LMFDB - Embedded newform 187.2.t.a.6.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [187,2,Mod(6,187)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(187, base_ring=CyclotomicField(80))

chi = DirichletCharacter(H, H._module([72, 75]))

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

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

chi := DirichletCharacter("187.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.t (of order $80$, degree $32$, 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:	$1.49320251780$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$16$ over $\Q(\zeta_{80})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{80}]$

Embedding invariants

Embedding label			6.15
Character	$\chi$	$=$	187.6
Dual form			187.2.t.a.156.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.13560 + 0.168075i) q^{2} +(0.194323 + 0.0895840i) q^{3} +(2.55715 + 0.405012i) q^{4} +(0.179483 + 0.227673i) q^{5} +(0.399938 + 0.223976i) q^{6} +(-0.474986 + 1.28751i) q^{7} +(1.22694 + 0.294561i) q^{8} +(-1.91861 - 2.24640i) q^{9} +O(q^{10})$	\(q+(2.13560 + 0.168075i) q^{2} +(0.194323 + 0.0895840i) q^{3} +(2.55715 + 0.405012i) q^{4} +(0.179483 + 0.227673i) q^{5} +(0.399938 + 0.223976i) q^{6} +(-0.474986 + 1.28751i) q^{7} +(1.22694 + 0.294561i) q^{8} +(-1.91861 - 2.24640i) q^{9} +(0.345037 + 0.516384i) q^{10} +(2.16691 - 2.51088i) q^{11} +(0.460629 + 0.307782i) q^{12} +(-2.54987 + 5.00439i) q^{13} +(-1.23078 + 2.66976i) q^{14} +(0.0144817 + 0.0603208i) q^{15} +(-2.35388 - 0.764822i) q^{16} +(1.58743 - 3.80527i) q^{17} +(-3.71981 - 5.11988i) q^{18} +(-2.53863 + 1.55567i) q^{19} +(0.366753 + 0.654885i) q^{20} +(-0.207641 + 0.207641i) q^{21} +(5.04966 - 4.99802i) q^{22} +(1.16600 + 0.231932i) q^{23} +(0.212033 + 0.167154i) q^{24} +(1.14761 - 4.78012i) q^{25} +(-6.28660 + 10.2588i) q^{26} +(-0.345834 - 1.22624i) q^{27} +(-1.73606 + 3.09997i) q^{28} +(0.316855 + 8.06449i) q^{29} +(0.0207887 + 0.131255i) q^{30} +(0.774079 - 0.433505i) q^{31} +(-7.22989 - 2.99472i) q^{32} +(0.646014 - 0.293800i) q^{33} +(4.02968 - 7.85971i) q^{34} +(-0.378382 + 0.122944i) q^{35} +(-3.99634 - 6.52143i) q^{36} +(-2.63092 + 2.84611i) q^{37} +(-5.68296 + 2.89561i) q^{38} +(-0.943810 + 0.744040i) q^{39} +(0.153150 + 0.332208i) q^{40} +(9.04541 + 0.355395i) q^{41} +(-0.478336 + 0.408537i) q^{42} +(-1.76689 - 4.26564i) q^{43} +(6.55803 - 5.54306i) q^{44} +(0.167087 - 0.840005i) q^{45} +(2.45113 + 0.691290i) q^{46} +(-9.61666 + 1.52313i) q^{47} +(-0.388896 - 0.359492i) q^{48} +(3.89078 + 3.32304i) q^{49} +(3.25424 - 10.0155i) q^{50} +(0.649365 - 0.597241i) q^{51} +(-8.54721 + 11.7642i) q^{52} +(-0.202261 + 2.56996i) q^{53} +(-0.532463 - 2.67687i) q^{54} +(0.960581 + 0.0426866i) q^{55} +(-0.962027 + 1.43978i) q^{56} +(-0.632677 + 0.0748823i) q^{57} +(-0.678766 + 17.2758i) q^{58} +(8.34877 + 5.11613i) q^{59} +(0.0126013 + 0.160114i) q^{60} +(9.86487 - 2.78218i) q^{61} +(1.72598 - 0.795688i) q^{62} +(3.80357 - 1.40321i) q^{63} +(-10.5263 - 5.36340i) q^{64} +(-1.59702 + 0.317667i) q^{65} +(1.42901 - 0.518860i) q^{66} -10.4656i q^{67} +(5.60047 - 9.08769i) q^{68} +(0.205803 + 0.149525i) q^{69} +(-0.828735 + 0.198962i) q^{70} +(0.768752 - 6.49515i) q^{71} +(-1.69231 - 3.32134i) q^{72} +(5.60663 - 0.220285i) q^{73} +(-6.09694 + 5.63595i) q^{74} +(0.651228 - 0.826079i) q^{75} +(-7.12171 + 2.94991i) q^{76} +(2.20352 + 3.98254i) q^{77} +(-2.14065 + 1.43034i) q^{78} +(0.443571 + 3.74771i) q^{79} +(-0.248352 - 0.673186i) q^{80} +(-1.34377 + 8.48426i) q^{81} +(19.2576 + 2.27929i) q^{82} +(-5.76670 + 6.75194i) q^{83} +(-0.615064 + 0.446870i) q^{84} +(1.15127 - 0.321565i) q^{85} +(-3.05641 - 9.40665i) q^{86} +(-0.660878 + 1.59550i) q^{87} +(3.39826 - 2.44240i) q^{88} +(5.07130 + 5.07130i) q^{89} +(0.498015 - 1.76583i) q^{90} +(-5.23204 - 5.65999i) q^{91} +(2.88770 + 1.06533i) q^{92} +(0.189256 - 0.0148948i) q^{93} +(-20.7933 + 1.63647i) q^{94} +(-0.809825 - 0.298760i) q^{95} +(-1.13665 - 1.22962i) q^{96} +(1.08135 - 3.83417i) q^{97} +(7.75061 + 7.75061i) q^{98} +(-9.79789 - 0.0503532i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q - 40 q^{2} - 24 q^{3} - 24 q^{4} - 24 q^{5} - 40 q^{6} - 40 q^{7} - 40 q^{8} - 24 q^{9}+O(q^{10}) $ 512 * q - 40 * q^2 - 24 * q^3 - 24 * q^4 - 24 * q^5 - 40 * q^6 - 40 * q^7 - 40 * q^8 - 24 * q^9	$ 512 q - 40 q^{2} - 24 q^{3} - 24 q^{4} - 24 q^{5} - 40 q^{6} - 40 q^{7} - 40 q^{8} - 24 q^{9} - 40 q^{11} - 16 q^{12} - 56 q^{14} - 24 q^{15} - 40 q^{17} - 80 q^{18} - 40 q^{19} - 24 q^{20} - 48 q^{22} - 48 q^{23} + 80 q^{24} - 40 q^{25} - 56 q^{26} + 48 q^{27} - 40 q^{28} - 40 q^{29} - 40 q^{30} + 40 q^{31} - 64 q^{34} - 80 q^{35} - 56 q^{36} - 56 q^{37} + 80 q^{38} - 40 q^{39} - 40 q^{40} + 80 q^{41} + 72 q^{42} + 32 q^{44} - 64 q^{45} - 40 q^{46} - 24 q^{47} - 72 q^{48} - 88 q^{49} - 40 q^{51} + 240 q^{52} - 24 q^{53} + 128 q^{55} - 64 q^{56} - 40 q^{57} + 88 q^{58} - 88 q^{59} - 152 q^{60} - 40 q^{61} - 40 q^{62} + 80 q^{63} - 88 q^{64} + 408 q^{66} - 40 q^{68} + 192 q^{69} - 168 q^{70} - 24 q^{71} - 40 q^{72} - 40 q^{73} - 40 q^{74} - 88 q^{75} + 192 q^{77} - 64 q^{78} - 40 q^{79} + 248 q^{80} - 40 q^{81} - 24 q^{82} - 40 q^{85} - 112 q^{86} + 128 q^{88} - 64 q^{89} - 40 q^{90} + 56 q^{91} + 136 q^{92} - 88 q^{93} + 440 q^{94} - 40 q^{95} - 40 q^{96} - 88 q^{97} + 72 q^{99}+O(q^{100}) $ 512 * q - 40 * q^2 - 24 * q^3 - 24 * q^4 - 24 * q^5 - 40 * q^6 - 40 * q^7 - 40 * q^8 - 24 * q^9 - 40 * q^11 - 16 * q^12 - 56 * q^14 - 24 * q^15 - 40 * q^17 - 80 * q^18 - 40 * q^19 - 24 * q^20 - 48 * q^22 - 48 * q^23 + 80 * q^24 - 40 * q^25 - 56 * q^26 + 48 * q^27 - 40 * q^28 - 40 * q^29 - 40 * q^30 + 40 * q^31 - 64 * q^34 - 80 * q^35 - 56 * q^36 - 56 * q^37 + 80 * q^38 - 40 * q^39 - 40 * q^40 + 80 * q^41 + 72 * q^42 + 32 * q^44 - 64 * q^45 - 40 * q^46 - 24 * q^47 - 72 * q^48 - 88 * q^49 - 40 * q^51 + 240 * q^52 - 24 * q^53 + 128 * q^55 - 64 * q^56 - 40 * q^57 + 88 * q^58 - 88 * q^59 - 152 * q^60 - 40 * q^61 - 40 * q^62 + 80 * q^63 - 88 * q^64 + 408 * q^66 - 40 * q^68 + 192 * q^69 - 168 * q^70 - 24 * q^71 - 40 * q^72 - 40 * q^73 - 40 * q^74 - 88 * q^75 + 192 * q^77 - 64 * q^78 - 40 * q^79 + 248 * q^80 - 40 * q^81 - 24 * q^82 - 40 * q^85 - 112 * q^86 + 128 * q^88 - 64 * q^89 - 40 * q^90 + 56 * q^91 + 136 * q^92 - 88 * q^93 + 440 * q^94 - 40 * q^95 - 40 * q^96 - 88 * q^97 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{15}{16}\right)$

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 $

$2$	2.13560	+	0.168075i	1.51009	+	0.118847i	0.806279	−	0.591536i	$-0.201478\pi$
$2$	2.13560	+	0.168075i	1.51009	+	0.118847i	0.703816	+	0.710383i	$0.251478\pi$
$3$	0.194323	+	0.0895840i	0.112192	+	0.0517213i	0.473956	−	0.880548i	$-0.342825\pi$
$3$	0.194323	+	0.0895840i	0.112192	+	0.0517213i	−0.361764	+	0.932270i	$0.617825\pi$
$4$	2.55715	+	0.405012i	1.27857	+	0.202506i
$5$	0.179483	+	0.227673i	0.0802671	+	0.101818i	0.823799	−	0.566883i	$-0.191851\pi$
$5$	0.179483	+	0.227673i	0.0802671	+	0.101818i	−0.743532	+	0.668701i	$0.766851\pi$
$6$	0.399938	+	0.223976i	0.163274	+	0.0914378i
$7$	−0.474986	+	1.28751i	−0.179528	+	0.486632i	−0.995855	−	0.0909586i	$-0.971007\pi$
$7$	−0.474986	+	1.28751i	−0.179528	+	0.486632i	0.816327	+	0.577590i	$0.196007\pi$
$8$	1.22694	+	0.294561i	0.433787	+	0.104143i
$9$	−1.91861	−	2.24640i	−0.639536	−	0.748800i
$10$	0.345037	+	0.516384i	0.109110	+	0.163295i
$11$	2.16691	−	2.51088i	0.653347	−	0.757058i
$11$	2.16691	−	2.51088i	0.653347	−	0.757058i
$12$	0.460629	+	0.307782i	0.132972	+	0.0888491i
$13$	−2.54987	+	5.00439i	−0.707205	+	1.38797i	0.205216	+	0.978717i	$0.434210\pi$
$13$	−2.54987	+	5.00439i	−0.707205	+	1.38797i	−0.912421	+	0.409252i	$0.865790\pi$
$14$	−1.23078	+	2.66976i	−0.328939	+	0.713524i
$15$	0.0144817	+	0.0603208i	0.00373917	+	0.0155748i
$16$	−2.35388	−	0.764822i	−0.588470	−	0.191205i
$17$	1.58743	−	3.80527i	0.385009	−	0.922913i
$17$	1.58743	−	3.80527i	0.385009	−	0.922913i
$18$	−3.71981	−	5.11988i	−0.876767	−	1.20677i
$19$	−2.53863	+	1.55567i	−0.582402	+	0.356896i	−0.782282	−	0.622924i	$-0.785945\pi$
$19$	−2.53863	+	1.55567i	−0.582402	+	0.356896i	0.199881	+	0.979820i	$0.435945\pi$
$20$	0.366753	+	0.654885i	0.0820085	+	0.146437i
$21$	−0.207641	+	0.207641i	−0.0453109	+	0.0453109i
$22$	5.04966	−	4.99802i	1.07659	−	1.06558i
$23$	1.16600	+	0.231932i	0.243128	+	0.0483612i	0.315150	−	0.949042i	$-0.397945\pi$
$23$	1.16600	+	0.231932i	0.243128	+	0.0483612i	−0.0720219	+	0.997403i	$0.522945\pi$
$24$	0.212033	+	0.167154i	0.0432812	+	0.0341201i
$25$	1.14761	−	4.78012i	0.229521	−	0.956025i
$26$	−6.28660	+	10.2588i	−1.23290	+	2.01191i
$27$	−0.345834	−	1.22624i	−0.0665559	−	0.235989i
$28$	−1.73606	+	3.09997i	−0.328085	+	0.585839i
$29$	0.316855	+	8.06449i	0.0588385	+	1.49754i	0.691086	+	0.722773i	$0.257133\pi$
$29$	0.316855	+	8.06449i	0.0588385	+	1.49754i	−0.632247	+	0.774766i	$0.717867\pi$
$30$	0.0207887	+	0.131255i	0.00379548	+	0.0239637i
$31$	0.774079	−	0.433505i	0.139029	−	0.0778598i	−0.417554	−	0.908652i	$-0.637112\pi$
$31$	0.774079	−	0.433505i	0.139029	−	0.0778598i	0.556582	+	0.830793i	$0.312112\pi$
$32$	−7.22989	−	2.99472i	−1.27808	−	0.529396i
$33$	0.646014	−	0.293800i	0.112457	−	0.0511441i
$34$	4.02968	−	7.85971i	0.691085	−	1.34793i
$35$	−0.378382	+	0.122944i	−0.0639583	+	0.0207813i
$36$	−3.99634	−	6.52143i	−0.666057	−	1.08691i
$37$	−2.63092	+	2.84611i	−0.432520	+	0.467898i	−0.912319	−	0.409481i	$-0.865710\pi$
$37$	−2.63092	+	2.84611i	−0.432520	+	0.467898i	0.479799	+	0.877379i	$0.340710\pi$
$38$	−5.68296	+	2.89561i	−0.921898	+	0.469730i
$39$	−0.943810	+	0.744040i	−0.151131	+	0.119142i
$40$	0.153150	+	0.332208i	0.0242152	+	0.0525268i
$41$	9.04541	+	0.355395i	1.41266	+	0.0555034i	0.734098	−	0.679044i	$-0.237605\pi$
$41$	9.04541	+	0.355395i	1.41266	+	0.0555034i	0.678557	+	0.734547i	$0.262605\pi$
$42$	−0.478336	+	0.408537i	−0.0738088	+	0.0630387i
$43$	−1.76689	−	4.26564i	−0.269447	−	0.650504i	0.730010	−	0.683436i	$-0.239515\pi$
$43$	−1.76689	−	4.26564i	−0.269447	−	0.650504i	−0.999458	+	0.0329326i	$0.989515\pi$
$44$	6.55803	−	5.54306i	0.988661	−	0.835647i
$45$	0.167087	−	0.840005i	0.0249079	−	0.125221i
$46$	2.45113	+	0.691290i	0.361399	+	0.101925i
$47$	−9.61666	+	1.52313i	−1.40273	+	0.222171i	−0.811511	−	0.584337i	$-0.801355\pi$
$47$	−9.61666	+	1.52313i	−1.40273	+	0.222171i	−0.591223	+	0.806508i	$0.701355\pi$
$48$	−0.388896	−	0.359492i	−0.0561324	−	0.0518882i
$49$	3.89078	+	3.32304i	0.555826	+	0.474720i
$50$	3.25424	−	10.0155i	0.460219	−	1.41641i
$51$	0.649365	−	0.597241i	0.0909293	−	0.0836305i
$52$	−8.54721	+	11.7642i	−1.18529	+	1.63141i
$53$	−0.202261	+	2.56996i	−0.0277826	+	0.353012i	0.967276	+	0.253725i	$0.0816559\pi$
$53$	−0.202261	+	2.56996i	−0.0277826	+	0.353012i	−0.995059	+	0.0992862i	$0.968344\pi$
$54$	−0.532463	−	2.67687i	−0.0724590	−	0.364276i
$55$	0.960581	+	0.0426866i	0.129525	+	0.00575586i
$56$	−0.962027	+	1.43978i	−0.128556	+	0.192398i
$57$	−0.632677	+	0.0748823i	−0.0838001	+	0.00991840i
$58$	−0.678766	+	17.2758i	−0.0891264	+	2.26842i
$59$	8.34877	+	5.11613i	1.08692	+	0.666064i	0.946068	−	0.323968i	$-0.105017\pi$
$59$	8.34877	+	5.11613i	1.08692	+	0.666064i	0.140849	+	0.990031i	$0.455017\pi$
$60$	0.0126013	+	0.160114i	0.00162682	+	0.0206707i
$61$	9.86487	−	2.78218i	1.26307	−	0.356222i	0.426701	−	0.904393i	$-0.359676\pi$
$61$	9.86487	−	2.78218i	1.26307	−	0.356222i	0.836366	+	0.548171i	$0.184676\pi$
$62$	1.72598	−	0.795688i	0.219200	−	0.101052i
$63$	3.80357	−	1.40321i	0.479205	−	0.176788i
$64$	−10.5263	−	5.36340i	−1.31578	−	0.670426i
$65$	−1.59702	+	0.317667i	−0.198086	+	0.0394018i
$66$	1.42901	−	0.518860i	0.175898	−	0.0638673i
$67$		−	10.4656i		−	1.27857i	−0.768968	−	0.639287i	$-0.779230\pi$
$67$		−	10.4656i		−	1.27857i	0.768968	−	0.639287i	$-0.220770\pi$
$68$	5.60047	−	9.08769i	0.679157	−	1.10204i
$69$	0.205803	+	0.149525i	0.0247758	+	0.0180007i
$70$	−0.828735	+	0.198962i	−0.0990528	+	0.0237805i
$71$	0.768752	−	6.49515i	0.0912341	−	0.770833i	−0.869609	−	0.493741i	$-0.835629\pi$
$71$	0.768752	−	6.49515i	0.0912341	−	0.770833i	0.960843	−	0.277092i	$-0.0893708\pi$
$72$	−1.69231	−	3.32134i	−0.199440	−	0.391423i
$73$	5.60663	−	0.220285i	0.656206	−	0.0257824i	0.291020	−	0.956717i	$-0.406005\pi$
$73$	5.60663	−	0.220285i	0.656206	−	0.0257824i	0.365186	+	0.930935i	$0.381005\pi$
$74$	−6.09694	+	5.63595i	−0.708754	+	0.655166i
$75$	0.651228	−	0.826079i	0.0751974	−	0.0953874i
$76$	−7.12171	+	2.94991i	−0.816916	+	0.338378i
$77$	2.20352	+	3.98254i	0.251115	+	0.453853i
$78$	−2.14065	+	1.43034i	−0.242381	+	0.161954i
$79$	0.443571	+	3.74771i	0.0499056	+	0.421651i	0.995384	+	0.0959672i	$0.0305944\pi$
$79$	0.443571	+	3.74771i	0.0499056	+	0.421651i	−0.945479	+	0.325683i	$0.894406\pi$
$80$	−0.248352	−	0.673186i	−0.0277666	−	0.0752645i
$81$	−1.34377	+	8.48426i	−0.149308	+	0.942696i
$82$	19.2576	+	2.27929i	2.12665	+	0.251705i
$83$	−5.76670	+	6.75194i	−0.632977	+	0.741121i	−0.980493	−	0.196553i	$-0.937025\pi$
$83$	−5.76670	+	6.75194i	−0.632977	+	0.741121i	0.347516	+	0.937674i	$0.387025\pi$
$84$	−0.615064	+	0.446870i	−0.0671090	+	0.0487575i
$85$	1.15127	−	0.321565i	0.124873	−	0.0348786i
$86$	−3.05641	−	9.40665i	−0.329581	−	1.01435i
$87$	−0.660878	+	1.59550i	−0.0708535	+	0.171056i
$88$	3.39826	−	2.44240i	0.362256	−	0.260361i
$89$	5.07130	+	5.07130i	0.537557	+	0.537557i	0.922811	−	0.385254i	$-0.125886\pi$
$89$	5.07130	+	5.07130i	0.537557	+	0.537557i	−0.385254	+	0.922811i	$0.625886\pi$
$90$	0.498015	−	1.76583i	0.0524954	−	0.186135i
$91$	−5.23204	−	5.65999i	−0.548467	−	0.593328i
$92$	2.88770	+	1.06533i	0.301064	+	0.111068i
$93$	0.189256	−	0.0148948i	0.0196250	−	0.00154452i
$94$	−20.7933	+	1.63647i	−2.14467	+	0.168789i
$95$	−0.809825	−	0.298760i	−0.0830863	−	0.0306522i
$96$	−1.13665	−	1.22962i	−0.116009	−	0.125498i
$97$	1.08135	−	3.83417i	0.109794	−	0.389301i	−0.887669	−	0.460482i	$-0.847677\pi$
$97$	1.08135	−	3.83417i	0.109794	−	0.389301i	0.997463	+	0.0711808i	$0.0226767\pi$
$98$	7.75061	+	7.75061i	0.782930	+	0.782930i
$99$	−9.79789	−	0.0503532i	−0.984725	−	0.00506069i
$100$	4.87060	−	11.7587i	0.487060	−	1.17587i
$101$	−0.920918	−	2.83429i	−0.0916347	−	0.282023i	0.894727	−	0.446613i	$-0.147370\pi$
$101$	−0.920918	−	2.83429i	−0.0916347	−	0.282023i	−0.986362	+	0.164590i	$0.947370\pi$
$102$	1.48716	−	1.16632i	0.147251	−	0.115483i
$103$	−3.31622	+	2.40937i	−0.326757	+	0.237403i	−0.739053	−	0.673647i	$-0.764727\pi$
$103$	−3.31622	+	2.40937i	−0.326757	+	0.237403i	0.412297	+	0.911050i	$0.364727\pi$
$104$	−4.60262	+	5.38898i	−0.451324	+	0.528432i
$105$	−0.0845420	−	0.0100062i	−0.00825046	−	0.000976506i
$106$	−0.863894	+	5.45441i	−0.0839088	+	0.529779i
$107$	−3.73555	−	10.1257i	−0.361129	−	0.978884i	−0.980970	−	0.194157i	$-0.937803\pi$
$107$	−3.73555	−	10.1257i	−0.361129	−	0.978884i	0.619841	−	0.784727i	$-0.287197\pi$
$108$	−0.387708	−	3.27573i	−0.0373073	−	0.315207i
$109$	1.65780	−	1.10770i	0.158788	−	0.106099i	−0.473638	−	0.880720i	$-0.657059\pi$
$109$	1.65780	−	1.10770i	0.158788	−	0.106099i	0.632426	+	0.774621i	$0.282059\pi$
$110$	2.04424	+	0.252611i	0.194911	+	0.0240855i
$111$	−0.766213	+	0.317376i	−0.0727257	+	0.0301240i
$112$	2.10277	−	2.66736i	0.198693	−	0.252041i
$113$	−7.54940	+	6.97859i	−0.710188	+	0.656491i	−0.949253	−	0.314513i	$-0.898159\pi$
$113$	−7.54940	+	6.97859i	−0.710188	+	0.656491i	0.239066	+	0.971003i	$0.423159\pi$
$114$	−1.36373	+	0.0535810i	−0.127725	+	0.00501832i
$115$	0.156473	+	0.307095i	0.0145911	+	0.0286367i
$116$	−2.45597	+	20.7504i	−0.228031	+	1.92663i
$117$	16.1341	−	3.87345i	1.49160	−	0.358100i
$118$	16.9697	+	12.3292i	1.56219	+	1.13500i
$119$	4.14530	+	3.85128i	0.379999	+	0.353046i
$120$			0.0782755i			0.00714554i
$121$	−1.60902	−	10.8817i	−0.146275	−	0.989244i
$122$	21.5350	−	4.28358i	1.94969	−	0.387817i
$123$	1.72589	+	0.879385i	0.155618	+	0.0792915i
$124$	2.15501	−	0.795024i	0.193525	−	0.0713952i
$125$	2.61069	−	1.20354i	0.233507	−	0.107648i
$126$	8.35873	−	2.35741i	0.744655	−	0.210014i
$127$	0.938751	+	11.9280i	0.0833007	+	1.05844i	0.886501	+	0.462726i	$0.153129\pi$
$127$	0.938751	+	11.9280i	0.0833007	+	1.05844i	−0.803200	+	0.595709i	$0.796871\pi$
$128$	−8.23362	−	5.04557i	−0.727756	−	0.445969i
$129$	0.0387870	−	0.987195i	0.00341501	−	0.0869177i
$130$	−3.46398	+	0.409989i	−0.303811	+	0.0359585i
$131$	−3.30042	+	4.93943i	−0.288359	+	0.431560i	−0.947162	−	0.320755i	$-0.896063\pi$
$131$	−3.30042	+	4.93943i	−0.288359	+	0.431560i	0.658803	+	0.752316i	$0.271063\pi$
$132$	1.77094	−	0.489647i	0.154141	−	0.0426183i
$133$	−0.797127	−	4.00743i	−0.0691197	−	0.347488i
$134$	1.75900	−	22.3503i	0.151955	−	1.93077i
$135$	0.217109	−	0.298825i	0.0186858	−	0.0257188i
$136$	3.06856	−	4.20122i	0.263127	−	0.360252i
$137$	−0.506443	+	1.55867i	−0.0432684	+	0.133166i	−0.970357	−	0.241676i	$-0.922303\pi$
$137$	−0.506443	+	1.55867i	−0.0432684	+	0.133166i	0.927089	+	0.374842i	$0.122303\pi$
$138$	0.414381	+	0.353915i	0.0352745	+	0.0301273i
$139$	5.97745	+	5.52550i	0.507001	+	0.468666i	0.890570	−	0.454845i	$-0.150305\pi$
$139$	5.97745	+	5.52550i	0.507001	+	0.468666i	−0.383570	+	0.923512i	$0.625305\pi$
$140$	−1.01737	+	0.161136i	−0.0859836	+	0.0136185i
$141$	−2.00518	−	0.565520i	−0.168867	−	0.0476254i
$142$	2.73342	−	13.7418i	0.229383	−	1.15319i
$143$	7.04010	+	17.2465i	0.588723	+	1.44222i
$144$	2.79807	+	6.75515i	0.233173	+	0.562929i
$145$	−1.77920	+	1.51958i	−0.147754	+	0.126194i
$146$	12.0105	+	0.471895i	0.993997	+	0.0390543i
$147$	0.458376	+	0.994294i	0.0378062	+	0.0820080i
$148$	−7.88034	+	6.21236i	−0.647760	+	0.510653i
$149$	6.02208	−	3.06840i	0.493348	−	0.251373i	−0.189572	−	0.981867i	$-0.560710\pi$
$149$	6.02208	−	3.06840i	0.493348	−	0.251373i	0.682920	+	0.730494i	$0.260710\pi$
$150$	1.52960	−	1.65472i	0.124892	−	0.135107i
$151$	−10.0919	−	16.4685i	−0.821269	−	1.34019i	−0.937862	−	0.347009i	$-0.887197\pi$
$151$	−10.0919	−	16.4685i	−0.821269	−	1.34019i	0.116593	−	0.993180i	$-0.462803\pi$
$152$	−3.57298	+	1.16093i	−0.289807	+	0.0941639i
$153$	−11.5938	+	3.73481i	−0.937305	+	0.301941i
$154$	4.03647	+	8.87546i	0.325268	+	0.715205i
$155$	0.237631	+	0.0984300i	0.0190870	+	0.00790609i
$156$	−2.71481	+	1.52036i	−0.217358	+	0.121727i
$157$	−2.06638	−	13.0466i	−0.164915	−	1.04123i	−0.921795	−	0.387679i	$-0.873277\pi$
$157$	−2.06638	−	13.0466i	−0.164915	−	1.04123i	0.756879	−	0.653555i	$-0.226723\pi$
$158$	0.317392	+	8.07816i	0.0252503	+	0.642664i
$159$	−0.269531	+	0.481283i	−0.0213752	+	0.0381682i
$160$	−0.615825	−	2.18355i	−0.0486852	−	0.172625i
$161$	−0.852449	+	1.39107i	−0.0671824	+	0.109632i
$162$	−4.29575	+	17.8931i	−0.337506	+	1.40581i
$163$	−18.3229	−	14.4446i	−1.43516	−	1.13139i	−0.969109	−	0.246632i	$-0.920676\pi$
$163$	−18.3229	−	14.4446i	−1.43516	−	1.13139i	−0.466051	−	0.884758i	$-0.654324\pi$
$164$	22.9865	+	4.57229i	1.79494	+	0.357036i
$165$	0.182839	+	0.0943477i	0.0142340	+	0.00734496i
$166$	−13.4502	+	13.4502i	−1.04394	+	1.04394i
$167$	−10.3172	−	18.4226i	−0.798366	−	1.42558i	−0.902349	−	0.431006i	$-0.858159\pi$
$167$	−10.3172	−	18.4226i	−0.798366	−	1.42558i	0.103984	−	0.994579i	$-0.466841\pi$
$168$	−0.315925	+	0.193599i	−0.0243741	+	0.0149365i
$169$	−10.9009	−	15.0038i	−0.838533	−	1.15414i
$170$	2.51270	−	0.493232i	0.192715	−	0.0378292i
$171$	8.36531	+	2.71805i	0.639711	+	0.207855i
$172$	−2.79055	−	11.6235i	−0.212777	−	0.886281i
$173$	−7.80126	+	16.9222i	−0.593119	+	1.28657i	0.344459	+	0.938801i	$0.388062\pi$
$173$	−7.80126	+	16.9222i	−0.593119	+	1.28657i	−0.937579	+	0.347774i	$0.886938\pi$
$174$	−1.67953	+	3.29627i	−0.127325	+	0.249889i
$175$	5.60934	+	3.74804i	0.424027	+	0.283325i
$176$	−7.02101	+	4.25301i	−0.529229	+	0.320582i
$177$	1.16403	+	1.74210i	0.0874940	+	0.130944i
$178$	9.97790	+	11.6826i	0.747875	+	0.875649i
$179$	−2.06019	−	0.494609i	−0.153986	−	0.0369688i	0.155719	−	0.987801i	$-0.450230\pi$
$179$	−2.06019	−	0.494609i	−0.153986	−	0.0369688i	−0.309705	+	0.950833i	$0.600230\pi$
$180$	0.767479	−	2.08034i	0.0572045	−	0.155060i
$181$	−9.36417	−	5.24419i	−0.696033	−	0.389797i	0.100052	−	0.994982i	$-0.468099\pi$
$181$	−9.36417	−	5.24419i	−0.696033	−	0.389797i	−0.796085	+	0.605185i	$0.793099\pi$
$182$	−10.2222	−	12.9668i	−0.757721	−	0.961165i
$183$	2.16621	+	0.343093i	0.160131	+	0.0253622i
$184$	1.36229	+	0.628025i	0.100429	+	0.0462986i
$185$	−1.12019	−	0.0881605i	−0.0823577	−	0.00648169i
$186$	0.406678			0.0298191
$187$	−6.11474	−	12.2315i	−0.447154	−	0.894457i
$188$	−25.2081			−1.83849
$189$	1.74305	+	0.137181i	0.126789	+	0.00997847i
$190$	−1.67925	−	0.774143i	−0.121825	−	0.0561622i
$191$	−17.2137	−	2.72638i	−1.24554	−	0.197274i	−0.501352	−	0.865244i	$-0.667164\pi$
$191$	−17.2137	−	2.72638i	−1.24554	−	0.197274i	−0.744189	+	0.667969i	$0.767164\pi$
$192$	−1.56502	−	1.98522i	−0.112946	−	0.143271i
$193$	−11.0481	−	6.18721i	−0.795257	−	0.445365i	0.0373005	−	0.999304i	$-0.488124\pi$
$193$	−11.0481	−	6.18721i	−0.795257	−	0.445365i	−0.832557	+	0.553939i	$0.813124\pi$
$194$	2.95375	−	8.00649i	0.212067	−	0.574832i
$195$	−0.338795	−	0.0813376i	−0.0242616	−	0.00582470i
$196$	8.60342	+	10.0733i	0.614530	+	0.719522i
$197$	12.9159	+	19.3300i	0.920220	+	1.37721i	0.926122	+	0.377223i	$0.123121\pi$
$197$	12.9159	+	19.3300i	0.920220	+	1.37721i	−0.00590281	+	0.999983i	$0.501879\pi$
$198$	−20.9159	−	1.75431i	−1.48643	−	0.124674i
$199$	−20.2299	−	13.5172i	−1.43406	−	0.958208i	−0.998308	−	0.0581412i	$-0.981483\pi$
$199$	−20.2299	−	13.5172i	−1.43406	−	0.958208i	−0.435752	−	0.900067i	$-0.643517\pi$
$200$	2.81608	−	5.52686i	0.199127	−	0.390808i
$201$	0.937549	−	2.03370i	0.0661296	−	0.143446i
$202$	−1.49033	−	6.20769i	−0.104860	−	0.436771i
$203$	−10.5336	−	3.42257i	−0.739313	−	0.240217i
$204$	1.90241	−	1.26423i	0.133195	−	0.0885140i
$205$	1.54258	+	2.12318i	0.107739	+	0.148289i
$206$	−7.48706	+	4.58807i	−0.521648	+	0.319666i
$207$	−1.71609	−	3.06430i	−0.119276	−	0.212983i
$208$	9.82954	−	9.82954i	0.681556	−	0.681556i
$209$	−1.59487	+	9.74520i	−0.110319	+	0.674089i
$210$	−0.178866	−	0.0355786i	−0.0123429	−	0.00245516i
$211$	2.21042	+	1.74256i	0.152172	+	0.119963i	0.692267	−	0.721641i	$-0.256612\pi$
$211$	2.21042	+	1.74256i	0.152172	+	0.119963i	−0.540095	+	0.841604i	$0.681612\pi$
$212$	−1.55808	+	6.48985i	−0.107009	+	0.445725i
$213$	0.731248	−	1.19329i	0.0501043	−	0.0817627i
$214$	−6.27576	−	22.2522i	−0.429002	−	1.52113i
$215$	0.654044	−	1.16788i	0.0446055	−	0.0796488i
$216$	−0.0631149	−	1.60638i	−0.00429443	−	0.109300i
$217$	0.190464	+	1.20254i	0.0129295	+	0.0816338i
$218$	3.72656	−	2.08697i	0.252395	−	0.141348i
$219$	1.10923	+	0.459458i	0.0749548	+	0.0310473i
$220$	2.43906	+	0.498203i	0.164441	+	0.0335888i
$221$	14.9953	+	17.6471i	1.00869	+	1.18707i
$222$	−1.68966	+	0.549005i	−0.113403	+	0.0368468i
$223$	−2.17651	−	3.55173i	−0.145750	−	0.237842i	0.771431	−	0.636312i	$-0.219541\pi$
$223$	−2.17651	−	3.55173i	−0.145750	−	0.237842i	−0.917181	+	0.398471i	$0.869541\pi$
$224$	7.28982	−	7.88608i	0.487071	−	0.526911i
$225$	−12.9399	+	6.59320i	−0.862659	+	0.439547i
$226$	−17.2954	+	13.6346i	−1.15047	+	0.906959i
$227$	9.50548	+	20.6190i	0.630901	+	1.36853i	0.912531	+	0.409007i	$0.134125\pi$
$227$	9.50548	+	20.6190i	0.630901	+	1.36853i	−0.281631	+	0.959523i	$0.590875\pi$
$228$	−1.64818	−	0.0647570i	−0.109153	−	0.00428864i
$229$	−7.99148	+	6.82537i	−0.528092	+	0.451033i	−0.873082	−	0.487573i	$-0.837882\pi$
$229$	−7.99148	+	6.82537i	−0.528092	+	0.451033i	0.344990	+	0.938606i	$0.387882\pi$
$230$	0.282547	+	0.682130i	0.0186306	+	0.0449783i
$231$	0.0714223	+	0.971299i	0.00469924	+	0.0639068i
$232$	−1.98673	+	9.98795i	−0.130435	+	0.655741i
$233$	−8.27798	−	2.33463i	−0.542309	−	0.152947i	−0.0107090	−	0.999943i	$-0.503409\pi$
$233$	−8.27798	−	2.33463i	−0.542309	−	0.152947i	−0.531600	+	0.846996i	$0.678409\pi$
$234$	35.1069	−	5.56038i	2.29501	−	0.363494i
$235$	−2.07280	−	1.91608i	−0.135215	−	0.124991i
$236$	19.2769	+	16.4640i	1.25482	+	1.07172i
$237$	−0.249539	+	0.768003i	−0.0162093	+	0.0498871i
$238$	8.20538	+	8.92150i	0.531876	+	0.578295i
$239$	17.7364	−	24.4120i	1.14727	−	1.57908i	0.397186	−	0.917738i	$-0.369987\pi$
$239$	17.7364	−	24.4120i	1.14727	−	1.57908i	0.750083	−	0.661343i	$-0.230013\pi$
$240$	0.0120464	−	0.153064i	0.000777590	−	0.00988022i
$241$	4.21185	+	21.1744i	0.271309	+	1.36396i	0.840524	+	0.541774i	$0.182247\pi$
$241$	4.21185	+	21.1744i	0.271309	+	1.36396i	−0.569215	+	0.822188i	$0.692753\pi$
$242$	−1.60728	−	23.5093i	−0.103320	−	1.51124i
$243$	−3.14469	+	4.70636i	−0.201732	+	0.301913i
$244$	26.3527	−	3.11905i	1.68706	−	0.199677i
$245$	−0.0582379	+	1.48225i	−0.00372068	+	0.0946977i
$246$	3.53800	+	2.16809i	0.225575	+	0.138232i
$247$	−1.31204	−	16.6711i	−0.0834832	−	1.06075i
$248$	1.07744	−	0.303869i	0.0684174	−	0.0192957i
$249$	−1.72547	+	0.795451i	−0.109347	+	0.0504096i
$250$	5.77766	−	2.13149i	0.365411	−	0.134807i
$251$	−2.04413	−	1.04153i	−0.129024	−	0.0657411i	0.388287	−	0.921539i	$-0.373067\pi$
$251$	−2.04413	−	1.04153i	−0.129024	−	0.0657411i	−0.517311	+	0.855797i	$0.673067\pi$
$252$	10.2946	−	2.04772i	0.648499	−	0.128994i
$253$	3.10897	−	2.42511i	0.195459	−	0.152466i
$254$			25.6311i			1.60824i
$255$	0.252525	+	0.0406483i	0.0158138	+	0.00254549i
$256$	2.37966	+	1.72893i	0.148729	+	0.108058i
$257$	14.7269	−	3.53562i	0.918640	−	0.220546i	0.253561	−	0.967319i	$-0.418398\pi$
$257$	14.7269	−	3.53562i	0.918640	−	0.220546i	0.665078	+	0.746774i	$0.268398\pi$
$258$	0.248756	−	2.10173i	0.0154869	−	0.130848i
$259$	−2.41474	−	4.73919i	−0.150044	−	0.294479i
$260$	−4.21247	+	0.165509i	−0.261246	+	0.0102644i
$261$	17.5082	−	16.1844i	1.08373	−	1.00179i
$262$	−7.87857	+	9.99392i	−0.486740	+	0.617426i
$263$	12.6457	−	5.23803i	0.779769	−	0.322991i	0.0429469	−	0.999077i	$-0.486325\pi$
$263$	12.6457	−	5.23803i	0.779769	−	0.322991i	0.736822	+	0.676086i	$0.236325\pi$
$264$	0.879160	−	0.170184i	0.0541085	−	0.0104741i
$265$	−0.621413	+	0.415215i	−0.0381731	+	0.0255064i
$266$	−1.02879	−	8.69222i	−0.0630793	−	0.532954i
$267$	0.531162	+	1.43978i	0.0325066	+	0.0881130i
$268$	4.23869	−	26.7620i	0.258919	−	1.63475i
$269$	−11.1033	−	1.31417i	−0.676982	−	0.0801261i	−0.227992	−	0.973663i	$-0.573216\pi$
$269$	−11.1033	−	1.31417i	−0.676982	−	0.0801261i	−0.448990	+	0.893537i	$0.648216\pi$
$270$	0.513883	−	0.601680i	0.0312739	−	0.0366171i
$271$	−7.52102	+	5.46434i	−0.456870	+	0.331935i	−0.792302	−	0.610129i	$-0.791118\pi$
$271$	−7.52102	+	5.46434i	−0.456870	+	0.331935i	0.335432	+	0.942064i	$0.391118\pi$
$272$	−6.64697	+	7.74304i	−0.403032	+	0.469491i
$273$	−0.509660	−	1.56857i	−0.0308460	−	0.0949342i
$274$	−1.34353	+	3.24357i	−0.0811658	+	0.195951i
$275$	−9.51555	−	13.2396i	−0.573809	−	0.798377i
$276$	0.465710	+	0.465710i	0.0280324	+	0.0280324i
$277$	−2.20848	+	7.83067i	−0.132695	+	0.470499i	−0.999609	−	0.0279575i	$-0.991100\pi$
$277$	−2.20848	+	7.83067i	−0.132695	+	0.470499i	0.866915	+	0.498457i	$0.166100\pi$
$278$	11.8367	+	12.8049i	0.709919	+	0.767986i
$279$	−2.45898	−	0.907165i	−0.147215	−	0.0543106i
$280$	−0.500465	+	0.0393874i	−0.0299085	+	0.00235385i
$281$	23.7982	−	1.87296i	1.41968	−	0.111732i	0.654753	−	0.755843i	$-0.272773\pi$
$281$	23.7982	−	1.87296i	1.41968	−	0.111732i	0.764931	+	0.644112i	$0.222773\pi$
$282$	−4.18721	−	1.54474i	−0.249345	−	0.0919882i
$283$	17.9470	+	19.4150i	1.06684	+	1.15410i	0.987559	+	0.157248i	$0.0502621\pi$
$283$	17.9470	+	19.4150i	1.06684	+	1.15410i	0.0792799	+	0.996852i	$0.474738\pi$
$284$	4.59642	−	16.2977i	0.272748	−	0.967090i
$285$	−0.130603	−	0.130603i	−0.00773627	−	0.00773627i
$286$	12.1361	+	38.0147i	0.717623	+	2.24786i
$287$	−4.75402	+	11.4772i	−0.280621	+	0.677478i
$288$	7.14398	+	21.9869i	0.420963	+	1.29559i
$289$	−11.9601	−	12.0812i	−0.703536	−	0.710659i
$290$	−4.05505	+	2.94616i	−0.238121	+	0.173005i
$291$	0.553611	−	0.648195i	0.0324532	−	0.0379978i
$292$	14.4262	+	1.70745i	0.844228	+	0.0999210i
$293$	−0.128934	+	0.814059i	−0.00753242	+	0.0475578i	−0.991168	−	0.132610i	$-0.957664\pi$
$293$	−0.128934	+	0.814059i	−0.00753242	+	0.0475578i	0.983636	+	0.180168i	$0.0576642\pi$
$294$	0.811790	+	2.20045i	0.0473445	+	0.128333i
$295$	0.333656	+	2.81904i	0.0194262	+	0.164131i
$296$	−4.06632	+	2.71703i	−0.236350	+	0.157924i
$297$	−3.82832	−	1.78879i	−0.222142	−	0.103796i
$298$	13.3765	−	5.54071i	0.774877	−	0.320965i
$299$	−4.13383	+	5.24374i	−0.239065	+	0.303253i
$300$	1.99986	−	1.84865i	0.115462	−	0.106732i
$301$	6.33128	−	0.248757i	0.364929	−	0.0143381i
$302$	−18.7843	−	36.8663i	−1.08092	−	2.12142i
$303$	0.0749521	−	0.633267i	0.00430589	−	0.0363802i
$304$	7.16544	−	1.72027i	0.410966	−	0.0986643i
$305$	2.40400	+	1.74661i	0.137653	+	0.100011i
$306$	−25.3874	+	6.02741i	−1.45130	+	0.344564i
$307$			0.0901450i			0.00514484i	0.999997	+	0.00257242i	$0.000818828\pi$
$307$			0.0901450i			0.00514484i	−0.999997	+	0.00257242i	$0.999181\pi$
$308$	4.02175	+	11.0764i	0.229160	+	0.631136i
$309$	−0.860258	+	0.171116i	−0.0489383	+	0.00973444i
$310$	0.490940	+	0.250147i	0.0278835	+	0.0142074i
$311$	2.41657	−	0.891519i	0.137031	−	0.0505534i	−0.276677	−	0.960963i	$-0.589233\pi$
$311$	2.41657	−	0.891519i	0.137031	−	0.0505534i	0.413708	+	0.910409i	$0.364233\pi$
$312$	−1.37716	+	0.634879i	−0.0779663	+	0.0359430i
$313$	22.1145	−	6.23693i	1.24998	−	0.352532i	0.418569	−	0.908185i	$-0.362532\pi$
$313$	22.1145	−	6.23693i	1.24998	−	0.352532i	0.831414	+	0.555653i	$0.187532\pi$
$314$	−2.22014	−	28.2096i	−0.125290	−	1.59196i
$315$	1.00215	+	0.614117i	0.0564647	+	0.0346016i
$316$	−0.383593	+	9.76310i	−0.0215788	+	0.549217i
$317$	22.9785	−	2.71969i	1.29060	−	0.152753i	0.555961	−	0.831208i	$-0.312350\pi$
$317$	22.9785	−	2.71969i	1.29060	−	0.152753i	0.734642	+	0.678455i	$0.237350\pi$
$318$	−0.656502	+	0.982525i	−0.0368148	+	0.0550972i
$319$	20.9356	+	16.6794i	1.17217	+	0.933869i
$320$	−0.668183	−	3.35919i	−0.0373526	−	0.187784i
$321$	0.181194	−	2.30229i	0.0101133	−	0.128501i
$322$	−2.05429	+	2.82749i	−0.114481	+	0.157570i
$323$	1.88985	+	12.1297i	0.105154	+	0.674914i
$324$	−6.87245	+	21.1512i	−0.381803	+	1.17507i
$325$	20.9954	+	17.9317i	1.16461	+	0.994674i
$326$	−36.7025	−	33.9275i	−2.03277	−	1.87907i
$327$	0.421380	−	0.0667401i	0.0233024	−	0.00369073i
$328$	10.9934	+	3.10047i	0.607011	+	0.171195i
$329$	2.60674	−	13.1050i	0.143714	−	0.722501i
$330$	0.374612	+	0.232219i	0.0206217	+	0.0127832i
$331$	−0.593085	−	1.43183i	−0.0325989	−	0.0787007i	0.906742	−	0.421687i	$-0.138562\pi$
$331$	−0.593085	−	1.43183i	−0.0325989	−	0.0787007i	−0.939341	+	0.342986i	$0.888562\pi$
$332$	−17.4809	+	14.9301i	−0.959389	+	0.819396i
$333$	11.4412	+	0.449526i	0.626974	+	0.0246339i
$334$	−18.9369	−	41.0773i	−1.03618	−	2.24765i
$335$	2.38273	−	1.87839i	0.130182	−	0.102627i
$336$	0.647569	−	0.329953i	0.0353278	−	0.0180004i
$337$	8.74796	−	9.46349i	0.476532	−	0.515509i	−0.449333	−	0.893364i	$-0.648338\pi$
$337$	8.74796	−	9.46349i	0.476532	−	0.515509i	0.925865	+	0.377855i	$0.123338\pi$
$338$	−20.7582	−	33.8743i	−1.12910	−	1.84252i
$339$	−2.09219	+	0.679794i	−0.113632	+	0.0369213i
$340$	3.07421	−	0.356009i	0.166722	−	0.0193073i
$341$	0.588879	−	2.88298i	0.0318896	−	0.156122i
$342$	17.4081	+	7.21066i	0.941321	+	0.389908i
$343$	−14.5080	+	8.12485i	−0.783356	+	0.438701i
$344$	−0.911363	−	5.75412i	−0.0491374	−	0.310241i
$345$	0.00289540	+	0.0736929i	0.000155883	+	0.00396749i
$346$	−19.5046	+	34.8279i	−1.04857	+	1.87236i
$347$	3.43709	+	12.1870i	0.184513	+	0.654232i	0.997417	+	0.0718345i	$0.0228853\pi$
$347$	3.43709	+	12.1870i	0.184513	+	0.654232i	−0.812904	+	0.582398i	$0.802115\pi$
$348$	−2.33616	+	3.81226i	−0.125231	+	0.204359i
$349$	4.66431	−	19.4282i	0.249675	−	1.03997i	−0.696819	−	0.717247i	$-0.745402\pi$
$349$	4.66431	−	19.4282i	0.249675	−	1.03997i	0.946494	−	0.322722i	$-0.104598\pi$
$350$	11.3493	+	8.94710i	0.606648	+	0.478242i
$351$	7.01840	+	1.39605i	0.374614	+	0.0745154i
$352$	−23.1859	+	11.6641i	−1.23581	+	0.621698i
$353$	−16.9506	+	16.9506i	−0.902192	+	0.902192i	−0.995625	−	0.0934338i	$-0.970216\pi$
$353$	−16.9506	+	16.9506i	−0.902192	+	0.902192i	0.0934338	+	0.995625i	$0.470216\pi$
$354$	2.19310	+	3.91606i	0.116562	+	0.208136i
$355$	1.61675	−	0.990744i	0.0858080	−	0.0525832i
$356$	10.9141	+	15.0220i	0.578447	+	0.796164i
$357$	0.460513	+	1.11974i	0.0243729	+	0.0592631i
$358$	−4.31661	−	1.40255i	−0.228140	−	0.0741272i
$359$	2.04271	+	8.50852i	0.107810	+	0.449063i	0.999997	−	0.00260519i	$-0.000829260\pi$
$359$	2.04271	+	8.50852i	0.107810	+	0.449063i	−0.892186	+	0.451668i	$0.850829\pi$
$360$	0.452438	−	0.981415i	0.0238456	−	0.0517251i
$361$	−4.60130	+	9.03056i	−0.242174	+	0.475293i
$362$	−19.1167	−	12.7734i	−1.00475	−	0.671352i
$363$	0.662155	−	2.25870i	0.0347542	−	0.118551i
$364$	−11.0867	−	16.5924i	−0.581102	−	0.869680i
$365$	1.05645	+	1.23694i	0.0552969	+	0.0647444i
$366$	4.56848	+	1.09679i	0.238798	+	0.0573304i
$367$	3.64525	−	9.88088i	0.190281	−	0.515778i	−0.806911	−	0.590673i	$-0.798862\pi$
$367$	3.64525	−	9.88088i	0.190281	−	0.515778i	0.997191	+	0.0748953i	$0.0238622\pi$
$368$	−2.56724	−	1.43772i	−0.133827	−	0.0749465i
$369$	−16.5562	−	21.0015i	−0.861883	−	1.09329i
$370$	−2.37745	−	0.376551i	−0.123598	−	0.0195759i
$371$	−3.21277	−	1.48111i	−0.166799	−	0.0768954i
$372$	0.489988	+	0.0385629i	0.0254047	+	0.00199939i
$373$	−1.94500			−0.100708			−0.0503542	−	0.998731i	$-0.516035\pi$
$373$	−1.94500			−0.100708			−0.0503542	+	0.998731i	$0.516035\pi$
$374$	−11.0028	−	27.1493i	−0.568942	−	1.40386i
$375$	0.615134			0.0317654
$376$	−12.2477	−	0.963913i	−0.631626	−	0.0497100i
$377$	−41.1658	−	18.9777i	−2.12015	−	0.977402i
$378$	3.69940	+	0.585928i	0.190277	+	0.0301369i
$379$	21.3819	+	27.1228i	1.09831	+	1.39320i	0.911743	+	0.410762i	$0.134737\pi$
$379$	21.3819	+	27.1228i	1.09831	+	1.39320i	0.186570	+	0.982442i	$0.440263\pi$
$380$	−1.94984	−	1.09196i	−0.100025	−	0.0560165i
$381$	−0.886134	+	2.40197i	−0.0453980	+	0.123057i
$382$	−36.3033	−	8.71565i	−1.85744	−	0.445932i
$383$	2.37225	+	2.77754i	0.121216	+	0.141926i	0.817696	−	0.575651i	$-0.195251\pi$
$383$	2.37225	+	2.77754i	0.121216	+	0.141926i	−0.696479	+	0.717577i	$0.745251\pi$
$384$	−1.14798	−	1.71807i	−0.0585825	−	0.0876749i
$385$	−0.511222	+	1.21648i	−0.0260543	+	0.0619975i
$386$	−22.5543	−	15.0703i	−1.14798	−	0.767058i
$387$	−6.19238	+	12.1532i	−0.314776	+	0.617783i
$388$	4.31805	−	9.36657i	0.219216	−	0.475515i
$389$	3.10639	+	12.9390i	0.157500	+	0.656035i	0.994123	+	0.108256i	$0.0345266\pi$
$389$	3.10639	+	12.9390i	0.157500	+	0.656035i	−0.836623	+	0.547779i	$0.815473\pi$
$390$	−0.709859	−	0.230647i	−0.0359451	−	0.0116793i
$391$	2.73351	−	4.06877i	0.138240	−	0.205767i
$392$	3.79490	+	5.22323i	0.191671	+	0.263813i
$393$	−1.08384	+	0.664179i	−0.0546726	+	0.0335034i
$394$	24.3342	+	43.4519i	1.22594	+	2.18908i
$395$	−0.773639	+	0.773639i	−0.0389260	+	0.0389260i
$396$	−25.0342	−	4.09702i	−1.25802	−	0.205883i
$397$	24.6400	+	4.90120i	1.23665	+	0.245984i	0.769760	−	0.638334i	$-0.220376\pi$
$397$	24.6400	+	4.90120i	1.23665	+	0.245984i	0.466886	+	0.884318i	$0.345376\pi$
$398$	−40.9310	−	32.2674i	−2.05169	−	1.61742i
$399$	0.204102	−	0.850144i	0.0102179	−	0.0425604i
$400$	−6.35727	+	10.3741i	−0.317863	+	0.518706i
$401$	−4.75557	−	16.8620i	−0.237482	−	0.842047i	−0.984223	−	0.176932i	$-0.943383\pi$
$401$	−4.75557	−	16.8620i	−0.237482	−	0.842047i	0.746741	−	0.665115i	$-0.231617\pi$
$402$	2.34404	−	4.18558i	0.116910	−	0.208758i
$403$	0.195632	+	4.97917i	0.00974513	+	0.248030i
$404$	−1.20700	−	7.62068i	−0.0600504	−	0.379143i
$405$	−2.17282	+	1.21684i	−0.107968	+	0.0604651i
$406$	−21.9203	−	9.07967i	−1.08788	−	0.450616i
$407$	1.44528	+	12.7732i	0.0716399	+	0.633142i
$408$	0.972653	−	0.541499i	0.0481535	−	0.0268082i
$409$	−14.3348	+	4.65765i	−0.708810	+	0.230306i	−0.641165	−	0.767403i	$-0.721548\pi$
$409$	−14.3348	+	4.65765i	−0.708810	+	0.230306i	−0.0676448	+	0.997709i	$0.521548\pi$
$410$	2.93748	+	4.79352i	0.145072	+	0.236735i
$411$	−0.238046	+	0.257516i	−0.0117419	+	0.0127023i
$412$	−9.45587	+	4.81801i	−0.465857	+	0.237366i
$413$	−10.5526	+	8.31900i	−0.519260	+	0.409351i
$414$	−3.14984	−	6.83253i	−0.154806	−	0.335801i
$415$	−2.57226	−	0.101064i	−0.126267	−	0.00496105i
$416$	33.4220	−	28.5451i	1.63865	−	1.39954i
$417$	0.666558	+	1.60921i	0.0326415	+	0.0788035i
$418$	−5.04392	+	20.5437i	−0.246706	+	1.00483i
$419$	5.94807	−	29.9030i	0.290582	−	1.46086i	−0.509243	−	0.860623i	$-0.670074\pi$
$419$	5.94807	−	29.9030i	0.290582	−	1.46086i	0.799825	−	0.600233i	$-0.204926\pi$
$420$	−0.212134	−	0.0598279i	−0.0103511	−	0.00291930i
$421$	16.6527	−	2.63753i	0.811603	−	0.128545i	0.263181	−	0.964747i	$-0.415229\pi$
$421$	16.6527	−	2.63753i	0.811603	−	0.128545i	0.548423	+	0.836201i	$0.315229\pi$
$422$	4.42769	+	4.09292i	0.215537	+	0.199240i
$423$	21.8722	+	18.6806i	1.06346	+	0.908282i
$424$	−1.00517	+	3.09360i	−0.0488155	+	0.150239i
$425$	−16.3679	−	11.9551i	−0.793960	−	0.579906i
$426$	1.76221	−	2.42548i	0.0853794	−	0.117515i
$427$	−1.10360	+	14.0226i	−0.0534070	+	0.678600i
$428$	−5.45134	−	27.4057i	−0.263500	−	1.32471i
$429$	−0.176956	+	3.98206i	−0.00854351	+	0.192256i
$430$	1.59307	−	2.38419i	0.0768245	−	0.114976i
$431$	29.8080	−	3.52800i	1.43580	−	0.169938i	0.636688	−	0.771122i	$-0.280304\pi$
$431$	29.8080	−	3.52800i	1.43580	−	0.169938i	0.799111	+	0.601184i	$0.205304\pi$
$432$	−0.123800	+	3.15091i	−0.00595632	+	0.151598i
$433$	6.42796	+	3.93906i	0.308908	+	0.189299i	0.668308	−	0.743884i	$-0.267019\pi$
$433$	6.42796	+	3.93906i	0.308908	+	0.189299i	−0.359400	+	0.933184i	$0.617019\pi$
$434$	0.204636	+	2.60015i	0.00982286	+	0.124811i
$435$	−0.481868	+	0.135901i	−0.0231038	+	0.00651595i
$436$	4.68786	−	2.16113i	0.224508	−	0.103500i
$437$	−3.32086	+	1.22513i	−0.158858	+	0.0586059i
$438$	2.29164	+	1.16765i	0.109499	+	0.0557925i
$439$	−22.6660	+	4.50856i	−1.08179	+	0.215182i	−0.703636	−	0.710561i	$-0.748441\pi$
$439$	−22.6660	+	4.50856i	−1.08179	+	0.215182i	−0.378155	+	0.925742i	$0.623441\pi$
$440$	1.16600	+	0.335324i	0.0555867	+	0.0159859i
$441$		−	15.1159i		−	0.719803i
$442$	29.0579	+	40.2073i	1.38214	+	1.91247i
$443$	−7.21411	−	5.24136i	−0.342753	−	0.249024i	0.403070	−	0.915169i	$-0.367943\pi$
$443$	−7.21411	−	5.24136i	−0.342753	−	0.249024i	−0.745822	+	0.666145i	$0.767943\pi$
$444$	−2.08786	+	0.501250i	−0.0990854	+	0.0237883i
$445$	−0.244386	+	2.06481i	−0.0115850	+	0.0978814i
$446$	−4.05118	−	7.95088i	−0.191829	−	0.376485i
$447$	1.44511	−	0.0567784i	0.0683512	−	0.00268553i
$448$	11.9053	−	11.0051i	0.562471	−	0.519942i
$449$	25.5077	−	32.3563i	1.20378	−	1.52699i	0.418047	−	0.908426i	$-0.362715\pi$
$449$	25.5077	−	32.3563i	1.20378	−	1.52699i	0.785735	−	0.618564i	$-0.212285\pi$
$450$	−28.7425	+	11.9055i	−1.35494	+	0.561232i
$451$	20.4929	−	21.9418i	0.964974	−	1.03320i
$452$	−22.1313	+	14.7877i	−1.04097	+	0.695554i
$453$	−0.485774	−	4.10428i	−0.0228236	−	0.192836i
$454$	16.8343	+	45.6314i	0.790074	+	2.14159i
$455$	0.349564	−	2.20706i	0.0163878	−	0.103469i
$456$	−0.798311	−	0.0944864i	−0.0373844	−	0.00442473i
$457$	−19.7683	+	23.1457i	−0.924723	+	1.08271i	0.0716339	+	0.997431i	$0.477179\pi$
$457$	−19.7683	+	23.1457i	−0.924723	+	1.08271i	−0.996357	+	0.0852806i	$0.972821\pi$
$458$	−18.2137	+	13.2331i	−0.851072	+	0.618340i
$459$	−5.21515	−	0.630574i	−0.243422	−	0.0294327i
$460$	0.275746	+	0.848659i	0.0128567	+	0.0395689i
$461$	−6.45043	+	15.5727i	−0.300426	+	0.725294i	0.699517	+	0.714616i	$0.253399\pi$
$461$	−6.45043	+	15.5727i	−0.300426	+	0.725294i	−0.999943	+	0.0106772i	$0.996601\pi$
$462$	−0.0107219	+	2.08631i	−0.000498829	+	0.0970637i
$463$	1.59350	+	1.59350i	0.0740563	+	0.0740563i	0.743165	−	0.669108i	$-0.233324\pi$
$463$	1.59350	+	1.59350i	0.0740563	+	0.0740563i	−0.669108	+	0.743165i	$0.733324\pi$
$464$	5.42206	−	19.2252i	0.251713	−	0.892507i
$465$	0.0373594	+	0.0404151i	0.00173250	+	0.00187421i
$466$	−17.2860	−	6.37715i	−0.800760	−	0.295416i
$467$	16.8483	−	1.32599i	0.779644	−	0.0613593i	0.317610	−	0.948221i	$-0.397120\pi$
$467$	16.8483	−	1.32599i	0.779644	−	0.0613593i	0.462034	+	0.886862i	$0.347120\pi$
$468$	42.8259	−	3.37047i	1.97963	−	0.155800i
$469$	13.4745	+	4.97101i	0.622195	+	0.229540i
$470$	−4.10462	−	4.44035i	−0.189332	−	0.204818i
$471$	0.767223	−	2.72037i	0.0353518	−	0.125348i
$472$	8.73638	+	8.73638i	0.402125	+	0.402125i
$473$	−14.5392	−	4.80681i	−0.668512	−	0.221017i
$474$	−0.661997	+	1.59820i	−0.0304065	+	0.0734079i
$475$	4.52297	+	13.9203i	0.207528	+	0.638706i
$476$	9.04032	+	11.5272i	0.414362	+	0.528347i
$477$	6.16123	−	4.47639i	0.282103	−	0.204960i
$478$	41.9808	−	49.1531i	1.92015	−	2.24821i
$479$	13.2329	+	1.56622i	0.604627	+	0.0715623i	0.414272	−	0.910153i	$-0.364036\pi$
$479$	13.2329	+	1.56622i	0.604627	+	0.0715623i	0.190355	+	0.981715i	$0.439036\pi$
$480$	0.0759424	−	0.479481i	0.00346628	−	0.0218852i
$481$	−7.53457	−	20.4233i	−0.343547	−	0.931224i
$482$	5.43592	+	45.9279i	0.247599	+	2.09196i
$483$	−0.290268	+	0.193951i	−0.0132077	+	0.00882507i
$484$	0.292712	−	28.4777i	0.0133051	−	1.29444i
$485$	1.06702	−	0.441974i	0.0484508	−	0.0200690i
$486$	−7.50680	+	9.52234i	−0.340516	+	0.431942i
$487$	−6.30601	+	5.82921i	−0.285753	+	0.264147i	−0.808704	−	0.588215i	$-0.799831\pi$
$487$	−6.30601	+	5.82921i	−0.285753	+	0.264147i	0.522952	+	0.852362i	$0.324831\pi$
$488$	12.9231	−	0.507749i	0.585000	−	0.0229847i
$489$	−2.26655	−	4.44836i	−0.102497	−	0.201162i
$490$	−0.373502	+	3.15571i	−0.0168731	+	0.142560i
$491$	1.08568	−	0.260648i	0.0489959	−	0.0117629i	−0.208873	−	0.977943i	$-0.566980\pi$
$491$	1.08568	−	0.260648i	0.0489959	−	0.0117629i	0.257869	+	0.966180i	$0.416980\pi$
$492$	4.05719	+	2.94772i	0.182912	+	0.132894i
$493$	31.1905	+	11.5961i	1.40475	+	0.522263i
$494$		−	35.8232i		−	1.61176i
$495$	−1.74709	−	2.23975i	−0.0785258	−	0.100669i
$496$	−2.15364	+	0.428386i	−0.0967013	+	0.0192351i
$497$	7.99741	+	4.07488i	0.358733	+	0.182783i
$498$	−3.81859	+	1.40875i	−0.171115	+	0.0631278i
$499$	6.71993	−	3.09793i	0.300825	−	0.138682i	−0.262465	−	0.964942i	$-0.584535\pi$
$499$	6.71993	−	3.09793i	0.300825	−	0.138682i	0.563290	+	0.826259i	$0.309535\pi$
$500$	7.16336	−	2.02028i	0.320355	−	0.0903495i
$501$	−0.354487	−	4.50418i	−0.0158373	−	0.201232i
$502$	−4.19037	−	2.56786i	−0.187026	−	0.114609i
$503$	0.438814	−	11.1686i	0.0195658	−	0.497982i	−0.957927	−	0.287012i	$-0.907338\pi$
$503$	0.438814	−	11.1686i	0.0195658	−	0.497982i	0.977493	−	0.210970i	$-0.0676621\pi$
$504$	5.08007	−	0.601265i	0.226284	−	0.0267825i
$505$	0.480003	−	0.718375i	0.0213598	−	0.0319673i
$506$	7.04711	−	4.65652i	0.313282	−	0.207008i
$507$	−0.774194	−	3.89213i	−0.0343831	−	0.172856i
$508$	−2.43044	+	30.8817i	−0.107834	+	1.37016i
$509$	−14.3069	+	19.6918i	−0.634142	+	0.872822i	−0.998286	−	0.0585207i	$-0.981362\pi$
$509$	−14.3069	+	19.6918i	−0.634142	+	0.872822i	0.364144	+	0.931343i	$0.381362\pi$
$510$	0.532460	+	0.129251i	0.0235777	+	0.00572335i
$511$	−2.37945	+	7.32320i	−0.105261	+	0.323959i
$512$	19.4773	+	16.6352i	0.860784	+	0.735179i
$513$	2.78557	+	2.57496i	0.122986	+	0.113687i
$514$	32.0450	−	5.07543i	1.41344	−	0.223868i
$515$	−1.14375	−	0.322572i	−0.0503998	−	0.0142142i
$516$	0.499010	−	2.50869i	0.0219677	−	0.110439i
$517$	−17.0140	+	27.4468i	−0.748276	+	1.20711i
$518$	−4.36036	−	10.5268i	−0.191583	−	0.462523i
$519$	−3.03193	+	2.58951i	−0.133087	+	0.113667i
$520$	−2.05301	−	0.0806631i	−0.0900306	−	0.00353731i
$521$	11.7428	+	25.4722i	0.514463	+	1.11596i	0.973740	+	0.227663i	$0.0731085\pi$
$521$	11.7428	+	25.4722i	0.514463	+	1.11596i	−0.459277	+	0.888293i	$0.651891\pi$
$522$	40.1106	−	31.6206i	1.75559	−	1.38400i
$523$	16.7623	−	8.54079i	0.732962	−	0.373463i	−0.0473289	−	0.998879i	$-0.515071\pi$
$523$	16.7623	−	8.54079i	0.732962	−	0.373463i	0.780291	+	0.625416i	$0.215071\pi$
$524$	−10.4402	+	11.2941i	−0.456082	+	0.493387i
$525$	0.754258	+	1.23084i	0.0329185	+	0.0537182i
$526$	27.8866	−	9.06089i	1.21591	−	0.395074i
$527$	−0.420805	−	3.63374i	−0.0183305	−	0.158288i
$528$	−1.74534	+	0.197485i	−0.0759563	+	0.00859444i
$529$	−19.9435	−	8.26085i	−0.867107	−	0.359167i
$530$	−1.39687	+	0.782287i	−0.0606764	+	0.0339804i
$531$	−4.52513	−	28.5705i	−0.196374	−	1.23986i
$532$	−0.415313	−	10.5704i	−0.0180061	−	0.458286i
$533$	−24.8431	+	44.3606i	−1.07607	+	1.92147i
$534$	0.892357	+	3.16406i	0.0386161	+	0.136922i
$535$	1.63487	−	2.66786i	0.0706816	−	0.115342i
$536$	3.08275	−	12.8406i	0.133155	−	0.554629i
$537$	−0.356034	−	0.280674i	−0.0153640	−	0.0121120i
$538$	−23.4913	−	4.67272i	−1.01278	−	0.201455i
$539$	16.7747	−	2.56855i	0.722538	−	0.110635i
$540$	0.676208	−	0.676208i	0.0290994	−	0.0290994i
$541$	−19.0558	−	34.0266i	−0.819273	−	1.46292i	−0.885260	−	0.465096i	$-0.846020\pi$
$541$	−19.0558	−	34.0266i	−0.819273	−	1.46292i	0.0659875	−	0.997820i	$-0.478980\pi$
$542$	−16.9803	+	10.4055i	−0.729366	+	0.446956i
$543$	−1.34988	−	1.85794i	−0.0579287	−	0.0797320i
$544$	−22.8727	+	22.7577i	−0.980657	+	0.975730i
$545$	0.549740	+	0.178621i	0.0235483	+	0.00765130i
$546$	−0.824789	−	3.43550i	−0.0352977	−	0.147026i
$547$	−15.7183	+	34.0956i	−0.672066	+	1.45782i	0.205642	+	0.978627i	$0.434072\pi$
$547$	−15.7183	+	34.0956i	−0.672066	+	1.45782i	−0.877708	+	0.479197i	$0.840928\pi$
$548$	−1.92633	+	3.78064i	−0.0822887	+	0.161501i
$549$	−25.1767	−	16.8225i	−1.07452	−	0.717968i
$550$	−18.0961	−	29.8737i	−0.771622	−	1.27382i
$551$	−13.3501	−	19.9798i	−0.568734	−	0.851170i
$552$	0.208463	+	0.244079i	0.00887278	+	0.0103887i
$553$	−5.03590	−	1.20901i	−0.214148	−	0.0514124i
$554$	−6.03255	+	16.3520i	−0.256299	+	0.694728i
$555$	−0.209780	−	0.117482i	−0.00890466	−	0.00498685i
$556$	13.0473	+	16.5504i	0.553329	+	0.701895i
$557$	−25.6582	−	4.06386i	−1.08717	−	0.172191i	−0.412975	−	0.910742i	$-0.635510\pi$
$557$	−25.6582	−	4.06386i	−1.08717	−	0.172191i	−0.674198	+	0.738551i	$0.735510\pi$
$558$	−5.09892	−	2.35063i	−0.215854	−	0.0995102i
$559$	25.8522	+	2.03462i	1.09343	+	0.0860551i
$560$	0.984696			0.0416110
$561$	−0.0924860	−	2.92464i	−0.00390476	−	0.123479i
$562$	51.1382			2.15714
$563$	−30.5394	−	2.40350i	−1.28708	−	0.101296i	−0.583620	−	0.812027i	$-0.698364\pi$
$563$	−30.5394	−	2.40350i	−1.28708	−	0.101296i	−0.703463	+	0.710731i	$0.748364\pi$
$564$	−4.89850	−	2.25824i	−0.206264	−	0.0950891i
$565$	−2.94382	−	0.466256i	−0.123848	−	0.0196155i
$566$	35.0644	+	44.4790i	1.47387	+	1.86959i
$567$	−10.2853	−	5.76003i	−0.431941	−	0.241898i
$568$	2.85643	−	7.74269i	0.119853	−	0.324876i
$569$	15.0157	+	3.60495i	0.629490	+	0.151127i	0.535623	−	0.844458i	$-0.320077\pi$
$569$	15.0157	+	3.60495i	0.629490	+	0.151127i	0.0938675	+	0.995585i	$0.470077\pi$
$570$	−0.256965	−	0.300867i	−0.0107631	−	0.0126019i
$571$	−10.9768	−	16.4279i	−0.459365	−	0.687488i	0.527405	−	0.849614i	$-0.323165\pi$
$571$	−10.9768	−	16.4279i	−0.459365	−	0.687488i	−0.986770	+	0.162126i	$0.948165\pi$
$572$	11.0175	+	46.9530i	0.460666	+	1.96320i
$573$	−3.10078	−	2.07187i	−0.129537	−	0.0865537i
$574$	−12.0817	+	23.7117i	−0.504280	+	0.989706i
$575$	2.44678	−	5.30747i	0.102038	−	0.221337i
$576$	8.14744	+	33.9365i	0.339476	+	1.41402i
$577$	−22.8170	−	7.41368i	−0.949882	−	0.308635i	−0.207214	−	0.978296i	$-0.566440\pi$
$577$	−22.8170	−	7.41368i	−0.949882	−	0.308635i	−0.742668	+	0.669660i	$0.766440\pi$
$578$	−23.5114	−	27.8108i	−0.977947	−	1.15678i
$579$	−1.59261	−	2.19205i	−0.0661868	−	0.0910983i
$580$	−5.16511	+	3.16518i	−0.214469	+	0.131427i
$581$	−5.95406	−	10.6317i	−0.247016	−	0.441079i
$582$	1.29123	−	1.29123i	0.0535234	−	0.0535234i
$583$	6.01459	+	6.07673i	0.249099	+	0.251672i
$584$	6.94386	+	1.38122i	0.287339	+	0.0571553i
$585$	3.77767	+	2.97807i	0.156187	+	0.123128i
$586$	−0.412175	+	1.71683i	−0.0170268	+	0.0709216i
$587$	9.89836	−	16.1526i	0.408549	−	0.666691i	−0.580503	−	0.814258i	$-0.697144\pi$
$587$	9.89836	−	16.1526i	0.408549	−	0.666691i	0.989052	+	0.147567i	$0.0471441\pi$
$588$	0.769432	+	2.72820i	0.0317309	+	0.112509i
$589$	−1.29071	+	2.30472i	−0.0531827	+	0.0949645i
$590$	0.238743	+	6.07642i	0.00982890	+	0.250162i
$591$	0.778193	+	4.91332i	0.0320106	+	0.202107i
$592$	8.36963	−	4.68722i	0.343989	−	0.192643i
$593$	−36.6377	−	15.1758i	−1.50453	−	0.623197i	−0.530109	−	0.847929i	$-0.677849\pi$
$593$	−36.6377	−	15.1758i	−1.50453	−	0.623197i	−0.974420	+	0.224733i	$0.927849\pi$
$594$	−7.87510	−	4.46358i	−0.323119	−	0.183143i
$595$	−0.132822	+	1.63501i	−0.00544517	+	0.0670289i
$596$	16.6421	−	5.40734i	0.681686	−	0.221493i
$597$	−2.72021	−	4.43897i	−0.111331	−	0.181675i
$598$	−9.70953	+	10.5037i	−0.397052	+	0.429529i
$599$	−24.2671	+	12.3647i	−0.991526	+	0.505208i	−0.872988	−	0.487742i	$-0.837821\pi$
$599$	−24.2671	+	12.3647i	−0.991526	+	0.505208i	−0.118538	+	0.992949i	$0.537821\pi$
$600$	1.04235	−	0.821719i	0.0425536	−	0.0335466i
$601$	−9.06920	−	19.6726i	−0.369941	−	0.802463i	−0.999671	−	0.0256493i	$-0.991835\pi$
$601$	−9.06920	−	19.6726i	−0.369941	−	0.802463i	0.629730	−	0.776814i	$-0.283165\pi$
$602$	13.5629	+	0.532887i	0.552782	+	0.0217188i
$603$	−23.5099	+	20.0794i	−0.957397	+	0.817694i
$604$	−19.1366	−	46.1997i	−0.778655	−	1.87984i
$605$	2.18867	−	2.31941i	0.0889822	−	0.0942972i
$606$	0.266504	−	1.33981i	0.0108260	−	0.0544259i
$607$	10.8265	+	3.05340i	0.439436	+	0.123934i	0.483991	−	0.875073i	$-0.339187\pi$
$607$	10.8265	+	3.05340i	0.439436	+	0.123934i	−0.0445548	+	0.999007i	$0.514187\pi$
$608$	23.0128	−	3.64487i	0.933293	−	0.147819i
$609$	−1.74031	−	1.60872i	−0.0705209	−	0.0651888i
$610$	4.84041	+	4.13410i	0.195983	+	0.167385i
$611$	16.8989	−	52.0093i	0.683655	−	2.10407i
$612$	−31.1597	+	4.85481i	−1.25956	+	0.196244i
$613$	8.97574	−	12.3540i	0.362527	−	0.498975i	−0.588324	−	0.808625i	$-0.700212\pi$
$613$	8.97574	−	12.3540i	0.362527	−	0.498975i	0.950851	+	0.309650i	$0.100212\pi$
$614$	−0.0151511	+	0.192513i	−0.000611449	+	0.00776920i
$615$	0.109556	+	0.550773i	0.00441770	+	0.0222093i
$616$	1.53048	+	5.53539i	0.0616647	+	0.223027i
$617$	5.45152	−	8.15877i	0.219470	−	0.328460i	−0.705354	−	0.708855i	$-0.749212\pi$
$617$	5.45152	−	8.15877i	0.219470	−	0.328460i	0.924824	+	0.380395i	$0.124212\pi$
$618$	−1.86592	+	0.220847i	−0.0750584	+	0.00888375i
$619$	−0.353139	+	8.98798i	−0.0141938	+	0.361257i	0.975671	+	0.219242i	$0.0703583\pi$
$619$	−0.353139	+	8.98798i	−0.0141938	+	0.361257i	−0.989864	+	0.142016i	$0.954642\pi$
$620$	0.567792	+	0.347943i	0.0228031	+	0.0139737i
$621$	−0.118840	−	1.51000i	−0.00476888	−	0.0605944i
$622$	5.31065	−	1.49776i	0.212938	−	0.0600547i
$623$	−8.93814	+	4.12054i	−0.358099	+	0.165086i
$624$	2.79067	−	1.02953i	0.111716	−	0.0412143i
$625$	−21.1581	−	10.7806i	−0.846325	−	0.431224i
$626$	48.2759	−	9.60266i	1.92949	−	0.383800i
$627$	−1.18293	+	1.75084i	−0.0472418	+	0.0699217i
$628$		−	34.1990i		−	1.36469i
$629$	6.65381	+	14.5293i	0.265305	+	0.579323i
$630$	2.03697	+	1.47994i	0.0811547	+	0.0589623i
$631$	13.1620	−	3.15992i	0.523971	−	0.125794i	0.0371730	−	0.999309i	$-0.488165\pi$
$631$	13.1620	−	3.15992i	0.523971	−	0.125794i	0.486798	+	0.873514i	$0.338165\pi$
$632$	−0.559698	+	4.72886i	−0.0222636	+	0.188104i
$633$	0.273430	+	0.536637i	0.0108679	+	0.0213294i
$634$	49.5300	−	1.94604i	1.96709	−	0.0772871i
$635$	−2.54718	+	2.35459i	−0.101082	+	0.0934391i
$636$	−0.884156	+	1.12155i	−0.0350591	+	0.0444722i
$637$	−26.5508	+	10.9977i	−1.05198	+	0.435744i
$638$	41.9065	+	39.1393i	1.65909	+	1.54954i
$639$	−16.0657	+	10.7347i	−0.635547	+	0.424659i
$640$	−0.329054	−	2.78016i	−0.0130070	−	0.109896i
$641$	14.8142	+	40.1556i	0.585124	+	1.58605i	0.793876	+	0.608080i	$0.208060\pi$
$641$	14.8142	+	40.1556i	0.585124	+	1.58605i	−0.208751	+	0.977969i	$0.566940\pi$
$642$	0.773915	−	4.88631i	0.0305440	−	0.192847i
$643$	20.2414	+	2.39573i	0.798244	+	0.0944784i	0.506749	−	0.862094i	$-0.330847\pi$
$643$	20.2414	+	2.39573i	0.798244	+	0.0944784i	0.291495	+	0.956572i	$0.405847\pi$
$644$	−2.74324	+	3.21192i	−0.108099	+	0.126567i
$645$	0.231719	−	0.168354i	0.00912393	−	0.00662892i
$646$	1.99727	+	26.2218i	0.0785814	+	1.03168i
$647$	13.7857	+	42.4280i	0.541971	+	1.66802i	0.728085	+	0.685487i	$0.240411\pi$
$647$	13.7857	+	42.4280i	0.541971	+	1.66802i	−0.186113	+	0.982528i	$0.559589\pi$
$648$	−4.14786	+	10.0138i	−0.162943	+	0.393380i
$649$	30.9370	−	9.87656i	1.21438	−	0.387689i
$650$	41.8238	+	41.8238i	1.64046	+	1.64046i
$651$	−0.0707170	+	0.250743i	−0.00277162	+	0.00982741i
$652$	−41.0041	−	44.3580i	−1.60584	−	1.73719i
$653$	−3.97566	−	1.46670i	−0.155580	−	0.0573963i	0.267135	−	0.963659i	$-0.413923\pi$
$653$	−3.97566	−	1.46670i	−0.155580	−	0.0573963i	−0.422715	+	0.906263i	$0.638923\pi$
$654$	0.911115	−	0.0717063i	0.0356274	−	0.00280394i
$655$	−1.71694	+	0.135126i	−0.0670866	+	0.00527983i
$656$	−21.0200	−	7.75468i	−0.820692	−	0.302769i
$657$	−11.2518	−	12.1721i	−0.438973	−	0.474879i
$658$	7.76957	−	27.5488i	0.302889	−	1.07397i
$659$	27.0007	+	27.0007i	1.05180	+	1.05180i	0.998583	+	0.0532157i	$0.0169471\pi$
$659$	27.0007	+	27.0007i	1.05180	+	1.05180i	0.0532157	+	0.998583i	$0.483053\pi$
$660$	0.429333	+	0.315313i	0.0167118	+	0.0122735i
$661$	−0.961861	+	2.32214i	−0.0374120	+	0.0903207i	−0.941481	−	0.337066i	$-0.890566\pi$
$661$	−0.961861	+	2.32214i	−0.0374120	+	0.0903207i	0.904069	+	0.427386i	$0.140566\pi$
$662$	−1.02593	−	3.15750i	−0.0398741	−	0.122720i
$663$	1.33304	+	4.77256i	0.0517709	+	0.185351i
$664$	−9.06423	+	6.58555i	−0.351760	+	0.255569i
$665$	0.769312	−	0.900748i	0.0298326	−	0.0349295i
$666$	24.3582	+	2.88299i	0.943862	+	0.111713i
$667$	−1.50096	+	9.47671i	−0.0581175	+	0.366940i
$668$	−18.9211	−	51.2879i	−0.732079	−	1.98439i
$669$	−0.104766	−	0.885163i	−0.00405048	−	0.0342224i
$670$	5.40426	−	3.61101i	0.208785	−	0.139505i
$671$	14.3905	−	30.7982i	0.555541	−	1.18895i
$672$	2.12304	−	0.879393i	0.0818982	−	0.0339233i
$673$	−13.0870	+	16.6008i	−0.504468	+	0.639915i	−0.969416	−	0.245423i	$-0.921073\pi$
$673$	−13.0870	+	16.6008i	−0.504468	+	0.639915i	0.464948	+	0.885338i	$0.346073\pi$
$674$	20.2727	−	18.7399i	0.780875	−	0.721834i
$675$	−6.25844	+	0.245895i	−0.240888	+	0.00946450i
$676$	−21.7985	−	42.7820i	−0.838404	−	1.64546i
$677$	−0.984748	+	8.32009i	−0.0378469	+	0.319767i	0.961190	+	0.275888i	$0.0889718\pi$
$677$	−0.984748	+	8.32009i	−0.0378469	+	0.319767i	−0.999037	+	0.0438795i	$0.986028\pi$
$678$	−4.58233	+	1.10012i	−0.175983	+	0.0422499i
$679$	4.42289	+	3.21342i	0.169735	+	0.123320i
$680$	1.50726	−	0.0554191i	0.0578007	−	0.00212523i
$681$			4.85827i			0.186169i
$682$	1.74217	−	6.05791i	0.0667110	−	0.231969i
$683$	23.1581	−	4.60643i	0.886119	−	0.176260i	0.269010	−	0.963137i	$-0.413304\pi$
$683$	23.1581	−	4.60643i	0.886119	−	0.176260i	0.617109	+	0.786877i	$0.288304\pi$
$684$	20.2905	+	10.3385i	0.775825	+	0.395303i
$685$	−0.445765	+	0.164451i	−0.0170318	+	0.00628337i
$686$	−32.3487	+	14.9130i	−1.23508	+	0.569380i
$687$	−2.16437	+	0.610415i	−0.0825758	+	0.0232888i
$688$	0.896582	+	11.3921i	0.0341818	+	0.434322i
$689$	−12.3454	−	7.56525i	−0.470321	−	0.288213i
$690$	−0.00620253	+	0.157865i	−0.000236126	+	0.00600982i
$691$	−35.3682	+	4.18610i	−1.34547	+	0.159247i	−0.759193	−	0.650865i	$-0.774406\pi$
$691$	−35.3682	+	4.18610i	−1.34547	+	0.159247i	−0.586275	+	0.810112i	$0.699406\pi$
$692$	−26.8027	+	40.1130i	−1.01888	+	1.52487i
$693$	4.71869	−	12.5909i	0.179248	−	0.478290i
$694$	5.29190	+	26.6042i	0.200878	+	1.00988i
$695$	−0.185156	+	2.35263i	−0.00702338	+	0.0892405i
$696$	−1.28083	+	1.76291i	−0.0485496	+	0.0668228i
$697$	15.7113	−	33.8560i	0.595109	−	1.28239i
$698$	13.2265	−	40.7069i	0.500629	−	1.54078i
$699$	−1.39945	−	1.19525i	−0.0529322	−	0.0452084i
$700$	12.8259	+	11.8561i	0.484774	+	0.448120i
$701$	−4.87920	+	0.772789i	−0.184285	+	0.0291878i	−0.247895	−	0.968787i	$-0.579739\pi$
$701$	−4.87920	+	0.772789i	−0.184285	+	0.0291878i	0.0636099	+	0.997975i	$0.479739\pi$
$702$	14.7538	+	4.16101i	0.556847	+	0.157047i
$703$	2.25130	−	11.3181i	0.0849095	−	0.426869i
$704$	−36.2763	+	14.8082i	−1.36722	+	0.558105i
$705$	−0.231142	−	0.558027i	−0.00870533	−	0.0210165i
$706$	−39.0487	+	33.3507i	−1.46962	+	1.25517i
$707$	4.08659	+	0.160563i	0.153692	+	0.00603858i
$708$	2.27103	+	4.92624i	0.0853505	+	0.185139i
$709$	−3.33306	+	2.62757i	−0.125176	+	0.0986805i	−0.679712	−	0.733479i	$-0.737895\pi$
$709$	−3.33306	+	2.62757i	−0.125176	+	0.0986805i	0.554537	+	0.832159i	$0.312895\pi$
$710$	3.61924	−	1.84409i	0.135828	−	0.0692076i
$711$	7.56783	−	8.18683i	0.283816	−	0.307030i
$712$	4.72835	+	7.71597i	0.177203	+	0.289168i
$713$	1.00312	−	0.325934i	0.0375672	−	0.0122063i
$714$	0.795268	+	2.46872i	0.0297622	+	0.0923896i
$715$	−2.66297	+	4.69828i	−0.0995896	+	0.175706i
$716$	−5.06789	−	2.09919i	−0.189396	−	0.0784504i
$717$	5.63350	−	3.15491i	0.210387	−	0.117822i
$718$	2.93234	+	18.5141i	0.109434	+	0.690940i
$719$	−0.00245977	−	0.0626053i	−9.17338e−5	−	0.00233478i	0.999182	−	0.0404272i	$-0.0128719\pi$
$719$	−0.00245977	−	0.0626053i	−9.17338e−5	−	0.00233478i	−0.999274	+	0.0380924i	$0.987872\pi$
$720$	−1.03576	+	1.84948i	−0.0386004	+	0.0689260i
$721$	−1.52693	−	5.41407i	−0.0568657	−	0.201631i
$722$	−11.3443	+	18.5123i	−0.422192	+	0.688955i
$723$	−1.07843	+	4.49198i	−0.0401072	+	0.167059i
$724$	−21.8216	−	17.2028i	−0.810993	−	0.639335i
$725$	38.9129	+	7.74026i	1.44519	+	0.287466i
$726$	1.79373	−	4.71238i	0.0665715	−	0.174893i
$727$	−29.7943	+	29.7943i	−1.10501	+	1.10501i	−0.111211	+	0.993797i	$0.535473\pi$
$727$	−29.7943	+	29.7943i	−1.10501	+	1.10501i	−0.993797	+	0.111211i	$0.964527\pi$
$728$	−4.75216	−	8.48559i	−0.176127	−	0.314497i
$729$	20.9399	−	12.8320i	0.775551	−	0.475258i
$730$	2.04824	+	2.81917i	0.0758089	+	0.104342i
$731$	−19.0367	−	0.0479402i	−0.704098	−	0.00177313i
$732$	5.40035	+	1.75468i	0.199603	+	0.0648548i
$733$	−10.5096	−	43.7755i	−0.388180	−	1.61689i	−0.734389	−	0.678729i	$-0.762531\pi$
$733$	−10.5096	−	43.7755i	−0.388180	−	1.61689i	0.346209	−	0.938158i	$-0.387469\pi$
$734$	9.44551	−	20.4889i	0.348640	−	0.756259i
$735$	−0.144103	+	0.282818i	−0.00531532	+	0.0104319i
$736$	−7.73549	−	5.16869i	−0.285134	−	0.190520i
$737$	−26.2778	−	22.6780i	−0.967955	−	0.835353i
$738$	−31.8276	−	47.6334i	−1.17159	−	1.75341i
$739$	−0.486727	−	0.569885i	−0.0179046	−	0.0209635i	0.751381	−	0.659868i	$-0.229388\pi$
$739$	−0.486727	−	0.569885i	−0.0179046	−	0.0209635i	−0.769286	+	0.638905i	$0.779388\pi$
$740$	−2.82877	−	0.679128i	−0.103988	−	0.0249652i
$741$	1.23850	−	3.35710i	0.0454975	−	0.123326i
$742$	−6.61225	−	3.70304i	−0.242743	−	0.135943i
$743$	17.1152	+	21.7105i	0.627894	+	0.796480i	0.990798	−	0.135346i	$-0.0432148\pi$
$743$	17.1152	+	21.7105i	0.627894	+	0.796480i	−0.362904	+	0.931826i	$0.618215\pi$
$744$	0.236593	+	0.0374726i	0.00867390	+	0.00137381i
$745$	1.77945	+	0.820338i	0.0651941	+	0.0300549i
$746$	−4.15374	−	0.326906i	−0.152079	−	0.0119689i
$747$	26.2316			0.959764
$748$	−10.6824	−	33.7543i	−0.390587	−	1.23418i
$749$	14.8112			0.541189
$750$	1.31368	+	0.103389i	0.0479687	+	0.00377522i
$751$	22.3144	+	10.2871i	0.814265	+	0.375381i	0.781363	−	0.624077i	$-0.214525\pi$
$751$	22.3144	+	10.2871i	0.814265	+	0.375381i	0.0329024	+	0.999459i	$0.489525\pi$
$752$	23.8014	+	3.76977i	0.867947	+	0.137469i
$753$	−0.303915	−	0.385515i	−0.0110753	−	0.0140489i
$754$	−84.7239	−	47.4477i	−3.08546	−	1.72794i
$755$	1.93811	−	5.25347i	0.0705349	−	0.191193i
$756$	4.40168	+	1.05675i	0.160088	+	0.0384336i
$757$	−6.18005	−	7.23591i	−0.224618	−	0.262994i	0.636641	−	0.771160i	$-0.280323\pi$
$757$	−6.18005	−	7.23591i	−0.224618	−	0.262994i	−0.861259	+	0.508167i	$0.830323\pi$
$758$	41.1044	+	61.5171i	1.49298	+	2.23440i
$759$	0.821395	−	0.192740i	0.0298148	−	0.00699604i
$760$	−0.905600	−	0.605103i	−0.0328496	−	0.0219494i
$761$	4.26920	−	8.37878i	0.154759	−	0.303731i	−0.800590	−	0.599213i	$-0.795480\pi$
$761$	4.26920	−	8.37878i	0.154759	−	0.303731i	0.955348	+	0.295482i	$0.0954803\pi$
$762$	−2.29614	+	4.98070i	−0.0831802	+	0.180432i
$763$	0.638746	+	2.66057i	0.0231242	+	0.0963191i
$764$	−42.9137	−	13.9435i	−1.55256	−	0.504459i
$765$	−2.93120	−	1.96926i	−0.105978	−	0.0711989i
$766$	4.59932	+	6.33043i	0.166180	+	0.228728i
$767$	−46.8914	+	28.7351i	−1.69315	+	1.03756i
$768$	0.307538	+	0.549149i	0.0110973	+	0.0198157i
$769$	−1.91514	+	1.91514i	−0.0690618	+	0.0690618i	−0.740794	−	0.671732i	$-0.765551\pi$
$769$	−1.91514	+	1.91514i	−0.0690618	+	0.0690618i	0.671732	+	0.740794i	$0.265551\pi$
$770$	−1.29622	+	2.51199i	−0.0467127	+	0.0905257i
$771$	3.17851	+	0.632245i	0.114471	+	0.0227697i
$772$	−25.7456	−	20.2962i	−0.926604	−	0.730476i
$773$	1.54201	−	6.42291i	0.0554621	−	0.231016i	−0.937754	−	0.347301i	$-0.887098\pi$
$773$	1.54201	−	6.42291i	0.0554621	−	0.231016i	0.993216	+	0.116284i	$0.0370984\pi$
$774$	−15.2671	+	24.9136i	−0.548763	+	0.895501i
$775$	−1.18387	−	4.19768i	−0.0425258	−	0.150785i
$776$	2.45614	−	4.38575i	0.0881703	−	0.157439i
$777$	−0.0446828	−	1.13725i	−0.00160299	−	0.0407987i
$778$	4.45926	+	28.1547i	0.159872	+	1.00939i
$779$	−23.5158	+	13.1695i	−0.842542	+	0.471846i
$780$	−0.833406	−	0.345208i	−0.0298407	−	0.0123604i
$781$	−14.6427	−	16.0046i	−0.523958	−	0.572691i
$782$	6.52154	−	8.22982i	0.233210	−	0.294298i
$783$	9.77940	−	3.17752i	0.349487	−	0.113555i
$784$	−6.61689	−	10.7978i	−0.236318	−	0.385635i
$785$	2.59948	−	2.81210i	0.0927794	−	0.100368i
$786$	−2.42628	+	1.23625i	−0.0865425	+	0.0440956i
$787$	−3.07794	+	2.42645i	−0.109717	+	0.0864938i	−0.672440	−	0.740152i	$-0.734754\pi$
$787$	−3.07794	+	2.42645i	−0.109717	+	0.0864938i	0.562723	+	0.826645i	$0.309754\pi$
$788$	25.1989	+	54.6607i	0.897675	+	1.94721i
$789$	2.92660	+	0.114986i	0.104190	+	0.00409362i
$790$	−1.78221	+	1.52215i	−0.0634082	+	0.0541557i
$791$	−5.39912	−	13.0346i	−0.191971	−	0.463458i
$792$	−12.0065	−	2.94786i	−0.426634	−	0.104748i
$793$	−11.2310	+	56.4619i	−0.398823	+	2.00502i
$794$	51.7973	+	14.6083i	1.83822	+	0.518431i
$795$	−0.157951	+	0.0250170i	−0.00560195	+	0.000887263i
$796$	−46.2562	−	42.7588i	−1.63951	−	1.51554i
$797$	17.5506	+	14.9896i	0.621672	+	0.530958i	0.903545	−	0.428493i	$-0.140955\pi$
$797$	17.5506	+	14.9896i	0.621672	+	0.530958i	−0.281872	+	0.959452i	$0.590955\pi$
$798$	0.578767	−	1.78126i	0.0204881	−	0.0630559i
$799$	−9.46988	+	39.0118i	−0.335020	+	1.38014i
$800$	−22.6122	+	31.1230i	−0.799461	+	1.10036i
$801$	1.66234	−	21.1220i	0.0587359	−	0.746310i
$802$	−7.32190	−	36.8097i	−0.258545	−	1.29979i
$803$	11.5959	−	14.5549i	0.409212	−	0.513631i
$804$	3.22112	−	4.82075i	0.113600	−	0.170015i
$805$	−0.469709	+	0.0555937i	−0.0165551	+	0.00195942i
$806$	−0.419083	+	10.6664i	−0.0147616	+	0.375707i
$807$	−2.03990	−	1.25005i	−0.0718079	−	0.0440039i
$808$	−0.295034	−	3.74876i	−0.0103793	−	0.131881i
$809$	−18.0738	+	5.09734i	−0.635441	+	0.179213i	−0.573944	−	0.818894i	$-0.694587\pi$
$809$	−18.0738	+	5.09734i	−0.635441	+	0.179213i	−0.0614969	+	0.998107i	$0.519587\pi$
$810$	−4.84478	+	2.23348i	−0.170228	+	0.0784764i
$811$	25.7955	−	9.51645i	0.905801	−	0.334168i	0.149784	−	0.988719i	$-0.452142\pi$
$811$	25.7955	−	9.51645i	0.905801	−	0.334168i	0.756018	+	0.654551i	$0.227142\pi$
$812$	−25.5497	−	13.0182i	−0.896620	−	0.456851i
$813$	−1.95102	+	0.388083i	−0.0684254	+	0.0136107i
$814$	0.939686	+	27.5212i	0.0329360	+	0.964619i
$815$		−	6.76419i		−	0.236939i
$816$	−1.98531	+	0.909185i	−0.0694998	+	0.0318279i
$817$	11.1214	+	8.08018i	0.389089	+	0.282690i
$818$	−31.3961	+	7.53755i	−1.09774	+	0.263544i
$819$	−2.67637	+	22.6126i	−0.0935200	+	0.790147i
$820$	3.08469	+	6.05404i	0.107722	+	0.211416i
$821$	11.6071	−	0.456043i	0.405089	−	0.0159160i	0.164100	−	0.986444i	$-0.447528\pi$
$821$	11.6071	−	0.456043i	0.405089	−	0.0159160i	0.240989	+	0.970528i	$0.422528\pi$
$822$	−0.551651	+	0.509941i	−0.0192410	+	0.0177862i
$823$	18.2799	−	23.1880i	0.637199	−	0.808283i	−0.354745	−	0.934963i	$-0.615432\pi$
$823$	18.2799	−	23.1880i	0.637199	−	0.808283i	0.991944	+	0.126680i	$0.0404322\pi$
$824$	−4.77849	+	1.97932i	−0.166467	+	0.0689527i
$825$	−0.663033	−	3.42519i	−0.0230838	−	0.119250i
$826$	−23.9343	+	15.9924i	−0.832781	+	0.556447i
$827$	−2.43679	−	20.5884i	−0.0847356	−	0.715927i	−0.968676	−	0.248328i	$-0.920119\pi$
$827$	−2.43679	−	20.5884i	−0.0847356	−	0.715927i	0.883941	−	0.467599i	$-0.154881\pi$
$828$	−3.14721	−	8.53089i	−0.109373	−	0.296469i
$829$	5.31259	−	33.5424i	0.184514	−	1.16498i	−0.705387	−	0.708822i	$-0.749227\pi$
$829$	5.31259	−	33.5424i	0.184514	−	1.16498i	0.889901	−	0.456153i	$-0.150773\pi$
$830$	−5.47631	−	0.648164i	−0.190086	−	0.0224981i
$831$	−1.13066	+	1.32383i	−0.0392222	+	0.0459232i
$832$	53.6812	−	39.0017i	1.86106	−	1.35214i
$833$	18.8214	−	9.53036i	0.652123	−	0.330207i
$834$	1.15303	+	3.54866i	0.0399262	+	0.122880i
$835$	2.34258	−	5.65548i	0.0810682	−	0.195716i
$836$	−8.02523	+	24.2739i	−0.277558	+	0.839532i
$837$	−0.799282	−	0.799282i	−0.0276272	−	0.0276272i
$838$	17.7286	−	62.8610i	0.612425	−	2.17150i
$839$	−29.4091	−	31.8146i	−1.01531	−	1.09836i	−0.995131	−	0.0985650i	$-0.968575\pi$
$839$	−29.4091	−	31.8146i	−1.01531	−	1.09836i	−0.0201841	−	0.999796i	$-0.506425\pi$
$840$	−0.100780	−	0.0371798i	−0.00347725	−	0.00128282i
$841$	−36.0251	+	2.83523i	−1.24224	+	0.0977667i
$842$	36.0068	−	2.83379i	1.24087	−	0.0976590i
$843$	4.79233	+	1.76798i	0.165056	+	0.0608926i
$844$	4.94662	+	5.35122i	0.170270	+	0.184197i
$845$	1.45944	−	5.17477i	0.0502062	−	0.178018i
$846$	43.5704	+	43.5704i	1.49798	+	1.49798i
$847$	14.7745	+	3.09703i	0.507658	+	0.106415i
$848$	2.44166	−	5.89469i	0.0838470	−	0.202424i
$849$	1.74824	+	5.38053i	0.0599995	+	0.184659i
$850$	−32.9459	−	28.2822i	−1.13003	−	0.970073i
$851$	−3.72776	+	2.70838i	−0.127786	+	0.0928419i
$852$	2.35320	−	2.75525i	0.0806194	−	0.0943932i
$853$	−4.99978	−	0.591763i	−0.171189	−	0.0202616i	0.0315053	−	0.999504i	$-0.489970\pi$
$853$	−4.99978	−	0.591763i	−0.171189	−	0.0202616i	−0.202695	+	0.979242i	$0.564970\pi$
$854$	−4.71369	+	29.7611i	−0.161299	+	1.01840i
$855$	0.882602	+	2.39240i	0.0301843	+	0.0818182i
$856$	−1.60066	−	13.5239i	−0.0547093	−	0.462237i
$857$	−18.6108	+	12.4353i	−0.635732	+	0.424782i	−0.831235	−	0.555921i	$-0.812366\pi$
$857$	−18.6108	+	12.4353i	−0.635732	+	0.424782i	0.195504	+	0.980703i	$0.437366\pi$
$858$	−1.04719	+	8.47433i	−0.0357505	+	0.289309i
$859$	−10.5800	+	4.38239i	−0.360986	+	0.149525i	−0.555802	−	0.831314i	$-0.687589\pi$
$859$	−10.5800	+	4.38239i	−0.360986	+	0.149525i	0.194816	+	0.980840i	$0.437589\pi$
$860$	2.14549	−	2.72154i	0.0731607	−	0.0928039i
$861$	−1.95199	+	1.80440i	−0.0665236	+	0.0614938i
$862$	64.2507	−	2.52442i	2.18839	−	0.0859820i
$863$	−13.6653	−	26.8197i	−0.465174	−	0.912955i	−0.997780	−	0.0665919i	$-0.978787\pi$
$863$	−13.6653	−	26.8197i	−0.465174	−	0.912955i	0.532607	−	0.846363i	$-0.321213\pi$
$864$	−1.17189	+	9.90123i	−0.0398684	+	0.336847i
$865$	−5.25293	+	1.26112i	−0.178605	+	0.0428792i
$866$	13.0655	+	9.49262i	0.443983	+	0.322572i
$867$	−1.24184	−	3.41909i	−0.0421751	−	0.116118i
$868$			3.15221i			0.106993i
$869$	10.3712	+	7.00720i	0.351820	+	0.237703i
$870$	−1.05192	+	0.209239i	−0.0356633	+	0.00709388i
$871$	52.3739	+	26.6858i	1.77462	+	0.904215i
$872$	2.36030	−	0.870759i	0.0799297	−	0.0294876i
$873$	−10.6878	+	4.92713i	−0.361726	+	0.166758i
$874$	−7.29793	+	2.05823i	−0.246856	+	0.0696206i
$875$	0.309529	+	3.93294i	0.0104640	+	0.132958i
$876$	2.65037	+	1.62415i	0.0895478	+	0.0548750i
$877$	−2.21604	+	56.4019i	−0.0748302	+	1.90456i	0.265283	+	0.964171i	$0.414535\pi$
$877$	−2.21604	+	56.4019i	−0.0748302	+	1.90456i	−0.340113	+	0.940385i	$0.610465\pi$
$878$	−49.1633	+	5.81886i	−1.65918	+	0.196377i
$879$	−0.0979815	+	0.146640i	−0.00330484	+	0.00494604i
$880$	−2.22844	−	0.835152i	−0.0751208	−	0.0281530i
$881$	−1.18638	−	5.96432i	−0.0399701	−	0.200943i	0.955641	−	0.294536i	$-0.0951649\pi$
$881$	−1.18638	−	5.96432i	−0.0399701	−	0.200943i	−0.995611	+	0.0935924i	$0.970165\pi$
$882$	2.54060	−	32.2814i	0.0855465	−	1.08697i
$883$	29.3664	−	40.4193i	0.988257	−	1.36022i	0.0559961	−	0.998431i	$-0.482167\pi$
$883$	29.3664	−	40.4193i	0.988257	−	1.36022i	0.932261	−	0.361788i	$-0.117833\pi$
$884$	31.1979	+	51.1994i	1.04930	+	1.72202i
$885$	−0.187704	+	0.577695i	−0.00630961	+	0.0194190i
$886$	−14.5255	−	12.4059i	−0.487993	−	0.416786i
$887$	−23.0066	−	21.2671i	−0.772487	−	0.714079i	0.191072	−	0.981576i	$-0.438804\pi$
$887$	−23.0066	−	21.2671i	−0.772487	−	0.714079i	−0.963559	+	0.267497i	$0.913804\pi$
$888$	−1.03358	+	0.163703i	−0.0346847	+	0.00549351i
$889$	−15.8032	−	4.45697i	−0.530023	−	0.149482i
$890$	−0.868954	+	4.36852i	−0.0291274	+	0.146433i
$891$	18.3911	+	21.7587i	0.616125	+	0.728943i
$892$	−4.12714	−	9.96381i	−0.138187	−	0.333613i
$893$	22.0437	−	18.8271i	0.737663	−	0.630024i
$894$	3.09571	+	0.121631i	0.103536	+	0.00406794i
$895$	−0.257160	−	0.557824i	−0.00859592	−	0.0186460i
$896$	10.4071	−	8.20427i	0.347675	−	0.274085i
$897$	−1.27305	+	0.648652i	−0.0425060	+	0.0216579i
$898$	59.9124	−	64.8128i	1.99930	−	2.16283i
$899$	3.74127	+	6.10519i	0.124778	+	0.203620i
$900$	−35.7595	+	11.6190i	−1.19198	+	0.387299i
$901$	9.45832	+	4.84930i	0.315102	+	0.161554i
$902$	47.4525	−	43.4145i	1.57999	−	1.44554i
$903$	1.25260	+	0.518843i	0.0416838	+	0.0172660i
$904$	−11.3182	+	6.33852i	−0.376439	+	0.210816i
$905$	−0.486748	−	3.07321i	−0.0161801	−	0.102157i
$906$	−0.347589	−	8.84673i	−0.0115479	−	0.293913i
$907$	5.52882	−	9.87242i	0.183581	−	0.327808i	−0.765172	−	0.643826i	$-0.777346\pi$
$907$	5.52882	−	9.87242i	0.183581	−	0.327808i	0.948753	+	0.316018i	$0.102346\pi$
$908$	15.9560	+	56.5755i	0.529517	+	1.87753i
$909$	−4.60008	+	7.50665i	−0.152575	+	0.248980i
$910$	1.11748	−	4.65464i	0.0370441	−	0.154300i
$911$	6.58616	+	5.19211i	0.218209	+	0.172022i	0.722195	−	0.691690i	$-0.243133\pi$
$911$	6.58616	+	5.19211i	0.218209	+	0.172022i	−0.503985	+	0.863712i	$0.668133\pi$
$912$	1.54652	+	0.307621i	0.0512103	+	0.0101864i
$913$	4.45739	+	29.1103i	0.147518	+	0.963410i
$914$	−46.1074	+	46.1074i	−1.52510	+	1.52510i
$915$	0.310684	+	0.554766i	0.0102709	+	0.0183400i
$916$	−23.1997	+	14.2168i	−0.766540	+	0.469737i
$917$	−4.79190	−	6.59548i	−0.158242	−	0.217802i
$918$	−11.0315	−	2.22319i	−0.364092	−	0.0733762i
$919$	−26.0164	−	8.45324i	−0.858201	−	0.278846i	−0.153324	−	0.988176i	$-0.548998\pi$
$919$	−26.0164	−	8.45324i	−0.858201	−	0.278846i	−0.704877	+	0.709329i	$0.748998\pi$
$920$	0.101524	+	0.422876i	0.00334713	+	0.0139418i
$921$	−0.00807555	+	0.0175172i	−0.000266098	+	0.000577212i
$922$	−16.3929	+	32.1729i	−0.539871	+	1.05956i
$923$	30.5441	+	20.4089i	1.00537	+	0.671767i
$924$	−0.210750	+	2.51268i	−0.00693318	+	0.0826610i
$925$	10.5855	+	15.8423i	0.348049	+	0.520892i
$926$	3.13525	+	3.67090i	0.103031	+	0.120633i
$927$	11.7749	+	2.82691i	0.386740	+	0.0928480i
$928$	21.8601	−	59.2543i	0.717592	−	1.94512i
$929$	30.1990	+	16.9123i	0.990798	+	0.554874i	0.897617	−	0.440776i	$-0.145297\pi$
$929$	30.1990	+	16.9123i	0.990798	+	0.554874i	0.0931807	+	0.995649i	$0.470297\pi$
$930$	0.0729917	+	0.0925896i	0.00239349	+	0.00303613i
$931$	−15.0468	−	2.38318i	−0.493140	−	0.0781056i
$932$	−20.2224	−	9.32268i	−0.662408	−	0.305374i
$933$	0.549460	+	0.0432434i	0.0179885	+	0.00141573i
$934$	36.2039			1.18463
$935$	1.68729	−	3.58751i	0.0551803	−	0.117324i
$936$	20.9364			0.684328
$937$	−29.2970	−	2.30573i	−0.957092	−	0.0753248i	−0.409717	−	0.912213i	$-0.634373\pi$
$937$	−29.2970	−	2.30573i	−0.957092	−	0.0753248i	−0.547375	+	0.836888i	$0.684373\pi$
$938$	27.9406	+	12.8808i	0.912293	+	0.420573i
$939$	4.85607	+	0.769126i	0.158472	+	0.0250995i
$940$	−4.52442	−	5.73920i	−0.147570	−	0.187192i
$941$	17.2155	+	9.64113i	0.561208	+	0.314292i	0.743266	−	0.668996i	$-0.233276\pi$
$941$	17.2155	+	9.64113i	0.561208	+	0.314292i	−0.182058	+	0.983288i	$0.558276\pi$
$942$	2.09571	−	5.68066i	0.0682818	−	0.185086i
$943$	10.4645	+	2.51231i	0.340772	+	0.0818122i
$944$	−15.7391	−	18.4281i	−0.512263	−	0.599783i
$945$	0.281616	+	0.421468i	0.00916096	+	0.0137103i
$946$	−30.2419	−	12.7091i	−0.983249	−	0.413208i
$947$	−6.82044	−	4.55728i	−0.221635	−	0.148092i	0.439796	−	0.898097i	$-0.355051\pi$
$947$	−6.82044	−	4.55728i	−0.221635	−	0.148092i	−0.661431	+	0.750006i	$0.730051\pi$
$948$	−0.949158	+	1.86283i	−0.0308272	+	0.0605018i
$949$	−13.1938	+	28.6195i	−0.428287	+	0.929027i
$950$	7.31959	+	30.4883i	0.237479	+	0.989170i
$951$	4.70889	+	1.53001i	0.152696	+	0.0496140i
$952$	3.95158	+	5.94631i	0.128071	+	0.192721i
$953$	−8.44915	−	11.6293i	−0.273695	−	0.376708i	0.649938	−	0.759987i	$-0.274795\pi$
$953$	−8.44915	−	11.6293i	−0.273695	−	0.376708i	−0.923633	+	0.383279i	$0.874795\pi$
$954$	13.9103	−	8.52422i	0.450361	−	0.275982i
$955$	−2.46884	−	4.40843i	−0.0798898	−	0.142654i
$956$	55.2416	−	55.2416i	1.78664	−	1.78664i
$957$	2.57404	+	5.11668i	0.0832071	+	0.165399i
$958$	27.9969	+	5.56893i	0.904539	+	0.179924i
$959$	−1.76625	−	1.39240i	−0.0570351	−	0.0449629i
$960$	0.171086	−	0.712625i	0.00552178	−	0.0229999i
$961$	−15.7862	+	25.7607i	−0.509232	+	0.830991i
$962$	−12.6581	−	44.8824i	−0.408115	−	1.44707i
$963$	−15.5792	+	27.8187i	−0.502034	+	0.896446i
$964$	2.19442	+	55.8518i	0.0706777	+	1.79887i
$965$	−0.574277	−	3.62584i	−0.0184866	−	0.116720i
$966$	−0.652494	+	0.365414i	−0.0209936	+	0.0117570i
$967$	21.1620	+	8.76560i	0.680525	+	0.281883i	0.696046	−	0.717997i	$-0.254941\pi$
$967$	21.1620	+	8.76560i	0.680525	+	0.281883i	−0.0155214	+	0.999880i	$0.504941\pi$
$968$	1.23116	−	13.8251i	0.0395709	−	0.444355i
$969$	−0.719385	+	2.52638i	−0.0231100	+	0.0811589i
$970$	2.35301	−	0.764538i	0.0755505	−	0.0245478i
$971$	25.1340	+	41.0149i	0.806588	+	1.31623i	0.945400	+	0.325913i	$0.105672\pi$
$971$	25.1340	+	41.0149i	0.806588	+	1.31623i	−0.138812	+	0.990319i	$0.544328\pi$
$972$	−9.94755	+	10.7612i	−0.319068	+	0.345166i
$973$	−9.95332	+	5.07147i	−0.319089	+	0.162584i
$974$	−14.4468	+	11.3890i	−0.462906	+	0.364926i
$975$	2.47348	+	5.36539i	0.0792148	+	0.171830i
$976$	−25.3486	−	0.995948i	−0.811388	−	0.0318795i
$977$	9.90783	−	8.46209i	0.316980	−	0.270726i	−0.476695	−	0.879069i	$-0.658165\pi$
$977$	9.90783	−	8.46209i	0.316980	−	0.270726i	0.793675	+	0.608343i	$0.208165\pi$
$978$	−4.09278	−	9.88084i	−0.130873	−	0.315954i
$979$	23.7225	−	1.74438i	0.758174	−	0.0557506i
$980$	−0.749253	+	3.76675i	−0.0239340	+	0.120324i
$981$	−5.66901	−	1.59883i	−0.180998	−	0.0510466i
$982$	2.36237	−	0.374163i	0.0753864	−	0.0119400i
$983$	−28.2256	−	26.0915i	−0.900258	−	0.832190i	0.0861877	−	0.996279i	$-0.472532\pi$
$983$	−28.2256	−	26.0915i	−0.900258	−	0.832190i	−0.986446	+	0.164089i	$0.947532\pi$
$984$	1.85852	+	1.58733i	0.0592476	+	0.0506022i
$985$	−2.08274	+	6.41000i	−0.0663615	+	0.204240i
$986$	64.6614	+	30.0070i	2.05924	+	0.955617i
$987$	1.68055	−	2.31307i	0.0534924	−	0.0736260i
$988$	3.39690	−	43.1617i	0.108070	−	1.37316i
$989$	−1.07085	−	5.38354i	−0.0340511	−	0.171187i
$990$	−3.35463	−	5.07684i	−0.106617	−	0.161353i
$991$	19.6262	−	29.3726i	0.623446	−	0.933053i	−0.376532	−	0.926404i	$-0.622884\pi$
$991$	19.6262	−	29.3726i	0.623446	−	0.933053i	0.999978	−	0.00664903i	$-0.00211647\pi$
$992$	−6.89473	+	0.816045i	−0.218908	+	0.0259094i
$993$	0.0130195	−	0.331369i	0.000413162	−	0.0105157i
$994$	16.3943	+	10.0465i	0.519997	+	0.318655i
$995$	−0.553423	−	7.03190i	−0.0175447	−	0.222926i
$996$	−4.73443	+	1.33525i	−0.150016	+	0.0423090i
$997$	31.3855	−	14.4689i	0.993990	−	0.458236i	0.146594	−	0.989197i	$-0.453169\pi$
$997$	31.3855	−	14.4689i	0.993990	−	0.458236i	0.847396	+	0.530961i	$0.178169\pi$
$998$	14.8717	−	5.48648i	0.470757	−	0.173671i
$999$	4.39986	+	2.24184i	0.139206	+	0.0709288i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.t.a.6.15	✓	512
11.2	odd	10	inner	187.2.t.a.57.15	yes	512
17.3	odd	16	inner	187.2.t.a.105.15	yes	512
187.156	even	80	inner	187.2.t.a.156.15	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.t.a.6.15	✓	512	1.1	even	1	trivial
187.2.t.a.57.15	yes	512	11.2	odd	10	inner
187.2.t.a.105.15	yes	512	17.3	odd	16	inner
187.2.t.a.156.15	yes	512	187.156	even	80	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.t (of order \(80\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(2.13560 + 0.168075i) q^{2} +(0.194323 + 0.0895840i) q^{3} +(2.55715 + 0.405012i) q^{4} +(0.179483 + 0.227673i) q^{5} +(0.399938 + 0.223976i) q^{6} +(-0.474986 + 1.28751i) q^{7} +(1.22694 + 0.294561i) q^{8} +(-1.91861 - 2.24640i) q^{9} +O(q^{10})\)	\(q+(2.13560 + 0.168075i) q^{2} +(0.194323 + 0.0895840i) q^{3} +(2.55715 + 0.405012i) q^{4} +(0.179483 + 0.227673i) q^{5} +(0.399938 + 0.223976i) q^{6} +(-0.474986 + 1.28751i) q^{7} +(1.22694 + 0.294561i) q^{8} +(-1.91861 - 2.24640i) q^{9} +(0.345037 + 0.516384i) q^{10} +(2.16691 - 2.51088i) q^{11} +(0.460629 + 0.307782i) q^{12} +(-2.54987 + 5.00439i) q^{13} +(-1.23078 + 2.66976i) q^{14} +(0.0144817 + 0.0603208i) q^{15} +(-2.35388 - 0.764822i) q^{16} +(1.58743 - 3.80527i) q^{17} +(-3.71981 - 5.11988i) q^{18} +(-2.53863 + 1.55567i) q^{19} +(0.366753 + 0.654885i) q^{20} +(-0.207641 + 0.207641i) q^{21} +(5.04966 - 4.99802i) q^{22} +(1.16600 + 0.231932i) q^{23} +(0.212033 + 0.167154i) q^{24} +(1.14761 - 4.78012i) q^{25} +(-6.28660 + 10.2588i) q^{26} +(-0.345834 - 1.22624i) q^{27} +(-1.73606 + 3.09997i) q^{28} +(0.316855 + 8.06449i) q^{29} +(0.0207887 + 0.131255i) q^{30} +(0.774079 - 0.433505i) q^{31} +(-7.22989 - 2.99472i) q^{32} +(0.646014 - 0.293800i) q^{33} +(4.02968 - 7.85971i) q^{34} +(-0.378382 + 0.122944i) q^{35} +(-3.99634 - 6.52143i) q^{36} +(-2.63092 + 2.84611i) q^{37} +(-5.68296 + 2.89561i) q^{38} +(-0.943810 + 0.744040i) q^{39} +(0.153150 + 0.332208i) q^{40} +(9.04541 + 0.355395i) q^{41} +(-0.478336 + 0.408537i) q^{42} +(-1.76689 - 4.26564i) q^{43} +(6.55803 - 5.54306i) q^{44} +(0.167087 - 0.840005i) q^{45} +(2.45113 + 0.691290i) q^{46} +(-9.61666 + 1.52313i) q^{47} +(-0.388896 - 0.359492i) q^{48} +(3.89078 + 3.32304i) q^{49} +(3.25424 - 10.0155i) q^{50} +(0.649365 - 0.597241i) q^{51} +(-8.54721 + 11.7642i) q^{52} +(-0.202261 + 2.56996i) q^{53} +(-0.532463 - 2.67687i) q^{54} +(0.960581 + 0.0426866i) q^{55} +(-0.962027 + 1.43978i) q^{56} +(-0.632677 + 0.0748823i) q^{57} +(-0.678766 + 17.2758i) q^{58} +(8.34877 + 5.11613i) q^{59} +(0.0126013 + 0.160114i) q^{60} +(9.86487 - 2.78218i) q^{61} +(1.72598 - 0.795688i) q^{62} +(3.80357 - 1.40321i) q^{63} +(-10.5263 - 5.36340i) q^{64} +(-1.59702 + 0.317667i) q^{65} +(1.42901 - 0.518860i) q^{66} -10.4656i q^{67} +(5.60047 - 9.08769i) q^{68} +(0.205803 + 0.149525i) q^{69} +(-0.828735 + 0.198962i) q^{70} +(0.768752 - 6.49515i) q^{71} +(-1.69231 - 3.32134i) q^{72} +(5.60663 - 0.220285i) q^{73} +(-6.09694 + 5.63595i) q^{74} +(0.651228 - 0.826079i) q^{75} +(-7.12171 + 2.94991i) q^{76} +(2.20352 + 3.98254i) q^{77} +(-2.14065 + 1.43034i) q^{78} +(0.443571 + 3.74771i) q^{79} +(-0.248352 - 0.673186i) q^{80} +(-1.34377 + 8.48426i) q^{81} +(19.2576 + 2.27929i) q^{82} +(-5.76670 + 6.75194i) q^{83} +(-0.615064 + 0.446870i) q^{84} +(1.15127 - 0.321565i) q^{85} +(-3.05641 - 9.40665i) q^{86} +(-0.660878 + 1.59550i) q^{87} +(3.39826 - 2.44240i) q^{88} +(5.07130 + 5.07130i) q^{89} +(0.498015 - 1.76583i) q^{90} +(-5.23204 - 5.65999i) q^{91} +(2.88770 + 1.06533i) q^{92} +(0.189256 - 0.0148948i) q^{93} +(-20.7933 + 1.63647i) q^{94} +(-0.809825 - 0.298760i) q^{95} +(-1.13665 - 1.22962i) q^{96} +(1.08135 - 3.83417i) q^{97} +(7.75061 + 7.75061i) q^{98} +(-9.79789 - 0.0503532i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q - 40 q^{2} - 24 q^{3} - 24 q^{4} - 24 q^{5} - 40 q^{6} - 40 q^{7} - 40 q^{8} - 24 q^{9}+O(q^{10}) \) 512 * q - 40 * q^2 - 24 * q^3 - 24 * q^4 - 24 * q^5 - 40 * q^6 - 40 * q^7 - 40 * q^8 - 24 * q^9	\( 512 q - 40 q^{2} - 24 q^{3} - 24 q^{4} - 24 q^{5} - 40 q^{6} - 40 q^{7} - 40 q^{8} - 24 q^{9} - 40 q^{11} - 16 q^{12} - 56 q^{14} - 24 q^{15} - 40 q^{17} - 80 q^{18} - 40 q^{19} - 24 q^{20} - 48 q^{22} - 48 q^{23} + 80 q^{24} - 40 q^{25} - 56 q^{26} + 48 q^{27} - 40 q^{28} - 40 q^{29} - 40 q^{30} + 40 q^{31} - 64 q^{34} - 80 q^{35} - 56 q^{36} - 56 q^{37} + 80 q^{38} - 40 q^{39} - 40 q^{40} + 80 q^{41} + 72 q^{42} + 32 q^{44} - 64 q^{45} - 40 q^{46} - 24 q^{47} - 72 q^{48} - 88 q^{49} - 40 q^{51} + 240 q^{52} - 24 q^{53} + 128 q^{55} - 64 q^{56} - 40 q^{57} + 88 q^{58} - 88 q^{59} - 152 q^{60} - 40 q^{61} - 40 q^{62} + 80 q^{63} - 88 q^{64} + 408 q^{66} - 40 q^{68} + 192 q^{69} - 168 q^{70} - 24 q^{71} - 40 q^{72} - 40 q^{73} - 40 q^{74} - 88 q^{75} + 192 q^{77} - 64 q^{78} - 40 q^{79} + 248 q^{80} - 40 q^{81} - 24 q^{82} - 40 q^{85} - 112 q^{86} + 128 q^{88} - 64 q^{89} - 40 q^{90} + 56 q^{91} + 136 q^{92} - 88 q^{93} + 440 q^{94} - 40 q^{95} - 40 q^{96} - 88 q^{97} + 72 q^{99}+O(q^{100}) \) 512 * q - 40 * q^2 - 24 * q^3 - 24 * q^4 - 24 * q^5 - 40 * q^6 - 40 * q^7 - 40 * q^8 - 24 * q^9 - 40 * q^11 - 16 * q^12 - 56 * q^14 - 24 * q^15 - 40 * q^17 - 80 * q^18 - 40 * q^19 - 24 * q^20 - 48 * q^22 - 48 * q^23 + 80 * q^24 - 40 * q^25 - 56 * q^26 + 48 * q^27 - 40 * q^28 - 40 * q^29 - 40 * q^30 + 40 * q^31 - 64 * q^34 - 80 * q^35 - 56 * q^36 - 56 * q^37 + 80 * q^38 - 40 * q^39 - 40 * q^40 + 80 * q^41 + 72 * q^42 + 32 * q^44 - 64 * q^45 - 40 * q^46 - 24 * q^47 - 72 * q^48 - 88 * q^49 - 40 * q^51 + 240 * q^52 - 24 * q^53 + 128 * q^55 - 64 * q^56 - 40 * q^57 + 88 * q^58 - 88 * q^59 - 152 * q^60 - 40 * q^61 - 40 * q^62 + 80 * q^63 - 88 * q^64 + 408 * q^66 - 40 * q^68 + 192 * q^69 - 168 * q^70 - 24 * q^71 - 40 * q^72 - 40 * q^73 - 40 * q^74 - 88 * q^75 + 192 * q^77 - 64 * q^78 - 40 * q^79 + 248 * q^80 - 40 * q^81 - 24 * q^82 - 40 * q^85 - 112 * q^86 + 128 * q^88 - 64 * q^89 - 40 * q^90 + 56 * q^91 + 136 * q^92 - 88 * q^93 + 440 * q^94 - 40 * q^95 - 40 * q^96 - 88 * q^97 + 72 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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