LMFDB - Embedded newform 1000.2.o.a.349.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1000,2,Mod(149,1000)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1000, 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("1000.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1000 = 2^{3} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1000.o (of order $10$, degree $4$, not 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:	$7.98504020213$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			349.21
Character	$\chi$	$=$	1000.349
Dual form			1000.2.o.a.149.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.01240 + 0.987445i) q^{2} +(-1.39188 + 1.01126i) q^{3} +(0.0499066 + 1.99938i) q^{4} +(-2.40770 - 0.350605i) q^{6} +4.42380i q^{7} +(-1.92375 + 2.07345i) q^{8} +(-0.0123697 + 0.0380700i) q^{9} +O(q^{10})$	\(q+(1.01240 + 0.987445i) q^{2} +(-1.39188 + 1.01126i) q^{3} +(0.0499066 + 1.99938i) q^{4} +(-2.40770 - 0.350605i) q^{6} +4.42380i q^{7} +(-1.92375 + 2.07345i) q^{8} +(-0.0123697 + 0.0380700i) q^{9} +(5.07953 - 1.65044i) q^{11} +(-2.09135 - 2.73242i) q^{12} +(0.237511 - 0.730985i) q^{13} +(-4.36826 + 4.47866i) q^{14} +(-3.99502 + 0.199564i) q^{16} +(-3.34610 + 4.60551i) q^{17} +(-0.0501151 + 0.0263277i) q^{18} +(-1.01760 + 1.40061i) q^{19} +(-4.47361 - 6.15740i) q^{21} +(6.77223 + 3.34485i) q^{22} +(5.01464 - 1.62935i) q^{23} +(0.580831 - 4.83140i) q^{24} +(0.962263 - 0.505520i) q^{26} +(-1.61623 - 4.97425i) q^{27} +(-8.84485 + 0.220777i) q^{28} +(1.21119 + 1.66707i) q^{29} +(-2.10890 - 1.53221i) q^{31} +(-4.24161 - 3.74282i) q^{32} +(-5.40106 + 7.43393i) q^{33} +(-7.93528 + 1.35853i) q^{34} +(-0.0767337 - 0.0228318i) q^{36} +(2.01004 - 6.18628i) q^{37} +(-2.41324 + 0.413150i) q^{38} +(0.408628 + 1.25763i) q^{39} +(-0.754681 + 2.32267i) q^{41} +(1.55101 - 10.6512i) q^{42} +6.65200 q^{43} +(3.55335 + 10.0735i) q^{44} +(6.68572 + 3.30212i) q^{46} +(-4.72720 - 6.50644i) q^{47} +(5.35877 - 4.31777i) q^{48} -12.5700 q^{49} -9.79409i q^{51} +(1.47337 + 0.438394i) q^{52} +(-3.77778 + 2.74471i) q^{53} +(3.27552 - 6.63187i) q^{54} +(-9.17253 - 8.51029i) q^{56} -2.97854i q^{57} +(-0.419923 + 2.88373i) q^{58} +(1.02828 + 0.334110i) q^{59} +(-6.86954 + 2.23205i) q^{61} +(-0.622082 - 3.63363i) q^{62} +(-0.168414 - 0.0547211i) q^{63} +(-0.598382 - 7.97759i) q^{64} +(-12.8086 + 2.19285i) q^{66} +(-5.12879 - 3.72628i) q^{67} +(-9.37515 - 6.46027i) q^{68} +(-5.33207 + 7.33896i) q^{69} +(0.472812 - 0.343518i) q^{71} +(-0.0551401 - 0.0988851i) q^{72} +(5.48432 - 1.78197i) q^{73} +(8.14357 - 4.27818i) q^{74} +(-2.85113 - 1.96467i) q^{76} +(7.30121 + 22.4708i) q^{77} +(-0.828143 + 1.67672i) q^{78} +(6.27011 - 4.55550i) q^{79} +(7.18270 + 5.21854i) q^{81} +(-3.05755 + 1.60627i) q^{82} +(5.49924 + 3.99543i) q^{83} +(12.0877 - 9.25173i) q^{84} +(6.73448 + 6.56848i) q^{86} +(-3.37167 - 1.09552i) q^{87} +(-6.34963 + 13.7072i) q^{88} +(3.89405 + 11.9847i) q^{89} +(3.23373 + 1.05070i) q^{91} +(3.50796 + 9.94484i) q^{92} +4.48479 q^{93} +(1.63893 - 11.2550i) q^{94} +(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} + 5 q^{12} - 3 q^{14} - 15 q^{16} + 10 q^{17} + 30 q^{22} + 10 q^{23} - 16 q^{24} - 14 q^{26} - 15 q^{28} - 18 q^{31} + 10 q^{33} + 9 q^{34} + 41 q^{36} - 45 q^{38} - 10 q^{39} - 10 q^{41} - 75 q^{42} - 32 q^{44} + 13 q^{46} + 10 q^{47} + 70 q^{48} - 80 q^{49} + 100 q^{52} + 43 q^{54} + 36 q^{56} + 30 q^{58} - 20 q^{62} - 60 q^{63} - 36 q^{64} + 40 q^{66} + 22 q^{71} + 65 q^{72} + 10 q^{73} + 4 q^{74} - 36 q^{76} + 55 q^{78} + 14 q^{79} - 6 q^{81} + 78 q^{84} - 59 q^{86} + 10 q^{87} - 110 q^{88} + 24 q^{89} - 90 q^{92} + 45 q^{94} + 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 + 5 * q^12 - 3 * q^14 - 15 * q^16 + 10 * q^17 + 30 * q^22 + 10 * q^23 - 16 * q^24 - 14 * q^26 - 15 * q^28 - 18 * q^31 + 10 * q^33 + 9 * q^34 + 41 * q^36 - 45 * q^38 - 10 * q^39 - 10 * q^41 - 75 * q^42 - 32 * q^44 + 13 * q^46 + 10 * q^47 + 70 * q^48 - 80 * q^49 + 100 * q^52 + 43 * q^54 + 36 * q^56 + 30 * q^58 - 20 * q^62 - 60 * q^63 - 36 * q^64 + 40 * q^66 + 22 * q^71 + 65 * q^72 + 10 * q^73 + 4 * q^74 - 36 * q^76 + 55 * q^78 + 14 * q^79 - 6 * q^81 + 78 * q^84 - 59 * q^86 + 10 * q^87 - 110 * q^88 + 24 * q^89 - 90 * q^92 + 45 * q^94 + 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 $\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times$.

$n$	$377$	$501$	$751$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$-1$	$1$

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	$-0.865438\pi$
$3$	−1.39188	+	1.01126i	−0.803601	+	0.583851i	0.108367	+	0.994111i	$0.465438\pi$
$4$	0.0499066	+	1.99938i	0.0249533	+	0.999689i
$5$		0			0
$5$		0			0
$6$	−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
$10$		0			0
$11$	5.07953	−	1.65044i	1.53153	−	0.497626i	0.582509	−	0.812824i	$-0.302071\pi$
$11$	5.07953	−	1.65044i	1.53153	−	0.497626i	0.949026	+	0.315199i	$0.102071\pi$
$12$	−2.09135	−	2.73242i	−0.603721	−	0.788782i
$13$	0.237511	−	0.730985i	0.0658738	−	0.202739i	−0.912702	−	0.408626i	$-0.866008\pi$
$13$	0.237511	−	0.730985i	0.0658738	−	0.202739i	0.978576	+	0.205887i	$0.0660080\pi$
$14$	−4.36826	+	4.47866i	−1.16747	+	1.19697i
$15$		0			0
$16$	−3.99502	+	0.199564i	−0.998755	+	0.0498910i
$17$	−3.34610	+	4.60551i	−0.811549	+	1.11700i	0.179534	+	0.983752i	$0.442541\pi$
$17$	−3.34610	+	4.60551i	−0.811549	+	1.11700i	−0.991083	+	0.133249i	$0.957459\pi$
$18$	−0.0501151	+	0.0263277i	−0.0118123	+	0.00620550i
$19$	−1.01760	+	1.40061i	−0.233454	+	0.321322i	−0.909631	−	0.415418i	$-0.863635\pi$
$19$	−1.01760	+	1.40061i	−0.233454	+	0.321322i	0.676177	+	0.736739i	$0.263635\pi$
$20$		0			0
$21$	−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	$-0.414735\pi$
$23$	5.01464	−	1.62935i	1.04562	−	0.339744i	0.780950	+	0.624594i	$0.214735\pi$
$24$	0.580831	−	4.83140i	0.118562	−	0.986205i
$25$		0			0
$26$	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	0.906529	−	0.422144i	$-0.138722\pi$
$29$	1.21119	+	1.66707i	0.224913	+	0.309567i	−0.681616	+	0.731710i	$0.738722\pi$
$30$		0			0
$31$	−2.10890	−	1.53221i	−0.378770	−	0.275192i	0.382068	−	0.924134i	$-0.375212\pi$
$31$	−2.10890	−	1.53221i	−0.378770	−	0.275192i	−0.760838	+	0.648942i	$0.775212\pi$
$32$	−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
$35$		0			0
$36$	−0.0767337	−	0.0228318i	−0.0127889	−	0.00380529i
$37$	2.01004	−	6.18628i	0.330449	−	1.01702i	−0.638471	−	0.769646i	$-0.720433\pi$
$37$	2.01004	−	6.18628i	0.330449	−	1.01702i	0.968921	−	0.247372i	$-0.0795670\pi$
$38$	−2.41324	+	0.413150i	−0.391480	+	0.0670219i
$39$	0.408628	+	1.25763i	0.0654328	+	0.201382i
$40$		0			0
$41$	−0.754681	+	2.32267i	−0.117861	+	0.362740i	−0.992533	−	0.121976i	$-0.961077\pi$
$41$	−0.754681	+	2.32267i	−0.117861	+	0.362740i	0.874672	+	0.484716i	$0.161077\pi$
$42$	1.55101	−	10.6512i	0.239325	−	1.64351i
$43$	6.65200			1.01442			0.507210	−	0.861822i	$-0.330677\pi$
$43$	6.65200			1.01442			0.507210	+	0.861822i	$0.330677\pi$
$44$	3.55335	+	10.0735i	0.535688	+	1.51864i
$45$		0			0
$46$	6.68572	+	3.30212i	0.985755	+	0.486871i
$47$	−4.72720	−	6.50644i	−0.689534	−	0.949062i	0.310465	−	0.950585i	$-0.399515\pi$
$47$	−4.72720	−	6.50644i	−0.689534	−	0.949062i	−0.999999	+	0.00152305i	$0.999515\pi$
$48$	5.35877	−	4.31777i	0.773472	−	0.623216i
$49$	−12.5700			−1.79572
$50$		0			0
$51$		−	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	$-0.803921\pi$
$53$	−3.77778	+	2.74471i	−0.518917	+	0.377016i	0.297279	+	0.954791i	$0.403921\pi$
$54$	3.27552	−	6.63187i	0.445742	−	0.902483i
$55$		0			0
$56$	−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	0.375186	−	0.926949i	$-0.377579\pi$
$59$	1.02828	+	0.334110i	0.133871	+	0.0434974i	−0.241315	+	0.970447i	$0.577579\pi$
$60$		0			0
$61$	−6.86954	+	2.23205i	−0.879554	+	0.285785i	−0.713772	−	0.700378i	$-0.753015\pi$
$61$	−6.86954	+	2.23205i	−0.879554	+	0.285785i	−0.165782	+	0.986162i	$0.553015\pi$
$62$	−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
$65$		0			0
$66$	−12.8086	+	2.19285i	−1.57663	+	0.269922i
$67$	−5.12879	−	3.72628i	−0.626581	−	0.455238i	0.228633	−	0.973513i	$-0.426574\pi$
$67$	−5.12879	−	3.72628i	−0.626581	−	0.455238i	−0.855214	+	0.518275i	$0.826574\pi$
$68$	−9.37515	−	6.46027i	−1.13690	−	0.783423i
$69$	−5.33207	+	7.33896i	−0.641905	+	0.883507i
$70$		0			0
$71$	0.472812	−	0.343518i	0.0561125	−	0.0407681i	−0.559375	−	0.828914i	$-0.688959\pi$
$71$	0.472812	−	0.343518i	0.0561125	−	0.0407681i	0.615488	+	0.788146i	$0.288959\pi$
$72$	−0.0551401	−	0.0988851i	−0.00649832	−	0.0116537i
$73$	5.48432	−	1.78197i	0.641892	−	0.208563i	0.0300561	−	0.999548i	$-0.490431\pi$
$73$	5.48432	−	1.78197i	0.641892	−	0.208563i	0.611836	+	0.790985i	$0.290431\pi$
$74$	8.14357	−	4.27818i	0.946671	−	0.497328i
$75$		0			0
$76$	−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	−0.176258	−	0.984344i	$-0.556399\pi$
$79$	6.27011	−	4.55550i	0.705442	−	0.512534i	0.881700	+	0.471810i	$0.156399\pi$
$80$		0			0
$81$	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	$-0.178309\pi$
$83$	5.49924	+	3.99543i	0.603619	+	0.438555i	−0.243542	+	0.969890i	$0.578309\pi$
$84$	12.0877	−	9.25173i	1.31888	−	1.00945i
$85$		0			0
$86$	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	0.914232	+	0.405192i	$0.132795\pi$
$89$	3.89405	+	11.9847i	0.412769	+	1.27037i	−0.501463	+	0.865179i	$0.667205\pi$
$90$		0			0
$91$	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
$95$		0			0
$96$	9.68877	+	0.920181i	0.988856	+	0.0939156i
$97$	1.90925	+	2.62786i	0.193855	+	0.266819i	0.894869	−	0.446329i	$-0.147269\pi$
$97$	1.90925	+	2.62786i	0.193855	+	0.266819i	−0.701014	+	0.713148i	$0.747269\pi$
$98$	−12.7259	−	12.4122i	−1.28551	−	1.25382i
$99$			0.213793i			0.0214870i
$100$		0			0
$101$			3.90261i			0.388325i	0.980969	+	0.194162i	$0.0621989\pi$
$101$			3.90261i			0.388325i	−0.980969	+	0.194162i	$0.937801\pi$
$102$	9.67112	−	9.91553i	0.957583	−	0.981784i
$103$	11.2306	+	15.4576i	1.10659	+	1.52308i	0.826354	+	0.563151i	$0.190411\pi$
$103$	11.2306	+	15.4576i	1.10659	+	1.52308i	0.280231	+	0.959933i	$0.409589\pi$
$104$	1.05875	+	1.89870i	0.103819	+	0.186183i
$105$		0			0
$106$	−6.53487	−	0.951595i	−0.634723	−	0.0924271i
$107$	12.2161			1.18098			0.590488	−	0.807046i	$-0.298935\pi$
$107$	12.2161			1.18098			0.590488	+	0.807046i	$0.298935\pi$
$108$	9.86475	−	3.47971i	0.949236	−	0.334835i
$109$	−8.01169	−	2.60316i	−0.767381	−	0.249337i	−0.100937	−	0.994893i	$-0.532184\pi$
$109$	−8.01169	−	2.60316i	−0.767381	−	0.249337i	−0.666443	+	0.745556i	$0.732184\pi$
$110$		0			0
$111$	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	$-0.481864\pi$
$113$	−5.14306	−	1.67108i	−0.483818	−	0.157202i	−0.540762	+	0.841175i	$0.681864\pi$
$114$	2.94114	−	3.01547i	0.275463	−	0.282424i
$115$		0			0
$116$	−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
$120$		0			0
$121$	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
$125$		0			0
$126$	−0.116469	−	0.221700i	−0.0103758	−	0.0197506i
$127$	−12.7192	+	4.13273i	−1.12865	+	0.366721i	−0.813063	−	0.582175i	$-0.802202\pi$
$127$	−12.7192	+	4.13273i	−1.12865	+	0.366721i	−0.315588	+	0.948896i	$0.602202\pi$
$128$	7.27163	−	8.66738i	0.642727	−	0.766095i
$129$	−9.25877	+	6.72689i	−0.815190	+	0.592270i
$130$		0			0
$131$	−2.07801	+	2.86013i	−0.181556	+	0.249891i	−0.890089	−	0.455788i	$-0.849358\pi$
$131$	−2.07801	+	2.86013i	−0.181556	+	0.249891i	0.708532	+	0.705678i	$0.249358\pi$
$132$	−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
$135$		0			0
$136$	−3.11224	−	15.7978i	−0.266872	−	1.35465i
$137$	20.5757	+	6.68544i	1.75790	+	0.571176i	0.996979	−	0.0776705i	$-0.0247482\pi$
$137$	20.5757	+	6.68544i	1.75790	+	0.571176i	0.760919	+	0.648846i	$0.224748\pi$
$138$	−12.6450	+	2.16484i	−1.07641	+	0.184284i
$139$	1.89983	−	0.617291i	0.161141	−	0.0523579i	−0.227336	−	0.973816i	$-0.573001\pi$
$139$	1.89983	−	0.617291i	0.161141	−	0.0523579i	0.388477	+	0.921459i	$0.373001\pi$
$140$		0			0
$141$	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
$145$		0			0
$146$	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	$0.0604247\pi$
$149$			4.60655i			0.377384i	−0.982036	+	0.188692i	$0.939575\pi$
$150$		0			0
$151$	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
$155$		0			0
$156$	−2.49408	+	0.879765i	−0.199686	+	0.0704376i
$157$	−4.33632			−0.346076			−0.173038	−	0.984915i	$-0.555358\pi$
$157$	−4.33632			−0.346076			−0.173038	+	0.984915i	$0.555358\pi$
$158$	10.8462	+	1.57940i	0.862874	+	0.125650i
$159$	2.48259	−	7.64062i	0.196882	−	0.605940i
$160$		0			0
$161$	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	$-0.808716\pi$
$163$	2.23193	−	6.86918i	0.174818	−	0.538036i	0.999625	+	0.0273790i	$0.00871610\pi$
$164$	−4.68156	−	1.39298i	−0.365568	−	0.108773i
$165$		0			0
$166$	1.62216	+	9.47516i	0.125904	+	0.735415i
$167$	−5.30895	+	7.30714i	−0.410819	+	0.565444i	−0.963418	−	0.268004i	$-0.913636\pi$
$167$	−5.30895	+	7.30714i	−0.410819	+	0.565444i	0.552599	+	0.833447i	$0.313636\pi$
$168$	21.3732	+	2.56948i	1.64897	+	0.198240i
$169$	10.0393	+	7.29397i	0.772253	+	0.561075i
$170$		0			0
$171$	−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	−0.972882	−	0.231301i	$-0.925702\pi$
$173$	−4.23208	−	13.0250i	−0.321759	−	0.990273i	0.651123	−	0.758972i	$-0.274298\pi$
$174$	−2.33171	−	4.43845i	−0.176767	−	0.336478i
$175$		0			0
$176$	−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	0.936455	−	0.350787i	$-0.114086\pi$
$179$	4.19376	+	5.77221i	0.313456	+	0.431435i	−0.622999	+	0.782223i	$0.714086\pi$
$180$		0			0
$181$	1.65805	−	2.28211i	0.123242	−	0.169628i	−0.742938	−	0.669360i	$-0.766568\pi$
$181$	1.65805	−	2.28211i	0.123242	−	0.169628i	0.866180	+	0.499732i	$0.166568\pi$
$182$	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
$185$		0			0
$186$	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
$190$		0			0
$191$	4.36011	−	13.4190i	0.315486	−	0.970968i	−0.660067	−	0.751206i	$-0.729472\pi$
$191$	4.36011	−	13.4190i	0.315486	−	0.970968i	0.975554	−	0.219761i	$-0.0705278\pi$
$192$	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
$195$		0			0
$196$	−0.627328	−	25.1322i	−0.0448091	−	1.79516i
$197$	−9.86331	+	7.16612i	−0.702732	+	0.510565i	−0.880821	−	0.473450i	$-0.843009\pi$
$197$	−9.86331	+	7.16612i	−0.702732	+	0.510565i	0.178089	+	0.984014i	$0.443009\pi$
$198$	−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	$0.324616\pi$
$200$		0			0
$201$	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
$205$		0			0
$206$	−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
$210$		0			0
$211$	2.19369	−	0.712773i	0.151020	−	0.0490693i	−0.232532	−	0.972589i	$-0.574701\pi$
$211$	2.19369	−	0.712773i	0.151020	−	0.0490693i	0.383551	+	0.923520i	$0.374701\pi$
$212$	−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			0
$216$	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
$220$		0			0
$221$	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	$-0.576203\pi$
$223$	2.12152	−	0.689324i	0.142068	−	0.0461606i	0.379188	+	0.925320i	$0.376203\pi$
$224$	16.5575	−	18.7641i	1.10629	−	1.25373i
$225$		0			0
$226$	−3.55673	−	6.77028i	−0.236590	−	0.450353i
$227$	2.05822	+	6.33454i	0.136609	+	0.420438i	0.995837	−	0.0911544i	$-0.0290557\pi$
$227$	2.05822	+	6.33454i	0.136609	+	0.420438i	−0.859228	+	0.511593i	$0.829056\pi$
$228$	5.95522	−	0.148649i	0.394394	−	0.00984449i
$229$	−6.45978	−	8.89112i	−0.426874	−	0.587542i	0.540358	−	0.841435i	$-0.318289\pi$
$229$	−6.45978	−	8.89112i	−0.426874	−	0.587542i	−0.967232	+	0.253893i	$0.918289\pi$
$230$		0			0
$231$	−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	−0.158092	+	0.987424i	$0.550534\pi$
$233$	−16.0021	+	22.0251i	−1.04834	+	1.44291i	−0.890243	+	0.455485i	$0.849466\pi$
$234$	0.00734223	+	0.0428865i	0.000479977	+	0.00280358i
$235$		0			0
$236$	−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	0.999095	+	0.0425450i	$0.0135466\pi$
$239$	3.33646	+	10.2686i	0.215817	+	0.664218i	−0.783277	+	0.621673i	$0.786453\pi$
$240$		0			0
$241$	−2.98946	+	9.20061i	−0.192568	+	0.592663i	0.807428	+	0.589966i	$0.200859\pi$
$241$	−2.98946	+	9.20061i	−0.192568	+	0.592663i	−0.999996	+	0.00269761i	$0.999141\pi$
$242$	24.5262	+	3.57145i	1.57660	+	0.229582i
$243$	0.415968			0.0266843
$244$	−4.80554	−	13.6234i	−0.307643	−	0.872149i
$245$		0			0
$246$	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
$250$		0			0
$251$			19.3541i			1.22162i	0.791778	+	0.610809i	$0.209156\pi$
$251$			19.3541i			1.22162i	−0.791778	+	0.610809i	$0.790844\pi$
$252$	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
$255$		0			0
$256$	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			0
$261$	−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	$-0.476646\pi$
$263$	−7.35613	−	2.39015i	−0.453598	−	0.147383i	−0.526901	+	0.849927i	$0.676646\pi$
$264$	−5.02358	−	25.4998i	−0.309180	−	1.56941i
$265$		0			0
$266$	−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	−0.360295	−	0.932838i	$-0.617324\pi$
$269$	10.4677	−	14.4075i	0.638224	−	0.878440i	0.998519	+	0.0543984i	$0.0173241\pi$
$270$		0			0
$271$	6.54444	−	4.75481i	0.397546	−	0.288834i	−0.370994	−	0.928635i	$-0.620983\pi$
$271$	6.54444	−	4.75481i	0.397546	−	0.288834i	0.768541	+	0.639801i	$0.220983\pi$
$272$	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
$275$		0			0
$276$	−14.9395	−	10.2946i	−0.899250	−	0.619659i
$277$	−6.31523	−	19.4363i	−0.379445	−	1.16781i	−0.940430	−	0.339987i	$-0.889577\pi$
$277$	−6.31523	−	19.4363i	−0.379445	−	1.16781i	0.560985	−	0.827826i	$-0.310423\pi$
$278$	2.53292	+	1.25103i	0.151915	+	0.0750317i
$279$	0.0844176	−	0.0613330i	0.00505395	−	0.00367191i
$280$		0			0
$281$	−26.1698	−	19.0135i	−1.56116	−	1.13425i	−0.935051	−	0.354513i	$-0.884647\pi$
$281$	−26.1698	−	19.0135i	−1.56116	−	1.13425i	−0.626108	−	0.779736i	$-0.715353\pi$
$282$	9.10050	+	17.3229i	0.541927	+	1.03157i
$283$	19.5207	+	14.1826i	1.16038	+	0.843067i	0.989826	−	0.142280i	$-0.0454435\pi$
$283$	19.5207	+	14.1826i	1.16038	+	0.843067i	0.170556	+	0.985348i	$0.445443\pi$
$284$	0.710419	+	0.928186i	0.0421556	+	0.0550777i
$285$		0			0
$286$	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
$290$		0			0
$291$	−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	$-0.597993\pi$
$293$	−10.3735			−0.606027			−0.303014	+	0.952986i	$0.597993\pi$
$294$	30.2649	+	4.40711i	1.76508	+	0.257028i
$295$		0			0
$296$	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
$300$		0			0
$301$			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
$305$		0			0
$306$	0.0464377	−	0.318901i	0.00265467	−	0.0182304i
$307$	−3.04330			−0.173690			−0.0868452	−	0.996222i	$-0.527679\pi$
$307$	−3.04330			−0.173690			−0.0868452	+	0.996222i	$0.527679\pi$
$308$	−44.5633	+	15.7193i	−2.53923	+	0.895691i
$309$	−31.2633	−	10.1581i	−1.77851	−	0.577872i
$310$		0			0
$311$	−4.69469	−	14.4488i	−0.266212	−	0.819315i	−0.991412	−	0.130777i	$-0.958253\pi$
$311$	−4.69469	−	14.4488i	−0.266212	−	0.819315i	0.725200	−	0.688538i	$-0.241747\pi$
$312$	−3.39372	−	1.57209i	−0.192132	−	0.0890021i
$313$	0.113450	+	0.0368620i	0.00641255	+	0.00208357i	0.312222	−	0.950009i	$-0.398927\pi$
$313$	0.113450	+	0.0368620i	0.00641255	+	0.00208357i	−0.305809	+	0.952093i	$0.598927\pi$
$314$	−4.39009	−	4.28187i	−0.247747	−	0.241640i
$315$		0			0
$316$	9.42109	+	12.3090i	0.529977	+	0.692433i
$317$	−23.7579	−	17.2612i	−1.33438	−	0.969483i	−0.999631	−	0.0271752i	$-0.991349\pi$
$317$	−23.7579	−	17.2612i	−1.33438	−	0.969483i	−0.334748	−	0.942308i	$-0.608651\pi$
$318$	10.0581	−	5.28394i	0.564028	−	0.296309i
$319$	8.90369	+	6.46891i	0.498511	+	0.362189i
$320$		0			0
$321$	−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			0
$326$	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
$330$		0			0
$331$	19.7316	−	27.1582i	1.08455	−	1.49275i	0.230129	−	0.973160i	$-0.426085\pi$
$331$	19.7316	−	27.1582i	1.08455	−	1.49275i	0.854416	−	0.519589i	$-0.173915\pi$
$332$	−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
$335$		0			0
$336$	19.1010	+	23.7061i	1.04204	+	1.29328i
$337$	28.0105	+	9.10115i	1.52583	+	0.495771i	0.947424	−	0.319980i	$-0.103676\pi$
$337$	28.0105	+	9.10115i	1.52583	+	0.495771i	0.578403	+	0.815751i	$0.303676\pi$
$338$	2.96138	+	17.2977i	0.161078	+	0.940869i
$339$	8.84840	−	2.87502i	0.480579	−	0.156150i
$340$		0			0
$341$	−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
$345$		0			0
$346$	8.57692	−	17.3655i	0.461098	−	0.933573i
$347$	−3.43363	+	2.49468i	−0.184327	+	0.133921i	−0.676122	−	0.736789i	$-0.736341\pi$
$347$	−3.43363	+	2.49468i	−0.184327	+	0.133921i	0.491795	+	0.870711i	$0.336341\pi$
$348$	2.02209	−	6.79592i	0.108396	−	0.364300i
$349$			16.7792i			0.898172i	0.893488	+	0.449086i	$0.148250\pi$
$349$			16.7792i			0.898172i	−0.893488	+	0.449086i	$0.851750\pi$
$350$		0			0
$351$	−4.01998			−0.214570
$352$	−27.7227	−	12.0112i	−1.47762	−	0.640201i
$353$	−20.2984	−	27.9383i	−1.08037	−	1.48701i	−0.859108	−	0.511794i	$-0.828981\pi$
$353$	−20.2984	−	27.9383i	−1.08037	−	1.48701i	−0.221266	−	0.975213i	$-0.571019\pi$
$354$	−2.35866	−	1.16496i	−0.125361	−	0.0619168i
$355$		0			0
$356$	−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	−0.920034	−	0.391838i	$-0.871839\pi$
$359$	1.03463	−	3.18426i	0.0546057	−	0.168059i	0.974640	+	0.223779i	$0.0718394\pi$
$360$		0			0
$361$	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
$365$		0			0
$366$	17.3224	−	2.96561i	0.905454	−	0.155015i
$367$	−5.73261	+	7.89027i	−0.299240	+	0.411869i	−0.931988	−	0.362489i	$-0.881927\pi$
$367$	−5.73261	+	7.89027i	−0.299240	+	0.411869i	0.632748	+	0.774358i	$0.281927\pi$
$368$	−19.7084	+	7.51004i	−1.02737	+	0.391488i
$369$	−0.0790890	−	0.0574615i	−0.00411721	−	0.00299133i
$370$		0			0
$371$	−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	0.983060	+	0.183286i	$0.0586733\pi$
$373$	5.70667	+	17.5633i	0.295480	+	0.909395i	−0.687579	+	0.726109i	$0.741327\pi$
$374$	−38.0653	+	19.9974i	−1.96831	+	1.03404i
$375$		0			0
$376$	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	−0.993142	−	0.116917i	$-0.962699\pi$
$379$	−15.5245	−	21.3676i	−0.797439	−	1.09758i	0.195703	−	0.980663i	$-0.437301\pi$
$380$		0			0
$381$	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	$-0.619716\pi$
$383$	12.3447	−	16.9911i	0.630787	−	0.868203i	0.998082	+	0.0619009i	$0.0197163\pi$
$384$	−1.35626	+	19.4174i	−0.0692111	+	0.990892i
$385$		0			0
$386$	−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	−0.642043	−	0.766669i	$-0.721913\pi$
$389$	−14.0198	+	4.55530i	−0.710830	+	0.230963i	−0.0687872	+	0.997631i	$0.521913\pi$
$390$		0			0
$391$	−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
$395$		0			0
$396$	−0.427453	+	0.0106697i	−0.0214803	+	0.000536172i
$397$	19.8855	−	14.4476i	0.998023	−	0.725106i	0.0363595	−	0.999339i	$-0.488424\pi$
$397$	19.8855	−	14.4476i	0.998023	−	0.725106i	0.961663	+	0.274233i	$0.0884239\pi$
$398$	14.9537	+	14.5851i	0.749559	+	0.731083i
$399$	13.1765			0.659648
$400$		0			0
$401$	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
$405$		0			0
$406$	−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	−0.981349	−	0.192233i	$-0.938427\pi$
$409$	−1.50524	+	4.63264i	−0.0744292	+	0.229069i	0.906920	+	0.421303i	$0.138427\pi$
$410$		0			0
$411$	−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
$415$		0			0
$416$	−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	−0.749610	−	0.661879i	$-0.769759\pi$
$419$	2.28269	−	3.14185i	0.111517	−	0.153489i	0.861127	+	0.508390i	$0.169759\pi$
$420$		0			0
$421$	−4.13220	−	5.68749i	−0.201391	−	0.277191i	0.696361	−	0.717691i	$-0.254801\pi$
$421$	−4.13220	−	5.68749i	−0.201391	−	0.277191i	−0.897753	+	0.440500i	$0.854801\pi$
$422$	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
$425$		0			0
$426$	−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
$430$		0			0
$431$	−1.52243	−	1.10611i	−0.0733329	−	0.0532795i	0.550515	−	0.834825i	$-0.314431\pi$
$431$	−1.52243	−	1.10611i	−0.0733329	−	0.0532795i	−0.623848	+	0.781546i	$0.714431\pi$
$432$	7.44956	+	19.5497i	0.358417	+	0.940585i
$433$	3.83776	−	5.28222i	0.184431	−	0.253847i	−0.706783	−	0.707430i	$-0.749854\pi$
$433$	3.83776	−	5.28222i	0.184431	−	0.253847i	0.891214	+	0.453583i	$0.149854\pi$
$434$	16.0745	−	2.75197i	0.771598	−	0.132099i
$435$		0			0
$436$	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	−0.909461	−	0.415789i	$-0.863506\pi$
$439$	−8.75988	−	26.9601i	−0.418086	−	1.28674i	0.491375	−	0.870948i	$-0.336494\pi$
$440$		0			0
$441$	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	$-0.709658\pi$
$443$	−25.7646			−1.22412			−0.612058	+	0.790813i	$0.709658\pi$
$444$	−21.1072	+	7.44540i	−1.00170	+	0.353343i
$445$		0			0
$446$	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			0
$451$			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
$455$		0			0
$456$	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
$460$		0			0
$461$	−29.9901	+	9.74436i	−1.39678	+	0.453840i	−0.908147	−	0.418651i	$-0.862503\pi$
$461$	−29.9901	+	9.74436i	−1.39678	+	0.453840i	−0.488630	+	0.872491i	$0.662503\pi$
$462$	−9.70076	−	56.6628i	−0.451320	−	2.63619i
$463$	−12.8107	−	4.16244i	−0.595362	−	0.193445i	−0.00419137	−	0.999991i	$-0.501334\pi$
$463$	−12.8107	−	4.16244i	−0.595362	−	0.193445i	−0.591171	+	0.806546i	$0.701334\pi$
$464$	−5.17143	−	6.41825i	−0.240078	−	0.297960i
$465$		0			0
$466$	−37.9491	+	6.49694i	−1.75796	+	0.300965i
$467$	15.5848	+	11.3230i	0.721180	+	0.523968i	0.886761	−	0.462228i	$-0.152950\pi$
$467$	15.5848	+	11.3230i	0.721180	+	0.523968i	−0.165581	+	0.986196i	$0.552950\pi$
$468$	−0.0349148	+	0.0506684i	−0.00161394	+	0.00234215i
$469$	16.4843	−	22.6888i	0.761176	−	1.04767i
$470$		0			0
$471$	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
$475$		0			0
$476$	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	−0.893964	−	0.448138i	$-0.852087\pi$
$479$	−16.2835	+	11.8306i	−0.744010	+	0.540555i	0.149954	+	0.988693i	$0.452087\pi$
$480$		0			0
$481$	−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
$485$		0			0
$486$	0.421126	+	0.410745i	0.0191027	+	0.0186318i
$487$	26.8399	+	8.72080i	1.21623	+	0.395177i	0.845708	−	0.533646i	$-0.179179\pi$
$487$	26.8399	+	8.72080i	1.21623	+	0.395177i	0.370523	+	0.928823i	$0.379179\pi$
$488$	8.58723	−	18.5375i	0.388726	−	0.839155i
$489$	3.83994	+	11.8181i	0.173648	+	0.534434i
$490$		0			0
$491$	34.0495	+	11.0634i	1.53663	+	0.499283i	0.950445	−	0.310892i	$-0.100628\pi$
$491$	34.0495	+	11.0634i	1.53663	+	0.499283i	0.586189	+	0.810174i	$0.300628\pi$
$492$	7.92482	−	2.79541i	0.357279	−	0.126027i
$493$	−11.7305			−0.528314
$494$	−0.271166	+	1.86217i	−0.0122003	+	0.0837831i
$495$		0			0
$496$	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	$-0.796994\pi$
$499$		−	26.6004i		−	1.19080i	0.803430	−	0.595399i	$-0.203006\pi$
$500$		0			0
$501$		−	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	$-0.0461185\pi$
$503$	12.2552	+	16.8678i	0.546430	+	0.752097i	−0.443092	+	0.896476i	$0.646118\pi$
$504$	0.437448	−	0.243929i	0.0194855	−	0.0108655i
$505$		0			0
$506$	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	−0.573115	−	0.819475i	$-0.694265\pi$
$509$	−34.2578	−	11.1310i	−1.51845	−	0.493374i	−0.945335	+	0.326101i	$0.894265\pi$
$510$		0			0
$511$	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
$515$		0			0
$516$	−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
$520$		0			0
$521$	27.8704	−	20.2490i	1.22102	−	0.887126i	0.224839	−	0.974396i	$-0.427814\pi$
$521$	27.8704	−	20.2490i	1.22102	−	0.887126i	0.996185	+	0.0872702i	$0.0278144\pi$
$522$	−0.104589	−	0.0516573i	−0.00457775	−	0.00226098i
$523$	9.84654	+	30.3045i	0.430559	+	1.32512i	0.897570	+	0.440873i	$0.145331\pi$
$523$	9.84654	+	30.3045i	0.430559	+	1.32512i	−0.467011	+	0.884252i	$0.654669\pi$
$524$	−5.82219	−	4.01198i	−0.254343	−	0.175264i
$525$		0			0
$526$	−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
$530$		0			0
$531$	−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
$535$		0			0
$536$	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
$540$		0			0
$541$	19.8645	+	6.45438i	0.854044	+	0.277496i	0.703139	−	0.711053i	$-0.251781\pi$
$541$	19.8645	+	6.45438i	0.854044	+	0.277496i	0.150905	+	0.988548i	$0.451781\pi$
$542$	11.3207	+	1.64850i	0.486266	+	0.0708091i
$543$			4.85313i			0.208268i
$544$	31.4305	−	7.01095i	1.34757	−	0.300592i
$545$		0			0
$546$	−7.41748	−	3.66354i	−0.317439	−	0.156785i
$547$	24.4151	−	17.7386i	1.04392	−	0.758450i	0.0728702	−	0.997341i	$-0.476784\pi$
$547$	24.4151	−	17.7386i	1.04392	−	0.758450i	0.971046	+	0.238892i	$0.0767841\pi$
$548$	−12.3399	+	41.4722i	−0.527133	+	1.77160i
$549$		−	0.289133i		−	0.0123399i
$550$		0			0
$551$	−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
$555$		0			0
$556$	1.32901	+	3.76766i	0.0563626	+	0.159784i
$557$	0.749572			0.0317604			0.0158802	−	0.999874i	$-0.494945\pi$
$557$	0.749572			0.0317604			0.0158802	+	0.999874i	$0.494945\pi$
$558$	0.146027	+	0.0212642i	0.00618183	+	0.000900186i
$559$	1.57993	−	4.86251i	0.0668237	−	0.205662i
$560$		0			0
$561$	−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	−0.676949	−	0.736030i	$-0.736698\pi$
$563$	7.19759	−	22.1519i	0.303342	−	0.933591i	0.980291	−	0.197561i	$-0.0633020\pi$
$564$	−7.89209	+	26.5240i	−0.332317	+	1.11686i
$565$		0			0
$566$	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	0.707877	−	0.706336i	$-0.249653\pi$
$569$	6.07930	+	4.41687i	0.254858	+	0.185165i	−0.453019	+	0.891501i	$0.649653\pi$
$570$		0			0
$571$	−1.37819	−	1.89691i	−0.0576753	−	0.0793832i	0.779205	−	0.626769i	$-0.215623\pi$
$571$	−1.37819	−	1.89691i	−0.0576753	−	0.0793832i	−0.836880	+	0.547386i	$0.815623\pi$
$572$	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
$575$		0			0
$576$	0.311109	+	0.0759000i	0.0129629	+	0.00316250i
$577$	20.3396	−	6.60875i	0.846750	−	0.275126i	0.146666	−	0.989186i	$-0.453146\pi$
$577$	20.3396	−	6.60875i	0.846750	−	0.275126i	0.700084	+	0.714060i	$0.253146\pi$
$578$	9.64897	−	19.5360i	0.401344	−	0.812592i
$579$	−6.95547	−	9.57339i	−0.289060	−	0.397856i
$580$		0			0
$581$	−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			0
$586$	−10.5021	−	10.2433i	−0.433840	−	0.423146i
$587$	−2.16490	+	6.66288i	−0.0893551	+	0.275007i	−0.985741	−	0.168267i	$-0.946183\pi$
$587$	−2.16490	+	6.66288i	−0.0893551	+	0.275007i	0.896386	+	0.443274i	$0.146183\pi$
$588$	26.2884	+	34.3466i	1.08411	+	1.41643i
$589$	4.29204	−	1.39457i	0.176850	−	0.0574622i
$590$		0			0
$591$	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
$595$		0			0
$596$	−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			0
$601$	−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
$605$		0			0
$606$	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
$610$		0			0
$611$	−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	$-0.938428\pi$
$613$	−1.84281	+	5.67158i	−0.0744303	+	0.229073i	0.906919	+	0.421304i	$0.138428\pi$
$614$	−3.08104	−	3.00509i	−0.124341	−	0.121276i
$615$		0			0
$616$	−60.6378	−	28.0895i	−2.44317	−	1.13176i
$617$	−4.47498	+	6.15928i	−0.180156	+	0.247963i	−0.889538	−	0.456860i	$-0.848974\pi$
$617$	−4.47498	+	6.15928i	−0.180156	+	0.247963i	0.709383	+	0.704824i	$0.248974\pi$
$618$	−21.6204	−	41.1548i	−0.869701	−	1.65549i
$619$	−16.7671	+	23.0779i	−0.673925	+	0.927579i	−0.999841	−	0.0178200i	$-0.994327\pi$
$619$	−16.7671	+	23.0779i	−0.673925	+	0.927579i	0.325916	+	0.945399i	$0.394327\pi$
$620$		0			0
$621$	−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
$625$		0			0
$626$	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			0
$631$	27.7571	+	20.1667i	1.10499	+	0.802823i	0.981868	−	0.189568i	$-0.0607089\pi$
$631$	27.7571	+	20.1667i	1.10499	+	0.802823i	0.123124	+	0.992391i	$0.460709\pi$
$632$	−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
$635$		0			0
$636$	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
$640$		0			0
$641$	11.8514	−	36.4748i	0.468102	−	1.44067i	−0.386938	−	0.922106i	$-0.626467\pi$
$641$	11.8514	−	36.4748i	0.468102	−	1.44067i	0.855039	−	0.518563i	$-0.173533\pi$
$642$	−29.4127	−	4.28303i	−1.16083	−	0.169038i
$643$	−4.80260			−0.189396			−0.0946980	−	0.995506i	$-0.530189\pi$
$643$	−4.80260			−0.189396			−0.0946980	+	0.995506i	$0.530189\pi$
$644$	−43.9940	+	15.5185i	−1.73361	+	0.611515i
$645$		0			0
$646$	6.17218	−	12.4967i	0.242841	−	0.491675i
$647$	−2.22128	−	3.05732i	−0.0873273	−	0.120196i	0.763118	−	0.646259i	$-0.223667\pi$
$647$	−2.22128	−	3.05732i	−0.0873273	−	0.120196i	−0.850445	+	0.526063i	$0.823667\pi$
$648$	−24.6381	+	4.85381i	−0.967876	+	0.190676i
$649$	5.77462			0.226674
$650$		0			0
$651$			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	$-0.983545\pi$
$653$	−32.1500	+	23.3583i	−1.25813	+	0.914082i	−0.259462	+	0.965753i	$0.583545\pi$
$654$	18.3771	+	9.07655i	0.718600	+	0.354921i
$655$		0			0
$656$	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	0.581258	−	0.813719i	$-0.302561\pi$
$659$	14.7150	+	4.78119i	0.573214	+	0.186249i	−0.00804417	+	0.999968i	$0.502561\pi$
$660$		0			0
$661$	29.4671	−	9.57445i	1.14614	−	0.372403i	0.326451	−	0.945214i	$-0.394147\pi$
$661$	29.4671	−	9.57445i	1.14614	−	0.372403i	0.819687	+	0.572811i	$0.194147\pi$
$662$	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
$665$		0			0
$666$	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
$670$		0			0
$671$	−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	$-0.786382\pi$
$673$	−27.2704	+	8.86070i	−1.05120	+	0.341555i	−0.268059	+	0.963402i	$0.586382\pi$
$674$	19.3709	+	36.8728i	0.746139	+	1.42029i
$675$		0			0
$676$	−14.0824	+	20.4364i	−0.541630	+	0.786014i
$677$	9.18195	+	28.2591i	0.352891	+	1.08609i	0.957222	+	0.289353i	$0.0934403\pi$
$677$	9.18195	+	28.2591i	0.352891	+	1.08609i	−0.604331	+	0.796733i	$0.706560\pi$
$678$	11.7970	+	5.82664i	0.453063	+	0.223771i
$679$	−11.6251	+	8.44616i	−0.446132	+	0.324134i
$680$		0			0
$681$	−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	$-0.310762\pi$
$683$	−1.42936	−	1.03849i	−0.0546928	−	0.0397366i	−0.614796	+	0.788686i	$0.710762\pi$
$684$	0.110063	−	0.0842402i	0.00420835	−	0.00322100i
$685$		0			0
$686$	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
$690$		0			0
$691$	−12.3432	−	4.01054i	−0.469556	−	0.152568i	0.0646751	−	0.997906i	$-0.479399\pi$
$691$	−12.3432	−	4.01054i	−0.469556	−	0.152568i	−0.534231	+	0.845338i	$0.679399\pi$
$692$	25.8307	−	9.11156i	0.981936	−	0.346370i
$693$	−0.945779			−0.0359272
$694$	−5.93957	−	0.864908i	−0.225463	−	0.0328315i
$695$		0			0
$696$	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
$700$		0			0
$701$		−	9.99937i		−	0.377671i	−0.982009	−	0.188835i	$-0.939529\pi$
$701$		−	9.99937i		−	0.377671i	0.982009	−	0.188835i	$-0.0604713\pi$
$702$	−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
$705$		0			0
$706$	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	0.933699	−	0.358058i	$-0.116561\pi$
$709$	39.3712	+	12.7925i	1.47862	+	0.480432i	0.544918	+	0.838490i	$0.316561\pi$
$710$		0			0
$711$	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
$715$		0			0
$716$	−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	−0.0480227	−	0.998846i	$-0.515292\pi$
$719$	−27.1580	−	19.7314i	−1.01282	−	0.735858i	−0.964799	+	0.262988i	$0.915292\pi$
$720$		0			0
$721$	−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
$725$		0			0
$726$	−37.7491	+	19.8313i	−1.40100	+	0.736008i
$727$	42.4290	−	13.7860i	1.57360	−	0.511295i	0.613204	−	0.789924i	$-0.289880\pi$
$727$	42.4290	−	13.7860i	1.57360	−	0.511295i	0.960399	+	0.278630i	$0.0898803\pi$
$728$	−8.39947	+	4.68369i	−0.311305	+	0.173589i
$729$	−22.1271	+	16.0763i	−0.819522	+	0.595417i
$730$		0			0
$731$	−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	$-0.596597\pi$
$733$	−35.1630	−	25.5474i	−1.29877	−	0.943615i	−0.999943	+	0.0106913i	$0.996597\pi$
$734$	−13.5949	+	2.32747i	−0.501797	+	0.0859083i
$735$		0			0
$736$	−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	−0.625347	−	0.780347i	$-0.715043\pi$
$739$	−18.2840	+	5.94083i	−0.672588	+	0.218537i	−0.0472404	+	0.998884i	$0.515043\pi$
$740$		0			0
$741$	−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
$745$		0			0
$746$	−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			0
$751$	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			0
$756$	15.3935	+	43.6397i	0.559858	+	1.58716i
$757$	42.4947			1.54450			0.772248	−	0.635321i	$-0.219132\pi$
$757$	42.4947			1.54450			0.772248	+	0.635321i	$0.219132\pi$
$758$	5.38235	−	36.9621i	0.195496	−	1.34253i
$759$	−14.9719	+	46.0787i	−0.543445	+	1.67255i
$760$		0			0
$761$	11.9096	+	36.6540i	0.431723	+	1.32871i	0.896407	+	0.443231i	$0.146168\pi$
$761$	11.9096	+	36.6540i	0.431723	+	1.32871i	−0.464684	+	0.885477i	$0.653832\pi$
$762$	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			0
$766$	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	0.971577	−	0.236723i	$-0.0760733\pi$
$769$	29.0252	+	21.0880i	1.04667	+	0.760454i	0.0750973	+	0.997176i	$0.476073\pi$
$770$		0			0
$771$	−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	$-0.110136\pi$
$773$	−0.547088	−	1.68376i	−0.0196774	−	0.0605607i	−0.960413	+	0.278580i	$0.910136\pi$
$774$	−0.333366	+	0.175132i	−0.0119826	+	0.00629498i
$775$		0			0
$776$	−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
$780$		0			0
$781$	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			0
$786$	6.00599	−	6.15778i	0.214227	−	0.219641i
$787$	0.356070	−	1.09587i	0.0126925	−	0.0390636i	−0.944510	−	0.328484i	$-0.893462\pi$
$787$	0.356070	−	1.09587i	0.0126925	−	0.0390636i	0.957202	+	0.289420i	$0.0934624\pi$
$788$	−14.8200	−	19.3628i	−0.527941	−	0.689773i
$789$	12.6559	−	4.11215i	0.450562	−	0.146396i
$790$		0			0
$791$	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
$795$		0			0
$796$	0.737145	+	29.5318i	0.0261274	+	1.04673i
$797$	34.5173	−	25.0783i	1.22267	−	0.888319i	0.226347	−	0.974047i	$-0.427322\pi$
$797$	34.5173	−	25.0783i	1.22267	−	0.888319i	0.996319	+	0.0857282i	$0.0273217\pi$
$798$	13.3398	+	13.0110i	0.472225	+	0.460585i
$799$	45.7832			1.61969
$800$		0			0
$801$	−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
$805$		0			0
$806$	−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	0.127999	−	0.991774i	$-0.459145\pi$
$809$	17.2761	−	53.1704i	0.607396	−	1.86937i	0.479397	−	0.877598i	$-0.340855\pi$
$810$		0			0
$811$	27.5933	−	8.96560i	0.968931	−	0.314825i	0.218547	−	0.975826i	$-0.429868\pi$
$811$	27.5933	−	8.96560i	0.968931	−	0.314825i	0.750384	+	0.661002i	$0.229868\pi$
$812$	−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
$815$		0			0
$816$	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
$820$		0			0
$821$	26.5861	+	36.5926i	0.927860	+	1.27709i	0.960689	+	0.277628i	$0.0895484\pi$
$821$	26.5861	+	36.5926i	0.927860	+	1.27709i	−0.0328288	+	0.999461i	$0.510452\pi$
$822$	−47.1961	−	23.3105i	−1.64615	−	0.813046i
$823$	22.3928	−	7.27585i	0.780562	−	0.253620i	0.108482	−	0.994098i	$-0.465401\pi$
$823$	22.3928	−	7.27585i	0.780562	−	0.253620i	0.672080	+	0.740478i	$0.265401\pi$
$824$	−53.6554	−	6.45046i	−1.86918	−	0.224712i
$825$		0			0
$826$	−5.98818	+	3.14585i	−0.208355	+	0.109458i
$827$	16.1742	+	49.7791i	0.562432	+	1.73099i	0.675460	+	0.737397i	$0.263945\pi$
$827$	16.1742	+	49.7791i	0.562432	+	1.73099i	−0.113028	+	0.993592i	$0.536055\pi$
$828$	−0.421993	+	0.0105334i	−0.0146653	+	0.000366060i
$829$	−14.8801	−	20.4807i	−0.516808	−	0.711325i	0.468241	−	0.883601i	$-0.344888\pi$
$829$	−14.8801	−	20.4807i	−0.516808	−	0.711325i	−0.985049	+	0.172276i	$0.944888\pi$
$830$		0			0
$831$	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
$835$		0			0
$836$	−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	0.968323	+	0.249699i	$0.0803318\pi$
$839$	9.60794	+	29.5702i	0.331703	+	1.02088i	−0.636620	+	0.771177i	$0.719668\pi$
$840$		0			0
$841$	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
$845$		0			0
$846$	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
$850$		0			0
$851$		−	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	$-0.451493\pi$
$853$	33.2584	−	24.1636i	1.13875	−	0.827347i	0.986944	+	0.161064i	$0.0514926\pi$
$854$	20.0114	−	40.5165i	0.684775	−	1.38645i
$855$		0			0
$856$	−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	−0.462791	−	0.886468i	$-0.653152\pi$
$859$	−39.8085	−	12.9346i	−1.35825	−	0.441322i	−0.895458	+	0.445146i	$0.853152\pi$
$860$		0			0
$861$	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	$-0.305048\pi$
$863$	16.4224	+	5.33595i	0.559024	+	0.181638i	−0.0158581	+	0.999874i	$0.505048\pi$
$864$	−11.7623	+	27.1481i	−0.400162	+	0.923598i
$865$		0			0
$866$	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
$870$		0			0
$871$	−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
$875$		0			0
$876$	−16.3387	−	11.2588i	−0.552035	−	0.380399i
$877$	4.64130	+	14.2844i	0.156725	+	0.482351i	0.998332	−	0.0577404i	$-0.0183896\pi$
$877$	4.64130	+	14.2844i	0.156725	+	0.482351i	−0.841606	+	0.540092i	$0.818390\pi$
$878$	17.7531	−	35.9443i	0.599139	−	1.21306i
$879$	14.4387	−	10.4903i	0.487004	−	0.353829i
$880$		0			0
$881$	37.8296	+	27.4848i	1.27451	+	0.925986i	0.999373	−	0.0354189i	$-0.0112766\pi$
$881$	37.8296	+	27.4848i	1.27451	+	0.925986i	0.275138	+	0.961405i	$0.411277\pi$
$882$	0.629949	−	0.330940i	0.0212115	−	0.0111433i
$883$	27.3068	+	19.8395i	0.918946	+	0.667653i	0.943261	−	0.332051i	$-0.107741\pi$
$883$	27.3068	+	19.8395i	0.918946	+	0.667653i	−0.0243155	+	0.999704i	$0.507741\pi$
$884$	−6.94907	+	5.31870i	−0.233722	+	0.178887i
$885$		0			0
$886$	−26.0841	−	25.4412i	−0.876313	−	0.854712i
$887$	3.96211	+	1.28737i	0.133035	+	0.0432256i	0.374778	−	0.927115i	$-0.377719\pi$
$887$	3.96211	+	1.28737i	0.133035	+	0.0432256i	−0.241743	+	0.970340i	$0.577719\pi$
$888$	−28.7209	−	13.3045i	−0.963809	−	0.446470i
$889$	−18.2824	−	56.2675i	−0.613172	−	1.88715i
$890$		0			0
$891$	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
$895$		0			0
$896$	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			0
$901$		−	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
$905$		0			0
$906$	−4.24181	−	0.617685i	−0.140925	−	0.0205212i
$907$	−44.9685			−1.49315			−0.746577	−	0.665299i	$-0.768304\pi$
$907$	−44.9685			−1.49315			−0.746577	+	0.665299i	$0.768304\pi$
$908$	−12.5624	+	4.43129i	−0.416898	+	0.147057i
$909$	−0.148573	−	0.0482742i	−0.00492784	−	0.00160115i
$910$		0			0
$911$	−3.92631	−	12.0839i	−0.130085	−	0.400359i	0.864709	−	0.502274i	$-0.167503\pi$
$911$	−3.92631	−	12.0839i	−0.130085	−	0.400359i	−0.994793	+	0.101915i	$0.967503\pi$
$912$	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
$915$		0			0
$916$	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	0.239537	−	0.970887i	$-0.423004\pi$
$919$	−18.4864	−	13.4312i	−0.609810	−	0.443053i	−0.849347	+	0.527834i	$0.823004\pi$
$920$		0			0
$921$	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
$925$		0			0
$926$	−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	−0.909236	−	0.416282i	$-0.863333\pi$
$929$	−24.2098	+	17.5894i	−0.794297	+	0.577090i	0.114939	+	0.993373i	$0.463333\pi$
$930$		0			0
$931$	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
$935$		0			0
$936$	−0.0853799	+	0.0168202i	−0.00279073	+	0.000549786i
$937$	−44.9541	−	14.6065i	−1.46859	−	0.477172i	−0.537905	−	0.843005i	$-0.680784\pi$
$937$	−44.9541	−	14.6065i	−1.46859	−	0.477172i	−0.930681	+	0.365833i	$0.880784\pi$
$938$	39.0926	−	6.69271i	1.27642	−	0.218525i
$939$	−0.195185	+	0.0634195i	−0.00636963	+	0.00206962i
$940$		0			0
$941$	−20.6937	−	6.72379i	−0.674595	−	0.219189i	−0.0483677	−	0.998830i	$-0.515402\pi$
$941$	−20.6937	−	6.72379i	−0.674595	−	0.219189i	−0.626228	+	0.779640i	$0.715402\pi$
$942$	10.4405	+	1.52033i	0.340171	+	0.0495351i
$943$			12.8770i			0.419333i
$944$	−4.17469	−	1.12957i	−0.135875	−	0.0367642i
$945$		0			0
$946$	45.0488	+	22.2499i	1.46466	+	0.723407i
$947$	43.9238	−	31.9125i	1.42733	−	1.03702i	0.436827	−	0.899546i	$-0.356102\pi$
$947$	43.9238	−	31.9125i	1.42733	−	1.03702i	0.990506	−	0.137472i	$-0.0438978\pi$
$948$	−25.5606	−	7.60543i	−0.830168	−	0.247013i
$949$		−	4.43220i		−	0.143875i
$950$		0			0
$951$	50.5237			1.63834
$952$	69.8864	−	13.7679i	2.26503	−	0.446221i
$953$	26.3956	+	36.3305i	0.855039	+	1.17686i	0.982730	+	0.185046i	$0.0592434\pi$
$953$	26.3956	+	36.3305i	0.855039	+	1.17686i	−0.127691	+	0.991814i	$0.540757\pi$
$954$	0.117062	−	0.237012i	0.00379001	−	0.00767354i
$955$		0			0
$956$	−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
$960$		0			0
$961$	−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
$965$		0			0
$966$	−9.57683	−	55.9390i	−0.308130	−	1.79981i
$967$	1.74121	−	2.39657i	0.0559936	−	0.0770686i	−0.780102	−	0.625652i	$-0.784833\pi$
$967$	1.74121	−	2.39657i	0.0559936	−	0.0770686i	0.836096	+	0.548584i	$0.184833\pi$
$968$	−5.91666	+	49.2153i	−0.190169	+	1.58184i
$969$	13.7177	+	9.96648i	0.440675	+	0.320169i
$970$		0			0
$971$	15.2206	+	20.9493i	0.488451	+	0.672295i	0.980101	−	0.198497i	$-0.0636062\pi$
$971$	15.2206	+	20.9493i	0.488451	+	0.672295i	−0.491650	+	0.870793i	$0.663606\pi$
$972$	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
$975$		0			0
$976$	26.9985	−	10.2880i	0.864201	−	0.329311i
$977$	−34.3875	+	11.1732i	−1.10015	+	0.357461i	−0.802161	−	0.597107i	$-0.796317\pi$
$977$	−34.3875	+	11.1732i	−1.10015	+	0.357461i	−0.297991	+	0.954569i	$0.596317\pi$
$978$	−7.78219	+	15.7564i	−0.248847	+	0.503834i
$979$	39.5599	+	54.4495i	1.26434	+	1.74021i
$980$		0			0
$981$	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	$-0.987161\pi$
$983$	−20.4443	+	28.1391i	−0.652071	+	0.897499i	0.347115	+	0.937822i	$0.387161\pi$
$984$	10.7834	+	4.99524i	0.343762	+	0.159243i
$985$		0			0
$986$	−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			0
$991$	−1.42805	+	4.39510i	−0.0453636	+	0.139615i	−0.971173	−	0.238376i	$-0.923385\pi$
$991$	−1.42805	+	4.39510i	−0.0453636	+	0.139615i	0.925809	+	0.377991i	$0.123385\pi$
$992$	3.21037	+	14.3923i	0.101929	+	0.456955i
$993$			57.7546i			1.83279i
$994$	−0.526867	+	3.61814i	−0.0167112	+	0.114760i
$995$		0			0
$996$	−0.583642	−	23.3821i	−0.0184934	−	0.740890i
$997$	−29.6486	+	21.5409i	−0.938979	+	0.682209i	−0.948175	−	0.317749i	$-0.897073\pi$
$997$	−29.6486	+	21.5409i	−0.938979	+	0.682209i	0.00919532	+	0.999958i	$0.497073\pi$
$998$	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	1000.2.o.a.349.21		112
5.2	odd	4		1000.2.t.b.901.16		224
5.3	odd	4		1000.2.t.b.901.41		224
5.4	even	2		200.2.o.a.69.8	yes	112
8.5	even	2	inner	1000.2.o.a.349.15		112
20.19	odd	2		800.2.be.a.369.7		112
25.3	odd	20		1000.2.t.b.101.4		224
25.4	even	10	inner	1000.2.o.a.149.15		112
25.21	even	5		200.2.o.a.29.14	yes	112
25.22	odd	20		1000.2.t.b.101.53		224
40.13	odd	4		1000.2.t.b.901.4		224
40.19	odd	2		800.2.be.a.369.22		112
40.29	even	2		200.2.o.a.69.14	yes	112
40.37	odd	4		1000.2.t.b.901.53		224
100.71	odd	10		800.2.be.a.529.22		112
200.21	even	10		200.2.o.a.29.8	✓	112
200.29	even	10	inner	1000.2.o.a.149.21		112
200.53	odd	20		1000.2.t.b.101.41		224
200.171	odd	10		800.2.be.a.529.7		112
200.197	odd	20		1000.2.t.b.101.16		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.29.8	✓	112	200.21	even	10
200.2.o.a.29.14	yes	112	25.21	even	5
200.2.o.a.69.8	yes	112	5.4	even	2
200.2.o.a.69.14	yes	112	40.29	even	2
800.2.be.a.369.7		112	20.19	odd	2
800.2.be.a.369.22		112	40.19	odd	2
800.2.be.a.529.7		112	200.171	odd	10
800.2.be.a.529.22		112	100.71	odd	10
1000.2.o.a.149.15		112	25.4	even	10	inner
1000.2.o.a.149.21		112	200.29	even	10	inner
1000.2.o.a.349.15		112	8.5	even	2	inner
1000.2.o.a.349.21		112	1.1	even	1	trivial
1000.2.t.b.101.4		224	25.3	odd	20
1000.2.t.b.101.16		224	200.197	odd	20
1000.2.t.b.101.41		224	200.53	odd	20
1000.2.t.b.101.53		224	25.22	odd	20
1000.2.t.b.901.4		224	40.13	odd	4
1000.2.t.b.901.16		224	5.2	odd	4
1000.2.t.b.901.41		224	5.3	odd	4
1000.2.t.b.901.53		224	40.37	odd	4

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:	\( N \)	\(=\)	\( 1000 = 2^{3} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1000.o (of order \(10\), degree \(4\), not minimal)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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