LMFDB - Embedded newform 805.2.bs.a.37.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [805,2,Mod(37,805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(805, base_ring=CyclotomicField(132))

chi = DirichletCharacter(H, H._module([33, 44, 126]))

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

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

chi := DirichletCharacter("805.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 805 = 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	805.bs (of order $132$, degree $40$, 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:	$6.42795736271$
Analytic rank:	$0$
Dimension:	$3680$
Relative dimension:	$92$ over $\Q(\zeta_{132})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{132}]$

Embedding invariants

Embedding label			37.2
Character	$\chi$	$=$	805.37
Dual form			805.2.bs.a.718.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.30557 + 1.40532i) q^{2} +(-1.13353 - 2.33346i) q^{3} +(2.42427 - 4.70243i) q^{4} +(-0.533908 + 2.17139i) q^{5} +(5.89267 + 3.78699i) q^{6} +(-0.0145566 + 2.64571i) q^{7} +(0.633836 + 8.86218i) q^{8} +(-2.30569 + 2.93193i) q^{9} +O(q^{10})$	\(q+(-2.30557 + 1.40532i) q^{2} +(-1.13353 - 2.33346i) q^{3} +(2.42427 - 4.70243i) q^{4} +(-0.533908 + 2.17139i) q^{5} +(5.89267 + 3.78699i) q^{6} +(-0.0145566 + 2.64571i) q^{7} +(0.633836 + 8.86218i) q^{8} +(-2.30569 + 2.93193i) q^{9} +(-1.82053 - 5.75660i) q^{10} +(-1.14864 + 0.278657i) q^{11} +(-13.7209 - 0.326619i) q^{12} +(-0.865793 - 0.322924i) q^{13} +(-3.68450 - 6.12032i) q^{14} +(5.67206 - 1.21548i) q^{15} +(-7.77788 - 10.9225i) q^{16} +(2.22621 + 2.44891i) q^{17} +(1.19564 - 9.99998i) q^{18} +(-0.191553 - 4.02120i) q^{19} +(8.91648 + 7.77471i) q^{20} +(6.19017 - 2.96502i) q^{21} +(2.25666 - 2.25666i) q^{22} +(-0.103641 + 4.79471i) q^{23} +(19.9611 - 11.5246i) q^{24} +(-4.42988 - 2.31865i) q^{25} +(2.44995 - 0.472190i) q^{26} +(1.85033 + 0.402514i) q^{27} +(12.4060 + 6.48237i) q^{28} +(-0.866841 + 1.34883i) q^{29} +(-11.3692 + 10.7734i) q^{30} +(6.93937 + 1.33745i) q^{31} +(16.9471 + 7.25716i) q^{32} +(1.95225 + 2.36444i) q^{33} +(-8.57416 - 2.51760i) q^{34} +(-5.73710 - 1.44417i) q^{35} +(8.19755 + 17.9501i) q^{36} +(2.99540 - 0.358143i) q^{37} +(6.09270 + 9.00195i) q^{38} +(0.227868 + 2.38634i) q^{39} +(-19.5817 - 3.35529i) q^{40} +(-1.72799 - 12.0184i) q^{41} +(-10.1051 + 15.5352i) q^{42} +(0.433768 - 6.06487i) q^{43} +(-1.47425 + 6.07694i) q^{44} +(-5.13533 - 6.57194i) q^{45} +(-6.49913 - 11.2002i) q^{46} +(-7.88864 + 2.11376i) q^{47} +(-16.6708 + 30.5303i) q^{48} +(-6.99958 - 0.0770252i) q^{49} +(13.4718 - 0.879593i) q^{50} +(3.19098 - 7.97068i) q^{51} +(-3.61744 + 3.28847i) q^{52} +(-7.71830 - 6.37276i) q^{53} +(-4.83171 + 1.67227i) q^{54} +(0.00819449 - 2.64292i) q^{55} +(-23.4560 + 1.54794i) q^{56} +(-9.16619 + 5.00512i) q^{57} +(0.103026 - 4.32801i) q^{58} +(12.2362 + 8.71333i) q^{59} +(8.03493 - 29.6191i) q^{60} +(-6.07208 + 2.10157i) q^{61} +(-17.8787 + 6.66842i) q^{62} +(-7.72347 - 6.14287i) q^{63} +(-22.7265 + 3.26758i) q^{64} +(1.16345 - 1.70756i) q^{65} +(-7.82383 - 2.70785i) q^{66} +(-4.31836 + 0.102796i) q^{67} +(16.9128 - 4.53176i) q^{68} +(11.3058 - 5.19309i) q^{69} +(15.2568 - 4.73280i) q^{70} +(-2.79135 + 0.819614i) q^{71} +(-27.4447 - 18.5751i) q^{72} +(-12.3369 + 3.94368i) q^{73} +(-6.40278 + 5.03520i) q^{74} +(-0.389086 + 12.9652i) q^{75} +(-19.3738 - 8.84771i) q^{76} +(-0.720526 - 3.04303i) q^{77} +(-3.87893 - 5.18164i) q^{78} +(-10.0212 - 0.956906i) q^{79} +(27.8697 - 11.0572i) q^{80} +(1.47995 + 6.10045i) q^{81} +(20.8737 + 25.2809i) q^{82} +(9.85926 - 7.38055i) q^{83} +(1.06387 - 36.2968i) q^{84} +(-6.50613 + 3.52648i) q^{85} +(7.52298 + 14.5925i) q^{86} +(4.13004 + 0.493806i) q^{87} +(-3.19756 - 10.0028i) q^{88} +(-4.51144 + 0.869509i) q^{89} +(21.0755 + 7.93528i) q^{90} +(0.866967 - 2.28594i) q^{91} +(22.2955 + 12.1110i) q^{92} +(-4.74506 - 17.7088i) q^{93} +(15.2173 - 15.9594i) q^{94} +(8.83387 + 1.73101i) q^{95} +(-2.27564 - 47.7715i) q^{96} +(-10.3341 - 7.73601i) q^{97} +(16.2462 - 9.65903i) q^{98} +(1.83141 - 4.01022i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3680 q - 18 q^{2} - 18 q^{3} - 22 q^{5} - 160 q^{6} - 44 q^{7} - 56 q^{8}+O(q^{10}) $ 3680 * q - 18 * q^2 - 18 * q^3 - 22 * q^5 - 160 * q^6 - 44 * q^7 - 56 * q^8	$ 3680 q - 18 q^{2} - 18 q^{3} - 22 q^{5} - 160 q^{6} - 44 q^{7} - 56 q^{8} - 22 q^{10} - 44 q^{11} + 14 q^{12} - 72 q^{13} - 88 q^{15} - 196 q^{16} - 22 q^{17} - 62 q^{18} - 88 q^{20} - 88 q^{21} - 44 q^{23} - 30 q^{25} - 28 q^{26} - 48 q^{27} + 132 q^{28} - 22 q^{30} - 40 q^{31} - 50 q^{32} - 22 q^{33} - 40 q^{35} - 416 q^{36} - 110 q^{37} - 22 q^{38} - 22 q^{40} - 192 q^{41} - 264 q^{42} - 88 q^{43} - 44 q^{47} + 24 q^{48} - 44 q^{51} - 374 q^{52} - 22 q^{53} - 32 q^{55} - 220 q^{56} + 88 q^{57} - 58 q^{58} - 22 q^{60} - 220 q^{61} + 8 q^{62} - 44 q^{63} - 22 q^{65} - 44 q^{66} - 22 q^{67} - 96 q^{70} - 136 q^{71} - 46 q^{72} + 18 q^{73} - 34 q^{75} - 176 q^{76} - 116 q^{77} + 80 q^{78} + 176 q^{80} - 236 q^{81} - 2 q^{82} - 88 q^{83} - 448 q^{85} - 86 q^{87} - 110 q^{88} - 88 q^{90} - 228 q^{92} + 4 q^{93} - 236 q^{95} - 332 q^{96} - 88 q^{97} + 84 q^{98}+O(q^{100}) $ 3680 * q - 18 * q^2 - 18 * q^3 - 22 * q^5 - 160 * q^6 - 44 * q^7 - 56 * q^8 - 22 * q^10 - 44 * q^11 + 14 * q^12 - 72 * q^13 - 88 * q^15 - 196 * q^16 - 22 * q^17 - 62 * q^18 - 88 * q^20 - 88 * q^21 - 44 * q^23 - 30 * q^25 - 28 * q^26 - 48 * q^27 + 132 * q^28 - 22 * q^30 - 40 * q^31 - 50 * q^32 - 22 * q^33 - 40 * q^35 - 416 * q^36 - 110 * q^37 - 22 * q^38 - 22 * q^40 - 192 * q^41 - 264 * q^42 - 88 * q^43 - 44 * q^47 + 24 * q^48 - 44 * q^51 - 374 * q^52 - 22 * q^53 - 32 * q^55 - 220 * q^56 + 88 * q^57 - 58 * q^58 - 22 * q^60 - 220 * q^61 + 8 * q^62 - 44 * q^63 - 22 * q^65 - 44 * q^66 - 22 * q^67 - 96 * q^70 - 136 * q^71 - 46 * q^72 + 18 * q^73 - 34 * q^75 - 176 * q^76 - 116 * q^77 + 80 * q^78 + 176 * q^80 - 236 * q^81 - 2 * q^82 - 88 * q^83 - 448 * q^85 - 86 * q^87 - 110 * q^88 - 88 * q^90 - 228 * q^92 + 4 * q^93 - 236 * q^95 - 332 * q^96 - 88 * q^97 + 84 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/805\mathbb{Z}\right)^\times$.

$n$	$162$	$281$	$346$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−2.30557	+	1.40532i	−1.63028	+	0.993709i	−0.660149	+	0.751135i	$0.729507\pi$
$2$	−2.30557	+	1.40532i	−1.63028	+	0.993709i	−0.970133	+	0.242574i	$0.922008\pi$
$3$	−1.13353	−	2.33346i	−0.654442	−	1.34723i	−0.923313	−	0.384049i	$-0.874529\pi$
$3$	−1.13353	−	2.33346i	−0.654442	−	1.34723i	0.268871	−	0.963176i	$-0.413350\pi$
$4$	2.42427	−	4.70243i	1.21214	−	2.35121i
$5$	−0.533908	+	2.17139i	−0.238771	+	0.971076i
$5$	−0.533908	+	2.17139i	−0.238771	+	0.971076i
$6$	5.89267	+	3.78699i	2.40567	+	1.54603i
$7$	−0.0145566	+	2.64571i	−0.00550188	+	0.999985i
$7$	−0.0145566	+	2.64571i	−0.00550188	+	0.999985i
$8$	0.633836	+	8.86218i	0.224095	+	3.13326i
$9$	−2.30569	+	2.93193i	−0.768564	+	0.977309i
$10$	−1.82053	−	5.75660i	−0.575703	−	1.82040i
$11$	−1.14864	+	0.278657i	−0.346328	+	0.0840182i	−0.405150	−	0.914250i	$-0.632781\pi$
$11$	−1.14864	+	0.278657i	−0.346328	+	0.0840182i	0.0588221	+	0.998268i	$0.481266\pi$
$12$	−13.7209	−	0.326619i	−3.96089	−	0.0942867i
$13$	−0.865793	−	0.322924i	−0.240128	−	0.0895630i	0.226519	−	0.974007i	$-0.427265\pi$
$13$	−0.865793	−	0.322924i	−0.240128	−	0.0895630i	−0.466647	+	0.884444i	$0.654538\pi$
$14$	−3.68450	−	6.12032i	−0.984724	−	1.63572i
$15$	5.67206	−	1.21548i	1.46452	−	0.313834i
$16$	−7.77788	−	10.9225i	−1.94447	−	2.73063i
$17$	2.22621	+	2.44891i	0.539935	+	0.593948i	0.947709	−	0.319134i	$-0.103392\pi$
$17$	2.22621	+	2.44891i	0.539935	+	0.593948i	−0.407775	+	0.913082i	$0.633695\pi$
$18$	1.19564	−	9.99998i	0.281816	−	2.35702i
$19$	−0.191553	−	4.02120i	−0.0439454	−	0.922527i	−0.907959	−	0.419059i	$-0.862360\pi$
$19$	−0.191553	−	4.02120i	−0.0439454	−	0.922527i	0.864014	−	0.503468i	$-0.167943\pi$
$20$	8.91648	+	7.77471i	1.99379	+	1.73848i
$21$	6.19017	−	2.96502i	1.35081	−	0.647020i
$22$	2.25666	−	2.25666i	0.481122	−	0.481122i
$23$	−0.103641	+	4.79471i	−0.0216106	+	0.999766i
$23$	−0.103641	+	4.79471i	−0.0216106	+	0.999766i
$24$	19.9611	−	11.5246i	4.07454	−	2.35244i
$25$	−4.42988	−	2.31865i	−0.885977	−	0.463729i
$26$	2.44995	−	0.472190i	0.480475	−	0.0926041i
$27$	1.85033	+	0.402514i	0.356095	+	0.0774638i
$28$	12.4060	+	6.48237i	2.34451	+	1.22505i
$29$	−0.866841	+	1.34883i	−0.160968	+	0.250472i	−0.912364	−	0.409381i	$-0.865745\pi$
$29$	−0.866841	+	1.34883i	−0.160968	+	0.250472i	0.751395	+	0.659852i	$0.229381\pi$
$30$	−11.3692	+	10.7734i	−2.07572	+	1.96694i
$31$	6.93937	+	1.33745i	1.24635	+	0.240214i	0.769428	−	0.638733i	$-0.220541\pi$
$31$	6.93937	+	1.33745i	1.24635	+	0.240214i	0.476919	+	0.878947i	$0.341753\pi$
$32$	16.9471	+	7.25716i	2.99585	+	1.28290i
$33$	1.95225	+	2.36444i	0.339843	+	0.411597i
$34$	−8.57416	−	2.51760i	−1.47046	−	0.431765i
$35$	−5.73710	−	1.44417i	−0.969748	−	0.244110i
$36$	8.19755	+	17.9501i	1.36626	+	2.99169i
$37$	2.99540	−	0.358143i	0.492440	−	0.0588784i	0.131209	−	0.991355i	$-0.458114\pi$
$37$	2.99540	−	0.358143i	0.492440	−	0.0588784i	0.361231	+	0.932476i	$0.382357\pi$
$38$	6.09270	+	9.00195i	0.988366	+	1.46031i
$39$	0.227868	+	2.38634i	0.0364880	+	0.382120i
$40$	−19.5817	−	3.35529i	−3.09614	−	0.530517i
$41$	−1.72799	−	12.0184i	−0.269866	−	1.87696i	−0.449577	−	0.893242i	$-0.648425\pi$
$41$	−1.72799	−	12.0184i	−0.269866	−	1.87696i	0.179711	−	0.983720i	$-0.442484\pi$
$42$	−10.1051	+	15.5352i	−1.55925	+	2.39713i
$43$	0.433768	−	6.06487i	0.0661490	−	0.924884i	−0.850700	−	0.525651i	$-0.823822\pi$
$43$	0.433768	−	6.06487i	0.0661490	−	0.924884i	0.916849	−	0.399233i	$-0.130724\pi$
$44$	−1.47425	+	6.07694i	−0.222251	+	0.916133i
$45$	−5.13533	−	6.57194i	−0.765530	−	0.979687i
$46$	−6.49913	−	11.2002i	−0.958245	−	1.65138i
$47$	−7.88864	+	2.11376i	−1.15068	+	0.308323i	−0.783236	−	0.621724i	$-0.786433\pi$
$47$	−7.88864	+	2.11376i	−1.15068	+	0.308323i	−0.367441	+	0.930047i	$0.619766\pi$
$48$	−16.6708	+	30.5303i	−2.40623	+	4.40668i
$49$	−6.99958	−	0.0770252i	−0.999939	−	0.0110036i
$50$	13.4718	−	0.879593i	1.90520	−	0.124393i
$51$	3.19098	−	7.97068i	0.446826	−	1.11612i
$52$	−3.61744	+	3.28847i	−0.501649	+	0.456029i
$53$	−7.71830	−	6.37276i	−1.06019	−	0.875366i	−0.0677012	−	0.997706i	$-0.521566\pi$
$53$	−7.71830	−	6.37276i	−1.06019	−	0.875366i	−0.992488	+	0.122339i	$0.960960\pi$
$54$	−4.83171	+	1.67227i	−0.657512	+	0.227567i
$55$	0.00819449	−	2.64292i	0.00110495	−	0.356372i
$56$	−23.4560	+	1.54794i	−3.13444	+	0.206853i
$57$	−9.16619	+	5.00512i	−1.21409	+	0.662944i
$58$	0.103026	−	4.32801i	0.0135279	−	0.568295i
$59$	12.2362	+	8.71333i	1.59301	+	1.13438i	0.918005	+	0.396569i	$0.129799\pi$
$59$	12.2362	+	8.71333i	1.59301	+	1.13438i	0.675008	+	0.737810i	$0.264140\pi$
$60$	8.03493	−	29.6191i	1.03730	−	3.82381i
$61$	−6.07208	+	2.10157i	−0.777450	+	0.269078i	−0.686840	−	0.726808i	$-0.741003\pi$
$61$	−6.07208	+	2.10157i	−0.777450	+	0.269078i	−0.0906099	+	0.995886i	$0.528882\pi$
$62$	−17.8787	+	6.66842i	−2.27060	+	0.846890i
$63$	−7.72347	−	6.14287i	−0.973065	−	0.773929i
$64$	−22.7265	+	3.26758i	−2.84081	+	0.408447i
$65$	1.16345	−	1.70756i	0.144308	−	0.211797i
$66$	−7.82383	−	2.70785i	−0.963047	−	0.333314i
$67$	−4.31836	+	0.102796i	−0.527572	+	0.0125586i	−0.286740	−	0.958008i	$-0.592572\pi$
$67$	−4.31836	+	0.102796i	−0.527572	+	0.0125586i	−0.240832	+	0.970567i	$0.577420\pi$
$68$	16.9128	−	4.53176i	2.05097	−	0.549557i
$69$	11.3058	−	5.19309i	1.36105	−	0.625175i
$70$	15.2568	−	4.73280i	1.82354	−	0.565678i
$71$	−2.79135	+	0.819614i	−0.331272	+	0.0972703i	−0.443139	−	0.896453i	$-0.646135\pi$
$71$	−2.79135	+	0.819614i	−0.331272	+	0.0972703i	0.111867	+	0.993723i	$0.464317\pi$
$72$	−27.4447	−	18.5751i	−3.23439	−	2.18910i
$73$	−12.3369	+	3.94368i	−1.44392	+	0.461572i	−0.920582	−	0.390550i	$-0.872285\pi$
$73$	−12.3369	+	3.94368i	−1.44392	+	0.461572i	−0.523342	+	0.852123i	$0.675315\pi$
$74$	−6.40278	+	5.03520i	−0.744308	+	0.585330i
$75$	−0.389086	+	12.9652i	−0.0449278	+	1.49709i
$76$	−19.3738	−	8.84771i	−2.22233	−	1.01490i
$77$	−0.720526	−	3.04303i	−0.0821115	−	0.346785i
$78$	−3.87893	−	5.18164i	−0.439202	−	0.586705i
$79$	−10.0212	−	0.956906i	−1.12747	−	0.107660i	−0.485390	−	0.874298i	$-0.661322\pi$
$79$	−10.0212	−	0.956906i	−1.12747	−	0.107660i	−0.642080	+	0.766637i	$0.721928\pi$
$80$	27.8697	−	11.0572i	3.11593	−	1.23623i
$81$	1.47995	+	6.10045i	0.164439	+	0.677828i
$82$	20.8737	+	25.2809i	2.30511	+	2.79181i
$83$	9.85926	−	7.38055i	1.08219	−	0.810121i	0.0994415	−	0.995043i	$-0.468294\pi$
$83$	9.85926	−	7.38055i	1.08219	−	0.810121i	0.982753	+	0.184923i	$0.0592035\pi$
$84$	1.06387	−	36.2968i	0.116078	−	3.96031i
$85$	−6.50613	+	3.52648i	−0.705689	+	0.382500i
$86$	7.52298	+	14.5925i	0.811224	+	1.57355i
$87$	4.13004	+	0.493806i	0.442786	+	0.0529416i
$88$	−3.19756	−	10.0028i	−0.340861	−	1.06631i
$89$	−4.51144	+	0.869509i	−0.478212	+	0.0921678i	−0.422661	−	0.906288i	$-0.638904\pi$
$89$	−4.51144	+	0.869509i	−0.478212	+	0.0921678i	−0.0555513	+	0.998456i	$0.517692\pi$
$90$	21.0755	+	7.93528i	2.22155	+	0.836452i
$91$	0.866967	−	2.28594i	0.0908828	−	0.239631i
$92$	22.2955	+	12.1110i	2.32447	+	1.26266i
$93$	−4.74506	−	17.7088i	−0.492040	−	1.83632i
$94$	15.2173	−	15.9594i	1.56954	−	1.64609i
$95$	8.83387	+	1.73101i	0.906336	+	0.177598i
$96$	−2.27564	−	47.7715i	−0.232256	−	4.87566i
$97$	−10.3341	−	7.73601i	−1.04927	−	0.785473i	−0.0719850	−	0.997406i	$-0.522933\pi$
$97$	−10.3341	−	7.73601i	−1.04927	−	0.785473i	−0.977284	+	0.211933i	$0.932024\pi$
$98$	16.2462	−	9.65903i	1.64112	−	0.975709i
$99$	1.83141	−	4.01022i	0.184063	−	0.403043i
$100$	−21.6425	+	15.2102i	−2.16425	+	1.52102i
$101$	−6.43898	+	2.57778i	−0.640702	+	0.256499i	−0.669185	−	0.743096i	$-0.733357\pi$
$101$	−6.43898	+	2.57778i	−0.640702	+	0.256499i	0.0284827	+	0.999594i	$0.490932\pi$
$102$	3.84431	+	22.8613i	0.380643	+	2.26360i
$103$	8.11941	+	0.193278i	0.800030	+	0.0190443i	0.421824	−	0.906678i	$-0.361390\pi$
$103$	8.11941	+	0.193278i	0.800030	+	0.0190443i	0.378205	+	0.925722i	$0.376541\pi$
$104$	2.31304	−	7.87750i	0.226812	−	0.772452i
$105$	3.13323	+	15.0243i	0.305772	+	1.46622i
$106$	26.7508	+	3.84618i	2.59827	+	0.373574i
$107$	−0.310050	−	0.150613i	−0.0299736	−	0.0145603i	0.421897	−	0.906644i	$-0.361364\pi$
$107$	−0.310050	−	0.150613i	−0.0299736	−	0.0145603i	−0.451871	+	0.892083i	$0.649243\pi$
$108$	6.37848	−	7.72523i	0.613770	−	0.743360i
$109$	0.0653627	−	1.37213i	0.00626062	−	0.131426i	−0.993573	−	0.113192i	$-0.963892\pi$
$109$	0.0653627	−	1.37213i	0.00626062	−	0.131426i	0.999834	−	0.0182344i	$-0.00580451\pi$
$110$	3.69525	+	6.10495i	0.352328	+	0.582084i
$111$	−4.23107	−	6.58368i	−0.401596	−	0.624895i
$112$	29.0110	−	20.4190i	2.74128	−	1.92942i
$113$	−10.1726	−	5.55467i	−0.956959	−	0.522539i	−0.0767115	−	0.997053i	$-0.524442\pi$
$113$	−10.1726	−	5.55467i	−0.956959	−	0.522539i	−0.880248	+	0.474514i	$0.842624\pi$
$114$	14.0995	−	24.4210i	1.32054	−	2.28724i
$115$	−10.3559	−	2.78498i	−0.965689	−	0.259701i
$116$	4.24133	+	7.34619i	0.393797	+	0.682077i
$117$	2.94304	−	1.79388i	0.272084	−	0.165844i
$118$	−40.4563	−	2.89349i	−3.72430	−	0.266367i
$119$	−6.51152	+	5.85425i	−0.596910	+	0.536659i
$120$	14.3669	+	49.4964i	1.31151	+	4.51839i
$121$	−8.53547	+	4.40034i	−0.775951	+	0.400031i
$122$	11.0462	−	13.3785i	1.00008	−	1.21123i
$123$	−26.0858	+	17.6554i	−2.35208	+	1.59193i
$124$	23.1122	−	29.3895i	2.07554	−	2.63926i
$125$	7.39984	−	8.38107i	0.661862	−	0.749626i
$126$	26.4396	+	3.30889i	2.35543	+	0.294780i
$127$	0.200627	+	0.367421i	0.0178028	+	0.0326034i	0.886429	−	0.462865i	$-0.153178\pi$
$127$	0.200627	+	0.367421i	0.0178028	+	0.0326034i	−0.868626	+	0.495468i	$0.834997\pi$
$128$	19.3735	−	15.9961i	1.71239	−	1.41387i
$129$	−14.6438	+	5.86251i	−1.28932	+	0.516165i
$130$	−0.282741	+	5.57192i	−0.0247980	+	0.488689i
$131$	−8.71319	−	12.2360i	−0.761275	−	1.06906i	−0.995301	−	0.0968311i	$-0.969129\pi$
$131$	−8.71319	−	12.2360i	−0.761275	−	1.06906i	0.234026	−	0.972230i	$-0.424810\pi$
$132$	15.8514	−	3.44826i	1.37969	−	0.300133i
$133$	10.6417	−	0.448260i	0.922754	−	0.0388691i
$134$	9.81181	−	6.30567i	0.847611	−	0.544727i
$135$	−1.86192	+	3.80288i	−0.160249	+	0.327300i
$136$	−20.2916	+	21.2813i	−1.73999	+	1.82485i
$137$	−11.0080	−	2.94958i	−0.940476	−	0.252000i	−0.244160	−	0.969735i	$-0.578512\pi$
$137$	−11.0080	−	2.94958i	−0.940476	−	0.252000i	−0.696316	+	0.717735i	$0.745179\pi$
$138$	−18.7683	+	27.8612i	−1.59766	+	2.37170i
$139$			4.53147i			0.384354i	0.981360	+	0.192177i	$0.0615548\pi$
$139$			4.53147i			0.384354i	−0.981360	+	0.192177i	$0.938445\pi$
$140$	−20.6994	+	23.4773i	−1.74942	+	1.98419i
$141$	13.8744	+	16.0119i	1.16843	+	1.34844i
$142$	5.28383	−	5.81240i	0.443409	−	0.487766i
$143$	1.08447	+	0.129664i	0.0906879	+	0.0108431i
$144$	49.9574	+	2.37976i	4.16311	+	0.198314i
$145$	−2.46603	−	2.60240i	−0.204793	−	0.216118i
$146$	22.9014	−	26.4296i	1.89533	−	2.18733i
$147$	7.75447	+	16.4206i	0.639578	+	1.35435i
$148$	5.57751	−	14.9539i	0.458468	−	1.22920i
$149$	−7.80946	+	7.44631i	−0.639776	+	0.610025i	−0.938900	−	0.344189i	$-0.888154\pi$
$149$	−7.80946	+	7.44631i	−0.639776	+	0.610025i	0.299124	+	0.954214i	$0.403305\pi$
$150$	−17.3232	−	30.4390i	−1.41443	−	2.48533i
$151$	5.93183	−	8.33008i	0.482725	−	0.677893i	−0.499346	−	0.866403i	$-0.666426\pi$
$151$	5.93183	−	8.33008i	0.482725	−	0.677893i	0.982071	+	0.188510i	$0.0603658\pi$
$152$	35.5152	−	4.24636i	2.88066	−	0.344425i
$153$	−12.3130	+	0.880641i	−0.995445	+	0.0711956i
$154$	5.93763	+	6.00333i	0.478468	+	0.483762i
$155$	−6.60912	+	14.3540i	−0.530858	+	1.15294i
$156$	11.7740	+	4.71360i	0.942675	+	0.377390i
$157$	4.57148	−	1.46134i	0.364844	−	0.116628i	−0.116428	−	0.993199i	$-0.537144\pi$
$157$	4.57148	−	1.46134i	0.364844	−	0.116628i	0.481272	+	0.876571i	$0.340175\pi$
$158$	24.4492	−	11.8767i	1.94508	−	0.944860i
$159$	−6.12172	+	25.2341i	−0.485484	+	2.00119i
$160$	−24.8063	+	32.9241i	−1.96111	+	2.60288i
$161$	−12.6839	−	0.343998i	−0.999632	−	0.0271109i
$162$	−11.9852	−	11.9852i	−0.941645	−	0.941645i
$163$	−6.33436	−	10.3922i	−0.496145	−	0.813978i	0.502576	−	0.864533i	$-0.332386\pi$
$163$	−6.33436	−	10.3922i	−0.496145	−	0.813978i	−0.998721	+	0.0505554i	$0.983901\pi$
$164$	−60.7049	−	21.0102i	−4.74025	−	1.64062i
$165$	−6.17646	+	2.97670i	−0.480836	+	0.231736i
$166$	−12.3592	+	30.8717i	−0.959258	+	2.39611i
$167$	1.07160	+	4.92605i	0.0829227	+	0.381189i	0.999840	−	0.0178878i	$-0.00569416\pi$
$167$	1.07160	+	4.92605i	0.0829227	+	0.381189i	−0.916917	+	0.399077i	$0.869331\pi$
$168$	30.2001	+	52.9791i	2.32999	+	4.08743i
$169$	−9.17943	−	7.95402i	−0.706110	−	0.611848i
$170$	10.0445	−	17.2737i	0.770379	−	1.32483i
$171$	12.2315	+	8.71003i	0.935368	+	0.666073i
$172$	−27.4680	−	16.7426i	−2.09442	−	1.27661i
$173$	−0.151149	+	6.34962i	−0.0114917	+	0.482752i	0.964394	+	0.264470i	$0.0851970\pi$
$173$	−0.151149	+	6.34962i	−0.0114917	+	0.482752i	−0.975886	+	0.218283i	$0.929955\pi$
$174$	−10.2160	+	4.66550i	−0.774475	+	0.353691i
$175$	6.19895	−	11.6864i	0.468597	−	0.883412i
$176$	11.9776	+	10.3787i	0.902847	+	0.782321i
$177$	6.46223	−	38.4294i	0.485731	−	2.88853i
$178$	9.17949	−	8.34471i	0.688032	−	0.625463i
$179$	14.5614	+	18.5163i	1.08837	+	1.38397i	0.917058	+	0.398754i	$0.130557\pi$
$179$	14.5614	+	18.5163i	1.08837	+	1.38397i	0.171309	+	0.985217i	$0.445200\pi$
$180$	−43.3535	+	8.21637i	−3.23138	+	0.612412i
$181$	2.07726	−	1.79996i	0.154402	−	0.133790i	−0.574234	−	0.818691i	$-0.694700\pi$
$181$	2.07726	−	1.79996i	0.154402	−	0.133790i	0.728636	+	0.684901i	$0.240155\pi$
$182$	1.21362	+	6.48874i	0.0899591	+	0.480978i
$183$	11.7868	+	11.7868i	0.871305	+	0.871305i
$184$	−42.5573	+	2.12058i	−3.13737	+	0.156331i
$185$	−0.821596	+	6.69539i	−0.0604049	+	0.492255i
$186$	35.8265	+	34.1605i	2.62693	+	2.50477i
$187$	−3.23952	−	2.19257i	−0.236897	−	0.160336i
$188$	−9.18442	+	42.2201i	−0.669843	+	3.07922i
$189$	−1.09187	+	4.88957i	−0.0794219	+	0.355664i
$190$	−22.7997	+	8.42342i	−1.65406	+	0.611099i
$191$	−4.92775	+	3.50903i	−0.356559	+	0.253905i	−0.744274	−	0.667875i	$-0.767204\pi$
$191$	−4.92775	+	3.50903i	−0.356559	+	0.253905i	0.387714	+	0.921780i	$0.373265\pi$
$192$	33.3859	+	49.3276i	2.40942	+	3.55991i
$193$	0.744748	−	1.73915i	0.0536082	−	0.125187i	−0.890323	−	0.455330i	$-0.849521\pi$
$193$	0.744748	−	1.73915i	0.0536082	−	0.125187i	0.943931	+	0.330143i	$0.107097\pi$
$194$	34.6975	+	3.31321i	2.49114	+	0.237875i
$195$	−5.30334	−	0.779295i	−0.379780	−	0.0558065i
$196$	−17.3311	+	32.7283i	−1.23793	+	2.33773i
$197$	3.07224	−	8.23698i	0.218888	−	0.586861i	−0.780373	−	0.625315i	$-0.784971\pi$
$197$	3.07224	−	8.23698i	0.218888	−	0.586861i	0.999260	+	0.0384540i	$0.0122433\pi$
$198$	1.41320	+	11.8195i	0.100432	+	0.839978i
$199$	9.64502	+	1.85892i	0.683717	+	0.131776i	0.519270	−	0.854610i	$-0.326204\pi$
$199$	9.64502	+	1.85892i	0.683717	+	0.131776i	0.164447	+	0.986386i	$0.447416\pi$
$200$	17.7405	−	40.7281i	1.25444	−	2.87991i
$201$	5.13485	+	9.96022i	0.362184	+	0.702539i
$202$	11.2229	−	14.9920i	0.789641	−	1.05484i
$203$	−3.55600	−	2.31305i	−0.249582	−	0.162344i
$204$	−29.7458	−	34.3284i	−2.08262	−	2.40347i
$205$	27.0193	+	2.66459i	1.88711	+	0.186103i
$206$	−18.9915	+	10.9647i	−1.32320	+	0.763949i
$207$	−13.8188	−	11.3590i	−0.960471	−	0.789505i
$208$	3.20689	+	11.9683i	0.222358	+	0.829852i
$209$	1.34056	+	4.56553i	0.0927286	+	0.315805i
$210$	−28.3378	−	30.2364i	−1.95549	−	2.08651i
$211$	−5.51840	+	3.54646i	−0.379902	+	0.244148i	−0.716630	−	0.697454i	$-0.754316\pi$
$211$	−5.51840	+	3.54646i	−0.379902	+	0.244148i	0.336728	+	0.941602i	$0.390680\pi$
$212$	−48.6787	+	20.8454i	−3.34327	+	1.43167i
$213$	5.07661	+	5.58446i	0.347844	+	0.382641i
$214$	0.926499	−	0.0884699i	0.0633341	−	0.00604768i
$215$	12.9376	+	4.17996i	0.882338	+	0.285071i
$216$	−2.39435	+	16.6531i	−0.162915	+	1.13310i
$217$	−3.63953	+	18.3401i	−0.247067	+	1.24501i
$218$	1.77758	+	3.25540i	0.120393	+	0.220483i
$219$	23.1866	+	24.3174i	1.56681	+	1.64322i
$220$	−12.4083	−	6.44570i	−0.836567	−	0.434569i
$221$	−1.13662	−	2.83915i	−0.0764575	−	0.190982i
$222$	19.0072	+	9.23312i	1.27568	+	0.619686i
$223$	−1.30606	−	3.50167i	−0.0874600	−	0.234489i	0.885855	−	0.463962i	$-0.153573\pi$
$223$	−1.30606	−	3.50167i	−0.0874600	−	0.234489i	−0.973315	+	0.229473i	$0.926300\pi$
$224$	−19.4470	+	44.7314i	−1.29936	+	2.98874i
$225$	17.0120	−	7.64201i	1.13414	−	0.509467i
$226$	31.2597	−	1.48908i	2.07937	−	0.0990524i
$227$	−10.3194	−	21.2433i	−0.684921	−	1.40997i	−0.901098	−	0.433616i	$-0.857237\pi$
$227$	−10.3194	−	21.2433i	−0.684921	−	1.40997i	0.216176	−	0.976354i	$-0.430641\pi$
$228$	1.31489	+	55.2371i	0.0870807	+	3.65817i
$229$	13.2377	−	22.9283i	0.874771	−	1.51515i	0.0177643	−	0.999842i	$-0.494345\pi$
$229$	13.2377	−	22.9283i	0.874771	−	1.51515i	0.857007	−	0.515305i	$-0.172322\pi$
$230$	27.7899	−	8.13230i	1.83241	−	0.536228i
$231$	−6.28405	+	5.13067i	−0.413460	+	0.337573i
$232$	−12.5030	−	6.82717i	−0.820864	−	0.448226i
$233$	−3.39818	+	5.02081i	−0.222622	+	0.328924i	−0.922966	−	0.384882i	$-0.874242\pi$
$233$	−3.39818	+	5.02081i	−0.222622	+	0.328924i	0.700344	+	0.713806i	$0.253030\pi$
$234$	−4.26441	+	8.27181i	−0.278773	+	0.540745i
$235$	−0.377982	−	18.2579i	−0.0246568	−	1.19101i
$236$	70.6376	−	36.4162i	4.59812	−	2.37049i
$237$	9.12636	+	24.4687i	0.592821	+	1.58941i
$238$	6.78566	−	22.6481i	0.439849	−	1.46806i
$239$	−5.24937	−	0.754746i	−0.339554	−	0.0488204i	−0.0295710	−	0.999563i	$-0.509414\pi$
$239$	−5.24937	−	0.754746i	−0.339554	−	0.0488204i	−0.309983	+	0.950742i	$0.600323\pi$
$240$	−57.3927	−	52.4993i	−3.70468	−	3.38882i
$241$	−0.461967	+	0.112072i	−0.0297579	+	0.00721919i	−0.250610	−	0.968088i	$-0.580631\pi$
$241$	−0.461967	+	0.112072i	−0.0297579	+	0.00721919i	0.220852	+	0.975307i	$0.429116\pi$
$242$	13.4952	−	22.1403i	0.867506	−	1.42323i
$243$	16.9382	−	13.9853i	1.08659	−	0.897160i
$244$	−4.83789	+	33.6483i	−0.309714	+	2.15411i
$245$	3.90438	−	15.1577i	0.249442	−	0.968390i
$246$	35.3312	−	77.3645i	2.25263	−	4.93258i
$247$	−1.13270	+	3.54338i	−0.0720718	+	0.225460i
$248$	−7.45434	+	62.3457i	−0.473351	+	3.95896i
$249$	−28.3980	−	14.6402i	−1.79965	−	0.927783i
$250$	−5.28277	+	29.7222i	−0.334112	+	1.87980i
$251$	−1.87839	−	6.39721i	−0.118563	−	0.403789i	0.878730	−	0.477319i	$-0.158391\pi$
$251$	−1.87839	−	6.39721i	−0.118563	−	0.403789i	−0.997293	+	0.0735307i	$0.976573\pi$
$252$	−47.6102	+	21.4271i	−2.99916	+	1.34978i
$253$	−1.21703	−	5.53628i	−0.0765143	−	0.348063i
$254$	−0.978903	−	0.565170i	−0.0614218	−	0.0354619i
$255$	15.6038	+	11.1845i	0.977146	+	0.700399i
$256$	−7.16816	+	20.7110i	−0.448010	+	1.29444i
$257$	8.58486	−	9.44366i	0.535509	−	0.589080i	−0.411049	−	0.911613i	$-0.634838\pi$
$257$	8.58486	−	9.44366i	0.535509	−	0.589080i	0.946558	+	0.322534i	$0.104535\pi$
$258$	25.5237	−	34.0956i	1.58903	−	2.12270i
$259$	0.903941	+	7.93016i	0.0561682	+	0.492756i
$260$	−5.20918	−	9.61063i	−0.323060	−	0.596026i
$261$	−1.95600	−	5.65150i	−0.121074	−	0.349819i
$262$	37.2843	+	15.9660i	2.30343	+	0.986386i
$263$	−31.0334	+	5.21852i	−1.91360	+	0.321788i	−0.996960	−	0.0779207i	$-0.975172\pi$
$263$	−31.0334	+	5.21852i	−1.91360	+	0.321788i	−0.916642	+	0.399709i	$0.869111\pi$
$264$	−19.7167	+	18.7999i	−1.21348	+	1.15705i
$265$	17.9586	−	13.3570i	1.10319	−	0.820512i
$266$	−23.9053	+	15.9885i	−1.46573	+	0.980317i
$267$	7.14281	+	9.54167i	0.437133	+	0.583941i
$268$	−9.98549	+	20.5560i	−0.609961	+	1.25566i
$269$	−0.0692669	−	0.725396i	−0.00422328	−	0.0442282i	0.993115	−	0.117147i	$-0.0373748\pi$
$269$	−0.0692669	−	0.725396i	−0.00422328	−	0.0442282i	−0.997338	+	0.0729185i	$0.976769\pi$
$270$	−1.05147	−	11.3844i	−0.0639902	−	0.692831i
$271$	28.1747	+	11.2794i	1.71149	+	0.685177i	0.999849	−	0.0173672i	$-0.00552842\pi$
$271$	28.1747	+	11.2794i	1.71149	+	0.685177i	0.711640	+	0.702544i	$0.247953\pi$
$272$	9.43306	−	43.3631i	0.571963	−	2.62927i
$273$	−6.31688	+	0.568135i	−0.382315	+	0.0343851i
$274$	29.5248	−	8.66925i	1.78366	−	0.523729i
$275$	5.73445	+	1.42887i	0.345800	+	0.0861642i
$276$	2.98809	−	65.7540i	0.179862	−	3.95793i
$277$	3.03008	−	11.3084i	0.182060	−	0.679457i	−0.813181	−	0.582011i	$-0.802266\pi$
$277$	3.03008	−	11.3084i	0.182060	−	0.679457i	0.995241	−	0.0974457i	$-0.0310672\pi$
$278$	−6.36815	−	10.4476i	−0.381936	−	0.626606i
$279$	−19.9214	+	17.2620i	−1.19266	+	1.03345i
$280$	9.16216	−	51.7586i	0.547544	−	3.09317i
$281$	−21.8037	+	3.13490i	−1.30070	+	0.187012i	−0.757635	−	0.652679i	$-0.773645\pi$
$281$	−21.8037	+	3.13490i	−1.30070	+	0.187012i	−0.543065	+	0.839691i	$0.682736\pi$
$282$	−54.4900	−	17.4186i	−3.24483	−	1.03726i
$283$	18.2003	+	15.0275i	1.08190	+	0.893290i	0.994692	−	0.102901i	$-0.0328124\pi$
$283$	18.2003	+	15.0275i	1.08190	+	0.893290i	0.0872056	+	0.996190i	$0.472206\pi$
$284$	−2.91281	+	15.1131i	−0.172843	+	0.896797i
$285$	−5.97417	−	22.5757i	−0.353879	−	1.33727i
$286$	−2.68254	+	1.22507i	−0.158622	+	0.0724401i
$287$	31.8224	−	4.39681i	1.87842	−	0.259535i
$288$	−60.3522	+	32.9548i	−3.55628	+	1.94188i
$289$	0.574789	−	6.01946i	0.0338111	−	0.354086i
$290$	9.34279	+	2.53447i	0.548628	+	0.148829i
$291$	−6.33772	+	32.8832i	−0.371524	+	1.92765i
$292$	−11.3631	+	67.5739i	−0.664976	+	3.95446i
$293$	5.85102	+	26.8967i	0.341820	+	1.57132i	0.751903	+	0.659274i	$0.229136\pi$
$293$	5.85102	+	26.8967i	0.341820	+	1.57132i	−0.410083	+	0.912048i	$0.634500\pi$
$294$	−40.9545	−	26.9612i	−2.38852	−	1.57241i
$295$	−25.4530	+	21.9174i	−1.48193	+	1.27608i
$296$	5.07252	+	26.3187i	0.294834	+	1.52975i
$297$	−2.23752	+	0.0532629i	−0.129834	+	0.00309063i
$298$	7.54082	−	28.1427i	0.436828	−	1.63026i
$299$	1.63806	−	4.11776i	0.0947314	−	0.238136i
$300$	60.0248	+	33.2609i	3.46553	+	1.92032i
$301$	16.0396	+	1.23591i	0.924506	+	0.0712366i
$302$	−1.96982	+	27.5416i	−0.113350	+	1.58484i
$303$	13.3139	+	12.1031i	0.764864	+	0.695307i
$304$	−42.4317	+	33.3687i	−2.43363	+	1.91382i
$305$	−1.32139	−	14.3069i	−0.0756628	−	0.819211i
$306$	27.1508	−	19.3340i	1.55211	−	1.10525i
$307$	−20.6449	+	1.47656i	−1.17827	+	0.0842714i	−0.646701	−	0.762744i	$-0.723852\pi$
$307$	−20.6449	+	1.47656i	−1.17827	+	0.0842714i	−0.531568	+	0.847015i	$0.678397\pi$
$308$	−16.0564	−	3.98890i	−0.914896	−	0.227288i
$309$	−8.75256	−	19.1654i	−0.497916	−	1.09028i
$310$	−4.93416	−	42.3820i	−0.280241	−	2.40714i
$311$	2.12213	+	8.74752i	0.120335	+	0.496026i	0.999799	+	0.0200610i	$0.00638605\pi$
$311$	2.12213	+	8.74752i	0.120335	+	0.496026i	−0.879464	+	0.475965i	$0.842099\pi$
$312$	−21.0037	+	3.53195i	−1.18910	+	0.199957i
$313$	3.08549	+	25.8060i	0.174402	+	1.45864i	0.760994	+	0.648759i	$0.224712\pi$
$313$	3.08549	+	25.8060i	0.174402	+	1.45864i	−0.586592	+	0.809883i	$0.699531\pi$
$314$	−8.48621	+	9.79361i	−0.478905	+	0.552685i
$315$	17.4622	−	13.4909i	0.983884	−	0.760128i
$316$	−28.7938	+	44.8041i	−1.61978	+	2.52043i
$317$	−8.88166	−	20.7406i	−0.498844	−	1.16491i	−0.960608	−	0.277908i	$-0.910359\pi$
$317$	−8.88166	−	20.7406i	−0.498844	−	1.16491i	0.461764	−	0.887003i	$-0.347217\pi$
$318$	−21.3478	−	66.7817i	−1.19713	−	3.74493i
$319$	0.619827	−	1.79087i	0.0347037	−	0.100270i
$320$	5.03867	−	51.0927i	0.281670	−	2.85617i
$321$			0.894213i			0.0499101i
$322$	29.7270	−	17.0318i	1.65662	−	0.949145i
$323$	9.42112	−	9.42112i	0.524205	−	0.524205i
$324$	32.2747	+	7.82976i	1.79304	+	0.434987i
$325$	3.08662	+	3.43798i	0.171215	+	0.190705i
$326$	29.2086	+	15.0581i	1.61771	+	0.833989i
$327$	−3.27591	+	1.40283i	−0.181158	+	0.0775765i
$328$	105.414	−	22.9314i	5.82052	−	1.26618i
$329$	−5.47756	−	20.9018i	−0.301987	−	1.15236i
$330$	10.0570	−	15.5429i	0.553621	−	0.855606i
$331$	−5.35641	−	4.21233i	−0.294415	−	0.231531i	0.460015	−	0.887911i	$-0.347844\pi$
$331$	−5.35641	−	4.21233i	−0.294415	−	0.231531i	−0.754430	+	0.656381i	$0.772087\pi$
$332$	−10.8050	−	64.2549i	−0.593001	−	3.52645i
$333$	−5.85641	+	9.60804i	−0.320929	+	0.526518i
$334$	−9.39330	−	9.85141i	−0.513979	−	0.539045i
$335$	2.08240	−	9.43174i	0.113774	−	0.515311i
$336$	−80.5318	−	44.5506i	−4.39337	−	2.43044i
$337$	−0.877591	−	12.2703i	−0.0478054	−	0.668407i	−0.963700	−	0.266988i	$-0.913972\pi$
$337$	−0.877591	−	12.2703i	−0.0478054	−	0.668407i	0.915894	−	0.401419i	$-0.131483\pi$
$338$	32.3417	+	5.43852i	1.75916	+	0.295817i
$339$	−1.43069	+	30.0338i	−0.0777042	+	1.63121i
$340$	0.810369	+	39.1438i	0.0439484	+	2.12287i
$341$	−8.34353	+	0.397451i	−0.451827	+	0.0215232i
$342$	−40.4409	−	2.89239i	−2.18680	−	0.156403i
$343$	0.305676	−	18.5177i	0.0165050	−	0.999864i
$344$	54.0229			2.91272
$345$	5.24000	+	27.3219i	0.282112	+	1.47096i
$346$	−8.57474	−	14.8519i	−0.460981	−	0.798442i
$347$	−0.291203	−	12.2331i	−0.0156326	−	0.656710i	−0.952071	−	0.305877i	$-0.901050\pi$
$347$	−0.291203	−	12.2331i	−0.0156326	−	0.656710i	0.936438	−	0.350832i	$-0.114101\pi$
$348$	12.3344	−	18.2241i	0.661194	−	0.976913i
$349$	9.86969	+	15.3575i	0.528312	+	0.822070i	0.998157	−	0.0606789i	$-0.0193266\pi$
$349$	9.86969	+	15.3575i	0.528312	+	0.822070i	−0.469845	+	0.882749i	$0.655690\pi$
$350$	2.13105	+	35.6554i	0.113909	+	1.90586i
$351$	−1.47202	−	0.946009i	−0.0785705	−	0.0504942i
$352$	−21.4883	−	3.61344i	−1.14533	−	0.192597i
$353$	22.7649	−	15.4077i	1.21165	−	0.820070i	0.223674	−	0.974664i	$-0.428195\pi$
$353$	22.7649	−	15.4077i	1.21165	−	0.820070i	0.987978	+	0.154594i	$0.0494069\pi$
$354$	39.1064	+	97.6831i	2.07848	+	5.19180i
$355$	−0.289380	−	6.49871i	−0.0153587	−	0.344916i
$356$	−6.84815	+	23.3227i	−0.362951	+	1.23610i
$357$	21.0417	+	8.55843i	1.11364	+	0.452960i
$358$	−59.5934	−	22.2272i	−3.14961	−	1.17474i
$359$	−22.2974	−	17.5348i	−1.17681	−	0.925453i	−0.178521	−	0.983936i	$-0.557131\pi$
$359$	−22.2974	−	17.5348i	−1.17681	−	0.925453i	−0.998288	+	0.0584832i	$0.981374\pi$
$360$	54.9868	−	49.6758i	2.89806	−	2.61814i
$361$	2.78061	−	0.265516i	0.146348	−	0.0139745i
$362$	−2.25976	+	7.06914i	−0.118770	+	0.371546i
$363$	19.9432	+	14.9293i	1.04675	+	0.783585i
$364$	−8.64770	−	9.61858i	−0.453262	−	0.504151i
$365$	−1.97650	−	28.8938i	−0.103455	−	1.51237i
$366$	−43.7394	−	10.6111i	−2.28630	−	0.554649i
$367$	9.99631	+	2.67850i	0.521803	+	0.139817i	0.510100	−	0.860115i	$-0.329608\pi$
$367$	9.99631	+	2.67850i	0.521803	+	0.139817i	0.0117025	+	0.999932i	$0.496275\pi$
$368$	53.1764	−	36.1607i	2.77201	−	1.88501i
$369$	39.2213	+	22.6444i	2.04178	+	1.17882i
$370$	−7.51490	−	16.5913i	−0.390681	−	0.862539i
$371$	16.9728	−	20.3276i	0.881186	−	1.05536i
$372$	−94.7777	−	20.6176i	−4.91400	−	1.06897i
$373$	−4.23533	−	9.89042i	−0.219297	−	0.512107i	0.773231	−	0.634124i	$-0.218639\pi$
$373$	−4.23533	−	9.89042i	−0.219297	−	0.512107i	−0.992528	+	0.122018i	$0.961064\pi$
$374$	10.5502	+	0.502567i	0.545536	+	0.0259871i
$375$	−27.9448	−	7.76709i	−1.44307	−	0.401091i
$376$	−23.7326	−	68.5708i	−1.22392	−	3.53627i
$377$	1.18608	−	0.887885i	0.0610860	−	0.0457284i
$378$	−4.35401	−	12.8077i	−0.223946	−	0.658755i
$379$	25.3008	+	7.42897i	1.29961	+	0.381601i	0.857095	−	0.515159i	$-0.172267\pi$
$379$	25.3008	+	7.42897i	1.29961	+	0.381601i	0.442518	+	0.896760i	$0.354085\pi$
$380$	29.5557	−	37.3442i	1.51617	−	1.91572i
$381$	0.629948	−	0.884638i	0.0322732	−	0.0453214i
$382$	6.42995	−	15.0154i	0.328985	−	0.768253i
$383$	3.89551	−	8.01924i	0.199051	−	0.409764i	−0.776319	−	0.630341i	$-0.782915\pi$
$383$	3.89551	−	8.01924i	0.199051	−	0.409764i	0.975370	+	0.220577i	$0.0707940\pi$
$384$	−59.2866	−	27.0753i	−3.02546	−	1.38168i
$385$	6.99229	+	0.0601523i	0.356360	+	0.00306564i
$386$	0.726992	+	5.05634i	0.0370029	+	0.257361i
$387$	16.7816	+	15.2555i	0.853057	+	0.775480i
$388$	−61.4307	+	29.8412i	−3.11867	+	1.51496i
$389$	−25.8282	−	24.6271i	−1.30954	−	1.24865i	−0.948761	−	0.315996i	$-0.897661\pi$
$389$	−25.8282	−	24.6271i	−1.30954	−	1.24865i	−0.360782	−	0.932650i	$-0.617490\pi$
$390$	13.3224	−	5.65615i	0.674604	−	0.286410i
$391$	−11.9725	+	10.4202i	−0.605478	+	0.526973i
$392$	−3.75397	−	62.0804i	−0.189604	−	3.13553i
$393$	−18.6755	+	34.2017i	−0.942057	+	1.72525i
$394$	4.49232	+	23.3084i	0.226320	+	1.17426i
$395$	7.42821	−	21.2490i	0.373754	−	1.06915i
$396$	−14.4180	−	18.3339i	−0.724530	−	0.921315i
$397$	−15.9320	−	5.09292i	−0.799606	−	0.255606i	−0.123436	−	0.992352i	$-0.539392\pi$
$397$	−15.9320	−	5.09292i	−0.799606	−	0.255606i	−0.676169	+	0.736746i	$0.736361\pi$
$398$	−24.8496	+	9.26842i	−1.24560	+	0.464584i
$399$	−13.1087	−	24.3240i	−0.656255	−	1.21772i
$400$	9.12968	+	66.4196i	0.456484	+	3.32098i
$401$	0.136226	−	1.42662i	0.00680280	−	0.0712422i	−0.991433	−	0.130616i	$-0.958304\pi$
$401$	0.136226	−	1.42662i	0.00680280	−	0.0712422i	0.998236	+	0.0593741i	$0.0189105\pi$
$402$	−25.8360	−	15.7479i	−1.28858	−	0.785432i
$403$	−5.57616	−	3.39885i	−0.277768	−	0.169309i
$404$	−3.48801	+	36.5281i	−0.173535	+	1.81734i
$405$	−14.0366	−	0.0435211i	−0.697485	−	0.00216258i
$406$	11.4492	+	0.335578i	0.568212	+	0.0166544i
$407$	−3.34083	+	1.24607i	−0.165599	+	0.0617652i
$408$	72.6602	+	23.2269i	3.59721	+	1.14990i
$409$	9.56750	+	12.1661i	0.473082	+	0.601573i	0.962769	−	0.270325i	$-0.0871313\pi$
$409$	9.56750	+	12.1661i	0.473082	+	0.601573i	−0.489687	+	0.871898i	$0.662889\pi$
$410$	−66.0393	+	31.8272i	−3.26145	+	1.57183i
$411$	5.59511	+	29.0302i	0.275986	+	1.43195i
$412$	20.5925	−	37.7124i	1.01452	−	1.85796i
$413$	−23.2311	+	32.2465i	−1.14313	+	1.58675i
$414$	47.8231	+	6.76917i	2.35038	+	0.332687i
$415$	10.7621	+	25.3489i	0.528292	+	1.24433i
$416$	−12.3291	−	11.7558i	−0.604486	−	0.576376i
$417$	10.5740	−	5.13654i	0.517812	−	0.251538i
$418$	−9.50677	−	8.64223i	−0.464991	−	0.422705i
$419$	−4.16753	−	28.9858i	−0.203597	−	1.41605i	−0.793498	−	0.608573i	$-0.791742\pi$
$419$	−4.16753	−	28.9858i	−0.203597	−	1.41605i	0.589901	−	0.807476i	$-0.299167\pi$
$420$	78.2466	+	21.6892i	3.81805	+	1.05833i
$421$	2.99875	+	1.36949i	0.146150	+	0.0667446i	0.487148	−	0.873320i	$-0.338037\pi$
$421$	2.99875	+	1.36949i	0.146150	+	0.0667446i	−0.340997	+	0.940064i	$0.610765\pi$
$422$	7.73914	−	15.9317i	0.376735	−	0.775542i
$423$	11.9914	−	28.0026i	0.583042	−	1.36153i
$424$	51.5845	−	72.4402i	2.50516	−	3.51801i
$425$	−4.18368	−	16.0102i	−0.202938	−	0.776608i
$426$	−19.5524	−	5.74110i	−0.947316	−	0.278157i
$427$	−5.47175	−	16.0956i	−0.264797	−	0.778919i
$428$	−1.45989	+	1.09286i	−0.0705665	+	0.0528254i
$429$	−0.926708	−	2.67755i	−0.0447419	−	0.129273i
$430$	−35.7027	+	8.54426i	−1.72174	+	0.412041i
$431$	7.19574	+	0.342775i	0.346607	+	0.0165109i	0.220164	−	0.975463i	$-0.429341\pi$
$431$	7.19574	+	0.342775i	0.346607	+	0.0165109i	0.126443	+	0.991974i	$0.459644\pi$
$432$	−9.99516	−	23.3409i	−0.480892	−	1.12299i
$433$	−4.26069	−	0.926856i	−0.204756	−	0.0445419i	0.109018	−	0.994040i	$-0.465230\pi$
$433$	−4.26069	−	0.926856i	−0.204756	−	0.0445419i	−0.313773	+	0.949498i	$0.601593\pi$
$434$	−17.3825	−	47.3990i	−0.834385	−	2.27523i
$435$	−3.27731	+	8.70428i	−0.157135	+	0.417338i
$436$	−6.29390	−	3.63378i	−0.301423	−	0.174027i
$437$	19.3003	−	0.501683i	0.923261	−	0.0239988i
$438$	−87.6320	−	23.4809i	−4.18722	−	1.12196i
$439$	0.566974	+	0.137546i	0.0270602	+	0.00656473i	0.249266	−	0.968435i	$-0.419811\pi$
$439$	0.566974	+	0.137546i	0.0270602	+	0.00656473i	−0.222206	+	0.975000i	$0.571326\pi$
$440$	23.4273	−	1.60256i	1.11685	−	0.0763990i
$441$	16.3647	−	20.3446i	0.779271	−	0.968792i
$442$	6.61046	+	4.94852i	0.314427	+	0.235377i
$443$	−10.9832	+	34.3585i	−0.521828	+	1.63242i	0.230095	+	0.973168i	$0.426096\pi$
$443$	−10.9832	+	34.3585i	−0.521828	+	1.63242i	−0.751923	+	0.659251i	$0.770873\pi$
$444$	−41.2166	+	3.93570i	−1.95605	+	0.186780i
$445$	0.520650	−	10.2603i	0.0246812	−	0.486387i
$446$	7.93216	+	6.23792i	0.375599	+	0.295374i
$447$	26.2279	+	9.78251i	1.24054	+	0.462697i
$448$	−8.31425	−	60.1753i	−0.392811	−	2.84302i
$449$	−5.11506	+	17.4203i	−0.241395	+	0.822114i	0.746285	+	0.665626i	$0.231835\pi$
$449$	−5.11506	+	17.4203i	−0.241395	+	0.822114i	−0.987680	+	0.156488i	$0.949983\pi$
$450$	−28.4830	+	41.5265i	−1.34270	+	1.95758i
$451$	5.33385	+	13.3233i	0.251161	+	0.627370i
$452$	−50.7816	+	34.3700i	−2.38857	+	1.61663i
$453$	−26.1618	−	4.39933i	−1.22919	−	0.206698i
$454$	53.6456	+	34.4760i	2.51771	+	1.61804i
$455$	4.50079	+	3.10301i	0.211000	+	0.145471i
$456$	−50.1662	−	78.0601i	−2.34925	−	3.65550i
$457$	5.12233	−	7.56823i	0.239612	−	0.354027i	−0.689204	−	0.724567i	$-0.742040\pi$
$457$	5.12233	−	7.56823i	0.239612	−	0.354027i	0.928816	+	0.370540i	$0.120828\pi$
$458$	1.70121	+	71.4660i	0.0794922	+	3.33938i
$459$	3.13349	+	5.42736i	0.146259	+	0.253328i
$460$	−38.2016	+	41.9462i	−1.78116	+	1.95575i
$461$	−6.23271			−0.290286			−0.145143	−	0.989411i	$-0.546364\pi$
$461$	−6.23271			−0.290286			−0.145143	+	0.989411i	$0.546364\pi$
$462$	7.27809	−	20.6602i	0.338607	−	0.961199i
$463$	−0.0234471	−	0.00167697i	−0.00108968	−	7.79354e-5i	0.0707943	−	0.997491i	$-0.477447\pi$
$463$	−0.0234471	−	0.00167697i	−0.00108968	−	7.79354e-5i	−0.0718840	+	0.997413i	$0.522901\pi$
$464$	21.4748	−	1.02297i	0.996943	−	0.0474902i
$465$	40.9862	−	0.848511i	1.90069	−	0.0393488i
$466$	0.778909	−	16.3513i	0.0360823	−	0.757460i
$467$	3.13875	+	0.527807i	0.145244	+	0.0244240i	0.238002	−	0.971265i	$-0.423508\pi$
$467$	3.13875	+	0.527807i	0.145244	+	0.0244240i	−0.0927576	+	0.995689i	$0.529568\pi$
$468$	−1.30085	−	18.1883i	−0.0601319	−	0.840754i
$469$	−0.209108	−	11.4266i	−0.00965572	−	0.527633i
$470$	26.5296	+	41.5636i	1.22372	+	1.91719i
$471$	−8.59189	−	9.01092i	−0.395894	−	0.415201i
$472$	−69.4634	+	113.962i	−3.19731	+	5.24553i
$473$	1.19178	+	7.08722i	0.0547979	+	0.325871i
$474$	−55.4277	−	43.5889i	−2.54588	−	2.00210i
$475$	−8.47519	+	18.2576i	−0.388868	+	0.837716i
$476$	11.7435	+	44.8122i	0.538264	+	2.05397i
$477$	36.4805	−	7.93584i	1.67033	−	0.363357i
$478$	13.1634	−	5.63691i	0.602081	−	0.257826i
$479$	−9.76276	−	5.03305i	−0.446072	−	0.229966i	0.220530	−	0.975380i	$-0.429221\pi$
$479$	−9.76276	−	5.03305i	−0.446072	−	0.229966i	−0.666602	+	0.745414i	$0.732252\pi$
$480$	104.946	+	20.5643i	4.79009	+	0.938628i
$481$	−2.70905	−	0.657207i	−0.123522	−	0.0299661i
$482$	0.907599	−	0.907599i	0.0413400	−	0.0413400i
$483$	13.5748	+	29.9874i	0.617677	+	1.36447i
$484$			50.8050i			2.30932i
$485$	22.3154	−	18.3091i	1.01329	−	0.831372i
$486$	−19.3983	+	56.0477i	−0.879924	+	2.54237i
$487$	10.3259	+	32.3021i	0.467910	+	1.46375i	0.843584	+	0.536997i	$0.180441\pi$
$487$	10.3259	+	32.3021i	0.467910	+	1.46375i	−0.375675	+	0.926752i	$0.622589\pi$
$488$	−22.4732	−	52.4798i	−1.01731	−	2.37565i
$489$	−17.0696	+	26.5608i	−0.771913	+	1.20112i
$490$	12.2995	+	40.4340i	0.555637	+	1.82662i
$491$	−14.5853	+	16.8323i	−0.658226	+	0.759633i	−0.982486	−	0.186335i	$-0.940339\pi$
$491$	−14.5853	+	16.8323i	−0.658226	+	0.759633i	0.324261	+	0.945968i	$0.394885\pi$
$492$	19.7841	+	165.468i	0.891938	+	7.45988i
$493$	−5.23294	+	0.879962i	−0.235680	+	0.0396315i
$494$	−2.36807	−	9.76131i	−0.106544	−	0.439182i
$495$	7.72996	+	6.11779i	0.347436	+	0.274974i
$496$	−39.3653	−	86.1979i	−1.76755	−	3.87040i
$497$	−2.12783	−	7.39704i	−0.0954462	−	0.331802i
$498$	86.0475	−	6.15424i	3.85588	−	0.275778i
$499$	−10.6079	+	7.55382i	−0.474873	+	0.338155i	−0.792305	−	0.610126i	$-0.791119\pi$
$499$	−10.6079	+	7.55382i	−0.474873	+	0.338155i	0.317432	+	0.948281i	$0.397180\pi$
$500$	−21.4722	−	55.1152i	−0.960265	−	2.46483i
$501$	10.2801	−	8.08434i	0.459280	−	0.361182i
$502$	13.3209	+	12.1095i	0.594539	+	0.540472i
$503$	−0.0245308	+	0.342986i	−0.00109378	+	0.0152930i	−0.997970	−	0.0636906i	$-0.979713\pi$
$503$	−0.0245308	+	0.342986i	−0.00109378	+	0.0152930i	0.996876	+	0.0789836i	$0.0251675\pi$
$504$	49.5439	−	72.3403i	2.20686	−	3.22230i
$505$	−2.15954	−	15.3578i	−0.0960985	−	0.683415i
$506$	10.5862	+	11.0539i	0.470613	+	0.491407i
$507$	−8.15529	+	30.4359i	−0.362189	+	1.35171i
$508$	2.21415	−	0.0527065i	0.0982369	−	0.00233847i
$509$	3.64867	+	18.9311i	0.161724	+	0.839105i	0.968646	+	0.248446i	$0.0799200\pi$
$509$	3.64867	+	18.9311i	0.161724	+	0.839105i	−0.806921	+	0.590659i	$0.798868\pi$
$510$	−51.6933	−	3.85831i	−2.28902	−	0.170849i
$511$	−10.2542	−	32.6973i	−0.453621	−	1.44644i
$512$	−1.89799	−	8.72492i	−0.0838801	−	0.385591i
$513$	1.26415	−	7.51764i	0.0558137	−	0.331912i
$514$	−6.52163	+	33.8374i	−0.287657	+	1.49251i
$515$	−4.75470	+	17.5272i	−0.209517	+	0.772342i
$516$	−7.93260	+	83.0739i	−0.349213	+	3.65713i
$517$	8.47220	−	4.62617i	0.372607	−	0.203459i
$518$	−13.2285	−	17.0132i	−0.581226	−	0.747517i
$519$	14.9879	−	6.84476i	0.657897	−	0.300452i
$520$	15.8702	+	9.22838i	0.695954	+	0.404691i
$521$	−2.08092	+	10.7968i	−0.0911667	+	0.473018i	0.907437	+	0.420188i	$0.138036\pi$
$521$	−2.08092	+	10.7968i	−0.0911667	+	0.473018i	−0.998604	+	0.0528292i	$0.983176\pi$
$522$	12.4518	+	10.2811i	0.545003	+	0.449992i
$523$	−22.2151	−	7.10138i	−0.971397	−	0.310522i	−0.223771	−	0.974642i	$-0.571837\pi$
$523$	−22.2151	−	7.10138i	−0.971397	−	0.310522i	−0.747626	+	0.664120i	$0.768806\pi$
$524$	−78.6619	+	11.3099i	−3.43636	+	0.494074i
$525$	−34.2966	−	1.21814i	−1.49682	−	0.0531640i
$526$	64.2159	−	55.6434i	2.79995	−	2.42617i
$527$	12.1732	+	19.9713i	0.530272	+	0.869966i
$528$	10.6413	−	39.7138i	0.463102	−	1.72832i
$529$	−22.9785	−	0.993855i	−0.999066	−	0.0432111i
$530$	−22.6340	+	56.0329i	−0.983160	+	2.43392i
$531$	−53.7597	+	15.7853i	−2.33297	+	0.685022i
$532$	23.6905	−	51.1287i	1.02711	−	2.21671i
$533$	−2.38496	+	10.9635i	−0.103304	+	0.474881i
$534$	−29.8773	−	11.9611i	−1.29292	−	0.517606i
$535$	0.492577	−	0.592826i	0.0212960	−	0.0256301i
$536$	−3.64813	−	38.2050i	−0.157575	−	1.65020i
$537$	26.7014	−	54.9671i	1.15225	−	2.37200i
$538$	1.17911	+	1.57511i	0.0508351	+	0.0679077i
$539$	8.06146	−	1.86201i	0.347231	−	0.0802023i
$540$	13.3690	+	17.9747i	0.575309	+	0.773510i
$541$	22.9038	−	21.8387i	0.984712	−	0.938921i	−0.0134263	−	0.999910i	$-0.504274\pi$
$541$	22.9038	−	21.8387i	0.984712	−	0.938921i	0.998138	+	0.0609887i	$0.0194254\pi$
$542$	−80.8098	+	13.5888i	−3.47108	+	0.583690i
$543$	−6.55477	−	2.80692i	−0.281292	−	0.120456i
$544$	19.9556	+	57.6578i	0.855587	+	2.47206i
$545$	2.94454	+	0.874521i	0.126130	+	0.0374604i
$546$	13.7656	−	10.1871i	0.589112	−	0.435967i
$547$	16.8015	−	22.4441i	0.718379	−	0.959642i	−0.281621	−	0.959526i	$-0.590872\pi$
$547$	16.8015	−	22.4441i	0.718379	−	0.959642i	1.00000		0.000116248i	$-3.70028e-5\pi$
$548$	−40.5566	+	44.6137i	−1.73249	+	1.90580i
$549$	7.83871	−	22.6485i	0.334548	−	0.966612i
$550$	−15.2292	+	4.76435i	−0.649374	+	0.203153i
$551$	5.58997	+	3.22737i	0.238141	+	0.137491i
$552$	53.1881	+	96.9022i	2.26384	+	4.12443i
$553$	2.67757	−	26.4992i	0.113862	−	1.12686i
$554$	8.90584	+	30.3305i	0.378373	+	1.28862i
$555$	16.5548	−	5.67224i	0.702710	−	0.240773i
$556$	21.3089	+	10.9855i	0.903699	+	0.465889i
$557$	−4.27296	+	35.7377i	−0.181051	+	1.51425i	0.551865	+	0.833934i	$0.313917\pi$
$557$	−4.27296	+	35.7377i	−0.181051	+	1.51425i	−0.732916	+	0.680320i	$0.761841\pi$
$558$	21.6715	−	67.7944i	0.917429	−	2.86997i
$559$	−2.33405	+	5.11085i	−0.0987196	+	0.216166i
$560$	28.8485	+	73.8962i	1.21907	+	3.12268i
$561$	−1.44420	+	10.0446i	−0.0609741	+	0.424084i
$562$	45.8644	−	37.8688i	1.93467	−	1.59740i
$563$	12.2825	−	20.1506i	0.517644	−	0.849248i	−0.481994	−	0.876175i	$-0.660087\pi$
$563$	12.2825	−	20.1506i	0.517644	−	0.849248i	0.999637	+	0.0269264i	$0.00857199\pi$
$564$	108.930	−	26.4261i	4.58677	−	1.11274i
$565$	17.4926	−	19.1231i	0.735920	−	0.804513i
$566$	−63.0804	−	9.06959i	−2.65147	−	0.381223i
$567$	−16.1616	+	3.82673i	−0.678722	+	0.160707i
$568$	−9.03283	−	24.2180i	−0.379009	−	1.01616i
$569$	−41.2142	+	21.2474i	−1.72779	+	0.890737i	−0.756107	+	0.654448i	$0.772901\pi$
$569$	−41.2142	+	21.2474i	−1.72779	+	0.890737i	−0.971683	+	0.236289i	$0.924069\pi$
$570$	45.4998	+	43.6541i	1.90578	+	1.82847i
$571$	−10.5651	+	20.4934i	−0.442136	+	0.857624i	0.557488	+	0.830185i	$0.311765\pi$
$571$	−10.5651	+	20.4934i	−0.442136	+	0.857624i	−0.999623	+	0.0274388i	$0.991265\pi$
$572$	3.23878	−	4.78530i	0.135420	−	0.200083i
$573$	13.7739	+	7.52114i	0.575414	+	0.314200i
$574$	−67.1898	+	54.8577i	−2.80445	+	2.28972i
$575$	11.5764	−	20.9997i	0.482768	−	0.875749i
$576$	42.8200	−	74.1665i	1.78417	−	3.09027i
$577$	0.198584	+	8.34231i	0.00826716	+	0.347295i	0.988654	+	0.150211i	$0.0479954\pi$
$577$	0.198584	+	8.34231i	0.00826716	+	0.347295i	−0.980387	+	0.197083i	$0.936853\pi$
$578$	7.13403	+	14.6860i	0.296736	+	0.610858i
$579$	−4.90244	+	0.233532i	−0.203738	+	0.00970526i
$580$	−18.2159	+	5.28739i	−0.756376	+	0.219547i
$581$	19.3833	+	26.1922i	0.804154	+	1.08664i
$582$	−31.5993	−	84.7210i	−1.30983	−	3.51180i
$583$	10.6414	+	5.16925i	0.440720	+	0.214089i
$584$	−42.7691	−	106.832i	−1.76980	−	4.42075i
$585$	2.32390	+	7.34826i	0.0960813	+	0.303813i
$586$	−51.2883	−	53.7896i	−2.11870	−	2.22203i
$587$	−1.71219	−	3.13564i	−0.0706696	−	0.129422i	0.839955	−	0.542655i	$-0.182581\pi$
$587$	−1.71219	−	3.13564i	−0.0706696	−	0.129422i	−0.910625	+	0.413234i	$0.864399\pi$
$588$	96.0155	+	3.34305i	3.95961	+	0.137865i
$589$	4.04891	−	28.1608i	0.166832	−	1.16035i
$590$	27.8828	−	86.3016i	1.14792	−	3.55298i
$591$	−22.7032	+	2.16789i	−0.933883	+	0.0891750i
$592$	−27.2097	−	29.9316i	−1.11831	−	1.23018i
$593$	−29.6338	+	12.6899i	−1.21691	+	0.521113i	−0.903535	−	0.428515i	$-0.859037\pi$
$593$	−29.6338	+	12.6899i	−1.21691	+	0.521113i	−0.313379	+	0.949628i	$0.601461\pi$
$594$	5.08390	−	3.26723i	0.208595	−	0.134056i
$595$	−9.23533	−	17.2647i	−0.378612	−	0.707783i
$596$	16.0835	+	54.7753i	0.658805	+	2.24368i
$597$	−6.59515	−	24.6134i	−0.269922	−	1.00736i
$598$	2.01010	+	11.7958i	0.0821991	+	0.482364i
$599$	6.58337	−	3.80091i	0.268989	−	0.155301i	−0.359439	−	0.933169i	$-0.617032\pi$
$599$	6.58337	−	3.80091i	0.268989	−	0.155301i	0.628428	+	0.777868i	$0.283699\pi$
$600$	−115.147	+	4.76967i	−4.70085	+	0.194721i
$601$	6.50087	+	7.50240i	0.265176	+	0.306029i	0.872685	−	0.488283i	$-0.162377\pi$
$601$	6.50087	+	7.50240i	0.265176	+	0.306029i	−0.607509	+	0.794313i	$0.707831\pi$
$602$	−38.7172	+	19.6912i	−1.57799	+	0.802554i
$603$	9.65542	−	12.8981i	0.393199	−	0.525253i
$604$	−24.7913	−	48.0884i	−1.00874	−	1.95669i
$605$	−4.99771	−	20.8832i	−0.203186	−	0.849024i
$606$	−47.7048	−	9.19435i	−1.93788	−	0.373495i
$607$	2.09012	+	17.4811i	0.0848354	+	0.709536i	0.969804	+	0.243885i	$0.0784220\pi$
$607$	2.09012	+	17.4811i	0.0848354	+	0.709536i	−0.884969	+	0.465650i	$0.845820\pi$
$608$	25.9362	−	69.5377i	1.05185	−	2.82013i
$609$	−1.36659	+	10.9197i	−0.0553770	+	0.442488i
$610$	23.1523	+	31.1286i	0.937409	+	1.26036i
$611$	7.51252	+	0.717358i	0.303924	+	0.0290212i
$612$	−25.7088	+	60.0358i	−1.03922	+	2.42680i
$613$	−18.4512	−	27.2616i	−0.745236	−	1.10109i	−0.991273	−	0.131825i	$-0.957916\pi$
$613$	−18.4512	−	27.2616i	−0.745236	−	1.10109i	0.246037	−	0.969260i	$-0.420871\pi$
$614$	45.5232	−	32.4170i	1.83717	−	1.30824i
$615$	−24.4093	−	66.0689i	−0.984280	−	2.66415i
$616$	26.5112	−	8.31421i	1.06816	−	0.334989i
$617$	0.582423	−	2.67735i	0.0234474	−	0.107786i	−0.963936	−	0.266135i	$-0.914253\pi$
$617$	0.582423	−	2.67735i	0.0234474	−	0.107786i	0.987383	+	0.158349i	$0.0506170\pi$
$618$	47.1131	+	31.8871i	1.89517	+	1.28269i
$619$	9.14448	+	8.71924i	0.367548	+	0.350456i	0.851235	−	0.524785i	$-0.175854\pi$
$619$	9.14448	+	8.71924i	0.367548	+	0.350456i	−0.483687	+	0.875241i	$0.660703\pi$
$620$	51.4764	+	65.8769i	2.06734	+	2.64568i
$621$	−2.12171	+	8.83006i	−0.0851412	+	0.354338i
$622$	−17.1857	−	17.1857i	−0.689085	−	0.689085i
$623$	−2.23480	−	11.9486i	−0.0895353	−	0.478712i
$624$	24.2925	−	21.0495i	0.972477	−	0.842656i
$625$	14.2478	+	20.5427i	0.569910	+	0.821707i
$626$	−43.3794	−	55.1614i	−1.73379	−	2.20469i
$627$	9.13394	−	8.30330i	0.364775	−	0.331602i
$628$	4.21065	−	25.0398i	0.168023	−	0.999196i
$629$	7.54543	+	6.53815i	0.300856	+	0.260693i
$630$	−21.3012	+	55.6442i	−0.848662	+	2.21692i
$631$	1.09193	−	0.498667i	0.0434690	−	0.0198516i	−0.393562	−	0.919298i	$-0.628757\pi$
$631$	1.09193	−	0.498667i	0.0434690	−	0.0198516i	0.437031	+	0.899446i	$0.356030\pi$
$632$	2.12850	−	89.4160i	0.0846671	−	3.55678i
$633$	14.5308	+	8.85697i	0.577547	+	0.352033i
$634$	49.6244	+	35.3374i	1.97084	+	1.40343i
$635$	−0.904932	+	0.239471i	−0.0359111	+	0.00950312i
$636$	103.821	+	89.9611i	4.11676	+	3.56719i
$637$	6.03531	+	2.32702i	0.239128	+	0.0921999i
$638$	1.08769	+	5.00003i	0.0430621	+	0.197953i
$639$	4.03294	−	10.0738i	0.159541	−	0.398514i
$640$	24.3901	+	50.6078i	0.964104	+	2.00045i
$641$	10.3882	+	3.59540i	0.410310	+	0.142010i	0.524422	−	0.851458i	$-0.324281\pi$
$641$	10.3882	+	3.59540i	0.410310	+	0.142010i	−0.114113	+	0.993468i	$0.536402\pi$
$642$	−1.25665	−	2.06167i	−0.0495961	−	0.0813675i
$643$	−11.4713	−	11.4713i	−0.452383	−	0.452383i	0.443762	−	0.896145i	$-0.353644\pi$
$643$	−11.4713	−	11.4713i	−0.452383	−	0.452383i	−0.896145	+	0.443762i	$0.853644\pi$
$644$	−32.3669	+	58.8113i	−1.27543	+	2.31749i
$645$	−4.91134	−	34.9276i	−0.193384	−	1.37527i
$646$	−8.48137	+	34.9607i	−0.333695	+	1.37551i
$647$	−2.86257	+	1.39055i	−0.112539	+	0.0546682i	−0.492358	−	0.870393i	$-0.663865\pi$
$647$	−2.86257	+	1.39055i	−0.112539	+	0.0546682i	0.379819	+	0.925061i	$0.375986\pi$
$648$	−53.1252	+	16.9823i	−2.08696	+	0.667128i
$649$	−16.4830	−	6.59879i	−0.647013	−	0.259025i
$650$	−11.9479	−	3.58883i	−0.468633	−	0.140766i
$651$	46.9215	−	12.2963i	1.83900	−	0.481929i
$652$	−64.2246	+	4.59344i	−2.51523	+	0.179893i
$653$	38.6791	−	4.62466i	1.51363	−	0.180977i	0.679965	−	0.733244i	$-0.261995\pi$
$653$	38.6791	−	4.62466i	1.51363	−	0.180977i	0.833667	+	0.552268i	$0.186237\pi$
$654$	5.58142	−	7.83800i	0.218251	−	0.306490i
$655$	31.2211	−	12.3869i	1.21991	−	0.483995i
$656$	−117.831	+	112.352i	−4.60053	+	4.38660i
$657$	16.8825	−	45.2637i	0.658649	−	1.76591i
$658$	42.0026	+	40.4929i	1.63743	+	1.57858i
$659$	−12.9101	+	14.8991i	−0.502907	+	0.580385i	−0.949268	−	0.314467i	$-0.898174\pi$
$659$	−12.9101	+	14.8991i	−0.502907	+	0.580385i	0.446361	+	0.894853i	$0.352720\pi$
$660$	−0.975665	+	36.2607i	−0.0379777	+	1.41144i
$661$	33.4379	+	1.59285i	1.30059	+	0.0619545i	0.686410	−	0.727215i	$-0.259186\pi$
$661$	33.4379	+	1.59285i	1.30059	+	0.0619545i	0.614176	+	0.789169i	$0.289489\pi$
$662$	18.2692	+	2.18435i	0.710053	+	0.0848973i
$663$	−5.33665	+	5.87051i	−0.207258	+	0.227992i
$664$	71.6570	+	82.6965i	2.78083	+	3.20925i
$665$	−4.70835	+	23.3467i	−0.182582	+	0.905345i
$666$		−	30.3821i		−	1.17728i
$667$	−6.37742	−	4.29605i	−0.246935	−	0.166344i
$668$	25.7623	+	6.90298i	0.996772	+	0.267084i
$669$	−6.69058	+	7.01687i	−0.258673	+	0.271288i
$670$	8.45347	+	24.6719i	0.326586	+	0.953160i
$671$	6.38902	−	4.10597i	0.246645	−	0.158509i
$672$	126.423	−	5.32529i	4.87687	−	0.205428i
$673$	−5.50971	+	1.19856i	−0.212384	+	0.0462012i	−0.317498	−	0.948259i	$-0.602843\pi$
$673$	−5.50971	+	1.19856i	−0.212384	+	0.0462012i	0.105114	+	0.994460i	$0.466479\pi$
$674$	19.2670	+	27.0568i	0.742138	+	1.04219i
$675$	−7.26344	−	6.07334i	−0.279570	−	0.233763i
$676$	−59.6566	+	23.8829i	−2.29449	+	0.918573i
$677$	−19.7915	+	16.3412i	−0.760648	+	0.628044i	−0.934187	−	0.356783i	$-0.883873\pi$
$677$	−19.7915	+	16.3412i	−0.760648	+	0.628044i	0.173540	+	0.984827i	$0.444480\pi$
$678$	−38.9084	−	71.2555i	−1.49427	−	2.73655i
$679$	20.6177	−	27.2284i	0.791234	−	1.04493i
$680$	−35.3761	−	55.4234i	−1.35661	−	2.12539i
$681$	−37.8733	+	48.1598i	−1.45131	+	1.84549i
$682$	18.6780	−	12.6416i	0.715218	−	0.484074i
$683$	17.4565	−	21.1423i	0.667956	−	0.808987i	−0.322536	−	0.946557i	$-0.604535\pi$
$683$	17.4565	−	21.1423i	0.667956	−	0.808987i	0.990492	+	0.137570i	$0.0439292\pi$
$684$	70.6108	−	36.4024i	2.69987	−	1.39188i
$685$	12.2820	−	22.3279i	0.469269	−	0.853104i
$686$	25.3185	+	43.1234i	0.966665	+	1.64646i
$687$	−68.5077	−	4.89977i	−2.61373	−	0.186938i
$688$	−69.6174	+	42.4340i	−2.65414	+	1.61778i
$689$	4.62453	+	8.00992i	0.176180	+	0.305154i
$690$	−50.4770	−	55.6285i	−1.92163	−	2.11774i
$691$	−9.56101	+	16.5602i	−0.363718	+	0.629978i	−0.988570	−	0.150766i	$-0.951826\pi$
$691$	−9.56101	+	16.5602i	−0.363718	+	0.629978i	0.624852	+	0.780744i	$0.285159\pi$
$692$	29.4922	+	16.1040i	1.12113	+	0.612181i
$693$	10.5832	+	4.90375i	0.402024	+	0.186278i
$694$	17.8628	+	27.7951i	0.678063	+	1.05509i
$695$	−9.83960	−	2.41939i	−0.373237	−	0.0917726i
$696$	−1.75844	+	36.9141i	−0.0666534	+	1.39923i
$697$	25.5852	−	30.9872i	0.969107	−	1.17372i
$698$	−44.3374	−	21.5378i	−1.67820	−	0.815217i
$699$	15.5678	+	2.23831i	0.588828	+	0.0846607i
$700$	−39.9267	−	57.4812i	−1.50909	−	2.17259i
$701$	−6.01780	+	20.4948i	−0.227289	+	0.774076i	0.764324	+	0.644833i	$0.223073\pi$
$701$	−6.01780	+	20.4948i	−0.227289	+	0.774076i	−0.991613	+	0.129243i	$0.958745\pi$
$702$	4.72328	+	0.112435i	0.178269	+	0.00424358i
$703$	−2.01394	−	11.9765i	−0.0759574	−	0.451702i
$704$	25.1940	−	10.0862i	0.949536	−	0.380137i
$705$	−42.1757	+	21.5778i	−1.58843	+	0.812667i
$706$	−30.8332	+	67.5154i	−1.16042	+	2.54097i
$707$	−6.72633	−	17.0732i	−0.252970	−	0.642104i
$708$	−165.046	−	123.552i	−6.20279	−	4.64335i
$709$	1.29426	+	27.1698i	0.0486069	+	1.02038i	0.883047	+	0.469285i	$0.155488\pi$
$709$	1.29426	+	27.1698i	0.0486069	+	1.02038i	−0.834440	+	0.551099i	$0.814209\pi$
$710$	9.79993	+	14.5765i	0.367785	+	0.547048i
$711$	25.9113	−	27.1750i	0.971750	−	1.01914i
$712$	−10.5653	−	39.4301i	−0.395950	−	1.47771i
$713$	−7.13191	+	33.1337i	−0.267092	+	1.24087i
$714$	−60.5403	+	9.83815i	−2.26566	+	0.368184i
$715$	−0.860559	+	2.28558i	−0.0321831	+	0.0854758i
$716$	122.372	−	23.5853i	4.57326	−	0.881424i
$717$	4.18913	+	13.1047i	0.156446	+	0.489405i
$718$	76.0500	+	9.09289i	2.83816	+	0.339344i
$719$	−12.0637	−	23.4003i	−0.449899	−	0.872683i	−0.999310	−	0.0371310i	$-0.988178\pi$
$719$	−12.0637	−	23.4003i	−0.449899	−	0.872683i	0.549411	−	0.835552i	$-0.314852\pi$
$720$	−31.8400	+	107.206i	−1.18661	+	3.99535i
$721$	−0.629549	+	21.4788i	−0.0234456	+	0.799913i
$722$	−6.03774	+	4.51979i	−0.224701	+	0.168209i
$723$	0.785168	+	0.950947i	0.0292007	+	0.0353661i
$724$	−3.42833	−	14.1318i	−0.127413	−	0.525203i
$725$	6.96747	−	3.96527i	0.258765	−	0.147266i
$726$	−66.9608	−	6.39398i	−2.48515	−	0.237303i
$727$	16.5167	+	22.0637i	0.612569	+	0.818296i	0.994372	−	0.105947i	$-0.0337875\pi$
$727$	16.5167	+	22.0637i	0.612569	+	0.818296i	−0.381803	+	0.924244i	$0.624697\pi$
$728$	20.8079	+	6.23431i	0.771193	+	0.231059i
$729$	−34.7038	−	15.8487i	−1.28533	−	0.586989i
$730$	45.1619	+	63.8389i	1.67152	+	2.36279i
$731$	15.8180	−	12.4394i	0.585049	−	0.460088i
$732$	84.0009	−	26.8522i	3.10476	−	0.992485i
$733$	0.475699	+	0.321963i	0.0175704	+	0.0118920i	0.569261	−	0.822157i	$-0.307229\pi$
$733$	0.475699	+	0.321963i	0.0175704	+	0.0118920i	−0.551691	+	0.834049i	$0.686017\pi$
$734$	−26.8113	+	7.87251i	−0.989623	+	0.290579i
$735$	−39.7957	+	8.07092i	−1.46788	+	0.297700i
$736$	−36.5524	+	80.5042i	−1.34734	+	2.96742i
$737$	4.93160	−	1.32142i	0.181658	−	0.0486750i
$738$	−122.250	+	2.91009i	−4.50008	+	0.107122i
$739$	−35.8180	−	12.3967i	−1.31759	−	0.456021i	−0.424305	−	0.905520i	$-0.639481\pi$
$739$	−35.8180	−	12.3967i	−1.31759	−	0.456021i	−0.893281	+	0.449499i	$0.851603\pi$
$740$	29.4928	+	20.0949i	1.08418	+	0.738705i
$741$	9.55230	−	1.37341i	0.350912	−	0.0504536i
$742$	−10.5653	+	70.7189i	−0.387864	+	2.59617i
$743$	−26.0808	+	9.72763i	−0.956811	+	0.356872i	−0.778881	−	0.627171i	$-0.784213\pi$
$743$	−26.0808	+	9.72763i	−0.956811	+	0.356872i	−0.177930	+	0.984043i	$0.556940\pi$
$744$	153.931	−	53.2761i	5.64339	−	1.95320i
$745$	−11.9993	−	20.9330i	−0.439621	−	0.766927i
$746$	23.6640	+	16.8511i	0.866401	+	0.616961i
$747$	−1.09319	+	45.9239i	−0.0399978	+	1.68027i
$748$	−18.1639	+	9.91822i	−0.664136	+	0.362646i
$749$	0.402991	−	0.818109i	0.0147250	−	0.0298931i
$750$	75.3439	−	21.3638i	2.75117	−	0.780095i
$751$	−13.4050	+	4.63952i	−0.489156	+	0.169299i	−0.560502	−	0.828153i	$-0.689392\pi$
$751$	−13.4050	+	4.63952i	−0.489156	+	0.169299i	0.0713458	+	0.997452i	$0.477271\pi$
$752$	84.4444	+	69.7232i	3.07937	+	2.54254i
$753$	−12.7985	+	11.6346i	−0.466402	+	0.423987i
$754$	−1.48682	+	3.71389i	−0.0541467	+	0.135252i
$755$	14.9208	+	17.3278i	0.543024	+	0.630624i
$756$	20.3459	+	16.9881i	0.739972	+	0.617851i
$757$	2.45541	−	4.49675i	0.0892435	−	0.163437i	−0.829245	−	0.558886i	$-0.811229\pi$
$757$	2.45541	−	4.49675i	0.0892435	−	0.163437i	0.918488	+	0.395449i	$0.129411\pi$
$758$	−68.7726	+	18.4276i	−2.49793	+	0.669320i
$759$	−11.5392	+	9.11542i	−0.418845	+	0.330869i
$760$	−9.74134	+	79.3846i	−0.353355	+	2.87958i
$761$	0.685433	−	2.82539i	0.0248469	−	0.102420i	−0.958038	−	0.286642i	$-0.907461\pi$
$761$	0.685433	−	2.82539i	0.0248469	−	0.102420i	0.982885	+	0.184221i	$0.0589763\pi$
$762$	−0.209191	+	2.92487i	−0.00757818	+	0.105957i
$763$	3.62932	+	0.192905i	0.131390	+	0.00698361i
$764$	4.55479	+	31.6792i	0.164786	+	1.14611i
$765$	4.66178	−	27.2065i	0.168547	−	0.983652i
$766$	2.28822	+	23.9633i	0.0826767	+	0.865829i
$767$	−7.78024	−	11.4953i	−0.280928	−	0.415071i
$768$	56.4538	−	6.74987i	2.03710	−	0.243565i
$769$	−4.14415	−	9.07443i	−0.149442	−	0.327232i	0.820075	−	0.572256i	$-0.193932\pi$
$769$	−4.14415	−	9.07443i	−0.149442	−	0.327232i	−0.969517	+	0.245023i	$0.921204\pi$
$770$	−16.2057	+	9.68770i	−0.584014	+	0.349120i
$771$	−31.7676	−	9.32781i	−1.14408	−	0.335933i
$772$	−6.37277	−	7.71830i	−0.229361	−	0.277788i
$773$	10.2623	+	4.39455i	0.369108	+	0.158061i	0.570189	−	0.821513i	$-0.306870\pi$
$773$	10.2623	+	4.39455i	0.369108	+	0.158061i	−0.201082	+	0.979574i	$0.564446\pi$
$774$	−60.1299	−	11.5891i	−2.16133	−	0.416561i
$775$	−27.6395	−	22.0147i	−0.992841	−	0.790792i
$776$	62.0078	−	96.4861i	2.22595	−	3.46365i
$777$	17.4801	−	11.0984i	0.627095	−	0.398152i
$778$	94.1576	+	20.4827i	3.37571	+	0.734341i
$779$	−47.9975	+	9.25075i	−1.71969	+	0.331443i
$780$	−16.5213	+	23.0493i	−0.591558	+	0.825299i
$781$	2.97786	−	1.71927i	0.106556	−	0.0615203i
$782$	12.9598	−	40.8497i	0.463442	−	1.46078i
$783$	−2.14686	+	2.14686i	−0.0767226	+	0.0767226i
$784$	53.6006	+	77.0520i	1.91431	+	2.75186i
$785$	0.732400	+	10.7067i	0.0261405	+	0.382139i
$786$	−5.00650	−	105.099i	−0.178576	−	3.74877i
$787$	−0.351751	+	2.94193i	−0.0125386	+	0.104869i	−0.997812	−	0.0661191i	$-0.978938\pi$
$787$	−0.351751	+	2.94193i	−0.0125386	+	0.104869i	0.985273	+	0.170988i	$0.0546958\pi$
$788$	−31.2859	−	34.4156i	−1.11451	−	1.22601i
$789$	47.3544	+	66.5000i	1.68586	+	2.36746i
$790$	12.7353	+	59.4300i	0.453103	+	2.11442i
$791$	14.8441	−	26.8330i	0.527797	−	0.954070i
$792$	36.7002	+	13.6884i	1.30408	+	0.486398i
$793$	5.93581	+	0.141299i	0.210787	+	0.00501766i
$794$	43.8895	−	10.6475i	1.55758	−	0.377865i
$795$	−51.5246	−	26.7653i	−1.82739	−	0.949268i
$796$	32.1236	−	40.8485i	1.13859	−	1.44784i
$797$	−2.18611	−	30.5659i	−0.0774361	−	1.08270i	−0.876484	−	0.481431i	$-0.840117\pi$
$797$	−2.18611	−	30.5659i	−0.0774361	−	1.08270i	0.799048	−	0.601267i	$-0.205337\pi$
$798$	64.4058	+	37.6587i	2.27994	+	1.33310i
$799$	−22.7382	−	14.6129i	−0.804418	−	0.516968i
$800$	−58.2468	−	71.4426i	−2.05933	−	2.52588i
$801$	7.85266	−	15.2320i	0.277460	−	0.538197i
$802$	1.69078	+	3.48062i	0.0597035	+	0.122905i
$803$	13.0717	−	7.96762i	0.461291	−	0.281171i
$804$	59.2855			2.09084
$805$	7.51900	−	27.3581i	0.265010	−	0.964246i
$806$	17.6327			0.621084
$807$	−1.61417	+	0.983888i	−0.0568215	+	0.0346345i
$808$	−26.9260	−	55.4295i	−0.947253	−	1.95000i
$809$	10.9142	−	21.1707i	0.383724	−	0.744321i	−0.615309	−	0.788286i	$-0.710969\pi$
$809$	10.9142	−	21.1707i	0.383724	−	0.744321i	0.999033	+	0.0439652i	$0.0139991\pi$
$810$	32.4235	−	19.6255i	1.13925	−	0.689572i
$811$	11.6767	+	7.50414i	0.410023	+	0.263506i	0.729353	−	0.684138i	$-0.239821\pi$
$811$	11.6767	+	7.50414i	0.410023	+	0.263506i	−0.319329	+	0.947644i	$0.603458\pi$
$812$	−19.4976	+	11.1144i	−0.684233	+	0.390039i
$813$	−5.61658	−	78.5301i	−0.196982	−	2.75417i
$814$	5.95139	−	7.56781i	0.208596	−	0.265252i
$815$	25.9474	−	8.20591i	0.908899	−	0.287441i
$816$	−111.879	+	27.1415i	−3.91654	+	0.950143i
$817$	−24.4711	−	0.582522i	−0.856137	−	0.0203799i
$818$	−39.1557	−	14.6043i	−1.36905	−	0.510628i
$819$	4.70324	+	7.81255i	0.164345	+	0.272993i
$820$	78.0321	−	120.597i	2.72500	−	4.21141i
$821$	19.7476	+	27.7316i	0.689196	+	0.967841i	0.999850	+	0.0173176i	$0.00551265\pi$
$821$	19.7476	+	27.7316i	0.689196	+	0.967841i	−0.310654	+	0.950523i	$0.600548\pi$
$822$	−53.6965	−	59.0681i	−1.87288	−	2.06024i
$823$	0.941315	−	7.87286i	0.0328122	−	0.274431i	−0.966995	−	0.254795i	$-0.917992\pi$
$823$	0.941315	−	7.87286i	0.0328122	−	0.274431i	0.999807	−	0.0196353i	$-0.00625050\pi$
$824$	3.43351	+	72.0783i	0.119612	+	2.51097i
$825$	−3.16593	−	15.0008i	−0.110224	−	0.522260i
$826$	8.24425	−	106.994i	0.286854	−	3.72278i
$827$	7.85954	−	7.85954i	0.273303	−	0.273303i	−0.557125	−	0.830428i	$-0.688096\pi$
$827$	7.85954	−	7.85954i	0.273303	−	0.273303i	0.830428	+	0.557125i	$0.188096\pi$
$828$	−86.9153	+	37.4445i	−3.02052	+	1.30129i
$829$	−17.0673	+	9.85382i	−0.592773	+	0.342237i	−0.766193	−	0.642610i	$-0.777851\pi$
$829$	−17.0673	+	9.85382i	−0.592773	+	0.342237i	0.173420	+	0.984848i	$0.444518\pi$
$830$	−60.4360	−	43.3193i	−2.09776	−	1.50363i
$831$	−29.8224	+	5.74780i	−1.03453	+	0.199389i
$832$	20.7316	+	4.50989i	0.718740	+	0.156352i
$833$	−15.3939	−	17.3128i	−0.533366	−	0.599853i
$834$	−17.1606	+	26.7025i	−0.594224	+	0.924631i
$835$	−11.2685	−	0.303202i	−0.389963	−	0.0104927i
$836$	24.7190	+	4.76419i	0.854924	+	0.164773i
$837$	12.3018	+	5.26792i	0.425211	+	0.182086i
$838$	50.3427	+	60.9720i	1.73906	+	2.10624i
$839$	−1.85726	−	0.545340i	−0.0641197	−	0.0188272i	0.249515	−	0.968371i	$-0.419729\pi$
$839$	−1.85726	−	0.545340i	−0.0641197	−	0.0188272i	−0.313635	+	0.949544i	$0.601547\pi$
$840$	−131.162	+	37.2902i	−4.52553	+	1.28664i
$841$	10.9791	+	24.0409i	0.378590	+	0.828996i
$842$	−8.83839	+	1.05676i	−0.304591	+	0.0364183i
$843$	32.0302	+	47.3246i	1.10318	+	1.62995i
$844$	3.29888	+	34.5474i	0.113552	+	1.18917i
$845$	22.1723	−	15.6854i	0.762749	−	0.539595i
$846$	11.7055	+	81.4135i	0.402443	+	2.79906i
$847$	−11.5178	−	22.6464i	−0.395756	−	0.778141i
$848$	−9.57455	+	133.870i	−0.328791	+	4.59711i
$849$	14.4355	−	59.5038i	0.495424	−	2.04217i
$850$	32.1451	+	31.0331i	1.10257	+	1.06443i
$851$	1.40675	+	14.3992i	0.0482227	+	0.493597i
$852$	38.5676	−	10.3342i	1.32130	−	0.354042i
$853$	−5.17422	+	9.47588i	−0.177162	+	0.324448i	−0.951138	−	0.308768i	$-0.900083\pi$
$853$	−5.17422	+	9.47588i	−0.177162	+	0.324448i	0.773976	+	0.633215i	$0.218265\pi$
$854$	35.2348	+	29.4199i	1.20571	+	1.00673i
$855$	−25.4434	+	21.9091i	−0.870146	+	0.749275i
$856$	1.13824	−	2.84318i	0.0389042	−	0.0971779i
$857$	0.0446087	−	0.0405520i	0.00152380	−	0.00138523i	−0.671898	−	0.740644i	$-0.734521\pi$
$857$	0.0446087	−	0.0405520i	0.00152380	−	0.00138523i	0.673422	+	0.739258i	$0.264824\pi$
$858$	5.89939	+	4.87095i	0.201402	+	0.166291i
$859$	−3.73878	+	1.29400i	−0.127566	+	0.0441509i	−0.390105	−	0.920770i	$-0.627561\pi$
$859$	−3.73878	+	1.29400i	−0.127566	+	0.0441509i	0.262539	+	0.964921i	$0.415440\pi$
$860$	51.0203	−	50.7049i	1.73978	−	1.72902i
$861$	−46.3313	−	69.2725i	−1.57897	−	2.36080i
$862$	−17.0720	+	9.32200i	−0.581473	+	0.317509i
$863$	0.282519	−	11.8683i	0.00961706	−	0.404003i	−0.974288	−	0.225308i	$-0.927661\pi$
$863$	0.282519	−	11.8683i	0.00961706	−	0.404003i	0.983905	−	0.178695i	$-0.0571874\pi$
$864$	28.4365	+	20.2495i	0.967429	+	0.688903i
$865$	−13.7068	−	3.71832i	−0.466045	−	0.126427i
$866$	11.1258	−	3.85069i	0.378071	−	0.130852i
$867$	−14.6977	+	5.48197i	−0.499161	+	0.186177i
$868$	77.4198	+	61.5760i	2.62780	+	2.09003i
$869$	11.7774	−	1.69333i	0.399520	−	0.0574423i
$870$	−4.67622	−	24.6740i	−0.158539	−	0.836525i
$871$	3.77200	+	1.30550i	0.127809	+	0.0442353i
$872$	12.2015	−	0.290450i	0.413196	−	0.00983589i
$873$	46.5087	−	12.4620i	1.57408	−	0.421773i
$874$	−43.7932	+	28.2798i	−1.48133	+	0.956577i
$875$	22.0662	+	19.6998i	0.745973	+	0.665976i
$876$	170.562	−	50.0814i	5.76274	−	1.69209i
$877$	22.0668	+	14.9352i	0.745142	+	0.504326i	0.873153	−	0.487446i	$-0.162072\pi$
$877$	22.0668	+	14.9352i	0.745142	+	0.504326i	−0.128011	+	0.991773i	$0.540859\pi$
$878$	−1.50049	+	0.479655i	−0.0506392	+	0.0161876i
$879$	56.1302	−	44.1413i	1.89322	−	1.48885i
$880$	−28.9311	+	20.4668i	−0.975267	+	0.689937i
$881$	7.37874	+	3.36976i	0.248596	+	0.113530i	0.535816	−	0.844335i	$-0.320004\pi$
$881$	7.37874	+	3.36976i	0.248596	+	0.113530i	−0.287220	+	0.957865i	$0.592731\pi$
$882$	−9.13925	+	69.9035i	−0.307734	+	2.35377i
$883$	12.8273	+	17.1353i	0.431674	+	0.576649i	0.962654	−	0.270736i	$-0.0872670\pi$
$883$	12.8273	+	17.1353i	0.431674	+	0.576649i	−0.530980	+	0.847384i	$0.678176\pi$
$884$	−16.1064	−	1.53797i	−0.541715	−	0.0517276i
$885$	79.9951	+	34.5498i	2.68901	+	1.16138i
$886$	−22.9620	−	94.6506i	−0.771423	−	3.17985i
$887$	−8.70922	−	10.5481i	−0.292427	−	0.354169i	0.604298	−	0.796759i	$-0.293454\pi$
$887$	−8.70922	−	10.5481i	−0.292427	−	0.354169i	−0.896724	+	0.442589i	$0.854060\pi$
$888$	55.6640	−	41.6695i	1.86796	−	1.39834i
$889$	−0.975011	+	0.525453i	−0.0327008	+	0.0176231i
$890$	13.2186	+	24.3876i	0.443090	+	0.817474i
$891$	−3.39986	−	6.59482i	−0.113900	−	0.220935i
$892$	−19.6326	−	2.34737i	−0.657348	−	0.0785956i
$893$	10.0109	+	31.3169i	0.335003	+	1.04798i
$894$	−74.2177	+	14.3043i	−2.48221	+	0.478407i
$895$	−47.9805	+	21.7324i	−1.60381	+	0.726435i
$896$	42.0390	+	51.4894i	1.40442	+	1.72014i
$897$	−11.4654	+	0.845238i	−0.382819	+	0.0282217i
$898$	−12.6879	−	47.3519i	−0.423401	−	1.58015i
$899$	−7.81933	+	8.20068i	−0.260789	+	0.273508i
$900$	5.30582	−	98.5242i	0.176861	−	3.28414i
$901$	−1.57620	−	33.0885i	−0.0525108	−	1.10234i
$902$	−31.0210	−	23.2220i	−1.03289	−	0.773209i
$903$	−15.2973	−	38.8287i	−0.509064	−	1.29214i
$904$	42.7787	−	93.6724i	1.42280	−	3.11550i
$905$	2.79935	+	5.47156i	0.0930535	+	0.181881i
$906$	66.5003	−	26.6227i	2.20932	−	0.884480i
$907$	4.77626	+	28.4033i	0.158593	+	0.943118i	0.945399	+	0.325917i	$0.105673\pi$
$907$	4.77626	+	28.4033i	0.158593	+	0.943118i	−0.786806	+	0.617201i	$0.788267\pi$
$908$	−124.912	−	2.97347i	−4.14536	−	0.0986780i
$909$	7.28845	−	24.8222i	0.241743	−	0.823299i
$910$	−14.7376	−	0.829159i	−0.488545	−	0.0274863i
$911$	31.7091	+	4.55908i	1.05057	+	0.151049i	0.645906	−	0.763417i	$-0.276480\pi$
$911$	31.7091	+	4.55908i	1.05057	+	0.151049i	0.404663	+	0.914466i	$0.367389\pi$
$912$	125.962	+	61.1886i	4.17102	+	2.02616i
$913$	−9.26810	+	11.2249i	−0.306729	+	0.371492i
$914$	−1.17411	+	24.6475i	−0.0388360	+	0.815268i
$915$	−31.8868	+	19.3007i	−1.05415	+	0.638061i
$916$	−75.7272	−	117.834i	−2.50210	−	3.89334i
$917$	32.4997	−	22.8745i	1.07323	−	0.755382i
$918$	−14.8516	−	8.10960i	−0.490177	−	0.267657i
$919$	−12.0057	+	20.7946i	−0.396033	+	0.685949i	−0.993232	−	0.116143i	$-0.962947\pi$
$919$	−12.0057	+	20.7946i	−0.396033	+	0.685949i	0.597199	+	0.802093i	$0.296280\pi$
$920$	18.1171	−	93.5408i	0.597303	−	3.08395i
$921$	26.8471	+	46.5005i	0.884641	+	1.53224i
$922$	14.3699	−	8.75893i	0.473249	−	0.288460i
$923$	2.68140	+	0.191778i	0.0882595	+	0.00631244i
$924$	8.89237	+	41.9884i	0.292537	+	1.38132i
$925$	−14.0997	−	5.35873i	−0.463594	−	0.176194i
$926$	0.0564155	−	0.0290842i	0.00185393	−	0.000955766i
$927$	−19.2875	+	23.3599i	−0.633486	+	0.767239i
$928$	−24.4791	+	16.5679i	−0.803566	+	0.543869i
$929$	20.8595	−	26.5250i	0.684377	−	0.870256i	−0.312444	−	0.949936i	$-0.601147\pi$
$929$	20.8595	−	26.5250i	0.684377	−	0.870256i	0.996820	+	0.0796802i	$0.0253899\pi$
$930$	−93.3039	+	59.5548i	−3.05956	+	1.95288i
$931$	1.03106	+	28.1615i	0.0337916	+	0.922954i
$932$	15.3719	+	28.1515i	0.503523	+	0.922133i
$933$	18.0065	−	14.8674i	0.589507	−	0.486738i
$934$	−7.97834	+	3.19405i	−0.261059	+	0.104512i
$935$	6.49053	−	5.86363i	0.212263	−	0.191761i
$936$	17.7631	+	24.9447i	0.580604	+	0.815345i
$937$	−16.8410	+	3.66353i	−0.550171	+	0.119682i	−0.479054	−	0.877786i	$-0.659020\pi$
$937$	−16.8410	+	3.66353i	−0.550171	+	0.119682i	−0.0711174	+	0.997468i	$0.522656\pi$
$938$	16.5401	+	26.0510i	0.540055	+	0.850595i
$939$	56.7199	−	36.4517i	1.85098	−	1.18956i
$940$	−86.7728	−	42.4846i	−2.83022	−	1.38570i
$941$	−7.55135	+	7.91963i	−0.246167	+	0.258173i	−0.835212	−	0.549927i	$-0.814655\pi$
$941$	−7.55135	+	7.91963i	−0.246167	+	0.258173i	0.589045	+	0.808100i	$0.299504\pi$
$942$	32.4724	+	8.70095i	1.05801	+	0.283492i
$943$	57.8039	−	7.03960i	1.88235	−	0.229241i
$944$		−	201.421i		−	6.55569i
$945$	−10.0342	−	4.98146i	−0.326413	−	0.162047i
$946$	−12.7075	−	14.6652i	−0.413157	−	0.476808i
$947$	−16.0096	+	17.6112i	−0.520244	+	0.572287i	−0.942507	−	0.334186i	$-0.891539\pi$
$947$	−16.0096	+	17.6112i	−0.520244	+	0.572287i	0.422264	+	0.906473i	$0.361236\pi$
$948$	137.187	+	16.4027i	4.45563	+	0.532736i
$949$	11.9547	+	0.569473i	0.388066	+	0.0184859i
$950$	−6.11759	−	54.0044i	−0.198481	−	1.75213i
$951$	−38.3299	+	44.2351i	−1.24293	+	1.43442i
$952$	−56.0087	−	53.9956i	−1.81525	−	1.75001i
$953$	−9.19439	+	24.6511i	−0.297836	+	0.798528i	0.698704	+	0.715411i	$0.253760\pi$
$953$	−9.19439	+	24.6511i	−0.297836	+	0.798528i	−0.996540	+	0.0831175i	$0.973512\pi$
$954$	−72.9558	+	69.5632i	−2.36203	+	2.25219i
$955$	−4.98852	−	12.5736i	−0.161425	−	0.406871i
$956$	−16.2750	+	22.8551i	−0.526372	+	0.739186i
$957$	−4.88153	+	0.583658i	−0.157797	+	0.0188670i
$958$	29.5817	−	2.11573i	0.955742	−	0.0683560i
$959$	7.96398	−	29.0810i	0.257170	−	0.939076i
$960$	−124.934	+	46.1574i	−4.03224	+	1.48972i
$961$	17.5867	+	7.04064i	0.567312	+	0.227118i
$962$	7.16947	−	2.29183i	0.231153	−	0.0738916i
$963$	1.15646	−	0.561776i	0.0372665	−	0.0181030i
$964$	−0.592923	+	2.44406i	−0.0190968	+	0.0787179i
$965$	3.37875	+	2.54569i	0.108766	+	0.0819486i
$966$	−73.4395	−	50.0609i	−2.36288	−	1.61068i
$967$	29.9313	+	29.9313i	0.962525	+	0.962525i	0.999323	−	0.0367975i	$-0.0117156\pi$
$967$	29.9313	+	29.9313i	0.962525	+	0.962525i	−0.0367975	+	0.999323i	$0.511716\pi$
$968$	−44.4067	−	72.8538i	−1.42729	−	2.34161i
$969$	−32.6629	−	11.3048i	−1.04928	−	0.363161i
$970$	−25.7196	+	73.5729i	−0.825805	+	2.36228i
$971$	−5.99532	+	14.9756i	−0.192399	+	0.480590i	−0.992930	−	0.118702i	$-0.962127\pi$
$971$	−5.99532	+	14.9756i	−0.192399	+	0.480590i	0.800531	+	0.599291i	$0.204551\pi$
$972$	−24.7024	−	113.555i	−0.792328	−	3.64227i
$973$	−11.9890	−	0.0659628i	−0.384348	−	0.00211467i
$974$	−69.2017	−	59.9636i	−2.21736	−	1.92136i
$975$	4.52365	−	11.0996i	0.144873	−	0.355470i
$976$	70.1823	+	49.9766i	2.24648	+	1.59971i
$977$	44.0846	+	26.8710i	1.41039	+	0.859679i	0.998666	−	0.0516290i	$-0.0164413\pi$
$977$	44.0846	+	26.8710i	1.41039	+	0.859679i	0.411726	+	0.911308i	$0.364926\pi$
$978$	2.02875	−	85.2258i	0.0648724	−	2.72522i
$979$	4.93973	−	2.25590i	0.157874	−	0.0720988i
$980$	−61.8127	−	55.1064i	−1.97453	−	1.76031i
$981$	3.87229	+	3.35535i	0.123633	+	0.107128i
$982$	9.97264	−	59.3051i	0.318240	−	1.89250i
$983$	−17.1636	+	15.6027i	−0.547433	+	0.497650i	−0.898663	−	0.438639i	$-0.855461\pi$
$983$	−17.1636	+	15.6027i	−0.547433	+	0.497650i	0.351230	+	0.936289i	$0.385764\pi$
$984$	−172.999	−	219.987i	−5.51502	−	7.01292i
$985$	16.2454	+	11.0688i	0.517622	+	0.352682i
$986$	10.8283	−	9.38274i	0.344842	−	0.298807i
$987$	−42.5647	+	36.4745i	−1.35485	+	1.16100i
$988$	13.9165	+	13.9165i	0.442744	+	0.442744i
$989$	29.0343	+	2.70836i	0.923238	+	0.0861208i
$990$	−26.4194	−	3.24194i	−0.839663	−	0.103036i
$991$	18.3019	+	17.4508i	0.581378	+	0.554343i	0.922658	−	0.385619i	$-0.126012\pi$
$991$	18.3019	+	17.4508i	0.581378	+	0.554343i	−0.341280	+	0.939962i	$0.610860\pi$
$992$	107.896	+	73.0260i	3.42570	+	2.31858i
$993$	−3.75768	+	17.2738i	−0.119246	+	0.548167i
$994$	15.3010	+	14.0641i	0.485319	+	0.446086i
$995$	−9.18601	+	19.9506i	−0.291216	+	0.632477i
$996$	−137.689	+	98.0477i	−4.36284	+	3.10676i
$997$	−28.5997	−	42.2560i	−0.905761	−	1.33826i	−0.940831	−	0.338876i	$-0.889953\pi$
$997$	−28.5997	−	42.2560i	−0.905761	−	1.33826i	0.0350699	−	0.999385i	$-0.488835\pi$
$998$	13.8416	−	32.3232i	0.438148	−	1.02317i
$999$	5.68662	+	0.543006i	0.179917	+	0.0171800i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	805.2.bs.a.37.2	✓	3680
5.3	odd	4	inner	805.2.bs.a.198.91	yes	3680
7.4	even	3	inner	805.2.bs.a.382.2	yes	3680
23.5	odd	22	inner	805.2.bs.a.212.2	yes	3680
35.18	odd	12	inner	805.2.bs.a.543.2	yes	3680
115.28	even	44	inner	805.2.bs.a.373.2	yes	3680
161.74	odd	66	inner	805.2.bs.a.557.91	yes	3680
805.718	even	132	inner	805.2.bs.a.718.2	yes	3680

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.bs.a.37.2	✓	3680	1.1	even	1	trivial
805.2.bs.a.198.91	yes	3680	5.3	odd	4	inner
805.2.bs.a.212.2	yes	3680	23.5	odd	22	inner
805.2.bs.a.373.2	yes	3680	115.28	even	44	inner
805.2.bs.a.382.2	yes	3680	7.4	even	3	inner
805.2.bs.a.543.2	yes	3680	35.18	odd	12	inner
805.2.bs.a.557.91	yes	3680	161.74	odd	66	inner
805.2.bs.a.718.2	yes	3680	805.718	even	132	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 805 = 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	805.bs (of order \(132\), degree \(40\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.30557 + 1.40532i) q^{2} +(-1.13353 - 2.33346i) q^{3} +(2.42427 - 4.70243i) q^{4} +(-0.533908 + 2.17139i) q^{5} +(5.89267 + 3.78699i) q^{6} +(-0.0145566 + 2.64571i) q^{7} +(0.633836 + 8.86218i) q^{8} +(-2.30569 + 2.93193i) q^{9} +O(q^{10})\)	\(q+(-2.30557 + 1.40532i) q^{2} +(-1.13353 - 2.33346i) q^{3} +(2.42427 - 4.70243i) q^{4} +(-0.533908 + 2.17139i) q^{5} +(5.89267 + 3.78699i) q^{6} +(-0.0145566 + 2.64571i) q^{7} +(0.633836 + 8.86218i) q^{8} +(-2.30569 + 2.93193i) q^{9} +(-1.82053 - 5.75660i) q^{10} +(-1.14864 + 0.278657i) q^{11} +(-13.7209 - 0.326619i) q^{12} +(-0.865793 - 0.322924i) q^{13} +(-3.68450 - 6.12032i) q^{14} +(5.67206 - 1.21548i) q^{15} +(-7.77788 - 10.9225i) q^{16} +(2.22621 + 2.44891i) q^{17} +(1.19564 - 9.99998i) q^{18} +(-0.191553 - 4.02120i) q^{19} +(8.91648 + 7.77471i) q^{20} +(6.19017 - 2.96502i) q^{21} +(2.25666 - 2.25666i) q^{22} +(-0.103641 + 4.79471i) q^{23} +(19.9611 - 11.5246i) q^{24} +(-4.42988 - 2.31865i) q^{25} +(2.44995 - 0.472190i) q^{26} +(1.85033 + 0.402514i) q^{27} +(12.4060 + 6.48237i) q^{28} +(-0.866841 + 1.34883i) q^{29} +(-11.3692 + 10.7734i) q^{30} +(6.93937 + 1.33745i) q^{31} +(16.9471 + 7.25716i) q^{32} +(1.95225 + 2.36444i) q^{33} +(-8.57416 - 2.51760i) q^{34} +(-5.73710 - 1.44417i) q^{35} +(8.19755 + 17.9501i) q^{36} +(2.99540 - 0.358143i) q^{37} +(6.09270 + 9.00195i) q^{38} +(0.227868 + 2.38634i) q^{39} +(-19.5817 - 3.35529i) q^{40} +(-1.72799 - 12.0184i) q^{41} +(-10.1051 + 15.5352i) q^{42} +(0.433768 - 6.06487i) q^{43} +(-1.47425 + 6.07694i) q^{44} +(-5.13533 - 6.57194i) q^{45} +(-6.49913 - 11.2002i) q^{46} +(-7.88864 + 2.11376i) q^{47} +(-16.6708 + 30.5303i) q^{48} +(-6.99958 - 0.0770252i) q^{49} +(13.4718 - 0.879593i) q^{50} +(3.19098 - 7.97068i) q^{51} +(-3.61744 + 3.28847i) q^{52} +(-7.71830 - 6.37276i) q^{53} +(-4.83171 + 1.67227i) q^{54} +(0.00819449 - 2.64292i) q^{55} +(-23.4560 + 1.54794i) q^{56} +(-9.16619 + 5.00512i) q^{57} +(0.103026 - 4.32801i) q^{58} +(12.2362 + 8.71333i) q^{59} +(8.03493 - 29.6191i) q^{60} +(-6.07208 + 2.10157i) q^{61} +(-17.8787 + 6.66842i) q^{62} +(-7.72347 - 6.14287i) q^{63} +(-22.7265 + 3.26758i) q^{64} +(1.16345 - 1.70756i) q^{65} +(-7.82383 - 2.70785i) q^{66} +(-4.31836 + 0.102796i) q^{67} +(16.9128 - 4.53176i) q^{68} +(11.3058 - 5.19309i) q^{69} +(15.2568 - 4.73280i) q^{70} +(-2.79135 + 0.819614i) q^{71} +(-27.4447 - 18.5751i) q^{72} +(-12.3369 + 3.94368i) q^{73} +(-6.40278 + 5.03520i) q^{74} +(-0.389086 + 12.9652i) q^{75} +(-19.3738 - 8.84771i) q^{76} +(-0.720526 - 3.04303i) q^{77} +(-3.87893 - 5.18164i) q^{78} +(-10.0212 - 0.956906i) q^{79} +(27.8697 - 11.0572i) q^{80} +(1.47995 + 6.10045i) q^{81} +(20.8737 + 25.2809i) q^{82} +(9.85926 - 7.38055i) q^{83} +(1.06387 - 36.2968i) q^{84} +(-6.50613 + 3.52648i) q^{85} +(7.52298 + 14.5925i) q^{86} +(4.13004 + 0.493806i) q^{87} +(-3.19756 - 10.0028i) q^{88} +(-4.51144 + 0.869509i) q^{89} +(21.0755 + 7.93528i) q^{90} +(0.866967 - 2.28594i) q^{91} +(22.2955 + 12.1110i) q^{92} +(-4.74506 - 17.7088i) q^{93} +(15.2173 - 15.9594i) q^{94} +(8.83387 + 1.73101i) q^{95} +(-2.27564 - 47.7715i) q^{96} +(-10.3341 - 7.73601i) q^{97} +(16.2462 - 9.65903i) q^{98} +(1.83141 - 4.01022i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3680 q - 18 q^{2} - 18 q^{3} - 22 q^{5} - 160 q^{6} - 44 q^{7} - 56 q^{8}+O(q^{10}) \) 3680 * q - 18 * q^2 - 18 * q^3 - 22 * q^5 - 160 * q^6 - 44 * q^7 - 56 * q^8	\( 3680 q - 18 q^{2} - 18 q^{3} - 22 q^{5} - 160 q^{6} - 44 q^{7} - 56 q^{8} - 22 q^{10} - 44 q^{11} + 14 q^{12} - 72 q^{13} - 88 q^{15} - 196 q^{16} - 22 q^{17} - 62 q^{18} - 88 q^{20} - 88 q^{21} - 44 q^{23} - 30 q^{25} - 28 q^{26} - 48 q^{27} + 132 q^{28} - 22 q^{30} - 40 q^{31} - 50 q^{32} - 22 q^{33} - 40 q^{35} - 416 q^{36} - 110 q^{37} - 22 q^{38} - 22 q^{40} - 192 q^{41} - 264 q^{42} - 88 q^{43} - 44 q^{47} + 24 q^{48} - 44 q^{51} - 374 q^{52} - 22 q^{53} - 32 q^{55} - 220 q^{56} + 88 q^{57} - 58 q^{58} - 22 q^{60} - 220 q^{61} + 8 q^{62} - 44 q^{63} - 22 q^{65} - 44 q^{66} - 22 q^{67} - 96 q^{70} - 136 q^{71} - 46 q^{72} + 18 q^{73} - 34 q^{75} - 176 q^{76} - 116 q^{77} + 80 q^{78} + 176 q^{80} - 236 q^{81} - 2 q^{82} - 88 q^{83} - 448 q^{85} - 86 q^{87} - 110 q^{88} - 88 q^{90} - 228 q^{92} + 4 q^{93} - 236 q^{95} - 332 q^{96} - 88 q^{97} + 84 q^{98}+O(q^{100}) \) 3680 * q - 18 * q^2 - 18 * q^3 - 22 * q^5 - 160 * q^6 - 44 * q^7 - 56 * q^8 - 22 * q^10 - 44 * q^11 + 14 * q^12 - 72 * q^13 - 88 * q^15 - 196 * q^16 - 22 * q^17 - 62 * q^18 - 88 * q^20 - 88 * q^21 - 44 * q^23 - 30 * q^25 - 28 * q^26 - 48 * q^27 + 132 * q^28 - 22 * q^30 - 40 * q^31 - 50 * q^32 - 22 * q^33 - 40 * q^35 - 416 * q^36 - 110 * q^37 - 22 * q^38 - 22 * q^40 - 192 * q^41 - 264 * q^42 - 88 * q^43 - 44 * q^47 + 24 * q^48 - 44 * q^51 - 374 * q^52 - 22 * q^53 - 32 * q^55 - 220 * q^56 + 88 * q^57 - 58 * q^58 - 22 * q^60 - 220 * q^61 + 8 * q^62 - 44 * q^63 - 22 * q^65 - 44 * q^66 - 22 * q^67 - 96 * q^70 - 136 * q^71 - 46 * q^72 + 18 * q^73 - 34 * q^75 - 176 * q^76 - 116 * q^77 + 80 * q^78 + 176 * q^80 - 236 * q^81 - 2 * q^82 - 88 * q^83 - 448 * q^85 - 86 * q^87 - 110 * q^88 - 88 * q^90 - 228 * q^92 + 4 * q^93 - 236 * q^95 - 332 * q^96 - 88 * q^97 + 84 * q^98

Introduction

L-functions

Modular forms

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