LMFDB - Embedded newform 504.2.bm.c.107.5

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			107.5
Character	$\chi$	$=$	504.107
Dual form			504.2.bm.c.179.5

$q$-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	$-0.596418\pi$
$5$	1.51483	−	2.62375i	0.677451	−	1.17338i	0.975746	−	0.218905i	$-0.0702486\pi$
$6$		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	0.287545	−	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	$0.0715618\pi$
$13$			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	−0.995047	−	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	$-0.475300\pi$
$23$	4.32670	−	7.49406i	0.902179	−	1.56262i	0.824660	−	0.565629i	$-0.191367\pi$
$24$		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	$-0.736478\pi$
$29$	−7.28547			−1.35288			−0.676439	+	0.736499i	$0.736478\pi$
$30$		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	$-0.864860\pi$
$41$		−	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	$0.576491\pi$
$44$	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	−0.846235	−	0.532810i	$-0.821136\pi$
$47$	0.262637	−	0.454901i	0.0383096	−	0.0663541i	0.884544	+	0.466456i	$0.154469\pi$
$48$		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	$-0.925593\pi$
$53$	−5.00146	−	8.66278i	−0.687003	−	1.18992i	0.285800	−	0.958289i	$-0.407741\pi$
$54$		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	−0.608840	−	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	0.944383	−	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	$-0.550494\pi$
$71$	−2.66212			−0.315936			−0.157968	+	0.987444i	$0.550494\pi$
$72$		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	$0.149115\pi$
$83$			8.22694i			0.903024i	−0.892265	+	0.451512i	$0.850885\pi$
$84$		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	0.907215	−	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
$94$	−0.689638	+	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	0.998469	−	0.0553102i	$-0.0176148\pi$
$101$	4.53586	+	7.85633i	0.451335	+	0.781734i	−0.547135	+	0.837045i	$0.684281\pi$
$102$		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	0.385342	−	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	−0.416812	−	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	$-0.958786\pi$
$113$		−	2.74503i		−	0.258231i	0.991630	−	0.129115i	$-0.0412137\pi$
$114$		0			0
$115$	−13.1084	−	22.7044i	−1.22236	−	2.11720i
$116$	−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	0.689939	−	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
$136$	1.80044	+	18.8539i	0.154387	+	1.61671i
$137$	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	$0.177874\pi$
$140$	−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	$0.374129\pi$
$149$	−7.40435	+	12.8247i	−0.606588	+	1.05064i	−0.991798	+	0.127813i	$0.959204\pi$
$150$		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	$-0.547322\pi$
$167$	−3.82827			−0.296240			−0.148120	+	0.988969i	$0.547322\pi$
$168$		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	−0.992600	−	0.121433i	$-0.961251\pi$
$173$	−5.14458	+	8.91068i	−0.391136	+	0.677467i	0.601464	+	0.798900i	$0.294584\pi$
$174$		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	−0.128192	−	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	$0.178495\pi$
$181$			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	−0.689921	−	0.723885i	$-0.742355\pi$
$191$	3.89652	−	6.74897i	0.281942	−	0.488338i	0.971863	+	0.235547i	$0.0756880\pi$
$192$		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	$-0.344837\pi$
$197$	13.1481			0.936763			0.468382	+	0.883526i	$0.344837\pi$
$198$		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	−0.403670	−	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	0.439445	−	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	0.676825	−	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
$236$	−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	$-0.463642\pi$
$239$	3.52397			0.227947			0.113973	+	0.993484i	$0.463642\pi$
$240$		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	$0.0655447\pi$
$251$			6.47860i			0.408926i	−0.978874	+	0.204463i	$0.934455\pi$
$252$		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	0.473234	−	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
$262$	−2.83435	−	7.07983i	−0.175107	−	0.437393i
$263$	5.56267	+	9.63482i	0.343009	+	0.594108i	0.984990	−	0.172612i	$-0.0552206\pi$
$263$	5.56267	+	9.63482i	0.343009	+	0.594108i	−0.641981	+	0.766720i	$0.721887\pi$
$264$		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	0.820161	−	0.572133i	$-0.193884\pi$
$269$	−1.40068	−	2.42605i	−0.0854011	−	0.147919i	−0.905562	+	0.424214i	$0.860551\pi$
$270$		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	$-0.866244\pi$
$281$		−	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	$0.907994\pi$
$284$	−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	$-0.282003\pi$
$293$	21.6555			1.26513			0.632563	+	0.774509i	$0.282003\pi$
$294$		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	$-0.951032\pi$
$311$	−11.0537	−	19.1456i	−0.626798	−	1.08565i	0.361392	−	0.932414i	$-0.382302\pi$
$312$		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	−0.933354	−	0.358957i	$-0.883132\pi$
$317$	−2.77413	+	4.80494i	−0.155811	+	0.269872i	0.777543	+	0.628830i	$0.216466\pi$
$318$		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	−0.904642	−	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	$-0.774014\pi$
$349$		−	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	−0.916562	−	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	$0.415003\pi$
$359$	−13.3275	+	23.0840i	−0.703400	+	1.21833i	−0.967266	+	0.253766i	$0.918331\pi$
$360$		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	$-0.633255\pi$
$383$	11.5071	−	19.9308i	0.587983	−	1.01842i	0.994496	−	0.104772i	$-0.0334113\pi$
$384$		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	$0.120722\pi$
$389$	15.4846	+	26.8201i	0.785101	+	1.35983i	−0.143838	+	0.989601i	$0.545944\pi$
$390$		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	0.776460	−	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
$404$	−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	$-0.914220\pi$
$419$		−	10.8994i		−	0.532471i	0.963908	−	0.266235i	$-0.0857798\pi$
$420$		0			0
$421$		−	12.1339i		−	0.591368i	−0.955286	−	0.295684i	$-0.904452\pi$
$421$		−	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	$-0.951189\pi$
$431$	−13.0047	−	22.5247i	−0.626413	−	1.08498i	0.361853	−	0.932235i	$-0.382144\pi$
$432$		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	$-0.987344\pi$
$443$	−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
$446$	−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	$-0.764354\pi$
$449$		−	28.5853i		−	1.34902i	0.738265	−	0.674511i	$-0.235646\pi$
$450$		0			0
$451$	−12.7351	−	22.0578i	−0.599672	−	1.03866i
$452$	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	$-0.903454\pi$
$461$	−40.9817			−1.90871			−0.954354	+	0.298678i	$0.903454\pi$
$462$		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	0.916105	−	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
$472$	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	0.641109	−	0.767450i	$-0.278475\pi$
$479$	−7.53048	−	13.0432i	−0.344077	−	0.595958i	−0.985186	+	0.171492i	$0.945141\pi$
$480$		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	$-0.908215\pi$
$491$		−	12.6025i		−	0.568743i	0.958714	−	0.284371i	$-0.0917848\pi$
$492$		0			0
$493$	42.2490	−	24.3925i	1.90280	−	1.09858i
$494$	1.12161	+	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	$-0.663916\pi$
$503$	−22.0912			−0.984998			−0.492499	+	0.870313i	$0.663916\pi$
$504$		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	−0.988610	−	0.150502i	$-0.951911\pi$
$509$	−8.21146	+	14.2227i	−0.363967	+	0.630409i	0.624643	+	0.780910i	$0.285244\pi$
$510$		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	$0.766903\pi$
$521$	−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
$530$	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	0.677593	−	0.735437i	$-0.263023\pi$
$557$	−7.03565	−	12.1861i	−0.298110	−	0.516342i	−0.975704	+	0.219095i	$0.929690\pi$
$558$		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	0.0924453	−	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	$0.577668\pi$
$572$	−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	$0.344214\pi$
$587$			42.7677i			1.76521i	−0.470112	+	0.882607i	$0.655786\pi$
$588$		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	0.755074	−	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
$598$	−7.31174	−	18.2637i	−0.298999	−	0.746860i
$599$	−20.2047	−	34.9955i	−0.825540	−	1.42988i	−0.901506	−	0.432766i	$-0.857537\pi$
$599$	−20.2047	−	34.9955i	−0.825540	−	1.42988i	0.0759664	−	0.997110i	$-0.475796\pi$
$600$		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	$0.282716\pi$
$617$			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	$0.912263\pi$
$620$	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	−0.642723	−	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	$0.596310\pi$
$644$	−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	$0.125194\pi$
$647$	20.1893	+	34.9689i	0.793724	+	1.37477i	−0.129923	+	0.991524i	$0.541473\pi$
$648$		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	−0.804028	−	0.594591i	$-0.797314\pi$
$653$	2.88547	−	4.99777i	0.112917	−	0.195578i	0.916945	+	0.399013i	$0.130647\pi$
$654$		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	$-0.941930\pi$
$659$		−	9.31457i		−	0.362844i	0.983405	−	0.181422i	$-0.0580700\pi$
$660$		0			0
$661$	−6.32010	+	3.64891i	−0.245823	+	0.141926i	−0.617850	−	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	$0.334214\pi$
$677$	−13.0719	+	22.6412i	−0.502393	+	0.870170i	−0.999996	+	0.00276538i	$0.999120\pi$
$678$		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	−0.676640	−	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
$686$	−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	$-0.550060\pi$
$701$	−8.29346			−0.313240			−0.156620	+	0.987659i	$0.550060\pi$
$702$		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	−0.946717	−	0.322067i	$-0.895622\pi$
$719$	−5.21376	+	9.03049i	−0.194440	+	0.336781i	0.752277	+	0.658847i	$0.228956\pi$
$720$		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	$-0.266351\pi$
$743$	36.5185			1.33973			0.669866	+	0.742482i	$0.266351\pi$
$744$		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	0.598636	−	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
$766$	−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	$0.0126846\pi$
$773$	14.8497	+	25.7204i	0.534105	+	0.925097i	−0.465101	+	0.885258i	$0.653982\pi$
$774$		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	$-0.903660\pi$
$797$	−53.8960			−1.90909			−0.954547	+	0.298061i	$0.903660\pi$
$798$		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	−0.737844	−	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	$0.609288\pi$
$812$	−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	−0.628974	−	0.777427i	$-0.716525\pi$
$821$	10.2803	−	17.8060i	0.358784	−	0.621433i	0.987758	+	0.155994i	$0.0498580\pi$
$822$		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	$-0.857751\pi$
$827$		−	24.8558i		−	0.864321i	0.901797	−	0.432160i	$-0.142249\pi$
$828$		0			0
$829$	7.94223	−	4.58545i	0.275845	−	0.159259i	−0.355696	−	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	$-0.545887\pi$
$839$	−8.32235			−0.287319			−0.143660	+	0.989627i	$0.545887\pi$
$840$		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	−0.764488	−	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	$0.438634\pi$
$863$	−22.1555	+	38.3745i	−0.754183	+	1.30628i	−0.945779	+	0.324810i	$0.894700\pi$
$864$		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	$-0.833883\pi$
$881$		−	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	$0.750500\pi$
$884$	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	−0.987040	−	0.160475i	$-0.948698\pi$
$887$	−10.5593	+	18.2892i	−0.354545	+	0.614090i	0.632495	+	0.774564i	$0.282031\pi$
$888$		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	$-0.256044\pi$
$911$	41.8668			1.38711			0.693554	+	0.720405i	$0.256044\pi$
$912$		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	0.916663	−	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
$934$	−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	0.995005	−	0.0998249i	$-0.0318283\pi$
$941$	12.6093	+	21.8400i	0.411052	+	0.711962i	−0.583953	+	0.811787i	$0.698495\pi$
$942$		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
$950$	−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	$0.0898361\pi$
$953$			17.1948i			0.556993i	−0.960437	+	0.278496i	$0.910164\pi$
$954$		0			0
$955$	−11.8051	−	20.4470i	−0.382004	−	0.661650i
$956$	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	0.777854	−	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
$976$	−40.7818	−	1.94235i	−1.30539	−	0.0621732i
$977$	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
$980$	−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	0.521892	−	0.853011i	$-0.325226\pi$
$983$	−14.9799	−	25.9459i	−0.477783	−	0.827545i	−0.999676	+	0.0254664i	$0.991893\pi$
$984$		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.107.5	yes	48
3.2	odd	2	inner	504.2.bm.c.107.20	yes	48
4.3	odd	2		2016.2.bu.c.1871.21		48
7.4	even	3	inner	504.2.bm.c.179.22	yes	48
8.3	odd	2	inner	504.2.bm.c.107.3	✓	48
8.5	even	2		2016.2.bu.c.1871.3		48
12.11	even	2		2016.2.bu.c.1871.4		48
21.11	odd	6	inner	504.2.bm.c.179.3	yes	48
24.5	odd	2		2016.2.bu.c.1871.22		48
24.11	even	2	inner	504.2.bm.c.107.22	yes	48
28.11	odd	6		2016.2.bu.c.431.22		48
56.11	odd	6	inner	504.2.bm.c.179.20	yes	48
56.53	even	6		2016.2.bu.c.431.4		48
84.11	even	6		2016.2.bu.c.431.3		48
168.11	even	6	inner	504.2.bm.c.179.5	yes	48
168.53	odd	6		2016.2.bu.c.431.21		48

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