LMFDB - Embedded newform 504.3.l.h.181.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,3,Mod(181,504)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("504.181"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	504.l (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,2,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$13.7330053238$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.8
Character	$\chi$	$=$	504.181
Dual form			504.3.l.h.181.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.44694 + 1.38071i) q^{2} +(0.187253 - 3.99561i) q^{4} +5.24467 q^{5} +(-6.31936 + 3.01094i) q^{7} +(5.24586 + 6.03995i) q^{8} +(-7.58871 + 7.24140i) q^{10} -3.67957i q^{11} -12.5108 q^{13} +(4.98647 - 13.0819i) q^{14} +(-15.9299 - 1.49638i) q^{16} +18.2226i q^{17} +4.94253 q^{19} +(0.982081 - 20.9557i) q^{20} +(5.08043 + 5.32410i) q^{22} -1.93648 q^{23} +2.50660 q^{25} +(18.1024 - 17.2739i) q^{26} +(10.8472 + 25.8135i) q^{28} +41.0446i q^{29} -22.7944i q^{31} +(25.1156 - 19.8294i) q^{32} +(-25.1602 - 26.3669i) q^{34} +(-33.1430 + 15.7914i) q^{35} +46.7736i q^{37} +(-7.15153 + 6.82422i) q^{38} +(27.5128 + 31.6775i) q^{40} +66.3075i q^{41} +41.9792i q^{43} +(-14.7021 - 0.689010i) q^{44} +(2.80196 - 2.67373i) q^{46} -53.3092i q^{47} +(30.8685 - 38.0544i) q^{49} +(-3.62689 + 3.46089i) q^{50} +(-2.34269 + 49.9885i) q^{52} +61.3279i q^{53} -19.2981i q^{55} +(-51.3364 - 22.3736i) q^{56} +(-56.6709 - 59.3889i) q^{58} -70.9445 q^{59} -82.0007 q^{61} +(31.4726 + 32.9821i) q^{62} +(-8.96188 + 63.3694i) q^{64} -65.6152 q^{65} +1.63710i q^{67} +(72.8104 + 3.41223i) q^{68} +(26.1524 - 68.6101i) q^{70} -10.0937 q^{71} -64.4337i q^{73} +(-64.5810 - 67.6784i) q^{74} +(0.925503 - 19.7484i) q^{76} +(11.0789 + 23.2525i) q^{77} -149.702 q^{79} +(-83.5470 - 7.84804i) q^{80} +(-91.5517 - 95.9427i) q^{82} -12.9895 q^{83} +95.5714i q^{85} +(-57.9614 - 60.7413i) q^{86} +(22.2244 - 19.3025i) q^{88} -130.681i q^{89} +(79.0604 - 37.6693i) q^{91} +(-0.362612 + 7.73743i) q^{92} +(73.6048 + 77.1351i) q^{94} +25.9219 q^{95} +103.630i q^{97} +(7.87741 + 97.6829i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} - 6 q^{4} + 2 q^{8} - 38 q^{14} - 46 q^{16} + 16 q^{22} - 64 q^{23} + 160 q^{25} - 122 q^{28} + 122 q^{32} + 216 q^{44} - 260 q^{46} - 16 q^{49} - 122 q^{50} - 98 q^{56} - 160 q^{58} - 174 q^{64}+ \cdots + 2 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 - 6 * q^4 + 2 * q^8 - 38 * q^14 - 46 * q^16 + 16 * q^22 - 64 * q^23 + 160 * q^25 - 122 * q^28 + 122 * q^32 + 216 * q^44 - 260 * q^46 - 16 * q^49 - 122 * q^50 - 98 * q^56 - 160 * q^58 - 174 * q^64 + 408 * q^70 + 640 * q^71 - 408 * q^74 - 64 * q^79 - 792 * q^86 - 592 * q^88 - 316 * q^92 + 768 * q^95 + 2 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$-1$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.44694	+	1.38071i	−0.723468	+	0.690357i
$2$	−1.44694	+	1.38071i	−0.723468	+	0.690357i
$3$		0			0
$3$		0			0
$4$	0.187253	−	3.99561i	0.0468133	−	0.998904i
$5$	5.24467			1.04893			0.524467	−	0.851431i	$-0.324264\pi$
$5$	5.24467			1.04893			0.524467	+	0.851431i	$0.324264\pi$
$6$		0			0
$7$	−6.31936	+	3.01094i	−0.902765	+	0.430134i
$7$	−6.31936	+	3.01094i	−0.902765	+	0.430134i
$8$	5.24586	+	6.03995i	0.655733	+	0.754993i
$9$		0			0
$10$	−7.58871	+	7.24140i	−0.758871	+	0.724140i
$11$		−	3.67957i		−	0.334506i	−0.985914	−	0.167253i	$-0.946510\pi$
$11$		−	3.67957i		−	0.334506i	0.985914	−	0.167253i	$-0.0534897\pi$
$12$		0			0
$13$	−12.5108			−0.962372			−0.481186	−	0.876619i	$-0.659794\pi$
$13$	−12.5108			−0.962372			−0.481186	+	0.876619i	$0.659794\pi$
$14$	4.98647	−	13.0819i	0.356176	−	0.934419i
$15$		0			0
$16$	−15.9299	−	1.49638i	−0.995617	−	0.0935239i
$17$			18.2226i			1.07192i	0.844245	+	0.535958i	$0.180049\pi$
$17$			18.2226i			1.07192i	−0.844245	+	0.535958i	$0.819951\pi$
$18$		0			0
$19$	4.94253			0.260133			0.130067	−	0.991505i	$-0.458481\pi$
$19$	4.94253			0.260133			0.130067	+	0.991505i	$0.458481\pi$
$20$	0.982081	−	20.9557i	0.0491041	−	1.04778i
$21$		0			0
$22$	5.08043	+	5.32410i	0.230929	+	0.242005i
$23$	−1.93648			−0.0841948			−0.0420974	−	0.999114i	$-0.513404\pi$
$23$	−1.93648			−0.0841948			−0.0420974	+	0.999114i	$0.513404\pi$
$24$		0			0
$25$	2.50660			0.100264
$26$	18.1024	−	17.2739i	0.696246	−	0.664380i
$27$		0			0
$28$	10.8472	+	25.8135i	0.387401	+	0.921911i
$29$			41.0446i			1.41533i	0.706548	+	0.707665i	$0.250252\pi$
$29$			41.0446i			1.41533i	−0.706548	+	0.707665i	$0.749748\pi$
$30$		0			0
$31$		−	22.7944i		−	0.735303i	−0.929964	−	0.367652i	$-0.880162\pi$
$31$		−	22.7944i		−	0.735303i	0.929964	−	0.367652i	$-0.119838\pi$
$32$	25.1156	−	19.8294i	0.784862	−	0.619670i
$33$		0			0
$34$	−25.1602	−	26.3669i	−0.740005	−	0.775497i
$35$	−33.1430	+	15.7914i	−0.946942	+	0.451182i
$36$		0			0
$37$			46.7736i			1.26415i	0.774907	+	0.632075i	$0.217797\pi$
$37$			46.7736i			1.26415i	−0.774907	+	0.632075i	$0.782203\pi$
$38$	−7.15153	+	6.82422i	−0.188198	+	0.179585i
$39$		0			0
$40$	27.5128	+	31.6775i	0.687821	+	0.791939i
$41$			66.3075i			1.61725i	0.588321	+	0.808627i	$0.299789\pi$
$41$			66.3075i			1.61725i	−0.588321	+	0.808627i	$0.700211\pi$
$42$		0			0
$43$			41.9792i			0.976261i	0.872771	+	0.488131i	$0.162321\pi$
$43$			41.9792i			0.976261i	−0.872771	+	0.488131i	$0.837679\pi$
$44$	−14.7021	−	0.689010i	−0.334139	−	0.0156593i
$45$		0			0
$46$	2.80196	−	2.67373i	0.0609123	−	0.0581245i
$47$		−	53.3092i		−	1.13424i	−0.823636	−	0.567119i	$-0.808058\pi$
$47$		−	53.3092i		−	1.13424i	0.823636	−	0.567119i	$-0.191942\pi$
$48$		0			0
$49$	30.8685	−	38.0544i	0.629970	−	0.776620i
$50$	−3.62689	+	3.46089i	−0.0725377	+	0.0692179i
$51$		0			0
$52$	−2.34269	+	49.9885i	−0.0450518	+	0.961317i
$53$			61.3279i			1.15713i	0.815636	+	0.578565i	$0.196387\pi$
$53$			61.3279i			1.15713i	−0.815636	+	0.578565i	$0.803613\pi$
$54$		0			0
$55$		−	19.2981i		−	0.350875i
$56$	−51.3364	−	22.3736i	−0.916721	−	0.399529i
$57$		0			0
$58$	−56.6709	−	59.3889i	−0.977084	−	1.02395i
$59$	−70.9445			−1.20245			−0.601225	−	0.799080i	$-0.705320\pi$
$59$	−70.9445			−1.20245			−0.601225	+	0.799080i	$0.705320\pi$
$60$		0			0
$61$	−82.0007			−1.34427			−0.672137	−	0.740427i	$-0.734623\pi$
$61$	−82.0007			−1.34427			−0.672137	+	0.740427i	$0.734623\pi$
$62$	31.4726	+	32.9821i	0.507622	+	0.531969i
$63$		0			0
$64$	−8.96188	+	63.3694i	−0.140029	+	0.990147i
$65$	−65.6152			−1.00947
$66$		0			0
$67$			1.63710i			0.0244344i	0.999925	+	0.0122172i	$0.00388895\pi$
$67$			1.63710i			0.0244344i	−0.999925	+	0.0122172i	$0.996111\pi$
$68$	72.8104	+	3.41223i	1.07074	+	0.0501799i
$69$		0			0
$70$	26.1524	−	68.6101i	0.373605	−	0.980144i
$71$	−10.0937			−0.142165			−0.0710823	−	0.997470i	$-0.522645\pi$
$71$	−10.0937			−0.142165			−0.0710823	+	0.997470i	$0.522645\pi$
$72$		0			0
$73$		−	64.4337i		−	0.882653i	−0.897347	−	0.441326i	$-0.854508\pi$
$73$		−	64.4337i		−	0.882653i	0.897347	−	0.441326i	$-0.145492\pi$
$74$	−64.5810	−	67.6784i	−0.872716	−	0.914573i
$75$		0			0
$76$	0.925503	−	19.7484i	0.0121777	−	0.259848i
$77$	11.0789	+	23.2525i	0.143882	+	0.301980i
$78$		0			0
$79$	−149.702			−1.89496			−0.947479	−	0.319818i	$-0.896378\pi$
$79$	−149.702			−1.89496			−0.947479	+	0.319818i	$0.896378\pi$
$80$	−83.5470	−	7.84804i	−1.04434	−	0.0981004i
$81$		0			0
$82$	−91.5517	−	95.9427i	−1.11648	−	1.17003i
$83$	−12.9895			−0.156500			−0.0782498	−	0.996934i	$-0.524933\pi$
$83$	−12.9895			−0.156500			−0.0782498	+	0.996934i	$0.524933\pi$
$84$		0			0
$85$			95.5714i			1.12437i
$86$	−57.9614	−	60.7413i	−0.673969	−	0.706294i
$87$		0			0
$88$	22.2244	−	19.3025i	0.252550	−	0.219347i
$89$		−	130.681i		−	1.46832i	−0.678976	−	0.734160i	$-0.737576\pi$
$89$		−	130.681i		−	1.46832i	0.678976	−	0.734160i	$-0.262424\pi$
$90$		0			0
$91$	79.0604	−	37.6693i	0.868796	−	0.413949i
$92$	−0.362612	+	7.73743i	−0.00394143	+	0.0841025i
$93$		0			0
$94$	73.6048	+	77.1351i	0.783030	+	0.820586i
$95$	25.9219			0.272863
$96$		0			0
$97$			103.630i			1.06835i	0.845373	+	0.534176i	$0.179378\pi$
$97$			103.630i			1.06835i	−0.845373	+	0.534176i	$0.820622\pi$
$98$	7.87741	+	97.6829i	0.0803818	+	0.996764i
$99$		0			0
$100$	0.469368	−	10.0154i	0.00469368	−	0.100154i
$101$	22.8199			0.225939			0.112970	−	0.993598i	$-0.463964\pi$
$101$	22.8199			0.225939			0.112970	+	0.993598i	$0.463964\pi$
$102$		0			0
$103$			158.219i			1.53611i	0.640386	+	0.768053i	$0.278774\pi$
$103$			158.219i			1.53611i	−0.640386	+	0.768053i	$0.721226\pi$
$104$	−65.6301	−	75.5648i	−0.631059	−	0.726584i
$105$		0			0
$106$	−84.6763	−	88.7376i	−0.798833	−	0.837147i
$107$			123.746i			1.15650i	0.815859	+	0.578251i	$0.196265\pi$
$107$			123.746i			1.15650i	−0.815859	+	0.578251i	$0.803735\pi$
$108$		0			0
$109$		−	39.5511i		−	0.362854i	−0.983404	−	0.181427i	$-0.941928\pi$
$109$		−	39.5511i		−	0.362854i	0.983404	−	0.181427i	$-0.0580716\pi$
$110$	26.6452	+	27.9232i	0.242229	+	0.253847i
$111$		0			0
$112$	105.172	−	38.5077i	0.939036	−	0.343818i
$113$	53.1831			0.470647			0.235324	−	0.971917i	$-0.424385\pi$
$113$	53.1831			0.470647			0.235324	+	0.971917i	$0.424385\pi$
$114$		0			0
$115$	−10.1562			−0.0883148
$116$	163.998	+	7.68572i	1.41378	+	0.0662562i
$117$		0			0
$118$	102.652	−	97.9541i	0.869934	−	0.830120i
$119$	−54.8670	−	115.155i	−0.461067	−	0.967688i
$120$		0			0
$121$	107.461			0.888106
$122$	118.650	−	113.220i	0.972539	−	0.928029i
$123$		0			0
$124$	−91.0776	−	4.26832i	−0.734497	−	0.0344219i
$125$	−117.971			−0.943764
$126$		0			0
$127$	−44.1953			−0.347994			−0.173997	−	0.984746i	$-0.555668\pi$
$127$	−44.1953			−0.347994			−0.173997	+	0.984746i	$0.555668\pi$
$128$	−74.5278	−	104.065i	−0.582249	−	0.813011i
$129$		0			0
$130$	94.9411	−	90.5959i	0.730316	−	0.696892i
$131$	192.217			1.46731			0.733654	−	0.679523i	$-0.237813\pi$
$131$	192.217			1.46731			0.733654	+	0.679523i	$0.237813\pi$
$132$		0			0
$133$	−31.2336	+	14.8816i	−0.234839	+	0.111892i
$134$	−2.26037	−	2.36879i	−0.0168685	−	0.0176775i
$135$		0			0
$136$	−110.063	+	95.5931i	−0.809289	+	0.702890i
$137$	265.473			1.93776			0.968879	−	0.247535i	$-0.0796206\pi$
$137$	265.473			1.93776			0.968879	+	0.247535i	$0.0796206\pi$
$138$		0			0
$139$	−15.5158			−0.111624			−0.0558122	−	0.998441i	$-0.517775\pi$
$139$	−15.5158			−0.111624			−0.0558122	+	0.998441i	$0.517775\pi$
$140$	56.8901	+	135.383i	0.406358	+	0.967025i
$141$		0			0
$142$	14.6049	−	13.9365i	0.102852	−	0.0981444i
$143$			46.0345i			0.321919i
$144$		0			0
$145$			215.265i			1.48459i
$146$	88.9645	+	93.2315i	0.609346	+	0.638572i
$147$		0			0
$148$	186.889	+	8.75850i	1.26276	+	0.0591790i
$149$			156.124i			1.04782i	0.851775	+	0.523908i	$0.175526\pi$
$149$			156.124i			1.04782i	−0.851775	+	0.523908i	$0.824474\pi$
$150$		0			0
$151$	83.2527			0.551342			0.275671	−	0.961252i	$-0.411100\pi$
$151$	83.2527			0.551342			0.275671	+	0.961252i	$0.411100\pi$
$152$	25.9278	+	29.8526i	0.170578	+	0.196399i
$153$		0			0
$154$	−48.1356	−	18.3480i	−0.312569	−	0.119143i
$155$		−	119.549i		−	0.771285i
$156$		0			0
$157$	−165.066			−1.05138			−0.525689	−	0.850677i	$-0.676192\pi$
$157$	−165.066			−1.05138			−0.525689	+	0.850677i	$0.676192\pi$
$158$	216.609	−	206.695i	1.37094	−	1.30820i
$159$		0			0
$160$	131.723	−	103.999i	0.823269	−	0.649993i
$161$	12.2373	−	5.83062i	0.0760081	−	0.0362150i
$162$		0			0
$163$		−	207.397i		−	1.27238i	−0.771534	−	0.636188i	$-0.780510\pi$
$163$		−	207.397i		−	1.27238i	0.771534	−	0.636188i	$-0.219490\pi$
$164$	264.939	+	12.4163i	1.61548	+	0.0757090i
$165$		0			0
$166$	18.7949	−	17.9348i	0.113223	−	0.108041i
$167$			170.091i			1.01851i	0.860617	+	0.509253i	$0.170078\pi$
$167$			170.091i			1.01851i	−0.860617	+	0.509253i	$0.829922\pi$
$168$		0			0
$169$	−12.4791			−0.0738406
$170$	−131.957	−	138.286i	−0.776217	−	0.813446i
$171$		0			0
$172$	167.733	+	7.86074i	0.975191	+	0.0457020i
$173$	−244.457			−1.41304			−0.706522	−	0.707691i	$-0.749737\pi$
$173$	−244.457			−1.41304			−0.706522	+	0.707691i	$0.749737\pi$
$174$		0			0
$175$	−15.8401	+	7.54720i	−0.0905147	+	0.0431269i
$176$	−5.50604	+	58.6150i	−0.0312843	+	0.333040i
$177$		0			0
$178$	180.433	+	189.086i	1.01367	+	1.06228i
$179$			51.4534i			0.287449i	0.989618	+	0.143725i	$0.0459079\pi$
$179$			51.4534i			0.287449i	−0.989618	+	0.143725i	$0.954092\pi$
$180$		0			0
$181$	281.237			1.55380			0.776898	−	0.629626i	$-0.216792\pi$
$181$	281.237			1.55380			0.776898	+	0.629626i	$0.216792\pi$
$182$	−62.3848	+	163.665i	−0.342774	+	0.899258i
$183$		0			0
$184$	−10.1585	−	11.6962i	−0.0552093	−	0.0635665i
$185$			245.312i			1.32601i
$186$		0			0
$187$	67.0512			0.358562
$188$	−213.003	−	9.98231i	−1.13299	−	0.0530974i
$189$		0			0
$190$	−37.5074	+	35.7908i	−0.197407	+	0.188373i
$191$	−126.618			−0.662921			−0.331460	−	0.943469i	$-0.607541\pi$
$191$	−126.618			−0.662921			−0.331460	+	0.943469i	$0.607541\pi$
$192$		0			0
$193$	328.592			1.70255			0.851275	−	0.524719i	$-0.175830\pi$
$193$	328.592			1.70255			0.851275	+	0.524719i	$0.175830\pi$
$194$	−143.084	−	149.946i	−0.737545	−	0.772919i
$195$		0			0
$196$	−146.270	−	130.465i	−0.746277	−	0.665635i
$197$			26.1931i			0.132960i	0.997788	+	0.0664799i	$0.0211768\pi$
$197$			26.1931i			0.132960i	−0.997788	+	0.0664799i	$0.978823\pi$
$198$		0			0
$199$		−	341.606i		−	1.71661i	−0.513137	−	0.858307i	$-0.671517\pi$
$199$		−	341.606i		−	1.71661i	0.513137	−	0.858307i	$-0.328483\pi$
$200$	13.1493	+	15.1397i	0.0657463	+	0.0756985i
$201$		0			0
$202$	−33.0189	+	31.5077i	−0.163460	+	0.155979i
$203$	−123.583	−	259.375i	−0.608782	−	1.27771i
$204$		0			0
$205$			347.761i			1.69639i
$206$	−218.455	−	228.933i	−1.06046	−	1.11132i
$207$		0			0
$208$	199.296	+	18.7210i	0.958154	+	0.0900047i
$209$		−	18.1864i		−	0.0870161i
$210$		0			0
$211$		−	89.5480i		−	0.424398i	−0.977226	−	0.212199i	$-0.931938\pi$
$211$		−	89.5480i		−	0.424398i	0.977226	−	0.212199i	$-0.0680625\pi$
$212$	245.043	+	11.4838i	1.15586	+	0.0541690i
$213$		0			0
$214$	−170.858	−	179.052i	−0.798400	−	0.836693i
$215$			220.167i			1.02403i
$216$		0			0
$217$	68.6325	+	144.046i	0.316279	+	0.663806i
$218$	54.6087	+	57.2279i	0.250499	+	0.262513i
$219$		0			0
$220$	−77.1079	−	3.61363i	−0.350490	−	0.0164256i
$221$		−	227.980i		−	1.03158i
$222$		0			0
$223$		−	391.913i		−	1.75746i	−0.477323	−	0.878728i	$-0.658393\pi$
$223$		−	391.913i		−	1.75746i	0.477323	−	0.878728i	$-0.341607\pi$
$224$	−99.0092	+	200.931i	−0.442005	+	0.897012i
$225$		0			0
$226$	−76.9526	+	73.4307i	−0.340498	+	0.324915i
$227$	306.142			1.34864			0.674322	−	0.738437i	$-0.264436\pi$
$227$	306.142			1.34864			0.674322	+	0.738437i	$0.264436\pi$
$228$		0			0
$229$	53.4932			0.233595			0.116797	−	0.993156i	$-0.462737\pi$
$229$	53.4932			0.233595			0.116797	+	0.993156i	$0.462737\pi$
$230$	14.6954	−	14.0228i	0.0638930	−	0.0609688i
$231$		0			0
$232$	−247.907	+	215.314i	−1.06856	+	0.928078i
$233$	28.7104			0.123221			0.0616103	−	0.998100i	$-0.480376\pi$
$233$	28.7104			0.123221			0.0616103	+	0.998100i	$0.480376\pi$
$234$		0			0
$235$		−	279.589i		−	1.18974i
$236$	−13.2846	+	283.467i	−0.0562906	+	1.20113i
$237$		0			0
$238$	238.385	+	90.8662i	1.00162	+	0.381791i
$239$	−214.671			−0.898207			−0.449103	−	0.893480i	$-0.648256\pi$
$239$	−214.671			−0.898207			−0.449103	+	0.893480i	$0.648256\pi$
$240$		0			0
$241$		−	355.937i		−	1.47692i	−0.674298	−	0.738459i	$-0.735554\pi$
$241$		−	355.937i		−	1.47692i	0.674298	−	0.738459i	$-0.264446\pi$
$242$	−155.489	+	148.373i	−0.642516	+	0.613110i
$243$		0			0
$244$	−15.3549	+	327.643i	−0.0629298	+	1.34280i
$245$	161.895	−	199.583i	0.660797	−	0.814623i
$246$		0			0
$247$	−61.8351			−0.250345
$248$	137.677	−	119.576i	0.555149	−	0.482162i
$249$		0			0
$250$	170.696	−	162.884i	0.682784	−	0.651535i
$251$	86.5294			0.344739			0.172369	−	0.985032i	$-0.444858\pi$
$251$	86.5294			0.344739			0.172369	+	0.985032i	$0.444858\pi$
$252$		0			0
$253$			7.12541i			0.0281637i
$254$	63.9478	−	61.0211i	0.251763	−	0.240240i
$255$		0			0
$256$	251.522	+	47.6744i	0.982507	+	0.186228i
$257$		−	289.039i		−	1.12466i	−0.826911	−	0.562332i	$-0.809904\pi$
$257$		−	289.039i		−	1.12466i	0.826911	−	0.562332i	$-0.190096\pi$
$258$		0			0
$259$	−140.832	−	295.579i	−0.543754	−	1.14123i
$260$	−12.2867	+	262.173i	−0.0472564	+	1.00836i
$261$		0			0
$262$	−278.126	+	265.397i	−1.06155	+	1.01297i
$263$	273.840			1.04122			0.520609	−	0.853795i	$-0.325705\pi$
$263$	273.840			1.04122			0.520609	+	0.853795i	$0.325705\pi$
$264$		0			0
$265$			321.645i			1.21375i
$266$	24.6457	−	64.6575i	0.0926532	−	0.243073i
$267$		0			0
$268$	6.54124	+	0.306553i	0.0244076	+	0.00114385i
$269$	115.065			0.427752			0.213876	−	0.976861i	$-0.431391\pi$
$269$	115.065			0.427752			0.213876	+	0.976861i	$0.431391\pi$
$270$		0			0
$271$		−	85.2047i		−	0.314409i	−0.987566	−	0.157204i	$-0.949752\pi$
$271$		−	85.2047i		−	0.314409i	0.987566	−	0.157204i	$-0.0502481\pi$
$272$	27.2679	−	290.283i	0.100250	−	1.06722i
$273$		0			0
$274$	−384.122	+	366.542i	−1.40191	+	1.33775i
$275$		−	9.22319i		−	0.0335389i
$276$		0			0
$277$			96.6558i			0.348938i	0.984663	+	0.174469i	$0.0558209\pi$
$277$			96.6558i			0.348938i	−0.984663	+	0.174469i	$0.944179\pi$
$278$	22.4504	−	21.4229i	0.0807568	−	0.0770607i
$279$		0			0
$280$	−269.242	−	117.342i	−0.961580	−	0.419080i
$281$	−49.2889			−0.175405			−0.0877026	−	0.996147i	$-0.527953\pi$
$281$	−49.2889			−0.175405			−0.0877026	+	0.996147i	$0.527953\pi$
$282$		0			0
$283$	435.567			1.53911			0.769553	−	0.638583i	$-0.220479\pi$
$283$	435.567			1.53911			0.769553	+	0.638583i	$0.220479\pi$
$284$	−1.89007	+	40.3305i	−0.00665519	+	0.142009i
$285$		0			0
$286$	−63.5605	−	66.6089i	−0.222239	−	0.232898i
$287$	−199.648	−	419.020i	−0.695636	−	1.46000i
$288$		0			0
$289$	−43.0622			−0.149004
$290$	−297.220	−	311.476i	−1.02490	−	1.07405i
$291$		0			0
$292$	−257.452	−	12.0654i	−0.881685	−	0.0413199i
$293$	92.1414			0.314476			0.157238	−	0.987561i	$-0.449741\pi$
$293$	92.1414			0.314476			0.157238	+	0.987561i	$0.449741\pi$
$294$		0			0
$295$	−372.081			−1.26129
$296$	−282.510	+	245.368i	−0.954425	+	0.828945i
$297$		0			0
$298$	−215.563	−	225.902i	−0.723367	−	0.758061i
$299$	24.2270			0.0810267
$300$		0			0
$301$	−126.397	−	265.282i	−0.419923	−	0.881335i
$302$	−120.461	+	114.948i	−0.398879	+	0.380623i
$303$		0			0
$304$	−78.7338	−	7.39591i	−0.258993	−	0.0243287i
$305$	−430.067			−1.41005
$306$		0			0
$307$	−554.865			−1.80738			−0.903689	−	0.428189i	$-0.859152\pi$
$307$	−554.865			−1.80738			−0.903689	+	0.428189i	$0.859152\pi$
$308$	94.9826	−	39.9131i	0.308385	−	0.129588i
$309$		0			0
$310$	165.063	+	172.980i	0.532462	+	0.558000i
$311$		−	12.8088i		−	0.0411860i	−0.999788	−	0.0205930i	$-0.993445\pi$
$311$		−	12.8088i		−	0.0411860i	0.999788	−	0.0205930i	$-0.00655542\pi$
$312$		0			0
$313$		−	9.52099i		−	0.0304185i	−0.999884	−	0.0152093i	$-0.995159\pi$
$313$		−	9.52099i		−	0.0304185i	0.999884	−	0.0152093i	$-0.00484144\pi$
$314$	238.840	−	227.909i	0.760638	−	0.725826i
$315$		0			0
$316$	−28.0321	+	598.150i	−0.0887092	+	1.89288i
$317$			322.997i			1.01892i	0.860495	+	0.509459i	$0.170154\pi$
$317$			322.997i			1.01892i	−0.860495	+	0.509459i	$0.829846\pi$
$318$		0			0
$319$	151.026			0.473437
$320$	−47.0022	+	332.352i	−0.146882	+	1.03860i
$321$		0			0
$322$	−9.65619	+	25.3328i	−0.0299882	+	0.0786732i
$323$			90.0656i			0.278841i
$324$		0			0
$325$	−31.3596			−0.0964911
$326$	286.357	+	300.091i	0.878395	+	0.920525i
$327$		0			0
$328$	−400.493	+	347.840i	−1.22102	+	1.06049i
$329$	160.511	+	336.880i	0.487874	+	1.02395i
$330$		0			0
$331$			605.748i			1.83005i	0.403392	+	0.915027i	$0.367831\pi$
$331$			605.748i			1.83005i	−0.403392	+	0.915027i	$0.632169\pi$
$332$	−2.43232	+	51.9009i	−0.00732626	+	0.156328i
$333$		0			0
$334$	−234.847	−	246.110i	−0.703133	−	0.736857i
$335$			8.58608i			0.0256301i
$336$		0			0
$337$	−378.648			−1.12359			−0.561793	−	0.827278i	$-0.689888\pi$
$337$	−378.648			−1.12359			−0.561793	+	0.827278i	$0.689888\pi$
$338$	18.0564	−	17.2300i	0.0534213	−	0.0509764i
$339$		0			0
$340$	381.867	+	17.8960i	1.12314	+	0.0526354i
$341$	−83.8735			−0.245963
$342$		0			0
$343$	−80.4899	+	333.422i	−0.234665	+	0.972076i
$344$	−253.552	+	220.217i	−0.737071	+	0.640166i
$345$		0			0
$346$	353.713	−	337.525i	1.02229	−	0.975506i
$347$		−	297.236i		−	0.856586i	−0.903640	−	0.428293i	$-0.859115\pi$
$347$		−	297.236i		−	0.856586i	0.903640	−	0.428293i	$-0.140885\pi$
$348$		0			0
$349$	107.718			0.308649			0.154324	−	0.988020i	$-0.450680\pi$
$349$	107.718			0.308649			0.154324	+	0.988020i	$0.450680\pi$
$350$	12.4991	−	32.7910i	0.0357116	−	0.0936884i
$351$		0			0
$352$	−72.9638	−	92.4145i	−0.207283	−	0.262541i
$353$			158.792i			0.449836i	0.974378	+	0.224918i	$0.0722115\pi$
$353$			158.792i			0.449836i	−0.974378	+	0.224918i	$0.927789\pi$
$354$		0			0
$355$	−52.9381			−0.149121
$356$	−522.149	−	24.4703i	−1.46671	−	0.0687369i
$357$		0			0
$358$	−71.0425	−	74.4498i	−0.198443	−	0.207960i
$359$	−202.772			−0.564825			−0.282412	−	0.959293i	$-0.591135\pi$
$359$	−202.772			−0.564825			−0.282412	+	0.959293i	$0.591135\pi$
$360$		0			0
$361$	−336.571			−0.932331
$362$	−406.932	+	388.308i	−1.12412	+	1.07267i
$363$		0			0
$364$	−135.708	−	322.949i	−0.372824	−	0.887221i
$365$		−	337.934i		−	0.925845i
$366$		0			0
$367$			669.013i			1.82292i	0.411383	+	0.911462i	$0.365046\pi$
$367$			669.013i			1.82292i	−0.411383	+	0.911462i	$0.634954\pi$
$368$	30.8479	+	2.89771i	0.0838258	+	0.00787422i
$369$		0			0
$370$	−338.706	−	354.951i	−0.915422	−	0.959327i
$371$	−184.654	−	387.553i	−0.497721	−	1.04462i
$372$		0			0
$373$			148.124i			0.397116i	0.980089	+	0.198558i	$0.0636258\pi$
$373$			148.124i			0.397116i	−0.980089	+	0.198558i	$0.936374\pi$
$374$	−97.0188	+	92.5786i	−0.259409	+	0.247536i
$375$		0			0
$376$	321.985	−	279.653i	0.856342	−	0.743757i
$377$		−	513.502i		−	1.36207i
$378$		0			0
$379$		−	3.50008i		−	0.00923505i	−0.999989	−	0.00461753i	$-0.998530\pi$
$379$		−	3.50008i		−	0.00923505i	0.999989	−	0.00461753i	$-0.00146981\pi$
$380$	4.85396	−	103.574i	0.0127736	−	0.272563i
$381$		0			0
$382$	183.208	−	174.823i	0.479602	−	0.457652i
$383$		−	113.064i		−	0.295206i	−0.989047	−	0.147603i	$-0.952844\pi$
$383$		−	113.064i		−	0.295206i	0.989047	−	0.147603i	$-0.0471558\pi$
$384$		0			0
$385$	58.1054	+	121.952i	0.150923	+	0.316758i
$386$	−475.452	+	453.692i	−1.23174	+	1.17537i
$387$		0			0
$388$	414.066	+	19.4051i	1.06718	+	0.0500130i
$389$		−	74.8109i		−	0.192316i	−0.995366	−	0.0961580i	$-0.969345\pi$
$389$		−	74.8109i		−	0.192316i	0.995366	−	0.0961580i	$-0.0306554\pi$
$390$		0			0
$391$		−	35.2877i		−	0.0902497i
$392$	391.778	−	13.1837i	0.999434	−	0.0336318i
$393$		0			0
$394$	−36.1652	−	37.8997i	−0.0917898	−	0.0961922i
$395$	−785.136			−1.98769
$396$		0			0
$397$	119.449			0.300880			0.150440	−	0.988619i	$-0.451931\pi$
$397$	119.449			0.300880			0.150440	+	0.988619i	$0.451931\pi$
$398$	471.661	+	494.283i	1.18508	+	1.24192i
$399$		0			0
$400$	−39.9298	−	3.75083i	−0.0998244	−	0.00937707i
$401$	497.793			1.24138			0.620689	−	0.784057i	$-0.286853\pi$
$401$	497.793			1.24138			0.620689	+	0.784057i	$0.286853\pi$
$402$		0			0
$403$			285.177i			0.707635i
$404$	4.27309	−	91.1794i	0.0105770	−	0.225692i
$405$		0			0
$406$	536.940	+	204.667i	1.32251	+	0.504107i
$407$	172.107			0.422866
$408$		0			0
$409$		−	241.893i		−	0.591425i	−0.955277	−	0.295713i	$-0.904443\pi$
$409$		−	241.893i		−	0.591425i	0.955277	−	0.295713i	$-0.0955571\pi$
$410$	−480.159	−	503.188i	−1.17112	−	1.22729i
$411$		0			0
$412$	632.182	+	29.6270i	1.53442	+	0.0719101i
$413$	448.324	−	213.609i	1.08553	−	0.517214i
$414$		0			0
$415$	−68.1255			−0.164158
$416$	−314.217	+	248.083i	−0.755329	+	0.596353i
$417$		0			0
$418$	25.1102	+	26.3145i	0.0600722	+	0.0629534i
$419$	719.154			1.71636			0.858179	−	0.513351i	$-0.171596\pi$
$419$	719.154			1.71636			0.858179	+	0.513351i	$0.171596\pi$
$420$		0			0
$421$		−	20.4985i		−	0.0486901i	−0.999704	−	0.0243450i	$-0.992250\pi$
$421$		−	20.4985i		−	0.0486901i	0.999704	−	0.0243450i	$-0.00775003\pi$
$422$	123.640	+	129.570i	0.292986	+	0.307039i
$423$		0			0
$424$	−370.417	+	321.717i	−0.873625	+	0.758768i
$425$			45.6766i			0.107474i
$426$		0			0
$427$	518.191	−	246.899i	1.21356	−	0.578217i
$428$	494.440	+	23.1718i	1.15523	+	0.0541396i
$429$		0			0
$430$	−303.988	−	318.568i	−0.706950	−	0.740857i
$431$	145.153			0.336782			0.168391	−	0.985720i	$-0.446143\pi$
$431$	145.153			0.336782			0.168391	+	0.985720i	$0.446143\pi$
$432$		0			0
$433$		−	52.0462i		−	0.120199i	−0.998192	−	0.0600996i	$-0.980858\pi$
$433$		−	52.0462i		−	0.120199i	0.998192	−	0.0600996i	$-0.0191418\pi$
$434$	−298.193	−	113.663i	−0.687081	−	0.261897i
$435$		0			0
$436$	−158.031	−	7.40606i	−0.362456	−	0.0169864i
$437$	−9.57111			−0.0219018
$438$		0			0
$439$		−	265.081i		−	0.603829i	−0.953335	−	0.301914i	$-0.902374\pi$
$439$		−	265.081i		−	0.603829i	0.953335	−	0.301914i	$-0.0976257\pi$
$440$	116.560	−	101.235i	0.264908	−	0.230080i
$441$		0			0
$442$	314.775	+	329.872i	0.712160	+	0.746317i
$443$			330.902i			0.746957i	0.927639	+	0.373478i	$0.121835\pi$
$443$			330.902i			0.746957i	−0.927639	+	0.373478i	$0.878165\pi$
$444$		0			0
$445$		−	685.377i		−	1.54017i
$446$	541.120	+	567.073i	1.21327	+	1.27146i
$447$		0			0
$448$	−134.168	−	427.438i	−0.299482	−	0.954102i
$449$	−625.698			−1.39354			−0.696768	−	0.717296i	$-0.745379\pi$
$449$	−625.698			−1.39354			−0.696768	+	0.717296i	$0.745379\pi$
$450$		0			0
$451$	243.983			0.540982
$452$	9.95870	−	212.499i	0.0220325	−	0.470131i
$453$		0			0
$454$	−442.969	+	422.695i	−0.975702	+	0.931047i
$455$	414.646	−	197.563i	0.911310	−	0.434205i
$456$		0			0
$457$	397.689			0.870217			0.435108	−	0.900378i	$-0.356710\pi$
$457$	397.689			0.870217			0.435108	+	0.900378i	$0.356710\pi$
$458$	−77.4012	+	73.8588i	−0.168998	+	0.161264i
$459$		0			0
$460$	−1.90178	+	40.5803i	−0.00413431	+	0.0882180i
$461$	−71.4288			−0.154943			−0.0774715	−	0.996995i	$-0.524685\pi$
$461$	−71.4288			−0.154943			−0.0774715	+	0.996995i	$0.524685\pi$
$462$		0			0
$463$	−88.0481			−0.190169			−0.0950844	−	0.995469i	$-0.530312\pi$
$463$	−88.0481			−0.190169			−0.0950844	+	0.995469i	$0.530312\pi$
$464$	61.4184	−	653.835i	0.132367	−	1.40913i
$465$		0			0
$466$	−41.5422	+	39.6409i	−0.0891462	+	0.0850663i
$467$	118.536			0.253824			0.126912	−	0.991914i	$-0.459493\pi$
$467$	118.536			0.253824			0.126912	+	0.991914i	$0.459493\pi$
$468$		0			0
$469$	−4.92922	−	10.3454i	−0.0105101	−	0.0220585i
$470$	386.033	+	404.548i	0.821347	+	0.860741i
$471$		0			0
$472$	−372.165	−	428.501i	−0.788485	−	0.907841i
$473$	154.465			0.326565
$474$		0			0
$475$	12.3889			0.0260819
$476$	−470.389	+	197.664i	−0.988212	+	0.415261i
$477$		0			0
$478$	310.616	−	296.400i	0.649824	−	0.620084i
$479$			138.101i			0.288311i	0.989555	+	0.144156i	$0.0460466\pi$
$479$			138.101i			0.288311i	−0.989555	+	0.144156i	$0.953953\pi$
$480$		0			0
$481$		−	585.176i		−	1.21658i
$482$	491.448	+	515.019i	1.01960	+	1.06850i
$483$		0			0
$484$	20.1224	−	429.372i	0.0415751	−	0.887132i
$485$			543.506i			1.12063i
$486$		0			0
$487$	311.781			0.640206			0.320103	−	0.947383i	$-0.396282\pi$
$487$	311.781			0.640206			0.320103	+	0.947383i	$0.396282\pi$
$488$	−430.164	−	495.280i	−0.881484	−	1.01492i
$489$		0			0
$490$	41.3145	+	512.315i	0.0843152	+	1.04554i
$491$		−	602.082i		−	1.22624i	−0.789991	−	0.613118i	$-0.789915\pi$
$491$		−	602.082i		−	1.22624i	0.789991	−	0.613118i	$-0.210085\pi$
$492$		0			0
$493$	−747.938			−1.51712
$494$	89.4715	−	85.3767i	0.181116	−	0.172827i
$495$		0			0
$496$	−34.1091	+	363.112i	−0.0687684	+	0.732080i
$497$	63.7856	−	30.3914i	0.128341	−	0.0611498i
$498$		0			0
$499$		−	209.915i		−	0.420671i	−0.977629	−	0.210335i	$-0.932544\pi$
$499$		−	209.915i		−	0.420671i	0.977629	−	0.210335i	$-0.0674556\pi$
$500$	−22.0903	+	471.365i	−0.0441807	+	0.942730i
$501$		0			0
$502$	−125.203	+	119.472i	−0.249408	+	0.237993i
$503$		−	8.12961i		−	0.0161622i	−0.999967	−	0.00808112i	$-0.997428\pi$
$503$		−	8.12961i		−	0.0161622i	0.999967	−	0.00808112i	$-0.00257233\pi$
$504$		0			0
$505$	119.683			0.236995
$506$	−9.83816	−	10.3100i	−0.0194430	−	0.0203755i
$507$		0			0
$508$	−8.27570	+	176.587i	−0.0162908	+	0.347613i
$509$	−116.510			−0.228899			−0.114449	−	0.993429i	$-0.536510\pi$
$509$	−116.510			−0.228899			−0.114449	+	0.993429i	$0.536510\pi$
$510$		0			0
$511$	194.006	+	407.179i	0.379659	+	0.796828i
$512$	−429.761	+	278.298i	−0.839376	+	0.543551i
$513$		0			0
$514$	399.080	+	418.221i	0.776421	+	0.813660i
$515$			829.807i			1.61128i
$516$		0			0
$517$	−196.155			−0.379410
$518$	611.886	+	233.235i	1.18125	+	0.450260i
$519$		0			0
$520$	−344.208	−	396.312i	−0.661939	−	0.762139i
$521$			459.362i			0.881693i	0.897583	+	0.440846i	$0.145322\pi$
$521$			459.362i			0.881693i	−0.897583	+	0.440846i	$0.854678\pi$
$522$		0			0
$523$	392.738			0.750933			0.375467	−	0.926836i	$-0.377482\pi$
$523$	392.738			0.750933			0.375467	+	0.926836i	$0.377482\pi$
$524$	35.9933	−	768.026i	0.0686895	−	1.46570i
$525$		0			0
$526$	−396.230	+	378.096i	−0.753289	+	0.718813i
$527$	415.373			0.788183
$528$		0			0
$529$	−525.250			−0.992911
$530$	−444.099	−	465.399i	−0.837924	−	0.878112i
$531$		0			0
$532$	53.6127	+	127.584i	0.100776	+	0.239820i
$533$		−	829.561i		−	1.55640i
$534$		0			0
$535$			649.006i			1.21309i
$536$	−9.88802	+	8.58802i	−0.0184478	+	0.0160224i
$537$		0			0
$538$	−166.492	+	158.872i	−0.309465	+	0.295302i
$539$	−140.024	−	113.583i	−0.259784	−	0.210729i
$540$		0			0
$541$		−	224.719i		−	0.415378i	−0.978195	−	0.207689i	$-0.933406\pi$
$541$		−	224.719i		−	0.415378i	0.978195	−	0.207689i	$-0.0665942\pi$
$542$	117.643	+	123.286i	0.217054	+	0.227465i
$543$		0			0
$544$	361.343	+	457.671i	0.664234	+	0.841307i
$545$		−	207.432i		−	0.380610i
$546$		0			0
$547$			650.761i			1.18969i	0.803840	+	0.594845i	$0.202787\pi$
$547$			650.761i			1.18969i	−0.803840	+	0.594845i	$0.797213\pi$
$548$	49.7106	−	1060.73i	0.0907128	−	1.93563i
$549$		0			0
$550$	12.7346	+	13.3454i	0.0231538	+	0.0242643i
$551$			202.864i			0.368174i
$552$		0			0
$553$	946.018	−	450.742i	1.71070	−	0.815086i
$554$	−133.454	−	139.855i	−0.240892	−	0.252446i
$555$		0			0
$556$	−2.90538	+	61.9951i	−0.00522550	+	0.111502i
$557$			269.480i			0.483806i	0.970300	+	0.241903i	$0.0777715\pi$
$557$			269.480i			0.483806i	−0.970300	+	0.241903i	$0.922228\pi$
$558$		0			0
$559$		−	525.195i		−	0.939526i
$560$	551.593	−	201.960i	0.984988	−	0.360643i
$561$		0			0
$562$	71.3179	−	68.0539i	0.126900	−	0.121092i
$563$	114.814			0.203932			0.101966	−	0.994788i	$-0.467487\pi$
$563$	114.814			0.203932			0.101966	+	0.994788i	$0.467487\pi$
$564$		0			0
$565$	278.928			0.493678
$566$	−630.238	+	601.394i	−1.11349	+	1.06253i
$567$		0			0
$568$	−52.9501	−	60.9653i	−0.0932220	−	0.107333i
$569$	−226.624			−0.398285			−0.199143	−	0.979971i	$-0.563816\pi$
$569$	−226.624			−0.398285			−0.199143	+	0.979971i	$0.563816\pi$
$570$		0			0
$571$			905.094i			1.58510i	0.609805	+	0.792551i	$0.291248\pi$
$571$			905.094i			1.58510i	−0.609805	+	0.792551i	$0.708752\pi$
$572$	183.936	+	8.62009i	0.321566	+	0.0150701i
$573$		0			0
$574$	867.425	+	330.640i	1.51119	+	0.576028i
$575$	−4.85397			−0.00844169
$576$		0			0
$577$			288.394i			0.499816i	0.968270	+	0.249908i	$0.0804004\pi$
$577$			288.394i			0.499816i	−0.968270	+	0.249908i	$0.919600\pi$
$578$	62.3082	−	59.4566i	0.107800	−	0.102866i
$579$		0			0
$580$	860.118	+	40.3091i	1.48296	+	0.0694985i
$581$	82.0851	−	39.1105i	0.141282	−	0.0673158i
$582$		0			0
$583$	225.660			0.387067
$584$	389.176	−	338.010i	0.666397	−	0.578784i
$585$		0			0
$586$	−133.323	+	127.221i	−0.227513	+	0.217101i
$587$	−478.167			−0.814594			−0.407297	−	0.913296i	$-0.633529\pi$
$587$	−478.167			−0.814594			−0.407297	+	0.913296i	$0.633529\pi$
$588$		0			0
$589$		−	112.662i		−	0.191277i
$590$	538.377	−	513.737i	0.912504	−	0.870742i
$591$		0			0
$592$	69.9911	−	745.097i	0.118228	−	1.25861i
$593$			350.708i			0.591414i	0.955279	+	0.295707i	$0.0955552\pi$
$593$			350.708i			0.591414i	−0.955279	+	0.295707i	$0.904445\pi$
$594$		0			0
$595$	−287.760	−	603.950i	−0.483629	−	1.01504i
$596$	623.813	+	29.2348i	1.04667	+	0.0490517i
$597$		0			0
$598$	−35.0549	+	33.4506i	−0.0586203	+	0.0559374i
$599$	−781.919			−1.30537			−0.652687	−	0.757627i	$-0.726358\pi$
$599$	−781.919			−1.30537			−0.652687	+	0.757627i	$0.726358\pi$
$600$		0			0
$601$		−	125.321i		−	0.208521i	−0.994550	−	0.104260i	$-0.966752\pi$
$601$		−	125.321i		−	0.208521i	0.994550	−	0.104260i	$-0.0332475\pi$
$602$	549.167	+	209.328i	0.912237	+	0.347721i
$603$		0			0
$604$	15.5893	−	332.646i	0.0258101	−	0.550738i
$605$	563.597			0.931565
$606$		0			0
$607$		−	25.4854i		−	0.0419859i	−0.999780	−	0.0209929i	$-0.993317\pi$
$607$		−	25.4854i		−	0.0419859i	0.999780	−	0.0209929i	$-0.00668275\pi$
$608$	124.135	−	98.0076i	0.204169	−	0.161197i
$609$		0			0
$610$	622.279	−	593.799i	1.02013	−	0.973442i
$611$			666.943i			1.09156i
$612$		0			0
$613$		−	1044.03i		−	1.70315i	−0.524230	−	0.851577i	$-0.675647\pi$
$613$		−	1044.03i		−	1.70315i	0.524230	−	0.851577i	$-0.324353\pi$
$614$	802.855	−	766.111i	1.30758	−	1.24774i
$615$		0			0
$616$	−82.3252	+	188.896i	−0.133645	+	0.306649i
$617$	540.524			0.876052			0.438026	−	0.898962i	$-0.355678\pi$
$617$	540.524			0.876052			0.438026	+	0.898962i	$0.355678\pi$
$618$		0			0
$619$	−295.065			−0.476680			−0.238340	−	0.971182i	$-0.576603\pi$
$619$	−295.065			−0.476680			−0.238340	+	0.971182i	$0.576603\pi$
$620$	−477.672	−	22.3860i	−0.770439	−	0.0361064i
$621$		0			0
$622$	17.6854	+	18.5336i	0.0284331	+	0.0297968i
$623$	393.471	+	825.817i	0.631574	+	1.32555i
$624$		0			0
$625$	−681.382			−1.09021
$626$	13.1458	+	13.7763i	0.0209996	+	0.0220068i
$627$		0			0
$628$	−30.9092	+	659.541i	−0.0492184	+	1.05022i
$629$	−852.335			−1.35506
$630$		0			0
$631$	787.813			1.24852			0.624258	−	0.781219i	$-0.285402\pi$
$631$	787.813			1.24852			0.624258	+	0.781219i	$0.285402\pi$
$632$	−785.314	−	904.190i	−1.24259	−	1.43068i
$633$		0			0
$634$	−445.967	−	467.356i	−0.703418	−	0.737155i
$635$	−231.790			−0.365023
$636$		0			0
$637$	−386.191	+	476.092i	−0.606265	+	0.747397i
$638$	−218.526	+	208.524i	−0.342517	+	0.326841i
$639$		0			0
$640$	−390.874	−	545.789i	−0.610741	−	0.852795i
$641$	−1170.55			−1.82613			−0.913066	−	0.407811i	$-0.866292\pi$
$641$	−1170.55			−1.82613			−0.913066	+	0.407811i	$0.866292\pi$
$642$		0			0
$643$	−570.395			−0.887085			−0.443542	−	0.896253i	$-0.646278\pi$
$643$	−570.395			−0.887085			−0.443542	+	0.896253i	$0.646278\pi$
$644$	−21.0054	−	49.9874i	−0.0326171	−	0.0776201i
$645$		0			0
$646$	−124.355	−	130.319i	−0.192500	−	0.201733i
$647$		−	869.330i		−	1.34363i	−0.740718	−	0.671816i	$-0.765515\pi$
$647$		−	869.330i		−	1.34363i	0.740718	−	0.671816i	$-0.234485\pi$
$648$		0			0
$649$			261.045i			0.402227i
$650$	45.3754	−	43.2987i	0.0698083	−	0.0666134i
$651$		0			0
$652$	−828.680	−	38.8358i	−1.27098	−	0.0595641i
$653$			1004.79i			1.53872i	0.638813	+	0.769362i	$0.279426\pi$
$653$			1004.79i			1.53872i	−0.638813	+	0.769362i	$0.720574\pi$
$654$		0			0
$655$	1008.12			1.53911
$656$	99.2213	−	1056.27i	0.151252	−	1.61017i
$657$		0			0
$658$	−697.384	−	265.824i	−1.05985	−	0.403989i
$659$			323.660i			0.491139i	0.969379	+	0.245569i	$0.0789749\pi$
$659$			323.660i			0.491139i	−0.969379	+	0.245569i	$0.921025\pi$
$660$		0			0
$661$	803.454			1.21551			0.607756	−	0.794124i	$-0.292070\pi$
$661$	803.454			1.21551			0.607756	+	0.794124i	$0.292070\pi$
$662$	−836.365	−	876.479i	−1.26339	−	1.32399i
$663$		0			0
$664$	−68.1410	−	78.4557i	−0.102622	−	0.118156i
$665$	−163.810	+	78.0493i	−0.246331	+	0.117367i
$666$		0			0
$667$		−	79.4820i		−	0.119163i
$668$	679.616	+	31.8500i	1.01739	+	0.0476796i
$669$		0			0
$670$	−11.8549	−	12.4235i	−0.0176939	−	0.0185426i
$671$			301.727i			0.449668i
$672$		0			0
$673$	−336.584			−0.500125			−0.250063	−	0.968230i	$-0.580451\pi$
$673$	−336.584			−0.500125			−0.250063	+	0.968230i	$0.580451\pi$
$674$	547.880	−	522.805i	0.812879	−	0.775676i
$675$		0			0
$676$	−2.33674	+	49.8615i	−0.00345672	+	0.0737596i
$677$	516.746			0.763289			0.381644	−	0.924309i	$-0.375358\pi$
$677$	516.746			0.763289			0.381644	+	0.924309i	$0.375358\pi$
$678$		0			0
$679$	−312.024	−	654.876i	−0.459534	−	0.964471i
$680$	−577.246	+	501.354i	−0.848892	+	0.737286i
$681$		0			0
$682$	121.360	−	115.805i	0.177947	−	0.169803i
$683$			587.298i			0.859879i	0.902858	+	0.429940i	$0.141465\pi$
$683$			587.298i			0.859879i	−0.902858	+	0.429940i	$0.858535\pi$
$684$		0			0
$685$	1392.32			2.03258
$686$	−343.897	−	593.575i	−0.501308	−	0.865269i
$687$		0			0
$688$	62.8170	−	668.724i	0.0913038	−	0.971982i
$689$		−	767.263i		−	1.11359i
$690$		0			0
$691$	−1102.12			−1.59497			−0.797483	−	0.603342i	$-0.793835\pi$
$691$	−1102.12			−1.59497			−0.797483	+	0.603342i	$0.793835\pi$
$692$	−45.7753	+	976.755i	−0.0661492	+	1.41150i
$693$		0			0
$694$	410.397	+	430.081i	0.591351	+	0.619713i
$695$	−81.3753			−0.117087
$696$		0			0
$697$	−1208.29			−1.73356
$698$	−155.862	+	148.728i	−0.223298	+	0.213078i
$699$		0			0
$700$	27.1896	+	64.7041i	0.0388423	+	0.0924344i
$701$		−	12.2107i		−	0.0174189i	−0.999962	−	0.00870946i	$-0.997228\pi$
$701$		−	12.2107i		−	0.0174189i	0.999962	−	0.00870946i	$-0.00277234\pi$
$702$		0			0
$703$			231.180i			0.328847i
$704$	233.172	+	32.9759i	0.331210	+	0.0468407i
$705$		0			0
$706$	−219.247	−	229.762i	−0.310548	−	0.325442i
$707$	−144.207	+	68.7092i	−0.203970	+	0.0971841i
$708$		0			0
$709$			1129.01i			1.59239i	0.605037	+	0.796197i	$0.293158\pi$
$709$			1129.01i			1.59239i	−0.605037	+	0.796197i	$0.706842\pi$
$710$	76.5981	−	73.0924i	0.107885	−	0.102947i
$711$		0			0
$712$	789.303	−	685.532i	1.10857	−	0.962826i
$713$			44.1409i			0.0619087i
$714$		0			0
$715$			241.436i			0.337672i
$716$	205.588	+	9.63481i	0.287134	+	0.0134564i
$717$		0			0
$718$	293.398	−	279.970i	0.408633	−	0.389931i
$719$			878.237i			1.22147i	0.791835	+	0.610735i	$0.209126\pi$
$719$			878.237i			1.22147i	−0.791835	+	0.610735i	$0.790874\pi$
$720$		0			0
$721$	−476.387	−	999.842i	−0.660731	−	1.38674i
$722$	486.998	−	464.709i	0.674512	−	0.643641i
$723$		0			0
$724$	52.6625	−	1123.72i	0.0727383	−	1.55209i
$725$			102.882i			0.141907i
$726$		0			0
$727$			226.673i			0.311793i	0.987773	+	0.155896i	$0.0498266\pi$
$727$			226.673i			0.311793i	−0.987773	+	0.155896i	$0.950173\pi$
$728$	642.261	+	279.913i	0.882226	+	0.384495i
$729$		0			0
$730$	466.590	+	488.968i	0.639164	+	0.669820i
$731$	−764.970			−1.04647
$732$		0			0
$733$	103.641			0.141393			0.0706964	−	0.997498i	$-0.477478\pi$
$733$	103.641			0.141393			0.0706964	+	0.997498i	$0.477478\pi$
$734$	−923.717	−	968.020i	−1.25847	−	1.31883i
$735$		0			0
$736$	−48.6359	+	38.3993i	−0.0660813	+	0.0521730i
$737$	6.02383			0.00817345
$738$		0			0
$739$			708.603i			0.958867i	0.877578	+	0.479434i	$0.159158\pi$
$739$			708.603i			0.958867i	−0.877578	+	0.479434i	$0.840842\pi$
$740$	980.173	+	45.9354i	1.32456	+	0.0620749i
$741$		0			0
$742$	802.283	+	305.809i	1.08124	+	0.412142i
$743$	64.3198			0.0865677			0.0432838	−	0.999063i	$-0.486218\pi$
$743$	64.3198			0.0865677			0.0432838	+	0.999063i	$0.486218\pi$
$744$		0			0
$745$			818.822i			1.09909i
$746$	−204.517	−	214.326i	−0.274152	−	0.287301i
$747$		0			0
$748$	12.5555	−	267.911i	0.0167855	−	0.358169i
$749$	−372.590	−	781.993i	−0.497451	−	1.04405i
$750$		0			0
$751$	−500.993			−0.667101			−0.333551	−	0.942732i	$-0.608247\pi$
$751$	−500.993			−0.667101			−0.333551	+	0.942732i	$0.608247\pi$
$752$	−79.7709	+	849.209i	−0.106078	+	1.12927i
$753$		0			0
$754$	709.000	+	743.005i	0.940318	+	0.985418i
$755$	436.633			0.578322
$756$		0			0
$757$		−	1207.70i		−	1.59537i	−0.603074	−	0.797685i	$-0.706058\pi$
$757$		−	1207.70i		−	1.59537i	0.603074	−	0.797685i	$-0.293942\pi$
$758$	4.83262	+	5.06440i	0.00637549	+	0.00668127i
$759$		0			0
$760$	135.983	+	156.567i	0.178925	+	0.206009i
$761$			389.162i			0.511382i	0.966759	+	0.255691i	$0.0823030\pi$
$761$			389.162i			0.511382i	−0.966759	+	0.255691i	$0.917697\pi$
$762$		0			0
$763$	119.086	+	249.937i	0.156076	+	0.327572i
$764$	−23.7096	+	505.916i	−0.0310335	+	0.662194i
$765$		0			0
$766$	156.109	+	163.596i	0.203798	+	0.213572i
$767$	887.575			1.15720
$768$		0			0
$769$			656.498i			0.853704i	0.904322	+	0.426852i	$0.140377\pi$
$769$			656.498i			0.853704i	−0.904322	+	0.426852i	$0.859623\pi$
$770$	−252.455	−	96.2294i	−0.327864	−	0.124973i
$771$		0			0
$772$	61.5299	−	1312.93i	0.0797020	−	1.70068i
$773$	369.776			0.478364			0.239182	−	0.970975i	$-0.423121\pi$
$773$	369.776			0.478364			0.239182	+	0.970975i	$0.423121\pi$
$774$		0			0
$775$		−	57.1364i		−	0.0737243i
$776$	−625.920	+	543.629i	−0.806598	+	0.700553i
$777$		0			0
$778$	103.293	+	108.247i	0.132767	+	0.139135i
$779$			327.726i			0.420701i
$780$		0			0
$781$			37.1404i			0.0475549i
$782$	48.7222	+	51.0590i	0.0623046	+	0.0652928i
$783$		0			0
$784$	−548.676	+	560.010i	−0.699841	+	0.714298i
$785$	−865.718			−1.10283
$786$		0			0
$787$	−590.922			−0.750854			−0.375427	−	0.926852i	$-0.622504\pi$
$787$	−590.922			−0.750854			−0.375427	+	0.926852i	$0.622504\pi$
$788$	104.657	+	4.90473i	0.132814	+	0.00622428i
$789$		0			0
$790$	1136.04	−	1084.05i	1.43803	−	1.37221i
$791$	−336.083	+	160.131i	−0.424884	+	0.202441i
$792$		0			0
$793$	1025.90			1.29369
$794$	−172.836	+	164.926i	−0.217677	+	0.207715i
$795$		0			0
$796$	−1364.93	−	63.9668i	−1.71473	−	0.0803603i
$797$	−1185.20			−1.48708			−0.743539	−	0.668692i	$-0.766854\pi$
$797$	−1185.20			−1.48708			−0.743539	+	0.668692i	$0.766854\pi$
$798$		0			0
$799$	971.431			1.21581
$800$	62.9547	−	49.7044i	0.0786933	−	0.0621305i
$801$		0			0
$802$	−720.274	+	687.310i	−0.898098	+	0.856994i
$803$	−237.088			−0.295253
$804$		0			0
$805$	64.1807	−	30.5797i	0.0797276	−	0.0379872i
$806$	−393.748	−	412.633i	−0.488521	−	0.511952i
$807$		0			0
$808$	119.710	+	137.831i	0.148156	+	0.170583i
$809$	697.293			0.861920			0.430960	−	0.902371i	$-0.358175\pi$
$809$	697.293			0.861920			0.430960	+	0.902371i	$0.358175\pi$
$810$		0			0
$811$	744.052			0.917450			0.458725	−	0.888578i	$-0.348306\pi$
$811$	744.052			0.917450			0.458725	+	0.888578i	$0.348306\pi$
$812$	−1059.51	+	445.220i	−1.30481	+	0.548300i
$813$		0			0
$814$	−249.027	+	237.630i	−0.305930	+	0.291929i
$815$		−	1087.73i		−	1.33464i
$816$		0			0
$817$			207.484i			0.253958i
$818$	333.985	+	350.004i	0.408295	+	0.427878i
$819$		0			0
$820$	1389.52	+	65.1193i	1.69453	+	0.0794138i
$821$			71.5020i			0.0870913i	0.999051	+	0.0435457i	$0.0138654\pi$
$821$			71.5020i			0.0870913i	−0.999051	+	0.0435457i	$0.986135\pi$
$822$		0			0
$823$	1001.05			1.21635			0.608174	−	0.793804i	$-0.291902\pi$
$823$	1001.05			1.21635			0.608174	+	0.793804i	$0.291902\pi$
$824$	−955.634	+	829.995i	−1.15975	+	1.00727i
$825$		0			0
$826$	−353.762	+	928.087i	−0.428284	+	1.12359i
$827$			504.214i			0.609691i	0.952402	+	0.304845i	$0.0986048\pi$
$827$			504.214i			0.609691i	−0.952402	+	0.304845i	$0.901395\pi$
$828$		0			0
$829$	709.973			0.856421			0.428210	−	0.903679i	$-0.359144\pi$
$829$	709.973			0.856421			0.428210	+	0.903679i	$0.359144\pi$
$830$	98.5734	−	94.0619i	0.118763	−	0.113328i
$831$		0			0
$832$	112.121	−	792.804i	0.134760	−	0.952890i
$833$	693.448	+	562.504i	0.832471	+	0.675275i
$834$		0			0
$835$			892.069i			1.06835i
$836$	−72.6657	−	3.40545i	−0.0869207	−	0.00407351i
$837$		0			0
$838$	−1040.57	+	992.946i	−1.24173	+	1.18490i
$839$			868.501i			1.03516i	0.855634	+	0.517581i	$0.173167\pi$
$839$			868.501i			1.03516i	−0.855634	+	0.517581i	$0.826833\pi$
$840$		0			0
$841$	−843.658			−1.00316
$842$	28.3026	+	29.6601i	0.0336136	+	0.0352257i
$843$		0			0
$844$	−357.799	−	16.7681i	−0.423933	−	0.0198675i
$845$	−65.4486			−0.0774539
$846$		0			0
$847$	−679.083	+	323.558i	−0.801751	+	0.382004i
$848$	91.7699	−	976.945i	0.108219	−	1.15206i
$849$		0			0
$850$	−63.0664	−	66.0912i	−0.0741958	−	0.0777544i
$851$		−	90.5761i		−	0.106435i
$852$		0			0
$853$	−404.626			−0.474356			−0.237178	−	0.971466i	$-0.576222\pi$
$853$	−404.626			−0.474356			−0.237178	+	0.971466i	$0.576222\pi$
$854$	−408.893	+	1072.72i	−0.478798	+	1.25611i
$855$		0			0
$856$	−747.417	+	649.153i	−0.873151	+	0.758356i
$857$		−	1427.04i		−	1.66515i	−0.553910	−	0.832577i	$-0.686865\pi$
$857$		−	1427.04i		−	1.66515i	0.553910	−	0.832577i	$-0.313135\pi$
$858$		0			0
$859$	−1004.69			−1.16960			−0.584801	−	0.811177i	$-0.698827\pi$
$859$	−1004.69			−1.16960			−0.584801	+	0.811177i	$0.698827\pi$
$860$	879.704	+	41.2270i	1.02291	+	0.0479384i
$861$		0			0
$862$	−210.027	+	200.415i	−0.243651	+	0.232500i
$863$	328.400			0.380533			0.190267	−	0.981732i	$-0.439065\pi$
$863$	328.400			0.380533			0.190267	+	0.981732i	$0.439065\pi$
$864$		0			0
$865$	−1282.10			−1.48219
$866$	71.8610	+	75.3076i	0.0829804	+	0.0869603i
$867$		0			0
$868$	588.404	−	247.256i	0.677884	−	0.284857i
$869$			550.837i			0.633875i
$870$		0			0
$871$		−	20.4815i		−	0.0235150i
$872$	238.886	−	207.479i	0.273952	−	0.237935i
$873$		0			0
$874$	13.8488	−	13.2150i	0.0158453	−	0.0151201i
$875$	745.498	−	355.202i	0.851998	−	0.405945i
$876$		0			0
$877$			924.919i			1.05464i	0.849667	+	0.527320i	$0.176803\pi$
$877$			924.919i			1.05464i	−0.849667	+	0.527320i	$0.823197\pi$
$878$	366.001	+	383.555i	0.416858	+	0.436851i
$879$		0			0
$880$	−28.8774	+	307.417i	−0.0328152	+	0.349337i
$881$		−	1330.68i		−	1.51042i	−0.655483	−	0.755210i	$-0.727535\pi$
$881$		−	1330.68i		−	1.51042i	0.655483	−	0.755210i	$-0.272465\pi$
$882$		0			0
$883$		−	1431.52i		−	1.62120i	−0.585601	−	0.810600i	$-0.699141\pi$
$883$		−	1431.52i		−	1.62120i	0.585601	−	0.810600i	$-0.300859\pi$
$884$	−910.918	−	42.6899i	−1.03045	−	0.0482917i
$885$		0			0
$886$	−456.881	−	478.794i	−0.515667	−	0.540400i
$887$		−	1257.50i		−	1.41770i	−0.705359	−	0.708850i	$-0.749214\pi$
$887$		−	1257.50i		−	1.41770i	0.705359	−	0.708850i	$-0.250786\pi$
$888$		0			0
$889$	279.286	−	133.069i	0.314157	−	0.149684i
$890$	946.310	+	991.697i	1.06327	+	1.11427i
$891$		0			0
$892$	−1565.93	−	73.3868i	−1.75553	−	0.0822722i
$893$		−	263.482i		−	0.295053i
$894$		0			0
$895$			269.856i			0.301515i
$896$	784.302	+	433.228i	0.875337	+	0.483513i
$897$		0			0
$898$	905.346	−	863.911i	1.00818	−	0.962038i
$899$	935.587			1.04070
$900$		0			0
$901$	−1117.55			−1.24035
$902$	−353.028	+	336.871i	−0.391383	+	0.373471i
$903$		0			0
$904$	278.991	+	321.223i	0.308619	+	0.355335i
$905$	1475.00			1.62983
$906$		0			0
$907$			1630.83i			1.79805i	0.437899	+	0.899024i	$0.355723\pi$
$907$			1630.83i			1.79805i	−0.437899	+	0.899024i	$0.644277\pi$
$908$	57.3261	−	1223.23i	0.0631344	−	1.34717i
$909$		0			0
$910$	−327.188	+	858.370i	−0.359547	+	0.943263i
$911$	778.173			0.854197			0.427098	−	0.904205i	$-0.359536\pi$
$911$	778.173			0.854197			0.427098	+	0.904205i	$0.359536\pi$
$912$		0			0
$913$			47.7956i			0.0523501i
$914$	−575.431	+	549.095i	−0.629574	+	0.600760i
$915$		0			0
$916$	10.0168	−	213.738i	0.0109353	−	0.233338i
$917$	−1214.69	+	578.754i	−1.32463	+	0.631139i
$918$		0			0
$919$	−116.976			−0.127286			−0.0636429	−	0.997973i	$-0.520272\pi$
$919$	−116.976			−0.127286			−0.0636429	+	0.997973i	$0.520272\pi$
$920$	−53.2780	−	61.3429i	−0.0579109	−	0.0666771i
$921$		0			0
$922$	103.353	−	98.6227i	0.112096	−	0.106966i
$923$	126.280			0.136815
$924$		0			0
$925$			117.242i			0.126749i
$926$	127.400	−	121.569i	0.137581	−	0.131284i
$927$		0			0
$928$	813.891	+	1030.86i	0.877038	+	1.11084i
$929$		−	631.449i		−	0.679709i	−0.940478	−	0.339854i	$-0.889622\pi$
$929$		−	631.449i		−	0.679709i	0.940478	−	0.339854i	$-0.110378\pi$
$930$		0			0
$931$	152.569	−	188.085i	0.163876	−	0.202024i
$932$	5.37611	−	114.716i	0.00576836	−	0.123086i
$933$		0			0
$934$	−171.514	+	163.664i	−0.183634	+	0.175229i
$935$	351.662			0.376109
$936$		0			0
$937$			50.0533i			0.0534187i	0.999643	+	0.0267093i	$0.00850286\pi$
$937$			50.0533i			0.0534187i	−0.999643	+	0.0267093i	$0.991497\pi$
$938$	21.4164	+	8.16336i	0.0228320	+	0.00870294i
$939$		0			0
$940$	−1117.13	−	52.3540i	−1.18844	−	0.0556957i
$941$	−272.536			−0.289623			−0.144812	−	0.989459i	$-0.546258\pi$
$941$	−272.536			−0.289623			−0.144812	+	0.989459i	$0.546258\pi$
$942$		0			0
$943$		−	128.403i		−	0.136164i
$944$	1130.14	+	106.160i	1.19718	+	0.112458i
$945$		0			0
$946$	−223.502	+	213.273i	−0.236260	+	0.225447i
$947$			1505.37i			1.58962i	0.606858	+	0.794810i	$0.292430\pi$
$947$			1505.37i			1.58962i	−0.606858	+	0.794810i	$0.707570\pi$
$948$		0			0
$949$			806.119i			0.849440i
$950$	−17.9260	+	17.1056i	−0.0188695	+	0.0180059i
$951$		0			0
$952$	407.705	−	935.480i	0.428261	−	0.982648i
$953$	714.817			0.750070			0.375035	−	0.927011i	$-0.377631\pi$
$953$	714.817			0.750070			0.375035	+	0.927011i	$0.377631\pi$
$954$		0			0
$955$	−664.069			−0.695360
$956$	−40.1979	+	857.744i	−0.0420480	+	0.897222i
$957$		0			0
$958$	−190.678	−	199.823i	−0.199038	−	0.208584i
$959$	−1677.62	+	799.322i	−1.74934	+	0.833495i
$960$		0			0
$961$	441.415			0.459329
$962$	807.962	+	846.713i	0.839877	+	0.880159i
$963$		0			0
$964$	−1422.19	−	66.6504i	−1.47530	−	0.0691394i
$965$	1723.36			1.78586
$966$		0			0
$967$	−982.093			−1.01561			−0.507804	−	0.861473i	$-0.669543\pi$
$967$	−982.093			−1.01561			−0.507804	+	0.861473i	$0.669543\pi$
$968$	563.724	+	649.057i	0.582360	+	0.670514i
$969$		0			0
$970$	−750.427	−	786.419i	−0.773636	−	0.810741i
$971$	−119.012			−0.122566			−0.0612832	−	0.998120i	$-0.519519\pi$
$971$	−119.012			−0.122566			−0.0612832	+	0.998120i	$0.519519\pi$
$972$		0			0
$973$	98.0498	−	46.7171i	0.100771	−	0.0480134i
$974$	−451.127	+	430.480i	−0.463169	+	0.441971i
$975$		0			0
$976$	1306.26	+	122.704i	1.33838	+	0.125722i
$977$	−1313.25			−1.34417			−0.672083	−	0.740476i	$-0.734600\pi$
$977$	−1313.25			−1.34417			−0.672083	+	0.740476i	$0.734600\pi$
$978$		0			0
$979$	−480.848			−0.491162
$980$	−767.140	−	684.244i	−0.782796	−	0.698208i
$981$		0			0
$982$	831.304	+	871.175i	0.846541	+	0.887143i
$983$			59.3222i			0.0603482i	0.999545	+	0.0301741i	$0.00960617\pi$
$983$			59.3222i			0.0603482i	−0.999545	+	0.0301741i	$0.990394\pi$
$984$		0			0
$985$			137.374i			0.139466i
$986$	1082.22	−	1032.69i	1.09759	−	1.04735i
$987$		0			0
$988$	−11.5788	+	247.069i	−0.0117195	+	0.250070i
$989$		−	81.2920i		−	0.0821961i
$990$		0			0
$991$	−790.745			−0.797927			−0.398963	−	0.916967i	$-0.630630\pi$
$991$	−790.745			−0.797927			−0.398963	+	0.916967i	$0.630630\pi$
$992$	−452.000	−	572.495i	−0.455645	−	0.577112i
$993$		0			0
$994$	−50.3318	+	132.044i	−0.0506356	+	0.132841i
$995$		−	1791.61i		−	1.80062i
$996$		0			0
$997$	−1034.13			−1.03724			−0.518622	−	0.855004i	$-0.673555\pi$
$997$	−1034.13			−1.03724			−0.518622	+	0.855004i	$0.673555\pi$
$998$	289.832	+	303.733i	0.290413	+	0.304342i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.3.l.h.181.8		32
3.2	odd	2		168.3.l.a.13.25	✓	32
4.3	odd	2		2016.3.l.h.433.24		32
7.6	odd	2	inner	504.3.l.h.181.7		32
8.3	odd	2		2016.3.l.h.433.9		32
8.5	even	2	inner	504.3.l.h.181.5		32
12.11	even	2		672.3.l.a.433.26		32
21.20	even	2		168.3.l.a.13.26	yes	32
24.5	odd	2		168.3.l.a.13.28	yes	32
24.11	even	2		672.3.l.a.433.7		32
28.27	even	2		2016.3.l.h.433.10		32
56.13	odd	2	inner	504.3.l.h.181.6		32
56.27	even	2		2016.3.l.h.433.23		32
84.83	odd	2		672.3.l.a.433.10		32
168.83	odd	2		672.3.l.a.433.23		32
168.125	even	2		168.3.l.a.13.27	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.3.l.a.13.25	✓	32	3.2	odd	2
168.3.l.a.13.26	yes	32	21.20	even	2
168.3.l.a.13.27	yes	32	168.125	even	2
168.3.l.a.13.28	yes	32	24.5	odd	2
504.3.l.h.181.5		32	8.5	even	2	inner
504.3.l.h.181.6		32	56.13	odd	2	inner
504.3.l.h.181.7		32	7.6	odd	2	inner
504.3.l.h.181.8		32	1.1	even	1	trivial
672.3.l.a.433.7		32	24.11	even	2
672.3.l.a.433.10		32	84.83	odd	2
672.3.l.a.433.23		32	168.83	odd	2
672.3.l.a.433.26		32	12.11	even	2
2016.3.l.h.433.9		32	8.3	odd	2
2016.3.l.h.433.10		32	28.27	even	2
2016.3.l.h.433.23		32	56.27	even	2
2016.3.l.h.433.24		32	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	504.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.44694 + 1.38071i) q^{2} +(0.187253 - 3.99561i) q^{4} +5.24467 q^{5} +(-6.31936 + 3.01094i) q^{7} +(5.24586 + 6.03995i) q^{8} +(-7.58871 + 7.24140i) q^{10} -3.67957i q^{11} -12.5108 q^{13} +(4.98647 - 13.0819i) q^{14} +(-15.9299 - 1.49638i) q^{16} +18.2226i q^{17} +4.94253 q^{19} +(0.982081 - 20.9557i) q^{20} +(5.08043 + 5.32410i) q^{22} -1.93648 q^{23} +2.50660 q^{25} +(18.1024 - 17.2739i) q^{26} +(10.8472 + 25.8135i) q^{28} +41.0446i q^{29} -22.7944i q^{31} +(25.1156 - 19.8294i) q^{32} +(-25.1602 - 26.3669i) q^{34} +(-33.1430 + 15.7914i) q^{35} +46.7736i q^{37} +(-7.15153 + 6.82422i) q^{38} +(27.5128 + 31.6775i) q^{40} +66.3075i q^{41} +41.9792i q^{43} +(-14.7021 - 0.689010i) q^{44} +(2.80196 - 2.67373i) q^{46} -53.3092i q^{47} +(30.8685 - 38.0544i) q^{49} +(-3.62689 + 3.46089i) q^{50} +(-2.34269 + 49.9885i) q^{52} +61.3279i q^{53} -19.2981i q^{55} +(-51.3364 - 22.3736i) q^{56} +(-56.6709 - 59.3889i) q^{58} -70.9445 q^{59} -82.0007 q^{61} +(31.4726 + 32.9821i) q^{62} +(-8.96188 + 63.3694i) q^{64} -65.6152 q^{65} +1.63710i q^{67} +(72.8104 + 3.41223i) q^{68} +(26.1524 - 68.6101i) q^{70} -10.0937 q^{71} -64.4337i q^{73} +(-64.5810 - 67.6784i) q^{74} +(0.925503 - 19.7484i) q^{76} +(11.0789 + 23.2525i) q^{77} -149.702 q^{79} +(-83.5470 - 7.84804i) q^{80} +(-91.5517 - 95.9427i) q^{82} -12.9895 q^{83} +95.5714i q^{85} +(-57.9614 - 60.7413i) q^{86} +(22.2244 - 19.3025i) q^{88} -130.681i q^{89} +(79.0604 - 37.6693i) q^{91} +(-0.362612 + 7.73743i) q^{92} +(73.6048 + 77.1351i) q^{94} +25.9219 q^{95} +103.630i q^{97} +(7.87741 + 97.6829i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} - 6 q^{4} + 2 q^{8} - 38 q^{14} - 46 q^{16} + 16 q^{22} - 64 q^{23} + 160 q^{25} - 122 q^{28} + 122 q^{32} + 216 q^{44} - 260 q^{46} - 16 q^{49} - 122 q^{50} - 98 q^{56} - 160 q^{58} - 174 q^{64}+ \cdots + 2 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 - 6 * q^4 + 2 * q^8 - 38 * q^14 - 46 * q^16 + 16 * q^22 - 64 * q^23 + 160 * q^25 - 122 * q^28 + 122 * q^32 + 216 * q^44 - 260 * q^46 - 16 * q^49 - 122 * q^50 - 98 * q^56 - 160 * q^58 - 174 * q^64 + 408 * q^70 + 640 * q^71 - 408 * q^74 - 64 * q^79 - 792 * q^86 - 592 * q^88 - 316 * q^92 + 768 * q^95 + 2 * q^98

Introduction

L-functions

Modular forms

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Database

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