LMFDB - Embedded newform 882.2.v.a.629.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(125,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 1]))

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

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

chi := DirichletCharacter("882.125");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.v (of order $14$, degree $6$, 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:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			629.14
Character	$\chi$	$=$	882.629
Dual form			882.2.v.a.251.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.781831 - 0.623490i) q^{2} +(0.222521 - 0.974928i) q^{4} +(1.35279 - 0.651468i) q^{5} +(1.05127 - 2.42793i) q^{7} +(-0.433884 - 0.900969i) q^{8} +O(q^{10})$	\(q+(0.781831 - 0.623490i) q^{2} +(0.222521 - 0.974928i) q^{4} +(1.35279 - 0.651468i) q^{5} +(1.05127 - 2.42793i) q^{7} +(-0.433884 - 0.900969i) q^{8} +(0.651468 - 1.35279i) q^{10} +(1.68791 - 1.34606i) q^{11} +(-2.26715 + 1.80799i) q^{13} +(-0.691870 - 2.55369i) q^{14} +(-0.900969 - 0.433884i) q^{16} +(-0.0455349 - 0.199501i) q^{17} -5.39752i q^{19} +(-0.334111 - 1.46384i) q^{20} +(0.480404 - 2.10479i) q^{22} +(-1.31536 - 0.300223i) q^{23} +(-1.71182 + 2.14656i) q^{25} +(-0.645265 + 2.82709i) q^{26} +(-2.13312 - 1.56518i) q^{28} +(9.29440 - 2.12139i) q^{29} +7.31951i q^{31} +(-0.974928 + 0.222521i) q^{32} +(-0.159988 - 0.127586i) q^{34} +(-0.159570 - 3.96934i) q^{35} +(-0.0944532 - 0.413827i) q^{37} +(-3.36530 - 4.21995i) q^{38} +(-1.17391 - 0.936158i) q^{40} +(1.15593 - 0.556665i) q^{41} +(-8.01852 - 3.86152i) q^{43} +(-0.936719 - 1.94512i) q^{44} +(-1.21558 + 0.585392i) q^{46} +(-2.87406 - 3.60396i) q^{47} +(-4.78966 - 5.10482i) q^{49} +2.74555i q^{50} +(1.25817 + 2.61263i) q^{52} +(7.68111 + 1.75316i) q^{53} +(1.40647 - 2.92056i) q^{55} +(-2.64362 + 0.106275i) q^{56} +(5.94399 - 7.45353i) q^{58} +(5.96899 + 2.87452i) q^{59} +(-1.14351 + 0.260999i) q^{61} +(4.56364 + 5.72263i) q^{62} +(-0.623490 + 0.781831i) q^{64} +(-1.88912 + 3.92281i) q^{65} -1.42683 q^{67} -0.204632 q^{68} +(-2.59960 - 3.00386i) q^{70} +(10.7059 + 2.44356i) q^{71} +(-5.67419 - 4.52502i) q^{73} +(-0.331863 - 0.264652i) q^{74} +(-5.26220 - 1.20106i) q^{76} +(-1.49369 - 5.51320i) q^{77} +10.0908 q^{79} -1.50148 q^{80} +(0.556665 - 1.15593i) q^{82} +(4.55824 - 5.71585i) q^{83} +(-0.191568 - 0.240219i) q^{85} +(-8.67675 + 1.98041i) q^{86} +(-1.94512 - 0.936719i) q^{88} +(-4.14732 + 5.20058i) q^{89} +(2.00628 + 7.40517i) q^{91} +(-0.585392 + 1.21558i) q^{92} +(-4.49406 - 1.02574i) q^{94} +(-3.51632 - 7.30170i) q^{95} +18.0992i q^{97} +(-6.92751 - 1.00481i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 16 q^{4}+O(q^{10}) $ 96 * q + 16 * q^4	$ 96 q + 16 q^{4} - 16 q^{16} + 20 q^{22} - 8 q^{25} + 76 q^{37} + 28 q^{40} - 8 q^{43} + 112 q^{49} + 28 q^{52} + 28 q^{55} + 20 q^{58} + 84 q^{61} + 16 q^{64} - 8 q^{67} + 28 q^{70} + 112 q^{85} + 8 q^{88} - 56 q^{91} - 56 q^{94}+O(q^{100}) $ 96 * q + 16 * q^4 - 16 * q^16 + 20 * q^22 - 8 * q^25 + 76 * q^37 + 28 * q^40 - 8 * q^43 + 112 * q^49 + 28 * q^52 + 28 * q^55 + 20 * q^58 + 84 * q^61 + 16 * q^64 - 8 * q^67 + 28 * q^70 + 112 * q^85 + 8 * q^88 - 56 * q^91 - 56 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{5}{14}\right)$	$-1$

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 $

$2$	0.781831	−	0.623490i	0.552838	−	0.440874i
$2$	0.781831	−	0.623490i	0.552838	−	0.440874i
$3$		0			0
$3$		0			0
$4$	0.222521	−	0.974928i	0.111260	−	0.487464i
$5$	1.35279	−	0.651468i	0.604985	−	0.291345i	−0.106206	−	0.994344i	$-0.533870\pi$
$5$	1.35279	−	0.651468i	0.604985	−	0.291345i	0.711191	+	0.702999i	$0.248156\pi$
$6$		0			0
$7$	1.05127	−	2.42793i	0.397343	−	0.917670i
$7$	1.05127	−	2.42793i	0.397343	−	0.917670i
$8$	−0.433884	−	0.900969i	−0.153401	−	0.318541i
$9$		0			0
$10$	0.651468	−	1.35279i	0.206012	−	0.427789i
$11$	1.68791	−	1.34606i	0.508924	−	0.405853i	−0.335081	−	0.942189i	$-0.608764\pi$
$11$	1.68791	−	1.34606i	0.508924	−	0.405853i	0.844004	+	0.536336i	$0.180192\pi$
$12$		0			0
$13$	−2.26715	+	1.80799i	−0.628795	+	0.501447i	−0.885254	−	0.465108i	$-0.846015\pi$
$13$	−2.26715	+	1.80799i	−0.628795	+	0.501447i	0.256459	+	0.966555i	$0.417444\pi$
$14$	−0.691870	−	2.55369i	−0.184910	−	0.682501i
$15$		0			0
$16$	−0.900969	−	0.433884i	−0.225242	−	0.108471i
$17$	−0.0455349	−	0.199501i	−0.0110438	−	0.0483862i	0.969106	−	0.246646i	$-0.0793283\pi$
$17$	−0.0455349	−	0.199501i	−0.0110438	−	0.0483862i	−0.980150	+	0.198259i	$0.936471\pi$
$18$		0			0
$19$		−	5.39752i		−	1.23828i	−0.785282	−	0.619138i	$-0.787482\pi$
$19$		−	5.39752i		−	1.23828i	0.785282	−	0.619138i	$-0.212518\pi$
$20$	−0.334111	−	1.46384i	−0.0747095	−	0.327324i
$21$		0			0
$22$	0.480404	−	2.10479i	0.102422	−	0.448742i
$23$	−1.31536	−	0.300223i	−0.274272	−	0.0626009i	0.0831723	−	0.996535i	$-0.473495\pi$
$23$	−1.31536	−	0.300223i	−0.274272	−	0.0626009i	−0.357445	+	0.933934i	$0.616352\pi$
$24$		0			0
$25$	−1.71182	+	2.14656i	−0.342365	+	0.429312i
$26$	−0.645265	+	2.82709i	−0.126547	+	0.554438i
$27$		0			0
$28$	−2.13312	−	1.56518i	−0.403122	−	0.295791i
$29$	9.29440	−	2.12139i	1.72593	−	0.393931i	0.759426	−	0.650594i	$-0.225480\pi$
$29$	9.29440	−	2.12139i	1.72593	−	0.393931i	0.966501	+	0.256663i	$0.0826229\pi$
$30$		0			0
$31$			7.31951i			1.31462i	0.753619	+	0.657312i	$0.228306\pi$
$31$			7.31951i			1.31462i	−0.753619	+	0.657312i	$0.771694\pi$
$32$	−0.974928	+	0.222521i	−0.172345	+	0.0393365i
$33$		0			0
$34$	−0.159988	−	0.127586i	−0.0274377	−	0.0218808i
$35$	−0.159570	−	3.96934i	−0.0269722	−	0.670941i
$36$		0			0
$37$	−0.0944532	−	0.413827i	−0.0155280	−	0.0680327i	0.966570	−	0.256402i	$-0.0825370\pi$
$37$	−0.0944532	−	0.413827i	−0.0155280	−	0.0680327i	−0.982098	+	0.188369i	$0.939680\pi$
$38$	−3.36530	−	4.21995i	−0.545924	−	0.684567i
$39$		0			0
$40$	−1.17391	−	0.936158i	−0.185611	−	0.148020i
$41$	1.15593	−	0.556665i	0.180525	−	0.0869364i	−0.341438	−	0.939904i	$-0.610914\pi$
$41$	1.15593	−	0.556665i	0.180525	−	0.0869364i	0.521963	+	0.852968i	$0.325200\pi$
$42$		0			0
$43$	−8.01852	−	3.86152i	−1.22281	−	0.588876i	−0.292719	−	0.956198i	$-0.594560\pi$
$43$	−8.01852	−	3.86152i	−1.22281	−	0.588876i	−0.930094	+	0.367323i	$0.880274\pi$
$44$	−0.936719	−	1.94512i	−0.141216	−	0.293237i
$45$		0			0
$46$	−1.21558	+	0.585392i	−0.179227	+	0.0863114i
$47$	−2.87406	−	3.60396i	−0.419225	−	0.525691i	0.526711	−	0.850044i	$-0.323425\pi$
$47$	−2.87406	−	3.60396i	−0.419225	−	0.525691i	−0.945936	+	0.324353i	$0.894853\pi$
$48$		0			0
$49$	−4.78966	−	5.10482i	−0.684237	−	0.729260i
$50$			2.74555i			0.388280i
$51$		0			0
$52$	1.25817	+	2.61263i	0.174477	+	0.362306i
$53$	7.68111	+	1.75316i	1.05508	+	0.240816i	0.714671	−	0.699461i	$-0.246577\pi$
$53$	7.68111	+	1.75316i	1.05508	+	0.240816i	0.340411	+	0.940277i	$0.389434\pi$
$54$		0			0
$55$	1.40647	−	2.92056i	0.189648	−	0.393808i
$56$	−2.64362	+	0.106275i	−0.353268	+	0.0142016i
$57$		0			0
$58$	5.94399	−	7.45353i	0.780484	−	0.978696i
$59$	5.96899	+	2.87452i	0.777097	+	0.374230i	0.780011	−	0.625766i	$-0.215213\pi$
$59$	5.96899	+	2.87452i	0.777097	+	0.374230i	−0.00291427	+	0.999996i	$0.500928\pi$
$60$		0			0
$61$	−1.14351	+	0.260999i	−0.146411	+	0.0334174i	−0.295098	−	0.955467i	$-0.595352\pi$
$61$	−1.14351	+	0.260999i	−0.146411	+	0.0334174i	0.148687	+	0.988884i	$0.452495\pi$
$62$	4.56364	+	5.72263i	0.579583	+	0.726774i
$63$		0			0
$64$	−0.623490	+	0.781831i	−0.0779362	+	0.0977289i
$65$	−1.88912	+	3.92281i	−0.234317	+	0.486564i
$66$		0			0
$67$	−1.42683			−0.174315			−0.0871573	−	0.996195i	$-0.527778\pi$
$67$	−1.42683			−0.174315			−0.0871573	+	0.996195i	$0.527778\pi$
$68$	−0.204632			−0.0248153
$69$		0			0
$70$	−2.59960	−	3.00386i	−0.310712	−	0.359031i
$71$	10.7059	+	2.44356i	1.27056	+	0.289998i	0.804074	−	0.594530i	$-0.202662\pi$
$71$	10.7059	+	2.44356i	1.27056	+	0.289998i	0.466489	+	0.884527i	$0.345519\pi$
$72$		0			0
$73$	−5.67419	−	4.52502i	−0.664114	−	0.529613i	0.232405	−	0.972619i	$-0.425341\pi$
$73$	−5.67419	−	4.52502i	−0.664114	−	0.529613i	−0.896519	+	0.443006i	$0.853912\pi$
$74$	−0.331863	−	0.264652i	−0.0385783	−	0.0307652i
$75$		0			0
$76$	−5.26220	−	1.20106i	−0.603615	−	0.137771i
$77$	−1.49369	−	5.51320i	−0.170222	−	0.628287i
$78$		0			0
$79$	10.0908			1.13531			0.567654	−	0.823267i	$-0.307851\pi$
$79$	10.0908			1.13531			0.567654	+	0.823267i	$0.307851\pi$
$80$	−1.50148			−0.167871
$81$		0			0
$82$	0.556665	−	1.15593i	0.0614733	−	0.127651i
$83$	4.55824	−	5.71585i	0.500332	−	0.627396i	−0.465972	−	0.884799i	$-0.654295\pi$
$83$	4.55824	−	5.71585i	0.500332	−	0.627396i	0.966304	+	0.257403i	$0.0828668\pi$
$84$		0			0
$85$	−0.191568	−	0.240219i	−0.0207785	−	0.0260554i
$86$	−8.67675	+	1.98041i	−0.935638	+	0.213553i
$87$		0			0
$88$	−1.94512	−	0.936719i	−0.207350	−	0.0998546i
$89$	−4.14732	+	5.20058i	−0.439615	+	0.551260i	−0.951442	−	0.307829i	$-0.900398\pi$
$89$	−4.14732	+	5.20058i	−0.439615	+	0.551260i	0.511827	+	0.859089i	$0.328969\pi$
$90$		0			0
$91$	2.00628	+	7.40517i	0.210316	+	0.776273i
$92$	−0.585392	+	1.21558i	−0.0610314	+	0.126733i
$93$		0			0
$94$	−4.49406	−	1.02574i	−0.463527	−	0.105797i
$95$	−3.51632	−	7.30170i	−0.360766	−	0.749139i
$96$		0			0
$97$			18.0992i			1.83770i	0.394612	+	0.918848i	$0.370879\pi$
$97$			18.0992i			1.83770i	−0.394612	+	0.918848i	$0.629121\pi$
$98$	−6.92751	−	1.00481i	−0.699784	−	0.101501i
$99$		0			0
$100$	1.71182	+	2.14656i	0.171182	+	0.214656i
$101$	−13.8795	+	6.68400i	−1.38106	+	0.665083i	−0.969225	−	0.246176i	$-0.920826\pi$
$101$	−13.8795	+	6.68400i	−1.38106	+	0.665083i	−0.411834	+	0.911259i	$0.635112\pi$
$102$		0			0
$103$	−0.0524422	−	0.108897i	−0.00516729	−	0.0107300i	0.898369	−	0.439241i	$-0.144753\pi$
$103$	−0.0524422	−	0.108897i	−0.00516729	−	0.0107300i	−0.903537	+	0.428511i	$0.859038\pi$
$104$	2.61263	+	1.25817i	0.256189	+	0.123374i
$105$		0			0
$106$	7.09842	−	3.41842i	0.689459	−	0.332026i
$107$	12.9825	+	10.3532i	1.25506	+	1.00088i	0.999418	+	0.0341092i	$0.0108594\pi$
$107$	12.9825	+	10.3532i	1.25506	+	1.00088i	0.255645	+	0.966771i	$0.417712\pi$
$108$		0			0
$109$	−6.79050	−	8.51501i	−0.650412	−	0.815590i	0.341850	−	0.939754i	$-0.388946\pi$
$109$	−6.79050	−	8.51501i	−0.650412	−	0.815590i	−0.992262	+	0.124164i	$0.960375\pi$
$110$	−0.721318	−	3.16030i	−0.0687750	−	0.301323i
$111$		0			0
$112$	−2.00060	+	1.73136i	−0.189039	+	0.163598i
$113$	2.73829	+	2.18372i	0.257597	+	0.205427i	0.743770	−	0.668436i	$-0.233036\pi$
$113$	2.73829	+	2.18372i	0.257597	+	0.205427i	−0.486173	+	0.873863i	$0.661607\pi$
$114$		0			0
$115$	−1.97500	+	0.450780i	−0.184169	+	0.0420354i
$116$		−	9.53342i		−	0.885156i
$117$		0			0
$118$	6.45898	−	1.47422i	0.594597	−	0.135713i
$119$	−0.532244	−	0.0991748i	−0.0487908	−	0.00909134i
$120$		0			0
$121$	−1.41058	+	6.18015i	−0.128234	+	0.561831i
$122$	−0.731302	+	0.917023i	−0.0662089	+	0.0830234i
$123$		0			0
$124$	7.13600	+	1.62874i	0.640831	+	0.146266i
$125$	−2.58787	+	11.3382i	−0.231467	+	1.01412i
$126$		0			0
$127$	−0.626861	−	2.74646i	−0.0556249	−	0.243709i	0.939470	−	0.342630i	$-0.111318\pi$
$127$	−0.626861	−	2.74646i	−0.0556249	−	0.243709i	−0.995095	+	0.0989216i	$0.968461\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	0.968854	+	4.24483i	0.0849741	+	0.372296i
$131$	5.11176	+	2.46170i	0.446617	+	0.215079i	0.643654	−	0.765317i	$-0.277418\pi$
$131$	5.11176	+	2.46170i	0.446617	+	0.215079i	−0.197037	+	0.980396i	$0.563132\pi$
$132$		0			0
$133$	−13.1048	−	5.67426i	−1.13633	−	0.492021i
$134$	−1.11554	+	0.889612i	−0.0963678	+	0.0768508i
$135$		0			0
$136$	−0.159988	+	0.127586i	−0.0137188	+	0.0109404i
$137$	2.38003	−	4.94219i	0.203340	−	0.422240i	−0.774214	−	0.632924i	$-0.781855\pi$
$137$	2.38003	−	4.94219i	0.203340	−	0.422240i	0.977554	+	0.210684i	$0.0675690\pi$
$138$		0			0
$139$	7.83497	+	16.2695i	0.664554	+	1.37996i	0.911650	+	0.410969i	$0.134809\pi$
$139$	7.83497	+	16.2695i	0.664554	+	1.37996i	−0.247096	+	0.968991i	$0.579476\pi$
$140$	−3.90533	−	0.727692i	−0.330060	−	0.0615012i
$141$		0			0
$142$	9.89378	−	4.76459i	0.830268	−	0.399836i
$143$	−1.39307	+	6.10345i	−0.116495	+	0.510397i
$144$		0			0
$145$	11.1913	−	8.92479i	0.929390	−	0.741164i
$146$	−7.25756			−0.600640
$147$		0			0
$148$	−0.424469			−0.0348911
$149$	−4.98163	+	3.97272i	−0.408111	+	0.325458i	−0.805935	−	0.592004i	$-0.798337\pi$
$149$	−4.98163	+	3.97272i	−0.408111	+	0.325458i	0.397824	+	0.917462i	$0.369765\pi$
$150$		0			0
$151$	0.923274	−	4.04513i	0.0751350	−	0.329188i	−0.923366	−	0.383921i	$-0.874574\pi$
$151$	0.923274	−	4.04513i	0.0751350	−	0.329188i	0.998501	+	0.0547329i	$0.0174307\pi$
$152$	−4.86300	+	2.34190i	−0.394441	+	0.189953i
$153$		0			0
$154$	−4.60524	−	3.37909i	−0.371100	−	0.272295i
$155$	4.76843	+	9.90175i	0.383010	+	0.795328i
$156$		0			0
$157$	−5.75842	+	11.9575i	−0.459572	+	0.954312i	0.534457	+	0.845196i	$0.320516\pi$
$157$	−5.75842	+	11.9575i	−0.459572	+	0.954312i	−0.994029	+	0.109116i	$0.965198\pi$
$158$	7.88933	−	6.29153i	0.627642	−	0.500527i
$159$		0			0
$160$	−1.17391	+	0.936158i	−0.0928054	+	0.0740098i
$161$	−2.11173	+	2.87799i	−0.166427	+	0.226818i
$162$		0			0
$163$	14.1708	+	6.82429i	1.10994	+	0.534519i	0.896771	−	0.442496i	$-0.145907\pi$
$163$	14.1708	+	6.82429i	1.10994	+	0.534519i	0.213170	+	0.977015i	$0.431621\pi$
$164$	−0.285490	−	1.25081i	−0.0222930	−	0.0976721i
$165$		0			0
$166$		−	7.31085i		−	0.567432i
$167$	−0.487595	−	2.13629i	−0.0377312	−	0.165311i	0.952552	−	0.304375i	$-0.0984477\pi$
$167$	−0.487595	−	2.13629i	−0.0377312	−	0.165311i	−0.990283	+	0.139064i	$0.955591\pi$
$168$		0			0
$169$	−1.02163	+	4.47608i	−0.0785873	+	0.344313i
$170$	−0.299548	−	0.0683698i	−0.0229743	−	0.00524372i
$171$		0			0
$172$	−5.54899	+	6.95821i	−0.423106	+	0.530559i
$173$	−2.37986	+	10.4268i	−0.180937	+	0.792738i	0.800248	+	0.599669i	$0.204701\pi$
$173$	−2.37986	+	10.4268i	−0.180937	+	0.792738i	−0.981185	+	0.193069i	$0.938156\pi$
$174$		0			0
$175$	3.41210	+	6.41280i	0.257930	+	0.484762i
$176$	−2.10479	+	0.480404i	−0.158654	+	0.0362118i
$177$		0			0
$178$			6.65179i			0.498573i
$179$	−6.12193	+	1.39729i	−0.457574	+	0.104438i	−0.445094	−	0.895484i	$-0.646830\pi$
$179$	−6.12193	+	1.39729i	−0.457574	+	0.104438i	−0.0124802	+	0.999922i	$0.503973\pi$
$180$		0			0
$181$	8.03542	+	6.40804i	0.597268	+	0.476306i	0.874848	−	0.484397i	$-0.160961\pi$
$181$	8.03542	+	6.40804i	0.597268	+	0.476306i	−0.277580	+	0.960703i	$0.589532\pi$
$182$	6.18562	+	4.53870i	0.458509	+	0.336431i
$183$		0			0
$184$	0.300223	+	1.31536i	0.0221328	+	0.0969699i
$185$	−0.397370	−	0.498286i	−0.0292152	−	0.0366347i
$186$		0			0
$187$	−0.345400	−	0.275447i	−0.0252582	−	0.0201427i
$188$	−4.15314	+	2.00005i	−0.302899	+	0.145868i
$189$		0			0
$190$	−7.30170	−	3.51632i	−0.529721	−	0.255100i
$191$	−7.78261	−	16.1607i	−0.563130	−	1.16935i	−0.967057	−	0.254560i	$-0.918069\pi$
$191$	−7.78261	−	16.1607i	−0.563130	−	1.16935i	0.403927	−	0.914791i	$-0.367645\pi$
$192$		0			0
$193$	−3.69255	+	1.77824i	−0.265796	+	0.128000i	−0.562035	−	0.827113i	$-0.689982\pi$
$193$	−3.69255	+	1.77824i	−0.265796	+	0.128000i	0.296240	+	0.955114i	$0.404267\pi$
$194$	11.2847	+	14.1505i	0.810192	+	1.01595i
$195$		0			0
$196$	−6.04263	+	3.53364i	−0.431617	+	0.252403i
$197$			14.7696i			1.05229i	0.850395	+	0.526144i	$0.176363\pi$
$197$			14.7696i			1.05229i	−0.850395	+	0.526144i	$0.823637\pi$
$198$		0			0
$199$	8.20609	+	17.0401i	0.581714	+	1.20794i	0.959411	+	0.282013i	$0.0910021\pi$
$199$	8.20609	+	17.0401i	0.581714	+	1.20794i	−0.377696	+	0.925930i	$0.623284\pi$
$200$	2.67672	+	0.610943i	0.189272	+	0.0432002i
$201$		0			0
$202$	−6.68400	+	13.8795i	−0.470285	+	0.976556i
$203$	4.62037	−	24.7963i	0.324286	−	1.74036i
$204$		0			0
$205$	1.20107	−	1.50610i	0.0838866	−	0.105190i
$206$	−0.108897	−	0.0524422i	−0.00758724	−	0.00365382i
$207$		0			0
$208$	2.82709	−	0.645265i	0.196024	−	0.0447411i
$209$	−7.26540	−	9.11053i	−0.502558	−	0.630188i
$210$		0			0
$211$	9.29395	−	11.6542i	0.639822	−	0.802311i	−0.351159	−	0.936316i	$-0.614212\pi$
$211$	9.29395	−	11.6542i	0.639822	−	0.802311i	0.990981	+	0.134005i	$0.0427838\pi$
$212$	3.41842	−	7.09842i	0.234778	−	0.487521i
$213$		0			0
$214$	16.6052			1.13511
$215$	−13.3630			−0.911350
$216$		0			0
$217$	17.7712	+	7.69480i	1.20639	+	0.522357i
$218$	−10.6180	−	2.42350i	−0.719145	−	0.164140i
$219$		0			0
$220$	−2.53436	−	2.02109i	−0.170867	−	0.136262i
$221$	0.463932	+	0.369973i	0.0312074	+	0.0248871i
$222$		0			0
$223$	13.7631	+	3.14133i	0.921644	+	0.210359i	0.656916	−	0.753964i	$-0.271861\pi$
$223$	13.7631	+	3.14133i	0.921644	+	0.210359i	0.264728	+	0.964323i	$0.414718\pi$
$224$	−0.484650	+	2.60098i	−0.0323820	+	0.173786i
$225$		0			0
$226$	3.50241			0.232977
$227$	−15.9299			−1.05731			−0.528654	−	0.848837i	$-0.677303\pi$
$227$	−15.9299			−1.05731			−0.528654	+	0.848837i	$0.677303\pi$
$228$		0			0
$229$	7.06838	−	14.6776i	0.467092	−	0.969926i	−0.525767	−	0.850629i	$-0.676222\pi$
$229$	7.06838	−	14.6776i	0.467092	−	0.969926i	0.992859	−	0.119297i	$-0.0380641\pi$
$230$	−1.26306	+	1.58382i	−0.0832835	+	0.104434i
$231$		0			0
$232$	−5.94399	−	7.45353i	−0.390242	−	0.489348i
$233$	−7.71873	+	1.76175i	−0.505671	+	0.115416i	−0.467743	−	0.883864i	$-0.654933\pi$
$233$	−7.71873	+	1.76175i	−0.505671	+	0.115416i	−0.0379277	+	0.999280i	$0.512076\pi$
$234$		0			0
$235$	−6.23586	−	3.00303i	−0.406783	−	0.195896i
$236$	4.13067	−	5.17970i	0.268884	−	0.337170i
$237$		0			0
$238$	−0.477960	+	0.254311i	−0.0309815	+	0.0164845i
$239$	8.84157	−	18.3597i	0.571914	−	1.18759i	−0.391650	−	0.920114i	$-0.628096\pi$
$239$	8.84157	−	18.3597i	0.571914	−	1.18759i	0.963564	−	0.267477i	$-0.0861900\pi$
$240$		0			0
$241$	−6.16349	−	1.40678i	−0.397025	−	0.0906185i	0.0193465	−	0.999813i	$-0.493841\pi$
$241$	−6.16349	−	1.40678i	−0.397025	−	0.0906185i	−0.416372	+	0.909194i	$0.636699\pi$
$242$	2.75042	+	5.71131i	0.176804	+	0.367137i
$243$		0			0
$244$			1.17292i			0.0750883i
$245$	−9.80502	−	3.78543i	−0.626420	−	0.241842i
$246$		0			0
$247$	9.75868	+	12.2370i	0.620930	+	0.778622i
$248$	6.59465	−	3.17582i	0.418761	−	0.201665i
$249$		0			0
$250$	5.04598	+	10.4781i	0.319136	+	0.662693i
$251$	0.781617	+	0.376407i	0.0493352	+	0.0237586i	0.458389	−	0.888752i	$-0.348427\pi$
$251$	0.781617	+	0.376407i	0.0493352	+	0.0237586i	−0.409053	+	0.912510i	$0.634141\pi$
$252$		0			0
$253$	−2.62433	+	1.26381i	−0.164990	+	0.0794552i
$254$	−2.20249	−	1.75643i	−0.138196	−	0.110208i
$255$		0			0
$256$	0.623490	+	0.781831i	0.0389681	+	0.0488645i
$257$	0.502741	+	2.20265i	0.0313601	+	0.137398i	0.988185	−	0.153269i	$-0.0489801\pi$
$257$	0.502741	+	2.20265i	0.0313601	+	0.137398i	−0.956824	+	0.290667i	$0.906123\pi$
$258$		0			0
$259$	−1.10404	−	0.205719i	−0.0686015	−	0.0127827i
$260$	3.40409	+	2.71467i	0.211112	+	0.168357i
$261$		0			0
$262$	5.53138	−	1.26250i	0.341730	−	0.0779976i
$263$		−	17.7691i		−	1.09569i	−0.836579	−	0.547846i	$-0.815448\pi$
$263$		−	17.7691i		−	1.09569i	0.836579	−	0.547846i	$-0.184552\pi$
$264$		0			0
$265$	11.5330	−	2.63234i	0.708470	−	0.161704i
$266$	−13.7836	+	3.73439i	−0.845126	+	0.228970i
$267$		0			0
$268$	−0.317499	+	1.39105i	−0.0193943	+	0.0849721i
$269$	−19.1598	+	24.0257i	−1.16820	+	1.46487i	−0.310605	+	0.950539i	$0.600532\pi$
$269$	−19.1598	+	24.0257i	−1.16820	+	1.46487i	−0.857591	+	0.514333i	$0.828040\pi$
$270$		0			0
$271$	−2.69899	−	0.616026i	−0.163952	−	0.0374209i	0.139757	−	0.990186i	$-0.455368\pi$
$271$	−2.69899	−	0.616026i	−0.163952	−	0.0374209i	−0.303709	+	0.952765i	$0.598225\pi$
$272$	−0.0455349	+	0.199501i	−0.00276096	+	0.0120965i
$273$		0			0
$274$	−1.22062	−	5.34789i	−0.0737404	−	0.323078i
$275$			5.92742i			0.357437i
$276$		0			0
$277$	−4.32785	−	18.9615i	−0.260035	−	1.13929i	−0.921213	−	0.389059i	$-0.872800\pi$
$277$	−4.32785	−	18.9615i	−0.260035	−	1.13929i	0.661178	−	0.750229i	$-0.270057\pi$
$278$	16.2695	+	7.83497i	0.975779	+	0.469910i
$279$		0			0
$280$	−3.50702	+	1.86600i	−0.209584	+	0.111515i
$281$	19.2555	−	15.3557i	1.14869	−	0.916047i	0.151314	−	0.988486i	$-0.451650\pi$
$281$	19.2555	−	15.3557i	1.14869	−	0.916047i	0.997373	+	0.0724387i	$0.0230782\pi$
$282$		0			0
$283$	−25.0714	+	19.9938i	−1.49034	+	1.18851i	−0.556487	+	0.830856i	$0.687851\pi$
$283$	−25.0714	+	19.9938i	−1.49034	+	1.18851i	−0.933855	+	0.357652i	$0.883577\pi$
$284$	4.76459	−	9.89378i	0.282727	−	0.587088i
$285$		0			0
$286$	2.71629	+	5.64044i	0.160618	+	0.333526i
$287$	−0.136349	−	3.39171i	−0.00804841	−	0.200206i
$288$		0			0
$289$	15.2787	−	7.35786i	0.898750	−	0.432815i
$290$	3.18522	−	13.9554i	0.187043	−	0.819487i
$291$		0			0
$292$	−5.67419	+	4.52502i	−0.332057	+	0.264807i
$293$	−24.7786			−1.44758			−0.723789	−	0.690021i	$-0.757601\pi$
$293$	−24.7786			−1.44758			−0.723789	+	0.690021i	$0.757601\pi$
$294$		0			0
$295$	9.94744			0.579162
$296$	−0.331863	+	0.264652i	−0.0192892	+	0.0153826i
$297$		0			0
$298$	−1.41785	+	6.21199i	−0.0821336	+	0.359851i
$299$	3.52493	−	1.69752i	0.203852	−	0.0981700i
$300$		0			0
$301$	−17.8051	+	15.4089i	−1.02627	+	0.888153i
$302$	−1.80025	−	3.73826i	−0.103593	−	0.215113i
$303$		0			0
$304$	−2.34190	+	4.86300i	−0.134317	+	0.278912i
$305$	−1.37689	+	1.09804i	−0.0788407	+	0.0628733i
$306$		0			0
$307$	−3.08325	+	2.45881i	−0.175971	+	0.140332i	−0.707514	−	0.706699i	$-0.750184\pi$
$307$	−3.08325	+	2.45881i	−0.175971	+	0.140332i	0.531544	+	0.847031i	$0.321612\pi$
$308$	−5.70735	+	0.229439i	−0.325206	+	0.0130735i
$309$		0			0
$310$	9.90175	+	4.76843i	0.562382	+	0.270829i
$311$	−1.45343	−	6.36788i	−0.0824163	−	0.361089i	0.916857	−	0.399217i	$-0.130718\pi$
$311$	−1.45343	−	6.36788i	−0.0824163	−	0.361089i	−0.999273	+	0.0381273i	$0.987861\pi$
$312$		0			0
$313$		−	22.9071i		−	1.29479i	−0.762156	−	0.647393i	$-0.775859\pi$
$313$		−	22.9071i		−	1.29479i	0.762156	−	0.647393i	$-0.224141\pi$
$314$	2.95326	+	12.9391i	0.166662	+	0.730194i
$315$		0			0
$316$	2.24542	−	9.83784i	0.126315	−	0.553422i
$317$	27.7501	+	6.33378i	1.55860	+	0.355740i	0.913008	−	0.407941i	$-0.133753\pi$
$317$	27.7501	+	6.33378i	1.55860	+	0.355740i	0.645593	+	0.763682i	$0.276610\pi$
$318$		0			0
$319$	12.8326	−	16.0915i	0.718487	−	0.900954i
$320$	−0.334111	+	1.46384i	−0.0186774	+	0.0818309i
$321$		0			0
$322$	0.143385	+	3.56674i	0.00799055	+	0.198767i
$323$	−1.07681	+	0.245776i	−0.0599155	+	0.0136753i
$324$		0			0
$325$		−	7.96154i		−	0.441627i
$326$	15.3340	−	3.49989i	0.849274	−	0.193841i
$327$		0			0
$328$	−1.00307	−	0.799925i	−0.0553855	−	0.0441685i
$329$	−11.7716	+	3.18927i	−0.648987	+	0.175830i
$330$		0			0
$331$	2.37205	+	10.3926i	0.130380	+	0.571230i	0.997342	+	0.0728573i	$0.0232118\pi$
$331$	2.37205	+	10.3926i	0.130380	+	0.571230i	−0.866963	+	0.498373i	$0.833931\pi$
$332$	−4.55824	−	5.71585i	−0.250166	−	0.313698i
$333$		0			0
$334$	−1.71317	−	1.36621i	−0.0937407	−	0.0747557i
$335$	−1.93019	+	0.929532i	−0.105458	+	0.0507858i
$336$		0			0
$337$	−7.10579	−	3.42197i	−0.387077	−	0.186406i	0.230216	−	0.973139i	$-0.426057\pi$
$337$	−7.10579	−	3.42197i	−0.387077	−	0.186406i	−0.617293	+	0.786733i	$0.711771\pi$
$338$	1.99204	+	4.13652i	0.108353	+	0.224997i
$339$		0			0
$340$	−0.276824	+	0.133311i	−0.0150129	+	0.00722982i
$341$	9.85252	+	12.3547i	0.533544	+	0.669043i
$342$		0			0
$343$	−17.4294	+	6.26238i	−0.941097	+	0.338137i
$344$			8.89989i			0.479850i
$345$		0			0
$346$	4.64038	+	9.63585i	0.249468	+	0.518027i
$347$	24.5003	+	5.59204i	1.31525	+	0.300196i	0.821898	−	0.569635i	$-0.192916\pi$
$347$	24.5003	+	5.59204i	1.31525	+	0.300196i	0.493349	+	0.869832i	$0.335773\pi$
$348$		0			0
$349$	11.6767	−	24.2469i	0.625038	−	1.29791i	−0.312465	−	0.949929i	$-0.601155\pi$
$349$	11.6767	−	24.2469i	0.625038	−	1.29791i	0.937503	−	0.347976i	$-0.113131\pi$
$350$	6.66600	+	2.88632i	0.356313	+	0.154280i
$351$		0			0
$352$	−1.34606	+	1.68791i	−0.0717454	+	0.0899658i
$353$	1.47598	+	0.710796i	0.0785586	+	0.0378318i	0.472751	−	0.881196i	$-0.343261\pi$
$353$	1.47598	+	0.710796i	0.0785586	+	0.0378318i	−0.394192	+	0.919028i	$0.628975\pi$
$354$		0			0
$355$	16.0748	−	3.66896i	0.853161	−	0.194728i
$356$	4.14732	+	5.20058i	0.219808	+	0.275630i
$357$		0			0
$358$	−3.91512	+	4.90941i	−0.206921	+	0.259470i
$359$	−4.20157	+	8.72464i	−0.221750	+	0.460469i	−0.981930	−	0.189243i	$-0.939396\pi$
$359$	−4.20157	+	8.72464i	−0.221750	+	0.460469i	0.760180	+	0.649713i	$0.225111\pi$
$360$		0			0
$361$	−10.1333			−0.533329
$362$	10.2777			0.540184
$363$		0			0
$364$	7.66595	−	0.308176i	0.401805	−	0.0161528i
$365$	−10.6239	−	2.42483i	−0.556079	−	0.126922i
$366$		0			0
$367$	−28.1872	−	22.4785i	−1.47136	−	1.17337i	−0.946725	−	0.322042i	$-0.895631\pi$
$367$	−28.1872	−	22.4785i	−1.47136	−	1.17337i	−0.524634	−	0.851328i	$-0.675798\pi$
$368$	1.05484	+	0.841207i	0.0549874	+	0.0438510i
$369$		0			0
$370$	−0.621353	−	0.141820i	−0.0323026	−	0.00737286i
$371$	12.3315	−	16.8061i	0.640219	−	0.872531i
$372$		0			0
$373$	−25.8009			−1.33592			−0.667959	−	0.744198i	$-0.732832\pi$
$373$	−25.8009			−1.33592			−0.667959	+	0.744198i	$0.732832\pi$
$374$	−0.441783			−0.0228441
$375$		0			0
$376$	−2.00005	+	4.15314i	−0.103145	+	0.214182i
$377$	−17.2364	+	21.6137i	−0.887718	+	1.11316i
$378$		0			0
$379$	−15.2588	−	19.1340i	−0.783794	−	0.982846i	−0.999979	−	0.00649407i	$-0.997933\pi$
$379$	−15.2588	−	19.1340i	−0.783794	−	0.982846i	0.216185	−	0.976352i	$-0.430639\pi$
$380$	−7.90109	+	1.80337i	−0.405317	+	0.0925110i
$381$		0			0
$382$	−16.1607	−	7.78261i	−0.826856	−	0.398193i
$383$	−9.10693	+	11.4197i	−0.465342	+	0.583521i	−0.958024	−	0.286689i	$-0.907445\pi$
$383$	−9.10693	+	11.4197i	−0.465342	+	0.583521i	0.492682	+	0.870210i	$0.336017\pi$
$384$		0			0
$385$	−5.61232	−	6.48509i	−0.286030	−	0.330511i
$386$	−1.77824	+	3.69255i	−0.0905100	+	0.187946i
$387$		0			0
$388$	17.6454	+	4.02745i	0.895810	+	0.204463i
$389$	−8.15516	−	16.9344i	−0.413483	−	0.858606i	−0.998855	−	0.0478415i	$-0.984766\pi$
$389$	−8.15516	−	16.9344i	−0.413483	−	0.858606i	0.585372	−	0.810765i	$-0.300949\pi$
$390$		0			0
$391$			0.276088i			0.0139624i
$392$	−2.52113	+	6.53023i	−0.127336	+	0.329826i
$393$		0			0
$394$	9.20868	+	11.5473i	0.463926	+	0.581745i
$395$	13.6508	−	6.57386i	0.686844	−	0.330767i
$396$		0			0
$397$	3.03244	+	6.29693i	0.152194	+	0.316034i	0.963101	−	0.269142i	$-0.0867400\pi$
$397$	3.03244	+	6.29693i	0.152194	+	0.316034i	−0.810907	+	0.585175i	$0.801026\pi$
$398$	17.0401	+	8.20609i	0.854144	+	0.411334i
$399$		0			0
$400$	2.47366	−	1.19125i	0.123683	−	0.0595626i
$401$	1.40707	+	1.12210i	0.0702658	+	0.0560351i	0.657993	−	0.753024i	$-0.271406\pi$
$401$	1.40707	+	1.12210i	0.0702658	+	0.0560351i	−0.587727	+	0.809059i	$0.699977\pi$
$402$		0			0
$403$	−13.2336	−	16.5944i	−0.659214	−	0.826628i
$404$	3.42795	+	15.0188i	0.170547	+	0.747214i
$405$		0			0
$406$	−11.8479	−	22.2673i	−0.588000	−	1.10511i
$407$	−0.716465	−	0.571362i	−0.0355138	−	0.0283213i
$408$		0			0
$409$	−1.27232	+	0.290399i	−0.0629121	+	0.0143593i	−0.253861	−	0.967241i	$-0.581701\pi$
$409$	−1.27232	+	0.290399i	−0.0629121	+	0.0143593i	0.190949	+	0.981600i	$0.438843\pi$
$410$		−	1.92637i		−	0.0951367i
$411$		0			0
$412$	−0.117837	+	0.0268954i	−0.00580539	+	0.00132504i
$413$	13.2541	−	11.4704i	0.652194	−	0.564421i
$414$		0			0
$415$	2.44264	−	10.7019i	0.119904	−	0.525335i
$416$	1.80799	−	2.26715i	0.0886441	−	0.111156i
$417$		0			0
$418$	−11.3606	−	2.59299i	−0.555667	−	0.126827i
$419$	5.85902	−	25.6701i	0.286232	−	1.25406i	−0.603419	−	0.797424i	$-0.706195\pi$
$419$	5.85902	−	25.6701i	0.286232	−	1.25406i	0.889651	−	0.456640i	$-0.150947\pi$
$420$		0			0
$421$	−1.79434	−	7.86150i	−0.0874506	−	0.383146i	0.912195	−	0.409756i	$-0.134386\pi$
$421$	−1.79434	−	7.86150i	−0.0874506	−	0.383146i	−0.999646	+	0.0266096i	$0.991529\pi$
$422$		−	14.9063i		−	0.725629i
$423$		0			0
$424$	−1.75316	−	7.68111i	−0.0851412	−	0.373028i
$425$	0.506190	+	0.243768i	0.0245538	+	0.0118245i
$426$		0			0
$427$	−0.568454	+	3.05074i	−0.0275094	+	0.147636i
$428$	12.9825	−	10.3532i	0.627532	−	0.500440i
$429$		0			0
$430$	−10.4476	+	8.33170i	−0.503829	+	0.401790i
$431$	−9.00171	+	18.6923i	−0.433597	+	0.900374i	0.563635	+	0.826024i	$0.309402\pi$
$431$	−9.00171	+	18.6923i	−0.433597	+	0.900374i	−0.997232	+	0.0743500i	$0.976312\pi$
$432$		0			0
$433$	−3.33827	−	6.93198i	−0.160427	−	0.333130i	0.805225	−	0.592970i	$-0.202045\pi$
$433$	−3.33827	−	6.93198i	−0.160427	−	0.333130i	−0.965652	+	0.259840i	$0.916330\pi$
$434$	18.6917	−	5.06415i	0.897232	−	0.243087i
$435$		0			0
$436$	−9.81255	+	4.72548i	−0.469936	+	0.226309i
$437$	−1.62046	+	7.09971i	−0.0775172	+	0.339625i
$438$		0			0
$439$	29.7877	−	23.7549i	1.42169	−	1.13376i	0.451254	−	0.892396i	$-0.350977\pi$
$439$	29.7877	−	23.7549i	1.42169	−	1.13376i	0.970435	−	0.241363i	$-0.0775946\pi$
$440$	−3.24157			−0.154536
$441$		0			0
$442$	0.593391			0.0282247
$443$	−12.9541	+	10.3305i	−0.615466	+	0.490818i	−0.880895	−	0.473313i	$-0.843058\pi$
$443$	−12.9541	+	10.3305i	−0.615466	+	0.490818i	0.265428	+	0.964131i	$0.414487\pi$
$444$		0			0
$445$	−2.22244	+	9.73713i	−0.105354	+	0.461584i
$446$	12.7190	−	6.12515i	0.602262	−	0.290034i
$447$		0			0
$448$	1.24277	+	2.33570i	0.0587155	+	0.110352i
$449$	7.88953	+	16.3828i	0.372330	+	0.773151i	0.999986	−	0.00534002i	$-0.00169979\pi$
$449$	7.88953	+	16.3828i	0.372330	+	0.773151i	−0.627656	+	0.778491i	$0.715986\pi$
$450$		0			0
$451$	1.20179	−	2.49555i	0.0565902	−	0.117511i
$452$	2.73829	−	2.18372i	0.128798	−	0.102713i
$453$		0			0
$454$	−12.4545	+	9.93216i	−0.584520	+	0.466139i
$455$	7.53831	+	8.71059i	0.353401	+	0.408359i
$456$		0			0
$457$	−26.4700	−	12.7473i	−1.23821	−	0.596292i	−0.303887	−	0.952708i	$-0.598284\pi$
$457$	−26.4700	−	12.7473i	−1.23821	−	0.596292i	−0.934327	+	0.356416i	$0.883999\pi$
$458$	−3.62508	−	15.8825i	−0.169389	−	0.742141i
$459$		0			0
$460$			2.02579i			0.0944527i
$461$	0.752767	+	3.29809i	0.0350599	+	0.153607i	0.989428	−	0.145026i	$-0.0463265\pi$
$461$	0.752767	+	3.29809i	0.0350599	+	0.153607i	−0.954368	+	0.298633i	$0.903469\pi$
$462$		0			0
$463$	−3.00074	+	13.1471i	−0.139456	+	0.610998i	0.856099	+	0.516813i	$0.172882\pi$
$463$	−3.00074	+	13.1471i	−0.139456	+	0.610998i	−0.995555	+	0.0941849i	$0.969976\pi$
$464$	−9.29440	−	2.12139i	−0.431482	−	0.0984829i
$465$		0			0
$466$	−4.93631	+	6.18994i	−0.228670	+	0.286744i
$467$	−0.900613	+	3.94584i	−0.0416754	+	0.182592i	−0.991482	−	0.130247i	$-0.958423\pi$
$467$	−0.900613	+	3.94584i	−0.0416754	+	0.182592i	0.949806	+	0.312839i	$0.101280\pi$
$468$		0			0
$469$	−1.49998	+	3.46423i	−0.0692628	+	0.159963i
$470$	−6.74775	+	1.54013i	−0.311251	+	0.0710409i
$471$		0			0
$472$		−	6.62508i		−	0.304944i
$473$	−18.7324	+	4.27554i	−0.861315	+	0.196590i
$474$		0			0
$475$	11.5861	+	9.23961i	0.531607	+	0.423943i
$476$	−0.215124	+	0.496831i	−0.00986018	+	0.0227722i
$477$		0			0
$478$	−4.53448	−	19.8668i	−0.207402	−	0.908688i
$479$	−23.4220	−	29.3703i	−1.07018	−	1.34196i	−0.936394	−	0.350951i	$-0.885858\pi$
$479$	−23.4220	−	29.3703i	−1.07018	−	1.34196i	−0.133784	−	0.991010i	$-0.542713\pi$
$480$		0			0
$481$	0.962335	+	0.767437i	0.0438787	+	0.0349921i
$482$	−5.69592	+	2.74301i	−0.259442	+	0.124941i
$483$		0			0
$484$	5.71131	+	2.75042i	0.259605	+	0.125019i
$485$	11.7911	+	24.4844i	0.535404	+	1.11178i
$486$		0			0
$487$	−24.7132	+	11.9012i	−1.11986	+	0.539296i	−0.899849	−	0.436201i	$-0.856324\pi$
$487$	−24.7132	+	11.9012i	−1.11986	+	0.539296i	−0.220011	+	0.975497i	$0.570609\pi$
$488$	0.731302	+	0.917023i	0.0331045	+	0.0415117i
$489$		0			0
$490$	−10.0260	+	3.15376i	−0.452931	+	0.142472i
$491$		−	8.06621i		−	0.364023i	−0.983296	−	0.182011i	$-0.941739\pi$
$491$		−	8.06621i		−	0.364023i	0.983296	−	0.182011i	$-0.0582608\pi$
$492$		0			0
$493$	−0.846439	−	1.75765i	−0.0381217	−	0.0791605i
$494$	15.2593	+	3.48283i	0.686548	+	0.156700i
$495$		0			0
$496$	3.17582	−	6.59465i	0.142598	−	0.296109i
$497$	17.1876	−	23.4244i	0.770971	−	1.05073i
$498$		0			0
$499$	2.05876	−	2.58161i	0.0921629	−	0.115569i	−0.733612	−	0.679569i	$-0.762167\pi$
$499$	2.05876	−	2.58161i	0.0921629	−	0.115569i	0.825775	+	0.564000i	$0.190738\pi$
$500$	10.4781	+	5.04598i	0.468595	+	0.225663i
$501$		0			0
$502$	0.845778	−	0.193043i	0.0377489	−	0.00861595i
$503$	−19.4857	−	24.4343i	−0.868825	−	1.08947i	−0.995236	−	0.0974941i	$-0.968917\pi$
$503$	−19.4857	−	24.4343i	−0.868825	−	1.08947i	0.126411	−	0.991978i	$-0.459654\pi$
$504$		0			0
$505$	−14.4216	+	18.0841i	−0.641751	+	0.804731i
$506$	−1.26381	+	2.62433i	−0.0561833	+	0.116666i
$507$		0			0
$508$	−2.81709			−0.124988
$509$	−1.19757			−0.0530814			−0.0265407	−	0.999648i	$-0.508449\pi$
$509$	−1.19757			−0.0530814			−0.0265407	+	0.999648i	$0.508449\pi$
$510$		0			0
$511$	−16.9515	+	9.01950i	−0.749891	+	0.398999i
$512$	0.974928	+	0.222521i	0.0430861	+	0.00983413i
$513$		0			0
$514$	1.76639	+	1.40865i	0.0779121	+	0.0621328i
$515$	−0.141886	−	0.113151i	−0.00625226	−	0.00498601i
$516$		0			0
$517$	−9.70231	−	2.21449i	−0.426707	−	0.0973931i
$518$	−0.991434	+	0.527518i	−0.0435611	+	0.0231778i
$519$		0			0
$520$	4.35399			0.190935
$521$	12.2679			0.537468			0.268734	−	0.963214i	$-0.413395\pi$
$521$	12.2679			0.537468			0.268734	+	0.963214i	$0.413395\pi$
$522$		0			0
$523$	−3.66609	+	7.61271i	−0.160307	+	0.332881i	−0.965615	−	0.259976i	$-0.916285\pi$
$523$	−3.66609	+	7.61271i	−0.160307	+	0.332881i	0.805308	+	0.592856i	$0.202000\pi$
$524$	3.53745	−	4.43582i	0.154534	−	0.193780i
$525$		0			0
$526$	−11.0789	−	13.8925i	−0.483062	−	0.605741i
$527$	1.46025	−	0.333293i	0.0636096	−	0.0145185i
$528$		0			0
$529$	−19.0822	−	9.18952i	−0.829662	−	0.399544i
$530$	7.37566	−	9.24879i	0.320378	−	0.401742i
$531$		0			0
$532$	−8.44809	+	11.5136i	−0.366271	+	0.499177i
$533$	−1.61421	+	3.35195i	−0.0699193	+	0.145189i
$534$		0			0
$535$	24.3073	+	5.54798i	1.05090	+	0.239860i
$536$	0.619077	+	1.28553i	0.0267401	+	0.0555263i
$537$		0			0
$538$			30.7300i			1.32486i
$539$	−14.9559	−	2.16930i	−0.644197	−	0.0934382i
$540$		0			0
$541$	9.44157	+	11.8394i	0.405925	+	0.509014i	0.942210	−	0.335023i	$-0.108744\pi$
$541$	9.44157	+	11.8394i	0.405925	+	0.509014i	−0.536285	+	0.844037i	$0.680173\pi$
$542$	−2.49424	+	1.20116i	−0.107137	+	0.0515944i
$543$		0			0
$544$	0.0887865	+	0.184367i	0.00380669	+	0.00790467i
$545$	−14.7334	−	7.09521i	−0.631108	−	0.303926i
$546$		0			0
$547$	17.5398	−	8.44673i	0.749948	−	0.361156i	−0.0195469	−	0.999809i	$-0.506222\pi$
$547$	17.5398	−	8.44673i	0.749948	−	0.361156i	0.769495	+	0.638653i	$0.220508\pi$
$548$	−4.28867	−	3.42010i	−0.183203	−	0.146100i
$549$		0			0
$550$	3.69569	+	4.63424i	0.157585	+	0.197605i
$551$	−11.4502	−	50.1667i	−0.487796	−	2.13717i
$552$		0			0
$553$	10.6082	−	24.4998i	0.451107	−	1.04184i
$554$	−15.2060	−	12.1264i	−0.646040	−	0.515199i
$555$		0			0
$556$	17.6050	−	4.01823i	0.746619	−	0.170411i
$557$		−	24.1887i		−	1.02491i	−0.858715	−	0.512454i	$-0.828736\pi$
$557$		−	24.1887i		−	1.02491i	0.858715	−	0.512454i	$-0.171264\pi$
$558$		0			0
$559$	25.1608	−	5.74279i	1.06419	−	0.242894i
$560$	−1.57846	+	3.64549i	−0.0667023	+	0.154050i
$561$		0			0
$562$	5.48040	−	24.0112i	0.231177	−	1.01285i
$563$	16.6035	−	20.8202i	0.699756	−	0.877466i	−0.297249	−	0.954800i	$-0.596069\pi$
$563$	16.6035	−	20.8202i	0.699756	−	0.877466i	0.997005	+	0.0773339i	$0.0246407\pi$
$564$		0			0
$565$	5.12695	+	1.17019i	0.215692	+	0.0492304i
$566$	−7.13571	+	31.2636i	−0.299936	+	1.31411i
$567$		0			0
$568$	−2.44356	−	10.7059i	−0.102530	−	0.449212i
$569$			44.6824i			1.87318i	0.350424	+	0.936591i	$0.386037\pi$
$569$			44.6824i			1.87318i	−0.350424	+	0.936591i	$0.613963\pi$
$570$		0			0
$571$	−6.67647	−	29.2515i	−0.279402	−	1.22414i	−0.898552	−	0.438866i	$-0.855380\pi$
$571$	−6.67647	−	29.2515i	−0.279402	−	1.22414i	0.619151	−	0.785272i	$-0.287477\pi$
$572$	5.64044	+	2.71629i	0.235839	+	0.113574i
$573$		0			0
$574$	−2.22130	−	2.56673i	−0.0927152	−	0.107133i
$575$	2.89612	−	2.30958i	0.120777	−	0.0963161i
$576$		0			0
$577$	−0.188795	+	0.150559i	−0.00785966	+	0.00626787i	−0.627412	−	0.778688i	$-0.715886\pi$
$577$	−0.188795	+	0.150559i	−0.00785966	+	0.00626787i	0.619552	+	0.784956i	$0.287314\pi$
$578$	7.35786	−	15.2787i	0.306046	−	0.635512i
$579$		0			0
$580$	−6.21072	−	12.8967i	−0.257886	−	0.535506i
$581$	−9.08572	−	17.0760i	−0.376939	−	0.708431i
$582$		0			0
$583$	15.3249	−	7.38008i	0.634692	−	0.305652i
$584$	−1.61496	+	7.07560i	−0.0668275	+	0.292790i
$585$		0			0
$586$	−19.3727	+	15.4492i	−0.800277	+	0.638200i
$587$	31.6533			1.30647			0.653235	−	0.757155i	$-0.273411\pi$
$587$	31.6533			1.30647			0.653235	+	0.757155i	$0.273411\pi$
$588$		0			0
$589$	39.5072			1.62787
$590$	7.77722	−	6.20213i	0.320183	−	0.255338i
$591$		0			0
$592$	−0.0944532	+	0.413827i	−0.00388200	+	0.0170082i
$593$	26.5558	−	12.7886i	1.09052	−	0.525165i	0.199851	−	0.979826i	$-0.435954\pi$
$593$	26.5558	−	12.7886i	1.09052	−	0.525165i	0.890664	+	0.454661i	$0.150240\pi$
$594$		0			0
$595$	−0.784623	+	0.212578i	−0.0321664	+	0.00871484i
$596$	2.76459	+	5.74074i	0.113242	+	0.235150i
$597$		0			0
$598$	1.69752	−	3.52493i	0.0694167	−	0.144145i
$599$	−28.6362	+	22.8366i	−1.17004	+	0.933079i	−0.998641	−	0.0521217i	$-0.983402\pi$
$599$	−28.6362	+	22.8366i	−1.17004	+	0.933079i	−0.171404	+	0.985201i	$0.554830\pi$
$600$		0			0
$601$	−29.5747	+	23.5851i	−1.20638	+	0.962054i	−0.999866	−	0.0163895i	$-0.994783\pi$
$601$	−29.5747	+	23.5851i	−1.20638	+	0.962054i	−0.206512	+	0.978444i	$0.566211\pi$
$602$	−4.31333	+	23.1485i	−0.175798	+	0.943461i
$603$		0			0
$604$	−3.73826	−	1.80025i	−0.152108	−	0.0732512i
$605$	2.11796	+	9.27937i	0.0861072	+	0.377260i
$606$		0			0
$607$		−	22.4274i		−	0.910300i	−0.890415	−	0.455150i	$-0.849586\pi$
$607$		−	22.4274i		−	0.910300i	0.890415	−	0.455150i	$-0.150414\pi$
$608$	1.20106	+	5.26220i	0.0487095	+	0.213410i
$609$		0			0
$610$	−0.391884	+	1.71696i	−0.0158669	+	0.0695176i
$611$	13.0319	+	2.97444i	0.527213	+	0.120333i
$612$		0			0
$613$	1.63843	−	2.05453i	0.0661757	−	0.0829817i	−0.747642	−	0.664102i	$-0.768814\pi$
$613$	1.63843	−	2.05453i	0.0661757	−	0.0829817i	0.813818	+	0.581120i	$0.197385\pi$
$614$	−0.877540	+	3.84476i	−0.0354146	+	0.155162i
$615$		0			0
$616$	−4.31913	+	3.73785i	−0.174023	+	0.150602i
$617$	42.2730	−	9.64854i	1.70185	−	0.388436i	0.742319	−	0.670046i	$-0.233726\pi$
$617$	42.2730	−	9.64854i	1.70185	−	0.388436i	0.959529	+	0.281610i	$0.0908686\pi$
$618$		0			0
$619$			3.81960i			0.153523i	0.997049	+	0.0767613i	$0.0244580\pi$
$619$			3.81960i			0.153523i	−0.997049	+	0.0767613i	$0.975542\pi$
$620$	10.7146	−	2.44553i	0.430307	−	0.0982148i
$621$		0			0
$622$	−5.10664	−	4.07241i	−0.204758	−	0.163289i
$623$	8.26666	+	15.5366i	0.331197	+	0.622461i
$624$		0			0
$625$	0.830930	+	3.64054i	0.0332372	+	0.145622i
$626$	−14.2824	−	17.9095i	−0.570838	−	0.715808i
$627$		0			0
$628$	10.3763	+	8.27484i	0.414060	+	0.330202i
$629$	−0.0782581	+	0.0376871i	−0.00312035	+	0.00150268i
$630$		0			0
$631$	−1.92471	−	0.926893i	−0.0766216	−	0.0368990i	0.395180	−	0.918603i	$-0.370682\pi$
$631$	−1.92471	−	0.926893i	−0.0766216	−	0.0368990i	−0.471802	+	0.881704i	$0.656396\pi$
$632$	−4.37825	−	9.09153i	−0.174157	−	0.361642i
$633$		0			0
$634$	25.6449	−	12.3500i	1.01849	−	0.490479i
$635$	−2.63724	−	3.30699i	−0.104656	−	0.131234i
$636$		0			0
$637$	20.0884	+	2.91374i	0.795930	+	0.115446i
$638$		−	20.5819i		−	0.814844i
$639$		0			0
$640$	0.651468	+	1.35279i	0.0257515	+	0.0534736i
$641$	−38.5724	−	8.80389i	−1.52352	−	0.347733i	−0.622884	−	0.782314i	$-0.714039\pi$
$641$	−38.5724	−	8.80389i	−1.52352	−	0.347733i	−0.900632	+	0.434582i	$0.856896\pi$
$642$		0			0
$643$	3.88449	−	8.06622i	0.153189	−	0.318101i	−0.810224	−	0.586120i	$-0.800655\pi$
$643$	3.88449	−	8.06622i	0.153189	−	0.318101i	0.963414	+	0.268019i	$0.0863691\pi$
$644$	2.33593	+	2.69919i	0.0920486	+	0.106363i
$645$		0			0
$646$	−0.688648	+	0.863537i	−0.0270945	+	0.0339754i
$647$	21.3106	+	10.2626i	0.837805	+	0.403466i	0.803036	−	0.595930i	$-0.203216\pi$
$647$	21.3106	+	10.2626i	0.837805	+	0.403466i	0.0347683	+	0.999395i	$0.488931\pi$
$648$		0			0
$649$	13.9444	−	3.18272i	0.547365	−	0.124933i
$650$	−4.96394	−	6.22459i	−0.194702	−	0.244148i
$651$		0			0
$652$	9.80648	−	12.2969i	0.384051	−	0.481585i
$653$	3.61275	−	7.50196i	0.141378	−	0.293574i	−0.818242	−	0.574874i	$-0.805051\pi$
$653$	3.61275	−	7.50196i	0.141378	−	0.293574i	0.959620	+	0.281299i	$0.0907654\pi$
$654$		0			0
$655$	8.51885			0.332859
$656$	−1.28298			−0.0500920
$657$		0			0
$658$	−7.21490	+	9.83292i	−0.281266	+	0.383327i
$659$	3.71159	+	0.847146i	0.144583	+	0.0330001i	0.294200	−	0.955744i	$-0.404947\pi$
$659$	3.71159	+	0.847146i	0.144583	+	0.0330001i	−0.149617	+	0.988744i	$0.547804\pi$
$660$		0			0
$661$	−17.1526	−	13.6787i	−0.667159	−	0.532041i	0.230311	−	0.973117i	$-0.426026\pi$
$661$	−17.1526	−	13.6787i	−0.667159	−	0.532041i	−0.897470	+	0.441076i	$0.854597\pi$
$662$	8.33424	+	6.64633i	0.323919	+	0.258317i
$663$		0			0
$664$	−7.12755	−	1.62682i	−0.276603	−	0.0631328i
$665$	−21.4246	+	0.861282i	−0.830810	+	0.0333991i
$666$		0			0
$667$	−12.8624			−0.498035
$668$	−2.19123			−0.0847813
$669$		0			0
$670$	−0.929532	+	1.93019i	−0.0359110	+	0.0745699i
$671$	−1.57882	+	1.97978i	−0.0609496	+	0.0764284i
$672$		0			0
$673$	−7.63064	−	9.56852i	−0.294139	−	0.368839i	0.612700	−	0.790316i	$-0.290083\pi$
$673$	−7.63064	−	9.56852i	−0.294139	−	0.368839i	−0.906839	+	0.421476i	$0.861512\pi$
$674$	−7.68909	+	1.75498i	−0.296173	+	0.0675995i
$675$		0			0
$676$	4.13652	+	1.99204i	0.159097	+	0.0766170i
$677$	14.0442	−	17.6109i	0.539764	−	0.676843i	−0.434910	−	0.900474i	$-0.643220\pi$
$677$	14.0442	−	17.6109i	0.539764	−	0.676843i	0.974674	+	0.223631i	$0.0717911\pi$
$678$		0			0
$679$	43.9435	+	19.0272i	1.68640	+	0.730196i
$680$	−0.133311	+	0.276824i	−0.00511225	+	0.0106157i
$681$		0			0
$682$	15.4060	+	3.51632i	0.589927	+	0.134647i
$683$	20.5392	+	42.6501i	0.785910	+	1.63196i	0.774952	+	0.632020i	$0.217774\pi$
$683$	20.5392	+	42.6501i	0.785910	+	1.63196i	0.0109579	+	0.999940i	$0.496512\pi$
$684$		0			0
$685$		−	8.23625i		−	0.314691i
$686$	−9.72229	+	15.7632i	−0.371199	+	0.601840i
$687$		0			0
$688$	5.54899	+	6.95821i	0.211553	+	0.265279i
$689$	−20.5840	+	9.91271i	−0.784186	+	0.377644i
$690$		0			0
$691$	8.05414	+	16.7246i	0.306394	+	0.636233i	0.996136	−	0.0878215i	$-0.0279905\pi$
$691$	8.05414	+	16.7246i	0.306394	+	0.636233i	−0.689742	+	0.724055i	$0.742276\pi$
$692$	9.63585	+	4.64038i	0.366300	+	0.176401i
$693$		0			0
$694$	22.6417	−	10.9037i	0.859467	−	0.413898i
$695$	21.1981	+	16.9049i	0.804090	+	0.641240i
$696$		0			0
$697$	−0.163690	−	0.205261i	−0.00620021	−	0.00777482i
$698$	−5.98848	−	26.2373i	−0.226667	−	0.993095i
$699$		0			0
$700$	7.01128	−	1.89957i	0.265002	−	0.0717969i
$701$	−22.2361	−	17.7327i	−0.839847	−	0.669756i	0.106000	−	0.994366i	$-0.466195\pi$
$701$	−22.2361	−	17.7327i	−0.839847	−	0.669756i	−0.945848	+	0.324610i	$0.894767\pi$
$702$		0			0
$703$	−2.23364	+	0.509813i	−0.0842433	+	0.0192280i
$704$			2.15892i			0.0813672i
$705$		0			0
$706$	1.59714	−	0.364538i	0.0601093	−	0.0137196i
$707$	1.63717	+	40.7250i	0.0615721	+	1.53162i
$708$		0			0
$709$	−8.81551	+	38.6233i	−0.331073	+	1.45053i	0.485983	+	0.873968i	$0.338462\pi$
$709$	−8.81551	+	38.6233i	−0.331073	+	1.45053i	−0.817056	+	0.576558i	$0.804395\pi$
$710$	10.2802	−	12.8910i	0.385809	−	0.483790i
$711$		0			0
$712$	6.48501	+	1.48016i	0.243036	+	0.0554714i
$713$	2.19749	−	9.62783i	0.0822966	−	0.360565i
$714$		0			0
$715$	2.09167	+	9.16422i	0.0782242	+	0.342723i
$716$			6.27937i			0.234671i
$717$		0			0
$718$	2.15481	+	9.44084i	0.0804168	+	0.352329i
$719$	−23.6541	−	11.3912i	−0.882148	−	0.424820i	−0.0627396	−	0.998030i	$-0.519984\pi$
$719$	−23.6541	−	11.3912i	−0.882148	−	0.424820i	−0.819409	+	0.573210i	$0.805698\pi$
$720$		0			0
$721$	−0.319526	+	0.0128451i	−0.0118998	+	0.000478378i
$722$	−7.92250	+	6.31798i	−0.294845	+	0.235131i
$723$		0			0
$724$	8.03542	−	6.40804i	0.298634	−	0.238153i
$725$	−11.3567	+	23.5824i	−0.421777	+	0.875830i
$726$		0			0
$727$	−17.3659	−	36.0607i	−0.644066	−	1.33742i	−0.925832	−	0.377934i	$-0.876635\pi$
$727$	−17.3659	−	36.0607i	−0.644066	−	1.33742i	0.281766	−	0.959483i	$-0.409080\pi$
$728$	5.80133	−	5.02058i	0.215012	−	0.186075i
$729$		0			0
$730$	−9.81794	+	4.72807i	−0.363378	+	0.174994i
$731$	−0.405255	+	1.77554i	−0.0149889	+	0.0656707i
$732$		0			0
$733$	−19.7378	+	15.7404i	−0.729032	+	0.581384i	−0.916094	−	0.400964i	$-0.868675\pi$
$733$	−19.7378	+	15.7404i	−0.729032	+	0.581384i	0.187061	+	0.982348i	$0.440104\pi$
$734$	−36.0528			−1.33073
$735$		0			0
$736$	1.34919			0.0497319
$737$	−2.40835	+	1.92060i	−0.0887128	+	0.0707461i
$738$		0			0
$739$	−9.00127	+	39.4372i	−0.331117	+	1.45072i	0.485854	+	0.874040i	$0.338509\pi$
$739$	−9.00127	+	39.4372i	−0.331117	+	1.45072i	−0.816971	+	0.576679i	$0.804348\pi$
$740$	−0.574216	+	0.276528i	−0.0211086	+	0.0101654i
$741$		0			0
$742$	−0.837303	−	20.8281i	−0.0307383	−	0.764624i
$743$	−1.11411	−	2.31348i	−0.0408729	−	0.0848734i	0.879532	−	0.475839i	$-0.157855\pi$
$743$	−1.11411	−	2.31348i	−0.0408729	−	0.0848734i	−0.920405	+	0.390965i	$0.872141\pi$
$744$		0			0
$745$	−4.15099	+	8.61961i	−0.152080	+	0.315798i
$746$	−20.1719	+	16.0866i	−0.738547	+	0.588972i
$747$		0			0
$748$	−0.345400	+	0.275447i	−0.0126291	+	0.0100714i
$749$	38.7849	−	20.6365i	1.41717	−	0.754041i
$750$		0			0
$751$	−7.83219	−	3.77178i	−0.285801	−	0.137634i	0.285491	−	0.958381i	$-0.407843\pi$
$751$	−7.83219	−	3.77178i	−0.285801	−	0.137634i	−0.571292	+	0.820747i	$0.693558\pi$
$752$	1.02574	+	4.49406i	0.0374049	+	0.163882i
$753$		0			0
$754$			27.6450i			1.00677i
$755$	−1.38628	−	6.07368i	−0.0504518	−	0.221044i
$756$		0			0
$757$	−9.55538	+	41.8649i	−0.347296	+	1.52160i	0.435995	+	0.899949i	$0.356397\pi$
$757$	−9.55538	+	41.8649i	−0.347296	+	1.52160i	−0.783291	+	0.621655i	$0.786460\pi$
$758$	−23.8597	−	5.44582i	−0.866623	−	0.197801i
$759$		0			0
$760$	−5.05294	+	6.33618i	−0.183289	+	0.229837i
$761$	−7.85501	+	34.4150i	−0.284744	+	1.24754i	0.606890	+	0.794786i	$0.292417\pi$
$761$	−7.85501	+	34.4150i	−0.284744	+	1.24754i	−0.891633	+	0.452758i	$0.850440\pi$
$762$		0			0
$763$	−27.8125	+	7.53524i	−1.00688	+	0.272794i
$764$	−17.4874	+	3.99138i	−0.632670	+	0.144403i
$765$		0			0
$766$			14.6064i			0.527750i
$767$	−18.7297	+	4.27494i	−0.676291	+	0.154359i
$768$		0			0
$769$	15.1641	+	12.0929i	0.546831	+	0.436083i	0.857536	−	0.514423i	$-0.171994\pi$
$769$	15.1641	+	12.0929i	0.546831	+	0.436083i	−0.310706	+	0.950506i	$0.600565\pi$
$770$	−8.43128	−	1.57103i	−0.303842	−	0.0566159i
$771$		0			0
$772$	0.911985	+	3.99567i	0.0328231	+	0.143807i
$773$	−33.2681	−	41.7169i	−1.19657	−	1.50045i	−0.818335	−	0.574742i	$-0.805102\pi$
$773$	−33.2681	−	41.7169i	−1.19657	−	1.50045i	−0.378236	−	0.925709i	$-0.623469\pi$
$774$		0			0
$775$	−15.7118	−	12.5297i	−0.564384	−	0.450081i
$776$	16.3068	−	7.85295i	0.585381	−	0.281904i
$777$		0			0
$778$	−16.9344	−	8.15516i	−0.607126	−	0.292377i
$779$	−3.00461	−	6.23914i	−0.107651	−	0.223540i
$780$		0			0
$781$	21.3598	−	10.2864i	0.764316	−	0.368075i
$782$	0.172138	+	0.215854i	0.00615564	+	0.00771892i
$783$		0			0
$784$	2.10043	+	6.67744i	0.0750154	+	0.238480i
$785$			19.9274i			0.711239i
$786$		0			0
$787$	22.0866	+	45.8633i	0.787303	+	1.63485i	0.772545	+	0.634960i	$0.218983\pi$
$787$	22.0866	+	45.8633i	0.787303	+	1.63485i	0.0147578	+	0.999891i	$0.495302\pi$
$788$	14.3993	+	3.28654i	0.512953	+	0.117078i
$789$		0			0
$790$	6.57386	−	13.6508i	0.233887	−	0.485672i
$791$	8.18059	−	4.35270i	0.290868	−	0.154764i
$792$		0			0
$793$	2.12063	−	2.65918i	0.0753056	−	0.0944303i
$794$	6.29693	+	3.03244i	0.223470	+	0.107617i
$795$		0			0
$796$	18.4389	−	4.20856i	0.653550	−	0.149169i
$797$	−7.93893	−	9.95510i	−0.281211	−	0.352628i	0.621086	−	0.783743i	$-0.286692\pi$
$797$	−7.93893	−	9.95510i	−0.281211	−	0.352628i	−0.902297	+	0.431115i	$0.858120\pi$
$798$		0			0
$799$	−0.588125	+	0.737485i	−0.0208064	+	0.0260903i
$800$	1.19125	−	2.47366i	0.0421171	−	0.0874570i
$801$		0			0
$802$	1.79971			0.0635500
$803$	−15.6685			−0.552928
$804$		0			0
$805$	−0.981796	+	5.26904i	−0.0346038	+	0.185709i
$806$	−20.6929	−	4.72303i	−0.728878	−	0.166362i
$807$		0			0
$808$	12.0442	+	9.60489i	0.423712	+	0.337899i
$809$	33.1701	+	26.4523i	1.16620	+	0.930013i	0.998441	−	0.0558151i	$-0.0177757\pi$
$809$	33.1701	+	26.4523i	1.16620	+	0.930013i	0.167758	+	0.985828i	$0.446347\pi$
$810$		0			0
$811$	34.7241	+	7.92555i	1.21933	+	0.278304i	0.783308	−	0.621633i	$-0.213531\pi$
$811$	34.7241	+	7.92555i	1.21933	+	0.278304i	0.436020	+	0.899937i	$0.356388\pi$
$812$	−23.1465	−	10.0222i	−0.812281	−	0.351711i
$813$		0			0
$814$	−0.916393			−0.0321196
$815$	23.6159			0.827228
$816$		0			0
$817$	−20.8426	+	43.2801i	−0.729191	+	1.51418i
$818$	−0.813679	+	1.02032i	−0.0284496	+	0.0356747i
$819$		0			0
$820$	−1.20107	−	1.50610i	−0.0419433	−	0.0525952i
$821$	−14.5214	+	3.31441i	−0.506800	+	0.115674i	−0.468273	−	0.883584i	$-0.655124\pi$
$821$	−14.5214	+	3.31441i	−0.506800	+	0.115674i	−0.0385270	+	0.999258i	$0.512267\pi$
$822$		0			0
$823$	12.7383	+	6.13444i	0.444029	+	0.213833i	0.642519	−	0.766270i	$-0.277889\pi$
$823$	12.7383	+	6.13444i	0.444029	+	0.213833i	−0.198490	+	0.980103i	$0.563604\pi$
$824$	−0.0753593	+	0.0944976i	−0.00262527	+	0.00329198i
$825$		0			0
$826$	3.21084	−	17.2317i	0.111720	−	0.599569i
$827$	6.99442	−	14.5241i	0.243220	−	0.505051i	−0.743246	−	0.669018i	$-0.766715\pi$
$827$	6.99442	−	14.5241i	0.243220	−	0.505051i	0.986466	+	0.163967i	$0.0524291\pi$
$828$		0			0
$829$	31.8673	+	7.27351i	1.10680	+	0.252619i	0.736597	−	0.676332i	$-0.236432\pi$
$829$	31.8673	+	7.27351i	1.10680	+	0.252619i	0.370201	+	0.928952i	$0.379289\pi$
$830$	−4.76279	−	9.89003i	−0.165319	−	0.343288i
$831$		0			0
$832$		−	2.89980i		−	0.100532i
$833$	−0.800322	+	1.18799i	−0.0277295	+	0.0411614i
$834$		0			0
$835$	−2.05134	−	2.57230i	−0.0709895	−	0.0890181i
$836$	−10.4988	+	5.05596i	−0.363109	+	0.174864i
$837$		0			0
$838$	−11.4243	−	23.7227i	−0.394644	−	0.819487i
$839$	11.4472	+	5.51269i	0.395202	+	0.190319i	0.620921	−	0.783873i	$-0.286759\pi$
$839$	11.4472	+	5.51269i	0.395202	+	0.190319i	−0.225719	+	0.974192i	$0.572473\pi$
$840$		0			0
$841$	55.7575	−	26.8514i	1.92267	−	0.925910i
$842$	−6.30443	−	5.02762i	−0.217265	−	0.173263i
$843$		0			0
$844$	−9.29395	−	11.6542i	−0.319911	−	0.401155i
$845$	1.53397	+	6.72074i	0.0527700	+	0.231201i
$846$		0			0
$847$	13.5220	+	9.92179i	0.464623	+	0.340917i
$848$	−6.15977	−	4.91226i	−0.211528	−	0.168688i
$849$		0			0
$850$	0.547742	−	0.125019i	0.0187874	−	0.00428810i
$851$			0.572690i			0.0196316i
$852$		0			0
$853$	−43.9508	+	10.0315i	−1.50485	+	0.343472i	−0.893924	−	0.448218i	$-0.852059\pi$
$853$	−43.9508	+	10.0315i	−1.50485	+	0.343472i	−0.610924	+	0.791690i	$0.709202\pi$
$854$	1.45767	+	2.73959i	0.0498804	+	0.0937468i
$855$		0			0
$856$	3.69501	−	16.1889i	0.126293	−	0.553325i
$857$	−2.57480	+	3.22870i	−0.0879534	+	0.110290i	−0.823861	−	0.566792i	$-0.808184\pi$
$857$	−2.57480	+	3.22870i	−0.0879534	+	0.110290i	0.735908	+	0.677082i	$0.236756\pi$
$858$		0			0
$859$	22.1087	+	5.04617i	0.754339	+	0.172173i	0.582364	−	0.812928i	$-0.302128\pi$
$859$	22.1087	+	5.04617i	0.754339	+	0.172173i	0.171975	+	0.985101i	$0.444985\pi$
$860$	−2.97355	+	13.0280i	−0.101397	+	0.444250i
$861$		0			0
$862$	4.61660	+	20.2267i	0.157242	+	0.688923i
$863$		−	34.9443i		−	1.18952i	−0.803905	−	0.594758i	$-0.797248\pi$
$863$		−	34.9443i		−	1.18952i	0.803905	−	0.594758i	$-0.202752\pi$
$864$		0			0
$865$	3.57331	+	15.6557i	0.121496	+	0.532310i
$866$	−6.93198	−	3.33827i	−0.235558	−	0.113439i
$867$		0			0
$868$	11.4563	−	15.6134i	0.388854	−	0.529954i
$869$	17.0324	−	13.5829i	0.577785	−	0.460768i
$870$		0			0
$871$	3.23483	−	2.57969i	0.109608	−	0.0874096i
$872$	−4.72548	+	9.81255i	−0.160025	+	0.332295i
$873$		0			0
$874$	3.15967	+	6.56112i	0.106877	+	0.221933i
$875$	24.8078	+	18.2027i	0.838657	+	0.615364i
$876$		0			0
$877$	−8.46027	+	4.07425i	−0.285683	+	0.137578i	−0.571238	−	0.820785i	$-0.693537\pi$
$877$	−8.46027	+	4.07425i	−0.285683	+	0.137578i	0.285554	+	0.958362i	$0.407822\pi$
$878$	8.47802	−	37.1446i	0.286119	−	1.25357i
$879$		0			0
$880$	−2.53436	+	2.02109i	−0.0854334	+	0.0681308i
$881$	14.3251			0.482624			0.241312	−	0.970448i	$-0.422422\pi$
$881$	14.3251			0.482624			0.241312	+	0.970448i	$0.422422\pi$
$882$		0			0
$883$	−18.7968			−0.632564			−0.316282	−	0.948665i	$-0.602435\pi$
$883$	−18.7968			−0.632564			−0.316282	+	0.948665i	$0.602435\pi$
$884$	0.463932	−	0.369973i	0.0156037	−	0.0124435i
$885$		0			0
$886$	−3.68692	+	16.1535i	−0.123865	+	0.542686i
$887$	−9.47248	+	4.56170i	−0.318055	+	0.153167i	−0.586099	−	0.810240i	$-0.699337\pi$
$887$	−9.47248	+	4.56170i	−0.318055	+	0.153167i	0.268044	+	0.963407i	$0.413623\pi$
$888$		0			0
$889$	−7.32720	−	1.36530i	−0.245746	−	0.0457907i
$890$	4.33343	+	8.99846i	0.145257	+	0.301629i
$891$		0			0
$892$	6.12515	−	12.7190i	0.205085	−	0.425864i
$893$	−19.4524	+	15.5128i	−0.650951	+	0.519116i
$894$		0			0
$895$	−7.37138	+	5.87848i	−0.246398	+	0.196496i
$896$	2.42793	+	1.05127i	0.0811113	+	0.0351205i
$897$		0			0
$898$	16.3828	+	7.88953i	0.546700	+	0.263277i
$899$	15.5275	+	68.0305i	0.517872	+	2.26894i
$900$		0			0
$901$		−	1.61222i		−	0.0537109i
$902$	−0.616349	−	2.70040i	−0.0205222	−	0.0899136i
$903$		0			0
$904$	0.779359	−	3.41459i	0.0259211	−	0.113568i
$905$	15.0449	+	3.43389i	0.500108	+	0.114146i
$906$		0			0
$907$	−20.5577	+	25.7785i	−0.682607	+	0.855962i	−0.995591	−	0.0937965i	$-0.970100\pi$
$907$	−20.5577	+	25.7785i	−0.682607	+	0.855962i	0.312985	+	0.949758i	$0.398671\pi$
$908$	−3.54475	+	15.5306i	−0.117637	+	0.515399i
$909$		0			0
$910$	11.3247	+	2.11016i	0.375409	+	0.0699511i
$911$	−33.9627	+	7.75176i	−1.12523	+	0.256827i	−0.744346	−	0.667794i	$-0.767239\pi$
$911$	−33.9627	+	7.75176i	−1.12523	+	0.256827i	−0.380888	+	0.924621i	$0.624382\pi$
$912$		0			0
$913$		−	15.7835i		−	0.522358i
$914$	−28.6429	+	6.53755i	−0.947422	+	0.216243i
$915$		0			0
$916$	−12.7368	−	10.1572i	−0.420835	−	0.335605i
$917$	11.3507	−	9.82308i	0.374832	−	0.324387i
$918$		0			0
$919$	1.75297	+	7.68026i	0.0578252	+	0.253349i	0.995576	−	0.0939603i	$-0.0299527\pi$
$919$	1.75297	+	7.68026i	0.0578252	+	0.253349i	−0.937751	+	0.347309i	$0.887096\pi$
$920$	1.26306	+	1.58382i	0.0416417	+	0.0522171i
$921$		0			0
$922$	2.64486	+	2.10921i	0.0871039	+	0.0694630i
$923$	−28.6899	+	13.8163i	−0.944341	+	0.454771i
$924$		0			0
$925$	1.04999	+	0.505649i	0.0345235	+	0.0166256i
$926$	5.85101	+	12.1497i	0.192276	+	0.399265i
$927$		0			0
$928$	−8.58932	+	4.13640i	−0.281958	+	0.135784i
$929$	−3.25281	−	4.07890i	−0.106721	−	0.133824i	0.725602	−	0.688114i	$-0.241561\pi$
$929$	−3.25281	−	4.07890i	−0.106721	−	0.133824i	−0.832324	+	0.554290i	$0.812990\pi$
$930$		0			0
$931$	−27.5534	+	25.8523i	−0.903026	+	0.847274i
$932$			7.91723i			0.259338i
$933$		0			0
$934$	1.75607	+	3.64651i	0.0574602	+	0.119317i
$935$	−0.646698	−	0.147605i	−0.0211493	−	0.00482719i
$936$		0			0
$937$	14.3858	−	29.8725i	0.469964	−	0.975891i	−0.522418	−	0.852690i	$-0.674970\pi$
$937$	14.3858	−	29.8725i	0.469964	−	0.975891i	0.992382	−	0.123201i	$-0.0393160\pi$
$938$	0.987179	+	3.64367i	0.0322325	+	0.118970i
$939$		0			0
$940$	−4.31535	+	5.41128i	−0.140751	+	0.176496i
$941$	46.1563	+	22.2277i	1.50465	+	0.724602i	0.991058	−	0.133431i	$-0.0425994\pi$
$941$	46.1563	+	22.2277i	1.50465	+	0.724602i	0.513594	+	0.858033i	$0.328314\pi$
$942$		0			0
$943$	−1.68759	+	0.385181i	−0.0549554	+	0.0125432i
$944$	−4.13067	−	5.17970i	−0.134442	−	0.168585i
$945$		0			0
$946$	−11.9798	+	15.0222i	−0.389497	+	0.488414i
$947$	−9.74277	+	20.2311i	−0.316598	+	0.657422i	−0.997164	−	0.0752651i	$-0.976020\pi$
$947$	−9.74277	+	20.2311i	−0.316598	+	0.657422i	0.680566	+	0.732687i	$0.261734\pi$
$948$		0			0
$949$	21.0455			0.683164
$950$	14.8192			0.480798
$951$		0			0
$952$	0.141579	+	0.522566i	0.00458859	+	0.0169365i
$953$	−37.7369	−	8.61320i	−1.22242	−	0.279009i	−0.437848	−	0.899049i	$-0.644259\pi$
$953$	−37.7369	−	8.61320i	−1.22242	−	0.279009i	−0.784570	+	0.620040i	$0.787116\pi$
$954$		0			0
$955$	−21.0564	−	16.7919i	−0.681370	−	0.543375i
$956$	−15.9320	−	12.7053i	−0.515277	−	0.410919i
$957$		0			0
$958$	−36.6241	−	8.35921i	−1.18327	−	0.270074i
$959$	−9.49721	−	10.9741i	−0.306681	−	0.354373i
$960$		0			0
$961$	−22.5753			−0.728235
$962$	1.23087			0.0396849
$963$		0			0
$964$	−2.74301	+	5.69592i	−0.0883465	+	0.183453i
$965$	−3.83677	+	4.81116i	−0.123510	+	0.154877i
$966$		0			0
$967$	−1.35041	−	1.69337i	−0.0434264	−	0.0544550i	0.759644	−	0.650339i	$-0.225373\pi$
$967$	−1.35041	−	1.69337i	−0.0434264	−	0.0544550i	−0.803070	+	0.595884i	$0.796802\pi$
$968$	6.18015	−	1.41058i	0.198637	−	0.0453377i
$969$		0			0
$970$	24.4844	+	11.7911i	0.786146	+	0.378588i
$971$	4.67261	−	5.85927i	0.149951	−	0.188033i	−0.701182	−	0.712982i	$-0.747344\pi$
$971$	4.67261	−	5.85927i	0.149951	−	0.188033i	0.851134	+	0.524949i	$0.175916\pi$
$972$		0			0
$973$	47.7378	−	1.91909i	1.53040	−	0.0615231i
$974$	−11.9012	+	24.7132i	−0.381340	+	0.791860i
$975$		0			0
$976$	1.14351	+	0.260999i	0.0366028	+	0.00835436i
$977$	−18.1863	−	37.7643i	−0.581832	−	1.20819i	−0.959359	−	0.282188i	$-0.908940\pi$
$977$	−18.1863	−	37.7643i	−0.581832	−	1.20819i	0.377527	−	0.925998i	$-0.376774\pi$
$978$		0			0
$979$			14.3607i			0.458968i
$980$	−5.87234	+	8.71685i	−0.187585	+	0.278449i
$981$		0			0
$982$	−5.02920	−	6.30642i	−0.160488	−	0.201246i
$983$	−24.5500	+	11.8227i	−0.783024	+	0.377084i	−0.782289	−	0.622915i	$-0.785948\pi$
$983$	−24.5500	+	11.8227i	−0.783024	+	0.377084i	−0.000734510		1.00000i	$0.500234\pi$
$984$		0			0
$985$	9.62191	+	19.9801i	0.306579	+	0.636619i
$986$	−1.75765	−	0.846439i	−0.0559749	−	0.0269561i
$987$		0			0
$988$	14.1017	−	6.79102i	0.448635	−	0.216051i
$989$	9.38796	+	7.48665i	0.298520	+	0.238062i
$990$		0			0
$991$	−11.0028	−	13.7971i	−0.349515	−	0.438279i	0.575734	−	0.817637i	$-0.304716\pi$
$991$	−11.0028	−	13.7971i	−0.349515	−	0.438279i	−0.925250	+	0.379358i	$0.876145\pi$
$992$	−1.62874	−	7.13600i	−0.0517127	−	0.226568i
$993$		0			0
$994$	−1.16703	−	29.0303i	−0.0370161	−	0.920784i
$995$	22.2022	+	17.7057i	0.703857	+	0.561307i
$996$		0			0
$997$	27.5656	−	6.29167i	0.873012	−	0.199259i	0.237535	−	0.971379i	$-0.423661\pi$
$997$	27.5656	−	6.29167i	0.873012	−	0.199259i	0.635477	+	0.772120i	$0.280803\pi$
$998$		−	3.30200i		−	0.104523i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.v.a.629.14	yes	96
3.2	odd	2	inner	882.2.v.a.629.3	yes	96
49.6	odd	14	inner	882.2.v.a.251.3	✓	96
147.104	even	14	inner	882.2.v.a.251.14	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.v.a.251.3	✓	96	49.6	odd	14	inner
882.2.v.a.251.14	yes	96	147.104	even	14	inner
882.2.v.a.629.3	yes	96	3.2	odd	2	inner
882.2.v.a.629.14	yes	96	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.v (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.781831 - 0.623490i) q^{2} +(0.222521 - 0.974928i) q^{4} +(1.35279 - 0.651468i) q^{5} +(1.05127 - 2.42793i) q^{7} +(-0.433884 - 0.900969i) q^{8} +O(q^{10})\)	\(q+(0.781831 - 0.623490i) q^{2} +(0.222521 - 0.974928i) q^{4} +(1.35279 - 0.651468i) q^{5} +(1.05127 - 2.42793i) q^{7} +(-0.433884 - 0.900969i) q^{8} +(0.651468 - 1.35279i) q^{10} +(1.68791 - 1.34606i) q^{11} +(-2.26715 + 1.80799i) q^{13} +(-0.691870 - 2.55369i) q^{14} +(-0.900969 - 0.433884i) q^{16} +(-0.0455349 - 0.199501i) q^{17} -5.39752i q^{19} +(-0.334111 - 1.46384i) q^{20} +(0.480404 - 2.10479i) q^{22} +(-1.31536 - 0.300223i) q^{23} +(-1.71182 + 2.14656i) q^{25} +(-0.645265 + 2.82709i) q^{26} +(-2.13312 - 1.56518i) q^{28} +(9.29440 - 2.12139i) q^{29} +7.31951i q^{31} +(-0.974928 + 0.222521i) q^{32} +(-0.159988 - 0.127586i) q^{34} +(-0.159570 - 3.96934i) q^{35} +(-0.0944532 - 0.413827i) q^{37} +(-3.36530 - 4.21995i) q^{38} +(-1.17391 - 0.936158i) q^{40} +(1.15593 - 0.556665i) q^{41} +(-8.01852 - 3.86152i) q^{43} +(-0.936719 - 1.94512i) q^{44} +(-1.21558 + 0.585392i) q^{46} +(-2.87406 - 3.60396i) q^{47} +(-4.78966 - 5.10482i) q^{49} +2.74555i q^{50} +(1.25817 + 2.61263i) q^{52} +(7.68111 + 1.75316i) q^{53} +(1.40647 - 2.92056i) q^{55} +(-2.64362 + 0.106275i) q^{56} +(5.94399 - 7.45353i) q^{58} +(5.96899 + 2.87452i) q^{59} +(-1.14351 + 0.260999i) q^{61} +(4.56364 + 5.72263i) q^{62} +(-0.623490 + 0.781831i) q^{64} +(-1.88912 + 3.92281i) q^{65} -1.42683 q^{67} -0.204632 q^{68} +(-2.59960 - 3.00386i) q^{70} +(10.7059 + 2.44356i) q^{71} +(-5.67419 - 4.52502i) q^{73} +(-0.331863 - 0.264652i) q^{74} +(-5.26220 - 1.20106i) q^{76} +(-1.49369 - 5.51320i) q^{77} +10.0908 q^{79} -1.50148 q^{80} +(0.556665 - 1.15593i) q^{82} +(4.55824 - 5.71585i) q^{83} +(-0.191568 - 0.240219i) q^{85} +(-8.67675 + 1.98041i) q^{86} +(-1.94512 - 0.936719i) q^{88} +(-4.14732 + 5.20058i) q^{89} +(2.00628 + 7.40517i) q^{91} +(-0.585392 + 1.21558i) q^{92} +(-4.49406 - 1.02574i) q^{94} +(-3.51632 - 7.30170i) q^{95} +18.0992i q^{97} +(-6.92751 - 1.00481i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 16 q^{4}+O(q^{10}) \) 96 * q + 16 * q^4	\( 96 q + 16 q^{4} - 16 q^{16} + 20 q^{22} - 8 q^{25} + 76 q^{37} + 28 q^{40} - 8 q^{43} + 112 q^{49} + 28 q^{52} + 28 q^{55} + 20 q^{58} + 84 q^{61} + 16 q^{64} - 8 q^{67} + 28 q^{70} + 112 q^{85} + 8 q^{88} - 56 q^{91} - 56 q^{94}+O(q^{100}) \) 96 * q + 16 * q^4 - 16 * q^16 + 20 * q^22 - 8 * q^25 + 76 * q^37 + 28 * q^40 - 8 * q^43 + 112 * q^49 + 28 * q^52 + 28 * q^55 + 20 * q^58 + 84 * q^61 + 16 * q^64 - 8 * q^67 + 28 * q^70 + 112 * q^85 + 8 * q^88 - 56 * q^91 - 56 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more