LMFDB - Embedded newform 448.2.z.a.271.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [448,2,Mod(47,448)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(448, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 10])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("448.47"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	448.z (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.57729801055$
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			271.12
Character	$\chi$	$=$	448.271
Dual form			448.2.z.a.367.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.48480 + 0.665801i) q^{3} +(-0.837076 - 3.12401i) q^{5} +(-1.56215 - 2.13534i) q^{7} +(3.13287 + 1.80877i) q^{9} +(1.40398 + 0.376195i) q^{11} +(3.11315 + 3.11315i) q^{13} -8.31987i q^{15} +(2.02443 - 1.16881i) q^{17} +(-1.18070 - 4.40643i) q^{19} +(-2.45991 - 6.34599i) q^{21} +(1.15450 - 1.99965i) q^{23} +(-4.72861 + 2.73006i) q^{25} +(1.12329 + 1.12329i) q^{27} +(-1.55163 + 1.55163i) q^{29} +(3.88952 + 6.73685i) q^{31} +(3.23814 + 1.86954i) q^{33} +(-5.36320 + 6.66761i) q^{35} +(-1.01669 + 0.272421i) q^{37} +(5.66282 + 9.80830i) q^{39} +2.77210 q^{41} +(-7.12142 + 7.12142i) q^{43} +(3.02815 - 11.3012i) q^{45} +(1.42516 - 2.46844i) q^{47} +(-2.11939 + 6.67144i) q^{49} +(5.80851 - 1.55638i) q^{51} +(-2.97221 + 11.0925i) q^{53} -4.70094i q^{55} -11.7352i q^{57} +(-1.01120 + 3.77383i) q^{59} +(-13.9045 + 3.72571i) q^{61} +(-1.03167 - 9.51532i) q^{63} +(7.11957 - 12.3315i) q^{65} +(0.695627 - 2.59612i) q^{67} +(4.20006 - 4.20006i) q^{69} +7.48345 q^{71} +(5.65210 + 9.78973i) q^{73} +(-13.5673 + 3.63536i) q^{75} +(-1.38991 - 3.58565i) q^{77} +(-0.706717 - 0.408024i) q^{79} +(-3.38303 - 5.85958i) q^{81} +(2.65285 - 2.65285i) q^{83} +(-5.34597 - 5.34597i) q^{85} +(-4.88857 + 2.82241i) q^{87} +(2.40944 - 4.17328i) q^{89} +(1.78445 - 11.5108i) q^{91} +(5.17929 + 19.3294i) q^{93} +(-12.7774 + 7.37703i) q^{95} +5.86541i q^{97} +(3.71804 + 3.71804i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

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
$3$	2.48480	+	0.665801i	1.43460	+	0.384400i	0.890640	−	0.454710i	$-0.150257\pi$
$3$	2.48480	+	0.665801i	1.43460	+	0.384400i	0.543962	+	0.839110i	$0.316924\pi$
$4$		0			0
$5$	−0.837076	−	3.12401i	−0.374352	−	1.39710i	−0.854290	−	0.519797i	$-0.826008\pi$
$5$	−0.837076	−	3.12401i	−0.374352	−	1.39710i	0.479938	−	0.877302i	$-0.340659\pi$
$6$		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
$11$	1.40398	+	0.376195i	0.423315	+	0.113427i	0.464187	−	0.885737i	$-0.346347\pi$
$11$	1.40398	+	0.376195i	0.423315	+	0.113427i	−0.0408713	+	0.999164i	$0.513013\pi$
$12$		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	−0.233991	−	0.972239i	$-0.575179\pi$
$17$	2.02443	−	1.16881i	0.490997	−	0.283477i	0.724988	+	0.688761i	$0.241845\pi$
$18$		0			0
$19$	−1.18070	−	4.40643i	−0.270871	−	1.01090i	−0.958558	−	0.284897i	$-0.908041\pi$
$19$	−1.18070	−	4.40643i	−0.270871	−	1.01090i	0.687687	−	0.726007i	$-0.258626\pi$
$20$		0			0
$21$	−2.45991	−	6.34599i	−0.536797	−	1.38481i
$22$		0			0
$23$	1.15450	−	1.99965i	0.240729	−	0.416955i	−0.720193	−	0.693774i	$-0.755947\pi$
$23$	1.15450	−	1.99965i	0.240729	−	0.416955i	0.960922	+	0.276819i	$0.0892802\pi$
$24$		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	−0.836341	−	0.548210i	$-0.815309\pi$
$29$	−1.55163	+	1.55163i	−0.288130	+	0.288130i	0.548210	+	0.836341i	$0.315309\pi$
$30$		0			0
$31$	3.88952	+	6.73685i	0.698579	+	1.20997i	0.968959	+	0.247221i	$0.0795172\pi$
$31$	3.88952	+	6.73685i	0.698579	+	1.20997i	−0.270380	+	0.962754i	$0.587149\pi$
$32$		0			0
$33$	3.23814	+	1.86954i	0.563687	+	0.325445i
$34$		0			0
$35$	−5.36320	+	6.66761i	−0.906546	+	1.12703i
$36$		0			0
$37$	−1.01669	+	0.272421i	−0.167142	+	0.0447857i	−0.341420	−	0.939911i	$-0.610908\pi$
$37$	−1.01669	+	0.272421i	−0.167142	+	0.0447857i	0.174277	+	0.984697i	$0.444241\pi$
$38$		0			0
$39$	5.66282	+	9.80830i	0.906778	+	1.57058i
$40$		0			0
$41$	2.77210			0.432929			0.216464	−	0.976290i	$-0.430547\pi$
$41$	2.77210			0.432929			0.216464	+	0.976290i	$0.430547\pi$
$42$		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
$45$	3.02815	−	11.3012i	0.451410	−	1.68468i
$46$		0			0
$47$	1.42516	−	2.46844i	0.207880	−	0.360059i	−0.743166	−	0.669107i	$-0.766677\pi$
$47$	1.42516	−	2.46844i	0.207880	−	0.360059i	0.951047	+	0.309047i	$0.100010\pi$
$48$		0			0
$49$	−2.11939	+	6.67144i	−0.302770	+	0.953064i
$50$		0			0
$51$	5.80851	−	1.55638i	0.813354	−	0.217937i
$52$		0			0
$53$	−2.97221	+	11.0925i	−0.408265	+	1.52367i	0.389689	+	0.920947i	$0.372583\pi$
$53$	−2.97221	+	11.0925i	−0.408265	+	1.52367i	−0.797954	+	0.602719i	$0.794084\pi$
$54$		0			0
$55$		−	4.70094i		−	0.633875i
$56$		0			0
$57$		−	11.7352i		−	1.55437i
$58$		0			0
$59$	−1.01120	+	3.77383i	−0.131646	+	0.491311i	−0.999989	−	0.00465348i	$-0.998519\pi$
$59$	−1.01120	+	3.77383i	−0.131646	+	0.491311i	0.868343	+	0.495965i	$0.165185\pi$
$60$		0			0
$61$	−13.9045	+	3.72571i	−1.78029	+	0.477028i	−0.990637	−	0.136523i	$-0.956407\pi$
$61$	−13.9045	+	3.72571i	−1.78029	+	0.477028i	−0.789655	+	0.613551i	$0.789741\pi$
$62$		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
$67$	0.695627	−	2.59612i	0.0849844	−	0.317166i	−0.910327	−	0.413890i	$-0.864170\pi$
$67$	0.695627	−	2.59612i	0.0849844	−	0.317166i	0.995311	+	0.0967240i	$0.0308364\pi$
$68$		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	0.980214	+	0.197941i	$0.0634253\pi$
$73$	5.65210	+	9.78973i	0.661529	+	1.14580i	−0.318685	+	0.947861i	$0.603241\pi$
$74$		0			0
$75$	−13.5673	+	3.63536i	−1.56662	+	0.419775i
$76$		0			0
$77$	−1.38991	−	3.58565i	−0.158395	−	0.408623i
$78$		0			0
$79$	−0.706717	−	0.408024i	−0.0795119	−	0.0459062i	0.459717	−	0.888066i	$-0.347951\pi$
$79$	−0.706717	−	0.408024i	−0.0795119	−	0.0459062i	−0.539229	+	0.842159i	$0.681284\pi$
$80$		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	$-0.751126\pi$
$89$	2.40944	−	4.17328i	0.255400	−	0.442367i	0.965004	+	0.262234i	$0.0844594\pi$
$90$		0			0
$91$	1.78445	−	11.5108i	0.187061	−	1.20666i
$92$		0			0
$93$	5.17929	+	19.3294i	0.537068	+	2.00436i
$94$		0			0
$95$	−12.7774	+	7.37703i	−1.31093	+	0.756867i
$96$		0			0
$97$			5.86541i			0.595542i	0.954637	+	0.297771i	$0.0962432\pi$
$97$			5.86541i			0.595542i	−0.954637	+	0.297771i	$0.903757\pi$
$98$		0			0
$99$	3.71804	+	3.71804i	0.373677	+	0.373677i
$100$		0			0
$101$	1.39442	+	0.373632i	0.138749	+	0.0371778i	0.327525	−	0.944842i	$-0.393785\pi$
$101$	1.39442	+	0.373632i	0.138749	+	0.0371778i	−0.188776	+	0.982020i	$0.560452\pi$
$102$		0			0
$103$	2.10134	+	1.21321i	0.207051	+	0.119541i	0.599940	−	0.800045i	$-0.295191\pi$
$103$	2.10134	+	1.21321i	0.207051	+	0.119541i	−0.392889	+	0.919586i	$0.628524\pi$
$104$		0			0
$105$	−17.7658	+	12.9969i	−1.73376	+	1.26836i
$106$		0			0
$107$	−1.16493	−	4.34758i	−0.112618	−	0.420297i	0.886480	−	0.462768i	$-0.153144\pi$
$107$	−1.16493	−	4.34758i	−0.112618	−	0.420297i	−0.999098	+	0.0424712i	$0.986477\pi$
$108$		0			0
$109$	−3.14518	−	0.842750i	−0.301254	−	0.0807208i	0.105026	−	0.994470i	$-0.466507\pi$
$109$	−3.14518	−	0.842750i	−0.301254	−	0.0807208i	−0.406280	+	0.913749i	$0.633174\pi$
$110$		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
$115$	−7.21331	−	1.93280i	−0.672645	−	0.180235i
$116$		0			0
$117$	4.12215	+	15.3841i	0.381093	+	1.42226i
$118$		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
$123$	6.88811	+	1.84566i	0.621080	+	0.166418i
$124$		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
$131$	3.58012	+	13.3612i	0.312796	+	1.16737i	0.926024	+	0.377465i	$0.123204\pi$
$131$	3.58012	+	13.3612i	0.312796	+	1.16737i	−0.613227	+	0.789907i	$0.710129\pi$
$132$		0			0
$133$	−7.56482	+	9.40469i	−0.655953	+	0.815490i
$134$		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	$-0.632305\pi$
$137$	2.18423	−	1.26106i	0.186611	−	0.107740i	0.590395	+	0.807114i	$0.298972\pi$
$138$		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
$147$	−9.70812	+	15.1661i	−0.800713	+	1.25088i
$148$		0			0
$149$	8.20870	−	2.19951i	0.672483	−	0.180191i	0.0936097	−	0.995609i	$-0.470159\pi$
$149$	8.20870	−	2.19951i	0.672483	−	0.180191i	0.578873	+	0.815418i	$0.303493\pi$
$150$		0			0
$151$	−5.11927	−	8.86683i	−0.416600	−	0.721572i	0.578995	−	0.815331i	$-0.303445\pi$
$151$	−5.11927	−	8.86683i	−0.416600	−	0.721572i	−0.995595	+	0.0937588i	$0.970112\pi$
$152$		0			0
$153$	8.45639			0.683659
$154$		0			0
$155$	17.7902	−	17.7902i	1.42894	−	1.42894i
$156$		0			0
$157$	3.79998	−	14.1817i	0.303272	−	1.13183i	−0.631151	−	0.775660i	$-0.717417\pi$
$157$	3.79998	−	14.1817i	0.303272	−	1.13183i	0.934423	−	0.356166i	$-0.115916\pi$
$158$		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
$163$	−22.2047	+	5.94974i	−1.73921	+	0.466019i	−0.982271	−	0.187468i	$-0.939972\pi$
$163$	−22.2047	+	5.94974i	−1.73921	+	0.466019i	−0.756937	+	0.653488i	$0.773305\pi$
$164$		0			0
$165$	3.12989	−	11.6809i	0.243662	−	0.909358i
$166$		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
$171$	4.27121	−	15.9404i	0.326628	−	1.21899i
$172$		0			0
$173$	8.02996	−	2.15162i	0.610506	−	0.163585i	0.0596981	−	0.998216i	$-0.480986\pi$
$173$	8.02996	−	2.15162i	0.610506	−	0.163585i	0.550808	+	0.834632i	$0.314320\pi$
$174$		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
$179$	5.00112	−	18.6644i	0.373801	−	1.39504i	−0.481288	−	0.876563i	$-0.659831\pi$
$179$	5.00112	−	18.6644i	0.373801	−	1.39504i	0.855089	−	0.518482i	$-0.173503\pi$
$180$		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
$187$	3.28196	−	0.879398i	0.240001	−	0.0643080i
$188$		0			0
$189$	0.643867	−	4.15336i	0.0468344	−	0.302112i
$190$		0			0
$191$	13.1707	+	7.60410i	0.952997	+	0.550213i	0.894011	−	0.448046i	$-0.147880\pi$
$191$	13.1707	+	7.60410i	0.952997	+	0.550213i	0.0589865	+	0.998259i	$0.481213\pi$
$192$		0			0
$193$	−11.2397	−	19.4678i	−0.809053	−	1.40132i	−0.913521	−	0.406792i	$-0.866647\pi$
$193$	−11.2397	−	19.4678i	−0.809053	−	1.40132i	0.104468	−	0.994528i	$-0.466686\pi$
$194$		0			0
$195$	25.9010	−	25.9010i	1.85481	−	1.85481i
$196$		0			0
$197$	−8.31581	−	8.31581i	−0.592477	−	0.592477i	0.345823	−	0.938300i	$-0.387600\pi$
$197$	−8.31581	−	8.31581i	−0.592477	−	0.592477i	−0.938300	+	0.345823i	$0.887600\pi$
$198$		0			0
$199$	−8.85088	+	5.11006i	−0.627422	+	0.362242i	−0.779753	−	0.626087i	$-0.784655\pi$
$199$	−8.85088	+	5.11006i	−0.627422	+	0.362242i	0.152331	+	0.988330i	$0.451322\pi$
$200$		0			0
$201$	3.45699	−	5.98769i	0.243837	−	0.422339i
$202$		0			0
$203$	5.73713	+	0.889390i	0.402668	+	0.0624229i
$204$		0			0
$205$	−2.32046	−	8.66006i	−0.162068	−	0.604845i
$206$		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
$213$	18.5949	+	4.98248i	1.27410	+	0.341394i
$214$		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
$219$	7.52635	+	28.0887i	0.508583	+	1.89806i
$220$		0			0
$221$	9.94104	+	2.66369i	0.668706	+	0.179179i
$222$		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
$227$	16.9291	+	4.53614i	1.12362	+	0.301074i	0.772349	−	0.635198i	$-0.219081\pi$
$227$	16.9291	+	4.53614i	1.12362	+	0.301074i	0.351275	+	0.936272i	$0.385748\pi$
$228$		0			0
$229$	1.80926	+	6.75227i	0.119560	+	0.446202i	0.999588	−	0.0287195i	$-0.00914296\pi$
$229$	1.80926	+	6.75227i	0.119560	+	0.446202i	−0.880028	+	0.474922i	$0.842476\pi$
$230$		0			0
$231$	−1.06634	−	9.83503i	−0.0701597	−	0.647098i
$232$		0			0
$233$	−25.0933	−	14.4876i	−1.64392	−	0.949116i	−0.979422	−	0.201823i	$-0.935313\pi$
$233$	−25.0933	−	14.4876i	−1.64392	−	0.949116i	−0.664495	−	0.747293i	$-0.731353\pi$
$234$		0			0
$235$	−8.90440	−	2.38593i	−0.580859	−	0.155641i
$236$		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	−0.120072	−	0.992765i	$-0.538313\pi$
$241$	10.5510	−	6.09164i	0.679651	−	0.392397i	0.799724	+	0.600368i	$0.204979\pi$
$242$		0			0
$243$	−5.73831	−	21.4157i	−0.368113	−	1.37381i
$244$		0			0
$245$	22.6157	+	1.03650i	1.44487	+	0.0662195i
$246$		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	0.600204	−	0.799847i	$-0.295086\pi$
$257$	3.32837	+	1.92163i	0.207618	+	0.119868i	−0.392586	+	0.919715i	$0.628419\pi$
$258$		0			0
$259$	2.16993	+	1.74542i	0.134833	+	0.108455i
$260$		0			0
$261$	−7.66759	+	2.05452i	−0.474612	+	0.127172i
$262$		0			0
$263$	−3.15784	−	5.46953i	−0.194720	−	0.337266i	0.752088	−	0.659062i	$-0.229047\pi$
$263$	−3.15784	−	5.46953i	−0.194720	−	0.337266i	−0.946809	+	0.321797i	$0.895713\pi$
$264$		0			0
$265$	37.1409			2.28155
$266$		0			0
$267$	8.76556	−	8.76556i	0.536444	−	0.536444i
$268$		0			0
$269$	−6.24090	+	23.2914i	−0.380514	+	1.42010i	0.464603	+	0.885519i	$0.346197\pi$
$269$	−6.24090	+	23.2914i	−0.380514	+	1.42010i	−0.845118	+	0.534580i	$0.820470\pi$
$270$		0			0
$271$	−4.73315	+	8.19805i	−0.287518	+	0.497996i	−0.973217	−	0.229890i	$-0.926163\pi$
$271$	−4.73315	+	8.19805i	−0.287518	+	0.497996i	0.685699	+	0.727886i	$0.259497\pi$
$272$		0			0
$273$	12.0979	−	27.4141i	0.732200	−	1.65918i
$274$		0			0
$275$	−7.66590	+	2.05407i	−0.462271	+	0.123865i
$276$		0			0
$277$	−3.03526	+	11.3278i	−0.182371	+	0.680619i	0.812807	+	0.582533i	$0.197938\pi$
$277$	−3.03526	+	11.3278i	−0.182371	+	0.680619i	−0.995178	+	0.0980853i	$0.968728\pi$
$278$		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
$283$	−0.992910	+	3.70559i	−0.0590224	+	0.220275i	−0.989137	−	0.146994i	$-0.953040\pi$
$283$	−0.992910	+	3.70559i	−0.0590224	+	0.220275i	0.930115	+	0.367268i	$0.119707\pi$
$284$		0			0
$285$	−36.6609	+	9.82326i	−2.17160	+	0.581880i
$286$		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
$291$	−3.90519	+	14.5744i	−0.228927	+	0.854365i
$292$		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
$299$	9.81932	−	2.63108i	0.567866	−	0.152159i
$300$		0			0
$301$	26.3314	+	4.08198i	1.51772	+	0.235282i
$302$		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	−0.513976	−	0.857804i	$-0.671828\pi$
$311$	−0.495271	+	0.285945i	−0.0280843	+	0.0162145i	0.485892	+	0.874019i	$0.338495\pi$
$312$		0			0
$313$	−0.707287	+	1.22506i	−0.0399782	+	0.0692443i	−0.885322	−	0.464978i	$-0.846062\pi$
$313$	−0.707287	+	1.22506i	−0.0399782	+	0.0692443i	0.845344	+	0.534222i	$0.179396\pi$
$314$		0			0
$315$	−28.8624	+	11.1880i	−1.62621	+	0.630372i
$316$		0			0
$317$	6.77681	+	25.2914i	0.380624	+	1.42051i	0.844951	+	0.534843i	$0.179629\pi$
$317$	6.77681	+	25.2914i	0.380624	+	1.42051i	−0.464328	+	0.885663i	$0.653704\pi$
$318$		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
$325$	−23.2200	−	6.22177i	−1.28801	−	0.345122i
$326$		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
$331$	0.727156	+	2.71378i	0.0399681	+	0.149163i	0.983026	−	0.183465i	$-0.0587313\pi$
$331$	0.727156	+	2.71378i	0.0399681	+	0.149163i	−0.943058	+	0.332628i	$0.892065\pi$
$332$		0			0
$333$	−3.67790	−	0.985490i	−0.201548	−	0.0540045i
$334$		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
$339$	28.6738	+	7.68312i	1.55735	+	0.417290i
$340$		0			0
$341$	2.92644	+	10.9216i	0.158475	+	0.591438i
$342$		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
$347$	−12.0814	−	3.23720i	−0.648563	−	0.173782i	−0.0804837	−	0.996756i	$-0.525647\pi$
$347$	−12.0814	−	3.23720i	−0.648563	−	0.173782i	−0.568079	+	0.822974i	$0.692313\pi$
$348$		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	−0.898810	−	0.438337i	$-0.855567\pi$
$353$	−18.1984	+	10.5069i	−0.968604	+	0.559224i	−0.0697939	+	0.997561i	$0.522234\pi$
$354$		0			0
$355$	−6.26421	−	23.3784i	−0.332470	−	1.24079i
$356$		0			0
$357$	−12.3972	−	9.97186i	−0.656127	−	0.527767i
$358$		0			0
$359$	−4.78310	+	8.28458i	−0.252443	+	0.437243i	−0.964198	−	0.265184i	$-0.914567\pi$
$359$	−4.78310	+	8.28458i	−0.252443	+	0.437243i	0.711755	+	0.702428i	$0.247901\pi$
$360$		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	$-0.217781\pi$
$367$	−3.06305	−	5.30536i	−0.159890	−	0.276938i	−0.934829	+	0.355099i	$0.884447\pi$
$368$		0			0
$369$	8.68463	+	5.01408i	0.452104	+	0.261022i
$370$		0			0
$371$	28.3292	−	10.9813i	1.47078	−	0.570123i
$372$		0			0
$373$	15.8673	−	4.25162i	0.821575	−	0.220140i	0.176540	−	0.984293i	$-0.443509\pi$
$373$	15.8673	−	4.25162i	0.821575	−	0.220140i	0.645035	+	0.764153i	$0.276843\pi$
$374$		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
$381$	2.99085	−	11.1620i	0.153226	−	0.571846i
$382$		0			0
$383$	9.64030	−	16.6975i	0.492596	−	0.853202i	−0.507367	−	0.861730i	$-0.669381\pi$
$383$	9.64030	−	16.6975i	0.492596	−	0.853202i	0.999964	+	0.00852805i	$0.00271459\pi$
$384$		0			0
$385$	−10.0381	+	7.34357i	−0.511591	+	0.374263i
$386$		0			0
$387$	−35.1915	+	9.42954i	−1.78889	+	0.479330i
$388$		0			0
$389$	7.40814	−	27.6476i	0.375608	−	1.40179i	−0.476847	−	0.878986i	$-0.658221\pi$
$389$	7.40814	−	27.6476i	0.375608	−	1.40179i	0.852455	−	0.522801i	$-0.175113\pi$
$390$		0			0
$391$		−	5.39753i		−	0.272965i
$392$		0			0
$393$			35.5835i			1.79495i
$394$		0			0
$395$	−0.683093	+	2.54934i	−0.0343701	+	0.128271i
$396$		0			0
$397$	−8.95799	+	2.40028i	−0.449588	+	0.120467i	−0.476507	−	0.879171i	$-0.658097\pi$
$397$	−8.95799	+	2.40028i	−0.449588	+	0.120467i	0.0269184	+	0.999638i	$0.491431\pi$
$398$		0			0
$399$	−25.0587	+	18.3321i	−1.25451	+	0.917754i
$400$		0			0
$401$	17.5281	−	30.3596i	0.875312	−	1.51609i	0.0188827	−	0.999822i	$-0.493989\pi$
$401$	17.5281	−	30.3596i	0.875312	−	1.51609i	0.856430	−	0.516264i	$-0.172678\pi$
$402$		0			0
$403$	−8.86416	+	33.0815i	−0.441555	+	1.64791i
$404$		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	0.869690	+	0.493598i	$0.164319\pi$
$409$	17.4392	+	30.2056i	0.862314	+	1.49357i	−0.00737621	+	0.999973i	$0.502348\pi$
$410$		0			0
$411$	6.26699	−	1.67923i	0.309128	−	0.0828306i
$412$		0			0
$413$	9.63807	−	3.73603i	0.474258	−	0.183838i
$414$		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	0.503035	−	0.864266i	$-0.332217\pi$
$421$	−7.41183	−	7.41183i	−0.361230	−	0.361230i	−0.864266	+	0.503035i	$0.832217\pi$
$422$		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
$427$	29.6766	+	23.8709i	1.43615	+	1.15519i
$428$		0			0
$429$	4.26065	+	15.9010i	0.205706	+	0.767706i
$430$		0			0
$431$	−1.39637	+	0.806195i	−0.0672608	+	0.0388331i	−0.533253	−	0.845956i	$-0.679031\pi$
$431$	−1.39637	+	0.806195i	−0.0672608	+	0.0388331i	0.465992	+	0.884789i	$0.345697\pi$
$432$		0			0
$433$			13.0869i			0.628917i	0.949271	+	0.314458i	$0.101823\pi$
$433$			13.0869i			0.628917i	−0.949271	+	0.314458i	$0.898177\pi$
$434$		0			0
$435$	12.9093	+	12.9093i	0.618956	+	0.618956i
$436$		0			0
$437$	−10.1744	−	2.72622i	−0.486708	−	0.130413i
$438$		0			0
$439$	−1.71358	−	0.989334i	−0.0817846	−	0.0472184i	0.458550	−	0.888669i	$-0.348369\pi$
$439$	−1.71358	−	0.989334i	−0.0817846	−	0.0472184i	−0.540335	+	0.841450i	$0.681702\pi$
$440$		0			0
$441$	−18.7069	+	17.0673i	−0.890803	+	0.812729i
$442$		0			0
$443$	−8.98048	−	33.5156i	−0.426675	−	1.59237i	−0.760237	−	0.649646i	$-0.774917\pi$
$443$	−8.98048	−	33.5156i	−0.426675	−	1.59237i	0.333562	−	0.942728i	$-0.391749\pi$
$444$		0			0
$445$	−15.0542	−	4.03377i	−0.713640	−	0.191219i
$446$		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
$451$	3.89196	+	1.04285i	0.183265	+	0.0491058i
$452$		0			0
$453$	−6.81682	−	25.4407i	−0.320282	−	1.19531i
$454$		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	$-0.0857088\pi$
$457$	25.9859	+	15.0030i	1.21557	+	0.701810i	0.251603	+	0.967830i	$0.419042\pi$
$458$		0			0
$459$	3.58693	+	0.961116i	0.167424	+	0.0448611i
$460$		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
$467$	6.17115	+	23.0310i	0.285567	+	1.06575i	0.948424	+	0.317004i	$0.102677\pi$
$467$	6.17115	+	23.0310i	0.285567	+	1.06575i	−0.662858	+	0.748745i	$0.730657\pi$
$468$		0			0
$469$	−6.63028	+	2.57011i	−0.306158	+	0.118677i
$470$		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	−0.914421	−	0.404764i	$-0.867354\pi$
$479$	−17.6784	−	30.6199i	−0.807747	−	1.39906i	0.106674	−	0.994294i	$-0.465980\pi$
$480$		0			0
$481$	−4.01319	−	2.31701i	−0.182986	−	0.105647i
$482$		0			0
$483$	−15.5297	−	2.40746i	−0.706625	−	0.109543i
$484$		0			0
$485$	18.3236	−	4.90979i	0.832032	−	0.222942i
$486$		0			0
$487$	−5.31153	−	9.19984i	−0.240688	−	0.416884i	0.720222	−	0.693743i	$-0.244040\pi$
$487$	−5.31153	−	9.19984i	−0.240688	−	0.416884i	−0.960911	+	0.276859i	$0.910706\pi$
$488$		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
$493$	−1.32761	+	4.95472i	−0.0597927	+	0.223149i
$494$		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
$499$	12.2441	−	3.28081i	0.548123	−	0.146869i	0.0258790	−	0.999665i	$-0.491762\pi$
$499$	12.2441	−	3.28081i	0.548123	−	0.146869i	0.522244	+	0.852796i	$0.325095\pi$
$500$		0			0
$501$	−2.54402	+	9.49441i	−0.113658	+	0.424179i
$502$		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
$507$	−4.25008	+	15.8615i	−0.188753	+	0.704434i
$508$		0			0
$509$	23.0168	−	6.16734i	1.02020	−	0.273363i	0.290317	−	0.956931i	$-0.406239\pi$
$509$	23.0168	−	6.16734i	1.02020	−	0.273363i	0.729887	+	0.683568i	$0.239573\pi$
$510$		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
$515$	2.03109	−	7.58014i	0.0895007	−	0.334021i
$516$		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	−0.999742	−	0.0227214i	$-0.992767\pi$
$521$	−11.8589	−	20.5402i	−0.519548	−	0.899884i	0.480194	−	0.877163i	$-0.340566\pi$
$522$		0			0
$523$	−18.1369	+	4.85978i	−0.793073	+	0.212503i	−0.632540	−	0.774527i	$-0.717988\pi$
$523$	−18.1369	+	4.85978i	−0.793073	+	0.212503i	−0.160532	+	0.987031i	$0.551321\pi$
$524$		0			0
$525$	28.9569	+	23.2920i	1.26378	+	1.01655i
$526$		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
$539$	−5.48534	+	8.56926i	−0.236271	+	0.369104i
$540$		0			0
$541$	−6.76561	−	25.2496i	−0.290876	−	1.08556i	−0.944437	−	0.328691i	$-0.893392\pi$
$541$	−6.76561	−	25.2496i	−0.290876	−	1.08556i	0.653561	−	0.756874i	$-0.273274\pi$
$542$		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
$549$	−50.3001	−	13.4779i	−2.14675	−	0.575221i
$550$		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
$555$	2.26650	+	8.45871i	0.0962077	+	0.359052i
$556$		0			0
$557$	−41.6206	−	11.1522i	−1.76352	−	0.472534i	−0.776094	−	0.630617i	$-0.782802\pi$
$557$	−41.6206	−	11.1522i	−1.76352	−	0.472534i	−0.987426	+	0.158083i	$0.949468\pi$
$558$		0			0
$559$	−44.3401			−1.87539
$560$		0			0
$561$	8.74052			0.369025
$562$		0			0
$563$	8.61735	+	2.30901i	0.363178	+	0.0973133i	0.435793	−	0.900047i	$-0.356468\pi$
$563$	8.61735	+	2.30901i	0.363178	+	0.0973133i	−0.0726153	+	0.997360i	$0.523135\pi$
$564$		0			0
$565$	−9.65958	−	36.0500i	−0.406382	−	1.51664i
$566$		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	$-0.290868\pi$
$569$	5.49552	+	3.17284i	0.230384	+	0.133012i	−0.380365	+	0.924836i	$0.624202\pi$
$570$		0			0
$571$	−36.2565	−	9.71490i	−1.51729	−	0.406556i	−0.598439	−	0.801168i	$-0.704212\pi$
$571$	−36.2565	−	9.71490i	−1.51729	−	0.406556i	−0.918848	+	0.394612i	$0.870879\pi$
$572$		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	−0.533729	−	0.845655i	$-0.679210\pi$
$577$	−1.63907	+	0.946316i	−0.0682353	+	0.0393957i	0.465494	+	0.885051i	$0.345877\pi$
$578$		0			0
$579$	−14.9668	−	55.8569i	−0.622000	−	2.32134i
$580$		0			0
$581$	−9.80889	−	1.52061i	−0.406941	−	0.0630854i
$582$		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	−0.0784171	−	0.996921i	$-0.524987\pi$
$593$	−23.8885	−	13.7920i	−0.980984	−	0.566372i	−0.902567	+	0.430549i	$0.858320\pi$
$594$		0			0
$595$	−3.06430	+	19.7667i	−0.125624	+	0.810354i
$596$		0			0
$597$	−25.3950	+	6.80456i	−1.03935	+	0.278492i
$598$		0			0
$599$	11.8101	+	20.4557i	0.482548	+	0.835797i	0.999799	−	0.0200365i	$-0.00637824\pi$
$599$	11.8101	+	20.4557i	0.482548	+	0.835797i	−0.517252	+	0.855833i	$0.673045\pi$
$600$		0			0
$601$	−5.61717			−0.229129			−0.114565	−	0.993416i	$-0.536547\pi$
$601$	−5.61717			−0.229129			−0.114565	+	0.993416i	$0.536547\pi$
$602$		0			0
$603$	6.87508	−	6.87508i	0.279975	−	0.279975i
$604$		0			0
$605$	−7.43936	+	27.7641i	−0.302453	+	1.12877i
$606$		0			0
$607$	−2.43281	+	4.21375i	−0.0987446	+	0.171031i	−0.911165	−	0.412041i	$-0.864816\pi$
$607$	−2.43281	+	4.21375i	−0.0987446	+	0.171031i	0.812421	+	0.583072i	$0.198149\pi$
$608$		0			0
$609$	13.6635	+	6.02975i	0.553672	+	0.244338i
$610$		0			0
$611$	12.1214	−	3.24791i	0.490378	−	0.131396i
$612$		0			0
$613$	−1.06941	+	3.99109i	−0.0431931	+	0.161199i	−0.984154	−	0.177317i	$-0.943258\pi$
$613$	−1.06941	+	3.99109i	−0.0431931	+	0.161199i	0.940961	+	0.338516i	$0.109925\pi$
$614$		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
$619$	4.75356	−	17.7405i	0.191062	−	0.713051i	−0.802190	−	0.597069i	$-0.796332\pi$
$619$	4.75356	−	17.7405i	0.191062	−	0.713051i	0.993251	−	0.115982i	$-0.0370015\pi$
$620$		0			0
$621$	3.54302	−	0.949348i	0.142176	−	0.0380960i
$622$		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
$627$	4.41472	−	16.4760i	0.176307	−	0.657987i
$628$		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
$635$	−14.0334	+	3.76023i	−0.556897	+	0.149220i
$636$		0			0
$637$	−27.3672	+	14.1712i	−1.08433	+	0.561484i
$638$		0			0
$639$	23.4447	+	13.5358i	0.927458	+	0.535468i
$640$		0			0
$641$	−17.0933	−	29.6065i	−0.675146	−	1.16939i	−0.976426	−	0.215852i	$-0.930747\pi$
$641$	−17.0933	−	29.6065i	−0.675146	−	1.16939i	0.301280	−	0.953536i	$-0.402586\pi$
$642$		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	−0.928957	−	0.370188i	$-0.879293\pi$
$647$	−27.2890	+	15.7553i	−1.07284	+	0.619406i	−0.143886	+	0.989594i	$0.545960\pi$
$648$		0			0
$649$	−2.83939	+	4.91797i	−0.111456	+	0.193047i
$650$		0			0
$651$	33.1841	−	41.2549i	1.30059	−	1.61691i
$652$		0			0
$653$	−5.18880	−	19.3649i	−0.203053	−	0.757805i	−0.990034	−	0.140828i	$-0.955024\pi$
$653$	−5.18880	−	19.3649i	−0.203053	−	0.757805i	0.786981	−	0.616977i	$-0.211643\pi$
$654$		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
$661$	46.8440	+	12.5518i	1.82202	+	0.488208i	0.997035	−	0.0769483i	$-0.0245176\pi$
$661$	46.8440	+	12.5518i	1.82202	+	0.488208i	0.824984	+	0.565157i	$0.191184\pi$
$662$		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
$667$	1.31136	+	4.89406i	0.0507760	+	0.189499i
$668$		0			0
$669$	43.4664	+	11.6468i	1.68051	+	0.450290i
$670$		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
$675$	−8.37826	−	2.24495i	−0.322479	−	0.0864080i
$676$		0			0
$677$	8.74138	+	32.6233i	0.335959	+	1.25381i	0.902826	+	0.430006i	$0.141488\pi$
$677$	8.74138	+	32.6233i	0.335959	+	1.25381i	−0.566868	+	0.823809i	$0.691845\pi$
$678$		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
$683$	6.57460	+	1.76166i	0.251570	+	0.0674080i	0.382400	−	0.923997i	$-0.375098\pi$
$683$	6.57460	+	1.76166i	0.251570	+	0.0674080i	−0.130830	+	0.991405i	$0.541764\pi$
$684$		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
$691$	−7.97267	−	29.7544i	−0.303295	−	1.13191i	−0.934403	−	0.356217i	$-0.884066\pi$
$691$	−7.97267	−	29.7544i	−0.303295	−	1.13191i	0.631108	−	0.775695i	$-0.282600\pi$
$692$		0			0
$693$	2.13117	−	13.7474i	0.0809565	−	0.522221i
$694$		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	$0.521708\pi$
$701$	−28.2191	+	28.2191i	−1.06582	+	1.06582i	−0.997675	+	0.0681440i	$0.978292\pi$
$702$		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
$707$	−1.38045	−	3.56123i	−0.0519171	−	0.133934i
$708$		0			0
$709$	18.5805	−	4.97862i	0.697804	−	0.186976i	0.107557	−	0.994199i	$-0.465697\pi$
$709$	18.5805	−	4.97862i	0.697804	−	0.186976i	0.590247	+	0.807223i	$0.299030\pi$
$710$		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
$717$	8.89426	−	33.1938i	0.332162	−	1.23965i
$718$		0			0
$719$	11.9289	−	20.6615i	0.444873	−	0.770543i	−0.553170	−	0.833068i	$-0.686582\pi$
$719$	11.9289	−	20.6615i	0.444873	−	0.770543i	0.998043	+	0.0625253i	$0.0199154\pi$
$720$		0			0
$721$	−0.691981	−	6.38229i	−0.0257707	−	0.237689i
$722$		0			0
$723$	30.2730	−	8.11163i	1.12587	−	0.301675i
$724$		0			0
$725$	3.10100	−	11.5731i	0.115168	−	0.429814i
$726$		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
$731$	−6.09328	+	22.7404i	−0.225368	+	0.841085i
$732$		0			0
$733$	22.5582	−	6.04445i	0.833206	−	0.223257i	0.183094	−	0.983095i	$-0.441389\pi$
$733$	22.5582	−	6.04445i	0.833206	−	0.223257i	0.650112	+	0.759839i	$0.274722\pi$
$734$		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
$739$	0.460947	−	1.72028i	0.0169562	−	0.0632814i	−0.956929	−	0.290321i	$-0.906238\pi$
$739$	0.460947	−	1.72028i	0.0169562	−	0.0632814i	0.973886	+	0.227039i	$0.0729046\pi$
$740$		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
$747$	13.1094	−	3.51266i	0.479649	−	0.128522i
$748$		0			0
$749$	−7.46379	+	9.27909i	−0.272721	+	0.339051i
$750$		0			0
$751$	1.51512	+	0.874754i	0.0552874	+	0.0319202i	0.527389	−	0.849624i	$-0.323171\pi$
$751$	1.51512	+	0.874754i	0.0552874	+	0.0319202i	−0.472101	+	0.881544i	$0.656504\pi$
$752$		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	0.362278	−	0.932070i	$-0.381999\pi$
$757$	−15.6771	−	15.6771i	−0.569792	−	0.569792i	−0.932070	+	0.362278i	$0.881999\pi$
$758$		0			0
$759$	7.47683	−	4.31675i	0.271392	−	0.156688i
$760$		0			0
$761$	25.9814	−	45.0012i	0.941826	−	1.63129i	0.179842	−	0.983695i	$-0.442441\pi$
$761$	25.9814	−	45.0012i	0.941826	−	1.63129i	0.761984	−	0.647596i	$-0.224225\pi$
$762$		0			0
$763$	3.11368	+	8.03255i	0.112723	+	0.290798i
$764$		0			0
$765$	−7.07864	−	26.4178i	−0.255929	−	0.955139i
$766$		0			0
$767$	−14.8965	+	8.60050i	−0.537882	+	0.310546i
$768$		0			0
$769$		−	34.9699i		−	1.26105i	−0.776170	−	0.630524i	$-0.782840\pi$
$769$		−	34.9699i		−	1.26105i	0.776170	−	0.630524i	$-0.217160\pi$
$770$		0			0
$771$	6.99090	+	6.99090i	0.251771	+	0.251771i
$772$		0			0
$773$	−13.2793	−	3.55817i	−0.477622	−	0.127978i	0.0119731	−	0.999928i	$-0.496189\pi$
$773$	−13.2793	−	3.55817i	−0.477622	−	0.127978i	−0.489595	+	0.871950i	$0.662855\pi$
$774$		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
$779$	−3.27301	−	12.2150i	−0.117268	−	0.437650i
$780$		0			0
$781$	10.5066	+	2.81523i	0.375956	+	0.100737i
$782$		0			0
$783$	−3.48586			−0.124574
$784$		0			0
$785$	−47.4847			−1.69480
$786$		0			0
$787$	−23.9812	−	6.42575i	−0.854838	−	0.229053i	−0.195318	−	0.980740i	$-0.562574\pi$
$787$	−23.9812	−	6.42575i	−0.854838	−	0.229053i	−0.659520	+	0.751687i	$0.729240\pi$
$788$		0			0
$789$	−4.20498	−	15.6932i	−0.149701	−	0.558692i
$790$		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
$795$	92.2878	+	24.7284i	3.27311	+	0.877027i
$796$		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
$803$	4.25258	+	15.8709i	0.150070	+	0.560070i
$804$		0			0
$805$	7.14106	+	18.4222i	0.251689	+	0.649298i
$806$		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	$-0.791019\pi$
$809$	−18.7601	+	10.8311i	−0.659569	+	0.380803i	0.132544	+	0.991177i	$0.457686\pi$
$810$		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
$819$	26.4109	−	32.8344i	0.922871	−	1.14733i
$820$		0			0
$821$	−46.3574	+	12.4214i	−1.61788	+	0.433511i	−0.950379	−	0.311094i	$-0.899305\pi$
$821$	−46.3574	+	12.4214i	−1.61788	+	0.433511i	−0.667506	+	0.744605i	$0.732638\pi$
$822$		0			0
$823$	15.0408	+	26.0514i	0.524290	+	0.908096i	0.999600	+	0.0282782i	$0.00900244\pi$
$823$	15.0408	+	26.0514i	0.524290	+	0.908096i	−0.475310	+	0.879818i	$0.657664\pi$
$824$		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
$829$	8.56747	−	31.9742i	0.297561	−	1.11051i	−0.641602	−	0.767038i	$-0.721730\pi$
$829$	8.56747	−	31.9742i	0.297561	−	1.11051i	0.939162	−	0.343473i	$-0.111603\pi$
$830$		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
$835$	11.9368	−	3.19846i	0.413091	−	0.110687i
$836$		0			0
$837$	−3.19838	+	11.9365i	−0.110552	+	0.412586i
$838$		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
$843$	3.72527	−	13.9029i	0.128305	−	0.478841i
$844$		0			0
$845$	19.9418	−	5.34340i	0.686020	−	0.183818i
$846$		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
$851$	−0.629017	+	2.34752i	−0.0215624	+	0.0804721i
$852$		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	0.994824	+	0.101614i	$0.0324008\pi$
$857$	17.1377	+	29.6834i	0.585412	+	1.01396i	−0.409411	+	0.912350i	$0.634266\pi$
$858$		0			0
$859$	43.1714	−	11.5677i	1.47299	−	0.394686i	0.569034	−	0.822314i	$-0.307317\pi$
$859$	43.1714	−	11.5677i	1.47299	−	0.394686i	0.903955	+	0.427628i	$0.140651\pi$
$860$		0			0
$861$	−6.81912	−	17.5917i	−0.232395	−	0.599523i
$862$		0			0
$863$	−32.5858	−	18.8134i	−1.10923	−	0.640416i	−0.170602	−	0.985340i	$-0.554571\pi$
$863$	−32.5858	−	18.8134i	−1.10923	−	0.640416i	−0.938631	+	0.344924i	$0.887905\pi$
$864$		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
$875$	0.603167	−	3.89081i	0.0203908	−	0.131533i
$876$		0			0
$877$	5.49616	+	20.5119i	0.185592	+	0.692639i	0.994503	+	0.104708i	$0.0333907\pi$
$877$	5.49616	+	20.5119i	0.185592	+	0.692639i	−0.808911	+	0.587931i	$0.799943\pi$
$878$		0			0
$879$	−30.7099	+	17.7304i	−1.03582	+	0.598031i
$880$		0			0
$881$		−	3.13017i		−	0.105458i	−0.998609	−	0.0527291i	$-0.983208\pi$
$881$		−	3.13017i		−	0.105458i	0.998609	−	0.0527291i	$-0.0167920\pi$
$882$		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
$885$	31.3978	+	8.41301i	1.05543	+	0.282800i
$886$		0			0
$887$	−41.9702	−	24.2315i	−1.40922	−	0.813615i	−0.413908	−	0.910318i	$-0.635837\pi$
$887$	−41.9702	−	24.2315i	−1.40922	−	0.813615i	−0.995313	+	0.0967040i	$0.969170\pi$
$888$		0			0
$889$	−9.59219	+	7.01733i	−0.321712	+	0.235354i
$890$		0			0
$891$	−2.54536	−	9.49940i	−0.0852727	−	0.318242i
$892$		0			0
$893$	−12.5597	−	3.36536i	−0.420294	−	0.112617i
$894$		0			0
$895$	−62.4941			−2.08895
$896$		0			0
$897$	26.1508			0.873151
$898$		0			0
$899$	−16.4882	−	4.41800i	−0.549912	−	0.147348i
$900$		0			0
$901$	6.94789	+	25.9299i	0.231468	+	0.863849i
$902$		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
$907$	−36.1999	−	9.69974i	−1.20200	−	0.322075i	−0.398381	−	0.917220i	$-0.630428\pi$
$907$	−36.1999	−	9.69974i	−1.20200	−	0.322075i	−0.803618	+	0.595146i	$0.797094\pi$
$908$		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
$915$	30.9974	+	115.684i	1.02474	+	3.82439i
$916$		0			0
$917$	22.9381	−	28.5169i	0.757481	−	0.941712i
$918$		0			0
$919$	−27.6308	+	47.8579i	−0.911455	+	1.57869i	−0.0994447	+	0.995043i	$0.531707\pi$
$919$	−27.6308	+	47.8579i	−0.911455	+	1.57869i	−0.812010	+	0.583643i	$0.801627\pi$
$920$		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	0.635096	−	0.772433i	$-0.280961\pi$
$929$	8.64695	+	4.99232i	0.283697	+	0.163793i	−0.351399	+	0.936226i	$0.614294\pi$
$930$		0			0
$931$	31.8996	+	1.46199i	1.04547	+	0.0479147i
$932$		0			0
$933$	−1.42103	+	0.380765i	−0.0465226	+	0.0124657i
$934$		0			0
$935$	−5.49450	−	9.51675i	−0.179689	−	0.311231i
$936$		0			0
$937$	7.92416			0.258871			0.129436	−	0.991588i	$-0.458683\pi$
$937$	7.92416			0.258871			0.129436	+	0.991588i	$0.458683\pi$
$938$		0			0
$939$	−2.57311	+	2.57311i	−0.0839703	+	0.0839703i
$940$		0			0
$941$	1.63637	−	6.10702i	0.0533441	−	0.199083i	−0.934111	−	0.356983i	$-0.883806\pi$
$941$	1.63637	−	6.10702i	0.0533441	−	0.199083i	0.987455	+	0.157900i	$0.0504722\pi$
$942$		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
$947$	−10.9891	+	2.94453i	−0.357098	+	0.0956843i	−0.432908	−	0.901438i	$-0.642513\pi$
$947$	−10.9891	+	2.94453i	−0.357098	+	0.0956843i	0.0758096	+	0.997122i	$0.475846\pi$
$948$		0			0
$949$	−12.8811	+	48.0727i	−0.418137	+	1.56051i
$950$		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
$955$	12.7304	−	47.5105i	0.411946	−	1.53741i
$956$		0			0
$957$	−7.92522	+	2.12356i	−0.256186	+	0.0686448i
$958$		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
$963$	4.21417	−	15.7275i	0.135800	−	0.506812i
$964$		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
$971$	−2.22623	+	0.596517i	−0.0714431	+	0.0191431i	−0.294364	−	0.955694i	$-0.595108\pi$
$971$	−2.22623	+	0.596517i	−0.0714431	+	0.0191431i	0.222920	+	0.974837i	$0.428441\pi$
$972$		0			0
$973$	3.44137	−	22.1990i	0.110325	−	0.711669i
$974$		0			0
$975$	−53.5546	−	30.9198i	−1.71512	−	0.990225i
$976$		0			0
$977$	7.66274	+	13.2723i	0.245153	+	0.424617i	0.962175	−	0.272434i	$-0.0878286\pi$
$977$	7.66274	+	13.2723i	0.245153	+	0.424617i	−0.717022	+	0.697051i	$0.754495\pi$
$978$		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	$-0.762591\pi$
$983$	−16.1184	+	9.30595i	−0.514097	+	0.296814i	0.220419	+	0.975405i	$0.429257\pi$
$984$		0			0
$985$	−19.0177	+	32.9396i	−0.605954	+	1.04954i
$986$		0			0
$987$	−19.1705	−	2.97187i	−0.610202	−	0.0945956i
$988$		0			0
$989$	6.01867	+	22.4620i	0.191383	+	0.714249i
$990$		0			0
$991$	23.7555	−	13.7153i	0.754619	−	0.435680i	−0.0727413	−	0.997351i	$-0.523175\pi$
$991$	23.7555	−	13.7153i	0.754619	−	0.435680i	0.827361	+	0.561671i	$0.189841\pi$
$992$		0			0
$993$			7.22736i			0.229353i
$994$		0			0
$995$	23.3727	+	23.3727i	0.740965	+	0.740965i
$996$		0			0
$997$	18.7595	+	5.02660i	0.594120	+	0.159194i	0.543335	−	0.839516i	$-0.317161\pi$
$997$	18.7595	+	5.02660i	0.594120	+	0.159194i	0.0507843	+	0.998710i	$0.483828\pi$
$998$		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	448.2.z.a.271.12		56
4.3	odd	2		112.2.v.a.75.13	yes	56
7.3	odd	6	inner	448.2.z.a.143.12		56
8.3	odd	2		896.2.z.b.159.12		56
8.5	even	2		896.2.z.a.159.3		56
16.3	odd	4	inner	448.2.z.a.47.12		56
16.5	even	4		896.2.z.b.607.12		56
16.11	odd	4		896.2.z.a.607.3		56
16.13	even	4		112.2.v.a.19.7	yes	56
28.3	even	6		112.2.v.a.59.7	yes	56
28.11	odd	6		784.2.w.f.619.7		56
28.19	even	6		784.2.j.a.587.5		56
28.23	odd	6		784.2.j.a.587.6		56
28.27	even	2		784.2.w.f.411.13		56
56.3	even	6		896.2.z.b.31.12		56
56.45	odd	6		896.2.z.a.31.3		56
112.3	even	12	inner	448.2.z.a.367.12		56
112.13	odd	4		784.2.w.f.19.7		56
112.45	odd	12		112.2.v.a.3.13	✓	56
112.59	even	12		896.2.z.a.479.3		56
112.61	odd	12		784.2.j.a.195.6		56
112.93	even	12		784.2.j.a.195.5		56
112.101	odd	12		896.2.z.b.479.12		56
112.109	even	12		784.2.w.f.227.13		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.13	✓	56	112.45	odd	12
112.2.v.a.19.7	yes	56	16.13	even	4
112.2.v.a.59.7	yes	56	28.3	even	6
112.2.v.a.75.13	yes	56	4.3	odd	2
448.2.z.a.47.12		56	16.3	odd	4	inner
448.2.z.a.143.12		56	7.3	odd	6	inner
448.2.z.a.271.12		56	1.1	even	1	trivial
448.2.z.a.367.12		56	112.3	even	12	inner
784.2.j.a.195.5		56	112.93	even	12
784.2.j.a.195.6		56	112.61	odd	12
784.2.j.a.587.5		56	28.19	even	6
784.2.j.a.587.6		56	28.23	odd	6
784.2.w.f.19.7		56	112.13	odd	4
784.2.w.f.227.13		56	112.109	even	12
784.2.w.f.411.13		56	28.27	even	2
784.2.w.f.619.7		56	28.11	odd	6
896.2.z.a.31.3		56	56.45	odd	6
896.2.z.a.159.3		56	8.5	even	2
896.2.z.a.479.3		56	112.59	even	12
896.2.z.a.607.3		56	16.11	odd	4
896.2.z.b.31.12		56	56.3	even	6
896.2.z.b.159.12		56	8.3	odd	2
896.2.z.b.479.12		56	112.101	odd	12
896.2.z.b.607.12		56	16.5	even	4

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:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	448.z (of order \(12\), degree \(4\), not minimal)

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