LMFDB - Embedded newform 216.2.t.a.13.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(13,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 8]))

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

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

chi := DirichletCharacter("216.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.t (of order $18$, degree $6$, 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:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			13.17
Character	$\chi$	$=$	216.13
Dual form			216.2.t.a.133.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0120789 + 1.41416i) q^{2} +(-0.919076 - 1.46809i) q^{3} +(-1.99971 - 0.0341629i) q^{4} +(0.185555 - 0.221136i) q^{5} +(2.08722 - 1.28199i) q^{6} +(-2.62731 - 0.956263i) q^{7} +(0.0724661 - 2.82750i) q^{8} +(-1.31060 + 2.69858i) q^{9} +O(q^{10})$	\(q+(-0.0120789 + 1.41416i) q^{2} +(-0.919076 - 1.46809i) q^{3} +(-1.99971 - 0.0341629i) q^{4} +(0.185555 - 0.221136i) q^{5} +(2.08722 - 1.28199i) q^{6} +(-2.62731 - 0.956263i) q^{7} +(0.0724661 - 2.82750i) q^{8} +(-1.31060 + 2.69858i) q^{9} +(0.310481 + 0.265076i) q^{10} +(-3.08006 - 3.67067i) q^{11} +(1.78773 + 2.96716i) q^{12} +(-3.17478 - 0.559799i) q^{13} +(1.38405 - 3.70389i) q^{14} +(-0.495188 - 0.0691714i) q^{15} +(3.99767 + 0.136632i) q^{16} +(2.81522 - 4.87610i) q^{17} +(-3.80040 - 1.88599i) q^{18} +(-0.00428975 + 0.00247669i) q^{19} +(-0.378611 + 0.435868i) q^{20} +(1.01082 + 4.73602i) q^{21} +(5.22813 - 4.31136i) q^{22} +(1.84294 - 0.670777i) q^{23} +(-4.21763 + 2.49230i) q^{24} +(0.853770 + 4.84197i) q^{25} +(0.829994 - 4.48289i) q^{26} +(5.16631 - 0.556122i) q^{27} +(5.22119 + 2.00200i) q^{28} +(-7.88122 + 1.38967i) q^{29} +(0.103801 - 0.699440i) q^{30} +(-5.45972 + 1.98718i) q^{31} +(-0.241507 + 5.65170i) q^{32} +(-2.55808 + 7.89544i) q^{33} +(6.86159 + 4.04007i) q^{34} +(-0.698975 + 0.403553i) q^{35} +(2.71300 - 5.35160i) q^{36} +(8.20717 + 4.73841i) q^{37} +(-0.00345063 - 0.00609632i) q^{38} +(2.09603 + 5.17537i) q^{39} +(-0.611815 - 0.540682i) q^{40} +(1.69965 - 9.63917i) q^{41} +(-6.70971 + 1.37225i) q^{42} +(-3.57494 - 4.26045i) q^{43} +(6.03382 + 7.44549i) q^{44} +(0.353565 + 0.790555i) q^{45} +(0.926326 + 2.61432i) q^{46} +(3.48835 + 1.26966i) q^{47} +(-3.47357 - 5.99452i) q^{48} +(0.626015 + 0.525289i) q^{49} +(-6.85765 + 1.14888i) q^{50} +(-9.74597 + 0.348505i) q^{51} +(6.32950 + 1.22789i) q^{52} +0.865665i q^{53} +(0.724043 + 7.31271i) q^{54} -1.38324 q^{55} +(-2.89422 + 7.35942i) q^{56} +(0.00757862 + 0.00402149i) q^{57} +(-1.87003 - 11.1621i) q^{58} +(3.57109 - 4.25586i) q^{59} +(0.987867 + 0.155240i) q^{60} +(-2.43327 + 6.68534i) q^{61} +(-2.74424 - 7.74493i) q^{62} +(6.02390 - 5.83673i) q^{63} +(-7.98950 - 0.409796i) q^{64} +(-0.712888 + 0.598184i) q^{65} +(-11.1345 - 3.71291i) q^{66} +(0.224950 + 0.0396647i) q^{67} +(-5.79620 + 9.65460i) q^{68} +(-2.67857 - 2.08912i) q^{69} +(-0.562247 - 0.993338i) q^{70} +(0.429923 - 0.744648i) q^{71} +(7.53526 + 3.90127i) q^{72} +(-2.02670 - 3.51035i) q^{73} +(-6.80001 + 11.5490i) q^{74} +(6.32379 - 5.70356i) q^{75} +(0.00866286 - 0.00480611i) q^{76} +(4.58214 + 12.5893i) q^{77} +(-7.34413 + 2.90161i) q^{78} +(-0.797428 - 4.52244i) q^{79} +(0.772001 - 0.858675i) q^{80} +(-5.56467 - 7.07350i) q^{81} +(13.6108 + 2.52001i) q^{82} +(4.00250 - 0.705749i) q^{83} +(-1.85954 - 9.50519i) q^{84} +(-0.555903 - 1.52733i) q^{85} +(6.06815 - 5.00408i) q^{86} +(9.28361 + 10.2932i) q^{87} +(-10.6020 + 8.44286i) q^{88} +(-1.77889 - 3.08112i) q^{89} +(-1.12224 + 0.490449i) q^{90} +(7.80581 + 4.50669i) q^{91} +(-3.70827 + 1.27840i) q^{92} +(7.93526 + 6.18901i) q^{93} +(-1.83764 + 4.91776i) q^{94} +(-0.000248300 + 0.00140818i) q^{95} +(8.51918 - 4.83979i) q^{96} +(6.04757 - 5.07452i) q^{97} +(-0.750405 + 0.878942i) q^{98} +(13.9423 - 3.50101i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9}+O(q^{10}) $ 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9	$ 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26} - 12 q^{28} - 39 q^{30} - 12 q^{31} - 36 q^{32} - 36 q^{36} - 42 q^{38} - 12 q^{39} - 21 q^{40} - 24 q^{41} - 66 q^{42} + 21 q^{44} - 3 q^{46} - 12 q^{47} + 51 q^{48} - 12 q^{49} - 99 q^{50} - 33 q^{52} - 90 q^{54} - 24 q^{55} + 99 q^{56} - 30 q^{57} + 21 q^{58} + 102 q^{60} - 36 q^{62} - 72 q^{63} - 3 q^{64} - 12 q^{65} - 9 q^{66} + 75 q^{68} + 9 q^{70} - 90 q^{71} + 60 q^{72} - 6 q^{73} + 9 q^{74} - 18 q^{76} + 12 q^{78} - 12 q^{79} + 78 q^{80} - 12 q^{81} - 12 q^{82} + 102 q^{84} - 30 q^{86} - 48 q^{87} - 30 q^{88} - 6 q^{89} + 6 q^{90} + 111 q^{92} - 33 q^{94} - 42 q^{95} + 126 q^{96} - 12 q^{97} + 54 q^{98}+O(q^{100}) $ 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{4}{9}\right)$

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 $

$2$	−0.0120789	+	1.41416i	−0.00854104	+	0.999964i
$2$	−0.0120789	+	1.41416i	−0.00854104	+	0.999964i
$3$	−0.919076	−	1.46809i	−0.530629	−	0.847604i
$3$	−0.919076	−	1.46809i	−0.530629	−	0.847604i
$4$	−1.99971	−	0.0341629i	−0.999854	−	0.0170815i
$5$	0.185555	−	0.221136i	0.0829828	−	0.0988950i	−0.722956	−	0.690895i	$-0.757217\pi$
$5$	0.185555	−	0.221136i	0.0829828	−	0.0988950i	0.805938	+	0.592000i	$0.201661\pi$
$6$	2.08722	−	1.28199i	0.852105	−	0.523370i
$7$	−2.62731	−	0.956263i	−0.993030	−	0.361433i	−0.206137	−	0.978523i	$-0.566089\pi$
$7$	−2.62731	−	0.956263i	−0.993030	−	0.361433i	−0.786893	+	0.617090i	$0.788312\pi$
$8$	0.0724661	−	2.82750i	0.0256206	−	0.999672i
$9$	−1.31060	+	2.69858i	−0.436866	+	0.899527i
$10$	0.310481	+	0.265076i	0.0981826	+	0.0838244i
$11$	−3.08006	−	3.67067i	−0.928672	−	1.10675i	−0.994054	−	0.108888i	$-0.965271\pi$
$11$	−3.08006	−	3.67067i	−0.928672	−	1.10675i	0.0653817	−	0.997860i	$-0.479174\pi$
$12$	1.78773	+	2.96716i	0.516073	+	0.856544i
$13$	−3.17478	−	0.559799i	−0.880525	−	0.155260i	−0.284933	−	0.958547i	$-0.591971\pi$
$13$	−3.17478	−	0.559799i	−0.880525	−	0.155260i	−0.595592	+	0.803287i	$0.703082\pi$
$14$	1.38405	−	3.70389i	0.369902	−	0.989907i
$15$	−0.495188	−	0.0691714i	−0.127857	−	0.0178600i
$16$	3.99767	+	0.136632i	0.999416	+	0.0341579i
$17$	2.81522	−	4.87610i	0.682791	−	1.18263i	−0.291335	−	0.956621i	$-0.594099\pi$
$17$	2.81522	−	4.87610i	0.682791	−	1.18263i	0.974126	−	0.226007i	$-0.0725672\pi$
$18$	−3.80040	−	1.88599i	−0.895763	−	0.444533i
$19$	−0.00428975	+	0.00247669i	−0.000984137	+	0.000568192i	−0.500492	−	0.865741i	$-0.666848\pi$
$19$	−0.00428975	+	0.00247669i	−0.000984137	+	0.000568192i	0.499508	+	0.866309i	$0.333514\pi$
$20$	−0.378611	+	0.435868i	−0.0846599	+	0.0974631i
$21$	1.01082	+	4.73602i	0.220578	+	1.03348i
$22$	5.22813	−	4.31136i	1.11464	−	0.919186i
$23$	1.84294	−	0.670777i	0.384280	−	0.139867i	−0.142654	−	0.989773i	$-0.545564\pi$
$23$	1.84294	−	0.670777i	0.384280	−	0.139867i	0.526934	+	0.849906i	$0.323341\pi$
$24$	−4.21763	+	2.49230i	−0.860921	+	0.508739i
$25$	0.853770	+	4.84197i	0.170754	+	0.968395i
$26$	0.829994	−	4.48289i	0.162775	−	0.879167i
$27$	5.16631	−	0.556122i	0.994256	−	0.107026i
$28$	5.22119	+	2.00200i	0.986712	+	0.378343i
$29$	−7.88122	+	1.38967i	−1.46351	+	0.258056i	−0.847966	−	0.530050i	$-0.822173\pi$
$29$	−7.88122	+	1.38967i	−1.46351	+	0.258056i	−0.615540	+	0.788106i	$0.711062\pi$
$30$	0.103801	−	0.699440i	0.0189514	−	0.127700i
$31$	−5.45972	+	1.98718i	−0.980595	+	0.356907i	−0.782071	−	0.623189i	$-0.785837\pi$
$31$	−5.45972	+	1.98718i	−0.980595	+	0.356907i	−0.198523	+	0.980096i	$0.563615\pi$
$32$	−0.241507	+	5.65170i	−0.0426927	+	0.999088i
$33$	−2.55808	+	7.89544i	−0.445304	+	1.37442i
$34$	6.86159	+	4.04007i	1.17675	+	0.692867i
$35$	−0.698975	+	0.403553i	−0.118148	+	0.0682130i
$36$	2.71300	−	5.35160i	0.452167	−	0.891933i
$37$	8.20717	+	4.73841i	1.34925	+	0.778990i	0.988143	−	0.153534i	$-0.0490656\pi$
$37$	8.20717	+	4.73841i	1.34925	+	0.778990i	0.361107	+	0.932524i	$0.382399\pi$
$38$	−0.00345063	−	0.00609632i	−0.000559765	−	0.000988954i
$39$	2.09603	+	5.17537i	0.335633	+	0.828722i
$40$	−0.611815	−	0.540682i	−0.0967365	−	0.0854893i
$41$	1.69965	−	9.63917i	0.265440	−	1.50539i	−0.502339	−	0.864671i	$-0.667527\pi$
$41$	1.69965	−	9.63917i	0.265440	−	1.50539i	0.767779	−	0.640715i	$-0.221362\pi$
$42$	−6.70971	+	1.37225i	−1.03533	+	0.211743i
$43$	−3.57494	−	4.26045i	−0.545173	−	0.649712i	0.421166	−	0.906984i	$-0.361621\pi$
$43$	−3.57494	−	4.26045i	−0.545173	−	0.649712i	−0.966339	+	0.257271i	$0.917177\pi$
$44$	6.03382	+	7.44549i	0.909632	+	1.12245i
$45$	0.353565	+	0.790555i	0.0527064	+	0.117849i
$46$	0.926326	+	2.61432i	0.136579	+	0.385461i
$47$	3.48835	+	1.26966i	0.508829	+	0.185199i	0.583661	−	0.811998i	$-0.301620\pi$
$47$	3.48835	+	1.26966i	0.508829	+	0.185199i	−0.0748320	+	0.997196i	$0.523842\pi$
$48$	−3.47357	−	5.99452i	−0.501367	−	0.865235i
$49$	0.626015	+	0.525289i	0.0894307	+	0.0750413i
$50$	−6.85765	+	1.14888i	−0.969818	+	0.162477i
$51$	−9.74597	+	0.348505i	−1.36471	+	0.0488005i
$52$	6.32950	+	1.22789i	0.877744	+	0.170278i
$53$			0.865665i			0.118908i	0.998231	+	0.0594541i	$0.0189360\pi$
$53$			0.865665i			0.118908i	−0.998231	+	0.0594541i	$0.981064\pi$
$54$	0.724043	+	7.31271i	0.0985298	+	0.995134i
$55$	−1.38324			−0.186516
$56$	−2.89422	+	7.35942i	−0.386757	+	0.983444i
$57$	0.00757862	+	0.00402149i	0.00100381	+	0.000532660i
$58$	−1.87003	−	11.1621i	−0.245546	−	1.46566i
$59$	3.57109	−	4.25586i	0.464916	−	0.554066i	−0.481739	−	0.876315i	$-0.659995\pi$
$59$	3.57109	−	4.25586i	0.464916	−	0.554066i	0.946655	+	0.322249i	$0.104439\pi$
$60$	0.987867	+	0.155240i	0.127533	+	0.0200414i
$61$	−2.43327	+	6.68534i	−0.311548	+	0.855970i	0.680797	+	0.732472i	$0.261634\pi$
$61$	−2.43327	+	6.68534i	−0.311548	+	0.855970i	−0.992345	+	0.123498i	$0.960589\pi$
$62$	−2.74424	−	7.74493i	−0.348519	−	0.983607i
$63$	6.02390	−	5.83673i	0.758940	−	0.735359i
$64$	−7.98950	−	0.409796i	−0.998687	−	0.0512244i
$65$	−0.712888	+	0.598184i	−0.0884228	+	0.0741956i
$66$	−11.1345	−	3.71291i	−1.37057	−	0.457027i
$67$	0.224950	+	0.0396647i	0.0274820	+	0.00484582i	0.187372	−	0.982289i	$-0.440003\pi$
$67$	0.224950	+	0.0396647i	0.0274820	+	0.00484582i	−0.159890	+	0.987135i	$0.551114\pi$
$68$	−5.79620	+	9.65460i	−0.702892	+	1.17079i
$69$	−2.67857	−	2.08912i	−0.322462	−	0.251500i
$70$	−0.562247	−	0.993338i	−0.0672014	−	0.118727i
$71$	0.429923	−	0.744648i	0.0510224	−	0.0883735i	−0.839386	−	0.543535i	$-0.817085\pi$
$71$	0.429923	−	0.744648i	0.0510224	−	0.0883735i	0.890409	+	0.455162i	$0.150419\pi$
$72$	7.53526	+	3.90127i	0.888039	+	0.459769i
$73$	−2.02670	−	3.51035i	−0.237208	−	0.410856i	0.722704	−	0.691157i	$-0.242899\pi$
$73$	−2.02670	−	3.51035i	−0.237208	−	0.410856i	−0.959912	+	0.280301i	$0.909566\pi$
$74$	−6.80001	+	11.5490i	−0.790486	+	1.34255i
$75$	6.32379	−	5.70356i	0.730208	−	0.658590i
$76$	0.00866286	−	0.00480611i	0.000993699	−	0.000551298i
$77$	4.58214	+	12.5893i	0.522184	+	1.43469i
$78$	−7.34413	+	2.90161i	−0.831558	+	0.328542i
$79$	−0.797428	−	4.52244i	−0.0897176	−	0.508814i	−0.996239	−	0.0866531i	$-0.972383\pi$
$79$	−0.797428	−	4.52244i	−0.0897176	−	0.508814i	0.906521	−	0.422161i	$-0.138728\pi$
$80$	0.772001	−	0.858675i	0.0863124	−	0.0960028i
$81$	−5.56467	−	7.07350i	−0.618297	−	0.785945i
$82$	13.6108	+	2.52001i	1.50306	+	0.278288i
$83$	4.00250	−	0.705749i	0.439332	−	0.0774660i	0.0503925	−	0.998729i	$-0.483953\pi$
$83$	4.00250	−	0.705749i	0.439332	−	0.0774660i	0.388939	+	0.921263i	$0.372842\pi$
$84$	−1.85954	−	9.50519i	−0.202893	−	1.03710i
$85$	−0.555903	−	1.52733i	−0.0602961	−	0.165662i
$86$	6.06815	−	5.00408i	0.654345	−	0.539604i
$87$	9.28361	+	10.2932i	0.995308	+	1.10354i
$88$	−10.6020	+	8.44286i	−1.13018	+	0.900012i
$89$	−1.77889	−	3.08112i	−0.188562	−	0.326599i	0.756209	−	0.654330i	$-0.227049\pi$
$89$	−1.77889	−	3.08112i	−0.188562	−	0.326599i	−0.944771	+	0.327731i	$0.893716\pi$
$90$	−1.12224	+	0.490449i	−0.118295	+	0.0516979i
$91$	7.80581	+	4.50669i	0.818272	+	0.472429i
$92$	−3.70827	+	1.27840i	−0.386613	+	0.133282i
$93$	7.93526	+	6.18901i	0.822848	+	0.641771i
$94$	−1.83764	+	4.91776i	−0.189538	+	0.507228i
$95$	−0.000248300		0.00140818i	−2.54751e−5		0.000144476i
$96$	8.51918	−	4.83979i	0.869485	−	0.493959i
$97$	6.04757	−	5.07452i	0.614038	−	0.515239i	−0.281885	−	0.959448i	$-0.590960\pi$
$97$	6.04757	−	5.07452i	0.614038	−	0.515239i	0.895923	+	0.444209i	$0.146515\pi$
$98$	−0.750405	+	0.878942i	−0.0758024	+	0.0887865i
$99$	13.9423	−	3.50101i	1.40126	−	0.351865i
$100$	−1.54188	−	9.71170i	−0.154188	−	0.971170i
$101$	6.35260	−	17.4536i	0.632107	−	1.73670i	−0.0430976	−	0.999071i	$-0.513723\pi$
$101$	6.35260	−	17.4536i	0.632107	−	1.73670i	0.675205	−	0.737630i	$-0.264055\pi$
$102$	−0.375123	−	13.7866i	−0.0371427	−	1.36508i
$103$	−3.47298	−	2.91418i	−0.342203	−	0.287143i	0.455447	−	0.890263i	$-0.349479\pi$
$103$	−3.47298	−	2.91418i	−0.342203	−	0.287143i	−0.797650	+	0.603120i	$0.793924\pi$
$104$	−1.81289	+	8.93611i	−0.177769	+	0.876258i
$105$	1.23487	+	0.655264i	0.120511	+	0.0639473i
$106$	−1.22419	−	0.0104562i	−0.118904	−	0.00101560i
$107$			3.74905i			0.362434i	0.983443	+	0.181217i	$0.0580036\pi$
$107$			3.74905i			0.362434i	−0.983443	+	0.181217i	$0.941996\pi$
$108$	−10.3501	+	0.935585i	−0.995939	+	0.0900267i
$109$		−	16.8471i		−	1.61366i	−0.590782	−	0.806831i	$-0.701181\pi$
$109$		−	16.8471i		−	1.61366i	0.590782	−	0.806831i	$-0.298819\pi$
$110$	0.0167079	−	1.95612i	0.00159304	−	0.186509i
$111$	−0.586584	−	16.4039i	−0.0556761	−	1.55698i
$112$	−10.3725	−	4.18179i	−0.980105	−	0.395142i
$113$	4.67369	+	3.92169i	0.439664	+	0.368921i	0.835583	−	0.549364i	$-0.185130\pi$
$113$	4.67369	+	3.92169i	0.439664	+	0.368921i	−0.395920	+	0.918285i	$0.629574\pi$
$114$	−0.00577858	+	0.0106688i	−0.000541214	+	0.000999227i
$115$	0.193635	−	0.532007i	0.0180565	−	0.0496099i
$116$	15.8076	−	2.50969i	1.46770	−	0.233019i
$117$	5.67152	−	7.83372i	0.524332	−	0.724228i
$118$	5.97534	+	5.10151i	0.550075	+	0.469632i
$119$	−12.0593	+	10.1189i	−1.10547	+	0.927602i
$120$	−0.231466	+	1.39513i	−0.0211299	+	0.127357i
$121$	−2.07693	+	11.7789i	−0.188812	+	1.07081i
$122$	−9.42477	−	3.52178i	−0.853278	−	0.318847i
$123$	−15.7133	+	6.36390i	−1.41682	+	0.573813i
$124$	10.9857	−	3.78725i	0.986548	−	0.340105i
$125$	2.47914	+	1.43133i	0.221741	+	0.128022i
$126$	8.18133	+	8.58927i	0.728850	+	0.765193i
$127$	−10.6004	−	18.3604i	−0.940632	−	1.62922i	−0.764270	−	0.644896i	$-0.776901\pi$
$127$	−10.6004	−	18.3604i	−0.940632	−	1.62922i	−0.176362	−	0.984325i	$-0.556433\pi$
$128$	0.676021	−	11.2935i	0.0597524	−	0.998213i
$129$	−2.96909	+	9.16403i	−0.261414	+	0.806847i
$130$	−0.837318	−	1.01536i	−0.0734376	−	0.0890533i
$131$	3.62600	+	9.96234i	0.316805	+	0.870414i	0.991239	+	0.132079i	$0.0421653\pi$
$131$	3.62600	+	9.96234i	0.316805	+	0.870414i	−0.674435	+	0.738335i	$0.735613\pi$
$132$	5.38514	−	15.7012i	0.468716	−	1.36661i
$133$	0.0136389	−	0.00240490i	0.00118264	−	0.000208532i
$134$	−0.0588095	+	0.317636i	−0.00508037	+	0.0274396i
$135$	0.835656	−	1.24565i	0.0719218	−	0.107208i
$136$	−13.5832	−	8.31338i	−1.16475	−	0.712866i
$137$	−2.46640	−	13.9877i	−0.210719	−	1.19505i	−0.888182	−	0.459491i	$-0.848032\pi$
$137$	−2.46640	−	13.9877i	−0.210719	−	1.19505i	0.677463	−	0.735557i	$-0.263079\pi$
$138$	2.98671	−	3.76270i	0.254245	−	0.320302i
$139$	3.33532	+	9.16372i	0.282898	+	0.777257i	0.997013	+	0.0772283i	$0.0246070\pi$
$139$	3.33532	+	9.16372i	0.282898	+	0.777257i	−0.714115	+	0.700028i	$0.753171\pi$
$140$	1.41153	−	0.783110i	0.119296	−	0.0661849i
$141$	−1.34209	−	6.28814i	−0.113024	−	0.529557i
$142$	1.04786	+	0.616975i	0.0879344	+	0.0517754i
$143$	7.72366	+	13.3778i	0.645885	+	1.11871i
$144$	−5.60804	+	10.6090i	−0.467337	+	0.884079i
$145$	−1.15509	+	2.00068i	−0.0959254	+	0.166148i
$146$	4.98869	−	2.82369i	0.412867	−	0.233690i
$147$	0.195818	−	1.40183i	0.0161508	−	0.115621i
$148$	−16.2501	−	9.75582i	−1.33575	−	0.801924i
$149$	−1.13973	−	0.200964i	−0.0933699	−	0.0164636i	0.126768	−	0.991932i	$-0.459540\pi$
$149$	−1.13973	−	0.200964i	−0.0933699	−	0.0164636i	−0.220138	+	0.975469i	$0.570651\pi$
$150$	7.98937	+	9.01175i	0.652329	+	0.735807i
$151$	−15.9973	+	13.4234i	−1.30184	+	1.09238i	−0.312022	+	0.950075i	$0.601006\pi$
$151$	−15.9973	+	13.4234i	−1.30184	+	1.09238i	−0.989823	+	0.142303i	$0.954549\pi$
$152$	0.00669198	+	0.0123087i	0.000542791	+	0.000998371i
$153$	9.46893	+	13.9877i	0.765518	+	1.13084i
$154$	−17.8587	+	6.32783i	−1.43910	+	0.509911i
$155$	−0.573643	+	1.57607i	−0.0460761	+	0.126593i
$156$	−4.01463	−	10.4208i	−0.321428	−	0.834334i
$157$	−12.0447	+	14.3543i	−0.961268	+	1.14560i	0.0280180	+	0.999607i	$0.491080\pi$
$157$	−12.0447	+	14.3543i	−0.961268	+	1.14560i	−0.989286	+	0.145988i	$0.953364\pi$
$158$	6.40509	−	1.07307i	0.509562	−	0.0853686i
$159$	1.27088	−	0.795612i	0.100787	−	0.0630961i
$160$	1.20498	+	1.10211i	0.0952621	+	0.0871292i
$161$	−5.48343			−0.432155
$162$	10.0703	−	7.78390i	0.791197	−	0.611561i
$163$			11.5772i			0.906795i	0.891308	+	0.453397i	$0.149788\pi$
$163$			11.5772i			0.906795i	−0.891308	+	0.453397i	$0.850212\pi$
$164$	−3.72810	+	19.2175i	−0.291116	+	1.50063i
$165$	1.27130	+	2.03072i	0.0989706	+	0.158091i
$166$	0.949698	+	5.66871i	0.0737108	+	0.439977i
$167$	7.59855	+	6.37594i	0.587994	+	0.493385i	0.887561	−	0.460690i	$-0.152398\pi$
$167$	7.59855	+	6.37594i	0.587994	+	0.493385i	−0.299568	+	0.954075i	$0.596842\pi$
$168$	13.4643	−	2.51488i	1.03880	−	0.194027i
$169$	−2.45017	−	0.891789i	−0.188475	−	0.0685991i
$170$	2.16661	−	0.767689i	0.166171	−	0.0588790i
$171$	−0.00106141	−	0.0148222i	−8.11679e−5	−	0.00113348i
$172$	7.00329	+	8.64178i	0.533996	+	0.658930i
$173$	−12.8453	−	15.3084i	−0.976609	−	1.16388i	−0.986473	−	0.163926i	$-0.947584\pi$
$173$	−12.8453	−	15.3084i	−0.976609	−	1.16388i	0.00986338	−	0.999951i	$-0.496860\pi$
$174$	−14.6683	+	13.0042i	−1.11200	+	0.985846i
$175$	2.38708	−	13.5378i	0.180446	−	1.02336i
$176$	−11.8115	−	15.0949i	−0.890326	−	1.13782i
$177$	−9.53010	−	1.33123i	−0.716326	−	0.100062i
$178$	4.37870	−	2.47842i	0.328197	−	0.185765i
$179$	−18.6622	−	10.7746i	−1.39488	−	0.805335i	−0.401030	−	0.916065i	$-0.631348\pi$
$179$	−18.6622	−	10.7746i	−1.39488	−	0.805335i	−0.993851	+	0.110730i	$0.964681\pi$
$180$	−0.680019	−	1.59296i	−0.0506856	−	0.118732i
$181$	17.9309	−	10.3524i	1.33280	−	0.769490i	0.347068	−	0.937840i	$-0.387177\pi$
$181$	17.9309	−	10.3524i	1.33280	−	0.769490i	0.985727	+	0.168350i	$0.0538440\pi$
$182$	−6.46747	+	10.9842i	−0.479401	+	0.814207i
$183$	12.0511	−	2.57208i	0.890840	−	0.190134i
$184$	−1.76307	−	5.25953i	−0.129975	−	0.387738i
$185$	2.57071	−	0.935664i	0.189003	−	0.0687914i
$186$	−8.84812	+	11.1470i	−0.648775	+	0.817337i
$187$	−26.5696	+	4.68494i	−1.94296	+	0.342596i
$188$	−6.93231	−	2.65812i	−0.505591	−	0.193863i
$189$	−14.1053	−	3.47924i	−1.02601	−	0.253078i
$190$	−0.00198840		0.000368146i	−0.000144253		2.67081e-5i
$191$	−0.173666	−	0.984911i	−0.0125661	−	0.0712657i	0.977880	−	0.209167i	$-0.0670753\pi$
$191$	−0.173666	−	0.984911i	−0.0125661	−	0.0712657i	−0.990446	+	0.137902i	$0.955964\pi$
$192$	6.74134	+	12.1060i	0.486514	+	0.873673i
$193$	18.6207	−	6.77739i	1.34035	−	0.487847i	0.430427	−	0.902625i	$-0.358363\pi$
$193$	18.6207	−	6.77739i	1.34035	−	0.487847i	0.909923	+	0.414778i	$0.136141\pi$
$194$	7.10314	+	8.61354i	0.509976	+	0.618416i
$195$	1.53339	+	0.496809i	0.109808	+	0.0355772i
$196$	−1.23390	−	1.07181i	−0.0881359	−	0.0765579i
$197$	5.14676	−	2.97148i	0.366691	−	0.211709i	−0.305321	−	0.952250i	$-0.598764\pi$
$197$	5.14676	−	2.97148i	0.366691	−	0.211709i	0.672012	+	0.740540i	$0.265430\pi$
$198$	4.78259	+	19.7590i	0.339884	+	1.40421i
$199$	−4.22572	+	7.31916i	−0.299553	+	0.518842i	−0.976034	−	0.217619i	$-0.930171\pi$
$199$	−4.22572	+	7.31916i	−0.299553	+	0.518842i	0.676480	+	0.736461i	$0.263504\pi$
$200$	13.7525	−	2.06316i	0.972452	−	0.145887i
$201$	−0.148515	−	0.366702i	−0.0104754	−	0.0258652i
$202$	24.6055	+	9.19443i	1.73124	+	0.646918i
$203$	22.0353	+	3.88542i	1.54658	+	0.272703i
$204$	19.5010	−	0.363958i	1.36534	−	0.0254822i
$205$	−1.81619	−	2.16445i	−0.126848	−	0.151172i
$206$	4.16307	−	4.87616i	0.290055	−	0.339738i
$207$	−0.605213	+	5.85245i	−0.0420652	+	0.406773i
$208$	−12.6152	−	2.67166i	−0.874708	−	0.185247i
$209$	0.0223038	+	0.00811792i	0.00154279	+	0.000561528i
$210$	−0.941566	+	1.73839i	−0.0649742	+	0.119960i
$211$	2.67743	−	3.19083i	0.184322	−	0.219666i	−0.665969	−	0.745980i	$-0.731982\pi$
$211$	2.67743	−	3.19083i	0.184322	−	0.219666i	0.850291	+	0.526313i	$0.176426\pi$
$212$	0.0295736	−	1.73108i	0.00203113	−	0.118891i
$213$	−1.48834	+	0.0532216i	−0.101980	+	0.00364668i
$214$	−5.30176	−	0.0452842i	−0.362421	−	0.00309556i
$215$	−1.60549			−0.109493
$216$	−1.19805	−	14.6480i	−0.0815171	−	0.996672i
$217$	16.2446			1.10276
$218$	23.8246	+	0.203494i	1.61360	+	0.0137824i
$219$	−3.29083	+	6.20168i	−0.222374	+	0.419070i
$220$	2.76607	+	0.0472554i	0.186488	+	0.00318596i
$221$	−11.6673	+	13.9046i	−0.784829	+	0.935323i
$222$	23.2048	−	0.631385i	1.55740	−	0.0423758i
$223$	13.7266	+	4.99606i	0.919198	+	0.334561i	0.757919	−	0.652348i	$-0.226216\pi$
$223$	13.7266	+	4.99606i	0.919198	+	0.334561i	0.161279	+	0.986909i	$0.448438\pi$
$224$	6.03902	−	14.6178i	0.403499	−	0.976694i
$225$	−14.1854	−	4.04191i	−0.945693	−	0.269461i
$226$	−5.60236	+	6.56198i	−0.372663	+	0.436496i
$227$	13.2187	+	15.7535i	0.877359	+	1.04560i	0.998596	+	0.0529722i	$0.0168695\pi$
$227$	13.2187	+	15.7535i	0.877359	+	1.04560i	−0.121237	+	0.992624i	$0.538686\pi$
$228$	−0.0150176	−	0.00830072i	−0.000994568	−	0.000549728i
$229$	−11.3156	−	1.99525i	−0.747759	−	0.131850i	−0.213232	−	0.977002i	$-0.568399\pi$
$229$	−11.3156	−	1.99525i	−0.747759	−	0.131850i	−0.534527	+	0.845151i	$0.679510\pi$
$230$	0.750005	+	0.280257i	0.0494539	+	0.0184796i
$231$	14.2710	−	18.2976i	0.938962	−	1.20389i
$232$	3.35817	+	22.3848i	0.220475	+	1.46964i
$233$	−2.16566	+	3.75103i	−0.141877	+	0.245738i	−0.928203	−	0.372073i	$-0.878647\pi$
$233$	−2.16566	+	3.75103i	−0.141877	+	0.245738i	0.786326	+	0.617811i	$0.211980\pi$
$234$	11.0096	+	8.11507i	0.719723	+	0.530498i
$235$	0.928049	−	0.535809i	0.0605392	−	0.0349523i
$236$	−7.28653	+	8.38848i	−0.474313	+	0.546043i
$237$	−5.90647	+	5.32717i	−0.383666	+	0.346037i
$238$	−14.1642	−	17.1760i	−0.918126	−	1.11336i
$239$	−13.2703	+	4.82998i	−0.858382	+	0.312426i	−0.733453	−	0.679740i	$-0.762093\pi$
$239$	−13.2703	+	4.82998i	−0.858382	+	0.312426i	−0.124929	+	0.992166i	$0.539870\pi$
$240$	−1.97014	−	0.344182i	−0.127172	−	0.0222169i
$241$	2.60609	+	14.7799i	0.167873	+	0.952056i	0.946052	+	0.324014i	$0.105032\pi$
$241$	2.60609	+	14.7799i	0.167873	+	0.952056i	−0.778179	+	0.628042i	$0.783856\pi$
$242$	−16.6321	−	3.07939i	−1.06915	−	0.197951i
$243$	−5.27021	+	14.6705i	−0.338084	+	0.941116i
$244$	5.09421	−	13.2856i	0.326124	−	0.850524i
$245$	0.232321	−	0.0409644i	0.0148424	−	0.00261712i
$246$	−8.80978	−	22.2980i	−0.561691	−	1.42167i
$247$	0.0150055	−	0.00546154i	0.000954774	−	0.000347509i
$248$	5.22309	+	15.5814i	0.331667	+	0.989417i
$249$	−4.71471	−	5.22741i	−0.298783	−	0.331274i
$250$	−2.05408	+	3.48862i	−0.129912	+	0.220640i
$251$	−26.0768	+	15.0554i	−1.64595	+	0.950290i	−0.667293	+	0.744795i	$0.732547\pi$
$251$	−26.0768	+	15.0554i	−1.64595	+	0.950290i	−0.978658	+	0.205495i	$0.934120\pi$
$252$	−12.2454	+	11.4660i	−0.771390	+	0.722288i
$253$	−8.13857	−	4.69881i	−0.511668	−	0.295412i
$254$	26.0926	−	14.7689i	1.63720	−	0.926682i
$255$	−1.73135	+	2.21985i	−0.108421	+	0.139012i
$256$	15.9627	+	1.09242i	0.997666	+	0.0682760i
$257$	−0.685637	+	3.88844i	−0.0427688	+	0.242554i	−0.998696	−	0.0510494i	$-0.983743\pi$
$257$	−0.685637	+	3.88844i	−0.0427688	+	0.242554i	0.955927	+	0.293603i	$0.0948545\pi$
$258$	−12.9236	−	4.30947i	−0.804585	−	0.268296i
$259$	−17.0316	−	20.2975i	−1.05829	−	1.26123i
$260$	1.44600	−	1.17184i	0.0896773	−	0.0726743i
$261$	6.57897	−	23.0894i	0.407228	−	1.42920i
$262$	−14.1322	+	5.00741i	−0.873088	+	0.309359i
$263$	12.3951	+	4.51144i	0.764313	+	0.278187i	0.694616	−	0.719381i	$-0.255575\pi$
$263$	12.3951	+	4.51144i	0.764313	+	0.278187i	0.0696970	+	0.997568i	$0.477797\pi$
$264$	22.1390	+	7.80511i	1.36256	+	0.480372i
$265$	0.191430	+	0.160629i	0.0117594	+	0.00986733i
$266$	0.00323618	+	0.0193166i	0.000198423	+	0.00118438i
$267$	−2.88844	+	5.44336i	−0.176770	+	0.333128i
$268$	−0.448479	−	0.0870028i	−0.0273952	−	0.00531454i
$269$			7.68651i			0.468655i	0.972158	+	0.234327i	$0.0752887\pi$
$269$			7.68651i			0.468655i	−0.972158	+	0.234327i	$0.924711\pi$
$270$	1.75145	+	1.19680i	0.106590	+	0.0728349i
$271$	21.3410			1.29637			0.648187	−	0.761481i	$-0.275528\pi$
$271$	21.3410			1.29637			0.648187	+	0.761481i	$0.275528\pi$
$272$	11.9205	−	19.1084i	0.722788	−	1.15862i
$273$	−0.557898	−	15.6017i	−0.0337655	−	0.944255i
$274$	19.8106	−	3.31894i	1.19680	−	0.200504i
$275$	15.1436	−	18.0475i	0.913195	−	1.08830i
$276$	5.28499	+	4.26914i	0.318119	+	0.256972i
$277$	7.73418	−	21.2495i	0.464702	−	1.27676i	−0.457210	−	0.889359i	$-0.651151\pi$
$277$	7.73418	−	21.2495i	0.464702	−	1.27676i	0.921912	−	0.387400i	$-0.126627\pi$
$278$	−12.9993	+	4.60600i	−0.779644	+	0.276249i
$279$	1.79294	−	17.3379i	0.107341	−	1.03799i
$280$	1.09039	+	2.00560i	0.0651636	+	0.119857i
$281$	−24.7061	+	20.7308i	−1.47384	+	1.23670i	−0.561363	+	0.827570i	$0.689723\pi$
$281$	−24.7061	+	20.7308i	−1.47384	+	1.23670i	−0.912477	+	0.409129i	$0.865833\pi$
$282$	8.90866	−	1.82198i	0.530503	−	0.108497i
$283$	20.0970	+	3.54364i	1.19464	+	0.210648i	0.735381	−	0.677653i	$-0.237003\pi$
$283$	20.0970	+	3.54364i	1.19464	+	0.210648i	0.459261	+	0.888301i	$0.348114\pi$
$284$	−0.885159	+	1.47439i	−0.0525245	+	0.0874890i
$285$	0.00229555		0.000929698i	0.000135977		5.50705e-5i
$286$	−19.0116	+	10.7609i	−1.12418	+	0.636306i
$287$	−13.6831	+	23.6998i	−0.807687	+	1.39896i
$288$	−14.9350	−	8.05882i	−0.880056	−	0.474871i
$289$	−7.35090	−	12.7321i	−0.432406	−	0.748949i
$290$	−2.81534	−	1.65766i	−0.165322	−	0.0973409i
$291$	−13.0080	−	4.21453i	−0.762545	−	0.247060i
$292$	3.93289	+	7.08892i	0.230155	+	0.414848i
$293$	1.43710	+	3.94839i	0.0839561	+	0.230667i	0.974566	−	0.224101i	$-0.0719444\pi$
$293$	1.43710	+	3.94839i	0.0839561	+	0.230667i	−0.890610	+	0.454768i	$0.849722\pi$
$294$	1.98005	+	0.293850i	0.115479	+	0.0171377i
$295$	−0.278490	−	1.57939i	−0.0162143	−	0.0919558i
$296$	13.9926	−	22.8624i	0.813303	−	1.32885i
$297$	−17.9539	−	17.2509i	−1.04179	−	1.00100i
$298$	0.297963	−	1.60933i	0.0172605	−	0.0932259i
$299$	−6.22644	+	1.09789i	−0.360084	+	0.0634926i
$300$	−12.8406	+	11.1894i	−0.741351	+	0.646021i
$301$	5.31837	+	14.6121i	0.306546	+	0.842228i
$302$	−18.7896	−	22.7850i	−1.08122	−	1.31113i
$303$	−31.4621	+	6.71500i	−1.80745	+	0.385767i
$304$	−0.0174874	+	0.00931486i	−0.00100297	+	0.000534244i
$305$	1.02686	+	1.77858i	0.0587981	+	0.101841i
$306$	−19.8952	+	13.2216i	−1.13734	+	0.755831i
$307$	16.4700	+	9.50896i	0.939993	+	0.542705i	0.889958	−	0.456043i	$-0.150734\pi$
$307$	16.4700	+	9.50896i	0.939993	+	0.542705i	0.0500346	+	0.998747i	$0.484067\pi$
$308$	−8.73286	−	25.3315i	−0.497601	−	1.44340i
$309$	−1.08635	+	7.77702i	−0.0618003	+	0.442419i
$310$	−2.22189	−	0.830261i	−0.126195	−	0.0471557i
$311$	3.01498	−	17.0988i	0.170964	−	0.969585i	−0.771736	−	0.635943i	$-0.780611\pi$
$311$	3.01498	−	17.0988i	0.170964	−	0.969585i	0.942700	−	0.333642i	$-0.108278\pi$
$312$	14.7852	−	5.55147i	0.837049	−	0.314290i
$313$	0.579959	−	0.486644i	0.0327812	−	0.0275067i	−0.626250	−	0.779622i	$-0.715411\pi$
$313$	0.579959	−	0.486644i	0.0327812	−	0.0275067i	0.659031	+	0.752116i	$0.270967\pi$
$314$	−20.1538	−	17.2065i	−1.13734	−	0.971018i
$315$	−0.172947	−	2.41514i	−0.00974443	−	0.136078i
$316$	1.44012	+	9.07080i	0.0810133	+	0.510272i
$317$	6.72476	−	18.4761i	0.377700	−	1.03772i	−0.594607	−	0.804016i	$-0.702692\pi$
$317$	6.72476	−	18.4761i	0.377700	−	1.03772i	0.972307	−	0.233706i	$-0.0750853\pi$
$318$	1.10977	+	1.80684i	0.0622330	+	0.101322i
$319$	29.3756	+	24.6491i	1.64472	+	1.38008i
$320$	−1.57311	+	1.69073i	−0.0879397	+	0.0945144i
$321$	5.50395	−	3.44566i	0.307201	−	0.192318i
$322$	0.0662335	−	7.75445i	0.00369105	−	0.432139i
$323$			0.0278897i			0.00155182i
$324$	10.8861	+	14.3350i	0.604781	+	0.796392i
$325$		−	15.8501i		−	0.879207i
$326$	−16.3720	−	0.139839i	−0.906762	−	0.00774497i
$327$	−24.7332	+	15.4838i	−1.36775	+	0.856256i
$328$	−27.1316	−	5.50426i	−1.49809	−	0.303922i
$329$	−7.95087	−	6.67157i	−0.438345	−	0.367815i
$330$	−2.88713	+	1.77330i	−0.158931	+	0.0976168i
$331$	8.42157	−	23.1381i	0.462891	−	1.27178i	−0.460409	−	0.887707i	$-0.652297\pi$
$331$	8.42157	−	23.1381i	0.462891	−	1.27178i	0.923301	−	0.384077i	$-0.125480\pi$
$332$	−8.02794	+	1.27455i	−0.440591	+	0.0699503i
$333$	−23.5433	+	15.9376i	−1.29016	+	0.873373i
$334$	−9.10840	+	10.6686i	−0.498389	+	0.583758i
$335$	0.0505119	−	0.0423845i	0.00275976	−	0.00231571i
$336$	3.39381	+	19.0711i	0.185148	+	1.04042i
$337$	−1.71929	+	9.75056i	−0.0936555	+	0.531147i	0.901496	+	0.432788i	$0.142470\pi$
$337$	−1.71929	+	9.75056i	−0.0936555	+	0.531147i	−0.995151	+	0.0983585i	$0.968641\pi$
$338$	1.29073	−	3.45416i	0.0702064	−	0.187882i
$339$	1.46193	−	10.4657i	0.0794012	−	0.568421i
$340$	1.05947	+	3.07321i	0.0574576	+	0.166668i
$341$	24.1105	+	13.9202i	1.30566	+	0.753822i
$342$	0.0209738	−	0.00132197i	0.00113413	−	7.14838e-5i
$343$	8.64332	+	14.9707i	0.466695	+	0.808340i
$344$	−12.3055	+	9.79940i	−0.663467	+	0.528348i
$345$	−0.959002	+	0.204681i	−0.0516309	+	0.0110197i
$346$	21.8037	−	17.9804i	1.17218	−	0.966633i
$347$	−7.12971	−	19.5887i	−0.382743	−	1.05158i	−0.970196	−	0.242320i	$-0.922092\pi$
$347$	−7.12971	−	19.5887i	−0.382743	−	1.05158i	0.587453	−	0.809258i	$-0.300131\pi$
$348$	−18.2129	−	20.9005i	−0.976313	−	1.12038i
$349$	14.8725	−	2.62242i	0.796107	−	0.140375i	0.239222	−	0.970965i	$-0.423108\pi$
$349$	14.8725	−	2.62242i	0.796107	−	0.140375i	0.556885	+	0.830590i	$0.311996\pi$
$350$	19.1158	+	3.53924i	1.02178	+	0.189180i
$351$	−16.7132	−	1.12653i	−0.892084	−	0.0601297i
$352$	21.4894	−	16.5211i	1.14539	−	0.880575i
$353$	−0.616217	−	3.49474i	−0.0327979	−	0.186006i	0.964007	−	0.265875i	$-0.0856609\pi$
$353$	−0.616217	−	3.49474i	−0.0327979	−	0.186006i	−0.996805	+	0.0798689i	$0.974550\pi$
$354$	1.99769	−	13.4610i	0.106176	−	0.715446i
$355$	−0.0848941	−	0.233245i	−0.00450571	−	0.0123793i
$356$	3.45200	+	6.22212i	0.182955	+	0.329772i
$357$	25.9390	+	8.40408i	1.37284	+	0.444791i
$358$	15.4625	−	26.2613i	0.817219	−	1.38795i
$359$	−11.0808	−	19.1925i	−0.584823	−	1.01294i	−0.994897	−	0.100891i	$-0.967831\pi$
$359$	−11.0808	−	19.1925i	−0.584823	−	1.01294i	0.410074	−	0.912052i	$-0.365503\pi$
$360$	2.26092	−	0.942416i	0.119161	−	0.0496697i
$361$	−9.49999	+	16.4545i	−0.499999	+	0.866024i
$362$	14.4234	+	25.4823i	0.758078	+	1.33932i
$363$	19.2013	−	7.77655i	1.00781	−	0.408163i
$364$	−15.4554	−	9.27873i	−0.810082	−	0.486338i
$365$	−1.15233	−	0.203187i	−0.0603158	−	0.0106353i
$366$	3.49177	+	17.0732i	0.182518	+	0.892432i
$367$	13.2887	−	11.1505i	0.693664	−	0.582053i	−0.226299	−	0.974058i	$-0.572663\pi$
$367$	13.2887	−	11.1505i	0.693664	−	0.582053i	0.919963	+	0.392005i	$0.128218\pi$
$368$	7.45912	−	2.42974i	0.388834	−	0.126659i
$369$	23.7845	+	17.2197i	1.23817	+	0.896422i
$370$	1.29213	+	3.64671i	0.0671746	+	0.189583i
$371$	0.827803	−	2.27437i	0.0429774	−	0.118079i
$372$	−15.6568	−	12.6473i	−0.811766	−	0.655733i
$373$	−10.6639	+	12.7087i	−0.552156	+	0.658034i	−0.967867	−	0.251463i	$-0.919088\pi$
$373$	−10.6639	+	12.7087i	−0.552156	+	0.658034i	0.415711	+	0.909497i	$0.363533\pi$
$374$	−6.30433	−	37.6303i	−0.325989	−	1.94582i
$375$	−0.177190	−	4.95512i	−0.00915004	−	0.255881i
$376$	3.84274	−	9.77131i	0.198174	−	0.503917i
$377$	25.7991			1.32872
$378$	5.09059	−	19.9051i	0.261832	−	1.02381i
$379$		−	9.64915i		−	0.495644i	−0.968806	−	0.247822i	$-0.920285\pi$
$379$		−	9.64915i		−	0.495644i	0.968806	−	0.247822i	$-0.0797148\pi$
$380$	0.000544636	−	0.00280747i	2.79392e−5	−	0.000144020i
$381$	−17.2122	+	32.4370i	−0.881809	+	1.66180i
$382$	1.39492	−	0.233696i	0.0713704	−	0.0119569i
$383$	−9.22574	−	7.74132i	−0.471414	−	0.395563i	0.375896	−	0.926662i	$-0.377335\pi$
$383$	−9.22574	−	7.74132i	−0.471414	−	0.395563i	−0.847310	+	0.531099i	$0.821779\pi$
$384$	−17.2012	+	9.38712i	−0.877796	+	0.479034i
$385$	3.63420	+	1.32274i	0.185216	+	0.0674130i
$386$	9.35941	+	26.4146i	0.476382	+	1.34447i
$387$	16.1825	−	4.06353i	0.822601	−	0.206561i
$388$	−12.2667	+	9.94095i	−0.622749	+	0.504675i
$389$	1.86623	+	2.22408i	0.0946216	+	0.112766i	0.811277	−	0.584661i	$-0.198773\pi$
$389$	1.86623	+	2.22408i	0.0946216	+	0.112766i	−0.716656	+	0.697427i	$0.754328\pi$
$390$	−0.721090	+	2.16246i	−0.0365138	+	0.109500i
$391$	1.91751	−	10.8748i	0.0969729	−	0.549960i
$392$	1.53062	−	1.73199i	0.0773079	−	0.0874788i
$393$	11.2931	−	14.4795i	0.569661	−	0.730392i
$394$	4.13999	+	7.31424i	0.208570	+	0.368486i
$395$	−1.14804	−	0.662821i	−0.0577642	−	0.0333502i
$396$	−28.0002	+	6.52469i	−1.40706	+	0.327878i
$397$	−3.53148	+	2.03890i	−0.177240	+	0.102330i	−0.585995	−	0.810314i	$-0.699296\pi$
$397$	−3.53148	+	2.03890i	−0.177240	+	0.102330i	0.408755	+	0.912644i	$0.365963\pi$
$398$	−10.2994	−	6.06426i	−0.516264	−	0.303974i
$399$	−0.0160658	−	0.0178129i	−0.000804296	−	0.000891759i
$400$	2.75152	+	19.4732i	0.137576	+	0.973662i
$401$	2.09322	−	0.761870i	0.104530	−	0.0380460i	−0.289226	−	0.957261i	$-0.593398\pi$
$401$	2.09322	−	0.761870i	0.104530	−	0.0380460i	0.393756	+	0.919215i	$0.371176\pi$
$402$	0.520370	−	0.205594i	0.0259537	−	0.0102541i
$403$	18.4458	−	3.25249i	0.918851	−	0.162018i
$404$	−13.2996	+	34.6851i	−0.661681	+	1.72565i
$405$	−2.59676	−	0.0819761i	−0.129034	−	0.00407343i
$406$	−5.76078	+	31.1146i	−0.285903	+	1.54419i
$407$	−7.88541	−	44.7204i	−0.390865	−	2.21671i
$408$	0.279146	+	27.5820i	0.0138198	+	1.36551i
$409$	17.7345	−	6.45483i	0.876914	−	0.319171i	0.135950	−	0.990716i	$-0.456591\pi$
$409$	17.7345	−	6.45483i	0.876914	−	0.319171i	0.740964	+	0.671545i	$0.234369\pi$
$410$	3.08282	−	2.54224i	0.152250	−	0.125552i
$411$	−18.2684	+	16.4767i	−0.901114	+	0.812733i
$412$	6.84540	+	5.94615i	0.337248	+	0.292946i
$413$	−13.4521	+	7.76657i	−0.661934	+	0.382168i
$414$	−8.26900	−	0.926560i	−0.406399	−	0.0455379i
$415$	0.586618	−	1.01605i	0.0287959	−	0.0498760i
$416$	3.93054	−	17.8077i	0.192711	−	0.873093i
$417$	10.3878	−	13.3187i	0.508692	−	0.652221i
$418$	−0.0117495	+	0.0314431i	−0.000574685	+	0.00153793i
$419$	−13.5715	−	2.39303i	−0.663013	−	0.116907i	−0.167992	−	0.985788i	$-0.553728\pi$
$419$	−13.5715	−	2.39303i	−0.663013	−	0.116907i	−0.495021	+	0.868881i	$0.664839\pi$
$420$	−2.44699	−	1.35252i	−0.119401	−	0.0659964i
$421$	23.8985	+	28.4811i	1.16474	+	1.38809i	0.906607	+	0.421977i	$0.138664\pi$
$421$	23.8985	+	28.4811i	1.16474	+	1.38809i	0.258135	+	0.966109i	$0.416892\pi$
$422$	4.48002	+	3.82486i	0.218084	+	0.186191i
$423$	−7.99810	+	7.74959i	−0.388881	+	0.376798i
$424$	2.44767	+	0.0627313i	0.118869	+	0.00304650i
$425$	26.0135	+	9.46814i	1.26184	+	0.459272i
$426$	−0.0572865	−	2.10540i	−0.00277554	−	0.102007i
$427$	12.7859	−	15.2376i	0.618753	−	0.737401i
$428$	0.128078	−	7.49700i	0.00619090	−	0.362381i
$429$	12.5412	−	23.6342i	0.605494	−	1.14107i
$430$	0.0193924	−	2.27042i	0.000935187	−	0.109489i
$431$	11.4089			0.549548			0.274774	−	0.961509i	$-0.411397\pi$
$431$	11.4089			0.549548			0.274774	+	0.961509i	$0.411397\pi$
$432$	20.7292	−	1.51731i	0.997332	−	0.0730015i
$433$	−7.51420			−0.361109			−0.180555	−	0.983565i	$-0.557789\pi$
$433$	−7.51420			−0.361109			−0.180555	+	0.983565i	$0.557789\pi$
$434$	−0.196217	+	22.9726i	−0.00941870	+	1.10272i
$435$	3.99881	−	0.142993i	0.191728	−	0.00685599i
$436$	−0.575547	+	33.6893i	−0.0275637	+	1.61343i
$437$	−0.00624447	+	0.00744187i	−0.000298713	+	0.000355993i
$438$	−8.73042	−	4.72868i	−0.417156	−	0.225945i
$439$	−19.2063	−	6.99052i	−0.916667	−	0.333639i	−0.159755	−	0.987157i	$-0.551070\pi$
$439$	−19.2063	−	6.99052i	−0.916667	−	0.333639i	−0.756912	+	0.653517i	$0.773293\pi$
$440$	−0.100238	+	3.91110i	−0.00477865	+	0.186454i
$441$	−2.23799	+	1.00091i	−0.106571	+	0.0476624i
$442$	−19.5224	−	16.6674i	−0.928586	−	0.792789i
$443$	18.1395	+	21.6178i	0.861832	+	1.02709i	0.999330	+	0.0365893i	$0.0116493\pi$
$443$	18.1395	+	21.6178i	0.861832	+	1.02709i	−0.137498	+	0.990502i	$0.543906\pi$
$444$	0.612594	+	32.8230i	0.0290724	+	1.55771i
$445$	−1.01143	−	0.178342i	−0.0479463	−	0.00845423i
$446$	−7.23103	+	19.3512i	−0.342399	+	0.916307i
$447$	0.752460	+	1.85793i	0.0355901	+	0.0878768i
$448$	20.5990	+	8.71672i	0.973212	+	0.411826i
$449$	−5.65025	+	9.78653i	−0.266652	+	0.461855i	−0.967995	−	0.250969i	$-0.919251\pi$
$449$	−5.65025	+	9.78653i	−0.266652	+	0.461855i	0.701343	+	0.712824i	$0.252584\pi$
$450$	5.88726	−	20.0116i	0.277528	−	0.943357i
$451$	−40.6172	+	23.4504i	−1.91259	+	1.10423i
$452$	−9.21203	−	8.00190i	−0.433298	−	0.376378i
$453$	34.4095	+	11.1485i	1.61670	+	0.523802i
$454$	−22.4377	+	18.5032i	−1.05305	+	0.868397i
$455$	2.44500	−	0.889907i	0.114623	−	0.0417195i
$456$	0.0119200	−	0.0211371i	0.000558203	−	0.000989837i
$457$	−6.59891	−	37.4243i	−0.308684	−	1.75063i	−0.605636	−	0.795742i	$-0.707081\pi$
$457$	−6.59891	−	37.4243i	−0.308684	−	1.75063i	0.296952	−	0.954892i	$-0.404030\pi$
$458$	2.95829	−	15.9781i	0.138232	−	0.746606i
$459$	11.8326	−	26.7570i	0.552297	−	1.24891i
$460$	−0.405388	+	1.05724i	−0.0189013	+	0.0492943i
$461$	7.55207	−	1.33163i	0.351735	−	0.0620204i	0.00501063	−	0.999987i	$-0.498405\pi$
$461$	7.55207	−	1.33163i	0.351735	−	0.0620204i	0.346724	+	0.937967i	$0.387294\pi$
$462$	25.7034	+	20.4025i	1.19583	+	0.949210i
$463$	−20.5953	+	7.49607i	−0.957144	+	0.348372i	−0.772914	−	0.634511i	$-0.781202\pi$
$463$	−20.5953	+	7.49607i	−0.957144	+	0.348372i	−0.184231	+	0.982883i	$0.558979\pi$
$464$	−31.6964	+	4.47862i	−1.47147	+	0.207915i
$465$	2.84104	−	0.606368i	0.131750	−	0.0281196i
$466$	−5.27840	−	3.10790i	−0.244517	−	0.143971i
$467$	−2.10941	+	1.21787i	−0.0976119	+	0.0563563i	−0.548011	−	0.836471i	$-0.684615\pi$
$467$	−2.10941	+	1.21787i	−0.0976119	+	0.0563563i	0.450399	+	0.892827i	$0.351282\pi$
$468$	−11.6090	+	15.4714i	−0.536626	+	0.715166i
$469$	−0.553083	−	0.319323i	−0.0255390	−	0.0147450i
$470$	0.746511	+	1.31888i	0.0344340	+	0.0608355i
$471$	32.1434	+	4.49002i	1.48109	+	0.206889i
$472$	−11.7747	−	10.4057i	−0.541972	−	0.478959i
$473$	−4.62768	+	26.2449i	−0.212781	+	1.20674i
$474$	−7.46213	−	8.41704i	−0.342747	−	0.386608i
$475$	−0.0156545	−	0.0186563i	−0.000718279	−	0.000856012i
$476$	24.4608	−	19.8230i	1.12116	−	0.908584i
$477$	−2.33607	−	1.13454i	−0.106961	−	0.0519469i
$478$	−6.67009	−	18.8246i	−0.305083	−	0.861019i
$479$	13.6689	+	4.97509i	0.624550	+	0.227318i	0.634857	−	0.772629i	$-0.281059\pi$
$479$	13.6689	+	4.97509i	0.624550	+	0.227318i	−0.0103076	+	0.999947i	$0.503281\pi$
$480$	0.510527	−	2.78194i	0.0233023	−	0.126978i
$481$	−23.4034	−	19.6378i	−1.06710	−	0.895405i
$482$	−20.9326	+	3.50691i	−0.953455	+	0.159736i
$483$	5.03969	+	8.05018i	0.229314	+	0.366296i
$484$	4.55566	−	23.4833i	0.207075	−	1.06742i
$485$		−	2.27894i		−	0.103481i
$486$	−20.6829	−	7.63013i	−0.938194	−	0.346110i
$487$	2.54679			0.115406			0.0577031	−	0.998334i	$-0.481622\pi$
$487$	2.54679			0.115406			0.0577031	+	0.998334i	$0.481622\pi$
$488$	18.7265	+	7.36452i	0.847707	+	0.333376i
$489$	16.9964	−	10.6403i	0.768603	−	0.481172i
$490$	0.0551241	+	0.329034i	0.00249025	+	0.0148642i
$491$	11.6939	−	13.9362i	0.527738	−	0.628933i	−0.434654	−	0.900597i	$-0.643129\pi$
$491$	11.6939	−	13.9362i	0.527738	−	0.628933i	0.962392	+	0.271664i	$0.0875739\pi$
$492$	31.6395	−	12.1891i	1.42642	−	0.549528i
$493$	−15.4112	+	42.3419i	−0.694085	+	1.90698i
$494$	0.00754225	+	0.0212861i	0.000339342	+	0.000957708i
$495$	1.81287	−	3.73278i	0.0814823	−	0.167776i
$496$	−22.0976	+	7.19809i	−0.992214	+	0.323204i
$497$	−1.84162	+	1.54530i	−0.0826080	+	0.0693163i
$498$	7.44935	−	6.60422i	0.333813	−	0.295942i
$499$	−2.03309	−	0.358488i	−0.0910134	−	0.0160481i	0.127956	−	0.991780i	$-0.459158\pi$
$499$	−2.03309	−	0.358488i	−0.0910134	−	0.0160481i	−0.218969	+	0.975732i	$0.570269\pi$
$500$	−4.90867	−	2.94695i	−0.219522	−	0.131791i
$501$	2.37683	−	17.0154i	0.106189	−	0.760190i
$502$	−20.9758	−	37.0586i	−0.936197	−	1.65401i
$503$	15.5785	−	26.9828i	0.694613	−	1.20310i	−0.275699	−	0.961244i	$-0.588909\pi$
$503$	15.5785	−	26.9828i	0.694613	−	1.20310i	0.970311	−	0.241860i	$-0.0777575\pi$
$504$	−16.0668	−	17.4555i	−0.715674	−	0.777531i
$505$	−2.68087	−	4.64340i	−0.119297	−	0.206628i
$506$	6.74318	−	11.4525i	0.299771	−	0.509126i
$507$	0.942664	+	4.41670i	0.0418652	+	0.196153i
$508$	20.5704	+	37.0776i	0.912665	+	1.64505i
$509$	0.653669	+	1.79594i	0.0289734	+	0.0796037i	0.953336	−	0.301911i	$-0.0976247\pi$
$509$	0.653669	+	1.79594i	0.0289734	+	0.0796037i	−0.924363	+	0.381515i	$0.875402\pi$
$510$	−3.11832	−	2.47522i	−0.138081	−	0.109605i
$511$	1.96796	+	11.1609i	0.0870574	+	0.493727i
$512$	−1.73766	+	22.5606i	−0.0767946	+	0.997047i
$513$	−0.0207848	+	0.0151810i	−0.000917673	+	0.000670256i
$514$	−5.49060	−	1.01657i	−0.242180	−	0.0448389i
$515$	−1.28886	+	0.227261i	−0.0567939	+	0.0100143i
$516$	6.25039	−	18.2239i	0.275158	−	0.802264i
$517$	−6.08384	−	16.7152i	−0.267567	−	0.735134i
$518$	28.9097	−	23.8403i	1.27022	−	1.04748i
$519$	−10.6684	+	32.9277i	−0.468290	+	1.44537i
$520$	1.63970	+	2.05904i	0.0719058	+	0.0902947i
$521$	4.36155	+	7.55442i	0.191083	+	0.330965i	0.945609	−	0.325304i	$-0.105467\pi$
$521$	4.36155	+	7.55442i	0.191083	+	0.330965i	−0.754527	+	0.656269i	$0.772133\pi$
$522$	32.5727	+	9.58262i	1.42567	+	0.419420i
$523$	−17.9490	−	10.3629i	−0.784855	−	0.453136i	0.0532932	−	0.998579i	$-0.483028\pi$
$523$	−17.9490	−	10.3629i	−0.784855	−	0.453136i	−0.838148	+	0.545443i	$0.816362\pi$
$524$	−6.91059	−	20.0456i	−0.301891	−	0.875698i
$525$	−22.0687	+	8.93782i	−0.963156	+	0.390078i
$526$	−6.52962	+	17.4741i	−0.284705	+	0.761909i
$527$	−5.68063	+	32.2165i	−0.247452	+	1.40337i
$528$	−11.3051	+	31.2138i	−0.491992	+	1.35841i
$529$	−14.6725	+	12.3117i	−0.637936	+	0.535292i
$530$	−0.229467	+	0.268772i	−0.00996741	+	0.0116747i
$531$	6.80452	+	15.2146i	0.295291	+	0.660257i
$532$	−0.0273559	+	0.00434316i	−0.00118603	+	0.000188300i
$533$	−10.7920	+	29.6508i	−0.467453	+	1.28432i
$534$	−7.66291	−	4.15048i	−0.331606	−	0.179609i
$535$	0.829049	+	0.695655i	0.0358429	+	0.0300758i
$536$	0.128453	−	0.633171i	0.00554833	−	0.0273488i
$537$	1.33383	+	37.3006i	0.0575590	+	1.60964i
$538$	−10.8700	−	0.0928442i	−0.468638	−	0.00400280i
$539$		−	3.91581i		−	0.168666i
$540$	−1.71362	+	2.46238i	−0.0737426	+	0.105964i
$541$			3.63212i			0.156157i	0.996947	+	0.0780785i	$0.0248785\pi$
$541$			3.63212i			0.156157i	−0.996947	+	0.0780785i	$0.975122\pi$
$542$	−0.257775	+	30.1796i	−0.0110724	+	1.29633i
$543$	−31.6782	−	16.8096i	−1.35944	−	0.721369i
$544$	26.8783	+	17.0884i	1.15240	+	0.732658i
$545$	−3.72551	−	3.12607i	−0.159583	−	0.133906i
$546$	22.0700	−	0.600509i	0.944509	−	0.0256994i
$547$	3.43081	−	9.42608i	0.146691	−	0.403030i	−0.844486	−	0.535578i	$-0.820094\pi$
$547$	3.43081	−	9.42608i	0.146691	−	0.403030i	0.991177	+	0.132548i	$0.0423159\pi$
$548$	4.45423	+	28.0555i	0.190275	+	1.19847i
$549$	−14.8519	−	15.3282i	−0.633864	−	0.654190i
$550$	25.3391	+	21.6335i	1.08046	+	0.922457i
$551$	0.0303667	−	0.0254807i	0.00129367	−	0.00108551i
$552$	−6.10109	+	7.42226i	−0.259680	+	0.315912i
$553$	−2.22955	+	12.6444i	−0.0948101	+	0.537695i
$554$	29.9568	+	11.1941i	1.27274	+	0.475590i
$555$	−3.73633	−	2.91410i	−0.158598	−	0.123697i
$556$	−6.35661	−	18.4387i	−0.269580	−	0.781975i
$557$	−9.46379	−	5.46392i	−0.400994	−	0.231514i	0.285919	−	0.958254i	$-0.407701\pi$
$557$	−9.46379	−	5.46392i	−0.400994	−	0.231514i	−0.686913	+	0.726740i	$0.741034\pi$
$558$	24.4969	+	2.74493i	1.03704	+	0.116202i
$559$	8.96465	+	15.5272i	0.379164	+	0.656732i
$560$	−2.84941	+	1.51777i	−0.120409	+	0.0641375i
$561$	31.2974	+	34.7008i	1.32138	+	1.46507i
$562$	−29.0183	−	35.1888i	−1.22407	−	1.48435i
$563$	−9.70697	−	26.6697i	−0.409100	−	1.12399i	−0.957665	−	0.287885i	$-0.907048\pi$
$563$	−9.70697	−	26.6697i	−0.409100	−	1.12399i	0.548565	−	0.836108i	$-0.315174\pi$
$564$	2.46896	+	12.6203i	0.103962	+	0.531410i
$565$	1.73445	−	0.305831i	0.0729690	−	0.0128664i
$566$	−5.25403	+	28.3776i	−0.220844	+	1.19280i
$567$	7.85599	+	23.9056i	0.329921	+	1.00394i
$568$	−2.07434	−	1.26957i	−0.0870372	−	0.0532699i
$569$	−2.42865	−	13.7735i	−0.101814	−	0.577417i	−0.992445	−	0.122690i	$-0.960848\pi$
$569$	−2.42865	−	13.7735i	−0.101814	−	0.577417i	0.890631	−	0.454727i	$-0.150263\pi$
$570$	0.00128702	+	0.00325751i	5.39071e−5	+	0.000136442i
$571$	5.30577	+	14.5775i	0.222040	+	0.610049i	0.999829	−	0.0184759i	$-0.00588139\pi$
$571$	5.30577	+	14.5775i	0.222040	+	0.610049i	−0.777790	+	0.628525i	$0.783659\pi$
$572$	−14.9880	−	27.0155i	−0.626682	−	1.12957i
$573$	−1.28633	+	1.16017i	−0.0537372	+	0.0484667i
$574$	−33.3501	−	19.6364i	−1.39201	−	0.819606i
$575$	4.82133	+	8.35080i	0.201064	+	0.348252i
$576$	11.5769	−	21.0232i	0.482370	−	0.875968i
$577$	−0.198083	+	0.343090i	−0.00824632	+	0.0142830i	−0.870119	−	0.492841i	$-0.835958\pi$
$577$	−0.198083	+	0.343090i	−0.00824632	+	0.0142830i	0.861873	+	0.507125i	$0.169292\pi$
$578$	18.0941	−	10.2416i	0.752615	−	0.425994i
$579$	−27.0637	−	21.1080i	−1.12473	−	0.877220i
$580$	2.37820	−	3.96132i	0.0987494	−	0.164485i
$581$	−11.1907	−	1.97322i	−0.464268	−	0.0818630i
$582$	6.11716	−	18.3446i	0.253564	−	0.760407i
$583$	3.17757	−	2.66630i	0.131602	−	0.110427i
$584$	−10.0724	+	5.47612i	−0.416799	+	0.226604i
$585$	−0.679938	−	2.70776i	−0.0281120	−	0.111952i
$586$	−5.60102	+	1.98460i	−0.231376	+	0.0819829i
$587$	4.01994	−	11.0447i	0.165921	−	0.455864i	−0.828670	−	0.559738i	$-0.810902\pi$
$587$	4.01994	−	11.0447i	0.165921	−	0.455864i	0.994590	+	0.103874i	$0.0331240\pi$
$588$	−0.439469	+	2.79656i	−0.0181234	+	0.115328i
$589$	0.0184992	−	0.0220465i	0.000762247	−	0.000908411i
$590$	2.23688	−	0.374752i	0.0920909	−	0.0154283i
$591$	−9.09268	−	4.82490i	−0.374023	−	0.198470i
$592$	32.1621	+	20.0639i	1.32185	+	0.824623i
$593$	−14.1087			−0.579377			−0.289688	−	0.957121i	$-0.593552\pi$
$593$	−14.1087			−0.579377			−0.289688	+	0.957121i	$0.593552\pi$
$594$	24.6125	−	25.1813i	1.00986	−	1.03320i
$595$			4.54436i			0.186301i
$596$	2.27225	+	0.440806i	0.0930751	+	0.0180561i
$597$	14.6290	−	0.523116i	0.598724	−	0.0214097i
$598$	−1.47738	−	8.81845i	−0.0604147	−	0.360613i
$599$	−28.5436	−	23.9509i	−1.16626	−	0.978607i	−0.166286	−	0.986077i	$-0.553178\pi$
$599$	−28.5436	−	23.9509i	−1.16626	−	0.978607i	−0.999972	+	0.00747033i	$0.997622\pi$
$600$	−15.6685	−	18.2938i	−0.639666	−	0.746842i
$601$	−11.4635	−	4.17236i	−0.467605	−	0.170194i	0.0974622	−	0.995239i	$-0.468927\pi$
$601$	−11.4635	−	4.17236i	−0.467605	−	0.170194i	−0.565067	+	0.825045i	$0.691150\pi$
$602$	−20.7281	+	7.34454i	−0.844815	+	0.299341i
$603$	−0.401857	+	0.555061i	−0.0163649	+	0.0226038i
$604$	32.4486	−	26.2963i	1.32031	−	1.06998i
$605$	2.21934	+	2.64491i	0.0902292	+	0.107531i
$606$	−9.11608	−	44.5736i	−0.370315	−	1.81068i
$607$	7.57443	−	42.9567i	0.307436	−	1.74356i	−0.304372	−	0.952553i	$-0.598447\pi$
$607$	7.57443	−	42.9567i	0.307436	−	1.74356i	0.611809	−	0.791006i	$-0.290442\pi$
$608$	−0.0129615	−	0.0248425i	−0.000525658	−	0.00100750i
$609$	−14.5480	−	35.9209i	−0.589514	−	1.45559i
$610$	−2.52761	+	1.43067i	−0.102340	+	0.0579261i
$611$	−10.3640	−	5.98365i	−0.419282	−	0.242073i
$612$	−18.4572	−	28.2948i	−0.746090	−	1.14375i
$613$	−24.6408	+	14.2264i	−0.995233	+	0.574598i	−0.906834	−	0.421487i	$-0.861508\pi$
$613$	−24.6408	+	14.2264i	−0.995233	+	0.574598i	−0.0883987	+	0.996085i	$0.528175\pi$
$614$	−13.6461	+	23.1764i	−0.550714	+	0.935323i
$615$	−1.50840	+	4.65563i	−0.0608245	+	0.187733i
$616$	35.9284	−	12.0437i	1.44760	−	0.485255i
$617$	−6.84389	+	2.49097i	−0.275525	+	0.100283i	−0.476087	−	0.879398i	$-0.657945\pi$
$617$	−6.84389	+	2.49097i	−0.275525	+	0.100283i	0.200562	+	0.979681i	$0.435723\pi$
$618$	−10.9848	−	1.63021i	−0.441875	−	0.0655768i
$619$	4.70638	−	0.829861i	0.189165	−	0.0333549i	−0.0782628	−	0.996933i	$-0.524937\pi$
$619$	4.70638	−	0.829861i	0.189165	−	0.0333549i	0.267428	+	0.963578i	$0.413826\pi$
$620$	1.20096	−	3.13208i	0.0482318	−	0.125788i
$621$	9.14818	−	4.49034i	0.367104	−	0.180191i
$622$	24.1441	+	4.47021i	0.968089	+	0.179239i
$623$	1.72733	+	9.79616i	0.0692039	+	0.392475i
$624$	7.67209	+	20.9758i	0.307129	+	0.839703i
$625$	−22.3242	+	8.12536i	−0.892970	+	0.325014i
$626$	0.681188	+	0.826035i	0.0272257	+	0.0330150i
$627$	−0.00858103	−	0.0402050i	−0.000342693	−	0.00160563i
$628$	24.5762	−	28.2929i	0.980697	−	1.12901i
$629$	46.2099	−	26.6793i	1.84251	−	1.06377i
$630$	3.41748	−	0.215402i	0.136156	−	0.00858183i
$631$	−10.2228	+	17.7064i	−0.406964	+	0.704882i	−0.994548	−	0.104281i	$-0.966746\pi$
$631$	−10.2228	+	17.7064i	−0.406964	+	0.704882i	0.587584	+	0.809163i	$0.300079\pi$
$632$	−12.8450	+	1.92700i	−0.510946	+	0.0766521i
$633$	−7.14521	−	0.998094i	−0.283996	−	0.0396707i
$634$	26.0470	+	9.73307i	1.03446	+	0.386549i
$635$	−6.02710	−	1.06274i	−0.239178	−	0.0421736i
$636$	−2.56856	+	1.54758i	−0.101850	+	0.0613654i
$637$	−1.69340	−	2.01812i	−0.0670950	−	0.0799607i
$638$	−35.2126	+	41.2442i	−1.39408	+	1.63287i
$639$	1.44604	+	2.13611i	0.0572043	+	0.0845034i
$640$	−2.37196	−	2.24506i	−0.0937599	−	0.0887437i
$641$	17.9357	+	6.52806i	0.708417	+	0.257843i	0.671000	−	0.741457i	$-0.265865\pi$
$641$	17.9357	+	6.52806i	0.708417	+	0.257843i	0.0374167	+	0.999300i	$0.488087\pi$
$642$	4.80624	+	7.82510i	0.189687	+	0.308832i
$643$	11.9937	−	14.2935i	0.472984	−	0.563680i	−0.475821	−	0.879542i	$-0.657849\pi$
$643$	11.9937	−	14.2935i	0.472984	−	0.563680i	0.948805	+	0.315862i	$0.102294\pi$
$644$	10.9653	+	0.187330i	0.432092	+	0.00738183i
$645$	1.47556	+	2.35700i	0.0581003	+	0.0928070i
$646$	−0.0394405		0.000336876i	−0.00155177		1.32542e-5i
$647$	1.28685			0.0505911			0.0252955	−	0.999680i	$-0.491947\pi$
$647$	1.28685			0.0505911			0.0252955	+	0.999680i	$0.491947\pi$
$648$	−20.4036	+	15.2215i	−0.801528	+	0.597957i
$649$	−26.6210			−1.04497
$650$	22.4146	+	0.191451i	0.879175	+	0.00750934i
$651$	−14.9301	−	23.8487i	−0.585156	−	0.934703i
$652$	0.395510	−	23.1510i	0.0154894	−	0.906662i
$653$	−4.80662	+	5.72830i	−0.188097	+	0.224166i	−0.851849	−	0.523787i	$-0.824519\pi$
$653$	−4.80662	+	5.72830i	−0.188097	+	0.224166i	0.663752	+	0.747953i	$0.268963\pi$
$654$	−21.5979	−	35.1637i	−0.844543	−	1.37501i
$655$	2.87585	+	1.04672i	0.112369	+	0.0408989i
$656$	8.11164	−	38.3020i	0.316706	−	1.49544i
$657$	12.1292	−	0.868563i	0.473204	−	0.0338859i
$658$	9.53072	−	11.1632i	0.371546	−	0.435188i
$659$	15.2256	+	18.1451i	0.593104	+	0.706834i	0.976199	−	0.216875i	$-0.0695864\pi$
$659$	15.2256	+	18.1451i	0.593104	+	0.706834i	−0.383095	+	0.923709i	$0.625142\pi$
$660$	−2.47286	−	4.10428i	−0.0962558	−	0.159759i
$661$	−4.78633	−	0.843960i	−0.186167	−	0.0328262i	0.0797873	−	0.996812i	$-0.474576\pi$
$661$	−4.78633	−	0.843960i	−0.186167	−	0.0328262i	−0.265954	+	0.963986i	$0.585687\pi$
$662$	32.6193	+	12.1889i	1.26778	+	0.473737i
$663$	31.1364	+	4.34936i	1.20924	+	0.168915i
$664$	−1.70546	−	11.3682i	−0.0661846	−	0.441172i
$665$	0.00199895	−	0.00346229i	7.75161e−5	−	0.000134262i
$666$	−22.2539	−	33.4865i	−0.862321	−	1.29758i
$667$	−13.5925	+	7.84763i	−0.526303	+	0.303861i
$668$	−14.9771	−	13.0096i	−0.579480	−	0.503357i
$669$	−5.28107	−	24.7436i	−0.204178	−	0.956644i
$670$	0.0593284	+	0.0719439i	0.00229206	+	0.00277944i
$671$	32.0343	−	11.6595i	1.23667	−	0.450111i
$672$	−27.0107	+	4.56905i	−1.04196	+	0.176255i
$673$	−6.24184	−	35.3992i	−0.240605	−	1.36454i	−0.830482	−	0.557046i	$-0.811935\pi$
$673$	−6.24184	−	35.3992i	−0.240605	−	1.36454i	0.589876	−	0.807494i	$-0.299176\pi$
$674$	−13.7681	−	2.54913i	−0.530328	−	0.0981887i
$675$	7.10357	+	24.5403i	0.273416	+	0.944557i
$676$	4.86916	+	1.86702i	0.187275	+	0.0718085i
$677$	−17.6982	+	3.12068i	−0.680199	+	0.119937i	−0.503064	−	0.864249i	$-0.667794\pi$
$677$	−17.6982	+	3.12068i	−0.680199	+	0.119937i	−0.177135	+	0.984187i	$0.556683\pi$
$678$	14.7826	+	2.19382i	0.567722	+	0.0842532i
$679$	−20.7414	+	7.54926i	−0.795983	+	0.289714i
$680$	−4.35881	+	1.46114i	−0.167153	+	0.0560320i
$681$	10.9786	−	33.8850i	0.420699	−	1.29848i
$682$	−19.9767	+	33.9280i	−0.764946	+	1.29917i
$683$	5.01354	−	2.89457i	0.191838	−	0.110758i	−0.401005	−	0.916076i	$-0.631339\pi$
$683$	5.01354	−	2.89457i	0.191838	−	0.110758i	0.592843	+	0.805318i	$0.298006\pi$
$684$	0.00161614	+	0.0296763i	6.17945e−5	+	0.00113470i
$685$	−3.55083	−	2.05007i	−0.135670	−	0.0783293i
$686$	−21.2754	+	12.0422i	−0.812297	+	0.459774i
$687$	7.47072	+	18.4462i	0.285026	+	0.703767i
$688$	−13.7093	−	17.5203i	−0.522662	−	0.667955i
$689$	0.484598	−	2.74829i	0.0184617	−	0.104702i
$690$	−0.277869	−	1.35866i	−0.0105783	−	0.0517231i
$691$	8.42802	+	10.0441i	0.320617	+	0.382097i	0.902147	−	0.431428i	$-0.141990\pi$
$691$	8.42802	+	10.0441i	0.320617	+	0.382097i	−0.581530	+	0.813525i	$0.697546\pi$
$692$	25.1638	+	31.0512i	0.956586	+	1.18039i
$693$	−39.9787	−	4.13427i	−1.51866	−	0.157048i
$694$	27.7878	−	9.84596i	1.05481	−	0.373748i
$695$	2.64531	+	0.962815i	0.100342	+	0.0365217i
$696$	29.7766	−	25.5035i	1.12868	−	0.966708i
$697$	−42.2167	−	35.4240i	−1.59907	−	1.34178i
$698$	3.52889	+	21.0638i	0.133570	+	0.797277i
$699$	7.49727	−	0.268094i	0.283573	−	0.0101403i
$700$	−5.23595	+	26.9901i	−0.197900	+	1.02013i
$701$		−	3.89204i		−	0.147000i	−0.997295	−	0.0735002i	$-0.976583\pi$
$701$		−	3.89204i		−	0.147000i	0.997295	−	0.0735002i	$-0.0234170\pi$
$702$	1.79497	−	23.6215i	0.0677469	−	0.891538i
$703$	−0.0469423			−0.00177046
$704$	23.1039	+	30.5890i	0.870761	+	1.15287i
$705$	−1.63957	−	0.870013i	−0.0617496	−	0.0327666i
$706$	4.94958	−	0.829219i	0.186280	−	0.0312081i
$707$	−33.3805	+	39.7814i	−1.25540	+	1.49613i
$708$	19.0119	+	2.98766i	0.714513	+	0.112283i
$709$	10.4928	−	28.8286i	0.394064	−	1.08268i	−0.571065	−	0.820905i	$-0.693469\pi$
$709$	10.4928	−	28.8286i	0.394064	−	1.08268i	0.965128	−	0.261777i	$-0.0843084\pi$
$710$	0.330871	−	0.117237i	0.0124174	−	0.00439981i
$711$	13.2493	+	3.77517i	0.496886	+	0.141580i
$712$	−8.84078	+	4.80653i	−0.331322	+	0.180132i
$713$	−8.72901	+	7.32451i	−0.326904	+	0.274305i
$714$	−12.1980	+	36.5804i	−0.456500	+	1.36899i
$715$	4.39147	+	0.774335i	0.164232	+	0.0289585i
$716$	36.9509	+	22.1837i	1.38092	+	0.829044i
$717$	19.2873	+	15.0429i	0.720296	+	0.561786i
$718$	27.2752	−	15.4382i	1.01790	−	0.576150i
$719$	10.3301	−	17.8922i	0.385246	−	0.667266i	−0.606557	−	0.795040i	$-0.707450\pi$
$719$	10.3301	−	17.8922i	0.385246	−	0.667266i	0.991803	+	0.127774i	$0.0407831\pi$
$720$	1.30542	+	3.20868i	0.0486501	+	0.119581i
$721$	6.33789	+	10.9775i	0.236035	+	0.408825i
$722$	−23.1545	−	13.6333i	−0.861722	−	0.507378i
$723$	19.3031	−	17.4098i	0.717889	−	0.647479i
$724$	−36.2103	+	20.0893i	−1.34574	+	0.746611i
$725$	−13.4575	−	36.9742i	−0.499799	−	1.37319i
$726$	10.7654	+	27.2477i	0.399540	+	1.01126i
$727$	5.27477	+	29.9147i	0.195630	+	1.10947i	0.911518	+	0.411259i	$0.134911\pi$
$727$	5.27477	+	29.9147i	0.195630	+	1.10947i	−0.715888	+	0.698215i	$0.753978\pi$
$728$	13.3083	−	21.7443i	0.493239	−	0.805899i
$729$	26.3815	−	5.74619i	0.977091	−	0.212822i
$730$	0.301258	−	1.62713i	0.0111501	−	0.0602227i
$731$	−30.8386	+	5.43768i	−1.14061	+	0.201120i
$732$	−24.1865	+	4.73171i	−0.893958	+	0.174889i
$733$	−12.3847	−	34.0267i	−0.457439	−	1.25680i	−0.927385	−	0.374108i	$-0.877949\pi$
$733$	−12.3847	−	34.0267i	−0.457439	−	1.25680i	0.469946	−	0.882695i	$-0.344273\pi$
$734$	15.6081	+	18.9270i	0.576107	+	0.698610i
$735$	−0.273660	−	0.303419i	−0.0100941	−	0.0111918i
$736$	3.34594	+	10.5778i	0.123333	+	0.389901i
$737$	−0.547262	−	0.947886i	−0.0201587	−	0.0349158i
$738$	−24.6387	+	33.4272i	−0.906965	+	1.23047i
$739$	−4.81815	−	2.78176i	−0.177239	−	0.102329i	0.408756	−	0.912644i	$-0.365963\pi$
$739$	−4.81815	−	2.78176i	−0.177239	−	0.102329i	−0.585995	+	0.810315i	$0.699296\pi$
$740$	−5.17264	+	1.78323i	−0.190150	+	0.0655529i
$741$	−0.0218092	−	0.0170098i	−0.000801181	−	0.000624872i
$742$	3.20633	+	1.19812i	0.117708	+	0.0439844i
$743$	6.80955	−	38.6189i	0.249818	−	1.41679i	−0.559214	−	0.829024i	$-0.688897\pi$
$743$	6.80955	−	38.6189i	0.249818	−	1.41679i	0.809032	−	0.587765i	$-0.199992\pi$
$744$	18.0745	−	21.9884i	0.662642	−	0.806135i
$745$	−0.255922	+	0.214744i	−0.00937627	+	0.00786762i
$746$	−17.8434	−	15.2340i	−0.653294	−	0.557756i
$747$	−3.34115	+	11.7260i	−0.122246	+	0.429033i
$748$	53.2915	−	8.46081i	1.94853	−	0.309358i
$749$	3.58507	−	9.84991i	0.130996	−	0.359908i
$750$	7.00948	−	0.190723i	0.255950	−	0.00696421i
$751$	20.3773	+	17.0986i	0.743579	+	0.623937i	0.933796	−	0.357805i	$-0.116475\pi$
$751$	20.3773	+	17.0986i	0.743579	+	0.623937i	−0.190217	+	0.981742i	$0.560919\pi$
$752$	13.7718	+	5.55228i	0.502206	+	0.202471i
$753$	46.0693	+	24.4460i	1.67886	+	0.890863i
$754$	−0.311623	+	36.4841i	−0.0113486	+	1.32867i
$755$			6.02836i			0.219394i
$756$	28.0876	+	7.43935i	1.02154	+	0.270567i
$757$			9.99796i			0.363382i	0.983356	+	0.181691i	$0.0581571\pi$
$757$			9.99796i			0.363382i	−0.983356	+	0.181691i	$0.941843\pi$
$758$	13.6455	+	0.116551i	0.495626	+	0.00423331i
$759$	0.581682	+	16.2668i	0.0211137	+	0.590446i
$760$	0.00396364		0.000804114i	0.000143776		2.91683e-5i
$761$	36.4687	+	30.6009i	1.32199	+	1.10928i	0.985879	+	0.167460i	$0.0535564\pi$
$761$	36.4687	+	30.6009i	1.32199	+	1.10928i	0.336112	+	0.941822i	$0.390888\pi$
$762$	−45.6632	−	24.7327i	−1.65420	−	0.895970i
$763$	−16.1103	+	44.2627i	−0.583232	+	1.60242i
$764$	0.313635	+	1.97547i	0.0113469	+	0.0714699i
$765$	4.85019	+	0.501567i	0.175359	+	0.0181342i
$766$	11.0589	−	12.9532i	0.399575	−	0.468018i
$767$	−13.7198	+	11.5123i	−0.495395	+	0.415685i
$768$	−13.0671	−	24.4387i	−0.471520	−	0.881856i
$769$	−7.87549	+	44.6641i	−0.283998	+	1.61063i	0.424847	+	0.905265i	$0.360328\pi$
$769$	−7.87549	+	44.6641i	−0.283998	+	1.61063i	−0.708844	+	0.705365i	$0.750783\pi$
$770$	−1.91446	+	5.12336i	−0.0689925	+	0.184633i
$771$	6.33874	−	2.56719i	0.228284	−	0.0924552i
$772$	−37.4676	+	12.9167i	−1.34849	+	0.464881i
$773$	7.37741	+	4.25935i	0.265347	+	0.153198i	0.626771	−	0.779203i	$-0.284376\pi$
$773$	7.37741	+	4.25935i	0.265347	+	0.153198i	−0.361424	+	0.932401i	$0.617709\pi$
$774$	5.55103	+	22.9337i	0.199528	+	0.824335i
$775$	−14.2832	−	24.7392i	−0.513068	−	0.888659i
$776$	−13.9099	−	17.4672i	−0.499338	−	0.627037i
$777$	−14.1453	+	43.6590i	−0.507458	+	1.56626i
$778$	−3.16776	+	2.61229i	−0.113570	+	0.0936550i
$779$	0.0165822	+	0.0455592i	0.000594118	+	0.00163233i
$780$	−3.04936	−	1.04586i	−0.109184	−	0.0374477i
$781$	−4.05754	+	0.715454i	−0.145190	+	0.0256010i
$782$	15.3555	+	2.84303i	0.549112	+	0.101667i
$783$	−39.9440	+	11.5624i	−1.42748	+	0.413206i
$784$	2.43083	+	2.18546i	0.0868153	+	0.0780523i
$785$	0.939296	+	5.32701i	0.0335249	+	0.190129i
$786$	20.3399	+	16.1451i	0.725500	+	0.575878i
$787$	−6.01089	−	16.5148i	−0.214265	−	0.588688i	0.785271	−	0.619152i	$-0.212524\pi$
$787$	−6.01089	−	16.5148i	−0.214265	−	0.588688i	−0.999536	+	0.0304642i	$0.990301\pi$
$788$	−10.3935	+	5.76627i	−0.370254	+	0.205415i
$789$	−4.76880	−	22.3435i	−0.169774	−	0.795449i
$790$	0.951204	−	1.61551i	0.0338423	−	0.0574772i
$791$	−8.52906	−	14.7728i	−0.303259	−	0.525259i
$792$	−8.88876	−	39.6756i	−0.315848	−	1.40981i
$793$	11.4675	−	19.8623i	0.407224	−	0.705332i
$794$	−2.84068	−	5.01871i	−0.100812	−	0.178108i
$795$	0.0598793	−	0.428666i	0.00212370	−	0.0152032i
$796$	8.70025	−	14.4918i	0.308372	−	0.513649i
$797$	14.0527	+	2.47787i	0.497773	+	0.0877708i	0.416898	−	0.908953i	$-0.363117\pi$
$797$	14.0527	+	2.47787i	0.497773	+	0.0877708i	0.0808752	+	0.996724i	$0.474228\pi$
$798$	0.0253843	−	0.0225045i	0.000898596	−	0.000796650i
$799$	16.0115	−	13.4352i	0.566444	−	0.475303i
$800$	−27.5716	+	3.65588i	−0.974802	+	0.129255i
$801$	10.6461	−	0.762359i	0.376160	−	0.0269366i
$802$	1.05212	+	2.96935i	0.0371518	+	0.104852i
$803$	−6.64299	+	18.2515i	−0.234426	+	0.644080i
$804$	0.284458	+	0.738371i	0.0100321	+	0.0260404i
$805$	−1.01748	+	1.21258i	−0.0358614	+	0.0427379i
$806$	4.37675	+	26.1246i	0.154164	+	0.920202i
$807$	11.2845	−	7.06449i	0.397234	−	0.248682i
$808$	−48.8898	−	19.2268i	−1.71994	−	0.676395i
$809$	−41.9742			−1.47573			−0.737867	−	0.674946i	$-0.764167\pi$
$809$	−41.9742			−1.47573			−0.737867	+	0.674946i	$0.764167\pi$
$810$	0.147293	−	3.67125i	0.00517536	−	0.128994i
$811$			34.8911i			1.22519i	0.790397	+	0.612595i	$0.209875\pi$
$811$			34.8911i			1.22519i	−0.790397	+	0.612595i	$0.790125\pi$
$812$	−43.9315	−	8.52250i	−1.54169	−	0.299081i
$813$	−19.6140	−	31.3306i	−0.687893	−	1.09881i
$814$	63.3371	−	10.6111i	2.21996	−	0.371918i
$815$	2.56013	+	2.14820i	0.0896775	+	0.0752483i
$816$	−39.0088	+	0.0615993i	−1.36558	+	0.00215641i
$817$	0.0258874	+	0.00942225i	0.000905686	+	0.000329643i
$818$	8.91396	+	25.1574i	0.311669	+	0.879608i
$819$	−22.3919	+	15.1582i	−0.782438	+	0.529669i
$820$	3.55791	+	4.39032i	0.124247	+	0.153316i
$821$	−2.36456	−	2.81797i	−0.0825236	−	0.0983478i	0.723203	−	0.690636i	$-0.242669\pi$
$821$	−2.36456	−	2.81797i	−0.0825236	−	0.0983478i	−0.805726	+	0.592288i	$0.798225\pi$
$822$	−23.0800	−	26.0335i	−0.805007	−	0.908022i
$823$	−4.05525	+	22.9985i	−0.141357	+	0.801676i	0.828863	+	0.559452i	$0.188988\pi$
$823$	−4.05525	+	22.9985i	−0.141357	+	0.801676i	−0.970220	+	0.242225i	$0.922123\pi$
$824$	−8.49151	+	9.60868i	−0.295816	+	0.334734i
$825$	−40.4135	−	5.64525i	−1.40702	−	0.196543i
$826$	−10.8207	−	19.1172i	−0.376500	−	0.665174i
$827$	17.6991	+	10.2186i	0.615456	+	0.355334i	0.775098	−	0.631841i	$-0.217701\pi$
$827$	17.6991	+	10.2186i	0.615456	+	0.355334i	−0.159642	+	0.987175i	$0.551034\pi$
$828$	1.41019	−	11.6825i	0.0490073	−	0.405996i
$829$	18.2976	−	10.5641i	0.635503	−	0.366908i	−0.147377	−	0.989080i	$-0.547083\pi$
$829$	18.2976	−	10.5641i	0.635503	−	0.366908i	0.782880	+	0.622173i	$0.213750\pi$
$830$	1.42978	+	0.841846i	0.0496283	+	0.0292209i
$831$	−38.3046	+	8.17540i	−1.32877	+	0.283602i
$832$	25.1355	+	5.77352i	0.871416	+	0.200161i
$833$	4.32373	−	1.57371i	0.149808	−	0.0545258i
$834$	18.7094	+	14.8509i	0.647852	+	0.514244i
$835$	2.81990	−	0.497224i	0.0975866	−	0.0172072i
$836$	−0.0443238	−	0.0169954i	−0.00153297	−	0.000587799i
$837$	−27.1015	+	13.3026i	−0.936764	+	0.459806i
$838$	3.54806	−	19.1634i	0.122566	−	0.661990i
$839$	−5.53919	−	31.4143i	−0.191234	−	1.08454i	−0.917680	−	0.397320i	$-0.869940\pi$
$839$	−5.53919	−	31.4143i	−0.191234	−	1.08454i	0.726446	−	0.687223i	$-0.241171\pi$
$840$	1.94225	−	3.44410i	0.0670138	−	0.118833i
$841$	32.9314	−	11.9860i	1.13557	−	0.413312i
$842$	−40.5656	+	33.4523i	−1.39798	+	1.15284i
$843$	53.1416	+	17.2176i	1.83029	+	0.593005i
$844$	−5.46308	+	6.28927i	−0.188047	+	0.216486i
$845$	−0.651848	+	0.376345i	−0.0224242	+	0.0129466i
$846$	−10.8626	−	11.4042i	−0.373463	−	0.392085i
$847$	16.7204	−	28.9607i	0.574521	−	0.995100i
$848$	−0.118277	+	3.46064i	−0.00406166	+	0.118839i
$849$	−13.2683	−	32.7612i	−0.455366	−	1.12436i
$850$	−13.7037	+	36.6729i	−0.470033	+	1.25787i
$851$	18.3038	+	3.22745i	0.627445	+	0.110636i
$852$	2.97807	−	0.0555815i	0.102027	−	0.00190419i
$853$	10.1055	+	12.0433i	0.346006	+	0.412354i	0.910780	−	0.412891i	$-0.135481\pi$
$853$	10.1055	+	12.0433i	0.346006	+	0.412354i	−0.564774	+	0.825246i	$0.691037\pi$
$854$	21.3940	+	18.2654i	0.732089	+	0.625028i
$855$	−0.00347467	−	0.00251562i	−0.000118831	−	8.60323e-5i
$856$	10.6004	+	0.271679i	0.362315	+	0.00928579i
$857$	30.3992	+	11.0644i	1.03842	+	0.377953i	0.804280	−	0.594250i	$-0.202551\pi$
$857$	30.3992	+	11.0644i	1.03842	+	0.377953i	0.234138	+	0.972203i	$0.424773\pi$
$858$	33.2712	+	18.0207i	1.13586	+	0.615218i
$859$	−7.62842	+	9.09120i	−0.260278	+	0.310188i	−0.880319	−	0.474382i	$-0.842672\pi$
$859$	−7.62842	+	9.09120i	−0.260278	+	0.310188i	0.620041	+	0.784570i	$0.287116\pi$
$860$	3.21050	+	0.0548481i	0.109477	+	0.00187030i
$861$	47.3693	−	1.69388i	1.61434	−	0.0577271i
$862$	−0.137807	+	16.1340i	−0.00469371	+	0.549528i
$863$	−25.9229			−0.882426			−0.441213	−	0.897402i	$-0.645452\pi$
$863$	−25.9229			−0.882426			−0.441213	+	0.897402i	$0.645452\pi$
$864$	1.89533	+	29.3327i	0.0644806	+	0.997919i
$865$	−5.76875			−0.196143
$866$	0.0907629	−	10.6263i	0.00308425	−	0.361096i
$867$	−11.9359	+	22.4936i	−0.405365	+	0.763923i
$868$	−32.4846	−	0.554964i	−1.10260	−	0.0188367i
$869$	−14.1443	+	16.8565i	−0.479811	+	0.571816i
$870$	0.153914	+	5.65669i	0.00521819	+	0.191780i
$871$	−0.691961	−	0.251853i	−0.0234462	−	0.00853373i
$872$	−47.6352	−	1.22085i	−1.61313	−	0.0413430i
$873$	5.76806	+	22.9705i	0.195219	+	0.777434i
$874$	−0.0104486	−	0.00892058i	−0.000353429	−	0.000301743i
$875$	−5.14475	−	6.13128i	−0.173924	−	0.207275i
$876$	6.79257	−	12.2891i	0.229500	−	0.415211i
$877$	23.4419	+	4.13345i	0.791578	+	0.139577i	0.554796	−	0.831986i	$-0.312796\pi$
$877$	23.4419	+	4.13345i	0.791578	+	0.139577i	0.236782	+	0.971563i	$0.423907\pi$
$878$	10.1177	−	27.0764i	0.341456	−	0.913784i
$879$	4.47580	−	5.73866i	0.150965	−	0.193560i
$880$	−5.52972	−	0.188994i	−0.186407	−	0.00637099i
$881$	19.7098	−	34.1384i	0.664040	−	1.15015i	−0.315504	−	0.948924i	$-0.602174\pi$
$881$	19.7098	−	34.1384i	0.664040	−	1.15015i	0.979545	−	0.201227i	$-0.0644930\pi$
$882$	−1.38842	−	3.17697i	−0.0467504	−	0.106974i
$883$	39.3493	−	22.7183i	1.32421	−	0.764533i	0.339812	−	0.940493i	$-0.389636\pi$
$883$	39.3493	−	22.7183i	1.32421	−	0.764533i	0.984397	+	0.175960i	$0.0563031\pi$
$884$	23.8063	−	27.4065i	0.800691	−	0.921781i
$885$	−2.06274	+	1.86043i	−0.0693383	+	0.0625377i
$886$	−30.7901	+	25.3910i	−1.03441	+	0.853028i
$887$	−3.61326	+	1.31512i	−0.121321	+	0.0441573i	−0.401967	−	0.915654i	$-0.631673\pi$
$887$	−3.61326	+	1.31512i	−0.121321	+	0.0441573i	0.280646	+	0.959811i	$0.409451\pi$
$888$	−46.4244	+	0.469843i	−1.55790	+	0.0157669i
$889$	10.2931	+	58.3752i	0.345220	+	1.95784i
$890$	0.264422	−	1.42817i	0.00886344	−	0.0478724i
$891$	−8.82499	+	42.2129i	−0.295648	+	1.41418i
$892$	−27.2784	−	10.4596i	−0.913349	−	0.350213i
$893$	−0.0181087	+	0.00319306i	−0.000605985	+	0.000106852i
$894$	−2.63650	+	1.04166i	−0.0881776	+	0.0348383i
$895$	−5.84553	+	2.12760i	−0.195395	+	0.0711178i
$896$	−12.5757	+	29.0251i	−0.420124	+	0.969660i
$897$	7.33437	+	8.13195i	0.244888	+	0.271518i
$898$	−13.7715	−	8.10858i	−0.459560	−	0.270587i
$899$	40.2677	−	23.2486i	1.34300	−	0.775384i
$900$	28.2286	+	8.56725i	0.940953	+	0.285575i
$901$	4.22107	+	2.43704i	0.140624	+	0.0811894i
$902$	−32.6720	−	57.7226i	−1.08786	−	1.92195i
$903$	16.5640	−	21.2375i	0.551214	−	0.706740i
$904$	11.4273	−	12.9307i	0.380065	−	0.430067i
$905$	1.03788	−	5.88612i	0.0345003	−	0.195661i
$906$	−16.1814	+	48.5260i	−0.537591	+	1.61217i
$907$	−6.16891	−	7.35182i	−0.204835	−	0.244113i	0.653840	−	0.756632i	$-0.273157\pi$
$907$	−6.16891	−	7.35182i	−0.204835	−	0.244113i	−0.858676	+	0.512519i	$0.828712\pi$
$908$	−25.8955	−	31.9540i	−0.859371	−	1.06043i
$909$	38.7743	+	40.0177i	1.28606	+	1.32730i
$910$	1.22894	+	3.46837i	0.0407390	+	0.114975i
$911$	27.8833	+	10.1487i	0.923814	+	0.336241i	0.759755	−	0.650210i	$-0.225319\pi$
$911$	27.8833	+	10.1487i	0.923814	+	0.336241i	0.164059	+	0.986451i	$0.447541\pi$
$912$	0.0297473	+	0.0171121i	0.000985033	+	0.000566637i
$913$	−14.9185	−	12.5181i	−0.493730	−	0.414289i
$914$	53.0037	−	8.87989i	1.75321	−	0.293720i
$915$	1.66736	−	3.14219i	0.0551211	−	0.103877i
$916$	22.5598	+	4.37650i	0.745398	+	0.144604i
$917$		−	29.6416i		−	0.978851i
$918$	37.6959	+	17.0564i	1.24415	+	0.562944i
$919$	−18.2259			−0.601217			−0.300608	−	0.953748i	$-0.597190\pi$
$919$	−18.2259			−0.601217			−0.300608	+	0.953748i	$0.597190\pi$
$920$	−1.49022	−	0.586055i	−0.0491310	−	0.0193216i
$921$	−1.17715	−	32.9190i	−0.0387883	−	1.08472i
$922$	1.79193	+	10.6959i	0.0590139	+	0.352252i
$923$	−1.78176	+	2.12342i	−0.0586474	+	0.0698933i
$924$	−29.1629	+	36.1023i	−0.959389	+	1.18768i
$925$	−15.9362	+	43.7844i	−0.523980	+	1.43962i
$926$	−10.3519	−	29.2156i	−0.340184	−	0.960085i
$927$	12.4158	−	5.55281i	0.407789	−	0.182378i
$928$	−5.95064	−	44.8779i	−0.195339	−	1.47319i
$929$	−1.32347	+	1.11052i	−0.0434216	+	0.0364351i	−0.664240	−	0.747519i	$-0.731245\pi$
$929$	−1.32347	+	1.11052i	−0.0434216	+	0.0364351i	0.620819	+	0.783954i	$0.286800\pi$
$930$	0.823186	+	4.02502i	0.0269933	+	0.131985i
$931$	−0.00398643		0.000702915i	−0.000130650		2.30371e-5i
$932$	4.45883	−	7.42698i	0.146054	−	0.243279i
$933$	−27.8737	+	11.2888i	−0.912543	+	0.369580i
$934$	−1.69679	−	2.99776i	−0.0555205	−	0.0980897i
$935$	−3.89411	+	6.74480i	−0.127351	+	0.220579i
$936$	−21.7388	−	16.6039i	−0.710556	−	0.542715i
$937$	−3.54099	−	6.13317i	−0.115679	−	0.200362i	0.802372	−	0.596824i	$-0.203571\pi$
$937$	−3.54099	−	6.13317i	−0.115679	−	0.200362i	−0.918051	+	0.396462i	$0.870238\pi$
$938$	0.458255	−	0.778293i	0.0149626	−	0.0254122i
$939$	−1.24747	−	0.404172i	−0.0407095	−	0.0131897i
$940$	−1.87413	+	1.03976i	−0.0611274	+	0.0339131i
$941$	3.52638	+	9.68865i	0.114957	+	0.315841i	0.983806	−	0.179235i	$-0.0573624\pi$
$941$	3.52638	+	9.68865i	0.114957	+	0.315841i	−0.868850	+	0.495076i	$0.835140\pi$
$942$	−6.73787	+	45.4017i	−0.219532	+	1.47927i
$943$	−3.33338	−	18.9045i	−0.108550	−	0.615617i
$944$	14.8575	−	16.5256i	0.483571	−	0.537862i
$945$	−3.38670	+	2.47360i	−0.110169	+	0.0804661i
$946$	−37.0586	−	6.86129i	−1.20488	−	0.223080i
$947$	10.4361	−	1.84016i	0.339127	−	0.0597973i	−0.00149128	−	0.999999i	$-0.500475\pi$
$947$	10.4361	−	1.84016i	0.339127	−	0.0597973i	0.340618	+	0.940202i	$0.389364\pi$
$948$	11.9932	−	10.4510i	0.389521	−	0.339432i
$949$	4.46924	+	12.2791i	0.145078	+	0.398598i
$950$	0.0265722	−	0.0219127i	0.000862115	−	0.000710942i
$951$	−33.3052	+	7.10839i	−1.08000	+	0.230505i
$952$	27.7374	+	34.8309i	0.898975	+	1.12888i
$953$	−3.01897	−	5.22901i	−0.0977940	−	0.169384i	0.812977	−	0.582295i	$-0.197845\pi$
$953$	−3.01897	−	5.22901i	−0.0977940	−	0.169384i	−0.910771	+	0.412911i	$0.864512\pi$
$954$	1.63264	−	3.28987i	0.0528586	−	0.106514i
$955$	−0.250024	−	0.144351i	−0.00809058	−	0.00467110i
$956$	26.7017	−	9.20520i	0.863594	−	0.297718i
$957$	9.18871	−	65.7806i	0.297029	−	2.12638i
$958$	−7.20068	+	19.2700i	−0.232644	+	0.622585i
$959$	−6.89588	+	39.1085i	−0.222680	+	1.26288i
$960$	3.92795	+	0.755570i	0.126774	+	0.0243859i
$961$	2.11229	−	1.77242i	0.0681384	−	0.0571749i
$962$	28.0537	−	32.8590i	0.904486	−	1.05942i
$963$	−10.1171	−	4.91349i	−0.326019	−	0.158335i
$964$	−4.70650	−	29.6445i	−0.151586	−	0.954785i
$965$	1.95645	−	5.37529i	0.0629802	−	0.173037i
$966$	−11.4451	+	7.02970i	−0.368241	+	0.226177i
$967$	15.4521	+	12.9658i	0.496906	+	0.416954i	0.856494	−	0.516158i	$-0.172638\pi$
$967$	15.4521	+	12.9658i	0.496906	+	0.416954i	−0.359588	+	0.933111i	$0.617083\pi$
$968$	33.1542	+	6.72609i	1.06562	+	0.216185i
$969$	0.0409447	−	0.0256328i	0.00131533	−	0.000823443i
$970$	3.22279	+	0.0275270i	0.103477	+	0.000883837i
$971$		−	31.1328i		−	0.999100i	−0.866285	−	0.499550i	$-0.833499\pi$
$971$		−	31.1328i		−	0.999100i	0.866285	−	0.499550i	$-0.166501\pi$
$972$	11.0401	−	29.1568i	0.354110	−	0.935204i
$973$		−	27.2654i		−	0.874088i
$974$	−0.0307623	+	3.60158i	−0.000985689	+	0.115402i
$975$	−23.2695	+	14.5675i	−0.745219	+	0.466533i
$976$	−10.6408	+	26.3933i	−0.340604	+	0.844829i
$977$	−14.4476	−	12.1229i	−0.462219	−	0.387848i	0.381728	−	0.924275i	$-0.375329\pi$
$977$	−14.4476	−	12.1229i	−0.462219	−	0.387848i	−0.843947	+	0.536427i	$0.819774\pi$
$978$	14.8418	+	24.1642i	0.474589	+	0.772685i
$979$	−5.83071	+	16.0198i	−0.186350	+	0.511993i
$980$	−0.465973	+	0.0739801i	−0.0148850	+	0.00236321i
$981$	45.4633	+	22.0798i	1.45153	+	0.704954i
$982$	19.5668	+	16.7054i	0.624403	+	0.533090i
$983$	24.2461	−	20.3449i	0.773330	−	0.648901i	−0.168229	−	0.985748i	$-0.553805\pi$
$983$	24.2461	−	20.3449i	0.773330	−	0.648901i	0.941559	+	0.336847i	$0.109361\pi$
$984$	16.8552	+	44.8905i	0.537325	+	1.43106i
$985$	0.297906	−	1.68951i	0.00949206	−	0.0538322i
$986$	−59.6921	−	22.3053i	−1.90098	−	0.710347i
$987$	−2.48703	+	17.8043i	−0.0791632	+	0.566717i
$988$	−0.0301931	+	0.0104089i	−0.000960571	+	0.000331150i
$989$	−9.44623	−	5.45378i	−0.300373	−	0.173420i
$990$	5.25685	+	2.60878i	0.167074	+	0.0829123i
$991$	22.5906	+	39.1281i	0.717614	+	1.24294i	0.961942	+	0.273252i	$0.0880993\pi$
$991$	22.5906	+	39.1281i	0.717614	+	1.24294i	−0.244328	+	0.969693i	$0.578567\pi$
$992$	−9.91235	−	31.3366i	−0.314718	−	0.994938i
$993$	−41.7089	+	8.90201i	−1.32359	+	0.282497i
$994$	−2.16306	−	2.62301i	−0.0686082	−	0.0831970i
$995$	0.834426	+	2.29257i	0.0264531	+	0.0726792i
$996$	9.24946	+	10.6144i	0.293080	+	0.336329i
$997$	20.6197	−	3.63580i	0.653031	−	0.115147i	0.162689	−	0.986677i	$-0.447983\pi$
$997$	20.6197	−	3.63580i	0.653031	−	0.115147i	0.490342	+	0.871530i	$0.336872\pi$
$998$	0.531517	−	2.87078i	0.0168249	−	0.0908730i
$999$	45.0359	+	19.9159i	1.42487	+	0.630111i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.t.a.13.17	✓	204
3.2	odd	2		648.2.t.a.253.18		204
4.3	odd	2		864.2.bf.a.337.24		204
8.3	odd	2		864.2.bf.a.337.11		204
8.5	even	2	inner	216.2.t.a.13.22	yes	204
24.5	odd	2		648.2.t.a.253.13		204
27.2	odd	18		648.2.t.a.397.13		204
27.25	even	9	inner	216.2.t.a.133.22	yes	204
108.79	odd	18		864.2.bf.a.241.11		204
216.29	odd	18		648.2.t.a.397.18		204
216.133	even	18	inner	216.2.t.a.133.17	yes	204
216.187	odd	18		864.2.bf.a.241.24		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.13.17	✓	204	1.1	even	1	trivial
216.2.t.a.13.22	yes	204	8.5	even	2	inner
216.2.t.a.133.17	yes	204	216.133	even	18	inner
216.2.t.a.133.22	yes	204	27.25	even	9	inner
648.2.t.a.253.13		204	24.5	odd	2
648.2.t.a.253.18		204	3.2	odd	2
648.2.t.a.397.13		204	27.2	odd	18
648.2.t.a.397.18		204	216.29	odd	18
864.2.bf.a.241.11		204	108.79	odd	18
864.2.bf.a.241.24		204	216.187	odd	18
864.2.bf.a.337.11		204	8.3	odd	2
864.2.bf.a.337.24		204	4.3	odd	2

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.t (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0120789 + 1.41416i) q^{2} +(-0.919076 - 1.46809i) q^{3} +(-1.99971 - 0.0341629i) q^{4} +(0.185555 - 0.221136i) q^{5} +(2.08722 - 1.28199i) q^{6} +(-2.62731 - 0.956263i) q^{7} +(0.0724661 - 2.82750i) q^{8} +(-1.31060 + 2.69858i) q^{9} +O(q^{10})\)	\(q+(-0.0120789 + 1.41416i) q^{2} +(-0.919076 - 1.46809i) q^{3} +(-1.99971 - 0.0341629i) q^{4} +(0.185555 - 0.221136i) q^{5} +(2.08722 - 1.28199i) q^{6} +(-2.62731 - 0.956263i) q^{7} +(0.0724661 - 2.82750i) q^{8} +(-1.31060 + 2.69858i) q^{9} +(0.310481 + 0.265076i) q^{10} +(-3.08006 - 3.67067i) q^{11} +(1.78773 + 2.96716i) q^{12} +(-3.17478 - 0.559799i) q^{13} +(1.38405 - 3.70389i) q^{14} +(-0.495188 - 0.0691714i) q^{15} +(3.99767 + 0.136632i) q^{16} +(2.81522 - 4.87610i) q^{17} +(-3.80040 - 1.88599i) q^{18} +(-0.00428975 + 0.00247669i) q^{19} +(-0.378611 + 0.435868i) q^{20} +(1.01082 + 4.73602i) q^{21} +(5.22813 - 4.31136i) q^{22} +(1.84294 - 0.670777i) q^{23} +(-4.21763 + 2.49230i) q^{24} +(0.853770 + 4.84197i) q^{25} +(0.829994 - 4.48289i) q^{26} +(5.16631 - 0.556122i) q^{27} +(5.22119 + 2.00200i) q^{28} +(-7.88122 + 1.38967i) q^{29} +(0.103801 - 0.699440i) q^{30} +(-5.45972 + 1.98718i) q^{31} +(-0.241507 + 5.65170i) q^{32} +(-2.55808 + 7.89544i) q^{33} +(6.86159 + 4.04007i) q^{34} +(-0.698975 + 0.403553i) q^{35} +(2.71300 - 5.35160i) q^{36} +(8.20717 + 4.73841i) q^{37} +(-0.00345063 - 0.00609632i) q^{38} +(2.09603 + 5.17537i) q^{39} +(-0.611815 - 0.540682i) q^{40} +(1.69965 - 9.63917i) q^{41} +(-6.70971 + 1.37225i) q^{42} +(-3.57494 - 4.26045i) q^{43} +(6.03382 + 7.44549i) q^{44} +(0.353565 + 0.790555i) q^{45} +(0.926326 + 2.61432i) q^{46} +(3.48835 + 1.26966i) q^{47} +(-3.47357 - 5.99452i) q^{48} +(0.626015 + 0.525289i) q^{49} +(-6.85765 + 1.14888i) q^{50} +(-9.74597 + 0.348505i) q^{51} +(6.32950 + 1.22789i) q^{52} +0.865665i q^{53} +(0.724043 + 7.31271i) q^{54} -1.38324 q^{55} +(-2.89422 + 7.35942i) q^{56} +(0.00757862 + 0.00402149i) q^{57} +(-1.87003 - 11.1621i) q^{58} +(3.57109 - 4.25586i) q^{59} +(0.987867 + 0.155240i) q^{60} +(-2.43327 + 6.68534i) q^{61} +(-2.74424 - 7.74493i) q^{62} +(6.02390 - 5.83673i) q^{63} +(-7.98950 - 0.409796i) q^{64} +(-0.712888 + 0.598184i) q^{65} +(-11.1345 - 3.71291i) q^{66} +(0.224950 + 0.0396647i) q^{67} +(-5.79620 + 9.65460i) q^{68} +(-2.67857 - 2.08912i) q^{69} +(-0.562247 - 0.993338i) q^{70} +(0.429923 - 0.744648i) q^{71} +(7.53526 + 3.90127i) q^{72} +(-2.02670 - 3.51035i) q^{73} +(-6.80001 + 11.5490i) q^{74} +(6.32379 - 5.70356i) q^{75} +(0.00866286 - 0.00480611i) q^{76} +(4.58214 + 12.5893i) q^{77} +(-7.34413 + 2.90161i) q^{78} +(-0.797428 - 4.52244i) q^{79} +(0.772001 - 0.858675i) q^{80} +(-5.56467 - 7.07350i) q^{81} +(13.6108 + 2.52001i) q^{82} +(4.00250 - 0.705749i) q^{83} +(-1.85954 - 9.50519i) q^{84} +(-0.555903 - 1.52733i) q^{85} +(6.06815 - 5.00408i) q^{86} +(9.28361 + 10.2932i) q^{87} +(-10.6020 + 8.44286i) q^{88} +(-1.77889 - 3.08112i) q^{89} +(-1.12224 + 0.490449i) q^{90} +(7.80581 + 4.50669i) q^{91} +(-3.70827 + 1.27840i) q^{92} +(7.93526 + 6.18901i) q^{93} +(-1.83764 + 4.91776i) q^{94} +(-0.000248300 + 0.00140818i) q^{95} +(8.51918 - 4.83979i) q^{96} +(6.04757 - 5.07452i) q^{97} +(-0.750405 + 0.878942i) q^{98} +(13.9423 - 3.50101i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9}+O(q^{10}) \) 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9	\( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26} - 12 q^{28} - 39 q^{30} - 12 q^{31} - 36 q^{32} - 36 q^{36} - 42 q^{38} - 12 q^{39} - 21 q^{40} - 24 q^{41} - 66 q^{42} + 21 q^{44} - 3 q^{46} - 12 q^{47} + 51 q^{48} - 12 q^{49} - 99 q^{50} - 33 q^{52} - 90 q^{54} - 24 q^{55} + 99 q^{56} - 30 q^{57} + 21 q^{58} + 102 q^{60} - 36 q^{62} - 72 q^{63} - 3 q^{64} - 12 q^{65} - 9 q^{66} + 75 q^{68} + 9 q^{70} - 90 q^{71} + 60 q^{72} - 6 q^{73} + 9 q^{74} - 18 q^{76} + 12 q^{78} - 12 q^{79} + 78 q^{80} - 12 q^{81} - 12 q^{82} + 102 q^{84} - 30 q^{86} - 48 q^{87} - 30 q^{88} - 6 q^{89} + 6 q^{90} + 111 q^{92} - 33 q^{94} - 42 q^{95} + 126 q^{96} - 12 q^{97} + 54 q^{98}+O(q^{100}) \) 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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