LMFDB - Embedded newform 675.2.ba.b.407.11

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)

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);

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")

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 = [192] 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:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			407.11
Character	$\chi$	$=$	675.407
Dual form			675.2.ba.b.68.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.761943 + 1.08817i) q^{2} +(-1.60100 + 0.660916i) q^{3} +(0.0804885 - 0.221140i) q^{4} +(-1.93906 - 1.23857i) q^{6} +(-1.77434 - 0.827388i) q^{7} +(2.86825 - 0.768546i) q^{8} +(2.12638 - 2.11625i) q^{9} +(-2.76562 + 3.29594i) q^{11} +(0.0172933 + 0.407241i) q^{12} +(4.15220 + 2.90740i) q^{13} +(-0.451609 - 2.56120i) q^{14} +(2.66120 + 2.23301i) q^{16} +(3.09176 + 0.828434i) q^{17} +(3.92301 + 0.701399i) q^{18} +(0.776109 + 0.448087i) q^{19} +(3.38755 + 0.151957i) q^{21} +(-5.69379 - 0.498142i) q^{22} +(2.36525 + 5.07230i) q^{23} +(-4.08412 + 3.12611i) q^{24} +6.73356i q^{26} +(-2.00567 + 4.79346i) q^{27} +(-0.325783 + 0.325783i) q^{28} +(-1.14702 + 6.50507i) q^{29} +(2.27652 + 0.828586i) q^{31} +(0.115398 - 1.31900i) q^{32} +(2.24941 - 7.10463i) q^{33} +(1.45427 + 3.99557i) q^{34} +(-0.296839 - 0.640563i) q^{36} +(1.86654 - 6.96604i) q^{37} +(0.103757 + 1.18595i) q^{38} +(-8.56920 - 1.91049i) q^{39} +(8.33680 - 1.47000i) q^{41} +(2.41576 + 3.80200i) q^{42} +(-1.28541 + 0.112459i) q^{43} +(0.506265 + 0.876877i) q^{44} +(-3.71732 + 6.43859i) q^{46} +(-3.48305 + 7.46943i) q^{47} +(-5.73641 - 1.81622i) q^{48} +(-2.03580 - 2.42617i) q^{49} +(-5.49742 + 0.717071i) q^{51} +(0.977148 - 0.684206i) q^{52} +(-0.947342 - 0.947342i) q^{53} +(-6.74430 + 1.46984i) q^{54} +(-5.72514 - 1.00950i) q^{56} +(-1.53869 - 0.204443i) q^{57} +(-7.95258 + 3.70835i) q^{58} +(3.72879 - 3.12883i) q^{59} +(-7.90101 + 2.87573i) q^{61} +(0.832940 + 3.10857i) q^{62} +(-5.52388 + 1.99560i) q^{63} +(7.54029 - 4.35339i) q^{64} +(9.44496 - 2.96559i) q^{66} +(-5.53556 + 7.90560i) q^{67} +(0.432051 - 0.617033i) q^{68} +(-7.13912 - 6.55750i) q^{69} +(4.92123 - 2.84127i) q^{71} +(4.47256 - 7.70415i) q^{72} +(1.32285 + 4.93694i) q^{73} +(9.00242 - 3.27661i) q^{74} +(0.161558 - 0.135563i) q^{76} +(7.63418 - 3.55988i) q^{77} +(-4.45032 - 10.7804i) q^{78} +(0.410612 + 0.0724019i) q^{79} +(0.0429919 - 8.99990i) q^{81} +(7.95178 + 7.95178i) q^{82} +(7.59392 - 5.31732i) q^{83} +(0.306263 - 0.736893i) q^{84} +(-1.10179 - 1.31306i) q^{86} +(-2.46293 - 11.1727i) q^{87} +(-5.39942 + 11.5791i) q^{88} +(0.974450 - 1.68780i) q^{89} +(-4.96186 - 8.59420i) q^{91} +(1.31207 - 0.114791i) q^{92} +(-4.19233 + 0.178025i) q^{93} +(-10.7819 + 1.90114i) q^{94} +(0.686998 + 2.18799i) q^{96} +(-1.17718 - 13.4552i) q^{97} +(1.08892 - 4.06390i) q^{98} +(1.09426 + 12.8612i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{3} - 36 q^{6} + 12 q^{7} + 18 q^{8} - 36 q^{11} + 12 q^{12} + 12 q^{13} - 24 q^{16} + 18 q^{17} + 54 q^{18} - 24 q^{21} + 12 q^{22} + 36 q^{23} + 36 q^{27} + 24 q^{28} - 24 q^{31}+ \cdots - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^3 - 36 * q^6 + 12 * q^7 + 18 * q^8 - 36 * q^11 + 12 * q^12 + 12 * q^13 - 24 * q^16 + 18 * q^17 + 54 * q^18 - 24 * q^21 + 12 * q^22 + 36 * q^23 + 36 * q^27 + 24 * q^28 - 24 * q^31 + 48 * q^32 + 6 * q^33 + 12 * q^36 + 6 * q^37 - 12 * q^38 + 24 * q^41 + 24 * q^42 + 12 * q^43 - 12 * q^46 + 6 * q^47 - 12 * q^48 + 144 * q^51 - 12 * q^52 + 180 * q^56 + 12 * q^57 + 12 * q^58 - 60 * q^61 + 18 * q^62 + 54 * q^63 + 72 * q^66 - 24 * q^67 + 60 * q^68 - 36 * q^71 - 180 * q^72 + 6 * q^73 - 72 * q^76 - 132 * q^77 - 78 * q^78 + 12 * q^81 + 24 * q^82 - 48 * q^83 + 12 * q^86 - 144 * q^87 + 48 * q^88 - 12 * q^91 - 258 * q^92 - 180 * q^93 - 12 * q^96 - 24 * q^97 - 324 * q^98

Character values

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

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.761943	+	1.08817i	0.538775	+	0.769451i	0.992573	−	0.121654i	$-0.0388198\pi$
$2$	0.761943	+	1.08817i	0.538775	+	0.769451i	−0.453797	+	0.891105i	$0.649931\pi$
$3$	−1.60100	+	0.660916i	−0.924336	+	0.381580i
$3$	−1.60100	+	0.660916i	−0.924336	+	0.381580i
$4$	0.0804885	−	0.221140i	0.0402443	−	0.110570i
$5$		0			0
$5$		0			0
$6$	−1.93906	−	1.23857i	−0.791616	−	0.505645i
$7$	−1.77434	−	0.827388i	−0.670638	−	0.312723i	0.0573098	−	0.998356i	$-0.481748\pi$
$7$	−1.77434	−	0.827388i	−0.670638	−	0.312723i	−0.727947	+	0.685633i	$0.759526\pi$
$8$	2.86825	−	0.768546i	1.01408	−	0.271722i
$9$	2.12638	−	2.11625i	0.708794	−	0.705416i
$10$		0			0
$11$	−2.76562	+	3.29594i	−0.833867	+	0.993764i	0.166104	+	0.986108i	$0.446881\pi$
$11$	−2.76562	+	3.29594i	−0.833867	+	0.993764i	−0.999971	+	0.00765542i	$0.997563\pi$
$12$	0.0172933	+	0.407241i	0.00499215	+	0.117560i
$13$	4.15220	+	2.90740i	1.15161	+	0.806368i	0.983768	−	0.179446i	$-0.0574305\pi$
$13$	4.15220	+	2.90740i	1.15161	+	0.806368i	0.167844	+	0.985814i	$0.446319\pi$
$14$	−0.451609	−	2.56120i	−0.120698	−	0.684510i
$15$		0			0
$16$	2.66120	+	2.23301i	0.665301	+	0.558253i
$17$	3.09176	+	0.828434i	0.749861	+	0.200925i	0.613456	−	0.789729i	$-0.289779\pi$
$17$	3.09176	+	0.828434i	0.749861	+	0.200925i	0.136405	+	0.990653i	$0.456445\pi$
$18$	3.92301	+	0.701399i	0.924663	+	0.165321i
$19$	0.776109	+	0.448087i	0.178052	+	0.102798i	0.586377	−	0.810038i	$-0.300554\pi$
$19$	0.776109	+	0.448087i	0.178052	+	0.102798i	−0.408325	+	0.912836i	$0.633887\pi$
$20$		0			0
$21$	3.38755	+	0.151957i	0.739223	+	0.0331597i
$22$	−5.69379	−	0.498142i	−1.21392	−	0.106204i
$23$	2.36525	+	5.07230i	0.493189	+	1.05765i	0.982624	+	0.185607i	$0.0594253\pi$
$23$	2.36525	+	5.07230i	0.493189	+	1.05765i	−0.489435	+	0.872040i	$0.662797\pi$
$24$	−4.08412	+	3.12611i	−0.833667	+	0.638115i
$25$		0			0
$26$			6.73356i			1.32056i
$27$	−2.00567	+	4.79346i	−0.385991	+	0.922503i
$28$	−0.325783	+	0.325783i	−0.0615672	+	0.0615672i
$29$	−1.14702	+	6.50507i	−0.212996	+	1.20796i	0.671354	+	0.741137i	$0.265713\pi$
$29$	−1.14702	+	6.50507i	−0.212996	+	1.20796i	−0.884350	+	0.466825i	$0.845398\pi$
$30$		0			0
$31$	2.27652	+	0.828586i	0.408875	+	0.148818i	0.538266	−	0.842775i	$-0.319080\pi$
$31$	2.27652	+	0.828586i	0.408875	+	0.148818i	−0.129390	+	0.991594i	$0.541302\pi$
$32$	0.115398	−	1.31900i	0.0203996	−	0.233169i
$33$	2.24941	−	7.10463i	0.391573	−	1.23676i
$34$	1.45427	+	3.99557i	0.249405	+	0.685235i
$35$		0			0
$36$	−0.296839	−	0.640563i	−0.0494731	−	0.106760i
$37$	1.86654	−	6.96604i	0.306858	−	1.14521i	−0.624476	−	0.781044i	$-0.714688\pi$
$37$	1.86654	−	6.96604i	0.306858	−	1.14521i	0.931334	−	0.364166i	$-0.118646\pi$
$38$	0.103757	+	1.18595i	0.0168317	+	0.192387i
$39$	−8.56920	−	1.91049i	−1.37217	−	0.305922i
$40$		0			0
$41$	8.33680	−	1.47000i	1.30199	−	0.229576i	0.520697	−	0.853742i	$-0.325672\pi$
$41$	8.33680	−	1.47000i	1.30199	−	0.229576i	0.781292	+	0.624166i	$0.214561\pi$
$42$	2.41576	+	3.80200i	0.372761	+	0.586662i
$43$	−1.28541	+	0.112459i	−0.196024	+	0.0171499i	−0.184745	−	0.982787i	$-0.559146\pi$
$43$	−1.28541	+	0.112459i	−0.196024	+	0.0171499i	−0.0112790	+	0.999936i	$0.503590\pi$
$44$	0.506265	+	0.876877i	0.0763223	+	0.132194i
$45$		0			0
$46$	−3.71732	+	6.43859i	−0.548090	+	0.949319i
$47$	−3.48305	+	7.46943i	−0.508055	+	1.08953i	0.470283	+	0.882516i	$0.344152\pi$
$47$	−3.48305	+	7.46943i	−0.508055	+	1.08953i	−0.978338	+	0.207013i	$0.933626\pi$
$48$	−5.73641	−	1.81622i	−0.827979	−	0.262148i
$49$	−2.03580	−	2.42617i	−0.290829	−	0.346596i
$50$		0			0
$51$	−5.49742	+	0.717071i	−0.769792	+	0.100410i
$52$	0.977148	−	0.684206i	0.135506	−	0.0948823i
$53$	−0.947342	−	0.947342i	−0.130127	−	0.130127i	0.639043	−	0.769171i	$-0.279330\pi$
$53$	−0.947342	−	0.947342i	−0.130127	−	0.130127i	−0.769171	+	0.639043i	$0.779330\pi$
$54$	−6.74430	+	1.46984i	−0.917783	+	0.200021i
$55$		0			0
$56$	−5.72514	−	1.00950i	−0.765054	−	0.134900i
$57$	−1.53869	−	0.204443i	−0.203805	−	0.0270791i
$58$	−7.95258	+	3.70835i	−1.04422	+	0.486930i
$59$	3.72879	−	3.12883i	0.485447	−	0.407339i	−0.366944	−	0.930243i	$-0.619596\pi$
$59$	3.72879	−	3.12883i	0.485447	−	0.407339i	0.852391	+	0.522904i	$0.175151\pi$
$60$		0			0
$61$	−7.90101	+	2.87573i	−1.01162	+	0.368200i	−0.794055	−	0.607846i	$-0.792034\pi$
$61$	−7.90101	+	2.87573i	−1.01162	+	0.368200i	−0.217566	+	0.976046i	$0.569812\pi$
$62$	0.832940	+	3.10857i	0.105783	+	0.394789i
$63$	−5.52388	+	1.99560i	−0.695944	+	0.251422i
$64$	7.54029	−	4.35339i	0.942536	−	0.544173i
$65$		0			0
$66$	9.44496	−	2.96559i	1.16259	−	0.365039i
$67$	−5.53556	+	7.90560i	−0.676276	+	0.965822i	0.323532	+	0.946217i	$0.395130\pi$
$67$	−5.53556	+	7.90560i	−0.676276	+	0.965822i	−0.999808	+	0.0196049i	$0.993759\pi$
$68$	0.432051	−	0.617033i	0.0523939	−	0.0748262i
$69$	−7.13912	−	6.55750i	−0.859449	−	0.789430i
$70$		0			0
$71$	4.92123	−	2.84127i	0.584043	−	0.337197i	−0.178696	−	0.983904i	$-0.557188\pi$
$71$	4.92123	−	2.84127i	0.584043	−	0.337197i	0.762738	+	0.646707i	$0.223854\pi$
$72$	4.47256	−	7.70415i	0.527097	−	0.907943i
$73$	1.32285	+	4.93694i	0.154828	+	0.577825i	0.999120	+	0.0419419i	$0.0133544\pi$
$73$	1.32285	+	4.93694i	0.154828	+	0.577825i	−0.844292	+	0.535883i	$0.819979\pi$
$74$	9.00242	−	3.27661i	1.04651	−	0.380898i
$75$		0			0
$76$	0.161558	−	0.135563i	0.0185320	−	0.0155502i
$77$	7.63418	−	3.55988i	0.869996	−	0.405686i
$78$	−4.45032	−	10.7804i	−0.503899	−	1.22064i
$79$	0.410612	+	0.0724019i	0.0461974	+	0.00814585i	0.196699	−	0.980464i	$-0.436978\pi$
$79$	0.410612	+	0.0724019i	0.0461974	+	0.00814585i	−0.150502	+	0.988610i	$0.548089\pi$
$80$		0			0
$81$	0.0429919	−	8.99990i	0.00477688	−	0.999989i
$82$	7.95178	+	7.95178i	0.878127	+	0.878127i
$83$	7.59392	−	5.31732i	0.833541	−	0.583652i	−0.0770185	−	0.997030i	$-0.524540\pi$
$83$	7.59392	−	5.31732i	0.833541	−	0.583652i	0.910560	+	0.413378i	$0.135651\pi$
$84$	0.306263	−	0.736893i	0.0334160	−	0.0804016i
$85$		0			0
$86$	−1.10179	−	1.31306i	−0.118809	−	0.141591i
$87$	−2.46293	−	11.1727i	−0.264054	−	1.19784i
$88$	−5.39942	+	11.5791i	−0.575580	+	1.23434i
$89$	0.974450	−	1.68780i	0.103292	−	0.178906i	−0.809747	−	0.586779i	$-0.800396\pi$
$89$	0.974450	−	1.68780i	0.103292	−	0.178906i	0.913039	+	0.407872i	$0.133729\pi$
$90$		0			0
$91$	−4.96186	−	8.59420i	−0.520144	−	0.900917i
$92$	1.31207	−	0.114791i	0.136792	−	0.0119678i
$93$	−4.19233	+	0.178025i	−0.434724	+	0.0184604i
$94$	−10.7819	+	1.90114i	−1.11207	+	0.196087i
$95$		0			0
$96$	0.686998	+	2.18799i	0.0701164	+	0.223310i
$97$	−1.17718	−	13.4552i	−0.119524	−	1.36617i	−0.784883	−	0.619644i	$-0.787277\pi$
$97$	−1.17718	−	13.4552i	−0.119524	−	1.36617i	0.665359	−	0.746524i	$-0.268279\pi$
$98$	1.08892	−	4.06390i	0.109997	−	0.410516i
$99$	1.09426	+	12.8612i	0.109977	+	1.29260i
$100$		0			0
$101$	−1.45521	−	3.99814i	−0.144798	−	0.397830i	0.845999	−	0.533185i	$-0.179005\pi$
$101$	−1.45521	−	3.99814i	−0.144798	−	0.397830i	−0.990797	+	0.135354i	$0.956783\pi$
$102$	−4.96901	−	5.43575i	−0.492006	−	0.538219i
$103$	1.16385	−	13.3028i	0.114677	−	1.31077i	−0.692912	−	0.721022i	$-0.743673\pi$
$103$	1.16385	−	13.3028i	0.114677	−	1.31077i	0.807589	−	0.589745i	$-0.200772\pi$
$104$	14.1440	+	5.14800i	1.38694	+	0.504803i
$105$		0			0
$106$	0.309046	−	1.75269i	0.0300172	−	0.170236i
$107$	−10.2616	+	10.2616i	−0.992026	+	0.992026i	−0.999968	−	0.00794276i	$-0.997472\pi$
$107$	−10.2616	+	10.2616i	−0.992026	+	0.992026i	0.00794276	+	0.999968i	$0.497472\pi$
$108$	0.898596	+	0.829353i	0.0864674	+	0.0798045i
$109$			14.3459i			1.37409i	0.726615	+	0.687045i	$0.241092\pi$
$109$			14.3459i			1.37409i	−0.726615	+	0.687045i	$0.758908\pi$
$110$		0			0
$111$	1.61563	+	12.3862i	0.153349	+	1.17565i
$112$	−2.87431	−	6.16397i	−0.271597	−	0.582441i
$113$	13.5865	+	1.18867i	1.27811	+	0.111821i	0.705916	−	0.708295i	$-0.250535\pi$
$113$	13.5865	+	1.18867i	1.27811	+	0.111821i	0.572198	+	0.820116i	$0.306091\pi$
$114$	−0.949930	−	1.83013i	−0.0889691	−	0.171408i
$115$		0			0
$116$	1.34621	+	0.777236i	0.124993	+	0.0721646i
$117$	14.9819	−	2.60484i	1.38508	−	0.240817i
$118$	6.24582	+	1.67356i	0.574974	+	0.154064i
$119$	−4.80039	−	4.02801i	−0.440051	−	0.369247i
$120$		0			0
$121$	−1.30443	−	7.39778i	−0.118584	−	0.672525i
$122$	−9.14940	−	6.40648i	−0.828348	−	0.580016i
$123$	−12.3756	+	7.86339i	−1.11587	+	0.709018i
$124$	0.366468	−	0.436739i	0.0329098	−	0.0392204i
$125$		0			0
$126$	−6.38043	−	4.49038i	−0.568414	−	0.400035i
$127$	3.47767	−	0.931838i	0.308593	−	0.0826872i	−0.101199	−	0.994866i	$-0.532268\pi$
$127$	3.47767	−	0.931838i	0.308593	−	0.0826872i	0.409792	+	0.912179i	$0.365601\pi$
$128$	8.08251	+	3.76894i	0.714400	+	0.333130i
$129$	1.98362	−	1.02960i	0.174648	−	0.0906510i
$130$		0			0
$131$	0.189922	−	0.521807i	0.0165936	−	0.0455905i	−0.931119	−	0.364715i	$-0.881167\pi$
$131$	0.189922	−	0.521807i	0.0165936	−	0.0455905i	0.947713	+	0.319124i	$0.103389\pi$
$132$	−1.39007	−	1.06928i	−0.120990	−	0.0930687i
$133$	−1.00634	−	1.43720i	−0.0872607	−	0.124621i
$134$	−12.8204			−1.10751
$135$		0			0
$136$	9.50463			0.815015
$137$	3.46624	+	4.95031i	0.296141	+	0.422934i	0.939457	−	0.342668i	$-0.111330\pi$
$137$	3.46624	+	4.95031i	0.296141	+	0.422934i	−0.643315	+	0.765601i	$0.722442\pi$
$138$	1.69606	−	12.7650i	0.144378	−	1.08663i
$139$	6.33390	−	17.4022i	0.537234	−	1.47604i	−0.313061	−	0.949733i	$-0.601354\pi$
$139$	6.33390	−	17.4022i	0.537234	−	1.47604i	0.850295	−	0.526306i	$-0.176423\pi$
$140$		0			0
$141$	0.639692	−	14.2605i	0.0538718	−	1.20095i
$142$	6.84148	+	3.19024i	0.574125	+	0.267719i
$143$	−21.0660	+	5.64463i	−1.76163	+	0.472027i
$144$	10.3843	−	0.883525i	0.865362	−	0.0736271i
$145$		0			0
$146$	−4.36428	+	5.20115i	−0.361190	+	0.430450i
$147$	4.86281	+	2.53880i	0.401078	+	0.209397i
$148$	−1.39024	−	0.973455i	−0.114277	−	0.0800175i
$149$	−1.50609	−	8.54145i	−0.123384	−	0.699743i	−0.982255	−	0.187551i	$-0.939945\pi$
$149$	−1.50609	−	8.54145i	−0.123384	−	0.699743i	0.858871	−	0.512192i	$-0.171166\pi$
$150$		0			0
$151$	−12.2052	−	10.2414i	−0.993244	−	0.833431i	−0.00721007	−	0.999974i	$-0.502295\pi$
$151$	−12.2052	−	10.2414i	−0.993244	−	0.833431i	−0.986034	+	0.166543i	$0.946740\pi$
$152$	2.57045	+	0.688750i	0.208491	+	0.0558650i
$153$	8.32742	−	4.78136i	0.673232	−	0.386550i
$154$	9.69056	+	5.59485i	0.780887	+	0.450846i
$155$		0			0
$156$	−1.11221	+	1.74122i	−0.0890479	+	0.139410i
$157$	−13.2243	−	1.15698i	−1.05541	−	0.0923367i	−0.453784	−	0.891112i	$-0.649926\pi$
$157$	−13.2243	−	1.15698i	−1.05541	−	0.0923367i	−0.601630	+	0.798775i	$0.705482\pi$
$158$	0.234077	+	0.501981i	0.0186222	+	0.0399354i
$159$	2.14280	+	0.890578i	0.169935	+	0.0706274i
$160$		0			0
$161$		−	10.9570i		−	0.863530i
$162$	9.82616	−	6.81063i	0.772016	−	0.535094i
$163$	−5.24760	+	5.24760i	−0.411024	+	0.411024i	−0.882095	−	0.471071i	$-0.843867\pi$
$163$	−5.24760	+	5.24760i	−0.411024	+	0.411024i	0.471071	+	0.882095i	$0.343867\pi$
$164$	0.345940	−	1.96192i	0.0270133	−	0.153200i
$165$		0			0
$166$	11.5723	+	4.21196i	0.898183	+	0.326912i
$167$	0.717512	−	8.20120i	0.0555227	−	0.634628i	−0.916546	−	0.399930i	$-0.869034\pi$
$167$	0.717512	−	8.20120i	0.0555227	−	0.634628i	0.972068	−	0.234698i	$-0.0754101\pi$
$168$	9.83313	−	2.16763i	0.758642	−	0.167237i
$169$	4.34150	+	11.9282i	0.333962	+	0.917553i
$170$		0			0
$171$	2.59856	−	0.689635i	0.198717	−	0.0527377i
$172$	−0.0785918	+	0.293309i	−0.00599257	+	0.0223646i
$173$	−0.677506	−	7.74393i	−0.0515098	−	0.588760i	−0.977461	−	0.211116i	$-0.932290\pi$
$173$	−0.677506	−	7.74393i	−0.0515098	−	0.588760i	0.925951	−	0.377643i	$-0.123265\pi$
$174$	10.2811	−	11.1930i	0.779412	−	0.848542i
$175$		0			0
$176$	−14.7198	+	2.59549i	−1.10954	+	0.195643i
$177$	−3.90189	+	7.47366i	−0.293284	+	0.561755i
$178$	2.57908	−	0.225641i	0.193310	−	0.0169125i
$179$	−2.19929	−	3.80928i	−0.164382	−	0.284719i	0.772053	−	0.635558i	$-0.219230\pi$
$179$	−2.19929	−	3.80928i	−0.164382	−	0.284719i	−0.936436	+	0.350839i	$0.885896\pi$
$180$		0			0
$181$	−2.85830	+	4.95072i	−0.212456	+	0.367984i	−0.952483	−	0.304593i	$-0.901479\pi$
$181$	−2.85830	+	4.95072i	−0.212456	+	0.367984i	0.740027	+	0.672577i	$0.234813\pi$
$182$	5.57127	−	11.9476i	0.412970	−	0.885617i
$183$	10.7489	−	9.82594i	0.794580	−	0.726355i
$184$	10.6824	+	12.7308i	0.787519	+	0.938529i
$185$		0			0
$186$	−3.38804	−	4.42631i	−0.248423	−	0.324553i
$187$	−11.2811	+	7.89911i	−0.824956	+	0.577640i
$188$	1.37145	+	1.37145i	0.100023	+	0.100023i
$189$	7.52479	−	6.84577i	0.547348	−	0.497957i
$190$		0			0
$191$	14.2067	+	2.50503i	1.02796	+	0.181258i	0.662104	−	0.749412i	$-0.269664\pi$
$191$	14.2067	+	2.50503i	1.02796	+	0.181258i	0.365860	+	0.930670i	$0.380775\pi$
$192$	−9.19475	+	11.9532i	−0.663574	+	0.862651i
$193$	−15.7247	+	7.33254i	−1.13189	+	0.527808i	−0.896036	−	0.443981i	$-0.853566\pi$
$193$	−15.7247	+	7.33254i	−1.13189	+	0.527808i	−0.235852	+	0.971789i	$0.575788\pi$
$194$	13.7446	−	11.5331i	0.986802	−	0.828025i
$195$		0			0
$196$	−0.700384	+	0.254919i	−0.0500274	+	0.0182085i
$197$	3.52289	+	13.1476i	0.250995	+	0.936727i	0.970275	+	0.242006i	$0.0778054\pi$
$197$	3.52289	+	13.1476i	0.250995	+	0.936727i	−0.719280	+	0.694721i	$0.755528\pi$
$198$	−13.1613	+	10.9902i	−0.935336	+	0.781041i
$199$	7.78555	−	4.49499i	0.551903	−	0.318641i	−0.197986	−	0.980205i	$-0.563440\pi$
$199$	7.78555	−	4.49499i	0.551903	−	0.318641i	0.749889	+	0.661564i	$0.230107\pi$
$200$		0			0
$201$	3.63748	−	16.3154i	0.256568	−	1.15080i
$202$	3.24187	−	4.62987i	0.228097	−	0.325756i
$203$	7.41743	−	10.5932i	0.520601	−	0.743496i
$204$	−0.283906	+	1.27342i	−0.0198774	+	0.0891570i
$205$		0			0
$206$	15.3625	−	8.86955i	1.07036	−	0.617971i
$207$	15.7637	+	5.78018i	1.09565	+	0.401750i
$208$	4.55757	+	17.0091i	0.316011	+	1.17937i
$209$	−3.62329	+	1.31877i	−0.250628	+	0.0912212i
$210$		0			0
$211$	−14.3607	+	12.0500i	−0.988631	+	0.829559i	−0.985369	−	0.170435i	$-0.945483\pi$
$211$	−14.3607	+	12.0500i	−0.988631	+	0.829559i	−0.00326162	+	0.999995i	$0.501038\pi$
$212$	−0.285746	+	0.133245i	−0.0196251	+	0.00915134i
$213$	−6.00103	+	7.80139i	−0.411184	+	0.534542i
$214$	−18.9851	−	3.34758i	−1.29779	−	0.228836i
$215$		0			0
$216$	−2.06876	+	15.2903i	−0.140762	+	1.04037i
$217$	−3.35376	−	3.35376i	−0.227668	−	0.227668i
$218$	−15.6108	+	10.9308i	−1.05729	+	0.740326i
$219$	−5.38077	−	7.02973i	−0.363599	−	0.475025i
$220$		0			0
$221$	10.4290	+	12.4288i	0.701530	+	0.836051i
$222$	−12.2473	+	11.1957i	−0.821984	+	0.751405i
$223$	7.00968	−	15.0323i	0.469403	−	1.00664i	−0.518999	−	0.854775i	$-0.673695\pi$
$223$	7.00968	−	15.0323i	0.469403	−	1.00664i	0.988402	−	0.151862i	$-0.0485270\pi$
$224$	−1.29608	+	2.24488i	−0.0865981	+	0.149992i
$225$		0			0
$226$	9.05870	+	15.6901i	0.602576	+	1.04369i
$227$	−18.0248	+	1.57696i	−1.19634	+	0.104667i	−0.667867	−	0.744281i	$-0.732793\pi$
$227$	−18.0248	+	1.57696i	−1.19634	+	0.104667i	−0.528478	+	0.848947i	$0.677237\pi$
$228$	−0.169058	+	0.323812i	−0.0111961	+	0.0214450i
$229$	−18.7074	+	3.29862i	−1.23622	+	0.217979i	−0.753294	−	0.657684i	$-0.771536\pi$
$229$	−18.7074	+	3.29862i	−1.23622	+	0.217979i	−0.482924	+	0.875662i	$0.660425\pi$
$230$		0			0
$231$	−9.86952	+	10.7449i	−0.649367	+	0.706963i
$232$	1.70951	+	19.5397i	0.112235	+	1.28285i
$233$	1.95750	−	7.30551i	0.128240	−	0.478600i	−0.871694	−	0.490050i	$-0.836978\pi$
$233$	1.95750	−	7.30551i	0.128240	−	0.478600i	0.999934	+	0.0114509i	$0.00364501\pi$
$234$	14.2499	+	14.3181i	0.931544	+	0.936005i
$235$		0			0
$236$	−0.391785	−	1.07642i	−0.0255031	−	0.0700691i
$237$	−0.705239	+	0.155464i	−0.0458102	+	0.0100985i
$238$	0.725521	−	8.29275i	0.0470286	−	0.537539i
$239$	−11.7518	−	4.27731i	−0.760162	−	0.276676i	−0.0672867	−	0.997734i	$-0.521434\pi$
$239$	−11.7518	−	4.27731i	−0.760162	−	0.276676i	−0.692875	+	0.721057i	$0.743656\pi$
$240$		0			0
$241$	2.97320	−	16.8619i	0.191521	−	1.08617i	−0.725766	−	0.687942i	$-0.758514\pi$
$241$	2.97320	−	16.8619i	0.191521	−	1.08617i	0.917287	−	0.398227i	$-0.130374\pi$
$242$	7.05612	−	7.05612i	0.453585	−	0.453585i
$243$	5.87934	+	14.4372i	0.377160	+	0.926148i
$244$			1.97870i			0.126673i
$245$		0			0
$246$	−17.9862	−	7.47531i	−1.14676	−	0.476609i
$247$	1.91979	+	4.11700i	0.122153	+	0.261958i
$248$	7.16645	+	0.626983i	0.455070	+	0.0398134i
$249$	−8.64354	+	13.5320i	−0.547762	+	0.857553i
$250$		0			0
$251$	4.66370	+	2.69259i	0.294370	+	0.169955i	0.639911	−	0.768449i	$-0.278971\pi$
$251$	4.66370	+	2.69259i	0.294370	+	0.169955i	−0.345541	+	0.938404i	$0.612304\pi$
$252$	−0.00330126	+	1.38218i	−0.000207960	+	0.0870690i
$253$	−23.2594	−	6.23233i	−1.46231	−	0.391823i
$254$	3.66378	+	3.07428i	0.229886	+	0.192897i
$255$		0			0
$256$	−0.966651	−	5.48215i	−0.0604157	−	0.342634i
$257$	10.0445	+	7.03325i	0.626560	+	0.438722i	0.843252	−	0.537518i	$-0.180638\pi$
$257$	10.0445	+	7.03325i	0.626560	+	0.438722i	−0.216692	+	0.976240i	$0.569527\pi$
$258$	2.63178	+	1.37401i	0.163847	+	0.0855424i
$259$	−9.07550	+	10.8158i	−0.563924	+	0.672059i
$260$		0			0
$261$	11.3273	+	16.2596i	0.701145	+	1.00645i
$262$	0.712524	−	0.190920i	0.0440199	−	0.0117951i
$263$	−12.3505	−	5.75913i	−0.761563	−	0.355123i	0.00272594	−	0.999996i	$-0.499132\pi$
$263$	−12.3505	−	5.75913i	−0.761563	−	0.355123i	−0.764289	+	0.644873i	$0.776910\pi$
$264$	0.991650	−	22.1067i	0.0610318	−	1.36057i
$265$		0			0
$266$	0.797143	−	2.19013i	0.0488760	−	0.134286i
$267$	−0.444600	+	3.34619i	−0.0272091	+	0.204783i
$268$	1.30270	+	1.86045i	0.0795749	+	0.113645i
$269$	−12.3342			−0.752028			−0.376014	−	0.926614i	$-0.622706\pi$
$269$	−12.3342			−0.752028			−0.376014	+	0.926614i	$0.622706\pi$
$270$		0			0
$271$	19.7578			1.20020			0.600099	−	0.799926i	$-0.295128\pi$
$271$	19.7578			1.20020			0.600099	+	0.799926i	$0.295128\pi$
$272$	6.37789	+	9.10856i	0.386716	+	0.552288i
$273$	13.6240	+	10.4799i	0.824560	+	0.634273i
$274$	−2.74569	+	7.54371i	−0.165873	+	0.455732i
$275$		0			0
$276$	−2.02475	+	1.05094i	−0.121875	+	0.0632594i
$277$	1.83776	+	0.856962i	0.110420	+	0.0514898i	0.477044	−	0.878880i	$-0.341708\pi$
$277$	1.83776	+	0.856962i	0.110420	+	0.0514898i	−0.366623	+	0.930370i	$0.619486\pi$
$278$	23.7626	−	6.36718i	1.42519	−	0.381878i
$279$	6.59425	−	3.05579i	0.394787	−	0.182946i
$280$		0			0
$281$	−16.8041	+	20.0263i	−1.00245	+	1.19467i	−0.0216244	+	0.999766i	$0.506884\pi$
$281$	−16.8041	+	20.0263i	−1.00245	+	1.19467i	−0.980822	+	0.194903i	$0.937561\pi$
$282$	16.0053	−	10.1696i	0.953100	−	0.605593i
$283$	1.89971	+	1.33019i	0.112926	+	0.0790717i	0.628675	−	0.777668i	$-0.283597\pi$
$283$	1.89971	+	1.33019i	0.112926	+	0.0790717i	−0.515749	+	0.856740i	$0.672486\pi$
$284$	−0.232218	−	1.31697i	−0.0137796	−	0.0781480i
$285$		0			0
$286$	−22.1934	−	18.6225i	−1.31232	−	1.10117i
$287$	−16.0086	−	4.28949i	−0.944956	−	0.253200i
$288$	−2.54596	−	3.04891i	−0.150022	−	0.179659i
$289$	−5.84978	−	3.37737i	−0.344105	−	0.198669i
$290$		0			0
$291$	10.7774	+	20.7637i	0.631783	+	1.21719i
$292$	1.19823	+	0.104832i	0.0701211	+	0.00613480i
$293$	−5.09445	−	10.9251i	−0.297621	−	0.638250i	0.699454	−	0.714677i	$-0.253426\pi$
$293$	−5.09445	−	10.9251i	−0.297621	−	0.638250i	−0.997075	+	0.0764274i	$0.975649\pi$
$294$	0.942540	+	7.22598i	0.0549701	+	0.421427i
$295$		0			0
$296$		−	21.4149i		−	1.24471i
$297$	−10.2521	−	19.8675i	−0.594885	−	1.15283i
$298$	8.14698	−	8.14698i	0.471942	−	0.471942i
$299$	−4.92621	+	27.9379i	−0.284890	+	1.61569i
$300$		0			0
$301$	2.37381	+	0.863996i	0.136824	+	0.0497999i
$302$	1.84467	−	21.0846i	0.106149	−	1.21328i
$303$	4.97222	+	5.43925i	0.285646	+	0.312477i
$304$	1.06480	+	2.92551i	0.0610704	+	0.167790i
$305$		0			0
$306$	11.5479	+	5.41851i	0.660152	+	0.309756i
$307$	6.08202	−	22.6984i	0.347119	−	1.29547i	−0.542998	−	0.839734i	$-0.682711\pi$
$307$	6.08202	−	22.6984i	0.347119	−	1.29547i	0.890117	−	0.455732i	$-0.150622\pi$
$308$	−0.172769	−	1.97476i	−0.00984441	−	0.112522i
$309$	6.92874	+	22.0670i	0.394162	+	1.25535i
$310$		0			0
$311$	3.91683	−	0.690642i	0.222103	−	0.0391627i	−0.0614891	−	0.998108i	$-0.519585\pi$
$311$	3.91683	−	0.690642i	0.222103	−	0.0391627i	0.283592	+	0.958945i	$0.408474\pi$
$312$	−26.0469	+	1.10607i	−1.47462	+	0.0626189i
$313$	0.911077	−	0.0797089i	0.0514971	−	0.00450541i	−0.0613781	−	0.998115i	$-0.519550\pi$
$313$	0.911077	−	0.0797089i	0.0514971	−	0.00450541i	0.112875	+	0.993609i	$0.463994\pi$
$314$	−8.81718	−	15.2718i	−0.497582	−	0.861838i
$315$		0			0
$316$	0.0490605	−	0.0849753i	0.00275987	−	0.00478023i
$317$	11.1443	−	23.8990i	0.625924	−	1.34230i	−0.296096	−	0.955158i	$-0.595685\pi$
$317$	11.1443	−	23.8990i	0.625924	−	1.34230i	0.922021	−	0.387141i	$-0.126537\pi$
$318$	0.663597	+	3.01030i	0.0372127	+	0.168809i
$319$	−18.2681	−	21.7711i	−1.02282	−	1.21895i
$320$		0			0
$321$	9.64673	−	23.2108i	0.538428	−	1.29550i
$322$	11.9230	−	8.34859i	0.664444	−	0.465249i
$323$	2.02833	+	2.02833i	0.112859	+	0.112859i
$324$	−1.98678	−	0.733896i	−0.110377	−	0.0407720i
$325$		0			0
$326$	−9.70865	−	1.71190i	−0.537712	−	0.0948132i
$327$	−9.48144	−	22.9678i	−0.524325	−	1.27012i
$328$	22.7823	−	10.6235i	1.25794	−	0.586587i
$329$	12.3602	−	10.3715i	0.681442	−	0.571798i
$330$		0			0
$331$	−12.0746	+	4.39481i	−0.663682	+	0.241561i	−0.651825	−	0.758369i	$-0.725996\pi$
$331$	−12.0746	+	4.39481i	−0.663682	+	0.241561i	−0.0118569	+	0.999930i	$0.503774\pi$
$332$	−0.564651	−	2.10731i	−0.0309893	−	0.115653i
$333$	−10.7729	−	18.7625i	−0.590350	−	1.02818i
$334$	9.47099	−	5.46808i	0.518229	−	0.299200i
$335$		0			0
$336$	8.67563	+	7.96883i	0.473294	+	0.434735i
$337$	−4.87543	+	6.96283i	−0.265581	+	0.379290i	−0.929688	−	0.368349i	$-0.879923\pi$
$337$	−4.87543	+	6.96283i	−0.265581	+	0.379290i	0.664106	+	0.747638i	$0.268812\pi$
$338$	−9.67189	+	13.8129i	−0.526081	+	0.751322i
$339$	−22.5376	+	7.07650i	−1.22408	+	0.384343i
$340$		0			0
$341$	−9.02697	+	5.21173i	−0.488838	+	0.282231i
$342$	2.73040	+	2.30221i	0.147643	+	0.124489i
$343$	5.15177	+	19.2267i	0.278169	+	1.03814i
$344$	−3.60046	+	1.31046i	−0.194124	+	0.0706553i
$345$		0			0
$346$	7.91047	−	6.63767i	0.425270	−	0.356844i
$347$	−4.76851	+	2.22359i	−0.255987	+	0.119369i	−0.546376	−	0.837540i	$-0.683993\pi$
$347$	−4.76851	+	2.22359i	−0.255987	+	0.119369i	0.290389	+	0.956909i	$0.406215\pi$
$348$	−2.66897	−	0.354620i	−0.143072	−	0.0190096i
$349$	20.3047	+	3.58026i	1.08688	+	0.191647i	0.688258	−	0.725466i	$-0.258376\pi$
$349$	20.3047	+	3.58026i	1.08688	+	0.191647i	0.398627	+	0.917113i	$0.369487\pi$
$350$		0			0
$351$	−22.2644	+	14.0721i	−1.18839	+	0.751115i
$352$	4.02821	+	4.02821i	0.214704	+	0.214704i
$353$	−23.6027	+	16.5268i	−1.25624	+	0.879631i	−0.996296	−	0.0859911i	$-0.972594\pi$
$353$	−23.6027	+	16.5268i	−1.25624	+	0.879631i	−0.259948	+	0.965623i	$0.583705\pi$
$354$	−11.1056	+	1.44859i	−0.590257	+	0.0769918i
$355$		0			0
$356$	−0.294808	−	0.351339i	−0.0156248	−	0.0186209i
$357$	10.3476	+	3.27617i	0.547652	+	0.173393i
$358$	2.46940	−	5.29565i	0.130512	−	0.279884i
$359$	−8.91393	+	15.4394i	−0.470459	+	0.814860i	−0.999429	−	0.0337810i	$-0.989245\pi$
$359$	−8.91393	+	15.4394i	−0.470459	+	0.814860i	0.528970	+	0.848641i	$0.322578\pi$
$360$		0			0
$361$	−9.09844	−	15.7590i	−0.478865	−	0.829419i
$362$	−7.56508	+	0.661859i	−0.397612	+	0.0347865i
$363$	6.97769	+	10.9817i	0.366234	+	0.576390i
$364$	−2.29990	+	0.405534i	−0.120547	+	0.0212558i
$365$		0			0
$366$	18.8823	+	4.20977i	0.986994	+	0.220048i
$367$	1.91117	+	21.8448i	0.0997623	+	1.14029i	0.866790	+	0.498674i	$0.166179\pi$
$367$	1.91117	+	21.8448i	0.0997623	+	1.14029i	−0.767028	+	0.641614i	$0.778265\pi$
$368$	−5.03210	+	18.7800i	−0.262316	+	0.978978i
$369$	14.6163	−	20.7685i	0.760895	−	1.08117i
$370$		0			0
$371$	0.897087	+	2.46473i	0.0465744	+	0.127962i
$372$	−0.298066	+	0.941423i	−0.0154540	+	0.0488105i
$373$	1.50421	−	17.1932i	0.0778848	−	0.890228i	−0.852280	−	0.523086i	$-0.824781\pi$
$373$	1.50421	−	17.1932i	0.0778848	−	0.890228i	0.930165	−	0.367142i	$-0.119664\pi$
$374$	−17.1911	−	6.25706i	−0.888932	−	0.323545i
$375$		0			0
$376$	−4.24967	+	24.1011i	−0.219160	+	1.24292i
$377$	−23.6755	+	23.6755i	−1.21935	+	1.21935i
$378$	13.1828	+	2.97215i	0.678051	+	0.152871i
$379$		−	27.1687i		−	1.39556i	−0.716312	−	0.697780i	$-0.754171\pi$
$379$		−	27.1687i		−	1.39556i	0.716312	−	0.697780i	$-0.245829\pi$
$380$		0			0
$381$	−4.95187	+	3.79031i	−0.253692	+	0.194184i
$382$	8.09883	+	17.3680i	0.414372	+	0.888624i
$383$	−7.32022	−	0.640436i	−0.374046	−	0.0327248i	−0.101417	−	0.994844i	$-0.532338\pi$
$383$	−7.32022	−	0.640436i	−0.374046	−	0.0327248i	−0.272629	+	0.962119i	$0.587893\pi$
$384$	−15.4310	−	0.692197i	−0.787461	−	0.0353235i
$385$		0			0
$386$	−19.9604	−	11.5241i	−1.01596	−	0.586562i
$387$	−2.49529	+	2.95939i	−0.126843	+	0.150434i
$388$	−3.07024	−	0.822667i	−0.155868	−	0.0417646i
$389$	23.9421	+	20.0898i	1.21391	+	1.01859i	0.999120	+	0.0419334i	$0.0133517\pi$
$389$	23.9421	+	20.0898i	1.21391	+	1.01859i	0.214792	+	0.976660i	$0.431093\pi$
$390$		0			0
$391$	3.11072	+	17.6418i	0.157316	+	0.892182i
$392$	−7.70382	−	5.39427i	−0.389102	−	0.272452i
$393$	0.0408056	+	0.960934i	0.00205837	+	0.0484727i
$394$	−11.6225	+	13.8512i	−0.585535	+	0.697814i
$395$		0			0
$396$	2.93220	+	0.793192i	0.147349	+	0.0398594i
$397$	15.9305	−	4.26857i	0.799531	−	0.214234i	0.164153	−	0.986435i	$-0.447511\pi$
$397$	15.9305	−	4.26857i	0.799531	−	0.214234i	0.635378	+	0.772201i	$0.280844\pi$
$398$	10.8234	+	5.04706i	0.542530	+	0.252986i
$399$	2.56101	+	1.63585i	0.128211	+	0.0818949i
$400$		0			0
$401$	−0.517022	+	1.42051i	−0.0258188	+	0.0709367i	−0.951932	−	0.306308i	$-0.900906\pi$
$401$	−0.517022	+	1.42051i	−0.0258188	+	0.0709367i	0.926114	+	0.377245i	$0.123128\pi$
$402$	20.5254	−	8.47320i	1.02371	−	0.422605i
$403$	7.04354	+	10.0592i	0.350864	+	0.501085i
$404$	−1.00128			−0.0498155
$405$		0			0
$406$	17.1788			0.852571
$407$	17.7975	+	25.4175i	0.882189	+	1.25990i
$408$	−15.2169	+	6.28176i	−0.753348	+	0.310993i
$409$	8.02778	−	22.0561i	0.396948	−	1.09061i	−0.566815	−	0.823845i	$-0.691825\pi$
$409$	8.02778	−	22.0561i	0.396948	−	1.09061i	0.963763	−	0.266760i	$-0.0859532\pi$
$410$		0			0
$411$	−8.82118	−	5.63453i	−0.435117	−	0.277931i
$412$	−2.84812	−	1.32810i	−0.140317	−	0.0654308i
$413$	−9.20490	+	2.46645i	−0.452944	+	0.121366i
$414$	5.72121	+	21.5577i	0.281182	+	1.05950i
$415$		0			0
$416$	4.31402	−	5.14125i	0.211512	−	0.252070i
$417$	1.36086	+	32.0471i	0.0666418	+	1.56935i
$418$	−4.19579	−	2.93792i	−0.205223	−	0.143698i
$419$	2.76242	+	15.6665i	0.134953	+	0.765357i	0.974892	+	0.222677i	$0.0714794\pi$
$419$	2.76242	+	15.6665i	0.134953	+	0.765357i	−0.839939	+	0.542680i	$0.817409\pi$
$420$		0			0
$421$	27.8051	+	23.3312i	1.35514	+	1.13709i	0.977452	+	0.211160i	$0.0677241\pi$
$421$	27.8051	+	23.3312i	1.35514	+	1.13709i	0.377685	+	0.925934i	$0.376720\pi$
$422$	−24.0545	−	6.44539i	−1.17096	−	0.313756i
$423$	8.40087	+	23.2539i	0.408464	+	1.13064i
$424$	−3.44529	−	1.98914i	−0.167318	−	0.0966012i
$425$		0			0
$426$	−13.0617	−	0.585914i	−0.632840	−	0.0283876i
$427$	16.3984	+	1.43468i	0.793576	+	0.0694289i
$428$	1.44331	+	3.09519i	0.0697652	+	0.149612i
$429$	29.9960	−	22.9599i	1.44822	−	1.10851i
$430$		0			0
$431$			10.7570i			0.518146i	0.965858	+	0.259073i	$0.0834169\pi$
$431$			10.7570i			0.518146i	−0.965858	+	0.259073i	$0.916583\pi$
$432$	−16.0414	+	8.27769i	−0.771790	+	0.398261i
$433$	25.8369	−	25.8369i	1.24164	−	1.24164i	0.282321	−	0.959320i	$-0.408896\pi$
$433$	25.8369	−	25.8369i	1.24164	−	1.24164i	0.959320	−	0.282321i	$-0.0911042\pi$
$434$	1.09408	−	6.20483i	0.0525175	−	0.297842i
$435$		0			0
$436$	3.17246	+	1.15468i	0.151933	+	0.0552992i
$437$	−0.437136	+	4.99649i	−0.0209111	+	0.239015i
$438$	3.54968	−	11.2114i	0.169610	−	0.535703i
$439$	−4.76440	−	13.0901i	−0.227393	−	0.624756i	0.772556	−	0.634947i	$-0.218978\pi$
$439$	−4.76440	−	13.0901i	−0.227393	−	0.624756i	−0.999948	+	0.0101913i	$0.996756\pi$
$440$		0			0
$441$	−9.46327	−	0.850709i	−0.450632	−	0.0405100i
$442$	−5.57831	+	20.8185i	−0.265333	+	0.990237i
$443$	−0.993879	−	11.3601i	−0.0472206	−	0.539734i	−0.982555	−	0.185970i	$-0.940457\pi$
$443$	−0.993879	−	11.3601i	−0.0472206	−	0.539734i	0.935335	−	0.353764i	$-0.115098\pi$
$444$	2.86914	+	0.639668i	0.136163	+	0.0303573i
$445$		0			0
$446$	21.6986	−	3.82606i	1.02746	−	0.181169i
$447$	8.05642	+	12.6794i	0.381056	+	0.599717i
$448$	−16.9810	+	1.48564i	−0.802276	+	0.0701900i
$449$	−0.807925	−	1.39937i	−0.0381283	−	0.0660402i	0.846332	−	0.532657i	$-0.178806\pi$
$449$	−0.807925	−	1.39937i	−0.0381283	−	0.0660402i	−0.884460	+	0.466616i	$0.845473\pi$
$450$		0			0
$451$	−18.2114	+	31.5431i	−0.857541	+	1.48530i
$452$	1.35642	−	2.90886i	0.0638008	−	0.136821i
$453$	26.3092	+	8.32980i	1.23611	+	0.391368i
$454$	−15.4498	−	18.4124i	−0.725097	−	0.864137i
$455$		0			0
$456$	−4.57049	+	0.596164i	−0.214033	+	0.0279180i
$457$	−4.53775	+	3.17737i	−0.212267	+	0.148631i	−0.674875	−	0.737932i	$-0.735803\pi$
$457$	−4.53775	+	3.17737i	−0.212267	+	0.148631i	0.462608	+	0.886563i	$0.346914\pi$
$458$	−17.8434	−	17.8434i	−0.833768	−	0.833768i
$459$	−10.1721	+	13.1587i	−0.474793	+	0.614194i
$460$		0			0
$461$	14.9666	+	2.63902i	0.697065	+	0.122911i	0.510942	−	0.859615i	$-0.329297\pi$
$461$	14.9666	+	2.63902i	0.697065	+	0.122911i	0.186123	+	0.982527i	$0.440408\pi$
$462$	−19.2123	−	2.55269i	−0.893836	−	0.118762i
$463$	29.9580	−	13.9696i	1.39226	−	0.649224i	0.425516	−	0.904951i	$-0.360093\pi$
$463$	29.9580	−	13.9696i	1.39226	−	0.649224i	0.966749	+	0.255727i	$0.0823148\pi$
$464$	−17.5784	+	14.7500i	−0.816056	+	0.684752i
$465$		0			0
$466$	9.44112	−	3.43629i	0.437352	−	0.159183i
$467$	−5.87822	−	21.9378i	−0.272012	−	1.01516i	−0.957818	−	0.287377i	$-0.907217\pi$
$467$	−5.87822	−	21.9378i	−0.272012	−	1.01516i	0.685806	−	0.727784i	$-0.259450\pi$
$468$	0.629839	−	3.52277i	0.0291143	−	0.162840i
$469$	16.3630	−	9.44716i	0.755571	−	0.436229i
$470$		0			0
$471$	21.9367	−	6.88783i	1.01079	−	0.317374i
$472$	8.29047	−	11.8400i	0.381600	−	0.544981i
$473$	3.18431	−	4.54767i	0.146415	−	0.209102i
$474$	−0.706524	−	0.648964i	−0.0324517	−	0.0298079i
$475$		0			0
$476$	−1.27713	+	0.737352i	−0.0585372	+	0.0337965i
$477$	−4.01922	−	0.00959972i	−0.184027	−	0.000439541i
$478$	−4.29979	−	16.0470i	−0.196668	−	0.733974i
$479$	−21.4594	+	7.81060i	−0.980507	+	0.356875i	−0.782037	−	0.623232i	$-0.785819\pi$
$479$	−21.4594	+	7.81060i	−0.980507	+	0.356875i	−0.198470	+	0.980107i	$0.563597\pi$
$480$		0			0
$481$	28.0033	−	23.4976i	1.27684	−	1.07140i
$482$	20.6140	−	9.61245i	0.938941	−	0.437835i
$483$	7.24163	+	17.5421i	0.329506	+	0.798191i
$484$	−1.74094	−	0.306975i	−0.0791336	−	0.0139534i
$485$		0			0
$486$	−11.2304	+	17.3981i	−0.509421	+	0.789192i
$487$	−13.1004	−	13.1004i	−0.593634	−	0.593634i	0.344977	−	0.938611i	$-0.387887\pi$
$487$	−13.1004	−	13.1004i	−0.593634	−	0.593634i	−0.938611	+	0.344977i	$0.887887\pi$
$488$	−20.4520	+	14.3206i	−0.925817	+	0.648264i
$489$	4.93317	−	11.8696i	0.223086	−	0.536762i
$490$		0			0
$491$	−5.95862	−	7.10121i	−0.268909	−	0.320473i	0.614644	−	0.788805i	$-0.289300\pi$
$491$	−5.95862	−	7.10121i	−0.268909	−	0.320473i	−0.883553	+	0.468332i	$0.844855\pi$
$492$	0.742816	+	3.36967i	0.0334887	+	0.151916i
$493$	−8.93533	+	19.1619i	−0.402427	+	0.863007i
$494$	−3.01722	+	5.22597i	−0.135751	+	0.235128i
$495$		0			0
$496$	4.20804	+	7.28854i	0.188947	+	0.327265i
$497$	−11.0828	+	0.969617i	−0.497131	+	0.0434933i
$498$	−21.3109	+	0.904958i	−0.954965	+	0.0405521i
$499$	20.3482	−	3.58794i	0.910911	−	0.160618i	0.301494	−	0.953468i	$-0.402515\pi$
$499$	20.3482	−	3.58794i	0.910911	−	0.160618i	0.609417	+	0.792850i	$0.291404\pi$
$500$		0			0
$501$	4.27157	+	13.6043i	0.190840	+	0.607796i
$502$	0.623488	+	7.12650i	0.0278276	+	0.318071i
$503$	−1.21585	+	4.53760i	−0.0542119	+	0.202322i	−0.987720	−	0.156235i	$-0.950064\pi$
$503$	−1.21585	+	4.53760i	−0.0542119	+	0.202322i	0.933508	+	0.358557i	$0.116731\pi$
$504$	−14.3102	+	9.96924i	−0.637426	+	0.444065i
$505$		0			0
$506$	−10.9405	−	30.0588i	−0.486365	−	1.33628i
$507$	−14.8343	−	16.2276i	−0.658813	−	0.720694i
$508$	0.0738452	−	0.844055i	0.00327635	−	0.0374489i
$509$	30.3526	+	11.0475i	1.34536	+	0.489670i	0.911496	−	0.411309i	$-0.134928\pi$
$509$	30.3526	+	11.0475i	1.34536	+	0.489670i	0.433862	+	0.900979i	$0.357151\pi$
$510$		0			0
$511$	1.73758	−	9.85432i	0.0768661	−	0.435929i
$512$	17.8410	−	17.8410i	0.788469	−	0.788469i
$513$	−3.70450	+	2.82154i	−0.163558	+	0.124574i
$514$			16.2891i			0.718480i
$515$		0			0
$516$	−0.0680271	−	0.521529i	−0.00299472	−	0.0229590i
$517$	−14.9860	−	32.1376i	−0.659083	−	1.41341i
$518$	−18.6844	−	1.63467i	−0.820945	−	0.0718234i
$519$	6.20277	+	11.9502i	0.272271	+	0.524557i
$520$		0			0
$521$	−2.29310	−	1.32392i	−0.100463	−	0.0580021i	0.448927	−	0.893568i	$-0.351806\pi$
$521$	−2.29310	−	1.32392i	−0.100463	−	0.0580021i	−0.549390	+	0.835566i	$0.685140\pi$
$522$	−9.06243	+	24.7150i	−0.396652	+	1.08175i
$523$	12.5901	+	3.37351i	0.550527	+	0.147513i	0.523351	−	0.852117i	$-0.324682\pi$
$523$	12.5901	+	3.37351i	0.550527	+	0.147513i	0.0271764	+	0.999631i	$0.491348\pi$
$524$	−0.100106	−	0.0839990i	−0.00437316	−	0.00366951i
$525$		0			0
$526$	−3.14347	−	17.8275i	−0.137062	−	0.777317i
$527$	6.35202	+	4.44773i	0.276698	+	0.193746i
$528$	21.8509	−	13.8839i	0.950938	−	0.604219i
$529$	−5.34967	+	6.37549i	−0.232594	+	0.277195i
$530$		0			0
$531$	1.30746	−	14.5441i	0.0567388	−	0.631161i
$532$	−0.398822	+	0.106864i	−0.0172911	+	0.00463314i
$533$	38.8899	+	18.1347i	1.68451	+	0.785499i
$534$	−3.97997	+	2.06581i	−0.172230	+	0.0893962i
$535$		0			0
$536$	−9.80156	+	26.9296i	−0.423363	+	1.16318i
$537$	6.03866	+	4.64510i	0.260587	+	0.200451i
$538$	−9.39794	−	13.4217i	−0.405174	−	0.578649i
$539$	13.6268			0.586947
$540$		0			0
$541$	−42.0435			−1.80759			−0.903796	−	0.427963i	$-0.859231\pi$
$541$	−42.0435			−1.80759			−0.903796	+	0.427963i	$0.859231\pi$
$542$	15.0543	+	21.4998i	0.646637	+	0.923494i
$543$	1.30412	−	9.81518i	0.0559651	−	0.421210i
$544$	1.44949	−	3.98243i	0.0621463	−	0.170745i
$545$		0			0
$546$	−1.02321	+	22.8103i	−0.0437894	+	0.976189i
$547$	20.8870	+	9.73975i	0.893062	+	0.416442i	0.814295	−	0.580451i	$-0.197124\pi$
$547$	20.8870	+	9.73975i	0.893062	+	0.416442i	0.0787671	+	0.996893i	$0.474902\pi$
$548$	1.37371	−	0.368084i	0.0586818	−	0.0157238i
$549$	−10.7148	+	22.8354i	−0.457296	+	0.974591i
$550$		0			0
$551$	−3.80505	+	4.53468i	−0.162101	+	0.193184i
$552$	−25.5165	−	13.3218i	−1.08606	−	0.567014i
$553$	−0.668660	−	0.468201i	−0.0284343	−	0.0199099i
$554$	0.467751	+	2.65275i	0.0198728	+	0.112704i
$555$		0			0
$556$	−3.33853	−	2.80136i	−0.141585	−	0.118804i
$557$	34.3132	+	9.19419i	1.45390	+	0.389570i	0.897377	−	0.441265i	$-0.145470\pi$
$557$	34.3132	+	9.19419i	1.45390	+	0.389570i	0.556519	+	0.830835i	$0.312137\pi$
$558$	8.34966	+	4.84731i	0.353469	+	0.205203i
$559$	−5.66426	−	3.27026i	−0.239572	−	0.138317i
$560$		0			0
$561$	12.8404	−	20.1023i	0.542120	−	0.848720i
$562$	−34.5957	−	3.02674i	−1.45933	−	0.127675i
$563$	−1.97748	−	4.24073i	−0.0833410	−	0.178725i	0.860221	−	0.509922i	$-0.170326\pi$
$563$	−1.97748	−	4.24073i	−0.0833410	−	0.178725i	−0.943562	+	0.331196i	$0.892548\pi$
$564$	−3.10209	−	1.28927i	−0.130622	−	0.0542881i
$565$		0			0
$566$			3.08073i			0.129493i
$567$	−7.52269	+	15.9333i	−0.315923	+	0.669136i
$568$	11.9317	−	11.9317i	0.500642	−	0.500642i
$569$	−1.37633	+	7.80556i	−0.0576988	+	0.327226i	−0.999971	−	0.00762185i	$-0.997574\pi$
$569$	−1.37633	+	7.80556i	−0.0576988	+	0.327226i	0.942272	+	0.334848i	$0.108685\pi$
$570$		0			0
$571$	4.65824	+	1.69546i	0.194941	+	0.0709528i	0.437646	−	0.899147i	$-0.355812\pi$
$571$	4.65824	+	1.69546i	0.194941	+	0.0709528i	−0.242705	+	0.970100i	$0.578035\pi$
$572$	−0.447319	+	5.11288i	−0.0187033	+	0.213780i
$573$	−24.4006	+	5.37891i	−1.01935	+	0.224707i
$574$	−7.52995	−	20.6884i	−0.314294	−	0.863516i
$575$		0			0
$576$	6.82068	−	25.2141i	0.284195	−	1.05059i
$577$	5.90200	−	22.0266i	0.245703	−	0.916977i	−0.727325	−	0.686293i	$-0.759237\pi$
$577$	5.90200	−	22.0266i	0.245703	−	0.916977i	0.973029	−	0.230684i	$-0.0740965\pi$
$578$	−0.782053	−	8.93890i	−0.0325291	−	0.371809i
$579$	20.3290	−	22.1321i	0.844844	−	0.919777i
$580$		0			0
$581$	−17.8737	+	3.15161i	−0.741526	+	0.130751i
$582$	−14.3826	+	27.5484i	−0.596179	+	1.14192i
$583$	5.74237	−	0.502393i	0.237825	−	0.0208070i
$584$	7.58853	+	13.1437i	0.314015	+	0.543891i
$585$		0			0
$586$	8.00664	−	13.8679i	0.330751	−	0.572878i
$587$	15.8151	−	33.9155i	0.652758	−	1.39984i	−0.249384	−	0.968405i	$-0.580228\pi$
$587$	15.8151	−	33.9155i	0.652758	−	1.39984i	0.902142	−	0.431439i	$-0.141994\pi$
$588$	0.952832	−	0.871019i	0.0392941	−	0.0359202i
$589$	1.39555	+	1.66315i	0.0575026	+	0.0685290i
$590$		0			0
$591$	−14.3296	−	18.7209i	−0.589440	−	0.770075i
$592$	20.5225	−	14.3700i	0.843470	−	0.590604i
$593$	−5.46266	−	5.46266i	−0.224324	−	0.224324i	0.585992	−	0.810317i	$-0.300705\pi$
$593$	−5.46266	−	5.46266i	−0.224324	−	0.224324i	−0.810317	+	0.585992i	$0.800705\pi$
$594$	13.8077	−	26.2939i	0.566535	−	1.07885i
$595$		0			0
$596$	−2.01008	−	0.354432i	−0.0823362	−	0.0145181i
$597$	−9.49383	+	12.3421i	−0.388556	+	0.505126i
$598$	−34.1546	+	15.9266i	−1.39669	+	0.651286i
$599$	1.79656	−	1.50749i	0.0734055	−	0.0615946i	−0.605347	−	0.795962i	$-0.706965\pi$
$599$	1.79656	−	1.50749i	0.0734055	−	0.0615946i	0.678752	+	0.734367i	$0.262521\pi$
$600$		0			0
$601$	38.1639	−	13.8905i	1.55674	−	0.566607i	0.586753	−	0.809766i	$-0.300406\pi$
$601$	38.1639	−	13.8905i	1.55674	−	0.566607i	0.969987	+	0.243159i	$0.0781836\pi$
$602$	0.868536	+	3.24142i	0.0353989	+	0.132110i
$603$	4.95949	+	28.5249i	0.201966	+	1.16162i
$604$	−3.24716	+	1.87475i	−0.132125	+	0.0762824i
$605$		0			0
$606$	−2.13027	+	9.55500i	−0.0865362	+	0.388146i
$607$	−1.07501	+	1.53527i	−0.0436332	+	0.0623147i	−0.840376	−	0.542004i	$-0.817666\pi$
$607$	−1.07501	+	1.53527i	−0.0436332	+	0.0623147i	0.796743	+	0.604319i	$0.206555\pi$
$608$	0.680588	−	0.971981i	0.0276015	−	0.0394190i
$609$	−4.87408	+	21.8619i	−0.197508	+	0.885891i
$610$		0			0
$611$	−36.1789	+	20.8879i	−1.46364	+	0.845035i
$612$	−0.387089	−	2.22637i	−0.0156472	−	0.0899958i
$613$	−4.71349	−	17.5910i	−0.190376	−	0.710494i	−0.993415	−	0.114568i	$-0.963452\pi$
$613$	−4.71349	−	17.5910i	−0.190376	−	0.710494i	0.803039	−	0.595926i	$-0.203215\pi$
$614$	29.3338	−	10.6766i	1.18382	−	0.430874i
$615$		0			0
$616$	19.1608	−	16.0778i	0.772012	−	0.647795i
$617$	−16.8885	+	7.87526i	−0.679907	+	0.317046i	−0.731715	−	0.681611i	$-0.761280\pi$
$617$	−16.8885	+	7.87526i	−0.679907	+	0.317046i	0.0518073	+	0.998657i	$0.483502\pi$
$618$	−18.7333	+	24.3534i	−0.753564	+	0.979639i
$619$	28.0130	+	4.93945i	1.12594	+	0.198533i	0.705447	−	0.708763i	$-0.250746\pi$
$619$	28.0130	+	4.93945i	1.12594	+	0.198533i	0.420492	+	0.907296i	$0.361858\pi$
$620$		0			0
$621$	−29.0578	+	1.16440i	−1.16605	+	0.0467259i
$622$	3.73594	+	3.73594i	0.149797	+	0.149797i
$623$	−3.12547	+	2.18848i	−0.125219	+	0.0876795i
$624$	−18.5382	−	24.2193i	−0.742123	−	0.969549i
$625$		0			0
$626$	0.780926	+	0.930671i	0.0312121	+	0.0371971i
$627$	4.92928	−	4.50604i	0.196857	−	0.179954i
$628$	−1.32026	+	2.83130i	−0.0526840	+	0.112981i
$629$	11.5418	−	19.9910i	0.460202	−	0.797093i
$630$		0			0
$631$	−16.2016	−	28.0619i	−0.644974	−	1.11713i	−0.984307	−	0.176462i	$-0.943535\pi$
$631$	−16.2016	−	28.0619i	−0.644974	−	1.11713i	0.339333	−	0.940666i	$-0.389799\pi$
$632$	1.23338	−	0.107907i	0.0490613	−	0.00429231i
$633$	15.0273	−	28.7833i	0.597283	−	1.14403i
$634$	34.4974	−	6.08282i	1.37007	−	0.241580i
$635$		0			0
$636$	0.369414	−	0.402179i	0.0146482	−	0.0159475i
$637$	−1.39919	−	15.9928i	−0.0554380	−	0.633659i
$638$	9.77134	−	36.4671i	0.386851	−	1.44375i
$639$	4.45157	−	16.4562i	0.176102	−	0.650996i
$640$		0			0
$641$	−7.10695	−	19.5262i	−0.280708	−	0.771238i	−0.997279	−	0.0737239i	$-0.976512\pi$
$641$	−7.10695	−	19.5262i	−0.280708	−	0.771238i	0.716571	−	0.697514i	$-0.245711\pi$
$642$	32.6075	−	7.18807i	1.28692	−	0.283691i
$643$	−3.44122	+	39.3334i	−0.135709	+	1.55116i	0.557351	+	0.830277i	$0.311818\pi$
$643$	−3.44122	+	39.3334i	−0.135709	+	1.55116i	−0.693060	+	0.720880i	$0.743738\pi$
$644$	−2.42303	−	0.881910i	−0.0954807	−	0.0347521i
$645$		0			0
$646$	−0.661691	+	3.75263i	−0.0260339	+	0.147645i
$647$	27.7872	−	27.7872i	1.09243	−	1.09243i	0.0971593	−	0.995269i	$-0.469024\pi$
$647$	27.7872	−	27.7872i	1.09243	−	1.09243i	0.995269	−	0.0971593i	$-0.0309756\pi$
$648$	−6.79352	−	25.8470i	−0.266875	−	1.01537i
$649$			20.9430i			0.822086i
$650$		0			0
$651$	7.58592	+	3.15281i	0.297315	+	0.123568i
$652$	0.738085	+	1.58283i	0.0289056	+	0.0619884i
$653$	−16.8852	−	1.47726i	−0.660770	−	0.0578098i	−0.248162	−	0.968719i	$-0.579826\pi$
$653$	−16.8852	−	1.47726i	−0.660770	−	0.0578098i	−0.412608	+	0.910909i	$0.635382\pi$
$654$	17.7685	−	27.8175i	0.694802	−	1.08775i
$655$		0			0
$656$	25.4684	+	14.7042i	0.994375	+	0.574103i
$657$	13.2607	+	7.69833i	0.517348	+	0.300341i
$658$	20.7037	+	5.54754i	0.807115	+	0.216266i
$659$	−36.7210	−	30.8125i	−1.43045	−	1.20029i	−0.945449	−	0.325770i	$-0.894376\pi$
$659$	−36.7210	−	30.8125i	−1.43045	−	1.20029i	−0.484997	−	0.874516i	$-0.661179\pi$
$660$		0			0
$661$	−0.726513	−	4.12026i	−0.0282581	−	0.160259i	0.967413	−	0.253202i	$-0.0814838\pi$
$661$	−0.726513	−	4.12026i	−0.0282581	−	0.160259i	−0.995671	+	0.0929427i	$0.970373\pi$
$662$	−13.9825	−	9.79064i	−0.543445	−	0.380524i
$663$	−24.9112	−	13.0058i	−0.967470	−	0.505102i
$664$	17.6947	−	21.0877i	0.686687	−	0.818361i
$665$		0			0
$666$	12.2084	−	26.0187i	0.473068	−	1.00820i
$667$	−35.7087	+	9.56811i	−1.38264	+	0.370479i
$668$	−1.75587	−	0.818774i	−0.0679365	−	0.0316793i
$669$	−1.28739	+	28.6995i	−0.0497732	+	1.10959i
$670$		0			0
$671$	12.3730	−	33.9945i	0.477653	−	1.31234i
$672$	0.591347	−	4.45065i	0.0228117	−	0.171687i
$673$	−13.6940	−	19.5570i	−0.527863	−	0.753867i	0.463345	−	0.886178i	$-0.346649\pi$
$673$	−13.6940	−	19.5570i	−0.527863	−	0.753867i	−0.991208	+	0.132311i	$0.957760\pi$
$674$	−11.2915			−0.434933
$675$		0			0
$676$	2.98725			0.114894
$677$	12.6903	+	18.1236i	0.487727	+	0.696547i	0.985292	−	0.170880i	$-0.0546611\pi$
$677$	12.6903	+	18.1236i	0.487727	+	0.696547i	−0.497565	+	0.867427i	$0.665772\pi$
$678$	−24.8728	−	19.1328i	−0.955235	−	0.734791i
$679$	−9.04396	+	24.8481i	−0.347075	+	0.953581i
$680$		0			0
$681$	27.8153	−	14.4376i	1.06589	−	0.553248i
$682$	−12.5493	−	5.85182i	−0.480537	−	0.224078i
$683$	−24.3829	+	6.53337i	−0.932985	+	0.249993i	−0.693127	−	0.720815i	$-0.743768\pi$
$683$	−24.3829	+	6.53337i	−0.932985	+	0.249993i	−0.239858	+	0.970808i	$0.577101\pi$
$684$	0.0566484	−	0.630155i	0.00216601	−	0.0240946i
$685$		0			0
$686$	−16.9965	+	20.2556i	−0.648929	+	0.773363i
$687$	27.7703	−	17.6451i	1.05950	−	0.673201i
$688$	−3.67187	−	2.57107i	−0.139989	−	0.0980212i
$689$	−1.17925	−	6.68785i	−0.0449258	−	0.254787i
$690$		0			0
$691$	25.5999	+	21.4808i	0.973865	+	0.817170i	0.983153	−	0.182787i	$-0.0585118\pi$
$691$	25.5999	+	21.4808i	0.973865	+	0.817170i	−0.00928734	+	0.999957i	$0.502956\pi$
$692$	−1.76703	−	0.473473i	−0.0671723	−	0.0179988i
$693$	8.69959	−	23.7255i	0.330470	−	0.901256i
$694$	−6.05298	−	3.49469i	−0.229768	−	0.132657i
$695$		0			0
$696$	−15.6510	−	30.1532i	−0.593251	−	1.14295i
$697$	26.9931	+	2.36159i	1.02244	+	0.0894517i
$698$	11.5751	+	24.8229i	0.438124	+	0.939559i
$699$	1.69437	+	12.9898i	0.0640868	+	0.491321i
$700$		0			0
$701$		−	12.4042i		−	0.468499i	−0.972177	−	0.234249i	$-0.924737\pi$
$701$		−	12.4042i		−	0.468499i	0.972177	−	0.234249i	$-0.0752632\pi$
$702$	−32.2771	−	13.5053i	−1.21822	−	0.509724i
$703$	4.57003	−	4.57003i	0.172362	−	0.172362i
$704$	−6.50508	+	36.8922i	−0.245170	+	1.39043i
$705$		0			0
$706$	−35.9678	−	13.0912i	−1.35367	−	0.492694i
$707$	−0.725989	+	8.29809i	−0.0273036	+	0.312082i
$708$	1.33867	+	1.46441i	0.0503103	+	0.0550359i
$709$	4.29127	+	11.7902i	0.161162	+	0.442789i	0.993821	−	0.110998i	$-0.0354046\pi$
$709$	4.29127	+	11.7902i	0.161162	+	0.442789i	−0.832659	+	0.553786i	$0.813182\pi$
$710$		0			0
$711$	1.02634	−	0.715002i	0.0384906	−	0.0268147i
$712$	1.49782	−	5.58994i	0.0561332	−	0.209492i
$713$	1.18171	+	13.5070i	0.0442554	+	0.505842i
$714$	4.31925	+	13.7562i	0.161644	+	0.514812i
$715$		0			0
$716$	−1.01940	+	0.179748i	−0.0380969	+	0.00671750i
$717$	21.6416	−	0.918999i	0.808219	−	0.0343206i
$718$	−23.5926	+	2.06408i	−0.880466	+	0.0770308i
$719$	−9.10268	−	15.7663i	−0.339473	−	0.587984i	0.644861	−	0.764300i	$-0.276915\pi$
$719$	−9.10268	−	15.7663i	−0.339473	−	0.587984i	−0.984334	+	0.176316i	$0.943582\pi$
$720$		0			0
$721$	−13.0717	+	22.6408i	−0.486815	+	0.843188i
$722$	10.2159	−	21.9081i	0.380196	−	0.815334i
$723$	6.38419	+	28.9608i	0.237431	+	1.07707i
$724$	0.864744	+	1.03056i	0.0321380	+	0.0383005i
$725$		0			0
$726$	−6.63333	+	15.9603i	−0.246186	+	0.592344i
$727$	−8.06014	+	5.64377i	−0.298934	+	0.209316i	−0.713414	−	0.700742i	$-0.752852\pi$
$727$	−8.06014	+	5.64377i	−0.298934	+	0.209316i	0.414480	+	0.910058i	$0.363963\pi$
$728$	−20.8369	−	20.8369i	−0.772267	−	0.772267i
$729$	−18.9546	−	19.2282i	−0.702022	−	0.712155i
$730$		0			0
$731$	−4.06735	−	0.717184i	−0.150436	−	0.0265260i
$732$	−1.30775	−	3.16789i	−0.0483359	−	0.117088i
$733$	33.5024	−	15.6224i	1.23744	−	0.577027i	0.309905	−	0.950767i	$-0.399703\pi$
$733$	33.5024	−	15.6224i	1.23744	−	0.577027i	0.927533	+	0.373740i	$0.121925\pi$
$734$	−22.3146	+	18.7242i	−0.823646	+	0.691121i
$735$		0			0
$736$	6.96332	−	2.53444i	0.256671	−	0.0934207i
$737$	−10.7471	−	40.1088i	−0.395875	−	1.47743i
$738$	33.7364	+	0.0805779i	1.24186	+	0.00296611i
$739$	7.02338	−	4.05495i	0.258359	−	0.149164i	−0.365227	−	0.930919i	$-0.619009\pi$
$739$	7.02338	−	4.05495i	0.258359	−	0.149164i	0.623586	+	0.781755i	$0.285675\pi$
$740$		0			0
$741$	−5.79457	−	5.32249i	−0.212869	−	0.195526i
$742$	−1.99851	+	2.85416i	−0.0733675	+	0.104780i
$743$	−17.8592	+	25.5056i	−0.655190	+	0.935709i	−0.999996	−	0.00296531i	$-0.999056\pi$
$743$	−17.8592	+	25.5056i	−0.655190	+	0.935709i	0.344805	+	0.938674i	$0.387945\pi$
$744$	−11.8878	+	3.73262i	−0.435829	+	0.136844i
$745$		0			0
$746$	19.8552	−	11.4634i	0.726949	−	0.419704i
$747$	4.89480	−	27.3773i	0.179091	−	1.00168i
$748$	0.838814	+	3.13050i	0.0306701	+	0.114462i
$749$	26.6979	−	9.71724i	0.975519	−	0.355060i
$750$		0			0
$751$	−13.4156	+	11.2570i	−0.489541	+	0.410774i	−0.853862	−	0.520500i	$-0.825746\pi$
$751$	−13.4156	+	11.2570i	−0.489541	+	0.410774i	0.364321	+	0.931273i	$0.381301\pi$
$752$	−25.9484	+	12.1000i	−0.946243	+	0.441240i
$753$	−9.24615	−	1.22851i	−0.336949	−	0.0447695i
$754$	−43.8023	−	7.72353i	−1.59519	−	0.281274i
$755$		0			0
$756$	−0.908217	−	2.21504i	−0.0330315	−	0.0805603i
$757$	20.1777	+	20.1777i	0.733371	+	0.733371i	0.971286	−	0.237915i	$-0.0764640\pi$
$757$	20.1777	+	20.1777i	0.733371	+	0.733371i	−0.237915	+	0.971286i	$0.576464\pi$
$758$	29.5641	−	20.7010i	1.07381	−	0.751893i
$759$	41.3572	−	5.39455i	1.50117	−	0.195810i
$760$		0			0
$761$	23.7584	+	28.3141i	0.861240	+	1.02639i	0.999353	+	0.0359689i	$0.0114517\pi$
$761$	23.7584	+	28.3141i	0.861240	+	1.02639i	−0.138113	+	0.990416i	$0.544104\pi$
$762$	−7.89754	−	2.50046i	−0.286098	−	0.0905820i
$763$	11.8696	−	25.4545i	0.429710	−	0.921516i
$764$	1.69744	−	2.94006i	0.0614113	−	0.106368i
$765$		0			0
$766$	−4.88069	−	8.45360i	−0.176346	−	0.305441i
$767$	24.5794	−	2.15042i	0.887512	−	0.0776472i
$768$	5.17084	+	8.13803i	0.186587	+	0.293656i
$769$	−8.53754	+	1.50540i	−0.307872	+	0.0542861i	−0.325450	−	0.945559i	$-0.605516\pi$
$769$	−8.53754	+	1.50540i	−0.307872	+	0.0542861i	0.0175779	+	0.999845i	$0.494405\pi$
$770$		0			0
$771$	−20.7296	−	4.62163i	−0.746559	−	0.166444i
$772$	0.355865	+	4.06755i	0.0128078	+	0.146394i
$773$	−3.05417	+	11.3983i	−0.109851	+	0.409969i	−0.998850	−	0.0479396i	$-0.984734\pi$
$773$	−3.05417	+	11.3983i	−0.109851	+	0.409969i	0.889000	+	0.457908i	$0.151401\pi$
$774$	−5.12158	−	0.460409i	−0.184091	−	0.0165491i
$775$		0			0
$776$	−13.7174	−	37.6882i	−0.492425	−	1.35293i
$777$	7.38154	−	23.3141i	0.264811	−	0.836390i
$778$	−3.61856	+	41.3603i	−0.129732	+	1.48284i
$779$	7.12895	+	2.59472i	0.255421	+	0.0929657i
$780$		0			0
$781$	−4.24560	+	24.0780i	−0.151919	+	0.861578i
$782$	−16.8270	+	16.8270i	−0.601733	+	0.601733i
$783$	−28.8813	−	18.5452i	−1.03213	−	0.662752i
$784$		−	11.0025i		−	0.392947i
$785$		0			0
$786$	−1.01457	+	0.776581i	−0.0361884	+	0.0276997i
$787$	−7.93722	−	17.0214i	−0.282931	−	0.606748i	0.712559	−	0.701612i	$-0.247536\pi$
$787$	−7.93722	−	17.0214i	−0.282931	−	0.606748i	−0.995490	+	0.0948643i	$0.969758\pi$
$788$	3.19101	+	0.279178i	0.113675	+	0.00994529i
$789$	23.5794	+	1.05771i	0.839448	+	0.0376556i
$790$		0			0
$791$	−23.1237	−	13.3505i	−0.822183	−	0.474687i
$792$	13.0230	+	36.0481i	0.462753	+	1.28091i
$793$	−41.1675	−	11.0308i	−1.46190	−	0.391715i
$794$	16.7831	+	14.0827i	0.595610	+	0.499776i
$795$		0			0
$796$	−0.367376	−	2.08349i	−0.0130213	−	0.0738475i
$797$	−17.6670	−	12.3706i	−0.625797	−	0.438188i	0.217184	−	0.976131i	$-0.430313\pi$
$797$	−17.6670	−	12.3706i	−0.625797	−	0.438188i	−0.842981	+	0.537943i	$0.819202\pi$
$798$	0.171269	+	4.03324i	0.00606287	+	0.142775i
$799$	−16.9567	+	20.2082i	−0.599884	+	0.714914i
$800$		0			0
$801$	−1.49974	−	5.65108i	−0.0529909	−	0.199671i
$802$	−1.93969	+	0.519739i	−0.0684929	+	0.0183526i
$803$	−19.9304	−	9.29368i	−0.703327	−	0.327967i
$804$	−3.31521	−	2.11759i	−0.116919	−	0.0746818i
$805$		0			0
$806$	−5.57934	+	15.3291i	−0.196524	+	0.539945i
$807$	19.7470	−	8.15185i	0.695126	−	0.286959i
$808$	−7.24665	−	10.3493i	−0.254936	−	0.364087i
$809$	4.46938			0.157135			0.0785676	−	0.996909i	$-0.474965\pi$
$809$	4.46938			0.157135			0.0785676	+	0.996909i	$0.474965\pi$
$810$		0			0
$811$	37.9099			1.33120			0.665598	−	0.746311i	$-0.268177\pi$
$811$	37.9099			1.33120			0.665598	+	0.746311i	$0.268177\pi$
$812$	−1.74556	−	2.49292i	−0.0612573	−	0.0874845i
$813$	−31.6321	+	13.0582i	−1.10939	+	0.457971i
$814$	−14.0978	+	38.7333i	−0.494127	+	1.35760i
$815$		0			0
$816$	−16.2310	−	10.3675i	−0.568197	−	0.362936i
$817$	−1.04801	−	0.488696i	−0.0366653	−	0.0170973i
$818$	30.1175	−	8.06996i	1.05303	−	0.282159i
$819$	−28.7383	−	7.77401i	−1.00420	−	0.271646i
$820$		0			0
$821$	23.1674	−	27.6099i	0.808549	−	0.963591i	−0.191290	−	0.981533i	$-0.561267\pi$
$821$	23.1674	−	27.6099i	0.808549	−	0.963591i	0.999839	+	0.0179428i	$0.00571166\pi$
$822$	−0.589922	−	13.8921i	−0.0205759	−	0.484544i
$823$	2.18095	+	1.52711i	0.0760230	+	0.0532319i	0.610970	−	0.791654i	$-0.290780\pi$
$823$	2.18095	+	1.52711i	0.0760230	+	0.0532319i	−0.534947	+	0.844886i	$0.679668\pi$
$824$	−6.88563	−	39.0504i	−0.239872	−	1.36038i
$825$		0			0
$826$	−9.69752	−	8.13719i	−0.337420	−	0.283129i
$827$	−39.8859	−	10.6874i	−1.38697	−	0.371637i	−0.513321	−	0.858197i	$-0.671585\pi$
$827$	−39.8859	−	10.6874i	−1.38697	−	0.371637i	−0.873647	+	0.486560i	$0.838252\pi$
$828$	2.54703	−	3.02075i	0.0885153	−	0.104978i
$829$	−19.6326	−	11.3349i	−0.681869	−	0.393677i	0.118690	−	0.992931i	$-0.462131\pi$
$829$	−19.6326	−	11.3349i	−0.681869	−	0.393677i	−0.800559	+	0.599254i	$0.795464\pi$
$830$		0			0
$831$	−3.50863	−	0.157388i	−0.121713	−	0.00545974i
$832$	43.9658	+	3.84651i	1.52424	+	0.133354i
$833$	−4.28428	−	9.18766i	−0.148441	−	0.318334i
$834$	−33.8357	+	25.8989i	−1.17164	+	0.896806i
$835$		0			0
$836$			0.907402i			0.0313832i
$837$	−8.53774	+	9.25056i	−0.295108	+	0.319746i
$838$	−14.9429	+	14.9429i	−0.516195	+	0.516195i
$839$	1.44230	−	8.17971i	0.0497938	−	0.282395i	−0.949736	−	0.313052i	$-0.898649\pi$
$839$	1.44230	−	8.17971i	0.0497938	−	0.282395i	0.999530	+	0.0306567i	$0.00975985\pi$
$840$		0			0
$841$	−13.7493	−	5.00432i	−0.474112	−	0.172563i
$842$	−4.20240	+	48.0337i	−0.144824	+	1.65535i
$843$	13.6676	−	43.1681i	0.470736	−	1.48679i
$844$	1.50888	+	4.14562i	0.0519379	+	0.142698i
$845$		0			0
$846$	−18.9031	+	26.8597i	−0.649902	+	0.923455i
$847$	−3.80634	+	14.2054i	−0.130787	+	0.488105i
$848$	−0.405641	−	4.63650i	−0.0139298	−	0.159218i
$849$	−3.92057	−	0.874084i	−0.134554	−	0.0299985i
$850$		0			0
$851$	39.7487	−	7.00876i	1.36257	−	0.240257i
$852$	1.24219	+	1.95499i	0.0425567	+	0.0669770i
$853$	6.11455	−	0.534954i	0.209358	−	0.0183165i	0.0180058	−	0.999838i	$-0.494268\pi$
$853$	6.11455	−	0.534954i	0.209358	−	0.0183165i	0.191352	+	0.981521i	$0.438713\pi$
$854$	10.9335	+	18.9374i	0.374137	+	0.648024i
$855$		0			0
$856$	−21.5463	+	37.3193i	−0.736439	+	1.27555i
$857$	−14.6042	+	31.3187i	−0.498869	+	1.06983i	0.482181	+	0.876072i	$0.339845\pi$
$857$	−14.6042	+	31.3187i	−0.498869	+	1.06983i	−0.981050	+	0.193756i	$0.937933\pi$
$858$	47.8395	+	15.1466i	1.63321	+	0.517095i
$859$	14.4078	+	17.1705i	0.491587	+	0.585850i	0.953620	−	0.301012i	$-0.0973245\pi$
$859$	14.4078	+	17.1705i	0.491587	+	0.585850i	−0.462034	+	0.886862i	$0.652880\pi$
$860$		0			0
$861$	28.4647	−	3.71287i	0.970073	−	0.126534i
$862$	−11.7054	+	8.19621i	−0.398688	+	0.279164i
$863$	34.4337	+	34.4337i	1.17214	+	1.17214i	0.981700	+	0.190436i	$0.0609900\pi$
$863$	34.4337	+	34.4337i	1.17214	+	1.17214i	0.190436	+	0.981700i	$0.439010\pi$
$864$	6.09114	+	3.19864i	0.207225	+	0.108820i
$865$		0			0
$866$	47.8011	+	8.42862i	1.62435	+	0.286416i
$867$	11.5976	+	1.54095i	0.393876	+	0.0523334i
$868$	−1.01159	+	0.471713i	−0.0343357	+	0.0160110i
$869$	−1.37423	+	1.15312i	−0.0466175	+	0.0391168i
$870$		0			0
$871$	−45.9694	+	16.7315i	−1.55762	+	0.566926i
$872$	11.0255	+	41.1477i	0.373370	+	1.39344i
$873$	−30.9776	−	26.1197i	−1.04843	−	0.884017i
$874$	−5.77009	+	3.33137i	−0.195176	+	0.112685i
$875$		0			0
$876$	−1.98765	+	0.624094i	−0.0671564	+	0.0210862i
$877$	7.94910	−	11.3525i	0.268422	−	0.383347i	−0.662201	−	0.749327i	$-0.730377\pi$
$877$	7.94910	−	11.3525i	0.268422	−	0.383347i	0.930623	+	0.365980i	$0.119266\pi$
$878$	10.6140	−	15.1584i	0.358206	−	0.511571i
$879$	15.3768	+	14.1240i	0.518645	+	0.476391i
$880$		0			0
$881$	−20.3929	+	11.7738i	−0.687054	+	0.396671i	−0.802507	−	0.596642i	$-0.796501\pi$
$881$	−20.3929	+	11.7738i	−0.687054	+	0.396671i	0.115453	+	0.993313i	$0.463168\pi$
$882$	−6.28476	−	10.9458i	−0.211619	−	0.368565i
$883$	−4.25489	−	15.8795i	−0.143188	−	0.534386i	−0.999829	−	0.0184733i	$-0.994119\pi$
$883$	−4.25489	−	15.8795i	−0.143188	−	0.534386i	0.856641	−	0.515913i	$-0.172547\pi$
$884$	3.58792	−	1.30590i	0.120675	−	0.0439221i
$885$		0			0
$886$	11.6044	−	9.73725i	0.389857	−	0.327129i
$887$	−9.29073	+	4.33234i	−0.311952	+	0.145466i	−0.572289	−	0.820052i	$-0.693944\pi$
$887$	−9.29073	+	4.33234i	−0.311952	+	0.145466i	0.260336	+	0.965518i	$0.416167\pi$
$888$	14.1534	+	34.2851i	0.474958	+	1.15053i
$889$	−6.94156	−	1.22398i	−0.232812	−	0.0410511i
$890$		0			0
$891$	29.5442	+	25.0320i	0.989769	+	0.838604i
$892$	−2.76005	−	2.76005i	−0.0924133	−	0.0924133i
$893$	−6.05018	+	4.23638i	−0.202461	+	0.141765i
$894$	−7.65882	+	18.4278i	−0.256149	+	0.616316i
$895$		0			0
$896$	−11.2227	−	13.3748i	−0.374926	−	0.446819i
$897$	−10.5778	−	47.9843i	−0.353181	−	1.60215i
$898$	0.907153	−	1.94540i	0.0302721	−	0.0649187i
$899$	−8.00123	+	13.8585i	−0.266856	+	0.462208i
$900$		0			0
$901$	−2.14414	−	3.71376i	−0.0714317	−	0.123723i
$902$	−48.2002	+	4.21697i	−1.60489	+	0.140410i
$903$	−4.37149	+	0.185633i	−0.145474	+	0.00617748i
$904$	39.8832	−	7.03248i	1.32649	−	0.233897i
$905$		0			0
$906$	10.9819	+	34.9756i	0.364848	+	1.16199i
$907$	1.17717	+	13.4551i	0.0390872	+	0.446769i	0.990370	+	0.138448i	$0.0442114\pi$
$907$	1.17717	+	13.4551i	0.0390872	+	0.446769i	−0.951283	+	0.308321i	$0.900233\pi$
$908$	−1.10206	+	4.11293i	−0.0365730	+	0.136492i
$909$	−11.5554	−	5.42200i	−0.383268	−	0.179836i
$910$		0			0
$911$	4.95701	+	13.6193i	0.164233	+	0.451227i	0.994323	−	0.106403i	$-0.0339332\pi$
$911$	4.95701	+	13.6193i	0.164233	+	0.451227i	−0.830090	+	0.557629i	$0.811711\pi$
$912$	−3.63825	−	3.97999i	−0.120475	−	0.131791i
$913$	−3.47635	+	39.7348i	−0.115050	+	1.31503i
$914$	−6.91502	−	2.51686i	−0.228729	−	0.0832504i
$915$		0			0
$916$	−0.776272	+	4.40246i	−0.0256488	+	0.145461i
$917$	−0.768724	+	0.768724i	−0.0253855	+	0.0253855i
$918$	−22.0694	−	1.04280i	−0.728399	−	0.0344176i
$919$		−	11.7599i		−	0.387925i	−0.981009	−	0.193962i	$-0.937866\pi$
$919$		−	11.7599i		−	0.387925i	0.981009	−	0.193962i	$-0.0621340\pi$
$920$		0			0
$921$	5.26444	+	40.3597i	0.173469	+	1.32990i
$922$	8.53202	+	18.2970i	0.280987	+	0.602579i
$923$	28.6946	+	2.51046i	0.944496	+	0.0826327i
$924$	1.58175	+	3.04739i	0.0520357	+	0.100252i
$925$		0			0
$926$	38.0276	+	21.9552i	1.24966	+	0.721494i
$927$	−25.6773	−	30.7499i	−0.843353	−	1.00996i
$928$	8.44784	+	2.26359i	0.277314	+	0.0743061i
$929$	−36.0388	−	30.2401i	−1.18239	−	0.992146i	−0.999960	−	0.00892776i	$-0.997158\pi$
$929$	−36.0388	−	30.2401i	−1.18239	−	0.992146i	−0.182433	−	0.983218i	$-0.558397\pi$
$930$		0			0
$931$	−0.492867	−	2.79519i	−0.0161531	−	0.0916086i
$932$	−1.45799	−	1.02089i	−0.0477579	−	0.0334405i
$933$	−5.81437	+	3.69441i	−0.190354	+	0.120950i
$934$	19.3932	−	23.1119i	0.634563	−	0.756243i
$935$		0			0
$936$	40.9700	−	18.9856i	1.33915	−	0.620565i
$937$	−36.6017	+	9.80740i	−1.19573	+	0.320394i	−0.801147	−	0.598468i	$-0.795776\pi$
$937$	−36.6017	+	9.80740i	−1.19573	+	0.320394i	−0.394580	+	0.918862i	$0.629110\pi$
$938$	22.7477	+	10.6074i	0.742740	+	0.346346i
$939$	−1.40595	+	0.729759i	−0.0458814	+	0.0238148i
$940$		0			0
$941$	−3.79401	+	10.4240i	−0.123681	+	0.339811i	−0.986045	−	0.166477i	$-0.946761\pi$
$941$	−3.79401	+	10.4240i	−0.123681	+	0.339811i	0.862364	+	0.506289i	$0.168983\pi$
$942$	24.2096	+	18.6227i	0.788793	+	0.606760i
$943$	27.1749	+	38.8098i	0.884937	+	1.26382i
$944$	16.9098			0.550367
$945$		0			0
$946$	7.37489			0.239778
$947$	9.12331	+	13.0294i	0.296468	+	0.423400i	0.939558	−	0.342391i	$-0.111237\pi$
$947$	9.12331	+	13.0294i	0.296468	+	0.423400i	−0.643090	+	0.765791i	$0.722348\pi$
$948$	−0.0223842	+	0.168470i	−0.000727006	+	0.00547165i
$949$	−8.86092	+	24.3452i	−0.287638	+	0.790278i
$950$		0			0
$951$	−2.04674	+	45.6276i	−0.0663701	+	1.47958i
$952$	−16.8644	−	7.86402i	−0.546580	−	0.254874i
$953$	35.2746	−	9.45180i	1.14266	−	0.306174i	0.362638	−	0.931930i	$-0.381876\pi$
$953$	35.2746	−	9.45180i	1.14266	−	0.306174i	0.780019	+	0.625756i	$0.215210\pi$
$954$	−3.05197	−	4.38090i	−0.0988113	−	0.141837i
$955$		0			0
$956$	−1.89177	+	2.25453i	−0.0611843	+	0.0729167i
$957$	43.6361	+	22.7818i	1.41055	+	0.736430i
$958$	−24.8501	−	17.4002i	−0.802871	−	0.562176i
$959$	−2.05447	−	11.6515i	−0.0663422	−	0.376245i
$960$		0			0
$961$	−19.2514	−	16.1538i	−0.621012	−	0.521091i
$962$	46.9062	+	12.5685i	1.51232	+	0.405224i
$963$	−0.103984	+	43.5361i	−0.00335084	+	1.40293i
$964$	−3.48953	−	2.01468i	−0.112390	−	0.0648886i
$965$		0			0
$966$	−13.5710	+	21.2462i	−0.436640	+	0.683584i
$967$	1.95128	+	0.170714i	0.0627488	+	0.00548981i	0.118487	−	0.992956i	$-0.462196\pi$
$967$	1.95128	+	0.170714i	0.0627488	+	0.00548981i	−0.0557381	+	0.998445i	$0.517751\pi$
$968$	−9.42696	−	20.2162i	−0.302994	−	0.649773i
$969$	−4.58790	−	1.90679i	−0.147385	−	0.0612550i
$970$		0			0
$971$			27.5442i			0.883934i	0.897031	+	0.441967i	$0.145719\pi$
$971$			27.5442i			0.883934i	−0.897031	+	0.441967i	$0.854281\pi$
$972$	3.66587	−	0.138130i	0.117583	−	0.00443052i
$973$	−25.6369	+	25.6369i	−0.821881	+	0.821881i
$974$	4.27366	−	24.2371i	0.136937	−	0.776607i
$975$		0			0
$976$	−27.4477	−	9.99016i	−0.878581	−	0.319777i
$977$	−2.84484	+	32.5167i	−0.0910146	+	1.04030i	0.804108	+	0.594483i	$0.202643\pi$
$977$	−2.84484	+	32.5167i	−0.0910146	+	1.04030i	−0.895123	+	0.445819i	$0.852912\pi$
$978$	16.6749	−	3.67586i	0.533205	−	0.117541i
$979$	2.86792	+	7.87954i	0.0916591	+	0.251831i
$980$		0			0
$981$	30.3595	+	30.5049i	0.969305	+	0.973946i
$982$	3.18718	−	11.8947i	0.101707	−	0.379575i
$983$	−2.79155	−	31.9076i	−0.0890367	−	1.01769i	−0.900952	−	0.433919i	$-0.857130\pi$
$983$	−2.79155	−	31.9076i	−0.0890367	−	1.01769i	0.811915	−	0.583775i	$-0.198425\pi$
$984$	−29.4531	+	32.0654i	−0.938930	+	1.02221i
$985$		0			0
$986$	−27.6596	+	4.87713i	−0.880860	+	0.155319i
$987$	−12.9340	+	24.7738i	−0.411695	+	0.788558i
$988$	1.06496	−	0.0931716i	0.0338808	−	0.00296418i
$989$	−3.61075	−	6.25401i	−0.114815	−	0.198866i
$990$		0			0
$991$	24.5859	−	42.5840i	0.780995	−	1.35272i	−0.150367	−	0.988630i	$-0.548046\pi$
$991$	24.5859	−	42.5840i	0.780995	−	1.35272i	0.931362	−	0.364094i	$-0.118621\pi$
$992$	1.35561	−	2.90712i	0.0430407	−	0.0923012i
$993$	16.4269	−	15.0164i	0.521291	−	0.476531i
$994$	−9.49956	−	11.3211i	−0.301308	−	0.359084i
$995$		0			0
$996$	2.29676	+	3.00060i	0.0727755	+	0.0950778i
$997$	−25.7299	+	18.0163i	−0.814874	+	0.570581i	−0.905031	−	0.425347i	$-0.860152\pi$
$997$	−25.7299	+	18.0163i	−0.814874	+	0.570581i	0.0901563	+	0.995928i	$0.471263\pi$
$998$	19.4085	+	19.4085i	0.614364	+	0.614364i
$999$	29.6478	+	22.9188i	0.938014	+	0.725118i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.ba.b.407.11		192
5.2	odd	4		135.2.q.a.83.6	yes	192
5.3	odd	4	inner	675.2.ba.b.218.11		192
5.4	even	2		135.2.q.a.2.6	✓	192
15.2	even	4		405.2.r.a.8.11		192
15.14	odd	2		405.2.r.a.332.11		192
27.14	odd	18	inner	675.2.ba.b.257.11		192
135.14	odd	18		135.2.q.a.122.6	yes	192
135.67	odd	36		405.2.r.a.233.11		192
135.68	even	36	inner	675.2.ba.b.68.11		192
135.94	even	18		405.2.r.a.152.11		192
135.122	even	36		135.2.q.a.68.6	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.6	✓	192	5.4	even	2
135.2.q.a.68.6	yes	192	135.122	even	36
135.2.q.a.83.6	yes	192	5.2	odd	4
135.2.q.a.122.6	yes	192	135.14	odd	18
405.2.r.a.8.11		192	15.2	even	4
405.2.r.a.152.11		192	135.94	even	18
405.2.r.a.233.11		192	135.67	odd	36
405.2.r.a.332.11		192	15.14	odd	2
675.2.ba.b.68.11		192	135.68	even	36	inner
675.2.ba.b.218.11		192	5.3	odd	4	inner
675.2.ba.b.257.11		192	27.14	odd	18	inner
675.2.ba.b.407.11		192	1.1	even	1	trivial

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+(0.761943 + 1.08817i) q^{2} +(-1.60100 + 0.660916i) q^{3} +(0.0804885 - 0.221140i) q^{4} +(-1.93906 - 1.23857i) q^{6} +(-1.77434 - 0.827388i) q^{7} +(2.86825 - 0.768546i) q^{8} +(2.12638 - 2.11625i) q^{9} +(-2.76562 + 3.29594i) q^{11} +(0.0172933 + 0.407241i) q^{12} +(4.15220 + 2.90740i) q^{13} +(-0.451609 - 2.56120i) q^{14} +(2.66120 + 2.23301i) q^{16} +(3.09176 + 0.828434i) q^{17} +(3.92301 + 0.701399i) q^{18} +(0.776109 + 0.448087i) q^{19} +(3.38755 + 0.151957i) q^{21} +(-5.69379 - 0.498142i) q^{22} +(2.36525 + 5.07230i) q^{23} +(-4.08412 + 3.12611i) q^{24} +6.73356i q^{26} +(-2.00567 + 4.79346i) q^{27} +(-0.325783 + 0.325783i) q^{28} +(-1.14702 + 6.50507i) q^{29} +(2.27652 + 0.828586i) q^{31} +(0.115398 - 1.31900i) q^{32} +(2.24941 - 7.10463i) q^{33} +(1.45427 + 3.99557i) q^{34} +(-0.296839 - 0.640563i) q^{36} +(1.86654 - 6.96604i) q^{37} +(0.103757 + 1.18595i) q^{38} +(-8.56920 - 1.91049i) q^{39} +(8.33680 - 1.47000i) q^{41} +(2.41576 + 3.80200i) q^{42} +(-1.28541 + 0.112459i) q^{43} +(0.506265 + 0.876877i) q^{44} +(-3.71732 + 6.43859i) q^{46} +(-3.48305 + 7.46943i) q^{47} +(-5.73641 - 1.81622i) q^{48} +(-2.03580 - 2.42617i) q^{49} +(-5.49742 + 0.717071i) q^{51} +(0.977148 - 0.684206i) q^{52} +(-0.947342 - 0.947342i) q^{53} +(-6.74430 + 1.46984i) q^{54} +(-5.72514 - 1.00950i) q^{56} +(-1.53869 - 0.204443i) q^{57} +(-7.95258 + 3.70835i) q^{58} +(3.72879 - 3.12883i) q^{59} +(-7.90101 + 2.87573i) q^{61} +(0.832940 + 3.10857i) q^{62} +(-5.52388 + 1.99560i) q^{63} +(7.54029 - 4.35339i) q^{64} +(9.44496 - 2.96559i) q^{66} +(-5.53556 + 7.90560i) q^{67} +(0.432051 - 0.617033i) q^{68} +(-7.13912 - 6.55750i) q^{69} +(4.92123 - 2.84127i) q^{71} +(4.47256 - 7.70415i) q^{72} +(1.32285 + 4.93694i) q^{73} +(9.00242 - 3.27661i) q^{74} +(0.161558 - 0.135563i) q^{76} +(7.63418 - 3.55988i) q^{77} +(-4.45032 - 10.7804i) q^{78} +(0.410612 + 0.0724019i) q^{79} +(0.0429919 - 8.99990i) q^{81} +(7.95178 + 7.95178i) q^{82} +(7.59392 - 5.31732i) q^{83} +(0.306263 - 0.736893i) q^{84} +(-1.10179 - 1.31306i) q^{86} +(-2.46293 - 11.1727i) q^{87} +(-5.39942 + 11.5791i) q^{88} +(0.974450 - 1.68780i) q^{89} +(-4.96186 - 8.59420i) q^{91} +(1.31207 - 0.114791i) q^{92} +(-4.19233 + 0.178025i) q^{93} +(-10.7819 + 1.90114i) q^{94} +(0.686998 + 2.18799i) q^{96} +(-1.17718 - 13.4552i) q^{97} +(1.08892 - 4.06390i) q^{98} +(1.09426 + 12.8612i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{3} - 36 q^{6} + 12 q^{7} + 18 q^{8} - 36 q^{11} + 12 q^{12} + 12 q^{13} - 24 q^{16} + 18 q^{17} + 54 q^{18} - 24 q^{21} + 12 q^{22} + 36 q^{23} + 36 q^{27} + 24 q^{28} - 24 q^{31}+ \cdots - 324 q^{98}+O(q^{100}) \) 192 * q + 12 * q^2 + 12 * q^3 - 36 * q^6 + 12 * q^7 + 18 * q^8 - 36 * q^11 + 12 * q^12 + 12 * q^13 - 24 * q^16 + 18 * q^17 + 54 * q^18 - 24 * q^21 + 12 * q^22 + 36 * q^23 + 36 * q^27 + 24 * q^28 - 24 * q^31 + 48 * q^32 + 6 * q^33 + 12 * q^36 + 6 * q^37 - 12 * q^38 + 24 * q^41 + 24 * q^42 + 12 * q^43 - 12 * q^46 + 6 * q^47 - 12 * q^48 + 144 * q^51 - 12 * q^52 + 180 * q^56 + 12 * q^57 + 12 * q^58 - 60 * q^61 + 18 * q^62 + 54 * q^63 + 72 * q^66 - 24 * q^67 + 60 * q^68 - 36 * q^71 - 180 * q^72 + 6 * q^73 - 72 * q^76 - 132 * q^77 - 78 * q^78 + 12 * q^81 + 24 * q^82 - 48 * q^83 + 12 * q^86 - 144 * q^87 + 48 * q^88 - 12 * q^91 - 258 * q^92 - 180 * q^93 - 12 * q^96 - 24 * q^97 - 324 * q^98

Introduction

L-functions

Modular forms

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