LMFDB - Embedded newform 1008.2.v.e.323.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(323,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2, 0]))

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

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

chi := DirichletCharacter("1008.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.v (of order $4$, 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:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			323.14
Character	$\chi$	$=$	1008.323
Dual form			1008.2.v.e.827.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.614527 - 1.27372i) q^{2} +(-1.24471 - 1.56547i) q^{4} +(2.62814 + 2.62814i) q^{5} +1.00000 q^{7} +(-2.75887 + 0.623393i) q^{8} +O(q^{10})$	\(q+(0.614527 - 1.27372i) q^{2} +(-1.24471 - 1.56547i) q^{4} +(2.62814 + 2.62814i) q^{5} +1.00000 q^{7} +(-2.75887 + 0.623393i) q^{8} +(4.96257 - 1.73245i) q^{10} +(0.583140 - 0.583140i) q^{11} +(1.76590 + 1.76590i) q^{13} +(0.614527 - 1.27372i) q^{14} +(-0.901375 + 3.89712i) q^{16} +3.63734i q^{17} +(0.963353 - 0.963353i) q^{19} +(0.842984 - 7.38555i) q^{20} +(-0.384401 - 1.10111i) q^{22} +3.77401i q^{23} +8.81423i q^{25} +(3.33446 - 1.16407i) q^{26} +(-1.24471 - 1.56547i) q^{28} +(4.76058 - 4.76058i) q^{29} -4.89207i q^{31} +(4.40991 + 3.54298i) q^{32} +(4.63295 + 2.23525i) q^{34} +(2.62814 + 2.62814i) q^{35} +(-4.66911 + 4.66911i) q^{37} +(-0.635034 - 1.81905i) q^{38} +(-8.88906 - 5.61234i) q^{40} +3.83668 q^{41} +(-3.45278 - 3.45278i) q^{43} +(-1.63873 - 0.187044i) q^{44} +(4.80702 + 2.31923i) q^{46} +11.6693 q^{47} +1.00000 q^{49} +(11.2268 + 5.41658i) q^{50} +(0.566419 - 4.96251i) q^{52} +(5.48624 + 5.48624i) q^{53} +3.06515 q^{55} +(-2.75887 + 0.623393i) q^{56} +(-3.13813 - 8.98914i) q^{58} +(4.40688 - 4.40688i) q^{59} +(-7.99959 - 7.99959i) q^{61} +(-6.23111 - 3.00630i) q^{62} +(7.22276 - 3.43972i) q^{64} +9.28208i q^{65} +(-11.3524 + 11.3524i) q^{67} +(5.69414 - 4.52745i) q^{68} +(4.96257 - 1.73245i) q^{70} -5.85120i q^{71} +0.564936i q^{73} +(3.07784 + 8.81643i) q^{74} +(-2.70720 - 0.308999i) q^{76} +(0.583140 - 0.583140i) q^{77} -16.4692i q^{79} +(-12.6111 + 7.87323i) q^{80} +(2.35774 - 4.88684i) q^{82} +(-6.92234 - 6.92234i) q^{83} +(-9.55945 + 9.55945i) q^{85} +(-6.51969 + 2.27604i) q^{86} +(-1.24528 + 1.97233i) q^{88} -10.7726 q^{89} +(1.76590 + 1.76590i) q^{91} +(5.90809 - 4.69756i) q^{92} +(7.17109 - 14.8634i) q^{94} +5.06365 q^{95} +8.64969 q^{97} +(0.614527 - 1.27372i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{7}+O(q^{10}) $ 40 * q + 40 * q^7	$ 40 q + 40 q^{7} + 48 q^{10} - 24 q^{13} + 12 q^{16} - 32 q^{19} - 8 q^{22} - 56 q^{34} - 8 q^{37} + 32 q^{43} - 52 q^{46} + 40 q^{49} - 8 q^{52} + 48 q^{55} + 56 q^{58} - 24 q^{61} + 48 q^{64} + 48 q^{70} - 24 q^{76} - 64 q^{82} + 64 q^{85} - 120 q^{88} - 24 q^{91} - 128 q^{94} + 64 q^{97}+O(q^{100}) $ 40 * q + 40 * q^7 + 48 * q^10 - 24 * q^13 + 12 * q^16 - 32 * q^19 - 8 * q^22 - 56 * q^34 - 8 * q^37 + 32 * q^43 - 52 * q^46 + 40 * q^49 - 8 * q^52 + 48 * q^55 + 56 * q^58 - 24 * q^61 + 48 * q^64 + 48 * q^70 - 24 * q^76 - 64 * q^82 + 64 * q^85 - 120 * q^88 - 24 * q^91 - 128 * q^94 + 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.614527	−	1.27372i	0.434536	−	0.900654i
$2$	0.614527	−	1.27372i	0.434536	−	0.900654i
$3$		0			0
$3$		0			0
$4$	−1.24471	−	1.56547i	−0.622357	−	0.782734i
$5$	2.62814	+	2.62814i	1.17534	+	1.17534i	0.980918	+	0.194421i	$0.0622829\pi$
$5$	2.62814	+	2.62814i	1.17534	+	1.17534i	0.194421	+	0.980918i	$0.437717\pi$
$6$		0			0
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	−2.75887	+	0.623393i	−0.975409	+	0.220403i
$9$		0			0
$10$	4.96257	−	1.73245i	1.56930	−	0.547847i
$11$	0.583140	−	0.583140i	0.175823	−	0.175823i	−0.613709	−	0.789532i	$-0.710323\pi$
$11$	0.583140	−	0.583140i	0.175823	−	0.175823i	0.789532	+	0.613709i	$0.210323\pi$
$12$		0			0
$13$	1.76590	+	1.76590i	0.489774	+	0.489774i	0.908235	−	0.418461i	$-0.137430\pi$
$13$	1.76590	+	1.76590i	0.489774	+	0.489774i	−0.418461	+	0.908235i	$0.637430\pi$
$14$	0.614527	−	1.27372i	0.164239	−	0.340415i
$15$		0			0
$16$	−0.901375	+	3.89712i	−0.225344	+	0.974279i
$17$			3.63734i			0.882186i	0.897462	+	0.441093i	$0.145409\pi$
$17$			3.63734i			0.882186i	−0.897462	+	0.441093i	$0.854591\pi$
$18$		0			0
$19$	0.963353	−	0.963353i	0.221008	−	0.221008i	−0.587915	−	0.808923i	$-0.700051\pi$
$19$	0.963353	−	0.963353i	0.221008	−	0.221008i	0.808923	+	0.587915i	$0.200051\pi$
$20$	0.842984	−	7.38555i	0.188497	−	1.65146i
$21$		0			0
$22$	−0.384401	−	1.10111i	−0.0819545	−	0.234758i
$23$			3.77401i			0.786935i	0.919338	+	0.393468i	$0.128725\pi$
$23$			3.77401i			0.786935i	−0.919338	+	0.393468i	$0.871275\pi$
$24$		0			0
$25$			8.81423i			1.76285i
$26$	3.33446	−	1.16407i	0.653941	−	0.228292i
$27$		0			0
$28$	−1.24471	−	1.56547i	−0.235229	−	0.295845i
$29$	4.76058	−	4.76058i	0.884018	−	0.884018i	−0.109922	−	0.993940i	$-0.535060\pi$
$29$	4.76058	−	4.76058i	0.884018	−	0.884018i	0.993940	+	0.109922i	$0.0350602\pi$
$30$		0			0
$31$		−	4.89207i		−	0.878641i	−0.898330	−	0.439320i	$-0.855219\pi$
$31$		−	4.89207i		−	0.878641i	0.898330	−	0.439320i	$-0.144781\pi$
$32$	4.40991	+	3.54298i	0.779569	+	0.626316i
$33$		0			0
$34$	4.63295	+	2.23525i	0.794544	+	0.383341i
$35$	2.62814	+	2.62814i	0.444237	+	0.444237i
$36$		0			0
$37$	−4.66911	+	4.66911i	−0.767598	+	0.767598i	−0.977683	−	0.210085i	$-0.932626\pi$
$37$	−4.66911	+	4.66911i	−0.767598	+	0.767598i	0.210085	+	0.977683i	$0.432626\pi$
$38$	−0.635034	−	1.81905i	−0.103016	−	0.295088i
$39$		0			0
$40$	−8.88906	−	5.61234i	−1.40548	−	0.887389i
$41$	3.83668			0.599188			0.299594	−	0.954067i	$-0.403149\pi$
$41$	3.83668			0.599188			0.299594	+	0.954067i	$0.403149\pi$
$42$		0			0
$43$	−3.45278	−	3.45278i	−0.526544	−	0.526544i	0.392996	−	0.919540i	$-0.371439\pi$
$43$	−3.45278	−	3.45278i	−0.526544	−	0.526544i	−0.919540	+	0.392996i	$0.871439\pi$
$44$	−1.63873	−	0.187044i	−0.247048	−	0.0281980i
$45$		0			0
$46$	4.80702	+	2.31923i	0.708757	+	0.341952i
$47$	11.6693			1.70214			0.851070	−	0.525052i	$-0.175954\pi$
$47$	11.6693			1.70214			0.851070	+	0.525052i	$0.175954\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$	11.2268	+	5.41658i	1.58771	+	0.766020i
$51$		0			0
$52$	0.566419	−	4.96251i	0.0785482	−	0.688176i
$53$	5.48624	+	5.48624i	0.753593	+	0.753593i	0.975148	−	0.221555i	$-0.0711133\pi$
$53$	5.48624	+	5.48624i	0.753593	+	0.753593i	−0.221555	+	0.975148i	$0.571113\pi$
$54$		0			0
$55$	3.06515			0.413304
$56$	−2.75887	+	0.623393i	−0.368670	+	0.0833044i
$57$		0			0
$58$	−3.13813	−	8.98914i	−0.412057	−	1.18033i
$59$	4.40688	−	4.40688i	0.573727	−	0.573727i	−0.359441	−	0.933168i	$-0.617033\pi$
$59$	4.40688	−	4.40688i	0.573727	−	0.573727i	0.933168	+	0.359441i	$0.117033\pi$
$60$		0			0
$61$	−7.99959	−	7.99959i	−1.02424	−	1.02424i	−0.999699	−	0.0245439i	$-0.992187\pi$
$61$	−7.99959	−	7.99959i	−1.02424	−	1.02424i	−0.0245439	−	0.999699i	$-0.507813\pi$
$62$	−6.23111	−	3.00630i	−0.791352	−	0.381801i
$63$		0			0
$64$	7.22276	−	3.43972i	0.902845	−	0.429965i
$65$			9.28208i			1.15130i
$66$		0			0
$67$	−11.3524	+	11.3524i	−1.38692	+	1.38692i	−0.555213	+	0.831708i	$0.687363\pi$
$67$	−11.3524	+	11.3524i	−1.38692	+	1.38692i	−0.831708	+	0.555213i	$0.812637\pi$
$68$	5.69414	−	4.52745i	0.690516	−	0.549034i
$69$		0			0
$70$	4.96257	−	1.73245i	0.593140	−	0.207067i
$71$		−	5.85120i		−	0.694409i	−0.937789	−	0.347205i	$-0.887131\pi$
$71$		−	5.85120i		−	0.694409i	0.937789	−	0.347205i	$-0.112869\pi$
$72$		0			0
$73$			0.564936i			0.0661207i	0.999453	+	0.0330604i	$0.0105254\pi$
$73$			0.564936i			0.0661207i	−0.999453	+	0.0330604i	$0.989475\pi$
$74$	3.07784	+	8.81643i	0.357791	+	1.02489i
$75$		0			0
$76$	−2.70720	−	0.308999i	−0.310537	−	0.0354446i
$77$	0.583140	−	0.583140i	0.0664550	−	0.0664550i
$78$		0			0
$79$		−	16.4692i		−	1.85293i	−0.376382	−	0.926465i	$-0.622832\pi$
$79$		−	16.4692i		−	1.85293i	0.376382	−	0.926465i	$-0.377168\pi$
$80$	−12.6111	+	7.87323i	−1.40996	+	0.880254i
$81$		0			0
$82$	2.35774	−	4.88684i	0.260369	−	0.539662i
$83$	−6.92234	−	6.92234i	−0.759826	−	0.759826i	0.216465	−	0.976290i	$-0.430547\pi$
$83$	−6.92234	−	6.92234i	−0.759826	−	0.759826i	−0.976290	+	0.216465i	$0.930547\pi$
$84$		0			0
$85$	−9.55945	+	9.55945i	−1.03687	+	1.03687i
$86$	−6.51969	+	2.27604i	−0.703037	+	0.245432i
$87$		0			0
$88$	−1.24528	+	1.97233i	−0.132748	+	0.210252i
$89$	−10.7726			−1.14189			−0.570946	−	0.820988i	$-0.693423\pi$
$89$	−10.7726			−1.14189			−0.570946	+	0.820988i	$0.693423\pi$
$90$		0			0
$91$	1.76590	+	1.76590i	0.185117	+	0.185117i
$92$	5.90809	−	4.69756i	0.615961	−	0.489755i
$93$		0			0
$94$	7.17109	−	14.8634i	0.739641	−	1.53304i
$95$	5.06365			0.519520
$96$		0			0
$97$	8.64969			0.878243			0.439122	−	0.898428i	$-0.355290\pi$
$97$	8.64969			0.878243			0.439122	+	0.898428i	$0.355290\pi$
$98$	0.614527	−	1.27372i	0.0620766	−	0.128665i
$99$		0			0
$100$	13.7984	−	10.9712i	1.37984	−	1.09712i
$101$	−10.9849	−	10.9849i	−1.09303	−	1.09303i	−0.995203	−	0.0978307i	$-0.968810\pi$
$101$	−10.9849	−	10.9849i	−1.09303	−	1.09303i	−0.0978307	−	0.995203i	$-0.531190\pi$
$102$		0			0
$103$	−2.31765			−0.228365			−0.114183	−	0.993460i	$-0.536425\pi$
$103$	−2.31765			−0.228365			−0.114183	+	0.993460i	$0.536425\pi$
$104$	−5.97276	−	3.77105i	−0.585677	−	0.369782i
$105$		0			0
$106$	10.3594	−	3.61648i	1.00619	−	0.351263i
$107$	4.38720	−	4.38720i	0.424127	−	0.424127i	−0.462495	−	0.886622i	$-0.653046\pi$
$107$	4.38720	−	4.38720i	0.424127	−	0.424127i	0.886622	+	0.462495i	$0.153046\pi$
$108$		0			0
$109$	1.97102	+	1.97102i	0.188790	+	0.188790i	0.795173	−	0.606383i	$-0.207380\pi$
$109$	1.97102	+	1.97102i	0.188790	+	0.188790i	−0.606383	+	0.795173i	$0.707380\pi$
$110$	1.88361	−	3.90413i	0.179596	−	0.372244i
$111$		0			0
$112$	−0.901375	+	3.89712i	−0.0851719	+	0.368243i
$113$		−	7.79490i		−	0.733283i	−0.930362	−	0.366641i	$-0.880508\pi$
$113$		−	7.79490i		−	0.733283i	0.930362	−	0.366641i	$-0.119492\pi$
$114$		0			0
$115$	−9.91862	+	9.91862i	−0.924916	+	0.924916i
$116$	−13.3781	−	1.52697i	−1.24213	−	0.141776i
$117$		0			0
$118$	−2.90498	−	8.32127i	−0.267425	−	0.766035i
$119$			3.63734i			0.333435i
$120$		0			0
$121$			10.3199i			0.938172i
$122$	−15.1052	+	5.27326i	−1.36756	+	0.477418i
$123$		0			0
$124$	−7.65837	+	6.08922i	−0.687742	+	0.546828i
$125$	−10.0243	+	10.0243i	−0.896603	+	0.896603i
$126$		0			0
$127$		−	5.11789i		−	0.454139i	−0.973879	−	0.227070i	$-0.927086\pi$
$127$		−	5.11789i		−	0.454139i	0.973879	−	0.227070i	$-0.0729145\pi$
$128$	0.0573446	−	11.3136i	0.00506860	−	0.999987i
$129$		0			0
$130$	11.8227	+	5.70409i	1.03692	+	0.500281i
$131$	6.29337	+	6.29337i	0.549854	+	0.549854i	0.926399	−	0.376544i	$-0.122888\pi$
$131$	6.29337	+	6.29337i	0.549854	+	0.549854i	−0.376544	+	0.926399i	$0.622888\pi$
$132$		0			0
$133$	0.963353	−	0.963353i	0.0835333	−	0.0835333i
$134$	7.48343	+	21.4362i	0.646470	+	1.85180i
$135$		0			0
$136$	−2.26749	−	10.0350i	−0.194436	−	0.860492i
$137$	−14.2421			−1.21678			−0.608392	−	0.793636i	$-0.708185\pi$
$137$	−14.2421			−1.21678			−0.608392	+	0.793636i	$0.708185\pi$
$138$		0			0
$139$	1.23142	+	1.23142i	0.104448	+	0.104448i	0.757400	−	0.652952i	$-0.226470\pi$
$139$	1.23142	+	1.23142i	0.104448	+	0.104448i	−0.652952	+	0.757400i	$0.726470\pi$
$140$	0.842984	−	7.38555i	0.0712452	−	0.624193i
$141$		0			0
$142$	−7.45277	−	3.59572i	−0.625423	−	0.301746i
$143$	2.05954			0.172227
$144$		0			0
$145$	25.0229			2.07804
$146$	0.719569	+	0.347168i	0.0595519	+	0.0287318i
$147$		0			0
$148$	13.1211	+	1.49763i	1.07854	+	0.123105i
$149$	14.2649	+	14.2649i	1.16863	+	1.16863i	0.982531	+	0.186098i	$0.0595841\pi$
$149$	14.2649	+	14.2649i	1.16863	+	1.16863i	0.186098	+	0.982531i	$0.440416\pi$
$150$		0			0
$151$	−15.2951			−1.24470			−0.622349	−	0.782740i	$-0.713822\pi$
$151$	−15.2951			−1.24470			−0.622349	+	0.782740i	$0.713822\pi$
$152$	−2.05722	+	3.25832i	−0.166863	+	0.264284i
$153$		0			0
$154$	−0.384401	−	1.10111i	−0.0309759	−	0.0887301i
$155$	12.8570	−	12.8570i	1.03270	−	1.03270i
$156$		0			0
$157$	−4.79120	−	4.79120i	−0.382379	−	0.382379i	0.489580	−	0.871959i	$-0.337150\pi$
$157$	−4.79120	−	4.79120i	−0.382379	−	0.382379i	−0.871959	+	0.489580i	$0.837150\pi$
$158$	−20.9771	−	10.1208i	−1.66885	−	0.805165i
$159$		0			0
$160$	2.27841	+	20.9013i	0.180124	+	1.65239i
$161$			3.77401i			0.297434i
$162$		0			0
$163$	3.28056	−	3.28056i	0.256953	−	0.256953i	−0.566861	−	0.823814i	$-0.691842\pi$
$163$	3.28056	−	3.28056i	0.256953	−	0.256953i	0.823814	+	0.566861i	$0.191842\pi$
$164$	−4.77556	−	6.00619i	−0.372909	−	0.469005i
$165$		0			0
$166$	−13.0711	+	4.56315i	−1.01451	+	0.354169i
$167$			21.8772i			1.69291i	0.532461	+	0.846455i	$0.321267\pi$
$167$			21.8772i			1.69291i	−0.532461	+	0.846455i	$0.678733\pi$
$168$		0			0
$169$		−	6.76317i		−	0.520244i
$170$	6.30150	+	18.0506i	0.483303	+	1.38442i
$171$		0			0
$172$	−1.10749	+	9.70294i	−0.0844454	+	0.739842i
$173$	−12.4598	+	12.4598i	−0.947304	+	0.947304i	−0.998679	−	0.0513757i	$-0.983639\pi$
$173$	−12.4598	+	12.4598i	−0.947304	+	0.947304i	0.0513757	+	0.998679i	$0.483639\pi$
$174$		0			0
$175$			8.81423i			0.666293i
$176$	1.74694	+	2.79819i	0.131680	+	0.210922i
$177$		0			0
$178$	−6.62004	+	13.7212i	−0.496193	+	1.02845i
$179$	9.24841	+	9.24841i	0.691259	+	0.691259i	0.962509	−	0.271250i	$-0.0874371\pi$
$179$	9.24841	+	9.24841i	0.691259	+	0.691259i	−0.271250	+	0.962509i	$0.587437\pi$
$180$		0			0
$181$	−16.6449	+	16.6449i	−1.23721	+	1.23721i	−0.276072	+	0.961137i	$0.589033\pi$
$181$	−16.6449	+	16.6449i	−1.23721	+	1.23721i	−0.961137	+	0.276072i	$0.910967\pi$
$182$	3.33446	−	1.16407i	0.247166	−	0.0862864i
$183$		0			0
$184$	−2.35269	−	10.4120i	−0.173443	−	0.767584i
$185$	−24.5422			−1.80438
$186$		0			0
$187$	2.12108	+	2.12108i	0.155109	+	0.155109i
$188$	−14.5249	−	18.2679i	−1.05934	−	1.33232i
$189$		0			0
$190$	3.11175	−	6.44966i	0.225750	−	0.467908i
$191$	1.93740			0.140185			0.0700927	−	0.997540i	$-0.477670\pi$
$191$	1.93740			0.140185			0.0700927	+	0.997540i	$0.477670\pi$
$192$		0			0
$193$	−10.0684			−0.724742			−0.362371	−	0.932034i	$-0.618033\pi$
$193$	−10.0684			−0.724742			−0.362371	+	0.932034i	$0.618033\pi$
$194$	5.31547	−	11.0173i	0.381628	−	0.790994i
$195$		0			0
$196$	−1.24471	−	1.56547i	−0.0889081	−	0.111819i
$197$	−1.45632	−	1.45632i	−0.103758	−	0.103758i	0.653322	−	0.757080i	$-0.273375\pi$
$197$	−1.45632	−	1.45632i	−0.103758	−	0.103758i	−0.757080	+	0.653322i	$0.773375\pi$
$198$		0			0
$199$	−16.3258			−1.15730			−0.578652	−	0.815574i	$-0.696421\pi$
$199$	−16.3258			−1.15730			−0.578652	+	0.815574i	$0.696421\pi$
$200$	−5.49473	−	24.3173i	−0.388536	−	1.71950i
$201$		0			0
$202$	−20.7421	+	7.24112i	−1.45941	+	0.509483i
$203$	4.76058	−	4.76058i	0.334127	−	0.334127i
$204$		0			0
$205$	10.0833	+	10.0833i	0.704250	+	0.704250i
$206$	−1.42426	+	2.95204i	−0.0992329	+	0.205678i
$207$		0			0
$208$	−8.47367	+	5.29019i	−0.587544	+	0.366809i
$209$		−	1.12354i		−	0.0777168i
$210$		0			0
$211$	−6.81896	+	6.81896i	−0.469437	+	0.469437i	−0.901732	−	0.432295i	$-0.857704\pi$
$211$	−6.81896	+	6.81896i	−0.469437	+	0.469437i	0.432295	+	0.901732i	$0.357704\pi$
$212$	1.75973	−	15.4173i	0.120859	−	1.05887i
$213$		0			0
$214$	−2.89200	−	8.28411i	−0.197693	−	0.566290i
$215$		−	18.1488i		−	1.23774i
$216$		0			0
$217$		−	4.89207i		−	0.332095i
$218$	3.72177	−	1.29928i	0.252070	−	0.0879984i
$219$		0			0
$220$	−3.81523	−	4.79839i	−0.257223	−	0.323507i
$221$	−6.42320	+	6.42320i	−0.432071	+	0.432071i
$222$		0			0
$223$			2.90066i			0.194243i	0.995273	+	0.0971213i	$0.0309635\pi$
$223$			2.90066i			0.194243i	−0.995273	+	0.0971213i	$0.969037\pi$
$224$	4.40991	+	3.54298i	0.294649	+	0.236725i
$225$		0			0
$226$	−9.92851	−	4.79018i	−0.660434	−	0.318638i
$227$	9.48182	+	9.48182i	0.629331	+	0.629331i	0.947900	−	0.318569i	$-0.103202\pi$
$227$	9.48182	+	9.48182i	0.629331	+	0.629331i	−0.318569	+	0.947900i	$0.603202\pi$
$228$		0			0
$229$	14.9933	−	14.9933i	0.990786	−	0.990786i	−0.00917178	−	0.999958i	$-0.502920\pi$
$229$	14.9933	−	14.9933i	0.990786	−	0.990786i	0.999958	+	0.00917178i	$0.00291951\pi$
$230$	6.53827	+	18.7288i	0.431121	+	1.23494i
$231$		0			0
$232$	−10.1661	+	16.1016i	−0.667439	+	1.05712i
$233$	11.9359			0.781945			0.390973	−	0.920402i	$-0.372139\pi$
$233$	11.9359			0.781945			0.390973	+	0.920402i	$0.372139\pi$
$234$		0			0
$235$	30.6685	+	30.6685i	2.00059	+	2.00059i
$236$	−12.3841	−	1.41352i	−0.806138	−	0.0920124i
$237$		0			0
$238$	4.63295	+	2.23525i	0.300310	+	0.144889i
$239$	−14.4892			−0.937227			−0.468614	−	0.883403i	$-0.655246\pi$
$239$	−14.4892			−0.937227			−0.468614	+	0.883403i	$0.655246\pi$
$240$		0			0
$241$	12.5295			0.807094			0.403547	−	0.914959i	$-0.367777\pi$
$241$	12.5295			0.807094			0.403547	+	0.914959i	$0.367777\pi$
$242$	13.1446	+	6.34185i	0.844969	+	0.407670i
$243$		0			0
$244$	−2.56590	+	22.4803i	−0.164265	+	1.43915i
$245$	2.62814	+	2.62814i	0.167906	+	0.167906i
$246$		0			0
$247$	3.40238			0.216488
$248$	3.04968	+	13.4966i	0.193655	+	0.857034i
$249$		0			0
$250$	6.60794	+	18.9284i	0.417923	+	1.19714i
$251$	12.1384	−	12.1384i	0.766166	−	0.766166i	−0.211263	−	0.977429i	$-0.567758\pi$
$251$	12.1384	−	12.1384i	0.766166	−	0.766166i	0.977429	+	0.211263i	$0.0677576\pi$
$252$		0			0
$253$	2.20078	+	2.20078i	0.138362	+	0.138362i
$254$	−6.51874	−	3.14508i	−0.409022	−	0.197340i
$255$		0			0
$256$	−14.3750	−	7.02553i	−0.898440	−	0.439095i
$257$		−	12.8533i		−	0.801764i	−0.916130	−	0.400882i	$-0.868704\pi$
$257$		−	12.8533i		−	0.801764i	0.916130	−	0.400882i	$-0.131296\pi$
$258$		0			0
$259$	−4.66911	+	4.66911i	−0.290125	+	0.290125i
$260$	14.5308	−	11.5535i	0.901161	−	0.716520i
$261$		0			0
$262$	11.8834	−	4.14853i	0.734160	−	0.256297i
$263$		−	25.0594i		−	1.54523i	−0.634877	−	0.772613i	$-0.718949\pi$
$263$		−	25.0594i		−	1.54523i	0.634877	−	0.772613i	$-0.281051\pi$
$264$		0			0
$265$			28.8372i			1.77145i
$266$	−0.635034	−	1.81905i	−0.0389364	−	0.111533i
$267$		0			0
$268$	31.9024	+	3.64133i	1.94875	+	0.222430i
$269$	−21.1085	+	21.1085i	−1.28701	+	1.28701i	−0.350409	+	0.936597i	$0.613957\pi$
$269$	−21.1085	+	21.1085i	−1.28701	+	1.28701i	−0.936597	+	0.350409i	$0.886043\pi$
$270$		0			0
$271$		−	27.0517i		−	1.64327i	−0.570013	−	0.821636i	$-0.693062\pi$
$271$		−	27.0517i		−	1.64327i	0.570013	−	0.821636i	$-0.306938\pi$
$272$	−14.1752	−	3.27861i	−0.859495	−	0.198795i
$273$		0			0
$274$	−8.75215	+	18.1404i	−0.528737	+	1.09590i
$275$	5.13993	+	5.13993i	0.309949	+	0.309949i
$276$		0			0
$277$	9.25373	−	9.25373i	0.556003	−	0.556003i	−0.372164	−	0.928167i	$-0.621384\pi$
$277$	9.25373	−	9.25373i	0.556003	−	0.556003i	0.928167	+	0.372164i	$0.121384\pi$
$278$	2.32522	−	0.811742i	0.139458	−	0.0486850i
$279$		0			0
$280$	−8.88906	−	5.61234i	−0.531223	−	0.335401i
$281$	16.2367			0.968600			0.484300	−	0.874902i	$-0.339074\pi$
$281$	16.2367			0.968600			0.484300	+	0.874902i	$0.339074\pi$
$282$		0			0
$283$	−9.02844	−	9.02844i	−0.536685	−	0.536685i	0.385869	−	0.922554i	$-0.373902\pi$
$283$	−9.02844	−	9.02844i	−0.536685	−	0.536685i	−0.922554	+	0.385869i	$0.873902\pi$
$284$	−9.15986	+	7.28307i	−0.543537	+	0.432170i
$285$		0			0
$286$	1.26564	−	2.62327i	0.0748389	−	0.155117i
$287$	3.83668			0.226472
$288$		0			0
$289$	3.76973			0.221749
$290$	15.3773	−	31.8722i	0.902984	−	1.87160i
$291$		0			0
$292$	0.884388	−	0.703183i	0.0517549	−	0.0411507i
$293$	−20.6256	−	20.6256i	−1.20496	−	1.20496i	−0.972639	−	0.232324i	$-0.925367\pi$
$293$	−20.6256	−	20.6256i	−1.20496	−	1.20496i	−0.232324	−	0.972639i	$-0.574633\pi$
$294$		0			0
$295$	23.1638			1.34865
$296$	9.97080	−	15.7922i	0.579541	−	0.917902i
$297$		0			0
$298$	26.9357	−	9.40332i	1.56034	−	0.544720i
$299$	−6.66454	+	6.66454i	−0.385420	+	0.385420i
$300$		0			0
$301$	−3.45278	−	3.45278i	−0.199015	−	0.199015i
$302$	−9.39925	+	19.4816i	−0.540866	+	1.12104i
$303$		0			0
$304$	2.88596	+	4.62264i	0.165521	+	0.265127i
$305$		−	42.0481i		−	2.40767i
$306$		0			0
$307$	9.53094	−	9.53094i	0.543959	−	0.543959i	−0.380728	−	0.924687i	$-0.624327\pi$
$307$	9.53094	−	9.53094i	0.543959	−	0.543959i	0.924687	+	0.380728i	$0.124327\pi$
$308$	−1.63873	−	0.187044i	−0.0933753	−	0.0106578i
$309$		0			0
$310$	−8.47524	−	24.2772i	−0.481361	−	1.37885i
$311$			4.39638i			0.249296i	0.992201	+	0.124648i	$0.0397802\pi$
$311$			4.39638i			0.249296i	−0.992201	+	0.124648i	$0.960220\pi$
$312$		0			0
$313$		−	27.8579i		−	1.57462i	−0.616558	−	0.787310i	$-0.711473\pi$
$313$		−	27.8579i		−	1.57462i	0.616558	−	0.787310i	$-0.288527\pi$
$314$	−9.04695	+	3.15831i	−0.510549	+	0.178234i
$315$		0			0
$316$	−25.7820	+	20.4994i	−1.45035	+	1.15318i
$317$	−11.5283	+	11.5283i	−0.647491	+	0.647491i	−0.952386	−	0.304895i	$-0.901379\pi$
$317$	−11.5283	+	11.5283i	−0.647491	+	0.647491i	0.304895	+	0.952386i	$0.401379\pi$
$318$		0			0
$319$		−	5.55217i		−	0.310862i
$320$	28.0225	+	9.94236i	1.56651	+	0.555795i
$321$		0			0
$322$	4.80702	+	2.31923i	0.267885	+	0.129246i
$323$	3.50405	+	3.50405i	0.194970	+	0.194970i
$324$		0			0
$325$	−15.5651	+	15.5651i	−0.863395	+	0.863395i
$326$	−2.16252	−	6.19450i	−0.119771	−	0.343082i
$327$		0			0
$328$	−10.5849	+	2.39176i	−0.584454	+	0.132063i
$329$	11.6693			0.643349
$330$		0			0
$331$	−21.4888	−	21.4888i	−1.18113	−	1.18113i	−0.979451	−	0.201682i	$-0.935359\pi$
$331$	−21.4888	−	21.4888i	−1.18113	−	1.18113i	−0.201682	−	0.979451i	$-0.564641\pi$
$332$	−2.22036	+	19.4530i	−0.121858	+	1.06762i
$333$		0			0
$334$	27.8654	+	13.4441i	1.52473	+	0.735630i
$335$	−59.6716			−3.26021
$336$		0			0
$337$	6.64762			0.362119			0.181059	−	0.983472i	$-0.442047\pi$
$337$	6.64762			0.362119			0.181059	+	0.983472i	$0.442047\pi$
$338$	−8.61437	−	4.15615i	−0.468560	−	0.226065i
$339$		0			0
$340$	26.8638	+	3.06622i	1.45689	+	0.166289i
$341$	−2.85276	−	2.85276i	−0.154486	−	0.154486i
$342$		0			0
$343$	1.00000			0.0539949
$344$	11.6782	+	7.37335i	0.629648	+	0.397544i
$345$		0			0
$346$	8.21341	+	23.5272i	0.441556	+	1.26483i
$347$	−19.4459	+	19.4459i	−1.04391	+	1.04391i	−0.0449218	+	0.998991i	$0.514304\pi$
$347$	−19.4459	+	19.4459i	−1.04391	+	1.04391i	−0.998991	+	0.0449218i	$0.985696\pi$
$348$		0			0
$349$	−6.38328	−	6.38328i	−0.341689	−	0.341689i	0.515313	−	0.857002i	$-0.327676\pi$
$349$	−6.38328	−	6.38328i	−0.341689	−	0.341689i	−0.857002	+	0.515313i	$0.827676\pi$
$350$	11.2268	+	5.41658i	0.600100	+	0.289528i
$351$		0			0
$352$	4.63765	−	0.505541i	0.247187	−	0.0269454i
$353$			7.05143i			0.375310i	0.982235	+	0.187655i	$0.0600886\pi$
$353$			7.05143i			0.375310i	−0.982235	+	0.187655i	$0.939911\pi$
$354$		0			0
$355$	15.3778	−	15.3778i	0.816167	−	0.816167i
$356$	13.4088	+	16.8641i	0.710664	+	0.893797i
$357$		0			0
$358$	17.4633	−	6.09647i	0.922962	−	0.322208i
$359$		−	28.7598i		−	1.51788i	−0.651159	−	0.758941i	$-0.725717\pi$
$359$		−	28.7598i		−	1.51788i	0.651159	−	0.758941i	$-0.274283\pi$
$360$		0			0
$361$			17.1439i			0.902311i
$362$	10.9722	+	31.4297i	0.576686	+	1.65191i
$363$		0			0
$364$	0.566419	−	4.96251i	0.0296884	−	0.260106i
$365$	−1.48473	+	1.48473i	−0.0777143	+	0.0777143i
$366$		0			0
$367$			9.89445i			0.516486i	0.966080	+	0.258243i	$0.0831435\pi$
$367$			9.89445i			0.516486i	−0.966080	+	0.258243i	$0.916856\pi$
$368$	−14.7078	−	3.40180i	−0.766695	−	0.177331i
$369$		0			0
$370$	−15.0818	+	31.2598i	−0.784066	+	1.62512i
$371$	5.48624	+	5.48624i	0.284831	+	0.284831i
$372$		0			0
$373$	−24.6444	+	24.6444i	−1.27604	+	1.27604i	−0.333175	+	0.942865i	$0.608120\pi$
$373$	−24.6444	+	24.6444i	−1.27604	+	1.27604i	−0.942865	+	0.333175i	$0.891880\pi$
$374$	4.00512	−	1.39820i	0.207100	−	0.0722991i
$375$		0			0
$376$	−32.1941	+	7.27455i	−1.66028	+	0.375156i
$377$	16.8135			0.865937
$378$		0			0
$379$	3.92064	+	3.92064i	0.201390	+	0.201390i	0.800595	−	0.599206i	$-0.204517\pi$
$379$	3.92064	+	3.92064i	0.201390	+	0.201390i	−0.599206	+	0.800595i	$0.704517\pi$
$380$	−6.30280	−	7.92698i	−0.323327	−	0.406645i
$381$		0			0
$382$	1.19059	−	2.46770i	0.0609156	−	0.126259i
$383$	−18.5474			−0.947730			−0.473865	−	0.880598i	$-0.657142\pi$
$383$	−18.5474			−0.947730			−0.473865	+	0.880598i	$0.657142\pi$
$384$		0			0
$385$	3.06515			0.156214
$386$	−6.18732	+	12.8243i	−0.314926	+	0.652742i
$387$		0			0
$388$	−10.7664	−	13.5408i	−0.546581	−	0.687431i
$389$	19.7437	+	19.7437i	1.00104	+	1.00104i	0.999999	+	0.00104509i	$0.000332661\pi$
$389$	19.7437	+	19.7437i	1.00104	+	1.00104i	0.00104509	+	0.999999i	$0.499667\pi$
$390$		0			0
$391$	−13.7274			−0.694223
$392$	−2.75887	+	0.623393i	−0.139344	+	0.0314861i
$393$		0			0
$394$	−2.74989	+	0.959993i	−0.138537	+	0.0483638i
$395$	43.2833	−	43.2833i	2.17782	−	2.17782i
$396$		0			0
$397$	13.4592	+	13.4592i	0.675497	+	0.675497i	0.958978	−	0.283481i	$-0.0914893\pi$
$397$	13.4592	+	13.4592i	0.675497	+	0.675497i	−0.283481	+	0.958978i	$0.591489\pi$
$398$	−10.0326	+	20.7945i	−0.502891	+	1.04233i
$399$		0			0
$400$	−34.3501	−	7.94492i	−1.71750	−	0.397246i
$401$		−	29.4638i		−	1.47135i	−0.677334	−	0.735676i	$-0.736865\pi$
$401$		−	29.4638i		−	1.47135i	0.677334	−	0.735676i	$-0.263135\pi$
$402$		0			0
$403$	8.63891	−	8.63891i	0.430335	−	0.430335i
$404$	−3.52343	+	30.8694i	−0.175297	+	1.53581i
$405$		0			0
$406$	−3.13813	−	8.98914i	−0.155743	−	0.446124i
$407$			5.44550i			0.269923i
$408$		0			0
$409$		−	15.9026i		−	0.786333i	−0.919467	−	0.393167i	$-0.871380\pi$
$409$		−	15.9026i		−	0.786333i	0.919467	−	0.393167i	$-0.128620\pi$
$410$	19.0398	−	6.64683i	0.940307	−	0.328264i
$411$		0			0
$412$	2.88482	+	3.62821i	0.142125	+	0.178749i
$413$	4.40688	−	4.40688i	0.216848	−	0.216848i
$414$		0			0
$415$		−	36.3858i		−	1.78611i
$416$	1.53091	+	14.0440i	0.0750591	+	0.688565i
$417$		0			0
$418$	−1.43107	−	0.690445i	−0.0699960	−	0.0337708i
$419$	−6.45606	−	6.45606i	−0.315399	−	0.315399i	0.531598	−	0.846997i	$-0.321592\pi$
$419$	−6.45606	−	6.45606i	−0.315399	−	0.315399i	−0.846997	+	0.531598i	$0.821592\pi$
$420$		0			0
$421$	11.8827	−	11.8827i	0.579126	−	0.579126i	−0.355536	−	0.934663i	$-0.615702\pi$
$421$	11.8827	−	11.8827i	0.579126	−	0.579126i	0.934663	+	0.355536i	$0.115702\pi$
$422$	4.49500	+	12.8759i	0.218813	+	0.626787i
$423$		0			0
$424$	−18.5559	−	11.7158i	−0.901155	−	0.568967i
$425$	−32.0604			−1.55516
$426$		0			0
$427$	−7.99959	−	7.99959i	−0.387127	−	0.387127i
$428$	−12.3288	−	1.40721i	−0.595937	−	0.0680200i
$429$		0			0
$430$	−23.1164	−	11.1529i	−1.11477	−	0.537841i
$431$	5.49791			0.264825			0.132412	−	0.991195i	$-0.457728\pi$
$431$	5.49791			0.264825			0.132412	+	0.991195i	$0.457728\pi$
$432$		0			0
$433$	20.0080			0.961522			0.480761	−	0.876852i	$-0.340360\pi$
$433$	20.0080			0.961522			0.480761	+	0.876852i	$0.340360\pi$
$434$	−6.23111	−	3.00630i	−0.299103	−	0.144307i
$435$		0			0
$436$	0.632212	−	5.53893i	0.0302775	−	0.265267i
$437$	3.63570	+	3.63570i	0.173919	+	0.173919i
$438$		0			0
$439$	−0.00616772			−0.000294369			−0.000147185	−	1.00000i	$-0.500047\pi$
$439$	−0.00616772			−0.000294369			−0.000147185		1.00000i	$0.500047\pi$
$440$	−8.45635	+	1.91079i	−0.403141	+	0.0910933i
$441$		0			0
$442$	4.23411	+	12.1286i	0.201396	+	0.576897i
$443$	−4.02537	+	4.02537i	−0.191251	+	0.191251i	−0.796237	−	0.604985i	$-0.793179\pi$
$443$	−4.02537	+	4.02537i	−0.191251	+	0.191251i	0.604985	+	0.796237i	$0.293179\pi$
$444$		0			0
$445$	−28.3118	−	28.3118i	−1.34211	−	1.34211i
$446$	3.69462	+	1.78253i	0.174946	+	0.0844054i
$447$		0			0
$448$	7.22276	−	3.43972i	0.341243	−	0.162512i
$449$			19.6378i			0.926765i	0.886158	+	0.463382i	$0.153364\pi$
$449$			19.6378i			0.926765i	−0.886158	+	0.463382i	$0.846636\pi$
$450$		0			0
$451$	2.23732	−	2.23732i	0.105351	−	0.105351i
$452$	−12.2027	+	9.70242i	−0.573965	+	0.456364i
$453$		0			0
$454$	17.9040	−	6.25033i	0.840276	−	0.293343i
$455$			9.28208i			0.435151i
$456$		0			0
$457$			18.0292i			0.843372i	0.906742	+	0.421686i	$0.138562\pi$
$457$			18.0292i			0.843372i	−0.906742	+	0.421686i	$0.861438\pi$
$458$	−9.88346	−	28.3110i	−0.461824	−	1.32289i
$459$		0			0
$460$	27.8731	+	3.18143i	1.29959	+	0.148335i
$461$	−2.06055	+	2.06055i	−0.0959694	+	0.0959694i	−0.753461	−	0.657492i	$-0.771617\pi$
$461$	−2.06055	+	2.06055i	−0.0959694	+	0.0959694i	0.657492	+	0.753461i	$0.271617\pi$
$462$		0			0
$463$		−	38.8765i		−	1.80674i	−0.428857	−	0.903372i	$-0.641084\pi$
$463$		−	38.8765i		−	1.80674i	0.428857	−	0.903372i	$-0.358916\pi$
$464$	14.2615	+	22.8436i	0.662072	+	1.06049i
$465$		0			0
$466$	7.33492	−	15.2029i	0.339783	−	0.704263i
$467$	−6.88850	−	6.88850i	−0.318762	−	0.318762i	0.529530	−	0.848291i	$-0.322368\pi$
$467$	−6.88850	−	6.88850i	−0.318762	−	0.318762i	−0.848291	+	0.529530i	$0.822368\pi$
$468$		0			0
$469$	−11.3524	+	11.3524i	−0.524207	+	0.524207i
$470$	57.9096	−	20.2164i	2.67117	−	0.932513i
$471$		0			0
$472$	−9.41081	+	14.9052i	−0.433167	+	0.686069i
$473$	−4.02691			−0.185157
$474$		0			0
$475$	8.49121	+	8.49121i	0.389604	+	0.389604i
$476$	5.69414	−	4.52745i	0.260991	−	0.207515i
$477$		0			0
$478$	−8.90399	+	18.4551i	−0.407259	+	0.844118i
$479$	3.25769			0.148848			0.0744239	−	0.997227i	$-0.476288\pi$
$479$	3.25769			0.148848			0.0744239	+	0.997227i	$0.476288\pi$
$480$		0			0
$481$	−16.4904			−0.751898
$482$	7.69970	−	15.9590i	0.350712	−	0.726913i
$483$		0			0
$484$	16.1555	−	12.8453i	0.734339	−	0.583878i
$485$	22.7326	+	22.7326i	1.03223	+	1.03223i
$486$		0			0
$487$	−27.6993			−1.25517			−0.627587	−	0.778547i	$-0.715957\pi$
$487$	−27.6993			−1.25517			−0.627587	+	0.778547i	$0.715957\pi$
$488$	27.0567	+	17.0830i	1.22480	+	0.773310i
$489$		0			0
$490$	4.96257	−	1.73245i	0.224186	−	0.0782639i
$491$	−20.9676	+	20.9676i	−0.946256	+	0.946256i	−0.998628	−	0.0523720i	$-0.983322\pi$
$491$	−20.9676	+	20.9676i	−0.946256	+	0.946256i	0.0523720	+	0.998628i	$0.483322\pi$
$492$		0			0
$493$	17.3159	+	17.3159i	0.779868	+	0.779868i
$494$	2.09085	−	4.33367i	0.0940718	−	0.194981i
$495$		0			0
$496$	19.0650	+	4.40958i	0.856042	+	0.197996i
$497$		−	5.85120i		−	0.262462i
$498$		0			0
$499$	2.46939	−	2.46939i	0.110545	−	0.110545i	−0.649671	−	0.760216i	$-0.725093\pi$
$499$	2.46939	−	2.46939i	0.110545	−	0.110545i	0.760216	+	0.649671i	$0.225093\pi$
$500$	28.1702	+	3.21534i	1.25981	+	0.143794i
$501$		0			0
$502$	−8.00150	−	22.9202i	−0.357124	−	1.02298i
$503$		−	19.9403i		−	0.889093i	−0.895756	−	0.444547i	$-0.853365\pi$
$503$		−	19.9403i		−	0.889093i	0.895756	−	0.444547i	$-0.146635\pi$
$504$		0			0
$505$		−	57.7394i		−	2.56937i
$506$	4.15560	−	1.45073i	0.184739	−	0.0644929i
$507$		0			0
$508$	−8.01188	+	6.37031i	−0.355470	+	0.282637i
$509$	7.45882	−	7.45882i	0.330606	−	0.330606i	−0.522210	−	0.852817i	$-0.674892\pi$
$509$	7.45882	−	7.45882i	0.330606	−	0.330606i	0.852817	+	0.522210i	$0.174892\pi$
$510$		0			0
$511$			0.564936i			0.0249913i
$512$	−17.7824	+	13.9924i	−0.785878	+	0.618382i
$513$		0			0
$514$	−16.3714	−	7.89867i	−0.722112	−	0.348395i
$515$	−6.09112	−	6.09112i	−0.268407	−	0.268407i
$516$		0			0
$517$	6.80483	−	6.80483i	0.299276	−	0.299276i
$518$	3.07784	+	8.81643i	0.135232	+	0.387372i
$519$		0			0
$520$	−5.78638	−	25.6081i	−0.253750	−	1.12299i
$521$	23.2354			1.01796			0.508981	−	0.860778i	$-0.330022\pi$
$521$	23.2354			1.01796			0.508981	+	0.860778i	$0.330022\pi$
$522$		0			0
$523$	19.1847	+	19.1847i	0.838888	+	0.838888i	0.988713	−	0.149824i	$-0.0478708\pi$
$523$	19.1847	+	19.1847i	0.838888	+	0.838888i	−0.149824	+	0.988713i	$0.547871\pi$
$524$	2.01862	−	17.6855i	0.0881838	−	0.772595i
$525$		0			0
$526$	−31.9185	−	15.3996i	−1.39171	−	0.671456i
$527$	17.7941			0.775124
$528$		0			0
$529$	8.75685			0.380733
$530$	36.7304	+	17.7212i	1.59547	+	0.769761i
$531$		0			0
$532$	−2.70720	−	0.308999i	−0.117372	−	0.0133968i
$533$	6.77520	+	6.77520i	0.293467	+	0.293467i
$534$		0			0
$535$	23.0604			0.996986
$536$	24.2429	−	38.3970i	1.04713	−	1.65850i
$537$		0			0
$538$	13.9145	+	39.8579i	0.599897	+	1.71840i
$539$	0.583140	−	0.583140i	0.0251176	−	0.0251176i
$540$		0			0
$541$	−9.33342	−	9.33342i	−0.401275	−	0.401275i	0.477407	−	0.878682i	$-0.341577\pi$
$541$	−9.33342	−	9.33342i	−0.401275	−	0.401275i	−0.878682	+	0.477407i	$0.841577\pi$
$542$	−34.4562	−	16.6240i	−1.48002	−	0.714061i
$543$		0			0
$544$	−12.8870	+	16.0404i	−0.552527	+	0.687725i
$545$			10.3602i			0.443784i
$546$		0			0
$547$	12.2760	−	12.2760i	0.524883	−	0.524883i	−0.394159	−	0.919042i	$-0.628964\pi$
$547$	12.2760	−	12.2760i	0.524883	−	0.524883i	0.919042	+	0.394159i	$0.128964\pi$
$548$	17.7273	+	22.2955i	0.757275	+	0.952418i
$549$		0			0
$550$	9.70544	−	3.38820i	0.413842	−	0.144473i
$551$		−	9.17224i		−	0.390751i
$552$		0			0
$553$		−	16.4692i		−	0.700342i
$554$	−6.09998	−	17.4733i	−0.259163	−	0.742370i
$555$		0			0
$556$	0.394982	−	3.46052i	0.0167510	−	0.146759i
$557$	14.3475	−	14.3475i	0.607923	−	0.607923i	−0.334480	−	0.942403i	$-0.608561\pi$
$557$	14.3475	−	14.3475i	0.607923	−	0.607923i	0.942403	+	0.334480i	$0.108561\pi$
$558$		0			0
$559$		−	12.1946i		−	0.515775i
$560$	−12.6111	+	7.87323i	−0.532916	+	0.332705i
$561$		0			0
$562$	9.97789	−	20.6810i	0.420892	−	0.872374i
$563$	14.8013	+	14.8013i	0.623802	+	0.623802i	0.946501	−	0.322700i	$-0.104590\pi$
$563$	14.8013	+	14.8013i	0.623802	+	0.623802i	−0.322700	+	0.946501i	$0.604590\pi$
$564$		0			0
$565$	20.4861	−	20.4861i	0.861856	−	0.861856i
$566$	−17.0479	+	5.95147i	−0.716577	+	0.250159i
$567$		0			0
$568$	3.64759	+	16.1427i	0.153050	+	0.677333i
$569$	−8.30895			−0.348329			−0.174165	−	0.984717i	$-0.555723\pi$
$569$	−8.30895			−0.348329			−0.174165	+	0.984717i	$0.555723\pi$
$570$		0			0
$571$	9.56981	+	9.56981i	0.400484	+	0.400484i	0.878404	−	0.477920i	$-0.158609\pi$
$571$	9.56981	+	9.56981i	0.400484	+	0.400484i	−0.477920	+	0.878404i	$0.658609\pi$
$572$	−2.56354	−	3.22414i	−0.107187	−	0.134808i
$573$		0			0
$574$	2.35774	−	4.88684i	0.0984102	−	0.203973i
$575$	−33.2650			−1.38725
$576$		0			0
$577$	36.5616			1.52208			0.761039	−	0.648706i	$-0.224690\pi$
$577$	36.5616			1.52208			0.761039	+	0.648706i	$0.224690\pi$
$578$	2.31660	−	4.80157i	0.0963578	−	0.199719i
$579$		0			0
$580$	−31.1464	−	39.1726i	−1.29328	−	1.62655i
$581$	−6.92234	−	6.92234i	−0.287187	−	0.287187i
$582$		0			0
$583$	6.39849			0.264998
$584$	−0.352177	−	1.55859i	−0.0145732	−	0.0644947i
$585$		0			0
$586$	−38.9462	+	13.5962i	−1.60885	+	0.561655i
$587$	2.86143	−	2.86143i	0.118104	−	0.118104i	−0.645585	−	0.763689i	$-0.723386\pi$
$587$	2.86143	−	2.86143i	0.118104	−	0.118104i	0.763689	+	0.645585i	$0.223386\pi$
$588$		0			0
$589$	−4.71279	−	4.71279i	−0.194187	−	0.194187i
$590$	14.2348	−	29.5041i	0.586036	−	1.21467i
$591$		0			0
$592$	−13.9875	−	22.4047i	−0.574881	−	0.920828i
$593$		−	40.5600i		−	1.66560i	−0.553575	−	0.832799i	$-0.686737\pi$
$593$		−	40.5600i		−	1.66560i	0.553575	−	0.832799i	$-0.313263\pi$
$594$		0			0
$595$	−9.55945	+	9.55945i	−0.391899	+	0.391899i
$596$	4.57553	−	40.0871i	0.187421	−	1.64203i
$597$		0			0
$598$	4.39320	+	12.5843i	0.179651	+	0.514609i
$599$			41.0811i			1.67853i	0.543725	+	0.839263i	$0.317013\pi$
$599$			41.0811i			1.67853i	−0.543725	+	0.839263i	$0.682987\pi$
$600$		0			0
$601$		−	26.2778i		−	1.07190i	−0.844251	−	0.535948i	$-0.819954\pi$
$601$		−	26.2778i		−	1.07190i	0.844251	−	0.535948i	$-0.180046\pi$
$602$	−6.51969	+	2.27604i	−0.265723	+	0.0927645i
$603$		0			0
$604$	19.0380	+	23.9440i	0.774646	+	0.974267i
$605$	−27.1221	+	27.1221i	−1.10267	+	1.10267i
$606$		0			0
$607$		−	47.8974i		−	1.94410i	−0.234784	−	0.972048i	$-0.575438\pi$
$607$		−	47.8974i		−	1.94410i	0.234784	−	0.972048i	$-0.424562\pi$
$608$	7.66144	−	0.835158i	0.310712	−	0.0338701i
$609$		0			0
$610$	−53.5574	−	25.8397i	−2.16847	−	1.04622i
$611$	20.6068	+	20.6068i	0.833663	+	0.833663i
$612$		0			0
$613$	0.694342	−	0.694342i	0.0280442	−	0.0280442i	−0.692946	−	0.720990i	$-0.743687\pi$
$613$	0.694342	−	0.694342i	0.0280442	−	0.0280442i	0.720990	+	0.692946i	$0.243687\pi$
$614$	−6.28271	−	17.9967i	−0.253549	−	0.726289i
$615$		0			0
$616$	−1.24528	+	1.97233i	−0.0501739	+	0.0794676i
$617$	4.60105			0.185231			0.0926156	−	0.995702i	$-0.470477\pi$
$617$	4.60105			0.185231			0.0926156	+	0.995702i	$0.470477\pi$
$618$		0			0
$619$	−6.50800	−	6.50800i	−0.261579	−	0.261579i	0.564117	−	0.825695i	$-0.309217\pi$
$619$	−6.50800	−	6.50800i	−0.261579	−	0.261579i	−0.825695	+	0.564117i	$0.809217\pi$
$620$	−36.1306	−	4.12393i	−1.45104	−	0.165621i
$621$		0			0
$622$	5.59975	+	2.70169i	0.224530	+	0.108328i
$623$	−10.7726			−0.431594
$624$		0			0
$625$	−8.61949			−0.344779
$626$	−35.4830	−	17.1194i	−1.41819	−	0.684229i
$627$		0			0
$628$	−1.53679	+	13.4641i	−0.0613247	+	0.537277i
$629$	−16.9832	−	16.9832i	−0.677164	−	0.677164i
$630$		0			0
$631$	30.8637			1.22867			0.614333	−	0.789047i	$-0.289425\pi$
$631$	30.8637			1.22867			0.614333	+	0.789047i	$0.289425\pi$
$632$	10.2668	+	45.4364i	0.408390	+	1.80736i
$633$		0			0
$634$	7.59932	+	21.7682i	0.301808	+	0.864524i
$635$	13.4505	−	13.4505i	0.533768	−	0.533768i
$636$		0			0
$637$	1.76590	+	1.76590i	0.0699676	+	0.0699676i
$638$	−7.07190	−	3.41196i	−0.279979	−	0.135081i
$639$		0			0
$640$	29.8843	−	29.5829i	1.18128	−	1.16937i
$641$			1.57360i			0.0621536i	0.999517	+	0.0310768i	$0.00989365\pi$
$641$			1.57360i			0.0621536i	−0.999517	+	0.0310768i	$0.990106\pi$
$642$		0			0
$643$	0.203779	−	0.203779i	0.00803626	−	0.00803626i	−0.703077	−	0.711113i	$-0.748191\pi$
$643$	0.203779	−	0.203779i	0.00803626	−	0.00803626i	0.711113	+	0.703077i	$0.248191\pi$
$644$	5.90809	−	4.69756i	0.232811	−	0.185110i
$645$		0			0
$646$	6.61650	−	2.30984i	0.260323	−	0.0908793i
$647$			7.73020i			0.303906i	0.988388	+	0.151953i	$0.0485562\pi$
$647$			7.73020i			0.303906i	−0.988388	+	0.151953i	$0.951444\pi$
$648$		0			0
$649$		−	5.13966i		−	0.201749i
$650$	10.2604	+	29.3907i	0.402444	+	1.15280i
$651$		0			0
$652$	−9.21897	−	1.05225i	−0.361043	−	0.0412093i
$653$	25.7507	−	25.7507i	1.00770	−	1.00770i	0.00773247	−	0.999970i	$-0.497539\pi$
$653$	25.7507	−	25.7507i	1.00770	−	1.00770i	0.999970	−	0.00773247i	$-0.00246135\pi$
$654$		0			0
$655$			33.0797i			1.29253i
$656$	−3.45828	+	14.9520i	−0.135023	+	0.583777i
$657$		0			0
$658$	7.17109	−	14.8634i	0.279558	−	0.579435i
$659$	14.1443	+	14.1443i	0.550984	+	0.550984i	0.926725	−	0.375741i	$-0.122612\pi$
$659$	14.1443	+	14.1443i	0.550984	+	0.550984i	−0.375741	+	0.926725i	$0.622612\pi$
$660$		0			0
$661$	−8.31619	+	8.31619i	−0.323462	+	0.323462i	−0.850094	−	0.526632i	$-0.823455\pi$
$661$	−8.31619	+	8.31619i	−0.323462	+	0.323462i	0.526632	+	0.850094i	$0.323455\pi$
$662$	−40.5762	+	14.1652i	−1.57704	+	0.550548i
$663$		0			0
$664$	23.4132	+	14.7825i	0.908609	+	0.573673i
$665$	5.06365			0.196360
$666$		0			0
$667$	17.9665	+	17.9665i	0.695665	+	0.695665i
$668$	34.2481	−	27.2309i	1.32510	−	1.05359i
$669$		0			0
$670$	−36.6698	+	76.0048i	−1.41668	+	2.93632i
$671$	−9.32976			−0.360172
$672$		0			0
$673$	34.9355			1.34667			0.673333	−	0.739339i	$-0.264862\pi$
$673$	34.9355			1.34667			0.673333	+	0.739339i	$0.264862\pi$
$674$	4.08514	−	8.46719i	0.157354	−	0.326144i
$675$		0			0
$676$	−10.5875	+	8.41821i	−0.407212	+	0.323777i
$677$	−5.44273	−	5.44273i	−0.209181	−	0.209181i	0.594738	−	0.803919i	$-0.297256\pi$
$677$	−5.44273	−	5.44273i	−0.209181	−	0.209181i	−0.803919	+	0.594738i	$0.797256\pi$
$678$		0			0
$679$	8.64969			0.331945
$680$	20.4140	−	32.3326i	0.782842	−	1.23990i
$681$		0			0
$682$	−5.38671	+	1.88051i	−0.206268	+	0.0720086i
$683$	−33.7753	+	33.7753i	−1.29238	+	1.29238i	−0.359063	+	0.933313i	$0.616904\pi$
$683$	−33.7753	+	33.7753i	−1.29238	+	1.29238i	−0.933313	+	0.359063i	$0.883096\pi$
$684$		0			0
$685$	−37.4302	−	37.4302i	−1.43014	−	1.43014i
$686$	0.614527	−	1.27372i	0.0234627	−	0.0486308i
$687$		0			0
$688$	16.5681	−	10.3436i	0.631654	−	0.394348i
$689$			19.3763i			0.738179i
$690$		0			0
$691$	−31.8468	+	31.8468i	−1.21151	+	1.21151i	−0.240979	+	0.970530i	$0.577469\pi$
$691$	−31.8468	+	31.8468i	−1.21151	+	1.21151i	−0.970530	+	0.240979i	$0.922531\pi$
$692$	35.0144	+	3.99653i	1.33105	+	0.151925i
$693$		0			0
$694$	12.8186	+	36.7187i	0.486587	+	1.39382i
$695$			6.47269i			0.245523i
$696$		0			0
$697$			13.9553i			0.528595i
$698$	−12.0532	+	4.20780i	−0.456220	+	0.159268i
$699$		0			0
$700$	13.7984	−	10.9712i	0.521530	−	0.414672i
$701$	17.0196	−	17.0196i	0.642822	−	0.642822i	−0.308426	−	0.951248i	$-0.599802\pi$
$701$	17.0196	−	17.0196i	0.642822	−	0.642822i	0.951248	+	0.308426i	$0.0998023\pi$
$702$		0			0
$703$			8.99601i			0.339291i
$704$	2.20604	−	6.21772i	0.0831433	−	0.234339i
$705$		0			0
$706$	8.98153	+	4.33329i	0.338024	+	0.163086i
$707$	−10.9849	−	10.9849i	−0.413128	−	0.413128i
$708$		0			0
$709$	4.45471	−	4.45471i	0.167300	−	0.167300i	−0.618491	−	0.785792i	$-0.712256\pi$
$709$	4.45471	−	4.45471i	0.167300	−	0.167300i	0.785792	+	0.618491i	$0.212256\pi$
$710$	−10.1369	−	29.0370i	−0.380430	−	1.08974i
$711$		0			0
$712$	29.7202	−	6.71555i	1.11381	−	0.251676i
$713$	18.4627			0.691434
$714$		0			0
$715$	5.41275	+	5.41275i	0.202425	+	0.202425i
$716$	2.96646	−	25.9897i	0.110862	−	0.971281i
$717$		0			0
$718$	−36.6318	−	17.6736i	−1.36709	−	0.659575i
$719$	17.3426			0.646771			0.323385	−	0.946267i	$-0.395179\pi$
$719$	17.3426			0.646771			0.323385	+	0.946267i	$0.395179\pi$
$720$		0			0
$721$	−2.31765			−0.0863139
$722$	21.8365	+	10.5354i	0.812670	+	0.392086i
$723$		0			0
$724$	46.7753	+	5.33892i	1.73839	+	0.198419i
$725$	41.9609	+	41.9609i	1.55839	+	1.55839i
$726$		0			0
$727$	0.938724			0.0348153			0.0174077	−	0.999848i	$-0.494459\pi$
$727$	0.938724			0.0348153			0.0174077	+	0.999848i	$0.494459\pi$
$728$	−5.97276	−	3.77105i	−0.221365	−	0.139765i
$729$		0			0
$730$	0.978720	+	2.80353i	0.0362241	+	0.103763i
$731$	12.5590	−	12.5590i	0.464510	−	0.464510i
$732$		0			0
$733$	−17.3212	−	17.3212i	−0.639775	−	0.639775i	0.310725	−	0.950500i	$-0.399428\pi$
$733$	−17.3212	−	17.3212i	−0.639775	−	0.639775i	−0.950500	+	0.310725i	$0.899428\pi$
$734$	12.6027	+	6.08040i	0.465175	+	0.224432i
$735$		0			0
$736$	−13.3712	+	16.6430i	−0.492871	+	0.613471i
$737$			13.2401i			0.487706i
$738$		0			0
$739$	−30.7806	+	30.7806i	−1.13228	+	1.13228i	−0.142486	+	0.989797i	$0.545510\pi$
$739$	−30.7806	+	30.7806i	−1.13228	+	1.13228i	−0.989797	+	0.142486i	$0.954490\pi$
$740$	30.5480	+	38.4200i	1.12297	+	1.41235i
$741$		0			0
$742$	10.3594	−	3.61648i	0.380304	−	0.132765i
$743$			41.3295i			1.51623i	0.652120	+	0.758116i	$0.273880\pi$
$743$			41.3295i			1.51623i	−0.652120	+	0.758116i	$0.726120\pi$
$744$		0			0
$745$			74.9805i			2.74707i
$746$	16.2454	+	46.5347i	0.594786	+	1.70376i
$747$		0			0
$748$	0.680344	−	5.96062i	0.0248758	−	0.217942i
$749$	4.38720	−	4.38720i	0.160305	−	0.160305i
$750$		0			0
$751$			50.1560i			1.83022i	0.403204	+	0.915110i	$0.367896\pi$
$751$			50.1560i			1.83022i	−0.403204	+	0.915110i	$0.632104\pi$
$752$	−10.5184	+	45.4766i	−0.383567	+	1.65836i
$753$		0			0
$754$	10.3323	−	21.4156i	0.376281	−	0.779910i
$755$	−40.1977	−	40.1977i	−1.46294	−	1.46294i
$756$		0			0
$757$	−2.81463	+	2.81463i	−0.102299	+	0.102299i	−0.756404	−	0.654105i	$-0.773046\pi$
$757$	−2.81463	+	2.81463i	−0.102299	+	0.102299i	0.654105	+	0.756404i	$0.273046\pi$
$758$	7.40312	−	2.58445i	0.268893	−	0.0938714i
$759$		0			0
$760$	−13.9700	+	3.15664i	−0.506744	+	0.114503i
$761$	−21.6910			−0.786297			−0.393149	−	0.919475i	$-0.628614\pi$
$761$	−21.6910			−0.786297			−0.393149	+	0.919475i	$0.628614\pi$
$762$		0			0
$763$	1.97102	+	1.97102i	0.0713558	+	0.0713558i
$764$	−2.41151	−	3.03294i	−0.0872454	−	0.109728i
$765$		0			0
$766$	−11.3979	+	23.6242i	−0.411823	+	0.853577i
$767$	15.5642			0.561992
$768$		0			0
$769$	−4.53040			−0.163371			−0.0816853	−	0.996658i	$-0.526030\pi$
$769$	−4.53040			−0.163371			−0.0816853	+	0.996658i	$0.526030\pi$
$770$	1.88361	−	3.90413i	0.0678807	−	0.140695i
$771$		0			0
$772$	12.5323	+	15.7618i	0.451048	+	0.567280i
$773$	−23.6600	−	23.6600i	−0.850990	−	0.850990i	0.139265	−	0.990255i	$-0.455526\pi$
$773$	−23.6600	−	23.6600i	−0.850990	−	0.850990i	−0.990255	+	0.139265i	$0.955526\pi$
$774$		0			0
$775$	43.1198			1.54891
$776$	−23.8634	+	5.39216i	−0.856646	+	0.193567i
$777$		0			0
$778$	37.2809	−	13.0149i	1.33659	−	0.466605i
$779$	3.69607	−	3.69607i	0.132426	−	0.132426i
$780$		0			0
$781$	−3.41207	−	3.41207i	−0.122093	−	0.122093i
$782$	−8.43584	+	17.4848i	−0.301665	+	0.625255i
$783$		0			0
$784$	−0.901375	+	3.89712i	−0.0321920	+	0.139183i
$785$		−	25.1839i		−	0.898850i
$786$		0			0
$787$	−1.29221	+	1.29221i	−0.0460623	+	0.0460623i	−0.729763	−	0.683700i	$-0.760369\pi$
$787$	−1.29221	+	1.29221i	−0.0460623	+	0.0460623i	0.683700	+	0.729763i	$0.260369\pi$
$788$	−0.467119	+	4.09252i	−0.0166404	+	0.145790i
$789$		0			0
$790$	−28.5320	−	81.7295i	−1.01512	−	2.90781i
$791$		−	7.79490i		−	0.277155i
$792$		0			0
$793$		−	28.2530i		−	1.00329i
$794$	25.4142	−	8.87217i	0.901917	−	0.314861i
$795$		0			0
$796$	20.3209	+	25.5575i	0.720257	+	0.905861i
$797$	6.95058	−	6.95058i	0.246202	−	0.246202i	−0.573208	−	0.819410i	$-0.694301\pi$
$797$	6.95058	−	6.95058i	0.246202	−	0.246202i	0.819410	+	0.573208i	$0.194301\pi$
$798$		0			0
$799$			42.4452i			1.50160i
$800$	−31.2286	+	38.8699i	−1.10410	+	1.37426i
$801$		0			0
$802$	−37.5286	−	18.1063i	−1.32518	−	0.639355i
$803$	0.329437	+	0.329437i	0.0116256	+	0.0116256i
$804$		0			0
$805$	−9.91862	+	9.91862i	−0.349586	+	0.349586i
$806$	−5.69470	−	16.3124i	−0.200587	−	0.574579i
$807$		0			0
$808$	37.1537	+	23.4579i	1.30706	+	0.825248i
$809$	20.9481			0.736495			0.368248	−	0.929728i	$-0.379958\pi$
$809$	20.9481			0.736495			0.368248	+	0.929728i	$0.379958\pi$
$810$		0			0
$811$	15.6400	+	15.6400i	0.549194	+	0.549194i	0.926208	−	0.377014i	$-0.123049\pi$
$811$	15.6400	+	15.6400i	0.549194	+	0.549194i	−0.377014	+	0.926208i	$0.623049\pi$
$812$	−13.3781	−	1.52697i	−0.469479	−	0.0535862i
$813$		0			0
$814$	6.93602	+	3.34640i	0.243108	+	0.117291i
$815$	17.2435			0.604015
$816$		0			0
$817$	−6.65249			−0.232741
$818$	−20.2554	−	9.77257i	−0.708214	−	0.341690i
$819$		0			0
$820$	3.23426	−	28.3360i	0.112945	−	0.989534i
$821$	7.17232	+	7.17232i	0.250316	+	0.250316i	0.821100	−	0.570784i	$-0.193361\pi$
$821$	7.17232	+	7.17232i	0.250316	+	0.250316i	−0.570784	+	0.821100i	$0.693361\pi$
$822$		0			0
$823$	−3.57692			−0.124684			−0.0623418	−	0.998055i	$-0.519857\pi$
$823$	−3.57692			−0.124684			−0.0623418	+	0.998055i	$0.519857\pi$
$824$	6.39411	−	1.44481i	0.222749	−	0.0503323i
$825$		0			0
$826$	−2.90498	−	8.32127i	−0.101077	−	0.289534i
$827$	−13.0753	+	13.0753i	−0.454672	+	0.454672i	−0.896902	−	0.442230i	$-0.854188\pi$
$827$	−13.0753	+	13.0753i	−0.454672	+	0.454672i	0.442230	+	0.896902i	$0.354188\pi$
$828$		0			0
$829$	2.86517	+	2.86517i	0.0995115	+	0.0995115i	0.755110	−	0.655598i	$-0.227584\pi$
$829$	2.86517	+	2.86517i	0.0995115	+	0.0995115i	−0.655598	+	0.755110i	$0.727584\pi$
$830$	−46.3452	−	22.3600i	−1.60866	−	0.776128i
$831$		0			0
$832$	18.8289	+	6.68048i	0.652775	+	0.231604i
$833$			3.63734i			0.126027i
$834$		0			0
$835$	−57.4963	+	57.4963i	−1.98974	+	1.98974i
$836$	−1.75886	+	1.39848i	−0.0608316	+	0.0483676i
$837$		0			0
$838$	−12.1906	+	4.25578i	−0.421118	+	0.147013i
$839$			53.9862i			1.86381i	0.362703	+	0.931905i	$0.381854\pi$
$839$			53.9862i			1.86381i	−0.362703	+	0.931905i	$0.618146\pi$
$840$		0			0
$841$		−	16.3263i		−	0.562975i
$842$	−7.83296	−	22.4374i	−0.269942	−	0.773244i
$843$		0			0
$844$	19.1625	+	2.18720i	0.659601	+	0.0752867i
$845$	17.7746	−	17.7746i	0.611463	−	0.611463i
$846$		0			0
$847$			10.3199i			0.354596i
$848$	−26.3257	+	16.4354i	−0.904027	+	0.564392i
$849$		0			0
$850$	−19.7020	+	40.8359i	−0.675772	+	1.40066i
$851$	−17.6213	−	17.6213i	−0.604050	−	0.604050i
$852$		0			0
$853$	25.3458	−	25.3458i	0.867823	−	0.867823i	−0.124408	−	0.992231i	$-0.539703\pi$
$853$	25.3458	−	25.3458i	0.867823	−	0.867823i	0.992231	+	0.124408i	$0.0397033\pi$
$854$	−15.1052	+	5.27326i	−0.516889	+	0.180447i
$855$		0			0
$856$	−9.36878	+	14.8387i	−0.320218	+	0.507176i
$857$	22.6403			0.773379			0.386689	−	0.922210i	$-0.373619\pi$
$857$	22.6403			0.773379			0.386689	+	0.922210i	$0.373619\pi$
$858$		0			0
$859$	−26.6166	−	26.6166i	−0.908146	−	0.908146i	0.0879765	−	0.996123i	$-0.471960\pi$
$859$	−26.6166	−	26.6166i	−0.908146	−	0.908146i	−0.996123	+	0.0879765i	$0.971960\pi$
$860$	−28.4113	+	22.5900i	−0.968818	+	0.770314i
$861$		0			0
$862$	3.37861	−	7.00278i	0.115076	−	0.238516i
$863$	24.5204			0.834683			0.417342	−	0.908750i	$-0.362962\pi$
$863$	24.5204			0.834683			0.417342	+	0.908750i	$0.362962\pi$
$864$		0			0
$865$	−65.4924			−2.22681
$866$	12.2954	−	25.4845i	0.417816	−	0.865999i
$867$		0			0
$868$	−7.65837	+	6.08922i	−0.259942	+	0.206682i
$869$	−9.60385	−	9.60385i	−0.325788	−	0.325788i
$870$		0			0
$871$	−40.0946			−1.35855
$872$	−6.66653	−	4.20908i	−0.225757	−	0.142538i
$873$		0			0
$874$	6.86510	−	2.39662i	0.232215	−	0.0810670i
$875$	−10.0243	+	10.0243i	−0.338884	+	0.338884i
$876$		0			0
$877$	28.9688	+	28.9688i	0.978206	+	0.978206i	0.999768	−	0.0215611i	$-0.00686364\pi$
$877$	28.9688	+	28.9688i	0.978206	+	0.978206i	−0.0215611	+	0.999768i	$0.506864\pi$
$878$	−0.00379023	+	0.00785593i	−0.000127914	+	0.000265125i
$879$		0			0
$880$	−2.76285	+	11.9452i	−0.0931355	+	0.402674i
$881$		−	30.1989i		−	1.01743i	−0.860936	−	0.508713i	$-0.830122\pi$
$881$		−	30.1989i		−	1.01743i	0.860936	−	0.508713i	$-0.169878\pi$
$882$		0			0
$883$	−3.28384	+	3.28384i	−0.110510	+	0.110510i	−0.760200	−	0.649690i	$-0.774899\pi$
$883$	−3.28384	+	3.28384i	−0.110510	+	0.110510i	0.649690	+	0.760200i	$0.274899\pi$
$884$	18.0504	+	2.06026i	0.607099	+	0.0692941i
$885$		0			0
$886$	2.65349	+	7.60088i	0.0891456	+	0.255357i
$887$		−	48.4792i		−	1.62777i	−0.581024	−	0.813886i	$-0.697348\pi$
$887$		−	48.4792i		−	1.62777i	0.581024	−	0.813886i	$-0.302652\pi$
$888$		0			0
$889$		−	5.11789i		−	0.171648i
$890$	−53.4597	+	18.6629i	−1.79197	+	0.625582i
$891$		0			0
$892$	4.54089	−	3.61049i	0.152040	−	0.120888i
$893$	11.2416	−	11.2416i	0.376187	−	0.376187i
$894$		0			0
$895$			48.6122i			1.62493i
$896$	0.0573446	−	11.3136i	0.00191575	−	0.377960i
$897$		0			0
$898$	25.0130	+	12.0679i	0.834695	+	0.402713i
$899$	−23.2891	−	23.2891i	−0.776734	−	0.776734i
$900$		0			0
$901$	−19.9553	+	19.9553i	−0.664808	+	0.664808i
$902$	−1.47482	−	4.22461i	−0.0491062	−	0.140664i
$903$		0			0
$904$	4.85929	+	21.5052i	0.161617	+	0.715251i
$905$	−87.4904			−2.90828
$906$		0			0
$907$	33.8236	+	33.8236i	1.12310	+	1.12310i	0.991273	+	0.131822i	$0.0420829\pi$
$907$	33.8236	+	33.8236i	1.12310	+	1.12310i	0.131822	+	0.991273i	$0.457917\pi$
$908$	3.04133	−	26.6456i	0.100930	−	0.884267i
$909$		0			0
$910$	11.8227	+	5.70409i	0.391920	+	0.189089i
$911$	−15.4793			−0.512852			−0.256426	−	0.966564i	$-0.582545\pi$
$911$	−15.4793			−0.512852			−0.256426	+	0.966564i	$0.582545\pi$
$912$		0			0
$913$	−8.07339			−0.267190
$914$	22.9642	+	11.0795i	0.759587	+	0.366476i
$915$		0			0
$916$	−42.1339	−	4.80916i	−1.39214	−	0.158899i
$917$	6.29337	+	6.29337i	0.207825	+	0.207825i
$918$		0			0
$919$	−49.5898			−1.63582			−0.817908	−	0.575349i	$-0.804866\pi$
$919$	−49.5898			−1.63582			−0.817908	+	0.575349i	$0.804866\pi$
$920$	21.1810	−	33.5474i	0.698318	−	1.10603i
$921$		0			0
$922$	1.35830	+	3.89082i	0.0447331	+	0.128137i
$923$	10.3326	−	10.3326i	0.340103	−	0.340103i
$924$		0			0
$925$	−41.1546	−	41.1546i	−1.35316	−	1.35316i
$926$	−49.5177	−	23.8907i	−1.62725	−	0.785096i
$927$		0			0
$928$	37.8604	−	4.12708i	1.24283	−	0.135478i
$929$			26.2852i			0.862391i	0.902259	+	0.431195i	$0.141908\pi$
$929$			26.2852i			0.862391i	−0.902259	+	0.431195i	$0.858092\pi$
$930$		0			0
$931$	0.963353	−	0.963353i	0.0315726	−	0.0315726i
$932$	−14.8568	−	18.6852i	−0.486649	−	0.612055i
$933$		0			0
$934$	−13.0072	+	4.54083i	−0.425607	+	0.148581i
$935$			11.1490i			0.364611i
$936$		0			0
$937$			2.51468i			0.0821510i	0.999156	+	0.0410755i	$0.0130784\pi$
$937$			2.51468i			0.0821510i	−0.999156	+	0.0410755i	$0.986922\pi$
$938$	7.48343	+	21.4362i	0.244343	+	0.699916i
$939$		0			0
$940$	9.83703	−	86.1841i	0.320848	−	2.81101i
$941$	15.4678	−	15.4678i	0.504237	−	0.504237i	−0.408514	−	0.912752i	$-0.633953\pi$
$941$	15.4678	−	15.4678i	0.504237	−	0.504237i	0.912752	+	0.408514i	$0.133953\pi$
$942$		0			0
$943$			14.4797i			0.471523i
$944$	13.2019	+	21.1464i	0.429684	+	0.688256i
$945$		0			0
$946$	−2.47464	+	5.12915i	−0.0804576	+	0.166763i
$947$	17.9424	+	17.9424i	0.583049	+	0.583049i	0.935740	−	0.352691i	$-0.114733\pi$
$947$	17.9424	+	17.9424i	0.583049	+	0.583049i	−0.352691	+	0.935740i	$0.614733\pi$
$948$		0			0
$949$	−0.997622	+	0.997622i	−0.0323842	+	0.0323842i
$950$	16.0335	−	5.59733i	0.520195	−	0.181601i
$951$		0			0
$952$	−2.26749	−	10.0350i	−0.0734899	−	0.325235i
$953$	−5.59267			−0.181164			−0.0905821	−	0.995889i	$-0.528873\pi$
$953$	−5.59267			−0.181164			−0.0905821	+	0.995889i	$0.528873\pi$
$954$		0			0
$955$	5.09176	+	5.09176i	0.164766	+	0.164766i
$956$	18.0349	+	22.6823i	0.583290	+	0.733599i
$957$		0			0
$958$	2.00194	−	4.14938i	0.0646797	−	0.134060i
$959$	−14.2421			−0.459901
$960$		0			0
$961$	7.06770			0.227990
$962$	−10.1338	+	21.0041i	−0.326727	+	0.677200i
$963$		0			0
$964$	−15.5956	−	19.6145i	−0.502301	−	0.631740i
$965$	−26.4612	−	26.4612i	−0.851818	−	0.851818i
$966$		0			0
$967$	31.6701			1.01844			0.509220	−	0.860636i	$-0.329934\pi$
$967$	31.6701			1.01844			0.509220	+	0.860636i	$0.329934\pi$
$968$	−6.43335	−	28.4713i	−0.206776	−	0.915102i
$969$		0			0
$970$	42.9247	−	14.9851i	1.37823	−	0.481143i
$971$	−19.7252	+	19.7252i	−0.633012	+	0.633012i	−0.948822	−	0.315810i	$-0.897724\pi$
$971$	−19.7252	+	19.7252i	−0.633012	+	0.633012i	0.315810	+	0.948822i	$0.397724\pi$
$972$		0			0
$973$	1.23142	+	1.23142i	0.0394775	+	0.0394775i
$974$	−17.0219	+	35.2810i	−0.545418	+	1.13048i
$975$		0			0
$976$	38.3860	−	23.9647i	1.22871	−	0.767092i
$977$			15.2206i			0.486951i	0.969907	+	0.243475i	$0.0782875\pi$
$977$			15.2206i			0.486951i	−0.969907	+	0.243475i	$0.921713\pi$
$978$		0			0
$979$	−6.28192	+	6.28192i	−0.200771	+	0.200771i
$980$	0.842984	−	7.38555i	0.0269281	−	0.235923i
$981$		0			0
$982$	13.8217	+	39.5920i	0.441067	+	1.26343i
$983$			39.8828i			1.27207i	0.771662	+	0.636033i	$0.219426\pi$
$983$			39.8828i			1.27207i	−0.771662	+	0.636033i	$0.780574\pi$
$984$		0			0
$985$		−	7.65482i		−	0.243903i
$986$	32.6966	−	11.4145i	1.04127	−	0.363511i
$987$		0			0
$988$	−4.23498	−	5.32631i	−0.134733	−	0.169452i
$989$	13.0308	−	13.0308i	0.414356	−	0.414356i
$990$		0			0
$991$		−	48.0864i		−	1.52752i	−0.645503	−	0.763758i	$-0.723352\pi$
$991$		−	48.0864i		−	1.52752i	0.645503	−	0.763758i	$-0.276648\pi$
$992$	17.3325	−	21.5736i	0.550307	−	0.684961i
$993$		0			0
$994$	−7.45277	−	3.59572i	−0.236388	−	0.114049i
$995$	−42.9065	−	42.9065i	−1.36023	−	1.36023i
$996$		0			0
$997$	−16.3703	+	16.3703i	−0.518452	+	0.518452i	−0.917103	−	0.398651i	$-0.869479\pi$
$997$	−16.3703	+	16.3703i	−0.518452	+	0.518452i	0.398651	+	0.917103i	$0.369479\pi$
$998$	−1.62780	−	4.66282i	−0.0515272	−	0.147599i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.v.e.323.14	yes	40
3.2	odd	2	inner	1008.2.v.e.323.7	✓	40
4.3	odd	2		4032.2.v.e.1583.19		40
12.11	even	2		4032.2.v.e.1583.2		40
16.5	even	4		4032.2.v.e.3599.2		40
16.11	odd	4	inner	1008.2.v.e.827.7	yes	40
48.5	odd	4		4032.2.v.e.3599.19		40
48.11	even	4	inner	1008.2.v.e.827.14	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.v.e.323.7	✓	40	3.2	odd	2	inner
1008.2.v.e.323.14	yes	40	1.1	even	1	trivial
1008.2.v.e.827.7	yes	40	16.11	odd	4	inner
1008.2.v.e.827.14	yes	40	48.11	even	4	inner
4032.2.v.e.1583.2		40	12.11	even	2
4032.2.v.e.1583.19		40	4.3	odd	2
4032.2.v.e.3599.2		40	16.5	even	4
4032.2.v.e.3599.19		40	48.5	odd	4

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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.v (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.614527 - 1.27372i) q^{2} +(-1.24471 - 1.56547i) q^{4} +(2.62814 + 2.62814i) q^{5} +1.00000 q^{7} +(-2.75887 + 0.623393i) q^{8} +O(q^{10})\)	\(q+(0.614527 - 1.27372i) q^{2} +(-1.24471 - 1.56547i) q^{4} +(2.62814 + 2.62814i) q^{5} +1.00000 q^{7} +(-2.75887 + 0.623393i) q^{8} +(4.96257 - 1.73245i) q^{10} +(0.583140 - 0.583140i) q^{11} +(1.76590 + 1.76590i) q^{13} +(0.614527 - 1.27372i) q^{14} +(-0.901375 + 3.89712i) q^{16} +3.63734i q^{17} +(0.963353 - 0.963353i) q^{19} +(0.842984 - 7.38555i) q^{20} +(-0.384401 - 1.10111i) q^{22} +3.77401i q^{23} +8.81423i q^{25} +(3.33446 - 1.16407i) q^{26} +(-1.24471 - 1.56547i) q^{28} +(4.76058 - 4.76058i) q^{29} -4.89207i q^{31} +(4.40991 + 3.54298i) q^{32} +(4.63295 + 2.23525i) q^{34} +(2.62814 + 2.62814i) q^{35} +(-4.66911 + 4.66911i) q^{37} +(-0.635034 - 1.81905i) q^{38} +(-8.88906 - 5.61234i) q^{40} +3.83668 q^{41} +(-3.45278 - 3.45278i) q^{43} +(-1.63873 - 0.187044i) q^{44} +(4.80702 + 2.31923i) q^{46} +11.6693 q^{47} +1.00000 q^{49} +(11.2268 + 5.41658i) q^{50} +(0.566419 - 4.96251i) q^{52} +(5.48624 + 5.48624i) q^{53} +3.06515 q^{55} +(-2.75887 + 0.623393i) q^{56} +(-3.13813 - 8.98914i) q^{58} +(4.40688 - 4.40688i) q^{59} +(-7.99959 - 7.99959i) q^{61} +(-6.23111 - 3.00630i) q^{62} +(7.22276 - 3.43972i) q^{64} +9.28208i q^{65} +(-11.3524 + 11.3524i) q^{67} +(5.69414 - 4.52745i) q^{68} +(4.96257 - 1.73245i) q^{70} -5.85120i q^{71} +0.564936i q^{73} +(3.07784 + 8.81643i) q^{74} +(-2.70720 - 0.308999i) q^{76} +(0.583140 - 0.583140i) q^{77} -16.4692i q^{79} +(-12.6111 + 7.87323i) q^{80} +(2.35774 - 4.88684i) q^{82} +(-6.92234 - 6.92234i) q^{83} +(-9.55945 + 9.55945i) q^{85} +(-6.51969 + 2.27604i) q^{86} +(-1.24528 + 1.97233i) q^{88} -10.7726 q^{89} +(1.76590 + 1.76590i) q^{91} +(5.90809 - 4.69756i) q^{92} +(7.17109 - 14.8634i) q^{94} +5.06365 q^{95} +8.64969 q^{97} +(0.614527 - 1.27372i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{7}+O(q^{10}) \) 40 * q + 40 * q^7	\( 40 q + 40 q^{7} + 48 q^{10} - 24 q^{13} + 12 q^{16} - 32 q^{19} - 8 q^{22} - 56 q^{34} - 8 q^{37} + 32 q^{43} - 52 q^{46} + 40 q^{49} - 8 q^{52} + 48 q^{55} + 56 q^{58} - 24 q^{61} + 48 q^{64} + 48 q^{70} - 24 q^{76} - 64 q^{82} + 64 q^{85} - 120 q^{88} - 24 q^{91} - 128 q^{94} + 64 q^{97}+O(q^{100}) \) 40 * q + 40 * q^7 + 48 * q^10 - 24 * q^13 + 12 * q^16 - 32 * q^19 - 8 * q^22 - 56 * q^34 - 8 * q^37 + 32 * q^43 - 52 * q^46 + 40 * q^49 - 8 * q^52 + 48 * q^55 + 56 * q^58 - 24 * q^61 + 48 * q^64 + 48 * q^70 - 24 * q^76 - 64 * q^82 + 64 * q^85 - 120 * q^88 - 24 * q^91 - 128 * q^94 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

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