LMFDB - Embedded newform 1008.2.v.e.323.20

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			323.20
Character	$\chi$	$=$	1008.323
Dual form			1008.2.v.e.827.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40729 + 0.139782i) q^{2} +(1.96092 + 0.393427i) q^{4} +(1.17902 + 1.17902i) q^{5} +1.00000 q^{7} +(2.70459 + 0.827766i) q^{8} +O(q^{10})$	\(q+(1.40729 + 0.139782i) q^{2} +(1.96092 + 0.393427i) q^{4} +(1.17902 + 1.17902i) q^{5} +1.00000 q^{7} +(2.70459 + 0.827766i) q^{8} +(1.49442 + 1.82403i) q^{10} +(-4.54895 + 4.54895i) q^{11} +(2.56073 + 2.56073i) q^{13} +(1.40729 + 0.139782i) q^{14} +(3.69043 + 1.54296i) q^{16} -2.05280i q^{17} +(-3.64422 + 3.64422i) q^{19} +(1.84811 + 2.77583i) q^{20} +(-7.03755 + 5.76583i) q^{22} -2.27140i q^{23} -2.21982i q^{25} +(3.24574 + 3.96163i) q^{26} +(1.96092 + 0.393427i) q^{28} +(0.544898 - 0.544898i) q^{29} -10.1006i q^{31} +(4.97782 + 2.68724i) q^{32} +(0.286943 - 2.88888i) q^{34} +(1.17902 + 1.17902i) q^{35} +(4.71698 - 4.71698i) q^{37} +(-5.63787 + 4.61908i) q^{38} +(2.21282 + 4.16472i) q^{40} -0.487549 q^{41} +(7.56607 + 7.56607i) q^{43} +(-10.7098 + 7.13046i) q^{44} +(0.317501 - 3.19652i) q^{46} +0.768184 q^{47} +1.00000 q^{49} +(0.310290 - 3.12392i) q^{50} +(4.01393 + 6.02885i) q^{52} +(-0.269015 - 0.269015i) q^{53} -10.7266 q^{55} +(2.70459 + 0.827766i) q^{56} +(0.842996 - 0.690662i) q^{58} +(-0.0979540 + 0.0979540i) q^{59} +(-7.41725 - 7.41725i) q^{61} +(1.41188 - 14.2144i) q^{62} +(6.62961 + 4.47753i) q^{64} +6.03831i q^{65} +(6.83972 - 6.83972i) q^{67} +(0.807624 - 4.02537i) q^{68} +(1.49442 + 1.82403i) q^{70} +8.66316i q^{71} -13.6358i q^{73} +(7.29750 - 5.97880i) q^{74} +(-8.57977 + 5.71231i) q^{76} +(-4.54895 + 4.54895i) q^{77} +9.29142i q^{79} +(2.53192 + 6.17028i) q^{80} +(-0.686123 - 0.0681505i) q^{82} +(-9.76640 - 9.76640i) q^{83} +(2.42029 - 2.42029i) q^{85} +(9.59004 + 11.7052i) q^{86} +(-16.0685 + 8.53758i) q^{88} -7.27355 q^{89} +(2.56073 + 2.56073i) q^{91} +(0.893630 - 4.45404i) q^{92} +(1.08106 + 0.107378i) q^{94} -8.59324 q^{95} +10.4508 q^{97} +(1.40729 + 0.139782i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.40729	+	0.139782i	0.995103	+	0.0988406i
$2$	1.40729	+	0.139782i	0.995103	+	0.0988406i
$3$		0			0
$3$		0			0
$4$	1.96092	+	0.393427i	0.980461	+	0.196713i
$5$	1.17902	+	1.17902i	0.527275	+	0.527275i	0.919759	−	0.392484i	$-0.128384\pi$
$5$	1.17902	+	1.17902i	0.527275	+	0.527275i	−0.392484	+	0.919759i	$0.628384\pi$
$6$		0			0
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	2.70459	+	0.827766i	0.956217	+	0.292659i
$9$		0			0
$10$	1.49442	+	1.82403i	0.472576	+	0.576809i
$11$	−4.54895	+	4.54895i	−1.37156	+	1.37156i	−0.513428	+	0.858133i	$0.671625\pi$
$11$	−4.54895	+	4.54895i	−1.37156	+	1.37156i	−0.858133	+	0.513428i	$0.828375\pi$
$12$		0			0
$13$	2.56073	+	2.56073i	0.710218	+	0.710218i	0.966581	−	0.256363i	$-0.0825241\pi$
$13$	2.56073	+	2.56073i	0.710218	+	0.710218i	−0.256363	+	0.966581i	$0.582524\pi$
$14$	1.40729	+	0.139782i	0.376114	+	0.0373582i
$15$		0			0
$16$	3.69043	+	1.54296i	0.922608	+	0.385739i
$17$		−	2.05280i		−	0.497876i	−0.968519	−	0.248938i	$-0.919918\pi$
$17$		−	2.05280i		−	0.497876i	0.968519	−	0.248938i	$-0.0800815\pi$
$18$		0			0
$19$	−3.64422	+	3.64422i	−0.836042	+	0.836042i	−0.988335	−	0.152293i	$-0.951334\pi$
$19$	−3.64422	+	3.64422i	−0.836042	+	0.836042i	0.152293	+	0.988335i	$0.451334\pi$
$20$	1.84811	+	2.77583i	0.413250	+	0.620694i
$21$		0			0
$22$	−7.03755	+	5.76583i	−1.50041	+	1.22928i
$23$		−	2.27140i		−	0.473620i	−0.971556	−	0.236810i	$-0.923898\pi$
$23$		−	2.27140i		−	0.473620i	0.971556	−	0.236810i	$-0.0761019\pi$
$24$		0			0
$25$		−	2.21982i		−	0.443963i
$26$	3.24574	+	3.96163i	0.636542	+	0.776939i
$27$		0			0
$28$	1.96092	+	0.393427i	0.370579	+	0.0743506i
$29$	0.544898	−	0.544898i	0.101185	−	0.101185i	−0.654702	−	0.755887i	$-0.727206\pi$
$29$	0.544898	−	0.544898i	0.101185	−	0.101185i	0.755887	+	0.654702i	$0.227206\pi$
$30$		0			0
$31$		−	10.1006i		−	1.81412i	−0.421004	−	0.907059i	$-0.638322\pi$
$31$		−	10.1006i		−	1.81412i	0.421004	−	0.907059i	$-0.361678\pi$
$32$	4.97782	+	2.68724i	0.879963	+	0.475042i
$33$		0			0
$34$	0.286943	−	2.88888i	0.0492104	−	0.495438i
$35$	1.17902	+	1.17902i	0.199291	+	0.199291i
$36$		0			0
$37$	4.71698	−	4.71698i	0.775467	−	0.775467i	−0.203590	−	0.979056i	$-0.565261\pi$
$37$	4.71698	−	4.71698i	0.775467	−	0.775467i	0.979056	+	0.203590i	$0.0652608\pi$
$38$	−5.63787	+	4.61908i	−0.914584	+	0.749314i
$39$		0			0
$40$	2.21282	+	4.16472i	0.349877	+	0.658501i
$41$	−0.487549			−0.0761424			−0.0380712	−	0.999275i	$-0.512121\pi$
$41$	−0.487549			−0.0761424			−0.0380712	+	0.999275i	$0.512121\pi$
$42$		0			0
$43$	7.56607	+	7.56607i	1.15381	+	1.15381i	0.985781	+	0.168033i	$0.0537416\pi$
$43$	7.56607	+	7.56607i	1.15381	+	1.15381i	0.168033	+	0.985781i	$0.446258\pi$
$44$	−10.7098	+	7.13046i	−1.61457	+	1.07496i
$45$		0			0
$46$	0.317501	−	3.19652i	0.0468129	−	0.471301i
$47$	0.768184			0.112051			0.0560256	−	0.998429i	$-0.482157\pi$
$47$	0.768184			0.112051			0.0560256	+	0.998429i	$0.482157\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$	0.310290	−	3.12392i	0.0438816	−	0.441789i
$51$		0			0
$52$	4.01393	+	6.02885i	0.556632	+	0.836050i
$53$	−0.269015	−	0.269015i	−0.0369520	−	0.0369520i	0.688389	−	0.725341i	$-0.258318\pi$
$53$	−0.269015	−	0.269015i	−0.0369520	−	0.0369520i	−0.725341	+	0.688389i	$0.758318\pi$
$54$		0			0
$55$	−10.7266			−1.44638
$56$	2.70459	+	0.827766i	0.361416	+	0.110615i
$57$		0			0
$58$	0.842996	−	0.690662i	0.110691	−	0.0906884i
$59$	−0.0979540	+	0.0979540i	−0.0127525	+	0.0127525i	−0.713454	−	0.700702i	$-0.752870\pi$
$59$	−0.0979540	+	0.0979540i	−0.0127525	+	0.0127525i	0.700702	+	0.713454i	$0.252870\pi$
$60$		0			0
$61$	−7.41725	−	7.41725i	−0.949682	−	0.949682i	0.0491117	−	0.998793i	$-0.484361\pi$
$61$	−7.41725	−	7.41725i	−0.949682	−	0.949682i	−0.998793	+	0.0491117i	$0.984361\pi$
$62$	1.41188	−	14.2144i	0.179309	−	1.80523i
$63$		0			0
$64$	6.62961	+	4.47753i	0.828701	+	0.559692i
$65$			6.03831i			0.748960i
$66$		0			0
$67$	6.83972	−	6.83972i	0.835604	−	0.835604i	−0.152672	−	0.988277i	$-0.548788\pi$
$67$	6.83972	−	6.83972i	0.835604	−	0.835604i	0.988277	+	0.152672i	$0.0487880\pi$
$68$	0.807624	−	4.02537i	0.0979388	−	0.488148i
$69$		0			0
$70$	1.49442	+	1.82403i	0.178617	+	0.218013i
$71$			8.66316i			1.02813i	0.857752	+	0.514064i	$0.171861\pi$
$71$			8.66316i			1.02813i	−0.857752	+	0.514064i	$0.828139\pi$
$72$		0			0
$73$		−	13.6358i		−	1.59594i	−0.602694	−	0.797972i	$-0.705906\pi$
$73$		−	13.6358i		−	1.59594i	0.602694	−	0.797972i	$-0.294094\pi$
$74$	7.29750	−	5.97880i	0.848317	−	0.695022i
$75$		0			0
$76$	−8.57977	+	5.71231i	−0.984168	+	0.655246i
$77$	−4.54895	+	4.54895i	−0.518401	+	0.518401i
$78$		0			0
$79$			9.29142i			1.04537i	0.852527	+	0.522683i	$0.175069\pi$
$79$			9.29142i			1.04537i	−0.852527	+	0.522683i	$0.824931\pi$
$80$	2.53192	+	6.17028i	0.283077	+	0.689858i
$81$		0			0
$82$	−0.686123	−	0.0681505i	−0.0757696	−	0.00752597i
$83$	−9.76640	−	9.76640i	−1.07200	−	1.07200i	−0.997198	−	0.0748037i	$-0.976167\pi$
$83$	−9.76640	−	9.76640i	−1.07200	−	1.07200i	−0.0748037	−	0.997198i	$-0.523833\pi$
$84$		0			0
$85$	2.42029	−	2.42029i	0.262517	−	0.262517i
$86$	9.59004	+	11.7052i	1.03412	+	1.26221i
$87$		0			0
$88$	−16.0685	+	8.53758i	−1.71291	+	0.910109i
$89$	−7.27355			−0.770995			−0.385497	−	0.922709i	$-0.625970\pi$
$89$	−7.27355			−0.770995			−0.385497	+	0.922709i	$0.625970\pi$
$90$		0			0
$91$	2.56073	+	2.56073i	0.268437	+	0.268437i
$92$	0.893630	−	4.45404i	0.0931673	−	0.464366i
$93$		0			0
$94$	1.08106	+	0.107378i	0.111502	+	0.0110752i
$95$	−8.59324			−0.881648
$96$		0			0
$97$	10.4508			1.06112			0.530561	−	0.847647i	$-0.321981\pi$
$97$	10.4508			1.06112			0.530561	+	0.847647i	$0.321981\pi$
$98$	1.40729	+	0.139782i	0.142158	+	0.0141201i
$99$		0			0
$100$	0.873334	−	4.35289i	0.0873334	−	0.435289i
$101$	5.75000	+	5.75000i	0.572147	+	0.572147i	0.932728	−	0.360581i	$-0.117422\pi$
$101$	5.75000	+	5.75000i	0.572147	+	0.572147i	−0.360581	+	0.932728i	$0.617422\pi$
$102$		0			0
$103$	7.11905			0.701460			0.350730	−	0.936477i	$-0.385933\pi$
$103$	7.11905			0.701460			0.350730	+	0.936477i	$0.385933\pi$
$104$	4.80603	+	9.04540i	0.471270	+	0.886974i
$105$		0			0
$106$	−0.340978	−	0.416185i	−0.0331187	−	0.0404234i
$107$	−6.13593	+	6.13593i	−0.593182	+	0.593182i	−0.938490	−	0.345307i	$-0.887775\pi$
$107$	−6.13593	+	6.13593i	−0.593182	+	0.593182i	0.345307	+	0.938490i	$0.387775\pi$
$108$		0			0
$109$	1.54344	+	1.54344i	0.147835	+	0.147835i	0.777150	−	0.629315i	$-0.216665\pi$
$109$	1.54344	+	1.54344i	0.147835	+	0.147835i	−0.629315	+	0.777150i	$0.716665\pi$
$110$	−15.0955	−	1.49939i	−1.43930	−	0.142961i
$111$		0			0
$112$	3.69043	+	1.54296i	0.348713	+	0.145796i
$113$			14.0023i			1.31723i	0.752481	+	0.658614i	$0.228857\pi$
$113$			14.0023i			1.31723i	−0.752481	+	0.658614i	$0.771143\pi$
$114$		0			0
$115$	2.67803	−	2.67803i	0.249728	−	0.249728i
$116$	1.28288	−	0.854126i	0.119112	−	0.0793036i
$117$		0			0
$118$	−0.151542	+	0.124157i	−0.0139505	+	0.0114296i
$119$		−	2.05280i		−	0.188179i
$120$		0			0
$121$		−	30.3859i		−	2.76236i
$122$	−9.40141	−	11.4750i	−0.851164	−	1.03890i
$123$		0			0
$124$	3.97384	−	19.8064i	0.356861	−	1.77867i
$125$	8.51232	−	8.51232i	0.761365	−	0.761365i
$126$		0			0
$127$		−	5.32939i		−	0.472906i	−0.971643	−	0.236453i	$-0.924015\pi$
$127$		−	5.32939i		−	0.472906i	0.971643	−	0.236453i	$-0.0759850\pi$
$128$	8.70389	+	7.22788i	0.769323	+	0.638860i
$129$		0			0
$130$	−0.844045	+	8.49764i	−0.0740277	+	0.745292i
$131$	−13.4364	−	13.4364i	−1.17395	−	1.17395i	−0.981261	−	0.192685i	$-0.938280\pi$
$131$	−13.4364	−	13.4364i	−1.17395	−	1.17395i	−0.192685	−	0.981261i	$-0.561720\pi$
$132$		0			0
$133$	−3.64422	+	3.64422i	−0.315994	+	0.315994i
$134$	10.5815	−	8.66939i	0.914104	−	0.748921i
$135$		0			0
$136$	1.69923	−	5.55197i	0.145708	−	0.476077i
$137$	10.1704			0.868914			0.434457	−	0.900693i	$-0.356940\pi$
$137$	10.1704			0.868914			0.434457	+	0.900693i	$0.356940\pi$
$138$		0			0
$139$	−6.90089	−	6.90089i	−0.585326	−	0.585326i	0.351036	−	0.936362i	$-0.385829\pi$
$139$	−6.90089	−	6.90089i	−0.585326	−	0.585326i	−0.936362	+	0.351036i	$0.885829\pi$
$140$	1.84811	+	2.77583i	0.156194	+	0.234600i
$141$		0			0
$142$	−1.21095	+	12.1916i	−0.101621	+	1.02309i
$143$	−23.2973			−1.94821
$144$		0			0
$145$	1.28489			0.106705
$146$	1.90603	−	19.1894i	0.157744	−	1.58813i
$147$		0			0
$148$	11.1054	−	7.39385i	0.912860	−	0.607770i
$149$	−0.134093	−	0.134093i	−0.0109853	−	0.0109853i	0.701593	−	0.712578i	$-0.252473\pi$
$149$	−0.134093	−	0.134093i	−0.0109853	−	0.0109853i	−0.712578	+	0.701593i	$0.752473\pi$
$150$		0			0
$151$	−13.7321			−1.11750			−0.558750	−	0.829336i	$-0.688719\pi$
$151$	−13.7321			−1.11750			−0.558750	+	0.829336i	$0.688719\pi$
$152$	−12.8727	+	6.83957i	−1.04411	+	0.554762i
$153$		0			0
$154$	−7.03755	+	5.76583i	−0.567102	+	0.464624i
$155$	11.9088	−	11.9088i	0.956538	−	0.956538i
$156$		0			0
$157$	−2.49258	−	2.49258i	−0.198929	−	0.198929i	0.600612	−	0.799541i	$-0.294924\pi$
$157$	−2.49258	−	2.49258i	−0.198929	−	0.198929i	−0.799541	+	0.600612i	$0.794924\pi$
$158$	−1.29877	+	13.0757i	−0.103325	+	1.04025i
$159$		0			0
$160$	2.70065	+	9.03728i	0.213505	+	0.714460i
$161$		−	2.27140i		−	0.179012i
$162$		0			0
$163$	6.43203	−	6.43203i	0.503796	−	0.503796i	−0.408820	−	0.912615i	$-0.634059\pi$
$163$	6.43203	−	6.43203i	0.503796	−	0.503796i	0.912615	+	0.408820i	$0.134059\pi$
$164$	−0.956046	−	0.191815i	−0.0746547	−	0.0149782i
$165$		0			0
$166$	−12.3790	−	15.1093i	−0.960795	−	1.17271i
$167$			4.38595i			0.339395i	0.985496	+	0.169697i	$0.0542790\pi$
$167$			4.38595i			0.339395i	−0.985496	+	0.169697i	$0.945721\pi$
$168$		0			0
$169$			0.114651i			0.00881930i
$170$	3.74436	−	3.06773i	0.287179	−	0.235285i
$171$		0			0
$172$	11.8598	+	17.8132i	0.904300	+	1.35824i
$173$	18.2846	−	18.2846i	1.39015	−	1.39015i	0.565191	−	0.824960i	$-0.308803\pi$
$173$	18.2846	−	18.2846i	1.39015	−	1.39015i	0.824960	−	0.565191i	$-0.191197\pi$
$174$		0			0
$175$		−	2.21982i		−	0.167802i
$176$	−23.8064	+	9.76875i	−1.79448	+	0.736348i
$177$		0			0
$178$	−10.2360	−	1.01671i	−0.767219	−	0.0762056i
$179$	3.18124	+	3.18124i	0.237777	+	0.237777i	0.815929	−	0.578152i	$-0.196226\pi$
$179$	3.18124	+	3.18124i	0.237777	+	0.237777i	−0.578152	+	0.815929i	$0.696226\pi$
$180$		0			0
$181$	−18.4064	+	18.4064i	−1.36813	+	1.36813i	−0.505036	+	0.863098i	$0.668521\pi$
$181$	−18.4064	+	18.4064i	−1.36813	+	1.36813i	−0.863098	+	0.505036i	$0.831479\pi$
$182$	3.24574	+	3.96163i	0.240590	+	0.293655i
$183$		0			0
$184$	1.88019	−	6.14321i	0.138609	−	0.452883i
$185$	11.1228			0.817768
$186$		0			0
$187$	9.33807	+	9.33807i	0.682867	+	0.682867i
$188$	1.50635	+	0.302224i	0.109862	+	0.0220419i
$189$		0			0
$190$	−12.0932	−	1.20118i	−0.877331	−	0.0871426i
$191$	−22.1964			−1.60607			−0.803037	−	0.595929i	$-0.796784\pi$
$191$	−22.1964			−1.60607			−0.803037	+	0.595929i	$0.796784\pi$
$192$		0			0
$193$	−6.93243			−0.499007			−0.249503	−	0.968374i	$-0.580267\pi$
$193$	−6.93243			−0.499007			−0.249503	+	0.968374i	$0.580267\pi$
$194$	14.7073	+	1.46084i	1.05593	+	0.104882i
$195$		0			0
$196$	1.96092	+	0.393427i	0.140066	+	0.0281019i
$197$	6.07895	+	6.07895i	0.433107	+	0.433107i	0.889684	−	0.456577i	$-0.150925\pi$
$197$	6.07895	+	6.07895i	0.433107	+	0.433107i	−0.456577	+	0.889684i	$0.650925\pi$
$198$		0			0
$199$	−10.9223			−0.774265			−0.387132	−	0.922024i	$-0.626534\pi$
$199$	−10.9223			−0.774265			−0.387132	+	0.922024i	$0.626534\pi$
$200$	1.83749	−	6.00369i	0.129930	−	0.424525i
$201$		0			0
$202$	7.28817	+	8.89566i	0.512794	+	0.625897i
$203$	0.544898	−	0.544898i	0.0382444	−	0.0382444i
$204$		0			0
$205$	−0.574831	−	0.574831i	−0.0401480	−	0.0401480i
$206$	10.0186	+	0.995113i	0.698026	+	0.0693328i
$207$		0			0
$208$	5.49909	+	13.4013i	0.381294	+	0.929212i
$209$		−	33.1548i		−	2.29337i
$210$		0			0
$211$	−9.67612	+	9.67612i	−0.666131	+	0.666131i	−0.956818	−	0.290687i	$-0.906116\pi$
$211$	−9.67612	+	9.67612i	−0.666131	+	0.666131i	0.290687	+	0.956818i	$0.406116\pi$
$212$	−0.421679	−	0.633354i	−0.0289611	−	0.0434990i
$213$		0			0
$214$	−9.49271	+	7.77733i	−0.648908	+	0.531647i
$215$			17.8411i			1.21675i
$216$		0			0
$217$		−	10.1006i		−	0.685672i
$218$	1.95632	+	2.38781i	0.132499	+	0.161723i
$219$		0			0
$220$	−21.0341	−	4.22014i	−1.41812	−	0.284522i
$221$	5.25665	−	5.25665i	0.353601	−	0.353601i
$222$		0			0
$223$			4.17535i			0.279602i	0.990180	+	0.139801i	$0.0446463\pi$
$223$			4.17535i			0.279602i	−0.990180	+	0.139801i	$0.955354\pi$
$224$	4.97782	+	2.68724i	0.332595	+	0.179549i
$225$		0			0
$226$	−1.95727	+	19.7053i	−0.130196	+	1.31078i
$227$	−21.2251	−	21.2251i	−1.40876	−	1.40876i	−0.766413	−	0.642348i	$-0.777961\pi$
$227$	−21.2251	−	21.2251i	−1.40876	−	1.40876i	−0.642348	−	0.766413i	$-0.722039\pi$
$228$		0			0
$229$	−6.46169	+	6.46169i	−0.427000	+	0.427000i	−0.887605	−	0.460605i	$-0.847633\pi$
$229$	−6.46169	+	6.46169i	−0.427000	+	0.427000i	0.460605	+	0.887605i	$0.347633\pi$
$230$	4.14310	−	3.39442i	0.273188	−	0.223822i
$231$		0			0
$232$	1.92477	−	1.02268i	0.126368	−	0.0671421i
$233$	−10.6456			−0.697413			−0.348707	−	0.937232i	$-0.613379\pi$
$233$	−10.6456			−0.697413			−0.348707	+	0.937232i	$0.613379\pi$
$234$		0			0
$235$	0.905705	+	0.905705i	0.0590817	+	0.0590817i
$236$	−0.230618	+	0.153542i	−0.0150119	+	0.00999476i
$237$		0			0
$238$	0.286943	−	2.88888i	0.0185998	−	0.187258i
$239$	10.2774			0.664792			0.332396	−	0.943140i	$-0.392143\pi$
$239$	10.2774			0.664792			0.332396	+	0.943140i	$0.392143\pi$
$240$		0			0
$241$	−0.195675			−0.0126045			−0.00630227	−	0.999980i	$-0.502006\pi$
$241$	−0.195675			−0.0126045			−0.00630227	+	0.999980i	$0.502006\pi$
$242$	4.24740	−	42.7618i	0.273033	−	2.74883i
$243$		0			0
$244$	−11.6265	−	17.4628i	−0.744311	−	1.11794i
$245$	1.17902	+	1.17902i	0.0753249	+	0.0753249i
$246$		0			0
$247$	−18.6637			−1.18754
$248$	8.36091	−	27.3179i	0.530919	−	1.73469i
$249$		0			0
$250$	13.1692	−	10.7894i	0.832891	−	0.682383i
$251$	8.95377	−	8.95377i	0.565157	−	0.565157i	−0.365611	−	0.930768i	$-0.619140\pi$
$251$	8.95377	−	8.95377i	0.565157	−	0.565157i	0.930768	+	0.365611i	$0.119140\pi$
$252$		0			0
$253$	10.3325	+	10.3325i	0.649599	+	0.649599i
$254$	0.744951	−	7.49998i	0.0467424	−	0.470591i
$255$		0			0
$256$	11.2386	+	11.3884i	0.702410	+	0.711772i
$257$			21.3928i			1.33445i	0.744858	+	0.667223i	$0.232517\pi$
$257$			21.3928i			1.33445i	−0.744858	+	0.667223i	$0.767483\pi$
$258$		0			0
$259$	4.71698	−	4.71698i	0.293099	−	0.293099i
$260$	−2.37563	+	11.8406i	−0.147330	+	0.734326i
$261$		0			0
$262$	−17.0308	−	20.7871i	−1.05216	−	1.28423i
$263$		−	31.7659i		−	1.95877i	−0.202006	−	0.979384i	$-0.564746\pi$
$263$		−	31.7659i		−	1.95877i	0.202006	−	0.979384i	$-0.435254\pi$
$264$		0			0
$265$		−	0.634348i		−	0.0389677i
$266$	−5.63787	+	4.61908i	−0.345680	+	0.283214i
$267$		0			0
$268$	16.1031	−	10.7212i	0.983652	−	0.654903i
$269$	−11.1414	+	11.1414i	−0.679301	+	0.679301i	−0.959842	−	0.280541i	$-0.909486\pi$
$269$	−11.1414	+	11.1414i	−0.679301	+	0.679301i	0.280541	+	0.959842i	$0.409486\pi$
$270$		0			0
$271$			19.1289i			1.16200i	0.813904	+	0.580999i	$0.197338\pi$
$271$			19.1289i			1.16200i	−0.813904	+	0.580999i	$0.802662\pi$
$272$	3.16738	−	7.57570i	0.192050	−	0.459344i
$273$		0			0
$274$	14.3126	+	1.42163i	0.864659	+	0.0858840i
$275$	10.0978	+	10.0978i	0.608922	+	0.608922i
$276$		0			0
$277$	−1.64734	+	1.64734i	−0.0989791	+	0.0989791i	−0.754862	−	0.655883i	$-0.772296\pi$
$277$	−1.64734	+	1.64734i	−0.0989791	+	0.0989791i	0.655883	+	0.754862i	$0.272296\pi$
$278$	−8.74692	−	10.6762i	−0.524605	−	0.640313i
$279$		0			0
$280$	2.21282	+	4.16472i	0.132241	+	0.248890i
$281$	−4.73918			−0.282716			−0.141358	−	0.989959i	$-0.545147\pi$
$281$	−4.73918			−0.282716			−0.141358	+	0.989959i	$0.545147\pi$
$282$		0			0
$283$	9.70607	+	9.70607i	0.576966	+	0.576966i	0.934066	−	0.357100i	$-0.116234\pi$
$283$	9.70607	+	9.70607i	0.576966	+	0.576966i	−0.357100	+	0.934066i	$0.616234\pi$
$284$	−3.40832	+	16.9878i	−0.202246	+	1.00804i
$285$		0			0
$286$	−32.7860	−	3.25653i	−1.93867	−	0.192563i
$287$	−0.487549			−0.0287791
$288$		0			0
$289$	12.7860			0.752119
$290$	1.80822	+	0.179605i	0.106182	+	0.0105468i
$291$		0			0
$292$	5.36467	−	26.7387i	0.313944	−	1.56476i
$293$	4.58419	+	4.58419i	0.267811	+	0.267811i	0.828218	−	0.560406i	$-0.189355\pi$
$293$	4.58419	+	4.58419i	0.267811	+	0.267811i	−0.560406	+	0.828218i	$0.689355\pi$
$294$		0			0
$295$	−0.230980			−0.0134482
$296$	16.6621	−	8.85294i	0.968462	−	0.514567i
$297$		0			0
$298$	−0.169963	−	0.207451i	−0.00984572	−	0.0120173i
$299$	5.81644	−	5.81644i	0.336373	−	0.336373i
$300$		0			0
$301$	7.56607	+	7.56607i	0.436101	+	0.436101i
$302$	−19.3250	−	1.91949i	−1.11203	−	0.110454i
$303$		0			0
$304$	−19.0716	+	7.82588i	−1.09383	+	0.448845i
$305$		−	17.4902i		−	1.00149i
$306$		0			0
$307$	−12.3272	+	12.3272i	−0.703552	+	0.703552i	−0.965171	−	0.261619i	$-0.915744\pi$
$307$	−12.3272	+	12.3272i	−0.703552	+	0.703552i	0.261619	+	0.965171i	$0.415744\pi$
$308$	−10.7098	+	7.13046i	−0.610249	+	0.406296i
$309$		0			0
$310$	18.4238	−	15.0945i	1.04640	−	0.857309i
$311$			1.24831i			0.0707852i	0.999373	+	0.0353926i	$0.0112682\pi$
$311$			1.24831i			0.0707852i	−0.999373	+	0.0353926i	$0.988732\pi$
$312$		0			0
$313$			23.1106i			1.30629i	0.757234	+	0.653144i	$0.226550\pi$
$313$			23.1106i			1.30629i	−0.757234	+	0.653144i	$0.773450\pi$
$314$	−3.15936	−	3.85619i	−0.178293	−	0.217618i
$315$		0			0
$316$	−3.65549	+	18.2198i	−0.205637	+	1.02494i
$317$	−6.92113	+	6.92113i	−0.388729	+	0.388729i	−0.874234	−	0.485505i	$-0.838636\pi$
$317$	−6.92113	+	6.92113i	−0.388729	+	0.388729i	0.485505	+	0.874234i	$0.338636\pi$
$318$		0			0
$319$			4.95743i			0.277563i
$320$	2.53734	+	13.0956i	0.141842	+	0.732064i
$321$		0			0
$322$	0.317501	−	3.19652i	0.0176936	−	0.178135i
$323$	7.48085	+	7.48085i	0.416245	+	0.416245i
$324$		0			0
$325$	5.68434	−	5.68434i	0.315311	−	0.315311i
$326$	9.95080	−	8.15264i	0.551124	−	0.451533i
$327$		0			0
$328$	−1.31862	−	0.403577i	−0.0728087	−	0.0222838i
$329$	0.768184			0.0423513
$330$		0			0
$331$	14.3780	+	14.3780i	0.790288	+	0.790288i	0.981541	−	0.191253i	$-0.0612550\pi$
$331$	14.3780	+	14.3780i	0.790288	+	0.790288i	−0.191253	+	0.981541i	$0.561255\pi$
$332$	−15.3088	−	22.9935i	−0.840179	−	1.26193i
$333$		0			0
$334$	−0.613075	+	6.17229i	−0.0335460	+	0.337733i
$335$	16.1283			0.881186
$336$		0			0
$337$	−5.99526			−0.326583			−0.163291	−	0.986578i	$-0.552211\pi$
$337$	−5.99526			−0.326583			−0.163291	+	0.986578i	$0.552211\pi$
$338$	−0.0160261	+	0.161347i	−0.000871705	+	0.00877611i
$339$		0			0
$340$	5.69821	−	3.79379i	0.309029	−	0.205747i
$341$	45.9471	+	45.9471i	2.48817	+	2.48817i
$342$		0			0
$343$	1.00000			0.0539949
$344$	14.2002	+	26.7260i	0.765622	+	1.44097i
$345$		0			0
$346$	28.2875	−	23.1758i	1.52075	−	1.24594i
$347$	11.6602	−	11.6602i	0.625954	−	0.625954i	−0.321094	−	0.947047i	$-0.604050\pi$
$347$	11.6602	−	11.6602i	0.625954	−	0.625954i	0.947047	+	0.321094i	$0.104050\pi$
$348$		0			0
$349$	−18.7098	−	18.7098i	−1.00151	−	1.00151i	−0.999999	−	0.00151266i	$-0.999519\pi$
$349$	−18.7098	−	18.7098i	−1.00151	−	1.00151i	−0.00151266	−	0.999999i	$-0.500481\pi$
$350$	0.310290	−	3.12392i	0.0165857	−	0.166981i
$351$		0			0
$352$	−34.8680	+	10.4198i	−1.85847	+	0.555375i
$353$		−	4.65833i		−	0.247938i	−0.992286	−	0.123969i	$-0.960438\pi$
$353$		−	4.65833i		−	0.247938i	0.992286	−	0.123969i	$-0.0395624\pi$
$354$		0			0
$355$	−10.2141	+	10.2141i	−0.542106	+	0.542106i
$356$	−14.2629	−	2.86161i	−0.755930	−	0.151665i
$357$		0			0
$358$	4.03224	+	4.92160i	0.213111	+	0.260115i
$359$			13.3794i			0.706140i	0.935597	+	0.353070i	$0.114862\pi$
$359$			13.3794i			0.706140i	−0.935597	+	0.353070i	$0.885138\pi$
$360$		0			0
$361$		−	7.56074i		−	0.397934i
$362$	−28.4759	+	23.3302i	−1.49666	+	1.22621i
$363$		0			0
$364$	4.01393	+	6.02885i	0.210387	+	0.315997i
$365$	16.0769	−	16.0769i	0.841501	−	0.841501i
$366$		0			0
$367$			20.7376i			1.08249i	0.840864	+	0.541247i	$0.182047\pi$
$367$			20.7376i			1.08249i	−0.840864	+	0.541247i	$0.817953\pi$
$368$	3.50468	−	8.38245i	0.182694	−	0.436966i
$369$		0			0
$370$	15.6531	+	1.55477i	0.813763	+	0.0808287i
$371$	−0.269015	−	0.269015i	−0.0139665	−	0.0139665i
$372$		0			0
$373$	6.84888	−	6.84888i	0.354622	−	0.354622i	−0.507204	−	0.861826i	$-0.669321\pi$
$373$	6.84888	−	6.84888i	0.354622	−	0.354622i	0.861826	+	0.507204i	$0.169321\pi$
$374$	11.8361	+	14.4466i	0.612028	+	0.747018i
$375$		0			0
$376$	2.07762	+	0.635876i	0.107145	+	0.0327928i
$377$	2.79067			0.143727
$378$		0			0
$379$	17.1046	+	17.1046i	0.878602	+	0.878602i	0.993390	−	0.114788i	$-0.0366189\pi$
$379$	17.1046	+	17.1046i	0.878602	+	0.878602i	−0.114788	+	0.993390i	$0.536619\pi$
$380$	−16.8507	−	3.38081i	−0.864421	−	0.173432i
$381$		0			0
$382$	−31.2367	−	3.10265i	−1.59821	−	0.158745i
$383$	14.7106			0.751678			0.375839	−	0.926685i	$-0.377355\pi$
$383$	14.7106			0.751678			0.375839	+	0.926685i	$0.377355\pi$
$384$		0			0
$385$	−10.7266			−0.546680
$386$	−9.75592	−	0.969027i	−0.496563	−	0.0493222i
$387$		0			0
$388$	20.4933	+	4.11164i	1.04039	+	0.208737i
$389$	−4.86662	−	4.86662i	−0.246747	−	0.246747i	0.572887	−	0.819634i	$-0.305823\pi$
$389$	−4.86662	−	4.86662i	−0.246747	−	0.246747i	−0.819634	+	0.572887i	$0.805823\pi$
$390$		0			0
$391$	−4.66272			−0.235804
$392$	2.70459	+	0.827766i	0.136602	+	0.0418085i
$393$		0			0
$394$	7.70511	+	9.40457i	0.388178	+	0.473795i
$395$	−10.9548	+	10.9548i	−0.551195	+	0.551195i
$396$		0			0
$397$	25.4535	+	25.4535i	1.27747	+	1.27747i	0.942077	+	0.335396i	$0.108870\pi$
$397$	25.4535	+	25.4535i	1.27747	+	1.27747i	0.335396	+	0.942077i	$0.391130\pi$
$398$	−15.3709	−	1.52675i	−0.770473	−	0.0765288i
$399$		0			0
$400$	3.42508	−	8.19208i	0.171254	−	0.409604i
$401$		−	21.0632i		−	1.05184i	−0.850533	−	0.525922i	$-0.823720\pi$
$401$		−	21.0632i		−	1.05184i	0.850533	−	0.525922i	$-0.176280\pi$
$402$		0			0
$403$	25.8648	−	25.8648i	1.28842	−	1.28842i
$404$	9.01311	+	13.5375i	0.448419	+	0.673517i
$405$		0			0
$406$	0.842996	−	0.690662i	0.0418372	−	0.0342770i
$407$			42.9146i			2.12720i
$408$		0			0
$409$		−	36.0796i		−	1.78402i	−0.452016	−	0.892010i	$-0.649295\pi$
$409$		−	36.0796i		−	1.78402i	0.452016	−	0.892010i	$-0.350705\pi$
$410$	−0.728603	−	0.889304i	−0.0359831	−	0.0439196i
$411$		0			0
$412$	13.9599	+	2.80082i	0.687755	+	0.137987i
$413$	−0.0979540	+	0.0979540i	−0.00482000	+	0.00482000i
$414$		0			0
$415$		−	23.0296i		−	1.13048i
$416$	5.86556	+	19.6281i	0.287583	+	0.962349i
$417$		0			0
$418$	4.63444	−	46.6584i	0.226678	−	2.28214i
$419$	−4.95680	−	4.95680i	−0.242155	−	0.242155i	0.575586	−	0.817741i	$-0.304774\pi$
$419$	−4.95680	−	4.95680i	−0.242155	−	0.242155i	−0.817741	+	0.575586i	$0.804774\pi$
$420$		0			0
$421$	−7.80250	+	7.80250i	−0.380271	+	0.380271i	−0.871200	−	0.490929i	$-0.836657\pi$
$421$	−7.80250	+	7.80250i	−0.380271	+	0.380271i	0.490929	+	0.871200i	$0.336657\pi$
$422$	−14.9696	+	12.2645i	−0.728710	+	0.597029i
$423$		0			0
$424$	−0.504893	−	0.950255i	−0.0245198	−	0.0461485i
$425$	−4.55683			−0.221039
$426$		0			0
$427$	−7.41725	−	7.41725i	−0.358946	−	0.358946i
$428$	−14.4461	+	9.61804i	−0.698279	+	0.464905i
$429$		0			0
$430$	−2.49386	+	25.1076i	−0.120265	+	1.21080i
$431$	4.41852			0.212832			0.106416	−	0.994322i	$-0.466062\pi$
$431$	4.41852			0.212832			0.106416	+	0.994322i	$0.466062\pi$
$432$		0			0
$433$	−3.06712			−0.147396			−0.0736981	−	0.997281i	$-0.523480\pi$
$433$	−3.06712			−0.147396			−0.0736981	+	0.997281i	$0.523480\pi$
$434$	1.41188	−	14.2144i	0.0677723	−	0.682314i
$435$		0			0
$436$	2.41934	+	3.63380i	0.115865	+	0.174028i
$437$	8.27750	+	8.27750i	0.395966	+	0.395966i
$438$		0			0
$439$	−4.24215			−0.202467			−0.101233	−	0.994863i	$-0.532279\pi$
$439$	−4.24215			−0.202467			−0.101233	+	0.994863i	$0.532279\pi$
$440$	−29.0111	−	8.87914i	−1.38305	−	0.423296i
$441$		0			0
$442$	8.13241	−	6.66284i	0.386819	−	0.316919i
$443$	−2.34161	+	2.34161i	−0.111253	+	0.111253i	−0.760542	−	0.649289i	$-0.775067\pi$
$443$	−2.34161	+	2.34161i	−0.111253	+	0.111253i	0.649289	+	0.760542i	$0.275067\pi$
$444$		0			0
$445$	−8.57567	−	8.57567i	−0.406526	−	0.406526i
$446$	−0.583638	+	5.87592i	−0.0276360	+	0.278233i
$447$		0			0
$448$	6.62961	+	4.47753i	0.313220	+	0.211544i
$449$		−	8.86849i		−	0.418530i	−0.977859	−	0.209265i	$-0.932893\pi$
$449$		−	8.86849i		−	0.418530i	0.977859	−	0.209265i	$-0.0671071\pi$
$450$		0			0
$451$	2.21784	−	2.21784i	0.104434	−	0.104434i
$452$	−5.50889	+	27.4575i	−0.259116	+	1.29149i
$453$		0			0
$454$	−26.9030	−	32.8368i	−1.26262	−	1.54111i
$455$			6.03831i			0.283080i
$456$		0			0
$457$			7.14847i			0.334392i	0.985924	+	0.167196i	$0.0534712\pi$
$457$			7.14847i			0.334392i	−0.985924	+	0.167196i	$0.946529\pi$
$458$	−9.99669	+	8.19023i	−0.467114	+	0.382704i
$459$		0			0
$460$	6.30502	−	4.19780i	0.293973	−	0.195724i
$461$	−17.8346	+	17.8346i	−0.830638	+	0.830638i	−0.987604	−	0.156966i	$-0.949829\pi$
$461$	−17.8346	+	17.8346i	−0.830638	+	0.830638i	0.156966	+	0.987604i	$0.449829\pi$
$462$		0			0
$463$		−	16.1618i		−	0.751102i	−0.926802	−	0.375551i	$-0.877453\pi$
$463$		−	16.1618i		−	0.751102i	0.926802	−	0.375551i	$-0.122547\pi$
$464$	2.85166	−	1.17015i	0.132385	−	0.0543231i
$465$		0			0
$466$	−14.9814	−	1.48805i	−0.693998	−	0.0689328i
$467$	13.5356	+	13.5356i	0.626352	+	0.626352i	0.947148	−	0.320797i	$-0.103951\pi$
$467$	13.5356	+	13.5356i	0.626352	+	0.626352i	−0.320797	+	0.947148i	$0.603951\pi$
$468$		0			0
$469$	6.83972	−	6.83972i	0.315829	−	0.315829i
$470$	1.14799	+	1.40119i	0.0529527	+	0.0646321i
$471$		0			0
$472$	−0.346008	+	0.183842i	−0.0159263	+	0.00846203i
$473$	−68.8354			−3.16505
$474$		0			0
$475$	8.08951	+	8.08951i	0.371172	+	0.371172i
$476$	0.807624	−	4.02537i	0.0370174	−	0.184503i
$477$		0			0
$478$	14.4633	+	1.43660i	0.661537	+	0.0657085i
$479$	−9.85872			−0.450456			−0.225228	−	0.974306i	$-0.572313\pi$
$479$	−9.85872			−0.450456			−0.225228	+	0.974306i	$0.572313\pi$
$480$		0			0
$481$	24.1578			1.10150
$482$	−0.275371	−	0.0273518i	−0.0125428	−	0.00124584i
$483$		0			0
$484$	11.9546	−	59.5845i	0.543392	−	2.70838i
$485$	12.3218	+	12.3218i	0.559503	+	0.559503i
$486$		0			0
$487$	−29.4055			−1.33249			−0.666245	−	0.745733i	$-0.732100\pi$
$487$	−29.4055			−1.33249			−0.666245	+	0.745733i	$0.732100\pi$
$488$	−13.9209	−	26.2004i	−0.630168	−	1.18603i
$489$		0			0
$490$	1.49442	+	1.82403i	0.0675109	+	0.0824013i
$491$	5.21529	−	5.21529i	0.235363	−	0.235363i	−0.579564	−	0.814927i	$-0.696777\pi$
$491$	5.21529	−	5.21529i	0.235363	−	0.235363i	0.814927	+	0.579564i	$0.196777\pi$
$492$		0			0
$493$	−1.11856	−	1.11856i	−0.0503776	−	0.0503776i
$494$	−26.2653	−	2.60885i	−1.18173	−	0.117378i
$495$		0			0
$496$	15.5848	−	37.2755i	0.699777	−	1.67372i
$497$			8.66316i			0.388596i
$498$		0			0
$499$	−11.8610	+	11.8610i	−0.530973	+	0.530973i	−0.920862	−	0.389889i	$-0.872513\pi$
$499$	−11.8610	+	11.8610i	−0.530973	+	0.530973i	0.389889	+	0.920862i	$0.372513\pi$
$500$	20.0410	−	13.3430i	0.896259	−	0.596718i
$501$		0			0
$502$	13.8521	−	11.3490i	0.618250	−	0.506529i
$503$			9.18051i			0.409339i	0.978831	+	0.204669i	$0.0656119\pi$
$503$			9.18051i			0.409339i	−0.978831	+	0.204669i	$0.934388\pi$
$504$		0			0
$505$			13.5588i			0.603357i
$506$	13.0965	+	15.9851i	0.582211	+	0.710624i
$507$		0			0
$508$	2.09672	−	10.4505i	0.0930270	−	0.463666i
$509$	15.7454	−	15.7454i	0.697902	−	0.697902i	−0.266056	−	0.963958i	$-0.585721\pi$
$509$	15.7454	−	15.7454i	0.697902	−	0.697902i	0.963958	+	0.266056i	$0.0857206\pi$
$510$		0			0
$511$		−	13.6358i		−	0.603210i
$512$	14.2240	+	17.5977i	0.628619	+	0.777714i
$513$		0			0
$514$	−2.99032	+	30.1058i	−0.131897	+	1.32791i
$515$	8.39351	+	8.39351i	0.369862	+	0.369862i
$516$		0			0
$517$	−3.49443	+	3.49443i	−0.153685	+	0.153685i
$518$	7.29750	−	5.97880i	0.320634	−	0.262694i
$519$		0			0
$520$	−4.99830	+	16.3311i	−0.219190	+	0.716168i
$521$	35.2555			1.54457			0.772286	−	0.635275i	$-0.219113\pi$
$521$	35.2555			1.54457			0.772286	+	0.635275i	$0.219113\pi$
$522$		0			0
$523$	13.3455	+	13.3455i	0.583559	+	0.583559i	0.935880	−	0.352320i	$-0.114607\pi$
$523$	13.3455	+	13.3455i	0.583559	+	0.583559i	−0.352320	+	0.935880i	$0.614607\pi$
$524$	−21.0615	−	31.6340i	−0.920077	−	1.38194i
$525$		0			0
$526$	4.44029	−	44.7038i	0.193606	−	1.94918i
$527$	−20.7344			−0.903206
$528$		0			0
$529$	17.8407			0.775684
$530$	0.0886703	−	0.892711i	0.00385159	−	0.0387769i
$531$		0			0
$532$	−8.57977	+	5.71231i	−0.371980	+	0.247660i
$533$	−1.24848	−	1.24848i	−0.0540777	−	0.0540777i
$534$		0			0
$535$	−14.4688			−0.625540
$536$	24.1603	−	12.8369i	1.04357	−	0.554471i
$537$		0			0
$538$	−17.2365	+	14.1217i	−0.743117	+	0.608832i
$539$	−4.54895	+	4.54895i	−0.195937	+	0.195937i
$540$		0			0
$541$	22.4225	+	22.4225i	0.964020	+	0.964020i	0.999375	−	0.0353552i	$-0.0112563\pi$
$541$	22.4225	+	22.4225i	0.964020	+	0.964020i	−0.0353552	+	0.999375i	$0.511256\pi$
$542$	−2.67387	+	26.9199i	−0.114853	+	1.15631i
$543$		0			0
$544$	5.51636	−	10.2185i	0.236512	−	0.438113i
$545$			3.63950i			0.155899i
$546$		0			0
$547$	−6.02624	+	6.02624i	−0.257664	+	0.257664i	−0.824103	−	0.566440i	$-0.808320\pi$
$547$	−6.02624	+	6.02624i	−0.257664	+	0.257664i	0.566440	+	0.824103i	$0.308320\pi$
$548$	19.9433	+	4.00129i	0.851936	+	0.170927i
$549$		0			0
$550$	12.7991	+	15.6221i	0.545754	+	0.666127i
$551$			3.97146i			0.169190i
$552$		0			0
$553$			9.29142i			0.395111i
$554$	−2.54855	+	2.08802i	−0.108278	+	0.0887113i
$555$		0			0
$556$	−10.8171	−	16.2471i	−0.458748	−	0.689030i
$557$	−19.9169	+	19.9169i	−0.843905	+	0.843905i	−0.989364	−	0.145459i	$-0.953534\pi$
$557$	−19.9169	+	19.9169i	−0.843905	+	0.843905i	0.145459	+	0.989364i	$0.453534\pi$
$558$		0			0
$559$			38.7493i			1.63892i
$560$	2.53192	+	6.17028i	0.106993	+	0.260742i
$561$		0			0
$562$	−6.66939	−	0.662451i	−0.281331	−	0.0279438i
$563$	−18.0269	−	18.0269i	−0.759743	−	0.759743i	0.216533	−	0.976275i	$-0.430525\pi$
$563$	−18.0269	−	18.0269i	−0.759743	−	0.759743i	−0.976275	+	0.216533i	$0.930525\pi$
$564$		0			0
$565$	−16.5090	+	16.5090i	−0.694541	+	0.694541i
$566$	12.3025	+	15.0160i	0.517113	+	0.631169i
$567$		0			0
$568$	−7.17107	+	23.4303i	−0.300891	+	0.983113i
$569$	28.6582			1.20142			0.600708	−	0.799469i	$-0.294885\pi$
$569$	28.6582			1.20142			0.600708	+	0.799469i	$0.294885\pi$
$570$		0			0
$571$	−4.74392	−	4.74392i	−0.198527	−	0.198527i	0.600841	−	0.799368i	$-0.294832\pi$
$571$	−4.74392	−	4.74392i	−0.198527	−	0.198527i	−0.799368	+	0.600841i	$0.794832\pi$
$572$	−45.6841	−	9.16576i	−1.91015	−	0.383240i
$573$		0			0
$574$	−0.686123	−	0.0681505i	−0.0286382	−	0.00284455i
$575$	−5.04209			−0.210270
$576$		0			0
$577$	−27.7361			−1.15467			−0.577335	−	0.816507i	$-0.695907\pi$
$577$	−27.7361			−1.15467			−0.577335	+	0.816507i	$0.695907\pi$
$578$	17.9936	+	1.78725i	0.748437	+	0.0743400i
$579$		0			0
$580$	2.51958	+	0.505511i	0.104620	+	0.0209902i
$581$	−9.76640	−	9.76640i	−0.405179	−	0.405179i
$582$		0			0
$583$	2.44747			0.101364
$584$	11.2872	−	36.8791i	0.467068	−	1.52607i
$585$		0			0
$586$	5.81050	+	7.09207i	0.240029	+	0.292971i
$587$	19.8086	−	19.8086i	0.817587	−	0.817587i	−0.168171	−	0.985758i	$-0.553786\pi$
$587$	19.8086	−	19.8086i	0.817587	−	0.817587i	0.985758	+	0.168171i	$0.0537860\pi$
$588$		0			0
$589$	36.8088	+	36.8088i	1.51668	+	1.51668i
$590$	−0.325055	−	0.0322867i	−0.0133823	−	0.00132922i
$591$		0			0
$592$	24.6858	−	10.1296i	1.01458	−	0.416324i
$593$			18.8296i			0.773239i	0.922239	+	0.386620i	$0.126357\pi$
$593$			18.8296i			0.773239i	−0.922239	+	0.386620i	$0.873643\pi$
$594$		0			0
$595$	2.42029	−	2.42029i	0.0992222	−	0.0992222i
$596$	−0.210190	−	0.315701i	−0.00860971	−	0.0129316i
$597$		0			0
$598$	8.99844	−	7.37238i	0.367974	−	0.301479i
$599$			24.0141i			0.981188i	0.871388	+	0.490594i	$0.163220\pi$
$599$			24.0141i			0.981188i	−0.871388	+	0.490594i	$0.836780\pi$
$600$		0			0
$601$		−	14.3602i		−	0.585766i	−0.956148	−	0.292883i	$-0.905385\pi$
$601$		−	14.3602i		−	0.585766i	0.956148	−	0.292883i	$-0.0946147\pi$
$602$	9.59004	+	11.7052i	0.390861	+	0.477070i
$603$		0			0
$604$	−26.9275	−	5.40256i	−1.09567	−	0.219827i
$605$	35.8257	−	35.8257i	1.45652	−	1.45652i
$606$		0			0
$607$		−	6.44642i		−	0.261652i	−0.991405	−	0.130826i	$-0.958237\pi$
$607$		−	6.44642i		−	0.261652i	0.991405	−	0.130826i	$-0.0417629\pi$
$608$	−27.9332	+	8.34740i	−1.13284	+	0.338532i
$609$		0			0
$610$	2.44481	−	24.6138i	0.0989875	−	0.996582i
$611$	1.96711	+	1.96711i	0.0795807	+	0.0795807i
$612$		0			0
$613$	−31.4106	+	31.4106i	−1.26866	+	1.26866i	−0.321884	+	0.946779i	$0.604316\pi$
$613$	−31.4106	+	31.4106i	−1.26866	+	1.26866i	−0.946779	+	0.321884i	$0.895684\pi$
$614$	−19.0711	+	15.6248i	−0.769646	+	0.630567i
$615$		0			0
$616$	−16.0685	+	8.53758i	−0.647419	+	0.343989i
$617$	−30.2797			−1.21902			−0.609508	−	0.792780i	$-0.708633\pi$
$617$	−30.2797			−1.21902			−0.609508	+	0.792780i	$0.708633\pi$
$618$		0			0
$619$	6.97556	+	6.97556i	0.280372	+	0.280372i	0.833257	−	0.552886i	$-0.186473\pi$
$619$	6.97556	+	6.97556i	0.280372	+	0.280372i	−0.552886	+	0.833257i	$0.686473\pi$
$620$	28.0375	−	18.6670i	1.12601	−	0.749685i
$621$		0			0
$622$	−0.174491	+	1.75673i	−0.00699645	+	0.0704386i
$623$	−7.27355			−0.291409
$624$		0			0
$625$	8.97334			0.358934
$626$	−3.23044	+	32.5233i	−0.129114	+	1.29989i
$627$		0			0
$628$	−3.90711	−	5.86840i	−0.155910	−	0.234175i
$629$	−9.68300	−	9.68300i	−0.386086	−	0.386086i
$630$		0			0
$631$	14.0268			0.558398			0.279199	−	0.960233i	$-0.409931\pi$
$631$	14.0268			0.558398			0.279199	+	0.960233i	$0.409931\pi$
$632$	−7.69112	+	25.1295i	−0.305936	+	0.999597i
$633$		0			0
$634$	−10.7075	+	8.77258i	−0.425248	+	0.348403i
$635$	6.28346	−	6.28346i	0.249352	−	0.249352i
$636$		0			0
$637$	2.56073	+	2.56073i	0.101460	+	0.101460i
$638$	−0.692959	+	6.97654i	−0.0274345	+	0.276204i
$639$		0			0
$640$	1.74025	+	18.7839i	0.0687895	+	0.742499i
$641$			20.9884i			0.828992i	0.910051	+	0.414496i	$0.136042\pi$
$641$			20.9884i			0.828992i	−0.910051	+	0.414496i	$0.863958\pi$
$642$		0			0
$643$	32.1818	−	32.1818i	1.26913	−	1.26913i	0.322589	−	0.946539i	$-0.395447\pi$
$643$	32.1818	−	32.1818i	1.26913	−	1.26913i	0.946539	−	0.322589i	$-0.104553\pi$
$644$	0.893630	−	4.45404i	0.0352139	−	0.175514i
$645$		0			0
$646$	9.48202	+	11.5734i	0.373065	+	0.455349i
$647$		−	0.647703i		−	0.0254638i	−0.999919	−	0.0127319i	$-0.995947\pi$
$647$		−	0.647703i		−	0.0254638i	0.999919	−	0.0127319i	$-0.00405280\pi$
$648$		0			0
$649$		−	0.891176i		−	0.0349817i
$650$	8.79408	−	7.20494i	0.344932	−	0.282601i
$651$		0			0
$652$	15.1432	−	10.0822i	0.593055	−	0.394849i
$653$	25.7373	−	25.7373i	1.00718	−	1.00718i	0.00720262	−	0.999974i	$-0.497707\pi$
$653$	25.7373	−	25.7373i	1.00718	−	1.00718i	0.999974	−	0.00720262i	$-0.00229269\pi$
$654$		0			0
$655$		−	31.6837i		−	1.23798i
$656$	−1.79927	−	0.752268i	−0.0702496	−	0.0293711i
$657$		0			0
$658$	1.08106	+	0.107378i	0.0421440	+	0.00418603i
$659$	17.0862	+	17.0862i	0.665583	+	0.665583i	0.956690	−	0.291108i	$-0.0940238\pi$
$659$	17.0862	+	17.0862i	0.665583	+	0.665583i	−0.291108	+	0.956690i	$0.594024\pi$
$660$		0			0
$661$	−8.34196	+	8.34196i	−0.324465	+	0.324465i	−0.850477	−	0.526012i	$-0.823687\pi$
$661$	−8.34196	+	8.34196i	−0.324465	+	0.324465i	0.526012	+	0.850477i	$0.323687\pi$
$662$	18.2243	+	22.2438i	0.708306	+	0.864531i
$663$		0			0
$664$	−18.3298	−	34.4984i	−0.711335	−	1.33880i
$665$	−8.59324			−0.333232
$666$		0			0
$667$	−1.23768	−	1.23768i	−0.0479233	−	0.0479233i
$668$	−1.72555	+	8.60050i	−0.0667635	+	0.332763i
$669$		0			0
$670$	22.6972	+	2.25445i	0.876871	+	0.0870970i
$671$	67.4814			2.60509
$672$		0			0
$673$	−1.69237			−0.0652361			−0.0326180	−	0.999468i	$-0.510384\pi$
$673$	−1.69237			−0.0652361			−0.0326180	+	0.999468i	$0.510384\pi$
$674$	−8.43706	−	0.838028i	−0.324984	−	0.0322796i
$675$		0			0
$676$	−0.0451067	+	0.224821i	−0.00173487	+	0.00864698i
$677$	−36.3935	−	36.3935i	−1.39872	−	1.39872i	−0.803749	−	0.594968i	$-0.797165\pi$
$677$	−36.3935	−	36.3935i	−1.39872	−	1.39872i	−0.594968	−	0.803749i	$-0.702835\pi$
$678$		0			0
$679$	10.4508			0.401066
$680$	8.54933	−	4.54246i	0.327852	−	0.174195i
$681$		0			0
$682$	58.2382	+	71.0833i	2.23006	+	2.72192i
$683$	13.6522	−	13.6522i	0.522388	−	0.522388i	−0.395904	−	0.918292i	$-0.629569\pi$
$683$	13.6522	−	13.6522i	0.522388	−	0.522388i	0.918292	+	0.395904i	$0.129569\pi$
$684$		0			0
$685$	11.9911	+	11.9911i	0.458156	+	0.458156i
$686$	1.40729	+	0.139782i	0.0537305	+	0.00533689i
$687$		0			0
$688$	16.2479	+	39.5962i	0.619447	+	1.50959i
$689$		−	1.37775i		−	0.0524880i
$690$		0			0
$691$	−2.36989	+	2.36989i	−0.0901550	+	0.0901550i	−0.750746	−	0.660591i	$-0.770306\pi$
$691$	−2.36989	+	2.36989i	−0.0901550	+	0.0901550i	0.660591	+	0.750746i	$0.270306\pi$
$692$	43.0483	−	28.6610i	1.63645	−	1.08953i
$693$		0			0
$694$	18.0392	−	14.7794i	0.684758	−	0.561019i
$695$		−	16.2726i		−	0.617254i
$696$		0			0
$697$			1.00084i			0.0379095i
$698$	−23.7148	−	28.9453i	−0.897617	−	1.09560i
$699$		0			0
$700$	0.873334	−	4.35289i	0.0330089	−	0.164524i
$701$	−27.6655	+	27.6655i	−1.04491	+	1.04491i	−0.0459668	+	0.998943i	$0.514637\pi$
$701$	−27.6655	+	27.6655i	−1.04491	+	1.04491i	−0.998943	+	0.0459668i	$0.985363\pi$
$702$		0			0
$703$			34.3795i			1.29665i
$704$	−50.5259	+	9.78968i	−1.90426	+	0.368963i
$705$		0			0
$706$	0.651150	−	6.55562i	0.0245064	−	0.246724i
$707$	5.75000	+	5.75000i	0.216251	+	0.216251i
$708$		0			0
$709$	4.38704	−	4.38704i	0.164759	−	0.164759i	−0.619912	−	0.784671i	$-0.712832\pi$
$709$	4.38704	−	4.38704i	0.164759	−	0.164759i	0.784671	+	0.619912i	$0.212832\pi$
$710$	−15.8019	+	12.9464i	−0.593033	+	0.485869i
$711$		0			0
$712$	−19.6720	−	6.02079i	−0.737238	−	0.225639i
$713$	−22.9425			−0.859202
$714$		0			0
$715$	−27.4680	−	27.4680i	−1.02724	−	1.02724i
$716$	4.98658	+	7.48975i	0.186357	+	0.279905i
$717$		0			0
$718$	−1.87020	+	18.8287i	−0.0697953	+	0.702682i
$719$	−18.2313			−0.679915			−0.339957	−	0.940441i	$-0.610413\pi$
$719$	−18.2313			−0.679915			−0.339957	+	0.940441i	$0.610413\pi$
$720$		0			0
$721$	7.11905			0.265127
$722$	1.05685	−	10.6401i	0.0393320	−	0.395985i
$723$		0			0
$724$	−43.3350	+	28.8519i	−1.61053	+	1.07227i
$725$	−1.20957	−	1.20957i	−0.0449224	−	0.0449224i
$726$		0			0
$727$	17.1985			0.637857			0.318928	−	0.947779i	$-0.396677\pi$
$727$	17.1985			0.637857			0.318928	+	0.947779i	$0.396677\pi$
$728$	4.80603	+	9.04540i	0.178123	+	0.335245i
$729$		0			0
$730$	24.8720	−	20.3775i	0.920555	−	0.754206i
$731$	15.5316	−	15.5316i	0.574457	−	0.574457i
$732$		0			0
$733$	1.76630	+	1.76630i	0.0652396	+	0.0652396i	0.738974	−	0.673734i	$-0.235311\pi$
$733$	1.76630	+	1.76630i	0.0652396	+	0.0652396i	−0.673734	+	0.738974i	$0.735311\pi$
$734$	−2.89874	+	29.1838i	−0.106994	+	1.07719i
$735$		0			0
$736$	6.10381	−	11.3066i	0.224989	−	0.416768i
$737$			62.2271i			2.29216i
$738$		0			0
$739$	20.8217	−	20.8217i	0.765939	−	0.765939i	−0.211450	−	0.977389i	$-0.567818\pi$
$739$	20.8217	−	20.8217i	0.765939	−	0.765939i	0.977389	+	0.211450i	$0.0678184\pi$
$740$	21.8110	+	4.37602i	0.801790	+	0.160866i
$741$		0			0
$742$	−0.340978	−	0.416185i	−0.0125177	−	0.0152786i
$743$		−	39.1460i		−	1.43613i	−0.695977	−	0.718064i	$-0.745029\pi$
$743$		−	39.1460i		−	1.43613i	0.695977	−	0.718064i	$-0.254971\pi$
$744$		0			0
$745$		−	0.316196i		−	0.0115845i
$746$	10.5957	−	8.68101i	0.387936	−	0.317834i
$747$		0			0
$748$	14.6374	+	21.9851i	0.535196	+	0.803854i
$749$	−6.13593	+	6.13593i	−0.224202	+	0.224202i
$750$		0			0
$751$		−	44.9147i		−	1.63896i	−0.573106	−	0.819481i	$-0.694262\pi$
$751$		−	44.9147i		−	1.63896i	0.573106	−	0.819481i	$-0.305738\pi$
$752$	2.83493	+	1.18527i	0.103379	+	0.0432225i
$753$		0			0
$754$	3.92728	+	0.390085i	0.143023	+	0.0142061i
$755$	−16.1904	−	16.1904i	−0.589229	−	0.589229i
$756$		0			0
$757$	−35.8730	+	35.8730i	−1.30383	+	1.30383i	−0.378036	+	0.925791i	$0.623400\pi$
$757$	−35.8730	+	35.8730i	−1.30383	+	1.30383i	−0.925791	+	0.378036i	$0.876600\pi$
$758$	21.6801	+	26.4620i	0.787458	+	0.961141i
$759$		0			0
$760$	−23.2412	−	7.11319i	−0.843046	−	0.258023i
$761$	47.4451			1.71988			0.859941	−	0.510393i	$-0.170500\pi$
$761$	47.4451			1.71988			0.859941	+	0.510393i	$0.170500\pi$
$762$		0			0
$763$	1.54344	+	1.54344i	0.0558764	+	0.0558764i
$764$	−43.5254	−	8.73265i	−1.57469	−	0.315936i
$765$		0			0
$766$	20.7021	+	2.05628i	0.747997	+	0.0742963i
$767$	−0.501667			−0.0181141
$768$		0			0
$769$	4.59306			0.165630			0.0828150	−	0.996565i	$-0.473609\pi$
$769$	4.59306			0.165630			0.0828150	+	0.996565i	$0.473609\pi$
$770$	−15.0955	−	1.49939i	−0.544003	−	0.0540342i
$771$		0			0
$772$	−13.5939	−	2.72740i	−0.489257	−	0.0981613i
$773$	1.66000	+	1.66000i	0.0597062	+	0.0597062i	0.736329	−	0.676623i	$-0.236557\pi$
$773$	1.66000	+	1.66000i	0.0597062	+	0.0597062i	−0.676623	+	0.736329i	$0.736557\pi$
$774$		0			0
$775$	−22.4214			−0.805401
$776$	28.2652	+	8.65085i	1.01466	+	0.310547i
$777$		0			0
$778$	−6.16848	−	7.52901i	−0.221151	−	0.269928i
$779$	1.77674	−	1.77674i	0.0636583	−	0.0636583i
$780$		0			0
$781$	−39.4083	−	39.4083i	−1.41014	−	1.41014i
$782$	−6.56180	−	0.651764i	−0.234649	−	0.0233070i
$783$		0			0
$784$	3.69043	+	1.54296i	0.131801	+	0.0551056i
$785$		−	5.87761i		−	0.209781i
$786$		0			0
$787$	−16.7673	+	16.7673i	−0.597688	+	0.597688i	−0.939697	−	0.342009i	$-0.888893\pi$
$787$	−16.7673	+	16.7673i	−0.597688	+	0.597688i	0.342009	+	0.939697i	$0.388893\pi$
$788$	9.52873	+	14.3120i	0.339447	+	0.509843i
$789$		0			0
$790$	−16.9478	+	13.8853i	−0.602977	+	0.494016i
$791$			14.0023i			0.497865i
$792$		0			0
$793$		−	37.9871i		−	1.34896i
$794$	32.2624	+	39.3783i	1.14495	+	1.39748i
$795$		0			0
$796$	−21.4179	−	4.29714i	−0.759137	−	0.152308i
$797$	−24.6258	+	24.6258i	−0.872290	+	0.872290i	−0.992722	−	0.120431i	$-0.961572\pi$
$797$	−24.6258	+	24.6258i	−0.872290	+	0.872290i	0.120431	+	0.992722i	$0.461572\pi$
$798$		0			0
$799$		−	1.57692i		−	0.0557876i
$800$	5.96518	−	11.0499i	0.210901	−	0.390671i
$801$		0			0
$802$	2.94425	−	29.6419i	0.103965	−	1.04669i
$803$	62.0284	+	62.0284i	2.18894	+	2.18894i
$804$		0			0
$805$	2.67803	−	2.67803i	0.0943882	−	0.0943882i
$806$	40.0147	−	32.7838i	1.40946	−	1.15476i
$807$		0			0
$808$	10.7917	+	20.3111i	0.379652	+	0.714541i
$809$	−41.1357			−1.44626			−0.723128	−	0.690714i	$-0.757296\pi$
$809$	−41.1357			−1.44626			−0.723128	+	0.690714i	$0.757296\pi$
$810$		0			0
$811$	−3.55287	−	3.55287i	−0.124758	−	0.124758i	0.641971	−	0.766729i	$-0.278117\pi$
$811$	−3.55287	−	3.55287i	−0.124758	−	0.124758i	−0.766729	+	0.641971i	$0.778117\pi$
$812$	1.28288	−	0.854126i	0.0450203	−	0.0299739i
$813$		0			0
$814$	−5.99868	+	60.3933i	−0.210254	+	2.11678i
$815$	15.1670			0.531277
$816$		0			0
$817$	−55.1449			−1.92928
$818$	5.04326	−	50.7743i	0.176334	−	1.77528i
$819$		0			0
$820$	−0.901046	−	1.35335i	−0.0314659	−	0.0472612i
$821$	0.376144	+	0.376144i	0.0131275	+	0.0131275i	0.713640	−	0.700513i	$-0.247045\pi$
$821$	0.376144	+	0.376144i	0.0131275	+	0.0131275i	−0.700513	+	0.713640i	$0.747045\pi$
$822$		0			0
$823$	6.94476			0.242079			0.121039	−	0.992648i	$-0.461377\pi$
$823$	6.94476			0.242079			0.121039	+	0.992648i	$0.461377\pi$
$824$	19.2541	+	5.89290i	0.670748	+	0.205289i
$825$		0			0
$826$	−0.151542	+	0.124157i	−0.00527281	+	0.00431999i
$827$	−7.45823	+	7.45823i	−0.259348	+	0.259348i	−0.824789	−	0.565441i	$-0.808706\pi$
$827$	−7.45823	+	7.45823i	−0.259348	+	0.259348i	0.565441	+	0.824789i	$0.308706\pi$
$828$		0			0
$829$	−15.4119	−	15.4119i	−0.535279	−	0.535279i	0.386860	−	0.922139i	$-0.373560\pi$
$829$	−15.4119	−	15.4119i	−0.535279	−	0.535279i	−0.922139	+	0.386860i	$0.873560\pi$
$830$	3.21912	−	32.4093i	0.111737	−	1.12494i
$831$		0			0
$832$	5.51088	+	28.4424i	0.191055	+	0.986061i
$833$		−	2.05280i		−	0.0711251i
$834$		0			0
$835$	−5.17113	+	5.17113i	−0.178954	+	0.178954i
$836$	13.0440	−	65.0140i	0.451136	−	2.24856i
$837$		0			0
$838$	−6.28278	−	7.66852i	−0.217035	−	0.264904i
$839$			17.2950i			0.597091i	0.954395	+	0.298545i	$0.0965014\pi$
$839$			17.2950i			0.597091i	−0.954395	+	0.298545i	$0.903499\pi$
$840$		0			0
$841$			28.4062i			0.979523i
$842$	−12.0710	+	9.88972i	−0.415995	+	0.340822i
$843$		0			0
$844$	−22.7810	+	15.1673i	−0.784153	+	0.522079i
$845$	−0.135176	+	0.135176i	−0.00465019	+	0.00465019i
$846$		0			0
$847$		−	30.3859i		−	1.04407i
$848$	−0.577702	−	1.40786i	−0.0198384	−	0.0483461i
$849$		0			0
$850$	−6.41277	−	0.636961i	−0.219956	−	0.0218476i
$851$	−10.7142	−	10.7142i	−0.367277	−	0.367277i
$852$		0			0
$853$	−17.7845	+	17.7845i	−0.608930	+	0.608930i	−0.942666	−	0.333736i	$-0.891690\pi$
$853$	−17.7845	+	17.7845i	−0.608930	+	0.608930i	0.333736	+	0.942666i	$0.391690\pi$
$854$	−9.40141	−	11.4750i	−0.321710	−	0.392667i
$855$		0			0
$856$	−21.6743	+	11.5161i	−0.740811	+	0.393611i
$857$	−4.25624			−0.145390			−0.0726952	−	0.997354i	$-0.523160\pi$
$857$	−4.25624			−0.145390			−0.0726952	+	0.997354i	$0.523160\pi$
$858$		0			0
$859$	27.8297	+	27.8297i	0.949539	+	0.949539i	0.998787	−	0.0492479i	$-0.0156824\pi$
$859$	27.8297	+	27.8297i	0.949539	+	0.949539i	−0.0492479	+	0.998787i	$0.515682\pi$
$860$	−7.01917	+	34.9850i	−0.239352	+	1.19298i
$861$		0			0
$862$	6.21813	+	0.617628i	0.211790	+	0.0210365i
$863$	−8.41542			−0.286464			−0.143232	−	0.989689i	$-0.545750\pi$
$863$	−8.41542			−0.286464			−0.143232	+	0.989689i	$0.545750\pi$
$864$		0			0
$865$	43.1158			1.46598
$866$	−4.31632	−	0.428727i	−0.146674	−	0.0145687i
$867$		0			0
$868$	3.97384	−	19.8064i	0.134881	−	0.672275i
$869$	−42.2662	−	42.2662i	−1.43378	−	1.43378i
$870$		0			0
$871$	35.0293			1.18692
$872$	2.89677	+	5.45199i	0.0980970	+	0.184628i
$873$		0			0
$874$	10.4918	+	12.8059i	0.354890	+	0.433165i
$875$	8.51232	−	8.51232i	0.287769	−	0.287769i
$876$		0			0
$877$	−14.9657	−	14.9657i	−0.505356	−	0.505356i	0.407742	−	0.913097i	$-0.366316\pi$
$877$	−14.9657	−	14.9657i	−0.505356	−	0.505356i	−0.913097	+	0.407742i	$0.866316\pi$
$878$	−5.96993	−	0.592975i	−0.201475	−	0.0200119i
$879$		0			0
$880$	−39.5859	−	16.5507i	−1.33444	−	0.557925i
$881$		−	16.9109i		−	0.569743i	−0.958566	−	0.284871i	$-0.908049\pi$
$881$		−	16.9109i		−	0.569743i	0.958566	−	0.284871i	$-0.0919509\pi$
$882$		0			0
$883$	21.0835	−	21.0835i	0.709518	−	0.709518i	−0.256916	−	0.966434i	$-0.582706\pi$
$883$	21.0835	−	21.0835i	0.709518	−	0.709518i	0.966434	+	0.256916i	$0.0827063\pi$
$884$	12.3760	−	8.23978i	0.416249	−	0.277134i
$885$		0			0
$886$	−3.62264	+	2.96801i	−0.121705	+	0.0997121i
$887$		−	41.4937i		−	1.39322i	−0.717450	−	0.696610i	$-0.754691\pi$
$887$		−	41.4937i		−	1.39322i	0.717450	−	0.696610i	$-0.245309\pi$
$888$		0			0
$889$		−	5.32939i		−	0.178742i
$890$	−10.8697	−	13.2672i	−0.364354	−	0.444716i
$891$		0			0
$892$	−1.64269	+	8.18753i	−0.0550014	+	0.274139i
$893$	−2.79943	+	2.79943i	−0.0936795	+	0.0936795i
$894$		0			0
$895$			7.50150i			0.250748i
$896$	8.70389	+	7.22788i	0.290777	+	0.241467i
$897$		0			0
$898$	1.23965	−	12.4805i	0.0413678	−	0.416481i
$899$	−5.50379	−	5.50379i	−0.183562	−	0.183562i
$900$		0			0
$901$	−0.552232	+	0.552232i	−0.0183975	+	0.0183975i
$902$	3.43115	−	2.81113i	0.114245	−	0.0936003i
$903$		0			0
$904$	−11.5906	+	37.8705i	−0.385499	+	1.25956i
$905$	−43.4030			−1.44276
$906$		0			0
$907$	−3.24476	−	3.24476i	−0.107740	−	0.107740i	0.651182	−	0.758922i	$-0.274274\pi$
$907$	−3.24476	−	3.24476i	−0.107740	−	0.107740i	−0.758922	+	0.651182i	$0.774274\pi$
$908$	−33.2703	−	49.9713i	−1.10411	−	1.65836i
$909$		0			0
$910$	−0.844045	+	8.49764i	−0.0279798	+	0.281694i
$911$	47.2047			1.56396			0.781980	−	0.623303i	$-0.214210\pi$
$911$	47.2047			1.56396			0.781980	+	0.623303i	$0.214210\pi$
$912$		0			0
$913$	88.8538			2.94063
$914$	−0.999226	+	10.0600i	−0.0330515	+	0.332754i
$915$		0			0
$916$	−15.2131	+	10.1287i	−0.502654	+	0.334661i
$917$	−13.4364	−	13.4364i	−0.443710	−	0.443710i
$918$		0			0
$919$	21.1617			0.698061			0.349030	−	0.937111i	$-0.386511\pi$
$919$	21.1617			0.698061			0.349030	+	0.937111i	$0.386511\pi$
$920$	9.45976	−	5.02619i	0.311879	−	0.165709i
$921$		0			0
$922$	−27.5913	+	22.6054i	−0.908671	+	0.744470i
$923$	−22.1840	+	22.1840i	−0.730195	+	0.730195i
$924$		0			0
$925$	−10.4708	−	10.4708i	−0.344279	−	0.344279i
$926$	2.25912	−	22.7443i	0.0742394	−	0.747424i
$927$		0			0
$928$	4.17668	−	1.24813i	0.137106	−	0.0409720i
$929$		−	54.4109i		−	1.78516i	−0.450886	−	0.892581i	$-0.648892\pi$
$929$		−	54.4109i		−	1.78516i	0.450886	−	0.892581i	$-0.351108\pi$
$930$		0			0
$931$	−3.64422	+	3.64422i	−0.119435	+	0.119435i
$932$	−20.8751	−	4.18824i	−0.683786	−	0.137190i
$933$		0			0
$934$	17.1564	+	20.9405i	0.561376	+	0.685194i
$935$			22.0196i			0.720117i
$936$		0			0
$937$			40.2919i			1.31628i	0.752895	+	0.658140i	$0.228657\pi$
$937$			40.2919i			1.31628i	−0.752895	+	0.658140i	$0.771343\pi$
$938$	10.5815	−	8.66939i	0.345499	−	0.283066i
$939$		0			0
$940$	1.41969	+	2.13235i	0.0463051	+	0.0695495i
$941$	−21.2053	+	21.2053i	−0.691272	+	0.691272i	−0.962512	−	0.271239i	$-0.912566\pi$
$941$	−21.2053	+	21.2053i	−0.691272	+	0.691272i	0.271239	+	0.962512i	$0.412566\pi$
$942$		0			0
$943$			1.10742i			0.0360626i
$944$	−0.512631	+	0.210354i	−0.0166847	+	0.00684642i
$945$		0			0
$946$	−96.8712	−	9.62193i	−3.14956	−	0.312836i
$947$	−37.6027	−	37.6027i	−1.22192	−	1.22192i	−0.966947	−	0.254977i	$-0.917932\pi$
$947$	−37.6027	−	37.6027i	−1.22192	−	1.22192i	−0.254977	−	0.966947i	$-0.582068\pi$
$948$		0			0
$949$	34.9175	−	34.9175i	1.13347	−	1.13347i
$950$	10.2535	+	12.5150i	0.332668	+	0.406041i
$951$		0			0
$952$	1.69923	−	5.55197i	0.0550725	−	0.179940i
$953$	19.9135			0.645062			0.322531	−	0.946559i	$-0.395466\pi$
$953$	19.9135			0.645062			0.322531	+	0.946559i	$0.395466\pi$
$954$		0			0
$955$	−26.1700	−	26.1700i	−0.846842	−	0.846842i
$956$	20.1533	+	4.04342i	0.651803	+	0.130773i
$957$		0			0
$958$	−13.8741	−	1.37807i	−0.448251	−	0.0445234i
$959$	10.1704			0.328418
$960$		0			0
$961$	−71.0217			−2.29102
$962$	33.9970	+	3.37682i	1.09611	+	0.108873i
$963$		0			0
$964$	−0.383704	−	0.0769838i	−0.0123583	−	0.00247948i
$965$	−8.17348	−	8.17348i	−0.263114	−	0.263114i
$966$		0			0
$967$	−24.5899			−0.790759			−0.395380	−	0.918518i	$-0.629387\pi$
$967$	−24.5899			−0.790759			−0.395380	+	0.918518i	$0.629387\pi$
$968$	25.1524	−	82.1815i	0.808430	−	2.64141i
$969$		0			0
$970$	15.6179	+	19.0626i	0.501461	+	0.612065i
$971$	19.9255	−	19.9255i	0.639438	−	0.639438i	−0.310979	−	0.950417i	$-0.600657\pi$
$971$	19.9255	−	19.9255i	0.639438	−	0.639438i	0.950417	+	0.310979i	$0.100657\pi$
$972$		0			0
$973$	−6.90089	−	6.90089i	−0.221232	−	0.221232i
$974$	−41.3820	−	4.11035i	−1.32597	−	0.131704i
$975$		0			0
$976$	−15.9283	−	38.8174i	−0.509854	−	1.24251i
$977$		−	50.0455i		−	1.60110i	−0.599267	−	0.800549i	$-0.704541\pi$
$977$		−	50.0455i		−	1.60110i	0.599267	−	0.800549i	$-0.295459\pi$
$978$		0			0
$979$	33.0870	−	33.0870i	1.05747	−	1.05747i
$980$	1.84811	+	2.77583i	0.0590358	+	0.0886706i
$981$		0			0
$982$	8.06843	−	6.61042i	0.257474	−	0.210947i
$983$		−	17.3760i		−	0.554207i	−0.960840	−	0.277104i	$-0.910625\pi$
$983$		−	17.3760i		−	0.554207i	0.960840	−	0.277104i	$-0.0893746\pi$
$984$		0			0
$985$			14.3344i			0.456733i
$986$	−1.41779	−	1.73050i	−0.0451516	−	0.0551103i
$987$		0			0
$988$	−36.5981	−	7.34281i	−1.16434	−	0.233606i
$989$	17.1856	−	17.1856i	0.546470	−	0.546470i
$990$		0			0
$991$		−	44.1839i		−	1.40355i	−0.712399	−	0.701774i	$-0.752391\pi$
$991$		−	44.1839i		−	1.40355i	0.712399	−	0.701774i	$-0.247609\pi$
$992$	27.1427	−	50.2789i	0.861781	−	1.59636i
$993$		0			0
$994$	−1.21095	+	12.1916i	−0.0384091	+	0.386693i
$995$	−12.8777	−	12.8777i	−0.408250	−	0.408250i
$996$		0			0
$997$	1.76515	−	1.76515i	0.0559030	−	0.0559030i	−0.678603	−	0.734506i	$-0.737414\pi$
$997$	1.76515	−	1.76515i	0.0559030	−	0.0559030i	0.734506	+	0.678603i	$0.237414\pi$
$998$	−18.3498	+	15.0339i	−0.580854	+	0.475891i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.v.e.323.20	yes	40
3.2	odd	2	inner	1008.2.v.e.323.1	✓	40
4.3	odd	2		4032.2.v.e.1583.15		40
12.11	even	2		4032.2.v.e.1583.6		40
16.5	even	4		4032.2.v.e.3599.6		40
16.11	odd	4	inner	1008.2.v.e.827.1	yes	40
48.5	odd	4		4032.2.v.e.3599.15		40
48.11	even	4	inner	1008.2.v.e.827.20	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.v.e.323.1	✓	40	3.2	odd	2	inner
1008.2.v.e.323.20	yes	40	1.1	even	1	trivial
1008.2.v.e.827.1	yes	40	16.11	odd	4	inner
1008.2.v.e.827.20	yes	40	48.11	even	4	inner
4032.2.v.e.1583.6		40	12.11	even	2
4032.2.v.e.1583.15		40	4.3	odd	2
4032.2.v.e.3599.6		40	16.5	even	4
4032.2.v.e.3599.15		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)

\(f(q)\)	\(=\)	\(q+(1.40729 + 0.139782i) q^{2} +(1.96092 + 0.393427i) q^{4} +(1.17902 + 1.17902i) q^{5} +1.00000 q^{7} +(2.70459 + 0.827766i) q^{8} +O(q^{10})\)	\(q+(1.40729 + 0.139782i) q^{2} +(1.96092 + 0.393427i) q^{4} +(1.17902 + 1.17902i) q^{5} +1.00000 q^{7} +(2.70459 + 0.827766i) q^{8} +(1.49442 + 1.82403i) q^{10} +(-4.54895 + 4.54895i) q^{11} +(2.56073 + 2.56073i) q^{13} +(1.40729 + 0.139782i) q^{14} +(3.69043 + 1.54296i) q^{16} -2.05280i q^{17} +(-3.64422 + 3.64422i) q^{19} +(1.84811 + 2.77583i) q^{20} +(-7.03755 + 5.76583i) q^{22} -2.27140i q^{23} -2.21982i q^{25} +(3.24574 + 3.96163i) q^{26} +(1.96092 + 0.393427i) q^{28} +(0.544898 - 0.544898i) q^{29} -10.1006i q^{31} +(4.97782 + 2.68724i) q^{32} +(0.286943 - 2.88888i) q^{34} +(1.17902 + 1.17902i) q^{35} +(4.71698 - 4.71698i) q^{37} +(-5.63787 + 4.61908i) q^{38} +(2.21282 + 4.16472i) q^{40} -0.487549 q^{41} +(7.56607 + 7.56607i) q^{43} +(-10.7098 + 7.13046i) q^{44} +(0.317501 - 3.19652i) q^{46} +0.768184 q^{47} +1.00000 q^{49} +(0.310290 - 3.12392i) q^{50} +(4.01393 + 6.02885i) q^{52} +(-0.269015 - 0.269015i) q^{53} -10.7266 q^{55} +(2.70459 + 0.827766i) q^{56} +(0.842996 - 0.690662i) q^{58} +(-0.0979540 + 0.0979540i) q^{59} +(-7.41725 - 7.41725i) q^{61} +(1.41188 - 14.2144i) q^{62} +(6.62961 + 4.47753i) q^{64} +6.03831i q^{65} +(6.83972 - 6.83972i) q^{67} +(0.807624 - 4.02537i) q^{68} +(1.49442 + 1.82403i) q^{70} +8.66316i q^{71} -13.6358i q^{73} +(7.29750 - 5.97880i) q^{74} +(-8.57977 + 5.71231i) q^{76} +(-4.54895 + 4.54895i) q^{77} +9.29142i q^{79} +(2.53192 + 6.17028i) q^{80} +(-0.686123 - 0.0681505i) q^{82} +(-9.76640 - 9.76640i) q^{83} +(2.42029 - 2.42029i) q^{85} +(9.59004 + 11.7052i) q^{86} +(-16.0685 + 8.53758i) q^{88} -7.27355 q^{89} +(2.56073 + 2.56073i) q^{91} +(0.893630 - 4.45404i) q^{92} +(1.08106 + 0.107378i) q^{94} -8.59324 q^{95} +10.4508 q^{97} +(1.40729 + 0.139782i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{7}+O(q^{10}) \) 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

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