LMFDB - Embedded newform 639.2.z.a.305.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [639,2,Mod(35,639)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(639, base_ring=CyclotomicField(70))

chi = DirichletCharacter(H, H._module([35, 29]))

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

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

chi := DirichletCharacter("639.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 639 = 3^{2} \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	639.z (of order $70$, degree $24$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.10244068916$
Analytic rank:	$0$
Dimension:	$576$
Relative dimension:	$24$ over $\Q(\zeta_{70})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{70}]$

Embedding invariants

Embedding label			305.20
Character	$\chi$	$=$	639.305
Dual form			639.2.z.a.44.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.46713 - 0.968447i) q^{2} +(0.428545 - 1.00263i) q^{4} +(0.365787 + 0.503462i) q^{5} +(1.05239 + 2.80407i) q^{7} +(0.285525 + 1.57337i) q^{8} +O(q^{10})$	\(q+(1.46713 - 0.968447i) q^{2} +(0.428545 - 1.00263i) q^{4} +(0.365787 + 0.503462i) q^{5} +(1.05239 + 2.80407i) q^{7} +(0.285525 + 1.57337i) q^{8} +(1.02423 + 0.384402i) q^{10} +(0.685905 + 5.06355i) q^{11} +(-1.95959 - 0.265444i) q^{13} +(4.25959 + 3.09477i) q^{14} +(3.44967 + 3.60807i) q^{16} +(-0.337004 - 1.03719i) q^{17} +(-5.50275 - 3.28774i) q^{19} +(0.661542 - 0.150993i) q^{20} +(5.91010 + 6.76465i) q^{22} +(0.865725 + 1.08558i) q^{23} +(1.42541 - 4.38696i) q^{25} +(-3.13205 + 1.50831i) q^{26} +(3.26244 + 0.146516i) q^{28} +(4.52536 - 5.17969i) q^{29} +(1.48527 + 1.42006i) q^{31} +(5.43740 + 1.24105i) q^{32} +(-1.49890 - 1.19533i) q^{34} +(-1.02680 + 1.55553i) q^{35} +(5.95288 - 7.46467i) q^{37} +(-11.2573 + 0.505565i) q^{38} +(-0.687693 + 0.719271i) q^{40} +(7.29489 + 3.51303i) q^{41} +(0.540273 - 12.0301i) q^{43} +(5.37081 + 1.48225i) q^{44} +(2.32147 + 0.754290i) q^{46} +(-10.8576 + 0.977206i) q^{47} +(-1.48381 + 1.29637i) q^{49} +(-2.15727 - 7.81670i) q^{50} +(-1.10591 + 1.85098i) q^{52} +(3.22128 + 7.53655i) q^{53} +(-2.29841 + 2.19751i) q^{55} +(-4.11138 + 2.45643i) q^{56} +(1.62306 - 11.9819i) q^{58} +(2.04696 - 3.80389i) q^{59} +(-0.550000 + 1.46547i) q^{61} +(3.55434 + 0.645018i) q^{62} +(-0.167772 + 0.0629659i) q^{64} +(-0.583149 - 1.08367i) q^{65} +(0.630195 + 0.269358i) q^{67} +(-1.18434 - 0.106593i) q^{68} +3.27657i q^{70} +(-8.10443 + 2.30612i) q^{71} +(3.11498 + 4.71900i) q^{73} +(1.50453 - 16.7167i) q^{74} +(-5.65456 + 4.10828i) q^{76} +(-13.4767 + 7.25214i) q^{77} +(8.42434 - 1.52879i) q^{79} +(-0.554684 + 3.05656i) q^{80} +(14.1048 - 1.91062i) q^{82} +(2.00194 + 1.07729i) q^{83} +(0.398915 - 0.549060i) q^{85} +(-10.8579 - 18.1730i) q^{86} +(-7.77102 + 2.52496i) q^{88} +(-8.45230 + 3.61269i) q^{89} +(-1.31792 - 5.77417i) q^{91} +(1.45944 - 0.402780i) q^{92} +(-14.9833 + 11.9488i) q^{94} +(-0.357580 - 3.97304i) q^{95} +(-6.69689 - 13.9062i) q^{97} +(-0.921491 + 3.33895i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 576 q - 24 q^{4}+O(q^{10}) $ 576 * q - 24 * q^4	$ 576 q - 24 q^{4} - 16 q^{10} + 76 q^{16} - 8 q^{19} + 20 q^{22} + 168 q^{25} - 20 q^{28} - 28 q^{31} + 40 q^{37} + 32 q^{40} + 52 q^{43} - 20 q^{46} - 208 q^{52} - 92 q^{55} + 56 q^{58} + 56 q^{61} - 144 q^{64} - 16 q^{67} - 44 q^{73} - 336 q^{76} + 88 q^{79} - 124 q^{82} + 60 q^{85} - 260 q^{88} + 80 q^{91} + 56 q^{94} - 56 q^{97}+O(q^{100}) $ 576 * q - 24 * q^4 - 16 * q^10 + 76 * q^16 - 8 * q^19 + 20 * q^22 + 168 * q^25 - 20 * q^28 - 28 * q^31 + 40 * q^37 + 32 * q^40 + 52 * q^43 - 20 * q^46 - 208 * q^52 - 92 * q^55 + 56 * q^58 + 56 * q^61 - 144 * q^64 - 16 * q^67 - 44 * q^73 - 336 * q^76 + 88 * q^79 - 124 * q^82 + 60 * q^85 - 260 * q^88 + 80 * q^91 + 56 * q^94 - 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/639\mathbb{Z}\right)^\times$.

$n$	$433$	$569$
$\chi(n)$	$e\left(\frac{27}{70}\right)$	$-1$

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 $

$2$	1.46713	−	0.968447i	1.03742	−	0.684796i	0.0871422	−	0.996196i	$-0.472227\pi$
$2$	1.46713	−	0.968447i	1.03742	−	0.684796i	0.950279	+	0.311400i	$0.100798\pi$
$3$		0			0
$3$		0			0
$4$	0.428545	−	1.00263i	0.214272	−	0.501315i
$5$	0.365787	+	0.503462i	0.163585	+	0.225155i	0.882938	−	0.469489i	$-0.155562\pi$
$5$	0.365787	+	0.503462i	0.163585	+	0.225155i	−0.719354	+	0.694644i	$0.755562\pi$
$6$		0			0
$7$	1.05239	+	2.80407i	0.397765	+	1.05984i	0.970712	+	0.240248i	$0.0772287\pi$
$7$	1.05239	+	2.80407i	0.397765	+	1.05984i	−0.572947	+	0.819593i	$0.694200\pi$
$8$	0.285525	+	1.57337i	0.100948	+	0.556272i
$9$		0			0
$10$	1.02423	+	0.384402i	0.323892	+	0.121559i
$11$	0.685905	+	5.06355i	0.206808	+	1.52672i	0.735278	+	0.677766i	$0.237052\pi$
$11$	0.685905	+	5.06355i	0.206808	+	1.52672i	−0.528470	+	0.848952i	$0.677234\pi$
$12$		0			0
$13$	−1.95959	−	0.265444i	−0.543491	−	0.0736209i	−0.142658	−	0.989772i	$-0.545565\pi$
$13$	−1.95959	−	0.265444i	−0.543491	−	0.0736209i	−0.400833	+	0.916151i	$0.631279\pi$
$14$	4.25959	+	3.09477i	1.13842	+	0.827113i
$15$		0			0
$16$	3.44967	+	3.60807i	0.862417	+	0.902018i
$17$	−0.337004	−	1.03719i	−0.0817355	−	0.251556i	0.901835	−	0.432081i	$-0.142220\pi$
$17$	−0.337004	−	1.03719i	−0.0817355	−	0.251556i	−0.983570	+	0.180525i	$0.942220\pi$
$18$		0			0
$19$	−5.50275	−	3.28774i	−1.26242	−	0.754259i	−0.283590	−	0.958946i	$-0.591525\pi$
$19$	−5.50275	−	3.28774i	−1.26242	−	0.754259i	−0.978828	+	0.204687i	$0.934383\pi$
$20$	0.661542	−	0.150993i	0.147925	−	0.0337630i
$21$		0			0
$22$	5.91010	+	6.76465i	1.26004	+	1.44223i
$23$	0.865725	+	1.08558i	0.180516	+	0.226360i	0.863854	−	0.503742i	$-0.168044\pi$
$23$	0.865725	+	1.08558i	0.180516	+	0.226360i	−0.683338	+	0.730102i	$0.739472\pi$
$24$		0			0
$25$	1.42541	−	4.38696i	0.285082	−	0.877393i
$26$	−3.13205	+	1.50831i	−0.614245	+	0.295805i
$27$		0			0
$28$	3.26244	+	0.146516i	0.616544	+	0.0276890i
$29$	4.52536	−	5.17969i	0.840339	−	0.961845i	−0.159339	−	0.987224i	$-0.550936\pi$
$29$	4.52536	−	5.17969i	0.840339	−	0.961845i	0.999678	+	0.0253789i	$0.00807923\pi$
$30$		0			0
$31$	1.48527	+	1.42006i	0.266762	+	0.255050i	0.812575	−	0.582856i	$-0.198065\pi$
$31$	1.48527	+	1.42006i	0.266762	+	0.255050i	−0.545813	+	0.837907i	$0.683779\pi$
$32$	5.43740	+	1.24105i	0.961205	+	0.219389i
$33$		0			0
$34$	−1.49890	−	1.19533i	−0.257058	−	0.204997i
$35$	−1.02680	+	1.55553i	−0.173560	+	0.262933i
$36$		0			0
$37$	5.95288	−	7.46467i	0.978647	−	1.22718i	0.00479828	−	0.999988i	$-0.498473\pi$
$37$	5.95288	−	7.46467i	0.978647	−	1.22718i	0.973849	−	0.227196i	$-0.0729559\pi$
$38$	−11.2573	+	0.505565i	−1.82617	+	0.0820135i
$39$		0			0
$40$	−0.687693	+	0.719271i	−0.108734	+	0.113727i
$41$	7.29489	+	3.51303i	1.13927	+	0.548644i	0.905794	−	0.423719i	$-0.139276\pi$
$41$	7.29489	+	3.51303i	1.13927	+	0.548644i	0.233476	+	0.972362i	$0.424990\pi$
$42$		0			0
$43$	0.540273	−	12.0301i	0.0823909	−	1.83458i	−0.354494	−	0.935058i	$-0.615347\pi$
$43$	0.540273	−	12.0301i	0.0823909	−	1.83458i	0.436885	−	0.899517i	$-0.356082\pi$
$44$	5.37081	+	1.48225i	0.809680	+	0.223457i
$45$		0			0
$46$	2.32147	+	0.754290i	0.342282	+	0.111214i
$47$	−10.8576	+	0.977206i	−1.58375	+	0.142540i	−0.846242	−	0.532798i	$-0.821140\pi$
$47$	−10.8576	+	0.977206i	−1.58375	+	0.142540i	−0.737508	+	0.675338i	$0.763998\pi$
$48$		0			0
$49$	−1.48381	+	1.29637i	−0.211974	+	0.185196i
$50$	−2.15727	−	7.81670i	−0.305084	−	1.10545i
$51$		0			0
$52$	−1.10591	+	1.85098i	−0.153362	+	0.256685i
$53$	3.22128	+	7.53655i	0.442476	+	1.03522i	0.981244	+	0.192770i	$0.0617473\pi$
$53$	3.22128	+	7.53655i	0.442476	+	1.03522i	−0.538768	+	0.842454i	$0.681110\pi$
$54$		0			0
$55$	−2.29841	+	2.19751i	−0.309918	+	0.296312i
$56$	−4.11138	+	2.45643i	−0.549406	+	0.328255i
$57$		0			0
$58$	1.62306	−	11.9819i	0.213118	−	1.57330i
$59$	2.04696	−	3.80389i	0.266492	−	0.495224i	−0.711820	−	0.702362i	$-0.752129\pi$
$59$	2.04696	−	3.80389i	0.266492	−	0.495224i	0.978312	+	0.207137i	$0.0664147\pi$
$60$		0			0
$61$	−0.550000	+	1.46547i	−0.0704203	+	0.187634i	−0.966733	−	0.255789i	$-0.917665\pi$
$61$	−0.550000	+	1.46547i	−0.0704203	+	0.187634i	0.896312	+	0.443423i	$0.146236\pi$
$62$	3.55434	+	0.645018i	0.451402	+	0.0819174i
$63$		0			0
$64$	−0.167772	+	0.0629659i	−0.0209715	+	0.00787074i
$65$	−0.583149	−	1.08367i	−0.0723308	−	0.134413i
$66$		0			0
$67$	0.630195	+	0.269358i	0.0769905	+	0.0329073i	0.431176	−	0.902268i	$-0.358099\pi$
$67$	0.630195	+	0.269358i	0.0769905	+	0.0329073i	−0.354185	+	0.935175i	$0.615242\pi$
$68$	−1.18434	−	0.106593i	−0.143622	−	0.0129262i
$69$		0			0
$70$			3.27657i			0.391625i
$71$	−8.10443	+	2.30612i	−0.961819	+	0.273686i
$71$	−8.10443	+	2.30612i	−0.961819	+	0.273686i
$72$		0			0
$73$	3.11498	+	4.71900i	0.364581	+	0.552317i	0.969850	−	0.243705i	$-0.0783627\pi$
$73$	3.11498	+	4.71900i	0.364581	+	0.552317i	−0.605268	+	0.796022i	$0.706934\pi$
$74$	1.50453	−	16.7167i	0.174898	−	1.94328i
$75$		0			0
$76$	−5.65456	+	4.10828i	−0.648622	+	0.471252i
$77$	−13.4767	+	7.25214i	−1.53582	+	0.826458i
$78$		0			0
$79$	8.42434	−	1.52879i	0.947812	−	0.172003i	0.317425	−	0.948283i	$-0.397182\pi$
$79$	8.42434	−	1.52879i	0.947812	−	0.172003i	0.630387	+	0.776281i	$0.282896\pi$
$80$	−0.554684	+	3.05656i	−0.0620156	+	0.341734i
$81$		0			0
$82$	14.1048	−	1.91062i	1.55761	−	0.210993i
$83$	2.00194	+	1.07729i	0.219741	+	0.118248i	0.580036	−	0.814591i	$-0.303038\pi$
$83$	2.00194	+	1.07729i	0.219741	+	0.118248i	−0.360295	+	0.932838i	$0.617324\pi$
$84$		0			0
$85$	0.398915	−	0.549060i	0.0432684	−	0.0595539i
$86$	−10.8579	−	18.1730i	−1.17084	−	1.95965i
$87$		0			0
$88$	−7.77102	+	2.52496i	−0.828393	+	0.269161i
$89$	−8.45230	+	3.61269i	−0.895942	+	0.382944i	−0.791202	−	0.611555i	$-0.790544\pi$
$89$	−8.45230	+	3.61269i	−0.895942	+	0.382944i	−0.104741	+	0.994500i	$0.533401\pi$
$90$		0			0
$91$	−1.31792	−	5.77417i	−0.138155	−	0.605298i
$92$	1.45944	−	0.402780i	0.152157	−	0.0419927i
$93$		0			0
$94$	−14.9833	+	11.9488i	−1.54541	+	1.23242i
$95$	−0.357580	−	3.97304i	−0.0366869	−	0.407625i
$96$		0			0
$97$	−6.69689	−	13.9062i	−0.679966	−	1.41196i	−0.899746	−	0.436415i	$-0.856248\pi$
$97$	−6.69689	−	13.9062i	−0.679966	−	1.41196i	0.219779	−	0.975550i	$-0.429466\pi$
$98$	−0.921491	+	3.33895i	−0.0930846	+	0.337284i
$99$		0			0
$100$	−3.78765	−	3.30917i	−0.378765	−	0.330917i
$101$	0.820719	−	1.70424i	0.0816646	−	0.169578i	−0.856138	−	0.516747i	$-0.827143\pi$
$101$	0.820719	−	1.70424i	0.0816646	−	0.169578i	0.937803	+	0.347169i	$0.112857\pi$
$102$		0			0
$103$	−3.17339	+	13.9035i	−0.312684	+	1.36996i	0.537408	+	0.843322i	$0.319403\pi$
$103$	−3.17339	+	13.9035i	−0.312684	+	1.36996i	−0.850092	+	0.526634i	$0.823454\pi$
$104$	−0.141869	−	3.15895i	−0.0139114	−	0.309761i
$105$		0			0
$106$	12.0248	+	7.93750i	1.16795	+	0.770958i
$107$	13.9497	+	9.20815i	1.34857	+	0.890185i	0.998909	−	0.0466904i	$-0.0148674\pi$
$107$	13.9497	+	9.20815i	1.34857	+	0.890185i	0.349663	+	0.936875i	$0.386296\pi$
$108$		0			0
$109$	−0.380823	−	8.47969i	−0.0364763	−	0.812207i	−0.930963	−	0.365113i	$-0.881030\pi$
$109$	−0.380823	−	8.47969i	−0.0364763	−	0.812207i	0.894487	−	0.447094i	$-0.147541\pi$
$110$	−1.24391	+	5.44993i	−0.118602	+	0.519630i
$111$		0			0
$112$	−6.48691	+	13.4702i	−0.612956	+	1.27282i
$113$	−4.61891	−	4.03542i	−0.434511	−	0.379621i	0.412709	−	0.910863i	$-0.364583\pi$
$113$	−4.61891	−	4.03542i	−0.434511	−	0.379621i	−0.847220	+	0.531242i	$0.821725\pi$
$114$		0			0
$115$	−0.229880	+	0.832952i	−0.0214364	+	0.0776732i
$116$	−3.25400	−	6.75699i	−0.302126	−	0.627371i
$117$		0			0
$118$	−0.680700	−	7.56319i	−0.0626635	−	0.696248i
$119$	2.55370	−	2.03651i	0.234098	−	0.186687i
$120$		0			0
$121$	−14.5655	+	4.01982i	−1.32414	+	0.365438i
$122$	0.612306	+	2.68269i	0.0554356	+	0.242879i
$123$		0			0
$124$	2.06030	−	0.880614i	0.185020	−	0.0790815i
$125$	5.68934	−	1.84858i	0.508870	−	0.165342i
$126$		0			0
$127$	−6.83494	−	11.4398i	−0.606503	−	1.01512i	−0.995581	−	0.0939101i	$-0.970063\pi$
$127$	−6.83494	−	11.4398i	−0.606503	−	1.01512i	0.389078	−	0.921205i	$-0.372794\pi$
$128$	−6.74159	+	9.27900i	−0.595878	+	0.820156i
$129$		0			0
$130$	−1.90504	−	1.02515i	−0.167083	−	0.0899112i
$131$	8.49169	−	1.15028i	0.741923	−	0.100500i	0.246488	−	0.969146i	$-0.420723\pi$
$131$	8.49169	−	1.15028i	0.741923	−	0.100500i	0.495434	+	0.868645i	$0.335009\pi$
$132$		0			0
$133$	3.42805	−	18.8901i	0.297249	−	1.63798i
$134$	1.18544	−	0.215126i	0.102406	−	0.0185840i
$135$		0			0
$136$	1.53567	−	0.826378i	0.131682	−	0.0708613i
$137$	15.0485	−	10.9334i	1.28568	−	0.934101i	0.285971	−	0.958238i	$-0.407684\pi$
$137$	15.0485	−	10.9334i	1.28568	−	0.934101i	0.999709	+	0.0241378i	$0.00768405\pi$
$138$		0			0
$139$	−1.38182	+	15.3533i	−0.117205	+	1.30225i	0.695056	+	0.718956i	$0.255380\pi$
$139$	−1.38182	+	15.3533i	−0.117205	+	1.30225i	−0.812260	+	0.583295i	$0.801763\pi$
$140$	1.11959	+	1.69611i	0.0946229	+	0.143347i
$141$		0			0
$142$	−9.65694	+	11.2321i	−0.810392	+	0.942577i
$143$		−	10.1045i		−	0.844983i
$144$		0			0
$145$	4.26310	+	0.383686i	0.354031	+	0.0318634i
$146$	9.14020	+	3.90671i	0.756448	+	0.323322i
$147$		0			0
$148$	−4.93323	−	9.16748i	−0.405509	−	0.753562i
$149$	7.71234	−	2.89449i	0.631820	−	0.237126i	−0.0148577	−	0.999890i	$-0.504730\pi$
$149$	7.71234	−	2.89449i	0.631820	−	0.237126i	0.646677	+	0.762764i	$0.276158\pi$
$150$		0			0
$151$	−7.21430	−	1.30920i	−0.587092	−	0.106541i	−0.123120	−	0.992392i	$-0.539290\pi$
$151$	−7.21430	−	1.30920i	−0.587092	−	0.106541i	−0.463971	+	0.885850i	$0.653576\pi$
$152$	3.60167	−	9.59662i	0.292134	−	0.778389i
$153$		0			0
$154$	−12.7489	+	23.6914i	−1.02733	+	1.90911i
$155$	−0.171656	+	1.26722i	−0.0137877	+	0.101785i
$156$		0			0
$157$	−8.81851	+	5.26881i	−0.703794	+	0.420497i	−0.819723	−	0.572760i	$-0.805873\pi$
$157$	−8.81851	+	5.26881i	−0.703794	+	0.420497i	0.115929	+	0.993257i	$0.463015\pi$
$158$	10.8791	−	10.4015i	0.865494	−	0.827497i
$159$		0			0
$160$	1.36410	+	3.19148i	0.107842	+	0.252309i
$161$	−2.13298	+	3.57001i	−0.168103	+	0.281356i
$162$		0			0
$163$	1.90460	+	6.90116i	0.149180	+	0.540541i	0.999889	+	0.0149041i	$0.00474431\pi$
$163$	1.90460	+	6.90116i	0.149180	+	0.540541i	−0.850709	+	0.525637i	$0.823827\pi$
$164$	6.64846	−	5.80858i	0.519157	−	0.453574i
$165$		0			0
$166$	3.98041	−	0.358243i	0.308940	−	0.0278051i
$167$	−9.46102	−	3.07407i	−0.732115	−	0.237879i	−0.0808474	−	0.996726i	$-0.525763\pi$
$167$	−9.46102	−	3.07407i	−0.732115	−	0.237879i	−0.651268	+	0.758848i	$0.725763\pi$
$168$		0			0
$169$	−8.76200	−	2.41816i	−0.674000	−	0.186012i
$170$	0.0535271	−	1.19187i	0.00410534	−	0.0914125i
$171$		0			0
$172$	−11.8302	−	5.69713i	−0.902046	−	0.434402i
$173$	−2.43133	+	2.54297i	−0.184851	+	0.193339i	−0.808727	−	0.588185i	$-0.799843\pi$
$173$	−2.43133	+	2.54297i	−0.184851	+	0.193339i	0.623876	+	0.781523i	$0.285557\pi$
$174$		0			0
$175$	13.8015	−	0.619824i	1.04329	−	0.0468543i
$176$	−15.9035	+	19.9424i	−1.19877	+	1.50321i
$177$		0			0
$178$	−8.90197	+	13.4859i	−0.667231	+	1.01081i
$179$	1.51844	+	1.21092i	0.113494	+	0.0905082i	0.678592	−	0.734515i	$-0.262590\pi$
$179$	1.51844	+	1.21092i	0.113494	+	0.0905082i	−0.565098	+	0.825023i	$0.691162\pi$
$180$		0			0
$181$	−2.92573	−	0.667779i	−0.217468	−	0.0496356i	0.112399	−	0.993663i	$-0.464147\pi$
$181$	−2.92573	−	0.667779i	−0.217468	−	0.0496356i	−0.329867	+	0.944028i	$0.607004\pi$
$182$	−7.52555	−	7.19516i	−0.557831	−	0.533341i
$183$		0			0
$184$	−1.46085	+	1.67207i	−0.107695	+	0.123267i
$185$	5.93566	+	0.266571i	0.436399	+	0.0195987i
$186$		0			0
$187$	5.02072	−	2.41785i	0.367151	−	0.176811i
$188$	−3.67321	+	11.3050i	−0.267896	+	0.824500i
$189$		0			0
$190$	−4.37229	−	5.48268i	−0.317200	−	0.397756i
$191$	−0.0696586	−	0.0797307i	−0.00504032	−	0.00576911i	0.750546	−	0.660818i	$-0.229791\pi$
$191$	−0.0696586	−	0.0797307i	−0.00504032	−	0.00576911i	−0.755586	+	0.655049i	$0.772648\pi$
$192$		0			0
$193$	3.83671	−	0.875704i	0.276172	−	0.0630346i	−0.0821914	−	0.996617i	$-0.526192\pi$
$193$	3.83671	−	0.875704i	0.276172	−	0.0630346i	0.358364	+	0.933582i	$0.383335\pi$
$194$	−23.2927	−	13.9167i	−1.67232	−	0.999164i
$195$		0			0
$196$	0.663898	+	2.04327i	0.0474213	+	0.145948i
$197$	5.89211	+	6.16266i	0.419795	+	0.439071i	0.898546	−	0.438880i	$-0.144625\pi$
$197$	5.89211	+	6.16266i	0.419795	+	0.439071i	−0.478751	+	0.877951i	$0.658910\pi$
$198$		0			0
$199$	20.2815	+	14.7354i	1.43772	+	1.04456i	0.988513	+	0.151133i	$0.0482921\pi$
$199$	20.2815	+	14.7354i	1.43772	+	1.04456i	0.449203	+	0.893430i	$0.351708\pi$
$200$	7.30933	+	0.990116i	0.516847	+	0.0700117i
$201$		0			0
$202$	−0.446362	−	3.29517i	−0.0314059	−	0.231848i
$203$	19.2867	+	7.23841i	1.35366	+	0.508037i
$204$		0			0
$205$	0.899694	+	4.95772i	0.0628373	+	0.346262i
$206$	8.80905	+	23.4716i	0.613756	+	1.63535i
$207$		0			0
$208$	−5.80218	−	7.98602i	−0.402309	−	0.553731i
$209$	12.8733	−	30.1185i	0.890463	−	2.08334i
$210$		0			0
$211$	−2.85544	+	1.88486i	−0.196577	+	0.129759i	−0.645352	−	0.763886i	$-0.723289\pi$
$211$	−2.85544	+	1.88486i	−0.196577	+	0.129759i	0.448775	+	0.893645i	$0.351861\pi$
$212$	8.93683			0.613784
$213$		0			0
$214$	29.3838			2.00863
$215$	6.25433	−	4.12845i	0.426542	−	0.281558i
$216$		0			0
$217$	−2.41888	+	5.65925i	−0.164204	+	0.384175i
$218$	−8.77085	−	12.0720i	−0.594037	−	0.817622i
$219$		0			0
$220$	1.21831	+	3.24619i	0.0821387	+	0.218858i
$221$	0.385072	+	2.12192i	0.0259027	+	0.142736i
$222$		0			0
$223$	0.351249	+	0.131826i	0.0235214	+	0.00882772i	0.363108	−	0.931747i	$-0.381716\pi$
$223$	0.351249	+	0.131826i	0.0235214	+	0.00882772i	−0.339586	+	0.940575i	$0.610287\pi$
$224$	2.24225	+	16.5529i	0.149816	+	1.10599i
$225$		0			0
$226$	−10.6847	−	1.44734i	−0.710733	−	0.0962754i
$227$	0.688417	+	0.500165i	0.0456919	+	0.0331971i	0.610397	−	0.792096i	$-0.291010\pi$
$227$	0.688417	+	0.500165i	0.0456919	+	0.0331971i	−0.564705	+	0.825293i	$0.691010\pi$
$228$		0			0
$229$	−8.29075	−	8.67144i	−0.547868	−	0.573025i	0.389649	−	0.920963i	$-0.372596\pi$
$229$	−8.29075	−	8.67144i	−0.547868	−	0.573025i	−0.937517	+	0.347938i	$0.886882\pi$
$230$	0.469405	+	1.44468i	0.0309517	+	0.0952594i
$231$		0			0
$232$	9.44170	+	5.64116i	0.619878	+	0.370360i
$233$	−0.453103	+	0.103418i	−0.0296837	+	0.00677512i	−0.237337	−	0.971427i	$-0.576275\pi$
$233$	−0.453103	+	0.103418i	−0.0296837	+	0.00677512i	0.207653	+	0.978202i	$0.433417\pi$
$234$		0			0
$235$	−4.46357	−	5.10897i	−0.291171	−	0.333272i
$236$	−2.93668	−	3.68248i	−0.191162	−	0.239709i
$237$		0			0
$238$	1.77437	−	5.46096i	0.115016	−	0.353982i
$239$	−9.04785	+	4.35722i	−0.585257	+	0.281845i	−0.702989	−	0.711201i	$-0.748152\pi$
$239$	−9.04785	+	4.35722i	−0.585257	+	0.281845i	0.117732	+	0.993045i	$0.462438\pi$
$240$		0			0
$241$	−25.1770	−	1.13070i	−1.62179	−	0.0728348i	−0.784693	−	0.619884i	$-0.787179\pi$
$241$	−25.1770	−	1.13070i	−1.62179	−	0.0728348i	−0.837100	+	0.547050i	$0.815751\pi$
$242$	−17.4766	+	20.0035i	−1.12344	+	1.28588i
$243$		0			0
$244$	1.23362	+	1.17947i	0.0789747	+	0.0755076i
$245$	−1.19543	−	0.272850i	−0.0763734	−	0.0174317i
$246$		0			0
$247$	9.91040	+	7.90328i	0.630584	+	0.502874i
$248$	−1.81021	+	2.74235i	−0.114948	+	0.174139i
$249$		0			0
$250$	6.55678	−	8.22194i	0.414687	−	0.520001i
$251$	−25.4885	+	1.14469i	−1.60882	+	0.0722523i	−0.831014	−	0.556251i	$-0.812239\pi$
$251$	−25.4885	+	1.14469i	−1.60882	+	0.0722523i	−0.777807	+	0.628503i	$0.783668\pi$
$252$		0			0
$253$	−4.90311	+	5.12825i	−0.308256	+	0.322410i
$254$	−21.1066	−	10.1644i	−1.32435	−	0.637771i
$255$		0			0
$256$	−0.888518	+	19.7844i	−0.0555324	+	1.23652i
$257$	−4.98701	−	1.37633i	−0.311081	−	0.0858529i	0.107010	−	0.994258i	$-0.465872\pi$
$257$	−4.98701	−	1.37633i	−0.311081	−	0.0858529i	−0.418091	+	0.908405i	$0.637301\pi$
$258$		0			0
$259$	27.1962	+	8.83659i	1.68989	+	0.549079i
$260$	−1.33643	+	0.120281i	−0.0828818	+	0.00745950i
$261$		0			0
$262$	11.3445	−	9.91137i	0.700864	−	0.612326i
$263$	−0.343429	−	1.24439i	−0.0211767	−	0.0767321i	0.952611	−	0.304192i	$-0.0983865\pi$
$263$	−0.343429	−	1.24439i	−0.0211767	−	0.0767321i	−0.973787	+	0.227460i	$0.926958\pi$
$264$		0			0
$265$	−2.61607	+	4.37856i	−0.160704	+	0.268973i
$266$	−13.2647	−	31.0342i	−0.813308	−	1.90283i
$267$		0			0
$268$	0.540133	−	0.516420i	0.0329939	−	0.0315454i
$269$	22.7255	−	13.5779i	1.38560	−	0.827858i	0.389933	−	0.920843i	$-0.372498\pi$
$269$	22.7255	−	13.5779i	1.38560	−	0.827858i	0.995667	+	0.0929853i	$0.0296410\pi$
$270$		0			0
$271$	2.30516	−	17.0174i	0.140029	−	1.03373i	−0.775462	−	0.631394i	$-0.782483\pi$
$271$	2.30516	−	17.0174i	0.140029	−	1.03373i	0.915491	−	0.402339i	$-0.131803\pi$
$272$	2.57971	−	4.79390i	0.156418	−	0.290673i
$273$		0			0
$274$	11.4898	−	30.6144i	0.694123	−	1.84948i
$275$	23.1913	+	4.20860i	1.39849	+	0.253788i
$276$		0			0
$277$	−7.99423	+	3.00028i	−0.480327	+	0.180270i	−0.579781	−	0.814773i	$-0.696862\pi$
$277$	−7.99423	+	3.00028i	−0.480327	+	0.180270i	0.0994540	+	0.995042i	$0.468290\pi$
$278$	12.8416	+	23.8636i	0.770185	+	1.43124i
$279$		0			0
$280$	−2.74061	−	1.17139i	−0.163783	−	0.0700041i
$281$	−23.2883	−	2.09599i	−1.38927	−	0.125036i	−0.630393	−	0.776276i	$-0.717106\pi$
$281$	−23.2883	−	2.09599i	−1.38927	−	0.125036i	−0.758872	+	0.651240i	$0.774249\pi$
$282$		0			0
$283$		−	13.5427i		−	0.805030i	−0.915413	−	0.402515i	$-0.868136\pi$
$283$		−	13.5427i		−	0.805030i	0.915413	−	0.402515i	$-0.131864\pi$
$284$	−1.16092	+	9.11402i	−0.0688882	+	0.540818i
$285$		0			0
$286$	−9.78571	−	14.8247i	−0.578641	−	0.876603i
$287$	−2.17376	+	24.1525i	−0.128313	+	1.42568i
$288$		0			0
$289$	12.7911	−	9.29327i	0.752417	−	0.546663i
$290$	6.62612	−	3.56567i	0.389099	−	0.209383i
$291$		0			0
$292$	6.06632	−	1.10087i	0.355004	−	0.0644238i
$293$	−3.75620	+	20.6984i	−0.219440	+	1.20921i	0.666534	+	0.745475i	$0.267777\pi$
$293$	−3.75620	+	20.6984i	−0.219440	+	1.20921i	−0.885973	+	0.463737i	$0.846508\pi$
$294$		0			0
$295$	2.66387	−	0.360845i	0.155096	−	0.0210092i
$296$	13.4444	+	7.23475i	0.781441	+	0.420512i
$297$		0			0
$298$	8.51188	−	11.7156i	0.493080	−	0.678667i
$299$	−1.40830	−	2.35710i	−0.0814441	−	0.136315i
$300$		0			0
$301$	34.3019	−	11.1454i	1.97713	−	0.642408i
$302$	−11.8522	+	5.06589i	−0.682020	+	0.291509i
$303$		0			0
$304$	−7.12027	−	31.1959i	−0.408375	−	1.78921i
$305$	−0.938992	+	0.259145i	−0.0537665	+	0.0148386i
$306$		0			0
$307$	24.6400	−	19.6497i	1.40628	−	1.12147i	0.430527	−	0.902578i	$-0.358328\pi$
$307$	24.6400	−	19.6497i	1.40628	−	1.12147i	0.975749	−	0.218891i	$-0.0702438\pi$
$308$	1.49583	+	16.6200i	0.0852329	+	0.947015i
$309$		0			0
$310$	0.975389	+	2.02542i	0.0553984	+	0.115036i
$311$	6.14284	−	22.2581i	0.348329	−	1.26214i	−0.554516	−	0.832173i	$-0.687096\pi$
$311$	6.14284	−	22.2581i	0.348329	−	1.26214i	0.902844	−	0.429967i	$-0.141475\pi$
$312$		0			0
$313$	−14.1405	−	12.3542i	−0.799271	−	0.698302i	0.158018	−	0.987436i	$-0.449490\pi$
$313$	−14.1405	−	12.3542i	−0.799271	−	0.698302i	−0.957289	+	0.289134i	$0.906633\pi$
$314$	−7.83537	+	16.2703i	−0.442176	+	0.918187i
$315$		0			0
$316$	2.07739	−	9.10165i	0.116862	−	0.512008i
$317$	−0.430853	−	9.59369i	−0.0241991	−	0.538835i	−0.974077	−	0.226215i	$-0.927365\pi$
$317$	−0.430853	−	9.59369i	−0.0241991	−	0.538835i	0.949878	−	0.312620i	$-0.101207\pi$
$318$		0			0
$319$	29.3316	+	19.3616i	1.64225	+	1.08404i
$320$	−0.0930697	−	0.0614348i	−0.00520276	−	0.00343431i
$321$		0			0
$322$	0.327995	+	7.30337i	0.0182784	+	0.407001i
$323$	−1.55557	+	6.81539i	−0.0865541	+	0.379218i
$324$		0			0
$325$	−3.95771	+	8.21826i	−0.219534	+	0.455867i
$326$	9.47772	+	8.28043i	0.524922	+	0.458611i
$327$		0			0
$328$	−3.44444	+	12.4807i	−0.190187	+	0.689129i
$329$	−14.1666	−	29.4172i	−0.781030	−	1.62183i
$330$		0			0
$331$	0.622447	+	6.91595i	0.0342128	+	0.380135i	0.994777	+	0.102076i	$0.0325484\pi$
$331$	0.622447	+	6.91595i	0.0342128	+	0.380135i	−0.960564	+	0.278059i	$0.910309\pi$
$332$	1.93804	−	1.54554i	0.106364	−	0.0848223i
$333$		0			0
$334$	−16.8577	+	4.65242i	−0.922410	+	0.254569i
$335$	0.0949052	+	0.415807i	0.00518522	+	0.0227180i
$336$		0			0
$337$	−10.1559	+	4.34085i	−0.553229	+	0.236461i	−0.651435	−	0.758705i	$-0.725833\pi$
$337$	−10.1559	+	4.34085i	−0.553229	+	0.236461i	0.0982058	+	0.995166i	$0.468690\pi$
$338$	−15.1969	+	4.93777i	−0.826602	+	0.268579i
$339$		0			0
$340$	−0.379551	−	0.635261i	−0.0205840	−	0.0344518i
$341$	−6.17180	+	8.49475i	−0.334222	+	0.460017i
$342$		0			0
$343$	13.2654	+	7.13839i	0.716262	+	0.385437i
$344$	19.0821	−	2.58485i	1.02884	−	0.139366i
$345$		0			0
$346$	−1.10436	+	6.08550i	−0.0593706	+	0.327159i
$347$	−9.82009	+	1.78208i	−0.527170	+	0.0956673i	−0.435616	−	0.900133i	$-0.643469\pi$
$347$	−9.82009	+	1.78208i	−0.527170	+	0.0956673i	−0.0915545	+	0.995800i	$0.529184\pi$
$348$		0			0
$349$	−16.7308	+	9.00325i	−0.895582	+	0.481933i	−0.855819	−	0.517276i	$-0.826946\pi$
$349$	−16.7308	+	9.00325i	−0.895582	+	0.481933i	−0.0397632	+	0.999209i	$0.512660\pi$
$350$	19.6483	−	14.2753i	1.05025	−	0.763049i
$351$		0			0
$352$	−2.55459	+	28.3838i	−0.136160	+	1.51286i
$353$	−14.3083	−	21.6761i	−0.761552	−	1.15370i	−0.983897	−	0.178734i	$-0.942800\pi$
$353$	−14.3083	−	21.6761i	−0.761552	−	1.15370i	0.222346	−	0.974968i	$-0.428629\pi$
$354$		0			0
$355$	−4.12554	−	3.23673i	−0.218961	−	0.171788i
$356$			10.0227i			0.531203i
$357$		0			0
$358$	3.40047	+	0.306048i	0.179720	+	0.0161751i
$359$	−16.4728	−	7.04080i	−0.869399	−	0.371599i	−0.0883658	−	0.996088i	$-0.528164\pi$
$359$	−16.4728	−	7.04080i	−0.869399	−	0.371599i	−0.781034	+	0.624489i	$0.785307\pi$
$360$		0			0
$361$	10.4675	+	19.4519i	0.550922	+	1.02378i
$362$	−4.93915	+	1.85369i	−0.259596	+	0.0974280i
$363$		0			0
$364$	−6.35415	−	1.15311i	−0.333048	−	0.0604392i
$365$	−1.23642	+	3.29442i	−0.0647171	+	0.172438i
$366$		0			0
$367$	6.39796	−	11.8894i	0.333971	−	0.620622i	−0.657124	−	0.753783i	$-0.728227\pi$
$367$	6.39796	−	11.8894i	0.333971	−	0.620622i	0.991094	+	0.133161i	$0.0425128\pi$
$368$	−0.930402	+	6.86851i	−0.0485006	+	0.358046i
$369$		0			0
$370$	8.96658	−	5.35728i	0.466150	−	0.278512i
$371$	−17.7430	+	16.9641i	−0.921172	+	0.880730i
$372$		0			0
$373$	−5.69548	−	13.3252i	−0.294901	−	0.689955i	0.704912	−	0.709295i	$-0.250986\pi$
$373$	−5.69548	−	13.3252i	−0.294901	−	0.689955i	−0.999813	+	0.0193398i	$0.993844\pi$
$374$	5.02451	−	8.40961i	0.259811	−	0.434851i
$375$		0			0
$376$	−4.63764	−	16.8041i	−0.239168	−	0.866607i
$377$	−10.2428	+	8.94882i	−0.527529	+	0.460888i
$378$		0			0
$379$	3.35576	−	0.302024i	0.172374	−	0.0155139i	−0.00311605	−	0.999995i	$-0.500992\pi$
$379$	3.35576	−	0.302024i	0.172374	−	0.0155139i	0.175490	+	0.984481i	$0.443849\pi$
$380$	−4.13672	−	1.34410i	−0.212209	−	0.0689510i
$381$		0			0
$382$	−0.179414	−	0.0495150i	−0.00917960	−	0.00253341i
$383$	−1.44960	+	32.2778i	−0.0740710	+	1.64932i	0.526812	+	0.849982i	$0.323387\pi$
$383$	−1.44960	+	32.2778i	−0.0740710	+	1.64932i	−0.600883	+	0.799337i	$0.705184\pi$
$384$		0			0
$385$	−8.58079	−	4.13229i	−0.437317	−	0.210601i
$386$	4.78090	−	5.00043i	0.243341	−	0.254515i
$387$		0			0
$388$	−16.8127	+	0.755060i	−0.853537	+	0.0383324i
$389$	15.4640	−	19.3913i	0.784058	−	0.983177i	−0.215920	−	0.976411i	$-0.569275\pi$
$389$	15.4640	−	19.3913i	0.784058	−	0.983177i	0.999977	−	0.00676593i	$-0.00215368\pi$
$390$		0			0
$391$	0.834207	−	1.26377i	0.0421876	−	0.0639115i
$392$	−2.46334	−	1.96445i	−0.124418	−	0.0992197i
$393$		0			0
$394$	14.6127	+	3.33526i	0.736178	+	0.168028i
$395$	3.85120	+	3.68212i	0.193775	+	0.185268i
$396$		0			0
$397$	−1.59787	+	1.82891i	−0.0801947	+	0.0917902i	−0.791769	−	0.610821i	$-0.790840\pi$
$397$	−1.59787	+	1.82891i	−0.0801947	+	0.0917902i	0.711574	+	0.702611i	$0.247983\pi$
$398$	44.0261	+	1.97721i	2.20683	+	0.0991088i
$399$		0			0
$400$	20.7457	−	9.99059i	1.03728	−	0.499529i
$401$	−1.39493	+	4.29315i	−0.0696595	+	0.214390i	−0.979826	−	0.199853i	$-0.935954\pi$
$401$	−1.39493	+	4.29315i	−0.0696595	+	0.214390i	0.910166	+	0.414243i	$0.135954\pi$
$402$		0			0
$403$	−2.53356	−	3.17699i	−0.126206	−	0.158257i
$404$	−1.35701	−	1.55322i	−0.0675137	−	0.0772756i
$405$		0			0
$406$	35.3062	−	8.05840i	1.75222	−	0.399932i
$407$	41.8809	+	25.0226i	2.07596	+	1.24033i
$408$		0			0
$409$	7.24662	+	22.3028i	0.358322	+	1.10280i	0.954058	+	0.299622i	$0.0968606\pi$
$409$	7.24662	+	22.3028i	0.358322	+	1.10280i	−0.595736	+	0.803181i	$0.703139\pi$
$410$	6.12126	+	6.40234i	0.302308	+	0.316189i
$411$		0			0
$412$	12.5802	+	9.14002i	0.619780	+	0.450297i
$413$	12.8206	+	1.73667i	0.630860	+	0.0854557i
$414$		0			0
$415$	0.189908	+	1.40196i	0.00932222	+	0.0688194i
$416$	−10.3256	−	3.87527i	−0.506255	−	0.190001i
$417$		0			0
$418$	−10.2814	−	56.6550i	−0.502878	−	2.77109i
$419$	−6.76730	−	18.0314i	−0.330604	−	0.880892i	−0.991464	−	0.130382i	$-0.958380\pi$
$419$	−6.76730	−	18.0314i	−0.330604	−	0.880892i	0.660860	−	0.750510i	$-0.270192\pi$
$420$		0			0
$421$	14.1764	+	19.5121i	0.690914	+	0.950962i	1.00000		7.22153e-5i	$-2.29869e-5\pi$
$421$	14.1764	+	19.5121i	0.690914	+	0.950962i	−0.309086	+	0.951034i	$0.600023\pi$
$422$	−2.36393	+	5.53069i	−0.115074	+	0.269230i
$423$		0			0
$424$	−10.9381	+	7.22015i	−0.531199	+	0.350642i
$425$	−5.03049			−0.244015
$426$		0			0
$427$	−4.68810			−0.226873
$428$	15.2104	−	10.0403i	0.735225	−	0.485318i
$429$		0			0
$430$	5.17776	−	12.1140i	0.249694	−	0.584188i
$431$	−15.6177	−	21.4960i	−0.752280	−	1.03542i	−0.997817	−	0.0660376i	$-0.978964\pi$
$431$	−15.6177	−	21.4960i	−0.752280	−	1.03542i	0.245537	−	0.969387i	$-0.421036\pi$
$432$		0			0
$433$	−3.07843	−	8.20244i	−0.147940	−	0.394184i	0.841284	−	0.540593i	$-0.181800\pi$
$433$	−3.07843	−	8.20244i	−0.147940	−	0.394184i	−0.989224	+	0.146409i	$0.953229\pi$
$434$	1.93186	+	10.6454i	0.0927324	+	0.510998i
$435$		0			0
$436$	−8.66519	−	3.25210i	−0.414987	−	0.155747i
$437$	−1.19475	−	8.81998i	−0.0571525	−	0.421917i
$438$		0			0
$439$	−10.7912	−	1.46177i	−0.515037	−	0.0697665i	−0.127897	−	0.991787i	$-0.540823\pi$
$439$	−10.7912	−	1.46177i	−0.515037	−	0.0697665i	−0.387140	+	0.922021i	$0.626537\pi$
$440$	−4.11376	−	2.98882i	−0.196116	−	0.142486i
$441$		0			0
$442$	2.61992	+	2.74022i	0.124617	+	0.130339i
$443$	2.70487	+	8.32474i	0.128512	+	0.395520i	0.994525	−	0.104502i	$-0.0333250\pi$
$443$	2.70487	+	8.32474i	0.128512	+	0.395520i	−0.866012	+	0.500023i	$0.833325\pi$
$444$		0			0
$445$	−4.91059	−	2.93394i	−0.232784	−	0.139082i
$446$	0.642996	−	0.146760i	0.0304468	−	0.00694927i
$447$		0			0
$448$	−0.353122	−	0.404181i	−0.0166835	−	0.0190957i
$449$	12.8195	+	16.0752i	0.604992	+	0.758636i	0.986147	−	0.165875i	$-0.0530450\pi$
$449$	12.8195	+	16.0752i	0.604992	+	0.758636i	−0.381155	+	0.924511i	$0.624474\pi$
$450$		0			0
$451$	−12.7848	+	39.3476i	−0.602014	+	1.85281i
$452$	−6.02545	+	2.90170i	−0.283413	+	0.136485i
$453$		0			0
$454$	1.49438	+	0.0671129i	0.0701349	+	0.00314976i
$455$	2.42500	−	2.77564i	0.113686	−	0.130124i
$456$		0			0
$457$	24.4295	+	23.3570i	1.14277	+	1.09260i	0.994616	+	0.103631i	$0.0330460\pi$
$457$	24.4295	+	23.3570i	1.14277	+	1.09260i	0.148149	+	0.988965i	$0.452668\pi$
$458$	−20.5615	−	4.69302i	−0.960775	−	0.219291i
$459$		0			0
$460$	0.736629	+	0.587442i	0.0343455	+	0.0273896i
$461$	9.64665	−	14.6141i	0.449289	−	0.680644i	−0.537388	−	0.843335i	$-0.680589\pi$
$461$	9.64665	−	14.6141i	0.449289	−	0.680644i	0.986677	+	0.162691i	$0.0520174\pi$
$462$		0			0
$463$	9.14254	−	11.4644i	0.424890	−	0.532795i	−0.522601	−	0.852577i	$-0.675038\pi$
$463$	9.14254	−	11.4644i	0.424890	−	0.532795i	0.947491	+	0.319782i	$0.103610\pi$
$464$	34.2997	−	1.54040i	1.59232	−	0.0715113i
$465$		0			0
$466$	−0.564608	+	0.590534i	−0.0261550	+	0.0273559i
$467$	−35.5988	−	17.1435i	−1.64732	−	0.793307i	−0.999503	−	0.0315088i	$-0.989969\pi$
$467$	−35.5988	−	17.1435i	−1.64732	−	0.793307i	−0.647815	−	0.761798i	$-0.724317\pi$
$468$		0			0
$469$	−0.0920917	+	2.05058i	−0.00425240	+	0.0946871i
$470$	−11.4964	−	3.17281i	−0.530290	−	0.146351i
$471$		0			0
$472$	6.56940	+	2.13453i	0.302381	+	0.0982496i
$473$	61.2857	−	5.51581i	2.81792	−	0.253617i
$474$		0			0
$475$	−22.2669	+	19.4540i	−1.02167	+	0.892610i
$476$	−0.947490	−	3.43315i	−0.0434282	−	0.157358i
$477$		0			0
$478$	−9.05468	+	15.1550i	−0.414152	+	0.693173i
$479$	14.1922	+	33.2042i	0.648456	+	1.51714i	0.843943	+	0.536433i	$0.180228\pi$
$479$	14.1922	+	33.2042i	0.648456	+	1.51714i	−0.195487	+	0.980706i	$0.562629\pi$
$480$		0			0
$481$	−13.6466	+	13.0475i	−0.622233	+	0.594915i
$482$	−38.0331	+	22.7237i	−1.73236	+	1.03504i
$483$		0			0
$484$	−2.21157	+	16.3265i	−0.100526	+	0.742112i
$485$	4.55163	−	8.45835i	0.206679	−	0.384074i
$486$		0			0
$487$	−3.93262	+	10.4784i	−0.178204	+	0.474823i	−0.994735	−	0.102478i	$-0.967323\pi$
$487$	−3.93262	+	10.4784i	−0.178204	+	0.474823i	0.816531	+	0.577301i	$0.195894\pi$
$488$	−2.46277	−	0.446927i	−0.111484	−	0.0202315i
$489$		0			0
$490$	−2.01810	+	0.757406i	−0.0911686	+	0.0342161i
$491$	9.03640	+	16.7924i	0.407807	+	0.757833i	0.998807	−	0.0488393i	$-0.0155522\pi$
$491$	9.03640	+	16.7924i	0.407807	+	0.757833i	−0.591000	+	0.806672i	$0.701267\pi$
$492$		0			0
$493$	−6.89740	−	2.94809i	−0.310643	−	0.132775i
$494$	22.1938	+	1.99748i	0.998546	+	0.0898708i
$495$		0			0
$496$			10.2577i			0.460584i
$497$	−14.9955	−	20.2985i	−0.672641	−	0.910512i
$498$		0			0
$499$	11.8151	+	17.8991i	0.528917	+	0.801276i	0.996580	−	0.0826313i	$-0.0263324\pi$
$499$	11.8151	+	17.8991i	0.528917	+	0.801276i	−0.467663	+	0.883907i	$0.654904\pi$
$500$	0.584696	−	6.49650i	0.0261484	−	0.290532i
$501$		0			0
$502$	−36.2865	+	26.3637i	−1.61955	+	1.17667i
$503$	−11.7026	+	6.29744i	−0.521793	+	0.280789i	−0.713490	−	0.700665i	$-0.752887\pi$
$503$	−11.7026	+	6.29744i	−0.521793	+	0.280789i	0.191697	+	0.981454i	$0.438601\pi$
$504$		0			0
$505$	1.15823	−	0.210188i	0.0515405	−	0.00935322i
$506$	−2.22708	+	12.2722i	−0.0990059	+	0.545567i
$507$		0			0
$508$	−14.3989	+	1.95047i	−0.638849	+	0.0865380i
$509$	26.2229	+	14.1111i	1.16231	+	0.625465i	0.937174	−	0.348863i	$-0.113432\pi$
$509$	26.2229	+	14.1111i	1.16231	+	0.625465i	0.225134	+	0.974328i	$0.427718\pi$
$510$		0			0
$511$	−9.95425	+	13.7009i	−0.440350	+	0.606090i
$512$	6.09118	+	10.1949i	0.269195	+	0.450556i
$513$		0			0
$514$	−8.64951	+	2.81040i	−0.381513	+	0.123961i
$515$	−8.16069	+	3.48805i	−0.359603	+	0.153702i
$516$		0			0
$517$	−12.3954	−	54.3080i	−0.545151	−	2.38846i
$518$	48.4583	−	13.3736i	2.12914	−	0.587604i
$519$		0			0
$520$	1.53852	−	1.22693i	0.0674686	−	0.0538044i
$521$	2.68911	+	29.8785i	0.117812	+	1.30900i	0.809636	+	0.586933i	$0.199665\pi$
$521$	2.68911	+	29.8785i	0.117812	+	1.30900i	−0.691823	+	0.722067i	$0.743192\pi$
$522$		0			0
$523$	−14.7040	−	30.5332i	−0.642961	−	1.33512i	−0.926548	−	0.376177i	$-0.877239\pi$
$523$	−14.7040	−	30.5332i	−0.642961	−	1.33512i	0.283587	−	0.958947i	$-0.408476\pi$
$524$	2.48577	−	9.00697i	0.108591	−	0.393471i
$525$		0			0
$526$	−1.70898	−	1.49309i	−0.0745150	−	0.0651018i
$527$	0.972334	−	2.01907i	0.0423555	−	0.0879522i
$528$		0			0
$529$	4.68897	−	20.5437i	0.203868	−	0.893205i
$530$	0.402280	+	8.95746i	0.0174739	+	0.389087i
$531$		0			0
$532$	−17.4707	−	11.5323i	−0.757451	−	0.499989i
$533$	−13.3624	−	8.82047i	−0.578792	−	0.382057i
$534$		0			0
$535$	0.466678	+	10.3914i	0.0201762	+	0.449259i
$536$	−0.243865	+	1.06844i	−0.0105333	+	0.0461496i
$537$		0			0
$538$	20.1920	−	41.9291i	0.870538	−	1.80769i
$539$	−7.58199	−	6.62419i	−0.326579	−	0.285324i
$540$		0			0
$541$	−10.9061	+	39.5173i	−0.468889	+	1.69898i	0.221177	+	0.975234i	$0.429010\pi$
$541$	−10.9061	+	39.5173i	−0.468889	+	1.69898i	−0.690065	+	0.723747i	$0.742418\pi$
$542$	−13.0985	−	27.1992i	−0.562627	−	1.16831i
$543$		0			0
$544$	−0.545217	−	6.05786i	−0.0233760	−	0.259729i
$545$	4.12990	−	3.29349i	0.176906	−	0.141078i
$546$		0			0
$547$	−18.7121	+	5.16421i	−0.800072	+	0.220806i	−0.642083	−	0.766635i	$-0.721930\pi$
$547$	−18.7121	+	5.16421i	−0.800072	+	0.220806i	−0.157989	+	0.987441i	$0.550501\pi$
$548$	−4.51317	−	19.7735i	−0.192793	−	0.844682i
$549$		0			0
$550$	38.1006	−	16.2850i	1.62461	−	0.694393i
$551$	−41.9314	+	13.6243i	−1.78634	+	0.580417i
$552$		0			0
$553$	13.1525	+	22.0136i	0.559302	+	0.936113i
$554$	−8.82300	+	12.1438i	−0.374853	+	0.515941i
$555$		0			0
$556$	14.8015	+	7.96504i	0.627724	+	0.337793i
$557$	−3.34422	+	0.453006i	−0.141699	+	0.0191945i	−0.204739	−	0.978817i	$-0.565635\pi$
$557$	−3.34422	+	0.453006i	−0.141699	+	0.0191945i	0.0630401	+	0.998011i	$0.479920\pi$
$558$		0			0
$559$	−4.25203	+	23.4306i	−0.179842	+	0.991010i
$560$	−9.15457	+	1.66131i	−0.386851	+	0.0702031i
$561$		0			0
$562$	−36.1970	+	19.4784i	−1.52688	+	0.821648i
$563$	−0.395740	+	0.287522i	−0.0166784	+	0.0121176i	−0.596093	−	0.802915i	$-0.703281\pi$
$563$	−0.395740	+	0.287522i	−0.0166784	+	0.0121176i	0.579415	+	0.815033i	$0.303281\pi$
$564$		0			0
$565$	0.342146	−	3.80155i	0.0143942	−	0.159933i
$566$	−13.1154	−	19.8690i	−0.551281	−	0.835155i
$567$		0			0
$568$	−5.94241	−	12.0929i	−0.249338	−	0.507405i
$569$			24.0017i			1.00621i	0.864227	+	0.503103i	$0.167808\pi$
$569$			24.0017i			1.00621i	−0.864227	+	0.503103i	$0.832192\pi$
$570$		0			0
$571$	−39.8006	−	3.58212i	−1.66560	−	0.149907i	−0.783638	−	0.621218i	$-0.786638\pi$
$571$	−39.8006	−	3.58212i	−1.66560	−	0.149907i	−0.881967	+	0.471311i	$0.843781\pi$
$572$	−10.1311	−	4.33024i	−0.423603	−	0.181056i
$573$		0			0
$574$	20.2012	+	37.5401i	0.843182	+	1.56689i
$575$	5.99643	−	2.25050i	0.250069	−	0.0938523i
$576$		0			0
$577$	−20.8079	−	3.77608i	−0.866245	−	0.157200i	−0.272796	−	0.962072i	$-0.587948\pi$
$577$	−20.8079	−	3.77608i	−0.866245	−	0.157200i	−0.593449	+	0.804871i	$0.702234\pi$
$578$	9.76621	−	26.0220i	0.406221	−	1.08237i
$579$		0			0
$580$	2.21162	−	4.10988i	0.0918326	−	0.170654i
$581$	−0.913985	+	6.74731i	−0.0379185	+	0.279925i
$582$		0			0
$583$	−35.9522	+	21.4805i	−1.48899	+	0.889629i
$584$	−6.53534	+	6.24843i	−0.270434	+	0.258562i
$585$		0			0
$586$	14.5344	+	34.0050i	0.600412	+	1.40473i
$587$	9.44416	−	15.8069i	0.389802	−	0.652419i	−0.599153	−	0.800635i	$-0.704496\pi$
$587$	9.44416	−	15.8069i	0.389802	−	0.652419i	0.988955	+	0.148215i	$0.0473529\pi$
$588$		0			0
$589$	−3.50426	−	12.6974i	−0.144391	−	0.523188i
$590$	3.55879	−	3.10922i	0.146513	−	0.128005i
$591$		0			0
$592$	47.4685	−	4.27225i	1.95094	−	0.175588i
$593$	−33.7417	−	10.9633i	−1.38561	−	0.450211i	−0.481098	−	0.876667i	$-0.659762\pi$
$593$	−33.7417	−	10.9633i	−1.38561	−	0.450211i	−0.904508	+	0.426456i	$0.859762\pi$
$594$		0			0
$595$	1.95942	+	0.540765i	0.0803282	+	0.0221692i
$596$	0.402980	−	8.97304i	0.0165067	−	0.367550i
$597$		0			0
$598$	−4.34889	−	2.09432i	−0.177839	−	0.0856430i
$599$	−9.98349	+	10.4419i	−0.407914	+	0.426645i	−0.894555	−	0.446957i	$-0.852508\pi$
$599$	−9.98349	+	10.4419i	−0.407914	+	0.426645i	0.486641	+	0.873602i	$0.338222\pi$
$600$		0			0
$601$	−24.4244	+	1.09690i	−0.996292	+	0.0447435i	−0.537035	−	0.843560i	$-0.680456\pi$
$601$	−24.4244	+	1.09690i	−0.996292	+	0.0447435i	−0.459257	+	0.888303i	$0.651884\pi$
$602$	39.5318	−	49.5713i	1.61120	−	2.02038i
$603$		0			0
$604$	−4.40430	+	6.67222i	−0.179208	+	0.271489i
$605$	−7.35169	−	5.86278i	−0.298889	−	0.238356i
$606$		0			0
$607$	29.4795	+	6.72850i	1.19654	+	0.273101i	0.773965	−	0.633229i	$-0.218271\pi$
$607$	29.4795	+	6.72850i	1.19654	+	0.273101i	0.422571	+	0.906330i	$0.361128\pi$
$608$	−25.8404	−	24.7059i	−1.04797	−	1.00196i
$609$		0			0
$610$	−1.12666	+	1.28956i	−0.0456171	+	0.0522130i
$611$	21.5359	+	0.967178i	0.871249	+	0.0391278i
$612$		0			0
$613$	−13.4511	+	6.47769i	−0.543283	+	0.261631i	−0.685335	−	0.728228i	$-0.740344\pi$
$613$	−13.4511	+	6.47769i	−0.543283	+	0.261631i	0.142052	+	0.989859i	$0.454630\pi$
$614$	17.1204	−	52.6913i	0.690924	−	2.12645i
$615$		0			0
$616$	−15.2583	−	19.1333i	−0.614774	−	0.770902i
$617$	−16.4430	−	18.8205i	−0.661970	−	0.757685i	0.319857	−	0.947466i	$-0.396365\pi$
$617$	−16.4430	−	18.8205i	−0.661970	−	0.757685i	−0.981827	+	0.189780i	$0.939222\pi$
$618$		0			0
$619$	23.4983	−	5.36333i	0.944476	−	0.215570i	0.277564	−	0.960707i	$-0.410473\pi$
$619$	23.4983	−	5.36333i	0.944476	−	0.215570i	0.666912	+	0.745137i	$0.267616\pi$
$620$	1.19699	+	0.715166i	0.0480721	+	0.0287217i
$621$		0			0
$622$	−12.5434	−	38.6046i	−0.502945	−	1.54791i
$623$	−19.0253	−	19.8989i	−0.762234	−	0.797234i
$624$		0			0
$625$	−15.6471	−	11.3683i	−0.625884	−	0.454731i
$626$	−32.7105	−	4.43094i	−1.30737	−	0.177096i
$627$		0			0
$628$	1.50355	+	11.0996i	0.0599980	+	0.442923i
$629$	−9.74844	−	3.65865i	−0.388696	−	0.145880i
$630$		0			0
$631$	−4.66849	−	25.7255i	−0.185850	−	1.02412i	−0.933112	−	0.359587i	$-0.882918\pi$
$631$	−4.66849	−	25.7255i	−0.185850	−	1.02412i	0.747262	−	0.664530i	$-0.231368\pi$
$632$	4.81073	+	12.8181i	0.191360	+	0.509878i
$633$		0			0
$634$	−9.92310	−	13.6580i	−0.394097	−	0.542428i
$635$	3.25936	−	7.62565i	0.129344	−	0.302615i
$636$		0			0
$637$	3.25178	−	2.14648i	0.128840	−	0.0850466i
$638$	61.7841			2.44606
$639$		0			0
$640$	−7.13761			−0.282139
$641$	12.7421	−	8.41098i	0.503283	−	0.332214i	−0.273617	−	0.961839i	$-0.588220\pi$
$641$	12.7421	−	8.41098i	0.503283	−	0.332214i	0.776899	+	0.629625i	$0.216791\pi$
$642$		0			0
$643$	14.4784	−	33.8739i	0.570972	−	1.33586i	−0.346498	−	0.938051i	$-0.612629\pi$
$643$	14.4784	−	33.8739i	0.570972	−	1.33586i	0.917470	−	0.397805i	$-0.130228\pi$
$644$	2.66532	+	3.66850i	0.105028	+	0.144559i
$645$		0			0
$646$	4.31811	+	11.5056i	0.169894	+	0.452681i
$647$	−2.43358	−	13.4102i	−0.0956740	−	0.527207i	−0.995798	−	0.0915741i	$-0.970810\pi$
$647$	−2.43358	−	13.4102i	−0.0956740	−	0.527207i	0.900124	−	0.435633i	$-0.143476\pi$
$648$		0			0
$649$	20.6652	+	7.75578i	0.811180	+	0.304441i
$650$	2.15246	+	15.8901i	0.0844266	+	0.623262i
$651$		0			0
$652$	7.73552	+	1.04785i	0.302946	+	0.0410369i
$653$	−17.3369	−	12.5960i	−0.678444	−	0.492918i	0.194397	−	0.980923i	$-0.437725\pi$
$653$	−17.3369	−	12.5960i	−0.678444	−	0.492918i	−0.872841	+	0.488005i	$0.837725\pi$
$654$		0			0
$655$	3.68527	+	3.85449i	0.143995	+	0.150607i
$656$	12.4897	+	38.4393i	0.487640	+	1.50080i
$657$		0			0
$658$	−49.2734	−	29.4395i	−1.92088	−	1.14767i
$659$	−37.1779	+	8.48560i	−1.44824	+	0.330552i	−0.873117	−	0.487512i	$-0.837905\pi$
$659$	−37.1779	+	8.48560i	−1.44824	+	0.330552i	−0.575127	+	0.818064i	$0.695048\pi$
$660$		0			0
$661$	14.9829	+	17.1493i	0.582767	+	0.667031i	0.966576	−	0.256382i	$-0.0825305\pi$
$661$	14.9829	+	17.1493i	0.582767	+	0.667031i	−0.383808	+	0.923413i	$0.625388\pi$
$662$	7.61095	+	9.54382i	0.295808	+	0.370931i
$663$		0			0
$664$	−1.12337	+	3.45739i	−0.0435954	+	0.134173i
$665$	10.7644	−	5.18385i	0.417425	−	0.201021i
$666$		0			0
$667$	9.54072	+	0.428474i	0.369418	+	0.0165906i
$668$	−7.13662	+	8.16852i	−0.276124	+	0.316050i
$669$		0			0
$670$	0.541926	+	0.518134i	0.0209364	+	0.0200173i
$671$	−7.79773	−	1.77978i	−0.301028	−	0.0687077i
$672$		0			0
$673$	−34.3897	−	27.4248i	−1.32562	−	1.05715i	−0.993490	−	0.113918i	$-0.963660\pi$
$673$	−34.3897	−	27.4248i	−1.32562	−	1.05715i	−0.332134	−	0.943232i	$-0.607769\pi$
$674$	−10.6962	+	16.2041i	−0.412003	+	0.624159i
$675$		0			0
$676$	−6.17943	+	7.74875i	−0.237670	+	0.298029i
$677$	−33.2326	+	1.49248i	−1.27723	+	0.0573605i	−0.673116	−	0.739537i	$-0.735045\pi$
$677$	−33.2326	+	1.49248i	−1.27723	+	0.0573605i	−0.604115	+	0.796897i	$0.706473\pi$
$678$		0			0
$679$	31.9464	−	33.4133i	1.22599	−	1.28229i
$680$	0.977777	+	0.470872i	0.0374960	+	0.0180571i
$681$		0			0
$682$	−0.828142	+	18.4400i	−0.0317112	+	0.706104i
$683$	−13.7960	−	3.80746i	−0.527889	−	0.145688i	−0.00807494	−	0.999967i	$-0.502570\pi$
$683$	−13.7960	−	3.80746i	−0.527889	−	0.145688i	−0.519814	+	0.854279i	$0.673999\pi$
$684$		0			0
$685$	11.0091	+	3.57706i	0.420635	+	0.136673i
$686$	26.3752	−	2.37381i	1.00701	−	0.0906326i
$687$		0			0
$688$	45.2693	−	39.5506i	1.72587	−	1.50785i
$689$	−4.31184	−	15.6236i	−0.164268	−	0.595211i
$690$		0			0
$691$	−6.61623	+	11.0737i	−0.251693	+	0.421264i	−0.958054	−	0.286589i	$-0.907479\pi$
$691$	−6.61623	+	11.0737i	−0.251693	+	0.421264i	0.706360	+	0.707852i	$0.250336\pi$
$692$	1.50773	+	3.52750i	0.0573152	+	0.134096i
$693$		0			0
$694$	−12.6815	+	12.1248i	−0.481385	+	0.460251i
$695$	−8.23527	+	4.92034i	−0.312381	+	0.186639i
$696$		0			0
$697$	1.18528	−	8.75010i	0.0448958	−	0.331434i
$698$	−15.8272	+	29.4119i	−0.599070	+	1.11326i
$699$		0			0
$700$	5.29308	−	14.1034i	0.200060	−	0.533057i
$701$	1.54976	+	0.281241i	0.0585337	+	0.0106223i	0.207745	−	0.978183i	$-0.433388\pi$
$701$	1.54976	+	0.281241i	0.0585337	+	0.0106223i	−0.149211	+	0.988805i	$0.547673\pi$
$702$		0			0
$703$	−57.2991	+	21.5047i	−2.16108	+	0.811066i
$704$	−0.433907	−	0.806334i	−0.0163535	−	0.0303898i
$705$		0			0
$706$	−41.9843	−	17.9449i	−1.58010	−	0.675367i
$707$	5.64253	+	0.507837i	0.212209	+	0.0190992i
$708$		0			0
$709$		−	20.7716i		−	0.780093i	−0.920795	−	0.390046i	$-0.872459\pi$
$709$		−	20.7716i		−	0.780093i	0.920795	−	0.390046i	$-0.127541\pi$
$710$	−9.18732	−	0.753349i	−0.344794	−	0.0282727i
$711$		0			0
$712$	−8.09746	−	12.2671i	−0.303465	−	0.459730i
$713$	−0.255764	+	2.84177i	−0.00957842	+	0.106425i
$714$		0			0
$715$	5.08725	−	3.69610i	0.190252	−	0.138226i
$716$	1.86482	−	1.00350i	0.0696916	−	0.0375027i
$717$		0			0
$718$	−30.9864	+	5.62320i	−1.15640	+	0.209856i
$719$	−2.47955	+	13.6634i	−0.0924715	+	0.509560i	0.904135	+	0.427247i	$0.140517\pi$
$719$	−2.47955	+	13.6634i	−0.0924715	+	0.509560i	−0.996607	+	0.0823132i	$0.973769\pi$
$720$		0			0
$721$	−42.3262	+	5.73347i	−1.57631	+	0.213526i
$722$	34.1954	+	18.4013i	1.27262	+	0.684826i
$723$		0			0
$724$	−1.92334	+	2.64725i	−0.0714804	+	0.0983843i
$725$	−16.2726	−	27.2358i	−0.604350	−	1.01151i
$726$		0			0
$727$	17.3722	−	5.64457i	0.644299	−	0.209345i	0.0314003	−	0.999507i	$-0.490003\pi$
$727$	17.3722	−	5.64457i	0.644299	−	0.209345i	0.612899	+	0.790161i	$0.290003\pi$
$728$	8.70864	−	3.72225i	0.322764	−	0.137956i
$729$		0			0
$730$	1.37648	+	6.03077i	0.0509459	+	0.223209i
$731$	−12.6596	+	3.49383i	−0.468232	+	0.129224i
$732$		0			0
$733$	37.7942	−	30.1399i	1.39596	−	1.11324i	0.417065	−	0.908877i	$-0.363059\pi$
$733$	37.7942	−	30.1399i	1.39596	−	1.11324i	0.978895	−	0.204364i	$-0.0655127\pi$
$734$	−2.12759	−	23.6394i	−0.0785307	−	0.872547i
$735$		0			0
$736$	3.36002	+	6.97716i	0.123852	+	0.257182i
$737$	−0.931655	+	3.37578i	−0.0343180	+	0.124348i
$738$		0			0
$739$	30.1887	+	26.3751i	1.11051	+	0.970222i	0.999721	−	0.0236217i	$-0.00751971\pi$
$739$	30.1887	+	26.3751i	1.11051	+	0.970222i	0.110788	+	0.993844i	$0.464663\pi$
$740$	2.81097	−	5.83704i	0.103333	−	0.214574i
$741$		0			0
$742$	−9.60260	+	42.0717i	−0.352523	+	1.54450i
$743$	2.30656	+	51.3595i	0.0846195	+	1.88420i	0.374629	+	0.927175i	$0.377770\pi$
$743$	2.30656	+	51.3595i	0.0846195	+	1.88420i	−0.290009	+	0.957024i	$0.593658\pi$
$744$		0			0
$745$	4.27834	+	2.82411i	0.156746	+	0.103467i
$746$	−21.2608	−	14.0342i	−0.778414	−	0.513827i
$747$		0			0
$748$	−0.272608	−	6.07008i	−0.00996752	−	0.221944i
$749$	−11.1398	+	48.8066i	−0.407039	+	1.78336i
$750$		0			0
$751$	−14.8250	+	30.7844i	−0.540971	+	1.12334i	0.433980	+	0.900922i	$0.357109\pi$
$751$	−14.8250	+	30.7844i	−0.540971	+	1.12334i	−0.974952	+	0.222416i	$0.928606\pi$
$752$	−40.9811	−	35.8041i	−1.49443	−	1.30564i
$753$		0			0
$754$	−6.36104	+	23.0487i	−0.231655	+	0.839384i
$755$	−1.97976	−	4.11102i	−0.0720509	−	0.149615i
$756$		0			0
$757$	−2.96804	−	32.9777i	−0.107875	−	1.19859i	−0.849430	−	0.527701i	$-0.823054\pi$
$757$	−2.96804	−	32.9777i	−0.107875	−	1.19859i	0.741555	−	0.670892i	$-0.234089\pi$
$758$	4.63086	−	3.69299i	0.168201	−	0.134135i
$759$		0			0
$760$	6.14898	−	1.69701i	0.223047	−	0.0615570i
$761$	6.95931	+	30.4907i	0.252275	+	1.10529i	0.929299	+	0.369327i	$0.120412\pi$
$761$	6.95931	+	30.4907i	0.252275	+	1.10529i	−0.677025	+	0.735960i	$0.736731\pi$
$762$		0			0
$763$	23.3769	−	9.99177i	0.846301	−	0.361726i
$764$	−0.109792	+	0.0356737i	−0.00397214	+	0.00129063i
$765$		0			0
$766$	29.1326	+	48.7598i	1.05260	+	1.76176i
$767$	−5.02091	+	6.91070i	−0.181295	+	0.249531i
$768$		0			0
$769$	−12.2431	−	6.58830i	−0.441498	−	0.237580i	0.237989	−	0.971268i	$-0.423512\pi$
$769$	−12.2431	−	6.58830i	−0.441498	−	0.237580i	−0.679487	+	0.733688i	$0.737798\pi$
$770$	−16.5911	+	2.24741i	−0.597901	+	0.0809912i
$771$		0			0
$772$	0.766194	−	4.22208i	0.0275759	−	0.151956i
$773$	−17.4911	+	3.17417i	−0.629112	+	0.114167i	−0.483742	−	0.875210i	$-0.660723\pi$
$773$	−17.4911	+	3.17417i	−0.629112	+	0.114167i	−0.145370	+	0.989377i	$0.546437\pi$
$774$		0			0
$775$	8.34687	−	4.49164i	0.299828	−	0.161345i
$776$	19.9676	−	14.5073i	0.716795	−	0.520782i
$777$		0			0
$778$	3.90839	−	43.4257i	0.140122	−	1.55689i
$779$	−28.5920	−	43.3150i	−1.02441	−	1.55192i
$780$		0			0
$781$	−17.2360	−	39.4554i	−0.616753	−	1.41183i
$782$		−	2.66200i		−	0.0951931i
$783$		0			0
$784$	−9.79606	−	0.881662i	−0.349859	−	0.0314879i
$785$	−5.87834	−	2.51252i	−0.209807	−	0.0896758i
$786$		0			0
$787$	17.0048	+	31.6003i	0.606157	+	1.12643i	0.980011	+	0.198941i	$0.0637502\pi$
$787$	17.0048	+	31.6003i	0.606157	+	1.12643i	−0.373855	+	0.927487i	$0.621964\pi$
$788$	8.70390	−	3.26663i	0.310063	−	0.116369i
$789$		0			0
$790$	9.21617	+	1.67249i	0.327897	+	0.0595045i
$791$	6.45474	−	17.1986i	0.229504	−	0.611512i
$792$		0			0
$793$	1.46677	−	2.72572i	0.0520866	−	0.0967932i
$794$	−0.573088	+	4.23071i	−0.0203381	+	0.150142i
$795$		0			0
$796$	23.4656	−	14.0201i	0.831718	−	0.496928i
$797$	5.84664	−	5.58996i	0.207099	−	0.198007i	−0.580385	−	0.814342i	$-0.697098\pi$
$797$	5.84664	−	5.58996i	0.207099	−	0.198007i	0.787484	+	0.616336i	$0.211384\pi$
$798$		0			0
$799$	4.67262	+	10.9321i	0.165305	+	0.386751i
$800$	13.1950	−	22.0846i	0.466512	−	0.780810i
$801$		0			0
$802$	2.11114	+	7.64955i	0.0745470	+	0.270115i
$803$	−21.7583	+	19.0097i	−0.767834	+	0.670836i
$804$		0			0
$805$	−2.57758	+	0.231987i	−0.0908479	+	0.00817646i
$806$	−6.79382	−	2.20745i	−0.239302	−	0.0777540i
$807$		0			0
$808$	2.91575	+	0.804695i	0.102576	+	0.0283091i
$809$	1.42986	−	31.8383i	0.0502711	−	1.11937i	−0.802353	−	0.596849i	$-0.796419\pi$
$809$	1.42986	−	31.8383i	0.0502711	−	1.11937i	0.852624	−	0.522524i	$-0.175010\pi$
$810$		0			0
$811$	46.6697	+	22.4749i	1.63879	+	0.789202i	0.999800	+	0.0199904i	$0.00636357\pi$
$811$	46.6697	+	22.4749i	1.63879	+	0.789202i	0.638994	+	0.769211i	$0.279351\pi$
$812$	15.5226	−	16.2354i	0.544738	−	0.569751i
$813$		0			0
$814$	85.6780	−	3.84780i	3.00301	−	0.134865i
$815$	−2.77780	+	3.48325i	−0.0973020	+	0.122013i
$816$		0			0
$817$	−42.5249	+	64.4224i	−1.48776	+	2.25386i
$818$	32.2309	+	25.7032i	1.12693	+	0.898693i
$819$		0			0
$820$	5.35632	+	1.22254i	0.187051	+	0.0426931i
$821$	17.8933	+	17.1077i	0.624480	+	0.597064i	0.935495	−	0.353341i	$-0.114954\pi$
$821$	17.8933	+	17.1077i	0.624480	+	0.597064i	−0.311014	+	0.950405i	$0.600669\pi$
$822$		0			0
$823$	5.13389	−	5.87621i	0.178956	−	0.204832i	−0.656597	−	0.754242i	$-0.728005\pi$
$823$	5.13389	−	5.87621i	0.178956	−	0.204832i	0.835553	+	0.549410i	$0.185147\pi$
$824$	−22.7816	−	1.02312i	−0.793633	−	0.0356421i
$825$		0			0
$826$	20.4914	−	9.86813i	0.712987	−	0.343356i
$827$	−3.79022	+	11.6651i	−0.131799	+	0.405636i	−0.995078	−	0.0990907i	$-0.968407\pi$
$827$	−3.79022	+	11.6651i	−0.131799	+	0.405636i	0.863279	+	0.504726i	$0.168407\pi$
$828$		0			0
$829$	20.0739	+	25.1718i	0.697194	+	0.874254i	0.996810	−	0.0798057i	$-0.0254300\pi$
$829$	20.0739	+	25.1718i	0.697194	+	0.874254i	−0.299616	+	0.954060i	$0.596859\pi$
$830$	1.63634	+	1.87295i	0.0567983	+	0.0650109i
$831$		0			0
$832$	0.345478	−	0.0788530i	0.0119773	−	0.00273374i
$833$	1.84464	+	1.10212i	0.0639128	+	0.0381861i
$834$		0			0
$835$	−1.91304	−	5.88772i	−0.0662033	−	0.203753i
$836$	−24.6810	−	25.8143i	−0.853609	−	0.892805i
$837$		0			0
$838$	−27.3910	−	19.9007i	−0.946207	−	0.687459i
$839$	30.5695	+	4.14093i	1.05538	+	0.142961i	0.641307	−	0.767284i	$-0.278392\pi$
$839$	30.5695	+	4.14093i	1.05538	+	0.142961i	0.414071	+	0.910245i	$0.364107\pi$
$840$		0			0
$841$	−2.45756	−	18.1424i	−0.0847434	−	0.625601i
$842$	39.6951	+	14.8978i	1.36798	+	0.513413i
$843$		0			0
$844$	0.666134	+	3.67070i	0.0229293	+	0.126351i
$845$	−1.98757	−	5.29587i	−0.0683745	−	0.182183i
$846$		0			0
$847$	−26.6004	−	36.6123i	−0.914000	−	1.25801i
$848$	−16.0801	+	37.6212i	−0.552192	+	1.29192i
$849$		0			0
$850$	−7.38041	+	4.87176i	−0.253146	+	0.167100i
$851$	13.2571			0.454447
$852$		0			0
$853$	29.8546			1.02220			0.511101	−	0.859520i	$-0.329238\pi$
$853$	29.8546			1.02220			0.511101	+	0.859520i	$0.329238\pi$
$854$	−6.87808	+	4.54018i	−0.235363	+	0.155362i
$855$		0			0
$856$	−10.5049	+	24.5773i	−0.359049	+	0.840036i
$857$	1.71847	+	2.36527i	0.0587017	+	0.0807959i	0.837359	−	0.546654i	$-0.184099\pi$
$857$	1.71847	+	2.36527i	0.0587017	+	0.0807959i	−0.778657	+	0.627450i	$0.784099\pi$
$858$		0			0
$859$	11.9526	+	31.8476i	0.407817	+	1.08662i	0.966370	+	0.257156i	$0.0827854\pi$
$859$	11.9526	+	31.8476i	0.407817	+	1.08662i	−0.558553	+	0.829469i	$0.688643\pi$
$860$	−1.45905	−	8.04000i	−0.0497530	−	0.274162i
$861$		0			0
$862$	−43.7311	−	16.4125i	−1.48949	−	0.559013i
$863$	−0.209749	−	1.54843i	−0.00713996	−	0.0527093i	0.987029	−	0.160540i	$-0.0513237\pi$
$863$	−0.209749	−	1.54843i	−0.00713996	−	0.0527093i	−0.994169	+	0.107831i	$0.965609\pi$
$864$		0			0
$865$	−2.16964	−	0.293898i	−0.0737700	−	0.00999282i
$866$	−12.4601	−	9.05279i	−0.423411	−	0.307626i
$867$		0			0
$868$	4.63754	+	4.85048i	0.157408	+	0.164636i
$869$	13.5194	+	41.6085i	0.458615	+	1.41147i
$870$		0			0
$871$	−1.16342	−	0.695112i	−0.0394210	−	0.0235530i
$872$	13.2330	−	3.02035i	0.448126	−	0.102282i
$873$		0			0
$874$	−10.2945	−	11.7831i	−0.348218	−	0.398568i
$875$	11.1709	+	14.0079i	0.377647	+	0.473554i
$876$		0			0
$877$	−13.6596	+	42.0398i	−0.461250	+	1.41958i	0.402387	+	0.915470i	$0.368181\pi$
$877$	−13.6596	+	42.0398i	−0.461250	+	1.41958i	−0.863637	+	0.504113i	$0.831819\pi$
$878$	−17.2478	+	8.30611i	−0.582086	+	0.280318i
$879$		0			0
$880$	−15.8575	−	0.712162i	−0.534557	−	0.0240070i
$881$	−16.1130	+	18.4428i	−0.542861	+	0.621354i	−0.957431	−	0.288663i	$-0.906789\pi$
$881$	−16.1130	+	18.4428i	−0.542861	+	0.621354i	0.414570	+	0.910018i	$0.363932\pi$
$882$		0			0
$883$	35.5482	+	33.9876i	1.19629	+	1.14377i	0.986107	+	0.166113i	$0.0531216\pi$
$883$	35.5482	+	33.9876i	1.19629	+	1.14377i	0.210187	+	0.977661i	$0.432593\pi$
$884$	2.29252	+	0.523253i	0.0771059	+	0.0175989i
$885$		0			0
$886$	12.0305	+	9.59399i	0.404172	+	0.322316i
$887$	17.5743	−	26.6239i	0.590087	−	0.893944i	−0.409746	−	0.912200i	$-0.634383\pi$
$887$	17.5743	−	26.6239i	0.590087	−	0.893944i	0.999833	+	0.0182554i	$0.00581120\pi$
$888$		0			0
$889$	24.8850	−	31.2047i	0.834614	−	1.04657i
$890$	−10.0459	+	0.451160i	−0.336738	+	0.0151229i
$891$		0			0
$892$	0.282699	−	0.295679i	0.00946545	−	0.00990008i
$893$	62.9597	+	30.3198i	2.10687	+	1.01461i
$894$		0			0
$895$	−0.0542251	+	1.20742i	−0.00181254	+	0.0403594i
$896$	−33.1138	−	9.13882i	−1.10625	−	0.305307i
$897$		0			0
$898$	34.3760	+	11.1694i	1.14714	+	0.372729i
$899$	14.0769	−	1.26694i	0.469489	−	0.0422548i
$900$		0			0
$901$	6.73126	−	5.88093i	0.224251	−	0.195922i
$902$	19.3491	+	70.1097i	0.644253	+	2.33440i
$903$		0			0
$904$	5.03042	−	8.41950i	0.167309	−	0.280028i
$905$	−0.733992	−	1.71726i	−0.0243987	−	0.0570836i
$906$		0			0
$907$	11.7079	−	11.1939i	0.388753	−	0.371686i	−0.471228	−	0.882011i	$-0.656189\pi$
$907$	11.7079	−	11.1939i	0.388753	−	0.371686i	0.859982	+	0.510325i	$0.170475\pi$
$908$	0.796497	−	0.475885i	0.0264327	−	0.0157928i
$909$		0			0
$910$	0.869746	−	6.42072i	0.0288318	−	0.212845i
$911$	0.794976	−	1.47731i	0.0263387	−	0.0489455i	−0.867086	−	0.498158i	$-0.834010\pi$
$911$	0.794976	−	1.47731i	0.0263387	−	0.0489455i	0.893425	+	0.449213i	$0.148296\pi$
$912$		0			0
$913$	−4.08177	+	10.8758i	−0.135087	+	0.359937i
$914$	58.4615	+	10.6092i	1.93373	+	0.350921i
$915$		0			0
$916$	−12.2472	+	4.59645i	−0.404659	+	0.151871i
$917$	12.1620	+	22.6008i	0.401625	+	0.746344i
$918$		0			0
$919$	−37.1060	−	15.8599i	−1.22401	−	0.523169i	−0.318678	−	0.947863i	$-0.603239\pi$
$919$	−37.1060	−	15.8599i	−1.22401	−	0.523169i	−0.905337	+	0.424694i	$0.860382\pi$
$920$	−1.37618	−	0.123859i	−0.0453714	−	0.00408350i
$921$		0			0
$922$		−	30.7831i		−	1.01379i
$923$	16.4935	−	2.36777i	0.542889	−	0.0779361i
$924$		0			0
$925$	−24.2620	−	36.7553i	−0.797728	−	1.20851i
$926$	2.31069	−	25.6739i	0.0759340	−	0.843695i
$927$		0			0
$928$	31.0344	−	22.5478i	1.01876	−	0.740169i
$929$	−34.2498	+	18.4306i	−1.12370	+	0.604689i	−0.926733	−	0.375721i	$-0.877395\pi$
$929$	−34.2498	+	18.4306i	−1.12370	+	0.604689i	−0.196967	+	0.980410i	$0.563109\pi$
$930$		0			0
$931$	12.4272	−	2.25520i	0.407285	−	0.0739113i
$932$	−0.0904850	+	0.498613i	−0.00296393	+	0.0163326i
$933$		0			0
$934$	−68.8309	+	9.32378i	−2.25222	+	0.305083i
$935$	3.05381	+	1.64332i	0.0998702	+	0.0537425i
$936$		0			0
$937$	−20.9140	+	28.7856i	−0.683230	+	0.940386i	−0.999967	−	0.00812768i	$-0.997413\pi$
$937$	−20.9140	+	28.7856i	−0.683230	+	0.940386i	0.316737	+	0.948514i	$0.397413\pi$
$938$	1.85077	+	3.09767i	0.0604298	+	0.101142i
$939$		0			0
$940$	−7.03524	+	2.28589i	−0.229464	+	0.0745574i
$941$	38.4528	−	16.4355i	1.25353	−	0.535783i	0.339182	−	0.940721i	$-0.389850\pi$
$941$	38.4528	−	16.4355i	1.25353	−	0.535783i	0.914344	+	0.404938i	$0.132707\pi$
$942$		0			0
$943$	2.50167	+	10.9605i	0.0814657	+	0.356924i
$944$	20.7860	−	5.73658i	0.676528	−	0.186710i
$945$		0			0
$946$	84.5726	−	67.4444i	2.74969	−	2.19281i
$947$	−1.87676	−	20.8525i	−0.0609864	−	0.677614i	−0.967069	−	0.254514i	$-0.918085\pi$
$947$	−1.87676	−	20.8525i	−0.0609864	−	0.677614i	0.906083	−	0.423101i	$-0.139058\pi$
$948$		0			0
$949$	−4.85145	−	10.0741i	−0.157485	−	0.327020i
$950$	−13.8283	+	50.1059i	−0.448651	+	1.62565i
$951$		0			0
$952$	3.93334	+	3.43646i	0.127480	+	0.111376i
$953$	12.5631	−	26.0875i	0.406957	−	0.845056i	−0.592269	−	0.805740i	$-0.701768\pi$
$953$	12.5631	−	26.0875i	0.406957	−	0.845056i	0.999227	−	0.0393158i	$-0.0125178\pi$
$954$		0			0
$955$	0.0146612	−	0.0642349i	0.000474425	−	0.00207859i
$956$	0.491267	+	10.9389i	0.0158887	+	0.353790i
$957$		0			0
$958$	52.9783	+	34.9707i	1.71165	+	1.12985i
$959$	46.4948	+	30.6910i	1.50140	+	0.991063i
$960$		0			0
$961$	−1.20136	−	26.7504i	−0.0387537	−	0.862918i
$962$	−7.38562	+	32.3585i	−0.238122	+	1.04328i
$963$		0			0
$964$	−11.9231	+	24.7587i	−0.384019	+	0.797423i
$965$	1.84430	+	1.61132i	0.0593702	+	0.0518702i
$966$		0			0
$967$	0.993913	−	3.60136i	0.0319621	−	0.115812i	−0.946241	−	0.323462i	$-0.895153\pi$
$967$	0.993913	−	3.60136i	0.0319621	−	0.115812i	0.978203	+	0.207650i	$0.0665816\pi$
$968$	−10.4835	−	21.7692i	−0.336952	−	0.699689i
$969$		0			0
$970$	−1.51361	−	16.8176i	−0.0485990	−	0.539979i
$971$	10.8719	−	8.67005i	0.348896	−	0.278235i	−0.433323	−	0.901238i	$-0.642659\pi$
$971$	10.8719	−	8.67005i	0.348896	−	0.278235i	0.782219	+	0.623004i	$0.214088\pi$
$972$		0			0
$973$	−44.5060	+	12.2829i	−1.42680	+	0.393771i
$974$	4.37812	+	19.1818i	0.140284	+	0.614625i
$975$		0			0
$976$	−7.18484	+	3.07095i	−0.229981	+	0.0982986i
$977$	12.3426	−	4.01036i	0.394875	−	0.128303i	−0.104847	−	0.994488i	$-0.533435\pi$
$977$	12.3426	−	4.01036i	0.394875	−	0.128303i	0.499722	+	0.866186i	$0.333435\pi$
$978$		0			0
$979$	−24.0905	−	40.3207i	−0.769936	−	1.28866i
$980$	−0.785864	+	1.08165i	−0.0251035	+	0.0345520i
$981$		0			0
$982$	29.5202	+	15.8855i	0.942028	+	0.506927i
$983$	5.77178	−	0.781840i	0.184091	−	0.0249368i	−0.0416074	−	0.999134i	$-0.513248\pi$
$983$	5.77178	−	0.781840i	0.184091	−	0.0249368i	0.225698	+	0.974197i	$0.427534\pi$
$984$		0			0
$985$	−0.947412	+	5.22067i	−0.0301871	+	0.166344i
$986$	−12.9745	+	2.35452i	−0.413192	+	0.0749832i
$987$		0			0
$988$	12.1711	−	6.54955i	0.387215	−	0.208369i
$989$	13.5274	−	9.82826i	0.430148	−	0.312520i
$990$		0			0
$991$	−3.70692	+	41.1872i	−0.117754	+	1.30835i	0.692134	+	0.721769i	$0.256671\pi$
$991$	−3.70692	+	41.1872i	−0.117754	+	1.30835i	−0.809888	+	0.586585i	$0.800472\pi$
$992$	6.31362	+	9.56472i	0.200458	+	0.303680i
$993$		0			0
$994$	−41.6585	−	15.2583i	−1.32133	−	0.483962i
$995$			15.6010i			0.494584i
$996$		0			0
$997$	60.5684	+	5.45126i	1.91822	+	0.172643i	0.983273	−	0.182141i	$-0.0583026\pi$
$997$	60.5684	+	5.45126i	1.91822	+	0.172643i	0.934948	+	0.354784i	$0.115445\pi$
$998$	34.6687	+	14.8181i	1.09742	+	0.469060i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	639.2.z.a.305.20	yes	576
3.2	odd	2	inner	639.2.z.a.305.5	yes	576
71.44	odd	70	inner	639.2.z.a.44.5	✓	576
213.44	even	70	inner	639.2.z.a.44.20	yes	576

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
639.2.z.a.44.5	✓	576	71.44	odd	70	inner
639.2.z.a.44.20	yes	576	213.44	even	70	inner
639.2.z.a.305.5	yes	576	3.2	odd	2	inner
639.2.z.a.305.20	yes	576	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:	\( N \)	\(=\)	\( 639 = 3^{2} \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	639.z (of order \(70\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(1.46713 - 0.968447i) q^{2} +(0.428545 - 1.00263i) q^{4} +(0.365787 + 0.503462i) q^{5} +(1.05239 + 2.80407i) q^{7} +(0.285525 + 1.57337i) q^{8} +O(q^{10})\)	\(q+(1.46713 - 0.968447i) q^{2} +(0.428545 - 1.00263i) q^{4} +(0.365787 + 0.503462i) q^{5} +(1.05239 + 2.80407i) q^{7} +(0.285525 + 1.57337i) q^{8} +(1.02423 + 0.384402i) q^{10} +(0.685905 + 5.06355i) q^{11} +(-1.95959 - 0.265444i) q^{13} +(4.25959 + 3.09477i) q^{14} +(3.44967 + 3.60807i) q^{16} +(-0.337004 - 1.03719i) q^{17} +(-5.50275 - 3.28774i) q^{19} +(0.661542 - 0.150993i) q^{20} +(5.91010 + 6.76465i) q^{22} +(0.865725 + 1.08558i) q^{23} +(1.42541 - 4.38696i) q^{25} +(-3.13205 + 1.50831i) q^{26} +(3.26244 + 0.146516i) q^{28} +(4.52536 - 5.17969i) q^{29} +(1.48527 + 1.42006i) q^{31} +(5.43740 + 1.24105i) q^{32} +(-1.49890 - 1.19533i) q^{34} +(-1.02680 + 1.55553i) q^{35} +(5.95288 - 7.46467i) q^{37} +(-11.2573 + 0.505565i) q^{38} +(-0.687693 + 0.719271i) q^{40} +(7.29489 + 3.51303i) q^{41} +(0.540273 - 12.0301i) q^{43} +(5.37081 + 1.48225i) q^{44} +(2.32147 + 0.754290i) q^{46} +(-10.8576 + 0.977206i) q^{47} +(-1.48381 + 1.29637i) q^{49} +(-2.15727 - 7.81670i) q^{50} +(-1.10591 + 1.85098i) q^{52} +(3.22128 + 7.53655i) q^{53} +(-2.29841 + 2.19751i) q^{55} +(-4.11138 + 2.45643i) q^{56} +(1.62306 - 11.9819i) q^{58} +(2.04696 - 3.80389i) q^{59} +(-0.550000 + 1.46547i) q^{61} +(3.55434 + 0.645018i) q^{62} +(-0.167772 + 0.0629659i) q^{64} +(-0.583149 - 1.08367i) q^{65} +(0.630195 + 0.269358i) q^{67} +(-1.18434 - 0.106593i) q^{68} +3.27657i q^{70} +(-8.10443 + 2.30612i) q^{71} +(3.11498 + 4.71900i) q^{73} +(1.50453 - 16.7167i) q^{74} +(-5.65456 + 4.10828i) q^{76} +(-13.4767 + 7.25214i) q^{77} +(8.42434 - 1.52879i) q^{79} +(-0.554684 + 3.05656i) q^{80} +(14.1048 - 1.91062i) q^{82} +(2.00194 + 1.07729i) q^{83} +(0.398915 - 0.549060i) q^{85} +(-10.8579 - 18.1730i) q^{86} +(-7.77102 + 2.52496i) q^{88} +(-8.45230 + 3.61269i) q^{89} +(-1.31792 - 5.77417i) q^{91} +(1.45944 - 0.402780i) q^{92} +(-14.9833 + 11.9488i) q^{94} +(-0.357580 - 3.97304i) q^{95} +(-6.69689 - 13.9062i) q^{97} +(-0.921491 + 3.33895i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 576 q - 24 q^{4}+O(q^{10}) \) 576 * q - 24 * q^4	\( 576 q - 24 q^{4} - 16 q^{10} + 76 q^{16} - 8 q^{19} + 20 q^{22} + 168 q^{25} - 20 q^{28} - 28 q^{31} + 40 q^{37} + 32 q^{40} + 52 q^{43} - 20 q^{46} - 208 q^{52} - 92 q^{55} + 56 q^{58} + 56 q^{61} - 144 q^{64} - 16 q^{67} - 44 q^{73} - 336 q^{76} + 88 q^{79} - 124 q^{82} + 60 q^{85} - 260 q^{88} + 80 q^{91} + 56 q^{94} - 56 q^{97}+O(q^{100}) \) 576 * q - 24 * q^4 - 16 * q^10 + 76 * q^16 - 8 * q^19 + 20 * q^22 + 168 * q^25 - 20 * q^28 - 28 * q^31 + 40 * q^37 + 32 * q^40 + 52 * q^43 - 20 * q^46 - 208 * q^52 - 92 * q^55 + 56 * q^58 + 56 * q^61 - 144 * q^64 - 16 * q^67 - 44 * q^73 - 336 * q^76 + 88 * q^79 - 124 * q^82 + 60 * q^85 - 260 * q^88 + 80 * q^91 + 56 * q^94 - 56 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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