LMFDB - Embedded newform 513.2.t.a.179.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [513,2,Mod(179,513)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(513, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("513.179"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 513 = 3^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	513.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.09632562369$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 171)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			179.16
Character	$\chi$	$=$	513.179
Dual form			513.2.t.a.278.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.15080 q^{2} +2.62595 q^{4} +(2.61989 - 1.51259i) q^{5} +(1.86959 + 3.23822i) q^{7} +1.34630 q^{8} +(5.63486 - 3.25329i) q^{10} +(-4.41421 + 2.54855i) q^{11} -2.07051i q^{13} +(4.02111 + 6.96477i) q^{14} -2.35628 q^{16} +(-4.50968 - 2.60366i) q^{17} +(4.31830 - 0.593520i) q^{19} +(6.87970 - 3.97200i) q^{20} +(-9.49410 + 5.48142i) q^{22} -6.34770i q^{23} +(2.07588 - 3.59553i) q^{25} -4.45327i q^{26} +(4.90944 + 8.50340i) q^{28} +(-0.805794 + 1.39568i) q^{29} +(1.31340 + 0.758293i) q^{31} -7.76049 q^{32} +(-9.69943 - 5.59997i) q^{34} +(9.79622 + 5.65585i) q^{35} +4.54399i q^{37} +(9.28782 - 1.27654i) q^{38} +(3.52715 - 2.03640i) q^{40} +(-1.01280 - 1.75421i) q^{41} -1.94650 q^{43} +(-11.5915 + 6.69236i) q^{44} -13.6527i q^{46} +(2.96939 + 1.71438i) q^{47} +(-3.49070 + 6.04608i) q^{49} +(4.46481 - 7.73327i) q^{50} -5.43707i q^{52} +(-4.49378 - 7.78345i) q^{53} +(-7.70983 + 13.3538i) q^{55} +(2.51702 + 4.35961i) q^{56} +(-1.73310 + 3.00183i) q^{58} +(3.60454 + 6.24324i) q^{59} +(3.87522 - 6.71208i) q^{61} +(2.82487 + 1.63094i) q^{62} -11.9787 q^{64} +(-3.13185 - 5.42452i) q^{65} +0.658050i q^{67} +(-11.8422 - 6.83709i) q^{68} +(21.0697 + 12.1646i) q^{70} +(-2.68449 + 4.64968i) q^{71} +(-1.90331 + 3.29663i) q^{73} +9.77323i q^{74} +(11.3397 - 1.55855i) q^{76} +(-16.5055 - 9.52945i) q^{77} +10.4891i q^{79} +(-6.17320 + 3.56410i) q^{80} +(-2.17832 - 3.77297i) q^{82} +(4.06246 - 2.34546i) q^{83} -15.7531 q^{85} -4.18654 q^{86} +(-5.94284 + 3.43110i) q^{88} +(1.49289 + 2.58575i) q^{89} +(6.70478 - 3.87100i) q^{91} -16.6688i q^{92} +(6.38657 + 3.68729i) q^{94} +(10.4157 - 8.08679i) q^{95} -5.46067i q^{97} +(-7.50782 + 13.0039i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 6 q^{2} + 30 q^{4} + 3 q^{5} - q^{7} + 12 q^{8} - 6 q^{10} + 9 q^{11} + 3 q^{14} + 18 q^{16} - 27 q^{17} + q^{19} - 9 q^{20} - 6 q^{22} + 11 q^{25} + 2 q^{28} + 12 q^{29} - 12 q^{31} + 30 q^{32}+ \cdots - 84 q^{98}+O(q^{100}) $ 36 * q + 6 * q^2 + 30 * q^4 + 3 * q^5 - q^7 + 12 * q^8 - 6 * q^10 + 9 * q^11 + 3 * q^14 + 18 * q^16 - 27 * q^17 + q^19 - 9 * q^20 - 6 * q^22 + 11 * q^25 + 2 * q^28 + 12 * q^29 - 12 * q^31 + 30 * q^32 - 21 * q^34 + 15 * q^35 + 36 * q^38 - 30 * q^40 - 18 * q^41 - 6 * q^43 + 66 * q^44 - 45 * q^47 - 9 * q^49 + 3 * q^50 - 12 * q^53 - 7 * q^55 + 6 * q^56 - 6 * q^58 + 9 * q^59 + 8 * q^61 - 12 * q^62 + 12 * q^64 - 18 * q^65 - 60 * q^68 - 24 * q^70 + 9 * q^71 - 18 * q^73 + 10 * q^76 + 6 * q^77 - 12 * q^80 - 9 * q^82 + 9 * q^83 - 22 * q^85 - 102 * q^86 - 3 * q^88 - 18 * q^89 + 27 * q^91 - 12 * q^94 + 21 * q^95 - 84 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/513\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	2.15080			1.52085			0.760424	−	0.649427i	$-0.224991\pi$
$2$	2.15080			1.52085			0.760424	+	0.649427i	$0.224991\pi$
$3$		0			0
$3$		0			0
$4$	2.62595			1.31298
$5$	2.61989	−	1.51259i	1.17165	−	0.676452i	0.217582	−	0.976042i	$-0.430183\pi$
$5$	2.61989	−	1.51259i	1.17165	−	0.676452i	0.954068	+	0.299590i	$0.0968497\pi$
$6$		0			0
$7$	1.86959	+	3.23822i	0.706637	+	1.22393i	0.966097	+	0.258178i	$0.0831220\pi$
$7$	1.86959	+	3.23822i	0.706637	+	1.22393i	−0.259460	+	0.965754i	$0.583545\pi$
$8$	1.34630			0.475988
$9$		0			0
$10$	5.63486	−	3.25329i	1.78190	−	1.02878i
$11$	−4.41421	+	2.54855i	−1.33093	+	0.768415i	−0.985443	−	0.170006i	$-0.945621\pi$
$11$	−4.41421	+	2.54855i	−1.33093	+	0.768415i	−0.345492	+	0.938422i	$0.612288\pi$
$12$		0			0
$13$		−	2.07051i		−	0.574257i	−0.957892	−	0.287129i	$-0.907299\pi$
$13$		−	2.07051i		−	0.574257i	0.957892	−	0.287129i	$-0.0927007\pi$
$14$	4.02111	+	6.96477i	1.07469	+	1.86141i
$15$		0			0
$16$	−2.35628			−0.589071
$17$	−4.50968	−	2.60366i	−1.09376	−	0.631481i	−0.159183	−	0.987249i	$-0.550886\pi$
$17$	−4.50968	−	2.60366i	−1.09376	−	0.631481i	−0.934574	+	0.355768i	$0.884219\pi$
$18$		0			0
$19$	4.31830	−	0.593520i	0.990686	−	0.136163i
$19$	4.31830	−	0.593520i	0.990686	−	0.136163i
$20$	6.87970	−	3.97200i	1.53835	−	0.888166i
$21$		0			0
$22$	−9.49410	+	5.48142i	−2.02415	+	1.16864i
$23$		−	6.34770i		−	1.32359i	−0.749686	−	0.661794i	$-0.769795\pi$
$23$		−	6.34770i		−	1.32359i	0.749686	−	0.661794i	$-0.230205\pi$
$24$		0			0
$25$	2.07588	−	3.59553i	0.415176	−	0.719106i
$26$		−	4.45327i		−	0.873357i
$27$		0			0
$28$	4.90944	+	8.50340i	0.927797	+	1.60699i
$29$	−0.805794	+	1.39568i	−0.149632	+	0.259171i	−0.931092	−	0.364786i	$-0.881142\pi$
$29$	−0.805794	+	1.39568i	−0.149632	+	0.259171i	0.781459	+	0.623956i	$0.214476\pi$
$30$		0			0
$31$	1.31340	+	0.758293i	0.235894	+	0.136194i	0.613288	−	0.789859i	$-0.289846\pi$
$31$	1.31340	+	0.758293i	0.235894	+	0.136194i	−0.377394	+	0.926053i	$0.623180\pi$
$32$	−7.76049			−1.37187
$33$		0			0
$34$	−9.69943	−	5.59997i	−1.66344	−	0.960386i
$35$	9.79622	+	5.65585i	1.65586	+	0.956013i
$36$		0			0
$37$			4.54399i			0.747028i	0.927625	+	0.373514i	$0.121847\pi$
$37$			4.54399i			0.747028i	−0.927625	+	0.373514i	$0.878153\pi$
$38$	9.28782	−	1.27654i	1.50668	−	0.207083i
$39$		0			0
$40$	3.52715	−	2.03640i	0.557692	−	0.321983i
$41$	−1.01280	−	1.75421i	−0.158172	−	0.273962i	0.776037	−	0.630687i	$-0.217227\pi$
$41$	−1.01280	−	1.75421i	−0.158172	−	0.273962i	−0.934210	+	0.356725i	$0.883893\pi$
$42$		0			0
$43$	−1.94650			−0.296838			−0.148419	−	0.988925i	$-0.547418\pi$
$43$	−1.94650			−0.296838			−0.148419	+	0.988925i	$0.547418\pi$
$44$	−11.5915	+	6.69236i	−1.74748	+	1.00891i
$45$		0			0
$46$		−	13.6527i		−	2.01297i
$47$	2.96939	+	1.71438i	0.433130	+	0.250068i	0.700679	−	0.713476i	$-0.252880\pi$
$47$	2.96939	+	1.71438i	0.433130	+	0.250068i	−0.267549	+	0.963544i	$0.586214\pi$
$48$		0			0
$49$	−3.49070	+	6.04608i	−0.498672	+	0.863725i
$50$	4.46481	−	7.73327i	0.631419	−	1.09365i
$51$		0			0
$52$		−	5.43707i		−	0.753986i
$53$	−4.49378	−	7.78345i	−0.617268	−	1.06914i	−0.989982	−	0.141193i	$-0.954906\pi$
$53$	−4.49378	−	7.78345i	−0.617268	−	1.06914i	0.372714	−	0.927946i	$-0.378427\pi$
$54$		0			0
$55$	−7.70983	+	13.3538i	−1.03959	+	1.80063i
$56$	2.51702	+	4.35961i	0.336351	+	0.582577i
$57$		0			0
$58$	−1.73310	+	3.00183i	−0.227568	+	0.394159i
$59$	3.60454	+	6.24324i	0.469271	+	0.812800i	0.999383	−	0.0351270i	$-0.0111836\pi$
$59$	3.60454	+	6.24324i	0.469271	+	0.812800i	−0.530112	+	0.847927i	$0.677850\pi$
$60$		0			0
$61$	3.87522	−	6.71208i	0.496171	−	0.859394i	−0.503819	−	0.863809i	$-0.668072\pi$
$61$	3.87522	−	6.71208i	0.496171	−	0.859394i	0.999990	+	0.00441560i	$0.00140553\pi$
$62$	2.82487	+	1.63094i	0.358759	+	0.207129i
$63$		0			0
$64$	−11.9787			−1.49734
$65$	−3.13185	−	5.42452i	−0.388458	−	0.672829i
$66$		0			0
$67$			0.658050i			0.0803936i	0.999192	+	0.0401968i	$0.0127985\pi$
$67$			0.658050i			0.0803936i	−0.999192	+	0.0401968i	$0.987202\pi$
$68$	−11.8422	−	6.83709i	−1.43608	−	0.829119i
$69$		0			0
$70$	21.0697	+	12.1646i	2.51831	+	1.45395i
$71$	−2.68449	+	4.64968i	−0.318591	+	0.551815i	−0.980194	−	0.198039i	$-0.936543\pi$
$71$	−2.68449	+	4.64968i	−0.318591	+	0.551815i	0.661604	+	0.749854i	$0.269876\pi$
$72$		0			0
$73$	−1.90331	+	3.29663i	−0.222765	+	0.385841i	−0.955647	−	0.294516i	$-0.904842\pi$
$73$	−1.90331	+	3.29663i	−0.222765	+	0.385841i	0.732881	+	0.680357i	$0.238175\pi$
$74$			9.77323i			1.13612i
$75$		0			0
$76$	11.3397	−	1.55855i	1.30075	−	0.178778i
$77$	−16.5055	−	9.52945i	−1.88098	−	1.08598i
$78$		0			0
$79$			10.4891i			1.18012i	0.807360	+	0.590059i	$0.200895\pi$
$79$			10.4891i			1.18012i	−0.807360	+	0.590059i	$0.799105\pi$
$80$	−6.17320	+	3.56410i	−0.690185	+	0.398478i
$81$		0			0
$82$	−2.17832	−	3.77297i	−0.240556	−	0.416655i
$83$	4.06246	−	2.34546i	0.445913	−	0.257448i	−0.260190	−	0.965558i	$-0.583785\pi$
$83$	4.06246	−	2.34546i	0.445913	−	0.257448i	0.706102	+	0.708110i	$0.250452\pi$
$84$		0			0
$85$	−15.7531			−1.70867
$86$	−4.18654			−0.451446
$87$		0			0
$88$	−5.94284	+	3.43110i	−0.633509	+	0.365757i
$89$	1.49289	+	2.58575i	0.158246	+	0.274089i	0.934236	−	0.356655i	$-0.116083\pi$
$89$	1.49289	+	2.58575i	0.158246	+	0.274089i	−0.775991	+	0.630745i	$0.782750\pi$
$90$		0			0
$91$	6.70478	−	3.87100i	0.702851	−	0.405791i
$92$		−	16.6688i		−	1.73784i
$93$		0			0
$94$	6.38657	+	3.68729i	0.658725	+	0.380315i
$95$	10.4157	−	8.08679i	1.06863	−	0.829687i
$96$		0			0
$97$		−	5.46067i		−	0.554447i	−0.960805	−	0.277224i	$-0.910586\pi$
$97$		−	5.46067i		−	0.554447i	0.960805	−	0.277224i	$-0.0894143\pi$
$98$	−7.50782	+	13.0039i	−0.758404	+	1.31359i
$99$		0			0
$100$	5.45116	−	9.44168i	0.545116	−	0.944168i
$101$	1.39704	+	0.806582i	0.139011	+	0.0802579i	0.567892	−	0.823103i	$-0.307759\pi$
$101$	1.39704	+	0.806582i	0.139011	+	0.0802579i	−0.428882	+	0.903361i	$0.641092\pi$
$102$		0			0
$103$	−9.11427	−	5.26213i	−0.898056	−	0.518493i	−0.0214871	−	0.999769i	$-0.506840\pi$
$103$	−9.11427	−	5.26213i	−0.898056	−	0.518493i	−0.876569	+	0.481276i	$0.840173\pi$
$104$		−	2.78753i		−	0.273340i
$105$		0			0
$106$	−9.66523	−	16.7407i	−0.938770	−	1.62600i
$107$	10.3237			0.998028			0.499014	−	0.866594i	$-0.333696\pi$
$107$	10.3237			0.998028			0.499014	+	0.866594i	$0.333696\pi$
$108$		0			0
$109$	−5.10016	−	2.94458i	−0.488506	−	0.282039i	0.235448	−	0.971887i	$-0.424344\pi$
$109$	−5.10016	−	2.94458i	−0.488506	−	0.282039i	−0.723955	+	0.689848i	$0.757677\pi$
$110$	−16.5823	+	28.7214i	−1.58106	+	2.73848i
$111$		0			0
$112$	−4.40527	−	7.63016i	−0.416259	−	0.720982i
$113$	−7.68377	+	13.3087i	−0.722828	+	1.25197i	0.237034	+	0.971501i	$0.423825\pi$
$113$	−7.68377	+	13.3087i	−0.722828	+	1.25197i	−0.959862	+	0.280473i	$0.909509\pi$
$114$		0			0
$115$	−9.60150	−	16.6303i	−0.895344	−	1.55078i
$116$	−2.11598	+	3.66498i	−0.196464	+	0.340285i
$117$		0			0
$118$	7.75264	+	13.4280i	0.713689	+	1.23615i
$119$		−	19.4711i		−	1.78491i
$120$		0			0
$121$	7.49017	−	12.9734i	0.680925	−	1.17940i
$122$	8.33483	−	14.4364i	0.754600	−	1.30701i
$123$		0			0
$124$	3.44893	+	1.99124i	0.309723	+	0.178819i
$125$			2.56609i			0.229518i
$126$		0			0
$127$	1.69680	−	0.979649i	0.150567	−	0.0869298i	−0.422824	−	0.906212i	$-0.638961\pi$
$127$	1.69680	−	0.979649i	0.150567	−	0.0869298i	0.573391	+	0.819282i	$0.305628\pi$
$128$	−10.2429			−0.905351
$129$		0			0
$130$	−6.73598	−	11.6671i	−0.590785	−	1.02327i
$131$	−11.2918	+	6.51931i	−0.986567	+	0.569595i	−0.904246	−	0.427011i	$-0.859566\pi$
$131$	−11.2918	+	6.51931i	−0.986567	+	0.569595i	−0.0823204	+	0.996606i	$0.526233\pi$
$132$		0			0
$133$	9.99538	+	12.8740i	0.866710	+	1.11631i
$134$			1.41534i			0.122266i
$135$		0			0
$136$	−6.07137	−	3.50531i	−0.520616	−	0.300578i
$137$	9.92118	+	5.72800i	0.847624	+	0.489376i	0.859848	−	0.510549i	$-0.170558\pi$
$137$	9.92118	+	5.72800i	0.847624	+	0.489376i	−0.0122245	+	0.999925i	$0.503891\pi$
$138$		0			0
$139$	18.5228			1.57108			0.785541	−	0.618810i	$-0.212385\pi$
$139$	18.5228			1.57108			0.785541	+	0.618810i	$0.212385\pi$
$140$	25.7244	+	14.8520i	2.17411	+	1.25522i
$141$		0			0
$142$	−5.77381	+	10.0005i	−0.484528	+	0.839226i
$143$	5.27680	+	9.13968i	0.441268	+	0.764299i
$144$		0			0
$145$			4.87536i			0.404876i
$146$	−4.09364	+	7.09039i	−0.338792	+	0.586805i
$147$		0			0
$148$			11.9323i			0.980830i
$149$	6.30799	−	3.64192i	0.516771	−	0.298358i	−0.218842	−	0.975760i	$-0.570228\pi$
$149$	6.30799	−	3.64192i	0.516771	−	0.298358i	0.735612	+	0.677403i	$0.236894\pi$
$150$		0			0
$151$	−1.90838	+	1.10180i	−0.155302	+	0.0896635i	−0.575637	−	0.817705i	$-0.695246\pi$
$151$	−1.90838	+	1.10180i	−0.155302	+	0.0896635i	0.420335	+	0.907369i	$0.361913\pi$
$152$	5.81372	−	0.799054i	0.471555	−	0.0648118i
$153$		0			0
$154$	−35.5001	−	20.4960i	−2.86068	−	1.65161i
$155$	4.58796			0.368514
$156$		0			0
$157$	6.78596	+	11.7536i	0.541579	+	0.938041i	0.998814	+	0.0486957i	$0.0155064\pi$
$157$	6.78596	+	11.7536i	0.541579	+	0.938041i	−0.457235	+	0.889346i	$0.651160\pi$
$158$			22.5600i			1.79478i
$159$		0			0
$160$	−20.3316	+	11.7385i	−1.60736	+	0.928008i
$161$	20.5552	−	11.8676i	1.61998	−	0.935296i
$162$		0			0
$163$	3.00114			0.235067			0.117534	−	0.993069i	$-0.462501\pi$
$163$	3.00114			0.235067			0.117534	+	0.993069i	$0.462501\pi$
$164$	−2.65955	−	4.60648i	−0.207676	−	0.359706i
$165$		0			0
$166$	8.73755	−	5.04462i	0.678165	−	0.391539i
$167$	5.96291			0.461424			0.230712	−	0.973022i	$-0.425894\pi$
$167$	5.96291			0.461424			0.230712	+	0.973022i	$0.425894\pi$
$168$		0			0
$169$	8.71297			0.670229
$170$	−33.8819			−2.59862
$171$		0			0
$172$	−5.11141			−0.389742
$173$	−18.7882			−1.42844			−0.714220	−	0.699921i	$-0.753218\pi$
$173$	−18.7882			−1.42844			−0.714220	+	0.699921i	$0.753218\pi$
$174$		0			0
$175$	15.5241			1.17351
$176$	10.4011	−	6.00509i	0.784014	−	0.452651i
$177$		0			0
$178$	3.21090	+	5.56144i	0.240667	+	0.416848i
$179$	14.8755			1.11184			0.555922	−	0.831235i	$-0.312365\pi$
$179$	14.8755			1.11184			0.555922	+	0.831235i	$0.312365\pi$
$180$		0			0
$181$	−3.85625	+	2.22640i	−0.286633	+	0.165487i	−0.636422	−	0.771341i	$-0.719586\pi$
$181$	−3.85625	+	2.22640i	−0.286633	+	0.165487i	0.349790	+	0.936828i	$0.386253\pi$
$182$	14.4206	−	8.32577i	1.06893	−	0.617147i
$183$		0			0
$184$		−	8.54590i		−	0.630012i
$185$	6.87322	+	11.9048i	0.505329	+	0.875255i
$186$		0			0
$187$	26.5422			1.94096
$188$	7.79748	+	4.50187i	0.568689	+	0.328333i
$189$		0			0
$190$	22.4022	−	17.3931i	1.62522	−	1.26183i
$191$	20.1652	−	11.6424i	1.45910	−	0.842414i	0.460136	−	0.887848i	$-0.347801\pi$
$191$	20.1652	−	11.6424i	1.45910	−	0.842414i	0.998967	+	0.0454345i	$0.0144672\pi$
$192$		0			0
$193$	19.5461	−	11.2849i	1.40696	−	0.812308i	0.411865	−	0.911245i	$-0.364878\pi$
$193$	19.5461	−	11.2849i	1.40696	−	0.812308i	0.995094	+	0.0989370i	$0.0315442\pi$
$194$		−	11.7448i		−	0.843230i
$195$		0			0
$196$	−9.16642	+	15.8767i	−0.654744	+	1.13405i
$197$		−	2.10025i		−	0.149637i	−0.997197	−	0.0748184i	$-0.976162\pi$
$197$		−	2.10025i		−	0.149637i	0.997197	−	0.0748184i	$-0.0238377\pi$
$198$		0			0
$199$	−6.81724	−	11.8078i	−0.483261	−	0.837033i	0.516554	−	0.856255i	$-0.327215\pi$
$199$	−6.81724	−	11.8078i	−0.483261	−	0.837033i	−0.999815	+	0.0192216i	$0.993881\pi$
$200$	2.79475	−	4.84065i	0.197619	−	0.342286i
$201$		0			0
$202$	3.00476	+	1.73480i	0.211414	+	0.122060i
$203$	−6.02601			−0.422943
$204$		0			0
$205$	−5.30683	−	3.06390i	−0.370645	−	0.213992i
$206$	−19.6030	−	11.3178i	−1.36581	−	0.788548i
$207$		0			0
$208$			4.87871i			0.338278i
$209$	−17.5493	+	13.6253i	−1.21391	+	0.942482i
$210$		0			0
$211$	−23.7174	+	13.6933i	−1.63277	+	0.942683i	−0.649542	+	0.760325i	$0.725039\pi$
$211$	−23.7174	+	13.6933i	−1.63277	+	0.942683i	−0.983232	+	0.182357i	$0.941627\pi$
$212$	−11.8004	−	20.4390i	−0.810458	−	1.40375i
$213$		0			0
$214$	22.2042			1.51785
$215$	−5.09961	+	2.94426i	−0.347791	+	0.200797i
$216$		0			0
$217$			5.67078i			0.384958i
$218$	−10.9694	−	6.33320i	−0.742943	−	0.428939i
$219$		0			0
$220$	−20.2456	+	35.0665i	−1.36496	+	2.36418i
$221$	−5.39092	+	9.33735i	−0.362633	+	0.628098i
$222$		0			0
$223$			2.30986i			0.154679i	0.997005	+	0.0773397i	$0.0246426\pi$
$223$			2.30986i			0.154679i	−0.997005	+	0.0773397i	$0.975357\pi$
$224$	−14.5089	−	25.1302i	−0.969417	−	1.67908i
$225$		0			0
$226$	−16.5263	+	28.6243i	−1.09931	+	1.90406i
$227$	5.87376	+	10.1737i	0.389855	+	0.675249i	0.992430	−	0.122813i	$-0.0391917\pi$
$227$	5.87376	+	10.1737i	0.389855	+	0.675249i	−0.602574	+	0.798063i	$0.705858\pi$
$228$		0			0
$229$	−3.31652	+	5.74438i	−0.219162	+	0.379599i	−0.954552	−	0.298045i	$-0.903666\pi$
$229$	−3.31652	+	5.74438i	−0.219162	+	0.379599i	0.735390	+	0.677644i	$0.236999\pi$
$230$	−20.6509	−	35.7684i	−1.36168	−	2.35850i
$231$		0			0
$232$	−1.08484	+	1.87900i	−0.0712232	+	0.123362i
$233$	−3.13882	−	1.81220i	−0.205631	−	0.118721i	0.393648	−	0.919261i	$-0.371213\pi$
$233$	−3.13882	−	1.81220i	−0.205631	−	0.118721i	−0.599279	+	0.800540i	$0.704546\pi$
$234$		0			0
$235$	10.3726			0.676636
$236$	9.46533	+	16.3944i	0.616141	+	1.06719i
$237$		0			0
$238$		−	41.8785i		−	2.71458i
$239$	−13.1428	−	7.58803i	−0.850140	−	0.490829i	0.0105580	−	0.999944i	$-0.496639\pi$
$239$	−13.1428	−	7.58803i	−0.850140	−	0.490829i	−0.860698	+	0.509116i	$0.829973\pi$
$240$		0			0
$241$	−21.2378	−	12.2617i	−1.36805	−	0.789844i	−0.377371	−	0.926062i	$-0.623172\pi$
$241$	−21.2378	−	12.2617i	−1.36805	−	0.789844i	−0.990679	+	0.136218i	$0.956505\pi$
$242$	16.1099	−	27.9031i	1.03558	−	1.79368i
$243$		0			0
$244$	10.1761	−	17.6256i	0.651461	−	1.12836i
$245$			21.1201i			1.34931i
$246$		0			0
$247$	−1.22889	−	8.94110i	−0.0781924	−	0.568909i
$248$	1.76823	+	1.02089i	0.112283	+	0.0648265i
$249$		0			0
$250$			5.51915i			0.349061i
$251$	−3.73240	+	2.15490i	−0.235587	+	0.136016i	−0.613147	−	0.789969i	$-0.710097\pi$
$251$	−3.73240	+	2.15490i	−0.235587	+	0.136016i	0.377560	+	0.925985i	$0.376763\pi$
$252$		0			0
$253$	16.1774	+	28.0201i	1.01707	+	1.76161i
$254$	3.64949	−	2.10703i	0.228989	−	0.132207i
$255$		0			0
$256$	1.92703			0.120439
$257$	25.2532			1.57525			0.787626	−	0.616154i	$-0.211310\pi$
$257$	25.2532			1.57525			0.787626	+	0.616154i	$0.211310\pi$
$258$		0			0
$259$	−14.7144	+	8.49539i	−0.914311	+	0.527878i
$260$	−8.22408	−	14.2445i	−0.510036	−	0.883408i
$261$		0			0
$262$	−24.2864	+	14.0217i	−1.50042	+	0.866266i
$263$		−	20.1838i		−	1.24459i	−0.782784	−	0.622293i	$-0.786201\pi$
$263$		−	20.1838i		−	1.24459i	0.782784	−	0.622293i	$-0.213799\pi$
$264$		0			0
$265$	−23.5464	−	13.5945i	−1.44644	−	0.835105i
$266$	21.4981	+	27.6894i	1.31813	+	1.69774i
$267$		0			0
$268$			1.72801i			0.105555i
$269$	−2.92165	+	5.06044i	−0.178136	+	0.308540i	−0.941242	−	0.337733i	$-0.890340\pi$
$269$	−2.92165	+	5.06044i	−0.178136	+	0.308540i	0.763106	+	0.646273i	$0.223673\pi$
$270$		0			0
$271$	7.53980	−	13.0593i	0.458010	−	0.793297i	−0.540845	−	0.841122i	$-0.681896\pi$
$271$	7.53980	−	13.0593i	0.458010	−	0.793297i	0.998856	+	0.0478248i	$0.0152289\pi$
$272$	10.6261	+	6.13497i	0.644300	+	0.371987i
$273$		0			0
$274$	21.3385	+	12.3198i	1.28911	+	0.744266i
$275$			21.1619i			1.27611i
$276$		0			0
$277$	−8.02211	−	13.8947i	−0.482002	−	0.834852i	0.517785	−	0.855511i	$-0.326757\pi$
$277$	−8.02211	−	13.8947i	−0.482002	−	0.834852i	−0.999787	+	0.0206591i	$0.993424\pi$
$278$	39.8388			2.38937
$279$		0			0
$280$	13.1886	+	7.61446i	0.788171	+	0.455051i
$281$	8.49793	−	14.7188i	0.506944	−	0.878052i	−0.493024	−	0.870016i	$-0.664108\pi$
$281$	8.49793	−	14.7188i	0.506944	−	0.878052i	0.999968	−	0.00803669i	$-0.00255819\pi$
$282$		0			0
$283$	7.76431	+	13.4482i	0.461540	+	0.799411i	0.999038	−	0.0438543i	$-0.0139637\pi$
$283$	7.76431	+	13.4482i	0.461540	+	0.799411i	−0.537498	+	0.843265i	$0.680630\pi$
$284$	−7.04935	+	12.2098i	−0.418302	+	0.724520i
$285$		0			0
$286$	11.3494	+	19.6577i	0.671101	+	1.16238i
$287$	3.78702	−	6.55931i	0.223541	−	0.387184i
$288$		0			0
$289$	5.05813	+	8.76093i	0.297537	+	0.515349i
$290$			10.4859i			0.615755i
$291$		0			0
$292$	−4.99800	+	8.65678i	−0.292486	+	0.506600i
$293$	−15.1343	+	26.2134i	−0.884156	+	1.53140i	−0.0374772	+	0.999297i	$0.511932\pi$
$293$	−15.1343	+	26.2134i	−0.884156	+	1.53140i	−0.846678	+	0.532105i	$0.821401\pi$
$294$		0			0
$295$	18.8870	+	10.9044i	1.09964	+	0.634878i
$296$			6.11757i			0.355576i
$297$		0			0
$298$	13.5672	−	7.83305i	0.785929	−	0.453757i
$299$	−13.1430			−0.760080
$300$		0			0
$301$	−3.63915	−	6.30319i	−0.209757	−	0.363310i
$302$	−4.10455	+	2.36976i	−0.236190	+	0.136365i
$303$		0			0
$304$	−10.1751	+	1.39850i	−0.583584	+	0.0802095i
$305$		−	23.4465i		−	1.34254i
$306$		0			0
$307$	−24.4373	−	14.1089i	−1.39471	−	0.805235i	−0.400876	−	0.916132i	$-0.631294\pi$
$307$	−24.4373	−	14.1089i	−1.39471	−	0.805235i	−0.993832	+	0.110897i	$0.964628\pi$
$308$	−43.3426	−	25.0239i	−2.46968	−	1.42587i
$309$		0			0
$310$	9.86779			0.560453
$311$	−16.5220	−	9.53896i	−0.936875	−	0.540905i	−0.0478956	−	0.998852i	$-0.515251\pi$
$311$	−16.5220	−	9.53896i	−0.936875	−	0.540905i	−0.888979	+	0.457947i	$0.848585\pi$
$312$		0			0
$313$	5.61840	−	9.73135i	0.317571	−	0.550049i	−0.662410	−	0.749142i	$-0.730466\pi$
$313$	5.61840	−	9.73135i	0.317571	−	0.550049i	0.979981	+	0.199093i	$0.0637996\pi$
$314$	14.5953	+	25.2797i	0.823658	+	1.42662i
$315$		0			0
$316$			27.5439i			1.54947i
$317$	0.188031	−	0.325679i	0.0105608	−	0.0182919i	−0.860697	−	0.509118i	$-0.829972\pi$
$317$	0.188031	−	0.325679i	0.0105608	−	0.0182919i	0.871258	+	0.490826i	$0.163305\pi$
$318$		0			0
$319$		−	8.21441i		−	0.459919i
$320$	−31.3829	+	18.1189i	−1.75436	+	1.01288i
$321$		0			0
$322$	44.2103	−	25.5248i	2.46374	−	1.42244i
$323$	−21.0195	−	8.56682i	−1.16955	−	0.476671i
$324$		0			0
$325$	−7.44459	−	4.29814i	−0.412952	−	0.238418i
$326$	6.45486			0.357501
$327$		0			0
$328$	−1.36353	−	2.36170i	−0.0752881	−	0.130403i
$329$			12.8207i			0.706829i
$330$		0			0
$331$	27.1452	−	15.6723i	1.49204	−	0.861428i	0.492078	−	0.870551i	$-0.336237\pi$
$331$	27.1452	−	15.6723i	1.49204	−	0.861428i	0.999958	+	0.00912336i	$0.00290410\pi$
$332$	10.6678	−	6.15907i	0.585473	−	0.338023i
$333$		0			0
$334$	12.8250			0.701755
$335$	0.995362	+	1.72402i	0.0543825	+	0.0941932i
$336$		0			0
$337$	−0.985879	+	0.569198i	−0.0537043	+	0.0310062i	−0.526612	−	0.850106i	$-0.676538\pi$
$337$	−0.985879	+	0.569198i	−0.0537043	+	0.0310062i	0.472907	+	0.881112i	$0.343204\pi$
$338$	18.7399			1.01932
$339$		0			0
$340$	−41.3670			−2.24344
$341$	−7.73018			−0.418613
$342$		0			0
$343$	0.0695125			0.00375332
$344$	−2.62057			−0.141292
$345$		0			0
$346$	−40.4097			−2.17244
$347$	28.1036	−	16.2256i	1.50868	−	0.871036i	0.508730	−	0.860926i	$-0.330115\pi$
$347$	28.1036	−	16.2256i	1.50868	−	0.871036i	0.999949	−	0.0101104i	$-0.00321829\pi$
$348$		0			0
$349$	−3.78030	−	6.54768i	−0.202355	−	0.350489i	0.746932	−	0.664901i	$-0.231526\pi$
$349$	−3.78030	−	6.54768i	−0.202355	−	0.350489i	−0.949287	+	0.314412i	$0.898193\pi$
$350$	33.3894			1.78474
$351$		0			0
$352$	34.2565	−	19.7780i	1.82587	−	1.05417i
$353$	4.45738	−	2.57347i	0.237242	−	0.136972i	−0.376666	−	0.926349i	$-0.622930\pi$
$353$	4.45738	−	2.57347i	0.237242	−	0.136972i	0.613909	+	0.789377i	$0.289596\pi$
$354$		0			0
$355$			16.2422i			0.862046i
$356$	3.92024	+	6.79006i	0.207773	+	0.359873i
$357$		0			0
$358$	31.9942			1.69094
$359$	5.46349	+	3.15435i	0.288352	+	0.166480i	0.637198	−	0.770700i	$-0.280093\pi$
$359$	5.46349	+	3.15435i	0.288352	+	0.166480i	−0.348846	+	0.937180i	$0.613426\pi$
$360$		0			0
$361$	18.2955	−	5.12599i	0.962919	−	0.269789i
$362$	−8.29402	+	4.78856i	−0.435924	+	0.251681i
$363$		0			0
$364$	17.6064	−	10.1651i	0.922827	−	0.532794i
$365$			11.5157i			0.602761i
$366$		0			0
$367$	−3.71164	+	6.42875i	−0.193746	+	0.335578i	−0.946489	−	0.322737i	$-0.895397\pi$
$367$	−3.71164	+	6.42875i	−0.193746	+	0.335578i	0.752743	+	0.658315i	$0.228730\pi$
$368$			14.9570i			0.779686i
$369$		0			0
$370$	14.7829	+	25.6048i	0.768528	+	1.33113i
$371$	16.8030	−	29.1037i	0.872369	−	1.51099i
$372$		0			0
$373$	−21.2019	−	12.2409i	−1.09779	−	0.633811i	−0.162153	−	0.986766i	$-0.551844\pi$
$373$	−21.2019	−	12.2409i	−1.09779	−	0.633811i	−0.935641	+	0.352954i	$0.885177\pi$
$374$	57.0871			2.95190
$375$		0			0
$376$	3.99768	+	2.30806i	0.206165	+	0.119029i
$377$	2.88977	+	1.66841i	0.148831	+	0.0859274i
$378$		0			0
$379$			27.3088i			1.40276i	0.712788	+	0.701380i	$0.247432\pi$
$379$			27.3088i			1.40276i	−0.712788	+	0.701380i	$0.752568\pi$
$380$	27.3512	−	21.2355i	1.40309	−	1.08936i
$381$		0			0
$382$	43.3714	−	25.0405i	2.21907	−	1.28118i
$383$	0.563982	+	0.976845i	0.0288181	+	0.0499144i	0.880075	−	0.474835i	$-0.157492\pi$
$383$	0.563982	+	0.976845i	0.0288181	+	0.0499144i	−0.851257	+	0.524750i	$0.824159\pi$
$384$		0			0
$385$	−57.6568			−2.93846
$386$	42.0398	−	24.2717i	2.13977	−	1.23540i
$387$		0			0
$388$		−	14.3395i		−	0.727976i
$389$	−1.70122	−	0.982200i	−0.0862553	−	0.0497995i	0.456252	−	0.889851i	$-0.349192\pi$
$389$	−1.70122	−	0.982200i	−0.0862553	−	0.0497995i	−0.542507	+	0.840051i	$0.682525\pi$
$390$		0			0
$391$	−16.5273	+	28.6261i	−0.835821	+	1.44768i
$392$	−4.69953	+	8.13982i	−0.237362	+	0.411123i
$393$		0			0
$394$		−	4.51723i		−	0.227575i
$395$	15.8658	+	27.4803i	0.798293	+	1.38268i
$396$		0			0
$397$	16.7936	−	29.0874i	0.842848	−	1.45985i	−0.0446298	−	0.999004i	$-0.514211\pi$
$397$	16.7936	−	29.0874i	0.842848	−	1.45985i	0.887477	−	0.460851i	$-0.152456\pi$
$398$	−14.6625	−	25.3963i	−0.734966	−	1.27300i
$399$		0			0
$400$	−4.89136	+	8.47208i	−0.244568	+	0.423604i
$401$	−3.07664	−	5.32889i	−0.153640	−	0.266112i	0.778923	−	0.627120i	$-0.215766\pi$
$401$	−3.07664	−	5.32889i	−0.153640	−	0.266112i	−0.932563	+	0.361007i	$0.882433\pi$
$402$		0			0
$403$	1.57006	−	2.71942i	0.0782101	−	0.135464i
$404$	3.66856	+	2.11805i	0.182518	+	0.105377i
$405$		0			0
$406$	−12.9608			−0.643231
$407$	−11.5806	−	20.0581i	−0.574028	−	0.994245i
$408$		0			0
$409$		−	3.74581i		−	0.185218i	−0.995703	−	0.0926091i	$-0.970479\pi$
$409$		−	3.74581i		−	0.185218i	0.995703	−	0.0926091i	$-0.0295207\pi$
$410$	−11.4139	−	6.58984i	−0.563694	−	0.325449i
$411$		0			0
$412$	−23.9336	−	13.8181i	−1.17913	−	0.680769i
$413$	−13.4780	+	23.3445i	−0.663208	+	1.14871i
$414$		0			0
$415$	7.09546	−	12.2897i	0.348302	−	0.603278i
$416$			16.0682i			0.787809i
$417$		0			0
$418$	−37.7450	+	29.3054i	−1.84617	+	1.43337i
$419$	3.16792	+	1.82900i	0.154763	+	0.0893526i	0.575382	−	0.817885i	$-0.304854\pi$
$419$	3.16792	+	1.82900i	0.154763	+	0.0893526i	−0.420618	+	0.907238i	$0.638187\pi$
$420$		0			0
$421$		−	7.39683i		−	0.360499i	−0.983621	−	0.180250i	$-0.942309\pi$
$421$		−	7.39683i		−	0.360499i	0.983621	−	0.180250i	$-0.0576906\pi$
$422$	−51.0115	+	29.4515i	−2.48320	+	1.43368i
$423$		0			0
$424$	−6.04996	−	10.4788i	−0.293812	−	0.508898i
$425$	−18.7231	+	10.8098i	−0.908204	+	0.524352i
$426$		0			0
$427$	28.9802			1.40245
$428$	27.1095			1.31039
$429$		0			0
$430$	−10.9683	+	6.33253i	−0.528936	+	0.305382i
$431$	5.78011	+	10.0114i	0.278418	+	0.482234i	0.970992	−	0.239113i	$-0.0768566\pi$
$431$	5.78011	+	10.0114i	0.278418	+	0.482234i	−0.692574	+	0.721347i	$0.743523\pi$
$432$		0			0
$433$	−2.95790	+	1.70774i	−0.142148	+	0.0820689i	−0.569387	−	0.822070i	$-0.692819\pi$
$433$	−2.95790	+	1.70774i	−0.142148	+	0.0820689i	0.427240	+	0.904138i	$0.359486\pi$
$434$			12.1967i			0.585462i
$435$		0			0
$436$	−13.3928	−	7.73231i	−0.641397	−	0.370311i
$437$	−3.76749	−	27.4113i	−0.180223	−	1.31126i
$438$		0			0
$439$			24.4034i			1.16471i	0.812934	+	0.582355i	$0.197869\pi$
$439$			24.4034i			1.16471i	−0.812934	+	0.582355i	$0.802131\pi$
$440$	−10.3797	+	17.9782i	−0.494834	+	0.857078i
$441$		0			0
$442$	−11.5948	+	20.0828i	−0.551509	+	0.955241i
$443$	−33.7632	−	19.4932i	−1.60414	−	0.926150i	−0.990647	−	0.136448i	$-0.956431\pi$
$443$	−33.7632	−	19.4932i	−1.60414	−	0.926150i	−0.613491	−	0.789702i	$-0.710235\pi$
$444$		0			0
$445$	7.82239	+	4.51626i	0.370817	+	0.214091i
$446$			4.96805i			0.235244i
$447$		0			0
$448$	−22.3953	−	38.7897i	−1.05808	−	1.83264i
$449$	−26.0848			−1.23102			−0.615509	−	0.788130i	$-0.711050\pi$
$449$	−26.0848			−1.23102			−0.615509	+	0.788130i	$0.711050\pi$
$450$		0			0
$451$	8.94139	+	5.16231i	0.421034	+	0.243084i
$452$	−20.1772	+	34.9479i	−0.949056	+	1.64381i
$453$		0			0
$454$	12.6333	+	21.8815i	0.592910	+	1.02695i
$455$	11.7105	−	20.2832i	0.548997	−	0.950891i
$456$		0			0
$457$	8.91236	+	15.4367i	0.416903	+	0.722096i	0.995626	−	0.0934274i	$-0.0297823\pi$
$457$	8.91236	+	15.4367i	0.416903	+	0.722096i	−0.578724	+	0.815524i	$0.696449\pi$
$458$	−7.13318	+	12.3550i	−0.333312	+	0.577313i
$459$		0			0
$460$	−25.2131	−	43.6703i	−1.17557	−	2.03614i
$461$			35.6170i			1.65885i	0.558620	+	0.829424i	$0.311331\pi$
$461$			35.6170i			1.65885i	−0.558620	+	0.829424i	$0.688669\pi$
$462$		0			0
$463$	−5.50447	+	9.53403i	−0.255815	+	0.443084i	−0.965116	−	0.261821i	$-0.915677\pi$
$463$	−5.50447	+	9.53403i	−0.255815	+	0.443084i	0.709302	+	0.704905i	$0.249010\pi$
$464$	1.89868	−	3.28861i	0.0881440	−	0.152670i
$465$		0			0
$466$	−6.75098	−	3.89768i	−0.312733	−	0.180557i
$467$			23.7561i			1.09930i	0.835394	+	0.549651i	$0.185239\pi$
$467$			23.7561i			1.09930i	−0.835394	+	0.549651i	$0.814761\pi$
$468$		0			0
$469$	−2.13091	+	1.23028i	−0.0983963	+	0.0568091i
$470$	22.3095			1.02906
$471$		0			0
$472$	4.85278	+	8.40526i	0.223367	+	0.386883i
$473$	8.59226	−	4.96074i	0.395072	−	0.228095i
$474$		0			0
$475$	6.83026	−	16.7587i	0.313394	−	0.768940i
$476$		−	51.1301i		−	2.34355i
$477$		0			0
$478$	−28.2677	−	16.3203i	−1.29293	−	0.746475i
$479$	35.8666	+	20.7076i	1.63879	+	0.946153i	0.981252	+	0.192728i	$0.0617334\pi$
$479$	35.8666	+	20.7076i	1.63879	+	0.946153i	0.657533	+	0.753425i	$0.271600\pi$
$480$		0			0
$481$	9.40840			0.428986
$482$	−45.6784	−	26.3724i	−2.08059	−	1.20123i
$483$		0			0
$484$	19.6688	−	34.0674i	0.894037	−	1.54852i
$485$	−8.25978	−	14.3064i	−0.375057	−	0.649618i
$486$		0			0
$487$		−	15.0755i		−	0.683134i	−0.939857	−	0.341567i	$-0.889042\pi$
$487$		−	15.0755i		−	0.683134i	0.939857	−	0.341567i	$-0.110958\pi$
$488$	5.21720	−	9.03646i	0.236172	−	0.409061i
$489$		0			0
$490$			45.4251i			2.05210i
$491$	−36.6408	+	21.1546i	−1.65357	+	0.954691i	−0.677988	+	0.735073i	$0.737148\pi$
$491$	−36.6408	+	21.1546i	−1.65357	+	0.954691i	−0.975586	+	0.219619i	$0.929519\pi$
$492$		0			0
$493$	7.26775	−	4.19603i	0.327323	−	0.188980i
$494$	−2.64310	−	19.2306i	−0.118919	−	0.865223i
$495$		0			0
$496$	−3.09475	−	1.78675i	−0.138958	−	0.0802276i
$497$	−20.0756			−0.900512
$498$		0			0
$499$	−21.6295	−	37.4634i	−0.968268	−	1.67709i	−0.700565	−	0.713589i	$-0.747068\pi$
$499$	−21.6295	−	37.4634i	−0.968268	−	1.67709i	−0.267704	−	0.963501i	$-0.586265\pi$
$500$			6.73842i			0.301351i
$501$		0			0
$502$	−8.02766	+	4.63477i	−0.358292	+	0.206860i
$503$	5.29464	−	3.05686i	0.236077	−	0.136299i	−0.377296	−	0.926093i	$-0.623146\pi$
$503$	5.29464	−	3.05686i	0.236077	−	0.136299i	0.613372	+	0.789794i	$0.289813\pi$
$504$		0			0
$505$	4.88012			0.217163
$506$	34.7944	+	60.2657i	1.54680	+	2.67914i
$507$		0			0
$508$	4.45572	−	2.57251i	0.197691	−	0.114137i
$509$	−27.7660			−1.23071			−0.615353	−	0.788252i	$-0.710986\pi$
$509$	−27.7660			−1.23071			−0.615353	+	0.788252i	$0.710986\pi$
$510$		0			0
$511$	−14.2336			−0.629657
$512$	24.6304			1.08852
$513$		0			0
$514$	54.3147			2.39572
$515$	−31.8379			−1.40294
$516$		0			0
$517$	−17.4767			−0.768624
$518$	−31.6479	+	18.2719i	−1.39053	+	0.802821i
$519$		0			0
$520$	−4.21640	−	7.30302i	−0.184901	−	0.320258i
$521$	−3.72919			−0.163379			−0.0816894	−	0.996658i	$-0.526032\pi$
$521$	−3.72919			−0.163379			−0.0816894	+	0.996658i	$0.526032\pi$
$522$		0			0
$523$	−38.8829	+	22.4491i	−1.70023	+	0.981629i	−0.754715	+	0.656053i	$0.772225\pi$
$523$	−38.8829	+	22.4491i	−1.70023	+	0.981629i	−0.945516	+	0.325575i	$0.894442\pi$
$524$	−29.6516	+	17.1194i	−1.29534	+	0.747864i
$525$		0			0
$526$		−	43.4114i		−	1.89283i
$527$	−3.94868	−	6.83932i	−0.172007	−	0.297925i
$528$		0			0
$529$	−17.2933			−0.751884
$530$	−50.6437	−	29.2391i	−2.19982	−	1.27007i
$531$		0			0
$532$	26.2474	+	33.8064i	1.13797	+	1.46569i
$533$	−3.63213	+	2.09701i	−0.157325	+	0.0908315i
$534$		0			0
$535$	27.0469	−	15.6155i	1.16934	−	0.675118i
$536$			0.885931i			0.0382664i
$537$		0			0
$538$	−6.28388	+	10.8840i	−0.270917	+	0.469243i
$539$		−	35.5849i		−	1.53275i
$540$		0			0
$541$	−16.3200	−	28.2670i	−0.701651	−	1.21530i	−0.967887	−	0.251387i	$-0.919113\pi$
$541$	−16.3200	−	28.2670i	−0.701651	−	1.21530i	0.266236	−	0.963908i	$-0.414220\pi$
$542$	16.2166	−	28.0880i	0.696564	−	1.20648i
$543$		0			0
$544$	34.9973	+	20.2057i	1.50050	+	0.866313i
$545$	−17.8158			−0.763145
$546$		0			0
$547$	−8.90948	−	5.14389i	−0.380942	−	0.219937i	0.297286	−	0.954788i	$-0.403918\pi$
$547$	−8.90948	−	5.14389i	−0.380942	−	0.219937i	−0.678228	+	0.734852i	$0.737252\pi$
$548$	26.0525	+	15.0414i	1.11291	+	0.642539i
$549$		0			0
$550$			45.5151i			1.94077i
$551$	−2.65130	+	6.50521i	−0.112949	+	0.277131i
$552$		0			0
$553$	−33.9660	+	19.6103i	−1.44438	+	0.833915i
$554$	−17.2540	−	29.8848i	−0.733051	−	1.26968i
$555$		0			0
$556$	48.6399			2.06279
$557$	1.55437	−	0.897418i	0.0658609	−	0.0380248i	−0.466708	−	0.884411i	$-0.654560\pi$
$557$	1.55437	−	0.897418i	0.0658609	−	0.0380248i	0.532569	+	0.846387i	$0.321227\pi$
$558$		0			0
$559$			4.03025i			0.170462i
$560$	−23.0827	−	13.3268i	−0.975420	−	0.563159i
$561$		0			0
$562$	18.2774	−	31.6573i	0.770984	−	1.33538i
$563$	2.51042	−	4.34817i	0.105801	−	0.183254i	−0.808264	−	0.588820i	$-0.799593\pi$
$563$	2.51042	−	4.34817i	0.105801	−	0.183254i	0.914065	+	0.405567i	$0.132926\pi$
$564$		0			0
$565$			46.4897i			1.95584i
$566$	16.6995	+	28.9244i	0.701932	+	1.21578i
$567$		0			0
$568$	−3.61413	+	6.25985i	−0.151645	+	0.262657i
$569$	−10.4266	−	18.0595i	−0.437107	−	0.757092i	0.560358	−	0.828251i	$-0.310664\pi$
$569$	−10.4266	−	18.0595i	−0.437107	−	0.757092i	−0.997465	+	0.0711585i	$0.977330\pi$
$570$		0			0
$571$	−18.2645	+	31.6350i	−0.764345	+	1.32388i	0.176248	+	0.984346i	$0.443604\pi$
$571$	−18.2645	+	31.6350i	−0.764345	+	1.32388i	−0.940592	+	0.339538i	$0.889729\pi$
$572$	13.8566	+	24.0004i	0.579374	+	1.00351i
$573$		0			0
$574$	8.14513	−	14.1078i	0.339971	−	0.588847i
$575$	−22.8234	−	13.1771i	−0.951800	−	0.549522i
$576$		0			0
$577$	−13.8317			−0.575822			−0.287911	−	0.957657i	$-0.592961\pi$
$577$	−13.8317			−0.575822			−0.287911	+	0.957657i	$0.592961\pi$
$578$	10.8790	+	18.8430i	0.452508	+	0.783767i
$579$		0			0
$580$			12.8025i			0.531593i
$581$	15.1902	+	8.77008i	0.630197	+	0.363844i
$582$		0			0
$583$	39.6730	+	22.9052i	1.64309	+	0.948636i
$584$	−2.56242	+	4.43824i	−0.106034	+	0.183656i
$585$		0			0
$586$	−32.5509	+	56.3798i	−1.34467	+	2.32903i
$587$		−	3.52537i		−	0.145508i	−0.997350	−	0.0727539i	$-0.976821\pi$
$587$		−	3.52537i		−	0.145508i	0.997350	−	0.0727539i	$-0.0231788\pi$
$588$		0			0
$589$	6.12173	+	2.49501i	0.252242	+	0.102805i
$590$	40.6221	+	23.4532i	1.67239	+	0.965553i
$591$		0			0
$592$		−	10.7069i		−	0.440052i
$593$	3.25664	−	1.88022i	0.133734	−	0.0772113i	−0.431640	−	0.902046i	$-0.642065\pi$
$593$	3.25664	−	1.88022i	0.133734	−	0.0772113i	0.565374	+	0.824834i	$0.308732\pi$
$594$		0			0
$595$	−29.4519	−	51.0121i	−1.20741	−	2.09129i
$596$	16.5645	−	9.56351i	0.678508	−	0.391737i
$597$		0			0
$598$	−28.2680			−1.15597
$599$	2.69993			0.110316			0.0551580	−	0.998478i	$-0.482434\pi$
$599$	2.69993			0.110316			0.0551580	+	0.998478i	$0.482434\pi$
$600$		0			0
$601$	−3.51336	+	2.02844i	−0.143313	+	0.0827417i	−0.569942	−	0.821685i	$-0.693034\pi$
$601$	−3.51336	+	2.02844i	−0.143313	+	0.0827417i	0.426629	+	0.904427i	$0.359701\pi$
$602$	−7.82709	−	13.5569i	−0.319008	−	0.552539i
$603$		0			0
$604$	−5.01131	+	2.89328i	−0.203907	+	0.117726i
$605$		−	45.3183i		−	1.84245i
$606$		0			0
$607$	−4.17611	−	2.41108i	−0.169503	−	0.0978627i	0.412848	−	0.910800i	$-0.364534\pi$
$607$	−4.17611	−	2.41108i	−0.169503	−	0.0978627i	−0.582352	+	0.812937i	$0.697867\pi$
$608$	−33.5122	+	4.60600i	−1.35910	+	0.186798i
$609$		0			0
$610$		−	50.4289i		−	2.04181i
$611$	3.54964	−	6.14817i	0.143603	−	0.248728i
$612$		0			0
$613$	4.89396	−	8.47658i	0.197665	−	0.342366i	−0.750106	−	0.661318i	$-0.769997\pi$
$613$	4.89396	−	8.47658i	0.197665	−	0.342366i	0.947771	+	0.318952i	$0.103331\pi$
$614$	−52.5597	−	30.3454i	−2.12114	−	1.22464i
$615$		0			0
$616$	−22.2213	−	12.8295i	−0.895322	−	0.516914i
$617$		−	3.89095i		−	0.156644i	−0.996928	−	0.0783219i	$-0.975044\pi$
$617$		−	3.89095i		−	0.156644i	0.996928	−	0.0783219i	$-0.0249562\pi$
$618$		0			0
$619$	−9.13436	−	15.8212i	−0.367141	−	0.635907i	0.621976	−	0.783036i	$-0.286330\pi$
$619$	−9.13436	−	15.8212i	−0.367141	−	0.635907i	−0.989117	+	0.147129i	$0.952997\pi$
$620$	12.0478			0.483850
$621$		0			0
$622$	−35.5355	−	20.5164i	−1.42484	−	0.822634i
$623$	−5.58216	+	9.66858i	−0.223644	+	0.387363i
$624$		0			0
$625$	14.2608	+	24.7005i	0.570434	+	0.988020i
$626$	12.0841	−	20.9302i	0.482976	−	0.836540i
$627$		0			0
$628$	17.8196	+	30.8645i	0.711079	+	1.23163i
$629$	11.8310	−	20.4919i	0.471734	−	0.817067i
$630$		0			0
$631$	−7.88091	−	13.6501i	−0.313734	−	0.543404i	0.665433	−	0.746457i	$-0.268247\pi$
$631$	−7.88091	−	13.6501i	−0.313734	−	0.543404i	−0.979168	+	0.203054i	$0.934913\pi$
$632$			14.1215i			0.561722i
$633$		0			0
$634$	0.404417	−	0.700470i	0.0160614	−	0.0278192i
$635$	2.96362	−	5.13314i	0.117608	−	0.203703i
$636$		0			0
$637$	12.5185	+	7.22755i	0.496001	+	0.286366i
$638$		−	17.6676i		−	0.699466i
$639$		0			0
$640$	−26.8352	+	15.4933i	−1.06076	+	0.612427i
$641$	7.87357			0.310987			0.155494	−	0.987837i	$-0.450303\pi$
$641$	7.87357			0.310987			0.155494	+	0.987837i	$0.450303\pi$
$642$		0			0
$643$	−14.0900	−	24.4046i	−0.555656	−	0.962424i	−0.997852	−	0.0655057i	$-0.979134\pi$
$643$	−14.0900	−	24.4046i	−0.555656	−	0.962424i	0.442197	−	0.896918i	$-0.354199\pi$
$644$	53.9771	−	31.1637i	2.12700	−	1.22802i
$645$		0			0
$646$	−45.2087	−	18.4255i	−1.77871	−	0.724943i
$647$			41.2832i			1.62301i	0.584346	+	0.811504i	$0.301351\pi$
$647$			41.2832i			1.62301i	−0.584346	+	0.811504i	$0.698649\pi$
$648$		0			0
$649$	−31.8224	−	18.3726i	−1.24914	−	0.721189i
$650$	−16.0118	−	9.24445i	−0.628036	−	0.362597i
$651$		0			0
$652$	7.88084			0.308638
$653$	30.9349	+	17.8602i	1.21057	+	0.698925i	0.962884	−	0.269914i	$-0.0869953\pi$
$653$	30.9349	+	17.8602i	1.21057	+	0.698925i	0.247690	+	0.968839i	$0.420329\pi$
$654$		0			0
$655$	−19.7221	+	34.1597i	−0.770607	+	1.33473i
$656$	2.38643	+	4.13342i	0.0931746	+	0.161383i
$657$		0			0
$658$			27.5748i			1.07498i
$659$	−16.5224	+	28.6176i	−0.643621	+	1.11478i	0.340997	+	0.940064i	$0.389235\pi$
$659$	−16.5224	+	28.6176i	−0.643621	+	1.11478i	−0.984618	+	0.174720i	$0.944098\pi$
$660$		0			0
$661$		−	44.6790i		−	1.73781i	−0.494979	−	0.868905i	$-0.664824\pi$
$661$		−	44.6790i		−	1.73781i	0.494979	−	0.868905i	$-0.335176\pi$
$662$	58.3840	−	33.7080i	2.26916	−	1.31010i
$663$		0			0
$664$	5.46928	−	3.15769i	0.212249	−	0.122542i
$665$	45.6599	+	18.6094i	1.77061	+	0.721642i
$666$		0			0
$667$	8.85934	+	5.11494i	0.343035	+	0.198051i
$668$	15.6583			0.605839
$669$		0			0
$670$	2.14083	+	3.70802i	0.0827074	+	0.143253i
$671$			39.5047i			1.52506i
$672$		0			0
$673$	−15.8318	+	9.14047i	−0.610269	+	0.352339i	−0.773071	−	0.634320i	$-0.781280\pi$
$673$	−15.8318	+	9.14047i	−0.610269	+	0.352339i	0.162802	+	0.986659i	$0.447947\pi$
$674$	−2.12043	+	1.22423i	−0.0816760	+	0.0471556i
$675$		0			0
$676$	22.8798			0.879994
$677$	12.5993	+	21.8227i	0.484232	+	0.838715i	0.999836	−	0.0181123i	$-0.00576565\pi$
$677$	12.5993	+	21.8227i	0.484232	+	0.838715i	−0.515604	+	0.856827i	$0.672432\pi$
$678$		0			0
$679$	17.6829	−	10.2092i	0.678606	−	0.391793i
$680$	−21.2084			−0.813306
$681$		0			0
$682$	−16.6261			−0.636646
$683$	−13.1758			−0.504159			−0.252080	−	0.967706i	$-0.581114\pi$
$683$	−13.1758			−0.504159			−0.252080	+	0.967706i	$0.581114\pi$
$684$		0			0
$685$	34.6565			1.32416
$686$	0.149508			0.00570823
$687$		0			0
$688$	4.58650			0.174859
$689$	−16.1157	+	9.30443i	−0.613961	+	0.354470i
$690$		0			0
$691$	25.6729	+	44.4667i	0.976641	+	1.69159i	0.674409	+	0.738358i	$0.264399\pi$
$691$	25.6729	+	44.4667i	0.976641	+	1.69159i	0.302233	+	0.953234i	$0.402268\pi$
$692$	−49.3369			−1.87551
$693$		0			0
$694$	60.4452	−	34.8981i	2.29447	−	1.32471i
$695$	48.5276	−	28.0174i	1.84076	−	1.06276i
$696$		0			0
$697$			10.5479i			0.399531i
$698$	−8.13069	−	14.0828i	−0.307751	−	0.533040i
$699$		0			0
$700$	40.7656			1.54080
$701$	25.4463	+	14.6914i	0.961092	+	0.554887i	0.896509	−	0.443025i	$-0.146095\pi$
$701$	25.4463	+	14.6914i	0.961092	+	0.554887i	0.0645833	+	0.997912i	$0.479428\pi$
$702$		0			0
$703$	2.69695	+	19.6223i	0.101717	+	0.740071i
$704$	52.8766	−	30.5283i	1.99286	−	1.15058i
$705$		0			0
$706$	9.58693	−	5.53502i	0.360809	−	0.208313i
$707$			6.03190i			0.226853i
$708$		0			0
$709$	−23.0980	+	40.0068i	−0.867462	+	1.50249i	−0.00288007	+	0.999996i	$0.500917\pi$
$709$	−23.0980	+	40.0068i	−0.867462	+	1.50249i	−0.864582	+	0.502492i	$0.832417\pi$
$710$			34.9337i			1.31104i
$711$		0			0
$712$	2.00987	+	3.48119i	0.0753230	+	0.130463i
$713$	4.81342	−	8.33709i	0.180264	−	0.312226i
$714$		0			0
$715$	27.6493	+	15.9633i	1.03402	+	0.596994i
$716$	39.0622			1.45982
$717$		0			0
$718$	11.7509	+	6.78438i	0.438540	+	0.253191i
$719$	−5.87831	−	3.39385i	−0.219224	−	0.126569i	0.386367	−	0.922345i	$-0.373730\pi$
$719$	−5.87831	−	3.39385i	−0.219224	−	0.126569i	−0.605591	+	0.795776i	$0.707063\pi$
$720$		0			0
$721$		−	39.3520i		−	1.46555i
$722$	39.3499	−	11.0250i	1.46445	−	0.410308i
$723$		0			0
$724$	−10.1263	+	5.84643i	−0.376342	+	0.217281i
$725$	3.34546	+	5.79451i	0.124247	+	0.215203i
$726$		0			0
$727$	2.67494			0.0992081			0.0496040	−	0.998769i	$-0.484204\pi$
$727$	2.67494			0.0992081			0.0496040	+	0.998769i	$0.484204\pi$
$728$	9.02663	−	5.21152i	0.334549	−	0.193152i
$729$		0			0
$730$			24.7681i			0.916707i
$731$	8.77808	+	5.06803i	0.324669	+	0.187448i
$732$		0			0
$733$	11.4965	−	19.9126i	0.424634	−	0.735488i	−0.571752	−	0.820426i	$-0.693736\pi$
$733$	11.4965	−	19.9126i	0.424634	−	0.735488i	0.996386	+	0.0849388i	$0.0270695\pi$
$734$	−7.98301	+	13.8270i	−0.294658	+	0.510363i
$735$		0			0
$736$			49.2613i			1.81580i
$737$	−1.67707	−	2.90477i	−0.0617757	−	0.106999i
$738$		0			0
$739$	−14.6521	+	25.3781i	−0.538985	+	0.933550i	0.459974	+	0.887933i	$0.347859\pi$
$739$	−14.6521	+	25.3781i	−0.538985	+	0.933550i	−0.998959	+	0.0456175i	$0.985474\pi$
$740$	18.0487	+	31.2613i	0.663485	+	1.14919i
$741$		0			0
$742$	36.1400	−	62.5962i	1.32674	−	2.29798i
$743$	−6.75825	−	11.7056i	−0.247936	−	0.429438i	0.715017	−	0.699107i	$-0.246419\pi$
$743$	−6.75825	−	11.7056i	−0.247936	−	0.429438i	−0.962953	+	0.269669i	$0.913086\pi$
$744$		0			0
$745$	11.0175	−	19.0829i	0.403650	−	0.699142i
$746$	−45.6011	−	26.3278i	−1.66958	−	0.963930i
$747$		0			0
$748$	69.6986			2.54843
$749$	19.3010	+	33.4303i	0.705243	+	1.22152i
$750$		0			0
$751$			31.6955i			1.15659i	0.815829	+	0.578293i	$0.196281\pi$
$751$			31.6955i			1.15659i	−0.815829	+	0.578293i	$0.803719\pi$
$752$	−6.99672	−	4.03956i	−0.255144	−	0.147308i
$753$		0			0
$754$	6.21532	+	3.58842i	0.226349	+	0.130682i
$755$	−3.33316	+	5.77321i	−0.121306	+	0.210109i
$756$		0			0
$757$	−2.36484	+	4.09603i	−0.0859517	+	0.148873i	−0.905796	−	0.423713i	$-0.860726\pi$
$757$	−2.36484	+	4.09603i	−0.0859517	+	0.148873i	0.819845	+	0.572586i	$0.194060\pi$
$758$			58.7359i			2.13338i
$759$		0			0
$760$	14.0227	−	10.8872i	0.508655	−	0.394921i
$761$	−0.577494	−	0.333416i	−0.0209342	−	0.0120863i	0.489496	−	0.872005i	$-0.337181\pi$
$761$	−0.577494	−	0.333416i	−0.0209342	−	0.0120863i	−0.510431	+	0.859919i	$0.670514\pi$
$762$		0			0
$763$		−	22.0206i		−	0.797198i
$764$	52.9529	−	30.5724i	1.91577	−	1.10607i
$765$		0			0
$766$	1.21301	+	2.10100i	0.0438279	+	0.0759122i
$767$	12.9267	−	7.46324i	0.466757	−	0.269482i
$768$		0			0
$769$	23.8082			0.858546			0.429273	−	0.903175i	$-0.358770\pi$
$769$	23.8082			0.858546			0.429273	+	0.903175i	$0.358770\pi$
$770$	−124.008			−4.46895
$771$		0			0
$772$	51.3271	−	29.6337i	1.84730	−	1.06654i
$773$	−5.80883	−	10.0612i	−0.208929	−	0.361876i	0.742448	−	0.669903i	$-0.233664\pi$
$773$	−5.80883	−	10.0612i	−0.208929	−	0.361876i	−0.951377	+	0.308027i	$0.900331\pi$
$774$		0			0
$775$	5.45293	−	3.14825i	0.195875	−	0.113089i
$776$		−	7.35169i		−	0.263910i
$777$		0			0
$778$	−3.65899	−	2.11252i	−0.131181	−	0.0757375i
$779$	−5.41472	−	6.97411i	−0.194003	−	0.249874i
$780$		0			0
$781$		−	27.3662i		−	0.979240i
$782$	−35.5469	+	61.5691i	−1.27116	+	2.20171i
$783$		0			0
$784$	8.22509	−	14.2463i	0.293753	−	0.508795i
$785$	35.5569	+	20.5288i	1.26908	+	0.732704i
$786$		0			0
$787$	−8.15629	−	4.70904i	−0.290740	−	0.167859i	0.347535	−	0.937667i	$-0.387019\pi$
$787$	−8.15629	−	4.70904i	−0.290740	−	0.167859i	−0.638276	+	0.769808i	$0.720352\pi$
$788$		−	5.51516i		−	0.196470i
$789$		0			0
$790$	34.1241	+	59.1047i	1.21408	+	2.10285i
$791$	−57.4619			−2.04311
$792$		0			0
$793$	−13.8975	−	8.02370i	−0.493513	−	0.284930i
$794$	36.1198	−	62.5613i	1.28184	−	2.22022i
$795$		0			0
$796$	−17.9017	−	31.0067i	−0.634510	−	1.09900i
$797$	22.1959	−	38.4444i	0.786218	−	1.36177i	−0.142051	−	0.989859i	$-0.545370\pi$
$797$	22.1959	−	38.4444i	0.786218	−	1.36177i	0.928269	−	0.371910i	$-0.121297\pi$
$798$		0			0
$799$	−8.92733	−	15.4626i	−0.315826	−	0.547027i
$800$	−16.1099	+	27.9031i	−0.569569	+	0.986523i
$801$		0			0
$802$	−6.61724	−	11.4614i	−0.233663	−	0.404716i
$803$		−	19.4027i		−	0.684706i
$804$		0			0
$805$	35.9016	−	62.1835i	1.26537	−	2.19168i
$806$	3.37688	−	5.84893i	0.118946	−	0.206020i
$807$		0			0
$808$	1.88083	+	1.08590i	0.0661675	+	0.0382018i
$809$		−	4.81244i		−	0.169196i	−0.996415	−	0.0845982i	$-0.973039\pi$
$809$		−	4.81244i		−	0.169196i	0.996415	−	0.0845982i	$-0.0269607\pi$
$810$		0			0
$811$	−17.1253	+	9.88731i	−0.601351	+	0.347190i	−0.769573	−	0.638559i	$-0.779531\pi$
$811$	−17.1253	+	9.88731i	−0.601351	+	0.347190i	0.168222	+	0.985749i	$0.446198\pi$
$812$	−15.8240			−0.555314
$813$		0			0
$814$	−24.9075	−	43.1411i	−0.873009	−	1.51210i
$815$	7.86265	−	4.53950i	0.275417	−	0.159012i
$816$		0			0
$817$	−8.40557	+	1.15529i	−0.294074	+	0.0404183i
$818$		−	8.05649i		−	0.281689i
$819$		0			0
$820$	−13.9355	−	8.04565i	−0.486648	−	0.280966i
$821$	−5.41819	−	3.12820i	−0.189096	−	0.109175i	0.402463	−	0.915436i	$-0.368154\pi$
$821$	−5.41819	−	3.12820i	−0.189096	−	0.109175i	−0.591559	+	0.806261i	$0.701487\pi$
$822$		0			0
$823$	14.2365			0.496255			0.248127	−	0.968727i	$-0.420185\pi$
$823$	14.2365			0.496255			0.248127	+	0.968727i	$0.420185\pi$
$824$	−12.2705	−	7.08439i	−0.427464	−	0.246796i
$825$		0			0
$826$	−28.9885	+	50.2095i	−1.00864	+	1.74701i
$827$	6.98747	+	12.1027i	0.242978	+	0.420851i	0.961561	−	0.274590i	$-0.0885423\pi$
$827$	6.98747	+	12.1027i	0.242978	+	0.420851i	−0.718583	+	0.695441i	$0.755209\pi$
$828$		0			0
$829$			6.20264i			0.215427i	0.994182	+	0.107713i	$0.0343529\pi$
$829$			6.20264i			0.215427i	−0.994182	+	0.107713i	$0.965647\pi$
$830$	15.2609	−	26.4327i	0.529715	−	0.917493i
$831$		0			0
$832$			24.8021i			0.859859i
$833$	31.4839	−	18.1772i	1.09085	−	0.629804i
$834$		0			0
$835$	15.6222	−	9.01946i	0.540628	−	0.312131i
$836$	−46.0836	+	35.7794i	−1.59383	+	1.23746i
$837$		0			0
$838$	6.81358	+	3.93382i	0.235371	+	0.135892i
$839$	22.4066			0.773563			0.386781	−	0.922171i	$-0.373587\pi$
$839$	22.4066			0.773563			0.386781	+	0.922171i	$0.373587\pi$
$840$		0			0
$841$	13.2014	+	22.8655i	0.455220	+	0.788465i
$842$		−	15.9091i		−	0.548264i
$843$		0			0
$844$	−62.2808	+	35.9578i	−2.14379	+	1.23772i
$845$	22.8270	−	13.1792i	0.785273	−	0.453378i
$846$		0			0
$847$	56.0141			1.92467
$848$	10.5886	+	18.3400i	0.363614	+	0.629798i
$849$		0			0
$850$	−40.2697	+	23.2497i	−1.38124	+	0.797459i
$851$	28.8439			0.988757
$852$		0			0
$853$	12.0171			0.411457			0.205728	−	0.978609i	$-0.434044\pi$
$853$	12.0171			0.411457			0.205728	+	0.978609i	$0.434044\pi$
$854$	62.3308			2.13291
$855$		0			0
$856$	13.8987			0.475049
$857$	−36.1476			−1.23478			−0.617389	−	0.786658i	$-0.711810\pi$
$857$	−36.1476			−1.23478			−0.617389	+	0.786658i	$0.711810\pi$
$858$		0			0
$859$	35.6504			1.21637			0.608187	−	0.793794i	$-0.291897\pi$
$859$	35.6504			1.21637			0.608187	+	0.793794i	$0.291897\pi$
$860$	−13.3913	+	7.73149i	−0.456641	+	0.263642i
$861$		0			0
$862$	12.4319	+	21.5326i	0.423431	+	0.733404i
$863$	21.0718			0.717294			0.358647	−	0.933473i	$-0.383238\pi$
$863$	21.0718			0.717294			0.358647	+	0.933473i	$0.383238\pi$
$864$		0			0
$865$	−49.2230	+	28.4189i	−1.67363	+	0.966271i
$866$	−6.36186	+	3.67302i	−0.216185	+	0.124814i
$867$		0			0
$868$			14.8912i			0.505440i
$869$	−26.7320	−	46.3012i	−0.906820	−	1.57066i
$870$		0			0
$871$	1.36250			0.0461666
$872$	−6.86633	−	3.96428i	−0.232523	−	0.134247i
$873$		0			0
$874$	−8.10312	−	58.9563i	−0.274092	−	1.99423i
$875$	−8.30955	+	4.79752i	−0.280914	+	0.162186i
$876$		0			0
$877$	−44.3724	+	25.6184i	−1.49835	+	0.865073i	−0.999998	−	0.00190079i	$-0.999395\pi$
$877$	−44.3724	+	25.6184i	−1.49835	+	0.865073i	−0.498353	+	0.866974i	$0.666062\pi$
$878$			52.4869i			1.77135i
$879$		0			0
$880$	18.1665	−	31.4654i	0.612394	−	1.06070i
$881$			11.1100i			0.374304i	0.982331	+	0.187152i	$0.0599257\pi$
$881$			11.1100i			0.374304i	−0.982331	+	0.187152i	$0.940074\pi$
$882$		0			0
$883$	15.1216	+	26.1914i	0.508883	+	0.881411i	0.999947	+	0.0102875i	$0.00327469\pi$
$883$	15.1216	+	26.1914i	0.508883	+	0.881411i	−0.491064	+	0.871123i	$0.663392\pi$
$884$	−14.1563	+	24.5194i	−0.476128	+	0.824678i
$885$		0			0
$886$	−72.6180	−	41.9260i	−2.43965	−	1.40853i
$887$	−1.29765			−0.0435708			−0.0217854	−	0.999763i	$-0.506935\pi$
$887$	−1.29765			−0.0435708			−0.0217854	+	0.999763i	$0.506935\pi$
$888$		0			0
$889$	6.34463	+	3.66308i	0.212792	+	0.122856i
$890$	16.8244	+	9.71358i	0.563956	+	0.325600i
$891$		0			0
$892$			6.06557i			0.203090i
$893$	13.8402	+	5.64081i	0.463146	+	0.188763i
$894$		0			0
$895$	38.9720	−	22.5005i	1.30269	−	0.752109i
$896$	−19.1500	−	33.1687i	−0.639755	−	1.10809i
$897$		0			0
$898$	−56.1033			−1.87219
$899$	−2.11666	+	1.22206i	−0.0705947	+	0.0407579i
$900$		0			0
$901$			46.8011i			1.55917i
$902$	19.2312	+	11.1031i	0.640328	+	0.369693i
$903$		0			0
$904$	−10.3446	+	17.9174i	−0.344058	+	0.595925i
$905$	−6.73529	+	11.6659i	−0.223889	+	0.387787i
$906$		0			0
$907$		−	35.9791i		−	1.19467i	−0.801993	−	0.597333i	$-0.796227\pi$
$907$		−	35.9791i		−	1.19467i	0.801993	−	0.597333i	$-0.203773\pi$
$908$	15.4242	+	26.7155i	0.511871	+	0.886586i
$909$		0			0
$910$	25.1870	−	43.6252i	0.834941	−	1.44616i
$911$	−6.18966	−	10.7208i	−0.205073	−	0.355196i	0.745083	−	0.666972i	$-0.232410\pi$
$911$	−6.18966	−	10.7208i	−0.205073	−	0.355196i	−0.950156	+	0.311775i	$0.899076\pi$
$912$		0			0
$913$	−11.9550	+	20.7067i	−0.395654	+	0.685292i
$914$	19.1687	+	33.2012i	0.634045	+	1.09820i
$915$		0			0
$916$	−8.70902	+	15.0845i	−0.287754	+	0.498405i
$917$	−42.2219	−	24.3768i	−1.39429	−	0.804993i
$918$		0			0
$919$	−10.1943			−0.336279			−0.168139	−	0.985763i	$-0.553776\pi$
$919$	−10.1943			−0.336279			−0.168139	+	0.985763i	$0.553776\pi$
$920$	−12.9265	−	22.3893i	−0.426173	−	0.738154i
$921$		0			0
$922$			76.6051i			2.52285i
$923$	9.62722	+	5.55828i	0.316884	+	0.182953i
$924$		0			0
$925$	16.3381	+	9.43279i	0.537192	+	0.310148i
$926$	−11.8390	+	20.5058i	−0.389055	+	0.673863i
$927$		0			0
$928$	6.25336	−	10.8311i	0.205277	−	0.355550i
$929$			0.907754i			0.0297824i	0.999889	+	0.0148912i	$0.00474020\pi$
$929$			0.907754i			0.0297824i	−0.999889	+	0.0148912i	$0.995260\pi$
$930$		0			0
$931$	−11.4855	+	28.1806i	−0.376421	+	0.923582i
$932$	−8.24239	−	4.75875i	−0.269989	−	0.155878i
$933$		0			0
$934$			51.0947i			1.67187i
$935$	69.5377	−	40.1476i	2.27413	−	1.31297i
$936$		0			0
$937$	−23.0292	−	39.8878i	−0.752332	−	1.30308i	−0.946690	−	0.322146i	$-0.895596\pi$
$937$	−23.0292	−	39.8878i	−0.752332	−	1.30308i	0.194358	−	0.980931i	$-0.437738\pi$
$938$	−4.58317	+	2.64609i	−0.149646	+	0.0863980i
$939$		0			0
$940$	27.2380			0.888407
$941$	−52.8596			−1.72317			−0.861587	−	0.507610i	$-0.830529\pi$
$941$	−52.8596			−1.72317			−0.861587	+	0.507610i	$0.830529\pi$
$942$		0			0
$943$	−11.1352	+	6.42893i	−0.362613	+	0.209355i
$944$	−8.49330	−	14.7108i	−0.276433	−	0.478797i
$945$		0			0
$946$	18.4803	−	10.6696i	0.600845	−	0.346898i
$947$			6.62284i			0.215214i	0.994194	+	0.107607i	$0.0343187\pi$
$947$			6.62284i			0.215214i	−0.994194	+	0.107607i	$0.965681\pi$
$948$		0			0
$949$	6.82571	+	3.94083i	0.221572	+	0.127925i
$950$	14.6905	−	36.0446i	0.476624	−	1.16944i
$951$		0			0
$952$		−	26.2139i		−	0.849597i
$953$	−7.59011	+	13.1465i	−0.245868	+	0.425855i	−0.962375	−	0.271724i	$-0.912406\pi$
$953$	−7.59011	+	13.1465i	−0.245868	+	0.425855i	0.716508	+	0.697579i	$0.245740\pi$
$954$		0			0
$955$	35.2204	−	61.0035i	1.13971	−	1.97403i
$956$	−34.5125	−	19.9258i	−1.11621	−	0.644446i
$957$		0			0
$958$	77.1419	+	44.5379i	2.49234	+	1.43895i
$959$			42.8359i			1.38324i
$960$		0			0
$961$	−14.3500	−	24.8549i	−0.462903	−	0.801771i
$962$	20.2356			0.652422
$963$		0			0
$964$	−55.7696	−	32.1986i	−1.79622	−	1.03705i
$965$	34.1391	−	59.1306i	1.09898	−	1.90348i
$966$		0			0
$967$	−14.7829	−	25.6048i	−0.475387	−	0.823395i	0.524215	−	0.851586i	$-0.324359\pi$
$967$	−14.7829	−	25.6048i	−0.475387	−	0.823395i	−0.999603	+	0.0281906i	$0.991025\pi$
$968$	10.0840	−	17.4660i	0.324112	−	0.561378i
$969$		0			0
$970$	−17.7652	−	30.7702i	−0.570405	−	0.987970i
$971$	−17.8609	+	30.9360i	−0.573184	+	0.992784i	0.423052	+	0.906105i	$0.360959\pi$
$971$	−17.8609	+	30.9360i	−0.573184	+	0.992784i	−0.996236	+	0.0866789i	$0.972375\pi$
$972$		0			0
$973$	34.6299	+	59.9808i	1.11018	+	1.92290i
$974$		−	32.4243i		−	1.03894i
$975$		0			0
$976$	−9.13111	+	15.8155i	−0.292280	+	0.506243i
$977$	0.303010	−	0.524829i	0.00969416	−	0.0167908i	−0.861138	−	0.508372i	$-0.830248\pi$
$977$	0.303010	−	0.524829i	0.00969416	−	0.0167908i	0.870832	+	0.491581i	$0.163581\pi$
$978$		0			0
$979$	−13.1798	−	7.60937i	−0.421229	−	0.243197i
$980$			55.4603i			1.77161i
$981$		0			0
$982$	−78.8070	+	45.4993i	−2.51483	+	1.45194i
$983$	28.3050			0.902790			0.451395	−	0.892324i	$-0.350927\pi$
$983$	28.3050			0.902790			0.451395	+	0.892324i	$0.350927\pi$
$984$		0			0
$985$	−3.17683	−	5.50243i	−0.101222	−	0.175322i
$986$	15.6315	−	9.02484i	0.497808	−	0.287410i
$987$		0			0
$988$	−3.22701	−	23.4789i	−0.102665	−	0.746964i
$989$			12.3558i			0.392892i
$990$		0			0
$991$	49.4706	+	28.5619i	1.57149	+	0.907298i	0.995987	+	0.0894946i	$0.0285252\pi$
$991$	49.4706	+	28.5619i	1.57149	+	0.907298i	0.575498	+	0.817803i	$0.304808\pi$
$992$	−10.1927	−	5.88473i	−0.323617	−	0.186840i
$993$		0			0
$994$	−43.1786			−1.36954
$995$	−35.7208	−	20.6234i	−1.13243	−	0.653806i
$996$		0			0
$997$	18.3712	−	31.8199i	0.581823	−	1.00775i	−0.413441	−	0.910531i	$-0.635673\pi$
$997$	18.3712	−	31.8199i	0.581823	−	1.00775i	0.995263	−	0.0972153i	$-0.0309935\pi$
$998$	−46.5207	−	80.5763i	−1.47259	−	2.55060i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	513.2.t.a.179.16		36
3.2	odd	2		171.2.t.a.122.3	yes	36
9.2	odd	6		513.2.k.a.8.16		36
9.7	even	3		171.2.k.a.65.3	yes	36
19.12	odd	6		513.2.k.a.449.16		36
57.50	even	6		171.2.k.a.50.3	✓	36
171.88	odd	6		171.2.t.a.164.3	yes	36
171.164	even	6	inner	513.2.t.a.278.16		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.k.a.50.3	✓	36	57.50	even	6
171.2.k.a.65.3	yes	36	9.7	even	3
171.2.t.a.122.3	yes	36	3.2	odd	2
171.2.t.a.164.3	yes	36	171.88	odd	6
513.2.k.a.8.16		36	9.2	odd	6
513.2.k.a.449.16		36	19.12	odd	6
513.2.t.a.179.16		36	1.1	even	1	trivial
513.2.t.a.278.16		36	171.164	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 513 = 3^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	513.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.15080 q^{2} +2.62595 q^{4} +(2.61989 - 1.51259i) q^{5} +(1.86959 + 3.23822i) q^{7} +1.34630 q^{8} +(5.63486 - 3.25329i) q^{10} +(-4.41421 + 2.54855i) q^{11} -2.07051i q^{13} +(4.02111 + 6.96477i) q^{14} -2.35628 q^{16} +(-4.50968 - 2.60366i) q^{17} +(4.31830 - 0.593520i) q^{19} +(6.87970 - 3.97200i) q^{20} +(-9.49410 + 5.48142i) q^{22} -6.34770i q^{23} +(2.07588 - 3.59553i) q^{25} -4.45327i q^{26} +(4.90944 + 8.50340i) q^{28} +(-0.805794 + 1.39568i) q^{29} +(1.31340 + 0.758293i) q^{31} -7.76049 q^{32} +(-9.69943 - 5.59997i) q^{34} +(9.79622 + 5.65585i) q^{35} +4.54399i q^{37} +(9.28782 - 1.27654i) q^{38} +(3.52715 - 2.03640i) q^{40} +(-1.01280 - 1.75421i) q^{41} -1.94650 q^{43} +(-11.5915 + 6.69236i) q^{44} -13.6527i q^{46} +(2.96939 + 1.71438i) q^{47} +(-3.49070 + 6.04608i) q^{49} +(4.46481 - 7.73327i) q^{50} -5.43707i q^{52} +(-4.49378 - 7.78345i) q^{53} +(-7.70983 + 13.3538i) q^{55} +(2.51702 + 4.35961i) q^{56} +(-1.73310 + 3.00183i) q^{58} +(3.60454 + 6.24324i) q^{59} +(3.87522 - 6.71208i) q^{61} +(2.82487 + 1.63094i) q^{62} -11.9787 q^{64} +(-3.13185 - 5.42452i) q^{65} +0.658050i q^{67} +(-11.8422 - 6.83709i) q^{68} +(21.0697 + 12.1646i) q^{70} +(-2.68449 + 4.64968i) q^{71} +(-1.90331 + 3.29663i) q^{73} +9.77323i q^{74} +(11.3397 - 1.55855i) q^{76} +(-16.5055 - 9.52945i) q^{77} +10.4891i q^{79} +(-6.17320 + 3.56410i) q^{80} +(-2.17832 - 3.77297i) q^{82} +(4.06246 - 2.34546i) q^{83} -15.7531 q^{85} -4.18654 q^{86} +(-5.94284 + 3.43110i) q^{88} +(1.49289 + 2.58575i) q^{89} +(6.70478 - 3.87100i) q^{91} -16.6688i q^{92} +(6.38657 + 3.68729i) q^{94} +(10.4157 - 8.08679i) q^{95} -5.46067i q^{97} +(-7.50782 + 13.0039i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{2} + 30 q^{4} + 3 q^{5} - q^{7} + 12 q^{8} - 6 q^{10} + 9 q^{11} + 3 q^{14} + 18 q^{16} - 27 q^{17} + q^{19} - 9 q^{20} - 6 q^{22} + 11 q^{25} + 2 q^{28} + 12 q^{29} - 12 q^{31} + 30 q^{32}+ \cdots - 84 q^{98}+O(q^{100}) \) 36 * q + 6 * q^2 + 30 * q^4 + 3 * q^5 - q^7 + 12 * q^8 - 6 * q^10 + 9 * q^11 + 3 * q^14 + 18 * q^16 - 27 * q^17 + q^19 - 9 * q^20 - 6 * q^22 + 11 * q^25 + 2 * q^28 + 12 * q^29 - 12 * q^31 + 30 * q^32 - 21 * q^34 + 15 * q^35 + 36 * q^38 - 30 * q^40 - 18 * q^41 - 6 * q^43 + 66 * q^44 - 45 * q^47 - 9 * q^49 + 3 * q^50 - 12 * q^53 - 7 * q^55 + 6 * q^56 - 6 * q^58 + 9 * q^59 + 8 * q^61 - 12 * q^62 + 12 * q^64 - 18 * q^65 - 60 * q^68 - 24 * q^70 + 9 * q^71 - 18 * q^73 + 10 * q^76 + 6 * q^77 - 12 * q^80 - 9 * q^82 + 9 * q^83 - 22 * q^85 - 102 * q^86 - 3 * q^88 - 18 * q^89 + 27 * q^91 - 12 * q^94 + 21 * q^95 - 84 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more