LMFDB - Embedded newform 637.2.q.h.589.4

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			589.4
Root			$-1.08105 - 0.911778i$ of defining polynomial
Character	$\chi$	$=$	637.589
Dual form			637.2.q.h.491.4

$q$-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 $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

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

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	0.730497	−	0.682916i	$-0.239288\pi$
$2$	0.713220	+	0.411778i	0.504323	+	0.291171i	−0.226174	+	0.974087i	$0.572622\pi$
$3$	1.33015	−	2.30388i	0.767960	−	1.33015i	−0.170707	−	0.985322i	$-0.554605\pi$
$3$	1.33015	−	2.30388i	0.767960	−	1.33015i	0.938667	−	0.344824i	$-0.112061\pi$
$4$	−0.660878	−	1.14467i	−0.330439	−	0.572337i
$5$		−	3.16209i		−	1.41413i	−0.707148	−	0.707065i	$-0.750019\pi$
$5$		−	3.16209i		−	1.41413i	0.707148	−	0.707065i	$-0.249981\pi$
$6$	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	0.998001	+	0.0632025i	$0.0201314\pi$
$11$	5.14653	+	2.97135i	1.55174	+	0.895895i	0.553735	+	0.832693i	$0.313202\pi$
$12$	−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	0.981991	−	0.188927i	$-0.0605010\pi$
$17$	1.34982	+	2.33796i	0.327380	+	0.567038i	−0.654611	+	0.755966i	$0.727168\pi$
$18$		−	3.35776i		−	0.791433i
$19$	−1.69485	+	0.978524i	−0.388826	+	0.224489i	−0.681651	−	0.731677i	$-0.738738\pi$
$19$	−1.69485	+	0.978524i	−0.388826	+	0.224489i	0.292825	+	0.956166i	$0.405405\pi$
$20$	−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	−0.972503	−	0.232892i	$-0.925181\pi$
$23$	−1.36471	+	2.36374i	−0.284561	+	0.492874i	0.687941	+	0.725766i	$0.258515\pi$
$24$	−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	−0.440807	−	0.897602i	$-0.645308\pi$
$29$	2.99923	−	5.19481i	0.556942	−	0.964652i	0.997750	−	0.0670505i	$-0.0213589\pi$
$30$	−3.46391	−	5.99967i	−0.632421	−	1.09539i
$31$		−	1.15155i		−	0.206824i	−0.994639	−	0.103412i	$-0.967024\pi$
$31$		−	1.15155i		−	0.206824i	0.994639	−	0.103412i	$-0.0329760\pi$
$32$	−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	−0.0405072	−	0.999179i	$-0.512897\pi$
$37$	−5.63310	−	3.25227i	−0.926075	−	0.534670i	−0.885568	+	0.464509i	$0.846231\pi$
$38$	−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	0.730772	−	0.682622i	$-0.239160\pi$
$41$	3.23351	+	1.86687i	0.504990	+	0.291556i	−0.225782	+	0.974178i	$0.572494\pi$
$42$		0			0
$43$	3.49562	+	6.05460i	0.533078	+	0.923318i	0.999254	+	0.0386258i	$0.0122980\pi$
$43$	3.49562	+	6.05460i	0.533078	+	0.923318i	−0.466176	+	0.884692i	$0.654369\pi$
$44$		−	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	$0.0105897\pi$
$47$			0.456071i			0.0665248i	−0.999447	+	0.0332624i	$0.989410\pi$
$48$	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	−0.745827	−	0.666140i	$-0.767945\pi$
$59$	−4.16200	+	2.40293i	−0.541846	+	0.312835i	0.203981	+	0.978975i	$0.434612\pi$
$60$			11.1187i			1.43542i
$61$	−0.578514	−	1.00201i	−0.0740711	−	0.128295i	0.826611	−	0.562774i	$-0.190266\pi$
$61$	−0.578514	−	1.00201i	−0.0740711	−	0.128295i	−0.900682	+	0.434479i	$0.856933\pi$
$62$	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	0.129583	−	0.991569i	$-0.458636\pi$
$67$	−5.43793	−	3.13959i	−0.664349	−	0.383562i	−0.793932	+	0.608007i	$0.791969\pi$
$68$	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	−0.250165	−	0.968203i	$-0.580485\pi$
$71$	3.90335	−	2.25360i	0.463242	−	0.267453i	0.713406	+	0.700751i	$0.247151\pi$
$72$	−9.65936	+	5.57684i	−1.13837	+	0.657236i
$73$			8.30575i			0.972115i	0.873927	+	0.486057i	$0.161565\pi$
$73$			8.30575i			0.972115i	−0.873927	+	0.486057i	$0.838435\pi$
$74$	−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	$0.110480\pi$
$83$			6.19795i			0.680313i	−0.940369	+	0.340156i	$0.889520\pi$
$84$		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	0.327549	−	0.944834i	$-0.393778\pi$
$89$	−3.08423	−	1.78068i	−0.326928	−	0.188752i	−0.654476	+	0.756083i	$0.727111\pi$
$90$	−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	−0.341679	−	0.939817i	$-0.610996\pi$
$97$	2.96831	−	1.71375i	0.301386	−	0.174005i	0.643065	+	0.765811i	$0.277662\pi$
$98$		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	−0.316612	−	0.948555i	$-0.602545\pi$
$101$	6.66474	−	11.5437i	0.663167	−	1.14864i	0.979779	−	0.200084i	$-0.0641214\pi$
$102$	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	−0.945232	−	0.326398i	$-0.894165\pi$
$107$	−1.96483	+	3.40318i	−0.189947	+	0.328998i	0.755285	+	0.655396i	$0.227498\pi$
$108$	1.89377	+	3.28011i	0.182228	+	0.315629i
$109$		−	11.2533i		−	1.07787i	−0.842346	−	0.538936i	$-0.818826\pi$
$109$		−	11.2533i		−	1.07787i	0.842346	−	0.538936i	$-0.181174\pi$
$110$	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	0.969270	−	0.245998i	$-0.0791157\pi$
$113$	2.88709	+	5.00059i	0.271595	+	0.470416i	−0.697676	+	0.716414i	$0.745782\pi$
$114$	−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	−0.697354	−	0.716727i	$-0.745639\pi$
$127$	3.06558	−	5.30975i	0.272027	−	0.471164i	0.969381	+	0.245563i	$0.0789728\pi$
$128$	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	−0.999631	−	0.0271788i	$-0.991348\pi$
$137$	−17.2751	+	9.97376i	−1.47591	+	0.852116i	−0.476278	+	0.879295i	$0.658014\pi$
$138$			5.97987i			0.509041i
$139$	−10.1637	−	17.6041i	−0.862077	−	1.49316i	−0.869921	−	0.493192i	$-0.835830\pi$
$139$	−10.1637	−	17.6041i	−0.862077	−	1.49316i	0.00784365	−	0.999969i	$-0.497503\pi$
$140$		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	−0.829398	−	0.558658i	$-0.811316\pi$
$149$	−9.28046	+	5.35808i	−0.760285	+	0.438951i	0.0691132	+	0.997609i	$0.477983\pi$
$150$	−9.48465	+	5.47597i	−0.774418	+	0.447111i
$151$			8.74416i			0.711590i	0.934564	+	0.355795i	$0.115790\pi$
$151$			8.74416i			0.711590i	−0.934564	+	0.355795i	$0.884210\pi$
$152$	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	−0.408764	−	0.912640i	$-0.634040\pi$
$163$	2.26264	−	1.30634i	0.177224	−	0.102320i	0.585988	+	0.810320i	$0.300707\pi$
$164$		−	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	0.624534	−	0.780998i	$-0.285289\pi$
$167$	3.36558	+	1.94312i	0.260436	+	0.150363i	−0.364097	+	0.931361i	$0.618622\pi$
$168$		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	−0.999332	−	0.0365470i	$-0.988364\pi$
$173$	−6.98838	−	12.1042i	−0.531317	−	0.920267i	0.468015	−	0.883720i	$-0.344969\pi$
$174$		−	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	−0.189005	+	0.981976i	$0.560526\pi$
$179$	−12.6422	+	21.8968i	−0.944919	+	1.63665i	−0.755914	+	0.654671i	$0.772807\pi$
$180$	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	−0.999360	−	0.0357690i	$-0.988612\pi$
$191$	−7.33382	−	12.7026i	−0.530657	−	0.919125i	0.468703	−	0.883356i	$-0.344721\pi$
$192$	−5.30690	+	9.19182i	−0.382993	+	0.663363i
$193$	14.2859	+	8.24794i	1.02832	+	0.593700i	0.916503	−	0.400029i	$-0.131000\pi$
$193$	14.2859	+	8.24794i	1.02832	+	0.593700i	0.111816	+	0.993729i	$0.464333\pi$
$194$	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	0.799609	−	0.600521i	$-0.205040\pi$
$197$	9.53510	+	5.50509i	0.679348	+	0.392222i	−0.120262	+	0.992742i	$0.538373\pi$
$198$	9.97709	−	17.2808i	0.709041	−	1.22809i
$199$	10.6059	+	18.3699i	0.751829	+	1.30221i	0.946935	+	0.321425i	$0.104162\pi$
$199$	10.6059	+	18.3699i	0.751829	+	1.30221i	−0.195106	+	0.980782i	$0.562505\pi$
$200$			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	−0.372588	−	0.927997i	$-0.621530\pi$
$211$	8.96788	−	15.5328i	0.617375	−	1.06932i	0.989963	−	0.141327i	$-0.0451370\pi$
$212$	−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	0.886717	−	0.462313i	$-0.152980\pi$
$223$	13.8834	+	8.01558i	0.929700	+	0.536763i	0.0429835	+	0.999076i	$0.486314\pi$
$224$		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	0.0508902	−	0.998704i	$-0.483794\pi$
$227$	14.1812	−	8.18751i	0.941239	−	0.543424i	0.890348	+	0.455280i	$0.150461\pi$
$228$	5.95954	−	3.44074i	0.394680	−	0.227869i
$229$			27.0104i			1.78490i	0.451148	+	0.892449i	$0.351015\pi$
$229$			27.0104i			1.78490i	−0.451148	+	0.892449i	$0.648985\pi$
$230$	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	$0.157393\pi$
$239$			14.6731i			0.949122i	−0.880223	+	0.474561i	$0.842607\pi$
$240$	2.84518	−	1.64267i	0.183656	−	0.106034i
$241$	−12.4246	+	7.17334i	−0.800338	+	0.462076i	−0.843589	−	0.536989i	$-0.819562\pi$
$241$	−12.4246	+	7.17334i	−0.800338	+	0.462076i	0.0432510	+	0.999064i	$0.486228\pi$
$242$			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	0.697469	−	0.716615i	$-0.254309\pi$
$251$	−4.30726	−	7.46040i	−0.271872	−	0.470896i	−0.969341	+	0.245719i	$0.920976\pi$
$252$		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	−0.981155	−	0.193222i	$-0.938106\pi$
$257$	−5.18197	+	8.97544i	−0.323243	+	0.559873i	0.657912	+	0.753094i	$0.271440\pi$
$258$	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	−0.293891	−	0.955839i	$-0.594950\pi$
$263$	11.0413	−	19.1241i	0.680835	−	1.17924i	0.974726	−	0.223403i	$-0.0717165\pi$
$264$	−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	0.993035	−	0.117823i	$-0.0375915\pi$
$269$	6.46995	+	11.2063i	0.394480	+	0.683259i	−0.598555	+	0.801082i	$0.704258\pi$
$270$	−3.73117	+	6.46257i	−0.227072	+	0.393299i
$271$	15.3069	+	8.83745i	0.929829	+	0.536837i	0.886757	−	0.462235i	$-0.152952\pi$
$271$	15.3069	+	8.83745i	0.929829	+	0.536837i	0.0430712	+	0.999072i	$0.486286\pi$
$272$	−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	−0.998835	−	0.0482562i	$-0.984634\pi$
$277$	−9.00751	−	15.6015i	−0.541209	−	0.937401i	0.457626	−	0.889145i	$-0.348700\pi$
$278$		−	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	$-0.976796\pi$
$281$		−	2.44178i		−	0.145665i	0.997344	−	0.0728323i	$-0.0232038\pi$
$282$	0.499603	+	0.865337i	0.0297509	+	0.0515301i
$283$	14.3620	−	24.8757i	0.853732	−	1.47871i	−0.0240853	−	0.999710i	$-0.507667\pi$
$283$	14.3620	−	24.8757i	0.853732	−	1.47871i	0.877817	−	0.478996i	$-0.158999\pi$
$284$	−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	−0.999834	−	0.0182359i	$-0.994195\pi$
$293$	−25.4013	+	14.6654i	−1.48396	+	0.856763i	−0.484124	+	0.874999i	$0.660862\pi$
$294$		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	$-0.935344\pi$
$307$		−	7.06910i		−	0.403455i	0.979442	−	0.201728i	$-0.0646555\pi$
$308$		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	$0.184629\pi$
$317$			19.5155i			1.09610i	−0.836446	+	0.548049i	$0.815371\pi$
$318$	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	−0.0794953	−	0.996835i	$-0.525331\pi$
$331$	13.5367	−	7.81539i	0.744042	−	0.429573i	0.823537	+	0.567263i	$0.191998\pi$
$332$	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	0.996728	−	0.0808303i	$-0.0257572\pi$
$347$	7.97952	+	13.8209i	0.428363	+	0.741946i	−0.568365	+	0.822777i	$0.692424\pi$
$348$	−10.5460	+	18.2663i	−0.565327	+	0.979176i
$349$	−5.90375	−	3.40853i	−0.316021	−	0.182455i	0.333597	−	0.942716i	$-0.391738\pi$
$349$	−5.90375	−	3.40853i	−0.316021	−	0.182455i	−0.649617	+	0.760261i	$0.725071\pi$
$350$		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	0.141252	−	0.989974i	$-0.454887\pi$
$353$	−12.1272	−	7.00163i	−0.645465	−	0.372659i	−0.786716	+	0.617314i	$0.788221\pi$
$354$	−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	$-0.954359\pi$
$359$		−	5.41494i		−	0.285789i	0.989738	−	0.142895i	$-0.0456410\pi$
$360$	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	−0.145878	−	0.989303i	$-0.546601\pi$
$367$	15.0159	−	26.0083i	0.783822	−	1.35762i	0.929700	−	0.368317i	$-0.120066\pi$
$368$	−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	−0.997959	−	0.0638526i	$-0.979661\pi$
$373$	−10.7049	−	18.5414i	−0.554278	−	0.960037i	0.443682	−	0.896184i	$-0.353672\pi$
$374$	−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	0.274184	−	0.961677i	$-0.411592\pi$
$379$	−8.20693	−	4.73827i	−0.421562	−	0.243389i	−0.695745	+	0.718289i	$0.744926\pi$
$380$	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	−0.375007	−	0.927022i	$-0.622360\pi$
$383$	4.70304	−	2.71530i	0.240314	−	0.138746i	0.615321	+	0.788277i	$0.289026\pi$
$384$	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	−0.628367	+	0.777917i	$0.716276\pi$
$397$	−32.2035	+	18.5927i	−1.61625	+	0.933140i	−0.987879	+	0.155223i	$0.950390\pi$
$398$			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	0.480487	−	0.877002i	$-0.340460\pi$
$401$	−0.776487	−	0.448305i	−0.0387759	−	0.0223873i	−0.519263	+	0.854615i	$0.673793\pi$
$402$	−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	−0.923335	−	0.383995i	$-0.874548\pi$
$409$	−21.2846	+	12.2886i	−1.05245	+	0.607635i	−0.129119	+	0.991629i	$0.541215\pi$
$410$	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	−0.944167	−	0.329468i	$-0.893131\pi$
$419$	−3.82279	+	6.62126i	−0.186755	+	0.323470i	0.757411	+	0.652938i	$0.226464\pi$
$420$		0			0
$421$		−	25.0780i		−	1.22223i	−0.791544	−	0.611113i	$-0.790722\pi$
$421$		−	25.0780i		−	1.22223i	0.791544	−	0.611113i	$-0.209278\pi$
$422$	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	0.652934	−	0.757415i	$-0.273538\pi$
$431$	6.71520	+	3.87702i	0.323460	+	0.186750i	−0.329474	+	0.944165i	$0.606871\pi$
$432$	0.559567	−	0.969199i	0.0269222	−	0.0466306i
$433$	−17.9880	−	31.1561i	−0.864448	−	1.49727i	−0.867594	−	0.497273i	$-0.834335\pi$
$433$	−17.9880	−	31.1561i	−0.864448	−	1.49727i	0.00314644	−	0.999995i	$-0.498998\pi$
$434$		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	−0.303028	−	0.952982i	$-0.597998\pi$
$439$	14.1175	−	24.4523i	0.673792	−	1.16704i	0.976820	−	0.214061i	$-0.0686691\pi$
$440$	−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	−0.958988	−	0.283446i	$-0.908522\pi$
$449$	−25.2795	+	14.5951i	−1.19301	+	0.688785i	−0.234023	+	0.972231i	$0.575189\pi$
$450$			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	−0.306081	−	0.952006i	$-0.599018\pi$
$457$	−27.4399	−	15.8424i	−1.28358	−	0.741077i	−0.977501	+	0.210929i	$0.932351\pi$
$458$	−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	0.0170480	−	0.999855i	$-0.494573\pi$
$461$	19.1407	−	11.0509i	0.891471	−	0.514691i	0.874424	+	0.485163i	$0.161240\pi$
$462$		0			0
$463$			38.8811i			1.80696i	0.428632	+	0.903479i	$0.358996\pi$
$463$			38.8811i			1.80696i	−0.428632	+	0.903479i	$0.641004\pi$
$464$	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	0.362947	−	0.931810i	$-0.381770\pi$
$479$	−5.74618	−	3.31756i	−0.262550	−	0.151583i	−0.625497	+	0.780226i	$0.715104\pi$
$480$	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	0.330809	−	0.943698i	$-0.392678\pi$
$487$	28.9860	−	16.7351i	1.31348	−	0.758338i	0.982671	+	0.185359i	$0.0593449\pi$
$488$	−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	0.0456264	+	0.998959i	$0.485472\pi$
$491$	−18.6643	+	32.3276i	−0.842310	+	1.45892i	−0.887937	+	0.459966i	$0.847862\pi$
$492$	−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	$0.276764\pi$
$499$			34.1327i			1.52799i	−0.645223	+	0.763994i	$0.723236\pi$
$500$	−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	0.984674	−	0.174407i	$-0.0558008\pi$
$503$	7.65447	+	13.2579i	0.341296	+	0.591142i	−0.643378	+	0.765549i	$0.722467\pi$
$504$		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	0.811070	−	0.584949i	$-0.198885\pi$
$509$	16.0189	+	9.24851i	0.710025	+	0.409933i	−0.101046	+	0.994882i	$0.532219\pi$
$510$	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	−0.699567	−	0.714567i	$-0.746624\pi$
$523$	6.15294	−	10.6572i	0.269049	−	0.466007i	0.968617	+	0.248560i	$0.0799572\pi$
$524$	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	$-0.862760\pi$
$541$		−	19.4411i		−	0.835838i	0.908484	−	0.417919i	$-0.137240\pi$
$542$	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	0.638950	−	0.769248i	$-0.279369\pi$
$557$	6.89702	+	3.98199i	0.292236	+	0.168722i	−0.346714	+	0.937971i	$0.612703\pi$
$558$	−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	0.880639	−	0.473789i	$-0.157114\pi$
$563$	0.711981	+	1.23319i	0.0300064	+	0.0519726i	−0.850632	+	0.525761i	$0.823781\pi$
$564$		−	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	−0.992204	−	0.124622i	$-0.960228\pi$
$569$	−9.25946	+	16.0379i	−0.388177	+	0.672342i	0.604028	+	0.796963i	$0.293562\pi$
$570$	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	$0.0637955\pi$
$577$			9.56416i			0.398161i	−0.979983	+	0.199081i	$0.936204\pi$
$578$	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	0.541595	−	0.840640i	$-0.317821\pi$
$587$	2.04428	+	1.18027i	0.0843765	+	0.0487148i	−0.457218	+	0.889355i	$0.651154\pi$
$588$		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	$0.311725\pi$
$593$			40.4292i			1.66023i	−0.557594	+	0.830114i	$0.688275\pi$
$594$	−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	−0.770704	−	0.637193i	$-0.780095\pi$
$601$	4.08115	−	7.06877i	0.166474	−	0.288341i	0.937178	+	0.348852i	$0.113429\pi$
$602$		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	0.932672	−	0.360726i	$-0.117471\pi$
$607$	3.79263	+	6.56902i	0.153938	+	0.266628i	−0.778734	+	0.627354i	$0.784138\pi$
$608$	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	0.202169	−	0.979351i	$-0.435201\pi$
$613$	−13.4908	−	7.78892i	−0.544889	−	0.314592i	−0.747058	+	0.664759i	$0.768534\pi$
$614$	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	−0.0224202	−	0.999749i	$-0.507137\pi$
$617$	20.6709	−	11.9343i	0.832177	−	0.480458i	0.854598	+	0.519291i	$0.173804\pi$
$618$	22.0948	−	12.7565i	0.888785	−	0.513140i
$619$		−	19.4963i		−	0.783622i	−0.920046	−	0.391811i	$-0.871849\pi$
$619$		−	19.4963i		−	0.783622i	0.920046	−	0.391811i	$-0.128151\pi$
$620$	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	−0.872211	−	0.489130i	$-0.837314\pi$
$631$	−22.2239	+	12.8309i	−0.884718	+	0.510792i	−0.0125066	+	0.999922i	$0.503981\pi$
$632$			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	0.854897	−	0.518797i	$-0.173620\pi$
$641$	−0.553020	−	0.957859i	−0.0218430	−	0.0378332i	−0.876740	+	0.480964i	$0.840287\pi$
$642$			8.60949i			0.339789i
$643$	−10.9437	+	6.31833i	−0.431576	+	0.249171i	−0.700018	−	0.714125i	$-0.746825\pi$
$643$	−10.9437	+	6.31833i	−0.431576	+	0.249171i	0.268442	+	0.963296i	$0.413491\pi$
$644$		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	0.494503	+	0.869176i	$0.335350\pi$
$647$	−12.8574	+	22.2697i	−0.505477	+	0.875512i	−0.999980	+	0.00633579i	$0.997983\pi$
$648$	−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	−0.999978	−	0.00661158i	$-0.997895\pi$
$653$	−12.6303	+	21.8764i	−0.494263	+	0.856089i	0.505715	+	0.862701i	$0.331229\pi$
$654$	−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	0.550707	−	0.834699i	$-0.314358\pi$
$659$	−11.4882	−	19.8982i	−0.447517	−	0.775123i	−0.998224	+	0.0595764i	$0.981025\pi$
$660$	−33.0376	+	57.2228i	−1.28599	+	2.22739i
$661$	−26.3554	−	15.2163i	−1.02511	−	0.591845i	−0.109528	−	0.993984i	$-0.534934\pi$
$661$	−26.3554	−	15.2163i	−1.02511	−	0.591845i	−0.915579	+	0.402138i	$0.868267\pi$
$662$	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	−0.742468	−	0.669881i	$-0.766345\pi$
$673$	5.41933	−	9.38656i	0.208900	−	0.361825i	0.951368	+	0.308056i	$0.0996784\pi$
$674$	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	0.281909	−	0.959441i	$-0.409032\pi$
$683$	32.7662	−	18.9176i	1.25376	−	0.723861i	0.971855	+	0.235580i	$0.0756990\pi$
$684$		−	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	−0.0841761	−	0.996451i	$-0.526826\pi$
$691$	−26.0034	−	15.0131i	−0.989216	−	0.571124i	−0.905040	+	0.425327i	$0.860159\pi$
$692$	−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	−0.386548	−	0.922269i	$-0.626333\pi$
$709$	5.82829	−	3.36497i	0.218886	−	0.126374i	0.605434	+	0.795895i	$0.292999\pi$
$710$		−	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	−0.859069	−	0.511860i	$-0.828957\pi$
$719$	−23.4039	−	40.5367i	−0.872818	−	1.51177i	−0.0137492	−	0.999905i	$-0.504377\pi$
$720$		−	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	$0.183124\pi$
$733$			29.4612i			1.08817i	−0.839029	+	0.544087i	$0.816876\pi$
$734$	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	0.295982	−	0.955193i	$-0.404353\pi$
$739$	−10.4184	−	6.01509i	−0.383249	−	0.221269i	−0.679231	+	0.733925i	$0.737686\pi$
$740$	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	0.110331	−	0.993895i	$-0.464809\pi$
$743$	−18.9509	−	10.9413i	−0.695242	−	0.401398i	−0.805573	+	0.592497i	$0.798142\pi$
$744$	−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	−0.352717	−	0.935730i	$-0.614742\pi$
$751$	17.3746	−	30.0937i	0.634008	−	1.09813i	0.986724	−	0.162403i	$-0.0519245\pi$
$752$	−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	0.122481	+	0.992471i	$0.460915\pi$
$757$	−21.9632	+	38.0413i	−0.798265	+	1.38264i	−0.920745	+	0.390164i	$0.872418\pi$
$758$	−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	−0.502218	−	0.864741i	$-0.667482\pi$
$761$	−0.122449	+	0.0706957i	−0.00443876	+	0.00256272i	0.497779	+	0.867304i	$0.334149\pi$
$762$		−	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	0.271503	−	0.962438i	$-0.412479\pi$
$769$	−11.8200	−	6.82429i	−0.426241	−	0.246090i	−0.697744	+	0.716347i	$0.745813\pi$
$770$		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	−0.748269	−	0.663395i	$-0.769115\pi$
$773$	−15.2328	+	8.79469i	−0.547887	+	0.316323i	0.200382	+	0.979718i	$0.435782\pi$
$774$	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	−0.545118	−	0.838359i	$-0.683515\pi$
$787$	−2.57075	+	1.48422i	−0.0916374	+	0.0529069i	0.453481	+	0.891266i	$0.350182\pi$
$788$		−	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	0.770100	−	0.637923i	$-0.220206\pi$
$797$	−4.72611	−	8.18586i	−0.167407	−	0.289958i	−0.937508	+	0.347965i	$0.886873\pi$
$798$		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	−0.855626	−	0.517594i	$-0.826828\pi$
$809$	0.581273	−	1.00679i	0.0204365	−	0.0353970i	0.876063	+	0.482197i	$0.160161\pi$
$810$	−6.00035	−	10.3929i	−0.210831	−	0.365170i
$811$			19.5561i			0.686706i	0.939206	+	0.343353i	$0.111563\pi$
$811$			19.5561i			0.686706i	−0.939206	+	0.343353i	$0.888437\pi$
$812$		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	0.678427	−	0.734668i	$-0.262662\pi$
$821$	10.9283	+	6.30945i	0.381400	+	0.220201i	−0.297027	+	0.954869i	$0.595995\pi$
$822$	−21.8515	+	37.8479i	−0.762159	+	1.32010i
$823$	−3.28404	−	5.68812i	−0.114474	−	0.198275i	0.803095	−	0.595851i	$-0.203185\pi$
$823$	−3.28404	−	5.68812i	−0.114474	−	0.198275i	−0.917570	+	0.397575i	$0.869852\pi$
$824$		−	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	$0.0972794\pi$
$827$			17.3050i			0.601754i	−0.953663	+	0.300877i	$0.902721\pi$
$828$	−7.35441	−	12.7382i	−0.255583	−	0.442683i
$829$	1.87837	−	3.25343i	0.0652385	−	0.112996i	−0.831561	−	0.555433i	$-0.812553\pi$
$829$	1.87837	−	3.25343i	0.0652385	−	0.112996i	0.896800	+	0.442437i	$0.145886\pi$
$830$	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	0.392766	−	0.919638i	$-0.371518\pi$
$839$	40.1340	−	23.1714i	1.38558	−	0.799965i	0.992813	+	0.119674i	$0.0381849\pi$
$840$		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	$-0.915583\pi$
$853$		−	15.3103i		−	0.524215i	0.965039	−	0.262107i	$-0.0844174\pi$
$854$		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	$-0.830936\pi$
$863$		−	29.7592i		−	1.01302i	0.862235	−	0.506508i	$-0.169064\pi$
$864$	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	−0.520955	−	0.853584i	$-0.674424\pi$
$877$	−1.24995	+	0.721660i	−0.0422079	+	0.0243687i	0.478748	+	0.877953i	$0.341091\pi$
$878$	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	−0.387723	−	0.921776i	$-0.626738\pi$
$881$	17.9402	−	31.0733i	0.604420	−	1.04689i	0.992143	−	0.125110i	$-0.0399284\pi$
$882$		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	−0.744936	−	0.667136i	$-0.767520\pi$
$887$	6.11401	−	10.5898i	0.205288	−	0.355570i	0.950225	+	0.311566i	$0.100853\pi$
$888$	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	−0.826010	−	0.563655i	$-0.809395\pi$
$907$	2.26278	−	3.91924i	0.0751343	−	0.130136i	0.901145	+	0.433519i	$0.142728\pi$
$908$	−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	0.977281	+	0.211948i	$0.0679809\pi$
$919$	20.3775	+	35.2949i	0.672193	+	1.16427i	−0.305088	+	0.952324i	$0.598686\pi$
$920$	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	−0.999862	−	0.0165897i	$-0.994719\pi$
$929$	−45.2751	+	26.1396i	−1.48543	+	0.857611i	−0.485564	+	0.874201i	$0.661386\pi$
$930$	−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	$-0.864293\pi$
$941$		−	25.3711i		−	0.827073i	0.910488	−	0.413536i	$-0.135707\pi$
$942$	−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	0.831315	−	0.555801i	$-0.187588\pi$
$947$	23.5612	+	13.6031i	0.765635	+	0.442040i	−0.0656800	+	0.997841i	$0.520922\pi$
$948$	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	0.996928	−	0.0783248i	$-0.0249571\pi$
$953$	13.2939	+	23.0258i	0.430633	+	0.745878i	−0.566295	+	0.824203i	$0.691624\pi$
$954$		−	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	$-0.808209\pi$
$967$		−	35.2467i		−	1.13346i	0.823904	−	0.566729i	$-0.191791\pi$
$968$	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	0.993778	+	0.111377i	$0.0355261\pi$
$971$	18.4891	+	32.0241i	0.593344	+	1.02770i	−0.400434	+	0.916326i	$0.631141\pi$
$972$	−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	0.116232	−	0.993222i	$-0.462918\pi$
$977$	−21.4363	−	12.3762i	−0.685807	−	0.395951i	−0.802039	+	0.597271i	$0.796252\pi$
$978$	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	$0.0231547\pi$
$983$			4.55736i			0.145357i	−0.997355	+	0.0726786i	$0.976845\pi$
$984$	−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	−0.565082	−	0.825034i	$-0.691156\pi$
$991$	13.5982	−	23.5527i	0.431960	−	0.748176i	0.997042	+	0.0768584i	$0.0244890\pi$
$992$	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	0.521044	−	0.853530i	$-0.325543\pi$
$997$	−15.1137	−	26.1777i	−0.478656	−	0.829057i	−0.999700	+	0.0244727i	$0.992209\pi$
$998$	−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.589.4		12
7.2	even	3		637.2.k.g.459.3		12
7.3	odd	6		637.2.u.h.30.3		12
7.4	even	3		637.2.u.i.30.3		12
7.5	odd	6		637.2.k.h.459.3		12
7.6	odd	2		91.2.q.a.43.4	yes	12
13.6	odd	12		8281.2.a.ch.1.2		6
13.7	odd	12		8281.2.a.by.1.5		6
13.10	even	6	inner	637.2.q.h.491.4		12
21.20	even	2		819.2.ct.a.316.3		12
28.27	even	2		1456.2.cc.c.225.6		12
91.6	even	12		1183.2.a.p.1.2		6
91.10	odd	6		637.2.k.h.569.4		12
91.20	even	12		1183.2.a.m.1.5		6
91.23	even	6		637.2.u.i.361.3		12
91.48	odd	6		1183.2.c.i.337.5		12
91.62	odd	6		91.2.q.a.36.4	✓	12
91.69	odd	6		1183.2.c.i.337.8		12
91.75	odd	6		637.2.u.h.361.3		12
91.88	even	6		637.2.k.g.569.4		12
273.62	even	6		819.2.ct.a.127.3		12
364.335	even	6		1456.2.cc.c.673.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.q.a.36.4	✓	12	91.62	odd	6
91.2.q.a.43.4	yes	12	7.6	odd	2
637.2.k.g.459.3		12	7.2	even	3
637.2.k.g.569.4		12	91.88	even	6
637.2.k.h.459.3		12	7.5	odd	6
637.2.k.h.569.4		12	91.10	odd	6
637.2.q.h.491.4		12	13.10	even	6	inner
637.2.q.h.589.4		12	1.1	even	1	trivial
637.2.u.h.30.3		12	7.3	odd	6
637.2.u.h.361.3		12	91.75	odd	6
637.2.u.i.30.3		12	7.4	even	3
637.2.u.i.361.3		12	91.23	even	6
819.2.ct.a.127.3		12	273.62	even	6
819.2.ct.a.316.3		12	21.20	even	2
1183.2.a.m.1.5		6	91.20	even	12
1183.2.a.p.1.2		6	91.6	even	12
1183.2.c.i.337.5		12	91.48	odd	6
1183.2.c.i.337.8		12	91.69	odd	6
1456.2.cc.c.225.6		12	28.27	even	2
1456.2.cc.c.673.6		12	364.335	even	6
8281.2.a.by.1.5		6	13.7	odd	12
8281.2.a.ch.1.2		6	13.6	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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