LMFDB - Embedded newform 675.2.ba.b.257.3

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			257.3
Character	$\chi$	$=$	675.257
Dual form			675.2.ba.b.218.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.65044 - 1.15565i) q^{2} +(1.69572 - 0.352907i) q^{3} +(0.704386 + 1.93528i) q^{4} +(-3.20652 - 1.37721i) q^{6} +(-0.618828 - 1.32708i) q^{7} +(0.0310202 - 0.115769i) q^{8} +(2.75091 - 1.19686i) q^{9} +(1.86051 + 2.21727i) q^{11} +(1.87741 + 3.03311i) q^{12} +(3.51558 + 5.02076i) q^{13} +(-0.512304 + 2.90542i) q^{14} +(2.97033 - 2.49240i) q^{16} +(0.833002 + 3.10881i) q^{17} +(-5.92337 - 1.20375i) q^{18} +(3.51741 - 2.03078i) q^{19} +(-1.51769 - 2.03197i) q^{21} +(-0.508272 - 5.80958i) q^{22} +(-4.58997 - 2.14034i) q^{23} +(0.0117458 - 0.207259i) q^{24} -12.3493i q^{26} +(4.24239 - 3.00035i) q^{27} +(2.13239 - 2.13239i) q^{28} +(0.368261 + 2.08851i) q^{29} +(-3.20394 + 1.16614i) q^{31} +(-8.02150 + 0.701790i) q^{32} +(3.93739 + 3.10328i) q^{33} +(2.21787 - 6.09356i) q^{34} +(4.25397 + 4.48075i) q^{36} +(11.3656 - 3.04540i) q^{37} +(-8.15214 - 0.713220i) q^{38} +(7.73328 + 7.27312i) q^{39} +(0.839107 + 0.147957i) q^{41} +(0.156621 + 5.10757i) q^{42} +(0.0641287 - 0.732994i) q^{43} +(-2.98053 + 5.16243i) q^{44} +(5.10199 + 8.83690i) q^{46} +(-2.61254 + 1.21825i) q^{47} +(4.15725 - 5.27466i) q^{48} +(3.12132 - 3.71984i) q^{49} +(2.50966 + 4.97768i) q^{51} +(-7.24028 + 10.3402i) q^{52} +(0.0757900 + 0.0757900i) q^{53} +(-10.4692 + 0.0491845i) q^{54} +(-0.172831 + 0.0304748i) q^{56} +(5.24785 - 4.68494i) q^{57} +(1.80580 - 3.87255i) q^{58} +(-2.89613 - 2.43014i) q^{59} +(-4.21993 - 1.53593i) q^{61} +(6.63556 + 1.77799i) q^{62} +(-3.29067 - 2.91003i) q^{63} +(7.33402 + 4.23430i) q^{64} +(-2.91213 - 9.67203i) q^{66} +(-3.65313 + 2.55795i) q^{67} +(-5.42967 + 3.80189i) q^{68} +(-8.53862 - 2.00957i) q^{69} +(-7.84988 - 4.53213i) q^{71} +(-0.0532255 - 0.355597i) q^{72} +(8.04880 + 2.15667i) q^{73} +(-22.2777 - 8.10840i) q^{74} +(6.40774 + 5.37673i) q^{76} +(1.79116 - 3.84116i) q^{77} +(-4.35814 - 20.9408i) q^{78} +(1.44073 - 0.254040i) q^{79} +(6.13505 - 6.58492i) q^{81} +(-1.21391 - 1.21391i) q^{82} +(9.69375 - 13.8441i) q^{83} +(2.86339 - 4.36846i) q^{84} +(-0.952926 + 1.13565i) q^{86} +(1.36152 + 3.41157i) q^{87} +(0.314404 - 0.146609i) q^{88} +(3.05075 + 5.28406i) q^{89} +(4.48742 - 7.77244i) q^{91} +(0.909052 - 10.3905i) q^{92} +(-5.02144 + 3.10813i) q^{93} +(5.71971 + 1.00854i) q^{94} +(-13.3545 + 4.02088i) q^{96} +(-16.1512 - 1.41304i) q^{97} +(-9.45039 + 2.53222i) q^{98} +(7.77187 + 3.87275i) 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 $

$2$	−1.65044	−	1.15565i	−1.16704	−	0.817169i	−0.180966	−	0.983489i	$-0.557923\pi$
$2$	−1.65044	−	1.15565i	−1.16704	−	0.817169i	−0.986072	+	0.166320i	$0.946811\pi$
$3$	1.69572	−	0.352907i	0.979023	−	0.203751i
$3$	1.69572	−	0.352907i	0.979023	−	0.203751i
$4$	0.704386	+	1.93528i	0.352193	+	0.967642i
$5$		0			0
$5$		0			0
$6$	−3.20652	−	1.37721i	−1.30906	−	0.562242i
$7$	−0.618828	−	1.32708i	−0.233895	−	0.501590i	0.753969	−	0.656910i	$-0.228137\pi$
$7$	−0.618828	−	1.32708i	−0.233895	−	0.501590i	−0.987864	+	0.155320i	$0.950359\pi$
$8$	0.0310202	−	0.115769i	0.0109673	−	0.0409305i
$9$	2.75091	−	1.19686i	0.916971	−	0.398954i
$10$		0			0
$11$	1.86051	+	2.21727i	0.560965	+	0.668532i	0.969751	−	0.244098i	$-0.0784919\pi$
$11$	1.86051	+	2.21727i	0.560965	+	0.668532i	−0.408785	+	0.912631i	$0.634047\pi$
$12$	1.87741	+	3.03311i	0.541963	+	0.875584i
$13$	3.51558	+	5.02076i	0.975045	+	1.39251i	0.919078	+	0.394076i	$0.128935\pi$
$13$	3.51558	+	5.02076i	0.975045	+	1.39251i	0.0559675	+	0.998433i	$0.482176\pi$
$14$	−0.512304	+	2.90542i	−0.136919	+	0.776506i
$15$		0			0
$16$	2.97033	−	2.49240i	0.742582	−	0.623101i
$17$	0.833002	+	3.10881i	0.202033	+	0.753996i	0.990334	+	0.138706i	$0.0442944\pi$
$17$	0.833002	+	3.10881i	0.202033	+	0.753996i	−0.788301	+	0.615290i	$0.789039\pi$
$18$	−5.92337	−	1.20375i	−1.39615	−	0.283726i
$19$	3.51741	−	2.03078i	0.806949	−	0.465892i	−0.0389464	−	0.999241i	$-0.512400\pi$
$19$	3.51741	−	2.03078i	0.806949	−	0.465892i	0.845895	+	0.533349i	$0.179067\pi$
$20$		0			0
$21$	−1.51769	−	2.03197i	−0.331188	−	0.443411i
$22$	−0.508272	−	5.80958i	−0.108364	−	1.23861i
$23$	−4.58997	−	2.14034i	−0.957074	−	0.446291i	−0.119633	−	0.992818i	$-0.538172\pi$
$23$	−4.58997	−	2.14034i	−0.957074	−	0.446291i	−0.837441	+	0.546527i	$0.815949\pi$
$24$	0.0117458	−	0.207259i	0.00239760	−	0.0423065i
$25$		0			0
$26$		−	12.3493i		−	2.42189i
$27$	4.24239	−	3.00035i	0.816448	−	0.577418i
$28$	2.13239	−	2.13239i	0.402983	−	0.402983i
$29$	0.368261	+	2.08851i	0.0683844	+	0.387827i	0.999720	+	0.0236650i	$0.00753352\pi$
$29$	0.368261	+	2.08851i	0.0683844	+	0.387827i	−0.931336	+	0.364162i	$0.881355\pi$
$30$		0			0
$31$	−3.20394	+	1.16614i	−0.575445	+	0.209445i	−0.613316	−	0.789838i	$-0.710165\pi$
$31$	−3.20394	+	1.16614i	−0.575445	+	0.209445i	0.0378710	+	0.999283i	$0.487942\pi$
$32$	−8.02150	+	0.701790i	−1.41801	+	0.124060i
$33$	3.93739	+	3.10328i	0.685412	+	0.540211i
$34$	2.21787	−	6.09356i	0.380362	−	1.04504i
$35$		0			0
$36$	4.25397	+	4.48075i	0.708995	+	0.746791i
$37$	11.3656	−	3.04540i	1.86849	−	0.500661i	0.868503	−	0.495683i	$-0.165082\pi$
$37$	11.3656	−	3.04540i	1.86849	−	0.500661i	0.999988	−	0.00497757i	$-0.00158442\pi$
$38$	−8.15214	−	0.713220i	−1.32245	−	0.115700i
$39$	7.73328	+	7.27312i	1.23832	+	1.16463i
$40$		0			0
$41$	0.839107	+	0.147957i	0.131046	+	0.0231070i	0.238787	−	0.971072i	$-0.423250\pi$
$41$	0.839107	+	0.147957i	0.131046	+	0.0231070i	−0.107740	+	0.994179i	$0.534361\pi$
$42$	0.156621	+	5.10757i	0.0241671	+	0.788114i
$43$	0.0641287	−	0.732994i	0.00977953	−	0.111781i	−0.989736	−	0.142909i	$-0.954354\pi$
$43$	0.0641287	−	0.732994i	0.00977953	−	0.111781i	0.999515	+	0.0311282i	$0.00991001\pi$
$44$	−2.98053	+	5.16243i	−0.449332	+	0.778266i
$45$		0			0
$46$	5.10199	+	8.83690i	0.752247	+	1.30293i
$47$	−2.61254	+	1.21825i	−0.381078	+	0.177700i	−0.603712	−	0.797203i	$-0.706312\pi$
$47$	−2.61254	+	1.21825i	−0.381078	+	0.177700i	0.222634	+	0.974902i	$0.428535\pi$
$48$	4.15725	−	5.27466i	0.600048	−	0.761332i
$49$	3.12132	−	3.71984i	0.445902	−	0.531406i
$50$		0			0
$51$	2.50966	+	4.97768i	0.351422	+	0.697015i
$52$	−7.24028	+	10.3402i	−1.00405	+	1.43393i
$53$	0.0757900	+	0.0757900i	0.0104106	+	0.0104106i	0.712293	−	0.701882i	$-0.247657\pi$
$53$	0.0757900	+	0.0757900i	0.0104106	+	0.0104106i	−0.701882	+	0.712293i	$0.747657\pi$
$54$	−10.4692	+	0.0491845i	−1.42467	+	0.00669316i
$55$		0			0
$56$	−0.172831	+	0.0304748i	−0.0230955	+	0.00407236i
$57$	5.24785	−	4.68494i	0.695095	−	0.620536i
$58$	1.80580	−	3.87255i	0.237113	−	0.508491i
$59$	−2.89613	−	2.43014i	−0.377044	−	0.316377i	0.434497	−	0.900673i	$-0.356926\pi$
$59$	−2.89613	−	2.43014i	−0.377044	−	0.316377i	−0.811540	+	0.584296i	$0.801371\pi$
$60$		0			0
$61$	−4.21993	−	1.53593i	−0.540306	−	0.196655i	0.0574282	−	0.998350i	$-0.481710\pi$
$61$	−4.21993	−	1.53593i	−0.540306	−	0.196655i	−0.597734	+	0.801694i	$0.703932\pi$
$62$	6.63556	+	1.77799i	0.842717	+	0.225805i
$63$	−3.29067	−	2.91003i	−0.414586	−	0.366630i
$64$	7.33402	+	4.23430i	0.916753	+	0.529287i
$65$		0			0
$66$	−2.91213	−	9.67203i	−0.358458	−	1.19054i
$67$	−3.65313	+	2.55795i	−0.446301	+	0.312504i	−0.775034	−	0.631919i	$-0.782267\pi$
$67$	−3.65313	+	2.55795i	−0.446301	+	0.312504i	0.328733	+	0.944423i	$0.393378\pi$
$68$	−5.42967	+	3.80189i	−0.658444	+	0.461047i
$69$	−8.53862	−	2.00957i	−1.02793	−	0.241924i
$70$		0			0
$71$	−7.84988	−	4.53213i	−0.931609	−	0.537865i	−0.0442890	−	0.999019i	$-0.514102\pi$
$71$	−7.84988	−	4.53213i	−0.931609	−	0.537865i	−0.887320	+	0.461154i	$0.847436\pi$
$72$	−0.0532255	−	0.355597i	−0.00627268	−	0.0419075i
$73$	8.04880	+	2.15667i	0.942041	+	0.252419i	0.696982	−	0.717089i	$-0.254526\pi$
$73$	8.04880	+	2.15667i	0.942041	+	0.252419i	0.245059	+	0.969508i	$0.421193\pi$
$74$	−22.2777	−	8.10840i	−2.58972	−	0.942583i
$75$		0			0
$76$	6.40774	+	5.37673i	0.735018	+	0.616754i
$77$	1.79116	−	3.84116i	0.204122	−	0.437741i
$78$	−4.35814	−	20.9408i	−0.493462	−	2.37108i
$79$	1.44073	−	0.254040i	0.162095	−	0.0285818i	−0.0920115	−	0.995758i	$-0.529330\pi$
$79$	1.44073	−	0.254040i	0.162095	−	0.0285818i	0.254107	+	0.967176i	$0.418219\pi$
$80$		0			0
$81$	6.13505	−	6.58492i	0.681672	−	0.731658i
$82$	−1.21391	−	1.21391i	−0.134054	−	0.134054i
$83$	9.69375	−	13.8441i	1.06403	−	1.51959i	0.225872	−	0.974157i	$-0.427477\pi$
$83$	9.69375	−	13.8441i	1.06403	−	1.51959i	0.838155	−	0.545431i	$-0.183634\pi$
$84$	2.86339	−	4.36846i	0.312421	−	0.476638i
$85$		0			0
$86$	−0.952926	+	1.13565i	−0.102757	+	0.122461i
$87$	1.36152	+	3.41157i	0.145970	+	0.365758i
$88$	0.314404	−	0.146609i	0.0335156	−	0.0156286i
$89$	3.05075	+	5.28406i	0.323379	+	0.560109i	0.981183	−	0.193080i	$-0.0618477\pi$
$89$	3.05075	+	5.28406i	0.323379	+	0.560109i	−0.657804	+	0.753189i	$0.728514\pi$
$90$		0			0
$91$	4.48742	−	7.77244i	0.470410	−	0.814774i
$92$	0.909052	−	10.3905i	0.0947752	−	1.08329i
$93$	−5.02144	+	3.10813i	−0.520699	+	0.322299i
$94$	5.71971	+	1.00854i	0.589943	+	0.104023i
$95$		0			0
$96$	−13.3545	+	4.02088i	−1.36299	+	0.410379i
$97$	−16.1512	−	1.41304i	−1.63990	−	0.143473i	−0.770453	−	0.637496i	$-0.779970\pi$
$97$	−16.1512	−	1.41304i	−1.63990	−	0.143473i	−0.869449	+	0.494023i	$0.835526\pi$
$98$	−9.45039	+	2.53222i	−0.954633	+	0.255793i
$99$	7.77187	+	3.87275i	0.781102	+	0.389226i
$100$		0			0
$101$	−1.88053	+	5.16673i	−0.187120	+	0.514108i	−0.997410	−	0.0719204i	$-0.977087\pi$
$101$	−1.88053	+	5.16673i	−0.187120	+	0.514108i	0.810290	+	0.586029i	$0.199309\pi$
$102$	1.61043	−	11.1157i	0.159456	−	1.10061i
$103$	−3.90922	+	0.342012i	−0.385186	+	0.0336994i	−0.278105	−	0.960551i	$-0.589706\pi$
$103$	−3.90922	+	0.342012i	−0.385186	+	0.0336994i	−0.107082	+	0.994250i	$0.534151\pi$
$104$	0.690302	−	0.251249i	0.0676897	−	0.0246370i
$105$		0			0
$106$	−0.0375001	−	0.212674i	−0.00364233	−	0.0206567i
$107$	10.5329	−	10.5329i	1.01825	−	1.01825i	0.0184189	−	0.999830i	$-0.494137\pi$
$107$	10.5329	−	10.5329i	1.01825	−	1.01825i	0.999830	−	0.0184189i	$-0.00586325\pi$
$108$	8.79481	+	6.09682i	0.846281	+	0.586667i
$109$		−	9.91447i		−	0.949634i	−0.880085	−	0.474817i	$-0.842514\pi$
$109$		−	9.91447i		−	0.949634i	0.880085	−	0.474817i	$-0.157486\pi$
$110$		0			0
$111$	18.1981	−	9.17513i	1.72729	−	0.870865i
$112$	−5.14574	−	2.39950i	−0.486227	−	0.226731i
$113$	1.32748	+	15.1732i	0.124879	+	1.42737i	0.757462	+	0.652879i	$0.226439\pi$
$113$	1.32748	+	15.1732i	0.124879	+	1.42737i	−0.632583	+	0.774492i	$0.718005\pi$
$114$	−14.0754	+	1.66753i	−1.31829	+	0.156178i
$115$		0			0
$116$	−3.78247	+	2.18381i	−0.351193	+	0.202762i
$117$	15.6802	+	9.60403i	1.44963	+	0.887893i
$118$	1.97149	+	7.35771i	0.181491	+	0.677332i
$119$	3.61015	−	3.02928i	0.330942	−	0.277693i
$120$		0			0
$121$	0.455341	−	2.58237i	0.0413946	−	0.234761i
$122$	5.18974	+	7.41172i	0.469857	+	0.671026i
$123$	1.47510	−	0.0452332i	0.133006	−	0.00407854i
$124$	−4.51362	−	5.37912i	−0.405335	−	0.483059i
$125$		0			0
$126$	2.06808	+	8.60571i	0.184239	+	0.766658i
$127$	−2.58018	+	9.62937i	−0.228954	+	0.854468i	0.751828	+	0.659360i	$0.229173\pi$
$127$	−2.58018	+	9.62937i	−0.228954	+	0.854468i	−0.980782	+	0.195109i	$0.937494\pi$
$128$	−0.405037	−	0.868604i	−0.0358005	−	0.0767745i
$129$	−0.149935	−	1.26558i	−0.0132010	−	0.111428i
$130$		0			0
$131$	3.84111	+	10.5534i	0.335599	+	0.922051i	0.986627	+	0.162997i	$0.0521159\pi$
$131$	3.84111	+	10.5534i	0.335599	+	0.922051i	−0.651028	+	0.759054i	$0.725662\pi$
$132$	−3.23228	+	9.80587i	−0.281334	+	0.853492i
$133$	−4.87168	−	3.41119i	−0.422428	−	0.295787i
$134$	8.98538			0.776219
$135$		0			0
$136$	0.385743			0.0330772
$137$	−16.1027	−	11.2752i	−1.37574	−	0.963306i	−0.999320	−	0.0368588i	$-0.988265\pi$
$137$	−16.1027	−	11.2752i	−1.37574	−	0.963306i	−0.376424	−	0.926448i	$-0.622846\pi$
$138$	11.7701	+	13.1844i	1.00194	+	1.12233i
$139$	0.508611	+	1.39740i	0.0431398	+	0.118526i	0.959392	−	0.282076i	$-0.0910232\pi$
$139$	0.508611	+	1.39740i	0.0431398	+	0.118526i	−0.916252	+	0.400602i	$0.868801\pi$
$140$		0			0
$141$	−4.00020	+	2.98779i	−0.336878	+	0.251617i
$142$	7.71820	+	16.5517i	0.647697	+	1.38899i
$143$	−4.59162	+	17.1362i	−0.383971	+	1.43300i
$144$	5.18806	−	10.4115i	0.432338	−	0.867621i
$145$		0			0
$146$	−10.7917	−	12.8611i	−0.893129	−	1.06439i
$147$	3.98011	−	7.40933i	0.328274	−	0.611111i
$148$	13.8995	+	19.8505i	1.14253	+	1.63170i
$149$	0.861743	−	4.88719i	0.0705968	−	0.400374i	−0.928948	−	0.370210i	$-0.879286\pi$
$149$	0.861743	−	4.88719i	0.0705968	−	0.400374i	0.999545	−	0.0301644i	$-0.00960308\pi$
$150$		0			0
$151$	−15.8833	+	13.3277i	−1.29257	+	1.08459i	−0.301186	+	0.953565i	$0.597383\pi$
$151$	−15.8833	+	13.3277i	−1.29257	+	1.08459i	−0.991379	+	0.131025i	$0.958173\pi$
$152$	−0.125990	−	0.470202i	−0.0102191	−	0.0381384i
$153$	6.01232	+	7.55507i	0.486068	+	0.610791i
$154$	−7.39525	+	4.26965i	−0.595926	+	0.344058i
$155$		0			0
$156$	−8.62834	+	20.0892i	−0.690820	+	1.60842i
$157$	−0.591932	−	6.76582i	−0.0472413	−	0.539971i	−0.982532	−	0.186092i	$-0.940418\pi$
$157$	−0.591932	−	6.76582i	−0.0472413	−	0.539971i	0.935291	−	0.353879i	$-0.115138\pi$
$158$	−2.67143	−	1.24571i	−0.212528	−	0.0991032i
$159$	0.155265	+	0.101772i	0.0123133	+	0.00807101i
$160$		0			0
$161$			7.41576i			0.584444i
$162$	−17.7354	+	3.77805i	−1.39343	+	0.296832i
$163$	−14.3864	+	14.3864i	−1.12683	+	1.12683i	−0.136142	+	0.990689i	$0.543470\pi$
$163$	−14.3864	+	14.3864i	−1.12683	+	1.12683i	−0.990689	+	0.136142i	$0.956530\pi$
$164$	0.304716	+	1.72813i	0.0237943	+	0.134944i
$165$		0			0
$166$	−31.9979	+	11.6463i	−2.48352	+	0.903928i
$167$	0.469806	−	0.0411027i	0.0363547	−	0.00318063i	−0.0689639	−	0.997619i	$-0.521969\pi$
$167$	0.469806	−	0.0411027i	0.0363547	−	0.00318063i	0.105319	+	0.994439i	$0.466414\pi$
$168$	−0.282318	+	0.112670i	−0.0217813	+	0.00869266i
$169$	−8.40252	+	23.0857i	−0.646348	+	1.77583i
$170$		0			0
$171$	7.24553	−	9.79634i	0.554079	−	0.749145i
$172$	1.46372	−	0.392203i	0.111608	−	0.0299052i
$173$	18.3690	+	1.60708i	1.39657	+	0.122184i	0.760446	−	0.649402i	$-0.224981\pi$
$173$	18.3690	+	1.60708i	1.39657	+	0.122184i	0.636125	+	0.771586i	$0.280536\pi$
$174$	1.69548	−	7.20403i	0.128534	−	0.546136i
$175$		0			0
$176$	11.0527	+	1.94888i	0.833126	+	0.146903i
$177$	−5.76862	−	3.09876i	−0.433596	−	0.232917i
$178$	1.07144	−	12.2466i	0.0803080	−	0.917925i
$179$	−3.95796	+	6.85540i	−0.295832	+	0.512396i	−0.975178	−	0.221422i	$-0.928930\pi$
$179$	−3.95796	+	6.85540i	−0.295832	+	0.512396i	0.679346	+	0.733818i	$0.262264\pi$
$180$		0			0
$181$	9.86110	+	17.0799i	0.732970	+	1.26954i	0.955608	+	0.294640i	$0.0951998\pi$
$181$	9.86110	+	17.0799i	0.732970	+	1.26954i	−0.222638	+	0.974901i	$0.571467\pi$
$182$	−16.3885	+	7.64207i	−1.21479	+	0.566468i
$183$	−7.69784	−	1.11526i	−0.569041	−	0.0824421i
$184$	−0.390166	+	0.464982i	−0.0287634	+	0.0342789i
$185$		0			0
$186$	11.8795	+	0.673238i	0.871048	+	0.0493642i
$187$	−5.34326	+	7.63096i	−0.390738	+	0.558031i
$188$	−4.19789	−	4.19789i	−0.306162	−	0.306162i
$189$	−6.60703	−	3.77329i	−0.480590	−	0.274467i
$190$		0			0
$191$	−8.60644	+	1.51755i	−0.622740	+	0.109806i	−0.476110	−	0.879386i	$-0.657954\pi$
$191$	−8.60644	+	1.51755i	−0.622740	+	0.109806i	−0.146630	+	0.989191i	$0.546843\pi$
$192$	13.9307	+	4.59195i	1.00536	+	0.331395i
$193$	3.65180	−	7.83132i	0.262863	−	0.563711i	−0.729935	−	0.683517i	$-0.760450\pi$
$193$	3.65180	−	7.83132i	0.262863	−	0.563711i	0.992797	+	0.119806i	$0.0382273\pi$
$194$	25.0236	+	20.9973i	1.79659	+	1.50752i
$195$		0			0
$196$	9.39756	+	3.42043i	0.671254	+	0.244316i
$197$	−1.93720	−	0.519071i	−0.138020	−	0.0369822i	0.189148	−	0.981949i	$-0.439427\pi$
$197$	−1.93720	−	0.519071i	−0.138020	−	0.0369822i	−0.327167	+	0.944966i	$0.606094\pi$
$198$	−8.35147	−	15.3733i	−0.593513	−	1.09253i
$199$	15.5130	+	8.95641i	1.09968	+	0.634903i	0.936138	−	0.351633i	$-0.114373\pi$
$199$	15.5130	+	8.95641i	1.09968	+	0.634903i	0.163546	+	0.986536i	$0.447707\pi$
$200$		0			0
$201$	−5.29196	+	5.62678i	−0.373266	+	0.396883i
$202$	9.07464	−	6.35413i	0.638490	−	0.447075i
$203$	2.54374	−	1.78114i	0.178535	−	0.125012i
$204$	−7.86546	+	8.36310i	−0.550693	+	0.585534i
$205$		0			0
$206$	6.84718	+	3.95322i	0.477065	+	0.275434i
$207$	−15.1883	−	0.394328i	−1.05566	−	0.0274077i
$208$	22.9562	+	6.15109i	1.59172	+	0.426501i
$209$	11.0470	+	4.02077i	0.764134	+	0.278122i
$210$		0			0
$211$	−8.17709	−	6.86139i	−0.562934	−	0.472358i	0.316359	−	0.948640i	$-0.397540\pi$
$211$	−8.17709	−	6.86139i	−0.562934	−	0.472358i	−0.879293	+	0.476282i	$0.841984\pi$
$212$	−0.0932898	+	0.200061i	−0.00640717	+	0.0137402i
$213$	−14.9106	−	4.91493i	−1.02166	−	0.336766i
$214$	−29.5562	+	5.21155i	−2.02042	+	0.356254i
$215$		0			0
$216$	−0.215748	−	0.584208i	−0.0146798	−	0.0397503i
$217$	3.53025	+	3.53025i	0.239649	+	0.239649i
$218$	−11.4577	+	16.3632i	−0.776011	+	1.10826i
$219$	14.4096	+	0.816623i	0.973710	+	0.0551823i
$220$		0			0
$221$	−12.6801	+	15.1115i	−0.852955	+	1.01651i
$222$	−40.6381	−	5.88762i	−2.72745	−	0.395151i
$223$	−10.8301	+	5.05016i	−0.725238	+	0.338184i	−0.749936	−	0.661511i	$-0.769916\pi$
$223$	−10.8301	+	5.05016i	−0.725238	+	0.338184i	0.0246975	+	0.999695i	$0.492138\pi$
$224$	5.89526	+	10.2109i	0.393894	+	0.682244i
$225$		0			0
$226$	15.3440	−	26.5765i	1.02067	−	1.76784i
$227$	−0.100851	+	1.15273i	−0.00669369	+	0.0765092i	−0.998807	−	0.0488368i	$-0.984449\pi$
$227$	−0.100851	+	1.15273i	−0.00669369	+	0.0765092i	0.992113	+	0.125346i	$0.0400041\pi$
$228$	12.7632	+	6.85608i	0.845264	+	0.454055i
$229$	−8.62548	−	1.52090i	−0.569988	−	0.100504i	−0.118776	−	0.992921i	$-0.537897\pi$
$229$	−8.62548	−	1.52090i	−0.569988	−	0.100504i	−0.451212	+	0.892417i	$0.649008\pi$
$230$		0			0
$231$	1.68173	−	7.14564i	0.110650	−	0.470148i
$232$	0.253208	+	0.0221529i	0.0166240	+	0.00145441i
$233$	15.8052	−	4.23498i	1.03543	−	0.277443i	0.299213	−	0.954186i	$-0.403276\pi$
$233$	15.8052	−	4.23498i	1.03543	−	0.277443i	0.736219	+	0.676743i	$0.236609\pi$
$234$	−14.7803	−	33.9717i	−0.966221	−	2.22080i
$235$		0			0
$236$	2.66302	−	7.31658i	0.173348	−	0.476269i
$237$	2.35343	−	0.939226i	0.152871	−	0.0610093i
$238$	−9.45913	+	0.827567i	−0.613145	+	0.0536432i
$239$	−8.07123	+	2.93769i	−0.522085	+	0.190023i	−0.589601	−	0.807695i	$-0.700715\pi$
$239$	−8.07123	+	2.93769i	−0.522085	+	0.190023i	0.0675160	+	0.997718i	$0.478493\pi$
$240$		0			0
$241$	0.358872	+	2.03527i	0.0231170	+	0.131103i	0.994182	−	0.107712i	$-0.0343523\pi$
$241$	0.358872	+	2.03527i	0.0231170	+	0.131103i	−0.971065	+	0.238815i	$0.923241\pi$
$242$	−3.73583	+	3.73583i	−0.240148	+	0.240148i
$243$	8.07944	−	13.3313i	0.518296	−	0.855201i
$244$		−	9.24864i		−	0.592083i
$245$		0			0
$246$	−2.48684	−	1.63005i	−0.158555	−	0.103928i
$247$	22.5618	+	10.5207i	1.43557	+	0.669417i
$248$	0.0356158	+	0.407090i	0.00226161	+	0.0258503i
$249$	11.5522	−	26.8967i	0.732089	−	1.70451i
$250$		0			0
$251$	9.55376	−	5.51587i	0.603028	−	0.348158i	−0.167204	−	0.985922i	$-0.553474\pi$
$251$	9.55376	−	5.51587i	0.603028	−	0.348158i	0.770232	+	0.637764i	$0.220140\pi$
$252$	3.31384	−	8.41818i	0.208752	−	0.530295i
$253$	−3.79398	−	14.1593i	−0.238525	−	0.890189i
$254$	15.3866	−	12.9109i	0.965443	−	0.810103i
$255$		0			0
$256$	2.60580	−	14.7782i	0.162862	−	0.923639i
$257$	3.31253	+	4.73079i	0.206630	+	0.295098i	0.909069	−	0.416646i	$-0.136794\pi$
$257$	3.31253	+	4.73079i	0.206630	+	0.295098i	−0.702439	+	0.711744i	$0.747906\pi$
$258$	−1.21511	+	2.26204i	−0.0756496	+	0.140829i
$259$	−11.0748	−	13.1985i	−0.688157	−	0.820114i
$260$		0			0
$261$	3.51272	+	5.30456i	0.217432	+	0.328344i
$262$	5.85647	−	21.8567i	0.361814	−	1.35031i
$263$	−7.79728	−	16.7213i	−0.480801	−	1.03108i	−0.985794	−	0.167958i	$-0.946283\pi$
$263$	−7.79728	−	16.7213i	−0.480801	−	1.03108i	0.504993	−	0.863123i	$-0.331495\pi$
$264$	0.481402	−	0.359563i	0.0296282	−	0.0221296i
$265$		0			0
$266$	4.09828	+	11.2599i	0.251281	+	0.690390i
$267$	7.03800	+	7.88364i	0.430719	+	0.482471i
$268$	−7.52358	−	5.26807i	−0.459576	−	0.321798i
$269$	−15.7262			−0.958842			−0.479421	−	0.877585i	$-0.659153\pi$
$269$	−15.7262			−0.958842			−0.479421	+	0.877585i	$0.659153\pi$
$270$		0			0
$271$	−17.4326			−1.05895			−0.529477	−	0.848324i	$-0.677612\pi$
$271$	−17.4326			−1.05895			−0.529477	+	0.848324i	$0.677612\pi$
$272$	10.2227	+	7.15800i	0.619841	+	0.434018i
$273$	4.86645	−	14.7635i	0.294531	−	0.893528i
$274$	13.5463	+	37.2181i	0.818362	+	2.24843i
$275$		0			0
$276$	−2.12539	−	17.9402i	−0.127933	−	1.07987i
$277$	−6.49002	−	13.9179i	−0.389947	−	0.836245i	−0.999068	−	0.0431672i	$-0.986255\pi$
$277$	−6.49002	−	13.9179i	−0.389947	−	0.836245i	0.609120	−	0.793078i	$-0.291523\pi$
$278$	0.775471	−	2.89410i	0.0465097	−	0.173576i
$279$	−7.41806	+	7.04262i	−0.444107	+	0.421630i
$280$		0			0
$281$	4.76302	+	5.67634i	0.284138	+	0.338622i	0.889168	−	0.457580i	$-0.151284\pi$
$281$	4.76302	+	5.67634i	0.284138	+	0.338622i	−0.605031	+	0.796202i	$0.706839\pi$
$282$	10.0549	−	0.308329i	0.598763	−	0.0183607i
$283$	−8.24647	−	11.7772i	−0.490202	−	0.700081i	0.495495	−	0.868611i	$-0.334987\pi$
$283$	−8.24647	−	11.7772i	−0.490202	−	0.700081i	−0.985696	+	0.168530i	$0.946098\pi$
$284$	3.24161	−	18.3841i	0.192354	−	1.09090i
$285$		0			0
$286$	27.3816	−	22.9759i	1.61911	−	1.35859i
$287$	−0.322912	−	1.20512i	−0.0190609	−	0.0711362i
$288$	−21.2265	+	11.5312i	−1.25078	+	0.679481i
$289$	5.75165	−	3.32072i	0.338332	−	0.195336i
$290$		0			0
$291$	−27.8865	+	3.30374i	−1.63473	+	0.193668i
$292$	1.49569	+	17.0958i	0.0875288	+	1.00046i
$293$	−18.2561	−	8.51297i	−1.06653	−	0.497333i	−0.191549	−	0.981483i	$-0.561351\pi$
$293$	−18.2561	−	8.51297i	−1.06653	−	0.497333i	−0.874985	+	0.484150i	$0.839129\pi$
$294$	−15.1315	+	7.62904i	−0.882490	+	0.444935i
$295$		0			0
$296$		−	1.41025i		−	0.0819691i
$297$	14.5456	+	3.82434i	0.844022	+	0.221910i
$298$	−7.07014	+	7.07014i	−0.409562	+	0.409562i
$299$	−5.39025	−	30.5696i	−0.311726	−	1.76789i
$300$		0			0
$301$	−1.01243	+	0.368493i	−0.0583553	+	0.0212396i
$302$	41.6166	−	3.64098i	2.39477	−	0.209515i
$303$	−1.36548	+	9.42496i	−0.0784448	+	0.541450i
$304$	5.38635	−	14.7989i	0.308928	−	0.848774i
$305$		0			0
$306$	−1.19196	−	19.4173i	−0.0681401	−	1.11002i
$307$	−11.5423	+	3.09276i	−0.658756	+	0.176513i	−0.572684	−	0.819776i	$-0.694098\pi$
$307$	−11.5423	+	3.09276i	−0.658756	+	0.176513i	−0.0860714	+	0.996289i	$0.527431\pi$
$308$	8.69540	+	0.760749i	0.495467	+	0.0433477i
$309$	−6.50822	+	1.95955i	−0.370240	+	0.111475i
$310$		0			0
$311$	2.38442	+	0.420438i	0.135208	+	0.0238408i	0.240843	−	0.970564i	$-0.422576\pi$
$311$	2.38442	+	0.420438i	0.135208	+	0.0238408i	−0.105634	+	0.994405i	$0.533687\pi$
$312$	1.08189	−	0.669660i	0.0612499	−	0.0379120i
$313$	−1.06842	+	12.2121i	−0.0603905	+	0.690267i	0.904303	+	0.426891i	$0.140391\pi$
$313$	−1.06842	+	12.2121i	−0.0603905	+	0.690267i	−0.964693	+	0.263375i	$0.915164\pi$
$314$	−6.84198	+	11.8506i	−0.386115	+	0.668771i
$315$		0			0
$316$	1.50647	+	2.60929i	0.0847457	+	0.146784i
$317$	−20.5585	+	9.58656i	−1.15468	+	0.538435i	−0.903112	−	0.429405i	$-0.858723\pi$
$317$	−20.5585	+	9.58656i	−1.15468	+	0.538435i	−0.251566	+	0.967840i	$0.580945\pi$
$318$	−0.138644	−	0.347401i	−0.00777475	−	0.0194813i
$319$	−3.94565	+	4.70224i	−0.220914	+	0.263275i
$320$		0			0
$321$	14.1436	−	21.5779i	0.789420	−	1.20436i
$322$	8.57003	−	12.2393i	0.477589	−	0.682068i
$323$	9.24330	+	9.24330i	0.514311	+	0.514311i
$324$	17.0651	+	7.23473i	0.948063	+	0.401930i
$325$		0			0
$326$	40.3696	−	7.11825i	2.23587	−	0.394243i
$327$	−3.49889	−	16.8121i	−0.193489	−	0.929713i
$328$	0.0431581	−	0.0925528i	0.00238301	−	0.00511038i
$329$	3.23343	+	2.71317i	0.178265	+	0.149582i
$330$		0			0
$331$	15.3336	+	5.58098i	0.842812	+	0.306758i	0.727106	−	0.686525i	$-0.240865\pi$
$331$	15.3336	+	5.58098i	0.842812	+	0.306758i	0.115706	+	0.993284i	$0.463087\pi$
$332$	33.6204	+	9.00856i	1.84516	+	0.494409i
$333$	27.6208	−	21.9807i	1.51361	−	1.20453i
$334$	−0.822888	−	0.475095i	−0.0450264	−	0.0259960i
$335$		0			0
$336$	−9.57253	−	2.25290i	−0.522224	−	0.122906i
$337$	3.28511	−	2.30026i	0.178951	−	0.125303i	−0.480669	−	0.876902i	$-0.659606\pi$
$337$	3.28511	−	2.30026i	0.178951	−	0.125303i	0.659620	+	0.751599i	$0.270717\pi$
$338$	40.5469	−	28.3913i	2.20546	−	1.54428i
$339$	7.60575	+	25.2609i	0.413088	+	1.37198i
$340$		0			0
$341$	−8.54661	−	4.93439i	−0.462825	−	0.267212i
$342$	−23.2795	+	7.79498i	−1.25881	+	0.421504i
$343$	−16.7687	−	4.49317i	−0.905427	−	0.242608i
$344$	−0.0828686	−	0.0301617i	−0.00446798	−	0.00162621i
$345$		0			0
$346$	−28.4598	−	23.8806i	−1.53001	−	1.28383i
$347$	5.24496	−	11.2479i	0.281564	−	0.603816i	−0.713762	−	0.700389i	$-0.753010\pi$
$347$	5.24496	−	11.2479i	0.281564	−	0.603816i	0.995326	+	0.0965722i	$0.0307879\pi$
$348$	−5.64331	+	5.03798i	−0.302513	+	0.270064i
$349$	−7.52479	+	1.32682i	−0.402793	+	0.0710232i	−0.371375	−	0.928483i	$-0.621113\pi$
$349$	−7.52479	+	1.32682i	−0.402793	+	0.0710232i	−0.0314181	+	0.999506i	$0.510002\pi$
$350$		0			0
$351$	29.9785	+	10.7521i	1.60013	+	0.573902i
$352$	−16.4801	−	16.4801i	−0.878395	−	0.878395i
$353$	−10.2693	+	14.6661i	−0.546579	+	0.780595i	−0.993482	−	0.113987i	$-0.963638\pi$
$353$	−10.2693	+	14.6661i	−0.546579	+	0.780595i	0.446904	+	0.894582i	$0.352527\pi$
$354$	5.93968	+	11.7808i	0.315691	+	0.626145i
$355$		0			0
$356$	−8.07725	+	9.62609i	−0.428093	+	0.510182i
$357$	5.05275	−	6.41085i	0.267420	−	0.339298i
$358$	14.4548	−	6.74040i	0.763962	−	0.356241i
$359$	6.26521	+	10.8517i	0.330665	+	0.572729i	0.982642	−	0.185510i	$-0.0593936\pi$
$359$	6.26521	+	10.8517i	0.330665	+	0.572729i	−0.651977	+	0.758239i	$0.726060\pi$
$360$		0			0
$361$	−1.25189	+	2.16834i	−0.0658891	+	0.114123i
$362$	3.46328	−	39.5854i	0.182026	−	2.08056i
$363$	−0.139206	−	4.53966i	−0.00730642	−	0.238270i
$364$	18.2028	+	3.20964i	0.954084	+	0.168231i
$365$		0			0
$366$	11.4160	+	10.7367i	0.596723	+	0.561215i
$367$	13.6352	+	1.19292i	0.711750	+	0.0622701i	0.437280	−	0.899325i	$-0.355942\pi$
$367$	13.6352	+	1.19292i	0.711750	+	0.0622701i	0.274470	+	0.961596i	$0.411497\pi$
$368$	−18.9683	+	5.08254i	−0.988790	+	0.264946i
$369$	2.48539	−	0.597277i	0.129384	−	0.0310930i
$370$		0			0
$371$	0.0536785	−	0.147481i	0.00278685	−	0.00765681i
$372$	−9.55215	−	7.52858i	−0.495256	−	0.390339i
$373$	12.0608	−	1.05518i	0.624485	−	0.0546353i	0.229478	−	0.973314i	$-0.426298\pi$
$373$	12.0608	−	1.05518i	0.624485	−	0.0546353i	0.395006	+	0.918678i	$0.370742\pi$
$374$	17.6375	−	6.41951i	0.912011	−	0.331945i
$375$		0			0
$376$	0.0599937	+	0.340241i	0.00309394	+	0.0175466i
$377$	−9.19128	+	9.19128i	−0.473375	+	0.473375i
$378$	6.54389	+	13.8630i	0.336582	+	0.713037i
$379$		−	22.5213i		−	1.15684i	−0.815738	−	0.578421i	$-0.803669\pi$
$379$		−	22.5213i		−	1.15684i	0.815738	−	0.578421i	$-0.196331\pi$
$380$		0			0
$381$	−0.976986	+	17.2393i	−0.0500525	+	0.883194i
$382$	15.9582	+	7.44142i	0.816491	+	0.380736i
$383$	−1.26087	−	14.4118i	−0.0644275	−	0.736410i	−0.957864	−	0.287221i	$-0.907269\pi$
$383$	−1.26087	−	14.4118i	−0.0644275	−	0.736410i	0.893437	−	0.449189i	$-0.148287\pi$
$384$	−0.993364	−	1.32997i	−0.0506924	−	0.0678695i
$385$		0			0
$386$	−15.0774	+	8.70492i	−0.767417	+	0.443069i
$387$	−0.700880	−	2.09316i	−0.0356277	−	0.106401i
$388$	−8.64201	−	32.2524i	−0.438731	−	1.63737i
$389$	−9.68308	+	8.12507i	−0.490951	+	0.411957i	−0.854367	−	0.519670i	$-0.826055\pi$
$389$	−9.68308	+	8.12507i	−0.490951	+	0.411957i	0.363416	+	0.931627i	$0.381610\pi$
$390$		0			0
$391$	2.83044	−	16.0522i	0.143141	−	0.811795i
$392$	−0.333818	−	0.476742i	−0.0168604	−	0.0240791i
$393$	10.2378	+	16.5399i	0.516428	+	0.834330i
$394$	2.59737	+	3.09542i	0.130853	+	0.155945i
$395$		0			0
$396$	−2.02047	+	17.7687i	−0.101532	+	0.892910i
$397$	−3.89075	+	14.5205i	−0.195271	+	0.728761i	0.796926	+	0.604077i	$0.206458\pi$
$397$	−3.89075	+	14.5205i	−0.195271	+	0.728761i	−0.992197	+	0.124684i	$0.960208\pi$
$398$	−15.2527	−	32.7096i	−0.764550	−	1.63958i
$399$	−9.46482	−	4.06516i	−0.473834	−	0.203512i
$400$		0			0
$401$	−8.96818	−	24.6399i	−0.447849	−	1.23046i	−0.934218	−	0.356703i	$-0.883901\pi$
$401$	−8.96818	−	24.6399i	−0.447849	−	1.23046i	0.486369	−	0.873754i	$-0.338321\pi$
$402$	15.2367	−	3.17101i	0.759936	−	0.158155i
$403$	−17.1186	−	11.9866i	−0.852738	−	0.597094i
$404$	−11.3237			−0.563375
$405$		0			0
$406$	−6.25667			−0.310513
$407$	27.8983	+	19.5346i	1.38287	+	0.968294i
$408$	0.654111	−	0.136131i	0.0323833	−	0.00673951i
$409$	−2.57831	−	7.08384i	−0.127489	−	0.350273i	0.859483	−	0.511164i	$-0.170786\pi$
$409$	−2.57831	−	7.08384i	−0.127489	−	0.350273i	−0.986972	+	0.160891i	$0.948563\pi$
$410$		0			0
$411$	−31.2847	−	13.4368i	−1.54316	−	0.662790i
$412$	−3.41549	−	7.32453i	−0.168269	−	0.360854i
$413$	−1.43279	+	5.34723i	−0.0705028	+	0.263120i
$414$	24.6117	+	18.2032i	1.20960	+	0.894637i
$415$		0			0
$416$	−31.7237	−	37.8068i	−1.55538	−	1.85363i
$417$	1.35561	+	2.19010i	0.0663846	+	0.107250i
$418$	−13.5858	−	19.4025i	−0.664501	−	0.949006i
$419$	3.59622	−	20.3952i	0.175687	−	0.996370i	−0.761661	−	0.647975i	$-0.775616\pi$
$419$	3.59622	−	20.3952i	0.175687	−	0.996370i	0.937348	−	0.348394i	$-0.113273\pi$
$420$		0			0
$421$	−5.26964	+	4.42176i	−0.256827	+	0.215503i	−0.762105	−	0.647453i	$-0.775834\pi$
$421$	−5.26964	+	4.42176i	−0.256827	+	0.215503i	0.505279	+	0.862956i	$0.331390\pi$
$422$	5.56643	+	20.7742i	0.270969	+	1.01127i
$423$	−5.72880	+	6.47814i	−0.278544	+	0.314978i
$424$	0.0111251	−	0.00642311i	0.000540285	−	0.000311934i
$425$		0			0
$426$	18.9291	+	25.3433i	0.917118	+	1.22788i
$427$	0.573108	+	6.55066i	0.0277347	+	0.317009i
$428$	27.8032	+	12.9649i	1.34392	+	0.626680i
$429$	−1.73862	+	30.6785i	−0.0839413	+	1.48117i
$430$		0			0
$431$		−	2.91928i		−	0.140617i	−0.997525	−	0.0703084i	$-0.977602\pi$
$431$		−	2.91928i		−	0.140617i	0.997525	−	0.0703084i	$-0.0223983\pi$
$432$	5.12321	−	19.4858i	0.246490	−	0.937510i
$433$	−3.01763	+	3.01763i	−0.145018	+	0.145018i	−0.775888	−	0.630870i	$-0.782698\pi$
$433$	−3.01763	+	3.01763i	−0.145018	+	0.145018i	0.630870	+	0.775888i	$0.282698\pi$
$434$	−1.74673	−	9.90621i	−0.0838458	−	0.475513i
$435$		0			0
$436$	19.1873	−	6.98361i	0.918905	−	0.334454i
$437$	−20.4913	+	1.79276i	−0.980233	+	0.0857593i
$438$	−22.8385	−	18.0003i	−1.09126	−	0.860085i
$439$	−1.28129	+	3.52030i	−0.0611524	+	0.168015i	−0.966506	−	0.256643i	$-0.917383\pi$
$439$	−1.28129	+	3.52030i	−0.0611524	+	0.168015i	0.905354	+	0.424658i	$0.139606\pi$
$440$		0			0
$441$	4.13434	−	13.9687i	0.196873	−	0.665178i
$442$	38.3914	−	10.2870i	1.82609	−	0.489300i
$443$	27.8809	+	2.43927i	1.32466	+	0.115893i	0.727434	−	0.686177i	$-0.240713\pi$
$443$	27.8809	+	2.43927i	1.32466	+	0.115893i	0.597229	+	0.802070i	$0.296268\pi$
$444$	30.5749	+	28.7556i	1.45102	+	1.36468i
$445$		0			0
$446$	23.7107	+	4.18083i	1.12273	+	0.197968i
$447$	−0.263451	−	8.59141i	−0.0124608	−	0.406360i
$448$	1.08076	−	12.3531i	0.0510611	−	0.583631i
$449$	4.77256	−	8.26631i	0.225231	−	0.390111i	−0.731158	−	0.682208i	$-0.761020\pi$
$449$	4.77256	−	8.26631i	0.225231	−	0.390111i	0.956389	+	0.292097i	$0.0943530\pi$
$450$		0			0
$451$	1.23311	+	2.13580i	0.0580647	+	0.100571i
$452$	−28.4293	+	13.2568i	−1.33720	+	0.623548i
$453$	−22.2302	+	28.2053i	−1.04446	+	1.32520i
$454$	1.49860	−	1.78596i	0.0703328	−	0.0838193i
$455$		0			0
$456$	−0.379581	−	0.752866i	−0.0177755	−	0.0352562i
$457$	−20.3246	+	29.0265i	−0.950745	+	1.35780i	−0.0170039	+	0.999855i	$0.505413\pi$
$457$	−20.3246	+	29.0265i	−0.950745	+	1.35780i	−0.933741	+	0.357949i	$0.883476\pi$
$458$	12.4782	+	12.4782i	0.583068	+	0.583068i
$459$	12.8614	+	10.6895i	0.600321	+	0.498942i
$460$		0			0
$461$	24.4088	−	4.30393i	1.13683	−	0.200454i	0.426612	−	0.904435i	$-0.359707\pi$
$461$	24.4088	−	4.30393i	1.13683	−	0.200454i	0.710219	+	0.703981i	$0.248596\pi$
$462$	−11.0335	+	9.84995i	−0.513323	+	0.458261i
$463$	2.28775	−	4.90609i	0.106321	−	0.228005i	−0.845949	−	0.533264i	$-0.820965\pi$
$463$	2.28775	−	4.90609i	0.106321	−	0.228005i	0.952269	+	0.305259i	$0.0987430\pi$
$464$	6.29927	+	5.28572i	0.292436	+	0.245383i
$465$		0			0
$466$	−30.9797	−	11.2757i	−1.43511	−	0.522336i
$467$	−39.5591	−	10.5998i	−1.83058	−	0.490502i	−0.832589	−	0.553891i	$-0.813143\pi$
$467$	−39.5591	−	10.5998i	−1.83058	−	0.490502i	−0.997989	+	0.0633888i	$0.979809\pi$
$468$	−7.54161	+	37.1106i	−0.348611	+	1.71544i
$469$	5.65527	+	3.26507i	0.261136	+	0.150767i
$470$		0			0
$471$	−3.39145	−	11.2640i	−0.156270	−	0.519018i
$472$	−0.371173	+	0.259898i	−0.0170846	+	0.0119628i
$473$	1.74456	−	1.22155i	0.0802149	−	0.0561671i
$474$	−4.96961	−	1.16960i	−0.228262	−	0.0537216i
$475$		0			0
$476$	8.40545	+	4.85289i	0.385263	+	0.222432i
$477$	0.299202	+	0.117782i	0.0136995	+	0.00539285i
$478$	16.7160	+	4.47905i	0.764574	+	0.204867i
$479$	−25.9636	−	9.44996i	−1.18631	−	0.431780i	−0.327880	−	0.944719i	$-0.606334\pi$
$479$	−25.9636	−	9.44996i	−1.18631	−	0.431780i	−0.858425	+	0.512940i	$0.828556\pi$
$480$		0			0
$481$	55.2468	+	46.3576i	2.51904	+	2.11372i
$482$	1.75976	−	3.77382i	0.0801549	−	0.171893i
$483$	2.61707	+	12.5750i	0.119081	+	0.572184i
$484$	5.31835	−	0.937769i	0.241743	−	0.0426258i
$485$		0			0
$486$	−28.7409	+	12.6655i	−1.30372	+	0.574517i
$487$	−28.3122	−	28.3122i	−1.28295	−	1.28295i	−0.938981	−	0.343969i	$-0.888228\pi$
$487$	−28.3122	−	28.3122i	−1.28295	−	1.28295i	−0.343969	−	0.938981i	$-0.611772\pi$
$488$	−0.308715	+	0.440891i	−0.0139749	+	0.0199582i
$489$	−19.3182	+	29.4724i	−0.873600	+	1.33279i
$490$		0			0
$491$	15.4259	−	18.3839i	0.696161	−	0.829652i	−0.295925	−	0.955211i	$-0.595628\pi$
$491$	15.4259	−	18.3839i	0.696161	−	0.829652i	0.992086	+	0.125559i	$0.0400724\pi$
$492$	1.12658	+	2.82288i	0.0507902	+	0.127265i
$493$	−6.18602	+	2.88459i	−0.278604	+	0.129915i
$494$	−25.0786	−	43.4374i	−1.12834	−	1.95434i
$495$		0			0
$496$	−6.61027	+	11.4493i	−0.296810	+	0.514090i
$497$	−1.15678	+	13.2220i	−0.0518886	+	0.593089i
$498$	−50.1494	+	31.0411i	−2.24725	+	1.39099i
$499$	−31.1017	−	5.48406i	−1.39230	−	0.245500i	−0.573325	−	0.819328i	$-0.694347\pi$
$499$	−31.1017	−	5.48406i	−1.39230	−	0.245500i	−0.818976	+	0.573828i	$0.805458\pi$
$500$		0			0
$501$	0.782153	−	0.235497i	0.0349440	−	0.0105212i
$502$	−22.1423	−	1.93720i	−0.988261	−	0.0864616i
$503$	2.72503	−	0.730168i	0.121503	−	0.0325566i	−0.197555	−	0.980292i	$-0.563300\pi$
$503$	2.72503	−	0.730168i	0.121503	−	0.0325566i	0.319058	+	0.947735i	$0.396634\pi$
$504$	−0.438969	+	0.290688i	−0.0195532	+	0.0129483i
$505$		0			0
$506$	−10.1015	+	27.7536i	−0.449066	+	1.23380i
$507$	−6.10118	+	42.1122i	−0.270963	+	1.87027i
$508$	−20.4530	+	1.78941i	−0.907455	+	0.0793920i
$509$	20.7599	−	7.55598i	0.920166	−	0.334913i	0.161861	−	0.986814i	$-0.448250\pi$
$509$	20.7599	−	7.55598i	0.920166	−	0.334913i	0.758304	+	0.651901i	$0.226028\pi$
$510$		0			0
$511$	−2.11875	−	12.0160i	−0.0937279	−	0.531557i
$512$	−22.7346	+	22.7346i	−1.00474	+	1.00474i
$513$	8.82917	−	19.1688i	0.389817	−	0.846324i
$514$		−	11.6360i		−	0.513243i
$515$		0			0
$516$	2.34365	−	1.18162i	0.103173	−	0.0520181i
$517$	−7.56184	−	3.52615i	−0.332569	−	0.155080i
$518$	3.02553	+	34.5820i	0.132934	+	1.51944i
$519$	31.7158	−	3.75740i	1.39217	−	0.164932i
$520$		0			0
$521$	−7.62484	+	4.40220i	−0.334050	+	0.192864i	−0.657638	−	0.753334i	$-0.728444\pi$
$521$	−7.62484	+	4.40220i	−0.334050	+	0.192864i	0.323588	+	0.946198i	$0.395111\pi$
$522$	0.332694	−	12.8143i	0.0145616	−	0.560868i
$523$	0.332937	+	1.24254i	0.0145583	+	0.0543324i	0.972823	−	0.231550i	$-0.0743798\pi$
$523$	0.332937	+	1.24254i	0.0145583	+	0.0543324i	−0.958265	+	0.285883i	$0.907713\pi$
$524$	−17.7181	+	14.8673i	−0.774019	+	0.649479i
$525$		0			0
$526$	−6.45507	+	36.6085i	−0.281454	+	1.59621i
$527$	−6.29419	−	8.98903i	−0.274179	−	0.391568i
$528$	19.4300	−	0.595809i	0.845581	−	0.0259293i
$529$	1.70263	+	2.02911i	0.0740274	+	0.0882224i
$530$		0			0
$531$	−10.8755	−	3.21884i	−0.471958	−	0.139686i
$532$	3.17007	−	11.8309i	0.137440	−	0.512933i
$533$	2.20709	+	4.73311i	0.0955995	+	0.205014i
$534$	−2.50506	−	21.1450i	−0.108405	−	0.915032i
$535$		0			0
$536$	0.182810	+	0.502268i	0.00789621	+	0.0216947i
$537$	−4.29227	+	13.0216i	−0.185225	+	0.561924i
$538$	25.9551	+	18.1740i	1.11900	+	0.783535i
$539$	14.0551			0.605398
$540$		0			0
$541$	−9.16794			−0.394160			−0.197080	−	0.980387i	$-0.563146\pi$
$541$	−9.16794			−0.394160			−0.197080	+	0.980387i	$0.563146\pi$
$542$	28.7714	+	20.1460i	1.23584	+	0.865344i
$543$	22.7493	+	25.4827i	0.976265	+	1.09357i
$544$	−8.86365	−	24.3527i	−0.380026	−	1.04411i
$545$		0			0
$546$	−25.0933	+	18.7424i	−1.07389	+	0.802100i
$547$	−1.95267	−	4.18752i	−0.0834904	−	0.179046i	0.860130	−	0.510074i	$-0.170382\pi$
$547$	−1.95267	−	4.18752i	−0.0834904	−	0.179046i	−0.943621	+	0.331029i	$0.892604\pi$
$548$	10.4782	−	39.1053i	0.447608	−	1.67050i
$549$	−13.4469	+	0.825461i	−0.573901	+	0.0352298i
$550$		0			0
$551$	5.53663	+	6.59830i	0.235868	+	0.281097i
$552$	−0.497516	+	0.926170i	−0.0211757	+	0.0394204i
$553$	−1.22870	−	1.75476i	−0.0522496	−	0.0746202i
$554$	−5.37283	+	30.4709i	−0.228270	+	1.29458i
$555$		0			0
$556$	−2.34610	+	1.96861i	−0.0994968	+	0.0834878i
$557$	−2.60809	−	9.73354i	−0.110509	−	0.412423i	0.888403	−	0.459064i	$-0.151815\pi$
$557$	−2.60809	−	9.73354i	−0.110509	−	0.412423i	−0.998912	+	0.0466405i	$0.985148\pi$
$558$	20.3819	−	3.05074i	0.862833	−	0.129148i
$559$	3.90564	−	2.25492i	0.165191	−	0.0953730i
$560$		0			0
$561$	−6.36763	+	14.8256i	−0.268842	+	0.625938i
$562$	−1.30121	−	14.8729i	−0.0548881	−	0.627373i
$563$	15.0076	+	6.99817i	0.632496	+	0.294938i	0.712302	−	0.701873i	$-0.247652\pi$
$563$	15.0076	+	6.99817i	0.632496	+	0.294938i	−0.0798064	+	0.996810i	$0.525430\pi$
$564$	−8.59990	−	5.63697i	−0.362121	−	0.237359i
$565$		0			0
$566$			28.9676i			1.21760i
$567$	−12.5353	−	4.06677i	−0.526432	−	0.170788i
$568$	−0.768184	+	0.768184i	−0.0322323	+	0.0322323i
$569$	1.89828	+	10.7657i	0.0795799	+	0.451320i	0.998395	+	0.0566320i	$0.0180362\pi$
$569$	1.89828	+	10.7657i	0.0795799	+	0.451320i	−0.918815	+	0.394688i	$0.870853\pi$
$570$		0			0
$571$	15.2515	−	5.55110i	0.638256	−	0.232306i	−0.00256475	−	0.999997i	$-0.500816\pi$
$571$	15.2515	−	5.55110i	0.638256	−	0.232306i	0.640821	+	0.767691i	$0.278594\pi$
$572$	−36.3976	+	3.18438i	−1.52186	+	0.133146i
$573$	−14.0585	+	5.61060i	−0.587304	+	0.234386i
$574$	−0.859755	+	2.36216i	−0.0358855	+	0.0985946i
$575$		0			0
$576$	25.2431	+	2.87039i	1.05180	+	0.119599i
$577$	−17.0234	+	4.56140i	−0.708693	+	0.189894i	−0.595121	−	0.803636i	$-0.702896\pi$
$577$	−17.0234	+	4.56140i	−0.708693	+	0.189894i	−0.113572	+	0.993530i	$0.536229\pi$
$578$	−13.3304	−	1.16625i	−0.554469	−	0.0485098i
$579$	3.42870	−	14.5684i	0.142492	−	0.605444i
$580$		0			0
$581$	−24.3710	−	4.29727i	−1.01108	−	0.178281i
$582$	49.8430	+	26.7744i	2.06606	+	1.10984i
$583$	−0.0270388	+	0.309055i	−0.00111983	+	0.0127998i
$584$	0.499351	−	0.864901i	0.0206633	−	0.0357898i
$585$		0			0
$586$	20.2926	+	35.1479i	0.838280	+	1.45194i
$587$	7.40736	−	3.45411i	0.305734	−	0.142566i	−0.263696	−	0.964606i	$-0.584942\pi$
$587$	7.40736	−	3.45411i	0.305734	−	0.142566i	0.569430	+	0.822040i	$0.307164\pi$
$588$	17.1427	+	2.48362i	0.706953	+	0.102423i
$589$	−8.90140	+	10.6083i	−0.366776	+	0.437106i
$590$		0			0
$591$	−3.46812	−	0.196546i	−0.142660	−	0.00808483i
$592$	26.1692	−	37.3735i	1.07555	−	1.53604i
$593$	−28.1239	−	28.1239i	−1.15491	−	1.15491i	−0.985555	−	0.169357i	$-0.945831\pi$
$593$	−28.1239	−	28.1239i	−1.15491	−	1.15491i	−0.169357	−	0.985555i	$-0.554169\pi$
$594$	−19.5871	−	23.1215i	−0.803668	−	0.948687i
$595$		0			0
$596$	10.0651	−	1.77475i	0.412282	−	0.0726965i
$597$	29.4664	+	9.71291i	1.20598	+	0.397523i
$598$	−26.4315	+	56.6826i	−1.08087	+	2.31793i
$599$	−27.5968	−	23.1564i	−1.12757	−	0.946147i	−0.128612	−	0.991695i	$-0.541052\pi$
$599$	−27.5968	−	23.1564i	−1.12757	−	0.946147i	−0.998962	+	0.0455483i	$0.985496\pi$
$600$		0			0
$601$	−21.4617	−	7.81141i	−0.875440	−	0.318634i	−0.135072	−	0.990836i	$-0.543126\pi$
$601$	−21.4617	−	7.81141i	−0.875440	−	0.318634i	−0.740368	+	0.672202i	$0.765349\pi$
$602$	2.09680	+	0.561836i	0.0854593	+	0.0228987i
$603$	−6.98794	+	11.4090i	−0.284571	+	0.464610i
$604$	−36.9808	−	21.3509i	−1.50473	−	0.868755i
$605$		0			0
$606$	13.1456	−	13.9773i	0.534004	−	0.567790i
$607$	7.00562	−	4.90539i	0.284349	−	0.199104i	−0.422696	−	0.906271i	$-0.638916\pi$
$607$	7.00562	−	4.90539i	0.284349	−	0.199104i	0.707046	+	0.707168i	$0.250027\pi$
$608$	−26.7897	+	18.7583i	−1.08647	+	0.760751i
$609$	3.68488	−	3.91802i	0.149319	−	0.158766i
$610$		0			0
$611$	−15.3011	−	8.83410i	−0.619017	−	0.357389i
$612$	−10.3862	+	16.9572i	−0.419837	+	0.685456i
$613$	35.7827	+	9.58796i	1.44525	+	0.387254i	0.894369	−	0.447329i	$-0.147625\pi$
$613$	35.7827	+	9.58796i	1.44525	+	0.387254i	0.550882	+	0.834583i	$0.314291\pi$
$614$	22.6241	+	8.23450i	0.913034	+	0.332317i
$615$		0			0
$616$	−0.389125	−	0.326514i	−0.0156783	−	0.0131556i
$617$	5.17963	−	11.1077i	0.208524	−	0.447181i	−0.774032	−	0.633146i	$-0.781763\pi$
$617$	5.17963	−	11.1077i	0.208524	−	0.447181i	0.982556	+	0.185965i	$0.0595411\pi$
$618$	13.0060	+	4.28712i	0.523178	+	0.172453i
$619$	8.63834	−	1.52317i	0.347204	−	0.0612215i	0.00267331	−	0.999996i	$-0.499149\pi$
$619$	8.63834	−	1.52317i	0.347204	−	0.0612215i	0.344531	+	0.938775i	$0.388038\pi$
$620$		0			0
$621$	−25.8942	+	4.69138i	−1.03910	+	0.188259i
$622$	−3.44947	−	3.44947i	−0.138311	−	0.138311i
$623$	5.12449	−	7.31853i	0.205308	−	0.293211i
$624$	41.0979	+	2.32911i	1.64523	+	0.0932391i
$625$		0			0
$626$	15.8763	−	18.9206i	0.634543	−	0.756218i
$627$	20.1515	+	2.91953i	0.804773	+	0.116595i
$628$	12.6768	−	5.91130i	0.505860	−	0.235887i
$629$	18.9351	+	32.7966i	0.754992	+	1.30769i
$630$		0			0
$631$	16.1540	−	27.9796i	0.643083	−	1.11385i	−0.341658	−	0.939824i	$-0.610989\pi$
$631$	16.1540	−	27.9796i	0.643083	−	1.11385i	0.984741	−	0.174027i	$-0.0556781\pi$
$632$	0.0152819	−	0.174673i	0.000607880	−	0.00694810i
$633$	−16.2875	−	8.74923i	−0.647368	−	0.347751i
$634$	45.0092	+	7.93634i	1.78755	+	0.315192i
$635$		0			0
$636$	−0.0875903	+	0.372169i	−0.00347318	+	0.0147575i
$637$	29.6497	+	2.59401i	1.17476	+	0.102778i
$638$	11.9462	−	3.20098i	0.472955	−	0.126728i
$639$	−27.0187	−	3.07228i	−1.06884	−	0.121538i
$640$		0			0
$641$	−3.35944	+	9.23000i	−0.132690	+	0.364563i	−0.988189	−	0.153242i	$-0.951029\pi$
$641$	−3.35944	+	9.23000i	−0.132690	+	0.364563i	0.855499	+	0.517805i	$0.173251\pi$
$642$	−48.2797	+	19.2679i	−1.90545	+	0.760443i
$643$	−18.5293	+	1.62110i	−0.730723	+	0.0639299i	−0.446444	−	0.894812i	$-0.647310\pi$
$643$	−18.5293	+	1.62110i	−0.730723	+	0.0639299i	−0.284279	+	0.958742i	$0.591754\pi$
$644$	−14.3516	+	5.22355i	−0.565532	+	0.205837i
$645$		0			0
$646$	−4.57349	−	25.9375i	−0.179942	−	1.02050i
$647$	14.2018	−	14.2018i	0.558331	−	0.558331i	−0.370501	−	0.928832i	$-0.620814\pi$
$647$	14.2018	−	14.2018i	0.558331	−	0.558331i	0.928832	+	0.370501i	$0.120814\pi$
$648$	−0.572019	−	0.914513i	−0.0224710	−	0.0359255i
$649$		−	10.9428i		−	0.429542i
$650$		0			0
$651$	7.23215	+	4.74045i	0.283450	+	0.185793i
$652$	−37.9754	−	17.7082i	−1.48723	−	0.693507i
$653$	−1.73834	−	19.8693i	−0.0680265	−	0.777546i	−0.951215	−	0.308528i	$-0.900164\pi$
$653$	−1.73834	−	19.8693i	−0.0680265	−	0.777546i	0.883189	−	0.469018i	$-0.155392\pi$
$654$	−13.6543	+	31.7909i	−0.533924	+	1.24312i
$655$		0			0
$656$	2.86119	−	1.65191i	0.111711	−	0.0644963i
$657$	24.7228	−	3.70048i	0.964528	−	0.144370i
$658$	−2.20110	−	8.21463i	−0.0858080	−	0.320240i
$659$	0.815140	−	0.683983i	0.0317533	−	0.0266442i	−0.626773	−	0.779202i	$-0.715625\pi$
$659$	0.815140	−	0.683983i	0.0317533	−	0.0266442i	0.658526	+	0.752558i	$0.271180\pi$
$660$		0			0
$661$	−5.78183	+	32.7904i	−0.224887	+	1.27540i	0.638014	+	0.770025i	$0.279756\pi$
$661$	−5.78183	+	32.7904i	−0.224887	+	1.27540i	−0.862901	+	0.505373i	$0.831355\pi$
$662$	−18.8576	−	26.9314i	−0.732920	−	1.04672i
$663$	−16.1689	+	30.0998i	−0.627947	+	1.16898i
$664$	−1.30202	−	1.55168i	−0.0505280	−	0.0602169i
$665$		0			0
$666$	−70.9885	+	4.35774i	−2.75075	+	0.168859i
$667$	2.77981	−	10.3744i	0.107635	−	0.401699i
$668$	0.410470	+	0.880256i	0.0158816	+	0.0340581i
$669$	−16.5826	+	12.3857i	−0.641119	+	0.478858i
$670$		0			0
$671$	−4.44565	−	12.2143i	−0.171622	−	0.471529i
$672$	13.6002	+	15.2343i	0.524639	+	0.587676i
$673$	20.0466	+	14.0367i	0.772738	+	0.541077i	0.892135	−	0.451770i	$-0.149207\pi$
$673$	20.0466	+	14.0367i	0.772738	+	0.541077i	−0.119397	+	0.992847i	$0.538096\pi$
$674$	−8.08017			−0.311236
$675$		0			0
$676$	−50.5961			−1.94600
$677$	16.7682	+	11.7412i	0.644455	+	0.451252i	0.849563	−	0.527487i	$-0.176866\pi$
$677$	16.7682	+	11.7412i	0.644455	+	0.451252i	−0.205108	+	0.978739i	$0.565755\pi$
$678$	16.6400	−	50.4813i	0.639055	−	1.93872i
$679$	8.11957	+	22.3083i	0.311601	+	0.856115i
$680$		0			0
$681$	0.235792	+	1.99029i	0.00903556	+	0.0762681i
$682$	8.40325	+	18.0208i	0.321777	+	0.690053i
$683$	5.71751	−	21.3380i	0.218774	−	0.816477i	−0.766029	−	0.642806i	$-0.777770\pi$
$683$	5.71751	−	21.3380i	0.218774	−	0.816477i	0.984804	−	0.173671i	$-0.0555630\pi$
$684$	24.0623	+	7.12175i	0.920047	+	0.272307i
$685$		0			0
$686$	22.4833	+	26.7945i	0.858416	+	1.02302i
$687$	−15.1631	+	0.464968i	−0.578509	+	0.0177396i
$688$	−1.63643	−	2.33707i	−0.0623884	−	0.0890999i
$689$	−0.114078	+	0.646969i	−0.00434603	+	0.0246476i
$690$		0			0
$691$	13.7398	−	11.5291i	0.522688	−	0.438587i	−0.342880	−	0.939379i	$-0.611402\pi$
$691$	13.7398	−	11.5291i	0.522688	−	0.438587i	0.865568	+	0.500792i	$0.166958\pi$
$692$	9.82872	+	36.6813i	0.373632	+	1.39441i
$693$	0.329998	−	12.7105i	0.0125356	−	0.482831i
$694$	−21.6551	+	12.5026i	−0.822016	+	0.474591i
$695$		0			0
$696$	0.437188	−	0.0517940i	0.0165716	−	0.00196325i
$697$	0.239008	+	2.73187i	0.00905306	+	0.103477i
$698$	13.9526	+	6.50619i	0.528112	+	0.246263i
$699$	25.3066	−	12.7591i	0.957182	−	0.482593i
$700$		0			0
$701$		−	11.4005i		−	0.430590i	−0.976549	−	0.215295i	$-0.930929\pi$
$701$		−	11.4005i		−	0.430590i	0.976549	−	0.215295i	$-0.0690713\pi$
$702$	−37.0521	−	52.3903i	−1.39844	−	1.97735i
$703$	33.7929	−	33.7929i	1.27452	−	1.27452i
$704$	4.25644	+	24.1395i	0.160421	+	0.909791i
$705$		0			0
$706$	33.8977	−	12.3377i	1.27576	−	0.464337i
$707$	8.02039	−	0.701693i	0.301638	−	0.0263899i
$708$	1.93365	−	13.3466i	0.0726711	−	0.501598i
$709$	5.28444	−	14.5189i	0.198461	−	0.545268i	−0.800043	−	0.599943i	$-0.795190\pi$
$709$	5.28444	−	14.5189i	0.198461	−	0.545268i	0.998504	+	0.0546749i	$0.0174122\pi$
$710$		0			0
$711$	3.65928	−	2.42320i	0.137234	−	0.0908772i
$712$	0.706365	−	0.189270i	0.0264722	−	0.00709319i
$713$	17.2019	+	1.50497i	0.644216	+	0.0563616i
$714$	−15.7480	+	4.74151i	−0.589353	+	0.177447i
$715$		0			0
$716$	−16.0551	−	2.83094i	−0.600006	−	0.105797i
$717$	−12.6498	+	7.82988i	−0.472415	+	0.292412i
$718$	2.20038	−	25.1504i	0.0821174	−	0.938606i
$719$	4.71157	−	8.16068i	0.175712	−	0.304342i	−0.764695	−	0.644392i	$-0.777111\pi$
$719$	4.71157	−	8.16068i	0.175712	−	0.304342i	0.940407	+	0.340050i	$0.110444\pi$
$720$		0			0
$721$	2.87301	+	4.97620i	0.106997	+	0.185323i
$722$	4.57202	−	2.13197i	0.170153	−	0.0793437i
$723$	1.32681	+	3.32459i	0.0493444	+	0.123643i
$724$	−26.1085	+	31.1149i	−0.970315	+	1.15638i
$725$		0			0
$726$	−5.01651	+	7.65331i	−0.186180	+	0.284041i
$727$	24.6272	−	35.1712i	0.913371	−	1.30443i	−0.0389219	−	0.999242i	$-0.512392\pi$
$727$	24.6272	−	35.1712i	0.913371	−	1.30443i	0.952293	−	0.305186i	$-0.0987187\pi$
$728$	−0.760607	−	0.760607i	−0.0281900	−	0.0281900i
$729$	8.99575	−	25.4573i	0.333176	−	0.942865i
$730$		0			0
$731$	2.33216	−	0.411222i	0.0862579	−	0.0152096i
$732$	−3.26391	−	15.6831i	−0.120638	−	0.579663i
$733$	−0.264636	+	0.567513i	−0.00977454	+	0.0209616i	−0.911134	−	0.412109i	$-0.864792\pi$
$733$	−0.264636	+	0.567513i	−0.00977454	+	0.0209616i	0.901360	+	0.433071i	$0.142570\pi$
$734$	−21.1255	−	17.7264i	−0.779755	−	0.654292i
$735$		0			0
$736$	38.3205	+	13.9475i	1.41251	+	0.514112i
$737$	−12.4684	−	3.34089i	−0.459278	−	0.123063i
$738$	−4.79224	−	1.88648i	−0.176405	−	0.0694423i
$739$	23.6846	+	13.6743i	0.871251	+	0.503017i	0.867764	−	0.496977i	$-0.165557\pi$
$739$	23.6846	+	13.6743i	0.871251	+	0.503017i	0.00348723	+	0.999994i	$0.498890\pi$
$740$		0			0
$741$	41.9712	+	9.87796i	1.54185	+	0.362876i
$742$	−0.259029	+	0.181374i	−0.00950927	+	0.00665846i
$743$	−29.3796	+	20.5718i	−1.07783	+	0.754706i	−0.970882	−	0.239558i	$-0.922997\pi$
$743$	−29.3796	+	20.5718i	−1.07783	+	0.754706i	−0.106950	+	0.994264i	$0.534109\pi$
$744$	0.204059	+	0.677741i	0.00748118	+	0.0248472i
$745$		0			0
$746$	−21.1251	−	12.1966i	−0.773444	−	0.446548i
$747$	10.0972	−	49.6860i	0.369437	−	1.81792i
$748$	−18.5318	−	4.96558i	−0.677589	−	0.181559i
$749$	−20.4960	−	7.45993i	−0.748907	−	0.272580i
$750$		0			0
$751$	−27.0935	−	22.7342i	−0.988657	−	0.829582i	−0.00328459	−	0.999995i	$-0.501046\pi$
$751$	−27.0935	−	22.7342i	−0.988657	−	0.829582i	−0.985373	+	0.170413i	$0.945490\pi$
$752$	−4.72374	+	10.1301i	−0.172257	+	0.369407i
$753$	14.2539	−	12.7249i	0.519441	−	0.463723i
$754$	25.7916	−	4.54775i	0.939274	−	0.165619i
$755$		0			0
$756$	2.64850	−	15.4443i	0.0963250	−	0.561705i
$757$	26.1262	+	26.1262i	0.949573	+	0.949573i	0.998788	−	0.0492153i	$-0.0156721\pi$
$757$	26.1262	+	26.1262i	0.949573	+	0.949573i	−0.0492153	+	0.998788i	$0.515672\pi$
$758$	−26.0268	+	37.1701i	−0.945336	+	1.35008i
$759$	−11.4304	−	22.6713i	−0.414899	−	0.822915i
$760$		0			0
$761$	5.19201	−	6.18759i	0.188210	−	0.224300i	−0.663685	−	0.748012i	$-0.731009\pi$
$761$	5.19201	−	6.18759i	0.188210	−	0.224300i	0.851896	+	0.523712i	$0.175453\pi$
$762$	21.5350	−	27.3233i	0.780132	−	0.989819i
$763$	−13.1573	+	6.13535i	−0.476326	+	0.222115i
$764$	−8.99914	−	15.5870i	−0.325577	−	0.563917i
$765$		0			0
$766$	−14.5740	+	25.2430i	−0.526582	+	0.912066i
$767$	2.01960	−	23.0841i	0.0729234	−	0.833519i
$768$	−0.796640	−	25.9793i	−0.0287463	−	0.937447i
$769$	−16.0619	−	2.83215i	−0.579208	−	0.102130i	−0.123634	−	0.992328i	$-0.539455\pi$
$769$	−16.0619	−	2.83215i	−0.579208	−	0.102130i	−0.455574	+	0.890198i	$0.650566\pi$
$770$		0			0
$771$	7.28665	+	6.85306i	0.262422	+	0.246807i
$772$	17.7281	+	1.55101i	0.638048	+	0.0558220i
$773$	−11.4302	+	3.06271i	−0.411116	+	0.110158i	−0.458448	−	0.888721i	$-0.651595\pi$
$773$	−11.4302	+	3.06271i	−0.411116	+	0.110158i	0.0473325	+	0.998879i	$0.484928\pi$
$774$	−1.26220	+	4.26460i	−0.0453688	+	0.153288i
$775$		0			0
$776$	−0.664599	+	1.82597i	−0.0238577	+	0.0655485i
$777$	−23.4376	−	18.4725i	−0.840820	−	0.662697i
$778$	25.3711	−	2.21968i	0.909598	−	0.0795795i
$779$	3.25195	−	1.18361i	0.116513	−	0.0424073i
$780$		0			0
$781$	−4.55583	−	25.8374i	−0.163020	−	0.924534i
$782$	−23.2222	+	23.2222i	−0.830425	+	0.830425i
$783$	7.82859	+	7.75538i	0.279771	+	0.277154i
$784$		−	18.8287i		−	0.672455i
$785$		0			0
$786$	2.21756	−	39.1295i	0.0790976	−	1.39570i
$787$	43.1572	+	20.1245i	1.53839	+	0.717361i	0.992698	−	0.120627i	$-0.0384904\pi$
$787$	43.1572	+	20.1245i	1.53839	+	0.717361i	0.545689	+	0.837988i	$0.316268\pi$
$788$	−0.359985	−	4.11465i	−0.0128240	−	0.146578i
$789$	−19.1231	−	25.6029i	−0.680799	−	0.911488i
$790$		0			0
$791$	19.3145	−	11.1513i	0.686746	−	0.396493i
$792$	0.689429	−	0.779608i	0.0244978	−	0.0277022i
$793$	−7.12394	−	26.5869i	−0.252979	−	0.944129i
$794$	23.2020	−	19.4688i	0.823409	−	0.690922i
$795$		0			0
$796$	−6.40609	+	36.3307i	−0.227058	+	1.28771i
$797$	−9.48608	−	13.5475i	−0.336014	−	0.479878i	0.615216	−	0.788358i	$-0.289069\pi$
$797$	−9.48608	−	13.5475i	−0.336014	−	0.479878i	−0.951231	+	0.308480i	$0.900180\pi$
$798$	10.9232	+	17.6473i	0.386678	+	0.624709i
$799$	−5.96354	−	7.10708i	−0.210975	−	0.251430i
$800$		0			0
$801$	14.7166	+	10.8847i	0.519987	+	0.384591i
$802$	−13.6736	+	51.0307i	−0.482833	+	1.80196i
$803$	10.1930	+	21.8589i	0.359702	+	0.771383i
$804$	−14.6170	−	6.27803i	−0.515502	−	0.221409i
$805$		0			0
$806$	14.4009	+	39.5663i	0.507252	+	1.39366i
$807$	−26.6671	+	5.54988i	−0.938728	+	0.195365i
$808$	0.539812	+	0.377980i	0.0189905	+	0.0132973i
$809$	−21.1013			−0.741881			−0.370941	−	0.928657i	$-0.620965\pi$
$809$	−21.1013			−0.741881			−0.370941	+	0.928657i	$0.620965\pi$
$810$		0			0
$811$	3.03312			0.106507			0.0532537	−	0.998581i	$-0.483041\pi$
$811$	3.03312			0.106507			0.0532537	+	0.998581i	$0.483041\pi$
$812$	5.23879	+	3.66824i	0.183845	+	0.128730i
$813$	−29.5607	+	6.15208i	−1.03674	+	0.215763i
$814$	−23.4693	−	64.4814i	−0.822599	−	2.26007i
$815$		0			0
$816$	19.8609	+	8.53029i	0.695270	+	0.298620i
$817$	−1.26298	−	2.70847i	−0.0441861	−	0.0947574i
$818$	−3.93110	+	14.6711i	−0.137448	+	0.512962i
$819$	3.04198	−	26.7521i	0.106295	−	0.934795i
$820$		0			0
$821$	7.72326	+	9.20422i	0.269544	+	0.321230i	0.883789	−	0.467885i	$-0.154984\pi$
$821$	7.72326	+	9.20422i	0.269544	+	0.321230i	−0.614246	+	0.789115i	$0.710540\pi$
$822$	36.1052	+	58.3309i	1.25931	+	2.03452i
$823$	−13.6442	−	19.4859i	−0.475607	−	0.679237i	0.507629	−	0.861576i	$-0.330522\pi$
$823$	−13.6442	−	19.4859i	−0.475607	−	0.679237i	−0.983236	+	0.182339i	$0.941633\pi$
$824$	−0.0816702	+	0.463175i	−0.00284512	+	0.0161355i
$825$		0			0
$826$	8.54427	−	7.16949i	0.297293	−	0.249459i
$827$	12.0136	+	44.8353i	0.417753	+	1.55907i	0.779257	+	0.626704i	$0.215597\pi$
$827$	12.0136	+	44.8353i	0.417753	+	1.55907i	−0.361504	+	0.932370i	$0.617737\pi$
$828$	−9.93527	−	29.6714i	−0.345275	−	1.03115i
$829$	−27.8169	+	16.0601i	−0.966123	+	0.557791i	−0.898052	−	0.439889i	$-0.855018\pi$
$829$	−27.8169	+	16.0601i	−0.966123	+	0.557791i	−0.0680706	+	0.997681i	$0.521684\pi$
$830$		0			0
$831$	−15.9170	−	21.3104i	−0.552153	−	0.739251i
$832$	4.52390	+	51.7084i	0.156838	+	1.79267i
$833$	14.1643	+	6.60493i	0.490765	+	0.228847i
$834$	0.293632	−	5.18124i	0.0101677	−	0.179412i
$835$		0			0
$836$			24.2112i			0.837361i
$837$	−10.0935	+	14.5602i	−0.348884	+	0.503273i
$838$	−29.5051	+	29.5051i	−1.01924	+	1.01924i
$839$	8.77845	+	49.7851i	0.303066	+	1.71877i	0.632472	+	0.774583i	$0.282040\pi$
$839$	8.77845	+	49.7851i	0.303066	+	1.71877i	−0.329406	+	0.944188i	$0.606849\pi$
$840$		0			0
$841$	23.0248	−	8.38035i	0.793959	−	0.288977i
$842$	13.8072	−	1.20798i	0.475829	−	0.0416296i
$843$	10.0799	+	7.94457i	0.347172	+	0.273625i
$844$	7.51891	−	20.6580i	0.258812	−	0.711079i
$845$		0			0
$846$	16.9415	−	4.07129i	0.582461	−	0.139974i
$847$	−3.70879	+	0.993767i	−0.127436	+	0.0341463i
$848$	0.414021	+	0.0362221i	0.0142175	+	0.00124387i
$849$	−18.1399	−	17.0605i	−0.622561	−	0.585516i
$850$		0			0
$851$	−58.6858	−	10.3479i	−2.01172	−	0.354721i
$852$	−0.991020	−	32.3182i	−0.0339518	−	1.10720i
$853$	−4.44262	+	50.7794i	−0.152112	+	1.73865i	0.410438	+	0.911889i	$0.365376\pi$
$853$	−4.44262	+	50.7794i	−0.152112	+	1.73865i	−0.562550	+	0.826763i	$0.690180\pi$
$854$	6.62440	−	11.4738i	0.226682	−	0.392625i
$855$		0			0
$856$	−0.892646	−	1.54611i	−0.0305100	−	0.0528449i
$857$	9.12817	−	4.25654i	0.311812	−	0.145400i	−0.260412	−	0.965498i	$-0.583858\pi$
$857$	9.12817	−	4.25654i	0.311812	−	0.145400i	0.572224	+	0.820097i	$0.306081\pi$
$858$	38.3232	−	48.6238i	1.30833	−	1.65999i
$859$	−8.01487	+	9.55175i	−0.273464	+	0.325902i	−0.885245	−	0.465126i	$-0.846009\pi$
$859$	−8.01487	+	9.55175i	−0.273464	+	0.325902i	0.611781	+	0.791027i	$0.290453\pi$
$860$		0			0
$861$	−0.972864	−	1.92959i	−0.0331551	−	0.0657603i
$862$	−3.37367	+	4.81810i	−0.114908	+	0.164105i
$863$	−23.9621	−	23.9621i	−0.815678	−	0.815678i	0.169800	−	0.985479i	$-0.445688\pi$
$863$	−23.9621	−	23.9621i	−0.815678	−	0.815678i	−0.985479	+	0.169800i	$0.945688\pi$
$864$	−31.9247	+	27.0446i	−1.08610	+	0.920076i
$865$		0			0
$866$	8.46774	−	1.49309i	0.287745	−	0.0507373i
$867$	8.58127	−	7.66079i	0.291435	−	0.260174i
$868$	−4.34538	+	9.31869i	−0.147492	+	0.316297i
$869$	3.24378	+	2.72185i	0.110038	+	0.0923326i
$870$		0			0
$871$	−25.6857	−	9.34885i	−0.870328	−	0.316774i
$872$	−1.14779	−	0.307549i	−0.0388690	−	0.0104149i
$873$	−46.1217	+	15.4435i	−1.56098	+	0.522685i
$874$	35.8915	+	20.7220i	1.21405	+	0.700932i
$875$		0			0
$876$	8.56951	+	28.4619i	0.289537	+	0.961637i
$877$	−38.4629	+	26.9320i	−1.29880	+	0.909430i	−0.999006	−	0.0445739i	$-0.985807\pi$
$877$	−38.4629	+	26.9320i	−1.29880	+	0.909430i	−0.299794	+	0.954004i	$0.596918\pi$
$878$	6.18293	−	4.32933i	0.208664	−	0.146108i
$879$	−33.9615	−	7.99287i	−1.14549	−	0.269593i
$880$		0			0
$881$	20.2756	+	11.7061i	0.683103	+	0.394390i	0.801023	−	0.598633i	$-0.204289\pi$
$881$	20.2756	+	11.7061i	0.683103	+	0.394390i	−0.117920	+	0.993023i	$0.537623\pi$
$882$	−22.9665	+	18.2767i	−0.773321	+	0.615409i
$883$	−6.11319	−	1.63802i	−0.205725	−	0.0551239i	0.154485	−	0.987995i	$-0.450628\pi$
$883$	−6.11319	−	1.63802i	−0.205725	−	0.0551239i	−0.360210	+	0.932871i	$0.617295\pi$
$884$	−38.1768	−	13.8952i	−1.28402	−	0.467347i
$885$		0			0
$886$	−43.1969	−	36.2465i	−1.45123	−	1.21773i
$887$	13.8426	−	29.6855i	0.464788	−	0.996741i	−0.524587	−	0.851357i	$-0.675780\pi$
$887$	13.8426	−	29.6855i	0.464788	−	0.996741i	0.989375	−	0.145384i	$-0.0464419\pi$
$888$	−0.497687	−	2.39139i	−0.0167013	−	0.0802497i
$889$	14.3756	−	2.53481i	0.482144	−	0.0850149i
$890$		0			0
$891$	26.0149	+	1.35174i	0.871531	+	0.0452851i
$892$	−17.4021	−	17.4021i	−0.582665	−	0.582665i
$893$	−6.71538	+	9.59056i	−0.224722	+	0.320936i
$894$	−9.49386	+	14.4841i	−0.317522	+	0.484420i
$895$		0			0
$896$	−0.902060	+	1.07503i	−0.0301357	+	0.0359143i
$897$	−19.9286	−	49.9352i	−0.665396	−	1.66729i
$898$	−17.4298	+	8.12765i	−0.581640	+	0.271223i
$899$	−3.61538	−	6.26203i	−0.120580	−	0.208850i
$900$		0			0
$901$	−0.172483	+	0.298750i	−0.00574625	+	0.00995280i
$902$	0.433074	−	4.95006i	0.0144198	−	0.164819i
$903$	−1.58675	+	0.982153i	−0.0528036	+	0.0326840i
$904$	1.79776	+	0.316994i	0.0597926	+	0.0105430i
$905$		0			0
$906$	69.2851	−	20.8609i	2.30184	−	0.693056i
$907$	−28.5313	−	2.49616i	−0.947365	−	0.0828837i	−0.397010	−	0.917814i	$-0.629952\pi$
$907$	−28.5313	−	2.49616i	−0.947365	−	0.0828837i	−0.550355	+	0.834931i	$0.685508\pi$
$908$	−2.30189	+	0.616790i	−0.0763910	+	0.0204689i
$909$	1.01067	+	16.4640i	0.0335217	+	0.546075i
$910$		0			0
$911$	−6.61616	+	18.1777i	−0.219203	+	0.602255i	−0.999739	−	0.0228557i	$-0.992724\pi$
$911$	−6.61616	+	18.1777i	−0.219203	+	0.602255i	0.780536	+	0.625111i	$0.214946\pi$
$912$	3.91110	−	26.9956i	0.129509	−	0.893913i
$913$	48.7315	−	4.26345i	1.61278	−	0.141100i
$914$	67.0891	−	24.4184i	2.21911	−	0.807690i
$915$		0			0
$916$	−3.13228	−	17.7641i	−0.103493	−	0.586941i
$917$	11.6282	−	11.6282i	0.383996	−	0.383996i
$918$	−8.87375	−	32.5057i	−0.292877	−	1.07285i
$919$			44.6775i			1.47377i	0.676016	+	0.736887i	$0.263705\pi$
$919$			44.6775i			1.47377i	−0.676016	+	0.736887i	$0.736295\pi$
$920$		0			0
$921$	−18.4811	+	9.31782i	−0.608972	+	0.307032i
$922$	−45.2591	−	21.1047i	−1.49053	−	0.695046i
$923$	−4.84210	−	55.3454i	−0.159380	−	1.82172i
$924$	15.0134	−	1.77865i	0.493905	−	0.0585134i
$925$		0			0
$926$	−9.44552	+	5.45337i	−0.310399	+	0.179209i
$927$	−10.3446	+	5.61963i	−0.339760	+	0.184573i
$928$	−4.41970	−	16.4946i	−0.145084	−	0.541461i
$929$	40.3230	−	33.8350i	1.32296	−	1.11009i	0.337286	−	0.941402i	$-0.390491\pi$
$929$	40.3230	−	33.8350i	1.32296	−	1.11009i	0.985669	−	0.168689i	$-0.0539535\pi$
$930$		0			0
$931$	3.42478	−	19.4229i	0.112243	−	0.636560i
$932$	19.3288	+	27.6044i	0.633137	+	0.904213i
$933$	4.19168	−	0.128535i	0.137229	−	0.00420806i
$934$	53.0403	+	63.2110i	1.73553	+	2.06833i
$935$		0			0
$936$	1.59825	−	1.51736i	0.0522404	−	0.0495965i
$937$	−3.71263	+	13.8557i	−0.121286	+	0.452647i	−0.999680	−	0.0252908i	$-0.991949\pi$
$937$	−3.71263	+	13.8557i	−0.121286	+	0.452647i	0.878394	+	0.477938i	$0.158616\pi$
$938$	−5.56041	−	11.9243i	−0.181554	−	0.389343i
$939$	2.49799	+	21.0853i	0.0815188	+	0.688092i
$940$		0			0
$941$	−0.0906224	−	0.248983i	−0.00295420	−	0.00811661i	0.938207	−	0.346075i	$-0.112486\pi$
$941$	−0.0906224	−	0.248983i	−0.00295420	−	0.00811661i	−0.941161	+	0.337959i	$0.890264\pi$
$942$	−7.41988	+	22.5099i	−0.241753	+	0.733413i
$943$	−3.53479	−	2.47509i	−0.115109	−	0.0806000i
$944$	−14.6593			−0.477121
$945$		0			0
$946$	−4.29098			−0.139512
$947$	27.9252	+	19.5534i	0.907446	+	0.635401i	0.931276	−	0.364315i	$-0.118697\pi$
$947$	27.9252	+	19.5534i	0.907446	+	0.635401i	−0.0238294	+	0.999716i	$0.507586\pi$
$948$	3.47539	+	3.89297i	0.112875	+	0.126438i
$949$	17.4680	+	47.9930i	0.567037	+	1.55792i
$950$		0			0
$951$	−31.4782	+	23.5113i	−1.02075	+	0.762407i
$952$	−0.238709	−	0.511912i	−0.00773659	−	0.0165912i
$953$	−6.91874	+	25.8211i	−0.224120	+	0.836427i	0.758635	+	0.651516i	$0.225867\pi$
$953$	−6.91874	+	25.8211i	−0.224120	+	0.836427i	−0.982755	+	0.184912i	$0.940800\pi$
$954$	−0.357701	−	0.540165i	−0.0115810	−	0.0174885i
$955$		0			0
$956$	−11.3705	−	13.5509i	−0.367749	−	0.438266i
$957$	−5.03125	+	9.36611i	−0.162637	+	0.302763i
$958$	31.9305	+	45.6014i	1.03163	+	1.47331i
$959$	−4.99834	+	28.3470i	−0.161405	+	0.915372i
$960$		0			0
$961$	−14.8420	+	12.4539i	−0.478775	+	0.401740i
$962$	−37.6084	−	140.356i	−1.21254	−	4.52528i
$963$	16.3686	−	41.5813i	0.527471	−	1.33994i
$964$	−3.68603	+	2.12813i	−0.118719	+	0.0685425i
$965$		0			0
$966$	10.2130	−	23.7788i	0.328599	−	0.765069i
$967$	1.77416	+	20.2788i	0.0570532	+	0.652121i	0.969849	+	0.243706i	$0.0783631\pi$
$967$	1.77416	+	20.2788i	0.0570532	+	0.652121i	−0.912796	+	0.408416i	$0.866081\pi$
$968$	−0.284833	−	0.132820i	−0.00915488	−	0.00426899i
$969$	18.9360	+	12.4120i	0.608313	+	0.398731i
$970$		0			0
$971$		−	40.5268i		−	1.30057i	−0.759692	−	0.650284i	$-0.774650\pi$
$971$		−	40.5268i		−	1.30057i	0.759692	−	0.650284i	$-0.225350\pi$
$972$	31.4908	+	6.24566i	1.01007	+	0.200329i
$973$	1.53972	−	1.53972i	0.0493610	−	0.0493610i
$974$	14.0086	+	79.4468i	0.448865	+	2.54564i
$975$		0			0
$976$	−16.3627	+	5.95554i	−0.523758	+	0.190632i
$977$	35.4680	−	3.10305i	1.13472	−	0.0992752i	0.495721	−	0.868482i	$-0.334904\pi$
$977$	35.4680	−	3.10305i	1.13472	−	0.0992752i	0.639000	+	0.769207i	$0.279348\pi$
$978$	65.9434	−	26.3173i	2.10864	−	0.841533i
$979$	−6.04024	+	16.5954i	−0.193047	+	0.530392i
$980$		0			0
$981$	−11.8662	−	27.2738i	−0.378860	−	0.870787i
$982$	−46.7049	+	12.5145i	−1.49041	+	0.399355i
$983$	−36.5814	−	3.20046i	−1.16677	−	0.102079i	−0.512735	−	0.858547i	$-0.671368\pi$
$983$	−36.5814	−	3.20046i	−1.16677	−	0.102079i	−0.654030	+	0.756468i	$0.726923\pi$
$984$	0.0405214	−	0.172174i	0.00129177	−	0.00548871i
$985$		0			0
$986$	13.5432	+	2.38804i	0.431305	+	0.0760507i
$987$	6.44047	+	3.45966i	0.205002	+	0.110122i
$988$	−4.46840	+	51.0740i	−0.142159	+	1.62488i
$989$	−1.86320	+	3.22716i	−0.0592464	+	0.102618i
$990$		0			0
$991$	6.40763	+	11.0983i	0.203545	+	0.352550i	0.949668	−	0.313258i	$-0.101420\pi$
$991$	6.40763	+	11.0983i	0.203545	+	0.352550i	−0.746123	+	0.665808i	$0.768087\pi$
$992$	24.8820	−	11.6027i	0.790005	−	0.368385i
$993$	27.9710	+	4.05242i	0.887634	+	0.128600i
$994$	17.1893	−	20.4854i	0.545210	−	0.649756i
$995$		0			0
$996$	60.1899	+	3.41109i	1.90719	+	0.108085i
$997$	−31.6947	+	45.2647i	−1.00378	+	1.43355i	−0.105349	+	0.994435i	$0.533596\pi$
$997$	−31.6947	+	45.2647i	−1.00378	+	1.43355i	−0.898432	+	0.439113i	$0.855293\pi$
$998$	44.9938	+	44.9938i	1.42425	+	1.42425i
$999$	39.0800	−	47.0206i	1.23644	−	1.48766i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.ba.b.257.3		192
5.2	odd	4		135.2.q.a.68.14	yes	192
5.3	odd	4	inner	675.2.ba.b.68.3		192
5.4	even	2		135.2.q.a.122.14	yes	192
15.2	even	4		405.2.r.a.233.3		192
15.14	odd	2		405.2.r.a.152.3		192
27.2	odd	18	inner	675.2.ba.b.407.3		192
135.2	even	36		135.2.q.a.83.14	yes	192
135.29	odd	18		135.2.q.a.2.14	✓	192
135.52	odd	36		405.2.r.a.8.3		192
135.79	even	18		405.2.r.a.332.3		192
135.83	even	36	inner	675.2.ba.b.218.3		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.14	✓	192	135.29	odd	18
135.2.q.a.68.14	yes	192	5.2	odd	4
135.2.q.a.83.14	yes	192	135.2	even	36
135.2.q.a.122.14	yes	192	5.4	even	2
405.2.r.a.8.3		192	135.52	odd	36
405.2.r.a.152.3		192	15.14	odd	2
405.2.r.a.233.3		192	15.2	even	4
405.2.r.a.332.3		192	135.79	even	18
675.2.ba.b.68.3		192	5.3	odd	4	inner
675.2.ba.b.218.3		192	135.83	even	36	inner
675.2.ba.b.257.3		192	1.1	even	1	trivial
675.2.ba.b.407.3		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+(-1.65044 - 1.15565i) q^{2} +(1.69572 - 0.352907i) q^{3} +(0.704386 + 1.93528i) q^{4} +(-3.20652 - 1.37721i) q^{6} +(-0.618828 - 1.32708i) q^{7} +(0.0310202 - 0.115769i) q^{8} +(2.75091 - 1.19686i) q^{9} +(1.86051 + 2.21727i) q^{11} +(1.87741 + 3.03311i) q^{12} +(3.51558 + 5.02076i) q^{13} +(-0.512304 + 2.90542i) q^{14} +(2.97033 - 2.49240i) q^{16} +(0.833002 + 3.10881i) q^{17} +(-5.92337 - 1.20375i) q^{18} +(3.51741 - 2.03078i) q^{19} +(-1.51769 - 2.03197i) q^{21} +(-0.508272 - 5.80958i) q^{22} +(-4.58997 - 2.14034i) q^{23} +(0.0117458 - 0.207259i) q^{24} -12.3493i q^{26} +(4.24239 - 3.00035i) q^{27} +(2.13239 - 2.13239i) q^{28} +(0.368261 + 2.08851i) q^{29} +(-3.20394 + 1.16614i) q^{31} +(-8.02150 + 0.701790i) q^{32} +(3.93739 + 3.10328i) q^{33} +(2.21787 - 6.09356i) q^{34} +(4.25397 + 4.48075i) q^{36} +(11.3656 - 3.04540i) q^{37} +(-8.15214 - 0.713220i) q^{38} +(7.73328 + 7.27312i) q^{39} +(0.839107 + 0.147957i) q^{41} +(0.156621 + 5.10757i) q^{42} +(0.0641287 - 0.732994i) q^{43} +(-2.98053 + 5.16243i) q^{44} +(5.10199 + 8.83690i) q^{46} +(-2.61254 + 1.21825i) q^{47} +(4.15725 - 5.27466i) q^{48} +(3.12132 - 3.71984i) q^{49} +(2.50966 + 4.97768i) q^{51} +(-7.24028 + 10.3402i) q^{52} +(0.0757900 + 0.0757900i) q^{53} +(-10.4692 + 0.0491845i) q^{54} +(-0.172831 + 0.0304748i) q^{56} +(5.24785 - 4.68494i) q^{57} +(1.80580 - 3.87255i) q^{58} +(-2.89613 - 2.43014i) q^{59} +(-4.21993 - 1.53593i) q^{61} +(6.63556 + 1.77799i) q^{62} +(-3.29067 - 2.91003i) q^{63} +(7.33402 + 4.23430i) q^{64} +(-2.91213 - 9.67203i) q^{66} +(-3.65313 + 2.55795i) q^{67} +(-5.42967 + 3.80189i) q^{68} +(-8.53862 - 2.00957i) q^{69} +(-7.84988 - 4.53213i) q^{71} +(-0.0532255 - 0.355597i) q^{72} +(8.04880 + 2.15667i) q^{73} +(-22.2777 - 8.10840i) q^{74} +(6.40774 + 5.37673i) q^{76} +(1.79116 - 3.84116i) q^{77} +(-4.35814 - 20.9408i) q^{78} +(1.44073 - 0.254040i) q^{79} +(6.13505 - 6.58492i) q^{81} +(-1.21391 - 1.21391i) q^{82} +(9.69375 - 13.8441i) q^{83} +(2.86339 - 4.36846i) q^{84} +(-0.952926 + 1.13565i) q^{86} +(1.36152 + 3.41157i) q^{87} +(0.314404 - 0.146609i) q^{88} +(3.05075 + 5.28406i) q^{89} +(4.48742 - 7.77244i) q^{91} +(0.909052 - 10.3905i) q^{92} +(-5.02144 + 3.10813i) q^{93} +(5.71971 + 1.00854i) q^{94} +(-13.3545 + 4.02088i) q^{96} +(-16.1512 - 1.41304i) q^{97} +(-9.45039 + 2.53222i) q^{98} +(7.77187 + 3.87275i) 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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Groups

Database

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