LMFDB - Embedded newform 684.2.bo.c.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,2,Mod(73,684)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("684.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	684.bo (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} - 3 x^{10} + 70 x^{9} - 15 x^{8} - 426 x^{7} + 64 x^{6} + 1659 x^{5} + 267 x^{4} + \cdots + 4161 $ x^12 - 6x^11 - 3x^10 + 70x^9 - 15x^8 - 426x^7 + 64x^6 + 1659x^5 + 267x^4 - 3969x^3 - 2088x^2 + 4446*x + 4161
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 76)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			289.1
Root			$-1.75227 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	684.289
Dual form			684.2.bo.c.613.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.216181 + 0.181398i) q^{5} +(-0.579936 + 1.00448i) q^{7} +(0.622469 + 1.07815i) q^{11} +(0.977096 - 5.54139i) q^{13} +(6.25251 + 2.27573i) q^{17} +(3.09208 + 3.07231i) q^{19} +(4.65029 + 3.90205i) q^{23} +(-0.854412 + 4.84561i) q^{25} +(-3.64892 + 1.32810i) q^{29} +(-0.0400606 + 0.0693870i) q^{31} +(-0.0568388 - 0.322349i) q^{35} +3.71365 q^{37} +(-1.11697 - 6.33464i) q^{41} +(0.189407 - 0.158931i) q^{43} +(10.8939 - 3.96505i) q^{47} +(2.82735 + 4.89711i) q^{49} +(-3.50255 - 2.93899i) q^{53} +(-0.330140 - 0.120161i) q^{55} +(9.32947 + 3.39565i) q^{59} +(-4.27534 - 3.58744i) q^{61} +(0.793965 + 1.37519i) q^{65} +(-3.47734 + 1.26565i) q^{67} +(-7.14016 + 5.99131i) q^{71} +(0.191208 + 1.08439i) q^{73} -1.44397 q^{77} +(-1.50923 - 8.55928i) q^{79} +(-5.77114 + 9.99591i) q^{83} +(-1.76449 + 0.642221i) q^{85} +(0.418534 - 2.37362i) q^{89} +(4.99955 + 4.19512i) q^{91} +(-1.22576 - 0.103280i) q^{95} +(-13.4638 - 4.90042i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{7} - 3 q^{11} - 9 q^{13} + 3 q^{17} - 12 q^{19} + 12 q^{23} - 18 q^{25} - 27 q^{29} + 6 q^{31} - 33 q^{35} - 12 q^{37} - 3 q^{41} + 27 q^{43} + 15 q^{47} + 9 q^{49} + 21 q^{53} - 27 q^{55} + 48 q^{59}+ \cdots + 12 q^{97}+O(q^{100}) $ 12 * q + 3 * q^7 - 3 * q^11 - 9 * q^13 + 3 * q^17 - 12 * q^19 + 12 * q^23 - 18 * q^25 - 27 * q^29 + 6 * q^31 - 33 * q^35 - 12 * q^37 - 3 * q^41 + 27 * q^43 + 15 * q^47 + 9 * q^49 + 21 * q^53 - 27 * q^55 + 48 * q^59 - 6 * q^61 + 33 * q^65 + 24 * q^67 + 30 * q^73 - 24 * q^77 + 3 * q^79 - 3 * q^83 - 42 * q^85 + 18 * q^89 - 24 * q^91 - 9 * q^95 + 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.216181	+	0.181398i	−0.0966793	+	0.0811235i	−0.689846	−	0.723956i	$-0.742322\pi$
$5$	−0.216181	+	0.181398i	−0.0966793	+	0.0811235i	0.593167	+	0.805079i	$0.297877\pi$
$6$		0			0
$7$	−0.579936	+	1.00448i	−0.219195	+	0.379657i	−0.954562	−	0.298012i	$-0.903677\pi$
$7$	−0.579936	+	1.00448i	−0.219195	+	0.379657i	0.735367	+	0.677669i	$0.237010\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.622469	+	1.07815i	0.187682	+	0.325074i	0.944477	−	0.328578i	$-0.106569\pi$
$11$	0.622469	+	1.07815i	0.187682	+	0.325074i	−0.756795	+	0.653652i	$0.773236\pi$
$12$		0			0
$13$	0.977096	−	5.54139i	0.270998	−	1.53690i	−0.480397	−	0.877051i	$-0.659508\pi$
$13$	0.977096	−	5.54139i	0.270998	−	1.53690i	0.751395	−	0.659853i	$-0.229381\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	6.25251	+	2.27573i	1.51646	+	0.551945i	0.960260	−	0.279106i	$-0.0900381\pi$
$17$	6.25251	+	2.27573i	1.51646	+	0.551945i	0.556196	+	0.831051i	$0.312260\pi$
$18$		0			0
$19$	3.09208	+	3.07231i	0.709371	+	0.704835i
$19$	3.09208	+	3.07231i	0.709371	+	0.704835i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.65029	+	3.90205i	0.969652	+	0.813635i	0.982496	−	0.186283i	$-0.0596441\pi$
$23$	4.65029	+	3.90205i	0.969652	+	0.813635i	−0.0128443	+	0.999918i	$0.504089\pi$
$24$		0			0
$25$	−0.854412	+	4.84561i	−0.170882	+	0.969122i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.64892	+	1.32810i	−0.677587	+	0.246621i	−0.657811	−	0.753183i	$-0.728517\pi$
$29$	−3.64892	+	1.32810i	−0.677587	+	0.246621i	−0.0197756	+	0.999804i	$0.506295\pi$
$30$		0			0
$31$	−0.0400606	+	0.0693870i	−0.00719510	+	0.0124623i	−0.869601	−	0.493756i	$-0.835624\pi$
$31$	−0.0400606	+	0.0693870i	−0.00719510	+	0.0124623i	0.862405	+	0.506218i	$0.168957\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.0568388	−	0.322349i	−0.00960751	−	0.0544869i
$36$		0			0
$37$	3.71365			0.610521			0.305260	−	0.952269i	$-0.401256\pi$
$37$	3.71365			0.610521			0.305260	+	0.952269i	$0.401256\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.11697	−	6.33464i	−0.174441	−	0.989305i	−0.938787	−	0.344498i	$-0.888049\pi$
$41$	−1.11697	−	6.33464i	−0.174441	−	0.989305i	0.764346	−	0.644806i	$-0.223062\pi$
$42$		0			0
$43$	0.189407	−	0.158931i	0.0288842	−	0.0242368i	−0.628231	−	0.778027i	$-0.716221\pi$
$43$	0.189407	−	0.158931i	0.0288842	−	0.0242368i	0.657115	+	0.753790i	$0.271776\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	10.8939	−	3.96505i	1.58904	−	0.578362i	0.611893	−	0.790940i	$-0.290408\pi$
$47$	10.8939	−	3.96505i	1.58904	−	0.578362i	0.977144	+	0.212578i	$0.0681859\pi$
$48$		0			0
$49$	2.82735	+	4.89711i	0.403907	+	0.699587i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−3.50255	−	2.93899i	−0.481113	−	0.403702i	0.369716	−	0.929145i	$-0.379455\pi$
$53$	−3.50255	−	2.93899i	−0.481113	−	0.403702i	−0.850829	+	0.525443i	$0.823900\pi$
$54$		0			0
$55$	−0.330140	−	0.120161i	−0.0445161	−	0.0162025i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	9.32947	+	3.39565i	1.21459	+	0.442076i	0.868295	−	0.496049i	$-0.165216\pi$
$59$	9.32947	+	3.39565i	1.21459	+	0.442076i	0.346298	+	0.938124i	$0.387438\pi$
$60$		0			0
$61$	−4.27534	−	3.58744i	−0.547401	−	0.459324i	0.326659	−	0.945142i	$-0.394077\pi$
$61$	−4.27534	−	3.58744i	−0.547401	−	0.459324i	−0.874060	+	0.485818i	$0.838522\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.793965	+	1.37519i	0.0984792	+	0.170571i
$66$		0			0
$67$	−3.47734	+	1.26565i	−0.424824	+	0.154623i	−0.545580	−	0.838059i	$-0.683691\pi$
$67$	−3.47734	+	1.26565i	−0.424824	+	0.154623i	0.120756	+	0.992682i	$0.461468\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−7.14016	+	5.99131i	−0.847382	+	0.711038i	−0.959211	−	0.282690i	$-0.908773\pi$
$71$	−7.14016	+	5.99131i	−0.847382	+	0.711038i	0.111830	+	0.993727i	$0.464329\pi$
$72$		0			0
$73$	0.191208	+	1.08439i	0.0223792	+	0.126919i	0.993951	−	0.109828i	$-0.0350300\pi$
$73$	0.191208	+	1.08439i	0.0223792	+	0.126919i	−0.971571	+	0.236747i	$0.923919\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.44397			−0.164556
$78$		0			0
$79$	−1.50923	−	8.55928i	−0.169802	−	0.962994i	−0.943974	−	0.330019i	$-0.892945\pi$
$79$	−1.50923	−	8.55928i	−0.169802	−	0.962994i	0.774172	−	0.632975i	$-0.218166\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−5.77114	+	9.99591i	−0.633465	+	1.09719i	0.353373	+	0.935483i	$0.385035\pi$
$83$	−5.77114	+	9.99591i	−0.633465	+	1.09719i	−0.986838	+	0.161711i	$0.948299\pi$
$84$		0			0
$85$	−1.76449	+	0.642221i	−0.191386	+	0.0696587i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	0.418534	−	2.37362i	0.0443645	−	0.251603i	−0.954557	−	0.298027i	$-0.903671\pi$
$89$	0.418534	−	2.37362i	0.0443645	−	0.251603i	0.998922	+	0.0464239i	$0.0147825\pi$
$90$		0			0
$91$	4.99955	+	4.19512i	0.524095	+	0.439768i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.22576	−	0.103280i	−0.125760	−	0.0105963i
$96$		0			0
$97$	−13.4638	−	4.90042i	−1.36704	−	0.497562i	−0.448816	−	0.893624i	$-0.648154\pi$
$97$	−13.4638	−	4.90042i	−1.36704	−	0.497562i	−0.918224	+	0.396062i	$0.870376\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	2.97288	−	16.8600i	0.295813	−	1.67764i	−0.368068	−	0.929799i	$-0.619981\pi$
$101$	2.97288	−	16.8600i	0.295813	−	1.67764i	0.663881	−	0.747838i	$-0.268908\pi$
$102$		0			0
$103$	6.64081	+	11.5022i	0.654339	+	1.13335i	0.982059	+	0.188573i	$0.0603863\pi$
$103$	6.64081	+	11.5022i	0.654339	+	1.13335i	−0.327720	+	0.944775i	$0.606280\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.494870	−	0.857140i	0.0478409	−	0.0828628i	−0.841113	−	0.540859i	$-0.818099\pi$
$107$	0.494870	−	0.857140i	0.0478409	−	0.0828628i	0.888954	+	0.457996i	$0.151433\pi$
$108$		0			0
$109$	10.3519	−	8.68625i	0.991529	−	0.831991i	0.00574045	−	0.999984i	$-0.498173\pi$
$109$	10.3519	−	8.68625i	0.991529	−	0.831991i	0.985788	+	0.167992i	$0.0537283\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−16.5369			−1.55566			−0.777829	−	0.628476i	$-0.783679\pi$
$113$	−16.5369			−1.55566			−0.777829	+	0.628476i	$0.783679\pi$
$114$		0			0
$115$	−1.71313			−0.159750
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−5.91198	+	4.96074i	−0.541950	+	0.454750i
$120$		0			0
$121$	4.72506	−	8.18405i	0.429551	−	0.744005i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−1.39979	−	2.42450i	−0.125201	−	0.216854i
$126$		0			0
$127$	−0.388935	+	2.20576i	−0.0345124	+	0.195729i	−0.997189	−	0.0749239i	$-0.976129\pi$
$127$	−0.388935	+	2.20576i	−0.0345124	+	0.195729i	0.962677	+	0.270653i	$0.0872397\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−16.5173	−	6.01181i	−1.44313	−	0.525255i	−0.502463	−	0.864599i	$-0.667573\pi$
$131$	−16.5173	−	6.01181i	−1.44313	−	0.525255i	−0.940662	+	0.339344i	$0.889795\pi$
$132$		0			0
$133$	−4.87927	+	1.32418i	−0.423087	+	0.114821i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−4.36728	−	3.66458i	−0.373122	−	0.313086i	0.436873	−	0.899523i	$-0.356086\pi$
$137$	−4.36728	−	3.66458i	−0.373122	−	0.313086i	−0.809995	+	0.586437i	$0.800530\pi$
$138$		0			0
$139$	0.891090	−	5.05362i	0.0755813	−	0.428643i	−0.923413	−	0.383808i	$-0.874613\pi$
$139$	0.891090	−	5.05362i	0.0755813	−	0.428643i	0.998994	−	0.0448352i	$-0.0142763\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	6.58265	−	2.39589i	0.550469	−	0.200354i
$144$		0			0
$145$	0.547914	−	0.949015i	0.0455018	−	0.0788114i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	2.06723	+	11.7238i	0.169354	+	0.960454i	0.944461	+	0.328624i	$0.106585\pi$
$149$	2.06723	+	11.7238i	0.169354	+	0.960454i	−0.775107	+	0.631830i	$0.782304\pi$
$150$		0			0
$151$	−14.8628			−1.20952			−0.604759	−	0.796409i	$-0.706731\pi$
$151$	−14.8628			−1.20952			−0.604759	+	0.796409i	$0.706731\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.00392629	−	0.0222671i	−0.000315367	−	0.00178854i
$156$		0			0
$157$	−8.45258	+	7.09255i	−0.674589	+	0.566047i	−0.914420	−	0.404767i	$-0.867353\pi$
$157$	−8.45258	+	7.09255i	−0.674589	+	0.566047i	0.239831	+	0.970815i	$0.422908\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−6.61640	+	2.40817i	−0.521446	+	0.189791i
$162$		0			0
$163$	−1.99237	−	3.45089i	−0.156055	−	0.270295i	0.777388	−	0.629021i	$-0.216544\pi$
$163$	−1.99237	−	3.45089i	−0.156055	−	0.270295i	−0.933443	+	0.358727i	$0.883211\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	6.19785	+	5.20061i	0.479604	+	0.402436i	0.850283	−	0.526325i	$-0.176431\pi$
$167$	6.19785	+	5.20061i	0.479604	+	0.402436i	−0.370679	+	0.928761i	$0.620875\pi$
$168$		0			0
$169$	−17.5362	−	6.38267i	−1.34894	−	0.490974i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−6.13327	−	2.23233i	−0.466304	−	0.169721i	0.0981735	−	0.995169i	$-0.468700\pi$
$173$	−6.13327	−	2.23233i	−0.466304	−	0.169721i	−0.564477	+	0.825449i	$0.690922\pi$
$174$		0			0
$175$	−4.37181	−	3.66838i	−0.330478	−	0.277304i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−4.91617	−	8.51506i	−0.367452	−	0.636445i	0.621715	−	0.783244i	$-0.286436\pi$
$179$	−4.91617	−	8.51506i	−0.367452	−	0.636445i	−0.989166	+	0.146799i	$0.953103\pi$
$180$		0			0
$181$	12.9463	−	4.71208i	0.962293	−	0.350246i	0.187361	−	0.982291i	$-0.440007\pi$
$181$	12.9463	−	4.71208i	0.962293	−	0.350246i	0.774932	+	0.632045i	$0.217784\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.802823	+	0.673648i	−0.0590247	+	0.0495276i
$186$		0			0
$187$	1.43842	+	8.15771i	0.105188	+	0.596551i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.03137			−0.0746275			−0.0373137	−	0.999304i	$-0.511880\pi$
$191$	−1.03137			−0.0746275			−0.0373137	+	0.999304i	$0.511880\pi$
$192$		0			0
$193$	−0.407183	−	2.30925i	−0.0293097	−	0.166224i	0.966640	−	0.256140i	$-0.0824510\pi$
$193$	−0.407183	−	2.30925i	−0.0293097	−	0.166224i	−0.995949	+	0.0899169i	$0.971340\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	7.78406	−	13.4824i	0.554592	−	0.960581i	−0.443344	−	0.896352i	$-0.646208\pi$
$197$	7.78406	−	13.4824i	0.554592	−	0.960581i	0.997935	−	0.0642291i	$-0.0204588\pi$
$198$		0			0
$199$	12.8701	−	4.68434i	0.912339	−	0.332064i	0.157153	−	0.987574i	$-0.449769\pi$
$199$	12.8701	−	4.68434i	0.912339	−	0.332064i	0.755186	+	0.655510i	$0.227546\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.782093	−	4.43547i	0.0548922	−	0.311309i
$204$		0			0
$205$	1.39056	+	1.16682i	0.0971207	+	0.0814940i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.38768	+	5.24614i	−0.0959878	+	0.362883i
$210$		0			0
$211$	20.2595	+	7.37386i	1.39472	+	0.507638i	0.926608	−	0.376030i	$-0.122711\pi$
$211$	20.2595	+	7.37386i	1.39472	+	0.507638i	0.468116	+	0.883667i	$0.344933\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−0.0121165	+	0.0687159i	−0.000826336	+	0.00468638i
$216$		0			0
$217$	−0.0464652	−	0.0804801i	−0.00315426	−	0.00546335i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	18.7200	−	32.4240i	1.25924	−	2.18107i
$222$		0			0
$223$	−19.9848	+	16.7693i	−1.33828	+	1.12295i	−0.356220	+	0.934402i	$0.615935\pi$
$223$	−19.9848	+	16.7693i	−1.33828	+	1.12295i	−0.982063	+	0.188551i	$0.939621\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−21.7357			−1.44265			−0.721325	−	0.692596i	$-0.756467\pi$
$227$	−21.7357			−1.44265			−0.721325	+	0.692596i	$0.756467\pi$
$228$		0			0
$229$	−20.1255			−1.32993			−0.664964	−	0.746875i	$-0.731553\pi$
$229$	−20.1255			−1.32993			−0.664964	+	0.746875i	$0.731553\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−16.8667	+	14.1529i	−1.10498	+	0.927184i	−0.997750	−	0.0670504i	$-0.978641\pi$
$233$	−16.8667	+	14.1529i	−1.10498	+	0.927184i	−0.107226	+	0.994235i	$0.534197\pi$
$234$		0			0
$235$	−1.63581	+	2.83330i	−0.106708	+	0.184824i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	2.18637	+	3.78691i	0.141425	+	0.244955i	0.928033	−	0.372497i	$-0.121498\pi$
$239$	2.18637	+	3.78691i	0.141425	+	0.244955i	−0.786609	+	0.617452i	$0.788165\pi$
$240$		0			0
$241$	−2.60506	+	14.7740i	−0.167807	+	0.951679i	0.778317	+	0.627872i	$0.216074\pi$
$241$	−2.60506	+	14.7740i	−0.167807	+	0.951679i	−0.946123	+	0.323807i	$0.895037\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−1.49954	−	0.545790i	−0.0958024	−	0.0348692i
$246$		0			0
$247$	20.0461	−	14.1325i	1.27550	−	0.899226i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	17.9754	+	15.0832i	1.13460	+	0.952042i	0.999249	−	0.0387556i	$-0.0123394\pi$
$251$	17.9754	+	15.0832i	1.13460	+	0.952042i	0.135351	+	0.990798i	$0.456784\pi$
$252$		0			0
$253$	−1.31233	+	7.44261i	−0.0825057	+	0.467913i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	0.0996901	−	0.0362842i	0.00621850	−	0.00226335i	−0.338909	−	0.940819i	$-0.610058\pi$
$257$	0.0996901	−	0.0362842i	0.00621850	−	0.00226335i	0.345128	+	0.938556i	$0.387836\pi$
$258$		0			0
$259$	−2.15368	+	3.73029i	−0.133823	+	0.231789i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	2.70397	+	15.3350i	0.166734	+	0.945594i	0.947259	+	0.320469i	$0.103841\pi$
$263$	2.70397	+	15.3350i	0.166734	+	0.945594i	−0.780525	+	0.625124i	$0.785048\pi$
$264$		0			0
$265$	1.29031			0.0792633
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−2.43886	−	13.8315i	−0.148700	−	0.843321i	−0.964321	−	0.264734i	$-0.914716\pi$
$269$	−2.43886	−	13.8315i	−0.148700	−	0.843321i	0.815621	−	0.578586i	$-0.196395\pi$
$270$		0			0
$271$	8.77391	−	7.36218i	0.532977	−	0.447221i	−0.336151	−	0.941808i	$-0.609125\pi$
$271$	8.77391	−	7.36218i	0.532977	−	0.447221i	0.869128	+	0.494587i	$0.164681\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−5.75613	+	2.09506i	−0.347108	+	0.126337i
$276$		0			0
$277$	−12.8642	−	22.2814i	−0.772932	−	1.33876i	−0.935949	−	0.352135i	$-0.885456\pi$
$277$	−12.8642	−	22.2814i	−0.772932	−	1.33876i	0.163017	−	0.986623i	$-0.447878\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	20.6252	+	17.3066i	1.23039	+	1.03242i	0.998213	+	0.0597510i	$0.0190307\pi$
$281$	20.6252	+	17.3066i	1.23039	+	1.03242i	0.232181	+	0.972673i	$0.425414\pi$
$282$		0			0
$283$	−2.78007	−	1.01186i	−0.165258	−	0.0601491i	0.258066	−	0.966127i	$-0.416915\pi$
$283$	−2.78007	−	1.01186i	−0.165258	−	0.0601491i	−0.423324	+	0.905978i	$0.639137\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	7.01078	+	2.55172i	0.413834	+	0.150623i
$288$		0			0
$289$	20.8922	+	17.5306i	1.22895	+	1.03121i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	5.01204	+	8.68111i	0.292807	+	0.507156i	0.974472	−	0.224508i	$-0.0720775\pi$
$293$	5.01204	+	8.68111i	0.292807	+	0.507156i	−0.681666	+	0.731664i	$0.738744\pi$
$294$		0			0
$295$	−2.63282	+	0.958268i	−0.153289	+	0.0557925i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	26.1666	−	21.9564i	1.51325	−	1.26977i
$300$		0			0
$301$	0.0497991	+	0.282425i	0.00287037	+	0.0162787i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	1.57500			0.0901844
$306$		0			0
$307$	−2.87822	−	16.3232i	−0.164269	−	0.931614i	−0.949815	−	0.312811i	$-0.898729\pi$
$307$	−2.87822	−	16.3232i	−0.164269	−	0.931614i	0.785547	−	0.618802i	$-0.212382\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	0.215620	−	0.373465i	0.0122267	−	0.0211772i	−0.859847	−	0.510551i	$-0.829441\pi$
$311$	0.215620	−	0.373465i	0.0122267	−	0.0211772i	0.872074	+	0.489374i	$0.162775\pi$
$312$		0			0
$313$	13.0841	−	4.76223i	0.739557	−	0.269177i	0.0553527	−	0.998467i	$-0.482372\pi$
$313$	13.0841	−	4.76223i	0.739557	−	0.269177i	0.684205	+	0.729290i	$0.260149\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2.87712	−	16.3170i	0.161595	−	0.916452i	−0.790911	−	0.611932i	$-0.790393\pi$
$317$	2.87712	−	16.3170i	0.161595	−	0.916452i	0.952506	−	0.304521i	$-0.0984962\pi$
$318$		0			0
$319$	−3.70322	−	3.10737i	−0.207341	−	0.173980i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	12.3415	+	26.2463i	0.686700	+	1.46039i
$324$		0			0
$325$	26.0165	+	9.46925i	1.44314	+	0.525259i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−2.33495	+	13.2422i	−0.128730	+	0.730064i
$330$		0			0
$331$	−4.74773	−	8.22332i	−0.260959	−	0.451994i	0.705538	−	0.708672i	$-0.250705\pi$
$331$	−4.74773	−	8.22332i	−0.260959	−	0.451994i	−0.966497	+	0.256678i	$0.917372\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	0.522150	−	0.904390i	0.0285281	−	0.0494121i
$336$		0			0
$337$	9.65934	−	8.10515i	0.526178	−	0.441515i	−0.340601	−	0.940208i	$-0.610631\pi$
$337$	9.65934	−	8.10515i	0.526178	−	0.441515i	0.866779	+	0.498692i	$0.166186\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−0.0997461			−0.00540155
$342$		0			0
$343$	−14.6778			−0.792529
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−8.36688	+	7.02065i	−0.449158	+	0.376888i	−0.839123	−	0.543941i	$-0.816931\pi$
$347$	−8.36688	+	7.02065i	−0.449158	+	0.376888i	0.389965	+	0.920830i	$0.372487\pi$
$348$		0			0
$349$	−4.20032	+	7.27517i	−0.224838	+	0.389431i	−0.956271	−	0.292483i	$-0.905519\pi$
$349$	−4.20032	+	7.27517i	−0.224838	+	0.389431i	0.731433	+	0.681913i	$0.238852\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	6.69379	+	11.5940i	0.356274	+	0.617086i	0.987335	−	0.158648i	$-0.0507135\pi$
$353$	6.69379	+	11.5940i	0.356274	+	0.617086i	−0.631061	+	0.775733i	$0.717380\pi$
$354$		0			0
$355$	0.456761	−	2.59042i	0.0242423	−	0.137485i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−26.6099	−	9.68521i	−1.40442	−	0.511166i	−0.474931	−	0.880023i	$-0.657527\pi$
$359$	−26.6099	−	9.68521i	−1.40442	−	0.511166i	−0.929486	+	0.368857i	$0.879749\pi$
$360$		0			0
$361$	0.121876	+	18.9996i	0.00641452	+	0.999979i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−0.238042	−	0.199741i	−0.0124597	−	0.0104549i
$366$		0			0
$367$	0.0720091	−	0.408384i	0.00375884	−	0.0213175i	−0.982871	−	0.184297i	$-0.940999\pi$
$367$	0.0720091	−	0.408384i	0.00375884	−	0.0213175i	0.986629	+	0.162979i	$0.0521104\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	4.98342	−	1.81381i	0.258726	−	0.0941686i
$372$		0			0
$373$	2.01032	−	3.48198i	0.104090	−	0.180290i	−0.809276	−	0.587429i	$-0.800140\pi$
$373$	2.01032	−	3.48198i	0.104090	−	0.180290i	0.913366	+	0.407139i	$0.133474\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	3.79416	+	21.5177i	0.195409	+	1.10822i
$378$		0			0
$379$	14.1791			0.728332			0.364166	−	0.931334i	$-0.381354\pi$
$379$	14.1791			0.728332			0.364166	+	0.931334i	$0.381354\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−1.88738	−	10.7039i	−0.0964407	−	0.546943i	−0.994296	−	0.106653i	$-0.965987\pi$
$383$	−1.88738	−	10.7039i	−0.0964407	−	0.546943i	0.897856	−	0.440290i	$-0.145124\pi$
$384$		0			0
$385$	0.312160	−	0.261933i	0.0159091	−	0.0133493i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	24.0167	−	8.74136i	1.21769	−	0.443205i	0.348328	−	0.937373i	$-0.386749\pi$
$389$	24.0167	−	8.74136i	1.21769	−	0.443205i	0.869367	+	0.494168i	$0.164527\pi$
$390$		0			0
$391$	20.1960	+	34.9804i	1.02135	+	1.76904i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	1.87890	+	1.57659i	0.0945378	+	0.0793267i
$396$		0			0
$397$	16.1594	+	5.88155i	0.811018	+	0.295186i	0.714044	−	0.700101i	$-0.246862\pi$
$397$	16.1594	+	5.88155i	0.811018	+	0.295186i	0.0969735	+	0.995287i	$0.469084\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	14.4376	+	5.25485i	0.720979	+	0.262415i	0.676341	−	0.736588i	$-0.263564\pi$
$401$	14.4376	+	5.25485i	0.720979	+	0.262415i	0.0446377	+	0.999003i	$0.485787\pi$
$402$		0			0
$403$	0.345357	+	0.289789i	0.0172035	+	0.0144354i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	2.31164	+	4.00387i	0.114584	+	0.198465i
$408$		0			0
$409$	−13.4638	+	4.90042i	−0.665741	+	0.242310i	−0.652713	−	0.757605i	$-0.726369\pi$
$409$	−13.4638	+	4.90042i	−0.665741	+	0.242310i	−0.0130280	+	0.999915i	$0.504147\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−8.82135	+	7.40200i	−0.434070	+	0.364228i
$414$		0			0
$415$	−0.565622	−	3.20780i	−0.0277653	−	0.157465i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	17.2723			0.843805			0.421902	−	0.906641i	$-0.361363\pi$
$419$	17.2723			0.843805			0.421902	+	0.906641i	$0.361363\pi$
$420$		0			0
$421$	−4.83458	−	27.4183i	−0.235623	−	1.33629i	−0.841297	−	0.540573i	$-0.818208\pi$
$421$	−4.83458	−	27.4183i	−0.235623	−	1.33629i	0.605674	−	0.795713i	$-0.292903\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−16.3695	+	28.3528i	−0.794038	+	1.37531i
$426$		0			0
$427$	6.08293	−	2.21401i	0.294374	−	0.107143i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	6.57872	−	37.3098i	0.316886	−	1.79715i	−0.244558	−	0.969635i	$-0.578643\pi$
$431$	6.57872	−	37.3098i	0.316886	−	1.79715i	0.561444	−	0.827515i	$-0.310246\pi$
$432$		0			0
$433$	5.76405	+	4.83661i	0.277003	+	0.232433i	0.770696	−	0.637204i	$-0.219909\pi$
$433$	5.76405	+	4.83661i	0.277003	+	0.232433i	−0.493693	+	0.869636i	$0.664353\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	2.39074	+	26.3526i	0.114365	+	1.26061i
$438$		0			0
$439$	−19.9813	−	7.27259i	−0.953655	−	0.347102i	−0.182111	−	0.983278i	$-0.558293\pi$
$439$	−19.9813	−	7.27259i	−0.953655	−	0.347102i	−0.771544	+	0.636176i	$0.780515\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	2.59412	−	14.7120i	0.123250	−	0.698988i	−0.859081	−	0.511839i	$-0.828964\pi$
$443$	2.59412	−	14.7120i	0.123250	−	0.698988i	0.982332	−	0.187149i	$-0.0599246\pi$
$444$		0			0
$445$	0.340090	+	0.589054i	0.0161218	+	0.0279238i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	8.47286	−	14.6754i	0.399859	−	0.692576i	−0.593849	−	0.804576i	$-0.702392\pi$
$449$	8.47286	−	14.6754i	0.399859	−	0.692576i	0.993708	+	0.112000i	$0.0357258\pi$
$450$		0			0
$451$	6.13441	−	5.14738i	0.288858	−	0.242381i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−1.84180			−0.0863447
$456$		0			0
$457$	−10.2922			−0.481448			−0.240724	−	0.970594i	$-0.577385\pi$
$457$	−10.2922			−0.481448			−0.240724	+	0.970594i	$0.577385\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−4.59397	+	3.85480i	−0.213962	+	0.179536i	−0.743470	−	0.668770i	$-0.766821\pi$
$461$	−4.59397	+	3.85480i	−0.213962	+	0.179536i	0.529507	+	0.848305i	$0.322377\pi$
$462$		0			0
$463$	−1.69033	+	2.92774i	−0.0785563	+	0.136063i	−0.902627	−	0.430423i	$-0.858364\pi$
$463$	−1.69033	+	2.92774i	−0.0785563	+	0.136063i	0.824071	+	0.566487i	$0.191698\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	1.03045	+	1.78480i	0.0476837	+	0.0825906i	0.888882	−	0.458136i	$-0.151483\pi$
$467$	1.03045	+	1.78480i	0.0476837	+	0.0825906i	−0.841198	+	0.540727i	$0.818149\pi$
$468$		0			0
$469$	0.745318	−	4.22691i	0.0344156	−	0.195180i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.289251	+	0.105279i	0.0132998	+	0.00484073i
$474$		0			0
$475$	−17.5291	+	12.3580i	−0.804290	+	0.567023i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	4.53663	+	3.80668i	0.207284	+	0.173932i	0.740519	−	0.672035i	$-0.234580\pi$
$479$	4.53663	+	3.80668i	0.207284	+	0.173932i	−0.533235	+	0.845967i	$0.679024\pi$
$480$		0			0
$481$	3.62860	−	20.5788i	0.165450	−	0.938312i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	3.79954	−	1.38292i	0.172528	−	0.0627952i
$486$		0			0
$487$	13.3232	−	23.0764i	0.603731	−	1.04569i	−0.388520	−	0.921440i	$-0.627013\pi$
$487$	13.3232	−	23.0764i	0.603731	−	1.04569i	0.992251	−	0.124252i	$-0.0396532\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−6.15100	−	34.8841i	−0.277591	−	1.57430i	−0.730610	−	0.682795i	$-0.760764\pi$
$491$	−6.15100	−	34.8841i	−0.277591	−	1.57430i	0.453019	−	0.891501i	$-0.350347\pi$
$492$		0			0
$493$	−25.8373			−1.16365
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.87730	−	10.6467i	−0.0842086	−	0.477571i
$498$		0			0
$499$	−26.5322	+	22.2631i	−1.18774	+	0.996634i	−0.187846	+	0.982198i	$0.560151\pi$
$499$	−26.5322	+	22.2631i	−1.18774	+	0.996634i	−0.999896	+	0.0144356i	$0.995405\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	29.0173	−	10.5614i	1.29382	−	0.470912i	0.398840	−	0.917020i	$-0.369413\pi$
$503$	29.0173	−	10.5614i	1.29382	−	0.470912i	0.894979	+	0.446109i	$0.147190\pi$
$504$		0			0
$505$	2.41569	+	4.18410i	0.107497	+	0.186190i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−11.9255	−	10.0067i	−0.528590	−	0.443540i	0.339024	−	0.940778i	$-0.389903\pi$
$509$	−11.9255	−	10.0067i	−0.528590	−	0.443540i	−0.867614	+	0.497238i	$0.834348\pi$
$510$		0			0
$511$	−1.20014	−	0.436815i	−0.0530910	−	0.0193235i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−3.52210	−	1.28194i	−0.155202	−	0.0564890i
$516$		0			0
$517$	11.0560	+	9.27711i	0.486244	+	0.408007i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	11.1132	+	19.2486i	0.486877	+	0.843295i	0.999886	−	0.0150876i	$-0.00480270\pi$
$521$	11.1132	+	19.2486i	0.486877	+	0.843295i	−0.513009	+	0.858383i	$0.671469\pi$
$522$		0			0
$523$	−10.1135	+	3.68103i	−0.442234	+	0.160960i	−0.553534	−	0.832827i	$-0.686721\pi$
$523$	−10.1135	+	3.68103i	−0.442234	+	0.160960i	0.111299	+	0.993787i	$0.464499\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−0.408385	+	0.342676i	−0.0177895	+	0.0149272i
$528$		0			0
$529$	2.40523	+	13.6408i	0.104575	+	0.593077i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−36.1941			−1.56774
$534$		0			0
$535$	0.0485015	+	0.275066i	0.00209690	+	0.0118921i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−3.51988	+	6.09660i	−0.151612	+	0.262599i
$540$		0			0
$541$	11.5235	−	4.19422i	0.495435	−	0.180323i	−0.0822049	−	0.996615i	$-0.526196\pi$
$541$	11.5235	−	4.19422i	0.495435	−	0.180323i	0.577639	+	0.816292i	$0.303974\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−0.662215	+	3.75561i	−0.0283662	+	0.160873i
$546$		0			0
$547$	14.2562	+	11.9624i	0.609552	+	0.511475i	0.894500	−	0.447068i	$-0.147532\pi$
$547$	14.2562	+	11.9624i	0.609552	+	0.511475i	−0.284948	+	0.958543i	$0.591976\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−15.3630	−	7.10401i	−0.654488	−	0.302641i
$552$		0			0
$553$	9.47288	+	3.44785i	0.402828	+	0.146617i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	0.706865	−	4.00883i	0.0299508	−	0.169860i	−0.966163	−	0.257931i	$-0.916959\pi$
$557$	0.706865	−	4.00883i	0.0299508	−	0.169860i	0.996114	+	0.0880715i	$0.0280704\pi$
$558$		0			0
$559$	−0.695630	−	1.20487i	−0.0294220	−	0.0509604i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−12.4377	+	21.5428i	−0.524188	+	0.907920i	0.475416	+	0.879761i	$0.342298\pi$
$563$	−12.4377	+	21.5428i	−0.524188	+	0.907920i	−0.999603	+	0.0281586i	$0.991036\pi$
$564$		0			0
$565$	3.57496	−	2.99975i	0.150400	−	0.126201i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−19.2420			−0.806667			−0.403334	−	0.915053i	$-0.632149\pi$
$569$	−19.2420			−0.806667			−0.403334	+	0.915053i	$0.632149\pi$
$570$		0			0
$571$	13.5395			0.566612			0.283306	−	0.959030i	$-0.408569\pi$
$571$	13.5395			0.566612			0.283306	+	0.959030i	$0.408569\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−22.8811	+	19.1995i	−0.954207	+	0.800675i
$576$		0			0
$577$	−12.8402	+	22.2398i	−0.534543	+	0.925855i	0.464643	+	0.885498i	$0.346183\pi$
$577$	−12.8402	+	22.2398i	−0.534543	+	0.925855i	−0.999185	+	0.0403567i	$0.987151\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−6.69379	−	11.5940i	−0.277705	−	0.481000i
$582$		0			0
$583$	0.988438	−	5.60571i	0.0409369	−	0.232165i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−17.4378	−	6.34683i	−0.719734	−	0.261962i	−0.0439211	−	0.999035i	$-0.513985\pi$
$587$	−17.4378	−	6.34683i	−0.719734	−	0.261962i	−0.675813	+	0.737073i	$0.736207\pi$
$588$		0			0
$589$	−0.337049	+	0.0914715i	−0.0138878	+	0.00376902i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−2.75772	−	2.31400i	−0.113246	−	0.0950248i	0.584406	−	0.811461i	$-0.301327\pi$
$593$	−2.75772	−	2.31400i	−0.113246	−	0.0950248i	−0.697652	+	0.716437i	$0.745772\pi$
$594$		0			0
$595$	0.378193	−	2.14484i	0.0155044	−	0.0879298i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−12.3328	+	4.48878i	−0.503905	+	0.183407i	−0.581450	−	0.813582i	$-0.697514\pi$
$599$	−12.3328	+	4.48878i	−0.503905	+	0.183407i	0.0775443	+	0.996989i	$0.475292\pi$
$600$		0			0
$601$	−6.78825	+	11.7576i	−0.276898	+	0.479602i	−0.970612	−	0.240649i	$-0.922640\pi$
$601$	−6.78825	+	11.7576i	−0.276898	+	0.479602i	0.693714	+	0.720251i	$0.255973\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.463097	+	2.62635i	0.0188276	+	0.106777i
$606$		0			0
$607$	−18.3633			−0.745343			−0.372672	−	0.927963i	$-0.621558\pi$
$607$	−18.3633			−0.745343			−0.372672	+	0.927963i	$0.621558\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−11.3275	−	64.2415i	−0.458262	−	2.59893i
$612$		0			0
$613$	4.42518	−	3.71316i	0.178731	−	0.149973i	−0.549033	−	0.835801i	$-0.685004\pi$
$613$	4.42518	−	3.71316i	0.178731	−	0.149973i	0.727764	+	0.685827i	$0.240559\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	39.3443	−	14.3201i	1.58394	−	0.576507i	0.607885	−	0.794025i	$-0.292018\pi$
$617$	39.3443	−	14.3201i	1.58394	−	0.576507i	0.976056	+	0.217518i	$0.0697961\pi$
$618$		0			0
$619$	−18.0480	−	31.2601i	−0.725412	−	1.25645i	−0.958804	−	0.284068i	$-0.908316\pi$
$619$	−18.0480	−	31.2601i	−0.725412	−	1.25645i	0.233392	−	0.972383i	$-0.425017\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	2.14153	+	1.79696i	0.0857986	+	0.0719936i
$624$		0			0
$625$	−22.3757	−	8.14410i	−0.895029	−	0.325764i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	23.2197	+	8.45126i	0.925828	+	0.336974i
$630$		0			0
$631$	−29.6886	−	24.9117i	−1.18188	−	0.991717i	−0.999965	−	0.00840360i	$-0.997325\pi$
$631$	−29.6886	−	24.9117i	−1.18188	−	0.991717i	−0.181918	−	0.983314i	$-0.558231\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.316039	−	0.547396i	−0.0125416	−	0.0217227i
$636$		0			0
$637$	29.8994	−	10.8825i	1.18466	−	0.431179i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−5.24003	+	4.39691i	−0.206969	+	0.173667i	−0.740380	−	0.672189i	$-0.765354\pi$
$641$	−5.24003	+	4.39691i	−0.206969	+	0.173667i	0.533411	+	0.845856i	$0.320910\pi$
$642$		0			0
$643$	−2.89363	−	16.4106i	−0.114114	−	0.647171i	−0.987185	−	0.159579i	$-0.948986\pi$
$643$	−2.89363	−	16.4106i	−0.114114	−	0.647171i	0.873072	−	0.487592i	$-0.162125\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−36.1664			−1.42185			−0.710924	−	0.703269i	$-0.751723\pi$
$647$	−36.1664			−1.42185			−0.710924	+	0.703269i	$0.751723\pi$
$648$		0			0
$649$	2.14629	+	12.1722i	0.0842494	+	0.477802i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−4.83426	+	8.37319i	−0.189179	+	0.327668i	−0.944977	−	0.327137i	$-0.893916\pi$
$653$	−4.83426	+	8.37319i	−0.189179	+	0.327668i	0.755798	+	0.654805i	$0.227249\pi$
$654$		0			0
$655$	4.66127	−	1.69656i	0.182131	−	0.0662902i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−4.94409	+	28.0393i	−0.192594	+	1.09226i	0.723209	+	0.690629i	$0.242666\pi$
$659$	−4.94409	+	28.0393i	−0.192594	+	1.09226i	−0.915803	+	0.401627i	$0.868445\pi$
$660$		0			0
$661$	−19.5360	−	16.3927i	−0.759863	−	0.637601i	0.178228	−	0.983989i	$-0.442964\pi$
$661$	−19.5360	−	16.3927i	−0.759863	−	0.637601i	−0.938091	+	0.346388i	$0.887408\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	0.814604	−	1.17135i	0.0315890	−	0.0454231i
$666$		0			0
$667$	−22.1508	−	8.06223i	−0.857683	−	0.312171i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	1.20652	−	6.84252i	0.0465772	−	0.264153i
$672$		0			0
$673$	20.3192	+	35.1938i	0.783246	+	1.35662i	0.930041	+	0.367456i	$0.119771\pi$
$673$	20.3192	+	35.1938i	0.783246	+	1.35662i	−0.146795	+	0.989167i	$0.546896\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	10.2220	−	17.7050i	0.392862	−	0.680457i	−0.599964	−	0.800027i	$-0.704818\pi$
$677$	10.2220	−	17.7050i	0.392862	−	0.680457i	0.992826	+	0.119570i	$0.0381517\pi$
$678$		0			0
$679$	12.7305	−	10.6822i	0.488552	−	0.409944i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−39.8318			−1.52412			−0.762061	−	0.647505i	$-0.775813\pi$
$683$	−39.8318			−1.52412			−0.762061	+	0.647505i	$0.775813\pi$
$684$		0			0
$685$	1.60887			0.0614718
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−19.7084	+	16.5373i	−0.750831	+	0.630022i
$690$		0			0
$691$	14.0389	−	24.3160i	0.534064	−	0.925025i	−0.465144	−	0.885235i	$-0.653998\pi$
$691$	14.0389	−	24.3160i	0.534064	−	0.925025i	0.999208	−	0.0397906i	$-0.0126691\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	0.724079	+	1.25414i	0.0274659	+	0.0475723i
$696$		0			0
$697$	7.43206	−	42.1493i	0.281509	−	1.59652i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	4.02822	+	1.46615i	0.152144	+	0.0553757i	0.416969	−	0.908921i	$-0.363092\pi$
$701$	4.02822	+	1.46615i	0.152144	+	0.0553757i	−0.264826	+	0.964296i	$0.585314\pi$
$702$		0			0
$703$	11.4829	+	11.4095i	0.433086	+	0.430317i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	15.2115	+	12.7639i	0.572087	+	0.480038i
$708$		0			0
$709$	−0.715927	+	4.06022i	−0.0268872	+	0.152485i	−0.995296	−	0.0968845i	$-0.969112\pi$
$709$	−0.715927	+	4.06022i	−0.0268872	+	0.152485i	0.968408	+	0.249369i	$0.0802234\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−0.457045	+	0.166351i	−0.0171165	+	0.00622989i
$714$		0			0
$715$	−0.988438	+	1.71202i	−0.0369655	+	0.0640261i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	7.79796	+	44.2244i	0.290815	+	1.64929i	0.683742	+	0.729724i	$0.260351\pi$
$719$	7.79796	+	44.2244i	0.290815	+	1.64929i	−0.392927	+	0.919570i	$0.628538\pi$
$720$		0			0
$721$	−15.4050			−0.573712
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−3.31776	−	18.8160i	−0.123219	−	0.698807i
$726$		0			0
$727$	−26.7341	+	22.4326i	−0.991514	+	0.831979i	−0.985786	−	0.168005i	$-0.946268\pi$
$727$	−26.7341	+	22.4326i	−0.991514	+	0.831979i	−0.00572754	+	0.999984i	$0.501823\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	1.54595	−	0.562680i	0.0571791	−	0.0208115i
$732$		0			0
$733$	0.524006	+	0.907605i	0.0193546	+	0.0335232i	0.875540	−	0.483145i	$-0.160506\pi$
$733$	0.524006	+	0.907605i	0.0193546	+	0.0335232i	−0.856186	+	0.516668i	$0.827172\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−3.52909	−	2.96126i	−0.129996	−	0.109079i
$738$		0			0
$739$	−20.8426	−	7.58607i	−0.766706	−	0.279058i	−0.0710882	−	0.997470i	$-0.522647\pi$
$739$	−20.8426	−	7.58607i	−0.766706	−	0.279058i	−0.695618	+	0.718412i	$0.744869\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−35.7965	−	13.0288i	−1.31325	−	0.477982i	−0.411957	−	0.911203i	$-0.635155\pi$
$743$	−35.7965	−	13.0288i	−1.31325	−	0.477982i	−0.901288	+	0.433221i	$0.857377\pi$
$744$		0			0
$745$	−2.57357	−	2.15948i	−0.0942884	−	0.0791174i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	0.573986	+	0.994173i	0.0209730	+	0.0363263i
$750$		0			0
$751$	11.9657	−	4.35515i	0.436634	−	0.158922i	−0.114345	−	0.993441i	$-0.536477\pi$
$751$	11.9657	−	4.35515i	0.436634	−	0.158922i	0.550979	+	0.834519i	$0.314255\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	3.21306	−	2.69608i	0.116935	−	0.0981203i
$756$		0			0
$757$	7.21125	+	40.8970i	0.262097	+	1.48643i	0.777175	+	0.629284i	$0.216652\pi$
$757$	7.21125	+	40.8970i	0.262097	+	1.48643i	−0.515078	+	0.857143i	$0.672237\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−36.4398			−1.32094			−0.660471	−	0.750851i	$-0.729643\pi$
$761$	−36.4398			−1.32094			−0.660471	+	0.750851i	$0.729643\pi$
$762$		0			0
$763$	2.72173	+	15.4357i	0.0985333	+	0.558810i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	27.9324	−	48.3803i	1.00858	−	1.74691i
$768$		0			0
$769$	−11.0091	+	4.00697i	−0.396997	+	0.144495i	−0.532801	−	0.846241i	$-0.678860\pi$
$769$	−11.0091	+	4.00697i	−0.396997	+	0.144495i	0.135804	+	0.990736i	$0.456638\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−6.22310	+	35.2929i	−0.223829	+	1.26940i	0.641081	+	0.767473i	$0.278486\pi$
$773$	−6.22310	+	35.2929i	−0.223829	+	1.26940i	−0.864911	+	0.501926i	$0.832625\pi$
$774$		0			0
$775$	−0.301994	−	0.253403i	−0.0108480	−	0.00910251i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	16.0082	−	23.0189i	0.573553	−	0.824736i
$780$		0			0
$781$	−10.9041	−	3.96875i	−0.390178	−	0.142013i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	0.540717	−	3.06656i	0.0192990	−	0.109450i
$786$		0			0
$787$	−1.05573	−	1.82858i	−0.0376328	−	0.0651819i	0.846596	−	0.532237i	$-0.178648\pi$
$787$	−1.05573	−	1.82858i	−0.0376328	−	0.0651819i	−0.884228	+	0.467055i	$0.845315\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	9.59033	−	16.6109i	0.340993	−	0.590617i
$792$		0			0
$793$	−24.0568	+	20.1860i	−0.854282	+	0.716827i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−14.9794			−0.530596			−0.265298	−	0.964166i	$-0.585470\pi$
$797$	−14.9794			−0.530596			−0.265298	+	0.964166i	$0.585470\pi$
$798$		0			0
$799$	77.1376			2.72893
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−1.05012	+	0.881152i	−0.0370578	+	0.0310952i
$804$		0			0
$805$	0.993506	−	1.72080i	0.0350165	−	0.0606503i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−19.1248	−	33.1251i	−0.672392	−	1.16462i	−0.977224	−	0.212211i	$-0.931933\pi$
$809$	−19.1248	−	33.1251i	−0.672392	−	1.16462i	0.304831	−	0.952406i	$-0.401400\pi$
$810$		0			0
$811$	5.50463	−	31.2183i	0.193294	−	1.09622i	−0.721534	−	0.692379i	$-0.756563\pi$
$811$	5.50463	−	31.2183i	0.193294	−	1.09622i	0.914828	−	0.403844i	$-0.132326\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1.05670	+	0.384606i	0.0370145	+	0.0134722i
$816$		0			0
$817$	1.07394	+	0.0904882i	0.0375726	+	0.00316578i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	10.7629	+	9.03111i	0.375627	+	0.315188i	0.810983	−	0.585070i	$-0.198933\pi$
$821$	10.7629	+	9.03111i	0.375627	+	0.315188i	−0.435356	+	0.900258i	$0.643378\pi$
$822$		0			0
$823$	−3.19150	+	18.0999i	−0.111249	+	0.630923i	0.877291	+	0.479960i	$0.159349\pi$
$823$	−3.19150	+	18.0999i	−0.111249	+	0.630923i	−0.988539	+	0.150963i	$0.951762\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−5.23011	+	1.90360i	−0.181869	+	0.0661948i	−0.431349	−	0.902185i	$-0.641962\pi$
$827$	−5.23011	+	1.90360i	−0.181869	+	0.0661948i	0.249481	+	0.968380i	$0.419740\pi$
$828$		0			0
$829$	21.0061	−	36.3837i	0.729573	−	1.26366i	−0.227490	−	0.973780i	$-0.573052\pi$
$829$	21.0061	−	36.3837i	0.729573	−	1.26366i	0.957064	−	0.289878i	$-0.0936146\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	6.53353	+	37.0535i	0.226373	+	1.28383i
$834$		0			0
$835$	−2.28324			−0.0790148
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−5.46639	−	31.0014i	−0.188721	−	1.07029i	−0.921081	−	0.389371i	$-0.872692\pi$
$839$	−5.46639	−	31.0014i	−0.188721	−	1.07029i	0.732360	−	0.680918i	$-0.238419\pi$
$840$		0			0
$841$	−10.6645	+	8.94862i	−0.367743	+	0.308573i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	4.94881	−	1.80122i	0.170244	−	0.0619638i
$846$		0			0
$847$	5.48047	+	9.49246i	0.188311	+	0.326165i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	17.2696	+	14.4909i	0.591993	+	0.496741i
$852$		0			0
$853$	−10.6345	−	3.87065i	−0.364119	−	0.132529i	0.153480	−	0.988152i	$-0.450952\pi$
$853$	−10.6345	−	3.87065i	−0.364119	−	0.132529i	−0.517599	+	0.855623i	$0.673174\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	46.2117	+	16.8197i	1.57856	+	0.574550i	0.974891	−	0.222683i	$-0.0714814\pi$
$857$	46.2117	+	16.8197i	1.57856	+	0.574550i	0.603672	+	0.797233i	$0.293704\pi$
$858$		0			0
$859$	19.9118	+	16.7080i	0.679382	+	0.570069i	0.915826	−	0.401576i	$-0.131537\pi$
$859$	19.9118	+	16.7080i	0.679382	+	0.570069i	−0.236444	+	0.971645i	$0.575982\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−0.199487	−	0.345522i	−0.00679062	−	0.0117617i	0.862610	−	0.505869i	$-0.168828\pi$
$863$	−0.199487	−	0.345522i	−0.00679062	−	0.0117617i	−0.869401	+	0.494108i	$0.835495\pi$
$864$		0			0
$865$	1.73084	−	0.629973i	0.0588502	−	0.0214197i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	8.28873	−	6.95507i	0.281176	−	0.235935i
$870$		0			0
$871$	3.61575	+	20.5059i	0.122515	+	0.694817i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	3.24715			0.109774
$876$		0			0
$877$	1.98754	+	11.2719i	0.0671145	+	0.380625i	0.999801	+	0.0199377i	$0.00634679\pi$
$877$	1.98754	+	11.2719i	0.0671145	+	0.380625i	−0.932687	+	0.360687i	$0.882542\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−8.37742	+	14.5101i	−0.282242	+	0.488858i	−0.971937	−	0.235242i	$-0.924412\pi$
$881$	−8.37742	+	14.5101i	−0.282242	+	0.488858i	0.689694	+	0.724101i	$0.257745\pi$
$882$		0			0
$883$	−43.5805	+	15.8620i	−1.46660	+	0.533799i	−0.947175	−	0.320718i	$-0.896076\pi$
$883$	−43.5805	+	15.8620i	−1.46660	+	0.533799i	−0.519425	+	0.854516i	$0.673854\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	3.45930	−	19.6187i	0.116152	−	0.658730i	−0.870022	−	0.493014i	$-0.835895\pi$
$887$	3.45930	−	19.6187i	0.116152	−	0.658730i	0.986173	−	0.165717i	$-0.0529937\pi$
$888$		0			0
$889$	−1.99008	−	1.66988i	−0.0667452	−	0.0560059i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	45.8666	+	21.2091i	1.53487	+	0.709736i
$894$		0			0
$895$	2.60740	+	0.949015i	0.0871557	+	0.0317221i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	0.0540251	−	0.306392i	0.00180184	−	0.0102187i
$900$		0			0
$901$	−15.2114	−	26.3469i	−0.506766	−	0.877744i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−1.94399	+	3.36710i	−0.0646206	+	0.111926i
$906$		0			0
$907$	8.40693	−	7.05425i	0.279147	−	0.234232i	−0.492455	−	0.870338i	$-0.663900\pi$
$907$	8.40693	−	7.05425i	0.279147	−	0.234232i	0.771602	+	0.636106i	$0.219456\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	1.79760			0.0595572			0.0297786	−	0.999557i	$-0.490520\pi$
$911$	1.79760			0.0595572			0.0297786	+	0.999557i	$0.490520\pi$
$912$		0			0
$913$	−14.3694			−0.475559
$914$		0			0
$915$		0			0
$916$		0			0
$917$	15.6177	−	13.1048i	0.515743	−	0.432760i
$918$		0			0
$919$	−2.62319	+	4.54349i	−0.0865309	+	0.149876i	−0.906043	−	0.423187i	$-0.860911\pi$
$919$	−2.62319	+	4.54349i	−0.0865309	+	0.149876i	0.819512	+	0.573063i	$0.194245\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	26.2235	+	45.4205i	0.863158	+	1.49503i
$924$		0			0
$925$	−3.17299	+	17.9949i	−0.104327	+	0.591669i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−24.9915	−	9.09617i	−0.819946	−	0.298436i	−0.102220	−	0.994762i	$-0.532595\pi$
$929$	−24.9915	−	9.09617i	−0.819946	−	0.298436i	−0.717726	+	0.696326i	$0.754817\pi$
$930$		0			0
$931$	−6.30304	+	23.8287i	−0.206574	+	0.780955i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−1.79075	−	1.50262i	−0.0585638	−	0.0491408i
$936$		0			0
$937$	1.97310	−	11.1900i	0.0644582	−	0.365561i	−0.935468	−	0.353411i	$-0.885022\pi$
$937$	1.97310	−	11.1900i	0.0644582	−	0.365561i	0.999926	−	0.0121492i	$-0.00386732\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	46.0984	−	16.7785i	1.50277	−	0.546962i	0.545991	−	0.837791i	$-0.316153\pi$
$941$	46.0984	−	16.7785i	1.50277	−	0.546962i	0.956775	+	0.290829i	$0.0939309\pi$
$942$		0			0
$943$	19.5239	−	33.8164i	0.635785	−	1.10121i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	0.862194	+	4.88975i	0.0280175	+	0.158895i	0.995607	−	0.0936345i	$-0.0298485\pi$
$947$	0.862194	+	4.88975i	0.0280175	+	0.158895i	−0.967589	+	0.252530i	$0.918737\pi$
$948$		0			0
$949$	6.19587			0.201126
$950$		0			0
$951$		0			0
$952$		0			0
$953$	7.05030	+	39.9842i	0.228382	+	1.29522i	0.856114	+	0.516787i	$0.172872\pi$
$953$	7.05030	+	39.9842i	0.228382	+	1.29522i	−0.627732	+	0.778429i	$0.716017\pi$
$954$		0			0
$955$	0.222964	−	0.187089i	0.00721493	−	0.00605405i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	6.21374	−	2.26162i	0.200652	−	0.0730314i
$960$		0			0
$961$	15.4968	+	26.8412i	0.499896	+	0.865846i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	0.506918	+	0.425355i	0.0163183	+	0.0136927i
$966$		0			0
$967$	−4.40584	−	1.60359i	−0.141682	−	0.0515681i	0.270206	−	0.962803i	$-0.412908\pi$
$967$	−4.40584	−	1.60359i	−0.141682	−	0.0515681i	−0.411888	+	0.911234i	$0.635130\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	31.9910	+	11.6438i	1.02664	+	0.373666i	0.799800	−	0.600266i	$-0.204939\pi$
$971$	31.9910	+	11.6438i	1.02664	+	0.373666i	0.226839	+	0.973932i	$0.427161\pi$
$972$		0			0
$973$	4.55948	+	3.82586i	0.146170	+	0.122651i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	5.37934	+	9.31729i	0.172100	+	0.298086i	0.939154	−	0.343497i	$-0.111611\pi$
$977$	5.37934	+	9.31729i	0.172100	+	0.298086i	−0.767054	+	0.641583i	$0.778278\pi$
$978$		0			0
$979$	2.81964	−	1.02627i	0.0901161	−	0.0327996i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−46.0661	+	38.6540i	−1.46928	+	1.23287i	−0.552480	+	0.833526i	$0.686318\pi$
$983$	−46.0661	+	38.6540i	−1.46928	+	1.23287i	−0.916800	+	0.399346i	$0.869237\pi$
$984$		0			0
$985$	0.762906	+	4.32665i	0.0243082	+	0.137859i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	1.50095			0.0477275
$990$		0			0
$991$	−6.88681	−	39.0571i	−0.218767	−	1.24069i	−0.874249	−	0.485478i	$-0.838646\pi$
$991$	−6.88681	−	39.0571i	−0.218767	−	1.24069i	0.655482	−	0.755211i	$-0.272465\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−1.93255	+	3.34728i	−0.0612660	+	0.106116i
$996$		0			0
$997$	13.8021	−	5.02356i	0.437117	−	0.159098i	−0.114082	−	0.993471i	$-0.536393\pi$
$997$	13.8021	−	5.02356i	0.437117	−	0.159098i	0.551199	+	0.834374i	$0.314170\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.bo.c.289.1		12
3.2	odd	2		76.2.i.a.61.2	yes	12
12.11	even	2		304.2.u.e.289.1		12
19.5	even	9	inner	684.2.bo.c.613.1		12
57.5	odd	18		76.2.i.a.5.2	✓	12
57.23	odd	18		1444.2.e.g.653.3		12
57.29	even	18		1444.2.a.g.1.3		6
57.32	even	18		1444.2.e.h.429.4		12
57.44	odd	18		1444.2.e.g.429.3		12
57.47	odd	18		1444.2.a.h.1.4		6
57.53	even	18		1444.2.e.h.653.4		12
228.47	even	18		5776.2.a.bw.1.3		6
228.119	even	18		304.2.u.e.81.1		12
228.143	odd	18		5776.2.a.by.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.2.i.a.5.2	✓	12	57.5	odd	18
76.2.i.a.61.2	yes	12	3.2	odd	2
304.2.u.e.81.1		12	228.119	even	18
304.2.u.e.289.1		12	12.11	even	2
684.2.bo.c.289.1		12	1.1	even	1	trivial
684.2.bo.c.613.1		12	19.5	even	9	inner
1444.2.a.g.1.3		6	57.29	even	18
1444.2.a.h.1.4		6	57.47	odd	18
1444.2.e.g.429.3		12	57.44	odd	18
1444.2.e.g.653.3		12	57.23	odd	18
1444.2.e.h.429.4		12	57.32	even	18
1444.2.e.h.653.4		12	57.53	even	18
5776.2.a.bw.1.3		6	228.47	even	18
5776.2.a.by.1.4		6	228.143	odd	18

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.bo (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.216181 + 0.181398i) q^{5} +(-0.579936 + 1.00448i) q^{7} +(0.622469 + 1.07815i) q^{11} +(0.977096 - 5.54139i) q^{13} +(6.25251 + 2.27573i) q^{17} +(3.09208 + 3.07231i) q^{19} +(4.65029 + 3.90205i) q^{23} +(-0.854412 + 4.84561i) q^{25} +(-3.64892 + 1.32810i) q^{29} +(-0.0400606 + 0.0693870i) q^{31} +(-0.0568388 - 0.322349i) q^{35} +3.71365 q^{37} +(-1.11697 - 6.33464i) q^{41} +(0.189407 - 0.158931i) q^{43} +(10.8939 - 3.96505i) q^{47} +(2.82735 + 4.89711i) q^{49} +(-3.50255 - 2.93899i) q^{53} +(-0.330140 - 0.120161i) q^{55} +(9.32947 + 3.39565i) q^{59} +(-4.27534 - 3.58744i) q^{61} +(0.793965 + 1.37519i) q^{65} +(-3.47734 + 1.26565i) q^{67} +(-7.14016 + 5.99131i) q^{71} +(0.191208 + 1.08439i) q^{73} -1.44397 q^{77} +(-1.50923 - 8.55928i) q^{79} +(-5.77114 + 9.99591i) q^{83} +(-1.76449 + 0.642221i) q^{85} +(0.418534 - 2.37362i) q^{89} +(4.99955 + 4.19512i) q^{91} +(-1.22576 - 0.103280i) q^{95} +(-13.4638 - 4.90042i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{7} - 3 q^{11} - 9 q^{13} + 3 q^{17} - 12 q^{19} + 12 q^{23} - 18 q^{25} - 27 q^{29} + 6 q^{31} - 33 q^{35} - 12 q^{37} - 3 q^{41} + 27 q^{43} + 15 q^{47} + 9 q^{49} + 21 q^{53} - 27 q^{55} + 48 q^{59}+ \cdots + 12 q^{97}+O(q^{100}) \) 12 * q + 3 * q^7 - 3 * q^11 - 9 * q^13 + 3 * q^17 - 12 * q^19 + 12 * q^23 - 18 * q^25 - 27 * q^29 + 6 * q^31 - 33 * q^35 - 12 * q^37 - 3 * q^41 + 27 * q^43 + 15 * q^47 + 9 * q^49 + 21 * q^53 - 27 * q^55 + 48 * q^59 - 6 * q^61 + 33 * q^65 + 24 * q^67 + 30 * q^73 - 24 * q^77 + 3 * q^79 - 3 * q^83 - 42 * q^85 + 18 * q^89 - 24 * q^91 - 9 * q^95 + 12 * q^97

Introduction

L-functions

Modular forms

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