LMFDB - Embedded newform 216.2.t.a.133.22

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			133.22
Character	$\chi$	$=$	216.133
Dual form			216.2.t.a.13.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.495022 - 1.32475i) q^{2} +(0.919076 - 1.46809i) q^{3} +(-1.50991 - 1.31156i) q^{4} +(-0.185555 - 0.221136i) q^{5} +(-1.48989 - 1.94428i) q^{6} +(-2.62731 + 0.956263i) q^{7} +(-2.48492 + 1.35099i) q^{8} +(-1.31060 - 2.69858i) q^{9} +O(q^{10})$	\(q+(0.495022 - 1.32475i) q^{2} +(0.919076 - 1.46809i) q^{3} +(-1.50991 - 1.31156i) q^{4} +(-0.185555 - 0.221136i) q^{5} +(-1.48989 - 1.94428i) q^{6} +(-2.62731 + 0.956263i) q^{7} +(-2.48492 + 1.35099i) q^{8} +(-1.31060 - 2.69858i) q^{9} +(-0.384803 + 0.136346i) q^{10} +(3.08006 - 3.67067i) q^{11} +(-3.31321 + 1.01126i) q^{12} +(3.17478 - 0.559799i) q^{13} +(-0.0337716 + 3.95389i) q^{14} +(-0.495188 + 0.0691714i) q^{15} +(0.559631 + 3.96066i) q^{16} +(2.81522 + 4.87610i) q^{17} +(-4.22371 + 0.400352i) q^{18} +(0.00428975 + 0.00247669i) q^{19} +(-0.00986189 + 0.577261i) q^{20} +(-1.01082 + 4.73602i) q^{21} +(-3.33801 - 5.89736i) q^{22} +(1.84294 + 0.670777i) q^{23} +(-0.300448 + 4.88976i) 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} +(-0.153494 + 0.690239i) q^{30} +(-5.45972 - 1.98718i) q^{31} +(5.52390 + 1.21924i) q^{32} +(-2.55808 - 7.89544i) q^{33} +(7.85319 - 1.31567i) q^{34} +(0.698975 + 0.403553i) q^{35} +(-1.56047 + 5.79353i) q^{36} +(-8.20717 + 4.73841i) q^{37} +(0.00540451 - 0.00445682i) q^{38} +(2.09603 - 5.17537i) q^{39} +(0.759842 + 0.298821i) q^{40} +(1.69965 + 9.63917i) q^{41} +(5.77365 + 3.68351i) q^{42} +(3.57494 - 4.26045i) q^{43} +(-9.46489 + 1.50269i) q^{44} +(-0.353565 + 0.790555i) q^{45} +(1.80091 - 2.10938i) q^{46} +(3.48835 - 1.26966i) q^{47} +(6.32896 + 2.81856i) q^{48} +(0.626015 - 0.525289i) q^{49} +(-5.99175 - 3.52791i) q^{50} +(9.74597 + 0.348505i) q^{51} +(-5.52782 - 3.31866i) q^{52} +0.865665i q^{53} +(-3.29416 + 6.56875i) q^{54} -1.38324 q^{55} +(5.23675 - 5.92571i) q^{56} +(0.00757862 - 0.00402149i) q^{57} +(5.74234 - 9.75270i) q^{58} +(-3.57109 - 4.25586i) q^{59} +(0.838409 + 0.545025i) q^{60} +(2.43327 + 6.68534i) q^{61} +(-5.33519 + 6.24905i) q^{62} +(6.02390 + 5.83673i) q^{63} +(4.34964 - 6.71421i) q^{64} +(-0.712888 - 0.598184i) q^{65} +(-11.7258 - 0.519613i) q^{66} +(-0.224950 + 0.0396647i) q^{67} +(2.14457 - 11.0548i) q^{68} +(2.67857 - 2.08912i) q^{69} +(0.880614 - 0.726197i) q^{70} +(0.429923 + 0.744648i) q^{71} +(6.90249 + 4.93515i) q^{72} +(-2.02670 + 3.51035i) q^{73} +(2.21446 + 13.2180i) q^{74} +(-6.32379 - 5.70356i) q^{75} +(-0.00322880 - 0.00936583i) q^{76} +(-4.58214 + 12.5893i) q^{77} +(-5.81847 - 5.33862i) 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} +(7.73780 - 5.82520i) q^{84} +(0.555903 - 1.52733i) q^{85} +(-3.87434 - 6.84491i) q^{86} +(9.28361 - 10.2932i) q^{87} +(-2.69465 + 13.2824i) q^{88} +(-1.77889 + 3.08112i) q^{89} +(0.872263 + 0.859727i) q^{90} +(-7.80581 + 4.50669i) q^{91} +(-1.90291 - 3.42994i) q^{92} +(-7.93526 + 6.18901i) q^{93} +(0.0448395 - 5.24969i) q^{94} +(-0.000248300 - 0.00140818i) q^{95} +(6.86685 - 6.98902i) q^{96} +(6.04757 + 5.07452i) q^{97} +(-0.385983 - 1.08934i) 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 $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{9}\right)$

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 $

$2$	0.495022	−	1.32475i	0.350034	−	0.936737i
$2$	0.495022	−	1.32475i	0.350034	−	0.936737i
$3$	0.919076	−	1.46809i	0.530629	−	0.847604i
$3$	0.919076	−	1.46809i	0.530629	−	0.847604i
$4$	−1.50991	−	1.31156i	−0.754953	−	0.655779i
$5$	−0.185555	−	0.221136i	−0.0829828	−	0.0988950i	0.722956	−	0.690895i	$-0.242783\pi$
$5$	−0.185555	−	0.221136i	−0.0829828	−	0.0988950i	−0.805938	+	0.592000i	$0.798339\pi$
$6$	−1.48989	−	1.94428i	−0.608244	−	0.793750i
$7$	−2.62731	+	0.956263i	−0.993030	+	0.361433i	−0.786893	−	0.617090i	$-0.788312\pi$
$7$	−2.62731	+	0.956263i	−0.993030	+	0.361433i	−0.206137	+	0.978523i	$0.566089\pi$
$8$	−2.48492	+	1.35099i	−0.878551	+	0.477648i
$9$	−1.31060	−	2.69858i	−0.436866	−	0.899527i
$10$	−0.384803	+	0.136346i	−0.121685	+	0.0431165i
$11$	3.08006	−	3.67067i	0.928672	−	1.10675i	−0.0653817	−	0.997860i	$-0.520826\pi$
$11$	3.08006	−	3.67067i	0.928672	−	1.10675i	0.994054	−	0.108888i	$-0.0347291\pi$
$12$	−3.31321	+	1.01126i	−0.956441	+	0.291926i
$13$	3.17478	−	0.559799i	0.880525	−	0.155260i	0.284933	−	0.958547i	$-0.408029\pi$
$13$	3.17478	−	0.559799i	0.880525	−	0.155260i	0.595592	+	0.803287i	$0.296918\pi$
$14$	−0.0337716	+	3.95389i	−0.00902584	+	1.05672i
$15$	−0.495188	+	0.0691714i	−0.127857	+	0.0178600i
$16$	0.559631	+	3.96066i	0.139908	+	0.990165i
$17$	2.81522	+	4.87610i	0.682791	+	1.18263i	0.974126	+	0.226007i	$0.0725672\pi$
$17$	2.81522	+	4.87610i	0.682791	+	1.18263i	−0.291335	+	0.956621i	$0.594099\pi$
$18$	−4.22371	+	0.400352i	−0.995538	+	0.0943638i
$19$	0.00428975	+	0.00247669i	0.000984137	+	0.000568192i	0.500492	−	0.865741i	$-0.333152\pi$
$19$	0.00428975	+	0.00247669i	0.000984137	+	0.000568192i	−0.499508	+	0.866309i	$0.666486\pi$
$20$	−0.00986189	+	0.577261i	−0.00220519	+	0.129079i
$21$	−1.01082	+	4.73602i	−0.220578	+	1.03348i
$22$	−3.33801	−	5.89736i	−0.711666	−	1.25732i
$23$	1.84294	+	0.670777i	0.384280	+	0.139867i	0.526934	−	0.849906i	$-0.323341\pi$
$23$	1.84294	+	0.670777i	0.384280	+	0.139867i	−0.142654	+	0.989773i	$0.545564\pi$
$24$	−0.300448	+	4.88976i	−0.0613286	+	0.998118i
$25$	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	$-0.177827\pi$
$29$	7.88122	+	1.38967i	1.46351	+	0.258056i	0.615540	+	0.788106i	$0.288938\pi$
$30$	−0.153494	+	0.690239i	−0.0280241	+	0.126020i
$31$	−5.45972	−	1.98718i	−0.980595	−	0.356907i	−0.198523	−	0.980096i	$-0.563615\pi$
$31$	−5.45972	−	1.98718i	−0.980595	−	0.356907i	−0.782071	+	0.623189i	$0.785837\pi$
$32$	5.52390	+	1.21924i	0.976496	+	0.215534i
$33$	−2.55808	−	7.89544i	−0.445304	−	1.37442i
$34$	7.85319	−	1.31567i	1.34681	−	0.225636i
$35$	0.698975	+	0.403553i	0.118148	+	0.0682130i
$36$	−1.56047	+	5.79353i	−0.260078	+	0.965588i
$37$	−8.20717	+	4.73841i	−1.34925	+	0.778990i	−0.988143	−	0.153534i	$-0.950934\pi$
$37$	−8.20717	+	4.73841i	−1.34925	+	0.778990i	−0.361107	+	0.932524i	$0.617601\pi$
$38$	0.00540451	−	0.00445682i	0.000876727	−	0.000722991i
$39$	2.09603	−	5.17537i	0.335633	−	0.828722i
$40$	0.759842	+	0.298821i	0.120142	+	0.0472478i
$41$	1.69965	+	9.63917i	0.265440	+	1.50539i	0.767779	+	0.640715i	$0.221362\pi$
$41$	1.69965	+	9.63917i	0.265440	+	1.50539i	−0.502339	+	0.864671i	$0.667527\pi$
$42$	5.77365	+	3.68351i	0.890893	+	0.568378i
$43$	3.57494	−	4.26045i	0.545173	−	0.649712i	−0.421166	−	0.906984i	$-0.638379\pi$
$43$	3.57494	−	4.26045i	0.545173	−	0.649712i	0.966339	+	0.257271i	$0.0828234\pi$
$44$	−9.46489	+	1.50269i	−1.42689	+	0.226539i
$45$	−0.353565	+	0.790555i	−0.0527064	+	0.117849i
$46$	1.80091	−	2.10938i	0.265529	−	0.311012i
$47$	3.48835	−	1.26966i	0.508829	−	0.185199i	−0.0748320	−	0.997196i	$-0.523842\pi$
$47$	3.48835	−	1.26966i	0.508829	−	0.185199i	0.583661	+	0.811998i	$0.301620\pi$
$48$	6.32896	+	2.81856i	0.913507	+	0.406824i
$49$	0.626015	−	0.525289i	0.0894307	−	0.0750413i
$50$	−5.99175	−	3.52791i	−0.847362	−	0.498922i
$51$	9.74597	+	0.348505i	1.36471	+	0.0488005i
$52$	−5.52782	−	3.31866i	−0.766571	−	0.460215i
$53$			0.865665i			0.118908i	0.998231	+	0.0594541i	$0.0189360\pi$
$53$			0.865665i			0.118908i	−0.998231	+	0.0594541i	$0.981064\pi$
$54$	−3.29416	+	6.56875i	−0.448278	+	0.893894i
$55$	−1.38324			−0.186516
$56$	5.23675	−	5.92571i	0.699790	−	0.791857i
$57$	0.00757862	−	0.00402149i	0.00100381	−	0.000532660i
$58$	5.74234	−	9.75270i	0.754007	−	1.28059i
$59$	−3.57109	−	4.25586i	−0.464916	−	0.554066i	0.481739	−	0.876315i	$-0.340005\pi$
$59$	−3.57109	−	4.25586i	−0.464916	−	0.554066i	−0.946655	+	0.322249i	$0.895561\pi$
$60$	0.838409	+	0.545025i	0.108238	+	0.0703624i
$61$	2.43327	+	6.68534i	0.311548	+	0.855970i	0.992345	+	0.123498i	$0.0394113\pi$
$61$	2.43327	+	6.68534i	0.311548	+	0.855970i	−0.680797	+	0.732472i	$0.738366\pi$
$62$	−5.33519	+	6.24905i	−0.677569	+	0.793630i
$63$	6.02390	+	5.83673i	0.758940	+	0.735359i
$64$	4.34964	−	6.71421i	0.543705	−	0.839276i
$65$	−0.712888	−	0.598184i	−0.0884228	−	0.0741956i
$66$	−11.7258	−	0.519613i	−1.44334	−	0.0639599i
$67$	−0.224950	+	0.0396647i	−0.0274820	+	0.00484582i	−0.187372	−	0.982289i	$-0.559997\pi$
$67$	−0.224950	+	0.0396647i	−0.0274820	+	0.00484582i	0.159890	+	0.987135i	$0.448886\pi$
$68$	2.14457	−	11.0548i	0.260068	−	1.34059i
$69$	2.67857	−	2.08912i	0.322462	−	0.251500i
$70$	0.880614	−	0.726197i	0.105254	−	0.0867971i
$71$	0.429923	+	0.744648i	0.0510224	+	0.0883735i	0.890409	−	0.455162i	$-0.150419\pi$
$71$	0.429923	+	0.744648i	0.0510224	+	0.0883735i	−0.839386	+	0.543535i	$0.817085\pi$
$72$	6.90249	+	4.93515i	0.813466	+	0.581613i
$73$	−2.02670	+	3.51035i	−0.237208	+	0.410856i	−0.959912	−	0.280301i	$-0.909566\pi$
$73$	−2.02670	+	3.51035i	−0.237208	+	0.410856i	0.722704	+	0.691157i	$0.242899\pi$
$74$	2.21446	+	13.2180i	0.257426	+	1.53657i
$75$	−6.32379	−	5.70356i	−0.730208	−	0.658590i
$76$	−0.00322880	−	0.00936583i	−0.000370369	−	0.00107433i
$77$	−4.58214	+	12.5893i	−0.522184	+	1.43469i
$78$	−5.81847	−	5.33862i	−0.658812	−	0.604480i
$79$	−0.797428	+	4.52244i	−0.0897176	+	0.508814i	0.906521	+	0.422161i	$0.138728\pi$
$79$	−0.797428	+	4.52244i	−0.0897176	+	0.508814i	−0.996239	+	0.0866531i	$0.972383\pi$
$80$	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	$-0.516047\pi$
$83$	−4.00250	−	0.705749i	−0.439332	−	0.0774660i	−0.388939	+	0.921263i	$0.627158\pi$
$84$	7.73780	−	5.82520i	0.844263	−	0.635581i
$85$	0.555903	−	1.52733i	0.0602961	−	0.165662i
$86$	−3.87434	−	6.84491i	−0.417781	−	0.738105i
$87$	9.28361	−	10.2932i	0.995308	−	1.10354i
$88$	−2.69465	+	13.2824i	−0.287250	+	1.41591i
$89$	−1.77889	+	3.08112i	−0.188562	+	0.326599i	−0.944771	−	0.327731i	$-0.893716\pi$
$89$	−1.77889	+	3.08112i	−0.188562	+	0.326599i	0.756209	+	0.654330i	$0.227049\pi$
$90$	0.872263	+	0.859727i	0.0919446	+	0.0906231i
$91$	−7.80581	+	4.50669i	−0.818272	+	0.472429i
$92$	−1.90291	−	3.42994i	−0.198392	−	0.357596i
$93$	−7.93526	+	6.18901i	−0.822848	+	0.641771i
$94$	0.0448395	−	5.24969i	0.00462484	−	0.541464i
$95$	−0.000248300	−	0.00140818i	−2.54751e−5	−	0.000144476i
$96$	6.86685	−	6.98902i	0.700845	−	0.713314i
$97$	6.04757	+	5.07452i	0.614038	+	0.515239i	0.895923	−	0.444209i	$-0.146515\pi$
$97$	6.04757	+	5.07452i	0.614038	+	0.515239i	−0.281885	+	0.959448i	$0.590960\pi$
$98$	−0.385983	−	1.08934i	−0.0389902	−	0.110040i
$99$	−13.9423	−	3.50101i	−1.40126	−	0.351865i
$100$	−7.63964	+	6.19115i	−0.763964	+	0.619115i
$101$	−6.35260	−	17.4536i	−0.632107	−	1.73670i	−0.675205	−	0.737630i	$-0.735945\pi$
$101$	−6.35260	−	17.4536i	−0.632107	−	1.73670i	0.0430976	−	0.999071i	$-0.486277\pi$
$102$	5.28615	−	12.7384i	0.523407	−	1.26129i
$103$	−3.47298	+	2.91418i	−0.342203	+	0.287143i	−0.797650	−	0.603120i	$-0.793924\pi$
$103$	−3.47298	+	2.91418i	−0.342203	+	0.287143i	0.455447	+	0.890263i	$0.349479\pi$
$104$	−7.13278	+	5.68015i	−0.699427	+	0.556985i
$105$	1.23487	−	0.655264i	0.120511	−	0.0639473i
$106$	1.14679	+	0.428523i	0.111386	+	0.0416219i
$107$			3.74905i			0.362434i	0.983443	+	0.181217i	$0.0580036\pi$
$107$			3.74905i			0.362434i	−0.983443	+	0.181217i	$0.941996\pi$
$108$	7.07125	+	7.61560i	0.680431	+	0.732812i
$109$		−	16.8471i		−	1.61366i	−0.590782	−	0.806831i	$-0.701181\pi$
$109$		−	16.8471i		−	1.61366i	0.590782	−	0.806831i	$-0.298819\pi$
$110$	−0.684733	+	1.83244i	−0.0652868	+	0.174716i
$111$	−0.586584	+	16.4039i	−0.0556761	+	1.55698i
$112$	−5.25776	−	9.87073i	−0.496811	−	0.932696i
$113$	4.67369	−	3.92169i	0.439664	−	0.368921i	−0.395920	−	0.918285i	$-0.629574\pi$
$113$	4.67369	−	3.92169i	0.439664	−	0.368921i	0.835583	+	0.549364i	$0.185130\pi$
$114$	−0.00157587	−	0.0120305i	−0.000147594	−	0.00112676i
$115$	−0.193635	−	0.532007i	−0.0180565	−	0.0496099i
$116$	−10.0773	−	12.4350i	−0.935651	−	1.15456i
$117$	−5.67152	−	7.83372i	−0.524332	−	0.724228i
$118$	−7.40570	+	2.62404i	−0.681750	+	0.241563i
$119$	−12.0593	−	10.1189i	−1.10547	−	0.927602i
$120$	1.13705	−	0.840880i	0.103798	−	0.0767615i
$121$	−2.07693	−	11.7789i	−0.188812	−	1.07081i
$122$	10.0609	+	0.0859337i	0.910871	+	0.00778007i
$123$	15.7133	+	6.36390i	1.41682	+	0.573813i
$124$	5.63737	+	10.1612i	0.506250	+	0.912501i
$125$	−2.47914	+	1.43133i	−0.221741	+	0.128022i
$126$	10.7142	−	5.09083i	0.954493	−	0.453527i
$127$	−10.6004	+	18.3604i	−0.940632	+	1.62922i	−0.176362	+	0.984325i	$0.556433\pi$
$127$	−10.6004	+	18.3604i	−0.940632	+	1.62922i	−0.764270	+	0.644896i	$0.776901\pi$
$128$	−6.74146	−	9.08586i	−0.595866	−	0.803084i
$129$	−2.96909	−	9.16403i	−0.261414	−	0.806847i
$130$	−1.14534	+	0.648281i	−0.100453	+	0.0568580i
$131$	−3.62600	+	9.96234i	−0.316805	+	0.870414i	0.674435	+	0.738335i	$0.264387\pi$
$131$	−3.62600	+	9.96234i	−0.316805	+	0.870414i	−0.991239	+	0.132079i	$0.957835\pi$
$132$	−6.49287	+	15.2764i	−0.565132	+	1.32964i
$133$	−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	0.677463	+	0.735557i	$0.263079\pi$
$137$	−2.46640	+	13.9877i	−0.210719	+	1.19505i	−0.888182	+	0.459491i	$0.848032\pi$
$138$	−1.44160	−	4.58259i	−0.122717	−	0.390096i
$139$	−3.33532	+	9.16372i	−0.282898	+	0.777257i	0.714115	+	0.700028i	$0.246829\pi$
$139$	−3.33532	+	9.16372i	−0.282898	+	0.777257i	−0.997013	+	0.0772283i	$0.975393\pi$
$140$	−0.526103	−	1.52607i	−0.0444638	−	0.128977i
$141$	1.34209	−	6.28814i	0.113024	−	0.529557i
$142$	1.19929	−	0.200921i	0.100642	−	0.0168609i
$143$	7.72366	−	13.3778i	0.645885	−	1.11871i
$144$	9.95470	−	6.70104i	0.829558	−	0.558420i
$145$	−1.15509	−	2.00068i	−0.0959254	−	0.166148i
$146$	3.64707	+	4.42257i	0.301833	+	0.366015i
$147$	−0.195818	−	1.40183i	−0.0161508	−	0.115621i
$148$	18.6068	+	3.60962i	1.52947	+	0.296709i
$149$	1.13973	−	0.200964i	0.0933699	−	0.0164636i	−0.126768	−	0.991932i	$-0.540460\pi$
$149$	1.13973	−	0.200964i	0.0933699	−	0.0164636i	0.220138	+	0.975469i	$0.429349\pi$
$150$	−10.6862	+	5.55403i	−0.872523	+	0.453485i
$151$	−15.9973	−	13.4234i	−1.30184	−	1.09238i	−0.989823	−	0.142303i	$-0.954549\pi$
$151$	−15.9973	−	13.4234i	−1.30184	−	1.09238i	−0.312022	−	0.950075i	$-0.601006\pi$
$152$	−0.0140057		0.000358952i	−0.00113601		2.91149e-5i
$153$	9.46893	−	13.9877i	0.765518	−	1.13084i
$154$	14.4094	+	12.3022i	1.16114	+	0.991338i
$155$	0.573643	+	1.57607i	0.0460761	+	0.126593i
$156$	−9.95260	+	5.06526i	−0.796845	+	0.405545i
$157$	12.0447	+	14.3543i	0.961268	+	1.14560i	0.989286	+	0.145988i	$0.0466360\pi$
$157$	12.0447	+	14.3543i	0.961268	+	1.14560i	−0.0280180	+	0.999607i	$0.508920\pi$
$158$	5.59634	+	3.29510i	0.445221	+	0.262144i
$159$	1.27088	+	0.795612i	0.100787	+	0.0630961i
$160$	−0.755368	−	1.44777i	−0.0597171	−	0.114456i
$161$	−5.48343			−0.432155
$162$	6.61596	+	10.8733i	0.519799	+	0.854289i
$163$			11.5772i			0.906795i	0.891308	+	0.453397i	$0.149788\pi$
$163$			11.5772i			0.906795i	−0.891308	+	0.453397i	$0.850212\pi$
$164$	10.0760	−	16.7834i	0.786806	−	1.31057i
$165$	−1.27130	+	2.03072i	−0.0989706	+	0.158091i
$166$	−2.91627	+	4.95294i	−0.226346	+	0.384422i
$167$	7.59855	−	6.37594i	0.587994	−	0.493385i	−0.299568	−	0.954075i	$-0.596842\pi$
$167$	7.59855	−	6.37594i	0.587994	−	0.493385i	0.887561	+	0.460690i	$0.152398\pi$
$168$	−3.88653	−	13.1342i	−0.299852	−	1.01333i
$169$	−2.45017	+	0.891789i	−0.188475	+	0.0685991i
$170$	−1.74814	−	1.49249i	−0.134076	−	0.114469i
$171$	0.00106141	−	0.0148222i	8.11679e−5	−	0.00113348i
$172$	−10.9856	+	1.74413i	−0.837648	+	0.132989i
$173$	12.8453	−	15.3084i	0.976609	−	1.16388i	−0.00986338	−	0.999951i	$-0.503140\pi$
$173$	12.8453	−	15.3084i	0.976609	−	1.16388i	0.986473	−	0.163926i	$-0.0524159\pi$
$174$	−9.04023	−	17.3938i	−0.685338	−	1.31862i
$175$	2.38708	+	13.5378i	0.180446	+	1.02336i
$176$	16.2620	+	10.1448i	1.22579	+	0.764696i
$177$	−9.53010	+	1.33123i	−0.716326	+	0.100062i
$178$	3.20112	+	3.88180i	0.239934	+	0.290953i
$179$	18.6622	−	10.7746i	1.39488	−	0.805335i	0.401030	−	0.916065i	$-0.368652\pi$
$179$	18.6622	−	10.7746i	1.39488	−	0.805335i	0.993851	+	0.110730i	$0.0353188\pi$
$180$	1.57071	−	0.729943i	0.117074	−	0.0544068i
$181$	−17.9309	−	10.3524i	−1.33280	−	0.769490i	−0.347068	−	0.937840i	$-0.612823\pi$
$181$	−17.9309	−	10.3524i	−1.33280	−	0.769490i	−0.985727	+	0.168350i	$0.946156\pi$
$182$	2.10617	+	12.5716i	0.156120	+	0.931871i
$183$	12.0511	+	2.57208i	0.890840	+	0.190134i
$184$	−5.48578	+	0.822977i	−0.404417	+	0.0606706i
$185$	2.57071	+	0.935664i	0.189003	+	0.0687914i
$186$	4.27074	+	13.5759i	0.313146	+	0.995434i
$187$	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	−0.990446	−	0.137902i	$-0.955964\pi$
$191$	−0.173666	+	0.984911i	−0.0125661	+	0.0712657i	0.977880	+	0.209167i	$0.0670753\pi$
$192$	−5.85943	−	12.5566i	−0.422868	−	0.906191i
$193$	18.6207	+	6.77739i	1.34035	+	0.487847i	0.909923	−	0.414778i	$-0.136141\pi$
$193$	18.6207	+	6.77739i	1.34035	+	0.487847i	0.430427	+	0.902625i	$0.358363\pi$
$194$	9.71613	−	5.49950i	0.697577	−	0.394841i
$195$	−1.53339	+	0.496809i	−0.109808	+	0.0355772i
$196$	−1.63417	−	0.0279181i	−0.116726	−	0.00199415i
$197$	−5.14676	−	2.97148i	−0.366691	−	0.211709i	0.305321	−	0.952250i	$-0.401236\pi$
$197$	−5.14676	−	2.97148i	−0.366691	−	0.211709i	−0.672012	+	0.740540i	$0.734570\pi$
$198$	−11.5397	+	16.7369i	−0.820091	+	1.18944i
$199$	−4.22572	−	7.31916i	−0.299553	−	0.518842i	0.676480	−	0.736461i	$-0.263504\pi$
$199$	−4.22572	−	7.31916i	−0.299553	−	0.518842i	−0.976034	+	0.217619i	$0.930171\pi$
$200$	4.41992	+	13.1853i	0.312535	+	0.932345i
$201$	−0.148515	+	0.366702i	−0.0104754	+	0.0258652i
$202$	−26.2663	−	0.224350i	−1.84809	−	0.0157852i
$203$	−22.0353	+	3.88542i	−1.54658	+	0.272703i
$204$	−14.2584	−	13.3086i	−0.998289	−	0.931790i
$205$	1.81619	−	2.16445i	0.126848	−	0.151172i
$206$	2.14134	+	6.04341i	0.149194	+	0.421064i
$207$	−0.605213	−	5.85245i	−0.0420652	−	0.406773i
$208$	3.99388	+	12.2609i	0.276926	+	0.850142i
$209$	0.0223038	−	0.00811792i	0.00154279	−	0.000561528i
$210$	−0.256773	−	1.96025i	−0.0177190	−	0.135270i
$211$	−2.67743	−	3.19083i	−0.184322	−	0.219666i	0.665969	−	0.745980i	$-0.268018\pi$
$211$	−2.67743	−	3.19083i	−0.184322	−	0.219666i	−0.850291	+	0.526313i	$0.823574\pi$
$212$	1.13537	−	1.30707i	0.0779775	−	0.0897701i
$213$	1.48834	+	0.0532216i	0.101980	+	0.00364668i
$214$	4.96654	+	1.85586i	0.339505	+	0.126864i
$215$	−1.60549			−0.109493
$216$	13.5892	−	5.59772i	0.924626	−	0.380877i
$217$	16.2446			1.10276
$218$	−22.3182	−	8.33971i	−1.51158	−	0.564836i
$219$	3.29083	+	6.20168i	0.222374	+	0.419070i
$220$	2.08856	+	1.81420i	0.140811	+	0.122313i
$221$	11.6673	+	13.9046i	0.784829	+	0.935323i
$222$	21.4406	+	8.89735i	1.43900	+	0.597151i
$223$	13.7266	−	4.99606i	0.919198	−	0.334561i	0.161279	−	0.986909i	$-0.448438\pi$
$223$	13.7266	−	4.99606i	0.919198	−	0.334561i	0.757919	+	0.652348i	$0.226216\pi$
$224$	−15.6789	+	2.07896i	−1.04759	+	0.138907i
$225$	−14.1854	+	4.04191i	−0.945693	+	0.269461i
$226$	−2.88166	−	8.13277i	−0.191685	−	0.540984i
$227$	−13.2187	+	15.7535i	−0.877359	+	1.04560i	0.121237	+	0.992624i	$0.461314\pi$
$227$	−13.2187	+	15.7535i	−0.877359	+	1.04560i	−0.998596	+	0.0529722i	$0.983131\pi$
$228$	−0.0167174	−	0.00386773i	−0.00110714	−	0.000256147i
$229$	11.3156	−	1.99525i	0.747759	−	0.131850i	0.213232	−	0.977002i	$-0.431601\pi$
$229$	11.3156	−	1.99525i	0.747759	−	0.131850i	0.534527	+	0.845151i	$0.320490\pi$
$230$	−0.800628	−	0.00683845i	−0.0527919	−	0.000450914i
$231$	14.2710	+	18.2976i	0.938962	+	1.20389i
$232$	−21.4616	+	7.19424i	−1.40903	+	0.472325i
$233$	−2.16566	−	3.75103i	−0.141877	−	0.245738i	0.786326	−	0.617811i	$-0.211980\pi$
$233$	−2.16566	−	3.75103i	−0.141877	−	0.245738i	−0.928203	+	0.372073i	$0.878647\pi$
$234$	−13.1852	+	3.63545i	−0.861945	+	0.237657i
$235$	−0.928049	−	0.535809i	−0.0605392	−	0.0349523i
$236$	−0.189797	+	11.1096i	−0.0123547	+	0.723176i
$237$	5.90647	+	5.32717i	0.383666	+	0.346037i
$238$	−19.3747	+	10.9664i	−1.25587	+	0.710846i
$239$	−13.2703	−	4.82998i	−0.858382	−	0.312426i	−0.124929	−	0.992166i	$-0.539870\pi$
$239$	−13.2703	−	4.82998i	−0.858382	−	0.312426i	−0.733453	+	0.679740i	$0.762093\pi$
$240$	−0.551087	−	1.92256i	−0.0355725	−	0.124101i
$241$	2.60609	−	14.7799i	0.167873	−	0.952056i	−0.778179	−	0.628042i	$-0.783856\pi$
$241$	2.60609	−	14.7799i	0.167873	−	0.952056i	0.946052	−	0.324014i	$-0.105032\pi$
$242$	−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
$246$	16.2090	−	17.6659i	1.03345	−	1.12634i
$247$	0.0150055	+	0.00546154i	0.000954774	+	0.000347509i
$248$	16.2516	−	2.43807i	1.03198	−	0.154817i
$249$	−4.71471	+	5.22741i	−0.298783	+	0.331274i
$250$	0.668924	+	3.99278i	0.0423064	+	0.252526i
$251$	26.0768	+	15.0554i	1.64595	+	0.950290i	0.978658	+	0.205495i	$0.0658804\pi$
$251$	26.0768	+	15.0554i	1.64595	+	0.950290i	0.667293	+	0.744795i	$0.267453\pi$
$252$	−1.44031	−	16.7136i	−0.0907308	−	1.05286i
$253$	8.13857	−	4.69881i	0.511668	−	0.295412i
$254$	19.0754	+	23.1316i	1.19690	+	1.45141i
$255$	−1.73135	−	2.21985i	−0.108421	−	0.139012i
$256$	−15.3736	+	4.43302i	−0.960852	+	0.277064i
$257$	−0.685637	−	3.88844i	−0.0427688	−	0.242554i	0.955927	−	0.293603i	$-0.0948545\pi$
$257$	−0.685637	−	3.88844i	−0.0427688	−	0.242554i	−0.998696	+	0.0510494i	$0.983743\pi$
$258$	−13.6098	−	0.603101i	−0.847308	−	0.0375474i
$259$	17.0316	−	20.2975i	1.05829	−	1.26123i
$260$	0.291841	+	1.83819i	0.0180992	+	0.114000i
$261$	−6.57897	−	23.0894i	−0.407228	−	1.42920i
$262$	11.4026	+	9.73510i	0.704457	+	0.601437i
$263$	12.3951	−	4.51144i	0.764313	−	0.278187i	0.0696970	−	0.997568i	$-0.477797\pi$
$263$	12.3951	−	4.51144i	0.764313	−	0.278187i	0.694616	+	0.719381i	$0.255575\pi$
$264$	17.0233	+	16.1636i	1.04771	+	0.994800i
$265$	0.191430	−	0.160629i	0.0117594	−	0.00986733i
$266$	−0.00993744	+	0.0168776i	−0.000609303	+	0.00103483i
$267$	2.88844	+	5.44336i	0.176770	+	0.333128i
$268$	0.391676	+	0.235145i	0.0239254	+	0.0143638i
$269$			7.68651i			0.468655i	0.972158	+	0.234327i	$0.0752887\pi$
$269$			7.68651i			0.468655i	−0.972158	+	0.234327i	$0.924711\pi$
$270$	2.06384	−	0.490409i	0.125601	−	0.0298453i
$271$	21.3410			1.29637			0.648187	−	0.761481i	$-0.275528\pi$
$271$	21.3410			1.29637			0.648187	+	0.761481i	$0.275528\pi$
$272$	−17.7371	+	13.8789i	−1.07547	+	0.841534i
$273$	−0.557898	+	15.6017i	−0.0337655	+	0.944255i
$274$	17.3092	+	10.1916i	1.04569	+	0.615695i
$275$	−15.1436	−	18.0475i	−0.913195	−	1.08830i
$276$	−6.78439	−	0.358726i	−0.408372	−	0.0215928i
$277$	−7.73418	−	21.2495i	−0.464702	−	1.27676i	−0.921912	−	0.387400i	$-0.873373\pi$
$277$	−7.73418	−	21.2495i	−0.464702	−	1.27676i	0.457210	−	0.889359i	$-0.348849\pi$
$278$	10.4885	+	8.95470i	0.629061	+	0.537067i
$279$	1.79294	+	17.3379i	0.107341	+	1.03799i
$280$	−2.28209	−	0.0584879i	−0.136381	−	0.00349532i
$281$	−24.7061	−	20.7308i	−1.47384	−	1.23670i	−0.912477	−	0.409129i	$-0.865833\pi$
$281$	−24.7061	−	20.7308i	−1.47384	−	1.23670i	−0.561363	−	0.827570i	$-0.689723\pi$
$282$	−7.66583	−	4.89070i	−0.456493	−	0.291237i
$283$	−20.0970	+	3.54364i	−1.19464	+	0.210648i	−0.735381	−	0.677653i	$-0.762997\pi$
$283$	−20.0970	+	3.54364i	−1.19464	+	0.210648i	−0.459261	+	0.888301i	$0.651886\pi$
$284$	0.327506	−	1.68822i	0.0194339	−	0.100177i
$285$	−0.00229555		0.000929698i	−0.000135977		5.50705e-5i
$286$	−13.8988	−	16.8542i	−0.821851	−	0.996609i
$287$	−13.6831	−	23.6998i	−0.807687	−	1.39896i
$288$	−3.94938	−	16.5046i	−0.232719	−	0.972544i
$289$	−7.35090	+	12.7321i	−0.432406	+	0.748949i
$290$	−3.22219	+	0.539825i	−0.189214	+	0.0316996i
$291$	13.0080	−	4.21453i	0.762545	−	0.247060i
$292$	7.66417	−	2.64217i	0.448511	−	0.154621i
$293$	−1.43710	+	3.94839i	−0.0839561	+	0.230667i	−0.974566	−	0.224101i	$-0.928056\pi$
$293$	−1.43710	+	3.94839i	−0.0839561	+	0.230667i	0.890610	+	0.454768i	$0.150278\pi$
$294$	−1.95400	−	0.434528i	−0.113960	−	0.0253422i
$295$	−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
$300$	2.06778	+	16.9059i	0.119383	+	0.976060i
$301$	−5.31837	+	14.6121i	−0.306546	+	0.842228i
$302$	−25.7016	+	14.5476i	−1.47896	+	0.837118i
$303$	−31.4621	−	6.71500i	−1.80745	−	0.385767i
$304$	−0.00740864	+	0.0183763i	−0.000424915	+	0.00105395i
$305$	1.02686	−	1.77858i	0.0587981	−	0.101841i
$306$	−13.8428	−	19.4682i	−0.791341	−	1.11292i
$307$	−16.4700	+	9.50896i	−0.939993	+	0.542705i	−0.889958	−	0.456043i	$-0.849266\pi$
$307$	−16.4700	+	9.50896i	−0.939993	+	0.542705i	−0.0500346	+	0.998747i	$0.515933\pi$
$308$	23.4303	−	12.9990i	1.33506	−	0.740685i
$309$	1.08635	+	7.77702i	0.0618003	+	0.442419i
$310$	2.37186	+	0.0202589i	0.134713	+	0.00115063i
$311$	3.01498	+	17.0988i	0.170964	+	0.969585i	0.942700	+	0.333642i	$0.108278\pi$
$311$	3.01498	+	17.0988i	0.170964	+	0.969585i	−0.771736	+	0.635943i	$0.780611\pi$
$312$	1.78343	+	15.6921i	0.100967	+	0.888389i
$313$	0.579959	+	0.486644i	0.0327812	+	0.0275067i	0.659031	−	0.752116i	$-0.270967\pi$
$313$	0.579959	+	0.486644i	0.0327812	+	0.0275067i	−0.626250	+	0.779622i	$0.715411\pi$
$314$	24.9781	−	8.85044i	1.40960	−	0.499459i
$315$	0.172947	−	2.41514i	0.00974443	−	0.136078i
$316$	7.13548	−	5.78258i	0.401402	−	0.325296i
$317$	−6.72476	−	18.4761i	−0.377700	−	1.03772i	−0.972307	−	0.233706i	$-0.924915\pi$
$317$	−6.72476	−	18.4761i	−0.377700	−	1.03772i	0.594607	−	0.804016i	$-0.297308\pi$
$318$	1.68310	−	1.28974i	0.0943834	−	0.0723253i
$319$	29.3756	−	24.6491i	1.64472	−	1.38008i
$320$	−2.29185	+	0.283994i	−0.128118	+	0.0158757i
$321$	5.50395	+	3.44566i	0.307201	+	0.192318i
$322$	−2.71442	+	7.26415i	−0.151269	+	0.404815i
$323$			0.0278897i			0.00155182i
$324$	17.6794	−	3.38194i	0.982191	−	0.187885i
$325$		−	15.8501i		−	0.879207i
$326$	15.3368	+	5.73096i	0.849428	+	0.317409i
$327$	−24.7332	−	15.4838i	−1.36775	−	0.856256i
$328$	−17.2459	−	21.6564i	−0.952247	−	1.19577i
$329$	−7.95087	+	6.67157i	−0.438345	+	0.367815i
$330$	2.06087	+	2.68940i	0.113447	+	0.148047i
$331$	−8.42157	−	23.1381i	−0.462891	−	1.27178i	−0.923301	−	0.384077i	$-0.874520\pi$
$331$	−8.42157	−	23.1381i	−0.462891	−	1.27178i	0.460409	−	0.887707i	$-0.347703\pi$
$332$	5.11777	+	6.31513i	0.280874	+	0.346588i
$333$	23.5433	+	15.9376i	1.29016	+	0.873373i
$334$	−4.68505	−	13.2224i	−0.256355	−	0.723497i
$335$	0.0505119	+	0.0423845i	0.00275976	+	0.00231571i
$336$	−19.3234	−	1.35307i	−1.05418	−	0.0738162i
$337$	−1.71929	−	9.75056i	−0.0936555	−	0.531147i	−0.995151	−	0.0983585i	$-0.968641\pi$
$337$	−1.71929	−	9.75056i	−0.0936555	−	0.531147i	0.901496	−	0.432788i	$-0.142470\pi$
$338$	−0.0314946	+	3.68731i	−0.00171308	+	0.200563i
$339$	−1.46193	−	10.4657i	−0.0794012	−	0.568421i
$340$	−2.84254	+	1.57703i	−0.154159	+	0.0855263i
$341$	−24.1105	+	13.9202i	−1.30566	+	0.753822i
$342$	−0.0191102	−	0.00874341i	−0.00103336	−	0.000472789i
$343$	8.64332	−	14.9707i	0.466695	−	0.808340i
$344$	−3.12761	+	15.4166i	−0.168629	+	0.831207i
$345$	−0.959002	−	0.204681i	−0.0516309	−	0.0110197i
$346$	−13.9211	−	24.5948i	−0.748401	−	1.32222i
$347$	7.12971	−	19.5887i	0.382743	−	1.05158i	−0.587453	−	0.809258i	$-0.699869\pi$
$347$	7.12971	−	19.5887i	0.382743	−	1.05158i	0.970196	−	0.242320i	$-0.0779084\pi$
$348$	−27.5175	+	3.36570i	−1.47509	+	0.180420i
$349$	−14.8725	−	2.62242i	−0.796107	−	0.140375i	−0.239222	−	0.970965i	$-0.576892\pi$
$349$	−14.8725	−	2.62242i	−0.796107	−	0.140375i	−0.556885	+	0.830590i	$0.688004\pi$
$350$	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	−0.996805	−	0.0798689i	$-0.974550\pi$
$353$	−0.616217	+	3.49474i	−0.0327979	+	0.186006i	0.964007	+	0.265875i	$0.0856609\pi$
$354$	−2.95407	+	13.2840i	−0.157007	+	0.706035i
$355$	0.0848941	−	0.233245i	0.00450571	−	0.0123793i
$356$	6.72703	−	2.31909i	0.356532	−	0.122912i
$357$	−25.9390	+	8.40408i	−1.37284	+	0.444791i
$358$	−5.03545	−	30.0564i	−0.266132	−	1.58853i
$359$	−11.0808	+	19.1925i	−0.584823	+	1.01294i	0.410074	+	0.912052i	$0.365503\pi$
$359$	−11.0808	+	19.1925i	−0.584823	+	1.01294i	−0.994897	+	0.100891i	$0.967831\pi$
$360$	−0.189453	−	2.44213i	−0.00998508	−	0.128712i
$361$	−9.49999	−	16.4545i	−0.499999	−	0.866024i
$362$	−22.5905	+	18.6292i	−1.18733	+	0.979131i
$363$	−19.2013	−	7.77655i	−1.00781	−	0.408163i
$364$	17.6968	+	3.43310i	0.927566	+	0.179943i
$365$	1.15233	−	0.203187i	0.0603158	−	0.0106353i
$366$	9.37290	−	14.6914i	0.489929	−	0.767930i
$367$	13.2887	+	11.1505i	0.693664	+	0.582053i	0.919963	−	0.392005i	$-0.128218\pi$
$367$	13.2887	+	11.1505i	0.693664	+	0.582053i	−0.226299	+	0.974058i	$0.572663\pi$
$368$	−1.62535	+	7.67466i	−0.0847271	+	0.400069i
$369$	23.7845	−	17.2197i	1.23817	−	0.896422i
$370$	2.51208	−	2.94237i	0.130597	−	0.152967i
$371$	−0.827803	−	2.27437i	−0.0429774	−	0.118079i
$372$	20.0987	+	1.06272i	1.04207	+	0.0550997i
$373$	10.6639	+	12.7087i	0.552156	+	0.658034i	0.967867	−	0.251463i	$-0.0809116\pi$
$373$	10.6639	+	12.7087i	0.552156	+	0.658034i	−0.415711	+	0.909497i	$0.636467\pi$
$374$	19.3589	−	32.8788i	1.00102	−	1.70012i
$375$	−0.177190	+	4.95512i	−0.00915004	+	0.255881i
$376$	−6.95298	+	7.86773i	−0.358573	+	0.405747i
$377$	25.7991			1.32872
$378$	2.37332	−	20.4082i	0.122070	−	1.04969i
$379$		−	9.64915i		−	0.495644i	−0.968806	−	0.247822i	$-0.920285\pi$
$379$		−	9.64915i		−	0.495644i	0.968806	−	0.247822i	$-0.0797148\pi$
$380$	−0.00147200	+	0.00245188i	−7.55120e−5	+	0.000125779i
$381$	17.2122	+	32.4370i	0.881809	+	1.66180i
$382$	1.21879	+	0.717617i	0.0623586	+	0.0367165i
$383$	−9.22574	+	7.74132i	−0.471414	+	0.395563i	−0.847310	−	0.531099i	$-0.821779\pi$
$383$	−9.22574	+	7.74132i	−0.471414	+	0.395563i	0.375896	+	0.926662i	$0.377335\pi$
$384$	−19.5348	+	1.54649i	−0.996881	+	0.0789191i
$385$	3.63420	−	1.32274i	0.185216	−	0.0674130i
$386$	18.1960	−	21.3128i	0.926152	−	1.08479i
$387$	−16.1825	−	4.06353i	−0.822601	−	0.206561i
$388$	−2.47574	−	15.5938i	−0.125687	−	0.791654i
$389$	−1.86623	+	2.22408i	−0.0946216	+	0.112766i	−0.811277	−	0.584661i	$-0.801227\pi$
$389$	−1.86623	+	2.22408i	−0.0946216	+	0.112766i	0.716656	+	0.697427i	$0.245672\pi$
$390$	−0.100915	+	2.27728i	−0.00511003	+	0.115315i
$391$	1.91751	+	10.8748i	0.0969729	+	0.549960i
$392$	−0.845935	+	2.15104i	−0.0427262	+	0.108644i
$393$	11.2931	+	14.4795i	0.569661	+	0.730392i
$394$	−6.48422	+	5.34720i	−0.326670	+	0.269388i
$395$	1.14804	−	0.662821i	0.0577642	−	0.0333502i
$396$	16.4598	+	23.5723i	0.827136	+	1.18456i
$397$	3.53148	+	2.03890i	0.177240	+	0.102330i	0.585995	−	0.810314i	$-0.300704\pi$
$397$	3.53148	+	2.03890i	0.177240	+	0.102330i	−0.408755	+	0.912644i	$0.634037\pi$
$398$	−11.7879	+	1.97486i	−0.590872	+	0.0989907i
$399$	−0.0160658	+	0.0178129i	−0.000804296	+	0.000891759i
$400$	19.6552	+	0.671773i	0.982760	+	0.0335886i
$401$	2.09322	+	0.761870i	0.104530	+	0.0380460i	0.393756	−	0.919215i	$-0.371176\pi$
$401$	2.09322	+	0.761870i	0.104530	+	0.0380460i	−0.289226	+	0.957261i	$0.593398\pi$
$402$	0.412270	+	0.378270i	0.0205621	+	0.0188664i
$403$	−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
$408$	−24.6888	+	12.3007i	−1.22228	+	0.608976i
$409$	17.7345	+	6.45483i	0.876914	+	0.319171i	0.740964	−	0.671545i	$-0.234369\pi$
$409$	17.7345	+	6.45483i	0.876914	+	0.319171i	0.135950	+	0.990716i	$0.456591\pi$
$410$	−1.96829	−	3.47744i	−0.0972071	−	0.171739i
$411$	18.2684	+	16.4767i	0.901114	+	0.812733i
$412$	9.06599	+	0.154883i	0.446649	+	0.00763054i
$413$	13.4521	+	7.76657i	0.661934	+	0.382168i
$414$	−8.05261	−	2.09534i	−0.395764	−	0.102980i
$415$	0.586618	+	1.01605i	0.0287959	+	0.0498760i
$416$	18.2197	+	0.778558i	0.893293	+	0.0381719i
$417$	10.3878	+	13.3187i	0.508692	+	0.652221i
$418$	0.000286694	−	0.0335654i	1.40227e−5	−	0.00164174i
$419$	13.5715	−	2.39303i	0.663013	−	0.116907i	0.167992	−	0.985788i	$-0.446272\pi$
$419$	13.5715	−	2.39303i	0.663013	−	0.116907i	0.495021	+	0.868881i	$0.335161\pi$
$420$	−2.72395	−	0.630210i	−0.132915	−	0.0307511i
$421$	−23.8985	+	28.4811i	−1.16474	+	1.38809i	−0.258135	+	0.966109i	$0.583108\pi$
$421$	−23.8985	+	28.4811i	−1.16474	+	1.38809i	−0.906607	+	0.421977i	$0.861336\pi$
$422$	−5.55243	+	1.96738i	−0.270288	+	0.0957705i
$423$	−7.99810	−	7.74959i	−0.388881	−	0.376798i
$424$	−1.16951	−	2.15111i	−0.0567962	−	0.104467i
$425$	26.0135	−	9.46814i	1.26184	−	0.459272i
$426$	0.807269	−	1.94533i	0.0391123	−	0.0942517i
$427$	−12.7859	−	15.2376i	−0.618753	−	0.737401i
$428$	4.91709	−	5.66071i	0.237677	−	0.273621i
$429$	−12.5412	−	23.6342i	−0.605494	−	1.14107i
$430$	−0.794752	+	2.12686i	−0.0383263	+	0.102566i
$431$	11.4089			0.549548			0.274774	−	0.961509i	$-0.411397\pi$
$431$	11.4089			0.549548			0.274774	+	0.961509i	$0.411397\pi$
$432$	−0.688619	−	20.7732i	−0.0331312	−	0.999451i
$433$	−7.51420			−0.361109			−0.180555	−	0.983565i	$-0.557789\pi$
$433$	−7.51420			−0.361109			−0.180555	+	0.983565i	$0.557789\pi$
$434$	8.04146	−	21.5200i	0.386003	−	1.03299i
$435$	−3.99881	−	0.142993i	−0.191728	−	0.00685599i
$436$	−22.0960	+	25.4376i	−1.05821	+	1.21824i
$437$	0.00624447	+	0.00744187i	0.000298713	+	0.000355993i
$438$	9.84468	−	1.28955i	0.470397	−	0.0616172i
$439$	−19.2063	+	6.99052i	−0.916667	+	0.333639i	−0.756912	−	0.653517i	$-0.773293\pi$
$439$	−19.2063	+	6.99052i	−0.916667	+	0.333639i	−0.159755	+	0.987157i	$0.551070\pi$
$440$	3.43723	−	1.86874i	0.163864	−	0.0890888i
$441$	−2.23799	−	1.00091i	−0.106571	−	0.0476624i
$442$	24.1956	−	8.57317i	1.15087	−	0.407784i
$443$	−18.1395	+	21.6178i	−0.861832	+	1.02709i	0.137498	+	0.990502i	$0.456094\pi$
$443$	−18.1395	+	21.6178i	−0.861832	+	1.02709i	−0.999330	+	0.0365893i	$0.988351\pi$
$444$	22.4003	−	23.9989i	1.06307	−	1.13894i
$445$	1.01143	−	0.178342i	0.0479463	−	0.00845423i
$446$	0.176442	−	20.6574i	0.00835476	−	0.978154i
$447$	0.752460	−	1.85793i	0.0355901	−	0.0878768i
$448$	−5.00731	+	21.7997i	−0.236573	+	1.02994i
$449$	−5.65025	−	9.78653i	−0.266652	−	0.461855i	0.701343	−	0.712824i	$-0.252584\pi$
$449$	−5.65025	−	9.78653i	−0.266652	−	0.461855i	−0.967995	+	0.250969i	$0.919251\pi$
$450$	−1.66759	+	20.7929i	−0.0786108	+	0.980186i
$451$	40.6172	+	23.4504i	1.91259	+	1.10423i
$452$	−12.2004	−	0.208430i	−0.573856	−	0.00980373i
$453$	−34.4095	+	11.1485i	−1.61670	+	0.523802i
$454$	14.3258	+	25.3098i	0.672343	+	1.18785i
$455$	2.44500	+	0.889907i	0.114623	+	0.0417195i
$456$	−0.0133993	+	0.0202317i	−0.000627478	+	0.000947438i
$457$	−6.59891	+	37.4243i	−0.308684	+	1.75063i	0.296952	+	0.954892i	$0.404030\pi$
$457$	−6.59891	+	37.4243i	−0.308684	+	1.75063i	−0.605636	+	0.795742i	$0.707081\pi$
$458$	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	$-0.501595\pi$
$461$	−7.55207	−	1.33163i	−0.351735	−	0.0620204i	−0.346724	+	0.937967i	$0.612706\pi$
$462$	31.3041	−	9.84773i	1.45640	−	0.458158i
$463$	−20.5953	−	7.49607i	−0.957144	−	0.348372i	−0.184231	−	0.982883i	$-0.558979\pi$
$463$	−20.5953	−	7.49607i	−0.957144	−	0.348372i	−0.772914	+	0.634511i	$0.781202\pi$
$464$	−1.09344	+	31.9925i	−0.0507615	+	1.48522i
$465$	2.84104	+	0.606368i	0.131750	+	0.0281196i
$466$	−6.04121	+	1.01210i	−0.279854	+	0.0468848i
$467$	2.10941	+	1.21787i	0.0976119	+	0.0563563i	0.548011	−	0.836471i	$-0.315385\pi$
$467$	2.10941	+	1.21787i	0.0976119	+	0.0563563i	−0.450399	+	0.892827i	$0.648718\pi$
$468$	−1.71092	+	19.2667i	−0.0790874	+	0.890604i
$469$	0.553083	−	0.319323i	0.0255390	−	0.0147450i
$470$	−1.16922	+	0.964192i	−0.0539319	+	0.0444748i
$471$	32.1434	−	4.49002i	1.48109	−	0.206889i
$472$	14.6235	+	5.75095i	0.673101	+	0.264709i
$473$	−4.62768	−	26.2449i	−0.212781	−	1.20674i
$474$	9.98097	−	5.18750i	0.458441	−	0.238270i
$475$	0.0156545	−	0.0186563i	0.000718279	−	0.000856012i
$476$	4.93681	+	31.0951i	0.226278	+	1.42524i
$477$	2.33607	−	1.13454i	0.106961	−	0.0519469i
$478$	−12.9676	+	15.1888i	−0.593123	+	0.694719i
$479$	13.6689	−	4.97509i	0.624550	−	0.227318i	−0.0103076	−	0.999947i	$-0.503281\pi$
$479$	13.6689	−	4.97509i	0.624550	−	0.227318i	0.634857	+	0.772629i	$0.281059\pi$
$480$	−2.81970	−	0.221659i	−0.128701	−	0.0101173i
$481$	−23.4034	+	19.6378i	−1.06710	+	0.895405i
$482$	−18.2895	−	10.7688i	−0.833065	−	0.490505i
$483$	−5.03969	+	8.05018i	−0.229314	+	0.366296i
$484$	−12.3127	+	20.5090i	−0.559668	+	0.932227i
$485$		−	2.27894i		−	0.103481i
$486$	22.0436	+	0.280557i	0.999919	+	0.0127263i
$487$	2.54679			0.115406			0.0577031	−	0.998334i	$-0.481622\pi$
$487$	2.54679			0.115406			0.0577031	+	0.998334i	$0.481622\pi$
$488$	−15.0783	−	13.3252i	−0.682563	−	0.603204i
$489$	16.9964	+	10.6403i	0.768603	+	0.481172i
$490$	−0.169271	+	0.287487i	−0.00764690	+	0.0129874i
$491$	−11.6939	−	13.9362i	−0.527738	−	0.628933i	0.434654	−	0.900597i	$-0.356871\pi$
$491$	−11.6939	−	13.9362i	−0.527738	−	0.628933i	−0.962392	+	0.271664i	$0.912426\pi$
$492$	−15.3790	−	30.2178i	−0.693339	−	1.36232i
$493$	15.4112	+	42.3419i	0.694085	+	1.90698i
$494$	0.0146632	−	0.0171748i	0.000659728	−	0.000772733i
$495$	1.81287	+	3.73278i	0.0814823	+	0.167776i
$496$	4.81509	−	22.7362i	0.216204	−	1.02088i
$497$	−1.84162	−	1.54530i	−0.0826080	−	0.0693163i
$498$	4.59110	+	8.83348i	0.205732	+	0.395838i
$499$	2.03309	−	0.358488i	0.0910134	−	0.0160481i	−0.127956	−	0.991780i	$-0.540842\pi$
$499$	2.03309	−	0.358488i	0.0910134	−	0.0160481i	0.218969	+	0.975732i	$0.429731\pi$
$500$	5.62055	+	1.09036i	0.251359	+	0.0487624i
$501$	−2.37683	−	17.0154i	−0.106189	−	0.760190i
$502$	32.8532	−	27.0923i	1.46631	−	1.20919i
$503$	15.5785	+	26.9828i	0.694613	+	1.20310i	0.970311	+	0.241860i	$0.0777575\pi$
$503$	15.5785	+	26.9828i	0.694613	+	1.20310i	−0.275699	+	0.961244i	$0.588909\pi$
$504$	−22.8543	−	6.36557i	−1.01801	−	0.283545i
$505$	−2.68087	+	4.64340i	−0.119297	+	0.206628i
$506$	−2.19595	−	13.1076i	−0.0976220	−	0.582702i
$507$	−0.942664	+	4.41670i	−0.0418652	+	0.196153i
$508$	40.0863	−	13.8195i	1.77854	−	0.613139i
$509$	−0.653669	+	1.79594i	−0.0289734	+	0.0796037i	−0.953336	−	0.301911i	$-0.902375\pi$
$509$	−0.653669	+	1.79594i	−0.0289734	+	0.0796037i	0.924363	+	0.381515i	$0.124598\pi$
$510$	−3.79780	+	1.19472i	−0.168169	+	0.0529031i
$511$	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
$516$	−7.53610	+	17.7310i	−0.331758	+	0.780562i
$517$	6.08384	−	16.7152i	0.267567	−	0.735134i
$518$	−18.4580	−	32.6103i	−0.810998	−	1.43281i
$519$	−10.6684	−	32.9277i	−0.468290	−	1.44537i
$520$	2.57961	+	0.523333i	0.113123	+	0.0229497i
$521$	4.36155	−	7.55442i	0.191083	−	0.330965i	−0.754527	−	0.656269i	$-0.772133\pi$
$521$	4.36155	−	7.55442i	0.191083	−	0.330965i	0.945609	+	0.325304i	$0.105467\pi$
$522$	−33.8443	−	2.71431i	−1.48133	−	0.118802i
$523$	17.9490	−	10.3629i	0.784855	−	0.453136i	−0.0532932	−	0.998579i	$-0.516972\pi$
$523$	17.9490	−	10.3629i	0.784855	−	0.453136i	0.838148	+	0.545443i	$0.183638\pi$
$524$	18.5411	−	10.2865i	0.809972	−	0.449367i
$525$	22.0687	+	8.93782i	0.963156	+	0.390078i
$526$	0.159327	−	18.6536i	0.00694698	−	0.813335i
$527$	−5.68063	−	32.2165i	−0.247452	−	1.40337i
$528$	29.8396	−	14.5502i	1.29860	−	0.633217i
$529$	−14.6725	−	12.3117i	−0.637936	−	0.535292i
$530$	−0.118030	−	0.333110i	−0.00512690	−	0.0144694i
$531$	−6.80452	+	15.2146i	−0.295291	+	0.660257i
$532$	0.0174393	+	0.0215194i	0.000756088	+	0.000932983i
$533$	10.7920	+	29.6508i	0.467453	+	1.28432i
$534$	8.64092	−	1.13187i	0.373929	−	0.0489809i
$535$	0.829049	−	0.695655i	0.0358429	−	0.0300758i
$536$	0.505395	−	0.402469i	0.0218298	−	0.0173840i
$537$	1.33383	−	37.3006i	0.0575590	−	1.60964i
$538$	10.1827	+	3.80499i	0.439006	+	0.164045i
$539$		−	3.91581i		−	0.168666i
$540$	0.371977	−	2.97682i	0.0160073	−	0.128102i
$541$			3.63212i			0.156157i	0.996947	+	0.0780785i	$0.0248785\pi$
$541$			3.63212i			0.156157i	−0.996947	+	0.0780785i	$0.975122\pi$
$542$	10.5643	−	28.2714i	0.453774	−	1.21436i
$543$	−31.6782	+	16.8096i	−1.35944	+	0.721369i
$544$	9.60582	+	30.3675i	0.411846	+	1.30200i
$545$	−3.72551	+	3.12607i	−0.159583	+	0.133906i
$546$	20.3921	+	8.46224i	0.872700	+	0.362150i
$547$	−3.43081	−	9.42608i	−0.146691	−	0.403030i	0.844486	−	0.535578i	$-0.179906\pi$
$547$	−3.43081	−	9.42608i	−0.146691	−	0.403030i	−0.991177	+	0.132548i	$0.957684\pi$
$548$	22.0697	−	17.8852i	0.942770	−	0.764019i
$549$	14.8519	−	15.3282i	0.633864	−	0.654190i
$550$	−31.4047	+	11.1276i	−1.33910	+	0.474481i
$551$	0.0303667	+	0.0254807i	0.00129367	+	0.00108551i
$552$	−3.83364	+	8.81002i	−0.163171	+	0.374979i
$553$	−2.22955	−	12.6444i	−0.0948101	−	0.537695i
$554$	−31.9788	−	0.273142i	−1.35865	−	0.0116047i
$555$	3.73633	−	2.91410i	0.158598	−	0.123697i
$556$	17.0548	−	9.46189i	0.723283	−	0.401273i
$557$	9.46379	−	5.46392i	0.400994	−	0.231514i	−0.285919	−	0.958254i	$-0.592299\pi$
$557$	9.46379	−	5.46392i	0.400994	−	0.231514i	0.686913	+	0.726740i	$0.258966\pi$
$558$	23.8558	+	6.20744i	1.00990	+	0.262782i
$559$	8.96465	−	15.5272i	0.379164	−	0.656732i
$560$	−1.20717	+	2.99424i	−0.0510122	+	0.126530i
$561$	31.2974	−	34.7008i	1.32138	−	1.46507i
$562$	−39.6932	+	22.4670i	−1.67435	+	0.947714i
$563$	9.70697	−	26.6697i	0.409100	−	1.12399i	−0.548565	−	0.836108i	$-0.684826\pi$
$563$	9.70697	−	26.6697i	0.409100	−	1.12399i	0.957665	−	0.287885i	$-0.0929521\pi$
$564$	−10.2737	+	7.73428i	−0.432600	+	0.325672i
$565$	−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	0.890631	+	0.454727i	$0.150263\pi$
$569$	−2.42865	+	13.7735i	−0.101814	+	0.577417i	−0.992445	+	0.122690i	$0.960848\pi$
$570$	−0.00236796	+	0.00258080i	−9.91830e−5	+	0.000108098i
$571$	−5.30577	+	14.5775i	−0.222040	+	0.610049i	−0.999829	−	0.0184759i	$-0.994119\pi$
$571$	−5.30577	+	14.5775i	−0.222040	+	0.610049i	0.777790	+	0.628525i	$0.216341\pi$
$572$	−29.2077	+	10.0691i	−1.22124	+	0.421012i
$573$	1.28633	+	1.16017i	0.0537372	+	0.0484667i
$574$	−38.1697	+	6.39469i	−1.59317	+	0.266909i
$575$	4.82133	−	8.35080i	0.201064	−	0.348252i
$576$	−23.8195	−	2.93823i	−0.992478	−	0.122426i
$577$	−0.198083	−	0.343090i	−0.00824632	−	0.0142830i	0.861873	−	0.507125i	$-0.169292\pi$
$577$	−0.198083	−	0.343090i	−0.00824632	−	0.0142830i	−0.870119	+	0.492841i	$0.835958\pi$
$578$	13.2280	+	16.0408i	0.550212	+	0.667208i
$579$	27.0637	−	21.1080i	1.12473	−	0.877220i
$580$	−0.879927	+	4.53581i	−0.0365370	+	0.188339i
$581$	11.1907	−	1.97322i	0.464268	−	0.0818630i
$582$	0.856083	−	19.3186i	0.0354858	−	0.800784i
$583$	3.17757	+	2.66630i	0.131602	+	0.110427i
$584$	0.293735	−	11.4610i	0.0121548	−	0.474260i
$585$	−0.679938	+	2.70776i	−0.0281120	+	0.111952i
$586$	4.51922	+	3.85833i	0.186687	+	0.159386i
$587$	−4.01994	−	11.0447i	−0.165921	−	0.455864i	0.828670	−	0.559738i	$-0.189098\pi$
$587$	−4.01994	−	11.0447i	−0.165921	−	0.455864i	−0.994590	+	0.103874i	$0.966876\pi$
$588$	−1.54291	+	2.37346i	−0.0636287	+	0.0978797i
$589$	−0.0184992	−	0.0220465i	−0.000762247	−	0.000908411i
$590$	1.95444	+	1.15076i	0.0804629	+	0.0473761i
$591$	−9.09268	+	4.82490i	−0.374023	+	0.198470i
$592$	−23.3602	−	29.8540i	−0.960099	−	1.22699i
$593$	−14.1087			−0.579377			−0.289688	−	0.957121i	$-0.593552\pi$
$593$	−14.1087			−0.579377			−0.289688	+	0.957121i	$0.593552\pi$
$594$	13.9655	+	32.3239i	0.573013	+	1.32627i
$595$			4.54436i			0.186301i
$596$	−1.98445	−	1.19138i	−0.0812864	−	0.0488008i
$597$	−14.6290	−	0.523116i	−0.598724	−	0.0214097i
$598$	4.53665	−	7.70497i	0.185517	−	0.315080i
$599$	−28.5436	+	23.9509i	−1.16626	+	0.978607i	−0.999972	−	0.00747033i	$-0.997622\pi$
$599$	−28.5436	+	23.9509i	−1.16626	+	0.978607i	−0.166286	+	0.986077i	$0.553178\pi$
$600$	23.4196	+	5.62949i	0.956100	+	0.229823i
$601$	−11.4635	+	4.17236i	−0.467605	+	0.170194i	−0.565067	−	0.825045i	$-0.691150\pi$
$601$	−11.4635	+	4.17236i	−0.467605	+	0.170194i	0.0974622	+	0.995239i	$0.468927\pi$
$602$	16.7246	+	14.2788i	0.681645	+	0.581961i
$603$	0.401857	+	0.555061i	0.0163649	+	0.0226038i
$604$	6.54896	+	41.2494i	0.266473	+	1.67842i
$605$	−2.21934	+	2.64491i	−0.0902292	+	0.107531i
$606$	−24.4701	+	38.3552i	−0.994030	+	1.55807i
$607$	7.57443	+	42.9567i	0.307436	+	1.74356i	0.611809	+	0.791006i	$0.290442\pi$
$607$	7.57443	+	42.9567i	0.307436	+	1.74356i	−0.304372	+	0.952553i	$0.598447\pi$
$608$	0.0206765	+	0.0189112i	0.000838541	+	0.000766952i
$609$	−14.5480	+	35.9209i	−0.589514	+	1.45559i
$610$	−1.84785	−	2.24077i	−0.0748172	−	0.0907262i
$611$	10.3640	−	5.98365i	0.419282	−	0.242073i
$612$	−32.6429	+	8.70105i	−1.31951	+	0.351719i
$613$	24.6408	+	14.2264i	0.995233	+	0.574598i	0.906834	−	0.421487i	$-0.138492\pi$
$613$	24.6408	+	14.2264i	0.995233	+	0.574598i	0.0883987	+	0.996085i	$0.471825\pi$
$614$	4.44394	+	26.5257i	0.179343	+	1.07049i
$615$	−1.50840	−	4.65563i	−0.0608245	−	0.187733i
$616$	−5.62184	−	37.4739i	−0.226510	−	1.50987i
$617$	−6.84389	−	2.49097i	−0.275525	−	0.100283i	0.200562	−	0.979681i	$-0.435723\pi$
$617$	−6.84389	−	2.49097i	−0.275525	−	0.100283i	−0.476087	+	0.879398i	$0.657945\pi$
$618$	10.8403	+	2.41066i	0.436063	+	0.0969709i
$619$	−4.70638	−	0.829861i	−0.189165	−	0.0333549i	0.0782628	−	0.996933i	$-0.475063\pi$
$619$	−4.70638	−	0.829861i	−0.189165	−	0.0333549i	−0.267428	+	0.963578i	$0.586174\pi$
$620$	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
$624$	21.6709	+	5.40534i	0.867529	+	0.216387i
$625$	−22.3242	−	8.12536i	−0.892970	−	0.325014i
$626$	0.931772	−	0.527400i	0.0372411	−	0.0210791i
$627$	0.00858103	−	0.0402050i	0.000342693	−	0.00160563i
$628$	0.640150	−	37.4709i	0.0255448	−	1.49525i
$629$	−46.2099	−	26.6793i	−1.84251	−	1.06377i
$630$	−3.11383	−	1.42466i	−0.124058	−	0.0567597i
$631$	−10.2228	−	17.7064i	−0.406964	−	0.704882i	0.587584	−	0.809163i	$-0.300079\pi$
$631$	−10.2228	−	17.7064i	−0.406964	−	0.704882i	−0.994548	+	0.104281i	$0.966746\pi$
$632$	−4.12823	−	12.3152i	−0.164212	−	0.489873i
$633$	−7.14521	+	0.998094i	−0.283996	+	0.0396707i
$634$	−27.8051	−	0.237493i	−1.10428	−	0.00943205i
$635$	6.02710	−	1.06274i	0.239178	−	0.0421736i
$636$	−0.875413	−	2.86813i	−0.0347124	−	0.113729i
$637$	1.69340	−	2.01812i	0.0670950	−	0.0799607i
$638$	−18.1122	−	51.1171i	−0.717069	−	2.02375i
$639$	1.44604	−	2.13611i	0.0572043	−	0.0845034i
$640$	−0.758298	+	3.17670i	−0.0299744	+	0.125570i
$641$	17.9357	−	6.52806i	0.708417	−	0.257843i	0.0374167	−	0.999300i	$-0.488087\pi$
$641$	17.9357	−	6.52806i	0.708417	−	0.257843i	0.671000	+	0.741457i	$0.265865\pi$
$642$	7.28920	−	5.58566i	0.287682	−	0.220448i
$643$	−11.9937	−	14.2935i	−0.472984	−	0.563680i	0.475821	−	0.879542i	$-0.342151\pi$
$643$	−11.9937	−	14.2935i	−0.472984	−	0.563680i	−0.948805	+	0.315862i	$0.897706\pi$
$644$	8.27946	+	7.19183i	0.326256	+	0.283398i
$645$	−1.47556	+	2.35700i	−0.0581003	+	0.0928070i
$646$	0.0369468	+	0.0138060i	0.00145365	+	0.000543190i
$647$	1.28685			0.0505911			0.0252955	−	0.999680i	$-0.491947\pi$
$647$	1.28685			0.0505911			0.0252955	+	0.999680i	$0.491947\pi$
$648$	4.27151	−	25.0949i	0.167801	−	0.985821i
$649$	−26.6210			−1.04497
$650$	−20.9974	−	7.84617i	−0.823586	−	0.307752i
$651$	14.9301	−	23.8487i	0.585156	−	0.934703i
$652$	15.1841	−	17.4805i	0.594657	−	0.684587i
$653$	4.80662	+	5.72830i	0.188097	+	0.224166i	0.851849	−	0.523787i	$-0.175481\pi$
$653$	4.80662	+	5.72830i	0.188097	+	0.224166i	−0.663752	+	0.747953i	$0.731037\pi$
$654$	−32.7556	+	25.1003i	−1.28084	+	0.981501i
$655$	2.87585	−	1.04672i	0.112369	−	0.0408989i
$656$	−37.2263	+	12.1261i	−1.45344	+	0.473445i
$657$	12.1292	+	0.868563i	0.473204	+	0.0338859i
$658$	4.90228	+	13.8355i	0.191111	+	0.539362i
$659$	−15.2256	+	18.1451i	−0.593104	+	0.706834i	−0.976199	−	0.216875i	$-0.930414\pi$
$659$	−15.2256	+	18.1451i	−0.593104	+	0.706834i	0.383095	+	0.923709i	$0.374858\pi$
$660$	4.58295	−	1.39881i	0.178391	−	0.0544488i
$661$	4.78633	−	0.843960i	0.186167	−	0.0328262i	−0.0797873	−	0.996812i	$-0.525424\pi$
$661$	4.78633	−	0.843960i	0.186167	−	0.0328262i	0.265954	+	0.963986i	$0.414313\pi$
$662$	−34.8210	−	0.297418i	−1.35335	−	0.0115595i
$663$	31.1364	−	4.34936i	1.20924	−	0.168915i
$664$	10.8994	−	3.65362i	0.422977	−	0.141788i
$665$	0.00199895	+	0.00346229i	7.75161e−5	+	0.000134262i
$666$	32.7677	−	23.2994i	1.26972	−	0.902834i
$667$	13.5925	+	7.84763i	0.526303	+	0.303861i
$668$	−19.8355	−	0.338869i	−0.767459	−	0.0131112i
$669$	5.28107	−	24.7436i	0.204178	−	0.956644i
$670$	0.0811532	−	0.0459342i	0.00313522	−	0.00177459i
$671$	32.0343	+	11.6595i	1.23667	+	0.450111i
$672$	−11.3580	+	24.9288i	−0.438145	+	0.961651i
$673$	−6.24184	+	35.3992i	−0.240605	+	1.36454i	0.589876	+	0.807494i	$0.299176\pi$
$673$	−6.24184	+	35.3992i	−0.240605	+	1.36454i	−0.830482	+	0.557046i	$0.811935\pi$
$674$	−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	$-0.332206\pi$
$677$	17.6982	+	3.12068i	0.680199	+	0.119937i	0.177135	+	0.984187i	$0.443317\pi$
$678$	−14.5881	−	3.24409i	−0.560254	−	0.124588i
$679$	−20.7414	−	7.54926i	−0.795983	−	0.289714i
$680$	0.682038	+	4.54631i	0.0261550	+	0.174343i
$681$	10.9786	+	33.8850i	0.420699	+	1.29848i
$682$	6.50551	+	38.8311i	0.249109	+	1.48692i
$683$	−5.01354	−	2.89457i	−0.191838	−	0.110758i	0.401005	−	0.916076i	$-0.368661\pi$
$683$	−5.01354	−	2.89457i	−0.191838	−	0.110758i	−0.592843	+	0.805318i	$0.701994\pi$
$684$	−0.0210428	+	0.0209880i	−0.000804591	+	0.000802496i
$685$	3.55083	−	2.05007i	0.135670	−	0.0783293i
$686$	−15.5537	−	18.8610i	−0.593843	−	0.720117i
$687$	7.47072	−	18.4462i	0.285026	−	0.703767i
$688$	18.8748	+	11.7748i	0.719596	+	0.448911i
$689$	0.484598	+	2.74829i	0.0184617	+	0.104702i
$690$	−0.745878	+	1.16911i	−0.0283951	+	0.0445073i
$691$	−8.42802	+	10.0441i	−0.320617	+	0.382097i	−0.902147	−	0.431428i	$-0.858010\pi$
$691$	−8.42802	+	10.0441i	−0.320617	+	0.382097i	0.581530	+	0.813525i	$0.302454\pi$
$692$	−39.4731	+	6.26693i	−1.50054	+	0.238233i
$693$	39.9787	−	4.13427i	1.51866	−	0.157048i
$694$	−22.4207	−	19.1419i	−0.851079	−	0.726617i
$695$	2.64531	−	0.962815i	0.100342	−	0.0365217i
$696$	−9.16305	+	38.1197i	−0.347325	+	1.44493i
$697$	−42.2167	+	35.4240i	−1.59907	+	1.34178i
$698$	−10.8363	+	18.4041i	−0.410159	+	0.696607i
$699$	−7.49727	−	0.268094i	−0.283573	−	0.0101403i
$700$	14.1513	−	23.5716i	0.534871	−	0.890923i
$701$		−	3.89204i		−	0.147000i	−0.997295	−	0.0735002i	$-0.976583\pi$
$701$		−	3.89204i		−	0.147000i	0.997295	−	0.0735002i	$-0.0234170\pi$
$702$	−6.78104	+	22.6984i	−0.255934	+	0.856696i
$703$	−0.0469423			−0.00177046
$704$	−11.2485	−	36.6463i	−0.423944	−	1.38116i
$705$	−1.63957	+	0.870013i	−0.0617496	+	0.0327666i
$706$	4.32461	+	2.54631i	0.162759	+	0.0958315i
$707$	33.3805	+	39.7814i	1.25540	+	1.49613i
$708$	16.1355	+	10.4892i	0.606411	+	0.394210i
$709$	−10.4928	−	28.8286i	−0.394064	−	1.08268i	−0.965128	−	0.261777i	$-0.915692\pi$
$709$	−10.4928	−	28.8286i	−0.394064	−	1.08268i	0.571065	−	0.820905i	$-0.306531\pi$
$710$	−0.266965	−	0.227924i	−0.0100190	−	0.00855385i
$711$	13.2493	−	3.77517i	0.496886	−	0.141580i
$712$	0.257818	−	10.0596i	0.00966214	−	0.377000i
$713$	−8.72901	−	7.32451i	−0.326904	−	0.274305i
$714$	−1.70709	+	38.5228i	−0.0638862	+	1.44168i
$715$	−4.39147	+	0.774335i	−0.164232	+	0.0289585i
$716$	−42.3098	−	8.20790i	−1.58119	−	0.306744i
$717$	−19.2873	+	15.0429i	−0.720296	+	0.561786i
$718$	19.9400	+	24.1800i	0.744154	+	0.902390i
$719$	10.3301	+	17.8922i	0.385246	+	0.667266i	0.991803	−	0.127774i	$-0.0407831\pi$
$719$	10.3301	+	17.8922i	0.385246	+	0.667266i	−0.606557	+	0.795040i	$0.707450\pi$
$720$	−3.32899	−	0.957931i	−0.124064	−	0.0357000i
$721$	6.33789	−	10.9775i	0.236035	−	0.408825i
$722$	−26.5007	+	4.43975i	−0.986254	+	0.165230i
$723$	−19.3031	−	17.4098i	−0.717889	−	0.647479i
$724$	13.4962	+	39.1486i	0.501582	+	1.45495i
$725$	13.4575	−	36.9742i	0.499799	−	1.37319i
$726$	−19.8070	+	21.5873i	−0.735108	+	0.801181i
$727$	5.27477	−	29.9147i	0.195630	−	1.10947i	−0.715888	−	0.698215i	$-0.753978\pi$
$727$	5.27477	−	29.9147i	0.195630	−	1.10947i	0.911518	−	0.411259i	$-0.134911\pi$
$728$	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
$732$	−14.8225	−	19.6893i	−0.547857	−	0.727736i
$733$	12.3847	−	34.0267i	0.457439	−	1.25680i	−0.469946	−	0.882695i	$-0.655727\pi$
$733$	12.3847	−	34.0267i	0.457439	−	1.25680i	0.927385	−	0.374108i	$-0.122051\pi$
$734$	21.3498	−	12.0844i	0.788036	−	0.446042i
$735$	−0.273660	+	0.303419i	−0.0100941	+	0.0111918i
$736$	9.36239	+	5.95230i	0.345102	+	0.219405i
$737$	−0.547262	+	0.947886i	−0.0201587	+	0.0349158i
$738$	−11.0379	−	40.0326i	−0.406310	−	1.47362i
$739$	4.81815	−	2.78176i	0.177239	−	0.102329i	−0.408756	−	0.912644i	$-0.634037\pi$
$739$	4.81815	−	2.78176i	0.177239	−	0.102329i	0.585995	+	0.810315i	$0.300704\pi$
$740$	−2.65436	−	4.78441i	−0.0975762	−	0.175878i
$741$	0.0218092	−	0.0170098i	0.000801181	−	0.000624872i
$742$	−3.42275	−	0.0292349i	−0.125653	−	0.00107325i
$743$	6.80955	+	38.6189i	0.249818	+	1.41679i	0.809032	+	0.587765i	$0.199992\pi$
$743$	6.80955	+	38.6189i	0.249818	+	1.41679i	−0.559214	+	0.829024i	$0.688897\pi$
$744$	11.3572	−	26.0997i	0.416374	−	0.956860i
$745$	−0.255922	−	0.214744i	−0.00937627	−	0.00786762i
$746$	22.1147	−	7.83586i	0.809678	−	0.286891i
$747$	3.34115	+	11.7260i	0.122246	+	0.429033i
$748$	−33.9730	−	41.9214i	−1.24218	−	1.53280i
$749$	−3.58507	−	9.84991i	−0.130996	−	0.359908i
$750$	6.47657	+	2.68763i	0.236491	+	0.0981383i
$751$	20.3773	−	17.0986i	0.743579	−	0.623937i	−0.190217	−	0.981742i	$-0.560919\pi$
$751$	20.3773	−	17.0986i	0.743579	−	0.623937i	0.933796	+	0.357805i	$0.116475\pi$
$752$	6.98087	+	13.1056i	0.254566	+	0.477913i
$753$	46.0693	−	24.4460i	1.67886	−	0.890863i
$754$	12.7711	−	34.1772i	0.465096	−	1.24466i
$755$			6.02836i			0.219394i
$756$	−25.8609	−	13.2466i	−0.940552	−	0.481774i
$757$			9.99796i			0.363382i	0.983356	+	0.181691i	$0.0581571\pi$
$757$			9.99796i			0.363382i	−0.983356	+	0.181691i	$0.941843\pi$
$758$	−12.7827	−	4.77655i	−0.464288	−	0.173492i
$759$	0.581682	−	16.2668i	0.0211137	−	0.590446i
$760$	0.00251945	+	0.00316376i	9.13899e−5	+	0.000114762i
$761$	36.4687	−	30.6009i	1.32199	−	1.10928i	0.336112	−	0.941822i	$-0.390888\pi$
$761$	36.4687	−	30.6009i	1.32199	−	1.10928i	0.985879	−	0.167460i	$-0.0535564\pi$
$762$	51.4912	−	6.74481i	1.86533	−	0.244339i
$763$	16.1103	+	44.2627i	0.583232	+	1.60242i
$764$	1.55399	−	1.25935i	0.0562213	−	0.0455617i
$765$	−4.85019	+	0.501567i	−0.175359	+	0.0181342i
$766$	5.68833	+	16.0539i	0.205528	+	0.580051i
$767$	−13.7198	−	11.5123i	−0.495395	−	0.415685i
$768$	−7.62145	+	26.6442i	−0.275015	+	0.961440i
$769$	−7.87549	−	44.6641i	−0.283998	−	1.61063i	−0.708844	−	0.705365i	$-0.750783\pi$
$769$	−7.87549	−	44.6641i	−0.283998	−	1.61063i	0.424847	−	0.905265i	$-0.360328\pi$
$770$	0.0467141	−	5.46917i	0.00168346	−	0.197095i
$771$	−6.33874	−	2.56719i	−0.228284	−	0.0924552i
$772$	−19.2266	−	34.6554i	−0.691981	−	1.24728i
$773$	−7.37741	+	4.25935i	−0.265347	+	0.153198i	−0.626771	−	0.779203i	$-0.715624\pi$
$773$	−7.37741	+	4.25935i	−0.265347	+	0.153198i	0.361424	+	0.932401i	$0.382291\pi$
$774$	−13.3938	+	19.4261i	−0.481431	+	0.698258i
$775$	−14.2832	+	24.7392i	−0.513068	+	0.888659i
$776$	−21.8834	−	4.43954i	−0.785567	−	0.159370i
$777$	−14.1453	−	43.6590i	−0.507458	−	1.56626i
$778$	2.02252	+	3.57325i	0.0725110	+	0.128107i
$779$	−0.0165822	+	0.0455592i	−0.000594118	+	0.00163233i
$780$	2.96687	+	1.26099i	0.106231	+	0.0451508i
$781$	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
$786$	24.7719	−	7.79282i	0.883585	−	0.277961i
$787$	6.01089	−	16.5148i	0.214265	−	0.588688i	−0.785271	−	0.619152i	$-0.787476\pi$
$787$	6.01089	−	16.5148i	0.214265	−	0.588688i	0.999536	+	0.0304642i	$0.00969856\pi$
$788$	3.87385	+	11.2369i	0.138000	+	0.400299i
$789$	4.76880	−	22.3435i	0.169774	−	0.795449i
$790$	−0.309765	−	1.84897i	−0.0110209	−	0.0657835i
$791$	−8.52906	+	14.7728i	−0.303259	+	0.525259i
$792$	39.3754	−	10.1362i	1.39914	−	0.360175i
$793$	11.4675	+	19.8623i	0.407224	+	0.705332i
$794$	4.44919	−	3.66902i	0.157896	−	0.130208i
$795$	−0.0598793	−	0.428666i	−0.00212370	−	0.0152032i
$796$	−3.21907	+	16.5935i	−0.114097	+	0.588142i
$797$	−14.0527	+	2.47787i	−0.497773	+	0.0877708i	−0.416898	−	0.908953i	$-0.636883\pi$
$797$	−14.0527	+	2.47787i	−0.497773	+	0.0877708i	−0.0808752	+	0.996724i	$0.525772\pi$
$798$	0.0156446	+	0.0301009i	0.000553813	+	0.00106556i
$799$	16.0115	+	13.4352i	0.566444	+	0.475303i
$800$	10.6197	−	25.7056i	0.375463	−	0.908830i
$801$	10.6461	+	0.762359i	0.376160	+	0.0269366i
$802$	2.04547	−	2.39584i	0.0722282	−	0.0846001i
$803$	6.64299	+	18.2515i	0.234426	+	0.644080i
$804$	0.705194	−	0.358901i	0.0248703	−	0.0126574i
$805$	1.01748	+	1.21258i	0.0358614	+	0.0427379i
$806$	−13.4398	+	22.8260i	−0.473397	+	0.804010i
$807$	11.2845	+	7.06449i	0.397234	+	0.248682i
$808$	39.3654	+	34.7885i	1.38487	+	1.22386i
$809$	−41.9742			−1.47573			−0.737867	−	0.674946i	$-0.764167\pi$
$809$	−41.9742			−1.47573			−0.737867	+	0.674946i	$0.764167\pi$
$810$	1.17686	−	3.48063i	0.0413505	−	0.122297i
$811$			34.8911i			1.22519i	0.790397	+	0.612595i	$0.209875\pi$
$811$			34.8911i			1.22519i	−0.790397	+	0.612595i	$0.790125\pi$
$812$	38.3672	+	23.0340i	1.34643	+	0.808334i
$813$	19.6140	−	31.3306i	0.687893	−	1.09881i
$814$	55.3397	+	32.5838i	1.93966	+	1.14206i
$815$	2.56013	−	2.14820i	0.0896775	−	0.0752483i
$816$	4.07384	+	38.7955i	0.142613	+	1.35811i
$817$	0.0258874	−	0.00942225i	0.000905686	−	0.000329643i
$818$	17.3300	−	20.2984i	0.605928	−	0.709718i
$819$	22.3919	+	15.1582i	0.782438	+	0.529669i
$820$	−5.58108	+	0.886079i	−0.194900	+	0.0309432i
$821$	2.36456	−	2.81797i	0.0825236	−	0.0983478i	−0.723203	−	0.690636i	$-0.757331\pi$
$821$	2.36456	−	2.81797i	0.0825236	−	0.0983478i	0.805726	+	0.592288i	$0.201775\pi$
$822$	30.8706	−	16.0447i	1.07674	−	0.559623i
$823$	−4.05525	−	22.9985i	−0.141357	−	0.801676i	−0.970220	−	0.242225i	$-0.922123\pi$
$823$	−4.05525	−	22.9985i	−0.141357	−	0.801676i	0.828863	−	0.559452i	$-0.188988\pi$
$824$	4.69305	−	11.9335i	0.163490	−	0.415722i
$825$	−40.4135	+	5.64525i	−1.40702	+	0.196543i
$826$	16.9478	−	13.9760i	0.589690	−	0.486287i
$827$	−17.6991	+	10.2186i	−0.615456	+	0.355334i	−0.775098	−	0.631841i	$-0.782299\pi$
$827$	−17.6991	+	10.2186i	−0.615456	+	0.355334i	0.159642	+	0.987175i	$0.448966\pi$
$828$	−6.76201	+	9.63042i	−0.234996	+	0.334680i
$829$	−18.2976	−	10.5641i	−0.635503	−	0.366908i	0.147377	−	0.989080i	$-0.452917\pi$
$829$	−18.2976	−	10.5641i	−0.635503	−	0.366908i	−0.782880	+	0.622173i	$0.786250\pi$
$830$	1.63640	−	0.274152i	0.0568003	−	0.00951594i
$831$	−38.3046	−	8.17540i	−1.32877	−	0.283602i
$832$	10.0505	−	23.7510i	0.348440	−	0.823419i
$833$	4.32373	+	1.57371i	0.149808	+	0.0545258i
$834$	22.7861	−	7.16811i	0.789018	−	0.248211i
$835$	−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	0.726446	+	0.687223i	$0.241171\pi$
$839$	−5.53919	+	31.4143i	−0.191234	+	1.08454i	−0.917680	+	0.397320i	$0.869940\pi$
$840$	−2.18328	+	3.29657i	−0.0753305	+	0.113743i
$841$	32.9314	+	11.9860i	1.13557	+	0.413312i
$842$	25.9000	+	45.7583i	0.892572	+	1.57693i
$843$	−53.1416	+	17.2176i	−1.83029	+	0.593005i
$844$	−0.142300	+	8.32946i	−0.00489817	+	0.286712i
$845$	0.651848	+	0.376345i	0.0224242	+	0.0129466i
$846$	−14.2255	+	6.75923i	−0.489082	+	0.232387i
$847$	16.7204	+	28.9607i	0.574521	+	0.995100i
$848$	−3.42860	+	0.484453i	−0.117739	+	0.0166362i
$849$	−13.2683	+	32.7612i	−0.455366	+	1.12436i
$850$	0.334379	−	39.1482i	0.0114691	−	1.34277i
$851$	−18.3038	+	3.22745i	−0.627445	+	0.110636i
$852$	−2.17746	−	2.03241i	−0.0745985	−	0.0696292i
$853$	−10.1055	+	12.0433i	−0.346006	+	0.412354i	−0.910780	−	0.412891i	$-0.864519\pi$
$853$	−10.1055	+	12.0433i	−0.346006	+	0.412354i	0.564774	+	0.825246i	$0.308963\pi$
$854$	−26.5153	+	9.39510i	−0.907335	+	0.321494i
$855$	−0.00347467	+	0.00251562i	−0.000118831	+	8.60323e-5i
$856$	−5.06493	−	9.31608i	−0.173116	−	0.318417i
$857$	30.3992	−	11.0644i	1.03842	−	0.377953i	0.234138	−	0.972203i	$-0.424773\pi$
$857$	30.3992	−	11.0644i	1.03842	−	0.377953i	0.804280	+	0.594250i	$0.202551\pi$
$858$	−37.5176	+	4.91441i	−1.28083	+	0.167775i
$859$	7.62842	+	9.09120i	0.260278	+	0.310188i	0.880319	−	0.474382i	$-0.157328\pi$
$859$	7.62842	+	9.09120i	0.260278	+	0.310188i	−0.620041	+	0.784570i	$0.712884\pi$
$860$	2.42413	+	2.10569i	0.0826623	+	0.0718034i
$861$	−47.3693	−	1.69388i	−1.61434	−	0.0577271i
$862$	5.64766	−	15.1139i	0.192360	−	0.514782i
$863$	−25.9229			−0.882426			−0.441213	−	0.897402i	$-0.645452\pi$
$863$	−25.9229			−0.882426			−0.441213	+	0.897402i	$0.645452\pi$
$864$	−27.8601	−	9.37095i	−0.947820	−	0.318806i
$865$	−5.76875			−0.196143
$866$	−3.71970	+	9.95441i	−0.126400	+	0.338265i
$867$	11.9359	+	22.4936i	0.405365	+	0.763923i
$868$	−24.5279	−	21.3058i	−0.832531	−	0.723166i
$869$	14.1443	+	16.8565i	0.479811	+	0.571816i
$870$	−2.16893	+	5.22662i	−0.0735336	+	0.177199i
$871$	−0.691961	+	0.251853i	−0.0234462	+	0.00853373i
$872$	22.7603	+	41.8637i	0.770762	+	1.41769i
$873$	5.76806	−	22.9705i	0.195219	−	0.777434i
$874$	0.0129497	−	0.00458845i	0.000438031	−	0.000155207i
$875$	5.14475	−	6.13128i	0.173924	−	0.207275i
$876$	3.16501	−	13.6801i	0.106936	−	0.462207i
$877$	−23.4419	+	4.13345i	−0.791578	+	0.139577i	−0.554796	−	0.831986i	$-0.687204\pi$
$877$	−23.4419	+	4.13345i	−0.791578	+	0.139577i	−0.236782	+	0.971563i	$0.576093\pi$
$878$	−0.246879	+	28.9039i	−0.00833175	+	0.975461i
$879$	4.47580	+	5.73866i	0.150965	+	0.193560i
$880$	−0.774103	−	5.47853i	−0.0260950	−	0.184681i
$881$	19.7098	+	34.1384i	0.664040	+	1.15015i	0.979545	+	0.201227i	$0.0644930\pi$
$881$	19.7098	+	34.1384i	0.664040	+	1.15015i	−0.315504	+	0.948924i	$0.602174\pi$
$882$	−2.43380	+	2.46929i	−0.0819505	+	0.0831454i
$883$	−39.3493	−	22.7183i	−1.32421	−	0.764533i	−0.339812	−	0.940493i	$-0.610364\pi$
$883$	−39.3493	−	22.7183i	−1.32421	−	0.764533i	−0.984397	+	0.175960i	$0.943697\pi$
$884$	0.620096	−	36.2970i	0.0208561	−	1.22080i
$885$	2.06274	+	1.86043i	0.0693383	+	0.0625377i
$886$	19.6586	+	34.7315i	0.660444	+	1.16683i
$887$	−3.61326	−	1.31512i	−0.121321	−	0.0441573i	0.280646	−	0.959811i	$-0.409451\pi$
$887$	−3.61326	−	1.31512i	−0.121321	−	0.0441573i	−0.401967	+	0.915654i	$0.631673\pi$
$888$	−20.7039	−	41.5547i	−0.694776	−	1.39448i
$889$	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
$894$	−2.08879	−	1.91653i	−0.0698598	−	0.0640985i
$895$	−5.84553	−	2.12760i	−0.195395	−	0.0711178i
$896$	26.4004	+	17.4248i	0.881975	+	0.582121i
$897$	7.33437	−	8.13195i	0.244888	−	0.271518i
$898$	−15.7617	+	2.64060i	−0.525974	+	0.0881181i
$899$	−40.2677	−	23.2486i	−1.34300	−	0.775384i
$900$	26.7198	+	12.5021i	0.890661	+	0.416736i
$901$	−4.22107	+	2.43704i	−0.140624	+	0.0811894i
$902$	51.1722	−	42.1991i	1.70385	−	1.40508i
$903$	16.5640	+	21.2375i	0.551214	+	0.706740i
$904$	−6.31556	+	16.0592i	−0.210052	+	0.534121i
$905$	1.03788	+	5.88612i	0.0345003	+	0.195661i
$906$	−2.26455	+	51.1026i	−0.0752347	+	1.69777i
$907$	6.16891	−	7.35182i	0.204835	−	0.244113i	−0.653840	−	0.756632i	$-0.726843\pi$
$907$	6.16891	−	7.35182i	0.204835	−	0.244113i	0.858676	+	0.512519i	$0.171288\pi$
$908$	40.6207	−	6.44913i	1.34804	−	0.214022i
$909$	−38.7743	+	40.0177i	−1.28606	+	1.32730i
$910$	2.38923	−	2.79848i	0.0792022	−	0.0927687i
$911$	27.8833	−	10.1487i	0.923814	−	0.336241i	0.164059	−	0.986451i	$-0.447541\pi$
$911$	27.8833	−	10.1487i	0.923814	−	0.336241i	0.759755	+	0.650210i	$0.225319\pi$
$912$	0.0201690	+	0.0277658i	0.000667862	+	0.000919417i
$913$	−14.9185	+	12.5181i	−0.493730	+	0.414289i
$914$	46.3111	+	27.2677i	1.53183	+	0.901936i
$915$	−1.66736	−	3.14219i	−0.0551211	−	0.103877i
$916$	−19.7025	−	11.8285i	−0.650987	−	0.390824i
$917$		−	29.6416i		−	0.978851i
$918$	−41.3037	+	2.42983i	−1.36322	+	0.0801963i
$919$	−18.2259			−0.601217			−0.300608	−	0.953748i	$-0.597190\pi$
$919$	−18.2259			−0.601217			−0.300608	+	0.953748i	$0.597190\pi$
$920$	1.19990	+	1.06040i	0.0395597	+	0.0349602i
$921$	−1.17715	+	32.9190i	−0.0387883	+	1.08472i
$922$	−5.50252	+	9.34539i	−0.181216	+	0.307774i
$923$	1.78176	+	2.12342i	0.0586474	+	0.0698933i
$924$	2.45049	−	46.3448i	0.0806153	−	1.52463i
$925$	15.9362	+	43.7844i	0.523980	+	1.43962i
$926$	−20.1255	+	23.5728i	−0.661366	+	0.774651i
$927$	12.4158	+	5.55281i	0.407789	+	0.182378i
$928$	41.8407	+	17.2855i	1.37349	+	0.567426i
$929$	−1.32347	−	1.11052i	−0.0434216	−	0.0364351i	0.620819	−	0.783954i	$-0.286800\pi$
$929$	−1.32347	−	1.11052i	−0.0434216	−	0.0364351i	−0.664240	+	0.747519i	$0.731245\pi$
$930$	2.20966	−	3.46349i	0.0724577	−	0.113572i
$931$	0.00398643		0.000702915i	0.000130650		2.30371e-5i
$932$	−1.64975	+	8.50409i	−0.0540395	+	0.278561i
$933$	27.8737	+	11.2888i	0.912543	+	0.369580i
$934$	2.65757	−	2.19156i	0.0869585	−	0.0717101i
$935$	−3.89411	−	6.74480i	−0.127351	−	0.220579i
$936$	24.6765	+	11.8040i	0.806578	+	0.385825i
$937$	−3.54099	+	6.13317i	−0.115679	+	0.200362i	−0.918051	−	0.396462i	$-0.870238\pi$
$937$	−3.54099	+	6.13317i	−0.115679	+	0.200362i	0.802372	+	0.596824i	$0.203571\pi$
$938$	−0.149233	−	0.890767i	−0.00487264	−	0.0290846i
$939$	1.24747	−	0.404172i	0.0407095	−	0.0131897i
$940$	0.698521	+	2.02621i	0.0227833	+	0.0660877i
$941$	−3.52638	+	9.68865i	−0.114957	+	0.315841i	−0.983806	−	0.179235i	$-0.942638\pi$
$941$	−3.52638	+	9.68865i	−0.114957	+	0.315841i	0.868850	+	0.495076i	$0.164860\pi$
$942$	9.96355	−	44.8045i	0.324630	−	1.45981i
$943$	−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	$-0.499525\pi$
$947$	−10.4361	−	1.84016i	−0.339127	−	0.0597973i	−0.340618	+	0.940202i	$0.610636\pi$
$948$	−1.93132	−	15.7902i	−0.0627264	−	0.512842i
$949$	−4.46924	+	12.2791i	−0.145078	+	0.398598i
$950$	−0.0169656	−	0.0299736i	−0.000550436	−	0.000972472i
$951$	−33.3052	−	7.10839i	−1.08000	−	0.230505i
$952$	43.6370	+	8.85275i	1.41428	+	0.286919i
$953$	−3.01897	+	5.22901i	−0.0977940	+	0.169384i	−0.910771	−	0.412911i	$-0.864512\pi$
$953$	−3.01897	+	5.22901i	−0.0977940	+	0.169384i	0.812977	+	0.582295i	$0.197845\pi$
$954$	−0.346570	−	3.65632i	−0.0112206	−	0.118378i
$955$	0.250024	−	0.144351i	0.00809058	−	0.00467110i
$956$	13.7021	+	24.6975i	0.443156	+	0.798776i
$957$	−9.18871	−	65.7806i	−0.297029	−	2.12638i
$958$	0.175701	−	20.5707i	0.00567665	−	0.664608i
$959$	−6.89588	−	39.1085i	−0.222680	−	1.26288i
$960$	−1.68946	+	3.62566i	−0.0545270	+	0.117018i
$961$	2.11229	+	1.77242i	0.0681384	+	0.0571749i
$962$	14.4299	+	40.7247i	0.465237	+	1.31302i
$963$	10.1171	−	4.91349i	0.326019	−	0.158335i
$964$	−23.3196	+	18.8982i	−0.751075	+	0.608670i
$965$	−1.95645	−	5.37529i	−0.0629802	−	0.173037i
$966$	8.16969	+	10.6613i	0.262856	+	0.343023i
$967$	15.4521	−	12.9658i	0.496906	−	0.416954i	−0.359588	−	0.933111i	$-0.617083\pi$
$967$	15.4521	−	12.9658i	0.496906	−	0.416954i	0.856494	+	0.516158i	$0.172638\pi$
$968$	21.0742	+	26.4636i	0.677349	+	0.850572i
$969$	0.0409447	+	0.0256328i	0.00131533	+	0.000823443i
$970$	−3.01901	−	1.12812i	−0.0969347	−	0.0362219i
$971$		−	31.1328i		−	0.999100i	−0.866285	−	0.499550i	$-0.833499\pi$
$971$		−	31.1328i		−	0.999100i	0.866285	−	0.499550i	$-0.166501\pi$
$972$	11.2838	−	29.0633i	0.361927	−	0.932207i
$973$		−	27.2654i		−	0.874088i
$974$	1.26072	−	3.37385i	0.0403961	−	0.108105i
$975$	−23.2695	−	14.5675i	−0.745219	−	0.466533i
$976$	−25.1166	+	13.3787i	−0.803964	+	0.428240i
$977$	−14.4476	+	12.1229i	−0.462219	+	0.387848i	−0.843947	−	0.536427i	$-0.819774\pi$
$977$	−14.4476	+	12.1229i	−0.462219	+	0.387848i	0.381728	+	0.924275i	$0.375329\pi$
$978$	22.5093	−	17.2487i	0.719768	−	0.551553i
$979$	5.83071	+	16.0198i	0.186350	+	0.511993i
$980$	0.297055	+	0.366554i	0.00948907	+	0.0117091i
$981$	−45.4633	+	22.0798i	−1.45153	+	0.704954i
$982$	−24.2507	+	8.59269i	−0.773871	+	0.274204i
$983$	24.2461	+	20.3449i	0.773330	+	0.648901i	0.941559	−	0.336847i	$-0.109361\pi$
$983$	24.2461	+	20.3449i	0.773330	+	0.648901i	−0.168229	+	0.985748i	$0.553805\pi$
$984$	−47.6439	+	5.41479i	−1.51883	+	0.172617i
$985$	0.297906	+	1.68951i	0.00949206	+	0.0538322i
$986$	63.7211	+	0.544264i	2.02929	+	0.0173329i
$987$	2.48703	+	17.8043i	0.0791632	+	0.566717i
$988$	−0.0154937	−	0.0279269i	−0.000492920	−	0.000888474i
$989$	9.44623	−	5.45378i	0.300373	−	0.173420i
$990$	5.84239	−	0.553781i	0.185683	−	0.0176003i
$991$	22.5906	−	39.1281i	0.717614	−	1.24294i	−0.244328	−	0.969693i	$-0.578567\pi$
$991$	22.5906	−	39.1281i	0.717614	−	1.24294i	0.961942	−	0.273252i	$-0.0880993\pi$
$992$	−27.7361	−	17.6337i	−0.880621	−	0.559870i
$993$	−41.7089	−	8.90201i	−1.32359	−	0.282497i
$994$	−2.95878	+	1.67472i	−0.0938467	+	0.0531189i
$995$	−0.834426	+	2.29257i	−0.0264531	+	0.0726792i
$996$	13.9748	−	1.70928i	0.442809	−	0.0541606i
$997$	−20.6197	−	3.63580i	−0.653031	−	0.115147i	−0.162689	−	0.986677i	$-0.552017\pi$
$997$	−20.6197	−	3.63580i	−0.653031	−	0.115147i	−0.490342	+	0.871530i	$0.663128\pi$
$998$	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.133.22	yes	204
3.2	odd	2		648.2.t.a.397.13		204
4.3	odd	2		864.2.bf.a.241.11		204
8.3	odd	2		864.2.bf.a.241.24		204
8.5	even	2	inner	216.2.t.a.133.17	yes	204
24.5	odd	2		648.2.t.a.397.18		204
27.13	even	9	inner	216.2.t.a.13.17	✓	204
27.14	odd	18		648.2.t.a.253.18		204
108.67	odd	18		864.2.bf.a.337.24		204
216.13	even	18	inner	216.2.t.a.13.22	yes	204
216.67	odd	18		864.2.bf.a.337.11		204
216.149	odd	18		648.2.t.a.253.13		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.13.17	✓	204	27.13	even	9	inner
216.2.t.a.13.22	yes	204	216.13	even	18	inner
216.2.t.a.133.17	yes	204	8.5	even	2	inner
216.2.t.a.133.22	yes	204	1.1	even	1	trivial
648.2.t.a.253.13		204	216.149	odd	18
648.2.t.a.253.18		204	27.14	odd	18
648.2.t.a.397.13		204	3.2	odd	2
648.2.t.a.397.18		204	24.5	odd	2
864.2.bf.a.241.11		204	4.3	odd	2
864.2.bf.a.241.24		204	8.3	odd	2
864.2.bf.a.337.11		204	216.67	odd	18
864.2.bf.a.337.24		204	108.67	odd	18

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)

\(f(q)\)	\(=\)	\(q+(0.495022 - 1.32475i) q^{2} +(0.919076 - 1.46809i) q^{3} +(-1.50991 - 1.31156i) q^{4} +(-0.185555 - 0.221136i) q^{5} +(-1.48989 - 1.94428i) q^{6} +(-2.62731 + 0.956263i) q^{7} +(-2.48492 + 1.35099i) q^{8} +(-1.31060 - 2.69858i) q^{9} +O(q^{10})\)	\(q+(0.495022 - 1.32475i) q^{2} +(0.919076 - 1.46809i) q^{3} +(-1.50991 - 1.31156i) q^{4} +(-0.185555 - 0.221136i) q^{5} +(-1.48989 - 1.94428i) q^{6} +(-2.62731 + 0.956263i) q^{7} +(-2.48492 + 1.35099i) q^{8} +(-1.31060 - 2.69858i) q^{9} +(-0.384803 + 0.136346i) q^{10} +(3.08006 - 3.67067i) q^{11} +(-3.31321 + 1.01126i) q^{12} +(3.17478 - 0.559799i) q^{13} +(-0.0337716 + 3.95389i) q^{14} +(-0.495188 + 0.0691714i) q^{15} +(0.559631 + 3.96066i) q^{16} +(2.81522 + 4.87610i) q^{17} +(-4.22371 + 0.400352i) q^{18} +(0.00428975 + 0.00247669i) q^{19} +(-0.00986189 + 0.577261i) q^{20} +(-1.01082 + 4.73602i) q^{21} +(-3.33801 - 5.89736i) q^{22} +(1.84294 + 0.670777i) q^{23} +(-0.300448 + 4.88976i) 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} +(-0.153494 + 0.690239i) q^{30} +(-5.45972 - 1.98718i) q^{31} +(5.52390 + 1.21924i) q^{32} +(-2.55808 - 7.89544i) q^{33} +(7.85319 - 1.31567i) q^{34} +(0.698975 + 0.403553i) q^{35} +(-1.56047 + 5.79353i) q^{36} +(-8.20717 + 4.73841i) q^{37} +(0.00540451 - 0.00445682i) q^{38} +(2.09603 - 5.17537i) q^{39} +(0.759842 + 0.298821i) q^{40} +(1.69965 + 9.63917i) q^{41} +(5.77365 + 3.68351i) q^{42} +(3.57494 - 4.26045i) q^{43} +(-9.46489 + 1.50269i) q^{44} +(-0.353565 + 0.790555i) q^{45} +(1.80091 - 2.10938i) q^{46} +(3.48835 - 1.26966i) q^{47} +(6.32896 + 2.81856i) q^{48} +(0.626015 - 0.525289i) q^{49} +(-5.99175 - 3.52791i) q^{50} +(9.74597 + 0.348505i) q^{51} +(-5.52782 - 3.31866i) q^{52} +0.865665i q^{53} +(-3.29416 + 6.56875i) q^{54} -1.38324 q^{55} +(5.23675 - 5.92571i) q^{56} +(0.00757862 - 0.00402149i) q^{57} +(5.74234 - 9.75270i) q^{58} +(-3.57109 - 4.25586i) q^{59} +(0.838409 + 0.545025i) q^{60} +(2.43327 + 6.68534i) q^{61} +(-5.33519 + 6.24905i) q^{62} +(6.02390 + 5.83673i) q^{63} +(4.34964 - 6.71421i) q^{64} +(-0.712888 - 0.598184i) q^{65} +(-11.7258 - 0.519613i) q^{66} +(-0.224950 + 0.0396647i) q^{67} +(2.14457 - 11.0548i) q^{68} +(2.67857 - 2.08912i) q^{69} +(0.880614 - 0.726197i) q^{70} +(0.429923 + 0.744648i) q^{71} +(6.90249 + 4.93515i) q^{72} +(-2.02670 + 3.51035i) q^{73} +(2.21446 + 13.2180i) q^{74} +(-6.32379 - 5.70356i) q^{75} +(-0.00322880 - 0.00936583i) q^{76} +(-4.58214 + 12.5893i) q^{77} +(-5.81847 - 5.33862i) 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} +(7.73780 - 5.82520i) q^{84} +(0.555903 - 1.52733i) q^{85} +(-3.87434 - 6.84491i) q^{86} +(9.28361 - 10.2932i) q^{87} +(-2.69465 + 13.2824i) q^{88} +(-1.77889 + 3.08112i) q^{89} +(0.872263 + 0.859727i) q^{90} +(-7.80581 + 4.50669i) q^{91} +(-1.90291 - 3.42994i) q^{92} +(-7.93526 + 6.18901i) q^{93} +(0.0448395 - 5.24969i) q^{94} +(-0.000248300 - 0.00140818i) q^{95} +(6.86685 - 6.98902i) q^{96} +(6.04757 + 5.07452i) q^{97} +(-0.385983 - 1.08934i) 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

Fields

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Database

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