LMFDB - Embedded newform 675.2.ba.b.218.4

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			218.4
Character	$\chi$	$=$	675.218
Dual form			675.2.ba.b.257.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.23715 + 0.866263i) q^{2} +(-1.45553 + 0.938839i) q^{3} +(0.0960923 - 0.264011i) q^{4} +(0.987435 - 2.42236i) q^{6} +(-0.677826 + 1.45360i) q^{7} +(-0.671958 - 2.50778i) q^{8} +(1.23716 - 2.73303i) q^{9} +(-1.78545 + 2.12782i) q^{11} +(0.107999 + 0.474493i) q^{12} +(-0.176418 + 0.251952i) q^{13} +(-0.420628 - 2.38550i) q^{14} +(3.43416 + 2.88160i) q^{16} +(1.88139 - 7.02145i) q^{17} +(0.836964 + 4.45287i) q^{18} +(-5.07203 - 2.92834i) q^{19} +(-0.378100 - 2.75214i) q^{21} +(0.365624 - 4.17910i) q^{22} +(-0.116642 + 0.0543910i) q^{23} +(3.33246 + 3.01930i) q^{24} -0.464527i q^{26} +(0.765143 + 5.13951i) q^{27} +(0.318634 + 0.318634i) q^{28} +(1.51659 - 8.60103i) q^{29} +(4.22026 + 1.53605i) q^{31} +(-1.57207 - 0.137538i) q^{32} +(0.601106 - 4.77337i) q^{33} +(3.75485 + 10.3164i) q^{34} +(-0.602668 - 0.589247i) q^{36} +(-2.08386 - 0.558369i) q^{37} +(8.81158 - 0.770913i) q^{38} +(0.0202409 - 0.532353i) q^{39} +(-4.62442 + 0.815410i) q^{41} +(2.85184 + 3.07728i) q^{42} +(0.429127 + 4.90494i) q^{43} +(0.390200 + 0.675847i) q^{44} +(0.0971868 - 0.168333i) q^{46} +(7.69135 + 3.58654i) q^{47} +(-7.70389 - 0.970146i) q^{48} +(2.84600 + 3.39173i) q^{49} +(3.85358 + 11.9863i) q^{51} +(0.0495656 + 0.0707870i) q^{52} +(-0.483003 + 0.483003i) q^{53} +(-5.39876 - 5.69554i) q^{54} +(4.10079 + 0.723079i) q^{56} +(10.1318 - 0.499526i) q^{57} +(5.57450 + 11.9546i) q^{58} +(7.43127 - 6.23558i) q^{59} +(2.50049 - 0.910105i) q^{61} +(-6.55173 + 1.75553i) q^{62} +(3.13415 + 3.65086i) q^{63} +(-5.70071 + 3.29131i) q^{64} +(3.39133 + 6.42609i) q^{66} +(0.884390 + 0.619257i) q^{67} +(-1.67295 - 1.17142i) q^{68} +(0.118712 - 0.188676i) q^{69} +(9.03942 - 5.21891i) q^{71} +(-7.68515 - 1.26605i) q^{72} +(6.65047 - 1.78199i) q^{73} +(3.06175 - 1.11439i) q^{74} +(-1.26050 + 1.05768i) q^{76} +(-1.88278 - 4.03763i) q^{77} +(0.436116 + 0.676135i) q^{78} +(2.04188 + 0.360038i) q^{79} +(-5.93887 - 6.76239i) q^{81} +(5.01475 - 5.01475i) q^{82} +(-7.55956 - 10.7962i) q^{83} +(-0.762929 - 0.164636i) q^{84} +(-4.77986 - 5.69642i) q^{86} +(5.86754 + 13.9429i) q^{87} +(6.53585 + 3.04772i) q^{88} +(-5.58181 + 9.66798i) q^{89} +(-0.246656 - 0.427222i) q^{91} +(0.00315146 + 0.0360214i) q^{92} +(-7.58484 + 1.72638i) q^{93} +(-12.6222 + 2.22564i) q^{94} +(2.41732 - 1.27573i) q^{96} +(11.8062 - 1.03291i) q^{97} +(-6.45906 - 1.73070i) q^{98} +(3.60649 + 7.51214i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{3} - 36 q^{6} + 12 q^{7} + 18 q^{8} - 36 q^{11} + 12 q^{12} + 12 q^{13} - 24 q^{16} + 18 q^{17} + 54 q^{18} - 24 q^{21} + 12 q^{22} + 36 q^{23} + 36 q^{27} + 24 q^{28} - 24 q^{31}+ \cdots - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^3 - 36 * q^6 + 12 * q^7 + 18 * q^8 - 36 * q^11 + 12 * q^12 + 12 * q^13 - 24 * q^16 + 18 * q^17 + 54 * q^18 - 24 * q^21 + 12 * q^22 + 36 * q^23 + 36 * q^27 + 24 * q^28 - 24 * q^31 + 48 * q^32 + 6 * q^33 + 12 * q^36 + 6 * q^37 - 12 * q^38 + 24 * q^41 + 24 * q^42 + 12 * q^43 - 12 * q^46 + 6 * q^47 - 12 * q^48 + 144 * q^51 - 12 * q^52 + 180 * q^56 + 12 * q^57 + 12 * q^58 - 60 * q^61 + 18 * q^62 + 54 * q^63 + 72 * q^66 - 24 * q^67 + 60 * q^68 - 36 * q^71 - 180 * q^72 + 6 * q^73 - 72 * q^76 - 132 * q^77 - 78 * q^78 + 12 * q^81 + 24 * q^82 - 48 * q^83 + 12 * q^86 - 144 * q^87 + 48 * q^88 - 12 * q^91 - 258 * q^92 - 180 * q^93 - 12 * q^96 - 24 * q^97 - 324 * q^98

Character values

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

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.23715	+	0.866263i	−0.874798	+	0.612540i	−0.922361	−	0.386328i	$-0.873743\pi$
$2$	−1.23715	+	0.866263i	−0.874798	+	0.612540i	0.0475633	+	0.998868i	$0.484854\pi$
$3$	−1.45553	+	0.938839i	−0.840353	+	0.542039i
$3$	−1.45553	+	0.938839i	−0.840353	+	0.542039i
$4$	0.0960923	−	0.264011i	0.0480461	−	0.132006i
$5$		0			0
$5$		0			0
$6$	0.987435	−	2.42236i	0.403119	−	0.988925i
$7$	−0.677826	+	1.45360i	−0.256194	+	0.549410i	−0.991770	−	0.128032i	$-0.959134\pi$
$7$	−0.677826	+	1.45360i	−0.256194	+	0.549410i	0.735576	+	0.677442i	$0.236912\pi$
$8$	−0.671958	−	2.50778i	−0.237573	−	0.886634i
$9$	1.23716	−	2.73303i	0.412387	−	0.911009i
$10$		0			0
$11$	−1.78545	+	2.12782i	−0.538334	+	0.641561i	−0.964813	−	0.262936i	$-0.915309\pi$
$11$	−1.78545	+	2.12782i	−0.538334	+	0.641561i	0.426479	+	0.904497i	$0.359754\pi$
$12$	0.107999	+	0.474493i	0.0311765	+	0.136974i
$13$	−0.176418	+	0.251952i	−0.0489296	+	0.0698788i	−0.842871	−	0.538115i	$-0.819137\pi$
$13$	−0.176418	+	0.251952i	−0.0489296	+	0.0698788i	0.793942	+	0.607994i	$0.208025\pi$
$14$	−0.420628	−	2.38550i	−0.112418	−	0.637552i
$15$		0			0
$16$	3.43416	+	2.88160i	0.858539	+	0.720400i
$17$	1.88139	−	7.02145i	0.456304	−	1.70295i	−0.227921	−	0.973680i	$-0.573193\pi$
$17$	1.88139	−	7.02145i	0.456304	−	1.70295i	0.684225	−	0.729271i	$-0.260141\pi$
$18$	0.836964	+	4.45287i	0.197274	+	1.04955i
$19$	−5.07203	−	2.92834i	−1.16360	−	0.671807i	−0.211439	−	0.977391i	$-0.567815\pi$
$19$	−5.07203	−	2.92834i	−1.16360	−	0.671807i	−0.952165	+	0.305584i	$0.901148\pi$
$20$		0			0
$21$	−0.378100	−	2.75214i	−0.0825083	−	0.600566i
$22$	0.365624	−	4.17910i	0.0779514	−	0.890988i
$23$	−0.116642	+	0.0543910i	−0.0243215	+	0.0113413i	−0.434741	−	0.900556i	$-0.643160\pi$
$23$	−0.116642	+	0.0543910i	−0.0243215	+	0.0113413i	0.410419	+	0.911897i	$0.365382\pi$
$24$	3.33246	+	3.01930i	0.680236	+	0.616312i
$25$		0			0
$26$		−	0.464527i		−	0.0911012i
$27$	0.765143	+	5.13951i	0.147252	+	0.989099i
$28$	0.318634	+	0.318634i	0.0602161	+	0.0602161i
$29$	1.51659	−	8.60103i	0.281625	−	1.59717i	−0.435475	−	0.900201i	$-0.643419\pi$
$29$	1.51659	−	8.60103i	0.281625	−	1.59717i	0.717099	−	0.696971i	$-0.245469\pi$
$30$		0			0
$31$	4.22026	+	1.53605i	0.757981	+	0.275883i	0.691960	−	0.721936i	$-0.256747\pi$
$31$	4.22026	+	1.53605i	0.757981	+	0.275883i	0.0660211	+	0.997818i	$0.478970\pi$
$32$	−1.57207	−	0.137538i	−0.277905	−	0.0243135i
$33$	0.601106	−	4.77337i	0.104639	−	0.830936i
$34$	3.75485	+	10.3164i	0.643952	+	1.76924i
$35$		0			0
$36$	−0.602668	−	0.589247i	−0.100445	−	0.0982079i
$37$	−2.08386	−	0.558369i	−0.342585	−	0.0917953i	0.0834245	−	0.996514i	$-0.473414\pi$
$37$	−2.08386	−	0.558369i	−0.342585	−	0.0917953i	−0.426009	+	0.904719i	$0.640081\pi$
$38$	8.81158	−	0.770913i	1.42943	−	0.125059i
$39$	0.0202409	−	0.532353i	0.00324114	−	0.0852446i
$40$		0			0
$41$	−4.62442	+	0.815410i	−0.722213	+	0.127346i	−0.522660	−	0.852541i	$-0.675060\pi$
$41$	−4.62442	+	0.815410i	−0.722213	+	0.127346i	−0.199553	+	0.979887i	$0.563949\pi$
$42$	2.85184	+	3.07728i	0.440049	+	0.474834i
$43$	0.429127	+	4.90494i	0.0654412	+	0.747997i	0.956046	+	0.293218i	$0.0947261\pi$
$43$	0.429127	+	4.90494i	0.0654412	+	0.747997i	−0.890604	+	0.454779i	$0.849718\pi$
$44$	0.390200	+	0.675847i	0.0588249	+	0.101888i
$45$		0			0
$46$	0.0971868	−	0.168333i	0.0143294	−	0.0248193i
$47$	7.69135	+	3.58654i	1.12190	+	0.523150i	0.892890	−	0.450274i	$-0.148674\pi$
$47$	7.69135	+	3.58654i	1.12190	+	0.523150i	0.229009	+	0.973424i	$0.426452\pi$
$48$	−7.70389	−	0.970146i	−1.11196	−	0.140028i
$49$	2.84600	+	3.39173i	0.406571	+	0.484533i
$50$		0			0
$51$	3.85358	+	11.9863i	0.539609	+	1.67841i
$52$	0.0495656	+	0.0707870i	0.00687352	+	0.00981640i
$53$	−0.483003	+	0.483003i	−0.0663456	+	0.0663456i	−0.739501	−	0.673155i	$-0.764938\pi$
$53$	−0.483003	+	0.483003i	−0.0663456	+	0.0663456i	0.673155	+	0.739501i	$0.264938\pi$
$54$	−5.39876	−	5.69554i	−0.734679	−	0.775064i
$55$		0			0
$56$	4.10079	+	0.723079i	0.547991	+	0.0966255i
$57$	10.1318	−	0.499526i	1.34198	−	0.0661638i
$58$	5.57450	+	11.9546i	0.731968	+	1.56971i
$59$	7.43127	−	6.23558i	0.967469	−	0.811803i	−0.0146830	−	0.999892i	$-0.504674\pi$
$59$	7.43127	−	6.23558i	0.967469	−	0.811803i	0.982152	+	0.188089i	$0.0602295\pi$
$60$		0			0
$61$	2.50049	−	0.910105i	0.320155	−	0.116527i	−0.176943	−	0.984221i	$-0.556621\pi$
$61$	2.50049	−	0.910105i	0.320155	−	0.116527i	0.497099	+	0.867694i	$0.334399\pi$
$62$	−6.55173	+	1.75553i	−0.832070	+	0.222952i
$63$	3.13415	+	3.65086i	0.394866	+	0.459965i
$64$	−5.70071	+	3.29131i	−0.712589	+	0.411413i
$65$		0			0
$66$	3.39133	+	6.42609i	0.417444	+	0.790997i
$67$	0.884390	+	0.619257i	0.108045	+	0.0756543i	0.626350	−	0.779542i	$-0.284548\pi$
$67$	0.884390	+	0.619257i	0.108045	+	0.0756543i	−0.518305	+	0.855196i	$0.673437\pi$
$68$	−1.67295	−	1.17142i	−0.202876	−	0.142055i
$69$	0.118712	−	0.188676i	0.0142912	−	0.0227139i
$70$		0			0
$71$	9.03942	−	5.21891i	1.07278	−	0.619371i	0.143842	−	0.989601i	$-0.454054\pi$
$71$	9.03942	−	5.21891i	1.07278	−	0.619371i	0.928940	+	0.370230i	$0.120721\pi$
$72$	−7.68515	−	1.26605i	−0.905703	−	0.149205i
$73$	6.65047	−	1.78199i	0.778378	−	0.208566i	0.152309	−	0.988333i	$-0.451329\pi$
$73$	6.65047	−	1.78199i	0.778378	−	0.208566i	0.626070	+	0.779767i	$0.284663\pi$
$74$	3.06175	−	1.11439i	0.355921	−	0.129545i
$75$		0			0
$76$	−1.26050	+	1.05768i	−0.144589	+	0.121325i
$77$	−1.88278	−	4.03763i	−0.214562	−	0.460130i
$78$	0.436116	+	0.676135i	0.0493804	+	0.0765572i
$79$	2.04188	+	0.360038i	0.229729	+	0.0405074i	0.287327	−	0.957832i	$-0.407233\pi$
$79$	2.04188	+	0.360038i	0.229729	+	0.0405074i	−0.0575985	+	0.998340i	$0.518344\pi$
$80$		0			0
$81$	−5.93887	−	6.76239i	−0.659874	−	0.751376i
$82$	5.01475	−	5.01475i	0.553787	−	0.553787i
$83$	−7.55956	−	10.7962i	−0.829770	−	1.18503i	−0.980512	−	0.196461i	$-0.937055\pi$
$83$	−7.55956	−	10.7962i	−0.829770	−	1.18503i	0.150742	−	0.988573i	$-0.451834\pi$
$84$	−0.762929	−	0.164636i	−0.0832423	−	0.0179633i
$85$		0			0
$86$	−4.77986	−	5.69642i	−0.515426	−	0.614261i
$87$	5.86754	+	13.9429i	0.629066	+	1.49484i
$88$	6.53585	+	3.04772i	0.696724	+	0.324888i
$89$	−5.58181	+	9.66798i	−0.591671	+	1.02480i	0.402337	+	0.915492i	$0.368198\pi$
$89$	−5.58181	+	9.66798i	−0.591671	+	1.02480i	−0.994007	+	0.109312i	$0.965135\pi$
$90$		0			0
$91$	−0.246656	−	0.427222i	−0.0258566	−	0.0447850i
$92$	0.00315146	+	0.0360214i	0.000328562	+	0.00375549i
$93$	−7.58484	+	1.72638i	−0.786511	+	0.179017i
$94$	−12.6222	+	2.22564i	−1.30189	+	0.229558i
$95$		0			0
$96$	2.41732	−	1.27573i	0.246717	−	0.130203i
$97$	11.8062	−	1.03291i	1.19874	−	0.104876i	0.529754	−	0.848151i	$-0.322284\pi$
$97$	11.8062	−	1.03291i	1.19874	−	0.104876i	0.668986	+	0.743275i	$0.266729\pi$
$98$	−6.45906	−	1.73070i	−0.652464	−	0.174827i
$99$	3.60649	+	7.51214i	0.362466	+	0.754999i
$100$		0			0
$101$	−4.61138	−	12.6697i	−0.458850	−	1.26068i	−0.926343	−	0.376682i	$-0.877065\pi$
$101$	−4.61138	−	12.6697i	−0.458850	−	1.26068i	0.467493	−	0.883997i	$-0.345157\pi$
$102$	−15.1507	−	11.4906i	−1.50015	−	1.13774i
$103$	−2.96335	−	0.259260i	−0.291988	−	0.0255456i	−0.0597791	−	0.998212i	$-0.519040\pi$
$103$	−2.96335	−	0.259260i	−0.291988	−	0.0255456i	−0.232209	+	0.972666i	$0.574595\pi$
$104$	0.750384	+	0.273118i	0.0735813	+	0.0267814i
$105$		0			0
$106$	0.179140	−	1.01596i	0.0173997	−	0.0986783i
$107$	−7.80800	−	7.80800i	−0.754828	−	0.754828i	0.220548	−	0.975376i	$-0.429215\pi$
$107$	−7.80800	−	7.80800i	−0.754828	−	0.754828i	−0.975376	+	0.220548i	$0.929215\pi$
$108$	1.43041	+	0.291861i	0.137642	+	0.0280843i
$109$			0.464359i			0.0444775i	0.999753	+	0.0222388i	$0.00707940\pi$
$109$			0.464359i			0.0444775i	−0.999753	+	0.0222388i	$0.992921\pi$
$110$		0			0
$111$	3.55735	−	1.14369i	0.337649	−	0.108554i
$112$	−6.51646	+	3.03868i	−0.615748	+	0.287128i
$113$	−0.0417367	+	0.477053i	−0.00392626	+	0.0448774i	−0.997905	−	0.0646950i	$-0.979393\pi$
$113$	−0.0417367	+	0.477053i	−0.00392626	+	0.0448774i	0.993979	+	0.109572i	$0.0349481\pi$
$114$	−12.1018	+	9.39475i	−1.13344	+	0.879899i
$115$		0			0
$116$	−2.12504	−	1.22689i	−0.197305	−	0.113914i
$117$	0.470332	+	0.793861i	0.0434822	+	0.0733924i
$118$	−3.79196	+	14.1518i	−0.349078	+	1.30278i
$119$	8.93114	+	7.49411i	0.818716	+	0.686984i
$120$		0			0
$121$	0.570356	+	3.23465i	0.0518506	+	0.294059i
$122$	−2.30510	+	3.29202i	−0.208694	+	0.298046i
$123$	5.96547	−	5.52845i	0.537888	−	0.498483i
$124$	0.811069	−	0.966595i	0.0728362	−	0.0868028i
$125$		0			0
$126$	−7.04003	−	1.80166i	−0.627175	−	0.160505i
$127$	−3.48210	−	12.9954i	−0.308987	−	1.15315i	−0.929459	−	0.368925i	$-0.879726\pi$
$127$	−3.48210	−	12.9954i	−0.308987	−	1.15315i	0.620473	−	0.784228i	$-0.286941\pi$
$128$	5.53535	−	11.8706i	0.489260	−	1.04922i
$129$	−5.22956	−	6.73643i	−0.460437	−	0.593110i
$130$		0			0
$131$	−2.11500	+	5.81092i	−0.184788	+	0.507702i	−0.997149	−	0.0754528i	$-0.975960\pi$
$131$	−2.11500	+	5.81092i	−0.184788	+	0.507702i	0.812361	+	0.583155i	$0.198182\pi$
$132$	−1.20246	−	0.617383i	−0.104661	−	0.0537363i
$133$	7.69460	−	5.38781i	0.667206	−	0.467183i
$134$	−1.63056			−0.140859
$135$		0			0
$136$	−18.8725			−1.61830
$137$	6.04873	−	4.23537i	0.516778	−	0.361852i	−0.285905	−	0.958258i	$-0.592294\pi$
$137$	6.04873	−	4.23537i	0.516778	−	0.361852i	0.802683	+	0.596406i	$0.203405\pi$
$138$	0.0165784	+	0.336257i	0.00141125	+	0.0286241i
$139$	3.50715	−	9.63582i	0.297473	−	0.817299i	−0.697448	−	0.716635i	$-0.745681\pi$
$139$	3.50715	−	9.63582i	0.297473	−	0.817299i	0.994921	−	0.100664i	$-0.0320966\pi$
$140$		0			0
$141$	−14.5622	+	2.00062i	−1.22636	+	0.168482i
$142$	−6.66218	+	14.2871i	−0.559078	+	1.19895i
$143$	−0.221121	−	0.825233i	−0.0184910	−	0.0690095i
$144$	12.1241	−	5.82064i	1.01034	−	0.485053i
$145$		0			0
$146$	−6.68396	+	7.96564i	−0.553169	+	0.659241i
$147$	−7.32674	−	2.26484i	−0.604300	−	0.186801i
$148$	−0.347659	+	0.496508i	−0.0285774	+	0.0408127i
$149$	−0.210055	−	1.19128i	−0.0172084	−	0.0975937i	0.974994	−	0.222232i	$-0.0713341\pi$
$149$	−0.210055	−	1.19128i	−0.0172084	−	0.0975937i	−0.992202	+	0.124638i	$0.960223\pi$
$150$		0			0
$151$	−12.3858	−	10.3930i	−1.00795	−	0.845766i	−0.0198800	−	0.999802i	$-0.506328\pi$
$151$	−12.3858	−	10.3930i	−1.00795	−	0.845766i	−0.988065	+	0.154036i	$0.950773\pi$
$152$	−3.93544	+	14.6873i	−0.319206	+	1.19129i
$153$	−16.8622	−	13.8285i	−1.36323	−	1.11797i
$154$	5.82693	+	3.36418i	0.469547	+	0.271093i
$155$		0			0
$156$	−0.138602	−	0.0564988i	−0.0110971	−	0.00452353i
$157$	1.80822	−	20.6680i	0.144311	−	1.64949i	−0.486596	−	0.873627i	$-0.661762\pi$
$157$	1.80822	−	20.6680i	0.144311	−	1.64949i	0.630907	−	0.775858i	$-0.282683\pi$
$158$	−2.83800	+	1.32338i	−0.225779	+	0.105282i
$159$	0.249565	−	1.15649i	0.0197918	−	0.0917156i
$160$		0			0
$161$		−	0.206419i		−	0.0162681i
$162$	13.2053	+	3.22148i	1.03750	+	0.253103i
$163$	−9.24417	−	9.24417i	−0.724060	−	0.724060i	0.245370	−	0.969430i	$-0.421091\pi$
$163$	−9.24417	−	9.24417i	−0.724060	−	0.724060i	−0.969430	+	0.245370i	$0.921091\pi$
$164$	−0.229094	+	1.29925i	−0.0178892	+	0.101455i
$165$		0			0
$166$	18.7046	+	6.80794i	1.45176	+	0.528398i
$167$	−16.0301	−	1.40245i	−1.24044	−	0.108525i	−0.552018	−	0.833832i	$-0.686142\pi$
$167$	−16.0301	−	1.40245i	−1.24044	−	0.108525i	−0.688425	+	0.725307i	$0.741698\pi$
$168$	−6.64769	+	2.79751i	−0.512880	+	0.215833i
$169$	4.41391	+	12.1271i	0.339531	+	0.932854i
$170$		0			0
$171$	−14.2781	+	10.2392i	−1.09188	+	0.783009i
$172$	1.33620	+	0.358033i	0.101884	+	0.0272997i
$173$	2.64260	−	0.231197i	0.200913	−	0.0175776i	0.0137449	−	0.999906i	$-0.495625\pi$
$173$	2.64260	−	0.231197i	0.200913	−	0.0175776i	0.187168	+	0.982328i	$0.440069\pi$
$174$	−19.3373	−	12.1667i	−1.46596	−	0.922355i
$175$		0			0
$176$	−12.2630	+	2.16231i	−0.924362	+	0.162990i
$177$	−4.96226	+	16.0529i	−0.372987	+	1.20661i
$178$	−1.46947	−	16.7961i	−0.110141	−	1.25892i
$179$	−3.43088	−	5.94245i	−0.256436	−	0.444160i	0.708849	−	0.705360i	$-0.249215\pi$
$179$	−3.43088	−	5.94245i	−0.256436	−	0.444160i	−0.965284	+	0.261201i	$0.915882\pi$
$180$		0			0
$181$	10.0120	−	17.3412i	0.744183	−	1.28896i	−0.206392	−	0.978469i	$-0.566172\pi$
$181$	10.0120	−	17.3412i	0.744183	−	1.28896i	0.950575	−	0.310494i	$-0.100494\pi$
$182$	0.675238	+	0.314868i	0.0500519	+	0.0233396i
$183$	−2.78511	+	3.67225i	−0.205881	+	0.271460i
$184$	0.214779	+	0.255964i	0.0158337	+	0.0188699i
$185$		0			0
$186$	7.88810	−	8.70625i	0.578384	−	0.638373i
$187$	11.5812	+	16.5397i	0.846903	+	1.20950i
$188$	1.68597	−	1.68597i	0.122962	−	0.122962i
$189$	−7.98944	−	2.37148i	−0.581146	−	0.172500i
$190$		0			0
$191$	9.22577	+	1.62675i	0.667553	+	0.117708i	0.497147	−	0.867666i	$-0.334381\pi$
$191$	9.22577	+	1.62675i	0.667553	+	0.117708i	0.170406	+	0.985374i	$0.445492\pi$
$192$	5.20757	−	10.1427i	0.375824	−	0.731984i
$193$	−8.90711	−	19.1014i	−0.641148	−	1.37495i	−0.911146	−	0.412085i	$-0.864801\pi$
$193$	−8.90711	−	19.1014i	−0.641148	−	1.37495i	0.269998	−	0.962861i	$-0.412977\pi$
$194$	−13.7113	+	11.5052i	−0.984414	+	0.826022i
$195$		0			0
$196$	1.16893	−	0.425457i	0.0834953	−	0.0303898i
$197$	−7.09801	+	1.90191i	−0.505712	+	0.135505i	−0.502650	−	0.864490i	$-0.667642\pi$
$197$	−7.09801	+	1.90191i	−0.505712	+	0.135505i	−0.00306257	+	0.999995i	$0.500975\pi$
$198$	−10.9693	−	6.16948i	−0.779552	−	0.438446i
$199$	22.3449	−	12.9008i	1.58399	−	0.914516i	0.589718	−	0.807609i	$-0.299239\pi$
$199$	22.3449	−	12.9008i	1.58399	−	0.914516i	0.994269	−	0.106906i	$-0.0340945\pi$
$200$		0			0
$201$	−1.86864	−	0.0710490i	−0.131804	−	0.00501141i
$202$	16.6802	+	11.6796i	1.17362	+	0.821776i
$203$	11.4745	+	8.03453i	0.805352	+	0.563914i
$204$	3.53481	+	0.134400i	0.247486	+	0.00940985i
$205$		0			0
$206$	3.89070	−	2.24630i	0.271078	−	0.156507i
$207$	0.00434728	+	0.386076i	0.000302157	+	0.0268341i
$208$	−1.33187	+	0.356874i	−0.0923487	+	0.0247448i
$209$	15.2868	−	5.56395i	1.05741	−	0.384867i
$210$		0			0
$211$	−0.268205	+	0.225051i	−0.0184640	+	0.0154932i	−0.651973	−	0.758242i	$-0.726058\pi$
$211$	−0.268205	+	0.225051i	−0.0184640	+	0.0154932i	0.633509	+	0.773735i	$0.281614\pi$
$212$	0.0811054	+	0.173931i	0.00557035	+	0.0119456i
$213$	−8.25747	+	16.0829i	−0.565792	+	1.10198i
$214$	16.4235	+	2.89590i	1.12268	+	0.197960i
$215$		0			0
$216$	12.3746	−	5.37234i	0.841986	−	0.365542i
$217$	−5.09341	+	5.09341i	−0.345763	+	0.345763i
$218$	−0.402257	−	0.574483i	−0.0272443	−	0.0389089i
$219$	−8.00698	+	8.83746i	−0.541062	+	0.597180i
$220$		0			0
$221$	1.43715	+	1.71273i	0.0966733	+	0.115211i
$222$	−3.41025	+	4.49652i	−0.228881	+	0.301786i
$223$	14.2401	+	6.64028i	0.953590	+	0.444666i	0.836203	−	0.548420i	$-0.184770\pi$
$223$	14.2401	+	6.64028i	0.953590	+	0.444666i	0.117387	+	0.993086i	$0.462548\pi$
$224$	1.26551	−	2.19193i	0.0845557	−	0.146455i
$225$		0			0
$226$	−0.361618	−	0.626342i	−0.0240545	−	0.0416636i
$227$	2.05222	+	23.4570i	0.136211	+	1.55690i	0.689733	+	0.724064i	$0.257728\pi$
$227$	2.05222	+	23.4570i	0.136211	+	1.55690i	−0.553522	+	0.832834i	$0.686717\pi$
$228$	0.841703	−	2.72290i	0.0557431	−	0.180328i
$229$	−22.8004	+	4.02032i	−1.50669	+	0.265671i	−0.865188	−	0.501448i	$-0.832801\pi$
$229$	−22.8004	+	4.02032i	−1.50669	+	0.265671i	−0.641505	+	0.767119i	$0.721690\pi$
$230$		0			0
$231$	6.53113	+	4.10928i	0.429717	+	0.270371i
$232$	−22.5886	+	1.97625i	−1.48301	+	0.129747i
$233$	20.8931	+	5.59828i	1.36875	+	0.366755i	0.867022	−	0.498270i	$-0.166031\pi$
$233$	20.8931	+	5.59828i	1.36875	+	0.366755i	0.501728	+	0.865026i	$0.332698\pi$
$234$	−1.26956	−	0.574694i	−0.0829940	−	0.0375689i
$235$		0			0
$236$	−0.932175	−	2.56113i	−0.0606794	−	0.166715i
$237$	−3.31004	+	1.39295i	−0.215010	+	0.0904816i
$238$	−17.5410	−	1.53464i	−1.13702	−	0.0994761i
$239$	−13.3597	−	4.86252i	−0.864165	−	0.314530i	−0.128363	−	0.991727i	$-0.540972\pi$
$239$	−13.3597	−	4.86252i	−0.864165	−	0.314530i	−0.735802	+	0.677197i	$0.763195\pi$
$240$		0			0
$241$	−1.44826	+	8.21348i	−0.0932905	+	0.529077i	0.901967	+	0.431804i	$0.142123\pi$
$241$	−1.44826	+	8.21348i	−0.0932905	+	0.529077i	−0.995258	+	0.0972724i	$0.968988\pi$
$242$	−3.50767	−	3.50767i	−0.225482	−	0.225482i
$243$	14.9930	+	4.26724i	0.961803	+	0.273744i
$244$		−	0.747612i		−	0.0478610i
$245$		0			0
$246$	−2.59110	+	12.0072i	−0.165202	+	0.765550i
$247$	1.63260	−	0.761293i	0.103880	−	0.0484399i
$248$	1.01624	−	11.6156i	0.0645311	−	0.737594i
$249$	21.1391	+	8.61699i	1.33963	+	0.546079i
$250$		0			0
$251$	4.13040	+	2.38469i	0.260708	+	0.150520i	0.624658	−	0.780899i	$-0.285239\pi$
$251$	4.13040	+	2.38469i	0.260708	+	0.150520i	−0.363949	+	0.931419i	$0.618572\pi$
$252$	1.26504	−	0.476633i	0.0796898	−	0.0300251i
$253$	0.0925243	−	0.345305i	0.00581695	−	0.0217092i
$254$	15.5653	+	13.0608i	0.976654	+	0.819510i
$255$		0			0
$256$	1.14887	+	6.51557i	0.0718045	+	0.407223i
$257$	2.70759	−	3.86684i	0.168895	−	0.241207i	−0.725778	−	0.687929i	$-0.758520\pi$
$257$	2.70759	−	3.86684i	0.168895	−	0.241207i	0.894673	+	0.446722i	$0.147409\pi$
$258$	12.3053	+	3.80381i	0.766093	+	0.236815i
$259$	2.22414	−	2.65063i	0.138202	−	0.164702i
$260$		0			0
$261$	−21.6306	−	14.7858i	−1.33890	−	0.915215i
$262$	−2.41720	−	9.02113i	−0.149335	−	0.557327i
$263$	−1.40761	+	3.01862i	−0.0867967	+	0.186136i	−0.944915	−	0.327316i	$-0.893856\pi$
$263$	−1.40761	+	3.01862i	−0.0867967	+	0.186136i	0.858118	+	0.513452i	$0.171634\pi$
$264$	−12.3745	+	1.70006i	−0.761596	+	0.104631i
$265$		0			0
$266$	−4.85212	+	13.3311i	−0.297502	+	0.817381i
$267$	−0.952164	−	19.3125i	−0.0582715	−	1.18191i
$268$	0.248474	−	0.173983i	0.0151780	−	0.0106277i
$269$	−8.37429			−0.510589			−0.255295	−	0.966863i	$-0.582172\pi$
$269$	−8.37429			−0.510589			−0.255295	+	0.966863i	$0.582172\pi$
$270$		0			0
$271$	−13.7893			−0.837641			−0.418821	−	0.908069i	$-0.637556\pi$
$271$	−13.7893			−0.837641			−0.418821	+	0.908069i	$0.637556\pi$
$272$	26.6940	−	18.6913i	1.61856	−	1.13333i
$273$	0.760109	+	0.390265i	0.0460039	+	0.0236199i
$274$	−3.81425	+	10.4796i	−0.230428	+	0.633094i
$275$		0			0
$276$	−0.0384053	−	0.0494716i	−0.00231173	−	0.00297784i
$277$	−0.0519757	+	0.111462i	−0.00312292	+	0.00669711i	−0.907863	−	0.419267i	$-0.862287\pi$
$277$	−0.0519757	+	0.111462i	−0.00312292	+	0.00669711i	0.904740	+	0.425964i	$0.140065\pi$
$278$	4.00827	+	14.9591i	0.240400	+	0.897186i
$279$	9.41921	−	9.63375i	0.563913	−	0.576757i
$280$		0			0
$281$	15.4444	−	18.4059i	0.921334	−	1.09800i	−0.0735813	−	0.997289i	$-0.523443\pi$
$281$	15.4444	−	18.4059i	0.921334	−	1.09800i	0.994915	−	0.100714i	$-0.0321127\pi$
$282$	16.2826	−	15.0898i	0.969614	−	0.898582i
$283$	9.14396	−	13.0589i	0.543552	−	0.776273i	−0.449584	−	0.893238i	$-0.648428\pi$
$283$	9.14396	−	13.0589i	0.543552	−	0.776273i	0.993136	+	0.116965i	$0.0373166\pi$
$284$	−0.509233	−	2.88801i	−0.0302174	−	0.171372i
$285$		0			0
$286$	0.988429	+	0.829390i	0.0584470	+	0.0490429i
$287$	1.94927	−	7.27478i	0.115062	−	0.429417i
$288$	−2.32079	+	4.12634i	−0.136754	+	0.243147i
$289$	−31.0386	−	17.9202i	−1.82580	−	1.05413i
$290$		0			0
$291$	−16.2146	+	12.5876i	−0.950518	+	0.737897i
$292$	0.168594	−	1.92703i	0.00986619	−	0.112771i
$293$	4.77657	−	2.22735i	0.279050	−	0.130123i	−0.278055	−	0.960565i	$-0.589690\pi$
$293$	4.77657	−	2.22735i	0.279050	−	0.130123i	0.557105	+	0.830442i	$0.311912\pi$
$294$	11.0262	−	3.54493i	0.643063	−	0.206744i
$295$		0			0
$296$			5.60107i			0.325555i
$297$	−12.3021	−	7.54826i	−0.713838	−	0.437994i
$298$	1.29183	+	1.29183i	0.0748340	+	0.0748340i
$299$	0.00687388	−	0.0389837i	0.000397526	−	0.00225448i
$300$		0			0
$301$	−7.42071	−	2.70092i	−0.427723	−	0.155678i
$302$	24.3262	+	2.12827i	1.39981	+	0.122468i
$303$	18.6068	+	14.1118i	1.06893	+	0.810701i
$304$	−8.97985	−	24.6719i	−0.515030	−	1.41503i
$305$		0			0
$306$	32.8403	+	2.50090i	1.87735	+	0.142967i
$307$	21.3785	+	5.72834i	1.22013	+	0.326934i	0.810730	−	0.585420i	$-0.199070\pi$
$307$	21.3785	+	5.72834i	1.22013	+	0.326934i	0.409403	+	0.912353i	$0.365737\pi$
$308$	−1.24690	+	0.109090i	−0.0710487	+	0.00621596i
$309$	4.55666	−	2.40475i	0.259220	−	0.136801i
$310$		0			0
$311$	14.1711	−	2.49874i	0.803567	−	0.141691i	0.243244	−	0.969965i	$-0.421788\pi$
$311$	14.1711	−	2.49874i	0.803567	−	0.141691i	0.560322	+	0.828275i	$0.310677\pi$
$312$	−1.34862	+	0.306959i	−0.0763508	+	0.0173781i
$313$	1.85245	+	21.1736i	0.104707	+	1.19680i	0.848795	+	0.528722i	$0.177329\pi$
$313$	1.85245	+	21.1736i	0.104707	+	1.19680i	−0.744088	+	0.668081i	$0.767116\pi$
$314$	15.6669	+	27.1358i	0.884133	+	1.53136i
$315$		0			0
$316$	0.291263	−	0.504482i	0.0163848	−	0.0283793i
$317$	−20.8348	−	9.71542i	−1.17020	−	0.545672i	−0.262350	−	0.964973i	$-0.584498\pi$
$317$	−20.8348	−	9.71542i	−1.17020	−	0.545672i	−0.907848	+	0.419300i	$0.862275\pi$
$318$	0.693074	+	1.64694i	0.0388657	+	0.0923559i
$319$	15.5936	+	18.5838i	0.873076	+	1.04049i
$320$		0			0
$321$	18.6953	+	4.03435i	1.04347	+	0.225176i
$322$	0.178813	+	0.255371i	0.00996485	+	0.0142313i
$323$	−30.1036	+	30.1036i	−1.67501	+	1.67501i
$324$	−2.35603	+	0.918115i	−0.130890	+	0.0510064i
$325$		0			0
$326$	19.4443	+	3.42856i	1.07692	+	0.189890i
$327$	−0.435959	−	0.675891i	−0.0241086	−	0.0373768i
$328$	5.15228	+	11.0491i	0.284487	+	0.610085i
$329$	−10.4268	+	8.74912i	−0.574848	+	0.482355i
$330$		0			0
$331$	13.1133	−	4.77285i	0.720772	−	0.262340i	0.0445184	−	0.999009i	$-0.485825\pi$
$331$	13.1133	−	4.77285i	0.720772	−	0.262340i	0.676253	+	0.736669i	$0.263602\pi$
$332$	−3.57673	+	0.958382i	−0.196298	+	0.0525980i
$333$	−4.10411	+	5.00446i	−0.224904	+	0.274243i
$334$	21.0465	−	12.1512i	1.15161	−	0.664884i
$335$		0			0
$336$	6.63211	−	10.5408i	0.361811	−	0.575049i
$337$	−11.8702	−	8.31162i	−0.646612	−	0.452763i	0.203705	−	0.979032i	$-0.434701\pi$
$337$	−11.8702	−	8.31162i	−0.646612	−	0.452763i	−0.850318	+	0.526269i	$0.823590\pi$
$338$	−15.9659	−	11.1795i	−0.868432	−	0.608083i
$339$	−0.387127	−	0.733551i	−0.0210258	−	0.0398410i
$340$		0			0
$341$	−10.8035	+	6.23741i	−0.585043	+	0.337775i
$342$	8.79441	−	25.0360i	0.475547	−	1.35379i
$343$	−17.7039	+	4.74374i	−0.955920	+	0.256138i
$344$	12.0122	−	4.37207i	0.647652	−	0.235726i
$345$		0			0
$346$	−3.06901	+	2.57521i	−0.164991	+	0.138444i
$347$	3.83685	+	8.22815i	0.205973	+	0.441710i	0.981973	−	0.189023i	$-0.0605320\pi$
$347$	3.83685	+	8.22815i	0.205973	+	0.441710i	−0.776000	+	0.630733i	$0.782754\pi$
$348$	4.24492	−	0.209287i	0.227552	−	0.0112190i
$349$	8.20842	+	1.44737i	0.439387	+	0.0774757i	0.388966	−	0.921252i	$-0.372833\pi$
$349$	8.20842	+	1.44737i	0.439387	+	0.0774757i	0.0504212	+	0.998728i	$0.483944\pi$
$350$		0			0
$351$	−1.42989	−	0.713925i	−0.0763220	−	0.0381065i
$352$	3.09950	−	3.09950i	0.165204	−	0.165204i
$353$	1.51501	+	2.16366i	0.0806358	+	0.115160i	0.857444	−	0.514578i	$-0.172051\pi$
$353$	1.51501	+	2.16366i	0.0806358	+	0.115160i	−0.776808	+	0.629738i	$0.783162\pi$
$354$	−7.76693	−	24.1585i	−0.412808	−	1.28401i
$355$		0			0
$356$	2.01609	+	2.40268i	0.106852	+	0.127342i
$357$	−20.0353	−	2.52304i	−1.06038	−	0.133533i
$358$	9.39224	+	4.37967i	0.496395	+	0.231473i
$359$	−7.06131	+	12.2306i	−0.372682	+	0.645504i	−0.989977	−	0.141228i	$-0.954895\pi$
$359$	−7.06131	+	12.2306i	−0.372682	+	0.645504i	0.617295	+	0.786732i	$0.288228\pi$
$360$		0			0
$361$	7.65033	+	13.2508i	0.402649	+	0.697408i
$362$	2.63575	+	30.1267i	0.138532	+	1.58342i
$363$	−3.86699	−	4.17267i	−0.202964	−	0.219009i
$364$	−0.136493	+	0.0240674i	−0.00715418	+	0.00126148i
$365$		0			0
$366$	0.264470	−	6.95577i	0.0138241	−	0.363584i
$367$	13.7173	−	1.20011i	0.716037	−	0.0626451i	0.276686	−	0.960961i	$-0.410764\pi$
$367$	13.7173	−	1.20011i	0.716037	−	0.0626451i	0.439351	+	0.898315i	$0.355208\pi$
$368$	−0.557300	−	0.149328i	−0.0290513	−	0.00778426i
$369$	−3.49262	+	13.6475i	−0.181818	+	0.710458i
$370$		0			0
$371$	−0.374703	−	1.02949i	−0.0194536	−	0.0534483i
$372$	−0.273062	+	2.16838i	−0.0141576	+	0.112425i
$373$	20.2366	+	1.77048i	1.04781	+	0.0916718i	0.598036	−	0.801469i	$-0.295948\pi$
$373$	20.2366	+	1.77048i	1.04781	+	0.0916718i	0.449777	+	0.893141i	$0.351503\pi$
$374$	−28.6555	−	10.4297i	−1.48174	−	0.539309i
$375$		0			0
$376$	3.82598	−	21.6982i	0.197310	−	1.11900i
$377$	1.89949	+	1.89949i	0.0978286	+	0.0978286i
$378$	11.9385	−	3.98707i	0.614049	−	0.205073i
$379$		−	20.8542i		−	1.07121i	−0.844469	−	0.535605i	$-0.820084\pi$
$379$		−	20.8542i		−	1.07121i	0.844469	−	0.535605i	$-0.179916\pi$
$380$		0			0
$381$	17.2689	+	15.6461i	0.884712	+	0.801573i
$382$	−12.8229	+	5.97940i	−0.656075	+	0.305933i
$383$	−1.27835	+	14.6116i	−0.0653206	+	0.746618i	0.890944	+	0.454114i	$0.150044\pi$
$383$	−1.27835	+	14.6116i	−0.0653206	+	0.746618i	−0.956264	+	0.292504i	$0.905512\pi$
$384$	3.08769	+	22.4749i	0.157568	+	1.14692i
$385$		0			0
$386$	27.5662	+	15.9154i	1.40308	+	0.810071i
$387$	13.9362	+	4.89539i	0.708419	+	0.248847i
$388$	0.861786	−	3.21623i	0.0437506	−	0.163279i
$389$	−4.79561	−	4.02400i	−0.243147	−	0.204025i	0.513067	−	0.858348i	$-0.328509\pi$
$389$	−4.79561	−	4.02400i	−0.243147	−	0.204025i	−0.756215	+	0.654323i	$0.772953\pi$
$390$		0			0
$391$	0.162455	+	0.921326i	0.00821568	+	0.0465934i
$392$	6.59332	−	9.41624i	0.333013	−	0.475592i
$393$	−2.37706	−	10.4436i	−0.119907	−	0.526812i
$394$	7.13377	−	8.50169i	0.359394	−	0.428309i
$395$		0			0
$396$	2.32985	−	0.230297i	0.117079	−	0.0115728i
$397$	−0.120732	−	0.450577i	−0.00605935	−	0.0226138i	0.962830	−	0.270108i	$-0.0870595\pi$
$397$	−0.120732	−	0.450577i	−0.00605935	−	0.0226138i	−0.968889	+	0.247494i	$0.920393\pi$
$398$	−16.4685	+	35.3168i	−0.825492	+	1.77027i
$399$	−6.14146	+	15.0661i	−0.307457	+	0.754250i
$400$		0			0
$401$	3.19304	−	8.77280i	0.159453	−	0.438093i	−0.834079	−	0.551644i	$-0.814001\pi$
$401$	3.19304	−	8.77280i	0.159453	−	0.438093i	0.993532	+	0.113552i	$0.0362228\pi$
$402$	2.37334	−	1.53084i	0.118372	−	0.0763513i
$403$	−1.13154	+	0.792314i	−0.0563661	+	0.0394680i
$404$	−3.78805			−0.188463
$405$		0			0
$406$	−21.1557			−1.04994
$407$	4.90874	−	3.43714i	0.243317	−	0.170373i
$408$	27.4695	−	17.7182i	1.35994	−	0.877182i
$409$	−0.240362	+	0.660389i	−0.0118851	+	0.0326541i	−0.945493	−	0.325641i	$-0.894420\pi$
$409$	−0.240362	+	0.660389i	−0.0118851	+	0.0326541i	0.933608	+	0.358296i	$0.116642\pi$
$410$		0			0
$411$	−4.82780	+	11.8435i	−0.238138	+	0.584197i
$412$	−0.353203	+	0.757446i	−0.0174010	+	0.0373167i
$413$	4.02694	+	15.0288i	0.198153	+	0.739517i
$414$	−0.339821	−	0.473869i	−0.0167013	−	0.0232894i
$415$		0			0
$416$	0.311994	−	0.371820i	0.0152968	−	0.0182300i
$417$	3.94171	+	17.3179i	0.193026	+	0.848062i
$418$	−14.0923	+	20.1259i	−0.689276	+	0.984389i
$419$	−3.72329	−	21.1158i	−0.181894	−	1.03157i	−0.929881	−	0.367861i	$-0.880090\pi$
$419$	−3.72329	−	21.1158i	−0.181894	−	1.03157i	0.747986	−	0.663714i	$-0.231021\pi$
$420$		0			0
$421$	13.6486	+	11.4526i	0.665194	+	0.558164i	0.911638	−	0.410993i	$-0.134818\pi$
$421$	13.6486	+	11.4526i	0.665194	+	0.558164i	−0.246445	+	0.969157i	$0.579262\pi$
$422$	0.136857	−	0.510759i	0.00666211	−	0.0248633i
$423$	19.3175	−	16.5835i	0.939251	−	0.806319i
$424$	1.53582	+	0.886708i	0.0745862	+	0.0430623i
$425$		0			0
$426$	−3.71625	−	27.0501i	−0.180053	−	1.31058i
$427$	−0.371968	+	4.25162i	−0.0180008	+	0.205750i
$428$	−2.81169	+	1.31111i	−0.135908	+	0.0633750i
$429$	1.09661	+	0.993559i	0.0529449	+	0.0479695i
$430$		0			0
$431$		−	13.6942i		−	0.659624i	−0.944047	−	0.329812i	$-0.893015\pi$
$431$		−	13.6942i		−	0.659624i	0.944047	−	0.329812i	$-0.106985\pi$
$432$	−12.1824	+	19.8547i	−0.586126	+	0.955261i
$433$	−22.8337	−	22.8337i	−1.09732	−	1.09732i	−0.994723	−	0.102594i	$-0.967286\pi$
$433$	−22.8337	−	22.8337i	−1.09732	−	1.09732i	−0.102594	−	0.994723i	$-0.532714\pi$
$434$	1.88909	−	10.7136i	0.0906791	−	0.514267i
$435$		0			0
$436$	0.122596	+	0.0446213i	0.00587129	+	0.00213697i
$437$	0.750887	+	0.0656941i	0.0359198	+	0.00314257i
$438$	2.25028	−	17.8694i	0.107523	−	0.853834i
$439$	3.85214	+	10.5837i	0.183852	+	0.505130i	0.997041	−	0.0768697i	$-0.0244925\pi$
$439$	3.85214	+	10.5837i	0.183852	+	0.505130i	−0.813189	+	0.582000i	$0.802270\pi$
$440$		0			0
$441$	12.7907	−	3.58208i	0.609079	−	0.170575i
$442$	−3.26165	−	0.873956i	−0.155141	−	0.0415699i
$443$	−6.73147	+	0.588927i	−0.319822	+	0.0279808i	−0.245936	−	0.969286i	$-0.579095\pi$
$443$	−6.73147	+	0.588927i	−0.319822	+	0.0279808i	−0.0738853	+	0.997267i	$0.523540\pi$
$444$	0.0398878	−	1.04908i	0.00189299	−	0.0497872i
$445$		0			0
$446$	−23.3694	+	4.12066i	−1.10657	+	0.195119i
$447$	1.42417	+	1.53674i	0.0673607	+	0.0726855i
$448$	−0.920162	−	10.5175i	−0.0434736	−	0.496905i
$449$	−5.70190	−	9.87598i	−0.269089	−	0.466076i	0.699538	−	0.714596i	$-0.253389\pi$
$449$	−5.70190	−	9.87598i	−0.269089	−	0.466076i	−0.968627	+	0.248519i	$0.920056\pi$
$450$		0			0
$451$	6.52164	−	11.2958i	0.307092	−	0.531899i
$452$	0.121937	+	0.0568601i	0.00573542	+	0.00267447i
$453$	27.7853	+	3.49899i	1.30547	+	0.164397i
$454$	−22.8589	−	27.2421i	−1.07282	−	1.27854i
$455$		0			0
$456$	−8.06081	−	25.0725i	−0.377482	−	1.17413i
$457$	4.25450	+	6.07605i	0.199017	+	0.284226i	0.906239	−	0.422766i	$-0.138941\pi$
$457$	4.25450	+	6.07605i	0.199017	+	0.284226i	−0.707222	+	0.706992i	$0.750052\pi$
$458$	24.7249	−	24.7249i	1.15532	−	1.15532i
$459$	37.5263	+	4.29701i	1.75158	+	0.200567i
$460$		0			0
$461$	−41.0458	−	7.23749i	−1.91170	−	0.337083i	−0.914046	−	0.405611i	$-0.867059\pi$
$461$	−41.0458	−	7.23749i	−1.91170	−	0.337083i	−0.997649	+	0.0685275i	$0.978170\pi$
$462$	−11.6397	+	0.573873i	−0.541529	+	0.0266990i
$463$	−1.40671	−	3.01669i	−0.0653752	−	0.140198i	0.870905	−	0.491451i	$-0.163533\pi$
$463$	−1.40671	−	3.01669i	−0.0653752	−	0.140198i	−0.936280	+	0.351253i	$0.885756\pi$
$464$	29.9930	−	25.1671i	1.39239	−	1.16835i
$465$		0			0
$466$	−30.6975	+	11.1730i	−1.42203	+	0.517577i
$467$	4.32129	−	1.15789i	0.199966	−	0.0535806i	−0.157446	−	0.987528i	$-0.550326\pi$
$467$	4.32129	−	1.15789i	0.199966	−	0.0535806i	0.357412	+	0.933947i	$0.383659\pi$
$468$	0.254784	−	0.0478892i	0.0117774	−	0.00221368i
$469$	−1.49962	+	0.865804i	−0.0692458	+	0.0399791i
$470$		0			0
$471$	16.7720	+	31.7806i	0.772813	+	1.46437i
$472$	−20.6309	−	14.4459i	−0.949616	−	0.664929i
$473$	−11.2030	−	7.84443i	−0.515115	−	0.360687i
$474$	2.88836	−	4.59065i	0.132667	−	0.210855i
$475$		0			0
$476$	2.83674	−	1.63780i	0.130022	−	0.0750682i
$477$	0.722508	+	1.91761i	0.0330814	+	0.0878015i
$478$	20.7402	−	5.55731i	0.948632	−	0.254185i
$479$	−34.5314	+	12.5684i	−1.57778	+	0.574264i	−0.974719	−	0.223432i	$-0.928274\pi$
$479$	−34.5314	+	12.5684i	−1.57778	+	0.574264i	−0.603059	+	0.797697i	$0.706052\pi$
$480$		0			0
$481$	0.508314	−	0.426526i	0.0231771	−	0.0194479i
$482$	−5.32332	−	11.4159i	−0.242470	−	0.519980i
$483$	0.193794	+	0.300450i	0.00881793	+	0.0136709i
$484$	0.908792	+	0.160244i	0.0413087	+	0.00728384i
$485$		0			0
$486$	−22.2452	+	7.70867i	−1.00906	+	0.349672i
$487$	−9.05628	+	9.05628i	−0.410379	+	0.410379i	−0.881871	−	0.471492i	$-0.843716\pi$
$487$	−9.05628	+	9.05628i	−0.410379	+	0.410379i	0.471492	+	0.881871i	$0.343716\pi$
$488$	−3.96257	−	5.65913i	−0.179377	−	0.256177i
$489$	22.1340	+	4.77642i	1.00093	+	0.215997i
$490$		0			0
$491$	14.7648	+	17.5960i	0.666326	+	0.794096i	0.988279	−	0.152660i	$-0.0487838\pi$
$491$	14.7648	+	17.5960i	0.666326	+	0.794096i	−0.321953	+	0.946756i	$0.604339\pi$
$492$	−0.886338	−	2.10619i	−0.0399592	−	0.0949545i
$493$	−57.5384	−	26.8306i	−2.59140	−	1.20839i
$494$	−1.36029	+	2.35609i	−0.0612024	+	0.106006i
$495$		0			0
$496$	10.0668	+	17.4361i	0.452011	+	0.782906i
$497$	1.45907	+	16.6772i	0.0654482	+	0.748076i
$498$	−33.6168	+	7.65148i	−1.50641	+	0.342871i
$499$	−9.11992	+	1.60809i	−0.408264	+	0.0719879i	−0.374009	−	0.927425i	$-0.622017\pi$
$499$	−9.11992	+	1.60809i	−0.408264	+	0.0719879i	−0.0342550	+	0.999413i	$0.510906\pi$
$500$		0			0
$501$	24.6490	−	13.0083i	1.10124	−	0.581170i
$502$	−7.17569	+	0.627792i	−0.320267	+	0.0280197i
$503$	−8.31780	−	2.22875i	−0.370873	−	0.0993750i	0.0685686	−	0.997646i	$-0.478157\pi$
$503$	−8.31780	−	2.22875i	−0.370873	−	0.0993750i	−0.439441	+	0.898271i	$0.644823\pi$
$504$	7.04953	−	10.3130i	0.314011	−	0.459377i
$505$		0			0
$506$	0.184659	+	0.507345i	0.00820908	+	0.0225543i
$507$	−17.8100	−	13.5075i	−0.790970	−	0.599888i
$508$	−3.76553	−	0.329441i	−0.167068	−	0.0146166i
$509$	20.6614	+	7.52013i	0.915799	+	0.333324i	0.756566	−	0.653917i	$-0.226876\pi$
$509$	20.6614	+	7.52013i	0.915799	+	0.333324i	0.159233	+	0.987241i	$0.449098\pi$
$510$		0			0
$511$	−1.91756	+	10.8750i	−0.0848278	+	0.481082i
$512$	11.4575	+	11.4575i	0.506354	+	0.506354i
$513$	11.1694	−	28.3083i	0.493141	−	1.24984i
$514$			7.12936i			0.314463i
$515$		0			0
$516$	−2.28102	+	0.733345i	−0.100416	+	0.0322837i
$517$	−21.3640	+	9.96221i	−0.939589	+	0.438138i
$518$	−0.455459	+	5.20593i	−0.0200117	+	0.228735i
$519$	−3.62933	+	2.81749i	−0.159310	+	0.123674i
$520$		0			0
$521$	−4.43677	−	2.56157i	−0.194378	−	0.112224i	0.399652	−	0.916667i	$-0.369131\pi$
$521$	−4.43677	−	2.56157i	−0.194378	−	0.112224i	−0.594031	+	0.804442i	$0.702464\pi$
$522$	39.5687	−	0.445550i	1.73187	−	0.0195012i
$523$	−2.02890	+	7.57196i	−0.0887177	+	0.331099i	−0.995992	−	0.0894400i	$-0.971492\pi$
$523$	−2.02890	+	7.57196i	−0.0887177	+	0.331099i	0.907275	+	0.420539i	$0.138159\pi$
$524$	1.33091	+	1.11677i	0.0581412	+	0.0487863i
$525$		0			0
$526$	−0.873497	−	4.95385i	−0.0380863	−	0.215998i
$527$	18.7252	−	26.7424i	0.815685	−	1.16492i
$528$	15.8192	−	14.6603i	0.688443	−	0.638009i
$529$	−14.7735	+	17.6063i	−0.642325	+	0.765493i
$530$		0			0
$531$	−7.84832	−	28.0243i	−0.340588	−	1.21615i
$532$	−0.683053	−	2.54919i	−0.0296141	−	0.110521i
$533$	0.610389	−	1.30898i	0.0264389	−	0.0566984i
$534$	17.9077	+	23.0677i	0.774941	+	0.998236i
$535$		0			0
$536$	0.958687	−	2.63397i	0.0414090	−	0.113770i
$537$	10.5728	+	5.42840i	0.456248	+	0.234253i
$538$	10.3603	−	7.25433i	0.446663	−	0.312757i
$539$	−12.2984			−0.529729
$540$		0			0
$541$	−12.2903			−0.528401			−0.264200	−	0.964468i	$-0.585108\pi$
$541$	−12.2903			−0.528401			−0.264200	+	0.964468i	$0.585108\pi$
$542$	17.0595	−	11.9452i	0.732767	−	0.513089i
$543$	1.70787	+	34.6404i	0.0732919	+	1.48656i
$544$	−3.92339	+	10.7794i	−0.168214	+	0.462164i
$545$		0			0
$546$	−1.27844	+	0.175638i	−0.0547123	+	0.00751660i
$547$	0.220177	−	0.472172i	0.00941410	−	0.0201886i	−0.901545	−	0.432686i	$-0.857566\pi$
$547$	0.220177	−	0.472172i	0.00941410	−	0.0201886i	0.910959	+	0.412498i	$0.135344\pi$
$548$	−0.536948	−	2.00392i	−0.0229373	−	0.0856032i
$549$	0.606171	−	7.95986i	0.0258707	−	0.339718i
$550$		0			0
$551$	−32.8789	+	39.1836i	−1.40069	+	1.66928i
$552$	−0.552927	−	0.170921i	−0.0235342	−	0.00727488i
$553$	−1.90739	+	2.72403i	−0.0811104	+	0.115838i
$554$	−0.0322538	−	0.182920i	−0.00137033	−	0.00777153i
$555$		0			0
$556$	−2.20695	−	1.85185i	−0.0935957	−	0.0785361i
$557$	−6.03527	+	22.5239i	−0.255723	+	0.954370i	0.711964	+	0.702216i	$0.247806\pi$
$557$	−6.03527	+	22.5239i	−0.255723	+	0.954370i	−0.967687	+	0.252155i	$0.918861\pi$
$558$	−3.30763	+	20.0779i	−0.140023	+	0.849966i
$559$	−1.31151	−	0.757203i	−0.0554711	−	0.0320263i
$560$		0			0
$561$	−32.3850	−	13.2012i	−1.36730	−	0.557355i
$562$	−3.16269	+	36.1498i	−0.133410	+	1.52489i
$563$	−31.1449	+	14.5231i	−1.31260	+	0.612076i	−0.947757	−	0.318993i	$-0.896656\pi$
$563$	−31.1449	+	14.5231i	−1.31260	+	0.612076i	−0.364844	+	0.931069i	$0.618878\pi$
$564$	−0.871130	+	4.03683i	−0.0366812	+	0.169981i
$565$		0			0
$566$			24.0770i			1.01203i
$567$	13.8553	−	4.04903i	0.581870	−	0.170043i
$568$	−19.1620	−	19.1620i	−0.804019	−	0.804019i
$569$	0.227444	−	1.28990i	0.00953495	−	0.0540754i	−0.979669	−	0.200620i	$-0.935704\pi$
$569$	0.227444	−	1.28990i	0.00953495	−	0.0540754i	0.989204	+	0.146545i	$0.0468153\pi$
$570$		0			0
$571$	−17.9969	−	6.55033i	−0.753146	−	0.274123i	−0.0632171	−	0.998000i	$-0.520136\pi$
$571$	−17.9969	−	6.55033i	−0.753146	−	0.274123i	−0.689929	+	0.723877i	$0.742358\pi$
$572$	−0.239119	−	0.0209202i	−0.00999807	−	0.000874718i
$573$	−14.9557	+	6.29372i	−0.624782	+	0.262924i
$574$	3.89033	+	10.6886i	0.162379	+	0.446133i
$575$		0			0
$576$	1.94253	+	19.6521i	0.0809389	+	0.818836i
$577$	12.6473	+	3.38883i	0.526514	+	0.141079i	0.512278	−	0.858820i	$-0.328802\pi$
$577$	12.6473	+	3.38883i	0.526514	+	0.141079i	0.0142358	+	0.999899i	$0.495468\pi$
$578$	53.9231	−	4.71766i	2.24290	−	0.196229i
$579$	30.8977	+	19.4403i	1.28406	+	0.807913i
$580$		0			0
$581$	20.8174	−	3.67067i	0.863652	−	0.152285i
$582$	9.15579	−	29.6189i	0.379520	−	1.22774i
$583$	−0.165364	−	1.89012i	−0.00684869	−	0.0782808i
$584$	−8.93766	−	15.4805i	−0.369843	−	0.640587i
$585$		0			0
$586$	−3.97987	+	6.89333i	−0.164407	+	0.284761i
$587$	−26.3137	−	12.2703i	−1.08608	−	0.506449i	−0.204687	−	0.978827i	$-0.565618\pi$
$587$	−26.3137	−	12.2703i	−1.08608	−	0.506449i	−0.881396	+	0.472379i	$0.843395\pi$
$588$	−1.30199	+	1.71671i	−0.0536931	+	0.0707959i
$589$	−16.9072	−	20.1492i	−0.696650	−	0.830235i
$590$		0			0
$591$	8.54582	−	9.43219i	0.351528	−	0.387988i
$592$	−5.54732	−	7.92239i	−0.227993	−	0.325608i
$593$	18.8092	−	18.8092i	0.772402	−	0.772402i	−0.206124	−	0.978526i	$-0.566085\pi$
$593$	18.8092	−	18.8092i	0.772402	−	0.772402i	0.978526	+	0.206124i	$0.0660851\pi$
$594$	21.7583	−	1.31848i	0.892754	−	0.0540980i
$595$		0			0
$596$	−0.334697	−	0.0590161i	−0.0137097	−	0.00241739i
$597$	−20.4120	+	39.7559i	−0.835406	+	1.62710i
$598$	0.0252661	+	0.0541833i	0.00103321	+	0.00221572i
$599$	3.51169	−	2.94665i	0.143484	−	0.120397i	−0.568221	−	0.822876i	$-0.692368\pi$
$599$	3.51169	−	2.94665i	0.143484	−	0.120397i	0.711704	+	0.702479i	$0.247924\pi$
$600$		0			0
$601$	25.1131	−	9.14041i	1.02438	−	0.372845i	0.225443	−	0.974256i	$-0.427617\pi$
$601$	25.1131	−	9.14041i	1.02438	−	0.372845i	0.798940	+	0.601411i	$0.205395\pi$
$602$	11.5202	−	3.08684i	0.469530	−	0.125810i
$603$	2.78658	−	1.65094i	0.113478	−	0.0672316i
$604$	−3.93404	+	2.27132i	−0.160074	+	0.0924187i
$605$		0			0
$606$	−35.2440	−	1.34003i	−1.43169	−	0.0544352i
$607$	−29.2803	−	20.5023i	−1.18845	−	0.832163i	−0.199428	−	0.979913i	$-0.563908\pi$
$607$	−29.2803	−	20.5023i	−1.18845	−	0.832163i	−0.989025	+	0.147749i	$0.952797\pi$
$608$	7.57081	+	5.30114i	0.307037	+	0.214990i
$609$	−24.2447	−	0.921823i	−0.982443	−	0.0373542i
$610$		0			0
$611$	−2.26053	+	1.30512i	−0.0914512	+	0.0527994i
$612$	−5.27122	+	3.12300i	−0.213077	+	0.126240i
$613$	35.8682	−	9.61085i	1.44870	−	0.388179i	0.553130	−	0.833095i	$-0.313433\pi$
$613$	35.8682	−	9.61085i	1.44870	−	0.388179i	0.895572	+	0.444916i	$0.146767\pi$
$614$	−31.4107	+	11.4325i	−1.26763	+	0.461380i
$615$		0			0
$616$	−8.86034	+	7.43471i	−0.356993	+	0.299553i
$617$	−19.6545	−	42.1491i	−0.791258	−	1.69686i	−0.714316	−	0.699824i	$-0.753262\pi$
$617$	−19.6545	−	42.1491i	−0.791258	−	1.69686i	−0.0769428	−	0.997036i	$-0.524516\pi$
$618$	−3.55414	+	6.92231i	−0.142968	+	0.278456i
$619$	−13.9352	−	2.45716i	−0.560104	−	0.0987615i	−0.113573	−	0.993530i	$-0.536230\pi$
$619$	−13.9352	−	2.45716i	−0.560104	−	0.0987615i	−0.446531	+	0.894768i	$0.647341\pi$
$620$		0			0
$621$	−0.368791	−	0.557865i	−0.0147991	−	0.0223864i
$622$	−15.3672	+	15.3672i	−0.616168	+	0.616168i
$623$	−10.2699	−	14.6669i	−0.411455	−	0.587619i
$624$	1.60354	−	1.76986i	0.0641929	−	0.0708510i
$625$		0			0
$626$	−20.6337	−	24.5903i	−0.824687	−	0.982824i
$627$	−17.0269	+	22.4504i	−0.679987	+	0.896583i
$628$	−5.28283	−	2.46342i	−0.210808	−	0.0983013i
$629$	−7.84112	+	13.5812i	−0.312646	+	0.541519i
$630$		0			0
$631$	16.2979	+	28.2288i	0.648810	+	1.12377i	0.983407	+	0.181411i	$0.0580664\pi$
$631$	16.2979	+	28.2288i	0.648810	+	1.12377i	−0.334597	+	0.942361i	$0.608600\pi$
$632$	−0.469158	−	5.36250i	−0.0186621	−	0.213309i
$633$	0.179095	−	0.579371i	0.00711840	−	0.0230279i
$634$	34.1919	−	6.02895i	1.35793	−	0.239440i
$635$		0			0
$636$	−0.281345	−	0.177018i	−0.0111561	−	0.00701921i
$637$	−1.35664	+	0.118690i	−0.0537520	+	0.00470269i
$638$	−35.3901	−	9.48275i	−1.40111	−	0.375426i
$639$	−3.08021	−	31.1616i	−0.121851	−	1.23273i
$640$		0			0
$641$	−11.8689	−	32.6096i	−0.468794	−	1.28800i	−0.918711	−	0.394931i	$-0.870768\pi$
$641$	−11.8689	−	32.6096i	−0.468794	−	1.28800i	0.449916	−	0.893071i	$-0.351454\pi$
$642$	−26.6237	+	11.2039i	−1.05075	+	0.442183i
$643$	−8.82626	−	0.772198i	−0.348074	−	0.0304525i	−0.0882215	−	0.996101i	$-0.528118\pi$
$643$	−8.82626	−	0.772198i	−0.348074	−	0.0304525i	−0.259852	+	0.965648i	$0.583674\pi$
$644$	−0.0544969	−	0.0198352i	−0.00214748	−	0.000781618i
$645$		0			0
$646$	11.1651	−	63.3204i	0.439285	−	2.49131i
$647$	14.1426	+	14.1426i	0.556003	+	0.556003i	0.928167	−	0.372164i	$-0.121384\pi$
$647$	14.1426	+	14.1426i	0.556003	+	0.556003i	−0.372164	+	0.928167i	$0.621384\pi$
$648$	−12.9679	+	19.4374i	−0.509428	+	0.763573i
$649$			26.9457i			1.05771i
$650$		0			0
$651$	2.63174	−	12.1955i	0.103146	−	0.477980i
$652$	−3.32886	+	1.55227i	−0.130368	+	0.0607917i
$653$	0.173231	−	1.98004i	0.00677904	−	0.0774848i	−0.992052	−	0.125832i	$-0.959840\pi$
$653$	0.173231	−	1.98004i	0.00677904	−	0.0774848i	0.998831	+	0.0483474i	$0.0153955\pi$
$654$	1.12485	+	0.458524i	0.0439850	+	0.0179297i
$655$		0			0
$656$	−18.2307	−	10.5255i	−0.711788	−	0.410951i
$657$	3.35748	−	20.3805i	0.130988	−	0.795119i
$658$	5.32049	−	19.8563i	0.207414	−	0.774081i
$659$	−9.93910	−	8.33989i	−0.387172	−	0.324876i	0.428338	−	0.903619i	$-0.359099\pi$
$659$	−9.93910	−	8.33989i	−0.387172	−	0.324876i	−0.815510	+	0.578742i	$0.803544\pi$
$660$		0			0
$661$	2.91716	+	16.5440i	0.113464	+	0.643489i	0.987499	+	0.157625i	$0.0503837\pi$
$661$	2.91716	+	16.5440i	0.113464	+	0.643489i	−0.874035	+	0.485864i	$0.838505\pi$
$662$	−12.0886	+	17.2643i	−0.469836	+	0.670996i
$663$	−3.69980	−	1.14368i	−0.143688	−	0.0444170i
$664$	−21.9947	+	26.2123i	−0.853561	+	1.01723i
$665$		0			0
$666$	0.742231	−	9.74651i	0.0287609	−	0.377670i
$667$	0.290921	+	1.08573i	0.0112645	+	0.0420396i
$668$	−1.91063	+	4.09735i	−0.0739244	+	0.158531i
$669$	−26.9612	+	3.70404i	−1.04238	+	0.143206i
$670$		0			0
$671$	−2.52797	+	6.94554i	−0.0975912	+	0.268130i
$672$	0.215875	+	4.37855i	0.00832758	+	0.168906i
$673$	−7.48390	+	5.24028i	−0.288483	+	0.201998i	−0.708856	−	0.705353i	$-0.750788\pi$
$673$	−7.48390	+	5.24028i	−0.288483	+	0.201998i	0.420373	+	0.907352i	$0.361899\pi$
$674$	21.8853			0.842991
$675$		0			0
$676$	3.62584			0.139455
$677$	0.0991212	−	0.0694054i	0.00380954	−	0.00266747i	−0.571670	−	0.820484i	$-0.693704\pi$
$677$	0.0991212	−	0.0694054i	0.00380954	−	0.00266747i	0.575480	+	0.817816i	$0.304815\pi$
$678$	1.11438	+	0.572160i	0.0427976	+	0.0219737i
$679$	−6.50112	+	17.8617i	−0.249490	+	0.685468i
$680$		0			0
$681$	−25.0095	−	32.2158i	−0.958365	−	1.23451i
$682$	7.96234	−	17.0753i	0.304894	−	0.653847i
$683$	−3.58403	−	13.3758i	−0.137139	−	0.511810i	−0.999980	−	0.00633429i	$-0.997984\pi$
$683$	−3.58403	−	13.3758i	−0.137139	−	0.511810i	0.862841	−	0.505476i	$-0.168683\pi$
$684$	1.33124	+	4.75350i	0.0509011	+	0.181755i
$685$		0			0
$686$	17.7931	−	21.2049i	0.679342	−	0.809608i
$687$	29.4123	−	27.2576i	1.12215	−	1.03994i
$688$	−12.6604	+	18.0809i	−0.482673	+	0.689329i
$689$	−0.0364828	−	0.206904i	−0.00138988	−	0.00788241i
$690$		0			0
$691$	17.4891	+	14.6751i	0.665315	+	0.558266i	0.911675	−	0.410913i	$-0.134790\pi$
$691$	17.4891	+	14.6751i	0.665315	+	0.558266i	−0.246359	+	0.969179i	$0.579234\pi$
$692$	0.192894	−	0.719892i	0.00733274	−	0.0273662i
$693$	−13.3642	+	0.150484i	−0.507666	+	0.00571640i
$694$	−11.8745	−	6.85575i	−0.450750	−	0.260241i
$695$		0			0
$696$	31.0231	−	24.0835i	1.17593	−	0.912885i
$697$	−2.97498	+	34.0042i	−0.112686	+	1.28800i
$698$	−11.4089	+	5.32004i	−0.431832	+	0.201366i
$699$	−35.6664	+	11.4667i	−1.34903	+	0.433712i
$700$		0			0
$701$			15.6693i			0.591821i	0.955216	+	0.295910i	$0.0956230\pi$
$701$			15.6693i			0.591821i	−0.955216	+	0.295910i	$0.904377\pi$
$702$	2.38744	−	0.355429i	0.0901081	−	0.0134148i
$703$	8.93432	+	8.93432i	0.336964	+	0.336964i
$704$	3.17504	−	18.0065i	0.119664	−	0.678647i
$705$		0			0
$706$	−3.74859	−	1.36438i	−0.141080	−	0.0513490i
$707$	21.5424	+	1.88471i	0.810184	+	0.0708820i
$708$	3.76130	+	2.85265i	0.141358	+	0.107209i
$709$	−2.91839	−	8.01821i	−0.109602	−	0.301130i	0.872751	−	0.488166i	$-0.162334\pi$
$709$	−2.91839	−	8.01821i	−0.109602	−	0.301130i	−0.982353	+	0.187036i	$0.940112\pi$
$710$		0			0
$711$	3.51012	−	5.13508i	0.131640	−	0.192580i
$712$	27.9959	+	7.50148i	1.04919	+	0.281130i
$713$	−0.575807	+	0.0503766i	−0.0215641	+	0.00188662i
$714$	26.9724	−	14.2345i	1.00942	−	0.532713i
$715$		0			0
$716$	−1.89856	+	0.334767i	−0.0709523	+	0.0125108i
$717$	24.0106	−	5.46502i	0.896692	−	0.204095i
$718$	−1.85896	−	21.2480i	−0.0693758	−	0.792968i
$719$	19.9277	+	34.5157i	0.743176	+	1.28722i	0.951042	+	0.309062i	$0.100015\pi$
$719$	19.9277	+	34.5157i	0.743176	+	1.28722i	−0.207866	+	0.978157i	$0.566652\pi$
$720$		0			0
$721$	2.38550	−	4.13180i	0.0888406	−	0.153876i
$722$	−20.9433	−	9.76600i	−0.779427	−	0.363453i
$723$	−5.60315	−	13.3147i	−0.208383	−	0.495178i
$724$	−3.61621	−	4.30963i	−0.134395	−	0.160166i
$725$		0			0
$726$	8.39869	+	1.81240i	0.311704	+	0.0672644i
$727$	−26.2725	−	37.5210i	−0.974393	−	1.39158i	−0.919502	−	0.393085i	$-0.871408\pi$
$727$	−26.2725	−	37.5210i	−0.974393	−	1.39158i	−0.0548911	−	0.998492i	$-0.517481\pi$
$728$	−0.905635	+	0.905635i	−0.0335651	+	0.0335651i
$729$	−25.8291	+	7.86492i	−0.956634	+	0.291293i
$730$		0			0
$731$	35.2471	+	6.21502i	1.30366	+	0.229871i
$732$	0.701888	+	1.08818i	0.0259425	+	0.0402201i
$733$	15.6365	+	33.5325i	0.577546	+	1.23855i	0.950507	+	0.310704i	$0.100565\pi$
$733$	15.6365	+	33.5325i	0.577546	+	1.23855i	−0.372961	+	0.927847i	$0.621657\pi$
$734$	−15.9308	+	13.3675i	−0.588015	+	0.493403i
$735$		0			0
$736$	0.190850	−	0.0694636i	0.00703481	−	0.00256046i
$737$	−2.89670	+	0.776169i	−0.106701	+	0.0285906i
$738$	−7.50139	−	19.9095i	−0.276130	−	0.732879i
$739$	−9.45965	+	5.46153i	−0.347979	+	0.200906i	−0.663795	−	0.747915i	$-0.731055\pi$
$739$	−9.45965	+	5.46153i	−0.347979	+	0.200906i	0.315816	+	0.948820i	$0.397722\pi$
$740$		0			0
$741$	−1.66157	+	2.64084i	−0.0610393	+	0.0970135i
$742$	1.35537	+	0.949040i	0.0497572	+	0.0348404i
$743$	6.78635	+	4.75185i	0.248967	+	0.174329i	0.691398	−	0.722474i	$-0.256995\pi$
$743$	6.78635	+	4.75185i	0.248967	+	0.174329i	−0.442431	+	0.896802i	$0.645884\pi$
$744$	9.42606	+	17.8611i	0.345576	+	0.654818i
$745$		0			0
$746$	−26.5695	+	15.3399i	−0.972778	+	0.561633i
$747$	−38.8586	+	7.30388i	−1.42176	+	0.267235i
$748$	5.47954	−	1.46824i	0.200352	−	0.0536841i
$749$	16.6422	−	6.05726i	0.608093	−	0.221328i
$750$		0			0
$751$	1.01418	−	0.851000i	0.0370080	−	0.0310534i	−0.624096	−	0.781348i	$-0.714533\pi$
$751$	1.01418	−	0.851000i	0.0370080	−	0.0310534i	0.661104	+	0.750294i	$0.270088\pi$
$752$	16.0783	+	34.4801i	0.586317	+	1.25736i
$753$	−8.25077	+	0.406788i	−0.300675	+	0.0148242i
$754$	−3.99541	−	0.704499i	−0.145504	−	0.0256563i
$755$		0			0
$756$	−1.39382	+	1.88142i	−0.0506928	+	0.0684267i
$757$	26.5719	−	26.5719i	0.965772	−	0.965772i	−0.0336615	−	0.999433i	$-0.510717\pi$
$757$	26.5719	−	26.5719i	0.965772	−	0.965772i	0.999433	+	0.0336615i	$0.0107168\pi$
$758$	18.0652	+	25.7998i	0.656159	+	0.937092i
$759$	0.189514	+	0.589469i	0.00687892	+	0.0213964i
$760$		0			0
$761$	6.97127	+	8.30804i	0.252708	+	0.301166i	0.877453	−	0.479663i	$-0.159241\pi$
$761$	6.97127	+	8.30804i	0.252708	+	0.301166i	−0.624744	+	0.780829i	$0.714797\pi$
$762$	−34.9179	−	4.39718i	−1.26494	−	0.159293i
$763$	−0.674994	−	0.314755i	−0.0244364	−	0.0113949i
$764$	1.31601	−	2.27939i	0.0476114	−	0.0824654i
$765$		0			0
$766$	−11.0760	−	19.1841i	−0.400191	−	0.693151i
$767$	0.260050	+	2.97239i	0.00938988	+	0.107327i
$768$	−7.78930	−	8.40504i	−0.281072	−	0.303291i
$769$	44.1842	−	7.79087i	1.59332	−	0.280946i	0.694579	−	0.719417i	$-0.255591\pi$
$769$	44.1842	−	7.79087i	1.59332	−	0.280946i	0.898745	+	0.438471i	$0.144480\pi$
$770$		0			0
$771$	−0.310649	+	8.17032i	−0.0111878	+	0.294247i
$772$	−5.89888	+	0.516085i	−0.212305	+	0.0185743i
$773$	30.3757	+	8.13915i	1.09254	+	0.292745i	0.759723	−	0.650247i	$-0.225334\pi$
$773$	30.3757	+	8.13915i	1.09254	+	0.292745i	0.332816	+	0.942992i	$0.392001\pi$
$774$	−21.4819	+	6.01611i	−0.772152	+	0.216244i
$775$		0			0
$776$	−10.5236	−	28.9133i	−0.377775	−	1.03793i
$777$	−0.748800	+	5.94620i	−0.0268631	+	0.213319i
$778$	9.41874	+	0.824033i	0.337678	+	0.0295430i
$779$	25.8430	+	9.40608i	0.925922	+	0.337008i
$780$		0			0
$781$	−5.03455	+	28.5524i	−0.180150	+	1.02168i
$782$	−0.999091	−	0.999091i	−0.0357274	−	0.0357274i
$783$	45.3655	+	1.21353i	1.62123	+	0.0433680i
$784$			19.8488i			0.708885i
$785$		0			0
$786$	11.9877	+	10.8612i	0.427588	+	0.387406i
$787$	28.5680	−	13.3215i	1.01834	−	0.474860i	0.159552	−	0.987190i	$-0.448995\pi$
$787$	28.5680	−	13.3215i	1.01834	−	0.474860i	0.858789	+	0.512330i	$0.171217\pi$
$788$	−0.179939	+	2.05671i	−0.00641007	+	0.0732674i
$789$	−0.785181	−	5.71522i	−0.0279532	−	0.203467i
$790$		0			0
$791$	−0.665155	−	0.384027i	−0.0236502	−	0.0136544i
$792$	16.4154	−	14.0921i	0.583295	−	0.500742i
$793$	−0.211830	+	0.790562i	−0.00752232	+	0.0280737i
$794$	0.539681	+	0.452846i	0.0191526	+	0.0160709i
$795$		0			0
$796$	−1.25879	−	7.13898i	−0.0446168	−	0.253034i
$797$	3.73721	−	5.33729i	0.132379	−	0.189057i	−0.747490	−	0.664273i	$-0.768741\pi$
$797$	3.73721	−	5.33729i	0.132379	−	0.189057i	0.879869	+	0.475216i	$0.157630\pi$
$798$	−5.45332	−	23.9592i	−0.193046	−	0.848147i
$799$	39.6531	−	47.2567i	1.40283	−	1.67182i
$800$		0			0
$801$	19.5173	+	27.2161i	0.689608	+	0.961633i
$802$	3.64928	+	13.6193i	0.128860	+	0.480914i
$803$	−8.08234	+	17.3326i	−0.285220	+	0.611655i
$804$	−0.198320	+	0.486516i	−0.00699421	+	0.0171581i
$805$		0			0
$806$	0.713536	−	1.96042i	0.0251332	−	0.0690530i
$807$	12.1891	−	7.86211i	0.429075	−	0.276759i
$808$	−28.6741	+	20.0778i	−1.00875	+	0.706335i
$809$	−21.5117			−0.756312			−0.378156	−	0.925742i	$-0.623442\pi$
$809$	−21.5117			−0.756312			−0.378156	+	0.925742i	$0.623442\pi$
$810$		0			0
$811$	15.2216			0.534502			0.267251	−	0.963627i	$-0.413885\pi$
$811$	15.2216			0.534502			0.267251	+	0.963627i	$0.413885\pi$
$812$	3.22382	−	2.25734i	0.113134	−	0.0792172i
$813$	20.0708	−	12.9460i	0.703914	−	0.454034i
$814$	−3.09539	+	8.50453i	−0.108494	+	0.298083i
$815$		0			0
$816$	−21.3059	+	52.2673i	−0.745854	+	1.82972i
$817$	12.1868	−	26.1346i	0.426362	−	0.914335i
$818$	−0.274706	−	1.02522i	−0.00960488	−	0.0358459i
$819$	−1.47276	+	0.145577i	−0.0514624	+	0.00508687i
$820$		0			0
$821$	−32.2494	+	38.4334i	−1.12551	+	1.34133i	−0.192581	+	0.981281i	$0.561686\pi$
$821$	−32.2494	+	38.4334i	−1.12551	+	1.34133i	−0.932932	+	0.360053i	$0.882758\pi$
$822$	−4.28686	−	18.8344i	−0.149522	−	0.656924i
$823$	−2.01204	+	2.87349i	−0.0701354	+	0.100164i	−0.852687	−	0.522422i	$-0.825029\pi$
$823$	−2.01204	+	2.87349i	−0.0701354	+	0.100164i	0.782552	+	0.622585i	$0.213918\pi$
$824$	1.34108	+	7.60564i	0.0467187	+	0.264955i
$825$		0			0
$826$	−18.0008	−	15.1045i	−0.626327	−	0.525551i
$827$	−0.686704	+	2.56281i	−0.0238790	+	0.0891178i	−0.976837	−	0.213985i	$-0.931356\pi$
$827$	−0.686704	+	2.56281i	−0.0238790	+	0.0891178i	0.952958	+	0.303102i	$0.0980224\pi$
$828$	0.102346	+	0.0359512i	0.00355678	+	0.00124939i
$829$	13.2911	+	7.67359i	0.461617	+	0.266515i	0.712724	−	0.701444i	$-0.247461\pi$
$829$	13.2911	+	7.67359i	0.461617	+	0.266515i	−0.251107	+	0.967959i	$0.580794\pi$
$830$		0			0
$831$	−0.0289927	−	0.211034i	−0.00100575	−	0.00732068i
$832$	0.176460	−	2.01695i	0.00611766	−	0.0699251i
$833$	29.1693	−	13.6019i	1.01066	−	0.471277i
$834$	−19.8784	−	18.0103i	−0.688331	−	0.623647i
$835$		0			0
$836$		−	4.57055i		−	0.158076i
$837$	−4.66544	+	22.8654i	−0.161261	+	0.790343i
$838$	22.8981	+	22.8981i	0.791002	+	0.791002i
$839$	−2.05282	+	11.6421i	−0.0708712	+	0.401931i	0.928649	+	0.370960i	$0.120971\pi$
$839$	−2.05282	+	11.6421i	−0.0708712	+	0.401931i	−0.999520	+	0.0309713i	$0.990140\pi$
$840$		0			0
$841$	−44.4266	−	16.1700i	−1.53195	−	0.557585i
$842$	−26.8064	−	2.34525i	−0.923808	−	0.0808227i
$843$	−5.19964	+	41.2902i	−0.179085	+	1.42211i
$844$	0.0336436	+	0.0924350i	0.00115806	+	0.00318174i
$845$		0			0
$846$	−9.53301	+	37.2504i	−0.327752	+	1.28070i
$847$	−5.08850	−	1.36346i	−0.174843	−	0.0468490i
$848$	−3.05053	+	0.266887i	−0.104756	+	0.00916493i
$849$	−1.04911	+	27.5924i	−0.0360054	+	0.946970i
$850$		0			0
$851$	0.273436	−	0.0482142i	0.00937327	−	0.00165276i
$852$	3.45258	+	3.72550i	0.118283	+	0.127634i
$853$	2.93357	+	33.5308i	0.100443	+	1.14807i	0.864400	+	0.502805i	$0.167699\pi$
$853$	2.93357	+	33.5308i	0.100443	+	1.14807i	−0.763956	+	0.645268i	$0.776746\pi$
$854$	−3.22284	−	5.58211i	−0.110283	−	0.191016i
$855$		0			0
$856$	−14.3341	+	24.8274i	−0.489929	+	0.848583i
$857$	−33.6303	−	15.6821i	−1.14879	−	0.535689i	−0.247491	−	0.968890i	$-0.579606\pi$
$857$	−33.6303	−	15.6821i	−1.14879	−	0.535689i	−0.901297	+	0.433201i	$0.857384\pi$
$858$	−2.21736	−	0.279230i	−0.0756993	−	0.00953276i
$859$	18.6876	+	22.2710i	0.637613	+	0.759878i	0.983991	−	0.178217i	$-0.0570329\pi$
$859$	18.6876	+	22.2710i	0.637613	+	0.759878i	−0.346378	+	0.938095i	$0.612588\pi$
$860$		0			0
$861$	3.99262	+	12.4187i	0.136068	+	0.423230i
$862$	11.8627	+	16.9417i	0.404046	+	0.577038i
$863$	−9.57951	+	9.57951i	−0.326090	+	0.326090i	−0.851098	−	0.525007i	$-0.824063\pi$
$863$	−9.57951	+	9.57951i	−0.326090	+	0.326090i	0.525007	+	0.851098i	$0.324063\pi$
$864$	−0.495978	−	8.18489i	−0.0168735	−	0.278455i
$865$		0			0
$866$	48.0287	+	8.46876i	1.63208	+	0.287780i
$867$	62.0020	−	3.05688i	2.10570	−	0.103817i
$868$	0.855281	+	1.83416i	0.0290301	+	0.0622553i
$869$	−4.41177	+	3.70191i	−0.149659	+	0.125579i
$870$		0			0
$871$	−0.312045	+	0.113575i	−0.0105733	+	0.00384835i
$872$	1.16451	−	0.312030i	0.0394353	−	0.0105667i
$873$	11.7832	−	33.5446i	0.398801	−	1.13531i
$874$	−0.985869	+	0.569192i	−0.0333475	+	0.0192532i
$875$		0			0
$876$	1.56378	+	2.96315i	0.0528353	+	0.100115i
$877$	18.1337	+	12.6973i	0.612331	+	0.428759i	0.838172	−	0.545405i	$-0.183624\pi$
$877$	18.1337	+	12.6973i	0.612331	+	0.428759i	−0.225842	+	0.974164i	$0.572513\pi$
$878$	−13.9339	−	9.75663i	−0.470247	−	0.329270i
$879$	−4.86133	+	7.72641i	−0.163969	+	0.260605i
$880$		0			0
$881$	38.5171	−	22.2379i	1.29768	−	0.749213i	0.317673	−	0.948200i	$-0.397098\pi$
$881$	38.5171	−	22.2379i	1.29768	−	0.749213i	0.980002	+	0.198987i	$0.0637651\pi$
$882$	−12.7210	+	15.5116i	−0.428337	+	0.522304i
$883$	15.2412	−	4.08387i	0.512907	−	0.137433i	0.00692327	−	0.999976i	$-0.497796\pi$
$883$	15.2412	−	4.08387i	0.512907	−	0.137433i	0.505984	+	0.862543i	$0.331130\pi$
$884$	0.590280	−	0.214844i	0.0198533	−	0.00722599i
$885$		0			0
$886$	7.81768	−	6.55981i	0.262640	−	0.220381i
$887$	11.6632	+	25.0117i	0.391610	+	0.839811i	0.998970	+	0.0453839i	$0.0144511\pi$
$887$	11.6632	+	25.0117i	0.391610	+	0.839811i	−0.607359	+	0.794427i	$0.707771\pi$
$888$	−5.25850	−	8.15255i	−0.176464	−	0.273582i
$889$	21.2504	+	3.74702i	0.712715	+	0.125671i
$890$		0			0
$891$	24.9927	−	0.562915i	0.837287	−	0.0188584i
$892$	3.12148	−	3.12148i	0.104515	−	0.104515i
$893$	−28.5082	−	40.7139i	−0.953990	−	1.36244i
$894$	−3.09313	−	0.667484i	−0.103450	−	0.0223240i
$895$		0			0
$896$	13.5031	+	16.0924i	0.451108	+	0.537609i
$897$	0.0265943	+	0.0631956i	0.000887957	+	0.00211004i
$898$	15.6093	+	7.27874i	0.520890	+	0.242895i
$899$	19.6120	−	33.9690i	0.654098	−	1.13293i
$900$		0			0
$901$	2.48266	+	4.30010i	0.0827095	+	0.143257i
$902$	1.71688	+	19.6241i	0.0571660	+	0.653410i
$903$	13.3368	−	3.03558i	0.443822	−	0.101018i
$904$	1.22439	−	0.215893i	0.0407226	−	0.00718049i
$905$		0			0
$906$	−37.4057	+	19.7406i	−1.24272	+	0.655838i
$907$	3.71818	−	0.325298i	0.123460	−	0.0108014i	−0.0252582	−	0.999681i	$-0.508041\pi$
$907$	3.71818	−	0.325298i	0.123460	−	0.0108014i	0.148718	+	0.988880i	$0.452485\pi$
$908$	6.39013	+	1.71223i	0.212064	+	0.0568223i
$909$	−40.3316	−	3.07139i	−1.33771	−	0.101871i
$910$		0			0
$911$	−8.20345	−	22.5388i	−0.271792	−	0.746743i	−0.998228	−	0.0595086i	$-0.981047\pi$
$911$	−8.20345	−	22.5388i	−0.271792	−	0.746743i	0.726435	−	0.687235i	$-0.241176\pi$
$912$	36.2335	+	27.4802i	1.19981	+	0.909961i
$913$	36.4695	+	3.19067i	1.20697	+	0.105596i
$914$	−10.5269	−	3.83148i	−0.348199	−	0.126734i
$915$		0			0
$916$	−1.12953	+	6.40589i	−0.0373207	+	0.211656i
$917$	−7.01316	−	7.01316i	−0.231595	−	0.231595i
$918$	−50.1481	+	27.1916i	−1.65513	+	0.897456i
$919$		−	55.8452i		−	1.84216i	−0.389370	−	0.921081i	$-0.627307\pi$
$919$		−	55.8452i		−	1.84216i	0.389370	−	0.921081i	$-0.372693\pi$
$920$		0			0
$921$	−36.4951	+	11.7332i	−1.20255	+	0.386620i
$922$	57.0495	−	26.6026i	1.87882	−	0.876110i
$923$	−0.279807	+	3.19821i	−0.00920995	+	0.105270i
$924$	1.71249	−	1.32942i	0.0563367	−	0.0437348i
$925$		0			0
$926$	4.35356	+	2.51353i	0.143067	+	0.0825997i
$927$	−4.37471	+	7.77817i	−0.143684	+	0.255469i
$928$	−3.56716	+	13.3128i	−0.117098	+	0.437014i
$929$	43.9037	+	36.8395i	1.44043	+	1.20867i	0.939208	+	0.343349i	$0.111561\pi$
$929$	43.9037	+	36.8395i	1.44043	+	1.20867i	0.501224	+	0.865317i	$0.332883\pi$
$930$		0			0
$931$	−4.50286	−	25.5370i	−0.147575	−	0.836942i
$932$	3.48567	−	4.97805i	0.114177	−	0.163062i
$933$	−18.2805	+	16.9413i	−0.598478	+	0.554635i
$934$	−4.34306	+	5.17586i	−0.142109	+	0.169359i
$935$		0			0
$936$	1.67478	−	1.71293i	0.0547420	−	0.0559889i
$937$	14.6753	+	54.7688i	0.479420	+	1.78922i	0.603971	+	0.797006i	$0.293584\pi$
$937$	14.6753	+	54.7688i	0.479420	+	1.78922i	−0.124551	+	0.992213i	$0.539749\pi$
$938$	1.10524	−	2.37019i	0.0360873	−	0.0773895i
$939$	−22.5749	−	29.0798i	−0.736705	−	0.948982i
$940$		0			0
$941$	13.7044	−	37.6526i	0.446751	−	1.22744i	−0.488222	−	0.872719i	$-0.662354\pi$
$941$	13.7044	−	37.6526i	0.446751	−	1.22744i	0.934973	−	0.354719i	$-0.115423\pi$
$942$	−48.2799	−	24.7885i	−1.57304	−	0.807651i
$943$	0.495050	−	0.346638i	0.0161211	−	0.0112881i
$944$	43.4886			1.41543
$945$		0			0
$946$	20.6552			0.671557
$947$	−38.0843	+	26.6669i	−1.23757	+	0.866557i	−0.994631	−	0.103484i	$-0.967001\pi$
$947$	−38.0843	+	26.6669i	−1.23757	+	0.866557i	−0.242941	+	0.970041i	$0.578112\pi$
$948$	0.0496845	+	1.00774i	0.00161368	+	0.0327298i
$949$	−0.724290	+	1.98997i	−0.0235114	+	0.0645972i
$950$		0			0
$951$	39.4470	−	5.41939i	1.27916	−	0.175736i
$952$	12.7922	−	27.4331i	0.414599	−	0.889110i
$953$	−14.9234	−	55.6950i	−0.483417	−	1.80414i	−0.587085	−	0.809526i	$-0.699724\pi$
$953$	−14.9234	−	55.6950i	−0.483417	−	1.80414i	0.103668	−	0.994612i	$-0.466942\pi$
$954$	−2.55501	−	1.74650i	−0.0827214	−	0.0565449i
$955$		0			0
$956$	−2.56752	+	3.05985i	−0.0830396	+	0.0989627i
$957$	−40.1442	−	12.4094i	−1.29768	−	0.401139i
$958$	31.8330	−	45.4622i	1.02848	−	1.46882i
$959$	2.05655	+	11.6633i	0.0664095	+	0.376627i
$960$		0			0
$961$	−8.29622	−	6.96135i	−0.267620	−	0.224560i
$962$	−0.259378	+	0.968010i	−0.00836267	+	0.0312099i
$963$	−30.9992	+	11.6797i	−0.998936	+	0.376374i
$964$	2.02929	+	1.17161i	0.0653589	+	0.0377350i
$965$		0			0
$966$	−0.500021	−	0.203825i	−0.0160879	−	0.00655796i
$967$	−2.27121	+	25.9600i	−0.0730371	+	0.834818i	0.868011	+	0.496545i	$0.165398\pi$
$967$	−2.27121	+	25.9600i	−0.0730371	+	0.834818i	−0.941048	+	0.338273i	$0.890157\pi$
$968$	7.72854	−	3.60388i	0.248405	−	0.115833i
$969$	15.5544	−	72.0794i	0.499679	−	2.31552i
$970$		0			0
$971$		−	24.3222i		−	0.780536i	−0.920701	−	0.390268i	$-0.872382\pi$
$971$		−	24.3222i		−	0.780536i	0.920701	−	0.390268i	$-0.127618\pi$
$972$	2.56731	−	3.54828i	0.0823466	−	0.113811i
$973$	11.6294	+	11.6294i	0.372822	+	0.372822i
$974$	3.35887	−	19.0491i	0.107625	−	0.610372i
$975$		0			0
$976$	11.2096	+	4.07998i	0.358812	+	0.130597i
$977$	4.39652	+	0.384646i	0.140657	+	0.0123059i	0.157267	−	0.987556i	$-0.449732\pi$
$977$	4.39652	+	0.384646i	0.140657	+	0.0123059i	−0.0166097	+	0.999862i	$0.505287\pi$
$978$	−31.5208	+	13.2647i	−1.00792	+	0.424159i
$979$	−10.6057	−	29.1388i	−0.338958	−	0.931280i
$980$		0			0
$981$	1.26911	+	0.574487i	0.0405194	+	0.0183420i
$982$	−33.5090	−	8.97872i	−1.06932	−	0.286522i
$983$	−6.29396	+	0.550651i	−0.200746	+	0.0175630i	−0.187085	−	0.982344i	$-0.559904\pi$
$983$	−6.29396	+	0.550651i	−0.200746	+	0.0175630i	−0.0136609	+	0.999907i	$0.504349\pi$
$984$	−17.8727	−	11.2452i	−0.569760	−	0.358484i
$985$		0			0
$986$	94.4260	−	16.6499i	3.00714	−	0.530240i
$987$	6.96254	−	22.5237i	0.221620	−	0.716938i
$988$	−0.0441099	−	0.504179i	−0.00140332	−	0.0160401i
$989$	−0.316839	−	0.548781i	−0.0100749	−	0.0174502i
$990$		0			0
$991$	3.28793	−	5.69486i	0.104445	−	0.180903i	−0.809067	−	0.587717i	$-0.800027\pi$
$991$	3.28793	−	5.69486i	0.104445	−	0.180903i	0.913511	+	0.406814i	$0.133360\pi$
$992$	−6.42327	−	2.99522i	−0.203939	−	0.0950983i
$993$	−14.6059	+	19.2583i	−0.463505	+	0.611144i
$994$	−16.2520	−	19.3683i	−0.515481	−	0.614326i
$995$		0			0
$996$	4.30628	−	4.75293i	0.136450	−	0.150602i
$997$	−11.4987	−	16.4219i	−0.364168	−	0.520086i	0.594696	−	0.803951i	$-0.297272\pi$
$997$	−11.4987	−	16.4219i	−0.364168	−	0.520086i	−0.958864	+	0.283864i	$0.908383\pi$
$998$	9.88969	−	9.88969i	0.313053	−	0.313053i
$999$	1.27529	−	11.1373i	0.0403484	−	0.352367i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.ba.b.218.4		192
5.2	odd	4	inner	675.2.ba.b.407.4		192
5.3	odd	4		135.2.q.a.2.13	✓	192
5.4	even	2		135.2.q.a.83.13	yes	192
15.8	even	4		405.2.r.a.332.4		192
15.14	odd	2		405.2.r.a.8.4		192
27.14	odd	18	inner	675.2.ba.b.68.4		192
135.13	odd	36		405.2.r.a.152.4		192
135.14	odd	18		135.2.q.a.68.13	yes	192
135.68	even	36		135.2.q.a.122.13	yes	192
135.94	even	18		405.2.r.a.233.4		192
135.122	even	36	inner	675.2.ba.b.257.4		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.13	✓	192	5.3	odd	4
135.2.q.a.68.13	yes	192	135.14	odd	18
135.2.q.a.83.13	yes	192	5.4	even	2
135.2.q.a.122.13	yes	192	135.68	even	36
405.2.r.a.8.4		192	15.14	odd	2
405.2.r.a.152.4		192	135.13	odd	36
405.2.r.a.233.4		192	135.94	even	18
405.2.r.a.332.4		192	15.8	even	4
675.2.ba.b.68.4		192	27.14	odd	18	inner
675.2.ba.b.218.4		192	1.1	even	1	trivial
675.2.ba.b.257.4		192	135.122	even	36	inner
675.2.ba.b.407.4		192	5.2	odd	4	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+(-1.23715 + 0.866263i) q^{2} +(-1.45553 + 0.938839i) q^{3} +(0.0960923 - 0.264011i) q^{4} +(0.987435 - 2.42236i) q^{6} +(-0.677826 + 1.45360i) q^{7} +(-0.671958 - 2.50778i) q^{8} +(1.23716 - 2.73303i) q^{9} +(-1.78545 + 2.12782i) q^{11} +(0.107999 + 0.474493i) q^{12} +(-0.176418 + 0.251952i) q^{13} +(-0.420628 - 2.38550i) q^{14} +(3.43416 + 2.88160i) q^{16} +(1.88139 - 7.02145i) q^{17} +(0.836964 + 4.45287i) q^{18} +(-5.07203 - 2.92834i) q^{19} +(-0.378100 - 2.75214i) q^{21} +(0.365624 - 4.17910i) q^{22} +(-0.116642 + 0.0543910i) q^{23} +(3.33246 + 3.01930i) q^{24} -0.464527i q^{26} +(0.765143 + 5.13951i) q^{27} +(0.318634 + 0.318634i) q^{28} +(1.51659 - 8.60103i) q^{29} +(4.22026 + 1.53605i) q^{31} +(-1.57207 - 0.137538i) q^{32} +(0.601106 - 4.77337i) q^{33} +(3.75485 + 10.3164i) q^{34} +(-0.602668 - 0.589247i) q^{36} +(-2.08386 - 0.558369i) q^{37} +(8.81158 - 0.770913i) q^{38} +(0.0202409 - 0.532353i) q^{39} +(-4.62442 + 0.815410i) q^{41} +(2.85184 + 3.07728i) q^{42} +(0.429127 + 4.90494i) q^{43} +(0.390200 + 0.675847i) q^{44} +(0.0971868 - 0.168333i) q^{46} +(7.69135 + 3.58654i) q^{47} +(-7.70389 - 0.970146i) q^{48} +(2.84600 + 3.39173i) q^{49} +(3.85358 + 11.9863i) q^{51} +(0.0495656 + 0.0707870i) q^{52} +(-0.483003 + 0.483003i) q^{53} +(-5.39876 - 5.69554i) q^{54} +(4.10079 + 0.723079i) q^{56} +(10.1318 - 0.499526i) q^{57} +(5.57450 + 11.9546i) q^{58} +(7.43127 - 6.23558i) q^{59} +(2.50049 - 0.910105i) q^{61} +(-6.55173 + 1.75553i) q^{62} +(3.13415 + 3.65086i) q^{63} +(-5.70071 + 3.29131i) q^{64} +(3.39133 + 6.42609i) q^{66} +(0.884390 + 0.619257i) q^{67} +(-1.67295 - 1.17142i) q^{68} +(0.118712 - 0.188676i) q^{69} +(9.03942 - 5.21891i) q^{71} +(-7.68515 - 1.26605i) q^{72} +(6.65047 - 1.78199i) q^{73} +(3.06175 - 1.11439i) q^{74} +(-1.26050 + 1.05768i) q^{76} +(-1.88278 - 4.03763i) q^{77} +(0.436116 + 0.676135i) q^{78} +(2.04188 + 0.360038i) q^{79} +(-5.93887 - 6.76239i) q^{81} +(5.01475 - 5.01475i) q^{82} +(-7.55956 - 10.7962i) q^{83} +(-0.762929 - 0.164636i) q^{84} +(-4.77986 - 5.69642i) q^{86} +(5.86754 + 13.9429i) q^{87} +(6.53585 + 3.04772i) q^{88} +(-5.58181 + 9.66798i) q^{89} +(-0.246656 - 0.427222i) q^{91} +(0.00315146 + 0.0360214i) q^{92} +(-7.58484 + 1.72638i) q^{93} +(-12.6222 + 2.22564i) q^{94} +(2.41732 - 1.27573i) q^{96} +(11.8062 - 1.03291i) q^{97} +(-6.45906 - 1.73070i) q^{98} +(3.60649 + 7.51214i) 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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