LMFDB - Embedded newform 513.2.g.c.505.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [513,2,Mod(64,513)]

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([2, 2]))

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

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

chi := DirichletCharacter("513.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 513 = 3^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	513.g (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			505.9
Character	$\chi$	$=$	513.505
Dual form			513.2.g.c.64.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.185445 + 0.321199i) q^{2} +(0.931221 - 1.61292i) q^{4} +3.55521 q^{5} +(-0.124876 + 0.216291i) q^{7} +1.43254 q^{8} +(0.659294 + 1.14193i) q^{10} +(0.815815 - 1.41303i) q^{11} +(0.662707 - 1.14784i) q^{13} -0.0926300 q^{14} +(-1.59679 - 2.76571i) q^{16} +(-3.73000 + 6.46055i) q^{17} +(-4.07660 - 1.54315i) q^{19} +(3.31069 - 5.73428i) q^{20} +0.605154 q^{22} +(-2.24572 + 3.88969i) q^{23} +7.63952 q^{25} +0.491582 q^{26} +(0.232573 + 0.402829i) q^{28} +4.12725 q^{29} +(-4.32871 - 7.49755i) q^{31} +(2.02477 - 3.50700i) q^{32} -2.76683 q^{34} +(-0.443959 + 0.768960i) q^{35} +3.10599 q^{37} +(-0.260326 - 1.59557i) q^{38} +5.09297 q^{40} -5.54922 q^{41} +(5.02032 + 8.69544i) q^{43} +(-1.51941 - 2.63169i) q^{44} -1.66582 q^{46} -3.36575 q^{47} +(3.46881 + 6.00816i) q^{49} +(1.41671 + 2.45381i) q^{50} +(-1.23425 - 2.13779i) q^{52} +(-0.254182 - 0.440256i) q^{53} +(2.90039 - 5.02363i) q^{55} +(-0.178889 + 0.309845i) q^{56} +(0.765376 + 1.32567i) q^{58} +10.4624 q^{59} +4.14100 q^{61} +(1.60547 - 2.78076i) q^{62} -4.88521 q^{64} +(2.35606 - 4.08082i) q^{65} +(0.399675 - 0.692257i) q^{67} +(6.94690 + 12.0324i) q^{68} -0.329319 q^{70} +(-5.60051 + 9.70037i) q^{71} +(-1.84754 + 3.20004i) q^{73} +(0.575989 + 0.997642i) q^{74} +(-6.28519 + 5.13823i) q^{76} +(0.203751 + 0.352907i) q^{77} +(-4.92764 - 8.53493i) q^{79} +(-5.67691 - 9.83269i) q^{80} +(-1.02907 - 1.78241i) q^{82} +(-0.185251 + 0.320865i) q^{83} +(-13.2609 + 22.9686i) q^{85} +(-1.86198 + 3.22504i) q^{86} +(1.16868 - 2.02422i) q^{88} +(-4.01034 - 6.94611i) q^{89} +(0.165512 + 0.286675i) q^{91} +(4.18251 + 7.24433i) q^{92} +(-0.624161 - 1.08108i) q^{94} +(-14.4932 - 5.48621i) q^{95} +(-3.21577 - 5.56988i) q^{97} +(-1.28654 + 2.22836i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - q^{2} - 17 q^{4} + 6 q^{5} + q^{7} + 36 q^{8} - 8 q^{10} - 7 q^{11} - 4 q^{13} + 2 q^{14} - 11 q^{16} + 7 q^{17} + 7 q^{19} + 3 q^{20} + 16 q^{22} - 5 q^{23} + 18 q^{25} + 4 q^{26} - 10 q^{28}+ \cdots - 18 q^{98}+O(q^{100}) $ 32 * q - q^2 - 17 * q^4 + 6 * q^5 + q^7 + 36 * q^8 - 8 * q^10 - 7 * q^11 - 4 * q^13 + 2 * q^14 - 11 * q^16 + 7 * q^17 + 7 * q^19 + 3 * q^20 + 16 * q^22 - 5 * q^23 + 18 * q^25 + 4 * q^26 - 10 * q^28 + 20 * q^29 - 10 * q^31 - 17 * q^32 + 26 * q^34 + 3 * q^35 + 2 * q^37 - 38 * q^38 - 24 * q^40 + 12 * q^41 + 7 * q^43 - 20 * q^44 - 18 * q^47 - 13 * q^49 - q^50 + 19 * q^52 - 16 * q^53 + 15 * q^55 + 6 * q^56 + 74 * q^59 + 24 * q^61 - 54 * q^62 - 64 * q^64 - 54 * q^65 - 11 * q^67 + 2 * q^68 - 48 * q^70 - 9 * q^71 - 10 * q^73 - 6 * q^74 + 29 * q^76 - 46 * q^77 - 8 * q^79 + 24 * q^80 + 7 * q^82 - 3 * q^83 - 27 * q^85 - 17 * q^86 + 9 * q^88 - 30 * q^89 - q^91 + 17 * q^92 - 18 * q^94 + 6 * q^95 - 18 * q^98

Character values

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

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

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 $

$2$	0.185445	+	0.321199i	0.131129	+	0.227122i	0.924112	−	0.382122i	$-0.124806\pi$
$2$	0.185445	+	0.321199i	0.131129	+	0.227122i	−0.792983	+	0.609244i	$0.791473\pi$
$3$		0			0
$3$		0			0
$4$	0.931221	−	1.61292i	0.465610	−	0.806461i
$5$	3.55521			1.58994			0.794969	−	0.606650i	$-0.207487\pi$
$5$	3.55521			1.58994			0.794969	+	0.606650i	$0.207487\pi$
$6$		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
$13$	0.662707	−	1.14784i	0.183802	−	0.318354i	−0.759370	−	0.650659i	$-0.774493\pi$
$13$	0.662707	−	1.14784i	0.183802	−	0.318354i	0.943172	+	0.332305i	$0.107826\pi$
$14$	−0.0926300			−0.0247564
$15$		0			0
$16$	−1.59679	−	2.76571i	−0.399196	−	0.691428i
$17$	−3.73000	+	6.46055i	−0.904658	+	1.56691i	−0.0832816	+	0.996526i	$0.526540\pi$
$17$	−3.73000	+	6.46055i	−0.904658	+	1.56691i	−0.821376	+	0.570387i	$0.806793\pi$
$18$		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
$22$	0.605154			0.129019
$23$	−2.24572	+	3.88969i	−0.468264	+	0.811057i	−0.999342	−	0.0362656i	$-0.988454\pi$
$23$	−2.24572	+	3.88969i	−0.468264	+	0.811057i	0.531078	+	0.847323i	$0.321787\pi$
$24$		0			0
$25$	7.63952			1.52790
$26$	0.491582			0.0964071
$27$		0			0
$28$	0.232573	+	0.402829i	0.0439522	+	0.0761275i
$29$	4.12725			0.766411			0.383206	−	0.923663i	$-0.374820\pi$
$29$	4.12725			0.766411			0.383206	+	0.923663i	$0.374820\pi$
$30$		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	$-0.450159\pi$
$32$	2.02477	−	3.50700i	0.357932	−	0.619956i
$33$		0			0
$34$	−2.76683			−0.474508
$35$	−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	$0.417822\pi$
$38$	−0.260326	−	1.59557i	−0.0422305	−	0.258836i
$39$		0			0
$40$	5.09297			0.805269
$41$	−5.54922			−0.866643			−0.433322	−	0.901239i	$-0.642659\pi$
$41$	−5.54922			−0.866643			−0.433322	+	0.901239i	$0.642659\pi$
$42$		0			0
$43$	5.02032	+	8.69544i	0.765591	+	1.32604i	0.939934	+	0.341358i	$0.110887\pi$
$43$	5.02032	+	8.69544i	0.765591	+	1.32604i	−0.174342	+	0.984685i	$0.555780\pi$
$44$	−1.51941	−	2.63169i	−0.229059	−	0.396742i
$45$		0			0
$46$	−1.66582			−0.245612
$47$	−3.36575			−0.490946			−0.245473	−	0.969403i	$-0.578943\pi$
$47$	−3.36575			−0.490946			−0.245473	+	0.969403i	$0.578943\pi$
$48$		0			0
$49$	3.46881	+	6.00816i	0.495545	+	0.858308i
$50$	1.41671	+	2.45381i	0.200353	+	0.347021i
$51$		0			0
$52$	−1.23425	−	2.13779i	−0.171160	−	0.296458i
$53$	−0.254182	−	0.440256i	−0.0349146	−	0.0604739i	0.848040	−	0.529932i	$-0.177783\pi$
$53$	−0.254182	−	0.440256i	−0.0349146	−	0.0604739i	−0.882955	+	0.469458i	$0.844449\pi$
$54$		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
$59$	10.4624			1.36209			0.681045	−	0.732242i	$-0.261526\pi$
$59$	10.4624			1.36209			0.681045	+	0.732242i	$0.261526\pi$
$60$		0			0
$61$	4.14100			0.530201			0.265100	−	0.964221i	$-0.414595\pi$
$61$	4.14100			0.530201			0.265100	+	0.964221i	$0.414595\pi$
$62$	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
$67$	0.399675	−	0.692257i	0.0488281	−	0.0845727i	−0.840578	−	0.541690i	$-0.817785\pi$
$67$	0.399675	−	0.692257i	0.0488281	−	0.0845727i	0.889406	+	0.457117i	$0.151118\pi$
$68$	6.94690	+	12.0324i	0.842436	+	1.45914i
$69$		0			0
$70$	−0.329319			−0.0393612
$71$	−5.60051	+	9.70037i	−0.664658	+	1.15122i	0.314719	+	0.949185i	$0.398090\pi$
$71$	−5.60051	+	9.70037i	−0.664658	+	1.15122i	−0.979378	+	0.202037i	$0.935244\pi$
$72$		0			0
$73$	−1.84754	+	3.20004i	−0.216239	+	0.374537i	−0.953655	−	0.300902i	$-0.902712\pi$
$73$	−1.84754	+	3.20004i	−0.216239	+	0.374537i	0.737416	+	0.675439i	$0.236046\pi$
$74$	0.575989	+	0.997642i	0.0669573	+	0.115974i
$75$		0			0
$76$	−6.28519	+	5.13823i	−0.720961	+	0.589396i
$77$	0.203751	+	0.352907i	0.0232195	+	0.0402174i
$78$		0			0
$79$	−4.92764	−	8.53493i	−0.554403	−	0.960255i	−0.997950	−	0.0640032i	$-0.979613\pi$
$79$	−4.92764	−	8.53493i	−0.554403	−	0.960255i	0.443546	−	0.896251i	$-0.353720\pi$
$80$	−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
$85$	−13.2609	+	22.9686i	−1.43835	+	2.49130i
$86$	−1.86198	+	3.22504i	−0.200782	+	0.347765i
$87$		0			0
$88$	1.16868	−	2.02422i	0.124582	−	0.215783i
$89$	−4.01034	−	6.94611i	−0.425095	−	0.736286i	0.571334	−	0.820717i	$-0.306426\pi$
$89$	−4.01034	−	6.94611i	−0.425095	−	0.736286i	−0.996429	+	0.0844315i	$0.973093\pi$
$90$		0			0
$91$	0.165512	+	0.286675i	0.0173504	+	0.0300517i
$92$	4.18251	+	7.24433i	0.436057	+	0.755273i
$93$		0			0
$94$	−0.624161	−	1.08108i	−0.0643772	−	0.111505i
$95$	−14.4932	−	5.48621i	−1.48697	−	0.562873i
$96$		0			0
$97$	−3.21577	−	5.56988i	−0.326512	−	0.565536i	0.655305	−	0.755364i	$-0.272540\pi$
$97$	−3.21577	−	5.56988i	−0.326512	−	0.565536i	−0.981817	+	0.189829i	$0.939207\pi$
$98$	−1.28654	+	2.22836i	−0.129961	+	0.225098i
$99$		0			0
$100$	7.11408	−	12.3220i	0.711408	−	1.23220i
$101$	−7.56353			−0.752600			−0.376300	−	0.926498i	$-0.622804\pi$
$101$	−7.56353			−0.752600			−0.376300	+	0.926498i	$0.622804\pi$
$102$		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	$-0.405030\pi$
$104$	0.949353	−	1.64433i	0.0930917	−	0.161240i
$105$		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	0.226261	+	0.974067i	$0.427350\pi$
$109$	−7.62598	+	13.2086i	−0.730436	+	1.26515i	−0.956697	+	0.291086i	$0.905984\pi$
$110$	2.15145			0.205133
$111$		0			0
$112$	0.797598			0.0753659
$113$	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
$119$	−0.931572	−	1.61353i	−0.0853970	−	0.147912i
$120$		0			0
$121$	4.16889	+	7.22073i	0.378990	+	0.656430i
$122$	0.767926	+	1.33009i	0.0695248	+	0.120420i
$123$		0			0
$124$	−16.1240			−1.44797
$125$	9.38406			0.839336
$126$		0			0
$127$	−0.949181	−	1.64403i	−0.0842262	−	0.145884i	0.820835	−	0.571165i	$-0.193509\pi$
$127$	−0.949181	−	1.64403i	−0.0842262	−	0.145884i	−0.905061	+	0.425281i	$0.860175\pi$
$128$	−4.95547	−	8.58313i	−0.438006	−	0.758648i
$129$		0			0
$130$	1.74768			0.153281
$131$	3.02889			0.264636			0.132318	−	0.991207i	$-0.457758\pi$
$131$	3.02889			0.264636			0.132318	+	0.991207i	$0.457758\pi$
$132$		0			0
$133$	0.842837	−	0.689031i	0.0730832	−	0.0597465i
$134$	0.296470			0.0256111
$135$		0			0
$136$	−5.34336	+	9.25497i	−0.458190	+	0.793608i
$137$	−4.25747			−0.363741			−0.181870	−	0.983323i	$-0.558215\pi$
$137$	−4.25747			−0.363741			−0.181870	+	0.983323i	$0.558215\pi$
$138$		0			0
$139$	8.63607	−	14.9581i	0.732502	−	1.26873i	−0.223308	−	0.974748i	$-0.571686\pi$
$139$	8.63607	−	14.9581i	0.732502	−	1.26873i	0.955811	−	0.293983i	$-0.0949809\pi$
$140$	0.826848	+	1.43214i	0.0698814	+	0.121038i
$141$		0			0
$142$	−4.15434			−0.348624
$143$	−1.08129	−	1.87285i	−0.0904222	−	0.156616i
$144$		0			0
$145$	14.6732			1.21855
$146$	−1.37047			−0.113421
$147$		0			0
$148$	2.89236	−	5.00972i	0.237751	−	0.411796i
$149$	−1.84615			−0.151242			−0.0756211	−	0.997137i	$-0.524094\pi$
$149$	−1.84615			−0.151242			−0.0756211	+	0.997137i	$0.524094\pi$
$150$		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
$155$	−15.3895	−	26.6554i	−1.23611	−	2.14101i
$156$		0			0
$157$	20.7711			1.65772			0.828858	−	0.559459i	$-0.188991\pi$
$157$	20.7711			1.65772			0.828858	+	0.559459i	$0.188991\pi$
$158$	1.82761	−	3.16551i	0.145397	−	0.251835i
$159$		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
$166$	−0.137415			−0.0106655
$167$	−0.750032	+	1.29909i	−0.0580392	+	0.100527i	−0.893585	−	0.448894i	$-0.851818\pi$
$167$	−0.750032	+	1.29909i	−0.0580392	+	0.100527i	0.835546	+	0.549421i	$0.185152\pi$
$168$		0			0
$169$	5.62164	+	9.73696i	0.432434	+	0.748997i
$170$	−9.83667			−0.754438
$171$		0			0
$172$	18.7001			1.42587
$173$	11.2067	+	19.4106i	0.852031	+	1.47576i	0.879372	+	0.476135i	$0.157963\pi$
$173$	11.2067	+	19.4106i	0.852031	+	1.47576i	−0.0273414	+	0.999626i	$0.508704\pi$
$174$		0			0
$175$	−0.953990	+	1.65236i	−0.0721149	+	0.124907i
$176$	−5.21072			−0.392773
$177$		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	0.910644	−	0.413191i	$-0.135586\pi$
$181$	1.31157	+	2.27170i	0.0974880	+	0.168854i	−0.813156	+	0.582045i	$0.802253\pi$
$182$	−0.0613866	+	0.106325i	−0.00455027	+	0.00788131i
$183$		0			0
$184$	−3.21707	+	5.57213i	−0.237166	+	0.410783i
$185$	11.0425			0.811857
$186$		0			0
$187$	6.08598	+	10.5412i	0.445051	+	0.770850i
$188$	−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
$193$	0.497765			0.0358299			0.0179150	−	0.999840i	$-0.494297\pi$
$193$	0.497765			0.0358299			0.0179150	+	0.999840i	$0.494297\pi$
$194$	1.19269	−	2.06581i	0.0856305	−	0.148316i
$195$		0			0
$196$	12.9209			0.922923
$197$	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	0.869769	−	0.493459i	$-0.164268\pi$
$199$	0.106311	+	0.184136i	0.00753617	+	0.0130530i	−0.862233	+	0.506512i	$0.830934\pi$
$200$	10.9439			0.773851
$201$		0			0
$202$	−1.40262	−	2.42940i	−0.0986877	−	0.170932i
$203$	−0.515393	+	0.892687i	−0.0361735	+	0.0626543i
$204$		0			0
$205$	−19.7287			−1.37791
$206$	2.56257	−	4.43851i	0.178543	−	0.309245i
$207$		0			0
$208$	−4.23280			−0.293492
$209$	−5.50627	+	4.50145i	−0.380877	+	0.311372i
$210$		0			0
$211$	−8.52375			−0.586799			−0.293400	−	0.955990i	$-0.594787\pi$
$211$	−8.52375			−0.586799			−0.293400	+	0.955990i	$0.594787\pi$
$212$	−0.946799			−0.0650264
$213$		0			0
$214$	−2.22754	−	3.85821i	−0.152271	−	0.263742i
$215$	17.8483	+	30.9141i	1.21724	+	2.10833i
$216$		0			0
$217$	2.16220			0.146780
$218$	−5.65678			−0.383126
$219$		0			0
$220$	−5.40181	−	9.35621i	−0.364190	−	0.630796i
$221$	4.94380	+	8.56290i	0.332556	+	0.576003i
$222$		0			0
$223$	−7.80159	−	13.5127i	−0.522433	−	0.904880i	−0.999659	−	0.0260998i	$-0.991691\pi$
$223$	−7.80159	−	13.5127i	−0.522433	−	0.904880i	0.477227	−	0.878780i	$-0.341642\pi$
$224$	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	$-0.396021\pi$
$230$	−5.92235			−0.390508
$231$		0			0
$232$	5.91244			0.388171
$233$	−6.18432	+	10.7115i	−0.405148	+	0.701737i	−0.994339	−	0.106257i	$-0.966113\pi$
$233$	−6.18432	+	10.7115i	−0.405148	+	0.701737i	0.589191	+	0.807994i	$0.299447\pi$
$234$		0			0
$235$	−11.9660			−0.780573
$236$	9.74281	−	16.8750i	0.634203	−	1.09847i
$237$		0			0
$238$	0.345510	−	0.598440i	0.0223961	−	0.0387911i
$239$	−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
$241$	10.4869			0.675523			0.337762	−	0.941232i	$-0.390330\pi$
$241$	10.4869			0.675523			0.337762	+	0.941232i	$0.390330\pi$
$242$	−1.54620	+	2.67809i	−0.0993933	+	0.172154i
$243$		0			0
$244$	3.85619	−	6.67911i	0.246867	−	0.427586i
$245$	12.3324	+	21.3603i	0.787885	+	1.36466i
$246$		0			0
$247$	−4.47288	+	3.65665i	−0.284603	+	0.232667i
$248$	−6.20104	−	10.7405i	−0.393767	−	0.682024i
$249$		0			0
$250$	1.74022	+	3.01415i	0.110061	+	0.190632i
$251$	7.02198	+	12.1624i	0.443223	+	0.767685i	0.997927	−	0.0643630i	$-0.0205016\pi$
$251$	7.02198	+	12.1624i	0.443223	+	0.767685i	−0.554703	+	0.832048i	$0.687168\pi$
$252$		0			0
$253$	3.66418	+	6.34654i	0.230365	+	0.399004i
$254$	0.352041	−	0.609753i	0.0220890	−	0.0382593i
$255$		0			0
$256$	−3.04728	+	5.27805i	−0.190455	+	0.329878i
$257$	8.58033	−	14.8616i	0.535227	−	0.927040i	−0.463926	−	0.885874i	$-0.653560\pi$
$257$	8.58033	−	14.8616i	0.535227	−	0.927040i	0.999152	−	0.0411655i	$-0.0131071\pi$
$258$		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
$263$	9.74973	+	16.8870i	0.601194	+	1.04130i	0.992641	+	0.121098i	$0.0386415\pi$
$263$	9.74973	+	16.8870i	0.601194	+	1.04130i	−0.391446	+	0.920201i	$0.628025\pi$
$264$		0			0
$265$	−0.903671	−	1.56520i	−0.0555121	−	0.0961498i
$266$	0.377616	+	0.142942i	0.0231531	+	0.00876431i
$267$		0			0
$268$	−0.744371	−	1.28929i	−0.0454697	−	0.0787558i
$269$	11.5796	−	20.0564i	0.706020	−	1.22286i	−0.260303	−	0.965527i	$-0.583822\pi$
$269$	11.5796	−	20.0564i	0.706020	−	1.22286i	0.966322	−	0.257335i	$-0.0828443\pi$
$270$		0			0
$271$	−11.0388	+	19.1197i	−0.670557	+	1.16144i	0.307190	+	0.951648i	$0.400611\pi$
$271$	−11.0388	+	19.1197i	−0.670557	+	1.16144i	−0.977746	+	0.209790i	$0.932722\pi$
$272$	23.8240			1.44454
$273$		0			0
$274$	−0.789525	−	1.36750i	−0.0476970	−	0.0826136i
$275$	6.23244	−	10.7949i	0.375830	−	0.650957i
$276$		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
$281$	−28.8083			−1.71856			−0.859280	−	0.511506i	$-0.829088\pi$
$281$	−28.8083			−1.71856			−0.859280	+	0.511506i	$0.829088\pi$
$282$		0			0
$283$	16.0204			0.952314			0.476157	−	0.879360i	$-0.342029\pi$
$283$	16.0204			0.952314			0.476157	+	0.879360i	$0.342029\pi$
$284$	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
$290$	2.72107	+	4.71304i	0.159787	+	0.276759i
$291$		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
$295$	37.1961			2.16564
$296$	4.44945			0.258619
$297$		0			0
$298$	−0.342358	−	0.592981i	−0.0198322	−	0.0343504i
$299$	2.97650	+	5.15546i	0.172136	+	0.298148i
$300$		0			0
$301$	−2.50766			−0.144539
$302$	−4.15341			−0.239002
$303$		0			0
$304$	2.24156	+	13.7388i	0.128562	+	0.787974i
$305$	14.7221			0.842987
$306$		0			0
$307$	2.29987	−	3.98349i	0.131260	−	0.227350i	−0.792902	−	0.609349i	$-0.791431\pi$
$307$	2.29987	−	3.98349i	0.131260	−	0.227350i	0.924163	+	0.381999i	$0.124764\pi$
$308$	0.758947			0.0432450
$309$		0			0
$310$	5.70779	−	9.88619i	0.324181	−	0.561498i
$311$	−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
$313$	−18.3876			−1.03933			−0.519664	−	0.854371i	$-0.673943\pi$
$313$	−18.3876			−1.03933			−0.519664	+	0.854371i	$0.673943\pi$
$314$	3.85189	+	6.67167i	0.217375	+	0.376504i
$315$		0			0
$316$	−18.3549			−1.03254
$317$	−1.35820			−0.0762844			−0.0381422	−	0.999272i	$-0.512144\pi$
$317$	−1.35820			−0.0762844			−0.0381422	+	0.999272i	$0.512144\pi$
$318$		0			0
$319$	3.36707	−	5.83194i	0.188520	−	0.326526i
$320$	−17.3680			−0.970899
$321$		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
$326$	−1.00450	−	1.73984i	−0.0556341	−	0.0963610i
$327$		0			0
$328$	−7.94947			−0.438936
$329$	0.420300	−	0.727982i	0.0231719	−	0.0401349i
$330$		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
$337$	36.5224			1.98950			0.994750	−	0.102335i	$-0.0326312\pi$
$337$	36.5224			1.98950			0.994750	+	0.102335i	$0.0326312\pi$
$338$	−2.08500	+	3.61133i	−0.113409	+	0.196431i
$339$		0			0
$340$	24.6977	+	42.7777i	1.33942	+	2.31995i
$341$	−14.1257			−0.764951
$342$		0			0
$343$	−3.48094			−0.187953
$344$	7.19179	+	12.4565i	0.387755	+	0.671612i
$345$		0			0
$346$	−4.15645	+	7.19918i	−0.223452	+	0.387030i
$347$	10.1508			0.544926			0.272463	−	0.962166i	$-0.412162\pi$
$347$	10.1508			0.544926			0.272463	+	0.962166i	$0.412162\pi$
$348$		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
$355$	−19.9110	+	34.4869i	−1.05677	+	1.83037i
$356$	−14.9380			−0.791714
$357$		0			0
$358$	2.35762	+	4.08353i	0.124604	+	0.215821i
$359$	−3.82747	+	6.62938i	−0.202006	+	0.349885i	−0.949175	−	0.314750i	$-0.898079\pi$
$359$	−3.82747	+	6.62938i	−0.202006	+	0.349885i	0.747168	+	0.664635i	$0.231413\pi$
$360$		0			0
$361$	14.2374	+	12.5816i	0.749337	+	0.662189i
$362$	−0.486446	+	0.842549i	−0.0255670	+	0.0442834i
$363$		0			0
$364$	0.616512			0.0323140
$365$	−6.56841	+	11.3768i	−0.343806	+	0.595490i
$366$		0			0
$367$	−24.7775			−1.29338			−0.646688	−	0.762755i	$-0.723846\pi$
$367$	−24.7775			−1.29338			−0.646688	+	0.762755i	$0.723846\pi$
$368$	14.3437			0.747717
$369$		0			0
$370$	2.04776	+	3.54683i	0.106458	+	0.184391i
$371$	0.126965			0.00659167
$372$		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	$0.628534\pi$
$374$	−2.25722	+	3.90962i	−0.116718	+	0.202162i
$375$		0			0
$376$	−4.82157			−0.248653
$377$	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	$0.231555\pi$
$380$	−22.3452	+	18.2675i	−1.14628	+	0.937103i
$381$		0			0
$382$	1.26411			0.0646777
$383$	2.82855			0.144532			0.0722662	−	0.997385i	$-0.476977\pi$
$383$	2.82855			0.144532			0.0722662	+	0.997385i	$0.476977\pi$
$384$		0			0
$385$	0.724377	+	1.25466i	0.0369177	+	0.0639433i
$386$	0.0923078	+	0.159882i	0.00469834	+	0.00813777i
$387$		0			0
$388$	−11.9784			−0.608110
$389$	−19.1659			−0.971750			−0.485875	−	0.874028i	$-0.661499\pi$
$389$	−19.1659			−0.971750			−0.485875	+	0.874028i	$0.661499\pi$
$390$		0			0
$391$	−16.7530	−	29.0171i	−0.847238	−	1.46746i
$392$	4.96920	+	8.60691i	0.250983	+	0.434715i
$393$		0			0
$394$	0.490312	+	0.849245i	0.0247016	+	0.0427844i
$395$	−17.5188	−	30.3435i	−0.881467	−	1.52675i
$396$		0			0
$397$	15.9590	−	27.6417i	0.800958	−	1.38730i	−0.118029	−	0.993010i	$-0.537658\pi$
$397$	15.9590	−	27.6417i	0.800958	−	1.38730i	0.918986	−	0.394289i	$-0.129009\pi$
$398$	−0.0394295	+	0.0682939i	−0.00197642	+	0.00342326i
$399$		0			0
$400$	−12.1987	−	21.1287i	−0.609934	−	1.05644i
$401$	−38.3406			−1.91464			−0.957320	−	0.289030i	$-0.906667\pi$
$401$	−38.3406			−1.91464			−0.957320	+	0.289030i	$0.906667\pi$
$402$		0			0
$403$	−11.4747			−0.571595
$404$	−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
$409$	−1.14644	+	1.98569i	−0.0566877	+	0.0981860i	−0.892977	−	0.450103i	$-0.851387\pi$
$409$	−1.14644	+	1.98569i	−0.0566877	+	0.0981860i	0.836289	+	0.548289i	$0.184721\pi$
$410$	−3.65857	−	6.33683i	−0.180684	−	0.312954i
$411$		0			0
$412$	−25.7362			−1.26793
$413$	−1.30650	+	2.26292i	−0.0642886	+	0.111351i
$414$		0			0
$415$	−0.658608	+	1.14074i	−0.0323298	+	0.0559968i
$416$	−2.68366	−	4.64823i	−0.131577	−	0.227898i
$417$		0			0
$418$	−2.46697	−	0.933841i	−0.120663	−	0.0456756i
$419$	−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
$421$	−12.9323	−	22.3994i	−0.630280	−	1.09168i	−0.987494	−	0.157655i	$-0.949607\pi$
$421$	−12.9323	−	22.3994i	−0.630280	−	1.09168i	0.357214	−	0.934023i	$-0.383727\pi$
$422$	−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
$427$	−0.517110	+	0.895661i	−0.0250247	+	0.0433441i
$428$	−11.1857	+	19.3742i	−0.540682	+	0.936489i
$429$		0			0
$430$	−6.61973	+	11.4657i	−0.319232	+	0.552926i
$431$	9.52984	+	16.5062i	0.459036	+	0.795074i	0.998910	−	0.0466716i	$-0.0148614\pi$
$431$	9.52984	+	16.5062i	0.459036	+	0.795074i	−0.539874	+	0.841746i	$0.681528\pi$
$432$		0			0
$433$	13.3288	+	23.0861i	0.640540	+	1.10945i	0.985312	+	0.170761i	$0.0546226\pi$
$433$	13.3288	+	23.0861i	0.640540	+	1.10945i	−0.344773	+	0.938686i	$0.612044\pi$
$434$	0.400969	+	0.694498i	0.0192471	+	0.0333370i
$435$		0			0
$436$	14.2029	+	24.6002i	0.680197	+	1.17814i
$437$	15.1573	−	12.3913i	0.725070	−	0.592755i
$438$		0			0
$439$	0.973523	+	1.68619i	0.0464637	+	0.0804775i	0.888322	−	0.459221i	$-0.151871\pi$
$439$	0.973523	+	1.68619i	0.0464637	+	0.0804775i	−0.841858	+	0.539699i	$0.818538\pi$
$440$	4.15492	−	7.19653i	0.198078	−	0.343081i
$441$		0			0
$442$	−1.83360	+	3.17589i	−0.0872154	+	0.151062i
$443$	−6.56230			−0.311784			−0.155892	−	0.987774i	$-0.549825\pi$
$443$	−6.56230			−0.311784			−0.155892	+	0.987774i	$0.549825\pi$
$444$		0			0
$445$	−14.2576	−	24.6949i	−0.675875	−	1.17065i
$446$	2.89352	−	5.01173i	0.137012	−	0.237312i
$447$		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
$452$	5.45626			0.256641
$453$		0			0
$454$	0.441674			0.0207288
$455$	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
$461$	−3.48590	−	6.03776i	−0.162355	−	0.281207i	0.773358	−	0.633970i	$-0.218576\pi$
$461$	−3.48590	−	6.03776i	−0.162355	−	0.281207i	−0.935713	+	0.352763i	$0.885242\pi$
$462$		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
$466$	−4.58739			−0.212507
$467$	−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
$470$	−2.21902	−	3.84346i	−0.102356	−	0.177286i
$471$		0			0
$472$	14.9878			0.689869
$473$	16.3826			0.753272
$474$		0			0
$475$	−31.1433	−	11.7889i	−1.42895	−	0.540912i
$476$	−3.47000			−0.159047
$477$		0			0
$478$	3.01025	−	5.21391i	0.137686	−	0.238479i
$479$	19.9654			0.912242			0.456121	−	0.889918i	$-0.349238\pi$
$479$	19.9654			0.912242			0.456121	+	0.889918i	$0.349238\pi$
$480$		0			0
$481$	2.05836	−	3.56519i	0.0938533	−	0.162559i
$482$	1.94475	+	3.36840i	0.0885807	+	0.153426i
$483$		0			0
$484$	15.5286			0.705847
$485$	−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	$0.496095\pi$
$488$	5.93214			0.268535
$489$		0			0
$490$	−4.57394	+	7.92229i	−0.206629	+	0.357893i
$491$	7.34369			0.331416			0.165708	−	0.986175i	$-0.447009\pi$
$491$	7.34369			0.331416			0.165708	+	0.986175i	$0.447009\pi$
$492$		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
$497$	−1.39873	−	2.42268i	−0.0627418	−	0.108672i
$498$		0			0
$499$	−11.9475			−0.534842			−0.267421	−	0.963580i	$-0.586171\pi$
$499$	−11.9475			−0.534842			−0.267421	+	0.963580i	$0.586171\pi$
$500$	8.73863	−	15.1358i	0.390803	−	0.676891i
$501$		0			0
$502$	−2.60437	+	4.51091i	−0.116239	+	0.201332i
$503$	−14.7358	−	25.5232i	−0.657038	−	1.13802i	−0.981379	−	0.192083i	$-0.938476\pi$
$503$	−14.7358	−	25.5232i	−0.657038	−	1.13802i	0.324341	−	0.945940i	$-0.394858\pi$
$504$		0			0
$505$	−26.8900			−1.19659
$506$	−1.35900	+	2.35386i	−0.0604151	+	0.104642i
$507$		0			0
$508$	−3.53559			−0.156866
$509$	8.95222	−	15.5057i	0.396800	−	0.687278i	−0.596529	−	0.802592i	$-0.703454\pi$
$509$	8.95222	−	15.5057i	0.396800	−	0.687278i	0.993329	+	0.115314i	$0.0367873\pi$
$510$		0			0
$511$	−0.461426	−	0.799214i	−0.0204123	−	0.0353552i
$512$	−22.0823			−0.975909
$513$		0			0
$514$	6.36470			0.280735
$515$	−24.5639	−	42.5459i	−1.08242	−	1.87480i
$516$		0			0
$517$	−2.74583	+	4.75592i	−0.120762	+	0.209165i
$518$	−0.287708			−0.0126412
$519$		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	−0.996879	−	0.0789417i	$-0.974846\pi$
$523$	−12.9624	−	22.4515i	−0.566805	−	0.981735i	0.430074	−	0.902794i	$-0.358487\pi$
$524$	2.82057	−	4.88537i	0.123217	−	0.213418i
$525$		0			0
$526$	−3.61607	+	6.26321i	−0.157668	+	0.273089i
$527$	64.5844			2.81334
$528$		0			0
$529$	1.41352	+	2.44829i	0.0614573	+	0.106447i
$530$	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
$535$	−42.7048			−1.84629
$536$	0.572549	−	0.991684i	0.0247304	−	0.0428342i
$537$		0			0
$538$	8.58948			0.370319
$539$	11.3196			0.487571
$540$		0			0
$541$	−12.3043	−	21.3116i	−0.529001	−	0.916257i	−0.999428	−	0.0338181i	$-0.989233\pi$
$541$	−12.3043	−	21.3116i	−0.529001	−	0.916257i	0.470427	−	0.882439i	$-0.344100\pi$
$542$	−8.18831			−0.351718
$543$		0			0
$544$	15.1048	+	26.1622i	0.647611	+	1.12170i
$545$	−27.1120	+	46.9593i	−1.16135	+	2.01151i
$546$		0			0
$547$	12.8871			0.551014			0.275507	−	0.961299i	$-0.411154\pi$
$547$	12.8871			0.551014			0.275507	+	0.961299i	$0.411154\pi$
$548$	−3.96465	+	6.86697i	−0.169361	+	0.293343i
$549$		0			0
$550$	4.62308			0.197129
$551$	−16.8252	−	6.36895i	−0.716776	−	0.271327i
$552$		0			0
$553$	2.46137			0.104668
$554$	10.9777			0.466399
$555$		0			0
$556$	−16.0842	−	27.8586i	−0.682121	−	1.18147i
$557$	11.8767	+	20.5710i	0.503231	+	0.871622i	0.999993	+	0.00373498i	$0.00118888\pi$
$557$	11.8767	+	20.5710i	0.503231	+	0.871622i	−0.496762	+	0.867887i	$0.665478\pi$
$558$		0			0
$559$	13.3080			0.562868
$560$	2.83563			0.119827
$561$		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
$565$	5.20772	+	9.02003i	0.219090	+	0.379476i
$566$	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	$0.847734\pi$
$572$	−4.02769			−0.168406
$573$		0			0
$574$	0.514024			0.0214550
$575$	−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
$580$	13.6640	−	23.6668i	0.567368	−	0.982710i
$581$	−0.0462667	−	0.0801364i	−0.00191947	−	0.00332462i
$582$		0			0
$583$	−0.829462			−0.0343528
$584$	−2.64668	+	4.58418i	−0.109520	+	0.189695i
$585$		0			0
$586$	−0.148496	+	0.257202i	−0.00613430	+	0.0106249i
$587$	12.1339	+	21.0165i	0.500819	+	0.867444i	1.00000		0.000946197i	$0.000301184\pi$
$587$	12.1339	+	21.0165i	0.500819	+	0.867444i	−0.499180	+	0.866498i	$0.666365\pi$
$588$		0			0
$589$	6.07663	+	37.2444i	0.250383	+	1.53463i
$590$	6.89781	+	11.9474i	0.283978	+	0.491865i
$591$		0			0
$592$	−4.95960	−	8.59028i	−0.203838	−	0.353058i
$593$	−16.5350	−	28.6395i	−0.679013	−	1.17608i	−0.975279	−	0.220979i	$-0.929075\pi$
$593$	−16.5350	−	28.6395i	−0.679013	−	1.17608i	0.296266	−	0.955106i	$-0.404259\pi$
$594$		0			0
$595$	−3.31193	−	5.73644i	−0.135776	−	0.235171i
$596$	−1.71917	+	2.97769i	−0.0704199	+	0.121971i
$597$		0			0
$598$	−1.10395	+	1.91210i	−0.0451440	+	0.0781917i
$599$	−6.64241	+	11.5050i	−0.271401	+	0.470081i	−0.969221	−	0.246193i	$-0.920820\pi$
$599$	−6.64241	+	11.5050i	−0.271401	+	0.470081i	0.697820	+	0.716274i	$0.254154\pi$
$600$		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
$605$	14.8213	+	25.6712i	0.602571	+	1.04368i
$606$		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	$0.848753\pi$
$608$	−13.6660	+	11.1721i	−0.554229	+	0.453090i
$609$		0			0
$610$	2.73014	+	4.72874i	0.110540	+	0.191461i
$611$	−2.23051	+	3.86336i	−0.0902368	+	0.156295i
$612$		0			0
$613$	2.16079	−	3.74260i	0.0872736	−	0.151162i	−0.819084	−	0.573673i	$-0.805518\pi$
$613$	2.16079	−	3.74260i	0.0872736	−	0.151162i	0.906358	+	0.422511i	$0.138851\pi$
$614$	1.70599			0.0688482
$615$		0			0
$616$	0.291880	+	0.505552i	0.0117602	+	0.0203693i
$617$	−4.80522	+	8.32289i	−0.193451	+	0.335067i	−0.946392	−	0.323021i	$-0.895301\pi$
$617$	−4.80522	+	8.32289i	−0.193451	+	0.335067i	0.752941	+	0.658088i	$0.228635\pi$
$618$		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
$623$	2.00317			0.0802554
$624$		0			0
$625$	−4.83530			−0.193412
$626$	−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	0.999994	+	0.00331669i	$0.00105574\pi$
$631$	12.6319	+	21.8792i	0.502870	+	0.870996i	−0.497125	+	0.867679i	$0.665611\pi$
$632$	−7.05903	−	12.2266i	−0.280793	−	0.486348i
$633$		0			0
$634$	−0.251872	−	0.436254i	−0.0100031	−	0.0173259i
$635$	−3.37454	−	5.84487i	−0.133915	−	0.231947i
$636$		0			0
$637$	9.19523			0.364328
$638$	2.49762			0.0988818
$639$		0			0
$640$	−17.6177	−	30.5148i	−0.696402	−	1.20620i
$641$	−11.6521	−	20.1821i	−0.460231	−	0.797144i	0.538741	−	0.842472i	$-0.318900\pi$
$641$	−11.6521	−	20.1821i	−0.460231	−	0.797144i	−0.998972	+	0.0453273i	$0.985567\pi$
$642$		0			0
$643$	17.2596			0.680651			0.340325	−	0.940308i	$-0.389463\pi$
$643$	17.2596			0.680651			0.340325	+	0.940308i	$0.389463\pi$
$644$	−2.08918			−0.0823251
$645$		0			0
$646$	11.2793	+	4.26963i	0.443777	+	0.167986i
$647$	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
$650$	3.75545			0.147301
$651$		0			0
$652$	−5.04415	+	8.73673i	−0.197544	+	0.342157i
$653$	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
$655$	10.7684			0.420754
$656$	8.86092	+	15.3476i	0.345961	+	0.599222i
$657$		0			0
$658$	0.311770			0.0121540
$659$	4.52365			0.176216			0.0881082	−	0.996111i	$-0.471918\pi$
$659$	4.52365			0.176216			0.0881082	+	0.996111i	$0.471918\pi$
$660$		0			0
$661$	−10.0400	+	17.3898i	−0.390510	+	0.676384i	−0.992517	−	0.122107i	$-0.961035\pi$
$661$	−10.0400	+	17.3898i	−0.390510	+	0.676384i	0.602007	+	0.798491i	$0.294368\pi$
$662$	6.22996			0.242134
$663$		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
$668$	1.39689	+	2.41948i	0.0540473	+	0.0936127i
$669$		0			0
$670$	1.05401			0.0407201
$671$	3.37829	−	5.85137i	0.130417	−	0.225890i
$672$		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
$679$	1.60629			0.0616436
$680$	−18.9968	+	32.9034i	−0.728493	+	1.26179i
$681$		0			0
$682$	−2.61954	−	4.53717i	−0.100307	−	0.173737i
$683$	−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
$686$	−0.645521	−	1.11807i	−0.0246461	−	0.0426883i
$687$		0			0
$688$	16.0327	−	27.7695i	0.611242	−	1.05870i
$689$	−0.673794			−0.0256695
$690$		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
$697$	20.6986	−	35.8510i	0.784015	−	1.35795i
$698$	6.40610			0.242475
$699$		0			0
$700$	1.77675	+	3.07742i	0.0671548	+	0.116316i
$701$	1.32346	−	2.29231i	0.0499865	−	0.0865792i	−0.839950	−	0.542665i	$-0.817415\pi$
$701$	1.32346	−	2.29231i	0.0499865	−	0.0865792i	0.889936	+	0.456085i	$0.150749\pi$
$702$		0			0
$703$	−12.6619	−	4.79300i	−0.477552	−	0.180771i
$704$	−3.98543	+	6.90297i	−0.150207	+	0.260165i
$705$		0			0
$706$	6.26920			0.235944
$707$	0.944501	−	1.63592i	0.0355216	−	0.0615252i
$708$		0			0
$709$	26.8452			1.00819			0.504097	−	0.863647i	$-0.331825\pi$
$709$	26.8452			1.00819			0.504097	+	0.863647i	$0.331825\pi$
$710$	−14.7695			−0.554291
$711$		0			0
$712$	−5.74496	−	9.95056i	−0.215301	−	0.372913i
$713$	38.8843			1.45623
$714$		0			0
$715$	−3.84422	−	6.65839i	−0.143766	−	0.249010i
$716$	11.8390	−	20.5057i	0.442442	−	0.766333i
$717$		0			0
$718$	−2.83914			−0.105956
$719$	−1.94193	+	3.36352i	−0.0724217	+	0.125438i	−0.899962	−	0.435968i	$-0.856406\pi$
$719$	−1.94193	+	3.36352i	−0.0724217	+	0.125438i	0.827540	+	0.561406i	$0.189739\pi$
$720$		0			0
$721$	3.45120			0.128529
$722$	−1.40095	+	6.90623i	−0.0521381	+	0.257023i
$723$		0			0
$724$	4.88543			0.181566
$725$	31.5302			1.17100
$726$		0			0
$727$	26.1519	+	45.2965i	0.969922	+	1.67995i	0.695766	+	0.718269i	$0.255065\pi$
$727$	26.1519	+	45.2965i	0.969922	+	1.67995i	0.274156	+	0.961685i	$0.411602\pi$
$728$	0.237102	+	0.410673i	0.00878758	+	0.0152205i
$729$		0			0
$730$	−4.87230			−0.180332
$731$	−74.9031			−2.77039
$732$		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
$736$	9.09410	+	15.7515i	0.335213	+	0.580606i
$737$	−0.652121	−	1.12951i	−0.0240212	−	0.0416059i
$738$		0			0
$739$	−6.68714	+	11.5825i	−0.245990	+	0.426068i	−0.962410	−	0.271602i	$-0.912447\pi$
$739$	−6.68714	+	11.5825i	−0.245990	+	0.426068i	0.716419	+	0.697670i	$0.245780\pi$
$740$	10.2830	−	17.8106i	0.378009	−	0.654731i
$741$		0			0
$742$	0.0235449	+	0.0407809i	0.000864360	+	0.00149712i
$743$	2.74391			0.100664			0.0503321	−	0.998733i	$-0.483972\pi$
$743$	2.74391			0.100664			0.0503321	+	0.998733i	$0.483972\pi$
$744$		0			0
$745$	−6.56344			−0.240466
$746$	−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
$751$	10.4736	−	18.1408i	0.382187	−	0.661967i	−0.609188	−	0.793026i	$-0.708504\pi$
$751$	10.4736	−	18.1408i	0.382187	−	0.661967i	0.991375	+	0.131059i	$0.0418377\pi$
$752$	5.37439	+	9.30871i	0.195984	+	0.339454i
$753$		0			0
$754$	2.02888			0.0738875
$755$	−19.9065	+	34.4791i	−0.724473	+	1.25482i
$756$		0			0
$757$	3.65990	−	6.33913i	0.133021	−	0.230400i	−0.791819	−	0.610756i	$-0.790865\pi$
$757$	3.65990	−	6.33913i	0.133021	−	0.230400i	0.924840	+	0.380357i	$0.124199\pi$
$758$	5.39274	+	9.34049i	0.195873	+	0.339262i
$759$		0			0
$760$	−20.7620	−	7.85920i	−0.753118	−	0.285083i
$761$	−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
$763$	−1.90460	−	3.29886i	−0.0689510	−	0.119427i
$764$	−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
$769$	14.4830	−	25.0852i	0.522269	−	0.904597i	−0.477395	−	0.878689i	$-0.658419\pi$
$769$	14.4830	−	25.0852i	0.522269	−	0.904597i	0.999664	−	0.0259081i	$-0.00824772\pi$
$770$	−0.268663	+	0.465339i	−0.00968195	+	0.0167696i
$771$		0			0
$772$	0.463529	−	0.802856i	0.0166828	−	0.0288954i
$773$	−21.7876	−	37.7372i	−0.783645	−	1.35731i	−0.929805	−	0.368052i	$-0.880025\pi$
$773$	−21.7876	−	37.7372i	−0.783645	−	1.35731i	0.146160	−	0.989261i	$-0.453309\pi$
$774$		0			0
$775$	−33.0693	−	57.2777i	−1.18788	−	2.05748i
$776$	−4.60671	−	7.97906i	−0.165371	−	0.286432i
$777$		0			0
$778$	−3.55421	−	6.15608i	−0.127425	−	0.220706i
$779$	22.6220	+	8.56327i	0.810517	+	0.306811i
$780$		0			0
$781$	9.13796	+	15.8274i	0.326982	+	0.566349i
$782$	6.21352	−	10.7621i	0.222195	−	0.384853i
$783$		0			0
$784$	11.0779	−	19.1875i	0.395639	−	0.685267i
$785$	73.8457			2.63567
$786$		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	$0.798080\pi$
$788$	2.46213	−	4.26454i	0.0877098	−	0.151918i
$789$		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
$794$	11.8380			0.420115
$795$		0			0
$796$	0.395995			0.0140357
$797$	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
$803$	3.01451	+	5.22128i	0.106380	+	0.184255i
$804$		0			0
$805$	−1.99401	−	3.45373i	−0.0702797	−	0.121728i
$806$	−2.12792	−	3.68566i	−0.0749527	−	0.129822i
$807$		0			0
$808$	−10.8350			−0.381175
$809$	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	0.953632	+	0.300974i	$0.0973118\pi$
$811$	21.0016	+	36.3759i	0.737467	+	1.27733i	−0.216165	+	0.976357i	$0.569355\pi$
$812$	0.959889	+	1.66258i	0.0336855	+	0.0583450i
$813$		0			0
$814$	1.87960			0.0658800
$815$	−19.2575			−0.674562
$816$		0			0
$817$	−7.04750	−	43.1950i	−0.246561	−	1.51120i
$818$	−0.850402			−0.0297336
$819$		0			0
$820$	−18.3717	+	31.8208i	−0.641569	+	1.11123i
$821$	17.7203			0.618444			0.309222	−	0.950990i	$-0.399931\pi$
$821$	17.7203			0.618444			0.309222	+	0.950990i	$0.399931\pi$
$822$		0			0
$823$	14.6013	−	25.2903i	0.508971	−	0.881563i	−0.490975	−	0.871174i	$-0.663359\pi$
$823$	14.6013	−	25.2903i	0.508971	−	0.881563i	0.999946	−	0.0103898i	$-0.00330724\pi$
$824$	−9.89779	−	17.1435i	−0.344806	−	0.597221i
$825$		0			0
$826$	−0.969133			−0.0337204
$827$	−7.34515	−	12.7222i	−0.255416	−	0.442393i	0.709593	−	0.704612i	$-0.248879\pi$
$827$	−7.34515	−	12.7222i	−0.255416	−	0.442393i	−0.965008	+	0.262219i	$0.915546\pi$
$828$		0			0
$829$	−2.88680			−0.100263			−0.0501314	−	0.998743i	$-0.515964\pi$
$829$	−2.88680			−0.100263			−0.0501314	+	0.998743i	$0.515964\pi$
$830$	−0.488541			−0.0169575
$831$		0			0
$832$	−3.23747	+	5.60746i	−0.112239	+	0.194404i
$833$	−51.7547			−1.79319
$834$		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
$839$	−7.55921	−	13.0929i	−0.260973	−	0.452019i	0.705528	−	0.708682i	$-0.250710\pi$
$839$	−7.55921	−	13.0929i	−0.260973	−	0.452019i	−0.966501	+	0.256664i	$0.917377\pi$
$840$		0			0
$841$	−11.9658			−0.412614
$842$	4.79644	−	8.30768i	0.165296	−	0.286301i
$843$		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
$850$	−21.1373			−0.725002
$851$	−6.97517	+	12.0814i	−0.239106	+	0.414143i
$852$		0			0
$853$	−13.0507	−	22.6045i	−0.446848	−	0.773964i	0.551331	−	0.834287i	$-0.314120\pi$
$853$	−13.0507	−	22.6045i	−0.446848	−	0.773964i	−0.998179	+	0.0603231i	$0.980787\pi$
$854$	−0.383581			−0.0131259
$855$		0			0
$856$	−17.2075			−0.588139
$857$	20.8227	+	36.0660i	0.711291	+	1.23199i	0.964373	+	0.264547i	$0.0852224\pi$
$857$	20.8227	+	36.0660i	0.711291	+	1.23199i	−0.253082	+	0.967445i	$0.581444\pi$
$858$		0			0
$859$	−4.72015	+	8.17554i	−0.161049	+	0.278946i	−0.935245	−	0.354000i	$-0.884821\pi$
$859$	−4.72015	+	8.17554i	−0.161049	+	0.278946i	0.774196	+	0.632946i	$0.218155\pi$
$860$	66.4828			2.26704
$861$		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
$868$	2.01349	−	3.48746i	0.0683422	−	0.118372i
$869$	−16.0802			−0.545483
$870$		0			0
$871$	−0.529735	−	0.917528i	−0.0179494	−	0.0310892i
$872$	−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
$877$	−41.4554			−1.39985			−0.699924	−	0.714217i	$-0.746783\pi$
$877$	−41.4554			−1.39985			−0.699924	+	0.714217i	$0.746783\pi$
$878$	−0.361069	+	0.625390i	−0.0121855	+	0.0211059i
$879$		0			0
$880$	−18.5252			−0.624485
$881$	−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	0.860678	−	0.509149i	$-0.170040\pi$
$883$	−0.314882	−	0.545392i	−0.0105966	−	0.0183539i	−0.871275	+	0.490795i	$0.836706\pi$
$884$	18.4151			0.619365
$885$		0			0
$886$	−1.21694	−	2.10781i	−0.0408840	−	0.0708132i
$887$	−0.563597	+	0.976178i	−0.0189237	+	0.0327769i	−0.875332	−	0.483522i	$-0.839357\pi$
$887$	−0.563597	+	0.976178i	−0.0189237	+	0.0327769i	0.856408	+	0.516299i	$0.172691\pi$
$888$		0			0
$889$	0.474118			0.0159014
$890$	5.28798	−	9.15906i	0.177254	−	0.307012i
$891$		0			0
$892$	−29.0600			−0.973000
$893$	13.7208	+	5.19385i	0.459151	+	0.173806i
$894$		0			0
$895$	45.1987			1.51083
$896$	2.47527			0.0826929
$897$		0			0
$898$	6.58973	+	11.4137i	0.219902	+	0.380881i
$899$	−17.8657	−	30.9443i	−0.595854	−	1.03205i
$900$		0			0
$901$	3.79240			0.126343
$902$	−3.35813			−0.111814
$903$		0			0
$904$	2.09840	+	3.63453i	0.0697917	+	0.120883i
$905$	4.66290	+	8.07637i	0.155000	+	0.268468i
$906$		0			0
$907$	−14.3660	−	24.8826i	−0.477014	−	0.826213i	0.522639	−	0.852554i	$-0.324948\pi$
$907$	−14.3660	−	24.8826i	−0.477014	−	0.826213i	−0.999653	+	0.0263414i	$0.991614\pi$
$908$	−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
$914$	−2.46599			−0.0815678
$915$		0			0
$916$	−37.1908			−1.22882
$917$	−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
$922$	1.29288	−	2.23934i	0.0425788	−	0.0737487i
$923$	7.42300	+	12.8570i	0.244331	+	0.423194i
$924$		0			0
$925$	23.7283			0.780181
$926$	−3.18850	+	5.52264i	−0.104781	+	0.181485i
$927$		0			0
$928$	8.35672	−	14.4743i	0.274323	−	0.475141i
$929$	0.893942	+	1.54835i	0.0293293	+	0.0507998i	0.880317	−	0.474385i	$-0.157330\pi$
$929$	0.893942	+	1.54835i	0.0293293	+	0.0507998i	−0.850988	+	0.525185i	$0.823996\pi$
$930$		0			0
$931$	−4.86950	−	29.8458i	−0.159591	−	0.978156i
$932$	11.5179	+	19.9496i	0.377282	+	0.653472i
$933$		0			0
$934$	−6.77773	−	11.7394i	−0.221774	−	0.384124i
$935$	21.6369	+	37.4763i	0.707603	+	1.22560i
$936$		0			0
$937$	6.96721	+	12.0676i	0.227609	+	0.394230i	0.957099	−	0.289761i	$-0.0935759\pi$
$937$	6.96721	+	12.0676i	0.227609	+	0.394230i	−0.729490	+	0.683991i	$0.760243\pi$
$938$	−0.0370219	+	0.0641238i	−0.00120881	+	0.00209372i
$939$		0			0
$940$	−11.1430	+	19.3002i	−0.363443	+	0.629502i
$941$	−22.7165	+	39.3461i	−0.740535	+	1.28264i	0.211717	+	0.977331i	$0.432095\pi$
$941$	−22.7165	+	39.3461i	−0.740535	+	1.28264i	−0.952252	+	0.305314i	$0.901239\pi$
$942$		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
$947$	−2.58749	−	4.48167i	−0.0840823	−	0.145635i	0.820918	−	0.571047i	$-0.193463\pi$
$947$	−2.58749	−	4.48167i	−0.0840823	−	0.145635i	−0.905000	+	0.425412i	$0.860129\pi$
$948$		0			0
$949$	2.44876	+	4.24138i	0.0794902	+	0.137681i
$950$	−1.98877	−	12.1894i	−0.0645241	−	0.395476i
$951$		0			0
$952$	−1.33451	−	2.31144i	−0.0432517	−	0.0749142i
$953$	−12.9234	+	22.3840i	−0.418630	+	0.725088i	−0.995802	−	0.0915347i	$-0.970823\pi$
$953$	−12.9234	+	22.3840i	−0.418630	+	0.725088i	0.577172	+	0.816622i	$0.304156\pi$
$954$		0			0
$955$	6.05867	−	10.4939i	0.196054	−	0.339575i
$956$	−30.2323			−0.977783
$957$		0			0
$958$	3.70247	+	6.41287i	0.119621	+	0.207190i
$959$	0.531655	−	0.920853i	0.0171680	−	0.0297359i
$960$		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
$965$	1.76966			0.0569674
$966$		0			0
$967$	26.1397			0.840597			0.420299	−	0.907386i	$-0.361925\pi$
$967$	26.1397			0.840597			0.420299	+	0.907386i	$0.361925\pi$
$968$	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	−0.949116	−	0.314926i	$-0.898020\pi$
$971$	−6.28902	+	10.8929i	−0.201824	+	0.349570i	0.747292	+	0.664496i	$0.231354\pi$
$972$		0			0
$973$	2.15687	+	3.73581i	0.0691461	+	0.119764i
$974$	0.100402	+	0.173901i	0.00321708	+	0.00557215i
$975$		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
$979$	−13.0868			−0.418255
$980$	45.9366			1.46739
$981$		0			0
$982$	1.36185	+	2.35879i	0.0434583	+	0.0752719i
$983$	−11.6223	−	20.1305i	−0.370695	−	0.642063i	0.618977	−	0.785409i	$-0.287547\pi$
$983$	−11.6223	−	20.1305i	−0.370695	−	0.642063i	−0.989673	+	0.143346i	$0.954214\pi$
$984$		0			0
$985$	9.39991			0.299506
$986$	−11.4194			−0.363668
$987$		0			0
$988$	1.73264	+	10.6196i	0.0551226	+	0.337853i
$989$	−45.0968			−1.43400
$990$		0			0
$991$	−11.8484	+	20.5220i	−0.376376	+	0.651903i	−0.990532	−	0.137282i	$-0.956163\pi$
$991$	−11.8484	+	20.5220i	−0.376376	+	0.651903i	0.614156	+	0.789185i	$0.289497\pi$
$992$	−35.0586			−1.11311
$993$		0			0
$994$	0.518775	−	0.898545i	0.0164545	−	0.0285001i
$995$	0.377957	+	0.654641i	0.0119820	+	0.0207535i
$996$		0			0
$997$	−18.9313			−0.599559			−0.299780	−	0.954008i	$-0.596913\pi$
$997$	−18.9313			−0.599559			−0.299780	+	0.954008i	$0.596913\pi$
$998$	−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.g.c.505.9		32
3.2	odd	2		171.2.g.c.106.8	✓	32
9.4	even	3		513.2.h.c.334.8		32
9.5	odd	6		171.2.h.c.49.9	yes	32
19.7	even	3		513.2.h.c.235.8		32
57.26	odd	6		171.2.h.c.7.9	yes	32
171.121	even	3	inner	513.2.g.c.64.9		32
171.140	odd	6		171.2.g.c.121.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.g.c.106.8	✓	32	3.2	odd	2
171.2.g.c.121.8	yes	32	171.140	odd	6
171.2.h.c.7.9	yes	32	57.26	odd	6
171.2.h.c.49.9	yes	32	9.5	odd	6
513.2.g.c.64.9		32	171.121	even	3	inner
513.2.g.c.505.9		32	1.1	even	1	trivial
513.2.h.c.235.8		32	19.7	even	3
513.2.h.c.334.8		32	9.4	even	3

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.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.185445 + 0.321199i) q^{2} +(0.931221 - 1.61292i) q^{4} +3.55521 q^{5} +(-0.124876 + 0.216291i) q^{7} +1.43254 q^{8} +(0.659294 + 1.14193i) q^{10} +(0.815815 - 1.41303i) q^{11} +(0.662707 - 1.14784i) q^{13} -0.0926300 q^{14} +(-1.59679 - 2.76571i) q^{16} +(-3.73000 + 6.46055i) q^{17} +(-4.07660 - 1.54315i) q^{19} +(3.31069 - 5.73428i) q^{20} +0.605154 q^{22} +(-2.24572 + 3.88969i) q^{23} +7.63952 q^{25} +0.491582 q^{26} +(0.232573 + 0.402829i) q^{28} +4.12725 q^{29} +(-4.32871 - 7.49755i) q^{31} +(2.02477 - 3.50700i) q^{32} -2.76683 q^{34} +(-0.443959 + 0.768960i) q^{35} +3.10599 q^{37} +(-0.260326 - 1.59557i) q^{38} +5.09297 q^{40} -5.54922 q^{41} +(5.02032 + 8.69544i) q^{43} +(-1.51941 - 2.63169i) q^{44} -1.66582 q^{46} -3.36575 q^{47} +(3.46881 + 6.00816i) q^{49} +(1.41671 + 2.45381i) q^{50} +(-1.23425 - 2.13779i) q^{52} +(-0.254182 - 0.440256i) q^{53} +(2.90039 - 5.02363i) q^{55} +(-0.178889 + 0.309845i) q^{56} +(0.765376 + 1.32567i) q^{58} +10.4624 q^{59} +4.14100 q^{61} +(1.60547 - 2.78076i) q^{62} -4.88521 q^{64} +(2.35606 - 4.08082i) q^{65} +(0.399675 - 0.692257i) q^{67} +(6.94690 + 12.0324i) q^{68} -0.329319 q^{70} +(-5.60051 + 9.70037i) q^{71} +(-1.84754 + 3.20004i) q^{73} +(0.575989 + 0.997642i) q^{74} +(-6.28519 + 5.13823i) q^{76} +(0.203751 + 0.352907i) q^{77} +(-4.92764 - 8.53493i) q^{79} +(-5.67691 - 9.83269i) q^{80} +(-1.02907 - 1.78241i) q^{82} +(-0.185251 + 0.320865i) q^{83} +(-13.2609 + 22.9686i) q^{85} +(-1.86198 + 3.22504i) q^{86} +(1.16868 - 2.02422i) q^{88} +(-4.01034 - 6.94611i) q^{89} +(0.165512 + 0.286675i) q^{91} +(4.18251 + 7.24433i) q^{92} +(-0.624161 - 1.08108i) q^{94} +(-14.4932 - 5.48621i) q^{95} +(-3.21577 - 5.56988i) q^{97} +(-1.28654 + 2.22836i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - q^{2} - 17 q^{4} + 6 q^{5} + q^{7} + 36 q^{8} - 8 q^{10} - 7 q^{11} - 4 q^{13} + 2 q^{14} - 11 q^{16} + 7 q^{17} + 7 q^{19} + 3 q^{20} + 16 q^{22} - 5 q^{23} + 18 q^{25} + 4 q^{26} - 10 q^{28}+ \cdots - 18 q^{98}+O(q^{100}) \) 32 * q - q^2 - 17 * q^4 + 6 * q^5 + q^7 + 36 * q^8 - 8 * q^10 - 7 * q^11 - 4 * q^13 + 2 * q^14 - 11 * q^16 + 7 * q^17 + 7 * q^19 + 3 * q^20 + 16 * q^22 - 5 * q^23 + 18 * q^25 + 4 * q^26 - 10 * q^28 + 20 * q^29 - 10 * q^31 - 17 * q^32 + 26 * q^34 + 3 * q^35 + 2 * q^37 - 38 * q^38 - 24 * q^40 + 12 * q^41 + 7 * q^43 - 20 * q^44 - 18 * q^47 - 13 * q^49 - q^50 + 19 * q^52 - 16 * q^53 + 15 * q^55 + 6 * q^56 + 74 * q^59 + 24 * q^61 - 54 * q^62 - 64 * q^64 - 54 * q^65 - 11 * q^67 + 2 * q^68 - 48 * q^70 - 9 * q^71 - 10 * q^73 - 6 * q^74 + 29 * q^76 - 46 * q^77 - 8 * q^79 + 24 * q^80 + 7 * q^82 - 3 * q^83 - 27 * q^85 - 17 * q^86 + 9 * q^88 - 30 * q^89 - q^91 + 17 * q^92 - 18 * q^94 + 6 * q^95 - 18 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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