LMFDB - Embedded newform 840.2.da.a.89.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(89,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 3, 3, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.89"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.da (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.15
Character	$\chi$	$=$	840.89
Dual form			840.2.da.a.689.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.395473 - 1.68630i) q^{3} +(-2.06804 + 0.850426i) q^{5} +(0.514896 + 2.59517i) q^{7} +(-2.68720 - 1.33377i) q^{9} +(0.513340 - 0.296377i) q^{11} +3.52786 q^{13} +(0.616221 + 3.82365i) q^{15} +(5.41797 - 3.12807i) q^{17} +(-0.455153 - 0.262783i) q^{19} +(4.57985 + 0.158048i) q^{21} +(3.96748 - 6.87187i) q^{23} +(3.55355 - 3.51743i) q^{25} +(-3.31185 + 4.00396i) q^{27} -2.35134i q^{29} +(4.32575 - 2.49747i) q^{31} +(-0.296768 - 0.982854i) q^{33} +(-3.27182 - 4.92901i) q^{35} +(8.71989 + 5.03443i) q^{37} +(1.39517 - 5.94902i) q^{39} -4.64103 q^{41} +3.39515i q^{43} +(6.69151 + 0.473015i) q^{45} +(-7.55190 - 4.36009i) q^{47} +(-6.46976 + 2.67248i) q^{49} +(-3.13219 - 10.3734i) q^{51} +(4.45314 + 7.71307i) q^{53} +(-0.809560 + 1.04948i) q^{55} +(-0.623131 + 0.663601i) q^{57} +(-1.45156 - 2.51417i) q^{59} +(10.2693 + 5.92900i) q^{61} +(2.07772 - 7.66049i) q^{63} +(-7.29574 + 3.00018i) q^{65} +(2.49970 - 1.44320i) q^{67} +(-10.0190 - 9.40799i) q^{69} -1.36621i q^{71} +(-6.28839 - 10.8918i) q^{73} +(-4.52610 - 7.38339i) q^{75} +(1.03346 + 1.17960i) q^{77} +(-0.276768 + 0.479377i) q^{79} +(5.44212 + 7.16822i) q^{81} -2.27731i q^{83} +(-8.54437 + 11.0765i) q^{85} +(-3.96505 - 0.929889i) q^{87} +(-1.52477 + 2.64098i) q^{89} +(1.81648 + 9.15537i) q^{91} +(-2.50077 - 8.28218i) q^{93} +(1.16475 + 0.156370i) q^{95} +1.81647 q^{97} +(-1.77475 + 0.111748i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 3 q^{3} - 3 q^{5} - q^{9} - 14 q^{15} + 5 q^{21} - 2 q^{23} + q^{25} + 6 q^{31} - 24 q^{33} + 4 q^{35} + 2 q^{39} - 3 q^{45} + 12 q^{51} + 6 q^{53} - 20 q^{57} + 18 q^{61} + 26 q^{63} - 10 q^{65}+ \cdots - 12 q^{99}+O(q^{100}) $ 48 * q - 3 * q^3 - 3 * q^5 - q^9 - 14 * q^15 + 5 * q^21 - 2 * q^23 + q^25 + 6 * q^31 - 24 * q^33 + 4 * q^35 + 2 * q^39 - 3 * q^45 + 12 * q^51 + 6 * q^53 - 20 * q^57 + 18 * q^61 + 26 * q^63 - 10 * q^65 - 3 * q^75 - 2 * q^77 + 2 * q^79 - 9 * q^81 + 15 * q^87 + 24 * q^91 - 8 * q^93 - 6 * q^95 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$1$	$1$

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			0
$2$		0			0
$3$	0.395473	−	1.68630i	0.228326	−	0.973585i
$3$	0.395473	−	1.68630i	0.228326	−	0.973585i
$4$		0			0
$5$	−2.06804	+	0.850426i	−0.924854	+	0.380322i
$5$	−2.06804	+	0.850426i	−0.924854	+	0.380322i
$6$		0			0
$7$	0.514896	+	2.59517i	0.194612	+	0.980880i
$7$	0.514896	+	2.59517i	0.194612	+	0.980880i
$8$		0			0
$9$	−2.68720	−	1.33377i	−0.895734	−	0.444590i
$10$		0			0
$11$	0.513340	−	0.296377i	0.154778	−	0.0893611i	−0.420611	−	0.907241i	$-0.638184\pi$
$11$	0.513340	−	0.296377i	0.154778	−	0.0893611i	0.575389	+	0.817880i	$0.304851\pi$
$12$		0			0
$13$	3.52786			0.978452			0.489226	−	0.872157i	$-0.337279\pi$
$13$	3.52786			0.978452			0.489226	+	0.872157i	$0.337279\pi$
$14$		0			0
$15$	0.616221	+	3.82365i	0.159108	+	0.987261i
$16$		0			0
$17$	5.41797	−	3.12807i	1.31405	−	0.758667i	0.331286	−	0.943530i	$-0.392518\pi$
$17$	5.41797	−	3.12807i	1.31405	−	0.758667i	0.982764	+	0.184863i	$0.0591842\pi$
$18$		0			0
$19$	−0.455153	−	0.262783i	−0.104419	−	0.0602865i	0.446881	−	0.894593i	$-0.352535\pi$
$19$	−0.455153	−	0.262783i	−0.104419	−	0.0602865i	−0.551300	+	0.834307i	$0.685868\pi$
$20$		0			0
$21$	4.57985	+	0.158048i	0.999405	+	0.0344889i
$22$		0			0
$23$	3.96748	−	6.87187i	0.827276	−	1.43288i	−0.0728907	−	0.997340i	$-0.523222\pi$
$23$	3.96748	−	6.87187i	0.827276	−	1.43288i	0.900167	−	0.435545i	$-0.143444\pi$
$24$		0			0
$25$	3.55355	−	3.51743i	0.710710	−	0.703485i
$26$		0			0
$27$	−3.31185	+	4.00396i	−0.637365	+	0.770562i
$28$		0			0
$29$		−	2.35134i		−	0.436632i	−0.975878	−	0.218316i	$-0.929944\pi$
$29$		−	2.35134i		−	0.436632i	0.975878	−	0.218316i	$-0.0700564\pi$
$30$		0			0
$31$	4.32575	−	2.49747i	0.776927	−	0.448559i	−0.0584133	−	0.998292i	$-0.518604\pi$
$31$	4.32575	−	2.49747i	0.776927	−	0.448559i	0.835340	+	0.549734i	$0.185271\pi$
$32$		0			0
$33$	−0.296768	−	0.982854i	−0.0516607	−	0.171093i
$34$		0			0
$35$	−3.27182	−	4.92901i	−0.553039	−	0.833156i
$36$		0			0
$37$	8.71989	+	5.03443i	1.43354	+	0.827656i	0.997389	−	0.0722170i	$-0.0230074\pi$
$37$	8.71989	+	5.03443i	1.43354	+	0.827656i	0.436153	+	0.899873i	$0.356341\pi$
$38$		0			0
$39$	1.39517	−	5.94902i	0.223406	−	0.952606i
$40$		0			0
$41$	−4.64103			−0.724808			−0.362404	−	0.932021i	$-0.618044\pi$
$41$	−4.64103			−0.724808			−0.362404	+	0.932021i	$0.618044\pi$
$42$		0			0
$43$			3.39515i			0.517756i	0.965910	+	0.258878i	$0.0833528\pi$
$43$			3.39515i			0.517756i	−0.965910	+	0.258878i	$0.916647\pi$
$44$		0			0
$45$	6.69151	+	0.473015i	0.997511	+	0.0705129i
$46$		0			0
$47$	−7.55190	−	4.36009i	−1.10156	−	0.635985i	−0.164928	−	0.986306i	$-0.552739\pi$
$47$	−7.55190	−	4.36009i	−1.10156	−	0.635985i	−0.936630	+	0.350321i	$0.886073\pi$
$48$		0			0
$49$	−6.46976	+	2.67248i	−0.924252	+	0.381783i
$50$		0			0
$51$	−3.13219	−	10.3734i	−0.438595	−	1.45256i
$52$		0			0
$53$	4.45314	+	7.71307i	0.611686	+	1.05947i	0.990956	+	0.134186i	$0.0428419\pi$
$53$	4.45314	+	7.71307i	0.611686	+	1.05947i	−0.379270	+	0.925286i	$0.623825\pi$
$54$		0			0
$55$	−0.809560	+	1.04948i	−0.109161	+	0.141511i
$56$		0			0
$57$	−0.623131	+	0.663601i	−0.0825357	+	0.0878961i
$58$		0			0
$59$	−1.45156	−	2.51417i	−0.188977	−	0.327318i	0.755932	−	0.654650i	$-0.227184\pi$
$59$	−1.45156	−	2.51417i	−0.188977	−	0.327318i	−0.944909	+	0.327332i	$0.893850\pi$
$60$		0			0
$61$	10.2693	+	5.92900i	1.31485	+	0.759130i	0.982896	−	0.184164i	$-0.0589578\pi$
$61$	10.2693	+	5.92900i	1.31485	+	0.759130i	0.331957	+	0.943295i	$0.392291\pi$
$62$		0			0
$63$	2.07772	−	7.66049i	0.261768	−	0.965131i
$64$		0			0
$65$	−7.29574	+	3.00018i	−0.904925	+	0.372127i
$66$		0			0
$67$	2.49970	−	1.44320i	0.305387	−	0.176315i	−0.339474	−	0.940616i	$-0.610249\pi$
$67$	2.49970	−	1.44320i	0.305387	−	0.176315i	0.644860	+	0.764301i	$0.276916\pi$
$68$		0			0
$69$	−10.0190	−	9.40799i	−1.20615	−	1.13259i
$70$		0			0
$71$		−	1.36621i		−	0.162139i	−0.996708	−	0.0810695i	$-0.974166\pi$
$71$		−	1.36621i		−	0.162139i	0.996708	−	0.0810695i	$-0.0258336\pi$
$72$		0			0
$73$	−6.28839	−	10.8918i	−0.736001	−	1.27479i	−0.954283	−	0.298905i	$-0.903379\pi$
$73$	−6.28839	−	10.8918i	−0.736001	−	1.27479i	0.218282	−	0.975886i	$-0.429955\pi$
$74$		0			0
$75$	−4.52610	−	7.38339i	−0.522629	−	0.852560i
$76$		0			0
$77$	1.03346	+	1.17960i	0.117774	+	0.134428i
$78$		0			0
$79$	−0.276768	+	0.479377i	−0.0311389	+	0.0539341i	−0.881175	−	0.472790i	$-0.843247\pi$
$79$	−0.276768	+	0.479377i	−0.0311389	+	0.0539341i	0.850036	+	0.526725i	$0.176580\pi$
$80$		0			0
$81$	5.44212	+	7.16822i	0.604680	+	0.796469i
$82$		0			0
$83$		−	2.27731i		−	0.249967i	−0.992159	−	0.124983i	$-0.960112\pi$
$83$		−	2.27731i		−	0.249967i	0.992159	−	0.124983i	$-0.0398878\pi$
$84$		0			0
$85$	−8.54437	+	11.0765i	−0.926767	+	1.20142i
$86$		0			0
$87$	−3.96505	−	0.929889i	−0.425098	−	0.0996946i
$88$		0			0
$89$	−1.52477	+	2.64098i	−0.161625	+	0.279943i	−0.935452	−	0.353454i	$-0.885007\pi$
$89$	−1.52477	+	2.64098i	−0.161625	+	0.279943i	0.773826	+	0.633398i	$0.218340\pi$
$90$		0			0
$91$	1.81648	+	9.15537i	0.190419	+	0.959744i
$92$		0			0
$93$	−2.50077	−	8.28218i	−0.259317	−	0.858822i
$94$		0			0
$95$	1.16475	+	0.156370i	0.119501	+	0.0160433i
$96$		0			0
$97$	1.81647			0.184434			0.0922172	−	0.995739i	$-0.470605\pi$
$97$	1.81647			0.184434			0.0922172	+	0.995739i	$0.470605\pi$
$98$		0			0
$99$	−1.77475	+	0.111748i	−0.178369	+	0.0112311i
$100$		0			0
$101$	−3.40184	−	5.89216i	−0.338496	−	0.586292i	0.645654	−	0.763630i	$-0.276585\pi$
$101$	−3.40184	−	5.89216i	−0.338496	−	0.586292i	−0.984150	+	0.177338i	$0.943251\pi$
$102$		0			0
$103$	6.52606	−	11.3035i	0.643031	−	1.11376i	−0.341721	−	0.939801i	$-0.611010\pi$
$103$	6.52606	−	11.3035i	0.643031	−	1.11376i	0.984752	−	0.173962i	$-0.0556569\pi$
$104$		0			0
$105$	−9.60570	+	3.56798i	−0.937421	+	0.348199i
$106$		0			0
$107$	−0.906956	+	1.57089i	−0.0876787	+	0.151864i	−0.906530	−	0.422142i	$-0.861278\pi$
$107$	−0.906956	+	1.57089i	−0.0876787	+	0.151864i	0.818851	+	0.574006i	$0.194612\pi$
$108$		0			0
$109$	9.65478	+	16.7226i	0.924760	+	1.60173i	0.791947	+	0.610590i	$0.209068\pi$
$109$	9.65478	+	16.7226i	0.924760	+	1.60173i	0.132813	+	0.991141i	$0.457599\pi$
$110$		0			0
$111$	11.9380	−	12.7134i	1.13311	−	1.20670i
$112$		0			0
$113$	17.1285			1.61131			0.805656	−	0.592384i	$-0.201813\pi$
$113$	17.1285			1.61131			0.805656	+	0.592384i	$0.201813\pi$
$114$		0			0
$115$	−2.36087	+	17.5853i	−0.220152	+	1.63984i
$116$		0			0
$117$	−9.48007	−	4.70535i	−0.876433	−	0.435010i
$118$		0			0
$119$	10.9075	+	12.4499i	0.999892	+	1.14128i
$120$		0			0
$121$	−5.32432	+	9.22199i	−0.484029	+	0.838363i
$122$		0			0
$123$	−1.83540	+	7.82617i	−0.165493	+	0.705662i
$124$		0			0
$125$	−4.35756	+	10.2962i	−0.389752	+	0.920920i
$126$		0			0
$127$			5.58636i			0.495709i	0.968797	+	0.247855i	$0.0797255\pi$
$127$			5.58636i			0.495709i	−0.968797	+	0.247855i	$0.920275\pi$
$128$		0			0
$129$	5.72524	+	1.34269i	0.504079	+	0.118217i
$130$		0			0
$131$	−4.47664	+	7.75376i	−0.391125	+	0.677449i	−0.992598	−	0.121444i	$-0.961247\pi$
$131$	−4.47664	+	7.75376i	−0.391125	+	0.677449i	0.601473	+	0.798893i	$0.294581\pi$
$132$		0			0
$133$	0.447608	−	1.31650i	0.0388126	−	0.114155i
$134$		0			0
$135$	3.44395	−	11.0968i	0.296408	−	0.955061i
$136$		0			0
$137$	−0.822735	−	1.42502i	−0.0702910	−	0.121748i	0.828738	−	0.559637i	$-0.189059\pi$
$137$	−0.822735	−	1.42502i	−0.0702910	−	0.121748i	−0.899029	+	0.437889i	$0.855726\pi$
$138$		0			0
$139$		−	7.40264i		−	0.627883i	−0.949442	−	0.313942i	$-0.898350\pi$
$139$		−	7.40264i		−	0.627883i	0.949442	−	0.313942i	$-0.101650\pi$
$140$		0			0
$141$	−10.3390	+	11.0105i	−0.870700	+	0.927248i
$142$		0			0
$143$	1.81099	−	1.04558i	0.151443	−	0.0874355i
$144$		0			0
$145$	1.99964	+	4.86265i	0.166061	+	0.403821i
$146$		0			0
$147$	1.94799	+	11.9668i	0.160667	+	0.987009i
$148$		0			0
$149$	15.7660	+	9.10249i	1.29160	+	0.745705i	0.978938	−	0.204160i	$-0.0654463\pi$
$149$	15.7660	+	9.10249i	1.29160	+	0.745705i	0.312661	+	0.949865i	$0.398780\pi$
$150$		0			0
$151$	−8.90623	−	15.4260i	−0.724779	−	1.25535i	−0.959065	−	0.283186i	$-0.908609\pi$
$151$	−8.90623	−	15.4260i	−0.724779	−	1.25535i	0.234286	−	0.972168i	$-0.424725\pi$
$152$		0			0
$153$	−18.7313	+	1.17943i	−1.51434	+	0.0953510i
$154$		0			0
$155$	−6.82188	+	8.84359i	−0.547947	+	0.710334i
$156$		0			0
$157$	−9.04908	−	15.6735i	−0.722196	−	1.25088i	−0.960118	−	0.279595i	$-0.909800\pi$
$157$	−9.04908	−	15.6735i	−0.722196	−	1.25088i	0.237922	−	0.971284i	$-0.423534\pi$
$158$		0			0
$159$	14.7676	−	4.45902i	1.17115	−	0.353623i
$160$		0			0
$161$	19.8765	+	6.75796i	1.56649	+	0.532602i
$162$		0			0
$163$	−11.4627	−	6.61800i	−0.897829	−	0.518362i	−0.0213341	−	0.999772i	$-0.506791\pi$
$163$	−11.4627	−	6.61800i	−0.897829	−	0.518362i	−0.876495	+	0.481410i	$0.840125\pi$
$164$		0			0
$165$	1.44957	+	1.78020i	0.112849	+	0.138588i
$166$		0			0
$167$			13.6325i			1.05492i	0.849580	+	0.527459i	$0.176855\pi$
$167$			13.6325i			1.05492i	−0.849580	+	0.527459i	$0.823145\pi$
$168$		0			0
$169$	−0.554220			−0.0426323
$170$		0			0
$171$	0.872598	+	1.31322i	0.0667292	+	0.100425i
$172$		0			0
$173$	−9.61777	−	5.55282i	−0.731225	−	0.422173i	0.0876449	−	0.996152i	$-0.472066\pi$
$173$	−9.61777	−	5.55282i	−0.731225	−	0.422173i	−0.818870	+	0.573979i	$0.805399\pi$
$174$		0			0
$175$	10.9580	+	7.41094i	0.828348	+	0.560214i
$176$		0			0
$177$	−4.81370	+	1.45347i	−0.361820	+	0.109250i
$178$		0			0
$179$	3.67091	−	2.11940i	0.274377	−	0.158411i	−0.356498	−	0.934296i	$-0.616029\pi$
$179$	3.67091	−	2.11940i	0.274377	−	0.158411i	0.630875	+	0.775885i	$0.282696\pi$
$180$		0			0
$181$			8.96977i			0.666718i	0.942800	+	0.333359i	$0.108182\pi$
$181$			8.96977i			0.666718i	−0.942800	+	0.333359i	$0.891818\pi$
$182$		0			0
$183$	14.0593	−	14.9724i	1.03929	−	1.10679i
$184$		0			0
$185$	−22.3145	−	2.99576i	−1.64059	−	0.220253i
$186$		0			0
$187$	1.85417	−	3.21152i	0.135591	−	0.234850i
$188$		0			0
$189$	−12.0962	−	6.53317i	−0.879868	−	0.475218i
$190$		0			0
$191$	−10.1558	−	5.86347i	−0.734850	−	0.424266i	0.0853438	−	0.996352i	$-0.472801\pi$
$191$	−10.1558	−	5.86347i	−0.734850	−	0.424266i	−0.820194	+	0.572086i	$0.806134\pi$
$192$		0			0
$193$	17.4907	−	10.0983i	1.25901	−	0.726890i	0.286128	−	0.958191i	$-0.407632\pi$
$193$	17.4907	−	10.0983i	1.25901	−	0.726890i	0.972882	+	0.231301i	$0.0742983\pi$
$194$		0			0
$195$	2.17394	+	13.4893i	0.155679	+	0.965987i
$196$		0			0
$197$	11.0362			0.786296			0.393148	−	0.919475i	$-0.371386\pi$
$197$	11.0362			0.786296			0.393148	+	0.919475i	$0.371386\pi$
$198$		0			0
$199$	−5.81284	+	3.35604i	−0.412061	+	0.237904i	−0.691675	−	0.722209i	$-0.743127\pi$
$199$	−5.81284	+	3.35604i	−0.412061	+	0.237904i	0.279614	+	0.960113i	$0.409794\pi$
$200$		0			0
$201$	−1.44511	−	4.78598i	−0.101930	−	0.337577i
$202$		0			0
$203$	6.10211	−	1.21069i	0.428284	−	0.0849741i
$204$		0			0
$205$	9.59783	−	3.94686i	0.670341	−	0.275661i
$206$		0			0
$207$	−19.8269	+	13.1744i	−1.37807	+	0.915685i
$208$		0			0
$209$	−0.311532			−0.0215491
$210$		0			0
$211$	−15.7005			−1.08087			−0.540433	−	0.841387i	$-0.681740\pi$
$211$	−15.7005			−1.08087			−0.540433	+	0.841387i	$0.681740\pi$
$212$		0			0
$213$	−2.30383	−	0.540297i	−0.157856	−	0.0370206i
$214$		0			0
$215$	−2.88733	−	7.02130i	−0.196914	−	0.478849i
$216$		0			0
$217$	8.70866	+	9.94008i	0.591182	+	0.674777i
$218$		0			0
$219$	−20.8537	+	6.29669i	−1.40917	+	0.425491i
$220$		0			0
$221$	19.1138	−	11.0354i	1.28573	−	0.742319i
$222$		0			0
$223$	−27.7463			−1.85803			−0.929014	−	0.370044i	$-0.879343\pi$
$223$	−27.7463			−1.85803			−0.929014	+	0.370044i	$0.879343\pi$
$224$		0			0
$225$	−14.2405	+	4.71242i	−0.949370	+	0.314161i
$226$		0			0
$227$	−19.7971	+	11.4298i	−1.31398	+	0.758626i	−0.982752	−	0.184926i	$-0.940795\pi$
$227$	−19.7971	+	11.4298i	−1.31398	+	0.758626i	−0.331226	+	0.943552i	$0.607462\pi$
$228$		0			0
$229$	−1.64330	−	0.948762i	−0.108593	−	0.0626959i	0.444720	−	0.895670i	$-0.353303\pi$
$229$	−1.64330	−	0.948762i	−0.108593	−	0.0626959i	−0.553313	+	0.832974i	$0.686637\pi$
$230$		0			0
$231$	2.39786	−	1.27623i	0.157768	−	0.0839698i
$232$		0			0
$233$	0.969632	−	1.67945i	0.0635227	−	0.110025i	−0.832515	−	0.554002i	$-0.813100\pi$
$233$	0.969632	−	1.67945i	0.0635227	−	0.110025i	0.896038	+	0.443978i	$0.146433\pi$
$234$		0			0
$235$	19.3255	+	2.59449i	1.26066	+	0.169246i
$236$		0			0
$237$	0.698918	+	0.656294i	0.0453996	+	0.0426309i
$238$		0			0
$239$			27.3399i			1.76847i	0.467040	+	0.884236i	$0.345320\pi$
$239$			27.3399i			1.76847i	−0.467040	+	0.884236i	$0.654680\pi$
$240$		0			0
$241$	−8.99319	+	5.19222i	−0.579302	+	0.334460i	−0.760856	−	0.648921i	$-0.775221\pi$
$241$	−8.99319	+	5.19222i	−0.579302	+	0.334460i	0.181554	+	0.983381i	$0.441887\pi$
$242$		0			0
$243$	14.2400	−	6.34220i	0.913494	−	0.406852i
$244$		0			0
$245$	11.1070	−	11.0288i	0.709598	−	0.704607i
$246$		0			0
$247$	−1.60572	−	0.927061i	−0.102169	−	0.0589875i
$248$		0			0
$249$	−3.84022	−	0.900612i	−0.243364	−	0.0570740i
$250$		0			0
$251$	−28.7538			−1.81493			−0.907463	−	0.420131i	$-0.861984\pi$
$251$	−28.7538			−1.81493			−0.907463	+	0.420131i	$0.861984\pi$
$252$		0			0
$253$		−	4.70348i		−	0.295705i
$254$		0			0
$255$	15.2993	+	18.7888i	0.958078	+	1.17660i
$256$		0			0
$257$	−2.89420	−	1.67097i	−0.180535	−	0.104232i	0.407009	−	0.913424i	$-0.366572\pi$
$257$	−2.89420	−	1.67097i	−0.180535	−	0.104232i	−0.587544	+	0.809192i	$0.699905\pi$
$258$		0			0
$259$	−8.57534	+	25.2218i	−0.532846	+	1.56720i
$260$		0			0
$261$	−3.13614	+	6.31852i	−0.194122	+	0.391106i
$262$		0			0
$263$	−9.47670	−	16.4141i	−0.584358	−	1.01214i	−0.994955	−	0.100321i	$-0.968013\pi$
$263$	−9.47670	−	16.4141i	−0.584358	−	1.01214i	0.410597	−	0.911817i	$-0.365320\pi$
$264$		0			0
$265$	−15.7687	−	12.1638i	−0.968661	−	0.747219i
$266$		0			0
$267$	3.85048	+	3.61565i	0.235645	+	0.221274i
$268$		0			0
$269$	0.357429	+	0.619085i	0.0217928	+	0.0377463i	0.876716	−	0.481008i	$-0.159729\pi$
$269$	0.357429	+	0.619085i	0.0217928	+	0.0377463i	−0.854923	+	0.518754i	$0.826396\pi$
$270$		0			0
$271$	16.0639	+	9.27451i	0.975814	+	0.563386i	0.901004	−	0.433811i	$-0.142832\pi$
$271$	16.0639	+	9.27451i	0.975814	+	0.563386i	0.0748102	+	0.997198i	$0.476165\pi$
$272$		0			0
$273$	16.1571	+	0.557571i	0.977870	+	0.0337457i
$274$		0			0
$275$	0.781696	−	2.85883i	0.0471380	−	0.172394i
$276$		0			0
$277$	−23.1750	+	13.3801i	−1.39245	+	0.803932i	−0.993586	−	0.113077i	$-0.963929\pi$
$277$	−23.1750	+	13.3801i	−1.39245	+	0.803932i	−0.398866	+	0.917009i	$0.630596\pi$
$278$		0			0
$279$	−14.9552	+	0.941663i	−0.895345	+	0.0563759i
$280$		0			0
$281$		−	1.08018i		−	0.0644381i	−0.999481	−	0.0322191i	$-0.989743\pi$
$281$		−	1.08018i		−	0.0644381i	0.999481	−	0.0322191i	$-0.0102574\pi$
$282$		0			0
$283$	3.78268	+	6.55179i	0.224857	+	0.389463i	0.956276	−	0.292464i	$-0.0944753\pi$
$283$	3.78268	+	6.55179i	0.224857	+	0.389463i	−0.731420	+	0.681928i	$0.761142\pi$
$284$		0			0
$285$	0.724314	−	1.90228i	0.0429047	−	0.112681i
$286$		0			0
$287$	−2.38965	−	12.0442i	−0.141057	−	0.710950i
$288$		0			0
$289$	11.0696	−	19.1731i	0.651152	−	1.12783i
$290$		0			0
$291$	0.718364	−	3.06311i	0.0421112	−	0.179563i
$292$		0			0
$293$			1.61758i			0.0945000i	0.998883	+	0.0472500i	$0.0150458\pi$
$293$			1.61758i			0.0945000i	−0.998883	+	0.0472500i	$0.984954\pi$
$294$		0			0
$295$	5.14000	+	3.96496i	0.299262	+	0.230849i
$296$		0			0
$297$	−0.513424	+	3.03695i	−0.0297919	+	0.176222i
$298$		0			0
$299$	13.9967	−	24.2430i	0.809450	−	1.40201i
$300$		0			0
$301$	−8.81098	+	1.74815i	−0.507857	+	0.100762i
$302$		0			0
$303$	−11.2813	+	3.40633i	−0.648093	+	0.195689i
$304$		0			0
$305$	−26.2795	−	3.52808i	−1.50476	−	0.202017i
$306$		0			0
$307$	26.5559			1.51563			0.757813	−	0.652472i	$-0.226268\pi$
$307$	26.5559			1.51563			0.757813	+	0.652472i	$0.226268\pi$
$308$		0			0
$309$	−16.4801	−	15.4751i	−0.937522	−	0.880347i
$310$		0			0
$311$	−3.19106	−	5.52707i	−0.180948	−	0.313411i	0.761256	−	0.648452i	$-0.224583\pi$
$311$	−3.19106	−	5.52707i	−0.180948	−	0.313411i	−0.942204	+	0.335041i	$0.891250\pi$
$312$		0			0
$313$	−2.99675	+	5.19052i	−0.169386	+	0.293386i	−0.938204	−	0.346082i	$-0.887512\pi$
$313$	−2.99675	+	5.19052i	−0.169386	+	0.293386i	0.768818	+	0.639468i	$0.220845\pi$
$314$		0			0
$315$	2.21788	+	17.6091i	0.124963	+	0.992161i
$316$		0			0
$317$	−13.3260	+	23.0812i	−0.748461	+	1.29637i	0.200100	+	0.979776i	$0.435873\pi$
$317$	−13.3260	+	23.0812i	−0.748461	+	1.29637i	−0.948560	+	0.316596i	$0.897460\pi$
$318$		0			0
$319$	−0.696882	−	1.20704i	−0.0390179	−	0.0675810i
$320$		0			0
$321$	2.29032	+	2.15064i	0.127833	+	0.120037i
$322$		0			0
$323$	−3.28801			−0.182950
$324$		0			0
$325$	12.5364	−	12.4090i	0.695395	−	0.688326i
$326$		0			0
$327$	32.0174	−	9.66752i	1.77057	−	0.534615i
$328$		0			0
$329$	7.42672	−	21.8434i	0.409448	−	1.20427i
$330$		0			0
$331$	−2.62072	+	4.53922i	−0.144048	+	0.249498i	−0.929017	−	0.370036i	$-0.879345\pi$
$331$	−2.62072	+	4.53922i	−0.144048	+	0.249498i	0.784970	+	0.619534i	$0.212679\pi$
$332$		0			0
$333$	−16.7174	−	25.1589i	−0.916105	−	1.37870i
$334$		0			0
$335$	−3.94213	+	5.11040i	−0.215382	+	0.279211i
$336$		0			0
$337$			21.1800i			1.15375i	0.816834	+	0.576873i	$0.195727\pi$
$337$			21.1800i			1.15375i	−0.816834	+	0.576873i	$0.804273\pi$
$338$		0			0
$339$	6.77384	−	28.8837i	0.367905	−	1.56875i
$340$		0			0
$341$	1.48039	−	2.56410i	0.0801674	−	0.138854i
$342$		0			0
$343$	−10.2668	−	15.4141i	−0.554354	−	0.832281i
$344$		0			0
$345$	28.7205	+	10.9356i	1.54626	+	0.588755i
$346$		0			0
$347$	−6.35632	−	11.0095i	−0.341225	−	0.591019i	0.643435	−	0.765501i	$-0.277509\pi$
$347$	−6.35632	−	11.0095i	−0.341225	−	0.591019i	−0.984661	+	0.174481i	$0.944175\pi$
$348$		0			0
$349$		−	21.0822i		−	1.12851i	−0.825602	−	0.564253i	$-0.809164\pi$
$349$		−	21.0822i		−	1.12851i	0.825602	−	0.564253i	$-0.190836\pi$
$350$		0			0
$351$	−11.6837	+	14.1254i	−0.623631	+	0.753957i
$352$		0			0
$353$	31.8624	−	18.3958i	1.69587	−	0.979109i	0.746264	−	0.665650i	$-0.231846\pi$
$353$	31.8624	−	18.3958i	1.69587	−	0.979109i	0.949602	−	0.313458i	$-0.101488\pi$
$354$		0			0
$355$	1.16186	+	2.82537i	0.0616651	+	0.149955i
$356$		0			0
$357$	25.3079	−	13.4698i	1.33943	−	0.712896i
$358$		0			0
$359$	20.1910	+	11.6573i	1.06564	+	0.615248i	0.926987	−	0.375093i	$-0.122389\pi$
$359$	20.1910	+	11.6573i	1.06564	+	0.615248i	0.138653	+	0.990341i	$0.455723\pi$
$360$		0			0
$361$	−9.36189	−	16.2153i	−0.492731	−	0.853435i
$362$		0			0
$363$	13.4454	+	12.6254i	0.705701	+	0.662664i
$364$		0			0
$365$	22.2673	+	17.1769i	1.16552	+	0.899078i
$366$		0			0
$367$	−10.9958	−	19.0453i	−0.573977	−	0.994158i	−0.996152	−	0.0876432i	$-0.972066\pi$
$367$	−10.9958	−	19.0453i	−0.573977	−	0.994158i	0.422175	−	0.906514i	$-0.361267\pi$
$368$		0			0
$369$	12.4714	+	6.19007i	0.649235	+	0.322242i
$370$		0			0
$371$	−17.7238	+	15.5281i	−0.920173	+	0.806178i
$372$		0			0
$373$	1.06098	+	0.612559i	0.0549356	+	0.0317171i	0.527216	−	0.849731i	$-0.323236\pi$
$373$	1.06098	+	0.612559i	0.0549356	+	0.0317171i	−0.472281	+	0.881448i	$0.656569\pi$
$374$		0			0
$375$	15.6392	+	11.4200i	0.807603	+	0.589727i
$376$		0			0
$377$		−	8.29518i		−	0.427223i
$378$		0			0
$379$	22.9103			1.17683			0.588413	−	0.808561i	$-0.299753\pi$
$379$	22.9103			1.17683			0.588413	+	0.808561i	$0.299753\pi$
$380$		0			0
$381$	9.42026	+	2.20925i	0.482615	+	0.113183i
$382$		0			0
$383$	27.2371	+	15.7253i	1.39175	+	0.803527i	0.993509	−	0.113754i	$-0.0362875\pi$
$383$	27.2371	+	15.7253i	1.39175	+	0.803527i	0.398241	+	0.917281i	$0.369621\pi$
$384$		0			0
$385$	−3.14041	−	1.56057i	−0.160050	−	0.0795340i
$386$		0			0
$387$	4.52835	−	9.12346i	0.230189	−	0.463772i
$388$		0			0
$389$	−1.33122	+	0.768581i	−0.0674956	+	0.0389686i	−0.533368	−	0.845883i	$-0.679074\pi$
$389$	−1.33122	+	0.768581i	−0.0674956	+	0.0389686i	0.465872	+	0.884852i	$0.345741\pi$
$390$		0			0
$391$		−	49.6421i		−	2.51051i
$392$		0			0
$393$	11.3048	+	10.6153i	0.570250	+	0.535473i
$394$		0			0
$395$	0.164692	−	1.22674i	0.00828657	−	0.0617240i
$396$		0			0
$397$	7.62473	−	13.2064i	0.382674	−	0.662812i	−0.608769	−	0.793347i	$-0.708336\pi$
$397$	7.62473	−	13.2064i	0.382674	−	0.662812i	0.991444	+	0.130536i	$0.0416698\pi$
$398$		0			0
$399$	−2.04300	−	1.27544i	−0.102278	−	0.0638520i
$400$		0			0
$401$	−0.445950	−	0.257469i	−0.0222697	−	0.0128574i	0.488824	−	0.872383i	$-0.337426\pi$
$401$	−0.445950	−	0.257469i	−0.0222697	−	0.0128574i	−0.511094	+	0.859525i	$0.670759\pi$
$402$		0			0
$403$	15.2606	−	8.81072i	0.760185	−	0.438893i
$404$		0			0
$405$	−17.3505	−	10.1960i	−0.862155	−	0.506644i
$406$		0			0
$407$	5.96836			0.295841
$408$		0			0
$409$	−3.75167	+	2.16603i	−0.185508	+	0.107103i	−0.589878	−	0.807492i	$-0.700824\pi$
$409$	−3.75167	+	2.16603i	−0.185508	+	0.107103i	0.404370	+	0.914596i	$0.367491\pi$
$410$		0			0
$411$	−2.72838	+	0.823821i	−0.134581	+	0.0406361i
$412$		0			0
$413$	5.77730	−	5.06157i	0.284282	−	0.249064i
$414$		0			0
$415$	1.93668	+	4.70955i	0.0950679	+	0.231183i
$416$		0			0
$417$	−12.4831	−	2.92754i	−0.611298	−	0.143362i
$418$		0			0
$419$	−17.5359			−0.856685			−0.428342	−	0.903617i	$-0.640902\pi$
$419$	−17.5359			−0.856685			−0.428342	+	0.903617i	$0.640902\pi$
$420$		0			0
$421$	−26.3274			−1.28312			−0.641558	−	0.767074i	$-0.721712\pi$
$421$	−26.3274			−1.28312			−0.641558	+	0.767074i	$0.721712\pi$
$422$		0			0
$423$	14.4781	+	21.7890i	0.703951	+	1.05942i
$424$		0			0
$425$	8.25028	−	30.1730i	0.400197	−	1.46361i
$426$		0			0
$427$	−10.0991	+	29.7034i	−0.488729	+	1.43745i
$428$		0			0
$429$	−1.04696	−	3.46737i	−0.0505475	−	0.167406i
$430$		0			0
$431$	−8.92848	+	5.15486i	−0.430070	+	0.248301i	−0.699376	−	0.714754i	$-0.746539\pi$
$431$	−8.92848	+	5.15486i	−0.430070	+	0.248301i	0.269306	+	0.963055i	$0.413206\pi$
$432$		0			0
$433$	−6.23911			−0.299832			−0.149916	−	0.988699i	$-0.547900\pi$
$433$	−6.23911			−0.299832			−0.149916	+	0.988699i	$0.547900\pi$
$434$		0			0
$435$	8.99068	−	1.44894i	0.431070	−	0.0694715i
$436$		0			0
$437$	−3.61162	+	2.08517i	−0.172767	+	0.0997473i
$438$		0			0
$439$	−5.64405	−	3.25859i	−0.269376	−	0.155524i	0.359228	−	0.933250i	$-0.383040\pi$
$439$	−5.64405	−	3.25859i	−0.269376	−	0.155524i	−0.628604	+	0.777726i	$0.716373\pi$
$440$		0			0
$441$	20.9500	+	1.44767i	0.997621	+	0.0689368i
$442$		0			0
$443$	1.13138	−	1.95961i	0.0537537	−	0.0931041i	−0.837897	−	0.545829i	$-0.816215\pi$
$443$	1.13138	−	1.95961i	0.0537537	−	0.0931041i	0.891650	+	0.452725i	$0.149548\pi$
$444$		0			0
$445$	0.907322	−	6.75835i	0.0430112	−	0.320376i
$446$		0			0
$447$	21.5845	−	22.9863i	1.02091	−	1.08722i
$448$		0			0
$449$			17.1418i			0.808972i	0.914544	+	0.404486i	$0.132550\pi$
$449$			17.1418i			0.808972i	−0.914544	+	0.404486i	$0.867450\pi$
$450$		0			0
$451$	−2.38243	+	1.37550i	−0.112184	+	0.0647696i
$452$		0			0
$453$	−29.5351	+	8.91798i	−1.38768	+	0.419003i
$454$		0			0
$455$	−11.5425	−	17.3889i	−0.541122	−	0.815202i
$456$		0			0
$457$	13.1545	+	7.59478i	0.615343	+	0.355269i	0.775054	−	0.631895i	$-0.217723\pi$
$457$	13.1545	+	7.59478i	0.615343	+	0.355269i	−0.159710	+	0.987164i	$0.551056\pi$
$458$		0			0
$459$	−5.41885	+	32.0530i	−0.252930	+	1.49611i
$460$		0			0
$461$	15.2352			0.709572			0.354786	−	0.934948i	$-0.384554\pi$
$461$	15.2352			0.709572			0.354786	+	0.934948i	$0.384554\pi$
$462$		0			0
$463$			33.7527i			1.56862i	0.620369	+	0.784310i	$0.286983\pi$
$463$			33.7527i			1.56862i	−0.620369	+	0.784310i	$0.713017\pi$
$464$		0			0
$465$	12.2151	+	15.0011i	0.566460	+	0.695661i
$466$		0			0
$467$	7.08763	+	4.09205i	0.327976	+	0.189357i	0.654942	−	0.755679i	$-0.272693\pi$
$467$	7.08763	+	4.09205i	0.327976	+	0.189357i	−0.326966	+	0.945036i	$0.606026\pi$
$468$		0			0
$469$	5.03243	+	5.74403i	0.232376	+	0.265235i
$470$		0			0
$471$	−30.0088	+	9.06103i	−1.38273	+	0.417510i
$472$		0			0
$473$	1.00625	+	1.74287i	0.0462672	+	0.0801372i
$474$		0			0
$475$	−2.54173	+	0.667156i	−0.116623	+	0.0306112i
$476$		0			0
$477$	−1.67904	−	26.6661i	−0.0768781	−	1.22095i
$478$		0			0
$479$	19.6019	+	33.9515i	0.895635	+	1.55129i	0.833017	+	0.553248i	$0.186612\pi$
$479$	19.6019	+	33.9515i	0.895635	+	1.55129i	0.0626186	+	0.998038i	$0.480055\pi$
$480$		0			0
$481$	30.7625	+	17.7608i	1.40265	+	0.809821i
$482$		0			0
$483$	19.2565	−	30.8451i	0.876203	−	1.40350i
$484$		0			0
$485$	−3.75652	+	1.54477i	−0.170575	+	0.0701445i
$486$		0			0
$487$	20.1905	−	11.6570i	0.914920	−	0.528229i	0.0329090	−	0.999458i	$-0.489523\pi$
$487$	20.1905	−	11.6570i	0.914920	−	0.528229i	0.882011	+	0.471229i	$0.156190\pi$
$488$		0			0
$489$	−15.6931	+	16.7123i	−0.709667	+	0.755757i
$490$		0			0
$491$		−	26.3868i		−	1.19082i	−0.803423	−	0.595409i	$-0.796990\pi$
$491$		−	26.3868i		−	1.19082i	0.803423	−	0.595409i	$-0.203010\pi$
$492$		0			0
$493$	−7.35513	−	12.7395i	−0.331259	−	0.573757i
$494$		0			0
$495$	3.57521	−	1.74039i	0.160694	−	0.0782248i
$496$		0			0
$497$	3.54553	−	0.703455i	0.159039	−	0.0315543i
$498$		0			0
$499$	13.6823	−	23.6984i	0.612502	−	1.06088i	−0.378316	−	0.925677i	$-0.623497\pi$
$499$	13.6823	−	23.6984i	0.612502	−	1.06088i	0.990817	−	0.135207i	$-0.0431701\pi$
$500$		0			0
$501$	22.9885	+	5.39130i	1.02705	+	0.240865i
$502$		0			0
$503$			2.37035i			0.105689i	0.998603	+	0.0528444i	$0.0168287\pi$
$503$			2.37035i			0.105689i	−0.998603	+	0.0528444i	$0.983171\pi$
$504$		0			0
$505$	12.0460	+	9.29219i	0.536039	+	0.413497i
$506$		0			0
$507$	−0.219179	+	0.934581i	−0.00973408	+	0.0415062i
$508$		0			0
$509$	−8.37336	+	14.5031i	−0.371143	+	0.642838i	−0.989742	−	0.142869i	$-0.954367\pi$
$509$	−8.37336	+	14.5031i	−0.371143	+	0.642838i	0.618599	+	0.785707i	$0.287701\pi$
$510$		0			0
$511$	25.0282	−	21.9276i	1.10718	−	0.970019i
$512$		0			0
$513$	2.55957	−	0.952117i	0.113008	−	0.0420370i
$514$		0			0
$515$	−3.88336	+	28.9259i	−0.171121	+	1.27463i
$516$		0			0
$517$	−5.16893			−0.227329
$518$		0			0
$519$	−13.1673	+	14.0224i	−0.577979	+	0.615517i
$520$		0			0
$521$	−12.1895	−	21.1128i	−0.534030	−	0.924967i	−0.999210	−	0.0397506i	$-0.987344\pi$
$521$	−12.1895	−	21.1128i	−0.534030	−	0.924967i	0.465180	−	0.885216i	$-0.345990\pi$
$522$		0			0
$523$	−5.52273	+	9.56564i	−0.241492	+	0.418276i	−0.961139	−	0.276063i	$-0.910970\pi$
$523$	−5.52273	+	9.56564i	−0.241492	+	0.418276i	0.719647	+	0.694340i	$0.244303\pi$
$524$		0			0
$525$	16.8306	−	15.5476i	0.734550	−	0.678555i
$526$		0			0
$527$	15.6245	−	27.0624i	0.680614	−	1.17886i
$528$		0			0
$529$	−19.9818	−	34.6094i	−0.868772	−	1.50476i
$530$		0			0
$531$	0.547306	+	8.69214i	0.0237510	+	0.377207i
$532$		0			0
$533$	−16.3729			−0.709189
$534$		0			0
$535$	0.539688	−	4.01996i	0.0233328	−	0.173798i
$536$		0			0
$537$	−2.12220	−	7.02841i	−0.0915795	−	0.303298i
$538$		0			0
$539$	−2.52913	+	3.28938i	−0.108937	+	0.141684i
$540$		0			0
$541$	4.48534	−	7.76883i	0.192840	−	0.334008i	−0.753351	−	0.657619i	$-0.771564\pi$
$541$	4.48534	−	7.76883i	0.192840	−	0.334008i	0.946190	+	0.323611i	$0.104897\pi$
$542$		0			0
$543$	15.1257	+	3.54730i	0.649106	+	0.152229i
$544$		0			0
$545$	−34.1877	−	26.3722i	−1.46444	−	1.12966i
$546$		0			0
$547$			13.0695i			0.558813i	0.960173	+	0.279407i	$0.0901378\pi$
$547$			13.0695i			0.558813i	−0.960173	+	0.279407i	$0.909862\pi$
$548$		0			0
$549$	−19.6878	−	29.6293i	−0.840257	−	1.26455i
$550$		0			0
$551$	−0.617891	+	1.07022i	−0.0263230	+	0.0455929i
$552$		0			0
$553$	−1.38657	−	0.471430i	−0.0589629	−	0.0200473i
$554$		0			0
$555$	−13.8765	+	36.4441i	−0.589025	+	1.54697i
$556$		0			0
$557$	7.31816	+	12.6754i	0.310080	+	0.537075i	0.978380	−	0.206818i	$-0.0663107\pi$
$557$	7.31816	+	12.6754i	0.310080	+	0.537075i	−0.668299	+	0.743893i	$0.732977\pi$
$558$		0			0
$559$			11.9776i			0.506599i
$560$		0			0
$561$	−4.68231	−	4.39676i	−0.197687	−	0.185631i
$562$		0			0
$563$	−22.7880	+	13.1567i	−0.960400	+	0.554487i	−0.896296	−	0.443456i	$-0.853752\pi$
$563$	−22.7880	+	13.1567i	−0.960400	+	0.554487i	−0.0641038	+	0.997943i	$0.520419\pi$
$564$		0			0
$565$	−35.4223	+	14.5665i	−1.49023	+	0.612818i
$566$		0			0
$567$	−15.8006	+	17.8141i	−0.663562	+	0.748121i
$568$		0			0
$569$	−7.61500	−	4.39652i	−0.319237	−	0.184312i	0.331815	−	0.943344i	$-0.392339\pi$
$569$	−7.61500	−	4.39652i	−0.319237	−	0.184312i	−0.651053	+	0.759033i	$0.725672\pi$
$570$		0			0
$571$	−5.57694	−	9.65955i	−0.233388	−	0.404240i	0.725415	−	0.688312i	$-0.241648\pi$
$571$	−5.57694	−	9.65955i	−0.233388	−	0.404240i	−0.958803	+	0.284072i	$0.908315\pi$
$572$		0			0
$573$	−13.9039	+	14.8069i	−0.580844	+	0.618568i
$574$		0			0
$575$	−10.0727	−	38.3749i	−0.420060	−	1.60034i
$576$		0			0
$577$	−18.0251	−	31.2204i	−0.750394	−	1.29972i	−0.947632	−	0.319365i	$-0.896530\pi$
$577$	−18.0251	−	31.2204i	−0.750394	−	1.29972i	0.197238	−	0.980356i	$-0.436803\pi$
$578$		0			0
$579$	−10.1116	−	33.4882i	−0.420224	−	1.39172i
$580$		0			0
$581$	5.90998	−	1.17258i	0.245187	−	0.0486466i
$582$		0			0
$583$	4.57196	+	2.63962i	0.189351	+	0.109322i
$584$		0			0
$585$	23.6067	+	1.66873i	0.976016	+	0.0689935i
$586$		0			0
$587$			24.6334i			1.01673i	0.861142	+	0.508364i	$0.169749\pi$
$587$			24.6334i			1.01673i	−0.861142	+	0.508364i	$0.830251\pi$
$588$		0			0
$589$	−2.62517			−0.108168
$590$		0			0
$591$	4.36451	−	18.6103i	0.179532	−	0.765525i
$592$		0			0
$593$	10.2968	+	5.94488i	0.422841	+	0.244127i	0.696292	−	0.717759i	$-0.254832\pi$
$593$	10.2968	+	5.94488i	0.422841	+	0.244127i	−0.273451	+	0.961886i	$0.588165\pi$
$594$		0			0
$595$	−33.1449	−	16.4708i	−1.35881	−	0.675236i
$596$		0			0
$597$	3.36047	+	11.1294i	0.137535	+	0.455496i
$598$		0			0
$599$	13.6545	−	7.88342i	0.557907	−	0.322108i	−0.194398	−	0.980923i	$-0.562275\pi$
$599$	13.6545	−	7.88342i	0.557907	−	0.322108i	0.752305	+	0.658815i	$0.228942\pi$
$600$		0			0
$601$		−	0.994055i		−	0.0405483i	−0.999794	−	0.0202742i	$-0.993546\pi$
$601$		−	0.994055i		−	0.0405483i	0.999794	−	0.0202742i	$-0.00645391\pi$
$602$		0			0
$603$	−8.64209	+	0.544154i	−0.351933	+	0.0221597i
$604$		0			0
$605$	3.16826	−	23.5994i	0.128808	−	0.959451i
$606$		0			0
$607$	1.59944	−	2.77031i	0.0649193	−	0.112444i	−0.831739	−	0.555167i	$-0.812654\pi$
$607$	1.59944	−	2.77031i	0.0649193	−	0.112444i	0.896658	+	0.442723i	$0.145988\pi$
$608$		0			0
$609$	0.371624	−	10.7688i	0.0150590	−	0.436372i
$610$		0			0
$611$	−26.6420	−	15.3818i	−1.07782	−	0.622281i
$612$		0			0
$613$	27.5714	−	15.9183i	1.11360	−	0.642935i	0.173838	−	0.984774i	$-0.444383\pi$
$613$	27.5714	−	15.9183i	1.11360	−	0.642935i	0.939759	+	0.341839i	$0.111050\pi$
$614$		0			0
$615$	−2.85990	−	17.7457i	−0.115322	−	0.715575i
$616$		0			0
$617$	−37.2314			−1.49888			−0.749441	−	0.662071i	$-0.769678\pi$
$617$	−37.2314			−1.49888			−0.749441	+	0.662071i	$0.769678\pi$
$618$		0			0
$619$	13.9665	−	8.06355i	0.561360	−	0.324102i	−0.192331	−	0.981330i	$-0.561605\pi$
$619$	13.9665	−	8.06355i	0.561360	−	0.324102i	0.753691	+	0.657229i	$0.228271\pi$
$620$		0			0
$621$	14.3750	+	38.6442i	0.576849	+	1.55074i
$622$		0			0
$623$	−7.63888	−	2.59720i	−0.306045	−	0.104055i
$624$		0			0
$625$	0.255434	−	24.9987i	0.0102173	−	0.999948i
$626$		0			0
$627$	−0.123202	+	0.525335i	−0.00492022	+	0.0209799i
$628$		0			0
$629$	62.9921			2.51166
$630$		0			0
$631$	43.3819			1.72701			0.863503	−	0.504344i	$-0.168266\pi$
$631$	43.3819			1.72701			0.863503	+	0.504344i	$0.168266\pi$
$632$		0			0
$633$	−6.20912	+	26.4757i	−0.246790	+	1.05232i
$634$		0			0
$635$	−4.75079	−	11.5528i	−0.188529	−	0.458458i
$636$		0			0
$637$	−22.8244	+	9.42813i	−0.904336	+	0.373556i
$638$		0			0
$639$	−1.82221	+	3.67128i	−0.0720853	+	0.145233i
$640$		0			0
$641$	−5.95145	+	3.43607i	−0.235068	+	0.135717i	−0.612908	−	0.790154i	$-0.710000\pi$
$641$	−5.95145	+	3.43607i	−0.235068	+	0.135717i	0.377840	+	0.925871i	$0.376667\pi$
$642$		0			0
$643$	−5.95431			−0.234815			−0.117408	−	0.993084i	$-0.537458\pi$
$643$	−5.95431			−0.234815			−0.117408	+	0.993084i	$0.537458\pi$
$644$		0			0
$645$	−12.9819	+	2.09216i	−0.511160	+	0.0823789i
$646$		0			0
$647$	10.4558	−	6.03666i	0.411060	−	0.237325i	−0.280185	−	0.959946i	$-0.590396\pi$
$647$	10.4558	−	6.03666i	0.411060	−	0.237325i	0.691245	+	0.722621i	$0.257063\pi$
$648$		0			0
$649$	−1.49029	−	0.860418i	−0.0584989	−	0.0337744i
$650$		0			0
$651$	20.2060	−	10.7544i	0.791935	−	0.421497i
$652$		0			0
$653$	−20.6425	+	35.7539i	−0.807804	+	1.39916i	0.106578	+	0.994304i	$0.466010\pi$
$653$	−20.6425	+	35.7539i	−0.807804	+	1.39916i	−0.914382	+	0.404853i	$0.867323\pi$
$654$		0			0
$655$	2.66384	−	19.8421i	0.104085	−	0.775295i
$656$		0			0
$657$	2.37102	+	37.6558i	0.0925023	+	1.46909i
$658$		0			0
$659$			20.0620i			0.781506i	0.920496	+	0.390753i	$0.127785\pi$
$659$			20.0620i			0.781506i	−0.920496	+	0.390753i	$0.872215\pi$
$660$		0			0
$661$	−19.2634	+	11.1217i	−0.749260	+	0.432585i	−0.825426	−	0.564510i	$-0.809065\pi$
$661$	−19.2634	+	11.1217i	−0.749260	+	0.432585i	0.0761667	+	0.997095i	$0.475732\pi$
$662$		0			0
$663$	−11.0499	−	36.5958i	−0.429144	−	1.42126i
$664$		0			0
$665$	0.193919	+	3.10324i	0.00751988	+	0.120338i
$666$		0			0
$667$	−16.1581	−	9.32887i	−0.625644	−	0.361215i
$668$		0			0
$669$	−10.9729	+	46.7885i	−0.424237	+	1.80895i
$670$		0			0
$671$	7.02888			0.271347
$672$		0			0
$673$			12.6052i			0.485896i	0.970039	+	0.242948i	$0.0781144\pi$
$673$			12.6052i			0.485896i	−0.970039	+	0.242948i	$0.921886\pi$
$674$		0			0
$675$	2.31480	+	25.8774i	0.0890968	+	0.996023i
$676$		0			0
$677$	3.45389	+	1.99410i	0.132744	+	0.0766396i	0.564901	−	0.825159i	$-0.308914\pi$
$677$	3.45389	+	1.99410i	0.132744	+	0.0766396i	−0.432158	+	0.901798i	$0.642248\pi$
$678$		0			0
$679$	0.935293	+	4.71404i	0.0358932	+	0.180908i
$680$		0			0
$681$	11.4449	+	37.9040i	0.438571	+	1.45248i
$682$		0			0
$683$	4.40559	+	7.63071i	0.168575	+	0.291981i	0.937919	−	0.346854i	$-0.112750\pi$
$683$	4.40559	+	7.63071i	0.168575	+	0.291981i	−0.769344	+	0.638835i	$0.779417\pi$
$684$		0			0
$685$	2.91332	+	2.24732i	0.111312	+	0.0858655i
$686$		0			0
$687$	−2.24978	+	2.39589i	−0.0858343	+	0.0914089i
$688$		0			0
$689$	15.7101	+	27.2106i	0.598506	+	1.03664i
$690$		0			0
$691$	−25.3128	−	14.6144i	−0.962946	−	0.555957i	−0.0658672	−	0.997828i	$-0.520981\pi$
$691$	−25.3128	−	14.6144i	−0.962946	−	0.555957i	−0.897078	+	0.441872i	$0.854315\pi$
$692$		0			0
$693$	−1.20382	−	4.54823i	−0.0457292	−	0.172773i
$694$		0			0
$695$	6.29540	+	15.3089i	0.238798	+	0.580701i
$696$		0			0
$697$	−25.1450	+	14.5175i	−0.952434	+	0.549888i
$698$		0			0
$699$	−2.44859	−	2.29927i	−0.0926143	−	0.0869662i
$700$		0			0
$701$			5.79384i			0.218830i	0.993996	+	0.109415i	$0.0348978\pi$
$701$			5.79384i			0.218830i	−0.993996	+	0.109415i	$0.965102\pi$
$702$		0			0
$703$	−2.64593	−	4.58288i	−0.0997930	−	0.172847i
$704$		0			0
$705$	12.0178	−	31.5626i	0.452617	−	1.18872i
$706$		0			0
$707$	13.5395	−	11.8622i	0.509207	−	0.446124i
$708$		0			0
$709$	8.80248	−	15.2463i	0.330584	−	0.572589i	−0.652042	−	0.758183i	$-0.726088\pi$
$709$	8.80248	−	15.2463i	0.330584	−	0.572589i	0.982627	+	0.185594i	$0.0594209\pi$
$710$		0			0
$711$	1.38311	−	0.919038i	0.0518707	−	0.0344666i
$712$		0			0
$713$		−	39.6346i		−	1.48433i
$714$		0			0
$715$	−2.85601	+	3.70241i	−0.106809	+	0.138462i
$716$		0			0
$717$	46.1032	+	10.8122i	1.72176	+	0.403788i
$718$		0			0
$719$	15.5919	−	27.0059i	0.581479	−	1.00715i	−0.413826	−	0.910356i	$-0.635808\pi$
$719$	15.5919	−	27.0059i	0.581479	−	1.00715i	0.995304	−	0.0967945i	$-0.0308590\pi$
$720$		0			0
$721$	32.6946	+	11.1161i	1.21761	+	0.413985i
$722$		0			0
$723$	5.19907	+	17.2186i	0.193356	+	0.640366i
$724$		0			0
$725$	−8.27065	−	8.35559i	−0.307164	−	0.310319i
$726$		0			0
$727$	−10.1468			−0.376323			−0.188162	−	0.982138i	$-0.560253\pi$
$727$	−10.1468			−0.376323			−0.188162	+	0.982138i	$0.560253\pi$
$728$		0			0
$729$	−5.06333	−	26.5210i	−0.187531	−	0.982259i
$730$		0			0
$731$	10.6203	+	18.3948i	0.392804	+	0.680357i
$732$		0			0
$733$	−10.3136	+	17.8637i	−0.380942	+	0.659810i	−0.991197	−	0.132394i	$-0.957733\pi$
$733$	−10.3136	+	17.8637i	−0.380942	+	0.659810i	0.610255	+	0.792205i	$0.291067\pi$
$734$		0			0
$735$	−14.2054	−	23.0913i	−0.523975	−	0.851734i
$736$		0			0
$737$	0.855464	−	1.48171i	0.0315114	−	0.0545794i
$738$		0			0
$739$	5.78547	+	10.0207i	0.212822	+	0.368619i	0.952597	−	0.304236i	$-0.0984012\pi$
$739$	5.78547	+	10.0207i	0.212822	+	0.368619i	−0.739775	+	0.672855i	$0.765068\pi$
$740$		0			0
$741$	−2.19832	+	2.34109i	−0.0807572	+	0.0860021i
$742$		0			0
$743$	−38.5409			−1.41393			−0.706965	−	0.707249i	$-0.749936\pi$
$743$	−38.5409			−1.41393			−0.706965	+	0.707249i	$0.749936\pi$
$744$		0			0
$745$	−40.3456	−	5.41648i	−1.47815	−	0.198444i
$746$		0			0
$747$	−3.03740	+	6.11958i	−0.111133	+	0.223904i
$748$		0			0
$749$	−4.54372	−	1.54485i	−0.166024	−	0.0564477i
$750$		0			0
$751$	−18.1972	+	31.5186i	−0.664027	+	1.15013i	0.315521	+	0.948919i	$0.397821\pi$
$751$	−18.1972	+	31.5186i	−0.664027	+	1.15013i	−0.979548	+	0.201210i	$0.935513\pi$
$752$		0			0
$753$	−11.3714	+	48.4876i	−0.414395	+	1.76698i
$754$		0			0
$755$	31.5371	+	24.3275i	1.14775	+	0.885369i
$756$		0			0
$757$		−	42.1451i		−	1.53179i	−0.642966	−	0.765895i	$-0.722296\pi$
$757$		−	42.1451i		−	1.53179i	0.642966	−	0.765895i	$-0.277704\pi$
$758$		0			0
$759$	−7.93147	−	1.86010i	−0.287894	−	0.0675173i
$760$		0			0
$761$	−14.5480	+	25.1979i	−0.527365	+	0.913423i	0.472126	+	0.881531i	$0.343487\pi$
$761$	−14.5480	+	25.1979i	−0.527365	+	0.913423i	−0.999491	+	0.0318920i	$0.989847\pi$
$762$		0			0
$763$	−38.4266	+	33.6661i	−1.39114	+	1.21880i
$764$		0			0
$765$	37.7340	−	18.3687i	1.36428	−	0.664121i
$766$		0			0
$767$	−5.12089	−	8.86965i	−0.184905	−	0.320264i
$768$		0			0
$769$			38.1763i			1.37667i	0.725392	+	0.688336i	$0.241658\pi$
$769$			38.1763i			1.37667i	−0.725392	+	0.688336i	$0.758342\pi$
$770$		0			0
$771$	−3.96232	+	4.21966i	−0.142700	+	0.151967i
$772$		0			0
$773$	−37.7469	+	21.7932i	−1.35766	+	0.783846i	−0.989308	−	0.145840i	$-0.953411\pi$
$773$	−37.7469	+	21.7932i	−1.35766	+	0.783846i	−0.368353	+	0.929686i	$0.620078\pi$
$774$		0			0
$775$	6.58709	−	24.0904i	0.236615	−	0.865352i
$776$		0			0
$777$	39.1401	+	24.4351i	1.40414	+	0.876605i
$778$		0			0
$779$	2.11238	+	1.21958i	0.0756840	+	0.0436962i
$780$		0			0
$781$	−0.404913	−	0.701329i	−0.0144889	−	0.0250955i
$782$		0			0
$783$	9.41465	+	7.78727i	0.336452	+	0.278294i
$784$		0			0
$785$	32.0430	+	24.7177i	1.14366	+	0.882214i
$786$		0			0
$787$	−25.9626	−	44.9685i	−0.925465	−	1.60295i	−0.790811	−	0.612061i	$-0.790341\pi$
$787$	−25.9626	−	44.9685i	−0.925465	−	1.60295i	−0.134655	−	0.990893i	$-0.542993\pi$
$788$		0			0
$789$	−31.4269	+	9.48921i	−1.11883	+	0.337825i
$790$		0			0
$791$	8.81939	+	44.4512i	0.313581	+	1.58050i
$792$		0			0
$793$	36.2287	+	20.9167i	1.28652	+	0.742772i
$794$		0			0
$795$	−26.7479	+	21.7802i	−0.948652	+	0.772464i
$796$		0			0
$797$			5.63812i			0.199712i	0.995002	+	0.0998562i	$0.0318383\pi$
$797$			5.63812i			0.199712i	−0.995002	+	0.0998562i	$0.968162\pi$
$798$		0			0
$799$	−54.5546			−1.93000
$800$		0			0
$801$	7.61983	−	5.06316i	0.269233	−	0.178898i
$802$		0			0
$803$	−6.45617	−	3.72747i	−0.227833	−	0.131540i
$804$		0			0
$805$	−46.8524	+	2.92778i	−1.65133	+	0.103191i
$806$		0			0
$807$	1.18532	−	0.357901i	0.0417251	−	0.0125987i
$808$		0			0
$809$	−16.3536	+	9.44177i	−0.574963	+	0.331955i	−0.759129	−	0.650940i	$-0.774375\pi$
$809$	−16.3536	+	9.44177i	−0.574963	+	0.331955i	0.184166	+	0.982895i	$0.441042\pi$
$810$		0			0
$811$			3.44239i			0.120879i	0.998172	+	0.0604393i	$0.0192502\pi$
$811$			3.44239i			0.120879i	−0.998172	+	0.0604393i	$0.980750\pi$
$812$		0			0
$813$	21.9924	−	23.4208i	0.771308	−	0.821402i
$814$		0			0
$815$	29.3334	+	3.93807i	1.02751	+	0.137945i
$816$		0			0
$817$	0.892188	−	1.54532i	0.0312137	−	0.0540637i
$818$		0			0
$819$	7.32990	−	27.0251i	0.256128	−	0.944334i
$820$		0			0
$821$	−27.7709	−	16.0336i	−0.969213	−	0.559575i	−0.0702166	−	0.997532i	$-0.522369\pi$
$821$	−27.7709	−	16.0336i	−0.969213	−	0.559575i	−0.898996	+	0.437956i	$0.855702\pi$
$822$		0			0
$823$	−37.8755	+	21.8675i	−1.32026	+	0.762251i	−0.983770	−	0.179436i	$-0.942573\pi$
$823$	−37.8755	+	21.8675i	−1.32026	+	0.762251i	−0.336489	+	0.941688i	$0.609239\pi$
$824$		0			0
$825$	−4.51170	−	2.44876i	−0.157077	−	0.0852549i
$826$		0			0
$827$	23.6034			0.820771			0.410386	−	0.911912i	$-0.365394\pi$
$827$	23.6034			0.820771			0.410386	+	0.911912i	$0.365394\pi$
$828$		0			0
$829$	−9.47048	+	5.46778i	−0.328923	+	0.189904i	−0.655363	−	0.755314i	$-0.727484\pi$
$829$	−9.47048	+	5.46778i	−0.328923	+	0.189904i	0.326440	+	0.945218i	$0.394151\pi$
$830$		0			0
$831$	13.3978	+	44.3715i	0.464763	+	1.53923i
$832$		0			0
$833$	−26.6933	+	34.7173i	−0.924867	+	1.20288i
$834$		0			0
$835$	−11.5935	−	28.1926i	−0.401209	−	0.975645i
$836$		0			0
$837$	−4.32645	+	25.5913i	−0.149544	+	0.884566i
$838$		0			0
$839$	13.6819			0.472352			0.236176	−	0.971710i	$-0.424106\pi$
$839$	13.6819			0.472352			0.236176	+	0.971710i	$0.424106\pi$
$840$		0			0
$841$	23.4712			0.809352
$842$		0			0
$843$	−1.82151	−	0.427182i	−0.0627360	−	0.0147129i
$844$		0			0
$845$	1.14615	−	0.471324i	0.0394287	−	0.0162140i
$846$		0			0
$847$	−26.6741	−	9.06912i	−0.916532	−	0.311619i
$848$		0			0
$849$	12.5442	−	3.78767i	0.430516	−	0.129992i
$850$		0			0
$851$	69.1920	−	39.9480i	2.37187	−	1.36940i
$852$		0			0
$853$	41.0320			1.40491			0.702455	−	0.711728i	$-0.252087\pi$
$853$	41.0320			1.40491			0.702455	+	0.711728i	$0.252087\pi$
$854$		0			0
$855$	−2.92136	−	1.97371i	−0.0999085	−	0.0674994i
$856$		0			0
$857$	23.0360	−	13.2998i	0.786894	−	0.454313i	−0.0519741	−	0.998648i	$-0.516551\pi$
$857$	23.0360	−	13.2998i	0.786894	−	0.454313i	0.838868	+	0.544335i	$0.183218\pi$
$858$		0			0
$859$	−9.72479	−	5.61461i	−0.331805	−	0.191568i	0.324837	−	0.945770i	$-0.394691\pi$
$859$	−9.72479	−	5.61461i	−0.331805	−	0.191568i	−0.656642	+	0.754202i	$0.728024\pi$
$860$		0			0
$861$	−21.2552	−	0.733506i	−0.724377	−	0.0249978i
$862$		0			0
$863$	2.21291	−	3.83288i	0.0753284	−	0.130473i	−0.825901	−	0.563816i	$-0.809333\pi$
$863$	2.21291	−	3.83288i	0.0753284	−	0.130473i	0.901229	+	0.433343i	$0.142666\pi$
$864$		0			0
$865$	24.6122	+	3.30423i	0.836839	+	0.112347i
$866$		0			0
$867$	−27.9538	−	26.2490i	−0.949361	−	0.891464i
$868$		0			0
$869$			0.328111i			0.0111304i
$870$		0			0
$871$	8.81858	−	5.09141i	0.298806	−	0.172516i
$872$		0			0
$873$	−4.88122	−	2.42275i	−0.165204	−	0.0819977i
$874$		0			0
$875$	−28.9640	−	6.00711i	−0.979163	−	0.203077i
$876$		0			0
$877$	2.20861	+	1.27514i	0.0745796	+	0.0430585i	0.536826	−	0.843693i	$-0.319623\pi$
$877$	2.20861	+	1.27514i	0.0745796	+	0.0430585i	−0.462246	+	0.886751i	$0.652956\pi$
$878$		0			0
$879$	2.72772	+	0.639709i	0.0920038	+	0.0215768i
$880$		0			0
$881$	−7.69117			−0.259122			−0.129561	−	0.991571i	$-0.541357\pi$
$881$	−7.69117			−0.259122			−0.129561	+	0.991571i	$0.541357\pi$
$882$		0			0
$883$		−	1.64604i		−	0.0553937i	−0.999616	−	0.0276968i	$-0.991183\pi$
$883$		−	1.64604i		−	0.0553937i	0.999616	−	0.0276968i	$-0.00881730\pi$
$884$		0			0
$885$	8.71883	−	7.09954i	0.293080	−	0.238648i
$886$		0			0
$887$	2.13570	+	1.23305i	0.0717097	+	0.0414016i	0.535426	−	0.844582i	$-0.320151\pi$
$887$	2.13570	+	1.23305i	0.0717097	+	0.0414016i	−0.463716	+	0.885984i	$0.653484\pi$
$888$		0			0
$889$	−14.4975	+	2.87639i	−0.486231	+	0.0964712i
$890$		0			0
$891$	4.91816	+	2.06682i	0.164764	+	0.0692409i
$892$		0			0
$893$	2.29152	+	3.96902i	0.0766827	+	0.132818i
$894$		0			0
$895$	−5.78918	+	7.50483i	−0.193511	+	0.250859i
$896$		0			0
$897$	−35.3456	−	33.1900i	−1.18016	−	1.10818i
$898$		0			0
$899$	−5.87239	−	10.1713i	−0.195855	−	0.339231i
$900$		0			0
$901$	48.2540	+	27.8595i	1.60757	+	0.928133i
$902$		0			0
$903$	−0.536597	+	15.5493i	−0.0178568	+	0.517448i
$904$		0			0
$905$	−7.62813	−	18.5498i	−0.253568	−	0.616616i
$906$		0			0
$907$	25.5604	−	14.7573i	0.848718	−	0.490008i	−0.0114999	−	0.999934i	$-0.503661\pi$
$907$	25.5604	−	14.7573i	0.848718	−	0.490008i	0.860218	+	0.509926i	$0.170327\pi$
$908$		0			0
$909$	1.28265	+	20.3707i	0.0425429	+	0.675654i
$910$		0			0
$911$		−	41.8480i		−	1.38649i	−0.720704	−	0.693243i	$-0.756181\pi$
$911$		−	41.8480i		−	1.38649i	0.720704	−	0.693243i	$-0.243819\pi$
$912$		0			0
$913$	−0.674941	−	1.16903i	−0.0223373	−	0.0386893i
$914$		0			0
$915$	−16.3422	+	42.9198i	−0.540257	+	1.41889i
$916$		0			0
$917$	−22.4273	−	7.62523i	−0.740614	−	0.251807i
$918$		0			0
$919$	−21.5197	+	37.2732i	−0.709869	+	1.22953i	0.255036	+	0.966932i	$0.417913\pi$
$919$	−21.5197	+	37.2732i	−0.709869	+	1.22953i	−0.964905	+	0.262598i	$0.915421\pi$
$920$		0			0
$921$	10.5021	−	44.7812i	0.346057	−	1.47559i
$922$		0			0
$923$		−	4.81978i		−	0.158645i
$924$		0			0
$925$	48.6948	−	12.7815i	1.60108	−	0.420252i
$926$		0			0
$927$	−32.6130	+	21.6704i	−1.07115	+	0.711751i
$928$		0			0
$929$	−9.42759	+	16.3291i	−0.309309	+	0.535739i	−0.978211	−	0.207611i	$-0.933431\pi$
$929$	−9.42759	+	16.3291i	−0.309309	+	0.535739i	0.668902	+	0.743350i	$0.266765\pi$
$930$		0			0
$931$	3.64702	+	0.483755i	0.119526	+	0.0158544i
$932$		0			0
$933$	−10.5823	+	3.19527i	−0.346448	+	0.104608i
$934$		0			0
$935$	−1.10334	+	8.21839i	−0.0360829	+	0.268770i
$936$		0			0
$937$	6.81064			0.222494			0.111247	−	0.993793i	$-0.464516\pi$
$937$	6.81064			0.222494			0.111247	+	0.993793i	$0.464516\pi$
$938$		0			0
$939$	7.56764	+	7.10612i	0.246961	+	0.231900i
$940$		0			0
$941$	14.0242	+	24.2907i	0.457177	+	0.791853i	0.998810	−	0.0487612i	$-0.0155273\pi$
$941$	14.0242	+	24.2907i	0.457177	+	0.791853i	−0.541634	+	0.840615i	$0.682194\pi$
$942$		0			0
$943$	−18.4132	+	31.8926i	−0.599616	+	1.03857i
$944$		0			0
$945$	30.5713	+	3.22392i	0.994486	+	0.104874i
$946$		0			0
$947$	16.0004	−	27.7135i	0.519944	−	0.900569i	−0.479787	−	0.877385i	$-0.659286\pi$
$947$	16.0004	−	27.7135i	0.519944	−	0.900569i	0.999731	−	0.0231843i	$-0.00738045\pi$
$948$		0			0
$949$	−22.1846	−	38.4248i	−0.720141	−	1.24732i
$950$		0			0
$951$	33.6518	+	31.5996i	1.09123	+	1.02469i
$952$		0			0
$953$	−31.8127			−1.03051			−0.515257	−	0.857036i	$-0.672304\pi$
$953$	−31.8127			−1.03051			−0.515257	+	0.857036i	$0.672304\pi$
$954$		0			0
$955$	25.9891	+	3.48909i	0.840987	+	0.112904i
$956$		0			0
$957$	−2.31102	+	0.697802i	−0.0747047	+	0.0225567i
$958$		0			0
$959$	3.27454	−	2.86887i	0.105740	−	0.0926407i
$960$		0			0
$961$	−3.02529	+	5.23995i	−0.0975899	+	0.169031i
$962$		0			0
$963$	4.53238	−	3.01164i	0.146054	−	0.0970488i
$964$		0			0
$965$	−27.5836	+	35.7582i	−0.887948	+	1.15110i
$966$		0			0
$967$			20.9713i			0.674393i	0.941434	+	0.337196i	$0.109479\pi$
$967$			20.9713i			0.674393i	−0.941434	+	0.337196i	$0.890521\pi$
$968$		0			0
$969$	−1.30032	+	5.54456i	−0.0417722	+	0.178117i
$970$		0			0
$971$	−18.3558	+	31.7932i	−0.589066	+	1.02029i	0.405289	+	0.914189i	$0.367171\pi$
$971$	−18.3558	+	31.7932i	−0.589066	+	1.02029i	−0.994355	+	0.106104i	$0.966162\pi$
$972$		0			0
$973$	19.2111	−	3.81159i	0.615878	−	0.122194i
$974$		0			0
$975$	−15.9674	−	26.0475i	−0.511367	−	0.834189i
$976$		0			0
$977$	10.3346	+	17.9001i	0.330634	+	0.572676i	0.982636	−	0.185542i	$-0.0594040\pi$
$977$	10.3346	+	17.9001i	0.330634	+	0.572676i	−0.652002	+	0.758217i	$0.726071\pi$
$978$		0			0
$979$			1.80763i			0.0577721i
$980$		0			0
$981$	−3.64030	−	57.8142i	−0.116226	−	1.84586i
$982$		0			0
$983$	−9.22542	+	5.32630i	−0.294245	+	0.169883i	−0.639855	−	0.768496i	$-0.721006\pi$
$983$	−9.22542	+	5.32630i	−0.294245	+	0.169883i	0.345609	+	0.938378i	$0.387672\pi$
$984$		0			0
$985$	−22.8232	+	9.38546i	−0.727209	+	0.299046i
$986$		0			0
$987$	−33.8975	−	21.1621i	−1.07897	−	0.673598i
$988$		0			0
$989$	23.3311	+	13.4702i	0.741885	+	0.428327i
$990$		0			0
$991$	−19.0847	−	33.0557i	−0.606246	−	1.05005i	−0.991853	−	0.127386i	$-0.959341\pi$
$991$	−19.0847	−	33.0557i	−0.606246	−	1.05005i	0.385607	−	0.922663i	$-0.373992\pi$
$992$		0			0
$993$	6.61805	+	6.21445i	0.210018	+	0.197210i
$994$		0			0
$995$	9.16709	−	11.8838i	0.290616	−	0.376742i
$996$		0			0
$997$	20.1518	+	34.9040i	0.638215	+	1.10542i	0.985824	+	0.167781i	$0.0536603\pi$
$997$	20.1518	+	34.9040i	0.638215	+	1.10542i	−0.347609	+	0.937640i	$0.613006\pi$
$998$		0			0
$999$	−49.0366	+	18.2408i	−1.55145	+	0.577113i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.da.a.89.15	✓	48
3.2	odd	2		840.2.da.b.89.1	yes	48
5.4	even	2		840.2.da.b.89.10	yes	48
7.3	odd	6	inner	840.2.da.a.689.24	yes	48
15.14	odd	2	inner	840.2.da.a.89.24	yes	48
21.17	even	6		840.2.da.b.689.10	yes	48
35.24	odd	6		840.2.da.b.689.1	yes	48
105.59	even	6	inner	840.2.da.a.689.15	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.da.a.89.15	✓	48	1.1	even	1	trivial
840.2.da.a.89.24	yes	48	15.14	odd	2	inner
840.2.da.a.689.15	yes	48	105.59	even	6	inner
840.2.da.a.689.24	yes	48	7.3	odd	6	inner
840.2.da.b.89.1	yes	48	3.2	odd	2
840.2.da.b.89.10	yes	48	5.4	even	2
840.2.da.b.689.1	yes	48	35.24	odd	6
840.2.da.b.689.10	yes	48	21.17	even	6

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:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.da (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.395473 - 1.68630i) q^{3} +(-2.06804 + 0.850426i) q^{5} +(0.514896 + 2.59517i) q^{7} +(-2.68720 - 1.33377i) q^{9} +(0.513340 - 0.296377i) q^{11} +3.52786 q^{13} +(0.616221 + 3.82365i) q^{15} +(5.41797 - 3.12807i) q^{17} +(-0.455153 - 0.262783i) q^{19} +(4.57985 + 0.158048i) q^{21} +(3.96748 - 6.87187i) q^{23} +(3.55355 - 3.51743i) q^{25} +(-3.31185 + 4.00396i) q^{27} -2.35134i q^{29} +(4.32575 - 2.49747i) q^{31} +(-0.296768 - 0.982854i) q^{33} +(-3.27182 - 4.92901i) q^{35} +(8.71989 + 5.03443i) q^{37} +(1.39517 - 5.94902i) q^{39} -4.64103 q^{41} +3.39515i q^{43} +(6.69151 + 0.473015i) q^{45} +(-7.55190 - 4.36009i) q^{47} +(-6.46976 + 2.67248i) q^{49} +(-3.13219 - 10.3734i) q^{51} +(4.45314 + 7.71307i) q^{53} +(-0.809560 + 1.04948i) q^{55} +(-0.623131 + 0.663601i) q^{57} +(-1.45156 - 2.51417i) q^{59} +(10.2693 + 5.92900i) q^{61} +(2.07772 - 7.66049i) q^{63} +(-7.29574 + 3.00018i) q^{65} +(2.49970 - 1.44320i) q^{67} +(-10.0190 - 9.40799i) q^{69} -1.36621i q^{71} +(-6.28839 - 10.8918i) q^{73} +(-4.52610 - 7.38339i) q^{75} +(1.03346 + 1.17960i) q^{77} +(-0.276768 + 0.479377i) q^{79} +(5.44212 + 7.16822i) q^{81} -2.27731i q^{83} +(-8.54437 + 11.0765i) q^{85} +(-3.96505 - 0.929889i) q^{87} +(-1.52477 + 2.64098i) q^{89} +(1.81648 + 9.15537i) q^{91} +(-2.50077 - 8.28218i) q^{93} +(1.16475 + 0.156370i) q^{95} +1.81647 q^{97} +(-1.77475 + 0.111748i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 3 q^{3} - 3 q^{5} - q^{9} - 14 q^{15} + 5 q^{21} - 2 q^{23} + q^{25} + 6 q^{31} - 24 q^{33} + 4 q^{35} + 2 q^{39} - 3 q^{45} + 12 q^{51} + 6 q^{53} - 20 q^{57} + 18 q^{61} + 26 q^{63} - 10 q^{65}+ \cdots - 12 q^{99}+O(q^{100}) \) 48 * q - 3 * q^3 - 3 * q^5 - q^9 - 14 * q^15 + 5 * q^21 - 2 * q^23 + q^25 + 6 * q^31 - 24 * q^33 + 4 * q^35 + 2 * q^39 - 3 * q^45 + 12 * q^51 + 6 * q^53 - 20 * q^57 + 18 * q^61 + 26 * q^63 - 10 * q^65 - 3 * q^75 - 2 * q^77 + 2 * q^79 - 9 * q^81 + 15 * q^87 + 24 * q^91 - 8 * q^93 - 6 * q^95 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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