LMFDB - Embedded newform 1890.2.t.b.1151.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(1151,1890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1890, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0, 1]))

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

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

chi := DirichletCharacter("1890.1151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.t (of order $6$, degree $2$, not 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:	$15.0917259820$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1151.13
Character	$\chi$	$=$	1890.1151
Dual form			1890.2.t.b.1601.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(1.07313 + 2.41835i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(1.07313 + 2.41835i) q^{7} +1.00000i q^{8} +(0.866025 + 0.500000i) q^{10} -4.51143i q^{11} +(1.92602 + 1.11199i) q^{13} +(-0.279818 + 2.63091i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.31479 - 5.74138i) q^{17} +(6.71016 - 3.87412i) q^{19} +(0.500000 + 0.866025i) q^{20} +(2.25571 - 3.90701i) q^{22} -5.02232i q^{23} +1.00000 q^{25} +(1.11199 + 1.92602i) q^{26} +(-1.55779 + 2.13853i) q^{28} +(-1.08021 + 0.623662i) q^{29} +(-4.32162 + 2.49509i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(5.74138 - 3.31479i) q^{34} +(1.07313 + 2.41835i) q^{35} +(-0.475116 - 0.822924i) q^{37} +7.74823 q^{38} +1.00000i q^{40} +(-4.31268 + 7.46978i) q^{41} +(4.87159 + 8.43784i) q^{43} +(3.90701 - 2.25571i) q^{44} +(2.51116 - 4.34946i) q^{46} +(-2.53212 + 4.38576i) q^{47} +(-4.69680 + 5.19038i) q^{49} +(0.866025 + 0.500000i) q^{50} +2.22397i q^{52} +(4.68518 + 2.70499i) q^{53} -4.51143i q^{55} +(-2.41835 + 1.07313i) q^{56} -1.24732 q^{58} +(1.63861 + 2.83816i) q^{59} +(9.88563 + 5.70747i) q^{61} -4.99018 q^{62} -1.00000 q^{64} +(1.92602 + 1.11199i) q^{65} +(-2.76915 - 4.79631i) q^{67} +6.62958 q^{68} +(-0.279818 + 2.63091i) q^{70} +9.57979i q^{71} +(1.11202 + 0.642023i) q^{73} -0.950231i q^{74} +(6.71016 + 3.87412i) q^{76} +(10.9102 - 4.84133i) q^{77} +(1.98062 - 3.43054i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-7.46978 + 4.31268i) q^{82} +(-5.71593 - 9.90029i) q^{83} +(3.31479 - 5.74138i) q^{85} +9.74318i q^{86} +4.51143 q^{88} +(-8.89050 - 15.3988i) q^{89} +(-0.622308 + 5.85108i) q^{91} +(4.34946 - 2.51116i) q^{92} +(-4.38576 + 2.53212i) q^{94} +(6.71016 - 3.87412i) q^{95} +(-7.24779 + 4.18451i) q^{97} +(-6.66274 + 2.14660i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 14 q^{4} + 28 q^{5} - 4 q^{7}+O(q^{10}) $ 28 * q + 14 * q^4 + 28 * q^5 - 4 * q^7	$ 28 q + 14 q^{4} + 28 q^{5} - 4 q^{7} - 6 q^{14} - 14 q^{16} + 6 q^{17} - 6 q^{19} + 14 q^{20} - 6 q^{22} + 28 q^{25} - 12 q^{26} - 8 q^{28} - 12 q^{31} - 4 q^{35} + 4 q^{37} + 12 q^{38} - 18 q^{41} + 28 q^{43} - 18 q^{46} - 30 q^{47} - 14 q^{49} + 42 q^{53} - 6 q^{56} - 12 q^{58} + 24 q^{59} + 24 q^{61} + 12 q^{62} - 28 q^{64} - 40 q^{67} + 12 q^{68} - 6 q^{70} + 6 q^{73} - 6 q^{76} + 24 q^{77} + 2 q^{79} - 14 q^{80} + 24 q^{82} + 18 q^{83} + 6 q^{85} - 12 q^{88} - 6 q^{89} + 66 q^{91} + 30 q^{92} + 42 q^{94} - 6 q^{95} - 72 q^{97} + 24 q^{98}+O(q^{100}) $ 28 * q + 14 * q^4 + 28 * q^5 - 4 * q^7 - 6 * q^14 - 14 * q^16 + 6 * q^17 - 6 * q^19 + 14 * q^20 - 6 * q^22 + 28 * q^25 - 12 * q^26 - 8 * q^28 - 12 * q^31 - 4 * q^35 + 4 * q^37 + 12 * q^38 - 18 * q^41 + 28 * q^43 - 18 * q^46 - 30 * q^47 - 14 * q^49 + 42 * q^53 - 6 * q^56 - 12 * q^58 + 24 * q^59 + 24 * q^61 + 12 * q^62 - 28 * q^64 - 40 * q^67 + 12 * q^68 - 6 * q^70 + 6 * q^73 - 6 * q^76 + 24 * q^77 + 2 * q^79 - 14 * q^80 + 24 * q^82 + 18 * q^83 + 6 * q^85 - 12 * q^88 - 6 * q^89 + 66 * q^91 + 30 * q^92 + 42 * q^94 - 6 * q^95 - 72 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	1.07313	+	2.41835i	0.405604	+	0.914049i
$7$	1.07313	+	2.41835i	0.405604	+	0.914049i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	0.866025	+	0.500000i	0.273861	+	0.158114i
$11$		−	4.51143i		−	1.36025i	−0.733098	−	0.680123i	$-0.761926\pi$
$11$		−	4.51143i		−	1.36025i	0.733098	−	0.680123i	$-0.238074\pi$
$12$		0			0
$13$	1.92602	+	1.11199i	0.534181	+	0.308410i	0.742717	−	0.669605i	$-0.233537\pi$
$13$	1.92602	+	1.11199i	0.534181	+	0.308410i	−0.208536	+	0.978015i	$0.566870\pi$
$14$	−0.279818	+	2.63091i	−0.0747846	+	0.703141i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.31479	−	5.74138i	0.803954	−	1.39249i	−0.113041	−	0.993590i	$-0.536059\pi$
$17$	3.31479	−	5.74138i	0.803954	−	1.39249i	0.916995	−	0.398899i	$-0.130608\pi$
$18$		0			0
$19$	6.71016	−	3.87412i	1.53942	−	0.888783i	0.540545	−	0.841315i	$-0.318218\pi$
$19$	6.71016	−	3.87412i	1.53942	−	0.888783i	0.998873	−	0.0474677i	$-0.0151151\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$		0			0
$22$	2.25571	−	3.90701i	0.480920	−	0.832977i
$23$		−	5.02232i		−	1.04723i	−0.851956	−	0.523613i	$-0.824584\pi$
$23$		−	5.02232i		−	1.04723i	0.851956	−	0.523613i	$-0.175416\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	1.11199	+	1.92602i	0.218078	+	0.377723i
$27$		0			0
$28$	−1.55779	+	2.13853i	−0.294394	+	0.404144i
$29$	−1.08021	+	0.623662i	−0.200591	+	0.115811i	−0.596931	−	0.802293i	$-0.703613\pi$
$29$	−1.08021	+	0.623662i	−0.200591	+	0.115811i	0.396340	+	0.918104i	$0.370280\pi$
$30$		0			0
$31$	−4.32162	+	2.49509i	−0.776186	+	0.448131i	−0.835077	−	0.550133i	$-0.814577\pi$
$31$	−4.32162	+	2.49509i	−0.776186	+	0.448131i	0.0588911	+	0.998264i	$0.481244\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$	5.74138	−	3.31479i	0.984639	−	0.568481i
$35$	1.07313	+	2.41835i	0.181392	+	0.408775i
$36$		0			0
$37$	−0.475116	−	0.822924i	−0.0781085	−	0.135288i	0.824325	−	0.566116i	$-0.191555\pi$
$37$	−0.475116	−	0.822924i	−0.0781085	−	0.135288i	−0.902434	+	0.430828i	$0.858221\pi$
$38$	7.74823			1.25693
$39$		0			0
$40$			1.00000i			0.158114i
$41$	−4.31268	+	7.46978i	−0.673527	+	1.16658i	0.303370	+	0.952873i	$0.401888\pi$
$41$	−4.31268	+	7.46978i	−0.673527	+	1.16658i	−0.976897	+	0.213711i	$0.931445\pi$
$42$		0			0
$43$	4.87159	+	8.43784i	0.742911	+	1.28676i	0.951165	+	0.308684i	$0.0998887\pi$
$43$	4.87159	+	8.43784i	0.742911	+	1.28676i	−0.208254	+	0.978075i	$0.566778\pi$
$44$	3.90701	−	2.25571i	0.589004	−	0.340062i
$45$		0			0
$46$	2.51116	−	4.34946i	0.370251	−	0.641293i
$47$	−2.53212	+	4.38576i	−0.369348	+	0.639729i	−0.989464	−	0.144781i	$-0.953752\pi$
$47$	−2.53212	+	4.38576i	−0.369348	+	0.639729i	0.620116	+	0.784510i	$0.287086\pi$
$48$		0			0
$49$	−4.69680	+	5.19038i	−0.670971	+	0.741483i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$		0			0
$52$			2.22397i			0.308410i
$53$	4.68518	+	2.70499i	0.643559	+	0.371559i	0.785984	−	0.618246i	$-0.212157\pi$
$53$	4.68518	+	2.70499i	0.643559	+	0.371559i	−0.142425	+	0.989806i	$0.545490\pi$
$54$		0			0
$55$		−	4.51143i		−	0.608321i
$56$	−2.41835	+	1.07313i	−0.323165	+	0.143403i
$57$		0			0
$58$	−1.24732			−0.163782
$59$	1.63861	+	2.83816i	0.213329	+	0.369497i	0.952754	−	0.303742i	$-0.0982360\pi$
$59$	1.63861	+	2.83816i	0.213329	+	0.369497i	−0.739425	+	0.673239i	$0.764903\pi$
$60$		0			0
$61$	9.88563	+	5.70747i	1.26573	+	0.730767i	0.974176	−	0.225789i	$-0.0724960\pi$
$61$	9.88563	+	5.70747i	1.26573	+	0.730767i	0.291549	+	0.956556i	$0.405829\pi$
$62$	−4.99018			−0.633753
$63$		0			0
$64$	−1.00000			−0.125000
$65$	1.92602	+	1.11199i	0.238893	+	0.137925i
$66$		0			0
$67$	−2.76915	−	4.79631i	−0.338306	−	0.585963i	0.645808	−	0.763500i	$-0.276521\pi$
$67$	−2.76915	−	4.79631i	−0.338306	−	0.585963i	−0.984114	+	0.177537i	$0.943187\pi$
$68$	6.62958			0.803954
$69$		0			0
$70$	−0.279818	+	2.63091i	−0.0334447	+	0.314454i
$71$			9.57979i			1.13691i	0.822714	+	0.568456i	$0.192459\pi$
$71$			9.57979i			1.13691i	−0.822714	+	0.568456i	$0.807541\pi$
$72$		0			0
$73$	1.11202	+	0.642023i	0.130152	+	0.0751431i	0.563662	−	0.826005i	$-0.309392\pi$
$73$	1.11202	+	0.642023i	0.130152	+	0.0751431i	−0.433511	+	0.901148i	$0.642725\pi$
$74$		−	0.950231i		−	0.110462i
$75$		0			0
$76$	6.71016	+	3.87412i	0.769709	+	0.444392i
$77$	10.9102	−	4.84133i	1.24333	−	0.551721i
$78$		0			0
$79$	1.98062	−	3.43054i	0.222837	−	0.385966i	−0.732831	−	0.680411i	$-0.761801\pi$
$79$	1.98062	−	3.43054i	0.222837	−	0.385966i	0.955668	+	0.294445i	$0.0951348\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$		0			0
$82$	−7.46978	+	4.31268i	−0.824899	+	0.476256i
$83$	−5.71593	−	9.90029i	−0.627405	−	1.08670i	−0.988070	−	0.154003i	$-0.950784\pi$
$83$	−5.71593	−	9.90029i	−0.627405	−	1.08670i	0.360665	−	0.932695i	$-0.382550\pi$
$84$		0			0
$85$	3.31479	−	5.74138i	0.359539	−	0.622740i
$86$			9.74318i			1.05063i
$87$		0			0
$88$	4.51143			0.480920
$89$	−8.89050	−	15.3988i	−0.942392	−	1.63227i	−0.760892	−	0.648879i	$-0.775238\pi$
$89$	−8.89050	−	15.3988i	−0.942392	−	1.63227i	−0.181500	−	0.983391i	$-0.558095\pi$
$90$		0			0
$91$	−0.622308	+	5.85108i	−0.0652356	+	0.613360i
$92$	4.34946	−	2.51116i	0.453463	−	0.261807i
$93$		0			0
$94$	−4.38576	+	2.53212i	−0.452357	+	0.261168i
$95$	6.71016	−	3.87412i	0.688448	−	0.397476i
$96$		0			0
$97$	−7.24779	+	4.18451i	−0.735901	+	0.424873i	−0.820577	−	0.571536i	$-0.806348\pi$
$97$	−7.24779	+	4.18451i	−0.735901	+	0.424873i	0.0846758	+	0.996409i	$0.473015\pi$
$98$	−6.66274	+	2.14660i	−0.673038	+	0.216840i
$99$		0			0
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−11.6336			−1.15759			−0.578793	−	0.815475i	$-0.696476\pi$
$101$	−11.6336			−1.15759			−0.578793	+	0.815475i	$0.696476\pi$
$102$		0			0
$103$		−	13.3778i		−	1.31815i	−0.752077	−	0.659075i	$-0.770948\pi$
$103$		−	13.3778i		−	1.31815i	0.752077	−	0.659075i	$-0.229052\pi$
$104$	−1.11199	+	1.92602i	−0.109039	+	0.188862i
$105$		0			0
$106$	2.70499	+	4.68518i	0.262732	+	0.455065i
$107$	9.50931	−	5.49020i	0.919300	−	0.530758i	0.0358882	−	0.999356i	$-0.488574\pi$
$107$	9.50931	−	5.49020i	0.919300	−	0.530758i	0.883412	+	0.468598i	$0.155241\pi$
$108$		0			0
$109$	−7.73421	+	13.3960i	−0.740803	+	1.28311i	0.211327	+	0.977415i	$0.432221\pi$
$109$	−7.73421	+	13.3960i	−0.740803	+	1.28311i	−0.952130	+	0.305693i	$0.901112\pi$
$110$	2.25571	−	3.90701i	0.215074	−	0.372519i
$111$		0			0
$112$	−2.63091	−	0.279818i	−0.248598	−	0.0264403i
$113$	2.97068	+	1.71512i	0.279458	+	0.161345i	0.633178	−	0.774006i	$-0.281750\pi$
$113$	2.97068	+	1.71512i	0.279458	+	0.161345i	−0.353720	+	0.935351i	$0.615083\pi$
$114$		0			0
$115$		−	5.02232i		−	0.468334i
$116$	−1.08021	−	0.623662i	−0.100295	−	0.0579055i
$117$		0			0
$118$			3.27723i			0.301693i
$119$	17.4418	+	1.85508i	1.59889	+	0.170055i
$120$		0			0
$121$	−9.35297			−0.850270
$122$	5.70747	+	9.88563i	0.516730	+	0.895003i
$123$		0			0
$124$	−4.32162	−	2.49509i	−0.388093	−	0.224065i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−4.42037			−0.392244			−0.196122	−	0.980579i	$-0.562835\pi$
$127$	−4.42037			−0.392244			−0.196122	+	0.980579i	$0.562835\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	1.11199	+	1.92602i	0.0975277	+	0.168923i
$131$	8.34437			0.729051			0.364525	−	0.931193i	$-0.381231\pi$
$131$	8.34437			0.729051			0.364525	+	0.931193i	$0.381231\pi$
$132$		0			0
$133$	16.5698	+	12.0701i	1.43678	+	1.04661i
$134$		−	5.53831i		−	0.478437i
$135$		0			0
$136$	5.74138	+	3.31479i	0.492319	+	0.284241i
$137$		−	11.4602i		−	0.979113i	−0.871972	−	0.489556i	$-0.837159\pi$
$137$		−	11.4602i		−	0.979113i	0.871972	−	0.489556i	$-0.162841\pi$
$138$		0			0
$139$	−2.95770	−	1.70763i	−0.250869	−	0.144839i	0.369293	−	0.929313i	$-0.379600\pi$
$139$	−2.95770	−	1.70763i	−0.250869	−	0.144839i	−0.620162	+	0.784474i	$0.712933\pi$
$140$	−1.55779	+	2.13853i	−0.131657	+	0.180739i
$141$		0			0
$142$	−4.78989	+	8.29634i	−0.401959	+	0.696214i
$143$	5.01664	−	8.68908i	0.419513	−	0.726618i
$144$		0			0
$145$	−1.08021	+	0.623662i	−0.0897069	+	0.0517923i
$146$	0.642023	+	1.11202i	0.0531342	+	0.0920311i
$147$		0			0
$148$	0.475116	−	0.822924i	0.0390543	−	0.0676440i
$149$			17.7452i			1.45374i	0.686775	+	0.726870i	$0.259026\pi$
$149$			17.7452i			1.45374i	−0.686775	+	0.726870i	$0.740974\pi$
$150$		0			0
$151$	1.40189			0.114085			0.0570423	−	0.998372i	$-0.481833\pi$
$151$	1.40189			0.114085			0.0570423	+	0.998372i	$0.481833\pi$
$152$	3.87412	+	6.71016i	0.314232	+	0.544266i
$153$		0			0
$154$	11.8692	+	1.26238i	0.956445	+	0.101725i
$155$	−4.32162	+	2.49509i	−0.347121	+	0.200410i
$156$		0			0
$157$	−13.6405	+	7.87534i	−1.08863	+	0.628520i	−0.933211	−	0.359329i	$-0.883006\pi$
$157$	−13.6405	+	7.87534i	−1.08863	+	0.628520i	−0.155418	+	0.987849i	$0.549672\pi$
$158$	3.43054	−	1.98062i	0.272919	−	0.157570i
$159$		0			0
$160$	−0.866025	+	0.500000i	−0.0684653	+	0.0395285i
$161$	12.1457	−	5.38959i	0.957217	−	0.424759i
$162$		0			0
$163$	−0.789054	−	1.36668i	−0.0618035	−	0.107047i	0.833468	−	0.552568i	$-0.186352\pi$
$163$	−0.789054	−	1.36668i	−0.0618035	−	0.107047i	−0.895272	+	0.445521i	$0.853019\pi$
$164$	−8.62536			−0.673527
$165$		0			0
$166$		−	11.4319i		−	0.887285i
$167$	−4.60834	+	7.98188i	−0.356604	+	0.617656i	−0.987391	−	0.158300i	$-0.949399\pi$
$167$	−4.60834	+	7.98188i	−0.356604	+	0.617656i	0.630787	+	0.775956i	$0.282732\pi$
$168$		0			0
$169$	−4.02697	−	6.97492i	−0.309767	−	0.536532i
$170$	5.74138	−	3.31479i	0.440344	−	0.254233i
$171$		0			0
$172$	−4.87159	+	8.43784i	−0.371455	+	0.643380i
$173$	1.26455	−	2.19027i	0.0961423	−	0.166523i	−0.813942	−	0.580945i	$-0.802683\pi$
$173$	1.26455	−	2.19027i	0.0961423	−	0.166523i	0.910085	+	0.414422i	$0.136016\pi$
$174$		0			0
$175$	1.07313	+	2.41835i	0.0811207	+	0.182810i
$176$	3.90701	+	2.25571i	0.294502	+	0.170031i
$177$		0			0
$178$		−	17.7810i		−	1.33274i
$179$	9.58793	+	5.53559i	0.716635	+	0.413750i	0.813513	−	0.581547i	$-0.197552\pi$
$179$	9.58793	+	5.53559i	0.716635	+	0.413750i	−0.0968777	+	0.995296i	$0.530886\pi$
$180$		0			0
$181$		−	17.6466i		−	1.31166i	−0.754908	−	0.655831i	$-0.772318\pi$
$181$		−	17.6466i		−	1.31166i	0.754908	−	0.655831i	$-0.227682\pi$
$182$	−3.46447	+	4.75603i	−0.256804	+	0.352540i
$183$		0			0
$184$	5.02232			0.370251
$185$	−0.475116	−	0.822924i	−0.0349312	−	0.0605026i
$186$		0			0
$187$	−25.9018	−	14.9544i	−1.89413	−	1.09358i
$188$	−5.06424			−0.369348
$189$		0			0
$190$	7.74823			0.562116
$191$	8.00675	+	4.62270i	0.579348	+	0.334487i	0.760874	−	0.648899i	$-0.224770\pi$
$191$	8.00675	+	4.62270i	0.579348	+	0.334487i	−0.181526	+	0.983386i	$0.558104\pi$
$192$		0			0
$193$	8.98854	+	15.5686i	0.647010	+	1.12065i	0.983833	+	0.179086i	$0.0573140\pi$
$193$	8.98854	+	15.5686i	0.647010	+	1.12065i	−0.336824	+	0.941568i	$0.609353\pi$
$194$	−8.36903			−0.600861
$195$		0			0
$196$	−6.84340	−	1.47236i	−0.488815	−	0.105168i
$197$		−	11.1779i		−	0.796394i	−0.917300	−	0.398197i	$-0.869636\pi$
$197$		−	11.1779i		−	0.796394i	0.917300	−	0.398197i	$-0.130364\pi$
$198$		0			0
$199$	2.62204	+	1.51384i	0.185872	+	0.107313i	0.590048	−	0.807368i	$-0.299109\pi$
$199$	2.62204	+	1.51384i	0.185872	+	0.107313i	−0.404177	+	0.914681i	$0.632442\pi$
$200$			1.00000i			0.0707107i
$201$		0			0
$202$	−10.0750	−	5.81680i	−0.708874	−	0.409268i
$203$	−2.66744	−	1.94306i	−0.187217	−	0.136376i
$204$		0			0
$205$	−4.31268	+	7.46978i	−0.301211	+	0.521712i
$206$	6.68888	−	11.5855i	0.466037	−	0.807199i
$207$		0			0
$208$	−1.92602	+	1.11199i	−0.133545	+	0.0771024i
$209$	−17.4778	−	30.2724i	−1.20896	−	2.09399i
$210$		0			0
$211$	8.99690	−	15.5831i	0.619372	−	1.07278i	−0.370228	−	0.928941i	$-0.620721\pi$
$211$	8.99690	−	15.5831i	0.619372	−	1.07278i	0.989601	−	0.143843i	$-0.0459461\pi$
$212$			5.40998i			0.371559i
$213$		0			0
$214$	10.9804			0.750605
$215$	4.87159	+	8.43784i	0.332240	+	0.575456i
$216$		0			0
$217$	−10.6716	−	7.77363i	−0.724437	−	0.527708i
$218$	−13.3960	+	7.73421i	−0.907295	+	0.523827i
$219$		0			0
$220$	3.90701	−	2.25571i	0.263411	−	0.152080i
$221$	12.7687	−	7.37200i	0.858914	−	0.495894i
$222$		0			0
$223$	−10.6762	+	6.16390i	−0.714931	+	0.412765i	−0.812884	−	0.582426i	$-0.802104\pi$
$223$	−10.6762	+	6.16390i	−0.714931	+	0.412765i	0.0979533	+	0.995191i	$0.468770\pi$
$224$	−2.13853	−	1.55779i	−0.142886	−	0.104084i
$225$		0			0
$226$	1.71512	+	2.97068i	0.114088	+	0.197607i
$227$	−12.1983			−0.809627			−0.404813	−	0.914399i	$-0.632663\pi$
$227$	−12.1983			−0.809627			−0.404813	+	0.914399i	$0.632663\pi$
$228$		0			0
$229$			12.2318i			0.808302i	0.914692	+	0.404151i	$0.132433\pi$
$229$			12.2318i			0.808302i	−0.914692	+	0.404151i	$0.867567\pi$
$230$	2.51116	−	4.34946i	0.165581	−	0.286795i
$231$		0			0
$232$	−0.623662	−	1.08021i	−0.0409454	−	0.0709195i
$233$	0.604674	−	0.349109i	0.0396135	−	0.0228709i	−0.480062	−	0.877234i	$-0.659386\pi$
$233$	0.604674	−	0.349109i	0.0396135	−	0.0228709i	0.519676	+	0.854363i	$0.326053\pi$
$234$		0			0
$235$	−2.53212	+	4.38576i	−0.165177	+	0.286096i
$236$	−1.63861	+	2.83816i	−0.106665	+	0.184749i
$237$		0			0
$238$	14.1775	+	10.3275i	0.918993	+	0.669430i
$239$	4.76888	+	2.75332i	0.308473	+	0.178097i	0.646243	−	0.763132i	$-0.276339\pi$
$239$	4.76888	+	2.75332i	0.308473	+	0.178097i	−0.337770	+	0.941229i	$0.609673\pi$
$240$		0			0
$241$			17.6732i			1.13843i	0.822188	+	0.569215i	$0.192753\pi$
$241$			17.6732i			1.13843i	−0.822188	+	0.569215i	$0.807247\pi$
$242$	−8.09991	−	4.67648i	−0.520682	−	0.300616i
$243$		0			0
$244$			11.4149i			0.730767i
$245$	−4.69680	+	5.19038i	−0.300067	+	0.331601i
$246$		0			0
$247$	17.2319			1.09644
$248$	−2.49509	−	4.32162i	−0.158438	−	0.274423i
$249$		0			0
$250$	0.866025	+	0.500000i	0.0547723	+	0.0316228i
$251$	−27.8950			−1.76072			−0.880359	−	0.474308i	$-0.842698\pi$
$251$	−27.8950			−1.76072			−0.880359	+	0.474308i	$0.842698\pi$
$252$		0			0
$253$	−22.6578			−1.42449
$254$	−3.82815	−	2.21018i	−0.240199	−	0.138679i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−14.1508			−0.882701			−0.441351	−	0.897335i	$-0.645501\pi$
$257$	−14.1508			−0.882701			−0.441351	+	0.897335i	$0.645501\pi$
$258$		0			0
$259$	1.48026	−	2.03210i	0.0919787	−	0.126268i
$260$			2.22397i			0.137925i
$261$		0			0
$262$	7.22644	+	4.17218i	0.446451	+	0.257758i
$263$			30.7879i			1.89846i	0.314577	+	0.949232i	$0.398137\pi$
$263$			30.7879i			1.89846i	−0.314577	+	0.949232i	$0.601863\pi$
$264$		0			0
$265$	4.68518	+	2.70499i	0.287809	+	0.166166i
$266$	8.31483	+	18.7379i	0.509815	+	1.14889i
$267$		0			0
$268$	2.76915	−	4.79631i	0.169153	−	0.292982i
$269$	−0.272342	+	0.471711i	−0.0166050	+	0.0287607i	−0.874209	−	0.485551i	$-0.838619\pi$
$269$	−0.272342	+	0.471711i	−0.0166050	+	0.0287607i	0.857603	+	0.514311i	$0.171952\pi$
$270$		0			0
$271$	17.9370	−	10.3560i	1.08960	−	0.629079i	0.156128	−	0.987737i	$-0.450099\pi$
$271$	17.9370	−	10.3560i	1.08960	−	0.629079i	0.933469	+	0.358657i	$0.116765\pi$
$272$	3.31479	+	5.74138i	0.200989	+	0.348122i
$273$		0			0
$274$	5.73011	−	9.92484i	0.346169	−	0.599582i
$275$		−	4.51143i		−	0.272049i
$276$		0			0
$277$	−17.4909			−1.05093			−0.525464	−	0.850816i	$-0.676108\pi$
$277$	−17.4909			−1.05093			−0.525464	+	0.850816i	$0.676108\pi$
$278$	−1.70763	−	2.95770i	−0.102417	−	0.177391i
$279$		0			0
$280$	−2.41835	+	1.07313i	−0.144524	+	0.0641316i
$281$	−15.8222	+	9.13496i	−0.943874	+	0.544946i	−0.891173	−	0.453664i	$-0.850116\pi$
$281$	−15.8222	+	9.13496i	−0.943874	+	0.544946i	−0.0527014	+	0.998610i	$0.516783\pi$
$282$		0			0
$283$	7.97761	−	4.60587i	0.474219	−	0.273791i	−0.243785	−	0.969829i	$-0.578389\pi$
$283$	7.97761	−	4.60587i	0.474219	−	0.273791i	0.718004	+	0.696039i	$0.245056\pi$
$284$	−8.29634	+	4.78989i	−0.492297	+	0.284228i
$285$		0			0
$286$	8.68908	−	5.01664i	0.513796	−	0.296640i
$287$	−22.6926	−	2.41353i	−1.33950	−	0.142466i
$288$		0			0
$289$	−13.4756	−	23.3405i	−0.792685	−	1.37297i
$290$	−1.24732			−0.0732454
$291$		0			0
$292$			1.28405i			0.0751431i
$293$	−6.24576	+	10.8180i	−0.364881	+	0.631993i	−0.988757	−	0.149531i	$-0.952224\pi$
$293$	−6.24576	+	10.8180i	−0.364881	+	0.631993i	0.623876	+	0.781523i	$0.285557\pi$
$294$		0			0
$295$	1.63861	+	2.83816i	0.0954037	+	0.165244i
$296$	0.822924	−	0.475116i	0.0478315	−	0.0276155i
$297$		0			0
$298$	−8.87258	+	15.3678i	−0.513975	+	0.890231i
$299$	5.58476	−	9.67308i	0.322975	−	0.559409i
$300$		0			0
$301$	−15.1778	+	20.8361i	−0.874834	+	1.20097i
$302$	1.21408	+	0.700947i	0.0698623	+	0.0403350i
$303$		0			0
$304$			7.74823i			0.444392i
$305$	9.88563	+	5.70747i	0.566049	+	0.326809i
$306$		0			0
$307$		−	6.32444i		−	0.360955i	−0.983579	−	0.180477i	$-0.942236\pi$
$307$		−	6.32444i		−	0.360955i	0.983579	−	0.180477i	$-0.0577643\pi$
$308$	9.64781	+	7.02784i	0.549735	+	0.400448i
$309$		0			0
$310$	−4.99018			−0.283423
$311$	−11.2784	−	19.5347i	−0.639537	−	1.10771i	−0.985534	−	0.169475i	$-0.945793\pi$
$311$	−11.2784	−	19.5347i	−0.639537	−	1.10771i	0.345998	−	0.938235i	$-0.387541\pi$
$312$		0			0
$313$	9.10717	+	5.25803i	0.514768	+	0.297201i	0.734791	−	0.678293i	$-0.237280\pi$
$313$	9.10717	+	5.25803i	0.514768	+	0.297201i	−0.220024	+	0.975495i	$0.570613\pi$
$314$	−15.7507			−0.888862
$315$		0			0
$316$	3.96124			0.222837
$317$	−9.22254	−	5.32463i	−0.517989	−	0.299061i	0.218122	−	0.975921i	$-0.430007\pi$
$317$	−9.22254	−	5.32463i	−0.517989	−	0.299061i	−0.736112	+	0.676860i	$0.763340\pi$
$318$		0			0
$319$	2.81360	+	4.87330i	0.157532	+	0.272853i
$320$	−1.00000			−0.0559017
$321$		0			0
$322$	13.2133	+	1.40534i	0.736348	+	0.0783164i
$323$		−	51.3675i		−	2.85816i
$324$		0			0
$325$	1.92602	+	1.11199i	0.106836	+	0.0616819i
$326$		−	1.57811i		−	0.0874033i
$327$		0			0
$328$	−7.46978	−	4.31268i	−0.412450	−	0.238128i
$329$	−13.3236	−	1.41707i	−0.734553	−	0.0781255i
$330$		0			0
$331$	7.99412	−	13.8462i	0.439397	−	0.761057i	−0.558246	−	0.829675i	$-0.688526\pi$
$331$	7.99412	−	13.8462i	0.439397	−	0.761057i	0.997643	+	0.0686178i	$0.0218589\pi$
$332$	5.71593	−	9.90029i	0.313703	−	0.543349i
$333$		0			0
$334$	−7.98188	+	4.60834i	−0.436749	+	0.252157i
$335$	−2.76915	−	4.79631i	−0.151295	−	0.262051i
$336$		0			0
$337$	14.4075	−	24.9546i	0.784829	−	1.35936i	−0.144273	−	0.989538i	$-0.546084\pi$
$337$	14.4075	−	24.9546i	0.784829	−	1.35936i	0.929101	−	0.369825i	$-0.120582\pi$
$338$		−	8.05394i		−	0.438077i
$339$		0			0
$340$	6.62958			0.359539
$341$	11.2564	+	19.4967i	0.609568	+	1.05580i
$342$		0			0
$343$	−17.5924	−	5.78855i	−0.949901	−	0.312552i
$344$	−8.43784	+	4.87159i	−0.454938	+	0.262659i
$345$		0			0
$346$	2.19027	−	1.26455i	0.117750	−	0.0679829i
$347$	−0.234637	+	0.135468i	−0.0125960	+	0.00727228i	−0.506285	−	0.862366i	$-0.668982\pi$
$347$	−0.234637	+	0.135468i	−0.0125960	+	0.00727228i	0.493689	+	0.869639i	$0.335648\pi$
$348$		0			0
$349$	−21.0924	+	12.1777i	−1.12905	+	0.651857i	−0.943696	−	0.330814i	$-0.892677\pi$
$349$	−21.0924	+	12.1777i	−1.12905	+	0.651857i	−0.185354	+	0.982672i	$0.559343\pi$
$350$	−0.279818	+	2.63091i	−0.0149569	+	0.140628i
$351$		0			0
$352$	2.25571	+	3.90701i	0.120230	+	0.208244i
$353$	−15.7449			−0.838016			−0.419008	−	0.907982i	$-0.637622\pi$
$353$	−15.7449			−0.838016			−0.419008	+	0.907982i	$0.637622\pi$
$354$		0			0
$355$			9.57979i			0.508442i
$356$	8.89050	−	15.3988i	0.471196	−	0.816135i
$357$		0			0
$358$	5.53559	+	9.58793i	0.292565	+	0.506738i
$359$	12.5256	−	7.23168i	0.661078	−	0.381673i	−0.131610	−	0.991302i	$-0.542015\pi$
$359$	12.5256	−	7.23168i	0.661078	−	0.381673i	0.792688	+	0.609628i	$0.208681\pi$
$360$		0			0
$361$	20.5175	−	35.5374i	1.07987	−	1.87039i
$362$	8.82331	−	15.2824i	0.463743	−	0.803226i
$363$		0			0
$364$	−5.37834	+	2.38660i	−0.281901	+	0.125092i
$365$	1.11202	+	0.642023i	0.0582056	+	0.0336050i
$366$		0			0
$367$		−	32.5123i		−	1.69713i	−0.529092	−	0.848565i	$-0.677467\pi$
$367$		−	32.5123i		−	1.69713i	0.529092	−	0.848565i	$-0.322533\pi$
$368$	4.34946	+	2.51116i	0.226731	+	0.130903i
$369$		0			0
$370$		−	0.950231i		−	0.0494002i
$371$	−1.51381	+	14.2332i	−0.0785932	+	0.738951i
$372$		0			0
$373$	9.14687			0.473607			0.236803	−	0.971558i	$-0.423900\pi$
$373$	9.14687			0.473607			0.236803	+	0.971558i	$0.423900\pi$
$374$	−14.9544	−	25.9018i	−0.773275	−	1.33935i
$375$		0			0
$376$	−4.38576	−	2.53212i	−0.226178	−	0.130584i
$377$	−2.77401			−0.142869
$378$		0			0
$379$	−2.90816			−0.149382			−0.0746911	−	0.997207i	$-0.523797\pi$
$379$	−2.90816			−0.149382			−0.0746911	+	0.997207i	$0.523797\pi$
$380$	6.71016	+	3.87412i	0.344224	+	0.198738i
$381$		0			0
$382$	4.62270	+	8.00675i	0.236518	+	0.409661i
$383$	−3.17879			−0.162428			−0.0812142	−	0.996697i	$-0.525880\pi$
$383$	−3.17879			−0.162428			−0.0812142	+	0.996697i	$0.525880\pi$
$384$		0			0
$385$	10.9102	−	4.84133i	0.556035	−	0.246737i
$386$			17.9771i			0.915010i
$387$		0			0
$388$	−7.24779	−	4.18451i	−0.367951	−	0.212436i
$389$			12.6645i			0.642118i	0.947059	+	0.321059i	$0.104039\pi$
$389$			12.6645i			0.642118i	−0.947059	+	0.321059i	$0.895961\pi$
$390$		0			0
$391$	−28.8351	−	16.6479i	−1.45825	−	0.841922i
$392$	−5.19038	−	4.69680i	−0.262154	−	0.237224i
$393$		0			0
$394$	5.58896	−	9.68036i	0.281568	−	0.487690i
$395$	1.98062	−	3.43054i	0.0996559	−	0.172609i
$396$		0			0
$397$	−22.7136	+	13.1137i	−1.13996	+	0.658158i	−0.946421	−	0.322935i	$-0.895331\pi$
$397$	−22.7136	+	13.1137i	−1.13996	+	0.658158i	−0.193541	+	0.981092i	$0.561997\pi$
$398$	1.51384	+	2.62204i	0.0758817	+	0.131431i
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$			21.1817i			1.05776i	0.848696	+	0.528881i	$0.177388\pi$
$401$			21.1817i			1.05776i	−0.848696	+	0.528881i	$0.822612\pi$
$402$		0			0
$403$	−11.0980			−0.552832
$404$	−5.81680	−	10.0750i	−0.289396	−	0.501249i
$405$		0			0
$406$	−1.33854	−	3.01646i	−0.0664304	−	0.149704i
$407$	−3.71256	+	2.14345i	−0.184025	+	0.106247i
$408$		0			0
$409$	34.4207	−	19.8728i	1.70199	−	0.982646i	0.758250	−	0.651964i	$-0.226055\pi$
$409$	34.4207	−	19.8728i	1.70199	−	0.982646i	0.943742	−	0.330682i	$-0.107279\pi$
$410$	−7.46978	+	4.31268i	−0.368906	+	0.212988i
$411$		0			0
$412$	11.5855	−	6.68888i	0.570776	−	0.329538i
$413$	−5.10522	+	7.00844i	−0.251211	+	0.344863i
$414$		0			0
$415$	−5.71593	−	9.90029i	−0.280584	−	0.485986i
$416$	−2.22397			−0.109039
$417$		0			0
$418$		−	34.9556i		−	1.70973i
$419$	−3.05865	+	5.29774i	−0.149425	+	0.258811i	−0.931015	−	0.364981i	$-0.881076\pi$
$419$	−3.05865	+	5.29774i	−0.149425	+	0.258811i	0.781590	+	0.623792i	$0.214409\pi$
$420$		0			0
$421$	−0.503271	−	0.871691i	−0.0245279	−	0.0424836i	0.853501	−	0.521091i	$-0.174475\pi$
$421$	−0.503271	−	0.871691i	−0.0245279	−	0.0424836i	−0.878029	+	0.478608i	$0.841142\pi$
$422$	15.5831	−	8.99690i	0.758573	−	0.437962i
$423$		0			0
$424$	−2.70499	+	4.68518i	−0.131366	+	0.227533i
$425$	3.31479	−	5.74138i	0.160791	−	0.278498i
$426$		0			0
$427$	−3.19411	+	30.0317i	−0.154574	+	1.45334i
$428$	9.50931	+	5.49020i	0.459650	+	0.265379i
$429$		0			0
$430$			9.74318i			0.469858i
$431$	17.6560	+	10.1937i	0.850461	+	0.491014i	0.860806	−	0.508933i	$-0.169960\pi$
$431$	17.6560	+	10.1937i	0.850461	+	0.491014i	−0.0103455	+	0.999946i	$0.503293\pi$
$432$		0			0
$433$			9.53648i			0.458294i	0.973392	+	0.229147i	$0.0735937\pi$
$433$			9.53648i			0.458294i	−0.973392	+	0.229147i	$0.926406\pi$
$434$	−5.35509	−	12.0680i	−0.257053	−	0.579281i
$435$		0			0
$436$	−15.4684			−0.740803
$437$	−19.4571	−	33.7006i	−0.930757	−	1.61212i
$438$		0			0
$439$	−18.8382	−	10.8763i	−0.899100	−	0.519096i	−0.0221920	−	0.999754i	$-0.507065\pi$
$439$	−18.8382	−	10.8763i	−0.899100	−	0.519096i	−0.876908	+	0.480658i	$0.840398\pi$
$440$	4.51143			0.215074
$441$		0			0
$442$	14.7440			0.701300
$443$	−10.2965	−	5.94470i	−0.489203	−	0.282441i	0.235041	−	0.971985i	$-0.424478\pi$
$443$	−10.2965	−	5.94470i	−0.489203	−	0.282441i	−0.724244	+	0.689544i	$0.757811\pi$
$444$		0			0
$445$	−8.89050	−	15.3988i	−0.421450	−	0.729973i
$446$	−12.3278			−0.583738
$447$		0			0
$448$	−1.07313	−	2.41835i	−0.0507005	−	0.114256i
$449$			17.0757i			0.805853i	0.915232	+	0.402926i	$0.132007\pi$
$449$			17.0757i			0.805853i	−0.915232	+	0.402926i	$0.867993\pi$
$450$		0			0
$451$	33.6994	+	19.4563i	1.58684	+	0.916163i
$452$			3.43025i			0.161345i
$453$		0			0
$454$	−10.5640	−	6.09913i	−0.495793	−	0.286246i
$455$	−0.622308	+	5.85108i	−0.0291743	+	0.274303i
$456$		0			0
$457$	1.32533	−	2.29554i	0.0619964	−	0.107381i	−0.833361	−	0.552729i	$-0.813587\pi$
$457$	1.32533	−	2.29554i	0.0619964	−	0.107381i	0.895358	+	0.445348i	$0.146920\pi$
$458$	−6.11591	+	10.5931i	−0.285778	+	0.494982i
$459$		0			0
$460$	4.34946	−	2.51116i	0.202795	−	0.117084i
$461$	20.7077	+	35.8668i	0.964453	+	1.67048i	0.711077	+	0.703114i	$0.248208\pi$
$461$	20.7077	+	35.8668i	0.964453	+	1.67048i	0.253376	+	0.967368i	$0.418459\pi$
$462$		0			0
$463$	1.81970	−	3.15182i	0.0845687	−	0.146477i	−0.820639	−	0.571447i	$-0.806382\pi$
$463$	1.81970	−	3.15182i	0.0845687	−	0.146477i	0.905207	+	0.424970i	$0.139715\pi$
$464$		−	1.24732i		−	0.0579055i
$465$		0			0
$466$	0.698218			0.0323443
$467$	−16.1293	−	27.9368i	−0.746375	−	1.29276i	−0.949549	−	0.313617i	$-0.898459\pi$
$467$	−16.1293	−	27.9368i	−0.746375	−	1.29276i	0.203174	−	0.979143i	$-0.434874\pi$
$468$		0			0
$469$	8.62750	−	11.8438i	0.398381	−	0.546897i
$470$	−4.38576	+	2.53212i	−0.202300	+	0.116798i
$471$		0			0
$472$	−2.83816	+	1.63861i	−0.130637	+	0.0754233i
$473$	38.0667	−	21.9778i	1.75031	−	1.01054i
$474$		0			0
$475$	6.71016	−	3.87412i	0.307883	−	0.177757i
$476$	7.11437	+	16.0326i	0.326087	+	0.734854i
$477$		0			0
$478$	2.75332	+	4.76888i	0.125934	+	0.218124i
$479$	−5.07687			−0.231968			−0.115984	−	0.993251i	$-0.537002\pi$
$479$	−5.07687			−0.231968			−0.115984	+	0.993251i	$0.537002\pi$
$480$		0			0
$481$		−	2.11329i		−	0.0963576i
$482$	−8.83660	+	15.3054i	−0.402496	+	0.697144i
$483$		0			0
$484$	−4.67648	−	8.09991i	−0.212567	−	0.368178i
$485$	−7.24779	+	4.18451i	−0.329105	+	0.190009i
$486$		0			0
$487$	8.78880	−	15.2226i	0.398259	−	0.689804i	−0.595253	−	0.803539i	$-0.702948\pi$
$487$	8.78880	−	15.2226i	0.398259	−	0.689804i	0.993511	+	0.113735i	$0.0362814\pi$
$488$	−5.70747	+	9.88563i	−0.258365	+	0.447501i
$489$		0			0
$490$	−6.66274	+	2.14660i	−0.300992	+	0.0969737i
$491$	27.2873	+	15.7543i	1.23146	+	0.710984i	0.967334	−	0.253504i	$-0.0815833\pi$
$491$	27.2873	+	15.7543i	1.23146	+	0.710984i	0.264126	+	0.964488i	$0.414917\pi$
$492$		0			0
$493$			8.26922i			0.372427i
$494$	14.9232	+	8.61593i	0.671428	+	0.387649i
$495$		0			0
$496$		−	4.99018i		−	0.224065i
$497$	−23.1673	+	10.2803i	−1.03919	+	0.461136i
$498$		0			0
$499$	−34.1844			−1.53030			−0.765151	−	0.643851i	$-0.777336\pi$
$499$	−34.1844			−1.53030			−0.765151	+	0.643851i	$0.777336\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$		0			0
$502$	−24.1578	−	13.9475i	−1.07822	−	0.622508i
$503$	1.51617			0.0676028			0.0338014	−	0.999429i	$-0.489239\pi$
$503$	1.51617			0.0676028			0.0338014	+	0.999429i	$0.489239\pi$
$504$		0			0
$505$	−11.6336			−0.517688
$506$	−19.6223	−	11.3289i	−0.872316	−	0.503632i
$507$		0			0
$508$	−2.21018	−	3.82815i	−0.0980610	−	0.169847i
$509$	−8.51321			−0.377341			−0.188671	−	0.982040i	$-0.560418\pi$
$509$	−8.51321			−0.377341			−0.188671	+	0.982040i	$0.560418\pi$
$510$		0			0
$511$	−0.359299	+	3.37821i	−0.0158945	+	0.149443i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−12.2549	−	7.07539i	−0.540542	−	0.312082i
$515$		−	13.3778i		−	0.589495i
$516$		0			0
$517$	19.7860	+	11.4235i	0.870189	+	0.502404i
$518$	2.29799	−	1.01972i	0.100968	−	0.0448038i
$519$		0			0
$520$	−1.11199	+	1.92602i	−0.0487638	+	0.0844614i
$521$	−2.86246	+	4.95792i	−0.125407	+	0.217210i	−0.921892	−	0.387447i	$-0.873357\pi$
$521$	−2.86246	+	4.95792i	−0.125407	+	0.217210i	0.796485	+	0.604658i	$0.206690\pi$
$522$		0			0
$523$	25.1415	−	14.5154i	1.09936	−	0.634716i	0.163308	−	0.986575i	$-0.447784\pi$
$523$	25.1415	−	14.5154i	1.09936	−	0.634716i	0.936053	+	0.351859i	$0.114450\pi$
$524$	4.17218	+	7.22644i	0.182263	+	0.315688i
$525$		0			0
$526$	−15.3940	+	26.6631i	−0.671208	+	1.16257i
$527$			33.0827i			1.44111i
$528$		0			0
$529$	−2.22373			−0.0966840
$530$	2.70499	+	4.68518i	0.117497	+	0.203511i
$531$		0			0
$532$	−2.16810	+	20.3849i	−0.0939989	+	0.883798i
$533$	−16.6126	+	9.59128i	−0.719571	+	0.415445i
$534$		0			0
$535$	9.50931	−	5.49020i	0.411123	−	0.237362i
$536$	4.79631	−	2.76915i	0.207169	−	0.119609i
$537$		0			0
$538$	−0.471711	+	0.272342i	−0.0203369	+	0.0117415i
$539$	23.4160	+	21.1893i	1.00860	+	0.912686i
$540$		0			0
$541$	16.2086	+	28.0741i	0.696863	+	1.20700i	0.969549	+	0.244899i	$0.0787547\pi$
$541$	16.2086	+	28.0741i	0.696863	+	1.20700i	−0.272686	+	0.962103i	$0.587912\pi$
$542$	20.7119			0.889653
$543$		0			0
$544$			6.62958i			0.284241i
$545$	−7.73421	+	13.3960i	−0.331297	+	0.573823i
$546$		0			0
$547$	−14.7077	−	25.4744i	−0.628855	−	1.08921i	−0.987782	−	0.155843i	$-0.950191\pi$
$547$	−14.7077	−	25.4744i	−0.628855	−	1.08921i	0.358927	−	0.933366i	$-0.383143\pi$
$548$	9.92484	−	5.73011i	0.423968	−	0.244778i
$549$		0			0
$550$	2.25571	−	3.90701i	0.0961839	−	0.166595i
$551$	−4.83227	+	8.36975i	−0.205862	+	0.356563i
$552$		0			0
$553$	10.4217	+	1.10843i	0.443175	+	0.0471352i
$554$	−15.1476	−	8.74547i	−0.643560	−	0.371559i
$555$		0			0
$556$		−	3.41526i		−	0.144839i
$557$	−0.913577	−	0.527454i	−0.0387095	−	0.0223489i	0.480520	−	0.876984i	$-0.340448\pi$
$557$	−0.913577	−	0.527454i	−0.0387095	−	0.0223489i	−0.519230	+	0.854635i	$0.673781\pi$
$558$		0			0
$559$			21.6686i			0.916483i
$560$	−2.63091	−	0.279818i	−0.111176	−	0.0118245i
$561$		0			0
$562$	−18.2699			−0.770670
$563$	7.23900	+	12.5383i	0.305088	+	0.528427i	0.977281	−	0.211949i	$-0.0679809\pi$
$563$	7.23900	+	12.5383i	0.305088	+	0.528427i	−0.672193	+	0.740376i	$0.734648\pi$
$564$		0			0
$565$	2.97068	+	1.71512i	0.124978	+	0.0721558i
$566$	9.21175			0.387199
$567$		0			0
$568$	−9.57979			−0.401959
$569$	9.68190	+	5.58985i	0.405886	+	0.234339i	0.689021	−	0.724742i	$-0.258041\pi$
$569$	9.68190	+	5.58985i	0.405886	+	0.234339i	−0.283134	+	0.959080i	$0.591374\pi$
$570$		0			0
$571$	21.8476	+	37.8411i	0.914292	+	1.58360i	0.807934	+	0.589273i	$0.200586\pi$
$571$	21.8476	+	37.8411i	0.914292	+	1.58360i	0.106358	+	0.994328i	$0.466081\pi$
$572$	10.0333			0.419513
$573$		0			0
$574$	−18.4456	−	13.4365i	−0.769903	−	0.560827i
$575$		−	5.02232i		−	0.209445i
$576$		0			0
$577$	−16.6011	−	9.58466i	−0.691114	−	0.399015i	0.112915	−	0.993605i	$-0.463981\pi$
$577$	−16.6011	−	9.58466i	−0.691114	−	0.399015i	−0.804029	+	0.594590i	$0.797314\pi$
$578$		−	26.9513i		−	1.12103i
$579$		0			0
$580$	−1.08021	−	0.623662i	−0.0448534	−	0.0258961i
$581$	17.8084	−	24.4474i	0.738817	−	1.01425i
$582$		0			0
$583$	12.2034	−	21.1369i	0.505412	−	0.875399i
$584$	−0.642023	+	1.11202i	−0.0265671	+	0.0460155i
$585$		0			0
$586$	−10.8180	+	6.24576i	−0.446886	+	0.258010i
$587$	−0.776536	−	1.34500i	−0.0320511	−	0.0555141i	0.849555	−	0.527500i	$-0.176871\pi$
$587$	−0.776536	−	1.34500i	−0.0320511	−	0.0555141i	−0.881606	+	0.471986i	$0.843537\pi$
$588$		0			0
$589$	−19.3325	+	33.4849i	−0.796582	+	1.37972i
$590$			3.27723i			0.134921i
$591$		0			0
$592$	0.950231			0.0390543
$593$	5.43117	+	9.40706i	0.223031	+	0.386302i	0.955727	−	0.294255i	$-0.0950714\pi$
$593$	5.43117	+	9.40706i	0.223031	+	0.386302i	−0.732696	+	0.680556i	$0.761738\pi$
$594$		0			0
$595$	17.4418	+	1.85508i	0.715046	+	0.0760507i
$596$	−15.3678	+	8.87258i	−0.629488	+	0.363435i
$597$		0			0
$598$	9.67308	−	5.58476i	0.395562	−	0.228378i
$599$	7.28369	−	4.20524i	0.297603	−	0.171821i	−0.343762	−	0.939057i	$-0.611701\pi$
$599$	7.28369	−	4.20524i	0.297603	−	0.171821i	0.641366	+	0.767235i	$0.278368\pi$
$600$		0			0
$601$	−11.4553	+	6.61375i	−0.467273	+	0.269780i	−0.715098	−	0.699025i	$-0.753618\pi$
$601$	−11.4553	+	6.61375i	−0.467273	+	0.269780i	0.247824	+	0.968805i	$0.420284\pi$
$602$	−23.5624	+	10.4557i	−0.960331	+	0.426141i
$603$		0			0
$604$	0.700947	+	1.21408i	0.0285211	+	0.0494001i
$605$	−9.35297			−0.380252
$606$		0			0
$607$		−	12.6296i		−	0.512620i	−0.966595	−	0.256310i	$-0.917493\pi$
$607$		−	12.6296i		−	0.512620i	0.966595	−	0.256310i	$-0.0825067\pi$
$608$	−3.87412	+	6.71016i	−0.157116	+	0.272133i
$609$		0			0
$610$	5.70747	+	9.88563i	0.231089	+	0.400257i
$611$	−9.75381	+	5.63137i	−0.394597	+	0.227821i
$612$		0			0
$613$	−8.47611	+	14.6811i	−0.342347	+	0.592962i	−0.984868	−	0.173306i	$-0.944555\pi$
$613$	−8.47611	+	14.6811i	−0.342347	+	0.592962i	0.642521	+	0.766268i	$0.277889\pi$
$614$	3.16222	−	5.47713i	0.127617	−	0.221039i
$615$		0			0
$616$	4.84133	+	10.9102i	0.195063	+	0.439584i
$617$	−26.1121	−	15.0759i	−1.05124	−	0.606931i	−0.128240	−	0.991743i	$-0.540933\pi$
$617$	−26.1121	−	15.0759i	−1.05124	−	0.606931i	−0.922995	+	0.384812i	$0.874266\pi$
$618$		0			0
$619$		−	30.5258i		−	1.22694i	−0.789720	−	0.613468i	$-0.789774\pi$
$619$		−	30.5258i		−	1.22694i	0.789720	−	0.613468i	$-0.210226\pi$
$620$	−4.32162	−	2.49509i	−0.173560	−	0.100205i
$621$		0			0
$622$		−	22.5567i		−	0.904442i
$623$	27.6990	−	38.0252i	1.10974	−	1.52345i
$624$		0			0
$625$	1.00000			0.0400000
$626$	5.25803	+	9.10717i	0.210153	+	0.363996i
$627$		0			0
$628$	−13.6405	−	7.87534i	−0.544314	−	0.314260i
$629$	−6.29963			−0.251183
$630$		0			0
$631$	−23.7873			−0.946959			−0.473480	−	0.880805i	$-0.657002\pi$
$631$	−23.7873			−0.946959			−0.473480	+	0.880805i	$0.657002\pi$
$632$	3.43054	+	1.98062i	0.136459	+	0.0787849i
$633$		0			0
$634$	−5.32463	−	9.22254i	−0.211468	−	0.366274i
$635$	−4.42037			−0.175417
$636$		0			0
$637$	−14.8178	+	4.77399i	−0.587101	+	0.189152i
$638$			5.62721i			0.222783i
$639$		0			0
$640$	−0.866025	−	0.500000i	−0.0342327	−	0.0197642i
$641$			5.84348i			0.230804i	0.993319	+	0.115402i	$0.0368156\pi$
$641$			5.84348i			0.230804i	−0.993319	+	0.115402i	$0.963184\pi$
$642$		0			0
$643$	−0.948093	−	0.547382i	−0.0373891	−	0.0215866i	0.481189	−	0.876617i	$-0.340205\pi$
$643$	−0.948093	−	0.547382i	−0.0373891	−	0.0215866i	−0.518578	+	0.855030i	$0.673538\pi$
$644$	10.7404	+	7.82371i	0.423230	+	0.308297i
$645$		0			0
$646$	25.6837	−	44.4855i	1.01051	−	1.75026i
$647$	−1.97694	+	3.42416i	−0.0777216	+	0.134618i	−0.902267	−	0.431179i	$-0.858098\pi$
$647$	−1.97694	+	3.42416i	−0.0777216	+	0.134618i	0.824545	+	0.565796i	$0.191431\pi$
$648$		0			0
$649$	12.8042	−	7.39248i	0.502607	−	0.290180i
$650$	1.11199	+	1.92602i	0.0436157	+	0.0755446i
$651$		0			0
$652$	0.789054	−	1.36668i	0.0309017	−	0.0535234i
$653$		−	1.45438i		−	0.0569143i	−0.999595	−	0.0284572i	$-0.990941\pi$
$653$		−	1.45438i		−	0.0569143i	0.999595	−	0.0284572i	$-0.00905942\pi$
$654$		0			0
$655$	8.34437			0.326041
$656$	−4.31268	−	7.46978i	−0.168382	−	0.291646i
$657$		0			0
$658$	−10.8300	−	7.88900i	−0.422198	−	0.307545i
$659$	−4.32410	+	2.49652i	−0.168443	+	0.0972507i	−0.581852	−	0.813295i	$-0.697672\pi$
$659$	−4.32410	+	2.49652i	−0.168443	+	0.0972507i	0.413408	+	0.910546i	$0.364338\pi$
$660$		0			0
$661$	33.4204	−	19.2953i	1.29990	−	0.750500i	0.319517	−	0.947581i	$-0.396479\pi$
$661$	33.4204	−	19.2953i	1.29990	−	0.750500i	0.980387	+	0.197081i	$0.0631461\pi$
$662$	13.8462	−	7.99412i	0.538149	−	0.310700i
$663$		0			0
$664$	9.90029	−	5.71593i	0.384206	−	0.221821i
$665$	16.5698	+	12.0701i	0.642550	+	0.468058i
$666$		0			0
$667$	3.13223	+	5.42518i	0.121280	+	0.210064i
$668$	−9.21668			−0.356604
$669$		0			0
$670$		−	5.53831i		−	0.213963i
$671$	25.7488	−	44.5983i	0.994023	−	1.72170i
$672$		0			0
$673$	5.87005	+	10.1672i	0.226274	+	0.391918i	0.956701	−	0.291073i	$-0.0940122\pi$
$673$	5.87005	+	10.1672i	0.226274	+	0.391918i	−0.730427	+	0.682991i	$0.760679\pi$
$674$	24.9546	−	14.4075i	0.961215	−	0.554958i
$675$		0			0
$676$	4.02697	−	6.97492i	0.154884	−	0.268266i
$677$	14.5939	−	25.2774i	0.560889	−	0.971489i	−0.436530	−	0.899690i	$-0.643793\pi$
$677$	14.5939	−	25.2774i	0.560889	−	0.971489i	0.997419	−	0.0717989i	$-0.0228740\pi$
$678$		0			0
$679$	−17.8974	−	13.0372i	−0.686839	−	0.500320i
$680$	5.74138	+	3.31479i	0.220172	+	0.127116i
$681$		0			0
$682$			22.5128i			0.862060i
$683$	5.36086	+	3.09509i	0.205128	+	0.118431i	0.599045	−	0.800715i	$-0.295547\pi$
$683$	5.36086	+	3.09509i	0.205128	+	0.118431i	−0.393917	+	0.919146i	$0.628880\pi$
$684$		0			0
$685$		−	11.4602i		−	0.437873i
$686$	−12.3412	−	13.8092i	−0.471189	−	0.527239i
$687$		0			0
$688$	−9.74318			−0.371455
$689$	6.01583	+	10.4197i	0.229185	+	0.396960i
$690$		0			0
$691$	−25.0338	−	14.4533i	−0.952332	−	0.549829i	−0.0585274	−	0.998286i	$-0.518641\pi$
$691$	−25.0338	−	14.4533i	−0.952332	−	0.549829i	−0.893805	+	0.448457i	$0.851974\pi$
$692$	2.52911			0.0961423
$693$		0			0
$694$	−0.270935			−0.0102846
$695$	−2.95770	−	1.70763i	−0.112192	−	0.0647741i
$696$		0			0
$697$	28.5912	+	49.5215i	1.08297	+	1.87576i
$698$	−24.3554			−0.921866
$699$		0			0
$700$	−1.55779	+	2.13853i	−0.0588788	+	0.0808288i
$701$		−	15.3891i		−	0.581238i	−0.956839	−	0.290619i	$-0.906139\pi$
$701$		−	15.3891i		−	0.581238i	0.956839	−	0.290619i	$-0.0938612\pi$
$702$		0			0
$703$	−6.37621	−	3.68130i	−0.240483	−	0.138843i
$704$			4.51143i			0.170031i
$705$		0			0
$706$	−13.6355	−	7.87245i	−0.513178	−	0.296283i
$707$	−12.4843	−	28.1341i	−0.469521	−	1.05809i
$708$		0			0
$709$	−23.2331	+	40.2409i	−0.872538	+	1.51128i	−0.0131753	+	0.999913i	$0.504194\pi$
$709$	−23.2331	+	40.2409i	−0.872538	+	1.51128i	−0.859363	+	0.511367i	$0.829139\pi$
$710$	−4.78989	+	8.29634i	−0.179762	+	0.311356i
$711$		0			0
$712$	15.3988	−	8.89050i	0.577095	−	0.333186i
$713$	12.5311	+	21.7046i	0.469295	+	0.812842i
$714$		0			0
$715$	5.01664	−	8.68908i	0.187612	−	0.324953i
$716$			11.0712i			0.413750i
$717$		0			0
$718$	14.4634			0.539768
$719$	−2.95350	−	5.11561i	−0.110147	−	0.190780i	0.805682	−	0.592348i	$-0.201799\pi$
$719$	−2.95350	−	5.11561i	−0.110147	−	0.190780i	−0.915829	+	0.401568i	$0.868465\pi$
$720$		0			0
$721$	32.3521	−	14.3560i	1.20485	−	0.534647i
$722$	35.5374	−	20.5175i	1.32257	−	0.763584i
$723$		0			0
$724$	15.2824	−	8.82331i	0.567966	−	0.327916i
$725$	−1.08021	+	0.623662i	−0.0401181	+	0.0231622i
$726$		0			0
$727$	−4.73351	+	2.73289i	−0.175556	+	0.101357i	−0.585203	−	0.810887i	$-0.698985\pi$
$727$	−4.73351	+	2.73289i	−0.175556	+	0.101357i	0.409647	+	0.912244i	$0.365652\pi$
$728$	−5.85108	−	0.622308i	−0.216855	−	0.0230643i
$729$		0			0
$730$	0.642023	+	1.11202i	0.0237623	+	0.0411575i
$731$	64.5932			2.38906
$732$		0			0
$733$		−	24.0912i		−	0.889830i	−0.895573	−	0.444915i	$-0.853234\pi$
$733$		−	24.0912i		−	0.889830i	0.895573	−	0.444915i	$-0.146766\pi$
$734$	16.2562	−	28.1565i	0.600026	−	1.03928i
$735$		0			0
$736$	2.51116	+	4.34946i	0.0925626	+	0.160323i
$737$	−21.6382	+	12.4928i	−0.797054	+	0.460179i
$738$		0			0
$739$	−17.2995	+	29.9636i	−0.636373	+	1.10223i	0.349850	+	0.936806i	$0.386233\pi$
$739$	−17.2995	+	29.9636i	−0.636373	+	1.10223i	−0.986223	+	0.165424i	$0.947101\pi$
$740$	0.475116	−	0.822924i	0.0174656	−	0.0302513i
$741$		0			0
$742$	−8.42760	+	11.5694i	−0.309387	+	0.424726i
$743$	7.07661	+	4.08568i	0.259616	+	0.149889i	0.624159	−	0.781297i	$-0.285442\pi$
$743$	7.07661	+	4.08568i	0.259616	+	0.149889i	−0.364544	+	0.931186i	$0.618775\pi$
$744$		0			0
$745$			17.7452i			0.650133i
$746$	7.92142	+	4.57343i	0.290024	+	0.167445i
$747$		0			0
$748$		−	29.9088i		−	1.09358i
$749$	23.4819	+	17.1051i	0.858010	+	0.625008i
$750$		0			0
$751$	41.8027			1.52540			0.762702	−	0.646750i	$-0.223872\pi$
$751$	41.8027			1.52540			0.762702	+	0.646750i	$0.223872\pi$
$752$	−2.53212	−	4.38576i	−0.0923369	−	0.159932i
$753$		0			0
$754$	−2.40237	−	1.38701i	−0.0874890	−	0.0505118i
$755$	1.40189			0.0510202
$756$		0			0
$757$	1.75387			0.0637455			0.0318728	−	0.999492i	$-0.489853\pi$
$757$	1.75387			0.0637455			0.0318728	+	0.999492i	$0.489853\pi$
$758$	−2.51854	−	1.45408i	−0.0914776	−	0.0528146i
$759$		0			0
$760$	3.87412	+	6.71016i	0.140529	+	0.243403i
$761$	−40.0986			−1.45357			−0.726786	−	0.686864i	$-0.758987\pi$
$761$	−40.0986			−1.45357			−0.726786	+	0.686864i	$0.758987\pi$
$762$		0			0
$763$	−40.6961	−	4.32835i	−1.47330	−	0.156697i
$764$			9.24540i			0.334487i
$765$		0			0
$766$	−2.75291	−	1.58939i	−0.0994667	−	0.0574271i
$767$			7.28846i			0.263171i
$768$		0			0
$769$	5.48232	+	3.16522i	0.197698	+	0.114141i	0.595581	−	0.803295i	$-0.296922\pi$
$769$	5.48232	+	3.16522i	0.197698	+	0.114141i	−0.397883	+	0.917436i	$0.630255\pi$
$770$	11.8692	+	1.26238i	0.427735	+	0.0454930i
$771$		0			0
$772$	−8.98854	+	15.5686i	−0.323505	+	0.560327i
$773$	13.5247	−	23.4255i	0.486450	−	0.842556i	−0.513429	−	0.858132i	$-0.671625\pi$
$773$	13.5247	−	23.4255i	0.486450	−	0.842556i	0.999879	+	0.0155764i	$0.00495831\pi$
$774$		0			0
$775$	−4.32162	+	2.49509i	−0.155237	+	0.0896262i
$776$	−4.18451	−	7.24779i	−0.150215	−	0.260180i
$777$		0			0
$778$	−6.33227	+	10.9678i	−0.227023	+	0.393215i
$779$			66.8313i			2.39448i
$780$		0			0
$781$	43.2185			1.54648
$782$	−16.6479	−	28.8351i	−0.595329	−	1.03114i
$783$		0			0
$784$	−2.14660	−	6.66274i	−0.0766645	−	0.237955i
$785$	−13.6405	+	7.87534i	−0.486850	+	0.281083i
$786$		0			0
$787$	2.13740	−	1.23403i	0.0761901	−	0.0439884i	−0.461421	−	0.887181i	$-0.652660\pi$
$787$	2.13740	−	1.23403i	0.0761901	−	0.0439884i	0.537611	+	0.843193i	$0.319327\pi$
$788$	9.68036	−	5.58896i	0.344849	−	0.199098i
$789$		0			0
$790$	3.43054	−	1.98062i	0.122053	−	0.0704674i
$791$	−0.959847	+	9.02469i	−0.0341282	+	0.320881i
$792$		0			0
$793$	12.6933	+	21.9854i	0.450751	+	0.780723i
$794$	−26.2274			−0.930775
$795$		0			0
$796$			3.02767i			0.107313i
$797$	−25.8208	+	44.7230i	−0.914621	+	1.58417i	−0.107165	+	0.994241i	$0.534177\pi$
$797$	−25.8208	+	44.7230i	−0.914621	+	1.58417i	−0.807456	+	0.589928i	$0.799156\pi$
$798$		0			0
$799$	16.7869	+	29.0757i	0.593877	+	1.02863i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$		0			0
$802$	−10.5908	+	18.3439i	−0.373975	+	0.647744i
$803$	2.89644	−	5.01678i	0.102213	−	0.177038i
$804$		0			0
$805$	12.1457	−	5.38959i	0.428080	−	0.189958i
$806$	−9.61116	−	5.54901i	−0.338539	−	0.195455i
$807$		0			0
$808$		−	11.6336i		−	0.409268i
$809$	−4.28122	−	2.47177i	−0.150520	−	0.0869026i	0.422849	−	0.906200i	$-0.361030\pi$
$809$	−4.28122	−	2.47177i	−0.150520	−	0.0869026i	−0.573368	+	0.819298i	$0.694364\pi$
$810$		0			0
$811$			18.7591i			0.658720i	0.944204	+	0.329360i	$0.106833\pi$
$811$			18.7591i			0.658720i	−0.944204	+	0.329360i	$0.893167\pi$
$812$	0.349024	−	3.28160i	0.0122483	−	0.115162i
$813$		0			0
$814$	−4.28690			−0.150256
$815$	−0.789054	−	1.36668i	−0.0276393	−	0.0478728i
$816$		0			0
$817$	65.3784	+	37.7462i	2.28730	+	1.32057i
$818$	39.7456			1.38967
$819$		0			0
$820$	−8.62536			−0.301211
$821$	−44.8460	−	25.8919i	−1.56514	−	0.903632i	−0.996723	−	0.0808894i	$-0.974224\pi$
$821$	−44.8460	−	25.8919i	−1.56514	−	0.903632i	−0.568414	−	0.822743i	$-0.692443\pi$
$822$		0			0
$823$	−15.8652	−	27.4793i	−0.553026	−	0.957869i	−0.998054	−	0.0623527i	$-0.980140\pi$
$823$	−15.8652	−	27.4793i	−0.553026	−	0.957869i	0.445028	−	0.895517i	$-0.353194\pi$
$824$	13.3778			0.466037
$825$		0			0
$826$	−7.92547	+	3.51688i	−0.275762	+	0.122368i
$827$		−	44.9946i		−	1.56461i	−0.622893	−	0.782307i	$-0.714043\pi$
$827$		−	44.9946i		−	1.56461i	0.622893	−	0.782307i	$-0.285957\pi$
$828$		0			0
$829$	31.0372	+	17.9194i	1.07797	+	0.622365i	0.930347	−	0.366679i	$-0.119505\pi$
$829$	31.0372	+	17.9194i	1.07797	+	0.622365i	0.147620	+	0.989044i	$0.452839\pi$
$830$		−	11.4319i		−	0.396806i
$831$		0			0
$832$	−1.92602	−	1.11199i	−0.0667726	−	0.0385512i
$833$	14.2311	+	44.1711i	0.493078	+	1.53044i
$834$		0			0
$835$	−4.60834	+	7.98188i	−0.159478	+	0.276224i
$836$	17.4778	−	30.2724i	0.604482	−	1.04699i
$837$		0			0
$838$	−5.29774	+	3.05865i	−0.183007	+	0.105659i
$839$	−11.8062	−	20.4490i	−0.407596	−	0.705978i	0.587024	−	0.809570i	$-0.300300\pi$
$839$	−11.8062	−	20.4490i	−0.407596	−	0.705978i	−0.994620	+	0.103592i	$0.966966\pi$
$840$		0			0
$841$	−13.7221	+	23.7674i	−0.473176	+	0.819564i
$842$		−	1.00654i		−	0.0346877i
$843$		0			0
$844$	17.9938			0.619372
$845$	−4.02697	−	6.97492i	−0.138532	−	0.239945i
$846$		0			0
$847$	−10.0369	−	22.6187i	−0.344873	−	0.777188i
$848$	−4.68518	+	2.70499i	−0.160890	+	0.0928898i
$849$		0			0
$850$	5.74138	−	3.31479i	0.196928	−	0.113696i
$851$	−4.13299	+	2.38618i	−0.141677	+	0.0817973i
$852$		0			0
$853$	−49.7153	+	28.7031i	−1.70222	+	0.982777i	−0.758711	+	0.651427i	$0.774171\pi$
$853$	−49.7153	+	28.7031i	−1.70222	+	0.982777i	−0.943508	+	0.331349i	$0.892496\pi$
$854$	−17.7820	+	24.4112i	−0.608489	+	0.835333i
$855$		0			0
$856$	5.49020	+	9.50931i	0.187651	+	0.325022i
$857$	−29.8739			−1.02047			−0.510237	−	0.860034i	$-0.670442\pi$
$857$	−29.8739			−1.02047			−0.510237	+	0.860034i	$0.670442\pi$
$858$		0			0
$859$			3.85047i			0.131376i	0.997840	+	0.0656881i	$0.0209242\pi$
$859$			3.85047i			0.131376i	−0.997840	+	0.0656881i	$0.979076\pi$
$860$	−4.87159	+	8.43784i	−0.166120	+	0.287728i
$861$		0			0
$862$	10.1937	+	17.6560i	0.347199	+	0.601367i
$863$	−38.3566	+	22.1452i	−1.30567	+	0.753831i	−0.981371	−	0.192122i	$-0.938463\pi$
$863$	−38.3566	+	22.1452i	−1.30567	+	0.753831i	−0.324303	+	0.945953i	$0.605130\pi$
$864$		0			0
$865$	1.26455	−	2.19027i	0.0429961	−	0.0744715i
$866$	−4.76824	+	8.25884i	−0.162031	+	0.280647i
$867$		0			0
$868$	1.39634	−	13.1287i	0.0473950	−	0.445618i
$869$	−15.4766	−	8.93543i	−0.525008	−	0.303114i
$870$		0			0
$871$		−	12.3170i		−	0.417347i
$872$	−13.3960	−	7.73421i	−0.453647	−	0.261913i
$873$		0			0
$874$		−	38.9141i		−	1.31629i
$875$	1.07313	+	2.41835i	0.0362783	+	0.0817550i
$876$		0			0
$877$	−28.2949			−0.955451			−0.477725	−	0.878509i	$-0.658539\pi$
$877$	−28.2949			−0.955451			−0.477725	+	0.878509i	$0.658539\pi$
$878$	−10.8763	−	18.8382i	−0.367056	−	0.635760i
$879$		0			0
$880$	3.90701	+	2.25571i	0.131705	+	0.0760401i
$881$	−46.4649			−1.56544			−0.782721	−	0.622372i	$-0.786169\pi$
$881$	−46.4649			−1.56544			−0.782721	+	0.622372i	$0.786169\pi$
$882$		0			0
$883$	13.7476			0.462643			0.231322	−	0.972877i	$-0.425695\pi$
$883$	13.7476			0.462643			0.231322	+	0.972877i	$0.425695\pi$
$884$	12.7687	+	7.37200i	0.429457	+	0.247947i
$885$		0			0
$886$	−5.94470	−	10.2965i	−0.199716	−	0.345919i
$887$	−7.54100			−0.253202			−0.126601	−	0.991954i	$-0.540407\pi$
$887$	−7.54100			−0.253202			−0.126601	+	0.991954i	$0.540407\pi$
$888$		0			0
$889$	−4.74361	−	10.6900i	−0.159096	−	0.358530i
$890$		−	17.7810i		−	0.596021i
$891$		0			0
$892$	−10.6762	−	6.16390i	−0.357465	−	0.206383i
$893$			39.2389i			1.31308i
$894$		0			0
$895$	9.58793	+	5.53559i	0.320489	+	0.185034i
$896$	0.279818	−	2.63091i	0.00934807	−	0.0878926i
$897$		0			0
$898$	−8.53785	+	14.7880i	−0.284912	+	0.493482i
$899$	3.11218	−	5.39046i	0.103797	−	0.179782i
$900$		0			0
$901$	31.0608	−	17.9330i	1.03478	−	0.597433i
$902$	19.4563	+	33.6994i	0.647825	+	1.12207i
$903$		0			0
$904$	−1.71512	+	2.97068i	−0.0570442	+	0.0988034i
$905$		−	17.6466i		−	0.586593i
$906$		0			0
$907$	3.80480			0.126336			0.0631681	−	0.998003i	$-0.479880\pi$
$907$	3.80480			0.126336			0.0631681	+	0.998003i	$0.479880\pi$
$908$	−6.09913	−	10.5640i	−0.202407	−	0.350579i
$909$		0			0
$910$	−3.46447	+	4.75603i	−0.114846	+	0.157661i
$911$	14.3197	−	8.26749i	0.474433	−	0.273914i	−0.243660	−	0.969861i	$-0.578348\pi$
$911$	14.3197	−	8.26749i	0.474433	−	0.273914i	0.718094	+	0.695946i	$0.245015\pi$
$912$		0			0
$913$	−44.6644	+	25.7870i	−1.47818	+	0.853426i
$914$	2.29554	−	1.32533i	0.0759298	−	0.0438381i
$915$		0			0
$916$	−10.5931	+	6.11591i	−0.350005	+	0.202075i
$917$	8.95456	+	20.1796i	0.295706	+	0.666388i
$918$		0			0
$919$	20.4282	+	35.3826i	0.673863	+	1.16716i	0.976800	+	0.214154i	$0.0686994\pi$
$919$	20.4282	+	35.3826i	0.673863	+	1.16716i	−0.302937	+	0.953010i	$0.597967\pi$
$920$	5.02232			0.165581
$921$		0			0
$922$			41.4154i			1.36394i
$923$	−10.6526	+	18.4508i	−0.350634	+	0.607317i
$924$		0			0
$925$	−0.475116	−	0.822924i	−0.0156217	−	0.0270576i
$926$	3.15182	−	1.81970i	0.103575	−	0.0597991i
$927$		0			0
$928$	0.623662	−	1.08021i	0.0204727	−	0.0354598i
$929$	23.3606	−	40.4617i	0.766435	−	1.32750i	−0.173049	−	0.984913i	$-0.555362\pi$
$929$	23.3606	−	40.4617i	0.766435	−	1.32750i	0.939485	−	0.342591i	$-0.111305\pi$
$930$		0			0
$931$	−11.4081	+	53.0243i	−0.373887	+	1.73780i
$932$	0.604674	+	0.349109i	0.0198068	+	0.0114354i
$933$		0			0
$934$		−	32.2586i		−	1.05553i
$935$	−25.9018	−	14.9544i	−0.847080	−	0.489062i
$936$		0			0
$937$		−	4.60721i		−	0.150511i	−0.997164	−	0.0752555i	$-0.976023\pi$
$937$		−	4.60721i		−	0.150511i	0.997164	−	0.0752555i	$-0.0239772\pi$
$938$	13.3935	−	5.94330i	0.437315	−	0.194056i
$939$		0			0
$940$	−5.06424			−0.165177
$941$	1.29667	+	2.24590i	0.0422703	+	0.0732143i	0.886387	−	0.462946i	$-0.153208\pi$
$941$	1.29667	+	2.24590i	0.0422703	+	0.0732143i	−0.844116	+	0.536160i	$0.819874\pi$
$942$		0			0
$943$	37.5156	+	21.6597i	1.22168	+	0.705336i
$944$	−3.27723			−0.106665
$945$		0			0
$946$	43.9556			1.42912
$947$	−29.7197	−	17.1587i	−0.965762	−	0.557583i	−0.0678204	−	0.997698i	$-0.521604\pi$
$947$	−29.7197	−	17.1587i	−0.965762	−	0.557583i	−0.897942	+	0.440115i	$0.854938\pi$
$948$		0			0
$949$	1.42784	+	2.47309i	0.0463497	+	0.0802800i
$950$	7.74823			0.251386
$951$		0			0
$952$	−1.85508	+	17.4418i	−0.0601234	+	0.565293i
$953$			25.0785i			0.812372i	0.913791	+	0.406186i	$0.133141\pi$
$953$			25.0785i			0.812372i	−0.913791	+	0.406186i	$0.866859\pi$
$954$		0			0
$955$	8.00675	+	4.62270i	0.259092	+	0.149587i
$956$			5.50663i			0.178097i
$957$		0			0
$958$	−4.39670	−	2.53843i	−0.142051	−	0.0820131i
$959$	27.7148	−	12.2983i	0.894957	−	0.397132i
$960$		0			0
$961$	−3.04907	+	5.28115i	−0.0983572	+	0.170360i
$962$	1.05664	−	1.83016i	0.0340676	−	0.0590068i
$963$		0			0
$964$	−15.3054	+	8.83660i	−0.492955	+	0.284608i
$965$	8.98854	+	15.5686i	0.289351	+	0.501171i
$966$		0			0
$967$	9.16386	−	15.8723i	0.294690	−	0.510418i	−0.680223	−	0.733005i	$-0.738117\pi$
$967$	9.16386	−	15.8723i	0.294690	−	0.510418i	0.974913	+	0.222587i	$0.0714503\pi$
$968$		−	9.35297i		−	0.300616i
$969$		0			0
$970$	−8.36903			−0.268713
$971$	21.0601	+	36.4772i	0.675851	+	1.17061i	0.976219	+	0.216786i	$0.0695572\pi$
$971$	21.0601	+	36.4772i	0.675851	+	1.17061i	−0.300368	+	0.953823i	$0.597109\pi$
$972$		0			0
$973$	0.955653	−	8.98526i	0.0306368	−	0.288054i
$974$	15.2226	−	8.78880i	0.487765	−	0.281611i
$975$		0			0
$976$	−9.88563	+	5.70747i	−0.316431	+	0.182692i
$977$	44.2802	−	25.5652i	1.41665	−	0.817903i	0.420646	−	0.907225i	$-0.361803\pi$
$977$	44.2802	−	25.5652i	1.41665	−	0.817903i	0.996003	+	0.0893221i	$0.0284700\pi$
$978$		0			0
$979$	−69.4706	+	40.1089i	−2.22029	+	1.28188i
$980$	−6.84340	−	1.47236i	−0.218605	−	0.0470327i
$981$		0			0
$982$	15.7543	+	27.2873i	0.502741	+	0.870774i
$983$	51.7996			1.65215			0.826075	−	0.563560i	$-0.190569\pi$
$983$	51.7996			1.65215			0.826075	+	0.563560i	$0.190569\pi$
$984$		0			0
$985$		−	11.1779i		−	0.356158i
$986$	−4.13461	+	7.16136i	−0.131673	+	0.228064i
$987$		0			0
$988$	8.61593	+	14.9232i	0.274109	+	0.474771i
$989$	42.3776	−	24.4667i	1.34753	−	0.777996i
$990$		0			0
$991$	7.43685	−	12.8810i	0.236239	−	0.409178i	−0.723393	−	0.690437i	$-0.757418\pi$
$991$	7.43685	−	12.8810i	0.236239	−	0.409178i	0.959632	+	0.281258i	$0.0907518\pi$
$992$	2.49509	−	4.32162i	0.0792191	−	0.137212i
$993$		0			0
$994$	−25.2036	−	2.68060i	−0.799409	−	0.0850235i
$995$	2.62204	+	1.51384i	0.0831243	+	0.0479918i
$996$		0			0
$997$		−	57.8595i		−	1.83243i	−0.400687	−	0.916215i	$-0.631229\pi$
$997$		−	57.8595i		−	1.83243i	0.400687	−	0.916215i	$-0.368771\pi$
$998$	−29.6045	−	17.0922i	−0.937115	−	0.541043i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.t.b.1151.13		28
3.2	odd	2		630.2.t.b.311.4	✓	28
7.5	odd	6		1890.2.bk.b.341.2		28
9.2	odd	6		1890.2.bk.b.521.2		28
9.7	even	3		630.2.bk.b.101.2	yes	28
21.5	even	6		630.2.bk.b.131.9	yes	28
63.47	even	6	inner	1890.2.t.b.1601.13		28
63.61	odd	6		630.2.t.b.551.4	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.b.311.4	✓	28	3.2	odd	2
630.2.t.b.551.4	yes	28	63.61	odd	6
630.2.bk.b.101.2	yes	28	9.7	even	3
630.2.bk.b.131.9	yes	28	21.5	even	6
1890.2.t.b.1151.13		28	1.1	even	1	trivial
1890.2.t.b.1601.13		28	63.47	even	6	inner
1890.2.bk.b.341.2		28	7.5	odd	6
1890.2.bk.b.521.2		28	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(1.07313 + 2.41835i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(1.07313 + 2.41835i) q^{7} +1.00000i q^{8} +(0.866025 + 0.500000i) q^{10} -4.51143i q^{11} +(1.92602 + 1.11199i) q^{13} +(-0.279818 + 2.63091i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.31479 - 5.74138i) q^{17} +(6.71016 - 3.87412i) q^{19} +(0.500000 + 0.866025i) q^{20} +(2.25571 - 3.90701i) q^{22} -5.02232i q^{23} +1.00000 q^{25} +(1.11199 + 1.92602i) q^{26} +(-1.55779 + 2.13853i) q^{28} +(-1.08021 + 0.623662i) q^{29} +(-4.32162 + 2.49509i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(5.74138 - 3.31479i) q^{34} +(1.07313 + 2.41835i) q^{35} +(-0.475116 - 0.822924i) q^{37} +7.74823 q^{38} +1.00000i q^{40} +(-4.31268 + 7.46978i) q^{41} +(4.87159 + 8.43784i) q^{43} +(3.90701 - 2.25571i) q^{44} +(2.51116 - 4.34946i) q^{46} +(-2.53212 + 4.38576i) q^{47} +(-4.69680 + 5.19038i) q^{49} +(0.866025 + 0.500000i) q^{50} +2.22397i q^{52} +(4.68518 + 2.70499i) q^{53} -4.51143i q^{55} +(-2.41835 + 1.07313i) q^{56} -1.24732 q^{58} +(1.63861 + 2.83816i) q^{59} +(9.88563 + 5.70747i) q^{61} -4.99018 q^{62} -1.00000 q^{64} +(1.92602 + 1.11199i) q^{65} +(-2.76915 - 4.79631i) q^{67} +6.62958 q^{68} +(-0.279818 + 2.63091i) q^{70} +9.57979i q^{71} +(1.11202 + 0.642023i) q^{73} -0.950231i q^{74} +(6.71016 + 3.87412i) q^{76} +(10.9102 - 4.84133i) q^{77} +(1.98062 - 3.43054i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-7.46978 + 4.31268i) q^{82} +(-5.71593 - 9.90029i) q^{83} +(3.31479 - 5.74138i) q^{85} +9.74318i q^{86} +4.51143 q^{88} +(-8.89050 - 15.3988i) q^{89} +(-0.622308 + 5.85108i) q^{91} +(4.34946 - 2.51116i) q^{92} +(-4.38576 + 2.53212i) q^{94} +(6.71016 - 3.87412i) q^{95} +(-7.24779 + 4.18451i) q^{97} +(-6.66274 + 2.14660i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 14 q^{4} + 28 q^{5} - 4 q^{7}+O(q^{10}) \) 28 * q + 14 * q^4 + 28 * q^5 - 4 * q^7	\( 28 q + 14 q^{4} + 28 q^{5} - 4 q^{7} - 6 q^{14} - 14 q^{16} + 6 q^{17} - 6 q^{19} + 14 q^{20} - 6 q^{22} + 28 q^{25} - 12 q^{26} - 8 q^{28} - 12 q^{31} - 4 q^{35} + 4 q^{37} + 12 q^{38} - 18 q^{41} + 28 q^{43} - 18 q^{46} - 30 q^{47} - 14 q^{49} + 42 q^{53} - 6 q^{56} - 12 q^{58} + 24 q^{59} + 24 q^{61} + 12 q^{62} - 28 q^{64} - 40 q^{67} + 12 q^{68} - 6 q^{70} + 6 q^{73} - 6 q^{76} + 24 q^{77} + 2 q^{79} - 14 q^{80} + 24 q^{82} + 18 q^{83} + 6 q^{85} - 12 q^{88} - 6 q^{89} + 66 q^{91} + 30 q^{92} + 42 q^{94} - 6 q^{95} - 72 q^{97} + 24 q^{98}+O(q^{100}) \) 28 * q + 14 * q^4 + 28 * q^5 - 4 * q^7 - 6 * q^14 - 14 * q^16 + 6 * q^17 - 6 * q^19 + 14 * q^20 - 6 * q^22 + 28 * q^25 - 12 * q^26 - 8 * q^28 - 12 * q^31 - 4 * q^35 + 4 * q^37 + 12 * q^38 - 18 * q^41 + 28 * q^43 - 18 * q^46 - 30 * q^47 - 14 * q^49 + 42 * q^53 - 6 * q^56 - 12 * q^58 + 24 * q^59 + 24 * q^61 + 12 * q^62 - 28 * q^64 - 40 * q^67 + 12 * q^68 - 6 * q^70 + 6 * q^73 - 6 * q^76 + 24 * q^77 + 2 * q^79 - 14 * q^80 + 24 * q^82 + 18 * q^83 + 6 * q^85 - 12 * q^88 - 6 * q^89 + 66 * q^91 + 30 * q^92 + 42 * q^94 - 6 * q^95 - 72 * q^97 + 24 * q^98

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