LMFDB - Embedded newform 675.2.ba.b.257.11

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			257.11
Character	$\chi$	$=$	675.257
Dual form			675.2.ba.b.218.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.08817 + 0.761943i) q^{2} +(-0.660916 + 1.60100i) q^{3} +(-0.0804885 - 0.221140i) q^{4} +(-1.93906 + 1.23857i) q^{6} +(-0.827388 - 1.77434i) q^{7} +(0.768546 - 2.86825i) q^{8} +(-2.12638 - 2.11625i) q^{9} +(-2.76562 - 3.29594i) q^{11} +(0.407241 + 0.0172933i) q^{12} +(-2.90740 - 4.15220i) q^{13} +(0.451609 - 2.56120i) q^{14} +(2.66120 - 2.23301i) q^{16} +(0.828434 + 3.09176i) q^{17} +(-0.701399 - 3.92301i) q^{18} +(-0.776109 + 0.448087i) q^{19} +(3.38755 - 0.151957i) q^{21} +(-0.498142 - 5.69379i) q^{22} +(-5.07230 - 2.36525i) q^{23} +(4.08412 + 3.12611i) q^{24} -6.73356i q^{26} +(4.79346 - 2.00567i) q^{27} +(-0.325783 + 0.325783i) q^{28} +(1.14702 + 6.50507i) q^{29} +(2.27652 - 0.828586i) q^{31} +(-1.31900 + 0.115398i) q^{32} +(7.10463 - 2.24941i) q^{33} +(-1.45427 + 3.99557i) q^{34} +(-0.296839 + 0.640563i) q^{36} +(-6.96604 + 1.86654i) q^{37} +(-1.18595 - 0.103757i) q^{38} +(8.56920 - 1.91049i) q^{39} +(8.33680 + 1.47000i) q^{41} +(3.80200 + 2.41576i) q^{42} +(-0.112459 + 1.28541i) q^{43} +(-0.506265 + 0.876877i) q^{44} +(-3.71732 - 6.43859i) q^{46} +(7.46943 - 3.48305i) q^{47} +(1.81622 + 5.73641i) q^{48} +(2.03580 - 2.42617i) q^{49} +(-5.49742 - 0.717071i) q^{51} +(-0.684206 + 0.977148i) q^{52} +(0.947342 + 0.947342i) q^{53} +(6.74430 + 1.46984i) q^{54} +(-5.72514 + 1.00950i) q^{56} +(-0.204443 - 1.53869i) q^{57} +(-3.70835 + 7.95258i) q^{58} +(-3.72879 - 3.12883i) q^{59} +(-7.90101 - 2.87573i) q^{61} +(3.10857 + 0.832940i) q^{62} +(-1.99560 + 5.52388i) q^{63} +(-7.54029 - 4.35339i) q^{64} +(9.44496 + 2.96559i) q^{66} +(7.90560 - 5.53556i) q^{67} +(0.617033 - 0.432051i) q^{68} +(7.13912 - 6.55750i) q^{69} +(4.92123 + 2.84127i) q^{71} +(-7.70415 + 4.47256i) q^{72} +(-4.93694 - 1.32285i) q^{73} +(-9.00242 - 3.27661i) q^{74} +(0.161558 + 0.135563i) q^{76} +(-3.55988 + 7.63418i) q^{77} +(10.7804 + 4.45032i) q^{78} +(-0.410612 + 0.0724019i) q^{79} +(0.0429919 + 8.99990i) q^{81} +(7.95178 + 7.95178i) q^{82} +(5.31732 - 7.59392i) q^{83} +(-0.306263 - 0.736893i) q^{84} +(-1.10179 + 1.31306i) q^{86} +(-11.1727 - 2.46293i) q^{87} +(-11.5791 + 5.39942i) q^{88} +(-0.974450 - 1.68780i) q^{89} +(-4.96186 + 8.59420i) q^{91} +(-0.114791 + 1.31207i) q^{92} +(-0.178025 + 4.19233i) q^{93} +(10.7819 + 1.90114i) q^{94} +(0.686998 - 2.18799i) q^{96} +(-13.4552 - 1.17718i) q^{97} +(4.06390 - 1.08892i) 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 $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	1.08817	+	0.761943i	0.769451	+	0.538775i	0.891105	−	0.453797i	$-0.149931\pi$
$2$	1.08817	+	0.761943i	0.769451	+	0.538775i	−0.121654	+	0.992573i	$0.538820\pi$
$3$	−0.660916	+	1.60100i	−0.381580	+	0.924336i
$3$	−0.660916	+	1.60100i	−0.381580	+	0.924336i
$4$	−0.0804885	−	0.221140i	−0.0402443	−	0.110570i
$5$		0			0
$5$		0			0
$6$	−1.93906	+	1.23857i	−0.791616	+	0.505645i
$7$	−0.827388	−	1.77434i	−0.312723	−	0.670638i	0.685633	−	0.727947i	$-0.259526\pi$
$7$	−0.827388	−	1.77434i	−0.312723	−	0.670638i	−0.998356	+	0.0573098i	$0.981748\pi$
$8$	0.768546	−	2.86825i	0.271722	−	1.01408i
$9$	−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	$-0.446881\pi$
$12$	0.407241	+	0.0172933i	0.117560	+	0.00499215i
$13$	−2.90740	−	4.15220i	−0.806368	−	1.15161i	−0.985814	−	0.167844i	$-0.946319\pi$
$13$	−2.90740	−	4.15220i	−0.806368	−	1.15161i	0.179446	−	0.983768i	$-0.442569\pi$
$14$	0.451609	−	2.56120i	0.120698	−	0.684510i
$15$		0			0
$16$	2.66120	−	2.23301i	0.665301	−	0.558253i
$17$	0.828434	+	3.09176i	0.200925	+	0.749861i	0.990653	+	0.136405i	$0.0435547\pi$
$17$	0.828434	+	3.09176i	0.200925	+	0.749861i	−0.789729	+	0.613456i	$0.789779\pi$
$18$	−0.701399	−	3.92301i	−0.165321	−	0.924663i
$19$	−0.776109	+	0.448087i	−0.178052	+	0.102798i	−0.586377	−	0.810038i	$-0.699446\pi$
$19$	−0.776109	+	0.448087i	−0.178052	+	0.102798i	0.408325	+	0.912836i	$0.366113\pi$
$20$		0			0
$21$	3.38755	−	0.151957i	0.739223	−	0.0331597i
$22$	−0.498142	−	5.69379i	−0.106204	−	1.21392i
$23$	−5.07230	−	2.36525i	−1.05765	−	0.493189i	−0.185607	−	0.982624i	$-0.559425\pi$
$23$	−5.07230	−	2.36525i	−1.05765	−	0.493189i	−0.872040	+	0.489435i	$0.837203\pi$
$24$	4.08412	+	3.12611i	0.833667	+	0.638115i
$25$		0			0
$26$		−	6.73356i		−	1.32056i
$27$	4.79346	−	2.00567i	0.922503	−	0.385991i
$28$	−0.325783	+	0.325783i	−0.0615672	+	0.0615672i
$29$	1.14702	+	6.50507i	0.212996	+	1.20796i	0.884350	+	0.466825i	$0.154602\pi$
$29$	1.14702	+	6.50507i	0.212996	+	1.20796i	−0.671354	+	0.741137i	$0.734287\pi$
$30$		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	$0.319080\pi$
$32$	−1.31900	+	0.115398i	−0.233169	+	0.0203996i
$33$	7.10463	−	2.24941i	1.23676	−	0.391573i
$34$	−1.45427	+	3.99557i	−0.249405	+	0.685235i
$35$		0			0
$36$	−0.296839	+	0.640563i	−0.0494731	+	0.106760i
$37$	−6.96604	+	1.86654i	−1.14521	+	0.306858i	−0.781044	−	0.624476i	$-0.785312\pi$
$37$	−6.96604	+	1.86654i	−1.14521	+	0.306858i	−0.364166	+	0.931334i	$0.618646\pi$
$38$	−1.18595	−	0.103757i	−0.192387	−	0.0168317i
$39$	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	$0.325672\pi$
$42$	3.80200	+	2.41576i	0.586662	+	0.372761i
$43$	−0.112459	+	1.28541i	−0.0171499	+	0.196024i	0.982787	+	0.184745i	$0.0591459\pi$
$43$	−0.112459	+	1.28541i	−0.0171499	+	0.196024i	−0.999936	+	0.0112790i	$0.996410\pi$
$44$	−0.506265	+	0.876877i	−0.0763223	+	0.132194i
$45$		0			0
$46$	−3.71732	−	6.43859i	−0.548090	−	0.949319i
$47$	7.46943	−	3.48305i	1.08953	−	0.508055i	0.207013	−	0.978338i	$-0.433626\pi$
$47$	7.46943	−	3.48305i	1.08953	−	0.508055i	0.882516	+	0.470283i	$0.155848\pi$
$48$	1.81622	+	5.73641i	0.262148	+	0.827979i
$49$	2.03580	−	2.42617i	0.290829	−	0.346596i
$50$		0			0
$51$	−5.49742	−	0.717071i	−0.769792	−	0.100410i
$52$	−0.684206	+	0.977148i	−0.0948823	+	0.135506i
$53$	0.947342	+	0.947342i	0.130127	+	0.130127i	0.769171	−	0.639043i	$-0.220670\pi$
$53$	0.947342	+	0.947342i	0.130127	+	0.130127i	−0.639043	+	0.769171i	$0.720670\pi$
$54$	6.74430	+	1.46984i	0.917783	+	0.200021i
$55$		0			0
$56$	−5.72514	+	1.00950i	−0.765054	+	0.134900i
$57$	−0.204443	−	1.53869i	−0.0270791	−	0.203805i
$58$	−3.70835	+	7.95258i	−0.486930	+	1.04422i
$59$	−3.72879	−	3.12883i	−0.485447	−	0.407339i	0.366944	−	0.930243i	$-0.380404\pi$
$59$	−3.72879	−	3.12883i	−0.485447	−	0.407339i	−0.852391	+	0.522904i	$0.824849\pi$
$60$		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	$0.792034\pi$
$62$	3.10857	+	0.832940i	0.394789	+	0.105783i
$63$	−1.99560	+	5.52388i	−0.251422	+	0.695944i
$64$	−7.54029	−	4.35339i	−0.942536	−	0.544173i
$65$		0			0
$66$	9.44496	+	2.96559i	1.16259	+	0.365039i
$67$	7.90560	−	5.53556i	0.965822	−	0.676276i	0.0196049	−	0.999808i	$-0.493759\pi$
$67$	7.90560	−	5.53556i	0.965822	−	0.676276i	0.946217	+	0.323532i	$0.104870\pi$
$68$	0.617033	−	0.432051i	0.0748262	−	0.0523939i
$69$	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	$0.557188\pi$
$72$	−7.70415	+	4.47256i	−0.907943	+	0.527097i
$73$	−4.93694	−	1.32285i	−0.577825	−	0.154828i	−0.0419419	−	0.999120i	$-0.513354\pi$
$73$	−4.93694	−	1.32285i	−0.577825	−	0.154828i	−0.535883	+	0.844292i	$0.680021\pi$
$74$	−9.00242	−	3.27661i	−1.04651	−	0.380898i
$75$		0			0
$76$	0.161558	+	0.135563i	0.0185320	+	0.0155502i
$77$	−3.55988	+	7.63418i	−0.405686	+	0.869996i
$78$	10.7804	+	4.45032i	1.22064	+	0.503899i
$79$	−0.410612	+	0.0724019i	−0.0461974	+	0.00814585i	−0.196699	−	0.980464i	$-0.563022\pi$
$79$	−0.410612	+	0.0724019i	−0.0461974	+	0.00814585i	0.150502	+	0.988610i	$0.451911\pi$
$80$		0			0
$81$	0.0429919	+	8.99990i	0.00477688	+	0.999989i
$82$	7.95178	+	7.95178i	0.878127	+	0.878127i
$83$	5.31732	−	7.59392i	0.583652	−	0.833541i	−0.413378	−	0.910560i	$-0.635651\pi$
$83$	5.31732	−	7.59392i	0.583652	−	0.833541i	0.997030	+	0.0770185i	$0.0245401\pi$
$84$	−0.306263	−	0.736893i	−0.0334160	−	0.0804016i
$85$		0			0
$86$	−1.10179	+	1.31306i	−0.118809	+	0.141591i
$87$	−11.1727	−	2.46293i	−1.19784	−	0.264054i
$88$	−11.5791	+	5.39942i	−1.23434	+	0.575580i
$89$	−0.974450	−	1.68780i	−0.103292	−	0.178906i	0.809747	−	0.586779i	$-0.199604\pi$
$89$	−0.974450	−	1.68780i	−0.103292	−	0.178906i	−0.913039	+	0.407872i	$0.866271\pi$
$90$		0			0
$91$	−4.96186	+	8.59420i	−0.520144	+	0.900917i
$92$	−0.114791	+	1.31207i	−0.0119678	+	0.136792i
$93$	−0.178025	+	4.19233i	−0.0184604	+	0.434724i
$94$	10.7819	+	1.90114i	1.11207	+	0.196087i
$95$		0			0
$96$	0.686998	−	2.18799i	0.0701164	−	0.223310i
$97$	−13.4552	−	1.17718i	−1.36617	−	0.119524i	−0.619644	−	0.784883i	$-0.712723\pi$
$97$	−13.4552	−	1.17718i	−1.36617	−	0.119524i	−0.746524	+	0.665359i	$0.768279\pi$
$98$	4.06390	−	1.08892i	0.410516	−	0.109997i
$99$	−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	$0.179005\pi$
$102$	−5.43575	−	4.96901i	−0.538219	−	0.492006i
$103$	13.3028	−	1.16385i	1.31077	−	0.114677i	0.589745	−	0.807589i	$-0.299228\pi$
$103$	13.3028	−	1.16385i	1.31077	−	0.114677i	0.721022	+	0.692912i	$0.243673\pi$
$104$	−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	$-0.502528\pi$
$107$	10.2616	−	10.2616i	0.992026	−	0.992026i	0.999968	+	0.00794276i	$0.00252829\pi$
$108$	−0.829353	−	0.898596i	−0.0798045	−	0.0864674i
$109$			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
$112$	−6.16397	−	2.87431i	−0.582441	−	0.271597i
$113$	−1.18867	−	13.5865i	−0.111821	−	1.27811i	−0.820116	−	0.572198i	$-0.806091\pi$
$113$	−1.18867	−	13.5865i	−0.111821	−	1.27811i	0.708295	−	0.705916i	$-0.249465\pi$
$114$	0.949930	−	1.83013i	0.0889691	−	0.171408i
$115$		0			0
$116$	1.34621	−	0.777236i	0.124993	−	0.0721646i
$117$	−2.60484	+	14.9819i	−0.240817	+	1.38508i
$118$	−1.67356	−	6.24582i	−0.154064	−	0.574974i
$119$	4.80039	−	4.02801i	0.440051	−	0.369247i
$120$		0			0
$121$	−1.30443	+	7.39778i	−0.118584	+	0.672525i
$122$	−6.40648	−	9.14940i	−0.580016	−	0.828348i
$123$	−7.86339	+	12.3756i	−0.709018	+	1.11587i
$124$	−0.366468	−	0.436739i	−0.0329098	−	0.0392204i
$125$		0			0
$126$	−6.38043	+	4.49038i	−0.568414	+	0.400035i
$127$	−0.931838	+	3.47767i	−0.0826872	+	0.308593i	−0.994866	−	0.101199i	$-0.967732\pi$
$127$	−0.931838	+	3.47767i	−0.0826872	+	0.308593i	0.912179	+	0.409792i	$0.134399\pi$
$128$	−3.76894	−	8.08251i	−0.333130	−	0.714400i
$129$	−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	$0.881167\pi$
$132$	−1.06928	−	1.39007i	−0.0930687	−	0.120990i
$133$	1.43720	+	1.00634i	0.124621	+	0.0872607i
$134$	12.8204			1.10751
$135$		0			0
$136$	9.50463			0.815015
$137$	4.95031	+	3.46624i	0.422934	+	0.296141i	0.765601	−	0.643315i	$-0.222442\pi$
$137$	4.95031	+	3.46624i	0.422934	+	0.296141i	−0.342668	+	0.939457i	$0.611330\pi$
$138$	12.7650	−	1.69606i	1.08663	−	0.144378i
$139$	−6.33390	−	17.4022i	−0.537234	−	1.47604i	−0.850295	−	0.526306i	$-0.823577\pi$
$139$	−6.33390	−	17.4022i	−0.537234	−	1.47604i	0.313061	−	0.949733i	$-0.398646\pi$
$140$		0			0
$141$	0.639692	+	14.2605i	0.0538718	+	1.20095i
$142$	3.19024	+	6.84148i	0.267719	+	0.574125i
$143$	−5.64463	+	21.0660i	−0.472027	+	1.76163i
$144$	−10.3843	−	0.883525i	−0.865362	−	0.0736271i
$145$		0			0
$146$	−4.36428	−	5.20115i	−0.361190	−	0.430450i
$147$	2.53880	+	4.86281i	0.209397	+	0.401078i
$148$	0.973455	+	1.39024i	0.0800175	+	0.114277i
$149$	1.50609	−	8.54145i	0.123384	−	0.699743i	−0.858871	−	0.512192i	$-0.828834\pi$
$149$	1.50609	−	8.54145i	0.123384	−	0.699743i	0.982255	−	0.187551i	$-0.0600551\pi$
$150$		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	$0.502295\pi$
$152$	0.688750	+	2.57045i	0.0558650	+	0.208491i
$153$	4.78136	−	8.32742i	0.386550	−	0.673232i
$154$	−9.69056	+	5.59485i	−0.780887	+	0.450846i
$155$		0			0
$156$	−1.11221	−	1.74122i	−0.0890479	−	0.139410i
$157$	−1.15698	−	13.2243i	−0.0923367	−	1.05541i	−0.891112	−	0.453784i	$-0.850074\pi$
$157$	−1.15698	−	13.2243i	−0.0923367	−	1.05541i	0.798775	−	0.601630i	$-0.205482\pi$
$158$	−0.501981	−	0.234077i	−0.0399354	−	0.0186222i
$159$	−2.14280	+	0.890578i	−0.169935	+	0.0706274i
$160$		0			0
$161$			10.9570i			0.863530i
$162$	−6.81063	+	9.82616i	−0.535094	+	0.772016i
$163$	−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
$167$	−8.20120	+	0.717512i	−0.634628	+	0.0555227i	−0.399930	−	0.916546i	$-0.630966\pi$
$167$	−8.20120	+	0.717512i	−0.634628	+	0.0555227i	−0.234698	+	0.972068i	$0.575410\pi$
$168$	2.16763	−	9.83313i	0.167237	−	0.758642i
$169$	−4.34150	+	11.9282i	−0.333962	+	0.917553i
$170$		0			0
$171$	2.59856	+	0.689635i	0.198717	+	0.0527377i
$172$	0.293309	−	0.0785918i	0.0223646	−	0.00599257i
$173$	7.74393	+	0.677506i	0.588760	+	0.0515098i	0.377643	−	0.925951i	$-0.376735\pi$
$173$	7.74393	+	0.677506i	0.588760	+	0.0515098i	0.211116	+	0.977461i	$0.432290\pi$
$174$	−10.2811	−	11.1930i	−0.779412	−	0.848542i
$175$		0			0
$176$	−14.7198	−	2.59549i	−1.10954	−	0.195643i
$177$	7.47366	−	3.90189i	0.561755	−	0.293284i
$178$	0.225641	−	2.57908i	0.0169125	−	0.193310i
$179$	2.19929	−	3.80928i	0.164382	−	0.284719i	−0.772053	−	0.635558i	$-0.780770\pi$
$179$	2.19929	−	3.80928i	0.164382	−	0.284719i	0.936436	+	0.350839i	$0.114104\pi$
$180$		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	$0.901479\pi$
$182$	−11.9476	+	5.57127i	−0.885617	+	0.412970i
$183$	9.82594	−	10.7489i	0.726355	−	0.794580i
$184$	−10.6824	+	12.7308i	−0.787519	+	0.938529i
$185$		0			0
$186$	−3.38804	+	4.42631i	−0.248423	+	0.324553i
$187$	7.89911	−	11.2811i	0.577640	−	0.824956i
$188$	−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	$0.269664\pi$
$192$	11.9532	−	9.19475i	0.862651	−	0.663574i
$193$	−7.33254	+	15.7247i	−0.527808	+	1.13189i	0.443981	+	0.896036i	$0.353566\pi$
$193$	−7.33254	+	15.7247i	−0.527808	+	1.13189i	−0.971789	+	0.235852i	$0.924212\pi$
$194$	−13.7446	−	11.5331i	−0.986802	−	0.828025i
$195$		0			0
$196$	−0.700384	−	0.254919i	−0.0500274	−	0.0182085i
$197$	13.1476	+	3.52289i	0.936727	+	0.250995i	0.694721	−	0.719280i	$-0.255528\pi$
$197$	13.1476	+	3.52289i	0.936727	+	0.250995i	0.242006	+	0.970275i	$0.422195\pi$
$198$	−10.9902	+	13.1613i	−0.781041	+	0.935336i
$199$	−7.78555	−	4.49499i	−0.551903	−	0.318641i	0.197986	−	0.980205i	$-0.436560\pi$
$199$	−7.78555	−	4.49499i	−0.551903	−	0.318641i	−0.749889	+	0.661564i	$0.769893\pi$
$200$		0			0
$201$	3.63748	+	16.3154i	0.256568	+	1.15080i
$202$	−4.62987	+	3.24187i	−0.325756	+	0.228097i
$203$	10.5932	−	7.41743i	0.743496	−	0.520601i
$204$	0.283906	+	1.27342i	0.0198774	+	0.0891570i
$205$		0			0
$206$	15.3625	+	8.86955i	1.07036	+	0.617971i
$207$	5.78018	+	15.7637i	0.401750	+	1.09565i
$208$	−17.0091	−	4.55757i	−1.17937	−	0.316011i
$209$	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	$0.945483\pi$
$212$	0.133245	−	0.285746i	0.00915134	−	0.0196251i
$213$	−7.80139	+	6.00103i	−0.534542	+	0.411184i
$214$	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
$218$	−10.9308	+	15.6108i	−0.740326	+	1.05729i
$219$	5.38077	−	7.02973i	0.363599	−	0.475025i
$220$		0			0
$221$	10.4290	−	12.4288i	0.701530	−	0.836051i
$222$	11.1957	−	12.2473i	0.751405	−	0.821984i
$223$	15.0323	−	7.00968i	1.00664	−	0.469403i	0.151862	−	0.988402i	$-0.451473\pi$
$223$	15.0323	−	7.00968i	1.00664	−	0.469403i	0.854775	+	0.518999i	$0.173695\pi$
$224$	1.29608	+	2.24488i	0.0865981	+	0.149992i
$225$		0			0
$226$	9.05870	−	15.6901i	0.602576	−	1.04369i
$227$	1.57696	−	18.0248i	0.104667	−	1.19634i	−0.744281	−	0.667867i	$-0.767207\pi$
$227$	1.57696	−	18.0248i	0.104667	−	1.19634i	0.848947	−	0.528478i	$-0.177237\pi$
$228$	−0.323812	+	0.169058i	−0.0214450	+	0.0111961i
$229$	18.7074	+	3.29862i	1.23622	+	0.217979i	0.753294	−	0.657684i	$-0.228464\pi$
$229$	18.7074	+	3.29862i	1.23622	+	0.217979i	0.482924	+	0.875662i	$0.339575\pi$
$230$		0			0
$231$	−9.86952	−	10.7449i	−0.649367	−	0.706963i
$232$	19.5397	+	1.70951i	1.28285	+	0.112235i
$233$	7.30551	−	1.95750i	0.478600	−	0.128240i	−0.0114509	−	0.999934i	$-0.503645\pi$
$233$	7.30551	−	1.95750i	0.478600	−	0.128240i	0.490050	+	0.871694i	$0.336978\pi$
$234$	−14.2499	+	14.3181i	−0.931544	+	0.936005i
$235$		0			0
$236$	−0.391785	+	1.07642i	−0.0255031	+	0.0700691i
$237$	0.155464	−	0.705239i	0.0100985	−	0.0458102i
$238$	8.29275	−	0.725521i	0.537539	−	0.0470286i
$239$	11.7518	−	4.27731i	0.760162	−	0.276676i	0.0672867	−	0.997734i	$-0.478566\pi$
$239$	11.7518	−	4.27731i	0.760162	−	0.276676i	0.692875	+	0.721057i	$0.256344\pi$
$240$		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
$243$	−14.4372	−	5.87934i	−0.926148	−	0.377160i
$244$			1.97870i			0.126673i
$245$		0			0
$246$	−17.9862	+	7.47531i	−1.14676	+	0.476609i
$247$	4.11700	+	1.91979i	0.261958	+	0.122153i
$248$	−0.626983	−	7.16645i	−0.0398134	−	0.455070i
$249$	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	$0.278971\pi$
$252$	1.38218	−	0.00330126i	0.0870690	−	0.000207960i
$253$	6.23233	+	23.2594i	0.391823	+	1.46231i
$254$	−3.66378	+	3.07428i	−0.229886	+	0.192897i
$255$		0			0
$256$	−0.966651	+	5.48215i	−0.0604157	+	0.342634i
$257$	7.03325	+	10.0445i	0.438722	+	0.626560i	0.976240	−	0.216692i	$-0.0695268\pi$
$257$	7.03325	+	10.0445i	0.438722	+	0.626560i	−0.537518	+	0.843252i	$0.680638\pi$
$258$	−1.37401	−	2.63178i	−0.0855424	−	0.163847i
$259$	9.07550	+	10.8158i	0.563924	+	0.672059i
$260$		0			0
$261$	11.3273	−	16.2596i	0.701145	−	1.00645i
$262$	−0.190920	+	0.712524i	−0.0117951	+	0.0440199i
$263$	5.75913	+	12.3505i	0.355123	+	0.761563i	0.999996	−	0.00272594i	$-0.000867694\pi$
$263$	5.75913	+	12.3505i	0.355123	+	0.761563i	−0.644873	+	0.764289i	$0.723090\pi$
$264$	−0.991650	−	22.1067i	−0.0610318	−	1.36057i
$265$		0			0
$266$	0.797143	+	2.19013i	0.0488760	+	0.134286i
$267$	3.34619	−	0.444600i	0.204783	−	0.0272091i
$268$	−1.86045	−	1.30270i	−0.113645	−	0.0795749i
$269$	12.3342			0.752028			0.376014	−	0.926614i	$-0.377294\pi$
$269$	12.3342			0.752028			0.376014	+	0.926614i	$0.377294\pi$
$270$		0			0
$271$	19.7578			1.20020			0.600099	−	0.799926i	$-0.295128\pi$
$271$	19.7578			1.20020			0.600099	+	0.799926i	$0.295128\pi$
$272$	9.10856	+	6.37789i	0.552288	+	0.386716i
$273$	−10.4799	−	13.6240i	−0.634273	−	0.824560i
$274$	2.74569	+	7.54371i	0.165873	+	0.455732i
$275$		0			0
$276$	−2.02475	−	1.05094i	−0.121875	−	0.0632594i
$277$	0.856962	+	1.83776i	0.0514898	+	0.110420i	0.930370	−	0.366623i	$-0.119486\pi$
$277$	0.856962	+	1.83776i	0.0514898	+	0.110420i	−0.878880	+	0.477044i	$0.841708\pi$
$278$	6.36718	−	23.7626i	0.381878	−	1.42519i
$279$	−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	$-0.506884\pi$
$282$	−10.1696	+	16.0053i	−0.605593	+	0.953100i
$283$	−1.33019	−	1.89971i	−0.0790717	−	0.112926i	0.777668	−	0.628675i	$-0.216403\pi$
$283$	−1.33019	−	1.89971i	−0.0790717	−	0.112926i	−0.856740	+	0.515749i	$0.827514\pi$
$284$	0.232218	−	1.31697i	0.0137796	−	0.0781480i
$285$		0			0
$286$	−22.1934	+	18.6225i	−1.31232	+	1.10117i
$287$	−4.28949	−	16.0086i	−0.253200	−	0.944956i
$288$	3.04891	+	2.54596i	0.179659	+	0.150022i
$289$	5.84978	−	3.37737i	0.344105	−	0.198669i
$290$		0			0
$291$	10.7774	−	20.7637i	0.631783	−	1.21719i
$292$	0.104832	+	1.19823i	0.00613480	+	0.0701211i
$293$	10.9251	+	5.09445i	0.638250	+	0.297621i	0.714677	−	0.699454i	$-0.246574\pi$
$293$	10.9251	+	5.09445i	0.638250	+	0.297621i	−0.0764274	+	0.997075i	$0.524351\pi$
$294$	−0.942540	+	7.22598i	−0.0549701	+	0.421427i
$295$		0			0
$296$			21.4149i			1.24471i
$297$	−19.8675	−	10.2521i	−1.15283	−	0.594885i
$298$	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
$302$	−21.0846	+	1.84467i	−1.21328	+	0.106149i
$303$	−5.43925	−	4.97222i	−0.312477	−	0.285646i
$304$	−1.06480	+	2.92551i	−0.0610704	+	0.167790i
$305$		0			0
$306$	11.5479	−	5.41851i	0.660152	−	0.309756i
$307$	−22.6984	+	6.08202i	−1.29547	+	0.347119i	−0.839734	−	0.542998i	$-0.817289\pi$
$307$	−22.6984	+	6.08202i	−1.29547	+	0.347119i	−0.455732	+	0.890117i	$0.650622\pi$
$308$	1.97476	+	0.172769i	0.112522	+	0.00984441i
$309$	−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	$0.519585\pi$
$312$	1.10607	−	26.0469i	0.0626189	−	1.47462i
$313$	0.0797089	−	0.911077i	0.00450541	−	0.0514971i	−0.993609	−	0.112875i	$-0.963994\pi$
$313$	0.0797089	−	0.911077i	0.00450541	−	0.0514971i	0.998115	+	0.0613781i	$0.0195495\pi$
$314$	8.81718	−	15.2718i	0.497582	−	0.861838i
$315$		0			0
$316$	0.0490605	+	0.0849753i	0.00275987	+	0.00478023i
$317$	−23.8990	+	11.1443i	−1.34230	+	0.625924i	−0.955158	−	0.296096i	$-0.904315\pi$
$317$	−23.8990	+	11.1443i	−1.34230	+	0.625924i	−0.387141	+	0.922021i	$0.626537\pi$
$318$	−3.01030	−	0.663597i	−0.168809	−	0.0372127i
$319$	18.2681	−	21.7711i	1.02282	−	1.21895i
$320$		0			0
$321$	9.64673	+	23.2108i	0.538428	+	1.29550i
$322$	−8.34859	+	11.9230i	−0.465249	+	0.664444i
$323$	−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
$327$	−22.9678	−	9.48144i	−1.27012	−	0.524325i
$328$	10.6235	−	22.7823i	0.586587	−	1.25794i
$329$	−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	$0.725996\pi$
$332$	−2.10731	−	0.564651i	−0.115653	−	0.0309893i
$333$	18.7625	+	10.7729i	1.02818	+	0.590350i
$334$	−9.47099	−	5.46808i	−0.518229	−	0.299200i
$335$		0			0
$336$	8.67563	−	7.96883i	0.473294	−	0.434735i
$337$	6.96283	−	4.87543i	0.379290	−	0.265581i	−0.368349	−	0.929688i	$-0.620077\pi$
$337$	6.96283	−	4.87543i	0.379290	−	0.265581i	0.747638	+	0.664106i	$0.231188\pi$
$338$	−13.8129	+	9.67189i	−0.751322	+	0.526081i
$339$	22.5376	+	7.07650i	1.22408	+	0.384343i
$340$		0			0
$341$	−9.02697	−	5.21173i	−0.488838	−	0.282231i
$342$	2.30221	+	2.73040i	0.124489	+	0.147643i
$343$	−19.2267	−	5.15177i	−1.03814	−	0.278169i
$344$	3.60046	+	1.31046i	0.194124	+	0.0706553i
$345$		0			0
$346$	7.91047	+	6.63767i	0.425270	+	0.356844i
$347$	2.22359	−	4.76851i	0.119369	−	0.255987i	−0.837540	−	0.546376i	$-0.816007\pi$
$347$	2.22359	−	4.76851i	0.119369	−	0.255987i	0.956909	+	0.290389i	$0.0937847\pi$
$348$	0.354620	+	2.66897i	0.0190096	+	0.143072i
$349$	−20.3047	+	3.58026i	−1.08688	+	0.191647i	−0.688258	−	0.725466i	$-0.741624\pi$
$349$	−20.3047	+	3.58026i	−1.08688	+	0.191647i	−0.398627	+	0.917113i	$0.630513\pi$
$350$		0			0
$351$	−22.2644	−	14.0721i	−1.18839	−	0.751115i
$352$	4.02821	+	4.02821i	0.214704	+	0.214704i
$353$	−16.5268	+	23.6027i	−0.879631	+	1.25624i	0.0859911	+	0.996296i	$0.472594\pi$
$353$	−16.5268	+	23.6027i	−0.879631	+	1.25624i	−0.965623	+	0.259948i	$0.916295\pi$
$354$	11.1056	+	1.44859i	0.590257	+	0.0769918i
$355$		0			0
$356$	−0.294808	+	0.351339i	−0.0156248	+	0.0186209i
$357$	3.27617	+	10.3476i	0.173393	+	0.547652i
$358$	5.29565	−	2.46940i	0.279884	−	0.130512i
$359$	8.91393	+	15.4394i	0.470459	+	0.814860i	0.999429	−	0.0337810i	$-0.0107549\pi$
$359$	8.91393	+	15.4394i	0.470459	+	0.814860i	−0.528970	+	0.848641i	$0.677422\pi$
$360$		0			0
$361$	−9.09844	+	15.7590i	−0.478865	+	0.829419i
$362$	0.661859	−	7.56508i	0.0347865	−	0.397612i
$363$	−10.9817	−	6.97769i	−0.576390	−	0.366234i
$364$	2.29990	+	0.405534i	0.120547	+	0.0212558i
$365$		0			0
$366$	18.8823	−	4.20977i	0.986994	−	0.220048i
$367$	21.8448	+	1.91117i	1.14029	+	0.0997623i	0.641614	−	0.767028i	$-0.278265\pi$
$367$	21.8448	+	1.91117i	1.14029	+	0.0997623i	0.498674	+	0.866790i	$0.333821\pi$
$368$	−18.7800	+	5.03210i	−0.978978	+	0.262316i
$369$	−14.6163	−	20.7685i	−0.760895	−	1.08117i
$370$		0			0
$371$	0.897087	−	2.46473i	0.0465744	−	0.127962i
$372$	0.941423	−	0.298066i	0.0488105	−	0.0154540i
$373$	17.1932	−	1.50421i	0.890228	−	0.0778848i	0.367142	−	0.930165i	$-0.380336\pi$
$373$	17.1932	−	1.50421i	0.890228	−	0.0778848i	0.523086	+	0.852280i	$0.324781\pi$
$374$	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
$378$	−2.97215	−	13.1828i	−0.152871	−	0.678051i
$379$		−	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
$382$	17.3680	+	8.09883i	0.888624	+	0.414372i
$383$	0.640436	+	7.32022i	0.0327248	+	0.374046i	0.994844	+	0.101417i	$0.0323376\pi$
$383$	0.640436	+	7.32022i	0.0327248	+	0.374046i	−0.962119	+	0.272629i	$0.912107\pi$
$384$	15.4310	−	0.692197i	0.787461	−	0.0353235i
$385$		0			0
$386$	−19.9604	+	11.5241i	−1.01596	+	0.586562i
$387$	2.95939	−	2.49529i	0.150434	−	0.126843i
$388$	0.822667	+	3.07024i	0.0417646	+	0.155868i
$389$	−23.9421	+	20.0898i	−1.21391	+	1.01859i	−0.214792	+	0.976660i	$0.568907\pi$
$389$	−23.9421	+	20.0898i	−1.21391	+	1.01859i	−0.999120	+	0.0419334i	$0.986648\pi$
$390$		0			0
$391$	3.11072	−	17.6418i	0.157316	−	0.892182i
$392$	−5.39427	−	7.70382i	−0.272452	−	0.389102i
$393$	−0.960934	−	0.0408056i	−0.0484727	−	0.00205837i
$394$	11.6225	+	13.8512i	0.585535	+	0.697814i
$395$		0			0
$396$	2.93220	−	0.793192i	0.147349	−	0.0398594i
$397$	−4.26857	+	15.9305i	−0.214234	+	0.799531i	0.772201	+	0.635378i	$0.219156\pi$
$397$	−4.26857	+	15.9305i	−0.214234	+	0.799531i	−0.986435	+	0.164153i	$0.947511\pi$
$398$	−5.04706	−	10.8234i	−0.252986	−	0.542530i
$399$	−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	$0.900906\pi$
$402$	−8.47320	+	20.5254i	−0.422605	+	1.02371i
$403$	−10.0592	−	7.04354i	−0.501085	−	0.350864i
$404$	1.00128			0.0498155
$405$		0			0
$406$	17.1788			0.852571
$407$	25.4175	+	17.7975i	1.25990	+	0.882189i
$408$	−6.28176	+	15.2169i	−0.310993	+	0.753348i
$409$	−8.02778	−	22.0561i	−0.396948	−	1.09061i	−0.963763	−	0.266760i	$-0.914047\pi$
$409$	−8.02778	−	22.0561i	−0.396948	−	1.09061i	0.566815	−	0.823845i	$-0.308175\pi$
$410$		0			0
$411$	−8.82118	+	5.63453i	−0.435117	+	0.277931i
$412$	−1.32810	−	2.84812i	−0.0654308	−	0.140317i
$413$	−2.46645	+	9.20490i	−0.121366	+	0.452944i
$414$	−5.72121	+	21.5577i	−0.281182	+	1.05950i
$415$		0			0
$416$	4.31402	+	5.14125i	0.211512	+	0.252070i
$417$	32.0471	+	1.36086i	1.56935	+	0.0666418i
$418$	2.93792	+	4.19579i	0.143698	+	0.205223i
$419$	−2.76242	+	15.6665i	−0.134953	+	0.765357i	0.839939	+	0.542680i	$0.182591\pi$
$419$	−2.76242	+	15.6665i	−0.134953	+	0.765357i	−0.974892	+	0.222677i	$0.928521\pi$
$420$		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	$-0.0677241\pi$
$422$	−6.44539	−	24.0545i	−0.313756	−	1.17096i
$423$	−23.2539	−	8.40087i	−1.13064	−	0.408464i
$424$	3.44529	−	1.98914i	0.167318	−	0.0966012i
$425$		0			0
$426$	−13.0617	+	0.585914i	−0.632840	+	0.0283876i
$427$	1.43468	+	16.3984i	0.0694289	+	0.793576i
$428$	−3.09519	−	1.44331i	−0.149612	−	0.0697652i
$429$	−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	$-0.0834169\pi$
$432$	8.27769	−	16.0414i	0.398261	−	0.771790i
$433$	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
$437$	4.99649	−	0.437136i	0.239015	−	0.0209111i
$438$	11.2114	−	3.54968i	0.535703	−	0.169610i
$439$	4.76440	−	13.0901i	0.227393	−	0.624756i	−0.772556	−	0.634947i	$-0.781022\pi$
$439$	4.76440	−	13.0901i	0.227393	−	0.624756i	0.999948	+	0.0101913i	$0.00324405\pi$
$440$		0			0
$441$	−9.46327	+	0.850709i	−0.450632	+	0.0405100i
$442$	20.8185	−	5.57831i	0.990237	−	0.265333i
$443$	11.3601	+	0.993879i	0.539734	+	0.0472206i	0.353764	−	0.935335i	$-0.384902\pi$
$443$	11.3601	+	0.993879i	0.539734	+	0.0472206i	0.185970	+	0.982555i	$0.440457\pi$
$444$	−2.86914	+	0.639668i	−0.136163	+	0.0303573i
$445$		0			0
$446$	21.6986	+	3.82606i	1.02746	+	0.181169i
$447$	12.6794	+	8.05642i	0.599717	+	0.381056i
$448$	−1.48564	+	16.9810i	−0.0701900	+	0.802276i
$449$	0.807925	−	1.39937i	0.0381283	−	0.0660402i	−0.846332	−	0.532657i	$-0.821194\pi$
$449$	0.807925	−	1.39937i	0.0381283	−	0.0660402i	0.884460	+	0.466616i	$0.154527\pi$
$450$		0			0
$451$	−18.2114	−	31.5431i	−0.857541	−	1.48530i
$452$	−2.90886	+	1.35642i	−0.136821	+	0.0638008i
$453$	−8.32980	−	26.3092i	−0.391368	−	1.23611i
$454$	15.4498	−	18.4124i	0.725097	−	0.864137i
$455$		0			0
$456$	−4.57049	−	0.596164i	−0.214033	−	0.0279180i
$457$	3.17737	−	4.53775i	0.148631	−	0.212267i	−0.737932	−	0.674875i	$-0.764197\pi$
$457$	3.17737	−	4.53775i	0.148631	−	0.212267i	0.886563	+	0.462608i	$0.153086\pi$
$458$	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	$0.329297\pi$
$462$	−2.55269	−	19.2123i	−0.118762	−	0.893836i
$463$	13.9696	−	29.9580i	0.649224	−	1.39226i	−0.255727	−	0.966749i	$-0.582315\pi$
$463$	13.9696	−	29.9580i	0.649224	−	1.39226i	0.904951	−	0.425516i	$-0.139907\pi$
$464$	17.5784	+	14.7500i	0.816056	+	0.684752i
$465$		0			0
$466$	9.44112	+	3.43629i	0.437352	+	0.159183i
$467$	−21.9378	−	5.87822i	−1.01516	−	0.272012i	−0.287377	−	0.957818i	$-0.592783\pi$
$467$	−21.9378	−	5.87822i	−1.01516	−	0.272012i	−0.727784	+	0.685806i	$0.759450\pi$
$468$	3.52277	−	0.629839i	0.162840	−	0.0291143i
$469$	−16.3630	−	9.44716i	−0.755571	−	0.436229i
$470$		0			0
$471$	21.9367	+	6.88783i	1.01079	+	0.317374i
$472$	−11.8400	+	8.29047i	−0.544981	+	0.381600i
$473$	4.54767	−	3.18431i	0.209102	−	0.146415i
$474$	0.706524	−	0.648964i	0.0324517	−	0.0298079i
$475$		0			0
$476$	−1.27713	−	0.737352i	−0.0585372	−	0.0337965i
$477$	−0.00959972	−	4.01922i	−0.000439541	−	0.184027i
$478$	16.0470	+	4.29979i	0.733974	+	0.196668i
$479$	21.4594	+	7.81060i	0.980507	+	0.356875i	0.782037	−	0.623232i	$-0.214181\pi$
$479$	21.4594	+	7.81060i	0.980507	+	0.356875i	0.198470	+	0.980107i	$0.436403\pi$
$480$		0			0
$481$	28.0033	+	23.4976i	1.27684	+	1.07140i
$482$	−9.61245	+	20.6140i	−0.437835	+	0.938941i
$483$	−17.5421	−	7.24163i	−0.798191	−	0.329506i
$484$	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	$0.887887\pi$
$488$	−14.3206	+	20.4520i	−0.648264	+	0.925817i
$489$	−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	$0.289300\pi$
$492$	3.36967	+	0.742816i	0.151916	+	0.0334887i
$493$	−19.1619	+	8.93533i	−0.863007	+	0.402427i
$494$	3.01722	+	5.22597i	0.135751	+	0.235128i
$495$		0			0
$496$	4.20804	−	7.28854i	0.188947	−	0.327265i
$497$	0.969617	−	11.0828i	0.0434933	−	0.497131i
$498$	−0.904958	+	21.3109i	−0.0405521	+	0.954965i
$499$	−20.3482	−	3.58794i	−0.910911	−	0.160618i	−0.301494	−	0.953468i	$-0.597485\pi$
$499$	−20.3482	−	3.58794i	−0.910911	−	0.160618i	−0.609417	+	0.792850i	$0.708596\pi$
$500$		0			0
$501$	4.27157	−	13.6043i	0.190840	−	0.607796i
$502$	7.12650	+	0.623488i	0.318071	+	0.0278276i
$503$	−4.53760	+	1.21585i	−0.202322	+	0.0542119i	−0.358557	−	0.933508i	$-0.616731\pi$
$503$	−4.53760	+	1.21585i	−0.202322	+	0.0542119i	0.156235	+	0.987720i	$0.450064\pi$
$504$	14.3102	+	9.96924i	0.637426	+	0.444065i
$505$		0			0
$506$	−10.9405	+	30.0588i	−0.486365	+	1.33628i
$507$	−16.2276	−	14.8343i	−0.720694	−	0.658813i
$508$	0.844055	−	0.0738452i	0.0374489	−	0.00327635i
$509$	−30.3526	+	11.0475i	−1.34536	+	0.489670i	−0.911496	−	0.411309i	$-0.865072\pi$
$509$	−30.3526	+	11.0475i	−1.34536	+	0.489670i	−0.433862	+	0.900979i	$0.642849\pi$
$510$		0			0
$511$	1.73758	+	9.85432i	0.0768661	+	0.435929i
$512$	−17.8410	+	17.8410i	−0.788469	+	0.788469i
$513$	−2.82154	+	3.70450i	−0.124574	+	0.163558i
$514$			16.2891i			0.718480i
$515$		0			0
$516$	−0.0680271	+	0.521529i	−0.00299472	+	0.0229590i
$517$	−32.1376	−	14.9860i	−1.41341	−	0.659083i
$518$	1.63467	+	18.6844i	0.0718234	+	0.820945i
$519$	−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	$0.351806\pi$
$522$	24.7150	−	9.06243i	1.08175	−	0.396652i
$523$	−3.37351	−	12.5901i	−0.147513	−	0.550527i	−0.999631	−	0.0271764i	$-0.991348\pi$
$523$	−3.37351	−	12.5901i	−0.147513	−	0.550527i	0.852117	−	0.523351i	$-0.175318\pi$
$524$	0.100106	−	0.0839990i	0.00437316	−	0.00366951i
$525$		0			0
$526$	−3.14347	+	17.8275i	−0.137062	+	0.777317i
$527$	4.44773	+	6.35202i	0.193746	+	0.276698i
$528$	13.8839	−	21.8509i	0.604219	−	0.950938i
$529$	5.34967	+	6.37549i	0.232594	+	0.277195i
$530$		0			0
$531$	1.30746	+	14.5441i	0.0567388	+	0.631161i
$532$	0.106864	−	0.398822i	0.00463314	−	0.0172911i
$533$	−18.1347	−	38.8899i	−0.785499	−	1.68451i
$534$	3.97997	+	2.06581i	0.172230	+	0.0893962i
$535$		0			0
$536$	−9.80156	−	26.9296i	−0.423363	−	1.16318i
$537$	4.64510	+	6.03866i	0.200451	+	0.260587i
$538$	13.4217	+	9.39794i	0.578649	+	0.405174i
$539$	−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	$0.859231\pi$
$542$	21.4998	+	15.0543i	0.923494	+	0.646637i
$543$	9.81518	−	1.30412i	0.421210	−	0.0559651i
$544$	−1.44949	−	3.98243i	−0.0621463	−	0.170745i
$545$		0			0
$546$	−1.02321	−	22.8103i	−0.0437894	−	0.976189i
$547$	9.73975	+	20.8870i	0.416442	+	0.893062i	0.996893	+	0.0787671i	$0.0250984\pi$
$547$	9.73975	+	20.8870i	0.416442	+	0.893062i	−0.580451	+	0.814295i	$0.697124\pi$
$548$	0.368084	−	1.37371i	0.0157238	−	0.0586818i
$549$	10.7148	+	22.8354i	0.457296	+	0.974591i
$550$		0			0
$551$	−3.80505	−	4.53468i	−0.162101	−	0.193184i
$552$	−13.3218	−	25.5165i	−0.567014	−	1.08606i
$553$	0.468201	+	0.668660i	0.0199099	+	0.0284343i
$554$	−0.467751	+	2.65275i	−0.0198728	+	0.112704i
$555$		0			0
$556$	−3.33853	+	2.80136i	−0.141585	+	0.118804i
$557$	9.19419	+	34.3132i	0.389570	+	1.45390i	0.830835	+	0.556519i	$0.187863\pi$
$557$	9.19419	+	34.3132i	0.389570	+	1.45390i	−0.441265	+	0.897377i	$0.645470\pi$
$558$	−4.84731	−	8.34966i	−0.205203	−	0.353469i
$559$	5.66426	−	3.27026i	0.239572	−	0.138317i
$560$		0			0
$561$	12.8404	+	20.1023i	0.542120	+	0.848720i
$562$	−3.02674	−	34.5957i	−0.127675	−	1.45933i
$563$	4.24073	+	1.97748i	0.178725	+	0.0833410i	0.509922	−	0.860221i	$-0.329674\pi$
$563$	4.24073	+	1.97748i	0.178725	+	0.0833410i	−0.331196	+	0.943562i	$0.607452\pi$
$564$	3.10209	−	1.28927i	0.130622	−	0.0542881i
$565$		0			0
$566$		−	3.08073i		−	0.129493i
$567$	15.9333	−	7.52269i	0.669136	−	0.315923i
$568$	11.9317	−	11.9317i	0.500642	−	0.500642i
$569$	1.37633	+	7.80556i	0.0576988	+	0.327226i	0.999971	−	0.00762185i	$-0.00242613\pi$
$569$	1.37633	+	7.80556i	0.0576988	+	0.327226i	−0.942272	+	0.334848i	$0.891315\pi$
$570$		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	$0.355812\pi$
$572$	5.11288	−	0.447319i	0.213780	−	0.0187033i
$573$	−5.37891	+	24.4006i	−0.224707	+	1.01935i
$574$	7.52995	−	20.6884i	0.314294	−	0.863516i
$575$		0			0
$576$	6.82068	+	25.2141i	0.284195	+	1.05059i
$577$	−22.0266	+	5.90200i	−0.916977	+	0.245703i	−0.686293	−	0.727325i	$-0.740763\pi$
$577$	−22.0266	+	5.90200i	−0.916977	+	0.245703i	−0.230684	+	0.973029i	$0.574096\pi$
$578$	8.93890	+	0.782053i	0.371809	+	0.0325291i
$579$	−20.3290	−	22.1321i	−0.844844	−	0.919777i
$580$		0			0
$581$	−17.8737	−	3.15161i	−0.741526	−	0.130751i
$582$	27.5484	−	14.3826i	1.14192	−	0.596179i
$583$	0.502393	−	5.74237i	0.0208070	−	0.237825i
$584$	−7.58853	+	13.1437i	−0.314015	+	0.543891i
$585$		0			0
$586$	8.00664	+	13.8679i	0.330751	+	0.572878i
$587$	−33.9155	+	15.8151i	−1.39984	+	0.652758i	−0.968405	−	0.249384i	$-0.919772\pi$
$587$	−33.9155	+	15.8151i	−1.39984	+	0.652758i	−0.431439	+	0.902142i	$0.641994\pi$
$588$	0.871019	−	0.952832i	0.0359202	−	0.0392941i
$589$	−1.39555	+	1.66315i	−0.0575026	+	0.0685290i
$590$		0			0
$591$	−14.3296	+	18.7209i	−0.589440	+	0.770075i
$592$	−14.3700	+	20.5225i	−0.590604	+	0.843470i
$593$	5.46266	+	5.46266i	0.224324	+	0.224324i	0.810317	−	0.585992i	$-0.199295\pi$
$593$	5.46266	+	5.46266i	0.224324	+	0.224324i	−0.585992	+	0.810317i	$0.699295\pi$
$594$	−13.8077	−	26.2939i	−0.566535	−	1.07885i
$595$		0			0
$596$	−2.01008	+	0.354432i	−0.0823362	+	0.0145181i
$597$	12.3421	−	9.49383i	0.505126	−	0.388556i
$598$	−15.9266	+	34.1546i	−0.651286	+	1.39669i
$599$	−1.79656	−	1.50749i	−0.0734055	−	0.0615946i	0.605347	−	0.795962i	$-0.293035\pi$
$599$	−1.79656	−	1.50749i	−0.0734055	−	0.0615946i	−0.678752	+	0.734367i	$0.737479\pi$
$600$		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	$0.300406\pi$
$602$	3.24142	+	0.868536i	0.132110	+	0.0353989i
$603$	−28.5249	−	4.95949i	−1.16162	−	0.201966i
$604$	3.24716	+	1.87475i	0.132125	+	0.0762824i
$605$		0			0
$606$	−2.13027	−	9.55500i	−0.0865362	−	0.388146i
$607$	1.53527	−	1.07501i	0.0623147	−	0.0436332i	−0.542004	−	0.840376i	$-0.682334\pi$
$607$	1.53527	−	1.07501i	0.0623147	−	0.0436332i	0.604319	+	0.796743i	$0.293445\pi$
$608$	0.971981	−	0.680588i	0.0394190	−	0.0276015i
$609$	4.87408	+	21.8619i	0.197508	+	0.885891i
$610$		0			0
$611$	−36.1789	−	20.8879i	−1.46364	−	0.845035i
$612$	−2.22637	−	0.387089i	−0.0899958	−	0.0156472i
$613$	17.5910	+	4.71349i	0.710494	+	0.190376i	0.595926	−	0.803039i	$-0.296785\pi$
$613$	17.5910	+	4.71349i	0.710494	+	0.190376i	0.114568	+	0.993415i	$0.463452\pi$
$614$	−29.3338	−	10.6766i	−1.18382	−	0.430874i
$615$		0			0
$616$	19.1608	+	16.0778i	0.772012	+	0.647795i
$617$	7.87526	−	16.8885i	0.317046	−	0.679907i	−0.681611	−	0.731715i	$-0.738720\pi$
$617$	7.87526	−	16.8885i	0.317046	−	0.679907i	0.998657	+	0.0518073i	$0.0164982\pi$
$618$	−24.3534	+	18.7333i	−0.979639	+	0.753564i
$619$	−28.0130	+	4.93945i	−1.12594	+	0.198533i	−0.705447	−	0.708763i	$-0.749254\pi$
$619$	−28.0130	+	4.93945i	−1.12594	+	0.198533i	−0.420492	+	0.907296i	$0.638142\pi$
$620$		0			0
$621$	−29.0578	−	1.16440i	−1.16605	−	0.0467259i
$622$	3.73594	+	3.73594i	0.149797	+	0.149797i
$623$	−2.18848	+	3.12547i	−0.0876795	+	0.125219i
$624$	18.5382	−	24.2193i	0.742123	−	0.969549i
$625$		0			0
$626$	0.780926	−	0.930671i	0.0312121	−	0.0371971i
$627$	−4.50604	+	4.92928i	−0.179954	+	0.196857i
$628$	−2.83130	+	1.32026i	−0.112981	+	0.0526840i
$629$	−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	$0.943535\pi$
$632$	−0.107907	+	1.23338i	−0.00429231	+	0.0490613i
$633$	28.7833	−	15.0273i	1.14403	−	0.597283i
$634$	−34.4974	−	6.08282i	−1.37007	−	0.241580i
$635$		0			0
$636$	0.369414	+	0.402179i	0.0146482	+	0.0159475i
$637$	−15.9928	−	1.39919i	−0.633659	−	0.0554380i
$638$	36.4671	−	9.77134i	1.44375	−	0.386851i
$639$	−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	$0.976512\pi$
$642$	−7.18807	+	32.6075i	−0.283691	+	1.28692i
$643$	−39.3334	+	3.44122i	−1.55116	+	0.135709i	−0.830277	−	0.557351i	$-0.811818\pi$
$643$	−39.3334	+	3.44122i	−1.55116	+	0.135709i	−0.720880	+	0.693060i	$0.756262\pi$
$644$	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	$0.530976\pi$
$647$	−27.7872	+	27.7872i	−1.09243	+	1.09243i	−0.995269	+	0.0971593i	$0.969024\pi$
$648$	25.8470	+	6.79352i	1.01537	+	0.266875i
$649$			20.9430i			0.822086i
$650$		0			0
$651$	7.58592	−	3.15281i	0.297315	−	0.123568i
$652$	1.58283	+	0.738085i	0.0619884	+	0.0289056i
$653$	1.47726	+	16.8852i	0.0578098	+	0.660770i	0.968719	+	0.248162i	$0.0798264\pi$
$653$	1.47726	+	16.8852i	0.0578098	+	0.660770i	−0.910909	+	0.412608i	$0.864618\pi$
$654$	−17.7685	−	27.8175i	−0.694802	−	1.08775i
$655$		0			0
$656$	25.4684	−	14.7042i	0.994375	−	0.574103i
$657$	7.69833	+	13.2607i	0.300341	+	0.517348i
$658$	−5.54754	−	20.7037i	−0.216266	−	0.807115i
$659$	36.7210	−	30.8125i	1.43045	−	1.20029i	0.484997	−	0.874516i	$-0.338821\pi$
$659$	36.7210	−	30.8125i	1.43045	−	1.20029i	0.945449	−	0.325770i	$-0.105624\pi$
$660$		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	$0.0814838\pi$
$662$	−9.79064	−	13.9825i	−0.380524	−	0.543445i
$663$	13.0058	+	24.9112i	0.505102	+	0.967470i
$664$	−17.6947	−	21.0877i	−0.686687	−	0.818361i
$665$		0			0
$666$	12.2084	+	26.0187i	0.473068	+	1.00820i
$667$	9.56811	−	35.7087i	0.370479	−	1.38264i
$668$	0.818774	+	1.75587i	0.0316793	+	0.0679365i
$669$	1.28739	+	28.6995i	0.0497732	+	1.10959i
$670$		0			0
$671$	12.3730	+	33.9945i	0.477653	+	1.31234i
$672$	−4.45065	+	0.591347i	−0.171687	+	0.0228117i
$673$	19.5570	+	13.6940i	0.753867	+	0.527863i	0.886178	−	0.463345i	$-0.153351\pi$
$673$	19.5570	+	13.6940i	0.753867	+	0.527863i	−0.132311	+	0.991208i	$0.542240\pi$
$674$	11.2915			0.434933
$675$		0			0
$676$	2.98725			0.114894
$677$	18.1236	+	12.6903i	0.696547	+	0.487727i	0.867427	−	0.497565i	$-0.165772\pi$
$677$	18.1236	+	12.6903i	0.696547	+	0.487727i	−0.170880	+	0.985292i	$0.554661\pi$
$678$	19.1328	+	24.8728i	0.734791	+	0.955235i
$679$	9.04396	+	24.8481i	0.347075	+	0.953581i
$680$		0			0
$681$	27.8153	+	14.4376i	1.06589	+	0.553248i
$682$	−5.85182	−	12.5493i	−0.224078	−	0.480537i
$683$	−6.53337	+	24.3829i	−0.249993	+	0.932985i	0.720815	+	0.693127i	$0.243768\pi$
$683$	−6.53337	+	24.3829i	−0.249993	+	0.932985i	−0.970808	+	0.239858i	$0.922899\pi$
$684$	−0.0566484	−	0.630155i	−0.00216601	−	0.0240946i
$685$		0			0
$686$	−16.9965	−	20.2556i	−0.648929	−	0.773363i
$687$	−17.6451	+	27.7703i	−0.673201	+	1.05950i
$688$	2.57107	+	3.67187i	0.0980212	+	0.139989i
$689$	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	$0.0585118\pi$
$692$	−0.473473	−	1.76703i	−0.0179988	−	0.0671723i
$693$	23.7255	−	8.69959i	0.901256	−	0.330470i
$694$	6.05298	−	3.49469i	0.229768	−	0.132657i
$695$		0			0
$696$	−15.6510	+	30.1532i	−0.593251	+	1.14295i
$697$	2.36159	+	26.9931i	0.0894517	+	1.02244i
$698$	−24.8229	−	11.5751i	−0.939559	−	0.438124i
$699$	−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	$0.924737\pi$
$702$	−13.5053	−	32.2771i	−0.509724	−	1.21822i
$703$	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
$707$	8.29809	−	0.725989i	0.312082	−	0.0273036i
$708$	−1.46441	−	1.33867i	−0.0550359	−	0.0503103i
$709$	−4.29127	+	11.7902i	−0.161162	+	0.442789i	−0.993821	−	0.110998i	$-0.964595\pi$
$709$	−4.29127	+	11.7902i	−0.161162	+	0.442789i	0.832659	+	0.553786i	$0.186818\pi$
$710$		0			0
$711$	1.02634	+	0.715002i	0.0384906	+	0.0268147i
$712$	−5.58994	+	1.49782i	−0.209492	+	0.0561332i
$713$	−13.5070	−	1.18171i	−0.505842	−	0.0442554i
$714$	−4.31925	+	13.7562i	−0.161644	+	0.514812i
$715$		0			0
$716$	−1.01940	−	0.179748i	−0.0380969	−	0.00671750i
$717$	−0.918999	+	21.6416i	−0.0343206	+	0.808219i
$718$	−2.06408	+	23.5926i	−0.0770308	+	0.880466i
$719$	9.10268	−	15.7663i	0.339473	−	0.587984i	−0.644861	−	0.764300i	$-0.723085\pi$
$719$	9.10268	−	15.7663i	0.339473	−	0.587984i	0.984334	+	0.176316i	$0.0564181\pi$
$720$		0			0
$721$	−13.0717	−	22.6408i	−0.486815	−	0.843188i
$722$	−21.9081	+	10.2159i	−0.815334	+	0.380196i
$723$	−28.9608	−	6.38419i	−1.07707	−	0.237431i
$724$	−0.864744	+	1.03056i	−0.0321380	+	0.0383005i
$725$		0			0
$726$	−6.63333	−	15.9603i	−0.246186	−	0.592344i
$727$	5.64377	−	8.06014i	0.209316	−	0.298934i	−0.700742	−	0.713414i	$-0.747148\pi$
$727$	5.64377	−	8.06014i	0.209316	−	0.298934i	0.910058	+	0.414480i	$0.136037\pi$
$728$	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
$732$	−3.16789	−	1.30775i	−0.117088	−	0.0483359i
$733$	15.6224	−	33.5024i	0.577027	−	1.23744i	−0.373740	−	0.927533i	$-0.621925\pi$
$733$	15.6224	−	33.5024i	0.577027	−	1.23744i	0.950767	−	0.309905i	$-0.100297\pi$
$734$	22.3146	+	18.7242i	0.823646	+	0.691121i
$735$		0			0
$736$	6.96332	+	2.53444i	0.256671	+	0.0934207i
$737$	−40.1088	−	10.7471i	−1.47743	−	0.395875i
$738$	−0.0805779	−	33.7364i	−0.00296611	−	1.24186i
$739$	−7.02338	−	4.05495i	−0.258359	−	0.149164i	0.365227	−	0.930919i	$-0.380991\pi$
$739$	−7.02338	−	4.05495i	−0.258359	−	0.149164i	−0.623586	+	0.781755i	$0.714325\pi$
$740$		0			0
$741$	−5.79457	+	5.32249i	−0.212869	+	0.195526i
$742$	2.85416	−	1.99851i	0.104780	−	0.0733675i
$743$	−25.5056	+	17.8592i	−0.935709	+	0.655190i	−0.938674	−	0.344805i	$-0.887945\pi$
$743$	−25.5056	+	17.8592i	−0.935709	+	0.655190i	0.00296531	+	0.999996i	$0.499056\pi$
$744$	11.8878	+	3.73262i	0.435829	+	0.136844i
$745$		0			0
$746$	19.8552	+	11.4634i	0.726949	+	0.419704i
$747$	−27.3773	+	4.89480i	−1.00168	+	0.179091i
$748$	−3.13050	−	0.838814i	−0.114462	−	0.0306701i
$749$	−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	$0.825746\pi$
$752$	12.1000	−	25.9484i	0.441240	−	0.946243i
$753$	1.22851	+	9.24615i	0.0447695	+	0.336949i
$754$	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	$0.576464\pi$
$758$	20.7010	−	29.5641i	0.751893	−	1.07381i
$759$	−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	$-0.0114517\pi$
$762$	−2.50046	−	7.89754i	−0.0905820	−	0.286098i
$763$	25.4545	−	11.8696i	0.921516	−	0.429710i
$764$	−1.69744	−	2.94006i	−0.0614113	−	0.106368i
$765$		0			0
$766$	−4.88069	+	8.45360i	−0.176346	+	0.305441i
$767$	−2.15042	+	24.5794i	−0.0776472	+	0.887512i
$768$	−8.13803	−	5.17084i	−0.293656	−	0.186587i
$769$	8.53754	+	1.50540i	0.307872	+	0.0542861i	0.325450	−	0.945559i	$-0.394484\pi$
$769$	8.53754	+	1.50540i	0.307872	+	0.0542861i	−0.0175779	+	0.999845i	$0.505595\pi$
$770$		0			0
$771$	−20.7296	+	4.62163i	−0.746559	+	0.166444i
$772$	4.06755	+	0.355865i	0.146394	+	0.0128078i
$773$	−11.3983	+	3.05417i	−0.409969	+	0.109851i	−0.457908	−	0.889000i	$-0.651401\pi$
$773$	−11.3983	+	3.05417i	−0.409969	+	0.109851i	0.0479396	+	0.998850i	$0.484734\pi$
$774$	5.12158	−	0.460409i	0.184091	−	0.0165491i
$775$		0			0
$776$	−13.7174	+	37.6882i	−0.492425	+	1.35293i
$777$	−23.3141	+	7.38154i	−0.836390	+	0.264811i
$778$	−41.3603	+	3.61856i	−1.48284	+	0.129732i
$779$	−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
$783$	18.5452	+	28.8813i	0.662752	+	1.03213i
$784$		−	11.0025i		−	0.392947i
$785$		0			0
$786$	−1.01457	−	0.776581i	−0.0361884	−	0.0276997i
$787$	−17.0214	−	7.93722i	−0.606748	−	0.282931i	0.0948643	−	0.995490i	$-0.469758\pi$
$787$	−17.0214	−	7.93722i	−0.606748	−	0.282931i	−0.701612	+	0.712559i	$0.747536\pi$
$788$	−0.279178	−	3.19101i	−0.00994529	−	0.113675i
$789$	−23.5794	+	1.05771i	−0.839448	+	0.0376556i
$790$		0			0
$791$	−23.1237	+	13.3505i	−0.822183	+	0.474687i
$792$	36.0481	+	13.0230i	1.28091	+	0.462753i
$793$	11.0308	+	41.1675i	0.391715	+	1.46190i
$794$	−16.7831	+	14.0827i	−0.595610	+	0.499776i
$795$		0			0
$796$	−0.367376	+	2.08349i	−0.0130213	+	0.0738475i
$797$	−12.3706	−	17.6670i	−0.438188	−	0.625797i	0.537943	−	0.842981i	$-0.319202\pi$
$797$	−12.3706	−	17.6670i	−0.438188	−	0.625797i	−0.976131	+	0.217184i	$0.930313\pi$
$798$	−4.03324	−	0.171269i	−0.142775	−	0.00606287i
$799$	16.9567	+	20.2082i	0.599884	+	0.714914i
$800$		0			0
$801$	−1.49974	+	5.65108i	−0.0529909	+	0.199671i
$802$	0.519739	−	1.93969i	0.0183526	−	0.0684929i
$803$	9.29368	+	19.9304i	0.327967	+	0.703327i
$804$	3.31521	−	2.11759i	0.116919	−	0.0746818i
$805$		0			0
$806$	−5.57934	−	15.3291i	−0.196524	−	0.539945i
$807$	−8.15185	+	19.7470i	−0.286959	+	0.695126i
$808$	10.3493	+	7.24665i	0.364087	+	0.254936i
$809$	−4.46938			−0.157135			−0.0785676	−	0.996909i	$-0.525035\pi$
$809$	−4.46938			−0.157135			−0.0785676	+	0.996909i	$0.525035\pi$
$810$		0			0
$811$	37.9099			1.33120			0.665598	−	0.746311i	$-0.268177\pi$
$811$	37.9099			1.33120			0.665598	+	0.746311i	$0.268177\pi$
$812$	−2.49292	−	1.74556i	−0.0874845	−	0.0612573i
$813$	−13.0582	+	31.6321i	−0.457971	+	1.10939i
$814$	14.0978	+	38.7333i	0.494127	+	1.35760i
$815$		0			0
$816$	−16.2310	+	10.3675i	−0.568197	+	0.362936i
$817$	−0.488696	−	1.04801i	−0.0170973	−	0.0366653i
$818$	8.06996	−	30.1175i	0.282159	−	1.05303i
$819$	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	$0.561267\pi$
$822$	−13.8921	−	0.589922i	−0.484544	−	0.0205759i
$823$	−1.52711	−	2.18095i	−0.0532319	−	0.0760230i	0.791654	−	0.610970i	$-0.209220\pi$
$823$	−1.52711	−	2.18095i	−0.0532319	−	0.0760230i	−0.844886	+	0.534947i	$0.820332\pi$
$824$	6.88563	−	39.0504i	0.239872	−	1.36038i
$825$		0			0
$826$	−9.69752	+	8.13719i	−0.337420	+	0.283129i
$827$	−10.6874	−	39.8859i	−0.371637	−	1.38697i	−0.858197	−	0.513321i	$-0.828415\pi$
$827$	−10.6874	−	39.8859i	−0.371637	−	1.38697i	0.486560	−	0.873647i	$-0.338252\pi$
$828$	3.02075	−	2.54703i	0.104978	−	0.0885153i
$829$	19.6326	−	11.3349i	0.681869	−	0.393677i	−0.118690	−	0.992931i	$-0.537869\pi$
$829$	19.6326	−	11.3349i	0.681869	−	0.393677i	0.800559	+	0.599254i	$0.204536\pi$
$830$		0			0
$831$	−3.50863	+	0.157388i	−0.121713	+	0.00545974i
$832$	3.84651	+	43.9658i	0.133354	+	1.52424i
$833$	9.18766	+	4.28428i	0.318334	+	0.148441i
$834$	33.8357	+	25.8989i	1.17164	+	0.896806i
$835$		0			0
$836$		−	0.907402i		−	0.0313832i
$837$	9.25056	−	8.53774i	0.319746	−	0.295108i
$838$	−14.9429	+	14.9429i	−0.516195	+	0.516195i
$839$	−1.44230	−	8.17971i	−0.0497938	−	0.282395i	0.949736	−	0.313052i	$-0.101351\pi$
$839$	−1.44230	−	8.17971i	−0.0497938	−	0.282395i	−0.999530	+	0.0306567i	$0.990240\pi$
$840$		0			0
$841$	−13.7493	+	5.00432i	−0.474112	+	0.172563i
$842$	48.0337	−	4.20240i	1.65535	−	0.144824i
$843$	43.1681	−	13.6676i	1.48679	−	0.470736i
$844$	−1.50888	+	4.14562i	−0.0519379	+	0.142698i
$845$		0			0
$846$	−18.9031	−	26.8597i	−0.649902	−	0.923455i
$847$	14.2054	−	3.80634i	0.488105	−	0.130787i
$848$	4.63650	+	0.405641i	0.159218	+	0.0139298i
$849$	3.92057	−	0.874084i	0.134554	−	0.0299985i
$850$		0			0
$851$	39.7487	+	7.00876i	1.36257	+	0.240257i
$852$	1.95499	+	1.24219i	0.0669770	+	0.0425567i
$853$	0.534954	−	6.11455i	0.0183165	−	0.209358i	−0.981521	−	0.191352i	$-0.938713\pi$
$853$	0.534954	−	6.11455i	0.0183165	−	0.209358i	0.999838	−	0.0180058i	$-0.00573174\pi$
$854$	−10.9335	+	18.9374i	−0.374137	+	0.648024i
$855$		0			0
$856$	−21.5463	−	37.3193i	−0.736439	−	1.27555i
$857$	31.3187	−	14.6042i	1.06983	−	0.498869i	0.193756	−	0.981050i	$-0.437933\pi$
$857$	31.3187	−	14.6042i	1.06983	−	0.498869i	0.876072	+	0.482181i	$0.160155\pi$
$858$	−15.1466	−	47.8395i	−0.517095	−	1.63321i
$859$	−14.4078	+	17.1705i	−0.491587	+	0.585850i	−0.953620	−	0.301012i	$-0.902676\pi$
$859$	−14.4078	+	17.1705i	−0.491587	+	0.585850i	0.462034	+	0.886862i	$0.347120\pi$
$860$		0			0
$861$	28.4647	+	3.71287i	0.970073	+	0.126534i
$862$	8.19621	−	11.7054i	0.279164	−	0.398688i
$863$	−34.4337	−	34.4337i	−1.17214	−	1.17214i	−0.981700	−	0.190436i	$-0.939010\pi$
$863$	−34.4337	−	34.4337i	−1.17214	−	1.17214i	−0.190436	−	0.981700i	$-0.560990\pi$
$864$	−6.09114	+	3.19864i	−0.207225	+	0.108820i
$865$		0			0
$866$	47.8011	−	8.42862i	1.62435	−	0.286416i
$867$	1.54095	+	11.5976i	0.0523334	+	0.393876i
$868$	−0.471713	+	1.01159i	−0.0160110	+	0.0343357i
$869$	1.37423	+	1.15312i	0.0466175	+	0.0391168i
$870$		0			0
$871$	−45.9694	−	16.7315i	−1.55762	−	0.566926i
$872$	41.1477	+	11.0255i	1.39344	+	0.373370i
$873$	26.1197	+	30.9776i	0.884017	+	1.04843i
$874$	5.77009	+	3.33137i	0.195176	+	0.112685i
$875$		0			0
$876$	−1.98765	−	0.624094i	−0.0671564	−	0.0210862i
$877$	−11.3525	+	7.94910i	−0.383347	+	0.268422i	−0.749327	−	0.662201i	$-0.769623\pi$
$877$	−11.3525	+	7.94910i	−0.383347	+	0.268422i	0.365980	+	0.930623i	$0.380734\pi$
$878$	15.1584	−	10.6140i	0.511571	−	0.358206i
$879$	−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	$0.796501\pi$
$882$	−10.9458	−	6.28476i	−0.368565	−	0.211619i
$883$	15.8795	+	4.25489i	0.534386	+	0.143188i	0.515913	−	0.856641i	$-0.327453\pi$
$883$	15.8795	+	4.25489i	0.534386	+	0.143188i	0.0184733	+	0.999829i	$0.494119\pi$
$884$	−3.58792	−	1.30590i	−0.120675	−	0.0439221i
$885$		0			0
$886$	11.6044	+	9.73725i	0.389857	+	0.327129i
$887$	4.33234	−	9.29073i	0.145466	−	0.311952i	−0.820052	−	0.572289i	$-0.806056\pi$
$887$	4.33234	−	9.29073i	0.145466	−	0.311952i	0.965518	+	0.260336i	$0.0838335\pi$
$888$	−34.2851	−	14.1534i	−1.15053	−	0.474958i
$889$	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
$893$	−4.23638	+	6.05018i	−0.141765	+	0.202461i
$894$	7.65882	+	18.4278i	0.256149	+	0.616316i
$895$		0			0
$896$	−11.2227	+	13.3748i	−0.374926	+	0.446819i
$897$	−47.9843	−	10.5778i	−1.60215	−	0.353181i
$898$	1.94540	−	0.907153i	0.0649187	−	0.0302721i
$899$	8.00123	+	13.8585i	0.266856	+	0.462208i
$900$		0			0
$901$	−2.14414	+	3.71376i	−0.0714317	+	0.123723i
$902$	4.21697	−	48.2002i	0.140410	−	1.60489i
$903$	−0.185633	+	4.37149i	−0.00617748	+	0.145474i
$904$	−39.8832	−	7.03248i	−1.32649	−	0.233897i
$905$		0			0
$906$	10.9819	−	34.9756i	0.364848	−	1.16199i
$907$	13.4551	+	1.17717i	0.446769	+	0.0390872i	0.308321	−	0.951283i	$-0.400233\pi$
$907$	13.4551	+	1.17717i	0.446769	+	0.0390872i	0.138448	+	0.990370i	$0.455789\pi$
$908$	−4.11293	+	1.10206i	−0.136492	+	0.0365730i
$909$	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	$0.0339332\pi$
$912$	−3.97999	−	3.63825i	−0.131791	−	0.120475i
$913$	−39.7348	+	3.47635i	−1.31503	+	0.115050i
$914$	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
$918$	1.04280	+	22.0694i	0.0344176	+	0.728399i
$919$		−	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
$922$	18.2970	+	8.53202i	0.602579	+	0.280987i
$923$	−2.51046	−	28.6946i	−0.0826327	−	0.944496i
$924$	−1.58175	+	3.04739i	−0.0520357	+	0.100252i
$925$		0			0
$926$	38.0276	−	21.9552i	1.24966	−	0.721494i
$927$	−30.7499	−	25.6773i	−1.00996	−	0.843353i
$928$	−2.26359	−	8.44784i	−0.0743061	−	0.277314i
$929$	36.0388	−	30.2401i	1.18239	−	0.992146i	0.182433	−	0.983218i	$-0.441603\pi$
$929$	36.0388	−	30.2401i	1.18239	−	0.992146i	0.999960	−	0.00892776i	$-0.00284183\pi$
$930$		0			0
$931$	−0.492867	+	2.79519i	−0.0161531	+	0.0916086i
$932$	−1.02089	−	1.45799i	−0.0334405	−	0.0477579i
$933$	−3.69441	+	5.81437i	−0.120950	+	0.190354i
$934$	−19.3932	−	23.1119i	−0.634563	−	0.756243i
$935$		0			0
$936$	40.9700	+	18.9856i	1.33915	+	0.620565i
$937$	9.80740	−	36.6017i	0.320394	−	1.19573i	−0.598468	−	0.801147i	$-0.704224\pi$
$937$	9.80740	−	36.6017i	0.320394	−	1.19573i	0.918862	−	0.394580i	$-0.129110\pi$
$938$	−10.6074	−	22.7477i	−0.346346	−	0.742740i
$939$	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	$0.946761\pi$
$942$	18.6227	+	24.2096i	0.606760	+	0.788793i
$943$	−38.8098	−	27.1749i	−1.26382	−	0.884937i
$944$	−16.9098			−0.550367
$945$		0			0
$946$	7.37489			0.239778
$947$	13.0294	+	9.12331i	0.423400	+	0.296468i	0.765791	−	0.643090i	$-0.222348\pi$
$947$	13.0294	+	9.12331i	0.423400	+	0.296468i	−0.342391	+	0.939558i	$0.611237\pi$
$948$	−0.168470	+	0.0223842i	−0.00547165	+	0.000727006i
$949$	8.86092	+	24.3452i	0.287638	+	0.790278i
$950$		0			0
$951$	−2.04674	−	45.6276i	−0.0663701	−	1.47958i
$952$	−7.86402	−	16.8644i	−0.254874	−	0.546580i
$953$	9.45180	−	35.2746i	0.306174	−	1.14266i	−0.625756	−	0.780019i	$-0.715210\pi$
$953$	9.45180	−	35.2746i	0.306174	−	1.14266i	0.931930	−	0.362638i	$-0.118124\pi$
$954$	3.05197	−	4.38090i	0.0988113	−	0.141837i
$955$		0			0
$956$	−1.89177	−	2.25453i	−0.0611843	−	0.0729167i
$957$	22.7818	+	43.6361i	0.736430	+	1.41055i
$958$	17.4002	+	24.8501i	0.562176	+	0.802871i
$959$	2.05447	−	11.6515i	0.0663422	−	0.376245i
$960$		0			0
$961$	−19.2514	+	16.1538i	−0.621012	+	0.521091i
$962$	12.5685	+	46.9062i	0.405224	+	1.51232i
$963$	−43.5361	+	0.103984i	−1.40293	+	0.00335084i
$964$	3.48953	−	2.01468i	0.112390	−	0.0648886i
$965$		0			0
$966$	−13.5710	−	21.2462i	−0.436640	−	0.683584i
$967$	0.170714	+	1.95128i	0.00548981	+	0.0627488i	0.998445	−	0.0557381i	$-0.0177512\pi$
$967$	0.170714	+	1.95128i	0.00548981	+	0.0627488i	−0.992956	+	0.118487i	$0.962196\pi$
$968$	20.2162	+	9.42696i	0.649773	+	0.302994i
$969$	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	$-0.145719\pi$
$972$	−0.138130	+	3.66587i	−0.00443052	+	0.117583i
$973$	−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
$977$	32.5167	−	2.84484i	1.04030	−	0.0910146i	0.445819	−	0.895123i	$-0.352912\pi$
$977$	32.5167	−	2.84484i	1.04030	−	0.0910146i	0.594483	+	0.804108i	$0.297357\pi$
$978$	3.67586	−	16.6749i	0.117541	−	0.533205i
$979$	−2.86792	+	7.87954i	−0.0916591	+	0.251831i
$980$		0			0
$981$	30.3595	−	30.5049i	0.969305	−	0.973946i
$982$	−11.8947	+	3.18718i	−0.379575	+	0.101707i
$983$	31.9076	+	2.79155i	1.01769	+	0.0890367i	0.583775	−	0.811915i	$-0.301575\pi$
$983$	31.9076	+	2.79155i	1.01769	+	0.0890367i	0.433919	+	0.900952i	$0.357130\pi$
$984$	29.4531	+	32.0654i	0.938930	+	1.02221i
$985$		0			0
$986$	−27.6596	−	4.87713i	−0.880860	−	0.155319i
$987$	24.7738	−	12.9340i	0.788558	−	0.411695i
$988$	0.0931716	−	1.06496i	0.00296418	−	0.0338808i
$989$	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	$0.548046\pi$
$992$	−2.90712	+	1.35561i	−0.0923012	+	0.0430407i
$993$	15.0164	−	16.4269i	0.476531	−	0.521291i
$994$	9.49956	−	11.3211i	0.301308	−	0.359084i
$995$		0			0
$996$	2.29676	−	3.00060i	0.0727755	−	0.0950778i
$997$	18.0163	−	25.7299i	0.570581	−	0.814874i	−0.425347	−	0.905031i	$-0.639848\pi$
$997$	18.0163	−	25.7299i	0.570581	−	0.814874i	0.995928	+	0.0901563i	$0.0287367\pi$
$998$	−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.257.11		192
5.2	odd	4		135.2.q.a.68.6	yes	192
5.3	odd	4	inner	675.2.ba.b.68.11		192
5.4	even	2		135.2.q.a.122.6	yes	192
15.2	even	4		405.2.r.a.233.11		192
15.14	odd	2		405.2.r.a.152.11		192
27.2	odd	18	inner	675.2.ba.b.407.11		192
135.2	even	36		135.2.q.a.83.6	yes	192
135.29	odd	18		135.2.q.a.2.6	✓	192
135.52	odd	36		405.2.r.a.8.11		192
135.79	even	18		405.2.r.a.332.11		192
135.83	even	36	inner	675.2.ba.b.218.11		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.6	✓	192	135.29	odd	18
135.2.q.a.68.6	yes	192	5.2	odd	4
135.2.q.a.83.6	yes	192	135.2	even	36
135.2.q.a.122.6	yes	192	5.4	even	2
405.2.r.a.8.11		192	135.52	odd	36
405.2.r.a.152.11		192	15.14	odd	2
405.2.r.a.233.11		192	15.2	even	4
405.2.r.a.332.11		192	135.79	even	18
675.2.ba.b.68.11		192	5.3	odd	4	inner
675.2.ba.b.218.11		192	135.83	even	36	inner
675.2.ba.b.257.11		192	1.1	even	1	trivial
675.2.ba.b.407.11		192	27.2	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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