LMFDB - Embedded newform 135.2.q.a.32.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,2,Mod(2,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([2, 9]))

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

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

chi := DirichletCharacter("135.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.q (of order $36$, degree $12$, 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:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			32.12
Character	$\chi$	$=$	135.32
Dual form			135.2.q.a.38.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.119567 - 1.36666i) q^{2} +(-1.50279 + 0.861169i) q^{3} +(0.116159 + 0.0204819i) q^{4} +(1.52669 + 1.63378i) q^{5} +(0.997239 + 2.15677i) q^{6} +(1.87969 - 2.68447i) q^{7} +(0.752017 - 2.80657i) q^{8} +(1.51678 - 2.58832i) q^{9} +O(q^{10})$	\(q+(0.119567 - 1.36666i) q^{2} +(-1.50279 + 0.861169i) q^{3} +(0.116159 + 0.0204819i) q^{4} +(1.52669 + 1.63378i) q^{5} +(0.997239 + 2.15677i) q^{6} +(1.87969 - 2.68447i) q^{7} +(0.752017 - 2.80657i) q^{8} +(1.51678 - 2.58832i) q^{9} +(2.41535 - 1.89111i) q^{10} +(-1.85785 + 5.10439i) q^{11} +(-0.192201 + 0.0692523i) q^{12} +(2.45985 - 0.215209i) q^{13} +(-3.44400 - 2.88986i) q^{14} +(-3.70125 - 1.14049i) q^{15} +(-3.52402 - 1.28264i) q^{16} +(-0.925208 - 3.45292i) q^{17} +(-3.35599 - 2.38239i) q^{18} +(-0.417150 + 0.240842i) q^{19} +(0.143875 + 0.221047i) q^{20} +(-0.512998 + 5.65293i) q^{21} +(6.75381 + 3.14935i) q^{22} +(-5.73060 + 4.01261i) q^{23} +(1.28680 + 4.86530i) q^{24} +(-0.338453 + 4.98853i) q^{25} -3.38750i q^{26} +(-0.0504220 + 5.19591i) q^{27} +(0.273325 - 0.273325i) q^{28} +(-0.0993465 + 0.0833616i) q^{29} +(-2.00121 + 4.92198i) q^{30} +(0.509526 - 2.88966i) q^{31} +(0.281608 - 0.603911i) q^{32} +(-1.60378 - 9.27076i) q^{33} +(-4.82959 + 0.851587i) q^{34} +(7.25552 - 1.02736i) q^{35} +(0.229201 - 0.269590i) q^{36} +(-6.26774 + 1.67943i) q^{37} +(0.279271 + 0.598898i) q^{38} +(-3.51131 + 2.44176i) q^{39} +(5.73340 - 3.05612i) q^{40} +(0.215101 - 0.256347i) q^{41} +(7.66428 + 1.37700i) q^{42} +(-5.27405 + 2.45933i) q^{43} +(-0.320353 + 0.554867i) q^{44} +(6.54438 - 1.47348i) q^{45} +(4.79867 + 8.31155i) q^{46} +(-9.71652 - 6.80358i) q^{47} +(6.40045 - 1.10724i) q^{48} +(-1.27902 - 3.51408i) q^{49} +(6.77715 + 1.05901i) q^{50} +(4.36395 + 4.39227i) q^{51} +(0.290141 + 0.0253840i) q^{52} +(0.167838 + 0.167838i) q^{53} +(7.09500 + 0.690169i) q^{54} +(-11.1758 + 4.75750i) q^{55} +(-6.12058 - 7.29423i) q^{56} +(0.419485 - 0.721172i) q^{57} +(0.102048 + 0.145740i) q^{58} +(3.62976 - 1.32113i) q^{59} +(-0.406574 - 0.208287i) q^{60} +(-0.855508 - 4.85182i) q^{61} +(-3.88826 - 1.04186i) q^{62} +(-4.09720 - 8.93697i) q^{63} +(-7.28718 - 4.20726i) q^{64} +(4.10702 + 3.69029i) q^{65} +(-12.8617 + 1.08334i) q^{66} +(0.372661 + 4.25953i) q^{67} +(-0.0367485 - 0.420038i) q^{68} +(5.15637 - 10.9651i) q^{69} +(-0.536526 - 10.0386i) q^{70} +(7.10207 + 4.10038i) q^{71} +(-6.12364 - 6.20339i) q^{72} +(13.1228 + 3.51625i) q^{73} +(1.54580 + 8.76665i) q^{74} +(-3.78734 - 7.78820i) q^{75} +(-0.0533886 + 0.0194318i) q^{76} +(10.2104 + 14.5820i) q^{77} +(2.91721 + 5.09072i) q^{78} +(-6.44655 - 7.68270i) q^{79} +(-3.28453 - 7.71565i) q^{80} +(-4.39878 - 7.85180i) q^{81} +(-0.324619 - 0.324619i) q^{82} +(-0.0147020 - 0.00128626i) q^{83} +(-0.175372 + 0.646131i) q^{84} +(4.22880 - 6.78312i) q^{85} +(2.73046 + 7.50188i) q^{86} +(0.0775088 - 0.210829i) q^{87} +(12.9287 + 9.05275i) q^{88} +(2.55837 + 4.43123i) q^{89} +(-1.23125 - 9.12010i) q^{90} +(4.04602 - 7.00791i) q^{91} +(-0.747846 + 0.348726i) q^{92} +(1.72278 + 4.78135i) q^{93} +(-10.4599 + 12.4657i) q^{94} +(-1.03034 - 0.313840i) q^{95} +(0.0968703 + 1.15007i) q^{96} +(1.75805 + 3.77015i) q^{97} +(-4.95547 + 1.32781i) q^{98} +(10.3938 + 12.5509i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.119567	−	1.36666i	0.0845467	−	0.966373i	−0.828895	−	0.559404i	$-0.811030\pi$
$2$	0.119567	−	1.36666i	0.0845467	−	0.966373i	0.913442	−	0.406969i	$-0.133414\pi$
$3$	−1.50279	+	0.861169i	−0.867638	+	0.497196i
$3$	−1.50279	+	0.861169i	−0.867638	+	0.497196i
$4$	0.116159	+	0.0204819i	0.0580794	+	0.0102410i
$5$	1.52669	+	1.63378i	0.682755	+	0.730647i
$5$	1.52669	+	1.63378i	0.682755	+	0.730647i
$6$	0.997239	+	2.15677i	0.407121	+	0.880498i
$7$	1.87969	−	2.68447i	0.710455	−	1.01463i	−0.287921	−	0.957654i	$-0.592964\pi$
$7$	1.87969	−	2.68447i	0.710455	−	1.01463i	0.998375	−	0.0569801i	$-0.0181472\pi$
$8$	0.752017	−	2.80657i	0.265878	−	0.992271i
$9$	1.51678	−	2.58832i	0.505592	−	0.862773i
$10$	2.41535	−	1.89111i	0.763802	−	0.598022i
$11$	−1.85785	+	5.10439i	−0.560161	+	1.53903i	0.259241	+	0.965813i	$0.416527\pi$
$11$	−1.85785	+	5.10439i	−0.560161	+	1.53903i	−0.819403	+	0.573218i	$0.805695\pi$
$12$	−0.192201	+	0.0692523i	−0.0554837	+	0.0199914i
$13$	2.45985	−	0.215209i	0.682239	−	0.0596882i	0.259233	−	0.965815i	$-0.416530\pi$
$13$	2.45985	−	0.215209i	0.682239	−	0.0596882i	0.423006	+	0.906127i	$0.360975\pi$
$14$	−3.44400	−	2.88986i	−0.920449	−	0.772348i
$15$	−3.70125	−	1.14049i	−0.955659	−	0.294474i
$16$	−3.52402	−	1.28264i	−0.881006	−	0.320660i
$17$	−0.925208	−	3.45292i	−0.224396	−	0.837457i	−0.982646	−	0.185493i	$-0.940612\pi$
$17$	−0.925208	−	3.45292i	−0.224396	−	0.837457i	0.758250	−	0.651964i	$-0.226055\pi$
$18$	−3.35599	−	2.38239i	−0.791014	−	0.561535i
$19$	−0.417150	+	0.240842i	−0.0957007	+	0.0552529i	−0.547087	−	0.837076i	$-0.684263\pi$
$19$	−0.417150	+	0.240842i	−0.0957007	+	0.0552529i	0.451386	+	0.892329i	$0.350930\pi$
$20$	0.143875	+	0.221047i	0.0321715	+	0.0494276i
$21$	−0.512998	+	5.65293i	−0.111945	+	1.23357i
$22$	6.75381	+	3.14935i	1.43992	+	0.671445i
$23$	−5.73060	+	4.01261i	−1.19491	+	0.836687i	−0.989858	−	0.142063i	$-0.954626\pi$
$23$	−5.73060	+	4.01261i	−1.19491	+	0.836687i	−0.205055	+	0.978750i	$0.565737\pi$
$24$	1.28680	+	4.86530i	0.262667	+	0.993125i
$25$	−0.338453	+	4.98853i	−0.0676907	+	0.997706i
$26$		−	3.38750i		−	0.664344i
$27$	−0.0504220	+	5.19591i	−0.00970372	+	0.999953i
$28$	0.273325	−	0.273325i	0.0516536	−	0.0516536i
$29$	−0.0993465	+	0.0833616i	−0.0184482	+	0.0154799i	−0.651965	−	0.758249i	$-0.726055\pi$
$29$	−0.0993465	+	0.0833616i	−0.0184482	+	0.0154799i	0.633517	+	0.773729i	$0.281611\pi$
$30$	−2.00121	+	4.92198i	−0.365370	+	0.898627i
$31$	0.509526	−	2.88966i	0.0915135	−	0.518999i	−0.904247	−	0.427011i	$-0.859567\pi$
$31$	0.509526	−	2.88966i	0.0915135	−	0.518999i	0.995760	−	0.0919882i	$-0.0293222\pi$
$32$	0.281608	−	0.603911i	0.0497818	−	0.106757i
$33$	−1.60378	−	9.27076i	−0.279183	−	1.61383i
$34$	−4.82959	+	0.851587i	−0.828268	+	0.146046i
$35$	7.25552	−	1.02736i	1.22641	−	0.173655i
$36$	0.229201	−	0.269590i	0.0382001	−	0.0449316i
$37$	−6.26774	+	1.67943i	−1.03041	+	0.276097i	−0.734134	−	0.679005i	$-0.762411\pi$
$37$	−6.26774	+	1.67943i	−1.03041	+	0.276097i	−0.296276	+	0.955102i	$0.595745\pi$
$38$	0.279271	+	0.598898i	0.0453037	+	0.0971540i
$39$	−3.51131	+	2.44176i	−0.562260	+	0.390994i
$40$	5.73340	−	3.05612i	0.906529	−	0.483215i
$41$	0.215101	−	0.256347i	0.0335931	−	0.0400346i	−0.748986	−	0.662585i	$-0.769459\pi$
$41$	0.215101	−	0.256347i	0.0335931	−	0.0400346i	0.782579	+	0.622551i	$0.213904\pi$
$42$	7.66428	+	1.37700i	1.18262	+	0.212475i
$43$	−5.27405	+	2.45933i	−0.804285	+	0.375044i	−0.780880	−	0.624682i	$-0.785229\pi$
$43$	−5.27405	+	2.45933i	−0.804285	+	0.375044i	−0.0234058	+	0.999726i	$0.507451\pi$
$44$	−0.320353	+	0.554867i	−0.0482950	+	0.0836494i
$45$	6.54438	−	1.47348i	0.975578	−	0.219653i
$46$	4.79867	+	8.31155i	0.707526	+	1.22547i
$47$	−9.71652	−	6.80358i	−1.41730	−	0.992405i	−0.996354	−	0.0853195i	$-0.972809\pi$
$47$	−9.71652	−	6.80358i	−1.41730	−	0.992405i	−0.420947	−	0.907085i	$-0.638302\pi$
$48$	6.40045	−	1.10724i	0.923825	−	0.159816i
$49$	−1.27902	−	3.51408i	−0.182717	−	0.502011i
$50$	6.77715	+	1.05901i	0.958433	+	0.149767i
$51$	4.36395	+	4.39227i	0.611075	+	0.615041i
$52$	0.290141	+	0.0253840i	0.0402353	+	0.00352013i
$53$	0.167838	+	0.167838i	0.0230543	+	0.0230543i	0.718540	−	0.695486i	$-0.244811\pi$
$53$	0.167838	+	0.167838i	0.0230543	+	0.0230543i	−0.695486	+	0.718540i	$0.744811\pi$
$54$	7.09500	+	0.690169i	0.965507	+	0.0939201i
$55$	−11.1758	+	4.75750i	−1.50694	+	0.641501i
$56$	−6.12058	−	7.29423i	−0.817898	−	0.974732i
$57$	0.419485	−	0.721172i	0.0555621	−	0.0955215i
$58$	0.102048	+	0.145740i	0.0133996	+	0.0191366i
$59$	3.62976	−	1.32113i	0.472555	−	0.171996i	−0.0947544	−	0.995501i	$-0.530207\pi$
$59$	3.62976	−	1.32113i	0.472555	−	0.171996i	0.567309	+	0.823505i	$0.307984\pi$
$60$	−0.406574	−	0.208287i	−0.0524884	−	0.0268898i
$61$	−0.855508	−	4.85182i	−0.109537	−	0.621212i	−0.989311	−	0.145821i	$-0.953418\pi$
$61$	−0.855508	−	4.85182i	−0.109537	−	0.621212i	0.879774	−	0.475391i	$-0.157694\pi$
$62$	−3.88826	−	1.04186i	−0.493809	−	0.132316i
$63$	−4.09720	−	8.93697i	−0.516199	−	1.12595i
$64$	−7.28718	−	4.20726i	−0.910898	−	0.525907i
$65$	4.10702	+	3.69029i	0.509413	+	0.457724i
$66$	−12.8617	+	1.08334i	−1.58317	+	0.133350i
$67$	0.372661	+	4.25953i	0.0455277	+	0.520385i	0.984379	+	0.176062i	$0.0563359\pi$
$67$	0.372661	+	4.25953i	0.0455277	+	0.520385i	−0.938851	+	0.344323i	$0.888109\pi$
$68$	−0.0367485	−	0.420038i	−0.00445641	−	0.0509370i
$69$	5.15637	−	10.9651i	0.620755	−	1.32005i
$70$	−0.536526	−	10.0386i	−0.0641271	−	1.19985i
$71$	7.10207	+	4.10038i	0.842861	+	0.486626i	0.858236	−	0.513256i	$-0.171561\pi$
$71$	7.10207	+	4.10038i	0.842861	+	0.486626i	−0.0153747	+	0.999882i	$0.504894\pi$
$72$	−6.12364	−	6.20339i	−0.721678	−	0.731076i
$73$	13.1228	+	3.51625i	1.53591	+	0.411546i	0.924942	−	0.380108i	$-0.124113\pi$
$73$	13.1228	+	3.51625i	1.53591	+	0.411546i	0.610969	+	0.791654i	$0.290780\pi$
$74$	1.54580	+	8.76665i	0.179695	+	1.01910i
$75$	−3.78734	−	7.78820i	−0.437325	−	0.899304i
$76$	−0.0533886	+	0.0194318i	−0.00612409	+	0.00222899i
$77$	10.2104	+	14.5820i	1.16358	+	1.66177i
$78$	2.91721	+	5.09072i	0.330309	+	0.576410i
$79$	−6.44655	−	7.68270i	−0.725293	−	0.864371i	0.269840	−	0.962905i	$-0.413029\pi$
$79$	−6.44655	−	7.68270i	−0.725293	−	0.864371i	−0.995134	+	0.0985341i	$0.968585\pi$
$80$	−3.28453	−	7.71565i	−0.367222	−	0.862636i
$81$	−4.39878	−	7.85180i	−0.488753	−	0.872422i
$82$	−0.324619	−	0.324619i	−0.0358482	−	0.0358482i
$83$	−0.0147020	−	0.00128626i	−0.00161375	−	0.000141185i	0.0863488	−	0.996265i	$-0.472480\pi$
$83$	−0.0147020	−	0.00128626i	−0.00161375	−	0.000141185i	−0.0879626	+	0.996124i	$0.528036\pi$
$84$	−0.175372	+	0.646131i	−0.0191347	+	0.0704987i
$85$	4.22880	−	6.78312i	0.458678	−	0.735732i
$86$	2.73046	+	7.50188i	0.294433	+	0.808948i
$87$	0.0775088	−	0.210829i	0.00830982	−	0.0226033i
$88$	12.9287	+	9.05275i	1.37820	+	0.965026i
$89$	2.55837	+	4.43123i	0.271187	+	0.469709i	0.969166	−	0.246409i	$-0.0792506\pi$
$89$	2.55837	+	4.43123i	0.271187	+	0.469709i	−0.697979	+	0.716118i	$0.745917\pi$
$90$	−1.23125	−	9.12010i	−0.129785	−	0.961343i
$91$	4.04602	−	7.00791i	0.424138	−	0.734629i
$92$	−0.747846	+	0.348726i	−0.0779683	+	0.0363572i
$93$	1.72278	+	4.78135i	0.178644	+	0.495803i
$94$	−10.4599	+	12.4657i	−1.07886	+	1.28574i
$95$	−1.03034	−	0.313840i	−0.105711	−	0.0321993i
$96$	0.0968703	+	1.15007i	0.00988679	+	0.117378i
$97$	1.75805	+	3.77015i	0.178503	+	0.382800i	0.975118	−	0.221686i	$-0.0711561\pi$
$97$	1.75805	+	3.77015i	0.178503	+	0.382800i	−0.796615	+	0.604487i	$0.793378\pi$
$98$	−4.95547	+	1.32781i	−0.500578	+	0.134129i
$99$	10.3938	+	12.5509i	1.04462	+	1.26141i
$100$	−0.141489	+	0.572530i	−0.0141489	+	0.0572530i
$101$	7.79700	−	1.37482i	0.775831	−	0.136800i	0.228306	−	0.973589i	$-0.426681\pi$
$101$	7.79700	−	1.37482i	0.775831	−	0.136800i	0.547525	+	0.836789i	$0.315570\pi$
$102$	6.52451	−	5.43885i	0.646023	−	0.538526i
$103$	2.27837	−	4.88597i	0.224494	−	0.481429i	−0.761509	−	0.648154i	$-0.775541\pi$
$103$	2.27837	−	4.88597i	0.224494	−	0.481429i	0.986004	+	0.166725i	$0.0533191\pi$
$104$	1.24585	−	7.06556i	0.122166	−	0.692836i
$105$	−10.0188	+	7.79213i	−0.977736	+	0.760434i
$106$	0.249444	−	0.209309i	0.0242282	−	0.0203299i
$107$	6.45665	−	6.45665i	0.624188	−	0.624188i	−0.322412	−	0.946600i	$-0.604494\pi$
$107$	6.45665	−	6.45665i	0.624188	−	0.624188i	0.946600	+	0.322412i	$0.104494\pi$
$108$	−0.112279	+	0.602518i	−0.0108041	+	0.0579773i
$109$			10.2697i			0.983654i	0.870693	+	0.491827i	$0.163671\pi$
$109$			10.2697i			0.983654i	−0.870693	+	0.491827i	$0.836329\pi$
$110$	5.16562	+	15.8423i	0.492522	+	1.51050i
$111$	7.97284	−	7.92142i	0.756748	−	0.751868i
$112$	−10.0673	+	7.04917i	−0.951267	+	0.666084i
$113$	9.42875	+	4.39670i	0.886982	+	0.413607i	0.812054	−	0.583582i	$-0.198349\pi$
$113$	9.42875	+	4.39670i	0.886982	+	0.413607i	0.0749283	+	0.997189i	$0.476127\pi$
$114$	−0.935438	−	0.659520i	−0.0876118	−	0.0617697i
$115$	−15.3045	−	3.23652i	−1.42716	−	0.301807i
$116$	−0.0132474	+	0.00764838i	−0.00122999	+	0.000710134i
$117$	3.17401	−	6.69329i	0.293437	−	0.618795i
$118$	−1.37153	−	5.11861i	−0.126259	−	0.471206i
$119$	−11.0084	−	4.00672i	−1.00914	−	0.367295i
$120$	−5.98427	+	9.53014i	−0.546287	+	0.869979i
$121$	−14.1767	−	11.8957i	−1.28879	−	1.08142i
$122$	−6.73307	+	0.589068i	−0.609584	+	0.0533317i
$123$	−0.102494	+	0.570474i	−0.00924155	+	0.0514379i
$124$	0.118372	−	0.325224i	0.0106301	−	0.0292060i
$125$	−8.66686	+	7.06297i	−0.775187	+	0.631731i
$126$	−12.7037	+	4.53090i	−1.13173	+	0.403645i
$127$	−3.39311	+	12.6633i	−0.301090	+	1.12368i	0.635169	+	0.772373i	$0.280931\pi$
$127$	−3.39311	+	12.6633i	−0.301090	+	1.12368i	−0.936259	+	0.351311i	$0.885736\pi$
$128$	−5.85679	+	8.36436i	−0.517672	+	0.739312i
$129$	5.80791	−	8.23772i	0.511358	−	0.725290i
$130$	5.53442	−	5.17166i	0.485401	−	0.453584i
$131$	−3.19816	−	0.563922i	−0.279425	−	0.0492701i	0.0321796	−	0.999482i	$-0.489755\pi$
$131$	−3.19816	−	0.563922i	−0.279425	−	0.0492701i	−0.311604	+	0.950212i	$0.600866\pi$
$132$	0.00358957	−	1.10973i	0.000312432	−	0.0965895i
$133$	−0.137579	+	1.57253i	−0.0119296	+	0.136356i
$134$	5.86588			0.506735
$135$	−8.56593	+	7.85015i	−0.737238	+	0.675633i
$136$	−10.3866			−0.890646
$137$	0.410087	−	4.68732i	0.0350361	−	0.400465i	−0.958346	−	0.285609i	$-0.907804\pi$
$137$	0.410087	−	4.68732i	0.0350361	−	0.400465i	0.993382	−	0.114855i	$-0.0366404\pi$
$138$	−14.3691	−	8.35807i	−1.22318	−	0.711486i
$139$	11.3538	+	2.00197i	0.963013	+	0.169805i	0.632983	−	0.774165i	$-0.281830\pi$
$139$	11.3538	+	2.00197i	0.963013	+	0.169805i	0.330030	+	0.943971i	$0.392941\pi$
$140$	0.863835	+	0.0292703i	0.0730074	+	0.00247380i
$141$	20.4610	+	1.85681i	1.72312	+	0.156372i
$142$	6.45299	−	9.21583i	0.541523	−	0.773375i
$143$	−3.47151	+	12.9558i	−0.290302	+	1.08342i
$144$	−8.66503	+	7.17581i	−0.722086	+	0.597984i
$145$	−0.287865	−	0.0350429i	−0.0239059	−	0.00291015i
$146$	6.37457	−	17.5140i	0.527563	−	1.44947i
$147$	4.94831	+	4.17948i	0.408130	+	0.344718i
$148$	−0.762451	+	0.0667058i	−0.0626731	+	0.00548319i
$149$	−8.56384	−	7.18592i	−0.701577	−	0.588693i	0.220645	−	0.975354i	$-0.429184\pi$
$149$	−8.56384	−	7.18592i	−0.701577	−	0.588693i	−0.922222	+	0.386661i	$0.873628\pi$
$150$	−11.0966	+	4.24479i	−0.906037	+	0.346586i
$151$	11.0074	+	4.00638i	0.895773	+	0.326035i	0.748558	−	0.663070i	$-0.230747\pi$
$151$	11.0074	+	4.00638i	0.895773	+	0.326035i	0.147215	+	0.989104i	$0.452969\pi$
$152$	0.362234	+	1.35188i	0.0293810	+	0.109652i
$153$	−10.3406	−	2.84258i	−0.835988	−	0.229809i
$154$	21.1494	−	12.2106i	1.70427	−	0.983959i
$155$	5.49895	−	3.57916i	0.441686	−	0.287485i
$156$	−0.457882	+	0.211713i	−0.0366599	+	0.0169506i
$157$	−18.4349	−	8.59634i	−1.47127	−	0.686062i	−0.488781	−	0.872407i	$-0.662558\pi$
$157$	−18.4349	−	8.59634i	−1.47127	−	0.686062i	−0.982485	+	0.186344i	$0.940336\pi$
$158$	−11.2704	+	7.89163i	−0.896626	+	0.627824i
$159$	−0.396762	−	0.107689i	−0.0314653	−	0.00854027i
$160$	1.41658	−	0.461898i	0.111991	−	0.0365163i
$161$			22.9261i			1.80683i
$162$	−11.2567	+	5.07281i	−0.884407	+	0.398558i
$163$	−6.89303	+	6.89303i	−0.539904	+	0.539904i	−0.923501	−	0.383597i	$-0.874685\pi$
$163$	−6.89303	+	6.89303i	−0.539904	+	0.539904i	0.383597	+	0.923501i	$0.374685\pi$
$164$	0.0302363	−	0.0253713i	0.00236106	−	0.00198116i
$165$	12.6979	−	16.7738i	0.988528	−	1.30584i
$166$	−0.00351574	+	0.0199388i	−0.000272875	+	0.00154755i
$167$	3.38405	−	7.25712i	0.261866	−	0.561573i	−0.730782	−	0.682611i	$-0.760844\pi$
$167$	3.38405	−	7.25712i	0.261866	−	0.561573i	0.992648	+	0.121038i	$0.0386222\pi$
$168$	15.4795	+	5.69086i	1.19427	+	0.439060i
$169$	−6.79796	+	1.19866i	−0.522920	+	0.0922049i
$170$	−8.76457	−	6.59036i	−0.672212	−	0.505458i
$171$	−0.00934832	+	1.44502i	−0.000714884	+	0.110503i
$172$	−0.663000	+	0.177650i	−0.0505532	+	0.0135457i
$173$	−6.47315	−	13.8817i	−0.492145	−	1.05541i	−0.982905	−	0.184113i	$-0.941059\pi$
$173$	−6.47315	−	13.8817i	−0.492145	−	1.05541i	0.490760	−	0.871295i	$-0.336719\pi$
$174$	−0.278864	−	0.131136i	−0.0211406	−	0.00994141i
$175$	12.7554	+	10.2854i	0.964216	+	0.777506i
$176$	13.0942	−	15.6050i	0.987011	−	1.17627i
$177$	−4.31707	+	5.11122i	−0.324491	+	0.384183i
$178$	6.36186	−	2.96659i	0.476842	−	0.222355i
$179$	10.5577	−	18.2866i	0.789123	−	1.36680i	−0.137382	−	0.990518i	$-0.543869\pi$
$179$	10.5577	−	18.2866i	0.789123	−	1.36680i	0.926505	−	0.376283i	$-0.122798\pi$
$180$	0.790367	−	0.0371160i	0.0589105	−	0.00276646i
$181$	5.12182	+	8.87125i	0.380702	+	0.659395i	0.991163	−	0.132651i	$-0.0423491\pi$
$181$	5.12182	+	8.87125i	0.380702	+	0.659395i	−0.610461	+	0.792046i	$0.709016\pi$
$182$	−9.09365	−	6.36744i	−0.674066	−	0.471986i
$183$	5.46389	+	6.55455i	0.403902	+	0.484527i
$184$	6.95214	+	19.1009i	0.512519	+	1.40813i
$185$	−12.3127	−	7.67611i	−0.905247	−	0.564359i
$186$	6.74046	−	1.78275i	0.494235	−	0.130718i
$187$	19.3440	+	1.69238i	1.41457	+	0.123759i
$188$	−0.989310	−	0.989310i	−0.0721528	−	0.0721528i
$189$	13.8535	+	9.90203i	1.00769	+	0.720267i
$190$	−0.552106	+	1.37060i	−0.0400540	+	0.0994334i
$191$	−3.94811	−	4.70518i	−0.285676	−	0.340455i	0.604054	−	0.796944i	$-0.293551\pi$
$191$	−3.94811	−	4.70518i	−0.285676	−	0.340455i	−0.889729	+	0.456489i	$0.849107\pi$
$192$	14.5743	+	0.0471425i	1.05181	+	0.00340222i
$193$	−3.63906	−	5.19711i	−0.261945	−	0.374096i	0.666538	−	0.745471i	$-0.267775\pi$
$193$	−3.63906	−	5.19711i	−0.261945	−	0.374096i	−0.928483	+	0.371375i	$0.878887\pi$
$194$	5.36270	−	1.95186i	0.385020	−	0.140136i
$195$	−9.34996	−	2.00890i	−0.669565	−	0.143860i
$196$	−0.0765943	−	0.434388i	−0.00547102	−	0.0310277i
$197$	−0.329097	−	0.0881812i	−0.0234472	−	0.00628265i	0.247076	−	0.968996i	$-0.420530\pi$
$197$	−0.329097	−	0.0881812i	−0.0234472	−	0.00628265i	−0.270524	+	0.962713i	$0.587197\pi$
$198$	18.3956	−	12.7041i	1.30732	−	0.902845i
$199$	17.6952	+	10.2163i	1.25438	+	0.724216i	0.971976	−	0.235079i	$-0.0755350\pi$
$199$	17.6952	+	10.2163i	1.25438	+	0.724216i	0.282404	+	0.959296i	$0.408868\pi$
$200$	13.7461	+	4.70135i	0.971997	+	0.332436i
$201$	−4.22821	−	6.08027i	−0.298235	−	0.428869i
$202$	−0.946646	−	10.8202i	−0.0666058	−	0.761308i
$203$	0.0370415	+	0.423386i	0.00259980	+	0.0297159i
$204$	0.416949	+	0.599583i	0.0291923	+	0.0419792i
$205$	0.747205	−	0.0399351i	0.0521870	−	0.00278919i
$206$	−6.40504	−	3.69795i	−0.446260	−	0.257648i
$207$	1.69387	+	20.9189i	0.117732	+	1.45396i
$208$	−8.94459	−	2.39670i	−0.620196	−	0.166181i
$209$	−0.454349	−	2.57674i	−0.0314280	−	0.178237i
$210$	9.45126	+	14.6240i	0.652199	+	1.00915i
$211$	−5.48650	+	1.99692i	−0.377706	+	0.137474i	−0.523895	−	0.851783i	$-0.675522\pi$
$211$	−5.48650	+	1.99692i	−0.377706	+	0.137474i	0.146189	+	0.989257i	$0.453299\pi$
$212$	0.0160582	+	0.0229335i	0.00110288	+	0.00157508i
$213$	−14.2041	−	0.0459450i	−0.973247	−	0.00314810i
$214$	−8.05203	−	9.59603i	−0.550425	−	0.655971i
$215$	−12.0698	−	4.86199i	−0.823155	−	0.331585i
$216$	14.5447	+	4.04892i	0.989644	+	0.275494i
$217$	−6.79947	−	6.79947i	−0.461578	−	0.461578i
$218$	14.0351	+	1.22791i	0.950577	+	0.0831647i
$219$	−22.7490	+	6.01677i	−1.53723	+	0.406576i
$220$	−1.39561	+	0.323724i	−0.0940919	+	0.0218255i
$221$	−3.01897	−	8.29455i	−0.203078	−	0.557952i
$222$	−9.87259	−	11.8433i	−0.662605	−	0.794869i
$223$	16.0285	+	11.2233i	1.07335	+	0.751567i	0.970006	−	0.243079i	$-0.0781575\pi$
$223$	16.0285	+	11.2233i	1.07335	+	0.751567i	0.103342	+	0.994646i	$0.467046\pi$
$224$	−1.09185	−	1.89113i	−0.0729521	−	0.126357i
$225$	12.3985	+	8.44251i	0.826570	+	0.562834i
$226$	7.13615	−	12.3602i	0.474690	−	0.822187i
$227$	−9.06123	+	4.22532i	−0.601415	+	0.280444i	−0.699385	−	0.714745i	$-0.746543\pi$
$227$	−9.06123	+	4.22532i	−0.601415	+	0.280444i	0.0979701	+	0.995189i	$0.468765\pi$
$228$	0.0634979	−	0.0751786i	0.00420525	−	0.00497882i
$229$	8.12582	−	9.68397i	0.536969	−	0.639935i	−0.427536	−	0.903998i	$-0.640618\pi$
$229$	8.12582	−	9.68397i	0.536969	−	0.639935i	0.964505	+	0.264063i	$0.0850628\pi$
$230$	−6.25314	+	20.5291i	−0.412320	+	1.35365i
$231$	−27.9017	−	13.1208i	−1.83580	−	0.863286i
$232$	0.159249	+	0.341512i	0.0104552	+	0.0224213i
$233$	1.46682	−	0.393034i	0.0960947	−	0.0257485i	−0.210451	−	0.977604i	$-0.567493\pi$
$233$	1.46682	−	0.393034i	0.0960947	−	0.0257485i	0.306546	+	0.951856i	$0.400827\pi$
$234$	−8.76793	−	5.13808i	−0.573178	−	0.335887i
$235$	−3.71856	−	26.2616i	−0.242572	−	1.71312i
$236$	0.448688	−	0.0791159i	0.0292071	−	0.00515000i
$237$	16.3039	+	5.99394i	1.05905	+	0.389348i
$238$	−6.79205	+	14.5656i	−0.440263	+	0.944148i
$239$	3.47433	−	19.7039i	0.224735	−	1.27454i	−0.638455	−	0.769659i	$-0.720426\pi$
$239$	3.47433	−	19.7039i	0.224735	−	1.27454i	0.863190	−	0.504879i	$-0.168463\pi$
$240$	11.5805	+	8.76650i	0.747515	+	0.565875i
$241$	−8.08193	+	6.78155i	−0.520603	+	0.436838i	−0.864842	−	0.502044i	$-0.832581\pi$
$241$	−8.08193	+	6.78155i	−0.520603	+	0.436838i	0.344239	+	0.938882i	$0.388137\pi$
$242$	−17.9524	+	17.9524i	−1.15402	+	1.15402i
$243$	13.3722	+	8.01154i	0.857826	+	0.513940i
$244$		−	0.581105i		−	0.0372014i
$245$	3.78855	−	7.45452i	0.242042	−	0.476252i
$246$	0.767388	+	0.208284i	0.0489269	+	0.0132797i
$247$	−0.974294	+	0.682208i	−0.0619929	+	0.0434079i
$248$	−7.72686	−	3.60309i	−0.490656	−	0.228797i
$249$	0.0232017	−	0.0107279i	0.00147035	−	0.000679853i
$250$	8.61639	+	12.6891i	0.544948	+	0.802531i
$251$	−8.94339	+	5.16347i	−0.564502	+	0.325915i	−0.754950	−	0.655782i	$-0.772339\pi$
$251$	−8.94339	+	5.16347i	−0.564502	+	0.325915i	0.190449	+	0.981697i	$0.439006\pi$
$252$	−0.292880	−	1.12203i	−0.0184497	−	0.0706810i
$253$	−9.83535	−	36.7060i	−0.618343	−	2.30769i
$254$	16.9007	+	6.15134i	1.06044	+	0.385969i
$255$	−0.513608	+	13.8353i	−0.0321634	+	0.866402i
$256$	−2.16084	−	1.81316i	−0.135053	−	0.113323i
$257$	15.3834	−	1.34587i	0.959591	−	0.0839533i	0.403414	−	0.915017i	$-0.367823\pi$
$257$	15.3834	−	1.34587i	0.959591	−	0.0839533i	0.556177	+	0.831064i	$0.312268\pi$
$258$	−10.5637	−	8.92238i	−0.657667	−	0.555483i
$259$	−7.27299	+	19.9824i	−0.451921	+	1.24164i
$260$	0.401483	+	0.512779i	0.0248989	+	0.0318012i
$261$	0.0650799	+	0.383581i	0.00402835	+	0.0237431i
$262$	−1.15308	+	4.30336i	−0.0712377	+	0.265863i
$263$	7.80938	−	11.1530i	0.481547	−	0.687721i	−0.502712	−	0.864454i	$-0.667664\pi$
$263$	7.80938	−	11.1530i	0.481547	−	0.687721i	0.984259	+	0.176734i	$0.0565531\pi$
$264$	−27.2251	−	2.47065i	−1.67559	−	0.152058i
$265$	−0.0179737	+	0.530445i	−0.00110411	+	0.0325850i
$266$	2.13266	+	0.376046i	0.130762	+	0.0230569i
$267$	−7.66073	−	4.45603i	−0.468829	−	0.272705i
$268$	−0.0439556	+	0.502415i	−0.00268502	+	0.0306899i
$269$	11.6016			0.707363			0.353681	−	0.935366i	$-0.384930\pi$
$269$	11.6016			0.707363			0.353681	+	0.935366i	$0.384930\pi$
$270$	9.70426	+	12.6453i	0.590582	+	0.769569i
$271$	10.5393			0.640216			0.320108	−	0.947381i	$-0.396281\pi$
$271$	10.5393			0.640216			0.320108	+	0.947381i	$0.396281\pi$
$272$	−1.16840	+	13.3549i	−0.0708447	+	0.809759i
$273$	−0.0453358	+	14.0158i	−0.00274385	+	0.848272i
$274$	−6.35693	−	1.12090i	−0.384036	−	0.0677159i
$275$	−24.8346	−	10.9955i	−1.49758	−	0.663055i
$276$	0.823546	−	1.16809i	0.0495716	−	0.0703105i
$277$	−9.50648	+	13.5767i	−0.571189	+	0.815743i	−0.995983	−	0.0895477i	$-0.971458\pi$
$277$	−9.50648	+	13.5767i	−0.571189	+	0.815743i	0.424793	+	0.905290i	$0.360347\pi$
$278$	4.09355	−	15.2773i	0.245515	−	0.916273i
$279$	−6.70653	−	5.70179i	−0.401510	−	0.341357i
$280$	2.57292	−	21.1357i	0.153762	−	1.26310i
$281$	−4.02535	+	11.0596i	−0.240132	+	0.659758i	0.759821	+	0.650132i	$0.225286\pi$
$281$	−4.02535	+	11.0596i	−0.240132	+	0.659758i	−0.999954	+	0.00962623i	$0.996936\pi$
$282$	4.98408	−	27.7411i	0.296798	−	1.65196i
$283$	7.29153	−	0.637926i	0.433437	−	0.0379208i	0.131650	−	0.991296i	$-0.457973\pi$
$283$	7.29153	−	0.637926i	0.433437	−	0.0379208i	0.301787	+	0.953375i	$0.402417\pi$
$284$	0.740985	+	0.621760i	0.0439694	+	0.0368947i
$285$	1.81866	−	0.415659i	0.107728	−	0.0246215i
$286$	17.2911	+	6.29345i	1.02245	+	0.372140i
$287$	−0.283834	−	1.05928i	−0.0167542	−	0.0625275i
$288$	−1.13598	−	1.64489i	−0.0669381	−	0.0969261i
$289$	3.65576	−	2.11066i	0.215045	−	0.124156i
$290$	−0.0823108	+	0.389223i	−0.00483346	+	0.0228560i
$291$	−5.88872	−	4.15178i	−0.345203	−	0.243381i
$292$	1.45231	+	0.677225i	0.0849902	+	0.0396316i
$293$	−6.51480	+	4.56171i	−0.380599	+	0.266498i	−0.748183	−	0.663492i	$-0.769074\pi$
$293$	−6.51480	+	4.56171i	−0.380599	+	0.266498i	0.367585	+	0.929990i	$0.380185\pi$
$294$	6.30357	−	6.26292i	0.367632	−	0.365261i
$295$	7.69994	+	3.91328i	0.448308	+	0.227840i
$296$			18.8538i			1.09585i
$297$	−26.4283	−	9.91057i	−1.53352	−	0.575069i
$298$	−10.8446	+	10.8446i	−0.628213	+	0.628213i
$299$	−13.2329	+	11.1037i	−0.765276	+	0.642143i
$300$	−0.280416	−	0.982240i	−0.0161898	−	0.0567097i
$301$	−3.31156	+	18.7808i	−0.190875	+	1.08251i
$302$	6.79148	−	14.5644i	0.390806	−	0.838086i
$303$	−10.5333	+	8.78061i	−0.605124	+	0.504433i
$304$	1.77896	−	0.313678i	0.102030	−	0.0179907i
$305$	6.62071	−	8.80493i	0.379101	−	0.504169i
$306$	−5.12123	+	13.7922i	−0.292761	+	0.788446i
$307$	9.07696	−	2.43216i	0.518049	−	0.138811i	0.00968516	−	0.999953i	$-0.496917\pi$
$307$	9.07696	−	2.43216i	0.518049	−	0.138811i	0.508364	+	0.861142i	$0.330250\pi$
$308$	0.887362	+	1.90295i	0.0505622	+	0.108431i
$309$	0.783734	+	9.30467i	0.0445851	+	0.529324i
$310$	−4.23399	−	7.94313i	−0.240475	−	0.451140i
$311$	−3.85633	+	4.59579i	−0.218672	+	0.260603i	−0.864217	−	0.503119i	$-0.832186\pi$
$311$	−3.85633	+	4.59579i	−0.218672	+	0.260603i	0.645545	+	0.763722i	$0.276630\pi$
$312$	4.21239	+	11.6910i	0.238480	+	0.661871i
$313$	−8.36871	+	3.90239i	−0.473027	+	0.220576i	−0.644488	−	0.764615i	$-0.722929\pi$
$313$	−8.36871	+	3.90239i	−0.473027	+	0.220576i	0.171460	+	0.985191i	$0.445151\pi$
$314$	−13.9525	+	24.1664i	−0.787383	+	1.36379i
$315$	8.34587	−	20.3379i	0.470236	−	1.14591i
$316$	−0.591467	−	1.02445i	−0.0332726	−	0.0576299i
$317$	26.2573	+	18.3856i	1.47476	+	1.03264i	0.987190	+	0.159551i	$0.0510047\pi$
$317$	26.2573	+	18.3856i	1.47476	+	1.03264i	0.487568	+	0.873085i	$0.337884\pi$
$318$	−0.194613	+	0.529362i	−0.0109134	+	0.0296851i
$319$	−0.240939	−	0.661976i	−0.0134900	−	0.0370635i
$320$	−4.25153	−	18.3288i	−0.237668	−	1.02461i
$321$	−4.14274	+	15.2633i	−0.231225	+	0.851913i
$322$	31.3321	+	2.74120i	1.74607	+	0.152761i
$323$	1.21756	+	1.21756i	0.0677467	+	0.0677467i
$324$	−0.350137	−	1.00215i	−0.0194521	−	0.0556751i
$325$	0.241032	+	12.3439i	0.0133701	+	0.684715i
$326$	8.59623	+	10.2446i	0.476101	+	0.567396i
$327$	−8.84391	−	15.4332i	−0.489069	−	0.853456i
$328$	−0.557695	−	0.796471i	−0.0307935	−	0.0439777i
$329$	−36.5280	+	13.2951i	−2.01386	+	0.732984i
$330$	−21.4058	−	19.3592i	−1.17835	−	1.06569i
$331$	−5.34763	−	30.3279i	−0.293932	−	1.66697i	−0.671511	−	0.740995i	$-0.734354\pi$
$331$	−5.34763	−	30.3279i	−0.293932	−	1.66697i	0.377579	−	0.925977i	$-0.376757\pi$
$332$	−0.00168142		0.000450535i	−9.22799e−5		2.47263e-5i
$333$	−5.15984	+	18.7702i	−0.282758	+	1.02860i
$334$	−9.51338	−	5.49255i	−0.520549	−	0.300539i
$335$	−6.39019	+	7.11182i	−0.349133	+	0.388560i
$336$	9.05849	−	19.2631i	0.494181	−	1.05089i
$337$	0.275916	+	3.15374i	0.0150301	+	0.171795i	1.00000		0.000933572i	$-0.000297165\pi$
$337$	0.275916	+	3.15374i	0.0150301	+	0.171795i	−0.984969	+	0.172729i	$0.944742\pi$
$338$	0.825351	+	9.43381i	0.0448932	+	0.513132i
$339$	−17.9558	+	1.51242i	−0.975223	+	0.0821433i
$340$	0.630144	−	0.701305i	0.0341744	−	0.0380336i
$341$	13.8033	+	7.96936i	0.747493	+	0.431565i
$342$	1.97373	+	0.185553i	0.106727	+	0.0100335i
$343$	10.3207	+	2.76542i	0.557265	+	0.149319i
$344$	2.93610	+	16.6514i	0.158304	+	0.897785i
$345$	25.7868	−	8.31597i	1.38831	−	0.447717i
$346$	−19.7455	+	7.18679i	−1.06153	+	0.386364i
$347$	16.7182	+	23.8760i	0.897479	+	1.28173i	0.958936	+	0.283624i	$0.0915367\pi$
$347$	16.7182	+	23.8760i	0.897479	+	1.28173i	−0.0614562	+	0.998110i	$0.519574\pi$
$348$	0.0133215	−	0.0229022i	0.000714109	−	0.00122768i
$349$	−13.9918	−	16.6748i	−0.748963	−	0.892579i	0.248134	−	0.968726i	$-0.420183\pi$
$349$	−13.9918	−	16.6748i	−0.748963	−	0.892579i	−0.997097	+	0.0761464i	$0.975738\pi$
$350$	15.5818	−	16.2024i	0.832882	−	0.866057i
$351$	0.994175	+	12.7920i	0.0530651	+	0.682786i
$352$	2.55941	+	2.55941i	0.136417	+	0.136417i
$353$	4.00305	+	0.350221i	0.213061	+	0.0186404i	0.193186	−	0.981162i	$-0.438118\pi$
$353$	4.00305	+	0.350221i	0.213061	+	0.0186404i	0.0198744	+	0.999802i	$0.493673\pi$
$354$	6.46911	+	6.51109i	0.343829	+	0.346061i
$355$	4.14353	+	17.8632i	0.219916	+	0.948080i
$356$	0.206417	+	0.567126i	0.0109401	+	0.0300576i
$357$	19.9938	−	3.45880i	1.05818	−	0.183059i
$358$	−23.7291	−	16.6153i	−1.25412	−	0.878146i
$359$	4.90370	+	8.49346i	0.258807	+	0.448268i	0.965923	−	0.258831i	$-0.0833372\pi$
$359$	4.90370	+	8.49346i	0.258807	+	0.448268i	−0.707115	+	0.707098i	$0.750004\pi$
$360$	0.786069	−	19.4753i	0.0414295	−	1.02644i
$361$	−9.38399	+	16.2535i	−0.493894	+	0.855450i
$362$	12.7364	−	5.93907i	0.669409	−	0.312150i
$363$	31.5488	+	5.66819i	1.65588	+	0.297503i
$364$	0.613517	−	0.731161i	0.0321570	−	0.0383232i
$365$	14.2897	+	26.8080i	0.747956	+	1.40319i
$366$	9.61113	−	6.68356i	0.502382	−	0.349355i
$367$	−15.6137	−	33.4836i	−0.815027	−	1.74783i	−0.647650	−	0.761938i	$-0.724248\pi$
$367$	−15.6137	−	33.4836i	−0.815027	−	1.74783i	−0.167377	−	0.985893i	$-0.553530\pi$
$368$	25.3415	−	6.79023i	1.32102	−	0.353965i
$369$	−0.337248	−	0.945569i	−0.0175564	−	0.0492244i
$370$	−11.9628	+	15.9094i	−0.621917	+	0.827092i
$371$	0.766037	−	0.135073i	0.0397707	−	0.00701264i
$372$	0.102184	+	0.590682i	0.00529801	+	0.0306255i
$373$	11.0077	−	23.6061i	0.569958	−	1.22228i	−0.384276	−	0.923218i	$-0.625549\pi$
$373$	11.0077	−	23.6061i	0.569958	−	1.22228i	0.954234	−	0.299061i	$-0.0966735\pi$
$374$	4.62580	−	26.2342i	0.239194	−	1.35654i
$375$	6.94209	−	18.0778i	0.358488	−	0.933534i
$376$	−26.4017	+	22.1537i	−1.36156	+	1.14249i
$377$	−0.226437	+	0.226437i	−0.0116621	+	0.0116621i
$378$	15.1891	−	17.7490i	0.781243	−	0.912911i
$379$		−	25.9056i		−	1.33068i	−0.746541	−	0.665340i	$-0.768287\pi$
$379$		−	25.9056i		−	1.33068i	0.746541	−	0.665340i	$-0.231713\pi$
$380$	−0.113255	−	0.0575586i	−0.00580985	−	0.00295270i
$381$	−5.80607	−	21.9523i	−0.297454	−	1.12465i
$382$	−6.90243	+	4.83314i	−0.353159	+	0.247285i
$383$	−8.86756	−	4.13501i	−0.453111	−	0.211289i	0.182645	−	0.983179i	$-0.441534\pi$
$383$	−8.86756	−	4.13501i	−0.453111	−	0.211289i	−0.635757	+	0.771890i	$0.719312\pi$
$384$	1.59842	−	17.6136i	0.0815688	−	0.898840i
$385$	−8.23559	+	38.9436i	−0.419725	+	1.98475i
$386$	−7.53778	+	4.35194i	−0.383663	+	0.221508i
$387$	−1.63403	+	17.3812i	−0.0830622	+	0.883535i
$388$	0.126993	+	0.473944i	0.00644709	+	0.0240609i
$389$	−11.3841	−	4.14348i	−0.577198	−	0.210083i	0.0368917	−	0.999319i	$-0.488254\pi$
$389$	−11.3841	−	4.14348i	−0.577198	−	0.210083i	−0.614089	+	0.789236i	$0.710477\pi$
$390$	−3.86342	+	12.5380i	−0.195632	+	0.634886i
$391$	19.1572	+	16.0748i	0.968823	+	0.812939i
$392$	−10.8243	+	0.947006i	−0.546711	+	0.0478310i
$393$	5.29181	−	1.90670i	0.266936	−	0.0961802i
$394$	−0.159863	+	0.439219i	−0.00805376	+	0.0221275i
$395$	2.70995	−	22.2613i	0.136352	−	1.12009i
$396$	0.950270	+	1.67078i	0.0477529	+	0.0839601i
$397$	3.07416	−	11.4729i	0.154288	−	0.575810i	−0.844878	−	0.534960i	$-0.820327\pi$
$397$	3.07416	−	11.4729i	0.154288	−	0.575810i	0.999165	−	0.0408499i	$-0.0130066\pi$
$398$	16.0780	−	22.9617i	0.805917	−	1.15097i
$399$	−1.14746	−	2.48167i	−0.0574451	−	0.124239i
$400$	7.59120	−	17.1456i	0.379560	−	0.857279i
$401$	−31.8998	−	5.62479i	−1.59300	−	0.280889i	−0.694377	−	0.719612i	$-0.744320\pi$
$401$	−31.8998	−	5.62479i	−1.59300	−	0.280889i	−0.898622	+	0.438723i	$0.855431\pi$
$402$	−8.81520	+	5.05151i	−0.439662	+	0.251947i
$403$	0.631475	−	7.21779i	0.0314560	−	0.359544i
$404$	0.933850			0.0464608
$405$	6.11252	−	19.1739i	0.303734	−	0.952757i
$406$	0.583053			0.0289364
$407$	3.07200	−	35.1131i	0.152273	−	1.74049i
$408$	15.6090	−	8.94464i	0.772758	−	0.442826i
$409$	−4.62791	−	0.816026i	−0.228836	−	0.0403499i	0.0580544	−	0.998313i	$-0.481510\pi$
$409$	−4.62791	−	0.816026i	−0.228836	−	0.0403499i	−0.286890	+	0.957964i	$0.592621\pi$
$410$	0.0347634	−	1.02595i	0.00171684	−	0.0506680i
$411$	3.42030	+	7.39722i	0.168711	+	0.364878i
$412$	0.364727	−	0.520884i	0.0179688	−	0.0256621i
$413$	3.27629	−	12.2273i	0.161216	−	0.601666i
$414$	28.7914	+	0.186261i	1.41502	+	0.00915425i
$415$	−0.0203439	−	0.0259835i	−0.000998641	−	0.00127548i
$416$	0.562747	−	1.54613i	0.0275909	−	0.0758055i
$417$	−18.7864	+	6.76895i	−0.919973	+	0.331477i
$418$	−3.57585	+	0.312846i	−0.174900	+	0.0153018i
$419$	16.7939	+	14.0917i	0.820435	+	0.688427i	0.953074	−	0.302737i	$-0.0979005\pi$
$419$	16.7939	+	14.0917i	0.820435	+	0.688427i	−0.132639	+	0.991164i	$0.542345\pi$
$420$	−1.32337	+	0.699920i	−0.0645739	+	0.0341526i
$421$	26.6703	+	9.70721i	1.29983	+	0.473101i	0.896942	−	0.442148i	$-0.145783\pi$
$421$	26.6703	+	9.70721i	1.29983	+	0.473101i	0.402891	+	0.915248i	$0.368005\pi$
$422$	2.07311	+	7.73694i	0.100917	+	0.376628i
$423$	−32.3476	+	14.8299i	−1.57280	+	0.721057i
$424$	0.597264	−	0.344831i	0.0290057	−	0.0167465i
$425$	17.5382	−	3.44678i	0.850726	−	0.167193i
$426$	−1.76113	+	19.4066i	−0.0853270	+	0.940253i
$427$	−14.6327	−	6.82332i	−0.708124	−	0.330204i
$428$	0.882242	−	0.617752i	0.0426448	−	0.0298602i
$429$	−5.94021	−	22.4595i	−0.286796	−	1.08436i
$430$	−8.08784	+	15.9140i	−0.390030	+	0.767440i
$431$		−	34.6874i		−	1.67083i	−0.549617	−	0.835417i	$-0.685226\pi$
$431$		−	34.6874i		−	1.67083i	0.549617	−	0.835417i	$-0.314774\pi$
$432$	6.84216	−	18.2458i	0.329194	−	0.877852i
$433$	−3.65895	+	3.65895i	−0.175838	+	0.175838i	−0.789539	−	0.613701i	$-0.789680\pi$
$433$	−3.65895	+	3.65895i	−0.175838	+	0.175838i	0.613701	+	0.789539i	$0.289680\pi$
$434$	−10.1055	+	8.47955i	−0.485081	+	0.407031i
$435$	0.462780	−	0.195238i	0.0221886	−	0.00936096i
$436$	−0.210342	+	1.19291i	−0.0100736	+	0.0571301i
$437$	1.42412	−	3.05403i	0.0681247	−	0.146094i
$438$	5.50284	+	31.8095i	0.262936	+	1.51992i
$439$	30.7144	−	5.41577i	1.46592	−	0.258481i	0.616982	−	0.786977i	$-0.288355\pi$
$439$	30.7144	−	5.41577i	1.46592	−	0.258481i	0.848935	+	0.528496i	$0.177244\pi$
$440$	4.94785	+	34.9433i	0.235880	+	1.66585i
$441$	−11.0355	−	2.01956i	−0.525501	−	0.0961694i
$442$	−11.6968	+	3.13414i	−0.556359	+	0.149076i
$443$	13.1309	+	28.1594i	0.623869	+	1.33789i	0.923413	+	0.383809i	$0.125388\pi$
$443$	13.1309	+	28.1594i	0.623869	+	1.33789i	−0.299544	+	0.954083i	$0.596834\pi$
$444$	1.08836	−	0.756844i	0.0516514	−	0.0359182i
$445$	−3.33380	+	10.9449i	−0.158037	+	0.518838i
$446$	17.2549	−	20.5636i	0.817042	−	0.973712i
$447$	19.0580	+	3.42403i	0.901411	+	0.161951i
$448$	−24.9919	+	11.6539i	−1.18075	+	0.550595i
$449$	−5.46364	+	9.46330i	−0.257845	+	0.446601i	−0.965664	−	0.259793i	$-0.916346\pi$
$449$	−5.46364	+	9.46330i	−0.257845	+	0.446601i	0.707819	+	0.706394i	$0.249679\pi$
$450$	13.0205	−	15.9351i	0.613791	−	0.751189i
$451$	0.908870	+	1.57421i	0.0427970	+	0.0741266i
$452$	1.00518	+	0.703835i	0.0472797	+	0.0331056i
$453$	−19.9921	+	3.45850i	−0.939310	+	0.162495i
$454$	4.69114	+	12.8888i	0.220166	+	0.604902i
$455$	17.6264	−	4.08860i	0.826337	−	0.191676i
$456$	−1.70856	−	1.71964i	−0.0800105	−	0.0805297i
$457$	−25.8119	−	2.25825i	−1.20743	−	0.105637i	−0.534388	−	0.845239i	$-0.679458\pi$
$457$	−25.8119	−	2.25825i	−1.20743	−	0.105637i	−0.673044	+	0.739603i	$0.735013\pi$
$458$	−12.2631	−	12.2631i	−0.573017	−	0.573017i
$459$	17.9877	−	4.63319i	0.839595	−	0.216259i
$460$	−1.71147	−	0.689418i	−0.0797976	−	0.0321443i
$461$	−10.5103	−	12.5256i	−0.489512	−	0.583377i	0.463582	−	0.886054i	$-0.346564\pi$
$461$	−10.5103	−	12.5256i	−0.489512	−	0.583377i	−0.953093	+	0.302677i	$0.902120\pi$
$462$	−21.2678	+	36.5632i	−0.989467	+	1.70108i
$463$	−0.681583	−	0.973401i	−0.0316758	−	0.0452378i	0.803002	−	0.595977i	$-0.203235\pi$
$463$	−0.681583	−	0.973401i	−0.0316758	−	0.0452378i	−0.834678	+	0.550739i	$0.814346\pi$
$464$	0.457022	−	0.166342i	0.0212167	−	0.00772225i
$465$	−5.18153	+	10.1143i	−0.240288	+	0.469038i
$466$	−0.361759	−	2.05164i	−0.0167582	−	0.0950403i
$467$	−15.4210	−	4.13206i	−0.713601	−	0.191209i	−0.116286	−	0.993216i	$-0.537099\pi$
$467$	−15.4210	−	4.13206i	−0.713601	−	0.191209i	−0.597315	+	0.802007i	$0.703766\pi$
$468$	0.505781	−	0.712475i	0.0233797	−	0.0329342i
$469$	12.1351	+	7.00619i	0.560345	+	0.323516i
$470$	−36.3352	+	1.94197i	−1.67602	+	0.0895765i
$471$	35.1067	−	2.95705i	1.61763	−	0.136254i
$472$	−0.978183	−	11.1807i	−0.0450245	−	0.514632i
$473$	−2.75501	−	31.4899i	−0.126675	−	1.44791i
$474$	10.1411	−	21.5652i	0.465795	−	0.990523i
$475$	−1.06026	−	2.16248i	−0.0486481	−	0.0992213i
$476$	−1.19665	−	0.690889i	−0.0548486	−	0.0316668i
$477$	0.688989	−	0.179845i	0.0315467	−	0.00823454i
$478$	−26.5130	−	7.10415i	−1.21268	−	0.324936i
$479$	1.29177	+	7.32601i	0.0590226	+	0.334734i	0.999993	−	0.00375516i	$-0.00119531\pi$
$479$	1.29177	+	7.32601i	0.0590226	+	0.334734i	−0.940970	+	0.338489i	$0.890084\pi$
$480$	−1.73106	+	1.91406i	−0.0790118	+	0.0873643i
$481$	−15.0563	+	5.48003i	−0.686506	+	0.249868i
$482$	8.30172	+	11.8561i	0.378133	+	0.540030i
$483$	−19.7432	−	34.4532i	−0.898348	−	1.56767i
$484$	−1.40310	−	1.67215i	−0.0637774	−	0.0760069i
$485$	−3.47559	+	8.62809i	−0.157818	+	0.391782i
$486$	12.5479	−	17.3173i	0.569184	−	0.785528i
$487$	13.2649	+	13.2649i	0.601090	+	0.601090i	0.940602	−	0.339512i	$-0.110262\pi$
$487$	13.2649	+	13.2649i	0.601090	+	0.601090i	−0.339512	+	0.940602i	$0.610262\pi$
$488$	−14.2603	−	1.24762i	−0.645534	−	0.0564769i
$489$	4.42274	−	16.2949i	0.200003	−	0.736879i
$490$	−9.73480	−	6.06897i	−0.439773	−	0.274168i
$491$	12.3391	+	33.9013i	0.556855	+	1.52995i	0.824173	+	0.566337i	$0.191640\pi$
$491$	12.3391	+	33.9013i	0.556855	+	1.52995i	−0.267319	+	0.963608i	$0.586138\pi$
$492$	−0.0235900	+	0.0641664i	−0.00106352	+	0.00289284i
$493$	0.379757	+	0.265909i	0.0171034	+	0.0119759i
$494$	0.815851	+	1.41310i	0.0367069	+	0.0635782i
$495$	−4.63723	+	36.1425i	−0.208428	+	1.62449i
$496$	−5.50198	+	9.52970i	−0.247046	+	0.427896i
$497$	24.3570	−	11.3579i	1.09256	−	0.509470i
$498$	−0.0118872	−	0.0329915i	−0.000532679	−	0.00147838i
$499$	−20.6192	+	24.5730i	−0.923042	+	1.10004i	0.0716800	+	0.997428i	$0.477164\pi$
$499$	−20.6192	+	24.5730i	−0.923042	+	1.10004i	−0.994722	+	0.102610i	$0.967280\pi$
$500$	−1.15140	+	0.642912i	−0.0514920	+	0.0287519i
$501$	1.16408	+	13.8202i	0.0520072	+	0.617441i
$502$	5.98736	+	12.8399i	0.267229	+	0.573074i
$503$	−34.1605	+	9.15328i	−1.52314	+	0.408124i	−0.920775	−	0.390095i	$-0.872442\pi$
$503$	−34.1605	+	9.15328i	−1.52314	+	0.408124i	−0.602367	+	0.798220i	$0.705775\pi$
$504$	−28.1633	+	4.77831i	−1.25449	+	0.212843i
$505$	14.1497	+	10.6396i	0.629655	+	0.473458i
$506$	−51.3405	+	9.05272i	−2.28237	+	0.402443i
$507$	9.18368	−	7.65554i	0.407862	−	0.339994i
$508$	−0.653509	+	1.40145i	−0.0289948	+	0.0621795i
$509$	−3.11515	+	17.6669i	−0.138077	+	0.783072i	0.834591	+	0.550870i	$0.185704\pi$
$509$	−3.11515	+	17.6669i	−0.138077	+	0.783072i	−0.972668	+	0.232202i	$0.925407\pi$
$510$	18.8468	+	2.35618i	0.834548	+	0.104333i
$511$	34.1061	−	28.6184i	1.50876	−	1.26600i
$512$	−17.1769	+	17.1769i	−0.759118	+	0.759118i
$513$	−1.23036	−	2.17962i	−0.0543216	−	0.0962324i
$514$		−	21.1848i		−	0.934420i
$515$	11.4609	−	3.73701i	0.505030	−	0.164672i
$516$	0.843365	−	0.837926i	0.0371271	−	0.0368876i
$517$	52.7799	−	36.9569i	2.32126	−	1.62536i
$518$	26.4394	+	12.3289i	1.16168	+	0.541701i
$519$	21.6823	+	15.2869i	0.951748	+	0.671020i
$520$	13.4456	−	8.75147i	0.589628	−	0.383777i
$521$	5.38399	−	3.10845i	0.235877	−	0.136184i	−0.377403	−	0.926049i	$-0.623183\pi$
$521$	5.38399	−	3.10845i	0.235877	−	0.136184i	0.613280	+	0.789865i	$0.289850\pi$
$522$	0.532005	−	0.0430783i	0.0232852	−	0.00188549i
$523$	11.0715	+	41.3195i	0.484124	+	1.80677i	0.583975	+	0.811771i	$0.301497\pi$
$523$	11.0715	+	41.3195i	0.484124	+	1.80677i	−0.0998516	+	0.995002i	$0.531837\pi$
$524$	−0.359944	−	0.131009i	−0.0157242	−	0.00572316i
$525$	−28.0262	−	4.47236i	−1.22316	−	0.195190i
$526$	−14.3085	−	12.0063i	−0.623881	−	0.523499i
$527$	−10.4492	+	0.914187i	−0.455174	+	0.0398226i
$528$	−6.23927	+	34.7274i	−0.271529	+	1.51132i
$529$	8.87229	−	24.3764i	0.385752	−	1.05984i
$530$	0.722787	+	0.0879876i	0.0313959	+	0.00382194i
$531$	2.08604	−	11.3988i	0.0905266	−	0.494667i
$532$	−0.0481895	+	0.179846i	−0.00208928	+	0.00779730i
$533$	0.473947	−	0.676866i	0.0205289	−	0.0293183i
$534$	−7.00584	+	9.93681i	−0.303172	+	0.430008i
$535$	20.4060	+	0.691441i	0.882229	+	0.0298936i
$536$	12.2349	+	2.15734i	0.528467	+	0.0931830i
$537$	−0.118300	+	36.5729i	−0.00510502	+	1.57824i
$538$	1.38717	−	15.8554i	0.0598052	−	0.683576i
$539$	20.3134			0.874961
$540$	−1.15579	+	0.736417i	−0.0497375	+	0.0316903i
$541$	16.3822			0.704326			0.352163	−	0.935939i	$-0.385446\pi$
$541$	16.3822			0.704326			0.352163	+	0.935939i	$0.385446\pi$
$542$	1.26015	−	14.4036i	0.0541281	−	0.618687i
$543$	−15.3367	−	8.92091i	−0.658160	−	0.382833i
$544$	−2.34581	−	0.413629i	−0.100576	−	0.0177342i
$545$	−16.7783	+	15.6785i	−0.718704	+	0.671595i
$546$	19.1493	+	1.73778i	0.819515	+	0.0743702i
$547$	−12.1838	+	17.4002i	−0.520940	+	0.743980i	−0.990288	−	0.139034i	$-0.955600\pi$
$547$	−12.1838	+	17.4002i	−0.520940	+	0.743980i	0.469347	+	0.883014i	$0.344489\pi$
$548$	0.143641	−	0.536074i	0.00613602	−	0.0228999i
$549$	−13.8557	−	5.14481i	−0.591346	−	0.219575i
$550$	−17.9965	+	32.6257i	−0.767374	+	1.39116i
$551$	0.0213654	−	0.0587010i	0.000910198	−	0.00250075i
$552$	−26.8967	−	22.7177i	−1.14480	−	0.966928i
$553$	−32.7415	+	2.86451i	−1.39231	+	0.121811i
$554$	17.4180	+	14.6154i	0.740019	+	0.620950i
$555$	25.1139	+	0.932299i	1.06602	+	0.0395739i
$556$	1.27783	+	0.465094i	0.0541923	+	0.0197244i
$557$	4.42599	+	16.5180i	0.187535	+	0.699891i	0.994074	+	0.108709i	$0.0346718\pi$
$557$	4.42599	+	16.5180i	0.187535	+	0.699891i	−0.806538	+	0.591182i	$0.798662\pi$
$558$	−8.59427	+	8.48379i	−0.363824	+	0.359147i
$559$	−12.4441	+	7.18460i	−0.526329	+	0.303876i
$560$	−26.8863	−	5.68578i	−1.13616	−	0.240268i
$561$	−30.5274	+	14.1151i	−1.28887	+	0.595941i
$562$	14.6333	+	6.82364i	0.617270	+	0.287838i
$563$	35.9806	−	25.1939i	1.51640	−	1.06180i	0.541088	−	0.840966i	$-0.318013\pi$
$563$	35.9806	−	25.1939i	1.51640	−	1.06180i	0.975313	−	0.220829i	$-0.0708763\pi$
$564$	2.33869	+	0.634765i	0.0984767	+	0.0267284i
$565$	7.21153	+	22.1169i	0.303391	+	0.930463i
$566$		−	10.0413i		−	0.422067i
$567$	−29.3462	−	2.95052i	−1.23243	−	0.123910i
$568$	16.8489	−	16.8489i	0.706963	−	0.706963i
$569$	−31.1911	+	26.1725i	−1.30760	+	1.09721i	−0.318823	+	0.947814i	$0.603288\pi$
$569$	−31.1911	+	26.1725i	−1.30760	+	1.09721i	−0.988778	+	0.149393i	$0.952268\pi$
$570$	−0.350612	−	2.53518i	−0.0146855	−	0.106187i
$571$	6.97321	−	39.5470i	0.291820	−	1.65499i	−0.388035	−	0.921645i	$-0.626846\pi$
$571$	6.97321	−	39.5470i	0.291820	−	1.65499i	0.679855	−	0.733347i	$-0.262043\pi$
$572$	−0.668607	+	1.43383i	−0.0279559	+	0.0599515i
$573$	9.98516	+	3.67092i	0.417136	+	0.153355i
$574$	−1.48161	+	0.261248i	−0.0618414	+	0.0109043i
$575$	−18.0775	−	29.9454i	−0.753884	−	1.24881i
$576$	−21.9427	+	12.4801i	−0.914281	+	0.520003i
$577$	11.2139	−	3.00476i	0.466841	−	0.125090i	−0.0177276	−	0.999843i	$-0.505643\pi$
$577$	11.2139	−	3.00476i	0.466841	−	0.125090i	0.484569	+	0.874753i	$0.338976\pi$
$578$	−2.44743	−	5.24854i	−0.101800	−	0.218311i
$579$	9.94434	+	4.67634i	0.413273	+	0.194342i
$580$	−0.0327203	−	0.00996658i	−0.00135864	−	0.000413840i
$581$	−0.0310880	+	0.0370492i	−0.00128975	+	0.00153706i
$582$	−6.37815	+	7.55144i	−0.264383	+	0.313017i
$583$	−1.16852	+	0.544892i	−0.0483953	+	0.0225671i
$584$	19.7372	−	34.1858i	0.816730	−	1.41462i
$585$	15.7811	−	5.03294i	0.652467	−	0.208086i
$586$	5.45534	+	9.44893i	0.225358	+	0.390332i
$587$	−34.5111	−	24.1649i	−1.42442	−	0.997393i	−0.995570	−	0.0940196i	$-0.970028\pi$
$587$	−34.5111	−	24.1649i	−1.42442	−	0.997393i	−0.428855	−	0.903374i	$-0.641083\pi$
$588$	0.489187	+	0.586834i	0.0201737	+	0.0242006i
$589$	0.483403	+	1.32814i	0.0199183	+	0.0547250i
$590$	6.26877	−	10.0553i	0.258081	−	0.413969i
$591$	0.570503	−	0.150890i	0.0234674	−	0.00620677i
$592$	24.2418	+	2.12088i	0.996330	+	0.0871676i
$593$	10.2163	+	10.2163i	0.419534	+	0.419534i	0.885043	−	0.465509i	$-0.154129\pi$
$593$	10.2163	+	10.2163i	0.419534	+	0.419534i	−0.465509	+	0.885043i	$0.654129\pi$
$594$	−16.7043	+	34.9334i	−0.685386	+	1.43333i
$595$	−10.2603	−	24.1022i	−0.420629	−	0.988095i
$596$	−0.847584	−	1.01011i	−0.0347184	−	0.0413758i
$597$	−35.3902	−	0.114474i	−1.44843	−	0.00468513i
$598$	13.5927	+	19.4124i	0.555848	+	0.793833i
$599$	4.58046	−	1.66715i	0.187153	−	0.0681180i	−0.246744	−	0.969081i	$-0.579361\pi$
$599$	4.58046	−	1.66715i	0.187153	−	0.0681180i	0.433896	+	0.900963i	$0.357138\pi$
$600$	−24.7062	+	4.77257i	−1.00863	+	0.194839i
$601$	−6.94695	−	39.3981i	−0.283372	−	1.60708i	−0.711043	−	0.703149i	$-0.751777\pi$
$601$	−6.94695	−	39.3981i	−0.283372	−	1.60708i	0.427671	−	0.903935i	$-0.359334\pi$
$602$	25.2710	+	6.77134i	1.02997	+	0.275979i
$603$	11.5903	+	5.49619i	0.471992	+	0.223822i
$604$	1.19655	+	0.690830i	0.0486871	+	0.0281095i
$605$	−2.20852	−	41.3225i	−0.0897893	−	1.68000i
$606$	10.7407	+	15.4453i	0.436309	+	0.627424i
$607$	−0.829363	−	9.47967i	−0.0336628	−	0.384768i	−0.994273	−	0.106869i	$-0.965917\pi$
$607$	−0.829363	−	9.47967i	−0.0336628	−	0.384768i	0.960610	−	0.277899i	$-0.0896381\pi$
$608$	0.0279740	+	0.319745i	0.00113450	+	0.0129674i
$609$	−0.420273	−	0.604363i	−0.0170303	−	0.0244900i
$610$	−11.2417	−	10.1010i	−0.455163	−	0.408978i
$611$	−25.3654	−	14.6447i	−1.02617	−	0.592461i
$612$	−1.14293	−	0.541986i	−0.0462002	−	0.0219085i
$613$	−19.5042	−	5.22613i	−0.787766	−	0.211081i	−0.157560	−	0.987509i	$-0.550363\pi$
$613$	−19.5042	−	5.22613i	−0.787766	−	0.211081i	−0.630206	+	0.776428i	$0.717029\pi$
$614$	−2.23863	−	12.6959i	−0.0903437	−	0.512365i
$615$	−1.08850	+	0.703484i	−0.0438927	+	0.0283672i
$616$	48.6037	−	17.6903i	1.95830	−	0.712762i
$617$	−17.1129	−	24.4398i	−0.688940	−	0.983908i	−0.999444	−	0.0333358i	$-0.989387\pi$
$617$	−17.1129	−	24.4398i	−0.688940	−	0.983908i	0.310505	−	0.950572i	$-0.399502\pi$
$618$	12.8100	+	0.0414357i	0.515294	+	0.00166679i
$619$	−1.44832	−	1.72604i	−0.0582129	−	0.0693754i	0.736152	−	0.676816i	$-0.236641\pi$
$619$	−1.44832	−	1.72604i	−0.0582129	−	0.0693754i	−0.794365	+	0.607441i	$0.792196\pi$
$620$	0.712060	−	0.303122i	0.0285970	−	0.0121737i
$621$	−20.5602	−	29.9780i	−0.825053	−	1.20298i
$622$	5.81978	+	5.81978i	0.233352	+	0.233352i
$623$	16.7044	+	1.46145i	0.669249	+	0.0585517i
$624$	15.5058	−	4.10107i	0.620730	−	0.164174i
$625$	−24.7709	−	3.37677i	−0.990836	−	0.135071i
$626$	4.33261	+	11.9038i	0.173166	+	0.475770i
$627$	2.90180	+	3.48104i	0.115887	+	0.139019i
$628$	−1.96531	−	1.37612i	−0.0784243	−	0.0549133i
$629$	11.5979	+	20.0882i	0.462439	+	0.800968i
$630$	−26.7970	−	13.8377i	−1.06762	−	0.551306i
$631$	−10.8829	+	18.8498i	−0.433243	+	0.750399i	−0.997150	−	0.0754390i	$-0.975964\pi$
$631$	−10.8829	+	18.8498i	−0.433243	+	0.750399i	0.563907	+	0.825838i	$0.309298\pi$
$632$	−26.4099	+	12.3151i	−1.05053	+	0.489870i
$633$	6.52539	−	7.72577i	0.259361	−	0.307072i
$634$	28.2663	−	33.6864i	1.12260	−	1.33786i
$635$	−25.8692	+	13.7893i	−1.02659	+	0.547210i
$636$	−0.0438817	−	0.0206355i	−0.00174002	−	0.000818249i
$637$	−3.90245	−	8.36884i	−0.154621	−	0.331585i
$638$	−0.933502	+	0.250131i	−0.0369577	+	0.00990279i
$639$	21.3854	−	12.1631i	0.845991	−	0.481163i
$640$	−22.6070	+	3.20108i	−0.893619	+	0.126534i
$641$	−15.8779	+	2.79971i	−0.627141	+	0.110582i	−0.478181	−	0.878261i	$-0.658704\pi$
$641$	−15.8779	+	2.79971i	−0.627141	+	0.110582i	−0.148960	+	0.988843i	$0.547593\pi$
$642$	20.3643	+	7.48670i	0.803716	+	0.295476i
$643$	6.92110	−	14.8423i	0.272941	−	0.585325i	−0.721284	−	0.692640i	$-0.756448\pi$
$643$	6.92110	−	14.8423i	0.272941	−	0.585325i	0.994225	+	0.107315i	$0.0342254\pi$
$644$	−0.469571	+	2.66307i	−0.0185037	+	0.104940i
$645$	22.3255	−	3.08758i	0.879064	−	0.121573i
$646$	1.80956	−	1.51841i	0.0711964	−	0.0597408i
$647$	11.6159	−	11.6159i	0.456669	−	0.456669i	−0.440892	−	0.897560i	$-0.645338\pi$
$647$	11.6159	−	11.6159i	0.456669	−	0.456669i	0.897560	+	0.440892i	$0.145338\pi$
$648$	−25.3445	+	6.44078i	−0.995628	+	0.253018i
$649$			20.9822i			0.823622i
$650$	16.8987	+	1.14651i	0.662820	+	0.0449699i
$651$	16.0737	+	4.36270i	0.629977	+	0.170988i
$652$	−0.941869	+	0.659504i	−0.0368864	+	0.0258282i
$653$	40.4576	+	18.8657i	1.58323	+	0.738271i	0.997393	−	0.0721611i	$-0.0229896\pi$
$653$	40.4576	+	18.8657i	1.58323	+	0.738271i	0.585833	+	0.810432i	$0.300767\pi$
$654$	−22.1493	+	10.2413i	−0.866106	+	0.400466i
$655$	−3.96127	−	6.08601i	−0.154780	−	0.237800i
$656$	−1.08682	+	0.627476i	−0.0424332	+	0.0244988i
$657$	29.0056	−	28.6327i	1.13162	−	1.11707i
$658$	13.8023	+	51.5110i	0.538071	+	2.00811i
$659$	0.617551	+	0.224770i	0.0240564	+	0.00875580i	0.354020	−	0.935238i	$-0.384814\pi$
$659$	0.617551	+	0.224770i	0.0240564	+	0.00875580i	−0.329964	+	0.943994i	$0.607037\pi$
$660$	1.81853	−	1.68834i	0.0707862	−	0.0657187i
$661$	29.7997	+	25.0049i	1.15907	+	0.972578i	0.999892	−	0.0146714i	$-0.00467022\pi$
$661$	29.7997	+	25.0049i	1.15907	+	0.972578i	0.159181	+	0.987249i	$0.449115\pi$
$662$	−42.0873	+	3.68216i	−1.63577	+	0.143111i
$663$	11.6799	+	9.86516i	0.453610	+	0.383131i
$664$	−0.0146661	+	0.0402948i	−0.000569155	+	0.00156374i
$665$	−2.77921	+	2.17599i	−0.107773	+	0.0843814i
$666$	25.0355	+	9.29604i	0.970107	+	0.360214i
$667$	0.234817	−	0.876351i	0.00909217	−	0.0339324i
$668$	0.541728	−	0.773667i	0.0209601	−	0.0299341i
$669$	−33.7527	−	3.06302i	−1.30495	−	0.118423i
$670$	8.95536	+	9.58354i	0.345976	+	0.370244i
$671$	26.3550	+	4.64710i	1.01742	+	0.179399i
$672$	3.26940	+	1.90172i	0.126120	+	0.0733604i
$673$	−0.350216	+	4.00299i	−0.0134998	+	0.154304i	−0.999953	−	0.00974205i	$-0.996899\pi$
$673$	−0.350216	+	4.00299i	−0.0134998	+	0.154304i	0.986453	+	0.164046i	$0.0524545\pi$
$674$	4.34307			0.167289
$675$	−25.9029	−	2.01010i	−0.997003	−	0.0773689i
$676$	−0.814194			−0.0313152
$677$	−2.56187	+	29.2823i	−0.0984607	+	1.12541i	0.772820	+	0.634626i	$0.218846\pi$
$677$	−2.56187	+	29.2823i	−0.0984607	+	1.12541i	−0.871280	+	0.490786i	$0.836710\pi$
$678$	−0.0799609	+	24.7202i	−0.00307088	+	0.949374i
$679$	13.4254	+	2.36727i	0.515221	+	0.0908473i
$680$	−15.8571	−	16.9694i	−0.608093	−	0.650748i
$681$	9.97844	−	14.1530i	0.382375	−	0.542346i
$682$	12.5418	−	17.9116i	0.480251	−	0.685869i
$683$	1.99616	−	7.44976i	0.0763808	−	0.285057i	−0.917162	−	0.398515i	$-0.869526\pi$
$683$	1.99616	−	7.44976i	0.0763808	−	0.285057i	0.993543	+	0.113457i	$0.0361925\pi$
$684$	−0.0306827	+	0.167660i	−0.00117318	+	0.00641065i
$685$	8.28411	−	6.48608i	0.316519	−	0.247820i
$686$	5.01340	−	13.7742i	0.191412	−	0.525901i
$687$	−3.87189	+	21.5507i	−0.147722	+	0.822211i
$688$	21.7403	−	1.90203i	0.828841	−	0.0725142i
$689$	0.448975	+	0.376735i	0.0171046	+	0.0143525i
$690$	−8.28184	−	36.2360i	−0.315284	−	1.37948i
$691$	−32.4494	−	11.8106i	−1.23443	−	0.449297i	−0.359320	−	0.933215i	$-0.616991\pi$
$691$	−32.4494	−	11.8106i	−1.23443	−	0.449297i	−0.875114	+	0.483918i	$0.839213\pi$
$692$	−0.467589	−	1.74507i	−0.0177751	−	0.0663375i
$693$	53.2297	−	4.31019i	2.02203	−	0.163731i
$694$	34.6293	−	19.9933i	1.31451	−	0.758933i
$695$	14.0629	+	21.6059i	0.533434	+	0.819558i
$696$	−0.533418	−	0.376081i	−0.0202192	−	0.0142553i
$697$	−1.08416	−	0.505551i	−0.0410654	−	0.0191491i
$698$	−24.4616	+	17.1282i	−0.925887	+	0.648313i
$699$	−1.86586	+	1.85383i	−0.0705734	+	0.0701183i
$700$	1.27098	+	1.45600i	0.0480387	+	0.0550316i
$701$		−	2.02183i		−	0.0763636i	−0.999271	−	0.0381818i	$-0.987843\pi$
$701$		−	2.02183i		−	0.0763636i	0.999271	−	0.0381818i	$-0.0121566\pi$
$702$	17.6011	+	0.170805i	0.664313	+	0.00644660i
$703$	2.21011	−	2.21011i	0.0833558	−	0.0833558i
$704$	35.0139	−	29.3802i	1.31964	−	1.10731i
$705$	28.2039	+	36.2634i	1.06222	+	1.36576i
$706$	0.957265	−	5.42892i	0.0360272	−	0.204320i
$707$	10.9653	−	23.5151i	0.412391	−	0.884375i
$708$	−0.606154	+	0.505291i	−0.0227807	+	0.0189900i
$709$	−0.162501	+	0.0286532i	−0.00610284	+	0.00107609i	−0.176699	−	0.984265i	$-0.556542\pi$
$709$	−0.162501	+	0.0286532i	−0.00610284	+	0.00107609i	0.170596	+	0.985341i	$0.445431\pi$
$710$	24.9083	−	3.52694i	0.934792	−	0.132364i
$711$	−29.6632	+	5.03279i	−1.11246	+	0.188744i
$712$	14.3605	−	3.84787i	0.538181	−	0.144205i
$713$	8.67521	+	18.6040i	0.324889	+	0.696727i
$714$	−2.33639	−	27.7382i	−0.0874373	−	1.03808i
$715$	−26.4669	+	14.1078i	−0.989804	+	0.527604i
$716$	1.60092	−	1.90790i	0.0598292	−	0.0713017i
$717$	11.7472	+	32.6028i	0.438706	+	1.21758i
$718$	12.1940	−	5.68614i	0.455075	−	0.212205i
$719$	−0.704484	+	1.22020i	−0.0262728	+	0.0455059i	−0.878863	−	0.477074i	$-0.841697\pi$
$719$	−0.704484	+	1.22020i	−0.0262728	+	0.0455059i	0.852590	+	0.522580i	$0.175031\pi$
$720$	−24.9525	−	3.20150i	−0.929924	−	0.119313i
$721$	−8.83364	−	15.3003i	−0.328982	−	0.569813i
$722$	21.0910	+	14.7681i	0.784926	+	0.549611i
$723$	6.30542	−	17.1512i	0.234501	−	0.637859i
$724$	0.413244	+	1.13538i	0.0153581	+	0.0421960i
$725$	−0.382228	−	0.523807i	−0.0141956	−	0.0194537i
$726$	11.5187	−	42.4387i	0.427498	−	1.57505i
$727$	−32.9194	−	2.88007i	−1.22091	−	0.106816i	−0.541581	−	0.840648i	$-0.682174\pi$
$727$	−32.9194	−	2.88007i	−1.22091	−	0.106816i	−0.679330	+	0.733832i	$0.737730\pi$
$728$	−16.6255	−	16.6255i	−0.616182	−	0.616182i
$729$	−26.9949	−	0.523976i	−0.999812	−	0.0194065i
$730$	38.3459	−	16.3238i	1.41925	−	0.604169i
$731$	13.3715	+	15.9355i	0.494562	+	0.589396i
$732$	0.500429	+	0.873280i	0.0184964	+	0.0322774i
$733$	−8.49132	−	12.1269i	−0.313634	−	0.447916i	0.631125	−	0.775681i	$-0.282593\pi$
$733$	−8.49132	−	12.1269i	−0.313634	−	0.447916i	−0.944759	+	0.327765i	$0.893705\pi$
$734$	−47.6275	+	17.3350i	−1.75796	+	0.639847i
$735$	0.726192	+	14.4652i	0.0267860	+	0.533557i
$736$	0.809475	+	4.59076i	0.0298376	+	0.169218i
$737$	−22.4346	−	6.01134i	−0.826391	−	0.221431i
$738$	−1.33259	+	0.347843i	−0.0490534	+	0.0128043i
$739$	−10.7323	−	6.19632i	−0.394796	−	0.227935i	0.289440	−	0.957196i	$-0.406531\pi$
$739$	−10.7323	−	6.19632i	−0.394796	−	0.227935i	−0.684236	+	0.729261i	$0.739864\pi$
$740$	−1.27301	−	1.14384i	−0.0467967	−	0.0420482i
$741$	0.876666	−	1.86425i	0.0322051	−	0.0684849i
$742$	−0.0930058	−	1.06306i	−0.00341435	−	0.0390262i
$743$	−0.328934	−	3.75974i	−0.0120674	−	0.137931i	0.987771	−	0.155912i	$-0.0498317\pi$
$743$	−0.328934	−	3.75974i	−0.0120674	−	0.137931i	−0.999838	+	0.0179809i	$0.994276\pi$
$744$	14.7147	−	1.23943i	0.539469	−	0.0454395i
$745$	−1.33412	−	24.9621i	−0.0488785	−	0.914539i
$746$	−30.9454	−	17.8663i	−1.13299	−	0.654132i
$747$	−0.0256288	+	0.0361024i	−0.000937710	+	0.00132092i
$748$	2.21231	+	0.592786i	0.0808900	+	0.0216744i
$749$	−5.19621	−	29.4692i	−0.189865	−	1.07678i
$750$	−23.8761	−	11.6490i	−0.871833	−	0.425360i
$751$	−11.6339	+	4.23440i	−0.424528	+	0.154516i	−0.545444	−	0.838147i	$-0.683639\pi$
$751$	−11.6339	+	4.23440i	−0.424528	+	0.154516i	0.120916	+	0.992663i	$0.461417\pi$
$752$	25.5147	+	36.4388i	0.930426	+	1.32879i
$753$	8.99345	−	15.4614i	0.327739	−	0.563444i
$754$	0.282387	+	0.336536i	0.0102839	+	0.0122559i
$755$	10.2594	+	24.1002i	0.373377	+	0.877096i
$756$	1.40639	+	1.43395i	0.0511500	+	0.0521524i
$757$	14.6821	+	14.6821i	0.533632	+	0.533632i	0.921651	−	0.388019i	$-0.126841\pi$
$757$	14.6821	+	14.6821i	0.533632	+	0.533632i	−0.388019	+	0.921651i	$0.626841\pi$
$758$	−35.4040	−	3.09745i	−1.28593	−	0.112505i
$759$	46.3906	+	46.6917i	1.68387	+	1.69480i
$760$	−1.65564	+	2.65570i	−0.0600565	+	0.0963324i
$761$	−0.142795	−	0.392327i	−0.00517632	−	0.0142218i	0.937078	−	0.349121i	$-0.113520\pi$
$761$	−0.142795	−	0.392327i	−0.00517632	−	0.0142218i	−0.942254	+	0.334899i	$0.891298\pi$
$762$	−30.6955	+	5.31013i	−1.11198	+	0.192366i
$763$	27.5686	+	19.3037i	0.998050	+	0.698842i
$764$	−0.362237	−	0.627413i	−0.0131053	−	0.0226990i
$765$	−11.1427	−	21.2340i	−0.402866	−	0.767715i
$766$	−6.71141	+	11.6245i	−0.242493	+	0.420010i
$767$	8.64435	−	4.03093i	0.312129	−	0.145548i
$768$	4.80874	+	0.863958i	0.173520	+	0.0311754i
$769$	−11.9703	+	14.2656i	−0.431660	+	0.514432i	−0.937400	−	0.348254i	$-0.886775\pi$
$769$	−11.9703	+	14.2656i	−0.431660	+	0.514432i	0.505741	+	0.862685i	$0.331219\pi$
$770$	52.2379	+	15.9116i	1.88252	+	0.573415i
$771$	−21.9591	+	15.2703i	−0.790836	+	0.549946i
$772$	−0.316262	−	0.678225i	−0.0113825	−	0.0244099i
$773$	16.7325	−	4.48345i	0.601825	−	0.161259i	0.0549731	−	0.998488i	$-0.482493\pi$
$773$	16.7325	−	4.48345i	0.601825	−	0.161259i	0.546852	+	0.837229i	$0.315826\pi$
$774$	23.5587	+	4.31137i	0.846801	+	0.154969i
$775$	14.2427	+	3.51980i	0.511614	+	0.126435i
$776$	11.9032	−	2.09886i	0.427302	−	0.0753448i
$777$	−6.27840	−	36.2926i	−0.225236	−	1.30199i
$778$	−7.02388	+	15.0628i	−0.251818	+	0.540026i
$779$	−0.0279902	+	0.158740i	−0.00100285	+	0.00568746i
$780$	−1.04493	−	0.424857i	−0.0374147	−	0.0152123i
$781$	−34.1245	+	28.6339i	−1.22107	+	1.02460i
$782$	24.2594	−	24.2594i	0.867513	−	0.867513i
$783$	−0.428130	−	0.520398i	−0.0153001	−	0.0185975i
$784$			14.0242i			0.500864i
$785$	−14.0998	−	43.2424i	−0.503245	−	1.54339i
$786$	−1.97308	−	7.46007i	−0.0703774	−	0.266092i
$787$	−28.1240	+	19.6926i	−1.00251	+	0.701966i	−0.954909	−	0.296900i	$-0.904047\pi$
$787$	−28.1240	+	19.6926i	−1.00251	+	0.701966i	−0.0476032	+	0.998866i	$0.515158\pi$
$788$	−0.0364214	−	0.0169836i	−0.00129746	−	0.000605014i
$789$	−2.13131	+	23.4858i	−0.0758767	+	0.836116i
$790$	−30.0996	−	6.36529i	−1.07089	−	0.226467i
$791$	29.5259	−	17.0468i	1.04982	−	0.606114i
$792$	43.0413	−	19.7325i	1.52941	−	0.701164i
$793$	−3.14857	−	11.7506i	−0.111809	−	0.417277i
$794$	−15.3120	−	5.57311i	−0.543402	−	0.197782i
$795$	−0.429792	−	0.812627i	−0.0152431	−	0.0288209i
$796$	1.84620	+	1.54915i	0.0654370	+	0.0549081i
$797$	−37.0405	+	3.24062i	−1.31204	+	0.114789i	−0.721610	−	0.692300i	$-0.756598\pi$
$797$	−37.0405	+	3.24062i	−1.31204	+	0.114789i	−0.590431	+	0.807088i	$0.701042\pi$
$798$	−3.52879	+	1.27146i	−0.124918	+	0.0450094i
$799$	−14.5024	+	39.8451i	−0.513060	+	1.40962i
$800$	2.91732	+	1.60921i	0.103143	+	0.0568941i
$801$	15.3499	+	0.0993036i	0.542362	+	0.00350872i
$802$	−11.5013	+	42.9235i	−0.406126	+	1.51568i
$803$	−42.3285	+	60.4514i	−1.49374	+	2.13328i
$804$	−0.366608	−	0.792879i	−0.0129293	−	0.0279627i
$805$	−37.4561	+	35.0009i	−1.32015	+	1.23362i
$806$	−9.78874	−	1.72602i	−0.344794	−	0.0607964i
$807$	−17.4348	+	9.99095i	−0.613735	+	0.351698i
$808$	2.00495	−	22.9167i	0.0705339	−	0.806206i
$809$	−38.7711			−1.36312			−0.681560	−	0.731763i	$-0.738698\pi$
$809$	−38.7711			−1.36312			−0.681560	+	0.731763i	$0.738698\pi$
$810$	−25.4732	−	10.6463i	−0.895039	−	0.374072i
$811$	−15.0813			−0.529577			−0.264789	−	0.964307i	$-0.585302\pi$
$811$	−15.0813			−0.529577			−0.264789	+	0.964307i	$0.585302\pi$
$812$	−0.00436907	+	0.0499387i	−0.000153324	+	0.00175251i
$813$	−15.8384	+	9.07611i	−0.555476	+	0.318313i
$814$	−47.6203	−	8.39674i	−1.66909	−	0.294305i
$815$	−21.7852	−	0.738173i	−0.763101	−	0.0258571i
$816$	−9.74495	−	21.0758i	−0.341141	−	0.737801i
$817$	1.60776	−	2.29612i	0.0562484	−	0.0803311i
$818$	−1.66857	+	6.22720i	−0.0583403	+	0.217729i
$819$	−12.0018	−	21.1018i	−0.419377	−	0.737357i
$820$	0.0876124	+	0.0106654i	0.00305956	+	0.000372451i
$821$	−5.23862	+	14.3930i	−0.182829	+	0.502318i	−0.996921	−	0.0784180i	$-0.975013\pi$
$821$	−5.23862	+	14.3930i	−0.182829	+	0.502318i	0.814092	+	0.580736i	$0.197235\pi$
$822$	10.5184	−	3.78991i	0.366872	−	0.132188i
$823$	34.4798	−	3.01659i	1.20189	−	0.105152i	0.531434	−	0.847100i	$-0.321653\pi$
$823$	34.4798	−	3.01659i	1.20189	−	0.105152i	0.670458	+	0.741948i	$0.266098\pi$
$824$	−11.9994	−	10.0687i	−0.418020	−	0.350761i
$825$	46.7903	−	4.86280i	1.62903	−	0.169301i
$826$	−16.3188	−	5.93955i	−0.567803	−	0.206664i
$827$	−2.29823	−	8.57712i	−0.0799174	−	0.298256i	0.914386	−	0.404844i	$-0.132674\pi$
$827$	−2.29823	−	8.57712i	−0.0799174	−	0.298256i	−0.994303	+	0.106588i	$0.966007\pi$
$828$	−0.231700	+	2.46460i	−0.00805214	+	0.0856509i
$829$	−45.2184	+	26.1068i	−1.57050	+	0.906728i	−0.574391	+	0.818581i	$0.694761\pi$
$829$	−45.2184	+	26.1068i	−1.57050	+	0.906728i	−0.996108	+	0.0881465i	$0.971906\pi$
$830$	−0.0379429	+	0.0246963i	−0.00131702	+	0.000857222i
$831$	2.59448	−	28.5896i	0.0900014	−	0.991762i
$832$	−18.8308	−	8.78095i	−0.652840	−	0.304425i
$833$	−10.9505	+	7.66760i	−0.379411	+	0.265667i
$834$	7.00460	+	26.4839i	0.242550	+	0.917062i
$835$	17.0229	−	5.55057i	0.589102	−	0.192085i
$836$		−	0.308617i		−	0.0106737i
$837$	14.9887	+	2.79315i	0.518086	+	0.0965454i
$838$	21.2666	−	21.2666i	0.734642	−	0.734642i
$839$	11.8964	−	9.98230i	0.410711	−	0.344627i	−0.413905	−	0.910320i	$-0.635836\pi$
$839$	11.8964	−	9.98230i	0.410711	−	0.344627i	0.824616	+	0.565693i	$0.191391\pi$
$840$	14.3348	+	33.9783i	0.494598	+	1.17236i
$841$	−5.03288	+	28.5429i	−0.173547	+	0.984237i
$842$	16.4553	−	35.2886i	0.567088	−	1.21612i
$843$	−3.47488	−	20.0867i	−0.119681	−	0.691824i
$844$	−0.678207	+	0.119586i	−0.0233448	+	0.00411632i
$845$	−12.3367	−	9.27637i	−0.424396	−	0.319117i
$846$	16.3997	+	45.9813i	0.563835	+	1.58087i
$847$	−58.5813	+	15.6968i	−2.01288	+	0.539349i
$848$	−0.376188	−	0.806739i	−0.0129184	−	0.0277035i
$849$	−10.4083	+	7.23791i	−0.357212	+	0.248404i
$850$	−2.61358	−	24.3808i	−0.0896450	−	0.836254i
$851$	29.1790	−	34.7742i	1.00024	−	1.19204i
$852$	−1.64899	−	0.296264i	−0.0564934	−	0.0101498i
$853$	−24.4409	+	11.3970i	−0.836841	+	0.390225i	−0.793303	−	0.608826i	$-0.791641\pi$
$853$	−24.4409	+	11.3970i	−0.836841	+	0.390225i	−0.0435376	+	0.999052i	$0.513863\pi$
$854$	−11.0747	+	19.1820i	−0.378969	+	0.656394i
$855$	−2.37511	+	2.19082i	−0.0812271	+	0.0749244i
$856$	−13.2655	−	22.9765i	−0.453405	−	0.785321i
$857$	19.2394	+	13.4716i	0.657206	+	0.460181i	0.854006	−	0.520263i	$-0.174166\pi$
$857$	19.2394	+	13.4716i	0.657206	+	0.460181i	−0.196800	+	0.980444i	$0.563055\pi$
$858$	−31.4047	+	5.43282i	−1.07214	+	0.185473i
$859$	1.36480	+	3.74977i	0.0465665	+	0.127940i	0.960796	−	0.277257i	$-0.0894252\pi$
$859$	1.36480	+	3.74977i	0.0465665	+	0.127940i	−0.914229	+	0.405197i	$0.867203\pi$
$860$	−1.30243	−	0.811977i	−0.0444126	−	0.0276882i
$861$	1.33876	+	1.34745i	0.0456250	+	0.0459211i
$862$	−47.4058	−	4.14747i	−1.61465	−	0.141263i
$863$	−20.0386	−	20.0386i	−0.682123	−	0.682123i	0.278355	−	0.960478i	$-0.410211\pi$
$863$	−20.0386	−	20.0386i	−0.682123	−	0.682123i	−0.960478	+	0.278355i	$0.910211\pi$
$864$	3.12367	+	1.49366i	0.106269	+	0.0508154i
$865$	12.7972	−	31.7687i	0.435116	−	1.08017i
$866$	4.56305	+	5.43803i	0.155059	+	0.184792i
$867$	−3.67623	+	6.32011i	−0.124851	+	0.214642i
$868$	−0.650552	−	0.929084i	−0.0220812	−	0.0315352i
$869$	51.1922	−	18.6324i	1.73657	−	0.632062i
$870$	−0.211491	−	0.655805i	−0.00717021	−	0.0222339i
$871$	1.83338	+	10.3976i	0.0621216	+	0.352309i
$872$	28.8225	+	7.72295i	0.976051	+	0.261532i
$873$	12.4249	+	1.16808i	0.420519	+	0.0395335i
$874$	−4.00353	−	2.31144i	−0.135421	−	0.0781856i
$875$	2.66935	+	36.5421i	0.0902407	+	1.23535i
$876$	−2.76573	+	0.232958i	−0.0934454	+	0.00787093i
$877$	0.731178	+	8.35740i	0.0246901	+	0.282209i	0.998496	+	0.0548277i	$0.0174609\pi$
$877$	0.731178	+	8.35740i	0.0246901	+	0.282209i	−0.973806	+	0.227382i	$0.926984\pi$
$878$	−3.72908	−	42.6236i	−0.125850	−	1.43848i
$879$	5.86199	−	12.4657i	0.197720	−	0.420456i
$880$	45.4858	−	2.43104i	1.53333	−	0.0819503i
$881$	35.8317	+	20.6875i	1.20720	+	0.696978i	0.962147	−	0.272531i	$-0.0878608\pi$
$881$	35.8317	+	20.6875i	1.20720	+	0.696978i	0.245055	+	0.969509i	$0.421194\pi$
$882$	−4.07953	+	14.8403i	−0.137365	+	0.499700i
$883$	−47.4262	−	12.7078i	−1.59602	−	0.427652i	−0.652181	−	0.758063i	$-0.726146\pi$
$883$	−47.4262	−	12.7078i	−1.59602	−	0.427652i	−0.943837	+	0.330411i	$0.892813\pi$
$884$	−0.180792	−	1.02532i	−0.00608068	−	0.0344852i
$885$	−14.9414	+	0.750100i	−0.502250	+	0.0252143i
$886$	40.0542	−	14.5785i	1.34565	−	0.489776i
$887$	20.6509	+	29.4925i	0.693389	+	0.990261i	0.999270	+	0.0381920i	$0.0121598\pi$
$887$	20.6509	+	29.4925i	0.693389	+	0.990261i	−0.305882	+	0.952069i	$0.598951\pi$
$888$	−16.2363	−	28.3333i	−0.544854	−	0.950804i
$889$	27.6162	+	32.9117i	0.926218	+	1.10382i
$890$	14.5593	+	5.86482i	0.488029	+	0.196589i
$891$	48.2509	−	7.86566i	1.61647	−	0.263509i
$892$	1.63198	+	1.63198i	0.0546427	+	0.0546427i
$893$	5.69183	+	0.497971i	0.190470	+	0.0166640i
$894$	6.95819	−	25.6363i	0.232717	−	0.857407i
$895$	45.9945	−	10.6688i	1.53743	−	0.356620i
$896$	11.4450	+	31.4448i	0.382349	+	1.05050i
$897$	10.3241	−	28.0823i	0.344712	−	0.937640i
$898$	12.2798	+	8.59842i	0.409783	+	0.286933i
$899$	0.190267	+	0.329553i	0.00634577	+	0.0109912i
$900$	1.26728	+	1.23462i	0.0422427	+	0.0411540i
$901$	0.424246	−	0.734815i	0.0141337	−	0.0244802i
$902$	2.26008	−	1.05389i	0.0752523	−	0.0350907i
$903$	−11.1969	−	31.0755i	−0.372608	−	1.03413i
$904$	19.4302	−	23.1560i	0.646239	−	0.770158i
$905$	−6.67423	+	21.9115i	−0.221859	+	0.728364i
$906$	2.33620	+	27.7359i	0.0776149	+	0.921462i
$907$	12.3869	+	26.5638i	0.411300	+	0.882035i	0.997418	+	0.0718100i	$0.0228775\pi$
$907$	12.3869	+	26.5638i	0.411300	+	0.882035i	−0.586118	+	0.810225i	$0.699345\pi$
$908$	−1.13909	+	0.305217i	−0.0378019	+	0.0101290i
$909$	8.26783	−	22.2664i	0.274227	−	0.738531i
$910$	−3.48018	−	24.5781i	−0.115367	−	0.814755i
$911$	6.24634	−	1.10140i	0.206950	−	0.0364909i	−0.0692118	−	0.997602i	$-0.522048\pi$
$911$	6.24634	−	1.10140i	0.206950	−	0.0364909i	0.276162	+	0.961111i	$0.410937\pi$
$912$	−2.40328	+	2.00338i	−0.0795804	+	0.0663385i
$913$	0.0338795	−	0.0726549i	0.00112125	−	0.00240453i
$914$	−6.17252	+	35.0061i	−0.204169	+	1.15790i
$915$	−2.36702	+	18.9335i	−0.0782514	+	0.625923i
$916$	1.14223	−	0.958446i	0.0377404	−	0.0316680i
$917$	−7.52537	+	7.52537i	−0.248510	+	0.248510i
$918$	−4.18125	−	25.1370i	−0.138002	−	0.829646i
$919$		−	32.7220i		−	1.07940i	−0.841858	−	0.539699i	$-0.818538\pi$
$919$		−	32.7220i		−	1.07940i	0.841858	−	0.539699i	$-0.181462\pi$
$920$	−20.5928	+	40.5193i	−0.678924	+	1.33588i
$921$	−11.5463	+	11.4718i	−0.380463	+	0.378010i
$922$	−18.3749	+	12.8663i	−0.605146	+	0.423728i
$923$	18.3525	+	8.55789i	0.604079	+	0.281686i
$924$	−2.97229	−	2.09558i	−0.0977811	−	0.0689395i
$925$	−6.25658	−	31.8352i	−0.205715	−	1.04674i
$926$	−1.41180	+	0.815104i	−0.0463947	+	0.0267860i
$927$	−9.19068	−	13.3081i	−0.301862	−	0.437094i
$928$	0.0223662	+	0.0834718i	0.000734206	+	0.00274010i
$929$	43.8241	+	15.9507i	1.43782	+	0.523324i	0.939162	−	0.343474i	$-0.111604\pi$
$929$	43.8241	+	15.9507i	1.43782	+	0.523324i	0.498659	+	0.866798i	$0.333826\pi$
$930$	13.2032	+	8.29070i	0.432950	+	0.271863i
$931$	1.37988	+	1.15786i	0.0452237	+	0.0379472i
$932$	0.178434	−	0.0156110i	0.00584481	−	0.000511355i
$933$	1.83751	−	10.2275i	0.0601574	−	0.334833i
$934$	−7.49095	+	20.5812i	−0.245111	+	0.673438i
$935$	26.7672	+	34.1874i	0.875381	+	1.11805i
$936$	−16.3983	−	13.9415i	−0.535994	−	0.455693i
$937$	9.38138	−	35.0118i	0.306476	−	1.14379i	−0.625191	−	0.780472i	$-0.714979\pi$
$937$	9.38138	−	35.0118i	0.306476	−	1.14379i	0.931667	−	0.363313i	$-0.118355\pi$
$938$	11.0260	−	15.7468i	0.360012	−	0.514150i
$939$	9.21582	−	13.0714i	0.300747	−	0.426568i
$940$	0.105945	−	3.12668i	0.00345554	−	0.101981i
$941$	−57.6114	−	10.1585i	−1.87808	−	0.331156i	−0.886718	−	0.462312i	$-0.847020\pi$
$941$	−57.6114	−	10.1585i	−1.87808	−	0.331156i	−0.991362	+	0.131155i	$0.958131\pi$
$942$	0.156338	−	48.3325i	0.00509376	−	1.57476i
$943$	−0.204035	+	2.33214i	−0.00664431	+	0.0759448i
$944$	−14.4859			−0.471476
$945$	4.97222	+	37.7508i	0.161746	+	1.22803i
$946$	−43.3653			−1.40993
$947$	−3.10667	+	35.5094i	−0.100953	+	1.15390i	0.761639	+	0.648001i	$0.224395\pi$
$947$	−3.10667	+	35.5094i	−0.100953	+	1.15390i	−0.862592	+	0.505900i	$0.831161\pi$
$948$	1.77108	+	1.03019i	0.0575220	+	0.0334589i
$949$	33.0369	+	5.82530i	1.07242	+	0.189097i
$950$	−3.08214	+	1.19045i	−0.0999978	+	0.0386233i
$951$	−55.2924	−	5.01773i	−1.79298	−	0.162711i
$952$	−19.5236	+	27.8826i	−0.632763	+	0.903680i
$953$	−8.48031	+	31.6489i	−0.274704	+	1.02521i	0.681335	+	0.731971i	$0.261400\pi$
$953$	−8.48031	+	31.6489i	−0.274704	+	1.02521i	−0.956039	+	0.293238i	$0.905267\pi$
$954$	−0.163406	−	0.963116i	−0.00529047	−	0.0311820i
$955$	1.65968	−	13.6337i	0.0537059	−	0.441175i
$956$	0.807147	−	2.21762i	0.0261050	−	0.0717229i
$957$	0.932155	+	0.787323i	0.0301323	+	0.0254505i
$958$	10.1666	−	0.889462i	0.328468	−	0.0287372i
$959$	−11.8121	−	9.91155i	−0.381434	−	0.320061i
$960$	22.1734	+	23.8831i	0.715642	+	0.770824i
$961$	21.0399	+	7.65791i	0.678708	+	0.247029i
$962$	5.68909	+	21.2320i	0.183424	+	0.684546i
$963$	−6.91857	−	26.5052i	−0.222948	−	0.854117i
$964$	−1.07769	+	0.622203i	−0.0347100	+	0.0200398i
$965$	2.93522	−	13.8798i	0.0944881	−	0.446806i
$966$	−49.4463	+	22.8628i	−1.59091	+	0.735598i
$967$	20.7183	+	9.66112i	0.666257	+	0.310681i	0.726162	−	0.687523i	$-0.241302\pi$
$967$	20.7183	+	9.66112i	0.666257	+	0.310681i	−0.0599053	+	0.998204i	$0.519080\pi$
$968$	−44.0471	+	30.8421i	−1.41573	+	0.991302i
$969$	−2.87826	−	0.781215i	−0.0924631	−	0.0250962i
$970$	11.3761	+	5.78158i	0.365264	+	0.185635i
$971$		−	15.4621i		−	0.496202i	−0.968734	−	0.248101i	$-0.920193\pi$
$971$		−	15.4621i		−	0.496202i	0.968734	−	0.248101i	$-0.0798065\pi$
$972$	1.38921	+	1.20450i	0.0445588	+	0.0386343i
$973$	26.7157	−	26.7157i	0.856467	−	0.856467i
$974$	19.7146	−	16.5425i	0.631697	−	0.530057i
$975$	−10.9924	−	18.3427i	−0.352038	−	0.587437i
$976$	−3.20831	+	18.1952i	−0.102696	+	0.582416i
$977$	12.6029	−	27.0270i	0.403203	−	0.864672i	−0.594941	−	0.803770i	$-0.702824\pi$
$977$	12.6029	−	27.0270i	0.403203	−	0.864672i	0.998144	−	0.0609021i	$-0.0193977\pi$
$978$	−21.7407	−	7.99270i	−0.695191	−	0.255578i
$979$	−27.3717	+	4.82638i	−0.874805	+	0.154252i
$980$	0.592757	−	0.788312i	0.0189349	−	0.0251817i
$981$	26.5811	+	15.5768i	0.848670	+	0.497328i
$982$	47.8069	−	12.8098i	1.52558	−	0.408777i
$983$	−8.58979	−	18.4209i	−0.273972	−	0.587535i	0.720391	−	0.693569i	$-0.243963\pi$
$983$	−8.58979	−	18.4209i	−0.273972	−	0.587535i	−0.994363	+	0.106034i	$0.966185\pi$
$984$	1.52400	+	0.716662i	0.0485832	+	0.0228463i
$985$	−0.358359	−	0.672295i	−0.0114183	−	0.0214211i
$986$	0.408813	−	0.487204i	0.0130193	−	0.0155157i
$987$	43.4448	−	51.4366i	1.38286	−	1.63725i
$988$	−0.127146	+	0.0592891i	−0.00404505	+	0.00188624i
$989$	20.3552	−	35.2562i	0.647256	−	1.12108i
$990$	48.8400	+	10.6590i	1.55224	+	0.338764i
$991$	−13.3395	−	23.1047i	−0.423743	−	0.733944i	0.572559	−	0.819863i	$-0.305951\pi$
$991$	−13.3395	−	23.1047i	−0.423743	−	0.733944i	−0.996302	+	0.0859191i	$0.972617\pi$
$992$	−1.60161	−	1.12146i	−0.0508513	−	0.0356065i
$993$	34.1538	+	40.9714i	1.08384	+	1.30019i
$994$	−12.6100	−	34.6457i	−0.399965	−	1.09890i
$995$	10.3238	+	44.5072i	0.327288	+	1.41097i
$996$	0.00291481		0.000770925i	9.23594e−5		2.44277e-5i
$997$	−8.18529	−	0.716120i	−0.259231	−	0.0226798i	−0.0432005	−	0.999066i	$-0.513755\pi$
$997$	−8.18529	−	0.716120i	−0.259231	−	0.0226798i	−0.216030	+	0.976387i	$0.569311\pi$
$998$	31.1175	+	31.1175i	0.985007	+	0.985007i
$999$	−8.41016	−	32.6513i	−0.266086	−	1.03304i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.q.a.32.12	✓	192
3.2	odd	2		405.2.r.a.287.5		192
5.2	odd	4		675.2.ba.b.518.12		192
5.3	odd	4	inner	135.2.q.a.113.5	yes	192
5.4	even	2		675.2.ba.b.32.5		192
15.8	even	4		405.2.r.a.368.12		192
27.11	odd	18	inner	135.2.q.a.92.5	yes	192
27.16	even	9		405.2.r.a.197.12		192
135.38	even	36	inner	135.2.q.a.38.12	yes	192
135.43	odd	36		405.2.r.a.278.5		192
135.92	even	36		675.2.ba.b.443.5		192
135.119	odd	18		675.2.ba.b.632.12		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.12	✓	192	1.1	even	1	trivial
135.2.q.a.38.12	yes	192	135.38	even	36	inner
135.2.q.a.92.5	yes	192	27.11	odd	18	inner
135.2.q.a.113.5	yes	192	5.3	odd	4	inner
405.2.r.a.197.12		192	27.16	even	9
405.2.r.a.278.5		192	135.43	odd	36
405.2.r.a.287.5		192	3.2	odd	2
405.2.r.a.368.12		192	15.8	even	4
675.2.ba.b.32.5		192	5.4	even	2
675.2.ba.b.443.5		192	135.92	even	36
675.2.ba.b.518.12		192	5.2	odd	4
675.2.ba.b.632.12		192	135.119	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.q (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.119567 - 1.36666i) q^{2} +(-1.50279 + 0.861169i) q^{3} +(0.116159 + 0.0204819i) q^{4} +(1.52669 + 1.63378i) q^{5} +(0.997239 + 2.15677i) q^{6} +(1.87969 - 2.68447i) q^{7} +(0.752017 - 2.80657i) q^{8} +(1.51678 - 2.58832i) q^{9} +O(q^{10})\)	\(q+(0.119567 - 1.36666i) q^{2} +(-1.50279 + 0.861169i) q^{3} +(0.116159 + 0.0204819i) q^{4} +(1.52669 + 1.63378i) q^{5} +(0.997239 + 2.15677i) q^{6} +(1.87969 - 2.68447i) q^{7} +(0.752017 - 2.80657i) q^{8} +(1.51678 - 2.58832i) q^{9} +(2.41535 - 1.89111i) q^{10} +(-1.85785 + 5.10439i) q^{11} +(-0.192201 + 0.0692523i) q^{12} +(2.45985 - 0.215209i) q^{13} +(-3.44400 - 2.88986i) q^{14} +(-3.70125 - 1.14049i) q^{15} +(-3.52402 - 1.28264i) q^{16} +(-0.925208 - 3.45292i) q^{17} +(-3.35599 - 2.38239i) q^{18} +(-0.417150 + 0.240842i) q^{19} +(0.143875 + 0.221047i) q^{20} +(-0.512998 + 5.65293i) q^{21} +(6.75381 + 3.14935i) q^{22} +(-5.73060 + 4.01261i) q^{23} +(1.28680 + 4.86530i) q^{24} +(-0.338453 + 4.98853i) q^{25} -3.38750i q^{26} +(-0.0504220 + 5.19591i) q^{27} +(0.273325 - 0.273325i) q^{28} +(-0.0993465 + 0.0833616i) q^{29} +(-2.00121 + 4.92198i) q^{30} +(0.509526 - 2.88966i) q^{31} +(0.281608 - 0.603911i) q^{32} +(-1.60378 - 9.27076i) q^{33} +(-4.82959 + 0.851587i) q^{34} +(7.25552 - 1.02736i) q^{35} +(0.229201 - 0.269590i) q^{36} +(-6.26774 + 1.67943i) q^{37} +(0.279271 + 0.598898i) q^{38} +(-3.51131 + 2.44176i) q^{39} +(5.73340 - 3.05612i) q^{40} +(0.215101 - 0.256347i) q^{41} +(7.66428 + 1.37700i) q^{42} +(-5.27405 + 2.45933i) q^{43} +(-0.320353 + 0.554867i) q^{44} +(6.54438 - 1.47348i) q^{45} +(4.79867 + 8.31155i) q^{46} +(-9.71652 - 6.80358i) q^{47} +(6.40045 - 1.10724i) q^{48} +(-1.27902 - 3.51408i) q^{49} +(6.77715 + 1.05901i) q^{50} +(4.36395 + 4.39227i) q^{51} +(0.290141 + 0.0253840i) q^{52} +(0.167838 + 0.167838i) q^{53} +(7.09500 + 0.690169i) q^{54} +(-11.1758 + 4.75750i) q^{55} +(-6.12058 - 7.29423i) q^{56} +(0.419485 - 0.721172i) q^{57} +(0.102048 + 0.145740i) q^{58} +(3.62976 - 1.32113i) q^{59} +(-0.406574 - 0.208287i) q^{60} +(-0.855508 - 4.85182i) q^{61} +(-3.88826 - 1.04186i) q^{62} +(-4.09720 - 8.93697i) q^{63} +(-7.28718 - 4.20726i) q^{64} +(4.10702 + 3.69029i) q^{65} +(-12.8617 + 1.08334i) q^{66} +(0.372661 + 4.25953i) q^{67} +(-0.0367485 - 0.420038i) q^{68} +(5.15637 - 10.9651i) q^{69} +(-0.536526 - 10.0386i) q^{70} +(7.10207 + 4.10038i) q^{71} +(-6.12364 - 6.20339i) q^{72} +(13.1228 + 3.51625i) q^{73} +(1.54580 + 8.76665i) q^{74} +(-3.78734 - 7.78820i) q^{75} +(-0.0533886 + 0.0194318i) q^{76} +(10.2104 + 14.5820i) q^{77} +(2.91721 + 5.09072i) q^{78} +(-6.44655 - 7.68270i) q^{79} +(-3.28453 - 7.71565i) q^{80} +(-4.39878 - 7.85180i) q^{81} +(-0.324619 - 0.324619i) q^{82} +(-0.0147020 - 0.00128626i) q^{83} +(-0.175372 + 0.646131i) q^{84} +(4.22880 - 6.78312i) q^{85} +(2.73046 + 7.50188i) q^{86} +(0.0775088 - 0.210829i) q^{87} +(12.9287 + 9.05275i) q^{88} +(2.55837 + 4.43123i) q^{89} +(-1.23125 - 9.12010i) q^{90} +(4.04602 - 7.00791i) q^{91} +(-0.747846 + 0.348726i) q^{92} +(1.72278 + 4.78135i) q^{93} +(-10.4599 + 12.4657i) q^{94} +(-1.03034 - 0.313840i) q^{95} +(0.0968703 + 1.15007i) q^{96} +(1.75805 + 3.77015i) q^{97} +(-4.95547 + 1.32781i) q^{98} +(10.3938 + 12.5509i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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