LMFDB - Embedded newform 180.9.c.b.91.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [180,9,Mod(91,180)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(180, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 0])) N = Newforms(chi, 9, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("180.91"); S:= CuspForms(chi, 9); N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	180.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$73.3281498110$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.10
Character	$\chi$	$=$	180.91
Dual form			180.9.c.b.91.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-9.51821 + 12.8609i) q^{2} +(-74.8072 - 244.826i) q^{4} +279.508 q^{5} +2236.25i q^{7} +(3860.72 + 1368.22i) q^{8} +(-2660.42 + 3594.74i) q^{10} +11333.8i q^{11} +43422.0 q^{13} +(-28760.3 - 21285.1i) q^{14} +(-54343.8 + 36629.5i) q^{16} +106270. q^{17} +169252. i q^{19} +(-20909.3 - 68431.0i) q^{20} +(-145763. - 107877. i) q^{22} -301142. i q^{23} +78125.0 q^{25} +(-413299. + 558447. i) q^{26} +(547493. - 167288. i) q^{28} -1.13613e6 q^{29} -1.49838e6i q^{31} +(46165.6 - 1.04756e6i) q^{32} +(-1.01150e6 + 1.36673e6i) q^{34} +625051. i q^{35} +3.00588e6 q^{37} +(-2.17674e6 - 1.61098e6i) q^{38} +(1.07911e6 + 382429. i) q^{40} +1.45494e6 q^{41} -1.84278e6i q^{43} +(2.77481e6 - 847849. i) q^{44} +(3.87297e6 + 2.86634e6i) q^{46} +3.23470e6i q^{47} +763979. q^{49} +(-743610. + 1.00476e6i) q^{50} +(-3.24828e6 - 1.06308e7i) q^{52} +2.47758e6 q^{53} +3.16789e6i q^{55} +(-3.05968e6 + 8.63355e6i) q^{56} +(1.08139e7 - 1.46117e7i) q^{58} +1.98398e7i q^{59} +2.31511e7 q^{61} +(1.92706e7 + 1.42619e7i) q^{62} +(1.30332e7 + 1.05646e7i) q^{64} +1.21368e7 q^{65} +1.38239e7i q^{67} +(-7.94974e6 - 2.60176e7i) q^{68} +(-8.03874e6 - 5.94937e6i) q^{70} -3.24707e7i q^{71} -2.85975e7 q^{73} +(-2.86106e7 + 3.86584e7i) q^{74} +(4.14374e7 - 1.26613e7i) q^{76} -2.53452e7 q^{77} -5.42305e7i q^{79} +(-1.51895e7 + 1.02383e7i) q^{80} +(-1.38484e7 + 1.87119e7i) q^{82} +8.59356e7i q^{83} +2.97033e7 q^{85} +(2.36999e7 + 1.75400e7i) q^{86} +(-1.55071e7 + 4.37567e7i) q^{88} -4.60584e7 q^{89} +9.71024e7i q^{91} +(-7.37275e7 + 2.25276e7i) q^{92} +(-4.16013e7 - 3.07886e7i) q^{94} +4.73074e7i q^{95} -3.17442e7 q^{97} +(-7.27171e6 + 9.82548e6i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 610 q^{4} - 8750 q^{10} - 51392 q^{13} + 11986 q^{16} - 758068 q^{22} + 2500000 q^{25} + 976324 q^{28} - 6117428 q^{34} + 5152064 q^{37} - 96250 q^{40} - 10391752 q^{46} - 11002976 q^{49} + 13976584 q^{52}+ \cdots + 80579520 q^{97}+O(q^{100}) $ 32 * q + 610 * q^4 - 8750 * q^10 - 51392 * q^13 + 11986 * q^16 - 758068 * q^22 + 2500000 * q^25 + 976324 * q^28 - 6117428 * q^34 + 5152064 * q^37 - 96250 * q^40 - 10391752 * q^46 - 11002976 * q^49 + 13976584 * q^52 - 36333948 * q^58 - 7802048 * q^61 + 116259994 * q^64 - 49897500 * q^70 - 94303680 * q^73 + 248840592 * q^76 - 428557904 * q^82 + 106960000 * q^85 + 510719924 * q^88 - 692727576 * q^94 + 80579520 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	−9.51821	+	12.8609i	−0.594888	+	0.803808i
$2$	−9.51821	+	12.8609i	−0.594888	+	0.803808i
$3$		0			0
$3$		0			0
$4$	−74.8072	−	244.826i	−0.292216	−	0.956352i
$5$	279.508			0.447214
$5$	279.508			0.447214
$6$		0			0
$7$			2236.25i			0.931384i	0.884947	+	0.465692i	$0.154194\pi$
$7$			2236.25i			0.931384i	−0.884947	+	0.465692i	$0.845806\pi$
$8$	3860.72	+	1368.22i	0.942560	+	0.334038i
$9$		0			0
$10$	−2660.42	+	3594.74i	−0.266042	+	0.359474i
$11$			11333.8i			0.774113i	0.922056	+	0.387057i	$0.126508\pi$
$11$			11333.8i			0.774113i	−0.922056	+	0.387057i	$0.873492\pi$
$12$		0			0
$13$	43422.0			1.52032			0.760162	−	0.649734i	$-0.225120\pi$
$13$	43422.0			1.52032			0.760162	+	0.649734i	$0.225120\pi$
$14$	−28760.3	−	21285.1i	−0.748654	−	0.554069i
$15$		0			0
$16$	−54343.8	+	36629.5i	−0.829220	+	0.558922i
$17$	106270.			1.27237			0.636185	−	0.771536i	$-0.280511\pi$
$17$	106270.			1.27237			0.636185	+	0.771536i	$0.280511\pi$
$18$		0			0
$19$			169252.i			1.29873i	0.760476	+	0.649366i	$0.224966\pi$
$19$			169252.i			1.29873i	−0.760476	+	0.649366i	$0.775034\pi$
$20$	−20909.3	−	68431.0i	−0.130683	−	0.427694i
$21$		0			0
$22$	−145763.	−	107877.i	−0.622239	−	0.460511i
$23$		−	301142.i		−	1.07612i	−0.842907	−	0.538059i	$-0.819158\pi$
$23$		−	301142.i		−	1.07612i	0.842907	−	0.538059i	$-0.180842\pi$
$24$		0			0
$25$	78125.0			0.200000
$26$	−413299.	+	558447.i	−0.904423	+	1.22205i
$27$		0			0
$28$	547493.	−	167288.i	0.890731	−	0.272165i
$29$	−1.13613e6			−1.60633			−0.803166	−	0.595755i	$-0.796853\pi$
$29$	−1.13613e6			−1.60633			−0.803166	+	0.595755i	$0.796853\pi$
$30$		0			0
$31$		−	1.49838e6i		−	1.62246i	−0.584724	−	0.811232i	$-0.698797\pi$
$31$		−	1.49838e6i		−	1.62246i	0.584724	−	0.811232i	$-0.301203\pi$
$32$	46165.6	−	1.04756e6i	0.0440269	−	0.999030i
$33$		0			0
$34$	−1.01150e6	+	1.36673e6i	−0.756919	+	1.02274i
$35$			625051.i			0.416527i
$36$		0			0
$37$	3.00588e6			1.60385			0.801926	−	0.597424i	$-0.203809\pi$
$37$	3.00588e6			1.60385			0.801926	+	0.597424i	$0.203809\pi$
$38$	−2.17674e6	−	1.61098e6i	−1.04393	−	0.772601i
$39$		0			0
$40$	1.07911e6	+	382429.i	0.421526	+	0.149386i
$41$	1.45494e6			0.514884			0.257442	−	0.966294i	$-0.417120\pi$
$41$	1.45494e6			0.514884			0.257442	+	0.966294i	$0.417120\pi$
$42$		0			0
$43$		−	1.84278e6i		−	0.539015i	−0.962998	−	0.269507i	$-0.913139\pi$
$43$		−	1.84278e6i		−	0.539015i	0.962998	−	0.269507i	$-0.0868608\pi$
$44$	2.77481e6	−	847849.i	0.740325	−	0.226208i
$45$		0			0
$46$	3.87297e6	+	2.86634e6i	0.864993	+	0.640171i
$47$			3.23470e6i			0.662892i	0.943474	+	0.331446i	$0.107536\pi$
$47$			3.23470e6i			0.662892i	−0.943474	+	0.331446i	$0.892464\pi$
$48$		0			0
$49$	763979.			0.132525
$50$	−743610.	+	1.00476e6i	−0.118978	+	0.160762i
$51$		0			0
$52$	−3.24828e6	−	1.06308e7i	−0.444262	−	1.45396i
$53$	2.47758e6			0.313996			0.156998	−	0.987599i	$-0.449818\pi$
$53$	2.47758e6			0.313996			0.156998	+	0.987599i	$0.449818\pi$
$54$		0			0
$55$			3.16789e6i			0.346194i
$56$	−3.05968e6	+	8.63355e6i	−0.311117	+	0.877885i
$57$		0			0
$58$	1.08139e7	−	1.46117e7i	0.955589	−	1.29118i
$59$			1.98398e7i			1.63731i	0.574288	+	0.818654i	$0.305279\pi$
$59$			1.98398e7i			1.63731i	−0.574288	+	0.818654i	$0.694721\pi$
$60$		0			0
$61$	2.31511e7			1.67206			0.836032	−	0.548681i	$-0.184870\pi$
$61$	2.31511e7			1.67206			0.836032	+	0.548681i	$0.184870\pi$
$62$	1.92706e7	+	1.42619e7i	1.30415	+	0.965185i
$63$		0			0
$64$	1.30332e7	+	1.05646e7i	0.776838	+	0.629701i
$65$	1.21368e7			0.679909
$66$		0			0
$67$			1.38239e7i			0.686011i	0.939333	+	0.343006i	$0.111445\pi$
$67$			1.38239e7i			0.686011i	−0.939333	+	0.343006i	$0.888555\pi$
$68$	−7.94974e6	−	2.60176e7i	−0.371807	−	1.21684i
$69$		0			0
$70$	−8.03874e6	−	5.94937e6i	−0.334808	−	0.247787i
$71$		−	3.24707e7i		−	1.27779i	−0.769295	−	0.638894i	$-0.779392\pi$
$71$		−	3.24707e7i		−	1.27779i	0.769295	−	0.638894i	$-0.220608\pi$
$72$		0			0
$73$	−2.85975e7			−1.00702			−0.503508	−	0.863991i	$-0.667957\pi$
$73$	−2.85975e7			−1.00702			−0.503508	+	0.863991i	$0.667957\pi$
$74$	−2.86106e7	+	3.86584e7i	−0.954112	+	1.28919i
$75$		0			0
$76$	4.14374e7	−	1.26613e7i	1.24205	−	0.379510i
$77$	−2.53452e7			−0.720996
$78$		0			0
$79$		−	5.42305e7i		−	1.39231i	−0.717893	−	0.696154i	$-0.754893\pi$
$79$		−	5.42305e7i		−	1.39231i	0.717893	−	0.696154i	$-0.245107\pi$
$80$	−1.51895e7	+	1.02383e7i	−0.370838	+	0.249958i
$81$		0			0
$82$	−1.38484e7	+	1.87119e7i	−0.306298	+	0.413868i
$83$			8.59356e7i			1.81076i	0.424602	+	0.905380i	$0.360414\pi$
$83$			8.59356e7i			1.81076i	−0.424602	+	0.905380i	$0.639586\pi$
$84$		0			0
$85$	2.97033e7			0.569022
$86$	2.36999e7	+	1.75400e7i	0.433264	+	0.320654i
$87$		0			0
$88$	−1.55071e7	+	4.37567e7i	−0.258583	+	0.729648i
$89$	−4.60584e7			−0.734089			−0.367044	−	0.930203i	$-0.619630\pi$
$89$	−4.60584e7			−0.734089			−0.367044	+	0.930203i	$0.619630\pi$
$90$		0			0
$91$			9.71024e7i			1.41600i
$92$	−7.37275e7	+	2.25276e7i	−1.02915	+	0.314459i
$93$		0			0
$94$	−4.16013e7	−	3.07886e7i	−0.532838	−	0.394347i
$95$			4.73074e7i			0.580811i
$96$		0			0
$97$	−3.17442e7			−0.358572			−0.179286	−	0.983797i	$-0.557379\pi$
$97$	−3.17442e7			−0.358572			−0.179286	+	0.983797i	$0.557379\pi$
$98$	−7.27171e6	+	9.82548e6i	−0.0788374	+	0.106524i
$99$		0			0
$100$	−5.84431e6	−	1.91270e7i	−0.0584431	−	0.191270i
$101$	−1.18372e8			−1.13754			−0.568768	−	0.822498i	$-0.692580\pi$
$101$	−1.18372e8			−1.13754			−0.568768	+	0.822498i	$0.692580\pi$
$102$		0			0
$103$			1.85632e7i			0.164931i	0.996594	+	0.0824657i	$0.0262795\pi$
$103$			1.85632e7i			0.164931i	−0.996594	+	0.0824657i	$0.973721\pi$
$104$	1.67640e8	+	5.94107e7i	1.43300	+	0.507845i
$105$		0			0
$106$	−2.35822e7	+	3.18640e7i	−0.186793	+	0.252393i
$107$		−	3.88491e7i		−	0.296378i	−0.988959	−	0.148189i	$-0.952656\pi$
$107$		−	3.88491e7i		−	0.296378i	0.988959	−	0.148189i	$-0.0473444\pi$
$108$		0			0
$109$	8.82410e7			0.625121			0.312561	−	0.949898i	$-0.398813\pi$
$109$	8.82410e7			0.625121			0.312561	+	0.949898i	$0.398813\pi$
$110$	−4.07420e7	−	3.01527e7i	−0.278274	−	0.205947i
$111$		0			0
$112$	−8.19129e7	−	1.21526e8i	−0.520571	−	0.772322i
$113$	4.38503e7			0.268942			0.134471	−	0.990918i	$-0.457066\pi$
$113$	4.38503e7			0.268942			0.134471	+	0.990918i	$0.457066\pi$
$114$		0			0
$115$		−	8.41718e7i		−	0.481255i
$116$	8.49906e7	+	2.78154e8i	0.469396	+	1.53622i
$117$		0			0
$118$	−2.55159e8	−	1.88840e8i	−1.31608	−	0.974015i
$119$			2.37646e8i			1.18507i
$120$		0			0
$121$	8.59040e7			0.400749
$122$	−2.20357e8	+	2.97745e8i	−0.994691	+	1.34402i
$123$		0			0
$124$	−3.66843e8	+	1.12090e8i	−1.55165	+	0.474109i
$125$	2.18366e7			0.0894427
$126$		0			0
$127$			1.37839e8i			0.529856i	0.964268	+	0.264928i	$0.0853482\pi$
$127$			1.37839e8i			0.529856i	−0.964268	+	0.264928i	$0.914652\pi$
$128$	−2.59923e8	+	6.70624e7i	−0.968290	+	0.249827i
$129$		0			0
$130$	−1.15521e8	+	1.56091e8i	−0.404470	+	0.546517i
$131$			4.37311e8i			1.48493i	0.669886	+	0.742464i	$0.266343\pi$
$131$			4.37311e8i			1.48493i	−0.669886	+	0.742464i	$0.733657\pi$
$132$		0			0
$133$	−3.78490e8			−1.20962
$134$	−1.77788e8	−	1.31579e8i	−0.551421	−	0.408100i
$135$		0			0
$136$	4.10278e8	+	1.45400e8i	1.19929	+	0.425020i
$137$	2.80555e8			0.796407			0.398204	−	0.917297i	$-0.369634\pi$
$137$	2.80555e8			0.796407			0.398204	+	0.917297i	$0.369634\pi$
$138$		0			0
$139$			5.83632e8i			1.56343i	0.623633	+	0.781717i	$0.285656\pi$
$139$			5.83632e8i			1.56343i	−0.623633	+	0.781717i	$0.714344\pi$
$140$	1.53029e8	−	4.67584e7i	0.398347	−	0.121716i
$141$		0			0
$142$	4.17604e8	+	3.09063e8i	1.02710	+	0.760141i
$143$			4.92135e8i			1.17690i
$144$		0			0
$145$	−3.17558e8			−0.718374
$146$	2.72197e8	−	3.67790e8i	0.599062	−	0.809447i
$147$		0			0
$148$	−2.24861e8	−	7.35917e8i	−0.468670	−	1.53385i
$149$	−4.94113e8			−1.00249			−0.501246	−	0.865305i	$-0.667125\pi$
$149$	−4.94113e8			−1.00249			−0.501246	+	0.865305i	$0.667125\pi$
$150$		0			0
$151$			3.84901e8i			0.740358i	0.928960	+	0.370179i	$0.120704\pi$
$151$			3.84901e8i			0.740358i	−0.928960	+	0.370179i	$0.879296\pi$
$152$	−2.31574e8	+	6.53436e8i	−0.433825	+	1.22413i
$153$		0			0
$154$	2.41241e8	−	3.25963e8i	0.428912	−	0.579543i
$155$		−	4.18810e8i		−	0.725588i
$156$		0			0
$157$	6.31361e8			1.03915			0.519576	−	0.854424i	$-0.326090\pi$
$157$	6.31361e8			1.03915			0.519576	+	0.854424i	$0.326090\pi$
$158$	6.97454e8	+	5.16177e8i	1.11915	+	0.828267i
$159$		0			0
$160$	1.29037e7	−	2.92802e8i	0.0196894	−	0.446780i
$161$	6.73430e8			1.00228
$162$		0			0
$163$			1.12044e8i			0.158723i	0.996846	+	0.0793614i	$0.0252881\pi$
$163$			1.12044e8i			0.158723i	−0.996846	+	0.0793614i	$0.974712\pi$
$164$	−1.08840e8	−	3.56207e8i	−0.150457	−	0.492411i
$165$		0			0
$166$	−1.10521e9	−	8.17954e8i	−1.45550	−	1.07720i
$167$			3.81124e8i			0.490005i	0.969522	+	0.245003i	$0.0787889\pi$
$167$			3.81124e8i			0.490005i	−0.969522	+	0.245003i	$0.921211\pi$
$168$		0			0
$169$	1.06974e9			1.31138
$170$	−2.82722e8	+	3.82012e8i	−0.338504	+	0.457384i
$171$		0			0
$172$	−4.51162e8	+	1.37854e8i	−0.515488	+	0.157509i
$173$	−1.50210e9			−1.67693			−0.838465	−	0.544956i	$-0.816547\pi$
$173$	−1.50210e9			−1.67693			−0.838465	+	0.544956i	$0.816547\pi$
$174$		0			0
$175$			1.74707e8i			0.186277i
$176$	−4.15152e8	−	6.15921e8i	−0.432669	−	0.641910i
$177$		0			0
$178$	4.38393e8	−	5.92354e8i	0.436701	−	0.590067i
$179$			5.86501e7i			0.0571290i	0.999592	+	0.0285645i	$0.00909360\pi$
$179$			5.86501e7i			0.0571290i	−0.999592	+	0.0285645i	$0.990906\pi$
$180$		0			0
$181$	1.56353e9			1.45677			0.728385	−	0.685168i	$-0.240271\pi$
$181$	1.56353e9			1.45677			0.728385	+	0.685168i	$0.240271\pi$
$182$	−1.24883e9	−	9.24242e8i	−1.13820	−	0.842364i
$183$		0			0
$184$	4.12028e8	−	1.16263e9i	0.359464	−	1.01431i
$185$	8.40168e8			0.717264
$186$		0			0
$187$			1.20444e9i			0.984959i
$188$	7.91939e8	−	2.41979e8i	0.633958	−	0.193707i
$189$		0			0
$190$	−6.08417e8	−	4.50282e8i	−0.466861	−	0.345518i
$191$		−	6.82044e8i		−	0.512482i	−0.966613	−	0.256241i	$-0.917516\pi$
$191$		−	6.82044e8i		−	0.512482i	0.966613	−	0.256241i	$-0.0824841\pi$
$192$		0			0
$193$	1.54570e9			1.11403			0.557013	−	0.830504i	$-0.311947\pi$
$193$	1.54570e9			1.11403			0.557013	+	0.830504i	$0.311947\pi$
$194$	3.02148e8	−	4.08260e8i	0.213311	−	0.288223i
$195$		0			0
$196$	−5.71511e7	−	1.87042e8i	−0.0387258	−	0.126740i
$197$	−1.40479e7			−0.00932710			−0.00466355	−	0.999989i	$-0.501484\pi$
$197$	−1.40479e7			−0.00932710			−0.00466355	+	0.999989i	$0.501484\pi$
$198$		0			0
$199$		−	2.97076e8i		−	0.189433i	−0.995504	−	0.0947164i	$-0.969806\pi$
$199$		−	2.97076e8i		−	0.189433i	0.995504	−	0.0947164i	$-0.0301944\pi$
$200$	3.01619e8	+	1.06892e8i	0.188512	+	0.0668075i
$201$		0			0
$202$	1.12669e9	−	1.52238e9i	0.676707	−	0.914361i
$203$		−	2.54067e9i		−	1.49611i
$204$		0			0
$205$	4.06668e8			0.230263
$206$	−2.38740e8	−	1.76688e8i	−0.132573	−	0.0981158i
$207$		0			0
$208$	−2.35971e9	+	1.59053e9i	−1.26068	+	0.849743i
$209$	−1.91827e9			−1.00537
$210$		0			0
$211$			1.99442e9i			1.00621i	0.864226	+	0.503104i	$0.167809\pi$
$211$			1.99442e9i			1.00621i	−0.864226	+	0.503104i	$0.832191\pi$
$212$	−1.85341e8	−	6.06577e8i	−0.0917547	−	0.300291i
$213$		0			0
$214$	4.99636e8	+	3.69774e8i	0.238231	+	0.176312i
$215$		−	5.15074e8i		−	0.241055i
$216$		0			0
$217$	3.35075e9			1.51114
$218$	−8.39897e8	+	1.13486e9i	−0.371877	+	0.502478i
$219$		0			0
$220$	7.75583e8	−	2.36981e8i	0.331083	−	0.101163i
$221$	4.61444e9			1.93442
$222$		0			0
$223$			8.75699e8i			0.354108i	0.984201	+	0.177054i	$0.0566567\pi$
$223$			8.75699e8i			0.354108i	−0.984201	+	0.177054i	$0.943343\pi$
$224$	2.34261e9	+	1.03238e8i	0.930480	+	0.0410059i
$225$		0			0
$226$	−4.17377e8	+	5.63956e8i	−0.159991	+	0.216178i
$227$		−	2.71043e9i		−	1.02079i	−0.859941	−	0.510393i	$-0.829500\pi$
$227$		−	2.71043e9i		−	1.02079i	0.859941	−	0.510393i	$-0.170500\pi$
$228$		0			0
$229$	−1.61306e9			−0.586555			−0.293277	−	0.956027i	$-0.594746\pi$
$229$	−1.61306e9			−0.586555			−0.293277	+	0.956027i	$0.594746\pi$
$230$	1.08253e9	+	8.01165e8i	0.386837	+	0.286293i
$231$		0			0
$232$	−4.38628e9	−	1.55447e9i	−1.51406	−	0.536576i
$233$	2.02375e9			0.686647			0.343323	−	0.939217i	$-0.388447\pi$
$233$	2.02375e9			0.686647			0.343323	+	0.939217i	$0.388447\pi$
$234$		0			0
$235$			9.04126e8i			0.296454i
$236$	4.85731e9	−	1.48416e9i	1.56584	−	0.478447i
$237$		0			0
$238$	−3.05635e9	−	2.26196e9i	−0.952565	−	0.704982i
$239$			2.75210e9i			0.843474i	0.906718	+	0.421737i	$0.138579\pi$
$239$			2.75210e9i			0.843474i	−0.906718	+	0.421737i	$0.861421\pi$
$240$		0			0
$241$	−2.16446e8			−0.0641625			−0.0320812	−	0.999485i	$-0.510214\pi$
$241$	−2.16446e8			−0.0641625			−0.0320812	+	0.999485i	$0.510214\pi$
$242$	−8.17653e8	+	1.10481e9i	−0.238401	+	0.322125i
$243$		0			0
$244$	−1.73187e9	−	5.66800e9i	−0.488603	−	1.59908i
$245$	2.13539e8			0.0592669
$246$		0			0
$247$			7.34926e9i			1.97449i
$248$	2.05011e9	−	5.78483e9i	0.541964	−	1.52927i
$249$		0			0
$250$	−2.07845e8	+	2.80839e8i	−0.0532084	+	0.0718948i
$251$		−	5.89325e9i		−	1.48477i	−0.669972	−	0.742387i	$-0.733694\pi$
$251$		−	5.89325e9i		−	1.48477i	0.669972	−	0.742387i	$-0.266306\pi$
$252$		0			0
$253$	3.41308e9			0.833038
$254$	−1.77274e9	−	1.31198e9i	−0.425902	−	0.315205i
$255$		0			0
$256$	1.61152e9	−	3.98117e9i	0.375212	−	0.926939i
$257$	−6.27878e9			−1.43927			−0.719636	−	0.694352i	$-0.755691\pi$
$257$	−6.27878e9			−1.43927			−0.719636	+	0.694352i	$0.755691\pi$
$258$		0			0
$259$			6.72189e9i			1.49380i
$260$	−9.07920e8	−	2.97141e9i	−0.198680	−	0.650233i
$261$		0			0
$262$	−5.62423e9	−	4.16242e9i	−1.19360	−	0.883366i
$263$		−	4.86169e8i		−	0.101616i	−0.998708	−	0.0508082i	$-0.983820\pi$
$263$		−	4.86169e8i		−	0.101616i	0.998708	−	0.0508082i	$-0.0161797\pi$
$264$		0			0
$265$	6.92505e8			0.140423
$266$	3.60255e9	−	4.86774e9i	0.719588	−	0.972301i
$267$		0			0
$268$	3.38445e9	−	1.03413e9i	0.656068	−	0.200463i
$269$	3.48890e9			0.666315			0.333158	−	0.942871i	$-0.391886\pi$
$269$	3.48890e9			0.666315			0.333158	+	0.942871i	$0.391886\pi$
$270$		0			0
$271$		−	1.84408e8i		−	0.0341903i	−0.999854	−	0.0170952i	$-0.994558\pi$
$271$		−	1.84408e8i		−	0.0341903i	0.999854	−	0.0170952i	$-0.00544182\pi$
$272$	−5.77509e9	+	3.89261e9i	−1.05508	+	0.711157i
$273$		0			0
$274$	−2.67038e9	+	3.60819e9i	−0.473773	+	0.640159i
$275$			8.85452e8i			0.154823i
$276$		0			0
$277$	−1.04462e10			−1.77435			−0.887175	−	0.461433i	$-0.847335\pi$
$277$	−1.04462e10			−1.77435			−0.887175	+	0.461433i	$0.847335\pi$
$278$	−7.50605e9	−	5.55513e9i	−1.25670	−	0.930069i
$279$		0			0
$280$	−8.55206e8	+	2.41315e9i	−0.139136	+	0.392602i
$281$	−5.68155e8			−0.0911259			−0.0455629	−	0.998961i	$-0.514508\pi$
$281$	−5.68155e8			−0.0911259			−0.0455629	+	0.998961i	$0.514508\pi$
$282$		0			0
$283$			5.59784e9i			0.872720i	0.899772	+	0.436360i	$0.143733\pi$
$283$			5.59784e9i			0.872720i	−0.899772	+	0.436360i	$0.856267\pi$
$284$	−7.94968e9	+	2.42904e9i	−1.22201	+	0.373389i
$285$		0			0
$286$	−6.32932e9	−	4.68425e9i	−0.946004	−	0.700126i
$287$			3.25361e9i			0.479554i
$288$		0			0
$289$	4.31749e9			0.618928
$290$	3.02258e9	−	4.08409e9i	0.427352	−	0.577435i
$291$		0			0
$292$	2.13930e9	+	7.00141e9i	0.294266	+	0.963062i
$293$	6.86351e8			0.0931270			0.0465635	−	0.998915i	$-0.485173\pi$
$293$	6.86351e8			0.0931270			0.0465635	+	0.998915i	$0.485173\pi$
$294$		0			0
$295$			5.54540e9i			0.732226i
$296$	1.16049e10	+	4.11269e9i	1.51173	+	0.535746i
$297$		0			0
$298$	4.70307e9	−	6.35475e9i	0.596371	−	0.805812i
$299$		−	1.30762e10i		−	1.63605i
$300$		0			0
$301$	4.12093e9			0.502029
$302$	−4.95019e9	−	3.66357e9i	−0.595106	−	0.440430i
$303$		0			0
$304$	−6.19963e9	−	9.19780e9i	−0.725891	−	1.07694i
$305$	6.47094e9			0.747770
$306$		0			0
$307$		−	7.31673e9i		−	0.823690i	−0.911254	−	0.411845i	$-0.864885\pi$
$307$		−	7.31673e9i		−	0.823690i	0.911254	−	0.411845i	$-0.135115\pi$
$308$	1.89600e9	+	6.20517e9i	0.210686	+	0.689527i
$309$		0			0
$310$	5.38628e9	+	3.98632e9i	0.583234	+	0.431644i
$311$		−	2.18806e9i		−	0.233893i	−0.993138	−	0.116946i	$-0.962689\pi$
$311$		−	2.18806e9i		−	0.233893i	0.993138	−	0.116946i	$-0.0373106\pi$
$312$		0			0
$313$	8.81344e9			0.918266			0.459133	−	0.888368i	$-0.348160\pi$
$313$	8.81344e9			0.918266			0.459133	+	0.888368i	$0.348160\pi$
$314$	−6.00942e9	+	8.11989e9i	−0.618179	+	0.835279i
$315$		0			0
$316$	−1.32770e10	+	4.05683e9i	−1.33154	+	0.406854i
$317$	−7.70918e9			−0.763433			−0.381717	−	0.924279i	$-0.624667\pi$
$317$	−7.70918e9			−0.763433			−0.381717	+	0.924279i	$0.624667\pi$
$318$		0			0
$319$		−	1.28766e10i		−	1.24348i
$320$	3.64288e9	+	2.95290e9i	0.347412	+	0.281611i
$321$		0			0
$322$	−6.40985e9	+	8.66093e9i	−0.596244	+	0.805640i
$323$			1.79864e10i			1.65247i
$324$		0			0
$325$	3.39234e9			0.304065
$326$	−1.44099e9	−	1.06646e9i	−0.127583	−	0.0944223i
$327$		0			0
$328$	5.61712e9	+	1.99067e9i	0.485309	+	0.171991i
$329$	−7.23360e9			−0.617406
$330$		0			0
$331$			5.44067e9i			0.453252i	0.973982	+	0.226626i	$0.0727696\pi$
$331$			5.44067e9i			0.453252i	−0.973982	+	0.226626i	$0.927230\pi$
$332$	2.10393e10	−	6.42861e9i	1.73172	−	0.529132i
$333$		0			0
$334$	−4.90162e9	−	3.62762e9i	−0.393870	−	0.291499i
$335$			3.86389e9i			0.306793i
$336$		0			0
$337$	8.83055e9			0.684649			0.342325	−	0.939582i	$-0.388786\pi$
$337$	8.83055e9			0.684649			0.342325	+	0.939582i	$0.388786\pi$
$338$	−1.01820e10	+	1.37578e10i	−0.780126	+	1.05410i
$339$		0			0
$340$	−2.22202e9	−	7.27214e9i	−0.166277	−	0.544185i
$341$	1.69823e10			1.25597
$342$		0			0
$343$			1.46000e10i			1.05481i
$344$	2.52133e9	−	7.11448e9i	0.180051	−	0.508053i
$345$		0			0
$346$	1.42973e10	−	1.93184e10i	0.997586	−	1.34793i
$347$			1.82549e10i			1.25910i	0.776959	+	0.629551i	$0.216761\pi$
$347$			1.82549e10i			1.25910i	−0.776959	+	0.629551i	$0.783239\pi$
$348$		0			0
$349$	2.29945e10			1.54997			0.774984	−	0.631981i	$-0.217758\pi$
$349$	2.29945e10			1.54997			0.774984	+	0.631981i	$0.217758\pi$
$350$	−2.24690e9	−	1.66290e9i	−0.149731	−	0.110814i
$351$		0			0
$352$	1.18728e10	+	5.23231e8i	0.773363	+	0.0340818i
$353$	4.59432e9			0.295885			0.147942	−	0.988996i	$-0.452735\pi$
$353$	4.59432e9			0.295885			0.147942	+	0.988996i	$0.452735\pi$
$354$		0			0
$355$		−	9.07584e9i		−	0.571444i
$356$	3.44550e9	+	1.12763e10i	0.214512	+	0.702047i
$357$		0			0
$358$	−7.54295e8	−	5.58244e8i	−0.0459208	−	0.0339854i
$359$			1.90827e10i			1.14884i	0.818559	+	0.574422i	$0.194773\pi$
$359$			1.90827e10i			1.14884i	−0.818559	+	0.574422i	$0.805227\pi$
$360$		0			0
$361$	−1.16627e10			−0.686706
$362$	−1.48820e10	+	2.01084e10i	−0.866616	+	1.17096i
$363$		0			0
$364$	2.37732e10	−	7.26396e9i	1.35420	−	0.413779i
$365$	−7.99324e9			−0.450351
$366$		0			0
$367$			2.81013e10i			1.54904i	0.632552	+	0.774518i	$0.282008\pi$
$367$			2.81013e10i			1.54904i	−0.632552	+	0.774518i	$0.717992\pi$
$368$	1.10307e10	+	1.63652e10i	0.601467	+	0.892339i
$369$		0			0
$370$	−7.99690e9	+	1.08053e10i	−0.426692	+	0.576543i
$371$			5.54050e9i			0.292451i
$372$		0			0
$373$	−1.05420e10			−0.544612			−0.272306	−	0.962211i	$-0.587786\pi$
$373$	−1.05420e10			−0.544612			−0.272306	+	0.962211i	$0.587786\pi$
$374$	−1.54902e10	−	1.14641e10i	−0.791718	−	0.585941i
$375$		0			0
$376$	−4.42577e9	+	1.24883e10i	−0.221431	+	0.624815i
$377$	−4.93329e10			−2.44215
$378$		0			0
$379$		−	2.33524e10i		−	1.13181i	−0.824470	−	0.565906i	$-0.808527\pi$
$379$		−	2.33524e10i		−	1.13181i	0.824470	−	0.565906i	$-0.191473\pi$
$380$	1.15821e10	−	3.53894e9i	0.555460	−	0.169722i
$381$		0			0
$382$	8.77172e9	+	6.49184e9i	0.411937	+	0.304870i
$383$		−	3.00240e10i		−	1.39532i	−0.716429	−	0.697660i	$-0.754225\pi$
$383$		−	3.00240e10i		−	1.39532i	0.716429	−	0.697660i	$-0.245775\pi$
$384$		0			0
$385$	−7.08420e9			−0.322439
$386$	−1.47123e10	+	1.98791e10i	−0.662721	+	0.895463i
$387$		0			0
$388$	2.37469e9	+	7.77180e9i	0.104780	+	0.342922i
$389$	4.61263e9			0.201442			0.100721	−	0.994915i	$-0.467885\pi$
$389$	4.61263e9			0.201442			0.100721	+	0.994915i	$0.467885\pi$
$390$		0			0
$391$		−	3.20023e10i		−	1.36922i
$392$	2.94951e9	+	1.04529e9i	0.124912	+	0.0442682i
$393$		0			0
$394$	1.33711e8	−	1.80669e8i	0.00554858	−	0.00749720i
$395$		−	1.51579e10i		−	0.622659i
$396$		0			0
$397$	9.18645e8			0.0369816			0.0184908	−	0.999829i	$-0.494114\pi$
$397$	9.18645e8			0.0369816			0.0184908	+	0.999829i	$0.494114\pi$
$398$	3.82067e9	+	2.82763e9i	0.152268	+	0.112691i
$399$		0			0
$400$	−4.24561e9	+	2.86168e9i	−0.165844	+	0.111784i
$401$	3.49056e10			1.34995			0.674975	−	0.737840i	$-0.264154\pi$
$401$	3.49056e10			1.34995			0.674975	+	0.737840i	$0.264154\pi$
$402$		0			0
$403$		−	6.50626e10i		−	2.46667i
$404$	8.85511e9	+	2.89807e10i	0.332406	+	1.08789i
$405$		0			0
$406$	3.26754e10	+	2.41826e10i	1.20259	+	0.890020i
$407$			3.40680e10i			1.24156i
$408$		0			0
$409$	−2.87863e10			−1.02871			−0.514355	−	0.857577i	$-0.671969\pi$
$409$	−2.87863e10			−1.02871			−0.514355	+	0.857577i	$0.671969\pi$
$410$	−3.87075e9	+	5.23013e9i	−0.136981	+	0.185087i
$411$		0			0
$412$	4.54475e9	−	1.38866e9i	0.157733	−	0.0481955i
$413$	−4.43669e10			−1.52496
$414$		0			0
$415$			2.40197e10i			0.809797i
$416$	2.00460e9	−	4.54871e10i	0.0669351	−	1.51885i
$417$		0			0
$418$	1.82585e10	−	2.46707e10i	0.598081	−	0.808122i
$419$			2.41245e10i			0.782714i	0.920239	+	0.391357i	$0.127994\pi$
$419$			2.41245e10i			0.782714i	−0.920239	+	0.391357i	$0.872006\pi$
$420$		0			0
$421$	−4.05366e10			−1.29038			−0.645192	−	0.764021i	$-0.723223\pi$
$421$	−4.05366e10			−1.29038			−0.645192	+	0.764021i	$0.723223\pi$
$422$	−2.56502e10	−	1.89834e10i	−0.808798	−	0.598581i
$423$		0			0
$424$	9.56526e9	+	3.38987e9i	0.295960	+	0.104887i
$425$	8.30232e9			0.254474
$426$		0			0
$427$			5.17718e10i			1.55733i
$428$	−9.51128e9	+	2.90619e9i	−0.283442	+	0.0866063i
$429$		0			0
$430$	6.62433e9	+	4.90258e9i	0.193762	+	0.143401i
$431$			1.52760e10i			0.442691i	0.975195	+	0.221345i	$0.0710448\pi$
$431$			1.52760e10i			0.442691i	−0.975195	+	0.221345i	$0.928955\pi$
$432$		0			0
$433$	−1.50231e9			−0.0427375			−0.0213687	−	0.999772i	$-0.506802\pi$
$433$	−1.50231e9			−0.0427375			−0.0213687	+	0.999772i	$0.506802\pi$
$434$	−3.18932e10	+	4.30938e10i	−0.898957	+	1.21466i
$435$		0			0
$436$	−6.60106e9	−	2.16037e10i	−0.182670	−	0.597836i
$437$	5.09690e10			1.39759
$438$		0			0
$439$		−	4.28905e10i		−	1.15479i	−0.816465	−	0.577395i	$-0.804069\pi$
$439$		−	4.28905e10i		−	1.15479i	0.816465	−	0.577395i	$-0.195931\pi$
$440$	−4.33437e9	+	1.22304e10i	−0.115642	+	0.326309i
$441$		0			0
$442$	−4.39212e10	+	5.93460e10i	−1.15076	+	1.55490i
$443$		−	1.53896e10i		−	0.399587i	−0.979838	−	0.199793i	$-0.935973\pi$
$443$		−	1.53896e10i		−	0.399587i	0.979838	−	0.199793i	$-0.0640271\pi$
$444$		0			0
$445$	−1.28737e10			−0.328294
$446$	−1.12623e10	−	8.33509e9i	−0.284635	−	0.210654i
$447$		0			0
$448$	−2.36252e10	+	2.91455e10i	−0.586493	+	0.723534i
$449$	2.72593e10			0.670701			0.335351	−	0.942093i	$-0.391145\pi$
$449$	2.72593e10			0.670701			0.335351	+	0.942093i	$0.391145\pi$
$450$		0			0
$451$			1.64900e10i			0.398578i
$452$	−3.28032e9	−	1.07357e10i	−0.0785891	−	0.257204i
$453$		0			0
$454$	3.48586e10	+	2.57984e10i	0.820516	+	0.607253i
$455$			2.71410e10i			0.633256i
$456$		0			0
$457$	−6.24394e10			−1.43151			−0.715755	−	0.698352i	$-0.753917\pi$
$457$	−6.24394e10			−1.43151			−0.715755	+	0.698352i	$0.753917\pi$
$458$	1.53535e10	−	2.07455e10i	0.348935	−	0.471478i
$459$		0			0
$460$	−2.06075e10	+	6.29666e9i	−0.460249	+	0.140630i
$461$	−7.86871e10			−1.74221			−0.871103	−	0.491100i	$-0.836595\pi$
$461$	−7.86871e10			−1.74221			−0.871103	+	0.491100i	$0.836595\pi$
$462$		0			0
$463$		−	5.50659e10i		−	1.19828i	−0.800644	−	0.599140i	$-0.795509\pi$
$463$		−	5.50659e10i		−	1.19828i	0.800644	−	0.599140i	$-0.204491\pi$
$464$	6.17415e10	−	4.16159e10i	1.33200	−	0.897815i
$465$		0			0
$466$	−1.92625e10	+	2.60273e10i	−0.408478	+	0.551932i
$467$		−	5.90688e10i		−	1.24191i	−0.783845	−	0.620956i	$-0.786745\pi$
$467$		−	5.90688e10i		−	1.24191i	0.783845	−	0.620956i	$-0.213255\pi$
$468$		0			0
$469$	−3.09137e10			−0.638939
$470$	−1.16279e10	−	8.60567e9i	−0.238292	−	0.176357i
$471$		0			0
$472$	−2.71452e10	+	7.65962e10i	−0.546922	+	1.54326i
$473$	2.08857e10			0.417258
$474$		0			0
$475$			1.32228e10i			0.259747i
$476$	5.81819e10	−	1.77776e10i	1.13334	−	0.346295i
$477$		0			0
$478$	−3.53945e10	−	2.61950e10i	−0.677992	−	0.501773i
$479$		−	5.65594e9i		−	0.107439i	−0.998556	−	0.0537196i	$-0.982892\pi$
$479$		−	5.65594e9i		−	0.107439i	0.998556	−	0.0537196i	$-0.0171077\pi$
$480$		0			0
$481$	1.30521e11			2.43837
$482$	2.06018e9	−	2.78370e9i	0.0381695	−	0.0515743i
$483$		0			0
$484$	−6.42624e9	−	2.10316e10i	−0.117105	−	0.383257i
$485$	−8.87276e9			−0.160358
$486$		0			0
$487$		−	4.46018e10i		−	0.792934i	−0.918049	−	0.396467i	$-0.870236\pi$
$487$		−	4.46018e10i		−	0.792934i	0.918049	−	0.396467i	$-0.129764\pi$
$488$	8.93801e10	+	3.16758e10i	1.57602	+	0.558532i
$489$		0			0
$490$	−2.03251e9	+	2.74630e9i	−0.0352572	+	0.0476392i
$491$			8.46720e9i			0.145685i	0.997343	+	0.0728423i	$0.0232070\pi$
$491$			8.46720e9i			0.145685i	−0.997343	+	0.0728423i	$0.976793\pi$
$492$		0			0
$493$	−1.20736e11			−2.04385
$494$	−9.45183e10	−	6.99518e10i	−1.58711	−	1.17460i
$495$		0			0
$496$	5.48849e10	+	8.14276e10i	0.906831	+	1.34538i
$497$	7.26127e10			1.19011
$498$		0			0
$499$		−	9.22277e10i		−	1.48751i	−0.668453	−	0.743754i	$-0.733043\pi$
$499$		−	9.22277e10i		−	1.48751i	0.668453	−	0.743754i	$-0.266957\pi$
$500$	−1.63354e9	−	5.34617e9i	−0.0261366	−	0.0855388i
$501$		0			0
$502$	7.57927e10	+	5.60932e10i	1.19347	+	0.883274i
$503$		−	5.31873e9i		−	0.0830876i	−0.999137	−	0.0415438i	$-0.986772\pi$
$503$		−	5.31873e9i		−	0.0830876i	0.999137	−	0.0415438i	$-0.0132276\pi$
$504$		0			0
$505$	−3.30861e10			−0.508722
$506$	−3.24864e10	+	4.38954e10i	−0.495564	+	0.669603i
$507$		0			0
$508$	3.37466e10	−	1.03114e10i	0.506729	−	0.154832i
$509$	−6.32110e9			−0.0941720			−0.0470860	−	0.998891i	$-0.514993\pi$
$509$	−6.32110e9			−0.0941720			−0.0470860	+	0.998891i	$0.514993\pi$
$510$		0			0
$511$		−	6.39511e10i		−	0.937918i
$512$	3.58628e10	+	5.86193e10i	0.521872	+	0.853024i
$513$		0			0
$514$	5.97628e10	−	8.07509e10i	0.856206	−	1.15690i
$515$			5.18856e9i			0.0737596i
$516$		0			0
$517$	−3.66614e10			−0.513153
$518$	−8.64498e10	−	6.39804e10i	−1.20073	−	0.888645i
$519$		0			0
$520$	4.68569e10	+	1.66058e10i	0.640855	+	0.227115i
$521$	−2.88982e10			−0.392211			−0.196106	−	0.980583i	$-0.562830\pi$
$521$	−2.88982e10			−0.392211			−0.196106	+	0.980583i	$0.562830\pi$
$522$		0			0
$523$		−	6.89381e10i		−	0.921409i	−0.887554	−	0.460704i	$-0.847597\pi$
$523$		−	6.89381e10i		−	0.921409i	0.887554	−	0.460704i	$-0.152403\pi$
$524$	1.07065e11	−	3.27140e10i	1.42011	−	0.433919i
$525$		0			0
$526$	6.25259e9	+	4.62746e9i	0.0816802	+	0.0604505i
$527$		−	1.59232e11i		−	2.06438i
$528$		0			0
$529$	−1.23756e10			−0.158032
$530$	−6.59141e9	+	8.90626e9i	−0.0835363	+	0.112874i
$531$		0			0
$532$	2.83138e10	+	9.26644e10i	0.353469	+	1.15682i
$533$	6.31763e10			0.782790
$534$		0			0
$535$		−	1.08587e10i		−	0.132544i
$536$	−1.89141e10	+	5.33702e10i	−0.229153	+	0.646606i
$537$		0			0
$538$	−3.32081e10	+	4.48705e10i	−0.396383	+	0.535590i
$539$			8.65877e9i			0.102589i
$540$		0			0
$541$	−7.10155e10			−0.829018			−0.414509	−	0.910045i	$-0.636047\pi$
$541$	−7.10155e10			−0.829018			−0.414509	+	0.910045i	$0.636047\pi$
$542$	2.37166e9	+	1.75524e9i	0.0274825	+	0.0203394i
$543$		0			0
$544$	4.90600e9	−	1.11324e11i	0.0560186	−	1.27114i
$545$	2.46641e10			0.279563
$546$		0			0
$547$			1.29035e11i			1.44131i	0.693294	+	0.720654i	$0.256159\pi$
$547$			1.29035e11i			1.44131i	−0.693294	+	0.720654i	$0.743841\pi$
$548$	−2.09875e10	−	6.86871e10i	−0.232723	−	0.761646i
$549$		0			0
$550$	−1.13877e10	−	8.42793e9i	−0.124448	−	0.0921022i
$551$		−	1.92292e11i		−	2.08620i
$552$		0			0
$553$	1.21273e11			1.29677
$554$	9.94292e10	−	1.34348e11i	1.05554	−	1.42624i
$555$		0			0
$556$	1.42888e11	−	4.36599e10i	1.49519	−	0.456860i
$557$	1.02270e11			1.06250			0.531248	−	0.847216i	$-0.321723\pi$
$557$	1.02270e11			1.06250			0.531248	+	0.847216i	$0.321723\pi$
$558$		0			0
$559$		−	8.00173e10i		−	0.819476i
$560$	−2.28953e10	−	3.39676e10i	−0.232806	−	0.345393i
$561$		0			0
$562$	5.40782e9	−	7.30701e9i	0.0542097	−	0.0732477i
$563$			3.13822e10i			0.312356i	0.987729	+	0.156178i	$0.0499173\pi$
$563$			3.13822e10i			0.312356i	−0.987729	+	0.156178i	$0.950083\pi$
$564$		0			0
$565$	1.22565e10			0.120275
$566$	−7.19935e10	−	5.32815e10i	−0.701500	−	0.519171i
$567$		0			0
$568$	4.44270e10	−	1.25361e11i	0.426829	−	1.20439i
$569$	−5.63583e10			−0.537661			−0.268831	−	0.963187i	$-0.586637\pi$
$569$	−5.63583e10			−0.537661			−0.268831	+	0.963187i	$0.586637\pi$
$570$		0			0
$571$			1.11882e10i			0.105249i	0.998614	+	0.0526243i	$0.0167586\pi$
$571$			1.11882e10i			0.105249i	−0.998614	+	0.0526243i	$0.983241\pi$
$572$	1.20488e11	−	3.68153e10i	1.12553	−	0.343909i
$573$		0			0
$574$	−4.18445e10	−	3.09686e10i	−0.385470	−	0.285281i
$575$		−	2.35267e10i		−	0.215224i
$576$		0			0
$577$	−8.67948e10			−0.783051			−0.391526	−	0.920167i	$-0.628053\pi$
$577$	−8.67948e10			−0.783051			−0.391526	+	0.920167i	$0.628053\pi$
$578$	−4.10948e10	+	5.55269e10i	−0.368193	+	0.497499i
$579$		0			0
$580$	2.37556e10	+	7.77464e10i	0.209920	+	0.687019i
$581$	−1.92174e11			−1.68651
$582$		0			0
$583$			2.80804e10i			0.243069i
$584$	−1.10407e11	−	3.91276e10i	−0.949172	−	0.336381i
$585$		0			0
$586$	−6.53284e9	+	8.82711e9i	−0.0554002	+	0.0748563i
$587$			2.73633e10i			0.230471i	0.993338	+	0.115236i	$0.0367623\pi$
$587$			2.73633e10i			0.230471i	−0.993338	+	0.115236i	$0.963238\pi$
$588$		0			0
$589$	2.53604e11			2.10715
$590$	−7.13191e10	−	5.27823e10i	−0.588569	−	0.435593i
$591$		0			0
$592$	−1.63351e11	+	1.10104e11i	−1.32995	+	0.896428i
$593$	−1.70522e11			−1.37900			−0.689498	−	0.724288i	$-0.742169\pi$
$593$	−1.70522e11			−1.37900			−0.689498	+	0.724288i	$0.742169\pi$
$594$		0			0
$595$			6.64240e10i			0.529977i
$596$	3.69632e10	+	1.20972e11i	0.292944	+	0.958736i
$597$		0			0
$598$	1.68172e11	+	1.24462e11i	1.31507	+	0.973266i
$599$		−	5.31294e10i		−	0.412693i	−0.978479	−	0.206347i	$-0.933843\pi$
$599$		−	5.31294e10i		−	0.412693i	0.978479	−	0.206347i	$-0.0661575\pi$
$600$		0			0
$601$	−1.01471e11			−0.777758			−0.388879	−	0.921289i	$-0.627138\pi$
$601$	−1.01471e11			−0.777758			−0.388879	+	0.921289i	$0.627138\pi$
$602$	−3.92239e10	+	5.29990e10i	−0.298651	+	0.403535i
$603$		0			0
$604$	9.42340e10	−	2.87934e10i	0.708043	−	0.216344i
$605$	2.40109e10			0.179220
$606$		0			0
$607$			1.69027e11i			1.24509i	0.782583	+	0.622546i	$0.213902\pi$
$607$			1.69027e11i			1.24509i	−0.782583	+	0.622546i	$0.786098\pi$
$608$	1.77302e11	+	7.81362e9i	1.29747	+	0.0571792i
$609$		0			0
$610$	−6.15918e10	+	8.32223e10i	−0.444839	+	0.601064i
$611$			1.40457e11i			1.00781i
$612$		0			0
$613$	1.29478e11			0.916970			0.458485	−	0.888702i	$-0.348392\pi$
$613$	1.29478e11			0.916970			0.458485	+	0.888702i	$0.348392\pi$
$614$	9.41000e10	+	6.96422e10i	0.662089	+	0.490004i
$615$		0			0
$616$	−9.78509e10	−	3.46778e10i	−0.679582	−	0.240840i
$617$	−5.03702e10			−0.347563			−0.173781	−	0.984784i	$-0.555599\pi$
$617$	−5.03702e10			−0.347563			−0.173781	+	0.984784i	$0.555599\pi$
$618$		0			0
$619$		−	1.98244e11i		−	1.35032i	−0.737669	−	0.675162i	$-0.764074\pi$
$619$		−	1.98244e11i		−	1.35032i	0.737669	−	0.675162i	$-0.235926\pi$
$620$	−1.02536e11	+	3.13300e10i	−0.693918	+	0.212028i
$621$		0			0
$622$	2.81404e10	+	2.08264e10i	0.188005	+	0.139140i
$623$		−	1.02998e11i		−	0.683718i
$624$		0			0
$625$	6.10352e9			0.0400000
$626$	−8.38882e10	+	1.13349e11i	−0.546266	+	0.738110i
$627$		0			0
$628$	−4.72303e10	−	1.54574e11i	−0.303656	−	0.993795i
$629$	3.19433e11			2.04069
$630$		0			0
$631$		−	1.46853e11i		−	0.926326i	−0.886273	−	0.463163i	$-0.846714\pi$
$631$		−	1.46853e11i		−	0.926326i	0.886273	−	0.463163i	$-0.153286\pi$
$632$	7.41991e10	−	2.09369e11i	0.465083	−	1.31233i
$633$		0			0
$634$	7.33776e10	−	9.91472e10i	0.454158	−	0.613654i
$635$			3.85272e10i			0.236959i
$636$		0			0
$637$	3.31734e10			0.201480
$638$	1.65606e11	+	1.22563e11i	0.999522	+	0.739734i
$639$		0			0
$640$	−7.26508e10	+	1.87445e10i	−0.433033	+	0.111726i
$641$	9.36531e10			0.554741			0.277370	−	0.960763i	$-0.410537\pi$
$641$	9.36531e10			0.554741			0.277370	+	0.960763i	$0.410537\pi$
$642$		0			0
$643$		−	2.03358e11i		−	1.18964i	−0.803858	−	0.594821i	$-0.797223\pi$
$643$		−	2.03358e11i		−	1.18964i	0.803858	−	0.594821i	$-0.202777\pi$
$644$	−5.03774e10	−	1.64873e11i	−0.292882	−	0.958532i
$645$		0			0
$646$	−2.31322e11	−	1.71198e11i	−1.32827	−	0.983035i
$647$			1.34649e11i			0.768396i	0.923251	+	0.384198i	$0.125522\pi$
$647$			1.34649e11i			0.768396i	−0.923251	+	0.384198i	$0.874478\pi$
$648$		0			0
$649$	−2.24861e11			−1.26746
$650$	−3.22890e10	+	4.36287e10i	−0.180885	+	0.244410i
$651$		0			0
$652$	2.74314e10	−	8.38172e9i	0.151795	−	0.0463813i
$653$	1.33413e11			0.733747			0.366874	−	0.930271i	$-0.380428\pi$
$653$	1.33413e11			0.733747			0.366874	+	0.930271i	$0.380428\pi$
$654$		0			0
$655$			1.22232e11i			0.664080i
$656$	−7.90669e10	+	5.32937e10i	−0.426952	+	0.287780i
$657$		0			0
$658$	6.88510e10	−	9.30309e10i	0.367288	−	0.496276i
$659$			3.07029e11i			1.62794i	0.580909	+	0.813969i	$0.302697\pi$
$659$			3.07029e11i			1.62794i	−0.580909	+	0.813969i	$0.697303\pi$
$660$		0			0
$661$	−4.04970e10			−0.212137			−0.106069	−	0.994359i	$-0.533826\pi$
$661$	−4.04970e10			−0.212137			−0.106069	+	0.994359i	$0.533826\pi$
$662$	−6.99721e10	−	5.17854e10i	−0.364328	−	0.269635i
$663$		0			0
$664$	−1.17579e11	+	3.31774e11i	−0.604862	+	1.70675i
$665$	−1.05791e11			−0.540958
$666$		0			0
$667$			3.42136e11i			1.72861i
$668$	9.33093e10	−	2.85109e10i	0.468618	−	0.143187i
$669$		0			0
$670$	−4.96933e10	−	3.67774e10i	−0.246603	−	0.182508i
$671$			2.62390e11i			1.29437i
$672$		0			0
$673$	1.36014e10			0.0663016			0.0331508	−	0.999450i	$-0.489446\pi$
$673$	1.36014e10			0.0663016			0.0331508	+	0.999450i	$0.489446\pi$
$674$	−8.40511e10	+	1.13569e11i	−0.407290	+	0.550327i
$675$		0			0
$676$	−8.00239e10	−	2.61899e11i	−0.383207	−	1.25414i
$677$	1.81509e11			0.864060			0.432030	−	0.901859i	$-0.357798\pi$
$677$	1.81509e11			0.864060			0.432030	+	0.901859i	$0.357798\pi$
$678$		0			0
$679$		−	7.09879e10i		−	0.333968i
$680$	1.14676e11	+	4.06406e10i	0.536337	+	0.190075i
$681$		0			0
$682$	−1.61641e11	+	2.18409e11i	−0.747162	+	1.00956i
$683$		−	7.87512e10i		−	0.361888i	−0.983493	−	0.180944i	$-0.942085\pi$
$683$		−	7.87512e10i		−	0.361888i	0.983493	−	0.180944i	$-0.0579153\pi$
$684$		0			0
$685$	7.84174e10			0.356164
$686$	−1.87770e11	−	1.38966e11i	−0.847869	−	0.627497i
$687$		0			0
$688$	6.75003e10	+	1.00144e11i	0.301267	+	0.446962i
$689$	1.07581e11			0.477376
$690$		0			0
$691$			2.28485e11i			1.00218i	0.865396	+	0.501089i	$0.167067\pi$
$691$			2.28485e11i			1.00218i	−0.865396	+	0.501089i	$0.832933\pi$
$692$	1.12368e11	+	3.67754e11i	0.490025	+	1.60374i
$693$		0			0
$694$	−2.34775e11	−	1.73754e11i	−1.01208	−	0.749025i
$695$			1.63130e11i			0.699189i
$696$		0			0
$697$	1.54616e11			0.655123
$698$	−2.18867e11	+	2.95731e11i	−0.922058	+	1.24588i
$699$		0			0
$700$	4.27729e10	−	1.30694e10i	0.178146	−	0.0544330i
$701$	−3.61506e11			−1.49708			−0.748538	−	0.663092i	$-0.769244\pi$
$701$	−3.61506e11			−1.49708			−0.748538	+	0.663092i	$0.769244\pi$
$702$		0			0
$703$			5.08751e11i			2.08297i
$704$	−1.19737e11	+	1.47715e11i	−0.487460	+	0.601360i
$705$		0			0
$706$	−4.37297e10	+	5.90872e10i	−0.176018	+	0.237835i
$707$		−	2.64711e11i		−	1.05948i
$708$		0			0
$709$	4.37939e11			1.73312			0.866560	−	0.499073i	$-0.166326\pi$
$709$	4.37939e11			1.73312			0.866560	+	0.499073i	$0.166326\pi$
$710$	1.16724e11	+	8.63858e10i	0.459331	+	0.339945i
$711$		0			0
$712$	−1.77819e11	−	6.30179e10i	−0.691922	−	0.245213i
$713$	−4.51225e11			−1.74596
$714$		0			0
$715$			1.37556e11i			0.526327i
$716$	1.43591e10	−	4.38745e9i	0.0546354	−	0.0166940i
$717$		0			0
$718$	−2.45421e11	−	1.81633e11i	−0.923451	−	0.683435i
$719$			3.80190e11i			1.42261i	0.702885	+	0.711304i	$0.251895\pi$
$719$			3.80190e11i			1.42261i	−0.702885	+	0.711304i	$0.748105\pi$
$720$		0			0
$721$	−4.15119e10			−0.153614
$722$	1.11008e11	−	1.49993e11i	0.408514	−	0.551980i
$723$		0			0
$724$	−1.16963e11	−	3.82793e11i	−0.425691	−	1.39319i
$725$	−8.87601e10			−0.321267
$726$		0			0
$727$			3.48752e11i			1.24847i	0.781235	+	0.624236i	$0.214590\pi$
$727$			3.48752e11i			1.24847i	−0.781235	+	0.624236i	$0.785410\pi$
$728$	−1.32857e11	+	3.74886e11i	−0.472999	+	1.33467i
$729$		0			0
$730$	7.60813e10	−	1.02800e11i	0.267909	−	0.361996i
$731$		−	1.95832e11i		−	0.685827i
$732$		0			0
$733$	−2.14531e11			−0.743147			−0.371574	−	0.928403i	$-0.621182\pi$
$733$	−2.14531e11			−0.743147			−0.371574	+	0.928403i	$0.621182\pi$
$734$	−3.61408e11	−	2.67474e11i	−1.24513	−	0.921504i
$735$		0			0
$736$	−3.15464e11	−	1.39024e10i	−1.07508	−	0.0473782i
$737$	−1.56677e11			−0.531050
$738$		0			0
$739$		−	1.23753e11i		−	0.414932i	−0.978242	−	0.207466i	$-0.933478\pi$
$739$		−	1.23753e11i		−	0.414932i	0.978242	−	0.207466i	$-0.0665217\pi$
$740$	−6.28506e10	−	2.05695e11i	−0.209596	−	0.685957i
$741$		0			0
$742$	−7.12560e10	−	5.27356e10i	−0.235075	−	0.173976i
$743$		−	5.66350e11i		−	1.85836i	−0.369629	−	0.929180i	$-0.620515\pi$
$743$		−	5.66350e11i		−	1.85836i	0.369629	−	0.929180i	$-0.379485\pi$
$744$		0			0
$745$	−1.38109e11			−0.448328
$746$	1.00341e11	−	1.35580e11i	0.323983	−	0.437763i
$747$		0			0
$748$	2.94878e11	−	9.01007e10i	0.941968	−	0.287820i
$749$	8.68764e10			0.276042
$750$		0			0
$751$			5.84382e10i			0.183712i	0.995772	+	0.0918559i	$0.0292799\pi$
$751$			5.84382e10i			0.183712i	−0.995772	+	0.0918559i	$0.970720\pi$
$752$	−1.18486e11	−	1.75786e11i	−0.370505	−	0.549683i
$753$		0			0
$754$	4.69561e11	−	6.34467e11i	1.45280	−	1.96302i
$755$			1.07583e11i			0.331098i
$756$		0			0
$757$	−3.58426e11			−1.09148			−0.545740	−	0.837955i	$-0.683751\pi$
$757$	−3.58426e11			−1.09148			−0.545740	+	0.837955i	$0.683751\pi$
$758$	3.00333e11	+	2.22273e11i	0.909759	+	0.673301i
$759$		0			0
$760$	−6.47268e10	+	1.82641e11i	−0.194013	+	0.547449i
$761$	1.00991e10			0.0301123			0.0150562	−	0.999887i	$-0.495207\pi$
$761$	1.00991e10			0.0301123			0.0150562	+	0.999887i	$0.495207\pi$
$762$		0			0
$763$			1.97329e11i			0.582228i
$764$	−1.66982e11	+	5.10218e10i	−0.490114	+	0.149755i
$765$		0			0
$766$	3.86137e11	+	2.85775e11i	1.12157	+	0.830059i
$767$			8.61485e11i			2.48924i
$768$		0			0
$769$	−1.89952e11			−0.543173			−0.271587	−	0.962414i	$-0.587548\pi$
$769$	−1.89952e11			−0.543173			−0.271587	+	0.962414i	$0.587548\pi$
$770$	6.74290e10	−	9.11095e10i	0.191815	−	0.259179i
$771$		0			0
$772$	−1.15629e11	−	3.78427e11i	−0.325536	−	1.06540i
$773$	−2.78331e10			−0.0779550			−0.0389775	−	0.999240i	$-0.512410\pi$
$773$	−2.78331e10			−0.0779550			−0.0389775	+	0.999240i	$0.512410\pi$
$774$		0			0
$775$		−	1.17061e11i		−	0.324493i
$776$	−1.22555e11	−	4.34329e10i	−0.337976	−	0.119777i
$777$		0			0
$778$	−4.39040e10	+	5.93228e10i	−0.119836	+	0.161921i
$779$			2.46252e11i			0.668697i
$780$		0			0
$781$	3.68016e11			0.989152
$782$	4.11579e11	+	3.04605e11i	1.10059	+	0.814534i
$783$		0			0
$784$	−4.15175e10	+	2.79842e10i	−0.109892	+	0.0740710i
$785$	1.76471e11			0.464723
$786$		0			0
$787$			1.06011e11i			0.276344i	0.990408	+	0.138172i	$0.0441227\pi$
$787$			1.06011e11i			0.276344i	−0.990408	+	0.138172i	$0.955877\pi$
$788$	1.05088e9	+	3.43930e9i	0.00272552	+	0.00892000i
$789$		0			0
$790$	1.94944e11	+	1.44276e11i	0.500498	+	0.370412i
$791$			9.80604e10i			0.250488i
$792$		0			0
$793$	1.00527e12			2.54208
$794$	−8.74386e9	+	1.18146e10i	−0.0219999	+	0.0297261i
$795$		0			0
$796$	−7.27319e10	+	2.22234e10i	−0.181164	+	0.0553552i
$797$	−3.80945e11			−0.944125			−0.472062	−	0.881565i	$-0.656490\pi$
$797$	−3.80945e11			−0.944125			−0.472062	+	0.881565i	$0.656490\pi$
$798$		0			0
$799$			3.43751e11i			0.843444i
$800$	3.60668e9	−	8.18406e10i	0.00880538	−	0.199806i
$801$		0			0
$802$	−3.32239e11	+	4.48919e11i	−0.803070	+	1.08510i
$803$		−	3.24118e11i		−	0.779544i
$804$		0			0
$805$	1.88229e11			0.448233
$806$	8.36765e11	+	6.19279e11i	1.98273	+	1.46739i
$807$		0			0
$808$	−4.57003e11	−	1.61959e11i	−1.07220	−	0.379980i
$809$	4.11319e11			0.960251			0.480125	−	0.877200i	$-0.340591\pi$
$809$	4.11319e11			0.960251			0.480125	+	0.877200i	$0.340591\pi$
$810$		0			0
$811$		−	4.23775e10i		−	0.0979608i	−0.998800	−	0.0489804i	$-0.984403\pi$
$811$		−	4.23775e10i		−	0.0979608i	0.998800	−	0.0489804i	$-0.0155972\pi$
$812$	−6.22023e11	+	1.90060e11i	−1.43081	+	0.437187i
$813$		0			0
$814$	−4.38146e11	−	3.24266e11i	−0.997978	−	0.738591i
$815$			3.13173e10i			0.0709830i
$816$		0			0
$817$	3.11895e11			0.700036
$818$	2.73995e11	−	3.70219e11i	0.611968	−	0.826886i
$819$		0			0
$820$	−3.04217e10	−	9.95629e10i	−0.0672865	−	0.220213i
$821$	3.94688e11			0.868723			0.434361	−	0.900739i	$-0.356974\pi$
$821$	3.94688e11			0.868723			0.434361	+	0.900739i	$0.356974\pi$
$822$		0			0
$823$		−	8.07264e11i		−	1.75961i	−0.475335	−	0.879805i	$-0.657673\pi$
$823$		−	8.07264e11i		−	1.75961i	0.475335	−	0.879805i	$-0.342327\pi$
$824$	−2.53985e10	+	7.16673e10i	−0.0550933	+	0.155458i
$825$		0			0
$826$	4.22293e11	−	5.70600e11i	0.907181	−	1.22578i
$827$		−	3.75714e11i		−	0.803222i	−0.915810	−	0.401611i	$-0.868450\pi$
$827$		−	3.75714e11i		−	0.803222i	0.915810	−	0.401611i	$-0.131550\pi$
$828$		0			0
$829$	5.28969e11			1.11999			0.559993	−	0.828497i	$-0.310804\pi$
$829$	5.28969e11			1.11999			0.559993	+	0.828497i	$0.310804\pi$
$830$	−3.08916e11	−	2.28625e11i	−0.650921	−	0.481739i
$831$		0			0
$832$	5.65926e11	+	4.58737e11i	1.18104	+	0.957349i
$833$	8.11878e10			0.168621
$834$		0			0
$835$			1.06528e11i			0.219137i
$836$	1.43500e11	+	4.69642e11i	0.293784	+	0.961484i
$837$		0			0
$838$	−3.10264e11	−	2.29622e11i	−0.629152	−	0.465627i
$839$		−	7.36830e11i		−	1.48703i	−0.668719	−	0.743515i	$-0.733157\pi$
$839$		−	7.36830e11i		−	1.48703i	0.668719	−	0.743515i	$-0.266843\pi$
$840$		0			0
$841$	7.90542e11			1.58031
$842$	3.85836e11	−	5.21338e11i	0.767634	−	1.03722i
$843$		0			0
$844$	4.88287e11	−	1.49197e11i	0.962289	−	0.294030i
$845$	2.99000e11			0.586468
$846$		0			0
$847$			1.92103e11i			0.373251i
$848$	−1.34641e11	+	9.07527e10i	−0.260372	+	0.175500i
$849$		0			0
$850$	−7.90233e10	+	1.06776e11i	−0.151384	+	0.204548i
$851$		−	9.05196e11i		−	1.72593i
$852$		0			0
$853$	−1.74426e11			−0.329470			−0.164735	−	0.986338i	$-0.552677\pi$
$853$	−1.74426e11			−0.329470			−0.164735	+	0.986338i	$0.552677\pi$
$854$	−6.65833e11	−	4.92775e11i	−1.25180	−	0.926439i
$855$		0			0
$856$	5.31540e10	−	1.49986e11i	0.0990014	−	0.279354i
$857$	−4.27600e11			−0.792710			−0.396355	−	0.918097i	$-0.629725\pi$
$857$	−4.27600e11			−0.792710			−0.396355	+	0.918097i	$0.629725\pi$
$858$		0			0
$859$			4.34905e11i			0.798771i	0.916783	+	0.399385i	$0.130776\pi$
$859$			4.34905e11i			0.798771i	−0.916783	+	0.399385i	$0.869224\pi$
$860$	−1.26104e11	+	3.85312e10i	−0.230533	+	0.0704399i
$861$		0			0
$862$	−1.96464e11	−	1.45400e11i	−0.355838	−	0.263352i
$863$			9.81164e11i			1.76888i	0.466654	+	0.884440i	$0.345459\pi$
$863$			9.81164e11i			1.76888i	−0.466654	+	0.884440i	$0.654541\pi$
$864$		0			0
$865$	−4.19850e11			−0.749946
$866$	1.42993e10	−	1.93211e10i	0.0254240	−	0.0343527i
$867$		0			0
$868$	−2.50661e11	−	8.20352e11i	−0.441578	−	1.44518i
$869$	6.14637e11			1.07780
$870$		0			0
$871$			6.00260e11i			1.04296i
$872$	3.40674e11	+	1.20733e11i	0.589214	+	0.208814i
$873$		0			0
$874$	−4.85133e11	+	6.55508e11i	−0.831410	+	1.12339i
$875$			4.88321e10i			0.0833055i
$876$		0			0
$877$	5.03195e10			0.0850625			0.0425313	−	0.999095i	$-0.486458\pi$
$877$	5.03195e10			0.0850625			0.0425313	+	0.999095i	$0.486458\pi$
$878$	5.51612e11	+	4.08241e11i	0.928230	+	0.686972i
$879$		0			0
$880$	−1.16038e11	−	1.72155e11i	−0.193496	−	0.287071i
$881$	−3.73120e10			−0.0619362			−0.0309681	−	0.999520i	$-0.509859\pi$
$881$	−3.73120e10			−0.0619362			−0.0309681	+	0.999520i	$0.509859\pi$
$882$		0			0
$883$		−	8.62541e10i		−	0.141885i	−0.997480	−	0.0709426i	$-0.977399\pi$
$883$		−	8.62541e10i		−	0.141885i	0.997480	−	0.0709426i	$-0.0226007\pi$
$884$	−3.45193e11	−	1.12974e12i	−0.565266	−	1.84998i
$885$		0			0
$886$	1.97924e11	+	1.46481e11i	0.321191	+	0.237710i
$887$		−	6.97464e11i		−	1.12675i	−0.826201	−	0.563375i	$-0.809503\pi$
$887$		−	6.97464e11i		−	1.12675i	0.826201	−	0.563375i	$-0.190497\pi$
$888$		0			0
$889$	−3.08243e11			−0.493499
$890$	1.22535e11	−	1.65568e11i	0.195299	−	0.263886i
$891$		0			0
$892$	2.14394e11	−	6.55086e10i	0.338652	−	0.103476i
$893$	−5.47480e11			−0.860919
$894$		0			0
$895$			1.63932e10i			0.0255489i
$896$	−1.49969e11	−	5.81254e11i	−0.232685	−	0.901850i
$897$		0			0
$898$	−2.59460e11	+	3.50580e11i	−0.398992	+	0.539115i
$899$			1.70235e12i			2.60622i
$900$		0			0
$901$	2.63292e11			0.399520
$902$	−2.12076e11	−	1.56955e11i	−0.320381	−	0.237110i
$903$		0			0
$904$	1.69294e11	+	5.99968e10i	0.253494	+	0.0898368i
$905$	4.37019e11			0.651488
$906$		0			0
$907$		−	1.14603e12i		−	1.69343i	−0.532045	−	0.846716i	$-0.678576\pi$
$907$		−	1.14603e12i		−	1.69343i	0.532045	−	0.846716i	$-0.321424\pi$
$908$	−6.63584e11	+	2.02760e11i	−0.976231	+	0.298289i
$909$		0			0
$910$	−3.49058e11	−	2.58333e11i	−0.509017	−	0.376717i
$911$		−	1.19150e12i		−	1.72989i	−0.501863	−	0.864947i	$-0.667352\pi$
$911$		−	1.19150e12i		−	1.72989i	0.501863	−	0.864947i	$-0.332648\pi$
$912$		0			0
$913$	−9.73977e11			−1.40173
$914$	5.94312e11	−	8.03029e11i	0.851588	−	1.15066i
$915$		0			0
$916$	1.20669e11	+	3.94919e11i	0.171401	+	0.560953i
$917$	−9.77938e11			−1.38304
$918$		0			0
$919$		−	1.38895e11i		−	0.194726i	−0.995249	−	0.0973629i	$-0.968959\pi$
$919$		−	1.38895e11i		−	0.194726i	0.995249	−	0.0973629i	$-0.0310407\pi$
$920$	1.15165e11	−	3.24964e11i	0.160757	−	0.453612i
$921$		0			0
$922$	7.48960e11	−	1.01199e12i	1.03642	−	1.40040i
$923$		−	1.40994e12i		−	1.94265i
$924$		0			0
$925$	2.34834e11			0.320770
$926$	7.08198e11	+	5.24129e11i	0.963188	+	0.712843i
$927$		0			0
$928$	−5.24500e10	+	1.19016e12i	−0.0707219	+	1.60478i
$929$	−7.82376e10			−0.105040			−0.0525198	−	0.998620i	$-0.516725\pi$
$929$	−7.82376e10			−0.105040			−0.0525198	+	0.998620i	$0.516725\pi$
$930$		0			0
$931$			1.29305e11i			0.172114i
$932$	−1.51391e11	−	4.95467e11i	−0.200649	−	0.656676i
$933$		0			0
$934$	7.59680e11	+	5.62230e11i	0.998259	+	0.738799i
$935$			3.36651e11i			0.440487i
$936$		0			0
$937$	−1.86421e11			−0.241845			−0.120923	−	0.992662i	$-0.538585\pi$
$937$	−1.86421e11			−0.241845			−0.120923	+	0.992662i	$0.538585\pi$
$938$	2.94243e11	−	3.97579e11i	0.380098	−	0.513585i
$939$		0			0
$940$	2.21354e11	−	6.76352e10i	0.283515	−	0.0866286i
$941$	9.61073e11			1.22574			0.612870	−	0.790184i	$-0.290015\pi$
$941$	9.61073e11			1.22574			0.612870	+	0.790184i	$0.290015\pi$
$942$		0			0
$943$		−	4.38143e11i		−	0.554076i
$944$	−7.26724e11	−	1.07817e12i	−0.915127	−	1.35769i
$945$		0			0
$946$	−1.98795e11	+	2.68610e11i	−0.248222	+	0.335396i
$947$		−	2.98039e11i		−	0.370573i	−0.982685	−	0.185286i	$-0.940679\pi$
$947$		−	2.98039e11i		−	0.370573i	0.982685	−	0.185286i	$-0.0593212\pi$
$948$		0			0
$949$	−1.24176e12			−1.53099
$950$	−1.70058e11	−	1.25858e11i	−0.208786	−	0.154520i
$951$		0			0
$952$	−3.25151e11	+	9.17485e11i	−0.395856	+	1.11699i
$953$	3.08302e11			0.373770			0.186885	−	0.982382i	$-0.440161\pi$
$953$	3.08302e11			0.373770			0.186885	+	0.982382i	$0.440161\pi$
$954$		0			0
$955$		−	1.90637e11i		−	0.229189i
$956$	6.73785e11	−	2.05877e11i	0.806659	−	0.246476i
$957$		0			0
$958$	7.27406e10	+	5.38344e10i	0.0863605	+	0.0639143i
$959$			6.27391e11i			0.741761i
$960$		0			0
$961$	−1.39225e12			−1.63239
$962$	−1.24233e12	+	1.67862e12i	−1.45056	+	1.95998i
$963$		0			0
$964$	1.61917e10	+	5.29916e10i	0.0187493	+	0.0613620i
$965$	4.32036e11			0.498207
$966$		0			0
$967$			1.51625e12i			1.73407i	0.498249	+	0.867034i	$0.333977\pi$
$967$			1.51625e12i			1.73407i	−0.498249	+	0.867034i	$0.666023\pi$
$968$	3.31652e11	+	1.17535e11i	0.377730	+	0.133865i
$969$		0			0
$970$	8.44528e10	−	1.14112e11i	0.0953954	−	0.128897i
$971$		−	5.09948e11i		−	0.573653i	−0.957983	−	0.286826i	$-0.907400\pi$
$971$		−	5.09948e11i		−	0.573653i	0.957983	−	0.286826i	$-0.0926003\pi$
$972$		0			0
$973$	−1.30515e12			−1.45616
$974$	5.73621e11	+	4.24530e11i	0.637367	+	0.471707i
$975$		0			0
$976$	−1.25812e12	+	8.48015e11i	−1.38651	+	0.934554i
$977$	5.25454e11			0.576708			0.288354	−	0.957524i	$-0.406892\pi$
$977$	5.25454e11			0.576708			0.288354	+	0.957524i	$0.406892\pi$
$978$		0			0
$979$		−	5.22016e11i		−	0.568268i
$980$	−1.59742e10	−	5.22798e10i	−0.0173187	−	0.0566800i
$981$		0			0
$982$	−1.08896e11	−	8.05926e10i	−0.117103	−	0.0866661i
$983$		−	1.57970e12i		−	1.69184i	−0.533306	−	0.845922i	$-0.679051\pi$
$983$		−	1.57970e12i		−	1.69184i	0.533306	−	0.845922i	$-0.320949\pi$
$984$		0			0
$985$	−3.92651e9			−0.00417121
$986$	1.14919e12	−	1.55278e12i	1.21586	−	1.64286i
$987$		0			0
$988$	1.79929e12	−	5.49777e11i	1.88831	−	0.576978i
$989$	−5.54940e11			−0.580044
$990$		0			0
$991$		−	1.31555e12i		−	1.36400i	−0.731354	−	0.681999i	$-0.761111\pi$
$991$		−	1.31555e12i		−	1.36400i	0.731354	−	0.681999i	$-0.238889\pi$
$992$	−1.56964e12	−	6.91735e10i	−1.62089	−	0.0714321i
$993$		0			0
$994$	−6.91143e11	+	9.33867e11i	−0.707983	+	0.956620i
$995$		−	8.30352e10i		−	0.0847169i
$996$		0			0
$997$	1.29025e12			1.30585			0.652924	−	0.757424i	$-0.273542\pi$
$997$	1.29025e12			1.30585			0.652924	+	0.757424i	$0.273542\pi$
$998$	1.18613e12	+	8.77843e11i	1.19567	+	0.884901i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.9.c.b.91.10	yes	32
3.2	odd	2	inner	180.9.c.b.91.23	yes	32
4.3	odd	2	inner	180.9.c.b.91.9	✓	32
12.11	even	2	inner	180.9.c.b.91.24	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.9.c.b.91.9	✓	32	4.3	odd	2	inner
180.9.c.b.91.10	yes	32	1.1	even	1	trivial
180.9.c.b.91.23	yes	32	3.2	odd	2	inner
180.9.c.b.91.24	yes	32	12.11	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	180.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-9.51821 + 12.8609i) q^{2} +(-74.8072 - 244.826i) q^{4} +279.508 q^{5} +2236.25i q^{7} +(3860.72 + 1368.22i) q^{8} +(-2660.42 + 3594.74i) q^{10} +11333.8i q^{11} +43422.0 q^{13} +(-28760.3 - 21285.1i) q^{14} +(-54343.8 + 36629.5i) q^{16} +106270. q^{17} +169252. i q^{19} +(-20909.3 - 68431.0i) q^{20} +(-145763. - 107877. i) q^{22} -301142. i q^{23} +78125.0 q^{25} +(-413299. + 558447. i) q^{26} +(547493. - 167288. i) q^{28} -1.13613e6 q^{29} -1.49838e6i q^{31} +(46165.6 - 1.04756e6i) q^{32} +(-1.01150e6 + 1.36673e6i) q^{34} +625051. i q^{35} +3.00588e6 q^{37} +(-2.17674e6 - 1.61098e6i) q^{38} +(1.07911e6 + 382429. i) q^{40} +1.45494e6 q^{41} -1.84278e6i q^{43} +(2.77481e6 - 847849. i) q^{44} +(3.87297e6 + 2.86634e6i) q^{46} +3.23470e6i q^{47} +763979. q^{49} +(-743610. + 1.00476e6i) q^{50} +(-3.24828e6 - 1.06308e7i) q^{52} +2.47758e6 q^{53} +3.16789e6i q^{55} +(-3.05968e6 + 8.63355e6i) q^{56} +(1.08139e7 - 1.46117e7i) q^{58} +1.98398e7i q^{59} +2.31511e7 q^{61} +(1.92706e7 + 1.42619e7i) q^{62} +(1.30332e7 + 1.05646e7i) q^{64} +1.21368e7 q^{65} +1.38239e7i q^{67} +(-7.94974e6 - 2.60176e7i) q^{68} +(-8.03874e6 - 5.94937e6i) q^{70} -3.24707e7i q^{71} -2.85975e7 q^{73} +(-2.86106e7 + 3.86584e7i) q^{74} +(4.14374e7 - 1.26613e7i) q^{76} -2.53452e7 q^{77} -5.42305e7i q^{79} +(-1.51895e7 + 1.02383e7i) q^{80} +(-1.38484e7 + 1.87119e7i) q^{82} +8.59356e7i q^{83} +2.97033e7 q^{85} +(2.36999e7 + 1.75400e7i) q^{86} +(-1.55071e7 + 4.37567e7i) q^{88} -4.60584e7 q^{89} +9.71024e7i q^{91} +(-7.37275e7 + 2.25276e7i) q^{92} +(-4.16013e7 - 3.07886e7i) q^{94} +4.73074e7i q^{95} -3.17442e7 q^{97} +(-7.27171e6 + 9.82548e6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 610 q^{4} - 8750 q^{10} - 51392 q^{13} + 11986 q^{16} - 758068 q^{22} + 2500000 q^{25} + 976324 q^{28} - 6117428 q^{34} + 5152064 q^{37} - 96250 q^{40} - 10391752 q^{46} - 11002976 q^{49} + 13976584 q^{52}+ \cdots + 80579520 q^{97}+O(q^{100}) \) 32 * q + 610 * q^4 - 8750 * q^10 - 51392 * q^13 + 11986 * q^16 - 758068 * q^22 + 2500000 * q^25 + 976324 * q^28 - 6117428 * q^34 + 5152064 * q^37 - 96250 * q^40 - 10391752 * q^46 - 11002976 * q^49 + 13976584 * q^52 - 36333948 * q^58 - 7802048 * q^61 + 116259994 * q^64 - 49897500 * q^70 - 94303680 * q^73 + 248840592 * q^76 - 428557904 * q^82 + 106960000 * q^85 + 510719924 * q^88 - 692727576 * q^94 + 80579520 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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