LMFDB - Embedded newform 576.2.bm.a.517.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(13,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(48))

chi = DirichletCharacter(H, H._module([0, 45, 16]))

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

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

chi := DirichletCharacter("576.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.bm (of order $48$, degree $16$, 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:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$1504$
Relative dimension:	$94$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			517.18
Character	$\chi$	$=$	576.517
Dual form			576.2.bm.a.205.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.17666 + 0.784525i) q^{2} +(-1.47544 + 0.907238i) q^{3} +(0.769042 - 1.84623i) q^{4} +(-2.36898 + 2.70130i) q^{5} +(1.02433 - 2.22503i) q^{6} +(-4.85600 + 0.639304i) q^{7} +(0.543516 + 2.77571i) q^{8} +(1.35384 - 2.67715i) q^{9} +O(q^{10})$	\(q+(-1.17666 + 0.784525i) q^{2} +(-1.47544 + 0.907238i) q^{3} +(0.769042 - 1.84623i) q^{4} +(-2.36898 + 2.70130i) q^{5} +(1.02433 - 2.22503i) q^{6} +(-4.85600 + 0.639304i) q^{7} +(0.543516 + 2.77571i) q^{8} +(1.35384 - 2.67715i) q^{9} +(0.668237 - 5.03703i) q^{10} +(-2.39238 + 4.85126i) q^{11} +(0.540298 + 3.42171i) q^{12} +(-1.38803 + 4.08900i) q^{13} +(5.21229 - 4.56189i) q^{14} +(1.04456 - 6.13484i) q^{15} +(-2.81715 - 2.83966i) q^{16} +(2.53276 - 2.53276i) q^{17} +(0.507286 + 4.21220i) q^{18} +(-0.255110 - 1.28253i) q^{19} +(3.16539 + 6.45110i) q^{20} +(6.58473 - 5.34880i) q^{21} +(-0.990927 - 7.58515i) q^{22} +(-0.535956 + 4.07099i) q^{23} +(-3.32016 - 3.60230i) q^{24} +(-1.03235 - 7.84144i) q^{25} +(-1.57469 - 5.90029i) q^{26} +(0.431307 + 5.17822i) q^{27} +(-2.55416 + 9.45696i) q^{28} +(-1.21586 - 0.0796918i) q^{29} +(3.58384 + 8.03808i) q^{30} +(0.338001 + 0.195145i) q^{31} +(5.54260 + 1.13118i) q^{32} +(-0.871444 - 9.32820i) q^{33} +(-0.993175 + 4.96719i) q^{34} +(9.77681 - 14.6320i) q^{35} +(-3.90148 - 4.55834i) q^{36} +(-0.208376 + 1.04758i) q^{37} +(1.30635 + 1.30895i) q^{38} +(-1.66175 - 7.29234i) q^{39} +(-8.78563 - 5.10741i) q^{40} +(-0.197381 + 1.49926i) q^{41} +(-3.55170 + 11.4596i) q^{42} +(-1.18510 - 0.584427i) q^{43} +(7.11672 + 8.14771i) q^{44} +(4.02458 + 9.99924i) q^{45} +(-2.56315 - 5.21062i) q^{46} +(1.28250 + 0.343646i) q^{47} +(6.73278 + 1.63392i) q^{48} +(16.4105 - 4.39719i) q^{49} +(7.36652 + 8.41679i) q^{50} +(-1.43911 + 6.03474i) q^{51} +(6.48179 + 5.70724i) q^{52} +(1.84574 + 2.76234i) q^{53} +(-4.56994 - 5.75462i) q^{54} +(-7.43724 - 17.9551i) q^{55} +(-4.41384 - 13.1314i) q^{56} +(1.53996 + 1.66084i) q^{57} +(1.49317 - 0.860103i) q^{58} +(6.59505 - 7.52021i) q^{59} +(-10.5230 - 6.64645i) q^{60} +(0.245506 - 3.74569i) q^{61} +(-0.550807 + 0.0355514i) q^{62} +(-4.86272 + 13.8657i) q^{63} +(-7.40918 + 3.01729i) q^{64} +(-7.75742 - 13.4362i) q^{65} +(8.34359 + 10.2924i) q^{66} +(-2.51564 + 1.24057i) q^{67} +(-2.72826 - 6.62385i) q^{68} +(-2.90259 - 6.49273i) q^{69} +(-0.0247617 + 24.8870i) q^{70} +(-5.41313 + 13.0685i) q^{71} +(8.16683 + 2.30279i) q^{72} +(5.64462 + 13.6273i) q^{73} +(-0.576664 - 1.39612i) q^{74} +(8.63722 + 10.6330i) q^{75} +(-2.56403 - 0.515323i) q^{76} +(8.51595 - 25.0872i) q^{77} +(7.67633 + 7.27690i) q^{78} +(1.16935 - 4.36408i) q^{79} +(14.3446 - 0.882872i) q^{80} +(-5.33425 - 7.24885i) q^{81} +(-0.943954 - 1.91896i) q^{82} +(-2.73123 + 2.39522i) q^{83} +(-4.81120 - 16.2704i) q^{84} +(0.841695 + 12.8418i) q^{85} +(1.85295 - 0.242071i) q^{86} +(1.86623 - 0.985496i) q^{87} +(-14.7660 - 4.00382i) q^{88} +(-2.03872 - 0.844465i) q^{89} +(-12.5802 - 8.60829i) q^{90} +(4.12615 - 20.7436i) q^{91} +(7.10382 + 4.12026i) q^{92} +(-0.675742 + 0.0187230i) q^{93} +(-1.77867 + 0.601802i) q^{94} +(4.06884 + 2.34915i) q^{95} +(-9.20402 + 3.35947i) q^{96} +(8.16085 - 4.71167i) q^{97} +(-15.8599 + 18.0485i) q^{98} +(9.74866 + 12.9726i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1504 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{5} - 16 q^{6} - 8 q^{7} - 32 q^{8} - 16 q^{9}+O(q^{10}) $ 1504 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^5 - 16 * q^6 - 8 * q^7 - 32 * q^8 - 16 * q^9	\( 1504 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{5} - 16 q^{6} - 8 q^{7} - 32 q^{8} - 16 q^{9} - 32 q^{10} - 8 q^{11} - 16 q^{12} - 8 q^{13} - 8 q^{14} - 16 q^{15} - 8 q^{16} - 32 q^{17} - 16 q^{18} - 32 q^{19} - 8 q^{20} - 16 q^{21} - 8 q^{22} - 8 q^{23} + 64 q^{24} - 8 q^{25} - 32 q^{26} - 16 q^{27} - 32 q^{28} - 8 q^{29} - 96 q^{30} - 8 q^{32} - 8 q^{34} - 32 q^{35} - 96 q^{36} - 32 q^{37} - 8 q^{38} - 16 q^{39} - 8 q^{40} - 8 q^{41} + 64 q^{42} - 8 q^{43} - 32 q^{44} - 16 q^{45} - 32 q^{46} - 8 q^{47} - 16 q^{48} - 8 q^{49} - 8 q^{50} - 16 q^{51} - 8 q^{52} - 32 q^{53} - 16 q^{54} - 32 q^{55} - 8 q^{56} - 16 q^{57} - 80 q^{58} - 8 q^{59} - 16 q^{60} - 8 q^{61} - 64 q^{62} - 32 q^{63} - 32 q^{64} - 16 q^{65} - 32 q^{66} - 8 q^{67} - 8 q^{68} - 16 q^{69} - 8 q^{70} - 32 q^{71} - 16 q^{72} - 32 q^{73} - 8 q^{74} - 16 q^{75} + 40 q^{76} - 8 q^{77} - 40 q^{78} - 8 q^{79} - 160 q^{80} - 16 q^{81} - 32 q^{82} - 8 q^{83} - 128 q^{84} - 8 q^{85} - 216 q^{86} - 16 q^{87} - 8 q^{88} - 32 q^{89} - 160 q^{90} - 32 q^{91} + 144 q^{92} - 40 q^{93} - 8 q^{94} - 152 q^{96} - 304 q^{98} - 16 q^{99}+O(q^{100}) \) 1504 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^5 - 16 * q^6 - 8 * q^7 - 32 * q^8 - 16 * q^9 - 32 * q^10 - 8 * q^11 - 16 * q^12 - 8 * q^13 - 8 * q^14 - 16 * q^15 - 8 * q^16 - 32 * q^17 - 16 * q^18 - 32 * q^19 - 8 * q^20 - 16 * q^21 - 8 * q^22 - 8 * q^23 + 64 * q^24 - 8 * q^25 - 32 * q^26 - 16 * q^27 - 32 * q^28 - 8 * q^29 - 96 * q^30 - 8 * q^32 - 8 * q^34 - 32 * q^35 - 96 * q^36 - 32 * q^37 - 8 * q^38 - 16 * q^39 - 8 * q^40 - 8 * q^41 + 64 * q^42 - 8 * q^43 - 32 * q^44 - 16 * q^45 - 32 * q^46 - 8 * q^47 - 16 * q^48 - 8 * q^49 - 8 * q^50 - 16 * q^51 - 8 * q^52 - 32 * q^53 - 16 * q^54 - 32 * q^55 - 8 * q^56 - 16 * q^57 - 80 * q^58 - 8 * q^59 - 16 * q^60 - 8 * q^61 - 64 * q^62 - 32 * q^63 - 32 * q^64 - 16 * q^65 - 32 * q^66 - 8 * q^67 - 8 * q^68 - 16 * q^69 - 8 * q^70 - 32 * q^71 - 16 * q^72 - 32 * q^73 - 8 * q^74 - 16 * q^75 + 40 * q^76 - 8 * q^77 - 40 * q^78 - 8 * q^79 - 160 * q^80 - 16 * q^81 - 32 * q^82 - 8 * q^83 - 128 * q^84 - 8 * q^85 - 216 * q^86 - 16 * q^87 - 8 * q^88 - 32 * q^89 - 160 * q^90 - 32 * q^91 + 144 * q^92 - 40 * q^93 - 8 * q^94 - 152 * q^96 - 304 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{16}\right)$

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 $

$2$	−1.17666	+	0.784525i	−0.832022	+	0.554743i
$2$	−1.17666	+	0.784525i	−0.832022	+	0.554743i
$3$	−1.47544	+	0.907238i	−0.851845	+	0.523794i
$3$	−1.47544	+	0.907238i	−0.851845	+	0.523794i
$4$	0.769042	−	1.84623i	0.384521	−	0.923116i
$5$	−2.36898	+	2.70130i	−1.05944	+	1.20806i	−0.0820471	+	0.996628i	$0.526146\pi$
$5$	−2.36898	+	2.70130i	−1.05944	+	1.20806i	−0.977393	+	0.211431i	$0.932188\pi$
$6$	1.02433	−	2.22503i	0.418183	−	0.908363i
$7$	−4.85600	+	0.639304i	−1.83540	+	0.241634i	−0.967097	−	0.254408i	$-0.918119\pi$
$7$	−4.85600	+	0.639304i	−1.83540	+	0.241634i	−0.868298	+	0.496042i	$0.834786\pi$
$8$	0.543516	+	2.77571i	0.192162	+	0.981363i
$9$	1.35384	−	2.67715i	0.451279	−	0.892383i
$10$	0.668237	−	5.03703i	0.211315	−	1.59285i
$11$	−2.39238	+	4.85126i	−0.721329	+	1.46271i	0.158469	+	0.987364i	$0.449344\pi$
$11$	−2.39238	+	4.85126i	−0.721329	+	1.46271i	−0.879798	+	0.475347i	$0.842323\pi$
$12$	0.540298	+	3.42171i	0.155971	+	0.987762i
$13$	−1.38803	+	4.08900i	−0.384970	+	1.13408i	0.565895	+	0.824478i	$0.308531\pi$
$13$	−1.38803	+	4.08900i	−0.384970	+	1.13408i	−0.950865	+	0.309607i	$0.899802\pi$
$14$	5.21229	−	4.56189i	1.39304	−	1.21922i
$15$	1.04456	−	6.13484i	0.269704	−	1.58401i
$16$	−2.81715	−	2.83966i	−0.704287	−	0.709915i
$17$	2.53276	−	2.53276i	0.614283	−	0.614283i	−0.329776	−	0.944059i	$-0.606973\pi$
$17$	2.53276	−	2.53276i	0.614283	−	0.614283i	0.944059	+	0.329776i	$0.106973\pi$
$18$	0.507286	+	4.21220i	0.119569	+	0.992826i
$19$	−0.255110	−	1.28253i	−0.0585263	−	0.294231i	0.940426	−	0.339999i	$-0.110427\pi$
$19$	−0.255110	−	1.28253i	−0.0585263	−	0.294231i	−0.998952	+	0.0457674i	$0.985427\pi$
$20$	3.16539	+	6.45110i	0.707802	+	1.44251i
$21$	6.58473	−	5.34880i	1.43691	−	1.16720i
$22$	−0.990927	−	7.58515i	−0.211266	−	1.61716i
$23$	−0.535956	+	4.07099i	−0.111754	+	0.848859i	0.840126	+	0.542391i	$0.182481\pi$
$23$	−0.535956	+	4.07099i	−0.111754	+	0.848859i	−0.951881	+	0.306469i	$0.900853\pi$
$24$	−3.32016	−	3.60230i	−0.677725	−	0.735316i
$25$	−1.03235	−	7.84144i	−0.206469	−	1.56829i
$26$	−1.57469	−	5.90029i	−0.308822	−	1.15714i
$27$	0.431307	+	5.17822i	0.0830050	+	0.996549i
$28$	−2.55416	+	9.45696i	−0.482692	+	1.78720i
$29$	−1.21586	−	0.0796918i	−0.225780	−	0.0147984i	−0.0479067	−	0.998852i	$-0.515255\pi$
$29$	−1.21586	−	0.0796918i	−0.225780	−	0.0147984i	−0.177873	+	0.984053i	$0.556922\pi$
$30$	3.58384	+	8.03808i	0.654317	+	1.46755i
$31$	0.338001	+	0.195145i	0.0607067	+	0.0350490i	0.530046	−	0.847969i	$-0.322175\pi$
$31$	0.338001	+	0.195145i	0.0607067	+	0.0350490i	−0.469339	+	0.883018i	$0.655508\pi$
$32$	5.54260	+	1.13118i	0.979803	+	0.199967i
$33$	−0.871444	−	9.32820i	−0.151699	−	1.62383i
$34$	−0.993175	+	4.96719i	−0.170328	+	0.851867i
$35$	9.77681	−	14.6320i	1.65258	−	2.47326i
$36$	−3.90148	−	4.55834i	−0.650247	−	0.759723i
$37$	−0.208376	+	1.04758i	−0.0342569	+	0.172221i	−0.994126	−	0.108226i	$-0.965483\pi$
$37$	−0.208376	+	1.04758i	−0.0342569	+	0.172221i	0.959869	+	0.280447i	$0.0904828\pi$
$38$	1.30635	+	1.30895i	0.211918	+	0.212340i
$39$	−1.66175	−	7.29234i	−0.266092	−	1.16771i
$40$	−8.78563	−	5.10741i	−1.38913	−	0.807552i
$41$	−0.197381	+	1.49926i	−0.0308257	+	0.234145i	−0.999921	−	0.0125407i	$-0.996008\pi$
$41$	−0.197381	+	1.49926i	−0.0308257	+	0.234145i	0.969096	+	0.246685i	$0.0793414\pi$
$42$	−3.55170	+	11.4596i	−0.548039	+	1.76825i
$43$	−1.18510	−	0.584427i	−0.180726	−	0.0891243i	0.349675	−	0.936871i	$-0.386292\pi$
$43$	−1.18510	−	0.584427i	−0.180726	−	0.0891243i	−0.530401	+	0.847747i	$0.677959\pi$
$44$	7.11672	+	8.14771i	1.07289	+	1.22831i
$45$	4.02458	+	9.99924i	0.599948	+	1.49060i
$46$	−2.56315	−	5.21062i	−0.377916	−	0.768265i
$47$	1.28250	+	0.343646i	0.187072	+	0.0501259i	0.351139	−	0.936323i	$-0.385795\pi$
$47$	1.28250	+	0.343646i	0.187072	+	0.0501259i	−0.164067	+	0.986449i	$0.552461\pi$
$48$	6.73278	+	1.63392i	0.971793	+	0.235836i
$49$	16.4105	−	4.39719i	2.34436	−	0.628170i
$50$	7.36652	+	8.41679i	1.04178	+	1.19031i
$51$	−1.43911	+	6.03474i	−0.201516	+	0.845032i
$52$	6.48179	+	5.70724i	0.898863	+	0.791451i
$53$	1.84574	+	2.76234i	0.253531	+	0.379436i	0.936302	−	0.351197i	$-0.114225\pi$
$53$	1.84574	+	2.76234i	0.253531	+	0.379436i	−0.682771	+	0.730633i	$0.739225\pi$
$54$	−4.56994	−	5.75462i	−0.621890	−	0.783104i
$55$	−7.43724	−	17.9551i	−1.00284	−	2.42106i
$56$	−4.41384	−	13.1314i	−0.589824	−	1.75476i
$57$	1.53996	+	1.66084i	0.203972	+	0.219984i
$58$	1.49317	−	0.860103i	0.196063	−	0.112937i
$59$	6.59505	−	7.52021i	0.858602	−	0.979048i	−0.141338	−	0.989961i	$-0.545140\pi$
$59$	6.59505	−	7.52021i	0.858602	−	0.979048i	0.999940	+	0.0109131i	$0.00347381\pi$
$60$	−10.5230	−	6.64645i	−1.35852	−	0.858052i
$61$	0.245506	−	3.74569i	0.0314338	−	0.479587i	−0.952902	−	0.303280i	$-0.901918\pi$
$61$	0.245506	−	3.74569i	0.0314338	−	0.479587i	0.984335	−	0.176307i	$-0.0564151\pi$
$62$	−0.550807	+	0.0355514i	−0.0699525	+	0.00451503i
$63$	−4.86272	+	13.8657i	−0.612646	+	1.74692i
$64$	−7.40918	+	3.01729i	−0.926148	+	0.377161i
$65$	−7.75742	−	13.4362i	−0.962190	−	1.66656i
$66$	8.34359	+	10.2924i	1.02703	+	1.26691i
$67$	−2.51564	+	1.24057i	−0.307334	+	0.151560i	−0.589415	−	0.807830i	$-0.700642\pi$
$67$	−2.51564	+	1.24057i	−0.307334	+	0.151560i	0.282082	+	0.959390i	$0.408975\pi$
$68$	−2.72826	−	6.62385i	−0.330850	−	0.803260i
$69$	−2.90259	−	6.49273i	−0.349430	−	0.781633i
$70$	−0.0247617	+	24.8870i	−0.00295959	+	2.97457i
$71$	−5.41313	+	13.0685i	−0.642421	+	1.55094i	0.180984	+	0.983486i	$0.442072\pi$
$71$	−5.41313	+	13.0685i	−0.642421	+	1.55094i	−0.823404	+	0.567455i	$0.807928\pi$
$72$	8.16683	+	2.30279i	0.962470	+	0.271387i
$73$	5.64462	+	13.6273i	0.660653	+	1.59496i	0.796782	+	0.604267i	$0.206534\pi$
$73$	5.64462	+	13.6273i	0.660653	+	1.59496i	−0.136128	+	0.990691i	$0.543466\pi$
$74$	−0.576664	−	1.39612i	−0.0670358	−	0.162295i
$75$	8.63722	+	10.6330i	0.997340	+	1.22779i
$76$	−2.56403	−	0.515323i	−0.294114	−	0.0591117i
$77$	8.51595	−	25.0872i	0.970483	−	2.85895i
$78$	7.67633	+	7.27690i	0.869173	+	0.823947i
$79$	1.16935	−	4.36408i	0.131562	−	0.490997i	−0.868426	−	0.495819i	$-0.834868\pi$
$79$	1.16935	−	4.36408i	0.131562	−	0.490997i	0.999988	+	0.00482154i	$0.00153475\pi$
$80$	14.3446	−	0.882872i	1.60377	−	0.0987081i
$81$	−5.33425	−	7.24885i	−0.592694	−	0.805428i
$82$	−0.943954	−	1.91896i	−0.104242	−	0.211914i
$83$	−2.73123	+	2.39522i	−0.299791	+	0.262910i	−0.796004	−	0.605291i	$-0.793057\pi$
$83$	−2.73123	+	2.39522i	−0.299791	+	0.262910i	0.496213	+	0.868201i	$0.334723\pi$
$84$	−4.81120	−	16.2704i	−0.524945	−	1.77525i
$85$	0.841695	+	12.8418i	0.0912947	+	1.39289i
$86$	1.85295	−	0.242071i	0.199809	−	0.0261032i
$87$	1.86623	−	0.985496i	0.200081	−	0.105656i
$88$	−14.7660	−	4.00382i	−1.57406	−	0.426809i
$89$	−2.03872	−	0.844465i	−0.216104	−	0.0895131i	0.272005	−	0.962296i	$-0.412313\pi$
$89$	−2.03872	−	0.844465i	−0.216104	−	0.0895131i	−0.488109	+	0.872783i	$0.662313\pi$
$90$	−12.5802	−	8.60829i	−1.32607	−	0.907394i
$91$	4.12615	−	20.7436i	0.432538	−	2.17452i
$92$	7.10382	+	4.12026i	0.740624	+	0.429567i
$93$	−0.675742	+	0.0187230i	−0.0700712	+	0.00194148i
$94$	−1.77867	+	0.601802i	−0.183455	+	0.0620712i
$95$	4.06884	+	2.34915i	0.417454	+	0.241017i
$96$	−9.20402	+	3.35947i	−0.939381	+	0.342874i
$97$	8.16085	−	4.71167i	0.828609	−	0.478398i	−0.0247671	−	0.999693i	$-0.507884\pi$
$97$	8.16085	−	4.71167i	0.828609	−	0.478398i	0.853376	+	0.521296i	$0.174551\pi$
$98$	−15.8599	+	18.0485i	−1.60209	+	1.82317i
$99$	9.74866	+	12.9726i	0.979777	+	1.30379i
$100$	−15.2710	−	4.12445i	−1.52710	−	0.412445i
$101$	6.48052	−	2.19984i	0.644835	−	0.218892i	0.0201846	−	0.999796i	$-0.493575\pi$
$101$	6.48052	−	2.19984i	0.644835	−	0.218892i	0.624651	+	0.780904i	$0.285241\pi$
$102$	−3.04106	−	8.22983i	−0.301110	−	0.814875i
$103$	1.20258	−	0.922770i	0.118494	−	0.0909233i	−0.547815	−	0.836600i	$-0.684540\pi$
$103$	1.20258	−	0.922770i	0.118494	−	0.0909233i	0.666308	+	0.745676i	$0.267873\pi$
$104$	−12.1043	−	1.63033i	−1.18693	−	0.159867i
$105$	−1.15035	+	30.4586i	−0.112262	+	2.97245i
$106$	−4.33892	−	1.80230i	−0.421433	−	0.175055i
$107$	−9.80136	+	6.54906i	−0.947533	+	0.633121i	−0.930327	−	0.366731i	$-0.880477\pi$
$107$	−9.80136	+	6.54906i	−0.947533	+	0.633121i	−0.0172058	+	0.999852i	$0.505477\pi$
$108$	9.89189	+	3.18598i	0.951848	+	0.306571i
$109$	0.113874	+	0.572484i	0.0109072	+	0.0548340i	0.985856	−	0.167597i	$-0.0536008\pi$
$109$	0.113874	+	0.572484i	0.0109072	+	0.0548340i	−0.974948	+	0.222431i	$0.928601\pi$
$110$	22.8373	+	15.2923i	2.17745	+	1.45806i
$111$	−0.642957	−	1.73469i	−0.0610268	−	0.164649i
$112$	15.4955	+	11.9884i	1.46419	+	1.13280i
$113$	−18.2269	+	4.88387i	−1.71464	+	0.459436i	−0.976554	−	0.215272i	$-0.930936\pi$
$113$	−18.2269	+	4.88387i	−1.71464	+	0.459436i	−0.738085	+	0.674708i	$0.764270\pi$
$114$	−3.11497	−	0.746108i	−0.291744	−	0.0698794i
$115$	−9.72730	−	11.0919i	−0.907076	−	1.03432i
$116$	−1.08218	+	2.18348i	−0.100478	+	0.202731i
$117$	9.06769	+	9.25180i	0.838309	+	0.855329i
$118$	−1.86032	+	14.0227i	−0.171256	+	1.29089i
$119$	−10.6799	+	13.9183i	−0.979021	+	1.27588i
$120$	17.5963	−	0.434986i	1.60631	−	0.0397086i
$121$	−11.1149	−	14.4852i	−1.01045	−	1.31684i
$122$	2.64971	+	4.60000i	0.239894	+	0.416464i
$123$	−1.06896	−	2.39113i	−0.0963848	−	0.215601i
$124$	0.620219	−	0.473953i	0.0556973	−	0.0425622i
$125$	8.69069	+	5.80693i	0.777319	+	0.519388i
$126$	−5.15626	−	20.1301i	−0.459356	−	1.79334i
$127$	−9.58124			−0.850198			−0.425099	−	0.905147i	$-0.639761\pi$
$127$	−9.58124			−0.850198			−0.425099	+	0.905147i	$0.639761\pi$
$128$	6.35092	−	9.36300i	0.561348	−	0.827580i
$129$	2.27876	−	0.212883i	0.200633	−	0.0187433i
$130$	19.6689	+	9.72396i	1.72508	+	0.852848i
$131$	−14.9922	+	7.39336i	−1.30988	+	0.645960i	−0.957103	−	0.289748i	$-0.906429\pi$
$131$	−14.9922	+	7.39336i	−1.30988	+	0.645960i	−0.352775	+	0.935708i	$0.614762\pi$
$132$	−17.8922	−	5.56489i	−1.55732	−	0.484361i
$133$	2.05874	+	6.06485i	0.178515	+	0.525889i
$134$	1.98678	−	3.43331i	0.171632	−	0.296593i
$135$	−15.0097	−	11.1020i	−1.29183	−	0.955509i
$136$	8.40680	+	5.65361i	0.720877	+	0.484793i
$137$	−8.14499	+	10.6148i	−0.695874	+	0.906880i	−0.998937	−	0.0460900i	$-0.985324\pi$
$137$	−8.14499	+	10.6148i	−0.695874	+	0.906880i	0.303063	+	0.952970i	$0.401991\pi$
$138$	8.50905	+	5.36257i	0.724339	+	0.456492i
$139$	−13.6475	+	0.894507i	−1.15757	+	0.0758711i	−0.632062	−	0.774918i	$-0.717791\pi$
$139$	−13.6475	+	0.894507i	−1.15757	+	0.0758711i	−0.525508	+	0.850789i	$0.676125\pi$
$140$	−19.4953	−	29.3029i	−1.64766	−	2.47655i
$141$	−2.20402	+	0.656508i	−0.185612	+	0.0552879i
$142$	−3.88313	−	19.6238i	−0.325865	−	1.64680i
$143$	−16.5161	−	16.5161i	−1.38115	−	1.38115i
$144$	−11.4162	+	3.69748i	−0.951346	+	0.308124i
$145$	3.09562	−	3.09562i	0.257077	−	0.257077i
$146$	−17.3328	−	11.6063i	−1.43447	−	0.960548i
$147$	−20.2234	+	21.3761i	−1.66800	+	1.76307i
$148$	1.77382	+	1.19034i	0.145807	+	0.0978457i
$149$	0.581893	+	8.87797i	0.0476705	+	0.727311i	0.953070	+	0.302750i	$0.0979048\pi$
$149$	0.581893	+	8.87797i	0.0476705	+	0.727311i	−0.905399	+	0.424561i	$0.860428\pi$
$150$	−18.5049	−	5.73526i	−1.51092	−	0.468282i
$151$	−6.75471	−	5.18307i	−0.549691	−	0.421792i	0.296218	−	0.955120i	$-0.404275\pi$
$151$	−6.75471	−	5.18307i	−0.549691	−	0.421792i	−0.845909	+	0.533328i	$0.820941\pi$
$152$	3.42127	−	1.40519i	0.277501	−	0.113976i
$153$	−3.35162	−	10.2095i	−0.270963	−	0.825389i
$154$	9.66116	+	36.2000i	0.778519	+	2.91708i
$155$	−1.32786	+	0.450748i	−0.106656	+	0.0362050i
$156$	−14.7413	−	2.54015i	−1.18025	−	0.203375i
$157$	1.97598	+	4.00690i	0.157701	+	0.319785i	0.961355	−	0.275311i	$-0.0887807\pi$
$157$	1.97598	+	4.00690i	0.157701	+	0.319785i	−0.803655	+	0.595096i	$0.797114\pi$
$158$	2.04780	+	6.05241i	0.162914	+	0.481504i
$159$	−5.22937	−	2.40114i	−0.414716	−	0.190423i
$160$	−16.1860	+	12.2925i	−1.27961	+	0.971807i
$161$		−	20.1114i		−	1.58500i
$162$	11.9635	+	4.34456i	0.939940	+	0.341341i
$163$	9.45773	−	14.1545i	0.740787	−	1.10867i	−0.249330	−	0.968419i	$-0.580210\pi$
$163$	9.45773	−	14.1545i	0.740787	−	1.10867i	0.990117	−	0.140247i	$-0.0447897\pi$
$164$	2.61618	+	1.51740i	0.204290	+	0.118489i
$165$	27.2627	+	19.7443i	2.12240	+	1.53709i
$166$	1.33461	−	4.96107i	0.103586	−	0.385054i
$167$	13.5916	−	10.4292i	1.05175	−	0.807037i	0.0700651	−	0.997542i	$-0.477679\pi$
$167$	13.5916	−	10.4292i	1.05175	−	0.807037i	0.981686	+	0.190505i	$0.0610126\pi$
$168$	18.4257	+	15.3702i	1.42157	+	1.18583i
$169$	−4.47971	−	3.43740i	−0.344593	−	0.264415i
$170$	−11.0651	−	14.4500i	−0.848653	−	1.10827i
$171$	−3.77889	−	1.05336i	−0.288979	−	0.0805527i
$172$	−1.99038	+	1.73852i	−0.151765	+	0.132561i
$173$	6.05608	−	5.31104i	0.460435	−	0.403791i	−0.397457	−	0.917621i	$-0.630107\pi$
$173$	6.05608	−	5.31104i	0.460435	−	0.403791i	0.857892	+	0.513830i	$0.171774\pi$
$174$	−1.42276	+	2.62369i	−0.107859	+	0.198902i
$175$	10.0261	+	37.4181i	0.757905	+	2.82854i
$176$	20.5156	−	6.87318i	1.54642	−	0.518086i
$177$	−2.90797	+	17.0789i	−0.218576	+	1.28373i
$178$	3.06138	−	0.605780i	0.229460	−	0.0454051i
$179$	10.0838	−	2.00580i	0.753701	−	0.149920i	0.196736	−	0.980457i	$-0.436966\pi$
$179$	10.0838	−	2.00580i	0.753701	−	0.149920i	0.556965	+	0.830536i	$0.311966\pi$
$180$	21.5560	+	0.259533i	1.60669	+	0.0193444i
$181$	2.77999	+	4.16056i	0.206635	+	0.309252i	0.920283	−	0.391253i	$-0.127958\pi$
$181$	2.77999	+	4.16056i	0.206635	+	0.309252i	−0.713648	+	0.700505i	$0.752958\pi$
$182$	11.4188	+	27.6451i	0.846415	+	2.04919i
$183$	3.03601	+	5.74927i	0.224428	+	0.424998i
$184$	−11.5912	+	0.724987i	−0.854514	+	0.0534467i
$185$	−2.33619	−	3.04458i	−0.171760	−	0.223842i
$186$	0.780428	−	0.552167i	0.0572237	−	0.0404868i
$187$	6.22775	+	18.3464i	0.455418	+	1.34162i
$188$	1.62075	−	2.10352i	0.118205	−	0.153415i
$189$	−5.40489	−	24.8697i	−0.393148	−	1.80900i
$190$	−6.63059	+	0.427967i	−0.481034	+	0.0310480i
$191$	6.18316	+	10.7095i	0.447397	+	0.774915i	0.998216	−	0.0597100i	$-0.0190176\pi$
$191$	6.18316	+	10.7095i	0.447397	+	0.774915i	−0.550818	+	0.834625i	$0.685684\pi$
$192$	8.19439	−	11.1737i	0.591379	−	0.806394i
$193$	3.39482	−	5.88000i	0.244364	−	0.423251i	−0.717588	−	0.696467i	$-0.754754\pi$
$193$	3.39482	−	5.88000i	0.244364	−	0.423251i	0.961953	+	0.273216i	$0.0880874\pi$
$194$	−5.90610	+	11.9464i	−0.424033	+	0.857702i
$195$	23.6355	+	12.7865i	1.69257	+	0.915662i
$196$	4.50216	−	33.6793i	0.321583	−	2.40566i
$197$	−25.8621	−	5.14429i	−1.84260	−	0.366515i	−0.854389	−	0.519635i	$-0.826068\pi$
$197$	−25.8621	−	5.14429i	−1.84260	−	0.366515i	−0.988208	+	0.153119i	$0.951068\pi$
$198$	−21.6481	−	7.61620i	−1.53847	−	0.541260i
$199$	4.90493	−	11.8415i	0.347701	−	0.839425i	−0.649189	−	0.760627i	$-0.724892\pi$
$199$	4.90493	−	11.8415i	0.347701	−	0.839425i	0.996891	−	0.0787983i	$-0.0251083\pi$
$200$	21.2045	−	7.12745i	1.49939	−	0.503987i
$201$	2.58617	−	4.11267i	0.182414	−	0.290085i
$202$	−5.89952	+	7.67258i	−0.415088	+	0.539841i
$203$	5.95517	−	0.390322i	0.417971	−	0.0273953i
$204$	10.0348	+	7.29790i	0.702576	+	0.510955i
$205$	−3.58236	−	4.08490i	−0.250203	−	0.285301i
$206$	−0.691085	+	2.02924i	−0.0481502	+	0.141384i
$207$	10.1730	+	6.94629i	0.707075	+	0.482800i
$208$	15.5217	−	7.57779i	1.07623	−	0.525425i
$209$	6.83219	+	1.83068i	0.472592	+	0.126631i
$210$	−22.5419	−	36.7417i	−1.55554	−	2.53542i
$211$	24.4276	+	8.29204i	1.68166	+	0.570848i	0.988671	−	0.150097i	$-0.0479587\pi$
$211$	24.4276	+	8.29204i	1.68166	+	0.570848i	0.692992	+	0.720945i	$0.256292\pi$
$212$	6.51937	−	1.28330i	0.447752	−	0.0881375i
$213$	−3.86946	−	24.1927i	−0.265131	−	1.65766i
$214$	6.39494	−	15.3954i	0.437149	−	1.05241i
$215$	4.38620	−	1.81682i	0.299136	−	0.123906i
$216$	−14.1388	+	4.01163i	−0.962026	+	0.272957i
$217$	−1.76609	−	0.731537i	−0.119890	−	0.0496600i
$218$	−0.583119	−	0.584280i	−0.0394938	−	0.0395725i
$219$	−20.6915	−	14.9853i	−1.39820	−	1.01261i
$220$	−38.8688	−	0.0773462i	−2.62053	−	0.00521468i
$221$	6.84090	+	13.8720i	0.460169	+	0.933130i
$222$	2.11744	+	1.53671i	0.142114	+	0.103137i
$223$	−3.57594	+	2.06457i	−0.239463	+	0.138254i	−0.614930	−	0.788582i	$-0.710816\pi$
$223$	−3.57594	+	2.06457i	−0.239463	+	0.138254i	0.375467	+	0.926836i	$0.377482\pi$
$224$	−27.6380	−	1.94962i	−1.84664	−	0.130265i
$225$	−22.3903	−	7.85230i	−1.49269	−	0.523487i
$226$	17.6152	−	20.0461i	1.17175	−	1.33344i
$227$	13.0954	+	0.858316i	0.869170	+	0.0569684i	0.493460	−	0.869769i	$-0.335732\pi$
$227$	13.0954	+	0.858316i	0.869170	+	0.0569684i	0.375710	+	0.926737i	$0.377399\pi$
$228$	4.25059	−	1.56586i	0.281502	−	0.103701i
$229$	9.45514	+	8.29194i	0.624814	+	0.547947i	0.912136	−	0.409887i	$-0.134432\pi$
$229$	9.45514	+	8.29194i	0.624814	+	0.547947i	−0.287323	+	0.957834i	$0.592765\pi$
$230$	20.1475	+	5.42001i	1.32849	+	0.357385i
$231$	10.1953	+	44.7406i	0.670801	+	2.94372i
$232$	−0.439639	−	3.41820i	−0.0288637	−	0.224416i
$233$	8.70708	−	3.60659i	0.570420	−	0.236276i	−0.0787819	−	0.996892i	$-0.525103\pi$
$233$	8.70708	−	3.60659i	0.570420	−	0.236276i	0.649202	+	0.760616i	$0.275103\pi$
$234$	−17.9278	−	3.77237i	−1.17198	−	0.246607i
$235$	−3.96652	+	2.65034i	−0.258747	+	0.172889i
$236$	−8.81219	−	17.9594i	−0.573625	−	1.16905i
$237$	2.23395	+	7.49981i	0.145111	+	0.487165i
$238$	1.64731	−	24.7556i	0.106779	−	1.60467i
$239$	−4.29097	−	16.0141i	−0.277560	−	1.03587i	−0.954107	−	0.299467i	$-0.903191\pi$
$239$	−4.29097	−	16.0141i	−0.277560	−	1.03587i	0.676547	−	0.736399i	$-0.263476\pi$
$240$	−20.3635	+	14.3166i	−1.31446	+	0.924129i
$241$	5.91914	−	22.0905i	0.381285	−	1.42298i	−0.462654	−	0.886539i	$-0.653103\pi$
$241$	5.91914	−	22.0905i	0.381285	−	1.42298i	0.843940	−	0.536438i	$-0.180230\pi$
$242$	24.4424	+	8.32422i	1.57122	+	0.535101i
$243$	14.4468	+	5.85580i	0.926762	+	0.375650i
$244$	−6.72661	−	3.33386i	−0.430627	−	0.213428i
$245$	−26.9981	+	54.7467i	−1.72484	+	3.49764i
$246$	3.13370	+	1.97492i	0.199797	+	0.125916i
$247$	5.59835	+	0.737036i	0.356214	+	0.0468965i
$248$	−0.357957	+	1.04426i	−0.0227303	+	0.0663104i
$249$	1.85672	−	6.01188i	0.117665	−	0.380987i
$250$	−14.7816	−	0.0147072i	−0.934873	−	0.000930165i
$251$	−6.90438	−	1.37337i	−0.435801	−	0.0866861i	−0.0276857	−	0.999617i	$-0.508814\pi$
$251$	−6.90438	−	1.37337i	−0.435801	−	0.0866861i	−0.408115	+	0.912931i	$0.633814\pi$
$252$	21.8598	+	19.6411i	1.37703	+	1.23727i
$253$	−18.4672	−	12.3394i	−1.16102	−	0.775772i
$254$	11.2738	−	7.51672i	0.707383	−	0.471641i
$255$	−12.8924	−	18.1837i	−0.807355	−	1.13870i
$256$	−0.127354	+	15.9995i	−0.00795962	+	0.999968i
$257$	−0.0565236	+	0.0979018i	−0.00352585	+	0.00610695i	−0.867783	−	0.496943i	$-0.834456\pi$
$257$	−0.0565236	+	0.0979018i	−0.00352585	+	0.00610695i	0.864257	+	0.503050i	$0.167789\pi$
$258$	−2.51430	+	2.03823i	−0.156534	+	0.126895i
$259$	0.342154	−	5.22026i	0.0212604	−	0.324371i
$260$	−30.7722	+	3.98896i	−1.90841	+	0.247385i
$261$	−1.85943	+	3.14715i	−0.115096	+	0.194804i
$262$	11.8405	−	20.4612i	0.731506	−	1.26410i
$263$	11.9234	−	1.56975i	0.735231	−	0.0967950i	0.246394	−	0.969170i	$-0.420754\pi$
$263$	11.9234	−	1.56975i	0.735231	−	0.0967950i	0.488838	+	0.872375i	$0.337421\pi$
$264$	25.4188	−	7.48890i	1.56442	−	0.460910i
$265$	−11.8344	−	1.55803i	−0.726983	−	0.0957091i
$266$	−7.18045	−	5.52111i	−0.440262	−	0.338521i
$267$	3.77414	−	0.603648i	0.230973	−	0.0369426i
$268$	0.355758	+	5.59850i	0.0217314	+	0.341983i
$269$	11.1919	−	2.22621i	0.682384	−	0.135735i	0.158287	−	0.987393i	$-0.449403\pi$
$269$	11.1919	−	2.22621i	0.682384	−	0.135735i	0.524097	+	0.851659i	$0.324403\pi$
$270$	26.3711	+	1.28777i	1.60489	+	0.0783714i
$271$	9.59392	+	9.59392i	0.582789	+	0.582789i	0.935669	−	0.352879i	$-0.114797\pi$
$271$	9.59392	+	9.59392i	0.582789	+	0.582789i	−0.352879	+	0.935669i	$0.614797\pi$
$272$	−14.3273	−	0.0570209i	−0.868721	−	0.00345740i
$273$	12.7315	+	34.3492i	0.770543	+	2.07891i
$274$	1.25632	−	18.8799i	0.0758970	−	1.14058i
$275$	40.5107	+	13.7515i	2.44289	+	0.829248i
$276$	−14.2193	+	0.365663i	−0.855901	+	0.0220103i
$277$	−8.84680	−	4.36276i	−0.531552	−	0.262133i	0.156646	−	0.987655i	$-0.449932\pi$
$277$	−8.84680	−	4.36276i	−0.531552	−	0.262133i	−0.688199	+	0.725522i	$0.741598\pi$
$278$	15.3567	−	11.7594i	0.921034	−	0.705280i
$279$	0.980029	−	0.640683i	0.0586728	−	0.0383567i
$280$	45.9282	+	19.1849i	2.74473	+	1.14652i
$281$	2.06226	+	15.6644i	0.123024	+	0.934462i	0.935960	+	0.352108i	$0.114535\pi$
$281$	2.06226	+	15.6644i	0.123024	+	0.934462i	−0.812935	+	0.582354i	$0.802132\pi$
$282$	2.07833	−	2.50160i	0.123763	−	0.148968i
$283$	−10.5239	−	9.22925i	−0.625584	−	0.548622i	0.286783	−	0.957995i	$-0.407414\pi$
$283$	−10.5239	−	9.22925i	−0.625584	−	0.548622i	−0.912367	+	0.409373i	$0.865747\pi$
$284$	19.9645	+	20.0441i	1.18467	+	1.18940i
$285$	−8.13456	+	0.225387i	−0.481850	+	0.0133508i
$286$	32.3911	+	6.47650i	1.91533	+	0.382964i
$287$		−	7.40658i		−	0.437196i
$288$	10.5321	−	13.3069i	0.620612	−	0.784118i
$289$			4.17030i			0.245312i
$290$	−1.21389	+	6.07108i	−0.0712823	+	0.356506i
$291$	−7.76623	+	14.3556i	−0.455264	+	0.841541i
$292$	29.5002	+	0.0587033i	1.72637	+	0.00343535i
$293$	−21.2651	−	18.6490i	−1.24232	−	1.08949i	−0.992633	−	0.121161i	$-0.961338\pi$
$293$	−21.2651	−	18.6490i	−1.24232	−	1.08949i	−0.249689	−	0.968326i	$-0.580328\pi$
$294$	7.02601	−	41.0181i	0.409765	−	2.39222i
$295$	4.69084	+	35.6305i	0.273111	+	2.07449i
$296$	−3.02104	−	0.00901749i	−0.175594	−	0.000524131i
$297$	−26.1528	−	10.2959i	−1.51754	−	0.597428i
$298$	−7.64967	−	9.98981i	−0.443133	−	0.578694i
$299$	−15.9023	−	7.84217i	−0.919656	−	0.453524i
$300$	26.2733	−	7.76910i	1.51689	−	0.448549i
$301$	6.12848	+	2.08034i	0.353240	+	0.119909i
$302$	12.0142	+	0.799460i	0.691341	+	0.0460037i
$303$	−7.56583	+	9.12510i	−0.434645	+	0.524223i
$304$	−2.92325	+	4.33749i	−0.167660	+	0.248772i
$305$	9.53665	+	9.53665i	0.546067	+	0.546067i
$306$	11.9533	+	9.38365i	0.683325	+	0.536428i
$307$	25.1075	−	4.99419i	1.43296	−	0.285034i	0.583255	−	0.812289i	$-0.301779\pi$
$307$	25.1075	−	4.99419i	1.43296	−	0.285034i	0.849707	+	0.527256i	$0.176779\pi$
$308$	−39.7677	−	35.0155i	−2.26597	−	1.99520i
$309$	−0.937157	+	2.45252i	−0.0533130	+	0.139519i
$310$	1.20881	−	1.57212i	0.0686560	−	0.0892902i
$311$	4.03677	+	0.531451i	0.228904	+	0.0301358i	0.244106	−	0.969749i	$-0.421506\pi$
$311$	4.03677	+	0.531451i	0.228904	+	0.0301358i	−0.0152014	+	0.999884i	$0.504839\pi$
$312$	19.3383	−	8.57604i	1.09481	−	0.485522i
$313$	−1.92796	+	0.253821i	−0.108975	+	0.0143468i	−0.184816	−	0.982773i	$-0.559169\pi$
$313$	−1.92796	+	0.253821i	−0.108975	+	0.0143468i	0.0758414	+	0.997120i	$0.475836\pi$
$314$	−5.46856	−	3.16454i	−0.308609	−	0.178585i
$315$	−25.9359	−	45.9834i	−1.46132	−	2.59087i
$316$	−7.15782	−	5.51505i	−0.402659	−	0.310246i
$317$	−0.147088	+	2.24413i	−0.00826130	+	0.126043i	−0.999997	−	0.00225103i	$-0.999283\pi$
$317$	−0.147088	+	2.24413i	−0.00826130	+	0.126043i	0.991736	+	0.128294i	$0.0409501\pi$
$318$	8.03692	−	1.27725i	0.450688	−	0.0716247i
$319$	3.29541	−	5.70781i	0.184507	−	0.319576i
$320$	9.40158	−	27.1623i	0.525564	−	1.51842i
$321$	8.51975	−	18.5549i	0.475526	−	1.03563i
$322$	15.7778	+	23.6642i	0.879265	+	1.31875i
$323$	−3.89445	−	2.60219i	−0.216693	−	0.144790i
$324$	−17.4853	+	4.27359i	−0.971407	+	0.237422i
$325$	33.4966	+	6.66289i	1.85806	+	0.369590i
$326$	−0.0239536	+	24.0748i	−0.00132666	+	1.33338i
$327$	−0.687394	−	0.741354i	−0.0380130	−	0.0409970i
$328$	−4.26879	+	0.266997i	−0.235704	+	0.0147424i
$329$	−6.44753	−	0.848834i	−0.355464	−	0.0467977i
$330$	−47.5687	−	1.84395i	−2.61857	−	0.101506i
$331$	8.20321	−	16.6345i	0.450889	−	0.914313i	−0.546170	−	0.837674i	$-0.683915\pi$
$331$	8.20321	−	16.6345i	0.450889	−	0.914313i	0.997059	−	0.0766382i	$-0.0244186\pi$
$332$	2.32171	+	6.88451i	0.127420	+	0.377837i
$333$	2.52242	+	1.97611i	0.138228	+	0.108290i
$334$	−7.81070	+	22.9346i	−0.427382	+	1.25492i
$335$	2.60832	−	9.73439i	0.142508	−	0.531847i
$336$	−33.7389	−	3.63003i	−1.84061	−	0.198034i
$337$	6.13409	+	22.8927i	0.334145	+	1.24705i	0.904793	+	0.425852i	$0.140025\pi$
$337$	6.13409	+	22.8927i	0.334145	+	1.24705i	−0.570648	+	0.821195i	$0.693308\pi$
$338$	7.96780	+	0.530200i	0.433391	+	0.0288391i
$339$	22.4618	−	23.7420i	1.21996	−	1.28949i
$340$	24.3562	+	8.32191i	1.32090	+	0.451319i
$341$	−1.75532	+	1.17287i	−0.0950561	+	0.0635145i
$342$	5.27284	−	1.72518i	0.285123	−	0.0932872i
$343$	−45.2029	+	18.7237i	−2.44073	+	1.01098i
$344$	0.978081	−	3.60715i	0.0527346	−	0.194484i
$345$	24.4150	+	7.54038i	1.31446	+	0.405961i
$346$	−2.95929	+	11.0004i	−0.159092	+	0.591386i
$347$	−19.8216	−	17.3830i	−1.06408	−	0.933171i	−0.0661688	−	0.997808i	$-0.521078\pi$
$347$	−19.8216	−	17.3830i	−1.06408	−	0.933171i	−0.997909	+	0.0646374i	$0.979411\pi$
$348$	−0.384245	−	4.20338i	−0.0205977	−	0.225325i
$349$	−12.0838	−	0.792013i	−0.646830	−	0.0423955i	−0.261542	−	0.965192i	$-0.584231\pi$
$349$	−12.0838	−	0.792013i	−0.646830	−	0.0423955i	−0.385288	+	0.922797i	$0.625898\pi$
$350$	−41.1527	−	36.1625i	−2.19971	−	1.93297i
$351$	−21.7724	−	5.42391i	−1.16213	−	0.289507i
$352$	−18.7477	+	24.1824i	−0.999254	+	1.28893i
$353$	−3.70214	+	2.13743i	−0.197045	+	0.113764i	−0.595276	−	0.803521i	$-0.702957\pi$
$353$	−3.70214	+	2.13743i	−0.197045	+	0.113764i	0.398231	+	0.917285i	$0.369624\pi$
$354$	−9.97713	−	22.3774i	−0.530279	−	1.18934i
$355$	−22.4783	−	45.5814i	−1.19302	−	2.41921i
$356$	−3.12694	+	3.11452i	−0.165728	+	0.165069i
$357$	3.13030	−	30.2247i	0.165673	−	1.59966i
$358$	−10.2916	+	10.2711i	−0.543928	+	0.542847i
$359$	−23.4618	−	9.71821i	−1.23827	−	0.512907i	−0.335095	−	0.942184i	$-0.608768\pi$
$359$	−23.4618	−	9.71821i	−1.23827	−	0.512907i	−0.903173	+	0.429277i	$0.858768\pi$
$360$	−25.5676	+	16.6058i	−1.34753	+	0.875204i
$361$	15.9739	−	6.61661i	0.840733	−	0.348243i
$362$	−6.53516	−	2.71457i	−0.343480	−	0.142675i
$363$	29.5409	+	11.2882i	1.55050	+	0.592476i
$364$	−35.1242	−	23.5705i	−1.84101	−	1.23543i
$365$	−50.1836	−	17.0350i	−2.62673	−	0.891654i
$366$	−8.08278	−	4.38310i	−0.422494	−	0.229108i
$367$	24.9379	+	6.68210i	1.30175	+	0.348803i	0.842111	−	0.539304i	$-0.181312\pi$
$367$	24.9379	+	6.68210i	1.30175	+	0.348803i	0.459638	+	0.888106i	$0.347979\pi$
$368$	13.0701	−	9.94664i	0.681326	−	0.518504i
$369$	3.74651	+	2.55817i	0.195036	+	0.133173i
$370$	5.13744	+	1.74963i	0.267083	+	0.0909589i
$371$	−10.7289	−	12.2339i	−0.557015	−	0.635154i
$372$	−0.485107	+	1.26198i	−0.0251516	+	0.0654304i
$373$	−8.17465	+	0.535795i	−0.423267	+	0.0277424i	−0.275549	−	0.961287i	$-0.588860\pi$
$373$	−8.17465	+	0.535795i	−0.423267	+	0.0277424i	−0.147718	+	0.989029i	$0.547193\pi$
$374$	−21.7211	−	16.7016i	−1.12317	−	0.863617i
$375$	−18.0908	−	0.683248i	−0.934207	−	0.0352828i
$376$	−0.256801	+	3.74664i	−0.0132435	+	0.193218i
$377$	2.01351	−	4.86104i	0.103701	−	0.250356i
$378$	25.8706	+	25.0228i	1.33064	+	1.28704i
$379$	28.7613	+	5.72097i	1.47737	+	0.293866i	0.867022	−	0.498270i	$-0.166031\pi$
$379$	28.7613	+	5.72097i	1.47737	+	0.293866i	0.610344	+	0.792136i	$0.291031\pi$
$380$	7.46618	−	5.70543i	0.383007	−	0.292683i
$381$	14.1365	−	8.69247i	0.724237	−	0.445329i
$382$	−15.6774	−	7.75062i	−0.802123	−	0.396556i
$383$	−2.80086	+	4.85124i	−0.143117	+	0.247887i	−0.928669	−	0.370909i	$-0.879046\pi$
$383$	−2.80086	+	4.85124i	−0.143117	+	0.247887i	0.785552	+	0.618796i	$0.212379\pi$
$384$	−0.875927	+	19.5763i	−0.0446995	+	0.999000i
$385$	47.5940	+	82.4352i	2.42561	+	4.20129i
$386$	0.618467	+	9.58206i	0.0314791	+	0.487714i
$387$	−3.16903	+	2.38147i	−0.161091	+	0.121057i
$388$	−2.42280	−	18.6903i	−0.122999	−	0.948857i
$389$	2.91732	+	8.59415i	0.147914	+	0.435740i	0.995482	−	0.0949455i	$-0.0302677\pi$
$389$	2.91732	+	8.59415i	0.147914	+	0.435740i	−0.847569	+	0.530686i	$0.821934\pi$
$390$	−37.8422	+	3.49726i	−1.91621	+	0.177090i
$391$	8.95337	+	11.6683i	0.452791	+	0.590089i
$392$	21.1247	+	43.1610i	1.06696	+	2.17996i
$393$	15.4126	−	24.5100i	0.777463	−	1.23636i
$394$	34.4666	−	14.2364i	1.73640	−	0.717218i
$395$	9.01853	+	13.4972i	0.453771	+	0.679117i
$396$	31.4475	−	8.02183i	1.58030	−	0.403112i
$397$	−16.1277	+	3.20801i	−0.809428	+	0.161005i	−0.582421	−	0.812888i	$-0.697894\pi$
$397$	−16.1277	+	3.20801i	−0.809428	+	0.161005i	−0.227008	+	0.973893i	$0.572894\pi$
$398$	3.51857	+	17.7815i	0.176370	+	0.891305i
$399$	−8.53981	−	7.08055i	−0.427525	−	0.354471i
$400$	−19.3588	+	25.0220i	−0.967939	+	1.25110i
$401$	−0.446148	−	1.66505i	−0.0222796	−	0.0831486i	0.953891	−	0.300153i	$-0.0970379\pi$
$401$	−0.446148	−	1.66505i	−0.0222796	−	0.0831486i	−0.976171	+	0.217005i	$0.930371\pi$
$402$	0.183458	+	6.86812i	0.00915007	+	0.342550i
$403$	−1.26710	+	1.11122i	−0.0631188	+	0.0553537i
$404$	0.922377	−	13.6563i	0.0458900	−	0.679427i
$405$	32.2181	+	2.76296i	1.60093	+	0.137292i
$406$	−6.70097	+	5.13125i	−0.332564	+	0.254660i
$407$	−4.58357	−	3.51709i	−0.227199	−	0.174336i
$408$	−17.5329	−	0.714589i	−0.868007	−	0.0353774i
$409$	27.6238	−	21.1965i	1.36591	−	1.04810i	0.373178	−	0.927760i	$-0.378268\pi$
$409$	27.6238	−	21.1965i	1.36591	−	1.04810i	0.992733	−	0.120341i	$-0.0383988\pi$
$410$	7.41991	+	1.99607i	0.366443	+	0.0985790i
$411$	2.38732	−	23.0509i	0.117758	−	1.13702i
$412$	−0.778815	−	2.92989i	−0.0383695	−	0.144345i
$413$	−27.2179	+	40.7344i	−1.33930	+	2.00441i
$414$	−17.4197	−	0.192398i	−0.856132	−	0.00945585i
$415$		−	13.0521i		−	0.640703i
$416$	−12.3187	+	21.0936i	−0.603974	+	1.03420i
$417$	19.3246	−	13.7014i	0.946329	−	0.670959i
$418$	−9.47535	+	3.20594i	−0.463455	+	0.156808i
$419$	−0.834069	−	1.69133i	−0.0407470	−	0.0826267i	0.875547	−	0.483133i	$-0.160501\pi$
$419$	−0.834069	−	1.69133i	−0.0407470	−	0.0826267i	−0.916294	+	0.400506i	$0.868834\pi$
$420$	55.3489	+	25.5477i	2.70075	+	1.24660i
$421$	−37.9561	+	12.8843i	−1.84986	+	0.627944i	−0.856050	+	0.516893i	$0.827089\pi$
$421$	−37.9561	+	12.8843i	−1.84986	+	0.627944i	−0.993815	+	0.111052i	$0.964578\pi$
$422$	−35.2482	+	9.40714i	−1.71585	+	0.457933i
$423$	2.65629	−	2.96821i	0.129153	−	0.144319i
$424$	−6.66427	+	6.62461i	−0.323646	+	0.321719i
$425$	−22.4751	−	17.2458i	−1.09020	−	0.836543i
$426$	23.5328	+	25.4308i	1.14017	+	1.23213i
$427$	1.20246	+	18.3460i	0.0581912	+	0.887827i
$428$	4.55342	+	23.1321i	0.220098	+	1.11813i
$429$	39.3526	+	9.38447i	1.89996	+	0.453086i
$430$	−3.73571	+	5.57885i	−0.180152	+	0.269036i
$431$	10.2766	−	10.2766i	0.495005	−	0.495005i	−0.414874	−	0.909879i	$-0.636174\pi$
$431$	10.2766	−	10.2766i	0.495005	−	0.495005i	0.909879	+	0.414874i	$0.136174\pi$
$432$	13.4893	−	15.8126i	0.649006	−	0.760783i
$433$	−16.9308	−	16.9308i	−0.813644	−	0.813644i	0.171534	−	0.985178i	$-0.445128\pi$
$433$	−16.9308	−	16.9308i	−0.813644	−	0.813644i	−0.985178	+	0.171534i	$0.945128\pi$
$434$	2.65199	−	0.524771i	0.127300	−	0.0251898i
$435$	−1.75893	+	7.37587i	−0.0843344	+	0.353646i
$436$	1.14451	+	0.230026i	0.0548122	+	0.0110163i
$437$	5.35787	−	0.351173i	0.256302	−	0.0167989i
$438$	36.1031	+	1.39950i	1.72507	+	0.0668708i
$439$	−13.3471	+	17.3942i	−0.637020	+	0.830181i	−0.994609	−	0.103699i	$-0.966932\pi$
$439$	−13.3471	+	17.3942i	−0.637020	+	0.830181i	0.357589	+	0.933879i	$0.383599\pi$
$440$	45.7959	−	30.4025i	2.18324	−	1.44938i
$441$	10.4453	−	49.8865i	0.497394	−	2.37555i
$442$	−18.9323	−	10.9557i	−0.900518	−	0.521109i
$443$	−5.31446	−	15.6559i	−0.252498	−	0.743834i	−0.997084	−	0.0763083i	$-0.975687\pi$
$443$	−5.31446	−	15.6559i	−0.252498	−	0.743834i	0.744587	−	0.667526i	$-0.232647\pi$
$444$	−3.69709	−	0.146998i	−0.175456	−	0.00697623i
$445$	7.11084	−	3.50668i	0.337086	−	0.166233i
$446$	2.58795	−	5.23470i	0.122543	−	0.247870i
$447$	−8.91298	−	12.5710i	−0.421569	−	0.594587i
$448$	34.0500	−	19.3887i	1.60871	−	0.916029i
$449$	−37.1338			−1.75245			−0.876226	−	0.481901i	$-0.839947\pi$
$449$	−37.1338			−1.75245			−0.876226	+	0.481901i	$0.839947\pi$
$450$	32.5061	−	8.32631i	1.53235	−	0.392506i
$451$	−6.80108	−	4.54434i	−0.320250	−	0.213984i
$452$	−5.00046	+	37.4069i	−0.235202	+	1.75947i
$453$	14.6684	+	1.51917i	0.689183	+	0.0713770i
$454$	−16.0821	+	9.26369i	−0.754771	+	0.434767i
$455$	46.2599	+	60.2871i	2.16870	+	2.82630i
$456$	−3.77303	+	5.17717i	−0.176688	+	0.242443i
$457$	−17.4623	+	22.7574i	−0.816854	+	1.06454i	0.179872	+	0.983690i	$0.442432\pi$
$457$	−17.4623	+	22.7574i	−0.816854	+	1.06454i	−0.996726	+	0.0808547i	$0.974235\pi$
$458$	−17.6307	−	2.33897i	−0.823828	−	0.109293i
$459$	14.2076	+	12.0228i	0.663152	+	0.561175i
$460$	−27.9589	+	9.42875i	−1.30359	+	0.439618i
$461$	17.4974	+	19.9520i	0.814935	+	0.929255i	0.998555	−	0.0537420i	$-0.0171149\pi$
$461$	17.4974	+	19.9520i	0.814935	+	0.929255i	−0.183620	+	0.982997i	$0.558782\pi$
$462$	−47.0965	−	44.6459i	−2.19113	−	2.07711i
$463$	6.95851	−	1.86453i	0.323389	−	0.0866519i	−0.0934723	−	0.995622i	$-0.529797\pi$
$463$	6.95851	−	1.86453i	0.323389	−	0.0866519i	0.416862	+	0.908970i	$0.363130\pi$
$464$	3.19896	+	3.67714i	0.148508	+	0.170707i
$465$	1.55024	−	1.86974i	0.0718908	−	0.0867070i
$466$	−7.41579	+	11.0746i	−0.343530	+	0.513023i
$467$	1.60872	+	8.08756i	0.0744425	+	0.374248i	0.999990	−	0.00438292i	$-0.00139513\pi$
$467$	1.60872	+	8.08756i	0.0744425	+	0.374248i	−0.925548	+	0.378630i	$0.876395\pi$
$468$	24.0544	−	9.62605i	1.11192	−	0.444964i
$469$	11.4228	−	7.63248i	0.527457	−	0.352435i
$470$	2.58797	−	6.23037i	0.119374	−	0.287386i
$471$	−6.55065	−	4.11924i	−0.301838	−	0.189805i
$472$	24.4585	+	14.2186i	1.12579	+	0.654465i
$473$	5.67042	−	4.35107i	0.260726	−	0.200062i
$474$	−8.51238	−	7.07211i	−0.390987	−	0.324833i
$475$	−9.79349	+	3.32444i	−0.449356	+	0.152536i
$476$	17.4831	+	30.4212i	0.801336	+	1.39435i
$477$	9.89401	−	1.20155i	0.453016	−	0.0550152i
$478$	17.6125	+	15.4767i	0.805575	+	0.707890i
$479$	23.4713	−	13.5512i	1.07243	−	0.619169i	0.143587	−	0.989638i	$-0.454136\pi$
$479$	23.4713	−	13.5512i	1.07243	−	0.619169i	0.928845	+	0.370469i	$0.120803\pi$
$480$	12.7292	−	32.8214i	0.581006	−	1.49808i
$481$	−3.99432	−	2.30612i	−0.182125	−	0.105150i
$482$	10.3658	+	30.6367i	0.472148	+	1.39546i
$483$	18.2458	+	29.6731i	0.830212	+	1.35017i
$484$	−35.2909	+	9.38095i	−1.60413	+	0.426407i
$485$	−6.60524	+	33.2068i	−0.299929	+	1.50784i
$486$	−21.5929	+	4.44359i	−0.979475	+	0.201565i
$487$	8.90299	+	3.68774i	0.403433	+	0.167107i	0.575167	−	0.818036i	$-0.304937\pi$
$487$	8.90299	+	3.68774i	0.403433	+	0.167107i	−0.171734	+	0.985143i	$0.554937\pi$
$488$	10.5304	−	1.35439i	0.476689	−	0.0613104i
$489$	−1.11280	+	29.4645i	−0.0503227	+	1.33243i
$490$	−11.1827	−	85.5988i	−0.505181	−	3.86696i
$491$	1.40581	+	21.4486i	0.0634435	+	0.967961i	0.904353	+	0.426785i	$0.140354\pi$
$491$	1.40581	+	21.4486i	0.0634435	+	0.967961i	−0.840909	+	0.541176i	$0.817979\pi$
$492$	−5.23666	+	0.134666i	−0.236087	+	0.00607120i
$493$	−3.28132	+	2.87764i	−0.147783	+	0.129602i
$494$	−7.16555	+	3.52480i	−0.322394	+	0.158588i
$495$	−58.1372	−	4.39768i	−2.61307	−	0.197661i
$496$	−0.398053	−	1.50956i	−0.0178731	−	0.0677812i
$497$	17.9315	−	66.9211i	0.804336	−	3.00182i
$498$	2.53174	+	8.53056i	0.113450	+	0.382264i
$499$	0.902629	−	2.65906i	0.0404072	−	0.119036i	−0.924854	−	0.380322i	$-0.875813\pi$
$499$	0.902629	−	2.65906i	0.0404072	−	0.119036i	0.965261	+	0.261286i	$0.0841466\pi$
$500$	17.4045	−	11.5793i	0.778351	−	0.517840i
$501$	−10.5918	+	27.7185i	−0.473208	+	1.23837i
$502$	9.20153	−	3.80068i	0.410684	−	0.169632i
$503$	−13.5355	−	32.6776i	−0.603518	−	1.45702i	−0.869936	−	0.493164i	$-0.835840\pi$
$503$	−13.5355	−	32.6776i	−0.603518	−	1.45702i	0.266418	−	0.963857i	$-0.414160\pi$
$504$	−41.1303	−	5.96128i	−1.83209	−	0.265536i
$505$	−9.40978	+	22.7172i	−0.418730	+	1.01090i
$506$	31.4101	+	0.0312519i	1.39635	+	0.00138932i
$507$	9.72807	+	1.00751i	0.432039	+	0.0447452i
$508$	−7.36838	+	17.6892i	−0.326919	+	0.784831i
$509$	−16.8761	+	8.32238i	−0.748021	+	0.368883i	−0.776006	−	0.630725i	$-0.782757\pi$
$509$	−16.8761	+	8.32238i	−0.748021	+	0.368883i	0.0279856	+	0.999608i	$0.491091\pi$
$510$	29.4355	+	11.2815i	1.30343	+	0.499553i
$511$	−36.1223	−	62.5657i	−1.59796	−	2.76774i
$512$	−12.4021	−	18.9258i	−0.548103	−	0.836411i
$513$	6.53117	−	1.87418i	0.288358	−	0.0827470i
$514$	−0.0102975	−	0.159541i	−0.000454201	−	0.00703705i
$515$	−0.356199	+	5.43455i	−0.0156960	+	0.239475i
$516$	1.35943	−	4.37083i	0.0598456	−	0.192415i
$517$	−4.73535	+	5.39963i	−0.208260	+	0.237476i
$518$	3.69282	+	6.41088i	0.162253	+	0.281678i
$519$	−4.11700	+	13.3304i	−0.180716	+	0.585141i
$520$	33.0789	−	28.8352i	1.45061	−	1.26451i
$521$	−0.622985	−	1.50402i	−0.0272935	−	0.0658923i	0.909645	−	0.415386i	$-0.136354\pi$
$521$	−0.622985	−	1.50402i	−0.0272935	−	0.0658923i	−0.936939	+	0.349494i	$0.886354\pi$
$522$	−0.281112	−	5.16188i	−0.0123039	−	0.225929i
$523$	−11.7467	−	17.5802i	−0.513649	−	0.768729i	0.480472	−	0.877010i	$-0.340465\pi$
$523$	−11.7467	−	17.5802i	−0.513649	−	0.768729i	−0.994120	+	0.108281i	$0.965465\pi$
$524$	2.12018	+	33.3650i	0.0926207	+	1.45756i
$525$	−48.7401	−	46.1120i	−2.12719	−	2.01249i
$526$	−12.7983	+	11.2013i	−0.558032	+	0.488400i
$527$	1.35033	−	0.361819i	0.0588212	−	0.0157611i
$528$	−24.0339	+	28.7535i	−1.04594	+	1.25134i
$529$	5.93061	+	1.58910i	0.257853	+	0.0690914i
$530$	15.1474	−	7.45113i	0.657960	−	0.323656i
$531$	−11.2041	−	27.8371i	−0.486216	−	1.20803i
$532$	12.7804	+	0.863215i	0.554100	+	0.0374251i
$533$	−5.85649	−	2.88810i	−0.253673	−	0.125098i
$534$	−3.96729	+	3.67119i	−0.171681	+	0.158868i
$535$	5.52822	−	41.9910i	0.239006	−	1.81543i
$536$	−4.81077	−	6.30841i	−0.207793	−	0.272482i
$537$	−13.0583	+	12.1079i	−0.563509	+	0.522493i
$538$	−11.4225	+	11.3998i	−0.492460	+	0.491481i
$539$	−17.9283	+	90.1316i	−0.772226	+	3.88224i
$540$	−32.0400	+	19.1735i	−1.37878	+	0.825096i
$541$	−10.1174	+	15.1417i	−0.434979	+	0.650993i	−0.982600	−	0.185734i	$-0.940534\pi$
$541$	−10.1174	+	15.1417i	−0.434979	+	0.650993i	0.547621	+	0.836727i	$0.315534\pi$
$542$	−18.8154	−	3.76209i	−0.808192	−	0.161595i
$543$	−7.87633	−	3.61653i	−0.338005	−	0.155200i
$544$	16.9031	−	11.1730i	0.724713	−	0.479040i
$545$	−1.81622	−	1.04859i	−0.0777983	−	0.0449169i
$546$	−41.9284	−	30.4291i	−1.79437	−	1.30225i
$547$	18.7957	+	1.23194i	0.803647	+	0.0526738i	0.461690	−	0.887042i	$-0.347243\pi$
$547$	18.7957	+	1.23194i	0.803647	+	0.0526738i	0.341958	+	0.939715i	$0.388910\pi$
$548$	13.3335	+	23.2008i	0.569578	+	0.991087i
$549$	−9.69540	−	5.72831i	−0.413790	−	0.244478i
$550$	−58.4556	+	15.6008i	−2.49255	+	0.665220i
$551$	0.207972	+	1.57970i	0.00885990	+	0.0672976i
$552$	16.4444	−	11.5857i	0.699919	−	0.493118i
$553$	−2.88839	+	21.9395i	−0.122827	+	0.932964i
$554$	13.8323	−	1.80706i	0.587680	−	0.0767747i
$555$	6.20907	+	2.37261i	0.263560	+	0.100712i
$556$	−8.84407	+	25.8845i	−0.375072	+	1.09775i
$557$	−0.418181	−	2.10234i	−0.0177189	−	0.0890790i	0.970914	−	0.239429i	$-0.0769601\pi$
$557$	−0.418181	−	2.10234i	−0.0177189	−	0.0890790i	−0.988633	+	0.150350i	$0.951960\pi$
$558$	−0.650526	+	1.52272i	−0.0275390	+	0.0644619i
$559$	4.03468	−	4.03468i	0.170649	−	0.170649i
$560$	−69.0927	+	13.4578i	−2.91970	+	0.568694i
$561$	−25.8332	−	21.4189i	−1.09068	−	0.904306i
$562$	−14.7157	−	16.8138i	−0.620745	−	0.709246i
$563$	−2.21186	+	6.51592i	−0.0932187	+	0.274613i	−0.983532	−	0.180736i	$-0.942152\pi$
$563$	−2.21186	+	6.51592i	−0.0932187	+	0.274613i	0.890313	+	0.455349i	$0.150486\pi$
$564$	−0.482921	+	4.57402i	−0.0203347	+	0.192601i
$565$	29.9862	−	60.8061i	1.26153	−	2.55813i
$566$	19.6236	+	2.60337i	0.824843	+	0.109428i
$567$	30.5373	+	31.7902i	1.28245	+	1.33506i
$568$	−39.2164	−	7.92240i	−1.64549	−	0.332416i
$569$	6.32654	−	0.832905i	0.265223	−	0.0349172i	0.00325794	−	0.999995i	$-0.498963\pi$
$569$	6.32654	−	0.832905i	0.265223	−	0.0349172i	0.261965	+	0.965077i	$0.415630\pi$
$570$	9.39476	−	6.64697i	0.393503	−	0.278411i
$571$	−27.5041	+	31.3624i	−1.15101	+	1.31248i	−0.208607	+	0.978000i	$0.566893\pi$
$571$	−27.5041	+	31.3624i	−1.15101	+	1.31248i	−0.942404	+	0.334477i	$0.891440\pi$
$572$	−43.1942	+	17.7910i	−1.80604	+	0.743879i
$573$	−18.8390	−	10.1917i	−0.787009	−	0.425763i
$574$	5.81064	+	8.71500i	0.242532	+	0.363757i
$575$	32.4757			1.35433
$576$	−1.95310	+	23.9204i	−0.0813790	+	0.996683i
$577$	−14.5674			−0.606449			−0.303224	−	0.952919i	$-0.598063\pi$
$577$	−14.5674			−0.606449			−0.303224	+	0.952919i	$0.598063\pi$
$578$	−3.27170	−	4.90701i	−0.136085	−	0.204105i
$579$	0.325713	+	11.7555i	0.0135362	+	0.488541i
$580$	−3.33457	−	8.09590i	−0.138461	−	0.336164i
$581$	11.7316	−	13.3773i	0.486707	−	0.554984i
$582$	−2.12415	−	22.9844i	−0.0880488	−	0.952735i
$583$	−17.8165	+	2.34559i	−0.737885	+	0.0971444i
$584$	−34.7576	+	23.0745i	−1.43828	+	0.954831i
$585$	−46.4731	+	2.57727i	−1.92143	+	0.106557i
$586$	39.6524	+	5.26047i	1.63802	+	0.217308i
$587$	2.71163	−	5.49865i	0.111921	−	0.226953i	−0.833704	−	0.552211i	$-0.813784\pi$
$587$	2.71163	−	5.49865i	0.111921	−	0.226953i	0.945625	+	0.325258i	$0.105451\pi$
$588$	23.9125	+	53.7763i	0.986134	+	2.21770i
$589$	0.164051	−	0.483278i	0.00675959	−	0.0199131i
$590$	−33.4725	−	38.2447i	−1.37804	−	1.57451i
$591$	42.8250	−	15.8730i	1.76158	−	0.652927i
$592$	3.56180	−	2.35947i	0.146389	−	0.0969735i
$593$	−11.2215	+	11.2215i	−0.460813	+	0.460813i	−0.898922	−	0.438109i	$-0.855648\pi$
$593$	−11.2215	+	11.2215i	−0.460813	+	0.460813i	0.438109	+	0.898922i	$0.355648\pi$
$594$	38.8502	−	8.40277i	1.59404	−	0.344770i
$595$	−12.2971	−	61.8216i	−0.504131	−	2.53444i
$596$	16.8383	+	5.75322i	0.689723	+	0.235661i
$597$	3.50618	+	21.9214i	0.143498	+	0.897184i
$598$	24.8640	−	3.24824i	1.01676	−	0.132830i
$599$	1.95779	−	14.8709i	0.0799931	−	0.607608i	−0.903755	−	0.428051i	$-0.859200\pi$
$599$	1.95779	−	14.8709i	0.0799931	−	0.607608i	0.983748	−	0.179557i	$-0.0574664\pi$
$600$	−24.8197	+	29.7537i	−1.01326	+	1.21469i
$601$	0.382514	+	2.90548i	0.0156031	+	0.118517i	0.997474	−	0.0710343i	$-0.0226300\pi$
$601$	0.382514	+	2.90548i	0.0156031	+	0.118517i	−0.981871	+	0.189551i	$0.939297\pi$
$602$	−8.84319	+	2.36010i	−0.360422	+	0.0961904i
$603$	−0.0845614	+	8.41426i	−0.00344361	+	0.342655i
$604$	−14.7638	+	8.48476i	−0.600731	+	0.345240i
$605$	65.4600	+	4.29047i	2.66133	+	0.174433i
$606$	1.74352	−	16.6727i	0.0708255	−	0.677282i
$607$	−15.2857	−	8.82521i	−0.620428	−	0.358204i	0.156608	−	0.987661i	$-0.449944\pi$
$607$	−15.2857	−	8.82521i	−0.620428	−	0.358204i	−0.777036	+	0.629457i	$0.783278\pi$
$608$	0.0367995	−	7.39710i	0.00149242	−	0.299992i
$609$	−8.43237	+	5.97865i	−0.341697	+	0.242267i
$610$	−18.7031	−	3.73963i	−0.757267	−	0.151413i
$611$	−3.18532	+	4.76717i	−0.128864	+	0.192859i
$612$	−21.4267	−	1.66367i	−0.866121	−	0.0672497i
$613$	3.78132	−	19.0100i	0.152726	−	0.767806i	−0.826166	−	0.563427i	$-0.809482\pi$
$613$	3.78132	−	19.0100i	0.152726	−	0.767806i	0.978892	−	0.204379i	$-0.0655175\pi$
$614$	−25.6249	+	25.5739i	−1.03413	+	1.03208i
$615$	8.99152	+	2.77696i	0.362573	+	0.111978i
$616$	74.2634	+	10.0026i	2.99216	+	0.403015i
$617$	4.29209	−	32.6017i	0.172793	−	1.31249i	−0.656774	−	0.754088i	$-0.728079\pi$
$617$	4.29209	−	32.6017i	0.172793	−	1.31249i	0.829567	−	0.558407i	$-0.188587\pi$
$618$	−0.821347	−	3.62099i	−0.0330394	−	0.145658i
$619$	−27.3986	−	13.5115i	−1.10124	−	0.543073i	−0.201497	−	0.979489i	$-0.564581\pi$
$619$	−27.3986	−	13.5115i	−1.10124	−	0.543073i	−0.899745	+	0.436416i	$0.856247\pi$
$620$	−0.188996	+	2.79819i	−0.00759025	+	0.112378i
$621$	−21.3116	−	1.01945i	−0.855206	−	0.0409092i
$622$	−5.16683	+	2.54161i	−0.207171	+	0.101909i
$623$	10.4399	+	2.79736i	0.418265	+	0.112074i
$624$	−16.0264	+	25.2624i	−0.641569	+	1.01131i
$625$	1.92370	−	0.515454i	0.0769480	−	0.0206181i
$626$	2.06942	−	1.81120i	0.0827108	−	0.0723899i
$627$	−11.7413	+	3.49737i	−0.468904	+	0.139671i
$628$	8.91728	−	0.566651i	0.355838	−	0.0226118i
$629$	2.12550	+	3.18103i	0.0847490	+	0.126836i
$630$	66.5927	+	33.7593i	2.65312	+	1.34500i
$631$	15.7473	+	38.0175i	0.626892	+	1.51345i	0.843465	+	0.537184i	$0.180512\pi$
$631$	15.7473	+	38.0175i	0.626892	+	1.51345i	−0.216573	+	0.976266i	$0.569488\pi$
$632$	12.7490	+	0.873839i	0.507128	+	0.0347594i
$633$	−43.5642	+	9.92722i	−1.73152	+	0.394572i
$634$	−1.58751	−	2.75597i	−0.0630479	−	0.109453i
$635$	22.6978	−	25.8818i	0.900733	−	1.02709i
$636$	−8.45466	+	7.80805i	−0.335249	+	0.309609i
$637$	−4.79818	+	73.2061i	−0.190111	+	2.90053i
$638$	0.600356	+	9.30146i	0.0237683	+	0.368248i
$639$	27.6577	+	32.1843i	1.09412	+	1.27319i
$640$	10.2471	+	39.3365i	0.405052	+	1.55491i
$641$	6.16404	+	10.6764i	0.243465	+	0.421694i	0.961699	−	0.274108i	$-0.0883826\pi$
$641$	6.16404	+	10.6764i	0.243465	+	0.421694i	−0.718234	+	0.695802i	$0.755049\pi$
$642$	4.53196	+	28.5167i	0.178862	+	1.12546i
$643$	−1.25361	+	0.618214i	−0.0494377	+	0.0243800i	−0.466840	−	0.884342i	$-0.654607\pi$
$643$	−1.25361	+	0.618214i	−0.0494377	+	0.0243800i	0.417402	+	0.908722i	$0.362941\pi$
$644$	−37.1302	−	15.4665i	−1.46314	−	0.609465i
$645$	−4.82327	+	6.65993i	−0.189916	+	0.262235i
$646$	6.62392	+	0.00659056i	0.260615	+	0.000259302i
$647$	18.0722	−	43.6300i	0.710490	−	1.71527i	0.0117158	−	0.999931i	$-0.496271\pi$
$647$	18.0722	−	43.6300i	0.710490	−	1.71527i	0.698774	−	0.715343i	$-0.253729\pi$
$648$	17.2215	−	18.7462i	0.676524	−	0.736421i
$649$	20.7047	+	49.9855i	0.812730	+	1.96210i
$650$	−44.6412	+	18.4390i	−1.75097	+	0.723236i
$651$	3.26943	−	0.522924i	0.128139	−	0.0204950i
$652$	−18.8591	−	28.3466i	−0.738579	−	1.11014i
$653$	9.13490	−	26.9106i	0.357476	−	1.05309i	−0.608298	−	0.793709i	$-0.708147\pi$
$653$	9.13490	−	26.9106i	0.357476	−	1.05309i	0.965775	−	0.259383i	$-0.0835192\pi$
$654$	1.39044	+	0.333042i	0.0543704	+	0.0130230i
$655$	15.5446	−	58.0133i	0.607379	−	2.26677i
$656$	4.81343	−	3.66313i	0.187933	−	0.143021i
$657$	44.1243	+	3.33770i	1.72145	+	0.130216i
$658$	8.25246	−	4.05946i	0.321714	−	0.158254i
$659$	8.16966	−	7.16460i	0.318245	−	0.279093i	−0.485287	−	0.874355i	$-0.661285\pi$
$659$	8.16966	−	7.16460i	0.318245	−	0.279093i	0.803532	+	0.595262i	$0.202952\pi$
$660$	57.4187	−	35.1491i	2.23502	−	1.36818i
$661$	2.01792	+	30.7876i	0.0784881	+	1.19750i	0.837506	+	0.546428i	$0.184013\pi$
$661$	2.01792	+	30.7876i	0.0784881	+	1.19750i	−0.759018	+	0.651069i	$0.774321\pi$
$662$	3.39778	+	26.0087i	0.132059	+	1.01086i
$663$	−22.6785	−	14.2609i	−0.880760	−	0.553848i
$664$	−8.13292	−	6.27927i	−0.315619	−	0.243683i
$665$	−21.2601	−	8.80623i	−0.824432	−	0.341491i
$666$	−4.51832	−	0.346301i	−0.175081	−	0.0134189i
$667$	0.976072	−	4.90704i	0.0377937	−	0.190002i
$668$	−8.80223	−	33.1138i	−0.340568	−	1.28121i
$669$	3.40302	−	6.29038i	0.131569	−	0.243200i
$670$	4.56777	+	13.5003i	0.176468	+	0.521563i
$671$	17.5840	+	10.1521i	0.678823	+	0.391918i
$672$	42.5470	−	22.1977i	1.64129	−	0.856296i
$673$	−40.1707	+	23.1926i	−1.54847	+	0.894008i	−0.550209	+	0.835027i	$0.685452\pi$
$673$	−40.1707	+	23.1926i	−1.54847	+	0.894008i	−0.998259	+	0.0589813i	$0.981215\pi$
$674$	−25.1776	−	22.1245i	−0.969806	−	0.852206i
$675$	40.1595	−	8.72778i	1.54574	−	0.335932i
$676$	−9.79132	+	5.62707i	−0.376589	+	0.216426i
$677$	10.0627	−	3.41582i	0.386741	−	0.131281i	−0.121296	−	0.992616i	$-0.538705\pi$
$677$	10.0627	−	3.41582i	0.386741	−	0.131281i	0.508036	+	0.861336i	$0.330372\pi$
$678$	−7.80365	+	45.5580i	−0.299697	+	1.74964i
$679$	−36.6169	+	28.0971i	−1.40523	+	1.07827i
$680$	−35.1877	+	9.31602i	−1.34939	+	0.357253i
$681$	−20.1001	+	10.6142i	−0.770238	+	0.406738i
$682$	1.14527	−	2.75716i	0.0438546	−	0.105577i
$683$	31.4434	−	21.0098i	1.20315	−	0.803918i	0.218055	−	0.975936i	$-0.430029\pi$
$683$	31.4434	−	21.0098i	1.20315	−	0.803918i	0.985094	+	0.172018i	$0.0550288\pi$
$684$	−4.85088	+	6.16662i	−0.185478	+	0.235787i
$685$	−9.37837	−	47.1483i	−0.358329	−	1.80144i
$686$	38.4992	−	57.4942i	1.46991	−	2.19514i
$687$	−21.4732	−	3.65618i	−0.819256	−	0.139492i
$688$	1.67903	+	5.01170i	0.0640124	+	0.191069i
$689$	−13.8571	+	3.71301i	−0.527915	+	0.141454i
$690$	−34.6437	+	10.2817i	−1.31886	+	0.391419i
$691$	11.9652	+	13.6437i	0.455177	+	0.519030i	0.933219	−	0.359307i	$-0.116987\pi$
$691$	11.9652	+	13.6437i	0.455177	+	0.519030i	−0.478043	+	0.878337i	$0.658654\pi$
$692$	−5.14803	−	15.2654i	−0.195699	−	0.580302i
$693$	−55.6329	−	56.7625i	−2.11332	−	2.15623i
$694$	36.9606	+	4.90337i	1.40301	+	0.186130i
$695$	29.9144	−	38.9852i	1.13472	−	1.47879i
$696$	3.74978	+	4.64448i	0.142135	+	0.176049i
$697$	3.29733	+	4.29717i	0.124895	+	0.162767i
$698$	14.8398	−	8.54810i	0.561695	−	0.323550i
$699$	−9.57473	+	13.2207i	−0.362149	+	0.500053i
$700$	76.7930	+	10.2655i	2.90250	+	0.387999i
$701$	−11.0270	−	7.36803i	−0.416485	−	0.278287i	0.329621	−	0.944113i	$-0.393079\pi$
$701$	−11.0270	−	7.36803i	−0.416485	−	0.278287i	−0.746106	+	0.665827i	$0.768079\pi$
$702$	29.8738	−	10.6989i	1.12752	−	0.403805i
$703$	1.39671			0.0526777
$704$	3.08789	−	43.1624i	0.116379	−	1.62674i
$705$	3.44786	−	7.50899i	0.129854	−	0.282805i
$706$	2.67928	−	5.41944i	0.100836	−	0.203963i
$707$	−30.0630	+	14.8254i	−1.13064	+	0.557568i
$708$	29.2953	+	18.5032i	1.10098	+	0.695392i
$709$	−11.2485	−	33.1369i	−0.422445	−	1.24448i	−0.925010	−	0.379943i	$-0.875944\pi$
$709$	−11.2485	−	33.1369i	−0.422445	−	1.24448i	0.502565	−	0.864539i	$-0.332390\pi$
$710$	62.2090	+	35.9990i	2.33466	+	1.35102i
$711$	−10.1002	−	9.03878i	−0.378786	−	0.338981i
$712$	1.23592	−	6.11788i	0.0463180	−	0.229277i
$713$	−0.975585	+	1.27141i	−0.0365359	+	0.0476146i
$714$	20.0287	+	38.0199i	0.749557	+	1.42286i
$715$	83.7414	−	5.48870i	3.13175	−	0.205266i
$716$	4.05172	−	20.1596i	0.151420	−	0.753401i
$717$	20.8597	+	19.7349i	0.779019	+	0.737013i
$718$	35.2307	−	6.97139i	1.31480	−	0.260170i
$719$	35.9528	+	35.9528i	1.34081	+	1.34081i	0.895250	+	0.445564i	$0.146997\pi$
$719$	35.9528	+	35.9528i	1.34081	+	1.34081i	0.445564	+	0.895250i	$0.353003\pi$
$720$	17.0566	−	39.5978i	0.635663	−	1.47572i
$721$	−5.24979	+	5.24979i	−0.195512	+	0.195512i
$722$	−13.6049	+	20.3174i	−0.506323	+	0.756136i
$723$	11.3080	+	37.9633i	0.420551	+	1.41187i
$724$	9.81929	−	1.93287i	0.364931	−	0.0718346i
$725$	0.630291	+	9.61638i	0.0234084	+	0.357143i
$726$	−43.6154	+	9.89324i	−1.61872	+	0.367173i
$727$	27.1007	+	20.7951i	1.00511	+	0.771247i	0.973601	−	0.228256i	$-0.0733024\pi$
$727$	27.1007	+	20.7951i	1.00511	+	0.771247i	0.0315079	+	0.999504i	$0.489969\pi$
$728$	59.8208	+	0.178559i	2.21711	+	0.00661784i
$729$	−26.6279	+	4.46680i	−0.986220	+	0.165437i
$730$	72.4132	−	19.3259i	2.68013	−	0.715282i
$731$	−4.48178	+	1.52136i	−0.165765	+	0.0562695i
$732$	12.9493	−	1.18374i	0.478620	−	0.0437523i
$733$	−3.44727	−	6.99038i	−0.127328	−	0.258195i	0.823869	−	0.566780i	$-0.191811\pi$
$733$	−3.44727	−	6.99038i	−0.127328	−	0.258195i	−0.951197	+	0.308585i	$0.900145\pi$
$734$	−34.5857	+	11.7019i	−1.27658	+	0.431924i
$735$	−9.83428	−	105.269i	−0.362743	−	3.88291i
$736$	−7.57563	+	21.9576i	−0.279241	+	0.809367i
$737$		−	15.1719i		−	0.558865i
$738$	−6.41530	−	0.0708561i	−0.236151	−	0.00260825i
$739$	−13.7026	+	20.5075i	−0.504060	+	0.754379i	−0.993022	−	0.117926i	$-0.962376\pi$
$739$	−13.7026	+	20.5075i	−0.504060	+	0.754379i	0.488962	+	0.872305i	$0.337376\pi$
$740$	−7.41763	+	1.97174i	−0.272678	+	0.0724825i
$741$	−8.92868	+	3.99158i	−0.328003	+	0.146634i
$742$	22.2220	+	5.97807i	0.815795	+	0.219462i
$743$	−12.7876	+	9.81224i	−0.469130	+	0.359976i	−0.816110	−	0.577896i	$-0.803874\pi$
$743$	−12.7876	+	9.81224i	−0.469130	+	0.359976i	0.346980	+	0.937872i	$0.387207\pi$
$744$	−0.419246	−	1.86549i	−0.0153703	−	0.0683922i
$745$	−25.3606	−	19.4599i	−0.929139	−	0.712954i
$746$	9.19841	−	7.04366i	0.336778	−	0.257887i
$747$	2.71473	+	10.5546i	0.0993267	+	0.386174i
$748$	38.6611	+	2.61125i	1.41359	+	0.0954769i
$749$	43.4085	−	38.0683i	1.58611	−	1.39098i
$750$	21.8227	−	13.3888i	0.796854	−	0.488889i
$751$	−8.18195	−	30.5355i	−0.298564	−	1.11425i	−0.938346	−	0.345698i	$-0.887642\pi$
$751$	−8.18195	−	30.5355i	−0.298564	−	1.11425i	0.639782	−	0.768556i	$-0.279025\pi$
$752$	−2.63716	−	4.60998i	−0.0961675	−	0.168109i
$753$	11.4330	−	4.23760i	0.416640	−	0.154427i
$754$	1.44440	+	7.29943i	0.0526019	+	0.265829i
$755$	30.0028	−	5.96793i	1.09191	−	0.217195i
$756$	−50.0718	−	9.14718i	−1.82110	−	0.332680i
$757$	−11.0110	−	16.4792i	−0.400203	−	0.598946i	0.575564	−	0.817757i	$-0.304782\pi$
$757$	−11.0110	−	16.4792i	−0.400203	−	0.598946i	−0.975767	+	0.218810i	$0.929782\pi$
$758$	−38.3304	+	15.8323i	−1.39222	+	0.575055i
$759$	38.4420	+	1.45186i	1.39536	+	0.0526993i
$760$	−4.30908	+	12.5707i	−0.156307	+	0.455989i
$761$	28.5256	+	37.1753i	1.03405	+	1.34760i	0.935835	+	0.352439i	$0.114648\pi$
$761$	28.5256	+	37.1753i	1.03405	+	1.34760i	0.0982179	+	0.995165i	$0.468686\pi$
$762$	−9.81439	+	21.3185i	−0.355538	+	0.772288i
$763$	−0.918965	−	2.70718i	−0.0332688	−	0.0980066i
$764$	24.5274	−	3.17945i	0.887371	−	0.115029i
$765$	35.5189	+	15.1324i	1.28419	+	0.547111i
$766$	−0.510261	−	7.90559i	−0.0184365	−	0.285641i
$767$	21.5960	+	37.4054i	0.779788	+	1.35063i
$768$	−14.3274	−	23.7218i	−0.516997	−	0.855987i
$769$	7.33728	−	12.7085i	0.264589	−	0.458282i	−0.702867	−	0.711321i	$-0.748097\pi$
$769$	7.33728	−	12.7085i	0.264589	−	0.458282i	0.967456	+	0.253040i	$0.0814304\pi$
$770$	−120.674	−	59.6593i	−4.34880	−	2.14997i
$771$	−0.00542311	−	0.195728i	−0.000195308	−	0.00704899i
$772$	−8.24508	−	10.7896i	−0.296747	−	0.388326i
$773$	28.6795	+	5.70472i	1.03153	+	0.205184i	0.681703	−	0.731629i	$-0.261240\pi$
$773$	28.6795	+	5.70472i	1.03153	+	0.205184i	0.349829	+	0.936814i	$0.386240\pi$
$774$	1.86054	−	5.28836i	0.0668758	−	0.190086i
$775$	1.18128	−	2.85187i	0.0424329	−	0.102442i
$776$	17.5138	+	20.0913i	0.628709	+	0.721237i
$777$	4.23119	+	8.01259i	0.151793	+	0.287450i
$778$	−10.1750	−	7.82365i	−0.364791	−	0.280491i
$779$	1.97319	−	0.129330i	0.0706968	−	0.00463371i
$780$	41.7836	−	33.8032i	1.49609	−	1.21035i
$781$	−50.4483	−	57.5252i	−1.80518	−	2.05842i
$782$	−19.6891	−	6.70540i	−0.704080	−	0.239784i
$783$	−0.111748	−	6.33037i	−0.00399353	−	0.226229i
$784$	−58.7175	−	34.2128i	−2.09705	−	1.22189i
$785$	−15.5049	−	4.15453i	−0.553394	−	0.148281i
$786$	1.09334	+	40.9314i	0.0389982	+	1.45997i
$787$	−14.8020	−	5.02460i	−0.527635	−	0.179108i	0.0448952	−	0.998992i	$-0.485705\pi$
$787$	−14.8020	−	5.02460i	−0.527635	−	0.179108i	−0.572530	+	0.819884i	$0.694038\pi$
$788$	−29.3866	+	43.7912i	−1.04685	+	1.56000i
$789$	−16.1682	+	13.1335i	−0.575602	+	0.467564i
$790$	−21.2006	−	8.80629i	−0.754283	−	0.313314i
$791$	85.3873	−	35.3686i	3.03602	−	1.25756i
$792$	−30.7096	+	34.1103i	−1.09122	+	1.21206i
$793$	14.9754	+	6.20300i	0.531791	+	0.220275i
$794$	16.4601	−	16.4273i	0.584146	−	0.582984i
$795$	18.8745	−	8.43786i	0.669408	−	0.299260i
$796$	−18.0902	−	18.1623i	−0.641188	−	0.643745i
$797$	9.29186	+	18.8420i	0.329135	+	0.667419i	0.997045	−	0.0768231i	$-0.0244777\pi$
$797$	9.29186	+	18.8420i	0.329135	+	0.667419i	−0.667910	+	0.744242i	$0.732811\pi$
$798$	15.6033	+	1.63168i	0.552350	+	0.0577610i
$799$	4.11864	−	2.37790i	0.145707	−	0.0841240i
$800$	3.14824	−	44.6298i	0.111307	−	1.57790i
$801$	−5.02085	+	4.31469i	−0.177403	+	0.152452i
$802$	1.83124	+	1.60918i	0.0646632	+	0.0568220i
$803$	−79.6138	−	5.21817i	−2.80951	−	0.184145i
$804$	−5.60407	−	7.93749i	−0.197640	−	0.279934i
$805$	54.3269	+	47.6434i	1.91477	+	1.67921i
$806$	0.619165	−	2.30159i	0.0218092	−	0.0810702i
$807$	−14.4933	+	13.4384i	−0.510188	+	0.473053i
$808$	9.62839	+	16.7924i	0.338726	+	0.590755i
$809$	−21.7351	+	9.00296i	−0.764165	+	0.316527i	−0.730506	−	0.682906i	$-0.760716\pi$
$809$	−21.7351	+	9.00296i	−0.764165	+	0.316527i	−0.0336584	+	0.999433i	$0.510716\pi$
$810$	−40.0772	+	22.0248i	−1.40817	+	0.773873i
$811$	−32.1182	+	21.4607i	−1.12782	+	0.753586i	−0.972182	−	0.234228i	$-0.924744\pi$
$811$	−32.1182	+	21.4607i	−1.12782	+	0.753586i	−0.155640	+	0.987814i	$0.549744\pi$
$812$	3.85915	−	11.2948i	0.135430	−	0.396370i
$813$	−22.8592	−	5.45127i	−0.801708	−	0.191184i
$814$	8.15253	+	0.542492i	0.285746	+	0.0190143i
$815$	15.8304	+	59.0799i	0.554515	+	2.06948i
$816$	21.1908	−	12.9142i	0.741826	−	0.452086i
$817$	−0.447211	+	1.66902i	−0.0156459	+	0.0583915i
$818$	−15.8746	+	46.6126i	−0.555042	+	1.62977i
$819$	−49.9474	−	39.1297i	−1.74530	−	1.36730i
$820$	−10.2966	+	3.47241i	−0.359575	+	0.121262i
$821$	−12.0286	+	24.3915i	−0.419800	+	0.851270i	0.579540	+	0.814944i	$0.303232\pi$
$821$	−12.0286	+	24.3915i	−0.419800	+	0.851270i	−0.999340	+	0.0363265i	$0.988434\pi$
$822$	15.2749	+	28.9959i	0.532774	+	1.01135i
$823$	−54.3211	−	7.15151i	−1.89351	−	0.249286i	−0.908012	−	0.418945i	$-0.862400\pi$
$823$	−54.3211	−	7.15151i	−1.89351	−	0.249286i	−0.985503	+	0.169659i	$0.945733\pi$
$824$	3.21497	+	2.83647i	0.111999	+	0.0988132i
$825$	−72.2469	+	16.4633i	−2.51531	+	0.573179i
$826$	0.0689345	−	69.2835i	0.00239854	−	2.41068i
$827$	−21.6865	−	4.31372i	−0.754115	−	0.150003i	−0.196960	−	0.980411i	$-0.563107\pi$
$827$	−21.6865	−	4.31372i	−0.754115	−	0.150003i	−0.557155	+	0.830409i	$0.688107\pi$
$828$	20.6480	−	13.4398i	0.717566	−	0.467065i
$829$	−6.98330	−	4.66609i	−0.242540	−	0.162060i	0.428359	−	0.903608i	$-0.359092\pi$
$829$	−6.98330	−	4.66609i	−0.242540	−	0.162060i	−0.670899	+	0.741548i	$0.734092\pi$
$830$	10.2397	+	15.3579i	0.355425	+	0.533079i
$831$	17.0110	−	1.58917i	0.590104	−	0.0551277i
$832$	−2.05355	−	34.4842i	−0.0711939	−	1.19553i
$833$	30.4269	−	52.7009i	1.05423	−	1.82598i
$834$	−11.9893	+	31.2824i	−0.415157	+	1.08322i
$835$	−4.02579	+	61.4217i	−0.139318	+	2.12559i
$836$	8.63410	−	11.2059i	0.298617	−	0.387565i
$837$	−0.864721	+	1.83441i	−0.0298891	+	0.0634065i
$838$	2.30830	+	1.33576i	0.0797389	+	0.0461431i
$839$	−54.8081	+	7.21563i	−1.89219	+	0.249111i	−0.985119	−	0.171874i	$-0.945018\pi$
$839$	−54.8081	+	7.21563i	−1.89219	+	0.249111i	−0.907068	+	0.420985i	$0.861685\pi$
$840$	−85.1695	+	13.3617i	−2.93863	+	0.461022i
$841$	−27.2799	−	3.59147i	−0.940687	−	0.123844i
$842$	34.5532	−	44.9379i	1.19078	−	1.54866i
$843$	−17.2541	−	21.2409i	−0.594263	−	0.731577i
$844$	34.0949	−	38.7220i	1.17359	−	1.33287i
$845$	19.8978	−	3.95792i	0.684505	−	0.136157i
$846$	−0.796910	+	5.57649i	−0.0273983	+	0.191724i
$847$	63.2344	+	63.2344i	2.17276	+	2.17276i
$848$	2.64439	−	13.0232i	0.0908089	−	0.447218i
$849$	23.9006	+	4.06947i	0.820265	+	0.139664i
$850$	39.9753	+	2.66006i	1.37114	+	0.0912395i
$851$	−4.15300	−	1.40975i	−0.142363	−	0.0483257i
$852$	−47.6412	−	11.4613i	−1.63216	−	0.392658i
$853$	−10.5276	−	5.19163i	−0.360458	−	0.177758i	0.253037	−	0.967456i	$-0.418570\pi$
$853$	−10.5276	−	5.19163i	−0.360458	−	0.177758i	−0.613495	+	0.789698i	$0.710237\pi$
$854$	−15.8078	−	20.6436i	−0.540932	−	0.706410i
$855$	11.7976	−	7.71253i	0.403468	−	0.263763i
$856$	−23.5055	−	23.6463i	−0.803402	−	0.808212i
$857$	−4.94644	−	37.5720i	−0.168967	−	1.28343i	−0.840236	−	0.542220i	$-0.817584\pi$
$857$	−4.94644	−	37.5720i	−0.168967	−	1.28343i	0.671269	−	0.741214i	$-0.265750\pi$
$858$	−53.6668	+	19.8308i	−1.83216	+	0.677012i
$859$	40.0253	+	35.1013i	1.36565	+	1.19764i	0.958779	+	0.284153i	$0.0917124\pi$
$859$	40.0253	+	35.1013i	1.36565	+	1.19764i	0.406868	+	0.913487i	$0.366621\pi$
$860$	0.0188947	−	9.49515i	0.000644303	−	0.323782i
$861$	6.71953	+	10.9279i	0.229001	+	0.372424i
$862$	−4.02977	+	20.1542i	−0.137255	+	0.686455i
$863$			28.7562i			0.978874i	0.872039	+	0.489437i	$0.162798\pi$
$863$			28.7562i			0.978874i	−0.872039	+	0.489437i	$0.837202\pi$
$864$	−3.46696	+	29.1887i	−0.117949	+	0.993020i
$865$			28.9411i			0.984026i
$866$	33.2045	+	6.63913i	1.12833	+	0.225607i
$867$	−3.78346	−	6.15302i	−0.128493	−	0.208968i
$868$	−2.70878	+	2.69803i	−0.0919421	+	0.0915769i
$869$	18.3738	+	16.1134i	0.623287	+	0.546608i
$870$	−3.71689	−	10.0588i	−0.126014	−	0.341025i
$871$	−1.58093	−	12.0084i	−0.0535679	−	0.406889i
$872$	−1.52716	+	0.627237i	−0.0517162	+	0.0212409i
$873$	−1.56537	−	28.2267i	−0.0529798	−	0.955328i
$874$	−6.02887	+	4.61659i	−0.203930	+	0.156159i
$875$	−45.9144	−	22.6425i	−1.55219	−	0.765455i
$876$	−43.5789	+	26.6771i	−1.47240	+	0.901335i
$877$	−34.0075	−	11.5440i	−1.14835	−	0.389813i	−0.318569	−	0.947900i	$-0.603202\pi$
$877$	−34.0075	−	11.5440i	−1.14835	−	0.389813i	−0.829783	+	0.558087i	$0.811536\pi$
$878$	2.05871	−	30.9381i	0.0694780	−	1.04411i
$879$	48.2945	+	8.22294i	1.62893	+	0.277353i
$880$	−30.0346	+	71.7014i	−1.01246	+	2.41705i
$881$	0.990597	+	0.990597i	0.0333741	+	0.0333741i	0.723597	−	0.690223i	$-0.242488\pi$
$881$	0.990597	+	0.990597i	0.0333741	+	0.0333741i	−0.690223	+	0.723597i	$0.742488\pi$
$882$	26.8467	+	66.8939i	0.903976	+	2.25244i
$883$	5.60658	−	1.11522i	0.188677	−	0.0375301i	−0.0998475	−	0.995003i	$-0.531835\pi$
$883$	5.60658	−	1.11522i	0.188677	−	0.0375301i	0.288524	+	0.957473i	$0.406835\pi$
$884$	30.8718	−	1.96176i	1.03833	−	0.0659811i
$885$	−39.2464	−	48.3149i	−1.31925	−	1.62409i
$886$	18.5357	+	14.2523i	0.622720	+	0.478815i
$887$	20.6425	+	2.71764i	0.693108	+	0.0912495i	0.468847	−	0.883279i	$-0.344670\pi$
$887$	20.6425	+	2.71764i	0.693108	+	0.0912495i	0.224262	+	0.974529i	$0.428003\pi$
$888$	4.46553	−	2.72749i	0.149854	−	0.0915287i
$889$	46.5265	−	6.12533i	1.56045	−	0.205437i
$890$	−5.61595	+	9.70479i	−0.188247	+	0.325305i
$891$	47.9276	−	8.53584i	1.60564	−	0.285962i
$892$	1.06163	+	8.18976i	0.0355459	+	0.274213i
$893$	0.113555	−	1.73251i	0.00379996	−	0.0579763i
$894$	20.3498	+	7.79928i	0.680598	+	0.260847i
$895$	−18.4701	+	31.9912i	−0.617388	+	1.06935i
$896$	−24.8543	+	49.5269i	−0.830323	+	1.65458i
$897$	30.5776	−	2.85658i	1.02096	−	0.0953783i
$898$	43.6937	−	29.1324i	1.45808	−	0.972160i
$899$	−0.395410	−	0.264205i	−0.0131877	−	0.00881172i
$900$	−31.7163	+	35.2990i	−1.05721	+	1.17663i
$901$	11.6711	+	2.32153i	0.388821	+	0.0773414i
$902$	11.5677	+	0.0115094i	0.385162	+	0.000383222i
$903$	−10.9296	+	2.49058i	−0.363713	+	0.0828812i
$904$	−23.4628	−	47.9381i	−0.780362	−	1.59440i
$905$	−17.8247	−	2.34666i	−0.592512	−	0.0780057i
$906$	−18.4515	+	9.72021i	−0.613012	+	0.322932i
$907$	−2.50103	+	5.07159i	−0.0830453	+	0.168399i	−0.934434	−	0.356136i	$-0.884094\pi$
$907$	−2.50103	+	5.07159i	−0.0830453	+	0.168399i	0.851389	+	0.524535i	$0.175761\pi$
$908$	11.6555	−	23.5170i	0.386803	−	0.780439i
$909$	2.88427	−	20.3275i	0.0956653	−	0.674222i
$910$	−101.729	−	34.6452i	−3.37227	−	1.14848i
$911$	9.53854	−	35.5983i	0.316026	−	1.17943i	−0.607004	−	0.794698i	$-0.707629\pi$
$911$	9.53854	−	35.5983i	0.316026	−	1.17943i	0.923030	−	0.384727i	$-0.125704\pi$
$912$	0.377946	−	9.05179i	0.0125150	−	0.299735i
$913$	−5.08573	−	18.9802i	−0.168313	−	0.628153i
$914$	2.69347	−	40.4772i	0.0890920	−	1.33887i
$915$	−22.7228	−	5.41873i	−0.751191	−	0.179138i
$916$	22.5803	−	11.0795i	0.746073	−	0.366078i
$917$	68.0757	−	45.4867i	2.24806	−	1.50210i
$918$	−26.1496	−	3.00050i	−0.863065	−	0.0990311i
$919$	−2.42722	+	1.00539i	−0.0800667	+	0.0331647i	−0.422357	−	0.906429i	$-0.638797\pi$
$919$	−2.42722	+	1.00539i	−0.0800667	+	0.0331647i	0.342291	+	0.939594i	$0.388797\pi$
$920$	25.5009	−	33.0288i	0.840740	−	1.08893i
$921$	−32.5137	+	30.1471i	−1.07136	+	0.993381i
$922$	−36.2412	−	9.74947i	−1.19354	−	0.321082i
$923$	−45.9234	−	40.2737i	−1.51159	−	1.32563i
$924$	90.4422	+	15.5845i	2.97533	+	0.512694i
$925$	8.42965	+	0.552508i	0.277165	+	0.0181664i
$926$	−6.72501	+	7.65303i	−0.220997	+	0.251494i
$927$	−0.842298	−	4.46876i	−0.0276647	−	0.146773i
$928$	−6.64889	−	1.81706i	−0.218260	−	0.0596480i
$929$	26.8950	−	15.5278i	0.882396	−	0.509451i	0.0109481	−	0.999940i	$-0.496515\pi$
$929$	26.8950	−	15.5278i	0.882396	−	0.509451i	0.871448	+	0.490489i	$0.163182\pi$
$930$	−0.357247	+	3.41624i	−0.0117146	+	0.112023i
$931$	−9.82600	−	19.9252i	−0.322034	−	0.653021i
$932$	0.0375080	−	18.8489i	0.00122862	−	0.617417i
$933$	−6.43816	+	2.87819i	−0.210776	+	0.0942277i
$934$	−8.23779	−	8.25420i	−0.269549	−	0.270086i
$935$	−64.3125	−	26.6391i	−2.10325	−	0.871193i
$936$	−20.7519	+	30.1978i	−0.678298	+	0.987047i
$937$	17.0001	−	7.04168i	0.555370	−	0.230042i	−0.0873039	−	0.996182i	$-0.527825\pi$
$937$	17.0001	−	7.04168i	0.555370	−	0.230042i	0.642674	+	0.766140i	$0.277825\pi$
$938$	−7.45287	+	17.9423i	−0.243345	+	0.585837i
$939$	2.61432	−	2.12362i	0.0853150	−	0.0693017i
$940$	1.84273	+	9.36134i	0.0601032	+	0.305333i
$941$	−46.9152	−	15.9256i	−1.52939	−	0.519159i	−0.575113	−	0.818074i	$-0.695042\pi$
$941$	−46.9152	−	15.9256i	−1.52939	−	0.519159i	−0.954280	+	0.298915i	$0.903375\pi$
$942$	10.9395	−	0.292212i	0.356429	−	0.00952078i
$943$	−5.99767	−	1.60707i	−0.195311	−	0.0523334i
$944$	−39.9341	+	2.45784i	−1.29974	+	0.0799960i
$945$	79.9847	+	44.3156i	2.60190	+	1.44159i
$946$	−3.25862	+	9.56829i	−0.105947	+	0.311092i
$947$	21.3046	+	24.2932i	0.692306	+	0.789423i	0.986048	−	0.166461i	$-0.0532341\pi$
$947$	21.3046	+	24.2932i	0.692306	+	0.789423i	−0.293742	+	0.955885i	$0.594901\pi$
$948$	15.5644	+	1.64327i	0.505508	+	0.0533711i
$949$	−63.5571	+	4.16575i	−2.06315	+	0.135226i
$950$	8.91547	−	11.5950i	0.289256	−	0.376190i
$951$	−1.81894	−	3.44452i	−0.0589833	−	0.111696i
$952$	−44.4378	−	22.0794i	−1.44024	−	0.715599i
$953$	−13.0977	+	31.6206i	−0.424275	+	1.02429i	0.556797	+	0.830648i	$0.312030\pi$
$953$	−13.0977	+	31.6206i	−0.424275	+	1.02429i	−0.981072	+	0.193642i	$0.937970\pi$
$954$	−10.6992	+	9.17591i	−0.346400	+	0.297081i
$955$	−43.5775	−	8.66810i	−1.41013	−	0.280493i
$956$	−32.8657	−	4.39340i	−1.06295	−	0.142093i
$957$	0.316175	+	11.4112i	0.0102205	+	0.368873i
$958$	−16.9865	+	34.3589i	−0.548808	+	1.11009i
$959$	32.7660	−	56.7524i	1.05807	−	1.83263i
$960$	10.7713	+	48.6058i	0.347641	+	1.56875i
$961$	−15.4238	−	26.7149i	−0.497543	−	0.861770i
$962$	6.50915	−	0.420129i	0.209863	−	0.0135455i
$963$	4.26335	+	35.1061i	0.137385	+	1.13128i
$964$	−36.2322	−	27.9167i	−1.16696	−	0.899135i
$965$	7.84140	+	23.1000i	0.252424	+	0.743616i
$966$	−44.7483	−	20.6007i	−1.43975	−	0.662818i
$967$	11.6236	+	15.1482i	0.373789	+	0.487132i	0.941935	−	0.335797i	$-0.109005\pi$
$967$	11.6236	+	15.1482i	0.373789	+	0.487132i	−0.568145	+	0.822928i	$0.692339\pi$
$968$	34.1657	−	38.7247i	1.09813	−	1.24466i
$969$	8.10683	+	0.306176i	0.260429	+	0.00983578i
$970$	−18.2794	−	44.2550i	−0.586918	−	1.42094i
$971$	−19.4060	−	29.0431i	−0.622767	−	0.932036i	−0.999983	−	0.00591098i	$-0.998118\pi$
$971$	−19.4060	−	29.0431i	−0.622767	−	0.932036i	0.377216	−	0.926125i	$-0.376882\pi$
$972$	21.9214	−	22.1688i	0.703128	−	0.711063i
$973$	65.7006	−	13.0687i	2.10626	−	0.418962i
$974$	−13.3689	+	2.64541i	−0.428367	+	0.0847644i
$975$	−55.4670	+	20.5587i	−1.77637	+	0.658406i
$976$	−11.3281	+	9.85502i	−0.362604	+	0.315451i
$977$	1.70214	+	6.35247i	0.0544563	+	0.203234i	0.987794	−	0.155766i	$-0.0497846\pi$
$977$	1.70214	+	6.35247i	0.0544563	+	0.203234i	−0.933338	+	0.359000i	$0.883118\pi$
$978$	−21.8062	−	35.5426i	−0.697287	−	1.13653i
$979$	8.97411	−	7.87008i	0.286814	−	0.251529i
$980$	80.3125	+	91.9473i	2.56549	+	2.93715i
$981$	1.68679	+	0.470193i	0.0538551	+	0.0150121i
$982$	−18.4811	−	24.1347i	−0.589756	−	0.770170i
$983$	−17.9417	−	13.7671i	−0.572250	−	0.439103i	0.281667	−	0.959512i	$-0.409113\pi$
$983$	−17.9417	−	13.7671i	−0.572250	−	0.439103i	−0.853917	+	0.520409i	$0.825779\pi$
$984$	6.05611	−	4.26675i	0.193062	−	0.136019i
$985$	75.1630	−	57.6746i	2.39489	−	1.83767i
$986$	1.60341	−	5.96027i	0.0510629	−	0.189814i
$987$	10.2830	−	4.59704i	0.327312	−	0.146326i
$988$	5.66610	−	9.76904i	0.180263	−	0.310794i
$989$	3.01436	−	4.51130i	0.0958510	−	0.143451i
$990$	71.8577	−	40.4355i	2.28379	−	1.28513i
$991$		−	3.85319i		−	0.122400i	−0.998126	−	0.0612002i	$-0.980507\pi$
$991$		−	3.85319i		−	0.122400i	0.998126	−	0.0612002i	$-0.0194928\pi$
$992$	1.65266	+	1.46395i	0.0524719	+	0.0464805i
$993$	2.98809	+	31.9854i	0.0948241	+	1.01503i
$994$	31.4021	+	92.8108i	0.996013	+	2.94378i
$995$	20.3679	+	41.3021i	0.645707	+	1.30936i
$996$	−9.67143	−	8.05133i	−0.306451	−	0.255116i
$997$	36.6401	−	12.4376i	1.16040	−	0.393904i	0.326168	−	0.945312i	$-0.394242\pi$
$997$	36.6401	−	12.4376i	1.16040	−	0.393904i	0.834236	+	0.551408i	$0.185909\pi$
$998$	1.02401	+	3.83694i	0.0324146	+	0.121456i
$999$	−5.51447	−	0.627191i	−0.174470	−	0.0198435i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.bm.a.517.18	yes	1504
9.7	even	3	inner	576.2.bm.a.133.82	yes	1504
64.13	even	16	inner	576.2.bm.a.13.82	✓	1504
576.205	even	48	inner	576.2.bm.a.205.18	yes	1504

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
576.2.bm.a.13.82	✓	1504	64.13	even	16	inner
576.2.bm.a.133.82	yes	1504	9.7	even	3	inner
576.2.bm.a.205.18	yes	1504	576.205	even	48	inner
576.2.bm.a.517.18	yes	1504	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.bm (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.17666 + 0.784525i) q^{2} +(-1.47544 + 0.907238i) q^{3} +(0.769042 - 1.84623i) q^{4} +(-2.36898 + 2.70130i) q^{5} +(1.02433 - 2.22503i) q^{6} +(-4.85600 + 0.639304i) q^{7} +(0.543516 + 2.77571i) q^{8} +(1.35384 - 2.67715i) q^{9} +O(q^{10})\)	\(q+(-1.17666 + 0.784525i) q^{2} +(-1.47544 + 0.907238i) q^{3} +(0.769042 - 1.84623i) q^{4} +(-2.36898 + 2.70130i) q^{5} +(1.02433 - 2.22503i) q^{6} +(-4.85600 + 0.639304i) q^{7} +(0.543516 + 2.77571i) q^{8} +(1.35384 - 2.67715i) q^{9} +(0.668237 - 5.03703i) q^{10} +(-2.39238 + 4.85126i) q^{11} +(0.540298 + 3.42171i) q^{12} +(-1.38803 + 4.08900i) q^{13} +(5.21229 - 4.56189i) q^{14} +(1.04456 - 6.13484i) q^{15} +(-2.81715 - 2.83966i) q^{16} +(2.53276 - 2.53276i) q^{17} +(0.507286 + 4.21220i) q^{18} +(-0.255110 - 1.28253i) q^{19} +(3.16539 + 6.45110i) q^{20} +(6.58473 - 5.34880i) q^{21} +(-0.990927 - 7.58515i) q^{22} +(-0.535956 + 4.07099i) q^{23} +(-3.32016 - 3.60230i) q^{24} +(-1.03235 - 7.84144i) q^{25} +(-1.57469 - 5.90029i) q^{26} +(0.431307 + 5.17822i) q^{27} +(-2.55416 + 9.45696i) q^{28} +(-1.21586 - 0.0796918i) q^{29} +(3.58384 + 8.03808i) q^{30} +(0.338001 + 0.195145i) q^{31} +(5.54260 + 1.13118i) q^{32} +(-0.871444 - 9.32820i) q^{33} +(-0.993175 + 4.96719i) q^{34} +(9.77681 - 14.6320i) q^{35} +(-3.90148 - 4.55834i) q^{36} +(-0.208376 + 1.04758i) q^{37} +(1.30635 + 1.30895i) q^{38} +(-1.66175 - 7.29234i) q^{39} +(-8.78563 - 5.10741i) q^{40} +(-0.197381 + 1.49926i) q^{41} +(-3.55170 + 11.4596i) q^{42} +(-1.18510 - 0.584427i) q^{43} +(7.11672 + 8.14771i) q^{44} +(4.02458 + 9.99924i) q^{45} +(-2.56315 - 5.21062i) q^{46} +(1.28250 + 0.343646i) q^{47} +(6.73278 + 1.63392i) q^{48} +(16.4105 - 4.39719i) q^{49} +(7.36652 + 8.41679i) q^{50} +(-1.43911 + 6.03474i) q^{51} +(6.48179 + 5.70724i) q^{52} +(1.84574 + 2.76234i) q^{53} +(-4.56994 - 5.75462i) q^{54} +(-7.43724 - 17.9551i) q^{55} +(-4.41384 - 13.1314i) q^{56} +(1.53996 + 1.66084i) q^{57} +(1.49317 - 0.860103i) q^{58} +(6.59505 - 7.52021i) q^{59} +(-10.5230 - 6.64645i) q^{60} +(0.245506 - 3.74569i) q^{61} +(-0.550807 + 0.0355514i) q^{62} +(-4.86272 + 13.8657i) q^{63} +(-7.40918 + 3.01729i) q^{64} +(-7.75742 - 13.4362i) q^{65} +(8.34359 + 10.2924i) q^{66} +(-2.51564 + 1.24057i) q^{67} +(-2.72826 - 6.62385i) q^{68} +(-2.90259 - 6.49273i) q^{69} +(-0.0247617 + 24.8870i) q^{70} +(-5.41313 + 13.0685i) q^{71} +(8.16683 + 2.30279i) q^{72} +(5.64462 + 13.6273i) q^{73} +(-0.576664 - 1.39612i) q^{74} +(8.63722 + 10.6330i) q^{75} +(-2.56403 - 0.515323i) q^{76} +(8.51595 - 25.0872i) q^{77} +(7.67633 + 7.27690i) q^{78} +(1.16935 - 4.36408i) q^{79} +(14.3446 - 0.882872i) q^{80} +(-5.33425 - 7.24885i) q^{81} +(-0.943954 - 1.91896i) q^{82} +(-2.73123 + 2.39522i) q^{83} +(-4.81120 - 16.2704i) q^{84} +(0.841695 + 12.8418i) q^{85} +(1.85295 - 0.242071i) q^{86} +(1.86623 - 0.985496i) q^{87} +(-14.7660 - 4.00382i) q^{88} +(-2.03872 - 0.844465i) q^{89} +(-12.5802 - 8.60829i) q^{90} +(4.12615 - 20.7436i) q^{91} +(7.10382 + 4.12026i) q^{92} +(-0.675742 + 0.0187230i) q^{93} +(-1.77867 + 0.601802i) q^{94} +(4.06884 + 2.34915i) q^{95} +(-9.20402 + 3.35947i) q^{96} +(8.16085 - 4.71167i) q^{97} +(-15.8599 + 18.0485i) q^{98} +(9.74866 + 12.9726i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1504 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{5} - 16 q^{6} - 8 q^{7} - 32 q^{8} - 16 q^{9}+O(q^{10}) \) 1504 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^5 - 16 * q^6 - 8 * q^7 - 32 * q^8 - 16 * q^9	\( 1504 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{5} - 16 q^{6} - 8 q^{7} - 32 q^{8} - 16 q^{9} - 32 q^{10} - 8 q^{11} - 16 q^{12} - 8 q^{13} - 8 q^{14} - 16 q^{15} - 8 q^{16} - 32 q^{17} - 16 q^{18} - 32 q^{19} - 8 q^{20} - 16 q^{21} - 8 q^{22} - 8 q^{23} + 64 q^{24} - 8 q^{25} - 32 q^{26} - 16 q^{27} - 32 q^{28} - 8 q^{29} - 96 q^{30} - 8 q^{32} - 8 q^{34} - 32 q^{35} - 96 q^{36} - 32 q^{37} - 8 q^{38} - 16 q^{39} - 8 q^{40} - 8 q^{41} + 64 q^{42} - 8 q^{43} - 32 q^{44} - 16 q^{45} - 32 q^{46} - 8 q^{47} - 16 q^{48} - 8 q^{49} - 8 q^{50} - 16 q^{51} - 8 q^{52} - 32 q^{53} - 16 q^{54} - 32 q^{55} - 8 q^{56} - 16 q^{57} - 80 q^{58} - 8 q^{59} - 16 q^{60} - 8 q^{61} - 64 q^{62} - 32 q^{63} - 32 q^{64} - 16 q^{65} - 32 q^{66} - 8 q^{67} - 8 q^{68} - 16 q^{69} - 8 q^{70} - 32 q^{71} - 16 q^{72} - 32 q^{73} - 8 q^{74} - 16 q^{75} + 40 q^{76} - 8 q^{77} - 40 q^{78} - 8 q^{79} - 160 q^{80} - 16 q^{81} - 32 q^{82} - 8 q^{83} - 128 q^{84} - 8 q^{85} - 216 q^{86} - 16 q^{87} - 8 q^{88} - 32 q^{89} - 160 q^{90} - 32 q^{91} + 144 q^{92} - 40 q^{93} - 8 q^{94} - 152 q^{96} - 304 q^{98} - 16 q^{99}+O(q^{100}) \) 1504 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^5 - 16 * q^6 - 8 * q^7 - 32 * q^8 - 16 * q^9 - 32 * q^10 - 8 * q^11 - 16 * q^12 - 8 * q^13 - 8 * q^14 - 16 * q^15 - 8 * q^16 - 32 * q^17 - 16 * q^18 - 32 * q^19 - 8 * q^20 - 16 * q^21 - 8 * q^22 - 8 * q^23 + 64 * q^24 - 8 * q^25 - 32 * q^26 - 16 * q^27 - 32 * q^28 - 8 * q^29 - 96 * q^30 - 8 * q^32 - 8 * q^34 - 32 * q^35 - 96 * q^36 - 32 * q^37 - 8 * q^38 - 16 * q^39 - 8 * q^40 - 8 * q^41 + 64 * q^42 - 8 * q^43 - 32 * q^44 - 16 * q^45 - 32 * q^46 - 8 * q^47 - 16 * q^48 - 8 * q^49 - 8 * q^50 - 16 * q^51 - 8 * q^52 - 32 * q^53 - 16 * q^54 - 32 * q^55 - 8 * q^56 - 16 * q^57 - 80 * q^58 - 8 * q^59 - 16 * q^60 - 8 * q^61 - 64 * q^62 - 32 * q^63 - 32 * q^64 - 16 * q^65 - 32 * q^66 - 8 * q^67 - 8 * q^68 - 16 * q^69 - 8 * q^70 - 32 * q^71 - 16 * q^72 - 32 * q^73 - 8 * q^74 - 16 * q^75 + 40 * q^76 - 8 * q^77 - 40 * q^78 - 8 * q^79 - 160 * q^80 - 16 * q^81 - 32 * q^82 - 8 * q^83 - 128 * q^84 - 8 * q^85 - 216 * q^86 - 16 * q^87 - 8 * q^88 - 32 * q^89 - 160 * q^90 - 32 * q^91 + 144 * q^92 - 40 * q^93 - 8 * q^94 - 152 * q^96 - 304 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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