LMFDB - Embedded newform 936.2.dg.f.901.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [936,2,Mod(829,936)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(936, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 5]))

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

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

chi := DirichletCharacter("936.829");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.dg (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			901.7
Character	$\chi$	$=$	936.901
Dual form			936.2.dg.f.829.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.15325 + 0.818540i) q^{2} +(0.659986 - 1.88797i) q^{4} +2.34484 q^{5} +(3.69507 - 2.13335i) q^{7} +(0.784245 + 2.71753i) q^{8} +(-2.70420 + 1.91935i) q^{10} +(-1.33516 + 2.31256i) q^{11} +(-2.96097 + 2.05735i) q^{13} +(-2.51512 + 5.48486i) q^{14} +(-3.12884 - 2.49206i) q^{16} +(2.86144 + 4.95615i) q^{17} +(3.67163 + 6.35946i) q^{19} +(1.54756 - 4.42698i) q^{20} +(-0.353149 - 3.75985i) q^{22} +(-1.42407 + 2.46656i) q^{23} +0.498285 q^{25} +(1.73072 - 4.79631i) q^{26} +(-1.58900 - 8.38416i) q^{28} +(4.01604 + 2.31866i) q^{29} -6.91551i q^{31} +(5.64819 + 0.312900i) q^{32} +(-7.35677 - 3.37350i) q^{34} +(8.66436 - 5.00237i) q^{35} +(0.806558 - 1.39700i) q^{37} +(-9.43979 - 4.32869i) q^{38} +(1.83893 + 6.37217i) q^{40} +(-5.52067 - 3.18736i) q^{41} +(3.98283 - 2.29949i) q^{43} +(3.48486 + 4.04699i) q^{44} +(-0.376665 - 4.01023i) q^{46} -4.83325i q^{47} +(5.60238 - 9.70360i) q^{49} +(-0.574648 + 0.407866i) q^{50} +(1.93001 + 6.94803i) q^{52} +2.67224i q^{53} +(-3.13074 + 5.42260i) q^{55} +(8.69529 + 8.36839i) q^{56} +(-6.52943 + 0.613284i) q^{58} +(3.87932 + 6.71918i) q^{59} +(-1.83248 + 1.05798i) q^{61} +(5.66062 + 7.97534i) q^{62} +(-6.76992 + 4.26242i) q^{64} +(-6.94300 + 4.82416i) q^{65} +(4.32233 - 7.48649i) q^{67} +(11.2456 - 2.13131i) q^{68} +(-5.89756 + 12.8611i) q^{70} +(11.6191 - 6.70831i) q^{71} +10.5359i q^{73} +(0.213334 + 2.27129i) q^{74} +(14.4297 - 2.73477i) q^{76} +11.3935i q^{77} +1.92081 q^{79} +(-7.33663 - 5.84349i) q^{80} +(8.97571 - 0.843054i) q^{82} -2.73834 q^{83} +(6.70962 + 11.6214i) q^{85} +(-2.71099 + 5.91199i) q^{86} +(-7.33155 - 1.81472i) q^{88} +(-15.0637 - 8.69704i) q^{89} +(-6.55193 + 13.9188i) q^{91} +(3.71692 + 4.31649i) q^{92} +(3.95621 + 5.57396i) q^{94} +(8.60940 + 14.9119i) q^{95} +(4.06104 - 2.34464i) q^{97} +(1.48182 + 15.7765i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 4 q^{10} - 4 q^{16} + 64 q^{25} - 48 q^{28} - 48 q^{40} + 20 q^{49} - 12 q^{52} + 16 q^{55} + 12 q^{58} - 72 q^{64} - 84 q^{76} + 80 q^{79} - 12 q^{82} - 12 q^{88} - 24 q^{94} + 24 q^{97}+O(q^{100}) $ 56 * q - 4 * q^10 - 4 * q^16 + 64 * q^25 - 48 * q^28 - 48 * q^40 + 20 * q^49 - 12 * q^52 + 16 * q^55 + 12 * q^58 - 72 * q^64 - 84 * q^76 + 80 * q^79 - 12 * q^82 - 12 * q^88 - 24 * q^94 + 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$1$

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 $

$2$	−1.15325	+	0.818540i	−0.815473	+	0.578795i
$2$	−1.15325	+	0.818540i	−0.815473	+	0.578795i
$3$		0			0
$3$		0			0
$4$	0.659986	−	1.88797i	0.329993	−	0.943983i
$5$	2.34484			1.04865			0.524323	−	0.851520i	$-0.324319\pi$
$5$	2.34484			1.04865			0.524323	+	0.851520i	$0.324319\pi$
$6$		0			0
$7$	3.69507	−	2.13335i	1.39661	−	0.806331i	0.402571	−	0.915389i	$-0.368117\pi$
$7$	3.69507	−	2.13335i	1.39661	−	0.806331i	0.994035	+	0.109058i	$0.0347834\pi$
$8$	0.784245	+	2.71753i	0.277273	+	0.960791i
$9$		0			0
$10$	−2.70420	+	1.91935i	−0.855142	+	0.606951i
$11$	−1.33516	+	2.31256i	−0.402566	+	0.697264i	−0.994035	−	0.109063i	$-0.965215\pi$
$11$	−1.33516	+	2.31256i	−0.402566	+	0.697264i	0.591469	+	0.806328i	$0.298548\pi$
$12$		0			0
$13$	−2.96097	+	2.05735i	−0.821224	+	0.570606i
$13$	−2.96097	+	2.05735i	−0.821224	+	0.570606i
$14$	−2.51512	+	5.48486i	−0.672195	+	1.46589i
$15$		0			0
$16$	−3.12884	−	2.49206i	−0.782210	−	0.623015i
$17$	2.86144	+	4.95615i	0.694000	+	1.20204i	0.970517	+	0.241035i	$0.0774868\pi$
$17$	2.86144	+	4.95615i	0.694000	+	1.20204i	−0.276516	+	0.961009i	$0.589180\pi$
$18$		0			0
$19$	3.67163	+	6.35946i	0.842331	+	1.45896i	0.887919	+	0.459999i	$0.152150\pi$
$19$	3.67163	+	6.35946i	0.842331	+	1.45896i	−0.0455885	+	0.998960i	$0.514516\pi$
$20$	1.54756	−	4.42698i	0.346045	−	0.989904i
$21$		0			0
$22$	−0.353149	−	3.75985i	−0.0752915	−	0.801603i
$23$	−1.42407	+	2.46656i	−0.296939	+	0.514313i	−0.975434	−	0.220292i	$-0.929299\pi$
$23$	−1.42407	+	2.46656i	−0.296939	+	0.514313i	0.678495	+	0.734605i	$0.262632\pi$
$24$		0			0
$25$	0.498285			0.0996569
$26$	1.73072	−	4.79631i	0.339422	−	0.940634i
$27$		0			0
$28$	−1.58900	−	8.38416i	−0.300293	−	1.58446i
$29$	4.01604	+	2.31866i	0.745760	+	0.430565i	0.824160	−	0.566357i	$-0.191648\pi$
$29$	4.01604	+	2.31866i	0.745760	+	0.430565i	−0.0783999	+	0.996922i	$0.524981\pi$
$30$		0			0
$31$		−	6.91551i		−	1.24206i	−0.783786	−	0.621031i	$-0.786714\pi$
$31$		−	6.91551i		−	1.24206i	0.783786	−	0.621031i	$-0.213286\pi$
$32$	5.64819	+	0.312900i	0.998469	+	0.0553134i
$33$		0			0
$34$	−7.35677	−	3.37350i	−1.26168	−	0.578551i
$35$	8.66436	−	5.00237i	1.46454	−	0.845555i
$36$		0			0
$37$	0.806558	−	1.39700i	0.132597	−	0.229665i	−0.792080	−	0.610418i	$-0.791002\pi$
$37$	0.806558	−	1.39700i	0.132597	−	0.229665i	0.924677	+	0.380752i	$0.124335\pi$
$38$	−9.43979	−	4.32869i	−1.53134	−	0.702206i
$39$		0			0
$40$	1.83893	+	6.37217i	0.290761	+	1.00753i
$41$	−5.52067	−	3.18736i	−0.862184	−	0.497782i	0.00255936	−	0.999997i	$-0.499185\pi$
$41$	−5.52067	−	3.18736i	−0.862184	−	0.497782i	−0.864743	+	0.502215i	$0.832519\pi$
$42$		0			0
$43$	3.98283	−	2.29949i	0.607375	−	0.350668i	−0.164562	−	0.986367i	$-0.552621\pi$
$43$	3.98283	−	2.29949i	0.607375	−	0.350668i	0.771938	+	0.635698i	$0.219288\pi$
$44$	3.48486	+	4.04699i	0.525362	+	0.610107i
$45$		0			0
$46$	−0.376665	−	4.01023i	−0.0555362	−	0.591275i
$47$		−	4.83325i		−	0.705003i	−0.935811	−	0.352501i	$-0.885331\pi$
$47$		−	4.83325i		−	0.705003i	0.935811	−	0.352501i	$-0.114669\pi$
$48$		0			0
$49$	5.60238	−	9.70360i	0.800339	−	1.38623i
$50$	−0.574648	+	0.407866i	−0.0812675	+	0.0576809i
$51$		0			0
$52$	1.93001	+	6.94803i	0.267645	+	0.963518i
$53$			2.67224i			0.367060i	0.983014	+	0.183530i	$0.0587524\pi$
$53$			2.67224i			0.367060i	−0.983014	+	0.183530i	$0.941248\pi$
$54$		0			0
$55$	−3.13074	+	5.42260i	−0.422149	+	0.731183i
$56$	8.69529	+	8.36839i	1.16196	+	1.11827i
$57$		0			0
$58$	−6.52943	+	0.613284i	−0.857356	+	0.0805282i
$59$	3.87932	+	6.71918i	0.505045	+	0.874763i	0.999983	+	0.00583488i	$0.00185731\pi$
$59$	3.87932	+	6.71918i	0.505045	+	0.874763i	−0.494938	+	0.868928i	$0.664809\pi$
$60$		0			0
$61$	−1.83248	+	1.05798i	−0.234625	+	0.135461i	−0.612704	−	0.790312i	$-0.709918\pi$
$61$	−1.83248	+	1.05798i	−0.234625	+	0.135461i	0.378079	+	0.925773i	$0.376585\pi$
$62$	5.66062	+	7.97534i	0.718900	+	1.01287i
$63$		0			0
$64$	−6.76992	+	4.26242i	−0.846240	+	0.532802i
$65$	−6.94300	+	4.82416i	−0.861173	+	0.598363i
$66$		0			0
$67$	4.32233	−	7.48649i	0.528057	−	0.914621i	−0.471408	−	0.881915i	$-0.656254\pi$
$67$	4.32233	−	7.48649i	0.528057	−	0.914621i	0.999465	−	0.0327058i	$-0.0104124\pi$
$68$	11.2456	−	2.13131i	1.36372	−	0.258459i
$69$		0			0
$70$	−5.89756	+	12.8611i	−0.704894	+	1.53720i
$71$	11.6191	−	6.70831i	1.37894	−	0.796130i	0.386907	−	0.922119i	$-0.373544\pi$
$71$	11.6191	−	6.70831i	1.37894	−	0.796130i	0.992032	+	0.125988i	$0.0402102\pi$
$72$		0			0
$73$			10.5359i			1.23314i	0.787301	+	0.616569i	$0.211478\pi$
$73$			10.5359i			1.23314i	−0.787301	+	0.616569i	$0.788522\pi$
$74$	0.213334	+	2.27129i	0.0247996	+	0.264032i
$75$		0			0
$76$	14.4297	−	2.73477i	1.65520	−	0.313700i
$77$			11.3935i			1.29840i
$78$		0			0
$79$	1.92081			0.216109			0.108054	−	0.994145i	$-0.465538\pi$
$79$	1.92081			0.216109			0.108054	+	0.994145i	$0.465538\pi$
$80$	−7.33663	−	5.84349i	−0.820260	−	0.653322i
$81$		0			0
$82$	8.97571	−	0.843054i	0.991201	−	0.0930997i
$83$	−2.73834			−0.300572			−0.150286	−	0.988643i	$-0.548019\pi$
$83$	−2.73834			−0.300572			−0.150286	+	0.988643i	$0.548019\pi$
$84$		0			0
$85$	6.70962	+	11.6214i	0.727760	+	1.26052i
$86$	−2.71099	+	5.91199i	−0.292333	+	0.637506i
$87$		0			0
$88$	−7.33155	−	1.81472i	−0.781546	−	0.193449i
$89$	−15.0637	−	8.69704i	−1.59675	−	0.921884i	−0.992108	−	0.125388i	$-0.959983\pi$
$89$	−15.0637	−	8.69704i	−1.59675	−	0.921884i	−0.604643	−	0.796497i	$-0.706684\pi$
$90$		0			0
$91$	−6.55193	+	13.9188i	−0.686829	+	1.45909i
$92$	3.71692	+	4.31649i	0.387516	+	0.450025i
$93$		0			0
$94$	3.95621	+	5.57396i	0.408052	+	0.574911i
$95$	8.60940	+	14.9119i	0.883306	+	1.52993i
$96$		0			0
$97$	4.06104	−	2.34464i	0.412336	−	0.238062i	−0.279457	−	0.960158i	$-0.590154\pi$
$97$	4.06104	−	2.34464i	0.412336	−	0.238062i	0.691793	+	0.722096i	$0.256821\pi$
$98$	1.48182	+	15.7765i	0.149687	+	1.59366i
$99$		0			0
$100$	0.328861	−	0.940745i	0.0328861	−	0.0940745i
$101$	−9.77593	−	5.64414i	−0.972741	−	0.561612i	−0.0726704	−	0.997356i	$-0.523152\pi$
$101$	−9.77593	−	5.64414i	−0.972741	−	0.561612i	−0.900071	+	0.435744i	$0.856485\pi$
$102$		0			0
$103$	19.3944			1.91099			0.955495	−	0.295007i	$-0.0953219\pi$
$103$	19.3944			1.91099			0.955495	+	0.295007i	$0.0953219\pi$
$104$	−7.91303	−	6.43304i	−0.775936	−	0.630811i
$105$		0			0
$106$	−2.18733	−	3.08176i	−0.212452	−	0.299327i
$107$	−11.9910	−	6.92299i	−1.15921	−	0.669271i	−0.208096	−	0.978108i	$-0.566727\pi$
$107$	−11.9910	−	6.92299i	−1.15921	−	0.669271i	−0.951115	+	0.308838i	$0.900060\pi$
$108$		0			0
$109$	−6.87021			−0.658047			−0.329023	−	0.944322i	$-0.606720\pi$
$109$	−6.87021			−0.658047			−0.329023	+	0.944322i	$0.606720\pi$
$110$	−0.828078	−	8.81626i	−0.0789541	−	0.840597i
$111$		0			0
$112$	−16.8777	−	2.53344i	−1.59480	−	0.239387i
$113$	−9.79113	−	16.9587i	−0.921072	−	1.59534i	−0.797759	−	0.602977i	$-0.793981\pi$
$113$	−9.79113	−	16.9587i	−0.921072	−	1.59534i	−0.123313	−	0.992368i	$-0.539352\pi$
$114$		0			0
$115$	−3.33922	+	5.78369i	−0.311384	+	0.539332i
$116$	7.02809	−	6.05187i	0.652541	−	0.561902i
$117$		0			0
$118$	−9.97376	−	4.57354i	−0.918159	−	0.421028i
$119$	21.1464	+	12.2089i	1.93849	+	1.11919i
$120$		0			0
$121$	1.93470	+	3.35100i	0.175882	+	0.304636i
$122$	1.24731	−	2.72008i	0.112927	−	0.246265i
$123$		0			0
$124$	−13.0563	−	4.56414i	−1.17249	−	0.409872i
$125$	−10.5558			−0.944141
$126$		0			0
$127$	−1.64966	+	2.85730i	−0.146384	+	0.253544i	−0.929888	−	0.367842i	$-0.880097\pi$
$127$	−1.64966	+	2.85730i	−0.146384	+	0.253544i	0.783505	+	0.621386i	$0.213430\pi$
$128$	4.31847	−	10.4571i	0.381702	−	0.924285i
$129$		0			0
$130$	4.05827	−	11.2466i	0.355934	−	0.986392i
$131$		−	11.9694i		−	1.04577i	−0.852403	−	0.522885i	$-0.824856\pi$
$131$		−	11.9694i		−	1.04577i	0.852403	−	0.522885i	$-0.175144\pi$
$132$		0			0
$133$	27.1339	+	15.6658i	2.35281	+	1.35839i
$134$	1.14325	+	12.1718i	0.0987620	+	1.05149i
$135$		0			0
$136$	−11.2244	+	11.6629i	−0.962486	+	1.00008i
$137$	−7.47619	+	4.31638i	−0.638734	+	0.368773i	−0.784127	−	0.620601i	$-0.786889\pi$
$137$	−7.47619	+	4.31638i	−0.638734	+	0.368773i	0.145393	+	0.989374i	$0.453555\pi$
$138$		0			0
$139$	−0.164241	+	0.0948244i	−0.0139307	+	0.00804290i	−0.506949	−	0.861976i	$-0.669227\pi$
$139$	−0.164241	+	0.0948244i	−0.0139307	+	0.00804290i	0.493018	+	0.870019i	$0.335893\pi$
$140$	−3.72596	−	19.6595i	−0.314901	−	1.66153i
$141$		0			0
$142$	−7.90879	+	17.2471i	−0.663691	+	1.44735i
$143$	−0.804390	−	9.59431i	−0.0672665	−	0.802316i
$144$		0			0
$145$	9.41698	+	5.43690i	0.782038	+	0.451510i
$146$	−8.62408	−	12.1506i	−0.713734	−	1.00559i
$147$		0			0
$148$	−2.10517	−	2.44475i	−0.173044	−	0.200958i
$149$	8.56775	+	14.8398i	0.701897	+	1.21572i	0.967800	+	0.251722i	$0.0809968\pi$
$149$	8.56775	+	14.8398i	0.701897	+	1.21572i	−0.265902	+	0.964000i	$0.585670\pi$
$150$		0			0
$151$			3.17400i			0.258297i	0.991625	+	0.129148i	$0.0412243\pi$
$151$			3.17400i			0.258297i	−0.991625	+	0.129148i	$0.958776\pi$
$152$	−14.4025	+	14.9651i	−1.16820	+	1.21383i
$153$		0			0
$154$	−9.32599	−	13.1395i	−0.751510	−	1.05881i
$155$		−	16.2158i		−	1.30248i
$156$		0			0
$157$		−	17.7702i		−	1.41822i	−0.705099	−	0.709109i	$-0.749097\pi$
$157$		−	17.7702i		−	1.41822i	0.705099	−	0.709109i	$-0.250903\pi$
$158$	−2.21519	+	1.57226i	−0.176231	+	0.125083i
$159$		0			0
$160$	13.2441	+	0.733700i	1.04704	+	0.0580041i
$161$			12.1522i			0.957724i
$162$		0			0
$163$	−0.0275364	−	0.0476944i	−0.00215681	−	0.00373571i	0.864945	−	0.501867i	$-0.167353\pi$
$163$	−0.0275364	−	0.0476944i	−0.00215681	−	0.00373571i	−0.867102	+	0.498131i	$0.834020\pi$
$164$	−9.66119	+	8.31923i	−0.754412	+	0.649623i
$165$		0			0
$166$	3.15800	−	2.24144i	0.245108	−	0.173970i
$167$	11.6579	+	6.73072i	0.902119	+	0.520839i	0.877887	−	0.478868i	$-0.158953\pi$
$167$	11.6579	+	6.73072i	0.902119	+	0.520839i	0.0242321	+	0.999706i	$0.492286\pi$
$168$		0			0
$169$	4.53463	−	12.1835i	0.348818	−	0.937191i
$170$	−17.2505	−	7.91033i	−1.32305	−	0.606694i
$171$		0			0
$172$	−1.71275	−	9.03707i	−0.130596	−	0.689070i
$173$	13.8424	−	7.99194i	1.05242	−	0.607616i	0.129095	−	0.991632i	$-0.458793\pi$
$173$	13.8424	−	7.99194i	1.05242	−	0.607616i	0.923326	+	0.384016i	$0.125459\pi$
$174$		0			0
$175$	1.84120	−	1.06302i	0.139181	−	0.0803565i
$176$	9.94055	−	3.90834i	0.749297	−	0.294602i
$177$		0			0
$178$	24.4911	−	2.30036i	1.83569	−	0.172419i
$179$	−0.703881	−	0.406386i	−0.0526106	−	0.0303747i	0.473464	−	0.880813i	$-0.343003\pi$
$179$	−0.703881	−	0.406386i	−0.0526106	−	0.0303747i	−0.526075	+	0.850438i	$0.676337\pi$
$180$		0			0
$181$			4.40522i			0.327437i	0.986507	+	0.163719i	$0.0523489\pi$
$181$			4.40522i			0.327437i	−0.986507	+	0.163719i	$0.947651\pi$
$182$	−3.83708	−	21.4150i	−0.284423	−	1.58738i
$183$		0			0
$184$	−7.81977	−	1.93556i	−0.576481	−	0.142691i
$185$	1.89125	−	3.27574i	0.139048	−	0.240837i
$186$		0			0
$187$	−15.2819			−1.11752
$188$	−9.12502	−	3.18988i	−0.665511	−	0.232646i
$189$		0			0
$190$	−22.1348	−	10.1501i	−1.60583	−	0.736365i
$191$	−4.99011	−	8.64312i	−0.361072	−	0.625395i	0.627066	−	0.778966i	$-0.284256\pi$
$191$	−4.99011	−	8.64312i	−0.361072	−	0.625395i	−0.988138	+	0.153572i	$0.950922\pi$
$192$		0			0
$193$	−6.08787	−	3.51483i	−0.438215	−	0.253003i	0.264625	−	0.964351i	$-0.414752\pi$
$193$	−6.08787	−	3.51483i	−0.438215	−	0.253003i	−0.702840	+	0.711348i	$0.748085\pi$
$194$	−2.76422	+	6.02809i	−0.198460	+	0.432791i
$195$		0			0
$196$	−14.6226	−	16.9813i	−1.04447	−	1.21295i
$197$	−11.4687	+	19.8644i	−0.817111	+	1.41528i	0.0906911	+	0.995879i	$0.471092\pi$
$197$	−11.4687	+	19.8644i	−0.817111	+	1.41528i	−0.907802	+	0.419399i	$0.862241\pi$
$198$		0			0
$199$	−0.0585459	−	0.101404i	−0.00415021	−	0.00718837i	0.863943	−	0.503590i	$-0.167988\pi$
$199$	−0.0585459	−	0.101404i	−0.00415021	−	0.00718837i	−0.868093	+	0.496402i	$0.834654\pi$
$200$	0.390777	+	1.35410i	0.0276321	+	0.0957495i
$201$		0			0
$202$	15.8941	−	1.49287i	1.11830	−	0.105038i
$203$	19.7861			1.38871
$204$		0			0
$205$	−12.9451	−	7.47385i	−0.904125	−	0.521997i
$206$	−22.3667	+	15.8751i	−1.55836	+	1.10607i
$207$		0			0
$208$	14.3914	+	0.941797i	0.997866	+	0.0653018i
$209$	−19.6089			−1.35637
$210$		0			0
$211$	12.7439	+	7.35770i	0.877327	+	0.506525i	0.869776	−	0.493446i	$-0.164263\pi$
$211$	12.7439	+	7.35770i	0.877327	+	0.506525i	0.00755106	+	0.999971i	$0.497596\pi$
$212$	5.04509	+	1.76364i	0.346498	+	0.121127i
$213$		0			0
$214$	19.4954	−	1.83113i	1.33268	−	0.125173i
$215$	9.33910	−	5.39193i	0.636921	−	0.367727i
$216$		0			0
$217$	−14.7532	−	25.5533i	−1.00151	−	1.73467i
$218$	7.92309	−	5.62354i	0.536620	−	0.380874i
$219$		0			0
$220$	8.17144	+	9.48956i	0.550918	+	0.639786i
$221$	−18.6692	−	8.78803i	−1.25582	−	0.591147i
$222$		0			0
$223$	−10.9380	−	6.31505i	−0.732462	−	0.422887i	0.0868600	−	0.996221i	$-0.472317\pi$
$223$	−10.9380	−	6.31505i	−0.732462	−	0.422887i	−0.819322	+	0.573333i	$0.805650\pi$
$224$	21.5380	−	10.8934i	1.43907	−	0.727846i
$225$		0			0
$226$	25.1731	+	11.5433i	1.67449	+	0.767848i
$227$	−9.00775	−	15.6019i	−0.597865	−	1.03553i	−0.993136	−	0.116968i	$-0.962682\pi$
$227$	−9.00775	−	15.6019i	−0.597865	−	1.03553i	0.395270	−	0.918565i	$-0.370651\pi$
$228$		0			0
$229$	−5.09964			−0.336994			−0.168497	−	0.985702i	$-0.553891\pi$
$229$	−5.09964			−0.336994			−0.168497	+	0.985702i	$0.553891\pi$
$230$	−0.883220	−	9.40334i	−0.0582378	−	0.620038i
$231$		0			0
$232$	−3.15147	+	12.7321i	−0.206904	+	0.835903i
$233$	15.3036			1.00257			0.501286	−	0.865282i	$-0.332861\pi$
$233$	15.3036			1.00257			0.501286	+	0.865282i	$0.332861\pi$
$234$		0			0
$235$		−	11.3332i		−	0.739298i
$236$	15.2459	−	2.88947i	0.992423	−	0.188088i
$237$		0			0
$238$	−34.3807	+	3.22924i	−2.22857	+	0.209321i
$239$			10.7527i			0.695533i	0.937581	+	0.347766i	$0.113060\pi$
$239$			10.7527i			0.695533i	−0.937581	+	0.347766i	$0.886940\pi$
$240$		0			0
$241$	−4.82911	+	2.78809i	−0.311070	+	0.179596i	−0.647405	−	0.762146i	$-0.724146\pi$
$241$	−4.82911	+	2.78809i	−0.311070	+	0.179596i	0.336335	+	0.941742i	$0.390813\pi$
$242$	−4.97412	−	2.28092i	−0.319749	−	0.146623i
$243$		0			0
$244$	0.788028	+	4.15792i	0.0504483	+	0.266184i
$245$	13.1367	−	22.7534i	0.839272	−	1.45366i
$246$		0			0
$247$	−23.9552	−	11.2763i	−1.52423	−	0.717494i
$248$	18.7931	−	5.42346i	1.19336	−	0.344390i
$249$		0			0
$250$	12.1735	−	8.64035i	0.769921	−	0.546464i
$251$	−17.4469	+	10.0730i	−1.10124	+	0.635801i	−0.936546	−	0.350544i	$-0.885997\pi$
$251$	−17.4469	+	10.0730i	−1.10124	+	0.635801i	−0.164693	+	0.986345i	$0.552663\pi$
$252$		0			0
$253$	−3.80272	−	6.58650i	−0.239075	−	0.414090i
$254$	−0.436334	−	4.64550i	−0.0273780	−	0.291485i
$255$		0			0
$256$	3.57926	+	15.5945i	0.223704	+	0.974657i
$257$	2.14179	−	3.70969i	0.133601	−	0.231404i	−0.791461	−	0.611220i	$-0.790679\pi$
$257$	2.14179	−	3.70969i	0.133601	−	0.231404i	0.925062	+	0.379815i	$0.124012\pi$
$258$		0			0
$259$		−	6.88268i		−	0.427669i
$260$	4.52557	+	16.2920i	0.280664	+	1.01039i
$261$		0			0
$262$	9.79742	+	13.8037i	0.605287	+	0.852798i
$263$	10.7244	−	18.5751i	0.661293	−	1.14539i	−0.318984	−	0.947760i	$-0.603342\pi$
$263$	10.7244	−	18.5751i	0.661293	−	1.14539i	0.980276	−	0.197632i	$-0.0633251\pi$
$264$		0			0
$265$			6.26597i			0.384916i
$266$	−44.1153	+	4.14358i	−2.70488	+	0.254059i
$267$		0			0
$268$	−11.2816	−	13.1014i	−0.689132	−	0.800295i
$269$	5.23857	−	3.02449i	0.319401	−	0.184406i	−0.331724	−	0.943376i	$-0.607630\pi$
$269$	5.23857	−	3.02449i	0.319401	−	0.184406i	0.651126	+	0.758970i	$0.274297\pi$
$270$		0			0
$271$	9.09680	+	5.25204i	0.552591	+	0.319039i	0.750166	−	0.661249i	$-0.229973\pi$
$271$	9.09680	+	5.25204i	0.552591	+	0.319039i	−0.197575	+	0.980288i	$0.563307\pi$
$272$	3.39807	−	22.6379i	0.206038	−	1.37262i
$273$		0			0
$274$	5.08881	−	11.0974i	0.307426	−	0.670421i
$275$	−0.665289	+	1.15231i	−0.0401185	+	0.0694872i
$276$		0			0
$277$	4.73869	−	2.73588i	0.284720	−	0.164383i	−0.350838	−	0.936436i	$-0.614103\pi$
$277$	4.73869	−	2.73588i	0.284720	−	0.164383i	0.635558	+	0.772053i	$0.280770\pi$
$278$	0.111794	−	0.243794i	0.00670493	−	0.0146218i
$279$		0			0
$280$	20.3891	+	19.6226i	1.21848	+	1.17267i
$281$			13.2774i			0.792063i	0.918237	+	0.396032i	$0.129613\pi$
$281$			13.2774i			0.792063i	−0.918237	+	0.396032i	$0.870387\pi$
$282$		0			0
$283$	−14.8438	−	8.57010i	−0.882375	−	0.509439i	−0.0109341	−	0.999940i	$-0.503480\pi$
$283$	−14.8438	−	8.57010i	−0.882375	−	0.509439i	−0.871441	+	0.490501i	$0.836814\pi$
$284$	−4.99661	−	26.3639i	−0.296494	−	1.56441i
$285$		0			0
$286$	8.78099	+	10.4062i	0.519231	+	0.615334i
$287$	−27.1990			−1.60551
$288$		0			0
$289$	−7.87564	+	13.6410i	−0.463273	+	0.802413i
$290$	−15.3105	+	1.43805i	−0.899062	+	0.0844455i
$291$		0			0
$292$	19.8915	+	6.95356i	1.16406	+	0.406926i
$293$	−12.4999	−	21.6505i	−0.730254	−	1.26484i	−0.956775	−	0.290831i	$-0.906068\pi$
$293$	−12.4999	−	21.6505i	−0.730254	−	1.26484i	0.226521	−	0.974006i	$-0.427265\pi$
$294$		0			0
$295$	9.09640	+	15.7554i	0.529613	+	0.917316i
$296$	4.42892	+	1.09625i	0.257426	+	0.0637184i
$297$		0			0
$298$	−22.0277	−	10.1010i	−1.27603	−	0.585134i
$299$	−0.857955	−	10.2332i	−0.0496168	−	0.591802i
$300$		0			0
$301$	9.81122	−	16.9935i	0.565510	−	0.979491i
$302$	−2.59805	−	3.66043i	−0.149501	−	0.210634i
$303$		0			0
$304$	4.36021	−	29.0477i	0.250075	−	1.66600i
$305$	−4.29688	+	2.48081i	−0.246039	+	0.142051i
$306$		0			0
$307$	4.78769			0.273248			0.136624	−	0.990623i	$-0.456375\pi$
$307$	4.78769			0.273248			0.136624	+	0.990623i	$0.456375\pi$
$308$	21.5105	+	7.51951i	1.22567	+	0.428464i
$309$		0			0
$310$	13.2733	+	18.7009i	0.753871	+	1.06214i
$311$	15.0703			0.854556			0.427278	−	0.904120i	$-0.359473\pi$
$311$	15.0703			0.854556			0.427278	+	0.904120i	$0.359473\pi$
$312$		0			0
$313$	28.3272			1.60115			0.800573	−	0.599236i	$-0.204529\pi$
$313$	28.3272			1.60115			0.800573	+	0.599236i	$0.204529\pi$
$314$	14.5456	+	20.4936i	0.820858	+	1.15652i
$315$		0			0
$316$	1.26771	−	3.62643i	0.0713142	−	0.204003i
$317$	−14.9982			−0.842384			−0.421192	−	0.906972i	$-0.638388\pi$
$317$	−14.9982			−0.842384			−0.421192	+	0.906972i	$0.638388\pi$
$318$		0			0
$319$	−10.7241	+	6.19157i	−0.600435	+	0.346661i
$320$	−15.8744	+	9.99470i	−0.887405	+	0.558721i
$321$		0			0
$322$	−9.94702	−	14.0145i	−0.554326	−	0.780998i
$323$	−21.0123	+	36.3944i	−1.16916	+	2.02504i
$324$		0			0
$325$	−1.47540	+	1.02515i	−0.0818407	+	0.0568648i
$326$	0.0707961	+	0.0324641i	0.00392103	+	0.00179802i
$327$		0			0
$328$	4.33218	−	17.5022i	0.239205	−	0.966400i
$329$	−10.3110	−	17.8592i	−0.568465	−	0.984611i
$330$		0			0
$331$	−12.4044	−	21.4851i	−0.681808	−	1.18093i	−0.974429	−	0.224698i	$-0.927861\pi$
$331$	−12.4044	−	21.4851i	−0.681808	−	1.18093i	0.292620	−	0.956229i	$-0.405473\pi$
$332$	−1.80727	+	5.16990i	−0.0991866	+	0.283735i
$333$		0			0
$334$	−18.9539	+	1.78027i	−1.03711	+	0.0974121i
$335$	10.1352	−	17.5546i	0.553744	−	0.959113i
$336$		0			0
$337$	−31.0333			−1.69049			−0.845246	−	0.534378i	$-0.820546\pi$
$337$	−31.0333			−1.69049			−0.845246	+	0.534378i	$0.820546\pi$
$338$	4.74308	+	17.7624i	0.257990	+	0.966148i
$339$		0			0
$340$	26.3691	−	4.99758i	1.43006	−	0.271032i
$341$	15.9926	+	9.23331i	0.866046	+	0.500012i
$342$		0			0
$343$		−	17.9404i		−	0.968692i
$344$	9.37243	+	9.02008i	0.505328	+	0.486330i
$345$		0			0
$346$	−9.42212	+	20.5473i	−0.506536	+	1.10463i
$347$	9.66192	−	5.57831i	0.518679	−	0.299459i	−0.217715	−	0.976012i	$-0.569860\pi$
$347$	9.66192	−	5.57831i	0.518679	−	0.299459i	0.736394	+	0.676553i	$0.236527\pi$
$348$		0			0
$349$	−17.4633	+	30.2474i	−0.934791	+	1.61910i	−0.159784	+	0.987152i	$0.551080\pi$
$349$	−17.4633	+	30.2474i	−0.934791	+	1.61910i	−0.775007	+	0.631953i	$0.782254\pi$
$350$	−1.25325	+	2.73302i	−0.0669888	+	0.146086i
$351$		0			0
$352$	−8.26484	+	12.6440i	−0.440517	+	0.673929i
$353$	26.0211	+	15.0233i	1.38496	+	0.799610i	0.992742	−	0.120261i	$-0.0383730\pi$
$353$	26.0211	+	15.0233i	1.38496	+	0.799610i	0.392222	+	0.919870i	$0.371706\pi$
$354$		0			0
$355$	27.2451	−	15.7299i	1.44602	−	0.834858i
$356$	−26.3616	+	22.6999i	−1.39716	+	1.20309i
$357$		0			0
$358$	1.14440	−	0.107489i	0.0604832	−	0.00568096i
$359$		−	2.34283i		−	0.123650i	−0.998087	−	0.0618249i	$-0.980308\pi$
$359$		−	2.34283i		−	0.123650i	0.998087	−	0.0618249i	$-0.0196920\pi$
$360$		0			0
$361$	−17.4618	+	30.2447i	−0.919042	+	1.59183i
$362$	−3.60585	−	5.08033i	−0.189519	−	0.267016i
$363$		0			0
$364$	21.9541	+	21.5561i	1.15071	+	1.12984i
$365$			24.7051i			1.29312i
$366$		0			0
$367$	4.58886	−	7.94814i	0.239537	−	0.414890i	−0.721045	−	0.692889i	$-0.756338\pi$
$367$	4.58886	−	7.94814i	0.239537	−	0.414890i	0.960581	+	0.277999i	$0.0896711\pi$
$368$	10.6025	−	4.16860i	0.552694	−	0.217303i
$369$		0			0
$370$	0.500234	+	5.32582i	0.0260059	+	0.276876i
$371$	5.70082	+	9.87411i	0.295972	+	0.512638i
$372$		0			0
$373$	−1.54067	+	0.889508i	−0.0797731	+	0.0460570i	−0.539356	−	0.842078i	$-0.681332\pi$
$373$	−1.54067	+	0.889508i	−0.0797731	+	0.0460570i	0.459583	+	0.888135i	$0.347999\pi$
$374$	17.6239	−	12.5088i	0.911310	−	0.646817i
$375$		0			0
$376$	13.1345	−	3.79046i	0.677360	−	0.195478i
$377$	−16.6617	+	1.39692i	−0.858119	+	0.0719450i
$378$		0			0
$379$	−5.63066	+	9.75258i	−0.289227	+	0.500956i	−0.973626	−	0.228152i	$-0.926732\pi$
$379$	−5.63066	+	9.75258i	−0.289227	+	0.500956i	0.684398	+	0.729108i	$0.260065\pi$
$380$	33.8353	−	6.41261i	1.73571	−	0.328960i
$381$		0			0
$382$	12.8296	+	5.88311i	0.656420	+	0.301006i
$383$	−29.2793	+	16.9044i	−1.49610	+	0.863776i	−0.999990	−	0.00448179i	$-0.998573\pi$
$383$	−29.2793	+	16.9044i	−1.49610	+	0.863776i	−0.496114	+	0.868258i	$0.665240\pi$
$384$		0			0
$385$			26.7159i			1.36157i
$386$	9.89789	−	0.929671i	0.503789	−	0.0473190i
$387$		0			0
$388$	−1.74638	−	9.21454i	−0.0886590	−	0.467797i
$389$			29.7349i			1.50762i	0.657092	+	0.753811i	$0.271786\pi$
$389$			29.7349i			1.50762i	−0.657092	+	0.753811i	$0.728214\pi$
$390$		0			0
$391$	−16.2995			−0.824303
$392$	30.7634	+	7.61461i	1.55379	+	0.384596i
$393$		0			0
$394$	−3.03346	−	32.2962i	−0.152824	−	1.62706i
$395$	4.50401			0.226621
$396$		0			0
$397$	−9.49768	−	16.4505i	−0.476675	−	0.825625i	0.522968	−	0.852352i	$-0.324825\pi$
$397$	−9.49768	−	16.4505i	−0.476675	−	0.825625i	−0.999643	+	0.0267274i	$0.991491\pi$
$398$	0.150522	+	0.0690228i	0.00754497	+	0.00345980i
$399$		0			0
$400$	−1.55905	−	1.24176i	−0.0779526	−	0.0620878i
$401$	−10.5876	−	6.11273i	−0.528718	−	0.305255i	0.211776	−	0.977318i	$-0.432075\pi$
$401$	−10.5876	−	6.11273i	−0.528718	−	0.305255i	−0.740494	+	0.672063i	$0.765408\pi$
$402$		0			0
$403$	14.2276	+	20.4766i	0.708728	+	1.02001i
$404$	−17.1079	+	14.7316i	−0.851150	+	0.732924i
$405$		0			0
$406$	−22.8184	+	16.1957i	−1.13246	+	0.803779i
$407$	2.15377	+	3.73043i	0.106758	+	0.184911i
$408$		0			0
$409$	12.5862	−	7.26664i	0.622347	−	0.359312i	−0.155435	−	0.987846i	$-0.549678\pi$
$409$	12.5862	−	7.26664i	0.622347	−	0.359312i	0.777782	+	0.628534i	$0.216345\pi$
$410$	21.0466	−	1.97683i	1.03942	−	0.0976286i
$411$		0			0
$412$	12.8000	−	36.6160i	0.630613	−	1.80394i
$413$	28.6688	+	16.5519i	1.41070	+	0.814466i
$414$		0			0
$415$	−6.42098			−0.315193
$416$	−17.3678	+	10.6938i	−0.851529	+	0.524308i
$417$		0			0
$418$	22.6140	−	16.0506i	1.10609	−	0.785062i
$419$	9.78683	+	5.65043i	0.478118	+	0.276042i	0.719632	−	0.694356i	$-0.244311\pi$
$419$	9.78683	+	5.65043i	0.478118	+	0.276042i	−0.241514	+	0.970397i	$0.577644\pi$
$420$		0			0
$421$	−9.68826			−0.472177			−0.236088	−	0.971732i	$-0.575866\pi$
$421$	−9.68826			−0.472177			−0.236088	+	0.971732i	$0.575866\pi$
$422$	−20.7195	+	1.94611i	−1.00861	+	0.0947350i
$423$		0			0
$424$	−7.26188	+	2.09569i	−0.352668	+	0.101776i
$425$	1.42581	+	2.46958i	0.0691620	+	0.119792i
$426$		0			0
$427$	−4.51411	+	7.81866i	−0.218453	+	0.378372i
$428$	−20.9842	+	18.0695i	−1.01431	+	0.873421i
$429$		0			0
$430$	−6.35684	+	13.8627i	−0.306554	+	0.668518i
$431$	3.01093	+	1.73836i	0.145031	+	0.0837339i	0.570760	−	0.821117i	$-0.306649\pi$
$431$	3.01093	+	1.73836i	0.145031	+	0.0837339i	−0.425728	+	0.904851i	$0.639982\pi$
$432$		0			0
$433$	−6.49678	−	11.2528i	−0.312215	−	0.540773i	0.666626	−	0.745392i	$-0.267738\pi$
$433$	−6.49678	−	11.2528i	−0.312215	−	0.540773i	−0.978842	+	0.204619i	$0.934404\pi$
$434$	37.9306	+	17.3934i	1.82073	+	0.834908i
$435$		0			0
$436$	−4.53424	+	12.9707i	−0.217151	+	0.621185i
$437$	−20.9146			−1.00048
$438$		0			0
$439$	−13.8320	+	23.9578i	−0.660167	+	1.14344i	0.320405	+	0.947281i	$0.396181\pi$
$439$	−13.8320	+	23.9578i	−0.660167	+	1.14344i	−0.980572	+	0.196162i	$0.937152\pi$
$440$	−17.1913	−	4.25522i	−0.819564	−	0.202860i
$441$		0			0
$442$	28.7236	−	5.14662i	1.36624	−	0.244800i
$443$		−	27.0342i		−	1.28443i	−0.766523	−	0.642216i	$-0.778015\pi$
$443$		−	27.0342i		−	1.28443i	0.766523	−	0.642216i	$-0.221985\pi$
$444$		0			0
$445$	−35.3220	−	20.3932i	−1.67443	−	0.966730i
$446$	17.7834	−	1.67033i	0.842068	−	0.0790923i
$447$		0			0
$448$	−15.9221	+	30.1926i	−0.752249	+	1.42646i
$449$	−3.32814	+	1.92150i	−0.157064	+	0.0906812i	−0.576472	−	0.817117i	$-0.695571\pi$
$449$	−3.32814	+	1.92150i	−0.157064	+	0.0906812i	0.419408	+	0.907798i	$0.362238\pi$
$450$		0			0
$451$	14.7419	−	8.51126i	0.694171	−	0.400780i
$452$	−38.4796	+	7.29281i	−1.80993	+	0.343025i
$453$		0			0
$454$	23.1590	+	10.6197i	1.08690	+	0.498408i
$455$	−15.3633	+	32.6375i	−0.720240	+	1.53007i
$456$		0			0
$457$	−3.45666	−	1.99570i	−0.161696	−	0.0933550i	0.416969	−	0.908921i	$-0.363092\pi$
$457$	−3.45666	−	1.99570i	−0.161696	−	0.0933550i	−0.578664	+	0.815566i	$0.696426\pi$
$458$	5.88118	−	4.17426i	0.274809	−	0.195050i
$459$		0			0
$460$	8.71559	+	10.1215i	0.406366	+	0.471917i
$461$	−2.82779	−	4.89787i	−0.131703	−	0.228117i	0.792630	−	0.609703i	$-0.208711\pi$
$461$	−2.82779	−	4.89787i	−0.131703	−	0.228117i	−0.924333	+	0.381586i	$0.875378\pi$
$462$		0			0
$463$			11.5821i			0.538268i	0.963103	+	0.269134i	$0.0867374\pi$
$463$			11.5821i			0.538268i	−0.963103	+	0.269134i	$0.913263\pi$
$464$	−6.78729	−	17.2629i	−0.315092	−	0.801412i
$465$		0			0
$466$	−17.6489	+	12.5266i	−0.817570	+	0.580283i
$467$		−	18.5963i		−	0.860536i	−0.902701	−	0.430268i	$-0.858419\pi$
$467$		−	18.5963i		−	0.860536i	0.902701	−	0.430268i	$-0.141581\pi$
$468$		0			0
$469$		−	36.8842i		−	1.70315i
$470$	9.27669	+	13.0701i	0.427902	+	0.602877i
$471$		0			0
$472$	−15.2172	+	15.8117i	−0.700430	+	0.727790i
$473$			12.2807i			0.564668i
$474$		0			0
$475$	1.82952	+	3.16882i	0.0839441	+	0.145395i
$476$	37.0063	−	31.8661i	1.69618	−	1.46058i
$477$		0			0
$478$	−8.80149	−	12.4006i	−0.402571	−	0.567188i
$479$	17.3136	+	9.99603i	0.791080	+	0.456730i	0.840343	−	0.542056i	$-0.182354\pi$
$479$	17.3136	+	9.99603i	0.791080	+	0.456730i	−0.0492627	+	0.998786i	$0.515687\pi$
$480$		0			0
$481$	0.485925	+	5.79584i	0.0221563	+	0.264267i
$482$	3.28702	−	7.16819i	0.149720	−	0.326502i
$483$		0			0
$484$	7.60345	−	1.44104i	0.345611	−	0.0655018i
$485$	9.52249	−	5.49781i	0.432394	−	0.249643i
$486$		0			0
$487$	4.25869	−	2.45876i	0.192980	−	0.111417i	−0.400397	−	0.916342i	$-0.631128\pi$
$487$	4.25869	−	2.45876i	0.192980	−	0.111417i	0.593377	+	0.804925i	$0.297794\pi$
$488$	−4.31222	−	4.15011i	−0.195205	−	0.187866i
$489$		0			0
$490$	3.47464	+	36.9933i	0.156968	+	1.67119i
$491$	6.28406	+	3.62810i	0.283596	+	0.163734i	0.635050	−	0.772471i	$-0.280979\pi$
$491$	6.28406	+	3.62810i	0.283596	+	0.163734i	−0.351455	+	0.936205i	$0.614313\pi$
$492$		0			0
$493$			26.5388i			1.19525i
$494$	36.8565	−	6.60386i	1.65825	−	0.297122i
$495$		0			0
$496$	−17.2339	+	21.6375i	−0.773824	+	0.971553i
$497$	28.6224	−	49.5754i	1.28389	−	2.22376i
$498$		0			0
$499$	−11.7940			−0.527974			−0.263987	−	0.964526i	$-0.585038\pi$
$499$	−11.7940			−0.527974			−0.263987	+	0.964526i	$0.585038\pi$
$500$	−6.96668	+	19.9290i	−0.311560	+	0.891253i
$501$		0			0
$502$	11.8756	−	25.8977i	0.530033	−	1.15587i
$503$	−13.3082	−	23.0505i	−0.593383	−	1.02777i	−0.993773	−	0.111424i	$-0.964459\pi$
$503$	−13.3082	−	23.0505i	−0.593383	−	1.02777i	0.400390	−	0.916345i	$-0.368875\pi$
$504$		0			0
$505$	−22.9230	−	13.2346i	−1.02006	−	0.588932i
$506$	9.77681	+	4.48323i	0.434632	+	0.199304i
$507$		0			0
$508$	4.30573	+	5.00028i	0.191036	+	0.221852i
$509$	8.86015	−	15.3462i	0.392719	−	0.680210i	−0.600088	−	0.799934i	$-0.704868\pi$
$509$	8.86015	−	15.3462i	0.392719	−	0.680210i	0.992807	+	0.119724i	$0.0382011\pi$
$510$		0			0
$511$	22.4768	+	38.9310i	0.994317	+	1.72221i
$512$	−16.8925	−	15.0547i	−0.746551	−	0.665328i
$513$		0			0
$514$	0.566502	+	6.03136i	0.0249874	+	0.266032i
$515$	45.4769			2.00395
$516$		0			0
$517$	11.1772	+	6.45316i	0.491573	+	0.283810i
$518$	5.63375	+	7.93748i	0.247533	+	0.348753i
$519$		0			0
$520$	−18.5548	−	15.0845i	−0.813682	−	0.661497i
$521$	−4.65649			−0.204004			−0.102002	−	0.994784i	$-0.532525\pi$
$521$	−4.65649			−0.204004			−0.102002	+	0.994784i	$0.532525\pi$
$522$		0			0
$523$	−16.4234	−	9.48204i	−0.718144	−	0.414621i	0.0959250	−	0.995389i	$-0.469419\pi$
$523$	−16.4234	−	9.48204i	−0.718144	−	0.414621i	−0.814069	+	0.580768i	$0.802752\pi$
$524$	−22.5978	−	7.89963i	−0.987190	−	0.345097i
$525$		0			0
$526$	2.83659	+	30.2002i	0.123681	+	1.31679i
$527$	34.2743	−	19.7883i	1.49301	−	0.861992i
$528$		0			0
$529$	7.44405	+	12.8935i	0.323655	+	0.560586i
$530$	−5.12895	−	7.22625i	−0.222787	−	0.313888i
$531$		0			0
$532$	47.4845	−	40.8887i	2.05871	−	1.77275i
$533$	22.9040	−	1.92028i	0.992083	−	0.0831766i
$534$		0			0
$535$	−28.1169	−	16.2333i	−1.21560	−	0.701828i
$536$	23.7345	+	5.87480i	1.02518	+	0.253753i
$537$		0			0
$538$	−3.56573	+	7.77598i	−0.153730	+	0.335246i
$539$	14.9601	+	25.9117i	0.644378	+	1.11610i
$540$		0			0
$541$	31.4401			1.35172			0.675859	−	0.737031i	$-0.263773\pi$
$541$	31.4401			1.35172			0.675859	+	0.737031i	$0.263773\pi$
$542$	−14.7899	+	1.38916i	−0.635281	+	0.0596695i
$543$		0			0
$544$	14.6112	+	28.8887i	0.626449	+	1.23859i
$545$	−16.1096			−0.690058
$546$		0			0
$547$		−	32.9113i		−	1.40719i	−0.710603	−	0.703593i	$-0.751578\pi$
$547$		−	32.9113i		−	1.40719i	0.710603	−	0.703593i	$-0.248422\pi$
$548$	3.21501	+	16.9635i	0.137338	+	0.724647i
$549$		0			0
$550$	−0.175969	−	1.87348i	−0.00750332	−	0.0798853i
$551$			34.0531i			1.45071i
$552$		0			0
$553$	7.09755	−	4.09777i	0.301818	−	0.174255i
$554$	−3.22548	+	7.03397i	−0.137037	+	0.298845i
$555$		0			0
$556$	0.0706289	+	0.372664i	0.00299533	+	0.0158045i
$557$	15.3182	−	26.5319i	0.649054	−	1.12419i	−0.334295	−	0.942468i	$-0.608498\pi$
$557$	15.3182	−	26.5319i	0.649054	−	1.12419i	0.983349	−	0.181726i	$-0.0581685\pi$
$558$		0			0
$559$	−7.06217	+	15.0028i	−0.298698	+	0.634549i
$560$	−39.5756	−	5.94051i	−1.67237	−	0.251033i
$561$		0			0
$562$	−10.8681	−	15.3122i	−0.458442	−	0.645906i
$563$	−11.9974	+	6.92670i	−0.505630	+	0.291925i	−0.731035	−	0.682340i	$-0.760963\pi$
$563$	−11.9974	+	6.92670i	−0.505630	+	0.291925i	0.225406	+	0.974265i	$0.427629\pi$
$564$		0			0
$565$	−22.9587	−	39.7656i	−0.965878	−	1.67295i
$566$	24.1337	−	2.26678i	1.01441	−	0.0952800i
$567$		0			0
$568$	27.3423	+	26.3144i	1.14726	+	1.10413i
$569$	−1.42336	+	2.46532i	−0.0596702	+	0.103352i	−0.894317	−	0.447433i	$-0.852338\pi$
$569$	−1.42336	+	2.46532i	−0.0596702	+	0.103352i	0.834647	+	0.550785i	$0.185672\pi$
$570$		0			0
$571$		−	1.58567i		−	0.0663582i	−0.999449	−	0.0331791i	$-0.989437\pi$
$571$		−	1.58567i		−	0.0663582i	0.999449	−	0.0331791i	$-0.0105632\pi$
$572$	−18.6446	−	4.81344i	−0.779571	−	0.201260i
$573$		0			0
$574$	31.3674	−	22.2635i	1.30925	−	0.929260i
$575$	−0.709592	+	1.22905i	−0.0295920	+	0.0512549i
$576$		0			0
$577$			12.1207i			0.504591i	0.967650	+	0.252296i	$0.0811855\pi$
$577$			12.1207i			0.504591i	−0.967650	+	0.252296i	$0.918814\pi$
$578$	−2.08310	−	22.1781i	−0.0866456	−	0.922486i
$579$		0			0
$580$	16.4798	−	14.1907i	0.684284	−	0.589236i
$581$	−10.1184	+	5.84184i	−0.419781	+	0.242361i
$582$		0			0
$583$	−6.17972	−	3.56786i	−0.255938	−	0.147766i
$584$	−28.6317	+	8.26276i	−1.18479	+	0.341915i
$585$		0			0
$586$	32.1374	+	14.7368i	1.32758	+	0.608773i
$587$	−6.10053	+	10.5664i	−0.251796	+	0.436123i	−0.964020	−	0.265829i	$-0.914354\pi$
$587$	−6.10053	+	10.5664i	−0.251796	+	0.436123i	0.712225	+	0.701952i	$0.247688\pi$
$588$		0			0
$589$	43.9789	−	25.3912i	1.81212	−	1.04623i
$590$	−23.3869	−	10.7242i	−0.962823	−	0.441509i
$591$		0			0
$592$	−6.00500	+	2.36099i	−0.246804	+	0.0970362i
$593$			27.8522i			1.14375i	0.820340	+	0.571876i	$0.193784\pi$
$593$			27.8522i			1.14375i	−0.820340	+	0.571876i	$0.806216\pi$
$594$		0			0
$595$	49.5851	+	28.6279i	2.03279	+	1.17363i
$596$	33.6716	−	6.38159i	1.37924	−	0.261400i
$597$		0			0
$598$	9.36572	+	11.0992i	0.382993	+	0.453880i
$599$	2.82455			0.115408			0.0577040	−	0.998334i	$-0.481622\pi$
$599$	2.82455			0.115408			0.0577040	+	0.998334i	$0.481622\pi$
$600$		0			0
$601$	−12.3364	+	21.3673i	−0.503212	+	0.871589i	0.496781	+	0.867876i	$0.334515\pi$
$601$	−12.3364	+	21.3673i	−0.503212	+	0.871589i	−0.999993	+	0.00371312i	$0.998818\pi$
$602$	2.59506	+	27.6287i	0.105767	+	1.12606i
$603$		0			0
$604$	5.99241	+	2.09480i	0.243828	+	0.0852360i
$605$	4.53657	+	7.85756i	0.184438	+	0.319455i
$606$		0			0
$607$	−11.8980	−	20.6079i	−0.482925	−	0.836451i	0.516883	−	0.856056i	$-0.327092\pi$
$607$	−11.8980	−	20.6079i	−0.482925	−	0.836451i	−0.999808	+	0.0196055i	$0.993759\pi$
$608$	18.7482	+	37.0683i	0.760341	+	1.50332i
$609$		0			0
$610$	2.92476	−	6.37817i	0.118420	−	0.258245i
$611$	9.94369	+	14.3111i	0.402279	+	0.578965i
$612$		0			0
$613$	−16.8079	+	29.1122i	−0.678866	+	1.17583i	0.296456	+	0.955046i	$0.404195\pi$
$613$	−16.8079	+	29.1122i	−0.678866	+	1.17583i	−0.975323	+	0.220785i	$0.929138\pi$
$614$	−5.52142	+	3.91892i	−0.222826	+	0.158155i
$615$		0			0
$616$	−30.9620	+	8.93526i	−1.24750	+	0.360012i
$617$	4.78893	−	2.76489i	0.192795	−	0.111310i	−0.400495	−	0.916299i	$-0.631162\pi$
$617$	4.78893	−	2.76489i	0.192795	−	0.111310i	0.593290	+	0.804988i	$0.297829\pi$
$618$		0			0
$619$	−45.0671			−1.81140			−0.905700	−	0.423920i	$-0.860654\pi$
$619$	−45.0671			−1.81140			−0.905700	+	0.423920i	$0.860654\pi$
$620$	−30.6149	−	10.7022i	−1.22952	−	0.429810i
$621$		0			0
$622$	−17.3798	+	12.3356i	−0.696867	+	0.494613i
$623$	−74.2154			−2.97338
$624$		0			0
$625$	−27.2431			−1.08973
$626$	−32.6684	+	23.1869i	−1.30569	+	0.926735i
$627$		0			0
$628$	−33.5496	−	11.7281i	−1.33878	−	0.468002i
$629$	9.23166			0.368090
$630$		0			0
$631$	19.1700	−	11.0678i	0.763146	−	0.440603i	−0.0672781	−	0.997734i	$-0.521431\pi$
$631$	19.1700	−	11.0678i	0.763146	−	0.440603i	0.830424	+	0.557132i	$0.188098\pi$
$632$	1.50639	+	5.21987i	0.0599210	+	0.207635i
$633$		0			0
$634$	17.2967	−	12.2766i	0.686941	−	0.487568i
$635$	−3.86820	+	6.69991i	−0.153505	+	0.265878i
$636$		0			0
$637$	3.37525	+	40.2581i	0.133732	+	1.59508i
$638$	7.29957	−	15.9185i	0.288993	−	0.630221i
$639$		0			0
$640$	10.1261	−	24.5202i	0.400271	−	0.969247i
$641$	4.25471	+	7.36938i	0.168051	+	0.291073i	0.937735	−	0.347353i	$-0.112919\pi$
$641$	4.25471	+	7.36938i	0.168051	+	0.291073i	−0.769684	+	0.638426i	$0.779586\pi$
$642$		0			0
$643$	−16.6171	−	28.7817i	−0.655316	−	1.13504i	−0.981815	−	0.189842i	$-0.939202\pi$
$643$	−16.6171	−	28.7817i	−0.655316	−	1.13504i	0.326499	−	0.945198i	$-0.394131\pi$
$644$	22.9429	+	8.02025i	0.904076	+	0.316042i
$645$		0			0
$646$	−5.55774	−	59.1713i	−0.218666	−	2.32806i
$647$	−0.419692	+	0.726928i	−0.0164998	+	0.0285785i	−0.874157	−	0.485643i	$-0.838586\pi$
$647$	−0.419692	+	0.726928i	−0.0164998	+	0.0285785i	0.857658	+	0.514221i	$0.171919\pi$
$648$		0			0
$649$	−20.7180			−0.813254
$650$	0.862392	−	2.38993i	0.0338258	−	0.0937407i
$651$		0			0
$652$	−0.108219	+	0.0205101i	−0.00423818	+	0.000803239i
$653$	−17.5839	−	10.1521i	−0.688112	−	0.397282i	0.114792	−	0.993390i	$-0.463380\pi$
$653$	−17.5839	−	10.1521i	−0.688112	−	0.397282i	−0.802904	+	0.596108i	$0.796713\pi$
$654$		0			0
$655$		−	28.0663i		−	1.09664i
$656$	9.33018	+	23.7306i	0.364282	+	0.926523i
$657$		0			0
$658$	26.5097	+	12.1562i	1.03346	+	0.473899i
$659$	−14.9226	+	8.61559i	−0.581304	+	0.335616i	−0.761651	−	0.647987i	$-0.775611\pi$
$659$	−14.9226	+	8.61559i	−0.581304	+	0.335616i	0.180348	+	0.983603i	$0.442278\pi$
$660$		0			0
$661$	6.11325	−	10.5885i	0.237778	−	0.411844i	−0.722298	−	0.691582i	$-0.756914\pi$
$661$	6.11325	−	10.5885i	0.237778	−	0.411844i	0.960076	+	0.279738i	$0.0902476\pi$
$662$	31.8918	+	14.6242i	1.23951	+	0.568387i
$663$		0			0
$664$	−2.14753	−	7.44152i	−0.0833404	−	0.288787i
$665$	63.6247	+	36.7338i	2.46726	+	1.42447i
$666$		0			0
$667$	−11.4382	+	6.60387i	−0.442890	+	0.255703i
$668$	20.4015	−	17.5676i	0.789356	−	0.679713i
$669$		0			0
$670$	2.68075	+	28.5410i	0.103566	+	1.10263i
$671$		−	5.65031i		−	0.218128i
$672$		0			0
$673$	23.0768	−	39.9702i	0.889545	−	1.54074i	0.0491314	−	0.998792i	$-0.484355\pi$
$673$	23.0768	−	39.9702i	0.889545	−	1.54074i	0.840414	−	0.541945i	$-0.182312\pi$
$674$	35.7892	−	25.4020i	1.37855	−	0.978448i
$675$		0			0
$676$	−20.0092	−	16.6022i	−0.769585	−	0.638544i
$677$		−	37.1452i		−	1.42761i	−0.700346	−	0.713804i	$-0.746971\pi$
$677$		−	37.1452i		−	1.42761i	0.700346	−	0.713804i	$-0.253029\pi$
$678$		0			0
$679$	10.0039	−	17.3272i	0.383914	−	0.664959i
$680$	−26.3195	+	27.3476i	−1.00931	+	1.04873i
$681$		0			0
$682$	−26.0013	+	2.44220i	−0.995641	+	0.0935168i
$683$	12.9363	+	22.4064i	0.494994	+	0.857355i	0.999983	−	0.00577053i	$-0.00183683\pi$
$683$	12.9363	+	22.4064i	0.494994	+	0.857355i	−0.504989	+	0.863126i	$0.668503\pi$
$684$		0			0
$685$	−17.5305	+	10.1212i	−0.669805	+	0.386712i
$686$	14.6849	+	20.6898i	0.560674	+	0.789942i
$687$		0			0
$688$	−18.1921	−	2.73073i	−0.693567	−	0.104108i
$689$	−5.49772	−	7.91240i	−0.209447	−	0.301438i
$690$		0			0
$691$	−21.3019	+	36.8960i	−0.810363	+	1.40359i	0.102247	+	0.994759i	$0.467397\pi$
$691$	−21.3019	+	36.8960i	−0.810363	+	1.40359i	−0.912610	+	0.408831i	$0.865936\pi$
$692$	−5.95270	−	31.4086i	−0.226288	−	1.19398i
$693$		0			0
$694$	−6.57657	+	14.3419i	−0.249643	+	0.544410i
$695$	−0.385119	+	0.222348i	−0.0146084	+	0.00843415i
$696$		0			0
$697$		−	36.4817i		−	1.38184i
$698$	−4.61904	−	49.1773i	−0.174833	−	1.86139i
$699$		0			0
$700$	−0.791775	−	4.17770i	−0.0299263	−	0.157902i
$701$			23.0213i			0.869502i	0.900551	+	0.434751i	$0.143164\pi$
$701$			23.0213i			0.869502i	−0.900551	+	0.434751i	$0.856836\pi$
$702$		0			0
$703$	11.8455			0.446763
$704$	−0.818195	−	21.3469i	−0.0308369	−	0.804541i
$705$		0			0
$706$	−42.3061	+	3.97365i	−1.59221	+	0.149550i
$707$	−48.1637			−1.81138
$708$		0			0
$709$	−7.09063	−	12.2813i	−0.266294	−	0.461235i	0.701608	−	0.712563i	$-0.252466\pi$
$709$	−7.09063	−	12.2813i	−0.266294	−	0.461235i	−0.967902	+	0.251329i	$0.919133\pi$
$710$	−18.5449	+	40.4418i	−0.695976	+	1.51775i
$711$		0			0
$712$	11.8208	−	47.7567i	0.443003	−	1.78976i
$713$	17.0575	+	9.84817i	0.638809	+	0.368817i
$714$		0			0
$715$	−1.88617	−	22.4971i	−0.0705387	−	0.841345i
$716$	−1.23180	+	1.06070i	−0.0460343	+	0.0396401i
$717$		0			0
$718$	1.91770	+	2.70187i	0.0715679	+	0.100833i
$719$	7.72475	+	13.3797i	0.288085	+	0.498977i	0.973353	−	0.229314i	$-0.0736483\pi$
$719$	7.72475	+	13.3797i	0.288085	+	0.498977i	−0.685268	+	0.728291i	$0.740315\pi$
$720$		0			0
$721$	71.6638	−	41.3751i	2.66890	−	1.54089i
$722$	−4.61863	−	49.1730i	−0.171888	−	1.83003i
$723$		0			0
$724$	8.31691	+	2.90738i	0.309095	+	0.108052i
$725$	2.00113	+	1.15535i	0.0743201	+	0.0429088i
$726$		0			0
$727$	−4.72802			−0.175353			−0.0876763	−	0.996149i	$-0.527944\pi$
$727$	−4.72802			−0.175353			−0.0876763	+	0.996149i	$0.527944\pi$
$728$	−42.9631	−	6.88928i	−1.59232	−	0.255334i
$729$		0			0
$730$	−20.2221	−	28.4912i	−0.748453	−	1.05451i
$731$	22.7932	+	13.1597i	0.843038	+	0.486728i
$732$		0			0
$733$	49.7495			1.83754			0.918770	−	0.394793i	$-0.129184\pi$
$733$	49.7495			1.83754			0.918770	+	0.394793i	$0.129184\pi$
$734$	1.21375	+	12.9224i	0.0448004	+	0.476974i
$735$		0			0
$736$	−8.81520	+	13.4860i	−0.324933	+	0.497101i
$737$	11.5420	+	19.9913i	0.425155	+	0.736390i
$738$		0			0
$739$	18.1362	−	31.4129i	0.667152	−	1.15554i	−0.311545	−	0.950231i	$-0.600846\pi$
$739$	18.1362	−	31.4129i	0.667152	−	1.15554i	0.978697	−	0.205310i	$-0.0658202\pi$
$740$	−4.93630	−	5.73256i	−0.181462	−	0.210733i
$741$		0			0
$742$	−14.6568	−	6.72100i	−0.538069	−	0.246736i
$743$	−40.0642	−	23.1311i	−1.46981	−	0.848597i	−0.470387	−	0.882460i	$-0.655886\pi$
$743$	−40.0642	−	23.1311i	−1.46981	−	0.848597i	−0.999426	+	0.0338625i	$0.989219\pi$
$744$		0			0
$745$	20.0900	+	34.7969i	0.736041	+	1.27486i
$746$	1.04869	−	2.28693i	0.0383952	−	0.0837305i
$747$		0			0
$748$	−10.0858	+	28.8517i	−0.368774	+	1.05492i
$749$	−59.0767			−2.15861
$750$		0			0
$751$	−5.01579	+	8.68760i	−0.183029	+	0.317015i	−0.942911	−	0.333046i	$-0.891923\pi$
$751$	−5.01579	+	8.68760i	−0.183029	+	0.317015i	0.759882	+	0.650061i	$0.225257\pi$
$752$	−12.0448	+	15.1225i	−0.439227	+	0.551460i
$753$		0			0
$754$	18.0717	−	15.2492i	0.658131	−	0.555344i
$755$			7.44254i			0.270862i
$756$		0			0
$757$	12.5144	+	7.22517i	0.454842	+	0.262603i	0.709873	−	0.704330i	$-0.248752\pi$
$757$	12.5144	+	7.22517i	0.454842	+	0.262603i	−0.255031	+	0.966933i	$0.582086\pi$
$758$	−1.48930	−	15.8561i	−0.0540940	−	0.575920i
$759$		0			0
$760$	−33.7717	+	35.0909i	−1.22503	+	1.27288i
$761$	39.8657	−	23.0165i	1.44513	−	0.834347i	0.446947	−	0.894561i	$-0.352511\pi$
$761$	39.8657	−	23.0165i	1.44513	−	0.834347i	0.998186	+	0.0602132i	$0.0191781\pi$
$762$		0			0
$763$	−25.3859	+	14.6566i	−0.919032	+	0.530604i
$764$	−19.6113	+	3.71683i	−0.709513	+	0.134470i
$765$		0			0
$766$	19.9295	−	43.4614i	0.720083	−	1.57032i
$767$	−25.3102	−	11.9141i	−0.913900	−	0.430195i
$768$		0			0
$769$	−41.3732	−	23.8868i	−1.49196	−	0.861381i	−0.491998	−	0.870597i	$-0.663733\pi$
$769$	−41.3732	−	23.8868i	−1.49196	−	0.861381i	−0.999958	+	0.00921592i	$0.997066\pi$
$770$	−21.8680	−	30.8101i	−0.788067	−	1.11032i
$771$		0			0
$772$	−10.6538	+	9.17396i	−0.383439	+	0.330178i
$773$	−14.9570	−	25.9063i	−0.537966	−	0.931784i	−0.999013	−	0.0444085i	$-0.985860\pi$
$773$	−14.9570	−	25.9063i	−0.537966	−	0.931784i	0.461048	−	0.887375i	$-0.347474\pi$
$774$		0			0
$775$		−	3.44589i		−	0.123780i
$776$	9.55648	+	9.19721i	0.343058	+	0.330161i
$777$		0			0
$778$	−24.3392	−	34.2919i	−0.872604	−	1.22942i
$779$		−	46.8113i		−	1.67719i
$780$		0			0
$781$			35.8267i			1.28198i
$782$	18.7975	−	13.3418i	0.672197	−	0.477102i
$783$		0			0
$784$	−41.7109	+	16.3995i	−1.48967	+	0.585697i
$785$		−	41.6684i		−	1.48721i
$786$		0			0
$787$	12.5521	+	21.7409i	0.447435	+	0.774981i	0.998218	−	0.0596677i	$-0.0190041\pi$
$787$	12.5521	+	21.7409i	0.447435	+	0.774981i	−0.550783	+	0.834649i	$0.685671\pi$
$788$	29.9341	+	34.7627i	1.06636	+	1.23837i
$789$		0			0
$790$	−5.19426	+	3.68671i	−0.184803	+	0.131167i
$791$	−72.3579	−	41.7759i	−2.57275	−	1.48538i
$792$		0			0
$793$	3.24928	−	6.90271i	0.115385	−	0.245123i
$794$	24.4186	+	11.1973i	0.866583	+	0.397378i
$795$		0			0
$796$	−0.230088	+	0.0436072i	−0.00815524	+	0.00154562i
$797$	3.08814	−	1.78294i	0.109388	−	0.0631550i	−0.444308	−	0.895874i	$-0.646550\pi$
$797$	3.08814	−	1.78294i	0.109388	−	0.0631550i	0.553696	+	0.832719i	$0.313217\pi$
$798$		0			0
$799$	23.9544	−	13.8301i	0.847444	−	0.489272i
$800$	2.81441	+	0.155913i	0.0995044	+	0.00551236i
$801$		0			0
$802$	17.2137	−	1.61681i	0.607835	−	0.0570916i
$803$	−24.3650	−	14.0671i	−0.859822	−	0.496419i
$804$		0			0
$805$			28.4949i			1.00431i
$806$	−33.1690	−	11.9688i	−1.16833	−	0.421584i
$807$		0			0
$808$	7.67137	−	30.9927i	0.269878	−	1.09032i
$809$	−1.68066	+	2.91098i	−0.0590887	+	0.102345i	−0.894057	−	0.447954i	$-0.852153\pi$
$809$	−1.68066	+	2.91098i	−0.0590887	+	0.102345i	0.834968	+	0.550299i	$0.185486\pi$
$810$		0			0
$811$	−43.4005			−1.52400			−0.762000	−	0.647577i	$-0.775782\pi$
$811$	−43.4005			−1.52400			−0.762000	+	0.647577i	$0.775782\pi$
$812$	13.0585	−	37.3555i	0.458264	−	1.31092i
$813$		0			0
$814$	−5.53734	−	2.53919i	−0.194084	−	0.0889986i
$815$	−0.0645684	−	0.111836i	−0.00226173	−	0.00391744i
$816$		0			0
$817$	29.2470	+	16.8857i	1.02322	+	0.590757i
$818$	−8.56703	+	18.6826i	−0.299539	+	0.653221i
$819$		0			0
$820$	−22.6540	+	19.5073i	−0.791111	+	0.681224i
$821$	−2.76506	+	4.78922i	−0.0965011	+	0.167145i	−0.910234	−	0.414094i	$-0.864098\pi$
$821$	−2.76506	+	4.78922i	−0.0965011	+	0.167145i	0.813733	+	0.581239i	$0.197432\pi$
$822$		0			0
$823$	24.7831	+	42.9256i	0.863884	+	1.49629i	0.868151	+	0.496300i	$0.165308\pi$
$823$	24.7831	+	42.9256i	0.863884	+	1.49629i	−0.00426724	+	0.999991i	$0.501358\pi$
$824$	15.2100	+	52.7049i	0.529865	+	1.83606i
$825$		0			0
$826$	−46.6107	+	4.37797i	−1.62179	+	0.152329i
$827$	−49.4336			−1.71898			−0.859488	−	0.511156i	$-0.829217\pi$
$827$	−49.4336			−1.71898			−0.859488	+	0.511156i	$0.829217\pi$
$828$		0			0
$829$	43.7886	+	25.2814i	1.52084	+	0.878059i	0.999698	+	0.0245900i	$0.00782803\pi$
$829$	43.7886	+	25.2814i	1.52084	+	0.878059i	0.521144	+	0.853469i	$0.325505\pi$
$830$	7.40501	−	5.25583i	0.257032	−	0.182432i
$831$		0			0
$832$	11.2762	−	26.5490i	0.390932	−	0.920419i
$833$	64.1234			2.22174
$834$		0			0
$835$	27.3361	+	15.7825i	0.946003	+	0.546175i
$836$	−12.9416	+	37.0209i	−0.447593	+	1.28039i
$837$		0			0
$838$	−15.9118	+	1.49453i	−0.549664	+	0.0516278i
$839$	−8.26161	+	4.76984i	−0.285222	+	0.164673i	−0.635785	−	0.771866i	$-0.719324\pi$
$839$	−8.26161	+	4.76984i	−0.285222	+	0.164673i	0.350563	+	0.936539i	$0.385990\pi$
$840$		0			0
$841$	−3.74761	−	6.49106i	−0.129228	−	0.223830i
$842$	11.1730	−	7.93023i	0.385048	−	0.273294i
$843$		0			0
$844$	22.3019	−	19.2041i	0.767663	−	0.661033i
$845$	10.6330	−	28.5683i	0.365786	−	0.982780i
$846$		0			0
$847$	14.2977	+	8.25479i	0.491275	+	0.283638i
$848$	6.65938	−	8.36100i	0.228684	−	0.287118i
$849$		0			0
$850$	−3.66577	−	1.68096i	−0.125735	−	0.0576566i
$851$	2.29719	+	3.97885i	0.0787466	+	0.136393i
$852$		0			0
$853$	−19.1280			−0.654931			−0.327466	−	0.944863i	$-0.606195\pi$
$853$	−19.1280			−0.654931			−0.327466	+	0.944863i	$0.606195\pi$
$854$	−1.19398	−	12.7119i	−0.0408571	−	0.434991i
$855$		0			0
$856$	9.40955	−	38.0151i	0.321612	−	1.29933i
$857$	21.6279			0.738796			0.369398	−	0.929271i	$-0.379564\pi$
$857$	21.6279			0.738796			0.369398	+	0.929271i	$0.379564\pi$
$858$		0			0
$859$			6.82379i			0.232825i	0.993201	+	0.116412i	$0.0371394\pi$
$859$			6.82379i			0.232825i	−0.993201	+	0.116412i	$0.962861\pi$
$860$	−4.01612	−	21.1905i	−0.136948	−	0.722590i
$861$		0			0
$862$	−4.89528	+	0.459795i	−0.166734	+	0.0156607i
$863$		−	33.7913i		−	1.15027i	−0.818059	−	0.575134i	$-0.804950\pi$
$863$		−	33.7913i		−	1.15027i	0.818059	−	0.575134i	$-0.195050\pi$
$864$		0			0
$865$	32.4583	−	18.7398i	1.10362	−	0.637173i
$866$	16.7033	+	7.65940i	0.567600	+	0.260277i
$867$		0			0
$868$	−57.9807	+	10.9888i	−1.96799	+	0.372983i
$869$	−2.56459	+	4.44201i	−0.0869979	+	0.150685i
$870$		0			0
$871$	2.60406	+	31.0598i	0.0882353	+	1.05242i
$872$	−5.38793	−	18.6700i	−0.182458	−	0.632246i
$873$		0			0
$874$	24.1199	−	17.1195i	0.815867	−	0.579075i
$875$	−39.0045	+	22.5193i	−1.31859	+	0.761290i
$876$		0			0
$877$	−10.6606	−	18.4647i	−0.359983	−	0.623510i	0.627974	−	0.778234i	$-0.283884\pi$
$877$	−10.6606	−	18.4647i	−0.359983	−	0.623510i	−0.987958	+	0.154725i	$0.950551\pi$
$878$	−3.65856	−	38.9514i	−0.123470	−	1.31455i
$879$		0			0
$880$	23.3090	−	9.16444i	0.785747	−	0.308933i
$881$	4.05760	−	7.02796i	0.136704	−	0.236778i	−0.789543	−	0.613695i	$-0.789682\pi$
$881$	4.05760	−	7.02796i	0.136704	−	0.236778i	0.926247	+	0.376917i	$0.123016\pi$
$882$		0			0
$883$			51.4630i			1.73187i	0.500157	+	0.865935i	$0.333276\pi$
$883$			51.4630i			1.73187i	−0.500157	+	0.865935i	$0.666724\pi$
$884$	−28.9129	+	29.4468i	−0.972445	+	0.990402i
$885$		0			0
$886$	22.1285	+	31.1773i	0.743423	+	1.04742i
$887$	20.3583	−	35.2616i	0.683564	−	1.18397i	−0.290322	−	0.956929i	$-0.593762\pi$
$887$	20.3583	−	35.2616i	0.683564	−	1.18397i	0.973886	−	0.227038i	$-0.0729043\pi$
$888$		0			0
$889$			14.0772i			0.472135i
$890$	57.4279	−	5.39398i	1.92499	−	0.180807i
$891$		0			0
$892$	−19.1415	+	16.4827i	−0.640906	+	0.551883i
$893$	30.7369	−	17.7459i	1.02857	−	0.593845i
$894$		0			0
$895$	−1.65049	−	0.952911i	−0.0551698	−	0.0318523i
$896$	−6.35159	−	47.8525i	−0.212192	−	1.59864i
$897$		0			0
$898$	2.26536	−	4.94019i	0.0755960	−	0.164856i
$899$	16.0347	−	27.7730i	0.534788	−	0.926281i
$900$		0			0
$901$	−13.2440	+	7.64644i	−0.441222	+	0.254740i
$902$	−10.0344	+	21.8825i	−0.334108	+	0.728608i
$903$		0			0
$904$	38.4072	−	39.9075i	1.27740	−	1.32730i
$905$			10.3295i			0.343366i
$906$		0			0
$907$	21.6049	+	12.4736i	0.717380	+	0.414180i	0.813788	−	0.581162i	$-0.197402\pi$
$907$	21.6049	+	12.4736i	0.717380	+	0.414180i	−0.0964076	+	0.995342i	$0.530735\pi$
$908$	−35.4008	+	6.70932i	−1.17482	+	0.222657i
$909$		0			0
$910$	−8.99734	−	50.2147i	−0.298259	−	1.66460i
$911$	5.75030			0.190516			0.0952580	−	0.995453i	$-0.469632\pi$
$911$	5.75030			0.190516			0.0952580	+	0.995453i	$0.469632\pi$
$912$		0			0
$913$	3.65612	−	6.33259i	0.121000	−	0.209578i
$914$	5.61996	−	0.527862i	0.185892	−	0.0174601i
$915$		0			0
$916$	−3.36569	+	9.62795i	−0.111206	+	0.318117i
$917$	−25.5349	−	44.2278i	−0.843237	−	1.46053i
$918$		0			0
$919$	−11.6516	−	20.1812i	−0.384351	−	0.665716i	0.607328	−	0.794452i	$-0.292242\pi$
$919$	−11.6516	−	20.1812i	−0.384351	−	0.665716i	−0.991679	+	0.128735i	$0.958908\pi$
$920$	−18.3361	−	4.53858i	−0.604524	−	0.149633i
$921$		0			0
$922$	7.27025	+	3.33383i	0.239433	+	0.109794i
$923$	−20.6025	+	43.7677i	−0.678141	+	1.44063i
$924$		0			0
$925$	0.401895	−	0.696103i	0.0132142	−	0.0228877i
$926$	−9.48044	−	13.3571i	−0.311547	−	0.438943i
$927$		0			0
$928$	21.9579	+	14.3529i	0.720802	+	0.471156i
$929$	−3.29824	+	1.90424i	−0.108212	+	0.0624760i	−0.553129	−	0.833096i	$-0.686566\pi$
$929$	−3.29824	+	1.90424i	−0.108212	+	0.0624760i	0.444917	+	0.895572i	$0.353233\pi$
$930$		0			0
$931$	82.2795			2.69660
$932$	10.1002	−	28.8927i	0.330841	−	0.946411i
$933$		0			0
$934$	15.2218	+	21.4463i	0.498074	+	0.701744i
$935$	−35.8336			−1.17189
$936$		0			0
$937$	55.3478			1.80813			0.904067	−	0.427391i	$-0.140567\pi$
$937$	55.3478			1.80813			0.904067	+	0.427391i	$0.140567\pi$
$938$	30.1912	+	42.5368i	0.985777	+	1.38888i
$939$		0			0
$940$	−21.3967	−	7.47976i	−0.697885	−	0.243963i
$941$	45.3754			1.47920			0.739599	−	0.673048i	$-0.235015\pi$
$941$	45.3754			1.47920			0.739599	+	0.673048i	$0.235015\pi$
$942$		0			0
$943$	15.7236	−	9.07804i	0.512032	−	0.295622i
$944$	4.60685	−	30.6907i	0.149940	−	0.998899i
$945$		0			0
$946$	−10.0523	−	14.1628i	−0.326827	−	0.460472i
$947$	16.5629	−	28.6878i	0.538222	−	0.932229i	−0.460778	−	0.887516i	$-0.652429\pi$
$947$	16.5629	−	28.6878i	0.538222	−	0.932229i	0.999000	−	0.0447128i	$-0.0142373\pi$
$948$		0			0
$949$	−21.6761	−	31.1965i	−0.703635	−	1.01268i
$950$	−4.70370	−	2.15692i	−0.152608	−	0.0699797i
$951$		0			0
$952$	−16.5940	+	67.0408i	−0.537816	+	2.17281i
$953$	27.5249	+	47.6746i	0.891620	+	1.54433i	0.837933	+	0.545773i	$0.183764\pi$
$953$	27.5249	+	47.6746i	0.891620	+	1.54433i	0.0536867	+	0.998558i	$0.482903\pi$
$954$		0			0
$955$	−11.7010	−	20.2668i	−0.378636	−	0.655817i
$956$	20.3007	+	7.09661i	0.656571	+	0.229521i
$957$		0			0
$958$	−28.1491	+	2.64394i	−0.909458	+	0.0854219i
$959$	−18.4167	+	31.8987i	−0.594706	+	1.03006i
$960$		0			0
$961$	−16.8243			−0.542720
$962$	−5.30452	−	6.28632i	−0.171024	−	0.202679i
$963$		0			0
$964$	2.07667	+	10.9573i	0.0668852	+	0.352911i
$965$	−14.2751	−	8.24173i	−0.459532	−	0.265311i
$966$		0			0
$967$		−	32.3383i		−	1.03993i	−0.854188	−	0.519965i	$-0.825945\pi$
$967$		−	32.3383i		−	1.03993i	0.854188	−	0.519965i	$-0.174055\pi$
$968$	−7.58915	+	7.88561i	−0.243925	+	0.253453i
$969$		0			0
$970$	−6.48167	+	14.1349i	−0.208114	+	0.453845i
$971$	−31.4063	+	18.1325i	−1.00788	+	0.581898i	−0.910569	−	0.413356i	$-0.864356\pi$
$971$	−31.4063	+	18.1325i	−1.00788	+	0.581898i	−0.0973076	+	0.995254i	$0.531023\pi$
$972$		0			0
$973$	−0.404588	+	0.700766i	−0.0129705	+	0.0224655i
$974$	−2.89876	+	6.32148i	−0.0928822	+	0.202553i
$975$		0			0
$976$	8.37011	+	1.25640i	0.267921	+	0.0402163i
$977$	−17.6625	−	10.1975i	−0.565074	−	0.326246i	0.190105	−	0.981764i	$-0.439117\pi$
$977$	−17.6625	−	10.1975i	−0.565074	−	0.326246i	−0.755180	+	0.655518i	$0.772450\pi$
$978$		0			0
$979$	40.2249	−	23.2239i	1.28559	−	0.742238i
$980$	−34.2877	−	39.8185i	−1.09528	−	1.27196i
$981$		0			0
$982$	−10.2169	+	0.959630i	−0.326033	+	0.0306230i
$983$			28.2445i			0.900860i	0.892812	+	0.450430i	$0.148729\pi$
$983$			28.2445i			0.900860i	−0.892812	+	0.450430i	$0.851271\pi$
$984$		0			0
$985$	−26.8923	+	46.5788i	−0.856860	+	1.48412i
$986$	−21.7231	−	30.6060i	−0.691804	−	0.974693i
$987$		0			0
$988$	−37.0994	+	37.7844i	−1.18029	+	1.20208i
$989$			13.0985i			0.416508i
$990$		0			0
$991$	−4.37500	+	7.57772i	−0.138977	+	0.240714i	−0.927109	−	0.374791i	$-0.877715\pi$
$991$	−4.37500	+	7.57772i	−0.138977	+	0.240714i	0.788133	+	0.615505i	$0.211048\pi$
$992$	2.16386	−	39.0602i	0.0687027	−	1.24016i
$993$		0			0
$994$	7.57060	+	80.6016i	0.240125	+	2.55653i
$995$	−0.137281	−	0.237777i	−0.00435209	−	0.00753805i
$996$		0			0
$997$	9.67774	−	5.58745i	0.306497	−	0.176956i	−0.338861	−	0.940837i	$-0.610042\pi$
$997$	9.67774	−	5.58745i	0.306497	−	0.176956i	0.645358	+	0.763880i	$0.276708\pi$
$998$	13.6015	−	9.65389i	0.430549	−	0.305589i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.dg.f.901.7	yes	56
3.2	odd	2	inner	936.2.dg.f.901.22	yes	56
8.5	even	2	inner	936.2.dg.f.901.16	yes	56
13.10	even	6	inner	936.2.dg.f.829.16	yes	56
24.5	odd	2	inner	936.2.dg.f.901.13	yes	56
39.23	odd	6	inner	936.2.dg.f.829.13	yes	56
104.101	even	6	inner	936.2.dg.f.829.7	✓	56
312.101	odd	6	inner	936.2.dg.f.829.22	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.dg.f.829.7	✓	56	104.101	even	6	inner
936.2.dg.f.829.13	yes	56	39.23	odd	6	inner
936.2.dg.f.829.16	yes	56	13.10	even	6	inner
936.2.dg.f.829.22	yes	56	312.101	odd	6	inner
936.2.dg.f.901.7	yes	56	1.1	even	1	trivial
936.2.dg.f.901.13	yes	56	24.5	odd	2	inner
936.2.dg.f.901.16	yes	56	8.5	even	2	inner
936.2.dg.f.901.22	yes	56	3.2	odd	2	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:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.dg (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.15325 + 0.818540i) q^{2} +(0.659986 - 1.88797i) q^{4} +2.34484 q^{5} +(3.69507 - 2.13335i) q^{7} +(0.784245 + 2.71753i) q^{8} +(-2.70420 + 1.91935i) q^{10} +(-1.33516 + 2.31256i) q^{11} +(-2.96097 + 2.05735i) q^{13} +(-2.51512 + 5.48486i) q^{14} +(-3.12884 - 2.49206i) q^{16} +(2.86144 + 4.95615i) q^{17} +(3.67163 + 6.35946i) q^{19} +(1.54756 - 4.42698i) q^{20} +(-0.353149 - 3.75985i) q^{22} +(-1.42407 + 2.46656i) q^{23} +0.498285 q^{25} +(1.73072 - 4.79631i) q^{26} +(-1.58900 - 8.38416i) q^{28} +(4.01604 + 2.31866i) q^{29} -6.91551i q^{31} +(5.64819 + 0.312900i) q^{32} +(-7.35677 - 3.37350i) q^{34} +(8.66436 - 5.00237i) q^{35} +(0.806558 - 1.39700i) q^{37} +(-9.43979 - 4.32869i) q^{38} +(1.83893 + 6.37217i) q^{40} +(-5.52067 - 3.18736i) q^{41} +(3.98283 - 2.29949i) q^{43} +(3.48486 + 4.04699i) q^{44} +(-0.376665 - 4.01023i) q^{46} -4.83325i q^{47} +(5.60238 - 9.70360i) q^{49} +(-0.574648 + 0.407866i) q^{50} +(1.93001 + 6.94803i) q^{52} +2.67224i q^{53} +(-3.13074 + 5.42260i) q^{55} +(8.69529 + 8.36839i) q^{56} +(-6.52943 + 0.613284i) q^{58} +(3.87932 + 6.71918i) q^{59} +(-1.83248 + 1.05798i) q^{61} +(5.66062 + 7.97534i) q^{62} +(-6.76992 + 4.26242i) q^{64} +(-6.94300 + 4.82416i) q^{65} +(4.32233 - 7.48649i) q^{67} +(11.2456 - 2.13131i) q^{68} +(-5.89756 + 12.8611i) q^{70} +(11.6191 - 6.70831i) q^{71} +10.5359i q^{73} +(0.213334 + 2.27129i) q^{74} +(14.4297 - 2.73477i) q^{76} +11.3935i q^{77} +1.92081 q^{79} +(-7.33663 - 5.84349i) q^{80} +(8.97571 - 0.843054i) q^{82} -2.73834 q^{83} +(6.70962 + 11.6214i) q^{85} +(-2.71099 + 5.91199i) q^{86} +(-7.33155 - 1.81472i) q^{88} +(-15.0637 - 8.69704i) q^{89} +(-6.55193 + 13.9188i) q^{91} +(3.71692 + 4.31649i) q^{92} +(3.95621 + 5.57396i) q^{94} +(8.60940 + 14.9119i) q^{95} +(4.06104 - 2.34464i) q^{97} +(1.48182 + 15.7765i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 4 q^{10} - 4 q^{16} + 64 q^{25} - 48 q^{28} - 48 q^{40} + 20 q^{49} - 12 q^{52} + 16 q^{55} + 12 q^{58} - 72 q^{64} - 84 q^{76} + 80 q^{79} - 12 q^{82} - 12 q^{88} - 24 q^{94} + 24 q^{97}+O(q^{100}) \) 56 * q - 4 * q^10 - 4 * q^16 + 64 * q^25 - 48 * q^28 - 48 * q^40 + 20 * q^49 - 12 * q^52 + 16 * q^55 + 12 * q^58 - 72 * q^64 - 84 * q^76 + 80 * q^79 - 12 * q^82 - 12 * q^88 - 24 * q^94 + 24 * q^97

Introduction

L-functions

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