LMFDB - Embedded newform 675.2.ba.c.518.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(32,675)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([10, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("675.32"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.ba (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [288] 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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$24$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			518.17
Character	$\chi$	$=$	675.518
Dual form			675.2.ba.c.632.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.01137 + 0.0884834i) q^{2} +(-1.35601 + 1.07761i) q^{3} +(-0.954575 - 0.168317i) q^{4} +(-1.46678 + 0.969879i) q^{6} +(0.0780926 + 0.0546810i) q^{7} +(-2.91182 - 0.780219i) q^{8} +(0.677513 - 2.92249i) q^{9} +(1.08290 - 2.97524i) q^{11} +(1.47579 - 0.800420i) q^{12} +(0.0973814 + 1.11307i) q^{13} +(0.0741421 + 0.0622126i) q^{14} +(-1.05420 - 0.383697i) q^{16} +(5.36631 - 1.43790i) q^{17} +(0.943809 - 2.89578i) q^{18} +(1.63705 - 0.945151i) q^{19} +(-0.164819 + 0.0100055i) q^{21} +(1.35847 - 2.91325i) q^{22} +(-1.46883 - 2.09771i) q^{23} +(4.78922 - 2.07982i) q^{24} +1.13435i q^{26} +(2.23060 + 4.69302i) q^{27} +(-0.0653414 - 0.0653414i) q^{28} +(2.20954 - 1.85402i) q^{29} +(1.90673 - 10.8136i) q^{31} +(4.43196 + 2.06666i) q^{32} +(1.73773 + 5.20139i) q^{33} +(5.55456 - 0.979419i) q^{34} +(-1.13864 + 2.67570i) q^{36} +(-0.764839 - 2.85442i) q^{37} +(1.73929 - 0.811046i) q^{38} +(-1.33151 - 1.40440i) q^{39} +(-0.907830 + 1.08191i) q^{41} +(-0.167578 - 0.00446450i) q^{42} +(4.72655 + 10.1361i) q^{43} +(-1.53449 + 2.65782i) q^{44} +(-1.29992 - 2.25153i) q^{46} +(0.833027 - 1.18969i) q^{47} +(1.84298 - 0.615719i) q^{48} +(-2.39103 - 6.56931i) q^{49} +(-5.72726 + 7.73259i) q^{51} +(0.0943918 - 1.07890i) q^{52} +(4.90478 - 4.90478i) q^{53} +(1.84070 + 4.94375i) q^{54} +(-0.184728 - 0.220150i) q^{56} +(-1.20135 + 3.04573i) q^{57} +(2.39871 - 1.67959i) q^{58} +(-5.36820 + 1.95387i) q^{59} +(-0.783208 - 4.44180i) q^{61} +(2.88524 - 10.7679i) q^{62} +(0.212714 - 0.191178i) q^{63} +(6.24259 + 3.60416i) q^{64} +(1.29725 + 5.41429i) q^{66} +(-10.2362 + 0.895552i) q^{67} +(-5.36457 + 0.469339i) q^{68} +(4.25226 + 1.26168i) q^{69} +(-5.04685 - 2.91380i) q^{71} +(-4.25298 + 7.98116i) q^{72} +(0.754018 - 2.81403i) q^{73} +(-0.520967 - 2.95455i) q^{74} +(-1.72177 + 0.626673i) q^{76} +(0.247255 - 0.173130i) q^{77} +(-1.22238 - 1.53818i) q^{78} +(-5.79636 - 6.90783i) q^{79} +(-8.08195 - 3.96006i) q^{81} +(-1.01388 + 1.01388i) q^{82} +(1.07463 - 12.2831i) q^{83} +(0.159016 + 0.0181909i) q^{84} +(3.88341 + 10.6696i) q^{86} +(-0.998236 + 4.89509i) q^{87} +(-5.47454 + 7.81845i) q^{88} +(5.65298 + 9.79125i) q^{89} +(-0.0532593 + 0.0922477i) q^{91} +(1.04903 + 2.24965i) q^{92} +(9.06731 + 16.7180i) q^{93} +(0.947766 - 1.12950i) q^{94} +(-8.23681 + 1.97352i) q^{96} +(-1.82485 + 0.850941i) q^{97} +(-1.83694 - 6.85557i) q^{98} +(-7.96144 - 5.18053i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q + 24 q^{6} + 36 q^{11} + 48 q^{21} - 192 q^{36} - 180 q^{41} - 60 q^{51} - 288 q^{56} + 72 q^{61} + 144 q^{71} + 216 q^{76} + 24 q^{81} - 36 q^{91} - 168 q^{96}+O(q^{100}) $ 288 * q + 24 * q^6 + 36 * q^11 + 48 * q^21 - 192 * q^36 - 180 * q^41 - 60 * q^51 - 288 * q^56 + 72 * q^61 + 144 * q^71 + 216 * q^76 + 24 * q^81 - 36 * q^91 - 168 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.01137	+	0.0884834i	0.715147	+	0.0625672i	0.438921	−	0.898526i	$-0.355361\pi$
$2$	1.01137	+	0.0884834i	0.715147	+	0.0625672i	0.276226	+	0.961093i	$0.410916\pi$
$3$	−1.35601	+	1.07761i	−0.782891	+	0.622158i
$3$	−1.35601	+	1.07761i	−0.782891	+	0.622158i
$4$	−0.954575	−	0.168317i	−0.477287	−	0.0841586i
$5$		0			0
$5$		0			0
$6$	−1.46678	+	0.969879i	−0.598809	+	0.395951i
$7$	0.0780926	+	0.0546810i	0.0295162	+	0.0206675i	0.588241	−	0.808685i	$-0.299820\pi$
$7$	0.0780926	+	0.0546810i	0.0295162	+	0.0206675i	−0.558725	+	0.829353i	$0.688709\pi$
$8$	−2.91182	−	0.780219i	−1.02948	−	0.275849i
$9$	0.677513	−	2.92249i	0.225838	−	0.974165i
$10$		0			0
$11$	1.08290	−	2.97524i	0.326506	−	0.897068i	−0.662483	−	0.749077i	$-0.730497\pi$
$11$	1.08290	−	2.97524i	0.326506	−	0.897068i	0.988989	−	0.147991i	$-0.0472806\pi$
$12$	1.47579	−	0.800420i	0.426024	−	0.231061i
$13$	0.0973814	+	1.11307i	0.0270087	+	0.308711i	0.997668	+	0.0682525i	$0.0217423\pi$
$13$	0.0973814	+	1.11307i	0.0270087	+	0.308711i	−0.970659	+	0.240459i	$0.922702\pi$
$14$	0.0741421	+	0.0622126i	0.0198153	+	0.0166270i
$15$		0			0
$16$	−1.05420	−	0.383697i	−0.263550	−	0.0959243i
$17$	5.36631	−	1.43790i	1.30152	−	0.348742i	0.459496	−	0.888180i	$-0.348030\pi$
$17$	5.36631	−	1.43790i	1.30152	−	0.348742i	0.842025	+	0.539438i	$0.181363\pi$
$18$	0.943809	−	2.89578i	0.222458	−	0.682541i
$19$	1.63705	−	0.945151i	0.375565	−	0.216832i	−0.300322	−	0.953838i	$-0.597094\pi$
$19$	1.63705	−	0.945151i	0.375565	−	0.216832i	0.675887	+	0.737005i	$0.263761\pi$
$20$		0			0
$21$	−0.164819	+	0.0100055i	−0.0359664	+	0.00218337i
$22$	1.35847	−	2.91325i	0.289627	−	0.621107i
$23$	−1.46883	−	2.09771i	−0.306272	−	0.437402i	0.636281	−	0.771457i	$-0.280472\pi$
$23$	−1.46883	−	2.09771i	−0.306272	−	0.437402i	−0.942554	+	0.334055i	$0.891583\pi$
$24$	4.78922	−	2.07982i	0.977595	−	0.424541i
$25$		0			0
$26$			1.13435i			0.222464i
$27$	2.23060	+	4.69302i	0.429279	+	0.903172i
$28$	−0.0653414	−	0.0653414i	−0.0123484	−	0.0123484i
$29$	2.20954	−	1.85402i	0.410301	−	0.344283i	−0.414158	−	0.910205i	$-0.635924\pi$
$29$	2.20954	−	1.85402i	0.410301	−	0.344283i	0.824459	+	0.565922i	$0.191480\pi$
$30$		0			0
$31$	1.90673	−	10.8136i	0.342459	−	1.94218i	0.00743407	−	0.999972i	$-0.497634\pi$
$31$	1.90673	−	10.8136i	0.342459	−	1.94218i	0.335025	−	0.942209i	$-0.391255\pi$
$32$	4.43196	+	2.06666i	0.783467	+	0.365336i
$33$	1.73773	+	5.20139i	0.302500	+	0.905445i
$34$	5.55456	−	0.979419i	0.952599	−	0.167969i
$35$		0			0
$36$	−1.13864	+	2.67570i	−0.189774	+	0.445950i
$37$	−0.764839	−	2.85442i	−0.125739	−	0.469263i	0.874126	−	0.485699i	$-0.161435\pi$
$37$	−0.764839	−	2.85442i	−0.125739	−	0.469263i	−0.999865	+	0.0164356i	$0.994768\pi$
$38$	1.73929	−	0.811046i	0.282151	−	0.131569i
$39$	−1.33151	−	1.40440i	−0.213212	−	0.224884i
$40$		0			0
$41$	−0.907830	+	1.08191i	−0.141779	+	0.168966i	−0.832261	−	0.554384i	$-0.812954\pi$
$41$	−0.907830	+	1.08191i	−0.141779	+	0.168966i	0.690482	+	0.723350i	$0.257398\pi$
$42$	−0.167578	−	0.00446450i	−0.0258579	−	0.000688887i
$43$	4.72655	+	10.1361i	0.720792	+	1.54574i	0.833749	+	0.552144i	$0.186190\pi$
$43$	4.72655	+	10.1361i	0.720792	+	1.54574i	−0.112957	+	0.993600i	$0.536032\pi$
$44$	−1.53449	+	2.65782i	−0.231333	+	0.400681i
$45$		0			0
$46$	−1.29992	−	2.25153i	−0.191663	−	0.331970i
$47$	0.833027	−	1.18969i	0.121509	−	0.173534i	−0.753789	−	0.657116i	$-0.771776\pi$
$47$	0.833027	−	1.18969i	0.121509	−	0.173534i	0.875299	+	0.483583i	$0.160665\pi$
$48$	1.84298	−	0.615719i	0.266011	−	0.0888714i
$49$	−2.39103	−	6.56931i	−0.341576	−	0.938473i
$50$		0			0
$51$	−5.72726	+	7.73259i	−0.801977	+	1.08278i
$52$	0.0943918	−	1.07890i	0.0130898	−	0.149617i
$53$	4.90478	−	4.90478i	0.673723	−	0.673723i	−0.284849	−	0.958572i	$-0.591944\pi$
$53$	4.90478	−	4.90478i	0.673723	−	0.673723i	0.958572	+	0.284849i	$0.0919435\pi$
$54$	1.84070	+	4.94375i	0.250488	+	0.672760i
$55$		0			0
$56$	−0.184728	−	0.220150i	−0.0246853	−	0.0294188i
$57$	−1.20135	+	3.04573i	−0.159122	+	0.403417i
$58$	2.39871	−	1.67959i	0.314966	−	0.220542i
$59$	−5.36820	+	1.95387i	−0.698880	+	0.254372i	−0.666933	−	0.745118i	$-0.732393\pi$
$59$	−5.36820	+	1.95387i	−0.698880	+	0.254372i	−0.0319475	+	0.999490i	$0.510171\pi$
$60$		0			0
$61$	−0.783208	−	4.44180i	−0.100280	−	0.568714i	−0.993001	−	0.118105i	$-0.962318\pi$
$61$	−0.783208	−	4.44180i	−0.100280	−	0.568714i	0.892722	−	0.450609i	$-0.148793\pi$
$62$	2.88524	−	10.7679i	0.366425	−	1.36752i
$63$	0.212714	−	0.191178i	0.0267994	−	0.0240862i
$64$	6.24259	+	3.60416i	0.780324	+	0.450520i
$65$		0			0
$66$	1.29725	+	5.41429i	0.159680	+	0.666453i
$67$	−10.2362	+	0.895552i	−1.25055	+	0.109409i	−0.693125	−	0.720817i	$-0.743767\pi$
$67$	−10.2362	+	0.895552i	−1.25055	+	0.109409i	−0.557427	+	0.830226i	$0.688211\pi$
$68$	−5.36457	+	0.469339i	−0.650549	+	0.0569157i
$69$	4.25226	+	1.26168i	0.511912	+	0.151889i
$70$		0			0
$71$	−5.04685	−	2.91380i	−0.598951	−	0.345805i	0.169678	−	0.985500i	$-0.445727\pi$
$71$	−5.04685	−	2.91380i	−0.598951	−	0.345805i	−0.768629	+	0.639695i	$0.779061\pi$
$72$	−4.25298	+	7.98116i	−0.501218	+	0.940589i
$73$	0.754018	−	2.81403i	0.0882512	−	0.329358i	−0.907659	−	0.419709i	$-0.862132\pi$
$73$	0.754018	−	2.81403i	0.0882512	−	0.329358i	0.995910	+	0.0903509i	$0.0287989\pi$
$74$	−0.520967	−	2.95455i	−0.0605611	−	0.343459i
$75$		0			0
$76$	−1.72177	+	0.626673i	−0.197501	+	0.0718843i
$77$	0.247255	−	0.173130i	0.0281774	−	0.0197300i
$78$	−1.22238	−	1.53818i	−0.138408	−	0.174165i
$79$	−5.79636	−	6.90783i	−0.652141	−	0.777191i	0.334094	−	0.942540i	$-0.391570\pi$
$79$	−5.79636	−	6.90783i	−0.652141	−	0.777191i	−0.986235	+	0.165348i	$0.947125\pi$
$80$		0			0
$81$	−8.08195	−	3.96006i	−0.897995	−	0.440006i
$82$	−1.01388	+	1.01388i	−0.111965	+	0.111965i
$83$	1.07463	−	12.2831i	0.117956	−	1.34824i	−0.674483	−	0.738291i	$-0.735633\pi$
$83$	1.07463	−	12.2831i	0.117956	−	1.34824i	0.792439	−	0.609952i	$-0.208811\pi$
$84$	0.159016	+	0.0181909i	0.0173501	+	0.00198479i
$85$		0			0
$86$	3.88341	+	10.6696i	0.418759	+	1.15053i
$87$	−0.998236	+	4.89509i	−0.107022	+	0.524808i
$88$	−5.47454	+	7.81845i	−0.583588	+	0.833450i
$89$	5.65298	+	9.79125i	0.599215	+	1.03787i	0.992937	+	0.118641i	$0.0378538\pi$
$89$	5.65298	+	9.79125i	0.599215	+	1.03787i	−0.393722	+	0.919229i	$0.628813\pi$
$90$		0			0
$91$	−0.0532593	+	0.0922477i	−0.00558309	+	0.00967019i
$92$	1.04903	+	2.24965i	0.109369	+	0.234542i
$93$	9.06731	+	16.7180i	0.940237	+	1.73358i
$94$	0.947766	−	1.12950i	0.0977546	−	0.116499i
$95$		0			0
$96$	−8.23681	+	1.97352i	−0.840666	+	0.201422i
$97$	−1.82485	+	0.850941i	−0.185285	+	0.0864000i	−0.513047	−	0.858360i	$-0.671483\pi$
$97$	−1.82485	+	0.850941i	−0.185285	+	0.0864000i	0.327762	+	0.944760i	$0.393706\pi$
$98$	−1.83694	−	6.85557i	−0.185559	−	0.692517i
$99$	−7.96144	−	5.18053i	−0.800155	−	0.520663i
$100$		0			0
$101$	15.4928	−	2.73179i	1.54159	−	0.271824i	0.662713	−	0.748874i	$-0.269405\pi$
$101$	15.4928	−	2.73179i	1.54159	−	0.271824i	0.878876	+	0.477050i	$0.158294\pi$
$102$	−6.47659	+	7.31375i	−0.641278	+	0.724169i
$103$	−8.32832	−	3.88356i	−0.820614	−	0.382659i	−0.0334791	−	0.999439i	$-0.510659\pi$
$103$	−8.32832	−	3.88356i	−0.820614	−	0.382659i	−0.787135	+	0.616781i	$0.788436\pi$
$104$	0.584885	−	3.31705i	0.0573527	−	0.325263i
$105$		0			0
$106$	5.39454	−	4.52656i	0.523964	−	0.439658i
$107$	4.86588	+	4.86588i	0.470402	+	0.470402i	0.902045	−	0.431643i	$-0.142066\pi$
$107$	4.86588	+	4.86588i	0.470402	+	0.470402i	−0.431643	+	0.902045i	$0.642066\pi$
$108$	−1.33935	−	4.85529i	−0.128879	−	0.467200i
$109$			7.83089i			0.750063i	0.927012	+	0.375031i	$0.122368\pi$
$109$			7.83089i			0.750063i	−0.927012	+	0.375031i	$0.877632\pi$
$110$		0			0
$111$	4.11308	+	3.04641i	0.390396	+	0.289153i
$112$	−0.0613442	−	0.0876086i	−0.00579648	−	0.00827823i
$113$	−7.68065	+	16.4712i	−0.722535	+	1.54948i	0.109021	+	0.994039i	$0.465229\pi$
$113$	−7.68065	+	16.4712i	−0.722535	+	1.54948i	−0.831556	+	0.555442i	$0.812549\pi$
$114$	−1.48450	+	2.97406i	−0.139036	+	0.278547i
$115$		0			0
$116$	−2.42123	+	1.39790i	−0.224806	+	0.129792i
$117$	3.31893	+	0.469526i	0.306835	+	0.0434077i
$118$	−5.60212	+	1.50108i	−0.515717	+	0.138186i
$119$	0.497695	+	0.181146i	0.0456236	+	0.0166056i
$120$		0			0
$121$	0.747114	+	0.626903i	0.0679195	+	0.0569912i
$122$	−0.399088	−	4.56160i	−0.0361318	−	0.412988i
$123$	0.0651476	−	2.44536i	0.00587416	−	0.220491i
$124$	−3.64023	+	10.0015i	−0.326903	+	0.898158i
$125$		0			0
$126$	0.232048	−	0.174530i	0.0206725	−	0.0155484i
$127$	−18.4918	−	4.95487i	−1.64088	−	0.439673i	−0.683843	−	0.729629i	$-0.739693\pi$
$127$	−18.4918	−	4.95487i	−1.64088	−	0.439673i	−0.957040	+	0.289956i	$0.906359\pi$
$128$	−2.01684	−	1.41221i	−0.178265	−	0.124823i
$129$	−17.3320	−	8.65128i	−1.52600	−	0.761702i
$130$		0			0
$131$	19.0660	+	3.36186i	1.66581	+	0.293727i	0.925558	−	0.378605i	$-0.123596\pi$
$131$	19.0660	+	3.36186i	1.66581	+	0.293727i	0.740250	+	0.672332i	$0.234707\pi$
$132$	−0.783308	−	5.25760i	−0.0681782	−	0.457616i
$133$	0.179523	+	0.0157062i	0.0155666	+	0.00136190i
$134$	−10.4318			−0.901174
$135$		0			0
$136$	−16.7476			−1.43609
$137$	1.96913	+	0.172277i	0.168234	+	0.0147186i	0.170962	−	0.985278i	$-0.445313\pi$
$137$	1.96913	+	0.172277i	0.168234	+	0.0147186i	−0.00272729	+	0.999996i	$0.500868\pi$
$138$	4.18897	+	1.65228i	0.356589	+	0.140652i
$139$	−20.6650	−	3.64379i	−1.75278	−	0.309062i	−0.797182	−	0.603739i	$-0.793677\pi$
$139$	−20.6650	−	3.64379i	−1.75278	−	0.309062i	−0.955597	+	0.294677i	$0.904788\pi$
$140$		0			0
$141$	0.152427	+	2.51090i	0.0128366	+	0.211456i
$142$	−4.84641	−	3.39350i	−0.406702	−	0.284776i
$143$	3.41712	+	0.915613i	0.285754	+	0.0765674i
$144$	−1.83559	+	2.82093i	−0.152966	+	0.235078i
$145$		0			0
$146$	1.01159	−	2.77931i	0.0837196	−	0.230018i
$147$	10.3214	+	6.33143i	0.851296	+	0.522208i
$148$	0.249648	+	2.85349i	0.0205209	+	0.234555i
$149$	7.95475	+	6.67483i	0.651678	+	0.546823i	0.907580	−	0.419880i	$-0.137928\pi$
$149$	7.95475	+	6.67483i	0.651678	+	0.546823i	−0.255901	+	0.966703i	$0.582372\pi$
$150$		0			0
$151$	19.7123	+	7.17470i	1.60417	+	0.583869i	0.980274	−	0.197642i	$-0.0633285\pi$
$151$	19.7123	+	7.17470i	1.60417	+	0.583869i	0.623892	+	0.781511i	$0.285551\pi$
$152$	−5.50421	+	1.47485i	−0.446450	+	0.119626i
$153$	−0.566505	−	16.6572i	−0.0457992	−	1.34666i
$154$	0.265386	−	0.153221i	0.0213854	−	0.0123469i
$155$		0			0
$156$	1.03464	+	1.56472i	0.0828376	+	0.125278i
$157$	−4.97376	+	10.6663i	−0.396949	+	0.851260i	0.601671	+	0.798744i	$0.294502\pi$
$157$	−4.97376	+	10.6663i	−0.396949	+	0.851260i	−0.998620	+	0.0525161i	$0.983276\pi$
$158$	−5.25104	−	7.49926i	−0.417750	−	0.596609i
$159$	−1.36548	+	11.9364i	−0.108289	+	0.946615i
$160$		0			0
$161$		−	0.244133i		−	0.0192403i
$162$	−7.82345	−	4.72020i	−0.614668	−	0.370854i
$163$	−15.0223	−	15.0223i	−1.17663	−	1.17663i	−0.980596	−	0.196039i	$-0.937192\pi$
$163$	−15.0223	−	15.0223i	−1.17663	−	1.17663i	−0.196039	−	0.980596i	$-0.562808\pi$
$164$	1.04870	−	0.879960i	0.0818893	−	0.0687133i
$165$		0			0
$166$	2.17370	−	12.3277i	0.168712	−	0.956811i
$167$	−2.82971	−	1.31951i	−0.218969	−	0.102107i	0.310039	−	0.950724i	$-0.399658\pi$
$167$	−2.82971	−	1.31951i	−0.218969	−	0.102107i	−0.529008	+	0.848617i	$0.677436\pi$
$168$	0.487729	+	0.0994607i	0.0376291	+	0.00767356i
$169$	11.5730	−	2.04064i	0.890235	−	0.156972i
$170$		0			0
$171$	−1.65308	−	5.42462i	−0.126414	−	0.414831i
$172$	−2.80576	−	10.4712i	−0.213937	−	0.798425i
$173$	19.0541	−	8.88509i	1.44866	−	0.675521i	0.470314	−	0.882499i	$-0.344141\pi$
$173$	19.0541	−	8.88509i	1.44866	−	0.675521i	0.978345	+	0.206979i	$0.0663630\pi$
$174$	−1.44272	+	4.86242i	−0.109372	+	0.368619i
$175$		0			0
$176$	−2.28318	+	2.72099i	−0.172101	+	0.205102i
$177$	5.17382	−	8.43428i	0.388888	−	0.633960i
$178$	4.85089	+	10.4028i	0.363590	+	0.779721i
$179$	−6.25260	+	10.8298i	−0.467342	+	0.809459i	−0.999304	−	0.0373088i	$-0.988121\pi$
$179$	−6.25260	+	10.8298i	−0.467342	+	0.809459i	0.531962	+	0.846768i	$0.321455\pi$
$180$		0			0
$181$	−2.19207	−	3.79678i	−0.162935	−	0.282213i	0.772985	−	0.634425i	$-0.218763\pi$
$181$	−2.19207	−	3.79678i	−0.162935	−	0.282213i	−0.935920	+	0.352212i	$0.885430\pi$
$182$	−0.0620272	+	0.0885841i	−0.00459776	+	0.00656629i
$183$	5.84856	+	5.17912i	0.432338	+	0.382851i
$184$	2.64030	+	7.25415i	0.194645	+	0.534783i
$185$		0			0
$186$	7.69114	+	17.7104i	0.563942	+	1.29859i
$187$	1.53308	−	17.5232i	0.112110	−	1.28142i
$188$	−0.995431	+	0.995431i	−0.0725993	+	0.0725993i
$189$	−0.0824260	+	0.488461i	−0.00599561	+	0.0355303i
$190$		0			0
$191$	11.2869	+	13.4512i	0.816694	+	0.973298i	0.999952	−	0.00976704i	$-0.00310899\pi$
$191$	11.2869	+	13.4512i	0.816694	+	0.973298i	−0.183259	+	0.983065i	$0.558665\pi$
$192$	−12.3489	+	1.83981i	−0.891204	+	0.132777i
$193$	11.8555	−	8.30132i	0.853379	−	0.597542i	−0.0629287	−	0.998018i	$-0.520044\pi$
$193$	11.8555	−	8.30132i	0.853379	−	0.597542i	0.916307	+	0.400476i	$0.131155\pi$
$194$	−1.92089	+	0.699148i	−0.137912	+	0.0501959i
$195$		0			0
$196$	1.17669	+	6.67335i	0.0840494	+	0.476668i
$197$	1.79014	−	6.68089i	0.127542	−	0.475994i	−0.872375	−	0.488837i	$-0.837421\pi$
$197$	1.79014	−	6.68089i	0.127542	−	0.475994i	0.999918	+	0.0128429i	$0.00408812\pi$
$198$	−7.59357	−	5.94389i	−0.539652	−	0.422414i
$199$	9.64105	+	5.56626i	0.683436	+	0.394582i	0.801148	−	0.598466i	$-0.204223\pi$
$199$	9.64105	+	5.56626i	0.683436	+	0.394582i	−0.117712	+	0.993048i	$0.537556\pi$
$200$		0			0
$201$	12.9153	−	12.2450i	0.910977	−	0.863697i
$202$	15.9107	−	1.39200i	1.11947	−	0.0979409i
$203$	0.273928	−	0.0239656i	0.0192260	−	0.00168206i
$204$	6.76863	−	6.41734i	0.473899	−	0.449304i
$205$		0			0
$206$	−8.07939	−	4.66464i	−0.562918	−	0.325001i
$207$	−7.12569	+	2.87143i	−0.495270	+	0.199578i
$208$	0.324424	−	1.21077i	0.0224948	−	0.0839516i
$209$	−1.03929	−	5.89411i	−0.0718893	−	0.407704i
$210$		0			0
$211$	4.00924	−	1.45925i	0.276008	−	0.100459i	−0.200308	−	0.979733i	$-0.564194\pi$
$211$	4.00924	−	1.45925i	0.276008	−	0.100459i	0.476316	+	0.879274i	$0.341972\pi$
$212$	−5.50754	+	3.85642i	−0.378259	+	0.264860i
$213$	9.98351	−	1.48740i	0.684059	−	0.101915i
$214$	4.49066	+	5.35175i	0.306975	+	0.365838i
$215$		0			0
$216$	−2.83351	−	15.4056i	−0.192796	−	1.04822i
$217$	0.740201	−	0.740201i	0.0502481	−	0.0502481i
$218$	−0.692904	+	7.91993i	−0.0469294	+	0.536405i
$219$	2.00998	+	4.62839i	0.135822	+	0.312758i
$220$		0			0
$221$	2.12307	+	5.83308i	0.142813	+	0.392375i
$222$	3.89029	+	3.44499i	0.261099	+	0.231213i
$223$	−8.33967	+	11.9103i	−0.558466	+	0.797572i	−0.994761	−	0.102232i	$-0.967402\pi$
$223$	−8.33967	+	11.9103i	−0.558466	+	0.797572i	0.436295	+	0.899804i	$0.356290\pi$
$224$	0.233096	+	0.403734i	0.0155744	+	0.0269756i
$225$		0			0
$226$	−9.22541	+	15.9789i	−0.613665	+	1.06290i
$227$	−0.426342	−	0.914294i	−0.0282973	−	0.0606838i	0.891651	−	0.452723i	$-0.149547\pi$
$227$	−0.426342	−	0.914294i	−0.0282973	−	0.0606838i	−0.919948	+	0.392039i	$0.871770\pi$
$228$	1.65942	−	2.70517i	0.109898	−	0.179154i
$229$	−0.236161	+	0.281446i	−0.0156060	+	0.0185985i	−0.773791	−	0.633441i	$-0.781642\pi$
$229$	−0.236161	+	0.281446i	−0.0156060	+	0.0185985i	0.758185	+	0.652039i	$0.226086\pi$
$230$		0			0
$231$	−0.148713	+	0.501210i	−0.00978462	+	0.0329772i
$232$	−7.88031	+	3.67465i	−0.517367	+	0.241252i
$233$	0.254961	+	0.951529i	0.0167031	+	0.0623368i	0.973774	−	0.227516i	$-0.0730604\pi$
$233$	0.254961	+	0.951529i	0.0167031	+	0.0623368i	−0.957071	+	0.289853i	$0.906394\pi$
$234$	3.31512	+	0.768535i	0.216716	+	0.0502407i
$235$		0			0
$236$	5.45322	−	0.961549i	0.354974	−	0.0625915i
$237$	15.3038	+	3.12086i	0.994092	+	0.202721i
$238$	0.487325	+	0.227244i	0.0315886	+	0.0147300i
$239$	3.98223	−	22.5844i	0.257589	−	1.46086i	−0.531749	−	0.846902i	$-0.678465\pi$
$239$	3.98223	−	22.5844i	0.257589	−	1.46086i	0.789338	−	0.613959i	$-0.210424\pi$
$240$		0			0
$241$	−14.7217	+	12.3529i	−0.948306	+	0.795723i	−0.979011	−	0.203805i	$-0.934669\pi$
$241$	−14.7217	+	12.3529i	−0.948306	+	0.795723i	0.0307054	+	0.999528i	$0.490225\pi$
$242$	0.700139	+	0.700139i	0.0450066	+	0.0450066i
$243$	15.2266	−	3.33932i	0.976786	−	0.214218i
$244$			4.37185i			0.279879i
$245$		0			0
$246$	0.282263	−	2.46740i	0.0179964	−	0.157316i
$247$	1.21144	+	1.73012i	0.0770821	+	0.110085i
$248$	−13.9890	+	29.9996i	−0.888304	+	1.90497i
$249$	11.7792	+	17.8140i	0.746474	+	1.12891i
$250$		0			0
$251$	−7.72981	+	4.46281i	−0.487901	+	0.281690i	−0.723703	−	0.690111i	$-0.757562\pi$
$251$	−7.72981	+	4.46281i	−0.487901	+	0.281690i	0.235802	+	0.971801i	$0.424228\pi$
$252$	−0.235230	+	0.146690i	−0.0148181	+	0.00924062i
$253$	−7.83178	+	2.09852i	−0.492380	+	0.131933i
$254$	−18.2636	−	6.64742i	−1.14596	−	0.417097i
$255$		0			0
$256$	−12.9586	−	10.8736i	−0.809913	−	0.679598i
$257$	−1.17787	−	13.4631i	−0.0734736	−	0.839808i	−0.940111	−	0.340869i	$-0.889279\pi$
$257$	−1.17787	−	13.4631i	−0.0734736	−	0.839808i	0.866637	−	0.498939i	$-0.166277\pi$
$258$	−16.7636	−	10.2832i	−1.04366	−	0.640207i
$259$	0.0963542	−	0.264731i	0.00598716	−	0.0164496i
$260$		0			0
$261$	−3.92138	−	7.71348i	−0.242727	−	0.477453i
$262$	18.9854	+	5.08711i	1.17292	+	0.314283i
$263$	18.1928	+	12.7387i	1.12181	+	0.785503i	0.978922	−	0.204235i	$-0.0654706\pi$
$263$	18.1928	+	12.7387i	1.12181	+	0.785503i	0.142893	+	0.989738i	$0.454360\pi$
$264$	−1.00173	−	16.5013i	−0.0616520	−	1.01558i
$265$		0			0
$266$	0.180175	+	0.0317696i	0.0110472	+	0.00194792i
$267$	−18.2166	−	7.18530i	−1.11484	−	0.439733i
$268$	9.92197	+	0.868059i	0.606080	+	0.0530252i
$269$	23.2949			1.42032			0.710158	−	0.704042i	$-0.248623\pi$
$269$	23.2949			1.42032			0.710158	+	0.704042i	$0.248623\pi$
$270$		0			0
$271$	−10.6978			−0.649842			−0.324921	−	0.945741i	$-0.605338\pi$
$271$	−10.6978			−0.649842			−0.324921	+	0.945741i	$0.605338\pi$
$272$	−6.20888	−	0.543206i	−0.376469	−	0.0329367i
$273$	−0.0271871	−	0.182481i	−0.00164544	−	0.0110443i
$274$	1.97628	+	0.348471i	0.119391	+	0.0210519i
$275$		0			0
$276$	−3.84674	−	1.92010i	−0.231546	−	0.115576i
$277$	22.9557	+	16.0737i	1.37927	+	0.965776i	0.999166	+	0.0408334i	$0.0130013\pi$
$277$	22.9557	+	16.0737i	1.37927	+	0.965776i	0.380106	+	0.924943i	$0.375888\pi$
$278$	−20.5775	−	5.51373i	−1.23416	−	0.330691i
$279$	−30.3109	−	12.8988i	−1.81467	−	0.772229i
$280$		0			0
$281$	7.46331	−	20.5053i	0.445224	−	1.22324i	−0.490789	−	0.871278i	$-0.663292\pi$
$281$	7.46331	−	20.5053i	0.445224	−	1.22324i	0.936013	−	0.351965i	$-0.114486\pi$
$282$	−0.0680136	+	2.55294i	−0.00405015	+	0.152025i
$283$	−2.06294	−	23.5795i	−0.122629	−	1.40165i	−0.769301	−	0.638886i	$-0.779395\pi$
$283$	−2.06294	−	23.5795i	−0.122629	−	1.40165i	0.646672	−	0.762768i	$-0.276160\pi$
$284$	4.32715	+	3.63091i	0.256769	+	0.215455i
$285$		0			0
$286$	3.37495	+	1.22838i	0.199565	+	0.0726358i
$287$	−0.130055	+	0.0348480i	−0.00767688	+	0.00205701i
$288$	9.04250	−	11.5522i	0.532834	−	0.680719i
$289$	12.0073	−	6.93242i	0.706312	−	0.407790i
$290$		0			0
$291$	1.55753	−	3.12036i	0.0913038	−	0.182919i
$292$	−1.19342	+	2.55929i	−0.0698395	+	0.149771i
$293$	0.820761	+	1.17217i	0.0479493	+	0.0684788i	0.842411	−	0.538836i	$-0.181136\pi$
$293$	0.820761	+	1.17217i	0.0479493	+	0.0684788i	−0.794461	+	0.607315i	$0.792247\pi$
$294$	9.87854	+	7.31670i	0.576128	+	0.426718i
$295$		0			0
$296$			8.90828i			0.517783i
$297$	16.3784	−	1.55449i	0.950369	−	0.0902009i
$298$	7.45459	+	7.45459i	0.431833	+	0.431833i
$299$	2.19187	−	1.83920i	0.126759	−	0.106363i
$300$		0			0
$301$	−0.185145	+	1.05001i	−0.0106716	+	0.0605215i
$302$	19.3016	+	9.00049i	1.11068	+	0.517920i
$303$	−18.0645	+	20.3995i	−1.03778	+	1.17192i
$304$	−2.08843	+	0.368246i	−0.119779	+	0.0211204i
$305$		0			0
$306$	0.900941	−	16.8967i	0.0515034	−	0.965922i
$307$	1.29179	+	4.82104i	0.0737265	+	0.275151i	0.992942	−	0.118605i	$-0.0378422\pi$
$307$	1.29179	+	4.82104i	0.0737265	+	0.275151i	−0.919215	+	0.393756i	$0.871175\pi$
$308$	−0.265164	+	0.123648i	−0.0151091	+	0.00704551i
$309$	15.4782	−	3.70855i	0.880526	−	0.210972i
$310$		0			0
$311$	−12.6560	+	15.0828i	−0.717655	+	0.855268i	−0.994401	−	0.105675i	$-0.966300\pi$
$311$	−12.6560	+	15.0828i	−0.717655	+	0.855268i	0.276746	+	0.960943i	$0.410744\pi$
$312$	2.78137	+	5.12822i	0.157464	+	0.290328i
$313$	−2.47291	−	5.30318i	−0.139777	−	0.299753i	0.823941	−	0.566676i	$-0.191771\pi$
$313$	−2.47291	−	5.30318i	−0.139777	−	0.299753i	−0.963718	+	0.266923i	$0.913993\pi$
$314$	−5.97410	+	10.3474i	−0.337138	+	0.583940i
$315$		0			0
$316$	4.37035	+	7.56967i	0.245851	+	0.425827i
$317$	−13.4460	+	19.2029i	−0.755205	+	1.07854i	0.238997	+	0.971020i	$0.423181\pi$
$317$	−13.4460	+	19.2029i	−0.755205	+	1.07854i	−0.994202	+	0.107524i	$0.965708\pi$
$318$	−2.43717	+	11.9513i	−0.136670	+	0.670193i
$319$	−3.12345	−	8.58161i	−0.174880	−	0.480478i
$320$		0			0
$321$	−11.8417	−	1.35465i	−0.660938	−	0.0756091i
$322$	0.0216017	−	0.246908i	0.00120382	−	0.0137597i
$323$	7.42588	−	7.42588i	0.413187	−	0.413187i
$324$	7.04828	+	5.14050i	0.391571	+	0.285583i
$325$		0			0
$326$	−13.8639	−	16.5223i	−0.767848	−	0.915086i
$327$	−8.43864	−	10.6187i	−0.466658	−	0.587218i
$328$	3.48756	−	2.44201i	0.192568	−	0.134838i
$329$	0.130106	−	0.0473549i	0.00717300	−	0.00261076i
$330$		0			0
$331$	2.14790	+	12.1813i	0.118059	+	0.669546i	0.985190	+	0.171466i	$0.0548504\pi$
$331$	2.14790	+	12.1813i	0.118059	+	0.669546i	−0.867131	+	0.498080i	$0.834039\pi$
$332$	−3.09327	+	11.5442i	−0.169765	+	0.633572i
$333$	−8.86021	+	0.301332i	−0.485536	+	0.0165129i
$334$	−2.74513	−	1.58490i	−0.150207	−	0.0867218i
$335$		0			0
$336$	0.177591	+	0.0526928i	0.00968838	+	0.00287463i
$337$	1.27310	−	0.111382i	0.0693501	−	0.00606735i	−0.0524279	−	0.998625i	$-0.516696\pi$
$337$	1.27310	−	0.111382i	0.0693501	−	0.00606735i	0.121778	+	0.992557i	$0.461140\pi$
$338$	11.8852	−	1.03982i	0.646470	−	0.0565588i
$339$	−7.33452	−	30.6118i	−0.398356	−	1.66261i
$340$		0			0
$341$	−30.1083	−	17.3830i	−1.63045	−	0.941343i
$342$	−1.19188	−	5.63257i	−0.0644496	−	0.304574i
$343$	0.345213	−	1.28835i	0.0186398	−	0.0695645i
$344$	−5.85445	−	33.2023i	−0.315651	−	1.79015i
$345$		0			0
$346$	20.0570	−	7.30014i	1.07827	−	0.392458i
$347$	−12.1041	+	8.47537i	−0.649782	+	0.454982i	−0.851425	−	0.524477i	$-0.824261\pi$
$347$	−12.1041	+	8.47537i	−0.649782	+	0.454982i	0.201643	+	0.979459i	$0.435372\pi$
$348$	1.77682	−	4.50470i	0.0952475	−	0.241477i
$349$	−14.9928	−	17.8678i	−0.802548	−	0.956439i	0.197166	−	0.980370i	$-0.436826\pi$
$349$	−14.9928	−	17.8678i	−0.802548	−	0.956439i	−0.999714	+	0.0239312i	$0.992382\pi$
$350$		0			0
$351$	−5.00646	+	2.93983i	−0.267225	+	0.156917i
$352$	10.9481	−	10.9481i	0.583538	−	0.583538i
$353$	−0.0310525	+	0.354931i	−0.00165276	+	0.0188911i	−0.996976	−	0.0777063i	$-0.975240\pi$
$353$	−0.0310525	+	0.354931i	−0.00165276	+	0.0188911i	0.995324	+	0.0965974i	$0.0307959\pi$
$354$	5.97894	−	8.07239i	0.317777	−	0.429043i
$355$		0			0
$356$	−3.74816	−	10.2980i	−0.198652	−	0.545792i
$357$	−0.870083	+	0.290685i	−0.0460497	+	0.0153847i
$358$	−7.28196	+	10.3997i	−0.384863	+	0.549642i
$359$	4.55004	+	7.88090i	0.240142	+	0.415938i	0.960755	−	0.277400i	$-0.0894727\pi$
$359$	4.55004	+	7.88090i	0.240142	+	0.415938i	−0.720613	+	0.693338i	$0.756139\pi$
$360$		0			0
$361$	−7.71338	+	13.3600i	−0.405967	+	0.703156i
$362$	−1.88105	−	4.03391i	−0.0988655	−	0.212018i
$363$	−1.68865	−	0.0449878i	−0.0886312	−	0.00236125i
$364$	0.0663668	−	0.0790929i	0.00347857	−	0.00414559i
$365$		0			0
$366$	5.45679	+	5.75550i	0.285231	+	0.300845i
$367$	−22.0312	+	10.2733i	−1.15002	+	0.536262i	−0.901677	−	0.432410i	$-0.857663\pi$
$367$	−22.0312	+	10.2733i	−1.15002	+	0.536262i	−0.248341	+	0.968673i	$0.579885\pi$
$368$	0.743556	+	2.77499i	0.0387605	+	0.144656i
$369$	2.54681	+	3.38613i	0.132581	+	0.176275i
$370$		0			0
$371$	0.651225	−	0.114829i	0.0338099	−	0.00596160i
$372$	−5.84149	−	17.4848i	−0.302867	−	0.906545i
$373$	20.3805	+	9.50357i	1.05526	+	0.492076i	0.871246	−	0.490847i	$-0.163313\pi$
$373$	20.3805	+	9.50357i	1.05526	+	0.492076i	0.184015	+	0.982923i	$0.441090\pi$
$374$	3.10102	−	17.5867i	0.160350	−	0.909389i
$375$		0			0
$376$	−3.35384	+	2.81420i	−0.172961	+	0.145131i
$377$	2.27883	+	2.27883i	0.117366	+	0.117366i
$378$	−0.126584	+	0.486722i	−0.00651078	+	0.0250343i
$379$			3.33488i			0.171301i	0.996325	+	0.0856506i	$0.0272969\pi$
$379$			3.33488i			0.171301i	−0.996325	+	0.0856506i	$0.972703\pi$
$380$		0			0
$381$	30.4145	−	13.2081i	1.55818	−	0.676673i
$382$	10.2251	+	14.6029i	0.523159	+	0.747149i
$383$	−8.39456	+	18.0022i	−0.428942	+	0.919869i	0.566461	+	0.824089i	$0.308312\pi$
$383$	−8.39456	+	18.0022i	−0.428942	+	0.919869i	−0.995403	+	0.0957800i	$0.969465\pi$
$384$	4.25666	−	0.258404i	0.217222	−	0.0131866i
$385$		0			0
$386$	12.7248	−	7.34669i	0.647678	−	0.373937i
$387$	32.8251	−	6.94596i	1.66859	−	0.353083i
$388$	1.88518	−	0.505133i	0.0957056	−	0.0256443i
$389$	12.3541	+	4.49653i	0.626378	+	0.227983i	0.635654	−	0.771974i	$-0.280731\pi$
$389$	12.3541	+	4.49653i	0.626378	+	0.227983i	−0.00927617	+	0.999957i	$0.502953\pi$
$390$		0			0
$391$	−10.8985	−	9.14493i	−0.551161	−	0.462479i
$392$	1.83675	+	20.9941i	0.0927699	+	1.06036i
$393$	−29.4765	+	15.9871i	−1.48689	+	0.806441i
$394$	2.40164	−	6.59846i	0.120993	−	0.332425i
$395$		0			0
$396$	6.72782	+	6.28525i	0.338086	+	0.315846i
$397$	19.9480	+	5.34505i	1.00116	+	0.268260i	0.721932	−	0.691964i	$-0.243255\pi$
$397$	19.9480	+	5.34505i	1.00116	+	0.268260i	0.279229	+	0.960225i	$0.409921\pi$
$398$	9.25815	+	6.48263i	0.464069	+	0.324945i
$399$	−0.260360	+	0.172158i	−0.0130343	+	0.00861869i
$400$		0			0
$401$	−29.6077	−	5.22064i	−1.47854	−	0.260706i	−0.624545	−	0.780989i	$-0.714716\pi$
$401$	−29.6077	−	5.22064i	−1.47854	−	0.260706i	−0.853994	+	0.520282i	$0.825827\pi$
$402$	14.1457	−	11.2415i	0.705521	−	0.560673i
$403$	12.2220	+	1.06929i	0.608823	+	0.0532651i
$404$	−15.2488			−0.758657
$405$		0			0
$406$	0.279163			0.0138546
$407$	−9.32081	−	0.815466i	−0.462016	−	0.0404211i
$408$	22.7099	−	18.0474i	1.12431	−	0.893478i
$409$	0.0461503	+	0.00813754i	0.00228199	+	0.000402376i	0.174789	−	0.984606i	$-0.444076\pi$
$409$	0.0461503	+	0.00813754i	0.00228199	+	0.000402376i	−0.172507	+	0.985008i	$0.555187\pi$
$410$		0			0
$411$	−2.85581	+	1.88835i	−0.140867	+	0.0931454i
$412$	7.29634	+	5.10895i	0.359465	+	0.251700i
$413$	−0.526056	−	0.140956i	−0.0258855	−	0.00693600i
$414$	−7.46079	+	2.27357i	−0.366678	+	0.111740i
$415$		0			0
$416$	−1.86875	+	5.13435i	−0.0916230	+	0.251732i
$417$	31.9484	−	17.3278i	1.56452	−	0.848544i
$418$	−0.529577	−	6.05309i	−0.0259024	−	0.296066i
$419$	25.6941	+	21.5599i	1.25524	+	1.05327i	0.996172	+	0.0874108i	$0.0278593\pi$
$419$	25.6941	+	21.5599i	1.25524	+	1.05327i	0.259066	+	0.965860i	$0.416585\pi$
$420$		0			0
$421$	28.5935	+	10.4072i	1.39356	+	0.507215i	0.926260	−	0.376884i	$-0.123005\pi$
$421$	28.5935	+	10.4072i	1.39356	+	0.507215i	0.467300	+	0.884099i	$0.345227\pi$
$422$	4.18395	−	1.12109i	0.203671	−	0.0545736i
$423$	−2.91246	−	3.24055i	−0.141609	−	0.157561i
$424$	−18.1086	+	10.4550i	−0.879432	+	0.507740i
$425$		0			0
$426$	10.2286	−	0.620939i	0.495579	−	0.0300846i
$427$	0.181719	−	0.389698i	0.00879400	−	0.0188588i
$428$	−3.82583	−	5.46386i	−0.184929	−	0.264105i
$429$	−5.62031	+	2.44074i	−0.271351	+	0.117840i
$430$		0			0
$431$		−	13.0282i		−	0.627544i	−0.949498	−	0.313772i	$-0.898407\pi$
$431$		−	13.0282i		−	0.627544i	0.949498	−	0.313772i	$-0.101593\pi$
$432$	−0.550795	−	5.80325i	−0.0265001	−	0.279209i
$433$	−20.0186	−	20.0186i	−0.962033	−	0.962033i	0.0372720	−	0.999305i	$-0.488133\pi$
$433$	−20.0186	−	20.0186i	−0.962033	−	0.962033i	−0.999305	+	0.0372720i	$0.988133\pi$
$434$	0.814112	−	0.683121i	0.0390786	−	0.0327909i
$435$		0			0
$436$	1.31807	−	7.47517i	0.0631243	−	0.357996i
$437$	−4.38720	−	2.04578i	−0.209868	−	0.0978631i
$438$	1.62330	+	4.85887i	0.0775641	+	0.232166i
$439$	18.8026	−	3.31540i	0.897398	−	0.158236i	0.294122	−	0.955768i	$-0.404973\pi$
$439$	18.8026	−	3.31540i	0.897398	−	0.158236i	0.603276	+	0.797532i	$0.293862\pi$
$440$		0			0
$441$	−20.8187	+	2.53699i	−0.991368	+	0.120809i
$442$	1.63108	+	6.08726i	0.0775824	+	0.289541i
$443$	−1.25966	+	0.587391i	−0.0598485	+	0.0279078i	−0.452312	−	0.891860i	$-0.649401\pi$
$443$	−1.25966	+	0.587391i	−0.0598485	+	0.0279078i	0.392464	+	0.919768i	$0.371623\pi$
$444$	−3.41347	−	3.60033i	−0.161996	−	0.170864i
$445$		0			0
$446$	−9.48836	+	11.3078i	−0.449287	+	0.535439i
$447$	−17.9796	−	0.478999i	−0.850404	−	0.0226559i
$448$	0.290421	+	0.622810i	0.0137211	+	0.0294250i
$449$	11.4763	−	19.8775i	0.541600	−	0.938078i	−0.457213	−	0.889357i	$-0.651152\pi$
$449$	11.4763	−	19.8775i	0.541600	−	0.938078i	0.998812	−	0.0487209i	$-0.0155145\pi$
$450$		0			0
$451$	2.23585	+	3.87261i	0.105282	+	0.182354i
$452$	10.1041	−	14.4302i	0.475259	−	0.678740i
$453$	−34.4616	+	11.5132i	−1.61915	+	0.540940i
$454$	−0.350290	−	0.962414i	−0.0164399	−	0.0451683i
$455$		0			0
$456$	5.87444	−	7.93130i	0.275096	−	0.371417i
$457$	0.232947	−	2.66259i	0.0108968	−	0.124551i	−0.988798	−	0.149261i	$-0.952311\pi$
$457$	0.232947	−	2.66259i	0.0108968	−	0.124551i	0.999695	+	0.0247099i	$0.00786620\pi$
$458$	−0.263750	+	0.263750i	−0.0123242	+	0.0123242i
$459$	18.7182	+	21.9768i	0.873689	+	1.02579i
$460$		0			0
$461$	−13.5853	−	16.1904i	−0.632732	−	0.754061i	0.350471	−	0.936574i	$-0.386021\pi$
$461$	−13.5853	−	16.1904i	−0.632732	−	0.754061i	−0.983204	+	0.182512i	$0.941577\pi$
$462$	−0.194753	+	0.493751i	−0.00906074	+	0.0229714i
$463$	0.992726	−	0.695114i	0.0461359	−	0.0323047i	−0.550281	−	0.834980i	$-0.685479\pi$
$463$	0.992726	−	0.695114i	0.0461359	−	0.0323047i	0.596417	+	0.802675i	$0.296591\pi$
$464$	−3.04067	+	1.10671i	−0.141160	+	0.0513779i
$465$		0			0
$466$	0.173666	+	0.984908i	0.00804492	+	0.0456250i
$467$	−0.909385	+	3.39387i	−0.0420813	+	0.157050i	−0.983769	−	0.179438i	$-0.942572\pi$
$467$	−0.909385	+	3.39387i	−0.0420813	+	0.157050i	0.941688	+	0.336487i	$0.109239\pi$
$468$	−3.08914	−	1.00683i	−0.142795	−	0.0465408i
$469$	−0.848342	−	0.489790i	−0.0391728	−	0.0226164i
$470$		0			0
$471$	−4.74961	−	19.8233i	−0.218851	−	0.913410i
$472$	17.1557	−	1.50093i	0.789653	−	0.0690857i
$473$	35.2757	−	3.08623i	1.62198	−	0.141905i
$474$	15.2017	+	4.51048i	0.698238	+	0.207173i
$475$		0			0
$476$	−0.444597	−	0.256688i	−0.0203781	−	0.0117653i
$477$	−11.0111	−	17.6572i	−0.504165	−	0.808470i
$478$	6.02585	−	22.4888i	0.275616	−	1.02861i
$479$	6.70575	+	38.0302i	0.306393	+	1.73764i	0.616873	+	0.787063i	$0.288399\pi$
$479$	6.70575	+	38.0302i	0.306393	+	1.73764i	−0.310479	+	0.950580i	$0.600489\pi$
$480$		0			0
$481$	3.10270	−	1.12929i	0.141471	−	0.0514912i
$482$	−15.9821	+	11.1908i	−0.727964	+	0.509726i
$483$	0.263080	+	0.331046i	0.0119705	+	0.0150631i
$484$	−0.607658	−	0.724178i	−0.0276208	−	0.0329172i
$485$		0			0
$486$	15.6952	−	2.02999i	0.711948	−	0.0920824i
$487$	6.28015	−	6.28015i	0.284581	−	0.284581i	−0.550352	−	0.834933i	$-0.685506\pi$
$487$	6.28015	−	6.28015i	0.284581	−	0.284581i	0.834933	+	0.550352i	$0.185506\pi$
$488$	−1.18501	+	13.5448i	−0.0536430	+	0.613143i
$489$	36.5585	+	4.18216i	1.65323	+	0.189124i
$490$		0			0
$491$	6.13941	+	16.8679i	0.277068	+	0.761237i	0.997691	+	0.0679107i	$0.0216333\pi$
$491$	6.13941	+	16.8679i	0.277068	+	0.761237i	−0.720624	+	0.693326i	$0.756144\pi$
$492$	−0.473785	+	2.32332i	−0.0213599	+	0.104743i
$493$	9.19116	−	13.1263i	0.413949	−	0.591181i
$494$	1.07213	+	1.85698i	0.0482373	+	0.0835495i
$495$		0			0
$496$	−6.15923	+	10.6681i	−0.276557	+	0.479011i
$497$	−0.234792	−	0.503513i	−0.0105319	−	0.0225856i
$498$	10.3369	+	19.0588i	0.463205	+	0.854045i
$499$	−16.0337	+	19.1083i	−0.717769	+	0.855404i	−0.994412	−	0.105569i	$-0.966334\pi$
$499$	−16.0337	+	19.1083i	−0.717769	+	0.855404i	0.276643	+	0.960973i	$0.410778\pi$
$500$		0			0
$501$	5.25902	−	1.26005i	0.234956	−	0.0562949i
$502$	−8.21259	+	3.82959i	−0.366546	+	0.170923i
$503$	−9.95836	−	37.1651i	−0.444021	−	1.65711i	−0.718507	−	0.695519i	$-0.755174\pi$
$503$	−9.95836	−	37.1651i	−0.444021	−	1.65711i	0.274486	−	0.961591i	$-0.411492\pi$
$504$	−0.768544	+	0.390712i	−0.0342337	+	0.0174037i
$505$		0			0
$506$	−8.10651	+	1.42940i	−0.360378	+	0.0635444i
$507$	−13.4941	+	15.2384i	−0.599295	+	0.676759i
$508$	16.8178	+	7.84228i	0.746170	+	0.347945i
$509$	4.24058	−	24.0495i	0.187960	−	1.06598i	−0.734132	−	0.679007i	$-0.762411\pi$
$509$	4.24058	−	24.0495i	0.187960	−	1.06598i	0.922092	−	0.386970i	$-0.126478\pi$
$510$		0			0
$511$	0.212757	−	0.178525i	0.00941184	−	0.00789747i
$512$	−8.66188	−	8.66188i	−0.382805	−	0.382805i
$513$	8.08721	+	5.57445i	0.357059	+	0.246118i
$514$		−	13.7204i		−	0.605183i
$515$		0			0
$516$	15.0886	+	11.1756i	0.664236	+	0.491977i
$517$	−2.63752	−	3.76676i	−0.115998	−	0.165662i
$518$	0.120874	−	0.259215i	0.00531090	−	0.0113893i
$519$	−16.2629	+	32.5812i	−0.713862	+	1.43015i
$520$		0			0
$521$	−28.5328	+	16.4734i	−1.25004	+	0.721713i	−0.971118	−	0.238600i	$-0.923312\pi$
$521$	−28.5328	+	16.4734i	−1.25004	+	0.721713i	−0.278925	+	0.960313i	$0.589978\pi$
$522$	−3.28345	−	8.14816i	−0.143713	−	0.356635i
$523$	−12.9787	+	3.47763i	−0.567519	+	0.152066i	−0.531158	−	0.847273i	$-0.678243\pi$
$523$	−12.9787	+	3.47763i	−0.567519	+	0.152066i	−0.0363604	+	0.999339i	$0.511576\pi$
$524$	−17.6341	−	6.41829i	−0.770350	−	0.280384i
$525$		0			0
$526$	17.2725	+	14.4933i	0.753116	+	0.631939i
$527$	−5.31676	−	60.7709i	−0.231602	−	2.64722i
$528$	0.163845	−	6.15006i	0.00713046	−	0.267647i
$529$	5.62355	−	15.4506i	0.244502	−	0.671764i
$530$		0			0
$531$	2.07313	+	17.0123i	0.0899664	+	0.738271i
$532$	−0.168725	−	0.0452096i	−0.00731514	−	0.00196009i
$533$	−1.29265	−	0.905124i	−0.0559909	−	0.0392053i
$534$	−17.7880	−	8.87887i	−0.769761	−	0.384226i
$535$		0			0
$536$	30.5047	+	5.37880i	1.31760	+	0.232329i
$537$	−3.19175	−	21.4232i	−0.137734	−	0.924479i
$538$	23.5598	+	2.06121i	1.01573	+	0.0888653i
$539$	−22.1345			−0.953400
$540$		0			0
$541$	8.25433			0.354882			0.177441	−	0.984131i	$-0.443218\pi$
$541$	8.25433			0.354882			0.177441	+	0.984131i	$0.443218\pi$
$542$	−10.8194	−	0.946574i	−0.464733	−	0.0406588i
$543$	7.06392	+	2.78626i	0.303142	+	0.119570i
$544$	26.7549	+	4.71761i	1.14711	+	0.202266i
$545$		0			0
$546$	−0.0113497	−	0.186962i	−0.000485722	−	0.00800123i
$547$	15.0685	+	10.5511i	0.644281	+	0.451130i	0.849502	−	0.527585i	$-0.176902\pi$
$547$	15.0685	+	10.5511i	0.644281	+	0.451130i	−0.205221	+	0.978716i	$0.565791\pi$
$548$	−1.85069	−	0.495890i	−0.0790574	−	0.0211834i
$549$	−13.5118	−	0.720453i	−0.576668	−	0.0307482i
$550$		0			0
$551$	1.86479	−	5.12347i	0.0794427	−	0.218267i
$552$	−11.3974	−	6.99148i	−0.485106	−	0.297577i
$553$	−0.0749253	−	0.856401i	−0.00318615	−	0.0364179i
$554$	21.7944	+	18.2877i	0.925956	+	0.776969i
$555$		0			0
$556$	19.1129	+	6.95654i	0.810569	+	0.295023i
$557$	−24.2426	+	6.49580i	−1.02719	+	0.275236i	−0.732797	−	0.680448i	$-0.761785\pi$
$557$	−24.2426	+	6.49580i	−1.02719	+	0.275236i	−0.294397	+	0.955683i	$0.595119\pi$
$558$	−29.5142	−	15.7275i	−1.24944	−	0.665796i
$559$	−10.8220	+	6.24807i	−0.457721	+	0.264265i
$560$		0			0
$561$	16.8043	+	25.4136i	0.709476	+	1.07296i
$562$	9.36255	−	20.0781i	0.394935	−	0.846942i
$563$	−12.2869	−	17.5476i	−0.517833	−	0.739542i	0.472028	−	0.881584i	$-0.343522\pi$
$563$	−12.2869	−	17.5476i	−0.517833	−	0.739542i	−0.989861	+	0.142042i	$0.954633\pi$
$564$	0.277126	−	2.42250i	0.0116691	−	0.102006i
$565$		0			0
$566$		−	24.0301i		−	1.01006i
$567$	−0.414600	−	0.751180i	−0.0174116	−	0.0315466i
$568$	12.4221	+	12.4221i	0.521220	+	0.521220i
$569$	−28.2319	+	23.6893i	−1.18354	+	0.993109i	−0.183592	+	0.983002i	$0.558773\pi$
$569$	−28.2319	+	23.6893i	−1.18354	+	0.993109i	−0.999949	+	0.0101065i	$0.996783\pi$
$570$		0			0
$571$	−4.68121	+	26.5485i	−0.195903	+	1.11102i	0.715225	+	0.698894i	$0.246324\pi$
$571$	−4.68121	+	26.5485i	−0.195903	+	1.11102i	−0.911128	+	0.412124i	$0.864787\pi$
$572$	−3.10778	−	1.44918i	−0.129943	−	0.0605933i
$573$	−29.8004	−	6.07707i	−1.24493	−	0.253873i
$574$	−0.134617	+	0.0237366i	−0.00561880	+	0.000990746i
$575$		0			0
$576$	14.7626	−	15.8021i	0.615108	−	0.658420i
$577$	9.12335	+	34.0488i	0.379810	+	1.41747i	0.846188	+	0.532884i	$0.178892\pi$
$577$	9.12335	+	34.0488i	0.379810	+	1.41747i	−0.466378	+	0.884585i	$0.654441\pi$
$578$	12.7572	−	5.94880i	0.530631	−	0.247437i
$579$	−7.13058	+	24.0323i	−0.296337	+	0.998747i
$580$		0			0
$581$	0.755571	−	0.900455i	0.0313464	−	0.0373572i
$582$	1.85134	−	3.01802i	0.0767404	−	0.125101i
$583$	−9.28151	−	19.9043i	−0.384401	−	0.824350i
$584$	−4.39113	+	7.60565i	−0.181706	+	0.314724i
$585$		0			0
$586$	0.726376	+	1.25812i	0.0300063	+	0.0519724i
$587$	0.300699	−	0.429442i	0.0124112	−	0.0177250i	−0.812899	−	0.582405i	$-0.802112\pi$
$587$	0.300699	−	0.429442i	0.0124112	−	0.0177250i	0.825310	+	0.564680i	$0.191001\pi$
$588$	−8.78687	−	7.78110i	−0.362364	−	0.320887i
$589$	−7.09908	−	19.5046i	−0.292512	−	0.803671i
$590$		0			0
$591$	4.77195	+	10.9884i	0.196292	+	0.452003i
$592$	−0.288939	+	3.30259i	−0.0118753	+	0.135736i
$593$	−13.4237	+	13.4237i	−0.551245	+	0.551245i	−0.926800	−	0.375555i	$-0.877452\pi$
$593$	−13.4237	+	13.4237i	−0.551245	+	0.551245i	0.375555	+	0.926800i	$0.377452\pi$
$594$	16.7021	−	0.122955i	0.685297	−	0.00504491i
$595$		0			0
$596$	−6.46991	−	7.71054i	−0.265018	−	0.315836i
$597$	−19.0716	+	2.84140i	−0.780549	+	0.116291i
$598$	2.37953	−	1.66616i	0.0973062	−	0.0681345i
$599$	−22.1618	+	8.06622i	−0.905505	+	0.329577i	−0.752457	−	0.658642i	$-0.771131\pi$
$599$	−22.1618	+	8.06622i	−0.905505	+	0.329577i	−0.153049	+	0.988219i	$0.548909\pi$
$600$		0			0
$601$	−0.127390	−	0.722463i	−0.00519634	−	0.0294699i	0.982099	−	0.188364i	$-0.0603184\pi$
$601$	−0.127390	−	0.722463i	−0.00519634	−	0.0294699i	−0.987296	+	0.158894i	$0.949207\pi$
$602$	−0.280158	+	1.04556i	−0.0114184	+	0.0426140i
$603$	−4.31792	+	30.5220i	−0.175839	+	1.24295i
$604$	−17.6093	−	10.1667i	−0.716510	−	0.413677i
$605$		0			0
$606$	−20.0749	+	19.0330i	−0.815488	+	0.773165i
$607$	−24.4981	+	2.14331i	−0.994347	+	0.0869941i	−0.572699	−	0.819766i	$-0.694104\pi$
$607$	−24.4981	+	2.14331i	−0.994347	+	0.0869941i	−0.421648	+	0.906760i	$0.638548\pi$
$608$	9.20863	−	0.805651i	0.373459	−	0.0326734i
$609$	−0.345623	+	0.327685i	−0.0140054	+	0.0132785i
$610$		0			0
$611$	1.40533	+	0.811368i	0.0568536	+	0.0328244i
$612$	−2.26293	+	15.9959i	−0.0914733	+	0.646596i
$613$	−7.22014	+	26.9459i	−0.291619	+	1.08834i	0.652247	+	0.758007i	$0.273827\pi$
$613$	−7.22014	+	26.9459i	−0.291619	+	1.08834i	−0.943866	+	0.330330i	$0.892840\pi$
$614$	0.879899	+	4.99016i	0.0355098	+	0.201386i
$615$		0			0
$616$	−0.855041	+	0.311210i	−0.0344506	+	0.0125390i
$617$	−23.6349	+	16.5493i	−0.951506	+	0.666252i	−0.942676	−	0.333709i	$-0.891700\pi$
$617$	−23.6349	+	16.5493i	−0.951506	+	0.666252i	−0.00883005	+	0.999961i	$0.502811\pi$
$618$	15.9824	−	2.38115i	0.642905	−	0.0957838i
$619$	−17.6679	−	21.0558i	−0.710133	−	0.846304i	0.283499	−	0.958972i	$-0.408505\pi$
$619$	−17.6679	−	21.0558i	−0.710133	−	0.846304i	−0.993633	+	0.112669i	$0.964060\pi$
$620$		0			0
$621$	6.56822	−	11.5724i	0.263574	−	0.464384i
$622$	−14.1345	+	14.1345i	−0.566741	+	0.566741i
$623$	−0.0939396	+	1.07373i	−0.00376361	+	0.0430183i
$624$	0.864813	+	1.99141i	0.0346202	+	0.0797203i
$625$		0			0
$626$	−2.03179	−	5.58229i	−0.0812066	−	0.223113i
$627$	7.76084	+	6.87251i	0.309938	+	0.274462i
$628$	6.54314	−	9.34457i	0.261100	−	0.372889i
$629$	−8.20873	−	14.2179i	−0.327303	−	0.566906i
$630$		0			0
$631$	20.0750	−	34.7710i	0.799174	−	1.38421i	−0.120981	−	0.992655i	$-0.538604\pi$
$631$	20.0750	−	34.7710i	0.799174	−	1.38421i	0.920155	−	0.391555i	$-0.128063\pi$
$632$	11.4883	+	24.6368i	0.456980	+	0.979997i
$633$	−3.86407	+	6.29915i	−0.153583	+	0.250369i
$634$	−15.2981	+	18.2315i	−0.607564	+	0.724067i
$635$		0			0
$636$	3.31255	−	11.1643i	0.131351	−	0.442694i
$637$	7.07929	−	3.30113i	0.280492	−	0.130795i
$638$	−2.39964	−	8.95556i	−0.0950025	−	0.354554i
$639$	−11.9349	+	12.7753i	−0.472136	+	0.505381i
$640$		0			0
$641$	−18.1658	+	3.20312i	−0.717506	+	0.126516i	−0.520469	−	0.853880i	$-0.674243\pi$
$641$	−18.1658	+	3.20312i	−0.717506	+	0.126516i	−0.197037	+	0.980396i	$0.563132\pi$
$642$	−11.8565	−	2.41784i	−0.467937	−	0.0954247i
$643$	15.3029	+	7.13584i	0.603486	+	0.281410i	0.700251	−	0.713897i	$-0.253072\pi$
$643$	15.3029	+	7.13584i	0.603486	+	0.281410i	−0.0967645	+	0.995307i	$0.530849\pi$
$644$	−0.0410917	+	0.233043i	−0.00161924	+	0.00918317i
$645$		0			0
$646$	8.16738	−	6.85325i	0.321341	−	0.269638i
$647$	7.09292	+	7.09292i	0.278851	+	0.278851i	0.832650	−	0.553799i	$-0.186822\pi$
$647$	7.09292	+	7.09292i	0.278851	+	0.278851i	−0.553799	+	0.832650i	$0.686822\pi$
$648$	20.4434	+	17.8367i	0.803094	+	0.700690i
$649$			18.0875i			0.709997i
$650$		0			0
$651$	−0.206070	+	1.80137i	−0.00807652	+	0.0706011i
$652$	11.8114	+	16.8684i	0.462569	+	0.660617i
$653$	−9.19766	+	19.7244i	−0.359932	+	0.771877i	0.640062	+	0.768324i	$0.278909\pi$
$653$	−9.19766	+	19.7244i	−0.359932	+	0.771877i	−0.999994	+	0.00355334i	$0.998869\pi$
$654$	−7.59501	−	11.4862i	−0.296988	−	0.449144i
$655$		0			0
$656$	1.37216	−	0.792216i	0.0535738	−	0.0309308i
$657$	−7.71314	−	4.11016i	−0.300918	−	0.160353i
$658$	0.135776	−	0.0363810i	0.00529310	−	0.00141828i
$659$	−12.3875	−	4.50869i	−0.482550	−	0.175634i	0.0892792	−	0.996007i	$-0.471544\pi$
$659$	−12.3875	−	4.50869i	−0.482550	−	0.175634i	−0.571829	+	0.820373i	$0.693766\pi$
$660$		0			0
$661$	3.09314	+	2.59546i	0.120309	+	0.100952i	0.700957	−	0.713203i	$-0.252756\pi$
$661$	3.09314	+	2.59546i	0.120309	+	0.100952i	−0.580648	+	0.814155i	$0.697201\pi$
$662$	1.09447	+	12.5099i	0.0425379	+	0.486210i
$663$	−9.16468	−	5.62186i	−0.355927	−	0.218335i
$664$	−12.7126	+	34.9276i	−0.493345	+	1.35545i
$665$		0			0
$666$	−8.98762	−	0.479223i	−0.348263	−	0.0185695i
$667$	−7.13463	−	1.91172i	−0.276254	−	0.0740221i
$668$	2.47907	+	1.73586i	0.0959181	+	0.0671626i
$669$	−1.52598	−	25.1373i	−0.0589980	−	0.971866i
$670$		0			0
$671$	−14.0635	−	2.47978i	−0.542917	−	0.0957309i
$672$	−0.751148	−	0.296280i	−0.0289762	−	0.0114292i
$673$	−26.4671	−	2.31557i	−1.02023	−	0.0892588i	−0.435254	−	0.900308i	$-0.643341\pi$
$673$	−26.4671	−	2.31557i	−1.02023	−	0.0892588i	−0.584978	+	0.811049i	$0.698897\pi$
$674$	1.29743			0.0499752
$675$		0			0
$676$	−11.3908			−0.438108
$677$	29.9981	+	2.62449i	1.15292	+	0.100867i	0.647542	−	0.762030i	$-0.275797\pi$
$677$	29.9981	+	2.62449i	1.15292	+	0.100867i	0.505379	+	0.862898i	$0.331353\pi$
$678$	−4.70928	−	31.6089i	−0.180859	−	1.21393i
$679$	−0.189037	−	0.0333324i	−0.00725459	−	0.00127918i
$680$		0			0
$681$	1.56338	+	0.780359i	0.0599087	+	0.0299034i
$682$	−28.9125	−	20.2448i	−1.10712	−	0.775212i
$683$	3.13527	+	0.840092i	0.119968	+	0.0321452i	0.318303	−	0.947989i	$-0.396887\pi$
$683$	3.13527	+	0.840092i	0.119968	+	0.0321452i	−0.198336	+	0.980134i	$0.563554\pi$
$684$	0.664927	+	5.45644i	0.0254241	+	0.208632i
$685$		0			0
$686$	0.463136	−	1.27246i	0.0176826	−	0.0485826i
$687$	0.0169474	−	0.636133i	0.000646583	−	0.0242700i
$688$	−1.09353	−	12.4991i	−0.0416903	−	0.476522i
$689$	5.93702	+	4.98175i	0.226182	+	0.189790i
$690$		0			0
$691$	−10.0425	−	3.65517i	−0.382034	−	0.139049i	0.143862	−	0.989598i	$-0.454048\pi$
$691$	−10.0425	−	3.65517i	−0.382034	−	0.139049i	−0.525896	+	0.850549i	$0.676270\pi$
$692$	−19.6841	+	5.27434i	−0.748278	+	0.200500i
$693$	−0.338453	−	0.839900i	−0.0128568	−	0.0319052i
$694$	−12.9916	+	7.50073i	−0.493156	+	0.284724i
$695$		0			0
$696$	6.72592	−	13.4747i	0.254945	−	0.510759i
$697$	−3.31602	+	7.11123i	−0.125603	+	0.269357i
$698$	−13.5823	−	19.3975i	−0.514098	−	0.734208i
$699$	−1.37111	−	1.01553i	−0.0518600	−	0.0384109i
$700$		0			0
$701$			16.6810i			0.630034i	0.949086	+	0.315017i	$0.102010\pi$
$701$			16.6810i			0.630034i	−0.949086	+	0.315017i	$0.897990\pi$
$702$	−5.32351	+	2.53027i	−0.200923	+	0.0954989i
$703$	−3.94993	−	3.94993i	−0.148975	−	0.148975i
$704$	17.4833	−	14.6703i	0.658928	−	0.552906i
$705$		0			0
$706$	−0.0628111	+	0.356219i	−0.00236393	+	0.0134065i
$707$	1.35925	+	0.633828i	0.0511198	+	0.0238375i
$708$	−6.35843	+	7.18031i	−0.238964	+	0.269853i
$709$	25.9605	−	4.57754i	0.974967	−	0.171913i	0.336602	−	0.941647i	$-0.390722\pi$
$709$	25.9605	−	4.57754i	0.974967	−	0.171913i	0.638365	+	0.769734i	$0.279611\pi$
$710$		0			0
$711$	−24.1152	+	12.2597i	−0.904391	+	0.459774i
$712$	−8.82112	−	32.9209i	−0.330586	−	1.23376i
$713$	−25.4845	+	11.8836i	−0.954401	+	0.445044i
$714$	−0.905697	+	0.217003i	−0.0338948	+	0.00812112i
$715$		0			0
$716$	7.79142	−	9.28546i	0.291179	−	0.347014i
$717$	18.9372	+	34.9159i	0.707222	+	1.30396i
$718$	3.90445	+	8.37312i	0.145713	+	0.312482i
$719$	5.44851	−	9.43709i	0.203195	−	0.351944i	−0.746361	−	0.665541i	$-0.768201\pi$
$719$	5.44851	−	9.43709i	0.203195	−	0.351944i	0.949556	+	0.313597i	$0.101534\pi$
$720$		0			0
$721$	−0.438023	−	0.758678i	−0.0163128	−	0.0282547i
$722$	−8.98322	+	12.8294i	−0.334321	+	0.477460i
$723$	6.65104	−	32.6149i	0.247355	−	1.21296i
$724$	1.45343	+	3.99328i	0.0540164	+	0.148409i
$725$		0			0
$726$	−1.70387	−	0.194917i	−0.0632366	−	0.00723405i
$727$	0.274043	−	3.13232i	0.0101637	−	0.116171i	−0.989418	−	0.145093i	$-0.953652\pi$
$727$	0.274043	−	3.13232i	0.0101637	−	0.116171i	0.999582	+	0.0289218i	$0.00920737\pi$
$728$	0.227055	−	0.227055i	0.00841520	−	0.00841520i
$729$	−17.0489	+	20.9365i	−0.631440	+	0.775425i
$730$		0			0
$731$	39.9389	+	47.5973i	1.47719	+	1.76045i
$732$	−4.71115	−	5.92827i	−0.174129	−	0.219115i
$733$	7.67078	−	5.37114i	0.283327	−	0.198388i	−0.423271	−	0.906003i	$-0.639118\pi$
$733$	7.67078	−	5.37114i	0.283327	−	0.198388i	0.706597	+	0.707616i	$0.250229\pi$
$734$	−23.1907	+	8.44073i	−0.855984	+	0.311553i
$735$		0			0
$736$	−2.17456	−	12.3325i	−0.0801552	−	0.454583i
$737$	−8.42029	+	31.4250i	−0.310165	+	1.15755i
$738$	2.27615	+	3.64999i	0.0837862	+	0.134358i
$739$	6.38972	+	3.68911i	0.235050	+	0.135706i	0.612899	−	0.790161i	$-0.290003\pi$
$739$	6.38972	+	3.68911i	0.235050	+	0.135706i	−0.377850	+	0.925867i	$0.623336\pi$
$740$		0			0
$741$	−3.50711	−	1.04059i	−0.128837	−	0.0382271i
$742$	0.668790	−	0.0585116i	0.0245521	−	0.00214803i
$743$	32.2725	−	2.82348i	1.18396	−	0.103583i	0.521884	−	0.853017i	$-0.325229\pi$
$743$	32.2725	−	2.82348i	1.18396	−	0.103583i	0.662080	+	0.749433i	$0.269674\pi$
$744$	−13.3586	−	55.7544i	−0.489750	−	2.04405i
$745$		0			0
$746$	19.7713	+	11.4150i	0.723879	+	0.417932i
$747$	−35.1691	−	11.4625i	−1.28677	−	0.419393i
$748$	−4.41289	+	16.4691i	−0.161351	+	0.602170i
$749$	0.113918	+	0.646060i	0.00416247	+	0.0236065i
$750$		0			0
$751$	−17.0159	+	6.19326i	−0.620917	+	0.225995i	−0.633273	−	0.773928i	$-0.718289\pi$
$751$	−17.0159	+	6.19326i	−0.620917	+	0.225995i	0.0123561	+	0.999924i	$0.496067\pi$
$752$	−1.33466	+	0.934536i	−0.0486699	+	0.0340790i
$753$	5.67252	−	14.3813i	0.206718	−	0.524085i
$754$	2.10310	+	2.50638i	0.0765905	+	0.0912770i
$755$		0			0
$756$	0.160898	−	0.452399i	0.00585181	−	0.0164536i
$757$	−17.4396	+	17.4396i	−0.633854	+	0.633854i	−0.949033	−	0.315178i	$-0.897936\pi$
$757$	−17.4396	+	17.4396i	−0.633854	+	0.633854i	0.315178	+	0.949033i	$0.397936\pi$
$758$	−0.295082	+	3.37280i	−0.0107178	+	0.122506i
$759$	8.35856	−	11.2852i	0.303397	−	0.409627i
$760$		0			0
$761$	−13.1496	−	36.1282i	−0.476672	−	1.30965i	−0.912301	−	0.409520i	$-0.865696\pi$
$761$	−13.1496	−	36.1282i	−0.476672	−	1.30965i	0.435629	−	0.900126i	$-0.356526\pi$
$762$	31.9290	−	10.6671i	1.15666	−	0.386429i
$763$	−0.428201	+	0.611534i	−0.0155019	+	0.0221390i
$764$	−8.51014	−	14.7400i	−0.307886	−	0.533275i
$765$		0			0
$766$	−10.0829	+	17.4641i	−0.364310	+	0.631004i
$767$	−2.69756	−	5.78494i	−0.0974032	−	0.208882i
$768$	29.2894	+	0.780308i	1.05689	+	0.0281570i
$769$	−2.27346	+	2.70940i	−0.0819831	+	0.0977036i	−0.805477	−	0.592627i	$-0.798091\pi$
$769$	−2.27346	+	2.70940i	−0.0819831	+	0.0977036i	0.723494	+	0.690331i	$0.242535\pi$
$770$		0			0
$771$	16.1052	+	16.9868i	0.580015	+	0.611766i
$772$	−12.7142	+	5.92874i	−0.457595	+	0.213380i
$773$	12.2008	+	45.5341i	0.438833	+	1.63775i	0.731723	+	0.681602i	$0.238716\pi$
$773$	12.2008	+	45.5341i	0.438833	+	1.63775i	−0.292890	+	0.956146i	$0.594617\pi$
$774$	33.8129	−	4.12047i	1.21538	−	0.148107i
$775$		0			0
$776$	5.97754	−	1.05400i	0.214581	−	0.0378365i
$777$	0.154620	+	0.462809i	0.00554695	+	0.0166032i
$778$	12.0967	+	5.64079i	0.433688	+	0.202232i
$779$	−0.463594	+	2.62917i	−0.0166100	+	0.0941999i
$780$		0			0
$781$	−14.1345	+	11.8602i	−0.505771	+	0.424393i
$782$	−10.2132	−	10.2132i	−0.365225	−	0.365225i
$783$	13.6295	+	6.23383i	0.487080	+	0.222779i
$784$			7.84279i			0.280100i
$785$		0			0
$786$	−31.2262	+	13.5607i	−1.11380	+	0.483693i
$787$	−25.7839	−	36.8233i	−0.919098	−	1.31261i	−0.949728	−	0.313077i	$-0.898640\pi$
$787$	−25.7839	−	36.8233i	−0.919098	−	1.31261i	0.0306302	−	0.999531i	$-0.490249\pi$
$788$	−2.83333	+	6.07610i	−0.100933	+	0.216452i
$789$	−38.3969	+	2.33092i	−1.36697	+	0.0829829i
$790$		0			0
$791$	−1.50046	+	0.866293i	−0.0533504	+	0.0308018i
$792$	19.1403	+	21.2964i	0.680121	+	0.756735i
$793$	4.86778	−	1.30432i	0.172860	−	0.0463177i
$794$	19.7019	+	7.17089i	0.699193	+	0.254485i
$795$		0			0
$796$	−8.26620	−	6.93617i	−0.292988	−	0.245846i
$797$	−3.06411	−	35.0229i	−0.108536	−	1.24057i	−0.833786	−	0.552088i	$-0.813831\pi$
$797$	−3.06411	−	35.0229i	−0.108536	−	1.24057i	0.725249	−	0.688486i	$-0.241724\pi$
$798$	−0.278553	+	0.151078i	−0.00986068	+	0.00534811i
$799$	2.75963	−	7.58203i	0.0976288	−	0.268233i
$800$		0			0
$801$	32.4448	−	9.88711i	1.14638	−	0.349344i
$802$	−29.4824	−	7.89979i	−1.04106	−	0.278951i
$803$	−7.55590	−	5.29070i	−0.266642	−	0.186705i
$804$	−14.3897	+	9.51491i	−0.507485	+	0.335565i
$805$		0			0
$806$	12.2664	+	2.16289i	0.432065	+	0.0761847i
$807$	−31.5881	+	25.1028i	−1.11195	+	0.883662i
$808$	−47.2435	−	4.13327i	−1.66202	−	0.145408i
$809$	27.2053			0.956489			0.478244	−	0.878227i	$-0.341273\pi$
$809$	27.2053			0.956489			0.478244	+	0.878227i	$0.341273\pi$
$810$		0			0
$811$	7.54215			0.264841			0.132420	−	0.991194i	$-0.457725\pi$
$811$	7.54215			0.264841			0.132420	+	0.991194i	$0.457725\pi$
$812$	−0.265519	−	0.0232299i	−0.00931788	−	0.000815209i
$813$	14.5062	−	11.5280i	0.508756	−	0.404305i
$814$	−9.35464	−	1.64948i	−0.327880	−	0.0578141i
$815$		0			0
$816$	9.00465	−	5.95416i	0.315226	−	0.208437i
$817$	17.3178	+	12.1260i	0.605871	+	0.424236i
$818$	0.0459550	+	0.0123136i	0.00160678	+	0.000430535i
$819$	0.233510	+	0.218149i	0.00815949	+	0.00762274i
$820$		0			0
$821$	−2.67629	+	7.35304i	−0.0934031	+	0.256623i	−0.977593	−	0.210505i	$-0.932489\pi$
$821$	−2.67629	+	7.35304i	−0.0934031	+	0.256623i	0.884190	+	0.467128i	$0.154711\pi$
$822$	−3.05537	+	1.65713i	−0.106568	+	0.0577990i
$823$	0.836540	+	9.56170i	0.0291600	+	0.333300i	0.996737	+	0.0807223i	$0.0257227\pi$
$823$	0.836540	+	9.56170i	0.0291600	+	0.333300i	−0.967577	+	0.252577i	$0.918722\pi$
$824$	21.2205	+	17.8061i	0.739252	+	0.620306i
$825$		0			0
$826$	−0.519565	−	0.189106i	−0.0180780	−	0.00657985i
$827$	45.9650	−	12.3163i	1.59836	−	0.428279i	0.653812	−	0.756657i	$-0.273169\pi$
$827$	45.9650	−	12.3163i	1.59836	−	0.428279i	0.944546	+	0.328378i	$0.106502\pi$
$828$	7.28532	−	1.54161i	0.253182	−	0.0535748i
$829$	16.4702	−	9.50910i	0.572035	−	0.330265i	−0.185927	−	0.982564i	$-0.559529\pi$
$829$	16.4702	−	9.50910i	0.572035	−	0.330265i	0.757962	+	0.652299i	$0.226195\pi$
$830$		0			0
$831$	−48.4493	+	2.94115i	−1.68069	+	0.102028i
$832$	−3.40379	+	7.29945i	−0.118005	+	0.253063i
$833$	−22.2770	−	31.8149i	−0.771853	−	1.10232i
$834$	33.8449	−	14.6979i	1.17195	−	0.508946i
$835$		0			0
$836$			5.80130i			0.200642i
$837$	55.0016	−	15.1725i	1.90113	−	0.524437i
$838$	24.0786	+	24.0786i	0.831780	+	0.831780i
$839$	−10.3688	+	8.70044i	−0.357970	+	0.300373i	−0.803981	−	0.594655i	$-0.797289\pi$
$839$	−10.3688	+	8.70044i	−0.357970	+	0.300373i	0.446011	+	0.895028i	$0.352844\pi$
$840$		0			0
$841$	−3.59114	+	20.3664i	−0.123832	+	0.702289i
$842$	27.9977	+	13.0556i	0.964865	+	0.449924i
$843$	11.9764	+	35.8479i	0.412489	+	1.23467i
$844$	−4.07274	+	0.718134i	−0.140189	+	0.0247192i
$845$		0			0
$846$	−2.65885	−	3.53510i	−0.0914130	−	0.121539i
$847$	0.0240644	+	0.0898095i	0.000826862	+	0.00308589i
$848$	−7.05256	+	3.28866i	−0.242186	+	0.112933i
$849$	28.2068	+	29.7509i	0.968056	+	1.02105i
$850$		0			0
$851$	−4.86432	+	5.79707i	−0.166747	+	0.198721i
$852$	−9.78036	−	0.260561i	−0.335070	−	0.00892669i
$853$	−9.25913	−	19.8563i	−0.317026	−	0.679865i	0.681629	−	0.731698i	$-0.261272\pi$
$853$	−9.25913	−	19.8563i	−0.317026	−	0.679865i	−0.998656	+	0.0518322i	$0.983494\pi$
$854$	0.218267	−	0.378050i	0.00746895	−	0.0129366i
$855$		0			0
$856$	−10.3721	−	17.9650i	−0.354511	−	0.614031i
$857$	3.06418	−	4.37610i	0.104670	−	0.149485i	−0.763400	−	0.645926i	$-0.776471\pi$
$857$	3.06418	−	4.37610i	0.104670	−	0.149485i	0.868070	+	0.496441i	$0.165360\pi$
$858$	−5.90018	+	1.97119i	−0.201429	+	0.0672952i
$859$	18.0037	+	49.4648i	0.614279	+	1.68772i	0.720569	+	0.693383i	$0.243881\pi$
$859$	18.0037	+	49.4648i	0.614279	+	1.68772i	−0.106290	+	0.994335i	$0.533897\pi$
$860$		0			0
$861$	0.138802	−	0.187402i	0.00473038	−	0.00638665i
$862$	1.15278	−	13.1763i	0.0392637	−	0.448786i
$863$	13.4046	−	13.4046i	0.456299	−	0.456299i	−0.441139	−	0.897439i	$-0.645426\pi$
$863$	13.4046	−	13.4046i	0.456299	−	0.456299i	0.897439	+	0.441139i	$0.145426\pi$
$864$	0.187053	+	25.4091i	0.00636367	+	0.864436i
$865$		0			0
$866$	−18.4749	−	22.0175i	−0.627803	−	0.748187i
$867$	−8.81155	+	22.3396i	−0.299256	+	0.758693i
$868$	−0.831165	+	0.581988i	−0.0282116	+	0.0197540i
$869$	−26.8293	+	9.76507i	−0.910122	+	0.331257i
$870$		0			0
$871$	−1.99363	−	11.3065i	−0.0675517	−	0.383105i
$872$	6.10980	−	22.8021i	0.206904	−	0.772177i
$873$	1.25051	+	5.90964i	0.0423234	+	0.200011i
$874$	−4.25606	−	2.45724i	−0.143964	−	0.0831174i
$875$		0			0
$876$	−1.13964	−	4.75646i	−0.0385047	−	0.160706i
$877$	11.2439	−	0.983712i	0.379679	−	0.0332176i	0.104281	−	0.994548i	$-0.466746\pi$
$877$	11.2439	−	0.983712i	0.379679	−	0.0332176i	0.275398	+	0.961330i	$0.411190\pi$
$878$	19.3097	−	1.68938i	0.651672	−	0.0570139i
$879$	−2.37610	−	0.705008i	−0.0801438	−	0.0237793i
$880$		0			0
$881$	20.6068	+	11.8973i	0.694260	+	0.400831i	0.805206	−	0.592995i	$-0.202055\pi$
$881$	20.6068	+	11.8973i	0.694260	+	0.400831i	−0.110946	+	0.993826i	$0.535388\pi$
$882$	−21.2799	+	0.723722i	−0.716532	+	0.0243690i
$883$	−8.66082	+	32.3226i	−0.291460	+	1.08774i	0.652529	+	0.757764i	$0.273708\pi$
$883$	−8.66082	+	32.3226i	−0.291460	+	1.08774i	−0.943988	+	0.329978i	$0.892959\pi$
$884$	−1.04482	−	5.92546i	−0.0351410	−	0.199295i
$885$		0			0
$886$	−1.32596	+	0.482611i	−0.0445466	+	0.0162136i
$887$	20.4488	−	14.3184i	0.686603	−	0.480765i	−0.177473	−	0.984126i	$-0.556792\pi$
$887$	20.4488	−	14.3184i	0.686603	−	0.480765i	0.864076	+	0.503361i	$0.167903\pi$
$888$	−9.59965	−	12.0797i	−0.322143	−	0.405368i
$889$	−1.17314	−	1.39809i	−0.0393457	−	0.0468904i
$890$		0			0
$891$	−20.5340	+	19.7574i	−0.687916	+	0.661898i
$892$	9.96554	−	9.96554i	0.333671	−	0.333671i
$893$	0.239274	−	2.73491i	0.00800699	−	0.0915203i
$894$	−18.1416	−	2.07534i	−0.606746	−	0.0694097i
$895$		0			0
$896$	−0.0802794	−	0.220566i	−0.00268195	−	0.00736858i
$897$	−0.990254	+	4.85594i	−0.0330636	+	0.162135i
$898$	13.3656	−	19.0881i	0.446016	−	0.636977i
$899$	−15.8357	−	27.4282i	−0.528149	−	0.914781i
$900$		0			0
$901$	19.2680	−	33.3731i	0.641910	−	1.11182i
$902$	1.91861	+	4.11448i	0.0638828	+	0.136997i
$903$	−0.880442	−	1.62333i	−0.0292993	−	0.0540211i
$904$	35.2158	−	41.9685i	1.17126	−	1.39585i
$905$		0			0
$906$	−35.8722	+	8.59488i	−1.19177	+	0.285546i
$907$	37.0499	−	17.2767i	1.23022	−	0.573662i	0.304734	−	0.952438i	$-0.401433\pi$
$907$	37.0499	−	17.2767i	1.23022	−	0.573662i	0.925489	+	0.378776i	$0.123655\pi$
$908$	0.253084	+	0.944522i	0.00839889	+	0.0313451i
$909$	2.51290	−	47.1284i	0.0833478	−	1.56315i
$910$		0			0
$911$	36.3327	−	6.40644i	1.20376	−	0.212255i	0.464435	−	0.885607i	$-0.346258\pi$
$911$	36.3327	−	6.40644i	1.20376	−	0.212255i	0.739321	+	0.673353i	$0.235146\pi$
$912$	2.43510	−	2.74985i	0.0806341	−	0.0910568i
$913$	−35.3814	−	16.4986i	−1.17095	−	0.546024i
$914$	0.471191	−	2.67225i	0.0155856	−	0.0883903i
$915$		0			0
$916$	0.272806	−	0.228911i	0.00901376	−	0.00756344i
$917$	1.30509	+	1.30509i	0.0430978	+	0.0430978i
$918$	16.9864	+	23.8830i	0.560635	+	0.788255i
$919$			6.98816i			0.230518i	0.993335	+	0.115259i	$0.0367698\pi$
$919$			6.98816i			0.230518i	−0.993335	+	0.115259i	$0.963230\pi$
$920$		0			0
$921$	−6.94688	−	5.14531i	−0.228907	−	0.169544i
$922$	−12.3072	−	17.5765i	−0.405317	−	0.578853i
$923$	2.75181	−	5.90127i	0.0905769	−	0.194243i
$924$	0.226320	−	0.453412i	0.00744540	−	0.0149162i
$925$		0			0
$926$	1.06552	−	0.615178i	0.0350152	−	0.0202160i
$927$	−16.9922	+	21.7083i	−0.558098	+	0.712995i
$928$	13.6242	−	3.65059i	0.447236	−	0.119837i
$929$	26.6437	+	9.69750i	0.874150	+	0.318165i	0.739847	−	0.672776i	$-0.234898\pi$
$929$	26.6437	+	9.69750i	0.874150	+	0.318165i	0.134303	+	0.990940i	$0.457120\pi$
$930$		0			0
$931$	−10.1232	−	8.49439i	−0.331775	−	0.278392i
$932$	−0.0832210	−	0.951220i	−0.00272599	−	0.0311583i
$933$	0.908218	−	34.0906i	0.0297337	−	1.11608i
$934$	−1.22003	+	3.35199i	−0.0399205	+	0.109681i
$935$		0			0
$936$	−9.29778	−	3.95667i	−0.303908	−	0.129328i
$937$	23.2187	+	6.22144i	0.758523	+	0.203246i	0.617295	−	0.786732i	$-0.288228\pi$
$937$	23.2187	+	6.22144i	0.758523	+	0.203246i	0.141228	+	0.989977i	$0.454895\pi$
$938$	−0.814649	−	0.570424i	−0.0265992	−	0.0186250i
$939$	9.06805	+	4.52632i	0.295925	+	0.147711i
$940$		0			0
$941$	46.1660	+	8.14032i	1.50497	+	0.265367i	0.864506	−	0.502622i	$-0.167631\pi$
$941$	46.1660	+	8.14032i	1.50497	+	0.265367i	0.640463	+	0.767989i	$0.278742\pi$
$942$	−3.04959	−	20.4690i	−0.0993609	−	0.666915i
$943$	3.60298	+	0.315220i	0.117329	+	0.0102650i
$944$	6.40884			0.208590
$945$		0			0
$946$	35.9499			1.16883
$947$	38.6945	+	3.38533i	1.25740	+	0.110009i	0.696308	−	0.717743i	$-0.254825\pi$
$947$	38.6945	+	3.38533i	1.25740	+	0.110009i	0.561095	+	0.827751i	$0.310380\pi$
$948$	−14.0834	−	5.55499i	−0.457407	−	0.180418i
$949$	3.20566	+	0.565244i	0.104060	+	0.0183486i
$950$		0			0
$951$	−2.46034	−	40.5289i	−0.0797821	−	1.31424i
$952$	−1.30786	−	0.915775i	−0.0423880	−	0.0296804i
$953$	−27.5802	−	7.39010i	−0.893412	−	0.239389i	−0.217227	−	0.976121i	$-0.569701\pi$
$953$	−27.5802	−	7.39010i	−0.893412	−	0.239389i	−0.676185	+	0.736732i	$0.736368\pi$
$954$	−9.57397	−	18.8323i	−0.309969	−	0.609719i
$955$		0			0
$956$	−7.60268	+	20.8882i	−0.245888	+	0.675572i
$957$	13.4831	+	8.27087i	0.435845	+	0.267359i
$958$	3.41695	+	39.0559i	0.110397	+	1.26184i
$959$	0.144354	+	0.121128i	0.00466145	+	0.00391142i
$960$		0			0
$961$	−84.1681	−	30.6347i	−2.71510	−	0.988215i
$962$	3.23790	−	0.867593i	0.104394	−	0.0279723i
$963$	17.5172	−	10.9238i	0.564484	−	0.352015i
$964$	16.1321	−	9.31390i	0.519581	−	0.299981i
$965$		0			0
$966$	0.236779	+	0.358088i	0.00761824	+	0.0115213i
$967$	13.1114	−	28.1176i	0.421636	−	0.904201i	−0.574675	−	0.818382i	$-0.694872\pi$
$967$	13.1114	−	28.1176i	0.421636	−	0.904201i	0.996311	−	0.0858189i	$-0.0273507\pi$
$968$	−1.68634	−	2.40834i	−0.0542010	−	0.0774070i
$969$	−2.06735	+	18.0718i	−0.0664128	+	0.580548i
$970$		0			0
$971$			0.0712926i			0.00228789i	0.999999	+	0.00114394i	$0.000364129\pi$
$971$			0.0712926i			0.00228789i	−0.999999	+	0.00114394i	$0.999636\pi$
$972$	−15.0970	+	0.624737i	−0.484236	+	0.0200385i
$973$	−1.41453	−	1.41453i	−0.0453479	−	0.0453479i
$974$	6.90724	−	5.79587i	0.221322	−	0.185712i
$975$		0			0
$976$	−0.878647	+	4.98305i	−0.0281248	+	0.159504i
$977$	−9.45855	−	4.41060i	−0.302606	−	0.141107i	0.265384	−	0.964143i	$-0.414501\pi$
$977$	−9.45855	−	4.41060i	−0.302606	−	0.141107i	−0.567990	+	0.823035i	$0.692279\pi$
$978$	36.6041	+	7.46453i	1.17047	+	0.238689i
$979$	35.2529	−	6.21604i	1.12669	−	0.198665i
$980$		0			0
$981$	22.8857	+	5.30553i	0.730685	+	0.169392i
$982$	4.71669	+	17.6029i	0.150516	+	0.561732i
$983$	−16.9928	+	7.92390i	−0.541988	+	0.252733i	−0.674278	−	0.738478i	$-0.735545\pi$
$983$	−16.9928	+	7.92390i	−0.541988	+	0.252733i	0.132290	+	0.991211i	$0.457767\pi$
$984$	−2.09762	+	7.06962i	−0.0668696	+	0.225371i
$985$		0			0
$986$	10.4571	−	12.4623i	0.333023	−	0.396881i
$987$	−0.125395	+	0.204418i	−0.00399137	+	0.00650668i
$988$	−0.865202	−	1.85543i	−0.0275257	−	0.0590292i
$989$	14.3201	−	24.8032i	0.455353	−	0.788695i
$990$		0			0
$991$	5.25715	+	9.10566i	0.166999	+	0.289251i	0.937363	−	0.348353i	$-0.113259\pi$
$991$	5.25715	+	9.10566i	0.166999	+	0.289251i	−0.770364	+	0.637604i	$0.779926\pi$
$992$	30.7986	−	43.9849i	0.977855	−	1.39652i
$993$	−16.0393	−	14.2034i	−0.508991	−	0.450730i
$994$	−0.192909	−	0.530013i	−0.00611871	−	0.0168110i
$995$		0			0
$996$	−8.24569	−	18.9874i	−0.261275	−	0.601639i
$997$	0.374273	−	4.27796i	0.0118533	−	0.135484i	−0.987962	−	0.154696i	$-0.950560\pi$
$997$	0.374273	−	4.27796i	0.0118533	−	0.135484i	0.999815	+	0.0192119i	$0.00611571\pi$
$998$	−17.9068	+	17.9068i	−0.566831	+	0.566831i
$999$	11.6898	−	9.95646i	0.369849	−	0.315008i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.ba.c.518.17	yes	288
5.2	odd	4	inner	675.2.ba.c.32.8	✓	288
5.3	odd	4	inner	675.2.ba.c.32.17	yes	288
5.4	even	2	inner	675.2.ba.c.518.8	yes	288
27.11	odd	18	inner	675.2.ba.c.443.8	yes	288
135.38	even	36	inner	675.2.ba.c.632.8	yes	288
135.92	even	36	inner	675.2.ba.c.632.17	yes	288
135.119	odd	18	inner	675.2.ba.c.443.17	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
675.2.ba.c.32.8	✓	288	5.2	odd	4	inner
675.2.ba.c.32.17	yes	288	5.3	odd	4	inner
675.2.ba.c.443.8	yes	288	27.11	odd	18	inner
675.2.ba.c.443.17	yes	288	135.119	odd	18	inner
675.2.ba.c.518.8	yes	288	5.4	even	2	inner
675.2.ba.c.518.17	yes	288	1.1	even	1	trivial
675.2.ba.c.632.8	yes	288	135.38	even	36	inner
675.2.ba.c.632.17	yes	288	135.92	even	36	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.ba (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.01137 + 0.0884834i) q^{2} +(-1.35601 + 1.07761i) q^{3} +(-0.954575 - 0.168317i) q^{4} +(-1.46678 + 0.969879i) q^{6} +(0.0780926 + 0.0546810i) q^{7} +(-2.91182 - 0.780219i) q^{8} +(0.677513 - 2.92249i) q^{9} +(1.08290 - 2.97524i) q^{11} +(1.47579 - 0.800420i) q^{12} +(0.0973814 + 1.11307i) q^{13} +(0.0741421 + 0.0622126i) q^{14} +(-1.05420 - 0.383697i) q^{16} +(5.36631 - 1.43790i) q^{17} +(0.943809 - 2.89578i) q^{18} +(1.63705 - 0.945151i) q^{19} +(-0.164819 + 0.0100055i) q^{21} +(1.35847 - 2.91325i) q^{22} +(-1.46883 - 2.09771i) q^{23} +(4.78922 - 2.07982i) q^{24} +1.13435i q^{26} +(2.23060 + 4.69302i) q^{27} +(-0.0653414 - 0.0653414i) q^{28} +(2.20954 - 1.85402i) q^{29} +(1.90673 - 10.8136i) q^{31} +(4.43196 + 2.06666i) q^{32} +(1.73773 + 5.20139i) q^{33} +(5.55456 - 0.979419i) q^{34} +(-1.13864 + 2.67570i) q^{36} +(-0.764839 - 2.85442i) q^{37} +(1.73929 - 0.811046i) q^{38} +(-1.33151 - 1.40440i) q^{39} +(-0.907830 + 1.08191i) q^{41} +(-0.167578 - 0.00446450i) q^{42} +(4.72655 + 10.1361i) q^{43} +(-1.53449 + 2.65782i) q^{44} +(-1.29992 - 2.25153i) q^{46} +(0.833027 - 1.18969i) q^{47} +(1.84298 - 0.615719i) q^{48} +(-2.39103 - 6.56931i) q^{49} +(-5.72726 + 7.73259i) q^{51} +(0.0943918 - 1.07890i) q^{52} +(4.90478 - 4.90478i) q^{53} +(1.84070 + 4.94375i) q^{54} +(-0.184728 - 0.220150i) q^{56} +(-1.20135 + 3.04573i) q^{57} +(2.39871 - 1.67959i) q^{58} +(-5.36820 + 1.95387i) q^{59} +(-0.783208 - 4.44180i) q^{61} +(2.88524 - 10.7679i) q^{62} +(0.212714 - 0.191178i) q^{63} +(6.24259 + 3.60416i) q^{64} +(1.29725 + 5.41429i) q^{66} +(-10.2362 + 0.895552i) q^{67} +(-5.36457 + 0.469339i) q^{68} +(4.25226 + 1.26168i) q^{69} +(-5.04685 - 2.91380i) q^{71} +(-4.25298 + 7.98116i) q^{72} +(0.754018 - 2.81403i) q^{73} +(-0.520967 - 2.95455i) q^{74} +(-1.72177 + 0.626673i) q^{76} +(0.247255 - 0.173130i) q^{77} +(-1.22238 - 1.53818i) q^{78} +(-5.79636 - 6.90783i) q^{79} +(-8.08195 - 3.96006i) q^{81} +(-1.01388 + 1.01388i) q^{82} +(1.07463 - 12.2831i) q^{83} +(0.159016 + 0.0181909i) q^{84} +(3.88341 + 10.6696i) q^{86} +(-0.998236 + 4.89509i) q^{87} +(-5.47454 + 7.81845i) q^{88} +(5.65298 + 9.79125i) q^{89} +(-0.0532593 + 0.0922477i) q^{91} +(1.04903 + 2.24965i) q^{92} +(9.06731 + 16.7180i) q^{93} +(0.947766 - 1.12950i) q^{94} +(-8.23681 + 1.97352i) q^{96} +(-1.82485 + 0.850941i) q^{97} +(-1.83694 - 6.85557i) q^{98} +(-7.96144 - 5.18053i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q + 24 q^{6} + 36 q^{11} + 48 q^{21} - 192 q^{36} - 180 q^{41} - 60 q^{51} - 288 q^{56} + 72 q^{61} + 144 q^{71} + 216 q^{76} + 24 q^{81} - 36 q^{91} - 168 q^{96}+O(q^{100}) \) 288 * q + 24 * q^6 + 36 * q^11 + 48 * q^21 - 192 * q^36 - 180 * q^41 - 60 * q^51 - 288 * q^56 + 72 * q^61 + 144 * q^71 + 216 * q^76 + 24 * q^81 - 36 * q^91 - 168 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more