LMFDB - Embedded newform 218.2.c.c.63.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [218,2,Mod(45,218)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(218, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("218.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 218 = 2 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	218.c (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.74073876406$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 14x^{8} + 6x^{7} + 95x^{6} + 2x^{5} + 231x^{4} + 53x^{3} + 389x^{2} - 76x + 16 $ x^10 - 2x^9 + 14x^8 + 6x^7 + 95x^6 + 2x^5 + 231x^4 + 53x^3 + 389x^2 - 76*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			63.2
Root			$0.810249 - 1.40339i$ of defining polynomial
Character	$\chi$	$=$	218.63
Dual form			218.2.c.c.45.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-0.262161 - 0.454076i) q^{3} +1.00000 q^{4} +(-0.189751 - 0.328658i) q^{5} +(-0.262161 - 0.454076i) q^{6} +(1.23508 + 2.13922i) q^{7} +1.00000 q^{8} +(1.36254 - 2.35999i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-0.262161 - 0.454076i) q^{3} +1.00000 q^{4} +(-0.189751 - 0.328658i) q^{5} +(-0.262161 - 0.454076i) q^{6} +(1.23508 + 2.13922i) q^{7} +1.00000 q^{8} +(1.36254 - 2.35999i) q^{9} +(-0.189751 - 0.328658i) q^{10} +(2.04533 - 3.54262i) q^{11} +(-0.262161 - 0.454076i) q^{12} +(2.36254 + 4.09205i) q^{13} +(1.23508 + 2.13922i) q^{14} +(-0.0994903 + 0.172322i) q^{15} +1.00000 q^{16} -6.71116 q^{17} +(1.36254 - 2.35999i) q^{18} -3.04202 q^{19} +(-0.189751 - 0.328658i) q^{20} +(0.647579 - 1.12164i) q^{21} +(2.04533 - 3.54262i) q^{22} -5.86991 q^{23} +(-0.262161 - 0.454076i) q^{24} +(2.42799 - 4.20540i) q^{25} +(2.36254 + 4.09205i) q^{26} -3.00179 q^{27} +(1.23508 + 2.13922i) q^{28} +(3.45507 + 5.98436i) q^{29} +(-0.0994903 + 0.172322i) q^{30} +(-4.33270 + 7.50446i) q^{31} +1.00000 q^{32} -2.14482 q^{33} -6.71116 q^{34} +(0.468714 - 0.811837i) q^{35} +(1.36254 - 2.35999i) q^{36} +(-1.54533 + 2.67659i) q^{37} -3.04202 q^{38} +(1.23873 - 2.14555i) q^{39} +(-0.189751 - 0.328658i) q^{40} +7.14109 q^{41} +(0.647579 - 1.12164i) q^{42} -8.91192 q^{43} +(2.04533 - 3.54262i) q^{44} -1.03417 q^{45} -5.86991 q^{46} +(-0.262161 - 0.454076i) q^{48} +(0.449152 - 0.777955i) q^{49} +(2.42799 - 4.20540i) q^{50} +(1.75940 + 3.04737i) q^{51} +(2.36254 + 4.09205i) q^{52} +(-6.92944 - 12.0021i) q^{53} -3.00179 q^{54} -1.55241 q^{55} +(1.23508 + 2.13922i) q^{56} +(0.797497 + 1.38131i) q^{57} +(3.45507 + 5.98436i) q^{58} +(-1.06649 + 1.84722i) q^{59} +(-0.0994903 + 0.172322i) q^{60} +(-0.521009 - 0.902413i) q^{61} +(-4.33270 + 7.50446i) q^{62} +6.73140 q^{63} +1.00000 q^{64} +(0.896588 - 1.55294i) q^{65} -2.14482 q^{66} +(-7.60038 + 13.1642i) q^{67} -6.71116 q^{68} +(1.53886 + 2.66538i) q^{69} +(0.468714 - 0.811837i) q^{70} +6.23548 q^{71} +(1.36254 - 2.35999i) q^{72} +(7.62284 - 13.2031i) q^{73} +(-1.54533 + 2.67659i) q^{74} -2.54609 q^{75} -3.04202 q^{76} +10.1046 q^{77} +(1.23873 - 2.14555i) q^{78} +(7.31299 - 12.6665i) q^{79} +(-0.189751 - 0.328658i) q^{80} +(-3.30068 - 5.71695i) q^{81} +7.14109 q^{82} +(-0.282277 - 0.488917i) q^{83} +(0.647579 - 1.12164i) q^{84} +(1.27345 + 2.20567i) q^{85} -8.91192 q^{86} +(1.81157 - 3.13773i) q^{87} +(2.04533 - 3.54262i) q^{88} +(1.20711 + 2.09077i) q^{89} -1.03417 q^{90} +(-5.83586 + 10.1080i) q^{91} -5.86991 q^{92} +4.54346 q^{93} +(0.577224 + 0.999782i) q^{95} +(-0.262161 - 0.454076i) q^{96} +(6.33878 + 10.9791i) q^{97} +(0.449152 - 0.777955i) q^{98} +(-5.57370 - 9.65394i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} + q^{3} + 10 q^{4} - 8 q^{5} + q^{6} - q^{7} + 10 q^{8} - 10 q^{9}+O(q^{10}) $ 10 * q + 10 * q^2 + q^3 + 10 * q^4 - 8 * q^5 + q^6 - q^7 + 10 * q^8 - 10 * q^9	\( 10 q + 10 q^{2} + q^{3} + 10 q^{4} - 8 q^{5} + q^{6} - q^{7} + 10 q^{8} - 10 q^{9} - 8 q^{10} + q^{11} + q^{12} - q^{14} - q^{15} + 10 q^{16} - 16 q^{17} - 10 q^{18} - 6 q^{19} - 8 q^{20} + 4 q^{21} + q^{22} + 8 q^{23} + q^{24} - 11 q^{25} + 10 q^{27} - q^{28} + 9 q^{29} - q^{30} + 7 q^{31} + 10 q^{32} - 2 q^{33} - 16 q^{34} + 10 q^{35} - 10 q^{36} + 4 q^{37} - 6 q^{38} - 4 q^{39} - 8 q^{40} - 22 q^{41} + 4 q^{42} + 2 q^{43} + q^{44} + 38 q^{45} + 8 q^{46} + q^{48} - 10 q^{49} - 11 q^{50} - 3 q^{51} - 2 q^{53} + 10 q^{54} + 20 q^{55} - q^{56} - 49 q^{57} + 9 q^{58} - 12 q^{59} - q^{60} + 7 q^{61} + 7 q^{62} - 36 q^{63} + 10 q^{64} - 3 q^{65} - 2 q^{66} - 56 q^{67} - 16 q^{68} + 19 q^{69} + 10 q^{70} + 4 q^{71} - 10 q^{72} + 12 q^{73} + 4 q^{74} - 46 q^{75} - 6 q^{76} + 66 q^{77} - 4 q^{78} - 30 q^{79} - 8 q^{80} - 41 q^{81} - 22 q^{82} - 7 q^{83} + 4 q^{84} - 22 q^{85} + 2 q^{86} + 40 q^{87} + q^{88} + 9 q^{89} + 38 q^{90} + 20 q^{91} + 8 q^{92} + 10 q^{93} - 12 q^{95} + q^{96} + 35 q^{97} - 10 q^{98} + 19 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 + q^3 + 10 * q^4 - 8 * q^5 + q^6 - q^7 + 10 * q^8 - 10 * q^9 - 8 * q^10 + q^11 + q^12 - q^14 - q^15 + 10 * q^16 - 16 * q^17 - 10 * q^18 - 6 * q^19 - 8 * q^20 + 4 * q^21 + q^22 + 8 * q^23 + q^24 - 11 * q^25 + 10 * q^27 - q^28 + 9 * q^29 - q^30 + 7 * q^31 + 10 * q^32 - 2 * q^33 - 16 * q^34 + 10 * q^35 - 10 * q^36 + 4 * q^37 - 6 * q^38 - 4 * q^39 - 8 * q^40 - 22 * q^41 + 4 * q^42 + 2 * q^43 + q^44 + 38 * q^45 + 8 * q^46 + q^48 - 10 * q^49 - 11 * q^50 - 3 * q^51 - 2 * q^53 + 10 * q^54 + 20 * q^55 - q^56 - 49 * q^57 + 9 * q^58 - 12 * q^59 - q^60 + 7 * q^61 + 7 * q^62 - 36 * q^63 + 10 * q^64 - 3 * q^65 - 2 * q^66 - 56 * q^67 - 16 * q^68 + 19 * q^69 + 10 * q^70 + 4 * q^71 - 10 * q^72 + 12 * q^73 + 4 * q^74 - 46 * q^75 - 6 * q^76 + 66 * q^77 - 4 * q^78 - 30 * q^79 - 8 * q^80 - 41 * q^81 - 22 * q^82 - 7 * q^83 + 4 * q^84 - 22 * q^85 + 2 * q^86 + 40 * q^87 + q^88 + 9 * q^89 + 38 * q^90 + 20 * q^91 + 8 * q^92 + 10 * q^93 - 12 * q^95 + q^96 + 35 * q^97 - 10 * q^98 + 19 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/218\mathbb{Z}\right)^\times$.

$n$	$115$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−0.262161	−	0.454076i	−0.151359	−	0.262161i	0.780369	−	0.625320i	$-0.215031\pi$
$3$	−0.262161	−	0.454076i	−0.151359	−	0.262161i	−0.931727	+	0.363159i	$0.881698\pi$
$4$	1.00000			0.500000
$5$	−0.189751	−	0.328658i	−0.0848590	−	0.146980i	0.820472	−	0.571687i	$-0.193711\pi$
$5$	−0.189751	−	0.328658i	−0.0848590	−	0.146980i	−0.905331	+	0.424706i	$0.860377\pi$
$6$	−0.262161	−	0.454076i	−0.107027	−	0.185376i
$7$	1.23508	+	2.13922i	0.466817	+	0.808550i	0.999281	−	0.0379021i	$-0.0120675\pi$
$7$	1.23508	+	2.13922i	0.466817	+	0.808550i	−0.532465	+	0.846452i	$0.678734\pi$
$8$	1.00000			0.353553
$9$	1.36254	−	2.35999i	0.454181	−	0.786665i
$10$	−0.189751	−	0.328658i	−0.0600044	−	0.103931i
$11$	2.04533	−	3.54262i	0.616690	−	1.06814i	−0.373395	−	0.927672i	$-0.621806\pi$
$11$	2.04533	−	3.54262i	0.616690	−	1.06814i	0.990085	−	0.140466i	$-0.0448602\pi$
$12$	−0.262161	−	0.454076i	−0.0756793	−	0.131080i
$13$	2.36254	+	4.09205i	0.655252	+	1.13493i	0.981831	+	0.189759i	$0.0607708\pi$
$13$	2.36254	+	4.09205i	0.655252	+	1.13493i	−0.326579	+	0.945170i	$0.605896\pi$
$14$	1.23508	+	2.13922i	0.330089	+	0.571731i
$15$	−0.0994903	+	0.172322i	−0.0256883	+	0.0444934i
$16$	1.00000			0.250000
$17$	−6.71116			−1.62770			−0.813848	−	0.581078i	$-0.802631\pi$
$17$	−6.71116			−1.62770			−0.813848	+	0.581078i	$0.802631\pi$
$18$	1.36254	−	2.35999i	0.321155	−	0.556256i
$19$	−3.04202			−0.697887			−0.348943	−	0.937144i	$-0.613459\pi$
$19$	−3.04202			−0.697887			−0.348943	+	0.937144i	$0.613459\pi$
$20$	−0.189751	−	0.328658i	−0.0424295	−	0.0734901i
$21$	0.647579	−	1.12164i	0.141313	−	0.244762i
$22$	2.04533	−	3.54262i	0.436066	−	0.755288i
$23$	−5.86991			−1.22396			−0.611980	−	0.790873i	$-0.709627\pi$
$23$	−5.86991			−1.22396			−0.611980	+	0.790873i	$0.709627\pi$
$24$	−0.262161	−	0.454076i	−0.0535133	−	0.0926878i
$25$	2.42799	−	4.20540i	0.485598	−	0.841080i
$26$	2.36254	+	4.09205i	0.463333	+	0.802516i
$27$	−3.00179			−0.577694
$28$	1.23508	+	2.13922i	0.233408	+	0.404275i
$29$	3.45507	+	5.98436i	0.641590	+	1.11127i	0.985078	+	0.172110i	$0.0550584\pi$
$29$	3.45507	+	5.98436i	0.641590	+	1.11127i	−0.343487	+	0.939157i	$0.611608\pi$
$30$	−0.0994903	+	0.172322i	−0.0181644	+	0.0314616i
$31$	−4.33270	+	7.50446i	−0.778177	+	1.34784i	0.154815	+	0.987943i	$0.450522\pi$
$31$	−4.33270	+	7.50446i	−0.778177	+	1.34784i	−0.932992	+	0.359898i	$0.882811\pi$
$32$	1.00000			0.176777
$33$	−2.14482			−0.373365
$34$	−6.71116			−1.15095
$35$	0.468714	−	0.811837i	0.0792272	−	0.137226i
$36$	1.36254	−	2.35999i	0.227091	−	0.393332i
$37$	−1.54533	+	2.67659i	−0.254051	+	0.440029i	−0.964637	−	0.263581i	$-0.915096\pi$
$37$	−1.54533	+	2.67659i	−0.254051	+	0.440029i	0.710587	+	0.703610i	$0.248430\pi$
$38$	−3.04202			−0.493480
$39$	1.23873	−	2.14555i	0.198356	−	0.343562i
$40$	−0.189751	−	0.328658i	−0.0300022	−	0.0519653i
$41$	7.14109			1.11525			0.557625	−	0.830093i	$-0.311713\pi$
$41$	7.14109			1.11525			0.557625	+	0.830093i	$0.311713\pi$
$42$	0.647579	−	1.12164i	0.0999236	−	0.173073i
$43$	−8.91192			−1.35906			−0.679528	−	0.733650i	$-0.737815\pi$
$43$	−8.91192			−1.35906			−0.679528	+	0.733650i	$0.737815\pi$
$44$	2.04533	−	3.54262i	0.308345	−	0.534069i
$45$	−1.03417			−0.154166
$46$	−5.86991			−0.865471
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$	−0.262161	−	0.454076i	−0.0378396	−	0.0655402i
$49$	0.449152	−	0.777955i	0.0641646	−	0.111136i
$50$	2.42799	−	4.20540i	0.343370	−	0.594734i
$51$	1.75940	+	3.04737i	0.246366	+	0.426718i
$52$	2.36254	+	4.09205i	0.327626	+	0.567465i
$53$	−6.92944	−	12.0021i	−0.951831	−	1.64862i	−0.741458	−	0.670999i	$-0.765866\pi$
$53$	−6.92944	−	12.0021i	−0.951831	−	1.64862i	−0.210373	−	0.977621i	$-0.567468\pi$
$54$	−3.00179			−0.408491
$55$	−1.55241			−0.209327
$56$	1.23508	+	2.13922i	0.165045	+	0.285866i
$57$	0.797497	+	1.38131i	0.105631	+	0.182958i
$58$	3.45507	+	5.98436i	0.453673	+	0.785784i
$59$	−1.06649	+	1.84722i	−0.138846	+	0.240488i	−0.927060	−	0.374913i	$-0.877672\pi$
$59$	−1.06649	+	1.84722i	−0.138846	+	0.240488i	0.788214	+	0.615401i	$0.211006\pi$
$60$	−0.0994903	+	0.172322i	−0.0128441	+	0.0222467i
$61$	−0.521009	−	0.902413i	−0.0667083	−	0.115542i	0.830742	−	0.556657i	$-0.187916\pi$
$61$	−0.521009	−	0.902413i	−0.0667083	−	0.115542i	−0.897451	+	0.441115i	$0.854583\pi$
$62$	−4.33270	+	7.50446i	−0.550254	+	0.953068i
$63$	6.73140			0.848077
$64$	1.00000			0.125000
$65$	0.896588	−	1.55294i	0.111208	−	0.192618i
$66$	−2.14482			−0.264009
$67$	−7.60038	+	13.1642i	−0.928535	+	1.60827i	−0.142759	+	0.989758i	$0.545597\pi$
$67$	−7.60038	+	13.1642i	−0.928535	+	1.60827i	−0.785776	+	0.618512i	$0.787736\pi$
$68$	−6.71116			−0.813848
$69$	1.53886	+	2.66538i	0.185257	+	0.320874i
$70$	0.468714	−	0.811837i	0.0560221	−	0.0970331i
$71$	6.23548			0.740015			0.370008	−	0.929029i	$-0.379355\pi$
$71$	6.23548			0.740015			0.370008	+	0.929029i	$0.379355\pi$
$72$	1.36254	−	2.35999i	0.160577	−	0.278128i
$73$	7.62284	−	13.2031i	0.892186	−	1.54531i	0.0549362	−	0.998490i	$-0.482504\pi$
$73$	7.62284	−	13.2031i	0.892186	−	1.54531i	0.837249	−	0.546821i	$-0.184162\pi$
$74$	−1.54533	+	2.67659i	−0.179641	+	0.311147i
$75$	−2.54609			−0.293998
$76$	−3.04202			−0.348943
$77$	10.1046			1.15152
$78$	1.23873	−	2.14555i	0.140259	−	0.242935i
$79$	7.31299	−	12.6665i	0.822775	−	1.42509i	−0.0808322	−	0.996728i	$-0.525758\pi$
$79$	7.31299	−	12.6665i	0.822775	−	1.42509i	0.903608	−	0.428361i	$-0.140909\pi$
$80$	−0.189751	−	0.328658i	−0.0212148	−	0.0367450i
$81$	−3.30068	−	5.71695i	−0.366742	−	0.635216i
$82$	7.14109			0.788601
$83$	−0.282277	−	0.488917i	−0.0309839	−	0.0536657i	0.850118	−	0.526593i	$-0.176531\pi$
$83$	−0.282277	−	0.488917i	−0.0309839	−	0.0536657i	−0.881102	+	0.472927i	$0.843197\pi$
$84$	0.647579	−	1.12164i	0.0706567	−	0.122381i
$85$	1.27345	+	2.20567i	0.138125	+	0.239239i
$86$	−8.91192			−0.960998
$87$	1.81157	−	3.13773i	0.194220	−	0.336399i
$88$	2.04533	−	3.54262i	0.218033	−	0.377644i
$89$	1.20711	+	2.09077i	0.127953	+	0.221621i	0.922883	−	0.385079i	$-0.125826\pi$
$89$	1.20711	+	2.09077i	0.127953	+	0.221621i	−0.794930	+	0.606701i	$0.792493\pi$
$90$	−1.03417			−0.109011
$91$	−5.83586	+	10.1080i	−0.611765	+	1.05961i
$92$	−5.86991			−0.611980
$93$	4.54346			0.471135
$94$		0			0
$95$	0.577224	+	0.999782i	0.0592220	+	0.102575i
$96$	−0.262161	−	0.454076i	−0.0267567	−	0.0463439i
$97$	6.33878	+	10.9791i	0.643605	+	1.11476i	0.984622	+	0.174700i	$0.0558954\pi$
$97$	6.33878	+	10.9791i	0.643605	+	1.11476i	−0.341017	+	0.940057i	$0.610771\pi$
$98$	0.449152	−	0.777955i	0.0453712	−	0.0785853i
$99$	−5.57370	−	9.65394i	−0.560178	−	0.970257i
$100$	2.42799	−	4.20540i	0.242799	−	0.420540i
$101$	3.66073			0.364256			0.182128	−	0.983275i	$-0.441701\pi$
$101$	3.66073			0.364256			0.182128	+	0.983275i	$0.441701\pi$
$102$	1.75940	+	3.04737i	0.174207	+	0.301735i
$103$	3.65991	+	6.33915i	0.360622	+	0.624615i	0.988063	−	0.154048i	$-0.0492312\pi$
$103$	3.65991	+	6.33915i	0.360622	+	0.624615i	−0.627441	+	0.778664i	$0.715898\pi$
$104$	2.36254	+	4.09205i	0.231666	+	0.401258i
$105$	−0.491514			−0.0479669
$106$	−6.92944	−	12.0021i	−0.673046	−	1.16575i
$107$	−6.40207			−0.618912			−0.309456	−	0.950914i	$-0.600147\pi$
$107$	−6.40207			−0.618912			−0.309456	+	0.950914i	$0.600147\pi$
$108$	−3.00179			−0.288847
$109$	−2.26968	+	10.1906i	−0.217396	+	0.976084i
$109$	−2.26968	+	10.1906i	−0.217396	+	0.976084i
$110$	−1.55241			−0.148016
$111$	1.62050			0.153811
$112$	1.23508	+	2.13922i	0.116704	+	0.202137i
$113$	13.3766			1.25836			0.629181	−	0.777259i	$-0.283390\pi$
$113$	13.3766			1.25836			0.629181	+	0.777259i	$0.283390\pi$
$114$	0.797497	+	1.38131i	0.0746925	+	0.129371i
$115$	1.11382	+	1.92919i	0.103864	+	0.179898i
$116$	3.45507	+	5.98436i	0.320795	+	0.555634i
$117$	12.8763			1.19041
$118$	−1.06649	+	1.84722i	−0.0981786	+	0.170050i
$119$	−8.28882	−	14.3567i	−0.759835	−	1.31607i
$120$	−0.0994903	+	0.172322i	−0.00908218	+	0.0157308i
$121$	−2.86675	−	4.96535i	−0.260614	−	0.451396i
$122$	−0.521009	−	0.902413i	−0.0471699	−	0.0817007i
$123$	−1.87211	−	3.24259i	−0.168803	−	0.292375i
$124$	−4.33270	+	7.50446i	−0.389088	+	0.673921i
$125$	−3.74036			−0.334548
$126$	6.73140			0.599681
$127$	−1.80838	+	3.13221i	−0.160468	+	0.277939i	−0.935037	−	0.354551i	$-0.884634\pi$
$127$	−1.80838	+	3.13221i	−0.160468	+	0.277939i	0.774569	+	0.632490i	$0.217967\pi$
$128$	1.00000			0.0883883
$129$	2.33636	+	4.04669i	0.205705	+	0.356291i
$130$	0.896588	−	1.55294i	0.0786360	−	0.136201i
$131$	7.40877	−	12.8324i	0.647307	−	1.12117i	−0.336457	−	0.941699i	$-0.609229\pi$
$131$	7.40877	−	12.8324i	0.647307	−	1.12117i	0.983764	−	0.179469i	$-0.0574381\pi$
$132$	−2.14482			−0.186683
$133$	−3.75714	−	6.50755i	−0.325785	−	0.564276i
$134$	−7.60038	+	13.1642i	−0.656573	+	1.13722i
$135$	0.569590	+	0.986560i	0.0490225	+	0.0849095i
$136$	−6.71116			−0.575477
$137$	6.39002	+	11.0678i	0.545937	+	0.945590i	0.998547	+	0.0538816i	$0.0171594\pi$
$137$	6.39002	+	11.0678i	0.545937	+	0.945590i	−0.452611	+	0.891708i	$0.649507\pi$
$138$	1.53886	+	2.66538i	0.130996	+	0.226892i
$139$	2.02156	−	3.50145i	0.171467	−	0.296989i	−0.767466	−	0.641089i	$-0.778483\pi$
$139$	2.02156	−	3.50145i	0.171467	−	0.296989i	0.938933	+	0.344100i	$0.111816\pi$
$140$	0.468714	−	0.811837i	0.0396136	−	0.0686128i
$141$		0			0
$142$	6.23548			0.523270
$143$	19.3287			1.61635
$144$	1.36254	−	2.35999i	0.113545	−	0.196666i
$145$	1.31120	−	2.27107i	0.108889	−	0.188602i
$146$	7.62284	−	13.2031i	0.630871	−	1.09270i
$147$	−0.471000			−0.0388475
$148$	−1.54533	+	2.67659i	−0.127025	+	0.220014i
$149$	−6.16914	−	10.6853i	−0.505396	−	0.875371i	−0.999981	−	0.00624174i	$-0.998013\pi$
$149$	−6.16914	−	10.6853i	−0.505396	−	0.875371i	0.494585	−	0.869129i	$-0.335320\pi$
$150$	−2.54609			−0.207888
$151$	3.65991	−	6.33915i	0.297839	−	0.515873i	−0.677802	−	0.735244i	$-0.737067\pi$
$151$	3.65991	−	6.33915i	0.297839	−	0.515873i	0.975641	+	0.219372i	$0.0704007\pi$
$152$	−3.04202			−0.246740
$153$	−9.14425	+	15.8383i	−0.739268	+	1.28045i
$154$	10.1046			0.814251
$155$	3.28853			0.264141
$156$	1.23873	−	2.14555i	0.0991779	−	0.171781i
$157$	4.17108	+	7.22452i	0.332889	+	0.576580i	0.983077	−	0.183193i	$-0.0586434\pi$
$157$	4.17108	+	7.22452i	0.332889	+	0.576580i	−0.650188	+	0.759773i	$0.725310\pi$
$158$	7.31299	−	12.6665i	0.581790	−	1.00769i
$159$	−3.63325	+	6.29298i	−0.288136	+	0.499065i
$160$	−0.189751	−	0.328658i	−0.0150011	−	0.0259827i
$161$	−7.24981	−	12.5570i	−0.571365	−	0.989633i
$162$	−3.30068	−	5.71695i	−0.259326	−	0.449166i
$163$	5.30589			0.415590			0.207795	−	0.978172i	$-0.433371\pi$
$163$	5.30589			0.415590			0.207795	+	0.978172i	$0.433371\pi$
$164$	7.14109			0.557625
$165$	0.406981	+	0.704912i	0.0316834	+	0.0548773i
$166$	−0.282277	−	0.488917i	−0.0219089	−	0.0379474i
$167$	−8.74189	−	15.1414i	−0.676468	−	1.17168i	−0.976038	−	0.217602i	$-0.930176\pi$
$167$	−8.74189	−	15.1414i	−0.676468	−	1.17168i	0.299570	−	0.954074i	$-0.403157\pi$
$168$	0.647579	−	1.12164i	0.0499618	−	0.0865364i
$169$	−4.66322	+	8.07694i	−0.358710	+	0.621303i
$170$	1.27345	+	2.20567i	0.0976689	+	0.169167i
$171$	−4.14488	+	7.17914i	−0.316967	+	0.549003i
$172$	−8.91192			−0.679528
$173$	−6.96057			−0.529202			−0.264601	−	0.964358i	$-0.585240\pi$
$173$	−6.96057			−0.529202			−0.264601	+	0.964358i	$0.585240\pi$
$174$	1.81157	−	3.13773i	0.137335	−	0.237870i
$175$	11.9950			0.906741
$176$	2.04533	−	3.54262i	0.154173	−	0.267035i
$177$	1.11837			0.0840618
$178$	1.20711	+	2.09077i	0.0904765	+	0.156710i
$179$	−0.667695	+	1.15648i	−0.0499059	+	0.0864395i	−0.889899	−	0.456157i	$-0.849225\pi$
$179$	−0.667695	+	1.15648i	−0.0499059	+	0.0864395i	0.839993	+	0.542597i	$0.182559\pi$
$180$	−1.03417			−0.0770828
$181$	−0.775805	+	1.34373i	−0.0576652	+	0.0998790i	−0.893417	−	0.449228i	$-0.851699\pi$
$181$	−0.775805	+	1.34373i	−0.0576652	+	0.0998790i	0.835752	+	0.549107i	$0.185032\pi$
$182$	−5.83586	+	10.1080i	−0.432583	+	0.749256i
$183$	−0.273176	+	0.473155i	−0.0201937	+	0.0349766i
$184$	−5.86991			−0.432735
$185$	1.17291			0.0862340
$186$	4.54346			0.333143
$187$	−13.7265	+	23.7751i	−1.00378	+	1.73860i
$188$		0			0
$189$	−3.70745	−	6.42149i	−0.269677	−	0.467094i
$190$	0.577224	+	0.999782i	0.0418763	+	0.0725318i
$191$	−11.3551			−0.821627			−0.410813	−	0.911720i	$-0.634755\pi$
$191$	−11.3551			−0.821627			−0.410813	+	0.911720i	$0.634755\pi$
$192$	−0.262161	−	0.454076i	−0.0189198	−	0.0327701i
$193$	−0.494482	+	0.856468i	−0.0355936	+	0.0616499i	−0.883273	−	0.468858i	$-0.844666\pi$
$193$	−0.494482	+	0.856468i	−0.0355936	+	0.0616499i	0.847680	+	0.530508i	$0.177999\pi$
$194$	6.33878	+	10.9791i	0.455098	+	0.788252i
$195$	−0.940200			−0.0673291
$196$	0.449152	−	0.777955i	0.0320823	−	0.0555682i
$197$	2.76753	−	4.79350i	0.197178	−	0.341523i	−0.750434	−	0.660945i	$-0.770156\pi$
$197$	2.76753	−	4.79350i	0.197178	−	0.341523i	0.947612	+	0.319422i	$0.103489\pi$
$198$	−5.57370	−	9.65394i	−0.396106	−	0.686075i
$199$	−7.59180			−0.538169			−0.269084	−	0.963117i	$-0.586721\pi$
$199$	−7.59180			−0.538169			−0.269084	+	0.963117i	$0.586721\pi$
$200$	2.42799	−	4.20540i	0.171685	−	0.297367i
$201$	7.97009			0.562166
$202$	3.66073			0.257568
$203$	−8.53458	+	14.7823i	−0.599010	+	1.03752i
$204$	1.75940	+	3.04737i	0.123183	+	0.213359i
$205$	−1.35503	−	2.34697i	−0.0946391	−	0.163920i
$206$	3.65991	+	6.33915i	0.254998	+	0.441670i
$207$	−7.99800	+	13.8530i	−0.555900	+	0.962847i
$208$	2.36254	+	4.09205i	0.163813	+	0.283732i
$209$	−6.22193	+	10.7767i	−0.430380	+	0.745440i
$210$	−0.491514			−0.0339177
$211$	−0.998953	−	1.73024i	−0.0687708	−	0.119114i	0.829590	−	0.558373i	$-0.188574\pi$
$211$	−0.998953	−	1.73024i	−0.0687708	−	0.119114i	−0.898360	+	0.439259i	$0.855241\pi$
$212$	−6.92944	−	12.0021i	−0.475916	−	0.824310i
$213$	−1.63470	−	2.83138i	−0.112008	−	0.194003i
$214$	−6.40207			−0.437637
$215$	1.69104	+	2.92897i	0.115328	+	0.199754i
$216$	−3.00179			−0.204246
$217$	−21.4050			−1.45306
$218$	−2.26968	+	10.1906i	−0.153722	+	0.690195i
$219$	−7.99363			−0.540160
$220$	−1.55241			−0.104663
$221$	−15.8554	−	27.4624i	−1.06655	−	1.84732i
$222$	1.62050			0.108761
$223$	−1.47933	−	2.56228i	−0.0990633	−	0.171583i	0.812234	−	0.583332i	$-0.198251\pi$
$223$	−1.47933	−	2.56228i	−0.0990633	−	0.171583i	−0.911297	+	0.411749i	$0.864918\pi$
$224$	1.23508	+	2.13922i	0.0825223	+	0.142933i
$225$	−6.61648	−	11.4601i	−0.441099	−	0.764006i
$226$	13.3766			0.889796
$227$	−1.15034	+	1.99244i	−0.0763506	+	0.132243i	−0.901673	−	0.432419i	$-0.857660\pi$
$227$	−1.15034	+	1.99244i	−0.0763506	+	0.132243i	0.825322	+	0.564662i	$0.190993\pi$
$228$	0.797497	+	1.38131i	0.0528155	+	0.0914792i
$229$	−7.06226	+	12.2322i	−0.466687	+	0.808326i	−0.999276	−	0.0380480i	$-0.987886\pi$
$229$	−7.06226	+	12.2322i	−0.466687	+	0.808326i	0.532588	+	0.846374i	$0.321219\pi$
$230$	1.11382	+	1.92919i	0.0734430	+	0.127207i
$231$	−2.64903	−	4.58825i	−0.174293	−	0.301884i
$232$	3.45507	+	5.98436i	0.226836	+	0.392892i
$233$	7.74836	−	13.4206i	0.507612	−	0.879210i	−0.492349	−	0.870398i	$-0.663862\pi$
$233$	7.74836	−	13.4206i	0.507612	−	0.879210i	0.999961	−	0.00881204i	$-0.00280500\pi$
$234$	12.8763			0.841748
$235$		0			0
$236$	−1.06649	+	1.84722i	−0.0694228	+	0.120244i
$237$	−7.66871			−0.498136
$238$	−8.28882	−	14.3567i	−0.537284	−	0.930604i
$239$	−0.556899	+	0.964577i	−0.0360228	+	0.0623933i	−0.883475	−	0.468479i	$-0.844802\pi$
$239$	−0.556899	+	0.964577i	−0.0360228	+	0.0623933i	0.847452	+	0.530872i	$0.178136\pi$
$240$	−0.0994903	+	0.172322i	−0.00642207	+	0.0111234i
$241$	2.75028			0.177161			0.0885806	−	0.996069i	$-0.471767\pi$
$241$	2.75028			0.177161			0.0885806	+	0.996069i	$0.471767\pi$
$242$	−2.86675	−	4.96535i	−0.184282	−	0.319185i
$243$	−6.23330	+	10.7964i	−0.399866	+	0.692588i
$244$	−0.521009	−	0.902413i	−0.0333542	−	0.0577711i
$245$	−0.340908			−0.0217798
$246$	−1.87211	−	3.24259i	−0.119362	−	0.206740i
$247$	−7.18690	−	12.4481i	−0.457291	−	0.792052i
$248$	−4.33270	+	7.50446i	−0.275127	+	0.476534i
$249$	−0.148004	+	0.256350i	−0.00937935	+	0.0162455i
$250$	−3.74036			−0.236561
$251$	17.1335			1.08146			0.540728	−	0.841198i	$-0.318149\pi$
$251$	17.1335			1.08146			0.540728	+	0.841198i	$0.318149\pi$
$252$	6.73140			0.424039
$253$	−12.0059	+	20.7948i	−0.754804	+	1.30736i
$254$	−1.80838	+	3.13221i	−0.113468	+	0.196532i
$255$	0.667695	−	1.15648i	0.0418127	−	0.0724217i
$256$	1.00000			0.0625000
$257$	−8.21984	+	14.2372i	−0.512740	+	0.888091i	0.487151	+	0.873318i	$0.338036\pi$
$257$	−8.21984	+	14.2372i	−0.512740	+	0.888091i	−0.999891	+	0.0147733i	$0.995297\pi$
$258$	2.33636	+	4.04669i	0.145455	+	0.251936i
$259$	−7.63443			−0.474380
$260$	0.896588	−	1.55294i	0.0556040	−	0.0963090i
$261$	18.8307			1.16559
$262$	7.40877	−	12.8324i	0.457715	−	0.792786i
$263$	25.1569			1.55124			0.775621	−	0.631199i	$-0.217437\pi$
$263$	25.1569			1.55124			0.775621	+	0.631199i	$0.217437\pi$
$264$	−2.14482			−0.132005
$265$	−2.62973	+	4.55482i	−0.161543	+	0.279801i
$266$	−3.75714	−	6.50755i	−0.230365	−	0.399004i
$267$	0.632912	−	1.09624i	0.0387336	−	0.0670886i
$268$	−7.60038	+	13.1642i	−0.464267	+	0.804135i
$269$	1.05180	+	1.82177i	0.0641294	+	0.111075i	0.896307	−	0.443433i	$-0.146240\pi$
$269$	1.05180	+	1.82177i	0.0641294	+	0.111075i	−0.832178	+	0.554509i	$0.812906\pi$
$270$	0.569590	+	0.986560i	0.0346642	+	0.0600401i
$271$	3.19275	+	5.53001i	0.193946	+	0.335924i	0.946555	−	0.322544i	$-0.104538\pi$
$271$	3.19275	+	5.53001i	0.193946	+	0.335924i	−0.752608	+	0.658468i	$0.771205\pi$
$272$	−6.71116			−0.406924
$273$	6.11973			0.370383
$274$	6.39002	+	11.0678i	0.386035	+	0.668633i
$275$	−9.93208	−	17.2029i	−0.598927	−	1.03737i
$276$	1.53886	+	2.66538i	0.0926284	+	0.160437i
$277$	4.77710	−	8.27418i	0.287028	−	0.497147i	−0.686071	−	0.727535i	$-0.740666\pi$
$277$	4.77710	−	8.27418i	0.287028	−	0.497147i	0.973099	+	0.230388i	$0.0739994\pi$
$278$	2.02156	−	3.50145i	0.121245	−	0.210003i
$279$	11.8070	+	20.4503i	0.706866	+	1.22433i
$280$	0.468714	−	0.811837i	0.0280110	−	0.0485166i
$281$	−15.8073			−0.942987			−0.471493	−	0.881870i	$-0.656285\pi$
$281$	−15.8073			−0.942987			−0.471493	+	0.881870i	$0.656285\pi$
$282$		0			0
$283$	15.1467	−	26.2348i	0.900376	−	1.55950i	0.0733690	−	0.997305i	$-0.476625\pi$
$283$	15.1467	−	26.2348i	0.900376	−	1.55950i	0.827007	−	0.562192i	$-0.190042\pi$
$284$	6.23548			0.370008
$285$	0.302651	−	0.524207i	0.0179275	−	0.0310513i
$286$	19.3287			1.14293
$287$	8.81982	+	15.2764i	0.520617	+	0.901736i
$288$	1.36254	−	2.35999i	0.0802887	−	0.139064i
$289$	28.0397			1.64939
$290$	1.31120	−	2.27107i	0.0769965	−	0.133362i
$291$	3.32356	−	5.75657i	0.194830	−	0.337456i
$292$	7.62284	−	13.2031i	0.446093	−	0.772655i
$293$	−10.6352			−0.621317			−0.310658	−	0.950522i	$-0.600549\pi$
$293$	−10.6352			−0.621317			−0.310658	+	0.950522i	$0.600549\pi$
$294$	−0.471000			−0.0274693
$295$	0.809471			0.0471292
$296$	−1.54533	+	2.67659i	−0.0898205	+	0.155574i
$297$	−6.13964	+	10.6342i	−0.356258	+	0.617057i
$298$	−6.16914	−	10.6853i	−0.357369	−	0.618981i
$299$	−13.8679	−	24.0199i	−0.802002	−	1.38911i
$300$	−2.54609			−0.146999
$301$	−11.0069	−	19.0646i	−0.634430	−	1.09886i
$302$	3.65991	−	6.33915i	0.210604	−	0.364777i
$303$	−0.959700	−	1.66225i	−0.0551333	−	0.0954937i
$304$	−3.04202			−0.174472
$305$	−0.197723	+	0.342467i	−0.0113216	+	0.0196096i
$306$	−9.14425	+	15.8383i	−0.522742	+	0.905415i
$307$	5.09251	+	8.82048i	0.290645	+	0.503411i	0.973962	−	0.226710i	$-0.0727969\pi$
$307$	5.09251	+	8.82048i	0.290645	+	0.503411i	−0.683318	+	0.730121i	$0.739464\pi$
$308$	10.1046			0.575762
$309$	1.91897	−	3.32375i	0.109166	−	0.189082i
$310$	3.28853			0.186776
$311$	−1.22266			−0.0693307			−0.0346653	−	0.999399i	$-0.511037\pi$
$311$	−1.22266			−0.0693307			−0.0346653	+	0.999399i	$0.511037\pi$
$312$	1.23873	−	2.14555i	0.0701294	−	0.121468i
$313$	−14.7789	−	25.5979i	−0.835355	−	1.44688i	−0.893741	−	0.448584i	$-0.851929\pi$
$313$	−14.7789	−	25.5979i	−0.835355	−	1.44688i	0.0583855	−	0.998294i	$-0.481405\pi$
$314$	4.17108	+	7.22452i	0.235388	+	0.407704i
$315$	−1.27729	−	2.21233i	−0.0719670	−	0.124651i
$316$	7.31299	−	12.6665i	0.411388	−	0.712544i
$317$	12.8714	+	22.2938i	0.722927	+	1.25215i	0.959821	+	0.280611i	$0.0905372\pi$
$317$	12.8714	+	22.2938i	0.722927	+	1.25215i	−0.236894	+	0.971535i	$0.576129\pi$
$318$	−3.63325	+	6.29298i	−0.203743	+	0.352893i
$319$	28.2670			1.58265
$320$	−0.189751	−	0.328658i	−0.0106074	−	0.0183725i
$321$	1.67837	+	2.90702i	0.0936776	+	0.162254i
$322$	−7.24981	−	12.5570i	−0.404016	−	0.699776i
$323$	20.4155			1.13595
$324$	−3.30068	−	5.71695i	−0.183371	−	0.317608i
$325$	22.9449			1.27276
$326$	5.30589			0.293866
$327$	5.22233	−	1.64097i	0.288795	−	0.0907459i
$328$	7.14109			0.394301
$329$		0			0
$330$	0.406981	+	0.704912i	0.0224036	+	0.0388041i
$331$	−21.1881			−1.16460			−0.582301	−	0.812973i	$-0.697848\pi$
$331$	−21.1881			−1.16460			−0.582301	+	0.812973i	$0.697848\pi$
$332$	−0.282277	−	0.488917i	−0.0154919	−	0.0268328i
$333$	4.21116	+	7.29394i	0.230770	+	0.399705i
$334$	−8.74189	−	15.1414i	−0.478335	−	0.828500i
$335$	5.76871			0.315178
$336$	0.647579	−	1.12164i	0.0353283	−	0.0611905i
$337$	9.54346	+	16.5298i	0.519866	+	0.900434i	0.999733	+	0.0230928i	$0.00735131\pi$
$337$	9.54346	+	16.5298i	0.519866	+	0.900434i	−0.479868	+	0.877341i	$0.659315\pi$
$338$	−4.66322	+	8.07694i	−0.253646	+	0.439328i
$339$	−3.50681	−	6.07397i	−0.190464	−	0.329893i
$340$	1.27345	+	2.20567i	0.0690623	+	0.119619i
$341$	17.7236	+	30.6982i	0.959788	+	1.66240i
$342$	−4.14488	+	7.17914i	−0.224129	+	0.388204i
$343$	19.5101			1.05345
$344$	−8.91192			−0.480499
$345$	0.583999	−	1.01152i	0.0314414	−	0.0544582i
$346$	−6.96057			−0.374202
$347$	9.37845	+	16.2440i	0.503462	+	0.872021i	0.999992	+	0.00400196i	$0.00127387\pi$
$347$	9.37845	+	16.2440i	0.503462	+	0.872021i	−0.496530	+	0.868019i	$0.665393\pi$
$348$	1.81157	−	3.13773i	0.0971102	−	0.168200i
$349$	−4.61401	+	7.99170i	−0.246982	+	0.427786i	−0.962687	−	0.270617i	$-0.912772\pi$
$349$	−4.61401	+	7.99170i	−0.246982	+	0.427786i	0.715705	+	0.698403i	$0.246106\pi$
$350$	11.9950			0.641162
$351$	−7.09185	−	12.2834i	−0.378535	−	0.655642i
$352$	2.04533	−	3.54262i	0.109016	−	0.188822i
$353$	−14.2901	−	24.7512i	−0.760586	−	1.31737i	−0.942549	−	0.334068i	$-0.891578\pi$
$353$	−14.2901	−	24.7512i	−0.760586	−	1.31737i	0.181963	−	0.983305i	$-0.441755\pi$
$354$	1.11837			0.0594407
$355$	−1.18319	−	2.04934i	−0.0627970	−	0.108768i
$356$	1.20711	+	2.09077i	0.0639766	+	0.110811i
$357$	−4.34601	+	7.52750i	−0.230015	+	0.398398i
$358$	−0.667695	+	1.15648i	−0.0352888	+	0.0611220i
$359$	31.3287			1.65347			0.826733	−	0.562594i	$-0.190197\pi$
$359$	31.3287			1.65347			0.826733	+	0.562594i	$0.190197\pi$
$360$	−1.03417			−0.0545057
$361$	−9.74613			−0.512954
$362$	−0.775805	+	1.34373i	−0.0407754	+	0.0706251i
$363$	−1.50310	+	2.60344i	−0.0788922	+	0.136645i
$364$	−5.83586	+	10.1080i	−0.305882	+	0.529804i
$365$	−5.78575			−0.302840
$366$	−0.273176	+	0.473155i	−0.0142791	+	0.0247322i
$367$	−15.1212	−	26.1907i	−0.789319	−	1.36714i	−0.926384	−	0.376579i	$-0.877100\pi$
$367$	−15.1212	−	26.1907i	−0.789319	−	1.36714i	0.137065	−	0.990562i	$-0.456233\pi$
$368$	−5.86991			−0.305990
$369$	9.73004	−	16.8529i	0.506526	−	0.877328i
$370$	1.17291			0.0609766
$371$	17.1168	−	29.6472i	0.888661	−	1.53921i
$372$	4.54346			0.235567
$373$	−5.23811			−0.271219			−0.135610	−	0.990762i	$-0.543299\pi$
$373$	−5.23811			−0.271219			−0.135610	+	0.990762i	$0.543299\pi$
$374$	−13.7265	+	23.7751i	−0.709782	+	1.22938i
$375$	0.980574	+	1.69840i	0.0506366	+	0.0877052i
$376$		0			0
$377$	−16.3255	+	28.2766i	−0.840806	+	1.45632i
$378$	−3.70745	−	6.42149i	−0.190690	−	0.330286i
$379$	11.4617	+	19.8523i	0.588750	+	1.01974i	0.994397	+	0.105714i	$0.0337129\pi$
$379$	11.4617	+	19.8523i	0.588750	+	1.01974i	−0.405647	+	0.914030i	$0.632954\pi$
$380$	0.577224	+	0.999782i	0.0296110	+	0.0512877i
$381$	1.89635			0.0971528
$382$	−11.3551			−0.580978
$383$	−3.00206	−	5.19971i	−0.153398	−	0.265693i	0.779077	−	0.626929i	$-0.215688\pi$
$383$	−3.00206	−	5.19971i	−0.153398	−	0.265693i	−0.932475	+	0.361236i	$0.882355\pi$
$384$	−0.262161	−	0.454076i	−0.0133783	−	0.0231719i
$385$	−1.91735	−	3.32095i	−0.0977173	−	0.169251i
$386$	−0.494482	+	0.856468i	−0.0251685	+	0.0435931i
$387$	−12.1429	+	21.0321i	−0.617258	+	1.06912i
$388$	6.33878	+	10.9791i	0.321803	+	0.557378i
$389$	10.5938	−	18.3490i	0.537128	−	0.930333i	−0.461929	−	0.886917i	$-0.652843\pi$
$389$	10.5938	−	18.3490i	0.537128	−	0.930333i	0.999057	−	0.0434160i	$-0.0138241\pi$
$390$	−0.940200			−0.0476089
$391$	39.3939			1.99223
$392$	0.449152	−	0.777955i	0.0226856	−	0.0392926i
$393$	−7.76915			−0.391902
$394$	2.76753	−	4.79350i	0.139426	−	0.241493i
$395$	−5.55057			−0.279280
$396$	−5.57370	−	9.65394i	−0.280089	−	0.485129i
$397$	12.2021	−	21.1346i	0.612404	−	1.06071i	−0.378430	−	0.925630i	$-0.623536\pi$
$397$	12.2021	−	21.1346i	0.612404	−	1.06071i	0.990834	−	0.135085i	$-0.0431306\pi$
$398$	−7.59180			−0.380543
$399$	−1.96995	+	3.41205i	−0.0986207	+	0.170816i
$400$	2.42799	−	4.20540i	0.121399	−	0.210270i
$401$	9.32905	−	16.1584i	0.465871	−	0.806912i	−0.533370	−	0.845882i	$-0.679075\pi$
$401$	9.32905	−	16.1584i	0.465871	−	0.806912i	0.999240	+	0.0389706i	$0.0124079\pi$
$402$	7.97009			0.397512
$403$	−40.9448			−2.03961
$404$	3.66073			0.182128
$405$	−1.25261	+	2.16959i	−0.0622428	+	0.107808i
$406$	−8.53458	+	14.7823i	−0.423564	+	0.733634i
$407$	6.32142	+	10.9490i	0.313341	+	0.542723i
$408$	1.75940	+	3.04737i	0.0871034	+	0.150867i
$409$	−5.67577			−0.280649			−0.140324	−	0.990106i	$-0.544815\pi$
$409$	−5.67577			−0.280649			−0.140324	+	0.990106i	$0.544815\pi$
$410$	−1.35503	−	2.34697i	−0.0669199	−	0.115909i
$411$	3.35043	−	5.80311i	0.165264	−	0.286246i
$412$	3.65991	+	6.33915i	0.180311	+	0.312308i
$413$	−5.26882			−0.259262
$414$	−7.99800	+	13.8530i	−0.393080	+	0.680835i
$415$	−0.107124	+	0.185545i	−0.00525852	+	0.00910803i
$416$	2.36254	+	4.09205i	0.115833	+	0.200629i
$417$	−2.11990			−0.103812
$418$	−6.22193	+	10.7767i	−0.304324	+	0.527105i
$419$	−28.6563			−1.39995			−0.699975	−	0.714167i	$-0.746806\pi$
$419$	−28.6563			−1.39995			−0.699975	+	0.714167i	$0.746806\pi$
$420$	−0.491514			−0.0239834
$421$	4.33851	−	7.51451i	0.211446	−	0.366235i	−0.740721	−	0.671812i	$-0.765516\pi$
$421$	4.33851	−	7.51451i	0.211446	−	0.366235i	0.952167	+	0.305577i	$0.0988495\pi$
$422$	−0.998953	−	1.73024i	−0.0486283	−	0.0842266i
$423$		0			0
$424$	−6.92944	−	12.0021i	−0.336523	−	0.582875i
$425$	−16.2946	+	28.2231i	−0.790405	+	1.36902i
$426$	−1.63470	−	2.83138i	−0.0792014	−	0.137181i
$427$	1.28698	−	2.22911i	0.0622811	−	0.107874i
$428$	−6.40207			−0.309456
$429$	−5.06723	−	8.77670i	−0.244648	−	0.423743i
$430$	1.69104	+	2.92897i	0.0815493	+	0.141248i
$431$	−9.68733	−	16.7789i	−0.466622	−	0.808214i	0.532651	−	0.846335i	$-0.321196\pi$
$431$	−9.68733	−	16.7789i	−0.466622	−	0.808214i	−0.999273	+	0.0381216i	$0.987863\pi$
$432$	−3.00179			−0.144423
$433$	−9.54386	−	16.5305i	−0.458649	−	0.794403i	0.540241	−	0.841510i	$-0.318333\pi$
$433$	−9.54386	−	16.5305i	−0.458649	−	0.794403i	−0.998890	+	0.0471073i	$0.985000\pi$
$434$	−21.4050			−1.02747
$435$	−1.37498			−0.0659254
$436$	−2.26968	+	10.1906i	−0.108698	+	0.488042i
$437$	17.8564			0.854185
$438$	−7.99363			−0.381951
$439$	17.3605	+	30.0693i	0.828572	+	1.43513i	0.899159	+	0.437622i	$0.144179\pi$
$439$	17.3605	+	30.0693i	0.828572	+	1.43513i	−0.0705872	+	0.997506i	$0.522487\pi$
$440$	−1.55241			−0.0740082
$441$	−1.22398	−	2.11999i	−0.0582847	−	0.100952i
$442$	−15.8554	−	27.4624i	−0.754165	−	1.30625i
$443$	4.23030	+	7.32710i	0.200988	+	0.348121i	0.948847	−	0.315736i	$-0.102252\pi$
$443$	4.23030	+	7.32710i	0.200988	+	0.348121i	−0.747859	+	0.663857i	$0.768918\pi$
$444$	1.62050			0.0769055
$445$	0.458099	−	0.793450i	0.0217160	−	0.0376132i
$446$	−1.47933	−	2.56228i	−0.0700483	−	0.121327i
$447$	−3.23461	+	5.60251i	−0.152992	+	0.264990i
$448$	1.23508	+	2.13922i	0.0583521	+	0.101069i
$449$	10.2334	+	17.7247i	0.482943	+	0.836481i	0.999808	−	0.0195855i	$-0.00623467\pi$
$449$	10.2334	+	17.7247i	0.482943	+	0.836481i	−0.516866	+	0.856067i	$0.672901\pi$
$450$	−6.61648	−	11.4601i	−0.311904	−	0.540234i
$451$	14.6059	−	25.2981i	0.687764	−	1.19124i
$452$	13.3766			0.629181
$453$	−3.83794			−0.180322
$454$	−1.15034	+	1.99244i	−0.0539880	+	0.0935100i
$455$	4.42943			0.207655
$456$	0.797497	+	1.38131i	0.0373462	+	0.0646856i
$457$	19.6748	−	34.0778i	0.920349	−	1.59409i	0.121475	−	0.992595i	$-0.461238\pi$
$457$	19.6748	−	34.0778i	0.920349	−	1.59409i	0.798875	−	0.601497i	$-0.205429\pi$
$458$	−7.06226	+	12.2322i	−0.329998	+	0.571573i
$459$	20.1455			0.940309
$460$	1.11382	+	1.92919i	0.0519320	+	0.0899489i
$461$	−17.4583	+	30.2387i	−0.813114	+	1.40836i	0.0975600	+	0.995230i	$0.468896\pi$
$461$	−17.4583	+	30.2387i	−0.813114	+	1.40836i	−0.910674	+	0.413125i	$0.864437\pi$
$462$	−2.64903	−	4.58825i	−0.123244	−	0.213465i
$463$	37.5474			1.74498			0.872488	−	0.488635i	$-0.162505\pi$
$463$	37.5474			1.74498			0.872488	+	0.488635i	$0.162505\pi$
$464$	3.45507	+	5.98436i	0.160398	+	0.277817i
$465$	−0.862124	−	1.49324i	−0.0399800	−	0.0692475i
$466$	7.74836	−	13.4206i	0.358936	−	0.621695i
$467$	−9.02018	+	15.6234i	−0.417404	+	0.722966i	−0.995678	−	0.0928777i	$-0.970393\pi$
$467$	−9.02018	+	15.6234i	−0.417404	+	0.722966i	0.578273	+	0.815843i	$0.303727\pi$
$468$	12.8763			0.595206
$469$	−37.5483			−1.73382
$470$		0			0
$471$	2.18699	−	3.78797i	0.100771	−	0.174541i
$472$	−1.06649	+	1.84722i	−0.0490893	+	0.0850252i
$473$	−18.2278	+	31.5715i	−0.838116	+	1.45166i
$474$	−7.66871			−0.352236
$475$	−7.38599	+	12.7929i	−0.338892	+	0.586979i
$476$	−8.28882	−	14.3567i	−0.379917	−	0.658036i
$477$	−37.7666			−1.72922
$478$	−0.556899	+	0.964577i	−0.0254720	+	0.0441187i
$479$	−23.3335			−1.06613			−0.533066	−	0.846073i	$-0.678960\pi$
$479$	−23.3335			−1.06613			−0.533066	+	0.846073i	$0.678960\pi$
$480$	−0.0994903	+	0.172322i	−0.00454109	+	0.00786540i
$481$	−14.6036			−0.665869
$482$	2.75028			0.125272
$483$	−3.80123	+	6.58392i	−0.172962	+	0.299579i
$484$	−2.86675	−	4.96535i	−0.130307	−	0.225698i
$485$	2.40557	−	4.16657i	0.109231	−	0.189194i
$486$	−6.23330	+	10.7964i	−0.282748	+	0.489734i
$487$	−1.83586	−	3.17981i	−0.0831909	−	0.144091i	0.821428	−	0.570312i	$-0.193178\pi$
$487$	−1.83586	−	3.17981i	−0.0831909	−	0.144091i	−0.904619	+	0.426221i	$0.859844\pi$
$488$	−0.521009	−	0.902413i	−0.0235850	−	0.0408503i
$489$	−1.39100	−	2.40928i	−0.0629031	−	0.108951i
$490$	−0.340908			−0.0154006
$491$	−39.8496			−1.79839			−0.899193	−	0.437552i	$-0.855846\pi$
$491$	−39.8496			−1.79839			−0.899193	+	0.437552i	$0.855846\pi$
$492$	−1.87211	−	3.24259i	−0.0844013	−	0.146187i
$493$	−23.1875	−	40.1620i	−1.04431	−	1.80880i
$494$	−7.18690	−	12.4481i	−0.323354	−	0.560065i
$495$	−2.11523	+	3.66368i	−0.0950724	+	0.164670i
$496$	−4.33270	+	7.50446i	−0.194544	+	0.336960i
$497$	7.70132	+	13.3391i	0.345451	+	0.598339i
$498$	−0.148004	+	0.256350i	−0.00663220	+	0.0114873i
$499$	17.6328			0.789354			0.394677	−	0.918820i	$-0.370856\pi$
$499$	17.6328			0.789354			0.394677	+	0.918820i	$0.370856\pi$
$500$	−3.74036			−0.167274
$501$	−4.58356	+	7.93896i	−0.204778	+	0.354686i
$502$	17.1335			0.764704
$503$	−0.691192	+	1.19718i	−0.0308187	+	0.0533796i	−0.881023	−	0.473073i	$-0.843145\pi$
$503$	−0.691192	+	1.19718i	−0.0308187	+	0.0533796i	0.850205	+	0.526452i	$0.176478\pi$
$504$	6.73140			0.299841
$505$	−0.694626	−	1.20313i	−0.0309104	−	0.0535385i
$506$	−12.0059	+	20.7948i	−0.533727	+	0.924443i
$507$	4.89006			0.217175
$508$	−1.80838	+	3.13221i	−0.0802340	+	0.138969i
$509$	−11.3425	+	19.6458i	−0.502747	+	0.870783i	0.497248	+	0.867608i	$0.334344\pi$
$509$	−11.3425	+	19.6458i	−0.502747	+	0.870783i	−0.999995	+	0.00317483i	$0.998989\pi$
$510$	0.667695	−	1.15648i	0.0295660	−	0.0512099i
$511$	37.6593			1.66595
$512$	1.00000			0.0441942
$513$	9.13148			0.403165
$514$	−8.21984	+	14.2372i	−0.362562	+	0.627975i
$515$	1.38894	−	2.40572i	0.0612040	−	0.106008i
$516$	2.33636	+	4.04669i	0.102852	+	0.178145i
$517$		0			0
$518$	−7.63443			−0.335437
$519$	1.82479	+	3.16062i	0.0800993	+	0.138736i
$520$	0.896588	−	1.55294i	0.0393180	−	0.0681007i
$521$	−3.87212	−	6.70670i	−0.169641	−	0.293826i	0.768653	−	0.639666i	$-0.220927\pi$
$521$	−3.87212	−	6.70670i	−0.169641	−	0.293826i	−0.938294	+	0.345840i	$0.887594\pi$
$522$	18.8307			0.824199
$523$	−7.10280	+	12.3024i	−0.310584	+	0.537947i	−0.978489	−	0.206299i	$-0.933858\pi$
$523$	−7.10280	+	12.3024i	−0.310584	+	0.537947i	0.667905	+	0.744247i	$0.267191\pi$
$524$	7.40877	−	12.8324i	0.323653	−	0.560584i
$525$	−3.14463	−	5.44666i	−0.137243	−	0.237712i
$526$	25.1569			1.09689
$527$	29.0775	−	50.3637i	1.26663	−	2.19388i
$528$	−2.14482			−0.0933413
$529$	11.4558			0.498079
$530$	−2.62973	+	4.55482i	−0.114228	+	0.197849i
$531$	2.90629	+	5.03383i	0.126122	+	0.218450i
$532$	−3.75714	−	6.50755i	−0.162893	−	0.282138i
$533$	16.8711	+	29.2217i	0.730770	+	1.26573i
$534$	0.632912	−	1.09624i	0.0273888	−	0.0474388i
$535$	1.21480	+	2.10409i	0.0525202	+	0.0909677i
$536$	−7.60038	+	13.1642i	−0.328287	+	0.568609i
$537$	0.700173			0.0302147
$538$	1.05180	+	1.82177i	0.0453464	+	0.0785422i
$539$	−1.83733	−	3.18235i	−0.0791394	−	0.137073i
$540$	0.569590	+	0.986560i	0.0245113	+	0.0424548i
$541$	0.819898			0.0352502			0.0176251	−	0.999845i	$-0.494389\pi$
$541$	0.819898			0.0352502			0.0176251	+	0.999845i	$0.494389\pi$
$542$	3.19275	+	5.53001i	0.137141	+	0.237534i
$543$	0.813543			0.0349125
$544$	−6.71116			−0.287739
$545$	3.77989	−	1.18773i	0.161913	−	0.0508766i
$546$	6.11973			0.261900
$547$	1.95897			0.0837595			0.0418797	−	0.999123i	$-0.486665\pi$
$547$	1.95897			0.0837595			0.0418797	+	0.999123i	$0.486665\pi$
$548$	6.39002	+	11.0678i	0.272968	+	0.472795i
$549$	−2.83959			−0.121191
$550$	−9.93208	−	17.2029i	−0.423505	−	0.733533i
$551$	−10.5104	−	18.2045i	−0.447757	−	0.775538i
$552$	1.53886	+	2.66538i	0.0654982	+	0.113446i
$553$	36.1285			1.53634
$554$	4.77710	−	8.27418i	0.202959	−	0.351536i
$555$	−0.307491	−	0.532589i	−0.0130522	−	0.0226072i
$556$	2.02156	−	3.50145i	0.0857333	−	0.148495i
$557$	5.90285	+	10.2240i	0.250112	+	0.433206i	0.963556	−	0.267505i	$-0.0861993\pi$
$557$	5.90285	+	10.2240i	0.250112	+	0.433206i	−0.713445	+	0.700712i	$0.752866\pi$
$558$	11.8070	+	20.4503i	0.499830	+	0.865731i
$559$	−21.0548	−	36.4680i	−0.890524	−	1.54243i
$560$	0.468714	−	0.811837i	0.0198068	−	0.0343064i
$561$	14.3942			0.607725
$562$	−15.8073			−0.666792
$563$	−1.94756	+	3.37327i	−0.0820797	+	0.142166i	−0.904143	−	0.427230i	$-0.859490\pi$
$563$	−1.94756	+	3.37327i	−0.0820797	+	0.142166i	0.822063	+	0.569396i	$0.192823\pi$
$564$		0			0
$565$	−2.53821	−	4.39631i	−0.106783	−	0.184954i
$566$	15.1467	−	26.2348i	0.636662	−	1.10273i
$567$	8.15321	−	14.1218i	0.342403	−	0.593059i
$568$	6.23548			0.261635
$569$	−1.66052	−	2.87610i	−0.0696124	−	0.120572i	0.829118	−	0.559073i	$-0.188843\pi$
$569$	−1.66052	−	2.87610i	−0.0696124	−	0.120572i	−0.898731	+	0.438501i	$0.855510\pi$
$570$	0.302651	−	0.524207i	0.0126767	−	0.0219566i
$571$	2.83064	+	4.90280i	0.118458	+	0.205176i	0.919157	−	0.393892i	$-0.128871\pi$
$571$	2.83064	+	4.90280i	0.118458	+	0.205176i	−0.800699	+	0.599068i	$0.795538\pi$
$572$	19.3287			0.808175
$573$	2.97686	+	5.15608i	0.124360	+	0.215398i
$574$	8.81982	+	15.2764i	0.368132	+	0.637623i
$575$	−14.2521	+	24.6853i	−0.594353	+	1.02945i
$576$	1.36254	−	2.35999i	0.0567726	−	0.0983331i
$577$	−18.9105			−0.787255			−0.393628	−	0.919270i	$-0.628780\pi$
$577$	−18.9105			−0.787255			−0.393628	+	0.919270i	$0.628780\pi$
$578$	28.0397			1.16630
$579$	0.518535			0.0215496
$580$	1.31120	−	2.27107i	0.0544447	−	0.0943010i
$581$	0.697269	−	1.20770i	0.0289276	−	0.0501040i
$582$	3.32356	−	5.75657i	0.137766	−	0.238617i
$583$	−56.6919			−2.34794
$584$	7.62284	−	13.2031i	0.315435	−	0.546350i
$585$	−2.44328	−	4.23189i	−0.101017	−	0.174967i
$586$	−10.6352			−0.439337
$587$	9.12628	−	15.8072i	0.376682	−	0.652432i	−0.613895	−	0.789387i	$-0.710398\pi$
$587$	9.12628	−	15.8072i	0.376682	−	0.652432i	0.990577	+	0.136955i	$0.0437317\pi$
$588$	−0.471000			−0.0194237
$589$	13.1802	−	22.8287i	0.543079	−	0.940641i
$590$	0.809471			0.0333254
$591$	−2.90215			−0.119378
$592$	−1.54533	+	2.67659i	−0.0635127	+	0.110007i
$593$	16.1812	+	28.0266i	0.664482	+	1.15092i	0.979426	+	0.201806i	$0.0646809\pi$
$593$	16.1812	+	28.0266i	0.664482	+	1.15092i	−0.314944	+	0.949110i	$0.601986\pi$
$594$	−6.13964	+	10.6342i	−0.251913	+	0.436325i
$595$	−3.14562	+	5.44837i	−0.128958	+	0.223361i
$596$	−6.16914	−	10.6853i	−0.252698	−	0.437686i
$597$	1.99027	+	3.44725i	0.0814564	+	0.141087i
$598$	−13.8679	−	24.0199i	−0.567101	−	0.982248i
$599$	−5.23781			−0.214011			−0.107005	−	0.994258i	$-0.534126\pi$
$599$	−5.23781			−0.214011			−0.107005	+	0.994258i	$0.534126\pi$
$600$	−2.54609			−0.103944
$601$	1.44179	+	2.49725i	0.0588118	+	0.101865i	0.893932	−	0.448202i	$-0.147935\pi$
$601$	1.44179	+	2.49725i	0.0588118	+	0.101865i	−0.835120	+	0.550067i	$0.814602\pi$
$602$	−11.0069	−	19.0646i	−0.448610	−	0.777015i
$603$	20.7117	+	35.8737i	0.843446	+	1.46089i
$604$	3.65991	−	6.33915i	0.148920	−	0.257936i
$605$	−1.08793	+	1.88436i	−0.0442308	+	0.0766100i
$606$	−0.959700	−	1.66225i	−0.0389851	−	0.0675242i
$607$	−7.76752	+	13.4537i	−0.315274	+	0.546071i	−0.979496	−	0.201465i	$-0.935430\pi$
$607$	−7.76752	+	13.4537i	−0.315274	+	0.546071i	0.664222	+	0.747536i	$0.268763\pi$
$608$	−3.04202			−0.123370
$609$	8.94972			0.362661
$610$	−0.197723	+	0.342467i	−0.00800558	+	0.0138661i
$611$		0			0
$612$	−9.14425	+	15.8383i	−0.369634	+	0.640225i
$613$	32.1060			1.29675			0.648375	−	0.761321i	$-0.275449\pi$
$613$	32.1060			1.29675			0.648375	+	0.761321i	$0.275449\pi$
$614$	5.09251	+	8.82048i	0.205517	+	0.355966i
$615$	−0.710469	+	1.23057i	−0.0286489	+	0.0496213i
$616$	10.1046			0.407125
$617$	−16.4075	+	28.4185i	−0.660539	+	1.14409i	0.319935	+	0.947440i	$0.396339\pi$
$617$	−16.4075	+	28.4185i	−0.660539	+	1.14409i	−0.980474	+	0.196648i	$0.936994\pi$
$618$	1.91897	−	3.32375i	0.0771923	−	0.133701i
$619$	17.6616	−	30.5908i	0.709880	−	1.22955i	−0.255021	−	0.966936i	$-0.582082\pi$
$619$	17.6616	−	30.5908i	0.709880	−	1.22955i	0.964901	−	0.262613i	$-0.0845843\pi$
$620$	3.28853			0.132071
$621$	17.6202			0.707074
$622$	−1.22266			−0.0490242
$623$	−2.98175	+	5.16454i	−0.119461	+	0.206913i
$624$	1.23873	−	2.14555i	0.0495890	−	0.0858906i
$625$	−11.4302	−	19.7977i	−0.457209	−	0.791908i
$626$	−14.7789	−	25.5979i	−0.590685	−	1.02310i
$627$	6.52458			0.260567
$628$	4.17108	+	7.22452i	0.166444	+	0.288290i
$629$	10.3710	−	17.9630i	0.413517	−	0.716233i
$630$	−1.27729	−	2.21233i	−0.0508884	−	0.0881412i
$631$	−22.8724			−0.910535			−0.455267	−	0.890355i	$-0.650456\pi$
$631$	−22.8724			−0.910535			−0.455267	+	0.890355i	$0.650456\pi$
$632$	7.31299	−	12.6665i	0.290895	−	0.503845i
$633$	−0.523772	+	0.907200i	−0.0208181	+	0.0360580i
$634$	12.8714	+	22.2938i	0.511187	+	0.885401i
$635$	1.37257			0.0544687
$636$	−3.63325	+	6.29298i	−0.144068	+	0.249533i
$637$	4.24457			0.168176
$638$	28.2670			1.11910
$639$	8.49611	−	14.7157i	0.336101	−	0.582144i
$640$	−0.189751	−	0.328658i	−0.00750055	−	0.0129913i
$641$	11.5860	+	20.0675i	0.457618	+	0.792618i	0.998835	−	0.0482657i	$-0.0153694\pi$
$641$	11.5860	+	20.0675i	0.457618	+	0.792618i	−0.541217	+	0.840883i	$0.682036\pi$
$642$	1.67837	+	2.90702i	0.0662400	+	0.114731i
$643$	−21.4615	+	37.1724i	−0.846360	+	1.46594i	0.0380753	+	0.999275i	$0.487877\pi$
$643$	−21.4615	+	37.1724i	−0.846360	+	1.46594i	−0.884435	+	0.466663i	$0.845456\pi$
$644$	−7.24981	−	12.5570i	−0.285682	−	0.494817i
$645$	0.886650	−	1.53572i	0.0349118	−	0.0604690i
$646$	20.4155			0.803236
$647$	7.63034	+	13.2161i	0.299980	+	0.519580i	0.976131	−	0.217183i	$-0.0696868\pi$
$647$	7.63034	+	13.2161i	0.299980	+	0.519580i	−0.676151	+	0.736763i	$0.736353\pi$
$648$	−3.30068	−	5.71695i	−0.129663	−	0.224583i
$649$	4.36266	+	7.55635i	0.171249	+	0.296613i
$650$	22.9449			0.899974
$651$	5.61154	+	9.71947i	0.219933	+	0.380936i
$652$	5.30589			0.207795
$653$	−14.5861			−0.570798			−0.285399	−	0.958409i	$-0.592126\pi$
$653$	−14.5861			−0.570798			−0.285399	+	0.958409i	$0.592126\pi$
$654$	5.22233	−	1.64097i	0.204209	−	0.0641671i
$655$	−5.62327			−0.219719
$656$	7.14109			0.278813
$657$	−20.7729	−	35.9797i	−0.810428	−	1.40370i
$658$		0			0
$659$	−1.00405	−	1.73907i	−0.0391123	−	0.0677444i	0.845807	−	0.533490i	$-0.179120\pi$
$659$	−1.00405	−	1.73907i	−0.0391123	−	0.0677444i	−0.884919	+	0.465745i	$0.845786\pi$
$660$	0.406981	+	0.704912i	0.0158417	+	0.0274386i
$661$	−0.881835	−	1.52738i	−0.0342994	−	0.0594083i	0.848366	−	0.529410i	$-0.177587\pi$
$661$	−0.881835	−	1.52738i	−0.0342994	−	0.0594083i	−0.882666	+	0.470002i	$0.844253\pi$
$662$	−21.1881			−0.823499
$663$	−8.31333	+	14.3991i	−0.322863	+	0.559215i
$664$	−0.282277	−	0.488917i	−0.0109545	−	0.0189737i
$665$	−1.42584	+	2.46962i	−0.0552916	+	0.0957679i
$666$	4.21116	+	7.29394i	0.163179	+	0.282634i
$667$	−20.2809	−	35.1276i	−0.785281	−	1.36015i
$668$	−8.74189	−	15.1414i	−0.338234	−	0.585838i
$669$	−0.775644	+	1.34346i	−0.0299881	+	0.0519410i
$670$	5.76871			0.222865
$671$	−4.26254			−0.164553
$672$	0.647579	−	1.12164i	0.0249809	−	0.0432682i
$673$	26.0963			1.00594			0.502969	−	0.864305i	$-0.332241\pi$
$673$	26.0963			1.00594			0.502969	+	0.864305i	$0.332241\pi$
$674$	9.54346	+	16.5298i	0.367600	+	0.636703i
$675$	−7.28830	+	12.6237i	−0.280527	+	0.485887i
$676$	−4.66322	+	8.07694i	−0.179355	+	0.310652i
$677$	−49.9184			−1.91852			−0.959261	−	0.282523i	$-0.908829\pi$
$677$	−49.9184			−1.91852			−0.959261	+	0.282523i	$0.908829\pi$
$678$	−3.50681	−	6.07397i	−0.134678	−	0.233270i
$679$	−15.6578	+	27.1201i	−0.600891	+	1.04077i
$680$	1.27345	+	2.20567i	0.0488344	+	0.0845837i
$681$	1.20629			0.0462253
$682$	17.7236	+	30.6982i	0.678673	+	1.17550i
$683$	5.62415	+	9.74131i	0.215202	+	0.372741i	0.953335	−	0.301914i	$-0.0976256\pi$
$683$	5.62415	+	9.74131i	0.215202	+	0.372741i	−0.738133	+	0.674655i	$0.764292\pi$
$684$	−4.14488	+	7.17914i	−0.158483	+	0.274501i
$685$	2.42502	−	4.20026i	0.0926553	−	0.160484i
$686$	19.5101			0.744898
$687$	7.40579			0.282548
$688$	−8.91192			−0.339764
$689$	32.7422	−	56.7111i	1.24738	−	2.16052i
$690$	0.583999	−	1.01152i	0.0222324	−	0.0385077i
$691$	17.1718	−	29.7424i	0.653246	−	1.13146i	−0.329084	−	0.944301i	$-0.606740\pi$
$691$	17.1718	−	29.7424i	0.653246	−	1.13146i	0.982330	−	0.187155i	$-0.0599266\pi$
$692$	−6.96057			−0.264601
$693$	13.7679	−	23.8468i	0.523001	−	0.905864i
$694$	9.37845	+	16.2440i	0.356001	+	0.616612i
$695$	−1.53437			−0.0582020
$696$	1.81157	−	3.13773i	0.0686673	−	0.118935i
$697$	−47.9250			−1.81529
$698$	−4.61401	+	7.99170i	−0.174643	+	0.302490i
$699$	−8.12526			−0.307326
$700$	11.9950			0.453370
$701$	−25.0468	+	43.3822i	−0.946003	+	1.63852i	−0.192272	+	0.981342i	$0.561586\pi$
$701$	−25.0468	+	43.3822i	−0.946003	+	1.63852i	−0.753731	+	0.657183i	$0.771748\pi$
$702$	−7.09185	−	12.2834i	−0.267665	−	0.463609i
$703$	4.70092	−	8.14223i	0.177299	−	0.307090i
$704$	2.04533	−	3.54262i	0.0770863	−	0.133517i
$705$		0			0
$706$	−14.2901	−	24.7512i	−0.537816	−	0.931524i
$707$	4.52130	+	7.83112i	0.170041	+	0.294519i
$708$	1.11837			0.0420309
$709$	10.5175			0.394993			0.197497	−	0.980304i	$-0.436719\pi$
$709$	10.5175			0.394993			0.197497	+	0.980304i	$0.436719\pi$
$710$	−1.18319	−	2.04934i	−0.0444042	−	0.0769103i
$711$	−19.9285	−	34.5172i	−0.747378	−	1.29450i
$712$	1.20711	+	2.09077i	0.0452383	+	0.0783550i
$713$	25.4326	−	44.0505i	0.952457	−	1.64970i
$714$	−4.34601	+	7.52750i	−0.162645	+	0.281710i
$715$	−3.66764	−	6.35253i	−0.137162	−	0.237571i
$716$	−0.667695	+	1.15648i	−0.0249529	+	0.0432197i
$717$	0.583988			0.0218094
$718$	31.3287			1.16918
$719$	1.00212	−	1.73572i	0.0373726	−	0.0647313i	−0.846734	−	0.532016i	$-0.821434\pi$
$719$	1.00212	−	1.73572i	0.0373726	−	0.0647313i	0.884107	+	0.467285i	$0.154768\pi$
$720$	−1.03417			−0.0385414
$721$	−9.04057	+	15.6587i	−0.336688	+	0.583161i
$722$	−9.74613			−0.362713
$723$	−0.721016	−	1.24884i	−0.0268149	−	0.0464447i
$724$	−0.775805	+	1.34373i	−0.0288326	+	0.0499395i
$725$	33.5555			1.24622
$726$	−1.50310	+	2.60344i	−0.0557852	+	0.0966228i
$727$	−10.2012	+	17.6690i	−0.378343	+	0.655308i	−0.990821	−	0.135179i	$-0.956839\pi$
$727$	−10.2012	+	17.6690i	−0.378343	+	0.655308i	0.612479	+	0.790487i	$0.290173\pi$
$728$	−5.83586	+	10.1080i	−0.216291	+	0.374628i
$729$	−13.2676			−0.491392
$730$	−5.78575			−0.214140
$731$	59.8093			2.21213
$732$	−0.273176	+	0.473155i	−0.0100969	+	0.0174883i
$733$	−4.48704	+	7.77178i	−0.165733	+	0.287057i	−0.936915	−	0.349557i	$-0.886332\pi$
$733$	−4.48704	+	7.77178i	−0.165733	+	0.287057i	0.771183	+	0.636614i	$0.219666\pi$
$734$	−15.1212	−	26.1907i	−0.558133	−	0.966715i
$735$	0.0893726	+	0.154798i	0.00329656	+	0.00570980i
$736$	−5.86991			−0.216368
$737$	31.0906	+	53.8505i	1.14524	+	1.98361i
$738$	9.73004	−	16.8529i	0.358168	−	0.620365i
$739$	−14.7368	−	25.5248i	−0.542101	−	0.938946i	−0.998783	−	0.0493165i	$-0.984296\pi$
$739$	−14.7368	−	25.5248i	−0.542101	−	0.938946i	0.456682	−	0.889630i	$-0.349038\pi$
$740$	1.17291			0.0431170
$741$	−3.76824	+	6.52679i	−0.138430	+	0.239768i
$742$	17.1168	−	29.6472i	0.628378	−	1.08838i
$743$	−16.1501	−	27.9728i	−0.592490	−	1.02622i	−0.993896	−	0.110322i	$-0.964812\pi$
$743$	−16.1501	−	27.9728i	−0.592490	−	1.02622i	0.401406	−	0.915900i	$-0.368522\pi$
$744$	4.54346			0.166571
$745$	−2.34120	+	4.05507i	−0.0857748	+	0.148566i
$746$	−5.23811			−0.191781
$747$	−1.53846			−0.0562892
$748$	−13.7265	+	23.7751i	−0.501892	+	0.869302i
$749$	−7.90707	−	13.6955i	−0.288918	−	0.500421i
$750$	0.980574	+	1.69840i	0.0358055	+	0.0620169i
$751$	19.8628	+	34.4034i	0.724804	+	1.25540i	0.959055	+	0.283221i	$0.0914030\pi$
$751$	19.8628	+	34.4034i	0.724804	+	1.25540i	−0.234251	+	0.972176i	$0.575264\pi$
$752$		0			0
$753$	−4.49172	−	7.77989i	−0.163688	−	0.283515i
$754$	−16.3255	+	28.2766i	−0.594540	+	1.02977i
$755$	−2.77788			−0.101097
$756$	−3.70745	−	6.42149i	−0.134839	−	0.233547i
$757$	4.56144	+	7.90065i	0.165788	+	0.287154i	0.936935	−	0.349504i	$-0.113650\pi$
$757$	4.56144	+	7.90065i	0.165788	+	0.287154i	−0.771147	+	0.636658i	$0.780316\pi$
$758$	11.4617	+	19.8523i	0.416309	+	0.721068i
$759$	12.5899			0.456984
$760$	0.577224	+	0.999782i	0.0209381	+	0.0362659i
$761$	−36.2175			−1.31288			−0.656441	−	0.754377i	$-0.727939\pi$
$761$	−36.2175			−1.31288			−0.656441	+	0.754377i	$0.727939\pi$
$762$	1.89635			0.0686974
$763$	−24.6032	+	7.73088i	−0.890696	+	0.279877i
$764$	−11.3551			−0.410813
$765$	6.94050			0.250934
$766$	−3.00206	−	5.19971i	−0.108469	−	0.187873i
$767$	−10.0785			−0.363915
$768$	−0.262161	−	0.454076i	−0.00945991	−	0.0163850i
$769$	13.4151	+	23.2356i	0.483760	+	0.837897i	0.999826	−	0.0186516i	$-0.00593733\pi$
$769$	13.4151	+	23.2356i	0.483760	+	0.837897i	−0.516066	+	0.856549i	$0.672604\pi$
$770$	−1.91735	−	3.32095i	−0.0690965	−	0.119679i
$771$	8.61967			0.310430
$772$	−0.494482	+	0.856468i	−0.0177968	+	0.0308250i
$773$	11.8484	+	20.5221i	0.426158	+	0.738127i	0.996528	−	0.0832607i	$-0.0265334\pi$
$773$	11.8484	+	20.5221i	0.426158	+	0.738127i	−0.570370	+	0.821388i	$0.693200\pi$
$774$	−12.1429	+	21.0321i	−0.436467	+	0.755983i
$775$	21.0395	+	36.4415i	0.755762	+	1.30902i
$776$	6.33878	+	10.9791i	0.227549	+	0.394126i
$777$	2.00145	+	3.46661i	0.0718015	+	0.124364i
$778$	10.5938	−	18.3490i	0.379807	−	0.657845i
$779$	−21.7233			−0.778318
$780$	−0.940200			−0.0336646
$781$	12.7536	−	22.0899i	0.456360	−	0.790439i
$782$	39.3939			1.40872
$783$	−10.3714	−	17.9638i	−0.370643	−	0.641972i
$784$	0.449152	−	0.777955i	0.0160412	−	0.0277841i
$785$	1.58293	−	2.74172i	0.0564972	−	0.0978560i
$786$	−7.76915			−0.277116
$787$	14.7101	+	25.4786i	0.524358	+	0.908215i	0.999598	+	0.0283586i	$0.00902802\pi$
$787$	14.7101	+	25.4786i	0.524358	+	0.908215i	−0.475240	+	0.879856i	$0.657639\pi$
$788$	2.76753	−	4.79350i	0.0985891	−	0.170761i
$789$	−6.59516	−	11.4231i	−0.234794	−	0.406675i
$790$	−5.55057			−0.197481
$791$	16.5211	+	28.6155i	0.587424	+	1.01745i
$792$	−5.57370	−	9.65394i	−0.198053	−	0.343038i
$793$	2.46181	−	4.26398i	0.0874215	−	0.151418i
$794$	12.2021	−	21.1346i	0.433035	−	0.750038i
$795$	2.75765			0.0978036
$796$	−7.59180			−0.269084
$797$	−30.7024			−1.08753			−0.543767	−	0.839236i	$-0.683003\pi$
$797$	−30.7024			−1.08753			−0.543767	+	0.839236i	$0.683003\pi$
$798$	−1.96995	+	3.41205i	−0.0697354	+	0.120785i
$799$		0			0
$800$	2.42799	−	4.20540i	0.0858424	−	0.148683i
$801$	6.57895			0.232456
$802$	9.32905	−	16.1584i	0.329420	−	0.570573i
$803$	−31.1824	−	54.0096i	−1.10040	−	1.90596i
$804$	7.97009			0.281083
$805$	−2.75131	+	4.76541i	−0.0969709	+	0.167959i
$806$	−40.9448			−1.44222
$807$	0.551482	−	0.955194i	0.0194131	−	0.0336244i
$808$	3.66073			0.128784
$809$	−24.2634			−0.853056			−0.426528	−	0.904474i	$-0.640263\pi$
$809$	−24.2634			−0.853056			−0.426528	+	0.904474i	$0.640263\pi$
$810$	−1.25261	+	2.16959i	−0.0440123	+	0.0762315i
$811$	5.13932	+	8.90157i	0.180466	+	0.312576i	0.942039	−	0.335502i	$-0.108906\pi$
$811$	5.13932	+	8.90157i	0.180466	+	0.312576i	−0.761573	+	0.648079i	$0.775573\pi$
$812$	−8.53458	+	14.7823i	−0.299505	+	0.518758i
$813$	1.67403	−	2.89950i	0.0587108	−	0.101690i
$814$	6.32142	+	10.9490i	0.221566	+	0.383763i
$815$	−1.00680	−	1.74382i	−0.0352665	−	0.0610834i
$816$	1.75940	+	3.04737i	0.0615914	+	0.106679i
$817$	27.1102			0.948467
$818$	−5.67577			−0.198449
$819$	15.9032	+	27.5452i	0.555704	+	0.962508i
$820$	−1.35503	−	2.34697i	−0.0473195	−	0.0819599i
$821$	−13.7817	−	23.8706i	−0.480985	−	0.833090i	0.518777	−	0.854910i	$-0.326387\pi$
$821$	−13.7817	−	23.8706i	−0.480985	−	0.833090i	−0.999762	+	0.0218193i	$0.993054\pi$
$822$	3.35043	−	5.80311i	0.116860	−	0.202407i
$823$	−17.8530	+	30.9222i	−0.622315	+	1.07788i	0.366739	+	0.930324i	$0.380474\pi$
$823$	−17.8530	+	30.9222i	−0.622315	+	1.07788i	−0.989054	+	0.147557i	$0.952859\pi$
$824$	3.65991	+	6.33915i	0.127499	+	0.220835i
$825$	−5.20760	+	9.01983i	−0.181305	+	0.314030i
$826$	−5.26882			−0.183326
$827$	−8.37300			−0.291158			−0.145579	−	0.989347i	$-0.546504\pi$
$827$	−8.37300			−0.291158			−0.145579	+	0.989347i	$0.546504\pi$
$828$	−7.99800	+	13.8530i	−0.277950	+	0.481423i
$829$	19.5590			0.679314			0.339657	−	0.940549i	$-0.389689\pi$
$829$	19.5590			0.679314			0.339657	+	0.940549i	$0.389689\pi$
$830$	−0.107124	+	0.185545i	−0.00371834	+	0.00644035i
$831$	−5.00947			−0.173777
$832$	2.36254	+	4.09205i	0.0819065	+	0.141866i
$833$	−3.01433	+	5.22098i	−0.104440	+	0.180896i
$834$	−2.11990			−0.0734060
$835$	−3.31756	+	5.74618i	−0.114809	+	0.198855i
$836$	−6.22193	+	10.7767i	−0.215190	+	0.372720i
$837$	13.0058	−	22.5268i	0.449548	−	0.778640i
$838$	−28.6563			−0.989914
$839$	18.4598			0.637302			0.318651	−	0.947872i	$-0.396770\pi$
$839$	18.4598			0.637302			0.318651	+	0.947872i	$0.396770\pi$
$840$	−0.491514			−0.0169588
$841$	−9.37501	+	16.2380i	−0.323276	+	0.559931i
$842$	4.33851	−	7.51451i	0.149515	−	0.258967i
$843$	4.14406	+	7.17773i	0.142729	+	0.247214i
$844$	−0.998953	−	1.73024i	−0.0343854	−	0.0595572i
$845$	3.53940			0.121759
$846$		0			0
$847$	7.08133	−	12.2652i	0.243317	−	0.421438i
$848$	−6.92944	−	12.0021i	−0.237958	−	0.412155i
$849$	−15.8834			−0.545118
$850$	−16.2946	+	28.2231i	−0.558901	+	0.968045i
$851$	9.07094	−	15.7113i	0.310948	−	0.538578i
$852$	−1.63470	−	2.83138i	−0.0560038	−	0.0970015i
$853$	−5.44348			−0.186381			−0.0931906	−	0.995648i	$-0.529707\pi$
$853$	−5.44348			−0.186381			−0.0931906	+	0.995648i	$0.529707\pi$
$854$	1.28698	−	2.22911i	0.0440394	−	0.0762784i
$855$	3.14597			0.107590
$856$	−6.40207			−0.218818
$857$	26.1660	−	45.3208i	0.893814	−	1.54813i	0.0585476	−	0.998285i	$-0.481353\pi$
$857$	26.1660	−	45.3208i	0.893814	−	1.54813i	0.835266	−	0.549846i	$-0.185314\pi$
$858$	−5.06723	−	8.77670i	−0.172992	−	0.299632i
$859$	−4.71449	−	8.16574i	−0.160856	−	0.278611i	0.774320	−	0.632795i	$-0.218092\pi$
$859$	−4.71449	−	8.16574i	−0.160856	−	0.278611i	−0.935176	+	0.354183i	$0.884759\pi$
$860$	1.69104	+	2.92897i	0.0576641	+	0.0998771i
$861$	4.62442	−	8.00973i	0.157600	−	0.272971i
$862$	−9.68733	−	16.7789i	−0.329952	−	0.571493i
$863$	7.39383	−	12.8065i	0.251689	−	0.435938i	−0.712302	−	0.701873i	$-0.752347\pi$
$863$	7.39383	−	12.8065i	0.251689	−	0.435938i	0.963991	+	0.265935i	$0.0856807\pi$
$864$	−3.00179			−0.102123
$865$	1.32077	+	2.28764i	0.0449076	+	0.0777822i
$866$	−9.54386	−	16.5305i	−0.324314	−	0.561728i
$867$	−7.35089	−	12.7321i	−0.249649	−	0.432406i
$868$	−21.4050			−0.726532
$869$	−29.9149	−	51.8142i	−1.01480	−	1.75768i
$870$	−1.37498			−0.0466163
$871$	−71.8249			−2.43370
$872$	−2.26968	+	10.1906i	−0.0768610	+	0.345098i
$873$	34.5474			1.16925
$874$	17.8564			0.604000
$875$	−4.61964	−	8.00145i	−0.156172	−	0.270498i
$876$	−7.99363			−0.270080
$877$	−7.78384	−	13.4820i	−0.262842	−	0.455255i	0.704154	−	0.710047i	$-0.251326\pi$
$877$	−7.78384	−	13.4820i	−0.262842	−	0.455255i	−0.966996	+	0.254792i	$0.917993\pi$
$878$	17.3605	+	30.0693i	0.585889	+	1.01479i
$879$	2.78814	+	4.82920i	0.0940416	+	0.162885i
$880$	−1.55241			−0.0523317
$881$	−3.95699	+	6.85371i	−0.133314	+	0.230907i	−0.924952	−	0.380083i	$-0.875895\pi$
$881$	−3.95699	+	6.85371i	−0.133314	+	0.230907i	0.791638	+	0.610991i	$0.209229\pi$
$882$	−1.22398	−	2.11999i	−0.0412135	−	0.0713839i
$883$	−23.6166	+	40.9051i	−0.794761	+	1.37657i	0.128229	+	0.991745i	$0.459071\pi$
$883$	−23.6166	+	40.9051i	−0.794761	+	1.37657i	−0.922991	+	0.384823i	$0.874263\pi$
$884$	−15.8554	−	27.4624i	−0.533275	−	0.923659i
$885$	−0.212211	−	0.367561i	−0.00713341	−	0.0123554i
$886$	4.23030	+	7.32710i	0.142120	+	0.246159i
$887$	7.05085	−	12.2124i	0.236744	−	0.410053i	−0.723034	−	0.690813i	$-0.757253\pi$
$887$	7.05085	−	12.2124i	0.236744	−	0.410053i	0.959778	+	0.280759i	$0.0905863\pi$
$888$	1.62050			0.0543804
$889$	−8.93400			−0.299637
$890$	0.458099	−	0.793450i	0.0153555	−	0.0265965i
$891$	−27.0039			−0.904665
$892$	−1.47933	−	2.56228i	−0.0495316	−	0.0857913i
$893$		0			0
$894$	−3.23461	+	5.60251i	−0.108182	+	0.187376i
$895$	0.506782			0.0169399
$896$	1.23508	+	2.13922i	0.0412611	+	0.0714664i
$897$	−7.27124	+	12.5942i	−0.242780	+	0.420507i
$898$	10.2334	+	17.7247i	0.341492	+	0.591481i
$899$	−59.8792			−1.99708
$900$	−6.61648	−	11.4601i	−0.220549	−	0.382003i
$901$	46.5045	+	80.5482i	1.54929	+	2.68345i
$902$	14.6059	−	25.2981i	0.486323	−	0.842335i
$903$	−5.77118	+	9.99597i	−0.192053	+	0.332645i
$904$	13.3766			0.444898
$905$	0.588838			0.0195736
$906$	−3.83794			−0.127507
$907$	8.88142	−	15.3831i	0.294903	−	0.510787i	−0.680060	−	0.733157i	$-0.738046\pi$
$907$	8.88142	−	15.3831i	0.294903	−	0.510787i	0.974962	+	0.222370i	$0.0713794\pi$
$908$	−1.15034	+	1.99244i	−0.0381753	+	0.0661216i
$909$	4.98791	−	8.63931i	0.165438	−	0.286548i
$910$	4.42943			0.146834
$911$	−9.65517	+	16.7232i	−0.319890	+	0.554066i	−0.980465	−	0.196694i	$-0.936979\pi$
$911$	−9.65517	+	16.7232i	−0.319890	+	0.554066i	0.660575	+	0.750760i	$0.270313\pi$
$912$	0.797497	+	1.38131i	0.0264078	+	0.0457396i
$913$	−2.30940			−0.0764298
$914$	19.6748	−	34.0778i	0.650785	−	1.12719i
$915$	0.207341			0.00685449
$916$	−7.06226	+	12.2322i	−0.233344	+	0.404163i
$917$	36.6017			1.20869
$918$	20.1455			0.664899
$919$	11.7891	−	20.4193i	0.388885	−	0.673569i	−0.603414	−	0.797428i	$-0.706194\pi$
$919$	11.7891	−	20.4193i	0.388885	−	0.673569i	0.992300	+	0.123858i	$0.0395269\pi$
$920$	1.11382	+	1.92919i	0.0367215	+	0.0636035i
$921$	2.67011	−	4.62477i	0.0879831	−	0.152391i
$922$	−17.4583	+	30.2387i	−0.574959	+	0.995857i
$923$	14.7316	+	25.5159i	0.484896	+	0.839865i
$924$	−2.64903	−	4.58825i	−0.0871465	−	0.150942i
$925$	7.50409	+	12.9975i	0.246733	+	0.427354i
$926$	37.5474			1.23388
$927$	19.9472			0.655151
$928$	3.45507	+	5.98436i	0.113418	+	0.196446i
$929$	10.7198	+	18.5673i	0.351706	+	0.609172i	0.986548	−	0.163469i	$-0.0522684\pi$
$929$	10.7198	+	18.5673i	0.351706	+	0.609172i	−0.634843	+	0.772641i	$0.718935\pi$
$930$	−0.862124	−	1.49324i	−0.0282702	−	0.0489653i
$931$	−1.36633	+	2.36655i	−0.0447796	+	0.0775606i
$932$	7.74836	−	13.4206i	0.253806	−	0.439605i
$933$	0.320533	+	0.555180i	0.0104938	+	0.0181758i
$934$	−9.02018	+	15.6234i	−0.295149	+	0.511214i
$935$	10.4185			0.340720
$936$	12.8763			0.420874
$937$	−5.74877	+	9.95715i	−0.187804	+	0.325286i	−0.944518	−	0.328460i	$-0.893470\pi$
$937$	−5.74877	+	9.95715i	−0.187804	+	0.325286i	0.756714	+	0.653746i	$0.226804\pi$
$938$	−37.5483			−1.22600
$939$	−7.74892	+	13.4215i	−0.252876	+	0.437995i
$940$		0			0
$941$	3.74536	+	6.48715i	0.122095	+	0.211475i	0.920594	−	0.390522i	$-0.127705\pi$
$941$	3.74536	+	6.48715i	0.122095	+	0.211475i	−0.798499	+	0.601997i	$0.794372\pi$
$942$	2.18699	−	3.78797i	0.0712559	−	0.123419i
$943$	−41.9175			−1.36502
$944$	−1.06649	+	1.84722i	−0.0347114	+	0.0601219i
$945$	−1.40698	+	2.43696i	−0.0457691	+	0.0792743i
$946$	−18.2278	+	31.5715i	−0.592638	+	1.02648i
$947$	2.89476			0.0940670			0.0470335	−	0.998893i	$-0.485023\pi$
$947$	2.89476			0.0940670			0.0470335	+	0.998893i	$0.485023\pi$
$948$	−7.66871			−0.249068
$949$	72.0371			2.33842
$950$	−7.38599	+	12.7929i	−0.239633	+	0.415057i
$951$	6.74873	−	11.6891i	0.218842	−	0.379046i
$952$	−8.28882	−	14.3567i	−0.268642	−	0.465302i
$953$	−13.0154	−	22.5433i	−0.421609	−	0.730249i	0.574488	−	0.818513i	$-0.305201\pi$
$953$	−13.0154	−	22.5433i	−0.421609	−	0.730249i	−0.996097	+	0.0882644i	$0.971868\pi$
$954$	−37.7666			−1.22274
$955$	2.15464	+	3.73194i	0.0697224	+	0.120763i
$956$	−0.556899	+	0.964577i	−0.0180114	+	0.0311967i
$957$	−7.41050	−	12.8354i	−0.239548	−	0.414909i
$958$	−23.3335			−0.753870
$959$	−15.7844	+	27.3394i	−0.509704	+	0.882834i
$960$	−0.0994903	+	0.172322i	−0.00321103	+	0.00556168i
$961$	−22.0447	−	38.1825i	−0.711118	−	1.23169i
$962$	−14.6036			−0.470840
$963$	−8.72310	+	15.1089i	−0.281098	+	0.486876i
$964$	2.75028			0.0885806
$965$	0.375313			0.0120818
$966$	−3.80123	+	6.58392i	−0.122303	+	0.211834i
$967$	−10.3353	−	17.9013i	−0.332362	−	0.575667i	0.650613	−	0.759410i	$-0.274512\pi$
$967$	−10.3353	−	17.9013i	−0.332362	−	0.575667i	−0.982974	+	0.183742i	$0.941179\pi$
$968$	−2.86675	−	4.96535i	−0.0921408	−	0.159593i
$969$	−5.35213	−	9.27016i	−0.171935	−	0.297801i
$970$	2.40557	−	4.16657i	0.0772383	−	0.133781i
$971$	−4.43364	−	7.67929i	−0.142282	−	0.246440i	0.786073	−	0.618133i	$-0.212111\pi$
$971$	−4.43364	−	7.67929i	−0.142282	−	0.246440i	−0.928356	+	0.371693i	$0.878777\pi$
$972$	−6.23330	+	10.7964i	−0.199933	+	0.346294i
$973$	9.98717			0.320174
$974$	−1.83586	−	3.17981i	−0.0588248	−	0.101888i
$975$	−6.01526	−	10.4187i	−0.192642	−	0.333666i
$976$	−0.521009	−	0.902413i	−0.0166771	−	0.0288855i
$977$	−3.75081			−0.119999			−0.0599995	−	0.998198i	$-0.519110\pi$
$977$	−3.75081			−0.119999			−0.0599995	+	0.998198i	$0.519110\pi$
$978$	−1.39100	−	2.40928i	−0.0444792	−	0.0770402i
$979$	9.87573			0.315630
$980$	−0.340908			−0.0108899
$981$	20.9573	+	19.2416i	0.669114	+	0.614336i
$982$	−39.8496			−1.27165
$983$	−22.9774			−0.732865			−0.366432	−	0.930445i	$-0.619421\pi$
$983$	−22.9774			−0.732865			−0.366432	+	0.930445i	$0.619421\pi$
$984$	−1.87211	−	3.24259i	−0.0596808	−	0.103370i
$985$	−2.10056			−0.0669294
$986$	−23.1875	−	40.1620i	−0.738441	−	1.27902i
$987$		0			0
$988$	−7.18690	−	12.4481i	−0.228646	−	0.396026i
$989$	52.3122			1.66343
$990$	−2.11523	+	3.66368i	−0.0672263	+	0.116439i
$991$	−12.0594	−	20.8875i	−0.383080	−	0.663514i	0.608421	−	0.793614i	$-0.291803\pi$
$991$	−12.0594	−	20.8875i	−0.383080	−	0.663514i	−0.991501	+	0.130101i	$0.958470\pi$
$992$	−4.33270	+	7.50446i	−0.137564	+	0.238267i
$993$	5.55468	+	9.62100i	0.176273	+	0.305313i
$994$	7.70132	+	13.3391i	0.244271	+	0.423090i
$995$	1.44055	+	2.49510i	0.0456685	+	0.0791001i
$996$	−0.148004	+	0.256350i	−0.00468968	+	0.00812276i
$997$	28.2398			0.894364			0.447182	−	0.894443i	$-0.352428\pi$
$997$	28.2398			0.894364			0.447182	+	0.894443i	$0.352428\pi$
$998$	17.6328			0.558158
$999$	4.63875	−	8.03455i	0.146764	−	0.254202i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	218.2.c.c.63.2	yes	10
3.2	odd	2		1962.2.f.k.1153.2		10
109.45	even	3	inner	218.2.c.c.45.2	✓	10
327.263	odd	6		1962.2.f.k.1135.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
218.2.c.c.45.2	✓	10	109.45	even	3	inner
218.2.c.c.63.2	yes	10	1.1	even	1	trivial
1962.2.f.k.1135.2		10	327.263	odd	6
1962.2.f.k.1153.2		10	3.2	odd	2

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 218 = 2 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	218.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-0.262161 - 0.454076i) q^{3} +1.00000 q^{4} +(-0.189751 - 0.328658i) q^{5} +(-0.262161 - 0.454076i) q^{6} +(1.23508 + 2.13922i) q^{7} +1.00000 q^{8} +(1.36254 - 2.35999i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-0.262161 - 0.454076i) q^{3} +1.00000 q^{4} +(-0.189751 - 0.328658i) q^{5} +(-0.262161 - 0.454076i) q^{6} +(1.23508 + 2.13922i) q^{7} +1.00000 q^{8} +(1.36254 - 2.35999i) q^{9} +(-0.189751 - 0.328658i) q^{10} +(2.04533 - 3.54262i) q^{11} +(-0.262161 - 0.454076i) q^{12} +(2.36254 + 4.09205i) q^{13} +(1.23508 + 2.13922i) q^{14} +(-0.0994903 + 0.172322i) q^{15} +1.00000 q^{16} -6.71116 q^{17} +(1.36254 - 2.35999i) q^{18} -3.04202 q^{19} +(-0.189751 - 0.328658i) q^{20} +(0.647579 - 1.12164i) q^{21} +(2.04533 - 3.54262i) q^{22} -5.86991 q^{23} +(-0.262161 - 0.454076i) q^{24} +(2.42799 - 4.20540i) q^{25} +(2.36254 + 4.09205i) q^{26} -3.00179 q^{27} +(1.23508 + 2.13922i) q^{28} +(3.45507 + 5.98436i) q^{29} +(-0.0994903 + 0.172322i) q^{30} +(-4.33270 + 7.50446i) q^{31} +1.00000 q^{32} -2.14482 q^{33} -6.71116 q^{34} +(0.468714 - 0.811837i) q^{35} +(1.36254 - 2.35999i) q^{36} +(-1.54533 + 2.67659i) q^{37} -3.04202 q^{38} +(1.23873 - 2.14555i) q^{39} +(-0.189751 - 0.328658i) q^{40} +7.14109 q^{41} +(0.647579 - 1.12164i) q^{42} -8.91192 q^{43} +(2.04533 - 3.54262i) q^{44} -1.03417 q^{45} -5.86991 q^{46} +(-0.262161 - 0.454076i) q^{48} +(0.449152 - 0.777955i) q^{49} +(2.42799 - 4.20540i) q^{50} +(1.75940 + 3.04737i) q^{51} +(2.36254 + 4.09205i) q^{52} +(-6.92944 - 12.0021i) q^{53} -3.00179 q^{54} -1.55241 q^{55} +(1.23508 + 2.13922i) q^{56} +(0.797497 + 1.38131i) q^{57} +(3.45507 + 5.98436i) q^{58} +(-1.06649 + 1.84722i) q^{59} +(-0.0994903 + 0.172322i) q^{60} +(-0.521009 - 0.902413i) q^{61} +(-4.33270 + 7.50446i) q^{62} +6.73140 q^{63} +1.00000 q^{64} +(0.896588 - 1.55294i) q^{65} -2.14482 q^{66} +(-7.60038 + 13.1642i) q^{67} -6.71116 q^{68} +(1.53886 + 2.66538i) q^{69} +(0.468714 - 0.811837i) q^{70} +6.23548 q^{71} +(1.36254 - 2.35999i) q^{72} +(7.62284 - 13.2031i) q^{73} +(-1.54533 + 2.67659i) q^{74} -2.54609 q^{75} -3.04202 q^{76} +10.1046 q^{77} +(1.23873 - 2.14555i) q^{78} +(7.31299 - 12.6665i) q^{79} +(-0.189751 - 0.328658i) q^{80} +(-3.30068 - 5.71695i) q^{81} +7.14109 q^{82} +(-0.282277 - 0.488917i) q^{83} +(0.647579 - 1.12164i) q^{84} +(1.27345 + 2.20567i) q^{85} -8.91192 q^{86} +(1.81157 - 3.13773i) q^{87} +(2.04533 - 3.54262i) q^{88} +(1.20711 + 2.09077i) q^{89} -1.03417 q^{90} +(-5.83586 + 10.1080i) q^{91} -5.86991 q^{92} +4.54346 q^{93} +(0.577224 + 0.999782i) q^{95} +(-0.262161 - 0.454076i) q^{96} +(6.33878 + 10.9791i) q^{97} +(0.449152 - 0.777955i) q^{98} +(-5.57370 - 9.65394i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} + q^{3} + 10 q^{4} - 8 q^{5} + q^{6} - q^{7} + 10 q^{8} - 10 q^{9}+O(q^{10}) \) 10 * q + 10 * q^2 + q^3 + 10 * q^4 - 8 * q^5 + q^6 - q^7 + 10 * q^8 - 10 * q^9	\( 10 q + 10 q^{2} + q^{3} + 10 q^{4} - 8 q^{5} + q^{6} - q^{7} + 10 q^{8} - 10 q^{9} - 8 q^{10} + q^{11} + q^{12} - q^{14} - q^{15} + 10 q^{16} - 16 q^{17} - 10 q^{18} - 6 q^{19} - 8 q^{20} + 4 q^{21} + q^{22} + 8 q^{23} + q^{24} - 11 q^{25} + 10 q^{27} - q^{28} + 9 q^{29} - q^{30} + 7 q^{31} + 10 q^{32} - 2 q^{33} - 16 q^{34} + 10 q^{35} - 10 q^{36} + 4 q^{37} - 6 q^{38} - 4 q^{39} - 8 q^{40} - 22 q^{41} + 4 q^{42} + 2 q^{43} + q^{44} + 38 q^{45} + 8 q^{46} + q^{48} - 10 q^{49} - 11 q^{50} - 3 q^{51} - 2 q^{53} + 10 q^{54} + 20 q^{55} - q^{56} - 49 q^{57} + 9 q^{58} - 12 q^{59} - q^{60} + 7 q^{61} + 7 q^{62} - 36 q^{63} + 10 q^{64} - 3 q^{65} - 2 q^{66} - 56 q^{67} - 16 q^{68} + 19 q^{69} + 10 q^{70} + 4 q^{71} - 10 q^{72} + 12 q^{73} + 4 q^{74} - 46 q^{75} - 6 q^{76} + 66 q^{77} - 4 q^{78} - 30 q^{79} - 8 q^{80} - 41 q^{81} - 22 q^{82} - 7 q^{83} + 4 q^{84} - 22 q^{85} + 2 q^{86} + 40 q^{87} + q^{88} + 9 q^{89} + 38 q^{90} + 20 q^{91} + 8 q^{92} + 10 q^{93} - 12 q^{95} + q^{96} + 35 q^{97} - 10 q^{98} + 19 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 + q^3 + 10 * q^4 - 8 * q^5 + q^6 - q^7 + 10 * q^8 - 10 * q^9 - 8 * q^10 + q^11 + q^12 - q^14 - q^15 + 10 * q^16 - 16 * q^17 - 10 * q^18 - 6 * q^19 - 8 * q^20 + 4 * q^21 + q^22 + 8 * q^23 + q^24 - 11 * q^25 + 10 * q^27 - q^28 + 9 * q^29 - q^30 + 7 * q^31 + 10 * q^32 - 2 * q^33 - 16 * q^34 + 10 * q^35 - 10 * q^36 + 4 * q^37 - 6 * q^38 - 4 * q^39 - 8 * q^40 - 22 * q^41 + 4 * q^42 + 2 * q^43 + q^44 + 38 * q^45 + 8 * q^46 + q^48 - 10 * q^49 - 11 * q^50 - 3 * q^51 - 2 * q^53 + 10 * q^54 + 20 * q^55 - q^56 - 49 * q^57 + 9 * q^58 - 12 * q^59 - q^60 + 7 * q^61 + 7 * q^62 - 36 * q^63 + 10 * q^64 - 3 * q^65 - 2 * q^66 - 56 * q^67 - 16 * q^68 + 19 * q^69 + 10 * q^70 + 4 * q^71 - 10 * q^72 + 12 * q^73 + 4 * q^74 - 46 * q^75 - 6 * q^76 + 66 * q^77 - 4 * q^78 - 30 * q^79 - 8 * q^80 - 41 * q^81 - 22 * q^82 - 7 * q^83 + 4 * q^84 - 22 * q^85 + 2 * q^86 + 40 * q^87 + q^88 + 9 * q^89 + 38 * q^90 + 20 * q^91 + 8 * q^92 + 10 * q^93 - 12 * q^95 + q^96 + 35 * q^97 - 10 * q^98 + 19 * q^99

Introduction

L-functions

Modular forms

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