LMFDB - Embedded newform 418.2.v.b.13.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(13,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(90))

chi = DirichletCharacter(H, H._module([9, 25]))

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

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

chi := DirichletCharacter("418.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.v (of order $90$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$10$ over $\Q(\zeta_{90})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{90}]$

Embedding invariants

Embedding label			13.4
Character	$\chi$	$=$	418.13
Dual form			418.2.v.b.193.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.374607 - 0.927184i) q^{2} +(-0.414539 - 1.44567i) q^{3} +(-0.719340 + 0.694658i) q^{4} +(1.07843 - 0.573409i) q^{5} +(-1.18511 + 0.925911i) q^{6} +(1.15655 + 2.59766i) q^{7} +(0.913545 + 0.406737i) q^{8} +(0.626029 - 0.391186i) q^{9} +O(q^{10})$	\(q+(-0.374607 - 0.927184i) q^{2} +(-0.414539 - 1.44567i) q^{3} +(-0.719340 + 0.694658i) q^{4} +(1.07843 - 0.573409i) q^{5} +(-1.18511 + 0.925911i) q^{6} +(1.15655 + 2.59766i) q^{7} +(0.913545 + 0.406737i) q^{8} +(0.626029 - 0.391186i) q^{9} +(-0.935641 - 0.785096i) q^{10} +(1.24449 - 3.07429i) q^{11} +(1.30244 + 0.751964i) q^{12} +(-0.191039 - 5.47063i) q^{13} +(1.97526 - 2.04544i) q^{14} +(-1.27601 - 1.32135i) q^{15} +(0.0348995 - 0.999391i) q^{16} +(-1.20213 + 1.92381i) q^{17} +(-0.597216 - 0.433903i) q^{18} +(4.35393 - 0.208079i) q^{19} +(-0.377431 + 1.16161i) q^{20} +(3.27592 - 2.74882i) q^{21} +(-3.31662 - 0.00222434i) q^{22} +(-0.0120603 + 0.0683972i) q^{23} +(0.209306 - 1.48929i) q^{24} +(-1.96176 + 2.90843i) q^{25} +(-5.00072 + 2.22646i) q^{26} +(-4.17795 - 3.76184i) q^{27} +(-2.63644 - 1.06519i) q^{28} +(-2.10432 - 8.43997i) q^{29} +(-0.747130 + 1.67808i) q^{30} +(-6.55154 + 5.89903i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(-4.96029 - 0.524711i) q^{33} +(2.23405 + 0.393924i) q^{34} +(2.73678 + 2.13821i) q^{35} +(-0.178587 + 0.716272i) q^{36} +(-2.77108 + 3.81406i) q^{37} +(-1.82394 - 3.95895i) q^{38} +(-7.82953 + 2.54397i) q^{39} +(1.21842 - 0.0852001i) q^{40} +(3.30732 - 0.948358i) q^{41} +(-3.77585 - 2.00765i) q^{42} +(5.49515 - 0.968944i) q^{43} +(1.24037 + 3.07595i) q^{44} +(0.450816 - 0.780836i) q^{45} +(0.0679346 - 0.0144399i) q^{46} +(8.31458 + 0.581412i) q^{47} +(-1.45926 + 0.363833i) q^{48} +(-0.726315 + 0.806655i) q^{49} +(3.43154 + 0.729396i) q^{50} +(3.27952 + 0.940388i) q^{51} +(3.93764 + 3.80254i) q^{52} +(3.62120 - 6.81049i) q^{53} +(-1.92283 + 5.28294i) q^{54} +(-0.420733 - 4.02899i) q^{55} +2.84349i q^{56} +(-2.10569 - 6.20808i) q^{57} +(-7.03712 + 5.11276i) q^{58} +(-0.256685 - 3.67076i) q^{59} +(1.83577 + 0.0641065i) q^{60} +(-0.626225 - 4.45582i) q^{61} +(7.92373 + 3.86466i) q^{62} +(1.74020 + 1.17378i) q^{63} +(0.669131 + 0.743145i) q^{64} +(-3.34293 - 5.79013i) q^{65} +(1.37165 + 4.79566i) q^{66} +(-6.50963 + 7.75788i) q^{67} +(-0.471651 - 2.21894i) q^{68} +(0.103879 - 0.0109181i) q^{69} +(0.957295 - 3.33849i) q^{70} +(5.52499 + 10.3910i) q^{71} +(0.731015 - 0.102737i) q^{72} +(-1.82365 + 1.23007i) q^{73} +(4.57440 + 1.14053i) q^{74} +(5.01785 + 1.63040i) q^{75} +(-2.98741 + 3.17417i) q^{76} +(9.42528 - 0.322809i) q^{77} +(5.29172 + 6.30643i) q^{78} +(3.07372 - 3.93419i) q^{79} +(-0.535423 - 1.09778i) q^{80} +(-2.73564 + 5.60889i) q^{81} +(-2.11824 - 2.71123i) q^{82} +(-1.75683 + 8.26522i) q^{83} +(-0.447007 + 4.25299i) q^{84} +(-0.193278 + 2.76400i) q^{85} +(-2.95691 - 4.73204i) q^{86} +(-11.3291 + 6.54085i) q^{87} +(2.38732 - 2.30232i) q^{88} +(-1.05390 - 2.89557i) q^{89} +(-0.892857 - 0.125483i) q^{90} +(13.9899 - 6.82334i) q^{91} +(-0.0388372 - 0.0575786i) q^{92} +(11.2439 + 7.02597i) q^{93} +(-2.57562 - 7.92694i) q^{94} +(4.57608 - 2.72098i) q^{95} +(0.883987 + 1.21670i) q^{96} +(-17.1524 + 6.93002i) q^{97} +(1.02000 + 0.371250i) q^{98} +(-0.423531 - 2.41142i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 3 q^{3} - 3 q^{6} - 3 q^{7} + 30 q^{8} + 3 q^{9}+O(q^{10}) $ 240 * q + 3 * q^3 - 3 * q^6 - 3 * q^7 + 30 * q^8 + 3 * q^9	$ 240 q + 3 q^{3} - 3 q^{6} - 3 q^{7} + 30 q^{8} + 3 q^{9} - 3 q^{11} + 6 q^{13} - 18 q^{14} - 69 q^{15} + 9 q^{17} + 60 q^{18} - 45 q^{19} + 12 q^{20} - 48 q^{21} - 12 q^{22} + 3 q^{24} - 18 q^{25} + 84 q^{26} - 9 q^{27} + 6 q^{28} + 12 q^{29} + 9 q^{31} - 69 q^{33} - 24 q^{34} + 36 q^{35} + 3 q^{36} + 24 q^{38} - 30 q^{41} - 6 q^{42} + 12 q^{43} - 48 q^{44} + 48 q^{45} - 12 q^{46} - 54 q^{47} + 6 q^{48} - 81 q^{49} + 21 q^{50} + 45 q^{51} - 3 q^{52} + 81 q^{53} - 27 q^{54} - 72 q^{55} - 30 q^{57} - 24 q^{58} + 114 q^{59} + 78 q^{60} - 66 q^{61} - 45 q^{62} + 9 q^{63} + 30 q^{64} - 135 q^{66} - 9 q^{67} - 42 q^{68} - 54 q^{69} + 39 q^{70} - 102 q^{71} - 6 q^{72} + 12 q^{74} + 72 q^{77} + 36 q^{79} - 117 q^{81} + 30 q^{82} - 36 q^{83} - 36 q^{84} - 90 q^{85} + 3 q^{86} - 216 q^{87} - 3 q^{88} + 18 q^{89} - 24 q^{90} + 102 q^{91} + 30 q^{92} + 147 q^{93} + 18 q^{94} - 66 q^{95} - 24 q^{97} + 12 q^{98} - 195 q^{99}+O(q^{100}) $ 240 * q + 3 * q^3 - 3 * q^6 - 3 * q^7 + 30 * q^8 + 3 * q^9 - 3 * q^11 + 6 * q^13 - 18 * q^14 - 69 * q^15 + 9 * q^17 + 60 * q^18 - 45 * q^19 + 12 * q^20 - 48 * q^21 - 12 * q^22 + 3 * q^24 - 18 * q^25 + 84 * q^26 - 9 * q^27 + 6 * q^28 + 12 * q^29 + 9 * q^31 - 69 * q^33 - 24 * q^34 + 36 * q^35 + 3 * q^36 + 24 * q^38 - 30 * q^41 - 6 * q^42 + 12 * q^43 - 48 * q^44 + 48 * q^45 - 12 * q^46 - 54 * q^47 + 6 * q^48 - 81 * q^49 + 21 * q^50 + 45 * q^51 - 3 * q^52 + 81 * q^53 - 27 * q^54 - 72 * q^55 - 30 * q^57 - 24 * q^58 + 114 * q^59 + 78 * q^60 - 66 * q^61 - 45 * q^62 + 9 * q^63 + 30 * q^64 - 135 * q^66 - 9 * q^67 - 42 * q^68 - 54 * q^69 + 39 * q^70 - 102 * q^71 - 6 * q^72 + 12 * q^74 + 72 * q^77 + 36 * q^79 - 117 * q^81 + 30 * q^82 - 36 * q^83 - 36 * q^84 - 90 * q^85 + 3 * q^86 - 216 * q^87 - 3 * q^88 + 18 * q^89 - 24 * q^90 + 102 * q^91 + 30 * q^92 + 147 * q^93 + 18 * q^94 - 66 * q^95 - 24 * q^97 + 12 * q^98 - 195 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−0.374607	−	0.927184i	−0.264887	−	0.655618i
$2$	−0.374607	−	0.927184i	−0.264887	−	0.655618i
$3$	−0.414539	−	1.44567i	−0.239334	−	0.834657i	−0.985612	−	0.169023i	$-0.945939\pi$
$3$	−0.414539	−	1.44567i	−0.239334	−	0.834657i	0.746278	−	0.665634i	$-0.231839\pi$
$4$	−0.719340	+	0.694658i	−0.359670	+	0.347329i
$5$	1.07843	−	0.573409i	0.482287	−	0.256436i	−0.210480	−	0.977598i	$-0.567503\pi$
$5$	1.07843	−	0.573409i	0.482287	−	0.256436i	0.692767	+	0.721162i	$0.256392\pi$
$6$	−1.18511	+	0.925911i	−0.483820	+	0.378001i
$7$	1.15655	+	2.59766i	0.437136	+	0.981824i	0.989004	+	0.147892i	$0.0472488\pi$
$7$	1.15655	+	2.59766i	0.437136	+	0.981824i	−0.551867	+	0.833932i	$0.686085\pi$
$8$	0.913545	+	0.406737i	0.322987	+	0.143803i
$9$	0.626029	−	0.391186i	0.208676	−	0.130395i
$10$	−0.935641	−	0.785096i	−0.295876	−	0.248269i
$11$	1.24449	−	3.07429i	0.375228	−	0.926932i
$11$	1.24449	−	3.07429i	0.375228	−	0.926932i
$12$	1.30244	+	0.751964i	0.375982	+	0.217073i
$13$	−0.191039	−	5.47063i	−0.0529846	−	1.51728i	−0.677066	−	0.735922i	$-0.736749\pi$
$13$	−0.191039	−	5.47063i	−0.0529846	−	1.51728i	0.624082	−	0.781359i	$-0.285473\pi$
$14$	1.97526	−	2.04544i	0.527910	−	0.546667i
$15$	−1.27601	−	1.32135i	−0.329464	−	0.341170i
$16$	0.0348995	−	0.999391i	0.00872487	−	0.249848i
$17$	−1.20213	+	1.92381i	−0.291560	+	0.466593i	−0.961107	−	0.276177i	$-0.910933\pi$
$17$	−1.20213	+	1.92381i	−0.291560	+	0.466593i	0.669547	+	0.742769i	$0.266488\pi$
$18$	−0.597216	−	0.433903i	−0.140765	−	0.102272i
$19$	4.35393	−	0.208079i	0.998860	−	0.0477366i
$19$	4.35393	−	0.208079i	0.998860	−	0.0477366i
$20$	−0.377431	+	1.16161i	−0.0843962	+	0.259745i
$21$	3.27592	−	2.74882i	0.714865	−	0.599843i
$22$	−3.31662	−	0.00222434i	−0.707107	−	0.000474230i
$23$	−0.0120603	+	0.0683972i	−0.00251474	+	0.0142618i	−0.986039	−	0.166513i	$-0.946749\pi$
$23$	−0.0120603	+	0.0683972i	−0.00251474	+	0.0142618i	0.983525	+	0.180775i	$0.0578604\pi$
$24$	0.209306	−	1.48929i	0.0427245	−	0.304001i
$25$	−1.96176	+	2.90843i	−0.392352	+	0.581686i
$26$	−5.00072	+	2.22646i	−0.980722	+	0.436645i
$27$	−4.17795	−	3.76184i	−0.804047	−	0.723967i
$28$	−2.63644	−	1.06519i	−0.498241	−	0.201302i
$29$	−2.10432	−	8.43997i	−0.390763	−	1.56726i	−0.767566	−	0.640970i	$-0.778532\pi$
$29$	−2.10432	−	8.43997i	−0.390763	−	1.56726i	0.376803	−	0.926294i	$-0.377023\pi$
$30$	−0.747130	+	1.67808i	−0.136407	+	0.306374i
$31$	−6.55154	+	5.89903i	−1.17669	+	1.05950i	−0.179564	+	0.983746i	$0.557469\pi$
$31$	−6.55154	+	5.89903i	−1.17669	+	1.05950i	−0.997127	+	0.0757507i	$0.975865\pi$
$32$	−0.939693	+	0.342020i	−0.166116	+	0.0604612i
$33$	−4.96029	−	0.524711i	−0.863476	−	0.0913405i
$34$	2.23405	+	0.393924i	0.383137	+	0.0675574i
$35$	2.73678	+	2.13821i	0.462600	+	0.361423i
$36$	−0.178587	+	0.716272i	−0.0297644	+	0.119379i
$37$	−2.77108	+	3.81406i	−0.455562	+	0.627028i	−0.973581	−	0.228341i	$-0.926670\pi$
$37$	−2.77108	+	3.81406i	−0.455562	+	0.627028i	0.518019	+	0.855369i	$0.326670\pi$
$38$	−1.82394	−	3.95895i	−0.295882	−	0.642226i
$39$	−7.82953	+	2.54397i	−1.25373	+	0.407361i
$40$	1.21842	−	0.0852001i	0.192649	−	0.0134713i
$41$	3.30732	−	0.948358i	0.516516	−	0.148109i	−0.00724506	−	0.999974i	$-0.502306\pi$
$41$	3.30732	−	0.948358i	0.516516	−	0.148109i	0.523761	+	0.851865i	$0.324528\pi$
$42$	−3.77585	−	2.00765i	−0.582626	−	0.309788i
$43$	5.49515	−	0.968944i	0.838003	−	0.147763i	0.261854	−	0.965107i	$-0.415666\pi$
$43$	5.49515	−	0.968944i	0.838003	−	0.147763i	0.576149	+	0.817345i	$0.304555\pi$
$44$	1.24037	+	3.07595i	0.186992	+	0.463717i
$45$	0.450816	−	0.780836i	0.0672037	−	0.116400i
$46$	0.0679346	−	0.0144399i	0.0100164	−	0.00212905i
$47$	8.31458	+	0.581412i	1.21281	+	0.0848076i	0.661791	−	0.749688i	$-0.269796\pi$
$47$	8.31458	+	0.581412i	1.21281	+	0.0848076i	0.551014	+	0.834496i	$0.314241\pi$
$48$	−1.45926	+	0.363833i	−0.210625	+	0.0525148i
$49$	−0.726315	+	0.806655i	−0.103759	+	0.115236i
$50$	3.43154	+	0.729396i	0.485293	+	0.103152i
$51$	3.27952	+	0.940388i	0.459225	+	0.131681i
$52$	3.93764	+	3.80254i	0.546053	+	0.527317i
$53$	3.62120	−	6.81049i	0.497410	−	0.935493i	−0.500167	−	0.865929i	$-0.666728\pi$
$53$	3.62120	−	6.81049i	0.497410	−	0.935493i	0.997577	−	0.0695640i	$-0.0221608\pi$
$54$	−1.92283	+	5.28294i	−0.261664	+	0.718917i
$55$	−0.420733	−	4.02899i	−0.0567316	−	0.543269i
$56$			2.84349i			0.379978i
$57$	−2.10569	−	6.20808i	−0.278905	−	0.822281i
$58$	−7.03712	+	5.11276i	−0.924019	+	0.671339i
$59$	−0.256685	−	3.67076i	−0.0334175	−	0.477893i	−0.985233	−	0.171220i	$-0.945229\pi$
$59$	−0.256685	−	3.67076i	−0.0334175	−	0.477893i	0.951815	−	0.306672i	$-0.0992155\pi$
$60$	1.83577	+	0.0641065i	0.236997	+	0.00827611i
$61$	−0.626225	−	4.45582i	−0.0801799	−	0.570510i	−0.988383	−	0.151981i	$-0.951435\pi$
$61$	−0.626225	−	4.45582i	−0.0801799	−	0.570510i	0.908204	−	0.418529i	$-0.137454\pi$
$62$	7.92373	+	3.86466i	1.00632	+	0.490813i
$63$	1.74020	+	1.17378i	0.219245	+	0.147883i
$64$	0.669131	+	0.743145i	0.0836413	+	0.0928931i
$65$	−3.34293	−	5.79013i	−0.414640	−	0.718177i
$66$	1.37165	+	4.79566i	0.168839	+	0.590305i
$67$	−6.50963	+	7.75788i	−0.795278	+	0.947776i	−0.999515	−	0.0311457i	$-0.990084\pi$
$67$	−6.50963	+	7.75788i	−0.795278	+	0.947776i	0.204236	+	0.978922i	$0.434529\pi$
$68$	−0.471651	−	2.21894i	−0.0571961	−	0.269087i
$69$	0.103879	−	0.0109181i	0.0125056	−	0.00131439i
$70$	0.957295	−	3.33849i	0.114419	−	0.399025i
$71$	5.52499	+	10.3910i	0.655695	+	1.23318i	0.959837	+	0.280557i	$0.0905190\pi$
$71$	5.52499	+	10.3910i	0.655695	+	1.23318i	−0.304142	+	0.952627i	$0.598370\pi$
$72$	0.731015	−	0.102737i	0.0861510	−	0.0121077i
$73$	−1.82365	+	1.23007i	−0.213442	+	0.143968i	−0.661261	−	0.750156i	$-0.729978\pi$
$73$	−1.82365	+	1.23007i	−0.213442	+	0.143968i	0.447819	+	0.894124i	$0.352201\pi$
$74$	4.57440	+	1.14053i	0.531763	+	0.132583i
$75$	5.01785	+	1.63040i	0.579411	+	0.188262i
$76$	−2.98741	+	3.17417i	−0.342680	+	0.364103i
$77$	9.42528	−	0.322809i	1.07411	−	0.0367875i
$78$	5.29172	+	6.30643i	0.599170	+	0.714062i
$79$	3.07372	−	3.93419i	0.345821	−	0.442631i	−0.583383	−	0.812197i	$-0.698271\pi$
$79$	3.07372	−	3.93419i	0.345821	−	0.442631i	0.929204	+	0.369566i	$0.120494\pi$
$80$	−0.535423	−	1.09778i	−0.0598622	−	0.122736i
$81$	−2.73564	+	5.60889i	−0.303960	+	0.623210i
$82$	−2.11824	−	2.71123i	−0.233921	−	0.299405i
$83$	−1.75683	+	8.26522i	−0.192837	+	0.907226i	0.770189	+	0.637816i	$0.220162\pi$
$83$	−1.75683	+	8.26522i	−0.192837	+	0.907226i	−0.963026	+	0.269410i	$0.913171\pi$
$84$	−0.447007	+	4.25299i	−0.0487724	+	0.464039i
$85$	−0.193278	+	2.76400i	−0.0209639	+	0.299798i
$86$	−2.95691	−	4.73204i	−0.318852	−	0.510270i
$87$	−11.3291	+	6.54085i	−1.21461	+	0.701253i
$88$	2.38732	−	2.30232i	0.254490	−	0.245428i
$89$	−1.05390	−	2.89557i	−0.111713	−	0.306930i	0.871220	−	0.490893i	$-0.163329\pi$
$89$	−1.05390	−	2.89557i	−0.111713	−	0.306930i	−0.982933	+	0.183963i	$0.941107\pi$
$90$	−0.892857	−	0.125483i	−0.0941154	−	0.0132271i
$91$	13.9899	−	6.82334i	1.46654	−	0.715280i
$92$	−0.0388372	−	0.0575786i	−0.00404906	−	0.00600298i
$93$	11.2439	+	7.02597i	1.16594	+	0.728560i
$94$	−2.57562	−	7.92694i	−0.265655	−	0.817602i
$95$	4.57608	−	2.72098i	0.469496	−	0.279167i
$96$	0.883987	+	1.21670i	0.0902215	+	0.124179i
$97$	−17.1524	+	6.93002i	−1.74156	+	0.703637i	−0.742119	+	0.670268i	$0.766179\pi$
$97$	−17.1524	+	6.93002i	−1.74156	+	0.703637i	−0.999443	+	0.0333683i	$0.989377\pi$
$98$	1.02000	+	0.371250i	0.103036	+	0.0375019i
$99$	−0.423531	−	2.41142i	−0.0425665	−	0.242357i
$100$	−0.609192	−	3.45490i	−0.0609192	−	0.345490i
$101$	−0.813354	+	0.0284030i	−0.0809318	+	0.00282620i	−0.0753368	−	0.997158i	$-0.524003\pi$
$101$	−0.813354	+	0.0284030i	−0.0809318	+	0.00282620i	−0.00559501	+	0.999984i	$0.501781\pi$
$102$	−0.356618	−	3.39300i	−0.0353105	−	0.335957i
$103$	18.8130	+	1.97733i	1.85370	+	0.194832i	0.964751	−	0.263165i	$-0.0847663\pi$
$103$	18.8130	+	1.97733i	1.85370	+	0.194832i	0.888954	+	0.457997i	$0.151433\pi$
$104$	2.05058	−	5.07538i	0.201076	−	0.497682i
$105$	1.95664	−	4.84285i	0.190948	−	0.472614i
$106$	−7.67110	−	0.806266i	−0.745084	−	0.0783114i
$107$	1.72871	+	16.4475i	0.167120	+	1.59004i	0.681067	+	0.732221i	$0.261516\pi$
$107$	1.72871	+	16.4475i	0.167120	+	1.59004i	−0.513947	+	0.857822i	$0.671817\pi$
$108$	5.61856	−	0.196204i	0.540646	−	0.0188798i
$109$	−1.33603	−	7.57699i	−0.127968	−	0.725744i	−0.979500	−	0.201442i	$-0.935437\pi$
$109$	−1.33603	−	7.57699i	−0.127968	−	0.725744i	0.851532	−	0.524302i	$-0.175674\pi$
$110$	−3.57801	+	1.89938i	−0.341150	+	0.181099i
$111$	6.66259	+	2.42498i	0.632385	+	0.230169i
$112$	2.63644	−	1.06519i	0.249120	−	0.100651i
$113$	11.3494	+	15.6211i	1.06766	+	1.46951i	0.872421	+	0.488755i	$0.162549\pi$
$113$	11.3494	+	15.6211i	1.06766	+	1.46951i	0.195240	+	0.980755i	$0.437451\pi$
$114$	−4.96723	+	4.27795i	−0.465224	+	0.400666i
$115$	0.0262135	+	0.0806768i	0.00244442	+	0.00752315i
$116$	7.37662	+	4.60942i	0.684902	+	0.427974i
$117$	−2.25963	−	3.35004i	−0.208903	−	0.309711i
$118$	−3.30732	+	1.61309i	−0.304463	+	0.148497i
$119$	−6.38774	−	0.897738i	−0.585563	−	0.0822955i
$120$	−0.628253	−	1.72611i	−0.0573514	−	0.157572i
$121$	−7.90248	−	7.65185i	−0.718407	−	0.695623i
$122$	−3.89678	+	2.24981i	−0.352798	+	0.203688i
$123$	−2.74202	−	4.38815i	−0.247240	−	0.395666i
$124$	0.614970	−	8.79449i	0.0552260	−	0.789768i
$125$	−1.08624	+	10.3349i	−0.0971567	+	0.924384i
$126$	0.436420	−	2.05320i	0.0388794	−	0.182913i
$127$	1.70542	+	2.18284i	0.151332	+	0.193696i	0.857703	−	0.514146i	$-0.171891\pi$
$127$	1.70542	+	2.18284i	0.151332	+	0.193696i	−0.706371	+	0.707842i	$0.749669\pi$
$128$	0.438371	−	0.898794i	0.0387469	−	0.0794429i
$129$	−3.67873	−	7.54251i	−0.323894	−	0.664081i
$130$	−4.11623	+	5.26854i	−0.361017	+	0.462081i
$131$	6.97597	+	8.31364i	0.609494	+	0.726366i	0.979226	−	0.202772i	$-0.0649950\pi$
$131$	6.97597	+	8.31364i	0.609494	+	0.726366i	−0.369732	+	0.929138i	$0.620551\pi$
$132$	3.93263	−	3.06826i	0.342291	−	0.267058i
$133$	5.57607	+	11.0694i	0.483507	+	0.959837i
$134$	9.63153	+	3.12947i	0.832038	+	0.270345i
$135$	−6.66268	−	1.66119i	−0.573433	−	0.142973i
$136$	−1.88069	+	1.26854i	−0.161267	+	0.108776i
$137$	10.1707	−	1.42940i	0.868941	−	0.122122i	0.309407	−	0.950930i	$-0.399869\pi$
$137$	10.1707	−	1.42940i	0.868941	−	0.122122i	0.559533	+	0.828808i	$0.310980\pi$
$138$	−0.0490369	−	0.0922250i	−0.00417430	−	0.00785072i
$139$	−5.77929	+	20.1548i	−0.490193	+	1.70951i	0.194701	+	0.980863i	$0.437626\pi$
$139$	−5.77929	+	20.1548i	−0.490193	+	1.70951i	−0.684894	+	0.728643i	$0.740151\pi$
$140$	−3.45400	+	0.363030i	−0.291916	+	0.0306816i
$141$	−2.60619	−	12.2611i	−0.219480	−	1.03257i
$142$	7.56466	−	9.01521i	0.634812	−	0.756540i
$143$	−17.0560	−	6.22085i	−1.42630	−	0.520214i
$144$	−0.369100	−	0.639299i	−0.0307583	−	0.0532750i
$145$	−7.10892	−	7.89525i	−0.590363	−	0.655665i
$146$	1.82365	+	1.23007i	0.150926	+	0.101801i
$147$	1.46724	+	0.715621i	0.121016	+	0.0590235i
$148$	−0.656123	−	4.66856i	−0.0539330	−	0.383753i
$149$	0.152307	+	0.00531868i	0.0124775	+	0.000435723i	0.0411376	−	0.999153i	$-0.486902\pi$
$149$	0.152307	+	0.00531868i	0.0124775	+	0.000435723i	−0.0286601	+	0.999589i	$0.509124\pi$
$150$	−0.368041	−	5.26323i	−0.0300504	−	0.429741i
$151$	17.6064	−	12.7918i	1.43279	−	1.04098i	0.443299	−	0.896374i	$-0.353808\pi$
$151$	17.6064	−	12.7918i	1.43279	−	1.04098i	0.989489	−	0.144608i	$-0.0461921\pi$
$152$	4.06215	+	1.58081i	0.329484	+	0.128221i
$153$			1.67462i			0.135385i
$154$	−3.83007	−	8.61804i	−0.308636	−	0.694461i
$155$	−3.68279	+	10.1184i	−0.295809	+	0.812728i
$156$	3.86490	−	7.26883i	0.309440	−	0.581972i
$157$	7.32829	+	7.07684i	0.584861	+	0.564794i	0.927098	−	0.374820i	$-0.122296\pi$
$157$	7.32829	+	7.07684i	0.584861	+	0.564794i	−0.342237	+	0.939614i	$0.611184\pi$
$158$	−4.79915	−	1.37613i	−0.381800	−	0.109479i
$159$	−11.3468	−	2.41185i	−0.899863	−	0.191272i
$160$	−0.817271	+	0.907672i	−0.0646110	+	0.0717578i
$161$	−0.191621	+	0.0477765i	−0.0151019	+	0.00376532i
$162$	6.22526	+	0.435313i	0.489103	+	0.0342014i
$163$	−22.9234	+	4.87253i	−1.79550	+	0.381646i	−0.980298	−	0.197527i	$-0.936709\pi$
$163$	−22.9234	+	4.87253i	−1.79550	+	0.381646i	−0.815205	+	0.579172i	$0.803376\pi$
$164$	−1.72030	+	2.97965i	−0.134333	+	0.232671i
$165$	−5.65018	+	2.27841i	−0.439866	+	0.177374i
$166$	8.32150	−	1.46730i	0.645873	−	0.113885i
$167$	−12.3057	−	6.54304i	−0.952242	−	0.506316i	−0.0807545	−	0.996734i	$-0.525733\pi$
$167$	−12.3057	−	6.54304i	−0.952242	−	0.506316i	−0.871487	+	0.490418i	$0.836844\pi$
$168$	4.11075	−	1.17874i	0.317151	−	0.0909417i
$169$	−16.9230	+	1.18337i	−1.30177	+	0.0910287i
$170$	2.63514	−	0.856209i	0.202106	−	0.0656682i
$171$	2.64429	−	1.83346i	0.202214	−	0.140208i
$172$	−3.27980	+	4.51425i	−0.250082	+	0.344209i
$173$	3.38167	−	13.5631i	0.257104	−	1.03119i	−0.693420	−	0.720534i	$-0.743897\pi$
$173$	3.38167	−	13.5631i	0.257104	−	1.03119i	0.950523	−	0.310653i	$-0.100548\pi$
$174$	10.3085	+	8.05390i	0.781487	+	0.610565i
$175$	−9.82399	−	1.73224i	−0.742624	−	0.130945i
$176$	−3.02898	−	1.35102i	−0.228318	−	0.101837i
$177$	−5.20030	+	1.89275i	−0.390879	+	0.142268i
$178$	−2.28993	+	2.06186i	−0.171637	+	0.154543i
$179$	−2.51672	+	5.65264i	−0.188108	+	0.422498i	−0.982839	−	0.184464i	$-0.940945\pi$
$179$	−2.51672	+	5.65264i	−0.188108	+	0.422498i	0.794731	+	0.606962i	$0.207612\pi$
$180$	0.218124	+	0.874849i	0.0162580	+	0.0652074i
$181$	−7.59099	−	3.06696i	−0.564234	−	0.227965i	0.0747276	−	0.997204i	$-0.476191\pi$
$181$	−7.59099	−	3.06696i	−0.564234	−	0.227965i	−0.638962	+	0.769239i	$0.720636\pi$
$182$	−11.5672	−	10.4152i	−0.857418	−	0.772022i
$183$	−6.18205	+	2.75243i	−0.456990	+	0.203465i
$184$	−0.0388372	+	0.0575786i	−0.00286312	+	0.00424475i
$185$	−0.801384	+	5.70215i	−0.0589190	+	0.419230i
$186$	2.30233	−	13.0571i	0.168815	−	0.957396i
$187$	4.41831	+	6.08986i	0.323099	+	0.445335i
$188$	−6.38489	+	5.35756i	−0.465666	+	0.390740i
$189$	4.93997	−	15.2037i	0.359330	−	1.10590i
$190$	−4.23708	−	3.22357i	−0.307390	−	0.233862i
$191$	10.8664	+	7.89487i	0.786262	+	0.571253i	0.906852	−	0.421450i	$-0.138479\pi$
$191$	10.8664	+	7.89487i	0.786262	+	0.571253i	−0.120590	+	0.992702i	$0.538479\pi$
$192$	0.796961	−	1.27540i	0.0575157	−	0.0920443i
$193$	−0.672112	+	19.2468i	−0.0483797	+	1.38541i	0.696184	+	0.717863i	$0.254880\pi$
$193$	−0.672112	+	19.2468i	−0.0483797	+	1.38541i	−0.744564	+	0.667551i	$0.767343\pi$
$194$	12.8508	+	13.3074i	0.922634	+	0.955415i
$195$	−6.98484	+	7.23301i	−0.500195	+	0.517967i
$196$	−0.0378820	−	1.08480i	−0.00270586	−	0.0774857i
$197$	−6.53712	−	3.77421i	−0.465751	−	0.268901i	0.248709	−	0.968578i	$-0.419994\pi$
$197$	−6.53712	−	3.77421i	−0.465751	−	0.268901i	−0.714459	+	0.699677i	$0.753327\pi$
$198$	−2.07717	+	1.29602i	−0.147618	+	0.0921045i
$199$	1.88661	+	1.58305i	0.133738	+	0.112220i	0.707203	−	0.707010i	$-0.249957\pi$
$199$	1.88661	+	1.58305i	0.133738	+	0.112220i	−0.573465	+	0.819230i	$0.694401\pi$
$200$	−2.97512	+	1.85906i	−0.210373	+	0.131456i
$201$	13.9138	+	6.19483i	0.981405	+	0.436950i
$202$	0.331023	+	0.743489i	0.0232907	+	0.0523117i
$203$	19.4904	−	15.2276i	1.36796	−	1.06877i
$204$	−3.01234	+	1.60169i	−0.210906	+	0.112141i
$205$	3.02290	−	2.91918i	0.211128	−	0.203884i
$206$	−5.21414	−	18.1839i	−0.363286	−	1.26693i
$207$	0.0192059	+	0.0475364i	0.00133491	+	0.00330401i
$208$	−5.47397			−0.379551
$209$	4.77873	−	13.6442i	0.330552	−	0.943788i
$210$	−5.22318			−0.360434
$211$	−5.38438	−	13.3268i	−0.370676	−	0.917455i	−0.991092	−	0.133182i	$-0.957481\pi$
$211$	−5.38438	−	13.3268i	−0.370676	−	0.917455i	0.620416	−	0.784273i	$-0.286964\pi$
$212$	2.12609	+	7.41456i	0.146020	+	0.509234i
$213$	12.7316	−	12.2948i	0.872355	−	0.842423i
$214$	14.6023	−	7.76418i	0.998193	−	0.530748i
$215$	5.37052	−	4.19591i	0.366266	−	0.286158i
$216$	−2.28667	−	5.13594i	−0.155588	−	0.349456i
$217$	−22.9009	−	10.1961i	−1.55461	−	0.692158i
$218$	−6.52478	+	4.07714i	−0.441914	+	0.276138i
$219$	2.53424	+	2.12648i	0.171248	+	0.143694i
$220$	3.10142	+	2.60595i	0.209098	+	0.175693i
$221$	10.7541	+	6.20890i	0.723401	+	0.417656i
$222$	−0.247444	−	7.08586i	−0.0166073	−	0.475572i
$223$	−19.2041	+	19.8864i	−1.28600	+	1.33169i	−0.370793	+	0.928715i	$0.620914\pi$
$223$	−19.2041	+	19.8864i	−1.28600	+	1.33169i	−0.915209	+	0.402979i	$0.867975\pi$
$224$	−1.97526	−	2.04544i	−0.131977	−	0.136667i
$225$	−0.0903810	+	2.58817i	−0.00602540	+	0.172545i
$226$	10.2321	−	16.3747i	0.680628	−	1.08923i
$227$	−2.40724	−	1.74896i	−0.159774	−	0.116083i	0.505026	−	0.863104i	$-0.331483\pi$
$227$	−2.40724	−	1.74896i	−0.159774	−	0.116083i	−0.664800	+	0.747022i	$0.731483\pi$
$228$	5.82720	+	3.00299i	0.385916	+	0.198878i
$229$	−1.23777	+	3.80946i	−0.0817941	+	0.251736i	−0.983588	−	0.180431i	$-0.942251\pi$
$229$	−1.23777	+	3.80946i	−0.0817941	+	0.251736i	0.901794	+	0.432167i	$0.142251\pi$
$230$	0.0649825	−	0.0545268i	0.00428482	−	0.00359539i
$231$	−4.37382	−	13.4920i	−0.287776	−	0.887709i
$232$	1.51045	−	8.56621i	0.0991661	−	0.562399i
$233$	0.597087	−	4.24849i	0.0391165	−	0.278328i	−0.960883	−	0.276956i	$-0.910674\pi$
$233$	0.597087	−	4.24849i	0.0391165	−	0.278328i	0.999999	−	0.00137206i	$-0.000436741\pi$
$234$	−2.25963	+	3.35004i	−0.147717	+	0.218999i
$235$	9.30004	−	4.14065i	0.606668	−	0.270106i
$236$	2.73457	+	2.46222i	0.178005	+	0.160277i
$237$	−6.96171	−	2.81271i	−0.452212	−	0.182705i
$238$	1.56052	+	6.25891i	0.101154	+	0.405705i
$239$	0.452794	−	1.01699i	0.0292888	−	0.0657838i	−0.898309	−	0.439365i	$-0.855204\pi$
$239$	0.452794	−	1.01699i	0.0292888	−	0.0657838i	0.927598	+	0.373581i	$0.121870\pi$
$240$	−1.36507	+	1.22912i	−0.0881151	+	0.0793392i
$241$	6.84421	−	2.49109i	0.440874	−	0.160465i	−0.112039	−	0.993704i	$-0.535738\pi$
$241$	6.84421	−	2.49109i	0.440874	−	0.160465i	0.552913	+	0.833239i	$0.313516\pi$
$242$	−4.13435	+	10.1935i	−0.265766	+	0.655262i
$243$	−7.36709	−	1.29902i	−0.472599	−	0.0833320i
$244$	3.54574	+	2.77024i	0.226993	+	0.177346i
$245$	−0.320734	+	1.28639i	−0.0204909	+	0.0821847i
$246$	−3.04145	+	4.18619i	−0.193915	+	0.266902i
$247$	−1.97009	−	23.7790i	−0.125354	−	1.51302i
$248$	−8.38448	+	2.72428i	−0.532415	+	0.172992i
$249$	12.6770	−	0.886465i	0.803375	−	0.0561775i
$250$	9.98929	−	2.86438i	0.631778	−	0.181160i
$251$	−8.52427	−	4.53243i	−0.538047	−	0.286085i	0.178126	−	0.984008i	$-0.442997\pi$
$251$	−8.52427	−	4.53243i	−0.538047	−	0.286085i	−0.716173	+	0.697923i	$0.754108\pi$
$252$	−2.06718	+	0.364499i	−0.130220	+	0.0229613i
$253$	0.195264	+	0.122196i	0.0122761	+	0.00768242i
$254$	1.38503	−	2.39895i	0.0869046	−	0.150523i
$255$	4.07595	−	0.866370i	0.255246	−	0.0542542i
$256$	−0.997564	−	0.0697565i	−0.0623478	−	0.00435978i
$257$	0.0373141	−	0.00930344i	0.00232759	−	0.000580332i	−0.240758	−	0.970585i	$-0.577396\pi$
$257$	0.0373141	−	0.00930344i	0.00232759	−	0.000580332i	0.243086	+	0.970005i	$0.421840\pi$
$258$	−5.61522	+	6.23633i	−0.349588	+	0.388257i
$259$	−13.1125	−	2.78716i	−0.814774	−	0.173186i
$260$	6.42687	+	1.84287i	0.398577	+	0.114290i
$261$	−4.61897	−	4.46048i	−0.285907	−	0.276097i
$262$	5.09503	−	9.58236i	0.314772	−	0.592000i
$263$	−0.0637412	+	0.175128i	−0.00393045	+	0.0107988i	−0.941642	−	0.336615i	$-0.890718\pi$
$263$	−0.0637412	+	0.175128i	−0.00393045	+	0.0107988i	0.937712	+	0.347414i	$0.112940\pi$
$264$	−4.31803	−	2.49688i	−0.265756	−	0.153672i
$265$		−	9.42104i		−	0.578730i
$266$	8.17452	−	9.31671i	0.501212	−	0.571244i
$267$	−3.74915	+	2.72392i	−0.229444	+	0.166701i
$268$	−0.706437	−	10.1025i	−0.0431525	−	0.617110i
$269$	−2.50250	−	0.0873891i	−0.152580	−	0.00532821i	−0.0414923	−	0.999139i	$-0.513211\pi$
$269$	−2.50250	−	0.0873891i	−0.152580	−	0.00532821i	−0.111088	+	0.993811i	$0.535433\pi$
$270$	0.955653	+	6.79983i	0.0581592	+	0.413824i
$271$	−1.81929	−	0.887329i	−0.110514	−	0.0539014i	0.382285	−	0.924045i	$-0.375137\pi$
$271$	−1.81929	−	0.887329i	−0.110514	−	0.0539014i	−0.492799	+	0.870143i	$0.664026\pi$
$272$	1.88069	+	1.26854i	0.114033	+	0.0769164i
$273$	−15.6636	−	17.3962i	−0.948007	−	1.05287i
$274$	−5.13532	−	8.89464i	−0.310236	−	0.537345i
$275$	6.49995	+	9.65053i	0.391962	+	0.581949i
$276$	−0.0671400	+	0.0800143i	−0.00404135	+	0.00481630i
$277$	2.07772	+	9.77490i	0.124838	+	0.587317i	0.995445	+	0.0953376i	$0.0303930\pi$
$277$	2.07772	+	9.77490i	0.124838	+	0.587317i	−0.870607	+	0.491979i	$0.836274\pi$
$278$	20.8521	−	2.19165i	1.25063	−	0.131446i
$279$	−1.79383	+	6.25583i	−0.107394	+	0.374527i
$280$	1.63049	+	3.06650i	0.0974402	+	0.183258i
$281$	21.6794	−	3.04684i	1.29328	−	0.181759i	0.541237	−	0.840870i	$-0.317956\pi$
$281$	21.6794	−	3.04684i	1.29328	−	0.181759i	0.752045	+	0.659111i	$0.229067\pi$
$282$	−10.3920	+	7.00952i	−0.618837	+	0.417411i
$283$	−26.3704	−	6.57488i	−1.56756	−	0.390836i	−0.641167	−	0.767401i	$-0.721549\pi$
$283$	−26.3704	−	6.57488i	−1.56756	−	0.390836i	−0.926390	+	0.376566i	$0.877105\pi$
$284$	−11.1925	−	3.63667i	−0.664154	−	0.215797i
$285$	−5.83060	−	5.48754i	−0.345375	−	0.325054i
$286$	0.621435	+	18.1445i	0.0367462	+	1.07290i
$287$	6.28860	+	7.49446i	0.371204	+	0.442384i
$288$	−0.454481	+	0.581709i	−0.0267805	+	0.0342775i
$289$	5.19638	+	10.6542i	0.305669	+	0.626715i
$290$	−4.65730	+	9.54889i	−0.273486	+	0.560730i
$291$	17.1288	+	21.9239i	1.00411	+	1.28520i
$292$	0.457347	−	2.15165i	0.0267642	−	0.125916i
$293$	−0.770285	+	7.32877i	−0.0450005	+	0.428152i	0.948708	+	0.316154i	$0.102392\pi$
$293$	−0.770285	+	7.32877i	−0.0450005	+	0.428152i	−0.993708	+	0.111998i	$0.964275\pi$
$294$	0.113874	−	1.62848i	0.00664129	−	0.0949748i
$295$	−2.38166	−	3.81146i	−0.138666	−	0.221912i
$296$	−4.08282	+	2.35722i	−0.237309	+	0.137011i
$297$	−16.7644	+	8.16263i	−0.972769	+	0.473644i
$298$	−0.0521239	−	0.143209i	−0.00301945	−	0.00829588i
$299$	0.376480	+	0.0529108i	0.0217724	+	0.00305991i
$300$	−4.74211	+	2.31288i	−0.273786	+	0.133534i
$301$	8.87243	+	13.1539i	0.511398	+	0.758179i
$302$	−18.4558	−	11.5325i	−1.06201	−	0.663619i
$303$	0.378228	+	1.16407i	0.0217286	+	0.0668739i
$304$	−0.0560022	−	4.35854i	−0.00321195	−	0.249979i
$305$	−3.23035	−	4.44619i	−0.184969	−	0.254588i
$306$	1.55268	−	0.627323i	0.0887607	−	0.0358617i
$307$	6.46918	+	2.35459i	0.369215	+	0.134383i	0.519963	−	0.854189i	$-0.325946\pi$
$307$	6.46918	+	2.35459i	0.369215	+	0.134383i	−0.150747	+	0.988572i	$0.548168\pi$
$308$	−6.55574	+	6.77956i	−0.373548	+	0.386301i
$309$	−4.94017	−	28.0171i	−0.281037	−	1.59384i
$310$	10.7612	−	0.375789i	0.611195	−	0.0213434i
$311$	−0.556221	−	5.29209i	−0.0315404	−	0.300087i	−0.998908	−	0.0467113i	$-0.985126\pi$
$311$	−0.556221	−	5.29209i	−0.0315404	−	0.300087i	0.967368	−	0.253375i	$-0.0815408\pi$
$312$	−8.18736	−	0.860526i	−0.463518	−	0.0487177i
$313$	−4.99470	+	12.3623i	−0.282317	+	0.698759i	0.717680	+	0.696373i	$0.245204\pi$
$313$	−4.99470	+	12.3623i	−0.282317	+	0.698759i	−0.999997	+	0.00238620i	$0.999240\pi$
$314$	3.81631	−	9.44570i	0.215367	−	0.533052i
$315$	2.54974	+	0.267988i	0.143662	+	0.0150994i
$316$	0.521864	+	4.96521i	0.0293572	+	0.279315i
$317$	22.9482	−	0.801368i	1.28890	−	0.0450093i	0.617775	−	0.786355i	$-0.288034\pi$
$317$	22.9482	−	0.801368i	1.28890	−	0.0450093i	0.671123	+	0.741346i	$0.265812\pi$
$318$	2.01438	+	11.4241i	0.112961	+	0.640632i
$319$	−28.5657	−	4.03419i	−1.59937	−	0.225871i
$320$	1.14773	+	0.417741i	0.0641603	+	0.0233524i
$321$	23.0611	−	9.31728i	1.28714	−	0.520040i
$322$	0.116080	+	0.159771i	0.00646889	+	0.00890366i
$323$	−4.83369	+	8.62628i	−0.268954	+	0.479979i
$324$	−1.92841	−	5.93503i	−0.107134	−	0.329724i
$325$	16.2857	+	10.1764i	0.903369	+	0.564488i
$326$	13.1050	+	19.4290i	0.725819	+	1.07607i
$327$	−10.4000	+	5.07241i	−0.575121	+	0.280505i
$328$	3.40712	+	0.478839i	0.188127	+	0.0264395i
$329$	8.10594	+	22.2709i	0.446895	+	1.22783i
$330$	4.22910	+	4.38525i	0.232805	+	0.241400i
$331$	6.48619	−	3.74480i	0.356513	−	0.205833i	−0.311037	−	0.950398i	$-0.600676\pi$
$331$	6.48619	−	3.74480i	0.356513	−	0.205833i	0.667550	+	0.744565i	$0.267343\pi$
$332$	−4.47775	−	7.16590i	−0.245748	−	0.393280i
$333$	−0.242766	+	3.47172i	−0.0133035	+	0.190249i
$334$	−1.45682	+	13.8607i	−0.0797135	+	0.758423i
$335$	−2.57172	+	12.0990i	−0.140508	+	0.661038i
$336$	−2.63282	−	3.36986i	−0.143632	−	0.183841i
$337$	9.43123	−	19.3369i	0.513752	−	1.05335i	−0.471441	−	0.881897i	$-0.656266\pi$
$337$	9.43123	−	19.3369i	0.513752	−	1.05335i	0.985193	−	0.171449i	$-0.0548450\pi$
$338$	7.43668	+	15.2474i	0.404502	+	0.829352i
$339$	17.8782	−	22.8830i	0.971009	−	1.24284i
$340$	−1.78100	−	2.12252i	−0.0965885	−	0.115110i
$341$	9.98198	+	27.4826i	0.540554	+	1.48827i
$342$	−2.69052	−	1.76491i	−0.145487	−	0.0954356i
$343$	15.9948	+	5.19704i	0.863640	+	0.280614i
$344$	5.41418	+	1.34991i	0.291913	+	0.0727821i
$345$	0.105765	−	0.0713396i	0.00569422	−	0.00384080i
$346$	−13.8423	+	1.94541i	−0.744168	+	0.104586i
$347$	−3.32429	−	6.25208i	−0.178457	−	0.335629i	0.777625	−	0.628729i	$-0.216424\pi$
$347$	−3.32429	−	6.25208i	−0.178457	−	0.335629i	−0.956082	+	0.293099i	$0.905313\pi$
$348$	3.60581	−	12.5749i	0.193291	−	0.674087i
$349$	−8.37066	+	0.879792i	−0.448071	+	0.0470942i	−0.325877	−	0.945412i	$-0.605660\pi$
$349$	−8.37066	+	0.879792i	−0.448071	+	0.0470942i	−0.122194	+	0.992506i	$0.538993\pi$
$350$	2.07403	+	9.75755i	0.110862	+	0.521563i
$351$	−19.7815	+	23.5747i	−1.05586	+	1.25832i
$352$	−0.117971	+	3.31453i	−0.00628790	+	0.176665i
$353$	−10.2209	−	17.7031i	−0.544003	−	0.942240i	−0.998669	−	0.0515784i	$-0.983575\pi$
$353$	−10.2209	−	17.7031i	−0.544003	−	0.942240i	0.454666	−	0.890662i	$-0.349759\pi$
$354$	3.70300	+	4.11260i	0.196812	+	0.218582i
$355$	11.9166	+	8.03783i	0.632466	+	0.426604i
$356$	2.76954	+	1.35080i	0.146786	+	0.0715921i
$357$	1.35013	+	9.60670i	0.0714567	+	0.508441i
$358$	6.18381	+	0.215944i	0.326825	+	0.0114130i
$359$	−0.811789	−	11.6091i	−0.0428446	−	0.612706i	−0.970781	−	0.239968i	$-0.922863\pi$
$359$	−0.811789	−	11.6091i	−0.0428446	−	0.612706i	0.927936	−	0.372739i	$-0.121581\pi$
$360$	0.729435	−	0.529966i	0.0384446	−	0.0279316i
$361$	18.9134	−	1.81192i	0.995442	−	0.0953643i
$362$			8.18715i			0.430307i
$363$	−7.78615	+	14.5964i	−0.408667	+	0.766110i
$364$	−5.32361	+	14.6265i	−0.279033	+	0.766637i
$365$	−1.26134	+	2.37223i	−0.0660214	+	0.124168i
$366$	4.86784	+	4.70082i	0.254446	+	0.245716i
$367$	3.34996	+	0.960585i	0.174866	+	0.0501421i	0.361928	−	0.932206i	$-0.382119\pi$
$367$	3.34996	+	0.960585i	0.174866	+	0.0501421i	−0.187062	+	0.982348i	$0.559896\pi$
$368$	0.0679346	+	0.0144399i	0.00354134	+	0.000752734i
$369$	1.69949	−	1.88748i	0.0884719	−	0.0982580i
$370$	5.58714	−	1.39303i	0.290462	−	0.0724202i
$371$	21.8795	+	1.52996i	1.13593	+	0.0794316i
$372$	−12.9688	+	2.75661i	−0.672403	+	0.142924i
$373$	−9.41934	+	16.3148i	−0.487715	+	0.844747i	−0.999900	−	0.0141281i	$-0.995503\pi$
$373$	−9.41934	+	16.3148i	−0.487715	+	0.844747i	0.512185	+	0.858875i	$0.328836\pi$
$374$	3.99130	−	6.37789i	0.206385	−	0.329793i
$375$	15.3912	−	2.71388i	0.794797	−	0.140144i
$376$	7.35926	+	3.91299i	0.379525	+	0.201797i
$377$	−45.7700	+	13.1243i	−2.35728	+	0.675938i
$378$	−15.9471	+	1.11513i	−0.820232	+	0.0573562i
$379$	1.16577	−	0.378782i	0.0598816	−	0.0194567i	−0.278923	−	0.960313i	$-0.589977\pi$
$379$	1.16577	−	0.378782i	0.0598816	−	0.0194567i	0.338805	+	0.940857i	$0.389977\pi$
$380$	−1.40160	+	5.13612i	−0.0719006	+	0.263477i
$381$	2.44870	−	3.37035i	0.125451	−	0.172668i
$382$	3.24939	−	13.0326i	0.166253	−	0.666805i
$383$	−23.1672	−	18.1002i	−1.18379	−	0.924876i	−0.185458	−	0.982652i	$-0.559377\pi$
$383$	−23.1672	−	18.1002i	−1.18379	−	0.924876i	−0.998330	+	0.0577763i	$0.981599\pi$
$384$	−1.48108	−	0.261154i	−0.0755811	−	0.0133270i
$385$	9.97936	−	5.75267i	0.508595	−	0.293183i
$386$	18.0971	−	6.58680i	0.921117	−	0.335259i
$387$	3.06109	−	2.75621i	0.155604	−	0.140106i
$388$	7.52441	−	16.9001i	0.381994	−	0.857972i
$389$	−8.27548	−	33.1911i	−0.419583	−	1.68286i	−0.692981	−	0.720956i	$-0.743703\pi$
$389$	−8.27548	−	33.1911i	−0.419583	−	1.68286i	0.273397	−	0.961901i	$-0.411853\pi$
$390$	9.32290	+	3.76669i	0.472083	+	0.190734i
$391$	−0.117085	−	0.105424i	−0.00592126	−	0.00533152i
$392$	−0.991618	+	0.441497i	−0.0500843	+	0.0222990i
$393$	9.12696	−	13.5313i	0.460394	−	0.682563i
$394$	−1.05054	+	7.47496i	−0.0529253	+	0.376583i
$395$	1.05888	−	6.00523i	0.0532783	−	0.302156i
$396$	1.97978	+	1.44042i	0.0994875	+	0.0723839i
$397$	−6.07709	+	5.09929i	−0.305000	+	0.255926i	−0.782422	−	0.622749i	$-0.786016\pi$
$397$	−6.07709	+	5.09929i	−0.305000	+	0.255926i	0.477422	+	0.878674i	$0.341571\pi$
$398$	0.761045	−	2.34226i	0.0381478	−	0.117407i
$399$	13.6912	−	12.6498i	0.685415	−	0.633284i
$400$	2.83819	+	2.06207i	0.141910	+	0.103103i
$401$	7.56026	−	12.0989i	0.377541	−	0.604192i	−0.603646	−	0.797253i	$-0.706286\pi$
$401$	7.56026	−	12.0989i	0.377541	−	0.604192i	0.981187	+	0.193060i	$0.0618414\pi$
$402$	0.531539	−	15.2213i	0.0265108	−	0.759169i
$403$	33.5230	+	34.7141i	1.66990	+	1.72923i
$404$	0.565348	−	0.585435i	0.0281271	−	0.0291265i
$405$	0.266006	+	7.61742i	0.0132179	+	0.378512i
$406$	−21.4200	−	12.3669i	−1.06306	−	0.613757i
$407$	8.27694	+	13.2657i	0.410273	+	0.657554i
$408$	2.61350	+	2.19299i	0.129388	+	0.108569i
$409$	13.2165	−	8.25858i	0.653513	−	0.408360i	−0.162247	−	0.986750i	$-0.551874\pi$
$409$	13.2165	−	8.25858i	0.653513	−	0.408360i	0.815760	+	0.578390i	$0.196319\pi$
$410$	−3.83901	−	1.70924i	−0.189595	−	0.0844133i
$411$	−6.28258	−	14.1109i	−0.309897	−	0.696040i
$412$	−14.9065	+	11.6463i	−0.734393	+	0.573770i
$413$	9.23853	−	4.91221i	0.454598	−	0.241714i
$414$	0.0368803	−	0.0356149i	0.00181257	−	0.00175038i
$415$	2.84475	+	9.92081i	0.139643	+	0.486993i
$416$	2.05058	+	5.07538i	0.100538	+	0.248841i
$417$	31.5329			1.54417
$418$	−14.4408	+	0.680435i	−0.706323	+	0.0332812i
$419$	6.10708			0.298350			0.149175	−	0.988811i	$-0.452338\pi$
$419$	6.10708			0.298350			0.149175	+	0.988811i	$0.452338\pi$
$420$	1.95664	+	4.84285i	0.0954741	+	0.236307i
$421$	−4.11080	−	14.3361i	−0.200348	−	0.698698i	−0.995707	−	0.0925589i	$-0.970495\pi$
$421$	−4.11080	−	14.3361i	−0.200348	−	0.698698i	0.795359	−	0.606139i	$-0.207282\pi$
$422$	−10.3394	+	9.98461i	−0.503313	+	0.486043i
$423$	5.43260	−	2.88857i	0.264142	−	0.140447i
$424$	6.07821	−	4.74882i	0.295184	−	0.230623i
$425$	−3.23698	−	7.27037i	−0.157016	−	0.352665i
$426$	−16.1689	−	7.19884i	−0.783383	−	0.348785i
$427$	10.8505	−	6.78012i	0.525090	−	0.328113i
$428$	−12.6689	−	10.6305i	−0.612376	−	0.513845i
$429$	−1.92290	+	27.2362i	−0.0928383	+	1.31498i
$430$	−5.90221	−	3.40764i	−0.284630	−	0.164331i
$431$	0.710465	+	20.3451i	0.0342219	+	0.979987i	0.888138	+	0.459577i	$0.151999\pi$
$431$	0.710465	+	20.3451i	0.0342219	+	0.979987i	−0.853916	+	0.520411i	$0.825779\pi$
$432$	−3.90536	+	4.04412i	−0.187897	+	0.194573i
$433$	19.8153	+	20.5193i	0.952263	+	0.986097i	0.999919	−	0.0127668i	$-0.00406391\pi$
$433$	19.8153	+	20.5193i	0.952263	+	0.986097i	−0.0476557	+	0.998864i	$0.515175\pi$
$434$	−0.874865	+	25.0529i	−0.0419949	+	1.20258i
$435$	−8.46700	+	13.5500i	−0.405961	+	0.649674i
$436$	6.22448	+	4.52235i	0.298099	+	0.216581i
$437$	−0.0382775	+	0.300306i	−0.00183106	+	0.0143656i
$438$	1.02229	−	3.14630i	0.0488471	−	0.150336i
$439$	15.3819	−	12.9070i	0.734139	−	0.616016i	−0.197117	−	0.980380i	$-0.563158\pi$
$439$	15.3819	−	12.9070i	0.734139	−	0.616016i	0.931257	+	0.364364i	$0.118714\pi$
$440$	1.25438	−	3.85180i	0.0598003	−	0.183627i
$441$	−0.139142	+	0.789113i	−0.00662581	+	0.0375768i
$442$	1.72822	−	12.2969i	0.0822032	−	0.584906i
$443$	−10.3536	+	15.3498i	−0.491913	+	0.729291i	−0.990495	−	0.137552i	$-0.956077\pi$
$443$	−10.3536	+	15.3498i	−0.491913	+	0.729291i	0.498582	+	0.866843i	$0.333854\pi$
$444$	−6.47720	+	2.88384i	−0.307394	+	0.136861i
$445$	−2.79690	−	2.51834i	−0.132586	−	0.119381i
$446$	25.6324	+	10.3562i	1.21373	+	0.490378i
$447$	−0.0554482	−	0.222390i	−0.00262261	−	0.0105187i
$448$	−1.15655	+	2.59766i	−0.0546420	+	0.122728i
$449$	−30.8148	+	27.7458i	−1.45424	+	1.30940i	−0.588912	+	0.808197i	$0.700444\pi$
$449$	−30.8148	+	27.7458i	−1.45424	+	1.30940i	−0.865328	+	0.501207i	$0.832890\pi$
$450$	2.43357	−	0.885747i	0.114720	−	0.0417545i
$451$	1.20040	−	11.3479i	0.0565248	−	0.534350i
$452$	−19.0154	−	3.35293i	−0.894409	−	0.157709i
$453$	−25.7912	−	20.1503i	−1.21178	−	0.946745i
$454$	−0.719841	+	2.88713i	−0.0337838	+	0.135499i
$455$	11.1745	−	15.3804i	0.523870	−	0.721045i
$456$	0.601415	−	6.52783i	0.0281638	−	0.305693i
$457$	−2.05615	+	0.668083i	−0.0961826	+	0.0312516i	−0.356713	−	0.934214i	$-0.616103\pi$
$457$	−2.05615	+	0.668083i	−0.0961826	+	0.0312516i	0.260530	+	0.965466i	$0.416103\pi$
$458$	3.99575	−	0.279410i	0.186709	−	0.0130560i
$459$	12.2595	−	3.51536i	0.572225	−	0.164083i
$460$	−0.0748992	−	0.0398246i	−0.00349219	−	0.00185683i
$461$	−28.8983	+	5.09554i	−1.34593	+	0.237323i	−0.799743	−	0.600343i	$-0.795031\pi$
$461$	−28.8983	+	5.09554i	−1.34593	+	0.237323i	−0.546183	+	0.837666i	$0.683920\pi$
$462$	−10.8711	+	9.10953i	−0.505770	+	0.423814i
$463$	0.103964	−	0.180070i	0.00483160	−	0.00836857i	−0.863599	−	0.504178i	$-0.831795\pi$
$463$	0.103964	−	0.180070i	0.00483160	−	0.00836857i	0.868431	+	0.495810i	$0.165129\pi$
$464$	−8.50827	+	1.80849i	−0.394987	+	0.0839570i
$465$	16.1545	+	1.12963i	0.749146	+	0.0523854i
$466$	−4.16281	+	1.03790i	−0.192838	+	0.0480800i
$467$	4.60509	−	5.11447i	0.213098	−	0.236670i	−0.627114	−	0.778928i	$-0.715764\pi$
$467$	4.60509	−	5.11447i	0.213098	−	0.236670i	0.840212	+	0.542258i	$0.182431\pi$
$468$	3.95258	+	0.840146i	0.182708	+	0.0388358i
$469$	−27.6811	−	7.93742i	−1.27819	−	0.366516i
$470$	−7.32300	−	7.07174i	−0.337785	−	0.326195i
$471$	7.19291	−	13.5279i	0.331432	−	0.623333i
$472$	1.25854	−	3.45781i	0.0579290	−	0.159159i
$473$	3.85986	−	18.0995i	0.177477	−	0.832217i
$474$			7.50845i			0.344874i
$475$	−7.93618	+	13.0713i	−0.364137	+	0.599752i
$476$	5.21858	−	3.79152i	0.239193	−	0.173784i
$477$	−0.397193	−	5.68013i	−0.0181862	−	0.260075i
$478$	−1.11256	−	0.0388514i	−0.0508873	−	0.00177702i
$479$	−1.94493	−	13.8389i	−0.0888663	−	0.632317i	−0.982876	−	0.184269i	$-0.941008\pi$
$479$	−1.94493	−	13.8389i	−0.0888663	−	0.632317i	0.894010	−	0.448048i	$-0.147881\pi$
$480$	1.65098	+	0.805239i	0.0753568	+	0.0367539i
$481$	21.3947	+	14.4309i	0.975515	+	0.657993i
$482$	−4.87358	−	5.41266i	−0.221986	−	0.246540i
$483$	0.148503	+	0.257215i	0.00675714	+	0.0117037i
$484$	11.0000	+	0.0147546i	0.500000	+	0.000670662i
$485$	−14.5239	+	17.3089i	−0.659494	+	0.785955i
$486$	1.55533	+	7.31727i	0.0705514	+	0.331918i
$487$	−26.9102	+	2.82837i	−1.21942	+	0.128166i	−0.692289	−	0.721620i	$-0.743398\pi$
$487$	−26.9102	+	2.82837i	−1.21942	+	0.128166i	−0.527128	+	0.849786i	$0.676731\pi$
$488$	1.24026	−	4.32531i	0.0561440	−	0.195797i
$489$	16.5467	+	31.1199i	0.748269	+	1.40729i
$490$	1.31287	−	0.184512i	0.0593095	−	0.00833541i
$491$	16.1723	−	10.9084i	0.729846	−	0.492287i	−0.137183	−	0.990546i	$-0.543805\pi$
$491$	16.1723	−	10.9084i	0.729846	−	0.492287i	0.867029	+	0.498258i	$0.166027\pi$
$492$	5.02071	+	1.25180i	0.226351	+	0.0564357i
$493$	18.7666	+	6.09764i	0.845205	+	0.274624i
$494$	−21.3095	+	10.7344i	−0.958760	+	0.482964i
$495$	−1.83948	−	2.35768i	−0.0826783	−	0.105970i
$496$	5.66679	+	6.75342i	0.254446	+	0.303237i
$497$	−20.6023	+	26.3698i	−0.924141	+	1.18285i
$498$	−5.57082	−	11.4219i	−0.249634	−	0.511826i
$499$	−1.16845	+	2.39567i	−0.0523068	+	0.107245i	−0.923346	−	0.383968i	$-0.874557\pi$
$499$	−1.16845	+	2.39567i	−0.0523068	+	0.107245i	0.871040	+	0.491213i	$0.163446\pi$
$500$	−6.39786	−	8.18889i	−0.286121	−	0.366218i
$501$	−4.35789	+	20.5023i	−0.194696	+	0.915974i
$502$	−1.00915	+	9.60144i	−0.0450407	+	0.428533i
$503$	2.46985	−	35.3204i	0.110125	−	1.57486i	−0.557381	−	0.830257i	$-0.688194\pi$
$503$	2.46985	−	35.3204i	0.110125	−	1.57486i	0.667506	−	0.744604i	$-0.267362\pi$
$504$	1.11234	+	1.78011i	0.0495474	+	0.0792923i
$505$	−0.860856	+	0.497015i	−0.0383076	+	0.0221169i
$506$	0.0401515	−	0.226821i	0.00178495	−	0.0100834i
$507$	8.72601	+	23.9745i	0.387536	+	1.06475i
$508$	−2.74311	−	0.385518i	−0.121706	−	0.0171046i
$509$	−13.1399	+	6.40873i	−0.582414	+	0.284062i	−0.705931	−	0.708280i	$-0.749471\pi$
$509$	−13.1399	+	6.40873i	−0.582414	+	0.284062i	0.123518	+	0.992342i	$0.460582\pi$
$510$	−2.33016	−	3.45461i	−0.103181	−	0.152973i
$511$	−5.30444	−	3.31458i	−0.234655	−	0.146628i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	−18.9733	−	15.5095i	−0.837690	−	0.684759i
$514$	−0.0226041	−	0.0311119i	−0.000997024	−	0.00137229i
$515$	21.4223	−	8.65517i	0.943979	−	0.381392i
$516$	7.88572	+	2.87017i	0.347149	+	0.126352i
$517$	12.1348	−	24.8378i	0.533690	−	1.09237i
$518$	2.32784	+	13.2018i	0.102279	+	0.580055i
$519$	−21.0096	+	0.733673i	−0.922221	+	0.0322047i
$520$	−0.698864	−	6.64924i	−0.0306472	−	0.291589i
$521$	−15.1793	−	1.59541i	−0.665018	−	0.0698962i	−0.233996	−	0.972238i	$-0.575180\pi$
$521$	−15.1793	−	1.59541i	−0.665018	−	0.0698962i	−0.431022	+	0.902341i	$0.641847\pi$
$522$	−2.40539	+	5.95356i	−0.105281	+	0.260580i
$523$	−7.24200	+	17.9246i	−0.316670	+	0.783787i	0.681956	+	0.731393i	$0.261130\pi$
$523$	−7.24200	+	17.9246i	−0.316670	+	0.783787i	−0.998627	+	0.0523937i	$0.983315\pi$
$524$	−10.7932	−	1.13441i	−0.471505	−	0.0495571i
$525$	1.56819	+	14.9203i	0.0684414	+	0.651176i
$526$	0.186253	−	0.00650411i	0.00812103	−	0.000283593i
$527$	−3.47282	−	19.6953i	−0.151278	−	0.857942i
$528$	−0.697503	+	4.93896i	−0.0303549	+	0.214941i
$529$	21.6084	+	7.86481i	0.939496	+	0.341948i
$530$	−8.73504	+	3.52918i	−0.379426	+	0.153298i
$531$	−1.59664	−	2.19759i	−0.0692884	−	0.0953673i
$532$	−11.7005	−	4.08918i	−0.507282	−	0.177289i
$533$	−5.81995	−	17.9119i	−0.252090	−	0.775853i
$534$	3.93003	+	2.45575i	0.170069	+	0.106271i
$535$	11.2954	+	16.7462i	0.488345	+	0.724001i
$536$	−9.10226	+	4.43947i	−0.393158	+	0.191756i
$537$	9.21512	+	1.29510i	0.397662	+	0.0558877i
$538$	0.856426	+	2.35301i	0.0369231	+	0.101445i
$539$	1.57600	+	3.23678i	0.0678829	+	0.139418i
$540$	5.94670	−	3.43333i	0.255905	−	0.147747i
$541$	−1.62096	−	2.59407i	−0.0696904	−	0.111528i	0.811368	−	0.584536i	$-0.198724\pi$
$541$	−1.62096	−	2.59407i	−0.0696904	−	0.111528i	−0.881058	+	0.473008i	$0.843168\pi$
$542$	−0.141198	+	2.01922i	−0.00606496	+	0.0867329i
$543$	−1.28705	+	12.2454i	−0.0552325	+	0.525502i
$544$	0.471651	−	2.21894i	0.0202219	−	0.0951365i
$545$	−5.78553	−	7.40514i	−0.247825	−	0.317201i
$546$	−10.2618	+	21.0398i	−0.439165	+	0.900421i
$547$	2.05230	+	4.20785i	0.0877502	+	0.179915i	0.938156	−	0.346213i	$-0.112532\pi$
$547$	2.05230	+	4.20785i	0.0877502	+	0.179915i	−0.850406	+	0.526127i	$0.823644\pi$
$548$	−6.32324	+	8.09338i	−0.270115	+	0.345732i
$549$	−2.13509	−	2.54450i	−0.0911234	−	0.108597i
$550$	6.51289	−	9.64180i	0.277711	−	0.411128i
$551$	−10.9183	−	36.3092i	−0.465133	−	1.54682i
$552$	0.0993391	+	0.0322772i	0.00422815	+	0.00137381i
$553$	13.7746	+	3.43440i	0.585756	+	0.146045i
$554$	8.28480	−	5.58817i	0.351987	−	0.237419i
$555$	8.57562	−	1.20522i	0.364015	−	0.0511589i
$556$	−9.84341	−	18.5128i	−0.417454	−	0.785116i
$557$	6.63293	−	23.1318i	0.281046	−	0.980124i	−0.686437	−	0.727189i	$-0.740826\pi$
$557$	6.63293	−	23.1318i	0.281046	−	0.980124i	0.967483	−	0.252935i	$-0.0813959\pi$
$558$	6.47229	−	0.680265i	0.273994	−	0.0287979i
$559$	−6.35052	−	29.8769i	−0.268599	−	1.26366i
$560$	2.23242	−	2.66049i	0.0943368	−	0.112426i
$561$	6.97236	−	8.91189i	0.294373	−	0.376260i
$562$	−10.9462	−	18.9594i	−0.461738	−	0.799754i
$563$	3.77848	+	4.19643i	0.159244	+	0.176858i	0.817487	−	0.575947i	$-0.195367\pi$
$563$	3.77848	+	4.19643i	0.159244	+	0.176858i	−0.658243	+	0.752806i	$0.728700\pi$
$564$	10.3920	+	7.00952i	0.437584	+	0.295154i
$565$	21.1968	+	10.3384i	0.891755	+	0.434938i
$566$	3.78240	+	26.9132i	0.158986	+	1.13125i
$567$	−17.7339	−	0.619282i	−0.744754	−	0.0260074i
$568$	0.820930	+	11.7399i	0.0344455	+	0.492593i
$569$	−25.6032	+	18.6018i	−1.07334	+	0.779828i	−0.976510	−	0.215472i	$-0.930871\pi$
$569$	−25.6032	+	18.6018i	−1.07334	+	0.779828i	−0.0968317	+	0.995301i	$0.530871\pi$
$570$	−2.90378	+	7.46171i	−0.121626	+	0.312536i
$571$		−	20.0496i		−	0.839049i	−0.907744	−	0.419524i	$-0.862197\pi$
$571$		−	20.0496i		−	0.839049i	0.907744	−	0.419524i	$-0.137803\pi$
$572$	16.5905	−	7.37322i	0.693682	−	0.308290i
$573$	6.90884	−	18.9819i	0.288621	−	0.792979i
$574$	4.59299	−	8.63817i	0.191708	−	0.360550i
$575$	−0.175269	−	0.169255i	−0.00730922	−	0.00705843i
$576$	0.709603	+	0.203475i	0.0295668	+	0.00847814i
$577$	−19.4684	−	4.13814i	−0.810482	−	0.172273i	−0.216012	−	0.976391i	$-0.569305\pi$
$577$	−19.4684	−	4.13814i	−0.810482	−	0.172273i	−0.594470	+	0.804118i	$0.702638\pi$
$578$	7.93176	−	8.80911i	0.329918	−	0.366411i
$579$	28.1031	−	7.00689i	1.16792	−	0.291196i
$580$	10.5982	+	0.741100i	0.440067	+	0.0307725i
$581$	−23.5021	+	4.99553i	−0.975032	+	0.207249i
$582$	13.9109	−	24.0944i	0.576627	−	0.998746i
$583$	−16.4308	−	19.6082i	−0.680496	−	0.812089i
$584$	−2.16630	+	0.381977i	−0.0896420	+	0.0158063i
$585$	−4.35779	−	2.31708i	−0.180172	−	0.0957994i
$586$	7.08368	−	2.03121i	0.292624	−	0.0839086i
$587$	20.2825	−	1.41829i	0.837147	−	0.0585390i	0.355255	−	0.934769i	$-0.384394\pi$
$587$	20.2825	−	1.41829i	0.837147	−	0.0585390i	0.481892	+	0.876230i	$0.339950\pi$
$588$	−1.55256	+	0.504457i	−0.0640264	+	0.0208034i
$589$	−27.2975	+	27.0472i	−1.12477	+	1.11446i
$590$	−2.64174	+	3.63604i	−0.108759	+	0.149693i
$591$	−2.74636	+	11.0151i	−0.112970	+	0.453099i
$592$	3.71503	+	2.90250i	0.152687	+	0.119292i
$593$	−0.793100	−	0.139845i	−0.0325687	−	0.00574274i	0.157340	−	0.987544i	$-0.449708\pi$
$593$	−0.793100	−	0.139845i	−0.0325687	−	0.00574274i	−0.189909	+	0.981802i	$0.560819\pi$
$594$	13.8483	+	12.4859i	0.568203	+	0.512303i
$595$	−7.40348	+	2.69464i	−0.303513	+	0.110470i
$596$	−0.113255	+	0.101975i	−0.00463912	+	0.00417708i
$597$	1.50650	−	3.38365i	0.0616569	−	0.138484i
$598$	−0.0919738	−	0.368887i	−0.00376109	−	0.0150849i
$599$	−1.18295	−	0.477942i	−0.0483340	−	0.0195282i	0.350312	−	0.936633i	$-0.386075\pi$
$599$	−1.18295	−	0.477942i	−0.0483340	−	0.0195282i	−0.398646	+	0.917105i	$0.630520\pi$
$600$	3.92089	+	3.53039i	0.160070	+	0.144127i
$601$	13.2203	−	5.88606i	0.539267	−	0.240097i	−0.118983	−	0.992896i	$-0.537963\pi$
$601$	13.2203	−	5.88606i	0.539267	−	0.240097i	0.658251	+	0.752799i	$0.271297\pi$
$602$	8.87243	−	13.1539i	0.361613	−	0.536113i
$603$	−1.04044	+	7.40313i	−0.0423701	+	0.301479i
$604$	−3.77905	+	21.4321i	−0.153768	+	0.872059i
$605$	−12.9099	−	3.72060i	−0.524861	−	0.151264i
$606$	0.937617	−	0.786754i	0.0380881	−	0.0319597i
$607$	9.51612	−	29.2876i	0.386248	−	1.18875i	−0.549324	−	0.835610i	$-0.685115\pi$
$607$	9.51612	−	29.2876i	0.386248	−	1.18875i	0.935571	−	0.353138i	$-0.114885\pi$
$608$	−4.02019	+	1.68466i	−0.163040	+	0.0683221i
$609$	−30.0936	−	21.8643i	−1.21945	−	0.885986i
$610$	−2.91233	+	4.66070i	−0.117917	+	0.188706i
$611$	1.59229	−	45.5971i	0.0644170	−	1.84466i
$612$	−1.16329	−	1.20462i	−0.0470231	−	0.0486938i
$613$	−5.70196	+	5.90455i	−0.230300	+	0.238483i	−0.824538	−	0.565807i	$-0.808565\pi$
$613$	−5.70196	+	5.90455i	−0.230300	+	0.238483i	0.594238	+	0.804289i	$0.297454\pi$
$614$	−0.240260	−	6.88016i	−0.00969612	−	0.277661i
$615$	−5.47328	−	3.16000i	−0.220704	−	0.127423i
$616$	8.74172	+	3.53871i	0.352214	+	0.142578i
$617$	−17.8900	−	15.0115i	−0.720223	−	0.604339i	0.207224	−	0.978293i	$-0.433557\pi$
$617$	−17.8900	−	15.0115i	−0.720223	−	0.604339i	−0.927447	+	0.373955i	$0.878001\pi$
$618$	−24.1264	+	15.0758i	−0.970506	+	0.606439i
$619$	14.2243	+	6.33309i	0.571725	+	0.254548i	0.672173	−	0.740394i	$-0.265361\pi$
$619$	14.2243	+	6.33309i	0.571725	+	0.254548i	−0.100448	+	0.994942i	$0.532028\pi$
$620$	−4.37964	−	9.83683i	−0.175891	−	0.395057i
$621$	0.307687	−	0.240391i	0.0123470	−	0.00964656i
$622$	−4.69837	+	2.49817i	−0.188388	+	0.100167i
$623$	6.30282	−	6.08656i	0.252517	−	0.243853i
$624$	2.26917	+	7.91355i	0.0908396	+	0.316795i
$625$	−1.81626	−	4.49541i	−0.0726505	−	0.179816i
$626$	13.3332			0.532901
$627$	−21.7059	−	1.25242i	−0.866852	−	0.0500170i
$628$	−10.1875			−0.406526
$629$	−4.00634	−	9.91603i	−0.159743	−	0.395378i
$630$	−0.706675	−	2.46447i	−0.0281546	−	0.0981867i
$631$	6.04611	−	5.83867i	0.240692	−	0.232434i	−0.564522	−	0.825418i	$-0.690939\pi$
$631$	6.04611	−	5.83867i	0.240692	−	0.232434i	0.805214	+	0.592985i	$0.202050\pi$
$632$	4.40816	−	2.34386i	0.175347	−	0.0932339i
$633$	−17.0341	+	13.3085i	−0.677045	+	0.528965i
$634$	−9.33956	−	20.9770i	−0.370921	−	0.833103i
$635$	3.09083	+	1.37613i	0.122656	+	0.0546099i
$636$	9.83765	−	6.14724i	0.390088	−	0.243754i
$637$	4.55167	+	3.81930i	0.180344	+	0.151326i
$638$	6.96047	+	27.9969i	0.275568	+	1.10841i
$639$	7.52361	+	4.34376i	0.297629	+	0.171836i
$640$	−0.0426260	−	1.22065i	−0.00168494	−	0.0482504i
$641$	11.6968	−	12.1124i	0.461995	−	0.478409i	−0.447406	−	0.894331i	$-0.647652\pi$
$641$	11.6968	−	12.1124i	0.461995	−	0.478409i	0.909400	+	0.415922i	$0.136541\pi$
$642$	−17.2777	−	17.8915i	−0.681895	−	0.706123i
$643$	0.968061	−	27.7216i	0.0381766	−	1.09323i	−0.817567	−	0.575834i	$-0.804678\pi$
$643$	0.968061	−	27.7216i	0.0381766	−	1.09323i	0.855743	−	0.517400i	$-0.173100\pi$
$644$	0.104652	−	0.167479i	0.00412388	−	0.00659959i
$645$	−8.29218	−	6.02462i	−0.326504	−	0.237219i
$646$	9.80888	+	1.25026i	0.385925	+	0.0491907i
$647$	−3.51251	+	10.8104i	−0.138091	+	0.425000i	−0.996058	−	0.0887044i	$-0.971727\pi$
$647$	−3.51251	+	10.8104i	−0.138091	+	0.425000i	0.857967	+	0.513705i	$0.171727\pi$
$648$	−4.78047	+	4.01129i	−0.187795	+	0.157578i
$649$	−11.6044	−	3.77911i	−0.455513	−	0.148343i
$650$	3.33470	−	18.9120i	0.130798	−	0.741791i
$651$	−5.24692	+	37.3338i	−0.205643	+	1.46323i
$652$	13.1050	−	19.4290i	0.513232	−	0.760897i
$653$	33.5932	−	14.9567i	1.31460	−	0.585299i	0.374829	−	0.927094i	$-0.377701\pi$
$653$	33.5932	−	14.9567i	1.31460	−	0.585299i	0.939775	+	0.341795i	$0.111035\pi$
$654$	8.59896	+	7.74254i	0.336246	+	0.302757i
$655$	12.2902	+	4.96556i	0.480218	+	0.194020i
$656$	−0.832356	−	3.33840i	−0.0324981	−	0.130343i
$657$	−0.660471	+	1.48344i	−0.0257674	+	0.0578745i
$658$	17.6127	−	15.8585i	0.686613	−	0.618229i
$659$	11.9447	−	4.34753i	0.465301	−	0.169356i	−0.0987215	−	0.995115i	$-0.531475\pi$
$659$	11.9447	−	4.34753i	0.465301	−	0.169356i	0.564023	+	0.825759i	$0.309253\pi$
$660$	2.48168	−	5.56390i	0.0965993	−	0.216575i
$661$	−31.7908	−	5.60557i	−1.23652	−	0.218031i	−0.483095	−	0.875568i	$-0.660487\pi$
$661$	−31.7908	−	5.60557i	−1.23652	−	0.218031i	−0.753422	+	0.657537i	$0.771598\pi$
$662$	−5.90189	−	4.61106i	−0.229383	−	0.179214i
$663$	4.51801	−	18.1207i	0.175465	−	0.703751i
$664$	−4.96671	+	6.83609i	−0.192746	+	0.265292i
$665$	12.3607	+	8.74014i	0.479326	+	0.338928i
$666$	3.30986	−	1.07544i	0.128255	−	0.0416725i
$667$	0.602649	−	0.0421413i	0.0233347	−	0.00163172i
$668$	13.3971	−	3.84157i	0.518351	−	0.148635i
$669$	36.7101	+	19.5191i	1.41929	+	0.754651i
$670$	12.1814	−	2.14790i	0.470607	−	0.0829808i
$671$	−14.4778	−	3.62004i	−0.558910	−	0.139750i
$672$	−2.13821	+	3.70348i	−0.0824831	+	0.142865i
$673$	26.5604	−	5.64559i	1.02383	−	0.217622i	0.334749	−	0.942307i	$-0.391348\pi$
$673$	26.5604	−	5.64559i	1.02383	−	0.217622i	0.689080	+	0.724686i	$0.258015\pi$
$674$	−21.4618	−	1.50076i	−0.826679	−	0.0578070i
$675$	19.1372	−	4.77144i	0.736590	−	0.183653i
$676$	11.3514	−	12.6070i	0.436591	−	0.484883i
$677$	5.11473	+	1.08717i	0.196575	+	0.0417833i	0.305147	−	0.952305i	$-0.401294\pi$
$677$	5.11473	+	1.08717i	0.196575	+	0.0417833i	−0.108572	+	0.994089i	$0.534628\pi$
$678$	−27.9141	−	8.00423i	−1.07203	−	0.307400i
$679$	−37.8395	−	36.5412i	−1.45215	−	1.40232i
$680$	−1.30079	+	2.44643i	−0.0498830	+	0.0938162i
$681$	−1.53052	+	4.20508i	−0.0586498	+	0.161139i
$682$	21.7421	−	19.5503i	0.832548	−	0.748619i
$683$			4.26067i			0.163030i	0.996672	+	0.0815150i	$0.0259759\pi$
$683$			4.26067i			0.163030i	−0.996672	+	0.0815150i	$0.974024\pi$
$684$	−0.628512	+	3.15576i	−0.0240318	+	0.120663i
$685$	10.1487	−	7.37347i	0.387762	−	0.281726i
$686$	−1.17316	−	16.7770i	−0.0447915	−	0.640549i
$687$	6.02032	+	0.210234i	0.229690	+	0.00802094i
$688$	−0.776575	−	5.52562i	−0.0296067	−	0.210662i
$689$	−37.9495	−	18.5092i	−1.44576	−	0.705145i
$690$	−0.105765	−	0.0713396i	−0.00402642	−	0.00271585i
$691$	9.83095	+	10.9184i	0.373987	+	0.415355i	0.900530	−	0.434794i	$-0.143179\pi$
$691$	9.83095	+	10.9184i	0.373987	+	0.415355i	−0.526543	+	0.850148i	$0.676512\pi$
$692$	6.98918	+	12.1056i	0.265689	+	0.460186i
$693$	5.77421	−	3.88913i	0.219344	−	0.147736i
$694$	−4.55153	+	5.42430i	−0.172774	+	0.205904i
$695$	5.32440	+	25.0493i	0.201966	+	0.950175i
$696$	−13.0100	+	1.36741i	−0.493144	+	0.0518315i
$697$	−2.15137	+	7.50270i	−0.0814888	+	0.284185i
$698$	3.95143	+	7.43156i	0.149564	+	0.281289i
$699$	−6.38943	+	0.897976i	−0.241670	+	0.0339646i
$700$	8.27010	−	5.57825i	0.312580	−	0.210838i
$701$	20.4535	+	5.09964i	0.772520	+	0.192611i	0.608187	−	0.793794i	$-0.291897\pi$
$701$	20.4535	+	5.09964i	0.772520	+	0.192611i	0.164333	+	0.986405i	$0.447453\pi$
$702$	29.2684	+	9.50986i	1.10466	+	0.358927i
$703$	−11.2715	+	17.1828i	−0.425111	+	0.648060i
$704$	3.11737	−	1.13226i	0.117490	−	0.0426737i
$705$	−9.84123	−	11.7283i	−0.370642	−	0.441714i
$706$	−12.5852	+	16.1083i	−0.473650	+	0.606245i
$707$	−1.01447	−	2.07997i	−0.0381530	−	0.0782253i
$708$	2.42597	−	4.97397i	0.0911734	−	0.186933i
$709$	28.0729	+	35.9317i	1.05430	+	1.34944i	0.934227	+	0.356679i	$0.116091\pi$
$709$	28.0729	+	35.9317i	1.05430	+	1.34944i	0.120075	+	0.992765i	$0.461687\pi$
$710$	2.98852	−	14.0599i	0.112157	−	0.527658i
$711$	0.385240	−	3.66531i	0.0144476	−	0.137460i
$712$	0.214948	−	3.07389i	0.00805550	−	0.115199i
$713$	−0.324464	−	0.519250i	−0.0121513	−	0.0194461i
$714$	8.40141	−	4.85056i	0.314415	−	0.181528i
$715$	−21.9608	+	3.07137i	−0.821287	+	0.114863i
$716$	−2.11628	−	5.81443i	−0.0790890	−	0.217295i
$717$	−1.65794	−	0.233008i	−0.0619167	−	0.00870183i
$718$	−10.4597	+	5.10153i	−0.390352	+	0.190388i
$719$	−13.9003	−	20.6080i	−0.518392	−	0.768548i	0.475404	−	0.879768i	$-0.342302\pi$
$719$	−13.9003	−	20.6080i	−0.518392	−	0.768548i	−0.993796	+	0.111220i	$0.964524\pi$
$720$	−0.764627	−	0.477792i	−0.0284960	−	0.0178063i
$721$	16.6219	+	51.1568i	0.619030	+	1.90518i
$722$	−8.76507	−	16.8574i	−0.326202	−	0.627369i
$723$	−6.43848	−	8.86181i	−0.239450	−	0.329574i
$724$	7.59099	−	3.06696i	0.282117	−	0.113983i
$725$	28.6752	+	10.4369i	1.06497	+	0.387618i
$726$	16.4503	+	1.75130i	0.610526	+	0.0649970i
$727$	−1.30349	−	7.39246i	−0.0483438	−	0.274171i	0.951048	−	0.309043i	$-0.100009\pi$
$727$	−1.30349	−	7.39246i	−0.0483438	−	0.274171i	−0.999392	+	0.0348719i	$0.988898\pi$
$728$	15.5557	−	0.543218i	0.576533	−	0.0201330i
$729$	3.13292	+	29.8077i	0.116034	+	1.10399i
$730$	2.67200	+	0.280838i	0.0988951	+	0.0103943i
$731$	−4.74183	+	11.7364i	−0.175383	+	0.434088i
$732$	2.53500	−	6.27434i	0.0936962	−	0.231906i
$733$	3.36694	+	0.353880i	0.124361	+	0.0130709i	0.166504	−	0.986041i	$-0.446752\pi$
$733$	3.36694	+	0.353880i	0.124361	+	0.0130709i	−0.0421435	+	0.999112i	$0.513419\pi$
$734$	−0.364277	−	3.46587i	−0.0134457	−	0.127928i
$735$	1.99266	−	0.0695851i	0.0735002	−	0.00256668i
$736$	−0.0120603	−	0.0683972i	−0.000444547	−	0.00252115i
$737$	15.7488	+	29.6671i	0.580113	+	1.09280i
$738$	−2.38668	−	0.868679i	−0.0878548	−	0.0319765i
$739$	−16.5018	+	6.66718i	−0.607030	+	0.245256i	−0.657482	−	0.753470i	$-0.728378\pi$
$739$	−16.5018	+	6.66718i	−0.607030	+	0.245256i	0.0504518	+	0.998726i	$0.483934\pi$
$740$	−3.38458	−	4.65847i	−0.124419	−	0.171249i
$741$	−33.5599	+	12.7054i	−1.23285	+	0.466745i
$742$	−6.77764	−	20.8594i	−0.248815	−	0.765773i
$743$	6.18191	+	3.86289i	0.226792	+	0.141716i	0.638557	−	0.769575i	$-0.279532\pi$
$743$	6.18191	+	3.86289i	0.226792	+	0.141716i	−0.411764	+	0.911290i	$0.635087\pi$
$744$	7.41410	+	10.9919i	0.271814	+	0.402981i
$745$	0.167302	−	0.0815985i	0.00612946	−	0.00298954i
$746$	18.6553	+	2.62184i	0.683020	+	0.0959923i
$747$	2.13342	+	5.86151i	0.0780576	+	0.214461i
$748$	−7.40864	−	1.31147i	−0.270887	−	0.0479520i
$749$	−40.7258	+	23.5130i	−1.48809	+	0.859148i
$750$	−8.28190	−	13.2538i	−0.302412	−	0.483961i
$751$	1.69829	−	24.2866i	0.0619713	−	0.886232i	−0.862761	−	0.505613i	$-0.831267\pi$
$751$	1.69829	−	24.2866i	0.0619713	−	0.886232i	0.924732	−	0.380619i	$-0.124289\pi$
$752$	0.871232	−	8.28922i	0.0317706	−	0.302277i
$753$	−3.01876	+	14.2021i	−0.110010	+	0.517555i
$754$	29.3144	+	37.5208i	1.06757	+	1.36643i
$755$	11.6523	−	23.8907i	0.424069	−	0.869471i
$756$	7.00784	+	14.3682i	0.254873	+	0.522566i
$757$	−3.36685	+	4.30937i	−0.122370	+	0.156627i	−0.845295	−	0.534300i	$-0.820575\pi$
$757$	−3.36685	+	4.30937i	−0.122370	+	0.156627i	0.722925	+	0.690927i	$0.242797\pi$
$758$	−0.787906	−	0.938989i	−0.0286180	−	0.0341056i
$759$	0.0957112	−	0.332942i	0.00347410	−	0.0120850i
$760$	5.28718	−	0.624482i	0.191786	−	0.0226523i
$761$	39.8615	+	12.9518i	1.44498	+	0.469502i	0.923446	−	0.383729i	$-0.125360\pi$
$761$	39.8615	+	12.9518i	1.44498	+	0.469502i	0.521533	+	0.853231i	$0.325360\pi$
$762$	−4.04223	−	1.00784i	−0.146435	−	0.0365102i
$763$	18.1373	−	12.2337i	0.656613	−	0.442891i
$764$	−13.3008	+	1.86931i	−0.481207	+	0.0676293i
$765$	0.960241	+	1.80595i	0.0347176	+	0.0652943i
$766$	−8.10362	+	28.2607i	−0.292796	+	1.02110i
$767$	−20.0324	+	2.10549i	−0.723327	+	0.0760247i
$768$	0.312684	+	1.47106i	0.0112830	+	0.0530824i
$769$	7.39061	−	8.80779i	0.266512	−	0.317617i	−0.616146	−	0.787632i	$-0.711307\pi$
$769$	7.39061	−	8.80779i	0.266512	−	0.317617i	0.882659	+	0.470015i	$0.155751\pi$
$770$	−9.07212	−	7.09772i	−0.326936	−	0.255784i
$771$	−0.0289178	−	0.0500871i	−0.00104145	−	0.00180384i
$772$	−12.8865	−	14.3119i	−0.463794	−	0.515095i
$773$	−21.7373	−	14.6620i	−0.781837	−	0.527356i	0.102205	−	0.994763i	$-0.467410\pi$
$773$	−21.7373	−	14.6620i	−0.781837	−	0.527356i	−0.884042	+	0.467408i	$0.845188\pi$
$774$	−3.70222	−	1.80569i	−0.133074	−	0.0649043i
$775$	−4.30437	−	30.6272i	−0.154617	−	1.10016i
$776$	−18.4882	−	0.645622i	−0.663687	−	0.0231765i
$777$	1.40635	+	20.1118i	0.0504526	+	0.721506i
$778$	−27.6742	+	20.1065i	−0.992169	+	0.720853i
$779$	14.2025	−	4.81727i	0.508857	−	0.172596i
$780$		−	10.0551i		−	0.360029i
$781$	38.8207	−	4.05390i	1.38911	−	0.145060i
$782$	−0.0538866	+	0.148052i	−0.00192698	+	0.00529433i
$783$	−22.9581	+	43.1779i	−0.820456	+	1.54305i
$784$	0.780815	+	0.754025i	0.0278863	+	0.0269294i
$785$	11.9609	+	3.42975i	0.426904	+	0.122413i
$786$	−15.9650	−	3.39347i	−0.569453	−	0.121041i
$787$	−3.63268	+	4.03450i	−0.129491	+	0.143814i	−0.804403	−	0.594084i	$-0.797515\pi$
$787$	−3.63268	+	4.03450i	−0.129491	+	0.143814i	0.674912	+	0.737898i	$0.264181\pi$
$788$	7.32420	−	1.82613i	0.260914	−	0.0650531i
$789$	0.279600	+	0.0195515i	0.00995401	+	0.000696052i
$790$	−5.96462	+	1.26782i	−0.212212	+	0.0451070i
$791$	−27.4522	+	47.5485i	−0.976086	+	1.69063i
$792$	0.593898	−	2.37521i	0.0211032	−	0.0843993i
$793$	−24.2565	+	4.27708i	−0.861375	+	0.151884i
$794$	7.00449	+	3.72436i	0.248580	+	0.132172i
$795$	−13.6197	+	3.90539i	−0.483041	+	0.138510i
$796$	−2.45680	+	0.171796i	−0.0870788	+	0.00608914i
$797$	−22.9403	+	7.45377i	−0.812588	+	0.264026i	−0.685694	−	0.727890i	$-0.740501\pi$
$797$	−22.9403	+	7.45377i	−0.812588	+	0.264026i	−0.126895	+	0.991916i	$0.540501\pi$
$798$	−16.8575	−	7.95551i	−0.596750	−	0.281622i
$799$	−11.1137	+	15.2967i	−0.393176	+	0.541160i
$800$	0.848710	−	3.40399i	0.0300064	−	0.120349i
$801$	−1.79248	−	1.40044i	−0.0633341	−	0.0494820i
$802$	−14.0501	−	2.47741i	−0.496125	−	0.0874802i
$803$	1.51206	+	7.13722i	0.0533595	+	0.251867i
$804$	−14.3121	+	5.20916i	−0.504747	+	0.183713i
$805$	−0.179254	+	0.161401i	−0.00631786	+	0.00568863i
$806$	19.6284	−	44.0862i	0.691382	−	1.55287i
$807$	0.911046	+	3.65401i	0.0320703	+	0.128627i
$808$	−0.754589	−	0.304874i	−0.0265463	−	0.0107254i
$809$	−37.0613	−	33.3701i	−1.30301	−	1.17323i	−0.973400	−	0.229113i	$-0.926418\pi$
$809$	−37.0613	−	33.3701i	−1.30301	−	1.17323i	−0.329606	−	0.944119i	$-0.606916\pi$
$810$	6.96310	−	3.10017i	0.244658	−	0.108929i
$811$	−30.2514	+	44.8495i	−1.06227	+	1.57488i	−0.271822	+	0.962348i	$0.587626\pi$
$811$	−30.2514	+	44.8495i	−1.06227	+	1.57488i	−0.790447	+	0.612530i	$0.790152\pi$
$812$	−3.44227	+	24.4930i	−0.120800	+	0.859536i
$813$	−0.528616	+	2.99793i	−0.0185394	+	0.105142i
$814$	9.19911	−	12.6436i	0.322429	−	0.443160i
$815$	−21.9273	+	18.3992i	−0.768079	+	0.644495i
$816$	1.05427	−	3.24471i	0.0369068	−	0.113587i
$817$	23.7239	−	5.36214i	0.829994	−	0.187597i
$818$	−12.6082	−	9.16039i	−0.440835	−	0.320286i
$819$	6.08889	−	9.74426i	0.212763	−	0.340492i
$820$	−0.146659	+	4.19976i	−0.00512156	+	0.146662i
$821$	21.0267	+	21.7738i	0.733838	+	0.759912i	0.977725	−	0.209892i	$-0.0673112\pi$
$821$	21.0267	+	21.7738i	0.733838	+	0.759912i	−0.243886	+	0.969804i	$0.578422\pi$
$822$	−10.7299	+	11.1111i	−0.374249	+	0.387546i
$823$	−0.722798	−	20.6982i	−0.0251952	−	0.721495i	−0.944608	−	0.328201i	$-0.893558\pi$
$823$	−0.722798	−	20.6982i	−0.0251952	−	0.721495i	0.919413	−	0.393294i	$-0.128665\pi$
$824$	16.3823	+	9.45834i	0.570705	+	0.329497i
$825$	11.2570	−	13.3973i	0.391918	−	0.466434i
$826$	−8.01534	−	6.72567i	−0.278889	−	0.234016i
$827$	−26.2190	+	16.3834i	−0.911724	+	0.569708i	−0.902709	−	0.430251i	$-0.858425\pi$
$827$	−26.2190	+	16.3834i	−0.911724	+	0.569708i	−0.00901438	+	0.999959i	$0.502869\pi$
$828$	−0.0468372	−	0.0208532i	−0.00162770	−	0.000724700i
$829$	10.7845	+	24.2224i	0.374561	+	0.841278i	0.998223	+	0.0595837i	$0.0189773\pi$
$829$	10.7845	+	24.2224i	0.374561	+	0.841278i	−0.623662	+	0.781694i	$0.714356\pi$
$830$	8.13275	−	6.35400i	0.282292	−	0.220551i
$831$	13.2700	−	7.05577i	0.460330	−	0.244762i
$832$	3.93764	−	3.80254i	0.136513	−	0.131829i
$833$	−0.678726	−	2.36700i	−0.0235165	−	0.0820116i
$834$	−11.8124	−	29.2368i	−0.409031	−	1.01239i
$835$	−17.0226			−0.589092
$836$	6.04051	+	13.1344i	0.208915	+	0.454262i
$837$	49.5632			1.71315
$838$	−2.28775	−	5.66238i	−0.0790290	−	0.195604i
$839$	−9.97278	−	34.7792i	−0.344299	−	1.20071i	−0.922880	−	0.385088i	$-0.874171\pi$
$839$	−9.97278	−	34.7792i	−0.344299	−	1.20071i	0.578581	−	0.815625i	$-0.303607\pi$
$840$	3.75724	−	3.62833i	0.129637	−	0.125189i
$841$	−41.1995	+	21.9062i	−1.42067	+	0.755385i
$842$	−11.7522	+	9.18186i	−0.405009	+	0.316428i
$843$	−13.3917	−	30.0781i	−0.461233	−	1.03595i
$844$	13.1308	+	5.84619i	0.451980	+	0.201234i
$845$	−17.5717	+	10.9800i	−0.604484	+	0.377723i
$846$	−4.71332	−	3.95495i	−0.162047	−	0.135974i
$847$	10.7373	−	29.3777i	0.368937	−	1.00943i
$848$	−6.67996	−	3.85668i	−0.229391	−	0.132439i
$849$	1.42646	+	40.8484i	0.0489559	+	1.40191i
$850$	−5.52838	+	5.72480i	−0.189622	+	0.196359i
$851$	−0.227451	−	0.235533i	−0.00779692	−	0.00807395i
$852$	−0.617687	+	17.6882i	−0.0211616	+	0.605989i
$853$	3.29780	−	5.27758i	0.112914	−	0.180701i	−0.786764	−	0.617254i	$-0.788245\pi$
$853$	3.29780	−	5.27758i	0.112914	−	0.180701i	0.899679	+	0.436553i	$0.143801\pi$
$854$	−10.3511	−	7.52049i	−0.354206	−	0.257346i
$855$	1.80034	−	3.49351i	0.0615705	−	0.119476i
$856$	−5.11056	+	15.7287i	−0.174675	+	0.537596i
$857$	13.4430	−	11.2800i	0.459205	−	0.385319i	−0.383633	−	0.923485i	$-0.625327\pi$
$857$	13.4430	−	11.2800i	0.459205	−	0.385319i	0.842838	+	0.538167i	$0.180883\pi$
$858$	25.9733	−	8.41997i	0.886713	−	0.287453i
$859$	−4.19758	+	23.8057i	−0.143220	+	0.812239i	0.825560	+	0.564315i	$0.190859\pi$
$859$	−4.19758	+	23.8057i	−0.143220	+	0.812239i	−0.968779	+	0.247924i	$0.920252\pi$
$860$	−0.948504	+	6.74896i	−0.0323437	+	0.230137i
$861$	8.22764	−	12.1980i	0.280397	−	0.415706i
$862$	18.5975	−	8.28013i	0.633432	−	0.282022i
$863$	−1.89968	−	1.71048i	−0.0646659	−	0.0582254i	0.636164	−	0.771554i	$-0.280520\pi$
$863$	−1.89968	−	1.71048i	−0.0646659	−	0.0582254i	−0.700830	+	0.713328i	$0.747187\pi$
$864$	5.21261	+	2.10603i	0.177337	+	0.0716487i
$865$	−4.13035	−	16.5659i	−0.140436	−	0.563258i
$866$	11.6023	−	26.0591i	0.394261	−	0.885525i
$867$	13.2483	−	11.9288i	0.449935	−	0.405123i
$868$	23.5563	−	8.57381i	0.799554	−	0.291014i
$869$	−8.26960	−	14.3456i	−0.280527	−	0.486640i
$870$	15.7352	+	2.77453i	0.533472	+	0.0940655i
$871$	43.6841	+	34.1298i	1.48018	+	1.15644i
$872$	1.86132	−	7.46534i	0.0630322	−	0.252808i
$873$	−8.02696	+	11.0482i	−0.271672	+	0.373924i
$874$	0.292778	−	0.0770063i	0.00990336	−	0.00260478i
$875$	−28.1029	+	9.13120i	−0.950053	+	0.308691i
$876$	−3.30016	+	0.230769i	−0.111502	+	0.00779697i
$877$	−3.22491	+	0.924727i	−0.108897	+	0.0312258i	−0.329644	−	0.944105i	$-0.606929\pi$
$877$	−3.22491	+	0.924727i	−0.108897	+	0.0312258i	0.220746	+	0.975331i	$0.429151\pi$
$878$	−17.7293	−	9.42684i	−0.598335	−	0.318140i
$879$	10.9143	−	1.92448i	0.368130	−	0.0649113i
$880$	−4.04122	+	0.279866i	−0.136230	+	0.00943430i
$881$	15.6776	−	27.1544i	0.528192	−	0.914856i	−0.471267	−	0.881990i	$-0.656203\pi$
$881$	15.6776	−	27.1544i	0.528192	−	0.914856i	0.999460	−	0.0328656i	$-0.0104633\pi$
$882$	0.783777	−	0.166597i	0.0263911	−	0.00560961i
$883$	−38.1751	−	2.66947i	−1.28470	−	0.0898347i	−0.588977	−	0.808150i	$-0.700469\pi$
$883$	−38.1751	−	2.66947i	−1.28470	−	0.0898347i	−0.695718	+	0.718315i	$0.744914\pi$
$884$	−12.0489	+	3.00414i	−0.405249	+	0.101040i
$885$	−4.52282	+	5.02310i	−0.152033	+	0.168850i
$886$	18.1106	+	3.84953i	0.608437	+	0.129327i
$887$	−54.9255	−	15.7496i	−1.84422	−	0.528821i	−0.844242	−	0.535962i	$-0.819949\pi$
$887$	−54.9255	−	15.7496i	−1.84422	−	0.528821i	−0.999975	+	0.00714115i	$0.997727\pi$
$888$	5.10025	+	4.92525i	0.171153	+	0.165281i
$889$	−3.69787	+	6.95468i	−0.124023	+	0.233252i
$890$	−1.28723	+	3.53663i	−0.0431480	+	0.118548i
$891$	13.8389	+	15.3904i	0.463619	+	0.515596i
$892$		−	27.6454i		−	0.925637i
$893$	36.3221	+	0.801338i	1.21547	+	0.0268158i
$894$	−0.185426	+	0.134720i	−0.00620156	+	0.00450570i
$895$	0.527183	+	7.53906i	0.0176218	+	0.252003i
$896$	2.84176	+	0.0992365i	0.0949366	+	0.00331526i
$897$	−0.0795741	−	0.566199i	−0.00265690	−	0.0189048i
$898$	37.2688	+	18.1772i	1.24368	+	0.606582i
$899$	63.5742	+	42.8813i	2.12032	+	1.43017i
$900$	−1.73288	−	1.92456i	−0.0577627	−	0.0641520i
$901$	8.74894	+	15.1536i	0.291470	+	0.504840i
$902$	−10.9712	+	3.13799i	−0.365302	+	0.104484i
$903$	15.3382	−	18.2794i	0.510425	−	0.608300i
$904$	4.01451	+	18.8868i	0.133521	+	0.628166i
$905$	−9.94495	+	1.04526i	−0.330581	+	0.0347455i
$906$	−9.02149	+	31.4617i	−0.299719	+	1.04524i
$907$	−1.43306	−	2.69520i	−0.0475841	−	0.0894927i	0.858021	−	0.513615i	$-0.171694\pi$
$907$	−1.43306	−	2.69520i	−0.0475841	−	0.0894927i	−0.905605	+	0.424122i	$0.860583\pi$
$908$	2.94655	−	0.414111i	0.0977848	−	0.0137428i
$909$	−0.498072	+	0.335954i	−0.0165200	+	0.0111429i
$910$	−18.4465	−	4.59923i	−0.611496	−	0.152463i
$911$	−33.1581	−	10.7737i	−1.09858	−	0.356949i	−0.297022	−	0.954871i	$-0.595993\pi$
$911$	−33.1581	−	10.7737i	−1.09858	−	0.356949i	−0.801555	+	0.597922i	$0.795993\pi$
$912$	−6.27779	+	1.88774i	−0.207878	+	0.0625095i
$913$	23.2233	+	15.6870i	0.768579	+	0.519164i
$914$	1.38968	+	1.65616i	0.0459666	+	0.0547809i
$915$	−5.08862	+	6.51313i	−0.168224	+	0.215317i
$916$	−1.75590	−	3.60013i	−0.0580165	−	0.118951i
$917$	−13.5279	+	27.7364i	−0.446732	+	0.915936i
$918$	−7.85188	−	10.0499i	−0.259151	−	0.331698i
$919$	−1.01686	+	4.78395i	−0.0335431	+	0.157808i	−0.991731	−	0.128330i	$-0.959038\pi$
$919$	−1.01686	+	4.78395i	−0.0335431	+	0.157808i	0.958188	+	0.286138i	$0.0923716\pi$
$920$	−0.00886700	+	0.0843639i	−0.000292336	+	0.00278139i
$921$	0.722229	−	10.3284i	0.0237982	−	0.340331i
$922$	15.5500	+	24.8852i	0.512111	+	0.819549i
$923$	55.7898	−	32.2103i	1.83634	−	1.06021i
$924$	12.5186	+	6.66703i	0.411832	+	0.219329i
$925$	−5.65674	−	15.5418i	−0.185992	−	0.511010i
$926$	−0.205904	−	0.0289379i	−0.00676641	−	0.000950957i
$927$	12.5510	−	6.12154i	0.412229	−	0.201058i
$928$	4.86406	+	7.21126i	0.159671	+	0.236721i
$929$	−30.9110	−	19.3153i	−1.01416	−	0.633715i	−0.0823241	−	0.996606i	$-0.526234\pi$
$929$	−30.9110	−	19.3153i	−1.01416	−	0.633715i	−0.931832	+	0.362891i	$0.881790\pi$
$930$	−5.00420	−	15.4013i	−0.164094	−	0.505030i
$931$	−2.99448	+	3.66325i	−0.0981400	+	0.120058i
$932$	2.52174	+	3.47088i	0.0826024	+	0.113693i
$933$	−7.42003	+	2.99789i	−0.242921	+	0.0981464i
$934$	−6.46715	−	2.35385i	−0.211612	−	0.0770204i
$935$	8.25680	+	4.03397i	0.270026	+	0.131925i
$936$	−0.701692	−	3.97949i	−0.0229355	−	0.130074i
$937$	−44.4897	+	1.55362i	−1.45342	+	0.0507544i	−0.750666	−	0.660682i	$-0.770267\pi$
$937$	−44.4897	+	1.55362i	−1.45342	+	0.0507544i	−0.702750	+	0.711437i	$0.748045\pi$
$938$	3.01007	+	28.6389i	0.0982822	+	0.935092i
$939$	19.9423	+	2.09602i	0.650792	+	0.0684010i
$940$	−3.81356	+	9.43888i	−0.124385	+	0.307862i
$941$	−20.5316	+	50.8175i	−0.669312	+	1.65660i	0.0819795	+	0.996634i	$0.473876\pi$
$941$	−20.5316	+	50.8175i	−0.669312	+	1.65660i	−0.751291	+	0.659971i	$0.770569\pi$
$942$	−15.2374	−	1.60151i	−0.496460	−	0.0521801i
$943$	0.0249779	+	0.237649i	0.000813391	+	0.00773890i
$944$	−3.67748	+	0.128421i	−0.119692	+	0.00417973i
$945$	−3.39053	−	19.2287i	−0.110294	−	0.625508i
$946$	−18.2275	+	3.20140i	−0.592628	+	0.104086i
$947$	41.8475	+	15.2312i	1.35986	+	0.494949i	0.916011	−	0.401153i	$-0.131390\pi$
$947$	41.8475	+	15.2312i	1.35986	+	0.494949i	0.443849	+	0.896101i	$0.353612\pi$
$948$	6.96171	−	2.81271i	0.226106	−	0.0913527i
$949$	7.07762	+	9.74151i	0.229749	+	0.316223i
$950$	15.0924	+	2.46171i	0.489663	+	0.0798683i
$951$	−10.6714	−	32.8433i	−0.346045	−	1.06502i
$952$	−5.47035	−	3.41825i	−0.177295	−	0.110786i
$953$	9.75231	+	14.4584i	0.315908	+	0.468353i	0.953231	−	0.302244i	$-0.0977357\pi$
$953$	9.75231	+	14.4584i	0.315908	+	0.468353i	−0.637322	+	0.770597i	$0.719958\pi$
$954$	−5.11773	+	2.49608i	−0.165693	+	0.0808137i
$955$	16.2456	+	2.28316i	0.525694	+	0.0738814i
$956$	0.380749	+	1.04610i	0.0123143	+	0.0338333i
$957$	6.00950	+	42.9689i	0.194260	+	1.38899i
$958$	−12.1026	+	6.98747i	−0.391019	+	0.225755i
$959$	15.4760	+	24.7668i	0.499747	+	0.799763i
$960$	0.128135	−	1.83241i	0.00413553	−	0.0591409i
$961$	4.88369	−	46.4652i	0.157538	−	1.49888i
$962$	5.36551	−	25.2428i	0.172991	−	0.813859i
$963$	7.51626	+	9.62038i	0.242208	+	0.310012i
$964$	−3.19286	+	6.54633i	−0.102835	+	0.210843i
$965$	10.3115	+	21.1416i	0.331938	+	0.680573i
$966$	0.182856	−	0.234044i	0.00588328	−	0.00753026i
$967$	30.7972	+	36.7026i	0.990370	+	1.18028i	0.983612	+	0.180300i	$0.0577068\pi$
$967$	30.7972	+	36.7026i	0.990370	+	1.18028i	0.00675830	+	0.999977i	$0.497849\pi$
$968$	−4.10699	−	10.2045i	−0.132004	−	0.327986i
$969$	14.4745	+	3.41199i	0.464988	+	0.109609i
$970$	21.4892	+	6.98227i	0.689977	+	0.224187i
$971$	−13.0521	−	3.25427i	−0.418863	−	0.104434i	0.0267877	−	0.999641i	$-0.491472\pi$
$971$	−13.0521	−	3.25427i	−0.418863	−	0.104434i	−0.445651	+	0.895207i	$0.647028\pi$
$972$	6.20182	−	4.18318i	0.198923	−	0.134175i
$973$	−59.0393	+	8.29744i	−1.89271	+	0.266004i
$974$	12.7032	+	23.8912i	0.407035	+	0.765522i
$975$	7.96071	−	27.7623i	0.254947	−	0.889105i
$976$	−4.47496	+	0.470338i	−0.143240	+	0.0150551i
$977$	12.0534	+	56.7069i	0.385623	+	1.81421i	0.558776	+	0.829319i	$0.311271\pi$
$977$	12.0534	+	56.7069i	0.385623	+	1.81421i	−0.173153	+	0.984895i	$0.555395\pi$
$978$	22.6553	−	26.9996i	0.724437	−	0.863351i
$979$	−10.2134	−	0.363517i	−0.326421	−	0.0116181i
$980$	−0.662887	−	1.14815i	−0.0211752	−	0.0366764i
$981$	−3.80041	−	4.22078i	−0.121338	−	0.134759i
$982$	−16.1723	−	10.9084i	−0.516079	−	0.348100i
$983$	10.9091	+	5.32071i	0.347945	+	0.169704i	0.604053	−	0.796944i	$-0.293551\pi$
$983$	10.9091	+	5.32071i	0.347945	+	0.169704i	−0.256108	+	0.966648i	$0.582440\pi$
$984$	−0.720140	−	5.12406i	−0.0229572	−	0.163349i
$985$	−9.21397	−	0.321759i	−0.293581	−	0.0102521i
$986$	−1.37646	−	19.6843i	−0.0438354	−	0.626876i
$987$	28.8361	−	20.9507i	0.917863	−	0.666867i
$988$	17.9355	+	15.7366i	0.570603	+	0.500649i
$989$			0.387539i			0.0123230i
$990$	−1.49692	+	2.58874i	−0.0475753	+	0.0822754i
$991$	−10.4139	+	28.6121i	−0.330810	+	0.908893i	0.657092	+	0.753811i	$0.271786\pi$
$991$	−10.4139	+	28.6121i	−0.330810	+	0.908893i	−0.987902	+	0.155082i	$0.950436\pi$
$992$	4.13884	−	7.78403i	0.131408	−	0.247143i
$993$	−8.10252	−	7.82451i	−0.257126	−	0.248303i
$994$	32.1674	+	9.22385i	1.02029	+	0.292563i
$995$	2.94231	+	0.625407i	0.0932774	+	0.0198267i
$996$	−8.50331	+	9.44388i	−0.269438	+	0.299241i
$997$	−59.4879	+	14.8320i	−1.88400	+	0.469734i	−0.884002	+	0.467483i	$0.845161\pi$
$997$	−59.4879	+	14.8320i	−1.88400	+	0.469734i	−0.999997	+	0.00225104i	$0.999283\pi$
$998$	2.65893	+	0.185931i	0.0841670	+	0.00588553i
$999$	25.9253	−	5.51060i	0.820241	−	0.174348i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.v.b.13.4	yes	240
11.6	odd	10		418.2.v.a.127.7	yes	240
19.3	odd	18		418.2.v.a.79.7	✓	240
209.193	even	90	inner	418.2.v.b.193.4	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.v.a.79.7	✓	240	19.3	odd	18
418.2.v.a.127.7	yes	240	11.6	odd	10
418.2.v.b.13.4	yes	240	1.1	even	1	trivial
418.2.v.b.193.4	yes	240	209.193	even	90	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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.v (of order \(90\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.374607 - 0.927184i) q^{2} +(-0.414539 - 1.44567i) q^{3} +(-0.719340 + 0.694658i) q^{4} +(1.07843 - 0.573409i) q^{5} +(-1.18511 + 0.925911i) q^{6} +(1.15655 + 2.59766i) q^{7} +(0.913545 + 0.406737i) q^{8} +(0.626029 - 0.391186i) q^{9} +O(q^{10})\)	\(q+(-0.374607 - 0.927184i) q^{2} +(-0.414539 - 1.44567i) q^{3} +(-0.719340 + 0.694658i) q^{4} +(1.07843 - 0.573409i) q^{5} +(-1.18511 + 0.925911i) q^{6} +(1.15655 + 2.59766i) q^{7} +(0.913545 + 0.406737i) q^{8} +(0.626029 - 0.391186i) q^{9} +(-0.935641 - 0.785096i) q^{10} +(1.24449 - 3.07429i) q^{11} +(1.30244 + 0.751964i) q^{12} +(-0.191039 - 5.47063i) q^{13} +(1.97526 - 2.04544i) q^{14} +(-1.27601 - 1.32135i) q^{15} +(0.0348995 - 0.999391i) q^{16} +(-1.20213 + 1.92381i) q^{17} +(-0.597216 - 0.433903i) q^{18} +(4.35393 - 0.208079i) q^{19} +(-0.377431 + 1.16161i) q^{20} +(3.27592 - 2.74882i) q^{21} +(-3.31662 - 0.00222434i) q^{22} +(-0.0120603 + 0.0683972i) q^{23} +(0.209306 - 1.48929i) q^{24} +(-1.96176 + 2.90843i) q^{25} +(-5.00072 + 2.22646i) q^{26} +(-4.17795 - 3.76184i) q^{27} +(-2.63644 - 1.06519i) q^{28} +(-2.10432 - 8.43997i) q^{29} +(-0.747130 + 1.67808i) q^{30} +(-6.55154 + 5.89903i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(-4.96029 - 0.524711i) q^{33} +(2.23405 + 0.393924i) q^{34} +(2.73678 + 2.13821i) q^{35} +(-0.178587 + 0.716272i) q^{36} +(-2.77108 + 3.81406i) q^{37} +(-1.82394 - 3.95895i) q^{38} +(-7.82953 + 2.54397i) q^{39} +(1.21842 - 0.0852001i) q^{40} +(3.30732 - 0.948358i) q^{41} +(-3.77585 - 2.00765i) q^{42} +(5.49515 - 0.968944i) q^{43} +(1.24037 + 3.07595i) q^{44} +(0.450816 - 0.780836i) q^{45} +(0.0679346 - 0.0144399i) q^{46} +(8.31458 + 0.581412i) q^{47} +(-1.45926 + 0.363833i) q^{48} +(-0.726315 + 0.806655i) q^{49} +(3.43154 + 0.729396i) q^{50} +(3.27952 + 0.940388i) q^{51} +(3.93764 + 3.80254i) q^{52} +(3.62120 - 6.81049i) q^{53} +(-1.92283 + 5.28294i) q^{54} +(-0.420733 - 4.02899i) q^{55} +2.84349i q^{56} +(-2.10569 - 6.20808i) q^{57} +(-7.03712 + 5.11276i) q^{58} +(-0.256685 - 3.67076i) q^{59} +(1.83577 + 0.0641065i) q^{60} +(-0.626225 - 4.45582i) q^{61} +(7.92373 + 3.86466i) q^{62} +(1.74020 + 1.17378i) q^{63} +(0.669131 + 0.743145i) q^{64} +(-3.34293 - 5.79013i) q^{65} +(1.37165 + 4.79566i) q^{66} +(-6.50963 + 7.75788i) q^{67} +(-0.471651 - 2.21894i) q^{68} +(0.103879 - 0.0109181i) q^{69} +(0.957295 - 3.33849i) q^{70} +(5.52499 + 10.3910i) q^{71} +(0.731015 - 0.102737i) q^{72} +(-1.82365 + 1.23007i) q^{73} +(4.57440 + 1.14053i) q^{74} +(5.01785 + 1.63040i) q^{75} +(-2.98741 + 3.17417i) q^{76} +(9.42528 - 0.322809i) q^{77} +(5.29172 + 6.30643i) q^{78} +(3.07372 - 3.93419i) q^{79} +(-0.535423 - 1.09778i) q^{80} +(-2.73564 + 5.60889i) q^{81} +(-2.11824 - 2.71123i) q^{82} +(-1.75683 + 8.26522i) q^{83} +(-0.447007 + 4.25299i) q^{84} +(-0.193278 + 2.76400i) q^{85} +(-2.95691 - 4.73204i) q^{86} +(-11.3291 + 6.54085i) q^{87} +(2.38732 - 2.30232i) q^{88} +(-1.05390 - 2.89557i) q^{89} +(-0.892857 - 0.125483i) q^{90} +(13.9899 - 6.82334i) q^{91} +(-0.0388372 - 0.0575786i) q^{92} +(11.2439 + 7.02597i) q^{93} +(-2.57562 - 7.92694i) q^{94} +(4.57608 - 2.72098i) q^{95} +(0.883987 + 1.21670i) q^{96} +(-17.1524 + 6.93002i) q^{97} +(1.02000 + 0.371250i) q^{98} +(-0.423531 - 2.41142i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 3 q^{3} - 3 q^{6} - 3 q^{7} + 30 q^{8} + 3 q^{9}+O(q^{10}) \) 240 * q + 3 * q^3 - 3 * q^6 - 3 * q^7 + 30 * q^8 + 3 * q^9	\( 240 q + 3 q^{3} - 3 q^{6} - 3 q^{7} + 30 q^{8} + 3 q^{9} - 3 q^{11} + 6 q^{13} - 18 q^{14} - 69 q^{15} + 9 q^{17} + 60 q^{18} - 45 q^{19} + 12 q^{20} - 48 q^{21} - 12 q^{22} + 3 q^{24} - 18 q^{25} + 84 q^{26} - 9 q^{27} + 6 q^{28} + 12 q^{29} + 9 q^{31} - 69 q^{33} - 24 q^{34} + 36 q^{35} + 3 q^{36} + 24 q^{38} - 30 q^{41} - 6 q^{42} + 12 q^{43} - 48 q^{44} + 48 q^{45} - 12 q^{46} - 54 q^{47} + 6 q^{48} - 81 q^{49} + 21 q^{50} + 45 q^{51} - 3 q^{52} + 81 q^{53} - 27 q^{54} - 72 q^{55} - 30 q^{57} - 24 q^{58} + 114 q^{59} + 78 q^{60} - 66 q^{61} - 45 q^{62} + 9 q^{63} + 30 q^{64} - 135 q^{66} - 9 q^{67} - 42 q^{68} - 54 q^{69} + 39 q^{70} - 102 q^{71} - 6 q^{72} + 12 q^{74} + 72 q^{77} + 36 q^{79} - 117 q^{81} + 30 q^{82} - 36 q^{83} - 36 q^{84} - 90 q^{85} + 3 q^{86} - 216 q^{87} - 3 q^{88} + 18 q^{89} - 24 q^{90} + 102 q^{91} + 30 q^{92} + 147 q^{93} + 18 q^{94} - 66 q^{95} - 24 q^{97} + 12 q^{98} - 195 q^{99}+O(q^{100}) \) 240 * q + 3 * q^3 - 3 * q^6 - 3 * q^7 + 30 * q^8 + 3 * q^9 - 3 * q^11 + 6 * q^13 - 18 * q^14 - 69 * q^15 + 9 * q^17 + 60 * q^18 - 45 * q^19 + 12 * q^20 - 48 * q^21 - 12 * q^22 + 3 * q^24 - 18 * q^25 + 84 * q^26 - 9 * q^27 + 6 * q^28 + 12 * q^29 + 9 * q^31 - 69 * q^33 - 24 * q^34 + 36 * q^35 + 3 * q^36 + 24 * q^38 - 30 * q^41 - 6 * q^42 + 12 * q^43 - 48 * q^44 + 48 * q^45 - 12 * q^46 - 54 * q^47 + 6 * q^48 - 81 * q^49 + 21 * q^50 + 45 * q^51 - 3 * q^52 + 81 * q^53 - 27 * q^54 - 72 * q^55 - 30 * q^57 - 24 * q^58 + 114 * q^59 + 78 * q^60 - 66 * q^61 - 45 * q^62 + 9 * q^63 + 30 * q^64 - 135 * q^66 - 9 * q^67 - 42 * q^68 - 54 * q^69 + 39 * q^70 - 102 * q^71 - 6 * q^72 + 12 * q^74 + 72 * q^77 + 36 * q^79 - 117 * q^81 + 30 * q^82 - 36 * q^83 - 36 * q^84 - 90 * q^85 + 3 * q^86 - 216 * q^87 - 3 * q^88 + 18 * q^89 - 24 * q^90 + 102 * q^91 + 30 * q^92 + 147 * q^93 + 18 * q^94 - 66 * q^95 - 24 * q^97 + 12 * q^98 - 195 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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