LMFDB - Embedded newform 288.2.bf.a.11.35

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(11,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 15, 4]))

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

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

chi := DirichletCharacter("288.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.bf (of order $24$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			11.35
Character	$\chi$	$=$	288.11
Dual form			288.2.bf.a.131.35

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.857729 + 1.12441i) q^{2} +(0.978339 + 1.42928i) q^{3} +(-0.528601 + 1.92888i) q^{4} +(0.00231185 + 0.0175602i) q^{5} +(-0.767953 + 2.32599i) q^{6} +(-0.191417 - 0.714379i) q^{7} +(-2.62225 + 1.06009i) q^{8} +(-1.08571 + 2.79665i) q^{9} +O(q^{10})$	\(q+(0.857729 + 1.12441i) q^{2} +(0.978339 + 1.42928i) q^{3} +(-0.528601 + 1.92888i) q^{4} +(0.00231185 + 0.0175602i) q^{5} +(-0.767953 + 2.32599i) q^{6} +(-0.191417 - 0.714379i) q^{7} +(-2.62225 + 1.06009i) q^{8} +(-1.08571 + 2.79665i) q^{9} +(-0.0177620 + 0.0176614i) q^{10} +(0.235313 - 0.180562i) q^{11} +(-3.27407 + 1.13158i) q^{12} +(0.822172 - 1.07148i) q^{13} +(0.639071 - 0.827975i) q^{14} +(-0.0228368 + 0.0204841i) q^{15} +(-3.44116 - 2.03922i) q^{16} +3.82544 q^{17} +(-4.07582 + 1.17799i) q^{18} +(2.78801 - 1.15483i) q^{19} +(-0.0350936 - 0.00482307i) q^{20} +(0.833779 - 0.972494i) q^{21} +(0.404862 + 0.109715i) q^{22} +(-4.24462 - 1.13734i) q^{23} +(-4.08062 - 2.71081i) q^{24} +(4.82933 - 1.29401i) q^{25} +(1.90998 + 0.00542337i) q^{26} +(-5.05939 + 1.18429i) q^{27} +(1.47913 + 0.00840004i) q^{28} +(-0.0726193 - 0.00956051i) q^{29} +(-0.0426204 - 0.00810809i) q^{30} +(-1.05130 + 0.606969i) q^{31} +(-0.658670 - 5.61838i) q^{32} +(0.488291 + 0.159679i) q^{33} +(3.28119 + 4.30136i) q^{34} +(0.0121021 - 0.00501286i) q^{35} +(-4.82050 - 3.57251i) q^{36} +(3.37678 - 8.15228i) q^{37} +(3.68986 + 2.14433i) q^{38} +(2.33581 + 0.126852i) q^{39} +(-0.0246777 - 0.0435965i) q^{40} +(-2.68522 + 10.0214i) q^{41} +(1.80864 + 0.103374i) q^{42} +(-0.251160 - 0.327319i) q^{43} +(0.223896 + 0.549337i) q^{44} +(-0.0516197 - 0.0125998i) q^{45} +(-2.36190 - 5.74823i) q^{46} +(3.79608 + 2.19167i) q^{47} +(-0.452004 - 6.91344i) q^{48} +(5.58848 - 3.22651i) q^{49} +(5.59726 + 4.32023i) q^{50} +(3.74257 + 5.46764i) q^{51} +(1.63215 + 2.15225i) q^{52} +(0.729680 - 1.76160i) q^{53} +(-5.67121 - 4.67304i) q^{54} +(0.00371472 + 0.00371472i) q^{55} +(1.25925 + 1.67036i) q^{56} +(4.37820 + 2.85504i) q^{57} +(-0.0515377 - 0.0898542i) q^{58} +(-11.5055 + 1.51473i) q^{59} +(-0.0274399 - 0.0548773i) q^{60} +(1.53696 - 11.6744i) q^{61} +(-1.58421 - 0.661479i) q^{62} +(2.20569 + 0.240279i) q^{63} +(5.75240 - 5.55966i) q^{64} +(0.0207161 + 0.0119604i) q^{65} +(0.239277 + 0.686001i) q^{66} +(-4.33352 + 5.64755i) q^{67} +(-2.02213 + 7.37881i) q^{68} +(-2.52709 - 7.17948i) q^{69} +(0.0160169 + 0.00930808i) q^{70} +(3.05989 + 3.05989i) q^{71} +(-0.117712 - 8.48446i) q^{72} +(-4.64074 + 4.64074i) q^{73} +(12.0629 - 3.19556i) q^{74} +(6.57423 + 5.63650i) q^{75} +(0.753788 + 5.98818i) q^{76} +(-0.174033 - 0.133540i) q^{77} +(1.86086 + 2.73521i) q^{78} +(2.64432 - 4.58009i) q^{79} +(0.0278536 - 0.0651419i) q^{80} +(-6.64248 - 6.07268i) q^{81} +(-13.5713 + 5.57634i) q^{82} +(-3.87888 - 0.510664i) q^{83} +(1.43509 + 2.12232i) q^{84} +(0.00884382 + 0.0671755i) q^{85} +(0.152613 - 0.563158i) q^{86} +(-0.0573816 - 0.113147i) q^{87} +(-0.425638 + 0.722934i) q^{88} +(8.84724 - 8.84724i) q^{89} +(-0.0301084 - 0.0688491i) q^{90} +(-0.922817 - 0.382243i) q^{91} +(4.43751 - 7.58617i) q^{92} +(-1.89606 - 0.908786i) q^{93} +(0.791674 + 6.14822i) q^{94} +(0.0267245 + 0.0462882i) q^{95} +(7.38585 - 6.43810i) q^{96} +(6.08042 - 10.5316i) q^{97} +(8.42133 + 3.51628i) q^{98} +(0.249488 + 0.854127i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	0.857729	+	1.12441i	0.606506	+	0.795079i
$2$	0.857729	+	1.12441i	0.606506	+	0.795079i
$3$	0.978339	+	1.42928i	0.564844	+	0.825198i
$3$	0.978339	+	1.42928i	0.564844	+	0.825198i
$4$	−0.528601	+	1.92888i	−0.264300	+	0.964440i
$5$	0.00231185	+	0.0175602i	0.00103389	+	0.00785317i	0.991954	−	0.126599i	$-0.0404060\pi$
$5$	0.00231185	+	0.0175602i	0.00103389	+	0.00785317i	−0.990920	+	0.134452i	$0.957073\pi$
$6$	−0.767953	+	2.32599i	−0.313516	+	0.949583i
$7$	−0.191417	−	0.714379i	−0.0723489	−	0.270010i	0.920270	−	0.391283i	$-0.127969\pi$
$7$	−0.191417	−	0.714379i	−0.0723489	−	0.270010i	−0.992619	+	0.121274i	$0.961302\pi$
$8$	−2.62225	+	1.06009i	−0.927106	+	0.374800i
$9$	−1.08571	+	2.79665i	−0.361902	+	0.932216i
$10$	−0.0177620	+	0.0176614i	−0.00561683	+	0.00558502i
$11$	0.235313	−	0.180562i	0.0709497	−	0.0544416i	−0.572678	−	0.819781i	$-0.694095\pi$
$11$	0.235313	−	0.180562i	0.0709497	−	0.0544416i	0.643627	+	0.765339i	$0.277429\pi$
$12$	−3.27407	+	1.13158i	−0.945142	+	0.326658i
$13$	0.822172	−	1.07148i	0.228029	−	0.297174i	−0.665300	−	0.746576i	$-0.731696\pi$
$13$	0.822172	−	1.07148i	0.228029	−	0.297174i	0.893329	+	0.449402i	$0.148363\pi$
$14$	0.639071	−	0.827975i	0.170799	−	0.221286i
$15$	−0.0228368	+	0.0204841i	−0.00589643	+	0.00528898i
$16$	−3.44116	−	2.03922i	−0.860291	−	0.509804i
$17$	3.82544			0.927805			0.463902	−	0.885886i	$-0.346449\pi$
$17$	3.82544			0.927805			0.463902	+	0.885886i	$0.346449\pi$
$18$	−4.07582	+	1.17799i	−0.960681	+	0.277654i
$19$	2.78801	−	1.15483i	0.639613	−	0.264936i	−0.0392184	−	0.999231i	$-0.512487\pi$
$19$	2.78801	−	1.15483i	0.639613	−	0.264936i	0.678831	+	0.734294i	$0.262487\pi$
$20$	−0.0350936	−	0.00482307i	−0.00784717	−	0.00107847i
$21$	0.833779	−	0.972494i	0.181946	−	0.212216i
$22$	0.404862	+	0.109715i	0.0863168	+	0.0233914i
$23$	−4.24462	−	1.13734i	−0.885065	−	0.237152i	−0.212474	−	0.977167i	$-0.568152\pi$
$23$	−4.24462	−	1.13734i	−0.885065	−	0.237152i	−0.672591	+	0.740014i	$0.734819\pi$
$24$	−4.08062	−	2.71081i	−0.832954	−	0.553342i
$25$	4.82933	−	1.29401i	0.965865	−	0.258803i
$26$	1.90998	+	0.00542337i	0.374578	+	0.00106361i
$27$	−5.05939	+	1.18429i	−0.973681	+	0.227916i
$28$	1.47913	+	0.00840004i	0.279530	+	0.00158746i
$29$	−0.0726193	−	0.00956051i	−0.0134851	−	0.00177534i	0.123781	−	0.992310i	$-0.460498\pi$
$29$	−0.0726193	−	0.00956051i	−0.0134851	−	0.00177534i	−0.137266	+	0.990534i	$0.543831\pi$
$30$	−0.0426204	−	0.00810809i	−0.00778138	−	0.00148033i
$31$	−1.05130	+	0.606969i	−0.188819	+	0.109015i	−0.591430	−	0.806357i	$-0.701436\pi$
$31$	−1.05130	+	0.606969i	−0.188819	+	0.109015i	0.402610	+	0.915371i	$0.368103\pi$
$32$	−0.658670	−	5.61838i	−0.116438	−	0.993198i
$33$	0.488291	+	0.159679i	0.0850006	+	0.0277965i
$34$	3.28119	+	4.30136i	0.562719	+	0.737678i
$35$	0.0121021	−	0.00501286i	0.00204563	−	0.000847328i
$36$	−4.82050	−	3.57251i	−0.803416	−	0.595418i
$37$	3.37678	−	8.15228i	0.555140	−	1.34023i	−0.358434	−	0.933555i	$-0.616689\pi$
$37$	3.37678	−	8.15228i	0.555140	−	1.34023i	0.913574	−	0.406672i	$-0.133311\pi$
$38$	3.68986	+	2.14433i	0.598574	+	0.347857i
$39$	2.33581	+	0.126852i	0.374028	+	0.0203125i
$40$	−0.0246777	−	0.0435965i	−0.00390189	−	0.00689322i
$41$	−2.68522	+	10.0214i	−0.419361	+	1.56508i	0.356577	+	0.934266i	$0.383944\pi$
$41$	−2.68522	+	10.0214i	−0.419361	+	1.56508i	−0.775938	+	0.630809i	$0.782723\pi$
$42$	1.80864	+	0.103374i	0.279079	+	0.0159510i
$43$	−0.251160	−	0.327319i	−0.0383016	−	0.0499156i	0.773810	−	0.633418i	$-0.218349\pi$
$43$	−0.251160	−	0.327319i	−0.0383016	−	0.0499156i	−0.812111	+	0.583502i	$0.801682\pi$
$44$	0.223896	+	0.549337i	0.0337537	+	0.0828157i
$45$	−0.0516197	−	0.0125998i	−0.00769502	−	0.00187827i
$46$	−2.36190	−	5.74823i	−0.348242	−	0.847530i
$47$	3.79608	+	2.19167i	0.553716	+	0.319688i	0.750619	−	0.660735i	$-0.229755\pi$
$47$	3.79608	+	2.19167i	0.553716	+	0.319688i	−0.196904	+	0.980423i	$0.563089\pi$
$48$	−0.452004	−	6.91344i	−0.0652412	−	0.997870i
$49$	5.58848	−	3.22651i	0.798355	−	0.460930i
$50$	5.59726	+	4.32023i	0.791572	+	0.610973i
$51$	3.74257	+	5.46764i	0.524065	+	0.765622i
$52$	1.63215	+	2.15225i	0.226338	+	0.298464i
$53$	0.729680	−	1.76160i	0.100229	−	0.241975i	−0.865809	−	0.500375i	$-0.833195\pi$
$53$	0.729680	−	1.76160i	0.100229	−	0.241975i	0.966038	+	0.258400i	$0.0831954\pi$
$54$	−5.67121	−	4.67304i	−0.771755	−	0.635921i
$55$	0.00371472	+	0.00371472i	0.000500893	+	0.000500893i
$56$	1.25925	+	1.67036i	0.168275	+	0.223211i
$57$	4.37820	+	2.85504i	0.579906	+	0.378159i
$58$	−0.0515377	−	0.0898542i	−0.00676724	−	0.0117984i
$59$	−11.5055	+	1.51473i	−1.49789	+	0.197201i	−0.834473	−	0.551049i	$-0.814228\pi$
$59$	−11.5055	+	1.51473i	−1.49789	+	0.197201i	−0.663417	+	0.748250i	$0.730894\pi$
$60$	−0.0274399	−	0.0548773i	−0.00354248	−	0.00708463i
$61$	1.53696	−	11.6744i	0.196788	−	1.49475i	−0.553060	−	0.833141i	$-0.686540\pi$
$61$	1.53696	−	11.6744i	0.196788	−	1.49475i	0.749848	−	0.661610i	$-0.230127\pi$
$62$	−1.58421	−	0.661479i	−0.201195	−	0.0840079i
$63$	2.20569	+	0.240279i	0.277891	+	0.0302724i
$64$	5.75240	−	5.55966i	0.719050	−	0.694958i
$65$	0.0207161	+	0.0119604i	0.00256951	+	0.00148351i
$66$	0.239277	+	0.686001i	0.0294530	+	0.0844409i
$67$	−4.33352	+	5.64755i	−0.529424	+	0.689958i	−0.979134	−	0.203216i	$-0.934861\pi$
$67$	−4.33352	+	5.64755i	−0.529424	+	0.689958i	0.449710	+	0.893175i	$0.351527\pi$
$68$	−2.02213	+	7.37881i	−0.245219	+	0.894812i
$69$	−2.52709	−	7.17948i	−0.304226	−	0.864307i
$70$	0.0160169	+	0.00930808i	0.00191438	+	0.00111253i
$71$	3.05989	+	3.05989i	0.363142	+	0.363142i	0.864968	−	0.501827i	$-0.167338\pi$
$71$	3.05989	+	3.05989i	0.363142	+	0.363142i	−0.501827	+	0.864968i	$0.667338\pi$
$72$	−0.117712	−	8.48446i	−0.0138725	−	0.999904i
$73$	−4.64074	+	4.64074i	−0.543158	+	0.543158i	−0.924453	−	0.381296i	$-0.875478\pi$
$73$	−4.64074	+	4.64074i	−0.543158	+	0.543158i	0.381296	+	0.924453i	$0.375478\pi$
$74$	12.0629	−	3.19556i	1.40228	−	0.371476i
$75$	6.57423	+	5.63650i	0.759127	+	0.650846i
$76$	0.753788	+	5.98818i	0.0864654	+	0.686891i
$77$	−0.174033	−	0.133540i	−0.0198329	−	0.0152183i
$78$	1.86086	+	2.73521i	0.210700	+	0.309702i
$79$	2.64432	−	4.58009i	0.297509	−	0.515300i	−0.678057	−	0.735010i	$-0.737178\pi$
$79$	2.64432	−	4.58009i	0.297509	−	0.515300i	0.975565	+	0.219709i	$0.0705109\pi$
$80$	0.0278536	−	0.0651419i	0.00311413	−	0.00728309i
$81$	−6.64248	−	6.07268i	−0.738053	−	0.674742i
$82$	−13.5713	+	5.57634i	−1.49870	+	0.615803i
$83$	−3.87888	−	0.510664i	−0.425762	−	0.0560527i	−0.0853994	−	0.996347i	$-0.527217\pi$
$83$	−3.87888	−	0.510664i	−0.425762	−	0.0560527i	−0.340363	+	0.940294i	$0.610550\pi$
$84$	1.43509	+	2.12232i	0.156581	+	0.231564i
$85$	0.00884382	+	0.0671755i	0.000959247	+	0.00728621i
$86$	0.152613	−	0.563158i	0.0164567	−	0.0607269i
$87$	−0.0573816	−	0.113147i	−0.00615195	−	0.0121306i
$88$	−0.425638	+	0.722934i	−0.0453732	+	0.0770650i
$89$	8.84724	−	8.84724i	0.937806	−	0.937806i	−0.0603705	−	0.998176i	$-0.519228\pi$
$89$	8.84724	−	8.84724i	0.937806	−	0.937806i	0.998176	+	0.0603705i	$0.0192282\pi$
$90$	−0.0301084	−	0.0688491i	−0.00317370	−	0.00725733i
$91$	−0.922817	−	0.382243i	−0.0967375	−	0.0400700i
$92$	4.43751	−	7.58617i	0.462642	−	0.790913i
$93$	−1.89606	−	0.908786i	−0.196612	−	0.0942368i
$94$	0.791674	+	6.14822i	0.0816550	+	0.634140i
$95$	0.0267245	+	0.0462882i	0.00274188	+	0.00474907i
$96$	7.38585	−	6.43810i	0.753816	−	0.657086i
$97$	6.08042	−	10.5316i	0.617373	−	1.06932i	−0.372590	−	0.927996i	$-0.621530\pi$
$97$	6.08042	−	10.5316i	0.617373	−	1.06932i	0.989963	−	0.141326i	$-0.0451365\pi$
$98$	8.42133	+	3.51628i	0.850683	+	0.355198i
$99$	0.249488	+	0.854127i	0.0250745	+	0.0858430i
$100$	−0.0567858	+	9.99921i	−0.00567858	+	0.999921i
$101$	−9.90932	+	7.60369i	−0.986014	+	0.756595i	−0.969957	−	0.243276i	$-0.921778\pi$
$101$	−9.90932	+	7.60369i	−0.986014	+	0.756595i	−0.0160568	+	0.999871i	$0.505111\pi$
$102$	−2.93776	+	8.89794i	−0.290881	+	0.881028i
$103$	−14.6638	−	3.92917i	−1.44487	−	0.387152i	−0.550635	−	0.834746i	$-0.685614\pi$
$103$	−14.6638	−	3.92917i	−1.44487	−	0.387152i	−0.894237	+	0.447594i	$0.852281\pi$
$104$	−1.02008	+	3.68126i	−0.100027	+	0.360977i
$105$	0.0190048	+	0.0123931i	0.00185468	+	0.00120944i
$106$	2.60663	−	0.690519i	0.253179	−	0.0670691i
$107$	−4.90131	−	2.03019i	−0.473827	−	0.196266i	0.132974	−	0.991120i	$-0.457547\pi$
$107$	−4.90131	−	2.03019i	−0.473827	−	0.196266i	−0.606801	+	0.794854i	$0.707547\pi$
$108$	0.390054	−	10.3850i	0.0375330	−	0.999295i
$109$	−3.47774	−	8.39602i	−0.333108	−	0.804193i	−0.998342	−	0.0575583i	$-0.981668\pi$
$109$	−3.47774	−	8.39602i	−0.333108	−	0.804193i	0.665235	−	0.746634i	$-0.268332\pi$
$110$	−0.000990649		0.00736310i	−9.44546e−5		0.000702044i
$111$	14.9556	−	3.14930i	1.41952	−	0.298919i
$112$	−0.798074	+	2.84863i	−0.0754109	+	0.269171i
$113$	2.19726	+	3.80577i	0.206701	+	0.358017i	0.950673	−	0.310194i	$-0.100394\pi$
$113$	2.19726	+	3.80577i	0.206701	+	0.358017i	−0.743972	+	0.668211i	$0.767061\pi$
$114$	0.545069	+	7.37174i	0.0510504	+	0.690427i
$115$	0.0101591	−	0.0771658i	0.000947339	−	0.00719575i
$116$	0.0568277	−	0.135020i	0.00527632	−	0.0125363i
$117$	2.10390	+	3.46263i	0.194506	+	0.320121i
$118$	−11.5718	−	11.6377i	−1.06527	−	1.07134i
$119$	−0.732254	−	2.73281i	−0.0671256	−	0.250516i
$120$	0.0381687	−	0.0779236i	0.00348431	−	0.00711342i
$121$	−2.82424	+	10.5402i	−0.256749	+	0.958201i
$122$	14.4451	−	8.28528i	1.30780	−	0.750114i
$123$	−16.9504	+	5.96635i	−1.52837	+	0.537968i
$124$	−0.615052	−	2.34868i	−0.0552333	−	0.210917i
$125$	0.0677778	+	0.163630i	0.00606223	+	0.0146355i
$126$	1.62171	+	2.68620i	0.144473	+	0.239305i
$127$			10.9024i			0.967431i	0.875225	+	0.483715i	$0.160713\pi$
$127$			10.9024i			0.967431i	−0.875225	+	0.483715i	$0.839287\pi$
$128$	11.1854	+	1.69938i	0.988655	+	0.150205i
$129$	0.222111	−	0.679208i	0.0195558	−	0.0598009i
$130$	0.00432035	+	0.0335522i	0.000378919	+	0.00294272i
$131$	−6.74976	−	5.17927i	−0.589729	−	0.452515i	0.270289	−	0.962779i	$-0.412881\pi$
$131$	−6.74976	−	5.17927i	−0.589729	−	0.452515i	−0.860018	+	0.510264i	$0.829548\pi$
$132$	−0.566112	+	0.857449i	−0.0492737	+	0.0746314i
$133$	−1.35866	−	1.77064i	−0.117811	−	0.153534i
$134$	−10.0672	−	0.0285856i	−0.869670	−	0.00246942i
$135$	−0.0324928	−	0.0861062i	−0.00279654	−	0.00741084i
$136$	−10.0313	+	4.05532i	−0.860173	+	0.347741i
$137$	−3.49503	+	0.936491i	−0.298601	+	0.0800098i	−0.405009	−	0.914313i	$-0.632732\pi$
$137$	−3.49503	+	0.936491i	−0.298601	+	0.0800098i	0.106408	+	0.994323i	$0.466065\pi$
$138$	5.90512	−	8.99954i	0.502677	−	0.766091i
$139$	−8.84388	+	1.16432i	−0.750128	+	0.0987563i	−0.495890	−	0.868385i	$-0.665158\pi$
$139$	−8.84388	+	1.16432i	−0.750128	+	0.0987563i	−0.254238	+	0.967142i	$0.581825\pi$
$140$	0.00327203	+	0.0259933i	0.000276537	+	0.00219684i
$141$	0.581336	+	7.56988i	0.0489573	+	0.637499i
$142$	−0.816016	+	6.06512i	−0.0684785	+	0.508974i
$143$		−	0.400586i		−	0.0334987i
$144$	9.43906	−	7.40973i	0.786588	−	0.617478i
$145$		−	0.00129731i		−	0.000107736i
$146$	−9.19860	−	1.23760i	−0.761282	−	0.102425i
$147$	10.0790	+	4.83091i	0.831304	+	0.398447i
$148$	13.9398	+	10.8227i	1.14584	+	0.889622i
$149$	−15.4027	+	2.02781i	−1.26184	+	0.166124i	−0.731606	−	0.681727i	$-0.761229\pi$
$149$	−15.4027	+	2.02781i	−1.26184	+	0.166124i	−0.530233	+	0.847852i	$0.677896\pi$
$150$	−0.698828	+	12.2267i	−0.0570591	+	0.998308i
$151$	−8.53754	+	2.28763i	−0.694775	+	0.186164i	−0.588889	−	0.808214i	$-0.700435\pi$
$151$	−8.53754	+	2.28763i	−0.694775	+	0.186164i	−0.105886	+	0.994378i	$0.533768\pi$
$152$	−6.08663	+	5.98380i	−0.493691	+	0.485351i
$153$	−4.15330	+	10.6984i	−0.335775	+	0.864914i
$154$	0.000880883	−	0.310226i	7.09836e−5	−	0.0249987i
$155$	−0.0130889	−	0.0170578i	−0.00105133	−	0.00137012i
$156$	−1.47939	+	4.43844i	−0.118446	+	0.355359i
$157$	6.43378	+	4.93681i	0.513471	+	0.394000i	0.832740	−	0.553664i	$-0.186771\pi$
$157$	6.43378	+	4.93681i	0.513471	+	0.394000i	−0.319269	+	0.947664i	$0.603437\pi$
$158$	7.41801	−	0.955180i	0.590145	−	0.0759900i
$159$	3.23171	−	0.680524i	0.256291	−	0.0539691i
$160$	0.0971372	−	0.0245552i	0.00767937	−	0.00194126i
$161$			3.24997i			0.256134i
$162$	1.13074	−	12.6776i	0.0888392	−	0.996046i
$163$	2.65170	+	6.40178i	0.207697	+	0.501426i	0.993060	−	0.117610i	$-0.0375234\pi$
$163$	2.65170	+	6.40178i	0.207697	+	0.501426i	−0.785362	+	0.619036i	$0.787523\pi$
$164$	−17.9106	−	10.4768i	−1.39858	−	0.818098i
$165$	−0.00167514	+	0.00894365i	−0.000130409	+	0.000696262i
$166$	−2.75283	−	4.79947i	−0.213661	−	0.372511i
$167$	6.15993	−	22.9892i	0.476670	−	1.77896i	−0.138283	−	0.990393i	$-0.544158\pi$
$167$	6.15993	−	22.9892i	0.476670	−	1.77896i	0.614953	−	0.788564i	$-0.289175\pi$
$168$	−1.15544	+	3.43401i	−0.0891445	+	0.264939i
$169$	2.89255	+	10.7952i	0.222504	+	0.830397i
$170$	−0.0679473	+	0.0675625i	−0.00521132	+	0.00518181i
$171$	0.202695	+	9.05088i	0.0155005	+	0.692138i
$172$	0.764122	−	0.311438i	0.0582638	−	0.0237469i
$173$	−3.05018	+	23.1684i	−0.231901	+	1.76146i	0.339327	+	0.940669i	$0.389801\pi$
$173$	−3.05018	+	23.1684i	−0.231901	+	1.76146i	−0.571227	+	0.820792i	$0.693532\pi$
$174$	0.0780059	−	0.161570i	0.00591361	−	0.0122486i
$175$	−1.84883	−	3.20227i	−0.139759	−	0.242069i
$176$	−1.17796	+	0.141490i	−0.0887919	+	0.0106652i
$177$	−13.4213	−	14.9627i	−1.00880	−	1.12467i
$178$	17.5365	+	2.35940i	1.31441	+	0.176844i
$179$	−8.10557	−	19.5686i	−0.605839	−	1.46262i	−0.867486	−	0.497461i	$-0.834266\pi$
$179$	−8.10557	−	19.5686i	−0.605839	−	1.46262i	0.261648	−	0.965163i	$-0.415734\pi$
$180$	0.0515898	−	0.0929081i	0.00384528	−	0.00692496i
$181$	−18.5874	−	7.69916i	−1.38159	−	0.572274i	−0.436686	−	0.899614i	$-0.643848\pi$
$181$	−18.5874	−	7.69916i	−1.38159	−	0.572274i	−0.944907	+	0.327340i	$0.893848\pi$
$182$	−0.361729	−	1.36549i	−0.0268131	−	0.101217i
$183$	18.1897	−	9.22474i	1.34462	−	0.681913i
$184$	12.3362	−	1.51730i	0.909433	−	0.111857i
$185$	0.150962	+	0.0404503i	0.0110990	+	0.00297396i
$186$	−0.604456	−	2.91144i	−0.0443208	−	0.213477i
$187$	0.900177	−	0.690730i	0.0658274	−	0.0505112i
$188$	−6.23408	+	6.16367i	−0.454667	+	0.449532i
$189$	1.81448	+	3.38763i	0.131984	+	0.246414i
$190$	−0.0291246	+	0.0697521i	−0.00211292	+	0.00506035i
$191$	−9.08766	+	15.7403i	−0.657560	+	1.13893i	0.323686	+	0.946165i	$0.395078\pi$
$191$	−9.08766	+	15.7403i	−0.657560	+	1.13893i	−0.981246	+	0.192762i	$0.938255\pi$
$192$	13.5741	+	2.78259i	0.979629	+	0.200816i
$193$	3.90457	+	6.76291i	0.281057	+	0.486805i	0.971645	−	0.236443i	$-0.0759817\pi$
$193$	3.90457	+	6.76291i	0.281057	+	0.486805i	−0.690588	+	0.723248i	$0.742648\pi$
$194$	17.0572	−	2.19637i	1.22464	−	0.157690i
$195$	0.00317248	+	0.0413105i	0.000227186	+	0.00295831i
$196$	3.26948	+	12.4851i	0.233534	+	0.891789i
$197$	−6.81634	−	2.82342i	−0.485644	−	0.201160i	0.126407	−	0.991978i	$-0.459655\pi$
$197$	−6.81634	−	2.82342i	−0.485644	−	0.201160i	−0.612051	+	0.790818i	$0.709655\pi$
$198$	−0.746396	+	1.01314i	−0.0530441	+	0.0720005i
$199$	−0.978260	+	0.978260i	−0.0693470	+	0.0693470i	−0.740930	−	0.671583i	$-0.765615\pi$
$199$	−0.978260	+	0.978260i	−0.0693470	+	0.0693470i	0.671583	+	0.740930i	$0.265615\pi$
$200$	−11.2919	+	8.51277i	−0.798460	+	0.601944i
$201$	−12.3116	−	0.668612i	−0.868394	−	0.0471603i
$202$	−17.0492	−	4.62024i	−1.19958	−	0.325079i
$203$	0.00707075	+	0.0537077i	0.000496269	+	0.00376954i
$204$	−12.5247	+	4.32878i	−0.876908	+	0.303075i
$205$	−0.182185	−	0.0239851i	−0.0127244	−	0.00167520i
$206$	−8.15961	−	19.8584i	−0.568507	−	1.38360i
$207$	7.78916	−	10.6359i	0.541384	−	0.739245i
$208$	−5.01420	+	2.01054i	−0.347672	+	0.139406i
$209$	0.447537	−	0.775156i	0.0309568	−	0.0536187i
$210$	0.00236602	+	0.0319991i	0.000163271	+	0.00220815i
$211$	10.1971	+	7.82454i	0.702000	+	0.538664i	0.896940	−	0.442151i	$-0.145785\pi$
$211$	10.1971	+	7.82454i	0.702000	+	0.538664i	−0.194940	+	0.980815i	$0.562451\pi$
$212$	3.01221	+	2.33865i	0.206880	+	0.160619i
$213$	−1.37984	+	7.36705i	−0.0945452	+	0.504782i
$214$	−1.92123	−	7.25243i	−0.131332	−	0.495766i
$215$	0.00516714	−	0.00516714i	0.000352396	−	0.000352396i
$216$	12.0116	−	8.46892i	0.817282	−	0.576237i
$217$	0.634842	+	0.634842i	0.0430959	+	0.0430959i
$218$	6.45761	−	11.1119i	0.437365	−	0.752595i
$219$	−11.1732	−	2.09272i	−0.755012	−	0.141413i
$220$	−0.00912886	+	0.00520165i	−0.000615468	+	0.000350695i
$221$	3.14517	−	4.09886i	0.211567	−	0.275719i
$222$	16.3689	+	14.1150i	1.09861	+	0.947333i
$223$	23.4483	+	13.5379i	1.57022	+	0.906566i	0.996141	+	0.0877637i	$0.0279721\pi$
$223$	23.4483	+	13.5379i	1.57022	+	0.906566i	0.574076	+	0.818802i	$0.305361\pi$
$224$	−3.88757	+	1.54599i	−0.259749	+	0.103296i
$225$	−1.62433	+	14.9108i	−0.108289	+	0.994056i
$226$	−2.39460	+	5.73495i	−0.159286	+	0.381483i
$227$	1.53311	−	11.6452i	0.101756	−	0.772917i	−0.862146	−	0.506660i	$-0.830880\pi$
$227$	1.53311	−	11.6452i	0.101756	−	0.772917i	0.963902	−	0.266256i	$-0.0857868\pi$
$228$	−7.82135	+	6.93584i	−0.517981	+	0.459337i
$229$	24.1044	−	3.17341i	1.59286	−	0.209705i	0.718695	−	0.695326i	$-0.244740\pi$
$229$	24.1044	−	3.17341i	1.59286	−	0.209705i	0.874169	+	0.485621i	$0.161406\pi$
$230$	0.0954798	−	0.0547644i	0.00629575	−	0.00361106i
$231$	0.0206037	−	0.379390i	0.00135562	−	0.0249620i
$232$	0.200561	−	0.0519132i	0.0131675	−	0.00340827i
$233$	11.5840	+	11.5840i	0.758894	+	0.758894i	0.976121	−	0.217227i	$-0.0697013\pi$
$233$	11.5840	+	11.5840i	0.758894	+	0.758894i	−0.217227	+	0.976121i	$0.569701\pi$
$234$	−2.08885	+	5.33565i	−0.136552	+	0.348803i
$235$	−0.0297102	+	0.0717268i	−0.00193808	+	0.00467894i
$236$	3.16009	−	22.9934i	0.205704	−	1.49675i
$237$	9.13329	−	0.701400i	0.593271	−	0.0455608i
$238$	2.44473	−	3.16737i	0.158468	−	0.205310i
$239$	6.68306	−	3.85847i	0.432291	−	0.249584i	−0.268031	−	0.963410i	$-0.586373\pi$
$239$	6.68306	−	3.85847i	0.432291	−	0.249584i	0.700322	+	0.713827i	$0.253040\pi$
$240$	0.120357	−	0.0239201i	0.00776899	−	0.00154404i
$241$	8.39294	+	4.84567i	0.540637	+	0.312137i	0.745337	−	0.666688i	$-0.232289\pi$
$241$	8.39294	+	4.84567i	0.540637	+	0.312137i	−0.204700	+	0.978825i	$0.565622\pi$
$242$	−14.2740	+	5.86504i	−0.917565	+	0.377019i
$243$	2.18099	−	15.4351i	0.139911	−	0.990164i
$244$	21.7061	+	9.13570i	1.38959	+	0.584853i
$245$	0.0695780	+	0.0906758i	0.00444517	+	0.00579306i
$246$	−21.2475	−	13.9417i	−1.35469	−	0.888893i
$247$	1.05485	−	3.93675i	0.0671185	−	0.250489i
$248$	2.11333	−	2.70610i	0.134197	−	0.171838i
$249$	−3.06497	−	6.04363i	−0.194235	−	0.382999i
$250$	−0.125852	+	0.216560i	−0.00795961	+	0.0136965i
$251$	3.30095	−	7.96919i	0.208354	−	0.503011i	−0.784810	−	0.619736i	$-0.787240\pi$
$251$	3.30095	−	7.96919i	0.208354	−	0.503011i	0.993164	+	0.116725i	$0.0372397\pi$
$252$	−1.62940	+	4.12750i	−0.102642	+	0.260008i
$253$	−1.20418	+	0.498787i	−0.0757060	+	0.0313584i
$254$	−12.2588	+	9.35130i	−0.769184	+	0.586753i
$255$	−0.0873606	+	0.0783607i	−0.00547074	+	0.00490714i
$256$	7.68320	+	14.0345i	0.480200	+	0.877159i
$257$	10.7004	−	6.17788i	0.667473	−	0.385366i	−0.127645	−	0.991820i	$-0.540742\pi$
$257$	10.7004	−	6.17788i	0.667473	−	0.385366i	0.795118	+	0.606454i	$0.207409\pi$
$258$	0.954220	−	0.332832i	0.0594072	−	0.0207212i
$259$	−6.47019	−	0.851816i	−0.402038	−	0.0529293i
$260$	−0.0340208	+	0.0336366i	−0.00210988	+	0.00208605i
$261$	0.105581	−	0.192711i	0.00653528	−	0.0119285i
$262$	0.0341645	−	12.0319i	0.00211069	−	0.743334i
$263$	25.3222	−	6.78506i	1.56143	−	0.418384i	0.628315	−	0.777959i	$-0.283745\pi$
$263$	25.3222	−	6.78506i	1.56143	−	0.418384i	0.933116	+	0.359574i	$0.117078\pi$
$264$	−1.44970	+	0.0989167i	−0.0892226	+	0.00608790i
$265$	0.0326210	+	0.00874078i	0.00200390	+	0.000536942i
$266$	0.825564	−	3.04642i	0.0506186	−	0.186788i
$267$	21.3008	+	3.98962i	1.30359	+	0.244161i
$268$	−8.60276	−	11.3441i	−0.525497	−	0.692954i
$269$	3.33063	−	1.37959i	0.203072	−	0.0841152i	−0.278829	−	0.960341i	$-0.589946\pi$
$269$	3.33063	−	1.37959i	0.203072	−	0.0841152i	0.481901	+	0.876225i	$0.339946\pi$
$270$	0.0689487	−	0.110391i	0.00419608	−	0.00671819i
$271$	−15.5112			−0.942236			−0.471118	−	0.882070i	$-0.656149\pi$
$271$	−15.5112			−0.942236			−0.471118	+	0.882070i	$0.656149\pi$
$272$	−13.1639	−	7.80089i	−0.798182	−	0.472998i
$273$	−0.356493	−	1.69293i	−0.0215759	−	0.102461i
$274$	−4.05079	−	3.12660i	−0.244717	−	0.188885i
$275$	0.902755	−	1.17649i	0.0544382	−	0.0709452i
$276$	15.1842	−	1.07938i	0.913980	−	0.0649711i
$277$	−20.5068	+	15.7354i	−1.23213	+	0.945449i	−0.999631	−	0.0271468i	$-0.991358\pi$
$277$	−20.5068	+	15.7354i	−1.23213	+	0.945449i	−0.232502	+	0.972596i	$0.574691\pi$
$278$	−8.89483	−	8.94549i	−0.533477	−	0.536515i
$279$	−0.556073	−	3.59911i	−0.0332912	−	0.215473i
$280$	−0.0264207	+	0.0259744i	−0.00157894	+	0.00155226i
$281$	−6.51107	−	24.2996i	−0.388418	−	1.44959i	−0.832708	−	0.553712i	$-0.813211\pi$
$281$	−6.51107	−	24.2996i	−0.388418	−	1.44959i	0.444291	−	0.895883i	$-0.353456\pi$
$282$	−8.01302	+	7.14657i	−0.477169	+	0.425572i
$283$	−2.42080	−	18.3878i	−0.143902	−	1.09304i	−0.899161	−	0.437617i	$-0.855822\pi$
$283$	−2.42080	−	18.3878i	−0.143902	−	1.09304i	0.755259	−	0.655426i	$-0.227511\pi$
$284$	−7.51961	+	4.28470i	−0.446207	+	0.254250i
$285$	−0.0400134	+	0.0834825i	−0.00237019	+	0.00494508i
$286$	0.450423	−	0.343594i	0.0266341	−	0.0203172i
$287$	7.67305			0.452926
$288$	16.4277	+	4.25784i	0.968014	+	0.250896i
$289$	−2.36604			−0.139179
$290$	0.00145871	−	0.00111274i	8.56586e−5	−	6.53425e-5i
$291$	21.0014	−	1.61282i	1.23112	−	0.0945452i
$292$	−6.49834	−	11.4045i	−0.380286	−	0.667400i
$293$	0.0674140	+	0.512060i	0.00393837	+	0.0299149i	0.993301	−	0.115554i	$-0.0368643\pi$
$293$	0.0674140	+	0.512060i	0.00393837	+	0.0299149i	−0.989363	+	0.145469i	$0.953531\pi$
$294$	3.21315	+	15.4766i	0.187395	+	0.902613i
$295$	−0.0531979	−	0.198537i	−0.00309730	−	0.0115593i
$296$	−0.212600	+	24.9570i	−0.0123571	+	1.45060i
$297$	−0.976706	+	1.19221i	−0.0566742	+	0.0691793i
$298$	−15.4915	−	15.5797i	−0.897396	−	0.902507i
$299$	−4.70844	+	3.61292i	−0.272296	+	0.208940i
$300$	−14.3473	+	9.70145i	−0.828340	+	0.560114i
$301$	−0.185753	+	0.242078i	−0.0107066	+	0.0139531i
$302$	−9.89513	−	7.63754i	−0.569401	−	0.439491i
$303$	−20.5625	−	6.72425i	−1.18128	−	0.386298i
$304$	−11.9489	−	1.71139i	−0.685318	−	0.0981548i
$305$	0.208558			0.0119420
$306$	−15.5918	+	4.50631i	−0.891324	+	0.257609i
$307$	20.8701	−	8.64467i	1.19112	−	0.493377i	0.302999	−	0.952991i	$-0.402012\pi$
$307$	20.8701	−	8.64467i	1.19112	−	0.493377i	0.888119	+	0.459613i	$0.152012\pi$
$308$	0.349577	−	0.265099i	0.0199190	−	0.0151054i
$309$	−8.73031	−	24.8029i	−0.496650	−	1.41099i
$310$	0.00795326	−	0.0293484i	0.000451715	−	0.00166688i
$311$	−16.6074	−	4.44993i	−0.941718	−	0.252333i	−0.244874	−	0.969555i	$-0.578746\pi$
$311$	−16.6074	−	4.44993i	−0.941718	−	0.252333i	−0.696844	+	0.717223i	$0.745413\pi$
$312$	−6.25954	+	2.14354i	−0.354377	+	0.121354i
$313$	−11.3295	+	3.03572i	−0.640379	+	0.171589i	−0.564375	−	0.825519i	$-0.690883\pi$
$313$	−11.3295	+	3.03572i	−0.640379	+	0.171589i	−0.0760038	+	0.997108i	$0.524216\pi$
$314$	−0.0325651	+	11.4687i	−0.00183776	+	0.647214i
$315$	0.000879855		0.0392879i	4.95742e−5		0.00221362i
$316$	7.43666	+	7.52161i	0.418345	+	0.423124i
$317$	31.0320	+	4.08544i	1.74293	+	0.229461i	0.933707	−	0.358039i	$-0.116554\pi$
$317$	31.0320	+	4.08544i	1.74293	+	0.229461i	0.809224	+	0.587500i	$0.199888\pi$
$318$	3.53712	+	3.05006i	0.198352	+	0.171039i
$319$	−0.0188146	+	0.0108626i	−0.00105341	+	0.000608188i
$320$	0.110928	+	0.0881604i	0.00620104	+	0.00492832i
$321$	−1.89342	−	8.99157i	−0.105681	−	0.501860i
$322$	−3.65431	+	2.78760i	−0.203646	+	0.155347i
$323$	10.6653	−	4.41773i	0.593436	−	0.245809i
$324$	15.2247	−	9.60253i	0.845816	−	0.533474i
$325$	2.58403	−	6.23841i	0.143336	−	0.346045i
$326$	−4.92379	+	8.47260i	−0.272703	+	0.469254i
$327$	8.59789	−	13.1848i	0.475464	−	0.729123i
$328$	−3.58227	−	29.1251i	−0.197798	−	1.60817i
$329$	0.839046	−	3.13136i	0.0462581	−	0.172638i
$330$	−0.0114932	+	0.00578769i	−0.000632677	+	0.000318602i
$331$	9.79153	+	12.7606i	0.538191	+	0.701384i	0.980731	−	0.195365i	$-0.0625891\pi$
$331$	9.79153	+	12.7606i	0.538191	+	0.701384i	−0.442540	+	0.896749i	$0.645922\pi$
$332$	3.03539	−	7.21196i	0.166589	−	0.395808i
$333$	19.1329	+	18.2947i	1.04847	+	1.00254i
$334$	31.1328	−	12.7922i	1.70351	−	0.699958i
$335$	−0.109191	−	0.0630413i	−0.00596573	−	0.00344431i
$336$	−4.85229	+	1.64625i	−0.264714	+	0.0898105i
$337$	6.19533	−	3.57688i	0.337481	−	0.194845i	−0.321676	−	0.946850i	$-0.604246\pi$
$337$	6.19533	−	3.57688i	0.337481	−	0.194845i	0.659158	+	0.752005i	$0.270913\pi$
$338$	−9.65717	+	12.5117i	−0.525281	+	0.680549i
$339$	−3.28986	+	6.86385i	−0.178681	+	0.372793i
$340$	−0.134248	−	0.0184503i	−0.00728064	−	0.00100061i
$341$	−0.137789	+	0.332653i	−0.00746172	+	0.0180142i
$342$	−10.0031	+	7.99112i	−0.540903	+	0.432110i
$343$	−7.03541	−	7.03541i	−0.379877	−	0.379877i
$344$	1.00559	+	0.592058i	0.0542180	+	0.0319216i
$345$	0.120231	−	0.0609741i	0.00647301	−	0.00328274i
$346$	−28.6670	+	16.4426i	−1.54115	+	0.883958i
$347$	18.2812	−	2.40677i	0.981386	−	0.129202i	0.377274	−	0.926102i	$-0.376861\pi$
$347$	18.2812	−	2.40677i	0.981386	−	0.129202i	0.604112	+	0.796900i	$0.293528\pi$
$348$	0.248579	−	0.0508726i	0.0133252	−	0.00272706i
$349$	3.91068	−	29.7046i	0.209334	−	1.59005i	−0.487700	−	0.873011i	$-0.662164\pi$
$349$	3.91068	−	29.7046i	0.209334	−	1.59005i	0.697034	−	0.717038i	$-0.254503\pi$
$350$	2.01487	−	4.82553i	0.107699	−	0.257935i
$351$	−2.89076	+	6.39470i	−0.154297	+	0.341324i
$352$	−1.16946	−	1.20315i	−0.0623325	−	0.0641280i
$353$	12.8891	+	7.44153i	0.686018	+	0.396073i	0.802119	−	0.597165i	$-0.203706\pi$
$353$	12.8891	+	7.44153i	0.686018	+	0.396073i	−0.116100	+	0.993237i	$0.537039\pi$
$354$	5.31244	−	27.9250i	0.282353	−	1.48420i
$355$	−0.0466583	+	0.0608063i	−0.00247636	+	0.00322726i
$356$	12.3886	+	21.7419i	0.656595	+	1.15232i
$357$	3.18957	−	3.72021i	0.168810	−	0.196895i
$358$	15.0507	−	25.8985i	0.795456	−	1.36878i
$359$	20.1221	+	20.1221i	1.06200	+	1.06200i	0.997946	+	0.0640565i	$0.0204038\pi$
$359$	20.1221	+	20.1221i	1.06200	+	1.06200i	0.0640565	+	0.997946i	$0.479596\pi$
$360$	0.148717	−	0.0216818i	0.00783807	−	0.00114273i
$361$	−6.99568	+	6.99568i	−0.368194	+	0.368194i
$362$	−7.28596	−	27.5037i	−0.382941	−	1.44556i
$363$	−17.8280	+	6.27525i	−0.935728	+	0.329365i
$364$	1.22510	−	1.57795i	0.0642129	−	0.0827070i
$365$	−0.0922211	−	0.0707637i	−0.00482707	−	0.00370394i
$366$	25.9742	+	12.5403i	1.35769	+	0.655494i
$367$	−16.9472	+	29.3534i	−0.884636	+	1.53223i	−0.0385061	+	0.999258i	$0.512260\pi$
$367$	−16.9472	+	29.3534i	−0.884636	+	1.53223i	−0.846130	+	0.532976i	$0.821073\pi$
$368$	12.2871	+	12.5695i	0.640512	+	0.655229i
$369$	−25.1109	−	18.3899i	−1.30722	−	0.957339i
$370$	0.0840022	+	0.204439i	0.00436707	+	0.0106283i
$371$	−1.39812	−	0.184067i	−0.0725870	−	0.00955626i
$372$	2.75520	−	3.17689i	0.142850	−	0.164714i
$373$	0.284186	+	2.15861i	0.0147146	+	0.111769i	0.997226	−	0.0744344i	$-0.0237151\pi$
$373$	0.284186	+	2.15861i	0.0147146	+	0.111769i	−0.982511	+	0.186203i	$0.940382\pi$
$374$	1.54877	+	0.419709i	0.0800851	+	0.0217027i
$375$	−0.167564	+	0.256959i	−0.00865298	+	0.0132693i
$376$	−12.2777	−	1.72291i	−0.633172	−	0.0888521i
$377$	−0.0699494	+	0.0699494i	−0.00360258	+	0.00360258i
$378$	−2.25275	+	4.94589i	−0.115869	+	0.254389i
$379$	29.9450	+	12.4036i	1.53817	+	0.637132i	0.981130	−	0.193351i	$-0.0619356\pi$
$379$	29.9450	+	12.4036i	1.53817	+	0.637132i	0.557044	+	0.830483i	$0.311936\pi$
$380$	−0.103411	+	0.0270804i	−0.00530488	+	0.00138920i
$381$	−15.5826	+	10.6662i	−0.798322	+	0.546448i
$382$	−25.4933	+	3.28264i	−1.30435	+	0.167955i
$383$	3.71803	+	6.43982i	0.189983	+	0.329059i	0.945244	−	0.326364i	$-0.105824\pi$
$383$	3.71803	+	6.43982i	0.189983	+	0.329059i	−0.755262	+	0.655423i	$0.772490\pi$
$384$	8.51416	+	17.6496i	0.434487	+	0.900678i
$385$	0.00194266	−	0.00336478i	9.90069e−5	−	0.000171485i
$386$	−4.25523	+	10.1911i	−0.216585	+	0.518713i
$387$	1.18808	−	0.347035i	0.0603936	−	0.0176408i
$388$	17.1001	+	17.2954i	0.868125	+	0.878042i
$389$	−26.0271	+	19.9713i	−1.31963	+	1.01259i	−0.321793	+	0.946810i	$0.604285\pi$
$389$	−26.0271	+	19.9713i	−1.31963	+	1.01259i	−0.997834	+	0.0657753i	$0.979048\pi$
$390$	−0.0437289	+	0.0390004i	−0.00221430	+	0.00197486i
$391$	−16.2375	−	4.35083i	−0.821167	−	0.220031i
$392$	−11.2340	+	14.3850i	−0.567403	+	0.726554i
$393$	0.799102	−	14.7144i	0.0403094	−	0.742243i
$394$	−2.67189	−	10.0861i	−0.134608	−	0.508130i
$395$	0.0865407	+	0.0358463i	0.00435433	+	0.00180362i
$396$	−1.77939	+	0.0297406i	−0.0894176	+	0.00149452i
$397$	−1.58030	−	3.81517i	−0.0793128	−	0.191478i	0.879249	−	0.476362i	$-0.158045\pi$
$397$	−1.58030	−	3.81517i	−0.0793128	−	0.191478i	−0.958562	+	0.284884i	$0.908045\pi$
$398$	−1.93905	−	0.260884i	−0.0971957	−	0.0130769i
$399$	1.20152	−	3.67419i	0.0601511	−	0.183940i
$400$	−19.2573	−	5.39512i	−0.962864	−	0.269756i
$401$	2.56218	+	4.43782i	0.127949	+	0.221614i	0.922882	−	0.385083i	$-0.125827\pi$
$401$	2.56218	+	4.43782i	0.127949	+	0.221614i	−0.794933	+	0.606697i	$0.792494\pi$
$402$	−9.80823	−	14.4168i	−0.489190	−	0.719045i
$403$	−0.213998	+	1.62548i	−0.0106600	+	0.0809707i
$404$	−9.42853	−	23.1332i	−0.469087	−	1.15092i
$405$	0.0912812	−	0.130683i	0.00453580	−	0.00649367i
$406$	−0.0543247	+	0.0540171i	−0.00269609	+	0.00268082i
$407$	−0.677392	−	2.52806i	−0.0335771	−	0.125311i
$408$	−15.6102	−	10.3700i	−0.772819	−	0.513393i
$409$	−6.38784	+	23.8397i	−0.315858	+	1.17880i	0.607329	+	0.794450i	$0.292241\pi$
$409$	−6.38784	+	23.8397i	−0.315858	+	1.17880i	−0.923188	+	0.384349i	$0.874426\pi$
$410$	−0.129297	−	0.225424i	−0.00638550	−	0.0111329i
$411$	−4.75783	−	4.07919i	−0.234687	−	0.201211i
$412$	15.3302	−	26.2079i	0.755265	−	1.29117i
$413$	3.28444	+	7.92934i	0.161617	+	0.390178i
$414$	18.6401	−	0.364495i	0.916111	−	0.0179140i
$415$		−	0.0692946i		−	0.00340154i
$416$	−6.56149	−	3.91352i	−0.321704	−	0.191876i
$417$	−10.3165	−	11.5013i	−0.505199	−	0.563222i
$418$	1.25546	−	0.161659i	0.0614065	−	0.00790701i
$419$	0.926338	+	0.710804i	0.0452546	+	0.0347250i	0.631141	−	0.775668i	$-0.282587\pi$
$419$	0.926338	+	0.710804i	0.0452546	+	0.0347250i	−0.585887	+	0.810393i	$0.699254\pi$
$420$	−0.0339507	+	0.0301069i	−0.00165663	+	0.00146907i
$421$	11.4215	+	14.8848i	0.556650	+	0.725440i	0.983905	−	0.178691i	$-0.0571861\pi$
$421$	11.4215	+	14.8848i	0.556650	+	0.725440i	−0.427255	+	0.904131i	$0.640519\pi$
$422$	−0.0516137	+	18.1771i	−0.00251252	+	0.884848i
$423$	−10.2508	+	8.23680i	−0.498409	+	0.400487i
$424$	−0.0459402	+	5.39290i	−0.00223105	+	0.261902i
$425$	18.4743	−	4.95017i	0.896134	−	0.240118i
$426$	−9.46713	+	4.76743i	−0.458684	+	0.230983i
$427$	−8.63413	+	1.13670i	−0.417835	+	0.0550090i
$428$	6.50682	−	8.38088i	0.314519	−	0.405105i
$429$	0.572551	−	0.391909i	0.0276430	−	0.0189215i
$430$	0.0102420	+	0.00137798i	0.000493913	+	6.64522e-5i
$431$			38.4298i			1.85110i	0.378625	+	0.925550i	$0.376397\pi$
$431$			38.4298i			1.85110i	−0.378625	+	0.925550i	$0.623603\pi$
$432$	19.8252	+	6.24188i	0.953841	+	0.300312i
$433$			26.6567i			1.28104i	0.767941	+	0.640520i	$0.221281\pi$
$433$			26.6567i			1.28104i	−0.767941	+	0.640520i	$0.778719\pi$
$434$	−0.169301	+	1.25835i	−0.00812670	+	0.0604026i
$435$	0.00185423	−	0.00126921i	8.89035e−5	−	6.08540e-5i
$436$	18.0333	−	2.27001i	0.863636	−	0.108714i
$437$	−13.1475	+	1.73090i	−0.628929	+	0.0828001i
$438$	−7.23046	−	14.3582i	−0.345485	−	0.686062i
$439$	−39.7590	+	10.6534i	−1.89760	+	0.508459i	−0.900273	+	0.435325i	$0.856633\pi$
$439$	−39.7590	+	10.6534i	−1.89760	+	0.508459i	−0.997322	+	0.0731340i	$0.976700\pi$
$440$	−0.0136789	−	0.00580298i	−0.000652115	−	0.000276646i
$441$	2.95596	+	19.1321i	0.140760	+	0.911051i
$442$	7.30651	+	0.0207468i	0.347535	+	0.000986822i
$443$	19.0832	+	24.8697i	0.906670	+	1.18160i	0.982833	+	0.184500i	$0.0590665\pi$
$443$	19.0832	+	24.8697i	0.906670	+	1.18160i	−0.0761626	+	0.997095i	$0.524267\pi$
$444$	−1.83089	+	30.5122i	−0.0868900	+	1.44805i
$445$	0.175813	+	0.134906i	0.00833433	+	0.00639516i
$446$	4.89016	+	37.9774i	0.231556	+	1.79828i
$447$	−17.9674	−	20.0310i	−0.849828	−	0.947433i
$448$	−5.07281	−	3.04518i	−0.239668	−	0.143871i
$449$			0.439958i			0.0207629i	0.999946	+	0.0103815i	$0.00330458\pi$
$449$			0.439958i			0.0207629i	−0.999946	+	0.0103815i	$0.996695\pi$
$450$	−18.1592	+	10.9631i	−0.856031	+	0.516803i
$451$	1.17761	+	2.84301i	0.0554517	+	0.133872i
$452$	−8.50236	+	2.22653i	−0.399917	+	0.104727i
$453$	−11.6223	−	9.96450i	−0.546062	−	0.468173i
$454$	14.4089	−	8.26455i	0.676245	−	0.387874i
$455$	0.00457886	−	0.0170886i	0.000214660	−	0.000801124i
$456$	−14.5073	−	2.84533i	−0.679368	−	0.133245i
$457$	−6.44722	−	24.0614i	−0.301588	−	1.12554i	−0.935843	−	0.352418i	$-0.885359\pi$
$457$	−6.44722	−	24.0614i	−0.301588	−	1.12554i	0.634254	−	0.773125i	$-0.281307\pi$
$458$	24.2433	+	24.3813i	1.13281	+	1.13927i
$459$	−19.3544	+	4.53041i	−0.903386	+	0.211461i
$460$	0.143474	+	0.0603855i	0.00668949	+	0.00281549i
$461$	−0.690973	+	5.24846i	−0.0321818	+	0.244445i	−0.999973	−	0.00730792i	$-0.997674\pi$
$461$	−0.690973	+	5.24846i	−0.0321818	+	0.244445i	0.967791	+	0.251753i	$0.0810071\pi$
$462$	0.444263	−	0.302247i	0.0206690	−	0.0140618i
$463$	−4.97184	−	8.61148i	−0.231061	−	0.400210i	0.727060	−	0.686574i	$-0.240886\pi$
$463$	−4.97184	−	8.61148i	−0.231061	−	0.400210i	−0.958121	+	0.286365i	$0.907553\pi$
$464$	0.230399	+	0.180986i	0.0106960	+	0.00840204i
$465$	0.0115751	−	0.0353962i	0.000536782	−	0.00164146i
$466$	−3.08924	+	22.9611i	−0.143106	+	1.06365i
$467$	−11.0896	−	26.7726i	−0.513164	−	1.23889i	−0.942033	−	0.335521i	$-0.891088\pi$
$467$	−11.0896	−	26.7726i	−0.513164	−	1.23889i	0.428868	−	0.903367i	$-0.358912\pi$
$468$	−7.79113	+	2.22783i	−0.360145	+	0.102981i
$469$	4.86400	+	2.01474i	0.224599	+	0.0930318i
$470$	−0.106134	+	0.0281157i	−0.00489559	+	0.00129688i
$471$	−0.761693	+	14.0256i	−0.0350970	+	0.646264i
$472$	28.5646	−	16.1689i	1.31479	−	0.744235i
$473$	−0.118203	−	0.0316723i	−0.00543497	−	0.00145630i
$474$	8.62255	+	9.66796i	0.396047	+	0.444064i
$475$	11.9698	−	9.18477i	0.549213	−	0.421426i
$476$	5.65833	+	0.0321338i	0.259349	+	0.00147285i
$477$	4.13437	+	3.95324i	0.189300	+	0.181007i
$478$	10.0708	+	4.20499i	0.460626	+	0.192332i
$479$	−11.8540	+	20.5318i	−0.541625	+	0.938122i	0.457186	+	0.889371i	$0.348857\pi$
$479$	−11.8540	+	20.5318i	−0.541625	+	0.938122i	−0.998811	+	0.0487510i	$0.984476\pi$
$480$	0.130129	+	0.114813i	0.00593957	+	0.00524049i
$481$	−5.95867	−	10.3207i	−0.271692	−	0.470584i
$482$	1.75035	+	13.5934i	0.0797263	+	0.619162i
$483$	−4.64513	+	3.17957i	−0.211361	+	0.144676i
$484$	−18.8379	−	11.0192i	−0.856269	−	0.500872i
$485$	0.198994	+	0.0824261i	0.00903586	+	0.00374278i
$486$	19.2261	−	10.7868i	0.872115	−	0.489301i
$487$	5.94633	−	5.94633i	0.269454	−	0.269454i	−0.559426	−	0.828880i	$-0.688978\pi$
$487$	5.94633	−	5.94633i	0.269454	−	0.269454i	0.828880	+	0.559426i	$0.188978\pi$
$488$	8.34564	+	32.2425i	0.377789	+	1.45955i
$489$	−6.55570	+	10.0531i	−0.296459	+	0.454619i
$490$	−0.0422778	+	0.156009i	−0.00190992	+	0.00704779i
$491$	0.467966	+	3.55456i	0.0211190	+	0.160415i	0.998755	−	0.0498909i	$-0.0158874\pi$
$491$	0.467966	+	3.55456i	0.0211190	+	0.160415i	−0.977636	+	0.210306i	$0.932554\pi$
$492$	−2.54837	−	35.8492i	−0.114890	−	1.61621i
$493$	−0.277800	−	0.0365731i	−0.0125115	−	0.00164717i
$494$	5.33130	−	2.19058i	0.239867	−	0.0985590i
$495$	−0.0144219	+	0.00635567i	−0.000648215	+	0.000285666i
$496$	4.85544	+	0.0551501i	0.218016	+	0.00247631i
$497$	1.60020	−	2.77163i	0.0717789	−	0.124325i
$498$	4.16660	−	8.63009i	0.186710	−	0.386723i
$499$	12.6829	+	9.73192i	0.567764	+	0.435661i	0.852336	−	0.522994i	$-0.175185\pi$
$499$	12.6829	+	9.73192i	0.567764	+	0.435661i	−0.284572	+	0.958655i	$0.591852\pi$
$500$	−0.351450	+	0.0442403i	−0.0157173	+	0.00197849i
$501$	38.8846	−	13.6869i	1.73723	−	0.611486i
$502$	11.7920	−	3.12379i	0.526301	−	0.139421i
$503$	−0.702823	+	0.702823i	−0.0313373	+	0.0313373i	−0.722602	−	0.691264i	$-0.757054\pi$
$503$	−0.702823	+	0.702823i	−0.0313373	+	0.0313373i	0.691264	+	0.722602i	$0.257054\pi$
$504$	−6.03859	+	1.70816i	−0.268980	+	0.0760876i
$505$	−0.156431	−	0.156431i	−0.00696110	−	0.00696110i
$506$	−1.59370	−	0.926166i	−0.0708486	−	0.0411731i
$507$	−12.5995	+	14.6956i	−0.559561	+	0.652655i
$508$	−21.0294	−	5.76301i	−0.933029	−	0.255692i
$509$	12.0125	−	15.6550i	0.532445	−	0.693896i	−0.447245	−	0.894411i	$-0.647595\pi$
$509$	12.0125	−	15.6550i	0.532445	−	0.693896i	0.979691	+	0.200515i	$0.0642616\pi$
$510$	−0.163041	−	0.0310170i	−0.00721960	−	0.00137345i
$511$	4.20356	+	2.42693i	0.185955	+	0.107361i
$512$	−9.19049	+	20.6769i	−0.406166	+	0.913799i
$513$	−12.7380	+	9.14454i	−0.562396	+	0.403741i
$514$	16.1245	+	6.73270i	0.711223	+	0.296967i
$515$	0.0350964	−	0.266584i	0.00154653	−	0.0117471i
$516$	1.19270	+	0.787456i	0.0525058	+	0.0346658i
$517$	1.28900	−	0.169700i	0.0566902	−	0.00746341i
$518$	−4.59188	−	8.00578i	−0.201756	−	0.351754i
$519$	−36.0983	+	18.3070i	−1.58454	+	0.803587i
$520$	−0.0670019	−	0.00940228i	−0.00293823	−	0.000412317i
$521$	−5.69968	−	5.69968i	−0.249708	−	0.249708i	0.571143	−	0.820851i	$-0.306500\pi$
$521$	−5.69968	−	5.69968i	−0.249708	−	0.249708i	−0.820851	+	0.571143i	$0.806500\pi$
$522$	0.307246	−	0.0465775i	0.0134478	−	0.00203864i
$523$	12.8029	−	30.9088i	0.559830	−	1.35155i	−0.350071	−	0.936723i	$-0.613842\pi$
$523$	12.8029	−	30.9088i	0.559830	−	1.35155i	0.909901	−	0.414826i	$-0.136158\pi$
$524$	13.5581	−	10.2817i	0.592289	−	0.449159i
$525$	2.76817	−	5.77541i	0.120813	−	0.252060i
$526$	29.3488	+	22.6528i	1.27967	+	0.987708i
$527$	−4.02168	+	2.32192i	−0.175187	+	0.101144i
$528$	−1.35467	−	1.54521i	−0.0589544	−	0.0672467i
$529$	−3.19533	−	1.84482i	−0.138927	−	0.0802098i
$530$	0.0181518	+	0.0441767i	0.000788464	+	0.00191891i
$531$	8.25545	−	33.8214i	0.358256	−	1.46772i
$532$	4.13354	−	1.68473i	0.179212	−	0.0730423i
$533$	8.52994	+	11.1164i	0.369473	+	0.481506i
$534$	13.7844	+	27.3729i	0.596508	+	1.18454i
$535$	0.0243195	−	0.0907615i	0.00105142	−	0.00392396i
$536$	5.37664	−	19.4032i	0.232236	−	0.838092i
$537$	20.0391	−	30.7299i	0.864750	−	1.32609i
$538$	4.40801	+	2.56168i	0.190043	+	0.110442i
$539$	0.732458	−	1.76831i	0.0315492	−	0.0761665i
$540$	0.183264	−	0.0171591i	0.00788644	−	0.000738408i
$541$	−18.3962	+	7.61995i	−0.790914	+	0.327607i	−0.741311	−	0.671162i	$-0.765796\pi$
$541$	−18.3962	+	7.61995i	−0.790914	+	0.327607i	−0.0496028	+	0.998769i	$0.515796\pi$
$542$	−13.3044	−	17.4409i	−0.571472	−	0.749152i
$543$	−7.18050	−	34.0991i	−0.308145	−	1.46333i
$544$	−2.51970	−	21.4927i	−0.108031	−	0.921494i
$545$	0.139396	−	0.0804803i	0.00597106	−	0.00344740i
$546$	1.59778	−	1.85292i	0.0683785	−	0.0792977i
$547$	−22.1683	−	2.91852i	−0.947849	−	0.124787i	−0.359277	−	0.933231i	$-0.616977\pi$
$547$	−22.1683	−	2.91852i	−0.947849	−	0.124787i	−0.588573	+	0.808444i	$0.700310\pi$
$548$	0.0410964	−	7.23653i	0.00175555	−	0.309129i
$549$	30.9804	+	16.9733i	1.32221	+	0.724403i
$550$	2.09718	+	0.00595493i	0.0894241	+	0.000253919i
$551$	−0.213504	+	0.0572082i	−0.00909557	+	0.00243715i
$552$	14.2376	+	16.1474i	0.605992	+	0.687281i
$553$	−3.77809	−	1.01234i	−0.160661	−	0.0430489i
$554$	−35.2823	−	9.56133i	−1.49900	−	0.406222i
$555$	0.0898775	+	0.255342i	0.00381509	+	0.0108387i
$556$	2.42905	−	17.6743i	0.103015	−	0.749556i
$557$	15.5113	−	6.42500i	0.657235	−	0.272236i	−0.0290393	−	0.999578i	$-0.509245\pi$
$557$	15.5113	−	6.42500i	0.657235	−	0.272236i	0.686275	+	0.727342i	$0.259245\pi$
$558$	3.56992	−	3.71232i	0.151127	−	0.157155i
$559$	−0.557211			−0.0235675
$560$	−0.0518677	−	0.00742875i	−0.00219181	−	0.000313922i
$561$	1.86793	+	0.610841i	0.0788639	+	0.0257897i
$562$	21.7380	−	28.1636i	0.916964	−	1.18801i
$563$	−16.6816	+	21.7399i	−0.703046	+	0.916227i	−0.999243	−	0.0388997i	$-0.987615\pi$
$563$	−16.6816	+	21.7399i	−0.703046	+	0.916227i	0.296197	+	0.955127i	$0.404281\pi$
$564$	−14.9087	−	2.88011i	−0.627769	−	0.121275i
$565$	−0.0617505	+	0.0473828i	−0.00259786	+	0.00199341i
$566$	18.5991	−	18.4938i	0.781778	−	0.777351i
$567$	−3.06671	+	5.90766i	−0.128790	+	0.248098i
$568$	−11.2676	−	4.78003i	−0.472776	−	0.200565i
$569$	−10.2121	−	38.1119i	−0.428112	−	1.59774i	−0.757032	−	0.653378i	$-0.773351\pi$
$569$	−10.2121	−	38.1119i	−0.428112	−	1.59774i	0.328920	−	0.944358i	$-0.393315\pi$
$570$	−0.128189	+	0.0266139i	−0.00536926	+	0.00111473i
$571$	−2.35594	−	17.8952i	−0.0985931	−	0.748889i	−0.967313	−	0.253585i	$-0.918390\pi$
$571$	−2.35594	−	17.8952i	−0.0985931	−	0.748889i	0.868720	−	0.495304i	$-0.164943\pi$
$572$	0.772682	+	0.211750i	0.0323075	+	0.00885371i
$573$	−31.3881	+	2.41048i	−1.31126	+	0.100699i
$574$	6.58140	+	8.62766i	0.274702	+	0.360112i
$575$	−21.9704			−0.916229
$576$	9.30300	+	22.1236i	0.387625	+	0.921817i
$577$	−1.36524			−0.0568359			−0.0284179	−	0.999596i	$-0.509047\pi$
$577$	−1.36524			−0.0568359			−0.0284179	+	0.999596i	$0.509047\pi$
$578$	−2.02942	−	2.66040i	−0.0844127	−	0.110658i
$579$	−5.84613	+	12.1972i	−0.242957	+	0.506896i
$580$	0.00250236		0.000685760i	0.000103905		2.84746e-5i
$581$	0.377677	+	2.86874i	0.0156687	+	0.119015i
$582$	19.8270	+	22.2308i	0.821854	+	0.921496i
$583$	−0.146376	−	0.546282i	−0.00606226	−	0.0226247i
$584$	7.24957	−	17.0888i	0.299989	−	0.707140i
$585$	−0.0559407	+	0.0449501i	−0.00231286	+	0.00185846i
$586$	−0.517943	+	0.515010i	−0.0213960	+	0.0212749i
$587$	18.2224	−	13.9825i	0.752119	−	0.577121i	−0.159966	−	0.987122i	$-0.551139\pi$
$587$	18.2224	−	13.9825i	0.752119	−	0.577121i	0.912085	+	0.410002i	$0.134472\pi$
$588$	−14.6460	+	16.8876i	−0.603992	+	0.696434i
$589$	−2.23009	+	2.90631i	−0.0918892	+	0.119752i
$590$	0.177608	−	0.230108i	0.00731202	−	0.00947339i
$591$	−2.63322	−	12.5047i	−0.108316	−	0.514377i
$592$	−28.2443	+	21.1673i	−1.16083	+	0.869972i
$593$	−28.8818			−1.18603			−0.593016	−	0.805191i	$-0.702063\pi$
$593$	−28.8818			−1.18603			−0.593016	+	0.805191i	$0.702063\pi$
$594$	−2.17829	−	0.0756220i	−0.0893763	−	0.00310281i
$595$	0.0462959	−	0.0191764i	0.00189795	−	0.000786155i
$596$	4.23049	−	30.7819i	0.173288	−	1.26088i
$597$	−2.35528	−	0.441142i	−0.0963952	−	0.0180547i
$598$	−8.10097	−	2.19532i	−0.331273	−	0.0897734i
$599$	2.75303	+	0.737672i	0.112486	+	0.0301405i	0.314623	−	0.949217i	$-0.398122\pi$
$599$	2.75303	+	0.737672i	0.112486	+	0.0301405i	−0.202137	+	0.979357i	$0.564789\pi$
$600$	−23.2145	−	7.81101i	−0.947728	−	0.318883i
$601$	−0.389283	+	0.104308i	−0.0158792	+	0.00425482i	−0.266750	−	0.963766i	$-0.585950\pi$
$601$	−0.389283	+	0.104308i	−0.0158792	+	0.00425482i	0.250871	+	0.968021i	$0.419283\pi$
$602$	−0.431521	−	0.00122530i	−0.0175875	−	4.99395e-5i
$603$	−11.0893	−	18.2509i	−0.451591	−	0.743235i
$604$	0.100389	−	17.6771i	0.00408477	−	0.719273i
$605$	−0.191618	−	0.0252269i	−0.00779036	−	0.00102562i
$606$	−10.0762	−	28.8883i	−0.409319	−	1.17351i
$607$	26.8671	−	15.5117i	1.09050	−	0.629601i	0.156791	−	0.987632i	$-0.449885\pi$
$607$	26.8671	−	15.5117i	1.09050	−	0.629601i	0.933710	+	0.358031i	$0.116552\pi$
$608$	−8.32465	−	14.9034i	−0.337609	−	0.604414i
$609$	−0.0698460	+	0.0626504i	−0.00283030	+	0.00253872i
$610$	0.178886	+	0.234505i	0.00724289	+	0.00949482i
$611$	5.46935	−	2.26548i	0.221266	−	0.0916515i
$612$	−18.4405	−	13.6664i	−0.745413	−	0.552432i
$613$	−7.00368	+	16.9084i	−0.282876	+	0.682923i	−0.999900	−	0.0141250i	$-0.995504\pi$
$613$	−7.00368	+	16.9084i	−0.282876	+	0.682923i	0.717024	+	0.697048i	$0.245504\pi$
$614$	27.6210	+	16.0518i	1.11469	+	0.647796i
$615$	−0.143957	−	0.283860i	−0.00580492	−	0.0114463i
$616$	0.597923	+	0.165685i	0.0240910	+	0.00667563i
$617$	6.89253	−	25.7233i	0.277483	−	1.03558i	−0.676676	−	0.736281i	$-0.736580\pi$
$617$	6.89253	−	25.7233i	0.277483	−	1.03558i	0.954159	−	0.299300i	$-0.0967531\pi$
$618$	20.4004	−	31.0906i	0.820623	−	1.25065i
$619$	−5.77668	−	7.52832i	−0.232185	−	0.302589i	0.662701	−	0.748884i	$-0.269410\pi$
$619$	−5.77668	−	7.52832i	−0.232185	−	0.302589i	−0.894886	+	0.446295i	$0.852743\pi$
$620$	0.0398214	−	0.0162302i	0.00159927	−	0.000651822i
$621$	22.8221	+	0.727424i	0.915821	+	0.0291905i
$622$	−9.24108	−	22.4904i	−0.370534	−	0.901781i
$623$	−8.01379	−	4.62676i	−0.321066	−	0.185367i
$624$	−7.77921	−	5.19973i	−0.311418	−	0.208156i
$625$	21.6466	−	12.4976i	0.865862	−	0.499906i
$626$	−13.1310	−	10.1351i	−0.524820	−	0.405082i
$627$	1.54576	−	0.118708i	0.0617318	−	0.00474075i
$628$	−12.9234	+	9.80039i	−0.515701	+	0.391078i
$629$	12.9177	−	31.1860i	0.515061	−	1.24347i
$630$	−0.0434210	+	0.0346877i	−0.00172994	+	0.00138199i
$631$	12.7051	+	12.7051i	0.505783	+	0.505783i	0.913229	−	0.407447i	$-0.133581\pi$
$631$	12.7051	+	12.7051i	0.505783	+	0.505783i	−0.407447	+	0.913229i	$0.633581\pi$
$632$	−2.07874	+	14.8134i	−0.0826878	+	0.589244i
$633$	−1.20724	+	22.2297i	−0.0479834	+	0.883550i
$634$	22.0233	+	38.3969i	0.874659	+	1.52494i
$635$	−0.191448	+	0.0252047i	−0.00759740	+	0.00100022i
$636$	−0.395631	+	6.59330i	−0.0156878	+	0.261441i
$637$	1.13757	−	8.64067i	0.0450720	−	0.342356i
$638$	−0.0283518	−	0.0118381i	−0.00112246	−	0.000468676i
$639$	−11.8796	+	5.23528i	−0.469948	+	0.207105i
$640$	−0.00398268	+	0.200346i	−0.000157429	+	0.00791937i
$641$	4.57915	+	2.64377i	0.180865	+	0.104423i	0.587699	−	0.809079i	$-0.300034\pi$
$641$	4.57915	+	2.64377i	0.180865	+	0.104423i	−0.406834	+	0.913502i	$0.633367\pi$
$642$	8.48618	−	9.84132i	0.334923	−	0.388406i
$643$	4.70022	−	6.12544i	0.185359	−	0.241564i	−0.691426	−	0.722447i	$-0.743017\pi$
$643$	4.70022	−	6.12544i	0.185359	−	0.241564i	0.876785	+	0.480883i	$0.159684\pi$
$644$	−6.26881	−	1.71794i	−0.247026	−	0.0676962i
$645$	0.0124405	+	0.00233010i	0.000489845	+	9.17476e-5i
$646$	14.1153	+	8.20302i	0.555360	+	0.322743i
$647$	14.8116	+	14.8116i	0.582305	+	0.582305i	0.935536	−	0.353231i	$-0.114917\pi$
$647$	14.8116	+	14.8116i	0.582305	+	0.582305i	−0.353231	+	0.935536i	$0.614917\pi$
$648$	23.8559	+	8.88244i	0.937147	+	0.348935i
$649$	−2.43390	+	2.43390i	−0.0955388	+	0.0955388i
$650$	9.23093	−	2.44535i	0.362067	−	0.0959145i
$651$	−0.286279	+	1.52846i	−0.0112202	+	0.0599051i
$652$	−13.7500	+	1.73084i	−0.538490	+	0.0677848i
$653$	−21.1121	−	16.1999i	−0.826180	−	0.633950i	0.106638	−	0.994298i	$-0.465991\pi$
$653$	−21.1121	−	16.1999i	−0.826180	−	0.633950i	−0.932818	+	0.360348i	$0.882658\pi$
$654$	22.1998	−	1.64146i	0.868082	−	0.0641863i
$655$	0.0753447	−	0.130501i	0.00294396	−	0.00509909i
$656$	29.6760	−	29.0094i	1.15865	−	1.13263i
$657$	−7.94003	−	18.0170i	−0.309770	−	0.702910i
$658$	4.24061	−	1.74243i	0.165316	−	0.0679270i
$659$	−16.9799	−	2.23545i	−0.661444	−	0.0870808i	−0.207672	−	0.978199i	$-0.566589\pi$
$659$	−16.9799	−	2.23545i	−0.661444	−	0.0870808i	−0.453772	+	0.891118i	$0.649922\pi$
$660$	−0.0163658	−	0.00795876i	−0.000637036	−	0.000309794i
$661$	−0.270460	−	2.05435i	−0.0105197	−	0.0799049i	0.985380	−	0.170373i	$-0.0544971\pi$
$661$	−0.270460	−	2.05435i	−0.0105197	−	0.0799049i	−0.995899	+	0.0904677i	$0.971164\pi$
$662$	−5.94964	+	21.9548i	−0.231239	+	0.853298i
$663$	8.93548	+	0.485263i	0.347025	+	0.0188461i
$664$	10.7128	−	2.77289i	0.415735	−	0.107609i
$665$	0.0279518	−	0.0279518i	0.00108392	−	0.00108392i
$666$	−4.15991	+	37.2051i	−0.161193	+	1.44167i
$667$	0.297368	+	0.123174i	0.0115141	+	0.00476931i
$668$	41.0873	+	24.0339i	1.58971	+	0.929899i
$669$	3.59090	+	46.7590i	0.138832	+	1.80781i
$670$	−0.0227718	−	0.176848i	−0.000879750	−	0.00683222i
$671$	−1.74629	−	3.02466i	−0.0674146	−	0.116766i
$672$	−6.01302	−	4.04393i	−0.231957	−	0.155998i
$673$	16.4486	−	28.4897i	0.634045	−	1.09820i	−0.352671	−	0.935747i	$-0.614727\pi$
$673$	16.4486	−	28.4897i	0.634045	−	1.09820i	0.986717	−	0.162451i	$-0.0519400\pi$
$674$	9.33580	+	3.89811i	0.359602	+	0.150150i
$675$	−22.9010	+	12.2662i	−0.881459	+	0.472127i
$676$	−22.3516	−	0.126935i	−0.859676	−	0.00488212i
$677$	0.231655	−	0.177755i	0.00890321	−	0.00683167i	−0.604300	−	0.796757i	$-0.706547\pi$
$677$	0.231655	−	0.177755i	0.00890321	−	0.00683167i	0.613203	+	0.789925i	$0.289881\pi$
$678$	−10.5396	+	2.18817i	−0.404771	+	0.0840361i
$679$	−8.68745	−	2.32779i	−0.333394	−	0.0893325i
$680$	−0.0944030	−	0.166776i	−0.00362019	−	0.00639556i
$681$	18.1442	−	9.20166i	0.695285	−	0.352608i
$682$	−0.492225	+	0.130394i	−0.0188483	+	0.00499306i
$683$	−27.1904	−	11.2626i	−1.04041	−	0.430953i	−0.203952	−	0.978981i	$-0.565379\pi$
$683$	−27.1904	−	11.2626i	−1.04041	−	0.430953i	−0.836460	+	0.548028i	$0.815379\pi$
$684$	−17.5652	−	4.39333i	−0.671623	−	0.167983i
$685$	−0.0245250	−	0.0592085i	−0.000937050	−	0.00226224i
$686$	1.87622	−	13.9452i	0.0716342	−	0.532429i
$687$	28.1180	+	31.3474i	1.07277	+	1.19598i
$688$	0.196811	+	1.63853i	0.00750334	+	0.0624682i
$689$	−1.28759	−	2.23018i	−0.0490534	−	0.0849629i
$690$	0.171686	+	0.0828897i	0.00653596	+	0.00315556i
$691$	−2.82658	+	21.4700i	−0.107528	+	0.816757i	0.849668	+	0.527318i	$0.176802\pi$
$691$	−2.82658	+	21.4700i	−0.107528	+	0.816757i	−0.957196	+	0.289439i	$0.906531\pi$
$692$	−43.0768	−	18.1303i	−1.63753	−	0.689209i
$693$	0.562413	−	0.341723i	0.0213643	−	0.0129810i
$694$	18.3865	+	18.4912i	0.697943	+	0.701918i
$695$	−0.0408914	−	0.152609i	−0.00155110	−	0.00578878i
$696$	0.270415	+	0.235870i	0.0102501	+	0.00894063i
$697$	−10.2721	+	38.3361i	−0.389085	+	1.45208i
$698$	36.7545	−	21.0813i	1.39118	−	0.797938i
$699$	−5.22376	+	27.8899i	−0.197581	+	1.05489i
$700$	7.15409	−	1.87345i	0.270399	−	0.0708099i
$701$	0.577635	+	1.39453i	0.0218170	+	0.0526708i	0.934413	−	0.356193i	$-0.115925\pi$
$701$	0.577635	+	1.39453i	0.0218170	+	0.0526708i	−0.912596	+	0.408863i	$0.865925\pi$
$702$	−9.66976	+	2.23452i	−0.364962	+	0.0843366i
$703$		−	26.6282i		−	1.00430i
$704$	0.349752	−	2.34693i	0.0131818	−	0.0884533i
$705$	−0.131585	+	0.0277088i	−0.00495577	+	0.00104357i
$706$	2.68803	+	20.8755i	0.101165	+	0.785659i
$707$	7.32872	+	5.62353i	0.275625	+	0.211495i
$708$	35.9558	−	17.9787i	1.35130	−	0.675681i
$709$	12.4470	+	16.2212i	0.467455	+	0.609200i	0.966277	−	0.257505i	$-0.0829003\pi$
$709$	12.4470	+	16.2212i	0.467455	+	0.609200i	−0.498822	+	0.866705i	$0.666234\pi$
$710$	−0.108391		0.000307776i	−0.00406786		1.15506e-5i
$711$	9.93795	+	12.3679i	0.372702	+	0.463831i
$712$	−13.8208	+	32.5786i	−0.517956	+	1.22093i
$713$	5.15270	−	1.38066i	0.192970	−	0.0517062i
$714$	6.91884	+	0.395451i	0.258931	+	0.0147994i
$715$	0.00703438		0.000926093i	0.000263071		3.46339e-5i
$716$	42.0301	−	5.29072i	1.57074	−	0.197723i
$717$	12.0531	+	5.77711i	0.450133	+	0.215750i
$718$	−5.36619	+	39.8848i	−0.200264	+	1.48849i
$719$		−	14.3092i		−	0.533645i	−0.963746	−	0.266822i	$-0.914026\pi$
$719$		−	14.3092i		−	0.533645i	0.963746	−	0.266822i	$-0.0859737\pi$
$720$	0.151938	+	0.148622i	0.00566240	+	0.00553881i
$721$			11.2276i			0.418139i
$722$	−13.8664	−	1.86562i	−0.516054	−	0.0694311i
$723$	1.28530	+	16.7366i	0.0478010	+	0.622441i
$724$	24.6761	−	31.7831i	0.917080	−	1.18121i
$725$	−0.363074	+	0.0477995i	−0.0134842	+	0.00177523i
$726$	−22.3476	−	14.6636i	−0.829396	−	0.544215i
$727$	−12.1404	+	3.25301i	−0.450263	+	0.120647i	−0.476822	−	0.879000i	$-0.658211\pi$
$727$	−12.1404	+	3.25301i	−0.450263	+	0.120647i	0.0265597	+	0.999647i	$0.491545\pi$
$728$	2.82507	+	0.0240658i	0.104704	+	0.000891938i
$729$	24.1949	−	11.9835i	0.896109	−	0.443834i
$730$	0.000466785	−	0.164391i	1.72765e−5	−	0.00608437i
$731$	−0.960798	−	1.25214i	−0.0355364	−	0.0463119i
$732$	8.17836	+	39.9619i	0.302281	+	1.47704i
$733$	−15.2460	−	11.6987i	−0.563123	−	0.432100i	0.287572	−	0.957759i	$-0.407152\pi$
$733$	−15.2460	−	11.6987i	−0.563123	−	0.432100i	−0.850695	+	0.525659i	$0.823819\pi$
$734$	−47.5414	+	6.12166i	−1.75478	+	0.225955i
$735$	−0.0615306	+	0.188158i	−0.00226959	+	0.00694032i
$736$	−3.59421	+	24.5970i	−0.132484	+	0.906658i
$737$			2.11142i			0.0777750i
$738$	−0.860558	−	44.0085i	−0.0316776	−	1.61998i
$739$	4.66815	+	11.2699i	0.171721	+	0.414571i	0.986186	−	0.165642i	$-0.0529695\pi$
$739$	4.66815	+	11.2699i	0.171721	+	0.414571i	−0.814465	+	0.580212i	$0.802970\pi$
$740$	−0.157823	+	0.269806i	−0.00580167	+	0.00991828i
$741$	6.65874	−	2.34380i	0.244615	−	0.0861015i
$742$	−0.992246	−	1.72995i	−0.0364265	−	0.0635083i
$743$	−3.33507	+	12.4466i	−0.122352	+	0.456623i	−0.999731	−	0.0231738i	$-0.992623\pi$
$743$	−3.33507	+	12.4466i	−0.122352	+	0.456623i	0.877380	+	0.479797i	$0.159290\pi$
$744$	5.93534	+	0.373067i	0.217600	+	0.0136773i
$745$	−0.0712174	−	0.265787i	−0.00260921	−	0.00973769i
$746$	−2.18341	+	2.17105i	−0.0799403	+	0.0794876i
$747$	5.63948	−	10.2934i	0.206338	−	0.376617i
$748$	0.856502	+	2.10145i	0.0313168	+	0.0768367i
$749$	−0.512128	+	3.89000i	−0.0187128	+	0.142138i
$750$	−0.432653	+	0.0319905i	−0.0157982	+	0.00116813i
$751$	14.0978	+	24.4181i	0.514436	+	0.891029i	0.999860	+	0.0167503i	$0.00533204\pi$
$751$	14.0978	+	24.4181i	0.514436	+	0.891029i	−0.485424	+	0.874279i	$0.661335\pi$
$752$	−8.59365	−	15.2829i	−0.313378	−	0.557311i
$753$	14.6197	−	3.07858i	0.532771	−	0.112190i
$754$	−0.138650	−	0.0186542i	−0.00504932	−	0.000679347i
$755$	−0.0599087	−	0.144632i	−0.00218030	−	0.00526371i
$756$	−7.49347	+	1.70922i	−0.272535	+	0.0621636i
$757$	42.1796	+	17.4713i	1.53304	+	0.635007i	0.980152	−	0.198248i	$-0.0635250\pi$
$757$	42.1796	+	17.4713i	1.53304	+	0.635007i	0.552890	+	0.833254i	$0.313525\pi$
$758$	11.7379	+	44.3095i	0.426341	+	1.60939i
$759$	−1.89100	−	1.23313i	−0.0686390	−	0.0447598i
$760$	−0.119148	−	0.0930489i	−0.00432196	−	0.00337524i
$761$	−9.42510	−	2.52545i	−0.341660	−	0.0915475i	0.0839093	−	0.996473i	$-0.473259\pi$
$761$	−9.42510	−	2.52545i	−0.341660	−	0.0915475i	−0.425569	+	0.904926i	$0.639926\pi$
$762$	−25.3589	−	8.37253i	−0.918656	−	0.303305i
$763$	−5.33224	+	4.09157i	−0.193040	+	0.148125i
$764$	−25.5574	−	25.8493i	−0.924634	−	0.935196i
$765$	−0.197468	−	0.0481999i	−0.00713947	−	0.00174267i
$766$	−4.05194	+	9.70422i	−0.146403	+	0.350628i
$767$	−7.83651	+	13.5732i	−0.282960	+	0.490101i
$768$	−12.5426	+	24.7120i	−0.452591	+	0.891718i
$769$	−10.0638	−	17.4311i	−0.362911	−	0.628580i	0.625528	−	0.780202i	$-0.284884\pi$
$769$	−10.0638	−	17.4311i	−0.362911	−	0.628580i	−0.988439	+	0.151622i	$0.951550\pi$
$770$	0.00544967		0.000701726i	0.000196392		2.52884e-5i
$771$	19.2986	+	9.24986i	0.695021	+	0.333126i
$772$	−15.1088	+	3.95657i	−0.543778	+	0.142400i
$773$	−17.0413	−	7.05874i	−0.612933	−	0.253885i	0.0545490	−	0.998511i	$-0.482628\pi$
$773$	−17.0413	−	7.05874i	−0.612933	−	0.253885i	−0.667482	+	0.744626i	$0.732628\pi$
$774$	1.40926	+	1.03823i	0.0506549	+	0.0373184i
$775$	−4.29165	+	4.29165i	−0.154161	+	0.154161i
$776$	−4.77991	+	34.0623i	−0.171589	+	1.22277i
$777$	−5.11255	−	10.0811i	−0.183412	−	0.361658i
$778$	−44.7802	−	12.1352i	−1.60545	−	0.435068i
$779$	4.08658	+	31.0406i	0.146417	+	1.11215i
$780$	−0.0813601	−	0.0157174i	−0.00291316	−	0.000562774i
$781$	1.27253	+	0.167532i	0.0455348	+	0.00599477i
$782$	−9.03528	−	21.9895i	−0.323101	−	0.786343i
$783$	0.378732	−	0.0376315i	0.0135348	−	0.00134484i
$784$	−25.8104	−	0.293166i	−0.921801	−	0.0104702i
$785$	−0.0718176	+	0.124392i	−0.00256328	+	0.00443973i
$786$	17.2305	−	11.7225i	0.614590	−	0.418126i
$787$	17.5089	+	13.4351i	0.624126	+	0.478908i	0.871752	−	0.489947i	$-0.162984\pi$
$787$	17.5089	+	13.4351i	0.624126	+	0.478908i	−0.247627	+	0.968856i	$0.579651\pi$
$788$	9.04916	−	11.6554i	0.322363	−	0.415208i
$789$	34.4714	+	29.5545i	1.22722	+	1.05217i
$790$	0.0339225	+	0.128054i	0.00120691	+	0.00455595i
$791$	2.29817	−	2.29817i	0.0817135	−	0.0817135i
$792$	−1.55967	−	1.97525i	−0.0554206	−	0.0701876i
$793$	−11.2452	−	11.2452i	−0.399328	−	0.399328i
$794$	2.93436	−	5.04929i	0.104136	−	0.179193i
$795$	0.0194214	+	0.0551762i	0.000688805	+	0.00195690i
$796$	−1.36984	−	2.40406i	−0.0485526	−	0.0852095i
$797$	−16.8456	+	21.9536i	−0.596701	+	0.777635i	−0.989892	−	0.141821i	$-0.954704\pi$
$797$	−16.8456	+	21.9536i	−0.596701	+	0.777635i	0.393192	+	0.919456i	$0.371371\pi$
$798$	5.16188	−	1.80046i	0.182729	−	0.0637357i
$799$	14.5217	+	8.38409i	0.513740	+	0.296608i
$800$	−10.4512	−	26.2806i	−0.369505	−	0.929161i
$801$	15.1371	+	34.3481i	0.534843	+	1.21363i
$802$	−2.79228	+	6.68739i	−0.0985989	+	0.236140i
$803$	−0.254086	+	1.92997i	−0.00896649	+	0.0681072i
$804$	7.79760	−	23.3942i	0.275000	−	0.825050i
$805$	−0.0570702	+	0.00751344i	−0.00201146	+	0.000264814i
$806$	−2.01125	+	1.15360i	−0.0708434	+	0.0406337i
$807$	5.23031	+	3.41071i	0.184116	+	0.120063i
$808$	17.9241	−	30.4436i	0.630568	−	1.07100i
$809$	−11.7264	−	11.7264i	−0.412278	−	0.412278i	0.470253	−	0.882531i	$-0.344162\pi$
$809$	−11.7264	−	11.7264i	−0.412278	−	0.412278i	−0.882531	+	0.470253i	$0.844162\pi$
$810$	0.225235	−	0.00945264i	0.00791397	−	0.000332132i
$811$	13.3540	−	32.2393i	0.468921	−	1.13208i	−0.495714	−	0.868486i	$-0.665093\pi$
$811$	13.3540	−	32.2393i	0.468921	−	1.13208i	0.964635	−	0.263590i	$-0.0849065\pi$
$812$	−0.107333	−	0.0147513i	−0.00376666	−	0.000517668i
$813$	−15.1752	−	22.1699i	−0.532216	−	0.777531i
$814$	2.26156	−	2.93006i	0.0792677	−	0.102699i
$815$	−0.106286	+	0.0613644i	−0.00372305	+	0.00214950i
$816$	−1.72911	−	26.4469i	−0.0605311	−	0.925828i
$817$	−1.07823	−	0.622519i	−0.0377226	−	0.0217792i
$818$	−32.2847	+	13.2655i	−1.12881	+	0.463817i
$819$	2.07091	−	2.16579i	0.0723634	−	0.0756788i
$820$	0.142568	−	0.338735i	0.00497868	−	0.0118291i
$821$	−9.58463	−	12.4909i	−0.334506	−	0.435936i	0.595570	−	0.803303i	$-0.296926\pi$
$821$	−9.58463	−	12.4909i	−0.334506	−	0.435936i	−0.930076	+	0.367367i	$0.880259\pi$
$822$	0.505749	−	8.84860i	0.0176400	−	0.308630i
$823$	10.2737	−	38.3420i	0.358119	−	1.33652i	−0.518394	−	0.855142i	$-0.673470\pi$
$823$	10.2737	−	38.3420i	0.358119	−	1.33652i	0.876513	−	0.481377i	$-0.159863\pi$
$824$	42.6176	−	5.24179i	1.48465	−	0.182606i
$825$	2.56474	+	0.139285i	0.0892929	+	0.00484927i
$826$	−6.09868	+	10.4943i	−0.212200	+	0.365143i
$827$	−4.47074	+	10.7933i	−0.155463	+	0.375321i	−0.982351	−	0.187045i	$-0.940109\pi$
$827$	−4.47074	+	10.7933i	−0.155463	+	0.375321i	0.826888	+	0.562366i	$0.190109\pi$
$828$	16.3980	+	20.6465i	0.569870	+	0.717515i
$829$	−46.5111	+	19.2655i	−1.61540	+	0.669119i	−0.993484	−	0.113968i	$-0.963644\pi$
$829$	−46.5111	+	19.2655i	−1.61540	+	0.669119i	−0.621912	+	0.783087i	$0.713644\pi$
$830$	0.0779156	−	0.0594360i	0.00270449	−	0.00206305i
$831$	−42.5530	−	13.9155i	−1.47615	−	0.482722i
$832$	−1.22758	−	10.7346i	−0.0425586	−	0.372154i
$833$	21.3784	−	12.3428i	0.740717	−	0.427653i
$834$	4.08349	−	21.4650i	0.141400	−	0.743271i
$835$	0.417936	+	0.0550223i	0.0144633	+	0.00190413i
$836$	1.25862	+	1.27299i	0.0435301	+	0.0440274i
$837$	4.60012	−	4.31593i	0.159003	−	0.149180i
$838$	−0.00468874	+	1.65126i	−0.000161970	+	0.0570419i
$839$	−21.9100	+	5.87077i	−0.756418	+	0.202681i	−0.616363	−	0.787462i	$-0.711395\pi$
$839$	−21.9100	+	5.87077i	−0.756418	+	0.202681i	−0.140055	+	0.990144i	$0.544728\pi$
$840$	−0.0629731	−	0.0123510i	−0.00217278	−	0.000426149i
$841$	−28.0067	−	7.50436i	−0.965747	−	0.258771i
$842$	−6.94007	+	25.6096i	−0.239171	+	0.882565i
$843$	28.3611	−	33.0794i	0.976807	−	1.13932i
$844$	−20.4828	+	15.5330i	−0.705048	+	0.534668i
$845$	−0.182878	+	0.0757507i	−0.00629120	+	0.00260590i
$846$	−18.0539	−	4.46113i	−0.620707	−	0.153377i
$847$	8.07031			0.277299
$848$	−6.10324	+	4.57399i	−0.209586	+	0.157071i
$849$	23.9131	−	21.4495i	0.820695	−	0.736147i
$850$	21.4120	+	16.5268i	0.734424	+	0.566864i
$851$	−23.6051	+	30.7628i	−0.809173	+	1.05453i
$852$	−13.4808	−	6.55578i	−0.461844	−	0.224597i
$853$	2.89757	−	2.22339i	0.0992110	−	0.0761273i	−0.557965	−	0.829865i	$-0.688418\pi$
$853$	2.89757	−	2.22339i	0.0992110	−	0.0761273i	0.657176	+	0.753737i	$0.271751\pi$
$854$	−8.68387	−	8.73333i	−0.297156	−	0.298848i
$855$	−0.158467	+	0.0244836i	−0.00541945	+	0.000837322i
$856$	15.0046	+	0.127819i	0.512848	+	0.00436877i
$857$	−6.43398	−	24.0119i	−0.219781	−	0.820232i	−0.984429	−	0.175784i	$-0.943754\pi$
$857$	−6.43398	−	24.0119i	−0.219781	−	0.820232i	0.764648	−	0.644448i	$-0.222913\pi$
$858$	0.931760	+	0.307631i	0.0318098	+	0.0105024i
$859$	−4.28880	−	32.5767i	−0.146332	−	1.11150i	−0.894204	−	0.447660i	$-0.852258\pi$
$859$	−4.28880	−	32.5767i	−0.146332	−	1.11150i	0.747872	−	0.663843i	$-0.231076\pi$
$860$	0.00723545	+	0.0126982i	0.000246727	+	0.000433003i
$861$	7.50684	+	10.9670i	0.255832	+	0.373753i
$862$	−43.2109	+	32.9624i	−1.47177	+	1.12270i
$863$	35.4438			1.20652			0.603260	−	0.797545i	$-0.293868\pi$
$863$	35.4438			1.20652			0.603260	+	0.797545i	$0.293868\pi$
$864$	9.98623	+	27.6455i	0.339738	+	0.940520i
$865$	−0.413894			−0.0140728
$866$	−29.9731	+	22.8643i	−1.01853	+	0.776959i
$867$	−2.31478	−	3.38174i	−0.0786142	−	0.114850i
$868$	−1.56011	+	0.888957i	−0.0529537	+	0.0301732i
$869$	−0.204749	−	1.55522i	−0.00694562	−	0.0527573i
$870$	0.00301754		0.000996276i	0.000102304		3.37769e-5i
$871$	2.48832	+	9.28652i	0.0843134	+	0.314662i
$872$	18.0201	+	18.3297i	0.610237	+	0.620723i
$873$	22.8516	+	28.4390i	0.773410	+	0.962515i
$874$	−13.2232	−	13.2985i	−0.447282	−	0.449829i
$875$	0.103920	−	0.0797406i	0.00351314	−	0.00269572i
$876$	9.94275	−	20.4455i	0.335934	−	0.690788i
$877$	−8.89770	+	11.5957i	−0.300454	+	0.391559i	−0.919044	−	0.394154i	$-0.871038\pi$
$877$	−8.89770	+	11.5957i	−0.300454	+	0.391559i	0.618590	+	0.785714i	$0.287704\pi$
$878$	−46.0813	−	35.5678i	−1.55517	−	1.20035i
$879$	−0.665925	+	0.597322i	−0.0224611	+	0.0201472i
$880$	−0.00520785	−	0.0203581i	−0.000175556	−	0.000686271i
$881$	−22.1676			−0.746846			−0.373423	−	0.927661i	$-0.621816\pi$
$881$	−22.1676			−0.746846			−0.373423	+	0.927661i	$0.621816\pi$
$882$	−18.9769	+	19.7338i	−0.638985	+	0.664473i
$883$	−31.7946	+	13.1697i	−1.06997	+	0.443197i	−0.846981	−	0.531623i	$-0.821582\pi$
$883$	−31.7946	+	13.1697i	−1.06997	+	0.443197i	−0.222992	+	0.974820i	$0.571582\pi$
$884$	6.24368	+	8.23331i	0.209998	+	0.276916i
$885$	0.231721	−	0.270272i	0.00778921	−	0.00908509i
$886$	−11.5956	+	42.7888i	−0.389560	+	1.43752i
$887$	40.9370	+	10.9690i	1.37453	+	0.368304i	0.869131	−	0.494582i	$-0.164679\pi$
$887$	40.9370	+	10.9690i	1.37453	+	0.368304i	0.505399	+	0.862886i	$0.331345\pi$
$888$	−35.8787	+	24.1126i	−1.20401	+	0.809165i
$889$	7.78843	−	2.08690i	0.261216	−	0.0699925i
$890$	−0.000889893		0.313399i	−2.98293e−5		0.0105052i
$891$	−2.65956	−	0.229601i	−0.0890987	−	0.00769194i
$892$	−38.5078	+	38.0729i	−1.28934	+	1.27478i
$893$	13.1145	+	1.72656i	0.438860	+	0.0577771i
$894$	7.11190	−	37.3839i	0.237858	−	1.25030i
$895$	0.324890	−	0.187575i	0.0108599	−	0.00626995i
$896$	−0.927067	−	8.31587i	−0.0309711	−	0.277814i
$897$	−9.77033	−	3.19505i	−0.326222	−	0.106680i
$898$	−0.494694	+	0.377365i	−0.0165082	+	0.0125928i
$899$	0.0821476	−	0.0340267i	0.00273978	−	0.00113485i
$900$	−27.9026	−	11.0150i	−0.930087	−	0.367167i
$901$	2.79134	−	6.73890i	0.0929932	−	0.224505i
$902$	−2.18664	+	3.76266i	−0.0728072	+	0.125283i
$903$	−0.527727	−	0.0286595i	−0.0175617	−	0.000953730i
$904$	−9.79626	−	7.65039i	−0.325819	−	0.254448i
$905$	0.0922277	−	0.344199i	0.00306575	−	0.0114415i
$906$	1.23543	−	21.6151i	0.0410443	−	0.718112i
$907$	15.2692	+	19.8993i	0.507007	+	0.660744i	0.974797	−	0.223096i	$-0.0716162\pi$
$907$	15.2692	+	19.8993i	0.507007	+	0.660744i	−0.467790	+	0.883840i	$0.654950\pi$
$908$	21.6517	+	9.11284i	0.718538	+	0.302420i
$909$	−10.5062	−	35.9682i	−0.348469	−	1.19299i
$910$	0.0231420	−	0.00950883i	0.000767149	−	0.000315215i
$911$	−33.9124	−	19.5794i	−1.12357	−	0.648693i	−0.181260	−	0.983435i	$-0.558017\pi$
$911$	−33.9124	−	19.5794i	−1.12357	−	0.648693i	−0.942310	+	0.334742i	$0.891351\pi$
$912$	−9.24405	−	18.7527i	−0.306101	−	0.620965i
$913$	−1.00496	+	0.580214i	−0.0332593	+	0.0192023i
$914$	21.5249	−	27.8875i	0.711980	−	0.922435i
$915$	0.204040	+	0.298089i	0.00674536	+	0.00985450i
$916$	−6.62048	+	48.1720i	−0.218747	+	1.59165i
$917$	−2.40794	+	5.81328i	−0.0795172	+	0.191972i
$918$	−21.6949	−	17.8764i	−0.716037	−	0.590010i
$919$	38.7321	+	38.7321i	1.27765	+	1.27765i	0.941977	+	0.335677i	$0.108965\pi$
$919$	38.7321	+	38.7321i	1.27765	+	1.27765i	0.335677	+	0.941977i	$0.391035\pi$
$920$	0.0551633	+	0.213118i	0.00181868	+	0.00702628i
$921$	32.7737	+	21.3719i	1.07993	+	0.704227i
$922$	−6.49410	+	3.72482i	−0.213872	+	0.122671i
$923$	5.79435	−	0.762840i	0.190723	−	0.0251092i
$924$	0.720907	+	0.240288i	0.0237161	+	0.00790489i
$925$	5.75843	−	43.7396i	0.189336	−	1.43815i
$926$	5.41835	−	12.9767i	0.178058	−	0.426441i
$927$	26.9091	−	36.7437i	0.883812	−	1.20682i
$928$	−0.00588238	+	0.414300i	−0.000193098	+	0.0136001i
$929$	−35.5836	−	20.5442i	−1.16746	−	0.674034i	−0.214380	−	0.976750i	$-0.568773\pi$
$929$	−35.5836	−	20.5442i	−1.16746	−	0.674034i	−0.953081	+	0.302716i	$0.902106\pi$
$930$	0.0497282	−	0.0173452i	0.00163065	−	0.000568771i
$931$	11.8547	−	15.4493i	0.388521	−	0.506330i
$932$	−28.4675	+	16.2209i	−0.932484	+	0.531332i
$933$	−9.88742	−	28.0902i	−0.323700	−	0.919632i
$934$	20.5916	−	35.4329i	0.673776	−	1.15940i
$935$	0.0142104	+	0.0142104i	0.000464731	+	0.000464731i
$936$	−9.18768	−	6.84956i	−0.300309	−	0.223885i
$937$	15.8175	−	15.8175i	0.516736	−	0.516736i	−0.399846	−	0.916582i	$-0.630937\pi$
$937$	15.8175	−	15.8175i	0.516736	−	0.516736i	0.916582	+	0.399846i	$0.130937\pi$
$938$	1.90661	+	7.19723i	0.0622529	+	0.234998i
$939$	−15.4230	−	13.2231i	−0.503309	−	0.431518i
$940$	−0.122648	−	0.0952224i	−0.00400033	−	0.00310581i
$941$	−36.7163	−	28.1734i	−1.19692	−	0.918427i	−0.198818	−	0.980037i	$-0.563710\pi$
$941$	−36.7163	−	28.1734i	−1.19692	−	0.918427i	−0.998100	+	0.0616090i	$0.980377\pi$
$942$	−16.4238	+	11.1737i	−0.535117	+	0.364058i
$943$	22.7955	−	39.4829i	0.742323	−	1.28574i
$944$	42.6812	+	18.2498i	1.38915	+	0.593980i
$945$	−0.0552927	+	0.0396944i	−0.00179867	+	0.00129126i
$946$	−0.0657733	−	0.160075i	−0.00213847	−	0.00520448i
$947$	−17.0827	−	2.24898i	−0.555112	−	0.0730819i	−0.152249	−	0.988342i	$-0.548652\pi$
$947$	−17.0827	−	2.24898i	−0.555112	−	0.0730819i	−0.402863	+	0.915260i	$0.631985\pi$
$948$	−3.47495	+	17.9878i	−0.112861	+	0.584216i
$949$	1.15695	+	8.78793i	0.0375563	+	0.285268i
$950$	20.5943	+	5.58096i	0.668169	+	0.181070i
$951$	24.5206	+	48.3505i	0.795133	+	1.56787i
$952$	4.81719	+	6.38986i	0.156126	+	0.207096i
$953$	−19.8577	+	19.8577i	−0.643254	+	0.643254i	−0.951354	−	0.308100i	$-0.900307\pi$
$953$	−19.8577	+	19.8577i	−0.643254	+	0.643254i	0.308100	+	0.951354i	$0.400307\pi$
$954$	−0.898903	+	8.03954i	−0.0291031	+	0.260290i
$955$	−0.297412	−	0.123192i	−0.00962403	−	0.00398640i
$956$	3.90985	+	14.9304i	0.126454	+	0.482884i
$957$	−0.0339327	−	0.0162641i	−0.00109689	−	0.000525742i
$958$	−33.2538	+	4.28192i	−1.07438	+	0.138342i
$959$	1.33802	+	2.31751i	0.0432068	+	0.0748364i
$960$	−0.0174815	+	0.244798i	−0.000564214	+	0.00790081i
$961$	−14.7632	+	25.5706i	−0.476232	+	0.824857i
$962$	6.49380	−	15.5524i	0.209369	−	0.501429i
$963$	10.9991	−	11.5030i	0.354441	−	0.370680i
$964$	−13.7832	+	13.6276i	−0.443928	+	0.438914i
$965$	−0.109731	+	0.0841999i	−0.00353238	+	0.00271049i
$966$	−7.55942	−	2.49583i	−0.243220	−	0.0803019i
$967$	−17.1000	−	4.58194i	−0.549900	−	0.147345i	−0.0268380	−	0.999640i	$-0.508544\pi$
$967$	−17.1000	−	4.58194i	−0.549900	−	0.147345i	−0.523062	+	0.852294i	$0.675210\pi$
$968$	−3.76774	−	30.6330i	−0.121100	−	0.984583i
$969$	16.7485	+	10.9218i	0.538040	+	0.350858i
$970$	0.0780024	+	0.294451i	0.00250450	+	0.00945424i
$971$	27.8521	+	11.5367i	0.893817	+	0.370231i	0.781840	−	0.623480i	$-0.214282\pi$
$971$	27.8521	+	11.5367i	0.893817	+	0.370231i	0.111977	+	0.993711i	$0.464282\pi$
$972$	28.6197	+	12.3659i	0.917976	+	0.396636i
$973$	2.52464	+	6.09501i	0.0809361	+	0.195397i
$974$	11.7865	+	1.58578i	0.377663	+	0.0508116i
$975$	11.4445	−	2.40996i	0.366518	−	0.0771804i
$976$	−29.0955	+	37.0393i	−0.931325	+	1.18560i
$977$	29.9220	+	51.8264i	0.957290	+	1.65807i	0.729039	+	0.684472i	$0.239967\pi$
$977$	29.9220	+	51.8264i	0.957290	+	1.65807i	0.228251	+	0.973602i	$0.426699\pi$
$978$	−16.9269	+	1.25158i	−0.541262	+	0.0400211i
$979$	0.484396	−	3.67935i	0.0154814	−	0.117593i
$980$	−0.211682	+	0.0862763i	−0.00676192	+	0.00275600i
$981$	27.2565	−	0.610412i	0.870234	−	0.0194890i
$982$	−3.59539	+	3.57503i	−0.114734	+	0.114084i
$983$	−10.7240	−	40.0225i	−0.342043	−	1.27652i	−0.896029	−	0.443995i	$-0.853561\pi$
$983$	−10.7240	−	40.0225i	−0.342043	−	1.27652i	0.553987	−	0.832525i	$-0.313106\pi$
$984$	38.1234	−	33.6143i	1.21533	−	1.07159i
$985$	0.0338215	−	0.126224i	0.00107764	−	0.00402182i
$986$	−0.197154	−	0.343732i	−0.00627867	−	0.0109466i
$987$	5.29648	−	1.86430i	0.168589	−	0.0593413i
$988$	7.03593	+	4.11565i	0.223843	+	0.130936i
$989$	0.693807	+	1.67500i	0.0220618	+	0.0532618i
$990$	−0.0195165	−	0.0107647i	−0.000620274	−	0.000342124i
$991$		−	56.2448i		−	1.78667i	−0.449386	−	0.893337i	$-0.648357\pi$
$991$		−	56.2448i		−	1.78667i	0.449386	−	0.893337i	$-0.351643\pi$
$992$	4.10264	+	5.50681i	0.130259	+	0.174841i
$993$	−8.65905	+	26.4790i	−0.274787	+	0.840286i
$994$	4.48899	−	0.578025i	0.142382	−	0.0183338i
$995$	−0.0194400	−	0.0149169i	−0.000616291	−	0.000472897i
$996$	13.2776	−	2.71731i	0.420716	−	0.0861011i
$997$	2.87486	+	3.74659i	0.0910478	+	0.118656i	0.836656	−	0.547729i	$-0.184508\pi$
$997$	2.87486	+	3.74659i	0.0910478	+	0.118656i	−0.745608	+	0.666385i	$0.767841\pi$
$998$	−0.0641956	+	22.6081i	−0.00203208	+	0.715648i
$999$	−7.42986	+	45.2447i	−0.235070	+	1.43148i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.bf.a.11.35	✓	368
3.2	odd	2		864.2.bn.a.683.12		368
9.4	even	3		864.2.bn.a.395.2		368
9.5	odd	6	inner	288.2.bf.a.203.45	yes	368
32.3	odd	8	inner	288.2.bf.a.227.45	yes	368
96.35	even	8		864.2.bn.a.35.2		368
288.67	odd	24		864.2.bn.a.611.12		368
288.131	even	24	inner	288.2.bf.a.131.35	yes	368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.35	✓	368	1.1	even	1	trivial
288.2.bf.a.131.35	yes	368	288.131	even	24	inner
288.2.bf.a.203.45	yes	368	9.5	odd	6	inner
288.2.bf.a.227.45	yes	368	32.3	odd	8	inner
864.2.bn.a.35.2		368	96.35	even	8
864.2.bn.a.395.2		368	9.4	even	3
864.2.bn.a.611.12		368	288.67	odd	24
864.2.bn.a.683.12		368	3.2	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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.bf (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.857729 + 1.12441i) q^{2} +(0.978339 + 1.42928i) q^{3} +(-0.528601 + 1.92888i) q^{4} +(0.00231185 + 0.0175602i) q^{5} +(-0.767953 + 2.32599i) q^{6} +(-0.191417 - 0.714379i) q^{7} +(-2.62225 + 1.06009i) q^{8} +(-1.08571 + 2.79665i) q^{9} +O(q^{10})\)	\(q+(0.857729 + 1.12441i) q^{2} +(0.978339 + 1.42928i) q^{3} +(-0.528601 + 1.92888i) q^{4} +(0.00231185 + 0.0175602i) q^{5} +(-0.767953 + 2.32599i) q^{6} +(-0.191417 - 0.714379i) q^{7} +(-2.62225 + 1.06009i) q^{8} +(-1.08571 + 2.79665i) q^{9} +(-0.0177620 + 0.0176614i) q^{10} +(0.235313 - 0.180562i) q^{11} +(-3.27407 + 1.13158i) q^{12} +(0.822172 - 1.07148i) q^{13} +(0.639071 - 0.827975i) q^{14} +(-0.0228368 + 0.0204841i) q^{15} +(-3.44116 - 2.03922i) q^{16} +3.82544 q^{17} +(-4.07582 + 1.17799i) q^{18} +(2.78801 - 1.15483i) q^{19} +(-0.0350936 - 0.00482307i) q^{20} +(0.833779 - 0.972494i) q^{21} +(0.404862 + 0.109715i) q^{22} +(-4.24462 - 1.13734i) q^{23} +(-4.08062 - 2.71081i) q^{24} +(4.82933 - 1.29401i) q^{25} +(1.90998 + 0.00542337i) q^{26} +(-5.05939 + 1.18429i) q^{27} +(1.47913 + 0.00840004i) q^{28} +(-0.0726193 - 0.00956051i) q^{29} +(-0.0426204 - 0.00810809i) q^{30} +(-1.05130 + 0.606969i) q^{31} +(-0.658670 - 5.61838i) q^{32} +(0.488291 + 0.159679i) q^{33} +(3.28119 + 4.30136i) q^{34} +(0.0121021 - 0.00501286i) q^{35} +(-4.82050 - 3.57251i) q^{36} +(3.37678 - 8.15228i) q^{37} +(3.68986 + 2.14433i) q^{38} +(2.33581 + 0.126852i) q^{39} +(-0.0246777 - 0.0435965i) q^{40} +(-2.68522 + 10.0214i) q^{41} +(1.80864 + 0.103374i) q^{42} +(-0.251160 - 0.327319i) q^{43} +(0.223896 + 0.549337i) q^{44} +(-0.0516197 - 0.0125998i) q^{45} +(-2.36190 - 5.74823i) q^{46} +(3.79608 + 2.19167i) q^{47} +(-0.452004 - 6.91344i) q^{48} +(5.58848 - 3.22651i) q^{49} +(5.59726 + 4.32023i) q^{50} +(3.74257 + 5.46764i) q^{51} +(1.63215 + 2.15225i) q^{52} +(0.729680 - 1.76160i) q^{53} +(-5.67121 - 4.67304i) q^{54} +(0.00371472 + 0.00371472i) q^{55} +(1.25925 + 1.67036i) q^{56} +(4.37820 + 2.85504i) q^{57} +(-0.0515377 - 0.0898542i) q^{58} +(-11.5055 + 1.51473i) q^{59} +(-0.0274399 - 0.0548773i) q^{60} +(1.53696 - 11.6744i) q^{61} +(-1.58421 - 0.661479i) q^{62} +(2.20569 + 0.240279i) q^{63} +(5.75240 - 5.55966i) q^{64} +(0.0207161 + 0.0119604i) q^{65} +(0.239277 + 0.686001i) q^{66} +(-4.33352 + 5.64755i) q^{67} +(-2.02213 + 7.37881i) q^{68} +(-2.52709 - 7.17948i) q^{69} +(0.0160169 + 0.00930808i) q^{70} +(3.05989 + 3.05989i) q^{71} +(-0.117712 - 8.48446i) q^{72} +(-4.64074 + 4.64074i) q^{73} +(12.0629 - 3.19556i) q^{74} +(6.57423 + 5.63650i) q^{75} +(0.753788 + 5.98818i) q^{76} +(-0.174033 - 0.133540i) q^{77} +(1.86086 + 2.73521i) q^{78} +(2.64432 - 4.58009i) q^{79} +(0.0278536 - 0.0651419i) q^{80} +(-6.64248 - 6.07268i) q^{81} +(-13.5713 + 5.57634i) q^{82} +(-3.87888 - 0.510664i) q^{83} +(1.43509 + 2.12232i) q^{84} +(0.00884382 + 0.0671755i) q^{85} +(0.152613 - 0.563158i) q^{86} +(-0.0573816 - 0.113147i) q^{87} +(-0.425638 + 0.722934i) q^{88} +(8.84724 - 8.84724i) q^{89} +(-0.0301084 - 0.0688491i) q^{90} +(-0.922817 - 0.382243i) q^{91} +(4.43751 - 7.58617i) q^{92} +(-1.89606 - 0.908786i) q^{93} +(0.791674 + 6.14822i) q^{94} +(0.0267245 + 0.0462882i) q^{95} +(7.38585 - 6.43810i) q^{96} +(6.08042 - 10.5316i) q^{97} +(8.42133 + 3.51628i) q^{98} +(0.249488 + 0.854127i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more