LMFDB - Embedded newform 324.2.p.a.311.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,2,Mod(11,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([27, 13]))

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

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

chi := DirichletCharacter("324.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	324.p (of order $54$, degree $18$, 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:	$2.58715302549$
Analytic rank:	$0$
Dimension:	$936$
Relative dimension:	$52$ over $\Q(\zeta_{54})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label			311.4
Character	$\chi$	$=$	324.311
Dual form			324.2.p.a.299.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36306 - 0.376917i) q^{2} +(-1.73187 + 0.0251876i) q^{3} +(1.71587 + 1.02752i) q^{4} +(-0.958604 + 0.286987i) q^{5} +(2.37013 + 0.618439i) q^{6} +(1.31925 - 0.569068i) q^{7} +(-1.95154 - 2.04732i) q^{8} +(2.99873 - 0.0872431i) q^{9} +O(q^{10})$	\(q+(-1.36306 - 0.376917i) q^{2} +(-1.73187 + 0.0251876i) q^{3} +(1.71587 + 1.02752i) q^{4} +(-0.958604 + 0.286987i) q^{5} +(2.37013 + 0.618439i) q^{6} +(1.31925 - 0.569068i) q^{7} +(-1.95154 - 2.04732i) q^{8} +(2.99873 - 0.0872431i) q^{9} +(1.41480 - 0.0298662i) q^{10} +(-2.49854 + 0.592165i) q^{11} +(-2.99753 - 1.73631i) q^{12} +(-1.52037 - 0.999963i) q^{13} +(-2.01271 + 0.278427i) q^{14} +(1.65295 - 0.521169i) q^{15} +(1.88840 + 3.52618i) q^{16} +(0.373412 + 1.02594i) q^{17} +(-4.12033 - 1.01136i) q^{18} +(-0.642494 + 1.76524i) q^{19} +(-1.93972 - 0.492555i) q^{20} +(-2.27043 + 1.01878i) q^{21} +(3.62886 + 0.134587i) q^{22} +(-2.94887 + 6.83624i) q^{23} +(3.43137 + 3.49652i) q^{24} +(-3.34088 + 2.19733i) q^{25} +(1.69545 + 1.93606i) q^{26} +(-5.19121 + 0.226624i) q^{27} +(2.84839 + 0.379112i) q^{28} +(-1.06835 + 0.0622243i) q^{29} +(-2.44950 + 0.0873599i) q^{30} +(1.23361 + 10.5542i) q^{31} +(-1.24492 - 5.51817i) q^{32} +(4.31222 - 1.08848i) q^{33} +(-0.122288 - 1.53916i) q^{34} +(-1.10132 + 0.924118i) q^{35} +(5.23507 + 2.93157i) q^{36} +(-4.08066 - 3.42408i) q^{37} +(1.54111 - 2.16396i) q^{38} +(2.65827 + 1.69351i) q^{39} +(2.45830 + 1.40250i) q^{40} +(2.74509 + 5.46592i) q^{41} +(3.47873 - 0.532893i) q^{42} +(1.81801 - 1.71521i) q^{43} +(-4.89562 - 1.55123i) q^{44} +(-2.84956 + 0.944229i) q^{45} +(6.59618 - 8.20673i) q^{46} +(-2.78210 - 0.325180i) q^{47} +(-3.35927 - 6.05932i) q^{48} +(-3.38711 + 3.59013i) q^{49} +(5.38203 - 1.73586i) q^{50} +(-0.672541 - 1.76739i) q^{51} +(-1.58127 - 3.27802i) q^{52} +(-1.17840 - 0.680352i) q^{53} +(7.16135 + 1.64775i) q^{54} +(2.22517 - 1.28470i) q^{55} +(-3.73963 - 1.59036i) q^{56} +(1.06825 - 3.07334i) q^{57} +(1.47968 + 0.317864i) q^{58} +(-4.60689 - 1.09185i) q^{59} +(3.37175 + 0.804184i) q^{60} +(-4.28303 + 5.75311i) q^{61} +(2.29658 - 14.8510i) q^{62} +(3.90643 - 1.82158i) q^{63} +(-0.382998 + 7.99083i) q^{64} +(1.74441 + 0.522242i) q^{65} +(-6.28809 - 0.141685i) q^{66} +(-0.322457 - 0.0187810i) q^{67} +(-0.413452 + 2.14407i) q^{68} +(4.93486 - 11.9137i) q^{69} +(1.84948 - 0.844522i) q^{70} +(1.36586 - 7.74616i) q^{71} +(-6.03075 - 5.96909i) q^{72} +(-1.92114 - 10.8953i) q^{73} +(4.27159 + 6.20530i) q^{74} +(5.73062 - 3.88964i) q^{75} +(-2.91625 + 2.36873i) q^{76} +(-2.95921 + 2.20305i) q^{77} +(-2.98506 - 3.31030i) q^{78} +(4.89881 - 9.75434i) q^{79} +(-2.82219 - 2.83827i) q^{80} +(8.98478 - 0.523237i) q^{81} +(-1.68152 - 8.48505i) q^{82} +(0.440573 + 0.221264i) q^{83} +(-4.94258 - 0.584829i) q^{84} +(-0.652386 - 0.876306i) q^{85} +(-3.12456 + 1.65269i) q^{86} +(1.84867 - 0.134673i) q^{87} +(6.08834 + 3.95966i) q^{88} +(13.1105 - 2.31173i) q^{89} +(4.24001 - 0.212993i) q^{90} +(-2.57479 - 0.454006i) q^{91} +(-12.0843 + 8.70005i) q^{92} +(-2.40229 - 18.2474i) q^{93} +(3.66960 + 1.49186i) q^{94} +(0.109297 - 1.87655i) q^{95} +(2.29502 + 9.52538i) q^{96} +(-2.40082 + 8.01930i) q^{97} +(5.97002 - 3.61690i) q^{98} +(-7.44079 + 1.99372i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9}+O(q^{10}) $ 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9	$ 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 36 q^{13} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 36 q^{21} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 9 q^{28} - 36 q^{29} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 18 q^{36} - 36 q^{37} - 18 q^{38} - 18 q^{40} - 36 q^{41} - 63 q^{42} - 90 q^{44} - 36 q^{45} - 18 q^{46} - 117 q^{48} - 36 q^{49} - 135 q^{50} - 18 q^{52} - 54 q^{53} - 144 q^{54} - 144 q^{56} - 36 q^{57} - 18 q^{58} - 135 q^{60} - 36 q^{61} - 117 q^{62} - 18 q^{64} - 36 q^{65} - 90 q^{66} - 63 q^{68} - 36 q^{69} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 18 q^{76} - 36 q^{77} + 9 q^{78} - 36 q^{81} - 36 q^{82} - 45 q^{84} - 36 q^{85} - 18 q^{86} - 18 q^{88} - 54 q^{89} + 45 q^{90} + 72 q^{92} - 144 q^{93} - 18 q^{94} + 99 q^{96} - 36 q^{97} + 153 q^{98}+O(q^{100}) $ 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 18 * q^12 - 36 * q^13 - 18 * q^14 - 18 * q^16 - 36 * q^17 - 18 * q^18 - 18 * q^20 - 36 * q^21 - 18 * q^22 - 18 * q^24 - 36 * q^25 - 27 * q^26 - 9 * q^28 - 36 * q^29 - 18 * q^30 - 18 * q^32 - 36 * q^33 - 18 * q^34 - 18 * q^36 - 36 * q^37 - 18 * q^38 - 18 * q^40 - 36 * q^41 - 63 * q^42 - 90 * q^44 - 36 * q^45 - 18 * q^46 - 117 * q^48 - 36 * q^49 - 135 * q^50 - 18 * q^52 - 54 * q^53 - 144 * q^54 - 144 * q^56 - 36 * q^57 - 18 * q^58 - 135 * q^60 - 36 * q^61 - 117 * q^62 - 18 * q^64 - 36 * q^65 - 90 * q^66 - 63 * q^68 - 36 * q^69 - 18 * q^70 - 18 * q^72 - 36 * q^73 - 18 * q^74 - 18 * q^76 - 36 * q^77 + 9 * q^78 - 36 * q^81 - 36 * q^82 - 45 * q^84 - 36 * q^85 - 18 * q^86 - 18 * q^88 - 54 * q^89 + 45 * q^90 + 72 * q^92 - 144 * q^93 - 18 * q^94 + 99 * q^96 - 36 * q^97 + 153 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{35}{54}\right)$

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 $

$2$	−1.36306	−	0.376917i	−0.963829	−	0.266521i
$2$	−1.36306	−	0.376917i	−0.963829	−	0.266521i
$3$	−1.73187	+	0.0251876i	−0.999894	+	0.0145421i
$3$	−1.73187	+	0.0251876i	−0.999894	+	0.0145421i
$4$	1.71587	+	1.02752i	0.857933	+	0.513761i
$5$	−0.958604	+	0.286987i	−0.428701	+	0.128345i	−0.493882	−	0.869529i	$-0.664423\pi$
$5$	−0.958604	+	0.286987i	−0.428701	+	0.128345i	0.0651815	+	0.997873i	$0.479237\pi$
$6$	2.37013	+	0.618439i	0.967603	+	0.252477i
$7$	1.31925	−	0.569068i	0.498629	−	0.215088i	−0.131885	−	0.991265i	$-0.542103\pi$
$7$	1.31925	−	0.569068i	0.498629	−	0.215088i	0.630515	+	0.776177i	$0.282844\pi$
$8$	−1.95154	−	2.04732i	−0.689973	−	0.723835i
$9$	2.99873	−	0.0872431i	0.999577	−	0.0290810i
$10$	1.41480	−	0.0298662i	0.447401	−	0.00944453i
$11$	−2.49854	+	0.592165i	−0.753338	+	0.178544i	−0.589305	−	0.807911i	$-0.700598\pi$
$11$	−2.49854	+	0.592165i	−0.753338	+	0.178544i	−0.164033	+	0.986455i	$0.552450\pi$
$12$	−2.99753	−	1.73631i	−0.865314	−	0.501231i
$13$	−1.52037	−	0.999963i	−0.421675	−	0.277340i	0.320887	−	0.947117i	$-0.396019\pi$
$13$	−1.52037	−	0.999963i	−0.421675	−	0.277340i	−0.742562	+	0.669778i	$0.766389\pi$
$14$	−2.01271	+	0.278427i	−0.537919	+	0.0744126i
$15$	1.65295	−	0.521169i	0.426789	−	0.134565i
$16$	1.88840	+	3.52618i	0.472099	+	0.881546i
$17$	0.373412	+	1.02594i	0.0905657	+	0.248827i	0.976703	−	0.214596i	$-0.0688433\pi$
$17$	0.373412	+	1.02594i	0.0905657	+	0.248827i	−0.886137	+	0.463423i	$0.846621\pi$
$18$	−4.12033	−	1.01136i	−0.971172	−	0.238379i
$19$	−0.642494	+	1.76524i	−0.147398	+	0.404973i	−0.991316	−	0.131499i	$-0.958021\pi$
$19$	−0.642494	+	1.76524i	−0.147398	+	0.404973i	0.843918	+	0.536472i	$0.180243\pi$
$20$	−1.93972	−	0.492555i	−0.433735	−	0.110139i
$21$	−2.27043	+	1.01878i	−0.495449	+	0.222316i
$22$	3.62886	+	0.134587i	0.773675	+	0.0286940i
$23$	−2.94887	+	6.83624i	−0.614881	+	1.42545i	0.271472	+	0.962446i	$0.412489\pi$
$23$	−2.94887	+	6.83624i	−0.614881	+	1.42545i	−0.886354	+	0.463009i	$0.846770\pi$
$24$	3.43137	+	3.49652i	0.700426	+	0.713725i
$25$	−3.34088	+	2.19733i	−0.668176	+	0.439466i
$26$	1.69545	+	1.93606i	0.332506	+	0.379693i
$27$	−5.19121	+	0.226624i	−0.999048	+	0.0436139i
$28$	2.84839	+	0.379112i	0.538294	+	0.0716455i
$29$	−1.06835	+	0.0622243i	−0.198388	+	0.0115548i	−0.157051	−	0.987591i	$-0.550199\pi$
$29$	−1.06835	+	0.0622243i	−0.198388	+	0.0115548i	−0.0413368	+	0.999145i	$0.513162\pi$
$30$	−2.44950	+	0.0873599i	−0.447216	+	0.0159497i
$31$	1.23361	+	10.5542i	0.221563	+	1.89559i	0.407772	+	0.913084i	$0.366306\pi$
$31$	1.23361	+	10.5542i	0.221563	+	1.89559i	−0.186209	+	0.982510i	$0.559620\pi$
$32$	−1.24492	−	5.51817i	−0.220072	−	0.975484i
$33$	4.31222	−	1.08848i	0.750662	−	0.189481i
$34$	−0.122288	−	1.53916i	−0.0209722	−	0.263965i
$35$	−1.10132	+	0.924118i	−0.186157	+	0.156205i
$36$	5.23507	+	2.93157i	0.872511	+	0.488594i
$37$	−4.08066	−	3.42408i	−0.670857	−	0.562916i	0.242462	−	0.970161i	$-0.422045\pi$
$37$	−4.08066	−	3.42408i	−0.670857	−	0.562916i	−0.913319	+	0.407245i	$0.866489\pi$
$38$	1.54111	−	2.16396i	0.250000	−	0.351040i
$39$	2.65827	+	1.69351i	0.425663	+	0.271178i
$40$	2.45830	+	1.40250i	0.388692	+	0.221754i
$41$	2.74509	+	5.46592i	0.428711	+	0.853633i	0.999471	+	0.0325163i	$0.0103521\pi$
$41$	2.74509	+	5.46592i	0.428711	+	0.853633i	−0.570761	+	0.821116i	$0.693352\pi$
$42$	3.47873	−	0.532893i	0.536780	−	0.0822272i
$43$	1.81801	−	1.71521i	0.277245	−	0.261567i	−0.535042	−	0.844826i	$-0.679704\pi$
$43$	1.81801	−	1.71521i	0.277245	−	0.261567i	0.812286	+	0.583259i	$0.198223\pi$
$44$	−4.89562	−	1.55123i	−0.738043	−	0.233857i
$45$	−2.84956	+	0.944229i	−0.424787	+	0.140757i
$46$	6.59618	−	8.20673i	0.972554	−	1.21002i
$47$	−2.78210	−	0.325180i	−0.405810	−	0.0474324i	−0.0892606	−	0.996008i	$-0.528450\pi$
$47$	−2.78210	−	0.325180i	−0.405810	−	0.0474324i	−0.316550	+	0.948576i	$0.602524\pi$
$48$	−3.35927	−	6.05932i	−0.484868	−	0.874587i
$49$	−3.38711	+	3.59013i	−0.483873	+	0.512876i
$50$	5.38203	−	1.73586i	0.761134	−	0.245488i
$51$	−0.672541	−	1.76739i	−0.0941746	−	0.247484i
$52$	−1.58127	−	3.27802i	−0.219282	−	0.454579i
$53$	−1.17840	−	0.680352i	−0.161866	−	0.0934536i	0.416879	−	0.908962i	$-0.363124\pi$
$53$	−1.17840	−	0.680352i	−0.161866	−	0.0934536i	−0.578745	+	0.815509i	$0.696457\pi$
$54$	7.16135	+	1.64775i	0.974536	+	0.224231i
$55$	2.22517	−	1.28470i	0.300041	−	0.173229i
$56$	−3.73963	−	1.59036i	−0.499729	−	0.212521i
$57$	1.06825	−	3.07334i	0.141493	−	0.407074i
$58$	1.47968	+	0.317864i	0.194291	+	0.0417376i
$59$	−4.60689	−	1.09185i	−0.599767	−	0.142147i	−0.0804927	−	0.996755i	$-0.525649\pi$
$59$	−4.60689	−	1.09185i	−0.599767	−	0.142147i	−0.519274	+	0.854608i	$0.673798\pi$
$60$	3.37175	+	0.804184i	0.435291	+	0.103820i
$61$	−4.28303	+	5.75311i	−0.548386	+	0.736610i	−0.986761	−	0.162182i	$-0.948147\pi$
$61$	−4.28303	+	5.75311i	−0.548386	+	0.736610i	0.438375	+	0.898792i	$0.355554\pi$
$62$	2.29658	−	14.8510i	0.291666	−	1.88608i
$63$	3.90643	−	1.82158i	0.492163	−	0.229497i
$64$	−0.382998	+	7.99083i	−0.0478747	+	0.998853i
$65$	1.74441	+	0.522242i	0.216367	+	0.0647761i
$66$	−6.28809	−	0.141685i	−0.774010	−	0.0174402i
$67$	−0.322457	−	0.0187810i	−0.0393944	−	0.00229446i	0.0384363	−	0.999261i	$-0.487762\pi$
$67$	−0.322457	−	0.0187810i	−0.0393944	−	0.00229446i	−0.0778307	+	0.996967i	$0.524799\pi$
$68$	−0.413452	+	2.14407i	−0.0501385	+	0.260006i
$69$	4.93486	−	11.9137i	0.594087	−	1.43425i
$70$	1.84948	−	0.844522i	0.221056	−	0.100940i
$71$	1.36586	−	7.74616i	0.162097	−	0.919300i	−0.789909	−	0.613223i	$-0.789873\pi$
$71$	1.36586	−	7.74616i	0.162097	−	0.919300i	0.952007	−	0.306077i	$-0.0990164\pi$
$72$	−6.03075	−	5.96909i	−0.710731	−	0.703464i
$73$	−1.92114	−	10.8953i	−0.224852	−	1.27520i	−0.862968	−	0.505258i	$-0.831397\pi$
$73$	−1.92114	−	10.8953i	−0.224852	−	1.27520i	0.638116	−	0.769940i	$-0.279714\pi$
$74$	4.27159	+	6.20530i	0.496562	+	0.721352i
$75$	5.73062	−	3.88964i	0.661715	−	0.449136i
$76$	−2.91625	+	2.36873i	−0.334517	+	0.271712i
$77$	−2.95921	+	2.20305i	−0.337234	+	0.251061i
$78$	−2.98506	−	3.31030i	−0.337992	−	0.374818i
$79$	4.89881	−	9.75434i	0.551159	−	1.09745i	−0.429743	−	0.902951i	$-0.641396\pi$
$79$	4.89881	−	9.75434i	0.551159	−	1.09745i	0.980903	−	0.194498i	$-0.0623077\pi$
$80$	−2.82219	−	2.83827i	−0.315531	−	0.317328i
$81$	8.98478	−	0.523237i	0.998309	−	0.0581375i
$82$	−1.68152	−	8.48505i	−0.185693	−	0.937016i
$83$	0.440573	+	0.221264i	0.0483591	+	0.0242869i	0.472814	−	0.881162i	$-0.343238\pi$
$83$	0.440573	+	0.221264i	0.0483591	+	0.0242869i	−0.424455	+	0.905449i	$0.639534\pi$
$84$	−4.94258	−	0.584829i	−0.539279	−	0.0638100i
$85$	−0.652386	−	0.876306i	−0.0707612	−	0.0950488i
$86$	−3.12456	+	1.65269i	−0.336930	+	0.178214i
$87$	1.84867	−	0.134673i	0.198199	−	0.0144385i
$88$	6.08834	+	3.95966i	0.649019	+	0.422102i
$89$	13.1105	−	2.31173i	1.38971	−	0.245043i	0.571801	−	0.820392i	$-0.306245\pi$
$89$	13.1105	−	2.31173i	1.38971	−	0.245043i	0.817908	+	0.575349i	$0.195134\pi$
$90$	4.24001	−	0.212993i	0.446937	−	0.0224514i
$91$	−2.57479	−	0.454006i	−0.269912	−	0.0475927i
$92$	−12.0843	+	8.70005i	−1.25987	+	0.907043i
$93$	−2.40229	−	18.2474i	−0.249106	−	1.89217i
$94$	3.66960	+	1.49186i	0.378490	+	0.153874i
$95$	0.109297	−	1.87655i	0.0112136	−	0.192530i
$96$	2.29502	+	9.52538i	0.234235	+	0.972180i
$97$	−2.40082	+	8.01930i	−0.243766	+	0.814236i	0.745295	+	0.666734i	$0.232308\pi$
$97$	−2.40082	+	8.01930i	−0.243766	+	0.814236i	−0.989062	+	0.147502i	$0.952877\pi$
$98$	5.97002	−	3.61690i	0.603063	−	0.365362i
$99$	−7.44079	+	1.99372i	−0.747827	+	0.200377i
$100$	−7.99031	+	0.337498i	−0.799031	+	0.0337498i
$101$	10.2109	+	7.60175i	1.01602	+	0.756402i	0.970140	−	0.242545i	$-0.0779822\pi$
$101$	10.2109	+	7.60175i	1.01602	+	0.756402i	0.0458839	+	0.998947i	$0.485390\pi$
$102$	0.250554	+	2.66255i	0.0248086	+	0.263632i
$103$	−1.46841	+	6.19572i	−0.144687	+	0.610482i	0.851585	+	0.524216i	$0.175642\pi$
$103$	−1.46841	+	6.19572i	−0.144687	+	0.610482i	−0.996272	+	0.0862660i	$0.972506\pi$
$104$	0.919821	+	5.06414i	0.0901958	+	0.496580i
$105$	1.88407	−	1.62819i	0.183866	−	0.158895i
$106$	1.34980	+	1.37152i	0.131104	+	0.133214i
$107$	9.33476	+	16.1683i	0.902425	+	1.56305i	0.824337	+	0.566099i	$0.191548\pi$
$107$	9.33476	+	16.1683i	0.902425	+	1.56305i	0.0780877	+	0.996946i	$0.475119\pi$
$108$	−9.14028	−	4.94523i	−0.879524	−	0.475855i
$109$	−2.52690	+	4.37672i	−0.242033	+	0.419213i	−0.961293	−	0.275527i	$-0.911148\pi$
$109$	−2.52690	+	4.37672i	−0.242033	+	0.419213i	0.719260	+	0.694741i	$0.244481\pi$
$110$	−3.51726	+	0.912419i	−0.335358	+	0.0869958i
$111$	7.15341	+	5.82728i	0.678972	+	0.553100i
$112$	4.49790	+	3.57729i	0.425012	+	0.338022i
$113$	−10.7277	−	10.1211i	−1.00918	−	0.952109i	−0.0103217	−	0.999947i	$-0.503286\pi$
$113$	−10.7277	−	10.1211i	−1.00918	−	0.952109i	−0.998855	+	0.0478375i	$0.984767\pi$
$114$	−2.61449	+	3.78650i	−0.244869	+	0.354639i
$115$	0.864881	−	7.39953i	0.0806506	−	0.690010i
$116$	−1.89708	−	0.990985i	−0.176140	−	0.0920107i
$117$	−4.64642	−	2.86598i	−0.429562	−	0.264960i
$118$	5.86794	+	3.22468i	0.540187	+	0.296856i
$119$	1.07645	+	1.14097i	0.0986784	+	0.104593i
$120$	−4.29278	−	2.36702i	−0.391876	−	0.216078i
$121$	−3.93792	+	1.97770i	−0.357993	+	0.179791i
$122$	8.00647	−	6.22748i	0.724872	−	0.563810i
$123$	−4.89180	−	9.39710i	−0.441079	−	0.847308i
$124$	−8.72798	+	19.3772i	−0.783796	+	1.74012i
$125$	5.78797	−	6.89784i	0.517692	−	0.616961i
$126$	−6.01128	+	1.01052i	−0.535527	+	0.0900244i
$127$	−13.8456	−	16.5005i	−1.22860	−	1.46419i	−0.839829	−	0.542852i	$-0.817345\pi$
$127$	−13.8456	−	16.5005i	−1.22860	−	1.46419i	−0.388770	−	0.921335i	$-0.627100\pi$
$128$	3.53393	−	10.7476i	0.312358	−	0.949964i
$129$	−3.10536	+	3.01631i	−0.273412	+	0.265571i
$130$	−2.18089	−	1.36934i	−0.191277	−	0.120099i
$131$	−5.65418	+	0.660879i	−0.494008	+	0.0577412i	−0.359450	−	0.933164i	$-0.617036\pi$
$131$	−5.65418	+	0.660879i	−0.494008	+	0.0577412i	−0.134558	+	0.990906i	$0.542961\pi$
$132$	8.51764	+	2.56322i	0.741366	+	0.223099i
$133$	0.156931	+	2.69441i	0.0136077	+	0.233635i
$134$	0.432449	+	0.147139i	0.0373579	+	0.0127109i
$135$	4.91127	−	1.70705i	0.422695	−	0.146920i
$136$	1.37170	−	2.76666i	0.117622	−	0.237239i
$137$	9.75128	+	14.8261i	0.833108	+	1.26668i	0.961458	+	0.274951i	$0.0886615\pi$
$137$	9.75128	+	14.8261i	0.833108	+	1.26668i	−0.128350	+	0.991729i	$0.540968\pi$
$138$	−11.2170	+	14.3791i	−0.954855	+	1.22403i
$139$	12.1042	+	5.22123i	1.02666	+	0.442859i	0.841733	−	0.539893i	$-0.181535\pi$
$139$	12.1042	+	5.22123i	1.02666	+	0.442859i	0.184928	+	0.982752i	$0.440795\pi$
$140$	−2.83927	+	0.454031i	−0.239962	+	0.0383726i
$141$	4.82641	+	0.493095i	0.406457	+	0.0415261i
$142$	−4.78141	+	10.0437i	−0.401247	+	0.842846i
$143$	4.39085	+	1.59814i	0.367181	+	0.133643i
$144$	5.97042	+	10.4093i	0.497535	+	0.867444i
$145$	1.00627	−	0.366251i	0.0835659	−	0.0304155i
$146$	−1.48801	+	15.5751i	−0.123148	+	1.28900i
$147$	5.77560	−	6.30294i	0.476364	−	0.519858i
$148$	−3.48355	−	10.0682i	−0.286346	−	0.827604i
$149$	−9.38740	+	14.2728i	−0.769046	+	1.16928i	0.212334	+	0.977197i	$0.431894\pi$
$149$	−9.38740	+	14.2728i	−0.769046	+	1.16928i	−0.981379	+	0.192080i	$0.938477\pi$
$150$	−9.27725	+	3.14184i	−0.757484	+	0.256530i
$151$	−0.388145	−	1.63771i	−0.0315868	−	0.133275i	0.954967	−	0.296712i	$-0.0958901\pi$
$151$	−0.388145	−	1.63771i	−0.0315868	−	0.133275i	−0.986554	+	0.163437i	$0.947742\pi$
$152$	4.86785	−	2.12954i	0.394834	−	0.172728i
$153$	1.20927	+	3.04394i	0.0977636	+	0.246088i
$154$	4.86395	−	1.88751i	0.391949	−	0.152100i
$155$	−4.21147	−	9.76328i	−0.338273	−	0.784206i
$156$	2.82111	+	5.63726i	0.225870	+	0.451342i
$157$	3.29734	+	11.0139i	0.263157	+	0.879004i	0.982802	+	0.184663i	$0.0591192\pi$
$157$	3.29734	+	11.0139i	0.263157	+	0.879004i	−0.719645	+	0.694342i	$0.755696\pi$
$158$	−10.3540	+	11.4493i	−0.823717	+	0.910858i
$159$	2.05798	+	1.14860i	0.163208	+	0.0910898i
$160$	2.77702	+	4.93246i	0.219543	+	0.389945i
$161$			10.6968i			0.843027i
$162$	−12.4440	−	2.67332i	−0.977694	−	0.210036i
$163$		−	9.24166i		−	0.723862i	−0.932205	−	0.361931i	$-0.882118\pi$
$163$		−	9.24166i		−	0.723862i	0.932205	−	0.361931i	$-0.117882\pi$
$164$	−0.906150	+	12.1994i	−0.0707584	+	0.952615i
$165$	−3.82133	+	2.28098i	−0.297490	+	0.177574i
$166$	−0.517129	−	0.467656i	−0.0401370	−	0.0362971i
$167$	−1.27077	−	4.24468i	−0.0983354	−	0.328463i	0.894639	−	0.446789i	$-0.147432\pi$
$167$	−1.27077	−	4.24468i	−0.0983354	−	0.328463i	−0.992975	+	0.118326i	$0.962247\pi$
$168$	6.51660	+	2.66010i	0.502766	+	0.205231i
$169$	−3.83744	−	8.89618i	−0.295188	−	0.684322i
$170$	0.558946	+	1.44035i	0.0428692	+	0.110470i
$171$	−1.77266	+	5.34952i	−0.135559	+	0.409088i
$172$	4.88189	−	1.07502i	0.372240	−	0.0819693i
$173$	1.08188	+	4.56481i	0.0822537	+	0.347056i	0.998574	−	0.0533912i	$-0.0170030\pi$
$173$	1.08188	+	4.56481i	0.0822537	+	0.347056i	−0.916320	+	0.400447i	$0.868855\pi$
$174$	−2.57062	−	0.513230i	−0.194878	−	0.0389078i
$175$	−3.15702	+	4.80002i	−0.238648	+	0.362847i
$176$	−6.80631	−	7.69206i	−0.513045	−	0.579811i
$177$	8.00603	+	1.77491i	0.601770	+	0.133410i
$178$	−18.7417	−	1.79054i	−1.40475	−	0.134207i
$179$	20.6910	−	7.53089i	1.54651	−	0.562885i	0.578918	−	0.815386i	$-0.303475\pi$
$179$	20.6910	−	7.53089i	1.54651	−	0.562885i	0.967597	+	0.252501i	$0.0812529\pi$
$180$	−5.85968	−	1.30781i	−0.436754	−	0.0974787i
$181$	−21.9930	−	8.00478i	−1.63472	−	0.594991i	−0.648619	−	0.761114i	$-0.724653\pi$
$181$	−21.9930	−	8.00478i	−1.63472	−	0.594991i	−0.986105	+	0.166123i	$0.946875\pi$
$182$	3.33848	+	1.58932i	0.247464	+	0.117808i
$183$	7.27273	−	10.0715i	0.537616	−	0.744506i
$184$	19.7508	−	7.30393i	1.45605	−	0.538453i
$185$	4.89441	+	2.11124i	0.359844	+	0.155221i
$186$	−3.60332	+	25.7778i	−0.264208	+	1.89012i
$187$	−1.54051	−	2.34223i	−0.112653	−	0.171281i
$188$	−4.43958	−	3.41663i	−0.323789	−	0.249184i
$189$	−6.71953	+	3.25313i	−0.488774	+	0.236630i
$190$	−0.856282	+	2.51665i	−0.0621212	+	0.182577i
$191$	−0.920616	−	15.8064i	−0.0666135	−	1.14371i	−0.851599	−	0.524194i	$-0.824367\pi$
$191$	−0.920616	−	15.8064i	−0.0666135	−	1.14371i	0.784985	−	0.619515i	$-0.212671\pi$
$192$	0.462032	−	13.8487i	0.0333443	−	0.999444i
$193$	20.5708	−	2.40438i	1.48072	−	0.173071i	0.662970	−	0.748646i	$-0.269296\pi$
$193$	20.5708	−	2.40438i	1.48072	−	0.173071i	0.817749	+	0.575575i	$0.195222\pi$
$194$	6.29508	−	10.0259i	0.451960	−	0.719816i
$195$	−3.03424	−	0.860516i	−0.217286	−	0.0616228i
$196$	−9.50077	+	2.67985i	−0.678627	+	0.191418i
$197$	−0.281933	−	0.335995i	−0.0200869	−	0.0239386i	0.755907	−	0.654678i	$-0.227196\pi$
$197$	−0.281933	−	0.335995i	−0.0200869	−	0.0239386i	−0.775994	+	0.630740i	$0.782752\pi$
$198$	10.8937	+	0.0869973i	0.774182	+	0.00618263i
$199$	−9.60045	+	11.4414i	−0.680558	+	0.811058i	−0.990179	−	0.139802i	$-0.955353\pi$
$199$	−9.60045	+	11.4414i	−0.680558	+	0.811058i	0.309621	+	0.950860i	$0.399798\pi$
$200$	11.0185	+	2.55166i	0.779124	+	0.180429i
$201$	0.558925	+	0.0244042i	0.0394236	+	0.00172134i
$202$	−11.0529	−	14.2103i	−0.777677	−	0.999834i
$203$	−1.37401	+	0.690054i	−0.0964366	+	0.0484323i
$204$	0.662041	−	3.72365i	0.0463521	−	0.260708i
$205$	−4.20010	−	4.45184i	−0.293348	−	0.310930i
$206$	4.33681	−	7.89167i	0.302160	−	0.549839i
$207$	−8.24644	+	20.7573i	−0.573167	+	1.44273i
$208$	0.654993	−	7.24943i	0.0454156	−	0.502657i
$209$	0.559985	−	4.79098i	0.0387350	−	0.331399i
$210$	−3.18179	+	1.50918i	−0.219564	+	0.104144i
$211$	−13.2400	−	12.4913i	−0.911481	−	0.859938i	0.0790997	−	0.996867i	$-0.474795\pi$
$211$	−13.2400	−	12.4913i	−0.911481	−	0.859938i	−0.990581	+	0.136928i	$0.956277\pi$
$212$	−1.32291	−	2.37823i	−0.0908577	−	0.163338i
$213$	−2.17038	+	13.4497i	−0.148712	+	0.921560i
$214$	−6.62973	−	25.5568i	−0.453199	−	1.74702i
$215$	−1.25051	+	2.16595i	−0.0852843	+	0.147717i
$216$	10.5948	+	10.1858i	0.720886	+	0.693054i
$217$	7.63351	+	13.2216i	0.518197	+	0.897543i
$218$	5.09398	−	5.01330i	0.345008	−	0.339543i
$219$	3.60158	+	18.8208i	0.243372	+	1.27179i
$220$	5.13814	+	0.0820340i	0.346414	+	0.00553073i
$221$	0.458179	−	1.93321i	0.0308204	−	0.130042i
$222$	−7.55413	−	10.6392i	−0.507000	−	0.714055i
$223$	7.06016	+	5.25610i	0.472784	+	0.351974i	0.807029	−	0.590512i	$-0.201074\pi$
$223$	7.06016	+	5.25610i	0.472784	+	0.351974i	−0.334246	+	0.942486i	$0.608481\pi$
$224$	−4.78257	−	6.57139i	−0.319549	−	0.439070i
$225$	−9.82670	+	6.88067i	−0.655113	+	0.458712i
$226$	10.8077	+	17.8391i	0.718917	+	1.18664i
$227$	0.712444	−	2.37973i	0.0472866	−	0.157948i	−0.931085	−	0.364801i	$-0.881137\pi$
$227$	0.712444	−	2.37973i	0.0472866	−	0.157948i	0.978372	+	0.206853i	$0.0663222\pi$
$228$	4.99090	−	4.17579i	0.330531	−	0.276548i
$229$	1.09811	−	18.8538i	0.0725650	−	1.24589i	−0.743818	−	0.668382i	$-0.766987\pi$
$229$	1.09811	−	18.8538i	0.0725650	−	1.24589i	0.816383	−	0.577511i	$-0.195976\pi$
$230$	−3.96790	+	9.76002i	−0.261635	+	0.643557i
$231$	5.06948	−	3.88993i	0.333547	−	0.255939i
$232$	2.21232	+	2.06582i	0.145246	+	0.135628i
$233$	−13.4908	−	2.37880i	−0.883815	−	0.155840i	−0.286723	−	0.958014i	$-0.592566\pi$
$233$	−13.4908	−	2.37880i	−0.883815	−	0.155840i	−0.597091	+	0.802173i	$0.703677\pi$
$234$	5.25311	+	5.65782i	0.343407	+	0.369863i
$235$	2.76025	−	0.486707i	0.180059	−	0.0317492i
$236$	−6.78291	−	6.60716i	−0.441530	−	0.430090i
$237$	−8.23841	+	17.0166i	−0.535142	+	1.10535i
$238$	−1.03722	−	1.96095i	−0.0672329	−	0.127110i
$239$	−5.30471	−	7.12547i	−0.343133	−	0.460908i	0.596738	−	0.802436i	$-0.296463\pi$
$239$	−5.30471	−	7.12547i	−0.343133	−	0.460908i	−0.939872	+	0.341528i	$0.889056\pi$
$240$	4.95915	+	4.84442i	0.320112	+	0.312706i
$241$	11.5111	+	5.78111i	0.741497	+	0.372394i	0.779101	−	0.626899i	$-0.215676\pi$
$241$	11.5111	+	5.78111i	0.741497	+	0.372394i	−0.0376034	+	0.999293i	$0.511972\pi$
$242$	6.11305	−	1.21145i	0.392962	−	0.0778750i
$243$	−15.5473	+	1.13248i	−0.997358	+	0.0726488i
$244$	−13.2605	+	5.47065i	−0.848920	+	0.350223i
$245$	2.21658	−	4.41357i	0.141612	−	0.281973i
$246$	3.12589	+	14.6526i	0.199299	+	0.934217i
$247$	2.74200	−	2.04134i	0.174469	−	0.129888i
$248$	19.2004	−	23.1226i	1.21922	−	1.46828i
$249$	−0.768587	−	0.372103i	−0.0487072	−	0.0235811i
$250$	−10.4893	+	7.22058i	−0.663400	+	0.456670i
$251$	3.15290	+	17.8810i	0.199009	+	1.12864i	0.906592	+	0.422007i	$0.138674\pi$
$251$	3.15290	+	17.8810i	0.199009	+	1.12864i	−0.707583	+	0.706630i	$0.750215\pi$
$252$	8.57462	+	0.888354i	0.540150	+	0.0559611i
$253$	3.31968	−	18.8268i	0.208706	−	1.18363i
$254$	12.6530	+	27.7099i	0.793923	+	1.73867i
$255$	1.15192	+	1.50121i	0.0721359	+	0.0940097i
$256$	−8.86793	+	13.3177i	−0.554245	+	0.832353i
$257$	6.08497	+	0.354409i	0.379570	+	0.0221074i	0.246869	−	0.969049i	$-0.420598\pi$
$257$	6.08497	+	0.354409i	0.379570	+	0.0221074i	0.132700	+	0.991156i	$0.457635\pi$
$258$	5.36969	−	2.94094i	0.334302	−	0.183095i
$259$	−7.33195	−	2.19504i	−0.455585	−	0.136393i
$260$	2.45656	+	2.68852i	0.152349	+	0.166735i
$261$	−3.19827	+	0.279800i	−0.197968	+	0.0173192i
$262$	7.95608	+	1.23034i	0.491528	+	0.0760107i
$263$	7.37914	−	9.91191i	0.455017	−	0.611194i	−0.514119	−	0.857719i	$-0.671881\pi$
$263$	7.37914	−	9.91191i	0.455017	−	0.611194i	0.969137	+	0.246524i	$0.0792885\pi$
$264$	−10.6439	−	6.70427i	−0.655089	−	0.412619i
$265$	1.32488	+	0.314001i	0.0813865	+	0.0192889i
$266$	0.801663	−	3.73179i	0.0491531	−	0.228811i
$267$	−22.6474	+	4.33384i	−1.38600	+	0.265227i
$268$	−0.533995	−	0.363557i	−0.0326189	−	0.0222078i
$269$	−17.9683	+	10.3740i	−1.09555	+	0.632514i	−0.935048	−	0.354522i	$-0.884644\pi$
$269$	−17.9683	+	10.3740i	−1.09555	+	0.632514i	−0.160499	+	0.987036i	$0.551310\pi$
$270$	−7.33778	+	0.475671i	−0.446563	+	0.0289484i
$271$	−16.5506	−	9.55549i	−1.00538	−	0.580455i	−0.0955423	−	0.995425i	$-0.530459\pi$
$271$	−16.5506	−	9.55549i	−1.00538	−	0.580455i	−0.909835	+	0.414971i	$0.863792\pi$
$272$	−2.91251	+	3.25410i	−0.176597	+	0.197309i
$273$	4.47064	+	0.721425i	0.270575	+	0.0436626i
$274$	−7.70337	−	23.8843i	−0.465377	−	1.44290i
$275$	7.04614	−	7.46847i	0.424898	−	0.450366i
$276$	20.7092	−	15.3717i	1.24655	−	0.925268i
$277$	7.05354	+	0.824441i	0.423806	+	0.0495359i	0.325323	−	0.945603i	$-0.394527\pi$
$277$	7.05354	+	0.824441i	0.423806	+	0.0495359i	0.0984831	+	0.995139i	$0.468601\pi$
$278$	−14.5307	−	11.6791i	−0.871495	−	0.700467i
$279$	4.62005	+	31.5416i	0.276595	+	1.88835i
$280$	4.04123	+	0.451300i	0.241510	+	0.0269703i
$281$	10.6016	−	10.0021i	0.632438	−	0.596675i	−0.301780	−	0.953378i	$-0.597581\pi$
$281$	10.6016	−	10.0021i	0.632438	−	0.596675i	0.934218	+	0.356703i	$0.116099\pi$
$282$	−6.39284	−	2.49128i	−0.380688	−	0.148353i
$283$	10.3010	+	20.5111i	0.612334	+	1.21926i	0.959568	+	0.281478i	$0.0908246\pi$
$283$	10.3010	+	20.5111i	0.612334	+	1.21926i	−0.347234	+	0.937778i	$0.612879\pi$
$284$	10.3030	−	11.8879i	0.611369	−	0.705419i
$285$	−0.142021	+	3.25269i	−0.00841262	+	0.192673i
$286$	−5.38262	−	3.83334i	−0.318281	−	0.226670i
$287$	6.73193	+	5.64876i	0.397373	+	0.333436i
$288$	−4.21459	−	16.4389i	−0.248347	−	0.968671i
$289$	12.1096	−	10.1612i	0.712332	−	0.597717i
$290$	−1.50965	+	0.119943i	−0.0886496	+	0.00704329i
$291$	3.95592	−	13.9488i	0.231900	−	0.817695i
$292$	7.89875	−	20.6689i	0.462240	−	1.20956i
$293$	−3.87451	−	33.1486i	−0.226351	−	1.93656i	−0.334436	−	0.942418i	$-0.608546\pi$
$293$	−3.87451	−	33.1486i	−0.226351	−	1.93656i	0.108085	−	0.994142i	$-0.465528\pi$
$294$	−10.2482	+	6.41436i	−0.597686	+	0.374093i
$295$	4.72953	−	0.275464i	0.275364	−	0.0160381i
$296$	0.953393	+	15.0366i	0.0554148	+	0.873986i
$297$	12.8362	−	3.64028i	0.744834	−	0.211230i
$298$	18.1753	−	15.9165i	1.05287	−	0.922017i
$299$	11.3194	−	7.44486i	0.654615	−	0.430547i
$300$	13.8297	−	0.785758i	0.798456	−	0.0453658i
$301$	1.42234	−	3.29736i	0.0819825	−	0.190057i
$302$	−0.0882174	+	2.37860i	−0.00507634	+	0.136873i
$303$	−17.8754	−	12.9080i	−1.02692	−	0.741547i
$304$	−7.43783	+	1.06791i	−0.426589	+	0.0612491i
$305$	2.45466	−	6.74412i	0.140553	−	0.386167i
$306$	−0.500990	−	4.60487i	−0.0286397	−	0.263243i
$307$	6.17186	+	16.9571i	0.352247	+	0.967790i	0.981647	+	0.190708i	$0.0610785\pi$
$307$	6.17186	+	16.9571i	0.352247	+	0.967790i	−0.629400	+	0.777082i	$0.716699\pi$
$308$	−7.34130	+	0.739486i	−0.418309	+	0.0421361i
$309$	2.38704	−	10.7672i	0.135794	−	0.612522i
$310$	2.06053	+	14.8953i	0.117030	+	0.845997i
$311$	−7.77998	−	5.11697i	−0.441162	−	0.290157i	0.309431	−	0.950922i	$-0.399862\pi$
$311$	−7.77998	−	5.11697i	−0.441162	−	0.290157i	−0.750593	+	0.660765i	$0.770232\pi$
$312$	−1.72056	−	8.74726i	−0.0974076	−	0.495216i
$313$	−6.72739	+	1.59442i	−0.380255	+	0.0901220i	−0.416298	−	0.909228i	$-0.636673\pi$
$313$	−6.72739	+	1.59442i	−0.380255	+	0.0901220i	0.0360433	+	0.999350i	$0.488525\pi$
$314$	−0.343149	−	16.2554i	−0.0193650	−	0.917347i
$315$	−3.22194	+	2.86727i	−0.181536	+	0.161552i
$316$	18.4285	−	11.7035i	1.03668	−	0.658373i
$317$	−8.42376	+	3.63365i	−0.473125	+	0.204086i	−0.619272	−	0.785177i	$-0.712572\pi$
$317$	−8.42376	+	3.63365i	−0.473125	+	0.204086i	0.146147	+	0.989263i	$0.453313\pi$
$318$	−2.37222	−	2.34130i	−0.133028	−	0.131293i
$319$	2.63247	−	0.788109i	0.147390	−	0.0441257i
$320$	−1.92612	−	7.76995i	−0.107673	−	0.434353i
$321$	−16.5738	−	27.7662i	−0.925059	−	1.54976i
$322$	4.03181	−	14.5804i	0.224684	−	0.812534i
$323$	−2.05094			−0.114118
$324$	15.9543	+	8.33425i	0.886351	+	0.463014i
$325$	7.27662			0.403634
$326$	−3.48334	+	12.5969i	−0.192924	+	0.697680i
$327$	4.26601	−	7.64354i	0.235911	−	0.422689i
$328$	5.83331	−	16.2870i	0.322091	−	0.899299i
$329$	−3.85533	+	1.15421i	−0.212551	+	0.0636336i
$330$	6.06845	−	1.66878i	0.334057	−	0.0918634i
$331$	19.2827	−	8.31775i	1.05987	−	0.457185i	0.206479	−	0.978451i	$-0.433799\pi$
$331$	19.2827	−	8.31775i	1.05987	−	0.457185i	0.853394	+	0.521266i	$0.174540\pi$
$332$	0.528610	+	0.832358i	0.0290113	+	0.0456816i
$333$	−12.5355	−	9.91189i	−0.686943	−	0.543168i
$334$	0.132247	+	6.26473i	0.00723624	+	0.342791i
$335$	0.314498	−	0.0745374i	0.0171829	−	0.00407241i
$336$	−7.87987	−	6.08209i	−0.429882	−	0.331805i
$337$	−11.8724	−	7.80863i	−0.646734	−	0.425363i	0.183315	−	0.983054i	$-0.441317\pi$
$337$	−11.8724	−	7.80863i	−0.646734	−	0.425363i	−0.830049	+	0.557691i	$0.811687\pi$
$338$	1.87753	+	13.5724i	0.102124	+	0.738243i
$339$	18.8339	+	17.2581i	1.02292	+	0.937333i
$340$	−0.218983	−	2.17397i	−0.0118760	−	0.117900i
$341$	−9.33206	−	25.6396i	−0.505359	−	1.38846i
$342$	4.43257	−	6.62358i	0.239686	−	0.358162i
$343$	−5.86520	+	16.1145i	−0.316691	+	0.870102i
$344$	−7.05950	−	0.374754i	−0.380623	−	0.0202054i
$345$	−1.31148	+	12.8368i	−0.0706079	+	0.691110i
$346$	0.245889	−	6.62988i	0.0132191	−	0.356425i
$347$	−14.2256	+	32.9786i	−0.763668	+	1.77038i	−0.137790	+	0.990461i	$0.544000\pi$
$347$	−14.2256	+	32.9786i	−0.763668	+	1.77038i	−0.625878	+	0.779921i	$0.715259\pi$
$348$	3.31046	+	1.66847i	0.177459	+	0.0894395i
$349$	9.87341	−	6.49385i	0.528512	−	0.347608i	−0.257043	−	0.966400i	$-0.582748\pi$
$349$	9.87341	−	6.49385i	0.528512	−	0.347608i	0.785555	+	0.618792i	$0.212378\pi$
$350$	6.11242	−	5.35277i	0.326722	−	0.286118i
$351$	8.11917	+	4.84646i	0.433369	+	0.258685i
$352$	6.37814	+	13.0502i	0.339956	+	0.695576i
$353$	−5.37075	+	0.312810i	−0.285856	+	0.0166492i	−0.200474	−	0.979699i	$-0.564248\pi$
$353$	−5.37075	+	0.312810i	−0.285856	+	0.0166492i	−0.0853822	+	0.996348i	$0.527211\pi$
$354$	−10.2437	−	5.43692i	−0.544447	−	0.288969i
$355$	0.913732	+	7.81748i	0.0484959	+	0.414909i
$356$	24.8712	+	9.50470i	1.31817	+	0.503748i
$357$	−1.89301	−	1.94890i	−0.100189	−	0.103147i
$358$	−31.0415	+	2.46628i	−1.64060	+	0.130347i
$359$	−10.2142	+	8.57074i	−0.539085	+	0.452346i	−0.871225	−	0.490884i	$-0.836674\pi$
$359$	−10.2142	+	8.57074i	−0.539085	+	0.452346i	0.332140	+	0.943230i	$0.392229\pi$
$360$	7.49415	+	3.99124i	0.394977	+	0.210357i
$361$	11.8516	+	9.94466i	0.623767	+	0.523403i
$362$	26.9606	+	19.2005i	1.41702	+	1.00916i
$363$	6.77014	−	3.52430i	0.355340	−	0.184978i
$364$	−3.95150	−	3.42467i	−0.207115	−	0.179502i
$365$	4.96842	+	9.89293i	0.260059	+	0.517820i
$366$	−13.7093	+	10.9868i	−0.716596	+	0.574291i
$367$	−14.4345	+	13.6183i	−0.753475	+	0.710867i	−0.963759	−	0.266773i	$-0.914043\pi$
$367$	−14.4345	+	13.6183i	−0.753475	+	0.710867i	0.210284	+	0.977640i	$0.432561\pi$
$368$	−29.6745	+	2.51128i	−1.54689	+	0.130910i
$369$	8.70864	+	16.1513i	0.453354	+	0.840804i
$370$	−5.87561	−	4.72253i	−0.305458	−	0.245513i
$371$	−1.94178	−	0.226961i	−0.100812	−	0.0117832i
$372$	14.6276	−	33.7786i	0.758408	−	1.75134i
$373$	−5.30920	+	5.62742i	−0.274900	+	0.291377i	−0.850084	−	0.526647i	$-0.823449\pi$
$373$	−5.30920	+	5.62742i	−0.274900	+	0.291377i	0.575184	+	0.818024i	$0.304930\pi$
$374$	1.21698	+	3.77325i	0.0629286	+	0.195110i
$375$	−9.85026	+	12.0919i	−0.508665	+	0.624424i
$376$	4.76362	+	6.33043i	0.245665	+	0.326467i
$377$	1.68651	+	0.973707i	0.0868597	+	0.0501485i
$378$	10.3853	−	1.90150i	0.534161	−	0.0978025i
$379$	7.61424	−	4.39608i	0.391117	−	0.225812i	−0.291527	−	0.956563i	$-0.594163\pi$
$379$	7.61424	−	4.39608i	0.391117	−	0.225812i	0.682644	+	0.730751i	$0.260830\pi$
$380$	2.11574	−	3.10760i	0.108535	−	0.159417i
$381$	24.3944	+	28.2280i	1.24976	+	1.44617i
$382$	−4.70284	+	21.8920i	−0.240618	+	1.12009i
$383$	−19.4320	−	4.60548i	−0.992930	−	0.235329i	−0.298125	−	0.954527i	$-0.596361\pi$
$383$	−19.4320	−	4.60548i	−0.992930	−	0.235329i	−0.694805	+	0.719198i	$0.744509\pi$
$384$	−5.84959	+	18.7025i	−0.298511	+	0.954406i
$385$	2.20446	−	2.96111i	0.112350	−	0.150912i
$386$	−28.9455	−	4.47618i	−1.47329	−	0.227832i
$387$	5.30210	−	5.30206i	0.269521	−	0.269519i
$388$	−12.3595	+	11.2931i	−0.627458	+	0.573323i
$389$	−36.3467	−	10.8815i	−1.84285	−	0.551713i	−0.999906	−	0.0137091i	$-0.995636\pi$
$389$	−36.3467	−	10.8815i	−1.84285	−	0.551713i	−0.842943	−	0.538004i	$-0.819179\pi$
$390$	3.81151	+	2.31659i	0.193003	+	0.117305i
$391$	−8.11472	−	0.472629i	−0.410379	−	0.0239019i
$392$	13.9602	−	0.0717884i	0.705097	−	0.00362586i
$393$	9.77564	−	1.28697i	0.493116	−	0.0649190i
$394$	0.257649	+	0.564246i	0.0129802	+	0.0284263i
$395$	−1.89665	+	10.7564i	−0.0954308	+	0.541215i
$396$	−14.8160	−	4.22461i	−0.744531	−	0.212295i
$397$	5.63268	+	31.9445i	0.282696	+	1.60325i	0.713401	+	0.700756i	$0.247154\pi$
$397$	5.63268	+	31.9445i	0.282696	+	1.60325i	−0.430706	+	0.902493i	$0.641735\pi$
$398$	17.3985	−	11.9767i	0.872106	−	0.600338i
$399$	−0.339650	−	4.66241i	−0.0170038	−	0.233412i
$400$	−14.0571	−	7.63112i	−0.702855	−	0.381556i
$401$	18.6976	−	13.9198i	0.933712	−	0.695123i	−0.0187356	−	0.999824i	$-0.505964\pi$
$401$	18.6976	−	13.9198i	0.933712	−	0.695123i	0.952448	+	0.304701i	$0.0985567\pi$
$402$	−0.752651	−	0.243933i	−0.0375388	−	0.0121663i
$403$	8.67828	−	17.2799i	0.432296	−	0.860772i
$404$	9.70960	+	23.5355i	0.483071	+	1.17094i
$405$	−8.46268	+	3.08009i	−0.420514	+	0.153051i
$406$	2.13295	−	0.422697i	0.105857	−	0.0209781i
$407$	12.2233	+	6.13878i	0.605887	+	0.304288i
$408$	−2.30591	+	4.82603i	−0.114160	+	0.238924i
$409$	18.0356	+	24.2260i	0.891801	+	1.19790i	0.979438	+	0.201745i	$0.0646611\pi$
$409$	18.0356	+	24.2260i	0.891801	+	1.19790i	−0.0876369	+	0.996152i	$0.527932\pi$
$410$	4.04701	+	7.65122i	0.199868	+	0.377867i
$411$	−17.2614	−	25.4312i	−0.851440	−	1.25443i
$412$	−8.88584	+	9.12220i	−0.437774	+	0.449418i
$413$	−6.69898	+	1.18121i	−0.329635	+	0.0581236i
$414$	19.0642	−	25.1852i	0.936954	−	1.23779i
$415$	−0.485834	−	0.0856657i	−0.0238487	−	0.00420516i
$416$	−3.62523	+	9.63453i	−0.177742	+	0.472372i
$417$	−21.0943	−	8.73760i	−1.03299	−	0.427882i
$418$	−2.56910	+	6.31932i	−0.125659	+	0.309088i
$419$	−1.54380	+	26.5060i	−0.0754195	+	1.29490i	0.722176	+	0.691710i	$0.243142\pi$
$419$	−1.54380	+	26.5060i	−0.0754195	+	1.29490i	−0.797595	+	0.603193i	$0.793895\pi$
$420$	4.90581	−	0.857837i	0.239379	−	0.0418581i
$421$	4.67484	−	15.6151i	0.227838	−	0.761031i	−0.765258	−	0.643724i	$-0.777389\pi$
$421$	4.67484	−	15.6151i	0.227838	−	0.761031i	0.993096	−	0.117307i	$-0.0374263\pi$
$422$	13.3388	+	22.0168i	0.649321	+	1.07176i
$423$	−8.37113	−	0.732410i	−0.407018	−	0.0356110i
$424$	0.906806	+	3.74030i	0.0440384	+	0.181645i
$425$	−3.50186	−	2.60704i	−0.169865	−	0.126460i
$426$	8.02779	−	17.5147i	0.388948	−	0.848592i
$427$	−2.37647	+	10.0271i	−0.115005	+	0.485246i
$428$	−0.596067	+	37.3343i	−0.0288120	+	1.80462i
$429$	−7.64462	−	2.65717i	−0.369086	−	0.128289i
$430$	2.52091	−	2.48098i	0.121569	−	0.119644i
$431$	1.61367	+	2.79496i	0.0777279	+	0.134629i	0.902269	−	0.431173i	$-0.141900\pi$
$431$	1.61367	+	2.79496i	0.0777279	+	0.134629i	−0.824541	+	0.565802i	$0.808567\pi$
$432$	−10.6022	−	17.8772i	−0.510097	−	0.860117i
$433$	6.66675	−	11.5472i	0.320384	−	0.554921i	−0.660184	−	0.751104i	$-0.729522\pi$
$433$	6.66675	−	11.5472i	0.320384	−	0.554921i	0.980567	+	0.196184i	$0.0628548\pi$
$434$	−5.42147	−	20.8991i	−0.260239	−	1.00319i
$435$	−1.73350	+	0.659644i	−0.0831148	+	0.0316275i
$436$	−8.83299	+	4.91342i	−0.423024	+	0.235310i
$437$	−10.1730	−	9.59769i	−0.486639	−	0.459120i
$438$	2.18473	−	27.0114i	0.104390	−	1.29066i
$439$	−2.47906	+	21.2097i	−0.118319	+	1.01228i	0.795442	+	0.606030i	$0.207239\pi$
$439$	−2.47906	+	21.2097i	−0.118319	+	1.01228i	−0.913761	+	0.406253i	$0.866835\pi$
$440$	−6.97268	−	2.04847i	−0.332409	−	0.0976571i
$441$	−9.84383	+	11.0613i	−0.468754	+	0.526730i
$442$	−1.35319	+	2.46238i	−0.0643645	+	0.117124i
$443$	11.0913	+	11.7561i	0.526962	+	0.558547i	0.935105	−	0.354371i	$-0.115305\pi$
$443$	11.0913	+	11.7561i	0.526962	+	0.558547i	−0.408143	+	0.912918i	$0.633824\pi$
$444$	6.28664	+	17.3491i	0.298351	+	0.823353i
$445$	−11.9043	+	5.97858i	−0.564319	+	0.283412i
$446$	−7.64231	−	9.82548i	−0.361874	−	0.465250i
$447$	15.8982	−	24.9551i	0.751961	−	1.18034i
$448$	4.04206	+	10.7598i	0.190969	+	0.508355i
$449$	−5.44816	+	6.49286i	−0.257115	+	0.306417i	−0.879125	−	0.476592i	$-0.841872\pi$
$449$	−5.44816	+	6.49286i	−0.257115	+	0.306417i	0.622010	+	0.783009i	$0.286316\pi$
$450$	15.9878	−	5.67492i	0.753673	−	0.267518i
$451$	−10.0954	−	12.0313i	−0.475375	−	0.566530i
$452$	−8.00768	−	28.3893i	−0.376650	−	1.33532i
$453$	0.713466	+	2.82652i	0.0335215	+	0.132802i
$454$	−1.86807	+	2.97518i	−0.0876727	+	0.139632i
$455$	2.59850	−	0.303721i	0.121820	−	0.0142387i
$456$	−8.37683	+	3.81069i	−0.392281	+	0.178452i
$457$	1.90785	+	32.7565i	0.0892455	+	1.53229i	0.684657	+	0.728865i	$0.259952\pi$
$457$	1.90785	+	32.7565i	0.0892455	+	1.53229i	−0.595411	+	0.803421i	$0.703011\pi$
$458$	−8.60311	+	25.2849i	−0.401997	+	1.18149i
$459$	−2.17096	−	5.24125i	−0.101332	−	0.244641i
$460$	9.08721	−	11.8079i	0.423693	−	0.550547i
$461$	6.82770	+	10.3810i	0.317998	+	0.483492i	0.958748	−	0.284257i	$-0.0917470\pi$
$461$	6.82770	+	10.3810i	0.317998	+	0.483492i	−0.640750	+	0.767749i	$0.721377\pi$
$462$	−8.37618	+	3.39144i	−0.389695	+	0.157784i
$463$	1.20201	+	0.518496i	0.0558621	+	0.0240966i	0.423828	−	0.905743i	$-0.360686\pi$
$463$	1.20201	+	0.518496i	0.0558621	+	0.0240966i	−0.367965	+	0.929839i	$0.619946\pi$
$464$	−2.23688	−	3.64969i	−0.103845	−	0.169433i
$465$	7.53962	+	16.8026i	0.349642	+	0.779204i
$466$	17.4922	+	8.32738i	0.810312	+	0.385759i
$467$	0.279985	+	0.101906i	0.0129562	+	0.00471566i	0.348490	−	0.937312i	$-0.386694\pi$
$467$	0.279985	+	0.101906i	0.0129562	+	0.00471566i	−0.335534	+	0.942028i	$0.608917\pi$
$468$	−5.02778	−	9.69194i	−0.232409	−	0.448010i
$469$	−0.436088	+	0.158723i	−0.0201367	+	0.00732915i
$470$	−3.94584	−	0.376976i	−0.182008	−	0.0173886i
$471$	−5.98798	−	18.9916i	−0.275911	−	0.875085i
$472$	6.75516	+	11.5626i	0.310931	+	0.532210i
$473$	−3.52670	+	5.36208i	−0.162158	+	0.246549i
$474$	17.6433	−	20.0895i	0.810384	−	0.922740i
$475$	−1.73232	−	7.30921i	−0.0794841	−	0.335370i
$476$	0.674674	+	3.06384i	0.0309236	+	0.140431i
$477$	−3.59308	−	1.93739i	−0.164516	−	0.0887068i
$478$	4.54493	+	11.7119i	0.207880	+	0.535689i
$479$	−13.8993	−	32.2222i	−0.635075	−	1.47227i	−0.866379	−	0.499387i	$-0.833559\pi$
$479$	−13.8993	−	32.2222i	−0.635075	−	1.47227i	0.231304	−	0.972881i	$-0.425701\pi$
$480$	−4.93368	−	8.47242i	−0.225190	−	0.386711i
$481$	2.78016	+	9.28638i	0.126764	+	0.423423i
$482$	−13.5114	−	12.2187i	−0.615426	−	0.556549i
$483$	−0.269427	−	18.5255i	−0.0122593	−	0.842938i
$484$	−8.78907	−	0.652836i	−0.399503	−	0.0296744i
$485$		−	8.37633i		−	0.380350i
$486$	21.6187	+	4.31639i	0.980645	+	0.195796i
$487$			21.9973i			0.996791i	0.866950	+	0.498396i	$0.166077\pi$
$487$			21.9973i			0.996791i	−0.866950	+	0.498396i	$0.833923\pi$
$488$	20.1369	−	2.45870i	0.911555	−	0.111300i
$489$	0.232775	+	16.0053i	0.0105265	+	0.723786i
$490$	−4.68488	+	5.18049i	−0.211641	+	0.234031i
$491$	−5.26931	−	17.6007i	−0.237801	−	0.794310i	−0.990687	−	0.136159i	$-0.956524\pi$
$491$	−5.26931	−	17.6007i	−0.237801	−	0.794310i	0.752886	−	0.658151i	$-0.228661\pi$
$492$	1.26206	−	21.1506i	0.0568980	−	0.953543i
$493$	−0.462773	−	1.07283i	−0.0208423	−	0.0483178i
$494$	−4.50693	+	1.74897i	−0.202776	+	0.0786897i
$495$	6.56059	−	4.04660i	0.294877	−	0.181881i
$496$	−34.8866	+	24.2805i	−1.56645	+	1.09023i
$497$	−2.60619	−	10.9964i	−0.116904	−	0.493255i
$498$	0.907378	+	0.796892i	0.0406606	+	0.0357096i
$499$	−2.74935	+	4.18018i	−0.123078	+	0.187131i	−0.891771	−	0.452487i	$-0.850537\pi$
$499$	−2.74935	+	4.18018i	−0.123078	+	0.187131i	0.768693	+	0.639618i	$0.220907\pi$
$500$	17.0191	−	5.88849i	0.761116	−	0.263342i
$501$	2.30772	+	7.31921i	0.103102	+	0.326998i
$502$	2.44206	−	25.5612i	0.108995	−	1.14085i
$503$	−11.9947	+	4.36570i	−0.534815	+	0.194657i	−0.595287	−	0.803513i	$-0.702962\pi$
$503$	−11.9947	+	4.36570i	−0.534815	+	0.194657i	0.0604720	+	0.998170i	$0.480739\pi$
$504$	−11.3529	−	4.44280i	−0.505698	−	0.197898i
$505$	−11.9698	−	4.35666i	−0.532650	−	0.193869i
$506$	−11.6211	+	24.4109i	−0.516620	+	1.08520i
$507$	6.87001	+	15.3104i	0.305108	+	0.679957i
$508$	−6.80252	−	42.5394i	−0.301813	−	1.88738i
$509$	13.1590	+	5.67626i	0.583264	+	0.251596i	0.667204	−	0.744875i	$-0.267491\pi$
$509$	13.1590	+	5.67626i	0.583264	+	0.251596i	−0.0839395	+	0.996471i	$0.526750\pi$
$510$	−1.00430	−	2.48042i	−0.0444711	−	0.109835i
$511$	−8.73463	−	13.2804i	−0.386397	−	0.587488i
$512$	17.1072	−	14.8103i	0.756037	−	0.654528i
$513$	2.93527	−	9.30932i	0.129595	−	0.411016i
$514$	−8.16059	−	2.77661i	−0.359948	−	0.122471i
$515$	−0.370466	−	6.36065i	−0.0163247	−	0.280284i
$516$	−8.42770	+	1.98475i	−0.371009	+	0.0873738i
$517$	7.14374	−	0.834983i	0.314181	−	0.0367225i
$518$	9.16653	+	5.75551i	0.402754	+	0.252883i
$519$	−1.98865	−	7.87839i	−0.0872919	−	0.345823i
$520$	−2.33509	−	4.59053i	−0.102400	−	0.201308i
$521$	21.0911	+	25.1354i	0.924017	+	1.10120i	0.994609	+	0.103696i	$0.0330669\pi$
$521$	21.0911	+	25.1354i	0.924017	+	1.10120i	−0.0705916	+	0.997505i	$0.522489\pi$
$522$	4.46489	+	0.824098i	0.195423	+	0.0360698i
$523$	17.1999	−	20.4981i	0.752100	−	0.896318i	−0.245221	−	0.969467i	$-0.578861\pi$
$523$	17.1999	−	20.4981i	0.752100	−	0.896318i	0.997321	+	0.0731493i	$0.0233049\pi$
$524$	−10.3809	−	4.67581i	−0.453491	−	0.204264i
$525$	5.34664	−	8.39251i	0.233346	−	0.366279i
$526$	−13.7942	+	10.7292i	−0.601455	+	0.467815i
$527$	−10.3674	+	5.20668i	−0.451609	+	0.226807i
$528$	11.9814	+	13.1502i	0.521422	+	0.572289i
$529$	−22.2548	−	23.5887i	−0.967601	−	1.02560i
$530$	−1.68753	−	0.927371i	−0.0733017	−	0.0402824i
$531$	−13.9101	−	2.87226i	−0.603647	−	0.124645i
$532$	−2.49929	+	4.78450i	−0.108358	+	0.207434i
$533$	1.29217	−	11.0552i	0.0559700	−	0.478854i
$534$	32.5033	+	2.62892i	1.40655	+	0.113765i
$535$	−13.5884	−	12.8200i	−0.587478	−	0.554257i
$536$	0.590836	+	0.696822i	0.0255202	+	0.0300981i
$537$	−35.6443	+	13.5637i	−1.53817	+	0.585315i
$538$	28.4020	−	7.36783i	1.22450	−	0.317650i
$539$	6.33689	−	10.9758i	0.272949	−	0.472762i
$540$	10.1811	+	2.11737i	0.438126	+	0.0911170i
$541$	19.2897	+	33.4107i	0.829329	+	1.43644i	0.898566	+	0.438839i	$0.144610\pi$
$541$	19.2897	+	33.4107i	0.829329	+	1.43644i	−0.0692372	+	0.997600i	$0.522057\pi$
$542$	18.9578	+	19.2629i	0.814308	+	0.827413i
$543$	38.2905	+	13.3093i	1.64320	+	0.571156i
$544$	5.19645	−	3.33776i	0.222796	−	0.143105i
$545$	1.16623	−	4.92072i	0.0499559	−	0.210781i
$546$	−5.82183	−	2.66841i	−0.249151	−	0.114197i
$547$	13.6567	+	10.1671i	0.583920	+	0.434712i	0.848157	−	0.529746i	$-0.177713\pi$
$547$	13.6567	+	10.1671i	0.583920	+	0.434712i	−0.264237	+	0.964458i	$0.585120\pi$
$548$	1.49774	+	35.4593i	0.0639804	+	1.51475i
$549$	−12.3417	+	17.6257i	−0.526732	+	0.752246i
$550$	−12.4193	+	7.52416i	−0.529561	+	0.320831i
$551$	0.576568	−	1.92587i	0.0245626	−	0.0820448i
$552$	−34.0217	+	13.1469i	−1.44806	+	0.559570i
$553$	0.911867	−	15.6562i	0.0387765	−	0.665768i
$554$	−9.30366	−	3.78237i	−0.395275	−	0.160697i
$555$	−8.52964	−	3.53311i	−0.362063	−	0.149972i
$556$	15.4042	+	21.3962i	0.653284	+	0.907402i
$557$	22.0719	+	3.89187i	0.935216	+	0.164904i	0.620433	−	0.784260i	$-0.286957\pi$
$557$	22.0719	+	3.89187i	0.935216	+	0.164904i	0.314784	+	0.949163i	$0.398068\pi$
$558$	5.59119	−	44.7345i	0.236694	−	1.89376i
$559$	−4.47920	+	0.789804i	−0.189450	+	0.0334051i
$560$	−5.33834	−	2.13836i	−0.225586	−	0.0903622i
$561$	2.72696	+	4.01764i	0.115132	+	0.169625i
$562$	−18.2206	+	9.63752i	−0.768588	+	0.406534i
$563$	2.90352	+	3.90010i	0.122369	+	0.164370i	0.859086	−	0.511831i	$-0.171033\pi$
$563$	2.90352	+	3.90010i	0.122369	+	0.164370i	−0.736717	+	0.676201i	$0.763625\pi$
$564$	7.77481	+	5.80533i	0.327379	+	0.244449i
$565$	13.1882	+	6.62337i	0.554833	+	0.278647i
$566$	−6.30997	−	31.8405i	−0.265228	−	1.33835i
$567$	11.5554	−	5.80323i	0.485281	−	0.243713i
$568$	−18.5244	+	12.3206i	−0.777265	+	0.516960i
$569$	17.9499	−	35.7411i	0.752498	−	1.49835i	−0.110905	−	0.993831i	$-0.535375\pi$
$569$	17.9499	−	35.7411i	0.752498	−	1.49835i	0.863403	−	0.504515i	$-0.168329\pi$
$570$	1.41958	−	4.38008i	0.0594596	−	0.183461i
$571$	27.5700	−	20.5251i	1.15377	−	0.858950i	0.161976	−	0.986795i	$-0.448213\pi$
$571$	27.5700	−	20.5251i	1.15377	−	0.858950i	0.991794	+	0.127845i	$0.0408059\pi$
$572$	5.89198	+	7.25388i	0.246356	+	0.303300i
$573$	1.99251	+	27.3514i	0.0832383	+	1.14262i
$574$	−7.04691	−	10.2370i	−0.294132	−	0.427284i
$575$	−5.16968	−	29.3187i	−0.215590	−	1.22267i
$576$	−0.451362	+	23.9958i	−0.0188068	+	0.999823i
$577$	4.23015	−	23.9904i	0.176104	−	0.998733i	−0.760759	−	0.649035i	$-0.775173\pi$
$577$	4.23015	−	23.9904i	0.176104	−	0.998733i	0.936862	−	0.349698i	$-0.113716\pi$
$578$	−20.3361	+	9.28598i	−0.845870	+	0.386246i
$579$	−35.5654	+	4.68220i	−1.47805	+	0.194586i
$580$	2.10295	+	0.405524i	0.0873203	+	0.0168385i
$581$	0.707139	+	0.0411862i	0.0293371	+	0.00170869i
$582$	−10.6497	+	17.5220i	−0.441445	+	0.726312i
$583$	3.34717	+	1.00208i	0.138626	+	0.0415018i
$584$	−18.5569	+	25.1958i	−0.767892	+	1.04261i
$585$	5.27657	+	1.41387i	0.218159	+	0.0584565i
$586$	−7.21308	+	46.6439i	−0.297970	+	1.92684i
$587$	−16.1871	+	21.7430i	−0.668112	+	0.897430i	−0.998929	−	0.0462647i	$-0.985268\pi$
$587$	−16.1871	+	21.7430i	−0.668112	+	0.897430i	0.330817	+	0.943695i	$0.392676\pi$
$588$	16.3866	−	4.88045i	0.675771	−	0.201266i
$589$	−19.4233	−	4.60340i	−0.800322	−	0.189680i
$590$	−6.55047	−	1.40717i	−0.269678	−	0.0579323i
$591$	0.496734	+	0.574797i	0.0204329	+	0.0236440i
$592$	4.36804	−	20.8552i	0.179525	−	0.857143i
$593$	−27.2668	+	15.7425i	−1.11971	+	0.646467i	−0.941328	−	0.337494i	$-0.890421\pi$
$593$	−27.2668	+	15.7425i	−1.11971	+	0.646467i	−0.178386	+	0.983961i	$0.557088\pi$
$594$	−18.8687	+	0.123718i	−0.774190	+	0.00507622i
$595$	−1.35934	−	0.784814i	−0.0557274	−	0.0321742i
$596$	−30.7732	+	14.8445i	−1.26052	+	0.608056i
$597$	16.3385	−	20.0568i	0.668692	−	0.820869i
$598$	−18.2351	+	5.88133i	−0.745687	+	0.240505i
$599$	5.94320	−	6.29943i	0.242833	−	0.257388i	−0.594482	−	0.804109i	$-0.702643\pi$
$599$	5.94320	−	6.29943i	0.242833	−	0.257388i	0.837315	+	0.546721i	$0.184124\pi$
$600$	−19.1468	−	4.14160i	−0.781666	−	0.169080i
$601$	28.9379	+	3.38235i	1.18040	+	0.137969i	0.683574	−	0.729881i	$-0.260425\pi$
$601$	28.9379	+	3.38235i	1.18040	+	0.137969i	0.496826	+	0.867850i	$0.334499\pi$
$602$	−3.18157	+	3.95840i	−0.129671	+	0.161332i
$603$	−0.968599	−	0.0281869i	−0.0394444	−	0.00114786i
$604$	1.01678	−	3.20892i	0.0413722	−	0.130569i
$605$	3.20733	−	3.02596i	0.130397	−	0.123023i
$606$	19.5000	+	24.3320i	0.792134	+	0.988419i
$607$	8.92650	+	17.7741i	0.362316	+	0.721430i	0.998754	−	0.0498975i	$-0.0158895\pi$
$607$	8.92650	+	17.7741i	0.362316	+	0.721430i	−0.636439	+	0.771327i	$0.719593\pi$
$608$	10.5407	+	1.34782i	0.427483	+	0.0546611i
$609$	2.36222	−	1.22969i	0.0957221	−	0.0498296i
$610$	−5.88783	+	8.26744i	−0.238391	+	0.334739i
$611$	3.90465	+	3.27639i	0.157965	+	0.132548i
$612$	−1.05278	+	6.46555i	−0.0425560	+	0.261354i
$613$	−15.9496	+	13.3833i	−0.644199	+	0.540547i	−0.905305	−	0.424763i	$-0.860357\pi$
$613$	−15.9496	+	13.3833i	−0.644199	+	0.540547i	0.261105	+	0.965310i	$0.415913\pi$
$614$	−2.02121	−	25.4398i	−0.0815694	−	1.02667i
$615$	7.38614	+	7.60421i	0.297838	+	0.306631i
$616$	10.2854	+	1.75910i	0.414409	+	0.0708762i
$617$	−1.53283	−	13.1142i	−0.0617094	−	0.527958i	−0.988371	−	0.152061i	$-0.951409\pi$
$617$	−1.53283	−	13.1142i	−0.0617094	−	0.527958i	0.926662	−	0.375897i	$-0.122665\pi$
$618$	−7.31201	+	13.7766i	−0.294132	+	0.554174i
$619$	24.6667	−	1.43667i	0.991439	−	0.0577447i	0.445250	−	0.895406i	$-0.353115\pi$
$619$	24.6667	−	1.43667i	0.991439	−	0.0577447i	0.546189	+	0.837662i	$0.316078\pi$
$620$	2.80567	−	21.0799i	0.112679	−	0.846588i
$621$	13.7589	−	36.1566i	0.552127	−	1.45092i
$622$	8.67590	+	9.90715i	0.347872	+	0.397241i
$623$	15.9805	−	10.5105i	0.640244	−	0.421095i
$624$	−0.951765	+	12.5715i	−0.0381011	+	0.503265i
$625$	4.35027	−	10.0851i	0.174011	−	0.403403i
$626$	9.77081	+	0.362380i	0.390520	+	0.0144836i
$627$	−0.849146	+	8.31144i	−0.0339116	+	0.331927i
$628$	−5.65922	+	22.2865i	−0.225828	+	0.889327i
$629$	1.98914	−	5.46511i	0.0793121	−	0.217908i
$630$	5.47243	−	2.69385i	0.218027	−	0.107325i
$631$	6.58658	+	18.0965i	0.262208	+	0.720410i	0.999018	+	0.0443102i	$0.0141090\pi$
$631$	6.58658	+	18.0965i	0.262208	+	0.720410i	−0.736810	+	0.676100i	$0.763669\pi$
$632$	−29.5304	+	9.00655i	−1.17466	+	0.358261i
$633$	23.2446	+	21.2998i	0.923890	+	0.846592i
$634$	12.8517	−	1.77783i	0.510405	−	0.0706066i
$635$	18.0079	+	11.8440i	0.714621	+	0.470014i
$636$	2.35100	+	4.08546i	0.0932233	+	0.161999i
$637$	8.73966	−	2.07134i	0.346278	−	0.0820694i
$638$	−3.88527	+	0.0820171i	−0.153819	+	0.00324709i
$639$	3.42004	−	23.3478i	0.135295	−	0.923625i
$640$	−0.303211	+	11.3169i	−0.0119855	+	0.447340i
$641$	−31.4839	+	13.5808i	−1.24354	+	0.536410i	−0.913223	−	0.407460i	$-0.866414\pi$
$641$	−31.4839	+	13.5808i	−1.24354	+	0.536410i	−0.330316	+	0.943871i	$0.607155\pi$
$642$	12.1255	+	44.0939i	0.478556	+	1.74025i
$643$	24.9533	−	7.47053i	0.984063	−	0.294609i	0.245947	−	0.969283i	$-0.420901\pi$
$643$	24.9533	−	7.47053i	0.984063	−	0.294609i	0.738116	+	0.674674i	$0.235716\pi$
$644$	−10.9912	+	18.3543i	−0.433114	+	0.723261i
$645$	2.11117	−	3.78264i	0.0831271	−	0.148941i
$646$	2.79556	+	0.773037i	0.109990	+	0.0304147i
$647$	20.9588			0.823974			0.411987	−	0.911190i	$-0.364835\pi$
$647$	20.9588			0.823974			0.411987	+	0.911190i	$0.364835\pi$
$648$	−18.6054	−	17.3736i	−0.730888	−	0.682498i
$649$	12.1571			0.477206
$650$	−9.91847	−	2.74269i	−0.389035	−	0.107577i
$651$	−13.5533	−	22.7058i	−0.531194	−	0.889912i
$652$	9.49601	−	15.8574i	0.371892	−	0.621026i
$653$	−13.7311	+	4.11083i	−0.537341	+	0.160869i	−0.543964	−	0.839109i	$-0.683077\pi$
$653$	−13.7311	+	4.11083i	−0.537341	+	0.160869i	0.00662281	+	0.999978i	$0.497892\pi$
$654$	−8.69582	+	8.81067i	−0.340033	+	0.344524i
$655$	5.23045	−	2.25620i	0.204371	−	0.0881569i
$656$	−14.0900	+	20.0015i	−0.550123	+	0.780927i
$657$	−6.71151	−	32.5045i	−0.261841	−	1.26812i
$658$	5.69009	−	0.120116i	0.221823	−	0.00468263i
$659$	−14.2646	+	3.38078i	−0.555672	+	0.131697i	−0.498851	−	0.866688i	$-0.666244\pi$
$659$	−14.2646	+	3.38078i	−0.555672	+	0.131697i	−0.0568207	+	0.998384i	$0.518096\pi$
$660$	−8.90065	−	0.0126547i	−0.346457	−	0.000492583i
$661$	−23.3984	−	15.3894i	−0.910093	−	0.598578i	0.00580729	−	0.999983i	$-0.498151\pi$
$661$	−23.3984	−	15.3894i	−0.910093	−	0.598578i	−0.915900	+	0.401405i	$0.868522\pi$
$662$	−29.4186	+	4.06960i	−1.14339	+	0.158170i
$663$	−0.744812	+	3.35960i	−0.0289261	+	0.130476i
$664$	−0.406797	−	1.33380i	−0.0157868	−	0.0517613i
$665$	−0.923696	−	2.53783i	−0.0358194	−	0.0984130i
$666$	13.3507	+	18.2354i	0.517330	+	0.706606i
$667$	2.72504	−	7.48699i	0.105514	−	0.289898i
$668$	2.18102	−	8.58905i	0.0843864	−	0.332320i
$669$	−12.3597	−	8.92504i	−0.477852	−	0.345062i
$670$	−0.456774	−	0.0169408i	−0.0176467	−	0.000654482i
$671$	7.29453	−	16.9106i	0.281602	−	0.652827i
$672$	8.44830	+	11.2603i	0.325900	+	0.434376i
$673$	5.93296	−	3.90217i	0.228699	−	0.150417i	−0.429989	−	0.902834i	$-0.641482\pi$
$673$	5.93296	−	3.90217i	0.228699	−	0.150417i	0.658687	+	0.752417i	$0.271112\pi$
$674$	13.2397	+	15.1186i	0.509972	+	0.582346i
$675$	16.8452	−	12.1639i	0.648373	−	0.468190i
$676$	2.55650	−	19.2077i	0.0983267	−	0.738758i
$677$	45.3167	−	2.63940i	1.74166	−	0.101440i	0.842400	−	0.538852i	$-0.181142\pi$
$677$	45.3167	−	2.63940i	1.74166	−	0.101440i	0.899261	+	0.437412i	$0.144105\pi$
$678$	−19.1668	−	30.6227i	−0.736097	−	1.17606i
$679$	1.39625	+	11.9457i	0.0535832	+	0.458433i
$680$	−0.520919	+	3.04578i	−0.0199763	+	0.116801i
$681$	−1.17392	+	4.13932i	−0.0449847	+	0.158619i
$682$	3.05614	+	38.4658i	0.117026	+	1.47293i
$683$	−19.8981	+	16.6965i	−0.761381	+	0.638874i	−0.938486	−	0.345318i	$-0.887771\pi$
$683$	−19.8981	+	16.6965i	−0.761381	+	0.638874i	0.177105	+	0.984192i	$0.443327\pi$
$684$	−8.53840	+	7.35762i	−0.326474	+	0.281326i
$685$	−13.6025	−	11.4139i	−0.519725	−	0.436101i
$686$	14.0685	−	19.7544i	0.537136	−	0.754225i
$687$	−1.42690	+	32.6799i	−0.0544395	+	1.24682i
$688$	9.48127	+	3.17166i	0.361470	+	0.120918i
$689$	1.11128	+	2.21275i	0.0423365	+	0.0842990i
$690$	6.62604	−	17.0030i	0.252249	−	0.647293i
$691$	18.5679	−	17.5179i	0.706355	−	0.666412i	−0.246740	−	0.969082i	$-0.579359\pi$
$691$	18.5679	−	17.5179i	0.706355	−	0.666412i	0.953095	+	0.302670i	$0.0978780\pi$
$692$	−2.83408	+	8.94425i	−0.107736	+	0.340009i
$693$	−8.68168	+	6.86453i	−0.329790	+	0.260762i
$694$	31.8205	−	39.5899i	1.20789	−	1.50281i
$695$	−13.1015	−	1.53135i	−0.496969	−	0.0580873i
$696$	−3.88348	−	3.52200i	−0.147203	−	0.133501i
$697$	−4.58266	+	4.85734i	−0.173581	+	0.183985i
$698$	−15.9057	+	5.13004i	−0.602040	+	0.194175i
$699$	23.4243	+	3.77996i	0.885987	+	0.142971i
$700$	−10.3491	+	4.99228i	−0.391161	+	0.188690i
$701$	−18.4008	−	10.6237i	−0.694988	−	0.401251i	0.110490	−	0.993877i	$-0.464758\pi$
$701$	−18.4008	−	10.6237i	−0.694988	−	0.401251i	−0.805478	+	0.592626i	$0.798091\pi$
$702$	−9.24020	−	9.66628i	−0.348749	−	0.364830i
$703$	8.66612	−	5.00338i	0.326849	−	0.188706i
$704$	−3.77495	−	20.1922i	−0.142274	−	0.761022i
$705$	−4.76813	+	0.912436i	−0.179578	+	0.0343643i
$706$	7.43856	+	1.59795i	0.279954	+	0.0601396i
$707$	17.7967	+	4.21788i	0.669312	+	0.158630i
$708$	11.9135	+	11.2719i	0.447738	+	0.423623i
$709$	25.2931	−	33.9745i	0.949901	−	1.27594i	−0.0112555	−	0.999937i	$-0.503583\pi$
$709$	25.2931	−	33.9745i	0.949901	−	1.27594i	0.961157	−	0.276002i	$-0.0890098\pi$
$710$	1.70107	−	11.0001i	0.0638401	−	0.412826i
$711$	13.8392	−	29.6780i	0.519011	−	1.11301i
$712$	−30.3185	−	22.3299i	−1.13623	−	0.836847i
$713$	−75.7889	−	22.6897i	−2.83832	−	0.849737i
$714$	1.84572	+	3.36998i	0.0690742	+	0.126118i
$715$	−4.66773	−	0.271864i	−0.174563	−	0.0101671i
$716$	43.2411	+	8.33842i	1.61599	+	0.311621i
$717$	9.36654	+	12.2068i	0.349800	+	0.455870i
$718$	17.1530	−	7.83252i	0.640146	−	0.292307i
$719$	8.84369	−	50.1551i	0.329814	−	1.87047i	−0.143610	−	0.989634i	$-0.545871\pi$
$719$	8.84369	−	50.1551i	0.329814	−	1.87047i	0.473424	−	0.880835i	$-0.343018\pi$
$720$	−8.71061	−	8.26498i	−0.324625	−	0.308018i
$721$	1.58859	+	9.00932i	0.0591621	+	0.335525i
$722$	−12.4061	−	18.0222i	−0.461707	−	0.670718i
$723$	−20.0814	−	9.72218i	−0.746834	−	0.361572i
$724$	−29.5119	−	36.3334i	−1.09680	−	1.35032i
$725$	3.43250	−	2.55540i	0.127480	−	0.0949053i
$726$	−10.5565	+	2.25204i	−0.391788	+	0.0835812i
$727$	−11.6140	+	23.1254i	−0.430740	+	0.857674i	0.568644	+	0.822584i	$0.307468\pi$
$727$	−11.6140	+	23.1254i	−0.430740	+	0.857674i	−0.999384	+	0.0350901i	$0.988828\pi$
$728$	4.09532	+	6.15742i	0.151782	+	0.228209i
$729$	26.8973	−	2.35291i	0.996196	−	0.0871447i
$730$	−3.04343	−	15.3573i	−0.112643	−	0.568401i
$731$	2.43857	+	1.22470i	0.0901938	+	0.0452970i
$732$	22.8277	−	9.80845i	0.843737	−	0.362531i
$733$	0.251836	+	0.338275i	0.00930178	+	0.0124945i	0.806750	−	0.590893i	$-0.201225\pi$
$733$	0.251836	+	0.338275i	0.00930178	+	0.0124945i	−0.797448	+	0.603388i	$0.793817\pi$
$734$	24.8081	−	13.1219i	0.915683	−	0.484338i
$735$	−3.72765	+	7.69955i	−0.137497	+	0.284002i
$736$	41.3946	+	7.76179i	1.52583	+	0.286103i
$737$	0.816792	−	0.144022i	0.0300869	−	0.00530514i
$738$	−5.78268	−	25.2977i	−0.212864	−	0.931220i
$739$	−37.1598	−	6.55227i	−1.36695	−	0.241029i	−0.558453	−	0.829536i	$-0.688605\pi$
$739$	−37.1598	−	6.55227i	−1.36695	−	0.241029i	−0.808492	+	0.588507i	$0.799716\pi$
$740$	6.22880	+	8.65172i	0.228975	+	0.318043i
$741$	−4.69736	+	3.60440i	−0.172562	+	0.132411i
$742$	2.56121	+	1.04125i	0.0940251	+	0.0382255i
$743$	0.121233	−	2.08149i	0.00444762	−	0.0763626i	−0.995354	−	0.0962836i	$-0.969304\pi$
$743$	0.121233	−	2.08149i	0.00444762	−	0.0763626i	0.999802	+	0.0199210i	$0.00634146\pi$
$744$	−32.6701	+	40.5288i	−1.19774	+	1.48586i
$745$	4.90267	−	16.3761i	0.179620	−	0.599973i
$746$	9.35784	−	5.66939i	0.342615	−	0.207571i
$747$	1.34046	+	0.625074i	0.0490450	+	0.0228703i
$748$	−0.236614	−	5.60187i	−0.00865146	−	0.204825i
$749$	21.5157	+	16.0179i	0.786167	+	0.585280i
$750$	17.9842	−	12.7693i	0.656689	−	0.466268i
$751$	−4.70314	+	19.8441i	−0.171620	+	0.724122i	0.817367	+	0.576118i	$0.195433\pi$
$751$	−4.70314	+	19.8441i	−0.171620	+	0.724122i	−0.988987	+	0.148004i	$0.952715\pi$
$752$	−4.10705	−	10.4242i	−0.149769	−	0.380133i
$753$	−5.91078	−	30.8881i	−0.215401	−	1.12562i
$754$	−1.93181	−	1.96290i	−0.0703523	−	0.0714845i
$755$	0.842079	+	1.45852i	0.0306464	+	0.0530811i
$756$	−14.8725	−	1.32254i	−0.540907	−	0.0481002i
$757$	−10.9340	+	18.9382i	−0.397401	+	0.688319i	−0.993404	−	0.114663i	$-0.963421\pi$
$757$	−10.9340	+	18.9382i	−0.397401	+	0.688319i	0.596003	+	0.802982i	$0.296755\pi$
$758$	−12.0356	+	3.12219i	−0.437154	+	0.113403i
$759$	−5.27504	+	32.6892i	−0.191472	+	1.18654i
$760$	−4.05518	+	3.43839i	−0.147097	+	0.124724i
$761$	15.2568	+	14.3941i	0.553060	+	0.521786i	0.911245	−	0.411865i	$-0.135123\pi$
$761$	15.2568	+	14.3941i	0.553060	+	0.521786i	−0.358184	+	0.933651i	$0.616604\pi$
$762$	−22.6113	−	47.6712i	−0.819123	−	1.72694i
$763$	−0.842957	+	7.21196i	−0.0305171	+	0.261090i
$764$	14.6617	−	28.0676i	0.530443	−	1.01545i
$765$	−2.03278	−	2.57089i	−0.0734954	−	0.0929508i
$766$	24.7511	+	13.6018i	0.894295	+	0.491454i
$767$	5.91237	+	6.26675i	0.213483	+	0.226279i
$768$	15.0226	−	23.2878i	0.542083	−	0.840325i
$769$	−15.7427	+	7.90629i	−0.567697	+	0.285108i	−0.709406	−	0.704800i	$-0.751037\pi$
$769$	−15.7427	+	7.90629i	−0.567697	+	0.285108i	0.141709	+	0.989908i	$0.454740\pi$
$770$	−4.12091	+	3.20527i	−0.148507	+	0.115510i
$771$	−10.5473	−	0.460524i	−0.379851	−	0.0165854i
$772$	37.7673	+	17.0114i	1.35928	+	0.612253i
$773$	15.8164	−	18.8493i	0.568877	−	0.677962i	−0.402523	−	0.915410i	$-0.631867\pi$
$773$	15.8164	−	18.8493i	0.568877	−	0.677962i	0.971400	+	0.237448i	$0.0763110\pi$
$774$	−9.22552	+	5.22857i	−0.331604	+	0.187937i
$775$	−27.3125	−	32.5497i	−0.981093	−	1.16922i
$776$	21.1033	−	10.7347i	0.757565	−	0.385354i
$777$	12.7532	+	3.61685i	0.457520	+	0.129754i
$778$	45.4413	+	28.5318i	1.62915	+	1.02291i
$779$	−11.4123	+	1.33391i	−0.408889	+	0.0477923i
$780$	−4.32215	−	4.59428i	−0.154758	−	0.164502i
$781$	1.17436	+	20.1629i	0.0420217	+	0.721485i
$782$	10.8827	+	3.70280i	0.389165	+	0.132412i
$783$	5.53193	−	0.565134i	0.197695	−	0.0201962i
$784$	−19.0557	−	5.16399i	−0.680559	−	0.184428i
$785$	−6.32169	−	9.61166i	−0.225631	−	0.343055i
$786$	−13.8099	−	1.93039i	−0.492582	−	0.0688548i
$787$	−15.5833	−	6.72199i	−0.555485	−	0.239613i	0.0997829	−	0.995009i	$-0.468185\pi$
$787$	−15.5833	−	6.72199i	−0.555485	−	0.239613i	−0.655268	+	0.755396i	$0.727444\pi$
$788$	−0.138517	−	0.866215i	−0.00493448	−	0.0308576i
$789$	−12.5300	+	17.3520i	−0.446081	+	0.617747i
$790$	6.63954	−	13.9468i	0.236224	−	0.496205i
$791$	−19.9121	−	7.24740i	−0.707992	−	0.257688i
$792$	18.6028	+	11.3428i	0.661020	+	0.403049i
$793$	12.2647	−	4.46398i	0.435532	−	0.158521i
$794$	4.36276	−	45.6653i	0.154829	−	1.62060i
$795$	−2.30242	−	0.510438i	−0.0816583	−	0.0181034i
$796$	−28.2294	+	9.76719i	−1.00056	+	0.346189i
$797$	1.34214	−	2.04063i	0.0475412	−	0.0722829i	−0.810935	−	0.585136i	$-0.801041\pi$
$797$	1.34214	−	2.04063i	0.0475412	−	0.0722829i	0.858476	+	0.512853i	$0.171411\pi$
$798$	−1.29438	+	6.48316i	−0.0458205	+	0.229501i
$799$	−0.705252	−	2.97569i	−0.0249500	−	0.105272i
$800$	16.2844	+	15.7000i	0.575739	+	0.555080i
$801$	39.1132	−	8.07607i	1.38200	−	0.285354i
$802$	−30.7325	+	11.9261i	−1.08520	+	0.421126i
$803$	11.2518	+	26.0847i	0.397069	+	0.920509i
$804$	0.933965	+	0.616183i	0.0329384	+	0.0217311i
$805$	−3.06985	−	10.2540i	−0.108198	−	0.361406i
$806$	−18.3421	+	20.2825i	−0.646073	+	0.714421i
$807$	30.8574	−	18.4190i	1.08623	−	0.648379i
$808$	−4.36382	−	35.7401i	−0.153519	−	1.25733i
$809$			45.9010i			1.61379i	0.590694	+	0.806896i	$0.298854\pi$
$809$			45.9010i			1.61379i	−0.590694	+	0.806896i	$0.701146\pi$
$810$	12.6961	−	1.00862i	0.446095	−	0.0354393i
$811$		−	2.60086i		−	0.0913286i	−0.998957	−	0.0456643i	$-0.985460\pi$
$811$		−	2.60086i		−	0.0913286i	0.998957	−	0.0456643i	$-0.0145404\pi$
$812$	−3.06666	−	0.227786i	−0.107619	−	0.00799372i
$813$	28.9041	+	16.1320i	1.01371	+	0.565773i
$814$	−14.3473	−	12.9747i	−0.502873	−	0.454763i
$815$	2.65224	+	8.85909i	0.0929038	+	0.310320i
$816$	4.96211	−	5.70903i	0.173709	−	0.199856i
$817$	1.85969	+	4.31124i	0.0650622	+	0.150831i
$818$	−15.4524	−	39.8194i	−0.540279	−	1.39225i
$819$	−7.76072	−	1.13681i	−0.271182	−	0.0397233i
$820$	−2.63244	−	11.9545i	−0.0919287	−	0.417468i
$821$	5.37575	+	22.6821i	0.187615	+	0.791609i	0.982714	+	0.185130i	$0.0592706\pi$
$821$	5.37575	+	22.6821i	0.187615	+	0.791609i	−0.795099	+	0.606479i	$0.792581\pi$
$822$	13.9428	+	41.1704i	0.486311	+	1.43598i
$823$	9.67119	−	14.7043i	0.337117	−	0.512561i	−0.626653	−	0.779299i	$-0.715575\pi$
$823$	9.67119	−	14.7043i	0.337117	−	0.512561i	0.963769	+	0.266738i	$0.0859458\pi$
$824$	15.5503	−	9.08488i	0.541719	−	0.316487i
$825$	−12.0149	+	13.1119i	−0.418304	+	0.456497i
$826$	9.57633	+	0.914901i	0.333203	+	0.0318335i
$827$	−1.34429	+	0.489280i	−0.0467454	+	0.0170139i	−0.365287	−	0.930895i	$-0.619029\pi$
$827$	−1.34429	+	0.489280i	−0.0467454	+	0.0170139i	0.318542	+	0.947909i	$0.396807\pi$
$828$	−35.4784	+	27.1434i	−1.23296	+	0.943298i
$829$	6.31861	+	2.29979i	0.219454	+	0.0798749i	0.449408	−	0.893327i	$-0.351635\pi$
$829$	6.31861	+	2.29979i	0.219454	+	0.0798749i	−0.229953	+	0.973202i	$0.573857\pi$
$830$	0.629933	+	0.299887i	0.0218653	+	0.0104092i
$831$	−12.2366	−	1.25016i	−0.424482	−	0.0433676i
$832$	8.57283	−	11.7660i	0.297209	−	0.407914i
$833$	−4.94805	−	2.13438i	−0.171440	−	0.0739519i
$834$	25.4595	+	19.8607i	0.881590	+	0.687719i
$835$	2.43634	+	3.70427i	0.0843129	+	0.128191i
$836$	5.88369	−	7.64528i	0.203492	−	0.264417i
$837$	−8.79578	−	54.5096i	−0.304026	−	1.88413i
$838$	12.0949	−	35.5474i	0.417810	−	1.22796i
$839$	0.987205	+	16.9497i	0.0340821	+	0.585167i	0.971512	+	0.236992i	$0.0761615\pi$
$839$	0.987205	+	16.9497i	0.0340821	+	0.585167i	−0.937430	+	0.348175i	$0.886801\pi$
$840$	−7.01025	−	0.679802i	−0.241876	−	0.0234554i
$841$	−27.6664	+	3.23374i	−0.954014	+	0.111508i
$842$	−12.2577	+	19.5222i	−0.422427	+	0.672781i
$843$	−18.1086	+	17.5893i	−0.623694	+	0.605808i
$844$	−9.88301	−	35.0379i	−0.340187	−	1.20605i
$845$	6.23167	+	7.42662i	0.214376	+	0.255483i
$846$	11.1343	+	4.15354i	0.382805	+	0.142802i
$847$	−4.06965	+	4.85002i	−0.139835	+	0.166649i
$848$	0.173752	−	5.44004i	0.00596668	−	0.186812i
$849$	−18.3567	−	35.2630i	−0.629999	−	1.21022i
$850$	3.79060	+	4.87346i	0.130017	+	0.167158i
$851$	35.4412	−	17.7992i	1.21491	−	0.610150i
$852$	−17.5440	+	20.8478i	−0.601047	+	0.714235i
$853$	−0.567586	−	0.601606i	−0.0194338	−	0.0205986i	0.717584	−	0.696472i	$-0.245248\pi$
$853$	−0.567586	−	0.601606i	−0.0194338	−	0.0205986i	−0.737018	+	0.675874i	$0.763767\pi$
$854$	7.01867	−	12.7718i	0.240174	−	0.437043i
$855$	0.164035	−	5.63680i	0.00560988	−	0.192775i
$856$	14.8844	−	50.6642i	0.508739	−	1.73167i
$857$	−4.59923	+	39.3489i	−0.157107	+	1.34413i	0.652781	+	0.757547i	$0.273602\pi$
$857$	−4.59923	+	39.3489i	−0.157107	+	1.34413i	−0.809887	+	0.586586i	$0.800472\pi$
$858$	9.41854	+	6.50327i	0.321544	+	0.222018i
$859$	−40.9649	−	38.6484i	−1.39770	−	1.31867i	−0.889134	−	0.457646i	$-0.848693\pi$
$859$	−40.9649	−	38.6484i	−1.39770	−	1.31867i	−0.508571	−	0.861020i	$-0.669826\pi$
$860$	−4.37128	+	2.43155i	−0.149059	+	0.0829153i
$861$	−11.8011	−	9.61335i	−0.402180	−	0.327622i
$862$	−1.14606	−	4.41792i	−0.0390350	−	0.150475i
$863$	8.24290	−	14.2771i	0.280592	−	0.485999i	−0.690939	−	0.722913i	$-0.742803\pi$
$863$	8.24290	−	14.2771i	0.280592	−	0.485999i	0.971531	+	0.236914i	$0.0761360\pi$
$864$	7.71317	+	28.3638i	0.262407	+	0.964957i
$865$	−2.34713	−	4.06535i	−0.0798049	−	0.138226i
$866$	−13.4395	+	13.2266i	−0.456693	+	0.449460i
$867$	−20.7164	+	17.9029i	−0.703564	+	0.608013i
$868$	−0.487435	+	30.5302i	−0.0165446	+	1.03626i
$869$	−6.46370	+	27.2725i	−0.219266	+	0.925156i
$870$	2.61149	−	0.245750i	0.0885379	−	0.00833169i
$871$	0.471473	+	0.350999i	0.0159753	+	0.0118931i
$872$	13.8919	−	3.36797i	0.470438	−	0.114054i
$873$	−6.49979	+	24.2572i	−0.219984	+	0.820981i
$874$	10.2488	+	16.9166i	0.346671	+	0.572212i
$875$	3.71043	−	12.3937i	0.125436	−	0.418984i
$876$	−13.1590	+	35.9947i	−0.444601	+	1.21615i
$877$	0.866926	−	14.8845i	0.0292740	−	0.502615i	−0.951522	−	0.307580i	$-0.900481\pi$
$877$	0.866926	−	14.8845i	0.0292740	−	0.502615i	0.980796	−	0.195035i	$-0.0624821\pi$
$878$	11.3734	−	27.9757i	0.383834	−	0.944134i
$879$	7.54507	+	57.3113i	0.254489	+	1.93306i
$880$	8.73208	+	5.42032i	0.294358	+	0.182719i
$881$	16.0425	+	2.82873i	0.540486	+	0.0953023i	0.437225	−	0.899352i	$-0.355961\pi$
$881$	16.0425	+	2.82873i	0.540486	+	0.0953023i	0.103261	+	0.994654i	$0.467072\pi$
$882$	17.5869	−	11.3670i	0.592183	−	0.382745i
$883$	19.1174	−	3.37092i	0.643353	−	0.113440i	0.157553	−	0.987511i	$-0.449640\pi$
$883$	19.1174	−	3.37092i	0.643353	−	0.113440i	0.485800	+	0.874070i	$0.338528\pi$
$884$	2.77259	−	2.84634i	0.0932522	−	0.0957327i
$885$	−8.18399	+	0.596193i	−0.275102	+	0.0200408i
$886$	−10.6870	−	20.2047i	−0.359037	−	0.678790i
$887$	13.4396	+	18.0526i	0.451259	+	0.606146i	0.968293	−	0.249819i	$-0.0803711\pi$
$887$	13.4396	+	18.0526i	0.451259	+	0.606146i	−0.517033	+	0.855965i	$0.672964\pi$
$888$	−2.02989	−	26.0174i	−0.0681185	−	0.873088i
$889$	−27.6557	−	13.8892i	−0.927543	−	0.465830i
$890$	18.4797	−	3.66221i	0.619442	−	0.122758i
$891$	−22.1390	+	6.62780i	−0.741684	+	0.222040i
$892$	6.71354	+	16.2732i	0.224786	+	0.544868i
$893$	2.36150	−	4.70213i	0.0790246	−	0.157351i
$894$	−31.0763	+	28.0230i	−1.03935	+	0.937230i
$895$	−17.6732	+	13.1572i	−0.590748	+	0.439796i
$896$	−1.45400	−	16.1898i	−0.0485746	−	0.540864i
$897$	−19.4161	+	13.1786i	−0.648285	+	0.440021i
$898$	9.87344	−	6.79666i	0.329481	−	0.226807i
$899$	−1.97466	−	11.1988i	−0.0658585	−	0.373502i
$900$	−23.9313	+	1.70917i	−0.797712	+	0.0569722i
$901$	0.257971	−	1.46303i	0.00859426	−	0.0487404i
$902$	9.22588	+	20.2045i	0.307188	+	0.672736i
$903$	−2.38026	+	5.74642i	−0.0792100	+	0.191229i
$904$	0.214511	+	41.7146i	0.00713454	+	1.38741i
$905$	23.3798	+	1.36172i	0.777171	+	0.0452650i
$906$	0.0928698	−	4.12164i	0.00308539	−	0.136932i
$907$	−28.5292	−	8.54108i	−0.947296	−	0.283602i	−0.224352	−	0.974508i	$-0.572026\pi$
$907$	−28.5292	−	8.54108i	−0.947296	−	0.283602i	−0.722944	+	0.690906i	$0.757212\pi$
$908$	3.66768	−	3.35124i	0.121716	−	0.111215i
$909$	31.2830	+	21.9048i	1.03759	+	0.726535i
$910$	−3.65639	−	0.565430i	−0.121208	−	0.0187438i
$911$	−4.27433	+	5.74143i	−0.141615	+	0.190222i	−0.867272	−	0.497835i	$-0.834129\pi$
$911$	−4.27433	+	5.74143i	−0.141615	+	0.190222i	0.725657	+	0.688057i	$0.241536\pi$
$912$	12.8544	−	2.03683i	0.425653	−	0.0674461i
$913$	−1.23181	−	0.291945i	−0.0407670	−	0.00966197i
$914$	9.74600	−	45.3682i	0.322369	−	1.50065i
$915$	−4.08128	+	11.7418i	−0.134923	+	0.388170i
$916$	21.2569	−	31.2222i	0.702347	−	1.03161i
$917$	−7.08318	+	4.08948i	−0.233907	+	0.135046i
$918$	0.983634	+	7.96241i	0.0324648	+	0.262799i
$919$	16.0333	+	9.25686i	0.528891	+	0.305355i	0.740565	−	0.671985i	$-0.234558\pi$
$919$	16.0333	+	9.25686i	0.528891	+	0.305355i	−0.211674	+	0.977340i	$0.567891\pi$
$920$	−16.8370	+	12.6698i	−0.555100	+	0.417710i
$921$	−11.1160	−	29.2119i	−0.366283	−	0.962565i
$922$	−5.39378	−	16.7234i	−0.177635	−	0.550757i
$923$	−9.82248	+	10.4112i	−0.323311	+	0.342690i
$924$	12.6955	−	1.46560i	0.417652	−	0.0482147i
$925$	21.1568	+	2.47288i	0.695633	+	0.0813078i
$926$	−1.44298	−	1.15980i	−0.0474193	−	0.0381134i
$927$	−3.86284	+	18.7074i	−0.126872	+	0.614432i
$928$	1.67337	+	5.81787i	0.0549311	+	0.190981i
$929$	41.4455	−	39.1018i	1.35978	−	1.28289i	0.436011	−	0.899941i	$-0.356391\pi$
$929$	41.4455	−	39.1018i	1.35978	−	1.28289i	0.923771	−	0.382946i	$-0.125091\pi$
$930$	−3.94375	−	25.7448i	−0.129321	−	0.844206i
$931$	−4.16123	−	8.28569i	−0.136379	−	0.271553i
$932$	−20.7042	−	17.9438i	−0.678189	−	0.587770i
$933$	13.6028	+	8.66596i	0.445335	+	0.283711i
$934$	−0.343227	−	0.244436i	−0.0112307	−	0.00799818i
$935$	2.14893	+	1.80317i	0.0702775	+	0.0589698i
$936$	3.20011	+	15.1058i	0.104599	+	0.493747i
$937$	−31.7853	+	26.6711i	−1.03838	+	0.871305i	−0.991824	−	0.127610i	$-0.959269\pi$
$937$	−31.7853	+	26.6711i	−1.03838	+	0.871305i	−0.0465568	+	0.998916i	$0.514825\pi$
$938$	0.654240	−	0.0519799i	0.0213617	−	0.00169720i
$939$	11.6108	−	2.93077i	0.378904	−	0.0956422i
$940$	5.23632	+	2.00110i	0.170790	+	0.0652685i
$941$	2.09560	+	17.9290i	0.0683145	+	0.584468i	0.983432	+	0.181280i	$0.0580240\pi$
$941$	2.09560	+	17.9290i	0.0683145	+	0.584468i	−0.915117	+	0.403188i	$0.867902\pi$
$942$	1.00372	+	28.1436i	0.0327031	+	0.916968i
$943$	−45.4612	+	2.64781i	−1.48042	+	0.0862247i
$944$	−4.84956	−	18.3066i	−0.157840	−	0.595829i
$945$	5.50776	−	5.04688i	0.179167	−	0.164175i
$946$	6.82816	−	5.97956i	0.222003	−	0.194412i
$947$	−21.0414	+	13.8391i	−0.683753	+	0.449711i	−0.843274	−	0.537483i	$-0.819375\pi$
$947$	−21.0414	+	13.8391i	−0.683753	+	0.449711i	0.159522	+	0.987194i	$0.449005\pi$
$948$	−31.6210	+	20.7331i	−1.02700	+	0.673379i
$949$	−7.97406	+	18.4859i	−0.258849	+	0.600079i
$950$	−0.393720	+	10.6158i	−0.0127740	+	0.344423i
$951$	14.4973	−	6.50518i	0.470107	−	0.210945i
$952$	0.235193	−	4.43050i	0.00762266	−	0.143593i
$953$	−18.0948	+	49.7150i	−0.586148	+	1.61043i	0.191336	+	0.981525i	$0.438718\pi$
$953$	−18.0948	+	49.7150i	−0.586148	+	1.61043i	−0.777484	+	0.628903i	$0.783504\pi$
$954$	4.16734	+	3.99507i	0.134923	+	0.129345i
$955$	5.41873	+	14.8878i	0.175346	+	0.481759i
$956$	−1.78060	−	17.6771i	−0.0575888	−	0.571717i
$957$	−4.53924	+	1.43121i	−0.146733	+	0.0462643i
$958$	6.80047	+	49.1596i	0.219713	+	1.58828i
$959$	21.3014	+	14.0102i	0.687859	+	0.452412i
$960$	3.53149	+	13.4080i	0.113978	+	0.432742i
$961$	−79.7054	+	18.8905i	−2.57114	+	0.609371i
$962$	−0.289326	−	13.7058i	−0.00932825	−	0.441892i
$963$	29.4030	+	47.6699i	0.947498	+	1.53614i
$964$	13.8113	+	21.7476i	0.444834	+	0.700442i
$965$	−19.0292	+	8.20841i	−0.612573	+	0.264238i
$966$	−6.61532	+	25.3529i	−0.212845	+	0.815715i
$967$	51.7521	−	15.4936i	1.66424	−	0.498239i	0.690007	−	0.723803i	$-0.257608\pi$
$967$	51.7521	−	15.4936i	1.66424	−	0.498239i	0.974228	+	0.225564i	$0.0724223\pi$
$968$	11.7340	+	4.20261i	0.377144	+	0.135077i
$969$	3.55196	−	0.0516583i	0.114105	−	0.00165950i
$970$	−3.15719	+	11.4174i	−0.101371	+	0.366592i
$971$	−48.7414			−1.56419			−0.782093	−	0.623162i	$-0.785848\pi$
$971$	−48.7414			−1.56419			−0.782093	+	0.623162i	$0.785848\pi$
$972$	−27.8407	−	14.0320i	−0.892990	−	0.450076i
$973$	18.9396			0.607177
$974$	8.29115	−	29.9836i	0.265666	−	0.960736i
$975$	−12.6021	+	0.183281i	−0.403592	+	0.00586967i
$976$	−28.3745	−	4.23860i	−0.908247	−	0.135674i
$977$	6.74623	−	2.01969i	0.215831	−	0.0646155i	−0.177062	−	0.984200i	$-0.556659\pi$
$977$	6.74623	−	2.01969i	0.215831	−	0.0646155i	0.392893	+	0.919584i	$0.371474\pi$
$978$	5.71540	−	21.9040i	0.182758	−	0.700411i
$979$	−31.3882	+	13.5395i	−1.00317	+	0.432725i
$980$	8.33839	−	5.29551i	0.266360	−	0.169159i
$981$	−7.19565	+	13.3451i	−0.229739	+	0.426075i
$982$	0.548368	+	25.9770i	0.0174991	+	0.828958i
$983$	−14.8829	+	3.52730i	−0.474690	+	0.112503i	−0.460995	−	0.887403i	$-0.652507\pi$
$983$	−14.8829	+	3.52730i	−0.474690	+	0.112503i	−0.0136945	+	0.999906i	$0.504359\pi$
$984$	−9.69229	+	28.3539i	−0.308979	+	0.903888i
$985$	0.366688	+	0.241175i	0.0116837	+	0.00768446i
$986$	0.226420	+	1.63676i	0.00721068	+	0.0521250i
$987$	6.64785	−	2.09604i	0.211603	−	0.0667178i
$988$	6.80243	−	0.685206i	0.216414	−	0.0217993i
$989$	6.36450	+	17.4863i	0.202379	+	0.556032i
$990$	−10.4677	+	3.04296i	−0.332686	+	0.0967115i
$991$	−10.4780	+	28.7881i	−0.332845	+	0.914485i	0.654523	+	0.756042i	$0.272870\pi$
$991$	−10.4780	+	28.7881i	−0.332845	+	0.914485i	−0.987368	+	0.158443i	$0.949353\pi$
$992$	56.7042	−	19.9464i	1.80036	−	0.633299i
$993$	−33.1856	+	14.8909i	−1.05311	+	0.472549i
$994$	−0.592334	+	15.9710i	−0.0187877	+	0.506571i
$995$	5.91950	−	13.7230i	0.187661	−	0.435047i
$996$	−0.936448	−	1.42822i	−0.0296725	−	0.0452548i
$997$	−20.8344	+	13.7030i	−0.659834	+	0.433979i	−0.834769	−	0.550601i	$-0.814399\pi$
$997$	−20.8344	+	13.7030i	−0.659834	+	0.433979i	0.174935	+	0.984580i	$0.444028\pi$
$998$	5.32311	−	4.66156i	0.168500	−	0.147559i
$999$	21.9595	+	16.8503i	0.694769	+	0.533121i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.p.a.311.4	yes	936
3.2	odd	2		972.2.p.a.719.49		936
4.3	odd	2	inner	324.2.p.a.311.42	yes	936
12.11	even	2		972.2.p.a.719.11		936
81.25	even	27		972.2.p.a.899.11		936
81.56	odd	54	inner	324.2.p.a.299.42	yes	936
324.187	odd	54		972.2.p.a.899.49		936
324.299	even	54	inner	324.2.p.a.299.4	✓	936

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.2.p.a.299.4	✓	936	324.299	even	54	inner
324.2.p.a.299.42	yes	936	81.56	odd	54	inner
324.2.p.a.311.4	yes	936	1.1	even	1	trivial
324.2.p.a.311.42	yes	936	4.3	odd	2	inner
972.2.p.a.719.11		936	12.11	even	2
972.2.p.a.719.49		936	3.2	odd	2
972.2.p.a.899.11		936	81.25	even	27
972.2.p.a.899.49		936	324.187	odd	54

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	324.p (of order \(54\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36306 - 0.376917i) q^{2} +(-1.73187 + 0.0251876i) q^{3} +(1.71587 + 1.02752i) q^{4} +(-0.958604 + 0.286987i) q^{5} +(2.37013 + 0.618439i) q^{6} +(1.31925 - 0.569068i) q^{7} +(-1.95154 - 2.04732i) q^{8} +(2.99873 - 0.0872431i) q^{9} +O(q^{10})\)	\(q+(-1.36306 - 0.376917i) q^{2} +(-1.73187 + 0.0251876i) q^{3} +(1.71587 + 1.02752i) q^{4} +(-0.958604 + 0.286987i) q^{5} +(2.37013 + 0.618439i) q^{6} +(1.31925 - 0.569068i) q^{7} +(-1.95154 - 2.04732i) q^{8} +(2.99873 - 0.0872431i) q^{9} +(1.41480 - 0.0298662i) q^{10} +(-2.49854 + 0.592165i) q^{11} +(-2.99753 - 1.73631i) q^{12} +(-1.52037 - 0.999963i) q^{13} +(-2.01271 + 0.278427i) q^{14} +(1.65295 - 0.521169i) q^{15} +(1.88840 + 3.52618i) q^{16} +(0.373412 + 1.02594i) q^{17} +(-4.12033 - 1.01136i) q^{18} +(-0.642494 + 1.76524i) q^{19} +(-1.93972 - 0.492555i) q^{20} +(-2.27043 + 1.01878i) q^{21} +(3.62886 + 0.134587i) q^{22} +(-2.94887 + 6.83624i) q^{23} +(3.43137 + 3.49652i) q^{24} +(-3.34088 + 2.19733i) q^{25} +(1.69545 + 1.93606i) q^{26} +(-5.19121 + 0.226624i) q^{27} +(2.84839 + 0.379112i) q^{28} +(-1.06835 + 0.0622243i) q^{29} +(-2.44950 + 0.0873599i) q^{30} +(1.23361 + 10.5542i) q^{31} +(-1.24492 - 5.51817i) q^{32} +(4.31222 - 1.08848i) q^{33} +(-0.122288 - 1.53916i) q^{34} +(-1.10132 + 0.924118i) q^{35} +(5.23507 + 2.93157i) q^{36} +(-4.08066 - 3.42408i) q^{37} +(1.54111 - 2.16396i) q^{38} +(2.65827 + 1.69351i) q^{39} +(2.45830 + 1.40250i) q^{40} +(2.74509 + 5.46592i) q^{41} +(3.47873 - 0.532893i) q^{42} +(1.81801 - 1.71521i) q^{43} +(-4.89562 - 1.55123i) q^{44} +(-2.84956 + 0.944229i) q^{45} +(6.59618 - 8.20673i) q^{46} +(-2.78210 - 0.325180i) q^{47} +(-3.35927 - 6.05932i) q^{48} +(-3.38711 + 3.59013i) q^{49} +(5.38203 - 1.73586i) q^{50} +(-0.672541 - 1.76739i) q^{51} +(-1.58127 - 3.27802i) q^{52} +(-1.17840 - 0.680352i) q^{53} +(7.16135 + 1.64775i) q^{54} +(2.22517 - 1.28470i) q^{55} +(-3.73963 - 1.59036i) q^{56} +(1.06825 - 3.07334i) q^{57} +(1.47968 + 0.317864i) q^{58} +(-4.60689 - 1.09185i) q^{59} +(3.37175 + 0.804184i) q^{60} +(-4.28303 + 5.75311i) q^{61} +(2.29658 - 14.8510i) q^{62} +(3.90643 - 1.82158i) q^{63} +(-0.382998 + 7.99083i) q^{64} +(1.74441 + 0.522242i) q^{65} +(-6.28809 - 0.141685i) q^{66} +(-0.322457 - 0.0187810i) q^{67} +(-0.413452 + 2.14407i) q^{68} +(4.93486 - 11.9137i) q^{69} +(1.84948 - 0.844522i) q^{70} +(1.36586 - 7.74616i) q^{71} +(-6.03075 - 5.96909i) q^{72} +(-1.92114 - 10.8953i) q^{73} +(4.27159 + 6.20530i) q^{74} +(5.73062 - 3.88964i) q^{75} +(-2.91625 + 2.36873i) q^{76} +(-2.95921 + 2.20305i) q^{77} +(-2.98506 - 3.31030i) q^{78} +(4.89881 - 9.75434i) q^{79} +(-2.82219 - 2.83827i) q^{80} +(8.98478 - 0.523237i) q^{81} +(-1.68152 - 8.48505i) q^{82} +(0.440573 + 0.221264i) q^{83} +(-4.94258 - 0.584829i) q^{84} +(-0.652386 - 0.876306i) q^{85} +(-3.12456 + 1.65269i) q^{86} +(1.84867 - 0.134673i) q^{87} +(6.08834 + 3.95966i) q^{88} +(13.1105 - 2.31173i) q^{89} +(4.24001 - 0.212993i) q^{90} +(-2.57479 - 0.454006i) q^{91} +(-12.0843 + 8.70005i) q^{92} +(-2.40229 - 18.2474i) q^{93} +(3.66960 + 1.49186i) q^{94} +(0.109297 - 1.87655i) q^{95} +(2.29502 + 9.52538i) q^{96} +(-2.40082 + 8.01930i) q^{97} +(5.97002 - 3.61690i) q^{98} +(-7.44079 + 1.99372i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9}+O(q^{10}) \) 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9	\( 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 36 q^{13} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 36 q^{21} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 9 q^{28} - 36 q^{29} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 18 q^{36} - 36 q^{37} - 18 q^{38} - 18 q^{40} - 36 q^{41} - 63 q^{42} - 90 q^{44} - 36 q^{45} - 18 q^{46} - 117 q^{48} - 36 q^{49} - 135 q^{50} - 18 q^{52} - 54 q^{53} - 144 q^{54} - 144 q^{56} - 36 q^{57} - 18 q^{58} - 135 q^{60} - 36 q^{61} - 117 q^{62} - 18 q^{64} - 36 q^{65} - 90 q^{66} - 63 q^{68} - 36 q^{69} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 18 q^{76} - 36 q^{77} + 9 q^{78} - 36 q^{81} - 36 q^{82} - 45 q^{84} - 36 q^{85} - 18 q^{86} - 18 q^{88} - 54 q^{89} + 45 q^{90} + 72 q^{92} - 144 q^{93} - 18 q^{94} + 99 q^{96} - 36 q^{97} + 153 q^{98}+O(q^{100}) \) 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 18 * q^12 - 36 * q^13 - 18 * q^14 - 18 * q^16 - 36 * q^17 - 18 * q^18 - 18 * q^20 - 36 * q^21 - 18 * q^22 - 18 * q^24 - 36 * q^25 - 27 * q^26 - 9 * q^28 - 36 * q^29 - 18 * q^30 - 18 * q^32 - 36 * q^33 - 18 * q^34 - 18 * q^36 - 36 * q^37 - 18 * q^38 - 18 * q^40 - 36 * q^41 - 63 * q^42 - 90 * q^44 - 36 * q^45 - 18 * q^46 - 117 * q^48 - 36 * q^49 - 135 * q^50 - 18 * q^52 - 54 * q^53 - 144 * q^54 - 144 * q^56 - 36 * q^57 - 18 * q^58 - 135 * q^60 - 36 * q^61 - 117 * q^62 - 18 * q^64 - 36 * q^65 - 90 * q^66 - 63 * q^68 - 36 * q^69 - 18 * q^70 - 18 * q^72 - 36 * q^73 - 18 * q^74 - 18 * q^76 - 36 * q^77 + 9 * q^78 - 36 * q^81 - 36 * q^82 - 45 * q^84 - 36 * q^85 - 18 * q^86 - 18 * q^88 - 54 * q^89 + 45 * q^90 + 72 * q^92 - 144 * q^93 - 18 * q^94 + 99 * q^96 - 36 * q^97 + 153 * q^98

Introduction

L-functions

Modular forms

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