LMFDB - Embedded newform 1274.2.m.g.491.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1274,2,Mod(491,1274)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1274, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1274.491"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1274 = 2 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1274.m (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,2,10,0,0,0,0,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$10.1729412175$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 46 x^{18} + 895 x^{16} + 9634 x^{14} + 62977 x^{12} + 257850 x^{10} + 656102 x^{8} + \cdots + 32041 $ x^20 + 46x^18 + 895x^16 + 9634x^14 + 62977x^12 + 257850x^10 + 656102x^8 + 989866x^6 + 795896x^4 + 273668*x^2 + 32041
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			491.5
Root			$-2.49593i$ of defining polynomial
Character	$\chi$	$=$	1274.491
Dual form			1274.2.m.g.589.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(1.24796 + 2.16154i) q^{3} +(0.500000 - 0.866025i) q^{4} +2.78680i q^{5} +(-2.16154 - 1.24796i) q^{6} +1.00000i q^{8} +(-1.61483 + 2.79697i) q^{9} +(-1.39340 - 2.41344i) q^{10} +(3.26564 - 1.88542i) q^{11} +2.49593 q^{12} +(3.40109 + 1.19690i) q^{13} +(-6.02377 + 3.47782i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.50662 + 4.34160i) q^{17} -3.22966i q^{18} +(2.68042 + 1.54754i) q^{19} +(2.41344 + 1.39340i) q^{20} +(-1.88542 + 3.26564i) q^{22} +(0.0487130 + 0.0843734i) q^{23} +(-2.16154 + 1.24796i) q^{24} -2.76624 q^{25} +(-3.54388 + 0.664005i) q^{26} -0.573226 q^{27} +(-1.34957 - 2.33752i) q^{29} +(3.47782 - 6.02377i) q^{30} +8.24042i q^{31} +(0.866025 + 0.500000i) q^{32} +(8.15081 + 4.70587i) q^{33} -5.01324i q^{34} +(1.61483 + 2.79697i) q^{36} +(0.424045 - 0.244823i) q^{37} -3.09508 q^{38} +(1.65731 + 8.84528i) q^{39} -2.78680 q^{40} +(-8.29797 + 4.79084i) q^{41} +(0.642640 - 1.11309i) q^{43} -3.77084i q^{44} +(-7.79459 - 4.50021i) q^{45} +(-0.0843734 - 0.0487130i) q^{46} -9.86141i q^{47} +(1.24796 - 2.16154i) q^{48} +(2.39563 - 1.38312i) q^{50} -12.5127 q^{51} +(2.73709 - 2.34699i) q^{52} -10.2775 q^{53} +(0.496428 - 0.286613i) q^{54} +(5.25428 + 9.10068i) q^{55} +7.72510i q^{57} +(2.33752 + 1.34957i) q^{58} +(-4.70984 - 2.71923i) q^{59} +6.95565i q^{60} +(1.31592 - 2.27924i) q^{61} +(-4.12021 - 7.13641i) q^{62} -1.00000 q^{64} +(-3.33551 + 9.47816i) q^{65} -9.41175 q^{66} +(7.32268 - 4.22775i) q^{67} +(2.50662 + 4.34160i) q^{68} +(-0.121584 + 0.210590i) q^{69} +(-5.07078 - 2.92762i) q^{71} +(-2.79697 - 1.61483i) q^{72} -15.3226i q^{73} +(-0.244823 + 0.424045i) q^{74} +(-3.45217 - 5.97933i) q^{75} +(2.68042 - 1.54754i) q^{76} +(-5.85791 - 6.83158i) q^{78} +11.1089 q^{79} +(2.41344 - 1.39340i) q^{80} +(4.12913 + 7.15186i) q^{81} +(4.79084 - 8.29797i) q^{82} -16.0283i q^{83} +(-12.0992 - 6.98545i) q^{85} +1.28528i q^{86} +(3.36843 - 5.83429i) q^{87} +(1.88542 + 3.26564i) q^{88} +(12.4082 - 7.16387i) q^{89} +9.00042 q^{90} +0.0974260 q^{92} +(-17.8120 + 10.2837i) q^{93} +(4.93071 + 8.54023i) q^{94} +(-4.31268 + 7.46978i) q^{95} +2.49593i q^{96} +(5.50865 + 3.18042i) q^{97} +12.1785i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{3} + 10 q^{4} - 16 q^{9} - 4 q^{10} + 6 q^{11} + 4 q^{12} + 6 q^{13} - 12 q^{15} - 10 q^{16} - 10 q^{17} + 24 q^{19} + 2 q^{22} - 36 q^{25} - 28 q^{27} + 2 q^{29} - 2 q^{30} - 12 q^{33} + 16 q^{36}+ \cdots + 78 q^{97}+O(q^{100}) $ 20 * q + 2 * q^3 + 10 * q^4 - 16 * q^9 - 4 * q^10 + 6 * q^11 + 4 * q^12 + 6 * q^13 - 12 * q^15 - 10 * q^16 - 10 * q^17 + 24 * q^19 + 2 * q^22 - 36 * q^25 - 28 * q^27 + 2 * q^29 - 2 * q^30 - 12 * q^33 + 16 * q^36 + 36 * q^37 + 28 * q^38 + 4 * q^39 - 8 * q^40 + 18 * q^41 + 8 * q^43 + 60 * q^45 - 12 * q^46 + 2 * q^48 - 12 * q^50 + 44 * q^51 + 6 * q^52 + 8 * q^53 + 18 * q^54 + 2 * q^55 + 24 * q^58 - 4 * q^61 - 24 * q^62 - 20 * q^64 + 24 * q^65 - 64 * q^66 + 60 * q^67 + 10 * q^68 - 34 * q^69 - 18 * q^71 + 24 * q^72 + 12 * q^74 - 18 * q^75 + 24 * q^76 + 20 * q^78 - 84 * q^79 - 2 * q^81 - 16 * q^82 - 12 * q^85 - 64 * q^87 - 2 * q^88 + 18 * q^89 + 52 * q^90 - 60 * q^93 + 16 * q^94 - 12 * q^95 + 78 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times$.

$n$	$197$	$885$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	1.24796	+	2.16154i	0.720513	+	1.24796i	0.960794	+	0.277262i	$0.0894269\pi$
$3$	1.24796	+	2.16154i	0.720513	+	1.24796i	−0.240282	+	0.970703i	$0.577240\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$			2.78680i			1.24629i	0.782105	+	0.623147i	$0.214146\pi$
$5$			2.78680i			1.24629i	−0.782105	+	0.623147i	$0.785854\pi$
$6$	−2.16154	−	1.24796i	−0.882444	−	0.509479i
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	−1.61483	+	2.79697i	−0.538277	+	0.932324i
$10$	−1.39340	−	2.41344i	−0.440631	−	0.763196i
$11$	3.26564	−	1.88542i	0.984628	−	0.568475i	0.0809639	−	0.996717i	$-0.474200\pi$
$11$	3.26564	−	1.88542i	0.984628	−	0.568475i	0.903664	+	0.428242i	$0.140867\pi$
$12$	2.49593			0.720513
$13$	3.40109	+	1.19690i	0.943294	+	0.331959i
$13$	3.40109	+	1.19690i	0.943294	+	0.331959i
$14$		0			0
$15$	−6.02377	+	3.47782i	−1.55533	+	0.897970i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.50662	+	4.34160i	−0.607945	+	1.05299i	0.383633	+	0.923485i	$0.374673\pi$
$17$	−2.50662	+	4.34160i	−0.607945	+	1.05299i	−0.991579	+	0.129506i	$0.958661\pi$
$18$		−	3.22966i		−	0.761239i
$19$	2.68042	+	1.54754i	0.614930	+	0.355030i	0.774892	−	0.632093i	$-0.217804\pi$
$19$	2.68042	+	1.54754i	0.614930	+	0.355030i	−0.159963	+	0.987123i	$0.551137\pi$
$20$	2.41344	+	1.39340i	0.539661	+	0.311573i
$21$		0			0
$22$	−1.88542	+	3.26564i	−0.401973	+	0.696237i
$23$	0.0487130	+	0.0843734i	0.0101574	+	0.0175931i	0.871059	−	0.491178i	$-0.163433\pi$
$23$	0.0487130	+	0.0843734i	0.0101574	+	0.0175931i	−0.860902	+	0.508771i	$0.830100\pi$
$24$	−2.16154	+	1.24796i	−0.441222	+	0.254740i
$25$	−2.76624			−0.553248
$26$	−3.54388	+	0.664005i	−0.695012	+	0.130222i
$27$	−0.573226			−0.110317
$28$		0			0
$29$	−1.34957	−	2.33752i	−0.250609	−	0.434067i	0.713085	−	0.701078i	$-0.247297\pi$
$29$	−1.34957	−	2.33752i	−0.250609	−	0.434067i	−0.963694	+	0.267011i	$0.913964\pi$
$30$	3.47782	−	6.02377i	0.634961	−	1.09978i
$31$			8.24042i			1.48002i	0.672594	+	0.740011i	$0.265180\pi$
$31$			8.24042i			1.48002i	−0.672594	+	0.740011i	$0.734820\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	8.15081	+	4.70587i	1.41887	+	0.819188i
$34$		−	5.01324i		−	0.859764i
$35$		0			0
$36$	1.61483	+	2.79697i	0.269139	+	0.466162i
$37$	0.424045	−	0.244823i	0.0697126	−	0.0402486i	−0.464739	−	0.885448i	$-0.653852\pi$
$37$	0.424045	−	0.244823i	0.0697126	−	0.0402486i	0.534451	+	0.845199i	$0.320518\pi$
$38$	−3.09508			−0.502088
$39$	1.65731	+	8.84528i	0.265382	+	1.41638i
$40$	−2.78680			−0.440631
$41$	−8.29797	+	4.79084i	−1.29593	+	0.748203i	−0.979698	−	0.200481i	$-0.935750\pi$
$41$	−8.29797	+	4.79084i	−1.29593	+	0.748203i	−0.316228	+	0.948683i	$0.602416\pi$
$42$		0			0
$43$	0.642640	−	1.11309i	0.0980017	−	0.169744i	−0.812856	−	0.582465i	$-0.802088\pi$
$43$	0.642640	−	1.11309i	0.0980017	−	0.169744i	0.910857	+	0.412721i	$0.135422\pi$
$44$		−	3.77084i		−	0.568475i
$45$	−7.79459	−	4.50021i	−1.16195	−	0.670852i
$46$	−0.0843734	−	0.0487130i	−0.0124402	−	0.00718234i
$47$		−	9.86141i		−	1.43843i	−0.694785	−	0.719217i	$-0.744501\pi$
$47$		−	9.86141i		−	1.43843i	0.694785	−	0.719217i	$-0.255499\pi$
$48$	1.24796	−	2.16154i	0.180128	−	0.311991i
$49$		0			0
$50$	2.39563	−	1.38312i	0.338794	−	0.195603i
$51$	−12.5127			−1.75213
$52$	2.73709	−	2.34699i	0.379566	−	0.325468i
$53$	−10.2775			−1.41172			−0.705859	−	0.708352i	$-0.749439\pi$
$53$	−10.2775			−1.41172			−0.705859	+	0.708352i	$0.749439\pi$
$54$	0.496428	−	0.286613i	0.0675553	−	0.0390031i
$55$	5.25428	+	9.10068i	0.708487	+	1.22714i
$56$		0			0
$57$			7.72510i			1.02321i
$58$	2.33752	+	1.34957i	0.306932	+	0.177207i
$59$	−4.70984	−	2.71923i	−0.613169	−	0.354014i	0.161035	−	0.986949i	$-0.448517\pi$
$59$	−4.70984	−	2.71923i	−0.613169	−	0.354014i	−0.774205	+	0.632935i	$0.781850\pi$
$60$			6.95565i			0.897970i
$61$	1.31592	−	2.27924i	0.168486	−	0.291826i	−0.769402	−	0.638765i	$-0.779446\pi$
$61$	1.31592	−	2.27924i	0.168486	−	0.291826i	0.937888	+	0.346939i	$0.112779\pi$
$62$	−4.12021	−	7.13641i	−0.523267	−	0.906325i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−3.33551	+	9.47816i	−0.413719	+	1.17562i
$66$	−9.41175			−1.15851
$67$	7.32268	−	4.22775i	0.894608	−	0.516502i	0.0191607	−	0.999816i	$-0.493901\pi$
$67$	7.32268	−	4.22775i	0.894608	−	0.516502i	0.875447	+	0.483315i	$0.160567\pi$
$68$	2.50662	+	4.34160i	0.303973	+	0.526496i
$69$	−0.121584	+	0.210590i	−0.0146370	+	0.0253521i
$70$		0			0
$71$	−5.07078	−	2.92762i	−0.601791	−	0.347444i	0.167955	−	0.985795i	$-0.446284\pi$
$71$	−5.07078	−	2.92762i	−0.601791	−	0.347444i	−0.769746	+	0.638350i	$0.779617\pi$
$72$	−2.79697	−	1.61483i	−0.329626	−	0.190310i
$73$		−	15.3226i		−	1.79338i	−0.442663	−	0.896688i	$-0.645966\pi$
$73$		−	15.3226i		−	1.79338i	0.442663	−	0.896688i	$-0.354034\pi$
$74$	−0.244823	+	0.424045i	−0.0284600	+	0.0492942i
$75$	−3.45217	−	5.97933i	−0.398622	−	0.690434i
$76$	2.68042	−	1.54754i	0.307465	−	0.177515i
$77$		0			0
$78$	−5.85791	−	6.83158i	−0.663278	−	0.773524i
$79$	11.1089			1.24985			0.624923	−	0.780686i	$-0.285130\pi$
$79$	11.1089			1.24985			0.624923	+	0.780686i	$0.285130\pi$
$80$	2.41344	−	1.39340i	0.269830	−	0.155787i
$81$	4.12913	+	7.15186i	0.458792	+	0.794652i
$82$	4.79084	−	8.29797i	0.529059	−	0.916358i
$83$		−	16.0283i		−	1.75933i	−0.475594	−	0.879665i	$-0.657767\pi$
$83$		−	16.0283i		−	1.75933i	0.475594	−	0.879665i	$-0.342233\pi$
$84$		0			0
$85$	−12.0992	−	6.98545i	−1.31234	−	0.757678i
$86$			1.28528i			0.138595i
$87$	3.36843	−	5.83429i	0.361134	−	0.625502i
$88$	1.88542	+	3.26564i	0.200986	+	0.348119i
$89$	12.4082	−	7.16387i	1.31527	−	0.759369i	0.332302	−	0.943173i	$-0.392175\pi$
$89$	12.4082	−	7.16387i	1.31527	−	0.759369i	0.982963	+	0.183804i	$0.0588412\pi$
$90$	9.00042			0.948727
$91$		0			0
$92$	0.0974260			0.0101574
$93$	−17.8120	+	10.2837i	−1.84702	+	1.06638i
$94$	4.93071	+	8.54023i	0.508563	+	0.880858i
$95$	−4.31268	+	7.46978i	−0.442471	+	0.766383i
$96$			2.49593i			0.254740i
$97$	5.50865	+	3.18042i	0.559318	+	0.322923i	0.752872	−	0.658167i	$-0.228668\pi$
$97$	5.50865	+	3.18042i	0.559318	+	0.322923i	−0.193554	+	0.981090i	$0.562001\pi$
$98$		0			0
$99$			12.1785i			1.22399i
$100$	−1.38312	+	2.39563i	−0.138312	+	0.239563i
$101$	4.82460	+	8.35645i	0.480065	+	0.831497i	0.999739	−	0.0228677i	$-0.00727965\pi$
$101$	4.82460	+	8.35645i	0.480065	+	0.831497i	−0.519673	+	0.854365i	$0.673946\pi$
$102$	10.8363	−	6.25635i	1.07296	−	0.619471i
$103$	−7.74925			−0.763556			−0.381778	−	0.924254i	$-0.624688\pi$
$103$	−7.74925			−0.763556			−0.381778	+	0.924254i	$0.624688\pi$
$104$	−1.19690	+	3.40109i	−0.117365	+	0.333505i
$105$		0			0
$106$	8.90055	−	5.13873i	0.864498	−	0.499118i
$107$	8.62343	+	14.9362i	0.833658	+	1.44394i	0.895118	+	0.445829i	$0.147091\pi$
$107$	8.62343	+	14.9362i	0.833658	+	1.44394i	−0.0614597	+	0.998110i	$0.519576\pi$
$108$	−0.286613	+	0.496428i	−0.0275793	+	0.0477688i
$109$		−	17.3545i		−	1.66226i	−0.556079	−	0.831129i	$-0.687695\pi$
$109$		−	17.3545i		−	1.66226i	0.556079	−	0.831129i	$-0.312305\pi$
$110$	−9.10068	−	5.25428i	−0.867716	−	0.500976i
$111$	1.05839	+	0.611060i	0.100458	+	0.0579992i
$112$		0			0
$113$	−1.23746	+	2.14334i	−0.116410	+	0.201628i	−0.918343	−	0.395787i	$-0.870472\pi$
$113$	−1.23746	+	2.14334i	−0.116410	+	0.201628i	0.801932	+	0.597415i	$0.203805\pi$
$114$	−3.86255	−	6.69013i	−0.361761	−	0.626588i
$115$	−0.235131	+	0.135753i	−0.0219261	+	0.0126591i
$116$	−2.69914			−0.250609
$117$	−8.83988	+	7.57998i	−0.817247	+	0.700769i
$118$	5.43846			0.500651
$119$		0			0
$120$	−3.47782	−	6.02377i	−0.317481	−	0.549892i
$121$	1.60961	−	2.78793i	0.146328	−	0.253448i
$122$			2.63184i			0.238275i
$123$	−20.7111	−	11.9576i	−1.86746	−	1.07818i
$124$	7.13641	+	4.12021i	0.640869	+	0.370006i
$125$			6.22504i			0.556785i
$126$		0			0
$127$	−3.06965	−	5.31678i	−0.272387	−	0.471788i	0.697086	−	0.716988i	$-0.254480\pi$
$127$	−3.06965	−	5.31678i	−0.272387	−	0.471788i	−0.969473	+	0.245200i	$0.921146\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	3.20797			0.282446
$130$	−1.85045	−	9.87608i	−0.162295	−	0.866189i
$131$	−8.81308			−0.770002			−0.385001	−	0.922916i	$-0.625799\pi$
$131$	−8.81308			−0.770002			−0.385001	+	0.922916i	$0.625799\pi$
$132$	8.15081	−	4.70587i	0.709437	−	0.409594i
$133$		0			0
$134$	−4.22775	+	7.32268i	−0.365222	+	0.632583i
$135$		−	1.59746i		−	0.137488i
$136$	−4.34160	−	2.50662i	−0.372289	−	0.214941i
$137$	−4.47276	−	2.58235i	−0.382134	−	0.220625i	0.296612	−	0.954998i	$-0.404143\pi$
$137$	−4.47276	−	2.58235i	−0.382134	−	0.220625i	−0.678746	+	0.734373i	$0.737476\pi$
$138$		−	0.243168i		−	0.0206999i
$139$	−3.44149	+	5.96083i	−0.291903	+	0.505591i	−0.974260	−	0.225428i	$-0.927622\pi$
$139$	−3.44149	+	5.96083i	−0.291903	+	0.505591i	0.682357	+	0.731020i	$0.260955\pi$
$140$		0			0
$141$	21.3158	−	12.3067i	1.79512	−	1.03641i
$142$	5.85524			0.491361
$143$	13.3634	−	2.50385i	1.11750	−	0.209383i
$144$	3.22966			0.269139
$145$	6.51420	−	3.76098i	0.540975	−	0.312332i
$146$	7.66130	+	13.2698i	0.634054	+	1.09821i
$147$		0			0
$148$		−	0.489645i		−	0.0402486i
$149$	−8.20500	−	4.73716i	−0.672180	−	0.388083i	0.124722	−	0.992192i	$-0.460196\pi$
$149$	−8.20500	−	4.73716i	−0.672180	−	0.388083i	−0.796902	+	0.604109i	$0.793529\pi$
$150$	5.97933	+	3.45217i	0.488210	+	0.281868i
$151$			12.8603i			1.04656i	0.852161	+	0.523280i	$0.175292\pi$
$151$			12.8603i			1.04656i	−0.852161	+	0.523280i	$0.824708\pi$
$152$	−1.54754	+	2.68042i	−0.125522	+	0.217410i
$153$	−8.09555	−	14.0219i	−0.654486	−	1.13360i
$154$		0			0
$155$	−22.9644			−1.84454
$156$	8.48889	+	2.98737i	0.679655	+	0.239181i
$157$	−2.00489			−0.160008			−0.0800039	−	0.996795i	$-0.525493\pi$
$157$	−2.00489			−0.160008			−0.0800039	+	0.996795i	$0.525493\pi$
$158$	−9.62057	+	5.55444i	−0.765372	+	0.441888i
$159$	−12.8259	−	22.2151i	−1.01716	−	1.76178i
$160$	−1.39340	+	2.41344i	−0.110158	+	0.190799i
$161$		0			0
$162$	−7.15186	−	4.12913i	−0.561904	−	0.324415i
$163$	−8.88376	−	5.12904i	−0.695830	−	0.401738i	0.109962	−	0.993936i	$-0.464927\pi$
$163$	−8.88376	−	5.12904i	−0.695830	−	0.401738i	−0.805792	+	0.592198i	$0.798260\pi$
$164$			9.58167i			0.748203i
$165$	−13.1143	+	22.7147i	−1.02095	+	1.76833i
$166$	8.01413	+	13.8809i	0.622017	+	1.07737i
$167$	−2.85452	+	1.64806i	−0.220889	+	0.127530i	−0.606362	−	0.795189i	$-0.707372\pi$
$167$	−2.85452	+	1.64806i	−0.220889	+	0.127530i	0.385473	+	0.922719i	$0.374038\pi$
$168$		0			0
$169$	10.1349	+	8.14151i	0.779606	+	0.626270i
$170$	13.9709			1.07152
$171$	−8.65684	+	4.99803i	−0.662005	+	0.382209i
$172$	−0.642640	−	1.11309i	−0.0490009	−	0.0848720i
$173$	2.72291	−	4.71621i	0.207019	−	0.358567i	−0.743755	−	0.668452i	$-0.766957\pi$
$173$	2.72291	−	4.71621i	0.207019	−	0.358567i	0.950774	+	0.309885i	$0.100291\pi$
$174$			6.73686i			0.510720i
$175$		0			0
$176$	−3.26564	−	1.88542i	−0.246157	−	0.142119i
$177$		−	13.5740i		−	1.02029i
$178$	−7.16387	+	12.4082i	−0.536955	+	0.930033i
$179$	3.00769	+	5.20948i	0.224806	+	0.389375i	0.956261	−	0.292514i	$-0.0944920\pi$
$179$	3.00769	+	5.20948i	0.224806	+	0.389375i	−0.731456	+	0.681889i	$0.761159\pi$
$180$	−7.79459	+	4.50021i	−0.580975	+	0.335426i
$181$	−14.2195			−1.05692			−0.528462	−	0.848957i	$-0.677231\pi$
$181$	−14.2195			−1.05692			−0.528462	+	0.848957i	$0.677231\pi$
$182$		0			0
$183$	6.56888			0.485585
$184$	−0.0843734	+	0.0487130i	−0.00622009	+	0.00359117i
$185$	0.682271	+	1.18173i	0.0501616	+	0.0868824i
$186$	10.2837	−	17.8120i	0.754041	−	1.30604i
$187$			18.9041i			1.38241i
$188$	−8.54023	−	4.93071i	−0.622860	−	0.359609i
$189$		0			0
$190$		−	8.62535i		−	0.625749i
$191$	−5.89482	+	10.2101i	−0.426534	+	0.738778i	−0.996562	−	0.0828466i	$-0.973599\pi$
$191$	−5.89482	+	10.2101i	−0.426534	+	0.738778i	0.570028	+	0.821625i	$0.306932\pi$
$192$	−1.24796	−	2.16154i	−0.0900641	−	0.155996i
$193$	4.19609	−	2.42261i	0.302041	−	0.174384i	−0.341318	−	0.939948i	$-0.610873\pi$
$193$	4.19609	−	2.42261i	0.302041	−	0.174384i	0.643359	+	0.765564i	$0.277540\pi$
$194$	−6.36084			−0.456681
$195$	−24.6500	+	4.61858i	−1.76522	+	0.330744i
$196$		0			0
$197$	5.26154	−	3.03775i	0.374869	−	0.216431i	−0.300714	−	0.953714i	$-0.597225\pi$
$197$	5.26154	−	3.03775i	0.374869	−	0.216431i	0.675584	+	0.737283i	$0.263892\pi$
$198$	−6.08927	−	10.5469i	−0.432746	−	0.749538i
$199$	−2.82739	+	4.89718i	−0.200428	+	0.347152i	−0.948666	−	0.316278i	$-0.897567\pi$
$199$	−2.82739	+	4.89718i	−0.200428	+	0.347152i	0.748238	+	0.663430i	$0.230900\pi$
$200$		−	2.76624i		−	0.195603i
$201$	18.2769	+	10.5522i	1.28915	+	0.744292i
$202$	−8.35645	−	4.82460i	−0.587957	−	0.339457i
$203$		0			0
$204$	−6.25635	+	10.8363i	−0.438032	+	0.758694i
$205$	−13.3511	−	23.1248i	−0.932480	−	1.61510i
$206$	6.71105	−	3.87462i	0.467581	−	0.269958i
$207$	−0.314653			−0.0218699
$208$	−0.664005	−	3.54388i	−0.0460404	−	0.245724i
$209$	11.6710			0.807303
$210$		0			0
$211$	6.03845	+	10.4589i	0.415704	+	0.720020i	0.995502	−	0.0947401i	$-0.0302020\pi$
$211$	6.03845	+	10.4589i	0.415704	+	0.720020i	−0.579798	+	0.814760i	$0.696869\pi$
$212$	−5.13873	+	8.90055i	−0.352930	+	0.611292i
$213$		−	14.6143i		−	1.00135i
$214$	−14.9362	−	8.62343i	−1.02102	−	0.589486i
$215$	3.10194	+	1.79091i	0.211551	+	0.122139i
$216$		−	0.573226i		−	0.0390031i
$217$		0			0
$218$	8.67725	+	15.0294i	0.587697	+	1.01792i
$219$	33.1204	−	19.1221i	2.23807	−	1.29215i
$220$	10.5086			0.708487
$221$	−13.7217	+	11.7660i	−0.923021	+	0.791468i
$222$	−1.22212			−0.0820233
$223$	18.6878	−	10.7894i	1.25143	−	0.722514i	0.280037	−	0.959989i	$-0.409653\pi$
$223$	18.6878	−	10.7894i	1.25143	−	0.722514i	0.971394	+	0.237475i	$0.0763198\pi$
$224$		0			0
$225$	4.46701	−	7.73709i	0.297801	−	0.515806i
$226$		−	2.47491i		−	0.164629i
$227$	2.61224	+	1.50818i	0.173381	+	0.100101i	0.584179	−	0.811625i	$-0.301417\pi$
$227$	2.61224	+	1.50818i	0.173381	+	0.100101i	−0.410798	+	0.911726i	$0.634750\pi$
$228$	6.69013	+	3.86255i	0.443065	+	0.255803i
$229$			12.5934i			0.832196i	0.909320	+	0.416098i	$0.136603\pi$
$229$			12.5934i			0.832196i	−0.909320	+	0.416098i	$0.863397\pi$
$230$	0.135753	−	0.235131i	0.00895130	−	0.0155041i
$231$		0			0
$232$	2.33752	−	1.34957i	0.153466	−	0.0886036i
$233$	17.2952			1.13305			0.566524	−	0.824045i	$-0.308288\pi$
$233$	17.2952			1.13305			0.566524	+	0.824045i	$0.308288\pi$
$234$	3.86557	−	10.9844i	0.252700	−	0.718072i
$235$	27.4818			1.79271
$236$	−4.70984	+	2.71923i	−0.306585	+	0.177007i
$237$	13.8635	+	24.0123i	0.900530	+	1.55976i
$238$		0			0
$239$			15.6915i			1.01500i	0.861652	+	0.507500i	$0.169430\pi$
$239$			15.6915i			1.01500i	−0.861652	+	0.507500i	$0.830570\pi$
$240$	6.02377	+	3.47782i	0.388833	+	0.224493i
$241$	16.1878	+	9.34601i	1.04275	+	0.602029i	0.920610	−	0.390484i	$-0.127692\pi$
$241$	16.1878	+	9.34601i	1.04275	+	0.602029i	0.122136	+	0.992513i	$0.461026\pi$
$242$			3.21923i			0.206940i
$243$	−11.1659	+	19.3398i	−0.716290	+	1.24065i
$244$	−1.31592	−	2.27924i	−0.0842430	−	0.145913i
$245$		0			0
$246$	23.9152			1.52478
$247$	7.26410	+	8.47150i	0.462204	+	0.539029i
$248$	−8.24042			−0.523267
$249$	34.6457	−	20.0027i	2.19558	−	1.26762i
$250$	−3.11252	−	5.39104i	−0.196853	−	0.340960i
$251$	−4.76111	+	8.24648i	−0.300518	+	0.520513i	−0.976253	−	0.216631i	$-0.930493\pi$
$251$	−4.76111	+	8.24648i	−0.300518	+	0.520513i	0.675735	+	0.737145i	$0.263826\pi$
$252$		0			0
$253$	0.318158	+	0.183689i	0.0200024	+	0.0115484i
$254$	5.31678	+	3.06965i	0.333605	+	0.192607i
$255$		−	34.8704i		−	2.18367i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−1.50574	−	2.60801i	−0.0939253	−	0.162683i	0.815234	−	0.579131i	$-0.196608\pi$
$257$	−1.50574	−	2.60801i	−0.0939253	−	0.162683i	−0.909160	+	0.416448i	$0.863275\pi$
$258$	−2.77818	+	1.60399i	−0.172962	+	0.0998597i
$259$		0			0
$260$	6.54057	+	7.62771i	0.405629	+	0.473051i
$261$	8.71731			0.539588
$262$	7.63235	−	4.40654i	0.471528	−	0.272237i
$263$	−1.13508	−	1.96602i	−0.0699922	−	0.121230i	0.828905	−	0.559389i	$-0.188964\pi$
$263$	−1.13508	−	1.96602i	−0.0699922	−	0.121230i	−0.898898	+	0.438159i	$0.855631\pi$
$264$	−4.70587	+	8.15081i	−0.289627	+	0.501648i
$265$		−	28.6412i		−	1.75942i
$266$		0			0
$267$	30.9700	+	17.8805i	1.89533	+	1.09427i
$268$		−	8.45550i		−	0.516502i
$269$	1.46983	−	2.54582i	0.0896172	−	0.155222i	−0.817732	−	0.575599i	$-0.804769\pi$
$269$	1.46983	−	2.54582i	0.0896172	−	0.155222i	0.907349	+	0.420377i	$0.138102\pi$
$270$	0.798732	+	1.38344i	0.0486093	+	0.0841937i
$271$	−13.7231	+	7.92301i	−0.833616	+	0.481289i	−0.855089	−	0.518481i	$-0.826498\pi$
$271$	−13.7231	+	7.92301i	−0.833616	+	0.481289i	0.0214729	+	0.999769i	$0.493164\pi$
$272$	5.01324			0.303973
$273$		0			0
$274$	5.16470			0.312011
$275$	−9.03354	+	5.21552i	−0.544743	+	0.314508i
$276$	0.121584	+	0.210590i	0.00731851	+	0.0126760i
$277$	11.1111	−	19.2451i	0.667604	−	1.15632i	−0.310968	−	0.950420i	$-0.600653\pi$
$277$	11.1111	−	19.2451i	0.667604	−	1.15632i	0.978572	−	0.205904i	$-0.0660134\pi$
$278$		−	6.88298i		−	0.412814i
$279$	−23.0482	−	13.3069i	−1.37986	−	0.796663i
$280$		0			0
$281$		−	9.18876i		−	0.548156i	−0.961708	−	0.274078i	$-0.911627\pi$
$281$		−	9.18876i		−	0.548156i	0.961708	−	0.274078i	$-0.0883726\pi$
$282$	−12.3067	+	21.3158i	−0.732853	+	1.26934i
$283$	8.52808	+	14.7711i	0.506942	+	0.878049i	0.999968	+	0.00803458i	$0.00255751\pi$
$283$	8.52808	+	14.7711i	0.506942	+	0.878049i	−0.493026	+	0.870015i	$0.664109\pi$
$284$	−5.07078	+	2.92762i	−0.300896	+	0.173722i
$285$	−21.5283			−1.27522
$286$	−10.3211	+	8.85011i	−0.610301	+	0.523318i
$287$		0			0
$288$	−2.79697	+	1.61483i	−0.164813	+	0.0951549i
$289$	−4.06631	−	7.04306i	−0.239195	−	0.414297i
$290$	−3.76098	+	6.51420i	−0.220852	+	0.382527i
$291$			15.8762i			0.930679i
$292$	−13.2698	−	7.66130i	−0.776554	−	0.448344i
$293$	22.2433	+	12.8422i	1.29947	+	0.750248i	0.980312	−	0.197455i	$-0.0632675\pi$
$293$	22.2433	+	12.8422i	1.29947	+	0.750248i	0.319155	+	0.947702i	$0.396601\pi$
$294$		0			0
$295$	7.57794	−	13.1254i	0.441205	−	0.764189i
$296$	0.244823	+	0.424045i	0.0142300	+	0.0246471i
$297$	−1.87195	+	1.08077i	−0.108622	+	0.0627127i
$298$	9.47431			0.548832
$299$	0.0646913	+	0.345266i	0.00374119	+	0.0199673i
$300$	−6.90434			−0.398622
$301$		0			0
$302$	−6.43017	−	11.1374i	−0.370015	−	0.640885i
$303$	−12.0419	+	20.8571i	−0.691786	+	1.19821i
$304$		−	3.09508i		−	0.177515i
$305$	6.35177	+	3.66720i	0.363701	+	0.209983i
$306$	14.0219	+	8.09555i	0.801579	+	0.462792i
$307$		−	19.1987i		−	1.09573i	−0.836568	−	0.547863i	$-0.815442\pi$
$307$		−	19.1987i		−	1.09573i	0.836568	−	0.547863i	$-0.184558\pi$
$308$		0			0
$309$	−9.67079	−	16.7503i	−0.550152	−	0.952891i
$310$	19.8877	−	11.4822i	1.12955	−	0.652144i
$311$	−6.69185			−0.379460			−0.189730	−	0.981836i	$-0.560761\pi$
$311$	−6.69185			−0.379460			−0.189730	+	0.981836i	$0.560761\pi$
$312$	−8.84528	+	1.65731i	−0.500765	+	0.0938266i
$313$	−8.63310			−0.487972			−0.243986	−	0.969779i	$-0.578455\pi$
$313$	−8.63310			−0.487972			−0.243986	+	0.969779i	$0.578455\pi$
$314$	1.73629	−	1.00245i	0.0979844	−	0.0565713i
$315$		0			0
$316$	5.55444	−	9.62057i	0.312462	−	0.541199i
$317$		−	14.7971i		−	0.831089i	−0.909573	−	0.415545i	$-0.863591\pi$
$317$		−	14.7971i		−	0.831089i	0.909573	−	0.415545i	$-0.136409\pi$
$318$	22.2151	+	12.8259i	1.24576	+	0.719242i
$319$	−8.81442	−	5.08901i	−0.493513	−	0.284930i
$320$		−	2.78680i		−	0.155787i
$321$	−21.5235	+	37.2797i	−1.20132	+	2.08075i
$322$		0			0
$323$	−13.4376	+	7.75819i	−0.747687	+	0.431677i
$324$	8.25826			0.458792
$325$	−9.40824	−	3.31090i	−0.521875	−	0.183656i
$326$	10.2581			0.568143
$327$	37.5124	−	21.6578i	2.07444	−	1.19768i
$328$	−4.79084	−	8.29797i	−0.264530	−	0.458179i
$329$		0			0
$330$		−	26.2286i		−	1.44384i
$331$	−0.551753	−	0.318555i	−0.0303271	−	0.0175093i	0.484760	−	0.874647i	$-0.338907\pi$
$331$	−0.551753	−	0.318555i	−0.0303271	−	0.0175093i	−0.515087	+	0.857138i	$0.672240\pi$
$332$	−13.8809	−	8.01413i	−0.761812	−	0.439833i
$333$			1.58139i			0.0866596i
$334$	1.64806	−	2.85452i	0.0901776	−	0.156192i
$335$	11.7819	+	20.4068i	0.643713	+	1.11494i
$336$		0			0
$337$	−16.4026			−0.893508			−0.446754	−	0.894657i	$-0.647420\pi$
$337$	−16.4026			−0.893508			−0.446754	+	0.894657i	$0.647420\pi$
$338$	−12.8478	−	1.98332i	−0.698829	−	0.107878i
$339$	−6.17720			−0.335500
$340$	−12.0992	+	6.98545i	−0.656169	+	0.378839i
$341$	15.5366	+	26.9103i	0.841356	+	1.45727i
$342$	4.99803	−	8.65684i	0.270263	−	0.468108i
$343$		0			0
$344$	1.11309	+	0.642640i	0.0600136	+	0.0346488i
$345$	−0.586872	−	0.338830i	−0.0315961	−	0.0182420i
$346$			5.44581i			0.292769i
$347$	14.9194	−	25.8411i	0.800915	−	1.38722i	−0.118100	−	0.993002i	$-0.537680\pi$
$347$	14.9194	−	25.8411i	0.800915	−	1.38722i	0.919015	−	0.394223i	$-0.128986\pi$
$348$	−3.36843	−	5.83429i	−0.180567	−	0.312751i
$349$	4.10228	−	2.36845i	0.219590	−	0.126780i	−0.386170	−	0.922427i	$-0.626202\pi$
$349$	4.10228	−	2.36845i	0.219590	−	0.126780i	0.605760	+	0.795647i	$0.292869\pi$
$350$		0			0
$351$	−1.94959	−	0.686092i	−0.104062	−	0.0366209i
$352$	3.77084			0.200986
$353$	21.7703	−	12.5691i	1.15872	−	0.668985i	0.207720	−	0.978188i	$-0.433396\pi$
$353$	21.7703	−	12.5691i	1.15872	−	0.668985i	0.950996	+	0.309204i	$0.100063\pi$
$354$	6.78701	+	11.7554i	0.360725	+	0.624794i
$355$	8.15868	−	14.1312i	0.433018	−	0.750009i
$356$		−	14.3277i		−	0.759369i
$357$		0			0
$358$	−5.20948	−	3.00769i	−0.275329	−	0.158962i
$359$			35.0580i			1.85029i	0.379614	+	0.925145i	$0.376057\pi$
$359$			35.0580i			1.85029i	−0.379614	+	0.925145i	$0.623943\pi$
$360$	4.50021	−	7.79459i	0.237182	−	0.410811i
$361$	−4.71025	−	8.15839i	−0.247908	−	0.429389i
$362$	12.3144	−	7.10973i	0.647231	−	0.373679i
$363$	8.03496			0.421726
$364$		0			0
$365$	42.7010			2.23507
$366$	−5.68881	+	3.28444i	−0.297359	+	0.171680i
$367$	−4.00248	−	6.93250i	−0.208928	−	0.361874i	0.742449	−	0.669902i	$-0.233664\pi$
$367$	−4.00248	−	6.93250i	−0.208928	−	0.361874i	−0.951377	+	0.308029i	$0.900331\pi$
$368$	0.0487130	−	0.0843734i	0.00253934	−	0.00439827i
$369$		−	30.9456i		−	1.61096i
$370$	−1.18173	−	0.682271i	−0.0614351	−	0.0354696i
$371$		0			0
$372$			20.5675i			1.06638i
$373$	14.3631	−	24.8776i	0.743694	−	1.28812i	−0.207108	−	0.978318i	$-0.566405\pi$
$373$	14.3631	−	24.8776i	0.743694	−	1.28812i	0.950802	−	0.309798i	$-0.100261\pi$
$374$	−9.45207	−	16.3715i	−0.488755	−	0.846548i
$375$	−13.4557	+	7.76863i	−0.694848	+	0.401170i
$376$	9.86141			0.508563
$377$	−1.79224	−	9.56543i	−0.0923051	−	0.492645i
$378$		0			0
$379$	21.9159	−	12.6531i	1.12574	−	0.649947i	0.182881	−	0.983135i	$-0.441458\pi$
$379$	21.9159	−	12.6531i	1.12574	−	0.649947i	0.942861	+	0.333188i	$0.108124\pi$
$380$	4.31268	+	7.46978i	0.221236	+	0.383191i
$381$	7.66162	−	13.2703i	0.392517	−	0.679859i
$382$		−	11.7896i		−	0.603210i
$383$	−6.54979	−	3.78152i	−0.334679	−	0.193227i	0.323238	−	0.946318i	$-0.395229\pi$
$383$	−6.54979	−	3.78152i	−0.334679	−	0.193227i	−0.657916	+	0.753091i	$0.728562\pi$
$384$	2.16154	+	1.24796i	0.110306	+	0.0636849i
$385$		0			0
$386$	−2.42261	+	4.19609i	−0.123308	+	0.213575i
$387$	2.07551	+	3.59489i	0.105504	+	0.182739i
$388$	5.50865	−	3.18042i	0.279659	−	0.161461i
$389$	−6.27513			−0.318162			−0.159081	−	0.987266i	$-0.550853\pi$
$389$	−6.27513			−0.318162			−0.159081	+	0.987266i	$0.550853\pi$
$390$	19.0382	−	16.3248i	0.964038	−	0.826639i
$391$	−0.488420			−0.0247005
$392$		0			0
$393$	−10.9984	−	19.0498i	−0.554797	−	0.960936i
$394$	−3.03775	+	5.26154i	−0.153040	+	0.265073i
$395$			30.9582i			1.55768i
$396$	10.5469	+	6.08927i	0.530003	+	0.305997i
$397$	−1.46669	−	0.846796i	−0.0736113	−	0.0424995i	0.462743	−	0.886493i	$-0.346865\pi$
$397$	−1.46669	−	0.846796i	−0.0736113	−	0.0424995i	−0.536354	+	0.843993i	$0.680199\pi$
$398$		−	5.65478i		−	0.283448i
$399$		0			0
$400$	1.38312	+	2.39563i	0.0691560	+	0.119782i
$401$	−0.233348	+	0.134724i	−0.0116528	+	0.00672777i	−0.505815	−	0.862642i	$-0.668808\pi$
$401$	−0.233348	+	0.134724i	−0.0116528	+	0.00672777i	0.494162	+	0.869370i	$0.335475\pi$
$402$	−21.1043			−1.05259
$403$	−9.86292	+	28.0264i	−0.491307	+	1.39610i
$404$	9.64919			0.480065
$405$	−19.9308	+	11.5071i	−0.990369	+	0.571790i
$406$		0			0
$407$	0.923187	−	1.59901i	0.0457607	−	0.0792598i
$408$		−	12.5127i		−	0.619471i
$409$	27.7947	+	16.0473i	1.37436	+	0.793487i	0.991473	−	0.130309i	$-0.0415969\pi$
$409$	27.7947	+	16.0473i	1.37436	+	0.793487i	0.382886	+	0.923796i	$0.374930\pi$
$410$	23.1248	+	13.3511i	1.14205	+	0.659363i
$411$		−	12.8907i		−	0.635853i
$412$	−3.87462	+	6.71105i	−0.190889	+	0.330629i
$413$		0			0
$414$	0.272498	−	0.157327i	0.0133925	−	0.00773218i
$415$	44.6675			2.19264
$416$	2.34699	+	2.73709i	0.115070	+	0.134197i
$417$	−17.1794			−0.841280
$418$	−10.1074	+	5.83552i	−0.494370	+	0.285425i
$419$	3.42135	+	5.92595i	0.167144	+	0.289502i	0.937415	−	0.348215i	$-0.113212\pi$
$419$	3.42135	+	5.92595i	0.167144	+	0.289502i	−0.770271	+	0.637717i	$0.779879\pi$
$420$		0			0
$421$		−	13.2165i		−	0.644132i	−0.946717	−	0.322066i	$-0.895623\pi$
$421$		−	13.2165i		−	0.644132i	0.946717	−	0.322066i	$-0.104377\pi$
$422$	−10.4589	−	6.03845i	−0.509131	−	0.293947i
$423$	27.5821	+	15.9245i	1.34109	+	0.774277i
$424$		−	10.2775i		−	0.499118i
$425$	6.93391	−	12.0099i	0.336344	−	0.582565i
$426$	7.30713	+	12.6563i	0.354032	+	0.613201i
$427$		0			0
$428$	17.2469			0.833658
$429$	22.0892	+	25.7608i	1.06648	+	1.24374i
$430$	−3.58182			−0.172731
$431$	21.1031	−	12.1839i	1.01650	−	0.586876i	0.103412	−	0.994639i	$-0.467024\pi$
$431$	21.1031	−	12.1839i	1.01650	−	0.586876i	0.913088	+	0.407762i	$0.133691\pi$
$432$	0.286613	+	0.496428i	0.0137897	+	0.0238844i
$433$	9.31448	−	16.1331i	0.447625	−	0.775310i	−0.550606	−	0.834765i	$-0.685603\pi$
$433$	9.31448	−	16.1331i	0.447625	−	0.775310i	0.998231	+	0.0594558i	$0.0189365\pi$
$434$		0			0
$435$	16.2590	+	9.38713i	0.779559	+	0.450079i
$436$	−15.0294	−	8.67725i	−0.719779	−	0.415565i
$437$			0.301541i			0.0144247i
$438$	−19.1221	+	33.1204i	−0.913688	+	1.58255i
$439$	2.17594	+	3.76884i	0.103852	+	0.179877i	0.913269	−	0.407358i	$-0.133550\pi$
$439$	2.17594	+	3.76884i	0.103852	+	0.179877i	−0.809417	+	0.587235i	$0.800217\pi$
$440$	−9.10068	+	5.25428i	−0.433858	+	0.250488i
$441$		0			0
$442$	6.00033	−	17.0505i	0.285407	−	0.811010i
$443$	2.32788			0.110601			0.0553005	−	0.998470i	$-0.482388\pi$
$443$	2.32788			0.110601			0.0553005	+	0.998470i	$0.482388\pi$
$444$	1.05839	−	0.611060i	0.0502288	−	0.0289996i
$445$	19.9643	+	34.5791i	0.946396	+	1.63921i
$446$	−10.7894	+	18.6878i	−0.510895	+	0.884895i
$447$		−	23.6472i		−	1.11848i
$448$		0			0
$449$	−17.4514	−	10.0756i	−0.823582	−	0.475495i	0.0280681	−	0.999606i	$-0.491064\pi$
$449$	−17.4514	−	10.0756i	−0.823582	−	0.475495i	−0.851650	+	0.524111i	$0.824398\pi$
$450$			8.93402i			0.421154i
$451$	−18.0655	+	31.2903i	−0.850670	+	1.47340i
$452$	1.23746	+	2.14334i	0.0582050	+	0.100814i
$453$	−27.7981	+	16.0493i	−1.30607	+	0.754060i
$454$	−3.01636			−0.141565
$455$		0			0
$456$	−7.72510			−0.361761
$457$	3.47125	−	2.00413i	0.162378	−	0.0937492i	−0.416609	−	0.909086i	$-0.636781\pi$
$457$	3.47125	−	2.00413i	0.162378	−	0.0937492i	0.578987	+	0.815337i	$0.303448\pi$
$458$	−6.29670	−	10.9062i	−0.294226	−	0.509614i
$459$	1.43686	−	2.48872i	0.0670669	−	0.116163i
$460$			0.271506i			0.0126591i
$461$	11.6606	+	6.73224i	0.543088	+	0.313552i	0.746329	−	0.665577i	$-0.231814\pi$
$461$	11.6606	+	6.73224i	0.543088	+	0.313552i	−0.203242	+	0.979129i	$0.565148\pi$
$462$		0			0
$463$		−	1.46774i		−	0.0682116i	−0.999418	−	0.0341058i	$-0.989142\pi$
$463$		−	1.46774i		−	0.0682116i	0.999418	−	0.0341058i	$-0.0108583\pi$
$464$	−1.34957	+	2.33752i	−0.0626522	+	0.108517i
$465$	−28.6587	−	49.6384i	−1.32902	−	2.30192i
$466$	−14.9781	+	8.64761i	−0.693847	+	0.400593i
$467$	10.0177			0.463564			0.231782	−	0.972768i	$-0.425544\pi$
$467$	10.0177			0.463564			0.231782	+	0.972768i	$0.425544\pi$
$468$	2.14451	+	11.4455i	0.0991301	+	0.529071i
$469$		0			0
$470$	−23.7999	+	13.7409i	−1.09781	+	0.633819i
$471$	−2.50203	−	4.33365i	−0.115288	−	0.199684i
$472$	2.71923	−	4.70984i	0.125163	−	0.216788i
$473$		−	4.84659i		−	0.222846i
$474$	−24.0123	−	13.8635i	−1.10292	−	0.636771i
$475$	−7.41467	−	4.28086i	−0.340208	−	0.196419i
$476$		0			0
$477$	16.5964	−	28.7458i	0.759896	−	1.31618i
$478$	−7.84576	−	13.5893i	−0.358857	−	0.621558i
$479$	−7.74369	+	4.47082i	−0.353818	+	0.204277i	−0.666366	−	0.745625i	$-0.732151\pi$
$479$	−7.74369	+	4.47082i	−0.353818	+	0.204277i	0.312547	+	0.949902i	$0.398818\pi$
$480$	−6.95565			−0.317481
$481$	1.73524	−	0.325127i	0.0791203	−	0.0148245i
$482$	−18.6920			−0.851398
$483$		0			0
$484$	−1.60961	−	2.78793i	−0.0731642	−	0.126724i
$485$	−8.86318	+	15.3515i	−0.402456	+	0.697075i
$486$		−	22.3317i		−	1.01299i
$487$	−18.4298	−	10.6404i	−0.835133	−	0.482164i	0.0204740	−	0.999790i	$-0.493482\pi$
$487$	−18.4298	−	10.6404i	−0.835133	−	0.482164i	−0.855607	+	0.517626i	$0.826816\pi$
$488$	2.27924	+	1.31592i	0.103176	+	0.0595688i
$489$		−	25.6035i		−	1.15783i
$490$		0			0
$491$	3.45976	+	5.99247i	0.156137	+	0.270437i	0.933472	−	0.358649i	$-0.116763\pi$
$491$	3.45976	+	5.99247i	0.156137	+	0.270437i	−0.777336	+	0.629086i	$0.783429\pi$
$492$	−20.7111	+	11.9576i	−0.933731	+	0.539090i
$493$	13.5314			0.609426
$494$	−10.5267	−	3.70449i	−0.473616	−	0.166673i
$495$	−33.9391			−1.52545
$496$	7.13641	−	4.12021i	0.320434	−	0.185003i
$497$		0			0
$498$	−20.0027	+	34.6457i	−0.896343	+	1.55251i
$499$		−	20.3813i		−	0.912394i	−0.889879	−	0.456197i	$-0.849211\pi$
$499$		−	20.3813i		−	0.912394i	0.889879	−	0.456197i	$-0.150789\pi$
$500$	5.39104	+	3.11252i	0.241095	+	0.139196i
$501$	−7.12467	−	4.11343i	−0.318307	−	0.183775i
$502$		−	9.52221i		−	0.424997i
$503$	−19.0046	+	32.9170i	−0.847375	+	1.46770i	0.0361679	+	0.999346i	$0.488485\pi$
$503$	−19.0046	+	32.9170i	−0.847375	+	1.46770i	−0.883543	+	0.468351i	$0.844848\pi$
$504$		0			0
$505$	−23.2877	+	13.4452i	−1.03629	+	0.598302i
$506$	−0.367378			−0.0163319
$507$	−4.95021	+	32.0673i	−0.219847	+	1.42416i
$508$	−6.13929			−0.272387
$509$	−1.12000	+	0.646632i	−0.0496431	+	0.0286615i	−0.524616	−	0.851339i	$-0.675791\pi$
$509$	−1.12000	+	0.646632i	−0.0496431	+	0.0286615i	0.474973	+	0.880000i	$0.342458\pi$
$510$	17.4352	+	30.1986i	0.772043	+	1.33722i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	−1.53648	−	0.887089i	−0.0678374	−	0.0391659i
$514$	2.60801	+	1.50574i	0.115034	+	0.0664152i
$515$		−	21.5956i		−	0.951615i
$516$	1.60399	−	2.77818i	0.0706115	−	0.122303i
$517$	−18.5929	−	32.2038i	−0.817715	−	1.41632i
$518$		0			0
$519$	13.5924			0.596638
$520$	−9.47816	−	3.33551i	−0.415645	−	0.146272i
$521$	−33.4103			−1.46373			−0.731865	−	0.681449i	$-0.761350\pi$
$521$	−33.4103			−1.46373			−0.731865	+	0.681449i	$0.761350\pi$
$522$	−7.54942	+	4.35866i	−0.330429	+	0.190773i
$523$	21.2753	+	36.8499i	0.930303	+	1.61133i	0.782803	+	0.622270i	$0.213789\pi$
$523$	21.2753	+	36.8499i	0.930303	+	1.61133i	0.147500	+	0.989062i	$0.452877\pi$
$524$	−4.40654	+	7.63235i	−0.192501	+	0.333421i
$525$		0			0
$526$	1.96602	+	1.13508i	0.0857226	+	0.0494920i
$527$	−35.7766	−	20.6556i	−1.55845	−	0.899773i
$528$		−	9.41175i		−	0.409594i
$529$	11.4953	−	19.9104i	0.499794	−	0.865668i
$530$	14.3206	+	24.8040i	0.622048	+	1.07742i
$531$	15.2112	−	8.78220i	0.660110	−	0.381115i
$532$		0			0
$533$	−33.9563	+	6.36227i	−1.47081	+	0.275581i
$534$	−35.7610			−1.54753
$535$	−41.6242	+	24.0317i	−1.79957	+	1.03898i
$536$	4.22775	+	7.32268i	0.182611	+	0.316292i
$537$	−7.50699	+	13.0025i	−0.323951	+	0.561099i
$538$			2.93966i			0.126738i
$539$		0			0
$540$	−1.38344	−	0.798732i	−0.0595340	−	0.0343719i
$541$		−	29.4589i		−	1.26654i	−0.773932	−	0.633269i	$-0.781713\pi$
$541$		−	29.4589i		−	1.26654i	0.773932	−	0.633269i	$-0.218287\pi$
$542$	7.92301	−	13.7231i	0.340322	−	0.589456i
$543$	−17.7454	−	30.7359i	−0.761527	−	1.31900i
$544$	−4.34160	+	2.50662i	−0.186144	+	0.107471i
$545$	48.3634			2.07166
$546$		0			0
$547$	−9.59486			−0.410246			−0.205123	−	0.978736i	$-0.565760\pi$
$547$	−9.59486			−0.410246			−0.205123	+	0.978736i	$0.565760\pi$
$548$	−4.47276	+	2.58235i	−0.191067	+	0.110313i
$549$	4.24997	+	7.36117i	0.181384	+	0.314167i
$550$	5.21552	−	9.03354i	0.222391	−	0.385192i
$551$		−	8.35405i		−	0.355894i
$552$	−0.210590	−	0.121584i	−0.00896330	−	0.00517497i
$553$		0			0
$554$			22.2223i			0.944135i
$555$	−1.70290	+	2.94951i	−0.0722841	+	0.125200i
$556$	3.44149	+	5.96083i	0.145952	+	0.252796i
$557$	−2.30315	+	1.32973i	−0.0975877	+	0.0563423i	−0.548000	−	0.836479i	$-0.684610\pi$
$557$	−2.30315	+	1.32973i	−0.0975877	+	0.0563423i	0.450412	+	0.892821i	$0.351277\pi$
$558$	26.6138			1.12665
$559$	3.51793	−	3.01654i	0.148793	−	0.127586i
$560$		0			0
$561$	−40.8620	+	23.5917i	−1.72520	+	0.996042i
$562$	4.59438	+	7.95770i	0.193802	+	0.335675i
$563$	8.24254	−	14.2765i	0.347382	−	0.601683i	−0.638402	−	0.769703i	$-0.720404\pi$
$563$	8.24254	−	14.2765i	0.347382	−	0.601683i	0.985783	+	0.168021i	$0.0537375\pi$
$564$		−	24.6134i		−	1.03641i
$565$	−5.97304	−	3.44854i	−0.251288	−	0.145081i
$566$	−14.7711	−	8.52808i	−0.620875	−	0.358462i
$567$		0			0
$568$	2.92762	−	5.07078i	0.122840	−	0.212765i
$569$	4.38749	+	7.59936i	0.183933	+	0.318582i	0.943217	−	0.332179i	$-0.107784\pi$
$569$	4.38749	+	7.59936i	0.183933	+	0.318582i	−0.759283	+	0.650760i	$0.774450\pi$
$570$	18.6440	−	10.7641i	0.780913	−	0.450860i
$571$	16.6346			0.696134			0.348067	−	0.937470i	$-0.386838\pi$
$571$	16.6346			0.696134			0.348067	+	0.937470i	$0.386838\pi$
$572$	4.51330	−	12.8250i	0.188711	−	0.536239i
$573$	−29.4261			−1.22929
$574$		0			0
$575$	−0.134752	−	0.233397i	−0.00561954	−	0.00973332i
$576$	1.61483	−	2.79697i	0.0672847	−	0.116540i
$577$		−	12.3608i		−	0.514586i	−0.966333	−	0.257293i	$-0.917169\pi$
$577$		−	12.3608i		−	0.514586i	0.966333	−	0.257293i	$-0.0828305\pi$
$578$	7.04306	+	4.06631i	0.292953	+	0.169136i
$579$	10.4731	+	6.04667i	0.435249	+	0.251291i
$580$		−	7.52195i		−	0.312332i
$581$		0			0
$582$	−7.93810	−	13.7492i	−0.329045	−	0.569922i
$583$	−33.5625	+	19.3773i	−1.39002	+	0.802527i
$584$	15.3226			0.634054
$585$	−21.1239	−	24.6350i	−0.873364	−	1.01853i
$586$	−25.6843			−1.06101
$587$	11.1764	−	6.45268i	0.461298	−	0.266331i	−0.251292	−	0.967911i	$-0.580855\pi$
$587$	11.1764	−	6.45268i	0.461298	−	0.266331i	0.712590	+	0.701581i	$0.247522\pi$
$588$		0			0
$589$	−12.7524	+	22.0877i	−0.525452	+	0.910110i
$590$			15.1559i			0.623958i
$591$	13.1324	+	7.58202i	0.540196	+	0.311882i
$592$	−0.424045	−	0.244823i	−0.0174281	−	0.0100621i
$593$		−	27.0616i		−	1.11129i	−0.831420	−	0.555644i	$-0.812472\pi$
$593$		−	27.0616i		−	1.11129i	0.831420	−	0.555644i	$-0.187528\pi$
$594$	1.08077	−	1.87195i	0.0443446	−	0.0768070i
$595$		0			0
$596$	−8.20500	+	4.73716i	−0.336090	+	0.194042i
$597$	−14.1139			−0.577644
$598$	−0.228657	−	0.266664i	−0.00935050	−	0.0109047i
$599$	5.75554			0.235165			0.117582	−	0.993063i	$-0.462486\pi$
$599$	5.75554			0.235165			0.117582	+	0.993063i	$0.462486\pi$
$600$	5.97933	−	3.45217i	0.244105	−	0.140934i
$601$	12.5000	+	21.6506i	0.509886	+	0.883148i	0.999934	+	0.0114531i	$0.00364571\pi$
$601$	12.5000	+	21.6506i	0.509886	+	0.883148i	−0.490049	+	0.871695i	$0.663021\pi$
$602$		0			0
$603$			27.3084i			1.11209i
$604$	11.1374	+	6.43017i	0.453174	+	0.261640i
$605$	7.76940	+	4.48566i	0.315871	+	0.182368i
$606$		−	24.0837i		−	0.978334i
$607$	−16.4581	+	28.5062i	−0.668012	+	1.15703i	0.310447	+	0.950591i	$0.399521\pi$
$607$	−16.4581	+	28.5062i	−0.668012	+	1.15703i	−0.978459	+	0.206441i	$0.933812\pi$
$608$	1.54754	+	2.68042i	0.0627610	+	0.108705i
$609$		0			0
$610$	−7.33439			−0.296961
$611$	11.8031	−	33.5396i	0.477502	−	1.35687i
$612$	−16.1911			−0.654486
$613$	−40.1590	+	23.1858i	−1.62201	+	0.936467i	−0.635626	+	0.771997i	$0.719258\pi$
$613$	−40.1590	+	23.1858i	−1.62201	+	0.936467i	−0.986382	+	0.164469i	$0.947409\pi$
$614$	9.59933	+	16.6265i	0.387398	+	0.670992i
$615$	33.3234	−	57.7178i	1.34373	−	2.32741i
$616$		0			0
$617$	1.15943	+	0.669398i	0.0466769	+	0.0269489i	0.523157	−	0.852236i	$-0.324754\pi$
$617$	1.15943	+	0.669398i	0.0466769	+	0.0269489i	−0.476480	+	0.879185i	$0.658088\pi$
$618$	16.7503	+	9.67079i	0.673796	+	0.389016i
$619$		−	35.4593i		−	1.42523i	−0.701555	−	0.712615i	$-0.747511\pi$
$619$		−	35.4593i		−	1.42523i	0.701555	−	0.712615i	$-0.252489\pi$
$620$	−11.4822	+	19.8877i	−0.461136	+	0.798710i
$621$	−0.0279235	−	0.0483650i	−0.00112053	−	0.00194082i
$622$	5.79531	−	3.34592i	0.232371	−	0.134159i
$623$		0			0
$624$	6.83158	−	5.85791i	0.273482	−	0.234504i
$625$	−31.1791			−1.24716
$626$	7.47648	−	4.31655i	0.298820	−	0.172524i
$627$	14.5650	+	25.2274i	0.581672	+	1.00749i
$628$	−1.00245	+	1.73629i	−0.0400020	+	0.0692854i
$629$			2.45471i			0.0978757i
$630$		0			0
$631$	−16.2308	−	9.37087i	−0.646139	−	0.373049i	0.140836	−	0.990033i	$-0.455021\pi$
$631$	−16.2308	−	9.37087i	−0.646139	−	0.373049i	−0.786975	+	0.616984i	$0.788354\pi$
$632$			11.1089i			0.441888i
$633$	−15.0715	+	26.1047i	−0.599040	+	1.03757i
$634$	7.39856	+	12.8147i	0.293834	+	0.508936i
$635$	14.8168	−	8.55448i	0.587987	−	0.339474i
$636$	−25.6518			−1.01716
$637$		0			0
$638$	10.1780			0.402952
$639$	16.3769	−	9.45523i	0.647861	−	0.374043i
$640$	1.39340	+	2.41344i	0.0550789	+	0.0953995i
$641$	−6.90063	+	11.9522i	−0.272559	+	0.472085i	−0.969516	−	0.245027i	$-0.921203\pi$
$641$	−6.90063	+	11.9522i	−0.272559	+	0.472085i	0.696958	+	0.717112i	$0.254537\pi$
$642$		−	43.0469i		−	1.69893i
$643$	−8.54461	−	4.93323i	−0.336967	−	0.194548i	0.321963	−	0.946752i	$-0.395657\pi$
$643$	−8.54461	−	4.93323i	−0.336967	−	0.194548i	−0.658930	+	0.752204i	$0.728991\pi$
$644$		0			0
$645$			8.93996i			0.352011i
$646$	7.75819	−	13.4376i	0.305242	−	0.528695i
$647$	15.0867	+	26.1310i	0.593120	+	1.02731i	0.993809	+	0.111101i	$0.0354375\pi$
$647$	15.0867	+	26.1310i	0.593120	+	1.02731i	−0.400689	+	0.916214i	$0.631229\pi$
$648$	−7.15186	+	4.12913i	−0.280952	+	0.162208i
$649$	−20.5076			−0.804992
$650$	9.80322	−	1.83680i	0.384514	−	0.0720450i
$651$		0			0
$652$	−8.88376	+	5.12904i	−0.347915	+	0.200869i
$653$	−3.66066	−	6.34046i	−0.143253	−	0.248121i	0.785467	−	0.618904i	$-0.212423\pi$
$653$	−3.66066	−	6.34046i	−0.143253	−	0.248121i	−0.928720	+	0.370782i	$0.879090\pi$
$654$	−21.6578	+	37.5124i	−0.846887	+	1.46685i
$655$		−	24.5603i		−	0.959649i
$656$	8.29797	+	4.79084i	0.323981	+	0.187051i
$657$	42.8569	+	24.7434i	1.67201	+	0.965334i
$658$		0			0
$659$	9.37228	−	16.2333i	0.365092	−	0.632358i	−0.623699	−	0.781665i	$-0.714371\pi$
$659$	9.37228	−	16.2333i	0.365092	−	0.632358i	0.988791	+	0.149307i	$0.0477042\pi$
$660$	13.1143	+	22.7147i	0.510474	+	0.884167i
$661$	−28.2737	+	16.3238i	−1.09972	+	0.634924i	−0.936148	−	0.351607i	$-0.885635\pi$
$661$	−28.2737	+	16.3238i	−1.09972	+	0.634924i	−0.163573	+	0.986531i	$0.552302\pi$
$662$	0.637109			0.0247620
$663$	−42.5569	−	14.9764i	−1.65277	−	0.581635i
$664$	16.0283			0.622017
$665$		0			0
$666$	−0.790695	−	1.36952i	−0.0306388	−	0.0530680i
$667$	0.131483	−	0.227735i	0.00509105	−	0.00881795i
$668$			3.29611i			0.127530i
$669$	46.6436	+	26.9297i	1.80334	+	1.04116i
$670$	−20.4068	−	11.7819i	−0.788384	−	0.455174i
$671$		−	9.92423i		−	0.383121i
$672$		0			0
$673$	−5.06141	−	8.76662i	−0.195103	−	0.337928i	0.751831	−	0.659356i	$-0.229171\pi$
$673$	−5.06141	−	8.76662i	−0.195103	−	0.337928i	−0.946934	+	0.321427i	$0.895837\pi$
$674$	14.2051	−	8.20131i	0.547159	−	0.315903i
$675$	1.58568			0.0610328
$676$	12.1182	−	4.70631i	0.466084	−	0.181012i
$677$	17.5227			0.673451			0.336725	−	0.941603i	$-0.390681\pi$
$677$	17.5227			0.673451			0.336725	+	0.941603i	$0.390681\pi$
$678$	5.34962	−	3.08860i	0.205451	−	0.118617i
$679$		0			0
$680$	6.98545	−	12.0992i	0.267880	−	0.463981i
$681$			7.52862i			0.288497i
$682$	−26.9103	−	15.5366i	−1.03045	−	0.594929i
$683$	16.9201	+	9.76885i	0.647432	+	0.373795i	0.787471	−	0.616351i	$-0.211390\pi$
$683$	16.9201	+	9.76885i	0.647432	+	0.373795i	−0.140040	+	0.990146i	$0.544723\pi$
$684$			9.99606i			0.382209i
$685$	7.19649	−	12.4647i	0.274964	−	0.476251i
$686$		0			0
$687$	−27.2211	+	15.7161i	−1.03855	+	0.599608i
$688$	−1.28528			−0.0490009
$689$	−34.9546	−	12.3011i	−1.33167	−	0.468633i
$690$	0.677661			0.0257981
$691$	24.6690	−	14.2427i	0.938453	−	0.541816i	0.0489782	−	0.998800i	$-0.484404\pi$
$691$	24.6690	−	14.2427i	0.938453	−	0.541816i	0.889475	+	0.456984i	$0.151070\pi$
$692$	−2.72291	−	4.71621i	−0.103509	−	0.179283i
$693$		0			0
$694$			29.8388i			1.13266i
$695$	−16.6116	−	9.59073i	−0.630115	−	0.363797i
$696$	5.83429	+	3.36843i	0.221148	+	0.127680i
$697$		−	48.0353i		−	1.81947i
$698$	−2.36845	+	4.10228i	−0.0896473	+	0.155274i
$699$	21.5838	+	37.3843i	0.816376	+	1.41400i
$700$		0			0
$701$	−18.5649			−0.701186			−0.350593	−	0.936528i	$-0.614020\pi$
$701$	−18.5649			−0.701186			−0.350593	+	0.936528i	$0.614020\pi$
$702$	2.03144	−	0.380625i	0.0766719	−	0.0143657i
$703$	1.51549			0.0571578
$704$	−3.26564	+	1.88542i	−0.123079	+	0.0710594i
$705$	34.2963	+	59.4029i	1.29167	+	2.23724i
$706$	−12.5691	+	21.7703i	−0.473044	+	0.819335i
$707$		0			0
$708$	−11.7554	−	6.78701i	−0.441796	−	0.255071i
$709$	44.2691	+	25.5588i	1.66256	+	0.959880i	0.971486	+	0.237095i	$0.0761953\pi$
$709$	44.2691	+	25.5588i	1.66256	+	0.959880i	0.691074	+	0.722784i	$0.257138\pi$
$710$			16.3174i			0.612380i
$711$	−17.9390	+	31.0712i	−0.672764	+	1.16526i
$712$	7.16387	+	12.4082i	0.268477	+	0.465017i
$713$	−0.695272	+	0.401415i	−0.0260381	+	0.0150331i
$714$		0			0
$715$	6.97774	+	37.2411i	0.260953	+	1.39274i
$716$	6.01539			0.224806
$717$	−33.9178	+	19.5825i	−1.26668	+	0.731320i
$718$	−17.5290	−	30.3611i	−0.654176	−	1.13307i
$719$	11.1514	−	19.3147i	0.415876	−	0.720318i	−0.579644	−	0.814870i	$-0.696809\pi$
$719$	11.1514	−	19.3147i	0.415876	−	0.720318i	0.995520	+	0.0945520i	$0.0301419\pi$
$720$			9.00042i			0.335426i
$721$		0			0
$722$	8.15839	+	4.71025i	0.303624	+	0.175297i
$723$			46.6540i			1.73508i
$724$	−7.10973	+	12.3144i	−0.264231	+	0.457662i
$725$	3.73323	+	6.46615i	0.138649	+	0.240147i
$726$	−6.95848	+	4.01748i	−0.258253	+	0.149103i
$727$	−17.2920			−0.641324			−0.320662	−	0.947194i	$-0.603905\pi$
$727$	−17.2920			−0.641324			−0.320662	+	0.947194i	$0.603905\pi$
$728$		0			0
$729$	−30.9636			−1.14680
$730$	−36.9802	+	21.3505i	−1.36870	+	0.790218i
$731$	3.22171	+	5.58017i	0.119159	+	0.206390i
$732$	3.28444	−	5.68881i	0.121396	−	0.210265i
$733$			41.8019i			1.54399i	0.635629	+	0.771995i	$0.280741\pi$
$733$			41.8019i			1.54399i	−0.635629	+	0.771995i	$0.719259\pi$
$734$	6.93250	+	4.00248i	0.255883	+	0.147734i
$735$		0			0
$736$			0.0974260i			0.00359117i
$737$	15.9422	−	27.6126i	0.587237	−	1.01712i
$738$	15.4728	+	26.7997i	0.569561	+	0.986509i
$739$	−32.8076	+	18.9415i	−1.20685	+	0.696774i	−0.962069	−	0.272806i	$-0.912048\pi$
$739$	−32.8076	+	18.9415i	−1.20685	+	0.696774i	−0.244778	+	0.969579i	$0.578715\pi$
$740$	1.36454			0.0501616
$741$	−9.24614	+	26.2738i	−0.339665	+	0.965191i
$742$		0			0
$743$	−8.61540	+	4.97411i	−0.316069	+	0.182482i	−0.649639	−	0.760243i	$-0.725080\pi$
$743$	−8.61540	+	4.97411i	−0.316069	+	0.182482i	0.333570	+	0.942725i	$0.391747\pi$
$744$	−10.2837	−	17.8120i	−0.377021	−	0.653019i
$745$	13.2015	−	22.8657i	0.483665	−	0.837733i
$746$			28.7262i			1.05174i
$747$	44.8306	+	25.8830i	1.64027	+	0.947008i
$748$	16.3715	+	9.45207i	0.598600	+	0.345602i
$749$		0			0
$750$	7.76863	−	13.4557i	0.283670	−	0.491331i
$751$	−18.2470	−	31.6048i	−0.665843	−	1.15327i	−0.979056	−	0.203592i	$-0.934739\pi$
$751$	−18.2470	−	31.6048i	−0.665843	−	1.15327i	0.313212	−	0.949683i	$-0.398595\pi$
$752$	−8.54023	+	4.93071i	−0.311430	+	0.179804i
$753$	−23.7668			−0.866109
$754$	6.33484	+	7.38779i	0.230701	+	0.269047i
$755$	−35.8392			−1.30432
$756$		0			0
$757$	1.82304	+	3.15759i	0.0662594	+	0.114765i	0.897252	−	0.441519i	$-0.145560\pi$
$757$	1.82304	+	3.15759i	0.0662594	+	0.114765i	−0.830993	+	0.556284i	$0.812227\pi$
$758$	−12.6531	+	21.9159i	−0.459582	+	0.796020i
$759$			0.916949i			0.0332831i
$760$	−7.46978	−	4.31268i	−0.270957	−	0.156437i
$761$	−27.6262	−	15.9500i	−1.00145	−	0.578187i	−0.0927724	−	0.995687i	$-0.529573\pi$
$761$	−27.6262	−	15.9500i	−1.00145	−	0.578187i	−0.908677	+	0.417500i	$0.862906\pi$
$762$			15.3232i			0.555103i
$763$		0			0
$764$	5.89482	+	10.2101i	0.213267	+	0.369389i
$765$	39.0762	−	22.5607i	1.41280	−	0.815682i
$766$	7.56305			0.273264
$767$	−12.7640	−	14.8855i	−0.460881	−	0.537486i
$768$	−2.49593			−0.0900641
$769$	44.8246	−	25.8795i	1.61642	−	0.933238i	0.628578	−	0.777747i	$-0.283637\pi$
$769$	44.8246	−	25.8795i	1.61642	−	0.933238i	0.987837	−	0.155491i	$-0.0496960\pi$
$770$		0			0
$771$	3.75821	−	6.50941i	0.135349	−	0.234431i
$772$		−	4.84523i		−	0.174384i
$773$	−47.5454	−	27.4504i	−1.71009	−	0.987321i	−0.934413	−	0.356192i	$-0.884075\pi$
$773$	−47.5454	−	27.4504i	−1.71009	−	0.987321i	−0.775678	−	0.631129i	$-0.782592\pi$
$774$	−3.59489	−	2.07551i	−0.129216	−	0.0746028i
$775$		−	22.7950i		−	0.818819i
$776$	−3.18042	+	5.50865i	−0.114170	+	0.197749i
$777$		0			0
$778$	5.43442	−	3.13757i	0.194833	−	0.112487i
$779$	−29.6560			−1.06254
$780$	−8.32519	+	23.6568i	−0.298090	+	0.847050i
$781$	−22.0792			−0.790054
$782$	0.422984	−	0.244210i	0.0151259	−	0.00873294i
$783$	0.773608	+	1.33993i	0.0276465	+	0.0478851i
$784$		0			0
$785$		−	5.58723i		−	0.199417i
$786$	19.0498	+	10.9984i	0.679484	+	0.392300i
$787$	25.4568	+	14.6975i	0.907438	+	0.523909i	0.879606	−	0.475703i	$-0.157806\pi$
$787$	25.4568	+	14.6975i	0.907438	+	0.523909i	0.0278319	+	0.999613i	$0.491140\pi$
$788$		−	6.07551i		−	0.216431i
$789$	2.83309	−	4.90705i	0.100861	−	0.174696i
$790$	−15.4791	−	26.8106i	−0.550722	−	0.953878i
$791$		0			0
$792$	−12.1785			−0.432746
$793$	7.20357	−	6.17688i	0.255806	−	0.219348i
$794$	1.69359			0.0601033
$795$	61.9091	−	35.7432i	2.19569	−	1.26768i
$796$	2.82739	+	4.89718i	0.100214	+	0.173576i
$797$	−1.82440	+	3.15995i	−0.0646234	+	0.111931i	−0.896527	−	0.442989i	$-0.853918\pi$
$797$	−1.82440	+	3.15995i	−0.0646234	+	0.111931i	0.831903	+	0.554920i	$0.187251\pi$
$798$		0			0
$799$	42.8143	+	24.7188i	1.51466	+	0.874489i
$800$	−2.39563	−	1.38312i	−0.0846984	−	0.0489006i
$801$			46.2738i			1.63500i
$802$	0.134724	−	0.233348i	0.00475725	−	0.00823980i
$803$	−28.8895	−	50.0382i	−1.01949	−	1.76581i
$804$	18.2769	−	10.5522i	0.644576	−	0.372146i
$805$		0			0
$806$	−5.47168	−	29.2031i	−0.192732	−	1.02863i
$807$	7.33719			0.258281
$808$	−8.35645	+	4.82460i	−0.293979	+	0.169729i
$809$	21.0289	+	36.4231i	0.739336	+	1.28057i	0.952795	+	0.303615i	$0.0981936\pi$
$809$	21.0289	+	36.4231i	0.739336	+	1.28057i	−0.213459	+	0.976952i	$0.568473\pi$
$810$	11.5071	−	19.9308i	0.404317	−	0.700297i
$811$			53.2847i			1.87108i	0.353222	+	0.935539i	$0.385086\pi$
$811$			53.2847i			1.87108i	−0.353222	+	0.935539i	$0.614914\pi$
$812$		0			0
$813$	−34.2518	−	19.7753i	−1.20126	−	0.693549i
$814$			1.84637i			0.0647153i
$815$	14.2936	−	24.7572i	0.500683	−	0.867209i
$816$	6.25635	+	10.8363i	0.219016	+	0.379347i
$817$	3.44509	−	1.98902i	0.120528	−	0.0695871i
$818$	−32.0946			−1.12216
$819$		0			0
$820$	−26.7022			−0.932480
$821$	−13.7097	+	7.91527i	−0.478470	+	0.276245i	−0.719779	−	0.694203i	$-0.755757\pi$
$821$	−13.7097	+	7.91527i	−0.478470	+	0.276245i	0.241308	+	0.970448i	$0.422423\pi$
$822$	6.44537	+	11.1637i	0.224808	+	0.389379i
$823$	13.5651	−	23.4955i	0.472851	−	0.819003i	−0.526666	−	0.850072i	$-0.676558\pi$
$823$	13.5651	−	23.4955i	0.472851	−	0.819003i	0.999517	+	0.0310699i	$0.00989144\pi$
$824$		−	7.74925i		−	0.269958i
$825$	−22.5471	−	13.0176i	−0.784989	−	0.453214i
$826$		0			0
$827$			18.8496i			0.655464i	0.944771	+	0.327732i	$0.106284\pi$
$827$			18.8496i			0.655464i	−0.944771	+	0.327732i	$0.893716\pi$
$828$	−0.157327	+	0.272498i	−0.00546748	+	0.00946995i
$829$	−8.03188	−	13.9116i	−0.278959	−	0.483171i	0.692168	−	0.721737i	$-0.256656\pi$
$829$	−8.03188	−	13.9116i	−0.278959	−	0.483171i	−0.971126	+	0.238566i	$0.923323\pi$
$830$	−38.6832	+	22.3338i	−1.34271	+	0.775216i
$831$	55.4653			1.92407
$832$	−3.40109	−	1.19690i	−0.117912	−	0.0414949i
$833$		0			0
$834$	14.8778	−	8.58971i	0.515177	−	0.297437i
$835$	−4.59280	−	7.95496i	−0.158940	−	0.275293i
$836$	5.83552	−	10.1074i	0.201826	−	0.349572i
$837$		−	4.72362i		−	0.163272i
$838$	−5.92595	−	3.42135i	−0.204709	−	0.118189i
$839$	5.87434	+	3.39155i	0.202805	+	0.117089i	0.597963	−	0.801524i	$-0.295977\pi$
$839$	5.87434	+	3.39155i	0.202805	+	0.117089i	−0.395158	+	0.918613i	$0.629310\pi$
$840$		0			0
$841$	10.8573	−	18.8054i	0.374390	−	0.648463i
$842$	6.60824	+	11.4458i	0.227735	+	0.394449i
$843$	19.8619	−	11.4673i	0.684079	−	0.394953i
$844$	12.0769			0.415704
$845$	−22.6887	+	28.2439i	−0.780516	+	0.971618i
$846$	−31.8490			−1.09499
$847$		0			0
$848$	5.13873	+	8.90055i	0.176465	+	0.305646i
$849$	−21.2855	+	36.8676i	−0.730516	+	1.26529i
$850$			13.8678i			0.475663i
$851$	0.0413130	+	0.0238521i	0.00141619	+	0.000817639i
$852$	−12.6563	−	7.30713i	−0.433598	−	0.250338i
$853$		−	12.9032i		−	0.441796i	−0.975297	−	0.220898i	$-0.929101\pi$
$853$		−	12.9032i		−	0.441796i	0.975297	−	0.220898i	$-0.0708988\pi$
$854$		0			0
$855$	−13.9285	−	24.1249i	−0.476345	−	0.825053i
$856$	−14.9362	+	8.62343i	−0.510509	+	0.294743i
$857$	−4.90661			−0.167606			−0.0838032	−	0.996482i	$-0.526707\pi$
$857$	−4.90661			−0.167606			−0.0838032	+	0.996482i	$0.526707\pi$
$858$	−32.0102	−	11.2649i	−1.09281	−	0.384577i
$859$	−11.4512			−0.390709			−0.195354	−	0.980733i	$-0.562586\pi$
$859$	−11.4512			−0.390709			−0.195354	+	0.980733i	$0.562586\pi$
$860$	3.10194	−	1.79091i	0.105775	−	0.0610695i
$861$		0			0
$862$	−12.1839	+	21.1031i	−0.414984	+	0.718774i
$863$			21.7298i			0.739692i	0.929093	+	0.369846i	$0.120590\pi$
$863$			21.7298i			0.739692i	−0.929093	+	0.369846i	$0.879410\pi$
$864$	−0.496428	−	0.286613i	−0.0168888	−	0.00975077i
$865$	13.1431	+	7.58819i	0.446880	+	0.258006i
$866$			18.6290i			0.633038i
$867$	10.1492	−	17.5790i	0.344686	−	0.597013i
$868$		0			0
$869$	36.2776	−	20.9449i	1.23063	−	0.710507i
$870$	−18.7743			−0.636507
$871$	29.9653	−	5.61449i	1.01534	−	0.190240i
$872$	17.3545			0.587697
$873$	−17.7911	+	10.2717i	−0.602137	+	0.347644i
$874$	−0.150770	−	0.261142i	−0.00509989	−	0.00883326i
$875$		0			0
$876$		−	38.2442i		−	1.29215i
$877$	−14.1349	−	8.16076i	−0.477300	−	0.275569i	0.241990	−	0.970279i	$-0.422200\pi$
$877$	−14.1349	−	8.16076i	−0.477300	−	0.275569i	−0.719291	+	0.694709i	$0.755533\pi$
$878$	−3.76884	−	2.17594i	−0.127192	−	0.0734344i
$879$			64.1063i			2.16225i
$880$	5.25428	−	9.10068i	0.177122	−	0.306784i
$881$	−4.59758	−	7.96324i	−0.154896	−	0.268289i	0.778125	−	0.628110i	$-0.216171\pi$
$881$	−4.59758	−	7.96324i	−0.154896	−	0.268289i	−0.933021	+	0.359821i	$0.882838\pi$
$882$		0			0
$883$	44.7661			1.50650			0.753249	−	0.657735i	$-0.228485\pi$
$883$	44.7661			1.50650			0.753249	+	0.657735i	$0.228485\pi$
$884$	3.32882	+	17.7663i	0.111960	+	0.597547i
$885$	37.8280			1.27157
$886$	−2.01601	+	1.16394i	−0.0677291	+	0.0391034i
$887$	−13.2472	−	22.9448i	−0.444797	−	0.770411i	0.553241	−	0.833021i	$-0.313391\pi$
$887$	−13.2472	−	22.9448i	−0.444797	−	0.770411i	−0.998038	+	0.0626102i	$0.980058\pi$
$888$	−0.611060	+	1.05839i	−0.0205058	+	0.0355171i
$889$		0			0
$890$	−34.5791	−	19.9643i	−1.15909	−	0.669203i
$891$	26.9685	+	15.5703i	0.903480	+	0.521624i
$892$		−	21.5789i		−	0.722514i
$893$	15.2609	−	26.4327i	0.510687	−	0.884536i
$894$	11.8236	+	20.4791i	0.395441	+	0.684923i
$895$	−14.5178	+	8.38183i	−0.485275	+	0.280174i
$896$		0			0
$897$	−0.665573	+	0.570713i	−0.0222229	+	0.0190555i
$898$	20.1511			0.672452
$899$	19.2622	−	11.1210i	0.642429	−	0.370907i
$900$	−4.46701	−	7.73709i	−0.148900	−	0.257903i
$901$	25.7617	−	44.6206i	0.858248	−	1.48653i
$902$		−	36.1309i		−	1.20303i
$903$		0			0
$904$	−2.14334	−	1.23746i	−0.0712863	−	0.0411572i
$905$		−	39.6268i		−	1.31724i
$906$	16.0493	−	27.7981i	0.533201	−	0.923531i
$907$	16.0687	+	27.8319i	0.533554	+	0.924142i	0.999232	+	0.0391879i	$0.0124771\pi$
$907$	16.0687	+	27.8319i	0.533554	+	0.924142i	−0.465678	+	0.884954i	$0.654190\pi$
$908$	2.61224	−	1.50818i	0.0866903	−	0.0500507i
$909$	−31.1637			−1.03363
$910$		0			0
$911$	32.8753			1.08921			0.544603	−	0.838694i	$-0.316680\pi$
$911$	32.8753			1.08921			0.544603	+	0.838694i	$0.316680\pi$
$912$	6.69013	−	3.86255i	0.221532	−	0.127902i
$913$	−30.2200	−	52.3426i	−1.00014	−	1.73229i
$914$	−2.00413	+	3.47125i	−0.0662907	+	0.114819i
$915$			18.3061i			0.605182i
$916$	10.9062	+	6.29670i	0.360351	+	0.208049i
$917$		0			0
$918$			2.87372i			0.0948469i
$919$	−1.48641	+	2.57454i	−0.0490321	+	0.0849262i	−0.889500	−	0.456936i	$-0.848947\pi$
$919$	−1.48641	+	2.57454i	−0.0490321	+	0.0849262i	0.840468	+	0.541862i	$0.182280\pi$
$920$	−0.135753	−	0.235131i	−0.00447565	−	0.00775205i
$921$	41.4987	−	23.9593i	1.36743	−	0.789485i
$922$	−13.4645			−0.443429
$923$	−13.7422	−	16.0263i	−0.452329	−	0.527512i
$924$		0			0
$925$	−1.17301	+	0.677238i	−0.0385683	+	0.0222674i
$926$	0.733869	+	1.27110i	0.0241164	+	0.0417709i
$927$	12.5137	−	21.6744i	0.411005	−	0.711881i
$928$		−	2.69914i		−	0.0886036i
$929$	−32.5418	−	18.7880i	−1.06766	−	0.616414i	−0.140120	−	0.990135i	$-0.544749\pi$
$929$	−32.5418	−	18.7880i	−1.06766	−	0.616414i	−0.927541	+	0.373720i	$0.878082\pi$
$930$	49.6384	+	28.6587i	1.62771	+	0.939757i
$931$		0			0
$932$	8.64761	−	14.9781i	0.283262	−	0.490624i
$933$	−8.35119	−	14.4647i	−0.273406	−	0.473552i
$934$	−8.67558	+	5.00885i	−0.283874	+	0.163895i
$935$	−52.6820			−1.72289
$936$	−7.57998	−	8.83988i	−0.247759	−	0.288940i
$937$	−39.5464			−1.29192			−0.645962	−	0.763369i	$-0.723544\pi$
$937$	−39.5464			−1.29192			−0.645962	+	0.763369i	$0.723544\pi$
$938$		0			0
$939$	−10.7738	−	18.6608i	−0.351590	−	0.608971i
$940$	13.7409	−	23.7999i	0.448178	−	0.776267i
$941$		−	35.4992i		−	1.15724i	−0.815597	−	0.578620i	$-0.803591\pi$
$941$		−	35.4992i		−	1.15724i	0.815597	−	0.578620i	$-0.196409\pi$
$942$	4.33365	+	2.50203i	0.141198	+	0.0815207i
$943$	−0.808438	−	0.466752i	−0.0263264	−	0.0151995i
$944$			5.43846i			0.177007i
$945$		0			0
$946$	2.42329	+	4.19727i	0.0787881	+	0.136465i
$947$	−31.7413	+	18.3258i	−1.03145	+	0.595509i	−0.917400	−	0.397965i	$-0.869716\pi$
$947$	−31.7413	+	18.3258i	−1.03145	+	0.595509i	−0.114052	+	0.993475i	$0.536383\pi$
$948$	27.7270			0.900530
$949$	18.3396	−	52.1136i	0.595328	−	1.69168i
$950$	8.56172			0.277779
$951$	31.9846	−	18.4663i	1.03717	−	0.598810i
$952$		0			0
$953$	13.1191	−	22.7230i	0.424971	−	0.736071i	−0.571447	−	0.820639i	$-0.693618\pi$
$953$	13.1191	−	22.7230i	0.424971	−	0.736071i	0.996418	+	0.0845679i	$0.0269510\pi$
$954$			33.1928i			1.07466i
$955$	−28.4535	−	16.4277i	−0.920735	−	0.531586i
$956$	13.5893	+	7.84576i	0.439508	+	0.253750i
$957$		−	25.4036i		−	0.821182i
$958$	4.47082	−	7.74369i	0.144446	−	0.250187i
$959$		0			0
$960$	6.02377	−	3.47782i	0.194416	−	0.112246i
$961$	−36.9045			−1.19047
$962$	−1.34020	+	1.14919i	−0.0432099	+	0.0370514i
$963$	−55.7016			−1.79496
$964$	16.1878	−	9.34601i	0.521373	−	0.301015i
$965$	6.75133	+	11.6937i	0.217333	+	0.376432i
$966$		0			0
$967$			9.22945i			0.296799i	0.988927	+	0.148400i	$0.0474122\pi$
$967$			9.22945i			0.296799i	−0.988927	+	0.148400i	$0.952588\pi$
$968$	2.78793	+	1.60961i	0.0896075	+	0.0517349i
$969$	−33.5393	−	19.3639i	−1.07744	−	0.622058i
$970$		−	17.7264i		−	0.569159i
$971$	5.05018	−	8.74717i	0.162068	−	0.280710i	−0.773542	−	0.633745i	$-0.781517\pi$
$971$	5.05018	−	8.74717i	0.162068	−	0.280710i	0.935610	+	0.353035i	$0.114850\pi$
$972$	11.1659	+	19.3398i	0.358145	+	0.620325i
$973$		0			0
$974$	21.2809			0.681883
$975$	−4.58451	−	24.4682i	−0.146822	−	0.783608i
$976$	−2.63184			−0.0842430
$977$	39.8299	−	22.9958i	1.27427	−	0.735701i	0.298482	−	0.954415i	$-0.403520\pi$
$977$	39.8299	−	22.9958i	1.27427	−	0.735701i	0.975789	+	0.218715i	$0.0701864\pi$
$978$	12.8017	+	22.1733i	0.409354	+	0.709022i
$979$	27.0138	−	46.7893i	0.863365	−	1.49539i
$980$		0			0
$981$	48.5400	+	28.0246i	1.54976	+	0.894756i
$982$	−5.99247	−	3.45976i	−0.191228	−	0.110405i
$983$			25.5285i			0.814232i	0.913376	+	0.407116i	$0.133466\pi$
$983$			25.5285i			0.814232i	−0.913376	+	0.407116i	$0.866534\pi$
$984$	11.9576	−	20.7111i	0.381194	−	0.660247i
$985$	8.46560	+	14.6629i	0.269736	+	0.467197i
$986$	−11.7186	+	6.76572i	−0.373196	+	0.215465i
$987$		0			0
$988$	10.9686	−	2.05515i	0.348957	−	0.0653829i
$989$	0.125220			0.00398176
$990$	29.3921	−	16.9696i	0.934144	−	0.539328i
$991$	22.5708	+	39.0937i	0.716984	+	1.24185i	0.962189	+	0.272382i	$0.0878113\pi$
$991$	22.5708	+	39.0937i	0.716984	+	1.24185i	−0.245205	+	0.969471i	$0.578855\pi$
$992$	−4.12021	+	7.13641i	−0.130817	+	0.226581i
$993$		−	1.59018i		−	0.0504628i
$994$		0			0
$995$	−13.6474	−	7.87936i	−0.432653	−	0.249792i
$996$		−	40.0054i		−	1.26762i
$997$	1.83618	−	3.18035i	0.0581523	−	0.100723i	−0.835484	−	0.549515i	$-0.814812\pi$
$997$	1.83618	−	3.18035i	0.0581523	−	0.100723i	0.893636	+	0.448792i	$0.148146\pi$
$998$	10.1907	+	17.6508i	0.322580	+	0.558725i
$999$	−0.243074	+	0.140339i	−0.00769051	+	0.00444012i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1274.2.m.g.491.5		20
7.2	even	3		182.2.v.a.179.6	yes	20
7.3	odd	6		1274.2.o.h.569.1		20
7.4	even	3		182.2.o.a.23.5	✓	20
7.5	odd	6		1274.2.v.h.361.10		20
7.6	odd	2		1274.2.m.f.491.1		20
13.4	even	6	inner	1274.2.m.g.589.5		20
21.2	odd	6		1638.2.cr.c.361.2		20
21.11	odd	6		1638.2.dt.c.1297.9		20
91.4	even	6		182.2.v.a.121.6	yes	20
91.17	odd	6		1274.2.v.h.667.10		20
91.30	even	6		182.2.o.a.95.10	yes	20
91.69	odd	6		1274.2.m.f.589.1		20
91.82	odd	6		1274.2.o.h.459.6		20
273.95	odd	6		1638.2.cr.c.667.2		20
273.212	odd	6		1638.2.dt.c.1369.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.o.a.23.5	✓	20	7.4	even	3
182.2.o.a.95.10	yes	20	91.30	even	6
182.2.v.a.121.6	yes	20	91.4	even	6
182.2.v.a.179.6	yes	20	7.2	even	3
1274.2.m.f.491.1		20	7.6	odd	2
1274.2.m.f.589.1		20	91.69	odd	6
1274.2.m.g.491.5		20	1.1	even	1	trivial
1274.2.m.g.589.5		20	13.4	even	6	inner
1274.2.o.h.459.6		20	91.82	odd	6
1274.2.o.h.569.1		20	7.3	odd	6
1274.2.v.h.361.10		20	7.5	odd	6
1274.2.v.h.667.10		20	91.17	odd	6
1638.2.cr.c.361.2		20	21.2	odd	6
1638.2.cr.c.667.2		20	273.95	odd	6
1638.2.dt.c.1297.9		20	21.11	odd	6
1638.2.dt.c.1369.4		20	273.212	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1274 = 2 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1274.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(1.24796 + 2.16154i) q^{3} +(0.500000 - 0.866025i) q^{4} +2.78680i q^{5} +(-2.16154 - 1.24796i) q^{6} +1.00000i q^{8} +(-1.61483 + 2.79697i) q^{9} +(-1.39340 - 2.41344i) q^{10} +(3.26564 - 1.88542i) q^{11} +2.49593 q^{12} +(3.40109 + 1.19690i) q^{13} +(-6.02377 + 3.47782i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.50662 + 4.34160i) q^{17} -3.22966i q^{18} +(2.68042 + 1.54754i) q^{19} +(2.41344 + 1.39340i) q^{20} +(-1.88542 + 3.26564i) q^{22} +(0.0487130 + 0.0843734i) q^{23} +(-2.16154 + 1.24796i) q^{24} -2.76624 q^{25} +(-3.54388 + 0.664005i) q^{26} -0.573226 q^{27} +(-1.34957 - 2.33752i) q^{29} +(3.47782 - 6.02377i) q^{30} +8.24042i q^{31} +(0.866025 + 0.500000i) q^{32} +(8.15081 + 4.70587i) q^{33} -5.01324i q^{34} +(1.61483 + 2.79697i) q^{36} +(0.424045 - 0.244823i) q^{37} -3.09508 q^{38} +(1.65731 + 8.84528i) q^{39} -2.78680 q^{40} +(-8.29797 + 4.79084i) q^{41} +(0.642640 - 1.11309i) q^{43} -3.77084i q^{44} +(-7.79459 - 4.50021i) q^{45} +(-0.0843734 - 0.0487130i) q^{46} -9.86141i q^{47} +(1.24796 - 2.16154i) q^{48} +(2.39563 - 1.38312i) q^{50} -12.5127 q^{51} +(2.73709 - 2.34699i) q^{52} -10.2775 q^{53} +(0.496428 - 0.286613i) q^{54} +(5.25428 + 9.10068i) q^{55} +7.72510i q^{57} +(2.33752 + 1.34957i) q^{58} +(-4.70984 - 2.71923i) q^{59} +6.95565i q^{60} +(1.31592 - 2.27924i) q^{61} +(-4.12021 - 7.13641i) q^{62} -1.00000 q^{64} +(-3.33551 + 9.47816i) q^{65} -9.41175 q^{66} +(7.32268 - 4.22775i) q^{67} +(2.50662 + 4.34160i) q^{68} +(-0.121584 + 0.210590i) q^{69} +(-5.07078 - 2.92762i) q^{71} +(-2.79697 - 1.61483i) q^{72} -15.3226i q^{73} +(-0.244823 + 0.424045i) q^{74} +(-3.45217 - 5.97933i) q^{75} +(2.68042 - 1.54754i) q^{76} +(-5.85791 - 6.83158i) q^{78} +11.1089 q^{79} +(2.41344 - 1.39340i) q^{80} +(4.12913 + 7.15186i) q^{81} +(4.79084 - 8.29797i) q^{82} -16.0283i q^{83} +(-12.0992 - 6.98545i) q^{85} +1.28528i q^{86} +(3.36843 - 5.83429i) q^{87} +(1.88542 + 3.26564i) q^{88} +(12.4082 - 7.16387i) q^{89} +9.00042 q^{90} +0.0974260 q^{92} +(-17.8120 + 10.2837i) q^{93} +(4.93071 + 8.54023i) q^{94} +(-4.31268 + 7.46978i) q^{95} +2.49593i q^{96} +(5.50865 + 3.18042i) q^{97} +12.1785i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{3} + 10 q^{4} - 16 q^{9} - 4 q^{10} + 6 q^{11} + 4 q^{12} + 6 q^{13} - 12 q^{15} - 10 q^{16} - 10 q^{17} + 24 q^{19} + 2 q^{22} - 36 q^{25} - 28 q^{27} + 2 q^{29} - 2 q^{30} - 12 q^{33} + 16 q^{36}+ \cdots + 78 q^{97}+O(q^{100}) \) 20 * q + 2 * q^3 + 10 * q^4 - 16 * q^9 - 4 * q^10 + 6 * q^11 + 4 * q^12 + 6 * q^13 - 12 * q^15 - 10 * q^16 - 10 * q^17 + 24 * q^19 + 2 * q^22 - 36 * q^25 - 28 * q^27 + 2 * q^29 - 2 * q^30 - 12 * q^33 + 16 * q^36 + 36 * q^37 + 28 * q^38 + 4 * q^39 - 8 * q^40 + 18 * q^41 + 8 * q^43 + 60 * q^45 - 12 * q^46 + 2 * q^48 - 12 * q^50 + 44 * q^51 + 6 * q^52 + 8 * q^53 + 18 * q^54 + 2 * q^55 + 24 * q^58 - 4 * q^61 - 24 * q^62 - 20 * q^64 + 24 * q^65 - 64 * q^66 + 60 * q^67 + 10 * q^68 - 34 * q^69 - 18 * q^71 + 24 * q^72 + 12 * q^74 - 18 * q^75 + 24 * q^76 + 20 * q^78 - 84 * q^79 - 2 * q^81 - 16 * q^82 - 12 * q^85 - 64 * q^87 - 2 * q^88 + 18 * q^89 + 52 * q^90 - 60 * q^93 + 16 * q^94 - 12 * q^95 + 78 * q^97

Introduction

L-functions

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