LMFDB - Embedded newform 675.2.ba.b.68.11

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			68.11
Character	$\chi$	$=$	675.68
Dual form			675.2.ba.b.407.11

$q$-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 $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.761943	−	1.08817i	0.538775	−	0.769451i	−0.453797	−	0.891105i	$-0.649931\pi$
$2$	0.761943	−	1.08817i	0.538775	−	0.769451i	0.992573	+	0.121654i	$0.0388198\pi$
$3$	−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	−0.727947	−	0.685633i	$-0.759526\pi$
$7$	−1.77434	+	0.827388i	−0.670638	+	0.312723i	0.0573098	+	0.998356i	$0.481748\pi$
$8$	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	−0.999971	−	0.00765542i	$-0.997563\pi$
$11$	−2.76562	−	3.29594i	−0.833867	−	0.993764i	0.166104	−	0.986108i	$-0.446881\pi$
$12$	0.0172933	−	0.407241i	0.00499215	−	0.117560i
$13$	4.15220	−	2.90740i	1.15161	−	0.806368i	0.167844	−	0.985814i	$-0.446319\pi$
$13$	4.15220	−	2.90740i	1.15161	−	0.806368i	0.983768	+	0.179446i	$0.0574305\pi$
$14$	−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	0.136405	−	0.990653i	$-0.456445\pi$
$17$	3.09176	−	0.828434i	0.749861	−	0.200925i	0.613456	+	0.789729i	$0.289779\pi$
$18$	3.92301	−	0.701399i	0.924663	−	0.165321i
$19$	0.776109	−	0.448087i	0.178052	−	0.102798i	−0.408325	−	0.912836i	$-0.633887\pi$
$19$	0.776109	−	0.448087i	0.178052	−	0.102798i	0.586377	+	0.810038i	$0.300554\pi$
$20$		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	−0.489435	−	0.872040i	$-0.662797\pi$
$23$	2.36525	−	5.07230i	0.493189	−	1.05765i	0.982624	−	0.185607i	$-0.0594253\pi$
$24$	−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	−0.884350	−	0.466825i	$-0.845398\pi$
$29$	−1.14702	−	6.50507i	−0.212996	−	1.20796i	0.671354	−	0.741137i	$-0.265713\pi$
$30$		0			0
$31$	2.27652	−	0.828586i	0.408875	−	0.148818i	−0.129390	−	0.991594i	$-0.541302\pi$
$31$	2.27652	−	0.828586i	0.408875	−	0.148818i	0.538266	+	0.842775i	$0.319080\pi$
$32$	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	0.931334	+	0.364166i	$0.118646\pi$
$37$	1.86654	+	6.96604i	0.306858	+	1.14521i	−0.624476	+	0.781044i	$0.714688\pi$
$38$	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	0.781292	−	0.624166i	$-0.214561\pi$
$41$	8.33680	+	1.47000i	1.30199	+	0.229576i	0.520697	+	0.853742i	$0.325672\pi$
$42$	2.41576	−	3.80200i	0.372761	−	0.586662i
$43$	−1.28541	−	0.112459i	−0.196024	−	0.0171499i	−0.0112790	−	0.999936i	$-0.503590\pi$
$43$	−1.28541	−	0.112459i	−0.196024	−	0.0171499i	−0.184745	+	0.982787i	$0.559146\pi$
$44$	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	−0.978338	−	0.207013i	$-0.933626\pi$
$47$	−3.48305	−	7.46943i	−0.508055	−	1.08953i	0.470283	−	0.882516i	$-0.344152\pi$
$48$	−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	−0.769171	−	0.639043i	$-0.779330\pi$
$53$	−0.947342	+	0.947342i	−0.130127	+	0.130127i	0.639043	+	0.769171i	$0.279330\pi$
$54$	−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	0.852391	−	0.522904i	$-0.175151\pi$
$59$	3.72879	+	3.12883i	0.485447	+	0.407339i	−0.366944	+	0.930243i	$0.619596\pi$
$60$		0			0
$61$	−7.90101	−	2.87573i	−1.01162	−	0.368200i	−0.217566	−	0.976046i	$-0.569812\pi$
$61$	−7.90101	−	2.87573i	−1.01162	−	0.368200i	−0.794055	+	0.607846i	$0.792034\pi$
$62$	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	−0.999808	−	0.0196049i	$-0.993759\pi$
$67$	−5.53556	−	7.90560i	−0.676276	−	0.965822i	0.323532	−	0.946217i	$-0.395130\pi$
$68$	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	0.762738	−	0.646707i	$-0.223854\pi$
$71$	4.92123	+	2.84127i	0.584043	+	0.337197i	−0.178696	+	0.983904i	$0.557188\pi$
$72$	4.47256	+	7.70415i	0.527097	+	0.907943i
$73$	1.32285	−	4.93694i	0.154828	−	0.577825i	−0.844292	−	0.535883i	$-0.819979\pi$
$73$	1.32285	−	4.93694i	0.154828	−	0.577825i	0.999120	−	0.0419419i	$-0.0133544\pi$
$74$	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	−0.150502	−	0.988610i	$-0.548089\pi$
$79$	0.410612	−	0.0724019i	0.0461974	−	0.00814585i	0.196699	+	0.980464i	$0.436978\pi$
$80$		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	0.910560	−	0.413378i	$-0.135651\pi$
$83$	7.59392	+	5.31732i	0.833541	+	0.583652i	−0.0770185	+	0.997030i	$0.524540\pi$
$84$	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	0.913039	−	0.407872i	$-0.133729\pi$
$89$	0.974450	+	1.68780i	0.103292	+	0.178906i	−0.809747	+	0.586779i	$0.800396\pi$
$90$		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	0.665359	+	0.746524i	$0.268279\pi$
$97$	−1.17718	+	13.4552i	−0.119524	+	1.36617i	−0.784883	+	0.619644i	$0.787277\pi$
$98$	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	−0.990797	−	0.135354i	$-0.956783\pi$
$101$	−1.45521	+	3.99814i	−0.144798	+	0.397830i	0.845999	+	0.533185i	$0.179005\pi$
$102$	−4.96901	+	5.43575i	−0.492006	+	0.538219i
$103$	1.16385	+	13.3028i	0.114677	+	1.31077i	0.807589	+	0.589745i	$0.200772\pi$
$103$	1.16385	+	13.3028i	0.114677	+	1.31077i	−0.692912	+	0.721022i	$0.743673\pi$
$104$	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	0.00794276	−	0.999968i	$-0.497472\pi$
$107$	−10.2616	−	10.2616i	−0.992026	−	0.992026i	−0.999968	+	0.00794276i	$0.997472\pi$
$108$	0.898596	−	0.829353i	0.0864674	−	0.0798045i
$109$		−	14.3459i		−	1.37409i	−0.726615	−	0.687045i	$-0.758908\pi$
$109$		−	14.3459i		−	1.37409i	0.726615	−	0.687045i	$-0.241092\pi$
$110$		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	0.572198	−	0.820116i	$-0.306091\pi$
$113$	13.5865	−	1.18867i	1.27811	−	0.111821i	0.705916	+	0.708295i	$0.250535\pi$
$114$	−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	0.409792	−	0.912179i	$-0.365601\pi$
$127$	3.47767	+	0.931838i	0.308593	+	0.0826872i	−0.101199	+	0.994866i	$0.532268\pi$
$128$	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	0.947713	−	0.319124i	$-0.103389\pi$
$131$	0.189922	+	0.521807i	0.0165936	+	0.0455905i	−0.931119	+	0.364715i	$0.881167\pi$
$132$	−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	−0.643315	−	0.765601i	$-0.722442\pi$
$137$	3.46624	−	4.95031i	0.296141	−	0.422934i	0.939457	+	0.342668i	$0.111330\pi$
$138$	1.69606	+	12.7650i	0.144378	+	1.08663i
$139$	6.33390	+	17.4022i	0.537234	+	1.47604i	0.850295	+	0.526306i	$0.176423\pi$
$139$	6.33390	+	17.4022i	0.537234	+	1.47604i	−0.313061	+	0.949733i	$0.601354\pi$
$140$		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	0.858871	+	0.512192i	$0.171166\pi$
$149$	−1.50609	+	8.54145i	−0.123384	+	0.699743i	−0.982255	+	0.187551i	$0.939945\pi$
$150$		0			0
$151$	−12.2052	+	10.2414i	−0.993244	+	0.833431i	−0.986034	−	0.166543i	$-0.946740\pi$
$151$	−12.2052	+	10.2414i	−0.993244	+	0.833431i	−0.00721007	+	0.999974i	$0.502295\pi$
$152$	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	−0.601630	−	0.798775i	$-0.705482\pi$
$157$	−13.2243	+	1.15698i	−1.05541	+	0.0923367i	−0.453784	+	0.891112i	$0.649926\pi$
$158$	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	0.471071	−	0.882095i	$-0.343867\pi$
$163$	−5.24760	−	5.24760i	−0.411024	−	0.411024i	−0.882095	+	0.471071i	$0.843867\pi$
$164$	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	0.972068	+	0.234698i	$0.0754101\pi$
$167$	0.717512	+	8.20120i	0.0555227	+	0.634628i	−0.916546	+	0.399930i	$0.869034\pi$
$168$	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	0.925951	+	0.377643i	$0.123265\pi$
$173$	−0.677506	+	7.74393i	−0.0515098	+	0.588760i	−0.977461	+	0.211116i	$0.932290\pi$
$174$	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	−0.936436	−	0.350839i	$-0.885896\pi$
$179$	−2.19929	+	3.80928i	−0.164382	+	0.284719i	0.772053	+	0.635558i	$0.219230\pi$
$180$		0			0
$181$	−2.85830	−	4.95072i	−0.212456	−	0.367984i	0.740027	−	0.672577i	$-0.234813\pi$
$181$	−2.85830	−	4.95072i	−0.212456	−	0.367984i	−0.952483	+	0.304593i	$0.901479\pi$
$182$	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	0.365860	−	0.930670i	$-0.380775\pi$
$191$	14.2067	−	2.50503i	1.02796	−	0.181258i	0.662104	+	0.749412i	$0.269664\pi$
$192$	−9.19475	−	11.9532i	−0.663574	−	0.862651i
$193$	−15.7247	−	7.33254i	−1.13189	−	0.527808i	−0.235852	−	0.971789i	$-0.575788\pi$
$193$	−15.7247	−	7.33254i	−1.13189	−	0.527808i	−0.896036	+	0.443981i	$0.853566\pi$
$194$	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	−0.719280	−	0.694721i	$-0.755528\pi$
$197$	3.52289	−	13.1476i	0.250995	−	0.936727i	0.970275	−	0.242006i	$-0.0778054\pi$
$198$	−13.1613	−	10.9902i	−0.935336	−	0.781041i
$199$	7.78555	+	4.49499i	0.551903	+	0.318641i	0.749889	−	0.661564i	$-0.230107\pi$
$199$	7.78555	+	4.49499i	0.551903	+	0.318641i	−0.197986	+	0.980205i	$0.563440\pi$
$200$		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	−0.00326162	−	0.999995i	$-0.501038\pi$
$211$	−14.3607	−	12.0500i	−0.988631	−	0.829559i	−0.985369	+	0.170435i	$0.945483\pi$
$212$	−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	0.988402	+	0.151862i	$0.0485270\pi$
$223$	7.00968	+	15.0323i	0.469403	+	1.00664i	−0.518999	+	0.854775i	$0.673695\pi$
$224$	−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	−0.528478	−	0.848947i	$-0.677237\pi$
$227$	−18.0248	−	1.57696i	−1.19634	−	0.104667i	−0.667867	+	0.744281i	$0.732793\pi$
$228$	−0.169058	−	0.323812i	−0.0111961	−	0.0214450i
$229$	−18.7074	−	3.29862i	−1.23622	−	0.217979i	−0.482924	−	0.875662i	$-0.660425\pi$
$229$	−18.7074	−	3.29862i	−1.23622	−	0.217979i	−0.753294	+	0.657684i	$0.771536\pi$
$230$		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	0.999934	−	0.0114509i	$-0.00364501\pi$
$233$	1.95750	+	7.30551i	0.128240	+	0.478600i	−0.871694	+	0.490050i	$0.836978\pi$
$234$	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	−0.692875	−	0.721057i	$-0.743656\pi$
$239$	−11.7518	+	4.27731i	−0.760162	+	0.276676i	−0.0672867	+	0.997734i	$0.521434\pi$
$240$		0			0
$241$	2.97320	+	16.8619i	0.191521	+	1.08617i	0.917287	+	0.398227i	$0.130374\pi$
$241$	2.97320	+	16.8619i	0.191521	+	1.08617i	−0.725766	+	0.687942i	$0.758514\pi$
$242$	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	−0.345541	−	0.938404i	$-0.612304\pi$
$251$	4.66370	−	2.69259i	0.294370	−	0.169955i	0.639911	+	0.768449i	$0.278971\pi$
$252$	−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	−0.216692	−	0.976240i	$-0.569527\pi$
$257$	10.0445	−	7.03325i	0.626560	−	0.438722i	0.843252	+	0.537518i	$0.180638\pi$
$258$	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	−0.764289	−	0.644873i	$-0.776910\pi$
$263$	−12.3505	+	5.75913i	−0.761563	+	0.355123i	0.00272594	+	0.999996i	$0.499132\pi$
$264$	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	−0.366623	−	0.930370i	$-0.619486\pi$
$277$	1.83776	−	0.856962i	0.110420	−	0.0514898i	0.477044	+	0.878880i	$0.341708\pi$
$278$	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	−0.980822	−	0.194903i	$-0.937561\pi$
$281$	−16.8041	−	20.0263i	−1.00245	−	1.19467i	−0.0216244	−	0.999766i	$-0.506884\pi$
$282$	16.0053	+	10.1696i	0.953100	+	0.605593i
$283$	1.89971	−	1.33019i	0.112926	−	0.0790717i	−0.515749	−	0.856740i	$-0.672486\pi$
$283$	1.89971	−	1.33019i	0.112926	−	0.0790717i	0.628675	+	0.777668i	$0.283597\pi$
$284$	−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	−0.997075	−	0.0764274i	$-0.975649\pi$
$293$	−5.09445	+	10.9251i	−0.297621	+	0.638250i	0.699454	+	0.714677i	$0.253426\pi$
$294$	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	0.890117	+	0.455732i	$0.150622\pi$
$307$	6.08202	+	22.6984i	0.347119	+	1.29547i	−0.542998	+	0.839734i	$0.682711\pi$
$308$	−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	0.283592	−	0.958945i	$-0.408474\pi$
$311$	3.91683	+	0.690642i	0.222103	+	0.0391627i	−0.0614891	+	0.998108i	$0.519585\pi$
$312$	−26.0469	−	1.10607i	−1.47462	−	0.0626189i
$313$	0.911077	+	0.0797089i	0.0514971	+	0.00450541i	0.112875	−	0.993609i	$-0.463994\pi$
$313$	0.911077	+	0.0797089i	0.0514971	+	0.00450541i	−0.0613781	+	0.998115i	$0.519550\pi$
$314$	−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	0.922021	+	0.387141i	$0.126537\pi$
$317$	11.1443	+	23.8990i	0.625924	+	1.34230i	−0.296096	+	0.955158i	$0.595685\pi$
$318$	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	−0.0118569	−	0.999930i	$-0.503774\pi$
$331$	−12.0746	−	4.39481i	−0.663682	−	0.241561i	−0.651825	+	0.758369i	$0.725996\pi$
$332$	−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	0.664106	−	0.747638i	$-0.268812\pi$
$337$	−4.87543	−	6.96283i	−0.265581	−	0.379290i	−0.929688	+	0.368349i	$0.879923\pi$
$338$	−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	0.290389	−	0.956909i	$-0.406215\pi$
$347$	−4.76851	−	2.22359i	−0.255987	−	0.119369i	−0.546376	+	0.837540i	$0.683993\pi$
$348$	−2.66897	+	0.354620i	−0.143072	+	0.0190096i
$349$	20.3047	−	3.58026i	1.08688	−	0.191647i	0.398627	−	0.917113i	$-0.369487\pi$
$349$	20.3047	−	3.58026i	1.08688	−	0.191647i	0.688258	+	0.725466i	$0.258376\pi$
$350$		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	−0.259948	−	0.965623i	$-0.583705\pi$
$353$	−23.6027	−	16.5268i	−1.25624	−	0.879631i	−0.996296	+	0.0859911i	$0.972594\pi$
$354$	−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	0.528970	−	0.848641i	$-0.322578\pi$
$359$	−8.91393	−	15.4394i	−0.470459	−	0.814860i	−0.999429	+	0.0337810i	$0.989245\pi$
$360$		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	−0.767028	−	0.641614i	$-0.778265\pi$
$367$	1.91117	−	21.8448i	0.0997623	−	1.14029i	0.866790	−	0.498674i	$-0.166179\pi$
$368$	−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	0.930165	+	0.367142i	$0.119664\pi$
$373$	1.50421	+	17.1932i	0.0778848	+	0.890228i	−0.852280	+	0.523086i	$0.824781\pi$
$374$	−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	$0.245829\pi$
$379$			27.1687i			1.39556i	−0.716312	+	0.697780i	$0.754171\pi$
$380$		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	−0.272629	−	0.962119i	$-0.587893\pi$
$383$	−7.32022	+	0.640436i	−0.374046	+	0.0327248i	−0.101417	+	0.994844i	$0.532338\pi$
$384$	−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	0.214792	−	0.976660i	$-0.431093\pi$
$389$	23.9421	−	20.0898i	1.21391	−	1.01859i	0.999120	−	0.0419334i	$-0.0133517\pi$
$390$		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	0.635378	−	0.772201i	$-0.280844\pi$
$397$	15.9305	+	4.26857i	0.799531	+	0.214234i	0.164153	+	0.986435i	$0.447511\pi$
$398$	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	0.926114	−	0.377245i	$-0.123128\pi$
$401$	−0.517022	−	1.42051i	−0.0258188	−	0.0709367i	−0.951932	+	0.306308i	$0.900906\pi$
$402$	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	0.963763	+	0.266760i	$0.0859532\pi$
$409$	8.02778	+	22.0561i	0.396948	+	1.09061i	−0.566815	+	0.823845i	$0.691825\pi$
$410$		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	−0.839939	−	0.542680i	$-0.817409\pi$
$419$	2.76242	−	15.6665i	0.134953	−	0.765357i	0.974892	−	0.222677i	$-0.0714794\pi$
$420$		0			0
$421$	27.8051	−	23.3312i	1.35514	−	1.13709i	0.377685	−	0.925934i	$-0.376720\pi$
$421$	27.8051	−	23.3312i	1.35514	−	1.13709i	0.977452	−	0.211160i	$-0.0677241\pi$
$422$	−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	$-0.916583\pi$
$431$		−	10.7570i		−	0.518146i	0.965858	−	0.259073i	$-0.0834169\pi$
$432$	−16.0414	−	8.27769i	−0.771790	−	0.398261i
$433$	25.8369	+	25.8369i	1.24164	+	1.24164i	0.959320	+	0.282321i	$0.0911042\pi$
$433$	25.8369	+	25.8369i	1.24164	+	1.24164i	0.282321	+	0.959320i	$0.408896\pi$
$434$	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	−0.999948	−	0.0101913i	$-0.996756\pi$
$439$	−4.76440	+	13.0901i	−0.227393	+	0.624756i	0.772556	+	0.634947i	$0.218978\pi$
$440$		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	0.935335	+	0.353764i	$0.115098\pi$
$443$	−0.993879	+	11.3601i	−0.0472206	+	0.539734i	−0.982555	+	0.185970i	$0.940457\pi$
$444$	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	−0.884460	−	0.466616i	$-0.845473\pi$
$449$	−0.807925	+	1.39937i	−0.0381283	+	0.0660402i	0.846332	+	0.532657i	$0.178806\pi$
$450$		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	0.462608	−	0.886563i	$-0.346914\pi$
$457$	−4.53775	−	3.17737i	−0.212267	−	0.148631i	−0.674875	+	0.737932i	$0.735803\pi$
$458$	−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	0.186123	−	0.982527i	$-0.440408\pi$
$461$	14.9666	−	2.63902i	0.697065	−	0.122911i	0.510942	+	0.859615i	$0.329297\pi$
$462$	−19.2123	+	2.55269i	−0.893836	+	0.118762i
$463$	29.9580	+	13.9696i	1.39226	+	0.649224i	0.966749	−	0.255727i	$-0.0823148\pi$
$463$	29.9580	+	13.9696i	1.39226	+	0.649224i	0.425516	+	0.904951i	$0.360093\pi$
$464$	−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	0.685806	+	0.727784i	$0.259450\pi$
$467$	−5.87822	+	21.9378i	−0.272012	+	1.01516i	−0.957818	+	0.287377i	$0.907217\pi$
$468$	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	−0.198470	−	0.980107i	$-0.563597\pi$
$479$	−21.4594	−	7.81060i	−0.980507	−	0.356875i	−0.782037	+	0.623232i	$0.785819\pi$
$480$		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	−0.938611	−	0.344977i	$-0.887887\pi$
$487$	−13.1004	+	13.1004i	−0.593634	+	0.593634i	0.344977	+	0.938611i	$0.387887\pi$
$488$	−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	−0.883553	−	0.468332i	$-0.844855\pi$
$491$	−5.95862	+	7.10121i	−0.268909	+	0.320473i	0.614644	+	0.788805i	$0.289300\pi$
$492$	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	0.609417	−	0.792850i	$-0.291404\pi$
$499$	20.3482	+	3.58794i	0.910911	+	0.160618i	0.301494	+	0.953468i	$0.402515\pi$
$500$		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	0.933508	−	0.358557i	$-0.116731\pi$
$503$	−1.21585	−	4.53760i	−0.0542119	−	0.202322i	−0.987720	+	0.156235i	$0.950064\pi$
$504$	−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	0.433862	−	0.900979i	$-0.357151\pi$
$509$	30.3526	−	11.0475i	1.34536	−	0.489670i	0.911496	+	0.411309i	$0.134928\pi$
$510$		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	−0.549390	−	0.835566i	$-0.685140\pi$
$521$	−2.29310	+	1.32392i	−0.100463	+	0.0580021i	0.448927	+	0.893568i	$0.351806\pi$
$522$	−9.06243	−	24.7150i	−0.396652	−	1.08175i
$523$	12.5901	−	3.37351i	0.550527	−	0.147513i	0.0271764	−	0.999631i	$-0.491348\pi$
$523$	12.5901	−	3.37351i	0.550527	−	0.147513i	0.523351	+	0.852117i	$0.324682\pi$
$524$	−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	0.0787671	−	0.996893i	$-0.474902\pi$
$547$	20.8870	−	9.73975i	0.893062	−	0.416442i	0.814295	+	0.580451i	$0.197124\pi$
$548$	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	0.556519	−	0.830835i	$-0.312137\pi$
$557$	34.3132	−	9.19419i	1.45390	−	0.389570i	0.897377	+	0.441265i	$0.145470\pi$
$558$	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	−0.943562	−	0.331196i	$-0.892548\pi$
$563$	−1.97748	+	4.24073i	−0.0833410	+	0.178725i	0.860221	+	0.509922i	$0.170326\pi$
$564$	−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	0.942272	−	0.334848i	$-0.108685\pi$
$569$	−1.37633	−	7.80556i	−0.0576988	−	0.327226i	−0.999971	+	0.00762185i	$0.997574\pi$
$570$		0			0
$571$	4.65824	−	1.69546i	0.194941	−	0.0709528i	−0.242705	−	0.970100i	$-0.578035\pi$
$571$	4.65824	−	1.69546i	0.194941	−	0.0709528i	0.437646	+	0.899147i	$0.355812\pi$
$572$	−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	0.973029	+	0.230684i	$0.0740965\pi$
$577$	5.90200	+	22.0266i	0.245703	+	0.916977i	−0.727325	+	0.686293i	$0.759237\pi$
$578$	−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	0.902142	+	0.431439i	$0.141994\pi$
$587$	15.8151	+	33.9155i	0.652758	+	1.39984i	−0.249384	+	0.968405i	$0.580228\pi$
$588$	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	−0.810317	−	0.585992i	$-0.800705\pi$
$593$	−5.46266	+	5.46266i	−0.224324	+	0.224324i	0.585992	+	0.810317i	$0.300705\pi$
$594$	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	0.678752	−	0.734367i	$-0.262521\pi$
$599$	1.79656	+	1.50749i	0.0734055	+	0.0615946i	−0.605347	+	0.795962i	$0.706965\pi$
$600$		0			0
$601$	38.1639	+	13.8905i	1.55674	+	0.566607i	0.969987	−	0.243159i	$-0.0781836\pi$
$601$	38.1639	+	13.8905i	1.55674	+	0.566607i	0.586753	+	0.809766i	$0.300406\pi$
$602$	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	0.796743	−	0.604319i	$-0.206555\pi$
$607$	−1.07501	−	1.53527i	−0.0436332	−	0.0623147i	−0.840376	+	0.542004i	$0.817666\pi$
$608$	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	0.803039	+	0.595926i	$0.203215\pi$
$613$	−4.71349	+	17.5910i	−0.190376	+	0.710494i	−0.993415	+	0.114568i	$0.963452\pi$
$614$	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	0.0518073	−	0.998657i	$-0.483502\pi$
$617$	−16.8885	−	7.87526i	−0.679907	−	0.317046i	−0.731715	+	0.681611i	$0.761280\pi$
$618$	−18.7333	−	24.3534i	−0.753564	−	0.979639i
$619$	28.0130	−	4.93945i	1.12594	−	0.198533i	0.420492	−	0.907296i	$-0.361858\pi$
$619$	28.0130	−	4.93945i	1.12594	−	0.198533i	0.705447	+	0.708763i	$0.250746\pi$
$620$		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	0.339333	+	0.940666i	$0.389799\pi$
$631$	−16.2016	+	28.0619i	−0.644974	+	1.11713i	−0.984307	+	0.176462i	$0.943535\pi$
$632$	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	0.716571	+	0.697514i	$0.245711\pi$
$641$	−7.10695	+	19.5262i	−0.280708	+	0.771238i	−0.997279	+	0.0737239i	$0.976512\pi$
$642$	32.6075	+	7.18807i	1.28692	+	0.283691i
$643$	−3.44122	−	39.3334i	−0.135709	−	1.55116i	−0.693060	−	0.720880i	$-0.743738\pi$
$643$	−3.44122	−	39.3334i	−0.135709	−	1.55116i	0.557351	−	0.830277i	$-0.311818\pi$
$644$	−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	0.995269	+	0.0971593i	$0.0309756\pi$
$647$	27.7872	+	27.7872i	1.09243	+	1.09243i	0.0971593	+	0.995269i	$0.469024\pi$
$648$	−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	−0.412608	−	0.910909i	$-0.635382\pi$
$653$	−16.8852	+	1.47726i	−0.660770	+	0.0578098i	−0.248162	+	0.968719i	$0.579826\pi$
$654$	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	−0.484997	+	0.874516i	$0.661179\pi$
$659$	−36.7210	+	30.8125i	−1.43045	+	1.20029i	−0.945449	+	0.325770i	$0.894376\pi$
$660$		0			0
$661$	−0.726513	+	4.12026i	−0.0282581	+	0.160259i	−0.995671	−	0.0929427i	$-0.970373\pi$
$661$	−0.726513	+	4.12026i	−0.0282581	+	0.160259i	0.967413	+	0.253202i	$0.0814838\pi$
$662$	−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	−0.991208	−	0.132311i	$-0.957760\pi$
$673$	−13.6940	+	19.5570i	−0.527863	+	0.753867i	0.463345	+	0.886178i	$0.346649\pi$
$674$	−11.2915			−0.434933
$675$		0			0
$676$	2.98725			0.114894
$677$	12.6903	−	18.1236i	0.487727	−	0.696547i	−0.497565	−	0.867427i	$-0.665772\pi$
$677$	12.6903	−	18.1236i	0.487727	−	0.696547i	0.985292	+	0.170880i	$0.0546611\pi$
$678$	−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	−0.239858	−	0.970808i	$-0.577101\pi$
$683$	−24.3829	−	6.53337i	−0.932985	−	0.249993i	−0.693127	+	0.720815i	$0.743768\pi$
$684$	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	−0.00928734	−	0.999957i	$-0.502956\pi$
$691$	25.5999	−	21.4808i	0.973865	−	0.817170i	0.983153	+	0.182787i	$0.0585118\pi$
$692$	−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	$0.0752632\pi$
$701$			12.4042i			0.468499i	−0.972177	+	0.234249i	$0.924737\pi$
$702$	−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	−0.832659	−	0.553786i	$-0.813182\pi$
$709$	4.29127	−	11.7902i	0.161162	−	0.442789i	0.993821	+	0.110998i	$0.0354046\pi$
$710$		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	−0.984334	−	0.176316i	$-0.943582\pi$
$719$	−9.10268	+	15.7663i	−0.339473	+	0.587984i	0.644861	+	0.764300i	$0.276915\pi$
$720$		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	0.414480	−	0.910058i	$-0.363963\pi$
$727$	−8.06014	−	5.64377i	−0.298934	−	0.209316i	−0.713414	+	0.700742i	$0.752852\pi$
$728$	−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	0.927533	−	0.373740i	$-0.121925\pi$
$733$	33.5024	+	15.6224i	1.23744	+	0.577027i	0.309905	+	0.950767i	$0.399703\pi$
$734$	−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	0.623586	−	0.781755i	$-0.285675\pi$
$739$	7.02338	+	4.05495i	0.258359	+	0.149164i	−0.365227	+	0.930919i	$0.619009\pi$
$740$		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	0.344805	−	0.938674i	$-0.387945\pi$
$743$	−17.8592	−	25.5056i	−0.655190	−	0.935709i	−0.999996	+	0.00296531i	$0.999056\pi$
$744$	−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	0.364321	−	0.931273i	$-0.381301\pi$
$751$	−13.4156	−	11.2570i	−0.489541	−	0.410774i	−0.853862	+	0.520500i	$0.825746\pi$
$752$	−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	−0.237915	−	0.971286i	$-0.576464\pi$
$757$	20.1777	−	20.1777i	0.733371	−	0.733371i	0.971286	+	0.237915i	$0.0764640\pi$
$758$	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	−0.138113	−	0.990416i	$-0.544104\pi$
$761$	23.7584	−	28.3141i	0.861240	−	1.02639i	0.999353	−	0.0359689i	$-0.0114517\pi$
$762$	−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	0.0175779	−	0.999845i	$-0.494405\pi$
$769$	−8.53754	−	1.50540i	−0.307872	−	0.0542861i	−0.325450	+	0.945559i	$0.605516\pi$
$770$		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	0.889000	−	0.457908i	$-0.151401\pi$
$773$	−3.05417	−	11.3983i	−0.109851	−	0.409969i	−0.998850	+	0.0479396i	$0.984734\pi$
$774$	−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	−0.995490	−	0.0948643i	$-0.969758\pi$
$787$	−7.93722	+	17.0214i	−0.282931	+	0.606748i	0.712559	+	0.701612i	$0.247536\pi$
$788$	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	−0.842981	−	0.537943i	$-0.819202\pi$
$797$	−17.6670	+	12.3706i	−0.625797	+	0.438188i	0.217184	+	0.976131i	$0.430313\pi$
$798$	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	0.999839	−	0.0179428i	$-0.00571166\pi$
$821$	23.1674	+	27.6099i	0.808549	+	0.963591i	−0.191290	+	0.981533i	$0.561267\pi$
$822$	−0.589922	+	13.8921i	−0.0205759	+	0.484544i
$823$	2.18095	−	1.52711i	0.0760230	−	0.0532319i	−0.534947	−	0.844886i	$-0.679668\pi$
$823$	2.18095	−	1.52711i	0.0760230	−	0.0532319i	0.610970	+	0.791654i	$0.290780\pi$
$824$	−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	−0.873647	−	0.486560i	$-0.838252\pi$
$827$	−39.8859	+	10.6874i	−1.38697	+	0.371637i	−0.513321	+	0.858197i	$0.671585\pi$
$828$	2.54703	+	3.02075i	0.0885153	+	0.104978i
$829$	−19.6326	+	11.3349i	−0.681869	+	0.393677i	−0.800559	−	0.599254i	$-0.795464\pi$
$829$	−19.6326	+	11.3349i	−0.681869	+	0.393677i	0.118690	+	0.992931i	$0.462131\pi$
$830$		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	0.999530	−	0.0306567i	$-0.00975985\pi$
$839$	1.44230	+	8.17971i	0.0497938	+	0.282395i	−0.949736	+	0.313052i	$0.898649\pi$
$840$		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	0.191352	−	0.981521i	$-0.438713\pi$
$853$	6.11455	+	0.534954i	0.209358	+	0.0183165i	0.0180058	+	0.999838i	$0.494268\pi$
$854$	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	−0.981050	−	0.193756i	$-0.937933\pi$
$857$	−14.6042	−	31.3187i	−0.498869	−	1.06983i	0.482181	−	0.876072i	$-0.339845\pi$
$858$	47.8395	−	15.1466i	1.63321	−	0.517095i
$859$	14.4078	−	17.1705i	0.491587	−	0.585850i	−0.462034	−	0.886862i	$-0.652880\pi$
$859$	14.4078	−	17.1705i	0.491587	−	0.585850i	0.953620	+	0.301012i	$0.0973245\pi$
$860$		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	0.190436	−	0.981700i	$-0.439010\pi$
$863$	34.4337	−	34.4337i	1.17214	−	1.17214i	0.981700	−	0.190436i	$-0.0609900\pi$
$864$	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	0.930623	−	0.365980i	$-0.119266\pi$
$877$	7.94910	+	11.3525i	0.268422	+	0.383347i	−0.662201	+	0.749327i	$0.730377\pi$
$878$	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	0.115453	−	0.993313i	$-0.463168\pi$
$881$	−20.3929	−	11.7738i	−0.687054	−	0.396671i	−0.802507	+	0.596642i	$0.796501\pi$
$882$	−6.28476	+	10.9458i	−0.211619	+	0.368565i
$883$	−4.25489	+	15.8795i	−0.143188	+	0.534386i	0.856641	+	0.515913i	$0.172547\pi$
$883$	−4.25489	+	15.8795i	−0.143188	+	0.534386i	−0.999829	+	0.0184733i	$0.994119\pi$
$884$	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	0.260336	−	0.965518i	$-0.416167\pi$
$887$	−9.29073	−	4.33234i	−0.311952	−	0.145466i	−0.572289	+	0.820052i	$0.693944\pi$
$888$	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	−0.951283	−	0.308321i	$-0.900233\pi$
$907$	1.17717	−	13.4551i	0.0390872	−	0.446769i	0.990370	−	0.138448i	$-0.0442114\pi$
$908$	−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	−0.830090	−	0.557629i	$-0.811711\pi$
$911$	4.95701	−	13.6193i	0.164233	−	0.451227i	0.994323	+	0.106403i	$0.0339332\pi$
$912$	−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	$0.0621340\pi$
$919$			11.7599i			0.387925i	−0.981009	+	0.193962i	$0.937866\pi$
$920$		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	−0.182433	+	0.983218i	$0.558397\pi$
$929$	−36.0388	+	30.2401i	−1.18239	+	0.992146i	−0.999960	+	0.00892776i	$0.997158\pi$
$930$		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	−0.394580	−	0.918862i	$-0.629110\pi$
$937$	−36.6017	−	9.80740i	−1.19573	−	0.320394i	−0.801147	+	0.598468i	$0.795776\pi$
$938$	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	0.862364	−	0.506289i	$-0.168983\pi$
$941$	−3.79401	−	10.4240i	−0.123681	−	0.339811i	−0.986045	+	0.166477i	$0.946761\pi$
$942$	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	−0.643090	−	0.765791i	$-0.722348\pi$
$947$	9.12331	−	13.0294i	0.296468	−	0.423400i	0.939558	+	0.342391i	$0.111237\pi$
$948$	−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	0.780019	−	0.625756i	$-0.215210\pi$
$953$	35.2746	+	9.45180i	1.14266	+	0.306174i	0.362638	+	0.931930i	$0.381876\pi$
$954$	−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	−0.0557381	−	0.998445i	$-0.517751\pi$
$967$	1.95128	−	0.170714i	0.0627488	−	0.00548981i	0.118487	+	0.992956i	$0.462196\pi$
$968$	−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	$-0.854281\pi$
$971$		−	27.5442i		−	0.883934i	0.897031	−	0.441967i	$-0.145719\pi$
$972$	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	−0.895123	−	0.445819i	$-0.852912\pi$
$977$	−2.84484	−	32.5167i	−0.0910146	−	1.04030i	0.804108	−	0.594483i	$-0.202643\pi$
$978$	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	0.811915	+	0.583775i	$0.198425\pi$
$983$	−2.79155	+	31.9076i	−0.0890367	+	1.01769i	−0.900952	+	0.433919i	$0.857130\pi$
$984$	−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	0.931362	+	0.364094i	$0.118621\pi$
$991$	24.5859	+	42.5840i	0.780995	+	1.35272i	−0.150367	+	0.988630i	$0.548046\pi$
$992$	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	0.0901563	−	0.995928i	$-0.471263\pi$
$997$	−25.7299	−	18.0163i	−0.814874	−	0.570581i	−0.905031	+	0.425347i	$0.860152\pi$
$998$	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.68.11		192
5.2	odd	4	inner	675.2.ba.b.257.11		192
5.3	odd	4		135.2.q.a.122.6	yes	192
5.4	even	2		135.2.q.a.68.6	yes	192
15.8	even	4		405.2.r.a.152.11		192
15.14	odd	2		405.2.r.a.233.11		192
27.2	odd	18	inner	675.2.ba.b.218.11		192
135.2	even	36	inner	675.2.ba.b.407.11		192
135.29	odd	18		135.2.q.a.83.6	yes	192
135.79	even	18		405.2.r.a.8.11		192
135.83	even	36		135.2.q.a.2.6	✓	192
135.133	odd	36		405.2.r.a.332.11		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.6	✓	192	135.83	even	36
135.2.q.a.68.6	yes	192	5.4	even	2
135.2.q.a.83.6	yes	192	135.29	odd	18
135.2.q.a.122.6	yes	192	5.3	odd	4
405.2.r.a.8.11		192	135.79	even	18
405.2.r.a.152.11		192	15.8	even	4
405.2.r.a.233.11		192	15.14	odd	2
405.2.r.a.332.11		192	135.133	odd	36
675.2.ba.b.68.11		192	1.1	even	1	trivial
675.2.ba.b.218.11		192	27.2	odd	18	inner
675.2.ba.b.257.11		192	5.2	odd	4	inner
675.2.ba.b.407.11		192	135.2	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+(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

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