LMFDB - Embedded newform 200.2.o.a.29.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [200,2,Mod(29,200)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(200, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 1]))

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

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

chi := DirichletCharacter("200.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	200.o (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.59700804043$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			29.8
Character	$\chi$	$=$	200.29
Dual form			200.2.o.a.69.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.01240 + 0.987445i) q^{2} +(1.39188 + 1.01126i) q^{3} +(0.0499066 - 1.99938i) q^{4} +(0.122399 - 2.23272i) q^{5} +(-2.40770 + 0.350605i) q^{6} +4.42380i q^{7} +(1.92375 + 2.07345i) q^{8} +(-0.0123697 - 0.0380700i) q^{9} +O(q^{10})$	\(q+(-1.01240 + 0.987445i) q^{2} +(1.39188 + 1.01126i) q^{3} +(0.0499066 - 1.99938i) q^{4} +(0.122399 - 2.23272i) q^{5} +(-2.40770 + 0.350605i) q^{6} +4.42380i q^{7} +(1.92375 + 2.07345i) q^{8} +(-0.0123697 - 0.0380700i) q^{9} +(2.08077 + 2.38126i) q^{10} +(5.07953 + 1.65044i) q^{11} +(2.09135 - 2.73242i) q^{12} +(-0.237511 - 0.730985i) q^{13} +(-4.36826 - 4.47866i) q^{14} +(2.42822 - 2.98389i) q^{15} +(-3.99502 - 0.199564i) q^{16} +(3.34610 + 4.60551i) q^{17} +(0.0501151 + 0.0263277i) q^{18} +(-1.01760 - 1.40061i) q^{19} +(-4.45793 - 0.356148i) q^{20} +(-4.47361 + 6.15740i) q^{21} +(-6.77223 + 3.34485i) q^{22} +(-5.01464 - 1.62935i) q^{23} +(0.580831 + 4.83140i) q^{24} +(-4.97004 - 0.546563i) q^{25} +(0.962263 + 0.505520i) q^{26} +(1.61623 - 4.97425i) q^{27} +(8.84485 + 0.220777i) q^{28} +(1.21119 - 1.66707i) q^{29} +(0.488101 + 5.41862i) q^{30} +(-2.10890 + 1.53221i) q^{31} +(4.24161 - 3.74282i) q^{32} +(5.40106 + 7.43393i) q^{33} +(-7.93528 - 1.35853i) q^{34} +(9.87709 + 0.541468i) q^{35} +(-0.0767337 + 0.0228318i) q^{36} +(-2.01004 - 6.18628i) q^{37} +(2.41324 + 0.413150i) q^{38} +(0.408628 - 1.25763i) q^{39} +(4.86489 - 4.04140i) q^{40} +(-0.754681 - 2.32267i) q^{41} +(-1.55101 - 10.6512i) q^{42} -6.65200 q^{43} +(3.55335 - 10.0735i) q^{44} +(-0.0865136 + 0.0229583i) q^{45} +(6.68572 - 3.30212i) q^{46} +(4.72720 - 6.50644i) q^{47} +(-5.35877 - 4.31777i) q^{48} -12.5700 q^{49} +(5.57137 - 4.35430i) q^{50} +9.79409i q^{51} +(-1.47337 + 0.438394i) q^{52} +(3.77778 + 2.74471i) q^{53} +(3.27552 + 6.63187i) q^{54} +(4.30669 - 11.1391i) q^{55} +(-9.17253 + 8.51029i) q^{56} -2.97854i q^{57} +(0.419923 + 2.88373i) q^{58} +(1.02828 - 0.334110i) q^{59} +(-5.84474 - 5.00384i) q^{60} +(-6.86954 - 2.23205i) q^{61} +(0.622082 - 3.63363i) q^{62} +(0.168414 - 0.0547211i) q^{63} +(-0.598382 + 7.97759i) q^{64} +(-1.66115 + 0.440824i) q^{65} +(-12.8086 - 2.19285i) q^{66} +(5.12879 - 3.72628i) q^{67} +(9.37515 - 6.46027i) q^{68} +(-5.33207 - 7.33896i) q^{69} +(-10.5342 + 9.20490i) q^{70} +(0.472812 + 0.343518i) q^{71} +(0.0551401 - 0.0988851i) q^{72} +(-5.48432 - 1.78197i) q^{73} +(8.14357 + 4.27818i) q^{74} +(-6.36497 - 5.78674i) q^{75} +(-2.85113 + 1.96467i) q^{76} +(-7.30121 + 22.4708i) q^{77} +(0.828143 + 1.67672i) q^{78} +(6.27011 + 4.55550i) q^{79} +(-0.934555 + 8.89531i) q^{80} +(7.18270 - 5.21854i) q^{81} +(3.05755 + 1.60627i) q^{82} +(-5.49924 + 3.99543i) q^{83} +(12.0877 + 9.25173i) q^{84} +(10.6924 - 6.90718i) q^{85} +(6.73448 - 6.56848i) q^{86} +(3.37167 - 1.09552i) q^{87} +(6.34963 + 13.7072i) q^{88} +(3.89405 - 11.9847i) q^{89} +(0.0649163 - 0.108670i) q^{90} +(3.23373 - 1.05070i) q^{91} +(-3.50796 + 9.94484i) q^{92} -4.48479 q^{93} +(1.63893 + 11.2550i) q^{94} +(-3.25171 + 2.10058i) q^{95} +(9.68877 - 0.920181i) q^{96} +(-1.90925 + 2.62786i) q^{97} +(12.7259 - 12.4122i) q^{98} -0.213793i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 5 q^{2} - 3 q^{4} + q^{6} + 10 q^{8} - 30 q^{9}+O(q^{10}) $ 112 * q - 5 * q^2 - 3 * q^4 + q^6 + 10 * q^8 - 30 * q^9	$ 112 q - 5 q^{2} - 3 q^{4} + q^{6} + 10 q^{8} - 30 q^{9} - 9 q^{10} - 5 q^{12} - 3 q^{14} - 2 q^{15} - 15 q^{16} - 10 q^{17} - 17 q^{20} - 30 q^{22} - 10 q^{23} - 16 q^{24} - 6 q^{25} - 14 q^{26} + 15 q^{28} - 33 q^{30} - 18 q^{31} - 10 q^{33} + 9 q^{34} + 41 q^{36} + 45 q^{38} - 10 q^{39} - 14 q^{40} - 10 q^{41} + 75 q^{42} - 32 q^{44} + 13 q^{46} - 10 q^{47} - 70 q^{48} - 80 q^{49} - 19 q^{50} - 100 q^{52} + 43 q^{54} - 34 q^{55} + 36 q^{56} - 30 q^{58} - 28 q^{60} + 20 q^{62} + 60 q^{63} - 36 q^{64} + 40 q^{65} + 40 q^{66} + 42 q^{70} + 22 q^{71} - 65 q^{72} - 10 q^{73} + 4 q^{74} - 36 q^{76} - 55 q^{78} + 14 q^{79} - 76 q^{80} - 6 q^{81} + 78 q^{84} - 59 q^{86} - 10 q^{87} + 110 q^{88} + 24 q^{89} + 49 q^{90} + 90 q^{92} + 45 q^{94} - 86 q^{95} + 46 q^{96} - 50 q^{97} + 90 q^{98}+O(q^{100}) $ 112 * q - 5 * q^2 - 3 * q^4 + q^6 + 10 * q^8 - 30 * q^9 - 9 * q^10 - 5 * q^12 - 3 * q^14 - 2 * q^15 - 15 * q^16 - 10 * q^17 - 17 * q^20 - 30 * q^22 - 10 * q^23 - 16 * q^24 - 6 * q^25 - 14 * q^26 + 15 * q^28 - 33 * q^30 - 18 * q^31 - 10 * q^33 + 9 * q^34 + 41 * q^36 + 45 * q^38 - 10 * q^39 - 14 * q^40 - 10 * q^41 + 75 * q^42 - 32 * q^44 + 13 * q^46 - 10 * q^47 - 70 * q^48 - 80 * q^49 - 19 * q^50 - 100 * q^52 + 43 * q^54 - 34 * q^55 + 36 * q^56 - 30 * q^58 - 28 * q^60 + 20 * q^62 + 60 * q^63 - 36 * q^64 + 40 * q^65 + 40 * q^66 + 42 * q^70 + 22 * q^71 - 65 * q^72 - 10 * q^73 + 4 * q^74 - 36 * q^76 - 55 * q^78 + 14 * q^79 - 76 * q^80 - 6 * q^81 + 78 * q^84 - 59 * q^86 - 10 * q^87 + 110 * q^88 + 24 * q^89 + 49 * q^90 + 90 * q^92 + 45 * q^94 - 86 * q^95 + 46 * q^96 - 50 * q^97 + 90 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/200\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$177$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−1.01240	+	0.987445i	−0.715875	+	0.698229i
$2$	−1.01240	+	0.987445i	−0.715875	+	0.698229i
$3$	1.39188	+	1.01126i	0.803601	+	0.583851i	0.911968	−	0.410260i	$-0.134562\pi$
$3$	1.39188	+	1.01126i	0.803601	+	0.583851i	−0.108367	+	0.994111i	$0.534562\pi$
$4$	0.0499066	−	1.99938i	0.0249533	−	0.999689i
$5$	0.122399	−	2.23272i	0.0547384	−	0.998501i
$5$	0.122399	−	2.23272i	0.0547384	−	0.998501i
$6$	−2.40770	+	0.350605i	−0.982939	+	0.143134i
$7$			4.42380i			1.67204i	0.548699	+	0.836020i	$0.315123\pi$
$7$			4.42380i			1.67204i	−0.548699	+	0.836020i	$0.684877\pi$
$8$	1.92375	+	2.07345i	0.680148	+	0.733075i
$9$	−0.0123697	−	0.0380700i	−0.00412323	−	0.0126900i
$10$	2.08077	+	2.38126i	0.657996	+	0.753021i
$11$	5.07953	+	1.65044i	1.53153	+	0.497626i	0.949026	−	0.315199i	$-0.102071\pi$
$11$	5.07953	+	1.65044i	1.53153	+	0.497626i	0.582509	+	0.812824i	$0.302071\pi$
$12$	2.09135	−	2.73242i	0.603721	−	0.788782i
$13$	−0.237511	−	0.730985i	−0.0658738	−	0.202739i	0.912702	−	0.408626i	$-0.133992\pi$
$13$	−0.237511	−	0.730985i	−0.0658738	−	0.202739i	−0.978576	+	0.205887i	$0.933992\pi$
$14$	−4.36826	−	4.47866i	−1.16747	−	1.19697i
$15$	2.42822	−	2.98389i	0.626963	−	0.770438i
$16$	−3.99502	−	0.199564i	−0.998755	−	0.0498910i
$17$	3.34610	+	4.60551i	0.811549	+	1.11700i	0.991083	+	0.133249i	$0.0425410\pi$
$17$	3.34610	+	4.60551i	0.811549	+	1.11700i	−0.179534	+	0.983752i	$0.557459\pi$
$18$	0.0501151	+	0.0263277i	0.0118123	+	0.00620550i
$19$	−1.01760	−	1.40061i	−0.233454	−	0.321322i	0.676177	−	0.736739i	$-0.263635\pi$
$19$	−1.01760	−	1.40061i	−0.233454	−	0.321322i	−0.909631	+	0.415418i	$0.863635\pi$
$20$	−4.45793	−	0.356148i	−0.996824	−	0.0796372i
$21$	−4.47361	+	6.15740i	−0.976222	+	1.34365i
$22$	−6.77223	+	3.34485i	−1.44384	+	0.713124i
$23$	−5.01464	−	1.62935i	−1.04562	−	0.339744i	−0.264675	−	0.964338i	$-0.585265\pi$
$23$	−5.01464	−	1.62935i	−1.04562	−	0.339744i	−0.780950	+	0.624594i	$0.785265\pi$
$24$	0.580831	+	4.83140i	0.118562	+	0.986205i
$25$	−4.97004	−	0.546563i	−0.994007	−	0.109313i
$26$	0.962263	+	0.505520i	0.188715	+	0.0991405i
$27$	1.61623	−	4.97425i	0.311044	−	0.957295i
$28$	8.84485	+	0.220777i	1.67152	+	0.0417229i
$29$	1.21119	−	1.66707i	0.224913	−	0.309567i	−0.681616	−	0.731710i	$-0.738722\pi$
$29$	1.21119	−	1.66707i	0.224913	−	0.309567i	0.906529	+	0.422144i	$0.138722\pi$
$30$	0.488101	+	5.41862i	0.0891146	+	0.989301i
$31$	−2.10890	+	1.53221i	−0.378770	+	0.275192i	−0.760838	−	0.648942i	$-0.775212\pi$
$31$	−2.10890	+	1.53221i	−0.378770	+	0.275192i	0.382068	+	0.924134i	$0.375212\pi$
$32$	4.24161	−	3.74282i	0.749819	−	0.661643i
$33$	5.40106	+	7.43393i	0.940204	+	1.29408i
$34$	−7.93528	−	1.35853i	−1.36089	−	0.232986i
$35$	9.87709	+	0.541468i	1.66953	+	0.0915248i
$36$	−0.0767337	+	0.0228318i	−0.0127889	+	0.00380529i
$37$	−2.01004	−	6.18628i	−0.330449	−	1.01702i	−0.968921	−	0.247372i	$-0.920433\pi$
$37$	−2.01004	−	6.18628i	−0.330449	−	1.01702i	0.638471	−	0.769646i	$-0.279567\pi$
$38$	2.41324	+	0.413150i	0.391480	+	0.0670219i
$39$	0.408628	−	1.25763i	0.0654328	−	0.201382i
$40$	4.86489	−	4.04140i	0.769206	−	0.639001i
$41$	−0.754681	−	2.32267i	−0.117861	−	0.362740i	0.874672	−	0.484716i	$-0.161077\pi$
$41$	−0.754681	−	2.32267i	−0.117861	−	0.362740i	−0.992533	+	0.121976i	$0.961077\pi$
$42$	−1.55101	−	10.6512i	−0.239325	−	1.64351i
$43$	−6.65200			−1.01442			−0.507210	−	0.861822i	$-0.669323\pi$
$43$	−6.65200			−1.01442			−0.507210	+	0.861822i	$0.669323\pi$
$44$	3.55335	−	10.0735i	0.535688	−	1.51864i
$45$	−0.0865136	+	0.0229583i	−0.0128967	+	0.00342242i
$46$	6.68572	−	3.30212i	0.985755	−	0.486871i
$47$	4.72720	−	6.50644i	0.689534	−	0.949062i	−0.310465	−	0.950585i	$-0.600485\pi$
$47$	4.72720	−	6.50644i	0.689534	−	0.949062i	0.999999	+	0.00152305i	$0.000484802\pi$
$48$	−5.35877	−	4.31777i	−0.773472	−	0.623216i
$49$	−12.5700			−1.79572
$50$	5.57137	−	4.35430i	0.787910	−	0.615790i
$51$			9.79409i			1.37145i
$52$	−1.47337	+	0.438394i	−0.204319	+	0.0607943i
$53$	3.77778	+	2.74471i	0.518917	+	0.377016i	0.816196	−	0.577775i	$-0.196079\pi$
$53$	3.77778	+	2.74471i	0.518917	+	0.377016i	−0.297279	+	0.954791i	$0.596079\pi$
$54$	3.27552	+	6.63187i	0.445742	+	0.902483i
$55$	4.30669	−	11.1391i	0.580713	−	1.50200i
$56$	−9.17253	+	8.51029i	−1.22573	+	1.13723i
$57$		−	2.97854i		−	0.394517i
$58$	0.419923	+	2.88373i	0.0551385	+	0.378652i
$59$	1.02828	−	0.334110i	0.133871	−	0.0434974i	−0.241315	−	0.970447i	$-0.577579\pi$
$59$	1.02828	−	0.334110i	0.133871	−	0.0434974i	0.375186	+	0.926949i	$0.377579\pi$
$60$	−5.84474	−	5.00384i	−0.754553	−	0.645993i
$61$	−6.86954	−	2.23205i	−0.879554	−	0.285785i	−0.165782	−	0.986162i	$-0.553015\pi$
$61$	−6.86954	−	2.23205i	−0.879554	−	0.285785i	−0.713772	+	0.700378i	$0.753015\pi$
$62$	0.622082	−	3.63363i	0.0790045	−	0.461471i
$63$	0.168414	−	0.0547211i	0.0212182	−	0.00689422i
$64$	−0.598382	+	7.97759i	−0.0747977	+	0.997199i
$65$	−1.66115	+	0.440824i	−0.206041	+	0.0546775i
$66$	−12.8086	−	2.19285i	−1.57663	−	0.269922i
$67$	5.12879	−	3.72628i	0.626581	−	0.455238i	−0.228633	−	0.973513i	$-0.573426\pi$
$67$	5.12879	−	3.72628i	0.626581	−	0.455238i	0.855214	+	0.518275i	$0.173426\pi$
$68$	9.37515	−	6.46027i	1.13690	−	0.783423i
$69$	−5.33207	−	7.33896i	−0.641905	−	0.883507i
$70$	−10.5342	+	9.20490i	−1.25908	+	1.10020i
$71$	0.472812	+	0.343518i	0.0561125	+	0.0407681i	0.615488	−	0.788146i	$-0.288959\pi$
$71$	0.472812	+	0.343518i	0.0561125	+	0.0407681i	−0.559375	+	0.828914i	$0.688959\pi$
$72$	0.0551401	−	0.0988851i	0.00649832	−	0.0116537i
$73$	−5.48432	−	1.78197i	−0.641892	−	0.208563i	−0.0300561	−	0.999548i	$-0.509569\pi$
$73$	−5.48432	−	1.78197i	−0.641892	−	0.208563i	−0.611836	+	0.790985i	$0.709569\pi$
$74$	8.14357	+	4.27818i	0.946671	+	0.497328i
$75$	−6.36497	−	5.78674i	−0.734964	−	0.668196i
$76$	−2.85113	+	1.96467i	−0.327047	+	0.225363i
$77$	−7.30121	+	22.4708i	−0.832050	+	2.56079i
$78$	0.828143	+	1.67672i	0.0937687	+	0.189851i
$79$	6.27011	+	4.55550i	0.705442	+	0.512534i	0.881700	−	0.471810i	$-0.156399\pi$
$79$	6.27011	+	4.55550i	0.705442	+	0.512534i	−0.176258	+	0.984344i	$0.556399\pi$
$80$	−0.934555	+	8.89531i	−0.104486	+	0.994526i
$81$	7.18270	−	5.21854i	0.798078	−	0.579838i
$82$	3.05755	+	1.60627i	0.337650	+	0.177382i
$83$	−5.49924	+	3.99543i	−0.603619	+	0.438555i	−0.847162	−	0.531335i	$-0.821691\pi$
$83$	−5.49924	+	3.99543i	−0.603619	+	0.438555i	0.243542	+	0.969890i	$0.421691\pi$
$84$	12.0877	+	9.25173i	1.31888	+	1.00945i
$85$	10.6924	−	6.90718i	1.15975	−	0.749189i
$86$	6.73448	−	6.56848i	0.726198	−	0.708297i
$87$	3.37167	−	1.09552i	0.361481	−	0.117452i
$88$	6.34963	+	13.7072i	0.676873	+	1.46119i
$89$	3.89405	−	11.9847i	0.412769	−	1.27037i	−0.501463	−	0.865179i	$-0.667205\pi$
$89$	3.89405	−	11.9847i	0.412769	−	1.27037i	0.914232	−	0.405192i	$-0.132795\pi$
$90$	0.0649163	−	0.108670i	0.00684278	−	0.0114549i
$91$	3.23373	−	1.05070i	0.338987	−	0.110144i
$92$	−3.50796	+	9.94484i	−0.365730	+	1.03682i
$93$	−4.48479			−0.465051
$94$	1.63893	+	11.2550i	0.169042	+	1.16086i
$95$	−3.25171	+	2.10058i	−0.333619	+	0.215515i
$96$	9.68877	−	0.920181i	0.988856	−	0.0939156i
$97$	−1.90925	+	2.62786i	−0.193855	+	0.266819i	−0.894869	−	0.446329i	$-0.852731\pi$
$97$	−1.90925	+	2.62786i	−0.193855	+	0.266819i	0.701014	+	0.713148i	$0.252731\pi$
$98$	12.7259	−	12.4122i	1.28551	−	1.25382i
$99$		−	0.213793i		−	0.0214870i
$100$	−1.34082	+	9.90970i	−0.134082	+	0.990970i
$101$		−	3.90261i		−	0.388325i	−0.980969	−	0.194162i	$-0.937801\pi$
$101$		−	3.90261i		−	0.388325i	0.980969	−	0.194162i	$-0.0621989\pi$
$102$	−9.67112	−	9.91553i	−0.957583	−	0.981784i
$103$	−11.2306	+	15.4576i	−1.10659	+	1.52308i	−0.280231	+	0.959933i	$0.590411\pi$
$103$	−11.2306	+	15.4576i	−1.10659	+	1.52308i	−0.826354	+	0.563151i	$0.809589\pi$
$104$	1.05875	−	1.89870i	0.103819	−	0.186183i
$105$	13.2002	+	10.7420i	1.28820	+	1.04831i
$106$	−6.53487	+	0.951595i	−0.634723	+	0.0924271i
$107$	−12.2161			−1.18098			−0.590488	−	0.807046i	$-0.701065\pi$
$107$	−12.2161			−1.18098			−0.590488	+	0.807046i	$0.701065\pi$
$108$	−9.86475	−	3.47971i	−0.949236	−	0.334835i
$109$	−8.01169	+	2.60316i	−0.767381	+	0.249337i	−0.666443	−	0.745556i	$-0.732184\pi$
$109$	−8.01169	+	2.60316i	−0.767381	+	0.249337i	−0.100937	+	0.994893i	$0.532184\pi$
$110$	6.63918	+	15.5299i	0.633021	+	1.48071i
$111$	3.45819	−	10.6432i	0.328237	−	1.01021i
$112$	0.882833	−	17.6732i	0.0834198	−	1.66996i
$113$	5.14306	−	1.67108i	0.483818	−	0.157202i	−0.0569445	−	0.998377i	$-0.518136\pi$
$113$	5.14306	−	1.67108i	0.483818	−	0.157202i	0.540762	+	0.841175i	$0.318136\pi$
$114$	2.94114	+	3.01547i	0.275463	+	0.282424i
$115$	−4.25167	+	10.9968i	−0.396470	+	1.02546i
$116$	−3.27265	−	2.50483i	−0.303858	−	0.232568i
$117$	−0.0248907	+	0.0180841i	−0.00230114	+	0.00167188i
$118$	−0.711120	+	1.35363i	−0.0654639	+	0.124611i
$119$	−20.3739	+	14.8025i	−1.86767	+	1.35694i
$120$	10.8582	−	0.705473i	0.991216	−	0.0644006i
$121$	14.1785	+	10.3012i	1.28895	+	0.936477i
$122$	9.15875	−	4.52356i	0.829194	−	0.409544i
$123$	1.29840	−	3.99605i	0.117072	−	0.360312i
$124$	2.95821	+	4.29295i	0.265655	+	0.385519i
$125$	−1.82865	+	11.0298i	−0.163559	+	0.986534i
$126$	−0.116469	+	0.221700i	−0.0103758	+	0.0197506i
$127$	12.7192	+	4.13273i	1.12865	+	0.366721i	0.813063	−	0.582175i	$-0.197798\pi$
$127$	12.7192	+	4.13273i	1.12865	+	0.366721i	0.315588	+	0.948896i	$0.397798\pi$
$128$	−7.27163	−	8.66738i	−0.642727	−	0.766095i
$129$	−9.25877	−	6.72689i	−0.815190	−	0.592270i
$130$	1.24646	−	2.08659i	0.109322	−	0.183006i
$131$	−2.07801	−	2.86013i	−0.181556	−	0.249891i	0.708532	−	0.705678i	$-0.249358\pi$
$131$	−2.07801	−	2.86013i	−0.181556	−	0.249891i	−0.890089	+	0.455788i	$0.849358\pi$
$132$	15.1328	−	10.4278i	1.31714	−	0.907620i
$133$	6.19602	−	4.50167i	0.537263	−	0.390344i
$134$	−1.51289	+	8.83688i	−0.130694	+	0.763391i
$135$	−10.9083	−	4.21743i	−0.938834	−	0.362979i
$136$	−3.11224	+	15.7978i	−0.266872	+	1.35465i
$137$	−20.5757	+	6.68544i	−1.75790	+	0.571176i	−0.996979	−	0.0776705i	$-0.975252\pi$
$137$	−20.5757	+	6.68544i	−1.75790	+	0.571176i	−0.760919	+	0.648846i	$0.775252\pi$
$138$	12.6450	+	2.16484i	1.07641	+	0.184284i
$139$	1.89983	+	0.617291i	0.161141	+	0.0523579i	0.388477	−	0.921459i	$-0.373001\pi$
$139$	1.89983	+	0.617291i	0.161141	+	0.0523579i	−0.227336	+	0.973816i	$0.573001\pi$
$140$	1.57553	−	19.7210i	0.133157	−	1.66673i
$141$	13.1594	−	4.27575i	1.10822	−	0.360083i
$142$	−0.817880	+	0.119098i	−0.0686350	+	0.00999449i
$143$		−	4.10505i		−	0.343282i
$144$	0.0418198	+	0.154559i	0.00348498	+	0.0128799i
$145$	−3.57384	−	2.90830i	−0.296791	−	0.241521i
$146$	7.31192	−	3.61141i	0.605139	−	0.298882i
$147$	−17.4960	−	12.7116i	−1.44304	−	1.04843i
$148$	−12.4690	+	3.71010i	−1.02495	+	0.304968i
$149$		−	4.60655i		−	0.377384i	−0.982036	−	0.188692i	$-0.939575\pi$
$149$		−	4.60655i		−	0.377384i	0.982036	−	0.188692i	$-0.0604247\pi$
$150$	12.1580	−	0.426558i	0.992695	−	0.0348283i
$151$	1.76177			0.143371			0.0716854	−	0.997427i	$-0.477162\pi$
$151$	1.76177			0.143371			0.0716854	+	0.997427i	$0.477162\pi$
$152$	0.946480	−	4.80436i	0.0767697	−	0.389685i
$153$	0.133942	−	0.184355i	0.0108285	−	0.0149042i
$154$	−14.7969	−	29.9590i	−1.19237	−	2.41417i
$155$	3.16285	+	4.89611i	0.254046	+	0.393265i
$156$	−2.49408	−	0.879765i	−0.199686	−	0.0704376i
$157$	4.33632			0.346076			0.173038	−	0.984915i	$-0.444642\pi$
$157$	4.33632			0.346076			0.173038	+	0.984915i	$0.444642\pi$
$158$	−10.8462	+	1.57940i	−0.862874	+	0.125650i
$159$	2.48259	+	7.64062i	0.196882	+	0.605940i
$160$	−7.83749	−	9.92843i	−0.619608	−	0.784912i
$161$	7.20794	−	22.1838i	0.568066	−	1.74833i
$162$	−2.11875	+	12.3758i	−0.166465	+	0.972332i
$163$	−2.23193	−	6.86918i	−0.174818	−	0.538036i	0.824807	−	0.565415i	$-0.191284\pi$
$163$	−2.23193	−	6.86918i	−0.174818	−	0.538036i	−0.999625	+	0.0273790i	$0.991284\pi$
$164$	−4.68156	+	1.39298i	−0.365568	+	0.108773i
$165$	17.2589	−	11.1491i	1.34361	−	0.867959i
$166$	1.62216	−	9.47516i	0.125904	−	0.735415i
$167$	5.30895	+	7.30714i	0.410819	+	0.565444i	0.963418	−	0.268004i	$-0.0863639\pi$
$167$	5.30895	+	7.30714i	0.410819	+	0.565444i	−0.552599	+	0.833447i	$0.686364\pi$
$168$	−21.3732	+	2.56948i	−1.64897	+	0.198240i
$169$	10.0393	−	7.29397i	0.772253	−	0.561075i
$170$	−4.00448	+	17.5509i	−0.307130	+	1.34610i
$171$	−0.0407338	+	0.0560652i	−0.00311499	+	0.00428742i
$172$	−0.331978	+	13.2999i	−0.0253131	+	1.01410i
$173$	4.23208	−	13.0250i	0.321759	−	0.990273i	−0.651123	−	0.758972i	$-0.725702\pi$
$173$	4.23208	−	13.0250i	0.321759	−	0.990273i	0.972882	−	0.231301i	$-0.0742982\pi$
$174$	−2.33171	+	4.43845i	−0.176767	+	0.336478i
$175$	2.41789	−	21.9865i	0.182775	−	1.66202i
$176$	−19.9634	−	7.60722i	−1.50480	−	0.573416i
$177$	1.76912	+	0.574821i	0.132975	+	0.0432062i
$178$	7.89185	+	15.9784i	0.591519	+	1.19763i
$179$	4.19376	−	5.77221i	0.313456	−	0.431435i	−0.622999	−	0.782223i	$-0.714086\pi$
$179$	4.19376	−	5.77221i	0.313456	−	0.431435i	0.936455	+	0.350787i	$0.114086\pi$
$180$	0.0415847	+	0.174119i	0.00309954	+	0.0129781i
$181$	1.65805	+	2.28211i	0.123242	+	0.169628i	0.866180	−	0.499732i	$-0.166568\pi$
$181$	1.65805	+	2.28211i	0.123242	+	0.169628i	−0.742938	+	0.669360i	$0.766568\pi$
$182$	−2.23632	+	4.25686i	−0.165767	+	0.315540i
$183$	−7.30439	−	10.0536i	−0.539956	−	0.743185i
$184$	−6.26852	−	13.5321i	−0.462121	−	0.997597i
$185$	−14.0582	+	3.73066i	−1.03358	+	0.274284i
$186$	4.54040	−	4.42848i	0.332918	−	0.324712i
$187$	9.39549	+	28.9163i	0.687066	+	2.11457i
$188$	−12.7729	−	9.77618i	−0.931560	−	0.713001i
$189$	22.0051	+	7.14989i	1.60064	+	0.520078i
$190$	1.21783	−	5.33751i	0.0883503	−	0.387224i
$191$	4.36011	+	13.4190i	0.315486	+	0.970968i	0.975554	+	0.219761i	$0.0705278\pi$
$191$	4.36011	+	13.4190i	0.315486	+	0.970968i	−0.660067	+	0.751206i	$0.729472\pi$
$192$	−8.90028	+	10.4987i	−0.642323	+	0.757680i
$193$			6.87803i			0.495092i	0.968876	+	0.247546i	$0.0796241\pi$
$193$			6.87803i			0.495092i	−0.968876	+	0.247546i	$0.920376\pi$
$194$	−0.661940	−	4.54573i	−0.0475245	−	0.326364i
$195$	−2.75791	−	1.06628i	−0.197498	−	0.0763580i
$196$	−0.627328	+	25.1322i	−0.0448091	+	1.79516i
$197$	9.86331	+	7.16612i	0.702732	+	0.510565i	0.880821	−	0.473450i	$-0.156991\pi$
$197$	9.86331	+	7.16612i	0.702732	+	0.510565i	−0.178089	+	0.984014i	$0.556991\pi$
$198$	0.211109	+	0.216444i	0.0150029	+	0.0153820i
$199$	14.7705			1.04705			0.523527	−	0.852009i	$-0.324616\pi$
$199$	14.7705			1.04705			0.523527	+	0.852009i	$0.324616\pi$
$200$	−8.42783	−	11.3566i	−0.595938	−	0.803031i
$201$	10.9069			0.769313
$202$	3.85362	+	3.95101i	0.271139	+	0.277992i
$203$	7.37478	+	5.35809i	0.517608	+	0.376064i
$204$	19.5821	+	0.488789i	1.37102	+	0.0342221i
$205$	−5.27823	+	1.40070i	−0.368648	+	0.0978289i
$206$	−3.89366	−	26.7389i	−0.271284	−	1.86299i
$207$			0.211062i			0.0146698i
$208$	0.802984	+	2.96770i	0.0556769	+	0.205773i
$209$	−2.85732	−	8.79391i	−0.197645	−	0.608288i
$210$	−23.9709	+	2.15926i	−1.65415	+	0.149003i
$211$	2.19369	+	0.712773i	0.151020	+	0.0490693i	0.383551	−	0.923520i	$-0.374701\pi$
$211$	2.19369	+	0.712773i	0.151020	+	0.0490693i	−0.232532	+	0.972589i	$0.574701\pi$
$212$	5.67626	−	7.41622i	0.389847	−	0.509348i
$213$	0.310711	+	0.956271i	0.0212896	+	0.0655226i
$214$	12.3676	−	12.0627i	0.845431	−	0.824592i
$215$	−0.814196	+	14.8520i	−0.0555277	+	1.01290i
$216$	13.4231	−	6.21804i	0.913325	−	0.423084i
$217$	−6.77818	−	9.32936i	−0.460133	−	0.633318i
$218$	5.54056	−	10.5465i	0.375254	−	0.714301i
$219$	−5.83149	−	8.02635i	−0.394055	−	0.542371i
$220$	−22.0564	−	9.16661i	−1.48704	−	0.618012i
$221$	2.57182	−	3.53981i	0.173000	−	0.238113i
$222$	7.00852	+	14.1900i	0.470381	+	0.952368i
$223$	−2.12152	−	0.689324i	−0.142068	−	0.0461606i	0.237120	−	0.971480i	$-0.423797\pi$
$223$	−2.12152	−	0.689324i	−0.142068	−	0.0461606i	−0.379188	+	0.925320i	$0.623797\pi$
$224$	16.5575	+	18.7641i	1.10629	+	1.25373i
$225$	0.0406702	+	0.195970i	0.00271135	+	0.0130647i
$226$	−3.55673	+	6.77028i	−0.236590	+	0.450353i
$227$	−2.05822	+	6.33454i	−0.136609	+	0.420438i	−0.995837	−	0.0911544i	$-0.970944\pi$
$227$	−2.05822	+	6.33454i	−0.136609	+	0.420438i	0.859228	+	0.511593i	$0.170944\pi$
$228$	−5.95522	−	0.148649i	−0.394394	−	0.00984449i
$229$	−6.45978	+	8.89112i	−0.426874	+	0.587542i	−0.967232	−	0.253893i	$-0.918289\pi$
$229$	−6.45978	+	8.89112i	−0.426874	+	0.587542i	0.540358	+	0.841435i	$0.318289\pi$
$230$	−6.55437	−	15.3315i	−0.432182	−	1.01093i
$231$	−32.8862	+	23.8932i	−2.16375	+	1.57206i
$232$	5.78661	−	0.695667i	0.379910	−	0.0456728i
$233$	16.0021	+	22.0251i	1.04834	+	1.44291i	0.890243	+	0.455485i	$0.150534\pi$
$233$	16.0021	+	22.0251i	1.04834	+	1.44291i	0.158092	+	0.987424i	$0.449466\pi$
$234$	0.00734223	−	0.0428865i	0.000479977	−	0.00280358i
$235$	−13.9484	−	11.3509i	−0.909895	−	0.740450i
$236$	−0.616693	−	2.07260i	−0.0401433	−	0.134915i
$237$	4.12044	+	12.6814i	0.267651	+	0.823746i
$238$	6.00987	−	35.1041i	0.389562	−	2.27546i
$239$	3.33646	−	10.2686i	0.215817	−	0.664218i	−0.783277	−	0.621673i	$-0.786453\pi$
$239$	3.33646	−	10.2686i	0.215817	−	0.664218i	0.999095	−	0.0425450i	$-0.0135466\pi$
$240$	−10.2963	+	11.4361i	−0.664620	+	0.738198i
$241$	−2.98946	−	9.20061i	−0.192568	−	0.592663i	−0.999996	−	0.00269761i	$-0.999141\pi$
$241$	−2.98946	−	9.20061i	−0.192568	−	0.592663i	0.807428	−	0.589966i	$-0.200859\pi$
$242$	−24.5262	+	3.57145i	−1.57660	+	0.229582i
$243$	−0.415968			−0.0266843
$244$	−4.80554	+	13.6234i	−0.307643	+	0.872149i
$245$	−1.53856	+	28.0653i	−0.0982947	+	1.79303i
$246$	2.63139	+	5.32770i	0.167771	+	0.339682i
$247$	−0.782131	+	1.07651i	−0.0497658	+	0.0684968i
$248$	−7.23394	−	1.42512i	−0.459356	−	0.0904951i
$249$	−11.6947			−0.741120
$250$	−9.03998	−	12.9722i	−0.571738	−	0.820436i
$251$		−	19.3541i		−	1.22162i	−0.791778	−	0.610809i	$-0.790844\pi$
$251$		−	19.3541i		−	1.22162i	0.791778	−	0.610809i	$-0.209156\pi$
$252$	−0.101003	−	0.339455i	−0.00636260	−	0.0213836i
$253$	−22.7828	−	16.5527i	−1.43234	−	1.04066i
$254$	−16.9578	+	8.37557i	−1.06403	+	0.525530i
$255$	21.8674	+	1.19878i	1.36939	+	0.0750707i
$256$	15.9203	+	1.59453i	0.995022	+	0.0996578i
$257$			11.0336i			0.688257i	0.938923	+	0.344129i	$0.111826\pi$
$257$			11.0336i			0.688257i	−0.938923	+	0.344129i	$0.888174\pi$
$258$	16.0160	−	2.33222i	0.997114	−	0.145198i
$259$	27.3669	−	8.89204i	1.70049	−	0.552524i
$260$	0.798471	+	3.34327i	0.0495190	+	0.207341i
$261$	−0.0784474	−	0.0254891i	−0.00485577	−	0.00157774i
$262$	4.92799	+	0.843679i	0.304452	+	0.0521227i
$263$	7.35613	−	2.39015i	0.453598	−	0.147383i	−0.0733026	−	0.997310i	$-0.523354\pi$
$263$	7.35613	−	2.39015i	0.453598	−	0.147383i	0.526901	+	0.849927i	$0.323354\pi$
$264$	−5.02358	+	25.4998i	−0.309180	+	1.56941i
$265$	6.59056	−	8.09875i	0.404855	−	0.497502i
$266$	−1.82770	+	10.6757i	−0.112063	+	0.654570i
$267$	17.5396	−	12.7433i	1.07341	−	0.779877i
$268$	−7.19429	−	10.4404i	−0.439461	−	0.637746i
$269$	10.4677	+	14.4075i	0.638224	+	0.878440i	0.998519	−	0.0543984i	$-0.0173241\pi$
$269$	10.4677	+	14.4075i	0.638224	+	0.878440i	−0.360295	+	0.932838i	$0.617324\pi$
$270$	15.2080	−	6.50158i	0.925530	−	0.395674i
$271$	6.54444	+	4.75481i	0.397546	+	0.288834i	0.768541	−	0.639801i	$-0.220983\pi$
$271$	6.54444	+	4.75481i	0.397546	+	0.288834i	−0.370994	+	0.928635i	$0.620983\pi$
$272$	−12.4486	−	19.0669i	−0.754810	−	1.15610i
$273$	5.56350	+	1.80769i	0.336718	+	0.109406i
$274$	14.2293	−	27.0857i	0.859624	−	1.63631i
$275$	−24.3434	−	10.9790i	−1.46796	−	0.662060i
$276$	−14.9395	+	10.2946i	−0.899250	+	0.619659i
$277$	6.31523	−	19.4363i	0.379445	−	1.16781i	−0.560985	−	0.827826i	$-0.689577\pi$
$277$	6.31523	−	19.4363i	0.379445	−	1.16781i	0.940430	−	0.339987i	$-0.110423\pi$
$278$	−2.53292	+	1.25103i	−0.151915	+	0.0750317i
$279$	0.0844176	+	0.0613330i	0.00505395	+	0.00367191i
$280$	17.8783	+	21.5213i	1.06844	+	1.28614i
$281$	−26.1698	+	19.0135i	−1.56116	+	1.13425i	−0.626108	+	0.779736i	$0.715353\pi$
$281$	−26.1698	+	19.0135i	−1.56116	+	1.13425i	−0.935051	+	0.354513i	$0.884647\pi$
$282$	−9.10050	+	17.3229i	−0.541927	+	1.03157i
$283$	−19.5207	+	14.1826i	−1.16038	+	0.843067i	−0.989826	−	0.142280i	$-0.954557\pi$
$283$	−19.5207	+	14.1826i	−1.16038	+	0.843067i	−0.170556	+	0.985348i	$0.554557\pi$
$284$	0.710419	−	0.928186i	0.0421556	−	0.0550777i
$285$	−6.65022	−	0.364569i	−0.393925	−	0.0215952i
$286$	4.05351	+	4.15596i	0.239689	+	0.245747i
$287$	10.2750	−	3.33856i	0.606516	−	0.197069i
$288$	−0.194957	−	0.115181i	−0.0114879	−	0.00678710i
$289$	−4.76106	+	14.6531i	−0.280063	+	0.861944i
$290$	6.48994	−	0.584603i	0.381102	−	0.0343291i
$291$	−5.31490	+	1.72691i	−0.311565	+	0.101234i
$292$	−3.83652	+	10.8763i	−0.224516	+	0.636487i
$293$	10.3735			0.606027			0.303014	−	0.952986i	$-0.402007\pi$
$293$	10.3735			0.606027			0.303014	+	0.952986i	$0.402007\pi$
$294$	30.2649	−	4.40711i	1.76508	−	0.257028i
$295$	−0.620111	−	2.33676i	−0.0361043	−	0.136051i
$296$	8.96011	−	16.0686i	0.520796	−	0.933966i
$297$	16.4194	−	22.5994i	0.952750	−	1.31135i
$298$	4.54872	+	4.66367i	0.263500	+	0.270159i
$299$			4.05261i			0.234369i
$300$	−11.8875	+	12.4372i	−0.686327	+	0.718061i
$301$		−	29.4271i		−	1.69615i
$302$	−1.78362	+	1.73965i	−0.102636	+	0.100106i
$303$	3.94655	−	5.43197i	0.226724	−	0.312058i
$304$	3.78583	+	5.79853i	0.217132	+	0.332569i
$305$	−5.82435	+	15.0645i	−0.333501	+	0.862592i
$306$	0.0464377	+	0.318901i	0.00265467	+	0.0182304i
$307$	3.04330			0.173690			0.0868452	−	0.996222i	$-0.472321\pi$
$307$	3.04330			0.173690			0.0868452	+	0.996222i	$0.472321\pi$
$308$	44.5633	+	15.7193i	2.53923	+	0.895691i
$309$	−31.2633	+	10.1581i	−1.77851	+	0.577872i
$310$	−8.03671	−	1.83368i	−0.456455	−	0.104146i
$311$	−4.69469	+	14.4488i	−0.266212	+	0.819315i	0.725200	+	0.688538i	$0.241747\pi$
$311$	−4.69469	+	14.4488i	−0.266212	+	0.819315i	−0.991412	+	0.130777i	$0.958253\pi$
$312$	3.39372	−	1.57209i	0.192132	−	0.0890021i
$313$	−0.113450	+	0.0368620i	−0.00641255	+	0.00208357i	−0.312222	−	0.950009i	$-0.601073\pi$
$313$	−0.113450	+	0.0368620i	−0.00641255	+	0.00208357i	0.305809	+	0.952093i	$0.401073\pi$
$314$	−4.39009	+	4.28187i	−0.247747	+	0.241640i
$315$	−0.101563	−	0.382719i	−0.00572243	−	0.0215638i
$316$	9.42109	−	12.3090i	0.529977	−	0.692433i
$317$	23.7579	−	17.2612i	1.33438	−	0.969483i	0.334748	−	0.942308i	$-0.391349\pi$
$317$	23.7579	−	17.2612i	1.33438	−	0.969483i	0.999631	−	0.0271752i	$-0.00865119\pi$
$318$	−10.0581	−	5.28394i	−0.564028	−	0.296309i
$319$	8.90369	−	6.46891i	0.498511	−	0.362189i
$320$	17.7384	+	2.31246i	0.991609	+	0.129271i
$321$	−17.0033	−	12.3537i	−0.949034	−	0.689514i
$322$	14.6079	+	29.5763i	0.814068	+	1.64822i
$323$	3.04552	−	9.37315i	0.169457	−	0.521536i
$324$	−10.0754	−	14.6214i	−0.559743	−	0.812299i
$325$	0.780911	+	3.76284i	0.0433172	+	0.208725i
$326$	9.04254	+	4.75045i	0.500820	+	0.263103i
$327$	−13.7838	−	4.47862i	−0.762244	−	0.247668i
$328$	3.36412	−	6.03303i	0.185753	−	0.333118i
$329$	28.7832	+	20.9122i	1.58687	+	1.15293i
$330$	−6.46378	+	28.3296i	−0.355819	+	1.55949i
$331$	19.7316	+	27.1582i	1.08455	+	1.49275i	0.854416	+	0.519589i	$0.173915\pi$
$331$	19.7316	+	27.1582i	1.08455	+	1.49275i	0.230129	+	0.973160i	$0.426085\pi$
$332$	7.71392	+	11.1944i	0.423356	+	0.614375i
$333$	−0.210648	+	0.153045i	−0.0115434	+	0.00838681i
$334$	−12.5902	−	2.15546i	−0.688904	−	0.117941i
$335$	−7.69197	−	11.9072i	−0.420257	−	0.650561i
$336$	19.1010	−	23.7061i	1.04204	−	1.29328i
$337$	−28.0105	+	9.10115i	−1.52583	+	0.495771i	−0.947424	−	0.319980i	$-0.896324\pi$
$337$	−28.0105	+	9.10115i	−1.52583	+	0.495771i	−0.578403	+	0.815751i	$0.696324\pi$
$338$	−2.96138	+	17.2977i	−0.161078	+	0.940869i
$339$	8.84840	+	2.87502i	0.480579	+	0.156150i
$340$	−13.2764	−	21.7228i	−0.720016	−	1.17808i
$341$	−13.2410	+	4.30227i	−0.717042	+	0.232981i
$342$	−0.0141224	−	0.0969828i	−0.000763654	−	0.00524423i
$343$		−	24.6407i		−	1.33048i
$344$	−12.7968	−	13.7926i	−0.689956	−	0.743646i
$345$	−17.0385	+	11.0067i	−0.917319	+	0.592581i
$346$	8.57692	+	17.3655i	0.461098	+	0.933573i
$347$	3.43363	+	2.49468i	0.184327	+	0.133921i	0.676122	−	0.736789i	$-0.263659\pi$
$347$	3.43363	+	2.49468i	0.184327	+	0.133921i	−0.491795	+	0.870711i	$0.663659\pi$
$348$	−2.02209	−	6.79592i	−0.108396	−	0.364300i
$349$		−	16.7792i		−	0.898172i	−0.893488	−	0.449086i	$-0.851750\pi$
$349$		−	16.7792i		−	0.898172i	0.893488	−	0.449086i	$-0.148250\pi$
$350$	19.2625	+	24.6466i	1.02963	+	1.31742i
$351$	−4.01998			−0.214570
$352$	27.7227	−	12.0112i	1.47762	−	0.640201i
$353$	20.2984	−	27.9383i	1.08037	−	1.48701i	0.221266	−	0.975213i	$-0.428981\pi$
$353$	20.2984	−	27.9383i	1.08037	−	1.48701i	0.859108	−	0.511794i	$-0.171019\pi$
$354$	−2.35866	+	1.16496i	−0.125361	+	0.0619168i
$355$	0.824850	−	1.01361i	0.0437785	−	0.0537968i
$356$	−23.7675	−	8.38379i	−1.25968	−	0.444340i
$357$	−43.3271			−2.29311
$358$	1.45398	+	9.98489i	0.0768452	+	0.527718i
$359$	1.03463	+	3.18426i	0.0546057	+	0.168059i	0.974640	−	0.223779i	$-0.0718394\pi$
$359$	1.03463	+	3.18426i	0.0546057	+	0.168059i	−0.920034	+	0.391838i	$0.871839\pi$
$360$	−0.214033	−	0.135216i	−0.0112805	−	0.00712648i
$361$	4.94513	−	15.2196i	0.260270	−	0.801029i
$362$	−3.93206	−	0.673175i	−0.206665	−	0.0353813i
$363$	9.31745	+	28.6762i	0.489039	+	1.50511i
$364$	−1.93937	−	6.51789i	−0.101651	−	0.341630i
$365$	−4.64990	+	12.0268i	−0.243387	+	0.629513i
$366$	17.3224	+	2.96561i	0.905454	+	0.155015i
$367$	5.73261	+	7.89027i	0.299240	+	0.411869i	0.931988	−	0.362489i	$-0.118073\pi$
$367$	5.73261	+	7.89027i	0.299240	+	0.411869i	−0.632748	+	0.774358i	$0.718073\pi$
$368$	19.7084	+	7.51004i	1.02737	+	0.391488i
$369$	−0.0790890	+	0.0574615i	−0.00411721	+	0.00299133i
$370$	10.5487	−	17.6586i	0.548402	−	0.918029i
$371$	−12.1421	+	16.7121i	−0.630385	+	0.867651i
$372$	−0.223821	+	8.96679i	−0.0116046	+	0.464906i
$373$	−5.70667	+	17.5633i	−0.295480	+	0.909395i	0.687579	+	0.726109i	$0.258673\pi$
$373$	−5.70667	+	17.5633i	−0.295480	+	0.909395i	−0.983060	+	0.183286i	$0.941327\pi$
$374$	−38.0653	−	19.9974i	−1.96831	−	1.03404i
$375$	−13.6992	+	13.5029i	−0.707425	+	0.697286i
$376$	22.5847	−	2.71514i	1.16472	−	0.140022i
$377$	−1.50627	−	0.489418i	−0.0775770	−	0.0252063i
$378$	−29.3381	+	14.4903i	−1.50899	+	0.745299i
$379$	−15.5245	+	21.3676i	−0.797439	+	1.09758i	0.195703	+	0.980663i	$0.437301\pi$
$379$	−15.5245	+	21.3676i	−0.797439	+	1.09758i	−0.993142	+	0.116917i	$0.962699\pi$
$380$	4.03757	+	6.60623i	0.207123	+	0.338893i
$381$	13.5244	+	18.6147i	0.692875	+	0.953661i
$382$	−17.6647	−	9.28006i	−0.903806	−	0.474809i
$383$	−12.3447	−	16.9911i	−0.630787	−	0.868203i	0.367296	−	0.930104i	$-0.380284\pi$
$383$	−12.3447	−	16.9911i	−0.630787	−	0.868203i	−0.998082	+	0.0619009i	$0.980284\pi$
$384$	−1.35626	−	19.4174i	−0.0692111	−	0.990892i
$385$	49.2773	+	19.0519i	2.51140	+	0.970976i
$386$	−6.79168	−	6.96332i	−0.345687	−	0.354424i
$387$	0.0822833	+	0.253242i	0.00418269	+	0.0128730i
$388$	5.15880	+	3.94846i	0.261899	+	0.200453i
$389$	−14.0198	−	4.55530i	−0.710830	−	0.230963i	−0.0687872	−	0.997631i	$-0.521913\pi$
$389$	−14.0198	−	4.55530i	−0.710830	−	0.230963i	−0.642043	+	0.766669i	$0.721913\pi$
$390$	3.84500	−	1.64378i	0.194699	−	0.0832360i
$391$	−9.27547	−	28.5470i	−0.469081	−	1.44368i
$392$	−24.1816	−	26.0633i	−1.22135	−	1.31640i
$393$		−	6.08236i		−	0.306814i
$394$	−17.0618	+	2.48450i	−0.859559	+	0.125167i
$395$	10.9386	−	13.4418i	0.550380	−	0.676330i
$396$	−0.427453	−	0.0106697i	−0.0214803	−	0.000536172i
$397$	−19.8855	−	14.4476i	−0.998023	−	0.725106i	−0.0363595	−	0.999339i	$-0.511576\pi$
$397$	−19.8855	−	14.4476i	−0.998023	−	0.725106i	−0.961663	+	0.274233i	$0.911576\pi$
$398$	−14.9537	+	14.5851i	−0.749559	+	0.731083i
$399$	13.1765			0.659648
$400$	19.7463	+	3.17537i	0.987316	+	0.158769i
$401$	3.41803			0.170688			0.0853441	−	0.996352i	$-0.472801\pi$
$401$	3.41803			0.170688			0.0853441	+	0.996352i	$0.472801\pi$
$402$	−11.0421	+	10.7699i	−0.550732	+	0.537156i
$403$	1.62091	+	1.17766i	0.0807431	+	0.0586633i
$404$	−7.80280	−	0.194766i	−0.388204	−	0.00968998i
$405$	−10.7724	−	16.6757i	−0.535283	−	0.828621i
$406$	−12.7570	+	1.85765i	−0.633121	+	0.0921939i
$407$		−	34.7408i		−	1.72204i
$408$	−20.3075	+	18.8414i	−1.00537	+	0.932787i
$409$	−1.50524	−	4.63264i	−0.0744292	−	0.229069i	0.906920	−	0.421303i	$-0.138427\pi$
$409$	−1.50524	−	4.63264i	−0.0744292	−	0.229069i	−0.981349	+	0.192233i	$0.938427\pi$
$410$	3.96057	−	6.63003i	0.195599	−	0.327434i
$411$	−35.3996	−	11.5020i	−1.74613	−	0.567352i
$412$	30.3451	+	23.2257i	1.49500	+	1.14425i
$413$	1.47804	+	4.54893i	0.0727294	+	0.223838i
$414$	−0.208412	−	0.213679i	−0.0102429	−	0.0105018i
$415$	8.24756	+	12.7673i	0.404857	+	0.626720i
$416$	−3.74338	−	2.21159i	−0.183534	−	0.108432i
$417$	2.02009	+	2.78041i	0.0989240	+	0.136157i
$418$	11.5762	+	6.08152i	0.566213	+	0.297457i
$419$	2.28269	+	3.14185i	0.111517	+	0.153489i	0.861127	−	0.508390i	$-0.169759\pi$
$419$	2.28269	+	3.14185i	0.111517	+	0.153489i	−0.749610	+	0.661879i	$0.769759\pi$
$420$	22.1360	−	25.8560i	1.08013	−	1.26164i
$421$	−4.13220	+	5.68749i	−0.201391	+	0.277191i	−0.897753	−	0.440500i	$-0.854801\pi$
$421$	−4.13220	+	5.68749i	−0.201391	+	0.277191i	0.696361	+	0.717691i	$0.254801\pi$
$422$	−2.92471	+	1.44454i	−0.142373	+	0.0703189i
$423$	−0.306175	−	0.0994821i	−0.0148867	−	0.00483699i
$424$	1.57646	+	13.1132i	0.0765599	+	0.636832i
$425$	−14.1130	−	24.7184i	−0.684583	−	1.19902i
$426$	−1.25883	−	0.661319i	−0.0609905	−	0.0320410i
$427$	9.87415	−	30.3895i	0.477843	−	1.47065i
$428$	−0.609664	+	24.4246i	−0.0294692	+	1.18061i
$429$	4.15127	−	5.71374i	0.200425	−	0.275862i
$430$	−13.8413	−	15.8402i	−0.667485	−	0.763880i
$431$	−1.52243	+	1.10611i	−0.0733329	+	0.0532795i	−0.623848	−	0.781546i	$-0.714431\pi$
$431$	−1.52243	+	1.10611i	−0.0733329	+	0.0532795i	0.550515	+	0.834825i	$0.314431\pi$
$432$	−7.44956	+	19.5497i	−0.358417	+	0.940585i
$433$	−3.83776	−	5.28222i	−0.184431	−	0.253847i	0.706783	−	0.707430i	$-0.250146\pi$
$433$	−3.83776	−	5.28222i	−0.184431	−	0.253847i	−0.891214	+	0.453583i	$0.850146\pi$
$434$	16.0745	+	2.75197i	0.771598	+	0.132099i
$435$	−2.03330	−	7.66208i	−0.0974894	−	0.367368i
$436$	4.80485	+	16.1483i	0.230111	+	0.773363i
$437$	2.82082	+	8.68158i	0.134938	+	0.415296i
$438$	13.8294	+	2.36761i	0.660793	+	0.113129i
$439$	−8.75988	+	26.9601i	−0.418086	+	1.28674i	0.491375	+	0.870948i	$0.336494\pi$
$439$	−8.75988	+	26.9601i	−0.418086	+	1.28674i	−0.909461	+	0.415789i	$0.863506\pi$
$440$	31.3814	−	12.4992i	1.49605	−	0.595875i
$441$	0.155488	+	0.478542i	0.00740417	+	0.0227877i
$442$	0.891654	+	6.12324i	0.0424116	+	0.291253i
$443$	25.7646			1.22412			0.612058	−	0.790813i	$-0.290342\pi$
$443$	25.7646			1.22412			0.612058	+	0.790813i	$0.290342\pi$
$444$	−21.1072	−	7.44540i	−1.00170	−	0.353343i
$445$	−26.2817	−	10.1612i	−1.24587	−	0.481688i
$446$	2.82850	−	1.39701i	0.133933	−	0.0661505i
$447$	4.65842	−	6.41176i	0.220336	−	0.303266i
$448$	−35.2913	−	2.64712i	−1.66736	−	0.125065i
$449$	4.58045			0.216165			0.108082	−	0.994142i	$-0.465529\pi$
$449$	4.58045			0.216165			0.108082	+	0.994142i	$0.465529\pi$
$450$	−0.234684	−	0.158241i	−0.0110631	−	0.00745954i
$451$		−	13.0436i		−	0.614200i
$452$	−3.08445	−	10.3663i	−0.145080	−	0.487590i
$453$	2.45217	+	1.78161i	0.115213	+	0.0837072i
$454$	−4.17127	−	8.44546i	−0.195767	−	0.396365i
$455$	−1.95012	−	7.34861i	−0.0914229	−	0.344508i
$456$	6.17584	−	5.72995i	0.289210	−	0.268330i
$457$		−	10.4431i		−	0.488509i	−0.969711	−	0.244255i	$-0.921457\pi$
$457$		−	10.4431i		−	0.488509i	0.969711	−	0.244255i	$-0.0785433\pi$
$458$	−2.23961	−	15.3800i	−0.104650	−	0.718662i
$459$	28.3171	−	9.20077i	1.32173	−	0.429455i
$460$	21.7746	+	9.04951i	1.01525	+	0.421935i
$461$	−29.9901	−	9.74436i	−1.39678	−	0.453840i	−0.488630	−	0.872491i	$-0.662503\pi$
$461$	−29.9901	−	9.74436i	−1.39678	−	0.453840i	−0.908147	+	0.418651i	$0.862503\pi$
$462$	9.70076	−	56.6628i	0.451320	−	2.63619i
$463$	12.8107	−	4.16244i	0.595362	−	0.193445i	0.00419137	−	0.999991i	$-0.498666\pi$
$463$	12.8107	−	4.16244i	0.595362	−	0.193445i	0.591171	+	0.806546i	$0.298666\pi$
$464$	−5.17143	+	6.41825i	−0.240078	+	0.297960i
$465$	−0.548932	+	10.0133i	−0.0254561	+	0.464354i
$466$	−37.9491	−	6.49694i	−1.75796	−	0.300965i
$467$	−15.5848	+	11.3230i	−0.721180	+	0.523968i	−0.886761	−	0.462228i	$-0.847050\pi$
$467$	−15.5848	+	11.3230i	−0.721180	+	0.523968i	0.165581	+	0.986196i	$0.447050\pi$
$468$	0.0349148	+	0.0506684i	0.00161394	+	0.00234215i
$469$	16.4843	+	22.6888i	0.761176	+	1.04767i
$470$	25.3297	−	2.28166i	1.16837	−	0.105245i
$471$	6.03563	+	4.38514i	0.278107	+	0.202057i
$472$	2.67092	+	1.48935i	0.122939	+	0.0685530i
$473$	−33.7890	−	10.9787i	−1.55362	−	0.504802i
$474$	−16.6937	−	8.76995i	−0.766768	−	0.402817i
$475$	4.29200	+	7.51726i	0.196930	+	0.344915i
$476$	28.5790	+	41.4738i	1.30992	+	1.90095i
$477$	0.0577614	−	0.177771i	0.00264471	−	0.00813959i
$478$	6.76180	+	13.6905i	0.309278	+	0.626187i
$479$	−16.2835	−	11.8306i	−0.744010	−	0.540555i	0.149954	−	0.988693i	$-0.452087\pi$
$479$	−16.2835	−	11.8306i	−0.744010	−	0.540555i	−0.893964	+	0.448138i	$0.852087\pi$
$480$	−0.868609	−	21.7449i	−0.0396464	−	0.992515i
$481$	−4.04467	+	2.93862i	−0.184421	+	0.133990i
$482$	12.1116	+	6.36277i	0.551669	+	0.289816i
$483$	32.4661	−	23.5880i	1.47726	−	1.07329i
$484$	21.3037	−	27.8340i	0.968349	−	1.26518i
$485$	5.63358	+	4.58447i	0.255808	+	0.208170i
$486$	0.421126	−	0.410745i	0.0191027	−	0.0186318i
$487$	−26.8399	+	8.72080i	−1.21623	+	0.395177i	−0.845708	−	0.533646i	$-0.820821\pi$
$487$	−26.8399	+	8.72080i	−1.21623	+	0.395177i	−0.370523	+	0.928823i	$0.620821\pi$
$488$	−8.58723	−	18.5375i	−0.388726	−	0.839155i
$489$	3.83994	−	11.8181i	0.173648	−	0.534434i
$490$	−26.1553	−	29.9326i	−1.18158	−	1.35222i
$491$	34.0495	−	11.0634i	1.53663	−	0.499283i	0.586189	−	0.810174i	$-0.300628\pi$
$491$	34.0495	−	11.0634i	1.53663	−	0.499283i	0.950445	+	0.310892i	$0.100628\pi$
$492$	−7.92482	−	2.79541i	−0.357279	−	0.126027i
$493$	11.7305			0.528314
$494$	−0.271166	−	1.86217i	−0.0122003	−	0.0837831i
$495$	−0.477339	−	0.0261680i	−0.0214548	−	0.00117616i
$496$	8.73087	−	5.70033i	0.392028	−	0.255952i
$497$	−1.51966	+	2.09163i	−0.0681659	+	0.0938224i
$498$	11.8397	−	11.5478i	0.530549	−	0.517471i
$499$			26.6004i			1.19080i	0.803430	+	0.595399i	$0.203006\pi$
$499$			26.6004i			1.19080i	−0.803430	+	0.595399i	$0.796994\pi$
$500$	21.9614	+	4.20661i	0.982145	+	0.188125i
$501$			15.5394i			0.694248i
$502$	19.1111	+	19.5941i	0.852969	+	0.874526i
$503$	−12.2552	+	16.8678i	−0.546430	+	0.752097i	−0.989522	−	0.144379i	$-0.953882\pi$
$503$	−12.2552	+	16.8678i	−0.546430	+	0.752097i	0.443092	+	0.896476i	$0.353882\pi$
$504$	0.437448	+	0.243929i	0.0194855	+	0.0108655i
$505$	−8.71343	−	0.477675i	−0.387742	−	0.0212563i
$506$	39.4102	−	5.73884i	1.75200	−	0.255122i
$507$	21.3496			0.948168
$508$	8.89767	−	25.2243i	0.394770	−	1.11915i
$509$	−34.2578	+	11.1310i	−1.51845	+	0.493374i	−0.945335	−	0.326101i	$-0.894265\pi$
$509$	−34.2578	+	11.1310i	−1.51845	+	0.493374i	−0.573115	+	0.819475i	$0.694265\pi$
$510$	−23.3223	+	20.3792i	−1.03273	+	0.902407i
$511$	7.88306	−	24.2616i	0.348726	−	1.07327i
$512$	−17.6923	+	14.1062i	−0.781895	+	0.623410i
$513$	−8.61166	+	2.79810i	−0.380214	+	0.123539i
$514$	−10.8951	−	11.1704i	−0.480561	−	0.492706i
$515$	33.1378	+	26.9668i	1.46023	+	1.18830i
$516$	−13.9117	+	18.1761i	−0.612427	+	0.800157i
$517$	34.7504	−	25.2477i	1.52832	−	1.11039i
$518$	−18.9258	+	36.0256i	−0.831553	+	1.58287i
$519$	19.0622	−	13.8495i	0.836738	−	0.607926i
$520$	−4.10967	−	2.59628i	−0.180221	−	0.113854i
$521$	27.8704	+	20.2490i	1.22102	+	0.887126i	0.996185	−	0.0872702i	$-0.0278144\pi$
$521$	27.8704	+	20.2490i	1.22102	+	0.887126i	0.224839	+	0.974396i	$0.427814\pi$
$522$	0.104589	−	0.0516573i	0.00457775	−	0.00226098i
$523$	−9.84654	+	30.3045i	−0.430559	+	1.32512i	0.467011	+	0.884252i	$0.345331\pi$
$523$	−9.84654	+	30.3045i	−0.430559	+	1.32512i	−0.897570	+	0.440873i	$0.854669\pi$
$524$	−5.82219	+	4.01198i	−0.254343	+	0.175264i
$525$	25.5994	−	28.1574i	1.11725	−	1.22889i
$526$	−5.08720	+	9.68356i	−0.221812	+	0.422223i
$527$	−14.1132	−	4.58565i	−0.614780	−	0.199754i
$528$	−20.0938	−	30.7765i	−0.874471	−	1.33938i
$529$	3.88440	+	2.82218i	0.168887	+	0.122704i
$530$	1.32478	+	14.7070i	0.0575448	+	0.638831i
$531$	−0.0254391	−	0.0350140i	−0.00110396	−	0.00151948i
$532$	−8.69131	−	12.6128i	−0.376816	−	0.546836i
$533$	−1.51859	+	1.10332i	−0.0657775	+	0.0477902i
$534$	−5.17383	+	30.2207i	−0.223894	+	1.30778i
$535$	−1.49524	+	27.2751i	−0.0646447	+	1.17921i
$536$	17.5928	+	3.46585i	0.759892	+	0.149702i
$537$	11.6744	−	3.79324i	0.503788	−	0.163691i
$538$	−24.8240	−	4.24991i	−1.07024	−	0.183227i
$539$	−63.8498	−	20.7461i	−2.75021	−	0.893596i
$540$	−8.97663	+	21.5993i	−0.386292	+	0.929484i
$541$	19.8645	−	6.45438i	0.854044	−	0.277496i	0.150905	−	0.988548i	$-0.451781\pi$
$541$	19.8645	−	6.45438i	0.854044	−	0.277496i	0.703139	+	0.711053i	$0.251781\pi$
$542$	−11.3207	+	1.64850i	−0.486266	+	0.0708091i
$543$			4.85313i			0.208268i
$544$	31.4305	+	7.01095i	1.34757	+	0.300592i
$545$	4.83148	+	18.2064i	0.206958	+	0.779878i
$546$	−7.41748	+	3.66354i	−0.317439	+	0.156785i
$547$	−24.4151	−	17.7386i	−1.04392	−	0.758450i	−0.0728702	−	0.997341i	$-0.523216\pi$
$547$	−24.4151	−	17.7386i	−1.04392	−	0.758450i	−0.971046	+	0.238892i	$0.923216\pi$
$548$	12.3399	+	41.4722i	0.527133	+	1.77160i
$549$			0.289133i			0.0123399i
$550$	35.4864	−	12.9226i	1.51314	−	0.551020i
$551$	−3.56742			−0.151977
$552$	4.95940	−	25.1741i	0.211086	−	1.07148i
$553$	−20.1526	+	27.7377i	−0.856978	+	1.17953i
$554$	12.7987	+	25.9132i	0.543765	+	1.10095i
$555$	−23.3400	−	9.02388i	−0.990728	−	0.383042i
$556$	1.32901	−	3.76766i	0.0563626	−	0.159784i
$557$	−0.749572			−0.0317604			−0.0158802	−	0.999874i	$-0.505055\pi$
$557$	−0.749572			−0.0317604			−0.0158802	+	0.999874i	$0.505055\pi$
$558$	−0.146027	+	0.0212642i	−0.00618183	+	0.000900186i
$559$	1.57993	+	4.86251i	0.0668237	+	0.205662i
$560$	−39.3511	−	4.13429i	−1.66289	−	0.174706i
$561$	−16.1645	+	49.7493i	−0.682467	+	2.10042i
$562$	7.71955	−	45.0905i	0.325630	−	1.90203i
$563$	−7.19759	−	22.1519i	−0.303342	−	0.933591i	−0.980291	−	0.197561i	$-0.936698\pi$
$563$	−7.19759	−	22.1519i	−0.303342	−	0.933591i	0.676949	−	0.736030i	$-0.263302\pi$
$564$	−7.89209	−	26.5240i	−0.332317	−	1.11686i
$565$	−3.10154	−	11.6875i	−0.130483	−	0.491698i
$566$	5.75819	−	33.6340i	0.242035	−	1.41374i
$567$	23.0858	+	31.7749i	0.969512	+	1.33442i
$568$	0.197305	+	1.64120i	0.00827871	+	0.0688630i
$569$	6.07930	−	4.41687i	0.254858	−	0.185165i	−0.453019	−	0.891501i	$-0.649653\pi$
$569$	6.07930	−	4.41687i	0.254858	−	0.185165i	0.707877	+	0.706336i	$0.249653\pi$
$570$	7.09267	−	6.19764i	0.297079	−	0.259590i
$571$	−1.37819	+	1.89691i	−0.0576753	+	0.0793832i	−0.836880	−	0.547386i	$-0.815623\pi$
$571$	−1.37819	+	1.89691i	−0.0576753	+	0.0793832i	0.779205	+	0.626769i	$0.215623\pi$
$572$	−8.20755	−	0.204869i	−0.343175	−	0.00856601i
$573$	−7.50138	+	23.0869i	−0.313375	+	0.964468i
$574$	−7.10580	+	13.5260i	−0.296590	+	0.564564i
$575$	24.0324	+	10.8388i	1.00222	+	0.452008i
$576$	0.311109	−	0.0759000i	0.0129629	−	0.00316250i
$577$	−20.3396	−	6.60875i	−0.846750	−	0.275126i	−0.146666	−	0.989186i	$-0.546854\pi$
$577$	−20.3396	−	6.60875i	−0.846750	−	0.275126i	−0.700084	+	0.714060i	$0.746854\pi$
$578$	−9.64897	−	19.5360i	−0.401344	−	0.812592i
$579$	−6.95547	+	9.57339i	−0.289060	+	0.397856i
$580$	−5.99315	+	7.00031i	−0.248852	+	0.290672i
$581$	−17.6750	−	24.3275i	−0.733282	−	1.00928i
$582$	3.67557	−	6.99649i	0.152357	−	0.290014i
$583$	14.6593	+	20.1768i	0.607127	+	0.835639i
$584$	−6.85565	−	14.7995i	−0.283689	−	0.612409i
$585$	0.0373301	+	0.0577873i	0.00154341	+	0.00238921i
$586$	−10.5021	+	10.2433i	−0.433840	+	0.423146i
$587$	2.16490	+	6.66288i	0.0893551	+	0.275007i	0.985741	−	0.168267i	$-0.0538170\pi$
$587$	2.16490	+	6.66288i	0.0893551	+	0.275007i	−0.896386	+	0.443274i	$0.853817\pi$
$588$	−26.2884	+	34.3466i	−1.08411	+	1.41643i
$589$	4.29204	+	1.39457i	0.176850	+	0.0574622i
$590$	2.93522	+	1.75341i	0.120841	+	0.0721867i
$591$	6.48173	+	19.9487i	0.266623	+	0.820581i
$592$	6.79560	+	25.1154i	0.279298	+	1.03224i
$593$		−	28.8406i		−	1.18434i	−0.805812	−	0.592171i	$-0.798271\pi$
$593$		−	28.8406i		−	1.18434i	0.805812	−	0.592171i	$-0.201729\pi$
$594$	5.69262	+	39.0928i	0.233571	+	1.60400i
$595$	30.5560	+	47.3009i	1.25267	+	1.93915i
$596$	−9.21024	−	0.229897i	−0.377266	−	0.00941696i
$597$	20.5587	+	14.9368i	0.841414	+	0.611323i
$598$	−4.00173	−	4.10287i	−0.163643	−	0.167779i
$599$	2.36104			0.0964695			0.0482347	−	0.998836i	$-0.484640\pi$
$599$	2.36104			0.0964695			0.0482347	+	0.998836i	$0.484640\pi$
$600$	−0.246087	−	24.3297i	−0.0100465	−	0.993255i
$601$	−15.1806			−0.619228			−0.309614	−	0.950862i	$-0.600200\pi$
$601$	−15.1806			−0.619228			−0.309614	+	0.950862i	$0.600200\pi$
$602$	29.0577	+	29.7920i	1.18430	+	1.21423i
$603$	−0.205301	−	0.149160i	−0.00836052	−	0.00607427i
$604$	0.0879239	−	3.52244i	0.00357757	−	0.143326i
$605$	24.7352	−	30.3956i	1.00563	−	1.23576i
$606$	1.36827	+	9.39632i	0.0555823	+	0.381700i
$607$		−	34.1325i		−	1.38540i	−0.721227	−	0.692699i	$-0.756422\pi$
$607$		−	34.1325i		−	1.38540i	0.721227	−	0.692699i	$-0.243578\pi$
$608$	−9.55850	−	2.13214i	−0.387648	−	0.0864697i
$609$	4.84638	+	14.9156i	0.196385	+	0.604411i
$610$	−8.97881	−	21.0026i	−0.363542	−	0.850368i
$611$	−5.87887	−	1.91016i	−0.237834	−	0.0772769i
$612$	−0.361911	−	0.277001i	−0.0146294	−	0.0111971i
$613$	1.84281	+	5.67158i	0.0744303	+	0.229073i	0.981350	−	0.192231i	$-0.0615724\pi$
$613$	1.84281	+	5.67158i	0.0744303	+	0.229073i	−0.906919	+	0.421304i	$0.861572\pi$
$614$	−3.08104	+	3.00509i	−0.124341	+	0.121276i
$615$	−8.76313	−	3.38806i	−0.353363	−	0.136620i
$616$	−60.6378	+	28.0895i	−2.44317	+	1.13176i
$617$	4.47498	+	6.15928i	0.180156	+	0.247963i	0.889538	−	0.456860i	$-0.151026\pi$
$617$	4.47498	+	6.15928i	0.180156	+	0.247963i	−0.709383	+	0.704824i	$0.751026\pi$
$618$	21.6204	−	41.1548i	0.869701	−	1.65549i
$619$	−16.7671	−	23.0779i	−0.673925	−	0.927579i	0.325916	−	0.945399i	$-0.394327\pi$
$619$	−16.7671	−	23.0779i	−0.673925	−	0.927579i	−0.999841	+	0.0178200i	$0.994327\pi$
$620$	9.94703	−	6.07939i	0.399482	−	0.244154i
$621$	−16.2096	+	22.3107i	−0.650470	+	0.895296i
$622$	−9.51446	−	19.2637i	−0.381495	−	0.772403i
$623$	53.0178	+	17.2265i	2.12411	+	0.690166i
$624$	−1.88345	+	4.94270i	−0.0753985	+	0.197866i
$625$	24.4025	+	5.43288i	0.976102	+	0.217315i
$626$	0.0784572	−	0.149344i	0.00313578	−	0.00596900i
$627$	4.91589	−	15.1295i	0.196322	−	0.604216i
$628$	0.216411	−	8.66993i	0.00863573	−	0.345968i
$629$	21.7652	−	29.9572i	0.867834	−	1.19447i
$630$	0.480736	+	0.287177i	0.0191530	+	0.0114414i
$631$	27.7571	−	20.1667i	1.10499	−	0.802823i	0.123124	−	0.992391i	$-0.460709\pi$
$631$	27.7571	−	20.1667i	1.10499	−	0.802823i	0.981868	+	0.189568i	$0.0607089\pi$
$632$	2.61652	+	21.7644i	0.104079	+	0.865741i
$633$	2.33255	+	3.21048i	0.0927106	+	0.127605i
$634$	−7.00810	+	40.9348i	−0.278327	+	1.62573i
$635$	10.7840	−	27.8926i	0.427952	−	1.10689i
$636$	15.4004	−	4.58231i	0.610665	−	0.181700i
$637$	2.98553	+	9.18851i	0.118291	+	0.364062i
$638$	−2.62640	+	15.3410i	−0.103980	+	0.607357i
$639$	0.00722920	−	0.0222492i	0.000285983	−	0.000880165i
$640$	−20.2418	+	15.1746i	−0.800129	+	0.599829i
$641$	11.8514	+	36.4748i	0.468102	+	1.44067i	0.855039	+	0.518563i	$0.173533\pi$
$641$	11.8514	+	36.4748i	0.468102	+	1.44067i	−0.386938	+	0.922106i	$0.626467\pi$
$642$	29.4127	−	4.28303i	1.16083	−	0.169038i
$643$	4.80260			0.189396			0.0946980	−	0.995506i	$-0.469811\pi$
$643$	4.80260			0.189396			0.0946980	+	0.995506i	$0.469811\pi$
$644$	−43.9940	−	15.5185i	−1.73361	−	0.611515i
$645$	−16.1525	+	19.8488i	−0.636004	+	0.781548i
$646$	6.17218	+	12.4967i	0.242841	+	0.491675i
$647$	2.22128	−	3.05732i	0.0873273	−	0.120196i	−0.763118	−	0.646259i	$-0.776333\pi$
$647$	2.22128	−	3.05732i	0.0873273	−	0.120196i	0.850445	+	0.526063i	$0.176333\pi$
$648$	24.6381	+	4.85381i	0.967876	+	0.190676i
$649$	5.77462			0.226674
$650$	−4.50619	−	3.03839i	−0.176747	−	0.119175i
$651$		−	19.8398i		−	0.777584i
$652$	−13.8455	+	4.11966i	−0.542231	+	0.161338i
$653$	32.1500	+	23.3583i	1.25813	+	0.914082i	0.998664	−	0.0516709i	$-0.0164547\pi$
$653$	32.1500	+	23.3583i	1.25813	+	0.914082i	0.259462	+	0.965753i	$0.416455\pi$
$654$	18.3771	−	9.07655i	0.718600	−	0.354921i
$655$	−6.64020	+	4.28952i	−0.259454	+	0.167605i
$656$	2.55144	+	9.42972i	0.0996172	+	0.368169i
$657$			0.230831i			0.00900557i
$658$	−49.7898	+	7.25029i	−1.94101	+	0.282646i
$659$	14.7150	−	4.78119i	0.573214	−	0.186249i	−0.00804417	−	0.999968i	$-0.502561\pi$
$659$	14.7150	−	4.78119i	0.573214	−	0.186249i	0.581258	+	0.813719i	$0.302561\pi$
$660$	−21.4300	−	35.0635i	−0.834161	−	1.36485i
$661$	29.4671	+	9.57445i	1.14614	+	0.372403i	0.819687	−	0.572811i	$-0.194147\pi$
$661$	29.4671	+	9.57445i	1.14614	+	0.372403i	0.326451	+	0.945214i	$0.394147\pi$
$662$	−46.7934	−	8.01110i	−1.81868	−	0.311360i
$663$	7.15933	−	2.32621i	0.278045	−	0.0903424i
$664$	−18.8635	−	3.71618i	−0.732044	−	0.144216i
$665$	−9.29256	−	14.3849i	−0.360350	−	0.557824i
$666$	0.0621369	−	0.362946i	0.00240775	−	0.0140639i
$667$	−8.78995	+	6.38627i	−0.340348	+	0.247277i
$668$	14.8747	−	10.2499i	0.575519	−	0.396581i
$669$	−2.25582	−	3.10486i	−0.0872149	−	0.120041i
$670$	19.5451	+	4.45947i	0.755092	+	0.172284i
$671$	−31.2101	−	22.6755i	−1.20485	−	0.875378i
$672$	4.07070	+	42.8612i	0.157031	+	1.65341i
$673$	27.2704	+	8.86070i	1.05120	+	0.341555i	0.783138	−	0.621848i	$-0.213618\pi$
$673$	27.2704	+	8.86070i	1.05120	+	0.341555i	0.268059	+	0.963402i	$0.413618\pi$
$674$	19.3709	−	36.8728i	0.746139	−	1.42029i
$675$	−10.7515	+	23.8388i	−0.413825	+	0.917558i
$676$	−14.0824	−	20.4364i	−0.541630	−	0.786014i
$677$	−9.18195	+	28.2591i	−0.352891	+	1.08609i	0.604331	+	0.796733i	$0.293440\pi$
$677$	−9.18195	+	28.2591i	−0.352891	+	1.08609i	−0.957222	+	0.289353i	$0.906560\pi$
$678$	−11.7970	+	5.82664i	−0.453063	+	0.223771i
$679$	−11.6251	−	8.44616i	−0.446132	−	0.324134i
$680$	34.8911	+	8.88237i	1.33801	+	0.340624i
$681$	−9.27065	+	6.73552i	−0.355252	+	0.258106i
$682$	9.15696	−	17.4304i	0.350638	−	0.667444i
$683$	1.42936	−	1.03849i	0.0546928	−	0.0397366i	−0.560103	−	0.828423i	$-0.689238\pi$
$683$	1.42936	−	1.03849i	0.0546928	−	0.0397366i	0.614796	+	0.788686i	$0.289238\pi$
$684$	0.110063	+	0.0842402i	0.00420835	+	0.00322100i
$685$	12.4083	+	46.7579i	0.474095	+	1.78653i
$686$	24.3314	+	24.9463i	0.928976	+	0.952454i
$687$	−17.9825	+	5.84285i	−0.686073	+	0.222919i
$688$	26.5749	+	1.32750i	1.01316	+	0.0506105i
$689$	1.10908	−	3.41340i	0.0422526	−	0.130040i
$690$	6.38121	−	27.9677i	0.242928	−	1.06471i
$691$	−12.3432	+	4.01054i	−0.469556	+	0.152568i	−0.534231	−	0.845338i	$-0.679399\pi$
$691$	−12.3432	+	4.01054i	−0.469556	+	0.152568i	0.0646751	+	0.997906i	$0.479399\pi$
$692$	−25.8307	−	9.11156i	−0.981936	−	0.346370i
$693$	0.945779			0.0359272
$694$	−5.93957	+	0.864908i	−0.225463	+	0.0328315i
$695$	1.61077	−	4.16622i	0.0611000	−	0.158034i
$696$	8.75776	+	4.88348i	0.331962	+	0.185108i
$697$	8.17185	−	11.2476i	0.309531	−	0.426033i
$698$	16.5686	+	16.9873i	0.627130	+	0.642979i
$699$			46.8385i			1.77160i
$700$	−43.8386	−	5.93154i	−1.65694	−	0.224191i
$701$			9.99937i			0.377671i	0.982009	+	0.188835i	$0.0604713\pi$
$701$			9.99937i			0.377671i	−0.982009	+	0.188835i	$0.939529\pi$
$702$	4.06982	−	3.96950i	0.153606	−	0.149819i
$703$	−6.61913	+	9.11045i	−0.249645	+	0.343607i
$704$	−16.2060	+	39.5348i	−0.610787	+	1.49002i
$705$	−7.93583	−	29.9045i	−0.298881	−	1.12627i
$706$	7.03747	+	48.3283i	0.264859	+	1.81886i
$707$	17.2644			0.649295
$708$	1.23758	−	3.50845i	0.0465109	−	0.131856i
$709$	39.3712	−	12.7925i	1.47862	−	0.480432i	0.544918	−	0.838490i	$-0.316561\pi$
$709$	39.3712	−	12.7925i	1.47862	−	0.480432i	0.933699	+	0.358058i	$0.116561\pi$
$710$	0.165805	+	1.84067i	0.00622254	+	0.0690792i
$711$	0.0958687	−	0.295054i	0.00359536	−	0.0110654i
$712$	32.3408	−	14.9814i	1.21202	−	0.561450i
$713$	13.0719	−	4.24731i	0.489546	−	0.159063i
$714$	43.8644	−	42.7831i	1.64158	−	1.60112i
$715$	−9.16542	−	0.502453i	−0.342767	−	0.0187907i
$716$	−11.3315	−	8.67298i	−0.423479	−	0.324124i
$717$	15.0281	−	10.9186i	0.561235	−	0.407761i
$718$	−4.19174	−	2.20211i	−0.156434	−	0.0821819i
$719$	−27.1580	+	19.7314i	−1.01282	+	0.735858i	−0.964799	−	0.262988i	$-0.915292\pi$
$719$	−27.1580	+	19.7314i	−1.01282	+	0.735858i	−0.0480227	+	0.998846i	$0.515292\pi$
$720$	0.350205	−	0.0744539i	0.0130514	−	0.00277473i
$721$	−68.3814	−	49.6820i	−2.54666	−	1.85026i
$722$	10.0220	+	20.2913i	0.372981	+	0.755165i
$723$	5.14323	−	15.8292i	0.191279	−	0.588696i
$724$	4.64554	−	3.20117i	0.172650	−	0.118971i
$725$	−6.93084	+	7.62339i	−0.257405	+	0.283126i
$726$	−37.7491	−	19.8313i	−1.40100	−	0.736008i
$727$	−42.4290	−	13.7860i	−1.57360	−	0.511295i	−0.613204	−	0.789924i	$-0.710120\pi$
$727$	−42.4290	−	13.7860i	−1.57360	−	0.511295i	−0.960399	+	0.278630i	$0.910120\pi$
$728$	8.39947	+	4.68369i	0.311305	+	0.173589i
$729$	−22.1271	−	16.0763i	−0.819522	−	0.595417i
$730$	−7.16827	−	16.7675i	−0.265310	−	0.620592i
$731$	−22.2583	−	30.6359i	−0.823251	−	1.13311i
$732$	−20.4655	+	14.1025i	−0.756428	+	0.521243i
$733$	35.1630	−	25.5474i	1.29877	−	0.943615i	0.298831	−	0.954306i	$-0.403403\pi$
$733$	35.1630	−	25.5474i	1.29877	−	0.943615i	0.999943	+	0.0106913i	$0.00340322\pi$
$734$	−13.5949	−	2.32747i	−0.501797	−	0.0859083i
$735$	−30.5228	+	37.5076i	−1.12585	+	1.38349i
$736$	−27.3685	+	11.8578i	−1.00882	+	0.437084i
$737$	32.2018	−	10.4630i	1.18617	−	0.385410i
$738$	0.0233296	−	0.136270i	0.000858775	−	0.00501617i
$739$	−18.2840	−	5.94083i	−0.672588	−	0.218537i	−0.0472404	−	0.998884i	$-0.515043\pi$
$739$	−18.2840	−	5.94083i	−0.672588	−	0.218537i	−0.625347	+	0.780347i	$0.715043\pi$
$740$	6.75740	+	28.2939i	0.248407	+	1.04010i
$741$	−2.17726	+	0.707436i	−0.0799838	+	0.0259883i
$742$	−4.20967	−	28.9090i	−0.154542	−	1.06128i
$743$			35.7627i			1.31200i	0.754759	+	0.656002i	$0.227754\pi$
$743$			35.7627i			1.31200i	−0.754759	+	0.656002i	$0.772246\pi$
$744$	−8.62761	−	9.29898i	−0.316303	−	0.340917i
$745$	−10.2851	−	0.563836i	−0.376818	−	0.0206574i
$746$	−11.5654	−	23.4161i	−0.423439	−	0.857326i
$747$	0.220130	+	0.159934i	0.00805414	+	0.00585167i
$748$	58.2836	−	17.3420i	2.13106	−	0.634087i
$749$		−	54.0417i		−	1.97464i
$750$	0.535739	−	27.1975i	0.0195624	−	0.993113i
$751$	8.13835			0.296972			0.148486	−	0.988914i	$-0.452560\pi$
$751$	8.13835			0.296972			0.148486	+	0.988914i	$0.452560\pi$
$752$	−20.1837	+	25.0500i	−0.736025	+	0.913478i
$753$	19.5720	−	26.9385i	0.713243	−	0.981695i
$754$	2.00822	−	0.991875i	0.0731352	−	0.0361219i
$755$	0.215638	−	3.93353i	0.00784789	−	0.143156i
$756$	15.3935	−	43.6397i	0.559858	−	1.58716i
$757$	−42.4947			−1.54450			−0.772248	−	0.635321i	$-0.780868\pi$
$757$	−42.4947			−1.54450			−0.772248	+	0.635321i	$0.780868\pi$
$758$	−5.38235	−	36.9621i	−0.195496	−	1.34253i
$759$	−14.9719	−	46.0787i	−0.543445	−	1.67255i
$760$	−10.6109	−	2.70127i	−0.384899	−	0.0979853i
$761$	11.9096	−	36.6540i	0.431723	−	1.32871i	−0.464684	−	0.885477i	$-0.653832\pi$
$761$	11.9096	−	36.6540i	0.431723	−	1.32871i	0.896407	−	0.443231i	$-0.146168\pi$
$762$	−32.0731	−	5.49096i	−1.16189	−	0.198916i
$763$	−11.5158	−	35.4421i	−0.416902	−	1.28309i
$764$	27.0473	−	8.04781i	0.978538	−	0.291159i
$765$	−0.395218	−	0.321619i	−0.0142891	−	0.0116281i
$766$	29.2756	+	5.01202i	1.05777	+	0.181091i
$767$	−0.488458	−	0.672305i	−0.0176372	−	0.0242755i
$768$	20.5467	+	18.3190i	0.741416	+	0.661029i
$769$	29.0252	−	21.0880i	1.04667	−	0.760454i	0.0750973	−	0.997176i	$-0.476073\pi$
$769$	29.0252	−	21.0880i	1.04667	−	0.760454i	0.971577	+	0.236723i	$0.0760733\pi$
$770$	−68.7011	+	29.3704i	−2.47581	+	1.05844i
$771$	−11.1578	+	15.3574i	−0.401839	+	0.553084i
$772$	13.7518	+	0.343259i	0.494937	+	0.0123542i
$773$	0.547088	−	1.68376i	0.0196774	−	0.0605607i	−0.940736	−	0.339141i	$-0.889864\pi$
$773$	0.547088	−	1.68376i	0.0196774	−	0.0605607i	0.960413	+	0.278580i	$0.0898637\pi$
$774$	−0.333366	−	0.175132i	−0.0119826	−	0.00629498i
$775$	11.3188	−	6.46247i	0.406582	−	0.232139i
$776$	−9.12166	+	1.09661i	−0.327449	+	0.0393659i
$777$	47.0835	+	15.2984i	1.68911	+	0.548826i
$778$	18.6917	−	9.23196i	0.670130	−	0.330982i
$779$	−2.48519	+	3.42057i	−0.0890411	+	0.122554i
$780$	−2.26954	+	5.46089i	−0.0812625	+	0.195531i
$781$	1.83471	+	2.52526i	0.0656510	+	0.0903608i
$782$	37.5790	+	19.7419i	1.34382	+	0.705970i
$783$	−6.33484	−	8.71916i	−0.226389	−	0.311597i
$784$	50.2175	+	2.50853i	1.79348	+	0.0895903i
$785$	0.530760	−	9.68176i	0.0189436	−	0.345557i
$786$	6.00599	+	6.15778i	0.214227	+	0.219641i
$787$	−0.356070	−	1.09587i	−0.0126925	−	0.0390636i	0.944510	−	0.328484i	$-0.106538\pi$
$787$	−0.356070	−	1.09587i	−0.0126925	−	0.0390636i	−0.957202	+	0.289420i	$0.906538\pi$
$788$	14.8200	−	19.3628i	0.527941	−	0.689773i
$789$	12.6559	+	4.11215i	0.450562	+	0.146396i
$790$	2.19879	+	24.4097i	0.0782294	+	0.868459i
$791$	7.39253	+	22.7519i	0.262848	+	0.808963i
$792$	0.443289	−	0.411284i	0.0157516	−	0.0146144i
$793$			5.55167i			0.197145i
$794$	34.3983	−	5.00901i	1.22075	−	0.177763i
$795$	17.3632	−	4.60771i	0.615809	−	0.163419i
$796$	0.737145	−	29.5318i	0.0261274	−	1.04673i
$797$	−34.5173	−	25.0783i	−1.22267	−	0.888319i	−0.226347	−	0.974047i	$-0.572678\pi$
$797$	−34.5173	−	25.0783i	−1.22267	−	0.888319i	−0.996319	+	0.0857282i	$0.972678\pi$
$798$	−13.3398	+	13.0110i	−0.472225	+	0.460585i
$799$	45.7832			1.61969
$800$	−23.1267	+	16.2836i	−0.817651	+	0.575714i
$801$	−0.504425			−0.0178230
$802$	−3.46041	+	3.37511i	−0.122191	+	0.119179i
$803$	−24.9167	−	18.1031i	−0.879293	−	0.638844i
$804$	0.544326	−	21.8070i	0.0191969	−	0.769073i
$805$	−48.6478	−	18.8086i	−1.71461	−	0.662914i
$806$	−2.80388	+	0.408295i	−0.0987624	+	0.0143816i
$807$			30.6390i			1.07854i
$808$	8.09187	−	7.50765i	0.284671	−	0.264118i
$809$	17.2761	+	53.1704i	0.607396	+	1.86937i	0.479397	+	0.877598i	$0.340855\pi$
$809$	17.2761	+	53.1704i	0.607396	+	1.86937i	0.127999	+	0.991774i	$0.459145\pi$
$810$	27.3722	+	6.24534i	0.961763	+	0.219439i
$811$	27.5933	+	8.96560i	0.968931	+	0.314825i	0.750384	−	0.661002i	$-0.229868\pi$
$811$	27.5933	+	8.96560i	0.968931	+	0.314825i	0.218547	+	0.975826i	$0.429868\pi$
$812$	11.0809	−	14.4776i	0.388863	−	0.508063i
$813$	4.30072	+	13.2362i	0.150833	+	0.464216i
$814$	34.3046	+	35.1716i	1.20238	+	1.23276i
$815$	−15.6101	+	4.14249i	−0.546798	+	0.145105i
$816$	1.95455	−	39.1276i	0.0684229	−	1.36974i
$817$	6.76908	+	9.31684i	0.236820	+	0.325955i
$818$	6.09838	+	3.20375i	0.213225	+	0.112016i
$819$	−0.0800007	−	0.110111i	−0.00279545	−	0.00384761i
$820$	2.53710	+	10.6231i	0.0885995	+	0.370974i
$821$	26.5861	−	36.5926i	0.927860	−	1.27709i	−0.0328288	−	0.999461i	$-0.510452\pi$
$821$	26.5861	−	36.5926i	0.927860	−	1.27709i	0.960689	−	0.277628i	$-0.0895484\pi$
$822$	47.1961	−	23.3105i	1.64615	−	0.813046i
$823$	−22.3928	−	7.27585i	−0.780562	−	0.253620i	−0.108482	−	0.994098i	$-0.534599\pi$
$823$	−22.3928	−	7.27585i	−0.780562	−	0.253620i	−0.672080	+	0.740478i	$0.734599\pi$
$824$	−53.6554	+	6.45046i	−1.86918	+	0.224712i
$825$	−22.7804	−	39.8989i	−0.793111	−	1.38910i
$826$	−5.98818	−	3.14585i	−0.208355	−	0.109458i
$827$	−16.1742	+	49.7791i	−0.562432	+	1.73099i	0.113028	+	0.993592i	$0.463945\pi$
$827$	−16.1742	+	49.7791i	−0.562432	+	1.73099i	−0.675460	+	0.737397i	$0.736055\pi$
$828$	0.421993	+	0.0105334i	0.0146653	+	0.000366060i
$829$	−14.8801	+	20.4807i	−0.516808	+	0.711325i	−0.985049	−	0.172276i	$-0.944888\pi$
$829$	−14.8801	+	20.4807i	−0.516808	+	0.711325i	0.468241	+	0.883601i	$0.344888\pi$
$830$	−20.9568	−	4.78157i	−0.727421	−	0.165971i
$831$	28.4451	−	20.6666i	0.986751	−	0.716917i
$832$	5.97362	−	1.45736i	0.207098	−	0.0505249i
$833$	−42.0606	−	57.8915i	−1.45731	−	2.00582i
$834$	−4.79064	−	0.820163i	−0.165886	−	0.0283999i
$835$	16.9646	−	10.9590i	0.587083	−	0.379251i
$836$	−17.7250	+	5.27398i	−0.613030	+	0.182404i
$837$	4.21310	+	12.9666i	0.145626	+	0.448191i
$838$	−5.41339	−	0.926780i	−0.187003	−	0.0320151i
$839$	9.60794	−	29.5702i	0.331703	−	1.02088i	−0.636620	−	0.771177i	$-0.719668\pi$
$839$	9.60794	−	29.5702i	0.331703	−	1.02088i	0.968323	−	0.249699i	$-0.0803318\pi$
$840$	3.12087	+	48.0347i	0.107680	+	1.65735i
$841$	7.64937	+	23.5424i	0.263772	+	0.811805i
$842$	−1.43264	−	9.83834i	−0.0493720	−	0.339052i
$843$	−55.6527			−1.91678
$844$	1.53458	−	4.35044i	0.0528225	−	0.149748i
$845$	−15.0566	−	23.3077i	−0.517962	−	0.801808i
$846$	0.408204	−	0.201615i	0.0140343	−	0.00693165i
$847$	−45.5707	+	62.7227i	−1.56583	+	2.15518i
$848$	−14.5445	−	11.7191i	−0.499461	−	0.402435i
$849$	−41.5127			−1.42471
$850$	38.6961	+	11.0891i	1.32727	+	0.380352i
$851$			34.2970i			1.17569i
$852$	1.92745	−	0.573505i	0.0660335	−	0.0196480i
$853$	−33.2584	−	24.1636i	−1.13875	−	0.827347i	−0.151801	−	0.988411i	$-0.548507\pi$
$853$	−33.2584	−	24.1636i	−1.13875	−	0.827347i	−0.986944	+	0.161064i	$0.948507\pi$
$854$	20.0114	+	40.5165i	0.684775	+	1.38645i
$855$	0.120192	+	0.0978092i	0.00411048	+	0.00334501i
$856$	−23.5007	−	25.3295i	−0.803239	−	0.865744i
$857$			7.69778i			0.262951i	0.991319	+	0.131476i	$0.0419715\pi$
$857$			7.69778i			0.262951i	−0.991319	+	0.131476i	$0.958029\pi$
$858$	1.43925	+	9.88374i	0.0491352	+	0.337425i
$859$	−39.8085	+	12.9346i	−1.35825	+	0.441322i	−0.895458	−	0.445146i	$-0.853152\pi$
$859$	−39.8085	+	12.9346i	−1.35825	+	0.441322i	−0.462791	+	0.886468i	$0.653152\pi$
$860$	29.6542	+	2.36910i	1.01120	+	0.0807856i
$861$	17.6778	+	5.74385i	0.602456	+	0.195750i
$862$	0.449086	−	2.62314i	0.0152959	−	0.0893446i
$863$	−16.4224	+	5.33595i	−0.559024	+	0.181638i	−0.574882	−	0.818236i	$-0.694952\pi$
$863$	−16.4224	+	5.33595i	−0.559024	+	0.181638i	0.0158581	+	0.999874i	$0.494952\pi$
$864$	−11.7623	−	27.1481i	−0.400162	−	0.923598i
$865$	−28.5631	−	11.0433i	−0.971176	−	0.375483i
$866$	9.10124	+	1.55815i	0.309273	+	0.0529479i
$867$	−21.4449	+	15.5806i	−0.728305	+	0.529145i
$868$	−18.9912	+	13.0865i	−0.644603	+	0.444186i
$869$	24.3306	+	33.4882i	0.825359	+	1.13601i
$870$	9.62439	+	5.74931i	0.326297	+	0.194920i
$871$	−3.94200	−	2.86403i	−0.133570	−	0.0970441i
$872$	−20.8100	−	11.6040i	−0.704715	−	0.392961i
$873$	0.123660	+	0.0401795i	0.00418525	+	0.00135987i
$874$	−11.4284	−	6.00383i	−0.386570	−	0.203082i
$875$	−48.7936	−	8.08957i	−1.64952	−	0.273477i
$876$	−16.3387	+	11.2588i	−0.552035	+	0.380399i
$877$	−4.64130	+	14.2844i	−0.156725	+	0.482351i	−0.998332	−	0.0577404i	$-0.981610\pi$
$877$	−4.64130	+	14.2844i	−0.156725	+	0.482351i	0.841606	+	0.540092i	$0.181610\pi$
$878$	−17.7531	−	35.9443i	−0.599139	−	1.21306i
$879$	14.4387	+	10.4903i	0.487004	+	0.353829i
$880$	−19.4283	+	43.6416i	−0.654927	+	1.47116i
$881$	37.8296	−	27.4848i	1.27451	−	0.925986i	0.275138	−	0.961405i	$-0.411277\pi$
$881$	37.8296	−	27.4848i	1.27451	−	0.925986i	0.999373	+	0.0354189i	$0.0112766\pi$
$882$	−0.629949	−	0.330940i	−0.0212115	−	0.0111433i
$883$	−27.3068	+	19.8395i	−0.918946	+	0.667653i	−0.943261	−	0.332051i	$-0.892259\pi$
$883$	−27.3068	+	19.8395i	−0.918946	+	0.667653i	0.0243155	+	0.999704i	$0.492259\pi$
$884$	−6.94907	−	5.31870i	−0.233722	−	0.178887i
$885$	1.49995	−	3.87958i	0.0504203	−	0.130411i
$886$	−26.0841	+	25.4412i	−0.876313	+	0.854712i
$887$	−3.96211	+	1.28737i	−0.133035	+	0.0432256i	−0.374778	−	0.927115i	$-0.622281\pi$
$887$	−3.96211	+	1.28737i	−0.133035	+	0.0432256i	0.241743	+	0.970340i	$0.422281\pi$
$888$	28.7209	−	13.3045i	0.963809	−	0.446470i
$889$	−18.2824	+	56.2675i	−0.613172	+	1.88715i
$890$	36.6412	−	15.6645i	1.22822	−	0.525076i
$891$	45.0976	−	14.6531i	1.51083	−	0.490897i
$892$	−1.48410	+	4.20732i	−0.0496913	+	0.140872i
$893$	−13.9234			−0.465928
$894$	1.61508	+	11.0912i	0.0540163	+	0.370945i
$895$	−12.3744	−	10.0700i	−0.413630	−	0.336602i
$896$	38.3428	−	32.1682i	1.28094	−	1.07467i
$897$	−4.09824	+	5.64075i	−0.136836	+	0.188339i
$898$	−4.63725	+	4.52294i	−0.154747	+	0.150933i
$899$			5.37148i			0.179149i
$900$	0.393848	−	0.0715349i	0.0131283	−	0.00238450i
$901$			26.5827i			0.885597i
$902$	12.8799	+	13.2054i	0.428852	+	0.439690i
$903$	29.7585	−	40.9590i	0.990299	−	1.36303i
$904$	13.3588	+	7.44912i	0.444309	+	0.247754i
$905$	5.29824	−	3.42262i	0.176120	−	0.113772i
$906$	−4.24181	+	0.617685i	−0.140925	+	0.0205212i
$907$	44.9685			1.49315			0.746577	−	0.665299i	$-0.231696\pi$
$907$	44.9685			1.49315			0.746577	+	0.665299i	$0.231696\pi$
$908$	12.5624	+	4.43129i	0.416898	+	0.147057i
$909$	−0.148573	+	0.0482742i	−0.00492784	+	0.00160115i
$910$	9.23064	+	5.51410i	0.305993	+	0.182791i
$911$	−3.92631	+	12.0839i	−0.130085	+	0.400359i	−0.994793	−	0.101915i	$-0.967503\pi$
$911$	−3.92631	+	12.0839i	−0.130085	+	0.400359i	0.864709	+	0.502274i	$0.167503\pi$
$912$	−0.594409	+	11.8993i	−0.0196828	+	0.394025i
$913$	−34.5277	+	11.2187i	−1.14270	+	0.371286i
$914$	10.3120	+	10.5726i	0.341091	+	0.349711i
$915$	−23.3409	+	15.0781i	−0.771627	+	0.498465i
$916$	17.4543	+	13.3593i	0.576707	+	0.441402i
$917$	12.6527	−	9.19269i	0.417827	−	0.303569i
$918$	−19.5829	+	37.2764i	−0.646333	+	1.23030i
$919$	−18.4864	+	13.4312i	−0.609810	+	0.443053i	−0.849347	−	0.527834i	$-0.823004\pi$
$919$	−18.4864	+	13.4312i	−0.609810	+	0.443053i	0.239537	+	0.970887i	$0.423004\pi$
$920$	−30.9805	+	12.3395i	−1.02140	+	0.406822i
$921$	4.23591	+	3.07757i	0.139578	+	0.101409i
$922$	39.9840	−	19.7483i	1.31680	−	0.650377i
$923$	0.138808	−	0.427208i	0.00456893	−	0.0140617i
$924$	46.1304	+	66.9444i	1.51758	+	2.20231i
$925$	6.60880	+	31.8446i	0.217296	+	1.04705i
$926$	−8.85934	+	16.8639i	−0.291136	+	0.554181i
$927$	0.727391	+	0.236344i	0.0238907	+	0.00776255i
$928$	−1.10211	−	11.6043i	−0.0361785	−	0.380931i
$929$	−24.2098	−	17.5894i	−0.794297	−	0.577090i	0.114939	−	0.993373i	$-0.463333\pi$
$929$	−24.2098	−	17.5894i	−0.794297	−	0.577090i	−0.909236	+	0.416282i	$0.863333\pi$
$930$	−9.33180	−	10.6795i	−0.306002	−	0.350193i
$931$	12.7913	+	17.6057i	0.419218	+	0.577003i
$932$	44.8350	−	30.8951i	1.46862	−	1.01200i
$933$	−21.1459	+	15.3634i	−0.692286	+	0.502975i
$934$	4.59720	−	26.8526i	0.150425	−	0.878644i
$935$	65.7120	−	17.4381i	2.14901	−	0.570288i
$936$	−0.0853799	−	0.0168202i	−0.00279073	−	0.000549786i
$937$	44.9541	−	14.6065i	1.46859	−	0.477172i	0.537905	−	0.843005i	$-0.319216\pi$
$937$	44.9541	−	14.6065i	1.46859	−	0.477172i	0.930681	+	0.365833i	$0.119216\pi$
$938$	−39.0926	−	6.69271i	−1.27642	−	0.218525i
$939$	−0.195185	−	0.0634195i	−0.00636963	−	0.00206962i
$940$	−23.3908	+	27.3217i	−0.762924	+	0.891135i
$941$	−20.6937	+	6.72379i	−0.674595	+	0.219189i	−0.626228	−	0.779640i	$-0.715402\pi$
$941$	−20.6937	+	6.72379i	−0.674595	+	0.219189i	−0.0483677	+	0.998830i	$0.515402\pi$
$942$	−10.4405	+	1.52033i	−0.340171	+	0.0495351i
$943$			12.8770i			0.419333i
$944$	−4.17469	+	1.12957i	−0.135875	+	0.0367642i
$945$	18.6571	−	48.2560i	0.606915	−	1.56977i
$946$	45.0488	−	22.2499i	1.46466	−	0.723407i
$947$	−43.9238	−	31.9125i	−1.42733	−	1.03702i	−0.990506	−	0.137472i	$-0.956102\pi$
$947$	−43.9238	−	31.9125i	−1.42733	−	1.03702i	−0.436827	−	0.899546i	$-0.643898\pi$
$948$	25.5606	−	7.60543i	0.830168	−	0.247013i
$949$			4.43220i			0.143875i
$950$	−11.7681	−	3.37236i	−0.381807	−	0.109414i
$951$	50.5237			1.63834
$952$	−69.8864	−	13.7679i	−2.26503	−	0.446221i
$953$	−26.3956	+	36.3305i	−0.855039	+	1.17686i	0.127691	+	0.991814i	$0.459243\pi$
$953$	−26.3956	+	36.3305i	−0.855039	+	1.17686i	−0.982730	+	0.185046i	$0.940757\pi$
$954$	0.117062	+	0.237012i	0.00379001	+	0.00767354i
$955$	30.4946	−	8.09241i	0.986781	−	0.261864i
$956$	−20.3642	−	7.18330i	−0.658626	−	0.232325i
$957$	18.9346			0.612068
$958$	28.1675	−	4.10169i	0.910049	−	0.132520i
$959$	−29.5751	−	91.0227i	−0.955029	−	2.93928i
$960$	22.3513	+	21.1568i	0.721384	+	0.682834i
$961$	−7.47972	+	23.0202i	−0.241281	+	0.742588i
$962$	1.19309	−	6.96894i	0.0384669	−	0.224688i
$963$	0.151110	+	0.465068i	0.00486944	+	0.0149866i
$964$	−18.5447	+	5.51788i	−0.597284	+	0.177719i
$965$	15.3567	+	0.841862i	0.494349	+	0.0271005i
$966$	−9.57683	+	55.9390i	−0.308130	+	1.79981i
$967$	−1.74121	−	2.39657i	−0.0559936	−	0.0770686i	0.780102	−	0.625652i	$-0.215167\pi$
$967$	−1.74121	−	2.39657i	−0.0559936	−	0.0770686i	−0.836096	+	0.548584i	$0.815167\pi$
$968$	5.91666	+	49.2153i	0.190169	+	1.58184i
$969$	13.7177	−	9.96648i	0.440675	−	0.320169i
$970$	−10.2303	+	0.921533i	−0.328476	+	0.0295886i
$971$	15.2206	−	20.9493i	0.488451	−	0.672295i	−0.491650	−	0.870793i	$-0.663606\pi$
$971$	15.2206	−	20.9493i	0.488451	−	0.672295i	0.980101	+	0.198497i	$0.0636062\pi$
$972$	−0.0207595	+	0.831677i	−0.000665862	+	0.0266760i
$973$	−2.73077	+	8.40446i	−0.0875446	+	0.269435i
$974$	18.5614	−	35.3318i	0.594745	−	1.13210i
$975$	−2.71827	+	6.02712i	−0.0870543	+	0.193022i
$976$	26.9985	+	10.2880i	0.864201	+	0.329311i
$977$	34.3875	+	11.1732i	1.10015	+	0.357461i	0.802161	−	0.597107i	$-0.203683\pi$
$977$	34.3875	+	11.1732i	1.10015	+	0.357461i	0.297991	+	0.954569i	$0.403683\pi$
$978$	7.78219	+	15.7564i	0.248847	+	0.503834i
$979$	39.5599	−	54.4495i	1.26434	−	1.74021i
$980$	56.0364	+	4.47680i	1.79002	+	0.143006i
$981$	0.198204	+	0.272805i	0.00632818	+	0.00870999i
$982$	−23.5473	+	44.8226i	−0.751424	+	1.43035i
$983$	20.4443	+	28.1391i	0.652071	+	0.897499i	0.999187	−	0.0403234i	$-0.0128388\pi$
$983$	20.4443	+	28.1391i	0.652071	+	0.897499i	−0.347115	+	0.937822i	$0.612839\pi$
$984$	10.7834	−	4.99524i	0.343762	−	0.159243i
$985$	17.2072	−	21.1448i	0.548265	−	0.673731i
$986$	−11.8759	+	11.5832i	−0.378207	+	0.368884i
$987$	18.9151	+	58.2146i	0.602073	+	1.85299i
$988$	2.11332	+	1.61750i	0.0672336	+	0.0514596i
$989$	33.3574	+	10.8385i	1.06070	+	0.344643i
$990$	0.509098	−	0.444854i	0.0161802	−	0.0141384i
$991$	−1.42805	−	4.39510i	−0.0453636	−	0.139615i	0.925809	−	0.377991i	$-0.123385\pi$
$991$	−1.42805	−	4.39510i	−0.0453636	−	0.139615i	−0.971173	+	0.238376i	$0.923385\pi$
$992$	−3.21037	+	14.3923i	−0.101929	+	0.456955i
$993$			57.7546i			1.83279i
$994$	−0.526867	−	3.61814i	−0.0167112	−	0.114760i
$995$	1.80789	−	32.9783i	0.0573140	−	1.04548i
$996$	−0.583642	+	23.3821i	−0.0184934	+	0.740890i
$997$	29.6486	+	21.5409i	0.938979	+	0.682209i	0.948175	−	0.317749i	$-0.102927\pi$
$997$	29.6486	+	21.5409i	0.938979	+	0.682209i	−0.00919532	+	0.999958i	$0.502927\pi$
$998$	−26.2665	−	26.9303i	−0.831450	−	0.852463i
$999$	−34.0208			−1.07637

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.2.o.a.29.8	✓	112
4.3	odd	2		800.2.be.a.529.7		112
5.2	odd	4		1000.2.t.b.101.16		224
5.3	odd	4		1000.2.t.b.101.41		224
5.4	even	2		1000.2.o.a.149.21		112
8.3	odd	2		800.2.be.a.529.22		112
8.5	even	2	inner	200.2.o.a.29.14	yes	112
25.6	even	5		1000.2.o.a.349.15		112
25.8	odd	20		1000.2.t.b.901.4		224
25.17	odd	20		1000.2.t.b.901.53		224
25.19	even	10	inner	200.2.o.a.69.14	yes	112
40.13	odd	4		1000.2.t.b.101.4		224
40.29	even	2		1000.2.o.a.149.15		112
40.37	odd	4		1000.2.t.b.101.53		224
100.19	odd	10		800.2.be.a.369.22		112
200.19	odd	10		800.2.be.a.369.7		112
200.69	even	10	inner	200.2.o.a.69.8	yes	112
200.117	odd	20		1000.2.t.b.901.16		224
200.133	odd	20		1000.2.t.b.901.41		224
200.181	even	10		1000.2.o.a.349.21		112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.29.8	✓	112	1.1	even	1	trivial
200.2.o.a.29.14	yes	112	8.5	even	2	inner
200.2.o.a.69.8	yes	112	200.69	even	10	inner
200.2.o.a.69.14	yes	112	25.19	even	10	inner
800.2.be.a.369.7		112	200.19	odd	10
800.2.be.a.369.22		112	100.19	odd	10
800.2.be.a.529.7		112	4.3	odd	2
800.2.be.a.529.22		112	8.3	odd	2
1000.2.o.a.149.15		112	40.29	even	2
1000.2.o.a.149.21		112	5.4	even	2
1000.2.o.a.349.15		112	25.6	even	5
1000.2.o.a.349.21		112	200.181	even	10
1000.2.t.b.101.4		224	40.13	odd	4
1000.2.t.b.101.16		224	5.2	odd	4
1000.2.t.b.101.41		224	5.3	odd	4
1000.2.t.b.101.53		224	40.37	odd	4
1000.2.t.b.901.4		224	25.8	odd	20
1000.2.t.b.901.16		224	200.117	odd	20
1000.2.t.b.901.41		224	200.133	odd	20
1000.2.t.b.901.53		224	25.17	odd	20

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:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	200.o (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.01240 + 0.987445i) q^{2} +(1.39188 + 1.01126i) q^{3} +(0.0499066 - 1.99938i) q^{4} +(0.122399 - 2.23272i) q^{5} +(-2.40770 + 0.350605i) q^{6} +4.42380i q^{7} +(1.92375 + 2.07345i) q^{8} +(-0.0123697 - 0.0380700i) q^{9} +O(q^{10})\)	\(q+(-1.01240 + 0.987445i) q^{2} +(1.39188 + 1.01126i) q^{3} +(0.0499066 - 1.99938i) q^{4} +(0.122399 - 2.23272i) q^{5} +(-2.40770 + 0.350605i) q^{6} +4.42380i q^{7} +(1.92375 + 2.07345i) q^{8} +(-0.0123697 - 0.0380700i) q^{9} +(2.08077 + 2.38126i) q^{10} +(5.07953 + 1.65044i) q^{11} +(2.09135 - 2.73242i) q^{12} +(-0.237511 - 0.730985i) q^{13} +(-4.36826 - 4.47866i) q^{14} +(2.42822 - 2.98389i) q^{15} +(-3.99502 - 0.199564i) q^{16} +(3.34610 + 4.60551i) q^{17} +(0.0501151 + 0.0263277i) q^{18} +(-1.01760 - 1.40061i) q^{19} +(-4.45793 - 0.356148i) q^{20} +(-4.47361 + 6.15740i) q^{21} +(-6.77223 + 3.34485i) q^{22} +(-5.01464 - 1.62935i) q^{23} +(0.580831 + 4.83140i) q^{24} +(-4.97004 - 0.546563i) q^{25} +(0.962263 + 0.505520i) q^{26} +(1.61623 - 4.97425i) q^{27} +(8.84485 + 0.220777i) q^{28} +(1.21119 - 1.66707i) q^{29} +(0.488101 + 5.41862i) q^{30} +(-2.10890 + 1.53221i) q^{31} +(4.24161 - 3.74282i) q^{32} +(5.40106 + 7.43393i) q^{33} +(-7.93528 - 1.35853i) q^{34} +(9.87709 + 0.541468i) q^{35} +(-0.0767337 + 0.0228318i) q^{36} +(-2.01004 - 6.18628i) q^{37} +(2.41324 + 0.413150i) q^{38} +(0.408628 - 1.25763i) q^{39} +(4.86489 - 4.04140i) q^{40} +(-0.754681 - 2.32267i) q^{41} +(-1.55101 - 10.6512i) q^{42} -6.65200 q^{43} +(3.55335 - 10.0735i) q^{44} +(-0.0865136 + 0.0229583i) q^{45} +(6.68572 - 3.30212i) q^{46} +(4.72720 - 6.50644i) q^{47} +(-5.35877 - 4.31777i) q^{48} -12.5700 q^{49} +(5.57137 - 4.35430i) q^{50} +9.79409i q^{51} +(-1.47337 + 0.438394i) q^{52} +(3.77778 + 2.74471i) q^{53} +(3.27552 + 6.63187i) q^{54} +(4.30669 - 11.1391i) q^{55} +(-9.17253 + 8.51029i) q^{56} -2.97854i q^{57} +(0.419923 + 2.88373i) q^{58} +(1.02828 - 0.334110i) q^{59} +(-5.84474 - 5.00384i) q^{60} +(-6.86954 - 2.23205i) q^{61} +(0.622082 - 3.63363i) q^{62} +(0.168414 - 0.0547211i) q^{63} +(-0.598382 + 7.97759i) q^{64} +(-1.66115 + 0.440824i) q^{65} +(-12.8086 - 2.19285i) q^{66} +(5.12879 - 3.72628i) q^{67} +(9.37515 - 6.46027i) q^{68} +(-5.33207 - 7.33896i) q^{69} +(-10.5342 + 9.20490i) q^{70} +(0.472812 + 0.343518i) q^{71} +(0.0551401 - 0.0988851i) q^{72} +(-5.48432 - 1.78197i) q^{73} +(8.14357 + 4.27818i) q^{74} +(-6.36497 - 5.78674i) q^{75} +(-2.85113 + 1.96467i) q^{76} +(-7.30121 + 22.4708i) q^{77} +(0.828143 + 1.67672i) q^{78} +(6.27011 + 4.55550i) q^{79} +(-0.934555 + 8.89531i) q^{80} +(7.18270 - 5.21854i) q^{81} +(3.05755 + 1.60627i) q^{82} +(-5.49924 + 3.99543i) q^{83} +(12.0877 + 9.25173i) q^{84} +(10.6924 - 6.90718i) q^{85} +(6.73448 - 6.56848i) q^{86} +(3.37167 - 1.09552i) q^{87} +(6.34963 + 13.7072i) q^{88} +(3.89405 - 11.9847i) q^{89} +(0.0649163 - 0.108670i) q^{90} +(3.23373 - 1.05070i) q^{91} +(-3.50796 + 9.94484i) q^{92} -4.48479 q^{93} +(1.63893 + 11.2550i) q^{94} +(-3.25171 + 2.10058i) q^{95} +(9.68877 - 0.920181i) q^{96} +(-1.90925 + 2.62786i) q^{97} +(12.7259 - 12.4122i) q^{98} -0.213793i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 5 q^{2} - 3 q^{4} + q^{6} + 10 q^{8} - 30 q^{9}+O(q^{10}) \) 112 * q - 5 * q^2 - 3 * q^4 + q^6 + 10 * q^8 - 30 * q^9	\( 112 q - 5 q^{2} - 3 q^{4} + q^{6} + 10 q^{8} - 30 q^{9} - 9 q^{10} - 5 q^{12} - 3 q^{14} - 2 q^{15} - 15 q^{16} - 10 q^{17} - 17 q^{20} - 30 q^{22} - 10 q^{23} - 16 q^{24} - 6 q^{25} - 14 q^{26} + 15 q^{28} - 33 q^{30} - 18 q^{31} - 10 q^{33} + 9 q^{34} + 41 q^{36} + 45 q^{38} - 10 q^{39} - 14 q^{40} - 10 q^{41} + 75 q^{42} - 32 q^{44} + 13 q^{46} - 10 q^{47} - 70 q^{48} - 80 q^{49} - 19 q^{50} - 100 q^{52} + 43 q^{54} - 34 q^{55} + 36 q^{56} - 30 q^{58} - 28 q^{60} + 20 q^{62} + 60 q^{63} - 36 q^{64} + 40 q^{65} + 40 q^{66} + 42 q^{70} + 22 q^{71} - 65 q^{72} - 10 q^{73} + 4 q^{74} - 36 q^{76} - 55 q^{78} + 14 q^{79} - 76 q^{80} - 6 q^{81} + 78 q^{84} - 59 q^{86} - 10 q^{87} + 110 q^{88} + 24 q^{89} + 49 q^{90} + 90 q^{92} + 45 q^{94} - 86 q^{95} + 46 q^{96} - 50 q^{97} + 90 q^{98}+O(q^{100}) \) 112 * q - 5 * q^2 - 3 * q^4 + q^6 + 10 * q^8 - 30 * q^9 - 9 * q^10 - 5 * q^12 - 3 * q^14 - 2 * q^15 - 15 * q^16 - 10 * q^17 - 17 * q^20 - 30 * q^22 - 10 * q^23 - 16 * q^24 - 6 * q^25 - 14 * q^26 + 15 * q^28 - 33 * q^30 - 18 * q^31 - 10 * q^33 + 9 * q^34 + 41 * q^36 + 45 * q^38 - 10 * q^39 - 14 * q^40 - 10 * q^41 + 75 * q^42 - 32 * q^44 + 13 * q^46 - 10 * q^47 - 70 * q^48 - 80 * q^49 - 19 * q^50 - 100 * q^52 + 43 * q^54 - 34 * q^55 + 36 * q^56 - 30 * q^58 - 28 * q^60 + 20 * q^62 + 60 * q^63 - 36 * q^64 + 40 * q^65 + 40 * q^66 + 42 * q^70 + 22 * q^71 - 65 * q^72 - 10 * q^73 + 4 * q^74 - 36 * q^76 - 55 * q^78 + 14 * q^79 - 76 * q^80 - 6 * q^81 + 78 * q^84 - 59 * q^86 - 10 * q^87 + 110 * q^88 + 24 * q^89 + 49 * q^90 + 90 * q^92 + 45 * q^94 - 86 * q^95 + 46 * q^96 - 50 * q^97 + 90 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more