LMFDB - Embedded newform 1000.2.t.b.901.41

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1000,2,Mod(101,1000)]

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, 6]))

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

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

chi := DirichletCharacter("1000.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1000 = 2^{3} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1000.t (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:	$224$
Relative dimension:	$56$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			901.41
Character	$\chi$	$=$	1000.901
Dual form			1000.2.t.b.101.41

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.987445 - 1.01240i) q^{2} +(-1.01126 - 1.39188i) q^{3} +(-0.0499066 - 1.99938i) q^{4} +(-2.40770 - 0.350605i) q^{6} +4.42380 q^{7} +(-2.07345 - 1.92375i) q^{8} +(0.0123697 - 0.0380700i) q^{9} +O(q^{10})$	\(q+(0.987445 - 1.01240i) q^{2} +(-1.01126 - 1.39188i) q^{3} +(-0.0499066 - 1.99938i) q^{4} +(-2.40770 - 0.350605i) q^{6} +4.42380 q^{7} +(-2.07345 - 1.92375i) q^{8} +(0.0123697 - 0.0380700i) q^{9} +(5.07953 - 1.65044i) q^{11} +(-2.73242 + 2.09135i) q^{12} +(0.730985 + 0.237511i) q^{13} +(4.36826 - 4.47866i) q^{14} +(-3.99502 + 0.199564i) q^{16} +(4.60551 + 3.34610i) q^{17} +(-0.0263277 - 0.0501151i) q^{18} +(1.01760 - 1.40061i) q^{19} +(-4.47361 - 6.15740i) q^{21} +(3.34485 - 6.77223i) q^{22} +(1.62935 + 5.01464i) q^{23} +(-0.580831 + 4.83140i) q^{24} +(0.962263 - 0.505520i) q^{26} +(-4.97425 + 1.61623i) q^{27} +(-0.220777 - 8.84485i) q^{28} +(-1.21119 - 1.66707i) q^{29} +(-2.10890 - 1.53221i) q^{31} +(-3.74282 + 4.24161i) q^{32} +(-7.43393 - 5.40106i) q^{33} +(7.93528 - 1.35853i) q^{34} +(-0.0767337 - 0.0228318i) q^{36} +(-6.18628 - 2.01004i) q^{37} +(-0.413150 - 2.41324i) q^{38} +(-0.408628 - 1.25763i) q^{39} +(-0.754681 + 2.32267i) q^{41} +(-10.6512 - 1.55101i) q^{42} +6.65200i q^{43} +(-3.55335 - 10.0735i) q^{44} +(6.68572 + 3.30212i) q^{46} +(-6.50644 + 4.72720i) q^{47} +(4.31777 + 5.35877i) q^{48} +12.5700 q^{49} -9.79409i q^{51} +(0.438394 - 1.47337i) q^{52} +(-2.74471 - 3.77778i) q^{53} +(-3.27552 + 6.63187i) q^{54} +(-9.17253 - 8.51029i) q^{56} -2.97854 q^{57} +(-2.88373 - 0.419923i) q^{58} +(-1.02828 - 0.334110i) q^{59} +(-6.86954 + 2.23205i) q^{61} +(-3.63363 + 0.622082i) q^{62} +(0.0547211 - 0.168414i) q^{63} +(0.598382 + 7.97759i) q^{64} +(-12.8086 + 2.19285i) q^{66} +(-3.72628 + 5.12879i) q^{67} +(6.46027 - 9.37515i) q^{68} +(5.33207 - 7.33896i) q^{69} +(0.472812 - 0.343518i) q^{71} +(-0.0988851 + 0.0551401i) q^{72} +(1.78197 + 5.48432i) q^{73} +(-8.14357 + 4.27818i) q^{74} +(-2.85113 - 1.96467i) q^{76} +(22.4708 - 7.30121i) q^{77} +(-1.67672 - 0.828143i) q^{78} +(-6.27011 + 4.55550i) q^{79} +(7.18270 + 5.21854i) q^{81} +(1.60627 + 3.05755i) q^{82} +(-3.99543 + 5.49924i) q^{83} +(-12.0877 + 9.25173i) q^{84} +(6.73448 + 6.56848i) q^{86} +(-1.09552 + 3.37167i) q^{87} +(-13.7072 - 6.34963i) q^{88} +(-3.89405 - 11.9847i) q^{89} +(3.23373 + 1.05070i) q^{91} +(9.94484 - 3.50796i) q^{92} +4.48479i q^{93} +(-1.63893 + 11.2550i) q^{94} +(9.68877 + 0.920181i) q^{96} +(2.62786 - 1.90925i) q^{97} +(12.4122 - 12.7259i) q^{98} -0.213793i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 6 q^{4} + 2 q^{6} + 60 q^{9}+O(q^{10}) $ 224 * q + 6 * q^4 + 2 * q^6 + 60 * q^9	$ 224 q + 6 q^{4} + 2 q^{6} + 60 q^{9} + 6 q^{14} - 30 q^{16} + 32 q^{24} - 28 q^{26} - 36 q^{31} - 18 q^{34} + 82 q^{36} + 20 q^{39} - 20 q^{41} + 64 q^{44} + 26 q^{46} + 160 q^{49} - 86 q^{54} + 72 q^{56} + 72 q^{64} + 80 q^{66} + 44 q^{71} - 8 q^{74} - 72 q^{76} - 28 q^{79} - 12 q^{81} - 156 q^{84} - 118 q^{86} - 48 q^{89} - 90 q^{94} + 92 q^{96}+O(q^{100}) $ 224 * q + 6 * q^4 + 2 * q^6 + 60 * q^9 + 6 * q^14 - 30 * q^16 + 32 * q^24 - 28 * q^26 - 36 * q^31 - 18 * q^34 + 82 * q^36 + 20 * q^39 - 20 * q^41 + 64 * q^44 + 26 * q^46 + 160 * q^49 - 86 * q^54 + 72 * q^56 + 72 * q^64 + 80 * q^66 + 44 * q^71 - 8 * q^74 - 72 * q^76 - 28 * q^79 - 12 * q^81 - 156 * q^84 - 118 * q^86 - 48 * q^89 - 90 * q^94 + 92 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times$.

$n$	$377$	$501$	$751$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$-1$	$1$

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 $

$2$	0.987445	−	1.01240i	0.698229	−	0.715875i
$2$	0.987445	−	1.01240i	0.698229	−	0.715875i
$3$	−1.01126	−	1.39188i	−0.583851	−	0.803601i	0.410260	−	0.911968i	$-0.365438\pi$
$3$	−1.01126	−	1.39188i	−0.583851	−	0.803601i	−0.994111	+	0.108367i	$0.965438\pi$
$4$	−0.0499066	−	1.99938i	−0.0249533	−	0.999689i
$5$		0			0
$5$		0			0
$6$	−2.40770	−	0.350605i	−0.982939	−	0.143134i
$7$	4.42380			1.67204			0.836020	−	0.548699i	$-0.184877\pi$
$7$	4.42380			1.67204			0.836020	+	0.548699i	$0.184877\pi$
$8$	−2.07345	−	1.92375i	−0.733075	−	0.680148i
$9$	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	$0.102071\pi$
$12$	−2.73242	+	2.09135i	−0.788782	+	0.603721i
$13$	0.730985	+	0.237511i	0.202739	+	0.0658738i	0.408626	−	0.912702i	$-0.366008\pi$
$13$	0.730985	+	0.237511i	0.202739	+	0.0658738i	−0.205887	+	0.978576i	$0.566008\pi$
$14$	4.36826	−	4.47866i	1.16747	−	1.19697i
$15$		0			0
$16$	−3.99502	+	0.199564i	−0.998755	+	0.0498910i
$17$	4.60551	+	3.34610i	1.11700	+	0.811549i	0.983752	−	0.179534i	$-0.0574590\pi$
$17$	4.60551	+	3.34610i	1.11700	+	0.811549i	0.133249	+	0.991083i	$0.457459\pi$
$18$	−0.0263277	−	0.0501151i	−0.00620550	−	0.0118123i
$19$	1.01760	−	1.40061i	0.233454	−	0.321322i	−0.676177	−	0.736739i	$-0.736365\pi$
$19$	1.01760	−	1.40061i	0.233454	−	0.321322i	0.909631	+	0.415418i	$0.136365\pi$
$20$		0			0
$21$	−4.47361	−	6.15740i	−0.976222	−	1.34365i
$22$	3.34485	−	6.77223i	0.713124	−	1.44384i
$23$	1.62935	+	5.01464i	0.339744	+	1.04562i	0.964338	+	0.264675i	$0.0852645\pi$
$23$	1.62935	+	5.01464i	0.339744	+	1.04562i	−0.624594	+	0.780950i	$0.714735\pi$
$24$	−0.580831	+	4.83140i	−0.118562	+	0.986205i
$25$		0			0
$26$	0.962263	−	0.505520i	0.188715	−	0.0991405i
$27$	−4.97425	+	1.61623i	−0.957295	+	0.311044i
$28$	−0.220777	−	8.84485i	−0.0417229	−	1.67152i
$29$	−1.21119	−	1.66707i	−0.224913	−	0.309567i	0.681616	−	0.731710i	$-0.261278\pi$
$29$	−1.21119	−	1.66707i	−0.224913	−	0.309567i	−0.906529	+	0.422144i	$0.861278\pi$
$30$		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	$0.775212\pi$
$32$	−3.74282	+	4.24161i	−0.661643	+	0.749819i
$33$	−7.43393	−	5.40106i	−1.29408	−	0.940204i
$34$	7.93528	−	1.35853i	1.36089	−	0.232986i
$35$		0			0
$36$	−0.0767337	−	0.0228318i	−0.0127889	−	0.00380529i
$37$	−6.18628	−	2.01004i	−1.01702	−	0.330449i	−0.247372	−	0.968921i	$-0.579567\pi$
$37$	−6.18628	−	2.01004i	−1.01702	−	0.330449i	−0.769646	+	0.638471i	$0.779567\pi$
$38$	−0.413150	−	2.41324i	−0.0670219	−	0.391480i
$39$	−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	$0.161077\pi$
$42$	−10.6512	−	1.55101i	−1.64351	−	0.239325i
$43$			6.65200i			1.01442i	0.861822	+	0.507210i	$0.169323\pi$
$43$			6.65200i			1.01442i	−0.861822	+	0.507210i	$0.830677\pi$
$44$	−3.55335	−	10.0735i	−0.535688	−	1.51864i
$45$		0			0
$46$	6.68572	+	3.30212i	0.985755	+	0.486871i
$47$	−6.50644	+	4.72720i	−0.949062	+	0.689534i	−0.950585	−	0.310465i	$-0.899515\pi$
$47$	−6.50644	+	4.72720i	−0.949062	+	0.689534i	0.00152305	+	0.999999i	$0.499515\pi$
$48$	4.31777	+	5.35877i	0.623216	+	0.773472i
$49$	12.5700			1.79572
$50$		0			0
$51$		−	9.79409i		−	1.37145i
$52$	0.438394	−	1.47337i	0.0607943	−	0.204319i
$53$	−2.74471	−	3.77778i	−0.377016	−	0.518917i	0.577775	−	0.816196i	$-0.303921\pi$
$53$	−2.74471	−	3.77778i	−0.377016	−	0.518917i	−0.954791	+	0.297279i	$0.903921\pi$
$54$	−3.27552	+	6.63187i	−0.445742	+	0.902483i
$55$		0			0
$56$	−9.17253	−	8.51029i	−1.22573	−	1.13723i
$57$	−2.97854			−0.394517
$58$	−2.88373	−	0.419923i	−0.378652	−	0.0551385i
$59$	−1.02828	−	0.334110i	−0.133871	−	0.0434974i	0.241315	−	0.970447i	$-0.422421\pi$
$59$	−1.02828	−	0.334110i	−0.133871	−	0.0434974i	−0.375186	+	0.926949i	$0.622421\pi$
$60$		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	$0.553015\pi$
$62$	−3.63363	+	0.622082i	−0.461471	+	0.0790045i
$63$	0.0547211	−	0.168414i	0.00689422	−	0.0212182i
$64$	0.598382	+	7.97759i	0.0747977	+	0.997199i
$65$		0			0
$66$	−12.8086	+	2.19285i	−1.57663	+	0.269922i
$67$	−3.72628	+	5.12879i	−0.455238	+	0.626581i	−0.973513	−	0.228633i	$-0.926574\pi$
$67$	−3.72628	+	5.12879i	−0.455238	+	0.626581i	0.518275	+	0.855214i	$0.326574\pi$
$68$	6.46027	−	9.37515i	0.783423	−	1.13690i
$69$	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	$0.288959\pi$
$72$	−0.0988851	+	0.0551401i	−0.0116537	+	0.00649832i
$73$	1.78197	+	5.48432i	0.208563	+	0.641892i	0.999548	+	0.0300561i	$0.00956859\pi$
$73$	1.78197	+	5.48432i	0.208563	+	0.641892i	−0.790985	+	0.611836i	$0.790431\pi$
$74$	−8.14357	+	4.27818i	−0.946671	+	0.497328i
$75$		0			0
$76$	−2.85113	−	1.96467i	−0.327047	−	0.225363i
$77$	22.4708	−	7.30121i	2.56079	−	0.832050i
$78$	−1.67672	−	0.828143i	−0.189851	−	0.0937687i
$79$	−6.27011	+	4.55550i	−0.705442	+	0.512534i	−0.881700	−	0.471810i	$-0.843601\pi$
$79$	−6.27011	+	4.55550i	−0.705442	+	0.512534i	0.176258	+	0.984344i	$0.443601\pi$
$80$		0			0
$81$	7.18270	+	5.21854i	0.798078	+	0.579838i
$82$	1.60627	+	3.05755i	0.177382	+	0.337650i
$83$	−3.99543	+	5.49924i	−0.438555	+	0.603619i	−0.969890	−	0.243542i	$-0.921691\pi$
$83$	−3.99543	+	5.49924i	−0.438555	+	0.603619i	0.531335	+	0.847162i	$0.321691\pi$
$84$	−12.0877	+	9.25173i	−1.31888	+	1.00945i
$85$		0			0
$86$	6.73448	+	6.56848i	0.726198	+	0.708297i
$87$	−1.09552	+	3.37167i	−0.117452	+	0.361481i
$88$	−13.7072	−	6.34963i	−1.46119	−	0.676873i
$89$	−3.89405	−	11.9847i	−0.412769	−	1.27037i	−0.914232	−	0.405192i	$-0.867205\pi$
$89$	−3.89405	−	11.9847i	−0.412769	−	1.27037i	0.501463	−	0.865179i	$-0.332795\pi$
$90$		0			0
$91$	3.23373	+	1.05070i	0.338987	+	0.110144i
$92$	9.94484	−	3.50796i	1.03682	−	0.365730i
$93$			4.48479i			0.465051i
$94$	−1.63893	+	11.2550i	−0.169042	+	1.16086i
$95$		0			0
$96$	9.68877	+	0.920181i	0.988856	+	0.0939156i
$97$	2.62786	−	1.90925i	0.266819	−	0.193855i	−0.446329	−	0.894869i	$-0.647269\pi$
$97$	2.62786	−	1.90925i	0.266819	−	0.193855i	0.713148	+	0.701014i	$0.247269\pi$
$98$	12.4122	−	12.7259i	1.25382	−	1.28551i
$99$		−	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	$0.937801\pi$
$102$	−9.91553	−	9.67112i	−0.981784	−	0.957583i
$103$	−15.4576	+	11.2306i	−1.52308	+	1.10659i	−0.563151	+	0.826354i	$0.690411\pi$
$103$	−15.4576	+	11.2306i	−1.52308	+	1.10659i	−0.959933	+	0.280231i	$0.909589\pi$
$104$	−1.05875	−	1.89870i	−0.103819	−	0.186183i
$105$		0			0
$106$	−6.53487	−	0.951595i	−0.634723	−	0.0924271i
$107$		−	12.2161i		−	1.18098i	−0.807046	−	0.590488i	$-0.798935\pi$
$107$		−	12.2161i		−	1.18098i	0.807046	−	0.590488i	$-0.201065\pi$
$108$	3.47971	+	9.86475i	0.334835	+	0.949236i
$109$	8.01169	+	2.60316i	0.767381	+	0.249337i	0.666443	−	0.745556i	$-0.267816\pi$
$109$	8.01169	+	2.60316i	0.767381	+	0.249337i	0.100937	+	0.994893i	$0.467816\pi$
$110$		0			0
$111$	3.45819	+	10.6432i	0.328237	+	1.01021i
$112$	−17.6732	+	0.882833i	−1.66996	+	0.0834198i
$113$	1.67108	−	5.14306i	0.157202	−	0.483818i	−0.841175	−	0.540762i	$-0.818136\pi$
$113$	1.67108	−	5.14306i	0.157202	−	0.483818i	0.998377	+	0.0569445i	$0.0181358\pi$
$114$	−2.94114	+	3.01547i	−0.275463	+	0.282424i
$115$		0			0
$116$	−3.27265	+	2.50483i	−0.303858	+	0.232568i
$117$	0.0180841	−	0.0248907i	0.00167188	−	0.00230114i
$118$	−1.35363	+	0.711120i	−0.124611	+	0.0654639i
$119$	20.3739	+	14.8025i	1.86767	+	1.35694i
$120$		0			0
$121$	14.1785	−	10.3012i	1.28895	−	0.936477i
$122$	−4.52356	+	9.15875i	−0.409544	+	0.829194i
$123$	3.99605	−	1.29840i	0.360312	−	0.117072i
$124$	−2.95821	+	4.29295i	−0.265655	+	0.385519i
$125$		0			0
$126$	−0.116469	−	0.221700i	−0.0103758	−	0.0197506i
$127$	4.13273	+	12.7192i	0.366721	+	1.12865i	0.948896	+	0.315588i	$0.102202\pi$
$127$	4.13273	+	12.7192i	0.366721	+	1.12865i	−0.582175	+	0.813063i	$0.697798\pi$
$128$	8.66738	+	7.27163i	0.766095	+	0.642727i
$129$	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	$0.249358\pi$
$132$	−10.4278	+	15.1328i	−0.907620	+	1.31714i
$133$	4.50167	−	6.19602i	0.390344	−	0.537263i
$134$	1.51289	+	8.83688i	0.130694	+	0.763391i
$135$		0			0
$136$	−3.11224	−	15.7978i	−0.266872	−	1.35465i
$137$	6.68544	−	20.5757i	0.571176	−	1.75790i	−0.0776705	−	0.996979i	$-0.524748\pi$
$137$	6.68544	−	20.5757i	0.571176	−	1.75790i	0.648846	−	0.760919i	$-0.275252\pi$
$138$	−2.16484	−	12.6450i	−0.184284	−	1.07641i
$139$	−1.89983	+	0.617291i	−0.161141	+	0.0523579i	−0.388477	−	0.921459i	$-0.626999\pi$
$139$	−1.89983	+	0.617291i	−0.161141	+	0.0523579i	0.227336	+	0.973816i	$0.426999\pi$
$140$		0			0
$141$	13.1594	+	4.27575i	1.10822	+	0.360083i
$142$	0.119098	−	0.817880i	0.00999449	−	0.0686350i
$143$	4.10505			0.343282
$144$	−0.0418198	+	0.154559i	−0.00348498	+	0.0128799i
$145$		0			0
$146$	7.31192	+	3.61141i	0.605139	+	0.298882i
$147$	−12.7116	−	17.4960i	−1.04843	−	1.44304i
$148$	−3.71010	+	12.4690i	−0.304968	+	1.02495i
$149$		−	4.60655i		−	0.377384i	−0.982036	−	0.188692i	$-0.939575\pi$
$149$		−	4.60655i		−	0.377384i	0.982036	−	0.188692i	$-0.0604247\pi$
$150$		0			0
$151$	1.76177			0.143371			0.0716854	−	0.997427i	$-0.477162\pi$
$151$	1.76177			0.143371			0.0716854	+	0.997427i	$0.477162\pi$
$152$	−4.80436	+	0.946480i	−0.389685	+	0.0767697i
$153$	0.184355	−	0.133942i	0.0149042	−	0.0108285i
$154$	14.7969	−	29.9590i	1.19237	−	2.41417i
$155$		0			0
$156$	−2.49408	+	0.879765i	−0.199686	+	0.0704376i
$157$			4.33632i			0.346076i	0.984915	+	0.173038i	$0.0553583\pi$
$157$			4.33632i			0.346076i	−0.984915	+	0.173038i	$0.944642\pi$
$158$	−1.57940	+	10.8462i	−0.125650	+	0.862874i
$159$	−2.48259	+	7.64062i	−0.196882	+	0.605940i
$160$		0			0
$161$	7.20794	+	22.1838i	0.568066	+	1.74833i
$162$	12.3758	−	2.11875i	0.972332	−	0.166465i
$163$	6.86918	+	2.23193i	0.538036	+	0.174818i	0.565415	−	0.824807i	$-0.308716\pi$
$163$	6.86918	+	2.23193i	0.538036	+	0.174818i	−0.0273790	+	0.999625i	$0.508716\pi$
$164$	4.68156	+	1.39298i	0.365568	+	0.108773i
$165$		0			0
$166$	1.62216	+	9.47516i	0.125904	+	0.735415i
$167$	7.30714	+	5.30895i	0.565444	+	0.410819i	0.833447	−	0.552599i	$-0.186364\pi$
$167$	7.30714	+	5.30895i	0.565444	+	0.410819i	−0.268004	+	0.963418i	$0.586364\pi$
$168$	−2.56948	+	21.3732i	−0.198240	+	1.64897i
$169$	−10.0393	−	7.29397i	−0.772253	−	0.561075i
$170$		0			0
$171$	−0.0407338	−	0.0560652i	−0.00311499	−	0.00428742i
$172$	13.2999	−	0.331978i	1.01410	−	0.0253131i
$173$	13.0250	−	4.23208i	0.990273	−	0.321759i	0.231301	−	0.972882i	$-0.425702\pi$
$173$	13.0250	−	4.23208i	0.990273	−	0.321759i	0.758972	+	0.651123i	$0.225702\pi$
$174$	2.33171	+	4.43845i	0.176767	+	0.336478i
$175$		0			0
$176$	−19.9634	+	7.60722i	−1.50480	+	0.573416i
$177$	0.574821	+	1.76912i	0.0432062	+	0.132975i
$178$	−15.9784	−	7.89185i	−1.19763	−	0.591519i
$179$	−4.19376	−	5.77221i	−0.313456	−	0.431435i	0.622999	−	0.782223i	$-0.285914\pi$
$179$	−4.19376	−	5.77221i	−0.313456	−	0.431435i	−0.936455	+	0.350787i	$0.885914\pi$
$180$		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	$0.166568\pi$
$182$	4.25686	−	2.23632i	0.315540	−	0.165767i
$183$	10.0536	+	7.30439i	0.743185	+	0.539956i
$184$	6.26852	−	13.5321i	0.462121	−	0.997597i
$185$		0			0
$186$	4.54040	+	4.42848i	0.332918	+	0.324712i
$187$	28.9163	+	9.39549i	2.11457	+	0.687066i
$188$	9.77618	+	12.7729i	0.713001	+	0.931560i
$189$	−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	$-0.0705278\pi$
$192$	10.4987	−	8.90028i	0.757680	−	0.642323i
$193$	−6.87803			−0.495092			−0.247546	−	0.968876i	$-0.579624\pi$
$193$	−6.87803			−0.495092			−0.247546	+	0.968876i	$0.579624\pi$
$194$	0.661940	−	4.54573i	0.0475245	−	0.326364i
$195$		0			0
$196$	−0.627328	−	25.1322i	−0.0448091	−	1.79516i
$197$	7.16612	+	9.86331i	0.510565	+	0.702732i	0.984014	−	0.178089i	$-0.0569915\pi$
$197$	7.16612	+	9.86331i	0.510565	+	0.702732i	−0.473450	+	0.880821i	$0.656991\pi$
$198$	−0.216444	−	0.211109i	−0.0153820	−	0.0150029i
$199$	−14.7705			−1.04705			−0.523527	−	0.852009i	$-0.675384\pi$
$199$	−14.7705			−1.04705			−0.523527	+	0.852009i	$0.675384\pi$
$200$		0			0
$201$	10.9069			0.769313
$202$	3.95101	+	3.85362i	0.277992	+	0.271139i
$203$	−5.35809	−	7.37478i	−0.376064	−	0.517608i
$204$	−19.5821	+	0.488789i	−1.37102	+	0.0342221i
$205$		0			0
$206$	−3.89366	+	26.7389i	−0.271284	+	1.86299i
$207$	0.211062			0.0146698
$208$	−2.96770	−	0.802984i	−0.205773	−	0.0556769i
$209$	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	$0.374701\pi$
$212$	−7.41622	+	5.67626i	−0.509348	+	0.389847i
$213$	−0.956271	−	0.310711i	−0.0655226	−	0.0212896i
$214$	−12.3676	−	12.0627i	−0.845431	−	0.824592i
$215$		0			0
$216$	13.4231	+	6.21804i	0.913325	+	0.423084i
$217$	−9.32936	−	6.77818i	−0.633318	−	0.460133i
$218$	10.5465	−	5.54056i	0.714301	−	0.375254i
$219$	5.83149	−	8.02635i	0.394055	−	0.542371i
$220$		0			0
$221$	2.57182	+	3.53981i	0.173000	+	0.238113i
$222$	14.1900	+	7.00852i	0.952368	+	0.470381i
$223$	0.689324	+	2.12152i	0.0461606	+	0.142068i	0.971480	−	0.237120i	$-0.0762035\pi$
$223$	0.689324	+	2.12152i	0.0461606	+	0.142068i	−0.925320	+	0.379188i	$0.876203\pi$
$224$	−16.5575	+	18.7641i	−1.10629	+	1.25373i
$225$		0			0
$226$	−3.55673	−	6.77028i	−0.236590	−	0.450353i
$227$	6.33454	−	2.05822i	0.420438	−	0.136609i	−0.0911544	−	0.995837i	$-0.529056\pi$
$227$	6.33454	−	2.05822i	0.420438	−	0.136609i	0.511593	+	0.859228i	$0.329056\pi$
$228$	0.148649	+	5.95522i	0.00984449	+	0.394394i
$229$	6.45978	+	8.89112i	0.426874	+	0.587542i	0.967232	−	0.253893i	$-0.0817112\pi$
$229$	6.45978	+	8.89112i	0.426874	+	0.587542i	−0.540358	+	0.841435i	$0.681711\pi$
$230$		0			0
$231$	−32.8862	−	23.8932i	−2.16375	−	1.57206i
$232$	−0.695667	+	5.78661i	−0.0456728	+	0.379910i
$233$	−22.0251	−	16.0021i	−1.44291	−	1.04834i	−0.987424	−	0.158092i	$-0.949466\pi$
$233$	−22.0251	−	16.0021i	−1.44291	−	1.04834i	−0.455485	−	0.890243i	$-0.650534\pi$
$234$	−0.00734223	−	0.0428865i	−0.000479977	−	0.00280358i
$235$		0			0
$236$	−0.616693	+	2.07260i	−0.0401433	+	0.134915i
$237$	12.6814	+	4.12044i	0.823746	+	0.267651i
$238$	35.1041	−	6.00987i	2.27546	−	0.389562i
$239$	−3.33646	−	10.2686i	−0.215817	−	0.664218i	−0.999095	−	0.0425450i	$-0.986453\pi$
$239$	−3.33646	−	10.2686i	−0.215817	−	0.664218i	0.783277	−	0.621673i	$-0.213547\pi$
$240$		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	$0.999141\pi$
$242$	3.57145	−	24.5262i	0.229582	−	1.57660i
$243$			0.415968i			0.0266843i
$244$	4.80554	+	13.6234i	0.307643	+	0.872149i
$245$		0			0
$246$	2.63139	−	5.32770i	0.167771	−	0.339682i
$247$	1.07651	−	0.782131i	0.0684968	−	0.0497658i
$248$	1.42512	+	7.23394i	0.0904951	+	0.459356i
$249$	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	$0.790844\pi$
$252$	−0.339455	−	0.101003i	−0.0213836	−	0.00636260i
$253$	16.5527	+	22.7828i	1.04066	+	1.43234i
$254$	16.9578	+	8.37557i	1.06403	+	0.525530i
$255$		0			0
$256$	15.9203	−	1.59453i	0.995022	−	0.0996578i
$257$	11.0336			0.688257			0.344129	−	0.938923i	$-0.388174\pi$
$257$	11.0336			0.688257			0.344129	+	0.938923i	$0.388174\pi$
$258$	2.33222	−	16.0160i	0.145198	−	0.997114i
$259$	−27.3669	−	8.89204i	−1.70049	−	0.552524i
$260$		0			0
$261$	−0.0784474	+	0.0254891i	−0.00485577	+	0.00157774i
$262$	0.843679	+	4.92799i	0.0521227	+	0.304452i
$263$	2.39015	−	7.35613i	0.147383	−	0.453598i	−0.849927	−	0.526901i	$-0.823354\pi$
$263$	2.39015	−	7.35613i	0.147383	−	0.453598i	0.997310	+	0.0733026i	$0.0233539\pi$
$264$	5.02358	+	25.4998i	0.309180	+	1.56941i
$265$		0			0
$266$	−1.82770	−	10.6757i	−0.112063	−	0.654570i
$267$	−12.7433	+	17.5396i	−0.779877	+	1.07341i
$268$	10.4404	+	7.19429i	0.637746	+	0.439461i
$269$	−10.4677	+	14.4075i	−0.638224	+	0.878440i	−0.998519	−	0.0543984i	$-0.982676\pi$
$269$	−10.4677	+	14.4075i	−0.638224	+	0.878440i	0.360295	+	0.932838i	$0.382676\pi$
$270$		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	$0.220983\pi$
$272$	−19.0669	−	12.4486i	−1.15610	−	0.754810i
$273$	−1.80769	−	5.56350i	−0.109406	−	0.336718i
$274$	−14.2293	−	27.0857i	−0.859624	−	1.63631i
$275$		0			0
$276$	−14.9395	−	10.2946i	−0.899250	−	0.619659i
$277$	−19.4363	+	6.31523i	−1.16781	+	0.379445i	−0.827826	−	0.560985i	$-0.810423\pi$
$277$	−19.4363	+	6.31523i	−1.16781	+	0.379445i	−0.339987	+	0.940430i	$0.610423\pi$
$278$	−1.25103	+	2.53292i	−0.0750317	+	0.151915i
$279$	−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	$-0.715353\pi$
$282$	17.3229	−	9.10050i	1.03157	−	0.541927i
$283$	−14.1826	+	19.5207i	−0.843067	+	1.16038i	0.142280	+	0.989826i	$0.454557\pi$
$283$	−14.1826	+	19.5207i	−0.843067	+	1.16038i	−0.985348	+	0.170556i	$0.945443\pi$
$284$	−0.710419	−	0.928186i	−0.0421556	−	0.0550777i
$285$		0			0
$286$	4.05351	−	4.15596i	0.239689	−	0.245747i
$287$	−3.33856	+	10.2750i	−0.197069	+	0.606516i
$288$	0.115181	+	0.194957i	0.00678710	+	0.0114879i
$289$	4.76106	+	14.6531i	0.280063	+	0.861944i
$290$		0			0
$291$	−5.31490	−	1.72691i	−0.311565	−	0.101234i
$292$	10.8763	−	3.83652i	0.636487	−	0.224516i
$293$		−	10.3735i		−	0.606027i	−0.952986	−	0.303014i	$-0.902007\pi$
$293$		−	10.3735i		−	0.606027i	0.952986	−	0.303014i	$-0.0979928\pi$
$294$	−30.2649	−	4.40711i	−1.76508	−	0.257028i
$295$		0			0
$296$	8.96011	+	16.0686i	0.520796	+	0.933966i
$297$	−22.5994	+	16.4194i	−1.31135	+	0.952750i
$298$	−4.66367	−	4.54872i	−0.270159	−	0.263500i
$299$			4.05261i			0.234369i
$300$		0			0
$301$			29.4271i			1.69615i
$302$	1.73965	−	1.78362i	0.100106	−	0.102636i
$303$	5.43197	−	3.94655i	0.312058	−	0.226724i
$304$	−3.78583	+	5.79853i	−0.217132	+	0.332569i
$305$		0			0
$306$	0.0464377	−	0.318901i	0.00265467	−	0.0182304i
$307$			3.04330i			0.173690i	0.996222	+	0.0868452i	$0.0276786\pi$
$307$			3.04330i			0.173690i	−0.996222	+	0.0868452i	$0.972321\pi$
$308$	−15.7193	−	44.5633i	−0.895691	−	2.53923i
$309$	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	$-0.241747\pi$
$312$	−1.57209	+	3.39372i	−0.0890021	+	0.192132i
$313$	−0.0368620	+	0.113450i	−0.00208357	+	0.00641255i	−0.952093	−	0.305809i	$-0.901073\pi$
$313$	−0.0368620	+	0.113450i	−0.00208357	+	0.00641255i	0.950009	+	0.312222i	$0.101073\pi$
$314$	4.39009	+	4.28187i	0.247747	+	0.241640i
$315$		0			0
$316$	9.42109	+	12.3090i	0.529977	+	0.692433i
$317$	−17.2612	+	23.7579i	−0.969483	+	1.33438i	−0.0271752	+	0.999631i	$0.508651\pi$
$317$	−17.2612	+	23.7579i	−0.969483	+	1.33438i	−0.942308	+	0.334748i	$0.891349\pi$
$318$	5.28394	+	10.0581i	0.296309	+	0.564028i
$319$	−8.90369	−	6.46891i	−0.498511	−	0.362189i
$320$		0			0
$321$	−17.0033	+	12.3537i	−0.949034	+	0.689514i
$322$	29.5763	+	14.6079i	1.64822	+	0.814068i
$323$	9.37315	−	3.04552i	0.521536	−	0.169457i
$324$	10.0754	−	14.6214i	0.559743	−	0.812299i
$325$		0			0
$326$	9.04254	−	4.75045i	0.500820	−	0.263103i
$327$	−4.47862	−	13.7838i	−0.247668	−	0.762244i
$328$	6.03303	−	3.36412i	0.333118	−	0.185753i
$329$	−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	$-0.173915\pi$
$332$	11.1944	+	7.71392i	0.614375	+	0.423356i
$333$	−0.153045	+	0.210648i	−0.00838681	+	0.0115434i
$334$	12.5902	−	2.15546i	0.688904	−	0.117941i
$335$		0			0
$336$	19.1010	+	23.7061i	1.04204	+	1.29328i
$337$	9.10115	−	28.0105i	0.495771	−	1.52583i	−0.319980	−	0.947424i	$-0.603676\pi$
$337$	9.10115	−	28.0105i	0.495771	−	1.52583i	0.815751	−	0.578403i	$-0.196324\pi$
$338$	−17.2977	+	2.96138i	−0.940869	+	0.161078i
$339$	−8.84840	+	2.87502i	−0.480579	+	0.156150i
$340$		0			0
$341$	−13.2410	−	4.30227i	−0.717042	−	0.232981i
$342$	−0.0969828	−	0.0141224i	−0.00524423	−	0.000763654i
$343$	24.6407			1.33048
$344$	12.7968	−	13.7926i	0.689956	−	0.743646i
$345$		0			0
$346$	8.57692	−	17.3655i	0.461098	−	0.933573i
$347$	2.49468	+	3.43363i	0.133921	+	0.184327i	0.870711	−	0.491795i	$-0.163659\pi$
$347$	2.49468	+	3.43363i	0.133921	+	0.184327i	−0.736789	+	0.676122i	$0.763659\pi$
$348$	6.79592	+	2.02209i	0.364300	+	0.108396i
$349$		−	16.7792i		−	0.898172i	−0.893488	−	0.449086i	$-0.851750\pi$
$349$		−	16.7792i		−	0.898172i	0.893488	−	0.449086i	$-0.148250\pi$
$350$		0			0
$351$	−4.01998			−0.214570
$352$	−12.0112	+	27.7227i	−0.640201	+	1.47762i
$353$	27.9383	−	20.2984i	1.48701	−	1.08037i	0.511794	−	0.859108i	$-0.328981\pi$
$353$	27.9383	−	20.2984i	1.48701	−	1.08037i	0.975213	−	0.221266i	$-0.0710189\pi$
$354$	2.35866	+	1.16496i	0.125361	+	0.0619168i
$355$		0			0
$356$	−23.7675	+	8.38379i	−1.25968	+	0.444340i
$357$		−	43.3271i		−	2.29311i
$358$	−9.98489	−	1.45398i	−0.527718	−	0.0768452i
$359$	−1.03463	+	3.18426i	−0.0546057	+	0.168059i	−0.974640	−	0.223779i	$-0.928161\pi$
$359$	−1.03463	+	3.18426i	−0.0546057	+	0.168059i	0.920034	+	0.391838i	$0.128161\pi$
$360$		0			0
$361$	4.94513	+	15.2196i	0.260270	+	0.801029i
$362$	−0.673175	−	3.93206i	−0.0353813	−	0.206665i
$363$	−28.6762	−	9.31745i	−1.50511	−	0.489039i
$364$	1.93937	−	6.51789i	0.101651	−	0.341630i
$365$		0			0
$366$	17.3224	−	2.96561i	0.905454	−	0.155015i
$367$	7.89027	+	5.73261i	0.411869	+	0.299240i	0.774358	−	0.632748i	$-0.218073\pi$
$367$	7.89027	+	5.73261i	0.411869	+	0.299240i	−0.362489	+	0.931988i	$0.618073\pi$
$368$	−7.51004	−	19.7084i	−0.391488	−	1.02737i
$369$	0.0790890	+	0.0574615i	0.00411721	+	0.00299133i
$370$		0			0
$371$	−12.1421	−	16.7121i	−0.630385	−	0.867651i
$372$	8.96679	−	0.223821i	0.464906	−	0.0116046i
$373$	−17.5633	+	5.70667i	−0.909395	+	0.295480i	−0.726109	−	0.687579i	$-0.758673\pi$
$373$	−17.5633	+	5.70667i	−0.909395	+	0.295480i	−0.183286	+	0.983060i	$0.558673\pi$
$374$	38.0653	−	19.9974i	1.96831	−	1.03404i
$375$		0			0
$376$	22.5847	+	2.71514i	1.16472	+	0.140022i
$377$	−0.489418	−	1.50627i	−0.0252063	−	0.0775770i
$378$	−14.4903	+	29.3381i	−0.745299	+	1.50899i
$379$	15.5245	+	21.3676i	0.797439	+	1.09758i	0.993142	+	0.116917i	$0.0373013\pi$
$379$	15.5245	+	21.3676i	0.797439	+	1.09758i	−0.195703	+	0.980663i	$0.562699\pi$
$380$		0			0
$381$	13.5244	−	18.6147i	0.692875	−	0.953661i
$382$	−9.28006	−	17.6647i	−0.474809	−	0.903806i
$383$	16.9911	+	12.3447i	0.868203	+	0.630787i	0.930104	−	0.367296i	$-0.119716\pi$
$383$	16.9911	+	12.3447i	0.868203	+	0.630787i	−0.0619009	+	0.998082i	$0.519716\pi$
$384$	1.35626	−	19.4174i	0.0692111	−	0.990892i
$385$		0			0
$386$	−6.79168	+	6.96332i	−0.345687	+	0.354424i
$387$	0.253242	+	0.0822833i	0.0128730	+	0.00418269i
$388$	−3.94846	−	5.15880i	−0.200453	−	0.261899i
$389$	14.0198	−	4.55530i	0.710830	−	0.230963i	0.0687872	−	0.997631i	$-0.478087\pi$
$389$	14.0198	−	4.55530i	0.710830	−	0.230963i	0.642043	+	0.766669i	$0.278087\pi$
$390$		0			0
$391$	−9.27547	+	28.5470i	−0.469081	+	1.44368i
$392$	−26.0633	−	24.1816i	−1.31640	−	1.22135i
$393$	6.08236			0.306814
$394$	17.0618	+	2.48450i	0.859559	+	0.125167i
$395$		0			0
$396$	−0.427453	+	0.0106697i	−0.0214803	+	0.000536172i
$397$	−14.4476	−	19.8855i	−0.725106	−	0.998023i	−0.999339	−	0.0363595i	$-0.988424\pi$
$397$	−14.4476	−	19.8855i	−0.725106	−	0.998023i	0.274233	−	0.961663i	$-0.411576\pi$
$398$	−14.5851	+	14.9537i	−0.731083	+	0.749559i
$399$	−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	$0.472801\pi$
$402$	10.7699	−	11.0421i	0.537156	−	0.550732i
$403$	−1.17766	−	1.62091i	−0.0586633	−	0.0807431i
$404$	7.80280	−	0.194766i	0.388204	−	0.00968998i
$405$		0			0
$406$	−12.7570	−	1.85765i	−0.633121	−	0.0921939i
$407$	−34.7408			−1.72204
$408$	−18.8414	+	20.3075i	−0.932787	+	1.00537i
$409$	1.50524	−	4.63264i	0.0744292	−	0.229069i	−0.906920	−	0.421303i	$-0.861573\pi$
$409$	1.50524	−	4.63264i	0.0744292	−	0.229069i	0.981349	+	0.192233i	$0.0615730\pi$
$410$		0			0
$411$	−35.3996	+	11.5020i	−1.74613	+	0.567352i
$412$	23.2257	+	30.3451i	1.14425	+	1.49500i
$413$	−4.54893	−	1.47804i	−0.223838	−	0.0727294i
$414$	0.208412	−	0.213679i	0.0102429	−	0.0105018i
$415$		0			0
$416$	−3.74338	+	2.21159i	−0.183534	+	0.108432i
$417$	2.78041	+	2.02009i	0.136157	+	0.0989240i
$418$	−6.08152	−	11.5762i	−0.297457	−	0.566213i
$419$	−2.28269	+	3.14185i	−0.111517	+	0.153489i	−0.861127	−	0.508390i	$-0.830241\pi$
$419$	−2.28269	+	3.14185i	−0.111517	+	0.153489i	0.749610	+	0.661879i	$0.230241\pi$
$420$		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	$0.854801\pi$
$422$	1.44454	−	2.92471i	0.0703189	−	0.142373i
$423$	0.0994821	+	0.306175i	0.00483699	+	0.0148867i
$424$	−1.57646	+	13.1132i	−0.0765599	+	0.636832i
$425$		0			0
$426$	−1.25883	+	0.661319i	−0.0609905	+	0.0320410i
$427$	−30.3895	+	9.87415i	−1.47065	+	0.477843i
$428$	−24.4246	+	0.609664i	−1.18061	+	0.0294692i
$429$	−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	$0.714431\pi$
$432$	19.5497	−	7.44956i	0.940585	−	0.358417i
$433$	5.28222	+	3.83776i	0.253847	+	0.184431i	0.707430	−	0.706783i	$-0.249854\pi$
$433$	5.28222	+	3.83776i	0.253847	+	0.184431i	−0.453583	+	0.891214i	$0.649854\pi$
$434$	−16.0745	+	2.75197i	−0.771598	+	0.132099i
$435$		0			0
$436$	4.80485	−	16.1483i	0.230111	−	0.773363i
$437$	8.68158	+	2.82082i	0.415296	+	0.134938i
$438$	−2.36761	−	13.8294i	−0.113129	−	0.660793i
$439$	8.75988	+	26.9601i	0.418086	+	1.28674i	0.909461	+	0.415789i	$0.136494\pi$
$439$	8.75988	+	26.9601i	0.418086	+	1.28674i	−0.491375	+	0.870948i	$0.663506\pi$
$440$		0			0
$441$	0.155488	−	0.478542i	0.00740417	−	0.0227877i
$442$	6.12324	+	0.891654i	0.291253	+	0.0424116i
$443$		−	25.7646i		−	1.22412i	−0.790813	−	0.612058i	$-0.790342\pi$
$443$		−	25.7646i		−	1.22412i	0.790813	−	0.612058i	$-0.209658\pi$
$444$	21.1072	−	7.44540i	1.00170	−	0.353343i
$445$		0			0
$446$	2.82850	+	1.39701i	0.133933	+	0.0661505i
$447$	−6.41176	+	4.65842i	−0.303266	+	0.220336i
$448$	2.64712	+	35.2913i	0.125065	+	1.66736i
$449$	−4.58045			−0.216165			−0.108082	−	0.994142i	$-0.534471\pi$
$449$	−4.58045			−0.216165			−0.108082	+	0.994142i	$0.534471\pi$
$450$		0			0
$451$			13.0436i			0.614200i
$452$	−10.3663	−	3.08445i	−0.487590	−	0.145080i
$453$	−1.78161	−	2.45217i	−0.0837072	−	0.115213i
$454$	4.17127	−	8.44546i	0.195767	−	0.396365i
$455$		0			0
$456$	6.17584	+	5.72995i	0.289210	+	0.268330i
$457$	−10.4431			−0.488509			−0.244255	−	0.969711i	$-0.578543\pi$
$457$	−10.4431			−0.488509			−0.244255	+	0.969711i	$0.578543\pi$
$458$	15.3800	+	2.23961i	0.718662	+	0.104650i
$459$	−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	$0.662503\pi$
$462$	−56.6628	+	9.70076i	−2.63619	+	0.451320i
$463$	4.16244	−	12.8107i	0.193445	−	0.595362i	−0.806546	−	0.591171i	$-0.798666\pi$
$463$	4.16244	−	12.8107i	0.193445	−	0.595362i	0.999991	−	0.00419137i	$-0.00133416\pi$
$464$	5.17143	+	6.41825i	0.240078	+	0.297960i
$465$		0			0
$466$	−37.9491	+	6.49694i	−1.75796	+	0.300965i
$467$	11.3230	−	15.5848i	0.523968	−	0.721180i	−0.462228	−	0.886761i	$-0.652950\pi$
$467$	11.3230	−	15.5848i	0.523968	−	0.721180i	0.986196	+	0.165581i	$0.0529499\pi$
$468$	−0.0506684	−	0.0349148i	−0.00234215	−	0.00161394i
$469$	−16.4843	+	22.6888i	−0.761176	+	1.04767i
$470$		0			0
$471$	6.03563	−	4.38514i	0.278107	−	0.202057i
$472$	1.48935	+	2.67092i	0.0685530	+	0.122939i
$473$	10.9787	+	33.7890i	0.504802	+	1.55362i
$474$	16.6937	−	8.76995i	0.766768	−	0.402817i
$475$		0			0
$476$	28.5790	−	41.4738i	1.30992	−	1.90095i
$477$	−0.177771	+	0.0577614i	−0.00813959	+	0.00264471i
$478$	−13.6905	−	6.76180i	−0.626187	−	0.309278i
$479$	16.2835	−	11.8306i	0.744010	−	0.540555i	−0.149954	−	0.988693i	$-0.547913\pi$
$479$	16.2835	−	11.8306i	0.744010	−	0.540555i	0.893964	+	0.448138i	$0.147913\pi$
$480$		0			0
$481$	−4.04467	−	2.93862i	−0.184421	−	0.133990i
$482$	6.36277	+	12.1116i	0.289816	+	0.551669i
$483$	23.5880	−	32.4661i	1.07329	−	1.47726i
$484$	−21.3037	−	27.8340i	−0.968349	−	1.26518i
$485$		0			0
$486$	0.421126	+	0.410745i	0.0191027	+	0.0186318i
$487$	8.72080	−	26.8399i	0.395177	−	1.21623i	−0.533646	−	0.845708i	$-0.679179\pi$
$487$	8.72080	−	26.8399i	0.395177	−	1.21623i	0.928823	−	0.370523i	$-0.120821\pi$
$488$	18.5375	+	8.58723i	0.839155	+	0.388726i
$489$	−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	$0.300628\pi$
$492$	−2.79541	−	7.92482i	−0.126027	−	0.357279i
$493$		−	11.7305i		−	0.528314i
$494$	0.271166	−	1.86217i	0.0122003	−	0.0837831i
$495$		0			0
$496$	8.73087	+	5.70033i	0.392028	+	0.255952i
$497$	2.09163	−	1.51966i	0.0938224	−	0.0681659i
$498$	11.5478	−	11.8397i	0.517471	−	0.530549i
$499$			26.6004i			1.19080i	0.803430	+	0.595399i	$0.203006\pi$
$499$			26.6004i			1.19080i	−0.803430	+	0.595399i	$0.796994\pi$
$500$		0			0
$501$		−	15.5394i		−	0.694248i
$502$	19.5941	+	19.1111i	0.874526	+	0.852969i
$503$	−16.8678	+	12.2552i	−0.752097	+	0.546430i	−0.896476	−	0.443092i	$-0.853882\pi$
$503$	−16.8678	+	12.2552i	−0.752097	+	0.546430i	0.144379	+	0.989522i	$0.453882\pi$
$504$	−0.437448	+	0.243929i	−0.0194855	+	0.0108655i
$505$		0			0
$506$	39.4102	+	5.73884i	1.75200	+	0.255122i
$507$			21.3496i			0.948168i
$508$	25.2243	−	8.89767i	1.11915	−	0.394770i
$509$	34.2578	+	11.1310i	1.51845	+	0.493374i	0.945335	−	0.326101i	$-0.105735\pi$
$509$	34.2578	+	11.1310i	1.51845	+	0.493374i	0.573115	+	0.819475i	$0.305735\pi$
$510$		0			0
$511$	7.88306	+	24.2616i	0.348726	+	1.07327i
$512$	14.1062	−	17.6923i	0.623410	−	0.781895i
$513$	−2.79810	+	8.61166i	−0.123539	+	0.380214i
$514$	10.8951	−	11.1704i	0.480561	−	0.492706i
$515$		0			0
$516$	−13.9117	−	18.1761i	−0.612427	−	0.800157i
$517$	−25.2477	+	34.7504i	−1.11039	+	1.52832i
$518$	−36.0256	+	18.9258i	−1.58287	+	0.831553i
$519$	−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	$0.0278144\pi$
$522$	−0.0516573	+	0.104589i	−0.00226098	+	0.00457775i
$523$	−30.3045	+	9.84654i	−1.32512	+	0.430559i	−0.884252	−	0.467011i	$-0.845331\pi$
$523$	−30.3045	+	9.84654i	−1.32512	+	0.430559i	−0.440873	+	0.897570i	$0.645331\pi$
$524$	5.82219	+	4.01198i	0.254343	+	0.175264i
$525$		0			0
$526$	−5.08720	−	9.68356i	−0.221812	−	0.422223i
$527$	−4.58565	−	14.1132i	−0.199754	−	0.614780i
$528$	30.7765	+	20.0938i	1.33938	+	0.874471i
$529$	−3.88440	+	2.82218i	−0.168887	+	0.122704i
$530$		0			0
$531$	−0.0254391	+	0.0350140i	−0.00110396	+	0.00151948i
$532$	−12.6128	−	8.69131i	−0.546836	−	0.376816i
$533$	−1.10332	+	1.51859i	−0.0477902	+	0.0657775i
$534$	5.17383	+	30.2207i	0.223894	+	1.30778i
$535$		0			0
$536$	17.5928	−	3.46585i	0.759892	−	0.149702i
$537$	−3.79324	+	11.6744i	−0.163691	+	0.503788i
$538$	4.24991	+	24.8240i	0.183227	+	1.07024i
$539$	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	$0.451781\pi$
$542$	1.64850	−	11.3207i	0.0708091	−	0.486266i
$543$	−4.85313			−0.208268
$544$	−31.4305	+	7.01095i	−1.34757	+	0.300592i
$545$		0			0
$546$	−7.41748	−	3.66354i	−0.317439	−	0.156785i
$547$	−17.7386	−	24.4151i	−0.758450	−	1.04392i	−0.997341	−	0.0728702i	$-0.976784\pi$
$547$	−17.7386	−	24.4151i	−0.758450	−	1.04392i	0.238892	−	0.971046i	$-0.423216\pi$
$548$	−41.4722	−	12.3399i	−1.77160	−	0.527133i
$549$			0.289133i			0.0123399i
$550$		0			0
$551$	−3.56742			−0.151977
$552$	−25.1741	+	4.95940i	−1.07148	+	0.211086i
$553$	−27.7377	+	20.1526i	−1.17953	+	0.856978i
$554$	−12.7987	+	25.9132i	−0.543765	+	1.10095i
$555$		0			0
$556$	1.32901	+	3.76766i	0.0563626	+	0.159784i
$557$		−	0.749572i		−	0.0317604i	−0.999874	−	0.0158802i	$-0.994945\pi$
$557$		−	0.749572i		−	0.0317604i	0.999874	−	0.0158802i	$-0.00505504\pi$
$558$	−0.0212642	+	0.146027i	−0.000900186	+	0.00618183i
$559$	−1.57993	+	4.86251i	−0.0668237	+	0.205662i
$560$		0			0
$561$	−16.1645	−	49.7493i	−0.682467	−	2.10042i
$562$	−45.0905	+	7.71955i	−1.90203	+	0.325630i
$563$	22.1519	+	7.19759i	0.933591	+	0.303342i	0.736030	−	0.676949i	$-0.236698\pi$
$563$	22.1519	+	7.19759i	0.933591	+	0.303342i	0.197561	+	0.980291i	$0.436698\pi$
$564$	7.89209	−	26.5240i	0.332317	−	1.11686i
$565$		0			0
$566$	5.75819	+	33.6340i	0.242035	+	1.41374i
$567$	31.7749	+	23.0858i	1.33442	+	0.969512i
$568$	−1.64120	−	0.197305i	−0.0688630	−	0.00827871i
$569$	−6.07930	−	4.41687i	−0.254858	−	0.185165i	0.453019	−	0.891501i	$-0.350347\pi$
$569$	−6.07930	−	4.41687i	−0.254858	−	0.185165i	−0.707877	+	0.706336i	$0.750347\pi$
$570$		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	$0.815623\pi$
$572$	−0.204869	−	8.20755i	−0.00856601	−	0.343175i
$573$	−23.0869	+	7.50138i	−0.964468	+	0.313375i
$574$	7.10580	+	13.5260i	0.296590	+	0.564564i
$575$		0			0
$576$	0.311109	+	0.0759000i	0.0129629	+	0.00316250i
$577$	−6.60875	−	20.3396i	−0.275126	−	0.846750i	−0.989186	−	0.146666i	$-0.953146\pi$
$577$	−6.60875	−	20.3396i	−0.275126	−	0.846750i	0.714060	−	0.700084i	$-0.246854\pi$
$578$	19.5360	+	9.64897i	0.812592	+	0.401344i
$579$	6.95547	+	9.57339i	0.289060	+	0.397856i
$580$		0			0
$581$	−17.6750	+	24.3275i	−0.733282	+	1.00928i
$582$	−6.99649	+	3.67557i	−0.290014	+	0.152357i
$583$	−20.1768	−	14.6593i	−0.835639	−	0.607127i
$584$	6.85565	−	14.7995i	0.283689	−	0.612409i
$585$		0			0
$586$	−10.5021	−	10.2433i	−0.433840	−	0.423146i
$587$	6.66288	+	2.16490i	0.275007	+	0.0893551i	0.443274	−	0.896386i	$-0.353817\pi$
$587$	6.66288	+	2.16490i	0.275007	+	0.0893551i	−0.168267	+	0.985741i	$0.553817\pi$
$588$	−34.3466	+	26.2884i	−1.41643	+	1.08411i
$589$	−4.29204	+	1.39457i	−0.176850	+	0.0574622i
$590$		0			0
$591$	6.48173	−	19.9487i	0.266623	−	0.820581i
$592$	25.1154	+	6.79560i	1.03224	+	0.279298i
$593$	28.8406			1.18434			0.592171	−	0.805812i	$-0.298271\pi$
$593$	28.8406			1.18434			0.592171	+	0.805812i	$0.298271\pi$
$594$	−5.69262	+	39.0928i	−0.233571	+	1.60400i
$595$		0			0
$596$	−9.21024	+	0.229897i	−0.377266	+	0.00941696i
$597$	14.9368	+	20.5587i	0.611323	+	0.841414i
$598$	4.10287	+	4.00173i	0.167779	+	0.163643i
$599$	−2.36104			−0.0964695			−0.0482347	−	0.998836i	$-0.515360\pi$
$599$	−2.36104			−0.0964695			−0.0482347	+	0.998836i	$0.515360\pi$
$600$		0			0
$601$	−15.1806			−0.619228			−0.309614	−	0.950862i	$-0.600200\pi$
$601$	−15.1806			−0.619228			−0.309614	+	0.950862i	$0.600200\pi$
$602$	29.7920	+	29.0577i	1.21423	+	1.18430i
$603$	0.149160	+	0.205301i	0.00607427	+	0.00836052i
$604$	−0.0879239	−	3.52244i	−0.00357757	−	0.143326i
$605$		0			0
$606$	1.36827	−	9.39632i	0.0555823	−	0.381700i
$607$	−34.1325			−1.38540			−0.692699	−	0.721227i	$-0.743578\pi$
$607$	−34.1325			−1.38540			−0.692699	+	0.721227i	$0.743578\pi$
$608$	2.13214	+	9.55850i	0.0864697	+	0.387648i
$609$	−4.84638	+	14.9156i	−0.196385	+	0.604411i
$610$		0			0
$611$	−5.87887	+	1.91016i	−0.237834	+	0.0772769i
$612$	−0.277001	−	0.361911i	−0.0111971	−	0.0146294i
$613$	−5.67158	−	1.84281i	−0.229073	−	0.0744303i	0.192231	−	0.981350i	$-0.438428\pi$
$613$	−5.67158	−	1.84281i	−0.229073	−	0.0744303i	−0.421304	+	0.906919i	$0.638428\pi$
$614$	3.08104	+	3.00509i	0.124341	+	0.121276i
$615$		0			0
$616$	−60.6378	−	28.0895i	−2.44317	−	1.13176i
$617$	6.15928	+	4.47498i	0.247963	+	0.180156i	0.704824	−	0.709383i	$-0.251026\pi$
$617$	6.15928	+	4.47498i	0.247963	+	0.180156i	−0.456860	+	0.889538i	$0.651026\pi$
$618$	41.1548	−	21.6204i	1.65549	−	0.869701i
$619$	16.7671	−	23.0779i	0.673925	−	0.927579i	−0.325916	−	0.945399i	$-0.605673\pi$
$619$	16.7671	−	23.0779i	0.673925	−	0.927579i	0.999841	+	0.0178200i	$0.00567259\pi$
$620$		0			0
$621$	−16.2096	−	22.3107i	−0.650470	−	0.895296i
$622$	−19.2637	−	9.51446i	−0.772403	−	0.381495i
$623$	−17.2265	−	53.0178i	−0.690166	−	2.12411i
$624$	1.88345	+	4.94270i	0.0753985	+	0.197866i
$625$		0			0
$626$	0.0784572	+	0.149344i	0.00313578	+	0.00596900i
$627$	−15.1295	+	4.91589i	−0.604216	+	0.196322i
$628$	8.66993	−	0.216411i	0.345968	−	0.00863573i
$629$	−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	$0.460709\pi$
$632$	21.7644	+	2.61652i	0.865741	+	0.104079i
$633$	−3.21048	−	2.33255i	−0.127605	−	0.0927106i
$634$	7.00810	+	40.9348i	0.278327	+	1.62573i
$635$		0			0
$636$	15.4004	+	4.58231i	0.610665	+	0.181700i
$637$	9.18851	+	2.98553i	0.364062	+	0.118291i
$638$	−15.3410	+	2.62640i	−0.607357	+	0.103980i
$639$	−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	$-0.173533\pi$
$642$	−4.28303	+	29.4127i	−0.169038	+	1.16083i
$643$		−	4.80260i		−	0.189396i	−0.995506	−	0.0946980i	$-0.969811\pi$
$643$		−	4.80260i		−	0.189396i	0.995506	−	0.0946980i	$-0.0301885\pi$
$644$	43.9940	−	15.5185i	1.73361	−	0.611515i
$645$		0			0
$646$	6.17218	−	12.4967i	0.242841	−	0.491675i
$647$	−3.05732	+	2.22128i	−0.120196	+	0.0873273i	−0.646259	−	0.763118i	$-0.723667\pi$
$647$	−3.05732	+	2.22128i	−0.120196	+	0.0873273i	0.526063	+	0.850445i	$0.323667\pi$
$648$	−4.85381	−	24.6381i	−0.190676	−	0.967876i
$649$	−5.77462			−0.226674
$650$		0			0
$651$			19.8398i			0.777584i
$652$	4.11966	−	13.8455i	0.161338	−	0.542231i
$653$	−23.3583	−	32.1500i	−0.914082	−	1.25813i	−0.965753	−	0.259462i	$-0.916455\pi$
$653$	−23.3583	−	32.1500i	−0.914082	−	1.25813i	0.0516709	−	0.998664i	$-0.483545\pi$
$654$	−18.3771	−	9.07655i	−0.718600	−	0.354921i
$655$		0			0
$656$	2.55144	−	9.42972i	0.0996172	−	0.368169i
$657$	0.230831			0.00900557
$658$	−7.25029	+	49.7898i	−0.282646	+	1.94101i
$659$	−14.7150	−	4.78119i	−0.573214	−	0.186249i	0.00804417	−	0.999968i	$-0.497439\pi$
$659$	−14.7150	−	4.78119i	−0.573214	−	0.186249i	−0.581258	+	0.813719i	$0.697439\pi$
$660$		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	$0.194147\pi$
$662$	−8.01110	−	46.7934i	−0.311360	−	1.81868i
$663$	2.32621	−	7.15933i	0.0903424	−	0.278045i
$664$	18.8635	−	3.71618i	0.732044	−	0.144216i
$665$		0			0
$666$	0.0621369	+	0.362946i	0.00240775	+	0.0140639i
$667$	6.38627	−	8.78995i	0.247277	−	0.340348i
$668$	10.2499	−	14.8747i	0.396581	−	0.575519i
$669$	2.25582	−	3.10486i	0.0872149	−	0.120041i
$670$		0			0
$671$	−31.2101	+	22.6755i	−1.20485	+	0.875378i
$672$	42.8612	+	4.07070i	1.65341	+	0.157031i
$673$	−8.86070	−	27.2704i	−0.341555	−	1.05120i	−0.963402	−	0.268059i	$-0.913618\pi$
$673$	−8.86070	−	27.2704i	−0.341555	−	1.05120i	0.621848	−	0.783138i	$-0.286382\pi$
$674$	−19.3709	−	36.8728i	−0.746139	−	1.42029i
$675$		0			0
$676$	−14.0824	+	20.4364i	−0.541630	+	0.786014i
$677$	28.2591	−	9.18195i	1.08609	−	0.352891i	0.289353	−	0.957222i	$-0.406560\pi$
$677$	28.2591	−	9.18195i	1.08609	−	0.352891i	0.796733	+	0.604331i	$0.206560\pi$
$678$	−5.82664	+	11.7970i	−0.223771	+	0.453063i
$679$	11.6251	−	8.44616i	0.446132	−	0.324134i
$680$		0			0
$681$	−9.27065	−	6.73552i	−0.355252	−	0.258106i
$682$	−17.4304	+	9.15696i	−0.667444	+	0.350638i
$683$	1.03849	−	1.42936i	0.0397366	−	0.0546928i	−0.788686	−	0.614796i	$-0.789238\pi$
$683$	1.03849	−	1.42936i	0.0397366	−	0.0546928i	0.828423	+	0.560103i	$0.189238\pi$
$684$	−0.110063	+	0.0842402i	−0.00420835	+	0.00322100i
$685$		0			0
$686$	24.3314	−	24.9463i	0.928976	−	0.952454i
$687$	5.84285	−	17.9825i	0.222919	−	0.686073i
$688$	−1.32750	−	26.5749i	−0.0506105	−	1.01316i
$689$	−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	$0.679399\pi$
$692$	−9.11156	−	25.8307i	−0.346370	−	0.981936i
$693$		−	0.945779i		−	0.0359272i
$694$	5.93957	+	0.864908i	0.225463	+	0.0328315i
$695$		0			0
$696$	8.75776	−	4.88348i	0.331962	−	0.185108i
$697$	−11.2476	+	8.17185i	−0.426033	+	0.309531i
$698$	−16.9873	−	16.5686i	−0.642979	−	0.627130i
$699$			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	$-0.0604713\pi$
$702$	−3.96950	+	4.06982i	−0.149819	+	0.153606i
$703$	−9.11045	+	6.61913i	−0.343607	+	0.249645i
$704$	16.2060	+	39.5348i	0.610787	+	1.49002i
$705$		0			0
$706$	7.03747	−	48.3283i	0.264859	−	1.81886i
$707$			17.2644i			0.649295i
$708$	3.50845	−	1.23758i	0.131856	−	0.0465109i
$709$	−39.3712	−	12.7925i	−1.47862	−	0.480432i	−0.544918	−	0.838490i	$-0.683439\pi$
$709$	−39.3712	−	12.7925i	−1.47862	−	0.480432i	−0.933699	+	0.358058i	$0.883439\pi$
$710$		0			0
$711$	0.0958687	+	0.295054i	0.00359536	+	0.0110654i
$712$	−14.9814	+	32.3408i	−0.561450	+	1.21202i
$713$	4.24731	−	13.0719i	0.159063	−	0.489546i
$714$	−43.8644	−	42.7831i	−1.64158	−	1.60112i
$715$		0			0
$716$	−11.3315	+	8.67298i	−0.423479	+	0.324124i
$717$	−10.9186	+	15.0281i	−0.407761	+	0.561235i
$718$	2.20211	+	4.19174i	0.0821819	+	0.156434i
$719$	27.1580	+	19.7314i	1.01282	+	0.735858i	0.964799	−	0.262988i	$-0.0847080\pi$
$719$	27.1580	+	19.7314i	1.01282	+	0.735858i	0.0480227	+	0.998846i	$0.484708\pi$
$720$		0			0
$721$	−68.3814	+	49.6820i	−2.54666	+	1.85026i
$722$	20.2913	+	10.0220i	0.755165	+	0.372981i
$723$	15.8292	−	5.14323i	0.588696	−	0.191279i
$724$	−4.64554	−	3.20117i	−0.172650	−	0.118971i
$725$		0			0
$726$	−37.7491	+	19.8313i	−1.40100	+	0.736008i
$727$	−13.7860	−	42.4290i	−0.511295	−	1.57360i	−0.789924	−	0.613204i	$-0.789880\pi$
$727$	−13.7860	−	42.4290i	−0.511295	−	1.57360i	0.278630	−	0.960399i	$-0.410120\pi$
$728$	−4.68369	−	8.39947i	−0.173589	−	0.311305i
$729$	22.1271	−	16.0763i	0.819522	−	0.595417i
$730$		0			0
$731$	−22.2583	+	30.6359i	−0.823251	+	1.13311i
$732$	14.1025	−	20.4655i	0.521243	−	0.756428i
$733$	25.5474	−	35.1630i	0.943615	−	1.29877i	−0.0106913	−	0.999943i	$-0.503403\pi$
$733$	25.5474	−	35.1630i	0.943615	−	1.29877i	0.954306	−	0.298831i	$-0.0965968\pi$
$734$	13.5949	−	2.32747i	0.501797	−	0.0859083i
$735$		0			0
$736$	−27.3685	−	11.8578i	−1.00882	−	0.437084i
$737$	−10.4630	+	32.2018i	−0.385410	+	1.18617i
$738$	0.136270	−	0.0233296i	0.00501617	−	0.000858775i
$739$	18.2840	−	5.94083i	0.672588	−	0.218537i	0.0472404	−	0.998884i	$-0.484957\pi$
$739$	18.2840	−	5.94083i	0.672588	−	0.218537i	0.625347	+	0.780347i	$0.284957\pi$
$740$		0			0
$741$	−2.17726	−	0.707436i	−0.0799838	−	0.0259883i
$742$	−28.9090	−	4.20967i	−1.06128	−	0.154542i
$743$	−35.7627			−1.31200			−0.656002	−	0.754759i	$-0.727754\pi$
$743$	−35.7627			−1.31200			−0.656002	+	0.754759i	$0.727754\pi$
$744$	8.62761	−	9.29898i	0.316303	−	0.340917i
$745$		0			0
$746$	−11.5654	+	23.4161i	−0.423439	+	0.857326i
$747$	0.159934	+	0.220130i	0.00585167	+	0.00805414i
$748$	17.3420	−	58.2836i	0.634087	−	2.13106i
$749$		−	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	$0.452560\pi$
$752$	25.0500	−	20.1837i	0.913478	−	0.736025i
$753$	26.9385	−	19.5720i	0.981695	−	0.713243i
$754$	−2.00822	−	0.991875i	−0.0731352	−	0.0361219i
$755$		0			0
$756$	15.3935	+	43.6397i	0.559858	+	1.58716i
$757$		−	42.4947i		−	1.54450i	−0.635321	−	0.772248i	$-0.719132\pi$
$757$		−	42.4947i		−	1.54450i	0.635321	−	0.772248i	$-0.280868\pi$
$758$	36.9621	+	5.38235i	1.34253	+	0.195496i
$759$	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	$0.653832\pi$
$762$	−5.49096	−	32.0731i	−0.198916	−	1.16189i
$763$	35.4421	+	11.5158i	1.28309	+	0.416902i
$764$	−27.0473	−	8.04781i	−0.978538	−	0.291159i
$765$		0			0
$766$	29.2756	−	5.01202i	1.05777	−	0.181091i
$767$	−0.672305	−	0.488458i	−0.0242755	−	0.0176372i
$768$	−18.3190	−	20.5467i	−0.661029	−	0.741416i
$769$	−29.0252	−	21.0880i	−1.04667	−	0.760454i	−0.0750973	−	0.997176i	$-0.523927\pi$
$769$	−29.0252	−	21.0880i	−1.04667	−	0.760454i	−0.971577	+	0.236723i	$0.923927\pi$
$770$		0			0
$771$	−11.1578	−	15.3574i	−0.401839	−	0.553084i
$772$	0.343259	+	13.7518i	0.0123542	+	0.494937i
$773$	1.68376	−	0.547088i	0.0605607	−	0.0196774i	−0.278580	−	0.960413i	$-0.589864\pi$
$773$	1.68376	−	0.547088i	0.0605607	−	0.0196774i	0.339141	+	0.940736i	$0.389864\pi$
$774$	0.333366	−	0.175132i	0.0119826	−	0.00629498i
$775$		0			0
$776$	−9.12166	−	1.09661i	−0.327449	−	0.0393659i
$777$	15.2984	+	47.0835i	0.548826	+	1.68911i
$778$	9.23196	−	18.6917i	0.330982	−	0.670130i
$779$	2.48519	+	3.42057i	0.0890411	+	0.122554i
$780$		0			0
$781$	1.83471	−	2.52526i	0.0656510	−	0.0903608i
$782$	19.7419	+	37.5790i	0.705970	+	1.34382i
$783$	8.71916	+	6.33484i	0.311597	+	0.226389i
$784$	−50.2175	+	2.50853i	−1.79348	+	0.0895903i
$785$		0			0
$786$	6.00599	−	6.15778i	0.214227	−	0.219641i
$787$	−1.09587	−	0.356070i	−0.0390636	−	0.0126925i	0.289420	−	0.957202i	$-0.406538\pi$
$787$	−1.09587	−	0.356070i	−0.0390636	−	0.0126925i	−0.328484	+	0.944510i	$0.606538\pi$
$788$	19.3628	−	14.8200i	0.689773	−	0.527941i
$789$	−12.6559	+	4.11215i	−0.450562	+	0.146396i
$790$		0			0
$791$	7.39253	−	22.7519i	0.262848	−	0.808963i
$792$	−0.411284	+	0.443289i	−0.0146144	+	0.0157516i
$793$	−5.55167			−0.197145
$794$	−34.3983	−	5.00901i	−1.22075	−	0.177763i
$795$		0			0
$796$	0.737145	+	29.5318i	0.0261274	+	1.04673i
$797$	−25.0783	−	34.5173i	−0.888319	−	1.22267i	−0.974047	−	0.226347i	$-0.927322\pi$
$797$	−25.0783	−	34.5173i	−0.888319	−	1.22267i	0.0857282	−	0.996319i	$-0.472678\pi$
$798$	−13.0110	+	13.3398i	−0.460585	+	0.472225i
$799$	−45.7832			−1.61969
$800$		0			0
$801$	−0.504425			−0.0178230
$802$	3.37511	−	3.46041i	0.119179	−	0.122191i
$803$	18.1031	+	24.9167i	0.638844	+	0.879293i
$804$	−0.544326	−	21.8070i	−0.0191969	−	0.769073i
$805$		0			0
$806$	−2.80388	−	0.408295i	−0.0987624	−	0.0143816i
$807$	30.6390			1.07854
$808$	7.50765	−	8.09187i	0.264118	−	0.284671i
$809$	−17.2761	+	53.1704i	−0.607396	+	1.86937i	−0.127999	+	0.991774i	$0.540855\pi$
$809$	−17.2761	+	53.1704i	−0.607396	+	1.86937i	−0.479397	+	0.877598i	$0.659145\pi$
$810$		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	$0.229868\pi$
$812$	−14.4776	+	11.0809i	−0.508063	+	0.388863i
$813$	−13.2362	−	4.30072i	−0.464216	−	0.150833i
$814$	−34.3046	+	35.1716i	−1.20238	+	1.23276i
$815$		0			0
$816$	1.95455	+	39.1276i	0.0684229	+	1.36974i
$817$	9.31684	+	6.76908i	0.325955	+	0.236820i
$818$	−3.20375	−	6.09838i	−0.112016	−	0.213225i
$819$	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	$0.510452\pi$
$822$	−23.3105	+	47.1961i	−0.813046	+	1.64615i
$823$	7.27585	+	22.3928i	0.253620	+	0.780562i	0.994098	+	0.108482i	$0.0345990\pi$
$823$	7.27585	+	22.3928i	0.253620	+	0.780562i	−0.740478	+	0.672080i	$0.765401\pi$
$824$	53.6554	+	6.45046i	1.86918	+	0.224712i
$825$		0			0
$826$	−5.98818	+	3.14585i	−0.208355	+	0.109458i
$827$	49.7791	−	16.1742i	1.73099	−	0.562432i	0.737397	−	0.675460i	$-0.236055\pi$
$827$	49.7791	−	16.1742i	1.73099	−	0.562432i	0.993592	+	0.113028i	$0.0360549\pi$
$828$	−0.0105334	−	0.421993i	−0.000366060	−	0.0146653i
$829$	14.8801	+	20.4807i	0.516808	+	0.711325i	0.985049	−	0.172276i	$-0.0551120\pi$
$829$	14.8801	+	20.4807i	0.516808	+	0.711325i	−0.468241	+	0.883601i	$0.655112\pi$
$830$		0			0
$831$	28.4451	+	20.6666i	0.986751	+	0.716917i
$832$	−1.45736	+	5.97362i	−0.0505249	+	0.207098i
$833$	57.8915	+	42.0606i	2.00582	+	1.45731i
$834$	4.79064	−	0.820163i	0.165886	−	0.0283999i
$835$		0			0
$836$	−17.7250	−	5.27398i	−0.613030	−	0.182404i
$837$	12.9666	+	4.21310i	0.448191	+	0.145626i
$838$	0.926780	+	5.41339i	0.0320151	+	0.187003i
$839$	−9.60794	−	29.5702i	−0.331703	−	1.02088i	−0.968323	−	0.249699i	$-0.919668\pi$
$839$	−9.60794	−	29.5702i	−0.331703	−	1.02088i	0.636620	−	0.771177i	$-0.280332\pi$
$840$		0			0
$841$	7.64937	−	23.5424i	0.263772	−	0.811805i
$842$	−9.83834	−	1.43264i	−0.339052	−	0.0493720i
$843$			55.6527i			1.91678i
$844$	−1.53458	−	4.35044i	−0.0528225	−	0.149748i
$845$		0			0
$846$	0.408204	+	0.201615i	0.0140343	+	0.00693165i
$847$	62.7227	−	45.5707i	2.15518	−	1.56583i
$848$	11.7191	+	14.5445i	0.402435	+	0.499461i
$849$	41.5127			1.42471
$850$		0			0
$851$		−	34.2970i		−	1.17569i
$852$	−0.573505	+	1.92745i	−0.0196480	+	0.0660335i
$853$	24.1636	+	33.2584i	0.827347	+	1.13875i	0.988411	+	0.151801i	$0.0485074\pi$
$853$	24.1636	+	33.2584i	0.827347	+	1.13875i	−0.161064	+	0.986944i	$0.551493\pi$
$854$	−20.0114	+	40.5165i	−0.684775	+	1.38645i
$855$		0			0
$856$	−23.5007	+	25.3295i	−0.803239	+	0.865744i
$857$	7.69778			0.262951			0.131476	−	0.991319i	$-0.458029\pi$
$857$	7.69778			0.262951			0.131476	+	0.991319i	$0.458029\pi$
$858$	−9.88374	−	1.43925i	−0.337425	−	0.0491352i
$859$	39.8085	+	12.9346i	1.35825	+	0.441322i	0.895458	−	0.445146i	$-0.146848\pi$
$859$	39.8085	+	12.9346i	1.35825	+	0.441322i	0.462791	+	0.886468i	$0.346848\pi$
$860$		0			0
$861$	17.6778	−	5.74385i	0.602456	−	0.195750i
$862$	−2.62314	+	0.449086i	−0.0893446	+	0.0152959i
$863$	−5.33595	+	16.4224i	−0.181638	+	0.559024i	−0.999874	−	0.0158581i	$-0.994952\pi$
$863$	−5.33595	+	16.4224i	−0.181638	+	0.559024i	0.818236	+	0.574882i	$0.194952\pi$
$864$	11.7623	−	27.1481i	0.400162	−	0.923598i
$865$		0			0
$866$	9.10124	−	1.55815i	0.309273	−	0.0529479i
$867$	15.5806	−	21.4449i	0.529145	−	0.728305i
$868$	−13.0865	+	18.9912i	−0.444186	+	0.644603i
$869$	−24.3306	+	33.4882i	−0.825359	+	1.13601i
$870$		0			0
$871$	−3.94200	+	2.86403i	−0.133570	+	0.0970441i
$872$	−11.6040	−	20.8100i	−0.392961	−	0.704715i
$873$	−0.0401795	−	0.123660i	−0.00135987	−	0.00418525i
$874$	11.4284	−	6.00383i	0.386570	−	0.203082i
$875$		0			0
$876$	−16.3387	−	11.2588i	−0.552035	−	0.380399i
$877$	14.2844	−	4.64130i	0.482351	−	0.156725i	−0.0577404	−	0.998332i	$-0.518390\pi$
$877$	14.2844	−	4.64130i	0.482351	−	0.156725i	0.540092	+	0.841606i	$0.318390\pi$
$878$	35.9443	+	17.7531i	1.21306	+	0.599139i
$879$	−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	$0.411277\pi$
$882$	−0.330940	−	0.629949i	−0.0111433	−	0.0212115i
$883$	−19.8395	+	27.3068i	−0.667653	+	0.918946i	−0.999704	−	0.0243155i	$-0.992259\pi$
$883$	−19.8395	+	27.3068i	−0.667653	+	0.918946i	0.332051	+	0.943261i	$0.392259\pi$
$884$	6.94907	−	5.31870i	0.233722	−	0.178887i
$885$		0			0
$886$	−26.0841	−	25.4412i	−0.876313	−	0.854712i
$887$	1.28737	−	3.96211i	0.0432256	−	0.133035i	−0.927115	−	0.374778i	$-0.877719\pi$
$887$	1.28737	−	3.96211i	0.0432256	−	0.133035i	0.970340	+	0.241743i	$0.0777191\pi$
$888$	13.3045	−	28.7209i	0.446470	−	0.963809i
$889$	18.2824	+	56.2675i	0.613172	+	1.88715i
$890$		0			0
$891$	45.0976	+	14.6531i	1.51083	+	0.490897i
$892$	4.20732	−	1.48410i	0.140872	−	0.0496913i
$893$			13.9234i			0.465928i
$894$	−1.61508	+	11.0912i	−0.0540163	+	0.370945i
$895$		0			0
$896$	38.3428	+	32.1682i	1.28094	+	1.07467i
$897$	5.64075	−	4.09824i	0.188339	−	0.136836i
$898$	−4.52294	+	4.63725i	−0.150933	+	0.154747i
$899$			5.37148i			0.179149i
$900$		0			0
$901$		−	26.5827i		−	0.885597i
$902$	13.2054	+	12.8799i	0.439690	+	0.428852i
$903$	40.9590	−	29.7585i	1.36303	−	0.990299i
$904$	−13.3588	+	7.44912i	−0.444309	+	0.247754i
$905$		0			0
$906$	−4.24181	−	0.617685i	−0.140925	−	0.0205212i
$907$			44.9685i			1.49315i	0.665299	+	0.746577i	$0.268304\pi$
$907$			44.9685i			1.49315i	−0.665299	+	0.746577i	$0.731696\pi$
$908$	−4.43129	−	12.5624i	−0.147057	−	0.416898i
$909$	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	$0.967503\pi$
$912$	11.8993	−	0.594409i	0.394025	−	0.0196828i
$913$	−11.2187	+	34.5277i	−0.371286	+	1.14270i
$914$	−10.3120	+	10.5726i	−0.341091	+	0.349711i
$915$		0			0
$916$	17.4543	−	13.3593i	0.576707	−	0.441402i
$917$	−9.19269	+	12.6527i	−0.303569	+	0.417827i
$918$	−37.2764	+	19.5829i	−1.23030	+	0.646333i
$919$	18.4864	+	13.4312i	0.609810	+	0.443053i	0.849347	−	0.527834i	$-0.176996\pi$
$919$	18.4864	+	13.4312i	0.609810	+	0.443053i	−0.239537	+	0.970887i	$0.576996\pi$
$920$		0			0
$921$	4.23591	−	3.07757i	0.139578	−	0.101409i
$922$	−19.7483	+	39.9840i	−0.650377	+	1.31680i
$923$	0.427208	−	0.138808i	0.0140617	−	0.00456893i
$924$	−46.1304	+	66.9444i	−1.51758	+	2.20231i
$925$		0			0
$926$	−8.85934	−	16.8639i	−0.291136	−	0.554181i
$927$	0.236344	+	0.727391i	0.00776255	+	0.0238907i
$928$	11.6043	+	1.10211i	0.380931	+	0.0361785i
$929$	24.2098	−	17.5894i	0.794297	−	0.577090i	−0.114939	−	0.993373i	$-0.536667\pi$
$929$	24.2098	−	17.5894i	0.794297	−	0.577090i	0.909236	+	0.416282i	$0.136667\pi$
$930$		0			0
$931$	12.7913	−	17.6057i	0.419218	−	0.577003i
$932$	−30.8951	+	44.8350i	−1.01200	+	1.46862i
$933$	−15.3634	+	21.1459i	−0.502975	+	0.692286i
$934$	−4.59720	−	26.8526i	−0.150425	−	0.878644i
$935$		0			0
$936$	−0.0853799	+	0.0168202i	−0.00279073	+	0.000549786i
$937$	−14.6065	+	44.9541i	−0.477172	+	1.46859i	0.365833	+	0.930681i	$0.380784\pi$
$937$	−14.6065	+	44.9541i	−0.477172	+	1.46859i	−0.843005	+	0.537905i	$0.819216\pi$
$938$	6.69271	+	39.0926i	0.218525	+	1.27642i
$939$	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	$0.715402\pi$
$942$	1.52033	−	10.4405i	0.0495351	−	0.340171i
$943$	−12.8770			−0.419333
$944$	4.17469	+	1.12957i	0.135875	+	0.0367642i
$945$		0			0
$946$	45.0488	+	22.2499i	1.46466	+	0.723407i
$947$	−31.9125	−	43.9238i	−1.03702	−	1.42733i	−0.899546	−	0.436827i	$-0.856102\pi$
$947$	−31.9125	−	43.9238i	−1.03702	−	1.42733i	−0.137472	−	0.990506i	$-0.543898\pi$
$948$	7.60543	−	25.5606i	0.247013	−	0.830168i
$949$			4.43220i			0.143875i
$950$		0			0
$951$	50.5237			1.63834
$952$	−13.7679	−	69.8864i	−0.446221	−	2.26503i
$953$	−36.3305	+	26.3956i	−1.17686	+	0.855039i	−0.991814	−	0.127691i	$-0.959243\pi$
$953$	−36.3305	+	26.3956i	−1.17686	+	0.855039i	−0.185046	+	0.982730i	$0.559243\pi$
$954$	−0.117062	+	0.237012i	−0.00379001	+	0.00767354i
$955$		0			0
$956$	−20.3642	+	7.18330i	−0.658626	+	0.232325i
$957$			18.9346i			0.612068i
$958$	4.10169	−	28.1675i	0.132520	−	0.910049i
$959$	29.5751	−	91.0227i	0.955029	−	2.93928i
$960$		0			0
$961$	−7.47972	−	23.0202i	−0.241281	−	0.742588i
$962$	−6.96894	+	1.19309i	−0.224688	+	0.0384669i
$963$	−0.465068	−	0.151110i	−0.0149866	−	0.00486944i
$964$	18.5447	+	5.51788i	0.597284	+	0.177719i
$965$		0			0
$966$	−9.57683	−	55.9390i	−0.308130	−	1.79981i
$967$	−2.39657	−	1.74121i	−0.0770686	−	0.0559936i	0.548584	−	0.836096i	$-0.315167\pi$
$967$	−2.39657	−	1.74121i	−0.0770686	−	0.0559936i	−0.625652	+	0.780102i	$0.715167\pi$
$968$	−49.2153	−	5.91666i	−1.58184	−	0.190169i
$969$	−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	$0.663606\pi$
$972$	0.831677	−	0.0207595i	0.0266760	−	0.000665862i
$973$	−8.40446	+	2.73077i	−0.269435	+	0.0875446i
$974$	−18.5614	−	35.3318i	−0.594745	−	1.13210i
$975$		0			0
$976$	26.9985	−	10.2880i	0.864201	−	0.329311i
$977$	11.1732	+	34.3875i	0.357461	+	1.10015i	0.954569	+	0.297991i	$0.0963167\pi$
$977$	11.1732	+	34.3875i	0.357461	+	1.10015i	−0.597107	+	0.802161i	$0.703683\pi$
$978$	−15.7564	−	7.78219i	−0.503834	−	0.248847i
$979$	−39.5599	−	54.4495i	−1.26434	−	1.74021i
$980$		0			0
$981$	0.198204	−	0.272805i	0.00632818	−	0.00870999i
$982$	44.8226	−	23.5473i	1.43035	−	0.751424i
$983$	−28.1391	−	20.4443i	−0.897499	−	0.652071i	0.0403234	−	0.999187i	$-0.487161\pi$
$983$	−28.1391	−	20.4443i	−0.897499	−	0.652071i	−0.937822	+	0.347115i	$0.887161\pi$
$984$	−10.7834	−	4.99524i	−0.343762	−	0.159243i
$985$		0			0
$986$	−11.8759	−	11.5832i	−0.378207	−	0.368884i
$987$	58.2146	+	18.9151i	1.85299	+	0.602073i
$988$	−1.61750	−	2.11332i	−0.0514596	−	0.0672336i
$989$	−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	$0.123385\pi$
$992$	14.3923	−	3.21037i	0.456955	−	0.101929i
$993$	−57.7546			−1.83279
$994$	0.526867	−	3.61814i	0.0167112	−	0.114760i
$995$		0			0
$996$	−0.583642	−	23.3821i	−0.0184934	−	0.740890i
$997$	21.5409	+	29.6486i	0.682209	+	0.938979i	0.999958	−	0.00919532i	$-0.00292700\pi$
$997$	21.5409	+	29.6486i	0.682209	+	0.938979i	−0.317749	+	0.948175i	$0.602927\pi$
$998$	26.9303	+	26.2665i	0.852463	+	0.831450i
$999$	34.0208			1.07637

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.29.8	✓	112	200.197	odd	20
200.2.o.a.29.14	yes	112	25.22	odd	20
200.2.o.a.69.8	yes	112	5.3	odd	4
200.2.o.a.69.14	yes	112	40.13	odd	4
800.2.be.a.369.7		112	20.3	even	4
800.2.be.a.369.22		112	40.3	even	4
800.2.be.a.529.7		112	200.147	even	20
800.2.be.a.529.22		112	100.47	even	20
1000.2.o.a.149.15		112	25.3	odd	20
1000.2.o.a.149.21		112	200.53	odd	20
1000.2.o.a.349.15		112	40.37	odd	4
1000.2.o.a.349.21		112	5.2	odd	4
1000.2.t.b.101.4		224	25.21	even	5	inner
1000.2.t.b.101.16		224	200.29	even	10	inner
1000.2.t.b.101.41		224	200.21	even	10	inner
1000.2.t.b.101.53		224	25.4	even	10	inner
1000.2.t.b.901.4		224	8.5	even	2	inner
1000.2.t.b.901.16		224	5.4	even	2	inner
1000.2.t.b.901.41		224	1.1	even	1	trivial
1000.2.t.b.901.53		224	40.29	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.987445 - 1.01240i) q^{2} +(-1.01126 - 1.39188i) q^{3} +(-0.0499066 - 1.99938i) q^{4} +(-2.40770 - 0.350605i) q^{6} +4.42380 q^{7} +(-2.07345 - 1.92375i) q^{8} +(0.0123697 - 0.0380700i) q^{9} +O(q^{10})\)	\(q+(0.987445 - 1.01240i) q^{2} +(-1.01126 - 1.39188i) q^{3} +(-0.0499066 - 1.99938i) q^{4} +(-2.40770 - 0.350605i) q^{6} +4.42380 q^{7} +(-2.07345 - 1.92375i) q^{8} +(0.0123697 - 0.0380700i) q^{9} +(5.07953 - 1.65044i) q^{11} +(-2.73242 + 2.09135i) q^{12} +(0.730985 + 0.237511i) q^{13} +(4.36826 - 4.47866i) q^{14} +(-3.99502 + 0.199564i) q^{16} +(4.60551 + 3.34610i) q^{17} +(-0.0263277 - 0.0501151i) q^{18} +(1.01760 - 1.40061i) q^{19} +(-4.47361 - 6.15740i) q^{21} +(3.34485 - 6.77223i) q^{22} +(1.62935 + 5.01464i) q^{23} +(-0.580831 + 4.83140i) q^{24} +(0.962263 - 0.505520i) q^{26} +(-4.97425 + 1.61623i) q^{27} +(-0.220777 - 8.84485i) q^{28} +(-1.21119 - 1.66707i) q^{29} +(-2.10890 - 1.53221i) q^{31} +(-3.74282 + 4.24161i) q^{32} +(-7.43393 - 5.40106i) q^{33} +(7.93528 - 1.35853i) q^{34} +(-0.0767337 - 0.0228318i) q^{36} +(-6.18628 - 2.01004i) q^{37} +(-0.413150 - 2.41324i) q^{38} +(-0.408628 - 1.25763i) q^{39} +(-0.754681 + 2.32267i) q^{41} +(-10.6512 - 1.55101i) q^{42} +6.65200i q^{43} +(-3.55335 - 10.0735i) q^{44} +(6.68572 + 3.30212i) q^{46} +(-6.50644 + 4.72720i) q^{47} +(4.31777 + 5.35877i) q^{48} +12.5700 q^{49} -9.79409i q^{51} +(0.438394 - 1.47337i) q^{52} +(-2.74471 - 3.77778i) q^{53} +(-3.27552 + 6.63187i) q^{54} +(-9.17253 - 8.51029i) q^{56} -2.97854 q^{57} +(-2.88373 - 0.419923i) q^{58} +(-1.02828 - 0.334110i) q^{59} +(-6.86954 + 2.23205i) q^{61} +(-3.63363 + 0.622082i) q^{62} +(0.0547211 - 0.168414i) q^{63} +(0.598382 + 7.97759i) q^{64} +(-12.8086 + 2.19285i) q^{66} +(-3.72628 + 5.12879i) q^{67} +(6.46027 - 9.37515i) q^{68} +(5.33207 - 7.33896i) q^{69} +(0.472812 - 0.343518i) q^{71} +(-0.0988851 + 0.0551401i) q^{72} +(1.78197 + 5.48432i) q^{73} +(-8.14357 + 4.27818i) q^{74} +(-2.85113 - 1.96467i) q^{76} +(22.4708 - 7.30121i) q^{77} +(-1.67672 - 0.828143i) q^{78} +(-6.27011 + 4.55550i) q^{79} +(7.18270 + 5.21854i) q^{81} +(1.60627 + 3.05755i) q^{82} +(-3.99543 + 5.49924i) q^{83} +(-12.0877 + 9.25173i) q^{84} +(6.73448 + 6.56848i) q^{86} +(-1.09552 + 3.37167i) q^{87} +(-13.7072 - 6.34963i) q^{88} +(-3.89405 - 11.9847i) q^{89} +(3.23373 + 1.05070i) q^{91} +(9.94484 - 3.50796i) q^{92} +4.48479i q^{93} +(-1.63893 + 11.2550i) q^{94} +(9.68877 + 0.920181i) q^{96} +(2.62786 - 1.90925i) q^{97} +(12.4122 - 12.7259i) q^{98} -0.213793i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 6 q^{4} + 2 q^{6} + 60 q^{9}+O(q^{10}) \) 224 * q + 6 * q^4 + 2 * q^6 + 60 * q^9	\( 224 q + 6 q^{4} + 2 q^{6} + 60 q^{9} + 6 q^{14} - 30 q^{16} + 32 q^{24} - 28 q^{26} - 36 q^{31} - 18 q^{34} + 82 q^{36} + 20 q^{39} - 20 q^{41} + 64 q^{44} + 26 q^{46} + 160 q^{49} - 86 q^{54} + 72 q^{56} + 72 q^{64} + 80 q^{66} + 44 q^{71} - 8 q^{74} - 72 q^{76} - 28 q^{79} - 12 q^{81} - 156 q^{84} - 118 q^{86} - 48 q^{89} - 90 q^{94} + 92 q^{96}+O(q^{100}) \) 224 * q + 6 * q^4 + 2 * q^6 + 60 * q^9 + 6 * q^14 - 30 * q^16 + 32 * q^24 - 28 * q^26 - 36 * q^31 - 18 * q^34 + 82 * q^36 + 20 * q^39 - 20 * q^41 + 64 * q^44 + 26 * q^46 + 160 * q^49 - 86 * q^54 + 72 * q^56 + 72 * q^64 + 80 * q^66 + 44 * q^71 - 8 * q^74 - 72 * q^76 - 28 * q^79 - 12 * q^81 - 156 * q^84 - 118 * q^86 - 48 * q^89 - 90 * q^94 + 92 * q^96

Introduction

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