LMFDB - Embedded newform 304.2.u.d.161.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [304,2,Mod(17,304)] 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("304.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(304, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 0, 10])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	304.u (of order $9$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,6,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$2.42745222145$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 152)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			161.1
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	304.161
Dual form			304.2.u.d.17.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.17365 - 0.984808i) q^{3} +(1.76604 + 0.642788i) q^{5} +(1.03209 - 1.78763i) q^{7} +(-0.113341 + 0.642788i) q^{9} +(-1.03209 - 1.78763i) q^{11} +(1.17365 + 0.984808i) q^{13} +(2.70574 - 0.984808i) q^{15} +(0.0603074 + 0.342020i) q^{17} +(-3.75877 + 2.20718i) q^{19} +(-0.549163 - 3.11446i) q^{21} +(2.76604 - 1.00676i) q^{23} +(-1.12449 - 0.943555i) q^{25} +(2.79813 + 4.84651i) q^{27} +(1.81908 - 10.3165i) q^{29} +(-2.72668 + 4.72275i) q^{31} +(-2.97178 - 1.08164i) q^{33} +(2.97178 - 2.49362i) q^{35} +5.51754 q^{37} +2.34730 q^{39} +(-7.64930 + 6.41852i) q^{41} +(-6.52481 - 2.37484i) q^{43} +(-0.613341 + 1.06234i) q^{45} +(-0.897804 + 5.09170i) q^{47} +(1.36959 + 2.37219i) q^{49} +(0.407604 + 0.342020i) q^{51} +(-7.29813 + 2.65630i) q^{53} +(-0.673648 - 3.82045i) q^{55} +(-2.23783 + 6.29212i) q^{57} +(0.0457595 + 0.259515i) q^{59} +(9.97818 - 3.63176i) q^{61} +(1.03209 + 0.866025i) q^{63} +(1.43969 + 2.49362i) q^{65} +(-1.22281 + 6.93491i) q^{67} +(2.25490 - 3.90560i) q^{69} +(-6.07145 - 2.20983i) q^{71} +(-11.7777 + 9.88263i) q^{73} -2.24897 q^{75} -4.26083 q^{77} +(-9.64930 + 8.09672i) q^{79} +(6.21688 + 2.26276i) q^{81} +(6.54963 - 11.3443i) q^{83} +(-0.113341 + 0.642788i) q^{85} +(-8.02481 - 13.8994i) q^{87} +(-3.52094 - 2.95442i) q^{89} +(2.97178 - 1.08164i) q^{91} +(1.45084 + 8.22811i) q^{93} +(-8.05690 + 1.48189i) q^{95} +(0.301537 + 1.71010i) q^{97} +(1.26604 - 0.460802i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{3} + 6 q^{5} - 3 q^{7} + 6 q^{9} + 3 q^{11} + 6 q^{13} + 6 q^{15} + 6 q^{17} - 15 q^{21} + 12 q^{23} + 6 q^{25} + 3 q^{27} - 6 q^{29} - 3 q^{31} - 3 q^{33} + 3 q^{35} - 12 q^{37} + 12 q^{39}+ \cdots + 3 q^{99}+O(q^{100}) $ 6 * q + 6 * q^3 + 6 * q^5 - 3 * q^7 + 6 * q^9 + 3 * q^11 + 6 * q^13 + 6 * q^15 + 6 * q^17 - 15 * q^21 + 12 * q^23 + 6 * q^25 + 3 * q^27 - 6 * q^29 - 3 * q^31 - 3 * q^33 + 3 * q^35 - 12 * q^37 + 12 * q^39 - 6 * q^41 - 12 * q^43 + 3 * q^45 - 6 * q^47 - 6 * q^49 + 6 * q^51 - 30 * q^53 - 3 * q^55 + 6 * q^57 - 30 * q^59 + 6 * q^61 - 3 * q^63 + 3 * q^65 - 18 * q^67 + 15 * q^69 - 36 * q^71 + 6 * q^73 + 12 * q^75 - 54 * q^77 - 18 * q^79 + 21 * q^81 - 15 * q^83 + 6 * q^85 - 21 * q^87 - 18 * q^89 + 3 * q^91 - 3 * q^93 - 12 * q^95 + 30 * q^97 + 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.17365	−	0.984808i	0.677606	−	0.568579i	−0.237700	−	0.971339i	$-0.576393\pi$
$3$	1.17365	−	0.984808i	0.677606	−	0.568579i	0.915306	+	0.402760i	$0.131949\pi$
$4$		0			0
$5$	1.76604	+	0.642788i	0.789799	+	0.287463i	0.705253	−	0.708956i	$-0.250834\pi$
$5$	1.76604	+	0.642788i	0.789799	+	0.287463i	0.0845465	+	0.996420i	$0.473056\pi$
$6$		0			0
$7$	1.03209	−	1.78763i	0.390093	−	0.675661i	−0.602369	−	0.798218i	$-0.705776\pi$
$7$	1.03209	−	1.78763i	0.390093	−	0.675661i	0.992461	+	0.122557i	$0.0391095\pi$
$8$		0			0
$9$	−0.113341	+	0.642788i	−0.0377803	+	0.214263i
$10$		0			0
$11$	−1.03209	−	1.78763i	−0.311187	−	0.538991i	0.667433	−	0.744670i	$-0.267393\pi$
$11$	−1.03209	−	1.78763i	−0.311187	−	0.538991i	−0.978620	+	0.205679i	$0.934060\pi$
$12$		0			0
$13$	1.17365	+	0.984808i	0.325511	+	0.273137i	0.790868	−	0.611987i	$-0.209629\pi$
$13$	1.17365	+	0.984808i	0.325511	+	0.273137i	−0.465357	+	0.885123i	$0.654074\pi$
$14$		0			0
$15$	2.70574	−	0.984808i	0.698618	−	0.254276i
$16$		0			0
$17$	0.0603074	+	0.342020i	0.0146267	+	0.0829521i	0.991247	−	0.132018i	$-0.0421457\pi$
$17$	0.0603074	+	0.342020i	0.0146267	+	0.0829521i	−0.976621	+	0.214970i	$0.931035\pi$
$18$		0			0
$19$	−3.75877	+	2.20718i	−0.862321	+	0.506362i
$19$	−3.75877	+	2.20718i	−0.862321	+	0.506362i
$20$		0			0
$21$	−0.549163	−	3.11446i	−0.119837	−	0.679631i
$22$		0			0
$23$	2.76604	−	1.00676i	0.576760	−	0.209924i	−0.0371361	−	0.999310i	$-0.511824\pi$
$23$	2.76604	−	1.00676i	0.576760	−	0.209924i	0.613896	+	0.789387i	$0.289601\pi$
$24$		0			0
$25$	−1.12449	−	0.943555i	−0.224897	−	0.188711i
$26$		0			0
$27$	2.79813	+	4.84651i	0.538501	+	0.932711i
$28$		0			0
$29$	1.81908	−	10.3165i	0.337794	−	1.91573i	−0.0598915	−	0.998205i	$-0.519075\pi$
$29$	1.81908	−	10.3165i	0.337794	−	1.91573i	0.397686	−	0.917522i	$-0.369813\pi$
$30$		0			0
$31$	−2.72668	+	4.72275i	−0.489726	+	0.848231i	−0.999930	−	0.0118225i	$-0.996237\pi$
$31$	−2.72668	+	4.72275i	−0.489726	+	0.848231i	0.510204	+	0.860054i	$0.329570\pi$
$32$		0			0
$33$	−2.97178	−	1.08164i	−0.517321	−	0.188289i
$34$		0			0
$35$	2.97178	−	2.49362i	0.502323	−	0.421499i
$36$		0			0
$37$	5.51754			0.907078			0.453539	−	0.891236i	$-0.350161\pi$
$37$	5.51754			0.907078			0.453539	+	0.891236i	$0.350161\pi$
$38$		0			0
$39$	2.34730			0.375868
$40$		0			0
$41$	−7.64930	+	6.41852i	−1.19462	+	1.00241i	−0.194853	+	0.980833i	$0.562423\pi$
$41$	−7.64930	+	6.41852i	−1.19462	+	1.00241i	−0.999767	+	0.0215727i	$0.993133\pi$
$42$		0			0
$43$	−6.52481	−	2.37484i	−0.995025	−	0.362159i	−0.207361	−	0.978265i	$-0.566487\pi$
$43$	−6.52481	−	2.37484i	−0.995025	−	0.362159i	−0.787664	+	0.616105i	$0.788710\pi$
$44$		0			0
$45$	−0.613341	+	1.06234i	−0.0914314	+	0.158364i
$46$		0			0
$47$	−0.897804	+	5.09170i	−0.130958	+	0.742700i	0.846631	+	0.532180i	$0.178627\pi$
$47$	−0.897804	+	5.09170i	−0.130958	+	0.742700i	−0.977589	+	0.210520i	$0.932484\pi$
$48$		0			0
$49$	1.36959	+	2.37219i	0.195655	+	0.338884i
$50$		0			0
$51$	0.407604	+	0.342020i	0.0570759	+	0.0478924i
$52$		0			0
$53$	−7.29813	+	2.65630i	−1.00248	+	0.364871i	−0.790539	−	0.612412i	$-0.790199\pi$
$53$	−7.29813	+	2.65630i	−1.00248	+	0.364871i	−0.211937	+	0.977283i	$0.567977\pi$
$54$		0			0
$55$	−0.673648	−	3.82045i	−0.0908347	−	0.515149i
$56$		0			0
$57$	−2.23783	+	6.29212i	−0.296407	+	0.833412i
$58$		0			0
$59$	0.0457595	+	0.259515i	0.00595737	+	0.0337859i	0.987642	−	0.156730i	$-0.0500951\pi$
$59$	0.0457595	+	0.259515i	0.00595737	+	0.0337859i	−0.981684	+	0.190516i	$0.938984\pi$
$60$		0			0
$61$	9.97818	−	3.63176i	1.27757	−	0.464999i	0.387945	−	0.921682i	$-0.373185\pi$
$61$	9.97818	−	3.63176i	1.27757	−	0.464999i	0.889629	+	0.456683i	$0.150963\pi$
$62$		0			0
$63$	1.03209	+	0.866025i	0.130031	+	0.109109i
$64$		0			0
$65$	1.43969	+	2.49362i	0.178572	+	0.309296i
$66$		0			0
$67$	−1.22281	+	6.93491i	−0.149390	+	0.847234i	0.814347	+	0.580379i	$0.197096\pi$
$67$	−1.22281	+	6.93491i	−0.149390	+	0.847234i	−0.963737	+	0.266855i	$0.914016\pi$
$68$		0			0
$69$	2.25490	−	3.90560i	0.271458	−	0.470179i
$70$		0			0
$71$	−6.07145	−	2.20983i	−0.720549	−	0.262258i	−0.0443900	−	0.999014i	$-0.514134\pi$
$71$	−6.07145	−	2.20983i	−0.720549	−	0.262258i	−0.676159	+	0.736756i	$0.736357\pi$
$72$		0			0
$73$	−11.7777	+	9.88263i	−1.37847	+	1.15667i	−0.408696	+	0.912671i	$0.634016\pi$
$73$	−11.7777	+	9.88263i	−1.37847	+	1.15667i	−0.969774	+	0.244003i	$0.921539\pi$
$74$		0			0
$75$	−2.24897			−0.259689
$76$		0			0
$77$	−4.26083			−0.485567
$78$		0			0
$79$	−9.64930	+	8.09672i	−1.08563	+	0.910953i	−0.996376	−	0.0850562i	$-0.972893\pi$
$79$	−9.64930	+	8.09672i	−1.08563	+	0.910953i	−0.0892549	+	0.996009i	$0.528449\pi$
$80$		0			0
$81$	6.21688	+	2.26276i	0.690765	+	0.251418i
$82$		0			0
$83$	6.54963	−	11.3443i	0.718915	−	1.24520i	−0.242515	−	0.970148i	$-0.577972\pi$
$83$	6.54963	−	11.3443i	0.718915	−	1.24520i	0.961430	−	0.275050i	$-0.0886944\pi$
$84$		0			0
$85$	−0.113341	+	0.642788i	−0.0122935	+	0.0697201i
$86$		0			0
$87$	−8.02481	−	13.8994i	−0.860350	−	1.49017i
$88$		0			0
$89$	−3.52094	−	2.95442i	−0.373219	−	0.313168i	0.436814	−	0.899552i	$-0.356107\pi$
$89$	−3.52094	−	2.95442i	−0.373219	−	0.313168i	−0.810034	+	0.586384i	$0.800551\pi$
$90$		0			0
$91$	2.97178	−	1.08164i	0.311527	−	0.113387i
$92$		0			0
$93$	1.45084	+	8.22811i	0.150445	+	0.853215i
$94$		0			0
$95$	−8.05690	+	1.48189i	−0.826621	+	0.152038i
$96$		0			0
$97$	0.301537	+	1.71010i	0.0306164	+	0.173634i	0.996282	−	0.0861549i	$-0.0274580\pi$
$97$	0.301537	+	1.71010i	0.0306164	+	0.173634i	−0.965665	+	0.259789i	$0.916347\pi$
$98$		0			0
$99$	1.26604	−	0.460802i	0.127242	−	0.0463124i
$100$		0			0
$101$	−7.64930	−	6.41852i	−0.761134	−	0.638667i	0.177288	−	0.984159i	$-0.443268\pi$
$101$	−7.64930	−	6.41852i	−0.761134	−	0.638667i	−0.938422	+	0.345492i	$0.887712\pi$
$102$		0			0
$103$	0.642903	+	1.11354i	0.0633472	+	0.109721i	0.895960	−	0.444136i	$-0.146489\pi$
$103$	0.642903	+	1.11354i	0.0633472	+	0.109721i	−0.832612	+	0.553856i	$0.813156\pi$
$104$		0			0
$105$	1.03209	−	5.85327i	0.100722	−	0.571220i
$106$		0			0
$107$	0.337496	−	0.584561i	0.0326270	−	0.0565116i	−0.849251	−	0.527990i	$-0.822946\pi$
$107$	0.337496	−	0.584561i	0.0326270	−	0.0565116i	0.881878	+	0.471478i	$0.156279\pi$
$108$		0			0
$109$	9.28359	+	3.37895i	0.889206	+	0.323645i	0.745919	−	0.666037i	$-0.232011\pi$
$109$	9.28359	+	3.37895i	0.889206	+	0.323645i	0.143287	+	0.989681i	$0.454233\pi$
$110$		0			0
$111$	6.47565	−	5.43372i	0.614642	−	0.515746i
$112$		0			0
$113$	−4.61081			−0.433749			−0.216874	−	0.976199i	$-0.569586\pi$
$113$	−4.61081			−0.433749			−0.216874	+	0.976199i	$0.569586\pi$
$114$		0			0
$115$	5.53209			0.515870
$116$		0			0
$117$	−0.766044	+	0.642788i	−0.0708208	+	0.0594257i
$118$		0			0
$119$	0.673648	+	0.245188i	0.0617532	+	0.0224763i
$120$		0			0
$121$	3.36959	−	5.83629i	0.306326	−	0.530572i
$122$		0			0
$123$	−2.65657	+	15.0662i	−0.239535	+	1.35847i
$124$		0			0
$125$	−6.07785	−	10.5271i	−0.543619	−	0.941576i
$126$		0			0
$127$	7.15136	+	6.00070i	0.634581	+	0.532476i	0.902349	−	0.431007i	$-0.141842\pi$
$127$	7.15136	+	6.00070i	0.634581	+	0.532476i	−0.267768	+	0.963483i	$0.586286\pi$
$128$		0			0
$129$	−9.99660	+	3.63846i	−0.880151	+	0.320349i
$130$		0			0
$131$	−2.29473	−	13.0141i	−0.200491	−	1.13704i	−0.904378	−	0.426732i	$-0.859665\pi$
$131$	−2.29473	−	13.0141i	−0.200491	−	1.13704i	0.703887	−	0.710312i	$-0.251446\pi$
$132$		0			0
$133$	0.0662372	+	8.99730i	0.00574349	+	0.780165i
$134$		0			0
$135$	1.82635	+	10.3578i	0.157187	+	0.891454i
$136$		0			0
$137$	20.5599	−	7.48319i	1.75655	−	0.639332i	0.756655	−	0.653814i	$-0.226832\pi$
$137$	20.5599	−	7.48319i	1.75655	−	0.639332i	0.999895	+	0.0144818i	$0.00460986\pi$
$138$		0			0
$139$	15.7777	+	13.2390i	1.33824	+	1.12292i	0.982074	+	0.188498i	$0.0603620\pi$
$139$	15.7777	+	13.2390i	1.33824	+	1.12292i	0.356170	+	0.934421i	$0.384082\pi$
$140$		0			0
$141$	3.96064	+	6.86002i	0.333546	+	0.577718i
$142$		0			0
$143$	0.549163	−	3.11446i	0.0459233	−	0.260444i
$144$		0			0
$145$	9.84389	−	17.0501i	0.817491	−	1.41594i
$146$		0			0
$147$	3.94356	+	1.43534i	0.325260	+	0.118385i
$148$		0			0
$149$	6.23783	−	5.23416i	0.511023	−	0.428799i	−0.350466	−	0.936575i	$-0.613977\pi$
$149$	6.23783	−	5.23416i	0.511023	−	0.428799i	0.861489	+	0.507776i	$0.169532\pi$
$150$		0			0
$151$	16.0000			1.30206			0.651031	−	0.759051i	$-0.274337\pi$
$151$	16.0000			1.30206			0.651031	+	0.759051i	$0.274337\pi$
$152$		0			0
$153$	−0.226682			−0.0183261
$154$		0			0
$155$	−7.85117	+	6.58791i	−0.630621	+	0.529154i
$156$		0			0
$157$	5.07145	+	1.84586i	0.404746	+	0.147315i	0.536367	−	0.843985i	$-0.319796\pi$
$157$	5.07145	+	1.84586i	0.404746	+	0.147315i	−0.131622	+	0.991300i	$0.542018\pi$
$158$		0			0
$159$	−5.94949	+	10.3048i	−0.471825	+	0.817226i
$160$		0			0
$161$	1.05509	−	5.98373i	0.0831530	−	0.471584i
$162$		0			0
$163$	−11.2442	−	19.4756i	−0.880715	−	1.52544i	−0.850547	−	0.525899i	$-0.823729\pi$
$163$	−11.2442	−	19.4756i	−0.880715	−	1.52544i	−0.0301685	−	0.999545i	$-0.509604\pi$
$164$		0			0
$165$	−4.55303	−	3.82045i	−0.354453	−	0.297422i
$166$		0			0
$167$	16.6532	−	6.06126i	1.28866	−	0.469034i	0.395374	−	0.918520i	$-0.370615\pi$
$167$	16.6532	−	6.06126i	1.28866	−	0.469034i	0.893287	+	0.449486i	$0.148393\pi$
$168$		0			0
$169$	−1.84982	−	10.4909i	−0.142294	−	0.806990i
$170$		0			0
$171$	−0.992726	−	2.66625i	−0.0759157	−	0.203894i
$172$		0			0
$173$	−3.32888	−	18.8790i	−0.253090	−	1.43534i	−0.800928	−	0.598760i	$-0.795660\pi$
$173$	−3.32888	−	18.8790i	−0.253090	−	1.43534i	0.547839	−	0.836584i	$-0.315451\pi$
$174$		0			0
$175$	−2.84730	+	1.03633i	−0.215235	+	0.0783393i
$176$		0			0
$177$	0.309278	+	0.259515i	0.0232467	+	0.0195063i
$178$		0			0
$179$	2.27332	+	3.93750i	0.169916	+	0.294303i	0.938390	−	0.345578i	$-0.112317\pi$
$179$	2.27332	+	3.93750i	0.169916	+	0.294303i	−0.768474	+	0.639881i	$0.778984\pi$
$180$		0			0
$181$	−2.63429	+	14.9398i	−0.195805	+	1.11046i	0.715463	+	0.698651i	$0.246216\pi$
$181$	−2.63429	+	14.9398i	−0.195805	+	1.11046i	−0.911268	+	0.411814i	$0.864895\pi$
$182$		0			0
$183$	8.13429	−	14.0890i	0.601304	−	1.04149i
$184$		0			0
$185$	9.74422	+	3.54661i	0.716409	+	0.260752i
$186$		0			0
$187$	0.549163	−	0.460802i	0.0401588	−	0.0336972i
$188$		0			0
$189$	11.5517			0.840262
$190$		0			0
$191$	13.6459			0.987382			0.493691	−	0.869637i	$-0.335647\pi$
$191$	13.6459			0.987382			0.493691	+	0.869637i	$0.335647\pi$
$192$		0			0
$193$	−7.15136	+	6.00070i	−0.514766	+	0.431940i	−0.862803	−	0.505541i	$-0.831293\pi$
$193$	−7.15136	+	6.00070i	−0.514766	+	0.431940i	0.348037	+	0.937481i	$0.386849\pi$
$194$		0			0
$195$	4.14543	+	1.50881i	0.296860	+	0.108048i
$196$		0			0
$197$	−2.32295	+	4.02346i	−0.165503	+	0.286660i	−0.936834	−	0.349775i	$-0.886258\pi$
$197$	−2.32295	+	4.02346i	−0.165503	+	0.286660i	0.771331	+	0.636435i	$0.219591\pi$
$198$		0			0
$199$	−0.0748553	+	0.424525i	−0.00530635	+	0.0300938i	−0.987346	−	0.158581i	$-0.949308\pi$
$199$	−0.0748553	+	0.424525i	−0.00530635	+	0.0300938i	0.982040	+	0.188675i	$0.0604192\pi$
$200$		0			0
$201$	5.39440	+	9.34337i	0.380492	+	0.659031i
$202$		0			0
$203$	−16.5646	−	13.8994i	−1.16261	−	0.975546i
$204$		0			0
$205$	−17.6348	+	6.41852i	−1.23166	+	0.448289i
$206$		0			0
$207$	0.333626	+	1.89209i	0.0231886	+	0.131509i
$208$		0			0
$209$	7.82501	+	4.44129i	0.541267	+	0.307210i
$210$		0			0
$211$	−3.01842	−	17.1183i	−0.207796	−	1.17847i	−0.892978	−	0.450100i	$-0.851388\pi$
$211$	−3.01842	−	17.1183i	−0.207796	−	1.17847i	0.685182	−	0.728372i	$-0.259723\pi$
$212$		0			0
$213$	−9.30200	+	3.38565i	−0.637363	+	0.231981i
$214$		0			0
$215$	−9.99660	−	8.38814i	−0.681762	−	0.572066i
$216$		0			0
$217$	5.62836	+	9.74860i	0.382078	+	0.661778i
$218$		0			0
$219$	−4.09034	+	23.1975i	−0.276399	+	1.56754i
$220$		0			0
$221$	−0.266044	+	0.460802i	−0.0178961	+	0.0309969i
$222$		0			0
$223$	−12.4410	−	4.52817i	−0.833113	−	0.303228i	−0.109977	−	0.993934i	$-0.535078\pi$
$223$	−12.4410	−	4.52817i	−0.833113	−	0.303228i	−0.723136	+	0.690706i	$0.757300\pi$
$224$		0			0
$225$	0.733956	−	0.615862i	0.0489304	−	0.0410575i
$226$		0			0
$227$	7.77425			0.515995			0.257998	−	0.966146i	$-0.416937\pi$
$227$	7.77425			0.515995			0.257998	+	0.966146i	$0.416937\pi$
$228$		0			0
$229$	2.73917			0.181009			0.0905047	−	0.995896i	$-0.471152\pi$
$229$	2.73917			0.181009			0.0905047	+	0.995896i	$0.471152\pi$
$230$		0			0
$231$	−5.00072	+	4.19610i	−0.329023	+	0.276083i
$232$		0			0
$233$	1.76604	+	0.642788i	0.115697	+	0.0421104i	0.399220	−	0.916855i	$-0.369281\pi$
$233$	1.76604	+	0.642788i	0.115697	+	0.0421104i	−0.283523	+	0.958966i	$0.591503\pi$
$234$		0			0
$235$	−4.85844	+	8.41507i	−0.316930	+	0.548938i
$236$		0			0
$237$	−3.35117	+	19.0054i	−0.217682	+	1.23453i
$238$		0			0
$239$	−9.40167	−	16.2842i	−0.608144	−	1.05334i	−0.991546	−	0.129754i	$-0.958581\pi$
$239$	−9.40167	−	16.2842i	−0.608144	−	1.05334i	0.383402	−	0.923581i	$-0.374752\pi$
$240$		0			0
$241$	−8.91013	−	7.47649i	−0.573952	−	0.481603i	0.309003	−	0.951061i	$-0.400005\pi$
$241$	−8.91013	−	7.47649i	−0.573952	−	0.481603i	−0.882955	+	0.469458i	$0.844449\pi$
$242$		0			0
$243$	−6.25150	+	2.27536i	−0.401034	+	0.145964i
$244$		0			0
$245$	0.893933	+	5.06975i	0.0571113	+	0.323894i
$246$		0			0
$247$	−6.58512	−	1.11121i	−0.419001	−	0.0707048i
$248$		0			0
$249$	−3.48499	−	19.7643i	−0.220852	−	1.25251i
$250$		0			0
$251$	−7.60354	+	2.76746i	−0.479931	+	0.174681i	−0.570646	−	0.821196i	$-0.693307\pi$
$251$	−7.60354	+	2.76746i	−0.479931	+	0.174681i	0.0907147	+	0.995877i	$0.471085\pi$
$252$		0			0
$253$	−4.65451	−	3.90560i	−0.292627	−	0.245543i
$254$		0			0
$255$	0.500000	+	0.866025i	0.0313112	+	0.0542326i
$256$		0			0
$257$	−1.72756	+	9.79747i	−0.107762	+	0.611150i	0.882319	+	0.470652i	$0.155981\pi$
$257$	−1.72756	+	9.79747i	−0.107762	+	0.611150i	−0.990081	+	0.140497i	$0.955130\pi$
$258$		0			0
$259$	5.69459	−	9.86332i	0.353845	−	0.612877i
$260$		0			0
$261$	6.42514	+	2.33856i	0.397706	+	0.144753i
$262$		0			0
$263$	−12.4722	+	10.4655i	−0.769072	+	0.645328i	−0.940471	−	0.339874i	$-0.889616\pi$
$263$	−12.4722	+	10.4655i	−0.769072	+	0.645328i	0.171399	+	0.985202i	$0.445171\pi$
$264$		0			0
$265$	−14.5963			−0.896642
$266$		0			0
$267$	−7.04189			−0.430957
$268$		0			0
$269$	−10.9101	+	9.15469i	−0.665202	+	0.558171i	−0.911641	−	0.410987i	$-0.865184\pi$
$269$	−10.9101	+	9.15469i	−0.665202	+	0.558171i	0.246439	+	0.969158i	$0.420740\pi$
$270$		0			0
$271$	23.9440	+	8.71491i	1.45450	+	0.529393i	0.943843	−	0.330394i	$-0.107181\pi$
$271$	23.9440	+	8.71491i	1.45450	+	0.529393i	0.510653	+	0.859787i	$0.329404\pi$
$272$		0			0
$273$	2.42262	−	4.19610i	0.146624	−	0.253959i
$274$		0			0
$275$	−0.526159	+	2.98400i	−0.0317286	+	0.179942i
$276$		0			0
$277$	−5.62836	−	9.74860i	−0.338175	−	0.585736i	0.645914	−	0.763410i	$-0.276476\pi$
$277$	−5.62836	−	9.74860i	−0.338175	−	0.585736i	−0.984090	+	0.177673i	$0.943143\pi$
$278$		0			0
$279$	−2.72668	−	2.28796i	−0.163242	−	0.136976i
$280$		0			0
$281$	−2.15018	+	0.782601i	−0.128269	+	0.0466860i	−0.405357	−	0.914158i	$-0.632853\pi$
$281$	−2.15018	+	0.782601i	−0.128269	+	0.0466860i	0.277088	+	0.960844i	$0.410631\pi$
$282$		0			0
$283$	1.35117	+	7.66285i	0.0803185	+	0.455509i	0.998269	+	0.0588139i	$0.0187319\pi$
$283$	1.35117	+	7.66285i	0.0803185	+	0.455509i	−0.917950	+	0.396695i	$0.870157\pi$
$284$		0			0
$285$	−7.99660	+	9.67372i	−0.473677	+	0.573021i
$286$		0			0
$287$	3.57919	+	20.2986i	0.211273	+	1.19819i
$288$		0			0
$289$	15.8614	−	5.77309i	0.933026	−	0.339594i
$290$		0			0
$291$	2.03802	+	1.71010i	0.119471	+	0.100248i
$292$		0			0
$293$	2.04664	+	3.54488i	0.119566	+	0.207094i	0.919596	−	0.392866i	$-0.128516\pi$
$293$	2.04664	+	3.54488i	0.119566	+	0.207094i	−0.800030	+	0.599960i	$0.795183\pi$
$294$		0			0
$295$	−0.0859997	+	0.487728i	−0.00500709	+	0.0283966i
$296$		0			0
$297$	5.77584	−	10.0041i	0.335148	−	0.580494i
$298$		0			0
$299$	4.23783	+	1.54244i	0.245080	+	0.0892018i
$300$		0			0
$301$	−10.9795	+	9.21291i	−0.632849	+	0.531023i
$302$		0			0
$303$	−15.2986			−0.878882
$304$		0			0
$305$	19.9564			1.14270
$306$		0			0
$307$	13.0608	−	10.9593i	0.745418	−	0.625480i	−0.188869	−	0.982002i	$-0.560482\pi$
$307$	13.0608	−	10.9593i	0.745418	−	0.625480i	0.934287	+	0.356523i	$0.116038\pi$
$308$		0			0
$309$	1.85117	+	0.673770i	0.105309	+	0.0383294i
$310$		0			0
$311$	9.03209	−	15.6440i	0.512163	−	0.887092i	−0.487738	−	0.872990i	$-0.662178\pi$
$311$	9.03209	−	15.6440i	0.512163	−	0.887092i	0.999901	−	0.0141018i	$-0.00448888\pi$
$312$		0			0
$313$	−0.550507	+	3.12208i	−0.0311165	+	0.176470i	−0.996405	−	0.0847146i	$-0.973002\pi$
$313$	−0.550507	+	3.12208i	−0.0311165	+	0.176470i	0.965289	+	0.261185i	$0.0841133\pi$
$314$		0			0
$315$	1.26604	+	2.19285i	0.0713335	+	0.123553i
$316$		0			0
$317$	−11.7777	−	9.88263i	−0.661499	−	0.555064i	0.249037	−	0.968494i	$-0.419886\pi$
$317$	−11.7777	−	9.88263i	−0.661499	−	0.555064i	−0.910536	+	0.413430i	$0.864330\pi$
$318$		0			0
$319$	−20.3195	+	7.39571i	−1.13768	+	0.414080i
$320$		0			0
$321$	−0.179578	−	1.01844i	−0.0100231	−	0.0568436i
$322$		0			0
$323$	−0.981582	−	1.15247i	−0.0546167	−	0.0641249i
$324$		0			0
$325$	−0.390530	−	2.21480i	−0.0216627	−	0.122855i
$326$		0			0
$327$	14.2233	−	5.17685i	0.786549	−	0.286280i
$328$		0			0
$329$	8.17546	+	6.86002i	0.450728	+	0.378205i
$330$		0			0
$331$	12.8550	+	22.2656i	0.706577	+	1.22383i	0.966119	+	0.258095i	$0.0830948\pi$
$331$	12.8550	+	22.2656i	0.706577	+	1.22383i	−0.259543	+	0.965732i	$0.583572\pi$
$332$		0			0
$333$	−0.625362	+	3.54661i	−0.0342697	+	0.194353i
$334$		0			0
$335$	−6.61721	+	11.4613i	−0.361537	+	0.626200i
$336$		0			0
$337$	−32.7028	−	11.9028i	−1.78144	−	0.648389i	−0.999693	−	0.0247877i	$-0.992109\pi$
$337$	−32.7028	−	11.9028i	−1.78144	−	0.648389i	−0.781742	−	0.623602i	$-0.785669\pi$
$338$		0			0
$339$	−5.41147	+	4.54077i	−0.293911	+	0.246621i
$340$		0			0
$341$	11.2567			0.609585
$342$		0			0
$343$	20.1034			1.08548
$344$		0			0
$345$	6.49273	−	5.44804i	0.349557	−	0.293313i
$346$		0			0
$347$	−0.608593	−	0.221510i	−0.0326710	−	0.0118913i	0.325633	−	0.945496i	$-0.394423\pi$
$347$	−0.608593	−	0.221510i	−0.0326710	−	0.0118913i	−0.358304	+	0.933605i	$0.616645\pi$
$348$		0			0
$349$	−5.50000	+	9.52628i	−0.294408	+	0.509930i	−0.974847	−	0.222875i	$-0.928456\pi$
$349$	−5.50000	+	9.52628i	−0.294408	+	0.509930i	0.680439	+	0.732805i	$0.261789\pi$
$350$		0			0
$351$	−1.48886	+	8.44372i	−0.0794692	+	0.450692i
$352$		0			0
$353$	−8.69253	−	15.0559i	−0.462657	−	0.801345i	0.536436	−	0.843941i	$-0.319770\pi$
$353$	−8.69253	−	15.0559i	−0.462657	−	0.801345i	−0.999092	+	0.0425961i	$0.986437\pi$
$354$		0			0
$355$	−9.30200	−	7.80531i	−0.493699	−	0.414263i
$356$		0			0
$357$	1.03209	−	0.375650i	0.0546239	−	0.0198815i
$358$		0			0
$359$	3.18361	+	18.0552i	0.168025	+	0.952914i	0.945891	+	0.324485i	$0.105191\pi$
$359$	3.18361	+	18.0552i	0.168025	+	0.952914i	−0.777866	+	0.628430i	$0.783698\pi$
$360$		0			0
$361$	9.25671	−	16.5926i	0.487195	−	0.873293i
$362$		0			0
$363$	−1.79292	−	10.1681i	−0.0941038	−	0.533689i
$364$		0			0
$365$	−27.1523	+	9.88263i	−1.42122	+	0.517280i
$366$		0			0
$367$	−9.06077	−	7.60289i	−0.472969	−	0.396868i	0.374907	−	0.927062i	$-0.377674\pi$
$367$	−9.06077	−	7.60289i	−0.472969	−	0.396868i	−0.847876	+	0.530194i	$0.822119\pi$
$368$		0			0
$369$	−3.25877	−	5.64436i	−0.169645	−	0.293833i
$370$		0			0
$371$	−2.78383	+	15.7879i	−0.144529	+	0.819667i
$372$		0			0
$373$	−1.13041	+	1.95794i	−0.0585307	+	0.101378i	−0.893806	−	0.448454i	$-0.851975\pi$
$373$	−1.13041	+	1.95794i	−0.0585307	+	0.101378i	0.835275	+	0.549832i	$0.185308\pi$
$374$		0			0
$375$	−17.5005	−	6.36965i	−0.903720	−	0.328927i
$376$		0			0
$377$	12.2947	−	10.3165i	0.633211	−	0.531327i
$378$		0			0
$379$	12.4243			0.638192			0.319096	−	0.947722i	$-0.396621\pi$
$379$	12.4243			0.638192			0.319096	+	0.947722i	$0.396621\pi$
$380$		0			0
$381$	14.3027			0.732750
$382$		0			0
$383$	−14.8418	+	12.4538i	−0.758382	+	0.636358i	−0.937705	−	0.347432i	$-0.887054\pi$
$383$	−14.8418	+	12.4538i	−0.758382	+	0.636358i	0.179323	+	0.983790i	$0.442609\pi$
$384$		0			0
$385$	−7.52481	−	2.73881i	−0.383500	−	0.139583i
$386$		0			0
$387$	2.26604	−	3.92490i	0.115190	−	0.199514i
$388$		0			0
$389$	3.81908	−	21.6591i	0.193635	−	1.09816i	−0.720714	−	0.693232i	$-0.756186\pi$
$389$	3.81908	−	21.6591i	0.193635	−	1.09816i	0.914349	−	0.404926i	$-0.132703\pi$
$390$		0			0
$391$	0.511144	+	0.885328i	0.0258497	+	0.0447730i
$392$		0			0
$393$	−15.5096	−	13.0141i	−0.782353	−	0.656472i
$394$		0			0
$395$	−22.2456	+	8.09672i	−1.11930	+	0.407390i
$396$		0			0
$397$	−0.0234708	−	0.133109i	−0.00117796	−	0.00668056i	0.984213	−	0.176987i	$-0.0566352\pi$
$397$	−0.0234708	−	0.133109i	−0.00117796	−	0.00668056i	−0.985391	+	0.170307i	$0.945524\pi$
$398$		0			0
$399$	8.93835	+	10.4944i	0.447477	+	0.525379i
$400$		0			0
$401$	6.64203	+	37.6688i	0.331687	+	1.88109i	0.457770	+	0.889071i	$0.348648\pi$
$401$	6.64203	+	37.6688i	0.331687	+	1.88109i	−0.126083	+	0.992020i	$0.540241\pi$
$402$		0			0
$403$	−7.85117	+	2.85759i	−0.391094	+	0.142347i
$404$		0			0
$405$	9.52481	+	7.99227i	0.473292	+	0.397139i
$406$		0			0
$407$	−5.69459	−	9.86332i	−0.282270	−	0.488907i
$408$		0			0
$409$	−3.21600	+	18.2389i	−0.159021	+	0.901854i	0.795996	+	0.605302i	$0.206948\pi$
$409$	−3.21600	+	18.2389i	−0.159021	+	0.901854i	−0.955017	+	0.296552i	$0.904163\pi$
$410$		0			0
$411$	16.7606	−	29.0302i	0.826739	−	1.43195i
$412$		0			0
$413$	0.511144	+	0.186041i	0.0251518	+	0.00915450i
$414$		0			0
$415$	18.8589	−	15.8245i	0.925747	−	0.776794i
$416$		0			0
$417$	31.5553			1.54527
$418$		0			0
$419$	20.2567			0.989605			0.494803	−	0.869005i	$-0.335240\pi$
$419$	20.2567			0.989605			0.494803	+	0.869005i	$0.335240\pi$
$420$		0			0
$421$	−1.95883	+	1.64365i	−0.0954673	+	0.0801066i	−0.689272	−	0.724503i	$-0.742070\pi$
$421$	−1.95883	+	1.64365i	−0.0954673	+	0.0801066i	0.593805	+	0.804609i	$0.297625\pi$
$422$		0			0
$423$	−3.17112	−	1.15419i	−0.154185	−	0.0561188i
$424$		0			0
$425$	0.254900	−	0.441500i	0.0123645	−	0.0214159i
$426$		0			0
$427$	3.80612	−	21.5856i	0.184191	−	1.04460i
$428$		0			0
$429$	−2.42262	−	4.19610i	−0.116965	−	0.202590i
$430$		0			0
$431$	−7.43036	−	6.23481i	−0.357908	−	0.300320i	0.446048	−	0.895009i	$-0.352831\pi$
$431$	−7.43036	−	6.23481i	−0.357908	−	0.300320i	−0.803956	+	0.594689i	$0.797275\pi$
$432$		0			0
$433$	3.22890	−	1.17522i	0.155171	−	0.0564777i	−0.263267	−	0.964723i	$-0.584800\pi$
$433$	3.22890	−	1.17522i	0.155171	−	0.0564777i	0.418438	+	0.908245i	$0.362578\pi$
$434$		0			0
$435$	−5.23783	−	29.7052i	−0.251135	−	1.42425i
$436$		0			0
$437$	−8.17483	+	9.88933i	−0.391055	+	0.473071i
$438$		0			0
$439$	−6.61974	−	37.5424i	−0.315943	−	1.79180i	−0.566883	−	0.823798i	$-0.691851\pi$
$439$	−6.61974	−	37.5424i	−0.315943	−	1.79180i	0.250940	−	0.968003i	$-0.419260\pi$
$440$		0			0
$441$	−1.68004	+	0.611486i	−0.0800021	+	0.0291184i
$442$		0			0
$443$	3.64930	+	3.06213i	0.173383	+	0.145486i	0.725350	−	0.688380i	$-0.241678\pi$
$443$	3.64930	+	3.06213i	0.173383	+	0.145486i	−0.551967	+	0.833866i	$0.686122\pi$
$444$		0			0
$445$	−4.31908	−	7.48086i	−0.204744	−	0.354627i
$446$		0			0
$447$	2.16637	−	12.2861i	0.102466	−	0.581113i
$448$		0			0
$449$	−3.14590	+	5.44885i	−0.148464	+	0.257147i	−0.930660	−	0.365885i	$-0.880766\pi$
$449$	−3.14590	+	5.44885i	−0.148464	+	0.257147i	0.782196	+	0.623033i	$0.214100\pi$
$450$		0			0
$451$	19.3687	+	7.04963i	0.912037	+	0.331954i
$452$		0			0
$453$	18.7784	−	15.7569i	0.882285	−	0.740325i
$454$		0			0
$455$	5.94356			0.278639
$456$		0			0
$457$	35.6459			1.66744			0.833722	−	0.552184i	$-0.186205\pi$
$457$	35.6459			1.66744			0.833722	+	0.552184i	$0.186205\pi$
$458$		0			0
$459$	−1.48886	+	1.24930i	−0.0694938	+	0.0583122i
$460$		0			0
$461$	29.3282	+	10.6746i	1.36595	+	0.497165i	0.917888	−	0.396839i	$-0.129893\pi$
$461$	29.3282	+	10.6746i	1.36595	+	0.497165i	0.448060	+	0.894003i	$0.352115\pi$
$462$		0			0
$463$	2.94831	−	5.10662i	0.137020	−	0.237325i	−0.789348	−	0.613947i	$-0.789581\pi$
$463$	2.94831	−	5.10662i	0.137020	−	0.237325i	0.926367	+	0.376622i	$0.122914\pi$
$464$		0			0
$465$	−2.72668	+	15.4638i	−0.126447	+	0.717116i
$466$		0			0
$467$	16.7267	+	28.9715i	0.774019	+	1.34064i	0.935344	+	0.353738i	$0.115090\pi$
$467$	16.7267	+	28.9715i	0.774019	+	1.34064i	−0.161326	+	0.986901i	$0.551577\pi$
$468$		0			0
$469$	11.1350	+	9.34337i	0.514167	+	0.431437i
$470$		0			0
$471$	7.76991	−	2.82802i	0.358019	−	0.130308i
$472$		0			0
$473$	2.48886	+	14.1150i	0.114438	+	0.649008i
$474$		0			0
$475$	6.30928	+	1.06467i	0.289490	+	0.0488502i
$476$		0			0
$477$	−0.880263	−	4.99222i	−0.0403045	−	0.228578i
$478$		0			0
$479$	24.2545	−	8.82791i	1.10822	−	0.403358i	0.277877	−	0.960617i	$-0.410369\pi$
$479$	24.2545	−	8.82791i	1.10822	−	0.403358i	0.830339	+	0.557259i	$0.188147\pi$
$480$		0			0
$481$	6.47565	+	5.43372i	0.295264	+	0.247756i
$482$		0			0
$483$	−4.65451	−	8.06186i	−0.211788	−	0.366827i
$484$		0			0
$485$	−0.566704	+	3.21394i	−0.0257327	+	0.145937i
$486$		0			0
$487$	−16.8996	+	29.2710i	−0.765795	+	1.32640i	0.174031	+	0.984740i	$0.444321\pi$
$487$	−16.8996	+	29.2710i	−0.765795	+	1.32640i	−0.939825	+	0.341655i	$0.889013\pi$
$488$		0			0
$489$	−32.3764	−	11.7841i	−1.46411	−	0.532894i
$490$		0			0
$491$	5.12907	−	4.30380i	0.231472	−	0.194228i	−0.519673	−	0.854365i	$-0.673946\pi$
$491$	5.12907	−	4.30380i	0.231472	−	0.194228i	0.751145	+	0.660137i	$0.229502\pi$
$492$		0			0
$493$	3.63816			0.163854
$494$		0			0
$495$	2.53209			0.113809
$496$		0			0
$497$	−10.2166	+	8.57277i	−0.458279	+	0.384541i
$498$		0			0
$499$	3.15018	+	1.14657i	0.141021	+	0.0513276i	0.411567	−	0.911380i	$-0.364982\pi$
$499$	3.15018	+	1.14657i	0.141021	+	0.0513276i	−0.270545	+	0.962707i	$0.587204\pi$
$500$		0			0
$501$	13.5758	−	23.5140i	0.606522	−	1.05053i
$502$		0			0
$503$	3.95424	−	22.4256i	0.176311	−	0.999909i	−0.760309	−	0.649562i	$-0.774953\pi$
$503$	3.95424	−	22.4256i	0.176311	−	0.999909i	0.936620	−	0.350347i	$-0.113936\pi$
$504$		0			0
$505$	−9.38326	−	16.2523i	−0.417549	−	0.723217i
$506$		0			0
$507$	−12.5025	−	10.4909i	−0.555257	−	0.465916i
$508$		0			0
$509$	37.9937	−	13.8286i	1.68404	−	0.612940i	0.690185	−	0.723633i	$-0.257529\pi$
$509$	37.9937	−	13.8286i	1.68404	−	0.612940i	0.993855	+	0.110693i	$0.0353070\pi$
$510$		0			0
$511$	5.51090	+	31.2538i	0.243788	+	1.38259i
$512$		0			0
$513$	−21.2147	−	12.0409i	−0.936650	−	0.531620i
$514$		0			0
$515$	0.419625	+	2.37981i	0.0184909	+	0.104867i
$516$		0			0
$517$	10.0287	−	3.65014i	0.441061	−	0.160533i
$518$		0			0
$519$	−22.4991	−	18.8790i	−0.987602	−	0.828696i
$520$		0			0
$521$	5.80541	+	10.0553i	0.254340	+	0.440529i	0.964716	−	0.263293i	$-0.0848086\pi$
$521$	5.80541	+	10.0553i	0.254340	+	0.440529i	−0.710376	+	0.703822i	$0.751475\pi$
$522$		0			0
$523$	−1.96198	+	11.1269i	−0.0857915	+	0.486548i	0.911392	+	0.411540i	$0.135009\pi$
$523$	−1.96198	+	11.1269i	−0.0857915	+	0.486548i	−0.997183	+	0.0750072i	$0.976102\pi$
$524$		0			0
$525$	−2.32114	+	4.02033i	−0.101303	+	0.175461i
$526$		0			0
$527$	−1.77972	−	0.647763i	−0.0775256	−	0.0282170i
$528$		0			0
$529$	−10.9816	+	9.21464i	−0.477460	+	0.400637i
$530$		0			0
$531$	−0.171999			−0.00746413
$532$		0			0
$533$	−15.2986			−0.662656
$534$		0			0
$535$	0.971782	−	0.815422i	0.0420138	−	0.0352537i
$536$		0			0
$537$	6.54576	+	2.38246i	0.282470	+	0.102811i
$538$		0			0
$539$	2.82707	−	4.89662i	0.121770	−	0.210913i
$540$		0			0
$541$	2.48457	−	14.0907i	0.106820	−	0.605808i	−0.883657	−	0.468134i	$-0.844926\pi$
$541$	2.48457	−	14.0907i	0.106820	−	0.605808i	0.990478	−	0.137673i	$-0.0439625\pi$
$542$		0			0
$543$	11.6211	+	20.1283i	0.498708	+	0.863788i
$544$		0			0
$545$	14.2233	+	11.9347i	0.609258	+	0.511228i
$546$		0			0
$547$	−33.1657	+	12.0713i	−1.41806	+	0.516132i	−0.933485	−	0.358617i	$-0.883248\pi$
$547$	−33.1657	+	12.0713i	−1.41806	+	0.516132i	−0.484576	+	0.874749i	$0.661026\pi$
$548$		0			0
$549$	1.20352	+	6.82548i	0.0513648	+	0.291304i
$550$		0			0
$551$	15.9329	+	42.7924i	0.678764	+	1.82302i
$552$		0			0
$553$	4.51501	+	25.6059i	0.191998	+	1.08887i
$554$		0			0
$555$	14.9290	−	5.43372i	0.633701	−	0.230648i
$556$		0			0
$557$	−22.4277	−	18.8191i	−0.950291	−	0.797389i	0.0290556	−	0.999578i	$-0.490750\pi$
$557$	−22.4277	−	18.8191i	−0.950291	−	0.797389i	−0.979347	+	0.202189i	$0.935194\pi$
$558$		0			0
$559$	−5.31908	−	9.21291i	−0.224973	−	0.389665i
$560$		0			0
$561$	0.190722	−	1.08164i	0.00805230	−	0.0456669i
$562$		0			0
$563$	5.96791	−	10.3367i	0.251517	−	0.435641i	−0.712426	−	0.701747i	$-0.752404\pi$
$563$	5.96791	−	10.3367i	0.251517	−	0.435641i	0.963944	+	0.266106i	$0.0857371\pi$
$564$		0			0
$565$	−8.14290	−	2.96377i	−0.342575	−	0.124687i
$566$		0			0
$567$	10.4614	−	8.77812i	0.439336	−	0.368646i
$568$		0			0
$569$	−20.5526			−0.861611			−0.430805	−	0.902445i	$-0.641770\pi$
$569$	−20.5526			−0.861611			−0.430805	+	0.902445i	$0.641770\pi$
$570$		0			0
$571$	−34.7202			−1.45299			−0.726497	−	0.687169i	$-0.758853\pi$
$571$	−34.7202			−1.45299			−0.726497	+	0.687169i	$0.758853\pi$
$572$		0			0
$573$	16.0155	−	13.4386i	0.669056	−	0.561405i
$574$		0			0
$575$	−4.06031	−	1.47783i	−0.169327	−	0.0616298i
$576$		0			0
$577$	4.66756	−	8.08444i	0.194313	−	0.336560i	−0.752362	−	0.658750i	$-0.771086\pi$
$577$	4.66756	−	8.08444i	0.194313	−	0.336560i	0.946675	+	0.322190i	$0.104419\pi$
$578$		0			0
$579$	−2.48364	+	14.0854i	−0.103217	+	0.585370i
$580$		0			0
$581$	−13.5196	−	23.4166i	−0.560888	−	0.971486i
$582$		0			0
$583$	12.2808	+	10.3048i	0.508619	+	0.426782i
$584$		0			0
$585$	−1.76604	+	0.642788i	−0.0730170	+	0.0265760i
$586$		0			0
$587$	5.59240	+	31.7161i	0.230823	+	1.30906i	0.851235	+	0.524785i	$0.175854\pi$
$587$	5.59240	+	31.7161i	0.230823	+	1.30906i	−0.620412	+	0.784276i	$0.713034\pi$
$588$		0			0
$589$	−0.174992	−	23.7700i	−0.00721043	−	0.979426i
$590$		0			0
$591$	1.23601	+	7.00979i	0.0508429	+	0.288344i
$592$		0			0
$593$	−26.0920	+	9.49671i	−1.07147	+	0.389983i	−0.816726	−	0.577026i	$-0.804213\pi$
$593$	−26.0920	+	9.49671i	−1.07147	+	0.389983i	−0.254743	+	0.967009i	$0.581991\pi$
$594$		0			0
$595$	1.03209	+	0.866025i	0.0423115	+	0.0355036i
$596$		0			0
$597$	0.330222	+	0.571962i	0.0135151	+	0.0234088i
$598$		0			0
$599$	4.32383	−	24.5216i	0.176667	−	1.00193i	−0.759536	−	0.650466i	$-0.774574\pi$
$599$	4.32383	−	24.5216i	0.176667	−	1.00193i	0.936202	−	0.351461i	$-0.114315\pi$
$600$		0			0
$601$	−7.86959	+	13.6305i	−0.321007	+	0.556001i	−0.980696	−	0.195538i	$-0.937355\pi$
$601$	−7.86959	+	13.6305i	−0.321007	+	0.556001i	0.659689	+	0.751539i	$0.270688\pi$
$602$		0			0
$603$	−4.31908	−	1.57202i	−0.175886	−	0.0640174i
$604$		0			0
$605$	9.70233	−	8.14122i	0.394456	−	0.330988i
$606$		0			0
$607$	−4.16756			−0.169156			−0.0845779	−	0.996417i	$-0.526954\pi$
$607$	−4.16756			−0.169156			−0.0845779	+	0.996417i	$0.526954\pi$
$608$		0			0
$609$	−33.1293			−1.34247
$610$		0			0
$611$	−6.06805	+	5.09170i	−0.245487	+	0.205988i
$612$		0			0
$613$	−13.8252	−	5.03195i	−0.558393	−	0.203239i	0.0473784	−	0.998877i	$-0.484913\pi$
$613$	−13.8252	−	5.03195i	−0.558393	−	0.203239i	−0.605772	+	0.795638i	$0.707136\pi$
$614$		0			0
$615$	−14.3760	+	24.8999i	−0.579696	+	1.00406i
$616$		0			0
$617$	−5.53091	+	31.3673i	−0.222666	+	1.26280i	0.644431	+	0.764662i	$0.277094\pi$
$617$	−5.53091	+	31.3673i	−0.222666	+	1.26280i	−0.867097	+	0.498139i	$0.834017\pi$
$618$		0			0
$619$	−10.6334	−	18.4176i	−0.427393	−	0.740266i	0.569248	−	0.822166i	$-0.307235\pi$
$619$	−10.6334	−	18.4176i	−0.427393	−	0.740266i	−0.996641	+	0.0819000i	$0.973901\pi$
$620$		0			0
$621$	12.6190	+	10.5886i	0.506384	+	0.424907i
$622$		0			0
$623$	−8.91534	+	3.24492i	−0.357186	+	0.130005i
$624$		0			0
$625$	−2.69253	−	15.2701i	−0.107701	−	0.610805i
$626$		0			0
$627$	13.5576	−	2.49362i	0.541439	−	0.0995856i
$628$		0			0
$629$	0.332748	+	1.88711i	0.0132675	+	0.0752440i
$630$		0			0
$631$	−0.696814	+	0.253620i	−0.0277397	+	0.0100964i	−0.355853	−	0.934542i	$-0.615810\pi$
$631$	−0.696814	+	0.253620i	−0.0277397	+	0.0100964i	0.328113	+	0.944638i	$0.393587\pi$
$632$		0			0
$633$	−20.4008	−	17.1183i	−0.810859	−	0.680391i
$634$		0			0
$635$	8.77244	+	15.1943i	0.348124	+	0.602968i
$636$		0			0
$637$	−0.728741	+	4.13290i	−0.0288738	+	0.163751i
$638$		0			0
$639$	2.10859	−	3.65219i	0.0834147	−	0.144478i
$640$		0			0
$641$	23.3282	+	8.49076i	0.921407	+	0.335365i	0.758798	−	0.651326i	$-0.225787\pi$
$641$	23.3282	+	8.49076i	0.921407	+	0.335365i	0.162609	+	0.986691i	$0.448009\pi$
$642$		0			0
$643$	−35.6202	+	29.8889i	−1.40472	+	1.17870i	−0.445768	+	0.895149i	$0.647069\pi$
$643$	−35.6202	+	29.8889i	−1.40472	+	1.17870i	−0.958956	+	0.283554i	$0.908486\pi$
$644$		0			0
$645$	−19.9932			−0.787231
$646$		0			0
$647$	11.2918			0.443926			0.221963	−	0.975055i	$-0.428754\pi$
$647$	11.2918			0.443926			0.221963	+	0.975055i	$0.428754\pi$
$648$		0			0
$649$	0.416689	−	0.349643i	0.0163565	−	0.0137247i
$650$		0			0
$651$	16.2062	+	5.89858i	0.635171	+	0.231183i
$652$		0			0
$653$	−8.11081	+	14.0483i	−0.317401	+	0.549754i	−0.979945	−	0.199269i	$-0.936143\pi$
$653$	−8.11081	+	14.0483i	−0.317401	+	0.549754i	0.662544	+	0.749023i	$0.269477\pi$
$654$		0			0
$655$	4.31268	−	24.4584i	0.168510	−	0.955670i
$656$		0			0
$657$	−5.01754	−	8.69064i	−0.195753	−	0.339054i
$658$		0			0
$659$	−17.0608	−	14.3157i	−0.664593	−	0.557660i	0.246866	−	0.969050i	$-0.420599\pi$
$659$	−17.0608	−	14.3157i	−0.664593	−	0.557660i	−0.911460	+	0.411389i	$0.865044\pi$
$660$		0			0
$661$	11.2836	−	4.10689i	0.438881	−	0.159739i	−0.113123	−	0.993581i	$-0.536086\pi$
$661$	11.2836	−	4.10689i	0.438881	−	0.159739i	0.552004	+	0.833841i	$0.313863\pi$
$662$		0			0
$663$	0.141559	+	0.802823i	0.00549771	+	0.0311790i
$664$		0			0
$665$	−5.66637	+	15.9322i	−0.219733	+	0.617824i
$666$		0			0
$667$	−5.35457	−	30.3673i	−0.207330	−	1.17583i
$668$		0			0
$669$	−19.0608	+	6.93755i	−0.736932	+	0.268221i
$670$		0			0
$671$	−16.7906	−	14.0890i	−0.648194	−	0.543900i
$672$		0			0
$673$	−11.0175	−	19.0829i	−0.424695	−	0.735593i	0.571697	−	0.820465i	$-0.306285\pi$
$673$	−11.0175	−	19.0829i	−0.424695	−	0.735593i	−0.996392	+	0.0848716i	$0.972952\pi$
$674$		0			0
$675$	1.42649	−	8.09002i	0.0549056	−	0.311385i
$676$		0			0
$677$	−4.03714	+	6.99253i	−0.155160	+	0.268745i	−0.933117	−	0.359572i	$-0.882923\pi$
$677$	−4.03714	+	6.99253i	−0.155160	+	0.268745i	0.777957	+	0.628317i	$0.216256\pi$
$678$		0			0
$679$	3.36824	+	1.22594i	0.129261	+	0.0470472i
$680$		0			0
$681$	9.12424	−	7.65614i	0.349642	−	0.293384i
$682$		0			0
$683$	−23.0933			−0.883640			−0.441820	−	0.897104i	$-0.645667\pi$
$683$	−23.0933			−0.883640			−0.441820	+	0.897104i	$0.645667\pi$
$684$		0			0
$685$	41.1198			1.57111
$686$		0			0
$687$	3.21482	−	2.69756i	0.122653	−	0.102918i
$688$		0			0
$689$	−11.1814	−	4.06969i	−0.425977	−	0.155043i
$690$		0			0
$691$	−13.8746	+	24.0316i	−0.527816	+	0.914204i	0.471658	+	0.881781i	$0.343656\pi$
$691$	−13.8746	+	24.0316i	−0.527816	+	0.914204i	−0.999474	+	0.0324228i	$0.989678\pi$
$692$		0			0
$693$	0.482926	−	2.73881i	0.0183448	−	0.104039i
$694$		0			0
$695$	19.3542	+	33.5224i	0.734145	+	1.27158i
$696$		0			0
$697$	−2.65657	−	2.22913i	−0.100625	−	0.0844343i
$698$		0			0
$699$	2.70574	−	0.984808i	0.102340	−	0.0372489i
$700$		0			0
$701$	−0.678863	−	3.85002i	−0.0256403	−	0.145413i	0.969300	−	0.245881i	$-0.0790772\pi$
$701$	−0.678863	−	3.85002i	−0.0256403	−	0.145413i	−0.994940	+	0.100468i	$0.967966\pi$
$702$		0			0
$703$	−20.7392	+	12.1782i	−0.782193	+	0.459310i
$704$		0			0
$705$	2.58512	+	14.6610i	0.0973613	+	0.552164i
$706$		0			0
$707$	−19.3687	+	7.04963i	−0.728435	+	0.265129i
$708$		0			0
$709$	31.9675	+	26.8239i	1.20056	+	1.00739i	0.999614	+	0.0277921i	$0.00884763\pi$
$709$	31.9675	+	26.8239i	1.20056	+	1.00739i	0.200951	+	0.979601i	$0.435597\pi$
$710$		0			0
$711$	−4.11081	−	7.12014i	−0.154168	−	0.267026i
$712$		0			0
$713$	−2.78746	+	15.8084i	−0.104391	+	0.592031i
$714$		0			0
$715$	2.97178	−	5.14728i	0.111138	−	0.192497i
$716$		0			0
$717$	−27.0710	−	9.85305i	−1.01099	−	0.367969i
$718$		0			0
$719$	7.47494	−	6.27222i	0.278768	−	0.233914i	−0.492674	−	0.870214i	$-0.663980\pi$
$719$	7.47494	−	6.27222i	0.278768	−	0.233914i	0.771442	+	0.636300i	$0.219536\pi$
$720$		0			0
$721$	2.65413			0.0988451
$722$		0			0
$723$	−17.8203			−0.662743
$724$		0			0
$725$	−11.7797	+	9.88435i	−0.437488	+	0.367096i
$726$		0			0
$727$	−28.3828	−	10.3305i	−1.05266	−	0.383137i	−0.242995	−	0.970028i	$-0.578130\pi$
$727$	−28.3828	−	10.3305i	−1.05266	−	0.383137i	−0.809667	+	0.586890i	$0.800352\pi$
$728$		0			0
$729$	−15.0201	+	26.0155i	−0.556299	+	0.963538i
$730$		0			0
$731$	0.418748	−	2.37484i	0.0154880	−	0.0878366i
$732$		0			0
$733$	3.76083	+	6.51395i	0.138909	+	0.240598i	0.927084	−	0.374853i	$-0.122307\pi$
$733$	3.76083	+	6.51395i	0.138909	+	0.240598i	−0.788175	+	0.615452i	$0.788974\pi$
$734$		0			0
$735$	6.04189	+	5.06975i	0.222858	+	0.187000i
$736$		0			0
$737$	13.6591	−	4.97151i	0.503139	−	0.183128i
$738$		0			0
$739$	−0.654210	−	3.71021i	−0.0240655	−	0.136482i	0.970408	−	0.241472i	$-0.0776302\pi$
$739$	−0.654210	−	3.71021i	−0.0240655	−	0.136482i	−0.994473	+	0.104990i	$0.966519\pi$
$740$		0			0
$741$	−8.82295	+	5.18091i	−0.324119	+	0.190325i
$742$		0			0
$743$	4.52822	+	25.6808i	0.166124	+	0.942137i	0.947898	+	0.318575i	$0.103204\pi$
$743$	4.52822	+	25.6808i	0.166124	+	0.942137i	−0.781774	+	0.623563i	$0.785685\pi$
$744$		0			0
$745$	14.3807	−	5.23416i	0.526869	−	0.191765i
$746$		0			0
$747$	6.54963	+	5.49579i	0.239638	+	0.201081i
$748$		0			0
$749$	−0.696652	−	1.20664i	−0.0254551	−	0.0440896i
$750$		0			0
$751$	5.51098	−	31.2543i	0.201099	−	1.14049i	−0.702363	−	0.711819i	$-0.747872\pi$
$751$	5.51098	−	31.2543i	0.201099	−	1.14049i	0.903462	−	0.428668i	$-0.141017\pi$
$752$		0			0
$753$	−6.19846	+	10.7361i	−0.225885	+	0.391244i
$754$		0			0
$755$	28.2567	+	10.2846i	1.02837	+	0.374295i
$756$		0			0
$757$	14.8195	−	12.4351i	0.538626	−	0.451960i	−0.332442	−	0.943124i	$-0.607873\pi$
$757$	14.8195	−	12.4351i	0.538626	−	0.451960i	0.871068	+	0.491163i	$0.163428\pi$
$758$		0			0
$759$	−9.30903			−0.337896
$760$		0			0
$761$	12.1284			0.439653			0.219826	−	0.975539i	$-0.429451\pi$
$761$	12.1284			0.439653			0.219826	+	0.975539i	$0.429451\pi$
$762$		0			0
$763$	15.6218	−	13.1082i	0.565547	−	0.474550i
$764$		0			0
$765$	−0.400330	−	0.145708i	−0.0144740	−	0.00526809i
$766$		0			0
$767$	−0.201867	+	0.349643i	−0.00728898	+	0.0126249i
$768$		0			0
$769$	−4.71806	+	26.7575i	−0.170138	+	0.964899i	0.773470	+	0.633833i	$0.218519\pi$
$769$	−4.71806	+	26.7575i	−0.170138	+	0.964899i	−0.943608	+	0.331066i	$0.892592\pi$
$770$		0			0
$771$	7.62108	+	13.2001i	0.274467	+	0.475390i
$772$		0			0
$773$	9.99660	+	8.38814i	0.359553	+	0.301700i	0.804612	−	0.593800i	$-0.202373\pi$
$773$	9.99660	+	8.38814i	0.359553	+	0.301700i	−0.445060	+	0.895501i	$0.646818\pi$
$774$		0			0
$775$	7.52229	−	2.73789i	0.270209	−	0.0983479i
$776$		0			0
$777$	−3.03003	−	17.1842i	−0.108702	−	0.616478i
$778$		0			0
$779$	14.5851	−	41.0091i	0.522566	−	1.46931i
$780$		0			0
$781$	2.31592	+	13.1343i	0.0828702	+	0.469980i
$782$		0			0
$783$	55.0890	−	20.0508i	1.96872	−	0.716556i
$784$		0			0
$785$	7.76991	+	6.51973i	0.277320	+	0.232699i
$786$		0			0
$787$	−20.5942	−	35.6702i	−0.734104	−	1.27151i	−0.955115	−	0.296234i	$-0.904269\pi$
$787$	−20.5942	−	35.6702i	−0.734104	−	1.27151i	0.221011	−	0.975271i	$-0.429064\pi$
$788$		0			0
$789$	−4.33157	+	24.5655i	−0.154208	+	0.874556i
$790$		0			0
$791$	−4.75877	+	8.24243i	−0.169202	+	0.293067i
$792$		0			0
$793$	15.2875	+	5.56418i	0.542873	+	0.197590i
$794$		0			0
$795$	−17.1309	+	14.3745i	−0.607570	+	0.509812i
$796$		0			0
$797$	−4.20676			−0.149011			−0.0745055	−	0.997221i	$-0.523738\pi$
$797$	−4.20676			−0.149011			−0.0745055	+	0.997221i	$0.523738\pi$
$798$		0			0
$799$	−1.79561			−0.0635240
$800$		0			0
$801$	2.29813	−	1.92836i	0.0812005	−	0.0681354i
$802$		0			0
$803$	29.8221	+	10.8543i	1.05240	+	0.383042i
$804$		0			0
$805$	5.70961	−	9.88933i	0.201237	−	0.348553i
$806$		0			0
$807$	−3.78905	+	21.4888i	−0.133381	+	0.756440i
$808$		0			0
$809$	16.4263	+	28.4512i	0.577519	+	1.00029i	0.995763	+	0.0919574i	$0.0293124\pi$
$809$	16.4263	+	28.4512i	0.577519	+	1.00029i	−0.418244	+	0.908335i	$0.637354\pi$
$810$		0			0
$811$	25.9215	+	21.7507i	0.910227	+	0.763771i	0.972162	−	0.234309i	$-0.0752828\pi$
$811$	25.9215	+	21.7507i	0.910227	+	0.763771i	−0.0619354	+	0.998080i	$0.519727\pi$
$812$		0			0
$813$	36.6844	−	13.3520i	1.28658	−	0.468276i
$814$		0			0
$815$	−7.33915	−	41.6224i	−0.257079	−	1.45797i
$816$		0			0
$817$	29.7670	−	5.47497i	1.04141	−	0.191545i
$818$		0			0
$819$	0.358441	+	2.03282i	0.0125249	+	0.0710324i
$820$		0			0
$821$	−1.22446	+	0.445667i	−0.0427340	+	0.0155539i	−0.363299	−	0.931673i	$-0.618350\pi$
$821$	−1.22446	+	0.445667i	−0.0427340	+	0.0155539i	0.320565	+	0.947227i	$0.396127\pi$
$822$		0			0
$823$	−40.9188	−	34.3350i	−1.42634	−	1.19684i	−0.947837	−	0.318755i	$-0.896735\pi$
$823$	−40.9188	−	34.3350i	−1.42634	−	1.19684i	−0.478503	−	0.878086i	$-0.658820\pi$
$824$		0			0
$825$	2.32114	+	4.02033i	0.0808116	+	0.139970i
$826$		0			0
$827$	7.74211	−	43.9077i	0.269219	−	1.52682i	−0.487525	−	0.873109i	$-0.662100\pi$
$827$	7.74211	−	43.9077i	0.269219	−	1.52682i	0.756745	−	0.653710i	$-0.226789\pi$
$828$		0			0
$829$	−0.677052	+	1.17269i	−0.0235150	+	0.0407291i	−0.877543	−	0.479497i	$-0.840819\pi$
$829$	−0.677052	+	1.17269i	−0.0235150	+	0.0407291i	0.854028	+	0.520226i	$0.174152\pi$
$830$		0			0
$831$	−16.2062	−	5.89858i	−0.562187	−	0.204619i
$832$		0			0
$833$	−0.728741	+	0.611486i	−0.0252494	+	0.0211867i
$834$		0			0
$835$	33.3063			1.15261
$836$		0			0
$837$	−30.5185			−1.05487
$838$		0			0
$839$	−33.0094	+	27.6982i	−1.13961	+	0.956247i	−0.999426	−	0.0338785i	$-0.989214\pi$
$839$	−33.0094	+	27.6982i	−1.13961	+	0.956247i	−0.140185	+	0.990125i	$0.544770\pi$
$840$		0			0
$841$	−75.8701	−	27.6145i	−2.61621	−	0.952223i
$842$		0			0
$843$	−1.75284	+	3.03601i	−0.0603710	+	0.104566i
$844$		0			0
$845$	3.47653	−	19.7164i	0.119596	−	0.678264i
$846$		0			0
$847$	−6.95542	−	12.0471i	−0.238991	−	0.413945i
$848$		0			0
$849$	9.13223	+	7.66285i	0.313417	+	0.262988i
$850$		0			0
$851$	15.2618	−	5.55483i	0.523167	−	0.190417i
$852$		0			0
$853$	−7.00387	−	39.7209i	−0.239808	−	1.36002i	−0.832248	−	0.554404i	$-0.812946\pi$
$853$	−7.00387	−	39.7209i	−0.239808	−	1.36002i	0.592440	−	0.805615i	$-0.298165\pi$
$854$		0			0
$855$	−0.0393628	−	5.34684i	−0.00134618	−	0.182858i
$856$		0			0
$857$	−4.72344	−	26.7880i	−0.161350	−	0.915059i	−0.952749	−	0.303759i	$-0.901758\pi$
$857$	−4.72344	−	26.7880i	−0.161350	−	0.915059i	0.791399	−	0.611300i	$-0.209353\pi$
$858$		0			0
$859$	−16.1116	+	5.86414i	−0.549720	+	0.200082i	−0.601922	−	0.798555i	$-0.705598\pi$
$859$	−16.1116	+	5.86414i	−0.549720	+	0.200082i	0.0522020	+	0.998637i	$0.483376\pi$
$860$		0			0
$861$	24.1909	+	20.2986i	0.824425	+	0.691775i
$862$		0			0
$863$	19.1117	+	33.1025i	0.650571	+	1.12682i	0.982984	+	0.183689i	$0.0588039\pi$
$863$	19.1117	+	33.1025i	0.650571	+	1.12682i	−0.332413	+	0.943134i	$0.607863\pi$
$864$		0			0
$865$	6.25624	−	35.4809i	0.212719	−	1.20639i
$866$		0			0
$867$	12.9304	−	22.3960i	0.439138	−	0.760609i
$868$		0			0
$869$	24.4329	+	8.89284i	0.828829	+	0.301669i
$870$		0			0
$871$	−8.26470	+	6.93491i	−0.280039	+	0.234980i
$872$		0			0
$873$	−1.13341			−0.0383600
$874$		0			0
$875$	−25.0915			−0.848248
$876$		0			0
$877$	5.37030	−	4.50622i	0.181342	−	0.152164i	−0.547598	−	0.836742i	$-0.684458\pi$
$877$	5.37030	−	4.50622i	0.181342	−	0.152164i	0.728940	+	0.684577i	$0.240013\pi$
$878$		0			0
$879$	5.89306	+	2.14490i	0.198768	+	0.0723456i
$880$		0			0
$881$	14.2743	−	24.7237i	0.480912	−	0.832964i	−0.518848	−	0.854866i	$-0.673639\pi$
$881$	14.2743	−	24.7237i	0.480912	−	0.832964i	0.999760	+	0.0219027i	$0.00697240\pi$
$882$		0			0
$883$	−2.67206	+	15.1540i	−0.0899218	+	0.509972i	0.906264	+	0.422713i	$0.138922\pi$
$883$	−2.67206	+	15.1540i	−0.0899218	+	0.509972i	−0.996186	+	0.0872594i	$0.972189\pi$
$884$		0			0
$885$	0.379385	+	0.657115i	0.0127529	+	0.0220887i
$886$		0			0
$887$	34.4277	+	28.8882i	1.15597	+	0.969972i	0.999842	−	0.0177648i	$-0.00565501\pi$
$887$	34.4277	+	28.8882i	1.15597	+	0.969972i	0.156126	+	0.987737i	$0.450099\pi$
$888$		0			0
$889$	18.1079	−	6.59073i	0.607319	−	0.221046i
$890$		0			0
$891$	−2.37140	−	13.4489i	−0.0794448	−	0.450554i
$892$		0			0
$893$	−7.86366	−	21.1201i	−0.263147	−	0.706758i
$894$		0			0
$895$	1.48380	+	8.41507i	0.0495981	+	0.281285i
$896$		0			0
$897$	6.49273	−	2.36316i	0.216786	−	0.0789036i
$898$		0			0
$899$	43.7622	+	36.7209i	1.45955	+	1.22471i
$900$		0			0
$901$	−1.34864	−	2.33591i	−0.0449297	−	0.0778206i
$902$		0			0
$903$	−3.81315	+	21.6254i	−0.126894	+	0.719649i
$904$		0			0
$905$	−14.2554	+	24.6910i	−0.473864	+	0.820757i
$906$		0			0
$907$	42.4420	+	15.4476i	1.40926	+	0.512930i	0.930913	−	0.365240i	$-0.119013\pi$
$907$	42.4420	+	15.4476i	1.40926	+	0.512930i	0.478349	+	0.878170i	$0.341235\pi$
$908$		0			0
$909$	4.99273	−	4.18939i	0.165598	−	0.138953i
$910$		0			0
$911$	−47.2336			−1.56492			−0.782460	−	0.622701i	$-0.786035\pi$
$911$	−47.2336			−1.56492			−0.782460	+	0.622701i	$0.786035\pi$
$912$		0			0
$913$	−27.0392			−0.894867
$914$		0			0
$915$	23.4217	−	19.6532i	0.774299	−	0.649714i
$916$		0			0
$917$	−25.6327	−	9.32954i	−0.846466	−	0.308088i
$918$		0			0
$919$	18.3375	−	31.7615i	0.604898	−	1.04771i	−0.387169	−	0.922009i	$-0.626547\pi$
$919$	18.3375	−	31.7615i	0.604898	−	1.04771i	0.992068	−	0.125706i	$-0.0401195\pi$
$920$		0			0
$921$	4.53596	−	25.7247i	0.149465	−	0.847658i
$922$		0			0
$923$	−4.94949	−	8.57277i	−0.162915	−	0.282176i
$924$		0			0
$925$	−6.20439	−	5.20610i	−0.203999	−	0.171176i
$926$		0			0
$927$	−0.788638	+	0.287041i	−0.0259023	+	0.00942765i
$928$		0			0
$929$	−1.55463	−	8.81672i	−0.0510056	−	0.289267i	0.948626	−	0.316399i	$-0.102474\pi$
$929$	−1.55463	−	8.81672i	−0.0510056	−	0.289267i	−0.999632	+	0.0271316i	$0.991363\pi$
$930$		0			0
$931$	−10.3838	−	5.89360i	−0.340316	−	0.193155i
$932$		0			0
$933$	−4.80587	−	27.2555i	−0.157337	−	0.892304i
$934$		0			0
$935$	1.26604	−	0.460802i	0.0414041	−	0.0150699i
$936$		0			0
$937$	2.75949	+	2.31548i	0.0901485	+	0.0756435i	0.686748	−	0.726895i	$-0.259038\pi$
$937$	2.75949	+	2.31548i	0.0901485	+	0.0756435i	−0.596600	+	0.802539i	$0.703482\pi$
$938$		0			0
$939$	2.42855	+	4.20637i	0.0792527	+	0.137270i
$940$		0			0
$941$	4.62654	−	26.2384i	0.150821	−	0.855349i	−0.811686	−	0.584093i	$-0.801450\pi$
$941$	4.62654	−	26.2384i	0.150821	−	0.855349i	0.962507	−	0.271255i	$-0.0874387\pi$
$942$		0			0
$943$	−14.6964	+	25.4549i	−0.478581	+	0.828926i
$944$		0			0
$945$	20.4008	+	7.42528i	0.663638	+	0.241544i
$946$		0			0
$947$	−38.9857	+	32.7129i	−1.26686	+	1.06303i	−0.271949	+	0.962312i	$0.587668\pi$
$947$	−38.9857	+	32.7129i	−1.26686	+	1.06303i	−0.994915	+	0.100713i	$0.967887\pi$
$948$		0			0
$949$	−23.5553			−0.764638
$950$		0			0
$951$	−23.5553			−0.763833
$952$		0			0
$953$	31.8391	−	26.7162i	1.03137	−	0.865423i	0.0403576	−	0.999185i	$-0.487150\pi$
$953$	31.8391	−	26.7162i	1.03137	−	0.865423i	0.991013	+	0.133762i	$0.0427058\pi$
$954$		0			0
$955$	24.0993	+	8.77141i	0.779834	+	0.283836i
$956$		0			0
$957$	−16.5646	+	28.6908i	−0.535459	+	0.927442i
$958$		0			0
$959$	7.84246	−	44.4768i	0.253246	−	1.43623i
$960$		0			0
$961$	0.630415	+	1.09191i	0.0203360	+	0.0352229i
$962$		0			0
$963$	0.337496	+	0.283193i	0.0108757	+	0.00912576i
$964$		0			0
$965$	−16.4868	+	6.00070i	−0.530729	+	0.193169i
$966$		0			0
$967$	8.79503	+	49.8791i	0.282829	+	1.60400i	0.712938	+	0.701227i	$0.247364\pi$
$967$	8.79503	+	49.8791i	0.282829	+	1.60400i	−0.430109	+	0.902777i	$0.641525\pi$
$968$		0			0
$969$	−2.28699	−	0.385920i	−0.0734687	−	0.0123975i
$970$		0			0
$971$	2.52822	+	14.3382i	0.0811344	+	0.460136i	0.998124	+	0.0612249i	$0.0195007\pi$
$971$	2.52822	+	14.3382i	0.0811344	+	0.460136i	−0.916990	+	0.398911i	$0.869388\pi$
$972$		0			0
$973$	39.9504	−	14.5408i	1.28075	−	0.466156i
$974$		0			0
$975$	−2.63950	−	2.21480i	−0.0845316	−	0.0709305i
$976$		0			0
$977$	6.51548	+	11.2851i	0.208449	+	0.361044i	0.951226	−	0.308495i	$-0.0998252\pi$
$977$	6.51548	+	11.2851i	0.208449	+	0.361044i	−0.742777	+	0.669539i	$0.766492\pi$
$978$		0			0
$979$	−1.64749	+	9.34337i	−0.0526540	+	0.298616i
$980$		0			0
$981$	−3.22416	+	5.58440i	−0.102939	+	0.178296i
$982$		0			0
$983$	9.39141	+	3.41819i	0.299539	+	0.109023i	0.487418	−	0.873169i	$-0.337939\pi$
$983$	9.39141	+	3.41819i	0.299539	+	0.109023i	−0.187878	+	0.982192i	$0.560161\pi$
$984$		0			0
$985$	−6.68866	+	5.61245i	−0.213119	+	0.178828i
$986$		0			0
$987$	16.3509			0.520455
$988$		0			0
$989$	−20.4388			−0.649917
$990$		0			0
$991$	40.5337	−	34.0118i	1.28760	−	1.08042i	0.295448	−	0.955359i	$-0.404531\pi$
$991$	40.5337	−	34.0118i	1.28760	−	1.08042i	0.992149	−	0.125063i	$-0.0399133\pi$
$992$		0			0
$993$	37.0146	+	13.4722i	1.17462	+	0.427528i
$994$		0			0
$995$	−0.405078	+	0.701615i	−0.0128418	+	0.0222427i
$996$		0			0
$997$	−7.28430	+	41.3113i	−0.230696	+	1.30834i	0.620795	+	0.783973i	$0.286810\pi$
$997$	−7.28430	+	41.3113i	−0.230696	+	1.30834i	−0.851491	+	0.524370i	$0.824301\pi$
$998$		0			0
$999$	15.4388	+	26.7408i	0.488462	+	0.846042i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.2.u.d.161.1		6
4.3	odd	2		152.2.q.a.9.1	✓	6
19.6	even	9		5776.2.a.bl.1.3		3
19.13	odd	18		5776.2.a.bm.1.1		3
19.17	even	9	inner	304.2.u.d.17.1		6
76.51	even	18		2888.2.a.p.1.3		3
76.55	odd	18		152.2.q.a.17.1	yes	6
76.63	odd	18		2888.2.a.q.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.q.a.9.1	✓	6	4.3	odd	2
152.2.q.a.17.1	yes	6	76.55	odd	18
304.2.u.d.17.1		6	19.17	even	9	inner
304.2.u.d.161.1		6	1.1	even	1	trivial
2888.2.a.p.1.3		3	76.51	even	18
2888.2.a.q.1.1		3	76.63	odd	18
5776.2.a.bl.1.3		3	19.6	even	9
5776.2.a.bm.1.1		3	19.13	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	304.u (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.17365 - 0.984808i) q^{3} +(1.76604 + 0.642788i) q^{5} +(1.03209 - 1.78763i) q^{7} +(-0.113341 + 0.642788i) q^{9} +(-1.03209 - 1.78763i) q^{11} +(1.17365 + 0.984808i) q^{13} +(2.70574 - 0.984808i) q^{15} +(0.0603074 + 0.342020i) q^{17} +(-3.75877 + 2.20718i) q^{19} +(-0.549163 - 3.11446i) q^{21} +(2.76604 - 1.00676i) q^{23} +(-1.12449 - 0.943555i) q^{25} +(2.79813 + 4.84651i) q^{27} +(1.81908 - 10.3165i) q^{29} +(-2.72668 + 4.72275i) q^{31} +(-2.97178 - 1.08164i) q^{33} +(2.97178 - 2.49362i) q^{35} +5.51754 q^{37} +2.34730 q^{39} +(-7.64930 + 6.41852i) q^{41} +(-6.52481 - 2.37484i) q^{43} +(-0.613341 + 1.06234i) q^{45} +(-0.897804 + 5.09170i) q^{47} +(1.36959 + 2.37219i) q^{49} +(0.407604 + 0.342020i) q^{51} +(-7.29813 + 2.65630i) q^{53} +(-0.673648 - 3.82045i) q^{55} +(-2.23783 + 6.29212i) q^{57} +(0.0457595 + 0.259515i) q^{59} +(9.97818 - 3.63176i) q^{61} +(1.03209 + 0.866025i) q^{63} +(1.43969 + 2.49362i) q^{65} +(-1.22281 + 6.93491i) q^{67} +(2.25490 - 3.90560i) q^{69} +(-6.07145 - 2.20983i) q^{71} +(-11.7777 + 9.88263i) q^{73} -2.24897 q^{75} -4.26083 q^{77} +(-9.64930 + 8.09672i) q^{79} +(6.21688 + 2.26276i) q^{81} +(6.54963 - 11.3443i) q^{83} +(-0.113341 + 0.642788i) q^{85} +(-8.02481 - 13.8994i) q^{87} +(-3.52094 - 2.95442i) q^{89} +(2.97178 - 1.08164i) q^{91} +(1.45084 + 8.22811i) q^{93} +(-8.05690 + 1.48189i) q^{95} +(0.301537 + 1.71010i) q^{97} +(1.26604 - 0.460802i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{3} + 6 q^{5} - 3 q^{7} + 6 q^{9} + 3 q^{11} + 6 q^{13} + 6 q^{15} + 6 q^{17} - 15 q^{21} + 12 q^{23} + 6 q^{25} + 3 q^{27} - 6 q^{29} - 3 q^{31} - 3 q^{33} + 3 q^{35} - 12 q^{37} + 12 q^{39}+ \cdots + 3 q^{99}+O(q^{100}) \) 6 * q + 6 * q^3 + 6 * q^5 - 3 * q^7 + 6 * q^9 + 3 * q^11 + 6 * q^13 + 6 * q^15 + 6 * q^17 - 15 * q^21 + 12 * q^23 + 6 * q^25 + 3 * q^27 - 6 * q^29 - 3 * q^31 - 3 * q^33 + 3 * q^35 - 12 * q^37 + 12 * q^39 - 6 * q^41 - 12 * q^43 + 3 * q^45 - 6 * q^47 - 6 * q^49 + 6 * q^51 - 30 * q^53 - 3 * q^55 + 6 * q^57 - 30 * q^59 + 6 * q^61 - 3 * q^63 + 3 * q^65 - 18 * q^67 + 15 * q^69 - 36 * q^71 + 6 * q^73 + 12 * q^75 - 54 * q^77 - 18 * q^79 + 21 * q^81 - 15 * q^83 + 6 * q^85 - 21 * q^87 - 18 * q^89 + 3 * q^91 - 3 * q^93 - 12 * q^95 + 30 * q^97 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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