LMFDB - Embedded newform 637.2.q.h.491.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(491,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("637.491");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.q (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.58891012706304.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 $ x^12 - 5x^10 - 2x^9 + 15x^8 + 2x^7 - 30x^6 + 4x^5 + 60x^4 - 16x^3 - 80*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			491.4
Root			$-1.08105 + 0.911778i$ of defining polynomial
Character	$\chi$	$=$	637.491
Dual form			637.2.q.h.589.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.713220 - 0.411778i) q^{2} +(1.33015 + 2.30388i) q^{3} +(-0.660878 + 1.14467i) q^{4} +3.16209i q^{5} +(1.89737 + 1.09545i) q^{6} +2.73565i q^{8} +(-2.03858 + 3.53092i) q^{9} +O(q^{10})$	\(q+(0.713220 - 0.411778i) q^{2} +(1.33015 + 2.30388i) q^{3} +(-0.660878 + 1.14467i) q^{4} +3.16209i q^{5} +(1.89737 + 1.09545i) q^{6} +2.73565i q^{8} +(-2.03858 + 3.53092i) q^{9} +(1.30208 + 2.25527i) q^{10} +(5.14653 - 2.97135i) q^{11} -3.51626 q^{12} +(0.0766193 - 3.60474i) q^{13} +(-7.28508 + 4.20604i) q^{15} +(-0.195274 - 0.338225i) q^{16} +(1.34982 - 2.33796i) q^{17} +3.35776i q^{18} +(-1.69485 - 0.978524i) q^{19} +(-3.61956 - 2.08976i) q^{20} +(2.44707 - 4.23845i) q^{22} +(-1.36471 - 2.36374i) q^{23} +(-6.30261 + 3.63882i) q^{24} -4.99883 q^{25} +(-1.42970 - 2.60252i) q^{26} -2.86554 q^{27} +(2.99923 + 5.19481i) q^{29} +(-3.46391 + 5.99967i) q^{30} +1.15155i q^{31} +(-5.01684 - 2.89647i) q^{32} +(13.6913 + 7.90465i) q^{33} -2.22331i q^{34} +(-2.69450 - 4.66701i) q^{36} +(-5.63310 + 3.25227i) q^{37} -1.61174 q^{38} +(8.40680 - 4.61830i) q^{39} -8.65038 q^{40} +(3.23351 - 1.86687i) q^{41} +(3.49562 - 6.05460i) q^{43} +7.85479i q^{44} +(-11.1651 - 6.44617i) q^{45} +(-1.94667 - 1.12391i) q^{46} -0.456071i q^{47} +(0.519487 - 0.899778i) q^{48} +(-3.56527 + 2.05841i) q^{50} +7.18184 q^{51} +(4.07561 + 2.46999i) q^{52} +0.399286 q^{53} +(-2.04376 + 1.17997i) q^{54} +(9.39568 + 16.2738i) q^{55} -5.20632i q^{57} +(4.27822 + 2.47003i) q^{58} +(-4.16200 - 2.40293i) q^{59} -11.1187i q^{60} +(-0.578514 + 1.00201i) q^{61} +(0.474182 + 0.821308i) q^{62} -3.98971 q^{64} +(11.3985 + 0.242277i) q^{65} +13.0199 q^{66} +(-5.43793 + 3.13959i) q^{67} +(1.78413 + 3.09021i) q^{68} +(3.63052 - 6.28825i) q^{69} +(3.90335 + 2.25360i) q^{71} +(-9.65936 - 5.57684i) q^{72} -8.30575i q^{73} +(-2.67843 + 4.63917i) q^{74} +(-6.64917 - 11.5167i) q^{75} +(2.24018 - 1.29337i) q^{76} +(4.09418 - 6.75560i) q^{78} -7.91410 q^{79} +(1.06950 - 0.617476i) q^{80} +(2.30414 + 3.99089i) q^{81} +(1.53747 - 2.66298i) q^{82} -6.19795i q^{83} +(7.39284 + 4.26826i) q^{85} -5.75769i q^{86} +(-7.97882 + 13.8197i) q^{87} +(8.12857 + 14.0791i) q^{88} +(-3.08423 + 1.78068i) q^{89} -10.6176 q^{90} +3.60762 q^{92} +(-2.65303 + 1.53173i) q^{93} +(-0.187800 - 0.325279i) q^{94} +(3.09418 - 5.35928i) q^{95} -15.4109i q^{96} +(2.96831 + 1.71375i) q^{97} +24.2293i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4} + 18 q^{6} - 4 q^{9}+O(q^{10}) $ 12 * q + 4 * q^4 + 18 * q^6 - 4 * q^9	$ 12 q + 4 q^{4} + 18 q^{6} - 4 q^{9} - 12 q^{10} + 6 q^{11} + 4 q^{12} - 4 q^{13} + 6 q^{15} - 8 q^{16} + 4 q^{17} + 12 q^{20} + 6 q^{22} - 12 q^{23} - 12 q^{24} - 20 q^{25} + 42 q^{26} - 12 q^{27} + 8 q^{29} + 8 q^{30} + 36 q^{32} + 30 q^{33} - 10 q^{36} - 42 q^{37} - 4 q^{38} - 4 q^{39} - 92 q^{40} - 30 q^{41} + 2 q^{43} + 12 q^{46} + 2 q^{48} - 18 q^{50} + 52 q^{51} - 2 q^{52} - 44 q^{53} - 12 q^{54} + 6 q^{55} - 12 q^{58} - 18 q^{59} - 14 q^{61} + 4 q^{62} - 52 q^{64} + 60 q^{65} + 52 q^{66} - 24 q^{67} + 8 q^{68} - 4 q^{69} - 24 q^{71} + 60 q^{72} + 6 q^{74} - 46 q^{75} + 18 q^{76} - 10 q^{78} - 56 q^{79} + 72 q^{80} + 2 q^{81} - 14 q^{82} - 48 q^{85} + 2 q^{87} - 14 q^{88} + 12 q^{89} - 24 q^{90} + 24 q^{92} - 18 q^{93} - 4 q^{94} - 22 q^{95} - 6 q^{97}+O(q^{100}) $ 12 * q + 4 * q^4 + 18 * q^6 - 4 * q^9 - 12 * q^10 + 6 * q^11 + 4 * q^12 - 4 * q^13 + 6 * q^15 - 8 * q^16 + 4 * q^17 + 12 * q^20 + 6 * q^22 - 12 * q^23 - 12 * q^24 - 20 * q^25 + 42 * q^26 - 12 * q^27 + 8 * q^29 + 8 * q^30 + 36 * q^32 + 30 * q^33 - 10 * q^36 - 42 * q^37 - 4 * q^38 - 4 * q^39 - 92 * q^40 - 30 * q^41 + 2 * q^43 + 12 * q^46 + 2 * q^48 - 18 * q^50 + 52 * q^51 - 2 * q^52 - 44 * q^53 - 12 * q^54 + 6 * q^55 - 12 * q^58 - 18 * q^59 - 14 * q^61 + 4 * q^62 - 52 * q^64 + 60 * q^65 + 52 * q^66 - 24 * q^67 + 8 * q^68 - 4 * q^69 - 24 * q^71 + 60 * q^72 + 6 * q^74 - 46 * q^75 + 18 * q^76 - 10 * q^78 - 56 * q^79 + 72 * q^80 + 2 * q^81 - 14 * q^82 - 48 * q^85 + 2 * q^87 - 14 * q^88 + 12 * q^89 - 24 * q^90 + 24 * q^92 - 18 * q^93 - 4 * q^94 - 22 * q^95 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	0.713220	−	0.411778i	0.504323	−	0.291171i	−0.226174	−	0.974087i	$-0.572622\pi$
$2$	0.713220	−	0.411778i	0.504323	−	0.291171i	0.730497	+	0.682916i	$0.239288\pi$
$3$	1.33015	+	2.30388i	0.767960	+	1.33015i	0.938667	+	0.344824i	$0.112061\pi$
$3$	1.33015	+	2.30388i	0.767960	+	1.33015i	−0.170707	+	0.985322i	$0.554605\pi$
$4$	−0.660878	+	1.14467i	−0.330439	+	0.572337i
$5$			3.16209i			1.41413i	0.707148	+	0.707065i	$0.249981\pi$
$5$			3.16209i			1.41413i	−0.707148	+	0.707065i	$0.750019\pi$
$6$	1.89737	+	1.09545i	0.774600	+	0.447215i
$7$		0			0
$7$		0			0
$8$			2.73565i			0.967199i
$9$	−2.03858	+	3.53092i	−0.679526	+	1.17697i
$10$	1.30208	+	2.25527i	0.411754	+	0.713179i
$11$	5.14653	−	2.97135i	1.55174	−	0.895895i	0.553735	−	0.832693i	$-0.313202\pi$
$11$	5.14653	−	2.97135i	1.55174	−	0.895895i	0.998001	−	0.0632025i	$-0.0201314\pi$
$12$	−3.51626			−1.01506
$13$	0.0766193	−	3.60474i	0.0212504	−	0.999774i
$13$	0.0766193	−	3.60474i	0.0212504	−	0.999774i
$14$		0			0
$15$	−7.28508	+	4.20604i	−1.88100	+	1.08600i
$16$	−0.195274	−	0.338225i	−0.0488186	−	0.0845563i
$17$	1.34982	−	2.33796i	0.327380	−	0.567038i	−0.654611	−	0.755966i	$-0.727168\pi$
$17$	1.34982	−	2.33796i	0.327380	−	0.567038i	0.981991	+	0.188927i	$0.0605010\pi$
$18$			3.35776i			0.791433i
$19$	−1.69485	−	0.978524i	−0.388826	−	0.224489i	0.292825	−	0.956166i	$-0.405405\pi$
$19$	−1.69485	−	0.978524i	−0.388826	−	0.224489i	−0.681651	+	0.731677i	$0.738738\pi$
$20$	−3.61956	−	2.08976i	−0.809359	−	0.467284i
$21$		0			0
$22$	2.44707	−	4.23845i	0.521717	−	0.903641i
$23$	−1.36471	−	2.36374i	−0.284561	−	0.492874i	0.687941	−	0.725766i	$-0.258515\pi$
$23$	−1.36471	−	2.36374i	−0.284561	−	0.492874i	−0.972503	+	0.232892i	$0.925181\pi$
$24$	−6.30261	+	3.63882i	−1.28652	+	0.742770i
$25$	−4.99883			−0.999766
$26$	−1.42970	−	2.60252i	−0.280388	−	0.510397i
$27$	−2.86554			−0.551474
$28$		0			0
$29$	2.99923	+	5.19481i	0.556942	+	0.964652i	0.997750	+	0.0670505i	$0.0213589\pi$
$29$	2.99923	+	5.19481i	0.556942	+	0.964652i	−0.440807	+	0.897602i	$0.645308\pi$
$30$	−3.46391	+	5.99967i	−0.632421	+	1.09539i
$31$			1.15155i			0.206824i	0.994639	+	0.103412i	$0.0329760\pi$
$31$			1.15155i			0.206824i	−0.994639	+	0.103412i	$0.967024\pi$
$32$	−5.01684	−	2.89647i	−0.886860	−	0.512029i
$33$	13.6913	+	7.90465i	2.38334	+	1.37602i
$34$		−	2.22331i		−	0.381294i
$35$		0			0
$36$	−2.69450	−	4.66701i	−0.449083	−	0.777835i
$37$	−5.63310	+	3.25227i	−0.926075	+	0.534670i	−0.885568	−	0.464509i	$-0.846231\pi$
$37$	−5.63310	+	3.25227i	−0.926075	+	0.534670i	−0.0405072	+	0.999179i	$0.512897\pi$
$38$	−1.61174			−0.261459
$39$	8.40680	−	4.61830i	1.34617	−	0.739521i
$40$	−8.65038			−1.36775
$41$	3.23351	−	1.86687i	0.504990	−	0.291556i	−0.225782	−	0.974178i	$-0.572494\pi$
$41$	3.23351	−	1.86687i	0.504990	−	0.291556i	0.730772	+	0.682622i	$0.239160\pi$
$42$		0			0
$43$	3.49562	−	6.05460i	0.533078	−	0.923318i	−0.466176	−	0.884692i	$-0.654369\pi$
$43$	3.49562	−	6.05460i	0.533078	−	0.923318i	0.999254	−	0.0386258i	$-0.0122980\pi$
$44$			7.85479i			1.18415i
$45$	−11.1651	−	6.44617i	−1.66439	−	0.960938i
$46$	−1.94667	−	1.12391i	−0.287021	−	0.165712i
$47$		−	0.456071i		−	0.0665248i	−0.999447	−	0.0332624i	$-0.989410\pi$
$47$		−	0.456071i		−	0.0665248i	0.999447	−	0.0332624i	$-0.0105897\pi$
$48$	0.519487	−	0.899778i	0.0749815	−	0.129872i
$49$		0			0
$50$	−3.56527	+	2.05841i	−0.504205	+	0.291103i
$51$	7.18184			1.00566
$52$	4.07561	+	2.46999i	0.565186	+	0.342527i
$53$	0.399286			0.0548462			0.0274231	−	0.999624i	$-0.491270\pi$
$53$	0.399286			0.0548462			0.0274231	+	0.999624i	$0.491270\pi$
$54$	−2.04376	+	1.17997i	−0.278121	+	0.160573i
$55$	9.39568	+	16.2738i	1.26691	+	2.19436i
$56$		0			0
$57$		−	5.20632i		−	0.689594i
$58$	4.27822	+	2.47003i	0.561758	+	0.324331i
$59$	−4.16200	−	2.40293i	−0.541846	−	0.312835i	0.203981	−	0.978975i	$-0.434612\pi$
$59$	−4.16200	−	2.40293i	−0.541846	−	0.312835i	−0.745827	+	0.666140i	$0.767945\pi$
$60$		−	11.1187i		−	1.43542i
$61$	−0.578514	+	1.00201i	−0.0740711	+	0.128295i	−0.900682	−	0.434479i	$-0.856933\pi$
$61$	−0.578514	+	1.00201i	−0.0740711	+	0.128295i	0.826611	+	0.562774i	$0.190266\pi$
$62$	0.474182	+	0.821308i	0.0602212	+	0.104306i
$63$		0			0
$64$	−3.98971			−0.498714
$65$	11.3985	+	0.242277i	1.41381	+	0.0300508i
$66$	13.0199			1.60263
$67$	−5.43793	+	3.13959i	−0.664349	+	0.383562i	−0.793932	−	0.608007i	$-0.791969\pi$
$67$	−5.43793	+	3.13959i	−0.664349	+	0.383562i	0.129583	+	0.991569i	$0.458636\pi$
$68$	1.78413	+	3.09021i	0.216358	+	0.374743i
$69$	3.63052	−	6.28825i	0.437063	−	0.757016i
$70$		0			0
$71$	3.90335	+	2.25360i	0.463242	+	0.267453i	0.713406	−	0.700751i	$-0.247151\pi$
$71$	3.90335	+	2.25360i	0.463242	+	0.267453i	−0.250165	+	0.968203i	$0.580485\pi$
$72$	−9.65936	−	5.57684i	−1.13837	−	0.657236i
$73$		−	8.30575i		−	0.972115i	−0.873927	−	0.486057i	$-0.838435\pi$
$73$		−	8.30575i		−	0.972115i	0.873927	−	0.486057i	$-0.161565\pi$
$74$	−2.67843	+	4.63917i	−0.311361	+	0.539293i
$75$	−6.64917	−	11.5167i	−0.767780	−	1.32983i
$76$	2.24018	−	1.29337i	0.256966	−	0.148360i
$77$		0			0
$78$	4.09418	−	6.75560i	0.463575	−	0.764921i
$79$	−7.91410			−0.890405			−0.445203	−	0.895430i	$-0.646868\pi$
$79$	−7.91410			−0.890405			−0.445203	+	0.895430i	$0.646868\pi$
$80$	1.06950	−	0.617476i	0.119574	−	0.0690359i
$81$	2.30414	+	3.99089i	0.256016	+	0.443432i
$82$	1.53747	−	2.66298i	0.169785	−	0.294077i
$83$		−	6.19795i		−	0.680313i	−0.940369	−	0.340156i	$-0.889520\pi$
$83$		−	6.19795i		−	0.680313i	0.940369	−	0.340156i	$-0.110480\pi$
$84$		0			0
$85$	7.39284	+	4.26826i	0.801866	+	0.462958i
$86$		−	5.75769i		−	0.620867i
$87$	−7.97882	+	13.8197i	−0.855419	+	1.48163i
$88$	8.12857	+	14.0791i	0.866509	+	1.50084i
$89$	−3.08423	+	1.78068i	−0.326928	+	0.188752i	−0.654476	−	0.756083i	$-0.727111\pi$
$89$	−3.08423	+	1.78068i	−0.326928	+	0.188752i	0.327549	+	0.944834i	$0.393778\pi$
$90$	−10.6176			−1.11919
$91$		0			0
$92$	3.60762			0.376120
$93$	−2.65303	+	1.53173i	−0.275106	+	0.158833i
$94$	−0.187800	−	0.325279i	−0.0193701	−	0.0335500i
$95$	3.09418	−	5.35928i	0.317457	−	0.549851i
$96$		−	15.4109i		−	1.57287i
$97$	2.96831	+	1.71375i	0.301386	+	0.174005i	0.643065	−	0.765811i	$-0.277662\pi$
$97$	2.96831	+	1.71375i	0.301386	+	0.174005i	−0.341679	+	0.939817i	$0.610996\pi$
$98$		0			0
$99$			24.2293i			2.43513i
$100$	3.30361	−	5.72203i	0.330361	−	0.572203i
$101$	6.66474	+	11.5437i	0.663167	+	1.14864i	0.979779	+	0.200084i	$0.0641214\pi$
$101$	6.66474	+	11.5437i	0.663167	+	1.14864i	−0.316612	+	0.948555i	$0.602545\pi$
$102$	5.12223	−	2.95732i	0.507177	−	0.292819i
$103$	11.6450			1.14741			0.573706	−	0.819061i	$-0.305505\pi$
$103$	11.6450			1.14741			0.573706	+	0.819061i	$0.305505\pi$
$104$	9.86130	+	0.209604i	0.966981	+	0.0205533i
$105$		0			0
$106$	0.284779	−	0.164417i	0.0276602	−	0.0159696i
$107$	−1.96483	−	3.40318i	−0.189947	−	0.328998i	0.755285	−	0.655396i	$-0.227498\pi$
$107$	−1.96483	−	3.40318i	−0.189947	−	0.328998i	−0.945232	+	0.326398i	$0.894165\pi$
$108$	1.89377	−	3.28011i	0.182228	−	0.315629i
$109$			11.2533i			1.07787i	0.842346	+	0.538936i	$0.181174\pi$
$109$			11.2533i			1.07787i	−0.842346	+	0.538936i	$0.818826\pi$
$110$	13.4024	+	7.73787i	1.27787	+	0.737777i
$111$	−14.9857	−	8.65199i	−1.42238	−	0.821210i
$112$		0			0
$113$	2.88709	−	5.00059i	0.271595	−	0.470416i	−0.697676	−	0.716414i	$-0.745782\pi$
$113$	2.88709	−	5.00059i	0.271595	−	0.470416i	0.969270	+	0.245998i	$0.0791157\pi$
$114$	−2.14385	−	3.71325i	−0.200790	−	0.347778i
$115$	7.47437	−	4.31533i	0.696989	−	0.402407i
$116$	−7.92849			−0.736142
$117$	12.5718	+	7.61907i	1.16227	+	0.704383i
$118$	−3.95790			−0.364354
$119$		0			0
$120$	−11.5063	−	19.9294i	−1.05037	−	1.81930i
$121$	12.1578	−	21.0580i	1.10526	−	1.91436i
$122$			0.952877i			0.0862694i
$123$	8.60209	+	4.96642i	0.775625	+	0.447807i
$124$	−1.31815	−	0.761033i	−0.118373	−	0.0683428i
$125$			0.00370455i			0.000331345i
$126$		0			0
$127$	3.06558	+	5.30975i	0.272027	+	0.471164i	0.969381	−	0.245563i	$-0.0789728\pi$
$127$	3.06558	+	5.30975i	0.272027	+	0.471164i	−0.697354	+	0.716727i	$0.745639\pi$
$128$	7.18812	−	4.15007i	0.635346	−	0.366817i
$129$	18.5988			1.63753
$130$	8.22942	−	4.52086i	0.721767	−	0.396506i
$131$	−10.2217			−0.893073			−0.446537	−	0.894765i	$-0.647343\pi$
$131$	−10.2217			−0.893073			−0.446537	+	0.894765i	$0.647343\pi$
$132$	−18.0965	+	10.4480i	−1.57510	+	0.909383i
$133$		0			0
$134$	−2.58563	+	4.47844i	−0.223364	+	0.386878i
$135$		−	9.06111i		−	0.779856i
$136$	6.39584	+	3.69264i	0.548439	+	0.316641i
$137$	−17.2751	−	9.97376i	−1.47591	−	0.852116i	−0.476278	−	0.879295i	$-0.658014\pi$
$137$	−17.2751	−	9.97376i	−1.47591	−	0.852116i	−0.999631	+	0.0271788i	$0.991348\pi$
$138$		−	5.97987i		−	0.509041i
$139$	−10.1637	+	17.6041i	−0.862077	+	1.49316i	0.00784365	+	0.999969i	$0.497503\pi$
$139$	−10.1637	+	17.6041i	−0.862077	+	1.49316i	−0.869921	+	0.493192i	$0.835830\pi$
$140$		0			0
$141$	1.05073	−	0.606641i	0.0884877	−	0.0510884i
$142$	3.71193			0.311498
$143$	−10.3166	−	18.7795i	−0.862718	−	1.57042i
$144$	1.59233			0.132694
$145$	−16.4265	+	9.48383i	−1.36414	+	0.787589i
$146$	−3.42013	−	5.92383i	−0.283052	−	0.490260i
$147$		0			0
$148$		−	8.59741i		−	0.706703i
$149$	−9.28046	−	5.35808i	−0.760285	−	0.438951i	0.0691132	−	0.997609i	$-0.477983\pi$
$149$	−9.28046	−	5.35808i	−0.760285	−	0.438951i	−0.829398	+	0.558658i	$0.811316\pi$
$150$	−9.48465	−	5.47597i	−0.774418	−	0.447111i
$151$		−	8.74416i		−	0.711590i	−0.934564	−	0.355795i	$-0.884210\pi$
$151$		−	8.74416i		−	0.711590i	0.934564	−	0.355795i	$-0.115790\pi$
$152$	2.67690	−	4.63653i	0.217125	−	0.376072i
$153$	5.50343	+	9.53222i	0.444926	+	0.770634i
$154$		0			0
$155$	−3.64130			−0.292476
$156$	−0.269413	+	12.6752i	−0.0215703	+	1.01483i
$157$	−6.50734			−0.519342			−0.259671	−	0.965697i	$-0.583614\pi$
$157$	−6.50734			−0.519342			−0.259671	+	0.965697i	$0.583614\pi$
$158$	−5.64449	+	3.25885i	−0.449052	+	0.259260i
$159$	0.531109	+	0.919907i	0.0421197	+	0.0729534i
$160$	9.15891	−	15.8637i	0.724075	−	1.25414i
$161$		0			0
$162$	3.28672	+	1.89759i	0.258229	+	0.149089i
$163$	2.26264	+	1.30634i	0.177224	+	0.102320i	0.585988	−	0.810320i	$-0.300707\pi$
$163$	2.26264	+	1.30634i	0.177224	+	0.102320i	−0.408764	+	0.912640i	$0.634040\pi$
$164$			4.93509i			0.385366i
$165$	−24.9952	+	43.2930i	−1.94588	+	3.37036i
$166$	−2.55218	−	4.42050i	−0.198087	−	0.343097i
$167$	3.36558	−	1.94312i	0.260436	−	0.150363i	−0.364097	−	0.931361i	$-0.618622\pi$
$167$	3.36558	−	1.94312i	0.260436	−	0.150363i	0.624534	+	0.780998i	$0.285289\pi$
$168$		0			0
$169$	−12.9883	−	0.552385i	−0.999097	−	0.0424911i
$170$	7.03030			0.539200
$171$	6.91018	−	3.98959i	0.528434	−	0.305092i
$172$	4.62036	+	8.00270i	0.352299	+	0.610200i
$173$	−6.98838	+	12.1042i	−0.531317	+	0.920267i	0.468015	+	0.883720i	$0.344969\pi$
$173$	−6.98838	+	12.1042i	−0.531317	+	0.920267i	−0.999332	+	0.0365470i	$0.988364\pi$
$174$			13.1420i			0.996293i
$175$		0			0
$176$	−2.00997	−	1.16046i	−0.151507	−	0.0874727i
$177$		−	12.7850i		−	0.960979i
$178$	−1.46649	+	2.54004i	−0.109918	+	0.190384i
$179$	−12.6422	−	21.8968i	−0.944919	−	1.63665i	−0.755914	−	0.654671i	$-0.772807\pi$
$179$	−12.6422	−	21.8968i	−0.944919	−	1.63665i	−0.189005	−	0.981976i	$-0.560526\pi$
$180$	14.7575	−	8.52026i	1.09996	−	0.635063i
$181$	0.864474			0.0642559			0.0321279	−	0.999484i	$-0.489772\pi$
$181$	0.864474			0.0642559			0.0321279	+	0.999484i	$0.489772\pi$
$182$		0			0
$183$	−3.07803			−0.227535
$184$	6.46638	−	3.73336i	0.476708	−	0.275227i
$185$	−10.2840	−	17.8124i	−0.756093	−	1.30959i
$186$	−1.26146	+	2.18492i	−0.0924950	+	0.160206i
$187$		−	16.0432i		−	1.17319i
$188$	0.522052	+	0.301407i	0.0380746	+	0.0219824i
$189$		0			0
$190$		−	5.09647i		−	0.369737i
$191$	−7.33382	+	12.7026i	−0.530657	+	0.919125i	0.468703	+	0.883356i	$0.344721\pi$
$191$	−7.33382	+	12.7026i	−0.530657	+	0.919125i	−0.999360	+	0.0357690i	$0.988612\pi$
$192$	−5.30690	−	9.19182i	−0.382993	−	0.663363i
$193$	14.2859	−	8.24794i	1.02832	−	0.593700i	0.111816	−	0.993729i	$-0.464333\pi$
$193$	14.2859	−	8.24794i	1.02832	−	0.593700i	0.916503	+	0.400029i	$0.131000\pi$
$194$	2.82275			0.202661
$195$	14.6035	+	26.5831i	1.04578	+	1.90365i
$196$		0			0
$197$	9.53510	−	5.50509i	0.679348	−	0.392222i	−0.120262	−	0.992742i	$-0.538373\pi$
$197$	9.53510	−	5.50509i	0.679348	−	0.392222i	0.799609	+	0.600521i	$0.205040\pi$
$198$	9.97709	+	17.2808i	0.709041	+	1.22809i
$199$	10.6059	−	18.3699i	0.751829	−	1.30221i	−0.195106	−	0.980782i	$-0.562505\pi$
$199$	10.6059	−	18.3699i	0.751829	−	1.30221i	0.946935	−	0.321425i	$-0.104162\pi$
$200$		−	13.6751i		−	0.966972i
$201$	−14.4665	−	8.35223i	−1.02039	−	0.589121i
$202$	9.50686	+	5.48879i	0.668901	+	0.386190i
$203$		0			0
$204$	−4.74632	+	8.22086i	−0.332309	+	0.575576i
$205$	5.90322	+	10.2247i	0.412299	+	0.714122i
$206$	8.30542	−	4.79514i	0.578666	−	0.334093i
$207$	11.1282			0.773466
$208$	−1.23417	+	0.677998i	−0.0855746	+	0.0470107i
$209$	−11.6301			−0.804474
$210$		0			0
$211$	8.96788	+	15.5328i	0.617375	+	1.06932i	0.989963	+	0.141327i	$0.0451370\pi$
$211$	8.96788	+	15.5328i	0.617375	+	1.06932i	−0.372588	+	0.927997i	$0.621530\pi$
$212$	−0.263879	+	0.457052i	−0.0181233	+	0.0313905i
$213$			11.9905i			0.821572i
$214$	−2.80271	−	1.61815i	−0.191589	−	0.110614i
$215$	19.1452	+	11.0535i	1.30569	+	0.753842i
$216$		−	7.83913i		−	0.533385i
$217$		0			0
$218$	4.63387	+	8.02610i	0.313845	+	0.543596i
$219$	19.1355	−	11.0479i	1.29305	−	0.746545i
$220$	−24.8376			−1.67455
$221$	−8.32431	−	5.04488i	−0.559953	−	0.339356i
$222$	−14.2508			−0.956451
$223$	13.8834	−	8.01558i	0.929700	−	0.536763i	0.0429835	−	0.999076i	$-0.486314\pi$
$223$	13.8834	−	8.01558i	0.929700	−	0.536763i	0.886717	+	0.462313i	$0.152980\pi$
$224$		0			0
$225$	10.1905	−	17.6505i	0.679366	−	1.17670i
$226$		−	4.75536i		−	0.316322i
$227$	14.1812	+	8.18751i	0.941239	+	0.543424i	0.890348	−	0.455280i	$-0.150461\pi$
$227$	14.1812	+	8.18751i	0.941239	+	0.543424i	0.0508902	+	0.998704i	$0.483794\pi$
$228$	5.95954	+	3.44074i	0.394680	+	0.227869i
$229$		−	27.0104i		−	1.78490i	−0.451148	−	0.892449i	$-0.648985\pi$
$229$		−	27.0104i		−	1.78490i	0.451148	−	0.892449i	$-0.351015\pi$
$230$	3.55392	−	6.15556i	0.234338	−	0.405886i
$231$		0			0
$232$	−14.2112	+	8.20484i	−0.933011	+	0.538674i
$233$	−11.5681			−0.757853			−0.378926	−	0.925427i	$-0.623707\pi$
$233$	−11.5681			−0.757853			−0.378926	+	0.925427i	$0.623707\pi$
$234$	12.1039	+	0.257269i	0.791254	+	0.0168182i
$235$	1.44214			0.0940747
$236$	5.50114	−	3.17609i	0.358094	−	0.206746i
$237$	−10.5269	−	18.2331i	−0.683796	−	1.18437i
$238$		0			0
$239$		−	14.6731i		−	0.949122i	−0.880223	−	0.474561i	$-0.842607\pi$
$239$		−	14.6731i		−	0.949122i	0.880223	−	0.474561i	$-0.157393\pi$
$240$	2.84518	+	1.64267i	0.183656	+	0.106034i
$241$	−12.4246	−	7.17334i	−0.800338	−	0.462076i	0.0432510	−	0.999064i	$-0.486228\pi$
$241$	−12.4246	−	7.17334i	−0.800338	−	0.462076i	−0.843589	+	0.536989i	$0.819562\pi$
$242$		−	20.0253i		−	1.28727i
$243$	−10.4280	+	18.0618i	−0.668956	+	1.15867i
$244$	−0.764654	−	1.32442i	−0.0489519	−	0.0847872i
$245$		0			0
$246$	8.18025			0.521554
$247$	−3.65718	+	6.03453i	−0.232701	+	0.383968i
$248$	−3.15024			−0.200040
$249$	14.2793	−	8.24417i	0.904916	−	0.522453i
$250$	0.00152545	+	0.00264216i	9.64781e−5	+	0.000167105i
$251$	−4.30726	+	7.46040i	−0.271872	+	0.470896i	−0.969341	−	0.245719i	$-0.920976\pi$
$251$	−4.30726	+	7.46040i	−0.271872	+	0.470896i	0.697469	+	0.716615i	$0.254309\pi$
$252$		0			0
$253$	−14.0470	−	8.11004i	−0.883128	−	0.509874i
$254$	4.37287	+	2.52468i	0.274378	+	0.158412i
$255$			22.7096i			1.42213i
$256$	7.40753	−	12.8302i	0.462970	−	0.801888i
$257$	−5.18197	−	8.97544i	−0.323243	−	0.559873i	0.657912	−	0.753094i	$-0.271440\pi$
$257$	−5.18197	−	8.97544i	−0.323243	−	0.559873i	−0.981155	+	0.193222i	$0.938106\pi$
$258$	13.2650	−	7.65856i	0.825844	−	0.476801i
$259$		0			0
$260$	−7.81035	+	12.8875i	−0.484377	+	0.799247i
$261$	−24.4566			−1.51383
$262$	−7.29032	+	4.20907i	−0.450397	+	0.260037i
$263$	11.0413	+	19.1241i	0.680835	+	1.17924i	0.974726	+	0.223403i	$0.0717165\pi$
$263$	11.0413	+	19.1241i	0.680835	+	1.17924i	−0.293891	+	0.955839i	$0.594950\pi$
$264$	−21.6244	+	37.4545i	−1.33089	+	2.30517i
$265$			1.26258i			0.0775596i
$266$		0			0
$267$	−8.20495	−	4.73713i	−0.502135	−	0.289908i
$268$		−	8.29954i		−	0.506975i
$269$	6.46995	−	11.2063i	0.394480	−	0.683259i	−0.598555	−	0.801082i	$-0.704258\pi$
$269$	6.46995	−	11.2063i	0.394480	−	0.683259i	0.993035	+	0.117823i	$0.0375915\pi$
$270$	−3.73117	−	6.46257i	−0.227072	−	0.393299i
$271$	15.3069	−	8.83745i	0.929829	−	0.536837i	0.0430712	−	0.999072i	$-0.486286\pi$
$271$	15.3069	−	8.83745i	0.929829	−	0.536837i	0.886757	+	0.462235i	$0.152952\pi$
$272$	−1.05434			−0.0639289
$273$		0			0
$274$	−16.4279			−0.992446
$275$	−25.7266	+	14.8533i	−1.55137	+	0.895685i
$276$	4.79866	+	8.31152i	0.288845	+	0.500295i
$277$	−9.00751	+	15.6015i	−0.541209	+	0.937401i	0.457626	+	0.889145i	$0.348700\pi$
$277$	−9.00751	+	15.6015i	−0.541209	+	0.937401i	−0.998835	+	0.0482562i	$0.984634\pi$
$278$			16.7408i			1.00405i
$279$	−4.06602	−	2.34752i	−0.243426	−	0.140542i
$280$		0			0
$281$			2.44178i			0.145665i	0.997344	+	0.0728323i	$0.0232038\pi$
$281$			2.44178i			0.145665i	−0.997344	+	0.0728323i	$0.976796\pi$
$282$	0.499603	−	0.865337i	0.0297509	−	0.0515301i
$283$	14.3620	+	24.8757i	0.853732	+	1.47871i	0.877817	+	0.478996i	$0.158999\pi$
$283$	14.3620	+	24.8757i	0.853732	+	1.47871i	−0.0240853	+	0.999710i	$0.507667\pi$
$284$	−5.15927	+	2.97871i	−0.306146	+	0.176754i
$285$	16.4629			0.975176
$286$	−15.0910	−	9.14580i	−0.892350	−	0.540802i
$287$		0			0
$288$	20.4544	−	11.8094i	1.20529	−	0.695873i
$289$	4.85596	+	8.41078i	0.285645	+	0.494752i
$290$	−7.81046	+	13.5281i	−0.458646	+	0.794399i
$291$			9.11818i			0.534517i
$292$	9.50738	+	5.48909i	0.556377	+	0.321225i
$293$	−25.4013	−	14.6654i	−1.48396	−	0.856763i	−0.484124	−	0.874999i	$-0.660862\pi$
$293$	−25.4013	−	14.6654i	−1.48396	−	0.856763i	−0.999834	+	0.0182359i	$0.994195\pi$
$294$		0			0
$295$	7.59829	−	13.1606i	0.442390	−	0.766241i
$296$	−8.89708	−	15.4102i	−0.517132	−	0.895699i
$297$	−14.7476	+	8.51453i	−0.855742	+	0.494063i
$298$	−8.82535			−0.511239
$299$	−8.62523	+	4.73830i	−0.498810	+	0.274023i
$300$	17.5772			1.01482
$301$		0			0
$302$	−3.60065	−	6.23651i	−0.207194	−	0.358871i
$303$	−17.7302	+	30.7096i	−1.01857	+	1.76422i
$304$			0.764323i			0.0438369i
$305$	−3.16846	−	1.82931i	−0.181426	−	0.104746i
$306$	7.85032	+	4.53238i	0.448773	+	0.259099i
$307$			7.06910i			0.403455i	0.979442	+	0.201728i	$0.0646555\pi$
$307$			7.06910i			0.403455i	−0.979442	+	0.201728i	$0.935344\pi$
$308$		0			0
$309$	15.4895	+	26.8286i	0.881166	+	1.52623i
$310$	−2.59705	+	1.49941i	−0.147503	+	0.0851607i
$311$	−22.2686			−1.26274			−0.631368	−	0.775483i	$-0.717506\pi$
$311$	−22.2686			−1.26274			−0.631368	+	0.775483i	$0.717506\pi$
$312$	12.6341	+	22.9981i	0.715264	+	1.30201i
$313$	28.0840			1.58740			0.793700	−	0.608309i	$-0.208152\pi$
$313$	28.0840			1.58740			0.793700	+	0.608309i	$0.208152\pi$
$314$	−4.64117	+	2.67958i	−0.261916	+	0.151217i
$315$		0			0
$316$	5.23025	−	9.05906i	0.294225	−	0.509612i
$317$		−	19.5155i		−	1.09610i	−0.836446	−	0.548049i	$-0.815371\pi$
$317$		−	19.5155i		−	1.09610i	0.836446	−	0.548049i	$-0.184629\pi$
$318$	0.757595	+	0.437398i	0.0424838	+	0.0245281i
$319$	30.8712	+	17.8235i	1.72845	+	0.997924i
$320$		−	12.6158i		−	0.705247i
$321$	5.22702	−	9.05346i	0.291744	−	0.505315i
$322$		0			0
$323$	−4.57550	+	2.64167i	−0.254588	+	0.146986i
$324$	−6.09102			−0.338390
$325$	−0.383007	+	18.0195i	−0.0212454	+	0.999540i
$326$	2.15168			0.119171
$327$	−25.9263	+	14.9686i	−1.43373	+	0.827764i
$328$	5.10711	+	8.84577i	0.281993	+	0.488426i
$329$		0			0
$330$			41.1700i			2.26633i
$331$	13.5367	+	7.81539i	0.744042	+	0.429573i	0.823537	−	0.567263i	$-0.191998\pi$
$331$	13.5367	+	7.81539i	0.744042	+	0.429573i	−0.0794953	+	0.996835i	$0.525331\pi$
$332$	7.09463	+	4.09609i	0.389368	+	0.224802i
$333$		−	26.5200i		−	1.45329i
$334$	1.60027	−	2.77174i	0.0875627	−	0.151663i
$335$	−9.92767	−	17.1952i	−0.542407	−	0.939476i
$336$		0			0
$337$	21.7501			1.18480			0.592401	−	0.805643i	$-0.298180\pi$
$337$	21.7501			1.18480			0.592401	+	0.805643i	$0.298180\pi$
$338$	−9.49095	+	4.95431i	−0.516240	+	0.269479i
$339$	15.3610			0.834295
$340$	−9.77153	+	5.64160i	−0.529936	+	0.305959i
$341$	3.42165	+	5.92647i	0.185293	+	0.320937i
$342$	3.28565	−	5.69092i	0.177668	−	0.307730i
$343$		0			0
$344$	16.5633	+	9.56281i	0.893032	+	0.515592i
$345$	19.8840	+	11.4800i	1.07052	+	0.618065i
$346$			11.5106i			0.618816i
$347$	7.97952	−	13.8209i	0.428363	−	0.741946i	−0.568365	−	0.822777i	$-0.692424\pi$
$347$	7.97952	−	13.8209i	0.428363	−	0.741946i	0.996728	+	0.0808303i	$0.0257572\pi$
$348$	−10.5460	−	18.2663i	−0.565327	−	0.979176i
$349$	−5.90375	+	3.40853i	−0.316021	+	0.182455i	−0.649617	−	0.760261i	$-0.725071\pi$
$349$	−5.90375	+	3.40853i	−0.316021	+	0.182455i	0.333597	+	0.942716i	$0.391738\pi$
$350$		0			0
$351$	−0.219556	+	10.3295i	−0.0117190	+	0.551349i
$352$	−34.4257			−1.83490
$353$	−12.1272	+	7.00163i	−0.645465	+	0.372659i	−0.786716	−	0.617314i	$-0.788221\pi$
$353$	−12.1272	+	7.00163i	−0.645465	+	0.372659i	0.141252	+	0.989974i	$0.454887\pi$
$354$	−5.26458	−	9.11852i	−0.279809	−	0.484644i
$355$	−7.12608	+	12.3427i	−0.378213	+	0.655085i
$356$		−	4.70725i		−	0.249484i
$357$		0			0
$358$	−18.0333	−	10.4115i	−0.953088	−	0.550266i
$359$			5.41494i			0.285789i	0.989738	+	0.142895i	$0.0456410\pi$
$359$			5.41494i			0.285789i	−0.989738	+	0.142895i	$0.954359\pi$
$360$	17.6345	−	30.5438i	0.929418	−	1.60980i
$361$	−7.58498	−	13.1376i	−0.399210	−	0.691451i
$362$	0.616561	−	0.355972i	0.0324057	−	0.0187094i
$363$	64.6867			3.39517
$364$		0			0
$365$	26.2636			1.37470
$366$	−2.19531	+	1.26747i	−0.114751	+	0.0662515i
$367$	15.0159	+	26.0083i	0.783822	+	1.35762i	0.929700	+	0.368317i	$0.120066\pi$
$367$	15.0159	+	26.0083i	0.783822	+	1.35762i	−0.145878	+	0.989303i	$0.546601\pi$
$368$	−0.532985	+	0.923157i	−0.0277838	+	0.0481229i
$369$			15.2230i			0.792480i
$370$	−14.6695	−	8.46943i	−0.762630	−	0.440305i
$371$		0			0
$372$		−	4.04914i		−	0.209938i
$373$	−10.7049	+	18.5414i	−0.554278	+	0.960037i	0.443682	+	0.896184i	$0.353672\pi$
$373$	−10.7049	+	18.5414i	−0.554278	+	0.960037i	−0.997959	+	0.0638526i	$0.979661\pi$
$374$	−6.60622	−	11.4423i	−0.341599	−	0.591668i
$375$	−0.00853484	+	0.00492759i	−0.000440737	+	0.000254460i
$376$	1.24765			0.0643427
$377$	18.9557	−	10.4134i	0.976270	−	0.536317i
$378$		0			0
$379$	−8.20693	+	4.73827i	−0.421562	+	0.243389i	−0.695745	−	0.718289i	$-0.744926\pi$
$379$	−8.20693	+	4.73827i	−0.421562	+	0.243389i	0.274184	+	0.961677i	$0.411592\pi$
$380$	4.08975	+	7.08366i	0.209800	+	0.363384i
$381$	−8.15535	+	14.1255i	−0.417811	+	0.723670i
$382$			12.0796i			0.618048i
$383$	4.70304	+	2.71530i	0.240314	+	0.138746i	0.615321	−	0.788277i	$-0.289026\pi$
$383$	4.70304	+	2.71530i	0.240314	+	0.138746i	−0.375007	+	0.927022i	$0.622360\pi$
$384$	19.1225	+	11.0404i	0.975842	+	0.563402i
$385$		0			0
$386$	6.79264	−	11.7652i	0.345736	−	0.598833i
$387$	14.2522	+	24.6855i	0.724480	+	1.25484i
$388$	−3.92338	+	2.26516i	−0.199179	+	0.114996i
$389$	10.6422			0.539580			0.269790	−	0.962919i	$-0.413046\pi$
$389$	10.6422			0.539580			0.269790	+	0.962919i	$0.413046\pi$
$390$	21.3618	+	12.9462i	1.08170	+	0.655556i
$391$	−7.36845			−0.372638
$392$		0			0
$393$	−13.5963	−	23.5495i	−0.685845	−	1.18792i
$394$	4.53375	−	7.85269i	0.228407	−	0.395613i
$395$		−	25.0251i		−	1.25915i
$396$	−27.7346	−	16.0126i	−1.39372	−	0.804663i
$397$	−32.2035	−	18.5927i	−1.61625	−	0.933140i	−0.987879	−	0.155223i	$-0.950390\pi$
$397$	−32.2035	−	18.5927i	−1.61625	−	0.933140i	−0.628367	−	0.777917i	$-0.716276\pi$
$398$		−	17.4690i		−	0.875644i
$399$		0			0
$400$	0.976143	+	1.69073i	0.0488072	+	0.0845365i
$401$	−0.776487	+	0.448305i	−0.0387759	+	0.0223873i	−0.519263	−	0.854615i	$-0.673793\pi$
$401$	−0.776487	+	0.448305i	−0.0387759	+	0.0223873i	0.480487	+	0.877002i	$0.340460\pi$
$402$	−13.7571			−0.686139
$403$	4.15103	+	0.0882308i	0.206777	+	0.00439509i
$404$	−17.6183			−0.876545
$405$	−12.6196	+	7.28590i	−0.627071	+	0.362039i
$406$		0			0
$407$	−19.3273	+	33.4758i	−0.958016	+	1.65933i
$408$			19.6470i			0.972672i
$409$	−21.2846	−	12.2886i	−1.05245	−	0.607635i	−0.129119	−	0.991629i	$-0.541215\pi$
$409$	−21.2846	−	12.2886i	−1.05245	−	0.607635i	−0.923335	+	0.383995i	$0.874548\pi$
$410$	8.42059	+	4.86163i	0.415863	+	0.240099i
$411$		−	53.0662i		−	2.61756i
$412$	−7.69589	+	13.3297i	−0.379149	+	0.656706i
$413$		0			0
$414$	7.93689	−	4.58237i	0.390077	−	0.225211i
$415$	19.5985			0.962052
$416$	−10.8254	+	17.8624i	−0.530759	+	0.875778i
$417$	−54.0770			−2.64816
$418$	−8.29486	+	4.78904i	−0.405715	+	0.234239i
$419$	−3.82279	−	6.62126i	−0.186755	−	0.323470i	0.757411	−	0.652938i	$-0.226464\pi$
$419$	−3.82279	−	6.62126i	−0.186755	−	0.323470i	−0.944167	+	0.329468i	$0.893131\pi$
$420$		0			0
$421$			25.0780i			1.22223i	0.791544	+	0.611113i	$0.209278\pi$
$421$			25.0780i			1.22223i	−0.791544	+	0.611113i	$0.790722\pi$
$422$	12.7922	+	7.38555i	0.622712	+	0.359523i
$423$	1.61035	+	0.929736i	0.0782979	+	0.0452053i
$424$			1.09231i			0.0530471i
$425$	−6.74753	+	11.6871i	−0.327303	+	0.566906i
$426$	4.93741	+	8.55184i	0.239218	+	0.414338i
$427$		0			0
$428$	5.19405			0.251064
$429$	29.5432	−	48.7478i	1.42636	−	2.35356i
$430$	18.2063			0.877987
$431$	6.71520	−	3.87702i	0.323460	−	0.186750i	−0.329474	−	0.944165i	$-0.606871\pi$
$431$	6.71520	−	3.87702i	0.323460	−	0.186750i	0.652934	+	0.757415i	$0.273538\pi$
$432$	0.559567	+	0.969199i	0.0269222	+	0.0466306i
$433$	−17.9880	+	31.1561i	−0.864448	+	1.49727i	0.00314644	+	0.999995i	$0.498998\pi$
$433$	−17.9880	+	31.1561i	−0.864448	+	1.49727i	−0.867594	+	0.497273i	$0.834335\pi$
$434$		0			0
$435$	−43.6992	−	25.2298i	−2.09522	−	1.20967i
$436$	−12.8814	−	7.43707i	−0.616907	−	0.356171i
$437$			5.34160i			0.255523i
$438$	9.09853	−	15.7591i	0.434745	−	0.753000i
$439$	14.1175	+	24.4523i	0.673792	+	1.16704i	0.976820	+	0.214061i	$0.0686691\pi$
$439$	14.1175	+	24.4523i	0.673792	+	1.16704i	−0.303028	+	0.952982i	$0.597998\pi$
$440$	−44.5194	+	25.7033i	−2.12238	+	1.22536i
$441$		0			0
$442$	−8.01444	−	0.170348i	−0.381208	−	0.00810264i
$443$	28.7918			1.36794			0.683970	−	0.729511i	$-0.260252\pi$
$443$	28.7918			1.36794			0.683970	+	0.729511i	$0.260252\pi$
$444$	19.8074	−	11.4358i	0.940018	−	0.542720i
$445$	−5.63068	−	9.75262i	−0.266920	−	0.462319i
$446$	6.60128	−	11.4337i	0.312579	−	0.541404i
$447$		−	28.5081i		−	1.34839i
$448$		0			0
$449$	−25.2795	−	14.5951i	−1.19301	−	0.688785i	−0.234023	−	0.972231i	$-0.575189\pi$
$449$	−25.2795	−	14.5951i	−1.19301	−	0.688785i	−0.958988	+	0.283446i	$0.908522\pi$
$450$		−	16.7849i		−	0.791247i
$451$	11.0942	−	19.2158i	0.522408	−	0.904836i
$452$	3.81603	+	6.60955i	0.179491	+	0.310887i
$453$	20.1455	−	11.6310i	0.946518	−	0.546473i
$454$	13.4858			0.632918
$455$		0			0
$456$	14.2427			0.666974
$457$	−27.4399	+	15.8424i	−1.28358	+	0.741077i	−0.977501	−	0.210929i	$-0.932351\pi$
$457$	−27.4399	+	15.8424i	−1.28358	+	0.741077i	−0.306081	+	0.952006i	$0.599018\pi$
$458$	−11.1223	−	19.2644i	−0.519711	−	0.900165i
$459$	−3.86797	+	6.69952i	−0.180541	+	0.312707i
$460$			11.4076i			0.531883i
$461$	19.1407	+	11.0509i	0.891471	+	0.514691i	0.874424	−	0.485163i	$-0.161240\pi$
$461$	19.1407	+	11.0509i	0.891471	+	0.514691i	0.0170480	+	0.999855i	$0.494573\pi$
$462$		0			0
$463$		−	38.8811i		−	1.80696i	−0.428632	−	0.903479i	$-0.641004\pi$
$463$		−	38.8811i		−	1.80696i	0.428632	−	0.903479i	$-0.358996\pi$
$464$	1.17134	−	2.02883i	0.0543783	−	0.0941860i
$465$	−4.84346	−	8.38913i	−0.224610	−	0.389036i
$466$	−8.25062	+	4.76350i	−0.382202	+	0.220665i
$467$	13.2823			0.614632			0.307316	−	0.951607i	$-0.400569\pi$
$467$	13.2823			0.614632			0.307316	+	0.951607i	$0.400569\pi$
$468$	−17.0298	+	9.35538i	−0.787203	+	0.432453i
$469$		0			0
$470$	1.02856	−	0.593841i	0.0474440	−	0.0273918i
$471$	−8.65571	−	14.9921i	−0.398834	−	0.690801i
$472$	6.57358	−	11.3858i	0.302574	−	0.524073i
$473$		−	41.5469i		−	1.91033i
$474$	−15.0160	−	8.66949i	−0.689708	−	0.398203i
$475$	8.47228	+	4.89147i	0.388735	+	0.224436i
$476$		0			0
$477$	−0.813975	+	1.40985i	−0.0372694	+	0.0645524i
$478$	−6.04205	−	10.4651i	−0.276357	−	0.478664i
$479$	−5.74618	+	3.31756i	−0.262550	+	0.151583i	−0.625497	−	0.780226i	$-0.715104\pi$
$479$	−5.74618	+	3.31756i	−0.262550	+	0.151583i	0.362947	+	0.931810i	$0.381770\pi$
$480$	48.7307			2.22424
$481$	11.2920	+	20.5550i	0.514870	+	0.937228i
$482$	−11.8153			−0.538172
$483$		0			0
$484$	16.0697	+	27.8335i	0.730439	+	1.26516i
$485$	−5.41905	+	9.38607i	−0.246066	+	0.426200i
$486$			17.1761i			0.779123i
$487$	28.9860	+	16.7351i	1.31348	+	0.758338i	0.982671	−	0.185359i	$-0.0593449\pi$
$487$	28.9860	+	16.7351i	1.31348	+	0.758338i	0.330809	+	0.943698i	$0.392678\pi$
$488$	−2.74116	−	1.58261i	−0.124087	−	0.0716415i
$489$			6.95047i			0.314311i
$490$		0			0
$491$	−18.6643	−	32.3276i	−0.842310	−	1.45892i	−0.887937	−	0.459966i	$-0.847862\pi$
$491$	−18.6643	−	32.3276i	−0.842310	−	1.45892i	0.0456264	−	0.998959i	$-0.485472\pi$
$492$	−11.3699	+	6.56439i	−0.512593	+	0.295946i
$493$	16.1937			0.729327
$494$	−0.123490	+	5.80989i	−0.00555609	+	0.261399i
$495$	−76.6152			−3.44360
$496$	0.389483	−	0.224868i	0.0174883	−	0.0100969i
$497$		0			0
$498$	6.78954	−	11.7598i	0.304246	−	0.526970i
$499$		−	34.1327i		−	1.52799i	−0.645223	−	0.763994i	$-0.723236\pi$
$499$		−	34.1327i		−	1.52799i	0.645223	−	0.763994i	$-0.276764\pi$
$500$	−0.00424050	−	0.00244826i	−0.000189641	−	0.000109489i
$501$	8.95342	+	5.16926i	0.400009	+	0.230946i
$502$			7.09454i			0.316645i
$503$	7.65447	−	13.2579i	0.341296	−	0.591142i	−0.643378	−	0.765549i	$-0.722467\pi$
$503$	7.65447	−	13.2579i	0.341296	−	0.591142i	0.984674	+	0.174407i	$0.0558008\pi$
$504$		0			0
$505$	−36.5022	+	21.0745i	−1.62433	+	0.937805i
$506$	−13.3581			−0.593842
$507$	−16.0037	−	30.6581i	−0.710747	−	1.36158i
$508$	−8.10390			−0.359553
$509$	16.0189	−	9.24851i	0.710025	−	0.409933i	−0.101046	−	0.994882i	$-0.532219\pi$
$509$	16.0189	−	9.24851i	0.710025	−	0.409933i	0.811070	+	0.584949i	$0.198885\pi$
$510$	9.35133	+	16.1970i	0.414084	+	0.717214i
$511$		0			0
$512$			4.39924i			0.194421i
$513$	4.85668	+	2.80400i	0.214427	+	0.123800i
$514$	−7.39178	−	4.26765i	−0.326037	−	0.188238i
$515$			36.8224i			1.62259i
$516$	−12.2915	+	21.2895i	−0.541104	+	0.937219i
$517$	−1.35515	−	2.34718i	−0.0595992	−	0.103229i
$518$		0			0
$519$	−37.1823			−1.63212
$520$	−0.662786	+	31.1824i	−0.0290651	+	1.36744i
$521$	−23.5865			−1.03334			−0.516671	−	0.856184i	$-0.672829\pi$
$521$	−23.5865			−1.03334			−0.516671	+	0.856184i	$0.672829\pi$
$522$	−17.4430	+	10.0707i	−0.763457	+	0.440782i
$523$	6.15294	+	10.6572i	0.269049	+	0.466007i	0.968617	−	0.248560i	$-0.0799572\pi$
$523$	6.15294	+	10.6572i	0.269049	+	0.466007i	−0.699567	+	0.714567i	$0.746624\pi$
$524$	6.75529	−	11.7005i	0.295106	−	0.511139i
$525$		0			0
$526$	15.7498	+	9.09312i	0.686722	+	0.396479i
$527$	2.69227	+	1.55438i	0.117277	+	0.0677101i
$528$		−	6.17431i		−	0.268702i
$529$	7.77515	−	13.4670i	0.338050	−	0.585520i
$530$	0.519902	+	0.900497i	0.0225831	+	0.0391151i
$531$	16.9691	−	9.79712i	0.736397	−	0.425159i
$532$		0			0
$533$	−6.48183	−	11.7990i	−0.280759	−	0.511072i
$534$	−7.80259			−0.337651
$535$	10.7612	−	6.21297i	0.465246	−	0.268610i
$536$	−8.58883	−	14.8763i	−0.370981	−	0.642558i
$537$	33.6318	−	58.2520i	1.45132	−	2.51376i
$538$		−	10.6567i		−	0.459444i
$539$		0			0
$540$	10.3720	+	5.98829i	0.446341	+	0.257695i
$541$			19.4411i			0.835838i	0.908484	+	0.417919i	$0.137240\pi$
$541$			19.4411i			0.835838i	−0.908484	+	0.417919i	$0.862760\pi$
$542$	7.27813	−	12.6061i	0.312623	−	0.541478i
$543$	1.14988	+	1.99165i	0.0493460	+	0.0854697i
$544$	−13.5437	+	7.81944i	−0.580680	+	0.335256i
$545$	−35.5841			−1.52425
$546$		0			0
$547$	40.2163			1.71953			0.859763	−	0.510693i	$-0.170611\pi$
$547$	40.2163			1.71953			0.859763	+	0.510693i	$0.170611\pi$
$548$	22.8334	−	13.1829i	0.975395	−	0.563145i
$549$	−2.35869	−	4.08537i	−0.100666	−	0.174359i
$550$	−12.2325	+	21.1873i	−0.521595	+	0.903429i
$551$		−	11.7393i		−	0.500109i
$552$	17.2024	+	9.93184i	0.732185	+	0.422727i
$553$		0			0
$554$			14.8364i			0.630337i
$555$	27.3584	−	47.3861i	1.16130	−	2.01143i
$556$	−13.4340	−	23.2683i	−0.569727	−	0.986797i
$557$	6.89702	−	3.98199i	0.292236	−	0.168722i	−0.346714	−	0.937971i	$-0.612703\pi$
$557$	6.89702	−	3.98199i	0.292236	−	0.168722i	0.638950	+	0.769248i	$0.279369\pi$
$558$	−3.86663			−0.163687
$559$	−21.5574	−	13.0647i	−0.911781	−	0.552578i
$560$		0			0
$561$	36.9615	−	21.3397i	1.56052	−	0.900965i
$562$	1.00547	+	1.74153i	0.0424133	+	0.0734620i
$563$	0.711981	−	1.23319i	0.0300064	−	0.0519726i	−0.850632	−	0.525761i	$-0.823781\pi$
$563$	0.711981	−	1.23319i	0.0300064	−	0.0519726i	0.880639	+	0.473789i	$0.157114\pi$
$564$			1.60366i			0.0675263i
$565$	15.8123	+	9.12924i	0.665229	+	0.384070i
$566$	20.4865	+	11.8279i	0.861113	+	0.497164i
$567$		0			0
$568$	−6.16506	+	10.6782i	−0.258680	+	0.448047i
$569$	−9.25946	−	16.0379i	−0.388177	−	0.672342i	0.604028	−	0.796963i	$-0.293562\pi$
$569$	−9.25946	−	16.0379i	−0.388177	−	0.672342i	−0.992204	+	0.124622i	$0.960228\pi$
$570$	11.7417	−	6.77904i	0.491804	−	0.283943i
$571$	−4.35766			−0.182362			−0.0911812	−	0.995834i	$-0.529064\pi$
$571$	−4.35766			−0.182362			−0.0911812	+	0.995834i	$0.529064\pi$
$572$	28.3145	+	0.601828i	1.18389	+	0.0251637i
$573$	−39.0202			−1.63009
$574$		0			0
$575$	6.82194	+	11.8159i	0.284494	+	0.492759i
$576$	8.13334	−	14.0874i	0.338889	−	0.586973i
$577$		−	9.56416i		−	0.398161i	−0.979983	−	0.199081i	$-0.936204\pi$
$577$		−	9.56416i		−	0.398161i	0.979983	−	0.199081i	$-0.0637955\pi$
$578$	6.92674	+	3.99916i	0.288115	+	0.166343i
$579$	38.0046	+	21.9419i	1.57942	+	0.911876i
$580$		−	25.0706i		−	1.04100i
$581$		0			0
$582$	3.75466	+	6.50327i	0.155636	+	0.269569i
$583$	2.05494	−	1.18642i	0.0851068	−	0.0491364i
$584$	22.7216			0.940228
$585$	−24.0922	+	39.7533i	−0.996090	+	1.64360i
$586$	−24.1556			−0.997859
$587$	2.04428	−	1.18027i	0.0843765	−	0.0487148i	−0.457218	−	0.889355i	$-0.651154\pi$
$587$	2.04428	−	1.18027i	0.0843765	−	0.0487148i	0.541595	+	0.840640i	$0.317821\pi$
$588$		0			0
$589$	1.12682	−	1.95171i	0.0464297	−	0.0804186i
$590$		−	12.5152i		−	0.515244i
$591$	25.3661	+	14.6452i	1.04342	+	0.602421i
$592$	2.20000	+	1.27017i	0.0904194	+	0.0522037i
$593$		−	40.4292i		−	1.66023i	−0.557594	−	0.830114i	$-0.688275\pi$
$593$		−	40.4292i		−	1.66023i	0.557594	−	0.830114i	$-0.311725\pi$
$594$	−7.01219	+	12.1455i	−0.287714	+	0.498335i
$595$		0			0
$596$	12.2665	−	7.08207i	0.502455	−	0.290093i
$597$	56.4294			2.30950
$598$	−4.20056	+	6.93114i	−0.171774	+	0.283435i
$599$	−38.5873			−1.57663			−0.788316	−	0.615270i	$-0.789047\pi$
$599$	−38.5873			−1.57663			−0.788316	+	0.615270i	$0.789047\pi$
$600$	31.5057	−	18.1898i	1.28621	−	0.742596i
$601$	4.08115	+	7.06877i	0.166474	+	0.288341i	0.937178	−	0.348852i	$-0.113429\pi$
$601$	4.08115	+	7.06877i	0.166474	+	0.288341i	−0.770704	+	0.637193i	$0.780095\pi$
$602$		0			0
$603$		−	25.6012i		−	1.04256i
$604$	10.0092	+	5.77882i	0.407269	+	0.235137i
$605$	66.5872	+	38.4442i	2.70716	+	1.56298i
$606$			29.2036i			1.18631i
$607$	3.79263	−	6.56902i	0.153938	−	0.266628i	−0.778734	−	0.627354i	$-0.784138\pi$
$607$	3.79263	−	6.56902i	0.153938	−	0.266628i	0.932672	+	0.360726i	$0.117471\pi$
$608$	5.66853	+	9.81819i	0.229889	+	0.398180i
$609$		0			0
$610$	−3.01308			−0.121996
$611$	−1.64402	−	0.0349438i	−0.0665098	−	0.00141368i
$612$	−14.5484			−0.588083
$613$	−13.4908	+	7.78892i	−0.544889	+	0.314592i	−0.747058	−	0.664759i	$-0.768534\pi$
$613$	−13.4908	+	7.78892i	−0.544889	+	0.314592i	0.202169	+	0.979351i	$0.435201\pi$
$614$	2.91090	+	5.04183i	0.117474	+	0.203472i
$615$	−15.7043	+	27.2006i	−0.633258	+	1.09683i
$616$		0			0
$617$	20.6709	+	11.9343i	0.832177	+	0.480458i	0.854598	−	0.519291i	$-0.173804\pi$
$617$	20.6709	+	11.9343i	0.832177	+	0.480458i	−0.0224202	+	0.999749i	$0.507137\pi$
$618$	22.0948	+	12.7565i	0.888785	+	0.513140i
$619$			19.4963i			0.783622i	0.920046	+	0.391811i	$0.128151\pi$
$619$			19.4963i			0.783622i	−0.920046	+	0.391811i	$0.871849\pi$
$620$	2.40646	−	4.16810i	0.0966456	−	0.167395i
$621$	3.91063	+	6.77341i	0.156928	+	0.271807i
$622$	−15.8824	+	9.16972i	−0.636827	+	0.367672i
$623$		0			0
$624$	−3.20366	−	1.94155i	−0.128249	−	0.0777244i
$625$	−25.0059			−1.00023
$626$	20.0301	−	11.5644i	0.800562	−	0.462205i
$627$	−15.4698	−	26.7945i	−0.617804	−	1.07007i
$628$	4.30055	−	7.44878i	0.171611	−	0.297239i
$629$			17.5599i			0.700161i
$630$		0			0
$631$	−22.2239	−	12.8309i	−0.884718	−	0.510792i	−0.0125066	−	0.999922i	$-0.503981\pi$
$631$	−22.2239	−	12.8309i	−0.884718	−	0.510792i	−0.872211	+	0.489130i	$0.837314\pi$
$632$		−	21.6502i		−	0.861199i
$633$	−23.8572	+	41.3219i	−0.948238	+	1.64240i
$634$	−8.03604	−	13.9188i	−0.319152	−	0.552788i
$635$	−16.7899	+	9.69366i	−0.666287	+	0.384681i
$636$	−1.40399			−0.0556719
$637$		0			0
$638$	29.3573			1.16227
$639$	−15.9145	+	9.18826i	−0.629569	+	0.363482i
$640$	13.1229	+	22.7295i	0.518728	+	0.898463i
$641$	−0.553020	+	0.957859i	−0.0218430	+	0.0378332i	−0.876740	−	0.480964i	$-0.840287\pi$
$641$	−0.553020	+	0.957859i	−0.0218430	+	0.0378332i	0.854897	+	0.518797i	$0.173620\pi$
$642$		−	8.60949i		−	0.339789i
$643$	−10.9437	−	6.31833i	−0.431576	−	0.249171i	0.268442	−	0.963296i	$-0.413491\pi$
$643$	−10.9437	−	6.31833i	−0.431576	−	0.249171i	−0.700018	+	0.714125i	$0.746825\pi$
$644$		0			0
$645$			58.8110i			2.31568i
$646$	−2.17556	+	3.76818i	−0.0855962	+	0.148257i
$647$	−12.8574	−	22.2697i	−0.505477	−	0.875512i	−0.999980	−	0.00633579i	$-0.997983\pi$
$647$	−12.8574	−	22.2697i	−0.505477	−	0.875512i	0.494503	−	0.869176i	$-0.335350\pi$
$648$	−10.9177	+	6.30332i	−0.428887	+	0.247618i
$649$	−28.5598			−1.12107
$650$	7.14685	+	13.0096i	0.280323	+	0.510277i
$651$		0			0
$652$	−2.99066	+	1.72666i	−0.117123	+	0.0676211i
$653$	−12.6303	−	21.8764i	−0.494263	−	0.856089i	0.505715	−	0.862701i	$-0.331229\pi$
$653$	−12.6303	−	21.8764i	−0.494263	−	0.856089i	−0.999978	+	0.00661158i	$0.997895\pi$
$654$	−12.3275	+	21.3518i	−0.482041	+	0.834920i
$655$		−	32.3219i		−	1.26292i
$656$	−1.26285	−	0.729104i	−0.0493058	−	0.0284667i
$657$	29.3269	+	16.9319i	1.14415	+	0.660577i
$658$		0			0
$659$	−11.4882	+	19.8982i	−0.447517	+	0.775123i	−0.998224	−	0.0595764i	$-0.981025\pi$
$659$	−11.4882	+	19.8982i	−0.447517	+	0.775123i	0.550707	+	0.834699i	$0.314358\pi$
$660$	−33.0376	−	57.2228i	−1.28599	−	2.22739i
$661$	−26.3554	+	15.2163i	−1.02511	+	0.591845i	−0.915579	−	0.402138i	$-0.868267\pi$
$661$	−26.3554	+	15.2163i	−1.02511	+	0.591845i	−0.109528	+	0.993984i	$0.534934\pi$
$662$	12.8728			0.500316
$663$	0.550267	−	25.8886i	0.0213706	−	1.00543i
$664$	16.9554			0.657998
$665$		0			0
$666$	−10.9204	−	18.9146i	−0.423155	−	0.732926i
$667$	8.18613	−	14.1788i	0.316968	−	0.549005i
$668$			5.13665i			0.198743i
$669$	36.9339	+	21.3238i	1.42795	+	0.824425i
$670$	−14.1612	−	8.17600i	−0.547096	−	0.315866i
$671$			6.87586i			0.265440i
$672$		0			0
$673$	5.41933	+	9.38656i	0.208900	+	0.361825i	0.951368	−	0.308056i	$-0.0996784\pi$
$673$	5.41933	+	9.38656i	0.208900	+	0.361825i	−0.742468	+	0.669881i	$0.766345\pi$
$674$	15.5126	−	8.95620i	0.597523	−	0.344980i
$675$	14.3244			0.551345
$676$	9.21595	−	14.5023i	0.354460	−	0.557779i
$677$	18.1209			0.696442			0.348221	−	0.937412i	$-0.386786\pi$
$677$	18.1209			0.696442			0.348221	+	0.937412i	$0.386786\pi$
$678$	10.9558	−	6.32532i	0.420754	−	0.242923i
$679$		0			0
$680$	−11.6765	+	20.2242i	−0.447772	+	0.775564i
$681$			43.5624i			1.66931i
$682$	4.88078	+	2.81792i	0.186895	+	0.107904i
$683$	32.7662	+	18.9176i	1.25376	+	0.723861i	0.971855	−	0.235580i	$-0.0756990\pi$
$683$	32.7662	+	18.9176i	1.25376	+	0.723861i	0.281909	+	0.959441i	$0.409032\pi$
$684$			10.5465i			0.403257i
$685$	31.5380	−	54.6254i	1.20500	−	2.08713i
$686$		0			0
$687$	62.2288	−	35.9278i	2.37418	−	1.37073i
$688$	−2.73042			−0.104096
$689$	0.0305930	−	1.43932i	0.00116550	−	0.0548338i
$690$	18.9089			0.719850
$691$	−26.0034	+	15.0131i	−0.989216	+	0.571124i	−0.905040	−	0.425327i	$-0.860159\pi$
$691$	−26.0034	+	15.0131i	−0.989216	+	0.571124i	−0.0841761	+	0.996451i	$0.526826\pi$
$692$	−9.23693	−	15.9988i	−0.351135	−	0.608184i
$693$		0			0
$694$		−	13.1432i		−	0.498907i
$695$	−55.6658	−	32.1387i	−2.11152	−	1.21909i
$696$	−37.8059	−	21.8273i	−1.43303	−	0.827360i
$697$		−	10.0798i		−	0.381798i
$698$	−2.80712	+	4.86207i	−0.106251	+	0.184032i
$699$	−15.3873	−	26.6516i	−0.582001	−	1.00805i
$700$		0			0
$701$	0.116177			0.00438796			0.00219398	−	0.999998i	$-0.499302\pi$
$701$	0.116177			0.00438796			0.00219398	+	0.999998i	$0.499302\pi$
$702$	4.09688	+	7.45764i	0.154627	+	0.281470i
$703$	12.7297			0.480110
$704$	−20.5332	+	11.8548i	−0.773873	+	0.446796i
$705$	1.91825	+	3.32251i	0.0722456	+	0.125133i
$706$	−5.76624	+	9.98741i	−0.217015	+	0.375881i
$707$		0			0
$708$	14.6347	+	8.44932i	0.550004	+	0.317545i
$709$	5.82829	+	3.36497i	0.218886	+	0.126374i	0.605434	−	0.795895i	$-0.292999\pi$
$709$	5.82829	+	3.36497i	0.218886	+	0.126374i	−0.386548	+	0.922269i	$0.626333\pi$
$710$			11.7375i			0.440499i
$711$	16.1335	−	27.9440i	0.605053	−	1.04798i
$712$	−4.87132	−	8.43738i	−0.182561	−	0.316204i
$713$	2.72196	−	1.57153i	0.101938	−	0.0588541i
$714$		0			0
$715$	59.3826	−	32.6221i	2.22078	−	1.22000i
$716$	33.4197			1.24895
$717$	33.8050	−	19.5173i	1.26247	−	0.728888i
$718$	2.22975	+	3.86204i	0.0832136	+	0.144130i
$719$	−23.4039	+	40.5367i	−0.872818	+	1.51177i	−0.0137492	+	0.999905i	$0.504377\pi$
$719$	−23.4039	+	40.5367i	−0.872818	+	1.51177i	−0.859069	+	0.511860i	$0.828957\pi$
$720$			5.03509i			0.187647i
$721$		0			0
$722$	−10.8195	−	6.24666i	−0.402661	−	0.232476i
$723$		−	38.1664i		−	1.41942i
$724$	−0.571312	+	0.989541i	−0.0212326	+	0.0367760i
$725$	−14.9926	−	25.9680i	−0.556812	−	0.964426i
$726$	46.1359	−	26.6366i	1.71226	−	0.988576i
$727$	−13.3362			−0.494611			−0.247305	−	0.968938i	$-0.579545\pi$
$727$	−13.3362			−0.494611			−0.247305	+	0.968938i	$0.579545\pi$
$728$		0			0
$729$	−41.6582			−1.54290
$730$	18.7317	−	10.8148i	0.693291	−	0.400272i
$731$	−9.43694	−	16.3453i	−0.349038	−	0.604551i
$732$	2.03420	−	3.52334i	0.0751863	−	0.130226i
$733$		−	29.4612i		−	1.08817i	−0.839029	−	0.544087i	$-0.816876\pi$
$733$		−	29.4612i		−	1.08817i	0.839029	−	0.544087i	$-0.183124\pi$
$734$	21.4193	+	12.3664i	0.790599	+	0.456453i
$735$		0			0
$736$			15.8113i			0.582814i
$737$	−18.6576	+	32.3160i	−0.687263	+	1.19037i
$738$	6.26851	+	10.8574i	0.230747	+	0.399666i
$739$	−10.4184	+	6.01509i	−0.383249	+	0.221269i	−0.679231	−	0.733925i	$-0.737686\pi$
$739$	−10.4184	+	6.01509i	−0.383249	+	0.221269i	0.295982	+	0.955193i	$0.404353\pi$
$740$	27.1858			0.999370
$741$	−18.7674	−	0.398904i	−0.689438	−	0.0146541i
$742$		0			0
$743$	−18.9509	+	10.9413i	−0.695242	+	0.401398i	−0.805573	−	0.592497i	$-0.798142\pi$
$743$	−18.9509	+	10.9413i	−0.695242	+	0.401398i	0.110331	+	0.993895i	$0.464809\pi$
$744$	−4.19027	−	7.25777i	−0.153623	−	0.266083i
$745$	16.9427	−	29.3457i	0.620734	−	1.07514i
$746$			17.6321i			0.645558i
$747$	21.8844	+	12.6350i	0.800710	+	0.462290i
$748$	18.3642	+	10.6026i	0.671461	+	0.387668i
$749$		0			0
$750$	−0.00405815	+	0.00702892i	−0.000148183	+	0.000256660i
$751$	17.3746	+	30.0937i	0.634008	+	1.09813i	0.986724	+	0.162403i	$0.0519245\pi$
$751$	17.3746	+	30.0937i	0.634008	+	1.09813i	−0.352717	+	0.935730i	$0.614742\pi$
$752$	−0.154255	+	0.0890590i	−0.00562509	+	0.00324765i
$753$	−22.9172			−0.835147
$754$	9.23160	−	15.2326i	0.336195	−	0.554739i
$755$	27.6498			1.00628
$756$		0			0
$757$	−21.9632	−	38.0413i	−0.798265	−	1.38264i	−0.920745	−	0.390164i	$-0.872418\pi$
$757$	−21.9632	−	38.0413i	−0.798265	−	1.38264i	0.122481	−	0.992471i	$-0.460915\pi$
$758$	−3.90223	+	6.75887i	−0.141736	+	0.245493i
$759$		−	43.1502i		−	1.56625i
$760$	14.6611	+	8.46461i	0.531815	+	0.307044i
$761$	−0.122449	−	0.0706957i	−0.00443876	−	0.00256272i	0.497779	−	0.867304i	$-0.334149\pi$
$761$	−0.122449	−	0.0706957i	−0.00443876	−	0.00256272i	−0.502218	+	0.864741i	$0.667482\pi$
$762$			13.4328i			0.486618i
$763$		0			0
$764$	−9.69352	−	16.7897i	−0.350699	−	0.607429i
$765$	−30.1418	+	17.4024i	−1.08978	+	0.629183i
$766$	4.47241			0.161595
$767$	−8.98082	+	14.8188i	−0.324279	+	0.535076i
$768$	39.4124			1.42217
$769$	−11.8200	+	6.82429i	−0.426241	+	0.246090i	−0.697744	−	0.716347i	$-0.745813\pi$
$769$	−11.8200	+	6.82429i	−0.426241	+	0.246090i	0.271503	+	0.962438i	$0.412479\pi$
$770$		0			0
$771$	13.7856	−	23.8773i	0.496475	−	0.859920i
$772$			21.8035i			0.784726i
$773$	−15.2328	−	8.79469i	−0.547887	−	0.316323i	0.200382	−	0.979718i	$-0.435782\pi$
$773$	−15.2328	−	8.79469i	−0.547887	−	0.316323i	−0.748269	+	0.663395i	$0.769115\pi$
$774$	20.3299	+	11.7375i	0.730744	+	0.421895i
$775$		−	5.75639i		−	0.206776i
$776$	−4.68824	+	8.12026i	−0.168298	+	0.291500i
$777$		0			0
$778$	7.59022	−	4.38221i	0.272123	−	0.157110i
$779$	−7.30711			−0.261804
$780$	−40.0801	−	0.851909i	−1.43510	−	0.0305032i
$781$	26.7849			0.958439
$782$	−5.25533	+	3.03416i	−0.187930	+	0.108501i
$783$	−8.59441	−	14.8860i	−0.307139	−	0.531981i
$784$		0			0
$785$		−	20.5768i		−	0.734418i
$786$	−19.3944	−	11.1973i	−0.691774	−	0.399396i
$787$	−2.57075	−	1.48422i	−0.0916374	−	0.0529069i	0.453481	−	0.891266i	$-0.350182\pi$
$787$	−2.57075	−	1.48422i	−0.0916374	−	0.0529069i	−0.545118	+	0.838359i	$0.683515\pi$
$788$			14.5528i			0.518421i
$789$	−29.3731	+	50.8756i	−1.04571	+	1.81122i
$790$	−10.3048	−	17.8484i	−0.366628	−	0.635018i
$791$		0			0
$792$	−66.2829			−2.35526
$793$	3.56768	+	2.16216i	0.126692	+	0.0767807i
$794$	−30.6242			−1.08681
$795$	−2.90883	+	1.67941i	−0.103166	+	0.0595627i
$796$	14.0184	+	24.2805i	0.496867	+	0.860600i
$797$	−4.72611	+	8.18586i	−0.167407	+	0.289958i	−0.937508	−	0.347965i	$-0.886873\pi$
$797$	−4.72611	+	8.18586i	−0.167407	+	0.289958i	0.770100	+	0.637923i	$0.220206\pi$
$798$		0			0
$799$	−1.06628	−	0.615614i	−0.0377221	−	0.0217789i
$800$	25.0783	+	14.4790i	0.886652	+	0.511909i
$801$		−	14.5202i		−	0.513047i
$802$	−0.369204	+	0.639481i	−0.0130371	+	0.0225809i
$803$	−24.6793	−	42.7458i	−0.870913	−	1.50847i
$804$	19.1212	−	11.0396i	0.674351	−	0.389337i
$805$		0			0
$806$	2.99693	−	1.64637i	0.105562	−	0.0579911i
$807$	34.4239			1.21178
$808$	−31.5795	+	18.2324i	−1.11096	+	0.641414i
$809$	0.581273	+	1.00679i	0.0204365	+	0.0353970i	0.876063	−	0.482197i	$-0.160161\pi$
$809$	0.581273	+	1.00679i	0.0204365	+	0.0353970i	−0.855626	+	0.517594i	$0.826828\pi$
$810$	−6.00035	+	10.3929i	−0.210831	+	0.365170i
$811$		−	19.5561i		−	0.686706i	−0.939206	−	0.343353i	$-0.888437\pi$
$811$		−	19.5561i		−	0.686706i	0.939206	−	0.343353i	$-0.111563\pi$
$812$		0			0
$813$	40.7209	+	23.5102i	1.42814	+	0.824538i
$814$			31.8342i			1.11579i
$815$	−4.13075	+	7.15467i	−0.144694	+	0.250617i
$816$	−1.40243	−	2.42908i	−0.0490949	−	0.0850348i
$817$	−11.8491	+	6.84111i	−0.414549	+	0.239340i
$818$	−20.2408			−0.707702
$819$		0			0
$820$	−15.6052			−0.544958
$821$	10.9283	−	6.30945i	0.381400	−	0.220201i	−0.297027	−	0.954869i	$-0.595995\pi$
$821$	10.9283	−	6.30945i	0.381400	−	0.220201i	0.678427	+	0.734668i	$0.262662\pi$
$822$	−21.8515	−	37.8479i	−0.762159	−	1.32010i
$823$	−3.28404	+	5.68812i	−0.114474	+	0.198275i	−0.917570	−	0.397575i	$-0.869852\pi$
$823$	−3.28404	+	5.68812i	−0.114474	+	0.198275i	0.803095	+	0.595851i	$0.203185\pi$
$824$			31.8565i			1.10978i
$825$	−68.4403	−	39.5140i	−2.38278	−	1.37570i
$826$		0			0
$827$		−	17.3050i		−	0.601754i	−0.953663	−	0.300877i	$-0.902721\pi$
$827$		−	17.3050i		−	0.601754i	0.953663	−	0.300877i	$-0.0972794\pi$
$828$	−7.35441	+	12.7382i	−0.255583	+	0.442683i
$829$	1.87837	+	3.25343i	0.0652385	+	0.112996i	0.896800	−	0.442437i	$-0.145886\pi$
$829$	1.87837	+	3.25343i	0.0652385	+	0.112996i	−0.831561	+	0.555433i	$0.812553\pi$
$830$	13.9780	−	8.07022i	0.485185	−	0.280122i
$831$	−47.9252			−1.66251
$832$	−0.305689	+	14.3819i	−0.0105979	+	0.498602i
$833$		0			0
$834$	−38.5688	+	22.2677i	−1.33553	+	0.771068i
$835$	6.14432	+	10.6423i	0.212633	+	0.368291i
$836$	7.68610	−	13.3127i	0.265829	−	0.460430i
$837$		−	3.29981i		−	0.114058i
$838$	−5.45298	−	3.14828i	−0.188370	−	0.108756i
$839$	40.1340	+	23.1714i	1.38558	+	0.799965i	0.992813	−	0.119674i	$-0.0381849\pi$
$839$	40.1340	+	23.1714i	1.38558	+	0.799965i	0.392766	+	0.919638i	$0.371518\pi$
$840$		0			0
$841$	−3.49071	+	6.04609i	−0.120369	+	0.208486i
$842$	10.3266	+	17.8861i	0.355877	+	0.616396i
$843$	−5.62558	+	3.24793i	−0.193755	+	0.111865i
$844$	−23.7067			−0.816018
$845$	1.74669	−	41.0701i	0.0600880	−	1.41285i
$846$	1.53138			0.0526499
$847$		0			0
$848$	−0.0779704	−	0.135049i	−0.00267751	−	0.00463759i
$849$	−38.2071	+	66.1766i	−1.31126	+	2.27118i
$850$			11.1139i			0.381205i
$851$	15.3751	+	8.87679i	0.527050	+	0.304293i
$852$	−13.7252	−	7.92423i	−0.470216	−	0.271479i
$853$			15.3103i			0.524215i	0.965039	+	0.262107i	$0.0844174\pi$
$853$			15.3103i			0.524215i	−0.965039	+	0.262107i	$0.915583\pi$
$854$		0			0
$855$	12.6155	+	21.8506i	0.431440	+	0.747275i
$856$	9.30993	−	5.37509i	0.318207	−	0.183717i
$857$	2.59248			0.0885574			0.0442787	−	0.999019i	$-0.485901\pi$
$857$	2.59248			0.0885574			0.0442787	+	0.999019i	$0.485901\pi$
$858$	0.997571	−	46.9331i	0.0340565	−	1.60227i
$859$	13.7738			0.469955			0.234978	−	0.972001i	$-0.424498\pi$
$859$	13.7738			0.469955			0.234978	+	0.972001i	$0.424498\pi$
$860$	−25.3053	+	14.6100i	−0.862903	+	0.498197i
$861$		0			0
$862$	3.19294	−	5.53034i	0.108752	−	0.188364i
$863$			29.7592i			1.01302i	0.862235	+	0.506508i	$0.169064\pi$
$863$			29.7592i			1.01302i	−0.862235	+	0.506508i	$0.830936\pi$
$864$	14.3760	+	8.29996i	0.489080	+	0.282370i
$865$	−38.2747	−	22.0979i	−1.30138	−	0.751351i
$866$			29.6282i			1.00681i
$867$	−12.9183	+	22.3751i	−0.438728	+	0.759899i
$868$		0			0
$869$	−40.7301	+	23.5155i	−1.38167	+	0.797710i
$870$	−41.5562			−1.40889
$871$	10.9007	+	19.8429i	0.369358	+	0.672350i
$872$	−30.7852			−1.04252
$873$	−12.1023	+	6.98724i	−0.409599	+	0.236482i
$874$	2.19955	+	3.80974i	0.0744009	+	0.128866i
$875$		0			0
$876$			29.2051i			0.986750i
$877$	−1.24995	−	0.721660i	−0.0422079	−	0.0243687i	0.478748	−	0.877953i	$-0.341091\pi$
$877$	−1.24995	−	0.721660i	−0.0422079	−	0.0243687i	−0.520955	+	0.853584i	$0.674424\pi$
$878$	20.1378	+	11.6266i	0.679618	+	0.392378i
$879$		−	78.0286i		−	2.63184i
$880$	3.66947	−	6.35571i	0.123698	−	0.214251i
$881$	17.9402	+	31.0733i	0.604420	+	1.04689i	0.992143	+	0.125110i	$0.0399284\pi$
$881$	17.9402	+	31.0733i	0.604420	+	1.04689i	−0.387723	+	0.921776i	$0.626738\pi$
$882$		0			0
$883$	10.5626			0.355458			0.177729	−	0.984079i	$-0.443125\pi$
$883$	10.5626			0.355458			0.177729	+	0.984079i	$0.443125\pi$
$884$	11.2761	−	6.19456i	0.379256	−	0.208346i
$885$	40.4273			1.35895
$886$	20.5349	−	11.8558i	0.689883	−	0.398304i
$887$	6.11401	+	10.5898i	0.205288	+	0.355570i	0.950225	−	0.311566i	$-0.100853\pi$
$887$	6.11401	+	10.5898i	0.205288	+	0.355570i	−0.744936	+	0.667136i	$0.767520\pi$
$888$	23.6688	−	40.9956i	0.794274	−	1.37572i
$889$		0			0
$890$	−8.03183	−	4.63718i	−0.269228	−	0.155439i
$891$	23.7166	+	13.6928i	0.794537	+	0.458726i
$892$			21.1893i			0.709469i
$893$	−0.446276	+	0.772973i	−0.0149341	+	0.0258666i
$894$	−11.7390	−	20.3326i	−0.392611	−	0.680022i
$895$	69.2399	−	39.9757i	2.31443	−	1.33624i
$896$		0			0
$897$	−22.3893	−	13.5689i	−0.747557	−	0.453051i
$898$	−24.0398			−0.802217
$899$	−5.98208	+	3.45375i	−0.199513	+	0.115189i
$900$	13.4693	+	23.3296i	0.448978	+	0.777653i
$901$	0.538965	−	0.933515i	0.0179555	−	0.0310999i
$902$		−	18.2735i		−	0.608440i
$903$		0			0
$904$	13.6799	+	7.89807i	0.454985	+	0.262686i
$905$			2.73355i			0.0908662i
$906$	9.57879	−	16.5909i	0.318234	−	0.551197i
$907$	2.26278	+	3.91924i	0.0751343	+	0.130136i	0.901145	−	0.433519i	$-0.142728\pi$
$907$	2.26278	+	3.91924i	0.0751343	+	0.130136i	−0.826010	+	0.563655i	$0.809395\pi$
$908$	−18.7441	+	10.8219i	−0.622044	+	0.359137i
$909$	−54.3464			−1.80256
$910$		0			0
$911$	−57.2723			−1.89751			−0.948757	−	0.316006i	$-0.897658\pi$
$911$	−57.2723			−1.89751			−0.948757	+	0.316006i	$0.897658\pi$
$912$	−1.76091	+	1.01666i	−0.0583095	+	0.0336650i
$913$	−18.4163	−	31.8979i	−0.609489	−	1.05567i
$914$	−13.0471	+	22.5983i	−0.431560	+	0.747484i
$915$		−	9.73302i		−	0.321764i
$916$	30.9181	+	17.8506i	1.02156	+	0.589800i
$917$		0			0
$918$			6.37098i			0.210274i
$919$	20.3775	−	35.2949i	0.672193	−	1.16427i	−0.305088	−	0.952324i	$-0.598686\pi$
$919$	20.3775	−	35.2949i	0.672193	−	1.16427i	0.977281	−	0.211948i	$-0.0679809\pi$
$920$	11.8052	+	20.4473i	0.389207	+	0.674127i
$921$	−16.2864	+	9.40294i	−0.536654	+	0.309837i
$922$	18.2021			0.599453
$923$	8.42270	−	13.8979i	0.277236	−	0.457454i
$924$		0			0
$925$	28.1589	−	16.2575i	0.925858	−	0.534545i
$926$	−16.0104	−	27.7308i	−0.526134	−	0.911291i
$927$	−23.7391	+	41.1174i	−0.779696	+	1.35047i
$928$		−	34.7487i		−	1.14068i
$929$	−45.2751	−	26.1396i	−1.48543	−	0.857611i	−0.485564	−	0.874201i	$-0.661386\pi$
$929$	−45.2751	−	26.1396i	−1.48543	−	0.857611i	−0.999862	+	0.0165897i	$0.994719\pi$
$930$	−6.90891	−	3.98886i	−0.226552	−	0.130800i
$931$		0			0
$932$	7.64511	−	13.2417i	0.250424	−	0.433747i
$933$	−29.6205	−	51.3042i	−0.969731	−	1.67962i
$934$	9.47322	−	5.46937i	0.309973	−	0.178963i
$935$	50.7300			1.65905
$936$	−20.8431	+	34.3922i	−0.681279	+	1.12414i
$937$	6.38634			0.208633			0.104316	−	0.994544i	$-0.466735\pi$
$937$	6.38634			0.208633			0.104316	+	0.994544i	$0.466735\pi$
$938$		0			0
$939$	37.3558	+	64.7021i	1.21906	+	2.11147i
$940$	−0.953077	+	1.65078i	−0.0310859	+	0.0538424i
$941$			25.3711i			0.827073i	0.910488	+	0.413536i	$0.135707\pi$
$941$			25.3711i			0.827073i	−0.910488	+	0.413536i	$0.864293\pi$
$942$	−12.3469	−	7.12846i	−0.402282	−	0.232258i
$943$	−8.82560	−	5.09546i	−0.287401	−	0.165931i
$944$			1.87692i			0.0610887i
$945$		0			0
$946$	−17.1081	−	29.6321i	−0.556232	−	0.963422i
$947$	23.5612	−	13.6031i	0.765635	−	0.442040i	−0.0656800	−	0.997841i	$-0.520922\pi$
$947$	23.5612	−	13.6031i	0.765635	−	0.442040i	0.831315	+	0.555801i	$0.187588\pi$
$948$	27.8280			0.903811
$949$	−29.9401	−	0.636381i	−0.971895	−	0.0206578i
$950$	8.05681			0.261397
$951$	44.9613	−	25.9584i	1.45797	−	0.841760i
$952$		0			0
$953$	13.2939	−	23.0258i	0.430633	−	0.745878i	−0.566295	−	0.824203i	$-0.691624\pi$
$953$	13.2939	−	23.0258i	0.430633	−	0.745878i	0.996928	+	0.0783248i	$0.0249571\pi$
$954$			1.34071i			0.0434070i
$955$	−40.1667	−	23.1902i	−1.29976	−	0.750418i
$956$	16.7959	+	9.69711i	0.543218	+	0.313627i
$957$			94.8314i			3.06546i
$958$	−2.73220	+	4.73230i	−0.0882732	+	0.152894i
$959$		0			0
$960$	29.0654	−	16.7809i	0.938082	−	0.541602i
$961$	29.6739			0.957224
$962$	16.5178	+	10.0105i	0.532554	+	0.322751i
$963$	16.0218			0.516296
$964$	16.4223	−	9.48141i	0.528926	−	0.305376i
$965$	26.0808	+	45.1732i	0.839569	+	1.45418i
$966$		0			0
$967$			35.2467i			1.13346i	0.823904	+	0.566729i	$0.191791\pi$
$967$			35.2467i			1.13346i	−0.823904	+	0.566729i	$0.808209\pi$
$968$	57.6073	+	33.2596i	1.85157	+	1.06900i
$969$	−12.1722	−	7.02760i	−0.391026	−	0.225759i
$970$			8.92578i			0.286590i
$971$	18.4891	−	32.0241i	0.593344	−	1.02770i	−0.400434	−	0.916326i	$-0.631141\pi$
$971$	18.4891	−	32.0241i	0.593344	−	1.02770i	0.993778	−	0.111377i	$-0.0355261\pi$
$972$	−13.7833	−	23.8733i	−0.442098	−	0.765737i
$973$		0			0
$974$	27.5645			0.883224
$975$	−42.0241	+	23.0861i	−1.34585	+	0.739347i
$976$	0.451876			0.0144642
$977$	−21.4363	+	12.3762i	−0.685807	+	0.395951i	−0.802039	−	0.597271i	$-0.796252\pi$
$977$	−21.4363	+	12.3762i	−0.685807	+	0.395951i	0.116232	+	0.993222i	$0.462918\pi$
$978$	2.86205	+	4.95721i	0.0915182	+	0.158514i
$979$	−10.5820	+	18.3286i	−0.338204	+	0.585786i
$980$		0			0
$981$	−39.7346	−	22.9408i	−1.26863	−	0.732442i
$982$	−26.6236	−	15.3711i	−0.849593	−	0.490513i
$983$		−	4.55736i		−	0.145357i	−0.997355	−	0.0726786i	$-0.976845\pi$
$983$		−	4.55736i		−	0.145357i	0.997355	−	0.0726786i	$-0.0231547\pi$
$984$	−13.5864	+	23.5323i	−0.433119	+	0.750183i
$985$	17.4076	+	30.1509i	0.554652	+	0.960686i
$986$	11.5497	−	6.66820i	0.367816	−	0.212359i
$987$		0			0
$988$	−4.49062	−	8.17436i	−0.142866	−	0.260061i
$989$	−19.0820			−0.606773
$990$	−54.6436	+	31.5485i	−1.73669	+	1.00268i
$991$	13.5982	+	23.5527i	0.431960	+	0.748176i	0.997042	−	0.0768584i	$-0.0244890\pi$
$991$	13.5982	+	23.5527i	0.431960	+	0.748176i	−0.565082	+	0.825034i	$0.691156\pi$
$992$	3.33543	−	5.77713i	0.105900	−	0.183424i
$993$			41.5824i			1.31958i
$994$		0			0
$995$	58.0873	+	33.5367i	1.84149	+	1.06319i
$996$			21.7936i			0.690556i
$997$	−15.1137	+	26.1777i	−0.478656	+	0.829057i	−0.999700	−	0.0244727i	$-0.992209\pi$
$997$	−15.1137	+	26.1777i	−0.478656	+	0.829057i	0.521044	+	0.853530i	$0.325543\pi$
$998$	−14.0551	−	24.3441i	−0.444906	−	0.770600i
$999$	16.1419	−	9.31952i	0.510707	−	0.294857i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.q.h.491.4		12
7.2	even	3		637.2.u.i.361.3		12
7.3	odd	6		637.2.k.h.569.4		12
7.4	even	3		637.2.k.g.569.4		12
7.5	odd	6		637.2.u.h.361.3		12
7.6	odd	2		91.2.q.a.36.4	✓	12
13.2	odd	12		8281.2.a.by.1.5		6
13.4	even	6	inner	637.2.q.h.589.4		12
13.11	odd	12		8281.2.a.ch.1.2		6
21.20	even	2		819.2.ct.a.127.3		12
28.27	even	2		1456.2.cc.c.673.6		12
91.4	even	6		637.2.u.i.30.3		12
91.17	odd	6		637.2.u.h.30.3		12
91.30	even	6		637.2.k.g.459.3		12
91.41	even	12		1183.2.a.m.1.5		6
91.55	odd	6		1183.2.c.i.337.8		12
91.62	odd	6		1183.2.c.i.337.5		12
91.69	odd	6		91.2.q.a.43.4	yes	12
91.76	even	12		1183.2.a.p.1.2		6
91.82	odd	6		637.2.k.h.459.3		12
273.251	even	6		819.2.ct.a.316.3		12
364.251	even	6		1456.2.cc.c.225.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.q.a.36.4	✓	12	7.6	odd	2
91.2.q.a.43.4	yes	12	91.69	odd	6
637.2.k.g.459.3		12	91.30	even	6
637.2.k.g.569.4		12	7.4	even	3
637.2.k.h.459.3		12	91.82	odd	6
637.2.k.h.569.4		12	7.3	odd	6
637.2.q.h.491.4		12	1.1	even	1	trivial
637.2.q.h.589.4		12	13.4	even	6	inner
637.2.u.h.30.3		12	91.17	odd	6
637.2.u.h.361.3		12	7.5	odd	6
637.2.u.i.30.3		12	91.4	even	6
637.2.u.i.361.3		12	7.2	even	3
819.2.ct.a.127.3		12	21.20	even	2
819.2.ct.a.316.3		12	273.251	even	6
1183.2.a.m.1.5		6	91.41	even	12
1183.2.a.p.1.2		6	91.76	even	12
1183.2.c.i.337.5		12	91.62	odd	6
1183.2.c.i.337.8		12	91.55	odd	6
1456.2.cc.c.225.6		12	364.251	even	6
1456.2.cc.c.673.6		12	28.27	even	2
8281.2.a.by.1.5		6	13.2	odd	12
8281.2.a.ch.1.2		6	13.11	odd	12

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.713220 - 0.411778i) q^{2} +(1.33015 + 2.30388i) q^{3} +(-0.660878 + 1.14467i) q^{4} +3.16209i q^{5} +(1.89737 + 1.09545i) q^{6} +2.73565i q^{8} +(-2.03858 + 3.53092i) q^{9} +O(q^{10})\)	\(q+(0.713220 - 0.411778i) q^{2} +(1.33015 + 2.30388i) q^{3} +(-0.660878 + 1.14467i) q^{4} +3.16209i q^{5} +(1.89737 + 1.09545i) q^{6} +2.73565i q^{8} +(-2.03858 + 3.53092i) q^{9} +(1.30208 + 2.25527i) q^{10} +(5.14653 - 2.97135i) q^{11} -3.51626 q^{12} +(0.0766193 - 3.60474i) q^{13} +(-7.28508 + 4.20604i) q^{15} +(-0.195274 - 0.338225i) q^{16} +(1.34982 - 2.33796i) q^{17} +3.35776i q^{18} +(-1.69485 - 0.978524i) q^{19} +(-3.61956 - 2.08976i) q^{20} +(2.44707 - 4.23845i) q^{22} +(-1.36471 - 2.36374i) q^{23} +(-6.30261 + 3.63882i) q^{24} -4.99883 q^{25} +(-1.42970 - 2.60252i) q^{26} -2.86554 q^{27} +(2.99923 + 5.19481i) q^{29} +(-3.46391 + 5.99967i) q^{30} +1.15155i q^{31} +(-5.01684 - 2.89647i) q^{32} +(13.6913 + 7.90465i) q^{33} -2.22331i q^{34} +(-2.69450 - 4.66701i) q^{36} +(-5.63310 + 3.25227i) q^{37} -1.61174 q^{38} +(8.40680 - 4.61830i) q^{39} -8.65038 q^{40} +(3.23351 - 1.86687i) q^{41} +(3.49562 - 6.05460i) q^{43} +7.85479i q^{44} +(-11.1651 - 6.44617i) q^{45} +(-1.94667 - 1.12391i) q^{46} -0.456071i q^{47} +(0.519487 - 0.899778i) q^{48} +(-3.56527 + 2.05841i) q^{50} +7.18184 q^{51} +(4.07561 + 2.46999i) q^{52} +0.399286 q^{53} +(-2.04376 + 1.17997i) q^{54} +(9.39568 + 16.2738i) q^{55} -5.20632i q^{57} +(4.27822 + 2.47003i) q^{58} +(-4.16200 - 2.40293i) q^{59} -11.1187i q^{60} +(-0.578514 + 1.00201i) q^{61} +(0.474182 + 0.821308i) q^{62} -3.98971 q^{64} +(11.3985 + 0.242277i) q^{65} +13.0199 q^{66} +(-5.43793 + 3.13959i) q^{67} +(1.78413 + 3.09021i) q^{68} +(3.63052 - 6.28825i) q^{69} +(3.90335 + 2.25360i) q^{71} +(-9.65936 - 5.57684i) q^{72} -8.30575i q^{73} +(-2.67843 + 4.63917i) q^{74} +(-6.64917 - 11.5167i) q^{75} +(2.24018 - 1.29337i) q^{76} +(4.09418 - 6.75560i) q^{78} -7.91410 q^{79} +(1.06950 - 0.617476i) q^{80} +(2.30414 + 3.99089i) q^{81} +(1.53747 - 2.66298i) q^{82} -6.19795i q^{83} +(7.39284 + 4.26826i) q^{85} -5.75769i q^{86} +(-7.97882 + 13.8197i) q^{87} +(8.12857 + 14.0791i) q^{88} +(-3.08423 + 1.78068i) q^{89} -10.6176 q^{90} +3.60762 q^{92} +(-2.65303 + 1.53173i) q^{93} +(-0.187800 - 0.325279i) q^{94} +(3.09418 - 5.35928i) q^{95} -15.4109i q^{96} +(2.96831 + 1.71375i) q^{97} +24.2293i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} + 18 q^{6} - 4 q^{9}+O(q^{10}) \) 12 * q + 4 * q^4 + 18 * q^6 - 4 * q^9	\( 12 q + 4 q^{4} + 18 q^{6} - 4 q^{9} - 12 q^{10} + 6 q^{11} + 4 q^{12} - 4 q^{13} + 6 q^{15} - 8 q^{16} + 4 q^{17} + 12 q^{20} + 6 q^{22} - 12 q^{23} - 12 q^{24} - 20 q^{25} + 42 q^{26} - 12 q^{27} + 8 q^{29} + 8 q^{30} + 36 q^{32} + 30 q^{33} - 10 q^{36} - 42 q^{37} - 4 q^{38} - 4 q^{39} - 92 q^{40} - 30 q^{41} + 2 q^{43} + 12 q^{46} + 2 q^{48} - 18 q^{50} + 52 q^{51} - 2 q^{52} - 44 q^{53} - 12 q^{54} + 6 q^{55} - 12 q^{58} - 18 q^{59} - 14 q^{61} + 4 q^{62} - 52 q^{64} + 60 q^{65} + 52 q^{66} - 24 q^{67} + 8 q^{68} - 4 q^{69} - 24 q^{71} + 60 q^{72} + 6 q^{74} - 46 q^{75} + 18 q^{76} - 10 q^{78} - 56 q^{79} + 72 q^{80} + 2 q^{81} - 14 q^{82} - 48 q^{85} + 2 q^{87} - 14 q^{88} + 12 q^{89} - 24 q^{90} + 24 q^{92} - 18 q^{93} - 4 q^{94} - 22 q^{95} - 6 q^{97}+O(q^{100}) \) 12 * q + 4 * q^4 + 18 * q^6 - 4 * q^9 - 12 * q^10 + 6 * q^11 + 4 * q^12 - 4 * q^13 + 6 * q^15 - 8 * q^16 + 4 * q^17 + 12 * q^20 + 6 * q^22 - 12 * q^23 - 12 * q^24 - 20 * q^25 + 42 * q^26 - 12 * q^27 + 8 * q^29 + 8 * q^30 + 36 * q^32 + 30 * q^33 - 10 * q^36 - 42 * q^37 - 4 * q^38 - 4 * q^39 - 92 * q^40 - 30 * q^41 + 2 * q^43 + 12 * q^46 + 2 * q^48 - 18 * q^50 + 52 * q^51 - 2 * q^52 - 44 * q^53 - 12 * q^54 + 6 * q^55 - 12 * q^58 - 18 * q^59 - 14 * q^61 + 4 * q^62 - 52 * q^64 + 60 * q^65 + 52 * q^66 - 24 * q^67 + 8 * q^68 - 4 * q^69 - 24 * q^71 + 60 * q^72 + 6 * q^74 - 46 * q^75 + 18 * q^76 - 10 * q^78 - 56 * q^79 + 72 * q^80 + 2 * q^81 - 14 * q^82 - 48 * q^85 + 2 * q^87 - 14 * q^88 + 12 * q^89 - 24 * q^90 + 24 * q^92 - 18 * q^93 - 4 * q^94 - 22 * q^95 - 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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