LMFDB - Embedded newform 675.2.ba.b.218.3

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			218.3
Character	$\chi$	$=$	675.218
Dual form			675.2.ba.b.257.3

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

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

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 $

$2$	−1.65044	+	1.15565i	−1.16704	+	0.817169i	−0.986072	−	0.166320i	$-0.946811\pi$
$2$	−1.65044	+	1.15565i	−1.16704	+	0.817169i	−0.180966	+	0.983489i	$0.557923\pi$
$3$	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	−0.987864	−	0.155320i	$-0.950359\pi$
$7$	−0.618828	+	1.32708i	−0.233895	+	0.501590i	0.753969	+	0.656910i	$0.228137\pi$
$8$	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	−0.408785	−	0.912631i	$-0.634047\pi$
$11$	1.86051	−	2.21727i	0.560965	−	0.668532i	0.969751	+	0.244098i	$0.0784919\pi$
$12$	1.87741	−	3.03311i	0.541963	−	0.875584i
$13$	3.51558	−	5.02076i	0.975045	−	1.39251i	0.0559675	−	0.998433i	$-0.482176\pi$
$13$	3.51558	−	5.02076i	0.975045	−	1.39251i	0.919078	−	0.394076i	$-0.128935\pi$
$14$	−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	−0.788301	−	0.615290i	$-0.789039\pi$
$17$	0.833002	−	3.10881i	0.202033	−	0.753996i	0.990334	−	0.138706i	$-0.0442944\pi$
$18$	−5.92337	+	1.20375i	−1.39615	+	0.283726i
$19$	3.51741	+	2.03078i	0.806949	+	0.465892i	0.845895	−	0.533349i	$-0.179067\pi$
$19$	3.51741	+	2.03078i	0.806949	+	0.465892i	−0.0389464	+	0.999241i	$0.512400\pi$
$20$		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	−0.837441	−	0.546527i	$-0.815949\pi$
$23$	−4.58997	+	2.14034i	−0.957074	+	0.446291i	−0.119633	+	0.992818i	$0.538172\pi$
$24$	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	−0.931336	−	0.364162i	$-0.881355\pi$
$29$	0.368261	−	2.08851i	0.0683844	−	0.387827i	0.999720	−	0.0236650i	$-0.00753352\pi$
$30$		0			0
$31$	−3.20394	−	1.16614i	−0.575445	−	0.209445i	0.0378710	−	0.999283i	$-0.487942\pi$
$31$	−3.20394	−	1.16614i	−0.575445	−	0.209445i	−0.613316	+	0.789838i	$0.710165\pi$
$32$	−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	0.999988	+	0.00497757i	$0.00158442\pi$
$37$	11.3656	+	3.04540i	1.86849	+	0.500661i	0.868503	+	0.495683i	$0.165082\pi$
$38$	−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	−0.107740	−	0.994179i	$-0.534361\pi$
$41$	0.839107	−	0.147957i	0.131046	−	0.0231070i	0.238787	+	0.971072i	$0.423250\pi$
$42$	0.156621	−	5.10757i	0.0241671	−	0.788114i
$43$	0.0641287	+	0.732994i	0.00977953	+	0.111781i	0.999515	−	0.0311282i	$-0.00991001\pi$
$43$	0.0641287	+	0.732994i	0.00977953	+	0.111781i	−0.989736	+	0.142909i	$0.954354\pi$
$44$	−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	0.222634	−	0.974902i	$-0.428535\pi$
$47$	−2.61254	−	1.21825i	−0.381078	−	0.177700i	−0.603712	+	0.797203i	$0.706312\pi$
$48$	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	−0.701882	−	0.712293i	$-0.747657\pi$
$53$	0.0757900	−	0.0757900i	0.0104106	−	0.0104106i	0.712293	+	0.701882i	$0.247657\pi$
$54$	−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	−0.811540	−	0.584296i	$-0.801371\pi$
$59$	−2.89613	+	2.43014i	−0.377044	+	0.316377i	0.434497	+	0.900673i	$0.356926\pi$
$60$		0			0
$61$	−4.21993	+	1.53593i	−0.540306	+	0.196655i	−0.597734	−	0.801694i	$-0.703932\pi$
$61$	−4.21993	+	1.53593i	−0.540306	+	0.196655i	0.0574282	+	0.998350i	$0.481710\pi$
$62$	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	0.328733	−	0.944423i	$-0.393378\pi$
$67$	−3.65313	−	2.55795i	−0.446301	−	0.312504i	−0.775034	+	0.631919i	$0.782267\pi$
$68$	−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	−0.887320	−	0.461154i	$-0.847436\pi$
$71$	−7.84988	+	4.53213i	−0.931609	+	0.537865i	−0.0442890	+	0.999019i	$0.514102\pi$
$72$	−0.0532255	+	0.355597i	−0.00627268	+	0.0419075i
$73$	8.04880	−	2.15667i	0.942041	−	0.252419i	0.245059	−	0.969508i	$-0.421193\pi$
$73$	8.04880	−	2.15667i	0.942041	−	0.252419i	0.696982	+	0.717089i	$0.254526\pi$
$74$	−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	0.254107	−	0.967176i	$-0.418219\pi$
$79$	1.44073	+	0.254040i	0.162095	+	0.0285818i	−0.0920115	+	0.995758i	$0.529330\pi$
$80$		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	0.838155	+	0.545431i	$0.183634\pi$
$83$	9.69375	+	13.8441i	1.06403	+	1.51959i	0.225872	+	0.974157i	$0.427477\pi$
$84$	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	−0.657804	−	0.753189i	$-0.728514\pi$
$89$	3.05075	−	5.28406i	0.323379	−	0.560109i	0.981183	+	0.193080i	$0.0618477\pi$
$90$		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	−0.869449	−	0.494023i	$-0.835526\pi$
$97$	−16.1512	+	1.41304i	−1.63990	+	0.143473i	−0.770453	+	0.637496i	$0.779970\pi$
$98$	−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	0.810290	−	0.586029i	$-0.199309\pi$
$101$	−1.88053	−	5.16673i	−0.187120	−	0.514108i	−0.997410	+	0.0719204i	$0.977087\pi$
$102$	1.61043	+	11.1157i	0.159456	+	1.10061i
$103$	−3.90922	−	0.342012i	−0.385186	−	0.0336994i	−0.107082	−	0.994250i	$-0.534151\pi$
$103$	−3.90922	−	0.342012i	−0.385186	−	0.0336994i	−0.278105	+	0.960551i	$0.589706\pi$
$104$	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	0.999830	+	0.0184189i	$0.00586325\pi$
$107$	10.5329	+	10.5329i	1.01825	+	1.01825i	0.0184189	+	0.999830i	$0.494137\pi$
$108$	8.79481	−	6.09682i	0.846281	−	0.586667i
$109$			9.91447i			0.949634i	0.880085	+	0.474817i	$0.157486\pi$
$109$			9.91447i			0.949634i	−0.880085	+	0.474817i	$0.842514\pi$
$110$		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	−0.632583	−	0.774492i	$-0.718005\pi$
$113$	1.32748	−	15.1732i	0.124879	−	1.42737i	0.757462	−	0.652879i	$-0.226439\pi$
$114$	−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	−0.980782	−	0.195109i	$-0.937494\pi$
$127$	−2.58018	−	9.62937i	−0.228954	−	0.854468i	0.751828	−	0.659360i	$-0.229173\pi$
$128$	−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	−0.651028	−	0.759054i	$-0.725662\pi$
$131$	3.84111	−	10.5534i	0.335599	−	0.922051i	0.986627	−	0.162997i	$-0.0521159\pi$
$132$	−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	−0.376424	+	0.926448i	$0.622846\pi$
$137$	−16.1027	+	11.2752i	−1.37574	+	0.963306i	−0.999320	+	0.0368588i	$0.988265\pi$
$138$	11.7701	−	13.1844i	1.00194	−	1.12233i
$139$	0.508611	−	1.39740i	0.0431398	−	0.118526i	−0.916252	−	0.400602i	$-0.868801\pi$
$139$	0.508611	−	1.39740i	0.0431398	−	0.118526i	0.959392	+	0.282076i	$0.0910232\pi$
$140$		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	0.999545	+	0.0301644i	$0.00960308\pi$
$149$	0.861743	+	4.88719i	0.0705968	+	0.400374i	−0.928948	+	0.370210i	$0.879286\pi$
$150$		0			0
$151$	−15.8833	−	13.3277i	−1.29257	−	1.08459i	−0.991379	−	0.131025i	$-0.958173\pi$
$151$	−15.8833	−	13.3277i	−1.29257	−	1.08459i	−0.301186	−	0.953565i	$-0.597383\pi$
$152$	−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	0.935291	+	0.353879i	$0.115138\pi$
$157$	−0.591932	+	6.76582i	−0.0472413	+	0.539971i	−0.982532	+	0.186092i	$0.940418\pi$
$158$	−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	−0.990689	−	0.136142i	$-0.956530\pi$
$163$	−14.3864	−	14.3864i	−1.12683	−	1.12683i	−0.136142	−	0.990689i	$-0.543470\pi$
$164$	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	0.105319	−	0.994439i	$-0.466414\pi$
$167$	0.469806	+	0.0411027i	0.0363547	+	0.00318063i	−0.0689639	+	0.997619i	$0.521969\pi$
$168$	−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	0.636125	−	0.771586i	$-0.280536\pi$
$173$	18.3690	−	1.60708i	1.39657	−	0.122184i	0.760446	+	0.649402i	$0.224981\pi$
$174$	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	0.679346	−	0.733818i	$-0.262264\pi$
$179$	−3.95796	−	6.85540i	−0.295832	−	0.512396i	−0.975178	+	0.221422i	$0.928930\pi$
$180$		0			0
$181$	9.86110	−	17.0799i	0.732970	−	1.26954i	−0.222638	−	0.974901i	$-0.571467\pi$
$181$	9.86110	−	17.0799i	0.732970	−	1.26954i	0.955608	−	0.294640i	$-0.0951998\pi$
$182$	−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	−0.146630	−	0.989191i	$-0.546843\pi$
$191$	−8.60644	−	1.51755i	−0.622740	−	0.109806i	−0.476110	+	0.879386i	$0.657954\pi$
$192$	13.9307	−	4.59195i	1.00536	−	0.331395i
$193$	3.65180	+	7.83132i	0.262863	+	0.563711i	0.992797	−	0.119806i	$-0.0382273\pi$
$193$	3.65180	+	7.83132i	0.262863	+	0.563711i	−0.729935	+	0.683517i	$0.760450\pi$
$194$	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	−0.327167	−	0.944966i	$-0.606094\pi$
$197$	−1.93720	+	0.519071i	−0.138020	+	0.0369822i	0.189148	+	0.981949i	$0.439427\pi$
$198$	−8.35147	+	15.3733i	−0.593513	+	1.09253i
$199$	15.5130	−	8.95641i	1.09968	−	0.634903i	0.163546	−	0.986536i	$-0.447707\pi$
$199$	15.5130	−	8.95641i	1.09968	−	0.634903i	0.936138	+	0.351633i	$0.114373\pi$
$200$		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	−0.879293	−	0.476282i	$-0.841984\pi$
$211$	−8.17709	+	6.86139i	−0.562934	+	0.472358i	0.316359	+	0.948640i	$0.397540\pi$
$212$	−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	0.0246975	−	0.999695i	$-0.492138\pi$
$223$	−10.8301	−	5.05016i	−0.725238	−	0.338184i	−0.749936	+	0.661511i	$0.769916\pi$
$224$	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	0.992113	−	0.125346i	$-0.0400041\pi$
$227$	−0.100851	−	1.15273i	−0.00669369	−	0.0765092i	−0.998807	+	0.0488368i	$0.984449\pi$
$228$	12.7632	−	6.85608i	0.845264	−	0.454055i
$229$	−8.62548	+	1.52090i	−0.569988	+	0.100504i	−0.451212	−	0.892417i	$-0.649008\pi$
$229$	−8.62548	+	1.52090i	−0.569988	+	0.100504i	−0.118776	+	0.992921i	$0.537897\pi$
$230$		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	0.736219	−	0.676743i	$-0.236609\pi$
$233$	15.8052	+	4.23498i	1.03543	+	0.277443i	0.299213	+	0.954186i	$0.403276\pi$
$234$	−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	0.0675160	−	0.997718i	$-0.478493\pi$
$239$	−8.07123	−	2.93769i	−0.522085	−	0.190023i	−0.589601	+	0.807695i	$0.700715\pi$
$240$		0			0
$241$	0.358872	−	2.03527i	0.0231170	−	0.131103i	−0.971065	−	0.238815i	$-0.923241\pi$
$241$	0.358872	−	2.03527i	0.0231170	−	0.131103i	0.994182	+	0.107712i	$0.0343523\pi$
$242$	−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	0.770232	−	0.637764i	$-0.220140\pi$
$251$	9.55376	+	5.51587i	0.603028	+	0.348158i	−0.167204	+	0.985922i	$0.553474\pi$
$252$	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	−0.702439	−	0.711744i	$-0.747906\pi$
$257$	3.31253	−	4.73079i	0.206630	−	0.295098i	0.909069	+	0.416646i	$0.136794\pi$
$258$	−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	0.504993	+	0.863123i	$0.331495\pi$
$263$	−7.79728	+	16.7213i	−0.480801	+	1.03108i	−0.985794	+	0.167958i	$0.946283\pi$
$264$	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	0.609120	+	0.793078i	$0.291523\pi$
$277$	−6.49002	+	13.9179i	−0.389947	+	0.836245i	−0.999068	+	0.0431672i	$0.986255\pi$
$278$	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	−0.605031	−	0.796202i	$-0.706839\pi$
$281$	4.76302	−	5.67634i	0.284138	−	0.338622i	0.889168	+	0.457580i	$0.151284\pi$
$282$	10.0549	+	0.308329i	0.598763	+	0.0183607i
$283$	−8.24647	+	11.7772i	−0.490202	+	0.700081i	−0.985696	−	0.168530i	$-0.946098\pi$
$283$	−8.24647	+	11.7772i	−0.490202	+	0.700081i	0.495495	+	0.868611i	$0.334987\pi$
$284$	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	−0.874985	−	0.484150i	$-0.839129\pi$
$293$	−18.2561	+	8.51297i	−1.06653	+	0.497333i	−0.191549	+	0.981483i	$0.561351\pi$
$294$	−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	−0.0860714	−	0.996289i	$-0.527431\pi$
$307$	−11.5423	−	3.09276i	−0.658756	−	0.176513i	−0.572684	+	0.819776i	$0.694098\pi$
$308$	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	−0.105634	−	0.994405i	$-0.533687\pi$
$311$	2.38442	−	0.420438i	0.135208	−	0.0238408i	0.240843	+	0.970564i	$0.422576\pi$
$312$	1.08189	+	0.669660i	0.0612499	+	0.0379120i
$313$	−1.06842	−	12.2121i	−0.0603905	−	0.690267i	−0.964693	−	0.263375i	$-0.915164\pi$
$313$	−1.06842	−	12.2121i	−0.0603905	−	0.690267i	0.904303	−	0.426891i	$-0.140391\pi$
$314$	−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	−0.251566	−	0.967840i	$-0.580945\pi$
$317$	−20.5585	−	9.58656i	−1.15468	−	0.538435i	−0.903112	+	0.429405i	$0.858723\pi$
$318$	−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	0.115706	−	0.993284i	$-0.463087\pi$
$331$	15.3336	−	5.58098i	0.842812	−	0.306758i	0.727106	+	0.686525i	$0.240865\pi$
$332$	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	0.659620	−	0.751599i	$-0.270717\pi$
$337$	3.28511	+	2.30026i	0.178951	+	0.125303i	−0.480669	+	0.876902i	$0.659606\pi$
$338$	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	0.995326	−	0.0965722i	$-0.0307879\pi$
$347$	5.24496	+	11.2479i	0.281564	+	0.603816i	−0.713762	+	0.700389i	$0.753010\pi$
$348$	−5.64331	−	5.03798i	−0.302513	−	0.270064i
$349$	−7.52479	−	1.32682i	−0.402793	−	0.0710232i	−0.0314181	−	0.999506i	$-0.510002\pi$
$349$	−7.52479	−	1.32682i	−0.402793	−	0.0710232i	−0.371375	+	0.928483i	$0.621113\pi$
$350$		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	0.446904	−	0.894582i	$-0.352527\pi$
$353$	−10.2693	−	14.6661i	−0.546579	−	0.780595i	−0.993482	+	0.113987i	$0.963638\pi$
$354$	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	−0.651977	−	0.758239i	$-0.726060\pi$
$359$	6.26521	−	10.8517i	0.330665	−	0.572729i	0.982642	+	0.185510i	$0.0593936\pi$
$360$		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	0.274470	−	0.961596i	$-0.411497\pi$
$367$	13.6352	−	1.19292i	0.711750	−	0.0622701i	0.437280	+	0.899325i	$0.355942\pi$
$368$	−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	0.395006	−	0.918678i	$-0.370742\pi$
$373$	12.0608	+	1.05518i	0.624485	+	0.0546353i	0.229478	+	0.973314i	$0.426298\pi$
$374$	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	$0.196331\pi$
$379$			22.5213i			1.15684i	−0.815738	+	0.578421i	$0.803669\pi$
$380$		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	0.893437	+	0.449189i	$0.148287\pi$
$383$	−1.26087	+	14.4118i	−0.0644275	+	0.736410i	−0.957864	+	0.287221i	$0.907269\pi$
$384$	−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	0.363416	−	0.931627i	$-0.381610\pi$
$389$	−9.68308	−	8.12507i	−0.490951	−	0.411957i	−0.854367	+	0.519670i	$0.826055\pi$
$390$		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	−0.992197	−	0.124684i	$-0.960208\pi$
$397$	−3.89075	−	14.5205i	−0.195271	−	0.728761i	0.796926	−	0.604077i	$-0.206458\pi$
$398$	−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	0.486369	+	0.873754i	$0.338321\pi$
$401$	−8.96818	+	24.6399i	−0.447849	+	1.23046i	−0.934218	+	0.356703i	$0.883901\pi$
$402$	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	−0.986972	−	0.160891i	$-0.948563\pi$
$409$	−2.57831	+	7.08384i	−0.127489	+	0.350273i	0.859483	+	0.511164i	$0.170786\pi$
$410$		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	0.937348	+	0.348394i	$0.113273\pi$
$419$	3.59622	+	20.3952i	0.175687	+	0.996370i	−0.761661	+	0.647975i	$0.775616\pi$
$420$		0			0
$421$	−5.26964	−	4.42176i	−0.256827	−	0.215503i	0.505279	−	0.862956i	$-0.331390\pi$
$421$	−5.26964	−	4.42176i	−0.256827	−	0.215503i	−0.762105	+	0.647453i	$0.775834\pi$
$422$	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	$0.0223983\pi$
$431$			2.91928i			0.140617i	−0.997525	+	0.0703084i	$0.977602\pi$
$432$	5.12321	+	19.4858i	0.246490	+	0.937510i
$433$	−3.01763	−	3.01763i	−0.145018	−	0.145018i	0.630870	−	0.775888i	$-0.282698\pi$
$433$	−3.01763	−	3.01763i	−0.145018	−	0.145018i	−0.775888	+	0.630870i	$0.782698\pi$
$434$	−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	0.905354	−	0.424658i	$-0.139606\pi$
$439$	−1.28129	−	3.52030i	−0.0611524	−	0.168015i	−0.966506	+	0.256643i	$0.917383\pi$
$440$		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	0.597229	−	0.802070i	$-0.296268\pi$
$443$	27.8809	−	2.43927i	1.32466	−	0.115893i	0.727434	+	0.686177i	$0.240713\pi$
$444$	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	0.956389	−	0.292097i	$-0.0943530\pi$
$449$	4.77256	+	8.26631i	0.225231	+	0.390111i	−0.731158	+	0.682208i	$0.761020\pi$
$450$		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	−0.933741	−	0.357949i	$-0.883476\pi$
$457$	−20.3246	−	29.0265i	−0.950745	−	1.35780i	−0.0170039	−	0.999855i	$-0.505413\pi$
$458$	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	0.710219	−	0.703981i	$-0.248596\pi$
$461$	24.4088	+	4.30393i	1.13683	+	0.200454i	0.426612	+	0.904435i	$0.359707\pi$
$462$	−11.0335	−	9.84995i	−0.513323	−	0.458261i
$463$	2.28775	+	4.90609i	0.106321	+	0.228005i	0.952269	−	0.305259i	$-0.0987430\pi$
$463$	2.28775	+	4.90609i	0.106321	+	0.228005i	−0.845949	+	0.533264i	$0.820965\pi$
$464$	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	−0.997989	−	0.0633888i	$-0.979809\pi$
$467$	−39.5591	+	10.5998i	−1.83058	+	0.490502i	−0.832589	+	0.553891i	$0.813143\pi$
$468$	−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	−0.858425	−	0.512940i	$-0.828556\pi$
$479$	−25.9636	+	9.44996i	−1.18631	+	0.431780i	−0.327880	+	0.944719i	$0.606334\pi$
$480$		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	−0.343969	+	0.938981i	$0.611772\pi$
$487$	−28.3122	+	28.3122i	−1.28295	+	1.28295i	−0.938981	+	0.343969i	$0.888228\pi$
$488$	−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	0.992086	−	0.125559i	$-0.0400724\pi$
$491$	15.4259	+	18.3839i	0.696161	+	0.829652i	−0.295925	+	0.955211i	$0.595628\pi$
$492$	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	−0.818976	−	0.573828i	$-0.805458\pi$
$499$	−31.1017	+	5.48406i	−1.39230	+	0.245500i	−0.573325	+	0.819328i	$0.694347\pi$
$500$		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	0.319058	−	0.947735i	$-0.396634\pi$
$503$	2.72503	+	0.730168i	0.121503	+	0.0325566i	−0.197555	+	0.980292i	$0.563300\pi$
$504$	−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	0.758304	−	0.651901i	$-0.226028\pi$
$509$	20.7599	+	7.55598i	0.920166	+	0.334913i	0.161861	+	0.986814i	$0.448250\pi$
$510$		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	0.323588	−	0.946198i	$-0.395111\pi$
$521$	−7.62484	−	4.40220i	−0.334050	−	0.192864i	−0.657638	+	0.753334i	$0.728444\pi$
$522$	0.332694	+	12.8143i	0.0145616	+	0.560868i
$523$	0.332937	−	1.24254i	0.0145583	−	0.0543324i	−0.958265	−	0.285883i	$-0.907713\pi$
$523$	0.332937	−	1.24254i	0.0145583	−	0.0543324i	0.972823	+	0.231550i	$0.0743798\pi$
$524$	−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	−0.943621	−	0.331029i	$-0.892604\pi$
$547$	−1.95267	+	4.18752i	−0.0834904	+	0.179046i	0.860130	+	0.510074i	$0.170382\pi$
$548$	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	−0.998912	−	0.0466405i	$-0.985148\pi$
$557$	−2.60809	+	9.73354i	−0.110509	+	0.412423i	0.888403	+	0.459064i	$0.151815\pi$
$558$	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	−0.0798064	−	0.996810i	$-0.525430\pi$
$563$	15.0076	−	6.99817i	0.632496	−	0.294938i	0.712302	+	0.701873i	$0.247652\pi$
$564$	−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	−0.918815	−	0.394688i	$-0.870853\pi$
$569$	1.89828	−	10.7657i	0.0795799	−	0.451320i	0.998395	−	0.0566320i	$-0.0180362\pi$
$570$		0			0
$571$	15.2515	+	5.55110i	0.638256	+	0.232306i	0.640821	−	0.767691i	$-0.278594\pi$
$571$	15.2515	+	5.55110i	0.638256	+	0.232306i	−0.00256475	+	0.999997i	$0.500816\pi$
$572$	−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	−0.113572	−	0.993530i	$-0.536229\pi$
$577$	−17.0234	−	4.56140i	−0.708693	−	0.189894i	−0.595121	+	0.803636i	$0.702896\pi$
$578$	−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	0.569430	−	0.822040i	$-0.307164\pi$
$587$	7.40736	+	3.45411i	0.305734	+	0.142566i	−0.263696	+	0.964606i	$0.584942\pi$
$588$	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	−0.169357	+	0.985555i	$0.554169\pi$
$593$	−28.1239	+	28.1239i	−1.15491	+	1.15491i	−0.985555	+	0.169357i	$0.945831\pi$
$594$	−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	−0.998962	−	0.0455483i	$-0.985496\pi$
$599$	−27.5968	+	23.1564i	−1.12757	+	0.946147i	−0.128612	+	0.991695i	$0.541052\pi$
$600$		0			0
$601$	−21.4617	+	7.81141i	−0.875440	+	0.318634i	−0.740368	−	0.672202i	$-0.765349\pi$
$601$	−21.4617	+	7.81141i	−0.875440	+	0.318634i	−0.135072	+	0.990836i	$0.543126\pi$
$602$	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	0.707046	−	0.707168i	$-0.250027\pi$
$607$	7.00562	+	4.90539i	0.284349	+	0.199104i	−0.422696	+	0.906271i	$0.638916\pi$
$608$	−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	0.550882	−	0.834583i	$-0.314291\pi$
$613$	35.7827	−	9.58796i	1.44525	−	0.387254i	0.894369	+	0.447329i	$0.147625\pi$
$614$	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	0.982556	−	0.185965i	$-0.0595411\pi$
$617$	5.17963	+	11.1077i	0.208524	+	0.447181i	−0.774032	+	0.633146i	$0.781763\pi$
$618$	13.0060	−	4.28712i	0.523178	−	0.172453i
$619$	8.63834	+	1.52317i	0.347204	+	0.0612215i	0.344531	−	0.938775i	$-0.388038\pi$
$619$	8.63834	+	1.52317i	0.347204	+	0.0612215i	0.00267331	+	0.999996i	$0.499149\pi$
$620$		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	0.984741	+	0.174027i	$0.0556781\pi$
$631$	16.1540	+	27.9796i	0.643083	+	1.11385i	−0.341658	+	0.939824i	$0.610989\pi$
$632$	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	0.855499	−	0.517805i	$-0.173251\pi$
$641$	−3.35944	−	9.23000i	−0.132690	−	0.364563i	−0.988189	+	0.153242i	$0.951029\pi$
$642$	−48.2797	−	19.2679i	−1.90545	−	0.760443i
$643$	−18.5293	−	1.62110i	−0.730723	−	0.0639299i	−0.284279	−	0.958742i	$-0.591754\pi$
$643$	−18.5293	−	1.62110i	−0.730723	−	0.0639299i	−0.446444	+	0.894812i	$0.647310\pi$
$644$	−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	0.928832	−	0.370501i	$-0.120814\pi$
$647$	14.2018	+	14.2018i	0.558331	+	0.558331i	−0.370501	+	0.928832i	$0.620814\pi$
$648$	−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	0.883189	+	0.469018i	$0.155392\pi$
$653$	−1.73834	+	19.8693i	−0.0680265	+	0.777546i	−0.951215	+	0.308528i	$0.900164\pi$
$654$	−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	0.658526	−	0.752558i	$-0.271180\pi$
$659$	0.815140	+	0.683983i	0.0317533	+	0.0266442i	−0.626773	+	0.779202i	$0.715625\pi$
$660$		0			0
$661$	−5.78183	−	32.7904i	−0.224887	−	1.27540i	−0.862901	−	0.505373i	$-0.831355\pi$
$661$	−5.78183	−	32.7904i	−0.224887	−	1.27540i	0.638014	−	0.770025i	$-0.279756\pi$
$662$	−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	−0.119397	−	0.992847i	$-0.538096\pi$
$673$	20.0466	−	14.0367i	0.772738	−	0.541077i	0.892135	+	0.451770i	$0.149207\pi$
$674$	−8.08017			−0.311236
$675$		0			0
$676$	−50.5961			−1.94600
$677$	16.7682	−	11.7412i	0.644455	−	0.451252i	−0.205108	−	0.978739i	$-0.565755\pi$
$677$	16.7682	−	11.7412i	0.644455	−	0.451252i	0.849563	+	0.527487i	$0.176866\pi$
$678$	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	0.984804	+	0.173671i	$0.0555630\pi$
$683$	5.71751	+	21.3380i	0.218774	+	0.816477i	−0.766029	+	0.642806i	$0.777770\pi$
$684$	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	0.865568	−	0.500792i	$-0.166958\pi$
$691$	13.7398	+	11.5291i	0.522688	+	0.438587i	−0.342880	+	0.939379i	$0.611402\pi$
$692$	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	$0.0690713\pi$
$701$			11.4005i			0.430590i	−0.976549	+	0.215295i	$0.930929\pi$
$702$	−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	0.998504	−	0.0546749i	$-0.0174122\pi$
$709$	5.28444	+	14.5189i	0.198461	+	0.545268i	−0.800043	+	0.599943i	$0.795190\pi$
$710$		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	0.940407	−	0.340050i	$-0.110444\pi$
$719$	4.71157	+	8.16068i	0.175712	+	0.304342i	−0.764695	+	0.644392i	$0.777111\pi$
$720$		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	0.952293	+	0.305186i	$0.0987187\pi$
$727$	24.6272	+	35.1712i	0.913371	+	1.30443i	−0.0389219	+	0.999242i	$0.512392\pi$
$728$	−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	0.901360	−	0.433071i	$-0.142570\pi$
$733$	−0.264636	−	0.567513i	−0.00977454	−	0.0209616i	−0.911134	+	0.412109i	$0.864792\pi$
$734$	−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	0.00348723	−	0.999994i	$-0.498890\pi$
$739$	23.6846	−	13.6743i	0.871251	−	0.503017i	0.867764	+	0.496977i	$0.165557\pi$
$740$		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	−0.106950	−	0.994264i	$-0.534109\pi$
$743$	−29.3796	−	20.5718i	−1.07783	−	0.754706i	−0.970882	+	0.239558i	$0.922997\pi$
$744$	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	−0.985373	−	0.170413i	$-0.945490\pi$
$751$	−27.0935	+	22.7342i	−0.988657	+	0.829582i	−0.00328459	+	0.999995i	$0.501046\pi$
$752$	−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	−0.0492153	−	0.998788i	$-0.515672\pi$
$757$	26.1262	−	26.1262i	0.949573	−	0.949573i	0.998788	+	0.0492153i	$0.0156721\pi$
$758$	−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	0.851896	−	0.523712i	$-0.175453\pi$
$761$	5.19201	+	6.18759i	0.188210	+	0.224300i	−0.663685	+	0.748012i	$0.731009\pi$
$762$	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	−0.455574	−	0.890198i	$-0.650566\pi$
$769$	−16.0619	+	2.83215i	−0.579208	+	0.102130i	−0.123634	+	0.992328i	$0.539455\pi$
$770$		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	0.0473325	−	0.998879i	$-0.484928\pi$
$773$	−11.4302	−	3.06271i	−0.411116	−	0.110158i	−0.458448	+	0.888721i	$0.651595\pi$
$774$	−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	0.545689	−	0.837988i	$-0.316268\pi$
$787$	43.1572	−	20.1245i	1.53839	−	0.717361i	0.992698	+	0.120627i	$0.0384904\pi$
$788$	−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	−0.951231	−	0.308480i	$-0.900180\pi$
$797$	−9.48608	+	13.5475i	−0.336014	+	0.479878i	0.615216	+	0.788358i	$0.289069\pi$
$798$	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	−0.614246	−	0.789115i	$-0.710540\pi$
$821$	7.72326	−	9.20422i	0.269544	−	0.321230i	0.883789	+	0.467885i	$0.154984\pi$
$822$	36.1052	−	58.3309i	1.25931	−	2.03452i
$823$	−13.6442	+	19.4859i	−0.475607	+	0.679237i	−0.983236	−	0.182339i	$-0.941633\pi$
$823$	−13.6442	+	19.4859i	−0.475607	+	0.679237i	0.507629	+	0.861576i	$0.330522\pi$
$824$	−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	−0.361504	−	0.932370i	$-0.617737\pi$
$827$	12.0136	−	44.8353i	0.417753	−	1.55907i	0.779257	−	0.626704i	$-0.215597\pi$
$828$	−9.93527	+	29.6714i	−0.345275	+	1.03115i
$829$	−27.8169	−	16.0601i	−0.966123	−	0.557791i	−0.0680706	−	0.997681i	$-0.521684\pi$
$829$	−27.8169	−	16.0601i	−0.966123	−	0.557791i	−0.898052	+	0.439889i	$0.855018\pi$
$830$		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	−0.329406	−	0.944188i	$-0.606849\pi$
$839$	8.77845	−	49.7851i	0.303066	−	1.71877i	0.632472	−	0.774583i	$-0.282040\pi$
$840$		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	−0.562550	−	0.826763i	$-0.690180\pi$
$853$	−4.44262	−	50.7794i	−0.152112	−	1.73865i	0.410438	−	0.911889i	$-0.365376\pi$
$854$	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	0.572224	−	0.820097i	$-0.306081\pi$
$857$	9.12817	+	4.25654i	0.311812	+	0.145400i	−0.260412	+	0.965498i	$0.583858\pi$
$858$	38.3232	+	48.6238i	1.30833	+	1.65999i
$859$	−8.01487	−	9.55175i	−0.273464	−	0.325902i	0.611781	−	0.791027i	$-0.290453\pi$
$859$	−8.01487	−	9.55175i	−0.273464	−	0.325902i	−0.885245	+	0.465126i	$0.846009\pi$
$860$		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	−0.985479	−	0.169800i	$-0.945688\pi$
$863$	−23.9621	+	23.9621i	−0.815678	+	0.815678i	0.169800	+	0.985479i	$0.445688\pi$
$864$	−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	−0.299794	−	0.954004i	$-0.596918\pi$
$877$	−38.4629	−	26.9320i	−1.29880	−	0.909430i	−0.999006	+	0.0445739i	$0.985807\pi$
$878$	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	−0.117920	−	0.993023i	$-0.537623\pi$
$881$	20.2756	−	11.7061i	0.683103	−	0.394390i	0.801023	+	0.598633i	$0.204289\pi$
$882$	−22.9665	−	18.2767i	−0.773321	−	0.615409i
$883$	−6.11319	+	1.63802i	−0.205725	+	0.0551239i	−0.360210	−	0.932871i	$-0.617295\pi$
$883$	−6.11319	+	1.63802i	−0.205725	+	0.0551239i	0.154485	+	0.987995i	$0.450628\pi$
$884$	−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	0.989375	+	0.145384i	$0.0464419\pi$
$887$	13.8426	+	29.6855i	0.464788	+	0.996741i	−0.524587	+	0.851357i	$0.675780\pi$
$888$	−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	−0.550355	−	0.834931i	$-0.685508\pi$
$907$	−28.5313	+	2.49616i	−0.947365	+	0.0828837i	−0.397010	+	0.917814i	$0.629952\pi$
$908$	−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	0.780536	−	0.625111i	$-0.214946\pi$
$911$	−6.61616	−	18.1777i	−0.219203	−	0.602255i	−0.999739	+	0.0228557i	$0.992724\pi$
$912$	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	$-0.736295\pi$
$919$		−	44.6775i		−	1.47377i	0.676016	−	0.736887i	$-0.263705\pi$
$920$		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	0.985669	+	0.168689i	$0.0539535\pi$
$929$	40.3230	+	33.8350i	1.32296	+	1.11009i	0.337286	+	0.941402i	$0.390491\pi$
$930$		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	0.878394	−	0.477938i	$-0.158616\pi$
$937$	−3.71263	−	13.8557i	−0.121286	−	0.452647i	−0.999680	+	0.0252908i	$0.991949\pi$
$938$	−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	−0.941161	−	0.337959i	$-0.890264\pi$
$941$	−0.0906224	+	0.248983i	−0.00295420	+	0.00811661i	0.938207	+	0.346075i	$0.112486\pi$
$942$	−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	−0.0238294	−	0.999716i	$-0.507586\pi$
$947$	27.9252	−	19.5534i	0.907446	−	0.635401i	0.931276	+	0.364315i	$0.118697\pi$
$948$	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	−0.982755	−	0.184912i	$-0.940800\pi$
$953$	−6.91874	−	25.8211i	−0.224120	−	0.836427i	0.758635	−	0.651516i	$-0.225867\pi$
$954$	−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	−0.912796	−	0.408416i	$-0.866081\pi$
$967$	1.77416	−	20.2788i	0.0570532	−	0.652121i	0.969849	−	0.243706i	$-0.0783631\pi$
$968$	−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	$0.225350\pi$
$971$			40.5268i			1.30057i	−0.759692	+	0.650284i	$0.774650\pi$
$972$	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	0.639000	−	0.769207i	$-0.279348\pi$
$977$	35.4680	+	3.10305i	1.13472	+	0.0992752i	0.495721	+	0.868482i	$0.334904\pi$
$978$	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	−0.654030	−	0.756468i	$-0.726923\pi$
$983$	−36.5814	+	3.20046i	−1.16677	+	0.102079i	−0.512735	+	0.858547i	$0.671368\pi$
$984$	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	−0.746123	−	0.665808i	$-0.768087\pi$
$991$	6.40763	−	11.0983i	0.203545	−	0.352550i	0.949668	+	0.313258i	$0.101420\pi$
$992$	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	−0.898432	−	0.439113i	$-0.855293\pi$
$997$	−31.6947	−	45.2647i	−1.00378	−	1.43355i	−0.105349	−	0.994435i	$-0.533596\pi$
$998$	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.218.3		192
5.2	odd	4	inner	675.2.ba.b.407.3		192
5.3	odd	4		135.2.q.a.2.14	✓	192
5.4	even	2		135.2.q.a.83.14	yes	192
15.8	even	4		405.2.r.a.332.3		192
15.14	odd	2		405.2.r.a.8.3		192
27.14	odd	18	inner	675.2.ba.b.68.3		192
135.13	odd	36		405.2.r.a.152.3		192
135.14	odd	18		135.2.q.a.68.14	yes	192
135.68	even	36		135.2.q.a.122.14	yes	192
135.94	even	18		405.2.r.a.233.3		192
135.122	even	36	inner	675.2.ba.b.257.3		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.14	✓	192	5.3	odd	4
135.2.q.a.68.14	yes	192	135.14	odd	18
135.2.q.a.83.14	yes	192	5.4	even	2
135.2.q.a.122.14	yes	192	135.68	even	36
405.2.r.a.8.3		192	15.14	odd	2
405.2.r.a.152.3		192	135.13	odd	36
405.2.r.a.233.3		192	135.94	even	18
405.2.r.a.332.3		192	15.8	even	4
675.2.ba.b.68.3		192	27.14	odd	18	inner
675.2.ba.b.218.3		192	1.1	even	1	trivial
675.2.ba.b.257.3		192	135.122	even	36	inner
675.2.ba.b.407.3		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+(-1.65044 + 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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Database

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