LMFDB - Embedded newform 792.2.k.a.683.29

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [792,2,Mod(683,792)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("792.683"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(792, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 792 = 2^{3} \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	792.k (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$6.32415184009$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			683.29
Character	$\chi$	$=$	792.683
Dual form			792.2.k.a.683.30

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.885984 - 1.10229i) q^{2} +(-0.430065 - 1.95321i) q^{4} -3.67452 q^{5} -4.28843i q^{7} +(-2.53403 - 1.25646i) q^{8} +(-3.25556 + 4.05037i) q^{10} -1.00000i q^{11} +7.11160i q^{13} +(-4.72707 - 3.79948i) q^{14} +(-3.63009 + 1.68002i) q^{16} +4.85960i q^{17} +0.571401 q^{19} +(1.58028 + 7.17712i) q^{20} +(-1.10229 - 0.885984i) q^{22} -3.61453 q^{23} +8.50209 q^{25} +(7.83901 + 6.30076i) q^{26} +(-8.37621 + 1.84430i) q^{28} -3.99360 q^{29} -7.49755i q^{31} +(-1.36434 + 5.48986i) q^{32} +(5.35667 + 4.30553i) q^{34} +15.7579i q^{35} -5.62197i q^{37} +(0.506252 - 0.629847i) q^{38} +(9.31134 + 4.61689i) q^{40} -4.14379i q^{41} -7.29206 q^{43} +(-1.95321 + 0.430065i) q^{44} +(-3.20241 + 3.98424i) q^{46} -5.48001 q^{47} -11.3906 q^{49} +(7.53272 - 9.37173i) q^{50} +(13.8905 - 3.05845i) q^{52} -6.86693 q^{53} +3.67452i q^{55} +(-5.38824 + 10.8670i) q^{56} +(-3.53826 + 4.40208i) q^{58} +0.106064i q^{59} +4.52167i q^{61} +(-8.26444 - 6.64271i) q^{62} +(4.84261 + 6.36782i) q^{64} -26.1317i q^{65} +4.89107 q^{67} +(9.49184 - 2.08995i) q^{68} +(17.3697 + 13.9612i) q^{70} -0.651184 q^{71} -6.32539 q^{73} +(-6.19701 - 4.98097i) q^{74} +(-0.245740 - 1.11607i) q^{76} -4.28843 q^{77} -13.2255i q^{79} +(13.3388 - 6.17326i) q^{80} +(-4.56764 - 3.67133i) q^{82} -7.98402i q^{83} -17.8567i q^{85} +(-6.46064 + 8.03793i) q^{86} +(-1.25646 + 2.53403i) q^{88} +5.40135i q^{89} +30.4976 q^{91} +(1.55448 + 7.05995i) q^{92} +(-4.85520 + 6.04054i) q^{94} -2.09963 q^{95} -1.44563 q^{97} +(-10.0919 + 12.5557i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{4} + 8 q^{10} - 8 q^{16} + 32 q^{19} + 40 q^{25} - 32 q^{28} + 32 q^{34} + 16 q^{40} - 24 q^{46} - 8 q^{49} + 40 q^{52} - 8 q^{58} + 16 q^{64} + 72 q^{70} + 32 q^{73} - 8 q^{76} - 64 q^{82}+ \cdots - 32 q^{97}+O(q^{100}) $ 40 * q - 8 * q^4 + 8 * q^10 - 8 * q^16 + 32 * q^19 + 40 * q^25 - 32 * q^28 + 32 * q^34 + 16 * q^40 - 24 * q^46 - 8 * q^49 + 40 * q^52 - 8 * q^58 + 16 * q^64 + 72 * q^70 + 32 * q^73 - 8 * q^76 - 64 * q^82 - 24 * q^88 - 56 * q^94 - 32 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/792\mathbb{Z}\right)^\times$.

$n$	$145$	$199$	$353$	$397$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.885984	−	1.10229i	0.626485	−	0.779433i
$2$	0.885984	−	1.10229i	0.626485	−	0.779433i
$3$		0			0
$3$		0			0
$4$	−0.430065	−	1.95321i	−0.215033	−	0.976607i
$5$	−3.67452			−1.64330			−0.821648	−	0.569996i	$-0.806945\pi$
$5$	−3.67452			−1.64330			−0.821648	+	0.569996i	$0.806945\pi$
$6$		0			0
$7$		−	4.28843i		−	1.62087i	−0.585827	−	0.810436i	$-0.699230\pi$
$7$		−	4.28843i		−	1.62087i	0.585827	−	0.810436i	$-0.300770\pi$
$8$	−2.53403	−	1.25646i	−0.895915	−	0.444226i
$9$		0			0
$10$	−3.25556	+	4.05037i	−1.02950	+	1.28084i
$11$		−	1.00000i		−	0.301511i
$11$		−	1.00000i		−	0.301511i
$12$		0			0
$13$			7.11160i			1.97240i	0.165550	+	0.986201i	$0.447060\pi$
$13$			7.11160i			1.97240i	−0.165550	+	0.986201i	$0.552940\pi$
$14$	−4.72707	−	3.79948i	−1.26336	−	1.01545i
$15$		0			0
$16$	−3.63009	+	1.68002i	−0.907522	+	0.420005i
$17$			4.85960i			1.17863i	0.807905	+	0.589313i	$0.200602\pi$
$17$			4.85960i			1.17863i	−0.807905	+	0.589313i	$0.799398\pi$
$18$		0			0
$19$	0.571401			0.131088			0.0655442	−	0.997850i	$-0.479122\pi$
$19$	0.571401			0.131088			0.0655442	+	0.997850i	$0.479122\pi$
$20$	1.58028	+	7.17712i	0.353362	+	1.60485i
$21$		0			0
$22$	−1.10229	−	0.885984i	−0.235008	−	0.188892i
$23$	−3.61453			−0.753681			−0.376841	−	0.926278i	$-0.622990\pi$
$23$	−3.61453			−0.753681			−0.376841	+	0.926278i	$0.622990\pi$
$24$		0			0
$25$	8.50209			1.70042
$26$	7.83901	+	6.30076i	1.53736	+	1.23568i
$27$		0			0
$28$	−8.37621	+	1.84430i	−1.58296	+	0.348541i
$29$	−3.99360			−0.741592			−0.370796	−	0.928714i	$-0.620915\pi$
$29$	−3.99360			−0.741592			−0.370796	+	0.928714i	$0.620915\pi$
$30$		0			0
$31$		−	7.49755i		−	1.34660i	−0.739369	−	0.673300i	$-0.764876\pi$
$31$		−	7.49755i		−	1.34660i	0.739369	−	0.673300i	$-0.235124\pi$
$32$	−1.36434	+	5.48986i	−0.241183	+	0.970480i
$33$		0			0
$34$	5.35667	+	4.30553i	0.918661	+	0.738392i
$35$			15.7579i			2.66357i
$36$		0			0
$37$		−	5.62197i		−	0.924246i	−0.886816	−	0.462123i	$-0.847088\pi$
$37$		−	5.62197i		−	0.924246i	0.886816	−	0.462123i	$-0.152912\pi$
$38$	0.506252	−	0.629847i	0.0821250	−	0.102175i
$39$		0			0
$40$	9.31134	+	4.61689i	1.47225	+	0.729994i
$41$		−	4.14379i		−	0.647151i	−0.946202	−	0.323575i	$-0.895115\pi$
$41$		−	4.14379i		−	0.647151i	0.946202	−	0.323575i	$-0.104885\pi$
$42$		0			0
$43$	−7.29206			−1.11203			−0.556014	−	0.831173i	$-0.687670\pi$
$43$	−7.29206			−1.11203			−0.556014	+	0.831173i	$0.687670\pi$
$44$	−1.95321	+	0.430065i	−0.294458	+	0.0648348i
$45$		0			0
$46$	−3.20241	+	3.98424i	−0.472170	+	0.587444i
$47$	−5.48001			−0.799342			−0.399671	−	0.916659i	$-0.630876\pi$
$47$	−5.48001			−0.799342			−0.399671	+	0.916659i	$0.630876\pi$
$48$		0			0
$49$	−11.3906			−1.62723
$50$	7.53272	−	9.37173i	1.06529	−	1.32536i
$51$		0			0
$52$	13.8905	−	3.05845i	1.92626	−	0.424131i
$53$	−6.86693			−0.943246			−0.471623	−	0.881800i	$-0.656332\pi$
$53$	−6.86693			−0.943246			−0.471623	+	0.881800i	$0.656332\pi$
$54$		0			0
$55$			3.67452i			0.495472i
$56$	−5.38824	+	10.8670i	−0.720034	+	1.45216i
$57$		0			0
$58$	−3.53826	+	4.40208i	−0.464596	+	0.578022i
$59$			0.106064i			0.0138084i	0.999976	+	0.00690418i	$0.00219769\pi$
$59$			0.106064i			0.0138084i	−0.999976	+	0.00690418i	$0.997802\pi$
$60$		0			0
$61$			4.52167i			0.578941i	0.957187	+	0.289471i	$0.0934792\pi$
$61$			4.52167i			0.578941i	−0.957187	+	0.289471i	$0.906521\pi$
$62$	−8.26444	−	6.64271i	−1.04959	−	0.843625i
$63$		0			0
$64$	4.84261	+	6.36782i	0.605327	+	0.795977i
$65$		−	26.1317i		−	3.24124i
$66$		0			0
$67$	4.89107			0.597540			0.298770	−	0.954325i	$-0.403424\pi$
$67$	4.89107			0.597540			0.298770	+	0.954325i	$0.403424\pi$
$68$	9.49184	−	2.08995i	1.15105	−	0.253443i
$69$		0			0
$70$	17.3697	+	13.9612i	2.07608	+	1.66869i
$71$	−0.651184			−0.0772813			−0.0386407	−	0.999253i	$-0.512303\pi$
$71$	−0.651184			−0.0772813			−0.0386407	+	0.999253i	$0.512303\pi$
$72$		0			0
$73$	−6.32539			−0.740331			−0.370165	−	0.928966i	$-0.620699\pi$
$73$	−6.32539			−0.740331			−0.370165	+	0.928966i	$0.620699\pi$
$74$	−6.19701	−	4.98097i	−0.720388	−	0.579026i
$75$		0			0
$76$	−0.245740	−	1.11607i	−0.0281883	−	0.128022i
$77$	−4.28843			−0.488711
$78$		0			0
$79$		−	13.2255i		−	1.48799i	−0.668187	−	0.743993i	$-0.732930\pi$
$79$		−	13.2255i		−	1.48799i	0.668187	−	0.743993i	$-0.267070\pi$
$80$	13.3388	−	6.17326i	1.49133	−	0.690192i
$81$		0			0
$82$	−4.56764	−	3.67133i	−0.504411	−	0.405430i
$83$		−	7.98402i		−	0.876361i	−0.898887	−	0.438180i	$-0.855623\pi$
$83$		−	7.98402i		−	0.876361i	0.898887	−	0.438180i	$-0.144377\pi$
$84$		0			0
$85$		−	17.8567i		−	1.93683i
$86$	−6.46064	+	8.03793i	−0.696669	+	0.866752i
$87$		0			0
$88$	−1.25646	+	2.53403i	−0.133939	+	0.270128i
$89$			5.40135i			0.572542i	0.958149	+	0.286271i	$0.0924157\pi$
$89$			5.40135i			0.572542i	−0.958149	+	0.286271i	$0.907584\pi$
$90$		0			0
$91$	30.4976			3.19701
$92$	1.55448	+	7.05995i	0.162066	+	0.736050i
$93$		0			0
$94$	−4.85520	+	6.04054i	−0.500776	+	0.623034i
$95$	−2.09963			−0.215417
$96$		0			0
$97$	−1.44563			−0.146782			−0.0733908	−	0.997303i	$-0.523382\pi$
$97$	−1.44563			−0.146782			−0.0733908	+	0.997303i	$0.523382\pi$
$98$	−10.0919	+	12.5557i	−1.01943	+	1.26832i
$99$		0			0
$100$	−3.65646	−	16.6064i	−0.365646	−	1.66064i
$101$	11.5112			1.14541			0.572705	−	0.819762i	$-0.305894\pi$
$101$	11.5112			1.14541			0.572705	+	0.819762i	$0.305894\pi$
$102$		0			0
$103$			5.05511i			0.498095i	0.968491	+	0.249047i	$0.0801175\pi$
$103$			5.05511i			0.498095i	−0.968491	+	0.249047i	$0.919883\pi$
$104$	8.93545	−	18.0210i	0.876193	−	1.76710i
$105$		0			0
$106$	−6.08399	+	7.56932i	−0.590930	+	0.735197i
$107$		−	1.46547i		−	0.141673i	−0.997488	−	0.0708363i	$-0.977433\pi$
$107$		−	1.46547i		−	0.141673i	0.997488	−	0.0708363i	$-0.0225668\pi$
$108$		0			0
$109$			2.43341i			0.233079i	0.993186	+	0.116539i	$0.0371801\pi$
$109$			2.43341i			0.233079i	−0.993186	+	0.116539i	$0.962820\pi$
$110$	4.05037	+	3.25556i	0.386187	+	0.310406i
$111$		0			0
$112$	7.20464	+	15.5674i	0.680774	+	1.47098i
$113$		−	9.23698i		−	0.868942i	−0.900686	−	0.434471i	$-0.856935\pi$
$113$		−	9.23698i		−	0.868942i	0.900686	−	0.434471i	$-0.143065\pi$
$114$		0			0
$115$	13.2817			1.23852
$116$	1.71751	+	7.80035i	0.159467	+	0.724244i
$117$		0			0
$118$	0.116913	+	0.0939711i	0.0107627	+	0.00865074i
$119$	20.8400			1.91040
$120$		0			0
$121$	−1.00000			−0.0909091
$122$	4.98418	+	4.00613i	0.451246	+	0.362698i
$123$		0			0
$124$	−14.6443	+	3.22444i	−1.31510	+	0.289563i
$125$	−12.8685			−1.15099
$126$		0			0
$127$		−	1.21275i		−	0.107614i	−0.998551	−	0.0538071i	$-0.982864\pi$
$127$		−	1.21275i		−	0.107614i	0.998551	−	0.0538071i	$-0.0171356\pi$
$128$	11.3096	+	0.303843i	0.999639	+	0.0268562i
$129$		0			0
$130$	−28.8046	−	23.1523i	−2.52633	−	2.03059i
$131$		−	9.72206i		−	0.849420i	−0.905329	−	0.424710i	$-0.860376\pi$
$131$		−	9.72206i		−	0.849420i	0.905329	−	0.424710i	$-0.139624\pi$
$132$		0			0
$133$		−	2.45041i		−	0.212478i
$134$	4.33341	−	5.39136i	0.374350	−	0.465742i
$135$		0			0
$136$	6.10590	−	12.3144i	0.523576	−	1.05595i
$137$		−	9.97473i		−	0.852198i	−0.904676	−	0.426099i	$-0.859887\pi$
$137$		−	9.97473i		−	0.852198i	0.904676	−	0.426099i	$-0.140113\pi$
$138$		0			0
$139$	−19.0006			−1.61161			−0.805805	−	0.592181i	$-0.798267\pi$
$139$	−19.0006			−1.61161			−0.805805	+	0.592181i	$0.798267\pi$
$140$	30.7786	−	6.77693i	2.60126	−	0.572755i
$141$		0			0
$142$	−0.576938	+	0.717790i	−0.0484156	+	0.0602356i
$143$	7.11160			0.594702
$144$		0			0
$145$	14.6745			1.21865
$146$	−5.60419	+	6.97238i	−0.463806	+	0.577039i
$147$		0			0
$148$	−10.9809	+	2.41781i	−0.902625	+	0.198743i
$149$	−22.0567			−1.80696			−0.903480	−	0.428631i	$-0.858996\pi$
$149$	−22.0567			−1.80696			−0.903480	+	0.428631i	$0.858996\pi$
$150$		0			0
$151$			18.2008i			1.48116i	0.671970	+	0.740578i	$0.265448\pi$
$151$			18.2008i			1.48116i	−0.671970	+	0.740578i	$0.734552\pi$
$152$	−1.44795	−	0.717944i	−0.117444	−	0.0582329i
$153$		0			0
$154$	−3.79948	+	4.72707i	−0.306170	+	0.380918i
$155$			27.5499i			2.21286i
$156$		0			0
$157$			7.69643i			0.614242i	0.951670	+	0.307121i	$0.0993657\pi$
$157$			7.69643i			0.614242i	−0.951670	+	0.307121i	$0.900634\pi$
$158$	−14.5783	−	11.7176i	−1.15979	−	0.932201i
$159$		0			0
$160$	5.01329	−	20.1726i	0.396335	−	1.59478i
$161$			15.5006i			1.22162i
$162$		0			0
$163$	6.32104			0.495102			0.247551	−	0.968875i	$-0.420374\pi$
$163$	6.32104			0.495102			0.247551	+	0.968875i	$0.420374\pi$
$164$	−8.09370	+	1.78210i	−0.632012	+	0.139159i
$165$		0			0
$166$	−8.80067	−	7.07372i	−0.683065	−	0.549027i
$167$	13.2831			1.02788			0.513939	−	0.857827i	$-0.328186\pi$
$167$	13.2831			1.02788			0.513939	+	0.857827i	$0.328186\pi$
$168$		0			0
$169$	−37.5748			−2.89037
$170$	−19.6832	−	15.8207i	−1.50963	−	1.21340i
$171$		0			0
$172$	3.13606	+	14.2429i	0.239122	+	1.08601i
$173$	−3.07050			−0.233446			−0.116723	−	0.993165i	$-0.537239\pi$
$173$	−3.07050			−0.233446			−0.116723	+	0.993165i	$0.537239\pi$
$174$		0			0
$175$		−	36.4606i		−	2.75616i
$176$	1.68002	+	3.63009i	0.126636	+	0.273628i
$177$		0			0
$178$	5.95383	+	4.78551i	0.446258	+	0.358689i
$179$			0.702082i			0.0524761i	0.999656	+	0.0262380i	$0.00835279\pi$
$179$			0.702082i			0.0524761i	−0.999656	+	0.0262380i	$0.991647\pi$
$180$		0			0
$181$		−	17.3215i		−	1.28750i	−0.765237	−	0.643749i	$-0.777378\pi$
$181$		−	17.3215i		−	1.28750i	0.765237	−	0.643749i	$-0.222622\pi$
$182$	27.0203	−	33.6170i	2.00288	−	2.49186i
$183$		0			0
$184$	9.15932	+	4.54151i	0.675234	+	0.334805i
$185$			20.6580i			1.51881i
$186$		0			0
$187$	4.85960			0.355369
$188$	2.35676	+	10.7036i	0.171885	+	0.780643i
$189$		0			0
$190$	−1.86023	+	2.31439i	−0.134956	+	0.167903i
$191$	−5.73102			−0.414682			−0.207341	−	0.978269i	$-0.566481\pi$
$191$	−5.73102			−0.414682			−0.207341	+	0.978269i	$0.566481\pi$
$192$		0			0
$193$	−0.934136			−0.0672406			−0.0336203	−	0.999435i	$-0.510704\pi$
$193$	−0.934136			−0.0672406			−0.0336203	+	0.999435i	$0.510704\pi$
$194$	−1.28081	+	1.59350i	−0.0919565	+	0.114406i
$195$		0			0
$196$	4.89870	+	22.2483i	0.349907	+	1.58916i
$197$	23.0844			1.64469			0.822346	−	0.568987i	$-0.192665\pi$
$197$	23.0844			1.64469			0.822346	+	0.568987i	$0.192665\pi$
$198$		0			0
$199$		−	11.6214i		−	0.823816i	−0.911225	−	0.411908i	$-0.864863\pi$
$199$		−	11.6214i		−	0.823816i	0.911225	−	0.411908i	$-0.135137\pi$
$200$	−21.5446	−	10.6825i	−1.52343	−	0.755370i
$201$		0			0
$202$	10.1988	−	12.6887i	0.717582	−	0.892771i
$203$			17.1262i			1.20203i
$204$		0			0
$205$			15.2264i			1.06346i
$206$	5.57217	+	4.47874i	0.388232	+	0.312049i
$207$		0			0
$208$	−11.9476	−	25.8157i	−0.828419	−	1.79000i
$209$		−	0.571401i		−	0.0395247i
$210$		0			0
$211$	−15.3823			−1.05896			−0.529482	−	0.848321i	$-0.677614\pi$
$211$	−15.3823			−1.05896			−0.529482	+	0.848321i	$0.677614\pi$
$212$	2.95323	+	13.4126i	0.202829	+	0.921180i
$213$		0			0
$214$	−1.61537	−	1.29839i	−0.110424	−	0.0887558i
$215$	26.7948			1.82739
$216$		0			0
$217$	−32.1527			−2.18267
$218$	2.68231	+	2.15596i	0.181669	+	0.146020i
$219$		0			0
$220$	7.17712	−	1.58028i	0.483881	−	0.106543i
$221$	−34.5595			−2.32473
$222$		0			0
$223$			29.4476i			1.97195i	0.166880	+	0.985977i	$0.446631\pi$
$223$			29.4476i			1.97195i	−0.166880	+	0.985977i	$0.553369\pi$
$224$	23.5429	+	5.85086i	1.57302	+	0.390927i
$225$		0			0
$226$	−10.1818	−	8.18382i	−0.677283	−	0.544380i
$227$			21.0457i			1.39686i	0.715681	+	0.698428i	$0.246117\pi$
$227$			21.0457i			1.39686i	−0.715681	+	0.698428i	$0.753883\pi$
$228$		0			0
$229$		−	8.43517i		−	0.557412i	−0.960377	−	0.278706i	$-0.910095\pi$
$229$		−	8.43517i		−	0.557412i	0.960377	−	0.278706i	$-0.0899054\pi$
$230$	11.7673	−	14.6402i	0.775915	−	0.965344i
$231$		0			0
$232$	10.1199	+	5.01780i	0.664403	+	0.329435i
$233$		−	16.2145i		−	1.06224i	−0.847295	−	0.531122i	$-0.821771\pi$
$233$		−	16.2145i		−	1.06224i	0.847295	−	0.531122i	$-0.178229\pi$
$234$		0			0
$235$	20.1364			1.31356
$236$	0.207166	−	0.0456145i	0.0134853	−	0.00296925i
$237$		0			0
$238$	18.4639	−	22.9717i	1.19684	−	1.48903i
$239$	10.8146			0.699539			0.349769	−	0.936836i	$-0.386260\pi$
$239$	10.8146			0.699539			0.349769	+	0.936836i	$0.386260\pi$
$240$		0			0
$241$	23.5965			1.51998			0.759992	−	0.649932i	$-0.225203\pi$
$241$	23.5965			1.51998			0.759992	+	0.649932i	$0.225203\pi$
$242$	−0.885984	+	1.10229i	−0.0569532	+	0.0708576i
$243$		0			0
$244$	8.83180	−	1.94462i	0.565398	−	0.124491i
$245$	41.8550			2.67402
$246$		0			0
$247$			4.06358i			0.258559i
$248$	−9.42038	+	18.9990i	−0.598195	+	1.20644i
$249$		0			0
$250$	−11.4013	+	14.1848i	−0.721081	+	0.897124i
$251$		−	24.3292i		−	1.53564i	−0.640663	−	0.767822i	$-0.721341\pi$
$251$		−	24.3292i		−	1.53564i	0.640663	−	0.767822i	$-0.278659\pi$
$252$		0			0
$253$			3.61453i			0.227243i
$254$	−1.33680	−	1.07448i	−0.0838781	−	0.0674187i
$255$		0			0
$256$	10.3551	−	12.1972i	0.647192	−	0.762327i
$257$		−	15.7882i		−	0.984844i	−0.870357	−	0.492422i	$-0.836112\pi$
$257$		−	15.7882i		−	0.984844i	0.870357	−	0.492422i	$-0.163888\pi$
$258$		0			0
$259$	−24.1094			−1.49809
$260$	−51.0408	+	11.2383i	−3.16542	+	0.696973i
$261$		0			0
$262$	−10.7165	−	8.61359i	−0.662067	−	0.532149i
$263$	−12.3472			−0.761361			−0.380680	−	0.924707i	$-0.624310\pi$
$263$	−12.3472			−0.761361			−0.380680	+	0.924707i	$0.624310\pi$
$264$		0			0
$265$	25.2327			1.55003
$266$	−2.70105	−	2.17103i	−0.165612	−	0.133114i
$267$		0			0
$268$	−2.10348	−	9.55331i	−0.128491	−	0.583561i
$269$	−1.99457			−0.121611			−0.0608055	−	0.998150i	$-0.519367\pi$
$269$	−1.99457			−0.121611			−0.0608055	+	0.998150i	$0.519367\pi$
$270$		0			0
$271$		−	26.0744i		−	1.58391i	−0.610582	−	0.791953i	$-0.709065\pi$
$271$		−	26.0744i		−	1.58391i	0.610582	−	0.791953i	$-0.290935\pi$
$272$	−8.16422	−	17.6408i	−0.495029	−	1.06963i
$273$		0			0
$274$	−10.9950	−	8.83745i	−0.664232	−	0.533890i
$275$		−	8.50209i		−	0.512696i
$276$		0			0
$277$			13.1113i			0.787780i	0.919158	+	0.393890i	$0.128871\pi$
$277$			13.1113i			0.787780i	−0.919158	+	0.393890i	$0.871129\pi$
$278$	−16.8342	+	20.9441i	−1.00965	+	1.25614i
$279$		0			0
$280$	19.7992	−	39.9310i	1.18323	−	2.38633i
$281$		−	8.72948i		−	0.520757i	−0.965507	−	0.260379i	$-0.916153\pi$
$281$		−	8.72948i		−	0.520757i	0.965507	−	0.260379i	$-0.0838474\pi$
$282$		0			0
$283$	−11.1083			−0.660321			−0.330160	−	0.943925i	$-0.607103\pi$
$283$	−11.1083			−0.660321			−0.330160	+	0.943925i	$0.607103\pi$
$284$	0.280052	+	1.27190i	0.0166180	+	0.0754735i
$285$		0			0
$286$	6.30076	−	7.83901i	0.372572	−	0.463530i
$287$	−17.7703			−1.04895
$288$		0			0
$289$	−6.61572			−0.389160
$290$	13.0014	−	16.1755i	0.763469	−	0.949860i
$291$		0			0
$292$	2.72033	+	12.3548i	0.159195	+	0.723012i
$293$	9.60760			0.561282			0.280641	−	0.959813i	$-0.409453\pi$
$293$	9.60760			0.561282			0.280641	+	0.959813i	$0.409453\pi$
$294$		0			0
$295$		−	0.389735i		−	0.0226912i
$296$	−7.06378	+	14.2462i	−0.410574	+	0.828046i
$297$		0			0
$298$	−19.5419	+	24.3128i	−1.13203	+	1.40840i
$299$		−	25.7051i		−	1.48656i
$300$		0			0
$301$			31.2714i			1.80246i
$302$	20.0624	+	16.1256i	1.15446	+	0.927923i
$303$		0			0
$304$	−2.07424	+	0.959966i	−0.118966	+	0.0550578i
$305$		−	16.6150i		−	0.951371i
$306$		0			0
$307$	1.34324			0.0766628			0.0383314	−	0.999265i	$-0.487796\pi$
$307$	1.34324			0.0766628			0.0383314	+	0.999265i	$0.487796\pi$
$308$	1.84430	+	8.37621i	0.105089	+	0.477279i
$309$		0			0
$310$	30.3679	+	24.4088i	1.72478	+	1.38633i
$311$	9.54020			0.540975			0.270488	−	0.962723i	$-0.412815\pi$
$311$	9.54020			0.540975			0.270488	+	0.962723i	$0.412815\pi$
$312$		0			0
$313$	4.69540			0.265400			0.132700	−	0.991156i	$-0.457635\pi$
$313$	4.69540			0.265400			0.132700	+	0.991156i	$0.457635\pi$
$314$	8.48366	+	6.81892i	0.478761	+	0.384814i
$315$		0			0
$316$	−25.8322	+	5.68784i	−1.45318	+	0.319966i
$317$	−11.1383			−0.625587			−0.312794	−	0.949821i	$-0.601265\pi$
$317$	−11.1383			−0.625587			−0.312794	+	0.949821i	$0.601265\pi$
$318$		0			0
$319$			3.99360i			0.223598i
$320$	−17.7943	−	23.3987i	−0.994730	−	1.30803i
$321$		0			0
$322$	17.0861	+	13.7333i	0.952172	+	0.765328i
$323$			2.77678i			0.154504i
$324$		0			0
$325$			60.4635i			3.35391i
$326$	5.60033	−	6.96758i	0.310174	−	0.385899i
$327$		0			0
$328$	−5.20651	+	10.5005i	−0.287481	+	0.579792i
$329$			23.5006i			1.29563i
$330$		0			0
$331$	−24.2231			−1.33142			−0.665711	−	0.746210i	$-0.731872\pi$
$331$	−24.2231			−1.33142			−0.665711	+	0.746210i	$0.731872\pi$
$332$	−15.5945	+	3.43365i	−0.855860	+	0.188446i
$333$		0			0
$334$	11.7686	−	14.6418i	0.643951	−	0.801163i
$335$	−17.9723			−0.981934
$336$		0			0
$337$	6.42833			0.350173			0.175087	−	0.984553i	$-0.443979\pi$
$337$	6.42833			0.350173			0.175087	+	0.984553i	$0.443979\pi$
$338$	−33.2907	+	41.4182i	−1.81078	+	2.25285i
$339$		0			0
$340$	−34.8779	+	7.67955i	−1.89152	+	0.416482i
$341$	−7.49755			−0.406015
$342$		0			0
$343$			18.8287i			1.01666i
$344$	18.4783	+	9.16218i	0.996282	+	0.493992i
$345$		0			0
$346$	−2.72041	+	3.38457i	−0.146250	+	0.181956i
$347$		−	22.5860i		−	1.21248i	−0.795282	−	0.606239i	$-0.792677\pi$
$347$		−	22.5860i		−	1.21248i	0.795282	−	0.606239i	$-0.207323\pi$
$348$		0			0
$349$		−	7.23698i		−	0.387387i	−0.981062	−	0.193693i	$-0.937953\pi$
$349$		−	7.23698i		−	0.387387i	0.981062	−	0.193693i	$-0.0620467\pi$
$350$	−40.1900	−	32.3035i	−2.14824	−	1.72669i
$351$		0			0
$352$	5.48986	+	1.36434i	0.292611	+	0.0727195i
$353$		−	6.00677i		−	0.319708i	−0.987141	−	0.159854i	$-0.948898\pi$
$353$		−	6.00677i		−	0.319708i	0.987141	−	0.159854i	$-0.0511023\pi$
$354$		0			0
$355$	2.39279			0.126996
$356$	10.5500	−	2.32293i	0.559148	−	0.123115i
$357$		0			0
$358$	0.773895	+	0.622033i	0.0409016	+	0.0328755i
$359$	23.2718			1.22824			0.614120	−	0.789212i	$-0.289511\pi$
$359$	23.2718			1.22824			0.614120	+	0.789212i	$0.289511\pi$
$360$		0			0
$361$	−18.6735			−0.982816
$362$	−19.0933	−	15.3466i	−1.00352	−	0.806599i
$363$		0			0
$364$	−13.1160	−	59.5683i	−0.687463	−	3.12223i
$365$	23.2428			1.21658
$366$		0			0
$367$			18.7836i			0.980495i	0.871583	+	0.490248i	$0.163094\pi$
$367$			18.7836i			0.980495i	−0.871583	+	0.490248i	$0.836906\pi$
$368$	13.1211	−	6.07248i	0.683982	−	0.316550i
$369$		0			0
$370$	22.7710	+	18.3027i	1.18381	+	0.951511i
$371$			29.4483i			1.52888i
$372$		0			0
$373$			6.97688i			0.361249i	0.983552	+	0.180625i	$0.0578119\pi$
$373$			6.97688i			0.361249i	−0.983552	+	0.180625i	$0.942188\pi$
$374$	4.30553	−	5.35667i	0.222634	−	0.276987i
$375$		0			0
$376$	13.8865	+	6.88542i	0.716143	+	0.355089i
$377$		−	28.4009i		−	1.46272i
$378$		0			0
$379$	−20.4858			−1.05228			−0.526142	−	0.850396i	$-0.676362\pi$
$379$	−20.4858			−1.05228			−0.526142	+	0.850396i	$0.676362\pi$
$380$	0.902977	+	4.10102i	0.0463217	+	0.210378i
$381$		0			0
$382$	−5.07759	+	6.31722i	−0.259792	+	0.323217i
$383$	10.3791			0.530347			0.265174	−	0.964201i	$-0.414571\pi$
$383$	10.3791			0.530347			0.265174	+	0.964201i	$0.414571\pi$
$384$		0			0
$385$	15.7579			0.803097
$386$	−0.827629	+	1.02968i	−0.0421252	+	0.0524096i
$387$		0			0
$388$	0.621716	+	2.82363i	0.0315628	+	0.143348i
$389$	22.9562			1.16392			0.581962	−	0.813216i	$-0.302285\pi$
$389$	22.9562			1.16392			0.581962	+	0.813216i	$0.302285\pi$
$390$		0			0
$391$		−	17.5652i		−	0.888308i
$392$	28.8641	+	14.3118i	1.45786	+	0.722857i
$393$		0			0
$394$	20.4524	−	25.4455i	1.03038	−	1.28193i
$395$			48.5974i			2.44520i
$396$		0			0
$397$			4.90188i			0.246018i	0.992406	+	0.123009i	$0.0392545\pi$
$397$			4.90188i			0.246018i	−0.992406	+	0.123009i	$0.960746\pi$
$398$	−12.8100	−	10.2963i	−0.642110	−	0.516108i
$399$		0			0
$400$	−30.8633	+	14.2837i	−1.54317	+	0.714184i
$401$			8.20713i			0.409845i	0.978778	+	0.204922i	$0.0656942\pi$
$401$			8.20713i			0.409845i	−0.978778	+	0.204922i	$0.934306\pi$
$402$		0			0
$403$	53.3196			2.65604
$404$	−4.95058	−	22.4839i	−0.246301	−	1.11862i
$405$		0			0
$406$	18.8780	+	15.1736i	0.936900	+	0.753052i
$407$	−5.62197			−0.278671
$408$		0			0
$409$	6.42798			0.317843			0.158922	−	0.987291i	$-0.449198\pi$
$409$	6.42798			0.317843			0.158922	+	0.987291i	$0.449198\pi$
$410$	16.7839	+	13.4904i	0.828896	+	0.666242i
$411$		0			0
$412$	9.87371	−	2.17403i	0.486443	−	0.107107i
$413$	0.454848			0.0223816
$414$		0			0
$415$			29.3375i			1.44012i
$416$	−39.0417	−	9.70262i	−1.91418	−	0.475710i
$417$		0			0
$418$	−0.629847	−	0.506252i	−0.0308068	−	0.0247616i
$419$			0.627152i			0.0306384i	0.999883	+	0.0153192i	$0.00487644\pi$
$419$			0.627152i			0.0306384i	−0.999883	+	0.0153192i	$0.995124\pi$
$420$		0			0
$421$		−	6.92756i		−	0.337628i	−0.985648	−	0.168814i	$-0.946006\pi$
$421$		−	6.92756i		−	0.337628i	0.985648	−	0.168814i	$-0.0539938\pi$
$422$	−13.6285	+	16.9557i	−0.663425	+	0.825392i
$423$		0			0
$424$	17.4010	+	8.62803i	0.845068	+	0.419014i
$425$			41.3168i			2.00416i
$426$		0			0
$427$	19.3909			0.938390
$428$	−2.86238	+	0.630249i	−0.138358	+	0.0304642i
$429$		0			0
$430$	23.7398	−	29.5355i	1.14483	−	1.42433i
$431$	32.1099			1.54668			0.773339	−	0.633992i	$-0.218585\pi$
$431$	32.1099			1.54668			0.773339	+	0.633992i	$0.218585\pi$
$432$		0			0
$433$	17.0093			0.817416			0.408708	−	0.912665i	$-0.365979\pi$
$433$	17.0093			0.817416			0.408708	+	0.912665i	$0.365979\pi$
$434$	−28.4868	+	35.4414i	−1.36741	+	1.70124i
$435$		0			0
$436$	4.75297	−	1.04653i	0.227626	−	0.0501195i
$437$	−2.06535			−0.0987989
$438$		0			0
$439$			19.9250i			0.950967i	0.879725	+	0.475484i	$0.157727\pi$
$439$			19.9250i			0.950967i	−0.879725	+	0.475484i	$0.842273\pi$
$440$	4.61689	−	9.31134i	0.220102	−	0.443901i
$441$		0			0
$442$	−30.6192	+	38.0945i	−1.45641	+	1.81197i
$443$			21.3533i			1.01453i	0.861791	+	0.507264i	$0.169343\pi$
$443$			21.3533i			1.01453i	−0.861791	+	0.507264i	$0.830657\pi$
$444$		0			0
$445$		−	19.8474i		−	0.940855i
$446$	32.4596	+	26.0901i	1.53701	+	1.23540i
$447$		0			0
$448$	27.3079	−	20.7672i	1.29018	−	0.981157i
$449$			12.1619i			0.573957i	0.957937	+	0.286979i	$0.0926508\pi$
$449$			12.1619i			0.573957i	−0.957937	+	0.286979i	$0.907349\pi$
$450$		0			0
$451$	−4.14379			−0.195123
$452$	−18.0418	+	3.97251i	−0.848615	+	0.186851i
$453$		0			0
$454$	23.1984	+	18.6462i	1.08876	+	0.875109i
$455$	−112.064			−5.25364
$456$		0			0
$457$	29.8125			1.39457			0.697286	−	0.716793i	$-0.254391\pi$
$457$	29.8125			1.39457			0.697286	+	0.716793i	$0.254391\pi$
$458$	−9.29796	−	7.47342i	−0.434465	−	0.349210i
$459$		0			0
$460$	−5.71198	−	25.9419i	−0.266322	−	1.20955i
$461$	−3.21399			−0.149691			−0.0748453	−	0.997195i	$-0.523846\pi$
$461$	−3.21399			−0.149691			−0.0748453	+	0.997195i	$0.523846\pi$
$462$		0			0
$463$			31.0571i			1.44335i	0.692234	+	0.721673i	$0.256626\pi$
$463$			31.0571i			1.44335i	−0.692234	+	0.721673i	$0.743374\pi$
$464$	14.4971	−	6.70932i	0.673011	−	0.311472i
$465$		0			0
$466$	−17.8730	−	14.3657i	−0.827949	−	0.665480i
$467$		−	13.1669i		−	0.609293i	−0.952466	−	0.304646i	$-0.901462\pi$
$467$		−	13.1669i		−	0.609293i	0.952466	−	0.304646i	$-0.0985383\pi$
$468$		0			0
$469$		−	20.9750i		−	0.968535i
$470$	17.8405	−	22.1961i	0.822923	−	1.02383i
$471$		0			0
$472$	0.133265	−	0.268770i	0.00613404	−	0.0123711i
$473$			7.29206i			0.335289i
$474$		0			0
$475$	4.85811			0.222905
$476$	−8.96258	−	40.7050i	−0.410799	−	1.86571i
$477$		0			0
$478$	9.58156	−	11.9208i	0.438251	−	0.545244i
$479$	−29.5905			−1.35202			−0.676012	−	0.736890i	$-0.736293\pi$
$479$	−29.5905			−1.35202			−0.676012	+	0.736890i	$0.736293\pi$
$480$		0			0
$481$	39.9812			1.82299
$482$	20.9061	−	26.0101i	0.952248	−	1.18473i
$483$		0			0
$484$	0.430065	+	1.95321i	0.0195484	+	0.0887824i
$485$	5.31200			0.241205
$486$		0			0
$487$		−	1.62676i		−	0.0737154i	−0.999321	−	0.0368577i	$-0.988265\pi$
$487$		−	1.62676i		−	0.0737154i	0.999321	−	0.0368577i	$-0.0117348\pi$
$488$	5.68131	−	11.4581i	0.257181	−	0.518682i
$489$		0			0
$490$	37.0828	−	46.1361i	1.67523	−	2.08422i
$491$		−	24.9289i		−	1.12503i	−0.826788	−	0.562514i	$-0.809834\pi$
$491$		−	24.9289i		−	1.12503i	0.826788	−	0.562514i	$-0.190166\pi$
$492$		0			0
$493$		−	19.4073i		−	0.874060i
$494$	4.47922	+	3.60026i	0.201530	+	0.161984i
$495$		0			0
$496$	12.5960	+	27.2168i	0.565579	+	1.22207i
$497$			2.79255i			0.125263i
$498$		0			0
$499$	−15.3573			−0.687485			−0.343743	−	0.939064i	$-0.611695\pi$
$499$	−15.3573			−0.687485			−0.343743	+	0.939064i	$0.611695\pi$
$500$	5.53430	+	25.1350i	0.247502	+	1.12407i
$501$		0			0
$502$	−26.8177	−	21.5553i	−1.19693	−	0.962058i
$503$	5.70197			0.254238			0.127119	−	0.991887i	$-0.459427\pi$
$503$	5.70197			0.254238			0.127119	+	0.991887i	$0.459427\pi$
$504$		0			0
$505$	−42.2982			−1.88225
$506$	3.98424	+	3.20241i	0.177121	+	0.142365i
$507$		0			0
$508$	−2.36876	+	0.521562i	−0.105097	+	0.0231406i
$509$	−7.37472			−0.326879			−0.163439	−	0.986553i	$-0.552259\pi$
$509$	−7.37472			−0.326879			−0.163439	+	0.986553i	$0.552259\pi$
$510$		0			0
$511$			27.1260i			1.19998i
$512$	−4.27041	−	22.2208i	−0.188727	−	0.982030i
$513$		0			0
$514$	−17.4031	−	13.9881i	−0.767620	−	0.616990i
$515$		−	18.5751i		−	0.818516i
$516$		0			0
$517$			5.48001i			0.241011i
$518$	−21.3605	+	26.5754i	−0.938528	+	1.16766i
$519$		0			0
$520$	−32.8335	+	66.2185i	−1.43984	+	2.90387i
$521$			43.8704i			1.92200i	0.276555	+	0.960998i	$0.410807\pi$
$521$			43.8704i			1.92200i	−0.276555	+	0.960998i	$0.589193\pi$
$522$		0			0
$523$	−2.76514			−0.120911			−0.0604556	−	0.998171i	$-0.519255\pi$
$523$	−2.76514			−0.120911			−0.0604556	+	0.998171i	$0.519255\pi$
$524$	−18.9893	+	4.18112i	−0.829550	+	0.182653i
$525$		0			0
$526$	−10.9394	+	13.6101i	−0.476981	+	0.593430i
$527$	36.4351			1.58714
$528$		0			0
$529$	−9.93519			−0.431965
$530$	22.3557	−	27.8136i	0.971072	−	1.20815i
$531$		0			0
$532$	−4.78618	+	1.05384i	−0.207507	+	0.0456897i
$533$	29.4690			1.27644
$534$		0			0
$535$			5.38491i			0.232810i
$536$	−12.3941	−	6.14544i	−0.535344	−	0.265443i
$537$		0			0
$538$	−1.76716	+	2.19858i	−0.0761875	+	0.0947877i
$539$			11.3906i			0.490628i
$540$		0			0
$541$		−	22.6593i		−	0.974200i	−0.873346	−	0.487100i	$-0.838055\pi$
$541$		−	22.6593i		−	0.974200i	0.873346	−	0.487100i	$-0.161945\pi$
$542$	−28.7414	−	23.1015i	−1.23455	−	0.992293i
$543$		0			0
$544$	−26.6785	−	6.63014i	−1.14383	−	0.284265i
$545$		−	8.94162i		−	0.383017i
$546$		0			0
$547$	16.2215			0.693582			0.346791	−	0.937942i	$-0.387271\pi$
$547$	16.2215			0.693582			0.346791	+	0.937942i	$0.387271\pi$
$548$	−19.4828	+	4.28979i	−0.832263	+	0.183251i
$549$		0			0
$550$	−9.37173	−	7.53272i	−0.399612	−	0.321196i
$551$	−2.28195			−0.0972142
$552$		0			0
$553$	−56.7166			−2.41184
$554$	14.4524	+	11.6164i	0.614022	+	0.493532i
$555$		0			0
$556$	8.17150	+	37.1122i	0.346549	+	1.57391i
$557$	6.52782			0.276593			0.138296	−	0.990391i	$-0.455837\pi$
$557$	6.52782			0.276593			0.138296	+	0.990391i	$0.455837\pi$
$558$		0			0
$559$		−	51.8582i		−	2.19337i
$560$	−26.4736	−	57.2026i	−1.11871	−	2.41725i
$561$		0			0
$562$	−9.62238	−	7.73418i	−0.405896	−	0.326247i
$563$			8.89921i			0.375057i	0.982259	+	0.187529i	$0.0600477\pi$
$563$			8.89921i			0.375057i	−0.982259	+	0.187529i	$0.939952\pi$
$564$		0			0
$565$			33.9415i			1.42793i
$566$	−9.84179	+	12.2445i	−0.413681	+	0.514676i
$567$		0			0
$568$	1.65012	+	0.818187i	0.0692375	+	0.0343304i
$569$			2.33296i			0.0978026i	0.998804	+	0.0489013i	$0.0155720\pi$
$569$			2.33296i			0.0978026i	−0.998804	+	0.0489013i	$0.984428\pi$
$570$		0			0
$571$	9.91834			0.415070			0.207535	−	0.978228i	$-0.433456\pi$
$571$	9.91834			0.415070			0.207535	+	0.978228i	$0.433456\pi$
$572$	−3.05845	−	13.8905i	−0.127880	−	0.580790i
$573$		0			0
$574$	−15.7442	+	19.5880i	−0.657151	+	0.817586i
$575$	−30.7311			−1.28157
$576$		0			0
$577$	−29.7042			−1.23660			−0.618301	−	0.785941i	$-0.712179\pi$
$577$	−29.7042			−1.23660			−0.618301	+	0.785941i	$0.712179\pi$
$578$	−5.86142	+	7.29241i	−0.243803	+	0.303324i
$579$		0			0
$580$	−6.31102	−	28.6625i	−0.262051	−	1.19015i
$581$	−34.2389			−1.42047
$582$		0			0
$583$			6.86693i			0.284399i
$584$	16.0287	+	7.94760i	0.663273	+	0.328874i
$585$		0			0
$586$	8.51218	−	10.5903i	0.351635	−	0.437482i
$587$		−	24.6424i		−	1.01710i	−0.861033	−	0.508549i	$-0.830182\pi$
$587$		−	24.6424i		−	1.01710i	0.861033	−	0.508549i	$-0.169818\pi$
$588$		0			0
$589$		−	4.28411i		−	0.176524i
$590$	−0.429599	−	0.345299i	−0.0176863	−	0.0142157i
$591$		0			0
$592$	9.44502	+	20.4082i	0.388188	+	0.838773i
$593$			27.4755i			1.12828i	0.825678	+	0.564142i	$0.190793\pi$
$593$			27.4755i			1.12828i	−0.825678	+	0.564142i	$0.809207\pi$
$594$		0			0
$595$	−76.5771			−3.13936
$596$	9.48585	+	43.0815i	0.388555	+	1.76469i
$597$		0			0
$598$	−28.3343	−	22.7743i	−1.15868	−	0.931310i
$599$	−0.332844			−0.0135996			−0.00679982	−	0.999977i	$-0.502164\pi$
$599$	−0.332844			−0.0135996			−0.00679982	+	0.999977i	$0.502164\pi$
$600$		0			0
$601$	−6.25727			−0.255239			−0.127620	−	0.991823i	$-0.540734\pi$
$601$	−6.25727			−0.255239			−0.127620	+	0.991823i	$0.540734\pi$
$602$	34.4700	+	27.7060i	1.40489	+	1.12921i
$603$		0			0
$604$	35.5500	−	7.82752i	1.44651	−	0.318497i
$605$	3.67452			0.149390
$606$		0			0
$607$			16.5948i			0.673563i	0.941583	+	0.336781i	$0.109338\pi$
$607$			16.5948i			0.673563i	−0.941583	+	0.336781i	$0.890662\pi$
$608$	−0.779585	+	3.13692i	−0.0316163	+	0.127219i
$609$		0			0
$610$	−18.3144	−	14.7206i	−0.741530	−	0.596020i
$611$		−	38.9717i		−	1.57662i
$612$		0			0
$613$		−	20.9637i		−	0.846716i	−0.905963	−	0.423358i	$-0.860851\pi$
$613$		−	20.9637i		−	0.846716i	0.905963	−	0.423358i	$-0.139149\pi$
$614$	1.19009	−	1.48064i	0.0480281	−	0.0597536i
$615$		0			0
$616$	10.8670	+	5.38824i	0.437844	+	0.217098i
$617$		−	34.3728i		−	1.38380i	−0.721995	−	0.691898i	$-0.756775\pi$
$617$		−	34.3728i		−	1.38380i	0.721995	−	0.691898i	$-0.243225\pi$
$618$		0			0
$619$	−2.33014			−0.0936563			−0.0468282	−	0.998903i	$-0.514911\pi$
$619$	−2.33014			−0.0936563			−0.0468282	+	0.998903i	$0.514911\pi$
$620$	53.8109	−	11.8483i	2.16110	−	0.475838i
$621$		0			0
$622$	8.45246	−	10.5160i	0.338913	−	0.421654i
$623$	23.1633			0.928017
$624$		0			0
$625$	4.77513			0.191005
$626$	4.16005	−	5.17567i	0.166269	−	0.206861i
$627$		0			0
$628$	15.0328	−	3.30997i	0.599873	−	0.132082i
$629$	27.3205			1.08934
$630$		0			0
$631$		−	21.2012i		−	0.844008i	−0.906594	−	0.422004i	$-0.861327\pi$
$631$		−	21.2012i		−	0.844008i	0.906594	−	0.422004i	$-0.138673\pi$
$632$	−16.6173	+	33.5138i	−0.661002	+	1.33311i
$633$		0			0
$634$	−9.86832	+	12.2775i	−0.391921	+	0.487604i
$635$			4.45627i			0.176842i
$636$		0			0
$637$		−	81.0054i		−	3.20955i
$638$	4.40208	+	3.53826i	0.174280	+	0.140081i
$639$		0			0
$640$	−41.5574	−	1.11648i	−1.64270	−	0.0441327i
$641$			47.0298i			1.85756i	0.370627	+	0.928782i	$0.379143\pi$
$641$			47.0298i			1.85756i	−0.370627	+	0.928782i	$0.620857\pi$
$642$		0			0
$643$	−5.74124			−0.226413			−0.113206	−	0.993572i	$-0.536112\pi$
$643$	−5.74124			−0.226413			−0.113206	+	0.993572i	$0.536112\pi$
$644$	30.2761	−	6.66629i	1.19304	−	0.262689i
$645$		0			0
$646$	3.06081	+	2.46018i	0.120426	+	0.0967947i
$647$	6.61961			0.260244			0.130122	−	0.991498i	$-0.458463\pi$
$647$	6.61961			0.260244			0.130122	+	0.991498i	$0.458463\pi$
$648$		0			0
$649$	0.106064			0.00416338
$650$	66.6480	+	53.5697i	2.61415	+	2.10118i
$651$		0			0
$652$	−2.71846	−	12.3463i	−0.106463	−	0.483520i
$653$	−5.07600			−0.198639			−0.0993195	−	0.995056i	$-0.531667\pi$
$653$	−5.07600			−0.198639			−0.0993195	+	0.995056i	$0.531667\pi$
$654$		0			0
$655$			35.7239i			1.39585i
$656$	6.96164	+	15.0423i	0.271807	+	0.587304i
$657$		0			0
$658$	25.9044	+	20.8212i	1.00986	+	0.811694i
$659$		−	10.0947i		−	0.393233i	−0.980480	−	0.196617i	$-0.937005\pi$
$659$		−	10.0947i		−	0.393233i	0.980480	−	0.196617i	$-0.0629955\pi$
$660$		0			0
$661$		−	37.9561i		−	1.47632i	−0.674625	−	0.738161i	$-0.735695\pi$
$661$		−	37.9561i		−	1.47632i	0.674625	−	0.738161i	$-0.264305\pi$
$662$	−21.4613	+	26.7008i	−0.834116	+	1.03775i
$663$		0			0
$664$	−10.0316	+	20.2318i	−0.389302	+	0.785144i
$665$			9.00409i			0.349164i
$666$		0			0
$667$	14.4350			0.558924
$668$	−5.71261	−	25.9448i	−0.221028	−	1.00383i
$669$		0			0
$670$	−15.9232	+	19.8106i	−0.615167	+	0.765352i
$671$	4.52167			0.174557
$672$		0			0
$673$	32.7833			1.26370			0.631851	−	0.775090i	$-0.282295\pi$
$673$	32.7833			1.26370			0.631851	+	0.775090i	$0.282295\pi$
$674$	5.69540	−	7.08585i	0.219378	−	0.272937i
$675$		0			0
$676$	16.1596	+	73.3917i	0.621525	+	2.82276i
$677$	−43.6949			−1.67933			−0.839666	−	0.543103i	$-0.817249\pi$
$677$	−43.6949			−1.67933			−0.839666	+	0.543103i	$0.817249\pi$
$678$		0			0
$679$			6.19948i			0.237914i
$680$	−22.4362	+	45.2494i	−0.860391	+	1.73524i
$681$		0			0
$682$	−6.64271	+	8.26444i	−0.254363	+	0.316462i
$683$		−	37.2123i		−	1.42389i	−0.702236	−	0.711945i	$-0.747815\pi$
$683$		−	37.2123i		−	1.42389i	0.702236	−	0.711945i	$-0.252185\pi$
$684$		0			0
$685$			36.6523i			1.40041i
$686$	20.7546	+	16.6820i	0.792416	+	0.636920i
$687$		0			0
$688$	26.4708	−	12.2508i	1.00919	−	0.467057i
$689$		−	48.8349i		−	1.86046i
$690$		0			0
$691$	−43.3062			−1.64744			−0.823722	−	0.566994i	$-0.808106\pi$
$691$	−43.3062			−1.64744			−0.823722	+	0.566994i	$0.808106\pi$
$692$	1.32052	+	5.99735i	0.0501985	+	0.227985i
$693$		0			0
$694$	−24.8962	−	20.0108i	−0.945046	−	0.759600i
$695$	69.8181			2.64835
$696$		0			0
$697$	20.1372			0.762749
$698$	−7.97722	−	6.41185i	−0.301942	−	0.242692i
$699$		0			0
$700$	−71.2153	+	15.6804i	−2.69169	+	0.592665i
$701$	−8.83383			−0.333649			−0.166825	−	0.985987i	$-0.553351\pi$
$701$	−8.83383			−0.333649			−0.166825	+	0.985987i	$0.553351\pi$
$702$		0			0
$703$		−	3.21240i		−	0.121158i
$704$	6.36782	−	4.84261i	0.239996	−	0.182513i
$705$		0			0
$706$	−6.62117	−	5.32190i	−0.249191	−	0.200292i
$707$		−	49.3651i		−	1.85656i
$708$		0			0
$709$		−	0.293822i		−	0.0110347i	−0.999985	−	0.00551736i	$-0.998244\pi$
$709$		−	0.293822i		−	0.0110347i	0.999985	−	0.00551736i	$-0.00175624\pi$
$710$	2.11997	−	2.63753i	0.0795611	−	0.0989849i
$711$		0			0
$712$	6.78658	−	13.6872i	0.254338	−	0.512949i
$713$			27.1001i			1.01491i
$714$		0			0
$715$	−26.1317			−0.977271
$716$	1.37132	−	0.301941i	0.0512485	−	0.0112841i
$717$		0			0
$718$	20.6185	−	25.6522i	0.769474	−	0.957332i
$719$	46.7215			1.74242			0.871210	−	0.490911i	$-0.163336\pi$
$719$	46.7215			1.74242			0.871210	+	0.490911i	$0.163336\pi$
$720$		0			0
$721$	21.6785			0.807348
$722$	−16.5444	+	20.5835i	−0.615720	+	0.766039i
$723$		0			0
$724$	−33.8326	+	7.44939i	−1.25738	+	0.276854i
$725$	−33.9539			−1.26102
$726$		0			0
$727$		−	37.4050i		−	1.38727i	−0.720325	−	0.693637i	$-0.756007\pi$
$727$		−	37.4050i		−	1.38727i	0.720325	−	0.693637i	$-0.243993\pi$
$728$	−77.2817	−	38.3190i	−2.86425	−	1.42020i
$729$		0			0
$730$	20.5927	−	25.6202i	0.762171	−	0.948245i
$731$		−	35.4365i		−	1.31067i
$732$		0			0
$733$		−	29.3800i		−	1.08518i	−0.839999	−	0.542588i	$-0.817444\pi$
$733$		−	29.3800i		−	1.08518i	0.839999	−	0.542588i	$-0.182556\pi$
$734$	20.7049	+	16.6420i	0.764231	+	0.614266i
$735$		0			0
$736$	4.93144	−	19.8433i	0.181775	−	0.731432i
$737$		−	4.89107i		−	0.180165i
$738$		0			0
$739$	51.1151			1.88030			0.940149	−	0.340764i	$-0.110686\pi$
$739$	51.1151			1.88030			0.940149	+	0.340764i	$0.110686\pi$
$740$	40.3496	−	8.88431i	1.48328	−	0.326594i
$741$		0			0
$742$	32.4605	+	26.0907i	1.19166	+	0.957821i
$743$	−52.0471			−1.90942			−0.954712	−	0.297531i	$-0.903837\pi$
$743$	−52.0471			−1.90942			−0.954712	+	0.297531i	$0.903837\pi$
$744$		0			0
$745$	81.0479			2.96937
$746$	7.69051	+	6.18140i	0.281570	+	0.226317i
$747$		0			0
$748$	−2.08995	−	9.49184i	−0.0764160	−	0.347056i
$749$	−6.28457			−0.229633
$750$		0			0
$751$		−	19.4603i		−	0.710115i	−0.934844	−	0.355058i	$-0.884461\pi$
$751$		−	19.4603i		−	0.710115i	0.934844	−	0.355058i	$-0.115539\pi$
$752$	19.8929	−	9.20653i	0.725421	−	0.335728i
$753$		0			0
$754$	−31.3058	−	25.1627i	−1.14009	−	0.916371i
$755$		−	66.8790i		−	2.43398i
$756$		0			0
$757$			14.6495i			0.532445i	0.963912	+	0.266223i	$0.0857756\pi$
$757$			14.6495i			0.532445i	−0.963912	+	0.266223i	$0.914224\pi$
$758$	−18.1501	+	22.5812i	−0.659241	+	0.820186i
$759$		0			0
$760$	5.32051	+	2.63810i	0.192995	+	0.0956939i
$761$			44.5007i			1.61315i	0.591133	+	0.806574i	$0.298681\pi$
$761$			44.5007i			1.61315i	−0.591133	+	0.806574i	$0.701319\pi$
$762$		0			0
$763$	10.4355			0.377791
$764$	2.46472	+	11.1939i	0.0891703	+	0.404982i
$765$		0			0
$766$	9.19571	−	11.4407i	0.332255	−	0.413370i
$767$	−0.754285			−0.0272357
$768$		0			0
$769$	36.5828			1.31921			0.659605	−	0.751613i	$-0.270724\pi$
$769$	36.5828			1.31921			0.659605	+	0.751613i	$0.270724\pi$
$770$	13.9612	−	17.3697i	0.503128	−	0.625961i
$771$		0			0
$772$	0.401740	+	1.82457i	0.0144589	+	0.0656676i
$773$	44.3519			1.59523			0.797614	−	0.603169i	$-0.206095\pi$
$773$	44.3519			1.59523			0.797614	+	0.603169i	$0.206095\pi$
$774$		0			0
$775$		−	63.7449i		−	2.28978i
$776$	3.66327	+	1.81638i	0.131504	+	0.0652042i
$777$		0			0
$778$	20.3388	−	25.3043i	0.729181	−	0.907201i
$779$		−	2.36777i		−	0.0848340i
$780$		0			0
$781$			0.651184i			0.0233012i
$782$	−19.3618	−	15.5624i	−0.692377	−	0.556512i
$783$		0			0
$784$	41.3489	−	19.1364i	1.47674	−	0.683444i
$785$		−	28.2807i		−	1.00938i
$786$		0			0
$787$	28.9136			1.03066			0.515330	−	0.856992i	$-0.327669\pi$
$787$	28.9136			1.03066			0.515330	+	0.856992i	$0.327669\pi$
$788$	−9.92779	−	45.0887i	−0.353663	−	1.60622i
$789$		0			0
$790$	53.5682	+	43.0565i	1.90587	+	1.53188i
$791$	−39.6121			−1.40844
$792$		0			0
$793$	−32.1563			−1.14191
$794$	5.40327	+	4.34299i	0.191755	+	0.154127i
$795$		0			0
$796$	−22.6990	+	4.99794i	−0.804544	+	0.177147i
$797$	−10.1073			−0.358020			−0.179010	−	0.983847i	$-0.557290\pi$
$797$	−10.1073			−0.358020			−0.179010	+	0.983847i	$0.557290\pi$
$798$		0			0
$799$		−	26.6307i		−	0.942126i
$800$	−11.5997	+	46.6753i	−0.410112	+	1.65022i
$801$		0			0
$802$	9.04660	+	7.27139i	0.319447	+	0.256762i
$803$			6.32539i			0.223218i
$804$		0			0
$805$		−	56.9574i		−	2.00748i
$806$	47.2403	−	58.7734i	1.66397	−	2.07020i
$807$		0			0
$808$	−29.1698	−	14.4634i	−1.02619	−	0.508821i
$809$			26.4520i			0.930003i	0.885310	+	0.465001i	$0.153946\pi$
$809$			26.4520i			0.930003i	−0.885310	+	0.465001i	$0.846054\pi$
$810$		0			0
$811$	−44.1060			−1.54877			−0.774386	−	0.632714i	$-0.781941\pi$
$811$	−44.1060			−1.54877			−0.774386	+	0.632714i	$0.781941\pi$
$812$	33.4512	−	7.36540i	1.17391	−	0.258475i
$813$		0			0
$814$	−4.98097	+	6.19701i	−0.174583	+	0.217205i
$815$	−23.2268			−0.813598
$816$		0			0
$817$	−4.16669			−0.145774
$818$	5.69509	−	7.08547i	0.199124	−	0.247738i
$819$		0			0
$820$	29.7405	−	6.54836i	1.03858	−	0.228679i
$821$	3.46327			0.120869			0.0604344	−	0.998172i	$-0.480751\pi$
$821$	3.46327			0.120869			0.0604344	+	0.998172i	$0.480751\pi$
$822$		0			0
$823$		−	9.66899i		−	0.337040i	−0.985698	−	0.168520i	$-0.946101\pi$
$823$		−	9.66899i		−	0.337040i	0.985698	−	0.168520i	$-0.0538988\pi$
$824$	6.35155	−	12.8098i	0.221267	−	0.446250i
$825$		0			0
$826$	0.402988	−	0.501372i	0.0140217	−	0.0174450i
$827$			19.6246i			0.682413i	0.939988	+	0.341207i	$0.110836\pi$
$827$			19.6246i			0.682413i	−0.939988	+	0.341207i	$0.889164\pi$
$828$		0			0
$829$			31.9771i			1.11061i	0.831646	+	0.555306i	$0.187399\pi$
$829$			31.9771i			1.11061i	−0.831646	+	0.555306i	$0.812601\pi$
$830$	32.3382	+	25.9925i	1.12248	+	0.902213i
$831$		0			0
$832$	−45.2854	+	34.4387i	−1.56999	+	1.19395i
$833$		−	55.3537i		−	1.91789i
$834$		0			0
$835$	−48.8091			−1.68911
$836$	−1.11607	+	0.245740i	−0.0386001	+	0.00849910i
$837$		0			0
$838$	0.691300	+	0.555646i	0.0238806	+	0.0191945i
$839$	1.41283			0.0487761			0.0243881	−	0.999703i	$-0.492236\pi$
$839$	1.41283			0.0487761			0.0243881	+	0.999703i	$0.492236\pi$
$840$		0			0
$841$	−13.0512			−0.450041
$842$	−7.63614	−	6.13770i	−0.263159	−	0.211519i
$843$		0			0
$844$	6.61541	+	30.0450i	0.227712	+	1.03419i
$845$	138.070			4.74974
$846$		0			0
$847$			4.28843i			0.147352i
$848$	24.9276	−	11.5366i	0.856016	−	0.396168i
$849$		0			0
$850$	45.5429	+	36.6060i	1.56211	+	1.25558i
$851$			20.3208i			0.696587i
$852$		0			0
$853$			21.3955i			0.732567i	0.930503	+	0.366283i	$0.119370\pi$
$853$			21.3955i			0.732567i	−0.930503	+	0.366283i	$0.880630\pi$
$854$	17.1800	−	21.3743i	0.587887	−	0.731412i
$855$		0			0
$856$	−1.84131	+	3.71355i	−0.0629347	+	0.126927i
$857$			26.8542i			0.917323i	0.888611	+	0.458662i	$0.151671\pi$
$857$			26.8542i			0.917323i	−0.888611	+	0.458662i	$0.848329\pi$
$858$		0			0
$859$	38.2539			1.30521			0.652603	−	0.757700i	$-0.273677\pi$
$859$	38.2539			1.30521			0.652603	+	0.757700i	$0.273677\pi$
$860$	−11.5235	−	52.3360i	−0.392949	−	1.78464i
$861$		0			0
$862$	28.4488	−	35.3943i	0.968971	−	1.20553i
$863$	−49.3934			−1.68137			−0.840686	−	0.541523i	$-0.817848\pi$
$863$	−49.3934			−1.68137			−0.840686	+	0.541523i	$0.817848\pi$
$864$		0			0
$865$	11.2826			0.383620
$866$	15.0700	−	18.7491i	0.512099	−	0.637122i
$867$		0			0
$868$	13.8278	+	62.8011i	0.469345	+	2.13161i
$869$	−13.2255			−0.448645
$870$		0			0
$871$			34.7833i			1.17859i
$872$	3.05749	−	6.16634i	0.103540	−	0.208819i
$873$		0			0
$874$	−1.82986	+	2.27660i	−0.0618961	+	0.0770072i
$875$			55.1857i			1.86562i
$876$		0			0
$877$			5.68043i			0.191815i	0.995390	+	0.0959073i	$0.0305752\pi$
$877$			5.68043i			0.191815i	−0.995390	+	0.0959073i	$0.969425\pi$
$878$	21.9630	+	17.6532i	0.741215	+	0.595767i
$879$		0			0
$880$	−6.17326	−	13.3388i	−0.208101	−	0.449652i
$881$		−	30.5177i		−	1.02817i	−0.857740	−	0.514084i	$-0.828132\pi$
$881$		−	30.5177i		−	1.02817i	0.857740	−	0.514084i	$-0.171868\pi$
$882$		0			0
$883$	−1.35939			−0.0457470			−0.0228735	−	0.999738i	$-0.507281\pi$
$883$	−1.35939			−0.0457470			−0.0228735	+	0.999738i	$0.507281\pi$
$884$	14.8629	+	67.5021i	0.499892	+	2.27034i
$885$		0			0
$886$	23.5375	+	18.9187i	0.790757	+	0.635587i
$887$	−13.7129			−0.460434			−0.230217	−	0.973139i	$-0.573944\pi$
$887$	−13.7129			−0.460434			−0.230217	+	0.973139i	$0.573944\pi$
$888$		0			0
$889$	−5.20079			−0.174429
$890$	−21.8775	−	17.5844i	−0.733334	−	0.589432i
$891$		0			0
$892$	57.5174	−	12.6644i	1.92582	−	0.424035i
$893$	−3.13129			−0.104785
$894$		0			0
$895$		−	2.57981i		−	0.0862337i
$896$	1.30301	−	48.5005i	0.0435305	−	1.62029i
$897$		0			0
$898$	13.4059	+	10.7753i	0.447361	+	0.359576i
$899$			29.9422i			0.998628i
$900$		0			0
$901$		−	33.3706i		−	1.11173i
$902$	−3.67133	+	4.56764i	−0.122242	+	0.152086i
$903$		0			0
$904$	−11.6059	+	23.4068i	−0.386007	+	0.778498i
$905$			63.6483i			2.11574i
$906$		0			0
$907$	−26.2452			−0.871456			−0.435728	−	0.900078i	$-0.643509\pi$
$907$	−26.2452			−0.871456			−0.435728	+	0.900078i	$0.643509\pi$
$908$	41.1068	−	9.05105i	1.36418	−	0.300370i
$909$		0			0
$910$	−99.2868	+	123.526i	−3.29133	+	4.09486i
$911$	−21.5261			−0.713191			−0.356595	−	0.934259i	$-0.616062\pi$
$911$	−21.5261			−0.713191			−0.356595	+	0.934259i	$0.616062\pi$
$912$		0			0
$913$	−7.98402			−0.264233
$914$	26.4134	−	32.8619i	0.873679	−	1.08698i
$915$		0			0
$916$	−16.4757	+	3.62767i	−0.544372	+	0.119862i
$917$	−41.6923			−1.37680
$918$		0			0
$919$		−	31.2694i		−	1.03148i	−0.856745	−	0.515741i	$-0.827517\pi$
$919$		−	31.2694i		−	1.03148i	0.856745	−	0.515741i	$-0.172483\pi$
$920$	−33.6561	−	16.6879i	−1.10961	−	0.550183i
$921$		0			0
$922$	−2.84754	+	3.54274i	−0.0937789	+	0.116674i
$923$		−	4.63096i		−	0.152430i
$924$		0			0
$925$		−	47.7985i		−	1.57161i
$926$	34.2338	+	27.5161i	1.12499	+	0.904234i
$927$		0			0
$928$	5.44861	−	21.9243i	0.178860	−	0.719700i
$929$		−	45.9181i		−	1.50652i	−0.657721	−	0.753261i	$-0.728480\pi$
$929$		−	45.9181i		−	1.50652i	0.657721	−	0.753261i	$-0.271520\pi$
$930$		0			0
$931$	−6.50860			−0.213311
$932$	−31.6703	+	6.97328i	−1.03739	+	0.228417i
$933$		0			0
$934$	−14.5137	−	11.6657i	−0.474903	−	0.381713i
$935$	−17.8567			−0.583976
$936$		0			0
$937$	13.0922			0.427704			0.213852	−	0.976866i	$-0.431399\pi$
$937$	13.0922			0.427704			0.213852	+	0.976866i	$0.431399\pi$
$938$	−23.1204	−	18.5835i	−0.754909	−	0.606773i
$939$		0			0
$940$	−8.65998	−	39.3307i	−0.282457	−	1.28283i
$941$	39.4853			1.28718			0.643592	−	0.765368i	$-0.277443\pi$
$941$	39.4853			1.28718			0.643592	+	0.765368i	$0.277443\pi$
$942$		0			0
$943$			14.9778i			0.487745i
$944$	−0.178190	−	0.385022i	−0.00579958	−	0.0125314i
$945$		0			0
$946$	8.03793	+	6.46064i	0.261336	+	0.210054i
$947$			29.7163i			0.965651i	0.875717	+	0.482825i	$0.160389\pi$
$947$			29.7163i			0.965651i	−0.875717	+	0.482825i	$0.839611\pi$
$948$		0			0
$949$		−	44.9836i		−	1.46023i
$950$	4.30421	−	5.35502i	0.139647	−	0.173740i
$951$		0			0
$952$	−52.8093	−	26.1847i	−1.71156	−	0.848651i
$953$		−	7.56384i		−	0.245017i	−0.992467	−	0.122508i	$-0.960906\pi$
$953$		−	7.56384i		−	0.245017i	0.992467	−	0.122508i	$-0.0390938\pi$
$954$		0			0
$955$	21.0588			0.681445
$956$	−4.65099	−	21.1232i	−0.150424	−	0.683174i
$957$		0			0
$958$	−26.2167	+	32.6172i	−0.847023	+	1.05381i
$959$	−42.7759			−1.38130
$960$		0			0
$961$	−25.2133			−0.813333
$962$	35.4227	−	44.0707i	1.14207	−	1.42090i
$963$		0			0
$964$	−10.1480	−	46.0890i	−0.326846	−	1.48443i
$965$	3.43250			0.110496
$966$		0			0
$967$			29.2517i			0.940672i	0.882487	+	0.470336i	$0.155867\pi$
$967$			29.2517i			0.940672i	−0.882487	+	0.470336i	$0.844133\pi$
$968$	2.53403	+	1.25646i	0.0814468	+	0.0403842i
$969$		0			0
$970$	4.70634	−	5.85534i	0.151112	−	0.188004i
$971$			9.27409i			0.297620i	0.988866	+	0.148810i	$0.0475442\pi$
$971$			9.27409i			0.297620i	−0.988866	+	0.148810i	$0.952456\pi$
$972$		0			0
$973$			81.4826i			2.61221i
$974$	−1.79315	−	1.44128i	−0.0574562	−	0.0461816i
$975$		0			0
$976$	−7.59650	−	16.4141i	−0.243158	−	0.525402i
$977$			25.0267i			0.800676i	0.916368	+	0.400338i	$0.131107\pi$
$977$			25.0267i			0.800676i	−0.916368	+	0.400338i	$0.868893\pi$
$978$		0			0
$979$	5.40135			0.172628
$980$	−18.0004	−	81.7517i	−0.575001	−	2.61146i
$981$		0			0
$982$	−27.4788	−	22.0866i	−0.876884	−	0.704813i
$983$	−60.7052			−1.93619			−0.968097	−	0.250575i	$-0.919380\pi$
$983$	−60.7052			−1.93619			−0.968097	+	0.250575i	$0.919380\pi$
$984$		0			0
$985$	−84.8239			−2.70271
$986$	−21.3924	−	17.1945i	−0.681272	−	0.547586i
$987$		0			0
$988$	7.93704	−	1.74760i	0.252511	−	0.0555987i
$989$	26.3573			0.838115
$990$		0			0
$991$			55.0032i			1.74723i	0.486615	+	0.873617i	$0.338232\pi$
$991$			55.0032i			1.74723i	−0.486615	+	0.873617i	$0.661768\pi$
$992$	41.1605	+	10.2292i	1.30685	+	0.324777i
$993$		0			0
$994$	3.07819	+	2.47416i	0.0976343	+	0.0784755i
$995$			42.7029i			1.35377i
$996$		0			0
$997$			57.3394i			1.81596i	0.419015	+	0.907979i	$0.362375\pi$
$997$			57.3394i			1.81596i	−0.419015	+	0.907979i	$0.637625\pi$
$998$	−13.6063	+	16.9281i	−0.430699	+	0.535849i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	792.2.k.a.683.29	yes	40
3.2	odd	2	inner	792.2.k.a.683.12	yes	40
4.3	odd	2		3168.2.k.a.1871.6		40
8.3	odd	2	inner	792.2.k.a.683.11	✓	40
8.5	even	2		3168.2.k.a.1871.35		40
12.11	even	2		3168.2.k.a.1871.36		40
24.5	odd	2		3168.2.k.a.1871.5		40
24.11	even	2	inner	792.2.k.a.683.30	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
792.2.k.a.683.11	✓	40	8.3	odd	2	inner
792.2.k.a.683.12	yes	40	3.2	odd	2	inner
792.2.k.a.683.29	yes	40	1.1	even	1	trivial
792.2.k.a.683.30	yes	40	24.11	even	2	inner
3168.2.k.a.1871.5		40	24.5	odd	2
3168.2.k.a.1871.6		40	4.3	odd	2
3168.2.k.a.1871.35		40	8.5	even	2
3168.2.k.a.1871.36		40	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 792 = 2^{3} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	792.k (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.885984 - 1.10229i) q^{2} +(-0.430065 - 1.95321i) q^{4} -3.67452 q^{5} -4.28843i q^{7} +(-2.53403 - 1.25646i) q^{8} +(-3.25556 + 4.05037i) q^{10} -1.00000i q^{11} +7.11160i q^{13} +(-4.72707 - 3.79948i) q^{14} +(-3.63009 + 1.68002i) q^{16} +4.85960i q^{17} +0.571401 q^{19} +(1.58028 + 7.17712i) q^{20} +(-1.10229 - 0.885984i) q^{22} -3.61453 q^{23} +8.50209 q^{25} +(7.83901 + 6.30076i) q^{26} +(-8.37621 + 1.84430i) q^{28} -3.99360 q^{29} -7.49755i q^{31} +(-1.36434 + 5.48986i) q^{32} +(5.35667 + 4.30553i) q^{34} +15.7579i q^{35} -5.62197i q^{37} +(0.506252 - 0.629847i) q^{38} +(9.31134 + 4.61689i) q^{40} -4.14379i q^{41} -7.29206 q^{43} +(-1.95321 + 0.430065i) q^{44} +(-3.20241 + 3.98424i) q^{46} -5.48001 q^{47} -11.3906 q^{49} +(7.53272 - 9.37173i) q^{50} +(13.8905 - 3.05845i) q^{52} -6.86693 q^{53} +3.67452i q^{55} +(-5.38824 + 10.8670i) q^{56} +(-3.53826 + 4.40208i) q^{58} +0.106064i q^{59} +4.52167i q^{61} +(-8.26444 - 6.64271i) q^{62} +(4.84261 + 6.36782i) q^{64} -26.1317i q^{65} +4.89107 q^{67} +(9.49184 - 2.08995i) q^{68} +(17.3697 + 13.9612i) q^{70} -0.651184 q^{71} -6.32539 q^{73} +(-6.19701 - 4.98097i) q^{74} +(-0.245740 - 1.11607i) q^{76} -4.28843 q^{77} -13.2255i q^{79} +(13.3388 - 6.17326i) q^{80} +(-4.56764 - 3.67133i) q^{82} -7.98402i q^{83} -17.8567i q^{85} +(-6.46064 + 8.03793i) q^{86} +(-1.25646 + 2.53403i) q^{88} +5.40135i q^{89} +30.4976 q^{91} +(1.55448 + 7.05995i) q^{92} +(-4.85520 + 6.04054i) q^{94} -2.09963 q^{95} -1.44563 q^{97} +(-10.0919 + 12.5557i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{4} + 8 q^{10} - 8 q^{16} + 32 q^{19} + 40 q^{25} - 32 q^{28} + 32 q^{34} + 16 q^{40} - 24 q^{46} - 8 q^{49} + 40 q^{52} - 8 q^{58} + 16 q^{64} + 72 q^{70} + 32 q^{73} - 8 q^{76} - 64 q^{82}+ \cdots - 32 q^{97}+O(q^{100}) \) 40 * q - 8 * q^4 + 8 * q^10 - 8 * q^16 + 32 * q^19 + 40 * q^25 - 32 * q^28 + 32 * q^34 + 16 * q^40 - 24 * q^46 - 8 * q^49 + 40 * q^52 - 8 * q^58 + 16 * q^64 + 72 * q^70 + 32 * q^73 - 8 * q^76 - 64 * q^82 - 24 * q^88 - 56 * q^94 - 32 * q^97

Introduction

L-functions

Modular forms

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Groups

Database

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