LMFDB - Embedded newform 504.2.bm.c.107.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(107,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("504.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bm (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.3
Character	$\chi$	$=$	504.107
Dual form			504.2.bm.c.179.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31291 - 0.525613i) q^{2} +(1.44746 + 1.38016i) q^{4} +(-1.51483 + 2.62375i) q^{5} +(1.48957 + 2.18659i) q^{7} +(-1.17496 - 2.57283i) q^{8} +O(q^{10})$	\(q+(-1.31291 - 0.525613i) q^{2} +(1.44746 + 1.38016i) q^{4} +(-1.51483 + 2.62375i) q^{5} +(1.48957 + 2.18659i) q^{7} +(-1.17496 - 2.57283i) q^{8} +(3.36791 - 2.64854i) q^{10} +(4.18149 - 2.41419i) q^{11} -1.60756i q^{13} +(-0.806377 - 3.65373i) q^{14} +(0.190296 + 3.99547i) q^{16} +(-5.79907 + 3.34810i) q^{17} +(-0.663707 + 1.14957i) q^{19} +(-5.81387 + 1.70708i) q^{20} +(-6.75885 + 0.971762i) q^{22} +(-4.32670 + 7.49406i) q^{23} +(-2.08939 - 3.61894i) q^{25} +(-0.844956 + 2.11059i) q^{26} +(-0.861747 + 5.22086i) q^{28} +7.28547 q^{29} +(-6.89424 + 3.98039i) q^{31} +(1.85023 - 5.34571i) q^{32} +(9.37346 - 1.34768i) q^{34} +(-7.99352 + 0.595977i) q^{35} +(2.70074 + 1.55927i) q^{37} +(1.47562 - 1.16043i) q^{38} +(8.53034 + 0.814600i) q^{40} -5.27510i q^{41} -3.12131 q^{43} +(9.38453 + 2.27670i) q^{44} +(9.61954 - 7.56486i) q^{46} +(-0.262637 + 0.454901i) q^{47} +(-2.56234 + 6.51417i) q^{49} +(0.841026 + 5.84955i) q^{50} +(2.21870 - 2.32689i) q^{52} +(5.00146 + 8.66278i) q^{53} +14.6283i q^{55} +(3.87555 - 6.40157i) q^{56} +(-9.56517 - 3.82934i) q^{58} +(-1.73784 + 1.00334i) q^{59} +(-8.83953 - 5.10350i) q^{61} +(11.1437 - 1.60219i) q^{62} +(-5.23896 + 6.04593i) q^{64} +(4.21785 + 2.43518i) q^{65} +(0.979594 + 1.69671i) q^{67} +(-13.0149 - 3.15743i) q^{68} +(10.8080 + 3.41903i) q^{70} +2.66212 q^{71} +(-1.96808 - 3.40882i) q^{73} +(-2.72625 - 3.46672i) q^{74} +(-2.54729 + 0.747941i) q^{76} +(11.5075 + 5.54710i) q^{77} +(-2.66792 - 1.54032i) q^{79} +(-10.7714 - 5.55315i) q^{80} +(-2.77266 + 6.92574i) q^{82} +8.22694i q^{83} -20.2871i q^{85} +(4.09800 + 1.64060i) q^{86} +(-11.1244 - 7.92173i) q^{88} +(9.40108 + 5.42772i) q^{89} +(3.51508 - 2.39458i) q^{91} +(-16.6058 + 4.87582i) q^{92} +(0.583921 - 0.459198i) q^{94} +(-2.01080 - 3.48281i) q^{95} +15.3656 q^{97} +(6.78805 - 7.20572i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 8 q^{10} - 28 q^{16} - 32 q^{19} + 32 q^{22} + 4 q^{28} + 112 q^{34} - 36 q^{40} - 160 q^{43} + 40 q^{46} + 56 q^{49} - 36 q^{52} + 12 q^{58} - 24 q^{64} + 92 q^{70} + 16 q^{73} - 120 q^{76} + 20 q^{82} - 100 q^{88} - 32 q^{91} - 20 q^{94} + 240 q^{97}+O(q^{100}) $ 48 * q - 8 * q^10 - 28 * q^16 - 32 * q^19 + 32 * q^22 + 4 * q^28 + 112 * q^34 - 36 * q^40 - 160 * q^43 + 40 * q^46 + 56 * q^49 - 36 * q^52 + 12 * q^58 - 24 * q^64 + 92 * q^70 + 16 * q^73 - 120 * q^76 + 20 * q^82 - 100 * q^88 - 32 * q^91 - 20 * q^94 + 240 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.31291	−	0.525613i	−0.928367	−	0.371664i
$2$	−1.31291	−	0.525613i	−0.928367	−	0.371664i
$3$		0			0
$3$		0			0
$4$	1.44746	+	1.38016i	0.723731	+	0.690082i
$5$	−1.51483	+	2.62375i	−0.677451	+	1.17338i	0.298295	+	0.954474i	$0.403582\pi$
$5$	−1.51483	+	2.62375i	−0.677451	+	1.17338i	−0.975746	+	0.218905i	$0.929751\pi$
$6$		0			0
$7$	1.48957	+	2.18659i	0.563006	+	0.826453i
$7$	1.48957	+	2.18659i	0.563006	+	0.826453i
$8$	−1.17496	−	2.57283i	−0.415410	−	0.909634i
$9$		0			0
$10$	3.36791	−	2.64854i	1.06503	−	0.837542i
$11$	4.18149	−	2.41419i	1.26077	−	0.727905i	0.287545	−	0.957767i	$-0.407161\pi$
$11$	4.18149	−	2.41419i	1.26077	−	0.727905i	0.973223	+	0.229863i	$0.0738277\pi$
$12$		0			0
$13$		−	1.60756i		−	0.445858i	−0.974835	−	0.222929i	$-0.928438\pi$
$13$		−	1.60756i		−	0.445858i	0.974835	−	0.222929i	$-0.0715618\pi$
$14$	−0.806377	−	3.65373i	−0.215513	−	0.976501i
$15$		0			0
$16$	0.190296	+	3.99547i	0.0475740	+	0.998868i
$17$	−5.79907	+	3.34810i	−1.40648	+	0.812033i	−0.995047	−	0.0994061i	$-0.968306\pi$
$17$	−5.79907	+	3.34810i	−1.40648	+	0.812033i	−0.411435	+	0.911439i	$0.634972\pi$
$18$		0			0
$19$	−0.663707	+	1.14957i	−0.152265	+	0.263730i	−0.932060	−	0.362305i	$-0.881990\pi$
$19$	−0.663707	+	1.14957i	−0.152265	+	0.263730i	0.779795	+	0.626035i	$0.215323\pi$
$20$	−5.81387	+	1.70708i	−1.30002	+	0.381715i
$21$		0			0
$22$	−6.75885	+	0.971762i	−1.44099	+	0.207180i
$23$	−4.32670	+	7.49406i	−0.902179	+	1.56262i	−0.0775191	+	0.996991i	$0.524700\pi$
$23$	−4.32670	+	7.49406i	−0.902179	+	1.56262i	−0.824660	+	0.565629i	$0.808633\pi$
$24$		0			0
$25$	−2.08939	−	3.61894i	−0.417879	−	0.723787i
$26$	−0.844956	+	2.11059i	−0.165709	+	0.413920i
$27$		0			0
$28$	−0.861747	+	5.22086i	−0.162855	+	0.986650i
$29$	7.28547			1.35288			0.676439	−	0.736499i	$-0.263522\pi$
$29$	7.28547			1.35288			0.676439	+	0.736499i	$0.263522\pi$
$30$		0			0
$31$	−6.89424	+	3.98039i	−1.23824	+	0.714899i	−0.968735	−	0.248099i	$-0.920194\pi$
$31$	−6.89424	+	3.98039i	−1.23824	+	0.714899i	−0.269507	+	0.962998i	$0.586861\pi$
$32$	1.85023	−	5.34571i	0.327077	−	0.944998i
$33$		0			0
$34$	9.37346	−	1.34768i	1.60754	−	0.231125i
$35$	−7.99352	+	0.595977i	−1.35115	+	0.100738i
$36$		0			0
$37$	2.70074	+	1.55927i	0.443999	+	0.256343i	0.705292	−	0.708917i	$-0.250816\pi$
$37$	2.70074	+	1.55927i	0.443999	+	0.256343i	−0.261294	+	0.965259i	$0.584149\pi$
$38$	1.47562	−	1.16043i	0.239377	−	0.188247i
$39$		0			0
$40$	8.53034	+	0.814600i	1.34877	+	0.128800i
$41$		−	5.27510i		−	0.823833i	−0.911222	−	0.411916i	$-0.864860\pi$
$41$		−	5.27510i		−	0.823833i	0.911222	−	0.411916i	$-0.135140\pi$
$42$		0			0
$43$	−3.12131			−0.475995			−0.237998	−	0.971266i	$-0.576491\pi$
$43$	−3.12131			−0.475995			−0.237998	+	0.971266i	$0.576491\pi$
$44$	9.38453	+	2.27670i	1.41477	+	0.343226i
$45$		0			0
$46$	9.61954	−	7.56486i	1.41832	−	1.11538i
$47$	−0.262637	+	0.454901i	−0.0383096	+	0.0663541i	−0.884544	−	0.466456i	$-0.845531\pi$
$47$	−0.262637	+	0.454901i	−0.0383096	+	0.0663541i	0.846235	+	0.532810i	$0.178864\pi$
$48$		0			0
$49$	−2.56234	+	6.51417i	−0.366048	+	0.930596i
$50$	0.841026	+	5.84955i	0.118939	+	0.827251i
$51$		0			0
$52$	2.21870	−	2.32689i	0.307678	−	0.322681i
$53$	5.00146	+	8.66278i	0.687003	+	1.18992i	0.972803	+	0.231635i	$0.0744074\pi$
$53$	5.00146	+	8.66278i	0.687003	+	1.18992i	−0.285800	+	0.958289i	$0.592259\pi$
$54$		0			0
$55$			14.6283i			1.97248i
$56$	3.87555	−	6.40157i	0.517892	−	0.855446i
$57$		0			0
$58$	−9.56517	−	3.82934i	−1.25597	−	0.502817i
$59$	−1.73784	+	1.00334i	−0.226247	+	0.130624i	−0.608840	−	0.793293i	$-0.708365\pi$
$59$	−1.73784	+	1.00334i	−0.226247	+	0.130624i	0.382592	+	0.923917i	$0.375031\pi$
$60$		0			0
$61$	−8.83953	−	5.10350i	−1.13179	−	0.653437i	−0.187402	−	0.982283i	$-0.560007\pi$
$61$	−8.83953	−	5.10350i	−1.13179	−	0.653437i	−0.944383	+	0.328847i	$0.893340\pi$
$62$	11.1437	−	1.60219i	1.41525	−	0.203479i
$63$		0			0
$64$	−5.23896	+	6.04593i	−0.654870	+	0.755742i
$65$	4.21785	+	2.43518i	0.523160	+	0.302047i
$66$		0			0
$67$	0.979594	+	1.69671i	0.119676	+	0.207286i	0.919639	−	0.392764i	$-0.128481\pi$
$67$	0.979594	+	1.69671i	0.119676	+	0.207286i	−0.799963	+	0.600049i	$0.795148\pi$
$68$	−13.0149	−	3.15743i	−1.57828	−	0.382894i
$69$		0			0
$70$	10.8080	+	3.41903i	1.29181	+	0.408652i
$71$	2.66212			0.315936			0.157968	−	0.987444i	$-0.449506\pi$
$71$	2.66212			0.315936			0.157968	+	0.987444i	$0.449506\pi$
$72$		0			0
$73$	−1.96808	−	3.40882i	−0.230347	−	0.398972i	0.727563	−	0.686040i	$-0.240653\pi$
$73$	−1.96808	−	3.40882i	−0.230347	−	0.398972i	−0.957910	+	0.287068i	$0.907319\pi$
$74$	−2.72625	−	3.46672i	−0.316920	−	0.402999i
$75$		0			0
$76$	−2.54729	+	0.747941i	−0.292194	+	0.0857948i
$77$	11.5075	+	5.54710i	1.31140	+	0.632150i
$78$		0			0
$79$	−2.66792	−	1.54032i	−0.300164	−	0.173300i	0.342353	−	0.939572i	$-0.388776\pi$
$79$	−2.66792	−	1.54032i	−0.300164	−	0.173300i	−0.642517	+	0.766272i	$0.722110\pi$
$80$	−10.7714	−	5.55315i	−1.20428	−	0.620861i
$81$		0			0
$82$	−2.77266	+	6.92574i	−0.306189	+	0.764820i
$83$			8.22694i			0.903024i	0.892265	+	0.451512i	$0.149115\pi$
$83$			8.22694i			0.903024i	−0.892265	+	0.451512i	$0.850885\pi$
$84$		0			0
$85$		−	20.2871i		−	2.20045i
$86$	4.09800	+	1.64060i	0.441899	+	0.176910i
$87$		0			0
$88$	−11.1244	−	7.92173i	−1.18586	−	0.844459i
$89$	9.40108	+	5.42772i	0.996513	+	0.575337i	0.907215	−	0.420668i	$-0.138204\pi$
$89$	9.40108	+	5.42772i	0.996513	+	0.575337i	0.0892982	+	0.996005i	$0.471538\pi$
$90$		0			0
$91$	3.51508	−	2.39458i	0.368481	−	0.251021i
$92$	−16.6058	+	4.87582i	−1.73127	+	0.508340i
$93$		0			0
$94$	0.583921	−	0.459198i	0.0602268	−	0.0473627i
$95$	−2.01080	−	3.48281i	−0.206304	−	0.357329i
$96$		0			0
$97$	15.3656			1.56014			0.780072	−	0.625690i	$-0.215182\pi$
$97$	15.3656			1.56014			0.780072	+	0.625690i	$0.215182\pi$
$98$	6.78805	−	7.20572i	0.685697	−	0.727888i
$99$		0			0
$100$	1.97040	−	8.12198i	0.197040	−	0.812198i
$101$	−4.53586	−	7.85633i	−0.451335	−	0.781734i	0.547135	−	0.837045i	$-0.315719\pi$
$101$	−4.53586	−	7.85633i	−0.451335	−	0.781734i	−0.998469	+	0.0553102i	$0.982385\pi$
$102$		0			0
$103$	−2.91970	−	1.68569i	−0.287687	−	0.166096i	0.349211	−	0.937044i	$-0.386449\pi$
$103$	−2.91970	−	1.68569i	−0.287687	−	0.166096i	−0.636898	+	0.770948i	$0.719783\pi$
$104$	−4.13600	+	1.88882i	−0.405568	+	0.185214i
$105$		0			0
$106$	−2.01319	−	14.0023i	−0.195539	−	1.36002i
$107$	−2.28741	−	1.32064i	−0.221132	−	0.127671i	0.385342	−	0.922774i	$-0.374083\pi$
$107$	−2.28741	−	1.32064i	−0.221132	−	0.127671i	−0.606474	+	0.795103i	$0.707417\pi$
$108$		0			0
$109$	−1.69125	+	0.976445i	−0.161993	+	0.0935264i	−0.578805	−	0.815466i	$-0.696481\pi$
$109$	−1.69125	+	0.976445i	−0.161993	+	0.0935264i	0.416812	+	0.908993i	$0.363147\pi$
$110$	7.68881	−	19.2056i	0.733100	−	1.83118i
$111$		0			0
$112$	−8.45299	+	6.36765i	−0.798733	+	0.601686i
$113$		−	2.74503i		−	0.258231i	−0.991630	−	0.129115i	$-0.958786\pi$
$113$		−	2.74503i		−	0.258231i	0.991630	−	0.129115i	$-0.0412137\pi$
$114$		0			0
$115$	−13.1084	−	22.7044i	−1.22236	−	2.11720i
$116$	10.5454	+	10.0551i	0.979120	+	0.933597i
$117$		0			0
$118$	2.80899	−	0.403867i	0.258589	−	0.0371789i
$119$	−15.9591	−	7.69295i	−1.46296	−	0.705212i
$120$		0			0
$121$	6.15659	−	10.6635i	0.559690	−	0.969412i
$122$	8.92303	+	11.3466i	0.807853	+	1.02727i
$123$		0			0
$124$	−15.4727	−	3.75371i	−1.38949	−	0.337093i
$125$	−2.48799			−0.222532
$126$		0			0
$127$			8.70363i			0.772322i	0.922431	+	0.386161i	$0.126199\pi$
$127$			8.70363i			0.772322i	−0.922431	+	0.386161i	$0.873801\pi$
$128$	10.0561	−	5.18410i	0.888842	−	0.458214i
$129$		0			0
$130$	−4.25770	−	5.41413i	−0.373425	−	0.474850i
$131$	4.67002	+	2.69624i	0.408021	+	0.235571i	0.689939	−	0.723867i	$-0.257637\pi$
$131$	4.67002	+	2.69624i	0.408021	+	0.235571i	−0.281918	+	0.959439i	$0.590971\pi$
$132$		0			0
$133$	−3.50229	+	0.261122i	−0.303687	+	0.0226421i
$134$	−0.394308	−	2.74251i	−0.0340630	−	0.236917i
$135$		0			0
$136$	15.4278	+	10.9862i	1.32292	+	0.942058i
$137$	9.95066	−	5.74501i	0.850142	−	0.490830i	−0.0105568	−	0.999944i	$-0.503360\pi$
$137$	9.95066	−	5.74501i	0.850142	−	0.490830i	0.860699	+	0.509115i	$0.170027\pi$
$138$		0			0
$139$	19.9929			1.69578			0.847888	−	0.530175i	$-0.177874\pi$
$139$	19.9929			1.69578			0.847888	+	0.530175i	$0.177874\pi$
$140$	−12.3929	−	10.1697i	−1.04739	−	0.859497i
$141$		0			0
$142$	−3.49513	−	1.39925i	−0.293304	−	0.117422i
$143$	−3.88096	−	6.72202i	−0.324542	−	0.562123i
$144$		0			0
$145$	−11.0362	+	19.1153i	−0.916508	+	1.58744i
$146$	0.792196	+	5.50992i	0.0655626	+	0.456004i
$147$		0			0
$148$	1.75717	+	5.98445i	0.144438	+	0.491919i
$149$	7.40435	−	12.8247i	0.606588	−	1.05064i	−0.385210	−	0.922829i	$-0.625871\pi$
$149$	7.40435	−	12.8247i	0.606588	−	1.05064i	0.991798	−	0.127813i	$-0.0407956\pi$
$150$		0			0
$151$	−3.73528	+	2.15657i	−0.303973	+	0.175499i	−0.644226	−	0.764835i	$-0.722820\pi$
$151$	−3.73528	+	2.15657i	−0.303973	+	0.175499i	0.340253	+	0.940334i	$0.389487\pi$
$152$	3.73749	+	0.356909i	0.303151	+	0.0289492i
$153$		0			0
$154$	−12.1927	−	13.3313i	−0.982512	−	1.07427i
$155$		−	24.1184i		−	1.93724i
$156$		0			0
$157$	13.9896	−	8.07691i	1.11649	−	0.644608i	0.175990	−	0.984392i	$-0.443687\pi$
$157$	13.9896	−	8.07691i	1.11649	−	0.644608i	0.940503	+	0.339784i	$0.110354\pi$
$158$	2.69312	+	3.42459i	0.214253	+	0.272446i
$159$		0			0
$160$	11.2231	+	12.9524i	0.887262	+	1.02397i
$161$	−22.8314	+	1.70225i	−1.79936	+	0.134156i
$162$		0			0
$163$	−6.28004	+	10.8773i	−0.491890	+	0.851979i	−0.999956	−	0.00933901i	$-0.997027\pi$
$163$	−6.28004	+	10.8773i	−0.491890	+	0.851979i	0.508066	+	0.861318i	$0.330361\pi$
$164$	7.28051	−	7.63552i	0.568512	−	0.596234i
$165$		0			0
$166$	4.32418	−	10.8012i	0.335622	−	0.838338i
$167$	3.82827			0.296240			0.148120	−	0.988969i	$-0.452678\pi$
$167$	3.82827			0.296240			0.148120	+	0.988969i	$0.452678\pi$
$168$		0			0
$169$	10.4157			0.801211
$170$	−10.6632	+	26.6352i	−0.817828	+	2.04282i
$171$		0			0
$172$	−4.51798	−	4.30792i	−0.344493	−	0.328476i
$173$	5.14458	−	8.91068i	0.391136	−	0.677467i	−0.601464	−	0.798900i	$-0.705416\pi$
$173$	5.14458	−	8.91068i	0.391136	−	0.677467i	0.992600	+	0.121433i	$0.0387490\pi$
$174$		0			0
$175$	4.80082	−	9.95932i	0.362908	−	0.752854i
$176$	10.4415	+	16.2476i	0.787060	+	1.22471i
$177$		0			0
$178$	−9.48989	−	12.0674i	−0.711298	−	0.904492i
$179$	8.91839	−	5.14904i	0.666592	−	0.384857i	−0.128192	−	0.991749i	$-0.540917\pi$
$179$	8.91839	−	5.14904i	0.666592	−	0.384857i	0.794784	+	0.606892i	$0.207584\pi$
$180$		0			0
$181$		−	14.3100i		−	1.06366i	−0.846853	−	0.531828i	$-0.821505\pi$
$181$		−	14.3100i		−	1.06366i	0.846853	−	0.531828i	$-0.178495\pi$
$182$	−5.87361	+	1.29630i	−0.435381	+	0.0960883i
$183$		0			0
$184$	24.3647	+	2.32669i	1.79619	+	0.171526i
$185$	−8.18229	+	4.72405i	−0.601574	+	0.347319i
$186$		0			0
$187$	−16.1659	+	28.0001i	−1.18217	+	2.04757i
$188$	−1.00800	+	0.295970i	−0.0735156	+	0.0215858i
$189$		0			0
$190$	0.809391	+	5.62952i	0.0587194	+	0.408408i
$191$	−3.89652	+	6.74897i	−0.281942	+	0.488338i	−0.971863	−	0.235547i	$-0.924312\pi$
$191$	−3.89652	+	6.74897i	−0.281942	+	0.488338i	0.689921	+	0.723885i	$0.257645\pi$
$192$		0			0
$193$	−3.04215	−	5.26916i	−0.218979	−	0.379282i	0.735517	−	0.677506i	$-0.236939\pi$
$193$	−3.04215	−	5.26916i	−0.218979	−	0.379282i	−0.954496	+	0.298224i	$0.903606\pi$
$194$	−20.1737	−	8.07638i	−1.44839	−	0.579850i
$195$		0			0
$196$	−12.6995	+	5.89257i	−0.907108	+	0.420898i
$197$	−13.1481			−0.936763			−0.468382	−	0.883526i	$-0.655163\pi$
$197$	−13.1481			−0.936763			−0.468382	+	0.883526i	$0.655163\pi$
$198$		0			0
$199$	16.5572	−	9.55931i	1.17371	−	0.677642i	0.219159	−	0.975689i	$-0.429669\pi$
$199$	16.5572	−	9.55931i	1.17371	−	0.677642i	0.954551	+	0.298048i	$0.0963354\pi$
$200$	−6.85598	+	9.62775i	−0.484791	+	0.680785i
$201$		0			0
$202$	1.82578	+	12.6988i	0.128461	+	0.893482i
$203$	10.8523	+	15.9303i	0.761679	+	1.11809i
$204$		0			0
$205$	13.8406	+	7.99086i	0.966668	+	0.558106i
$206$	2.94728	+	3.74779i	0.205347	+	0.261121i
$207$		0			0
$208$	6.42297	−	0.305913i	0.445353	−	0.0212113i
$209$			6.40925i			0.443337i
$210$		0			0
$211$	9.86873			0.679391			0.339696	−	0.940535i	$-0.389676\pi$
$211$	9.86873			0.679391			0.339696	+	0.940535i	$0.389676\pi$
$212$	−4.71663	+	19.4419i	−0.323939	+	1.33527i
$213$		0			0
$214$	2.30902	+	2.93617i	0.157841	+	0.200712i
$215$	4.72824	−	8.18955i	0.322463	−	0.558523i
$216$		0			0
$217$	−18.9730	−	9.14578i	−1.28797	−	0.620856i
$218$	2.73369	−	0.393040i	0.185149	−	0.0266200i
$219$		0			0
$220$	−20.1894	+	21.1739i	−1.36117	+	1.42754i
$221$	5.38228	+	9.32238i	0.362051	+	0.627091i
$222$		0			0
$223$			15.1022i			1.01132i	0.862734	+	0.505658i	$0.168750\pi$
$223$			15.1022i			1.01132i	−0.862734	+	0.505658i	$0.831250\pi$
$224$	14.4449	−	3.91715i	0.965142	−	0.261725i
$225$		0			0
$226$	−1.44282	+	3.60397i	−0.0959751	+	0.239733i
$227$	2.81482	−	1.62514i	0.186826	−	0.107864i	−0.403670	−	0.914905i	$-0.632265\pi$
$227$	2.81482	−	1.62514i	0.186826	−	0.107864i	0.590496	+	0.807041i	$0.298932\pi$
$228$		0			0
$229$	1.79711	+	1.03756i	0.118757	+	0.0685642i	0.558202	−	0.829705i	$-0.311492\pi$
$229$	1.79711	+	1.03756i	0.118757	+	0.0685642i	−0.439445	+	0.898269i	$0.644825\pi$
$230$	5.27641	+	36.6987i	0.347916	+	2.41984i
$231$		0			0
$232$	−8.56011	−	18.7443i	−0.561999	−	1.23062i
$233$	5.76562	+	3.32878i	0.377718	+	0.218076i	0.676825	−	0.736144i	$-0.263355\pi$
$233$	5.76562	+	3.32878i	0.377718	+	0.218076i	−0.299107	+	0.954220i	$0.596689\pi$
$234$		0			0
$235$	−0.795699	−	1.37819i	−0.0519057	−	0.0899033i
$236$	−3.90023	−	0.946202i	−0.253883	−	0.0615925i
$237$		0			0
$238$	16.9093	+	18.4884i	1.09607	+	1.19843i
$239$	−3.52397			−0.227947			−0.113973	−	0.993484i	$-0.536358\pi$
$239$	−3.52397			−0.227947			−0.113973	+	0.993484i	$0.536358\pi$
$240$		0			0
$241$	10.5080	+	18.2003i	0.676878	+	1.17239i	0.975916	+	0.218146i	$0.0700007\pi$
$241$	10.5080	+	18.2003i	0.676878	+	1.17239i	−0.299039	+	0.954241i	$0.596666\pi$
$242$	−13.6879	+	10.7643i	−0.879894	+	0.691954i
$243$		0			0
$244$	−5.75121	−	19.5871i	−0.368184	−	1.25394i
$245$	−13.2101	−	16.5908i	−0.843962	−	1.05995i
$246$		0			0
$247$	1.84801	+	1.06695i	0.117586	+	0.0678885i
$248$	18.3413	+	13.0610i	1.16467	+	0.829371i
$249$		0			0
$250$	3.26650	+	1.30772i	0.206592	+	0.0827074i
$251$			6.47860i			0.408926i	0.978874	+	0.204463i	$0.0655447\pi$
$251$			6.47860i			0.408926i	−0.978874	+	0.204463i	$0.934455\pi$
$252$		0			0
$253$			41.7818i			2.62680i
$254$	4.57474	−	11.4271i	0.287045	−	0.716999i
$255$		0			0
$256$	−15.9276	+	1.52065i	−0.995473	+	0.0950403i
$257$	−0.850646	−	0.491121i	−0.0530618	−	0.0306353i	0.473234	−	0.880937i	$-0.343086\pi$
$257$	−0.850646	−	0.491121i	−0.0530618	−	0.0306353i	−0.526296	+	0.850301i	$0.676420\pi$
$258$		0			0
$259$	0.613463	+	8.22805i	0.0381187	+	0.511266i
$260$	2.74424	+	9.34616i	0.170191	+	0.579624i
$261$		0			0
$262$	−4.71413	−	5.99453i	−0.291240	−	0.370343i
$263$	−5.56267	−	9.63482i	−0.343009	−	0.594108i	0.641981	−	0.766720i	$-0.278113\pi$
$263$	−5.56267	−	9.63482i	−0.343009	−	0.594108i	−0.984990	+	0.172612i	$0.944779\pi$
$264$		0			0
$265$	−30.3053			−1.86164
$266$	4.73543	+	1.49802i	0.290348	+	0.0918493i
$267$		0			0
$268$	−0.923807	+	3.80792i	−0.0564305	+	0.232606i
$269$	1.40068	+	2.42605i	0.0854011	+	0.147919i	0.905562	−	0.424214i	$-0.139449\pi$
$269$	1.40068	+	2.42605i	0.0854011	+	0.147919i	−0.820161	+	0.572133i	$0.806116\pi$
$270$		0			0
$271$	7.96793	+	4.60029i	0.484017	+	0.279447i	0.722089	−	0.691800i	$-0.243182\pi$
$271$	7.96793	+	4.60029i	0.484017	+	0.279447i	−0.238072	+	0.971248i	$0.576515\pi$
$272$	−14.4808	−	22.5329i	−0.878025	−	1.36626i
$273$		0			0
$274$	−16.0840	+	2.31249i	−0.971668	+	0.139703i
$275$	−17.4736	−	10.0884i	−1.05370	−	0.608352i
$276$		0			0
$277$	14.7374	−	8.50866i	0.885487	−	0.511236i	0.0130233	−	0.999915i	$-0.495854\pi$
$277$	14.7374	−	8.50866i	0.885487	−	0.511236i	0.872464	+	0.488679i	$0.162521\pi$
$278$	−26.2489	−	10.5085i	−1.57430	−	0.630260i
$279$		0			0
$280$	10.9254	+	19.8658i	0.652916	+	1.18721i
$281$		−	13.6770i		−	0.815901i	−0.913004	−	0.407950i	$-0.866244\pi$
$281$		−	13.6770i		−	0.815901i	0.913004	−	0.407950i	$-0.133756\pi$
$282$		0			0
$283$	−3.90969	−	6.77179i	−0.232407	−	0.402541i	0.726109	−	0.687580i	$-0.241327\pi$
$283$	−3.90969	−	6.77179i	−0.232407	−	0.402541i	−0.958516	+	0.285039i	$0.907994\pi$
$284$	3.85332	+	3.67417i	0.228653	+	0.218022i
$285$		0			0
$286$	1.56217	+	10.8653i	0.0923730	+	0.642478i
$287$	11.5345	−	7.85766i	0.680859	−	0.463823i
$288$		0			0
$289$	13.9195	−	24.1093i	0.818795	−	1.41819i
$290$	24.5368	−	19.2959i	1.44085	−	1.13309i
$291$		0			0
$292$	1.85600	−	7.65042i	0.108614	−	0.447707i
$293$	−21.6555			−1.26513			−0.632563	−	0.774509i	$-0.717997\pi$
$293$	−21.6555			−1.26513			−0.632563	+	0.774509i	$0.717997\pi$
$294$		0			0
$295$		−	6.07955i		−	0.353965i
$296$	0.838501	−	8.78063i	0.0487369	−	0.510364i
$297$		0			0
$298$	−16.4621	+	12.9459i	−0.953622	+	0.749934i
$299$	12.0472	+	6.95544i	0.696706	+	0.402244i
$300$		0			0
$301$	−4.64942	−	6.82502i	−0.267988	−	0.393388i
$302$	6.03760	−	0.868064i	0.347425	−	0.0499515i
$303$		0			0
$304$	−4.71939	−	2.43306i	−0.270676	−	0.139546i
$305$	26.7807	−	15.4618i	1.53346	−	0.885342i
$306$		0			0
$307$	22.9124			1.30768			0.653840	−	0.756633i	$-0.273157\pi$
$307$	22.9124			1.30768			0.653840	+	0.756633i	$0.273157\pi$
$308$	9.00074	+	23.9114i	0.512865	+	1.36248i
$309$		0			0
$310$	−12.6769	+	31.6653i	−0.720001	+	1.79847i
$311$	11.0537	+	19.1456i	0.626798	+	1.08565i	0.988190	+	0.153233i	$0.0489684\pi$
$311$	11.0537	+	19.1456i	0.626798	+	1.08565i	−0.361392	+	0.932414i	$0.617698\pi$
$312$		0			0
$313$	5.12225	−	8.87199i	0.289527	−	0.501475i	−0.684170	−	0.729322i	$-0.739835\pi$
$313$	5.12225	−	8.87199i	0.289527	−	0.501475i	0.973697	+	0.227848i	$0.0731688\pi$
$314$	−22.6124	+	3.25113i	−1.27609	+	0.183472i
$315$		0			0
$316$	−1.73581	−	5.91172i	−0.0976471	−	0.332560i
$317$	2.77413	−	4.80494i	0.155811	−	0.269872i	−0.777543	−	0.628830i	$-0.783534\pi$
$317$	2.77413	−	4.80494i	0.155811	−	0.269872i	0.933354	+	0.358957i	$0.116868\pi$
$318$		0			0
$319$	30.4642	−	17.5885i	1.70567	−	0.984766i
$320$	−7.92694	−	22.9043i	−0.443130	−	1.28039i
$321$		0			0
$322$	30.8702	+	9.76555i	1.72033	+	0.544213i
$323$		−	8.88862i		−	0.494576i
$324$		0			0
$325$	−5.81767	+	3.35883i	−0.322706	+	0.186315i
$326$	13.9624	−	10.9801i	0.773305	−	0.608131i
$327$		0			0
$328$	−13.5720	+	6.19802i	−0.749387	+	0.342228i
$329$	−1.38590	+	0.103329i	−0.0764071	+	0.00569672i
$330$		0			0
$331$	12.6866	−	21.9739i	0.697320	−	1.20779i	−0.272072	−	0.962277i	$-0.587709\pi$
$331$	12.6866	−	21.9739i	0.697320	−	1.20779i	0.969392	−	0.245518i	$-0.0789579\pi$
$332$	−11.3545	+	11.9082i	−0.623160	+	0.653547i
$333$		0			0
$334$	−5.02617	−	2.01219i	−0.275020	−	0.110102i
$335$	−5.93566			−0.324300
$336$		0			0
$337$	18.5226			1.00899			0.504496	−	0.863414i	$-0.331678\pi$
$337$	18.5226			1.00899			0.504496	+	0.863414i	$0.331678\pi$
$338$	−13.6749	−	5.47464i	−0.743818	−	0.297781i
$339$		0			0
$340$	27.9996	−	29.3649i	1.51849	−	1.59253i
$341$	−19.2188	+	33.2880i	−1.04076	+	1.80264i
$342$		0			0
$343$	−18.0606	+	4.10056i	−0.975181	+	0.221409i
$344$	3.66740	+	8.03062i	0.197733	+	0.432982i
$345$		0			0
$346$	−11.4379	+	8.99486i	−0.614908	+	0.483567i
$347$	−18.4023	+	10.6246i	−0.987886	+	0.570356i	−0.904642	−	0.426173i	$-0.859862\pi$
$347$	−18.4023	+	10.6246i	−0.987886	+	0.570356i	−0.0832443	+	0.996529i	$0.526528\pi$
$348$		0			0
$349$			24.3533i			1.30360i	0.758391	+	0.651800i	$0.225986\pi$
$349$			24.3533i			1.30360i	−0.758391	+	0.651800i	$0.774014\pi$
$350$	−11.5378	+	10.5523i	−0.616720	+	0.564045i
$351$		0			0
$352$	−5.16883	−	26.8199i	−0.275500	−	1.42950i
$353$	−19.3242	+	11.1569i	−1.02853	+	0.593819i	−0.916562	−	0.399893i	$-0.869047\pi$
$353$	−19.3242	+	11.1569i	−1.02853	+	0.593819i	−0.111964	+	0.993712i	$0.535714\pi$
$354$		0			0
$355$	−4.03265	+	6.98476i	−0.214031	+	0.370712i
$356$	6.11658	+	20.8315i	0.324178	+	1.10406i
$357$		0			0
$358$	−14.4154	+	2.07260i	−0.761880	+	0.109540i
$359$	13.3275	−	23.0840i	0.703400	−	1.21833i	−0.263865	−	0.964560i	$-0.584997\pi$
$359$	13.3275	−	23.0840i	0.703400	−	1.21833i	0.967266	−	0.253766i	$-0.0816692\pi$
$360$		0			0
$361$	8.61899	+	14.9285i	0.453631	+	0.785712i
$362$	−7.52153	+	18.7878i	−0.395323	+	0.987463i
$363$		0			0
$364$	8.39287	+	1.38531i	0.439906	+	0.0726102i
$365$	11.9252			0.624194
$366$		0			0
$367$	3.73960	−	2.15906i	0.195206	−	0.112702i	−0.399212	−	0.916859i	$-0.630716\pi$
$367$	3.73960	−	2.15906i	0.195206	−	0.112702i	0.594417	+	0.804157i	$0.297383\pi$
$368$	−30.7657	−	15.8611i	−1.60377	−	0.826817i
$369$		0			0
$370$	13.2256	−	1.90153i	0.687568	−	0.0988559i
$371$	−11.4919	+	23.8400i	−0.596629	+	1.23771i
$372$		0			0
$373$	−9.70317	−	5.60213i	−0.502411	−	0.290067i	0.227298	−	0.973825i	$-0.427011\pi$
$373$	−9.70317	−	5.60213i	−0.502411	−	0.290067i	−0.729709	+	0.683758i	$0.760344\pi$
$374$	35.9415	−	28.2646i	1.85849	−	1.46153i
$375$		0			0
$376$	1.47897	+	0.141234i	0.0762722	+	0.00728357i
$377$		−	11.7119i		−	0.603191i
$378$		0			0
$379$	−28.2778			−1.45253			−0.726266	−	0.687414i	$-0.758746\pi$
$379$	−28.2778			−1.45253			−0.726266	+	0.687414i	$0.758746\pi$
$380$	1.89629	−	7.81647i	0.0972775	−	0.400976i
$381$		0			0
$382$	8.66312	−	6.81272i	0.443244	−	0.348569i
$383$	−11.5071	+	19.9308i	−0.587983	+	1.01842i	0.406513	+	0.913645i	$0.366745\pi$
$383$	−11.5071	+	19.9308i	−0.587983	+	1.01842i	−0.994496	+	0.104772i	$0.966589\pi$
$384$		0			0
$385$	−31.9860	+	21.7899i	−1.63016	+	1.11052i
$386$	1.22453	+	8.51692i	0.0623270	+	0.433500i
$387$		0			0
$388$	22.2412	+	21.2071i	1.12913	+	1.07663i
$389$	−15.4846	−	26.8201i	−0.785101	−	1.35983i	−0.928939	−	0.370233i	$-0.879278\pi$
$389$	−15.4846	−	26.8201i	−0.785101	−	1.35983i	0.143838	−	0.989601i	$-0.454056\pi$
$390$		0			0
$391$		−	57.9448i		−	2.93040i
$392$	19.7705	−	1.06139i	0.998562	−	0.0536082i
$393$		0			0
$394$	17.2623	+	6.91081i	0.869660	+	0.348161i
$395$	8.08285	−	4.66664i	0.406693	−	0.234804i
$396$		0			0
$397$	4.72823	+	2.72985i	0.237303	+	0.137007i	0.613937	−	0.789355i	$-0.289585\pi$
$397$	4.72823	+	2.72985i	0.237303	+	0.137007i	−0.376633	+	0.926362i	$0.622918\pi$
$398$	−26.7626	+	3.84783i	−1.34149	+	0.192874i
$399$		0			0
$400$	14.0617	−	9.03678i	0.703087	−	0.451839i
$401$	12.3944	+	7.15593i	0.618949	+	0.357350i	0.776460	−	0.630167i	$-0.217014\pi$
$401$	12.3944	+	7.15593i	0.618949	+	0.357350i	−0.157511	+	0.987517i	$0.550347\pi$
$402$		0			0
$403$	6.39873	+	11.0829i	0.318743	+	0.552080i
$404$	4.27754	−	17.6320i	0.212816	−	0.877223i
$405$		0			0
$406$	−5.87484	−	26.6192i	−0.291563	−	1.32109i
$407$	15.0575			0.746372
$408$		0			0
$409$	15.3274	+	26.5479i	0.757892	+	1.31271i	0.943924	+	0.330164i	$0.107104\pi$
$409$	15.3274	+	26.5479i	0.757892	+	1.31271i	−0.186031	+	0.982544i	$0.559563\pi$
$410$	−13.9713	−	17.7661i	−0.689995	−	0.877404i
$411$		0			0
$412$	−1.89963	−	6.46964i	−0.0935880	−	0.318736i
$413$	−4.78253	−	2.30539i	−0.235333	−	0.113441i
$414$		0			0
$415$	−21.5855	−	12.4624i	−1.05959	−	0.611754i
$416$	−8.59357	−	2.97436i	−0.421335	−	0.145830i
$417$		0			0
$418$	3.36878	−	8.41477i	0.164773	−	0.411580i
$419$		−	10.8994i		−	0.532471i	−0.963908	−	0.266235i	$-0.914220\pi$
$419$		−	10.8994i		−	0.532471i	0.963908	−	0.266235i	$-0.0857798\pi$
$420$		0			0
$421$			12.1339i			0.591368i	0.955286	+	0.295684i	$0.0955476\pi$
$421$			12.1339i			0.591368i	−0.955286	+	0.295684i	$0.904452\pi$
$422$	−12.9567	−	5.18713i	−0.630724	−	0.252505i
$423$		0			0
$424$	16.4114	−	23.0463i	0.797008	−	1.11923i
$425$	24.2331	+	13.9910i	1.17548	+	0.678662i
$426$		0			0
$427$	−2.00787	−	26.9305i	−0.0971675	−	1.30326i
$428$	−1.48825	−	5.06858i	−0.0719371	−	0.244999i
$429$		0			0
$430$	−10.5123	+	8.26692i	−0.506947	+	0.398666i
$431$	13.0047	+	22.5247i	0.626413	+	1.08498i	0.988266	+	0.152744i	$0.0488109\pi$
$431$	13.0047	+	22.5247i	0.626413	+	1.08498i	−0.361853	+	0.932235i	$0.617856\pi$
$432$		0			0
$433$	−8.47718			−0.407387			−0.203694	−	0.979035i	$-0.565295\pi$
$433$	−8.47718			−0.407387			−0.203694	+	0.979035i	$0.565295\pi$
$434$	20.1026	+	21.9800i	0.964957	+	1.05507i
$435$		0			0
$436$	−3.79568	−	0.920837i	−0.181780	−	0.0441001i
$437$	−5.74332	−	9.94772i	−0.274740	−	0.475864i
$438$		0			0
$439$	−17.5807	−	10.1502i	−0.839083	−	0.484445i	0.0178696	−	0.999840i	$-0.494312\pi$
$439$	−17.5807	−	10.1502i	−0.839083	−	0.484445i	−0.856952	+	0.515396i	$0.827645\pi$
$440$	37.6362	−	17.1876i	1.79423	−	0.819386i
$441$		0			0
$442$	−2.16648	−	15.0684i	−0.103049	−	0.716732i
$443$	−32.2709	−	18.6316i	−1.53324	−	0.885216i	−0.999210	−	0.0397494i	$-0.987344\pi$
$443$	−32.2709	−	18.6316i	−1.53324	−	0.885216i	−0.534029	−	0.845466i	$-0.679323\pi$
$444$		0			0
$445$	−28.4820	+	16.4441i	−1.35018	+	0.779525i
$446$	7.93789	−	19.8278i	0.375870	−	0.938873i
$447$		0			0
$448$	−21.0238	−	2.44958i	−0.993281	−	0.115732i
$449$		−	28.5853i		−	1.34902i	−0.738265	−	0.674511i	$-0.764354\pi$
$449$		−	28.5853i		−	1.34902i	0.738265	−	0.674511i	$-0.235646\pi$
$450$		0			0
$451$	−12.7351	−	22.0578i	−0.599672	−	1.03866i
$452$	3.78859	−	3.97333i	0.178200	−	0.186890i
$453$		0			0
$454$	−4.54980	+	0.654154i	−0.213533	+	0.0307010i
$455$	0.958071	+	12.8501i	0.0449150	+	0.602421i
$456$		0			0
$457$	5.19897	−	9.00489i	0.243198	−	0.421231i	−0.718426	−	0.695604i	$-0.755137\pi$
$457$	5.19897	−	9.00489i	0.243198	−	0.421231i	0.961623	+	0.274373i	$0.0884703\pi$
$458$	−1.81409	−	2.30681i	−0.0847669	−	0.107790i
$459$		0			0
$460$	12.3619	−	50.9555i	0.576376	−	2.37581i
$461$	40.9817			1.90871			0.954354	−	0.298678i	$-0.0965457\pi$
$461$	40.9817			1.90871			0.954354	+	0.298678i	$0.0965457\pi$
$462$		0			0
$463$		−	2.99890i		−	0.139371i	−0.997569	−	0.0696854i	$-0.977800\pi$
$463$		−	2.99890i		−	0.139371i	0.997569	−	0.0696854i	$-0.0221996\pi$
$464$	1.38640	+	29.1089i	0.0643619	+	1.35135i
$465$		0			0
$466$	−5.82009	−	7.40087i	−0.269610	−	0.342839i
$467$	22.1923	+	12.8127i	1.02694	+	0.592902i	0.916105	−	0.400938i	$-0.131316\pi$
$467$	22.1923	+	12.8127i	1.02694	+	0.592902i	0.110831	+	0.993839i	$0.464649\pi$
$468$		0			0
$469$	−2.25082	+	4.66934i	−0.103933	+	0.215610i
$470$	0.320286	+	2.22767i	0.0147737	+	0.102755i
$471$		0			0
$472$	4.62331	+	3.29229i	0.212805	+	0.151540i
$473$	−13.0517	+	7.53543i	−0.600120	+	0.346479i
$474$		0			0
$475$	5.54698			0.254513
$476$	−12.4826	−	33.1614i	−0.572140	−	1.51995i
$477$		0			0
$478$	4.62665	+	1.85224i	0.211618	+	0.0847197i
$479$	7.53048	+	13.0432i	0.344077	+	0.595958i	0.985186	−	0.171492i	$-0.0548587\pi$
$479$	7.53048	+	13.0432i	0.344077	+	0.595958i	−0.641109	+	0.767450i	$0.721525\pi$
$480$		0			0
$481$	2.50663	−	4.34161i	0.114292	−	0.197960i
$482$	−4.22968	−	29.4185i	−0.192657	−	1.33998i
$483$		0			0
$484$	23.6289	−	6.93796i	1.07404	−	0.315362i
$485$	−23.2763	+	40.3157i	−1.05692	+	1.83064i
$486$		0			0
$487$	−35.8325	+	20.6879i	−1.62373	+	0.937458i	−0.637814	+	0.770190i	$0.720161\pi$
$487$	−35.8325	+	20.6879i	−1.62373	+	0.937458i	−0.985911	+	0.167268i	$0.946506\pi$
$488$	−2.74442	+	28.7390i	−0.124234	+	1.30095i
$489$		0			0
$490$	8.62333	+	28.7256i	0.389562	+	1.29769i
$491$		−	12.6025i		−	0.568743i	−0.958714	−	0.284371i	$-0.908215\pi$
$491$		−	12.6025i		−	0.568743i	0.958714	−	0.284371i	$-0.0917848\pi$
$492$		0			0
$493$	−42.2490	+	24.3925i	−1.90280	+	1.09858i
$494$	−1.86547	−	2.37215i	−0.0839315	−	0.106728i
$495$		0			0
$496$	−17.2155	−	26.7883i	−0.772998	−	1.20283i
$497$	3.96543	+	5.82097i	0.177874	+	0.261106i
$498$		0			0
$499$	−20.6187	+	35.7126i	−0.923020	+	1.59872i	−0.128305	+	0.991735i	$0.540954\pi$
$499$	−20.6187	+	35.7126i	−0.923020	+	1.59872i	−0.794715	+	0.606983i	$0.792380\pi$
$500$	−3.60127	−	3.43383i	−0.161054	−	0.153566i
$501$		0			0
$502$	3.40523	−	8.50581i	0.151983	−	0.379633i
$503$	22.0912			0.984998			0.492499	−	0.870313i	$-0.336084\pi$
$503$	22.0912			0.984998			0.492499	+	0.870313i	$0.336084\pi$
$504$		0			0
$505$	27.4841			1.22303
$506$	21.9611	−	54.8558i	0.976288	−	2.43864i
$507$		0			0
$508$	−12.0124	+	12.5982i	−0.532966	+	0.558954i
$509$	8.21146	−	14.2227i	0.363967	−	0.630409i	−0.624643	−	0.780910i	$-0.714756\pi$
$509$	8.21146	−	14.2227i	0.363967	−	0.630409i	0.988610	+	0.150502i	$0.0480889\pi$
$510$		0			0
$511$	4.52208	−	9.38108i	0.200045	−	0.414994i
$512$	21.7107	+	6.37527i	0.959488	+	0.281750i
$513$		0			0
$514$	0.858682	+	1.09191i	0.0378748	+	0.0481620i
$515$	8.84568	−	5.10705i	0.389787	−	0.225044i
$516$		0			0
$517$			2.53622i			0.111543i
$518$	3.51935	−	11.1251i	0.154631	−	0.488810i
$519$		0			0
$520$	1.30952	−	13.7131i	0.0574263	−	0.601358i
$521$	−38.6770	+	22.3302i	−1.69447	+	0.978302i	−0.743642	+	0.668578i	$0.766903\pi$
$521$	−38.6770	+	22.3302i	−1.69447	+	0.978302i	−0.950826	+	0.309724i	$0.899763\pi$
$522$		0			0
$523$	9.50059	−	16.4555i	0.415432	−	0.719549i	−0.580042	−	0.814587i	$-0.696964\pi$
$523$	9.50059	−	16.4555i	0.415432	−	0.719549i	0.995474	+	0.0950376i	$0.0302971\pi$
$524$	3.03843	+	10.3481i	0.132734	+	0.452058i
$525$		0			0
$526$	2.23909	+	15.5735i	0.0976291	+	0.679035i
$527$	26.6535	−	46.1652i	1.16104	−	2.01099i
$528$		0			0
$529$	−25.9406	−	44.9305i	−1.12785	−	1.95350i
$530$	39.7882	+	15.9289i	1.72829	+	0.691906i
$531$		0			0
$532$	−5.42982	−	4.45577i	−0.235413	−	0.193182i
$533$	−8.48007			−0.367312
$534$		0			0
$535$	6.93006	−	4.00107i	0.299613	−	0.172981i
$536$	3.21437	−	4.51389i	0.138839	−	0.194970i
$537$		0			0
$538$	−0.563805	−	3.92141i	−0.0243074	−	0.169064i
$539$	5.01202	+	33.4249i	0.215883	+	1.43971i
$540$		0			0
$541$	−8.33522	−	4.81234i	−0.358359	−	0.206899i	0.310002	−	0.950736i	$-0.399670\pi$
$541$	−8.33522	−	4.81234i	−0.358359	−	0.206899i	−0.668361	+	0.743837i	$0.733004\pi$
$542$	−8.04320	−	10.2278i	−0.345485	−	0.439322i
$543$		0			0
$544$	7.16836	+	37.1949i	0.307341	+	1.59472i
$545$		−	5.91657i		−	0.253438i
$546$		0			0
$547$	18.2424			0.779990			0.389995	−	0.920817i	$-0.372477\pi$
$547$	18.2424			0.779990			0.389995	+	0.920817i	$0.372477\pi$
$548$	22.3323	+	5.41784i	0.953987	+	0.231439i
$549$		0			0
$550$	17.6386	+	22.4295i	0.752114	+	0.956395i
$551$	−4.83542	+	8.37519i	−0.205996	+	0.356795i
$552$		0			0
$553$	−0.606008	−	8.12806i	−0.0257701	−	0.345640i
$554$	−23.8212	+	3.42492i	−1.01207	+	0.145511i
$555$		0			0
$556$	28.9390	+	27.5935i	1.22729	+	1.17022i
$557$	7.03565	+	12.1861i	0.298110	+	0.516342i	0.975704	−	0.219095i	$-0.0703104\pi$
$557$	7.03565	+	12.1861i	0.298110	+	0.516342i	−0.677593	+	0.735437i	$0.736977\pi$
$558$		0			0
$559$			5.01771i			0.212226i
$560$	−3.90234	−	31.8245i	−0.164904	−	1.34483i
$561$		0			0
$562$	−7.18880	+	17.9566i	−0.303241	+	0.757455i
$563$	23.7510	−	13.7126i	1.00098	−	0.577919i	0.0924453	−	0.995718i	$-0.470532\pi$
$563$	23.7510	−	13.7126i	1.00098	−	0.577919i	0.908540	+	0.417799i	$0.137198\pi$
$564$		0			0
$565$	7.20228	+	4.15824i	0.303002	+	0.174938i
$566$	1.57374	+	10.9457i	0.0661491	+	0.460083i
$567$		0			0
$568$	−3.12788	−	6.84920i	−0.131243	−	0.287386i
$569$	−25.9776	−	14.9982i	−1.08904	−	0.628757i	−0.155719	−	0.987801i	$-0.549769\pi$
$569$	−25.9776	−	14.9982i	−1.08904	−	0.628757i	−0.933321	+	0.359044i	$0.883103\pi$
$570$		0			0
$571$	17.1948	+	29.7823i	0.719580	+	1.24635i	0.961166	+	0.275970i	$0.0889990\pi$
$571$	17.1948	+	29.7823i	0.719580	+	1.24635i	−0.241586	+	0.970379i	$0.577668\pi$
$572$	3.65994	−	15.0862i	0.153030	−	0.630787i
$573$		0			0
$574$	−19.2738	+	4.25372i	−0.804474	+	0.177547i
$575$	36.1607			1.50801
$576$		0			0
$577$	−10.8158	−	18.7335i	−0.450267	−	0.779886i	0.548135	−	0.836390i	$-0.315338\pi$
$577$	−10.8158	−	18.7335i	−0.450267	−	0.779886i	−0.998402	+	0.0565040i	$0.982005\pi$
$578$	−30.9472	+	24.3371i	−1.28723	+	1.01229i
$579$		0			0
$580$	−42.3568	+	12.4369i	−1.75877	+	0.516413i
$581$	−17.9889	+	12.2546i	−0.746307	+	0.508408i
$582$		0			0
$583$	41.8271	+	24.1489i	1.73230	+	1.00015i
$584$	−6.45792	+	9.06876i	−0.267231	+	0.375268i
$585$		0			0
$586$	28.4317	+	11.3824i	1.17450	+	0.470202i
$587$			42.7677i			1.76521i	0.470112	+	0.882607i	$0.344214\pi$
$587$			42.7677i			1.76521i	−0.470112	+	0.882607i	$0.655786\pi$
$588$		0			0
$589$		−	10.5673i		−	0.435416i
$590$	−3.19549	+	7.98190i	−0.131556	+	0.328609i
$591$		0			0
$592$	−5.71608	+	11.0874i	−0.234930	+	0.455691i
$593$	13.7540	+	7.94088i	0.564810	+	0.326093i	0.755074	−	0.655640i	$-0.227601\pi$
$593$	13.7540	+	7.94088i	0.564810	+	0.326093i	−0.190264	+	0.981733i	$0.560934\pi$
$594$		0			0
$595$	44.3596	−	30.2192i	1.81857	−	1.23887i
$596$	28.4177	−	8.34407i	1.16404	−	0.341787i
$597$		0			0
$598$	−12.1610	−	15.4640i	−0.497300	−	0.632371i
$599$	20.2047	+	34.9955i	0.825540	+	1.42988i	0.901506	+	0.432766i	$0.142463\pi$
$599$	20.2047	+	34.9955i	0.825540	+	1.42988i	−0.0759664	+	0.997110i	$0.524204\pi$
$600$		0			0
$601$	−32.2427			−1.31521			−0.657604	−	0.753364i	$-0.728430\pi$
$601$	−32.2427			−1.31521			−0.657604	+	0.753364i	$0.728430\pi$
$602$	2.51695	+	11.4044i	0.102583	+	0.464810i
$603$		0			0
$604$	−8.38309	−	2.03375i	−0.341103	−	0.0827522i
$605$	18.6523	+	32.3068i	0.758325	+	1.31346i
$606$		0			0
$607$	−29.2976	−	16.9150i	−1.18915	−	0.686557i	−0.231038	−	0.972945i	$-0.574212\pi$
$607$	−29.2976	−	16.9150i	−1.18915	−	0.686557i	−0.958114	+	0.286387i	$0.907546\pi$
$608$	4.91729	+	5.67496i	0.199422	+	0.230150i
$609$		0			0
$610$	−43.2876	+	6.22372i	−1.75266	+	0.251991i
$611$	0.731282	+	0.422206i	0.0295845	+	0.0170806i
$612$		0			0
$613$	6.60745	−	3.81481i	0.266872	−	0.154079i	−0.360593	−	0.932723i	$-0.617426\pi$
$613$	6.60745	−	3.81481i	0.266872	−	0.154079i	0.627465	+	0.778644i	$0.284092\pi$
$614$	−30.0819	−	12.0431i	−1.21401	−	0.486018i
$615$		0			0
$616$	0.750986	−	36.1244i	0.0302581	−	1.45549i
$617$			38.5471i			1.55185i	0.630827	+	0.775923i	$0.282716\pi$
$617$			38.5471i			1.55185i	−0.630827	+	0.775923i	$0.717284\pi$
$618$		0			0
$619$	−6.10624	−	10.5763i	−0.245430	−	0.425098i	0.716822	−	0.697256i	$-0.245596\pi$
$619$	−6.10624	−	10.5763i	−0.245430	−	0.425098i	−0.962253	+	0.272158i	$0.912263\pi$
$620$	33.2873	−	34.9105i	1.33685	−	1.40204i
$621$		0			0
$622$	−4.44936	−	30.9464i	−0.178403	−	1.24084i
$623$	2.13542	+	28.6413i	0.0855539	+	1.14749i
$624$		0			0
$625$	14.2158	−	24.6226i	0.568633	−	0.984902i
$626$	−11.3883	+	8.95581i	−0.455167	+	0.357946i
$627$		0			0
$628$	31.3969	+	7.61694i	1.25287	+	0.303949i
$629$	−20.8824			−0.832635
$630$		0			0
$631$		−	26.6937i		−	1.06266i	−0.847165	−	0.531331i	$-0.821692\pi$
$631$		−	26.6937i		−	1.06266i	0.847165	−	0.531331i	$-0.178308\pi$
$632$	−0.828310	+	8.67392i	−0.0329484	+	0.345030i
$633$		0			0
$634$	−6.16772	+	4.85033i	−0.244951	+	0.192631i
$635$	−22.8362	−	13.1845i	−0.906227	−	0.523210i
$636$		0			0
$637$	10.4719	+	4.11912i	0.414914	+	0.163206i
$638$	−49.2414	+	7.07975i	−1.94949	+	0.280290i
$639$		0			0
$640$	−1.63142	+	34.2377i	−0.0644875	+	1.35337i
$641$	−7.61117	+	4.39431i	−0.300623	+	0.173565i	−0.642723	−	0.766099i	$-0.722195\pi$
$641$	−7.61117	+	4.39431i	−0.300623	+	0.173565i	0.342100	+	0.939664i	$0.388862\pi$
$642$		0			0
$643$	−15.1116			−0.595943			−0.297972	−	0.954575i	$-0.596310\pi$
$643$	−15.1116			−0.595943			−0.297972	+	0.954575i	$0.596310\pi$
$644$	−35.3969	−	29.0471i	−1.39483	−	1.14462i
$645$		0			0
$646$	−4.67197	+	11.6700i	−0.183816	+	0.459148i
$647$	−20.1893	−	34.9689i	−0.793724	−	1.37477i	−0.923646	−	0.383246i	$-0.874806\pi$
$647$	−20.1893	−	34.9689i	−0.793724	−	1.37477i	0.129923	−	0.991524i	$-0.458527\pi$
$648$		0			0
$649$	−4.84451	+	8.39093i	−0.190163	+	0.329373i
$650$	9.40352	−	1.35200i	0.368836	−	0.0530299i
$651$		0			0
$652$	−24.1026	+	7.07707i	−0.943932	+	0.277159i
$653$	−2.88547	+	4.99777i	−0.112917	+	0.195578i	−0.916945	−	0.399013i	$-0.869353\pi$
$653$	−2.88547	+	4.99777i	−0.112917	+	0.195578i	0.804028	+	0.594591i	$0.202686\pi$
$654$		0			0
$655$	−14.1485	+	8.16865i	−0.552828	+	0.319176i
$656$	21.0765	−	1.00383i	0.822900	−	0.0391931i
$657$		0			0
$658$	1.87387	+	0.592784i	0.0730511	+	0.0231091i
$659$		−	9.31457i		−	0.362844i	−0.983405	−	0.181422i	$-0.941930\pi$
$659$		−	9.31457i		−	0.362844i	0.983405	−	0.181422i	$-0.0580700\pi$
$660$		0			0
$661$	6.32010	−	3.64891i	0.245823	−	0.141926i	−0.372027	−	0.928222i	$-0.621337\pi$
$661$	6.32010	−	3.64891i	0.245823	−	0.141926i	0.617850	+	0.786296i	$0.288004\pi$
$662$	−28.2062	+	22.1815i	−1.09626	+	0.862108i
$663$		0			0
$664$	21.1666	−	9.66629i	0.821422	−	0.375125i
$665$	4.62023	−	9.58470i	0.179165	−	0.371679i
$666$		0			0
$667$	−31.5220	+	54.5978i	−1.22054	+	2.11403i
$668$	5.54128	+	5.28364i	0.214398	+	0.204430i
$669$		0			0
$670$	7.79298	+	3.11986i	0.301069	+	0.120531i
$671$	−49.2832			−1.90256
$672$		0			0
$673$	−14.4504			−0.557022			−0.278511	−	0.960433i	$-0.589841\pi$
$673$	−14.4504			−0.557022			−0.278511	+	0.960433i	$0.589841\pi$
$674$	−24.3185	−	9.73573i	−0.936715	−	0.375006i
$675$		0			0
$676$	15.0764	+	14.3754i	0.579861	+	0.552901i
$677$	13.0719	−	22.6412i	0.502393	−	0.870170i	−0.497603	−	0.867405i	$-0.665786\pi$
$677$	13.0719	−	22.6412i	0.502393	−	0.870170i	0.999996	−	0.00276538i	$-0.000880250\pi$
$678$		0			0
$679$	22.8883	+	33.5983i	0.878371	+	1.28939i
$680$	−52.1954	+	23.8365i	−2.00160	+	0.914088i
$681$		0			0
$682$	42.7291	−	33.6024i	1.63618	−	1.28670i
$683$	−9.86031	+	5.69285i	−0.377294	+	0.217831i	−0.676640	−	0.736314i	$-0.736565\pi$
$683$	−9.86031	+	5.69285i	−0.377294	+	0.217831i	0.299346	+	0.954145i	$0.403231\pi$
$684$		0			0
$685$			34.8108i			1.33005i
$686$	25.8672	+	4.10922i	0.987616	+	0.156891i
$687$		0			0
$688$	−0.593973	−	12.4711i	−0.0226450	−	0.475456i
$689$	13.9260	−	8.04016i	0.530537	−	0.306306i
$690$		0			0
$691$	−3.65218	+	6.32576i	−0.138935	+	0.240643i	−0.927094	−	0.374829i	$-0.877701\pi$
$691$	−3.65218	+	6.32576i	−0.138935	+	0.240643i	0.788158	+	0.615472i	$0.211035\pi$
$692$	19.7448	−	5.79751i	0.750584	−	0.220388i
$693$		0			0
$694$	29.7449	−	4.27662i	1.12910	−	0.162338i
$695$	−30.2858	+	52.4565i	−1.14881	+	1.98979i
$696$		0			0
$697$	17.6616	+	30.5907i	0.668979	+	1.15871i
$698$	12.8004	−	31.9736i	0.484502	−	1.21022i
$699$		0			0
$700$	20.6945	−	7.78982i	0.782178	−	0.294428i
$701$	8.29346			0.313240			0.156620	−	0.987659i	$-0.449940\pi$
$701$	8.29346			0.313240			0.156620	+	0.987659i	$0.449940\pi$
$702$		0			0
$703$	−3.58500	+	2.06980i	−0.135211	+	0.0780640i
$704$	−7.31065	+	37.9289i	−0.275531	+	1.42950i
$705$		0			0
$706$	31.2352	−	4.49088i	1.17555	−	0.169016i
$707$	10.4221	−	21.6206i	0.391962	−	0.813128i
$708$		0			0
$709$	−4.76772	−	2.75264i	−0.179055	−	0.103378i	0.407793	−	0.913074i	$-0.366298\pi$
$709$	−4.76772	−	2.75264i	−0.179055	−	0.103378i	−0.586849	+	0.809697i	$0.699632\pi$
$710$	8.96578	−	7.05074i	0.336480	−	0.264610i
$711$		0			0
$712$	2.91876	−	30.5648i	0.109385	−	1.14546i
$713$		−	68.8878i		−	2.57987i
$714$		0			0
$715$	23.5159			0.879445
$716$	20.0156	+	4.85581i	0.748017	+	0.181470i
$717$		0			0
$718$	−29.6311	+	23.3020i	−1.10582	+	0.869624i
$719$	5.21376	−	9.03049i	0.194440	−	0.336781i	−0.752277	−	0.658847i	$-0.771044\pi$
$719$	5.21376	−	9.03049i	0.194440	−	0.336781i	0.946717	+	0.322067i	$0.104378\pi$
$720$		0			0
$721$	−0.663200	−	8.89515i	−0.0246989	−	0.331273i
$722$	−3.46933	−	24.1300i	−0.129115	−	0.898027i
$723$		0			0
$724$	19.7502	−	20.7132i	0.734009	−	0.769801i
$725$	−15.2222	−	26.3657i	−0.565339	−	0.979196i
$726$		0			0
$727$			2.87016i			0.106449i	0.998583	+	0.0532243i	$0.0169498\pi$
$727$			2.87016i			0.106449i	−0.998583	+	0.0532243i	$0.983050\pi$
$728$	−10.2909	−	6.23019i	−0.381407	−	0.230906i
$729$		0			0
$730$	−15.6567	−	6.26804i	−0.579481	−	0.231991i
$731$	18.1007	−	10.4505i	0.669479	−	0.386524i
$732$		0			0
$733$	31.8440	+	18.3851i	1.17618	+	0.679071i	0.955129	−	0.296191i	$-0.0957164\pi$
$733$	31.8440	+	18.3851i	1.17618	+	0.679071i	0.221056	+	0.975261i	$0.429050\pi$
$734$	−6.04459	+	0.869069i	−0.223110	+	0.0320779i
$735$		0			0
$736$	32.0557	+	36.9950i	1.18159	+	1.36365i
$737$	8.19233	+	4.72985i	0.301768	+	0.174226i
$738$		0			0
$739$	10.0420	+	17.3933i	0.369402	+	0.639823i	0.989472	−	0.144723i	$-0.0462292\pi$
$739$	10.0420	+	17.3933i	0.369402	+	0.639823i	−0.620070	+	0.784546i	$0.712896\pi$
$740$	−18.3635	−	4.45502i	−0.675057	−	0.163770i
$741$		0			0
$742$	27.6184	−	25.2594i	1.01390	−	0.927303i
$743$	−36.5185			−1.33973			−0.669866	−	0.742482i	$-0.733649\pi$
$743$	−36.5185			−1.33973			−0.669866	+	0.742482i	$0.733649\pi$
$744$		0			0
$745$	22.4326	+	38.8544i	0.821867	+	1.42352i
$746$	9.79483	+	12.4552i	0.358614	+	0.456017i
$747$		0			0
$748$	−62.0442	+	18.2176i	−2.26856	+	0.666100i
$749$	−0.519577	−	6.96881i	−0.0189849	−	0.254635i
$750$		0			0
$751$	−24.5567	−	14.1778i	−0.896087	−	0.517356i	−0.0201583	−	0.999797i	$-0.506417\pi$
$751$	−24.5567	−	14.1778i	−0.896087	−	0.517356i	−0.875929	+	0.482441i	$0.839750\pi$
$752$	−1.86752	−	0.962794i	−0.0681016	−	0.0351095i
$753$		0			0
$754$	−6.15590	+	15.3766i	−0.224185	+	0.559983i
$755$		−	13.0673i		−	0.475567i
$756$		0			0
$757$		−	10.5981i		−	0.385195i	−0.981278	−	0.192598i	$-0.938309\pi$
$757$		−	10.5981i		−	0.385195i	0.981278	−	0.192598i	$-0.0616912\pi$
$758$	37.1262	+	14.8632i	1.34848	+	0.539854i
$759$		0			0
$760$	−6.59809	+	9.26561i	−0.239338	+	0.336099i
$761$	5.63447	+	3.25306i	0.204249	+	0.117923i	0.598636	−	0.801021i	$-0.295710\pi$
$761$	5.63447	+	3.25306i	0.204249	+	0.117923i	−0.394387	+	0.918945i	$0.629043\pi$
$762$		0			0
$763$	−4.65433	−	2.24359i	−0.168498	−	0.0812232i
$764$	−14.9547	+	4.39104i	−0.541044	+	0.158862i
$765$		0			0
$766$	25.5836	−	20.1191i	0.924374	−	0.726932i
$767$	1.61293	+	2.79368i	0.0582397	+	0.100874i
$768$		0			0
$769$	−12.9001			−0.465190			−0.232595	−	0.972574i	$-0.574722\pi$
$769$	−12.9001			−0.465190			−0.232595	+	0.972574i	$0.574722\pi$
$770$	53.4478	−	11.7959i	1.92613	−	0.425095i
$771$		0			0
$772$	2.86890	−	11.8256i	0.103254	−	0.425612i
$773$	−14.8497	−	25.7204i	−0.534105	−	0.925097i	−0.999206	−	0.0398394i	$-0.987315\pi$
$773$	−14.8497	−	25.7204i	−0.534105	−	0.925097i	0.465101	−	0.885258i	$-0.346018\pi$
$774$		0			0
$775$	28.8096	+	16.6332i	1.03487	+	0.597482i
$776$	−18.0539	−	39.5333i	−0.648099	−	1.41916i
$777$		0			0
$778$	6.23289	+	43.3513i	0.223460	+	1.55422i
$779$	6.06413	+	3.50112i	0.217270	+	0.125441i
$780$		0			0
$781$	11.1316	−	6.42686i	0.398322	−	0.229971i
$782$	−30.4565	+	76.0763i	−1.08912	+	2.72048i
$783$		0			0
$784$	−26.5148	−	8.99813i	−0.946957	−	0.321362i
$785$			48.9405i			1.74676i
$786$		0			0
$787$	−26.2104	−	45.3978i	−0.934302	−	1.61826i	−0.775875	−	0.630887i	$-0.782691\pi$
$787$	−26.2104	−	45.3978i	−0.934302	−	1.61826i	−0.158427	−	0.987371i	$-0.550642\pi$
$788$	−19.0314	−	18.1465i	−0.677965	−	0.646443i
$789$		0			0
$790$	−13.0649	+	1.87842i	−0.464828	+	0.0668313i
$791$	6.00225	−	4.08892i	0.213415	−	0.145385i
$792$		0			0
$793$	−8.20421	+	14.2101i	−0.291340	+	0.504616i
$794$	−4.77290	−	6.06926i	−0.169384	−	0.215390i
$795$		0			0
$796$	37.1594	+	9.01492i	1.31708	+	0.319525i
$797$	53.8960			1.90909			0.954547	−	0.298061i	$-0.0963400\pi$
$797$	53.8960			1.90909			0.954547	+	0.298061i	$0.0963400\pi$
$798$		0			0
$799$		−	3.51734i		−	0.124435i
$800$	−23.2116	+	4.47344i	−0.820656	+	0.158160i
$801$		0			0
$802$	−12.5115	−	15.9098i	−0.441797	−	0.561793i
$803$	−16.4591	−	9.50264i	−0.580827	−	0.335341i
$804$		0			0
$805$	30.1193	−	62.4825i	1.06156	−	2.20222i
$806$	−2.57563	−	17.9141i	−0.0907226	−	0.630998i
$807$		0			0
$808$	−14.8836	+	20.9009i	−0.523604	+	0.735289i
$809$	−14.8536	+	8.57571i	−0.522223	+	0.301506i	−0.737844	−	0.674971i	$-0.764156\pi$
$809$	−14.8536	+	8.57571i	−0.522223	+	0.301506i	0.215620	+	0.976477i	$0.430823\pi$
$810$		0			0
$811$	−19.1733			−0.673265			−0.336632	−	0.941636i	$-0.609288\pi$
$811$	−19.1733			−0.673265			−0.336632	+	0.941636i	$0.609288\pi$
$812$	−6.27824	+	38.0364i	−0.220323	+	1.33482i
$813$		0			0
$814$	−19.7691	−	7.91441i	−0.692907	−	0.277400i
$815$	−19.0263	−	32.9546i	−0.666463	−	1.15435i
$816$		0			0
$817$	2.07164	−	3.58818i	0.0724774	−	0.125534i
$818$	−6.16962	−	42.9112i	−0.215716	−	1.50036i
$819$		0			0
$820$	9.00503	+	30.6687i	0.314469	+	1.07100i
$821$	−10.2803	+	17.8060i	−0.358784	+	0.621433i	−0.987758	−	0.155994i	$-0.950142\pi$
$821$	−10.2803	+	17.8060i	−0.358784	+	0.621433i	0.628974	+	0.777427i	$0.283475\pi$
$822$		0			0
$823$	−5.04464	+	2.91252i	−0.175845	+	0.101524i	−0.585339	−	0.810789i	$-0.699039\pi$
$823$	−5.04464	+	2.91252i	−0.175845	+	0.101524i	0.409494	+	0.912313i	$0.365705\pi$
$824$	−0.906483	+	9.49252i	−0.0315788	+	0.330688i
$825$		0			0
$826$	5.06729	+	5.54052i	0.176314	+	0.192779i
$827$		−	24.8558i		−	0.864321i	−0.901797	−	0.432160i	$-0.857751\pi$
$827$		−	24.8558i		−	0.864321i	0.901797	−	0.432160i	$-0.142249\pi$
$828$		0			0
$829$	−7.94223	+	4.58545i	−0.275845	+	0.159259i	−0.631541	−	0.775343i	$-0.717577\pi$
$829$	−7.94223	+	4.58545i	−0.275845	+	0.159259i	0.355696	+	0.934602i	$0.384244\pi$
$830$	21.7894	+	27.7076i	0.756321	+	0.961744i
$831$		0			0
$832$	9.71922	+	8.42196i	0.336953	+	0.291979i
$833$	−6.95088	−	46.3551i	−0.240834	−	1.60611i
$834$		0			0
$835$	−5.79916	+	10.0444i	−0.200688	+	0.347602i
$836$	−8.84582	+	9.27715i	−0.305939	+	0.320857i
$837$		0			0
$838$	−5.72886	+	14.3099i	−0.197900	+	0.494328i
$839$	8.32235			0.287319			0.143660	−	0.989627i	$-0.454113\pi$
$839$	8.32235			0.287319			0.143660	+	0.989627i	$0.454113\pi$
$840$		0			0
$841$	24.0781			0.830280
$842$	6.37771	−	15.9307i	0.219790	−	0.549007i
$843$		0			0
$844$	14.2846	+	13.6205i	0.491697	+	0.468835i
$845$	−15.7780	+	27.3283i	−0.542781	+	0.940124i
$846$		0			0
$847$	32.4875	−	2.42218i	1.11628	−	0.0832273i
$848$	−33.6601	+	21.6317i	−1.15589	+	0.742834i
$849$		0			0
$850$	−24.4620	−	31.1061i	−0.839041	−	1.06693i
$851$	−23.3706	+	13.4930i	−0.801132	+	0.462534i
$852$		0			0
$853$		−	38.7335i		−	1.32621i	−0.748527	−	0.663104i	$-0.769239\pi$
$853$		−	38.7335i		−	1.32621i	0.748527	−	0.663104i	$-0.230761\pi$
$854$	−11.5188	+	36.4126i	−0.394167	+	1.24601i
$855$		0			0
$856$	−0.710175	+	7.43682i	−0.0242733	+	0.254185i
$857$	−17.2269	+	9.94596i	−0.588460	+	0.339747i	−0.764488	−	0.644638i	$-0.777008\pi$
$857$	−17.2269	+	9.94596i	−0.588460	+	0.339747i	0.176028	+	0.984385i	$0.443675\pi$
$858$		0			0
$859$	10.0234	−	17.3611i	0.341995	−	0.592353i	−0.642808	−	0.766027i	$-0.722231\pi$
$859$	10.0234	−	17.3611i	0.341995	−	0.592353i	0.984803	+	0.173675i	$0.0555641\pi$
$860$	18.1469	−	5.32833i	0.618803	−	0.181694i
$861$		0			0
$862$	−5.23466	−	36.4084i	−0.178293	−	1.24007i
$863$	22.1555	−	38.3745i	0.754183	−	1.30628i	−0.191596	−	0.981474i	$-0.561366\pi$
$863$	22.1555	−	38.3745i	0.754183	−	1.30628i	0.945779	−	0.324810i	$-0.105300\pi$
$864$		0			0
$865$	15.5863	+	26.9963i	0.529950	+	0.917900i
$866$	11.1298	+	4.45571i	0.378205	+	0.151411i
$867$		0			0
$868$	−14.8400	−	39.4240i	−0.503702	−	1.33814i
$869$	−14.8745			−0.504583
$870$		0			0
$871$	2.72756	−	1.57476i	0.0924200	−	0.0533587i
$872$	4.49938	+	3.20403i	0.152368	+	0.108502i
$873$		0			0
$874$	2.31181	+	16.0792i	0.0781982	+	0.543888i
$875$	−3.70604	−	5.44021i	−0.125287	−	0.183913i
$876$		0			0
$877$	20.0853	+	11.5963i	0.678234	+	0.391578i	0.799189	−	0.601080i	$-0.205263\pi$
$877$	20.0853	+	11.5963i	0.678234	+	0.391578i	−0.120956	+	0.992658i	$0.538596\pi$
$878$	17.7468	+	22.5670i	0.598926	+	0.761600i
$879$		0			0
$880$	−58.4469	+	2.78371i	−1.97024	+	0.0938387i
$881$		−	29.5929i		−	0.997009i	−0.866887	−	0.498504i	$-0.833883\pi$
$881$		−	29.5929i		−	0.997009i	0.866887	−	0.498504i	$-0.166117\pi$
$882$		0			0
$883$	−42.0898			−1.41643			−0.708217	−	0.705995i	$-0.750500\pi$
$883$	−42.0898			−1.41643			−0.708217	+	0.705995i	$0.750500\pi$
$884$	−5.07576	+	20.9222i	−0.170716	+	0.703691i
$885$		0			0
$886$	32.5758	+	41.4237i	1.09441	+	1.39166i
$887$	10.5593	−	18.2892i	0.354545	−	0.614090i	−0.632495	−	0.774564i	$-0.717969\pi$
$887$	10.5593	−	18.2892i	0.354545	−	0.614090i	0.987040	+	0.160475i	$0.0513025\pi$
$888$		0			0
$889$	−19.0313	+	12.9647i	−0.638288	+	0.434822i
$890$	46.0375	−	6.61910i	1.54318	−	0.221873i
$891$		0			0
$892$	−20.8435	+	21.8598i	−0.697891	+	0.731921i
$893$	−0.348628	−	0.603842i	−0.0116664	−	0.0202068i
$894$		0			0
$895$			31.1996i			1.04289i
$896$	26.3148	+	14.2664i	0.879116	+	0.476608i
$897$		0			0
$898$	−15.0248	+	37.5299i	−0.501383	+	1.25239i
$899$	−50.2278	+	28.9990i	−1.67519	+	0.967172i
$900$		0			0
$901$	−58.0076	−	33.4907i	−1.93251	−	1.11574i
$902$	5.12615	+	35.6536i	0.170682	+	1.18714i
$903$		0			0
$904$	−7.06250	+	3.22529i	−0.234895	+	0.107271i
$905$	37.5460	+	21.6772i	1.24807	+	0.720574i
$906$		0			0
$907$	−1.86594	−	3.23191i	−0.0619576	−	0.107314i	0.833383	−	0.552696i	$-0.186401\pi$
$907$	−1.86594	−	3.23191i	−0.0619576	−	0.107314i	−0.895340	+	0.445383i	$0.853068\pi$
$908$	6.31731	+	1.53259i	0.209647	+	0.0508608i
$909$		0			0
$910$	5.49631	−	17.3746i	0.182201	−	0.575962i
$911$	−41.8668			−1.38711			−0.693554	−	0.720405i	$-0.743956\pi$
$911$	−41.8668			−1.38711			−0.693554	+	0.720405i	$0.743956\pi$
$912$		0			0
$913$	19.8614	+	34.4009i	0.657315	+	1.13850i
$914$	−11.5589	+	9.08996i	−0.382333	+	0.300669i
$915$		0			0
$916$	1.16925	+	3.98215i	0.0386330	+	0.131574i
$917$	1.06078	+	14.2276i	0.0350300	+	0.469838i
$918$		0			0
$919$	43.1798	+	24.9299i	1.42437	+	0.822361i	0.996669	−	0.0815583i	$-0.0259897\pi$
$919$	43.1798	+	24.9299i	1.42437	+	0.822361i	0.427703	+	0.903919i	$0.359323\pi$
$920$	−43.0129	+	60.4024i	−1.41809	+	1.99141i
$921$		0			0
$922$	−53.8053	−	21.5405i	−1.77198	−	0.709399i
$923$		−	4.27953i		−	0.140862i
$924$		0			0
$925$		−	13.0317i		−	0.428481i
$926$	−1.57626	+	3.93729i	−0.0517992	+	0.129387i
$927$		0			0
$928$	13.4798	−	38.9460i	0.442496	−	1.27847i
$929$	31.3597	+	18.1055i	1.02888	+	0.594023i	0.916663	−	0.399662i	$-0.130872\pi$
$929$	31.3597	+	18.1055i	1.02888	+	0.594023i	0.112214	+	0.993684i	$0.464206\pi$
$930$		0			0
$931$	−5.78788	−	7.26910i	−0.189690	−	0.238235i
$932$	3.75125	+	12.7758i	0.122876	+	0.418485i
$933$		0			0
$934$	−22.4019	−	28.4865i	−0.733013	−	0.932106i
$935$	−48.9769	−	84.8305i	−1.60172	−	2.77425i
$936$		0			0
$937$	−7.48145			−0.244408			−0.122204	−	0.992505i	$-0.538996\pi$
$937$	−7.48145			−0.244408			−0.122204	+	0.992505i	$0.538996\pi$
$938$	5.40939	−	4.94736i	0.176623	−	0.161537i
$939$		0			0
$940$	0.750385	−	3.09308i	0.0244749	−	0.100885i
$941$	−12.6093	−	21.8400i	−0.411052	−	0.711962i	0.583953	−	0.811787i	$-0.301505\pi$
$941$	−12.6093	−	21.8400i	−0.411052	−	0.711962i	−0.995005	+	0.0998249i	$0.968172\pi$
$942$		0			0
$943$	39.5320	+	22.8238i	1.28734	+	0.743245i
$944$	−4.33952	−	6.75255i	−0.141239	−	0.219777i
$945$		0			0
$946$	21.0965	−	3.03317i	0.685905	−	0.0986169i
$947$	17.0310	+	9.83284i	0.553432	+	0.319524i	0.750505	−	0.660865i	$-0.229810\pi$
$947$	17.0310	+	9.83284i	0.553432	+	0.319524i	−0.197073	+	0.980389i	$0.563144\pi$
$948$		0			0
$949$	−5.47989	+	3.16382i	−0.177885	+	0.102702i
$950$	−7.28268	−	2.91556i	−0.236281	−	0.0945934i
$951$		0			0
$952$	−1.04150	+	50.0989i	−0.0337552	+	1.62371i
$953$			17.1948i			0.556993i	0.960437	+	0.278496i	$0.0898361\pi$
$953$			17.1948i			0.556993i	−0.960437	+	0.278496i	$0.910164\pi$
$954$		0			0
$955$	−11.8051	−	20.4470i	−0.382004	−	0.661650i
$956$	−5.10082	−	4.86366i	−0.164972	−	0.157302i
$957$		0			0
$958$	−3.03118	−	21.0826i	−0.0979331	−	0.681149i
$959$	27.3842	+	13.2004i	0.884283	+	0.426262i
$960$		0			0
$961$	16.1870	−	28.0367i	0.522162	−	0.904411i
$962$	−5.57298	+	4.38262i	−0.179680	+	0.141301i
$963$		0			0
$964$	−9.90955	+	40.8470i	−0.319165	+	1.31559i
$965$	18.4333			0.593389
$966$		0			0
$967$			39.0833i			1.25683i	0.777877	+	0.628417i	$0.216297\pi$
$967$			39.0833i			1.25683i	−0.777877	+	0.628417i	$0.783703\pi$
$968$	−34.6692	−	3.31072i	−1.11431	−	0.106411i
$969$		0			0
$970$	51.7501	−	40.6965i	1.66159	−	1.30669i
$971$	19.3986	+	11.1998i	0.622531	+	0.359418i	0.777854	−	0.628446i	$-0.216309\pi$
$971$	19.3986	+	11.1998i	0.622531	+	0.359418i	−0.155323	+	0.987864i	$0.549642\pi$
$972$		0			0
$973$	29.7809	+	43.7163i	0.954733	+	1.40148i
$974$	57.9186	−	8.32733i	1.85583	−	0.266825i
$975$		0			0
$976$	18.7088	−	36.2893i	0.598853	−	1.16159i
$977$	31.8342	−	18.3795i	1.01846	−	0.588011i	0.104806	−	0.994493i	$-0.466578\pi$
$977$	31.8342	−	18.3795i	1.01846	−	0.588011i	0.913659	+	0.406482i	$0.133245\pi$
$978$		0			0
$979$	52.4141			1.67516
$980$	3.77688	−	42.2466i	0.120648	−	1.34952i
$981$		0			0
$982$	−6.62403	+	16.5459i	−0.211381	+	0.528002i
$983$	14.9799	+	25.9459i	0.477783	+	0.827545i	0.999676	−	0.0254664i	$-0.00810707\pi$
$983$	14.9799	+	25.9459i	0.477783	+	0.827545i	−0.521892	+	0.853011i	$0.674774\pi$
$984$		0			0
$985$	19.9171	−	34.4974i	0.634611	−	1.09918i
$986$	68.2901	−	9.81850i	2.17480	−	0.312685i
$987$		0			0
$988$	1.20236	+	4.09493i	0.0382523	+	0.130277i
$989$	13.5050	−	23.3913i	0.429433	−	0.743800i
$990$		0			0
$991$	−10.1390	+	5.85376i	−0.322076	+	0.185951i	−0.652318	−	0.757946i	$-0.726203\pi$
$991$	−10.1390	+	5.85376i	−0.322076	+	0.185951i	0.330241	+	0.943897i	$0.392870\pi$
$992$	8.52211	+	44.2193i	0.270577	+	1.40396i
$993$		0			0
$994$	−2.14667	−	9.72668i	−0.0680884	−	0.308512i
$995$			57.9228i			1.83628i
$996$		0			0
$997$	52.6239	−	30.3824i	1.66661	−	0.962221i	0.697172	−	0.716904i	$-0.254441\pi$
$997$	52.6239	−	30.3824i	1.66661	−	0.962221i	0.969443	−	0.245317i	$-0.0788919\pi$
$998$	45.8415	−	36.0500i	1.45109	−	1.14114i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bm.c.107.3	✓	48
3.2	odd	2	inner	504.2.bm.c.107.22	yes	48
4.3	odd	2		2016.2.bu.c.1871.3		48
7.4	even	3	inner	504.2.bm.c.179.20	yes	48
8.3	odd	2	inner	504.2.bm.c.107.5	yes	48
8.5	even	2		2016.2.bu.c.1871.21		48
12.11	even	2		2016.2.bu.c.1871.22		48
21.11	odd	6	inner	504.2.bm.c.179.5	yes	48
24.5	odd	2		2016.2.bu.c.1871.4		48
24.11	even	2	inner	504.2.bm.c.107.20	yes	48
28.11	odd	6		2016.2.bu.c.431.4		48
56.11	odd	6	inner	504.2.bm.c.179.22	yes	48
56.53	even	6		2016.2.bu.c.431.22		48
84.11	even	6		2016.2.bu.c.431.21		48
168.11	even	6	inner	504.2.bm.c.179.3	yes	48
168.53	odd	6		2016.2.bu.c.431.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bm.c.107.3	✓	48	1.1	even	1	trivial
504.2.bm.c.107.5	yes	48	8.3	odd	2	inner
504.2.bm.c.107.20	yes	48	24.11	even	2	inner
504.2.bm.c.107.22	yes	48	3.2	odd	2	inner
504.2.bm.c.179.3	yes	48	168.11	even	6	inner
504.2.bm.c.179.5	yes	48	21.11	odd	6	inner
504.2.bm.c.179.20	yes	48	7.4	even	3	inner
504.2.bm.c.179.22	yes	48	56.11	odd	6	inner
2016.2.bu.c.431.3		48	168.53	odd	6
2016.2.bu.c.431.4		48	28.11	odd	6
2016.2.bu.c.431.21		48	84.11	even	6
2016.2.bu.c.431.22		48	56.53	even	6
2016.2.bu.c.1871.3		48	4.3	odd	2
2016.2.bu.c.1871.4		48	24.5	odd	2
2016.2.bu.c.1871.21		48	8.5	even	2
2016.2.bu.c.1871.22		48	12.11	even	2

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31291 - 0.525613i) q^{2} +(1.44746 + 1.38016i) q^{4} +(-1.51483 + 2.62375i) q^{5} +(1.48957 + 2.18659i) q^{7} +(-1.17496 - 2.57283i) q^{8} +O(q^{10})\)	\(q+(-1.31291 - 0.525613i) q^{2} +(1.44746 + 1.38016i) q^{4} +(-1.51483 + 2.62375i) q^{5} +(1.48957 + 2.18659i) q^{7} +(-1.17496 - 2.57283i) q^{8} +(3.36791 - 2.64854i) q^{10} +(4.18149 - 2.41419i) q^{11} -1.60756i q^{13} +(-0.806377 - 3.65373i) q^{14} +(0.190296 + 3.99547i) q^{16} +(-5.79907 + 3.34810i) q^{17} +(-0.663707 + 1.14957i) q^{19} +(-5.81387 + 1.70708i) q^{20} +(-6.75885 + 0.971762i) q^{22} +(-4.32670 + 7.49406i) q^{23} +(-2.08939 - 3.61894i) q^{25} +(-0.844956 + 2.11059i) q^{26} +(-0.861747 + 5.22086i) q^{28} +7.28547 q^{29} +(-6.89424 + 3.98039i) q^{31} +(1.85023 - 5.34571i) q^{32} +(9.37346 - 1.34768i) q^{34} +(-7.99352 + 0.595977i) q^{35} +(2.70074 + 1.55927i) q^{37} +(1.47562 - 1.16043i) q^{38} +(8.53034 + 0.814600i) q^{40} -5.27510i q^{41} -3.12131 q^{43} +(9.38453 + 2.27670i) q^{44} +(9.61954 - 7.56486i) q^{46} +(-0.262637 + 0.454901i) q^{47} +(-2.56234 + 6.51417i) q^{49} +(0.841026 + 5.84955i) q^{50} +(2.21870 - 2.32689i) q^{52} +(5.00146 + 8.66278i) q^{53} +14.6283i q^{55} +(3.87555 - 6.40157i) q^{56} +(-9.56517 - 3.82934i) q^{58} +(-1.73784 + 1.00334i) q^{59} +(-8.83953 - 5.10350i) q^{61} +(11.1437 - 1.60219i) q^{62} +(-5.23896 + 6.04593i) q^{64} +(4.21785 + 2.43518i) q^{65} +(0.979594 + 1.69671i) q^{67} +(-13.0149 - 3.15743i) q^{68} +(10.8080 + 3.41903i) q^{70} +2.66212 q^{71} +(-1.96808 - 3.40882i) q^{73} +(-2.72625 - 3.46672i) q^{74} +(-2.54729 + 0.747941i) q^{76} +(11.5075 + 5.54710i) q^{77} +(-2.66792 - 1.54032i) q^{79} +(-10.7714 - 5.55315i) q^{80} +(-2.77266 + 6.92574i) q^{82} +8.22694i q^{83} -20.2871i q^{85} +(4.09800 + 1.64060i) q^{86} +(-11.1244 - 7.92173i) q^{88} +(9.40108 + 5.42772i) q^{89} +(3.51508 - 2.39458i) q^{91} +(-16.6058 + 4.87582i) q^{92} +(0.583921 - 0.459198i) q^{94} +(-2.01080 - 3.48281i) q^{95} +15.3656 q^{97} +(6.78805 - 7.20572i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 8 q^{10} - 28 q^{16} - 32 q^{19} + 32 q^{22} + 4 q^{28} + 112 q^{34} - 36 q^{40} - 160 q^{43} + 40 q^{46} + 56 q^{49} - 36 q^{52} + 12 q^{58} - 24 q^{64} + 92 q^{70} + 16 q^{73} - 120 q^{76} + 20 q^{82} - 100 q^{88} - 32 q^{91} - 20 q^{94} + 240 q^{97}+O(q^{100}) \) 48 * q - 8 * q^10 - 28 * q^16 - 32 * q^19 + 32 * q^22 + 4 * q^28 + 112 * q^34 - 36 * q^40 - 160 * q^43 + 40 * q^46 + 56 * q^49 - 36 * q^52 + 12 * q^58 - 24 * q^64 + 92 * q^70 + 16 * q^73 - 120 * q^76 + 20 * q^82 - 100 * q^88 - 32 * q^91 - 20 * q^94 + 240 * q^97

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