LMFDB - Embedded newform 896.2.z.b.31.12

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)

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")

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);

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			31.12
Character	$\chi$	$=$	896.31
Dual form			896.2.z.b.607.12

$q$-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	$0.183076\pi$
$3$	0.665801	+	2.48480i	0.384400	+	1.43460i	−0.454710	+	0.890640i	$0.650257\pi$
$4$		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	0.885737	−	0.464187i	$-0.153653\pi$
$11$	−0.376195	−	1.40398i	−0.113427	−	0.423315i	−0.999164	+	0.0408713i	$0.986987\pi$
$12$		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	−0.284897	−	0.958558i	$-0.591959\pi$
$19$	−4.40643	−	1.18070i	−1.01090	−	0.270871i	−0.726007	+	0.687687i	$0.758626\pi$
$20$		0			0
$21$	6.34599	+	2.45991i	1.38481	+	0.536797i
$22$		0			0
$23$	−1.15450	−	1.99965i	−0.240729	−	0.416955i	0.720193	−	0.693774i	$-0.244053\pi$
$23$	−1.15450	−	1.99965i	−0.240729	−	0.416955i	−0.960922	+	0.276819i	$0.910720\pi$
$24$		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	$-0.587149\pi$
$31$	3.88952	−	6.73685i	0.698579	−	1.20997i	0.968959	−	0.247221i	$-0.0795172\pi$
$32$		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	$0.528710\pi$
$43$	−7.12142	+	7.12142i	−1.08601	+	1.08601i	−0.995935	+	0.0900717i	$0.971290\pi$
$44$		0			0
$45$	−11.3012	+	3.02815i	−1.68468	+	0.451410i
$46$		0			0
$47$	1.42516	+	2.46844i	0.207880	+	0.360059i	0.951047	−	0.309047i	$-0.100010\pi$
$47$	1.42516	+	2.46844i	0.207880	+	0.360059i	−0.743166	+	0.669107i	$0.766677\pi$
$48$		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	−0.495965	−	0.868343i	$-0.665185\pi$
$59$	−3.77383	+	1.01120i	−0.491311	+	0.131646i	0.00465348	+	0.999989i	$0.498519\pi$
$60$		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	−0.413890	−	0.910327i	$-0.635830\pi$
$67$	−2.59612	+	0.695627i	−0.317166	+	0.0849844i	0.0967240	+	0.995311i	$0.469164\pi$
$68$		0			0
$69$	4.20006	−	4.20006i	0.505628	−	0.505628i
$70$		0			0
$71$	−7.48345			−0.888122			−0.444061	−	0.895997i	$-0.646463\pi$
$71$	−7.48345			−0.888122			−0.444061	+	0.895997i	$0.646463\pi$
$72$		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	−0.539229	−	0.842159i	$-0.681284\pi$
$79$	−0.706717	+	0.408024i	−0.0795119	+	0.0459062i	0.459717	+	0.888066i	$0.347951\pi$
$80$		0			0
$81$	−3.38303	+	5.85958i	−0.375892	+	0.651065i
$82$		0			0
$83$	−2.65285	+	2.65285i	−0.291188	+	0.291188i	−0.837550	−	0.546361i	$-0.816013\pi$
$83$	−2.65285	+	2.65285i	−0.291188	+	0.291188i	0.546361	+	0.837550i	$0.316013\pi$
$84$		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	−0.599940	−	0.800045i	$-0.704809\pi$
$103$	−2.10134	+	1.21321i	−0.207051	+	0.119541i	0.392889	+	0.919586i	$0.371476\pi$
$104$		0			0
$105$	17.7658	+	12.9969i	1.73376	+	1.26836i
$106$		0			0
$107$	4.34758	+	1.16493i	0.420297	+	0.112618i	0.462768	−	0.886480i	$-0.346856\pi$
$107$	4.34758	+	1.16493i	0.420297	+	0.112618i	−0.0424712	+	0.999098i	$0.513523\pi$
$108$		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	$0.0638684\pi$
$127$			4.49210i			0.398610i	−0.979938	+	0.199305i	$0.936132\pi$
$128$		0			0
$129$	−22.4368	−	12.9539i	−1.97545	−	1.14053i
$130$		0			0
$131$	13.3612	+	3.58012i	1.16737	+	0.312796i	0.789907	−	0.613227i	$-0.210129\pi$
$131$	13.3612	+	3.58012i	1.16737	+	0.312796i	0.377465	+	0.926024i	$0.376796\pi$
$132$		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	0.405055	−	0.914292i	$-0.367252\pi$
$139$	−6.00381	−	6.00381i	−0.509237	−	0.509237i	−0.914292	+	0.405055i	$0.867252\pi$
$140$		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	−0.578995	−	0.815331i	$-0.696555\pi$
$151$	5.11927	−	8.86683i	0.416600	−	0.721572i	0.995595	+	0.0937588i	$0.0298882\pi$
$152$		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	$-0.560028\pi$
$163$	5.94974	−	22.2047i	0.466019	−	1.73921i	0.653488	−	0.756937i	$-0.273305\pi$
$164$		0			0
$165$	11.6809	−	3.12989i	0.909358	−	0.243662i
$166$		0			0
$167$			3.82099i			0.295677i	0.989011	+	0.147839i	$0.0472316\pi$
$167$			3.82099i			0.295677i	−0.989011	+	0.147839i	$0.952768\pi$
$168$		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	−0.876563	−	0.481288i	$-0.840169\pi$
$179$	−18.6644	+	5.00112i	−1.39504	+	0.373801i	−0.518482	+	0.855089i	$0.673503\pi$
$180$		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	0.0589865	−	0.998259i	$-0.481213\pi$
$191$	13.1707	−	7.60410i	0.952997	−	0.550213i	0.894011	+	0.448046i	$0.147880\pi$
$192$		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	0.779753	−	0.626087i	$-0.215345\pi$
$199$	8.85088	+	5.11006i	0.627422	+	0.362242i	−0.152331	+	0.988330i	$0.548678\pi$
$200$		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	0.481467	−	0.876464i	$-0.340104\pi$
$211$	−5.73766	−	5.73766i	−0.394997	−	0.394997i	−0.876464	+	0.481467i	$0.840104\pi$
$212$		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	$-0.300818\pi$
$223$	17.4929			1.17141			0.585705	+	0.810524i	$0.300818\pi$
$224$		0			0
$225$	−19.7522			−1.31681
$226$		0			0
$227$	4.53614	+	16.9291i	0.301074	+	1.12362i	0.936272	+	0.351275i	$0.114252\pi$
$227$	4.53614	+	16.9291i	0.301074	+	1.12362i	−0.635198	+	0.772349i	$0.719081\pi$
$228$		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	$0.142211\pi$
$239$			13.3587i			0.864105i	−0.901848	+	0.432053i	$0.857789\pi$
$240$		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	0.885968	−	0.463746i	$-0.153495\pi$
$251$	6.68926	+	6.68926i	0.422223	+	0.422223i	−0.463746	+	0.885968i	$0.653495\pi$
$252$		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	−0.752088	−	0.659062i	$-0.770953\pi$
$263$	3.15784	−	5.46953i	0.194720	−	0.337266i	0.946809	+	0.321797i	$0.104287\pi$
$264$		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	0.685699	−	0.727886i	$-0.259497\pi$
$271$	−4.73315	−	8.19805i	−0.287518	−	0.497996i	−0.973217	+	0.229890i	$0.926163\pi$
$272$		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	−0.367268	−	0.930115i	$-0.619707\pi$
$283$	−3.70559	+	0.992910i	−0.220275	+	0.0590224i	0.146994	+	0.989137i	$0.453040\pi$
$284$		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	$-0.438182\pi$
$307$	20.5735	−	20.5735i	1.17419	−	1.17419i	0.981201	−	0.192988i	$-0.0618178\pi$
$308$		0			0
$309$	−4.41365	−	4.41365i	−0.251084	−	0.251084i
$310$		0			0
$311$	0.495271	+	0.285945i	0.0280843	+	0.0162145i	0.513976	−	0.857804i	$-0.328172\pi$
$311$	0.495271	+	0.285945i	0.0280843	+	0.0162145i	−0.485892	+	0.874019i	$0.661505\pi$
$312$		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	0.183465	−	0.983026i	$-0.441269\pi$
$331$	−2.71378	−	0.727156i	−0.149163	−	0.0399681i	−0.332628	+	0.943058i	$0.607935\pi$
$332$		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	$0.0256465\pi$
$347$	3.23720	+	12.0814i	0.173782	+	0.648563i	−0.822974	+	0.568079i	$0.807687\pi$
$348$		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	0.964198	−	0.265184i	$-0.0854328\pi$
$359$	4.78310	+	8.28458i	0.252443	+	0.437243i	−0.711755	+	0.702428i	$0.752099\pi$
$360$		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	−0.934829	−	0.355099i	$-0.884447\pi$
$367$	−3.06305	+	5.30536i	−0.159890	+	0.276938i	0.774939	+	0.632036i	$0.217781\pi$
$368$		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	−0.845257	−	0.534360i	$-0.820553\pi$
$379$	−6.05253	+	6.05253i	−0.310897	+	0.310897i	0.534360	+	0.845257i	$0.320553\pi$
$380$		0			0
$381$	−11.1620	+	2.99085i	−0.571846	+	0.153226i
$382$		0			0
$383$	9.64030	+	16.6975i	0.492596	+	0.853202i	0.999964	−	0.00852805i	$-0.00271459\pi$
$383$	9.64030	+	16.6975i	0.492596	+	0.853202i	−0.507367	+	0.861730i	$0.669381\pi$
$384$		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	−0.884885	−	0.465809i	$-0.845763\pi$
$419$	−8.57828	+	8.57828i	−0.419076	+	0.419076i	0.465809	+	0.884885i	$0.345763\pi$
$420$		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	0.465992	−	0.884789i	$-0.345697\pi$
$431$	−1.39637	−	0.806195i	−0.0672608	−	0.0388331i	−0.533253	+	0.845956i	$0.679031\pi$
$432$		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	−0.458550	−	0.888669i	$-0.651631\pi$
$439$	1.71358	−	0.989334i	0.0817846	−	0.0472184i	0.540335	+	0.841450i	$0.318298\pi$
$440$		0			0
$441$	18.7069	+	17.0673i	0.890803	+	0.812729i
$442$		0			0
$443$	33.5156	+	8.98048i	1.59237	+	0.426675i	0.942728	−	0.333562i	$-0.108251\pi$
$443$	33.5156	+	8.98048i	1.59237	+	0.426675i	0.649646	+	0.760237i	$0.274917\pi$
$444$		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	$-0.739899\pi$
$463$		−	31.3804i		−	1.45837i	0.684316	−	0.729186i	$-0.260101\pi$
$464$		0			0
$465$	56.0497	+	32.3603i	2.59924	+	1.50067i
$466$		0			0
$467$	23.0310	+	6.17115i	1.06575	+	0.285567i	0.748745	−	0.662858i	$-0.230657\pi$
$467$	23.0310	+	6.17115i	1.06575	+	0.285567i	0.317004	+	0.948424i	$0.397323\pi$
$468$		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	$0.465980\pi$
$479$	−17.6784	+	30.6199i	−0.807747	+	1.39906i	−0.914421	+	0.404764i	$0.867354\pi$
$480$		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	−0.720222	−	0.693743i	$-0.755960\pi$
$487$	5.31153	−	9.19984i	0.240688	−	0.416884i	0.960911	+	0.276859i	$0.0892935\pi$
$488$		0			0
$489$	59.1357			2.67421
$490$		0			0
$491$	−26.9088	+	26.9088i	−1.21438	+	1.21438i	−0.244806	+	0.969572i	$0.578724\pi$
$491$	−26.9088	+	26.9088i	−1.21438	+	1.21438i	−0.969572	+	0.244806i	$0.921276\pi$
$492$		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	$0.174905\pi$
$499$	−3.28081	+	12.2441i	−0.146869	+	0.548123i	−0.999665	+	0.0258790i	$0.991762\pi$
$500$		0			0
$501$	−9.49441	+	2.54402i	−0.424179	+	0.113658i
$502$		0			0
$503$			13.7074i			0.611183i	0.952163	+	0.305591i	$0.0988542\pi$
$503$			13.7074i			0.611183i	−0.952163	+	0.305591i	$0.901146\pi$
$504$		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	$0.217988\pi$
$523$	−4.85978	+	18.1369i	−0.212503	+	0.793073i	−0.987031	+	0.160532i	$0.948679\pi$
$524$		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	$0.00639620\pi$
$547$	23.8532	+	23.8532i	1.01989	+	1.01989i	0.0200929	+	0.999798i	$0.493604\pi$
$548$		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	0.997360	−	0.0726153i	$-0.0231345\pi$
$563$	2.30901	+	8.61735i	0.0973133	+	0.363178i	−0.900047	+	0.435793i	$0.856468\pi$
$564$		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	$0.204212\pi$
$571$	9.71490	+	36.2565i	0.406556	+	1.51729i	−0.394612	+	0.918848i	$0.629121\pi$
$572$		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	$-0.963338\pi$
$587$	−26.8519	−	26.8519i	−1.10830	−	1.10830i	−0.114923	−	0.993374i	$-0.536662\pi$
$588$		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	−0.999799	−	0.0200365i	$-0.993622\pi$
$599$	−11.8101	+	20.4557i	−0.482548	+	0.835797i	0.517252	+	0.855833i	$0.326955\pi$
$600$		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	0.812421	−	0.583072i	$-0.198149\pi$
$607$	−2.43281	−	4.21375i	−0.0987446	−	0.171031i	−0.911165	+	0.412041i	$0.864816\pi$
$608$		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	0.115982	−	0.993251i	$-0.462998\pi$
$619$	17.7405	−	4.75356i	0.713051	−	0.191062i	0.597069	+	0.802190i	$0.296332\pi$
$620$		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	$-0.808621\pi$
$631$	−41.4293			−1.64928			−0.824638	+	0.565661i	$0.808621\pi$
$632$		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	−0.635469	−	0.772126i	$-0.719193\pi$
$643$	3.46526	−	3.46526i	0.136657	−	0.136657i	0.772126	+	0.635469i	$0.219193\pi$
$644$		0			0
$645$	−59.2493	−	59.2493i	−2.33294	−	2.33294i
$646$		0			0
$647$	27.2890	+	15.7553i	1.07284	+	0.619406i	0.928957	−	0.370188i	$-0.120707\pi$
$647$	27.2890	+	15.7553i	1.07284	+	0.619406i	0.143886	+	0.989594i	$0.454040\pi$
$648$		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	$-0.949610\pi$
$659$	−29.3969	−	29.3969i	−1.14514	−	1.14514i	−0.157643	−	0.987496i	$-0.550390\pi$
$660$		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	0.923997	−	0.382400i	$-0.124902\pi$
$683$	−1.76166	−	6.57460i	−0.0674080	−	0.251570i	−0.991405	+	0.130830i	$0.958236\pi$
$684$		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	−0.356217	−	0.934403i	$-0.615934\pi$
$691$	−29.7544	−	7.97267i	−1.13191	−	0.303295i	−0.775695	+	0.631108i	$0.782600\pi$
$692$		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	0.998043	−	0.0625253i	$-0.0199154\pi$
$719$	11.9289	+	20.6615i	0.444873	+	0.770543i	−0.553170	+	0.833068i	$0.686582\pi$
$720$		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	$-0.822305\pi$
$727$		−	28.5645i		−	1.05940i	0.848185	−	0.529700i	$-0.177695\pi$
$728$		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	−0.290321	−	0.956929i	$-0.593762\pi$
$739$	−1.72028	+	0.460947i	−0.0632814	+	0.0169562i	0.227039	+	0.973886i	$0.427095\pi$
$740$		0			0
$741$	36.5335	−	36.5335i	1.34209	−	1.34209i
$742$		0			0
$743$	16.7041			0.612815			0.306407	−	0.951900i	$-0.400873\pi$
$743$	16.7041			0.612815			0.306407	+	0.951900i	$0.400873\pi$
$744$		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	−0.472101	−	0.881544i	$-0.656504\pi$
$751$	1.51512	−	0.874754i	0.0552874	−	0.0319202i	0.527389	+	0.849624i	$0.323171\pi$
$752$		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	$-0.937426\pi$
$787$	−6.42575	−	23.9812i	−0.229053	−	0.854838i	0.751687	−	0.659520i	$-0.229240\pi$
$788$		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	0.733176	−	0.680039i	$-0.238037\pi$
$811$	1.51326	+	1.51326i	0.0531379	+	0.0531379i	−0.680039	+	0.733176i	$0.738037\pi$
$812$		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	$0.342336\pi$
$823$	−15.0408	+	26.0514i	−0.524290	+	0.908096i	−0.999600	+	0.0282782i	$0.990998\pi$
$824$		0			0
$825$	20.4158			0.710789
$826$		0			0
$827$	−22.5866	+	22.5866i	−0.785414	+	0.785414i	−0.980739	−	0.195325i	$-0.937424\pi$
$827$	−22.5866	+	22.5866i	−0.785414	+	0.785414i	0.195325	+	0.980739i	$0.437424\pi$
$828$		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	$-0.788027\pi$
$839$		−	35.7894i		−	1.23559i	0.786340	−	0.617794i	$-0.211973\pi$
$840$		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	$-0.640651\pi$
$859$	11.5677	−	43.1714i	0.394686	−	1.47299i	0.822314	−	0.569034i	$-0.192683\pi$
$860$		0			0
$861$	−17.5917	−	6.81912i	−0.599523	−	0.232395i
$862$		0			0
$863$	−32.5858	+	18.8134i	−1.10923	+	0.640416i	−0.938631	−	0.344924i	$-0.887905\pi$
$863$	−32.5858	+	18.8134i	−1.10923	+	0.640416i	−0.170602	+	0.985340i	$0.554571\pi$
$864$		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	0.600702	−	0.799473i	$-0.294888\pi$
$883$	−5.90657	−	5.90657i	−0.198772	−	0.198772i	−0.799473	+	0.600702i	$0.794888\pi$
$884$		0			0
$885$	−8.41301	−	31.3978i	−0.282800	−	1.05543i
$886$		0			0
$887$	41.9702	−	24.2315i	1.40922	−	0.813615i	0.413908	−	0.910318i	$-0.364163\pi$
$887$	41.9702	−	24.2315i	1.40922	−	0.813615i	0.995313	+	0.0967040i	$0.0308300\pi$
$888$		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	$0.130428\pi$
$907$	9.69974	+	36.1999i	0.322075	+	1.20200i	−0.595146	+	0.803618i	$0.702906\pi$
$908$		0			0
$909$	3.69271	+	3.69271i	0.122480	+	0.122480i
$910$		0			0
$911$			12.0871i			0.400463i	0.979749	+	0.200231i	$0.0641694\pi$
$911$			12.0871i			0.400463i	−0.979749	+	0.200231i	$0.935831\pi$
$912$		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	$0.198373\pi$
$919$	27.6308	+	47.8579i	0.911455	+	1.57869i	0.0994447	+	0.995043i	$0.468293\pi$
$920$		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	−0.901438	−	0.432908i	$-0.857487\pi$
$947$	2.94453	−	10.9891i	0.0956843	−	0.357098i	0.997122	+	0.0758096i	$0.0241541\pi$
$948$		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	$-0.554852\pi$
$967$	−10.6644			−0.342944			−0.171472	+	0.985189i	$0.554852\pi$
$968$		0			0
$969$	13.7162	−	23.7571i	0.440628	−	0.763190i
$970$		0			0
$971$	−0.596517	+	2.22623i	−0.0191431	+	0.0714431i	−0.974837	−	0.222920i	$-0.928441\pi$
$971$	−0.596517	+	2.22623i	−0.0191431	+	0.0714431i	0.955694	+	0.294364i	$0.0951077\pi$
$972$		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	0.734516	−	0.678591i	$-0.237409\pi$
$983$	16.1184	+	9.30595i	0.514097	+	0.296814i	−0.220419	+	0.975405i	$0.570743\pi$
$984$		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	0.827361	−	0.561671i	$-0.189841\pi$
$991$	23.7555	+	13.7153i	0.754619	+	0.435680i	−0.0727413	+	0.997351i	$0.523175\pi$
$992$		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.b.31.12		56
4.3	odd	2		896.2.z.a.31.3		56
7.5	odd	6	inner	896.2.z.b.159.12		56
8.3	odd	2		448.2.z.a.143.12		56
8.5	even	2		112.2.v.a.59.7	yes	56
16.3	odd	4	inner	896.2.z.b.479.12		56
16.5	even	4		448.2.z.a.367.12		56
16.11	odd	4		112.2.v.a.3.13	✓	56
16.13	even	4		896.2.z.a.479.3		56
28.19	even	6		896.2.z.a.159.3		56
56.5	odd	6		112.2.v.a.75.13	yes	56
56.13	odd	2		784.2.w.f.619.7		56
56.19	even	6		448.2.z.a.271.12		56
56.37	even	6		784.2.w.f.411.13		56
56.45	odd	6		784.2.j.a.587.6		56
56.53	even	6		784.2.j.a.587.5		56
112.5	odd	12		448.2.z.a.47.12		56
112.11	odd	12		784.2.j.a.195.6		56
112.19	even	12	inner	896.2.z.b.607.12		56
112.27	even	4		784.2.w.f.227.13		56
112.59	even	12		784.2.j.a.195.5		56
112.61	odd	12		896.2.z.a.607.3		56
112.75	even	12		112.2.v.a.19.7	yes	56
112.107	odd	12		784.2.w.f.19.7		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.13	✓	56	16.11	odd	4
112.2.v.a.19.7	yes	56	112.75	even	12
112.2.v.a.59.7	yes	56	8.5	even	2
112.2.v.a.75.13	yes	56	56.5	odd	6
448.2.z.a.47.12		56	112.5	odd	12
448.2.z.a.143.12		56	8.3	odd	2
448.2.z.a.271.12		56	56.19	even	6
448.2.z.a.367.12		56	16.5	even	4
784.2.j.a.195.5		56	112.59	even	12
784.2.j.a.195.6		56	112.11	odd	12
784.2.j.a.587.5		56	56.53	even	6
784.2.j.a.587.6		56	56.45	odd	6
784.2.w.f.19.7		56	112.107	odd	12
784.2.w.f.227.13		56	112.27	even	4
784.2.w.f.411.13		56	56.37	even	6
784.2.w.f.619.7		56	56.13	odd	2
896.2.z.a.31.3		56	4.3	odd	2
896.2.z.a.159.3		56	28.19	even	6
896.2.z.a.479.3		56	16.13	even	4
896.2.z.a.607.3		56	112.61	odd	12
896.2.z.b.31.12		56	1.1	even	1	trivial
896.2.z.b.159.12		56	7.5	odd	6	inner
896.2.z.b.479.12		56	16.3	odd	4	inner
896.2.z.b.607.12		56	112.19	even	12	inner

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

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