LMFDB - Embedded newform 760.2.p.g.379.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [760,2,Mod(379,760)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(760, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 1]))

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

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

chi := DirichletCharacter("760.379");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 760 = 2^{3} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	760.p (of order $2$, degree $1$, 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:	$6.06863055362$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.1499238400.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 16x^{6} - 34x^{5} + 59x^{4} - 66x^{3} + 54x^{2} - 26x + 5 $ x^8 - 4x^7 + 16x^6 - 34x^5 + 59x^4 - 66x^3 + 54x^2 - 26*x + 5
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.8
Root			$0.500000 + 1.41267i$ of defining polynomial
Character	$\chi$	$=$	760.379
Dual form			760.2.p.g.379.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 + 1.00000i) q^{2} +1.00000 q^{3} +2.00000i q^{4} +(1.91267 - 1.15831i) q^{5} +(1.00000 + 1.00000i) q^{6} +3.21974 q^{7} +(-2.00000 + 2.00000i) q^{8} -2.00000 q^{9} +(3.07098 + 0.754359i) q^{10} -2.31662 q^{11} +2.00000i q^{12} +3.31662i q^{13} +(3.21974 + 3.21974i) q^{14} +(1.91267 - 1.15831i) q^{15} -4.00000 q^{16} +0.605599i q^{17} +(-2.00000 - 2.00000i) q^{18} +(4.31662 + 0.605599i) q^{19} +(2.31662 + 3.82534i) q^{20} +3.21974 q^{21} +(-2.31662 - 2.31662i) q^{22} +4.43094 q^{23} +(-2.00000 + 2.00000i) q^{24} +(2.31662 - 4.43094i) q^{25} +(-3.31662 + 3.31662i) q^{26} -5.00000 q^{27} +6.43949i q^{28} +5.64214 q^{29} +(3.07098 + 0.754359i) q^{30} -5.03654 q^{31} +(-4.00000 - 4.00000i) q^{32} -2.31662 q^{33} +(-0.605599 + 0.605599i) q^{34} +(6.15831 - 3.72947i) q^{35} -4.00000i q^{36} -6.63325i q^{37} +(3.71103 + 4.92222i) q^{38} +3.31662i q^{39} +(-1.50872 + 6.14197i) q^{40} -2.61414i q^{41} +(3.21974 + 3.21974i) q^{42} -12.6872i q^{43} -4.63325i q^{44} +(-3.82534 + 2.31662i) q^{45} +(4.43094 + 4.43094i) q^{46} -7.65069 q^{47} -4.00000 q^{48} +3.36675 q^{49} +(6.74757 - 2.11432i) q^{50} +0.605599i q^{51} -6.63325 q^{52} +13.3166i q^{53} +(-5.00000 - 5.00000i) q^{54} +(-4.43094 + 2.68338i) q^{55} +(-6.43949 + 6.43949i) q^{56} +(4.31662 + 0.605599i) q^{57} +(5.64214 + 5.64214i) q^{58} +9.46748i q^{59} +(2.31662 + 3.82534i) q^{60} -4.31662i q^{61} +(-5.03654 - 5.03654i) q^{62} -6.43949 q^{63} -8.00000i q^{64} +(3.84169 + 6.34361i) q^{65} +(-2.31662 - 2.31662i) q^{66} -11.6332 q^{67} -1.21120 q^{68} +4.43094 q^{69} +(9.88778 + 2.42884i) q^{70} +6.24774 q^{71} +(4.00000 - 4.00000i) q^{72} -7.04509i q^{73} +(6.63325 - 6.63325i) q^{74} +(2.31662 - 4.43094i) q^{75} +(-1.21120 + 8.63325i) q^{76} -7.45894 q^{77} +(-3.31662 + 3.31662i) q^{78} -16.5126 q^{79} +(-7.65069 + 4.63325i) q^{80} +1.00000 q^{81} +(2.61414 - 2.61414i) q^{82} +6.43949i q^{83} +6.43949i q^{84} +(0.701473 + 1.15831i) q^{85} +(12.6872 - 12.6872i) q^{86} +5.64214 q^{87} +(4.63325 - 4.63325i) q^{88} -12.6872i q^{89} +(-6.14197 - 1.50872i) q^{90} +10.6787i q^{91} +8.86188i q^{92} -5.03654 q^{93} +(-7.65069 - 7.65069i) q^{94} +(8.95776 - 3.84169i) q^{95} +(-4.00000 - 4.00000i) q^{96} +2.00000 q^{97} +(3.36675 + 3.36675i) q^{98} +4.63325 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{3} + 8 q^{6} - 16 q^{8} - 16 q^{9} - 4 q^{10} + 8 q^{11} - 32 q^{16} - 16 q^{18} + 8 q^{19} - 8 q^{20} + 8 q^{22} - 16 q^{24} - 8 q^{25} - 40 q^{27} - 4 q^{30} - 32 q^{32} + 8 q^{33}+ \cdots - 16 q^{99}+O(q^{100}) $ 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^6 - 16 * q^8 - 16 * q^9 - 4 * q^10 + 8 * q^11 - 32 * q^16 - 16 * q^18 + 8 * q^19 - 8 * q^20 + 8 * q^22 - 16 * q^24 - 8 * q^25 - 40 * q^27 - 4 * q^30 - 32 * q^32 + 8 * q^33 + 36 * q^35 + 8 * q^38 - 8 * q^40 - 32 * q^48 + 80 * q^49 - 8 * q^50 - 40 * q^54 + 8 * q^57 - 8 * q^60 + 44 * q^65 + 8 * q^66 - 40 * q^67 + 36 * q^70 + 32 * q^72 - 8 * q^75 + 8 * q^81 - 16 * q^88 + 8 * q^90 - 32 * q^96 + 16 * q^97 + 80 * q^98 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/760\mathbb{Z}\right)^\times$.

$n$	$191$	$381$	$401$	$457$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

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	+	1.00000i	0.707107	+	0.707107i
$2$	1.00000	+	1.00000i	0.707107	+	0.707107i
$3$	1.00000			0.577350			0.288675	−	0.957427i	$-0.406785\pi$
$3$	1.00000			0.577350			0.288675	+	0.957427i	$0.406785\pi$
$4$			2.00000i			1.00000i
$5$	1.91267	−	1.15831i	0.855373	−	0.518013i
$5$	1.91267	−	1.15831i	0.855373	−	0.518013i
$6$	1.00000	+	1.00000i	0.408248	+	0.408248i
$7$	3.21974			1.21695			0.608474	−	0.793574i	$-0.291782\pi$
$7$	3.21974			1.21695			0.608474	+	0.793574i	$0.291782\pi$
$8$	−2.00000	+	2.00000i	−0.707107	+	0.707107i
$9$	−2.00000			−0.666667
$10$	3.07098	+	0.754359i	0.971130	+	0.238549i
$11$	−2.31662			−0.698489			−0.349244	−	0.937032i	$-0.613562\pi$
$11$	−2.31662			−0.698489			−0.349244	+	0.937032i	$0.613562\pi$
$12$			2.00000i			0.577350i
$13$			3.31662i			0.919866i	0.887954	+	0.459933i	$0.152127\pi$
$13$			3.31662i			0.919866i	−0.887954	+	0.459933i	$0.847873\pi$
$14$	3.21974	+	3.21974i	0.860513	+	0.860513i
$15$	1.91267	−	1.15831i	0.493850	−	0.299075i
$16$	−4.00000			−1.00000
$17$			0.605599i			0.146879i	0.997300	+	0.0734397i	$0.0233976\pi$
$17$			0.605599i			0.146879i	−0.997300	+	0.0734397i	$0.976602\pi$
$18$	−2.00000	−	2.00000i	−0.471405	−	0.471405i
$19$	4.31662	+	0.605599i	0.990302	+	0.138934i
$19$	4.31662	+	0.605599i	0.990302	+	0.138934i
$20$	2.31662	+	3.82534i	0.518013	+	0.855373i
$21$	3.21974			0.702606
$22$	−2.31662	−	2.31662i	−0.493906	−	0.493906i
$23$	4.43094			0.923915			0.461958	−	0.886902i	$-0.347147\pi$
$23$	4.43094			0.923915			0.461958	+	0.886902i	$0.347147\pi$
$24$	−2.00000	+	2.00000i	−0.408248	+	0.408248i
$25$	2.31662	−	4.43094i	0.463325	−	0.886188i
$26$	−3.31662	+	3.31662i	−0.650444	+	0.650444i
$27$	−5.00000			−0.962250
$28$			6.43949i			1.21695i
$29$	5.64214			1.04772			0.523860	−	0.851805i	$-0.324492\pi$
$29$	5.64214			1.04772			0.523860	+	0.851805i	$0.324492\pi$
$30$	3.07098	+	0.754359i	0.560682	+	0.137727i
$31$	−5.03654			−0.904590			−0.452295	−	0.891869i	$-0.649395\pi$
$31$	−5.03654			−0.904590			−0.452295	+	0.891869i	$0.649395\pi$
$32$	−4.00000	−	4.00000i	−0.707107	−	0.707107i
$33$	−2.31662			−0.403273
$34$	−0.605599	+	0.605599i	−0.103859	+	0.103859i
$35$	6.15831	−	3.72947i	1.04094	−	0.630395i
$36$		−	4.00000i		−	0.666667i
$37$		−	6.63325i		−	1.09050i	−0.838274	−	0.545250i	$-0.816435\pi$
$37$		−	6.63325i		−	1.09050i	0.838274	−	0.545250i	$-0.183565\pi$
$38$	3.71103	+	4.92222i	0.602008	+	0.798490i
$39$			3.31662i			0.531085i
$40$	−1.50872	+	6.14197i	−0.238549	+	0.971130i
$41$		−	2.61414i		−	0.408261i	−0.978944	−	0.204130i	$-0.934563\pi$
$41$		−	2.61414i		−	0.408261i	0.978944	−	0.204130i	$-0.0654367\pi$
$42$	3.21974	+	3.21974i	0.496817	+	0.496817i
$43$		−	12.6872i		−	1.93478i	−0.253284	−	0.967392i	$-0.581511\pi$
$43$		−	12.6872i		−	1.93478i	0.253284	−	0.967392i	$-0.418489\pi$
$44$		−	4.63325i		−	0.698489i
$45$	−3.82534	+	2.31662i	−0.570248	+	0.345342i
$46$	4.43094	+	4.43094i	0.653307	+	0.653307i
$47$	−7.65069			−1.11597			−0.557984	−	0.829852i	$-0.688425\pi$
$47$	−7.65069			−1.11597			−0.557984	+	0.829852i	$0.688425\pi$
$48$	−4.00000			−0.577350
$49$	3.36675			0.480964
$50$	6.74757	−	2.11432i	0.954250	−	0.299010i
$51$			0.605599i			0.0848009i
$52$	−6.63325			−0.919866
$53$			13.3166i			1.82918i	0.404383	+	0.914590i	$0.367486\pi$
$53$			13.3166i			1.82918i	−0.404383	+	0.914590i	$0.632514\pi$
$54$	−5.00000	−	5.00000i	−0.680414	−	0.680414i
$55$	−4.43094	+	2.68338i	−0.597468	+	0.361826i
$56$	−6.43949	+	6.43949i	−0.860513	+	0.860513i
$57$	4.31662	+	0.605599i	0.571751	+	0.0802136i
$58$	5.64214	+	5.64214i	0.740849	+	0.740849i
$59$			9.46748i			1.23256i	0.787527	+	0.616281i	$0.211361\pi$
$59$			9.46748i			1.23256i	−0.787527	+	0.616281i	$0.788639\pi$
$60$	2.31662	+	3.82534i	0.299075	+	0.493850i
$61$		−	4.31662i		−	0.552687i	−0.961059	−	0.276344i	$-0.910877\pi$
$61$		−	4.31662i		−	0.552687i	0.961059	−	0.276344i	$-0.0891228\pi$
$62$	−5.03654	−	5.03654i	−0.639641	−	0.639641i
$63$	−6.43949			−0.811299
$64$		−	8.00000i		−	1.00000i
$65$	3.84169	+	6.34361i	0.476503	+	0.786828i
$66$	−2.31662	−	2.31662i	−0.285157	−	0.285157i
$67$	−11.6332			−1.42123			−0.710614	−	0.703582i	$-0.751583\pi$
$67$	−11.6332			−1.42123			−0.710614	+	0.703582i	$0.751583\pi$
$68$	−1.21120			−0.146879
$69$	4.43094			0.533423
$70$	9.88778	+	2.42884i	1.18182	+	0.290302i
$71$	6.24774			0.741470			0.370735	−	0.928739i	$-0.379106\pi$
$71$	6.24774			0.741470			0.370735	+	0.928739i	$0.379106\pi$
$72$	4.00000	−	4.00000i	0.471405	−	0.471405i
$73$		−	7.04509i		−	0.824565i	−0.911056	−	0.412283i	$-0.864732\pi$
$73$		−	7.04509i		−	0.824565i	0.911056	−	0.412283i	$-0.135268\pi$
$74$	6.63325	−	6.63325i	0.771100	−	0.771100i
$75$	2.31662	−	4.43094i	0.267501	−	0.511641i
$76$	−1.21120	+	8.63325i	−0.138934	+	0.990302i
$77$	−7.45894			−0.850025
$78$	−3.31662	+	3.31662i	−0.375534	+	0.375534i
$79$	−16.5126			−1.85781			−0.928905	−	0.370319i	$-0.879248\pi$
$79$	−16.5126			−1.85781			−0.928905	+	0.370319i	$0.879248\pi$
$80$	−7.65069	+	4.63325i	−0.855373	+	0.518013i
$81$	1.00000			0.111111
$82$	2.61414	−	2.61414i	0.288684	−	0.288684i
$83$			6.43949i			0.706826i	0.935467	+	0.353413i	$0.114979\pi$
$83$			6.43949i			0.706826i	−0.935467	+	0.353413i	$0.885021\pi$
$84$			6.43949i			0.702606i
$85$	0.701473	+	1.15831i	0.0760854	+	0.125637i
$86$	12.6872	−	12.6872i	1.36810	−	1.36810i
$87$	5.64214			0.604901
$88$	4.63325	−	4.63325i	0.493906	−	0.493906i
$89$		−	12.6872i		−	1.34484i	−0.740168	−	0.672422i	$-0.765254\pi$
$89$		−	12.6872i		−	1.34484i	0.740168	−	0.672422i	$-0.234746\pi$
$90$	−6.14197	−	1.50872i	−0.647420	−	0.159033i
$91$			10.6787i			1.11943i
$92$			8.86188i			0.923915i
$93$	−5.03654			−0.522265
$94$	−7.65069	−	7.65069i	−0.789108	−	0.789108i
$95$	8.95776	−	3.84169i	0.919047	−	0.394149i
$96$	−4.00000	−	4.00000i	−0.408248	−	0.408248i
$97$	2.00000			0.203069			0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000			0.203069			0.101535	+	0.994832i	$0.467625\pi$
$98$	3.36675	+	3.36675i	0.340093	+	0.340093i
$99$	4.63325			0.465659
$100$	8.86188	+	4.63325i	0.886188	+	0.463325i
$101$		−	4.31662i		−	0.429520i	−0.976667	−	0.214760i	$-0.931103\pi$
$101$		−	4.31662i		−	0.429520i	0.976667	−	0.214760i	$-0.0688970\pi$
$102$	−0.605599	+	0.605599i	−0.0599633	+	0.0599633i
$103$		−	1.68338i		−	0.165868i	−0.996555	−	0.0829339i	$-0.973571\pi$
$103$		−	1.68338i		−	0.165868i	0.996555	−	0.0829339i	$-0.0264291\pi$
$104$	−6.63325	−	6.63325i	−0.650444	−	0.650444i
$105$	6.15831	−	3.72947i	0.600990	−	0.363959i
$106$	−13.3166	+	13.3166i	−1.29342	+	1.29342i
$107$	−3.00000			−0.290021			−0.145010	−	0.989430i	$-0.546322\pi$
$107$	−3.00000			−0.290021			−0.145010	+	0.989430i	$0.546322\pi$
$108$		−	10.0000i		−	0.962250i
$109$	10.8704			1.04120			0.520599	−	0.853801i	$-0.325709\pi$
$109$	10.8704			1.04120			0.520599	+	0.853801i	$0.325709\pi$
$110$	−7.11432	−	1.74757i	−0.678324	−	0.166624i
$111$		−	6.63325i		−	0.629600i
$112$	−12.8790			−1.21695
$113$	−8.31662			−0.782362			−0.391181	−	0.920314i	$-0.627933\pi$
$113$	−8.31662			−0.782362			−0.391181	+	0.920314i	$0.627933\pi$
$114$	3.71103	+	4.92222i	0.347569	+	0.461009i
$115$	8.47494	−	5.13242i	0.790292	−	0.478600i
$116$			11.2843i			1.04772i
$117$		−	6.63325i		−	0.613244i
$118$	−9.46748	+	9.46748i	−0.871553	+	0.871553i
$119$			1.94987i			0.178745i
$120$	−1.50872	+	6.14197i	−0.137727	+	0.560682i
$121$	−5.63325			−0.512114
$122$	4.31662	−	4.31662i	0.390809	−	0.390809i
$123$		−	2.61414i		−	0.235709i
$124$		−	10.0731i		−	0.904590i
$125$	−0.701473	−	11.1583i	−0.0627417	−	0.998030i
$126$	−6.43949	−	6.43949i	−0.573675	−	0.573675i
$127$		−	8.00000i		−	0.709885i	−0.934888	−	0.354943i	$-0.884500\pi$
$127$		−	8.00000i		−	0.709885i	0.934888	−	0.354943i	$-0.115500\pi$
$128$	8.00000	−	8.00000i	0.707107	−	0.707107i
$129$		−	12.6872i		−	1.11705i
$130$	−2.50193	+	10.1853i	−0.219433	+	0.893310i
$131$	−6.63325			−0.579550			−0.289775	−	0.957095i	$-0.593580\pi$
$131$	−6.63325			−0.579550			−0.289775	+	0.957095i	$0.593580\pi$
$132$		−	4.63325i		−	0.403273i
$133$	13.8984	+	1.94987i	1.20515	+	0.169076i
$134$	−11.6332	−	11.6332i	−1.00496	−	1.00496i
$135$	−9.56336	+	5.79156i	−0.823083	+	0.498458i
$136$	−1.21120	−	1.21120i	−0.103859	−	0.103859i
$137$		−	15.9070i		−	1.35902i	−0.733664	−	0.679512i	$-0.762191\pi$
$137$		−	15.9070i		−	1.35902i	0.733664	−	0.679512i	$-0.237809\pi$
$138$	4.43094	+	4.43094i	0.377187	+	0.377187i
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$	7.45894	+	12.3166i	0.630395	+	1.04094i
$141$	−7.65069			−0.644304
$142$	6.24774	+	6.24774i	0.524299	+	0.524299i
$143$		−	7.68338i		−	0.642516i
$144$	8.00000			0.666667
$145$	10.7916	−	6.53536i	0.896190	−	0.542732i
$146$	7.04509	−	7.04509i	0.583056	−	0.583056i
$147$	3.36675			0.277685
$148$	13.2665			1.09050
$149$			14.0000i			1.14692i	0.819232	+	0.573462i	$0.194400\pi$
$149$			14.0000i			1.14692i	−0.819232	+	0.573462i	$0.805600\pi$
$150$	6.74757	−	2.11432i	0.550937	−	0.172633i
$151$	−7.65069			−0.622604			−0.311302	−	0.950311i	$-0.600765\pi$
$151$	−7.65069			−0.622604			−0.311302	+	0.950311i	$0.600765\pi$
$152$	−9.84445	+	7.42205i	−0.798490	+	0.602008i
$153$		−	1.21120i		−	0.0979196i
$154$	−7.45894	−	7.45894i	−0.601058	−	0.601058i
$155$	−9.63325	+	5.83389i	−0.773761	+	0.468589i
$156$	−6.63325			−0.531085
$157$	8.86188			0.707255			0.353628	−	0.935386i	$-0.384948\pi$
$157$	8.86188			0.707255			0.353628	+	0.935386i	$0.384948\pi$
$158$	−16.5126	−	16.5126i	−1.31367	−	1.31367i
$159$			13.3166i			1.05608i
$160$	−12.2839	−	3.01744i	−0.971130	−	0.238549i
$161$	14.2665			1.12436
$162$	1.00000	+	1.00000i	0.0785674	+	0.0785674i
$163$			9.05363i			0.709135i	0.935030	+	0.354568i	$0.115372\pi$
$163$			9.05363i			0.709135i	−0.935030	+	0.354568i	$0.884628\pi$
$164$	5.22829			0.408261
$165$	−4.43094	+	2.68338i	−0.344948	+	0.208900i
$166$	−6.43949	+	6.43949i	−0.499801	+	0.499801i
$167$		−	19.5831i		−	1.51539i	−0.652610	−	0.757694i	$-0.726326\pi$
$167$		−	19.5831i		−	1.51539i	0.652610	−	0.757694i	$-0.273674\pi$
$168$	−6.43949	+	6.43949i	−0.496817	+	0.496817i
$169$	2.00000			0.153846
$170$	−0.456839	+	1.85979i	−0.0350380	+	0.142639i
$171$	−8.63325	−	1.21120i	−0.660201	−	0.0926227i
$172$	25.3745			1.93478
$173$			14.0000i			1.06440i	0.846619	+	0.532200i	$0.178635\pi$
$173$			14.0000i			1.06440i	−0.846619	+	0.532200i	$0.821365\pi$
$174$	5.64214	+	5.64214i	0.427730	+	0.427730i
$175$	7.45894	−	14.2665i	0.563843	−	1.07845i
$176$	9.26650			0.698489
$177$			9.46748i			0.711620i
$178$	12.6872	−	12.6872i	0.950948	−	0.950948i
$179$			22.9521i			1.71552i	0.514053	+	0.857759i	$0.328144\pi$
$179$			22.9521i			1.71552i	−0.514053	+	0.857759i	$0.671856\pi$
$180$	−4.63325	−	7.65069i	−0.345342	−	0.570248i
$181$	14.0902			1.04731			0.523657	−	0.851929i	$-0.324567\pi$
$181$	14.0902			1.04731			0.523657	+	0.851929i	$0.324567\pi$
$182$	−10.6787	+	10.6787i	−0.791557	+	0.791557i
$183$		−	4.31662i		−	0.319094i
$184$	−8.86188	+	8.86188i	−0.653307	+	0.653307i
$185$	−7.68338	−	12.6872i	−0.564893	−	0.932784i
$186$	−5.03654	−	5.03654i	−0.369297	−	0.369297i
$187$		−	1.40295i		−	0.102594i
$188$		−	15.3014i		−	1.11597i
$189$	−16.0987			−1.17101
$190$	12.7994	+	5.11607i	0.928569	+	0.371159i
$191$			16.5831i			1.19991i	0.800033	+	0.599956i	$0.204815\pi$
$191$			16.5831i			1.19991i	−0.800033	+	0.599956i	$0.795185\pi$
$192$		−	8.00000i		−	0.577350i
$193$	16.0000			1.15171			0.575853	−	0.817554i	$-0.304670\pi$
$193$	16.0000			1.15171			0.575853	+	0.817554i	$0.304670\pi$
$194$	2.00000	+	2.00000i	0.143592	+	0.143592i
$195$	3.84169	+	6.34361i	0.275109	+	0.454276i
$196$			6.73350i			0.480964i
$197$	16.7043			1.19013			0.595067	−	0.803676i	$-0.297126\pi$
$197$	16.7043			1.19013			0.595067	+	0.803676i	$0.297126\pi$
$198$	4.63325	+	4.63325i	0.329271	+	0.329271i
$199$			11.9499i			0.847104i	0.905872	+	0.423552i	$0.139217\pi$
$199$			11.9499i			0.847104i	−0.905872	+	0.423552i	$0.860783\pi$
$200$	4.22864	+	13.4951i	0.299010	+	0.954250i
$201$	−11.6332			−0.820546
$202$	4.31662	−	4.31662i	0.303717	−	0.303717i
$203$	18.1662			1.27502
$204$	−1.21120			−0.0848009
$205$	−3.02800	−	5.00000i	−0.211484	−	0.349215i
$206$	1.68338	−	1.68338i	0.117286	−	0.117286i
$207$	−8.86188			−0.615944
$208$		−	13.2665i		−	0.919866i
$209$	−10.0000	−	1.40295i	−0.691714	−	0.0970438i
$210$	9.88778	+	2.42884i	0.682322	+	0.167606i
$211$		−	8.25629i		−	0.568386i	−0.958767	−	0.284193i	$-0.908274\pi$
$211$		−	8.25629i		−	0.568386i	0.958767	−	0.284193i	$-0.0917257\pi$
$212$	−26.6332			−1.82918
$213$	6.24774			0.428088
$214$	−3.00000	−	3.00000i	−0.205076	−	0.205076i
$215$	−14.6958	−	24.2665i	−1.00224	−	1.65496i
$216$	10.0000	−	10.0000i	0.680414	−	0.680414i
$217$	−16.2164			−1.10084
$218$	10.8704	+	10.8704i	0.736238	+	0.736238i
$219$		−	7.04509i		−	0.476063i
$220$	−5.36675	−	8.86188i	−0.361826	−	0.597468i
$221$	−2.00855			−0.135109
$222$	6.63325	−	6.63325i	0.445195	−	0.445195i
$223$		−	3.26650i		−	0.218741i	−0.994001	−	0.109370i	$-0.965117\pi$
$223$		−	3.26650i		−	0.218741i	0.994001	−	0.109370i	$-0.0348835\pi$
$224$	−12.8790	−	12.8790i	−0.860513	−	0.860513i
$225$	−4.63325	+	8.86188i	−0.308883	+	0.590792i
$226$	−8.31662	−	8.31662i	−0.553214	−	0.553214i
$227$	−1.63325			−0.108403			−0.0542013	−	0.998530i	$-0.517261\pi$
$227$	−1.63325			−0.108403			−0.0542013	+	0.998530i	$0.517261\pi$
$228$	−1.21120	+	8.63325i	−0.0802136	+	0.571751i
$229$			29.8997i			1.97583i	0.154993	+	0.987916i	$0.450464\pi$
$229$			29.8997i			1.97583i	−0.154993	+	0.987916i	$0.549536\pi$
$230$	13.6074	+	3.34252i	0.897242	+	0.220399i
$231$	−7.45894			−0.490762
$232$	−11.2843	+	11.2843i	−0.740849	+	0.740849i
$233$			12.4955i			0.818606i	0.912398	+	0.409303i	$0.134228\pi$
$233$			12.4955i			0.818606i	−0.912398	+	0.409303i	$0.865772\pi$
$234$	6.63325	−	6.63325i	0.433629	−	0.433629i
$235$	−14.6332	+	8.86188i	−0.954568	+	0.578086i
$236$	−18.9350			−1.23256
$237$	−16.5126			−1.07261
$238$	−1.94987	+	1.94987i	−0.126392	+	0.126392i
$239$			1.94987i			0.126127i	0.998010	+	0.0630634i	$0.0200870\pi$
$239$			1.94987i			0.126127i	−0.998010	+	0.0630634i	$0.979913\pi$
$240$	−7.65069	+	4.63325i	−0.493850	+	0.299075i
$241$		−	16.5126i		−	1.06367i	−0.846849	−	0.531834i	$-0.821503\pi$
$241$		−	16.5126i		−	1.06367i	0.846849	−	0.531834i	$-0.178497\pi$
$242$	−5.63325	−	5.63325i	−0.362119	−	0.362119i
$243$	16.0000			1.02640
$244$	8.63325			0.552687
$245$	6.43949	−	3.89975i	0.411404	−	0.249146i
$246$	2.61414	−	2.61414i	0.166672	−	0.166672i
$247$	−2.00855	+	14.3166i	−0.127801	+	0.910945i
$248$	10.0731	−	10.0731i	0.639641	−	0.639641i
$249$			6.43949i			0.408086i
$250$	10.4568	−	11.8598i	0.661349	−	0.750079i
$251$	4.94987			0.312433			0.156217	−	0.987723i	$-0.450070\pi$
$251$	4.94987			0.312433			0.156217	+	0.987723i	$0.450070\pi$
$252$		−	12.8790i		−	0.811299i
$253$	−10.2648			−0.645344
$254$	8.00000	−	8.00000i	0.501965	−	0.501965i
$255$	0.701473	+	1.15831i	0.0439279	+	0.0725363i
$256$	16.0000			1.00000
$257$	−9.58312			−0.597779			−0.298889	−	0.954288i	$-0.596616\pi$
$257$	−9.58312			−0.597779			−0.298889	+	0.954288i	$0.596616\pi$
$258$	12.6872	−	12.6872i	0.789872	−	0.789872i
$259$		−	21.3574i		−	1.32708i
$260$	−12.6872	+	7.68338i	−0.786828	+	0.476503i
$261$	−11.2843			−0.698479
$262$	−6.63325	−	6.63325i	−0.409804	−	0.409804i
$263$	−1.21120			−0.0746857			−0.0373428	−	0.999303i	$-0.511889\pi$
$263$	−1.21120			−0.0746857			−0.0373428	+	0.999303i	$0.511889\pi$
$264$	4.63325	−	4.63325i	0.285157	−	0.285157i
$265$	15.4248	+	25.4703i	0.947539	+	1.56463i
$266$	11.9486	+	15.8483i	0.732613	+	0.971722i
$267$		−	12.6872i		−	0.776446i
$268$		−	23.2665i		−	1.42123i
$269$	27.7969			1.69480			0.847402	−	0.530952i	$-0.178165\pi$
$269$	27.7969			1.69480			0.847402	+	0.530952i	$0.178165\pi$
$270$	−15.3549	−	3.77180i	−0.934471	−	0.229544i
$271$			9.31662i			0.565945i	0.959128	+	0.282972i	$0.0913205\pi$
$271$			9.31662i			0.565945i	−0.959128	+	0.282972i	$0.908680\pi$
$272$		−	2.42240i		−	0.146879i
$273$			10.6787i			0.646303i
$274$	15.9070	−	15.9070i	0.960975	−	0.960975i
$275$	−5.36675	+	10.2648i	−0.323627	+	0.618993i
$276$			8.86188i			0.533423i
$277$	−7.65069			−0.459685			−0.229843	−	0.973228i	$-0.573821\pi$
$277$	−7.65069			−0.459685			−0.229843	+	0.973228i	$0.573821\pi$
$278$		0			0
$279$	10.0731			0.603060
$280$	−4.85769	+	19.7756i	−0.290302	+	1.18182i
$281$		−	8.67014i		−	0.517217i	−0.965982	−	0.258609i	$-0.916736\pi$
$281$		−	8.67014i		−	0.517217i	0.965982	−	0.258609i	$-0.0832640\pi$
$282$	−7.65069	−	7.65069i	−0.455592	−	0.455592i
$283$			11.6678i			0.693577i	0.937943	+	0.346789i	$0.112728\pi$
$283$			11.6678i			0.693577i	−0.937943	+	0.346789i	$0.887272\pi$
$284$			12.4955i			0.741470i
$285$	8.95776	−	3.84169i	0.530612	−	0.227562i
$286$	7.68338	−	7.68338i	0.454328	−	0.454328i
$287$		−	8.41688i		−	0.496832i
$288$	8.00000	+	8.00000i	0.471405	+	0.471405i
$289$	16.6332			0.978426
$290$	17.3269	+	4.25620i	1.01747	+	0.249933i
$291$	2.00000			0.117242
$292$	14.0902			0.824565
$293$			3.31662i			0.193759i	0.995296	+	0.0968796i	$0.0308862\pi$
$293$			3.31662i			0.193759i	−0.995296	+	0.0968796i	$0.969114\pi$
$294$	3.36675	+	3.36675i	0.196353	+	0.196353i
$295$	10.9663	+	18.1082i	0.638483	+	1.05430i
$296$	13.2665	+	13.2665i	0.771100	+	0.771100i
$297$	11.5831			0.672121
$298$	−14.0000	+	14.0000i	−0.810998	+	0.810998i
$299$			14.6958i			0.849878i
$300$	8.86188	+	4.63325i	0.511641	+	0.267501i
$301$		−	40.8496i		−	2.35453i
$302$	−7.65069	−	7.65069i	−0.440248	−	0.440248i
$303$		−	4.31662i		−	0.247984i
$304$	−17.2665	−	2.42240i	−0.990302	−	0.138934i
$305$	−5.00000	−	8.25629i	−0.286299	−	0.472754i
$306$	1.21120	−	1.21120i	0.0692396	−	0.0692396i
$307$	−26.6332			−1.52004			−0.760020	−	0.649900i	$-0.774811\pi$
$307$	−26.6332			−1.52004			−0.760020	+	0.649900i	$0.774811\pi$
$308$		−	14.9179i		−	0.850025i
$309$		−	1.68338i		−	0.0957639i
$310$	−15.4671	−	3.79936i	−0.878474	−	0.215789i
$311$		−	9.31662i		−	0.528297i	−0.964482	−	0.264149i	$-0.914909\pi$
$311$		−	9.31662i		−	0.528297i	0.964482	−	0.264149i	$-0.0850910\pi$
$312$	−6.63325	−	6.63325i	−0.375534	−	0.375534i
$313$		−	28.7859i		−	1.62708i	−0.581510	−	0.813539i	$-0.697538\pi$
$313$		−	28.7859i		−	1.62708i	0.581510	−	0.813539i	$-0.302462\pi$
$314$	8.86188	+	8.86188i	0.500105	+	0.500105i
$315$	−12.3166	+	7.45894i	−0.693963	+	0.420264i
$316$		−	33.0251i		−	1.85781i
$317$		−	4.58312i		−	0.257414i	−0.991683	−	0.128707i	$-0.958917\pi$
$317$		−	4.58312i		−	0.257414i	0.991683	−	0.128707i	$-0.0410827\pi$
$318$	−13.3166	+	13.3166i	−0.746759	+	0.746759i
$319$	−13.0707			−0.731820
$320$	−9.26650	−	15.3014i	−0.518013	−	0.855373i
$321$	−3.00000			−0.167444
$322$	14.2665	+	14.2665i	0.795041	+	0.795041i
$323$	−0.366750	+	2.61414i	−0.0204065	+	0.145455i
$324$			2.00000i			0.111111i
$325$	14.6958	+	7.68338i	0.815175	+	0.426197i
$326$	−9.05363	+	9.05363i	−0.501434	+	0.501434i
$327$	10.8704			0.601136
$328$	5.22829	+	5.22829i	0.288684	+	0.288684i
$329$	−24.6332			−1.35808
$330$	−7.11432	−	1.74757i	−0.391630	−	0.0962004i
$331$		−	8.25629i		−	0.453806i	−0.973917	−	0.226903i	$-0.927140\pi$
$331$		−	8.25629i		−	0.453806i	0.973917	−	0.226903i	$-0.0728601\pi$
$332$	−12.8790			−0.706826
$333$			13.2665i			0.727000i
$334$	19.5831	−	19.5831i	1.07154	−	1.07154i
$335$	−22.2506	+	13.4749i	−1.21568	+	0.736214i
$336$	−12.8790			−0.702606
$337$	4.94987			0.269637			0.134818	−	0.990870i	$-0.456955\pi$
$337$	4.94987			0.269637			0.134818	+	0.990870i	$0.456955\pi$
$338$	2.00000	+	2.00000i	0.108786	+	0.108786i
$339$	−8.31662			−0.451697
$340$	−2.31662	+	1.40295i	−0.125637	+	0.0760854i
$341$	11.6678			0.631846
$342$	−7.42205	−	9.84445i	−0.401339	−	0.532327i
$343$	−11.6981			−0.631640
$344$	25.3745	+	25.3745i	1.36810	+	1.36810i
$345$	8.47494	−	5.13242i	0.456275	−	0.276320i
$346$	−14.0000	+	14.0000i	−0.752645	+	0.752645i
$347$			30.6027i			1.64284i	0.570323	+	0.821421i	$0.306818\pi$
$347$			30.6027i			1.64284i	−0.570323	+	0.821421i	$0.693182\pi$
$348$			11.2843i			0.604901i
$349$			28.5330i			1.52734i	0.645609	+	0.763668i	$0.276604\pi$
$349$			28.5330i			1.52734i	−0.645609	+	0.763668i	$0.723396\pi$
$350$	21.7254	−	6.80756i	1.16127	−	0.363879i
$351$		−	16.5831i		−	0.885142i
$352$	9.26650	+	9.26650i	0.493906	+	0.493906i
$353$			31.2083i			1.66105i	0.556979	+	0.830526i	$0.311960\pi$
$353$			31.2083i			1.66105i	−0.556979	+	0.830526i	$0.688040\pi$
$354$	−9.46748	+	9.46748i	−0.503191	+	0.503191i
$355$	11.9499	−	7.23683i	0.634233	−	0.384091i
$356$	25.3745			1.34484
$357$			1.94987i			0.103198i
$358$	−22.9521	+	22.9521i	−1.21305	+	1.21305i
$359$		−	2.58312i		−	0.136332i	−0.997674	−	0.0681660i	$-0.978285\pi$
$359$		−	2.58312i		−	0.136332i	0.997674	−	0.0681660i	$-0.0217148\pi$
$360$	3.01744	−	12.2839i	0.159033	−	0.647420i
$361$	18.2665	+	5.22829i	0.961395	+	0.275173i
$362$	14.0902	+	14.0902i	0.740563	+	0.740563i
$363$	−5.63325			−0.295669
$364$	−21.3574			−1.11943
$365$	−8.16041	−	13.4749i	−0.427135	−	0.705310i
$366$	4.31662	−	4.31662i	0.225634	−	0.225634i
$367$	−2.42240			−0.126448			−0.0632240	−	0.997999i	$-0.520138\pi$
$367$	−2.42240			−0.126448			−0.0632240	+	0.997999i	$0.520138\pi$
$368$	−17.7238			−0.923915
$369$			5.22829i			0.272174i
$370$	5.00385	−	20.3706i	0.260138	−	1.05902i
$371$			42.8761i			2.22602i
$372$		−	10.0731i		−	0.522265i
$373$		−	32.5831i		−	1.68709i	−0.537058	−	0.843545i	$-0.680465\pi$
$373$		−	32.5831i		−	1.68709i	0.537058	−	0.843545i	$-0.319535\pi$
$374$	1.40295	−	1.40295i	0.0725446	−	0.0725446i
$375$	−0.701473	−	11.1583i	−0.0362239	−	0.576213i
$376$	15.3014	−	15.3014i	0.789108	−	0.789108i
$377$			18.7129i			0.963762i
$378$	−16.0987	−	16.0987i	−0.828029	−	0.828029i
$379$		−	28.7859i		−	1.47863i	−0.673357	−	0.739317i	$-0.735148\pi$
$379$		−	28.7859i		−	1.47863i	0.673357	−	0.739317i	$-0.264852\pi$
$380$	7.68338	+	17.9155i	0.394149	+	0.919047i
$381$		−	8.00000i		−	0.409852i
$382$	−16.5831	+	16.5831i	−0.848466	+	0.848466i
$383$		−	7.58312i		−	0.387480i	−0.981053	−	0.193740i	$-0.937938\pi$
$383$		−	7.58312i		−	0.387480i	0.981053	−	0.193740i	$-0.0620617\pi$
$384$	8.00000	−	8.00000i	0.408248	−	0.408248i
$385$	−14.2665	+	8.63978i	−0.727088	+	0.440324i
$386$	16.0000	+	16.0000i	0.814379	+	0.814379i
$387$			25.3745i			1.28986i
$388$			4.00000i			0.203069i
$389$		−	3.05013i		−	0.154648i	−0.997006	−	0.0773238i	$-0.975362\pi$
$389$		−	3.05013i		−	0.154648i	0.997006	−	0.0773238i	$-0.0246375\pi$
$390$	−2.50193	+	10.1853i	−0.126690	+	0.515753i
$391$			2.68338i			0.135704i
$392$	−6.73350	+	6.73350i	−0.340093	+	0.340093i
$393$	−6.63325			−0.334603
$394$	16.7043	+	16.7043i	0.841551	+	0.841551i
$395$	−31.5831	+	19.1267i	−1.58912	+	0.962369i
$396$			9.26650i			0.465659i
$397$	−12.8790			−0.646377			−0.323189	−	0.946335i	$-0.604755\pi$
$397$	−12.8790			−0.646377			−0.323189	+	0.946335i	$0.604755\pi$
$398$	−11.9499	+	11.9499i	−0.598993	+	0.598993i
$399$	13.8984	+	1.94987i	0.695792	+	0.0976158i
$400$	−9.26650	+	17.7238i	−0.463325	+	0.886188i
$401$			24.3550i			1.21623i	0.793849	+	0.608115i	$0.208074\pi$
$401$			24.3550i			1.21623i	−0.793849	+	0.608115i	$0.791926\pi$
$402$	−11.6332	−	11.6332i	−0.580214	−	0.580214i
$403$		−	16.7043i		−	0.832101i
$404$	8.63325			0.429520
$405$	1.91267	−	1.15831i	0.0950414	−	0.0575570i
$406$	18.1662	+	18.1662i	0.901576	+	0.901576i
$407$			15.3668i			0.761702i
$408$	−1.21120	−	1.21120i	−0.0599633	−	0.0599633i
$409$			31.6222i			1.56362i	0.623519	+	0.781808i	$0.285703\pi$
$409$			31.6222i			1.56362i	−0.623519	+	0.781808i	$0.714297\pi$
$410$	1.97200	−	8.02800i	0.0973903	−	0.396474i
$411$		−	15.9070i		−	0.784633i
$412$	3.36675			0.165868
$413$			30.4829i			1.49996i
$414$	−8.86188	−	8.86188i	−0.435538	−	0.435538i
$415$	7.45894	+	12.3166i	0.366145	+	0.604599i
$416$	13.2665	−	13.2665i	0.650444	−	0.650444i
$417$		0			0
$418$	−8.59705	−	11.4029i	−0.420496	−	0.557736i
$419$	−7.05013			−0.344421			−0.172211	−	0.985060i	$-0.555091\pi$
$419$	−7.05013			−0.344421			−0.172211	+	0.985060i	$0.555091\pi$
$420$	7.45894	+	12.3166i	0.363959	+	0.600990i
$421$	9.27574			0.452072			0.226036	−	0.974119i	$-0.427423\pi$
$421$	9.27574			0.452072			0.226036	+	0.974119i	$0.427423\pi$
$422$	8.25629	−	8.25629i	0.401910	−	0.401910i
$423$	15.3014			0.743978
$424$	−26.6332	−	26.6332i	−1.29342	−	1.29342i
$425$	2.68338	+	1.40295i	0.130163	+	0.0680529i
$426$	6.24774	+	6.24774i	0.302704	+	0.302704i
$427$		−	13.8984i		−	0.672592i
$428$		−	6.00000i		−	0.290021i
$429$		−	7.68338i		−	0.370957i
$430$	9.57073	−	38.9623i	0.461541	−	1.87893i
$431$	−10.2648			−0.494439			−0.247220	−	0.968959i	$-0.579517\pi$
$431$	−10.2648			−0.494439			−0.247220	+	0.968959i	$0.579517\pi$
$432$	20.0000			0.962250
$433$	−28.3166			−1.36081			−0.680405	−	0.732836i	$-0.738196\pi$
$433$	−28.3166			−1.36081			−0.680405	+	0.732836i	$0.738196\pi$
$434$	−16.2164	−	16.2164i	−0.778411	−	0.778411i
$435$	10.7916	−	6.53536i	0.517416	−	0.313347i
$436$			21.7409i			1.04120i
$437$	19.1267	+	2.68338i	0.914955	+	0.128363i
$438$	7.04509	−	7.04509i	0.336627	−	0.336627i
$439$	30.4110			1.45144			0.725719	−	0.687991i	$-0.241507\pi$
$439$	30.4110			1.45144			0.725719	+	0.687991i	$0.241507\pi$
$440$	3.49513	−	14.2286i	0.166624	−	0.678324i
$441$	−6.73350			−0.320643
$442$	−2.00855	−	2.00855i	−0.0955368	−	0.0955368i
$443$			9.05363i			0.430151i	0.976597	+	0.215076i	$0.0689998\pi$
$443$			9.05363i			0.430151i	−0.976597	+	0.215076i	$0.931000\pi$
$444$	13.2665			0.629600
$445$	−14.6958	−	24.2665i	−0.696646	−	1.15034i
$446$	3.26650	−	3.26650i	0.154673	−	0.154673i
$447$			14.0000i			0.662177i
$448$		−	25.7580i		−	1.21695i
$449$			17.7238i			0.836436i	0.908347	+	0.418218i	$0.137345\pi$
$449$			17.7238i			0.836436i	−0.908347	+	0.418218i	$0.862655\pi$
$450$	−13.4951	+	4.22864i	−0.636167	+	0.199340i
$451$			6.05599i			0.285166i
$452$		−	16.6332i		−	0.782362i
$453$	−7.65069			−0.359461
$454$	−1.63325	−	1.63325i	−0.0766522	−	0.0766522i
$455$	12.3693	+	20.4248i	0.579879	+	0.957530i
$456$	−9.84445	+	7.42205i	−0.461009	+	0.347569i
$457$		−	9.85098i		−	0.460809i	−0.973095	−	0.230405i	$-0.925995\pi$
$457$		−	9.85098i		−	0.460809i	0.973095	−	0.230405i	$-0.0740050\pi$
$458$	−29.8997	+	29.8997i	−1.39712	+	1.39712i
$459$		−	3.02800i		−	0.141335i
$460$	10.2648	+	16.9499i	0.478600	+	0.790292i
$461$			21.5831i			1.00523i	0.864511	+	0.502613i	$0.167628\pi$
$461$			21.5831i			1.00523i	−0.864511	+	0.502613i	$0.832372\pi$
$462$	−7.45894	−	7.45894i	−0.347021	−	0.347021i
$463$	10.0731			0.468136			0.234068	−	0.972220i	$-0.424796\pi$
$463$	10.0731			0.468136			0.234068	+	0.972220i	$0.424796\pi$
$464$	−22.5686			−1.04772
$465$	−9.63325	+	5.83389i	−0.446731	+	0.270540i
$466$	−12.4955	+	12.4955i	−0.578842	+	0.578842i
$467$		−	10.2648i		−	0.475000i	−0.971388	−	0.237500i	$-0.923672\pi$
$467$		−	10.2648i		−	0.475000i	0.971388	−	0.237500i	$-0.0763279\pi$
$468$	13.2665			0.613244
$469$	−37.4561			−1.72956
$470$	−23.4951	−	5.77136i	−1.08375	−	0.266213i
$471$	8.86188			0.408334
$472$	−18.9350	−	18.9350i	−0.871553	−	0.871553i
$473$			29.3915i			1.35142i
$474$	−16.5126	−	16.5126i	−0.758447	−	0.758447i
$475$	12.6834	−	17.7238i	0.581953	−	0.813222i
$476$	−3.89975			−0.178745
$477$		−	26.6332i		−	1.21945i
$478$	−1.94987	+	1.94987i	−0.0891852	+	0.0891852i
$479$			24.0000i			1.09659i	0.836286	+	0.548294i	$0.184723\pi$
$479$			24.0000i			1.09659i	−0.836286	+	0.548294i	$0.815277\pi$
$480$	−12.2839	−	3.01744i	−0.560682	−	0.137727i
$481$	22.0000			1.00311
$482$	16.5126	−	16.5126i	0.752127	−	0.752127i
$483$	14.2665			0.649148
$484$		−	11.2665i		−	0.512114i
$485$	3.82534	−	2.31662i	0.173700	−	0.105193i
$486$	16.0000	+	16.0000i	0.725775	+	0.725775i
$487$			13.3668i			0.605705i	0.953037	+	0.302853i	$0.0979390\pi$
$487$			13.3668i			0.605705i	−0.953037	+	0.302853i	$0.902061\pi$
$488$	8.63325	+	8.63325i	0.390809	+	0.390809i
$489$			9.05363i			0.409419i
$490$	10.3392	+	2.53974i	0.467079	+	0.114734i
$491$	3.58312			0.161704			0.0808521	−	0.996726i	$-0.474236\pi$
$491$	3.58312			0.161704			0.0808521	+	0.996726i	$0.474236\pi$
$492$	5.22829			0.235709
$493$			3.41688i			0.153888i
$494$	−16.3252	+	12.3081i	−0.734504	+	0.553767i
$495$	8.86188	−	5.36675i	0.398312	−	0.241217i
$496$	20.1462			0.904590
$497$	20.1161			0.902331
$498$	−6.43949	+	6.43949i	−0.288560	+	0.288560i
$499$	−21.5831			−0.966193			−0.483097	−	0.875567i	$-0.660488\pi$
$499$	−21.5831			−0.966193			−0.483097	+	0.875567i	$0.660488\pi$
$500$	22.3166	−	1.40295i	0.998030	−	0.0627417i
$501$		−	19.5831i		−	0.874909i
$502$	4.94987	+	4.94987i	0.220924	+	0.220924i
$503$	−23.3659			−1.04183			−0.520917	−	0.853607i	$-0.674410\pi$
$503$	−23.3659			−1.04183			−0.520917	+	0.853607i	$0.674410\pi$
$504$	12.8790	−	12.8790i	0.573675	−	0.573675i
$505$	−5.00000	−	8.25629i	−0.222497	−	0.367400i
$506$	−10.2648	−	10.2648i	−0.456327	−	0.456327i
$507$	2.00000			0.0888231
$508$	16.0000			0.709885
$509$	−16.5126			−0.731907			−0.365953	−	0.930633i	$-0.619257\pi$
$509$	−16.5126			−0.731907			−0.365953	+	0.930633i	$0.619257\pi$
$510$	−0.456839	+	1.85979i	−0.0202292	+	0.0823527i
$511$		−	22.6834i		−	1.00345i
$512$	16.0000	+	16.0000i	0.707107	+	0.707107i
$513$	−21.5831	−	3.02800i	−0.952918	−	0.133689i
$514$	−9.58312	−	9.58312i	−0.422693	−	0.422693i
$515$	−1.94987	−	3.21974i	−0.0859217	−	0.141879i
$516$	25.3745			1.11705
$517$	17.7238			0.779490
$518$	21.3574	−	21.3574i	0.938389	−	0.938389i
$519$			14.0000i			0.614532i
$520$	−20.3706	−	5.00385i	−0.893310	−	0.219433i
$521$			11.2843i			0.494373i	0.968968	+	0.247187i	$0.0795061\pi$
$521$			11.2843i			0.494373i	−0.968968	+	0.247187i	$0.920494\pi$
$522$	−11.2843	−	11.2843i	−0.493900	−	0.493900i
$523$	5.10025			0.223018			0.111509	−	0.993763i	$-0.464432\pi$
$523$	5.10025			0.223018			0.111509	+	0.993763i	$0.464432\pi$
$524$		−	13.2665i		−	0.579550i
$525$	7.45894	−	14.2665i	0.325535	−	0.622641i
$526$	−1.21120	−	1.21120i	−0.0528108	−	0.0528108i
$527$		−	3.05013i		−	0.132866i
$528$	9.26650			0.403273
$529$	−3.36675			−0.146380
$530$	−10.0455	+	40.8951i	−0.436349	+	1.77637i
$531$		−	18.9350i		−	0.821708i
$532$	−3.89975	+	27.7969i	−0.169076	+	1.20515i
$533$	8.67014			0.375545
$534$	12.6872	−	12.6872i	0.549030	−	0.549030i
$535$	−5.73801	+	3.47494i	−0.248076	+	0.150235i
$536$	23.2665	−	23.2665i	1.00496	−	1.00496i
$537$			22.9521i			0.990454i
$538$	27.7969	+	27.7969i	1.19841	+	1.19841i
$539$	−7.79950			−0.335948
$540$	−11.5831	−	19.1267i	−0.498458	−	0.823083i
$541$			14.3166i			0.615520i	0.951464	+	0.307760i	$0.0995793\pi$
$541$			14.3166i			0.615520i	−0.951464	+	0.307760i	$0.900421\pi$
$542$	−9.31662	+	9.31662i	−0.400183	+	0.400183i
$543$	14.0902			0.604667
$544$	2.42240	−	2.42240i	0.103859	−	0.103859i
$545$	20.7916	−	12.5914i	0.890613	−	0.539354i
$546$	−10.6787	+	10.6787i	−0.457005	+	0.457005i
$547$	46.5330			1.98961			0.994804	−	0.101812i	$-0.0324640\pi$
$547$	46.5330			1.98961			0.994804	+	0.101812i	$0.0324640\pi$
$548$	31.8139			1.35902
$549$			8.63325i			0.368458i
$550$	−15.6316	+	4.89808i	−0.666533	+	0.208855i
$551$	24.3550	+	3.41688i	1.03756	+	0.145564i
$552$	−8.86188	+	8.86188i	−0.377187	+	0.377187i
$553$	−53.1662			−2.26086
$554$	−7.65069	−	7.65069i	−0.325047	−	0.325047i
$555$	−7.68338	−	12.6872i	−0.326141	−	0.538543i
$556$		0			0
$557$	−24.1633			−1.02383			−0.511915	−	0.859036i	$-0.671064\pi$
$557$	−24.1633			−1.02383			−0.511915	+	0.859036i	$0.671064\pi$
$558$	10.0731	+	10.0731i	0.426428	+	0.426428i
$559$	42.0788			1.77974
$560$	−24.6332	+	14.9179i	−1.04094	+	0.630395i
$561$		−	1.40295i		−	0.0592324i
$562$	8.67014	−	8.67014i	0.365728	−	0.365728i
$563$	−14.0000			−0.590030			−0.295015	−	0.955493i	$-0.595325\pi$
$563$	−14.0000			−0.590030			−0.295015	+	0.955493i	$0.595325\pi$
$564$		−	15.3014i		−	0.644304i
$565$	−15.9070	+	9.63325i	−0.669211	+	0.405274i
$566$	−11.6678	+	11.6678i	−0.490433	+	0.490433i
$567$	3.21974			0.135217
$568$	−12.4955	+	12.4955i	−0.524299	+	0.524299i
$569$			1.21120i			0.0507761i	0.999678	+	0.0253880i	$0.00808213\pi$
$569$			1.21120i			0.0507761i	−0.999678	+	0.0253880i	$0.991918\pi$
$570$	12.7994	+	5.11607i	0.536110	+	0.214289i
$571$	30.8496			1.29102			0.645508	−	0.763753i	$-0.276646\pi$
$571$	30.8496			1.29102			0.645508	+	0.763753i	$0.276646\pi$
$572$	15.3668			0.642516
$573$			16.5831i			0.692770i
$574$	8.41688	−	8.41688i	0.351314	−	0.351314i
$575$	10.2648	−	19.6332i	0.428073	−	0.818763i
$576$			16.0000i			0.666667i
$577$		−	5.45039i		−	0.226903i	−0.993544	−	0.113451i	$-0.963809\pi$
$577$		−	5.45039i		−	0.226903i	0.993544	−	0.113451i	$-0.0361906\pi$
$578$	16.6332	+	16.6332i	0.691852	+	0.691852i
$579$	16.0000			0.664937
$580$	13.0707	+	21.5831i	0.542732	+	0.896190i
$581$			20.7335i			0.860171i
$582$	2.00000	+	2.00000i	0.0829027	+	0.0829027i
$583$		−	30.8496i		−	1.27766i
$584$	14.0902	+	14.0902i	0.583056	+	0.583056i
$585$	−7.68338	−	12.6872i	−0.317668	−	0.524552i
$586$	−3.31662	+	3.31662i	−0.137009	+	0.137009i
$587$			1.01945i			0.0420772i	0.999779	+	0.0210386i	$0.00669729\pi$
$587$			1.01945i			0.0420772i	−0.999779	+	0.0210386i	$0.993303\pi$
$588$			6.73350i			0.277685i
$589$	−21.7409	−	3.05013i	−0.895817	−	0.125678i
$590$	−7.14188	+	29.0745i	−0.294027	+	1.19698i
$591$	16.7043			0.687124
$592$			26.5330i			1.09050i
$593$		−	37.0422i		−	1.52114i	−0.649255	−	0.760571i	$-0.724919\pi$
$593$		−	37.0422i		−	1.52114i	0.649255	−	0.760571i	$-0.275081\pi$
$594$	11.5831	+	11.5831i	0.475261	+	0.475261i
$595$	2.25856	+	3.72947i	0.0925921	+	0.152893i
$596$	−28.0000			−1.14692
$597$			11.9499i			0.489076i
$598$	−14.6958	+	14.6958i	−0.600955	+	0.600955i
$599$	−2.61414			−0.106811			−0.0534055	−	0.998573i	$-0.517008\pi$
$599$	−2.61414			−0.106811			−0.0534055	+	0.998573i	$0.517008\pi$
$600$	4.22864	+	13.4951i	0.172633	+	0.550937i
$601$			13.8984i			0.566929i	0.958983	+	0.283464i	$0.0914838\pi$
$601$			13.8984i			0.566929i	−0.958983	+	0.283464i	$0.908516\pi$
$602$	40.8496	−	40.8496i	1.66491	−	1.66491i
$603$	23.2665			0.947485
$604$		−	15.3014i		−	0.622604i
$605$	−10.7746	+	6.52506i	−0.438048	+	0.265282i
$606$	4.31662	−	4.31662i	0.175351	−	0.175351i
$607$			16.5330i			0.671054i	0.942031	+	0.335527i	$0.108914\pi$
$607$			16.5330i			0.671054i	−0.942031	+	0.335527i	$0.891086\pi$
$608$	−14.8441	−	19.6889i	−0.602008	−	0.798490i
$609$	18.1662			0.736134
$610$	3.25629	−	13.2563i	0.131843	−	0.536731i
$611$		−	25.3745i		−	1.02654i
$612$	2.42240			0.0979196
$613$	1.40295			0.0566645			0.0283322	−	0.999599i	$-0.490980\pi$
$613$	1.40295			0.0566645			0.0283322	+	0.999599i	$0.490980\pi$
$614$	−26.6332	−	26.6332i	−1.07483	−	1.07483i
$615$	−3.02800	−	5.00000i	−0.122101	−	0.201619i
$616$	14.9179	−	14.9179i	0.601058	−	0.601058i
$617$		−	2.42240i		−	0.0975220i	−0.998810	−	0.0487610i	$-0.984473\pi$
$617$		−	2.42240i		−	0.0975220i	0.998810	−	0.0487610i	$-0.0155273\pi$
$618$	1.68338	−	1.68338i	0.0677153	−	0.0677153i
$619$	31.5831			1.26943			0.634716	−	0.772745i	$-0.281117\pi$
$619$	31.5831			1.26943			0.634716	+	0.772745i	$0.281117\pi$
$620$	−11.6678	−	19.2665i	−0.468589	−	0.773761i
$621$	−22.1547			−0.889038
$622$	9.31662	−	9.31662i	0.373563	−	0.373563i
$623$		−	40.8496i		−	1.63661i
$624$		−	13.2665i		−	0.531085i
$625$	−14.2665	−	20.5297i	−0.570660	−	0.821186i
$626$	28.7859	−	28.7859i	1.15052	−	1.15052i
$627$	−10.0000	−	1.40295i	−0.399362	−	0.0560283i
$628$			17.7238i			0.707255i
$629$	4.01709			0.160172
$630$	−19.7756	−	4.85769i	−0.787877	−	0.193535i
$631$		−	4.10025i		−	0.163228i	−0.996664	−	0.0816142i	$-0.973992\pi$
$631$		−	4.10025i		−	0.163228i	0.996664	−	0.0816142i	$-0.0260075\pi$
$632$	33.0251	−	33.0251i	1.31367	−	1.31367i
$633$		−	8.25629i		−	0.328158i
$634$	4.58312	−	4.58312i	0.182019	−	0.182019i
$635$	−9.26650	−	15.3014i	−0.367730	−	0.607216i
$636$	−26.6332			−1.05608
$637$			11.1662i			0.442423i
$638$	−13.0707	−	13.0707i	−0.517475	−	0.517475i
$639$	−12.4955			−0.494314
$640$	6.03487	−	24.5679i	0.238549	−	0.971130i
$641$		−	30.4110i		−	1.20116i	−0.799564	−	0.600581i	$-0.794936\pi$
$641$		−	30.4110i		−	1.20116i	0.799564	−	0.600581i	$-0.205064\pi$
$642$	−3.00000	−	3.00000i	−0.118401	−	0.118401i
$643$		−	37.0422i		−	1.46080i	−0.683018	−	0.730402i	$-0.739333\pi$
$643$		−	37.0422i		−	1.46080i	0.683018	−	0.730402i	$-0.260667\pi$
$644$			28.5330i			1.12436i
$645$	−14.6958	−	24.2665i	−0.578645	−	0.955492i
$646$	−2.98090	+	2.24739i	−0.117282	+	0.0884225i
$647$	25.7883			1.01384			0.506921	−	0.861992i	$-0.330783\pi$
$647$	25.7883			1.01384			0.506921	+	0.861992i	$0.330783\pi$
$648$	−2.00000	+	2.00000i	−0.0785674	+	0.0785674i
$649$		−	21.9326i		−	0.860930i
$650$	7.01240	+	22.3791i	0.275049	+	0.877782i
$651$	−16.2164			−0.635570
$652$	−18.1073			−0.709135
$653$	10.0731			0.394190			0.197095	−	0.980384i	$-0.436849\pi$
$653$	10.0731			0.394190			0.197095	+	0.980384i	$0.436849\pi$
$654$	10.8704	+	10.8704i	0.425067	+	0.425067i
$655$	−12.6872	+	7.68338i	−0.495731	+	0.300214i
$656$			10.4566i			0.408261i
$657$			14.0902i			0.549710i
$658$	−24.6332	−	24.6332i	−0.960304	−	0.960304i
$659$		−	34.0142i		−	1.32501i	−0.749059	−	0.662503i	$-0.769494\pi$
$659$		−	34.0142i		−	1.32501i	0.749059	−	0.662503i	$-0.230506\pi$
$660$	−5.36675	−	8.86188i	−0.208900	−	0.344948i
$661$	−41.0897			−1.59820			−0.799102	−	0.601196i	$-0.794691\pi$
$661$	−41.0897			−1.59820			−0.799102	+	0.601196i	$0.794691\pi$
$662$	8.25629	−	8.25629i	0.320890	−	0.320890i
$663$	−2.00855			−0.0780054
$664$	−12.8790	−	12.8790i	−0.499801	−	0.499801i
$665$	28.8417	−	12.3693i	1.11843	−	0.479659i
$666$	−13.2665	+	13.2665i	−0.514066	+	0.514066i
$667$	25.0000			0.968004
$668$	39.1662			1.51539
$669$		−	3.26650i		−	0.126290i
$670$	−35.7255	−	8.77565i	−1.38020	−	0.339033i
$671$			10.0000i			0.386046i
$672$	−12.8790	−	12.8790i	−0.496817	−	0.496817i
$673$	−17.1662			−0.661710			−0.330855	−	0.943682i	$-0.607337\pi$
$673$	−17.1662			−0.661710			−0.330855	+	0.943682i	$0.607337\pi$
$674$	4.94987	+	4.94987i	0.190662	+	0.190662i
$675$	−11.5831	+	22.1547i	−0.445835	+	0.852735i
$676$			4.00000i			0.153846i
$677$			5.41688i			0.208187i	0.994567	+	0.104094i	$0.0331942\pi$
$677$			5.41688i			0.208187i	−0.994567	+	0.104094i	$0.966806\pi$
$678$	−8.31662	−	8.31662i	−0.319398	−	0.319398i
$679$	6.43949			0.247125
$680$	−3.71957	−	0.913679i	−0.142639	−	0.0350380i
$681$	−1.63325			−0.0625863
$682$	11.6678	+	11.6678i	0.446782	+	0.446782i
$683$	49.1662			1.88129			0.940647	−	0.339386i	$-0.110219\pi$
$683$	49.1662			1.88129			0.940647	+	0.339386i	$0.110219\pi$
$684$	2.42240	−	17.2665i	0.0926227	−	0.660201i
$685$	−18.4252	−	30.4248i	−0.703992	−	1.16247i
$686$	−11.6981	−	11.6981i	−0.446637	−	0.446637i
$687$			29.8997i			1.14075i
$688$			50.7489i			1.93478i
$689$	−44.1662			−1.68260
$690$	13.6074	+	3.34252i	0.518023	+	0.127248i
$691$	−13.8997			−0.528771			−0.264386	−	0.964417i	$-0.585169\pi$
$691$	−13.8997			−0.528771			−0.264386	+	0.964417i	$0.585169\pi$
$692$	−28.0000			−1.06440
$693$	14.9179			0.566683
$694$	−30.6027	+	30.6027i	−1.16166	+	1.16166i
$695$		0			0
$696$	−11.2843	+	11.2843i	−0.427730	+	0.427730i
$697$	1.58312			0.0599651
$698$	−28.5330	+	28.5330i	−1.07999	+	1.07999i
$699$			12.4955i			0.472622i
$700$	28.5330	+	14.9179i	1.07845	+	0.563843i
$701$		−	22.7335i		−	0.858632i	−0.903154	−	0.429316i	$-0.858755\pi$
$701$		−	22.7335i		−	0.858632i	0.903154	−	0.429316i	$-0.141245\pi$
$702$	16.5831	−	16.5831i	0.625890	−	0.625890i
$703$	4.01709	−	28.6332i	0.151507	−	1.07992i
$704$			18.5330i			0.698489i
$705$	−14.6332	+	8.86188i	−0.551120	+	0.333758i
$706$	−31.2083	+	31.2083i	−1.17454	+	1.17454i
$707$		−	13.8984i		−	0.522704i
$708$	−18.9350			−0.711620
$709$			15.3668i			0.577110i	0.957463	+	0.288555i	$0.0931749\pi$
$709$			15.3668i			0.577110i	−0.957463	+	0.288555i	$0.906825\pi$
$710$	19.1867	+	4.71304i	0.720064	+	0.176877i
$711$	33.0251			1.23854
$712$	25.3745	+	25.3745i	0.950948	+	0.950948i
$713$	−22.3166			−0.835764
$714$	−1.94987	+	1.94987i	−0.0729722	+	0.0729722i
$715$	−8.89975	−	14.6958i	−0.332832	−	0.549591i
$716$	−45.9041			−1.71552
$717$			1.94987i			0.0728194i
$718$	2.58312	−	2.58312i	0.0964013	−	0.0964013i
$719$			10.5831i			0.394684i	0.980335	+	0.197342i	$0.0632309\pi$
$719$			10.5831i			0.394684i	−0.980335	+	0.197342i	$0.936769\pi$
$720$	15.3014	−	9.26650i	0.570248	−	0.345342i
$721$		−	5.42004i		−	0.201853i
$722$	13.0382	+	23.4948i	0.485232	+	0.874385i
$723$		−	16.5126i		−	0.614109i
$724$			28.1803i			1.04731i
$725$	13.0707	−	25.0000i	0.485434	−	0.928477i
$726$	−5.63325	−	5.63325i	−0.209070	−	0.209070i
$727$	−2.00855			−0.0744928			−0.0372464	−	0.999306i	$-0.511859\pi$
$727$	−2.00855			−0.0744928			−0.0372464	+	0.999306i	$0.511859\pi$
$728$	−21.3574	−	21.3574i	−0.791557	−	0.791557i
$729$	13.0000			0.481481
$730$	5.31453	−	21.6353i	0.196699	−	0.800760i
$731$	7.68338			0.284180
$732$	8.63325			0.319094
$733$	−34.2363			−1.26455			−0.632274	−	0.774745i	$-0.717878\pi$
$733$	−34.2363			−1.26455			−0.632274	+	0.774745i	$0.717878\pi$
$734$	−2.42240	−	2.42240i	−0.0894123	−	0.0894123i
$735$	6.43949	−	3.89975i	0.237524	−	0.143844i
$736$	−17.7238	−	17.7238i	−0.653307	−	0.653307i
$737$	26.9499			0.992711
$738$	−5.22829	+	5.22829i	−0.192456	+	0.192456i
$739$	−20.2164			−0.743671			−0.371836	−	0.928299i	$-0.621272\pi$
$739$	−20.2164			−0.743671			−0.371836	+	0.928299i	$0.621272\pi$
$740$	25.3745	−	15.3668i	0.932784	−	0.564893i
$741$	−2.00855	+	14.3166i	−0.0737858	+	0.525934i
$742$	−42.8761	+	42.8761i	−1.57403	+	1.57403i
$743$			5.58312i			0.204825i	0.994742	+	0.102412i	$0.0326562\pi$
$743$			5.58312i			0.204825i	−0.994742	+	0.102412i	$0.967344\pi$
$744$	10.0731	−	10.0731i	0.369297	−	0.369297i
$745$	16.2164	+	26.7774i	0.594122	+	0.981048i
$746$	32.5831	−	32.5831i	1.19295	−	1.19295i
$747$		−	12.8790i		−	0.471217i
$748$	2.80589			0.102594
$749$	−9.65923			−0.352941
$750$	10.4568	−	11.8598i	0.381830	−	0.433058i
$751$	−26.7774			−0.977121			−0.488561	−	0.872530i	$-0.662478\pi$
$751$	−26.7774			−0.977121			−0.488561	+	0.872530i	$0.662478\pi$
$752$	30.6027			1.11597
$753$	4.94987			0.180383
$754$	−18.7129	+	18.7129i	−0.681482	+	0.681482i
$755$	−14.6332	+	8.86188i	−0.532558	+	0.322517i
$756$		−	32.1974i		−	1.17101i
$757$	−18.1073			−0.658120			−0.329060	−	0.944309i	$-0.606732\pi$
$757$	−18.1073			−0.658120			−0.329060	+	0.944309i	$0.606732\pi$
$758$	28.7859	−	28.7859i	1.04555	−	1.04555i
$759$	−10.2648			−0.372590
$760$	−10.2321	+	25.5989i	−0.371159	+	0.928569i
$761$	24.2665			0.879660			0.439830	−	0.898081i	$-0.355039\pi$
$761$	24.2665			0.879660			0.439830	+	0.898081i	$0.355039\pi$
$762$	8.00000	−	8.00000i	0.289809	−	0.289809i
$763$	35.0000			1.26709
$764$	−33.1662			−1.19991
$765$	−1.40295	−	2.31662i	−0.0507236	−	0.0837577i
$766$	7.58312	−	7.58312i	0.273989	−	0.273989i
$767$	−31.4001			−1.13379
$768$	16.0000			0.577350
$769$	48.1662			1.73692			0.868460	−	0.495760i	$-0.165110\pi$
$769$	48.1662			1.73692			0.868460	+	0.495760i	$0.165110\pi$
$770$	−22.9063	−	5.62672i	−0.825485	−	0.202773i
$771$	−9.58312			−0.345128
$772$			32.0000i			1.15171i
$773$		−	6.68338i		−	0.240384i	−0.992751	−	0.120192i	$-0.961649\pi$
$773$		−	6.68338i		−	0.240384i	0.992751	−	0.120192i	$-0.0383511\pi$
$774$	−25.3745	+	25.3745i	−0.912066	+	0.912066i
$775$	−11.6678	+	22.3166i	−0.419119	+	0.801637i
$776$	−4.00000	+	4.00000i	−0.143592	+	0.143592i
$777$		−	21.3574i		−	0.766191i
$778$	3.05013	−	3.05013i	0.109352	−	0.109352i
$779$	1.58312	−	11.2843i	0.0567213	−	0.404301i
$780$	−12.6872	+	7.68338i	−0.454276	+	0.275109i
$781$	−14.4737			−0.517909
$782$	−2.68338	+	2.68338i	−0.0959573	+	0.0959573i
$783$	−28.2107			−1.00817
$784$	−13.4670			−0.480964
$785$	16.9499	−	10.2648i	0.604967	−	0.366368i
$786$	−6.63325	−	6.63325i	−0.236600	−	0.236600i
$787$	11.5330			0.411107			0.205553	−	0.978646i	$-0.434101\pi$
$787$	11.5330			0.411107			0.205553	+	0.978646i	$0.434101\pi$
$788$			33.4086i			1.19013i
$789$	−1.21120			−0.0431198
$790$	−50.7098	−	12.4564i	−1.80418	−	0.443179i
$791$	−26.7774			−0.952095
$792$	−9.26650	+	9.26650i	−0.329271	+	0.329271i
$793$	14.3166			0.508398
$794$	−12.8790	−	12.8790i	−0.457058	−	0.457058i
$795$	15.4248	+	25.4703i	0.547062	+	0.903339i
$796$	−23.8997			−0.847104
$797$		−	33.2164i		−	1.17658i	−0.808648	−	0.588292i	$-0.799801\pi$
$797$		−	33.2164i		−	1.17658i	0.808648	−	0.588292i	$-0.200199\pi$
$798$	11.9486	+	15.8483i	0.422974	+	0.561024i
$799$		−	4.63325i		−	0.163913i
$800$	−26.9903	+	8.45727i	−0.954250	+	0.299010i
$801$			25.3745i			0.896562i
$802$	−24.3550	+	24.3550i	−0.860005	+	0.860005i
$803$			16.3208i			0.575949i
$804$		−	23.2665i		−	0.820546i
$805$	27.2871	−	16.5251i	0.961745	−	0.582432i
$806$	16.7043	−	16.7043i	0.588385	−	0.588385i
$807$	27.7969			0.978496
$808$	8.63325	+	8.63325i	0.303717	+	0.303717i
$809$	−26.7995			−0.942220			−0.471110	−	0.882074i	$-0.656147\pi$
$809$	−26.7995			−0.942220			−0.471110	+	0.882074i	$0.656147\pi$
$810$	3.07098	+	0.754359i	0.107903	+	0.0265055i
$811$			2.20029i			0.0772627i	0.999254	+	0.0386314i	$0.0122998\pi$
$811$			2.20029i			0.0772627i	−0.999254	+	0.0386314i	$0.987700\pi$
$812$			36.3325i			1.27502i
$813$			9.31662i			0.326748i
$814$	−15.3668	+	15.3668i	−0.538604	+	0.538604i
$815$	10.4869	+	17.3166i	0.367341	+	0.606575i
$816$		−	2.42240i		−	0.0848009i
$817$	7.68338	−	54.7660i	0.268807	−	1.91602i
$818$	−31.6222	+	31.6222i	−1.10564	+	1.10564i
$819$		−	21.3574i		−	0.746287i
$820$	10.0000	−	6.05599i	0.349215	−	0.211484i
$821$			43.1662i			1.50651i	0.657727	+	0.753256i	$0.271518\pi$
$821$			43.1662i			1.50651i	−0.657727	+	0.753256i	$0.728482\pi$
$822$	15.9070	−	15.9070i	0.554819	−	0.554819i
$823$	−18.1376			−0.632238			−0.316119	−	0.948720i	$-0.602380\pi$
$823$	−18.1376			−0.632238			−0.316119	+	0.948720i	$0.602380\pi$
$824$	3.36675	+	3.36675i	0.117286	+	0.117286i
$825$	−5.36675	+	10.2648i	−0.186846	+	0.357376i
$826$	−30.4829	+	30.4829i	−1.06063	+	1.06063i
$827$	−36.1662			−1.25762			−0.628812	−	0.777558i	$-0.716458\pi$
$827$	−36.1662			−1.25762			−0.628812	+	0.777558i	$0.716458\pi$
$828$		−	17.7238i		−	0.615944i
$829$	−10.8704			−0.377546			−0.188773	−	0.982021i	$-0.560451\pi$
$829$	−10.8704			−0.377546			−0.188773	+	0.982021i	$0.560451\pi$
$830$	−4.85769	+	19.7756i	−0.168613	+	0.686420i
$831$	−7.65069			−0.265399
$832$	26.5330			0.919866
$833$			2.03890i			0.0706437i
$834$		0			0
$835$	−22.6834	−	37.4561i	−0.784991	−	1.29622i
$836$	2.80589	−	20.0000i	0.0970438	−	0.691714i
$837$	25.1827			0.870442
$838$	−7.05013	−	7.05013i	−0.243543	−	0.243543i
$839$	−21.7409			−0.750578			−0.375289	−	0.926908i	$-0.622457\pi$
$839$	−21.7409			−0.750578			−0.375289	+	0.926908i	$0.622457\pi$
$840$	−4.85769	+	19.7756i	−0.167606	+	0.682322i
$841$	2.83375			0.0977156
$842$	9.27574	+	9.27574i	0.319663	+	0.319663i
$843$		−	8.67014i		−	0.298615i
$844$	16.5126			0.568386
$845$	3.82534	−	2.31662i	0.131596	−	0.0796943i
$846$	15.3014	+	15.3014i	0.526072	+	0.526072i
$847$	−18.1376			−0.623216
$848$		−	53.2665i		−	1.82918i
$849$			11.6678i			0.400437i
$850$	1.28043	+	4.08632i	0.0439184	+	0.140160i
$851$		−	29.3915i		−	1.00753i
$852$			12.4955i			0.428088i
$853$	21.3574			0.731262			0.365631	−	0.930760i	$-0.380853\pi$
$853$	21.3574			0.731262			0.365631	+	0.930760i	$0.380853\pi$
$854$	13.8984	−	13.8984i	0.475594	−	0.475594i
$855$	−17.9155	+	7.68338i	−0.612698	+	0.262766i
$856$	6.00000	−	6.00000i	0.205076	−	0.205076i
$857$	23.3668			0.798193			0.399096	−	0.916909i	$-0.369324\pi$
$857$	23.3668			0.798193			0.399096	+	0.916909i	$0.369324\pi$
$858$	7.68338	−	7.68338i	0.262306	−	0.262306i
$859$	32.9499			1.12424			0.562118	−	0.827057i	$-0.309987\pi$
$859$	32.9499			1.12424			0.562118	+	0.827057i	$0.309987\pi$
$860$	48.5330	−	29.3915i	1.65496	−	1.00224i
$861$		−	8.41688i		−	0.286846i
$862$	−10.2648	−	10.2648i	−0.349622	−	0.349622i
$863$			28.3166i			0.963909i	0.876196	+	0.481955i	$0.160073\pi$
$863$			28.3166i			0.963909i	−0.876196	+	0.481955i	$0.839927\pi$
$864$	20.0000	+	20.0000i	0.680414	+	0.680414i
$865$	16.2164	+	26.7774i	0.551373	+	0.910459i
$866$	−28.3166	−	28.3166i	−0.962238	−	0.962238i
$867$	16.6332			0.564895
$868$		−	32.4327i		−	1.10084i
$869$	38.2534			1.29766
$870$	17.3269	+	4.25620i	0.587438	+	0.144299i
$871$		−	38.5831i		−	1.30734i
$872$	−21.7409	+	21.7409i	−0.736238	+	0.736238i
$873$	−4.00000			−0.135379
$874$	16.4433	+	21.8101i	0.556204	+	0.737737i
$875$	−2.25856	−	35.9269i	−0.0763534	−	1.21455i
$876$	14.0902			0.476063
$877$		−	0.0501256i		−	0.00169262i	−1.00000		0.000846311i	$-0.999731\pi$
$877$		−	0.0501256i		−	0.00169262i	1.00000		0.000846311i	$-0.000269389\pi$
$878$	30.4110	+	30.4110i	1.02632	+	1.02632i
$879$			3.31662i			0.111867i
$880$	17.7238	−	10.7335i	0.597468	−	0.361826i
$881$	−33.8997			−1.14211			−0.571056	−	0.820911i	$-0.693466\pi$
$881$	−33.8997			−1.14211			−0.571056	+	0.820911i	$0.693466\pi$
$882$	−6.73350	−	6.73350i	−0.226729	−	0.226729i
$883$		−	30.9862i		−	1.04277i	−0.853322	−	0.521385i	$-0.825416\pi$
$883$		−	30.9862i		−	1.04277i	0.853322	−	0.521385i	$-0.174584\pi$
$884$		−	4.01709i		−	0.135109i
$885$	10.9663	+	18.1082i	0.368628	+	0.608700i
$886$	−9.05363	+	9.05363i	−0.304163	+	0.304163i
$887$			24.9499i			0.837735i	0.908047	+	0.418867i	$0.137573\pi$
$887$			24.9499i			0.837735i	−0.908047	+	0.418867i	$0.862427\pi$
$888$	13.2665	+	13.2665i	0.445195	+	0.445195i
$889$		−	25.7580i		−	0.863894i
$890$	9.57073	−	38.9623i	0.320811	−	1.30602i
$891$	−2.31662			−0.0776099
$892$	6.53300			0.218741
$893$	−33.0251	−	4.63325i	−1.10514	−	0.155046i
$894$	−14.0000	+	14.0000i	−0.468230	+	0.468230i
$895$	26.5857	+	43.8997i	0.888660	+	1.46741i
$896$	25.7580	−	25.7580i	0.860513	−	0.860513i
$897$			14.6958i			0.490678i
$898$	−17.7238	+	17.7238i	−0.591450	+	0.591450i
$899$	−28.4169			−0.947756
$900$	−17.7238	−	9.26650i	−0.590792	−	0.308883i
$901$	−8.06454			−0.268669
$902$	−6.05599	+	6.05599i	−0.201642	+	0.201642i
$903$		−	40.8496i		−	1.35939i
$904$	16.6332	−	16.6332i	0.553214	−	0.553214i
$905$	26.9499	−	16.3208i	0.895844	−	0.542523i
$906$	−7.65069	−	7.65069i	−0.254177	−	0.254177i
$907$	−26.1662			−0.868836			−0.434418	−	0.900711i	$-0.643046\pi$
$907$	−26.1662			−0.868836			−0.434418	+	0.900711i	$0.643046\pi$
$908$		−	3.26650i		−	0.108403i
$909$			8.63325i			0.286347i
$910$	−8.05556	+	32.7941i	−0.267039	+	1.08711i
$911$	−6.82298			−0.226056			−0.113028	−	0.993592i	$-0.536055\pi$
$911$	−6.82298			−0.226056			−0.113028	+	0.993592i	$0.536055\pi$
$912$	−17.2665	−	2.42240i	−0.571751	−	0.0802136i
$913$		−	14.9179i		−	0.493710i
$914$	9.85098	−	9.85098i	0.325841	−	0.325841i
$915$	−5.00000	−	8.25629i	−0.165295	−	0.272944i
$916$	−59.7995			−1.97583
$917$	−21.3574			−0.705282
$918$	3.02800	−	3.02800i	0.0999388	−	0.0999388i
$919$		−	41.2164i		−	1.35960i	−0.733396	−	0.679801i	$-0.762066\pi$
$919$		−	41.2164i		−	1.35960i	0.733396	−	0.679801i	$-0.237934\pi$
$920$	−6.68504	+	27.2147i	−0.220399	+	0.897242i
$921$	−26.6332			−0.877595
$922$	−21.5831	+	21.5831i	−0.710802	+	0.710802i
$923$			20.7214i			0.682053i
$924$		−	14.9179i		−	0.490762i
$925$	−29.3915	−	15.3668i	−0.966388	−	0.505256i
$926$	10.0731	+	10.0731i	0.331022	+	0.331022i
$927$			3.36675i			0.110579i
$928$	−22.5686	−	22.5686i	−0.740849	−	0.740849i
$929$	33.6332			1.10347			0.551736	−	0.834019i	$-0.313966\pi$
$929$	33.6332			1.10347			0.551736	+	0.834019i	$0.313966\pi$
$930$	−15.4671	−	3.79936i	−0.507187	−	0.124586i
$931$	14.5330	+	2.03890i	0.476300	+	0.0668223i
$932$	−24.9910			−0.818606
$933$		−	9.31662i		−	0.305013i
$934$	10.2648	−	10.2648i	0.335876	−	0.335876i
$935$	−1.62505	−	2.68338i	−0.0531448	−	0.0877558i
$936$	13.2665	+	13.2665i	0.433629	+	0.433629i
$937$		−	16.7347i		−	0.546698i	−0.961915	−	0.273349i	$-0.911869\pi$
$937$		−	16.7347i		−	0.546698i	0.961915	−	0.273349i	$-0.0881314\pi$
$938$	−37.4561	−	37.4561i	−1.22298	−	1.22298i
$939$		−	28.7859i		−	0.939394i
$940$	−17.7238	−	29.2665i	−0.578086	−	0.954568i
$941$	57.9857			1.89028			0.945141	−	0.326664i	$-0.105924\pi$
$941$	57.9857			1.89028			0.945141	+	0.326664i	$0.105924\pi$
$942$	8.86188	+	8.86188i	0.288736	+	0.288736i
$943$		−	11.5831i		−	0.377198i
$944$		−	37.8699i		−	1.23256i
$945$	−30.7916	+	18.6473i	−1.00165	+	0.606598i
$946$	−29.3915	+	29.3915i	−0.955602	+	0.955602i
$947$		−	18.9350i		−	0.615304i	−0.951499	−	0.307652i	$-0.900457\pi$
$947$		−	18.9350i		−	0.615304i	0.951499	−	0.307652i	$-0.0995432\pi$
$948$		−	33.0251i		−	1.07261i
$949$	23.3659			0.758490
$950$	30.4071	−	5.04039i	0.986538	−	0.163532i
$951$		−	4.58312i		−	0.148618i
$952$	−3.89975	−	3.89975i	−0.126392	−	0.126392i
$953$	−8.31662			−0.269402			−0.134701	−	0.990886i	$-0.543007\pi$
$953$	−8.31662			−0.269402			−0.134701	+	0.990886i	$0.543007\pi$
$954$	26.6332	−	26.6332i	0.862283	−	0.862283i
$955$	19.2084	+	31.7181i	0.621570	+	1.02637i
$956$	−3.89975			−0.126127
$957$	−13.0707			−0.422516
$958$	−24.0000	+	24.0000i	−0.775405	+	0.775405i
$959$		−	51.2164i		−	1.65386i
$960$	−9.26650	−	15.3014i	−0.299075	−	0.493850i
$961$	−5.63325			−0.181718
$962$	22.0000	+	22.0000i	0.709308	+	0.709308i
$963$	6.00000			0.193347
$964$	33.0251			1.06367
$965$	30.6027	−	18.5330i	0.985137	−	0.596598i
$966$	14.2665	+	14.2665i	0.459017	+	0.459017i
$967$	30.6027			0.984118			0.492059	−	0.870562i	$-0.336244\pi$
$967$	30.6027			0.984118			0.492059	+	0.870562i	$0.336244\pi$
$968$	11.2665	−	11.2665i	0.362119	−	0.362119i
$969$	−0.366750	+	2.61414i	−0.0117817	+	0.0839784i
$970$	6.14197	+	1.50872i	0.197207	+	0.0484420i
$971$		−	32.1974i		−	1.03326i	−0.856207	−	0.516632i	$-0.827185\pi$
$971$		−	32.1974i		−	1.03326i	0.856207	−	0.516632i	$-0.172815\pi$
$972$			32.0000i			1.02640i
$973$		0			0
$974$	−13.3668	+	13.3668i	−0.428298	+	0.428298i
$975$	14.6958	+	7.68338i	0.470641	+	0.246065i
$976$			17.2665i			0.552687i
$977$	−28.2164			−0.902722			−0.451361	−	0.892342i	$-0.649061\pi$
$977$	−28.2164			−0.902722			−0.451361	+	0.892342i	$0.649061\pi$
$978$	−9.05363	+	9.05363i	−0.289503	+	0.289503i
$979$			29.3915i			0.939358i
$980$	7.79950	+	12.8790i	0.249146	+	0.411404i
$981$	−21.7409			−0.694132
$982$	3.58312	+	3.58312i	0.114342	+	0.114342i
$983$		−	13.2665i		−	0.423136i	−0.977363	−	0.211568i	$-0.932143\pi$
$983$		−	13.2665i		−	0.423136i	0.977363	−	0.211568i	$-0.0678569\pi$
$984$	5.22829	+	5.22829i	0.166672	+	0.166672i
$985$	31.9499	−	19.3488i	1.01801	−	0.616505i
$986$	−3.41688	+	3.41688i	−0.108816	+	0.108816i
$987$	−24.6332			−0.784085
$988$	−28.6332	−	4.01709i	−0.910945	−	0.127801i
$989$		−	56.2164i		−	1.78758i
$990$	14.2286	+	3.49513i	0.452216	+	0.111083i
$991$	21.9326			0.696712			0.348356	−	0.937362i	$-0.386740\pi$
$991$	21.9326			0.696712			0.348356	+	0.937362i	$0.386740\pi$
$992$	20.1462	+	20.1462i	0.639641	+	0.639641i
$993$		−	8.25629i		−	0.262005i
$994$	20.1161	+	20.1161i	0.638045	+	0.638045i
$995$	13.8417	+	22.8562i	0.438811	+	0.724590i
$996$	−12.8790			−0.408086
$997$	38.4452			1.21757			0.608786	−	0.793335i	$-0.291657\pi$
$997$	38.4452			1.21757			0.608786	+	0.793335i	$0.291657\pi$
$998$	−21.5831	−	21.5831i	−0.683202	−	0.683202i
$999$			33.1662i			1.04933i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	760.2.p.g.379.8	yes	8
5.4	even	2		760.2.p.d.379.1	✓	8
8.3	odd	2	inner	760.2.p.g.379.1	yes	8
19.18	odd	2		760.2.p.d.379.4	yes	8
40.19	odd	2		760.2.p.d.379.8	yes	8
95.94	odd	2	inner	760.2.p.g.379.5	yes	8
152.75	even	2		760.2.p.d.379.5	yes	8
760.379	even	2	inner	760.2.p.g.379.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
760.2.p.d.379.1	✓	8	5.4	even	2
760.2.p.d.379.4	yes	8	19.18	odd	2
760.2.p.d.379.5	yes	8	152.75	even	2
760.2.p.d.379.8	yes	8	40.19	odd	2
760.2.p.g.379.1	yes	8	8.3	odd	2	inner
760.2.p.g.379.4	yes	8	760.379	even	2	inner
760.2.p.g.379.5	yes	8	95.94	odd	2	inner
760.2.p.g.379.8	yes	8	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 760 = 2^{3} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	760.p (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +1.00000 q^{3} +2.00000i q^{4} +(1.91267 - 1.15831i) q^{5} +(1.00000 + 1.00000i) q^{6} +3.21974 q^{7} +(-2.00000 + 2.00000i) q^{8} -2.00000 q^{9} +(3.07098 + 0.754359i) q^{10} -2.31662 q^{11} +2.00000i q^{12} +3.31662i q^{13} +(3.21974 + 3.21974i) q^{14} +(1.91267 - 1.15831i) q^{15} -4.00000 q^{16} +0.605599i q^{17} +(-2.00000 - 2.00000i) q^{18} +(4.31662 + 0.605599i) q^{19} +(2.31662 + 3.82534i) q^{20} +3.21974 q^{21} +(-2.31662 - 2.31662i) q^{22} +4.43094 q^{23} +(-2.00000 + 2.00000i) q^{24} +(2.31662 - 4.43094i) q^{25} +(-3.31662 + 3.31662i) q^{26} -5.00000 q^{27} +6.43949i q^{28} +5.64214 q^{29} +(3.07098 + 0.754359i) q^{30} -5.03654 q^{31} +(-4.00000 - 4.00000i) q^{32} -2.31662 q^{33} +(-0.605599 + 0.605599i) q^{34} +(6.15831 - 3.72947i) q^{35} -4.00000i q^{36} -6.63325i q^{37} +(3.71103 + 4.92222i) q^{38} +3.31662i q^{39} +(-1.50872 + 6.14197i) q^{40} -2.61414i q^{41} +(3.21974 + 3.21974i) q^{42} -12.6872i q^{43} -4.63325i q^{44} +(-3.82534 + 2.31662i) q^{45} +(4.43094 + 4.43094i) q^{46} -7.65069 q^{47} -4.00000 q^{48} +3.36675 q^{49} +(6.74757 - 2.11432i) q^{50} +0.605599i q^{51} -6.63325 q^{52} +13.3166i q^{53} +(-5.00000 - 5.00000i) q^{54} +(-4.43094 + 2.68338i) q^{55} +(-6.43949 + 6.43949i) q^{56} +(4.31662 + 0.605599i) q^{57} +(5.64214 + 5.64214i) q^{58} +9.46748i q^{59} +(2.31662 + 3.82534i) q^{60} -4.31662i q^{61} +(-5.03654 - 5.03654i) q^{62} -6.43949 q^{63} -8.00000i q^{64} +(3.84169 + 6.34361i) q^{65} +(-2.31662 - 2.31662i) q^{66} -11.6332 q^{67} -1.21120 q^{68} +4.43094 q^{69} +(9.88778 + 2.42884i) q^{70} +6.24774 q^{71} +(4.00000 - 4.00000i) q^{72} -7.04509i q^{73} +(6.63325 - 6.63325i) q^{74} +(2.31662 - 4.43094i) q^{75} +(-1.21120 + 8.63325i) q^{76} -7.45894 q^{77} +(-3.31662 + 3.31662i) q^{78} -16.5126 q^{79} +(-7.65069 + 4.63325i) q^{80} +1.00000 q^{81} +(2.61414 - 2.61414i) q^{82} +6.43949i q^{83} +6.43949i q^{84} +(0.701473 + 1.15831i) q^{85} +(12.6872 - 12.6872i) q^{86} +5.64214 q^{87} +(4.63325 - 4.63325i) q^{88} -12.6872i q^{89} +(-6.14197 - 1.50872i) q^{90} +10.6787i q^{91} +8.86188i q^{92} -5.03654 q^{93} +(-7.65069 - 7.65069i) q^{94} +(8.95776 - 3.84169i) q^{95} +(-4.00000 - 4.00000i) q^{96} +2.00000 q^{97} +(3.36675 + 3.36675i) q^{98} +4.63325 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{6} - 16 q^{8} - 16 q^{9} - 4 q^{10} + 8 q^{11} - 32 q^{16} - 16 q^{18} + 8 q^{19} - 8 q^{20} + 8 q^{22} - 16 q^{24} - 8 q^{25} - 40 q^{27} - 4 q^{30} - 32 q^{32} + 8 q^{33}+ \cdots - 16 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^6 - 16 * q^8 - 16 * q^9 - 4 * q^10 + 8 * q^11 - 32 * q^16 - 16 * q^18 + 8 * q^19 - 8 * q^20 + 8 * q^22 - 16 * q^24 - 8 * q^25 - 40 * q^27 - 4 * q^30 - 32 * q^32 + 8 * q^33 + 36 * q^35 + 8 * q^38 - 8 * q^40 - 32 * q^48 + 80 * q^49 - 8 * q^50 - 40 * q^54 + 8 * q^57 - 8 * q^60 + 44 * q^65 + 8 * q^66 - 40 * q^67 + 36 * q^70 + 32 * q^72 - 8 * q^75 + 8 * q^81 - 16 * q^88 + 8 * q^90 - 32 * q^96 + 16 * q^97 + 80 * q^98 - 16 * q^99

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