LMFDB - Embedded newform 896.2.z.a.31.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [896,2,Mod(31,896)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("896.31"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(896, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.z (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [56,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			31.3
Character	$\chi$	$=$	896.31
Dual form			896.2.z.a.607.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.665801 - 2.48480i) q^{3} +(3.12401 + 0.837076i) q^{5} +(-1.56215 + 2.13534i) q^{7} +(-3.13287 + 1.80877i) q^{9} +(0.376195 + 1.40398i) q^{11} +(3.11315 + 3.11315i) q^{13} -8.31987i q^{15} +(2.02443 + 1.16881i) q^{17} +(4.40643 + 1.18070i) q^{19} +(6.34599 + 2.45991i) q^{21} +(1.15450 + 1.99965i) q^{23} +(4.72861 + 2.73006i) q^{25} +(1.12329 + 1.12329i) q^{27} +(1.55163 - 1.55163i) q^{29} +(-3.88952 + 6.73685i) q^{31} +(3.23814 - 1.86954i) q^{33} +(-6.66761 + 5.36320i) q^{35} +(-0.272421 + 1.01669i) q^{37} +(5.66282 - 9.80830i) q^{39} -2.77210 q^{41} +(7.12142 - 7.12142i) q^{43} +(-11.3012 + 3.02815i) q^{45} +(-1.42516 - 2.46844i) q^{47} +(-2.11939 - 6.67144i) q^{49} +(1.55638 - 5.80851i) q^{51} +(-11.0925 + 2.97221i) q^{53} +4.70094i q^{55} -11.7352i q^{57} +(3.77383 - 1.01120i) q^{59} +(3.72571 - 13.9045i) q^{61} +(1.03167 - 9.51532i) q^{63} +(7.11957 + 12.3315i) q^{65} +(2.59612 - 0.695627i) q^{67} +(4.20006 - 4.20006i) q^{69} +7.48345 q^{71} +(-5.65210 + 9.78973i) q^{73} +(3.63536 - 13.5673i) q^{75} +(-3.58565 - 1.38991i) q^{77} +(0.706717 - 0.408024i) q^{79} +(-3.38303 + 5.85958i) q^{81} +(2.65285 - 2.65285i) q^{83} +(5.34597 + 5.34597i) q^{85} +(-4.88857 - 2.82241i) q^{87} +(-2.40944 - 4.17328i) q^{89} +(-11.5108 + 1.78445i) q^{91} +(19.3294 + 5.17929i) q^{93} +(12.7774 + 7.37703i) q^{95} -5.86541i q^{97} +(-3.71804 - 3.71804i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 6 q^{3} + 6 q^{5} + 8 q^{7} + 2 q^{11} - 12 q^{17} - 6 q^{19} + 10 q^{21} + 12 q^{23} + 24 q^{29} - 12 q^{33} - 2 q^{35} - 6 q^{37} + 4 q^{39} - 12 q^{45} - 8 q^{49} - 34 q^{51} - 6 q^{53} + 42 q^{59}+ \cdots - 16 q^{99}+O(q^{100}) $ 56 * q - 6 * q^3 + 6 * q^5 + 8 * q^7 + 2 * q^11 - 12 * q^17 - 6 * q^19 + 10 * q^21 + 12 * q^23 + 24 * q^29 - 12 * q^33 - 2 * q^35 - 6 * q^37 + 4 * q^39 - 12 * q^45 - 8 * q^49 - 34 * q^51 - 6 * q^53 + 42 * q^59 + 6 * q^61 - 4 * q^65 + 6 * q^67 + 80 * q^71 + 24 * q^75 - 10 * q^77 - 8 * q^81 + 28 * q^85 + 12 * q^87 + 16 * q^91 - 10 * q^93 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.665801	−	2.48480i	−0.384400	−	1.43460i	−0.839110	−	0.543962i	$-0.816924\pi$
$3$	−0.665801	−	2.48480i	−0.384400	−	1.43460i	0.454710	−	0.890640i	$-0.349743\pi$
$4$		0			0
$5$	3.12401	+	0.837076i	1.39710	+	0.374352i	0.877302	−	0.479938i	$-0.159341\pi$
$5$	3.12401	+	0.837076i	1.39710	+	0.374352i	0.519797	+	0.854290i	$0.326008\pi$
$6$		0			0
$7$	−1.56215	+	2.13534i	−0.590436	+	0.807084i
$7$	−1.56215	+	2.13534i	−0.590436	+	0.807084i
$8$		0			0
$9$	−3.13287	+	1.80877i	−1.04429	+	0.602922i
$10$		0			0
$11$	0.376195	+	1.40398i	0.113427	+	0.423315i	0.999164	−	0.0408713i	$-0.0130134\pi$
$11$	0.376195	+	1.40398i	0.113427	+	0.423315i	−0.885737	+	0.464187i	$0.846347\pi$
$12$		0			0
$13$	3.11315	+	3.11315i	0.863433	+	0.863433i	0.991735	−	0.128303i	$-0.0409528\pi$
$13$	3.11315	+	3.11315i	0.863433	+	0.863433i	−0.128303	+	0.991735i	$0.540953\pi$
$14$		0			0
$15$		−	8.31987i		−	2.14818i
$16$		0			0
$17$	2.02443	+	1.16881i	0.490997	+	0.283477i	0.724988	−	0.688761i	$-0.241845\pi$
$17$	2.02443	+	1.16881i	0.490997	+	0.283477i	−0.233991	+	0.972239i	$0.575179\pi$
$18$		0			0
$19$	4.40643	+	1.18070i	1.01090	+	0.270871i	0.726007	−	0.687687i	$-0.241374\pi$
$19$	4.40643	+	1.18070i	1.01090	+	0.270871i	0.284897	+	0.958558i	$0.408041\pi$
$20$		0			0
$21$	6.34599	+	2.45991i	1.38481	+	0.536797i
$22$		0			0
$23$	1.15450	+	1.99965i	0.240729	+	0.416955i	0.960922	−	0.276819i	$-0.0892802\pi$
$23$	1.15450	+	1.99965i	0.240729	+	0.416955i	−0.720193	+	0.693774i	$0.755947\pi$
$24$		0			0
$25$	4.72861	+	2.73006i	0.945722	+	0.546013i
$26$		0			0
$27$	1.12329	+	1.12329i	0.216177	+	0.216177i
$28$		0			0
$29$	1.55163	−	1.55163i	0.288130	−	0.288130i	−0.548210	−	0.836341i	$-0.684691\pi$
$29$	1.55163	−	1.55163i	0.288130	−	0.288130i	0.836341	+	0.548210i	$0.184691\pi$
$30$		0			0
$31$	−3.88952	+	6.73685i	−0.698579	+	1.20997i	0.270380	+	0.962754i	$0.412851\pi$
$31$	−3.88952	+	6.73685i	−0.698579	+	1.20997i	−0.968959	+	0.247221i	$0.920483\pi$
$32$		0			0
$33$	3.23814	−	1.86954i	0.563687	−	0.325445i
$34$		0			0
$35$	−6.66761	+	5.36320i	−1.12703	+	0.906546i
$36$		0			0
$37$	−0.272421	+	1.01669i	−0.0447857	+	0.167142i	−0.984697	−	0.174277i	$-0.944241\pi$
$37$	−0.272421	+	1.01669i	−0.0447857	+	0.167142i	0.939911	+	0.341420i	$0.110908\pi$
$38$		0			0
$39$	5.66282	−	9.80830i	0.906778	−	1.57058i
$40$		0			0
$41$	−2.77210			−0.432929			−0.216464	−	0.976290i	$-0.569453\pi$
$41$	−2.77210			−0.432929			−0.216464	+	0.976290i	$0.569453\pi$
$42$		0			0
$43$	7.12142	−	7.12142i	1.08601	−	1.08601i	0.0900717	−	0.995935i	$-0.471290\pi$
$43$	7.12142	−	7.12142i	1.08601	−	1.08601i	0.995935	−	0.0900717i	$-0.0287096\pi$
$44$		0			0
$45$	−11.3012	+	3.02815i	−1.68468	+	0.451410i
$46$		0			0
$47$	−1.42516	−	2.46844i	−0.207880	−	0.360059i	0.743166	−	0.669107i	$-0.233323\pi$
$47$	−1.42516	−	2.46844i	−0.207880	−	0.360059i	−0.951047	+	0.309047i	$0.899990\pi$
$48$		0			0
$49$	−2.11939	−	6.67144i	−0.302770	−	0.953064i
$50$		0			0
$51$	1.55638	−	5.80851i	0.217937	−	0.813354i
$52$		0			0
$53$	−11.0925	+	2.97221i	−1.52367	+	0.408265i	−0.920947	−	0.389689i	$-0.872583\pi$
$53$	−11.0925	+	2.97221i	−1.52367	+	0.408265i	−0.602719	+	0.797954i	$0.705916\pi$
$54$		0			0
$55$			4.70094i			0.633875i
$56$		0			0
$57$		−	11.7352i		−	1.55437i
$58$		0			0
$59$	3.77383	−	1.01120i	0.491311	−	0.131646i	−0.00465348	−	0.999989i	$-0.501481\pi$
$59$	3.77383	−	1.01120i	0.491311	−	0.131646i	0.495965	+	0.868343i	$0.334815\pi$
$60$		0			0
$61$	3.72571	−	13.9045i	0.477028	−	1.78029i	−0.136523	−	0.990637i	$-0.543593\pi$
$61$	3.72571	−	13.9045i	0.477028	−	1.78029i	0.613551	−	0.789655i	$-0.289741\pi$
$62$		0			0
$63$	1.03167	−	9.51532i	0.129978	−	1.19882i
$64$		0			0
$65$	7.11957	+	12.3315i	0.883074	+	1.52953i
$66$		0			0
$67$	2.59612	−	0.695627i	0.317166	−	0.0849844i	−0.0967240	−	0.995311i	$-0.530836\pi$
$67$	2.59612	−	0.695627i	0.317166	−	0.0849844i	0.413890	+	0.910327i	$0.364170\pi$
$68$		0			0
$69$	4.20006	−	4.20006i	0.505628	−	0.505628i
$70$		0			0
$71$	7.48345			0.888122			0.444061	−	0.895997i	$-0.353537\pi$
$71$	7.48345			0.888122			0.444061	+	0.895997i	$0.353537\pi$
$72$		0			0
$73$	−5.65210	+	9.78973i	−0.661529	+	1.14580i	0.318685	+	0.947861i	$0.396759\pi$
$73$	−5.65210	+	9.78973i	−0.661529	+	1.14580i	−0.980214	+	0.197941i	$0.936575\pi$
$74$		0			0
$75$	3.63536	−	13.5673i	0.419775	−	1.56662i
$76$		0			0
$77$	−3.58565	−	1.38991i	−0.408623	−	0.158395i
$78$		0			0
$79$	0.706717	−	0.408024i	0.0795119	−	0.0459062i	−0.459717	−	0.888066i	$-0.652049\pi$
$79$	0.706717	−	0.408024i	0.0795119	−	0.0459062i	0.539229	+	0.842159i	$0.318716\pi$
$80$		0			0
$81$	−3.38303	+	5.85958i	−0.375892	+	0.651065i
$82$		0			0
$83$	2.65285	−	2.65285i	0.291188	−	0.291188i	−0.546361	−	0.837550i	$-0.683987\pi$
$83$	2.65285	−	2.65285i	0.291188	−	0.291188i	0.837550	+	0.546361i	$0.183987\pi$
$84$		0			0
$85$	5.34597	+	5.34597i	0.579852	+	0.579852i
$86$		0			0
$87$	−4.88857	−	2.82241i	−0.524109	−	0.302595i
$88$		0			0
$89$	−2.40944	−	4.17328i	−0.255400	−	0.442367i	0.709604	−	0.704601i	$-0.248874\pi$
$89$	−2.40944	−	4.17328i	−0.255400	−	0.442367i	−0.965004	+	0.262234i	$0.915541\pi$
$90$		0			0
$91$	−11.5108	+	1.78445i	−1.20666	+	0.187061i
$92$		0			0
$93$	19.3294	+	5.17929i	2.00436	+	0.537068i
$94$		0			0
$95$	12.7774	+	7.37703i	1.31093	+	0.756867i
$96$		0			0
$97$		−	5.86541i		−	0.595542i	−0.954637	−	0.297771i	$-0.903757\pi$
$97$		−	5.86541i		−	0.595542i	0.954637	−	0.297771i	$-0.0962432\pi$
$98$		0			0
$99$	−3.71804	−	3.71804i	−0.373677	−	0.373677i
$100$		0			0
$101$	−0.373632	−	1.39442i	−0.0371778	−	0.138749i	0.944842	−	0.327525i	$-0.106215\pi$
$101$	−0.373632	−	1.39442i	−0.0371778	−	0.138749i	−0.982020	+	0.188776i	$0.939548\pi$
$102$		0			0
$103$	2.10134	−	1.21321i	0.207051	−	0.119541i	−0.392889	−	0.919586i	$-0.628524\pi$
$103$	2.10134	−	1.21321i	0.207051	−	0.119541i	0.599940	+	0.800045i	$0.295191\pi$
$104$		0			0
$105$	17.7658	+	12.9969i	1.73376	+	1.26836i
$106$		0			0
$107$	−4.34758	−	1.16493i	−0.420297	−	0.112618i	0.0424712	−	0.999098i	$-0.486477\pi$
$107$	−4.34758	−	1.16493i	−0.420297	−	0.112618i	−0.462768	+	0.886480i	$0.653144\pi$
$108$		0			0
$109$	−0.842750	−	3.14518i	−0.0807208	−	0.301254i	0.913749	−	0.406280i	$-0.133174\pi$
$109$	−0.842750	−	3.14518i	−0.0807208	−	0.301254i	−0.994470	+	0.105026i	$0.966507\pi$
$110$		0			0
$111$	2.70765			0.256998
$112$		0			0
$113$	11.5397			1.08556			0.542781	−	0.839875i	$-0.317372\pi$
$113$	11.5397			1.08556			0.542781	+	0.839875i	$0.317372\pi$
$114$		0			0
$115$	1.93280	+	7.21331i	0.180235	+	0.672645i
$116$		0			0
$117$	−15.3841	−	4.12215i	−1.42226	−	0.381093i
$118$		0			0
$119$	−5.65827	+	2.49701i	−0.518693	+	0.228901i
$120$		0			0
$121$	7.69665	−	4.44366i	0.699695	−	0.403969i
$122$		0			0
$123$	1.84566	+	6.88811i	0.166418	+	0.621080i
$124$		0			0
$125$	1.05228	+	1.05228i	0.0941192	+	0.0941192i
$126$		0			0
$127$		−	4.49210i		−	0.398610i	−0.979938	−	0.199305i	$-0.936132\pi$
$127$		−	4.49210i		−	0.398610i	0.979938	−	0.199305i	$-0.0638684\pi$
$128$		0			0
$129$	−22.4368	−	12.9539i	−1.97545	−	1.14053i
$130$		0			0
$131$	−13.3612	−	3.58012i	−1.16737	−	0.312796i	−0.377465	−	0.926024i	$-0.623204\pi$
$131$	−13.3612	−	3.58012i	−1.16737	−	0.312796i	−0.789907	+	0.613227i	$0.789871\pi$
$132$		0			0
$133$	−9.40469	+	7.56482i	−0.815490	+	0.655953i
$134$		0			0
$135$	2.56889	+	4.44945i	0.221095	+	0.382947i
$136$		0			0
$137$	−2.18423	−	1.26106i	−0.186611	−	0.107740i	0.403784	−	0.914854i	$-0.367695\pi$
$137$	−2.18423	−	1.26106i	−0.186611	−	0.107740i	−0.590395	+	0.807114i	$0.701028\pi$
$138$		0			0
$139$	6.00381	+	6.00381i	0.509237	+	0.509237i	0.914292	−	0.405055i	$-0.132748\pi$
$139$	6.00381	+	6.00381i	0.509237	+	0.509237i	−0.405055	+	0.914292i	$0.632748\pi$
$140$		0			0
$141$	−5.18472	+	5.18472i	−0.436632	+	0.436632i
$142$		0			0
$143$	−3.19964	+	5.54195i	−0.267568	+	0.463441i
$144$		0			0
$145$	6.14613	−	3.54847i	0.510409	−	0.294685i
$146$		0			0
$147$	−15.1661	+	9.70812i	−1.25088	+	0.800713i
$148$		0			0
$149$	2.19951	−	8.20870i	0.180191	−	0.672483i	−0.815418	−	0.578873i	$-0.803493\pi$
$149$	2.19951	−	8.20870i	0.180191	−	0.672483i	0.995609	−	0.0936097i	$-0.0298406\pi$
$150$		0			0
$151$	−5.11927	+	8.86683i	−0.416600	+	0.721572i	−0.995595	−	0.0937588i	$-0.970112\pi$
$151$	−5.11927	+	8.86683i	−0.416600	+	0.721572i	0.578995	+	0.815331i	$0.303445\pi$
$152$		0			0
$153$	−8.45639			−0.683659
$154$		0			0
$155$	−17.7902	+	17.7902i	−1.42894	+	1.42894i
$156$		0			0
$157$	−14.1817	+	3.79998i	−1.13183	+	0.303272i	−0.775660	−	0.631151i	$-0.782583\pi$
$157$	−14.1817	+	3.79998i	−1.13183	+	0.303272i	−0.356166	+	0.934423i	$0.615916\pi$
$158$		0			0
$159$	14.7707	+	25.5836i	1.17139	+	2.02892i
$160$		0			0
$161$	−6.07342	−	0.658494i	−0.478653	−	0.0518966i
$162$		0			0
$163$	−5.94974	+	22.2047i	−0.466019	+	1.73921i	0.187468	+	0.982271i	$0.439972\pi$
$163$	−5.94974	+	22.2047i	−0.466019	+	1.73921i	−0.653488	+	0.756937i	$0.726695\pi$
$164$		0			0
$165$	11.6809	−	3.12989i	0.909358	−	0.243662i
$166$		0			0
$167$		−	3.82099i		−	0.295677i	−0.989011	−	0.147839i	$-0.952768\pi$
$167$		−	3.82099i		−	0.295677i	0.989011	−	0.147839i	$-0.0472316\pi$
$168$		0			0
$169$			6.38341i			0.491032i
$170$		0			0
$171$	−15.9404	+	4.27121i	−1.21899	+	0.326628i
$172$		0			0
$173$	−2.15162	+	8.02996i	−0.163585	+	0.610506i	0.834632	+	0.550808i	$0.185680\pi$
$173$	−2.15162	+	8.02996i	−0.163585	+	0.610506i	−0.998216	+	0.0596981i	$0.980986\pi$
$174$		0			0
$175$	−13.2164	+	5.83245i	−0.999067	+	0.440892i
$176$		0			0
$177$	−5.02524	−	8.70397i	−0.377720	−	0.654230i
$178$		0			0
$179$	18.6644	−	5.00112i	1.39504	−	0.373801i	0.518482	−	0.855089i	$-0.326497\pi$
$179$	18.6644	−	5.00112i	1.39504	−	0.373801i	0.876563	+	0.481288i	$0.159831\pi$
$180$		0			0
$181$	6.07189	−	6.07189i	0.451320	−	0.451320i	−0.444472	−	0.895793i	$-0.646609\pi$
$181$	6.07189	−	6.07189i	0.451320	−	0.451320i	0.895793	+	0.444472i	$0.146609\pi$
$182$		0			0
$183$	−37.0306			−2.73738
$184$		0			0
$185$	−1.70209	+	2.94810i	−0.125140	+	0.216749i
$186$		0			0
$187$	−0.879398	+	3.28196i	−0.0643080	+	0.240001i
$188$		0			0
$189$	−4.15336	+	0.643867i	−0.302112	+	0.0468344i
$190$		0			0
$191$	−13.1707	+	7.60410i	−0.952997	+	0.550213i	−0.894011	−	0.448046i	$-0.852120\pi$
$191$	−13.1707	+	7.60410i	−0.952997	+	0.550213i	−0.0589865	+	0.998259i	$0.518787\pi$
$192$		0			0
$193$	−11.2397	+	19.4678i	−0.809053	+	1.40132i	0.104468	+	0.994528i	$0.466686\pi$
$193$	−11.2397	+	19.4678i	−0.809053	+	1.40132i	−0.913521	+	0.406792i	$0.866647\pi$
$194$		0			0
$195$	25.9010	−	25.9010i	1.85481	−	1.85481i
$196$		0			0
$197$	8.31581	+	8.31581i	0.592477	+	0.592477i	0.938300	−	0.345823i	$-0.112400\pi$
$197$	8.31581	+	8.31581i	0.592477	+	0.592477i	−0.345823	+	0.938300i	$0.612400\pi$
$198$		0			0
$199$	−8.85088	−	5.11006i	−0.627422	−	0.362242i	0.152331	−	0.988330i	$-0.451322\pi$
$199$	−8.85088	−	5.11006i	−0.627422	−	0.362242i	−0.779753	+	0.626087i	$0.784655\pi$
$200$		0			0
$201$	−3.45699	−	5.98769i	−0.243837	−	0.422339i
$202$		0			0
$203$	0.889390	+	5.73713i	0.0624229	+	0.402668i
$204$		0			0
$205$	−8.66006	−	2.32046i	−0.604845	−	0.162068i
$206$		0			0
$207$	−7.23378	−	4.17642i	−0.502782	−	0.290282i
$208$		0			0
$209$			6.63070i			0.458655i
$210$		0			0
$211$	5.73766	+	5.73766i	0.394997	+	0.394997i	0.876464	−	0.481467i	$-0.159896\pi$
$211$	5.73766	+	5.73766i	0.394997	+	0.394997i	−0.481467	+	0.876464i	$0.659896\pi$
$212$		0			0
$213$	−4.98248	−	18.5949i	−0.341394	−	1.27410i
$214$		0			0
$215$	28.2086	−	16.2862i	1.92381	−	1.11071i
$216$		0			0
$217$	−8.30949	−	18.8294i	−0.564085	−	1.27822i
$218$		0			0
$219$	28.0887	+	7.52635i	1.89806	+	0.508583i
$220$		0			0
$221$	2.66369	+	9.94104i	0.179179	+	0.668706i
$222$		0			0
$223$	−17.4929			−1.17141			−0.585705	−	0.810524i	$-0.699182\pi$
$223$	−17.4929			−1.17141			−0.585705	+	0.810524i	$0.699182\pi$
$224$		0			0
$225$	−19.7522			−1.31681
$226$		0			0
$227$	−4.53614	−	16.9291i	−0.301074	−	1.12362i	−0.936272	−	0.351275i	$-0.885748\pi$
$227$	−4.53614	−	16.9291i	−0.301074	−	1.12362i	0.635198	−	0.772349i	$-0.280919\pi$
$228$		0			0
$229$	−6.75227	−	1.80926i	−0.446202	−	0.119560i	0.0287195	−	0.999588i	$-0.490857\pi$
$229$	−6.75227	−	1.80926i	−0.446202	−	0.119560i	−0.474922	+	0.880028i	$0.657524\pi$
$230$		0			0
$231$	−1.06634	+	9.83503i	−0.0701597	+	0.647098i
$232$		0			0
$233$	25.0933	−	14.4876i	1.64392	−	0.949116i	0.664495	−	0.747293i	$-0.268647\pi$
$233$	25.0933	−	14.4876i	1.64392	−	0.949116i	0.979422	−	0.201823i	$-0.0646866\pi$
$234$		0			0
$235$	−2.38593	−	8.90440i	−0.155641	−	0.580859i
$236$		0			0
$237$	−1.48439	−	1.48439i	−0.0964215	−	0.0964215i
$238$		0			0
$239$		−	13.3587i		−	0.864105i	−0.901848	−	0.432053i	$-0.857789\pi$
$239$		−	13.3587i		−	0.864105i	0.901848	−	0.432053i	$-0.142211\pi$
$240$		0			0
$241$	10.5510	+	6.09164i	0.679651	+	0.392397i	0.799724	−	0.600368i	$-0.204979\pi$
$241$	10.5510	+	6.09164i	0.679651	+	0.392397i	−0.120072	+	0.992765i	$0.538313\pi$
$242$		0			0
$243$	21.4157	+	5.73831i	1.37381	+	0.368113i
$244$		0			0
$245$	−1.03650	−	22.6157i	−0.0662195	−	1.44487i
$246$		0			0
$247$	10.0422	+	17.3936i	0.638969	+	1.10673i
$248$		0			0
$249$	−8.35808	−	4.82554i	−0.529672	−	0.305806i
$250$		0			0
$251$	−6.68926	−	6.68926i	−0.422223	−	0.422223i	0.463746	−	0.885968i	$-0.346505\pi$
$251$	−6.68926	−	6.68926i	−0.422223	−	0.422223i	−0.885968	+	0.463746i	$0.846505\pi$
$252$		0			0
$253$	−2.37314	+	2.37314i	−0.149198	+	0.149198i
$254$		0			0
$255$	9.72432	−	16.8430i	0.608961	−	1.05475i
$256$		0			0
$257$	3.32837	−	1.92163i	0.207618	−	0.119868i	−0.392586	−	0.919715i	$-0.628419\pi$
$257$	3.32837	−	1.92163i	0.207618	−	0.119868i	0.600204	+	0.799847i	$0.295086\pi$
$258$		0			0
$259$	−1.74542	−	2.16993i	−0.108455	−	0.134833i
$260$		0			0
$261$	−2.05452	+	7.66759i	−0.127172	+	0.474612i
$262$		0			0
$263$	−3.15784	+	5.46953i	−0.194720	+	0.337266i	−0.946809	−	0.321797i	$-0.895713\pi$
$263$	−3.15784	+	5.46953i	−0.194720	+	0.337266i	0.752088	+	0.659062i	$0.229047\pi$
$264$		0			0
$265$	−37.1409			−2.28155
$266$		0			0
$267$	−8.76556	+	8.76556i	−0.536444	+	0.536444i
$268$		0			0
$269$	23.2914	−	6.24090i	1.42010	−	0.380514i	0.534580	−	0.845118i	$-0.320470\pi$
$269$	23.2914	−	6.24090i	1.42010	−	0.380514i	0.885519	+	0.464603i	$0.153803\pi$
$270$		0			0
$271$	4.73315	+	8.19805i	0.287518	+	0.497996i	0.973217	−	0.229890i	$-0.0738365\pi$
$271$	4.73315	+	8.19805i	0.287518	+	0.497996i	−0.685699	+	0.727886i	$0.740503\pi$
$272$		0			0
$273$	12.0979	+	27.4141i	0.732200	+	1.65918i
$274$		0			0
$275$	−2.05407	+	7.66590i	−0.123865	+	0.462271i
$276$		0			0
$277$	−11.3278	+	3.03526i	−0.680619	+	0.182371i	−0.582533	−	0.812807i	$-0.697938\pi$
$277$	−11.3278	+	3.03526i	−0.680619	+	0.182371i	−0.0980853	+	0.995178i	$0.531272\pi$
$278$		0			0
$279$		−	28.1409i		−	1.68475i
$280$		0			0
$281$		−	5.59517i		−	0.333780i	−0.985976	−	0.166890i	$-0.946628\pi$
$281$		−	5.59517i		−	0.333780i	0.985976	−	0.166890i	$-0.0533724\pi$
$282$		0			0
$283$	3.70559	−	0.992910i	0.220275	−	0.0590224i	−0.146994	−	0.989137i	$-0.546960\pi$
$283$	3.70559	−	0.992910i	0.220275	−	0.0590224i	0.367268	+	0.930115i	$0.380293\pi$
$284$		0			0
$285$	9.82326	−	36.6609i	0.581880	−	2.17160i
$286$		0			0
$287$	4.33042	−	5.91938i	0.255617	−	0.349410i
$288$		0			0
$289$	−5.76778	−	9.99009i	−0.339281	−	0.587652i
$290$		0			0
$291$	−14.5744	+	3.90519i	−0.854365	+	0.228927i
$292$		0			0
$293$	−9.74731	+	9.74731i	−0.569444	+	0.569444i	−0.931973	−	0.362529i	$-0.881913\pi$
$293$	−9.74731	+	9.74731i	−0.569444	+	0.569444i	0.362529	+	0.931973i	$0.381913\pi$
$294$		0			0
$295$	12.6359			0.735692
$296$		0			0
$297$	−1.15450	+	1.99965i	−0.0669908	+	0.116031i
$298$		0			0
$299$	−2.63108	+	9.81932i	−0.152159	+	0.567866i
$300$		0			0
$301$	4.08198	+	26.3314i	0.235282	+	1.51772i
$302$		0			0
$303$	−3.21608	+	1.85681i	−0.184759	+	0.106671i
$304$		0			0
$305$	23.2783	−	40.3192i	1.33291	−	2.30867i
$306$		0			0
$307$	−20.5735	+	20.5735i	−1.17419	+	1.17419i	−0.192988	+	0.981201i	$0.561818\pi$
$307$	−20.5735	+	20.5735i	−1.17419	+	1.17419i	−0.981201	+	0.192988i	$0.938182\pi$
$308$		0			0
$309$	−4.41365	−	4.41365i	−0.251084	−	0.251084i
$310$		0			0
$311$	−0.495271	−	0.285945i	−0.0280843	−	0.0162145i	0.485892	−	0.874019i	$-0.338495\pi$
$311$	−0.495271	−	0.285945i	−0.0280843	−	0.0162145i	−0.513976	+	0.857804i	$0.671828\pi$
$312$		0			0
$313$	0.707287	+	1.22506i	0.0399782	+	0.0692443i	0.885322	−	0.464978i	$-0.153938\pi$
$313$	0.707287	+	1.22506i	0.0399782	+	0.0692443i	−0.845344	+	0.534222i	$0.820604\pi$
$314$		0			0
$315$	11.1880	−	28.8624i	0.630372	−	1.62621i
$316$		0			0
$317$	25.2914	+	6.77681i	1.42051	+	0.380624i	0.885663	−	0.464328i	$-0.153704\pi$
$317$	25.2914	+	6.77681i	1.42051	+	0.380624i	0.534843	+	0.844951i	$0.320371\pi$
$318$		0			0
$319$	2.76217	+	1.59474i	0.154652	+	0.0892882i
$320$		0			0
$321$			11.5785i			0.646248i
$322$		0			0
$323$	7.54051	+	7.54051i	0.419565	+	0.419565i
$324$		0			0
$325$	6.22177	+	23.2200i	0.345122	+	1.28801i
$326$		0			0
$327$	−7.25406	+	4.18813i	−0.401150	+	0.231604i
$328$		0			0
$329$	7.49728	+	0.812871i	0.413338	+	0.0448150i
$330$		0			0
$331$	2.71378	+	0.727156i	0.149163	+	0.0399681i	0.332628	−	0.943058i	$-0.392065\pi$
$331$	2.71378	+	0.727156i	0.149163	+	0.0399681i	−0.183465	+	0.983026i	$0.558731\pi$
$332$		0			0
$333$	−0.985490	−	3.67790i	−0.0540045	−	0.201548i
$334$		0			0
$335$	8.69259			0.474927
$336$		0			0
$337$	−23.9205			−1.30303			−0.651517	−	0.758634i	$-0.725867\pi$
$337$	−23.9205			−1.30303			−0.651517	+	0.758634i	$0.725867\pi$
$338$		0			0
$339$	−7.68312	−	28.6738i	−0.417290	−	1.55735i
$340$		0			0
$341$	−10.9216	−	2.92644i	−0.591438	−	0.158475i
$342$		0			0
$343$	17.5566	+	5.89614i	0.947969	+	0.318362i
$344$		0			0
$345$	16.6368	−	9.60525i	0.895695	−	0.517130i
$346$		0			0
$347$	−3.23720	−	12.0814i	−0.173782	−	0.648563i	−0.996756	−	0.0804837i	$-0.974353\pi$
$347$	−3.23720	−	12.0814i	−0.173782	−	0.648563i	0.822974	−	0.568079i	$-0.192313\pi$
$348$		0			0
$349$	−21.9157	−	21.9157i	−1.17312	−	1.17312i	−0.981461	−	0.191662i	$-0.938612\pi$
$349$	−21.9157	−	21.9157i	−1.17312	−	1.17312i	−0.191662	−	0.981461i	$-0.561388\pi$
$350$		0			0
$351$			6.99394i			0.373309i
$352$		0			0
$353$	−18.1984	−	10.5069i	−0.968604	−	0.559224i	−0.0697939	−	0.997561i	$-0.522234\pi$
$353$	−18.1984	−	10.5069i	−0.968604	−	0.559224i	−0.898810	+	0.438337i	$0.855567\pi$
$354$		0			0
$355$	23.3784	+	6.26421i	1.24079	+	0.332470i
$356$		0			0
$357$	9.97186	+	12.3972i	0.527767	+	0.656127i
$358$		0			0
$359$	−4.78310	−	8.28458i	−0.252443	−	0.437243i	0.711755	−	0.702428i	$-0.247901\pi$
$359$	−4.78310	−	8.28458i	−0.252443	−	0.437243i	−0.964198	+	0.265184i	$0.914567\pi$
$360$		0			0
$361$	1.56807	+	0.905328i	0.0825302	+	0.0476488i
$362$		0			0
$363$	−16.1661	−	16.1661i	−0.848498	−	0.848498i
$364$		0			0
$365$	−25.8520	+	25.8520i	−1.35315	+	1.35315i
$366$		0			0
$367$	3.06305	−	5.30536i	0.159890	−	0.276938i	−0.774939	−	0.632036i	$-0.782219\pi$
$367$	3.06305	−	5.30536i	0.159890	−	0.276938i	0.934829	+	0.355099i	$0.115553\pi$
$368$		0			0
$369$	8.68463	−	5.01408i	0.452104	−	0.261022i
$370$		0			0
$371$	10.9813	−	28.3292i	0.570123	−	1.47078i
$372$		0			0
$373$	4.25162	−	15.8673i	0.220140	−	0.821575i	−0.764153	−	0.645035i	$-0.776843\pi$
$373$	4.25162	−	15.8673i	0.220140	−	0.821575i	0.984293	−	0.176540i	$-0.0564906\pi$
$374$		0			0
$375$	1.91411	−	3.31533i	0.0988440	−	0.171203i
$376$		0			0
$377$	9.66091			0.497562
$378$		0			0
$379$	6.05253	−	6.05253i	0.310897	−	0.310897i	−0.534360	−	0.845257i	$-0.679447\pi$
$379$	6.05253	−	6.05253i	0.310897	−	0.310897i	0.845257	+	0.534360i	$0.179447\pi$
$380$		0			0
$381$	−11.1620	+	2.99085i	−0.571846	+	0.153226i
$382$		0			0
$383$	−9.64030	−	16.6975i	−0.492596	−	0.853202i	0.507367	−	0.861730i	$-0.330619\pi$
$383$	−9.64030	−	16.6975i	−0.492596	−	0.853202i	−0.999964	+	0.00852805i	$0.997285\pi$
$384$		0			0
$385$	−10.0381	−	7.34357i	−0.511591	−	0.374263i
$386$		0			0
$387$	−9.42954	+	35.1915i	−0.479330	+	1.78889i
$388$		0			0
$389$	27.6476	−	7.40814i	1.40179	−	0.375608i	0.522801	−	0.852455i	$-0.324887\pi$
$389$	27.6476	−	7.40814i	1.40179	−	0.375608i	0.878986	+	0.476847i	$0.158221\pi$
$390$		0			0
$391$			5.39753i			0.272965i
$392$		0			0
$393$			35.5835i			1.79495i
$394$		0			0
$395$	2.54934	−	0.683093i	0.128271	−	0.0343701i
$396$		0			0
$397$	2.40028	−	8.95799i	0.120467	−	0.449588i	−0.879171	−	0.476507i	$-0.841903\pi$
$397$	2.40028	−	8.95799i	0.120467	−	0.449588i	0.999638	+	0.0269184i	$0.00856943\pi$
$398$		0			0
$399$	25.0587	+	18.3321i	1.25451	+	0.917754i
$400$		0			0
$401$	17.5281	+	30.3596i	0.875312	+	1.51609i	0.856430	+	0.516264i	$0.172678\pi$
$401$	17.5281	+	30.3596i	0.875312	+	1.51609i	0.0188827	+	0.999822i	$0.493989\pi$
$402$		0			0
$403$	−33.0815	+	8.86416i	−1.64791	+	0.441555i
$404$		0			0
$405$	−15.4735	+	15.4735i	−0.768886	+	0.768886i
$406$		0			0
$407$	−1.52989			−0.0758338
$408$		0			0
$409$	−17.4392	+	30.2056i	−0.862314	+	1.49357i	0.00737621	+	0.999973i	$0.497652\pi$
$409$	−17.4392	+	30.2056i	−0.862314	+	1.49357i	−0.869690	+	0.493598i	$0.835681\pi$
$410$		0			0
$411$	−1.67923	+	6.26699i	−0.0828306	+	0.309128i
$412$		0			0
$413$	−3.73603	+	9.63807i	−0.183838	+	0.474258i
$414$		0			0
$415$	10.5082	−	6.06689i	0.515826	−	0.297812i
$416$		0			0
$417$	10.9209	−	18.9156i	0.534801	−	0.926302i
$418$		0			0
$419$	8.57828	−	8.57828i	0.419076	−	0.419076i	−0.465809	−	0.884885i	$-0.654237\pi$
$419$	8.57828	−	8.57828i	0.419076	−	0.419076i	0.884885	+	0.465809i	$0.154237\pi$
$420$		0			0
$421$	7.41183	+	7.41183i	0.361230	+	0.361230i	0.864266	−	0.503035i	$-0.167783\pi$
$421$	7.41183	+	7.41183i	0.361230	+	0.361230i	−0.503035	+	0.864266i	$0.667783\pi$
$422$		0			0
$423$	8.92967	+	5.15555i	0.434175	+	0.250671i
$424$		0			0
$425$	6.38184	+	11.0537i	0.309565	+	0.536182i
$426$		0			0
$427$	23.8709	+	29.6766i	1.15519	+	1.43615i
$428$		0			0
$429$	15.9010	+	4.26065i	0.767706	+	0.205706i
$430$		0			0
$431$	1.39637	+	0.806195i	0.0672608	+	0.0388331i	0.533253	−	0.845956i	$-0.320969\pi$
$431$	1.39637	+	0.806195i	0.0672608	+	0.0388331i	−0.465992	+	0.884789i	$0.654303\pi$
$432$		0			0
$433$		−	13.0869i		−	0.628917i	−0.949271	−	0.314458i	$-0.898177\pi$
$433$		−	13.0869i		−	0.628917i	0.949271	−	0.314458i	$-0.101823\pi$
$434$		0			0
$435$	−12.9093	−	12.9093i	−0.618956	−	0.618956i
$436$		0			0
$437$	2.72622	+	10.1744i	0.130413	+	0.486708i
$438$		0			0
$439$	−1.71358	+	0.989334i	−0.0817846	+	0.0472184i	−0.540335	−	0.841450i	$-0.681702\pi$
$439$	−1.71358	+	0.989334i	−0.0817846	+	0.0472184i	0.458550	+	0.888669i	$0.348369\pi$
$440$		0			0
$441$	18.7069	+	17.0673i	0.890803	+	0.812729i
$442$		0			0
$443$	−33.5156	−	8.98048i	−1.59237	−	0.426675i	−0.649646	−	0.760237i	$-0.725083\pi$
$443$	−33.5156	−	8.98048i	−1.59237	−	0.426675i	−0.942728	+	0.333562i	$0.891749\pi$
$444$		0			0
$445$	−4.03377	−	15.0542i	−0.191219	−	0.713640i
$446$		0			0
$447$	−21.8614			−1.03401
$448$		0			0
$449$	20.0460			0.946031			0.473015	−	0.881054i	$-0.343166\pi$
$449$	20.0460			0.946031			0.473015	+	0.881054i	$0.343166\pi$
$450$		0			0
$451$	−1.04285	−	3.89196i	−0.0491058	−	0.183265i
$452$		0			0
$453$	25.4407	+	6.81682i	1.19531	+	0.320282i
$454$		0			0
$455$	−37.4537	−	4.06081i	−1.75586	−	0.190374i
$456$		0			0
$457$	−25.9859	+	15.0030i	−1.21557	+	0.701810i	−0.963967	−	0.266020i	$-0.914291\pi$
$457$	−25.9859	+	15.0030i	−1.21557	+	0.701810i	−0.251603	+	0.967830i	$0.580958\pi$
$458$		0			0
$459$	0.961116	+	3.58693i	0.0448611	+	0.167424i
$460$		0			0
$461$	−18.2334	−	18.2334i	−0.849213	−	0.849213i	0.140822	−	0.990035i	$-0.455026\pi$
$461$	−18.2334	−	18.2334i	−0.849213	−	0.849213i	−0.990035	+	0.140822i	$0.955026\pi$
$462$		0			0
$463$			31.3804i			1.45837i	0.684316	+	0.729186i	$0.260101\pi$
$463$			31.3804i			1.45837i	−0.684316	+	0.729186i	$0.739899\pi$
$464$		0			0
$465$	56.0497	+	32.3603i	2.59924	+	1.50067i
$466$		0			0
$467$	−23.0310	−	6.17115i	−1.06575	−	0.285567i	−0.317004	−	0.948424i	$-0.602677\pi$
$467$	−23.0310	−	6.17115i	−1.06575	−	0.285567i	−0.748745	+	0.662858i	$0.769343\pi$
$468$		0			0
$469$	−2.57011	+	6.63028i	−0.118677	+	0.306158i
$470$		0			0
$471$	18.8844	+	32.7088i	0.870148	+	1.50714i
$472$		0			0
$473$	12.6774	+	7.31928i	0.582906	+	0.336541i
$474$		0			0
$475$	17.6129	+	17.6129i	0.808135	+	0.808135i
$476$		0			0
$477$	29.3752	−	29.3752i	1.34500	−	1.34500i
$478$		0			0
$479$	17.6784	−	30.6199i	0.807747	−	1.39906i	−0.106674	−	0.994294i	$-0.534020\pi$
$479$	17.6784	−	30.6199i	0.807747	−	1.39906i	0.914421	−	0.404764i	$-0.132646\pi$
$480$		0			0
$481$	−4.01319	+	2.31701i	−0.182986	+	0.105647i
$482$		0			0
$483$	2.40746	+	15.5297i	0.109543	+	0.706625i
$484$		0			0
$485$	4.90979	−	18.3236i	0.222942	−	0.832032i
$486$		0			0
$487$	−5.31153	+	9.19984i	−0.240688	+	0.416884i	−0.960911	−	0.276859i	$-0.910706\pi$
$487$	−5.31153	+	9.19984i	−0.240688	+	0.416884i	0.720222	+	0.693743i	$0.244040\pi$
$488$		0			0
$489$	59.1357			2.67421
$490$		0			0
$491$	26.9088	−	26.9088i	1.21438	−	1.21438i	0.244806	−	0.969572i	$-0.421276\pi$
$491$	26.9088	−	26.9088i	1.21438	−	1.21438i	0.969572	−	0.244806i	$-0.0787243\pi$
$492$		0			0
$493$	4.95472	−	1.32761i	0.223149	−	0.0597927i
$494$		0			0
$495$	−8.50291	−	14.7275i	−0.382177	−	0.661950i
$496$		0			0
$497$	−11.6902	+	15.9797i	−0.524379	+	0.716789i
$498$		0			0
$499$	3.28081	−	12.2441i	0.146869	−	0.548123i	−0.852796	−	0.522244i	$-0.825095\pi$
$499$	3.28081	−	12.2441i	0.146869	−	0.548123i	0.999665	−	0.0258790i	$-0.00823846\pi$
$500$		0			0
$501$	−9.49441	+	2.54402i	−0.424179	+	0.113658i
$502$		0			0
$503$		−	13.7074i		−	0.611183i	−0.952163	−	0.305591i	$-0.901146\pi$
$503$		−	13.7074i		−	0.611183i	0.952163	−	0.305591i	$-0.0988542\pi$
$504$		0			0
$505$		−	4.66892i		−	0.207764i
$506$		0			0
$507$	15.8615	−	4.25008i	0.704434	−	0.188753i
$508$		0			0
$509$	−6.16734	+	23.0168i	−0.273363	+	1.02020i	0.683568	+	0.729887i	$0.260427\pi$
$509$	−6.16734	+	23.0168i	−0.273363	+	1.02020i	−0.956931	+	0.290317i	$0.906239\pi$
$510$		0			0
$511$	−12.0750	−	27.3622i	−0.534168	−	1.21043i
$512$		0			0
$513$	3.62343	+	6.27596i	0.159978	+	0.277091i
$514$		0			0
$515$	7.58014	−	2.03109i	0.334021	−	0.0895007i
$516$		0			0
$517$	2.92950	−	2.92950i	0.128839	−	0.128839i
$518$		0			0
$519$	21.3854			0.938715
$520$		0			0
$521$	11.8589	−	20.5402i	0.519548	−	0.899884i	−0.480194	−	0.877163i	$-0.659434\pi$
$521$	11.8589	−	20.5402i	0.519548	−	0.899884i	0.999742	−	0.0227214i	$-0.00723308\pi$
$522$		0			0
$523$	4.85978	−	18.1369i	0.212503	−	0.793073i	−0.774527	−	0.632540i	$-0.782012\pi$
$523$	4.85978	−	18.1369i	0.212503	−	0.793073i	0.987031	−	0.160532i	$-0.0513211\pi$
$524$		0			0
$525$	23.2920	+	28.9569i	1.01655	+	1.26378i
$526$		0			0
$527$	−15.7482	+	9.09220i	−0.686000	+	0.396063i
$528$		0			0
$529$	8.83428	−	15.3014i	0.384099	−	0.665279i
$530$		0			0
$531$	−9.99392	+	9.99392i	−0.433699	+	0.433699i
$532$		0			0
$533$	−8.62996	−	8.62996i	−0.373805	−	0.373805i
$534$		0			0
$535$	−12.6067	−	7.27851i	−0.545037	−	0.314677i
$536$		0			0
$537$	−24.8536	−	43.0476i	−1.07251	−	1.85764i
$538$		0			0
$539$	8.56926	−	5.48534i	0.369104	−	0.236271i
$540$		0			0
$541$	−25.2496	−	6.76561i	−1.08556	−	0.290876i	−0.328691	−	0.944437i	$-0.606608\pi$
$541$	−25.2496	−	6.76561i	−1.08556	−	0.290876i	−0.756874	+	0.653561i	$0.773274\pi$
$542$		0			0
$543$	−19.1301	−	11.0448i	−0.820952	−	0.473977i
$544$		0			0
$545$		−	10.5310i		−	0.451100i
$546$		0			0
$547$	−23.8532	−	23.8532i	−1.01989	−	1.01989i	−0.999798	−	0.0200929i	$-0.993604\pi$
$547$	−23.8532	−	23.8532i	−1.01989	−	1.01989i	−0.0200929	−	0.999798i	$-0.506396\pi$
$548$		0			0
$549$	13.4779	+	50.3001i	0.575221	+	2.14675i
$550$		0			0
$551$	8.66915	−	5.00513i	0.369318	−	0.213226i
$552$		0			0
$553$	−0.232726	+	2.14648i	−0.00989651	+	0.0912775i
$554$		0			0
$555$	8.45871	+	2.26650i	0.359052	+	0.0962077i
$556$		0			0
$557$	−11.1522	−	41.6206i	−0.472534	−	1.76352i	−0.630617	−	0.776094i	$-0.717198\pi$
$557$	−11.1522	−	41.6206i	−0.472534	−	1.76352i	0.158083	−	0.987426i	$-0.449468\pi$
$558$		0			0
$559$	44.3401			1.87539
$560$		0			0
$561$	8.74052			0.369025
$562$		0			0
$563$	−2.30901	−	8.61735i	−0.0973133	−	0.363178i	0.900047	−	0.435793i	$-0.143532\pi$
$563$	−2.30901	−	8.61735i	−0.0973133	−	0.363178i	−0.997360	+	0.0726153i	$0.976865\pi$
$564$		0			0
$565$	36.0500	+	9.65958i	1.51664	+	0.406382i
$566$		0			0
$567$	−7.22743	−	16.3775i	−0.303524	−	0.687789i
$568$		0			0
$569$	−5.49552	+	3.17284i	−0.230384	+	0.133012i	−0.610749	−	0.791824i	$-0.709132\pi$
$569$	−5.49552	+	3.17284i	−0.230384	+	0.133012i	0.380365	+	0.924836i	$0.375798\pi$
$570$		0			0
$571$	−9.71490	−	36.2565i	−0.406556	−	1.51729i	−0.801168	−	0.598439i	$-0.795788\pi$
$571$	−9.71490	−	36.2565i	−0.406556	−	1.51729i	0.394612	−	0.918848i	$-0.370879\pi$
$572$		0			0
$573$	27.6637	+	27.6637i	1.15567	+	1.15567i
$574$		0			0
$575$			12.6074i			0.525765i
$576$		0			0
$577$	−1.63907	−	0.946316i	−0.0682353	−	0.0393957i	0.465494	−	0.885051i	$-0.345877\pi$
$577$	−1.63907	−	0.946316i	−0.0682353	−	0.0393957i	−0.533729	+	0.845655i	$0.679210\pi$
$578$		0			0
$579$	55.8569	+	14.9668i	2.32134	+	0.622000i
$580$		0			0
$581$	1.52061	+	9.80889i	0.0630854	+	0.406941i
$582$		0			0
$583$	−8.34585	−	14.4554i	−0.345650	−	0.598683i
$584$		0			0
$585$	−44.6094	−	25.7553i	−1.84437	−	1.06485i
$586$		0			0
$587$	26.8519	+	26.8519i	1.10830	+	1.10830i	0.993374	+	0.114923i	$0.0366621\pi$
$587$	26.8519	+	26.8519i	1.10830	+	1.10830i	0.114923	+	0.993374i	$0.463338\pi$
$588$		0			0
$589$	−25.0931	+	25.0931i	−1.03394	+	1.03394i
$590$		0			0
$591$	15.1265	−	26.1998i	0.622220	−	1.07772i
$592$		0			0
$593$	−23.8885	+	13.7920i	−0.980984	+	0.566372i	−0.902567	−	0.430549i	$-0.858320\pi$
$593$	−23.8885	+	13.7920i	−0.980984	+	0.566372i	−0.0784171	+	0.996921i	$0.524987\pi$
$594$		0			0
$595$	−19.7667	+	3.06430i	−0.810354	+	0.125624i
$596$		0			0
$597$	−6.80456	+	25.3950i	−0.278492	+	1.03935i
$598$		0			0
$599$	11.8101	−	20.4557i	0.482548	−	0.835797i	−0.517252	−	0.855833i	$-0.673045\pi$
$599$	11.8101	−	20.4557i	0.482548	−	0.835797i	0.999799	+	0.0200365i	$0.00637824\pi$
$600$		0			0
$601$	5.61717			0.229129			0.114565	−	0.993416i	$-0.463453\pi$
$601$	5.61717			0.229129			0.114565	+	0.993416i	$0.463453\pi$
$602$		0			0
$603$	−6.87508	+	6.87508i	−0.279975	+	0.279975i
$604$		0			0
$605$	27.7641	−	7.43936i	1.12877	−	0.302453i
$606$		0			0
$607$	2.43281	+	4.21375i	0.0987446	+	0.171031i	0.911165	−	0.412041i	$-0.135184\pi$
$607$	2.43281	+	4.21375i	0.0987446	+	0.171031i	−0.812421	+	0.583072i	$0.801851\pi$
$608$		0			0
$609$	13.6635	−	6.02975i	0.553672	−	0.244338i
$610$		0			0
$611$	3.24791	−	12.1214i	0.131396	−	0.490378i
$612$		0			0
$613$	−3.99109	+	1.06941i	−0.161199	+	0.0431931i	−0.338516	−	0.940961i	$-0.609925\pi$
$613$	−3.99109	+	1.06941i	−0.161199	+	0.0431931i	0.177317	+	0.984154i	$0.443258\pi$
$614$		0			0
$615$			23.0635i			0.930010i
$616$		0			0
$617$			25.3025i			1.01864i	0.860578	+	0.509319i	$0.170103\pi$
$617$			25.3025i			1.01864i	−0.860578	+	0.509319i	$0.829897\pi$
$618$		0			0
$619$	−17.7405	+	4.75356i	−0.713051	+	0.191062i	−0.597069	−	0.802190i	$-0.703668\pi$
$619$	−17.7405	+	4.75356i	−0.713051	+	0.191062i	−0.115982	+	0.993251i	$0.537002\pi$
$620$		0			0
$621$	−0.949348	+	3.54302i	−0.0380960	+	0.142176i
$622$		0			0
$623$	12.6753	+	1.37428i	0.507825	+	0.0550595i
$624$		0			0
$625$	−11.2438	−	19.4749i	−0.449753	−	0.778995i
$626$		0			0
$627$	16.4760	−	4.41472i	0.657987	−	0.176307i
$628$		0			0
$629$	−1.73981	+	1.73981i	−0.0693707	+	0.0693707i
$630$		0			0
$631$	41.4293			1.64928			0.824638	−	0.565661i	$-0.191379\pi$
$631$	41.4293			1.64928			0.824638	+	0.565661i	$0.191379\pi$
$632$		0			0
$633$	10.4368	−	18.0771i	0.414826	−	0.718500i
$634$		0			0
$635$	3.76023	−	14.0334i	0.149220	−	0.556897i
$636$		0			0
$637$	14.1712	−	27.3672i	0.561484	−	1.08433i
$638$		0			0
$639$	−23.4447	+	13.5358i	−0.927458	+	0.535468i
$640$		0			0
$641$	−17.0933	+	29.6065i	−0.675146	+	1.16939i	0.301280	+	0.953536i	$0.402586\pi$
$641$	−17.0933	+	29.6065i	−0.675146	+	1.16939i	−0.976426	+	0.215852i	$0.930747\pi$
$642$		0			0
$643$	−3.46526	+	3.46526i	−0.136657	+	0.136657i	−0.772126	−	0.635469i	$-0.780807\pi$
$643$	−3.46526	+	3.46526i	−0.136657	+	0.136657i	0.635469	+	0.772126i	$0.280807\pi$
$644$		0			0
$645$	−59.2493	−	59.2493i	−2.33294	−	2.33294i
$646$		0			0
$647$	−27.2890	−	15.7553i	−1.07284	−	0.619406i	−0.143886	−	0.989594i	$-0.545960\pi$
$647$	−27.2890	−	15.7553i	−1.07284	−	0.619406i	−0.928957	+	0.370188i	$0.879293\pi$
$648$		0			0
$649$	2.83939	+	4.91797i	0.111456	+	0.193047i
$650$		0			0
$651$	−41.2549	+	33.1841i	−1.61691	+	1.30059i
$652$		0			0
$653$	−19.3649	−	5.18880i	−0.757805	−	0.203053i	−0.140828	−	0.990034i	$-0.544976\pi$
$653$	−19.3649	−	5.18880i	−0.757805	−	0.203053i	−0.616977	+	0.786981i	$0.711643\pi$
$654$		0			0
$655$	−38.7436	−	22.3686i	−1.51384	−	0.874015i
$656$		0			0
$657$		−	40.8933i		−	1.59540i
$658$		0			0
$659$	29.3969	+	29.3969i	1.14514	+	1.14514i	0.987496	+	0.157643i	$0.0503896\pi$
$659$	29.3969	+	29.3969i	1.14514	+	1.14514i	0.157643	+	0.987496i	$0.449610\pi$
$660$		0			0
$661$	−12.5518	−	46.8440i	−0.488208	−	1.82202i	−0.565157	−	0.824984i	$-0.691184\pi$
$661$	−12.5518	−	46.8440i	−0.488208	−	1.82202i	0.0769483	−	0.997035i	$-0.475482\pi$
$662$		0			0
$663$	22.9280	−	13.2375i	0.890450	−	0.514102i
$664$		0			0
$665$	−35.7127	+	15.7601i	−1.38488	+	0.611151i
$666$		0			0
$667$	4.89406	+	1.31136i	0.189499	+	0.0507760i
$668$		0			0
$669$	11.6468	+	43.4664i	0.450290	+	1.68051i
$670$		0			0
$671$	20.9232			0.807733
$672$		0			0
$673$	11.6457			0.448909			0.224454	−	0.974485i	$-0.427940\pi$
$673$	11.6457			0.448909			0.224454	+	0.974485i	$0.427940\pi$
$674$		0			0
$675$	2.24495	+	8.37826i	0.0864080	+	0.322479i
$676$		0			0
$677$	−32.6233	−	8.74138i	−1.25381	−	0.335959i	−0.430006	−	0.902826i	$-0.641488\pi$
$677$	−32.6233	−	8.74138i	−1.25381	−	0.335959i	−0.823809	+	0.566868i	$0.808155\pi$
$678$		0			0
$679$	12.5247	+	9.16263i	0.480653	+	0.351630i
$680$		0			0
$681$	−39.0453	+	22.5428i	−1.49622	+	0.863843i
$682$		0			0
$683$	1.76166	+	6.57460i	0.0674080	+	0.251570i	0.991405	−	0.130830i	$-0.0417643\pi$
$683$	1.76166	+	6.57460i	0.0674080	+	0.251570i	−0.923997	+	0.382400i	$0.875098\pi$
$684$		0			0
$685$	−5.76794	−	5.76794i	−0.220382	−	0.220382i
$686$		0			0
$687$			17.9827i			0.686081i
$688$		0			0
$689$	−43.7854	−	25.2795i	−1.66809	−	0.963073i
$690$		0			0
$691$	29.7544	+	7.97267i	1.13191	+	0.303295i	0.775695	−	0.631108i	$-0.217400\pi$
$691$	29.7544	+	7.97267i	1.13191	+	0.303295i	0.356217	+	0.934403i	$0.384066\pi$
$692$		0			0
$693$	13.7474	−	2.13117i	0.522221	−	0.0809565i
$694$		0			0
$695$	13.7303	+	23.7816i	0.520821	+	0.902088i
$696$		0			0
$697$	−5.61193	−	3.24005i	−0.212567	−	0.122726i
$698$		0			0
$699$	−52.7060	−	52.7060i	−1.99352	−	1.99352i
$700$		0			0
$701$	28.2191	−	28.2191i	1.06582	−	1.06582i	0.0681440	−	0.997675i	$-0.478292\pi$
$701$	28.2191	−	28.2191i	1.06582	−	1.06582i	0.997675	−	0.0681440i	$-0.0217077\pi$
$702$		0			0
$703$	−2.40080	+	4.15831i	−0.0905480	+	0.156834i
$704$		0			0
$705$	−20.5371	+	11.8571i	−0.773473	+	0.446565i
$706$		0			0
$707$	3.56123	+	1.38045i	0.133934	+	0.0519171i
$708$		0			0
$709$	4.97862	−	18.5805i	0.186976	−	0.697804i	−0.807223	−	0.590247i	$-0.799030\pi$
$709$	4.97862	−	18.5805i	0.186976	−	0.697804i	0.994199	−	0.107557i	$-0.0343028\pi$
$710$		0			0
$711$	−1.47604	+	2.55657i	−0.0553557	+	0.0958790i
$712$		0			0
$713$	−17.9618			−0.672673
$714$		0			0
$715$	−14.6347	+	14.6347i	−0.547308	+	0.547308i
$716$		0			0
$717$	−33.1938	+	8.89426i	−1.23965	+	0.332162i
$718$		0			0
$719$	−11.9289	−	20.6615i	−0.444873	−	0.770543i	0.553170	−	0.833068i	$-0.313418\pi$
$719$	−11.9289	−	20.6615i	−0.444873	−	0.770543i	−0.998043	+	0.0625253i	$0.980085\pi$
$720$		0			0
$721$	−0.691981	+	6.38229i	−0.0257707	+	0.237689i
$722$		0			0
$723$	8.11163	−	30.2730i	0.301675	−	1.12587i
$724$		0			0
$725$	11.5731	−	3.10100i	0.429814	−	0.115168i
$726$		0			0
$727$			28.5645i			1.05940i	0.848185	+	0.529700i	$0.177695\pi$
$727$			28.5645i			1.05940i	−0.848185	+	0.529700i	$0.822305\pi$
$728$		0			0
$729$		−	36.7360i		−	1.36059i
$730$		0			0
$731$	22.7404	−	6.09328i	0.841085	−	0.225368i
$732$		0			0
$733$	−6.04445	+	22.5582i	−0.223257	+	0.833206i	0.759839	+	0.650112i	$0.225278\pi$
$733$	−6.04445	+	22.5582i	−0.223257	+	0.833206i	−0.983095	+	0.183094i	$0.941389\pi$
$734$		0			0
$735$	−55.5055	+	17.6331i	−2.04735	+	0.650406i
$736$		0			0
$737$	1.95329	+	3.38320i	0.0719504	+	0.124622i
$738$		0			0
$739$	1.72028	−	0.460947i	0.0632814	−	0.0169562i	−0.227039	−	0.973886i	$-0.572905\pi$
$739$	1.72028	−	0.460947i	0.0632814	−	0.0169562i	0.290321	+	0.956929i	$0.406238\pi$
$740$		0			0
$741$	36.5335	−	36.5335i	1.34209	−	1.34209i
$742$		0			0
$743$	−16.7041			−0.612815			−0.306407	−	0.951900i	$-0.599127\pi$
$743$	−16.7041			−0.612815			−0.306407	+	0.951900i	$0.599127\pi$
$744$		0			0
$745$	13.7426	−	23.8029i	0.503490	−	0.872070i
$746$		0			0
$747$	−3.51266	+	13.1094i	−0.128522	+	0.479649i
$748$		0			0
$749$	9.27909	−	7.46379i	0.339051	−	0.272721i
$750$		0			0
$751$	−1.51512	+	0.874754i	−0.0552874	+	0.0319202i	−0.527389	−	0.849624i	$-0.676829\pi$
$751$	−1.51512	+	0.874754i	−0.0552874	+	0.0319202i	0.472101	+	0.881544i	$0.343496\pi$
$752$		0			0
$753$	−12.1678	+	21.0752i	−0.443419	+	0.768024i
$754$		0			0
$755$	−23.4148	+	23.4148i	−0.852153	+	0.852153i
$756$		0			0
$757$	15.6771	+	15.6771i	0.569792	+	0.569792i	0.932070	−	0.362278i	$-0.118001\pi$
$757$	15.6771	+	15.6771i	0.569792	+	0.569792i	−0.362278	+	0.932070i	$0.618001\pi$
$758$		0			0
$759$	7.47683	+	4.31675i	0.271392	+	0.156688i
$760$		0			0
$761$	−25.9814	−	45.0012i	−0.941826	−	1.63129i	−0.761984	−	0.647596i	$-0.775775\pi$
$761$	−25.9814	−	45.0012i	−0.941826	−	1.63129i	−0.179842	−	0.983695i	$-0.557559\pi$
$762$		0			0
$763$	8.03255	+	3.11368i	0.290798	+	0.112723i
$764$		0			0
$765$	−26.4178	−	7.07864i	−0.955139	−	0.255929i
$766$		0			0
$767$	14.8965	+	8.60050i	0.537882	+	0.310546i
$768$		0			0
$769$			34.9699i			1.26105i	0.776170	+	0.630524i	$0.217160\pi$
$769$			34.9699i			1.26105i	−0.776170	+	0.630524i	$0.782840\pi$
$770$		0			0
$771$	−6.99090	−	6.99090i	−0.251771	−	0.251771i
$772$		0			0
$773$	3.55817	+	13.2793i	0.127978	+	0.477622i	0.999928	−	0.0119731i	$-0.00381124\pi$
$773$	3.55817	+	13.2793i	0.127978	+	0.477622i	−0.871950	+	0.489595i	$0.837145\pi$
$774$		0			0
$775$	−36.7841	+	21.2373i	−1.32132	+	0.762866i
$776$		0			0
$777$	−4.22974	+	5.78176i	−0.151741	+	0.207419i
$778$		0			0
$779$	−12.2150	−	3.27301i	−0.437650	−	0.117268i
$780$		0			0
$781$	2.81523	+	10.5066i	0.100737	+	0.375956i
$782$		0			0
$783$	3.48586			0.124574
$784$		0			0
$785$	−47.4847			−1.69480
$786$		0			0
$787$	6.42575	+	23.9812i	0.229053	+	0.854838i	0.980740	+	0.195318i	$0.0625738\pi$
$787$	6.42575	+	23.9812i	0.229053	+	0.854838i	−0.751687	+	0.659520i	$0.770760\pi$
$788$		0			0
$789$	15.6932	+	4.20498i	0.558692	+	0.149701i
$790$		0			0
$791$	−18.0267	+	24.6412i	−0.640954	+	0.876139i
$792$		0			0
$793$	54.8856	−	31.6882i	1.94904	−	1.12528i
$794$		0			0
$795$	24.7284	+	92.2878i	0.877027	+	3.27311i
$796$		0			0
$797$	13.3302	+	13.3302i	0.472179	+	0.472179i	0.902619	−	0.430440i	$-0.141642\pi$
$797$	13.3302	+	13.3302i	0.472179	+	0.472179i	−0.430440	+	0.902619i	$0.641642\pi$
$798$		0			0
$799$		−	6.66293i		−	0.235717i
$800$		0			0
$801$	15.0970	+	8.71624i	0.533425	+	0.307973i
$802$		0			0
$803$	−15.8709	−	4.25258i	−0.560070	−	0.150070i
$804$		0			0
$805$	−18.4222	−	7.14106i	−0.649298	−	0.251689i
$806$		0			0
$807$	−31.0148	−	53.7192i	−1.09177	−	1.89101i
$808$		0			0
$809$	18.7601	+	10.8311i	0.659569	+	0.380803i	0.792113	−	0.610375i	$-0.208981\pi$
$809$	18.7601	+	10.8311i	0.659569	+	0.380803i	−0.132544	+	0.991177i	$0.542314\pi$
$810$		0			0
$811$	−1.51326	−	1.51326i	−0.0531379	−	0.0531379i	0.680039	−	0.733176i	$-0.261963\pi$
$811$	−1.51326	−	1.51326i	−0.0531379	−	0.0531379i	−0.733176	+	0.680039i	$0.761963\pi$
$812$		0			0
$813$	17.2192	−	17.2192i	0.603904	−	0.603904i
$814$		0			0
$815$	−37.1741	+	64.3874i	−1.30215	+	2.25539i
$816$		0			0
$817$	39.7883	−	22.9718i	1.39202	−	0.803681i
$818$		0			0
$819$	32.8344	−	26.4109i	1.14733	−	0.922871i
$820$		0			0
$821$	−12.4214	+	46.3574i	−0.433511	+	1.61788i	0.311094	+	0.950379i	$0.399305\pi$
$821$	−12.4214	+	46.3574i	−0.433511	+	1.61788i	−0.744605	+	0.667506i	$0.767362\pi$
$822$		0			0
$823$	15.0408	−	26.0514i	0.524290	−	0.908096i	−0.475310	−	0.879818i	$-0.657664\pi$
$823$	15.0408	−	26.0514i	0.524290	−	0.908096i	0.999600	−	0.0282782i	$-0.00900244\pi$
$824$		0			0
$825$	20.4158			0.710789
$826$		0			0
$827$	22.5866	−	22.5866i	0.785414	−	0.785414i	−0.195325	−	0.980739i	$-0.562576\pi$
$827$	22.5866	−	22.5866i	0.785414	−	0.785414i	0.980739	+	0.195325i	$0.0625760\pi$
$828$		0			0
$829$	−31.9742	+	8.56747i	−1.11051	+	0.297561i	−0.767038	−	0.641602i	$-0.778270\pi$
$829$	−31.9742	+	8.56747i	−1.11051	+	0.297561i	−0.343473	+	0.939162i	$0.611603\pi$
$830$		0			0
$831$	15.0840	+	26.1263i	0.523260	+	0.906313i
$832$		0			0
$833$	3.50706	−	15.9831i	0.121512	−	0.553780i
$834$		0			0
$835$	3.19846	−	11.9368i	0.110687	−	0.413091i
$836$		0			0
$837$	−11.9365	+	3.19838i	−0.412586	+	0.110552i
$838$		0			0
$839$			35.7894i			1.23559i	0.786340	+	0.617794i	$0.211973\pi$
$839$			35.7894i			1.23559i	−0.786340	+	0.617794i	$0.788027\pi$
$840$		0			0
$841$			24.1849i			0.833962i
$842$		0			0
$843$	−13.9029	+	3.72527i	−0.478841	+	0.128305i
$844$		0			0
$845$	−5.34340	+	19.9418i	−0.183818	+	0.686020i
$846$		0			0
$847$	−2.53455	+	23.3766i	−0.0870880	+	0.803231i
$848$		0			0
$849$	−4.93437	−	8.54658i	−0.169347	−	0.293318i
$850$		0			0
$851$	−2.34752	+	0.629017i	−0.0804721	+	0.0215624i
$852$		0			0
$853$	−1.27195	+	1.27195i	−0.0435507	+	0.0435507i	−0.728547	−	0.684996i	$-0.759804\pi$
$853$	−1.27195	+	1.27195i	−0.0435507	+	0.0435507i	0.684996	+	0.728547i	$0.259804\pi$
$854$		0			0
$855$	−53.3733			−1.82533
$856$		0			0
$857$	−17.1377	+	29.6834i	−0.585412	+	1.01396i	0.409411	+	0.912350i	$0.365734\pi$
$857$	−17.1377	+	29.6834i	−0.585412	+	1.01396i	−0.994824	+	0.101614i	$0.967599\pi$
$858$		0			0
$859$	−11.5677	+	43.1714i	−0.394686	+	1.47299i	0.427628	+	0.903955i	$0.359349\pi$
$859$	−11.5677	+	43.1714i	−0.394686	+	1.47299i	−0.822314	+	0.569034i	$0.807317\pi$
$860$		0			0
$861$	−17.5917	−	6.81912i	−0.599523	−	0.232395i
$862$		0			0
$863$	32.5858	−	18.8134i	1.10923	−	0.640416i	0.170602	−	0.985340i	$-0.445429\pi$
$863$	32.5858	−	18.8134i	1.10923	−	0.640416i	0.938631	+	0.344924i	$0.112095\pi$
$864$		0			0
$865$	−13.4434	+	23.2846i	−0.457088	+	0.791700i
$866$		0			0
$867$	−20.9832	+	20.9832i	−0.712627	+	0.712627i
$868$		0			0
$869$	0.838719	+	0.838719i	0.0284516	+	0.0284516i
$870$		0			0
$871$	10.2477	+	5.91651i	0.347230	+	0.200473i
$872$		0			0
$873$	10.6092	+	18.3756i	0.359065	+	0.621920i
$874$		0			0
$875$	−3.89081	+	0.603167i	−0.131533	+	0.0203908i
$876$		0			0
$877$	20.5119	+	5.49616i	0.692639	+	0.185592i	0.587931	−	0.808911i	$-0.299943\pi$
$877$	20.5119	+	5.49616i	0.692639	+	0.185592i	0.104708	+	0.994503i	$0.466609\pi$
$878$		0			0
$879$	30.7099	+	17.7304i	1.03582	+	0.598031i
$880$		0			0
$881$			3.13017i			0.105458i	0.998609	+	0.0527291i	$0.0167920\pi$
$881$			3.13017i			0.105458i	−0.998609	+	0.0527291i	$0.983208\pi$
$882$		0			0
$883$	5.90657	+	5.90657i	0.198772	+	0.198772i	0.799473	−	0.600702i	$-0.205112\pi$
$883$	5.90657	+	5.90657i	0.198772	+	0.198772i	−0.600702	+	0.799473i	$0.705112\pi$
$884$		0			0
$885$	−8.41301	−	31.3978i	−0.282800	−	1.05543i
$886$		0			0
$887$	−41.9702	+	24.2315i	−1.40922	+	0.813615i	−0.995313	−	0.0967040i	$-0.969170\pi$
$887$	−41.9702	+	24.2315i	−1.40922	+	0.813615i	−0.413908	+	0.910318i	$0.635837\pi$
$888$		0			0
$889$	9.59219	+	7.01733i	0.321712	+	0.235354i
$890$		0			0
$891$	−9.49940	−	2.54536i	−0.318242	−	0.0852727i
$892$		0			0
$893$	−3.36536	−	12.5597i	−0.112617	−	0.420294i
$894$		0			0
$895$	62.4941			2.08895
$896$		0			0
$897$	26.1508			0.873151
$898$		0			0
$899$	4.41800	+	16.4882i	0.147348	+	0.549912i
$900$		0			0
$901$	−25.9299	−	6.94789i	−0.863849	−	0.231468i
$902$		0			0
$903$	62.7105	−	27.6744i	2.08688	−	0.920946i
$904$		0			0
$905$	24.0513	−	13.8860i	0.799491	−	0.461587i
$906$		0			0
$907$	−9.69974	−	36.1999i	−0.322075	−	1.20200i	−0.917220	−	0.398381i	$-0.869572\pi$
$907$	−9.69974	−	36.1999i	−0.322075	−	1.20200i	0.595146	−	0.803618i	$-0.297094\pi$
$908$		0			0
$909$	3.69271	+	3.69271i	0.122480	+	0.122480i
$910$		0			0
$911$		−	12.0871i		−	0.400463i	−0.979749	−	0.200231i	$-0.935831\pi$
$911$		−	12.0871i		−	0.400463i	0.979749	−	0.200231i	$-0.0641694\pi$
$912$		0			0
$913$	4.72253	+	2.72656i	0.156293	+	0.0902358i
$914$		0			0
$915$	−115.684	−	30.9974i	−3.82439	−	1.02474i
$916$		0			0
$917$	28.5169	−	22.9381i	0.941712	−	0.757481i
$918$		0			0
$919$	−27.6308	−	47.8579i	−0.911455	−	1.57869i	−0.812010	−	0.583643i	$-0.801627\pi$
$919$	−27.6308	−	47.8579i	−0.911455	−	1.57869i	−0.0994447	−	0.995043i	$-0.531707\pi$
$920$		0			0
$921$	64.8188	+	37.4231i	2.13585	+	1.23313i
$922$		0			0
$923$	23.2971	+	23.2971i	0.766833	+	0.766833i
$924$		0			0
$925$	−4.06379	+	4.06379i	−0.133617	+	0.133617i
$926$		0			0
$927$	−4.38882	+	7.60165i	−0.144148	+	0.249671i
$928$		0			0
$929$	8.64695	−	4.99232i	0.283697	−	0.163793i	−0.351399	−	0.936226i	$-0.614294\pi$
$929$	8.64695	−	4.99232i	0.283697	−	0.163793i	0.635096	+	0.772433i	$0.280961\pi$
$930$		0			0
$931$	−1.46199	−	31.8996i	−0.0479147	−	1.04547i
$932$		0			0
$933$	−0.380765	+	1.42103i	−0.0124657	+	0.0465226i
$934$		0			0
$935$	−5.49450	+	9.51675i	−0.179689	+	0.311231i
$936$		0			0
$937$	−7.92416			−0.258871			−0.129436	−	0.991588i	$-0.541317\pi$
$937$	−7.92416			−0.258871			−0.129436	+	0.991588i	$0.541317\pi$
$938$		0			0
$939$	2.57311	−	2.57311i	0.0839703	−	0.0839703i
$940$		0			0
$941$	−6.10702	+	1.63637i	−0.199083	+	0.0533441i	−0.356983	−	0.934111i	$-0.616194\pi$
$941$	−6.10702	+	1.63637i	−0.199083	+	0.0533441i	0.157900	+	0.987455i	$0.449528\pi$
$942$		0			0
$943$	−3.20038	−	5.54321i	−0.104219	−	0.180512i
$944$		0			0
$945$	−13.5141	−	1.46523i	−0.439613	−	0.0476638i
$946$		0			0
$947$	−2.94453	+	10.9891i	−0.0956843	+	0.357098i	−0.997122	−	0.0758096i	$-0.975846\pi$
$947$	−2.94453	+	10.9891i	−0.0956843	+	0.357098i	0.901438	+	0.432908i	$0.142513\pi$
$948$		0			0
$949$	−48.0727	+	12.8811i	−1.56051	+	0.418137i
$950$		0			0
$951$		−	67.3561i		−	2.18417i
$952$		0			0
$953$			12.7329i			0.412460i	0.978504	+	0.206230i	$0.0661195\pi$
$953$			12.7329i			0.412460i	−0.978504	+	0.206230i	$0.933880\pi$
$954$		0			0
$955$	−47.5105	+	12.7304i	−1.53741	+	0.411946i
$956$		0			0
$957$	2.12356	−	7.92522i	0.0686448	−	0.256186i
$958$		0			0
$959$	6.10489	−	2.69411i	0.197137	−	0.0869974i
$960$		0			0
$961$	−14.7568	−	25.5595i	−0.476025	−	0.824500i
$962$		0			0
$963$	15.7275	−	4.21417i	0.506812	−	0.135800i
$964$		0			0
$965$	−51.4090	+	51.4090i	−1.65491	+	1.65491i
$966$		0			0
$967$	10.6644			0.342944			0.171472	−	0.985189i	$-0.445148\pi$
$967$	10.6644			0.342944			0.171472	+	0.985189i	$0.445148\pi$
$968$		0			0
$969$	13.7162	−	23.7571i	0.440628	−	0.763190i
$970$		0			0
$971$	0.596517	−	2.22623i	0.0191431	−	0.0714431i	−0.955694	−	0.294364i	$-0.904892\pi$
$971$	0.596517	−	2.22623i	0.0191431	−	0.0714431i	0.974837	+	0.222920i	$0.0715590\pi$
$972$		0			0
$973$	−22.1990	+	3.44137i	−0.711669	+	0.110325i
$974$		0			0
$975$	53.5546	−	30.9198i	1.71512	−	0.990225i
$976$		0			0
$977$	7.66274	−	13.2723i	0.245153	−	0.424617i	−0.717022	−	0.697051i	$-0.754495\pi$
$977$	7.66274	−	13.2723i	0.245153	−	0.424617i	0.962175	+	0.272434i	$0.0878286\pi$
$978$		0			0
$979$	4.95277	−	4.95277i	0.158291	−	0.158291i
$980$		0			0
$981$	8.32913	+	8.32913i	0.265929	+	0.265929i
$982$		0			0
$983$	−16.1184	−	9.30595i	−0.514097	−	0.296814i	0.220419	−	0.975405i	$-0.429257\pi$
$983$	−16.1184	−	9.30595i	−0.514097	−	0.296814i	−0.734516	+	0.678591i	$0.762591\pi$
$984$		0			0
$985$	19.0177	+	32.9396i	0.605954	+	1.04954i
$986$		0			0
$987$	−2.97187	−	19.1705i	−0.0945956	−	0.610202i
$988$		0			0
$989$	22.4620	+	6.01867i	0.714249	+	0.191383i
$990$		0			0
$991$	−23.7555	−	13.7153i	−0.754619	−	0.435680i	0.0727413	−	0.997351i	$-0.476825\pi$
$991$	−23.7555	−	13.7153i	−0.754619	−	0.435680i	−0.827361	+	0.561671i	$0.810159\pi$
$992$		0			0
$993$		−	7.22736i		−	0.229353i
$994$		0			0
$995$	−23.3727	−	23.3727i	−0.740965	−	0.740965i
$996$		0			0
$997$	−5.02660	−	18.7595i	−0.159194	−	0.594120i	−0.998710	−	0.0507843i	$-0.983828\pi$
$997$	−5.02660	−	18.7595i	−0.159194	−	0.594120i	0.839516	−	0.543335i	$-0.182839\pi$
$998$		0			0
$999$	−1.44804	+	0.836028i	−0.0458140	+	0.0264507i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.z.a.31.3		56
4.3	odd	2		896.2.z.b.31.12		56
7.5	odd	6	inner	896.2.z.a.159.3		56
8.3	odd	2		112.2.v.a.59.7	yes	56
8.5	even	2		448.2.z.a.143.12		56
16.3	odd	4	inner	896.2.z.a.479.3		56
16.5	even	4		112.2.v.a.3.13	✓	56
16.11	odd	4		448.2.z.a.367.12		56
16.13	even	4		896.2.z.b.479.12		56
28.19	even	6		896.2.z.b.159.12		56
56.3	even	6		784.2.j.a.587.6		56
56.5	odd	6		448.2.z.a.271.12		56
56.11	odd	6		784.2.j.a.587.5		56
56.19	even	6		112.2.v.a.75.13	yes	56
56.27	even	2		784.2.w.f.619.7		56
56.51	odd	6		784.2.w.f.411.13		56
112.5	odd	12		112.2.v.a.19.7	yes	56
112.19	even	12	inner	896.2.z.a.607.3		56
112.37	even	12		784.2.w.f.19.7		56
112.53	even	12		784.2.j.a.195.6		56
112.61	odd	12		896.2.z.b.607.12		56
112.69	odd	4		784.2.w.f.227.13		56
112.75	even	12		448.2.z.a.47.12		56
112.101	odd	12		784.2.j.a.195.5		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.13	✓	56	16.5	even	4
112.2.v.a.19.7	yes	56	112.5	odd	12
112.2.v.a.59.7	yes	56	8.3	odd	2
112.2.v.a.75.13	yes	56	56.19	even	6
448.2.z.a.47.12		56	112.75	even	12
448.2.z.a.143.12		56	8.5	even	2
448.2.z.a.271.12		56	56.5	odd	6
448.2.z.a.367.12		56	16.11	odd	4
784.2.j.a.195.5		56	112.101	odd	12
784.2.j.a.195.6		56	112.53	even	12
784.2.j.a.587.5		56	56.11	odd	6
784.2.j.a.587.6		56	56.3	even	6
784.2.w.f.19.7		56	112.37	even	12
784.2.w.f.227.13		56	112.69	odd	4
784.2.w.f.411.13		56	56.51	odd	6
784.2.w.f.619.7		56	56.27	even	2
896.2.z.a.31.3		56	1.1	even	1	trivial
896.2.z.a.159.3		56	7.5	odd	6	inner
896.2.z.a.479.3		56	16.3	odd	4	inner
896.2.z.a.607.3		56	112.19	even	12	inner
896.2.z.b.31.12		56	4.3	odd	2
896.2.z.b.159.12		56	28.19	even	6
896.2.z.b.479.12		56	16.13	even	4
896.2.z.b.607.12		56	112.61	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.z (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.665801 - 2.48480i) q^{3} +(3.12401 + 0.837076i) q^{5} +(-1.56215 + 2.13534i) q^{7} +(-3.13287 + 1.80877i) q^{9} +(0.376195 + 1.40398i) q^{11} +(3.11315 + 3.11315i) q^{13} -8.31987i q^{15} +(2.02443 + 1.16881i) q^{17} +(4.40643 + 1.18070i) q^{19} +(6.34599 + 2.45991i) q^{21} +(1.15450 + 1.99965i) q^{23} +(4.72861 + 2.73006i) q^{25} +(1.12329 + 1.12329i) q^{27} +(1.55163 - 1.55163i) q^{29} +(-3.88952 + 6.73685i) q^{31} +(3.23814 - 1.86954i) q^{33} +(-6.66761 + 5.36320i) q^{35} +(-0.272421 + 1.01669i) q^{37} +(5.66282 - 9.80830i) q^{39} -2.77210 q^{41} +(7.12142 - 7.12142i) q^{43} +(-11.3012 + 3.02815i) q^{45} +(-1.42516 - 2.46844i) q^{47} +(-2.11939 - 6.67144i) q^{49} +(1.55638 - 5.80851i) q^{51} +(-11.0925 + 2.97221i) q^{53} +4.70094i q^{55} -11.7352i q^{57} +(3.77383 - 1.01120i) q^{59} +(3.72571 - 13.9045i) q^{61} +(1.03167 - 9.51532i) q^{63} +(7.11957 + 12.3315i) q^{65} +(2.59612 - 0.695627i) q^{67} +(4.20006 - 4.20006i) q^{69} +7.48345 q^{71} +(-5.65210 + 9.78973i) q^{73} +(3.63536 - 13.5673i) q^{75} +(-3.58565 - 1.38991i) q^{77} +(0.706717 - 0.408024i) q^{79} +(-3.38303 + 5.85958i) q^{81} +(2.65285 - 2.65285i) q^{83} +(5.34597 + 5.34597i) q^{85} +(-4.88857 - 2.82241i) q^{87} +(-2.40944 - 4.17328i) q^{89} +(-11.5108 + 1.78445i) q^{91} +(19.3294 + 5.17929i) q^{93} +(12.7774 + 7.37703i) q^{95} -5.86541i q^{97} +(-3.71804 - 3.71804i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 6 q^{3} + 6 q^{5} + 8 q^{7} + 2 q^{11} - 12 q^{17} - 6 q^{19} + 10 q^{21} + 12 q^{23} + 24 q^{29} - 12 q^{33} - 2 q^{35} - 6 q^{37} + 4 q^{39} - 12 q^{45} - 8 q^{49} - 34 q^{51} - 6 q^{53} + 42 q^{59}+ \cdots - 16 q^{99}+O(q^{100}) \) 56 * q - 6 * q^3 + 6 * q^5 + 8 * q^7 + 2 * q^11 - 12 * q^17 - 6 * q^19 + 10 * q^21 + 12 * q^23 + 24 * q^29 - 12 * q^33 - 2 * q^35 - 6 * q^37 + 4 * q^39 - 12 * q^45 - 8 * q^49 - 34 * q^51 - 6 * q^53 + 42 * q^59 + 6 * q^61 - 4 * q^65 + 6 * q^67 + 80 * q^71 + 24 * q^75 - 10 * q^77 - 8 * q^81 + 28 * q^85 + 12 * q^87 + 16 * q^91 - 10 * q^93 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more