LMFDB - Embedded newform 504.2.bm.c.107.20

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			107.20
Character	$\chi$	$=$	504.107
Dual form			504.2.bm.c.179.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.11165 + 0.874207i) q^{2} +(0.471526 + 1.94362i) q^{4} +(-1.51483 + 2.62375i) q^{5} +(-1.48957 - 2.18659i) q^{7} +(-1.17496 + 2.57283i) q^{8} +O(q^{10})$	\(q+(1.11165 + 0.874207i) q^{2} +(0.471526 + 1.94362i) q^{4} +(-1.51483 + 2.62375i) q^{5} +(-1.48957 - 2.18659i) q^{7} +(-1.17496 + 2.57283i) q^{8} +(-3.97766 + 1.59242i) q^{10} +(-4.18149 + 2.41419i) q^{11} +1.60756i q^{13} +(0.255647 - 3.73291i) q^{14} +(-3.55533 + 1.83293i) q^{16} +(5.79907 - 3.34810i) q^{17} +(-0.663707 + 1.14957i) q^{19} +(-5.81387 - 1.70708i) q^{20} +(-6.75885 - 0.971762i) q^{22} +(-4.32670 + 7.49406i) q^{23} +(-2.08939 - 3.61894i) q^{25} +(-1.40534 + 1.78705i) q^{26} +(3.54753 - 3.92620i) q^{28} +7.28547 q^{29} +(6.89424 - 3.98039i) q^{31} +(-5.55464 - 1.07051i) q^{32} +(9.37346 + 1.34768i) q^{34} +(7.99352 - 0.595977i) q^{35} +(-2.70074 - 1.55927i) q^{37} +(-1.74277 + 0.697706i) q^{38} +(-4.97063 - 6.98019i) q^{40} +5.27510i q^{41} -3.12131 q^{43} +(-6.66395 - 6.98889i) q^{44} +(-11.3611 + 4.54833i) q^{46} +(-0.262637 + 0.454901i) q^{47} +(-2.56234 + 6.51417i) q^{49} +(0.841026 - 5.84955i) q^{50} +(-3.12449 + 0.758007i) q^{52} +(5.00146 + 8.66278i) q^{53} -14.6283i q^{55} +(7.37591 - 1.26328i) q^{56} +(8.09889 + 6.36901i) q^{58} +(1.73784 - 1.00334i) q^{59} +(8.83953 + 5.10350i) q^{61} +(11.1437 + 1.60219i) q^{62} +(-5.23896 - 6.04593i) q^{64} +(-4.21785 - 2.43518i) q^{65} +(0.979594 + 1.69671i) q^{67} +(9.24184 + 9.69249i) q^{68} +(9.40699 + 6.32547i) q^{70} +2.66212 q^{71} +(-1.96808 - 3.40882i) q^{73} +(-1.63915 - 4.09437i) q^{74} +(-2.54729 - 0.747941i) q^{76} +(11.5075 + 5.54710i) q^{77} +(2.66792 + 1.54032i) q^{79} +(0.576531 - 12.1049i) q^{80} +(-4.61153 + 5.86406i) q^{82} -8.22694i q^{83} +20.2871i q^{85} +(-3.46980 - 2.72867i) q^{86} +(-1.29823 - 13.5949i) q^{88} +(-9.40108 - 5.42772i) q^{89} +(3.51508 - 2.39458i) q^{91} +(-16.6058 - 4.87582i) q^{92} +(-0.689638 + 0.276091i) q^{94} +(-2.01080 - 3.48281i) q^{95} +15.3656 q^{97} +(-8.54315 + 5.00146i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.11165	+	0.874207i	0.786054	+	0.618157i
$2$	1.11165	+	0.874207i	0.786054	+	0.618157i
$3$		0			0
$3$		0			0
$4$	0.471526	+	1.94362i	0.235763	+	0.971811i
$5$	−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
$10$	−3.97766	+	1.59242i	−1.25785	+	0.503568i
$11$	−4.18149	+	2.41419i	−1.26077	+	0.727905i	−0.973223	−	0.229863i	$-0.926172\pi$
$11$	−4.18149	+	2.41419i	−1.26077	+	0.727905i	−0.287545	+	0.957767i	$0.592839\pi$
$12$		0			0
$13$			1.60756i			0.445858i	0.974835	+	0.222929i	$0.0715618\pi$
$13$			1.60756i			0.445858i	−0.974835	+	0.222929i	$0.928438\pi$
$14$	0.255647	−	3.73291i	0.0683246	−	0.997663i
$15$		0			0
$16$	−3.55533	+	1.83293i	−0.888832	+	0.458234i
$17$	5.79907	−	3.34810i	1.40648	−	0.812033i	0.411435	−	0.911439i	$-0.365028\pi$
$17$	5.79907	−	3.34810i	1.40648	−	0.812033i	0.995047	+	0.0994061i	$0.0316943\pi$
$18$		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
$26$	−1.40534	+	1.78705i	−0.275610	+	0.350469i
$27$		0			0
$28$	3.54753	−	3.92620i	0.670420	−	0.741982i
$29$	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	0.269507	−	0.962998i	$-0.413139\pi$
$31$	6.89424	−	3.98039i	1.23824	−	0.714899i	0.968735	+	0.248099i	$0.0798059\pi$
$32$	−5.55464	−	1.07051i	−0.981931	−	0.189242i
$33$		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	0.261294	−	0.965259i	$-0.415851\pi$
$37$	−2.70074	−	1.55927i	−0.443999	−	0.256343i	−0.705292	+	0.708917i	$0.749184\pi$
$38$	−1.74277	+	0.697706i	−0.282715	+	0.113183i
$39$		0			0
$40$	−4.97063	−	6.98019i	−0.785926	−	1.10367i
$41$			5.27510i			0.823833i	0.911222	+	0.411916i	$0.135140\pi$
$41$			5.27510i			0.823833i	−0.911222	+	0.411916i	$0.864860\pi$
$42$		0			0
$43$	−3.12131			−0.475995			−0.237998	−	0.971266i	$-0.576491\pi$
$43$	−3.12131			−0.475995			−0.237998	+	0.971266i	$0.576491\pi$
$44$	−6.66395	−	6.98889i	−1.00463	−	1.05361i
$45$		0			0
$46$	−11.3611	+	4.54833i	−1.67511	+	0.670615i
$47$	−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
$52$	−3.12449	+	0.758007i	−0.433289	+	0.105117i
$53$	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
$56$	7.37591	−	1.26328i	0.985648	−	0.168813i
$57$		0			0
$58$	8.09889	+	6.36901i	1.06344	+	0.836292i
$59$	1.73784	−	1.00334i	0.226247	−	0.130624i	−0.382592	−	0.923917i	$-0.624969\pi$
$59$	1.73784	−	1.00334i	0.226247	−	0.130624i	0.608840	+	0.793293i	$0.291635\pi$
$60$		0			0
$61$	8.83953	+	5.10350i	1.13179	+	0.653437i	0.944383	−	0.328847i	$-0.106660\pi$
$61$	8.83953	+	5.10350i	1.13179	+	0.653437i	0.187402	+	0.982283i	$0.439993\pi$
$62$	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	$0.795148\pi$
$68$	9.24184	+	9.69249i	1.12074	+	1.17539i
$69$		0			0
$70$	9.40699	+	6.32547i	1.12435	+	0.756038i
$71$	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	$0.907319\pi$
$74$	−1.63915	−	4.09437i	−0.190547	−	0.475960i
$75$		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	0.642517	−	0.766272i	$-0.277890\pi$
$79$	2.66792	+	1.54032i	0.300164	+	0.173300i	−0.342353	+	0.939572i	$0.611224\pi$
$80$	0.576531	−	12.1049i	0.0644581	−	1.35337i
$81$		0			0
$82$	−4.61153	+	5.86406i	−0.509258	+	0.647577i
$83$		−	8.22694i		−	0.903024i	−0.892265	−	0.451512i	$-0.850885\pi$
$83$		−	8.22694i		−	0.903024i	0.892265	−	0.451512i	$-0.149115\pi$
$84$		0			0
$85$			20.2871i			2.20045i
$86$	−3.46980	−	2.72867i	−0.374158	−	0.294240i
$87$		0			0
$88$	−1.29823	−	13.5949i	−0.138392	−	1.44922i
$89$	−9.40108	−	5.42772i	−0.996513	−	0.575337i	−0.0892982	−	0.996005i	$-0.528462\pi$
$89$	−9.40108	−	5.42772i	−0.996513	−	0.575337i	−0.907215	+	0.420668i	$0.861796\pi$
$90$		0			0
$91$	3.51508	−	2.39458i	0.368481	−	0.251021i
$92$	−16.6058	−	4.87582i	−1.73127	−	0.508340i
$93$		0			0
$94$	−0.689638	+	0.276091i	−0.0711307	+	0.0284766i
$95$	−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	$0.215182\pi$
$98$	−8.54315	+	5.00146i	−0.862989	+	0.505223i
$99$		0			0
$100$	6.04864	−	5.76741i	0.604864	−	0.576741i
$101$	−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	0.636898	−	0.770948i	$-0.280217\pi$
$103$	2.91970	+	1.68569i	0.287687	+	0.166096i	−0.349211	+	0.937044i	$0.613551\pi$
$104$	−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	0.606474	−	0.795103i	$-0.292583\pi$
$107$	2.28741	+	1.32064i	0.221132	+	0.127671i	−0.385342	+	0.922774i	$0.625917\pi$
$108$		0			0
$109$	1.69125	−	0.976445i	0.161993	−	0.0935264i	−0.416812	−	0.908993i	$-0.636853\pi$
$109$	1.69125	−	0.976445i	0.161993	−	0.0935264i	0.578805	+	0.815466i	$0.303519\pi$
$110$	12.7881	−	16.2615i	1.21930	−	1.55047i
$111$		0			0
$112$	9.30380	+	5.04375i	0.879126	+	0.476589i
$113$			2.74503i			0.258231i	0.991630	+	0.129115i	$0.0412137\pi$
$113$			2.74503i			0.258231i	−0.991630	+	0.129115i	$0.958786\pi$
$114$		0			0
$115$	−13.1084	−	22.7044i	−1.22236	−	2.11720i
$116$	3.43529	+	14.1602i	0.318958	+	1.31474i
$117$		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
$122$	5.36493	+	13.4009i	0.485718	+	1.21326i
$123$		0			0
$124$	10.9872	+	11.5229i	0.986678	+	1.03479i
$125$	−2.48799			−0.222532
$126$		0			0
$127$		−	8.70363i		−	0.772322i	−0.922431	−	0.386161i	$-0.873801\pi$
$127$		−	8.70363i		−	0.772322i	0.922431	−	0.386161i	$-0.126199\pi$
$128$	−0.538484	−	11.3009i	−0.0475957	−	0.998867i
$129$		0			0
$130$	−2.55992	−	6.39434i	−0.224520	−	0.560821i
$131$	−4.67002	−	2.69624i	−0.408021	−	0.235571i	0.281918	−	0.959439i	$-0.409029\pi$
$131$	−4.67002	−	2.69624i	−0.408021	−	0.235571i	−0.689939	+	0.723867i	$0.742363\pi$
$132$		0			0
$133$	3.50229	−	0.261122i	0.303687	−	0.0226421i
$134$	−0.394308	+	2.74251i	−0.0340630	+	0.236917i
$135$		0			0
$136$	1.80044	+	18.8539i	0.154387	+	1.61671i
$137$	−9.95066	+	5.74501i	−0.850142	+	0.490830i	−0.860699	−	0.509115i	$-0.829973\pi$
$137$	−9.95066	+	5.74501i	−0.850142	+	0.490830i	0.0105568	+	0.999944i	$0.496640\pi$
$138$		0			0
$139$	19.9929			1.69578			0.847888	−	0.530175i	$-0.177874\pi$
$139$	19.9929			1.69578			0.847888	+	0.530175i	$0.177874\pi$
$140$	4.92750	+	15.2554i	0.416450	+	1.28931i
$141$		0			0
$142$	2.95935	+	2.32725i	0.248343	+	0.195298i
$143$	−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	−0.340253	−	0.940334i	$-0.610513\pi$
$151$	3.73528	−	2.15657i	0.303973	−	0.175499i	0.644226	+	0.764835i	$0.277180\pi$
$152$	−2.17784	−	3.05831i	−0.176646	−	0.248062i
$153$		0			0
$154$	7.94296	+	16.2263i	0.640062	+	1.30756i
$155$			24.1184i			1.93724i
$156$		0			0
$157$	−13.9896	+	8.07691i	−1.11649	+	0.644608i	−0.940503	−	0.339784i	$-0.889646\pi$
$157$	−13.9896	+	8.07691i	−1.11649	+	0.644608i	−0.175990	+	0.984392i	$0.556313\pi$
$158$	1.61923	+	4.04461i	0.128819	+	0.321772i
$159$		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	$0.330361\pi$
$164$	−10.2528	+	2.48735i	−0.800610	+	0.194229i
$165$		0			0
$166$	7.19205	−	9.14547i	0.558211	−	0.709826i
$167$	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
$170$	−17.7351	+	22.5522i	−1.36022	+	1.72967i
$171$		0			0
$172$	−1.47178	−	6.06665i	−0.112222	−	0.462577i
$173$	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
$178$	−5.70575	−	14.2522i	−0.427664	−	1.06825i
$179$	−8.91839	+	5.14904i	−0.666592	+	0.384857i	−0.794784	−	0.606892i	$-0.792416\pi$
$179$	−8.91839	+	5.14904i	−0.666592	+	0.384857i	0.128192	+	0.991749i	$0.459083\pi$
$180$		0			0
$181$			14.3100i			1.06366i	0.846853	+	0.531828i	$0.178495\pi$
$181$			14.3100i			1.06366i	−0.846853	+	0.531828i	$0.821505\pi$
$182$	6.00090	+	0.410969i	0.444816	+	0.0304631i
$183$		0			0
$184$	−14.1973	−	19.9371i	−1.04664	−	1.46978i
$185$	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	$0.903606\pi$
$194$	17.0812	+	13.4327i	1.22636	+	0.964415i
$195$		0			0
$196$	−13.8693	−	1.90862i	−0.990663	−	0.136330i
$197$	−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	−0.954551	−	0.298048i	$-0.903665\pi$
$199$	−16.5572	+	9.55931i	−1.17371	+	0.677642i	−0.219159	+	0.975689i	$0.570331\pi$
$200$	11.7659	−	1.12357i	0.831973	−	0.0794487i
$201$		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
$206$	1.77204	+	4.42632i	0.123464	+	0.308396i
$207$		0			0
$208$	−2.94656	−	5.71541i	−0.204307	−	0.396293i
$209$		−	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	$0.389676\pi$
$212$	−14.4788	+	13.8057i	−0.994411	+	0.948176i
$213$		0			0
$214$	1.38829	+	3.46775i	0.0949014	+	0.237051i
$215$	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
$220$	28.4319	−	6.89761i	1.91687	−	0.465037i
$221$	5.38228	+	9.32238i	0.362051	+	0.627091i
$222$		0			0
$223$		−	15.1022i		−	1.01132i	−0.862734	−	0.505658i	$-0.831250\pi$
$223$		−	15.1022i		−	1.01132i	0.862734	−	0.505658i	$-0.168750\pi$
$224$	5.93328	+	13.7403i	0.396434	+	0.918063i
$225$		0			0
$226$	−2.39972	+	3.05151i	−0.159627	+	0.202983i
$227$	−2.81482	+	1.62514i	−0.186826	+	0.107864i	−0.590496	−	0.807041i	$-0.701068\pi$
$227$	−2.81482	+	1.62514i	−0.186826	+	0.107864i	0.403670	+	0.914905i	$0.367735\pi$
$228$		0			0
$229$	−1.79711	−	1.03756i	−0.118757	−	0.0685642i	0.439445	−	0.898269i	$-0.355175\pi$
$229$	−1.79711	−	1.03756i	−0.118757	−	0.0685642i	−0.558202	+	0.829705i	$0.688508\pi$
$230$	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	0.299107	−	0.954220i	$-0.403311\pi$
$233$	−5.76562	−	3.32878i	−0.377718	−	0.218076i	−0.676825	+	0.736144i	$0.736645\pi$
$234$		0			0
$235$	−0.795699	−	1.37819i	−0.0519057	−	0.0899033i
$236$	2.76955	+	2.90460i	0.180282	+	0.189073i
$237$		0			0
$238$	−11.0156	−	22.5034i	−0.714038	−	1.45868i
$239$	−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	$0.596666\pi$
$242$	16.1661	−	6.47197i	1.03920	−	0.416034i
$243$		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
$248$	2.14046	+	22.4145i	0.135919	+	1.42332i
$249$		0			0
$250$	−2.76577	−	2.17502i	−0.174923	−	0.137560i
$251$		−	6.47860i		−	0.408926i	−0.978874	−	0.204463i	$-0.934455\pi$
$251$		−	6.47860i		−	0.408926i	0.978874	−	0.204463i	$-0.0655447\pi$
$252$		0			0
$253$		−	41.7818i		−	2.62680i
$254$	7.60877	−	9.67538i	0.477417	−	0.607087i
$255$		0			0
$256$	9.28070	−	13.0334i	0.580044	−	0.814585i
$257$	0.850646	+	0.491121i	0.0530618	+	0.0306353i	0.526296	−	0.850301i	$-0.323580\pi$
$257$	0.850646	+	0.491121i	0.0530618	+	0.0306353i	−0.473234	+	0.880937i	$0.656914\pi$
$258$		0			0
$259$	0.613463	+	8.22805i	0.0381187	+	0.511266i
$260$	2.74424	−	9.34616i	0.170191	−	0.579624i
$261$		0			0
$262$	−2.83435	−	7.07983i	−0.175107	−	0.437393i
$263$	−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
$266$	4.12159	+	2.77145i	0.252711	+	0.169928i
$267$		0			0
$268$	−2.83585	+	2.70400i	−0.173227	+	0.165173i
$269$	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	0.238072	−	0.971248i	$-0.423485\pi$
$271$	−7.96793	−	4.60029i	−0.484017	−	0.279447i	−0.722089	+	0.691800i	$0.756818\pi$
$272$	−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	−0.872464	−	0.488679i	$-0.837479\pi$
$277$	−14.7374	+	8.50866i	−0.885487	+	0.511236i	−0.0130233	+	0.999915i	$0.504146\pi$
$278$	22.2251	+	17.4779i	1.33297	+	1.04826i
$279$		0			0
$280$	−7.85868	+	21.2662i	−0.469646	+	1.27090i
$281$			13.6770i			0.815901i	0.913004	+	0.407950i	$0.133756\pi$
$281$			13.6770i			0.815901i	−0.913004	+	0.407950i	$0.866244\pi$
$282$		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	$0.907994\pi$
$284$	1.25526	+	5.17416i	0.0744859	+	0.307030i
$285$		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
$290$	−28.9791	+	11.6016i	−1.70171	+	0.681267i
$291$		0			0
$292$	5.69745	−	5.43255i	0.333418	−	0.317916i
$293$	−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
$296$	7.18500	−	5.11648i	0.417619	−	0.297389i
$297$		0			0
$298$	19.4425	−	7.78364i	1.12627	−	0.450894i
$299$	−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
$304$	0.252602	−	5.30364i	0.0144877	−	0.304185i
$305$	−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	$0.273157\pi$
$308$	−5.35539	+	24.9818i	−0.305151	+	1.42347i
$309$		0			0
$310$	−21.0845	+	26.8112i	−1.19752	+	1.52277i
$311$	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
$320$	23.7992	−	4.58720i	1.33041	−	0.256433i
$321$		0			0
$322$	26.8686	+	18.0670i	1.49733	+	1.00684i
$323$			8.88862i			0.494576i
$324$		0			0
$325$	5.81767	−	3.35883i	0.322706	−	0.186315i
$326$	−16.4902	+	6.60173i	−0.913310	+	0.365636i
$327$		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	$-0.0789579\pi$
$332$	15.9901	−	3.87921i	0.877568	−	0.212899i
$333$		0			0
$334$	4.25569	+	3.34670i	0.232861	+	0.183123i
$335$	−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	$0.331678\pi$
$338$	11.5786	+	9.10551i	0.629795	+	0.495274i
$339$		0			0
$340$	−39.4305	+	9.56590i	−2.13842	+	0.518784i
$341$	−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
$346$	13.5087	−	5.40812i	0.726235	−	0.290742i
$347$	18.4023	−	10.6246i	0.987886	−	0.570356i	0.0832443	−	0.996529i	$-0.473472\pi$
$347$	18.4023	−	10.6246i	0.987886	−	0.570356i	0.904642	+	0.426173i	$0.140138\pi$
$348$		0			0
$349$		−	24.3533i		−	1.30360i	−0.758391	−	0.651800i	$-0.774014\pi$
$349$		−	24.3533i		−	1.30360i	0.758391	−	0.651800i	$-0.225986\pi$
$350$	−14.0433	+	6.87435i	−0.750647	+	0.367450i
$351$		0			0
$352$	25.8111	−	8.93359i	1.37574	−	0.476162i
$353$	19.3242	−	11.1569i	1.02853	−	0.593819i	0.111964	−	0.993712i	$-0.464286\pi$
$353$	19.3242	−	11.1569i	1.02853	−	0.593819i	0.916562	+	0.399893i	$0.130953\pi$
$354$		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
$362$	−12.5099	+	15.9077i	−0.657507	+	0.836091i
$363$		0			0
$364$	6.31162	+	5.70288i	0.330819	+	0.298912i
$365$	11.9252			0.624194
$366$		0			0
$367$	−3.73960	+	2.15906i	−0.195206	+	0.112702i	−0.594417	−	0.804157i	$-0.702617\pi$
$367$	−3.73960	+	2.15906i	−0.195206	+	0.112702i	0.399212	+	0.916859i	$0.369284\pi$
$368$	1.64671	−	34.5744i	0.0858406	−	1.80231i
$369$		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	0.729709	−	0.683758i	$-0.239656\pi$
$373$	9.70317	+	5.60213i	0.502411	+	0.290067i	−0.227298	+	0.973825i	$0.572989\pi$
$374$	−42.4486	+	16.9940i	−2.19497	+	0.878737i
$375$		0			0
$376$	−0.861798	−	1.21021i	−0.0444438	−	0.0624119i
$377$			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	$0.758746\pi$
$380$	5.82112	−	5.55047i	0.298617	−	0.284733i
$381$		0			0
$382$	−10.2316	+	4.09612i	−0.523492	+	0.209576i
$383$	−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
$388$	7.24529	+	29.8650i	0.367824	+	1.51616i
$389$	−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
$392$	−13.7493	−	14.2463i	−0.694442	−	0.719549i
$393$		0			0
$394$	−14.6161	−	11.4942i	−0.736347	−	0.579067i
$395$	−8.08285	+	4.66664i	−0.406693	+	0.234804i
$396$		0			0
$397$	−4.72823	−	2.72985i	−0.237303	−	0.137007i	0.376633	−	0.926362i	$-0.377082\pi$
$397$	−4.72823	−	2.72985i	−0.237303	−	0.137007i	−0.613937	+	0.789355i	$0.710415\pi$
$398$	−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	0.157511	−	0.987517i	$-0.449653\pi$
$401$	−12.3944	−	7.15593i	−0.618949	−	0.357350i	−0.776460	+	0.630167i	$0.782986\pi$
$402$		0			0
$403$	6.39873	+	11.0829i	0.318743	+	0.552080i
$404$	13.1310	−	12.5204i	0.653290	−	0.622916i
$405$		0			0
$406$	1.86251	−	27.1960i	0.0924349	−	1.34972i
$407$	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	$0.559563\pi$
$410$	−8.40020	−	20.9826i	−0.414856	−	1.03625i
$411$		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
$416$	1.72092	−	8.92943i	0.0843748	−	0.437802i
$417$		0			0
$418$	5.60301	−	7.12484i	0.274052	−	0.348487i
$419$			10.8994i			0.532471i	0.963908	+	0.266235i	$0.0857798\pi$
$419$			10.8994i			0.532471i	−0.963908	+	0.266235i	$0.914220\pi$
$420$		0			0
$421$		−	12.1339i		−	0.591368i	−0.955286	−	0.295684i	$-0.904452\pi$
$421$		−	12.1339i		−	0.591368i	0.955286	−	0.295684i	$-0.0955476\pi$
$422$	10.9706	+	8.62731i	0.534038	+	0.419971i
$423$		0			0
$424$	−28.1644	+	2.68954i	−1.36778	+	0.130616i
$425$	−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
$430$	12.4155	−	4.97045i	0.598729	−	0.239696i
$431$	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	$0.565295\pi$
$434$	−13.0960	−	26.7532i	−0.628626	−	1.28419i
$435$		0			0
$436$	2.69531	+	2.82673i	0.129082	+	0.135376i
$437$	−5.74332	−	9.94772i	−0.274740	−	0.475864i
$438$		0			0
$439$	17.5807	+	10.1502i	0.839083	+	0.484445i	0.856952	−	0.515396i	$-0.172355\pi$
$439$	17.5807	+	10.1502i	0.839083	+	0.484445i	−0.0178696	+	0.999840i	$0.505688\pi$
$440$	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	$0.0126560\pi$
$443$	32.2709	+	18.6316i	1.53324	+	0.885216i	0.534029	+	0.845466i	$0.320677\pi$
$444$		0			0
$445$	28.4820	−	16.4441i	1.35018	−	0.779525i
$446$	13.2024	−	16.7883i	0.625153	−	0.794949i
$447$		0			0
$448$	−5.41616	+	20.4613i	−0.255889	+	0.966706i
$449$			28.5853i			1.34902i	0.738265	+	0.674511i	$0.235646\pi$
$449$			28.5853i			1.34902i	−0.738265	+	0.674511i	$0.764354\pi$
$450$		0			0
$451$	−12.7351	−	22.0578i	−0.599672	−	1.03866i
$452$	−5.33530	+	1.29435i	−0.250951	+	0.0608811i
$453$		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	$0.0884703\pi$
$458$	−1.09071	−	2.72446i	−0.0509657	−	0.127305i
$459$		0			0
$460$	37.9478	−	36.1834i	1.76933	−	1.68706i
$461$	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	$0.0221996\pi$
$463$			2.99890i			0.139371i	−0.997569	+	0.0696854i	$0.977800\pi$
$464$	−25.9022	+	13.3538i	−1.20248	+	0.619934i
$465$		0			0
$466$	−3.49930	−	8.74078i	−0.162102	−	0.404909i
$467$	−22.1923	−	12.8127i	−1.02694	−	0.592902i	−0.110831	−	0.993839i	$-0.535351\pi$
$467$	−22.1923	−	12.8127i	−1.02694	−	0.592902i	−0.916105	+	0.400938i	$0.868684\pi$
$468$		0			0
$469$	2.25082	−	4.66934i	0.103933	−	0.215610i
$470$	0.320286	−	2.22767i	0.0147737	−	0.102755i
$471$		0			0
$472$	0.539548	+	5.65005i	0.0248347	+	0.260065i
$473$	13.0517	−	7.53543i	0.600120	−	0.346479i
$474$		0			0
$475$	5.54698			0.254513
$476$	7.42708	−	34.6458i	0.340420	−	1.58799i
$477$		0			0
$478$	−3.91742	−	3.08068i	−0.179179	−	0.140907i
$479$	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	$-0.279839\pi$
$487$	35.8325	−	20.6879i	1.62373	−	0.937458i	0.985911	−	0.167268i	$-0.0534945\pi$
$488$	−23.5165	+	16.7463i	−1.06454	+	0.758067i
$489$		0			0
$490$	−0.181209	−	29.9915i	−0.00818621	−	1.35488i
$491$			12.6025i			0.568743i	0.958714	+	0.284371i	$0.0917848\pi$
$491$			12.6025i			0.568743i	−0.958714	+	0.284371i	$0.908215\pi$
$492$		0			0
$493$	42.2490	−	24.3925i	1.90280	−	1.09858i
$494$	−1.12161	−	2.80162i	−0.0504634	−	0.126051i
$495$		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	$0.792380\pi$
$500$	−1.17315	−	4.83571i	−0.0524649	−	0.216259i
$501$		0			0
$502$	5.66363	−	7.20193i	0.252780	−	0.321438i
$503$	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
$506$	36.5260	−	46.4467i	1.62378	−	2.06481i
$507$		0			0
$508$	16.9166	−	4.10398i	0.750551	−	0.182085i
$509$	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
$514$	0.516278	+	1.28959i	0.0227721	+	0.0568815i
$515$	−8.84568	+	5.10705i	−0.389787	+	0.225044i
$516$		0			0
$517$		−	2.53622i		−	0.111543i
$518$	−6.51106	+	9.68300i	−0.286080	+	0.425446i
$519$		0			0
$520$	11.2211	−	7.99061i	0.492078	−	0.350411i
$521$	38.6770	−	22.3302i	1.69447	−	0.978302i	0.743642	−	0.668578i	$-0.233097\pi$
$521$	38.6770	−	22.3302i	1.69447	−	0.978302i	0.950826	−	0.309724i	$-0.100237\pi$
$522$		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
$530$	−33.6889	−	26.4931i	−1.46335	−	1.15079i
$531$		0			0
$532$	2.15894	+	6.68399i	0.0936019	+	0.289788i
$533$	−8.48007			−0.367312
$534$		0			0
$535$	−6.93006	+	4.00107i	−0.299613	+	0.172981i
$536$	−5.51633	+	0.526778i	−0.238269	+	0.0227534i
$537$		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	0.668361	−	0.743837i	$-0.266996\pi$
$541$	8.33522	+	4.81234i	0.358359	+	0.206899i	−0.310002	+	0.950736i	$0.600330\pi$
$542$	−4.83594	−	12.0795i	−0.207721	−	0.518860i
$543$		0			0
$544$	−35.7959	+	12.3895i	−1.53474	+	0.531195i
$545$			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	$0.372477\pi$
$548$	−15.8581	−	16.6314i	−0.677425	−	0.710458i
$549$		0			0
$550$	10.6052	+	26.4902i	0.452205	+	1.12955i
$551$	−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
$556$	9.42717	+	38.8587i	0.399801	+	1.64797i
$557$	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
$560$	−27.3272	+	16.7705i	−1.15478	+	0.708682i
$561$		0			0
$562$	−11.9565	+	15.2040i	−0.504355	+	0.641342i
$563$	−23.7510	+	13.7126i	−1.00098	+	0.577919i	−0.908540	−	0.417799i	$-0.862802\pi$
$563$	−23.7510	+	13.7126i	−1.00098	+	0.577919i	−0.0924453	+	0.995718i	$0.529468\pi$
$564$		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	0.933321	−	0.359044i	$-0.116897\pi$
$569$	25.9776	+	14.9982i	1.08904	+	0.628757i	0.155719	+	0.987801i	$0.450231\pi$
$570$		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	$0.577668\pi$
$572$	11.2351	−	10.7127i	0.469762	−	0.447921i
$573$		0			0
$574$	19.6915	+	1.34857i	0.821908	+	0.0562881i
$575$	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	$0.982005\pi$
$578$	36.5501	−	14.6325i	1.52028	−	0.608634i
$579$		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
$584$	11.0827	−	1.05834i	0.458607	−	0.0437944i
$585$		0			0
$586$	−24.0733	−	18.9314i	−0.994458	−	0.782047i
$587$		−	42.7677i		−	1.76521i	−0.470112	−	0.882607i	$-0.655786\pi$
$587$		−	42.7677i		−	1.76521i	0.470112	−	0.882607i	$-0.344214\pi$
$588$		0			0
$589$			10.5673i			0.435416i
$590$	−5.31478	+	6.75832i	−0.218806	+	0.278236i
$591$		0			0
$592$	12.4600	+	0.593447i	0.512105	+	0.0243905i
$593$	−13.7540	−	7.94088i	−0.564810	−	0.326093i	0.190264	−	0.981733i	$-0.439066\pi$
$593$	−13.7540	−	7.94088i	−0.564810	−	0.326093i	−0.755074	+	0.655640i	$0.772399\pi$
$594$		0			0
$595$	44.3596	−	30.2192i	1.81857	−	1.23887i
$596$	28.4177	+	8.34407i	1.16404	+	0.341787i
$597$		0			0
$598$	−7.31174	−	18.2637i	−0.298999	−	0.746860i
$599$	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	$0.728430\pi$
$602$	−0.797954	+	11.6516i	−0.0325222	+	0.474883i
$603$		0			0
$604$	5.95283	+	6.24310i	0.242217	+	0.254028i
$605$	18.6523	+	32.3068i	0.758325	+	1.31346i
$606$		0			0
$607$	29.2976	+	16.9150i	1.18915	+	0.686557i	0.958114	−	0.286387i	$-0.0924544\pi$
$607$	29.2976	+	16.9150i	1.18915	+	0.686557i	0.231038	+	0.972945i	$0.425788\pi$
$608$	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	−0.627465	−	0.778644i	$-0.715908\pi$
$613$	−6.60745	+	3.81481i	−0.266872	+	0.154079i	0.360593	+	0.932723i	$0.382574\pi$
$614$	25.4706	+	20.0302i	1.02791	+	0.808352i
$615$		0			0
$616$	−27.7925	+	23.0892i	−1.11979	+	0.930292i
$617$		−	38.5471i		−	1.55185i	−0.630827	−	0.775923i	$-0.717284\pi$
$617$		−	38.5471i		−	1.55185i	0.630827	−	0.775923i	$-0.282716\pi$
$618$		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	$0.912263\pi$
$620$	−46.8770	+	11.3724i	−1.88263	+	0.456728i
$621$		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
$626$	13.4501	−	5.38464i	0.537574	−	0.215213i
$627$		0			0
$628$	−22.2949	−	23.3821i	−0.889664	−	0.933046i
$629$	−20.8824			−0.832635
$630$		0			0
$631$			26.6937i			1.06266i	0.847165	+	0.531331i	$0.178308\pi$
$631$			26.6937i			1.06266i	−0.847165	+	0.531331i	$0.821692\pi$
$632$	−7.09768	+	5.05430i	−0.282330	+	0.201049i
$633$		0			0
$634$	7.28437	−	2.91624i	0.289299	−	0.115819i
$635$	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
$640$	30.4665	+	15.7060i	1.20429	+	0.620835i
$641$	7.61117	−	4.39431i	0.300623	−	0.173565i	−0.342100	−	0.939664i	$-0.611138\pi$
$641$	7.61117	−	4.39431i	0.300623	−	0.173565i	0.642723	+	0.766099i	$0.277805\pi$
$642$		0			0
$643$	−15.1116			−0.595943			−0.297972	−	0.954575i	$-0.596310\pi$
$643$	−15.1116			−0.595943			−0.297972	+	0.954575i	$0.596310\pi$
$644$	14.0741	+	43.5729i	0.554597	+	1.71701i
$645$		0			0
$646$	−7.77049	+	9.88103i	−0.305726	+	0.388764i
$647$	−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
$656$	−9.66892	−	18.7547i	−0.377508	−	0.732249i
$657$		0			0
$658$	1.63096	+	1.09670i	0.0635816	+	0.0427537i
$659$			9.31457i			0.362844i	0.983405	+	0.181422i	$0.0580700\pi$
$659$			9.31457i			0.362844i	−0.983405	+	0.181422i	$0.941930\pi$
$660$		0			0
$661$	−6.32010	+	3.64891i	−0.245823	+	0.141926i	−0.617850	−	0.786296i	$-0.711996\pi$
$661$	−6.32010	+	3.64891i	−0.245823	+	0.141926i	0.372027	+	0.928222i	$0.378663\pi$
$662$	33.3128	−	13.3365i	1.29474	−	0.518338i
$663$		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
$668$	1.80513	+	7.44071i	0.0698425	+	0.287890i
$669$		0			0
$670$	−6.59836	−	5.18899i	−0.254917	−	0.200468i
$671$	−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	$0.589841\pi$
$674$	20.5907	+	16.1926i	0.793122	+	0.623716i
$675$		0			0
$676$	4.91129	+	20.2443i	0.188896	+	0.778625i
$677$	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
$682$	−50.4651	+	20.2033i	−1.93241	+	0.773624i
$683$	9.86031	−	5.69285i	0.377294	−	0.217831i	−0.299346	−	0.954145i	$-0.596769\pi$
$683$	9.86031	−	5.69285i	0.377294	−	0.217831i	0.676640	+	0.736314i	$0.263435\pi$
$684$		0			0
$685$		−	34.8108i		−	1.33005i
$686$	23.6618	+	11.2303i	0.903411	+	0.428776i
$687$		0			0
$688$	11.0973	−	5.72116i	0.423080	−	0.218117i
$689$	−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
$698$	21.2898	−	27.0723i	0.805830	−	1.02470i
$699$		0			0
$700$	−21.6208	−	4.63490i	−0.817191	−	0.175183i
$701$	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
$704$	36.5027	+	12.6332i	1.37575	+	0.476132i
$705$		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	0.586849	−	0.809697i	$-0.300368\pi$
$709$	4.76772	+	2.75264i	0.179055	+	0.103378i	−0.407793	+	0.913074i	$0.633702\pi$
$710$	−10.5890	+	4.23923i	−0.397399	+	0.159095i
$711$		0			0
$712$	25.0105	−	17.8101i	0.937307	−	0.667462i
$713$			68.8878i			2.57987i
$714$		0			0
$715$	23.5159			0.879445
$716$	−14.2130	−	14.9061i	−0.531166	−	0.557066i
$717$		0			0
$718$	34.9957	−	14.0102i	1.30603	−	0.522858i
$719$	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
$724$	−27.8133	+	6.74754i	−1.03367	+	0.250770i
$725$	−15.2222	−	26.3657i	−0.565339	−	0.979196i
$726$		0			0
$727$		−	2.87016i		−	0.106449i	−0.998583	−	0.0532243i	$-0.983050\pi$
$727$		−	2.87016i		−	0.106449i	0.998583	−	0.0532243i	$-0.0169498\pi$
$728$	2.03081	+	11.8573i	0.0752667	+	0.439459i
$729$		0			0
$730$	13.2566	+	10.4251i	0.490650	+	0.385850i
$731$	−18.1007	+	10.4505i	−0.669479	+	0.386524i
$732$		0			0
$733$	−31.8440	−	18.3851i	−1.17618	−	0.679071i	−0.221056	−	0.975261i	$-0.570950\pi$
$733$	−31.8440	−	18.3851i	−1.17618	−	0.679071i	−0.955129	+	0.296191i	$0.904284\pi$
$734$	−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	$0.712896\pi$
$740$	13.0399	+	13.6758i	0.479357	+	0.502731i
$741$		0			0
$742$	33.6160	−	16.4554i	1.23408	−	0.604096i
$743$	−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
$746$	5.88910	+	14.7102i	0.215615	+	0.538578i
$747$		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	0.875929	−	0.482441i	$-0.160250\pi$
$751$	24.5567	+	14.1778i	0.896087	+	0.517356i	0.0201583	+	0.999797i	$0.493583\pi$
$752$	0.0999577	−	2.09872i	0.00364508	−	0.0765324i
$753$		0			0
$754$	−10.2386	+	13.0195i	−0.372867	+	0.474141i
$755$			13.0673i			0.475567i
$756$		0			0
$757$			10.5981i			0.385195i	0.981278	+	0.192598i	$0.0616912\pi$
$757$			10.5981i			0.385195i	−0.981278	+	0.192598i	$0.938309\pi$
$758$	−31.4350	−	24.7206i	−1.14177	−	0.897894i
$759$		0			0
$760$	11.3233	−	1.08131i	0.410739	−	0.0392233i
$761$	−5.63447	−	3.25306i	−0.204249	−	0.117923i	0.394387	−	0.918945i	$-0.370957\pi$
$761$	−5.63447	−	3.25306i	−0.204249	−	0.117923i	−0.598636	+	0.801021i	$0.704290\pi$
$762$		0			0
$763$	−4.65433	−	2.24359i	−0.168498	−	0.0812232i
$764$	−14.9547	−	4.39104i	−0.541044	−	0.158862i
$765$		0			0
$766$	−30.2155	+	12.0965i	−1.09173	+	0.437065i
$767$	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	$0.574722\pi$
$770$	−54.6061	−	3.73968i	−1.96787	−	0.134769i
$771$		0			0
$772$	8.80680	−	8.39733i	0.316964	−	0.302227i
$773$	−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
$782$	−50.6558	+	64.4143i	−1.81145	+	2.30345i
$783$		0			0
$784$	−2.83009	−	27.8566i	−0.101075	−	0.994879i
$785$		−	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	$-0.550642\pi$
$788$	−6.19966	−	25.5549i	−0.220854	−	0.910357i
$789$		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
$794$	−2.86968	−	7.16808i	−0.101841	−	0.254386i
$795$		0			0
$796$	−26.3868	−	27.6735i	−0.935256	−	0.980861i
$797$	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
$800$	7.73171	+	22.3386i	0.273357	+	0.789789i
$801$		0			0
$802$	−7.52249	−	18.7902i	−0.265629	−	0.663504i
$803$	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
$808$	25.5425	−	2.43916i	0.898581	−	0.0858095i
$809$	14.8536	−	8.57571i	0.522223	−	0.301506i	−0.215620	−	0.976477i	$-0.569177\pi$
$809$	14.8536	−	8.57571i	0.522223	−	0.301506i	0.737844	+	0.674971i	$0.235844\pi$
$810$		0			0
$811$	−19.1733			−0.673265			−0.336632	−	0.941636i	$-0.609288\pi$
$811$	−19.1733			−0.673265			−0.336632	+	0.941636i	$0.609288\pi$
$812$	25.8454	−	28.6042i	0.906996	−	1.00381i
$813$		0			0
$814$	16.7386	+	13.1634i	0.586689	+	0.461375i
$815$	−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	−0.409494	−	0.912313i	$-0.634295\pi$
$823$	5.04464	−	2.91252i	0.175845	−	0.101524i	0.585339	+	0.810789i	$0.300961\pi$
$824$	−7.76752	+	5.53130i	−0.270594	+	0.192692i
$825$		0			0
$826$	−3.30111	−	6.74370i	−0.114860	−	0.234643i
$827$			24.8558i			0.864321i	0.901797	+	0.432160i	$0.142249\pi$
$827$			24.8558i			0.864321i	−0.901797	+	0.432160i	$0.857751\pi$
$828$		0			0
$829$	7.94223	−	4.58545i	0.275845	−	0.159259i	−0.355696	−	0.934602i	$-0.615756\pi$
$829$	7.94223	−	4.58545i	0.275845	−	0.159259i	0.631541	+	0.775343i	$0.282423\pi$
$830$	13.1008	+	32.7240i	0.454734	+	1.13586i
$831$		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
$836$	12.4572	−	3.02213i	0.430840	−	0.104522i
$837$		0			0
$838$	−9.52833	+	12.1163i	−0.329151	+	0.418551i
$839$	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
$842$	10.6075	−	13.4886i	0.365559	−	0.464848i
$843$		0			0
$844$	4.65336	+	19.1811i	0.160175	+	0.660240i
$845$	−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
$850$	−14.7077	−	36.7378i	−0.504469	−	1.26010i
$851$	23.3706	−	13.4930i	0.801132	−	0.462534i
$852$		0			0
$853$			38.7335i			1.32621i	0.748527	+	0.663104i	$0.230761\pi$
$853$			38.7335i			1.32621i	−0.748527	+	0.663104i	$0.769239\pi$
$854$	21.3107	−	31.6925i	0.729238	−	1.08449i
$855$		0			0
$856$	−6.08539	+	4.33344i	−0.207994	+	0.148114i
$857$	17.2269	−	9.94596i	0.588460	−	0.339747i	−0.176028	−	0.984385i	$-0.556325\pi$
$857$	17.2269	−	9.94596i	0.588460	−	0.339747i	0.764488	+	0.644638i	$0.222992\pi$
$858$		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
$866$	−9.42364	−	7.41080i	−0.320228	−	0.251829i
$867$		0			0
$868$	8.82969	−	41.1887i	0.299699	−	1.39804i
$869$	−14.8745			−0.504583
$870$		0			0
$871$	−2.72756	+	1.57476i	−0.0924200	+	0.0533587i
$872$	0.525085	+	5.49859i	0.0177816	+	0.186206i
$873$		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	0.120956	−	0.992658i	$-0.461404\pi$
$877$	−20.0853	−	11.5963i	−0.678234	−	0.391578i	−0.799189	+	0.601080i	$0.794737\pi$
$878$	10.6702	+	26.6527i	0.360102	+	0.899485i
$879$		0			0
$880$	26.8127	+	52.0084i	0.903856	+	1.75320i
$881$			29.5929i			0.997009i	0.866887	+	0.498504i	$0.166117\pi$
$881$			29.5929i			0.997009i	−0.866887	+	0.498504i	$0.833883\pi$
$882$		0			0
$883$	−42.0898			−1.41643			−0.708217	−	0.705995i	$-0.750500\pi$
$883$	−42.0898			−1.41643			−0.708217	+	0.705995i	$0.750500\pi$
$884$	−15.5813	+	14.8569i	−0.524056	+	0.499690i
$885$		0			0
$886$	19.5860	+	48.9233i	0.658006	+	1.64361i
$887$	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
$892$	29.3529	−	7.12106i	0.982808	−	0.238431i
$893$	−0.348628	−	0.603842i	−0.0116664	−	0.0202068i
$894$		0			0
$895$		−	31.1996i		−	1.04289i
$896$	−23.9083	+	18.0109i	−0.798719	+	0.601704i
$897$		0			0
$898$	−24.9894	+	31.7768i	−0.833908	+	1.06040i
$899$	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	$0.853068\pi$
$908$	−4.48592	−	4.70466i	−0.148870	−	0.156130i
$909$		0			0
$910$	−10.1686	+	15.1223i	−0.337086	+	0.501300i
$911$	−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
$914$	13.6516	−	5.46529i	0.451554	−	0.180776i
$915$		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	−0.427703	−	0.903919i	$-0.640677\pi$
$919$	−43.1798	−	24.9299i	−1.42437	−	0.822361i	−0.996669	+	0.0815583i	$0.974010\pi$
$920$	73.8164	−	7.04906i	2.43366	−	0.232400i
$921$		0			0
$922$	45.5572	+	35.8265i	1.50035	+	1.17988i
$923$			4.27953i			0.140862i
$924$		0			0
$925$			13.0317i			0.428481i
$926$	−2.62166	+	3.33373i	−0.0861531	+	0.109553i
$927$		0			0
$928$	−40.4682	−	7.79918i	−1.32843	−	0.256021i
$929$	−31.3597	−	18.1055i	−1.02888	−	0.594023i	−0.112214	−	0.993684i	$-0.535794\pi$
$929$	−31.3597	−	18.1055i	−1.02888	−	0.594023i	−0.916663	+	0.399662i	$0.869128\pi$
$930$		0			0
$931$	−5.78788	−	7.26910i	−0.189690	−	0.238235i
$932$	3.75125	−	12.7758i	0.122876	−	0.418485i
$933$		0			0
$934$	−13.4690	−	33.6439i	−0.440721	−	1.10086i
$935$	−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	$0.538996\pi$
$938$	6.58409	−	3.22298i	0.214978	−	0.105234i
$939$		0			0
$940$	2.30349	−	2.19639i	0.0751316	−	0.0716384i
$941$	−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	0.197073	−	0.980389i	$-0.436856\pi$
$947$	−17.0310	−	9.83284i	−0.553432	−	0.319524i	−0.750505	+	0.660865i	$0.770190\pi$
$948$		0			0
$949$	5.47989	−	3.16382i	0.177885	−	0.102702i
$950$	6.16629	+	4.84921i	0.200061	+	0.157329i
$951$		0			0
$952$	38.5439	−	32.0212i	1.24921	−	1.03781i
$953$		−	17.1948i		−	0.556993i	−0.960437	−	0.278496i	$-0.910164\pi$
$953$		−	17.1948i		−	0.556993i	0.960437	−	0.278496i	$-0.0898361\pi$
$954$		0			0
$955$	−11.8051	−	20.4470i	−0.382004	−	0.661650i
$956$	−1.66164	−	6.84926i	−0.0537413	−	0.221521i
$957$		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
$962$	6.58195	−	2.63503i	0.212211	−	0.0849568i
$963$		0			0
$964$	−30.4198	+	29.0054i	−0.979755	+	0.934202i
$965$	18.4333			0.593389
$966$		0			0
$967$		−	39.0833i		−	1.25683i	−0.777877	−	0.628417i	$-0.783703\pi$
$967$		−	39.0833i		−	1.25683i	0.777877	−	0.628417i	$-0.216297\pi$
$968$	20.2018	+	28.3691i	0.649310	+	0.911817i
$969$		0			0
$970$	−61.1193	+	24.4686i	−1.96242	+	0.785639i
$971$	−19.3986	−	11.1998i	−0.622531	−	0.359418i	0.155323	−	0.987864i	$-0.450358\pi$
$971$	−19.3986	−	11.1998i	−0.622531	−	0.359418i	−0.777854	+	0.628446i	$0.783691\pi$
$972$		0			0
$973$	−29.7809	−	43.7163i	−0.954733	−	1.40148i
$974$	57.9186	+	8.32733i	1.85583	+	0.266825i
$975$		0			0
$976$	−40.7818	−	1.94235i	−1.30539	−	0.0621732i
$977$	−31.8342	+	18.3795i	−1.01846	+	0.588011i	−0.913659	−	0.406482i	$-0.866755\pi$
$977$	−31.8342	+	18.3795i	−1.01846	+	0.588011i	−0.104806	+	0.994493i	$0.533422\pi$
$978$		0			0
$979$	52.4141			1.67516
$980$	26.0173	−	33.4984i	0.831092	−	1.07007i
$981$		0			0
$982$	−11.0172	+	14.0095i	−0.351572	+	0.447063i
$983$	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	−0.330241	−	0.943897i	$-0.607130\pi$
$991$	10.1390	−	5.85376i	0.322076	−	0.185951i	0.652318	+	0.757946i	$0.273797\pi$
$992$	−42.5561	+	14.7293i	−1.35116	+	0.467655i
$993$		0			0
$994$	0.680564	−	9.93747i	0.0215862	−	0.315198i
$995$		−	57.9228i		−	1.83628i
$996$		0			0
$997$	−52.6239	+	30.3824i	−1.66661	+	0.962221i	−0.697172	+	0.716904i	$0.745559\pi$
$997$	−52.6239	+	30.3824i	−1.66661	+	0.962221i	−0.969443	+	0.245317i	$0.921108\pi$
$998$	−54.1410	+	21.6749i	−1.71380	+	0.686107i
$999$		0			0

Twists

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

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

\(f(q)\)	\(=\)	\(q+(1.11165 + 0.874207i) q^{2} +(0.471526 + 1.94362i) q^{4} +(-1.51483 + 2.62375i) q^{5} +(-1.48957 - 2.18659i) q^{7} +(-1.17496 + 2.57283i) q^{8} +O(q^{10})\)	\(q+(1.11165 + 0.874207i) q^{2} +(0.471526 + 1.94362i) q^{4} +(-1.51483 + 2.62375i) q^{5} +(-1.48957 - 2.18659i) q^{7} +(-1.17496 + 2.57283i) q^{8} +(-3.97766 + 1.59242i) q^{10} +(-4.18149 + 2.41419i) q^{11} +1.60756i q^{13} +(0.255647 - 3.73291i) q^{14} +(-3.55533 + 1.83293i) q^{16} +(5.79907 - 3.34810i) q^{17} +(-0.663707 + 1.14957i) q^{19} +(-5.81387 - 1.70708i) q^{20} +(-6.75885 - 0.971762i) q^{22} +(-4.32670 + 7.49406i) q^{23} +(-2.08939 - 3.61894i) q^{25} +(-1.40534 + 1.78705i) q^{26} +(3.54753 - 3.92620i) q^{28} +7.28547 q^{29} +(6.89424 - 3.98039i) q^{31} +(-5.55464 - 1.07051i) q^{32} +(9.37346 + 1.34768i) q^{34} +(7.99352 - 0.595977i) q^{35} +(-2.70074 - 1.55927i) q^{37} +(-1.74277 + 0.697706i) q^{38} +(-4.97063 - 6.98019i) q^{40} +5.27510i q^{41} -3.12131 q^{43} +(-6.66395 - 6.98889i) q^{44} +(-11.3611 + 4.54833i) q^{46} +(-0.262637 + 0.454901i) q^{47} +(-2.56234 + 6.51417i) q^{49} +(0.841026 - 5.84955i) q^{50} +(-3.12449 + 0.758007i) q^{52} +(5.00146 + 8.66278i) q^{53} -14.6283i q^{55} +(7.37591 - 1.26328i) q^{56} +(8.09889 + 6.36901i) q^{58} +(1.73784 - 1.00334i) q^{59} +(8.83953 + 5.10350i) q^{61} +(11.1437 + 1.60219i) q^{62} +(-5.23896 - 6.04593i) q^{64} +(-4.21785 - 2.43518i) q^{65} +(0.979594 + 1.69671i) q^{67} +(9.24184 + 9.69249i) q^{68} +(9.40699 + 6.32547i) q^{70} +2.66212 q^{71} +(-1.96808 - 3.40882i) q^{73} +(-1.63915 - 4.09437i) q^{74} +(-2.54729 - 0.747941i) q^{76} +(11.5075 + 5.54710i) q^{77} +(2.66792 + 1.54032i) q^{79} +(0.576531 - 12.1049i) q^{80} +(-4.61153 + 5.86406i) q^{82} -8.22694i q^{83} +20.2871i q^{85} +(-3.46980 - 2.72867i) q^{86} +(-1.29823 - 13.5949i) q^{88} +(-9.40108 - 5.42772i) q^{89} +(3.51508 - 2.39458i) q^{91} +(-16.6058 - 4.87582i) q^{92} +(-0.689638 + 0.276091i) q^{94} +(-2.01080 - 3.48281i) q^{95} +15.3656 q^{97} +(-8.54315 + 5.00146i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 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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