363724	+	0.175160i	0.243091	+	0.970004i	$0.421839\pi$
$692$	14.1777	−	1.59744i	0.538956	−	0.0607257i
$693$	24.3958	+	30.5914i	0.926719	+	1.16207i
$694$	0.0597999	−	0.170898i	0.00226997	−	0.00648722i
$695$		0			0
$696$	21.1106	−	40.1144i	0.800195	−	1.52053i
$697$	−30.5244	−	30.5244i	−1.15619	−	1.15619i
$698$	13.6125	+	28.2667i	0.515242	+	1.06991i
$699$	6.24653	−	55.4395i	0.236266	−	2.09691i
$700$		0			0
$701$	−7.04923	−	14.6379i	−0.266246	−	0.552865i	0.724391	−	0.689389i	$-0.242121\pi$
$701$	−7.04923	−	14.6379i	−0.266246	−	0.552865i	−0.990637	+	0.136524i	$0.956407\pi$
$702$	−24.5076	+	8.57558i	−0.924979	+	0.323664i
$703$	13.9518	+	1.57199i	0.526200	+	0.0592885i
$704$	−19.1727	−	30.5131i	−0.722597	−	1.15001i
$705$		0			0
$706$	18.8134	−	2.11976i	0.708052	−	0.0797782i
$707$	1.68304	+	7.37386i	0.0632971	+	0.277323i
$708$	12.0956			0.454582
$709$	5.20526	+	22.8057i	0.195488	+	0.856488i	0.973582	+	0.228340i	$0.0733296\pi$
$709$	5.20526	+	22.8057i	0.195488	+	0.856488i	−0.778094	+	0.628148i	$0.783813\pi$
$710$		0			0
$711$	−15.7256	−	44.9410i	−0.589754	−	1.68542i
$712$	−21.6185	+	34.4057i	−0.810189	+	1.28941i
$713$		−	9.84907i		−	0.368851i
$714$	17.3765	+	10.9184i	0.650298	+	0.408609i
$715$		0			0
$716$	−0.811905	+	3.55719i	−0.0303423	+	0.132938i
$717$	6.16634	−	27.0165i	0.230286	−	1.00895i
$718$	1.75085	−	15.5392i	0.0653411	−	0.579918i
$719$	14.4691	−	30.0454i	0.539606	−	1.12050i	−0.435790	−	0.900048i	$-0.643531\pi$
$719$	14.4691	−	30.0454i	0.539606	−	1.12050i	0.975397	−	0.220456i	$-0.0707546\pi$
$720$		0			0
$721$	−6.93522	+	8.69649i	−0.258281	+	0.323874i
$722$	3.55373	−	2.83401i	0.132256	−	0.105471i
$723$	51.5546	−	24.8274i	1.91734	−	0.923340i
$724$	−18.8346			−0.699983
$725$		0			0
$726$	53.7055			1.99320
$727$	13.9547	−	6.72024i	0.517552	−	0.249240i	−0.156826	−	0.987626i	$-0.550126\pi$
$727$	13.9547	−	6.72024i	0.517552	−	0.249240i	0.674378	+	0.738386i	$0.264412\pi$
$728$	14.8265	−	11.8238i	0.549508	−	0.438218i
$729$	26.5434	−	33.2844i	0.983089	−	1.23275i
$730$		0			0
$731$	−1.72287	+	3.57757i	−0.0637226	+	0.132321i
$732$	1.33701	−	11.8663i	0.0494173	−	0.438590i
$733$	6.90248	−	30.2417i	0.254949	−	1.11700i	−0.671625	−	0.740891i	$-0.734403\pi$
$733$	6.90248	−	30.2417i	0.254949	−	1.11700i	0.926574	−	0.376113i	$-0.122739\pi$
$734$	−3.01284	+	13.2001i	−0.111206	+	0.487224i
$735$		0			0
$736$	10.8570	+	6.82193i	0.400196	+	0.251460i
$737$		−	39.4306i		−	1.45244i
$738$	21.0489	−	33.4991i	0.774821	−	1.23312i
$739$	−3.03598	−	8.67634i	−0.111680	−	0.319164i	0.874455	−	0.485107i	$-0.161219\pi$
$739$	−3.03598	−	8.67634i	−0.111680	−	0.319164i	−0.986135	+	0.165942i	$0.946933\pi$
$740$		0			0
$741$	10.9393	+	47.9283i	0.401866	+	1.76069i
$742$	−2.35102			−0.0863087
$743$	4.77394	+	20.9160i	0.175139	+	0.767334i	0.983831	+	0.179101i	$0.0573189\pi$
$743$	4.77394	+	20.9160i	0.175139	+	0.767334i	−0.808692	+	0.588233i	$0.799824\pi$
$744$	33.5011	−	3.77466i	1.22821	−	0.138386i
$745$		0			0
$746$	−10.2992	−	16.3911i	−0.377081	−	0.600120i
$747$	74.6513	+	8.41118i	2.73135	+	0.307749i
$748$	−29.6846	+	10.3871i	−1.08538	+	0.379789i
$749$	6.90511	+	14.3386i	0.252307	+	0.523921i
$750$		0			0
$751$	−4.39473	+	39.0043i	−0.160366	+	1.42329i	0.613378	+	0.789790i	$0.289810\pi$
$751$	−4.39473	+	39.0043i	−0.160366	+	1.42329i	−0.773744	+	0.633499i	$0.781618\pi$
$752$	−0.00883409	−	0.0183442i	−0.000322146	−	0.000668943i
$753$	49.8722	+	49.8722i	1.81744	+	1.81744i
$754$	20.6284	−	11.9584i	0.751244	−	0.435501i
$755$		0			0
$756$	2.88134	−	8.23440i	0.104793	−	0.299482i
$757$	−26.9647	−	33.8127i	−0.980049	−	1.22894i	−0.973435	−	0.228965i	$-0.926466\pi$
$757$	−26.9647	−	33.8127i	−0.980049	−	1.22894i	−0.00661456	−	0.999978i	$-0.502105\pi$
$758$	−28.8534	+	3.25099i	−1.04800	+	0.118081i
$759$	−34.7785	+	16.7485i	−1.26238	+	0.607931i
$760$		0			0
$761$	−10.1735	−	12.7572i	−0.368791	−	0.462449i	0.562462	−	0.826823i	$-0.309854\pi$
$761$	−10.1735	−	12.7572i	−0.368791	−	0.462449i	−0.931253	+	0.364374i	$0.881283\pi$
$762$	1.98464	+	0.452982i	0.0718961	+	0.0164098i
$763$	−8.29920	+	5.21473i	−0.300451	+	0.188786i
$764$	−2.73753	−	24.2963i	−0.0990405	−	0.879009i
$765$		0			0
$766$	−3.26648	−	3.26648i	−0.118023	−	0.118023i
$767$	15.5095	+	9.74526i	0.560015	+	0.351881i
$768$	−20.9797	+	43.5649i	−0.757041	+	1.57201i
$769$	−35.8462	+	12.5431i	−1.29265	+	0.452317i	−0.887024	−	0.461723i	$-0.847232\pi$
$769$	−35.8462	+	12.5431i	−1.29265	+	0.452317i	−0.405624	+	0.914040i	$0.632946\pi$
$770$		0			0
$771$	2.06655	−	2.06655i	0.0744249	−	0.0744249i
$772$	−14.1043	+	3.21922i	−0.507625	+	0.115862i
$773$	−41.9634	−	33.4647i	−1.50932	−	1.20364i	−0.917604	−	0.397496i	$-0.869879\pi$
$773$	−41.9634	−	33.4647i	−1.50932	−	1.20364i	−0.591716	−	0.806147i	$-0.701549\pi$
$774$	−3.54798	−	0.809802i	−0.127529	−	0.0291077i
$775$		0			0
$776$	−20.3880	+	16.2589i	−0.731886	+	0.583659i
$777$	−4.86707	−	13.9093i	−0.174605	−	0.498993i
$778$	−5.18923	+	14.8300i	−0.186043	+	0.531680i
$779$	−23.8766	−	19.0409i	−0.855467	−	0.682212i
$780$		0			0
$781$	18.3184	+	6.40989i	0.655484	+	0.229364i
$782$	−8.99069	+	8.99069i	−0.321506	+	0.321506i
$783$	14.7067	−	27.9456i	0.525573	−	0.998696i
$784$			3.72518i			0.133042i
$785$		0			0
$786$	−40.0591	−	4.51357i	−1.42886	−	0.160994i
$787$	4.82326	+	42.8076i	0.171931	+	1.52593i	0.722637	+	0.691227i	$0.242930\pi$
$787$	4.82326	+	42.8076i	0.171931	+	1.52593i	−0.550707	+	0.834699i	$0.685642\pi$
$788$	−10.7499	−	3.76156i	−0.382950	−	0.134000i
$789$	10.1452	+	4.88565i	0.361177	+	0.173934i
$790$		0			0
$791$	17.4646	−	10.9737i	0.620969	−	0.390180i
$792$	−44.1483	−	70.2617i	−1.56874	−	2.49664i
$793$	11.2748	−	14.1382i	0.400381	−	0.502062i
$794$	−0.0310679	+	0.0494443i	−0.00110256	+	0.00175471i
$795$		0			0
$796$	−11.7834	+	2.68949i	−0.417653	+	0.0953266i
$797$	26.8505	+	12.9305i	0.951095	+	0.458023i	0.844070	−	0.536233i	$-0.180153\pi$
$797$	26.8505	+	12.9305i	0.951095	+	0.458023i	0.107025	+	0.994256i	$0.465868\pi$
$798$	13.0805	+	6.29926i	0.463046	+	0.222991i
$799$	−0.143745	+	0.0328089i	−0.00508534	+	0.00116070i
$800$		0			0
$801$	−36.9411	+	58.7914i	−1.30525	+	2.07729i
$802$	20.9608	−	26.2840i	0.740152	−	0.928121i
$803$	9.42451	+	14.9990i	0.332584	+	0.529304i
$804$	−18.2588	+	11.4728i	−0.643940	+	0.404614i
$805$		0			0
$806$	15.9772	+	7.69420i	0.562772	+	0.271017i
$807$	−19.3597	−	6.77426i	−0.681494	−	0.238465i
$808$	−1.79595	−	15.9395i	−0.0631812	−	0.560749i
$809$	−22.8571	−	2.57537i	−0.803612	−	0.0905453i	−0.299403	−	0.954127i	$-0.596787\pi$
$809$	−22.8571	−	2.57537i	−0.803612	−	0.0905453i	−0.504209	+	0.863582i	$0.668216\pi$
$810$		0			0
$811$			19.6076i			0.688516i	0.938875	+	0.344258i	$0.111869\pi$
$811$			19.6076i			0.688516i	−0.938875	+	0.344258i	$0.888131\pi$
$812$	−1.18006	+	7.92406i	−0.0414119	+	0.278080i
$813$	−2.07643	+	2.07643i	−0.0728236	+	0.0728236i
$814$	−18.7354	−	6.55581i	−0.656676	−	0.229781i
$815$		0			0
$816$	−8.76082	−	6.98652i	−0.306690	−	0.244577i
$817$	−0.927804	+	2.65151i	−0.0324598	+	0.0927646i
$818$	8.74954	+	25.0047i	0.305920	+	0.874270i
$819$	25.3351	−	20.2041i	0.885282	−	0.705988i
$820$		0			0
$821$	−3.20785	−	0.732172i	−0.111955	−	0.0255530i	0.166176	−	0.986096i	$-0.446858\pi$
$821$	−3.20785	−	0.732172i	−0.111955	−	0.0255530i	−0.278131	+	0.960543i	$0.589715\pi$
$822$	−14.0850	−	11.2324i	−0.491269	−	0.391774i
$823$	−16.4779	+	3.76096i	−0.574382	+	0.131099i	−0.499838	−	0.866119i	$-0.666607\pi$
$823$	−16.4779	+	3.76096i	−0.574382	+	0.131099i	−0.0745439	+	0.997218i	$0.523750\pi$
$824$	16.6804	−	16.6804i	0.581090	−	0.581090i
$825$		0			0
$826$	5.10588	−	1.78663i	0.177656	−	0.0621646i
$827$	−0.0579057	+	0.120242i	−0.00201358	+	0.00418124i	−0.901973	−	0.431792i	$-0.857881\pi$
$827$	−0.0579057	+	0.120242i	−0.00201358	+	0.00418124i	0.899960	+	0.435973i	$0.143596\pi$
$828$	11.2257	+	7.05358i	0.390120	+	0.245129i
$829$	28.0352	+	28.0352i	0.973704	+	0.973704i	0.999663	−	0.0259593i	$-0.00826403\pi$
$829$	28.0352	+	28.0352i	0.973704	+	0.973704i	−0.0259593	+	0.999663i	$0.508264\pi$
$830$		0			0
$831$	−5.28984	−	46.9486i	−0.183502	−	1.62863i
$832$	−25.2704	+	15.8784i	−0.876092	+	0.550485i
$833$	26.2998	+	6.00275i	0.911234	+	0.207983i
$834$	−7.83400	−	9.82352i	−0.271269	−	0.340161i
$835$		0			0
$836$	−20.0456	+	9.65345i	−0.693291	+	0.333871i
$837$	23.3385	−	2.62961i	0.806695	−	0.0908927i
$838$	4.58647	+	5.75126i	0.158437	+	0.198674i
$839$	−0.960023	+	2.74359i	−0.0331437	+	0.0947192i	−0.959266	−	0.282503i	$-0.908835\pi$
$839$	−0.960023	+	2.74359i	−0.0331437	+	0.0947192i	0.926123	+	0.377223i	$0.123121\pi$
$840$		0			0
$841$	−8.45001	+	27.7416i	−0.291380	+	0.956607i
$842$	15.5905	+	15.5905i	0.537285	+	0.537285i
$843$	−19.0572	−	39.5726i	−0.656364	−	1.36295i
$844$	−0.179623	+	1.59420i	−0.00618288	+	0.0548746i
$845$		0			0
$846$	−0.0586305	−	0.121748i	−0.00201576	−	0.00418577i
$847$	−25.7926	+	9.02522i	−0.886244	+	0.310110i
$848$	1.27564	+	0.143731i	0.0438058	+	0.00493573i
$849$	−5.74476	−	9.14273i	−0.197160	−	0.313778i
$850$		0			0
$851$	9.07268	−	1.02225i	0.311007	−	0.0350421i
$852$	−2.36177	−	10.3476i	−0.0809131	−	0.354503i
$853$	19.9191			0.682018			0.341009	−	0.940060i	$-0.389231\pi$
$853$	19.9191			0.682018			0.341009	+	0.940060i	$0.389231\pi$
$854$	−1.18836	−	5.20655i	−0.0406648	−	0.178164i
$855$		0			0
$856$	−11.1473	−	31.8571i	−0.381006	−	1.08885i
$857$	−17.6888	+	28.1515i	−0.604237	+	0.961638i	0.394843	+	0.918749i	$0.370799\pi$
$857$	−17.6888	+	28.1515i	−0.604237	+	0.961638i	−0.999080	+	0.0428889i	$0.986344\pi$
$858$		−	69.5018i		−	2.37275i
$859$	14.3941	+	9.04440i	0.491120	+	0.308591i	0.754727	−	0.656039i	$-0.227769\pi$
$859$	14.3941	+	9.04440i	0.491120	+	0.308591i	−0.263607	+	0.964630i	$0.584912\pi$
$860$		0			0
$861$	−7.13260	+	31.2500i	−0.243078	+	1.06500i
$862$	6.98469	−	30.6019i	0.237900	−	1.04231i
$863$	−1.07928	+	9.57890i	−0.0367392	+	0.326070i	0.961877	+	0.273482i	$0.0881754\pi$
$863$	−1.07928	+	9.57890i	−0.0367392	+	0.326070i	−0.998616	+	0.0525876i	$0.983253\pi$
$864$	−13.2666	+	27.5483i	−0.451338	+	0.937214i
$865$		0			0
$866$	19.5400	−	24.5024i	0.663996	−	0.832625i
$867$	−25.6969	+	20.4926i	−0.872712	+	0.695965i
$868$	−5.36823	+	2.58520i	−0.182210	+	0.0877475i
$869$	51.9599			1.76262
$870$		0			0
$871$	−32.6556			−1.10649
$872$	18.7282	−	9.01901i	0.634216	−	0.305422i
$873$	−34.8384	+	27.7827i	−1.17910	+	0.940301i
$874$	−5.60833	+	7.03263i	−0.189705	+	0.237882i
$875$		0			0
$876$	4.20332	−	8.72828i	0.142017	−	0.294901i
$877$	−2.98854	+	26.5240i	−0.100916	+	0.895652i	0.836625	+	0.547776i	$0.184525\pi$
$877$	−2.98854	+	26.5240i	−0.100916	+	0.895652i	−0.937541	+	0.347876i	$0.886903\pi$
$878$	3.63974	−	15.9467i	0.122835	−	0.538176i
$879$	−15.8875	+	69.6075i	−0.535871	+	2.34780i
$880$		0			0
$881$	19.0940	+	11.9976i	0.643294	+	0.404209i	0.813798	−	0.581148i	$-0.197396\pi$
$881$	19.0940	+	11.9976i	0.643294	+	0.404209i	−0.170503	+	0.985357i	$0.554539\pi$
$882$			24.7235i			0.832482i
$883$	−1.27154	+	2.02364i	−0.0427907	+	0.0681010i	−0.867435	−	0.497551i	$-0.834233\pi$
$883$	−1.27154	+	2.02364i	−0.0427907	+	0.0681010i	0.824644	+	0.565652i	$0.191376\pi$
$884$	8.60237	+	24.5842i	0.289329	+	0.826855i
$885$		0			0
$886$	−7.04143	−	30.8505i	−0.236561	−	1.03644i
$887$	−24.2760			−0.815109			−0.407554	−	0.913181i	$-0.633618\pi$
$887$	−24.2760			−0.815109			−0.407554	+	0.913181i	$0.633618\pi$
$888$	6.95422	+	30.4684i	0.233368	+	1.02245i
$889$	−1.02927	+	0.115971i	−0.0345206	+	0.00388953i
$890$		0			0
$891$	−4.28937	−	6.82649i	−0.143699	−	0.228696i
$892$	−9.27753	−	1.04533i	−0.310635	−	0.0350001i
$893$	−0.0984546	+	0.0344507i	−0.00329466	+	0.00115285i
$894$	9.64122	+	20.0202i	0.322451	+	0.669576i
$895$		0			0
$896$	0.645054	−	5.72501i	0.0215497	−	0.191259i
$897$	13.8707	+	28.8029i	0.463130	+	0.961700i
$898$	3.17594	+	3.17594i	0.105982	+	0.105982i
$899$	−20.5985	+	6.39363i	−0.686998	+	0.213240i
$900$		0			0
$901$	3.07031	−	8.77445i	0.102287	−	0.292319i
$902$	26.9194	+	33.7558i	0.896317	+	1.12395i
$903$	2.92991	−	0.330122i	0.0975013	−	0.0109858i
$904$	−39.4109	+	18.9793i	−1.31079	+	0.631242i
$905$		0			0
$906$	16.6513	+	20.8801i	0.553203	+	0.693694i
$907$	37.8499	+	8.63900i	1.25679	+	0.286853i	0.798523	−	0.601964i	$-0.205615\pi$
$907$	37.8499	+	8.63900i	1.25679	+	0.286853i	0.458262	+	0.888817i	$0.348472\pi$
$908$	18.7041	−	11.7525i	0.620716	−	0.390022i
$909$	−3.06886	−	27.2369i	−0.101788	−	0.903391i
$910$		0			0
$911$	42.3681	+	42.3681i	1.40372	+	1.40372i	0.787850	+	0.615867i	$0.211194\pi$
$911$	42.3681	+	42.3681i	1.40372	+	1.40372i	0.615867	+	0.787850i	$0.288806\pi$
$912$	−6.71228	−	4.21761i	−0.222266	−	0.139659i
$913$	−35.5708	+	73.8635i	−1.17722	+	2.44453i
$914$	−4.66615	+	1.63276i	−0.154343	+	0.0540068i
$915$		0			0
$916$	−4.05330	+	4.05330i	−0.133925	+	0.133925i
$917$	19.9973	−	4.56424i	0.660368	−	0.150725i
$918$	−23.7048	−	18.9040i	−0.782376	−	0.623924i
$919$	−35.7935	−	8.16963i	−1.18072	−	0.269491i	−0.413274	−	0.910607i	$-0.635615\pi$
$919$	−35.7935	−	8.16963i	−1.18072	−	0.269491i	−0.767444	+	0.641115i	$0.778472\pi$
$920$		0			0
$921$	−49.9374	+	39.8237i	−1.64549	+	1.31224i
$922$	3.40991	+	9.74496i	0.112299	+	0.320933i
$923$	5.30854	−	15.1709i	0.174733	−	0.499358i
$924$	18.2575	+	14.5598i	0.600627	+	0.478984i
$925$		0			0
$926$	−4.69781	−	1.64384i	−0.154380	−	0.0540198i
$927$	28.5030	−	28.5030i	0.936161	−	0.936161i
$928$	7.21951	−	27.1351i	0.236992	−	0.890753i
$929$		−	28.6797i		−	0.940951i	−0.882413	−	0.470476i	$-0.844082\pi$
$929$		−	28.6797i		−	0.940951i	0.882413	−	0.470476i	$-0.155918\pi$
$930$		0			0
$931$	18.9643	+	2.13676i	0.621530	+	0.0700296i
$932$	−2.34128	−	20.7794i	−0.0766912	−	0.680653i
$933$	−85.4925	−	29.9151i	−2.79890	−	0.979377i
$934$	3.99714	+	1.92492i	0.130790	+	0.0629854i
$935$		0			0
$936$	−58.1893	+	36.5628i	−1.90198	+	1.19509i
$937$	11.0928	+	17.6540i	0.362385	+	0.576732i	0.977300	−	0.211861i	$-0.0679525\pi$
$937$	11.0928	+	17.6540i	0.362385	+	0.576732i	−0.614915	+	0.788594i	$0.710810\pi$
$938$	−6.01290	+	7.53994i	−0.196328	+	0.246188i
$939$	−38.6107	+	61.4485i	−1.26001	+	2.00530i
$940$		0			0
$941$	25.0472	−	5.71686i	0.816515	−	0.186364i	0.206187	−	0.978513i	$-0.433895\pi$
$941$	25.0472	−	5.71686i	0.816515	−	0.186364i	0.610328	+	0.792148i	$0.291037\pi$
$942$	10.0263	+	4.82839i	0.326673	+	0.157318i
$943$	−17.8927	−	8.61666i	−0.582666	−	0.280597i
$944$	−2.87963	+	0.657257i	−0.0937241	+	0.0213919i
$945$		0			0
$946$	2.11295	−	3.36275i	0.0686980	−	0.109332i
$947$	−35.0919	+	44.0039i	−1.14033	+	1.42993i	−0.253809	+	0.967254i	$0.581683\pi$
$947$	−35.0919	+	44.0039i	−1.14033	+	1.42993i	−0.886526	+	0.462680i	$0.846888\pi$
$948$	−15.1184	−	24.0607i	−0.491021	−	0.781456i
$949$	12.4219	−	7.80519i	0.403232	−	0.253367i
$950$		0			0
$951$	−60.7902	−	29.2750i	−1.97126	−	0.949307i
$952$	20.9019	+	7.31391i	0.677436	+	0.237045i
$953$	1.11505	+	9.89638i	0.0361202	+	0.320575i	0.998760	+	0.0497894i	$0.0158550\pi$
$953$	1.11505	+	9.89638i	0.0361202	+	0.320575i	−0.962640	+	0.270786i	$0.912716\pi$
$954$	8.46626	+	0.953919i	0.274105	+	0.0308843i
$955$		0			0
$956$		−	10.3865i		−	0.335925i
$957$	57.6048	+	61.8638i	1.86210	+	1.99977i
$958$	21.3718	−	21.3718i	0.690493	−	0.690493i
$959$	8.65204	+	3.02748i	0.279389	+	0.0977624i
$960$		0			0
$961$	11.6958	+	9.32706i	0.377283	+	0.300873i
$962$	−5.42939	+	15.5163i	−0.175050	+	0.500265i
$963$	−19.0481	−	54.4365i	−0.613818	−	1.75419i
$964$	16.7681	−	13.3721i	0.540065	−	0.430688i
$965$		0			0
$966$	9.20440	+	2.10084i	0.296147	+	0.0675935i
$967$	27.7417	+	22.1233i	0.892114	+	0.711437i	0.958115	−	0.286383i	$-0.0924528\pi$
$967$	27.7417	+	22.1233i	0.892114	+	0.711437i	−0.0660016	+	0.997820i	$0.521024\pi$
$968$	56.4989	−	12.8955i	1.81594	−	0.414477i
$969$	−40.5925	+	40.5925i	−1.30402	+	1.30402i
$970$		0			0
$971$	−21.6352	+	7.57047i	−0.694306	+	0.242948i	−0.654282	−	0.756251i	$-0.727029\pi$
$971$	−21.6352	+	7.57047i	−0.694306	+	0.242948i	−0.0400236	+	0.999199i	$0.512743\pi$
$972$	6.21171	−	12.8987i	0.199241	−	0.413727i
$973$	5.41320	+	3.40134i	0.173539	+	0.109042i
$974$	3.56904	+	3.56904i	0.114359	+	0.114359i
$975$		0			0
$976$	0.326490	+	2.89768i	0.0104507	+	0.0927524i
$977$	0.884054	−	0.555488i	0.0282834	−	0.0177716i	−0.517816	−	0.855492i	$-0.673255\pi$
$977$	0.884054	−	0.555488i	0.0282834	−	0.0177716i	0.546100	+	0.837720i	$0.316112\pi$
$978$	−15.7854	−	3.60292i	−0.504762	−	0.115209i
$979$	−47.2438	−	59.2419i	−1.50992	−	1.89338i
$980$		0			0
$981$	32.0021	−	15.4114i	1.02175	−	0.492048i
$982$	−2.24751	+	0.253233i	−0.0717209	+	0.00808100i
$983$	16.0672	+	20.1477i	0.512465	+	0.642611i	0.968990	−	0.247100i	$-0.0794776\pi$
$983$	16.0672	+	20.1477i	0.512465	+	0.642611i	−0.456525	+	0.889710i	$0.650906\pi$
$984$	22.4517	−	64.1633i	0.715734	−	2.04545i
$985$		0			0
$986$	24.6396	+	12.9668i	0.784686	+	0.412948i
$987$	0.0774143	+	0.0774143i	0.00246412	+	0.00246412i
$988$	7.99479	+	16.6014i	0.254348	+	0.528159i
$989$	−0.204532	+	1.81528i	−0.00650375	+	0.0577224i
$990$		0			0
$991$	−10.0068	−	20.7794i	−0.317877	−	0.660078i	0.679405	−	0.733764i	$-0.262238\pi$
$991$	−10.0068	−	20.7794i	−0.317877	−	0.660078i	−0.997282	+	0.0736856i	$0.976524\pi$
$992$	19.7111	−	6.89723i	0.625830	−	0.218987i
$993$	−2.77399	−	0.312553i	−0.0880299	−	0.00991858i
$994$	−2.52539	−	4.01914i	−0.0801005	−	0.127479i
$995$		0			0
$996$	44.5532	−	5.01994i	1.41172	−	0.159063i
$997$	1.39888	+	6.12892i	0.0443031	+	0.194105i	0.992237	−	0.124363i	$-0.0396888\pi$
$997$	1.39888	+	6.12892i	0.0443031	+	0.194105i	−0.947934	+	0.318468i	$0.896832\pi$
$998$	21.8358			0.691199
$999$	4.84465	+	21.2258i	0.153278	+	0.671554i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	725.2.y.b.282.5		156
5.2	odd	4		145.2.t.a.108.5	yes	156
5.3	odd	4		725.2.bd.b.543.9		156
5.4	even	2		145.2.o.a.137.9	yes	156
29.18	odd	28		725.2.bd.b.482.9		156
145.18	even	28	inner	725.2.y.b.18.5		156
145.47	even	28		145.2.o.a.18.9	✓	156
145.134	odd	28		145.2.t.a.47.5	yes	156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
145.2.o.a.18.9	✓	156	145.47	even	28
145.2.o.a.137.9	yes	156	5.4	even	2
145.2.t.a.47.5	yes	156	145.134	odd	28
145.2.t.a.108.5	yes	156	5.2	odd	4
725.2.y.b.18.5		156	145.18	even	28	inner
725.2.y.b.282.5		156	1.1	even	1	trivial
725.2.bd.b.482.9		156	29.18	odd	28
725.2.bd.b.543.9		156	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	725.y (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.871464 + 0.419675i) q^{2} +(-2.22031 + 1.77064i) q^{3} +(-0.663657 + 0.832199i) q^{4} +(1.19183 - 2.47485i) q^{6} +(-0.156487 + 1.38886i) q^{7} +(0.659568 - 2.88975i) q^{8} +(1.12705 - 4.93793i) q^{9} +(4.68013 + 2.94072i) q^{11} -3.02283i q^{12} +(2.43545 - 3.87599i) q^{13} +(-0.446497 - 1.27601i) q^{14} +(0.164256 + 0.719651i) q^{16} +5.34543 q^{17} +(1.09014 + 4.77622i) q^{18} +(3.75785 - 0.423408i) q^{19} +(-2.11171 - 3.36077i) q^{21} +(-5.31271 - 0.598599i) q^{22} +(2.32115 - 0.812207i) q^{23} +(3.65226 + 7.58400i) q^{24} +(-0.495748 + 4.39988i) q^{26} +(2.54434 + 5.28338i) q^{27} +(-1.05195 - 1.05195i) q^{28} +(-3.20546 - 4.32724i) q^{29} +(1.32279 - 3.78032i) q^{31} +(3.25097 + 4.07659i) q^{32} +(-15.5983 + 1.75750i) q^{33} +(-4.65835 + 2.24334i) q^{34} +(3.36136 + 4.21502i) q^{36} +(3.61961 + 0.826152i) q^{37} +(-3.09714 + 1.94606i) q^{38} +(1.45553 + 12.9182i) q^{39} +(-5.71038 - 5.71038i) q^{41} +(3.25072 + 2.04256i) q^{42} +(-0.322307 + 0.669277i) q^{43} +(-5.55327 + 1.94317i) q^{44} +(-1.68194 + 1.68194i) q^{46} +(-0.0268913 + 0.00613776i) q^{47} +(-1.63894 - 1.30701i) q^{48} +(4.92005 + 1.12297i) q^{49} +(-11.8685 + 9.46480i) q^{51} +(1.60930 + 4.59910i) q^{52} +(0.574381 - 1.64149i) q^{53} +(-4.43460 - 3.53648i) q^{54} +(3.91025 + 1.36826i) q^{56} +(-7.59388 + 7.59388i) q^{57} +(4.60948 + 2.42578i) q^{58} +4.00143i q^{59} +(3.92555 + 0.442303i) q^{61} +(0.433740 + 3.84955i) q^{62} +(6.68171 + 2.33803i) q^{63} +(-5.87407 - 2.82880i) q^{64} +(12.8558 - 8.07781i) q^{66} +(-3.79538 - 6.04031i) q^{67} +(-3.54753 + 4.44846i) q^{68} +(-3.71555 + 5.91327i) q^{69} +(3.42315 - 0.781312i) q^{71} +(-13.5260 - 6.51379i) q^{72} +(2.88745 + 1.39052i) q^{73} +(-3.50108 + 0.799098i) q^{74} +(-2.14156 + 3.40828i) q^{76} +(-4.81662 + 6.03986i) q^{77} +(-6.68988 - 10.6469i) q^{78} +(7.95966 - 5.00139i) q^{79} +(-1.31416 - 0.632868i) q^{81} +(7.37289 + 2.57989i) q^{82} +(1.66068 + 14.7389i) q^{83} +(4.19829 + 0.473033i) q^{84} -0.718515i q^{86} +(14.7791 + 3.93209i) q^{87} +(11.5848 - 11.5848i) q^{88} +(-12.9395 - 4.52773i) q^{89} +(5.00209 + 3.98903i) q^{91} +(-0.864532 + 2.47069i) q^{92} +(3.75656 + 10.7356i) q^{93} +(0.0208589 - 0.0166344i) q^{94} +(-14.4363 - 3.29499i) q^{96} +(-6.87837 - 5.48532i) q^{97} +(-4.75893 + 1.08620i) q^{98} +(19.7958 - 19.7958i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q + 8 q^{2} + 14 q^{3} - 22 q^{4} - 28 q^{6} + 10 q^{7} - 4 q^{8} + 10 q^{9} - 20 q^{11} + 4 q^{14} - 34 q^{16} + 48 q^{17} + 94 q^{18} - 16 q^{21} + 6 q^{22} + 10 q^{23} + 56 q^{24} + 36 q^{26} + 56 q^{27}+ \cdots + 76 q^{99}+O(q^{100}) \) 156 * q + 8 * q^2 + 14 * q^3 - 22 * q^4 - 28 * q^6 + 10 * q^7 - 4 * q^8 + 10 * q^9 - 20 * q^11 + 4 * q^14 - 34 * q^16 + 48 * q^17 + 94 * q^18 - 16 * q^21 + 6 * q^22 + 10 * q^23 + 56 * q^24 + 36 * q^26 + 56 * q^27 - 8 * q^28 - 8 * q^31 - 28 * q^32 + 14 * q^33 - 24 * q^34 + 78 * q^36 - 28 * q^37 - 92 * q^38 + 16 * q^39 - 22 * q^41 + 10 * q^42 + 42 * q^43 - 112 * q^44 + 4 * q^46 + 14 * q^47 - 154 * q^48 + 84 * q^49 - 28 * q^51 + 166 * q^52 - 14 * q^53 + 4 * q^56 - 12 * q^57 - 126 * q^58 - 46 * q^61 - 84 * q^62 - 38 * q^63 - 30 * q^64 - 48 * q^66 + 46 * q^67 + 44 * q^68 - 124 * q^69 - 28 * q^71 - 60 * q^72 - 130 * q^73 + 112 * q^74 - 48 * q^76 + 44 * q^77 + 210 * q^78 - 4 * q^79 + 58 * q^81 - 72 * q^82 - 46 * q^83 + 120 * q^84 + 144 * q^87 - 40 * q^88 + 46 * q^89 - 28 * q^91 + 14 * q^92 + 6 * q^93 - 84 * q^94 - 28 * q^96 - 154 * q^97 - 98 * q^98 + 76 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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