LMFDB - Embedded newform 513.2.h.c.235.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [513,2,Mod(235,513)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(513, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 2]))

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

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

chi := DirichletCharacter("513.235");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.09632562369$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 171)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			235.8
Character	$\chi$	$=$	513.235
Dual form			513.2.h.c.334.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.370889 q^{2} -1.86244 q^{4} +(-1.77761 + 3.07890i) q^{5} +(-0.124876 + 0.216291i) q^{7} +1.43254 q^{8} +(0.659294 - 1.14193i) q^{10} +(0.815815 - 1.41303i) q^{11} -1.32541 q^{13} +(0.0463150 - 0.0802199i) q^{14} +3.19357 q^{16} +(-3.73000 - 6.46055i) q^{17} +(-4.07660 + 1.54315i) q^{19} +(3.31069 - 5.73428i) q^{20} +(-0.302577 + 0.524078i) q^{22} +4.49143 q^{23} +(-3.81976 - 6.61602i) q^{25} +0.491582 q^{26} +(0.232573 - 0.402829i) q^{28} +(-2.06363 - 3.57430i) q^{29} +(-4.32871 - 7.49755i) q^{31} -4.04953 q^{32} +(1.38342 + 2.39615i) q^{34} +(-0.443959 - 0.768960i) q^{35} +3.10599 q^{37} +(1.51197 - 0.572336i) q^{38} +(-2.54649 + 4.41064i) q^{40} +(2.77461 - 4.80577i) q^{41} -10.0406 q^{43} +(-1.51941 + 2.63169i) q^{44} -1.66582 q^{46} +(1.68288 + 2.91483i) q^{47} +(3.46881 + 6.00816i) q^{49} +(1.41671 + 2.45381i) q^{50} +2.46851 q^{52} +(-0.254182 + 0.440256i) q^{53} +(2.90039 + 5.02363i) q^{55} +(-0.178889 + 0.309845i) q^{56} +(0.765376 + 1.32567i) q^{58} +(-5.23121 + 9.06071i) q^{59} +(-2.07050 - 3.58621i) q^{61} +(1.60547 + 2.78076i) q^{62} -4.88521 q^{64} +(2.35606 - 4.08082i) q^{65} -0.799350 q^{67} +(6.94690 + 12.0324i) q^{68} +(0.164660 + 0.285199i) q^{70} +(-5.60051 - 9.70037i) q^{71} +(-1.84754 - 3.20004i) q^{73} -1.15198 q^{74} +(7.59244 - 2.87402i) q^{76} +(0.203751 + 0.352907i) q^{77} +9.85529 q^{79} +(-5.67691 + 9.83269i) q^{80} +(-1.02907 + 1.78241i) q^{82} +(-0.185251 + 0.320865i) q^{83} +26.5219 q^{85} +3.72396 q^{86} +(1.16868 - 2.02422i) q^{88} +(-4.01034 + 6.94611i) q^{89} +(0.165512 - 0.286675i) q^{91} -8.36503 q^{92} +(-0.624161 - 1.08108i) q^{94} +(2.49539 - 15.2946i) q^{95} +6.43155 q^{97} +(-1.28654 - 2.22836i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} + 34 q^{4} - 3 q^{5} + q^{7} + 36 q^{8} - 8 q^{10} - 7 q^{11} + 8 q^{13} - q^{14} + 22 q^{16} + 7 q^{17} + 7 q^{19} + 3 q^{20} - 8 q^{22} + 10 q^{23} - 9 q^{25} + 4 q^{26} - 10 q^{28} - 10 q^{29}+ \cdots - 18 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 + 34 * q^4 - 3 * q^5 + q^7 + 36 * q^8 - 8 * q^10 - 7 * q^11 + 8 * q^13 - q^14 + 22 * q^16 + 7 * q^17 + 7 * q^19 + 3 * q^20 - 8 * q^22 + 10 * q^23 - 9 * q^25 + 4 * q^26 - 10 * q^28 - 10 * q^29 - 10 * q^31 + 34 * q^32 - 13 * q^34 + 3 * q^35 + 2 * q^37 + 46 * q^38 + 12 * q^40 - 6 * q^41 - 14 * q^43 - 20 * q^44 + 9 * q^47 - 13 * q^49 - q^50 - 38 * q^52 - 16 * q^53 + 15 * q^55 + 6 * q^56 - 37 * q^59 - 12 * q^61 - 54 * q^62 - 64 * q^64 - 54 * q^65 + 22 * q^67 + 2 * q^68 + 24 * q^70 - 9 * q^71 - 10 * q^73 + 12 * q^74 - 40 * q^76 - 46 * q^77 + 16 * q^79 + 24 * q^80 + 7 * q^82 - 3 * q^83 + 54 * q^85 + 34 * q^86 + 9 * q^88 - 30 * q^89 - q^91 - 34 * q^92 - 18 * q^94 - 3 * q^95 - 18 * q^98

Character values

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

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.370889			−0.262258			−0.131129	−	0.991365i	$-0.541860\pi$
$2$	−0.370889			−0.262258			−0.131129	+	0.991365i	$0.541860\pi$
$3$		0			0
$3$		0			0
$4$	−1.86244			−0.931221
$5$	−1.77761	+	3.07890i	−0.794969	+	1.37693i	0.127889	+	0.991788i	$0.459180\pi$
$5$	−1.77761	+	3.07890i	−0.794969	+	1.37693i	−0.922859	+	0.385139i	$0.874154\pi$
$6$		0			0
$7$	−0.124876	+	0.216291i	−0.0471985	+	0.0817503i	−0.888660	−	0.458568i	$-0.848363\pi$
$7$	−0.124876	+	0.216291i	−0.0471985	+	0.0817503i	0.841461	+	0.540318i	$0.181696\pi$
$8$	1.43254			0.506478
$9$		0			0
$10$	0.659294	−	1.14193i	0.208487	−	0.361110i
$11$	0.815815	−	1.41303i	0.245977	−	0.426045i	−0.716429	−	0.697660i	$-0.754224\pi$
$11$	0.815815	−	1.41303i	0.245977	−	0.426045i	0.962406	+	0.271615i	$0.0875578\pi$
$12$		0			0
$13$	−1.32541			−0.367604			−0.183802	−	0.982963i	$-0.558841\pi$
$13$	−1.32541			−0.367604			−0.183802	+	0.982963i	$0.558841\pi$
$14$	0.0463150	−	0.0802199i	0.0123782	−	0.0214397i
$15$		0			0
$16$	3.19357			0.798393
$17$	−3.73000	−	6.46055i	−0.904658	−	1.56691i	−0.821376	−	0.570387i	$-0.806793\pi$
$17$	−3.73000	−	6.46055i	−0.904658	−	1.56691i	−0.0832816	−	0.996526i	$-0.526540\pi$
$18$		0			0
$19$	−4.07660	+	1.54315i	−0.935237	+	0.354022i
$19$	−4.07660	+	1.54315i	−0.935237	+	0.354022i
$20$	3.31069	−	5.73428i	0.740292	−	1.28222i
$21$		0			0
$22$	−0.302577	+	0.524078i	−0.0645096	+	0.111734i
$23$	4.49143			0.936528			0.468264	−	0.883589i	$-0.344880\pi$
$23$	4.49143			0.936528			0.468264	+	0.883589i	$0.344880\pi$
$24$		0			0
$25$	−3.81976	−	6.61602i	−0.763952	−	1.32320i
$26$	0.491582			0.0964071
$27$		0			0
$28$	0.232573	−	0.402829i	0.0439522	−	0.0761275i
$29$	−2.06363	−	3.57430i	−0.383206	−	0.663732i	0.608313	−	0.793697i	$-0.291847\pi$
$29$	−2.06363	−	3.57430i	−0.383206	−	0.663732i	−0.991518	+	0.129966i	$0.958513\pi$
$30$		0			0
$31$	−4.32871	−	7.49755i	−0.777460	−	1.34660i	−0.933401	−	0.358834i	$-0.883174\pi$
$31$	−4.32871	−	7.49755i	−0.777460	−	1.34660i	0.155941	−	0.987766i	$-0.450159\pi$
$32$	−4.04953			−0.715863
$33$		0			0
$34$	1.38342	+	2.39615i	0.237254	+	0.410936i
$35$	−0.443959	−	0.768960i	−0.0750428	−	0.129978i
$36$		0			0
$37$	3.10599			0.510622			0.255311	−	0.966859i	$-0.417822\pi$
$37$	3.10599			0.510622			0.255311	+	0.966859i	$0.417822\pi$
$38$	1.51197	−	0.572336i	0.245274	−	0.0928452i
$39$		0			0
$40$	−2.54649	+	4.41064i	−0.402635	+	0.697384i
$41$	2.77461	−	4.80577i	0.433322	−	0.750535i	−0.563835	−	0.825887i	$-0.690675\pi$
$41$	2.77461	−	4.80577i	0.433322	−	0.750535i	0.997157	+	0.0753521i	$0.0240081\pi$
$42$		0			0
$43$	−10.0406			−1.53118			−0.765591	−	0.643328i	$-0.777553\pi$
$43$	−10.0406			−1.53118			−0.765591	+	0.643328i	$0.777553\pi$
$44$	−1.51941	+	2.63169i	−0.229059	+	0.396742i
$45$		0			0
$46$	−1.66582			−0.245612
$47$	1.68288	+	2.91483i	0.245473	+	0.425171i	0.962264	−	0.272116i	$-0.0877235\pi$
$47$	1.68288	+	2.91483i	0.245473	+	0.425171i	−0.716792	+	0.697287i	$0.754390\pi$
$48$		0			0
$49$	3.46881	+	6.00816i	0.495545	+	0.858308i
$50$	1.41671	+	2.45381i	0.200353	+	0.347021i
$51$		0			0
$52$	2.46851			0.342320
$53$	−0.254182	+	0.440256i	−0.0349146	+	0.0604739i	−0.882955	−	0.469458i	$-0.844449\pi$
$53$	−0.254182	+	0.440256i	−0.0349146	+	0.0604739i	0.848040	+	0.529932i	$0.177783\pi$
$54$		0			0
$55$	2.90039	+	5.02363i	0.391089	+	0.677386i
$56$	−0.178889	+	0.309845i	−0.0239050	+	0.0414047i
$57$		0			0
$58$	0.765376	+	1.32567i	0.100499	+	0.174069i
$59$	−5.23121	+	9.06071i	−0.681045	+	1.17960i	0.293617	+	0.955923i	$0.405141\pi$
$59$	−5.23121	+	9.06071i	−0.681045	+	1.17960i	−0.974662	+	0.223681i	$0.928192\pi$
$60$		0			0
$61$	−2.07050	−	3.58621i	−0.265100	−	0.459168i	0.702489	−	0.711694i	$-0.252072\pi$
$61$	−2.07050	−	3.58621i	−0.265100	−	0.459168i	−0.967590	+	0.252527i	$0.918738\pi$
$62$	1.60547	+	2.78076i	0.203895	+	0.353157i
$63$		0			0
$64$	−4.88521			−0.610652
$65$	2.35606	−	4.08082i	0.292234	−	0.506164i
$66$		0			0
$67$	−0.799350			−0.0976561			−0.0488281	−	0.998807i	$-0.515549\pi$
$67$	−0.799350			−0.0976561			−0.0488281	+	0.998807i	$0.515549\pi$
$68$	6.94690	+	12.0324i	0.842436	+	1.45914i
$69$		0			0
$70$	0.164660	+	0.285199i	0.0196806	+	0.0340878i
$71$	−5.60051	−	9.70037i	−0.664658	−	1.15122i	−0.979378	−	0.202037i	$-0.935244\pi$
$71$	−5.60051	−	9.70037i	−0.664658	−	1.15122i	0.314719	−	0.949185i	$-0.398090\pi$
$72$		0			0
$73$	−1.84754	−	3.20004i	−0.216239	−	0.374537i	0.737416	−	0.675439i	$-0.236046\pi$
$73$	−1.84754	−	3.20004i	−0.216239	−	0.374537i	−0.953655	+	0.300902i	$0.902712\pi$
$74$	−1.15198			−0.133915
$75$		0			0
$76$	7.59244	−	2.87402i	0.870912	−	0.329673i
$77$	0.203751	+	0.352907i	0.0232195	+	0.0402174i
$78$		0			0
$79$	9.85529			1.10881			0.554403	−	0.832248i	$-0.312947\pi$
$79$	9.85529			1.10881			0.554403	+	0.832248i	$0.312947\pi$
$80$	−5.67691	+	9.83269i	−0.634698	+	1.09933i
$81$		0			0
$82$	−1.02907	+	1.78241i	−0.113642	+	0.196834i
$83$	−0.185251	+	0.320865i	−0.0203340	+	0.0352195i	−0.876013	−	0.482287i	$-0.839806\pi$
$83$	−0.185251	+	0.320865i	−0.0203340	+	0.0352195i	0.855679	+	0.517506i	$0.173140\pi$
$84$		0			0
$85$	26.5219			2.87670
$86$	3.72396			0.401565
$87$		0			0
$88$	1.16868	−	2.02422i	0.124582	−	0.215783i
$89$	−4.01034	+	6.94611i	−0.425095	+	0.736286i	−0.996429	−	0.0844315i	$-0.973093\pi$
$89$	−4.01034	+	6.94611i	−0.425095	+	0.736286i	0.571334	+	0.820717i	$0.306426\pi$
$90$		0			0
$91$	0.165512	−	0.286675i	0.0173504	−	0.0300517i
$92$	−8.36503			−0.872115
$93$		0			0
$94$	−0.624161	−	1.08108i	−0.0643772	−	0.111505i
$95$	2.49539	−	15.2946i	0.256022	−	1.56919i
$96$		0			0
$97$	6.43155			0.653024			0.326512	−	0.945193i	$-0.394127\pi$
$97$	6.43155			0.653024			0.326512	+	0.945193i	$0.394127\pi$
$98$	−1.28654	−	2.22836i	−0.129961	−	0.225098i
$99$		0			0
$100$	7.11408	+	12.3220i	0.711408	+	1.23220i
$101$	3.78177	+	6.55021i	0.376300	+	0.651771i	0.990521	−	0.137364i	$-0.0438629\pi$
$101$	3.78177	+	6.55021i	0.376300	+	0.651771i	−0.614221	+	0.789134i	$0.710530\pi$
$102$		0			0
$103$	−6.90927	−	11.9672i	−0.680791	−	1.17916i	−0.974740	−	0.223343i	$-0.928303\pi$
$103$	−6.90927	−	11.9672i	−0.680791	−	1.17916i	0.293949	−	0.955821i	$-0.405030\pi$
$104$	−1.89871			−0.186183
$105$		0			0
$106$	0.0942734	−	0.163286i	0.00915664	−	0.0158598i
$107$	−12.0119			−1.16123			−0.580616	−	0.814177i	$-0.697188\pi$
$107$	−12.0119			−1.16123			−0.580616	+	0.814177i	$0.697188\pi$
$108$		0			0
$109$	−7.62598	−	13.2086i	−0.730436	−	1.26515i	−0.956697	−	0.291086i	$-0.905984\pi$
$109$	−7.62598	−	13.2086i	−0.730436	−	1.26515i	0.226261	−	0.974067i	$-0.427350\pi$
$110$	−1.07572	−	1.86321i	−0.102566	−	0.177650i
$111$		0			0
$112$	−0.398799	+	0.690740i	−0.0376830	+	0.0652688i
$113$	1.46481	+	2.53713i	0.137798	+	0.238673i	0.926663	−	0.375894i	$-0.122664\pi$
$113$	1.46481	+	2.53713i	0.137798	+	0.238673i	−0.788865	+	0.614567i	$0.789331\pi$
$114$		0			0
$115$	−7.98399	+	13.8287i	−0.744511	+	1.28953i
$116$	3.84338	+	6.65693i	0.356849	+	0.618081i
$117$		0			0
$118$	1.94020	−	3.36052i	0.178610	−	0.309361i
$119$	1.86314			0.170794
$120$		0			0
$121$	4.16889	+	7.22073i	0.378990	+	0.656430i
$122$	0.767926	+	1.33009i	0.0695248	+	0.120420i
$123$		0			0
$124$	8.06198	+	13.9638i	0.723987	+	1.25398i
$125$	9.38406			0.839336
$126$		0			0
$127$	−0.949181	+	1.64403i	−0.0842262	+	0.145884i	−0.905061	−	0.425281i	$-0.860175\pi$
$127$	−0.949181	+	1.64403i	−0.0842262	+	0.145884i	0.820835	+	0.571165i	$0.193509\pi$
$128$	9.91094			0.876012
$129$		0			0
$130$	−0.873838	+	1.51353i	−0.0766407	+	0.132746i
$131$	−1.51445	+	2.62310i	−0.132318	+	0.229181i	−0.924570	−	0.381013i	$-0.875575\pi$
$131$	−1.51445	+	2.62310i	−0.132318	+	0.229181i	0.792252	+	0.610194i	$0.208909\pi$
$132$		0			0
$133$	0.175300	−	1.07443i	0.0152004	−	0.0931652i
$134$	0.296470			0.0256111
$135$		0			0
$136$	−5.34336	−	9.25497i	−0.458190	−	0.793608i
$137$	2.12874	+	3.68708i	0.181870	+	0.315009i	0.942517	−	0.334157i	$-0.108452\pi$
$137$	2.12874	+	3.68708i	0.181870	+	0.315009i	−0.760647	+	0.649166i	$0.775118\pi$
$138$		0			0
$139$	−17.2721			−1.46500			−0.732502	−	0.680765i	$-0.761648\pi$
$139$	−17.2721			−1.46500			−0.732502	+	0.680765i	$0.761648\pi$
$140$	0.826848	+	1.43214i	0.0698814	+	0.121038i
$141$		0			0
$142$	2.07717	+	3.59776i	0.174312	+	0.301917i
$143$	−1.08129	+	1.87285i	−0.0904222	+	0.156616i
$144$		0			0
$145$	14.6732			1.21855
$146$	0.685234	+	1.18686i	0.0567104	+	0.0982253i
$147$		0			0
$148$	−5.78473			−0.475501
$149$	0.923073	−	1.59881i	0.0756211	−	0.130980i	−0.825735	−	0.564058i	$-0.809239\pi$
$149$	0.923073	−	1.59881i	0.0756211	−	0.130980i	0.901356	+	0.433079i	$0.142573\pi$
$150$		0			0
$151$	−5.59926	+	9.69820i	−0.455661	+	0.789228i	−0.998726	−	0.0504626i	$-0.983930\pi$
$151$	−5.59926	+	9.69820i	−0.455661	+	0.789228i	0.543065	+	0.839691i	$0.317264\pi$
$152$	−5.83989	+	2.21061i	−0.473677	+	0.179305i
$153$		0			0
$154$	−0.0755689	−	0.130889i	−0.00608952	−	0.0105473i
$155$	30.7790			2.47223
$156$		0			0
$157$	−10.3856	+	17.9883i	−0.828858	+	1.43562i	0.0700766	+	0.997542i	$0.477676\pi$
$157$	−10.3856	+	17.9883i	−0.828858	+	1.43562i	−0.898935	+	0.438083i	$0.855658\pi$
$158$	−3.65522			−0.290794
$159$		0			0
$160$	7.19847	−	12.4681i	0.569089	−	0.985692i
$161$	−0.560870	+	0.971456i	−0.0442028	+	0.0765614i
$162$		0			0
$163$	−5.41671			−0.424269			−0.212135	−	0.977240i	$-0.568042\pi$
$163$	−5.41671			−0.424269			−0.212135	+	0.977240i	$0.568042\pi$
$164$	−5.16755	+	8.95046i	−0.403518	+	0.698914i
$165$		0			0
$166$	0.0687077	−	0.119005i	0.00533275	−	0.00923660i
$167$	1.50006			0.116078			0.0580392	−	0.998314i	$-0.481515\pi$
$167$	1.50006			0.116078			0.0580392	+	0.998314i	$0.481515\pi$
$168$		0			0
$169$	−11.2433			−0.864867
$170$	−9.83667			−0.754438
$171$		0			0
$172$	18.7001			1.42587
$173$	−22.4134			−1.70406			−0.852031	−	0.523491i	$-0.824629\pi$
$173$	−22.4134			−1.70406			−0.852031	+	0.523491i	$0.824629\pi$
$174$		0			0
$175$	1.90798			0.144230
$176$	2.60536	−	4.51262i	0.196387	−	0.340151i
$177$		0			0
$178$	1.48739	−	2.57623i	0.111485	−	0.193097i
$179$	12.7134			0.950242			0.475121	−	0.879920i	$-0.342404\pi$
$179$	12.7134			0.950242			0.475121	+	0.879920i	$0.342404\pi$
$180$		0			0
$181$	1.31157	−	2.27170i	0.0974880	−	0.168854i	−0.813156	−	0.582045i	$-0.802253\pi$
$181$	1.31157	−	2.27170i	0.0974880	−	0.168854i	0.910644	+	0.413191i	$0.135586\pi$
$182$	−0.0613866	+	0.106325i	−0.00455027	+	0.00788131i
$183$		0			0
$184$	6.43414			0.474331
$185$	−5.52123	+	9.56304i	−0.405929	+	0.703089i
$186$		0			0
$187$	−12.1720			−0.890101
$188$	−3.13426	−	5.42870i	−0.228589	−	0.395928i
$189$		0			0
$190$	−0.925514	+	5.67259i	−0.0671439	+	0.411533i
$191$	1.70417	−	2.95170i	0.123309	−	0.213578i	−0.797762	−	0.602973i	$-0.793983\pi$
$191$	1.70417	−	2.95170i	0.123309	−	0.213578i	0.921071	+	0.389395i	$0.127316\pi$
$192$		0			0
$193$	−0.248883	+	0.431077i	−0.0179150	+	0.0310296i	−0.874844	−	0.484405i	$-0.839036\pi$
$193$	−0.248883	+	0.431077i	−0.0179150	+	0.0310296i	0.856929	+	0.515435i	$0.172369\pi$
$194$	−2.38539			−0.171261
$195$		0			0
$196$	−6.46046	−	11.1898i	−0.461461	−	0.799275i
$197$	2.64398			0.188376			0.0941880	−	0.995554i	$-0.469975\pi$
$197$	2.64398			0.188376			0.0941880	+	0.995554i	$0.469975\pi$
$198$		0			0
$199$	0.106311	−	0.184136i	0.00753617	−	0.0130530i	−0.862233	−	0.506512i	$-0.830934\pi$
$199$	0.106311	−	0.184136i	0.00753617	−	0.0130530i	0.869769	+	0.493459i	$0.164268\pi$
$200$	−5.47195	−	9.47770i	−0.386925	−	0.670174i
$201$		0			0
$202$	−1.40262	−	2.42940i	−0.0986877	−	0.170932i
$203$	1.03079			0.0723470
$204$		0			0
$205$	9.86433	+	17.0855i	0.688955	+	1.19330i
$206$	2.56257	+	4.43851i	0.178543	+	0.309245i
$207$		0			0
$208$	−4.23280			−0.293492
$209$	−1.14524	+	7.01930i	−0.0792177	+	0.485535i
$210$		0			0
$211$	4.26187	−	7.38178i	0.293400	−	0.508183i	−0.681212	−	0.732086i	$-0.738547\pi$
$211$	4.26187	−	7.38178i	0.293400	−	0.508183i	0.974611	+	0.223903i	$0.0718800\pi$
$212$	0.473399	−	0.819952i	0.0325132	−	0.0563145i
$213$		0			0
$214$	4.45508			0.304543
$215$	17.8483	−	30.9141i	1.21724	−	2.10833i
$216$		0			0
$217$	2.16220			0.146780
$218$	2.82839	+	4.89892i	0.191563	+	0.331797i
$219$		0			0
$220$	−5.40181	−	9.35621i	−0.364190	−	0.630796i
$221$	4.94380	+	8.56290i	0.332556	+	0.576003i
$222$		0			0
$223$	15.6032			1.04487			0.522433	−	0.852680i	$-0.325025\pi$
$223$	15.6032			1.04487			0.522433	+	0.852680i	$0.325025\pi$
$224$	0.505688	−	0.875877i	0.0337877	−	0.0585220i
$225$		0			0
$226$	−0.543283	−	0.940994i	−0.0361386	−	0.0625940i
$227$	0.595426	−	1.03131i	0.0395198	−	0.0684503i	−0.845589	−	0.533835i	$-0.820751\pi$
$227$	0.595426	−	1.03131i	0.0395198	−	0.0684503i	0.885109	+	0.465384i	$0.154084\pi$
$228$		0			0
$229$	−9.98443	−	17.2935i	−0.659790	−	1.14279i	−0.980670	−	0.195669i	$-0.937312\pi$
$229$	−9.98443	−	17.2935i	−0.659790	−	1.14279i	0.320880	−	0.947120i	$-0.396021\pi$
$230$	2.96118	−	5.12891i	0.195254	−	0.338190i
$231$		0			0
$232$	−2.95622	−	5.12032i	−0.194085	−	0.336166i
$233$	−6.18432	−	10.7115i	−0.405148	−	0.701737i	0.589191	−	0.807994i	$-0.299447\pi$
$233$	−6.18432	−	10.7115i	−0.405148	−	0.701737i	−0.994339	+	0.106257i	$0.966113\pi$
$234$		0			0
$235$	−11.9660			−0.780573
$236$	9.74281	−	16.8750i	0.634203	−	1.09847i
$237$		0			0
$238$	−0.691019			−0.0447921
$239$	−8.11631	−	14.0579i	−0.525000	−	0.909327i	−0.999576	−	0.0291128i	$-0.990732\pi$
$239$	−8.11631	−	14.0579i	−0.525000	−	0.909327i	0.474576	−	0.880215i	$-0.342602\pi$
$240$		0			0
$241$	−5.24347	−	9.08196i	−0.337762	−	0.585020i	0.646250	−	0.763126i	$-0.276336\pi$
$241$	−5.24347	−	9.08196i	−0.337762	−	0.585020i	−0.984011	+	0.178106i	$0.943003\pi$
$242$	−1.54620	−	2.67809i	−0.0993933	−	0.172154i
$243$		0			0
$244$	3.85619	+	6.67911i	0.246867	+	0.427586i
$245$	−24.6647			−1.57577
$246$		0			0
$247$	5.40319	−	2.04531i	0.343797	−	0.130140i
$248$	−6.20104	−	10.7405i	−0.393767	−	0.682024i
$249$		0			0
$250$	−3.48044			−0.220123
$251$	7.02198	−	12.1624i	0.443223	−	0.767685i	−0.554703	−	0.832048i	$-0.687168\pi$
$251$	7.02198	−	12.1624i	0.443223	−	0.767685i	0.997927	+	0.0643630i	$0.0205016\pi$
$252$		0			0
$253$	3.66418	−	6.34654i	0.230365	−	0.399004i
$254$	0.352041	−	0.609753i	0.0220890	−	0.0382593i
$255$		0			0
$256$	6.09457			0.380910
$257$	−17.1607			−1.07045			−0.535227	−	0.844709i	$-0.679774\pi$
$257$	−17.1607			−1.07045			−0.535227	+	0.844709i	$0.679774\pi$
$258$		0			0
$259$	−0.387862	+	0.671797i	−0.0241006	+	0.0417435i
$260$	−4.38803	+	7.60029i	−0.272134	+	0.471350i
$261$		0			0
$262$	0.561691	−	0.972878i	0.0347014	−	0.0601046i
$263$	−19.4995			−1.20239			−0.601194	−	0.799103i	$-0.705308\pi$
$263$	−19.4995			−1.20239			−0.601194	+	0.799103i	$0.705308\pi$
$264$		0			0
$265$	−0.903671	−	1.56520i	−0.0555121	−	0.0961498i
$266$	−0.0650167	+	0.398496i	−0.00398643	+	0.0244333i
$267$		0			0
$268$	1.48874			0.0909394
$269$	11.5796	+	20.0564i	0.706020	+	1.22286i	0.966322	+	0.257335i	$0.0828443\pi$
$269$	11.5796	+	20.0564i	0.706020	+	1.22286i	−0.260303	+	0.965527i	$0.583822\pi$
$270$		0			0
$271$	−11.0388	−	19.1197i	−0.670557	−	1.16144i	−0.977746	−	0.209790i	$-0.932722\pi$
$271$	−11.0388	−	19.1197i	−0.670557	−	1.16144i	0.307190	−	0.951648i	$-0.400611\pi$
$272$	−11.9120	−	20.6322i	−0.722272	−	1.25101i
$273$		0			0
$274$	−0.789525	−	1.36750i	−0.0476970	−	0.0826136i
$275$	−12.4649			−0.751660
$276$		0			0
$277$	14.7992	−	25.6330i	0.889199	−	1.54014i	0.0483752	−	0.998829i	$-0.484596\pi$
$277$	14.7992	−	25.6330i	0.889199	−	1.54014i	0.840824	−	0.541309i	$-0.182071\pi$
$278$	6.40605			0.384209
$279$		0			0
$280$	−0.635988	−	1.10156i	−0.0380075	−	0.0658310i
$281$	14.4042	+	24.9487i	0.859280	+	1.48832i	0.872617	+	0.488406i	$0.162421\pi$
$281$	14.4042	+	24.9487i	0.859280	+	1.48832i	−0.0133368	+	0.999911i	$0.504245\pi$
$282$		0			0
$283$	−8.01020	+	13.8741i	−0.476157	+	0.824728i	−0.999627	−	0.0273162i	$-0.991304\pi$
$283$	−8.01020	+	13.8741i	−0.476157	+	0.824728i	0.523470	+	0.852044i	$0.324637\pi$
$284$	10.4306	+	18.0664i	0.618944	+	1.07204i
$285$		0			0
$286$	0.401040	−	0.694621i	0.0237140	−	0.0410738i
$287$	0.692963	+	1.20025i	0.0409043	+	0.0708483i
$288$		0			0
$289$	−19.3258	+	33.4732i	−1.13681	+	1.96901i
$290$	−5.44215			−0.319574
$291$		0			0
$292$	3.44094	+	5.95989i	0.201366	+	0.348776i
$293$	0.400378	+	0.693475i	0.0233903	+	0.0405132i	0.877484	−	0.479607i	$-0.159221\pi$
$293$	0.400378	+	0.693475i	0.0233903	+	0.0405132i	−0.854093	+	0.520120i	$0.825887\pi$
$294$		0			0
$295$	−18.5980	−	32.2127i	−1.08282	−	1.87550i
$296$	4.44945			0.258619
$297$		0			0
$298$	−0.342358	+	0.592981i	−0.0198322	+	0.0343504i
$299$	−5.95301			−0.344271
$300$		0			0
$301$	1.25383	−	2.17170i	0.0722696	−	0.125175i
$302$	2.07670	−	3.59696i	0.119501	−	0.206982i
$303$		0			0
$304$	−13.0189	+	4.92815i	−0.746686	+	0.282649i
$305$	14.7221			0.842987
$306$		0			0
$307$	2.29987	+	3.98349i	0.131260	+	0.227350i	0.924163	−	0.381999i	$-0.124764\pi$
$307$	2.29987	+	3.98349i	0.131260	+	0.227350i	−0.792902	+	0.609349i	$0.791431\pi$
$308$	−0.379474	−	0.657268i	−0.0216225	−	0.0374513i
$309$		0			0
$310$	−11.4156			−0.648362
$311$	−16.4116	−	28.4257i	−0.930615	−	1.61187i	−0.782273	−	0.622936i	$-0.785940\pi$
$311$	−16.4116	−	28.4257i	−0.930615	−	1.61187i	−0.148342	−	0.988936i	$-0.547394\pi$
$312$		0			0
$313$	9.19380	+	15.9241i	0.519664	+	0.900085i	0.999739	+	0.0228573i	$0.00727633\pi$
$313$	9.19380	+	15.9241i	0.519664	+	0.900085i	−0.480074	+	0.877228i	$0.659390\pi$
$314$	3.85189	−	6.67167i	0.217375	−	0.376504i
$315$		0			0
$316$	−18.3549			−1.03254
$317$	0.679102	+	1.17624i	0.0381422	+	0.0660642i	0.884466	−	0.466604i	$-0.154523\pi$
$317$	0.679102	+	1.17624i	0.0381422	+	0.0660642i	−0.846324	+	0.532668i	$0.821189\pi$
$318$		0			0
$319$	−6.73415			−0.377040
$320$	8.68398	−	15.0411i	0.485449	−	0.840823i
$321$		0			0
$322$	0.208021	−	0.360302i	0.0115925	−	0.0200789i
$323$	25.1753	+	20.5812i	1.40079	+	1.14517i
$324$		0			0
$325$	5.06277	+	8.76897i	0.280832	+	0.486415i
$326$	2.00900			0.111268
$327$		0			0
$328$	3.97473	−	6.88444i	0.219468	−	0.380130i
$329$	−0.840601			−0.0463438
$330$		0			0
$331$	8.39869	−	14.5470i	0.461634	−	0.799573i	−0.537409	−	0.843322i	$-0.680597\pi$
$331$	8.39869	−	14.5470i	0.461634	−	0.799573i	0.999043	+	0.0437490i	$0.0139302\pi$
$332$	0.345020	−	0.597592i	0.0189354	−	0.0327971i
$333$		0			0
$334$	−0.556357			−0.0304425
$335$	1.42093	−	2.46112i	0.0776336	−	0.134465i
$336$		0			0
$337$	−18.2612	+	31.6293i	−0.994750	+	1.72296i	−0.408751	+	0.912646i	$0.634035\pi$
$337$	−18.2612	+	31.6293i	−0.994750	+	1.72296i	−0.585999	+	0.810312i	$0.699298\pi$
$338$	4.17001			0.226819
$339$		0			0
$340$	−49.3954			−2.67884
$341$	−14.1257			−0.764951
$342$		0			0
$343$	−3.48094			−0.187953
$344$	−14.3836			−0.775511
$345$		0			0
$346$	8.31290			0.446904
$347$	−5.07542	+	8.79089i	−0.272463	+	0.471920i	−0.969492	−	0.245123i	$-0.921172\pi$
$347$	−5.07542	+	8.79089i	−0.272463	+	0.471920i	0.697029	+	0.717043i	$0.254505\pi$
$348$		0			0
$349$	8.63614	−	14.9582i	0.462282	−	0.800696i	−0.536792	−	0.843715i	$-0.680364\pi$
$349$	8.63614	−	14.9582i	0.462282	−	0.800696i	0.999074	+	0.0430183i	$0.0136974\pi$
$350$	−0.707649			−0.0378254
$351$		0			0
$352$	−3.30367	+	5.72212i	−0.176086	+	0.304990i
$353$	8.45158	−	14.6386i	0.449832	−	0.779132i	−0.548543	−	0.836123i	$-0.684817\pi$
$353$	8.45158	−	14.6386i	0.449832	−	0.779132i	0.998375	+	0.0569905i	$0.0181505\pi$
$354$		0			0
$355$	39.8220			2.11353
$356$	7.46902	−	12.9367i	0.395857	−	0.685645i
$357$		0			0
$358$	−4.71525			−0.249209
$359$	−3.82747	−	6.62938i	−0.202006	−	0.349885i	0.747168	−	0.664635i	$-0.231413\pi$
$359$	−3.82747	−	6.62938i	−0.202006	−	0.349885i	−0.949175	+	0.314750i	$0.898079\pi$
$360$		0			0
$361$	14.2374	−	12.5816i	0.749337	−	0.662189i
$362$	−0.486446	+	0.842549i	−0.0255670	+	0.0442834i
$363$		0			0
$364$	−0.308256	+	0.533915i	−0.0161570	+	0.0279848i
$365$	13.1368			0.687613
$366$		0			0
$367$	12.3888	+	21.4579i	0.646688	+	1.12010i	0.983909	+	0.178670i	$0.0571796\pi$
$367$	12.3888	+	21.4579i	0.646688	+	1.12010i	−0.337221	+	0.941425i	$0.609487\pi$
$368$	14.3437			0.747717
$369$		0			0
$370$	2.04776	−	3.54683i	0.106458	−	0.184391i
$371$	−0.0634823	−	0.109955i	−0.00329584	−	0.00570856i
$372$		0			0
$373$	11.5863	+	20.0681i	0.599917	+	1.03909i	0.992833	+	0.119512i	$0.0381330\pi$
$373$	11.5863	+	20.0681i	0.599917	+	1.03909i	−0.392916	+	0.919574i	$0.628534\pi$
$374$	4.51444			0.233436
$375$		0			0
$376$	2.41078	+	4.17560i	0.124327	+	0.215340i
$377$	2.73516	+	4.73744i	0.140868	+	0.243990i
$378$		0			0
$379$	29.0801			1.49374			0.746871	−	0.664969i	$-0.231555\pi$
$379$	29.0801			1.49374			0.746871	+	0.664969i	$0.231555\pi$
$380$	−4.64752	+	28.4852i	−0.238413	+	1.46126i
$381$		0			0
$382$	−0.632057	+	1.09475i	−0.0323388	+	0.0560125i
$383$	−1.41428	+	2.44960i	−0.0722662	+	0.125169i	−0.899894	−	0.436108i	$-0.856356\pi$
$383$	−1.41428	+	2.44960i	−0.0722662	+	0.125169i	0.827628	+	0.561277i	$0.189690\pi$
$384$		0			0
$385$	−1.44875			−0.0738353
$386$	0.0923078	−	0.159882i	0.00469834	−	0.00813777i
$387$		0			0
$388$	−11.9784			−0.608110
$389$	9.58295	+	16.5982i	0.485875	+	0.841560i	0.999868	−	0.0162341i	$-0.00516771\pi$
$389$	9.58295	+	16.5982i	0.485875	+	0.841560i	−0.513993	+	0.857794i	$0.671834\pi$
$390$		0			0
$391$	−16.7530	−	29.0171i	−0.847238	−	1.46746i
$392$	4.96920	+	8.60691i	0.250983	+	0.434715i
$393$		0			0
$394$	−0.980624			−0.0494031
$395$	−17.5188	+	30.3435i	−0.881467	+	1.52675i
$396$		0			0
$397$	15.9590	+	27.6417i	0.800958	+	1.38730i	0.918986	+	0.394289i	$0.129009\pi$
$397$	15.9590	+	27.6417i	0.800958	+	1.38730i	−0.118029	+	0.993010i	$0.537658\pi$
$398$	−0.0394295	+	0.0682939i	−0.00197642	+	0.00342326i
$399$		0			0
$400$	−12.1987	−	21.1287i	−0.609934	−	1.05644i
$401$	19.1703	−	33.2040i	0.957320	−	1.65813i	0.228353	−	0.973578i	$-0.426666\pi$
$401$	19.1703	−	33.2040i	0.957320	−	1.65813i	0.728967	−	0.684548i	$-0.240001\pi$
$402$		0			0
$403$	5.73734	+	9.93737i	0.285797	+	0.495015i
$404$	−7.04332	−	12.1994i	−0.350418	−	0.606942i
$405$		0			0
$406$	−0.382307			−0.0189736
$407$	2.53391	−	4.38887i	0.125601	−	0.217548i
$408$		0			0
$409$	2.29288			0.113375			0.0566877	−	0.998392i	$-0.481946\pi$
$409$	2.29288			0.113375			0.0566877	+	0.998392i	$0.481946\pi$
$410$	−3.65857	−	6.33683i	−0.180684	−	0.312954i
$411$		0			0
$412$	12.8681	+	22.2882i	0.633966	+	1.09806i
$413$	−1.30650	−	2.26292i	−0.0642886	−	0.111351i
$414$		0			0
$415$	−0.658608	−	1.14074i	−0.0323298	−	0.0559968i
$416$	5.36731			0.263154
$417$		0			0
$418$	0.424756	−	2.60338i	0.0207755	−	0.127335i
$419$	−5.32211	−	9.21817i	−0.260002	−	0.450337i	0.706240	−	0.707972i	$-0.250390\pi$
$419$	−5.32211	−	9.21817i	−0.260002	−	0.450337i	−0.966242	+	0.257636i	$0.917057\pi$
$420$		0			0
$421$	25.8645			1.26056			0.630280	−	0.776367i	$-0.282940\pi$
$421$	25.8645			1.26056			0.630280	+	0.776367i	$0.282940\pi$
$422$	−1.58068	+	2.73782i	−0.0769464	+	0.133275i
$423$		0			0
$424$	−0.364125	+	0.630684i	−0.0176835	+	0.0306287i
$425$	−28.4954	+	49.3555i	−1.38223	+	2.39409i
$426$		0			0
$427$	1.03422			0.0500494
$428$	22.3714			1.08136
$429$		0			0
$430$	−6.61973	+	11.4657i	−0.319232	+	0.552926i
$431$	9.52984	−	16.5062i	0.459036	−	0.795074i	−0.539874	−	0.841746i	$-0.681528\pi$
$431$	9.52984	−	16.5062i	0.459036	−	0.795074i	0.998910	+	0.0466716i	$0.0148614\pi$
$432$		0			0
$433$	13.3288	−	23.0861i	0.640540	−	1.10945i	−0.344773	−	0.938686i	$-0.612044\pi$
$433$	13.3288	−	23.0861i	0.640540	−	1.10945i	0.985312	−	0.170761i	$-0.0546226\pi$
$434$	−0.801937			−0.0384942
$435$		0			0
$436$	14.2029	+	24.6002i	0.680197	+	1.17814i
$437$	−18.3098	+	6.93094i	−0.875876	+	0.331552i
$438$		0			0
$439$	−1.94705			−0.0929274			−0.0464637	−	0.998920i	$-0.514795\pi$
$439$	−1.94705			−0.0929274			−0.0464637	+	0.998920i	$0.514795\pi$
$440$	4.15492	+	7.19653i	0.198078	+	0.343081i
$441$		0			0
$442$	−1.83360	−	3.17589i	−0.0872154	−	0.151062i
$443$	3.28115	+	5.68312i	0.155892	+	0.270013i	0.933384	−	0.358880i	$-0.116841\pi$
$443$	3.28115	+	5.68312i	0.155892	+	0.270013i	−0.777491	+	0.628894i	$0.783508\pi$
$444$		0			0
$445$	−14.2576	−	24.6949i	−0.675875	−	1.17065i
$446$	−5.78704			−0.274024
$447$		0			0
$448$	0.610044	−	1.05663i	0.0288219	−	0.0499209i
$449$	35.5348			1.67699			0.838495	−	0.544910i	$-0.183436\pi$
$449$	35.5348			1.67699			0.838495	+	0.544910i	$0.183436\pi$
$450$		0			0
$451$	−4.52714	−	7.84124i	−0.213175	−	0.369229i
$452$	−2.72813	−	4.72526i	−0.128320	−	0.222257i
$453$		0			0
$454$	−0.220837	+	0.382501i	−0.0103644	+	0.0179516i
$455$	0.588430	+	1.01919i	0.0275860	+	0.0477804i
$456$		0			0
$457$	−3.32444	+	5.75809i	−0.155511	+	0.269352i	−0.933245	−	0.359241i	$-0.883036\pi$
$457$	−3.32444	+	5.75809i	−0.155511	+	0.269352i	0.777734	+	0.628593i	$0.216369\pi$
$458$	3.70311	+	6.41398i	0.173035	+	0.299706i
$459$		0			0
$460$	14.8697	−	25.7551i	0.693304	−	1.20084i
$461$	6.97181			0.324709			0.162355	−	0.986732i	$-0.448091\pi$
$461$	6.97181			0.324709			0.162355	+	0.986732i	$0.448091\pi$
$462$		0			0
$463$	8.59691	+	14.8903i	0.399532	+	0.692010i	0.993668	−	0.112354i	$-0.0358392\pi$
$463$	8.59691	+	14.8903i	0.399532	+	0.692010i	−0.594136	+	0.804365i	$0.702506\pi$
$464$	−6.59033	−	11.4148i	−0.305949	−	0.529919i
$465$		0			0
$466$	2.29369	+	3.97280i	0.106253	+	0.184036i
$467$	−36.5485			−1.69126			−0.845632	−	0.533766i	$-0.820776\pi$
$467$	−36.5485			−1.69126			−0.845632	+	0.533766i	$0.820776\pi$
$468$		0			0
$469$	0.0998193	−	0.172892i	0.00460923	−	0.00798341i
$470$	4.43804			0.204712
$471$		0			0
$472$	−7.49390	+	12.9798i	−0.344935	+	0.597444i
$473$	−8.19130	+	14.1877i	−0.376636	+	0.652353i
$474$		0			0
$475$	25.7811	+	21.0764i	1.18292	+	0.967054i
$476$	−3.47000			−0.159047
$477$		0			0
$478$	3.01025	+	5.21391i	0.137686	+	0.238479i
$479$	−9.98270	−	17.2905i	−0.456121	−	0.790025i	0.542631	−	0.839971i	$-0.317428\pi$
$479$	−9.98270	−	17.2905i	−0.456121	−	0.790025i	−0.998752	+	0.0499464i	$0.984095\pi$
$480$		0			0
$481$	−4.11673			−0.187707
$482$	1.94475	+	3.36840i	0.0885807	+	0.153426i
$483$		0			0
$484$	−7.76432	−	13.4482i	−0.352924	−	0.611281i
$485$	−11.4327	+	19.8021i	−0.519134	+	0.899167i
$486$		0			0
$487$	0.541412			0.0245337			0.0122669	−	0.999925i	$-0.496095\pi$
$487$	0.541412			0.0245337			0.0122669	+	0.999925i	$0.496095\pi$
$488$	−2.96607	−	5.13738i	−0.134268	−	0.232558i
$489$		0			0
$490$	9.14787			0.413259
$491$	−3.67184	+	6.35982i	−0.165708	+	0.287015i	−0.936906	−	0.349580i	$-0.886324\pi$
$491$	−3.67184	+	6.35982i	−0.165708	+	0.287015i	0.771199	+	0.636595i	$0.219658\pi$
$492$		0			0
$493$	−15.3946	+	26.6643i	−0.693340	+	1.20090i
$494$	−2.00398	+	0.758583i	−0.0901635	+	0.0341302i
$495$		0			0
$496$	−13.8241	−	23.9440i	−0.620718	−	1.07512i
$497$	2.79747			0.125484
$498$		0			0
$499$	5.97373	−	10.3468i	0.267421	−	0.463187i	−0.700774	−	0.713383i	$-0.747162\pi$
$499$	5.97373	−	10.3468i	0.267421	−	0.463187i	0.968195	+	0.250197i	$0.0804952\pi$
$500$	−17.4773			−0.781607
$501$		0			0
$502$	−2.60437	+	4.51091i	−0.116239	+	0.201332i
$503$	−14.7358	+	25.5232i	−0.657038	+	1.13802i	0.324341	+	0.945940i	$0.394858\pi$
$503$	−14.7358	+	25.5232i	−0.657038	+	1.13802i	−0.981379	+	0.192083i	$0.938476\pi$
$504$		0			0
$505$	−26.8900			−1.19659
$506$	−1.35900	+	2.35386i	−0.0604151	+	0.104642i
$507$		0			0
$508$	1.76779	−	3.06191i	0.0784332	−	0.135850i
$509$	−17.9044			−0.793600			−0.396800	−	0.917905i	$-0.629879\pi$
$509$	−17.9044			−0.793600			−0.396800	+	0.917905i	$0.629879\pi$
$510$		0			0
$511$	0.922853			0.0408246
$512$	−22.0823			−0.975909
$513$		0			0
$514$	6.36470			0.280735
$515$	49.1278			2.16483
$516$		0			0
$517$	5.49166			0.241523
$518$	0.143854	−	0.249162i	0.00632058	−	0.0109476i
$519$		0			0
$520$	3.37515	−	5.84593i	0.148010	−	0.256361i
$521$	27.8411			1.21974			0.609871	−	0.792501i	$-0.291221\pi$
$521$	27.8411			1.21974			0.609871	+	0.792501i	$0.291221\pi$
$522$		0			0
$523$	−12.9624	+	22.4515i	−0.566805	+	0.981735i	0.430074	+	0.902794i	$0.358487\pi$
$523$	−12.9624	+	22.4515i	−0.566805	+	0.981735i	−0.996879	+	0.0789417i	$0.974846\pi$
$524$	2.82057	−	4.88537i	0.123217	−	0.213418i
$525$		0			0
$526$	7.23214			0.315336
$527$	−32.2922	+	55.9317i	−1.40667	+	2.43642i
$528$		0			0
$529$	−2.82704			−0.122915
$530$	0.335162	+	0.580517i	0.0145585	+	0.0252161i
$531$		0			0
$532$	−0.326485	+	2.00107i	−0.0141549	+	0.0867574i
$533$	−3.67751	+	6.36964i	−0.159291	+	0.275900i
$534$		0			0
$535$	21.3524	−	36.9834i	0.923144	−	1.59893i
$536$	−1.14510			−0.0494607
$537$		0			0
$538$	−4.29474	−	7.43871i	−0.185159	−	0.320705i
$539$	11.3196			0.487571
$540$		0			0
$541$	−12.3043	+	21.3116i	−0.529001	+	0.916257i	0.470427	+	0.882439i	$0.344100\pi$
$541$	−12.3043	+	21.3116i	−0.529001	+	0.916257i	−0.999428	+	0.0338181i	$0.989233\pi$
$542$	4.09415	+	7.09128i	0.175859	+	0.304597i
$543$		0			0
$544$	15.1048	+	26.1622i	0.647611	+	1.12170i
$545$	54.2239			2.32270
$546$		0			0
$547$	−6.44357	−	11.1606i	−0.275507	−	0.477192i	0.694756	−	0.719246i	$-0.255512\pi$
$547$	−6.44357	−	11.1606i	−0.275507	−	0.477192i	−0.970263	+	0.242054i	$0.922179\pi$
$548$	−3.96465	−	6.86697i	−0.169361	−	0.293343i
$549$		0			0
$550$	4.62308			0.197129
$551$	13.9283	+	11.3865i	0.593364	+	0.485083i
$552$		0			0
$553$	−1.23068	+	2.13161i	−0.0523340	+	0.0906452i
$554$	−5.48887	+	9.50700i	−0.233200	+	0.403914i
$555$		0			0
$556$	32.1684			1.36424
$557$	11.8767	−	20.5710i	0.503231	−	0.871622i	−0.496762	−	0.867887i	$-0.665478\pi$
$557$	11.8767	−	20.5710i	0.503231	−	0.871622i	0.999993	−	0.00373498i	$-0.00118888\pi$
$558$		0			0
$559$	13.3080			0.562868
$560$	−1.41781	−	2.45573i	−0.0599136	−	0.103773i
$561$		0			0
$562$	−5.34234	−	9.25321i	−0.225353	−	0.390323i
$563$	−13.3440	−	23.1125i	−0.562383	−	0.974077i	−0.997288	−	0.0735999i	$-0.976551\pi$
$563$	−13.3440	−	23.1125i	−0.562383	−	0.974077i	0.434904	−	0.900477i	$-0.356782\pi$
$564$		0			0
$565$	−10.4154			−0.438181
$566$	2.97090	−	5.14574i	0.124876	−	0.216292i
$567$		0			0
$568$	−8.02294	−	13.8961i	−0.336635	−	0.583069i
$569$	−6.57047	+	11.3804i	−0.275448	+	0.477090i	−0.970248	−	0.242113i	$-0.922160\pi$
$569$	−6.57047	+	11.3804i	−0.275448	+	0.477090i	0.694800	+	0.719203i	$0.255493\pi$
$570$		0			0
$571$	−1.08070	−	1.87182i	−0.0452258	−	0.0783333i	0.842526	−	0.538655i	$-0.181067\pi$
$571$	−1.08070	−	1.87182i	−0.0452258	−	0.0783333i	−0.887752	+	0.460322i	$0.847734\pi$
$572$	2.01384	−	3.48808i	0.0842031	−	0.145844i
$573$		0			0
$574$	−0.257012	−	0.445158i	−0.0107275	−	0.0185805i
$575$	−17.1562	−	29.7154i	−0.715463	−	1.23922i
$576$		0			0
$577$	4.53956			0.188985			0.0944923	−	0.995526i	$-0.469877\pi$
$577$	4.53956			0.188985			0.0944923	+	0.995526i	$0.469877\pi$
$578$	7.16772	−	12.4149i	0.298138	−	0.516390i
$579$		0			0
$580$	−27.3281			−1.13474
$581$	−0.0462667	−	0.0801364i	−0.00191947	−	0.00332462i
$582$		0			0
$583$	0.414731	+	0.718336i	0.0171764	+	0.0297504i
$584$	−2.64668	−	4.58418i	−0.109520	−	0.189695i
$585$		0			0
$586$	−0.148496	−	0.257202i	−0.00613430	−	0.0106249i
$587$	−24.2678			−1.00164			−0.500819	−	0.865552i	$-0.666968\pi$
$587$	−24.2678			−1.00164			−0.500819	+	0.865552i	$0.666968\pi$
$588$		0			0
$589$	29.2163	+	23.8847i	1.20384	+	0.984152i
$590$	6.89781	+	11.9474i	0.283978	+	0.491865i
$591$		0			0
$592$	9.91920			0.407677
$593$	−16.5350	+	28.6395i	−0.679013	+	1.17608i	0.296266	+	0.955106i	$0.404259\pi$
$593$	−16.5350	+	28.6395i	−0.679013	+	1.17608i	−0.975279	+	0.220979i	$0.929075\pi$
$594$		0			0
$595$	−3.31193	+	5.73644i	−0.135776	+	0.235171i
$596$	−1.71917	+	2.97769i	−0.0704199	+	0.121971i
$597$		0			0
$598$	2.20791			0.0902880
$599$	13.2848			0.542803			0.271401	−	0.962466i	$-0.412513\pi$
$599$	13.2848			0.542803			0.271401	+	0.962466i	$0.412513\pi$
$600$		0			0
$601$	−7.35146	+	12.7331i	−0.299872	+	0.519394i	−0.976106	−	0.217293i	$-0.930277\pi$
$601$	−7.35146	+	12.7331i	−0.299872	+	0.519394i	0.676234	+	0.736687i	$0.263611\pi$
$602$	−0.465032	+	0.805459i	−0.0189533	+	0.0328280i
$603$		0			0
$604$	10.4283	−	18.0623i	0.424321	−	0.734946i
$605$	−29.6426			−1.20514
$606$		0			0
$607$	−1.19304	−	2.06641i	−0.0484241	−	0.0838729i	0.840797	−	0.541350i	$-0.182087\pi$
$607$	−1.19304	−	2.06641i	−0.0484241	−	0.0838729i	−0.889221	+	0.457477i	$0.848753\pi$
$608$	16.5083	−	6.24903i	0.669502	−	0.253431i
$609$		0			0
$610$	−5.46028			−0.221080
$611$	−2.23051	−	3.86336i	−0.0902368	−	0.156295i
$612$		0			0
$613$	2.16079	+	3.74260i	0.0872736	+	0.151162i	0.906358	−	0.422511i	$-0.138851\pi$
$613$	2.16079	+	3.74260i	0.0872736	+	0.151162i	−0.819084	+	0.573673i	$0.805518\pi$
$614$	−0.852996	−	1.47743i	−0.0344241	−	0.0596243i
$615$		0			0
$616$	0.291880	+	0.505552i	0.0117602	+	0.0203693i
$617$	9.61045			0.386902			0.193451	−	0.981110i	$-0.438032\pi$
$617$	9.61045			0.386902			0.193451	+	0.981110i	$0.438032\pi$
$618$		0			0
$619$	−1.79677	+	3.11209i	−0.0722182	+	0.125086i	−0.899873	−	0.436152i	$-0.856341\pi$
$619$	−1.79677	+	3.11209i	−0.0722182	+	0.125086i	0.827655	+	0.561237i	$0.189674\pi$
$620$	−57.3241			−2.30219
$621$		0			0
$622$	6.08687	+	10.5428i	0.244061	+	0.422727i
$623$	−1.00159	−	1.73480i	−0.0401277	−	0.0695032i
$624$		0			0
$625$	2.41765	−	4.18750i	0.0967061	−	0.167500i
$626$	−3.40988	−	5.90608i	−0.136286	−	0.236055i
$627$		0			0
$628$	19.3425	−	33.5022i	0.771850	−	1.33688i
$629$	−11.5853	−	20.0664i	−0.461938	−	0.800100i
$630$		0			0
$631$	12.6319	−	21.8792i	0.502870	−	0.870996i	−0.497125	−	0.867679i	$-0.665611\pi$
$631$	12.6319	−	21.8792i	0.502870	−	0.870996i	0.999994	−	0.00331669i	$-0.00105574\pi$
$632$	14.1181			0.561586
$633$		0			0
$634$	−0.251872	−	0.436254i	−0.0100031	−	0.0173259i
$635$	−3.37454	−	5.84487i	−0.133915	−	0.231947i
$636$		0			0
$637$	−4.59761	−	7.96330i	−0.182164	−	0.315517i
$638$	2.49762			0.0988818
$639$		0			0
$640$	−17.6177	+	30.5148i	−0.696402	+	1.20620i
$641$	23.3043			0.920463			0.460231	−	0.887799i	$-0.347766\pi$
$641$	23.3043			0.920463			0.460231	+	0.887799i	$0.347766\pi$
$642$		0			0
$643$	−8.62978	+	14.9472i	−0.340325	+	0.589461i	−0.984493	−	0.175423i	$-0.943871\pi$
$643$	−8.62978	+	14.9472i	−0.340325	+	0.589461i	0.644168	+	0.764884i	$0.277204\pi$
$644$	1.04459	−	1.80928i	0.0411625	−	0.0712956i
$645$		0			0
$646$	−9.33724	−	7.63333i	−0.367369	−	0.300329i
$647$	35.6673			1.40223			0.701114	−	0.713049i	$-0.252686\pi$
$647$	35.6673			1.40223			0.701114	+	0.713049i	$0.252686\pi$
$648$		0			0
$649$	8.53539	+	14.7837i	0.335043	+	0.580312i
$650$	−1.87772	−	3.25231i	−0.0736504	−	0.127566i
$651$		0			0
$652$	10.0883			0.395088
$653$	8.46548	+	14.6626i	0.331280	+	0.573794i	0.982763	−	0.184869i	$-0.0591862\pi$
$653$	8.46548	+	14.6626i	0.331280	+	0.573794i	−0.651483	+	0.758663i	$0.725853\pi$
$654$		0			0
$655$	−5.38418	−	9.32566i	−0.210377	−	0.364384i
$656$	8.86092	−	15.3476i	0.345961	−	0.599222i
$657$		0			0
$658$	0.311770			0.0121540
$659$	−2.26182	−	3.91760i	−0.0881082	−	0.152608i	0.818603	−	0.574359i	$-0.194749\pi$
$659$	−2.26182	−	3.91760i	−0.0881082	−	0.152608i	−0.906711	+	0.421752i	$0.861415\pi$
$660$		0			0
$661$	20.0800			0.781021			0.390510	−	0.920599i	$-0.372299\pi$
$661$	20.0800			0.781021			0.390510	+	0.920599i	$0.372299\pi$
$662$	−3.11498	+	5.39530i	−0.121067	+	0.209694i
$663$		0			0
$664$	−0.265379	+	0.459651i	−0.0102987	+	0.0178379i
$665$	2.99646	+	2.44965i	0.116198	+	0.0949933i
$666$		0			0
$667$	−9.26864	−	16.0537i	−0.358883	−	0.621604i
$668$	−2.79378			−0.108095
$669$		0			0
$670$	−0.527007	+	0.912803i	−0.0203600	+	0.0352646i
$671$	−6.75658			−0.260835
$672$		0			0
$673$	8.72911	−	15.1193i	0.336482	−	0.582805i	−0.647286	−	0.762247i	$-0.724096\pi$
$673$	8.72911	−	15.1193i	0.336482	−	0.582805i	0.983768	+	0.179443i	$0.0574294\pi$
$674$	6.77287	−	11.7310i	0.260881	−	0.451860i
$675$		0			0
$676$	20.9399			0.805382
$677$	20.4904	−	35.4905i	0.787511	−	1.36401i	−0.139976	−	0.990155i	$-0.544703\pi$
$677$	20.4904	−	35.4905i	0.787511	−	1.36401i	0.927487	−	0.373854i	$-0.121964\pi$
$678$		0			0
$679$	−0.803143	+	1.39108i	−0.0308218	+	0.0533849i
$680$	37.9936			1.45699
$681$		0			0
$682$	5.23907			0.200614
$683$	−20.9461			−0.801480			−0.400740	−	0.916192i	$-0.631247\pi$
$683$	−20.9461			−0.801480			−0.400740	+	0.916192i	$0.631247\pi$
$684$		0			0
$685$	−15.1362			−0.578325
$686$	1.29104			0.0492922
$687$		0			0
$688$	−32.0655			−1.22248
$689$	0.336897	−	0.583522i	0.0128347	−	0.0222304i
$690$		0			0
$691$	−10.5768	+	18.3195i	−0.402359	+	0.696907i	−0.994010	−	0.109288i	$-0.965143\pi$
$691$	−10.5768	+	18.3195i	−0.402359	+	0.696907i	0.591651	+	0.806194i	$0.298476\pi$
$692$	41.7437			1.58686
$693$		0			0
$694$	1.88242	−	3.26044i	0.0714556	−	0.123765i
$695$	30.7031	−	53.1793i	1.16463	−	2.01720i
$696$		0			0
$697$	−41.3972			−1.56803
$698$	−3.20305	+	5.54785i	−0.121237	+	0.209989i
$699$		0			0
$700$	−3.55350			−0.134310
$701$	1.32346	+	2.29231i	0.0499865	+	0.0865792i	0.889936	−	0.456085i	$-0.150749\pi$
$701$	1.32346	+	2.29231i	0.0499865	+	0.0865792i	−0.839950	+	0.542665i	$0.817415\pi$
$702$		0			0
$703$	−12.6619	+	4.79300i	−0.477552	+	0.180771i
$704$	−3.98543	+	6.90297i	−0.150207	+	0.260165i
$705$		0			0
$706$	−3.13460	+	5.42928i	−0.117972	+	0.204334i
$707$	−1.88900			−0.0710432
$708$		0			0
$709$	−13.4226	−	23.2486i	−0.504097	−	0.873121i	−0.999989	−	0.00473700i	$-0.998492\pi$
$709$	−13.4226	−	23.2486i	−0.504097	−	0.873121i	0.495892	−	0.868384i	$-0.334841\pi$
$710$	−14.7695			−0.554291
$711$		0			0
$712$	−5.74496	+	9.95056i	−0.215301	+	0.372913i
$713$	−19.4421	−	33.6748i	−0.728113	−	1.26113i
$714$		0			0
$715$	−3.84422	−	6.65839i	−0.143766	−	0.249010i
$716$	−23.6779			−0.884885
$717$		0			0
$718$	1.41957	+	2.45876i	0.0529778	+	0.0917602i
$719$	−1.94193	−	3.36352i	−0.0724217	−	0.125438i	0.827540	−	0.561406i	$-0.189739\pi$
$719$	−1.94193	−	3.36352i	−0.0724217	−	0.125438i	−0.899962	+	0.435968i	$0.856406\pi$
$720$		0			0
$721$	3.45120			0.128529
$722$	−5.28049	+	4.66638i	−0.196520	+	0.173665i
$723$		0			0
$724$	−2.44272	+	4.23091i	−0.0907828	+	0.157240i
$725$	−15.7651	+	27.3060i	−0.585502	+	1.01412i
$726$		0			0
$727$	−52.3039			−1.93984			−0.969922	−	0.243417i	$-0.921732\pi$
$727$	−52.3039			−1.93984			−0.969922	+	0.243417i	$0.921732\pi$
$728$	0.237102	−	0.410673i	0.00878758	−	0.0152205i
$729$		0			0
$730$	−4.87230			−0.180332
$731$	37.4516	+	64.8680i	1.38520	+	2.39923i
$732$		0			0
$733$	3.06517	+	5.30902i	0.113215	+	0.196093i	0.917065	−	0.398739i	$-0.130552\pi$
$733$	3.06517	+	5.30902i	0.113215	+	0.196093i	−0.803850	+	0.594832i	$0.797219\pi$
$734$	−4.59485	−	7.95852i	−0.169599	−	0.293754i
$735$		0			0
$736$	−18.1882			−0.670426
$737$	−0.652121	+	1.12951i	−0.0240212	+	0.0416059i
$738$		0			0
$739$	−6.68714	−	11.5825i	−0.245990	−	0.426068i	0.716419	−	0.697670i	$-0.245780\pi$
$739$	−6.68714	−	11.5825i	−0.245990	−	0.426068i	−0.962410	+	0.271602i	$0.912447\pi$
$740$	10.2830	−	17.8106i	0.378009	−	0.654731i
$741$		0			0
$742$	0.0235449	+	0.0407809i	0.000864360	+	0.00149712i
$743$	−1.37195	+	2.37629i	−0.0503321	+	0.0871778i	−0.890094	−	0.455777i	$-0.849361\pi$
$743$	−1.37195	+	2.37629i	−0.0503321	+	0.0871778i	0.839762	+	0.542955i	$0.182695\pi$
$744$		0			0
$745$	3.28172	+	5.68410i	0.120233	+	0.208249i
$746$	−4.29724	−	7.44304i	−0.157333	−	0.272509i
$747$		0			0
$748$	22.6696			0.828881
$749$	1.49999	−	2.59806i	0.0548085	−	0.0949311i
$750$		0			0
$751$	−20.9472			−0.764374			−0.382187	−	0.924085i	$-0.624829\pi$
$751$	−20.9472			−0.764374			−0.382187	+	0.924085i	$0.624829\pi$
$752$	5.37439	+	9.30871i	0.195984	+	0.339454i
$753$		0			0
$754$	−1.01444	−	1.75706i	−0.0369438	−	0.0639885i
$755$	−19.9065	−	34.4791i	−0.724473	−	1.25482i
$756$		0			0
$757$	3.65990	+	6.33913i	0.133021	+	0.230400i	0.924840	−	0.380357i	$-0.124199\pi$
$757$	3.65990	+	6.33913i	0.133021	+	0.230400i	−0.791819	+	0.610756i	$0.790865\pi$
$758$	−10.7855			−0.391746
$759$		0			0
$760$	3.57474	−	21.9100i	0.129670	−	0.794761i
$761$	−6.05266	−	10.4835i	−0.219409	−	0.380027i	0.735219	−	0.677830i	$-0.237079\pi$
$761$	−6.05266	−	10.4835i	−0.219409	−	0.380027i	−0.954627	+	0.297803i	$0.903746\pi$
$762$		0			0
$763$	3.80919			0.137902
$764$	−3.17391	+	5.49737i	−0.114828	+	0.198888i
$765$		0			0
$766$	0.524540	−	0.908530i	0.0189524	−	0.0328265i
$767$	6.93352	−	12.0092i	0.250355	−	0.433627i
$768$		0			0
$769$	−28.9659			−1.04454			−0.522269	−	0.852781i	$-0.674914\pi$
$769$	−28.9659			−1.04454			−0.522269	+	0.852781i	$0.674914\pi$
$770$	0.537327			0.0193639
$771$		0			0
$772$	0.463529	−	0.802856i	0.0166828	−	0.0288954i
$773$	−21.7876	+	37.7372i	−0.783645	+	1.35731i	0.146160	+	0.989261i	$0.453309\pi$
$773$	−21.7876	+	37.7372i	−0.783645	+	1.35731i	−0.929805	+	0.368052i	$0.880025\pi$
$774$		0			0
$775$	−33.0693	+	57.2777i	−1.18788	+	2.05748i
$776$	9.21343			0.330743
$777$		0			0
$778$	−3.55421	−	6.15608i	−0.127425	−	0.220706i
$779$	−3.89499	+	23.8729i	−0.139552	+	0.855334i
$780$		0			0
$781$	−18.2759			−0.653964
$782$	6.21352	+	10.7621i	0.222195	+	0.384853i
$783$		0			0
$784$	11.0779	+	19.1875i	0.395639	+	0.685267i
$785$	−36.9229	−	63.9523i	−1.31783	−	2.28255i
$786$		0			0
$787$	3.10060	+	5.37040i	0.110525	+	0.191434i	0.915982	−	0.401220i	$-0.131414\pi$
$787$	3.10060	+	5.37040i	0.110525	+	0.191434i	−0.805457	+	0.592654i	$0.798080\pi$
$788$	−4.92426			−0.175420
$789$		0			0
$790$	6.49754	−	11.2541i	0.231172	−	0.400402i
$791$	−0.731677			−0.0260155
$792$		0			0
$793$	2.74427	+	4.75322i	0.0974520	+	0.168792i
$794$	−5.91901	−	10.2520i	−0.210058	−	0.363831i
$795$		0			0
$796$	−0.197997	+	0.342942i	−0.00701784	+	0.0121552i
$797$	19.1606	+	33.1871i	0.678702	+	1.17555i	0.975372	+	0.220566i	$0.0707904\pi$
$797$	19.1606	+	33.1871i	0.678702	+	1.17555i	−0.296671	+	0.954980i	$0.595876\pi$
$798$		0			0
$799$	12.5543	−	21.7446i	0.444138	−	0.769269i
$800$	15.4683	+	26.7918i	0.546885	+	0.947233i
$801$		0			0
$802$	−7.11006	+	12.3150i	−0.251065	+	0.434857i
$803$	−6.02902			−0.212759
$804$		0			0
$805$	−1.99401	−	3.45373i	−0.0702797	−	0.121728i
$806$	−2.12792	−	3.68566i	−0.0749527	−	0.129822i
$807$		0			0
$808$	5.41752	+	9.38342i	0.190588	+	0.330108i
$809$	36.9557			1.29929			0.649647	−	0.760236i	$-0.274917\pi$
$809$	36.9557			1.29929			0.649647	+	0.760236i	$0.274917\pi$
$810$		0			0
$811$	21.0016	−	36.3759i	0.737467	−	1.27733i	−0.216165	−	0.976357i	$-0.569355\pi$
$811$	21.0016	−	36.3759i	0.737467	−	1.27733i	0.953632	−	0.300974i	$-0.0973118\pi$
$812$	−1.91978			−0.0673710
$813$		0			0
$814$	−0.939801	+	1.62778i	−0.0329400	+	0.0570537i
$815$	9.62877	−	16.6775i	0.337281	−	0.584188i
$816$		0			0
$817$	40.9317	−	15.4942i	1.43202	−	0.542072i
$818$	−0.850402			−0.0297336
$819$		0			0
$820$	−18.3717	−	31.8208i	−0.641569	−	1.11123i
$821$	−8.86017	−	15.3463i	−0.309222	−	0.535588i	0.668970	−	0.743289i	$-0.266735\pi$
$821$	−8.86017	−	15.3463i	−0.309222	−	0.535588i	−0.978192	+	0.207701i	$0.933402\pi$
$822$		0			0
$823$	−29.2027			−1.01794			−0.508971	−	0.860784i	$-0.669974\pi$
$823$	−29.2027			−1.01794			−0.508971	+	0.860784i	$0.669974\pi$
$824$	−9.89779	−	17.1435i	−0.344806	−	0.597221i
$825$		0			0
$826$	0.484566	+	0.839294i	0.0168602	+	0.0292028i
$827$	−7.34515	+	12.7222i	−0.255416	+	0.442393i	−0.965008	−	0.262219i	$-0.915546\pi$
$827$	−7.34515	+	12.7222i	−0.255416	+	0.442393i	0.709593	+	0.704612i	$0.248879\pi$
$828$		0			0
$829$	−2.88680			−0.100263			−0.0501314	−	0.998743i	$-0.515964\pi$
$829$	−2.88680			−0.100263			−0.0501314	+	0.998743i	$0.515964\pi$
$830$	0.244270	+	0.423089i	0.00847875	+	0.0146856i
$831$		0			0
$832$	6.47493			0.224478
$833$	25.8773	−	44.8209i	0.896596	−	1.55295i
$834$		0			0
$835$	−2.66652	+	4.61855i	−0.0922788	+	0.159831i
$836$	2.13294	−	13.0730i	0.0737692	−	0.452140i
$837$		0			0
$838$	1.97391	+	3.41892i	0.0681877	+	0.118105i
$839$	15.1184			0.521946			0.260973	−	0.965346i	$-0.415957\pi$
$839$	15.1184			0.521946			0.260973	+	0.965346i	$0.415957\pi$
$840$		0			0
$841$	5.98290	−	10.3627i	0.206307	−	0.357334i
$842$	−9.59288			−0.330592
$843$		0			0
$844$	−7.93749	+	13.7481i	−0.273220	+	0.473230i
$845$	19.9861	−	34.6170i	0.687543	−	1.19086i
$846$		0			0
$847$	−2.08237			−0.0715511
$848$	−0.811749	+	1.40599i	−0.0278756	+	0.0482819i
$849$		0			0
$850$	10.5686	−	18.3054i	0.362501	−	0.627871i
$851$	13.9503			0.478212
$852$		0			0
$853$	26.1014			0.893696			0.446848	−	0.894610i	$-0.352546\pi$
$853$	26.1014			0.893696			0.446848	+	0.894610i	$0.352546\pi$
$854$	−0.383581			−0.0131259
$855$		0			0
$856$	−17.2075			−0.588139
$857$	−41.6454			−1.42258			−0.711291	−	0.702898i	$-0.751889\pi$
$857$	−41.6454			−1.42258			−0.711291	+	0.702898i	$0.751889\pi$
$858$		0			0
$859$	9.44030			0.322099			0.161049	−	0.986946i	$-0.448512\pi$
$859$	9.44030			0.322099			0.161049	+	0.986946i	$0.448512\pi$
$860$	−33.2414	+	57.5758i	−1.13352	+	1.96332i
$861$		0			0
$862$	−3.53451	+	6.12196i	−0.120386	+	0.208515i
$863$	−31.0403			−1.05662			−0.528311	−	0.849051i	$-0.677175\pi$
$863$	−31.0403			−1.05662			−0.528311	+	0.849051i	$0.677175\pi$
$864$		0			0
$865$	39.8422	−	69.0088i	1.35468	−	2.34637i
$866$	−4.94349	+	8.56238i	−0.167987	+	0.290962i
$867$		0			0
$868$	−4.02698			−0.136684
$869$	8.04009	−	13.9258i	0.272741	−	0.472402i
$870$		0			0
$871$	1.05947			0.0358988
$872$	−10.9245	−	18.9218i	−0.369950	−	0.640772i
$873$		0			0
$874$	6.79090	−	2.57061i	0.229706	−	0.0869522i
$875$	−1.17184	+	2.02969i	−0.0396154	+	0.0686159i
$876$		0			0
$877$	20.7277	−	35.9014i	0.699924	−	1.21230i	−0.268568	−	0.963261i	$-0.586550\pi$
$877$	20.7277	−	35.9014i	0.699924	−	1.21230i	0.968492	−	0.249044i	$-0.0801163\pi$
$878$	0.722138			0.0243710
$879$		0			0
$880$	9.26261	+	16.0433i	0.312243	+	0.540820i
$881$	−15.2233			−0.512886			−0.256443	−	0.966559i	$-0.582551\pi$
$881$	−15.2233			−0.512886			−0.256443	+	0.966559i	$0.582551\pi$
$882$		0			0
$883$	−0.314882	+	0.545392i	−0.0105966	+	0.0183539i	−0.871275	−	0.490795i	$-0.836706\pi$
$883$	−0.314882	+	0.545392i	−0.0105966	+	0.0183539i	0.860678	+	0.509149i	$0.170040\pi$
$884$	−9.20753	−	15.9479i	−0.309683	−	0.536386i
$885$		0			0
$886$	−1.21694	−	2.10781i	−0.0408840	−	0.0708132i
$887$	1.12719			0.0378474			0.0189237	−	0.999821i	$-0.493976\pi$
$887$	1.12719			0.0378474			0.0189237	+	0.999821i	$0.493976\pi$
$888$		0			0
$889$	−0.237059	−	0.410599i	−0.00795071	−	0.0137710i
$890$	5.28798	+	9.15906i	0.177254	+	0.307012i
$891$		0			0
$892$	−29.0600			−0.973000
$893$	−11.3584	−	9.28567i	−0.380095	−	0.310733i
$894$		0			0
$895$	−22.5994	+	39.1432i	−0.755413	+	1.30841i
$896$	−1.23763	+	2.14365i	−0.0413465	+	0.0716142i
$897$		0			0
$898$	−13.1795			−0.439804
$899$	−17.8657	+	30.9443i	−0.595854	+	1.03205i
$900$		0			0
$901$	3.79240			0.126343
$902$	1.67907	+	2.90823i	0.0559068	+	0.0968334i
$903$		0			0
$904$	2.09840	+	3.63453i	0.0697917	+	0.120883i
$905$	4.66290	+	8.07637i	0.155000	+	0.268468i
$906$		0			0
$907$	28.7319			0.954028			0.477014	−	0.878896i	$-0.341719\pi$
$907$	28.7319			0.954028			0.477014	+	0.878896i	$0.341719\pi$
$908$	−1.10895	+	1.92075i	−0.0368016	+	0.0637423i
$909$		0			0
$910$	−0.218242	−	0.378006i	−0.00723466	−	0.0125308i
$911$	19.6724	−	34.0735i	0.651774	−	1.12891i	−0.330918	−	0.943660i	$-0.607358\pi$
$911$	19.6724	−	34.0735i	0.651774	−	1.12891i	0.982692	−	0.185246i	$-0.0593083\pi$
$912$		0			0
$913$	0.302262	+	0.523532i	0.0100034	+	0.0173264i
$914$	1.23300	−	2.13561i	0.0407839	−	0.0706398i
$915$		0			0
$916$	18.5954	+	32.2082i	0.614410	+	1.06419i
$917$	−0.378235	−	0.655122i	−0.0124904	−	0.0216340i
$918$		0			0
$919$	14.3218			0.472433			0.236217	−	0.971700i	$-0.424093\pi$
$919$	14.3218			0.472433			0.236217	+	0.971700i	$0.424093\pi$
$920$	−11.4374	+	19.8101i	−0.377079	+	0.653120i
$921$		0			0
$922$	−2.58577			−0.0851577
$923$	7.42300	+	12.8570i	0.244331	+	0.423194i
$924$		0			0
$925$	−11.8641	−	20.5493i	−0.390091	−	0.675657i
$926$	−3.18850	−	5.52264i	−0.104781	−	0.181485i
$927$		0			0
$928$	8.35672	+	14.4743i	0.274323	+	0.475141i
$929$	−1.78788			−0.0586586			−0.0293293	−	0.999570i	$-0.509337\pi$
$929$	−1.78788			−0.0586586			−0.0293293	+	0.999570i	$0.509337\pi$
$930$		0			0
$931$	−23.4124	−	19.1400i	−0.767312	−	0.627288i
$932$	11.5179	+	19.9496i	0.377282	+	0.653472i
$933$		0			0
$934$	13.5555			0.443548
$935$	21.6369	−	37.4763i	0.707603	−	1.22560i
$936$		0			0
$937$	6.96721	−	12.0676i	0.227609	−	0.394230i	−0.729490	−	0.683991i	$-0.760243\pi$
$937$	6.96721	−	12.0676i	0.227609	−	0.394230i	0.957099	+	0.289761i	$0.0935759\pi$
$938$	−0.0370219	+	0.0641238i	−0.00120881	+	0.00209372i
$939$		0			0
$940$	22.2859			0.726886
$941$	45.4329			1.48107			0.740535	−	0.672017i	$-0.234572\pi$
$941$	45.4329			1.48107			0.740535	+	0.672017i	$0.234572\pi$
$942$		0			0
$943$	12.4620	−	21.5848i	0.405818	−	0.702897i
$944$	−16.7062	+	28.9360i	−0.543741	+	0.941787i
$945$		0			0
$946$	3.03806	−	5.26208i	0.0987759	−	0.171085i
$947$	5.17499			0.168165			0.0840823	−	0.996459i	$-0.473204\pi$
$947$	5.17499			0.168165			0.0840823	+	0.996459i	$0.473204\pi$
$948$		0			0
$949$	2.44876	+	4.24138i	0.0794902	+	0.137681i
$950$	−9.56194	−	7.81702i	−0.310230	−	0.253618i
$951$		0			0
$952$	2.66902			0.0865035
$953$	−12.9234	−	22.3840i	−0.418630	−	0.725088i	0.577172	−	0.816622i	$-0.304156\pi$
$953$	−12.9234	−	22.3840i	−0.418630	−	0.725088i	−0.995802	+	0.0915347i	$0.970823\pi$
$954$		0			0
$955$	6.05867	+	10.4939i	0.196054	+	0.339575i
$956$	15.1162	+	26.1819i	0.488891	+	0.846785i
$957$		0			0
$958$	3.70247	+	6.41287i	0.119621	+	0.207190i
$959$	−1.06331			−0.0343360
$960$		0			0
$961$	−21.9755	+	38.0628i	−0.708888	+	1.22783i
$962$	1.52685			0.0492276
$963$		0			0
$964$	9.76565	+	16.9146i	0.314531	+	0.544783i
$965$	−0.884830	−	1.53257i	−0.0284837	−	0.0493352i
$966$		0			0
$967$	−13.0699	+	22.6377i	−0.420299	+	0.727979i	−0.995969	−	0.0897035i	$-0.971408\pi$
$967$	−13.0699	+	22.6377i	−0.420299	+	0.727979i	0.575670	+	0.817682i	$0.304741\pi$
$968$	5.97209	+	10.3440i	0.191950	+	0.332468i
$969$		0			0
$970$	4.24028	−	7.34438i	0.136147	−	0.235814i
$971$	−6.28902	−	10.8929i	−0.201824	−	0.349570i	0.747292	−	0.664496i	$-0.231354\pi$
$971$	−6.28902	−	10.8929i	−0.201824	−	0.349570i	−0.949116	+	0.314926i	$0.898020\pi$
$972$		0			0
$973$	2.15687	−	3.73581i	0.0691461	−	0.119764i
$974$	−0.200804			−0.00643417
$975$		0			0
$976$	−6.61229	−	11.4528i	−0.211654	−	0.366596i
$977$	−18.8495	−	32.6483i	−0.603050	−	1.04451i	−0.992356	−	0.123405i	$-0.960619\pi$
$977$	−18.8495	−	32.6483i	−0.603050	−	1.04451i	0.389307	−	0.921108i	$-0.372715\pi$
$978$		0			0
$979$	6.54338	+	11.3335i	0.209127	+	0.362219i
$980$	45.9366			1.46739
$981$		0			0
$982$	1.36185	−	2.35879i	0.0434583	−	0.0752719i
$983$	23.2447			0.741390			0.370695	−	0.928755i	$-0.379119\pi$
$983$	23.2447			0.741390			0.370695	+	0.928755i	$0.379119\pi$
$984$		0			0
$985$	−4.69996	+	8.14056i	−0.149753	+	0.259380i
$986$	5.70970	−	9.88950i	0.181834	−	0.314946i
$987$		0			0
$988$	−10.0631	+	3.80927i	−0.320151	+	0.121189i
$989$	−45.0968			−1.43400
$990$		0			0
$991$	−11.8484	−	20.5220i	−0.376376	−	0.651903i	0.614156	−	0.789185i	$-0.289497\pi$
$991$	−11.8484	−	20.5220i	−0.376376	−	0.651903i	−0.990532	+	0.137282i	$0.956163\pi$
$992$	17.5293	+	30.3616i	0.556555	+	0.963982i
$993$		0			0
$994$	−1.03755			−0.0329091
$995$	0.377957	+	0.654641i	0.0119820	+	0.0207535i
$996$		0			0
$997$	9.46564	+	16.3950i	0.299780	+	0.519234i	0.976085	−	0.217387i	$-0.0697535\pi$
$997$	9.46564	+	16.3950i	0.299780	+	0.519234i	−0.676306	+	0.736621i	$0.736420\pi$
$998$	−2.21559	+	3.83752i	−0.0701333	+	0.121475i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	513.2.h.c.235.8		32
3.2	odd	2		171.2.h.c.7.9	yes	32
9.4	even	3		513.2.g.c.64.9		32
9.5	odd	6		171.2.g.c.121.8	yes	32
19.11	even	3		513.2.g.c.505.9		32
57.11	odd	6		171.2.g.c.106.8	✓	32
171.49	even	3	inner	513.2.h.c.334.8		32
171.68	odd	6		171.2.h.c.49.9	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.g.c.106.8	✓	32	57.11	odd	6
171.2.g.c.121.8	yes	32	9.5	odd	6
171.2.h.c.7.9	yes	32	3.2	odd	2
171.2.h.c.49.9	yes	32	171.68	odd	6
513.2.g.c.64.9		32	9.4	even	3
513.2.g.c.505.9		32	19.11	even	3
513.2.h.c.235.8		32	1.1	even	1	trivial
513.2.h.c.334.8		32	171.49	even	3	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.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-0.370889 q^{2} -1.86244 q^{4} +(-1.77761 + 3.07890i) q^{5} +(-0.124876 + 0.216291i) q^{7} +1.43254 q^{8} +(0.659294 - 1.14193i) q^{10} +(0.815815 - 1.41303i) q^{11} -1.32541 q^{13} +(0.0463150 - 0.0802199i) q^{14} +3.19357 q^{16} +(-3.73000 - 6.46055i) q^{17} +(-4.07660 + 1.54315i) q^{19} +(3.31069 - 5.73428i) q^{20} +(-0.302577 + 0.524078i) q^{22} +4.49143 q^{23} +(-3.81976 - 6.61602i) q^{25} +0.491582 q^{26} +(0.232573 - 0.402829i) q^{28} +(-2.06363 - 3.57430i) q^{29} +(-4.32871 - 7.49755i) q^{31} -4.04953 q^{32} +(1.38342 + 2.39615i) q^{34} +(-0.443959 - 0.768960i) q^{35} +3.10599 q^{37} +(1.51197 - 0.572336i) q^{38} +(-2.54649 + 4.41064i) q^{40} +(2.77461 - 4.80577i) q^{41} -10.0406 q^{43} +(-1.51941 + 2.63169i) q^{44} -1.66582 q^{46} +(1.68288 + 2.91483i) q^{47} +(3.46881 + 6.00816i) q^{49} +(1.41671 + 2.45381i) q^{50} +2.46851 q^{52} +(-0.254182 + 0.440256i) q^{53} +(2.90039 + 5.02363i) q^{55} +(-0.178889 + 0.309845i) q^{56} +(0.765376 + 1.32567i) q^{58} +(-5.23121 + 9.06071i) q^{59} +(-2.07050 - 3.58621i) q^{61} +(1.60547 + 2.78076i) q^{62} -4.88521 q^{64} +(2.35606 - 4.08082i) q^{65} -0.799350 q^{67} +(6.94690 + 12.0324i) q^{68} +(0.164660 + 0.285199i) q^{70} +(-5.60051 - 9.70037i) q^{71} +(-1.84754 - 3.20004i) q^{73} -1.15198 q^{74} +(7.59244 - 2.87402i) q^{76} +(0.203751 + 0.352907i) q^{77} +9.85529 q^{79} +(-5.67691 + 9.83269i) q^{80} +(-1.02907 + 1.78241i) q^{82} +(-0.185251 + 0.320865i) q^{83} +26.5219 q^{85} +3.72396 q^{86} +(1.16868 - 2.02422i) q^{88} +(-4.01034 + 6.94611i) q^{89} +(0.165512 - 0.286675i) q^{91} -8.36503 q^{92} +(-0.624161 - 1.08108i) q^{94} +(2.49539 - 15.2946i) q^{95} +6.43155 q^{97} +(-1.28654 - 2.22836i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 34 q^{4} - 3 q^{5} + q^{7} + 36 q^{8} - 8 q^{10} - 7 q^{11} + 8 q^{13} - q^{14} + 22 q^{16} + 7 q^{17} + 7 q^{19} + 3 q^{20} - 8 q^{22} + 10 q^{23} - 9 q^{25} + 4 q^{26} - 10 q^{28} - 10 q^{29}+ \cdots - 18 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 + 34 * q^4 - 3 * q^5 + q^7 + 36 * q^8 - 8 * q^10 - 7 * q^11 + 8 * q^13 - q^14 + 22 * q^16 + 7 * q^17 + 7 * q^19 + 3 * q^20 - 8 * q^22 + 10 * q^23 - 9 * q^25 + 4 * q^26 - 10 * q^28 - 10 * q^29 - 10 * q^31 + 34 * q^32 - 13 * q^34 + 3 * q^35 + 2 * q^37 + 46 * q^38 + 12 * q^40 - 6 * q^41 - 14 * q^43 - 20 * q^44 + 9 * q^47 - 13 * q^49 - q^50 - 38 * q^52 - 16 * q^53 + 15 * q^55 + 6 * q^56 - 37 * q^59 - 12 * q^61 - 54 * q^62 - 64 * q^64 - 54 * q^65 + 22 * q^67 + 2 * q^68 + 24 * q^70 - 9 * q^71 - 10 * q^73 + 12 * q^74 - 40 * q^76 - 46 * q^77 + 16 * q^79 + 24 * q^80 + 7 * q^82 - 3 * q^83 + 54 * q^85 + 34 * q^86 + 9 * q^88 - 30 * q^89 - q^91 - 34 * q^92 - 18 * q^94 - 3 * q^95 - 18 * q^98

Introduction

L-functions

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