LMFDB - Embedded newform 459.2.ba.a.25.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [459,2,Mod(25,459)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(459, base_ring=CyclotomicField(72))

chi = DirichletCharacter(H, H._module([40, 45]))

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

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

chi := DirichletCharacter("459.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 459 = 3^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	459.ba (of order $72$, degree $24$, 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:	$3.66513345278$
Analytic rank:	$0$
Dimension:	$1248$
Relative dimension:	$52$ over $\Q(\zeta_{72})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{72}]$

Embedding invariants

Embedding label			25.20
Character	$\chi$	$=$	459.25
Dual form			459.2.ba.a.202.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.442402 - 0.631815i) q^{2} +(1.70567 - 0.301145i) q^{3} +(0.480569 - 1.32035i) q^{4} +(-2.01144 + 0.634203i) q^{5} +(-0.944859 - 0.944442i) q^{6} +(1.40032 - 1.28316i) q^{7} +(-2.53687 + 0.679752i) q^{8} +(2.81862 - 1.02731i) q^{9} +(1.29056 + 0.990283i) q^{10} +(0.111384 - 0.353264i) q^{11} +(0.422075 - 2.39681i) q^{12} +(3.25736 - 0.574361i) q^{13} +(-1.43022 - 0.317073i) q^{14} +(-3.23986 + 1.68748i) q^{15} +(-0.600930 - 0.504240i) q^{16} +(-0.882834 - 4.02748i) q^{17} +(-1.89603 - 1.32637i) q^{18} +(-0.408167 - 1.52330i) q^{19} +(-0.129262 + 2.96058i) q^{20} +(2.00207 - 2.61034i) q^{21} +(-0.272474 + 0.0859108i) q^{22} +(-0.213726 - 4.89512i) q^{23} +(-4.12236 + 1.92340i) q^{24} +(-0.452098 + 0.316562i) q^{25} +(-1.80395 - 1.80395i) q^{26} +(4.49828 - 2.60106i) q^{27} +(-1.02127 - 2.46556i) q^{28} +(-1.71594 + 2.69349i) q^{29} +(2.49949 + 1.30045i) q^{30} +(0.390488 - 0.426143i) q^{31} +(-0.510539 + 5.83548i) q^{32} +(0.0836004 - 0.636095i) q^{33} +(-2.15406 + 2.33955i) q^{34} +(-2.00287 + 3.46908i) q^{35} +(-0.00186467 - 4.21527i) q^{36} +(-3.61407 + 0.475801i) q^{37} +(-0.781871 + 0.931797i) q^{38} +(5.38302 - 1.96061i) q^{39} +(4.67165 - 2.97617i) q^{40} +(4.41666 + 6.93277i) q^{41} +(-2.53497 - 0.110118i) q^{42} +(0.357735 + 4.08893i) q^{43} +(-0.412906 - 0.316834i) q^{44} +(-5.01796 + 3.85394i) q^{45} +(-2.99826 + 2.30065i) q^{46} +(2.50086 + 6.87104i) q^{47} +(-1.17684 - 0.679101i) q^{48} +(-0.295686 + 3.37970i) q^{49} +(0.400018 + 0.145595i) q^{50} +(-2.71868 - 6.60369i) q^{51} +(0.807029 - 4.57689i) q^{52} +(6.82673 - 6.82673i) q^{53} +(-3.63344 - 1.69136i) q^{54} +0.781209i q^{55} +(-2.68020 + 4.20707i) q^{56} +(-1.15493 - 2.47533i) q^{57} +(2.46092 - 0.107446i) q^{58} +(-3.35423 - 0.293457i) q^{59} +(0.671086 + 5.08871i) q^{60} +(8.55177 - 7.83625i) q^{61} +(-0.441996 - 0.0581899i) q^{62} +(2.62878 - 5.05530i) q^{63} +(2.55409 - 1.47460i) q^{64} +(-6.18772 + 3.22112i) q^{65} +(-0.438880 + 0.228590i) q^{66} +(0.552290 + 3.13219i) q^{67} +(-5.74196 - 0.769830i) q^{68} +(-1.83869 - 8.28511i) q^{69} +(3.07789 - 0.269280i) q^{70} +(1.87344 - 0.246643i) q^{71} +(-6.45216 + 4.52211i) q^{72} +(2.05957 - 1.58036i) q^{73} +(1.89949 + 2.07293i) q^{74} +(-0.675799 + 0.676098i) q^{75} +(-2.20745 - 0.193127i) q^{76} +(-0.297321 - 0.637606i) q^{77} +(-3.62020 - 2.53370i) q^{78} +(-10.1744 + 2.25561i) q^{79} +(1.52852 + 0.633135i) q^{80} +(6.88928 - 5.79119i) q^{81} +(2.42629 - 5.85758i) q^{82} +(5.80410 + 8.28911i) q^{83} +(-2.48444 - 3.89789i) q^{84} +(4.33001 + 7.54113i) q^{85} +(2.42519 - 2.03497i) q^{86} +(-2.11570 + 5.11095i) q^{87} +(-0.0424340 + 0.971898i) q^{88} +(4.34565 + 2.50897i) q^{89} +(4.65494 + 1.46543i) q^{90} +(3.82435 - 4.98400i) q^{91} +(-6.56600 - 2.07025i) q^{92} +(0.537713 - 0.844453i) q^{93} +(3.23485 - 4.61984i) q^{94} +(1.78709 + 2.80516i) q^{95} +(0.886515 + 10.1072i) q^{96} +(7.68940 + 14.7712i) q^{97} +(2.26616 - 1.30837i) q^{98} +(-0.0489620 - 1.11014i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1248 q - 24 q^{2} - 24 q^{3} - 24 q^{5} - 24 q^{6} - 24 q^{7} - 12 q^{8} - 24 q^{9} - 12 q^{10} - 36 q^{11} + 12 q^{12} - 24 q^{14} - 24 q^{15} - 48 q^{16} - 12 q^{17} - 48 q^{18} - 12 q^{19} - 24 q^{20}+ \cdots - 168 q^{99}+O(q^{100}) $ 1248 * q - 24 * q^2 - 24 * q^3 - 24 * q^5 - 24 * q^6 - 24 * q^7 - 12 * q^8 - 24 * q^9 - 12 * q^10 - 36 * q^11 + 12 * q^12 - 24 * q^14 - 24 * q^15 - 48 * q^16 - 12 * q^17 - 48 * q^18 - 12 * q^19 - 24 * q^20 - 24 * q^22 + 48 * q^23 - 84 * q^24 - 24 * q^25 - 48 * q^26 - 24 * q^27 - 48 * q^28 - 24 * q^29 - 24 * q^31 - 72 * q^32 - 48 * q^33 - 24 * q^34 - 216 * q^35 - 24 * q^36 - 12 * q^37 - 24 * q^39 - 72 * q^40 - 24 * q^41 + 96 * q^42 + 12 * q^43 - 12 * q^44 - 24 * q^45 - 12 * q^46 - 24 * q^48 - 24 * q^49 - 48 * q^50 - 24 * q^51 - 48 * q^52 - 48 * q^53 - 96 * q^54 + 96 * q^56 - 60 * q^57 - 24 * q^58 + 144 * q^59 - 480 * q^60 - 24 * q^61 - 12 * q^62 + 120 * q^63 - 72 * q^65 - 204 * q^66 - 48 * q^67 - 72 * q^68 + 96 * q^69 + 36 * q^71 - 12 * q^73 - 192 * q^74 - 24 * q^75 - 72 * q^76 - 60 * q^77 + 324 * q^78 - 24 * q^79 - 48 * q^80 - 48 * q^82 - 144 * q^83 - 48 * q^84 - 24 * q^85 + 72 * q^86 - 24 * q^87 + 192 * q^88 - 252 * q^90 - 12 * q^91 - 24 * q^92 - 24 * q^93 - 24 * q^94 + 192 * q^95 + 288 * q^96 - 132 * q^97 - 168 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/459\mathbb{Z}\right)^\times$.

$n$	$137$	$190$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{8}\right)$

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 $

$2$	−0.442402	−	0.631815i	−0.312825	−	0.446761i	0.631693	−	0.775218i	$-0.282360\pi$
$2$	−0.442402	−	0.631815i	−0.312825	−	0.446761i	−0.944519	+	0.328457i	$0.893471\pi$
$3$	1.70567	−	0.301145i	0.984769	−	0.173866i
$3$	1.70567	−	0.301145i	0.984769	−	0.173866i
$4$	0.480569	−	1.32035i	0.240285	−	0.660176i
$5$	−2.01144	+	0.634203i	−0.899542	+	0.283624i	−0.714937	−	0.699189i	$-0.753545\pi$
$5$	−2.01144	+	0.634203i	−0.899542	+	0.283624i	−0.184604	+	0.982813i	$0.559100\pi$
$6$	−0.944859	−	0.944442i	−0.385737	−	0.385567i
$7$	1.40032	−	1.28316i	0.529271	−	0.484988i	−0.365935	−	0.930641i	$-0.619251\pi$
$7$	1.40032	−	1.28316i	0.529271	−	0.484988i	0.895206	+	0.445653i	$0.147028\pi$
$8$	−2.53687	+	0.679752i	−0.896918	+	0.240329i
$9$	2.81862	−	1.02731i	0.939541	−	0.342436i
$10$	1.29056	+	0.990283i	0.408112	+	0.313155i
$11$	0.111384	−	0.353264i	0.0335835	−	0.106513i	−0.935437	−	0.353493i	$-0.884994\pi$
$11$	0.111384	−	0.353264i	0.0335835	−	0.106513i	0.969021	+	0.246980i	$0.0794382\pi$
$12$	0.422075	−	2.39681i	0.121843	−	0.691899i
$13$	3.25736	−	0.574361i	0.903430	−	0.159299i	0.297411	−	0.954749i	$-0.403877\pi$
$13$	3.25736	−	0.574361i	0.903430	−	0.159299i	0.606019	+	0.795450i	$0.292766\pi$
$14$	−1.43022	−	0.317073i	−0.382243	−	0.0847412i
$15$	−3.23986	+	1.68748i	−0.836528	+	0.435704i
$16$	−0.600930	−	0.504240i	−0.150233	−	0.126060i
$17$	−0.882834	−	4.02748i	−0.214119	−	0.976808i
$17$	−0.882834	−	4.02748i	−0.214119	−	0.976808i
$18$	−1.89603	−	1.32637i	−0.446899	−	0.312628i
$19$	−0.408167	−	1.52330i	−0.0936400	−	0.349469i	0.903170	−	0.429284i	$-0.141234\pi$
$19$	−0.408167	−	1.52330i	−0.0936400	−	0.349469i	−0.996810	+	0.0798144i	$0.974567\pi$
$20$	−0.129262	+	2.96058i	−0.0289038	+	0.662007i
$21$	2.00207	−	2.61034i	0.436887	−	0.569623i
$22$	−0.272474	+	0.0859108i	−0.0580917	+	0.0183162i
$23$	−0.213726	−	4.89512i	−0.0445649	−	1.02070i	−0.881141	−	0.472853i	$-0.843224\pi$
$23$	−0.213726	−	4.89512i	−0.0445649	−	1.02070i	0.836576	−	0.547851i	$-0.184554\pi$
$24$	−4.12236	+	1.92340i	−0.841473	+	0.392612i
$25$	−0.452098	+	0.316562i	−0.0904195	+	0.0633124i
$26$	−1.80395	−	1.80395i	−0.353784	−	0.353784i
$27$	4.49828	−	2.60106i	0.865693	−	0.500575i
$28$	−1.02127	−	2.46556i	−0.193002	−	0.465947i
$29$	−1.71594	+	2.69349i	−0.318642	+	0.500168i	−0.964782	−	0.263051i	$-0.915271\pi$
$29$	−1.71594	+	2.69349i	−0.318642	+	0.500168i	0.646140	+	0.763219i	$0.276382\pi$
$30$	2.49949	+	1.30045i	0.456343	+	0.237429i
$31$	0.390488	−	0.426143i	0.0701337	−	0.0765375i	−0.701217	−	0.712948i	$-0.747359\pi$
$31$	0.390488	−	0.426143i	0.0701337	−	0.0765375i	0.771350	+	0.636411i	$0.219582\pi$
$32$	−0.510539	+	5.83548i	−0.0902514	+	1.03158i
$33$	0.0836004	−	0.636095i	0.0145530	−	0.110730i
$34$	−2.15406	+	2.33955i	−0.369418	+	0.401230i
$35$	−2.00287	+	3.46908i	−0.338547	+	0.586381i
$36$	−0.00186467	−	4.21527i	−0.000310778	−	0.702545i
$37$	−3.61407	+	0.475801i	−0.594149	+	0.0782212i	−0.421603	−	0.906780i	$-0.638533\pi$
$37$	−3.61407	+	0.475801i	−0.594149	+	0.0782212i	−0.172546	+	0.985002i	$0.555199\pi$
$38$	−0.781871	+	0.931797i	−0.126836	+	0.151157i
$39$	5.38302	−	1.96061i	0.861973	−	0.313949i
$40$	4.67165	−	2.97617i	0.738653	−	0.470574i
$41$	4.41666	+	6.93277i	0.689766	+	1.08272i	0.991598	+	0.129355i	$0.0412907\pi$
$41$	4.41666	+	6.93277i	0.689766	+	1.08272i	−0.301832	+	0.953361i	$0.597598\pi$
$42$	−2.53497	−	0.110118i	−0.391155	−	0.0169915i
$43$	0.357735	+	4.08893i	0.0545541	+	0.623556i	0.973426	+	0.229001i	$0.0735458\pi$
$43$	0.357735	+	4.08893i	0.0545541	+	0.623556i	−0.918872	+	0.394555i	$0.870899\pi$
$44$	−0.412906	−	0.316834i	−0.0622479	−	0.0477645i
$45$	−5.01796	+	3.85394i	−0.748033	+	0.574512i
$46$	−2.99826	+	2.30065i	−0.442069	+	0.339212i
$47$	2.50086	+	6.87104i	0.364787	+	1.00224i	0.977314	+	0.211795i	$0.0679309\pi$
$47$	2.50086	+	6.87104i	0.364787	+	1.00224i	−0.612527	+	0.790450i	$0.709847\pi$
$48$	−1.17684	−	0.679101i	−0.169862	−	0.0980198i
$49$	−0.295686	+	3.37970i	−0.0422408	+	0.482815i
$50$	0.400018	+	0.145595i	0.0565710	+	0.0205902i
$51$	−2.71868	−	6.60369i	−0.380691	−	0.924702i
$52$	0.807029	−	4.57689i	0.111915	−	0.634700i
$53$	6.82673	−	6.82673i	0.937723	−	0.937723i	−0.0604483	−	0.998171i	$-0.519253\pi$
$53$	6.82673	−	6.82673i	0.937723	−	0.937723i	0.998171	+	0.0604483i	$0.0192530\pi$
$54$	−3.63344	−	1.69136i	−0.494448	−	0.230166i
$55$			0.781209i			0.105338i
$56$	−2.68020	+	4.20707i	−0.358157	+	0.562193i
$57$	−1.15493	−	2.47533i	−0.152975	−	0.327866i
$58$	2.46092	−	0.107446i	0.323135	−	0.0141084i
$59$	−3.35423	−	0.293457i	−0.436684	−	0.0382049i	−0.133305	−	0.991075i	$-0.542559\pi$
$59$	−3.35423	−	0.293457i	−0.436684	−	0.0382049i	−0.303379	+	0.952870i	$0.598115\pi$
$60$	0.671086	+	5.08871i	0.0866369	+	0.656949i
$61$	8.55177	−	7.83625i	1.09494	−	1.00333i	0.0949729	−	0.995480i	$-0.469724\pi$
$61$	8.55177	−	7.83625i	1.09494	−	1.00333i	0.999969	−	0.00784973i	$-0.00249867\pi$
$62$	−0.441996	−	0.0581899i	−0.0561336	−	0.00739012i
$63$	2.62878	−	5.05530i	0.331195	−	0.636907i
$64$	2.55409	−	1.47460i	0.319261	−	0.184325i
$65$	−6.18772	+	3.22112i	−0.767492	+	0.399531i
$66$	−0.438880	+	0.228590i	−0.0540223	+	0.0281374i
$67$	0.552290	+	3.13219i	0.0674730	+	0.382658i	0.999780	+	0.0209898i	$0.00668174\pi$
$67$	0.552290	+	3.13219i	0.0674730	+	0.382658i	−0.932307	+	0.361669i	$0.882207\pi$
$68$	−5.74196	−	0.769830i	−0.696315	−	0.0933557i
$69$	−1.83869	−	8.28511i	−0.221352	−	0.997410i
$70$	3.07789	−	0.269280i	0.367878	−	0.0321852i
$71$	1.87344	−	0.246643i	0.222336	−	0.0292711i	−0.0185351	−	0.999828i	$-0.505900\pi$
$71$	1.87344	−	0.246643i	0.222336	−	0.0292711i	0.240871	+	0.970557i	$0.422567\pi$
$72$	−6.45216	+	4.52211i	−0.760395	+	0.532936i
$73$	2.05957	−	1.58036i	0.241054	−	0.184968i	−0.481168	−	0.876628i	$-0.659787\pi$
$73$	2.05957	−	1.58036i	0.241054	−	0.184968i	0.722222	+	0.691661i	$0.243121\pi$
$74$	1.89949	+	2.07293i	0.220811	+	0.240973i
$75$	−0.675799	+	0.676098i	−0.0780345	+	0.0780690i
$76$	−2.20745	−	0.193127i	−0.253212	−	0.0221531i
$77$	−0.297321	−	0.637606i	−0.0338828	−	0.0726619i
$78$	−3.62020	−	2.53370i	−0.409907	−	0.286885i
$79$	−10.1744	+	2.25561i	−1.14471	+	0.253776i	−0.747699	−	0.664038i	$-0.768841\pi$
$79$	−10.1744	+	2.25561i	−1.14471	+	0.253776i	−0.397010	+	0.917814i	$0.629952\pi$
$80$	1.52852	+	0.633135i	0.170894	+	0.0707867i
$81$	6.88928	−	5.79119i	0.765475	−	0.643465i
$82$	2.42629	−	5.85758i	0.267939	−	0.646862i
$83$	5.80410	+	8.28911i	0.637082	+	0.909848i	0.999756	−	0.0220682i	$-0.00702509\pi$
$83$	5.80410	+	8.28911i	0.637082	+	0.909848i	−0.362674	+	0.931916i	$0.618136\pi$
$84$	−2.48444	−	3.89789i	−0.271075	−	0.425294i
$85$	4.33001	+	7.54113i	0.469655	+	0.817950i
$86$	2.42519	−	2.03497i	0.261514	−	0.219437i
$87$	−2.11570	+	5.11095i	−0.226827	+	0.547951i
$88$	−0.0424340	+	0.971898i	−0.00452348	+	0.103605i
$89$	4.34565	+	2.50897i	0.460638	+	0.265950i	0.712313	−	0.701862i	$-0.247648\pi$
$89$	4.34565	+	2.50897i	0.460638	+	0.265950i	−0.251674	+	0.967812i	$0.580981\pi$
$90$	4.65494	+	1.46543i	0.490673	+	0.154470i
$91$	3.82435	−	4.98400i	0.400901	−	0.522465i
$92$	−6.56600	−	2.07025i	−0.684553	−	0.215839i
$93$	0.537713	−	0.844453i	0.0557583	−	0.0875657i
$94$	3.23485	−	4.61984i	0.333649	−	0.476500i
$95$	1.78709	+	2.80516i	0.183351	+	0.287804i
$96$	0.886515	+	10.1072i	0.0904795	+	1.03156i
$97$	7.68940	+	14.7712i	0.780741	+	1.49979i	0.864128	+	0.503272i	$0.167871\pi$
$97$	7.68940	+	14.7712i	0.780741	+	1.49979i	−0.0833875	+	0.996517i	$0.526574\pi$
$98$	2.26616	−	1.30837i	0.228917	−	0.132165i
$99$	−0.0489620	−	1.11014i	−0.00492086	−	0.111574i
$100$	0.200710	+	0.749059i	0.0200710	+	0.0749059i
$101$	−2.08572	+	0.759140i	−0.207537	+	0.0755372i	−0.443697	−	0.896177i	$-0.646333\pi$
$101$	−2.08572	+	0.759140i	−0.207537	+	0.0755372i	0.236160	+	0.971714i	$0.424111\pi$
$102$	−2.96957	+	4.63919i	−0.294031	+	0.459348i
$103$	−4.25214	+	3.56797i	−0.418975	+	0.351562i	−0.827773	−	0.561063i	$-0.810393\pi$
$103$	−4.25214	+	3.56797i	−0.418975	+	0.351562i	0.408798	+	0.912625i	$0.365948\pi$
$104$	−7.87308	+	3.67128i	−0.772019	+	0.359998i
$105$	−2.37155	+	6.52026i	−0.231439	+	0.636312i
$106$	−7.33339	−	1.29307i	−0.712281	−	0.125594i
$107$	−1.11365	−	0.461289i	−0.107661	−	0.0445945i	0.328203	−	0.944607i	$-0.393557\pi$
$107$	−1.11365	−	0.461289i	−0.107661	−	0.0445945i	−0.435864	+	0.900013i	$0.643557\pi$
$108$	−1.27259	−	7.18930i	−0.122455	−	0.691791i
$109$	13.7564	−	5.69809i	1.31763	−	0.545778i	0.390526	−	0.920592i	$-0.372293\pi$
$109$	13.7564	−	5.69809i	1.31763	−	0.545778i	0.927100	+	0.374814i	$0.122293\pi$
$110$	0.493580	−	0.345608i	0.0470610	−	0.0329524i
$111$	−6.02112	+	1.89992i	−0.571500	+	0.180332i
$112$	−1.48851	+	0.0649899i	−0.140651	+	0.00614097i
$113$	−0.345817	−	0.180021i	−0.0325318	−	0.0169350i	0.445405	−	0.895329i	$-0.353060\pi$
$113$	−0.345817	−	0.180021i	−0.0325318	−	0.0169350i	−0.477937	+	0.878394i	$0.658615\pi$
$114$	−1.05301	+	1.82480i	−0.0986232	+	0.170908i
$115$	3.53440	+	9.71068i	0.329585	+	0.905526i
$116$	2.73172	+	3.56005i	0.253634	+	0.330543i
$117$	8.59123	−	4.96522i	0.794260	−	0.459035i
$118$	1.29851	+	2.24908i	0.119537	+	0.207045i
$119$	−6.40414	−	4.50695i	−0.587067	−	0.413151i
$120$	7.07204	−	6.48321i	0.645586	−	0.591833i
$121$	8.89828	+	6.23064i	0.808935	+	0.566422i
$122$	−8.73438	−	1.93637i	−0.790774	−	0.175310i
$123$	9.62113	+	10.4950i	0.867508	+	0.946299i
$124$	−0.375003	−	0.720373i	−0.0336762	−	0.0646914i
$125$	7.12814	−	9.28957i	0.637560	−	0.830885i
$126$	−4.35699	+	0.575569i	−0.388151	+	0.0512758i
$127$	−6.47260	+	1.73433i	−0.574351	+	0.153897i	−0.534291	−	0.845300i	$-0.679421\pi$
$127$	−6.47260	+	1.73433i	−0.574351	+	0.153897i	−0.0400595	+	0.999197i	$0.512755\pi$
$128$	8.55628	+	3.98986i	0.756276	+	0.352657i
$129$	1.84154	+	6.86664i	0.162138	+	0.604574i
$130$	4.77261	+	2.48446i	0.418586	+	0.217902i
$131$	3.16647	+	2.90153i	0.276656	+	0.253508i	0.801921	−	0.597430i	$-0.203812\pi$
$131$	3.16647	+	2.90153i	0.276656	+	0.253508i	−0.525265	+	0.850939i	$0.676034\pi$
$132$	−0.799694	−	0.416070i	−0.0696044	−	0.0362142i
$133$	−2.52620	−	1.60937i	−0.219049	−	0.139550i
$134$	1.73463	−	1.73463i	0.149850	−	0.149850i
$135$	−7.39839	+	8.08469i	−0.636752	+	0.695819i
$136$	4.97732	+	9.61708i	0.426802	+	0.824658i
$137$	−1.22606	+	6.95333i	−0.104749	+	0.594063i	0.886571	+	0.462593i	$0.153081\pi$
$137$	−1.22606	+	6.95333i	−0.104749	+	0.594063i	−0.991320	+	0.131470i	$0.958030\pi$
$138$	−4.42122	+	4.82706i	−0.376359	+	0.410906i
$139$	−10.2167	+	11.1496i	−0.866573	+	0.945699i	−0.998964	−	0.0454989i	$-0.985512\pi$
$139$	−10.2167	+	11.1496i	−0.866573	+	0.945699i	0.132391	+	0.991198i	$0.457734\pi$
$140$	3.61789	+	4.31163i	0.305767	+	0.364399i
$141$	6.33481	+	10.9666i	0.533488	+	0.923556i
$142$	−0.984644	−	1.07455i	−0.0826295	−	0.0901743i
$143$	0.159916	−	1.21468i	0.0133729	−	0.101577i
$144$	−2.21181	−	0.803924i	−0.184317	−	0.0669937i
$145$	1.74329	−	6.50603i	0.144772	−	0.540296i
$146$	−1.90965	−	0.602112i	−0.158044	−	0.0498311i
$147$	0.513437	+	5.85370i	0.0423476	+	0.482805i
$148$	−1.10858	+	5.00050i	−0.0911250	+	0.411038i
$149$	−22.0235	+	3.88333i	−1.80423	+	0.318135i	−0.971768	−	0.235940i	$-0.924183\pi$
$149$	−22.0235	+	3.88333i	−1.80423	+	0.318135i	−0.832466	+	0.554076i	$0.813072\pi$
$150$	0.726143	+	0.127873i	0.0592894	+	0.0104408i
$151$	−0.766916	+	0.0670965i	−0.0624108	+	0.00546023i	−0.118318	−	0.992976i	$-0.537750\pi$
$151$	−0.766916	+	0.0670965i	−0.0624108	+	0.00546023i	0.0559076	+	0.998436i	$0.482195\pi$
$152$	2.07093	+	3.58696i	0.167975	+	0.290941i
$153$	−6.62584	−	10.4450i	−0.535667	−	0.844429i
$154$	−0.271314	+	0.469930i	−0.0218631	+	0.0378680i
$155$	−0.515181	+	1.10481i	−0.0413803	+	0.0887403i
$156$	−0.00178043	−	8.04970i	−0.000142549	−	0.644491i
$157$	8.94393	+	10.6590i	0.713804	+	0.850678i	0.994013	−	0.109261i	$-0.0348484\pi$
$157$	8.94393	+	10.6590i	0.713804	+	0.850678i	−0.280210	+	0.959939i	$0.590404\pi$
$158$	5.92630	+	5.43045i	0.471471	+	0.432024i
$159$	9.58831	−	13.7000i	0.760403	−	1.08648i
$160$	−2.67397	−	12.0615i	−0.211396	−	0.953545i
$161$	−6.58050	−	6.58050i	−0.518616	−	0.518616i
$162$	−6.70679	−	1.79072i	−0.526935	−	0.140692i
$163$	1.37385	−	0.569066i	0.107608	−	0.0445727i	−0.328230	−	0.944598i	$-0.606452\pi$
$163$	1.37385	−	0.569066i	0.107608	−	0.0445727i	0.435838	+	0.900025i	$0.356452\pi$
$164$	11.2762	−	2.49987i	0.880524	−	0.195207i
$165$	0.235257	+	1.33248i	0.0183147	+	0.103734i
$166$	2.66944	−	7.33423i	0.207189	−	0.569247i
$167$	−2.60176	−	8.25174i	−0.201330	−	0.638539i	−0.999355	−	0.0359135i	$-0.988566\pi$
$167$	−2.60176	−	8.25174i	−0.201330	−	0.638539i	0.798024	−	0.602625i	$-0.205879\pi$
$168$	−3.30460	+	7.98300i	−0.254955	+	0.615902i
$169$	−1.93548	+	0.704459i	−0.148883	+	0.0541891i
$170$	2.84900	−	6.07197i	0.218508	−	0.465699i
$171$	−2.71537	−	3.87430i	−0.207649	−	0.296275i
$172$	5.57075	+	1.49268i	0.424765	+	0.113816i
$173$	−6.63518	+	3.45406i	−0.504463	+	0.262607i	−0.694918	−	0.719089i	$-0.744559\pi$
$173$	−6.63518	+	3.45406i	−0.504463	+	0.262607i	0.190455	+	0.981696i	$0.439004\pi$
$174$	4.16516	−	0.924361i	0.315760	−	0.0700756i
$175$	−0.226882	+	1.02340i	−0.0171507	+	0.0773618i
$176$	−0.245064	+	0.156123i	−0.0184724	+	0.0117682i
$177$	−5.80959	+	0.509568i	−0.436676	+	0.0383015i
$178$	−0.337323	−	3.85562i	−0.0252834	−	0.288991i
$179$	1.68166	−	6.27602i	0.125693	−	0.469092i	−0.874171	−	0.485619i	$-0.838594\pi$
$179$	1.68166	−	6.27602i	0.125693	−	0.469092i	0.999863	+	0.0165269i	$0.00526093\pi$
$180$	2.67709	+	8.47757i	0.199538	+	0.631880i
$181$	−26.2428	−	3.45492i	−1.95061	−	0.256803i	−0.951848	−	0.306570i	$-0.900819\pi$
$181$	−26.2428	−	3.45492i	−1.95061	−	0.256803i	−0.998761	+	0.0497673i	$0.984152\pi$
$182$	−4.84087	−	0.211357i	−0.358829	−	0.0156668i
$183$	12.2267	−	15.9414i	0.903820	−	1.17842i
$184$	3.86966	+	12.2730i	0.285275	+	0.904778i
$185$	6.96771	−	3.24910i	0.512276	−	0.238878i
$186$	−0.771423	+	0.0338520i	−0.0565635	+	0.00248215i
$187$	−1.52110	−	0.136722i	−0.111234	−	0.00999813i
$188$	10.2740			0.749311
$189$	2.96145	−	9.41431i	0.215414	−	0.684790i
$190$	0.981734	−	2.37012i	0.0712225	−	0.171946i
$191$	12.9958	+	2.29152i	0.940346	+	0.165808i	0.622753	−	0.782419i	$-0.286014\pi$
$191$	12.9958	+	2.29152i	0.940346	+	0.165808i	0.317593	+	0.948227i	$0.397125\pi$
$192$	3.91236	−	3.28434i	0.282351	−	0.237027i
$193$	0.314219	+	7.19680i	0.0226180	+	0.518037i	0.976196	+	0.216891i	$0.0695915\pi$
$193$	0.314219	+	7.19680i	0.0226180	+	0.518037i	−0.953578	+	0.301146i	$0.902631\pi$
$194$	5.93087	−	11.3931i	0.425811	−	0.817976i
$195$	−9.58418	+	7.35757i	−0.686337	+	0.526886i
$196$	4.32030	+	2.01459i	0.308593	+	0.143899i
$197$	2.22981	−	16.9371i	0.158867	−	1.20672i	−0.707282	−	0.706931i	$-0.750079\pi$
$197$	2.22981	−	16.9371i	0.158867	−	1.20672i	0.866150	−	0.499785i	$-0.166588\pi$
$198$	−0.679745	+	0.522065i	−0.0483074	+	0.0371015i
$199$	−3.53208	−	26.8288i	−0.250382	−	1.90184i	−0.405748	−	0.913985i	$-0.632989\pi$
$199$	−3.53208	−	26.8288i	−0.250382	−	1.90184i	0.155366	−	0.987857i	$-0.450344\pi$
$200$	0.931729	−	1.11039i	0.0658832	−	0.0785165i
$201$	1.88527	+	5.17617i	0.132977	+	0.365099i
$202$	1.40236	+	0.981944i	0.0986698	+	0.0690894i
$203$	1.05330	+	5.97356i	0.0739272	+	0.419262i
$204$	−10.0257	+	0.416084i	−0.701941	+	0.0291317i
$205$	−13.2806	−	11.1438i	−0.927558	−	0.778314i
$206$	4.13545	+	1.10809i	0.288130	+	0.0772043i
$207$	−5.63121	−	13.5780i	−0.391396	−	0.943733i
$208$	−2.24706	−	1.29734i	−0.155806	−	0.0899545i
$209$	−0.583591	−	0.0254801i	−0.0403678	−	0.00176250i
$210$	5.16877	−	1.38619i	0.356679	−	0.0956565i
$211$	8.32016	−	15.9829i	0.572784	−	1.10031i	−0.409395	−	0.912357i	$-0.634260\pi$
$211$	8.32016	−	15.9829i	0.572784	−	1.10031i	0.982179	−	0.187950i	$-0.0601843\pi$
$212$	−5.73297	−	12.2944i	−0.393742	−	0.844383i
$213$	3.12119	−	0.984866i	0.213860	−	0.0674819i
$214$	0.201232	+	0.907697i	0.0137559	+	0.0620489i
$215$	−3.31277	−	7.99775i	−0.225929	−	0.545442i
$216$	−9.64346	+	9.65626i	−0.656154	+	0.657025i
$217$		−	1.09779i		−	0.0745231i
$218$	−9.68601	−	6.17067i	−0.656019	−	0.417930i
$219$	3.03703	−	3.31581i	0.205223	−	0.224062i
$220$	1.03147	+	0.375425i	0.0695418	+	0.0253111i
$221$	−5.18894	−	12.6119i	−0.349046	−	0.848368i
$222$	3.86415	+	2.96371i	0.259345	+	0.198911i
$223$	−10.9435	+	23.4684i	−0.732830	+	1.57156i	0.0851866	+	0.996365i	$0.472851\pi$
$223$	−10.9435	+	23.4684i	−0.732830	+	1.57156i	−0.818017	+	0.575194i	$0.804926\pi$
$224$	6.77292	+	8.82665i	0.452535	+	0.589755i
$225$	−0.949087	+	1.35671i	−0.0632724	+	0.0904475i
$226$	0.0392501	+	0.298134i	0.00261088	+	0.0198316i
$227$	7.75900	−	24.6084i	0.514983	−	1.63332i	−0.235099	−	0.971972i	$-0.575541\pi$
$227$	7.75900	−	24.6084i	0.514983	−	1.63332i	0.750081	−	0.661345i	$-0.230014\pi$
$228$	−3.82334	+	0.335351i	−0.253207	+	0.0222091i
$229$	−7.20648	+	10.2919i	−0.476218	+	0.680110i	−0.983342	−	0.181763i	$-0.941820\pi$
$229$	−7.20648	+	10.2919i	−0.476218	+	0.680110i	0.507124	+	0.861873i	$0.330708\pi$
$230$	4.57173	−	6.52911i	0.301451	−	0.430517i
$231$	−0.699143	−	0.998009i	−0.0460002	−	0.0656642i
$232$	2.52221	−	7.99943i	0.165591	−	0.525189i
$233$	2.37199	+	18.0171i	0.155394	+	1.18034i	0.874355	+	0.485287i	$0.161285\pi$
$233$	2.37199	+	18.0171i	0.155394	+	1.18034i	−0.718961	+	0.695051i	$0.755382\pi$
$234$	−6.93788	−	3.23145i	−0.453543	−	0.211247i
$235$	−9.38795	−	12.2346i	−0.612402	−	0.798098i
$236$	−1.99941	+	4.28775i	−0.130150	+	0.279108i
$237$	−16.6749	+	6.91129i	−1.08315	+	0.448937i
$238$	−0.0143549	+	6.04011i	−0.000930493	+	0.391523i
$239$	−3.31573	−	1.20683i	−0.214477	−	0.0780631i	0.232547	−	0.972585i	$-0.425294\pi$
$239$	−3.31573	−	1.20683i	−0.214477	−	0.0780631i	−0.447024	+	0.894522i	$0.647516\pi$
$240$	2.79782	+	0.619613i	0.180599	+	0.0399959i
$241$	−8.65671	−	5.51493i	−0.557628	−	0.355248i	0.228276	−	0.973596i	$-0.426691\pi$
$241$	−8.65671	−	5.51493i	−0.557628	−	0.355248i	−0.785904	+	0.618348i	$0.787802\pi$
$242$		−	8.37852i		−	0.538592i
$243$	10.0069	−	11.9525i	0.641940	−	0.766755i
$244$	−6.23690	−	15.0572i	−0.399277	−	0.963940i
$245$	−1.54867	−	6.98558i	−0.0989406	−	0.446292i
$246$	2.37447	−	10.7218i	0.151391	−	0.683595i
$247$	−2.20447	−	4.72751i	−0.140267	−	0.300804i
$248$	−0.700945	+	1.34650i	−0.0445101	+	0.0855031i
$249$	12.3961	+	12.3906i	0.785571	+	0.785223i
$250$	−9.02280	−	0.393944i	−0.570652	−	0.0249152i
$251$	−15.8524	−	9.15241i	−1.00060	−	0.577695i	−0.0921719	−	0.995743i	$-0.529381\pi$
$251$	−15.8524	−	9.15241i	−1.00060	−	0.577695i	−0.908425	+	0.418048i	$0.862714\pi$
$252$	−5.41146	−	5.90033i	−0.340890	−	0.371686i
$253$	−1.75308	−	0.469736i	−0.110215	−	0.0295320i
$254$	3.95927	+	3.32222i	0.248426	+	0.208455i
$255$	9.65654	+	11.5587i	0.604716	+	0.723835i
$256$	−2.28871	−	12.9799i	−0.143044	−	0.811245i
$257$	−20.9505	−	14.6697i	−1.30686	−	0.915070i	−0.307521	−	0.951541i	$-0.599500\pi$
$257$	−20.9505	−	14.6697i	−1.30686	−	0.915070i	−0.999335	+	0.0364709i	$0.988388\pi$
$258$	3.52375	−	4.20132i	0.219379	−	0.261563i
$259$	−4.45032	+	5.30369i	−0.276530	+	0.329555i
$260$	1.27939	+	9.71794i	0.0793445	+	0.602681i
$261$	−2.06955	+	9.35472i	−0.128102	+	0.579043i
$262$	0.432382	−	3.28427i	0.0267127	−	0.202903i
$263$	20.7988	+	9.69865i	1.28251	+	0.598044i	0.939905	−	0.341435i	$-0.110913\pi$
$263$	20.7988	+	9.69865i	1.28251	+	0.598044i	0.342605	+	0.939480i	$0.388691\pi$
$264$	0.220304	+	1.67052i	0.0135588	+	0.102813i
$265$	−9.40199	+	18.0611i	−0.577560	+	1.10948i
$266$	0.100773	+	2.30808i	0.00617878	+	0.141517i
$267$	8.16782	+	2.97080i	0.499862	+	0.181810i
$268$	4.40102	+	0.776018i	0.268835	+	0.0474028i
$269$	−5.37869	+	12.9853i	−0.327944	+	0.791728i	0.670800	+	0.741638i	$0.265951\pi$
$269$	−5.37869	+	12.9853i	−0.327944	+	0.791728i	−0.998745	+	0.0500900i	$0.984049\pi$
$270$	8.38109	+	1.09773i	0.510057	+	0.0668060i
$271$	−3.99688			−0.242793			−0.121397	−	0.992604i	$-0.538737\pi$
$271$	−3.99688			−0.242793			−0.121397	+	0.992604i	$0.538737\pi$
$272$	−1.50030	+	2.86540i	−0.0909689	+	0.173740i
$273$	5.02218	−	9.65274i	0.303956	−	0.584210i
$274$	4.93563	−	2.30152i	0.298172	−	0.139040i
$275$	0.0614738	+	0.194970i	0.00370701	+	0.0117571i
$276$	−11.8229	−	1.55385i	−0.711654	−	0.0935309i
$277$	−25.1868	−	1.09968i	−1.51333	−	0.0660734i	−0.728183	−	0.685383i	$-0.759635\pi$
$277$	−25.1868	−	1.09968i	−1.51333	−	0.0660734i	−0.785147	+	0.619309i	$0.787413\pi$
$278$	11.5644	+	1.52248i	0.693587	+	0.0913125i
$279$	0.662859	−	1.60229i	0.0396843	−	0.0959265i
$280$	2.72291	−	10.1620i	0.162725	−	0.607298i
$281$	1.22446	+	13.9956i	0.0730450	+	0.834908i	0.941031	+	0.338320i	$0.109859\pi$
$281$	1.22446	+	13.9956i	0.0730450	+	0.834908i	−0.867986	+	0.496588i	$0.834586\pi$
$282$	4.12634	−	8.85408i	0.245720	−	0.527253i
$283$	16.4151	−	10.4576i	0.975779	−	0.621640i	0.0496179	−	0.998768i	$-0.484200\pi$
$283$	16.4151	−	10.4576i	0.975779	−	0.621640i	0.926161	+	0.377129i	$0.123089\pi$
$284$	0.574660	−	2.59213i	0.0340998	−	0.153814i
$285$	3.89294	+	4.24651i	0.230598	+	0.251542i
$286$	−0.838203	+	0.436341i	−0.0495640	+	0.0258014i
$287$	15.0806	+	4.04082i	0.890177	+	0.238522i
$288$	4.55582	+	16.9725i	0.268454	+	1.00012i
$289$	−15.4412	+	7.11120i	−0.908306	+	0.418306i
$290$	−4.88184	+	1.77685i	−0.286672	+	0.104340i
$291$	17.5639	+	22.8792i	1.02961	+	1.34120i
$292$	−1.09687	−	3.47883i	−0.0641896	−	0.203583i
$293$	8.73026	−	23.9862i	0.510027	−	1.40129i	−0.371181	−	0.928561i	$-0.621047\pi$
$293$	8.73026	−	23.9862i	0.510027	−	1.40129i	0.881208	−	0.472728i	$-0.156731\pi$
$294$	3.47131	−	2.91409i	0.202451	−	0.169953i
$295$	6.93294	−	1.53700i	0.403651	−	0.0894873i
$296$	8.84498	−	3.66371i	0.514104	−	0.212949i
$297$	−0.417827	−	1.87880i	−0.0242448	−	0.109019i
$298$	12.1968	+	12.1968i	0.706540	+	0.706540i
$299$	−3.50775	−	15.8224i	−0.202858	−	0.915035i
$300$	0.567920	+	1.21720i	0.0327889	+	0.0702753i
$301$	5.74768	+	5.26678i	0.331291	+	0.303572i
$302$	0.381678	+	0.454866i	0.0219631	+	0.0261746i
$303$	−3.32894	+	1.92295i	−0.191243	+	0.110470i
$304$	−0.522830	+	1.12121i	−0.0299863	+	0.0643059i
$305$	−12.2316	+	21.1857i	−0.700377	+	1.21309i
$306$	−3.66803	+	8.80720i	−0.209688	+	0.503474i
$307$	−15.8706	−	27.4886i	−0.905780	−	1.56886i	−0.819866	−	0.572555i	$-0.805952\pi$
$307$	−15.8706	−	27.4886i	−0.905780	−	1.56886i	−0.0859137	−	0.996303i	$-0.527381\pi$
$308$	−0.984748	+	0.0861543i	−0.0561112	+	0.00490910i
$309$	−6.17827	+	7.36628i	−0.351469	+	0.419053i
$310$	0.925951	−	0.163270i	0.0525905	−	0.00927313i
$311$	−1.15729	+	5.22021i	−0.0656240	+	0.296011i	−0.997824	−	0.0659327i	$-0.978998\pi$
$311$	−1.15729	+	5.22021i	−0.0656240	+	0.296011i	0.932200	+	0.361943i	$0.117887\pi$
$312$	−12.3233	+	8.63292i	−0.697669	+	0.488743i
$313$	0.0592687	+	0.0186873i	0.00335006	+	0.00105627i	0.302380	−	0.953187i	$-0.402219\pi$
$313$	0.0592687	+	0.0186873i	0.00335006	+	0.00105627i	−0.299030	+	0.954244i	$0.596663\pi$
$314$	2.77768	−	10.3665i	0.156754	−	0.585013i
$315$	−2.08154	+	11.8356i	−0.117281	+	0.666860i
$316$	−1.91130	+	14.5178i	−0.107519	+	0.816688i
$317$	4.47253	+	4.88091i	0.251202	+	0.274139i	0.850025	−	0.526742i	$-0.176587\pi$
$317$	4.47253	+	4.88091i	0.251202	+	0.274139i	−0.598823	+	0.800882i	$0.704365\pi$
$318$	−12.8977	+	0.00285272i	−0.723269	+	0.000159973i
$319$	0.760385	+	0.906191i	0.0425734	+	0.0507370i
$320$	−4.20219	+	4.58588i	−0.234909	+	0.256359i
$321$	−2.03844	−	0.451438i	−0.113774	−	0.0251968i
$322$	−1.24643	+	7.06888i	−0.0694611	+	0.393933i
$323$	−5.77472	+	2.98871i	−0.321314	+	0.166296i
$324$	−4.33563	−	11.8793i	−0.240869	−	0.659964i
$325$	−1.29083	+	1.29083i	−0.0716021	+	0.0716021i
$326$	−0.967337	−	0.616262i	−0.0535758	−	0.0341316i
$327$	21.7480	−	13.8617i	1.20267	−	0.766556i
$328$	−15.9170	−	14.5853i	−0.878872	−	0.805338i
$329$	12.3186	+	6.41267i	0.679148	+	0.353542i
$330$	0.737806	−	0.738132i	0.0406149	−	0.0406329i
$331$	12.9162	+	6.02290i	0.709936	+	0.331049i	0.743823	−	0.668377i	$-0.233011\pi$
$331$	12.9162	+	6.02290i	0.709936	+	0.331049i	−0.0338866	+	0.999426i	$0.510788\pi$
$332$	13.7338	−	3.67997i	0.753741	−	0.201964i
$333$	−9.69790	+	5.05386i	−0.531442	+	0.276950i
$334$	−4.06255	+	5.29442i	−0.222293	+	0.289698i
$335$	−3.09735	−	5.94995i	−0.169226	−	0.325080i
$336$	−2.51934	+	0.559110i	−0.137441	+	0.0305019i
$337$	11.1964	+	2.48218i	0.609906	+	0.135213i	0.510563	−	0.859840i	$-0.329437\pi$
$337$	11.1964	+	2.48218i	0.609906	+	0.135213i	0.0993427	+	0.995053i	$0.468326\pi$
$338$	1.30135	+	0.911215i	0.0707841	+	0.0495636i
$339$	−0.644063	−	0.202916i	−0.0349807	−	0.0110209i
$340$	12.0378	−	2.09311i	0.652842	−	0.113515i
$341$	−0.107047	−	0.185411i	−0.00579692	−	0.0100406i
$342$	−1.24656	+	3.42961i	−0.0674061	+	0.185452i
$343$	12.0162	+	15.6599i	0.648815	+	0.845553i
$344$	−3.68698	−	10.1299i	−0.198789	−	0.546168i
$345$	8.95284	+	15.4989i	0.482005	+	0.834431i
$346$	5.11774	+	2.66413i	0.275131	+	0.143224i
$347$	3.02773	−	0.132194i	0.162537	−	0.00709653i	0.0377938	−	0.999286i	$-0.487967\pi$
$347$	3.02773	−	0.132194i	0.162537	−	0.00709653i	0.124743	+	0.992189i	$0.460189\pi$
$348$	5.73151	+	5.24963i	0.307241	+	0.281410i
$349$	−12.3917	+	8.67677i	−0.663313	+	0.464457i	−0.856118	−	0.516780i	$-0.827130\pi$
$349$	−12.3917	+	8.67677i	−0.663313	+	0.464457i	0.192805	+	0.981237i	$0.438242\pi$
$350$	0.746973	−	0.309406i	0.0399274	−	0.0165385i
$351$	13.1586	−	11.0562i	0.702352	−	0.590138i
$352$	2.00460	+	0.830334i	0.106846	+	0.0442569i
$353$	11.5000	+	2.02776i	0.612082	+	0.107927i	0.471091	−	0.882084i	$-0.343860\pi$
$353$	11.5000	+	2.02776i	0.612082	+	0.107927i	0.140990	+	0.990011i	$0.454971\pi$
$354$	2.89213	+	3.44515i	0.153715	+	0.183108i
$355$	−3.61188	+	1.68425i	−0.191698	+	0.0893905i
$356$	5.40111	−	4.53207i	0.286258	−	0.240199i
$357$	−12.2806	−	5.75879i	−0.649958	−	0.304788i
$358$	−4.70925	+	1.71403i	−0.248892	+	0.0905892i
$359$	−3.84477	−	14.3489i	−0.202919	−	0.757305i	−0.990074	−	0.140549i	$-0.955113\pi$
$359$	−3.84477	−	14.3489i	−0.202919	−	0.757305i	0.787154	−	0.616756i	$-0.211553\pi$
$360$	10.1102	−	13.1879i	0.532853	−	0.695064i
$361$	14.3006	−	8.25648i	0.752665	−	0.434551i
$362$	9.42697	+	18.1090i	0.495471	+	0.951790i
$363$	17.0539	+	7.94776i	0.895096	+	0.417149i
$364$	−4.74277	−	7.44465i	−0.248589	−	0.390206i
$365$	−3.14042	+	4.48499i	−0.164377	+	0.234755i
$366$	−15.4811	−	0.672489i	−0.809210	−	0.0351516i
$367$	−28.5067	−	8.98812i	−1.48804	−	0.469176i	−0.555889	−	0.831256i	$-0.687622\pi$
$367$	−28.5067	−	8.98812i	−1.48804	−	0.469176i	−0.932147	+	0.362081i	$0.882067\pi$
$368$	−2.33989	+	3.04940i	−0.121975	+	0.158961i
$369$	19.5710	+	15.0036i	1.01882	+	0.781056i
$370$	−5.13536	−	2.96490i	−0.266974	−	0.154138i
$371$	0.799841	−	18.3194i	0.0415257	−	0.951094i
$372$	−0.856567	−	1.11579i	−0.0444109	−	0.0578510i
$373$	19.6057	−	16.4512i	1.01515	−	0.851809i	0.0261370	−	0.999658i	$-0.491679\pi$
$373$	19.6057	−	16.4512i	1.01515	−	0.851809i	0.989010	+	0.147849i	$0.0472349\pi$
$374$	0.586553	+	1.02154i	0.0303300	+	0.0528225i
$375$	9.36075	−	17.9916i	0.483387	−	0.929080i
$376$	−11.0149	−	15.7310i	−0.568052	−	0.811263i
$377$	−4.04241	+	9.75923i	−0.208194	+	0.502626i
$378$	−7.25826	+	2.29382i	−0.373324	+	0.117981i
$379$	7.64799	+	3.16790i	0.392851	+	0.162724i	0.570360	−	0.821395i	$-0.306804\pi$
$379$	7.64799	+	3.16790i	0.392851	+	0.162724i	−0.177509	+	0.984119i	$0.556804\pi$
$380$	4.56262	−	1.01151i	0.234058	−	0.0518893i
$381$	−10.5178	+	4.90738i	−0.538845	+	0.251413i
$382$	−4.30157	−	9.22474i	−0.220087	−	0.471979i
$383$	21.3967	+	1.87197i	1.09332	+	0.0956531i	0.619521	−	0.784980i	$-0.287327\pi$
$383$	21.3967	+	1.87197i	1.09332	+	0.0956531i	0.473799	+	0.880633i	$0.342882\pi$
$384$	15.7957	+	4.22871i	0.806072	+	0.215795i
$385$	1.00241	+	1.09394i	0.0510877	+	0.0557525i
$386$	4.40804	−	3.38240i	0.224363	−	0.172160i
$387$	5.20891	+	11.1577i	0.264784	+	0.567175i
$388$	23.1985	−	3.05414i	1.17773	−	0.155050i
$389$	−7.57792	+	0.662982i	−0.384216	+	0.0336145i	−0.277628	−	0.960689i	$-0.589548\pi$
$389$	−7.57792	+	0.662982i	−0.384216	+	0.0336145i	−0.106588	+	0.994303i	$0.533993\pi$
$390$	8.88868	+	2.80043i	0.450096	+	0.141805i
$391$	−19.5263	+	5.18236i	−0.987489	+	0.262083i
$392$	−1.54724	−	8.77485i	−0.0781476	−	0.443197i
$393$	6.27474	+	3.99550i	0.316519	+	0.201546i
$394$	−11.6876	+	6.08416i	−0.588811	+	0.306516i
$395$	19.0346	−	10.9897i	0.957737	−	0.552949i
$396$	−1.48931	−	0.468854i	−0.0748407	−	0.0235608i
$397$	−1.32465	−	0.174394i	−0.0664824	−	0.00875258i	0.0972116	−	0.995264i	$-0.469008\pi$
$397$	−1.32465	−	0.174394i	−0.0664824	−	0.00875258i	−0.163694	+	0.986511i	$0.552341\pi$
$398$	−15.3882	+	14.1007i	−0.771343	+	0.706805i
$399$	−4.79352	−	1.98430i	−0.239976	−	0.0993391i
$400$	0.431303	+	0.0377341i	0.0215651	+	0.00188670i
$401$	13.8805	−	0.606037i	0.693160	−	0.0302640i	0.305669	−	0.952138i	$-0.401120\pi$
$401$	13.8805	−	0.606037i	0.693160	−	0.0302640i	0.387491	+	0.921874i	$0.373342\pi$
$402$	2.43634	−	3.48109i	0.121514	−	0.173621i
$403$	1.02720	−	1.61238i	0.0511685	−	0.0803185i
$404$			3.11870i			0.155161i
$405$	−10.1846	+	16.0178i	−0.506075	+	0.795931i
$406$	3.30821	−	3.30821i	0.164183	−	0.164183i
$407$	−0.234465	+	1.32972i	−0.0116220	+	0.0659116i
$408$	11.3858	+	14.9047i	0.563681	+	0.737892i
$409$	−5.39642	−	1.96414i	−0.266836	−	0.0971204i	0.205137	−	0.978733i	$-0.434236\pi$
$409$	−5.39642	−	1.96414i	−0.266836	−	0.0971204i	−0.471973	+	0.881613i	$0.656458\pi$
$410$	−1.16543	+	13.3209i	−0.0575564	+	0.657873i
$411$	0.00270488	+	12.2293i	0.000133422	+	0.603227i
$412$	2.66753	+	7.32897i	0.131420	+	0.361073i
$413$	−5.07355	+	3.89307i	−0.249653	+	0.191566i
$414$	−6.08750	+	9.56479i	−0.299184	+	0.470084i
$415$	−16.9316	−	12.9920i	−0.831137	−	0.637754i
$416$	1.68866	+	19.3015i	0.0827936	+	0.946335i
$417$	−14.0688	+	22.0943i	−0.688950	+	1.08196i
$418$	0.242083	+	0.379994i	0.0118407	+	0.0185861i
$419$	−31.1266	+	19.8299i	−1.52064	+	0.968752i	−0.527787	+	0.849377i	$0.676978\pi$
$419$	−31.1266	+	19.8299i	−1.52064	+	0.968752i	−0.992849	+	0.119375i	$0.961911\pi$
$420$	7.46935	+	6.26471i	0.364467	+	0.305687i
$421$	−22.1788	+	26.4317i	−1.08093	+	1.28820i	−0.125786	+	0.992057i	$0.540145\pi$
$421$	−22.1788	+	26.4317i	−1.08093	+	1.28820i	−0.955143	+	0.296144i	$0.904299\pi$
$422$	−13.7791	+	1.81405i	−0.670755	+	0.0883066i
$423$	14.1076	+	16.7977i	0.685937	+	0.816734i
$424$	−12.6780	+	21.9590i	−0.615699	+	1.06642i
$425$	1.67408	+	1.54134i	0.0812046	+	0.0747661i
$426$	−2.00307	−	1.53631i	−0.0970492	−	0.0744344i
$427$	1.92007	−	21.9465i	0.0929188	−	1.06207i
$428$	−1.14425	+	1.24873i	−0.0553095	+	0.0603597i
$429$	−0.0930314	−	2.12001i	−0.00449160	−	0.102355i
$430$	−3.58752	+	5.63128i	−0.173006	+	0.271564i
$431$	2.54495	+	6.14406i	0.122586	+	0.295949i	0.973245	−	0.229768i	$-0.0737969\pi$
$431$	2.54495	+	6.14406i	0.122586	+	0.295949i	−0.850659	+	0.525718i	$0.823797\pi$
$432$	−4.01471	−	0.705155i	−0.193158	−	0.0339268i
$433$	26.6313	+	26.6313i	1.27982	+	1.27982i	0.940768	+	0.339050i	$0.110106\pi$
$433$	26.6313	+	26.6313i	1.27982	+	1.27982i	0.339050	+	0.940768i	$0.389894\pi$
$434$	−0.693603	+	0.485666i	−0.0332940	+	0.0233127i
$435$	1.01421	−	11.6221i	0.0486278	−	0.557238i
$436$	−0.912586	−	20.9017i	−0.0437049	−	1.00101i
$437$	−7.36951	+	2.32360i	−0.352532	+	0.111153i
$438$	−3.43856	−	0.451922i	−0.164301	−	0.0215937i
$439$	1.61836	−	37.0666i	0.0772401	−	1.76909i	−0.425791	−	0.904822i	$-0.640004\pi$
$439$	1.61836	−	37.0666i	0.0772401	−	1.76909i	0.503031	−	0.864268i	$-0.332218\pi$
$440$	−0.531028	−	1.98182i	−0.0253158	−	0.0944797i
$441$	2.63857	+	9.82987i	0.125646	+	0.468089i
$442$	−5.67279	+	8.85798i	−0.269827	+	0.421331i
$443$	22.0113	+	18.4697i	1.04579	+	0.877522i	0.992645	−	0.121064i	$-0.0386308\pi$
$443$	22.0113	+	18.4697i	1.04579	+	0.877522i	0.0531457	+	0.998587i	$0.483075\pi$
$444$	−0.385005	+	8.86305i	−0.0182715	+	0.420622i
$445$	−10.3322	−	2.29059i	−0.489793	−	0.108585i
$446$	19.6691	−	3.46819i	0.931359	−	0.164224i
$447$	−36.3954	+	13.2559i	−1.72144	+	0.626985i
$448$	1.68439	−	5.34221i	0.0795801	−	0.252396i
$449$	−11.0547	−	8.48253i	−0.521701	−	0.400315i	0.314065	−	0.949402i	$-0.398309\pi$
$449$	−11.0547	−	8.48253i	−0.521701	−	0.400315i	−0.835766	+	0.549086i	$0.814976\pi$
$450$	1.27707		0.000564924i	0.0602016		2.66308e-5i
$451$	2.94104	−	0.788050i	0.138488	−	0.0371078i
$452$	−0.403881	+	0.370088i	−0.0189969	+	0.0174075i
$453$	−1.28790	+	0.345397i	−0.0605108	+	0.0162282i
$454$	−18.9806	+	5.98455i	−0.890802	+	0.280869i
$455$	−4.53158	+	12.4504i	−0.212444	+	0.583684i
$456$	4.61252	+	5.49452i	0.216001	+	0.257305i
$457$	18.5004	+	26.4213i	0.865412	+	1.23594i	0.970410	+	0.241464i	$0.0776275\pi$
$457$	18.5004	+	26.4213i	0.865412	+	1.23594i	−0.104998	+	0.994472i	$0.533484\pi$
$458$	9.69076			0.452819
$459$	−14.4470	−	15.8204i	−0.674326	−	0.738434i
$460$	14.5201			0.677001
$461$	−20.7957	−	29.6993i	−0.968552	−	1.38324i	−0.923223	−	0.384264i	$-0.874455\pi$
$461$	−20.7957	−	29.6993i	−0.968552	−	1.38324i	−0.0453289	−	0.998972i	$-0.514434\pi$
$462$	−0.321255	+	0.883250i	−0.0149462	+	0.0410925i
$463$	0.514575	−	1.41378i	0.0239144	−	0.0657041i	−0.927161	−	0.374663i	$-0.877758\pi$
$463$	0.514575	−	1.41378i	0.0239144	−	0.0657041i	0.951075	+	0.308959i	$0.0999806\pi$
$464$	2.38932	−	0.753351i	0.110922	−	0.0349735i
$465$	−0.546021	+	2.03958i	−0.0253211	+	0.0945834i
$466$	10.3341	−	9.46945i	0.478717	−	0.438664i
$467$	−2.72375	+	0.729827i	−0.126040	+	0.0337724i	−0.321288	−	0.946982i	$-0.604116\pi$
$467$	−2.72375	+	0.729827i	−0.126040	+	0.0337724i	0.195248	+	0.980754i	$0.437449\pi$
$468$	−2.42716	−	13.7296i	−0.112196	−	0.634651i
$469$	4.79248	+	3.67740i	0.221296	+	0.169807i
$470$	−3.57677	+	11.3441i	−0.164984	+	0.523263i
$471$	18.4653	+	15.4873i	0.850836	+	0.713615i
$472$	8.70873	−	1.53558i	0.400852	−	0.0706810i
$473$	1.48432	+	0.329066i	0.0682490	+	0.0151304i
$474$	11.7437	+	7.47789i	0.539404	+	0.343471i
$475$	0.666751	+	0.559471i	0.0305926	+	0.0256703i
$476$	−9.02839	+	6.28983i	−0.413816	+	0.288294i
$477$	12.2288	−	26.2551i	0.559920	−	1.20214i
$478$	0.704393	+	2.62883i	0.0322182	+	0.120240i
$479$	1.34199	−	30.7366i	0.0613170	−	1.40439i	−0.679988	−	0.733223i	$-0.738015\pi$
$479$	1.34199	−	30.7366i	0.0613170	−	1.40439i	0.741305	−	0.671168i	$-0.234207\pi$
$480$	−8.19316	−	19.7677i	−0.373965	−	0.902267i
$481$	−11.4990	+	3.62563i	−0.524311	+	0.165315i
$482$	0.345326	+	7.90926i	0.0157292	+	0.360257i
$483$	−13.2058	−	9.24248i	−0.600887	−	0.420547i
$484$	12.5029	−	8.75462i	0.568313	−	0.397937i
$485$	−24.8347	−	24.8347i	−1.12769	−	1.12769i
$486$	−11.9788	−	1.03466i	−0.543371	−	0.0469334i
$487$	1.87686	+	4.53113i	0.0850484	+	0.205325i	0.960682	−	0.277651i	$-0.0895559\pi$
$487$	1.87686	+	4.53113i	0.0850484	+	0.205325i	−0.875634	+	0.482976i	$0.839556\pi$
$488$	−16.3680	+	25.6926i	−0.740945	+	1.16305i
$489$	2.17196	−	1.38437i	0.0982194	−	0.0626032i
$490$	−3.72846	+	4.06890i	−0.168435	+	0.183814i
$491$	2.03404	−	23.2492i	0.0917950	−	1.04922i	−0.800972	−	0.598702i	$-0.795683\pi$
$491$	2.03404	−	23.2492i	0.0917950	−	1.04922i	0.892767	−	0.450519i	$-0.148761\pi$
$492$	18.4807	−	7.65973i	0.833173	−	0.345327i
$493$	12.3629	+	4.53301i	0.556795	+	0.204157i
$494$	−2.01165	+	3.48428i	−0.0905084	+	0.156765i
$495$	0.802541	+	2.20193i	0.0360716	+	0.0989695i
$496$	−0.449535	+	0.0591823i	−0.0201847	+	0.00265737i
$497$	2.30693	−	2.74929i	0.103480	−	0.123323i
$498$	2.34452	−	13.3137i	0.105061	−	0.596600i
$499$	−12.9556	+	8.25363i	−0.579973	+	0.369483i	−0.794527	−	0.607229i	$-0.792281\pi$
$499$	−12.9556	+	8.25363i	−0.579973	+	0.369483i	0.214554	+	0.976712i	$0.431170\pi$
$500$	−8.83995	−	13.8759i	−0.395335	−	0.620551i
$501$	−6.92272	−	13.2912i	−0.309284	−	0.593809i
$502$	1.23051	+	14.0648i	0.0549206	+	0.627745i
$503$	−25.8182	−	19.8110i	−1.15117	−	0.883328i	−0.156632	−	0.987657i	$-0.550064\pi$
$503$	−25.8182	−	19.8110i	−1.15117	−	0.883328i	−0.994543	+	0.104329i	$0.966730\pi$
$504$	−3.23252	+	14.6115i	−0.143988	+	0.650850i
$505$	3.71384	−	2.84973i	0.165264	−	0.126811i
$506$	0.478779	+	1.31543i	0.0212843	+	0.0584781i
$507$	−3.08916	+	1.78444i	−0.137194	+	0.0792496i
$508$	−0.820607	+	9.37959i	−0.0364086	+	0.416152i
$509$	−16.4744	−	5.99619i	−0.730214	−	0.265776i	−0.0499588	−	0.998751i	$-0.515909\pi$
$509$	−16.4744	−	5.99619i	−0.730214	−	0.265776i	−0.680256	+	0.732975i	$0.738131\pi$
$510$	3.03090	−	11.2147i	0.134211	−	0.496597i
$511$	0.856202	−	4.85577i	0.0378762	−	0.214806i
$512$	6.16295	−	6.16295i	0.272366	−	0.272366i
$513$	−5.79825	−	5.79056i	−0.255999	−	0.255659i
$514$			19.7267i			0.870109i
$515$	6.29009	−	9.87346i	0.277174	−	0.435076i
$516$	9.95137	+	0.868414i	0.438085	+	0.0382298i
$517$	2.70585	−	0.118140i	0.119003	−	0.00519579i
$518$	5.31978	+	0.465421i	0.233738	+	0.0204494i
$519$	−10.2773	+	7.88963i	−0.451122	+	0.346316i
$520$	13.5079	−	12.3777i	0.592359	−	0.542797i
$521$	−19.6974	−	2.59321i	−0.862958	−	0.113611i	−0.313962	−	0.949436i	$-0.601656\pi$
$521$	−19.6974	−	2.59321i	−0.862958	−	0.113611i	−0.548996	+	0.835825i	$0.684990\pi$
$522$	6.82603	−	2.83097i	0.298767	−	0.123908i
$523$	25.8997	−	14.9532i	1.13251	−	0.653857i	0.187948	−	0.982179i	$-0.439816\pi$
$523$	25.8997	−	14.9532i	1.13251	−	0.653857i	0.944566	+	0.328322i	$0.106483\pi$
$524$	5.35276	−	2.78647i	0.233836	−	0.121727i
$525$	−0.0787950	+	1.81391i	−0.00343890	+	0.0791655i
$526$	−3.07368	−	17.4317i	−0.134019	−	0.760059i
$527$	−2.06102	−	1.19647i	−0.0897794	−	0.0521190i
$528$	−0.370983	+	0.340094i	−0.0161450	+	0.0148007i
$529$	−1.00408	+	0.0878457i	−0.0436557	+	0.00381938i
$530$	15.5707	−	2.04992i	0.676348	−	0.0890430i
$531$	−9.75579	+	2.61868i	−0.423365	+	0.113641i
$532$	−3.33894	+	2.56206i	−0.144762	+	0.111079i
$533$	18.3686	+	20.0458i	0.795631	+	0.868279i
$534$	−1.73646	−	6.47484i	−0.0751441	−	0.280194i
$535$	2.53259	+	0.221573i	0.109493	+	0.00957943i
$536$	−3.53020	−	7.57055i	−0.152482	−	0.326998i
$537$	0.978359	−	11.2113i	0.0422193	−	0.483801i
$538$	10.5839	−	2.34638i	0.456302	−	0.101160i
$539$	1.16099	+	0.480899i	0.0500075	+	0.0207138i
$540$	7.11921	+	13.6537i	0.306362	+	0.587563i
$541$	2.16987	−	5.23854i	0.0932901	−	0.225222i	−0.870346	−	0.492441i	$-0.836105\pi$
$541$	2.16987	−	5.23854i	0.0932901	−	0.225222i	0.963636	+	0.267219i	$0.0861047\pi$
$542$	1.76823	+	2.52529i	0.0759518	+	0.108470i
$543$	−45.8019	+	2.00991i	−1.96555	+	0.0862533i
$544$	23.9530	−	3.09558i	1.02698	−	0.132722i
$545$	−24.0564	+	20.1857i	−1.03046	+	0.864661i
$546$	−8.32057	+	1.09730i	−0.356088	+	0.0469599i
$547$	−0.937536	+	21.4731i	−0.0400862	+	0.918124i	0.867290	+	0.497804i	$0.165860\pi$
$547$	−0.937536	+	21.4731i	−0.0400862	+	0.918124i	−0.907376	+	0.420320i	$0.861918\pi$
$548$	8.59164	+	4.96039i	0.367017	+	0.211897i
$549$	16.0540	−	30.8728i	0.685167	−	1.31762i
$550$	0.0959888	−	0.125095i	0.00409298	−	0.00533407i
$551$	4.80338	+	1.51450i	0.204631	+	0.0645199i
$552$	10.2963	+	19.7684i	0.438241	+	0.841398i
$553$	−11.3531	+	16.2139i	−0.482783	+	0.689486i
$554$	10.4479	+	16.3999i	0.443889	+	0.696766i
$555$	10.9062	−	7.64018i	0.462941	−	0.324307i
$556$	9.81158	+	18.8479i	0.416104	+	0.799328i
$557$	3.41268	−	1.97031i	0.144600	−	0.0834849i	−0.425954	−	0.904745i	$-0.640062\pi$
$557$	3.41268	−	1.97031i	0.144600	−	0.0834849i	0.570555	+	0.821260i	$0.306728\pi$
$558$	−1.30560	+	0.290050i	−0.0552704	+	0.0122788i
$559$	3.51379	+	13.1137i	0.148618	+	0.554649i
$560$	2.95284	−	1.07474i	0.124780	−	0.0454162i
$561$	−2.63567	+	0.224868i	−0.111278	+	0.00949392i
$562$	8.30094	−	6.96531i	0.350154	−	0.293814i
$563$	−8.72326	+	4.06772i	−0.367642	+	0.171434i	−0.597655	−	0.801753i	$-0.703901\pi$
$563$	−8.72326	+	4.06772i	−0.367642	+	0.171434i	0.230013	+	0.973187i	$0.426123\pi$
$564$	17.5241	−	3.09397i	0.737899	−	0.130280i
$565$	0.809760	+	0.142782i	0.0340668	+	0.00600690i
$566$	−13.8694	−	5.74488i	−0.582972	−	0.241475i
$567$	2.21620	−	16.9495i	0.0930715	−	0.711814i
$568$	−4.58501	+	1.89917i	−0.192383	+	0.0796875i
$569$	13.5971	−	9.52079i	0.570020	−	0.399132i	−0.252729	−	0.967537i	$-0.581328\pi$
$569$	13.5971	−	9.52079i	0.570020	−	0.399132i	0.822749	+	0.568405i	$0.192439\pi$
$570$	0.960767	−	4.33828i	0.0402421	−	0.181711i
$571$	−18.3387	+	0.800687i	−0.767452	+	0.0335077i	−0.424000	−	0.905662i	$-0.639374\pi$
$571$	−18.3387	+	0.800687i	−0.767452	+	0.0335077i	−0.343453	+	0.939170i	$0.611597\pi$
$572$	−1.52696	−	0.794886i	−0.0638454	−	0.0332358i
$573$	22.8567	−	0.00505544i	0.954852	−	0.000211194i
$574$	−4.11861	−	11.3158i	−0.171908	−	0.472312i
$575$	1.64624	+	2.14542i	0.0686528	+	0.0894701i
$576$	5.68414	−	6.78019i	0.236839	−	0.282508i
$577$	11.5868	+	20.0689i	0.482364	+	0.835479i	0.999795	−	0.0202459i	$-0.00644491\pi$
$577$	11.5868	+	20.0689i	0.482364	+	0.835479i	−0.517431	+	0.855725i	$0.673112\pi$
$578$	11.3242	+	6.60998i	0.471024	+	0.274939i
$579$	2.70323	+	12.1807i	0.112342	+	0.506214i
$580$	−7.75249	−	5.42835i	−0.321905	−	0.225400i
$581$	18.7638	+	4.15984i	0.778454	+	0.172579i
$582$	6.68514	−	21.2189i	0.277108	−	0.879552i
$583$	−1.65125	−	3.17203i	−0.0683879	−	0.131372i
$584$	−4.15060	+	5.40917i	−0.171753	+	0.223833i
$585$	−14.1318	+	15.4358i	−0.584276	+	0.638192i
$586$	−19.0171	+	5.09562i	−0.785590	+	0.210498i
$587$	−10.2573	−	4.78307i	−0.423366	−	0.197419i	0.199246	−	0.979949i	$-0.436151\pi$
$587$	−10.2573	−	4.78307i	−0.423366	−	0.197419i	−0.622612	+	0.782531i	$0.713928\pi$
$588$	7.97570	+	2.13519i	0.328912	+	0.0880538i
$589$	−0.808528	−	0.420893i	−0.0333148	−	0.0173426i
$590$	−4.03824	−	3.70037i	−0.166252	−	0.152342i
$591$	−1.29719	−	29.5606i	−0.0533594	−	1.21596i
$592$	2.41172	+	1.53644i	0.0991211	+	0.0631471i
$593$	−15.3484	+	15.3484i	−0.630283	+	0.630283i	−0.948139	−	0.317856i	$-0.897037\pi$
$593$	−15.3484	+	15.3484i	−0.630283	+	0.630283i	0.317856	+	0.948139i	$0.397037\pi$
$594$	−1.00220	+	1.09517i	−0.0411209	+	0.0449355i
$595$	15.7398	+	5.00391i	0.645271	+	0.205140i
$596$	−5.45643	+	30.9450i	−0.223504	+	1.26756i
$597$	−14.1039	−	44.6974i	−0.577234	−	1.82934i
$598$	−8.44502	+	9.21612i	−0.345343	+	0.376875i
$599$	10.8373	+	12.9153i	0.442799	+	0.527707i	0.940569	−	0.339602i	$-0.110292\pi$
$599$	10.8373	+	12.9153i	0.442799	+	0.527707i	−0.497771	+	0.867309i	$0.665848\pi$
$600$	1.25483	−	2.17455i	0.0512284	−	0.0887755i
$601$	−5.39065	−	5.88286i	−0.219889	−	0.239967i	0.617504	−	0.786567i	$-0.288144\pi$
$601$	−5.39065	−	5.88286i	−0.219889	−	0.239967i	−0.837393	+	0.546601i	$0.815922\pi$
$602$	0.784847	−	5.96151i	0.0319880	−	0.242973i
$603$	4.77443	+	8.26111i	0.194430	+	0.336418i
$604$	−0.279965	+	1.04484i	−0.0113916	+	0.0425141i
$605$	−21.8498	−	6.88922i	−0.888322	−	0.280087i
$606$	2.68767	+	1.25256i	0.109179	+	0.0508818i
$607$	0.162180	−	0.731547i	0.00658269	−	0.0296926i	−0.972892	−	0.231261i	$-0.925715\pi$
$607$	0.162180	−	0.731547i	0.00658269	−	0.0296926i	0.979474	+	0.201568i	$0.0646038\pi$
$608$	9.09758	−	1.60415i	0.368956	−	0.0650569i
$609$	3.59549	+	9.87173i	0.145697	+	0.400023i
$610$	18.7967	−	1.64450i	0.761056	−	0.0665838i
$611$	12.0927	+	20.9451i	0.489216	+	0.847347i
$612$	−16.9753	+	3.72889i	−0.686185	+	0.150732i
$613$	−5.73710	+	9.93695i	−0.231719	+	0.401350i	−0.958314	−	0.285716i	$-0.907768\pi$
$613$	−5.73710	+	9.93695i	−0.231719	+	0.401350i	0.726595	+	0.687066i	$0.241102\pi$
$614$	−10.3466	+	22.1883i	−0.417553	+	0.895445i
$615$	−26.0082	−	15.0082i	−1.04875	−	0.605189i
$616$	1.18768	+	1.41542i	0.0478529	+	0.0570288i
$617$	−2.91968	−	2.67539i	−0.117542	−	0.107707i	0.614669	−	0.788785i	$-0.289289\pi$
$617$	−2.91968	−	2.67539i	−0.117542	−	0.107707i	−0.732211	+	0.681078i	$0.761512\pi$
$618$	7.38741	+	0.644668i	0.297165	+	0.0259323i
$619$	7.36464	+	33.2198i	0.296010	+	1.33521i	0.860363	+	0.509681i	$0.170237\pi$
$619$	7.36464	+	33.2198i	0.296010	+	1.33521i	−0.564353	+	0.825533i	$0.690874\pi$
$620$	1.21116	+	1.21116i	0.0486412	+	0.0486412i
$621$	−13.6939	−	21.4637i	−0.549518	−	0.861309i
$622$	3.81019	−	1.57823i	0.152775	−	0.0632814i
$623$	9.30470	−	2.06280i	0.372785	−	0.0826445i
$624$	−4.22344	−	1.53615i	−0.169073	−	0.0614951i
$625$	−7.50250	+	20.6130i	−0.300100	+	0.824518i
$626$	−0.0144136	−	0.0457142i	−0.000576084	−	0.00182710i
$627$	−1.00309	+	0.132285i	−0.0400594	+	0.00528294i
$628$	18.3718	−	6.68678i	0.733114	−	0.266832i
$629$	5.10690	+	14.1355i	0.203625	+	0.563621i
$630$	8.39878	−	3.92094i	0.334615	−	0.156214i
$631$	−9.62294	−	2.57846i	−0.383083	−	0.102647i	0.0621378	−	0.998068i	$-0.480208\pi$
$631$	−9.62294	−	2.57846i	−0.383083	−	0.102647i	−0.445221	+	0.895421i	$0.646875\pi$
$632$	24.2779	−	12.6382i	0.965721	−	0.502723i
$633$	9.37830	−	29.7671i	0.372754	−	1.18314i
$634$	1.10518	−	4.98514i	0.0438923	−	0.197985i
$635$	11.9193	−	7.59344i	0.473003	−	0.301336i
$636$	−13.4810	−	19.2437i	−0.534555	−	0.763064i
$637$	0.978014	+	11.1787i	0.0387503	+	0.442918i
$638$	0.236150	−	0.881323i	0.00934926	−	0.0348919i
$639$	5.02713	−	2.61979i	0.198870	−	0.103637i
$640$	−19.7408	−	2.59893i	−0.780324	−	0.102732i
$641$	−26.4921	−	1.15667i	−1.04638	−	0.0456857i	−0.486028	−	0.873943i	$-0.661555\pi$
$641$	−26.4921	−	1.15667i	−1.04638	−	0.0456857i	−0.560348	+	0.828258i	$0.689332\pi$
$642$	0.616583	+	1.48763i	0.0243346	+	0.0587122i
$643$	−8.79091	−	27.8812i	−0.346680	−	1.09953i	−0.952657	−	0.304046i	$-0.901662\pi$
$643$	−8.79091	−	27.8812i	−0.346680	−	1.09953i	0.605978	−	0.795481i	$-0.292782\pi$
$644$	−11.8510	+	5.52619i	−0.466993	+	0.217763i
$645$	−8.05898	−	12.6439i	−0.317322	−	0.497853i
$646$	4.44306	+	2.32635i	0.174810	+	0.0915289i
$647$	21.4217			0.842173			0.421087	−	0.907020i	$-0.361649\pi$
$647$	21.4217			0.842173			0.421087	+	0.907020i	$0.361649\pi$
$648$	−13.5406	+	19.3745i	−0.531926	+	0.761101i
$649$	−0.477275	+	1.15224i	−0.0187347	+	0.0452296i
$650$	1.38663	+	0.244500i	0.0543880	+	0.00959006i
$651$	−0.330595	−	1.87247i	−0.0129570	−	0.0733881i
$652$	−0.0911395	−	2.08744i	−0.00356930	−	0.0817504i
$653$	−15.1275	+	29.0597i	−0.591986	+	1.13719i	0.384804	+	0.922998i	$0.374269\pi$
$653$	−15.1275	+	29.0597i	−0.591986	+	1.13719i	−0.976791	+	0.214197i	$0.931287\pi$
$654$	−18.3794	−	7.60823i	−0.718691	−	0.297505i
$655$	−8.20932	−	3.82807i	−0.320765	−	0.149575i
$656$	0.841676	−	6.39317i	0.0328619	−	0.249611i
$657$	4.18163	−	6.57026i	0.163141	−	0.256330i
$658$	−1.39816	−	10.6201i	−0.0545059	−	0.414013i
$659$	23.4554	−	27.9531i	0.913695	−	1.08890i	−0.0820395	−	0.996629i	$-0.526143\pi$
$659$	23.4554	−	27.9531i	0.913695	−	1.08890i	0.995734	−	0.0922697i	$-0.0294122\pi$
$660$	1.87241	+	0.329729i	0.0728833	+	0.0128347i
$661$	15.7682	+	11.0410i	0.613313	+	0.429446i	0.838525	−	0.544864i	$-0.183419\pi$
$661$	15.7682	+	11.0410i	0.613313	+	0.429446i	−0.225212	+	0.974310i	$0.572307\pi$
$662$	−1.90877	−	10.8252i	−0.0741864	−	0.420732i
$663$	−12.6486	−	19.9491i	−0.491232	−	0.774760i
$664$	−20.3588	−	17.0830i	−0.790073	−	0.662950i
$665$	6.10195	+	1.63501i	0.236624	+	0.0634031i
$666$	7.48347	+	3.89144i	0.289979	+	0.150790i
$667$	13.5517	+	7.82407i	0.524723	+	0.302949i
$668$	−12.1455	−	0.530285i	−0.469925	−	0.0205174i
$669$	−11.5986	+	43.3249i	−0.448428	+	1.67504i
$670$	−2.38900	+	4.58922i	−0.0922949	+	0.177297i
$671$	−1.81574	−	3.89387i	−0.0700959	−	0.150321i
$672$	14.2105	+	13.0157i	0.548181	+	0.502092i
$673$	−2.65092	−	11.9575i	−0.102186	−	0.460929i	−0.999797	−	0.0201420i	$-0.993588\pi$
$673$	−2.65092	−	11.9575i	−0.102186	−	0.460929i	0.897612	−	0.440787i	$-0.145301\pi$
$674$	−3.38502	−	8.17216i	−0.130386	−	0.314780i
$675$	−1.21026	+	2.59992i	−0.0465830	+	0.100071i
$676$			2.89406i			0.111310i
$677$	−1.06609	−	0.679171i	−0.0409730	−	0.0261027i	0.516655	−	0.856194i	$-0.327177\pi$
$677$	−1.06609	−	0.679171i	−0.0409730	−	0.0261027i	−0.557628	+	0.830091i	$0.688288\pi$
$678$	0.156729	+	0.496699i	0.00601916	+	0.0190756i
$679$	29.7214	+	10.8177i	1.14060	+	0.415145i
$680$	−16.1108	−	16.1875i	−0.617819	−	0.620763i
$681$	5.82361	−	44.3104i	0.223161	−	1.69798i
$682$	−0.0697876	+	0.149660i	−0.00267231	+	0.00573078i
$683$	17.0343	+	22.1995i	0.651799	+	0.849441i	0.995991	−	0.0894588i	$-0.0285137\pi$
$683$	17.0343	+	22.1995i	0.651799	+	0.849441i	−0.344192	+	0.938899i	$0.611847\pi$
$684$	−6.42036	+	1.72338i	−0.245489	+	0.0658949i
$685$	−1.94369	−	14.7638i	−0.0742644	−	0.564094i
$686$	4.57813	−	14.5200i	0.174794	−	0.554376i
$687$	−9.19253	+	19.7248i	−0.350717	+	0.752549i
$688$	1.84683	−	2.63755i	0.0704097	−	0.100556i
$689$	18.3161	−	26.1581i	0.697789	−	0.996545i
$690$	5.83166	−	12.5133i	0.222008	−	0.476372i
$691$	12.4013	−	39.3318i	0.471767	−	1.49625i	−0.355625	−	0.934629i	$-0.615732\pi$
$691$	12.4013	−	39.3318i	0.471767	−	1.49625i	0.827392	−	0.561625i	$-0.189824\pi$
$692$	1.37191	+	10.4207i	0.0521522	+	0.396135i
$693$	−1.49305	−	1.49173i	−0.0567164	−	0.0566662i
$694$	−1.42300	−	1.85449i	−0.0540162	−	0.0703953i
$695$	13.4792	−	28.9063i	0.511295	−	1.09648i
$696$	1.89307	−	14.4039i	0.0717568	−	0.545980i
$697$	24.0224	−	23.9085i	0.909913	−	0.905599i
$698$	10.9642	+	3.99066i	0.415002	+	0.151049i
$699$	9.47159	+	30.0169i	0.358248	+	1.13534i
$700$	1.24222	+	0.791380i	0.0469514	+	0.0299113i
$701$			40.7151i			1.53779i	0.639377	+	0.768893i	$0.279192\pi$
$701$			40.7151i			1.53779i	−0.639377	+	0.768893i	$0.720808\pi$
$702$	−12.8069	−	3.42248i	−0.483364	−	0.129173i
$703$	2.19993	+	5.31110i	0.0829720	+	0.200312i
$704$	−0.236441	−	1.06652i	−0.00891120	−	0.0401958i
$705$	−19.6971	−	18.0411i	−0.741837	−	0.679467i
$706$	−3.80644	−	8.16294i	−0.143257	−	0.307216i
$707$	−1.94658	+	3.73934i	−0.0732086	+	0.140632i
$708$	−2.11910	+	7.91559i	−0.0796407	+	0.297486i
$709$	−29.3508	−	1.28148i	−1.10229	−	0.0481272i	−0.514765	−	0.857331i	$-0.672121\pi$
$709$	−29.3508	−	1.28148i	−1.10229	−	0.0481272i	−0.587528	+	0.809204i	$0.699899\pi$
$710$	2.66203	+	1.53693i	0.0999043	+	0.0576798i
$711$	−26.3606	+	16.8099i	−0.988599	+	0.630422i
$712$	−12.7298	−	3.41095i	−0.477071	−	0.127831i
$713$	−2.16948	−	1.82041i	−0.0812476	−	0.0681749i
$714$	1.79446	+	10.3068i	0.0671561	+	0.385721i
$715$	0.448696	+	2.54468i	0.0167803	+	0.0951656i
$716$	−7.47841	−	5.23644i	−0.279481	−	0.195695i
$717$	−6.01897	−	1.05993i	−0.224783	−	0.0395840i
$718$	−7.36491	+	8.77716i	−0.274856	+	0.327561i
$719$	−3.53914	−	26.8824i	−0.131988	−	1.00255i	−0.921382	−	0.388659i	$-0.872939\pi$
$719$	−3.53914	−	26.8824i	−0.131988	−	1.00255i	0.789394	−	0.613887i	$-0.210395\pi$
$720$	4.95876	+	0.214306i	0.184802	+	0.00798673i
$721$	−1.37609	+	10.4525i	−0.0512483	+	0.389270i
$722$	−11.5432	−	5.38268i	−0.429593	−	0.200323i
$723$	−16.4263	−	6.79973i	−0.610900	−	0.252885i
$724$	−17.1732	+	32.9894i	−0.638236	+	1.22604i
$725$	−0.0768835	−	1.76092i	−0.00285538	−	0.0653990i
$726$	−2.52315	−	14.2910i	−0.0936428	−	0.530388i
$727$	27.1404	+	4.78558i	1.00658	+	0.177487i	0.652550	−	0.757746i	$-0.273699\pi$
$727$	27.1404	+	4.78558i	1.00658	+	0.177487i	0.354032	+	0.935233i	$0.384810\pi$
$728$	−6.31400	+	15.2434i	−0.234013	+	0.564956i
$729$	13.4690	−	23.4006i	0.498850	−	0.866688i
$730$	4.22301			0.156301
$731$	16.1523	−	5.05062i	0.597413	−	0.186804i
$732$	−15.1725	−	23.8044i	−0.560792	−	0.879837i
$733$	39.3028	−	18.3272i	1.45168	−	0.676931i	0.472766	−	0.881188i	$-0.343256\pi$
$733$	39.3028	−	18.3272i	1.45168	−	0.676931i	0.978917	+	0.204258i	$0.0654780\pi$
$734$	6.93257	+	21.9873i	0.255886	+	0.811566i
$735$	−4.74519	−	11.4487i	−0.175029	−	0.422293i
$736$	28.6745	+	1.25196i	1.05696	+	0.0461478i
$737$	1.16801	+	0.153771i	0.0430242	+	0.00566424i
$738$	0.821261	−	19.0029i	0.0302310	−	0.699505i
$739$	−11.1550	+	41.6312i	−0.410345	+	1.53143i	0.383635	+	0.923485i	$0.374672\pi$
$739$	−11.1550	+	41.6312i	−0.410345	+	1.53143i	−0.793980	+	0.607944i	$0.791995\pi$
$740$	−0.941488	−	10.7613i	−0.0346098	−	0.395591i
$741$	−5.18377	−	7.39971i	−0.190431	−	0.271835i
$742$	−11.9283	+	7.59917i	−0.437902	+	0.278974i
$743$	−7.69697	+	34.7188i	−0.282375	+	1.27371i	0.598792	+	0.800904i	$0.295647\pi$
$743$	−7.69697	+	34.7188i	−0.282375	+	1.27371i	−0.881167	+	0.472805i	$0.843241\pi$
$744$	−0.790089	+	2.50778i	−0.0289661	+	0.0919396i
$745$	41.8360	−	21.7784i	1.53275	−	0.797901i
$746$	−19.0677	−	5.10918i	−0.698119	−	0.187060i
$747$	24.8750	+	17.4013i	0.910130	+	0.636680i
$748$	−0.911515	+	1.94268i	−0.0333283	+	0.0710315i
$749$	−2.15137	+	0.783036i	−0.0786095	+	0.0286115i
$750$	−15.5086	+	2.04523i	−0.566292	+	0.0746812i
$751$	−13.6682	−	43.3499i	−0.498758	−	1.58186i	−0.782302	−	0.622900i	$-0.785954\pi$
$751$	−13.6682	−	43.3499i	−0.498758	−	1.58186i	0.283544	−	0.958959i	$-0.408490\pi$
$752$	1.96182	−	5.39005i	0.0715401	−	0.196555i
$753$	−29.7952	−	10.8371i	−1.08580	−	0.394926i
$754$	7.95440	−	1.76345i	0.289682	−	0.0642210i
$755$	1.50005	−	0.621341i	0.0545924	−	0.0226129i
$756$	−11.0070	−	8.43439i	−0.400322	−	0.306756i
$757$	22.8209	+	22.8209i	0.829441	+	0.829441i	0.987439	−	0.157998i	$-0.0505041\pi$
$757$	22.8209	+	22.8209i	0.829441	+	0.829441i	−0.157998	+	0.987439i	$0.550504\pi$
$758$	−1.38196	−	6.23360i	−0.0501949	−	0.226415i
$759$	−3.13163	−	0.273284i	−0.113671	−	0.00991959i
$760$	−6.44041	−	5.90155i	−0.233618	−	0.214072i
$761$	7.47222	+	8.90505i	0.270868	+	0.322808i	0.884282	−	0.466954i	$-0.154649\pi$
$761$	7.47222	+	8.90505i	0.270868	+	0.322808i	−0.613414	+	0.789762i	$0.710204\pi$
$762$	7.75367	+	4.47430i	0.280886	+	0.162087i
$763$	11.9518	−	25.6308i	0.432686	−	0.927897i
$764$	9.27101	−	16.0579i	0.335413	−	0.580953i
$765$	19.9517	+	16.8073i	0.721356	+	0.607671i
$766$	−8.28320	−	14.3469i	−0.299284	−	0.518375i
$767$	−11.0945	+	0.970643i	−0.400599	+	0.0350479i
$768$	−7.81262	−	21.4502i	−0.281914	−	0.774018i
$769$	18.2185	−	3.21241i	0.656975	−	0.115842i	0.164784	−	0.986330i	$-0.447307\pi$
$769$	18.2185	−	3.21241i	0.656975	−	0.115842i	0.492191	+	0.870487i	$0.336196\pi$
$770$	0.247700	−	1.11730i	0.00892648	−	0.0402648i
$771$	−40.1523	−	18.7125i	−1.44605	−	0.673915i
$772$	9.65332	+	3.04368i	0.347430	+	0.109544i
$773$	−3.67349	+	13.7097i	−0.132126	+	0.493102i	−0.999993	−	0.00369477i	$-0.998824\pi$
$773$	−3.67349	+	13.7097i	−0.132126	+	0.493102i	0.867867	+	0.496797i	$0.165491\pi$
$774$	4.74514	−	8.22723i	0.170561	−	0.295722i
$775$	−0.0416380	+	0.316272i	−0.00149568	+	0.0113608i
$776$	−29.5478	−	32.2457i	−1.06070	−	1.15755i
$777$	−5.99361	+	10.3865i	−0.215019	+	0.372615i
$778$	3.77137	+	4.49454i	0.135210	+	0.161137i
$779$	8.75795	−	9.55763i	0.313786	−	0.342438i
$780$	5.10873	+	16.1903i	0.182922	+	0.579706i
$781$	0.121540	−	0.689290i	0.00434906	−	0.0246647i
$782$	11.9128	+	10.0444i	0.426000	+	0.359185i
$783$	−0.712846	+	16.5793i	−0.0254751	+	0.592496i
$784$	1.88187	−	1.88187i	0.0672096	−	0.0672096i
$785$	−24.7501	−	15.7676i	−0.883369	−	0.562768i
$786$	−0.251539	−	5.73209i	−0.00897209	−	0.204457i
$787$	13.9206	+	12.7559i	0.496217	+	0.454699i	0.884296	−	0.466927i	$-0.154639\pi$
$787$	13.9206	+	12.7559i	0.496217	+	0.454699i	−0.388079	+	0.921626i	$0.626861\pi$
$788$	−21.2913	−	11.0836i	−0.758472	−	0.394836i
$789$	38.3966	+	10.2792i	1.36696	+	0.365951i
$790$	−15.3644	−	7.16453i	−0.546640	−	0.254903i
$791$	−0.715250	+	0.191651i	−0.0254314	+	0.00681432i
$792$	0.878833	+	2.78301i	0.0312280	+	0.0988899i
$793$	23.3554	−	30.4373i	0.829374	−	1.08086i
$794$	0.475844	+	0.914088i	0.0168871	+	0.0324398i
$795$	−10.5977	+	33.6376i	−0.375862	+	1.19300i
$796$	−37.1209	−	8.22950i	−1.31571	−	0.291687i
$797$	3.01551	+	2.11148i	0.106815	+	0.0747926i	0.625764	−	0.780013i	$-0.284788\pi$
$797$	3.01551	+	2.11148i	0.106815	+	0.0747926i	−0.518949	+	0.854805i	$0.673676\pi$
$798$	0.866951	+	3.90647i	0.0306897	+	0.138288i
$799$	25.4652	−	16.1381i	0.900893	−	0.570926i
$800$	−1.61648	−	2.79983i	−0.0571512	−	0.0989888i
$801$	14.8262	+	2.60750i	0.523860	+	0.0921317i
$802$	−6.52367	−	8.50181i	−0.230359	−	0.300209i
$803$	−0.328883	−	0.903599i	−0.0116060	−	0.0318873i
$804$	7.74038	−	0.00171202i	0.272982	−	6.03781e-5i
$805$	17.4096	+	9.06288i	0.613609	+	0.319424i
$806$	−1.47316	+	0.0643197i	−0.0518900	+	0.00226557i
$807$	−5.26382	+	23.7684i	−0.185295	+	0.836688i
$808$	4.77517	−	3.34361i	0.167990	−	0.117628i
$809$	−26.6689	+	11.0466i	−0.937628	+	0.388378i	−0.798567	−	0.601906i	$-0.794408\pi$
$809$	−26.6689	+	11.0466i	−0.937628	+	0.388378i	−0.139061	+	0.990284i	$0.544408\pi$
$810$	14.6260	−	0.651548i	0.513904	−	0.0228931i
$811$	−40.4470	−	16.7537i	−1.42029	−	0.588302i	−0.465353	−	0.885125i	$-0.654073\pi$
$811$	−40.4470	−	16.7537i	−1.42029	−	0.588302i	−0.954932	+	0.296824i	$0.904073\pi$
$812$	8.39339	+	1.47998i	0.294550	+	0.0519372i
$813$	−6.81736	+	1.20364i	−0.239095	+	0.0422135i
$814$	0.943863	−	0.440131i	0.0330824	−	0.0154266i
$815$	−2.40250	+	2.01594i	−0.0841560	+	0.0706153i
$816$	−1.69611	+	5.33923i	−0.0593758	+	0.186910i
$817$	6.08266	−	2.21391i	0.212805	−	0.0774547i
$818$	1.14642	+	4.27848i	0.0400835	+	0.149594i
$819$	5.65932	−	17.9768i	0.197753	−	0.628160i
$820$	−21.0959	+	12.1797i	−0.736702	+	0.425335i
$821$	7.20288	+	13.8366i	0.251382	+	0.482901i	0.979207	−	0.202862i	$-0.0650243\pi$
$821$	7.20288	+	13.8366i	0.251382	+	0.482901i	−0.727825	+	0.685763i	$0.759469\pi$
$822$	7.72547	−	5.41198i	0.269457	−	0.188764i
$823$	4.40511	+	6.91464i	0.153553	+	0.241029i	0.911513	−	0.411271i	$-0.134915\pi$
$823$	4.40511	+	6.91464i	0.153553	+	0.241029i	−0.757960	+	0.652301i	$0.773804\pi$
$824$	8.36178	−	11.9419i	0.291296	−	0.416014i
$825$	0.163568	+	0.314042i	0.00569471	+	0.0109335i
$826$	4.70425	+	1.48324i	0.163682	+	0.0516087i
$827$	−30.5647	+	39.8327i	−1.06284	+	1.38512i	−0.144418	+	0.989517i	$0.546131\pi$
$827$	−30.5647	+	39.8327i	−1.06284	+	1.38512i	−0.918422	+	0.395603i	$0.870536\pi$
$828$	−20.6339	+	0.910039i	−0.717077	+	0.0316261i
$829$	−47.2945	−	27.3055i	−1.64261	−	0.948360i	−0.979902	−	0.199479i	$-0.936075\pi$
$829$	−47.2945	−	27.3055i	−1.64261	−	0.948360i	−0.662705	−	0.748880i	$-0.730592\pi$
$830$	−0.718018	+	16.4453i	−0.0249228	+	0.570825i
$831$	−43.2916	+	5.70919i	−1.50177	+	0.198050i
$832$	7.47264	−	6.27029i	0.259067	−	0.217383i
$833$	13.8727	−	1.79285i	0.480662	−	0.0621185i
$834$	20.1836	−	0.885706i	0.698899	−	0.0306695i
$835$	10.4666	+	14.9478i	0.362210	+	0.517290i
$836$	−0.314099	+	0.758301i	−0.0108633	+	0.0262264i
$837$	0.648099	−	2.93259i	0.0224016	−	0.101365i
$838$	26.2993	+	10.8935i	0.908494	+	0.376311i
$839$	17.5875	−	3.89905i	0.607187	−	0.134610i	0.0978848	−	0.995198i	$-0.468792\pi$
$839$	17.5875	−	3.89905i	0.607187	−	0.134610i	0.509303	+	0.860588i	$0.329903\pi$
$840$	1.58414	−	18.1531i	0.0546582	−	0.626341i
$841$	7.94551	+	17.0392i	0.273983	+	0.587559i
$842$	26.5119	+	2.31949i	0.913660	+	0.0799349i
$843$	6.30323	+	23.5032i	0.217095	+	0.809492i
$844$	−17.1046	−	18.6664i	−0.588766	−	0.642525i
$845$	3.44633	−	2.64447i	0.118558	−	0.0909724i
$846$	4.37182	−	16.3448i	0.150306	−	0.561945i
$847$	20.4553	−	2.69300i	0.702854	−	0.0925325i
$848$	−7.54470	+	0.660076i	−0.259086	+	0.0226671i
$849$	24.8496	−	22.7805i	0.852835	−	0.781826i
$850$	0.233230	−	1.73960i	0.00799972	−	0.0596678i
$851$	3.10152	+	17.5896i	0.106319	+	0.602964i
$852$	0.199576	−	4.59437i	0.00683737	−	0.157400i
$853$	6.57031	−	3.42029i	0.224963	−	0.117108i	−0.345539	−	0.938404i	$-0.612304\pi$
$853$	6.57031	−	3.42029i	0.224963	−	0.117108i	0.570503	+	0.821296i	$0.306748\pi$
$854$	−14.7156	+	8.49605i	−0.503557	+	0.290729i
$855$	7.91888	+	6.07081i	0.270820	+	0.207617i
$856$	3.13875	+	0.413224i	0.107280	+	0.0141237i
$857$	−1.94903	+	1.78596i	−0.0665776	+	0.0610071i	−0.708190	−	0.706022i	$-0.750488\pi$
$857$	−1.94903	+	1.78596i	−0.0665776	+	0.0610071i	0.641612	+	0.767029i	$0.278266\pi$
$858$	−1.29830	+	0.996674i	−0.0443231	+	0.0340259i
$859$	−35.1708	−	3.07705i	−1.20001	−	0.104987i	−0.530432	−	0.847727i	$-0.677970\pi$
$859$	−35.1708	−	3.07705i	−1.20001	−	0.104987i	−0.669580	+	0.742740i	$0.733526\pi$
$860$	−12.1519	+	0.530562i	−0.414375	+	0.0180920i
$861$	26.9393	+	2.35088i	0.918090	+	0.0801179i
$862$	2.75602	−	4.32608i	0.0938704	−	0.147347i
$863$			8.33045i			0.283572i	0.989897	+	0.141786i	$0.0452844\pi$
$863$			8.33045i			0.283572i	−0.989897	+	0.141786i	$0.954716\pi$
$864$	12.8819	+	27.5776i	0.438252	+	0.938208i
$865$	11.1557	−	11.1557i	0.379304	−	0.379304i
$866$	5.04433	−	28.6078i	0.171413	−	0.972132i
$867$	−24.1961	+	16.7794i	−0.821743	+	0.569858i
$868$	−1.44948	−	0.527566i	−0.0491984	−	0.0179068i
$869$	−0.336437	+	3.84549i	−0.0114128	+	0.130449i
$870$	−7.79173	+	4.50085i	−0.264164	+	0.152593i
$871$	3.59802	+	9.88548i	0.121914	+	0.334957i
$872$	−31.0249	+	23.8063i	−1.05064	+	0.806182i
$873$	36.8481	+	33.7351i	1.24712	+	1.14176i
$874$	4.72837	+	3.62821i	0.159939	+	0.122726i
$875$	−1.93830	−	22.1549i	−0.0655266	−	0.748972i
$876$	−2.91853	−	5.60342i	−0.0986081	−	0.189322i
$877$	2.56280	+	4.02280i	0.0865397	+	0.135840i	0.883922	−	0.467634i	$-0.154894\pi$
$877$	2.56280	+	4.02280i	0.0865397	+	0.135840i	−0.797382	+	0.603475i	$0.793782\pi$
$878$	−24.1352	+	15.3758i	−0.814523	+	0.518908i
$879$	7.66763	−	43.5416i	0.258623	−	1.46862i
$880$	0.393917	−	0.469452i	0.0132789	−	0.0158252i
$881$	−45.7738	+	6.02623i	−1.54216	+	0.203029i	−0.853127	−	0.521703i	$-0.825297\pi$
$881$	−45.7738	+	6.02623i	−1.54216	+	0.203029i	−0.689031	+	0.724732i	$0.741963\pi$
$882$	5.04335	−	6.01584i	0.169819	−	0.202564i
$883$	4.08636	−	7.07778i	0.137517	−	0.238186i	−0.789039	−	0.614343i	$-0.789421\pi$
$883$	4.08636	−	7.07778i	0.137517	−	0.238186i	0.926556	+	0.376157i	$0.122755\pi$
$884$	−19.1458	+	0.790340i	−0.643943	+	0.0265820i
$885$	11.3625	−	4.70943i	0.381945	−	0.158306i
$886$	1.93159	−	22.0781i	0.0648929	−	0.741729i
$887$	4.08343	−	4.45628i	0.137108	−	0.149627i	−0.664918	−	0.746917i	$-0.731533\pi$
$887$	4.08343	−	4.45628i	0.137108	−	0.149627i	0.802026	+	0.597289i	$0.203756\pi$
$888$	13.9833	−	8.91271i	0.469250	−	0.299091i
$889$	−6.83830	+	10.7340i	−0.229349	+	0.360006i
$890$	3.12375	+	7.54141i	0.104708	+	0.252789i
$891$	−1.27846	−	3.07878i	−0.0428302	−	0.103143i
$892$	25.7274	+	25.7274i	0.861419	+	0.861419i
$893$	9.44590	−	6.61409i	0.316095	−	0.221332i
$894$	24.4767	+	17.1307i	0.818623	+	0.572936i
$895$	0.597733	+	13.6903i	0.0199800	+	0.457617i
$896$	17.1012	−	5.39197i	0.571309	−	0.180133i
$897$	−10.7479	−	25.9315i	−0.358862	−	0.865828i
$898$	−0.468796	+	10.7372i	−0.0156439	+	0.358304i
$899$	0.477756	+	1.78301i	0.0159341	+	0.0594667i
$900$	1.33524	+	1.90512i	0.0445079	+	0.0635041i
$901$	−33.5214	−	21.4676i	−1.11676	−	0.715191i
$902$	−1.79902	−	1.50956i	−0.0599010	−	0.0502629i
$903$	11.3897	+	7.25251i	0.379026	+	0.241348i
$904$	0.999663	+	0.221620i	0.0332483	+	0.00737097i
$905$	54.9768	−	9.69389i	1.82749	−	0.322236i
$906$	0.787997	+	0.660911i	0.0261794	+	0.0219573i
$907$	8.01995	−	25.4360i	0.266298	−	0.844590i	−0.721979	−	0.691915i	$-0.756767\pi$
$907$	8.01995	−	25.4360i	0.266298	−	0.844590i	0.988277	−	0.152674i	$-0.0487885\pi$
$908$	−28.7630	−	22.0707i	−0.954535	−	0.732440i
$909$	−5.09899	+	4.28240i	−0.169123	+	0.142038i
$910$	9.87114	−	2.64496i	0.327225	−	0.0876797i
$911$	20.3072	−	18.6081i	0.672808	−	0.616515i	−0.264761	−	0.964314i	$-0.585293\pi$
$911$	20.3072	−	18.6081i	0.672808	−	0.616515i	0.937569	+	0.347799i	$0.113071\pi$
$912$	−0.554128	+	2.06987i	−0.0183490	+	0.0685401i
$913$	3.57473	−	1.12711i	0.118306	−	0.0373018i
$914$	8.50877	−	23.3777i	0.281445	−	0.773264i
$915$	−14.4831	+	39.8193i	−0.478795	+	1.31638i
$916$	10.1258	+	14.4611i	0.334565	+	0.477808i
$917$	8.15720			0.269374
$918$	−3.60422	+	16.1268i	−0.118957	+	0.532263i
$919$	6.90562			0.227795			0.113898	−	0.993492i	$-0.463666\pi$
$919$	6.90562			0.227795			0.113898	+	0.993492i	$0.463666\pi$
$920$	−15.5672	−	22.2322i	−0.513234	−	0.732974i
$921$	−35.3480	−	42.1072i	−1.16476	−	1.38748i
$922$	−9.56444	+	26.2781i	−0.314988	+	0.865422i
$923$	5.96080	−	1.87943i	0.196202	−	0.0618623i
$924$	−1.65371	+	0.443502i	−0.0544031	+	0.0145902i
$925$	1.48329	−	1.35919i	0.0487703	−	0.0446897i
$926$	−1.12090	+	0.300344i	−0.0368350	+	0.00986992i
$927$	−8.31977	+	14.4250i	−0.273257	+	0.473779i
$928$	−14.8417	−	11.3885i	−0.487204	−	0.373845i
$929$	−13.3790	+	42.4328i	−0.438951	+	1.39217i	0.432475	+	0.901646i	$0.357640\pi$
$929$	−13.3790	+	42.4328i	−0.438951	+	1.39217i	−0.871426	+	0.490528i	$0.836804\pi$
$930$	1.53020	−	0.557331i	0.0501772	−	0.0182756i
$931$	5.26899	−	0.929066i	0.172684	−	0.0304489i
$932$	24.9288	+	5.52658i	0.816570	+	0.181029i
$933$	−0.401921	+	9.25246i	−0.0131583	+	0.302912i
$934$	1.66611	+	1.39803i	0.0545167	+	0.0457449i
$935$	3.14630	−	0.689678i	0.102895	−	0.0225549i
$936$	−18.4197	+	18.4360i	−0.602067	+	0.602600i
$937$	12.6944	+	47.3760i	0.414707	+	1.54771i	0.785422	+	0.618961i	$0.212446\pi$
$937$	12.6944	+	47.3760i	0.414707	+	1.54771i	−0.370715	+	0.928747i	$0.620887\pi$
$938$	0.203235	−	4.65485i	0.00663586	−	0.151986i
$939$	0.106720	+	0.0140260i	0.00348269	+	0.000457721i
$940$	−20.6656	+	6.51583i	−0.674037	+	0.212523i
$941$	−0.433304	−	9.92429i	−0.0141253	−	0.323523i	−0.992928	−	0.118717i	$-0.962122\pi$
$941$	−0.433304	−	9.92429i	−0.0141253	−	0.323523i	0.978803	−	0.204805i	$-0.0656561\pi$
$942$	1.61601	−	18.5182i	0.0526524	−	0.603357i
$943$	32.9928	−	23.1018i	1.07439	−	0.752298i
$944$	1.86769	+	1.86769i	0.0607881	+	0.0607881i
$945$	0.0138112	+	20.8145i	0.000449279	+	0.677094i
$946$	−0.448757	−	1.08339i	−0.0145903	−	0.0352242i
$947$	−29.8442	+	46.8460i	−0.969805	+	1.52229i	−0.121628	+	0.992576i	$0.538812\pi$
$947$	−29.8442	+	46.8460i	−0.969805	+	1.52229i	−0.848177	+	0.529713i	$0.822300\pi$
$948$	1.11190	+	25.3381i	0.0361129	+	0.822944i
$949$	5.80107	−	6.33075i	0.188311	−	0.205505i
$950$	0.0585102	−	0.668774i	0.00189832	−	0.0216979i
$951$	9.09853	+	6.97835i	0.295040	+	0.226289i
$952$	19.3101	+	7.08031i	0.625843	+	0.229474i
$953$	−15.5096	+	26.8634i	−0.502405	+	0.870191i	0.497591	+	0.867412i	$0.334218\pi$
$953$	−15.5096	+	26.8634i	−0.502405	+	0.870191i	−0.999996	+	0.00277959i	$0.999115\pi$
$954$	−21.9984	+	3.88895i	−0.712226	+	0.125909i
$955$	−27.5936	+	3.63277i	−0.892908	+	0.117554i
$956$	−3.18687	+	3.79797i	−0.103071	+	0.122835i
$957$	1.56986	+	1.31668i	0.0507464	+	0.0425621i
$958$	−20.0135	+	12.7500i	−0.646608	+	0.411935i
$959$	7.20534	+	11.3101i	0.232672	+	0.365223i
$960$	−5.78653	+	9.08747i	−0.186760	+	0.293297i
$961$	2.67271	+	30.5492i	0.0862165	+	0.985459i
$962$	7.37793	+	5.66128i	0.237874	+	0.182527i
$963$	−3.61285	−	0.156139i	−0.116422	−	0.00503152i
$964$	−11.4418	+	8.77961i	−0.368516	+	0.282772i
$965$	−5.19627	−	14.2766i	−0.167274	−	0.459581i
$966$	0.00274983	+	12.4325i	8.84742e−5	+	0.400010i
$967$	2.26273	−	25.8631i	0.0727644	−	0.831701i	−0.868865	−	0.495049i	$-0.835150\pi$
$967$	2.26273	−	25.8631i	0.0727644	−	0.831701i	0.941629	−	0.336652i	$-0.109294\pi$
$968$	−26.8091	−	9.75770i	−0.861676	−	0.313624i
$969$	−8.94974	+	6.83678i	−0.287507	+	0.219629i
$970$	−4.70403	+	26.6779i	−0.151037	+	0.856574i
$971$	3.54063	−	3.54063i	0.113624	−	0.113624i	−0.648009	−	0.761633i	$-0.724398\pi$
$971$	3.54063	−	3.54063i	0.113624	−	0.113624i	0.761633	+	0.648009i	$0.224398\pi$
$972$	−10.9726	−	18.9566i	−0.351945	−	0.608033i
$973$			28.7227i			0.920808i
$974$	2.03251	−	3.19040i	0.0651259	−	0.102227i
$975$	−1.81300	+	2.59045i	−0.0580624	+	0.0829607i
$976$	−9.09038	+	0.396894i	−0.290976	+	0.0127043i
$977$	−30.6632	−	2.68268i	−0.981003	−	0.0858266i	−0.414643	−	0.909984i	$-0.636093\pi$
$977$	−30.6632	−	2.68268i	−0.981003	−	0.0858266i	−0.566360	+	0.824158i	$0.691649\pi$
$978$	−1.83554	−	0.759831i	−0.0586942	−	0.0242967i
$979$	1.37036	−	1.25571i	0.0437970	−	0.0401326i
$980$	−9.96767	−	1.31227i	−0.318406	−	0.0419189i
$981$	32.9205	−	30.1929i	1.05107	−	0.963984i
$982$	−15.5891	+	9.00035i	−0.497467	+	0.287213i
$983$	−6.28883	+	3.27376i	−0.200583	+	0.104417i	−0.559079	−	0.829114i	$-0.688845\pi$
$983$	−6.28883	+	3.27376i	−0.200583	+	0.104417i	0.358496	+	0.933531i	$0.383290\pi$
$984$	−31.5415	−	20.0844i	−1.00551	−	0.640266i
$985$	6.25643	+	35.4820i	0.199346	+	1.13055i
$986$	−2.60532	−	9.81645i	−0.0829703	−	0.312620i
$987$	22.9427	+	7.22821i	0.730273	+	0.230077i
$988$	−7.30138	+	0.638788i	−0.232288	+	0.0203226i
$989$	19.9394	−	2.62507i	0.634035	−	0.0834723i
$990$	1.03617	−	1.48120i	0.0329316	−	0.0470755i
$991$	28.7828	−	22.0858i	0.914315	−	0.701578i	−0.0403741	−	0.999185i	$-0.512855\pi$
$991$	28.7828	−	22.0858i	0.914315	−	0.701578i	0.954689	+	0.297606i	$0.0961883\pi$
$992$	2.28739	+	2.49625i	0.0726247	+	0.0792560i
$993$	23.8445	+	6.38345i	0.756681	+	0.202573i
$994$	−2.75763	−	0.241262i	−0.0874668	−	0.00765236i
$995$	24.1195	+	51.7243i	0.764638	+	1.63977i
$996$	22.3172	−	10.4127i	0.707146	−	0.329938i
$997$	28.9288	−	6.41337i	0.916185	−	0.203113i	0.266958	−	0.963708i	$-0.413981\pi$
$997$	28.9288	−	6.41337i	0.916185	−	0.203113i	0.649227	+	0.760595i	$0.275093\pi$
$998$	10.9464	+	4.53413i	0.346501	+	0.143525i
$999$	−15.0195	+	11.5407i	−0.475195	+	0.365131i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	459.2.ba.a.25.20	✓	1248
17.15	even	8	inner	459.2.ba.a.457.33	yes	1248
27.13	even	9	inner	459.2.ba.a.229.33	yes	1248
459.202	even	72	inner	459.2.ba.a.202.20	yes	1248

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
459.2.ba.a.25.20	✓	1248	1.1	even	1	trivial
459.2.ba.a.202.20	yes	1248	459.202	even	72	inner
459.2.ba.a.229.33	yes	1248	27.13	even	9	inner
459.2.ba.a.457.33	yes	1248	17.15	even	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 459 = 3^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	459.ba (of order \(72\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.442402 - 0.631815i) q^{2} +(1.70567 - 0.301145i) q^{3} +(0.480569 - 1.32035i) q^{4} +(-2.01144 + 0.634203i) q^{5} +(-0.944859 - 0.944442i) q^{6} +(1.40032 - 1.28316i) q^{7} +(-2.53687 + 0.679752i) q^{8} +(2.81862 - 1.02731i) q^{9} +(1.29056 + 0.990283i) q^{10} +(0.111384 - 0.353264i) q^{11} +(0.422075 - 2.39681i) q^{12} +(3.25736 - 0.574361i) q^{13} +(-1.43022 - 0.317073i) q^{14} +(-3.23986 + 1.68748i) q^{15} +(-0.600930 - 0.504240i) q^{16} +(-0.882834 - 4.02748i) q^{17} +(-1.89603 - 1.32637i) q^{18} +(-0.408167 - 1.52330i) q^{19} +(-0.129262 + 2.96058i) q^{20} +(2.00207 - 2.61034i) q^{21} +(-0.272474 + 0.0859108i) q^{22} +(-0.213726 - 4.89512i) q^{23} +(-4.12236 + 1.92340i) q^{24} +(-0.452098 + 0.316562i) q^{25} +(-1.80395 - 1.80395i) q^{26} +(4.49828 - 2.60106i) q^{27} +(-1.02127 - 2.46556i) q^{28} +(-1.71594 + 2.69349i) q^{29} +(2.49949 + 1.30045i) q^{30} +(0.390488 - 0.426143i) q^{31} +(-0.510539 + 5.83548i) q^{32} +(0.0836004 - 0.636095i) q^{33} +(-2.15406 + 2.33955i) q^{34} +(-2.00287 + 3.46908i) q^{35} +(-0.00186467 - 4.21527i) q^{36} +(-3.61407 + 0.475801i) q^{37} +(-0.781871 + 0.931797i) q^{38} +(5.38302 - 1.96061i) q^{39} +(4.67165 - 2.97617i) q^{40} +(4.41666 + 6.93277i) q^{41} +(-2.53497 - 0.110118i) q^{42} +(0.357735 + 4.08893i) q^{43} +(-0.412906 - 0.316834i) q^{44} +(-5.01796 + 3.85394i) q^{45} +(-2.99826 + 2.30065i) q^{46} +(2.50086 + 6.87104i) q^{47} +(-1.17684 - 0.679101i) q^{48} +(-0.295686 + 3.37970i) q^{49} +(0.400018 + 0.145595i) q^{50} +(-2.71868 - 6.60369i) q^{51} +(0.807029 - 4.57689i) q^{52} +(6.82673 - 6.82673i) q^{53} +(-3.63344 - 1.69136i) q^{54} +0.781209i q^{55} +(-2.68020 + 4.20707i) q^{56} +(-1.15493 - 2.47533i) q^{57} +(2.46092 - 0.107446i) q^{58} +(-3.35423 - 0.293457i) q^{59} +(0.671086 + 5.08871i) q^{60} +(8.55177 - 7.83625i) q^{61} +(-0.441996 - 0.0581899i) q^{62} +(2.62878 - 5.05530i) q^{63} +(2.55409 - 1.47460i) q^{64} +(-6.18772 + 3.22112i) q^{65} +(-0.438880 + 0.228590i) q^{66} +(0.552290 + 3.13219i) q^{67} +(-5.74196 - 0.769830i) q^{68} +(-1.83869 - 8.28511i) q^{69} +(3.07789 - 0.269280i) q^{70} +(1.87344 - 0.246643i) q^{71} +(-6.45216 + 4.52211i) q^{72} +(2.05957 - 1.58036i) q^{73} +(1.89949 + 2.07293i) q^{74} +(-0.675799 + 0.676098i) q^{75} +(-2.20745 - 0.193127i) q^{76} +(-0.297321 - 0.637606i) q^{77} +(-3.62020 - 2.53370i) q^{78} +(-10.1744 + 2.25561i) q^{79} +(1.52852 + 0.633135i) q^{80} +(6.88928 - 5.79119i) q^{81} +(2.42629 - 5.85758i) q^{82} +(5.80410 + 8.28911i) q^{83} +(-2.48444 - 3.89789i) q^{84} +(4.33001 + 7.54113i) q^{85} +(2.42519 - 2.03497i) q^{86} +(-2.11570 + 5.11095i) q^{87} +(-0.0424340 + 0.971898i) q^{88} +(4.34565 + 2.50897i) q^{89} +(4.65494 + 1.46543i) q^{90} +(3.82435 - 4.98400i) q^{91} +(-6.56600 - 2.07025i) q^{92} +(0.537713 - 0.844453i) q^{93} +(3.23485 - 4.61984i) q^{94} +(1.78709 + 2.80516i) q^{95} +(0.886515 + 10.1072i) q^{96} +(7.68940 + 14.7712i) q^{97} +(2.26616 - 1.30837i) q^{98} +(-0.0489620 - 1.11014i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1248 q - 24 q^{2} - 24 q^{3} - 24 q^{5} - 24 q^{6} - 24 q^{7} - 12 q^{8} - 24 q^{9} - 12 q^{10} - 36 q^{11} + 12 q^{12} - 24 q^{14} - 24 q^{15} - 48 q^{16} - 12 q^{17} - 48 q^{18} - 12 q^{19} - 24 q^{20}+ \cdots - 168 q^{99}+O(q^{100}) \) 1248 * q - 24 * q^2 - 24 * q^3 - 24 * q^5 - 24 * q^6 - 24 * q^7 - 12 * q^8 - 24 * q^9 - 12 * q^10 - 36 * q^11 + 12 * q^12 - 24 * q^14 - 24 * q^15 - 48 * q^16 - 12 * q^17 - 48 * q^18 - 12 * q^19 - 24 * q^20 - 24 * q^22 + 48 * q^23 - 84 * q^24 - 24 * q^25 - 48 * q^26 - 24 * q^27 - 48 * q^28 - 24 * q^29 - 24 * q^31 - 72 * q^32 - 48 * q^33 - 24 * q^34 - 216 * q^35 - 24 * q^36 - 12 * q^37 - 24 * q^39 - 72 * q^40 - 24 * q^41 + 96 * q^42 + 12 * q^43 - 12 * q^44 - 24 * q^45 - 12 * q^46 - 24 * q^48 - 24 * q^49 - 48 * q^50 - 24 * q^51 - 48 * q^52 - 48 * q^53 - 96 * q^54 + 96 * q^56 - 60 * q^57 - 24 * q^58 + 144 * q^59 - 480 * q^60 - 24 * q^61 - 12 * q^62 + 120 * q^63 - 72 * q^65 - 204 * q^66 - 48 * q^67 - 72 * q^68 + 96 * q^69 + 36 * q^71 - 12 * q^73 - 192 * q^74 - 24 * q^75 - 72 * q^76 - 60 * q^77 + 324 * q^78 - 24 * q^79 - 48 * q^80 - 48 * q^82 - 144 * q^83 - 48 * q^84 - 24 * q^85 + 72 * q^86 - 24 * q^87 + 192 * q^88 - 252 * q^90 - 12 * q^91 - 24 * q^92 - 24 * q^93 - 24 * q^94 + 192 * q^95 + 288 * q^96 - 132 * q^97 - 168 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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