LMFDB - Embedded newform 441.2.w.a.188.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(62,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 11]))

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

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

chi := DirichletCharacter("441.62");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.w (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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			188.17
Character	$\chi$	$=$	441.188
Dual form			441.2.w.a.251.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.61627 - 1.28893i) q^{2} +(0.505936 - 2.21665i) q^{4} +(3.93097 - 1.89305i) q^{5} +(-2.02319 - 1.70491i) q^{7} +(-0.245458 - 0.509698i) q^{8} +O(q^{10})$	\(q+(1.61627 - 1.28893i) q^{2} +(0.505936 - 2.21665i) q^{4} +(3.93097 - 1.89305i) q^{5} +(-2.02319 - 1.70491i) q^{7} +(-0.245458 - 0.509698i) q^{8} +(3.91348 - 8.12642i) q^{10} +(-3.17960 + 2.53564i) q^{11} +(-1.07613 + 0.858184i) q^{13} +(-5.46752 - 0.147843i) q^{14} +(3.04329 + 1.46557i) q^{16} +(-0.000551178 - 0.00241487i) q^{17} +4.84659i q^{19} +(-2.20742 - 9.67134i) q^{20} +(-1.87081 + 8.19655i) q^{22} +(-1.08174 - 0.246900i) q^{23} +(8.75139 - 10.9739i) q^{25} +(-0.633172 + 2.77411i) q^{26} +(-4.80279 + 3.62212i) q^{28} +(-1.58525 + 0.361823i) q^{29} +3.23885i q^{31} +(7.91087 - 1.80561i) q^{32} +(-0.00400344 - 0.00319264i) q^{34} +(-11.1806 - 2.87194i) q^{35} +(-2.10701 - 9.23141i) q^{37} +(6.24691 + 7.83338i) q^{38} +(-1.92977 - 1.53894i) q^{40} +(-7.61140 + 3.66546i) q^{41} +(-0.421609 - 0.203036i) q^{43} +(4.01196 + 8.33093i) q^{44} +(-2.06662 + 0.995232i) q^{46} +(1.51205 + 1.89605i) q^{47} +(1.18657 + 6.89870i) q^{49} -29.0167i q^{50} +(1.35784 + 2.81959i) q^{52} +(-6.81397 - 1.55524i) q^{53} +(-7.69878 + 15.9867i) q^{55} +(-0.372382 + 1.44970i) q^{56} +(-2.09582 + 2.62808i) q^{58} +(7.40362 + 3.56539i) q^{59} +(14.5677 - 3.32497i) q^{61} +(4.17465 + 5.23485i) q^{62} +(6.24673 - 7.83315i) q^{64} +(-2.60564 + 5.41066i) q^{65} +11.7825 q^{67} -0.00563178 q^{68} +(-21.7725 + 9.76913i) q^{70} +(4.38641 + 1.00117i) q^{71} +(-4.34434 - 3.46449i) q^{73} +(-15.3041 - 12.2046i) q^{74} +(10.7432 + 2.45206i) q^{76} +(10.7560 + 0.290843i) q^{77} -10.0580 q^{79} +14.7375 q^{80} +(-7.57754 + 15.7349i) q^{82} +(-10.4803 + 13.1419i) q^{83} +(-0.00673813 - 0.00844935i) q^{85} +(-0.943132 + 0.215264i) q^{86} +(2.07287 + 0.998241i) q^{88} +(-3.92695 + 4.92424i) q^{89} +(3.64033 + 0.0984354i) q^{91} +(-1.09458 + 2.27293i) q^{92} +(4.88775 + 1.11560i) q^{94} +(9.17485 + 19.0518i) q^{95} -2.91734i q^{97} +(10.8097 + 9.62073i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 24 q^{4}+O(q^{10}) $ 120 * q + 24 * q^4	$ 120 q + 24 q^{4} - 32 q^{16} - 44 q^{22} - 4 q^{25} - 56 q^{28} + 112 q^{34} - 76 q^{37} + 28 q^{40} + 8 q^{43} - 40 q^{46} - 84 q^{49} - 140 q^{52} + 12 q^{58} - 84 q^{61} + 24 q^{64} + 16 q^{67} + 112 q^{70} - 84 q^{76} - 24 q^{79} + 140 q^{82} - 96 q^{85} - 24 q^{88} - 112 q^{91} - 112 q^{94}+O(q^{100}) $ 120 * q + 24 * q^4 - 32 * q^16 - 44 * q^22 - 4 * q^25 - 56 * q^28 + 112 * q^34 - 76 * q^37 + 28 * q^40 + 8 * q^43 - 40 * q^46 - 84 * q^49 - 140 * q^52 + 12 * q^58 - 84 * q^61 + 24 * q^64 + 16 * q^67 + 112 * q^70 - 84 * q^76 - 24 * q^79 + 140 * q^82 - 96 * q^85 - 24 * q^88 - 112 * q^91 - 112 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{5}{14}\right)$	$-1$

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 $

$2$	1.61627	−	1.28893i	1.14287	−	0.911411i	0.145911	−	0.989298i	$-0.453389\pi$
$2$	1.61627	−	1.28893i	1.14287	−	0.911411i	0.996962	+	0.0778871i	$0.0248174\pi$
$3$		0			0
$3$		0			0
$4$	0.505936	−	2.21665i	0.252968	−	1.10832i
$5$	3.93097	−	1.89305i	1.75798	−	0.846599i	0.783741	−	0.621088i	$-0.213309\pi$
$5$	3.93097	−	1.89305i	1.75798	−	0.846599i	0.974241	−	0.225511i	$-0.0724052\pi$
$6$		0			0
$7$	−2.02319	−	1.70491i	−0.764693	−	0.644395i
$7$	−2.02319	−	1.70491i	−0.764693	−	0.644395i
$8$	−0.245458	−	0.509698i	−0.0867824	−	0.180206i
$9$		0			0
$10$	3.91348	−	8.12642i	1.23755	−	2.56980i
$11$	−3.17960	+	2.53564i	−0.958684	+	0.764525i	−0.971902	−	0.235387i	$-0.924364\pi$
$11$	−3.17960	+	2.53564i	−0.958684	+	0.764525i	0.0132172	+	0.999913i	$0.495793\pi$
$12$		0			0
$13$	−1.07613	+	0.858184i	−0.298464	+	0.238017i	−0.761259	−	0.648448i	$-0.775418\pi$
$13$	−1.07613	+	0.858184i	−0.298464	+	0.238017i	0.462794	+	0.886466i	$0.346847\pi$
$14$	−5.46752	−	0.147843i	−1.46126	−	0.0395126i
$15$		0			0
$16$	3.04329	+	1.46557i	0.760824	+	0.366393i
$17$	−0.000551178	−	0.00241487i	−0.000133680	−	0.000585691i	0.974861	−	0.222814i	$-0.0715242\pi$
$17$	−0.000551178	−	0.00241487i	−0.000133680	−	0.000585691i	−0.974995	+	0.222228i	$0.928667\pi$
$18$		0			0
$19$			4.84659i			1.11188i	0.831221	+	0.555942i	$0.187642\pi$
$19$			4.84659i			1.11188i	−0.831221	+	0.555942i	$0.812358\pi$
$20$	−2.20742	−	9.67134i	−0.493594	−	2.16258i
$21$		0			0
$22$	−1.87081	+	8.19655i	−0.398858	+	1.74751i
$23$	−1.08174	−	0.246900i	−0.225559	−	0.0514823i	0.108248	−	0.994124i	$-0.465476\pi$
$23$	−1.08174	−	0.246900i	−0.225559	−	0.0514823i	−0.333806	+	0.942642i	$0.608333\pi$
$24$		0			0
$25$	8.75139	−	10.9739i	1.75028	−	2.19478i
$26$	−0.633172	+	2.77411i	−0.124175	+	0.544047i
$27$		0			0
$28$	−4.80279	+	3.62212i	−0.907642	+	0.684517i
$29$	−1.58525	+	0.361823i	−0.294374	+	0.0671889i	−0.367157	−	0.930159i	$-0.619669\pi$
$29$	−1.58525	+	0.361823i	−0.294374	+	0.0671889i	0.0727835	+	0.997348i	$0.476812\pi$
$30$		0			0
$31$			3.23885i			0.581715i	0.956766	+	0.290857i	$0.0939405\pi$
$31$			3.23885i			0.581715i	−0.956766	+	0.290857i	$0.906059\pi$
$32$	7.91087	−	1.80561i	1.39846	−	0.319189i
$33$		0			0
$34$	−0.00400344	−	0.00319264i	−0.000686585	−	0.000547533i
$35$	−11.1806	−	2.87194i	−1.88986	−	0.485446i
$36$		0			0
$37$	−2.10701	−	9.23141i	−0.346390	−	1.51764i	−0.785306	−	0.619107i	$-0.787495\pi$
$37$	−2.10701	−	9.23141i	−0.346390	−	1.51764i	0.438916	−	0.898528i	$-0.355363\pi$
$38$	6.24691	+	7.83338i	1.01338	+	1.27074i
$39$		0			0
$40$	−1.92977	−	1.53894i	−0.305124	−	0.243328i
$41$	−7.61140	+	3.66546i	−1.18870	+	0.572449i	−0.920435	−	0.390896i	$-0.872165\pi$
$41$	−7.61140	+	3.66546i	−1.18870	+	0.572449i	−0.268267	+	0.963345i	$0.586451\pi$
$42$		0			0
$43$	−0.421609	−	0.203036i	−0.0642948	−	0.0309627i	0.401460	−	0.915877i	$-0.368503\pi$
$43$	−0.421609	−	0.203036i	−0.0642948	−	0.0309627i	−0.465755	+	0.884914i	$0.654217\pi$
$44$	4.01196	+	8.33093i	0.604826	+	1.25593i
$45$		0			0
$46$	−2.06662	+	0.995232i	−0.304706	+	0.146739i
$47$	1.51205	+	1.89605i	0.220555	+	0.276568i	0.879783	−	0.475376i	$-0.157688\pi$
$47$	1.51205	+	1.89605i	0.220555	+	0.276568i	−0.659227	+	0.751944i	$0.729117\pi$
$48$		0			0
$49$	1.18657	+	6.89870i	0.169510	+	0.985529i
$50$		−	29.0167i		−	4.10358i
$51$		0			0
$52$	1.35784	+	2.81959i	0.188299	+	0.391006i
$53$	−6.81397	−	1.55524i	−0.935970	−	0.213629i	−0.272777	−	0.962077i	$-0.587942\pi$
$53$	−6.81397	−	1.55524i	−0.935970	−	0.213629i	−0.663193	+	0.748448i	$0.730799\pi$
$54$		0			0
$55$	−7.69878	+	15.9867i	−1.03810	+	2.15564i
$56$	−0.372382	+	1.44970i	−0.0497617	+	0.193724i
$57$		0			0
$58$	−2.09582	+	2.62808i	−0.275195	+	0.345084i
$59$	7.40362	+	3.56539i	0.963869	+	0.464175i	0.848528	−	0.529151i	$-0.177490\pi$
$59$	7.40362	+	3.56539i	0.963869	+	0.464175i	0.115341	+	0.993326i	$0.463204\pi$
$60$		0			0
$61$	14.5677	−	3.32497i	1.86520	−	0.425719i	0.867742	−	0.497015i	$-0.165571\pi$
$61$	14.5677	−	3.32497i	1.86520	−	0.425719i	0.997455	+	0.0712956i	$0.0227134\pi$
$62$	4.17465	+	5.23485i	0.530181	+	0.664826i
$63$		0			0
$64$	6.24673	−	7.83315i	0.780841	−	0.979144i
$65$	−2.60564	+	5.41066i	−0.323189	+	0.671110i
$66$		0			0
$67$	11.7825			1.43946			0.719731	−	0.694253i	$-0.244265\pi$
$67$	11.7825			1.43946			0.719731	+	0.694253i	$0.244265\pi$
$68$	−0.00563178			−0.000682953
$69$		0			0
$70$	−21.7725	+	9.76913i	−2.60231	+	1.16763i
$71$	4.38641	+	1.00117i	0.520571	+	0.118817i	0.474729	−	0.880132i	$-0.342546\pi$
$71$	4.38641	+	1.00117i	0.520571	+	0.118817i	0.0458416	+	0.998949i	$0.485403\pi$
$72$		0			0
$73$	−4.34434	−	3.46449i	−0.508466	−	0.405488i	0.335372	−	0.942086i	$-0.391138\pi$
$73$	−4.34434	−	3.46449i	−0.508466	−	0.405488i	−0.843838	+	0.536597i	$0.819709\pi$
$74$	−15.3041	−	12.2046i	−1.77907	−	1.41876i
$75$		0			0
$76$	10.7432	+	2.45206i	1.23233	+	0.281271i
$77$	10.7560	+	0.290843i	1.22576	+	0.0331447i
$78$		0			0
$79$	−10.0580			−1.13162			−0.565809	−	0.824536i	$-0.691436\pi$
$79$	−10.0580			−1.13162			−0.565809	+	0.824536i	$0.691436\pi$
$80$	14.7375			1.64770
$81$		0			0
$82$	−7.57754	+	15.7349i	−0.836799	+	1.73763i
$83$	−10.4803	+	13.1419i	−1.15036	+	1.44251i	−0.273433	+	0.961891i	$0.588159\pi$
$83$	−10.4803	+	13.1419i	−1.15036	+	1.44251i	−0.876930	+	0.480618i	$0.840412\pi$
$84$		0			0
$85$	−0.00673813	−	0.00844935i	−0.000730853	−	0.000916461i
$86$	−0.943132	+	0.215264i	−0.101701	+	0.0232125i
$87$		0			0
$88$	2.07287	+	0.998241i	0.220969	+	0.106413i
$89$	−3.92695	+	4.92424i	−0.416256	+	0.521968i	−0.945113	−	0.326742i	$-0.894049\pi$
$89$	−3.92695	+	4.92424i	−0.416256	+	0.521968i	0.528858	+	0.848710i	$0.322620\pi$
$90$		0			0
$91$	3.64033	+	0.0984354i	0.381611	+	0.0103188i
$92$	−1.09458	+	2.27293i	−0.114118	+	0.236969i
$93$		0			0
$94$	4.88775	+	1.11560i	0.504133	+	0.115065i
$95$	9.17485	+	19.0518i	0.941320	+	1.95467i
$96$		0			0
$97$		−	2.91734i		−	0.296211i	−0.988972	−	0.148106i	$-0.952682\pi$
$97$		−	2.91734i		−	0.296211i	0.988972	−	0.148106i	$-0.0473176\pi$
$98$	10.8097	+	9.62073i	1.09195	+	0.971841i
$99$		0			0
$100$	−19.8976	−	24.9509i	−1.98976	−	2.49509i
$101$	−8.25227	+	3.97408i	−0.821131	+	0.395436i	−0.796781	−	0.604268i	$-0.793466\pi$
$101$	−8.25227	+	3.97408i	−0.821131	+	0.395436i	−0.0243497	+	0.999704i	$0.507752\pi$
$102$		0			0
$103$	−1.26385	−	2.62441i	−0.124531	−	0.258590i	0.829378	−	0.558688i	$-0.188695\pi$
$103$	−1.26385	−	2.62441i	−0.124531	−	0.258590i	−0.953909	+	0.300098i	$0.902981\pi$
$104$	0.701559	+	0.337853i	0.0687935	+	0.0331292i
$105$		0			0
$106$	−13.0178	+	6.26903i	−1.26440	+	0.608902i
$107$	−11.1132	−	8.86244i	−1.07435	−	0.856765i	−0.0841534	−	0.996453i	$-0.526819\pi$
$107$	−11.1132	−	8.86244i	−1.07435	−	0.856765i	−0.990196	+	0.139688i	$0.955390\pi$
$108$		0			0
$109$	−4.95739	−	6.21637i	−0.474831	−	0.595420i	0.485515	−	0.874228i	$-0.338632\pi$
$109$	−4.95739	−	6.21637i	−0.474831	−	0.595420i	−0.960347	+	0.278808i	$0.910061\pi$
$110$	8.16242	+	35.7619i	0.778256	+	3.40976i
$111$		0			0
$112$	−3.65848	−	8.15367i	−0.345694	−	0.770449i
$113$	11.6381	+	9.28105i	1.09482	+	0.873088i	0.992570	−	0.121671i	$-0.0388254\pi$
$113$	11.6381	+	9.28105i	1.09482	+	0.873088i	0.102247	+	0.994759i	$0.467397\pi$
$114$		0			0
$115$	−4.71969	+	1.07724i	−0.440113	+	0.100453i
$116$			3.69701i			0.343259i
$117$		0			0
$118$	16.5618	−	3.78011i	1.52463	−	0.347988i
$119$	−0.00300199	+	0.00582544i	−0.000275192	+	0.000534017i
$120$		0			0
$121$	1.23262	−	5.40044i	0.112056	−	0.490949i
$122$	19.2596	−	24.1507i	1.74368	−	2.18650i
$123$		0			0
$124$	7.17940	+	1.63865i	0.644729	+	0.147155i
$125$	8.77291	−	38.4366i	0.784673	−	3.43788i
$126$		0			0
$127$	−3.67465	−	16.0997i	−0.326073	−	1.42862i	−0.826547	−	0.562867i	$-0.809698\pi$
$127$	−3.67465	−	16.0997i	−0.326073	−	1.42862i	0.500474	−	0.865751i	$-0.333159\pi$
$128$		−	4.48341i		−	0.396282i
$129$		0			0
$130$	2.76256	+	12.1035i	0.242292	+	1.06155i
$131$	−3.65928	−	1.76222i	−0.319713	−	0.153966i	0.267143	−	0.963657i	$-0.413920\pi$
$131$	−3.65928	−	1.76222i	−0.319713	−	0.153966i	−0.586856	+	0.809691i	$0.699635\pi$
$132$		0			0
$133$	8.26300	−	9.80556i	0.716493	−	0.850250i
$134$	19.0437	−	15.1868i	1.64512	−	1.31194i
$135$		0			0
$136$	−0.00109556		0.000873682i	−9.39437e−5		7.49176e-5i
$137$	2.27979	−	4.73403i	0.194775	−	0.404455i	−0.780592	−	0.625041i	$-0.785082\pi$
$137$	2.27979	−	4.73403i	0.194775	−	0.404455i	0.975368	+	0.220585i	$0.0707967\pi$
$138$		0			0
$139$	−2.09638	−	4.35318i	−0.177813	−	0.369232i	0.792945	−	0.609293i	$-0.208547\pi$
$139$	−2.09638	−	4.35318i	−0.177813	−	0.369232i	−0.970758	+	0.240061i	$0.922832\pi$
$140$	−12.0227	+	23.3304i	−1.01611	+	1.97178i
$141$		0			0
$142$	8.38004	−	4.03562i	0.703238	−	0.338661i
$143$	1.24561	−	5.45736i	0.104163	−	0.456367i
$144$		0			0
$145$	−5.54662	+	4.42328i	−0.460622	+	0.367334i
$146$	−11.4871			−0.950679
$147$		0			0
$148$	−21.5288			−1.76966
$149$	8.30896	−	6.62617i	0.680696	−	0.542837i	−0.220964	−	0.975282i	$-0.570920\pi$
$149$	8.30896	−	6.62617i	0.680696	−	0.542837i	0.901660	+	0.432445i	$0.142349\pi$
$150$		0			0
$151$	1.62392	−	7.11488i	0.132153	−	0.579001i	−0.864877	−	0.501984i	$-0.832604\pi$
$151$	1.62392	−	7.11488i	0.132153	−	0.579001i	0.997030	−	0.0770162i	$-0.0245393\pi$
$152$	2.47030	−	1.18963i	0.200368	−	0.0964920i
$153$		0			0
$154$	17.7594	−	13.3936i	1.43109	−	1.07929i
$155$	6.13132	+	12.7318i	0.492479	+	1.02264i
$156$		0			0
$157$	−5.67493	+	11.7841i	−0.452909	+	0.940475i	0.542065	+	0.840337i	$0.317643\pi$
$157$	−5.67493	+	11.7841i	−0.452909	+	0.940475i	−0.994974	+	0.100138i	$0.968071\pi$
$158$	−16.2565	+	12.9641i	−1.29330	+	1.03137i
$159$		0			0
$160$	27.6793	−	22.0735i	2.18824	−	1.74506i
$161$	1.76762	+	2.34380i	0.139308	+	0.184717i
$162$		0			0
$163$	−0.348080	−	0.167627i	−0.0272638	−	0.0131295i	0.420202	−	0.907431i	$-0.361959\pi$
$163$	−0.348080	−	0.167627i	−0.0272638	−	0.0131295i	−0.447466	+	0.894301i	$0.647673\pi$
$164$	4.27416	+	18.7263i	0.333756	+	1.46228i
$165$		0			0
$166$			34.7492i			2.69706i
$167$	−1.61253	−	7.06498i	−0.124782	−	0.546704i	−0.998213	−	0.0597569i	$-0.980967\pi$
$167$	−1.61253	−	7.06498i	−0.124782	−	0.546704i	0.873431	−	0.486947i	$-0.161890\pi$
$168$		0			0
$169$	−2.47120	+	10.8270i	−0.190092	+	0.832849i
$170$	−0.0217812	−	0.00497143i	−0.00167054	−	0.000381291i
$171$		0			0
$172$	−0.663368	+	0.831837i	−0.0505813	+	0.0634269i
$173$	0.637002	−	2.79089i	0.0484304	−	0.212187i	−0.944923	−	0.327293i	$-0.893864\pi$
$173$	0.637002	−	2.79089i	0.0484304	−	0.212187i	0.993353	+	0.115106i	$0.0367207\pi$
$174$		0			0
$175$	−36.4152	+	7.28192i	−2.75273	+	0.550461i
$176$	−13.3926	+	3.05678i	−1.00951	+	0.230413i
$177$		0			0
$178$			13.0204i			0.975923i
$179$	−10.4981	+	2.39612i	−0.784665	+	0.179095i	−0.596040	−	0.802954i	$-0.703260\pi$
$179$	−10.4981	+	2.39612i	−0.784665	+	0.179095i	−0.188625	+	0.982049i	$0.560403\pi$
$180$		0			0
$181$	11.6008	+	9.25131i	0.862279	+	0.687645i	0.951260	−	0.308389i	$-0.0997897\pi$
$181$	11.6008	+	9.25131i	0.862279	+	0.687645i	−0.0889812	+	0.996033i	$0.528361\pi$
$182$	6.01062	−	4.53304i	0.445537	−	0.336011i
$183$		0			0
$184$	0.139677	+	0.611965i	0.0102971	+	0.0451147i
$185$	−25.7581	−	32.2997i	−1.89378	−	2.37472i
$186$		0			0
$187$	0.00787577	+	0.00628071i	0.000575933	+	0.000459291i
$188$	4.96788	−	2.39241i	0.362320	−	0.174484i
$189$		0			0
$190$	39.3854	+	18.9670i	2.85732	+	1.37601i
$191$	−5.09937	−	10.5890i	−0.368978	−	0.766190i	0.630976	−	0.775802i	$-0.282655\pi$
$191$	−5.09937	−	10.5890i	−0.368978	−	0.766190i	−0.999954	+	0.00961204i	$0.996940\pi$
$192$		0			0
$193$	−5.53509	+	2.66556i	−0.398424	+	0.191871i	−0.622357	−	0.782734i	$-0.713825\pi$
$193$	−5.53509	+	2.66556i	−0.398424	+	0.191871i	0.223933	+	0.974605i	$0.428110\pi$
$194$	−3.76025	−	4.71520i	−0.269970	−	0.338532i
$195$		0			0
$196$	15.8923	+	0.860093i	1.13517	+	0.0614352i
$197$		−	3.01370i		−	0.214717i	−0.994220	−	0.107359i	$-0.965761\pi$
$197$		−	3.01370i		−	0.214717i	0.994220	−	0.107359i	$-0.0342393\pi$
$198$		0			0
$199$	−9.17541	−	19.0529i	−0.650428	−	1.35063i	−0.921617	−	0.388101i	$-0.873131\pi$
$199$	−9.17541	−	19.0529i	−0.650428	−	1.35063i	0.271189	−	0.962526i	$-0.412583\pi$
$200$	−7.74147	−	1.76694i	−0.547405	−	0.124942i
$201$		0			0
$202$	−8.21555	+	17.0598i	−0.578044	+	1.20032i
$203$	3.82414	+	1.97067i	0.268402	+	0.138314i
$204$		0			0
$205$	−22.9813	+	28.8176i	−1.60508	+	2.01271i
$206$	−5.42539	−	2.61273i	−0.378005	−	0.182038i
$207$		0			0
$208$	−4.53271	+	1.03456i	−0.314287	+	0.0717339i
$209$	−12.2892	−	15.4102i	−0.850064	−	1.06595i
$210$		0			0
$211$	9.60477	−	12.0440i	0.661220	−	0.829144i	−0.332256	−	0.943189i	$-0.607810\pi$
$211$	9.60477	−	12.0440i	0.661220	−	0.829144i	0.993475	+	0.114046i	$0.0363811\pi$
$212$	−6.89486	+	14.3173i	−0.473541	+	0.983318i
$213$		0			0
$214$	−29.3849			−2.00871
$215$	−2.04169			−0.139242
$216$		0			0
$217$	5.52195	−	6.55280i	0.374854	−	0.444833i
$218$	−16.0249	−	3.65758i	−1.08534	−	0.247723i
$219$		0			0
$220$	31.5418	+	25.1537i	2.12655	+	1.69586i
$221$	0.00266554	+	0.00212570i	0.000179303	+	0.000142990i
$222$		0			0
$223$	4.82462	+	1.10119i	0.323080	+	0.0737410i	0.380985	−	0.924581i	$-0.375585\pi$
$223$	4.82462	+	1.10119i	0.323080	+	0.0737410i	−0.0579050	+	0.998322i	$0.518442\pi$
$224$	−19.0836	−	9.83424i	−1.27507	−	0.657078i
$225$		0			0
$226$	30.7728			2.04698
$227$	19.8226			1.31567			0.657835	−	0.753162i	$-0.271472\pi$
$227$	19.8226			1.31567			0.657835	+	0.753162i	$0.271472\pi$
$228$		0			0
$229$	5.43984	−	11.2959i	0.359475	−	0.746457i	−0.640290	−	0.768133i	$-0.721186\pi$
$229$	5.43984	−	11.2959i	0.359475	−	0.746457i	0.999765	+	0.0216759i	$0.00690019\pi$
$230$	−6.23979	+	7.82444i	−0.411439	+	0.515929i
$231$		0			0
$232$	0.573533	+	0.719188i	0.0376543	+	0.0472170i
$233$	−20.9996	+	4.79302i	−1.37573	+	0.314001i	−0.845556	−	0.533888i	$-0.820731\pi$
$233$	−20.9996	+	4.79302i	−1.37573	+	0.314001i	−0.530174	+	0.847889i	$0.677873\pi$
$234$		0			0
$235$	9.53315	+	4.59092i	0.621874	+	0.299479i
$236$	11.6490	−	14.6074i	0.758284	−	0.950858i
$237$		0			0
$238$	0.00265655	+	0.0132848i	0.000172199	+	0.000861127i
$239$	4.22999	−	8.78367i	0.273615	−	0.568168i	−0.718202	−	0.695835i	$-0.755034\pi$
$239$	4.22999	−	8.78367i	0.273615	−	0.568168i	0.991817	+	0.127667i	$0.0407488\pi$
$240$		0			0
$241$	9.34327	+	2.13254i	0.601853	+	0.137369i	0.512582	−	0.858638i	$-0.328689\pi$
$241$	9.34327	+	2.13254i	0.601853	+	0.137369i	0.0892712	+	0.996007i	$0.471546\pi$
$242$	−4.96855	−	10.3173i	−0.319391	−	0.663221i
$243$		0			0
$244$		−	33.9736i		−	2.17494i
$245$	17.7240	+	24.8723i	1.13234	+	1.58903i
$246$		0			0
$247$	−4.15927	−	5.21555i	−0.264648	−	0.331858i
$248$	1.65084	−	0.795001i	0.104828	−	0.0504826i
$249$		0			0
$250$	−35.3627	−	73.4315i	−2.23654	−	4.64421i
$251$	3.12043	+	1.50272i	0.196960	+	0.0948508i	0.529764	−	0.848145i	$-0.322281\pi$
$251$	3.12043	+	1.50272i	0.196960	+	0.0948508i	−0.332804	+	0.942996i	$0.607995\pi$
$252$		0			0
$253$	4.06555	−	1.95787i	0.255599	−	0.123090i
$254$	−26.6906	−	21.2851i	−1.67472	−	1.33554i
$255$		0			0
$256$	6.71465	+	8.41991i	0.419666	+	0.526244i
$257$	4.15911	+	18.2222i	0.259438	+	1.13667i	0.921854	+	0.387537i	$0.126674\pi$
$257$	4.15911	+	18.2222i	0.259438	+	1.13667i	−0.662416	+	0.749136i	$0.730469\pi$
$258$		0			0
$259$	−11.4758	+	22.2691i	−0.713075	+	1.38374i
$260$	10.6753	+	8.51323i	0.662051	+	0.527968i
$261$		0			0
$262$	−8.18575	+	1.86834i	−0.505717	+	0.115427i
$263$		−	20.9882i		−	1.29419i	−0.762410	−	0.647095i	$-0.775984\pi$
$263$		−	20.9882i		−	1.29419i	0.762410	−	0.647095i	$-0.224016\pi$
$264$		0			0
$265$	−29.7296	+	6.78559i	−1.82628	+	0.416836i
$266$	0.716533	−	26.4988i	0.0439335	−	1.62475i
$267$		0			0
$268$	5.96119	−	26.1177i	0.364138	−	1.59539i
$269$	−7.08941	+	8.88983i	−0.432249	+	0.542023i	−0.949482	−	0.313822i	$-0.898391\pi$
$269$	−7.08941	+	8.88983i	−0.432249	+	0.542023i	0.517233	+	0.855844i	$0.326962\pi$
$270$		0			0
$271$	−4.25141	−	0.970356i	−0.258255	−	0.0589449i	0.0914332	−	0.995811i	$-0.470855\pi$
$271$	−4.25141	−	0.970356i	−0.258255	−	0.0589449i	−0.349688	+	0.936866i	$0.613712\pi$
$272$	0.00186177	−	0.00815695i	0.000112886	−	0.000494587i
$273$		0			0
$274$	−2.41708	−	10.5899i	−0.146021	−	0.639761i
$275$			57.0830i			3.44223i
$276$		0			0
$277$	−3.49711	−	15.3218i	−0.210121	−	0.920599i	−0.964484	−	0.264142i	$-0.914911\pi$
$277$	−3.49711	−	15.3218i	−0.210121	−	0.920599i	0.754363	−	0.656457i	$-0.227946\pi$
$278$	−8.99926	−	4.33381i	−0.539739	−	0.259925i
$279$		0			0
$280$	1.28053	+	6.40365i	0.0765265	+	0.382691i
$281$	−12.2719	+	9.78649i	−0.732079	+	0.583813i	−0.916975	−	0.398945i	$-0.869377\pi$
$281$	−12.2719	+	9.78649i	−0.732079	+	0.583813i	0.184896	+	0.982758i	$0.440805\pi$
$282$		0			0
$283$	−0.591566	+	0.471759i	−0.0351650	+	0.0280431i	−0.640915	−	0.767612i	$-0.721445\pi$
$283$	−0.591566	+	0.471759i	−0.0351650	+	0.0280431i	0.605750	+	0.795655i	$0.292873\pi$
$284$	4.43848	−	9.21661i	0.263376	−	0.546905i
$285$		0			0
$286$	−5.02092	−	10.4260i	−0.296893	−	0.616505i
$287$	21.6486	+	5.56085i	1.27787	+	0.328246i
$288$		0			0
$289$	15.3165	−	7.37602i	0.900969	−	0.433884i
$290$	−3.26352	+	14.2984i	−0.191640	+	0.839631i
$291$		0			0
$292$	−9.87753	+	7.87707i	−0.578039	+	0.460970i
$293$	15.5966			0.911164			0.455582	−	0.890194i	$-0.349431\pi$
$293$	15.5966			0.911164			0.455582	+	0.890194i	$0.349431\pi$
$294$		0			0
$295$	35.8528			2.08743
$296$	−4.18805	+	3.33986i	−0.243426	+	0.194125i
$297$		0			0
$298$	4.88882	−	21.4193i	0.283202	−	1.24079i
$299$	1.37598	−	0.662637i	0.0795749	−	0.0383213i
$300$		0			0
$301$	0.506836	+	1.12959i	0.0292135	+	0.0651082i
$302$	−6.54588	−	13.5927i	−0.376673	−	0.782170i
$303$		0			0
$304$	−7.10304	+	14.7496i	−0.407387	+	0.845948i
$305$	50.9706	−	40.6477i	2.91857	−	2.32748i
$306$		0			0
$307$	1.03488	−	0.825290i	0.0590638	−	0.0471018i	−0.593513	−	0.804824i	$-0.702259\pi$
$307$	1.03488	−	0.825290i	0.0590638	−	0.0471018i	0.652577	+	0.757723i	$0.273688\pi$
$308$	6.08652	−	23.6950i	0.346812	−	1.35015i
$309$		0			0
$310$	26.3203	+	12.6752i	1.49489	+	0.719901i
$311$	−1.16016	−	5.08300i	−0.0657867	−	0.288230i	0.931324	−	0.364192i	$-0.118655\pi$
$311$	−1.16016	−	5.08300i	−0.0657867	−	0.288230i	−0.997111	+	0.0759611i	$0.975798\pi$
$312$		0			0
$313$			8.11203i			0.458519i	0.973365	+	0.229259i	$0.0736304\pi$
$313$			8.11203i			0.458519i	−0.973365	+	0.229259i	$0.926370\pi$
$314$	6.01669	+	26.3609i	0.339542	+	1.48763i
$315$		0			0
$316$	−5.08872	+	22.2952i	−0.286263	+	1.25420i
$317$	−8.11359	−	1.85187i	−0.455705	−	0.104012i	−0.0114939	−	0.999934i	$-0.503659\pi$
$317$	−8.11359	−	1.85187i	−0.455705	−	0.104012i	−0.444211	+	0.895922i	$0.646516\pi$
$318$		0			0
$319$	4.12301	−	5.17009i	0.230844	−	0.289469i
$320$	9.72710	−	42.6172i	0.543762	−	2.38238i
$321$		0			0
$322$	5.87794	+	1.50986i	0.327565	+	0.0841412i
$323$	0.0117039	−	0.00267133i	0.000651221	−	0.000148637i
$324$		0			0
$325$			19.3196i			1.07166i
$326$	−0.778649	+	0.177722i	−0.0431254	+	0.00984309i
$327$		0			0
$328$	3.73656	+	2.97980i	0.206317	+	0.164532i
$329$	0.173435	−	6.41398i	0.00956179	−	0.353614i
$330$		0			0
$331$	4.34040	+	19.0165i	0.238570	+	1.04524i	0.942299	+	0.334774i	$0.108660\pi$
$331$	4.34040	+	19.0165i	0.238570	+	1.04524i	−0.703729	+	0.710469i	$0.748483\pi$
$332$	23.8286	+	29.8801i	1.30776	+	1.63988i
$333$		0			0
$334$	−11.7125	−	9.34044i	−0.640882	−	0.511086i
$335$	46.3166	−	22.3049i	2.53055	−	1.21865i
$336$		0			0
$337$	20.7554	+	9.99525i	1.13062	+	0.544476i	0.903157	−	0.429311i	$-0.141244\pi$
$337$	20.7554	+	9.99525i	1.13062	+	0.544476i	0.227460	+	0.973787i	$0.426958\pi$
$338$	9.96116	+	20.6846i	0.541816	+	1.12509i
$339$		0			0
$340$	−0.0221383	+	0.0106613i	−0.00120062	+	0.000578188i
$341$	−8.21257	−	10.2982i	−0.444736	−	0.557681i
$342$		0			0
$343$	9.36101	−	15.9803i	0.505447	−	0.862858i
$344$			0.264730i			0.0142733i
$345$		0			0
$346$	−2.56769	−	5.33187i	−0.138040	−	0.286643i
$347$	−21.6884	−	4.95023i	−1.16429	−	0.265742i	−0.403650	−	0.914913i	$-0.632259\pi$
$347$	−21.6884	−	4.95023i	−1.16429	−	0.265742i	−0.760642	+	0.649171i	$0.775116\pi$
$348$		0			0
$349$	1.84031	−	3.82143i	0.0985093	−	0.204557i	−0.845890	−	0.533357i	$-0.820930\pi$
$349$	1.84031	−	3.82143i	0.0985093	−	0.204557i	0.944399	+	0.328801i	$0.106644\pi$
$350$	−49.4708	+	58.7061i	−2.64432	+	3.13798i
$351$		0			0
$352$	−20.5750	+	25.8002i	−1.09665	+	1.37516i
$353$	−4.11202	−	1.98025i	−0.218861	−	0.105398i	0.321241	−	0.946997i	$-0.395900\pi$
$353$	−4.11202	−	1.98025i	−0.218861	−	0.105398i	−0.540102	+	0.841600i	$0.681614\pi$
$354$		0			0
$355$	19.1381	−	4.36815i	1.01574	−	0.231837i
$356$	8.92852	+	11.1960i	0.473211	+	0.593388i
$357$		0			0
$358$	−13.8793	+	17.4041i	−0.733544	+	0.919835i
$359$	−7.99103	+	16.5935i	−0.421750	+	0.875774i	0.576525	+	0.817079i	$0.304408\pi$
$359$	−7.99103	+	16.5935i	−0.421750	+	0.875774i	−0.998276	+	0.0586947i	$0.981306\pi$
$360$		0			0
$361$	−4.48944			−0.236286
$362$	30.6742			1.61220
$363$		0			0
$364$	2.05997	−	8.01954i	0.107972	−	0.420338i
$365$	−23.6359	−	5.39474i	−1.23716	−	0.282374i
$366$		0			0
$367$	−26.5459	−	21.1697i	−1.38569	−	1.10505i	−0.981732	−	0.190269i	$-0.939064\pi$
$367$	−26.5459	−	21.1697i	−1.38569	−	1.10505i	−0.403955	−	0.914779i	$-0.632365\pi$
$368$	−2.93021	−	2.33676i	−0.152748	−	0.121812i
$369$		0			0
$370$	−83.2640	−	19.0045i	−4.32869	−	0.987996i
$371$	11.1344	+	14.7637i	0.578068	+	0.766495i
$372$		0			0
$373$	26.8836			1.39198			0.695990	−	0.718051i	$-0.254966\pi$
$373$	26.8836			1.39198			0.695990	+	0.718051i	$0.254966\pi$
$374$	0.0208247			0.00107682
$375$		0			0
$376$	0.595270	−	1.23609i	0.0306987	−	0.0637465i
$377$	1.39542	−	1.74981i	0.0718680	−	0.0901196i
$378$		0			0
$379$	−12.2638	−	15.3783i	−0.629948	−	0.789929i	0.359758	−	0.933046i	$-0.382859\pi$
$379$	−12.2638	−	15.3783i	−0.629948	−	0.789929i	−0.989706	+	0.143116i	$0.954288\pi$
$380$	46.8730	−	10.6985i	2.40454	−	0.548819i
$381$		0			0
$382$	−21.8904	−	10.5418i	−1.12001	−	0.539368i
$383$	14.9439	−	18.7390i	0.763597	−	0.957520i	−0.236303	−	0.971679i	$-0.575936\pi$
$383$	14.9439	−	18.7390i	0.763597	−	0.957520i	0.999900	+	0.0141595i	$0.00450726\pi$
$384$		0			0
$385$	42.8319	−	19.2183i	2.18292	−	0.979456i
$386$	−5.51046	+	11.4426i	−0.280475	+	0.582412i
$387$		0			0
$388$	−6.46673	−	1.47599i	−0.328298	−	0.0749320i
$389$	−9.56032	−	19.8522i	−0.484728	−	1.00655i	−0.989666	−	0.143392i	$-0.954199\pi$
$389$	−9.56032	−	19.8522i	−0.484728	−	1.00655i	0.504938	−	0.863155i	$-0.331515\pi$
$390$		0			0
$391$			0.00274835i			0.000138990i
$392$	3.22500	−	2.29813i	0.162887	−	0.116073i
$393$		0			0
$394$	−3.88445	−	4.87094i	−0.195696	−	0.245394i
$395$	−39.5378	+	19.0404i	−1.98936	+	0.958027i
$396$		0			0
$397$	10.8708	+	22.5735i	0.545592	+	1.13293i	0.973410	+	0.229069i	$0.0735680\pi$
$397$	10.8708	+	22.5735i	0.545592	+	1.13293i	−0.427818	+	0.903865i	$0.640718\pi$
$398$	−39.3878	−	18.9682i	−1.97433	−	0.950788i
$399$		0			0
$400$	42.7161	−	20.5710i	2.13581	−	1.02855i
$401$	11.8949	+	9.48584i	0.594002	+	0.473700i	0.873752	−	0.486372i	$-0.161680\pi$
$401$	11.8949	+	9.48584i	0.594002	+	0.473700i	−0.279750	+	0.960073i	$0.590252\pi$
$402$		0			0
$403$	−2.77953	−	3.48542i	−0.138458	−	0.173621i
$404$	4.63403	+	20.3030i	0.230552	+	1.01011i
$405$		0			0
$406$	8.72088	−	1.74391i	0.432810	−	0.0865486i
$407$	30.1070	+	24.0095i	1.49235	+	1.19011i
$408$		0			0
$409$	12.1656	−	2.77673i	0.601552	−	0.137300i	0.0891093	−	0.996022i	$-0.471598\pi$
$409$	12.1656	−	2.77673i	0.601552	−	0.137300i	0.512442	+	0.858722i	$0.328741\pi$
$410$			76.1981i			3.76316i
$411$		0			0
$412$	−6.45682	+	1.47373i	−0.318105	+	0.0726053i
$413$	−8.90022	−	19.8360i	−0.437951	−	0.976063i
$414$		0			0
$415$	−16.3194	+	71.5001i	−0.801089	+	3.50980i
$416$	−6.96357	+	8.73204i	−0.341417	+	0.428124i
$417$		0			0
$418$	−39.7253	−	9.06705i	−1.94303	−	0.443484i
$419$	−4.14796	+	18.1734i	−0.202641	+	0.887830i	0.766679	+	0.642030i	$0.221908\pi$
$419$	−4.14796	+	18.1734i	−0.202641	+	0.887830i	−0.969321	+	0.245799i	$0.920950\pi$
$420$		0			0
$421$	2.49894	+	10.9486i	0.121791	+	0.533600i	0.998606	+	0.0527737i	$0.0168062\pi$
$421$	2.49894	+	10.9486i	0.121791	+	0.533600i	−0.876816	+	0.480827i	$0.840337\pi$
$422$		−	31.8462i		−	1.55025i
$423$		0			0
$424$	0.879836	+	3.85481i	0.0427286	+	0.187206i
$425$	−0.0313241	−	0.0150849i	−0.00151944	−	0.000731724i
$426$		0			0
$427$	−35.1419	−	18.1095i	−1.70063	−	0.876380i
$428$	−25.2675	+	20.1501i	−1.22135	+	0.973994i
$429$		0			0
$430$	−3.29991	+	2.63159i	−0.159136	+	0.126907i
$431$	−17.6980	+	36.7503i	−0.852482	+	1.77020i	−0.257881	+	0.966177i	$0.583024\pi$
$431$	−17.6980	+	36.7503i	−0.852482	+	1.77020i	−0.594601	+	0.804021i	$0.702690\pi$
$432$		0			0
$433$	−5.73036	−	11.8992i	−0.275383	−	0.571840i	0.716706	−	0.697376i	$-0.245649\pi$
$433$	−5.73036	−	11.8992i	−0.275383	−	0.571840i	−0.992089	+	0.125536i	$0.959935\pi$
$434$	0.478841	−	17.7085i	0.0229851	−	0.850034i
$435$		0			0
$436$	−16.2876	+	7.84371i	−0.780036	+	0.375645i
$437$	1.19663	−	5.24276i	0.0572424	−	0.250795i
$438$		0			0
$439$	−14.0789	+	11.2275i	−0.671949	+	0.535861i	−0.898960	−	0.438031i	$-0.855676\pi$
$439$	−14.0789	+	11.2275i	−0.671949	+	0.535861i	0.227011	+	0.973892i	$0.427105\pi$
$440$	10.0381			0.478548
$441$		0			0
$442$	0.00704809			0.000335243
$443$	17.2953	−	13.7925i	0.821723	−	0.655302i	−0.119595	−	0.992823i	$-0.538160\pi$
$443$	17.2953	−	13.7925i	0.821723	−	0.655302i	0.941318	+	0.337520i	$0.109588\pi$
$444$		0			0
$445$	−6.11485	+	26.7909i	−0.289872	+	1.27001i
$446$	9.21722	−	4.43878i	0.436448	−	0.210182i
$447$		0			0
$448$	−25.9931	+	5.19782i	−1.22806	+	0.245574i
$449$	3.37716	+	7.01274i	0.159378	+	0.330952i	0.965331	−	0.261027i	$-0.0840612\pi$
$449$	3.37716	+	7.01274i	0.159378	+	0.330952i	−0.805953	+	0.591979i	$0.798347\pi$
$450$		0			0
$451$	14.9069	−	30.9545i	0.701938	−	1.45759i
$452$	26.4609	−	21.1019i	1.24462	−	0.992550i
$453$		0			0
$454$	32.0386	−	25.5499i	1.50364	−	1.19912i
$455$	14.4964	−	6.50440i	0.679600	−	0.304931i
$456$		0			0
$457$	16.4925	+	7.94239i	0.771488	+	0.371529i	0.777850	−	0.628451i	$-0.216311\pi$
$457$	16.4925	+	7.94239i	0.771488	+	0.371529i	−0.00636122	+	0.999980i	$0.502025\pi$
$458$	−5.76745	−	25.2688i	−0.269495	−	1.18073i
$459$		0			0
$460$			11.0069i			0.513200i
$461$	6.73601	+	29.5124i	0.313727	+	1.37453i	0.848349	+	0.529437i	$0.177597\pi$
$461$	6.73601	+	29.5124i	0.313727	+	1.37453i	−0.534622	+	0.845091i	$0.679546\pi$
$462$		0			0
$463$	−5.33895	+	23.3915i	−0.248122	+	1.08709i	0.685285	+	0.728275i	$0.259678\pi$
$463$	−5.33895	+	23.3915i	−0.248122	+	1.08709i	−0.933407	+	0.358819i	$0.883180\pi$
$464$	−5.35467	−	1.22217i	−0.248584	−	0.0567377i
$465$		0			0
$466$	−27.7631	+	34.8138i	−1.28610	+	1.61272i
$467$	3.08333	−	13.5090i	0.142679	−	0.625120i	−0.852127	−	0.523335i	$-0.824688\pi$
$467$	3.08333	−	13.5090i	0.142679	−	0.625120i	0.994806	−	0.101785i	$-0.0324552\pi$
$468$		0			0
$469$	−23.8382	−	20.0881i	−1.10075	−	0.927583i
$470$	21.3255	−	4.86740i	0.983671	−	0.224516i
$471$		0			0
$472$		−	4.64876i		−	0.213977i
$473$	1.85537	−	0.423477i	0.0853102	−	0.0194715i
$474$		0			0
$475$	53.1860	+	42.4144i	2.44034	+	1.94611i
$476$	0.0113941	+	0.00960167i	0.000522249	+	0.000440092i
$477$		0			0
$478$	−4.48474	−	19.6489i	−0.205127	−	0.898720i
$479$	6.76546	+	8.48362i	0.309122	+	0.387626i	0.911989	−	0.410215i	$-0.134546\pi$
$479$	6.76546	+	8.48362i	0.309122	+	0.387626i	−0.602867	+	0.797842i	$0.705975\pi$
$480$		0			0
$481$	10.1897	+	8.12599i	0.464609	+	0.370513i
$482$	17.8499	−	8.59607i	0.813041	−	0.391540i
$483$		0			0
$484$	−11.3473	−	5.46455i	−0.515785	−	0.248389i
$485$	−5.52269	−	11.4680i	−0.250772	−	0.520734i
$486$		0			0
$487$	12.1205	−	5.83690i	0.549230	−	0.264495i	−0.138623	−	0.990345i	$-0.544268\pi$
$487$	12.1205	−	5.83690i	0.549230	−	0.264495i	0.687853	+	0.725850i	$0.258553\pi$
$488$	−5.27048	−	6.60897i	−0.238583	−	0.299174i
$489$		0			0
$490$	60.7053	+	17.3553i	2.74239	+	0.784034i
$491$			32.1316i			1.45008i	0.688708	+	0.725039i	$0.258178\pi$
$491$			32.1316i			1.45008i	−0.688708	+	0.725039i	$0.741822\pi$
$492$		0			0
$493$	0.00174751	+	0.00362874i	7.87039e−5	+	0.000163430i
$494$	−13.4450	−	3.06872i	−0.604917	−	0.138068i
$495$		0			0
$496$	−4.74678	+	9.85678i	−0.213137	+	0.442583i
$497$	−7.16762	−	9.50398i	−0.321512	−	0.426312i
$498$		0			0
$499$	2.66616	−	3.34326i	0.119354	−	0.149665i	−0.718565	−	0.695460i	$-0.755201\pi$
$499$	2.66616	−	3.34326i	0.119354	−	0.149665i	0.837919	+	0.545795i	$0.183772\pi$
$500$	−80.7620	−	38.8929i	−3.61179	−	1.73934i
$501$		0			0
$502$	6.98034	−	1.59322i	0.311548	−	0.0711088i
$503$	15.4247	+	19.3419i	0.687752	+	0.862414i	0.996042	−	0.0888785i	$-0.0283283\pi$
$503$	15.4247	+	19.3419i	0.687752	+	0.862414i	−0.308290	+	0.951292i	$0.599757\pi$
$504$		0			0
$505$	−24.9162	+	31.2440i	−1.10876	+	1.39034i
$506$	4.04746	−	8.40465i	0.179932	−	0.373632i
$507$		0			0
$508$	−37.5466			−1.66586
$509$	−9.79261			−0.434050			−0.217025	−	0.976166i	$-0.569635\pi$
$509$	−9.79261			−0.434050			−0.217025	+	0.976166i	$0.569635\pi$
$510$		0			0
$511$	2.88276	+	14.4160i	0.127526	+	0.637727i
$512$	30.4473	+	6.94941i	1.34560	+	0.307123i
$513$		0			0
$514$	30.2094	+	24.0912i	1.33248	+	1.06262i
$515$	−9.93628	−	7.92392i	−0.437845	−	0.349170i
$516$		0			0
$517$	−9.61542	−	2.19466i	−0.422886	−	0.0965209i
$518$	10.1553	+	50.7844i	0.446199	+	2.23134i
$519$		0			0
$520$	3.39738			0.148985
$521$	12.2091			0.534892			0.267446	−	0.963573i	$-0.413820\pi$
$521$	12.2091			0.534892			0.267446	+	0.963573i	$0.413820\pi$
$522$		0			0
$523$	7.65067	−	15.8868i	0.334541	−	0.694681i	−0.664054	−	0.747685i	$-0.731165\pi$
$523$	7.65067	−	15.8868i	0.334541	−	0.694681i	0.998594	+	0.0530043i	$0.0168797\pi$
$524$	−5.75758	+	7.21978i	−0.251521	+	0.315397i
$525$		0			0
$526$	−27.0523	−	33.9226i	−1.17954	−	1.47909i
$527$	0.00782140	−	0.00178518i	0.000340705	−	7.77638e-5i
$528$		0			0
$529$	−19.6131	−	9.44516i	−0.852743	−	0.410659i
$530$	−39.3049	+	49.2867i	−1.70729	+	2.14088i
$531$		0			0
$532$	−17.5549	−	23.2772i	−0.761103	−	1.00919i
$533$	5.04521	−	10.4765i	0.218532	−	0.453787i
$534$		0			0
$535$	−60.4625	−	13.8002i	−2.61402	−	0.596633i
$536$	−2.89211	−	6.00552i	−0.124920	−	0.259399i
$537$		0			0
$538$			23.5061i			1.01342i
$539$	−21.2655	−	18.9264i	−0.915968	−	0.815216i
$540$		0			0
$541$	−6.97220	−	8.74286i	−0.299758	−	0.375885i	0.609027	−	0.793150i	$-0.291560\pi$
$541$	−6.97220	−	8.74286i	−0.299758	−	0.375885i	−0.908785	+	0.417265i	$0.862989\pi$
$542$	−8.12213	+	3.91141i	−0.348875	+	0.168009i
$543$		0			0
$544$	−0.00872059	−	0.0181085i	−0.000373892	−	0.000776396i
$545$	−31.2552	−	15.0517i	−1.33883	−	0.644745i
$546$		0			0
$547$	−13.9058	+	6.69667i	−0.594568	+	0.286329i	−0.706868	−	0.707346i	$-0.749893\pi$
$547$	−13.9058	+	6.69667i	−0.594568	+	0.286329i	0.112300	+	0.993674i	$0.464178\pi$
$548$	−9.34025	−	7.44860i	−0.398996	−	0.318189i
$549$		0			0
$550$	73.5759	+	92.2613i	3.13729	+	3.93404i
$551$	−1.75361	−	7.68307i	−0.0747063	−	0.327310i
$552$		0			0
$553$	20.3493	+	17.1480i	0.865340	+	0.729209i
$554$	−25.4010	−	20.2566i	−1.07919	−	0.860622i
$555$		0			0
$556$	−10.7101	+	2.44451i	−0.454210	+	0.103670i
$557$			18.1025i			0.767028i	0.923535	+	0.383514i	$0.125286\pi$
$557$			18.1025i			0.767028i	−0.923535	+	0.383514i	$0.874714\pi$
$558$		0			0
$559$	0.627948	−	0.143325i	0.0265594	−	0.00606200i
$560$	−29.8167	−	25.1261i	−1.25999	−	1.06177i
$561$		0			0
$562$	−7.22052	+	31.6352i	−0.304579	+	1.33445i
$563$	−5.44395	+	6.82650i	−0.229435	+	0.287703i	−0.883201	−	0.468994i	$-0.844617\pi$
$563$	−5.44395	+	6.82650i	−0.229435	+	0.287703i	0.653766	+	0.756697i	$0.273188\pi$
$564$		0			0
$565$	63.3184	+	14.4520i	2.66382	+	0.608000i
$566$	−0.348066	+	1.52497i	−0.0146303	+	0.0640995i
$567$		0			0
$568$	−0.566384	−	2.48149i	−0.0237649	−	0.104121i
$569$			0.531762i			0.0222926i	0.999938	+	0.0111463i	$0.00354806\pi$
$569$			0.531762i			0.0222926i	−0.999938	+	0.0111463i	$0.996452\pi$
$570$		0			0
$571$	−1.82542	−	7.99770i	−0.0763916	−	0.334693i	0.922262	−	0.386565i	$-0.126338\pi$
$571$	−1.82542	−	7.99770i	−0.0763916	−	0.334693i	−0.998654	+	0.0518716i	$0.983481\pi$
$572$	−11.4669	−	5.52214i	−0.479453	−	0.230892i
$573$		0			0
$574$	42.1574	−	18.9157i	1.75962	−	0.789525i
$575$	−12.1762	+	9.71020i	−0.507783	+	0.404943i
$576$		0			0
$577$	−7.32438	+	5.84100i	−0.304918	+	0.243164i	−0.763979	−	0.645241i	$-0.776757\pi$
$577$	−7.32438	+	5.84100i	−0.304918	+	0.243164i	0.459062	+	0.888404i	$0.348186\pi$
$578$	15.2483	−	31.6635i	0.634246	−	1.31703i
$579$		0			0
$580$	6.99863	+	14.5328i	0.290602	+	0.603442i
$581$	43.6093	−	8.72052i	1.80922	−	0.361788i
$582$		0			0
$583$	25.6092	−	12.3327i	1.06063	−	0.510770i
$584$	−0.699495	+	3.06469i	−0.0289453	+	0.126818i
$585$		0			0
$586$	25.2083	−	20.1029i	1.04134	−	0.830445i
$587$	22.2926			0.920113			0.460057	−	0.887890i	$-0.347829\pi$
$587$	22.2926			0.920113			0.460057	+	0.887890i	$0.347829\pi$
$588$		0			0
$589$	−15.6974			−0.646800
$590$	57.9477	−	46.2118i	2.38567	−	1.90251i
$591$		0			0
$592$	7.11706	−	31.1819i	0.292510	−	1.28157i
$593$	2.68385	−	1.29248i	0.110213	−	0.0530756i	−0.377965	−	0.925820i	$-0.623376\pi$
$593$	2.68385	−	1.29248i	0.110213	−	0.0530756i	0.488178	+	0.872744i	$0.337662\pi$
$594$		0			0
$595$	−0.000772877		0.0285825i	−3.16849e−5		0.00117177i
$596$	−10.4841	−	21.7705i	−0.429446	−	0.891753i
$597$		0			0
$598$	1.36986	−	2.84454i	0.0560176	−	0.116322i
$599$	6.09092	−	4.85734i	0.248868	−	0.198466i	−0.491108	−	0.871099i	$-0.663408\pi$
$599$	6.09092	−	4.85734i	0.248868	−	0.198466i	0.739976	+	0.672633i	$0.234837\pi$
$600$		0			0
$601$	−7.47364	+	5.96003i	−0.304856	+	0.243115i	−0.763953	−	0.645271i	$-0.776744\pi$
$601$	−7.47364	+	5.96003i	−0.304856	+	0.243115i	0.459097	+	0.888386i	$0.348173\pi$
$602$	2.27514	+	1.17244i	0.0927277	+	0.0477849i
$603$		0			0
$604$	−14.9496	−	7.19934i	−0.608290	−	0.292937i
$605$	−5.37795	−	23.5624i	−0.218645	−	0.957946i
$606$		0			0
$607$			40.3837i			1.63912i	0.572990	+	0.819562i	$0.305783\pi$
$607$			40.3837i			1.63912i	−0.572990	+	0.819562i	$0.694217\pi$
$608$	8.75103	+	38.3408i	0.354901	+	1.55492i
$609$		0			0
$610$	29.9901	−	131.395i	1.21426	−	5.32003i
$611$	−3.25432	−	0.742778i	−0.131656	−	0.0300496i
$612$		0			0
$613$	28.5198	−	35.7627i	1.15190	−	1.44444i	0.276523	−	0.961007i	$-0.410818\pi$
$613$	28.5198	−	35.7627i	1.15190	−	1.44444i	0.875381	−	0.483434i	$-0.160611\pi$
$614$	0.608903	−	2.66778i	0.0245733	−	0.107663i
$615$		0			0
$616$	−2.49189	−	5.55368i	−0.100401	−	0.223764i
$617$	16.4516	−	3.75497i	0.662316	−	0.151169i	0.121867	−	0.992546i	$-0.461112\pi$
$617$	16.4516	−	3.75497i	0.662316	−	0.151169i	0.540448	+	0.841377i	$0.318255\pi$
$618$		0			0
$619$			27.2418i			1.09494i	0.836825	+	0.547470i	$0.184409\pi$
$619$			27.2418i			1.09494i	−0.836825	+	0.547470i	$0.815591\pi$
$620$	31.3240	−	7.14951i	1.25800	−	0.287131i
$621$		0			0
$622$	−8.42676	−	6.72011i	−0.337882	−	0.269452i
$623$	16.3403	−	3.26756i	0.654661	−	0.130912i
$624$		0			0
$625$	−22.6599	−	99.2795i	−0.906396	−	3.97118i
$626$	10.4558	+	13.1112i	0.417899	+	0.524029i
$627$		0			0
$628$	23.2501	+	18.5413i	0.927781	+	0.739880i
$629$	−0.0211313	+	0.0101763i	−0.000842560	+	0.000405756i
$630$		0			0
$631$	−24.7711	−	11.9292i	−0.986124	−	0.474892i	−0.129917	−	0.991525i	$-0.541471\pi$
$631$	−24.7711	−	11.9292i	−0.986124	−	0.474892i	−0.856207	+	0.516633i	$0.827185\pi$
$632$	2.46882	+	5.12657i	0.0982045	+	0.203924i
$633$		0			0
$634$	−15.5007	+	7.46472i	−0.615610	+	0.296462i
$635$	−44.9226	−	56.3311i	−1.78270	−	2.23543i
$636$		0			0
$637$	−7.19725	−	6.40559i	−0.285165	−	0.253799i
$638$		−	13.6705i		−	0.541220i
$639$		0			0
$640$	−8.48734	−	17.6241i	−0.335492	−	0.696656i
$641$	14.5469	+	3.32024i	0.574569	+	0.131142i	0.499925	−	0.866069i	$-0.333361\pi$
$641$	14.5469	+	3.32024i	0.574569	+	0.131142i	0.0746437	+	0.997210i	$0.476218\pi$
$642$		0			0
$643$	9.62506	−	19.9866i	0.379575	−	0.788196i	−0.620417	−	0.784272i	$-0.713037\pi$
$643$	9.62506	−	19.9866i	0.379575	−	0.788196i	0.999992	−	0.00392394i	$-0.00124903\pi$
$644$	6.08968	−	2.73239i	0.239967	−	0.107671i
$645$		0			0
$646$	0.0154734	−	0.0194031i	0.000608793	−	0.000763403i
$647$	31.9879	+	15.4046i	1.25757	+	0.605616i	0.939532	−	0.342461i	$-0.111260\pi$
$647$	31.9879	+	15.4046i	1.25757	+	0.605616i	0.318042	+	0.948077i	$0.396975\pi$
$648$		0			0
$649$	−32.5811	+	7.43642i	−1.27892	+	0.291905i
$650$	24.9016	+	31.2257i	0.976722	+	1.22477i
$651$		0			0
$652$	−0.547676	+	0.686764i	−0.0214486	+	0.0268958i
$653$	−9.55151	+	19.8339i	−0.373780	+	0.776161i	−0.999994	−	0.00348962i	$-0.998889\pi$
$653$	−9.55151	+	19.8339i	−0.373780	+	0.776161i	0.626214	+	0.779651i	$0.284604\pi$
$654$		0			0
$655$	−17.7205			−0.692397
$656$	−28.5357			−1.11413
$657$		0			0
$658$	−7.98684	−	10.5902i	−0.311360	−	0.412850i
$659$	−22.7399	−	5.19024i	−0.885822	−	0.202183i	−0.244679	−	0.969604i	$-0.578683\pi$
$659$	−22.7399	−	5.19024i	−0.885822	−	0.202183i	−0.641143	+	0.767421i	$0.721540\pi$
$660$		0			0
$661$	4.64300	+	3.70267i	0.180592	+	0.144017i	0.709614	−	0.704591i	$-0.248870\pi$
$661$	4.64300	+	3.70267i	0.180592	+	0.144017i	−0.529022	+	0.848608i	$0.677441\pi$
$662$	31.5262	+	25.1413i	1.22530	+	0.977144i
$663$		0			0
$664$	9.27087	+	2.11602i	0.359779	+	0.0821173i
$665$	13.9191	−	54.1876i	0.539760	−	2.10131i
$666$		0			0
$667$	1.80417			0.0698576
$668$	−16.4764			−0.637492
$669$		0			0
$670$	46.1106	−	95.7496i	1.78141	−	3.69913i
$671$	−37.8883	+	47.5105i	−1.46266	+	1.83412i
$672$		0			0
$673$	−4.78696	−	6.00266i	−0.184524	−	0.231386i	0.680962	−	0.732319i	$-0.261562\pi$
$673$	−4.78696	−	6.00266i	−0.184524	−	0.231386i	−0.865486	+	0.500933i	$0.832990\pi$
$674$	46.4294	−	10.5972i	1.78839	−	0.408189i
$675$		0			0
$676$	22.7495	+	10.9556i	0.874980	+	0.421368i
$677$	−27.0462	+	33.9149i	−1.03947	+	1.30346i	−0.0878656	+	0.996132i	$0.528005\pi$
$677$	−27.0462	+	33.9149i	−1.03947	+	1.30346i	−0.951605	+	0.307323i	$0.900567\pi$
$678$		0			0
$679$	−4.97381	+	5.90233i	−0.190877	+	0.226511i
$680$	−0.00265269	+	0.00550837i	−0.000101726	+	0.000211237i
$681$		0			0
$682$	−26.5474	−	6.05927i	−1.01655	−	0.232022i
$683$	−9.51245	−	19.7528i	−0.363984	−	0.755820i	0.635889	−	0.771781i	$-0.280634\pi$
$683$	−9.51245	−	19.7528i	−0.363984	−	0.755820i	−0.999873	+	0.0159608i	$0.994919\pi$
$684$		0			0
$685$		−	22.9251i		−	0.875921i
$686$	−5.46766	−	37.8942i	−0.208756	−	1.44681i
$687$		0			0
$688$	−0.985517	−	1.23580i	−0.0375725	−	0.0471144i
$689$	8.66739	−	4.17399i	0.330201	−	0.159017i
$690$		0			0
$691$	−15.6054	−	32.4051i	−0.593659	−	1.23275i	−0.953967	−	0.299913i	$-0.903042\pi$
$691$	−15.6054	−	32.4051i	−0.593659	−	1.23275i	0.360307	−	0.932834i	$-0.382672\pi$
$692$	−5.86414	−	2.82402i	−0.222921	−	0.107353i
$693$		0			0
$694$	−41.4347	+	19.9539i	−1.57284	+	0.757439i
$695$	−16.4816	−	13.1436i	−0.625183	−	0.498567i
$696$		0			0
$697$	0.0130468	+	0.0163602i	0.000494184	+	0.000619687i
$698$	−1.95113	−	8.54848i	−0.0738515	−	0.323565i
$699$		0			0
$700$	−2.28230	+	84.4039i	−0.0862628	+	3.19017i
$701$	−7.18722	−	5.73162i	−0.271458	−	0.216480i	0.478294	−	0.878200i	$-0.341255\pi$
$701$	−7.18722	−	5.73162i	−0.271458	−	0.216480i	−0.749751	+	0.661720i	$0.769827\pi$
$702$		0			0
$703$	44.7409	−	10.2118i	1.68743	−	0.385146i
$704$			40.7457i			1.53566i
$705$		0			0
$706$	−9.19852	+	2.09950i	−0.346191	+	0.0790158i
$707$	23.4713	+	6.02906i	0.882730	+	0.226746i
$708$		0			0
$709$	7.15245	−	31.3369i	0.268616	−	1.17688i	−0.643009	−	0.765859i	$-0.722314\pi$
$709$	7.15245	−	31.3369i	0.268616	−	1.17688i	0.911625	−	0.411024i	$-0.134829\pi$
$710$	25.3020	−	31.7277i	0.949568	−	1.19072i
$711$		0			0
$712$	3.47377	+	0.792866i	0.130185	+	0.0297139i
$713$	0.799674	−	3.50360i	0.0299480	−	0.131211i
$714$		0			0
$715$	−5.43463	−	23.8107i	−0.203244	−	0.890469i
$716$			24.4829i			0.914969i
$717$		0			0
$718$	8.47228	+	37.1195i	0.316182	+	1.38529i
$719$	31.2682	+	15.0580i	1.16611	+	0.561568i	0.913834	−	0.406087i	$-0.133107\pi$
$719$	31.2682	+	15.0580i	1.16611	+	0.561568i	0.252274	+	0.967656i	$0.418821\pi$
$720$		0			0
$721$	−1.91738	+	7.46441i	−0.0714068	+	0.277989i
$722$	−7.25613	+	5.78657i	−0.270045	+	0.215354i
$723$		0			0
$724$	26.3762	−	21.0343i	0.980263	−	0.781734i
$725$	−9.90255	+	20.5629i	−0.367771	+	0.763685i
$726$		0			0
$727$	6.04878	+	12.5604i	0.224337	+	0.465840i	0.982509	−	0.186214i	$-0.0596217\pi$
$727$	6.04878	+	12.5604i	0.224337	+	0.465840i	−0.758172	+	0.652054i	$0.773907\pi$
$728$	−0.843376	−	1.87963i	−0.0312576	−	0.0696638i
$729$		0			0
$730$	−45.1554	+	21.7457i	−1.67128	+	0.804844i
$731$	−0.000257924		0.00113004i	−9.53967e−6		4.17960e-5i
$732$		0			0
$733$	29.0186	−	23.1416i	1.07183	−	0.854753i	0.0819430	−	0.996637i	$-0.473887\pi$
$733$	29.0186	−	23.1416i	1.07183	−	0.854753i	0.989883	+	0.141884i	$0.0453160\pi$
$734$	−70.1915			−2.59082
$735$		0			0
$736$	−9.00333			−0.331867
$737$	−37.4636	+	29.8762i	−1.37999	+	1.10051i
$738$		0			0
$739$	−5.18637	+	22.7230i	−0.190784	+	0.835878i	0.785410	+	0.618976i	$0.212452\pi$
$739$	−5.18637	+	22.7230i	−0.190784	+	0.835878i	−0.976193	+	0.216902i	$0.930405\pi$
$740$	−84.6291	+	40.7552i	−3.11103	+	1.49819i
$741$		0			0
$742$	37.0255	+	9.51072i	1.35925	+	0.349149i
$743$	2.69045	+	5.58678i	0.0987032	+	0.204959i	0.944473	−	0.328588i	$-0.106573\pi$
$743$	2.69045	+	5.58678i	0.0987032	+	0.204959i	−0.845770	+	0.533548i	$0.820859\pi$
$744$		0			0
$745$	20.1185	−	41.7766i	0.737086	−	1.53058i
$746$	43.4511	−	34.6511i	1.59086	−	1.26867i
$747$		0			0
$748$	0.0179068	−	0.0142802i	0.000654737	−	0.000522135i
$749$	7.37432	+	36.8773i	0.269452	+	1.34747i
$750$		0			0
$751$	6.48350	+	3.12229i	0.236586	+	0.113934i	0.548421	−	0.836202i	$-0.315229\pi$
$751$	6.48350	+	3.12229i	0.236586	+	0.113934i	−0.311835	+	0.950136i	$0.600943\pi$
$752$	1.82281	+	7.98627i	0.0664712	+	0.291229i
$753$		0			0
$754$		−	4.62675i		−	0.168496i
$755$	−7.08525	−	31.0425i	−0.257859	−	1.12975i
$756$		0			0
$757$	−7.52407	+	32.9651i	−0.273467	+	1.19814i	0.632423	+	0.774624i	$0.282061\pi$
$757$	−7.52407	+	32.9651i	−0.273467	+	1.19814i	−0.905890	+	0.423514i	$0.860796\pi$
$758$	−39.6430	−	9.04827i	−1.43990	−	0.328648i
$759$		0			0
$760$	7.45862	−	9.35281i	0.270553	−	0.339262i
$761$	7.11305	−	31.1643i	0.257848	−	1.12971i	−0.665699	−	0.746220i	$-0.731867\pi$
$761$	7.11305	−	31.1643i	0.257848	−	1.12971i	0.923547	−	0.383485i	$-0.125276\pi$
$762$		0			0
$763$	−0.568622	+	21.0288i	−0.0205855	+	0.761292i
$764$	−26.0520	+	5.94619i	−0.942527	+	0.215126i
$765$		0			0
$766$		−	49.5489i		−	1.79027i
$767$	−11.0270	+	2.51684i	−0.398162	+	0.0908779i
$768$		0			0
$769$	24.2017	+	19.3002i	0.872735	+	0.695983i	0.953708	−	0.300734i	$-0.0972315\pi$
$769$	24.2017	+	19.3002i	0.872735	+	0.695983i	−0.0809736	+	0.996716i	$0.525803\pi$
$770$	44.4567	−	86.2692i	1.60211	−	3.10893i
$771$		0			0
$772$	3.10821	+	13.6179i	0.111867	+	0.490121i
$773$	−5.89943	−	7.39765i	−0.212188	−	0.266075i	0.664336	−	0.747434i	$-0.268715\pi$
$773$	−5.89943	−	7.39765i	−0.212188	−	0.266075i	−0.876523	+	0.481359i	$0.840143\pi$
$774$		0			0
$775$	35.5428	+	28.3445i	1.27674	+	1.01816i
$776$	−1.48696	+	0.716084i	−0.0533789	+	0.0257059i
$777$		0			0
$778$	−41.0401	−	19.7639i	−1.47136	−	0.708570i
$779$	−17.7650	−	36.8894i	−0.636496	−	1.32170i
$780$		0			0
$781$	−16.4856	+	7.93906i	−0.589902	+	0.284082i
$782$	0.00354243	+	0.00444206i	0.000126677	+	0.000158848i
$783$		0			0
$784$	−6.49947	+	22.7338i	−0.232124	+	0.811921i
$785$			57.0659i			2.03677i
$786$		0			0
$787$	−1.28538	−	2.66912i	−0.0458189	−	0.0951439i	0.876803	−	0.480850i	$-0.159672\pi$
$787$	−1.28538	−	2.66912i	−0.0458189	−	0.0951439i	−0.922622	+	0.385707i	$0.873958\pi$
$788$	−6.68032	−	1.52474i	−0.237976	−	0.0543166i
$789$		0			0
$790$	−39.3619	+	81.7358i	−1.40043	+	2.90803i
$791$	−7.72264	−	38.6191i	−0.274585	−	1.37314i
$792$		0			0
$793$	−12.8232	+	16.0798i	−0.455366	+	0.571011i
$794$	46.6659	+	22.4731i	1.65611	+	0.797540i
$795$		0			0
$796$	−46.8759	+	10.6991i	−1.66147	+	0.379220i
$797$	−24.2657	−	30.4282i	−0.859535	−	1.07782i	−0.996190	−	0.0872044i	$-0.972207\pi$
$797$	−24.2657	−	30.4282i	−0.859535	−	1.07782i	0.136655	−	0.990619i	$-0.456365\pi$
$798$		0			0
$799$	0.00374531	−	0.00469646i	0.000132499	−	0.000166149i
$800$	49.4166	−	102.615i	1.74714	−	3.62798i
$801$		0			0
$802$	31.4519			1.11060
$803$	22.5980			0.797465
$804$		0			0
$805$	11.3854	+	5.86718i	0.401283	+	0.206791i
$806$	−8.98492	−	2.05075i	−0.316480	−	0.0722346i
$807$		0			0
$808$	4.05117	+	3.23070i	0.142519	+	0.113656i
$809$	−14.7897	−	11.7944i	−0.519979	−	0.414670i	0.328017	−	0.944672i	$-0.393620\pi$
$809$	−14.7897	−	11.7944i	−0.519979	−	0.414670i	−0.847996	+	0.530002i	$0.822191\pi$
$810$		0			0
$811$	−21.4007	−	4.88457i	−0.751480	−	0.171521i	−0.170409	−	0.985373i	$-0.554509\pi$
$811$	−21.4007	−	4.88457i	−0.751480	−	0.171521i	−0.581071	+	0.813853i	$0.697366\pi$
$812$	6.30306	−	7.47974i	0.221194	−	0.262487i
$813$		0			0
$814$	79.6076			2.79024
$815$	−1.68562			−0.0590446
$816$		0			0
$817$	0.984034	−	2.04337i	0.0344270	−	0.0714884i
$818$	16.0839	−	20.1686i	0.562360	−	0.705177i
$819$		0			0
$820$	52.2515	+	65.5213i	1.82470	+	2.28810i
$821$	11.7531	−	2.68256i	0.410185	−	0.0936221i	−0.0124488	−	0.999923i	$-0.503963\pi$
$821$	11.7531	−	2.68256i	0.410185	−	0.0936221i	0.422634	+	0.906300i	$0.361106\pi$
$822$		0			0
$823$	39.6190	+	19.0795i	1.38103	+	0.665070i	0.969219	−	0.246198i	$-0.0791814\pi$
$823$	39.6190	+	19.0795i	1.38103	+	0.665070i	0.411813	+	0.911268i	$0.364896\pi$
$824$	−1.02743	+	1.28836i	−0.0357924	+	0.0448822i
$825$		0			0
$826$	−39.9523	−	20.5884i	−1.39012	−	0.716363i
$827$	3.87859	−	8.05398i	0.134872	−	0.280064i	−0.822584	−	0.568643i	$-0.807468\pi$
$827$	3.87859	−	8.05398i	0.134872	−	0.280064i	0.957456	+	0.288579i	$0.0931828\pi$
$828$		0			0
$829$	41.1702	+	9.39684i	1.42990	+	0.326366i	0.866235	−	0.499637i	$-0.166533\pi$
$829$	41.1702	+	9.39684i	1.42990	+	0.326366i	0.563667	+	0.826002i	$0.309390\pi$
$830$	65.7820	+	136.598i	2.28333	+	4.74138i
$831$		0			0
$832$			13.7903i			0.478093i
$833$	0.0160054	−	0.00666782i	0.000554555	−	0.000231026i
$834$		0			0
$835$	−19.7132	−	24.7196i	−0.682203	−	0.855456i
$836$	−40.3766	+	19.4443i	−1.39645	+	0.672497i
$837$		0			0
$838$	16.7200	+	34.7195i	0.577584	+	1.19937i
$839$	22.0943	+	10.6400i	0.762779	+	0.367335i	0.774482	−	0.632596i	$-0.218011\pi$
$839$	22.0943	+	10.6400i	0.762779	+	0.367335i	−0.0117024	+	0.999932i	$0.503725\pi$
$840$		0			0
$841$	−23.7460	+	11.4355i	−0.818827	+	0.394326i
$842$	18.1509	+	14.4748i	0.625520	+	0.498836i
$843$		0			0
$844$	−21.8379	−	27.3839i	−0.751693	−	0.942593i
$845$	10.7819	+	47.2388i	0.370910	+	1.62506i
$846$		0			0
$847$	−11.7011	+	8.82460i	−0.402054	+	0.303217i
$848$	−18.4576	−	14.7194i	−0.633836	−	0.505468i
$849$		0			0
$850$	−0.0700714	+	0.0159933i	−0.00240343	+	0.000548567i
$851$			10.5062i			0.360149i
$852$		0			0
$853$	10.5434	−	2.40645i	0.360998	−	0.0823954i	−0.0381750	−	0.999271i	$-0.512154\pi$
$853$	10.5434	−	2.40645i	0.360998	−	0.0823954i	0.399173	+	0.916876i	$0.369297\pi$
$854$	−80.1405	+	16.0256i	−2.74235	+	0.548385i
$855$		0			0
$856$	−1.78936	+	7.83971i	−0.0611591	+	0.267956i
$857$	16.6335	−	20.8577i	0.568189	−	0.712486i	−0.411859	−	0.911248i	$-0.635120\pi$
$857$	16.6335	−	20.8577i	0.568189	−	0.712486i	0.980048	+	0.198761i	$0.0636919\pi$
$858$		0			0
$859$	−43.0235	−	9.81983i	−1.46794	−	0.335048i	−0.587509	−	0.809218i	$-0.699891\pi$
$859$	−43.0235	−	9.81983i	−1.46794	−	0.335048i	−0.880434	+	0.474170i	$0.842748\pi$
$860$	−1.03296	+	4.52571i	−0.0352238	+	0.154325i
$861$		0			0
$862$	18.7638	+	82.2097i	0.639098	+	2.80007i
$863$		−	8.40308i		−	0.286044i	−0.989719	−	0.143022i	$-0.954318\pi$
$863$		−	8.40308i		−	0.286044i	0.989719	−	0.143022i	$-0.0456820\pi$
$864$		0			0
$865$	−2.77927	−	12.1768i	−0.0944980	−	0.414023i
$866$	−24.5990	−	11.8463i	−0.835909	−	0.402553i
$867$		0			0
$868$	−11.7315	−	15.5555i	−0.398194	−	0.527989i
$869$	31.9805	−	25.5036i	1.08486	−	0.865151i
$870$		0			0
$871$	−12.6795	+	10.1116i	−0.429628	+	0.342617i
$872$	−1.95164	+	4.05263i	−0.0660909	+	0.137239i
$873$		0			0
$874$	−4.82348	−	10.0161i	−0.163157	−	0.338798i
$875$	−83.2802	+	62.8074i	−2.81538	+	2.12328i
$876$		0			0
$877$	−30.3155	+	14.5992i	−1.02368	+	0.492978i	−0.868909	−	0.494972i	$-0.835178\pi$
$877$	−30.3155	+	14.5992i	−1.02368	+	0.492978i	−0.154771	+	0.987950i	$0.549464\pi$
$878$	−8.28373	+	36.2934i	−0.279562	+	1.22484i
$879$		0			0
$880$	−46.8593	+	37.3690i	−1.57963	+	1.25971i
$881$	41.2262			1.38895			0.694474	−	0.719518i	$-0.255637\pi$
$881$	41.2262			1.38895			0.694474	+	0.719518i	$0.255637\pi$
$882$		0			0
$883$	−3.51281			−0.118215			−0.0591077	−	0.998252i	$-0.518826\pi$
$883$	−3.51281			−0.118215			−0.0591077	+	0.998252i	$0.518826\pi$
$884$	0.00606051	−	0.00483310i	0.000203837	−	0.000162555i
$885$		0			0
$886$	10.1762	−	44.5848i	0.341875	−	1.49785i
$887$	−28.6866	+	13.8147i	−0.963201	+	0.463853i	−0.848295	−	0.529523i	$-0.822371\pi$
$887$	−28.6866	+	13.8147i	−0.963201	+	0.463853i	−0.114906	+	0.993376i	$0.536657\pi$
$888$		0			0
$889$	−20.0140	+	38.8377i	−0.671249	+	1.30257i
$890$	24.6484	+	51.1829i	0.826215	+	1.71565i
$891$		0			0
$892$	4.88189	−	10.1374i	0.163458	−	0.339424i
$893$	−9.18939	+	7.32829i	−0.307511	+	0.245232i
$894$		0			0
$895$	−36.7317	+	29.2926i	−1.22781	+	0.979142i
$896$	−7.64381	+	9.07078i	−0.255362	+	0.303034i
$897$		0			0
$898$	14.4973	+	6.98154i	0.483782	+	0.232977i
$899$	−1.17189	−	5.13440i	−0.0390848	−	0.171242i
$900$		0			0
$901$			0.0173120i			0.000576748i
$902$	−15.8046	−	69.2446i	−0.526237	−	2.30559i
$903$		0			0
$904$	1.87388	−	8.21001i	0.0623243	−	0.273061i
$905$	63.1155	+	14.4057i	2.09803	+	0.478862i
$906$		0			0
$907$	15.5943	−	19.5546i	0.517800	−	0.649300i	−0.452340	−	0.891845i	$-0.649411\pi$
$907$	15.5943	−	19.5546i	0.517800	−	0.649300i	0.970140	+	0.242545i	$0.0779822\pi$
$908$	10.0290	−	43.9397i	0.332823	−	1.45819i
$909$		0			0
$910$	15.0463	−	29.1976i	0.498779	−	0.967892i
$911$	−26.2429	+	5.98976i	−0.869465	+	0.198450i	−0.633906	−	0.773410i	$-0.718549\pi$
$911$	−26.2429	+	5.98976i	−0.869465	+	0.198450i	−0.235559	+	0.971860i	$0.575692\pi$
$912$		0			0
$913$		−	68.3602i		−	2.26239i
$914$	36.8935	−	8.42070i	1.22033	−	0.278532i
$915$		0			0
$916$	−22.2869	−	17.7732i	−0.736382	−	0.587245i
$917$	4.39899	+	9.80404i	0.145267	+	0.323758i
$918$		0			0
$919$	7.60122	+	33.3031i	0.250741	+	1.09857i	0.930834	+	0.365443i	$0.119082\pi$
$919$	7.60122	+	33.3031i	0.250741	+	1.09857i	−0.680093	+	0.733126i	$0.738060\pi$
$920$	1.70755	+	2.14120i	0.0562962	+	0.0705932i
$921$		0			0
$922$	48.9265	+	39.0176i	1.61131	+	1.28498i
$923$	−5.57953	+	2.68696i	−0.183652	+	0.0884423i
$924$		0			0
$925$	−119.744	−	57.6656i	−3.93715	−	1.89603i
$926$	21.5208	+	44.6884i	0.707217	+	1.46855i
$927$		0			0
$928$	−11.8874	+	5.72468i	−0.390223	+	0.187922i
$929$	−18.3586	−	23.0210i	−0.602327	−	0.755294i	0.383412	−	0.923577i	$-0.374749\pi$
$929$	−18.3586	−	23.0210i	−0.602327	−	0.755294i	−0.985739	+	0.168284i	$0.946178\pi$
$930$		0			0
$931$	−33.4352	+	5.75081i	−1.09579	+	0.188475i
$932$			48.9737i			1.60419i
$933$		0			0
$934$	−12.4286	−	25.8083i	−0.406676	−	0.844472i
$935$	0.0428491	+	0.00978003i	0.00140132	+	0.000319841i
$936$		0			0
$937$	−16.6392	+	34.5516i	−0.543578	+	1.12875i	0.430511	+	0.902585i	$0.358333\pi$
$937$	−16.6392	+	34.5516i	−0.543578	+	1.12875i	−0.974089	+	0.226166i	$0.927381\pi$
$938$	−64.4210	−	1.74196i	−2.10342	−	0.0568770i
$939$		0			0
$940$	14.9996	−	18.8089i	0.489234	−	0.613480i
$941$	−34.8714	−	16.7932i	−1.13677	−	0.547442i	−0.231739	−	0.972778i	$-0.574442\pi$
$941$	−34.8714	−	16.7932i	−1.13677	−	0.547442i	−0.905035	+	0.425336i	$0.860156\pi$
$942$		0			0
$943$	9.13858	−	2.08582i	0.297593	−	0.0679237i
$944$	17.3060	+	21.7011i	0.563264	+	0.706310i
$945$		0			0
$946$	2.45295	−	3.07590i	0.0797522	−	0.100006i
$947$	−0.566474	+	1.17629i	−0.0184079	+	0.0382245i	−0.909970	−	0.414674i	$-0.863896\pi$
$947$	−0.566474	+	1.17629i	−0.0184079	+	0.0382245i	0.891562	+	0.452898i	$0.149610\pi$
$948$		0			0
$949$	7.64824			0.248272
$950$	140.632			4.56270
$951$		0			0
$952$	0.00370608		0.000100213i	0.000120115		3.24792e-6i
$953$	26.4806	+	6.04403i	0.857792	+	0.195785i	0.628727	−	0.777626i	$-0.283576\pi$
$953$	26.4806	+	6.04403i	0.857792	+	0.195785i	0.229065	+	0.973411i	$0.426433\pi$
$954$		0			0
$955$	−40.0909	−	31.9715i	−1.29731	−	1.03457i
$956$	−17.3302	−	13.8204i	−0.560499	−	0.446983i
$957$		0			0
$958$	21.8696	+	4.99159i	0.706574	+	0.161271i
$959$	−12.6835	+	5.69099i	−0.409572	+	0.183772i
$960$		0			0
$961$	20.5098			0.661608
$962$	26.9430			0.868678
$963$		0			0
$964$	9.45420	−	19.6318i	0.304499	−	0.632299i
$965$	−16.7122	+	20.9564i	−0.537985	+	0.674611i
$966$		0			0
$967$	15.4663	+	19.3941i	0.497362	+	0.623672i	0.965632	−	0.259913i	$-0.0836940\pi$
$967$	15.4663	+	19.3941i	0.497362	+	0.623672i	−0.468270	+	0.883585i	$0.655123\pi$
$968$	−3.05515	+	0.697318i	−0.0981962	+	0.0224127i
$969$		0			0
$970$	−23.7075	−	11.4169i	−0.761203	−	0.366576i
$971$	3.64436	−	4.56988i	0.116953	−	0.146654i	−0.719909	−	0.694069i	$-0.755816\pi$
$971$	3.64436	−	4.56988i	0.116953	−	0.146654i	0.836862	+	0.547414i	$0.184388\pi$
$972$		0			0
$973$	−3.18041	+	12.3814i	−0.101959	+	0.396931i
$974$	12.0665	−	25.0564i	0.386636	−	0.802859i
$975$		0			0
$976$	49.2067	+	11.2311i	1.57507	+	0.359499i
$977$	8.68106	+	18.0264i	0.277732	+	0.576716i	0.992443	−	0.122703i	$-0.0391564\pi$
$977$	8.68106	+	18.0264i	0.277732	+	0.576716i	−0.714712	+	0.699419i	$0.753442\pi$
$978$		0			0
$979$		−	25.6144i		−	0.818640i
$980$	64.1004	−	26.7040i	2.04761	−	0.853029i
$981$		0			0
$982$	41.4153	+	51.9332i	1.32162	+	1.65726i
$983$	−3.55339	+	1.71122i	−0.113336	+	0.0545796i	−0.489692	−	0.871895i	$-0.662891\pi$
$983$	−3.55339	+	1.71122i	−0.113336	+	0.0545796i	0.376357	+	0.926475i	$0.377177\pi$
$984$		0			0
$985$	−5.70509	−	11.8467i	−0.181779	−	0.377469i
$986$	0.00750164	+	0.00361260i	0.000238901	+	0.000115049i
$987$		0			0
$988$	−13.6654	+	6.58090i	−0.434754	+	0.209366i
$989$	0.405943	+	0.323728i	0.0129082	+	0.0102940i
$990$		0			0
$991$	−35.1091	−	44.0254i	−1.11528	−	1.39851i	−0.907354	−	0.420367i	$-0.861901\pi$
$991$	−35.1091	−	44.0254i	−1.11528	−	1.39851i	−0.207922	−	0.978145i	$-0.566670\pi$
$992$	5.84809	+	25.6221i	0.185677	+	0.813504i
$993$		0			0
$994$	−23.8347	−	6.12241i	−0.755992	−	0.194191i
$995$	−72.1365	−	57.5269i	−2.28688	−	1.82373i
$996$		0			0
$997$	43.1103	−	9.83965i	1.36532	−	0.311625i	0.523794	−	0.851845i	$-0.324516\pi$
$997$	43.1103	−	9.83965i	1.36532	−	0.311625i	0.841524	+	0.540220i	$0.181659\pi$
$998$		−	8.84009i		−	0.279828i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.w.a.188.17	yes	120
3.2	odd	2	inner	441.2.w.a.188.4	✓	120
49.6	odd	14	inner	441.2.w.a.251.4	yes	120
147.104	even	14	inner	441.2.w.a.251.17	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.w.a.188.4	✓	120	3.2	odd	2	inner
441.2.w.a.188.17	yes	120	1.1	even	1	trivial
441.2.w.a.251.4	yes	120	49.6	odd	14	inner
441.2.w.a.251.17	yes	120	147.104	even	14	inner

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.w (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.61627 - 1.28893i) q^{2} +(0.505936 - 2.21665i) q^{4} +(3.93097 - 1.89305i) q^{5} +(-2.02319 - 1.70491i) q^{7} +(-0.245458 - 0.509698i) q^{8} +O(q^{10})\)	\(q+(1.61627 - 1.28893i) q^{2} +(0.505936 - 2.21665i) q^{4} +(3.93097 - 1.89305i) q^{5} +(-2.02319 - 1.70491i) q^{7} +(-0.245458 - 0.509698i) q^{8} +(3.91348 - 8.12642i) q^{10} +(-3.17960 + 2.53564i) q^{11} +(-1.07613 + 0.858184i) q^{13} +(-5.46752 - 0.147843i) q^{14} +(3.04329 + 1.46557i) q^{16} +(-0.000551178 - 0.00241487i) q^{17} +4.84659i q^{19} +(-2.20742 - 9.67134i) q^{20} +(-1.87081 + 8.19655i) q^{22} +(-1.08174 - 0.246900i) q^{23} +(8.75139 - 10.9739i) q^{25} +(-0.633172 + 2.77411i) q^{26} +(-4.80279 + 3.62212i) q^{28} +(-1.58525 + 0.361823i) q^{29} +3.23885i q^{31} +(7.91087 - 1.80561i) q^{32} +(-0.00400344 - 0.00319264i) q^{34} +(-11.1806 - 2.87194i) q^{35} +(-2.10701 - 9.23141i) q^{37} +(6.24691 + 7.83338i) q^{38} +(-1.92977 - 1.53894i) q^{40} +(-7.61140 + 3.66546i) q^{41} +(-0.421609 - 0.203036i) q^{43} +(4.01196 + 8.33093i) q^{44} +(-2.06662 + 0.995232i) q^{46} +(1.51205 + 1.89605i) q^{47} +(1.18657 + 6.89870i) q^{49} -29.0167i q^{50} +(1.35784 + 2.81959i) q^{52} +(-6.81397 - 1.55524i) q^{53} +(-7.69878 + 15.9867i) q^{55} +(-0.372382 + 1.44970i) q^{56} +(-2.09582 + 2.62808i) q^{58} +(7.40362 + 3.56539i) q^{59} +(14.5677 - 3.32497i) q^{61} +(4.17465 + 5.23485i) q^{62} +(6.24673 - 7.83315i) q^{64} +(-2.60564 + 5.41066i) q^{65} +11.7825 q^{67} -0.00563178 q^{68} +(-21.7725 + 9.76913i) q^{70} +(4.38641 + 1.00117i) q^{71} +(-4.34434 - 3.46449i) q^{73} +(-15.3041 - 12.2046i) q^{74} +(10.7432 + 2.45206i) q^{76} +(10.7560 + 0.290843i) q^{77} -10.0580 q^{79} +14.7375 q^{80} +(-7.57754 + 15.7349i) q^{82} +(-10.4803 + 13.1419i) q^{83} +(-0.00673813 - 0.00844935i) q^{85} +(-0.943132 + 0.215264i) q^{86} +(2.07287 + 0.998241i) q^{88} +(-3.92695 + 4.92424i) q^{89} +(3.64033 + 0.0984354i) q^{91} +(-1.09458 + 2.27293i) q^{92} +(4.88775 + 1.11560i) q^{94} +(9.17485 + 19.0518i) q^{95} -2.91734i q^{97} +(10.8097 + 9.62073i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 24 q^{4}+O(q^{10}) \) 120 * q + 24 * q^4	\( 120 q + 24 q^{4} - 32 q^{16} - 44 q^{22} - 4 q^{25} - 56 q^{28} + 112 q^{34} - 76 q^{37} + 28 q^{40} + 8 q^{43} - 40 q^{46} - 84 q^{49} - 140 q^{52} + 12 q^{58} - 84 q^{61} + 24 q^{64} + 16 q^{67} + 112 q^{70} - 84 q^{76} - 24 q^{79} + 140 q^{82} - 96 q^{85} - 24 q^{88} - 112 q^{91} - 112 q^{94}+O(q^{100}) \) 120 * q + 24 * q^4 - 32 * q^16 - 44 * q^22 - 4 * q^25 - 56 * q^28 + 112 * q^34 - 76 * q^37 + 28 * q^40 + 8 * q^43 - 40 * q^46 - 84 * q^49 - 140 * q^52 + 12 * q^58 - 84 * q^61 + 24 * q^64 + 16 * q^67 + 112 * q^70 - 84 * q^76 - 24 * q^79 + 140 * q^82 - 96 * q^85 - 24 * q^88 - 112 * q^91 - 112 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more