LMFDB - Embedded newform 1000.2.t.b.101.53

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			101.53
Character	$\chi$	$=$	1000.101
Dual form			1000.2.t.b.901.53

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.39393 - 0.238643i) q^{2} +(-1.01126 + 1.39188i) q^{3} +(1.88610 - 0.665306i) q^{4} +(-1.07746 + 2.18152i) q^{6} -4.42380 q^{7} +(2.47032 - 1.37750i) q^{8} +(0.0123697 + 0.0380700i) q^{9} +O(q^{10})$	\(q+(1.39393 - 0.238643i) q^{2} +(-1.01126 + 1.39188i) q^{3} +(1.88610 - 0.665306i) q^{4} +(-1.07746 + 2.18152i) q^{6} -4.42380 q^{7} +(2.47032 - 1.37750i) q^{8} +(0.0123697 + 0.0380700i) q^{9} +(-5.07953 - 1.65044i) q^{11} +(-0.981310 + 3.29802i) q^{12} +(0.730985 - 0.237511i) q^{13} +(-6.16649 + 1.05571i) q^{14} +(3.11474 - 2.50966i) 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} +(-7.47439 - 1.08841i) 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} +(-8.34373 + 2.94318i) 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} +(-5.62125 + 5.76331i) q^{34} +(0.0486587 + 0.0635742i) q^{36} +(-6.18628 + 2.01004i) q^{37} +(-1.75271 - 1.70951i) q^{38} +(-0.408628 + 1.25763i) q^{39} +(-0.754681 - 2.32267i) q^{41} +(4.76649 - 9.65060i) q^{42} -6.65200i q^{43} +(-10.6785 + 0.266548i) q^{44} +(-1.07450 + 7.37890i) q^{46} +(6.50644 + 4.72720i) q^{47} +(0.343341 + 6.87326i) q^{48} +12.5700 q^{49} -9.79409i q^{51} +(1.22069 - 0.934298i) q^{52} +(-2.74471 + 3.77778i) q^{53} +(-7.31948 - 1.06585i) q^{54} +(-10.9282 + 6.09377i) q^{56} +2.97854 q^{57} +(1.29049 - 2.61282i) q^{58} +(1.02828 - 0.334110i) q^{59} +(6.86954 + 2.23205i) q^{61} +(-2.57402 + 2.63907i) q^{62} +(-0.0547211 - 0.168414i) q^{63} +(4.20501 - 6.80573i) q^{64} +(9.07347 - 9.30278i) 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} +(0.0829985 + 0.0770061i) 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} +(-0.269476 + 1.85057i) 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} +(4.34112 - 14.5898i) q^{84} +(-1.58745 - 9.27244i) q^{86} +(1.09552 + 3.37167i) q^{87} +(-14.8216 + 2.91991i) q^{88} +(-3.89405 + 11.9847i) q^{89} +(-3.23373 + 1.05070i) q^{91} +(0.263143 + 10.5421i) q^{92} -4.48479i q^{93} +(10.1977 + 5.03669i) q^{94} +(2.11885 + 9.49892i) q^{96} +(-2.62786 - 1.90925i) q^{97} +(17.5218 - 2.99975i) 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 $\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times$.

$n$	$377$	$501$	$751$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$-1$	$1$

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 $

$2$	1.39393	−	0.238643i	0.985660	−	0.168746i
$2$	1.39393	−	0.238643i	0.985660	−	0.168746i
$3$	−1.01126	+	1.39188i	−0.583851	+	0.803601i	−0.994111	−	0.108367i	$-0.965438\pi$
$3$	−1.01126	+	1.39188i	−0.583851	+	0.803601i	0.410260	+	0.911968i	$0.365438\pi$
$4$	1.88610	−	0.665306i	0.943049	−	0.332653i
$5$		0			0
$5$		0			0
$6$	−1.07746	+	2.18152i	−0.439873	+	0.890600i
$7$	−4.42380			−1.67204			−0.836020	−	0.548699i	$-0.815123\pi$
$7$	−4.42380			−1.67204			−0.836020	+	0.548699i	$0.815123\pi$
$8$	2.47032	−	1.37750i	0.873392	−	0.487018i
$9$	0.0123697	+	0.0380700i	0.00412323	+	0.0126900i
$10$		0			0
$11$	−5.07953	−	1.65044i	−1.53153	−	0.497626i	−0.582509	−	0.812824i	$-0.697929\pi$
$11$	−5.07953	−	1.65044i	−1.53153	−	0.497626i	−0.949026	+	0.315199i	$0.897929\pi$
$12$	−0.981310	+	3.29802i	−0.283280	+	0.952055i
$13$	0.730985	−	0.237511i	0.202739	−	0.0658738i	−0.205887	−	0.978576i	$-0.566008\pi$
$13$	0.730985	−	0.237511i	0.202739	−	0.0658738i	0.408626	+	0.912702i	$0.366008\pi$
$14$	−6.16649	+	1.05571i	−1.64806	+	0.282151i
$15$		0			0
$16$	3.11474	−	2.50966i	0.778684	−	0.627416i
$17$	−4.60551	+	3.34610i	−1.11700	+	0.811549i	−0.983752	−	0.179534i	$-0.942541\pi$
$17$	−4.60551	+	3.34610i	−1.11700	+	0.811549i	−0.133249	+	0.991083i	$0.542541\pi$
$18$	0.0263277	+	0.0501151i	0.00620550	+	0.0118123i
$19$	−1.01760	−	1.40061i	−0.233454	−	0.321322i	0.676177	−	0.736739i	$-0.263635\pi$
$19$	−1.01760	−	1.40061i	−0.233454	−	0.321322i	−0.909631	+	0.415418i	$0.863635\pi$
$20$		0			0
$21$	4.47361	−	6.15740i	0.976222	−	1.34365i
$22$	−7.47439	−	1.08841i	−1.59354	−	0.232049i
$23$	−1.62935	+	5.01464i	−0.339744	+	1.04562i	0.624594	+	0.780950i	$0.285265\pi$
$23$	−1.62935	+	5.01464i	−0.339744	+	1.04562i	−0.964338	+	0.264675i	$0.914735\pi$
$24$	−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
$28$	−8.34373	+	2.94318i	−1.57682	+	0.556209i
$29$	1.21119	−	1.66707i	0.224913	−	0.309567i	−0.681616	−	0.731710i	$-0.738722\pi$
$29$	1.21119	−	1.66707i	0.224913	−	0.309567i	0.906529	+	0.422144i	$0.138722\pi$
$30$		0			0
$31$	−2.10890	+	1.53221i	−0.378770	+	0.275192i	−0.760838	−	0.648942i	$-0.775212\pi$
$31$	−2.10890	+	1.53221i	−0.378770	+	0.275192i	0.382068	+	0.924134i	$0.375212\pi$
$32$	3.74282	−	4.24161i	0.661643	−	0.749819i
$33$	7.43393	−	5.40106i	1.29408	−	0.940204i
$34$	−5.62125	+	5.76331i	−0.964037	+	0.988400i
$35$		0			0
$36$	0.0486587	+	0.0635742i	0.00810978	+	0.0105957i
$37$	−6.18628	+	2.01004i	−1.01702	+	0.330449i	−0.769646	−	0.638471i	$-0.779567\pi$
$37$	−6.18628	+	2.01004i	−1.01702	+	0.330449i	−0.247372	+	0.968921i	$0.579567\pi$
$38$	−1.75271	−	1.70951i	−0.284328	−	0.277319i
$39$	−0.408628	+	1.25763i	−0.0654328	+	0.201382i
$40$		0			0
$41$	−0.754681	−	2.32267i	−0.117861	−	0.362740i	0.874672	−	0.484716i	$-0.161077\pi$
$41$	−0.754681	−	2.32267i	−0.117861	−	0.362740i	−0.992533	+	0.121976i	$0.961077\pi$
$42$	4.76649	−	9.65060i	0.735486	−	1.48912i
$43$		−	6.65200i		−	1.01442i	−0.861822	−	0.507210i	$-0.830677\pi$
$43$		−	6.65200i		−	1.01442i	0.861822	−	0.507210i	$-0.169323\pi$
$44$	−10.6785	+	0.266548i	−1.60985	+	0.0401836i
$45$		0			0
$46$	−1.07450	+	7.37890i	−0.158427	+	1.08796i
$47$	6.50644	+	4.72720i	0.949062	+	0.689534i	0.950585	−	0.310465i	$-0.100485\pi$
$47$	6.50644	+	4.72720i	0.949062	+	0.689534i	−0.00152305	+	0.999999i	$0.500485\pi$
$48$	0.343341	+	6.87326i	0.0495571	+	0.992069i
$49$	12.5700			1.79572
$50$		0			0
$51$		−	9.79409i		−	1.37145i
$52$	1.22069	−	0.934298i	0.169280	−	0.129564i
$53$	−2.74471	+	3.77778i	−0.377016	+	0.518917i	−0.954791	−	0.297279i	$-0.903921\pi$
$53$	−2.74471	+	3.77778i	−0.377016	+	0.518917i	0.577775	+	0.816196i	$0.303921\pi$
$54$	−7.31948	−	1.06585i	−0.996055	−	0.145044i
$55$		0			0
$56$	−10.9282	+	6.09377i	−1.46035	+	0.814315i
$57$	2.97854			0.394517
$58$	1.29049	−	2.61282i	0.169450	−	0.343080i
$59$	1.02828	−	0.334110i	0.133871	−	0.0434974i	−0.241315	−	0.970447i	$-0.577579\pi$
$59$	1.02828	−	0.334110i	0.133871	−	0.0434974i	0.375186	+	0.926949i	$0.377579\pi$
$60$		0			0
$61$	6.86954	+	2.23205i	0.879554	+	0.285785i	0.713772	−	0.700378i	$-0.246985\pi$
$61$	6.86954	+	2.23205i	0.879554	+	0.285785i	0.165782	+	0.986162i	$0.446985\pi$
$62$	−2.57402	+	2.63907i	−0.326900	+	0.335162i
$63$	−0.0547211	−	0.168414i	−0.00689422	−	0.0212182i
$64$	4.20501	−	6.80573i	0.525626	−	0.850716i
$65$		0			0
$66$	9.07347	−	9.30278i	1.11687	−	1.14509i
$67$	−3.72628	−	5.12879i	−0.455238	−	0.626581i	0.518275	−	0.855214i	$-0.326574\pi$
$67$	−3.72628	−	5.12879i	−0.455238	−	0.626581i	−0.973513	+	0.228633i	$0.926574\pi$
$68$	−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	0.615488	−	0.788146i	$-0.288959\pi$
$71$	0.472812	+	0.343518i	0.0561125	+	0.0407681i	−0.559375	+	0.828914i	$0.688959\pi$
$72$	0.0829985	+	0.0770061i	0.00978147	+	0.00907526i
$73$	−1.78197	+	5.48432i	−0.208563	+	0.641892i	0.790985	+	0.611836i	$0.209569\pi$
$73$	−1.78197	+	5.48432i	−0.208563	+	0.641892i	−0.999548	+	0.0300561i	$0.990431\pi$
$74$	−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
$78$	−0.269476	+	1.85057i	−0.0305121	+	0.209535i
$79$	−6.27011	−	4.55550i	−0.705442	−	0.512534i	0.176258	−	0.984344i	$-0.443601\pi$
$79$	−6.27011	−	4.55550i	−0.705442	−	0.512534i	−0.881700	+	0.471810i	$0.843601\pi$
$80$		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	0.531335	−	0.847162i	$-0.321691\pi$
$83$	−3.99543	−	5.49924i	−0.438555	−	0.603619i	−0.969890	+	0.243542i	$0.921691\pi$
$84$	4.34112	−	14.5898i	0.473655	−	1.59188i
$85$		0			0
$86$	−1.58745	−	9.27244i	−0.171180	−	0.999873i
$87$	1.09552	+	3.37167i	0.117452	+	0.361481i
$88$	−14.8216	+	2.91991i	−1.57998	+	0.311263i
$89$	−3.89405	+	11.9847i	−0.412769	+	1.27037i	0.501463	+	0.865179i	$0.332795\pi$
$89$	−3.89405	+	11.9847i	−0.412769	+	1.27037i	−0.914232	+	0.405192i	$0.867205\pi$
$90$		0			0
$91$	−3.23373	+	1.05070i	−0.338987	+	0.110144i
$92$	0.263143	+	10.5421i	0.0274345	+	1.09909i
$93$		−	4.48479i		−	0.465051i
$94$	10.1977	+	5.03669i	1.05181	+	0.519495i
$95$		0			0
$96$	2.11885	+	9.49892i	0.216254	+	0.969480i
$97$	−2.62786	−	1.90925i	−0.266819	−	0.193855i	0.446329	−	0.894869i	$-0.352731\pi$
$97$	−2.62786	−	1.90925i	−0.266819	−	0.193855i	−0.713148	+	0.701014i	$0.752731\pi$
$98$	17.5218	−	2.99975i	1.76997	−	0.303021i
$99$		−	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	$0.937801\pi$
$102$	−2.33729	−	13.6523i	−0.231427	−	1.35178i
$103$	15.4576	+	11.2306i	1.52308	+	1.10659i	0.959933	+	0.280231i	$0.0904111\pi$
$103$	15.4576	+	11.2306i	1.52308	+	1.10659i	0.563151	+	0.826354i	$0.309589\pi$
$104$	1.47860	−	1.59366i	0.144989	−	0.156271i
$105$		0			0
$106$	−2.92441	+	5.92097i	−0.284044	+	0.575096i
$107$			12.2161i			1.18098i	0.807046	+	0.590488i	$0.201065\pi$
$107$			12.2161i			1.18098i	−0.807046	+	0.590488i	$0.798935\pi$
$108$	−10.4572	+	0.261023i	−1.00625	+	0.0251170i
$109$	−8.01169	+	2.60316i	−0.767381	+	0.249337i	−0.666443	−	0.745556i	$-0.732184\pi$
$109$	−8.01169	+	2.60316i	−0.767381	+	0.249337i	−0.100937	+	0.994893i	$0.532184\pi$
$110$		0			0
$111$	3.45819	−	10.6432i	0.328237	−	1.01021i
$112$	−13.7790	+	11.1023i	−1.30199	+	1.04906i
$113$	−1.67108	−	5.14306i	−0.157202	−	0.483818i	0.841175	−	0.540762i	$-0.181864\pi$
$113$	−1.67108	−	5.14306i	−0.157202	−	0.483818i	−0.998377	+	0.0569445i	$0.981864\pi$
$114$	4.15188	−	0.710807i	0.388859	−	0.0665732i
$115$		0			0
$116$	1.17532	−	3.95007i	0.109126	−	0.366755i
$117$	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
$122$	10.1083	+	1.47196i	0.915166	+	0.133265i
$123$	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	0.582175	+	0.813063i	$0.302202\pi$
$127$	−4.13273	+	12.7192i	−0.366721	+	1.12865i	−0.948896	+	0.315588i	$0.897798\pi$
$128$	4.23736	−	10.4902i	0.374533	−	0.927213i
$129$	9.25877	+	6.72689i	0.815190	+	0.592270i
$130$		0			0
$131$	2.07801	+	2.86013i	0.181556	+	0.249891i	0.890089	−	0.455788i	$-0.150642\pi$
$131$	2.07801	+	2.86013i	0.181556	+	0.249891i	−0.708532	+	0.705678i	$0.750642\pi$
$132$	10.4278	−	15.1328i	0.907620	−	1.31714i
$133$	4.50167	+	6.19602i	0.390344	+	0.537263i
$134$	−6.41814	−	6.25994i	−0.554443	−	0.540776i
$135$		0			0
$136$	−6.76787	+	14.6100i	−0.580340	+	1.25280i
$137$	−6.68544	−	20.5757i	−0.571176	−	1.75790i	−0.648846	−	0.760919i	$-0.724748\pi$
$137$	−6.68544	−	20.5757i	−0.571176	−	1.75790i	0.0776705	−	0.996979i	$-0.475252\pi$
$138$	−9.18394	−	8.95756i	−0.781789	−	0.762518i
$139$	1.89983	+	0.617291i	0.161141	+	0.0523579i	0.388477	−	0.921459i	$-0.373001\pi$
$139$	1.89983	+	0.617291i	0.161141	+	0.0523579i	−0.227336	+	0.973816i	$0.573001\pi$
$140$		0			0
$141$	−13.1594	+	4.27575i	−1.10822	+	0.360083i
$142$	0.741047	+	0.366008i	0.0621873	+	0.0307147i
$143$	−4.10505			−0.343282
$144$	0.134071	+	0.0875344i	0.0111726	+	0.00729453i
$145$		0			0
$146$	−1.17514	+	8.07004i	−0.0972555	+	0.667881i
$147$	−12.7116	+	17.4960i	−1.04843	+	1.44304i
$148$	−10.3306	+	7.90690i	−0.849173	+	0.649944i
$149$		−	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	$0.477162\pi$
$152$	−4.44314	−	2.05822i	−0.360386	−	0.166943i
$153$	−0.184355	−	0.133942i	−0.0149042	−	0.0108285i
$154$	33.0652	+	4.81489i	2.66447	+	0.387995i
$155$		0			0
$156$	0.0659939	+	2.64387i	0.00528374	+	0.211679i
$157$		−	4.33632i		−	0.346076i	−0.984915	−	0.173038i	$-0.944642\pi$
$157$		−	4.33632i		−	0.346076i	0.984915	−	0.173038i	$-0.0553583\pi$
$158$	−9.82725	−	4.85374i	−0.781814	−	0.386143i
$159$	−2.48259	−	7.64062i	−0.196882	−	0.605940i
$160$		0			0
$161$	7.20794	−	22.1838i	0.568066	−	1.74833i
$162$	8.76684	−	8.98840i	0.688788	−	0.706195i
$163$	6.86918	−	2.23193i	0.538036	−	0.174818i	−0.0273790	−	0.999625i	$-0.508716\pi$
$163$	6.86918	−	2.23193i	0.538036	−	0.174818i	0.565415	+	0.824807i	$0.308716\pi$
$164$	−2.96869	−	3.87869i	−0.231816	−	0.302875i
$165$		0			0
$166$	−6.88172	−	6.71208i	−0.534125	−	0.520959i
$167$	−7.30714	+	5.30895i	−0.565444	+	0.410819i	−0.833447	−	0.552599i	$-0.813636\pi$
$167$	−7.30714	+	5.30895i	−0.565444	+	0.410819i	0.268004	+	0.963418i	$0.413636\pi$
$168$	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
$172$	−4.42561	−	12.5463i	−0.337450	−	0.956648i
$173$	13.0250	+	4.23208i	0.990273	+	0.321759i	0.758972	−	0.651123i	$-0.225702\pi$
$173$	13.0250	+	4.23208i	0.990273	+	0.321759i	0.231301	+	0.972882i	$0.425702\pi$
$174$	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
$178$	−2.56799	+	17.6351i	−0.192479	+	1.32181i
$179$	4.19376	−	5.77221i	0.313456	−	0.431435i	−0.622999	−	0.782223i	$-0.714086\pi$
$179$	4.19376	−	5.77221i	0.313456	−	0.431435i	0.936455	+	0.350787i	$0.114086\pi$
$180$		0			0
$181$	−1.65805	−	2.28211i	−0.123242	−	0.169628i	0.742938	−	0.669360i	$-0.233432\pi$
$181$	−1.65805	−	2.28211i	−0.123242	−	0.169628i	−0.866180	+	0.499732i	$0.833432\pi$
$182$	−4.25686	+	2.23632i	−0.315540	+	0.165767i
$183$	−10.0536	+	7.30439i	−0.743185	+	0.539956i
$184$	2.88261	+	14.6322i	0.212509	+	1.07870i
$185$		0			0
$186$	−1.07026	−	6.25150i	−0.0784756	−	0.458382i
$187$	28.9163	−	9.39549i	2.11457	−	0.687066i
$188$	15.4168	+	4.58721i	1.12439	+	0.334556i
$189$	22.0051	+	7.14989i	1.60064	+	0.520078i
$190$		0			0
$191$	4.36011	+	13.4190i	0.315486	+	0.970968i	0.975554	+	0.219761i	$0.0705278\pi$
$191$	4.36011	+	13.4190i	0.315486	+	0.970968i	−0.660067	+	0.751206i	$0.729472\pi$
$192$	5.22039	+	12.7352i	0.376749	+	0.919085i
$193$	6.87803			0.495092			0.247546	−	0.968876i	$-0.420376\pi$
$193$	6.87803			0.495092			0.247546	+	0.968876i	$0.420376\pi$
$194$	−4.11869	−	2.03425i	−0.295705	−	0.146051i
$195$		0			0
$196$	23.7083	−	8.36291i	1.69345	−	0.597351i
$197$	7.16612	−	9.86331i	0.510565	−	0.702732i	−0.473450	−	0.880821i	$-0.656991\pi$
$197$	7.16612	−	9.86331i	0.510565	−	0.702732i	0.984014	+	0.178089i	$0.0569915\pi$
$198$	−0.0510203	−	0.298013i	−0.00362586	−	0.0211789i
$199$	−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
$202$	0.931333	+	5.43998i	0.0655283	+	0.382756i
$203$	−5.35809	+	7.37478i	−0.376064	+	0.517608i
$204$	−6.51606	−	18.4726i	−0.456216	−	1.29334i
$205$		0			0
$206$	24.2270	+	11.9659i	1.68797	+	0.833701i
$207$	−0.211062			−0.0146698
$208$	1.68075	−	2.57431i	0.116539	−	0.178496i
$209$	2.85732	+	8.79391i	0.197645	+	0.608288i
$210$		0			0
$211$	−2.19369	−	0.712773i	−0.151020	−	0.0490693i	0.232532	−	0.972589i	$-0.425299\pi$
$211$	−2.19369	−	0.712773i	−0.151020	−	0.0490693i	−0.383551	+	0.923520i	$0.625299\pi$
$212$	−2.66343	+	8.95133i	−0.182925	+	0.614780i
$213$	−0.956271	+	0.310711i	−0.0655226	+	0.0212896i
$214$	2.91529	+	17.0284i	0.199285	+	1.16404i
$215$		0			0
$216$	−14.5144	+	2.85939i	−0.987578	+	0.194557i
$217$	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
$222$	2.28056	−	15.6612i	0.153061	−	1.05111i
$223$	−0.689324	+	2.12152i	−0.0461606	+	0.142068i	−0.971480	−	0.237120i	$-0.923797\pi$
$223$	−0.689324	+	2.12152i	−0.0461606	+	0.142068i	0.925320	+	0.379188i	$0.123797\pi$
$224$	−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	0.511593	−	0.859228i	$-0.329056\pi$
$227$	6.33454	+	2.05822i	0.420438	+	0.136609i	−0.0911544	+	0.995837i	$0.529056\pi$
$228$	5.61781	−	1.98164i	0.372049	−	0.131237i
$229$	−6.45978	+	8.89112i	−0.426874	+	0.587542i	−0.967232	−	0.253893i	$-0.918289\pi$
$229$	−6.45978	+	8.89112i	−0.426874	+	0.587542i	0.540358	+	0.841435i	$0.318289\pi$
$230$		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	0.455485	−	0.890243i	$-0.349466\pi$
$233$	22.0251	−	16.0021i	1.44291	−	1.04834i	0.987424	−	0.158092i	$-0.0505343\pi$
$234$	0.0311481	+	0.0303803i	0.00203621	+	0.00198602i
$235$		0			0
$236$	1.71716	−	1.31429i	0.111778	−	0.0855528i
$237$	12.6814	−	4.12044i	0.823746	−	0.267651i
$238$	24.8673	−	25.4958i	1.61191	−	1.65265i
$239$	−3.33646	+	10.2686i	−0.215817	+	0.664218i	0.783277	+	0.621673i	$0.213547\pi$
$239$	−3.33646	+	10.2686i	−0.215817	+	0.664218i	−0.999095	+	0.0425450i	$0.986453\pi$
$240$		0			0
$241$	−2.98946	−	9.20061i	−0.192568	−	0.592663i	−0.999996	−	0.00269761i	$-0.999141\pi$
$241$	−2.98946	−	9.20061i	−0.192568	−	0.592663i	0.807428	−	0.589966i	$-0.200859\pi$
$242$	22.2221	+	10.9757i	1.42849	+	0.705542i
$243$		−	0.415968i		−	0.0266843i
$244$	14.4416	−	0.360478i	0.924530	−	0.0230773i
$245$		0			0
$246$	5.88009	+	0.856247i	0.374901	+	0.0545923i
$247$	−1.07651	−	0.782131i	−0.0684968	−	0.0497658i
$248$	−3.09906	+	6.69005i	−0.196791	+	0.424818i
$249$	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	$0.790844\pi$
$252$	−0.215256	−	0.281240i	−0.0135599	−	0.0177164i
$253$	16.5527	−	22.7828i	1.04066	−	1.43234i
$254$	−2.72539	+	18.7160i	−0.171006	+	1.17435i
$255$		0			0
$256$	3.40317	−	15.6339i	0.212698	−	0.977118i
$257$	−11.0336			−0.688257			−0.344129	−	0.938923i	$-0.611826\pi$
$257$	−11.0336			−0.688257			−0.344129	+	0.938923i	$0.611826\pi$
$258$	14.5114	+	7.16729i	0.903443	+	0.446216i
$259$	27.3669	−	8.89204i	1.70049	−	0.552524i
$260$		0			0
$261$	0.0784474	+	0.0254891i	0.00485577	+	0.00157774i
$262$	3.57915	+	3.49093i	0.221121	+	0.215670i
$263$	−2.39015	−	7.35613i	−0.147383	−	0.453598i	0.849927	−	0.526901i	$-0.176646\pi$
$263$	−2.39015	−	7.35613i	−0.147383	−	0.453598i	−0.997310	+	0.0733026i	$0.976646\pi$
$264$	10.9243	−	23.5826i	0.672342	−	1.45141i
$265$		0			0
$266$	7.75366	+	7.56254i	0.475408	+	0.463689i
$267$	−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	$-0.0173241\pi$
$269$	10.4677	+	14.4075i	0.638224	+	0.878440i	−0.360295	+	0.932838i	$0.617324\pi$
$270$		0			0
$271$	6.54444	+	4.75481i	0.397546	+	0.288834i	0.768541	−	0.639801i	$-0.220983\pi$
$271$	6.54444	+	4.75481i	0.397546	+	0.288834i	−0.370994	+	0.928635i	$0.620983\pi$
$272$	−5.94737	+	21.9805i	−0.360612	+	1.33276i
$273$	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	−0.339987	−	0.940430i	$-0.610423\pi$
$277$	−19.4363	−	6.31523i	−1.16781	−	0.379445i	−0.827826	+	0.560985i	$0.810423\pi$
$278$	2.79554	+	0.407081i	0.167665	+	0.0244151i
$279$	−0.0844176	−	0.0613330i	−0.00505395	−	0.00367191i
$280$		0			0
$281$	−26.1698	+	19.0135i	−1.56116	+	1.13425i	−0.626108	+	0.779736i	$0.715353\pi$
$281$	−26.1698	+	19.0135i	−1.56116	+	1.13425i	−0.935051	+	0.354513i	$0.884647\pi$
$282$	−17.3229	+	9.10050i	−1.03157	+	0.541927i
$283$	−14.1826	−	19.5207i	−0.843067	−	1.16038i	−0.985348	−	0.170556i	$-0.945443\pi$
$283$	−14.1826	−	19.5207i	−0.843067	−	1.16038i	0.142280	−	0.989826i	$-0.454557\pi$
$284$	1.12032	+	0.333345i	0.0664785	+	0.0197804i
$285$		0			0
$286$	−5.72217	+	0.979644i	−0.338359	+	0.0579275i
$287$	3.33856	+	10.2750i	0.197069	+	0.606516i
$288$	0.207776	+	0.0900218i	0.0122433	+	0.00530459i
$289$	4.76106	−	14.6531i	0.280063	−	0.861944i
$290$		0			0
$291$	5.31490	−	1.72691i	0.311565	−	0.101234i
$292$	0.287789	+	11.5295i	0.0168416	+	0.674715i
$293$			10.3735i			0.606027i	0.952986	+	0.303014i	$0.0979928\pi$
$293$			10.3735i			0.606027i	−0.952986	+	0.303014i	$0.902007\pi$
$294$	−13.5438	+	27.4217i	−0.789889	+	1.59927i
$295$		0			0
$296$	−12.5133	+	13.4870i	−0.727320	+	0.783918i
$297$	22.5994	+	16.4194i	1.31135	+	0.952750i
$298$	−1.09932	−	6.42123i	−0.0636821	−	0.371972i
$299$			4.05261i			0.234369i
$300$		0			0
$301$			29.4271i			1.69615i
$302$	2.45579	−	0.420435i	0.141315	−	0.0241933i
$303$	−5.43197	−	3.94655i	−0.312058	−	0.226724i
$304$	−6.68462	−	1.80869i	−0.383389	−	0.103735i
$305$		0			0
$306$	−0.288943	−	0.142711i	−0.0165178	−	0.00815823i
$307$		−	3.04330i		−	0.173690i	−0.996222	−	0.0868452i	$-0.972321\pi$
$307$		−	3.04330i		−	0.173690i	0.996222	−	0.0868452i	$-0.0276786\pi$
$308$	47.2397	−	1.17915i	2.69173	−	0.0671885i
$309$	−31.2633	+	10.1581i	−1.77851	+	0.577872i
$310$		0			0
$311$	−4.69469	+	14.4488i	−0.266212	+	0.819315i	0.725200	+	0.688538i	$0.241747\pi$
$311$	−4.69469	+	14.4488i	−0.266212	+	0.819315i	−0.991412	+	0.130777i	$0.958253\pi$
$312$	0.722933	+	3.66963i	0.0409280	+	0.207752i
$313$	0.0368620	+	0.113450i	0.00208357	+	0.00641255i	0.952093	−	0.305809i	$-0.0989269\pi$
$313$	0.0368620	+	0.113450i	0.00208357	+	0.00641255i	−0.950009	+	0.312222i	$0.898927\pi$
$314$	−1.03483	−	6.04454i	−0.0583990	−	0.341113i
$315$		0			0
$316$	−14.8568	−	4.42059i	−0.835763	−	0.248677i
$317$	−17.2612	−	23.7579i	−0.969483	−	1.33438i	−0.942308	−	0.334748i	$-0.891349\pi$
$317$	−17.2612	−	23.7579i	−0.969483	−	1.33438i	−0.0271752	−	0.999631i	$-0.508651\pi$
$318$	−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
$322$	4.75338	−	32.6428i	0.264896	−	1.81911i
$323$	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
$328$	−5.06378	−	4.69818i	−0.279600	−	0.259414i
$329$	−28.7832	−	20.9122i	−1.58687	−	1.15293i
$330$		0			0
$331$	−19.7316	−	27.1582i	−1.08455	−	1.49275i	−0.854416	−	0.519589i	$-0.826085\pi$
$331$	−19.7316	−	27.1582i	−1.08455	−	1.49275i	−0.230129	−	0.973160i	$-0.573915\pi$
$332$	−11.1944	−	7.71392i	−0.614375	−	0.423356i
$333$	−0.153045	−	0.210648i	−0.00838681	−	0.0115434i
$334$	−8.91872	+	9.14412i	−0.488011	+	0.500344i
$335$		0			0
$336$	−1.51888	−	30.4059i	−0.0828614	−	1.65878i
$337$	−9.10115	−	28.0105i	−0.495771	−	1.52583i	−0.815751	−	0.578403i	$-0.803676\pi$
$337$	−9.10115	−	28.0105i	−0.495771	−	1.52583i	0.319980	−	0.947424i	$-0.396324\pi$
$338$	−12.2534	+	12.5631i	−0.666500	+	0.683344i
$339$	8.84840	+	2.87502i	0.480579	+	0.156150i
$340$		0			0
$341$	13.2410	−	4.30227i	0.717042	−	0.232981i
$342$	0.0434006	−	0.0878720i	0.00234683	−	0.00475158i
$343$	−24.6407			−1.33048
$344$	−9.16310	−	16.4326i	−0.494041	−	0.885986i
$345$		0			0
$346$	19.1659	+	2.79091i	1.03037	+	0.150040i
$347$	2.49468	−	3.43363i	0.133921	−	0.184327i	−0.736789	−	0.676122i	$-0.763659\pi$
$347$	2.49468	−	3.43363i	0.133921	−	0.184327i	0.870711	+	0.491795i	$0.163659\pi$
$348$	4.30946	+	5.63045i	0.231011	+	0.301824i
$349$		−	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
$352$	−26.0123	+	15.3681i	−1.38646	+	0.819122i
$353$	−27.9383	−	20.2984i	−1.48701	−	1.08037i	−0.975213	−	0.221266i	$-0.928981\pi$
$353$	−27.9383	−	20.2984i	−1.48701	−	1.08037i	−0.511794	−	0.859108i	$-0.671019\pi$
$354$	−0.379074	+	2.60321i	−0.0201476	+	0.138359i
$355$		0			0
$356$	0.628894	+	25.1950i	0.0333313	+	1.33533i
$357$			43.3271i			2.29311i
$358$	4.46832	−	9.04689i	0.236158	−	0.478143i
$359$	−1.03463	−	3.18426i	−0.0546057	−	0.168059i	0.920034	−	0.391838i	$-0.128161\pi$
$359$	−1.03463	−	3.18426i	−0.0546057	−	0.168059i	−0.974640	+	0.223779i	$0.928161\pi$
$360$		0			0
$361$	4.94513	−	15.2196i	0.260270	−	0.801029i
$362$	−2.85582	−	2.78542i	−0.150099	−	0.146399i
$363$	−28.6762	+	9.31745i	−1.50511	+	0.489039i
$364$	−5.40010	+	4.13315i	−0.283042	+	0.216636i
$365$		0			0
$366$	−12.2709	+	12.5811i	−0.641412	+	0.657622i
$367$	−7.89027	+	5.73261i	−0.411869	+	0.299240i	−0.774358	−	0.632748i	$-0.781927\pi$
$367$	−7.89027	+	5.73261i	−0.411869	+	0.299240i	0.362489	+	0.931988i	$0.381927\pi$
$368$	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
$372$	−2.98376	−	8.45876i	−0.154701	−	0.438566i
$373$	−17.5633	−	5.70667i	−0.909395	−	0.295480i	−0.183286	−	0.983060i	$-0.558673\pi$
$373$	−17.5633	−	5.70667i	−0.909395	−	0.295480i	−0.726109	+	0.687579i	$0.758673\pi$
$374$	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
$378$	32.3799	+	4.71510i	1.66544	+	0.242519i
$379$	−15.5245	+	21.3676i	−0.797439	+	1.09758i	0.195703	+	0.980663i	$0.437301\pi$
$379$	−15.5245	+	21.3676i	−0.797439	+	1.09758i	−0.993142	+	0.116917i	$0.962699\pi$
$380$		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	$-0.880284\pi$
$383$	−16.9911	+	12.3447i	−0.868203	+	0.630787i	0.0619009	+	0.998082i	$0.480284\pi$
$384$	10.3160	+	16.5062i	0.526439	+	0.842330i
$385$		0			0
$386$	9.58752	−	1.64140i	0.487992	−	0.0835449i
$387$	0.253242	−	0.0822833i	0.0128730	−	0.00418269i
$388$	−6.22664	−	1.85271i	−0.316110	−	0.0940571i
$389$	−14.0198	−	4.55530i	−0.710830	−	0.230963i	−0.0687872	−	0.997631i	$-0.521913\pi$
$389$	−14.0198	−	4.55530i	−0.710830	−	0.230963i	−0.642043	+	0.766669i	$0.721913\pi$
$390$		0			0
$391$	−9.27547	−	28.5470i	−0.469081	−	1.44368i
$392$	31.0521	−	17.3152i	1.56837	−	0.874549i
$393$	−6.08236			−0.306814
$394$	7.63527	−	15.4589i	0.384659	−	0.778810i
$395$		0			0
$396$	−0.142238	−	0.403235i	−0.00714772	−	0.0202633i
$397$	−14.4476	+	19.8855i	−0.725106	+	0.998023i	0.274233	+	0.961663i	$0.411576\pi$
$397$	−14.4476	+	19.8855i	−0.725106	+	0.998023i	−0.999339	+	0.0363595i	$0.988424\pi$
$398$	−20.5891	+	3.52488i	−1.03204	+	0.176686i
$399$	−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	$0.472801\pi$
$402$	15.2035	−	2.60286i	0.758280	−	0.129819i
$403$	−1.17766	+	1.62091i	−0.0586633	+	0.0807431i
$404$	2.59643	+	7.36072i	0.129177	+	0.366209i
$405$		0			0
$406$	−5.70888	+	11.5586i	−0.283327	+	0.573644i
$407$	34.7408			1.72204
$408$	−13.4913	−	24.1946i	−0.667920	−	1.19781i
$409$	1.50524	+	4.63264i	0.0744292	+	0.229069i	0.981349	−	0.192233i	$-0.0615730\pi$
$409$	1.50524	+	4.63264i	0.0744292	+	0.229069i	−0.906920	+	0.421303i	$0.861573\pi$
$410$		0			0
$411$	35.3996	+	11.5020i	1.74613	+	0.567352i
$412$	36.6264	+	10.8980i	1.80445	+	0.536906i
$413$	−4.54893	+	1.47804i	−0.223838	+	0.0727294i
$414$	−0.294206	+	0.0503685i	−0.0144595	+	0.00247548i
$415$		0			0
$416$	1.72851	−	3.98952i	0.0847473	−	0.195602i
$417$	−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	$-0.169759\pi$
$419$	2.28269	+	3.14185i	0.111517	+	0.153489i	−0.749610	+	0.661879i	$0.769759\pi$
$420$		0			0
$421$	4.13220	−	5.68749i	0.201391	−	0.277191i	−0.696361	−	0.717691i	$-0.745199\pi$
$421$	4.13220	−	5.68749i	0.201391	−	0.277191i	0.897753	+	0.440500i	$0.145199\pi$
$422$	−3.22795	−	0.470048i	−0.157134	−	0.0228816i
$423$	−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
$428$	8.12745	+	23.0408i	0.392855	+	1.11372i
$429$	4.15127	−	5.71374i	0.200425	−	0.275862i
$430$		0			0
$431$	−1.52243	+	1.10611i	−0.0733329	+	0.0532795i	−0.623848	−	0.781546i	$-0.714431\pi$
$431$	−1.52243	+	1.10611i	−0.0733329	+	0.0532795i	0.550515	+	0.834825i	$0.314431\pi$
$432$	−19.5497	+	7.44956i	−0.940585	+	0.358417i
$433$	−5.28222	+	3.83776i	−0.253847	+	0.184431i	−0.707430	−	0.706783i	$-0.750146\pi$
$433$	−5.28222	+	3.83776i	−0.253847	+	0.184431i	0.453583	+	0.891214i	$0.350146\pi$
$434$	11.3869	−	11.6747i	0.546590	−	0.560404i
$435$		0			0
$436$	−13.3789	+	10.2400i	−0.640735	+	0.490408i
$437$	8.68158	−	2.82082i	0.415296	−	0.134938i
$438$	−10.0441	−	9.79655i	−0.479927	−	0.468097i
$439$	8.75988	−	26.9601i	0.418086	−	1.28674i	−0.491375	−	0.870948i	$-0.663506\pi$
$439$	8.75988	−	26.9601i	0.418086	−	1.28674i	0.909461	−	0.415789i	$-0.136494\pi$
$440$		0			0
$441$	0.155488	+	0.478542i	0.00740417	+	0.0227877i
$442$	−2.74020	+	5.54801i	−0.130338	+	0.263892i
$443$			25.7646i			1.22412i	0.790813	+	0.612058i	$0.209658\pi$
$443$			25.7646i			1.22412i	−0.790813	+	0.612058i	$0.790342\pi$
$444$	−0.558502	−	22.3749i	−0.0265053	−	1.06187i
$445$		0			0
$446$	−0.454585	+	3.12176i	−0.0215252	+	0.147820i
$447$	6.41176	+	4.65842i	0.303266	+	0.220336i
$448$	−18.6021	+	30.1072i	−0.878868	+	1.42243i
$449$	−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
$452$	−6.57352	−	8.58853i	−0.309193	−	0.403971i
$453$	−1.78161	+	2.45217i	−0.0837072	+	0.115213i
$454$	9.32111	+	1.35732i	0.437461	+	0.0637022i
$455$		0			0
$456$	7.35795	−	4.10292i	0.344568	−	0.192137i
$457$	10.4431			0.488509			0.244255	−	0.969711i	$-0.421457\pi$
$457$	10.4431			0.488509			0.244255	+	0.969711i	$0.421457\pi$
$458$	−6.88269	+	13.9352i	−0.321607	+	0.651150i
$459$	28.3171	−	9.20077i	1.32173	−	0.429455i
$460$		0			0
$461$	29.9901	+	9.74436i	1.39678	+	0.453840i	0.908147	−	0.418651i	$-0.137497\pi$
$461$	29.9901	+	9.74436i	1.39678	+	0.453840i	0.488630	+	0.872491i	$0.337497\pi$
$462$	−40.1392	+	41.1537i	−1.86745	+	1.91464i
$463$	−4.16244	−	12.8107i	−0.193445	−	0.595362i	−0.999991	−	0.00419137i	$-0.998666\pi$
$463$	−4.16244	−	12.8107i	−0.193445	−	0.595362i	0.806546	−	0.591171i	$-0.201334\pi$
$464$	−0.411223	−	8.23217i	−0.0190906	−	0.382169i
$465$		0			0
$466$	26.8827	−	27.5621i	1.24532	−	1.27679i
$467$	11.3230	+	15.5848i	0.523968	+	0.721180i	0.986196	−	0.165581i	$-0.0529499\pi$
$467$	11.3230	+	15.5848i	0.523968	+	0.721180i	−0.462228	+	0.886761i	$0.652950\pi$
$468$	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
$472$	2.07996	−	2.24182i	0.0957379	−	0.103188i
$473$	−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
$478$	−2.20027	+	15.1099i	−0.100638	+	0.691111i
$479$	16.2835	+	11.8306i	0.744010	+	0.540555i	0.893964	−	0.448138i	$-0.147913\pi$
$479$	16.2835	+	11.8306i	0.744010	+	0.540555i	−0.149954	+	0.988693i	$0.547913\pi$
$480$		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
$484$	33.5954	+	9.99617i	1.52707	+	0.454371i
$485$		0			0
$486$	−0.0992679	−	0.579831i	−0.00450288	−	0.0263017i
$487$	−8.72080	−	26.8399i	−0.395177	−	1.21623i	−0.928823	−	0.370523i	$-0.879179\pi$
$487$	−8.72080	−	26.8399i	−0.395177	−	1.21623i	0.533646	−	0.845708i	$-0.320821\pi$
$488$	20.0446	−	3.94888i	0.907378	−	0.178757i
$489$	−3.83994	+	11.8181i	−0.173648	+	0.534434i
$490$		0			0
$491$	−34.0495	+	11.0634i	−1.53663	+	0.499283i	−0.950445	−	0.310892i	$-0.899372\pi$
$491$	−34.0495	+	11.0634i	−1.53663	+	0.499283i	−0.586189	+	0.810174i	$0.699372\pi$
$492$	8.40078	−	0.209692i	0.378737	−	0.00945367i
$493$			11.7305i			0.528314i
$494$	−1.68724	−	0.833337i	−0.0759123	−	0.0374936i
$495$		0			0
$496$	−2.72335	+	10.0650i	−0.122282	+	0.451934i
$497$	−2.09163	−	1.51966i	−0.0938224	−	0.0681659i
$498$	16.3016	−	2.79086i	0.730492	−	0.125061i
$499$			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
$502$	4.61872	+	26.9783i	0.206144	+	1.20410i
$503$	16.8678	+	12.2552i	0.752097	+	0.546430i	0.896476	−	0.443092i	$-0.146118\pi$
$503$	16.8678	+	12.2552i	0.752097	+	0.546430i	−0.144379	+	0.989522i	$0.546118\pi$
$504$	−0.367169	−	0.340660i	−0.0163550	−	0.0151742i
$505$		0			0
$506$	17.6364	−	35.7079i	0.784033	−	1.58741i
$507$		−	21.3496i		−	0.948168i
$508$	0.667441	+	26.7393i	0.0296129	+	1.18636i
$509$	−34.2578	+	11.1310i	−1.51845	+	0.493374i	−0.945335	−	0.326101i	$-0.894265\pi$
$509$	−34.2578	+	11.1310i	−1.51845	+	0.493374i	−0.573115	+	0.819475i	$0.694265\pi$
$510$		0			0
$511$	7.88306	−	24.2616i	0.348726	−	1.07327i
$512$	1.01288	−	22.6047i	0.0447632	−	0.998998i
$513$	2.79810	+	8.61166i	0.123539	+	0.380214i
$514$	−15.3801	+	2.63309i	−0.678387	+	0.116141i
$515$		0			0
$516$	21.9384	+	6.52767i	0.965784	+	0.287365i
$517$	−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	0.996185	−	0.0872702i	$-0.0278144\pi$
$521$	27.8704	+	20.2490i	1.22102	+	0.887126i	0.224839	+	0.974396i	$0.427814\pi$
$522$	0.115433	+	0.0168092i	0.00505238	+	0.000735717i
$523$	−30.3045	−	9.84654i	−1.32512	−	0.430559i	−0.440873	−	0.897570i	$-0.645331\pi$
$523$	−30.3045	−	9.84654i	−1.32512	−	0.430559i	−0.884252	+	0.467011i	$0.845331\pi$
$524$	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
$528$	9.59987	−	35.4795i	0.417781	−	1.54405i
$529$	−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
$534$	−21.9490	−	21.4080i	−0.949827	−	0.926414i
$535$		0			0
$536$	−16.2700	−	7.53683i	−0.702758	−	0.325542i
$537$	3.79324	+	11.6744i	0.163691	+	0.503788i
$538$	18.0295	+	17.5850i	0.777305	+	0.758145i
$539$	−63.8498	−	20.7461i	−2.75021	−	0.893596i
$540$		0			0
$541$	−19.8645	+	6.45438i	−0.854044	+	0.277496i	−0.703139	−	0.711053i	$-0.748219\pi$
$541$	−19.8645	+	6.45438i	−0.854044	+	0.277496i	−0.150905	+	0.988548i	$0.548219\pi$
$542$	10.2572	+	5.06611i	0.440585	+	0.217608i
$543$	4.85313			0.208268
$544$	−3.04474	+	32.0587i	−0.130542	+	1.37450i
$545$		0			0
$546$	1.19211	−	8.18654i	0.0510175	−	0.350351i
$547$	−17.7386	+	24.4151i	−0.758450	+	1.04392i	0.238892	+	0.971046i	$0.423216\pi$
$547$	−17.7386	+	24.4151i	−0.758450	+	1.04392i	−0.997341	+	0.0728702i	$0.976784\pi$
$548$	−26.2985	−	34.3599i	−1.12342	−	1.46778i
$549$			0.289133i			0.0123399i
$550$		0			0
$551$	−3.56742			−0.151977
$552$	−23.2813	−	10.7847i	−0.990919	−	0.459028i
$553$	27.7377	+	20.1526i	1.17953	+	0.856978i
$554$	−28.6000	−	4.16467i	−1.21510	−	0.176940i
$555$		0			0
$556$	3.99395	−	0.0996931i	0.169381	−	0.00422793i
$557$			0.749572i			0.0317604i	0.999874	+	0.0158802i	$0.00505504\pi$
$557$			0.749572i			0.0317604i	−0.999874	+	0.0158802i	$0.994945\pi$
$558$	−0.132309	−	0.0653484i	−0.00560109	−	0.00276642i
$559$	−1.57993	−	4.86251i	−0.0668237	−	0.205662i
$560$		0			0
$561$	−16.1645	+	49.7493i	−0.682467	+	2.10042i
$562$	−31.9415	+	32.7488i	−1.34737	+	1.38142i
$563$	22.1519	−	7.19759i	0.933591	−	0.303342i	0.197561	−	0.980291i	$-0.436698\pi$
$563$	22.1519	−	7.19759i	0.933591	−	0.303342i	0.736030	+	0.676949i	$0.236698\pi$
$564$	−21.9752	+	16.8195i	−0.925324	+	0.708228i
$565$		0			0
$566$	−24.4281	−	23.8259i	−1.02679	−	1.00148i
$567$	−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	−0.707877	−	0.706336i	$-0.750347\pi$
$569$	−6.07930	+	4.41687i	−0.254858	+	0.185165i	0.453019	+	0.891501i	$0.350347\pi$
$570$		0			0
$571$	1.37819	−	1.89691i	0.0576753	−	0.0793832i	−0.779205	−	0.626769i	$-0.784377\pi$
$571$	1.37819	−	1.89691i	0.0576753	−	0.0793832i	0.836880	+	0.547386i	$0.184377\pi$
$572$	−7.74254	+	2.73112i	−0.323732	+	0.114194i
$573$	−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	−0.714060	−	0.700084i	$-0.753146\pi$
$577$	6.60875	−	20.3396i	0.275126	−	0.846750i	0.989186	−	0.146666i	$-0.0468543\pi$
$578$	3.13975	−	21.5616i	0.130597	−	0.896843i
$579$	−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
$584$	3.15260	+	16.0027i	0.130456	+	0.662197i
$585$		0			0
$586$	2.47557	+	14.4600i	0.102265	+	0.597337i
$587$	6.66288	−	2.16490i	0.275007	−	0.0893551i	−0.168267	−	0.985741i	$-0.553817\pi$
$587$	6.66288	−	2.16490i	0.275007	−	0.0893551i	0.443274	+	0.896386i	$0.353817\pi$
$588$	−12.3351	+	41.4562i	−0.508691	+	1.70962i
$589$	4.29204	+	1.39457i	0.176850	+	0.0574622i
$590$		0			0
$591$	6.48173	+	19.9487i	0.266623	+	0.820581i
$592$	−14.2241	+	21.7862i	−0.584607	+	0.895409i
$593$	−28.8406			−1.18434			−0.592171	−	0.805812i	$-0.701729\pi$
$593$	−28.8406			−1.18434			−0.592171	+	0.805812i	$0.701729\pi$
$594$	35.4204	+	17.4943i	1.45331	+	0.717802i
$595$		0			0
$596$	−3.06477	−	8.68842i	−0.125538	−	0.355891i
$597$	14.9368	−	20.5587i	0.611323	−	0.841414i
$598$	0.967129	+	5.64907i	0.0395489	+	0.231008i
$599$	−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	$0.600200\pi$
$602$	7.02259	+	41.0195i	0.286219	+	1.67183i
$603$	0.149160	−	0.205301i	0.00607427	−	0.00836052i
$604$	3.32287	−	1.17212i	0.135206	−	0.0476927i
$605$		0			0
$606$	−8.51362	−	4.20493i	−0.345842	−	0.170814i
$607$	34.1325			1.38540			0.692699	−	0.721227i	$-0.256422\pi$
$607$	34.1325			1.38540			0.692699	+	0.721227i	$0.256422\pi$
$608$	−9.74954	−	0.925952i	−0.395396	−	0.0375523i
$609$	−4.84638	−	14.9156i	−0.196385	−	0.604411i
$610$		0			0
$611$	5.87887	+	1.91016i	0.237834	+	0.0772769i
$612$	−0.436824	−	0.129975i	−0.0176576	−	0.00525393i
$613$	−5.67158	+	1.84281i	−0.229073	+	0.0744303i	−0.421304	−	0.906919i	$-0.638428\pi$
$613$	−5.67158	+	1.84281i	−0.229073	+	0.0744303i	0.192231	+	0.981350i	$0.438428\pi$
$614$	−0.726264	−	4.24216i	−0.0293096	−	0.171200i
$615$		0			0
$616$	65.5676	−	12.9171i	2.64179	−	0.520445i
$617$	−6.15928	+	4.47498i	−0.247963	+	0.180156i	−0.704824	−	0.709383i	$-0.748974\pi$
$617$	−6.15928	+	4.47498i	−0.247963	+	0.180156i	0.456860	+	0.889538i	$0.348974\pi$
$618$	−41.1548	+	21.6204i	−1.65549	+	0.869701i
$619$	−16.7671	−	23.0779i	−0.673925	−	0.927579i	0.325916	−	0.945399i	$-0.394327\pi$
$619$	−16.7671	−	23.0779i	−0.673925	−	0.927579i	−0.999841	+	0.0178200i	$0.994327\pi$
$620$		0			0
$621$	16.2096	−	22.3107i	0.650470	−	0.895296i
$622$	−3.09598	+	21.2610i	−0.124138	+	0.852488i
$623$	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
$628$	−2.88498	−	8.17872i	−0.115123	−	0.326367i
$629$	21.7652	−	29.9572i	0.867834	−	1.19447i
$630$		0			0
$631$	27.7571	−	20.1667i	1.10499	−	0.802823i	0.123124	−	0.992391i	$-0.460709\pi$
$631$	27.7571	−	20.1667i	1.10499	−	0.802823i	0.981868	+	0.189568i	$0.0607089\pi$
$632$	−21.7644	−	2.61652i	−0.865741	−	0.104079i
$633$	3.21048	−	2.33255i	0.127605	−	0.0927106i
$634$	−29.7306	−	28.9977i	−1.18075	−	1.15165i
$635$		0			0
$636$	−9.76575	−	12.7593i	−0.387237	−	0.505938i
$637$	9.18851	−	2.98553i	0.364062	−	0.118291i
$638$	−10.8674	+	11.1420i	−0.430244	+	0.441117i
$639$	−0.00722920	+	0.0222492i	−0.000285983	+	0.000880165i
$640$		0			0
$641$	11.8514	+	36.4748i	0.468102	+	1.44067i	0.855039	+	0.518563i	$0.173533\pi$
$641$	11.8514	+	36.4748i	0.468102	+	1.44067i	−0.386938	+	0.922106i	$0.626467\pi$
$642$	−26.6496	−	13.1624i	−1.05178	−	0.519480i
$643$			4.80260i			0.189396i	0.995506	+	0.0946980i	$0.0301885\pi$
$643$			4.80260i			0.189396i	−0.995506	+	0.0946980i	$0.969811\pi$
$644$	−1.16409	−	46.6363i	−0.0458716	−	1.83773i
$645$		0			0
$646$	13.7923	+	2.00841i	0.542652	+	0.0790200i
$647$	3.05732	+	2.22128i	0.120196	+	0.0873273i	0.646259	−	0.763118i	$-0.276333\pi$
$647$	3.05732	+	2.22128i	0.120196	+	0.0873273i	−0.526063	+	0.850445i	$0.676333\pi$
$648$	10.5551	−	22.7856i	0.414643	−	0.895104i
$649$	−5.77462			−0.226674
$650$		0			0
$651$			19.8398i			0.777584i
$652$	11.4710	−	8.77975i	0.449241	−	0.343842i
$653$	−23.3583	+	32.1500i	−0.914082	+	1.25813i	0.0516709	+	0.998664i	$0.483545\pi$
$653$	−23.3583	+	32.1500i	−0.914082	+	1.25813i	−0.965753	+	0.259462i	$0.916455\pi$
$654$	2.95349	−	20.2824i	0.115491	−	0.793106i
$655$		0			0
$656$	−8.17976	−	5.34051i	−0.319366	−	0.208512i
$657$	−0.230831			−0.00900557
$658$	−45.1124	−	22.2813i	−1.75867	−	0.868616i
$659$	14.7150	−	4.78119i	0.573214	−	0.186249i	−0.00804417	−	0.999968i	$-0.502561\pi$
$659$	14.7150	−	4.78119i	0.573214	−	0.186249i	0.581258	+	0.813719i	$0.302561\pi$
$660$		0			0
$661$	−29.4671	−	9.57445i	−1.14614	−	0.372403i	−0.326451	−	0.945214i	$-0.605853\pi$
$661$	−29.4671	−	9.57445i	−1.14614	−	0.372403i	−0.819687	+	0.572811i	$0.805853\pi$
$662$	−33.9856	−	33.1479i	−1.32089	−	1.28833i
$663$	−2.32621	−	7.15933i	−0.0903424	−	0.278045i
$664$	−17.4452	−	8.08121i	−0.677004	−	0.313612i
$665$		0			0
$666$	−0.263604	−	0.257106i	−0.0102144	−	0.00996267i
$667$	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
$672$	−9.37338	−	42.0214i	−0.361586	−	1.62101i
$673$	8.86070	−	27.2704i	0.341555	−	1.05120i	−0.621848	−	0.783138i	$-0.713618\pi$
$673$	8.86070	−	27.2704i	0.341555	−	1.05120i	0.963402	−	0.268059i	$-0.0863823\pi$
$674$	−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	0.796733	−	0.604331i	$-0.206560\pi$
$677$	28.2591	+	9.18195i	1.08609	+	0.352891i	0.289353	+	0.957222i	$0.406560\pi$
$678$	13.0202	+	1.89597i	0.500037	+	0.0728144i
$679$	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	0.828423	−	0.560103i	$-0.189238\pi$
$683$	1.03849	+	1.42936i	0.0397366	+	0.0546928i	−0.788686	+	0.614796i	$0.789238\pi$
$684$	0.0395274	−	0.132845i	0.00151137	−	0.00507945i
$685$		0			0
$686$	−34.3476	+	5.88035i	−1.31140	+	0.224513i
$687$	−5.84285	−	17.9825i	−0.222919	−	0.686073i
$688$	−16.6943	−	20.7192i	−0.636463	−	0.789913i
$689$	−1.10908	+	3.41340i	−0.0422526	+	0.130040i
$690$		0			0
$691$	12.3432	−	4.01054i	0.469556	−	0.152568i	−0.0646751	−	0.997906i	$-0.520601\pi$
$691$	12.3432	−	4.01054i	0.469556	−	0.152568i	0.534231	+	0.845338i	$0.320601\pi$
$692$	27.3821	−	0.683486i	1.04091	−	0.0259822i
$693$			0.945779i			0.0359272i
$694$	2.65800	−	5.38159i	0.100896	−	0.204283i
$695$		0			0
$696$	7.35076	+	6.82005i	0.278630	+	0.258513i
$697$	11.2476	+	8.17185i	0.426033	+	0.309531i
$698$	−4.00425	−	23.3891i	−0.151563	−	0.885292i
$699$			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	$-0.0604713\pi$
$702$	−5.60358	+	0.959340i	−0.211493	+	0.0362080i
$703$	9.11045	+	6.61913i	0.343607	+	0.249645i
$704$	−32.5919	+	27.6298i	−1.22835	+	1.04134i
$705$		0			0
$706$	−43.7882	−	21.6273i	−1.64799	−	0.813954i
$707$		−	17.2644i		−	0.649295i
$708$	0.0928343	+	3.71916i	0.00348893	+	0.139775i
$709$	39.3712	−	12.7925i	1.47862	−	0.480432i	0.544918	−	0.838490i	$-0.316561\pi$
$709$	39.3712	−	12.7925i	1.47862	−	0.480432i	0.933699	+	0.358058i	$0.116561\pi$
$710$		0			0
$711$	0.0958687	−	0.295054i	0.00359536	−	0.0110654i
$712$	6.88925	+	34.9700i	0.258186	+	1.31056i
$713$	−4.24731	−	13.0719i	−0.159063	−	0.489546i
$714$	10.3397	+	60.3951i	0.386955	+	2.26023i
$715$		0			0
$716$	4.06956	−	13.6771i	0.152086	−	0.511137i
$717$	−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	0.0480227	−	0.998846i	$-0.484708\pi$
$719$	27.1580	−	19.7314i	1.01282	−	0.735858i	0.964799	+	0.262988i	$0.0847080\pi$
$720$		0			0
$721$	−68.3814	−	49.6820i	−2.54666	−	1.85026i
$722$	3.26114	−	22.3952i	0.121367	−	0.833462i
$723$	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	−0.278630	−	0.960399i	$-0.589880\pi$
$727$	13.7860	−	42.4290i	0.511295	−	1.57360i	0.789924	−	0.613204i	$-0.210120\pi$
$728$	−6.54103	+	7.05003i	−0.242427	+	0.261292i
$729$	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	0.954306	+	0.298831i	$0.0965968\pi$
$733$	25.5474	+	35.1630i	0.943615	+	1.29877i	−0.0106913	+	0.999943i	$0.503403\pi$
$734$	−9.63045	+	9.87384i	−0.355467	+	0.364450i
$735$		0			0
$736$	15.1718	+	25.6800i	0.559239	+	0.946577i
$737$	10.4630	+	32.2018i	0.385410	+	1.18617i
$738$	0.0965319	−	0.0989715i	0.00355339	−	0.00364319i
$739$	−18.2840	−	5.94083i	−0.672588	−	0.218537i	−0.0472404	−	0.998884i	$-0.515043\pi$
$739$	−18.2840	−	5.94083i	−0.672588	−	0.218537i	−0.625347	+	0.780347i	$0.715043\pi$
$740$		0			0
$741$	2.17726	−	0.707436i	0.0799838	−	0.0259883i
$742$	12.9370	−	26.1932i	0.474932	−	0.961583i
$743$	35.7627			1.31200			0.656002	−	0.754759i	$-0.272246\pi$
$743$	35.7627			1.31200			0.656002	+	0.754759i	$0.272246\pi$
$744$	−6.17778	−	11.0789i	−0.226488	−	0.406172i
$745$		0			0
$746$	−25.8440	−	3.76335i	−0.946215	−	0.137786i
$747$	0.159934	−	0.220130i	0.00585167	−	0.00805414i
$748$	48.2882	−	36.9590i	1.76559	−	1.35136i
$749$		−	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	$0.452560\pi$
$752$	32.1295	−	1.60498i	1.17164	−	0.0585274i
$753$	−26.9385	−	19.5720i	−0.981695	−	0.713243i
$754$	0.322754	−	2.21644i	0.0117540	−	0.0807180i
$755$		0			0
$756$	46.2607	−	1.15472i	1.68248	−	0.0419966i
$757$			42.4947i			1.54450i	0.635321	+	0.772248i	$0.280868\pi$
$757$			42.4947i			1.54450i	−0.635321	+	0.772248i	$0.719132\pi$
$758$	−16.5409	+	33.4898i	−0.600791	+	1.21641i
$759$	14.9719	+	46.0787i	0.543445	+	1.67255i
$760$		0			0
$761$	11.9096	−	36.6540i	0.431723	−	1.32871i	−0.464684	−	0.885477i	$-0.653832\pi$
$761$	11.9096	−	36.6540i	0.431723	−	1.32871i	0.896407	−	0.443231i	$-0.146168\pi$
$762$	−23.2944	−	22.7202i	−0.843866	−	0.823065i
$763$	35.4421	−	11.5158i	1.28309	−	0.416902i
$764$	17.1514	+	22.4088i	0.620514	+	0.810723i
$765$		0			0
$766$	−20.7384	+	21.2625i	−0.749310	+	0.768247i
$767$	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	−0.971577	−	0.236723i	$-0.923927\pi$
$769$	−29.0252	+	21.0880i	−1.04667	+	0.760454i	−0.0750973	+	0.997176i	$0.523927\pi$
$770$		0			0
$771$	11.1578	−	15.3574i	0.401839	−	0.553084i
$772$	12.9726	−	4.57599i	0.466896	−	0.164694i
$773$	1.68376	+	0.547088i	0.0605607	+	0.0196774i	0.339141	−	0.940736i	$-0.389864\pi$
$773$	1.68376	+	0.547088i	0.0605607	+	0.0196774i	−0.278580	+	0.960413i	$0.589864\pi$
$774$	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
$778$	−20.6297	−	3.00406i	−0.739611	−	0.107701i
$779$	−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
$784$	39.1524	−	31.5466i	1.39830	−	1.12666i
$785$		0			0
$786$	−8.47840	+	1.45151i	−0.302414	+	0.0517738i
$787$	−1.09587	+	0.356070i	−0.0390636	+	0.0126925i	−0.328484	−	0.944510i	$-0.606538\pi$
$787$	−1.09587	+	0.356070i	−0.0390636	+	0.0126925i	0.289420	+	0.957202i	$0.406538\pi$
$788$	6.95389	−	23.3708i	0.247722	−	0.832552i
$789$	12.6559	+	4.11215i	0.450562	+	0.146396i
$790$		0			0
$791$	7.39253	+	22.7519i	0.262848	+	0.808963i
$792$	−0.294499	−	0.528139i	−0.0104646	−	0.0187666i
$793$	5.55167			0.197145
$794$	−15.3935	+	31.1668i	−0.546295	+	1.10607i
$795$		0			0
$796$	−27.8586	+	9.82690i	−0.987423	+	0.348305i
$797$	−25.0783	+	34.5173i	−0.888319	+	1.22267i	0.0857282	+	0.996319i	$0.472678\pi$
$797$	−25.0783	+	34.5173i	−0.888319	+	1.22267i	−0.974047	+	0.226347i	$0.927322\pi$
$798$	−18.3671	+	3.14447i	−0.650188	+	0.111313i
$799$	−45.7832			−1.61969
$800$		0			0
$801$	−0.504425			−0.0178230
$802$	4.76450	−	0.815690i	0.168240	−	0.0288030i
$803$	18.1031	−	24.9167i	0.638844	−	0.879293i
$804$	20.5715	−	7.25641i	0.725500	−	0.255914i
$805$		0			0
$806$	−1.25476	+	2.54048i	−0.0441970	+	0.0894844i
$807$	−30.6390			−1.07854
$808$	5.37584	+	9.64073i	0.189121	+	0.339160i
$809$	−17.2761	−	53.1704i	−0.607396	−	1.86937i	−0.479397	−	0.877598i	$-0.659145\pi$
$809$	−17.2761	−	53.1704i	−0.607396	−	1.86937i	−0.127999	−	0.991774i	$-0.540855\pi$
$810$		0			0
$811$	−27.5933	−	8.96560i	−0.968931	−	0.314825i	−0.218547	−	0.975826i	$-0.570132\pi$
$811$	−27.5933	−	8.96560i	−0.968931	−	0.314825i	−0.750384	+	0.661002i	$0.770132\pi$
$812$	−5.19940	+	17.4743i	−0.182463	+	0.613228i
$813$	−13.2362	+	4.30072i	−0.464216	+	0.150833i
$814$	48.4264	−	8.29066i	1.69734	−	0.290588i
$815$		0			0
$816$	−24.5799	−	30.5060i	−0.860468	−	1.06792i
$817$	−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	0.0328288	+	0.999461i	$0.489548\pi$
$821$	−26.5861	+	36.5926i	−0.927860	+	1.27709i	−0.960689	+	0.277628i	$0.910452\pi$
$822$	52.0895	+	7.58517i	1.81683	+	0.264563i
$823$	−7.27585	+	22.3928i	−0.253620	+	0.780562i	0.740478	+	0.672080i	$0.234599\pi$
$823$	−7.27585	+	22.3928i	−0.253620	+	0.780562i	−0.994098	+	0.108482i	$0.965401\pi$
$824$	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	0.993592	−	0.113028i	$-0.0360549\pi$
$827$	49.7791	+	16.1742i	1.73099	+	0.562432i	0.737397	+	0.675460i	$0.236055\pi$
$828$	−0.398084	+	0.140421i	−0.0138344	+	0.00487996i
$829$	−14.8801	+	20.4807i	−0.516808	+	0.711325i	−0.985049	−	0.172276i	$-0.944888\pi$
$829$	−14.8801	+	20.4807i	−0.516808	+	0.711325i	0.468241	+	0.883601i	$0.344888\pi$
$830$		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
$834$	−3.39363	+	3.47939i	−0.117512	+	0.120481i
$835$		0			0
$836$	11.2398	+	14.6852i	0.388737	+	0.507898i
$837$	12.9666	−	4.21310i	0.448191	−	0.145626i
$838$	3.93169	+	3.83478i	0.135818	+	0.132470i
$839$	−9.60794	+	29.5702i	−0.331703	+	1.02088i	0.636620	+	0.771177i	$0.280332\pi$
$839$	−9.60794	+	29.5702i	−0.331703	+	1.02088i	−0.968323	+	0.249699i	$0.919668\pi$
$840$		0			0
$841$	7.64937	+	23.5424i	0.263772	+	0.811805i
$842$	4.40274	−	8.91411i	0.151728	−	0.307200i
$843$		−	55.6527i		−	1.91678i
$844$	−4.61173	+	0.115114i	−0.158742	+	0.00396237i
$845$		0			0
$846$	−0.0656049	+	0.450528i	−0.00225554	+	0.0154895i
$847$	−62.7227	−	45.5707i	−2.15518	−	1.56583i
$848$	0.931882	+	18.6551i	0.0320010	+	0.640618i
$849$	41.5127			1.42471
$850$		0			0
$851$		−	34.2970i		−	1.17569i
$852$	−1.59690	+	1.22225i	−0.0547090	+	0.0418734i
$853$	24.1636	−	33.2584i	0.827347	−	1.13875i	−0.161064	−	0.986944i	$-0.551493\pi$
$853$	24.1636	−	33.2584i	0.827347	−	1.13875i	0.988411	−	0.151801i	$-0.0485074\pi$
$854$	−44.7173	−	6.51165i	−1.53020	−	0.222824i
$855$		0			0
$856$	16.8277	+	30.1778i	0.575157	+	1.03145i
$857$	−7.69778			−0.262951			−0.131476	−	0.991319i	$-0.541971\pi$
$857$	−7.69778			−0.262951			−0.131476	+	0.991319i	$0.541971\pi$
$858$	4.42305	−	8.95524i	0.151000	−	0.305727i
$859$	−39.8085	+	12.9346i	−1.35825	+	0.441322i	−0.895458	−	0.445146i	$-0.853152\pi$
$859$	−39.8085	+	12.9346i	−1.35825	+	0.441322i	−0.462791	+	0.886468i	$0.653152\pi$
$860$		0			0
$861$	−17.6778	−	5.74385i	−0.602456	−	0.195750i
$862$	−1.85820	+	1.90516i	−0.0632906	+	0.0648901i
$863$	5.33595	+	16.4224i	0.181638	+	0.559024i	0.999874	−	0.0158581i	$-0.00504800\pi$
$863$	5.33595	+	16.4224i	0.181638	+	0.559024i	−0.818236	+	0.574882i	$0.805048\pi$
$864$	−25.4732	+	15.0496i	−0.866615	+	0.511998i
$865$		0			0
$866$	−6.44721	+	6.61014i	−0.219085	+	0.224622i
$867$	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
$872$	−16.2056	+	17.4667i	−0.548792	+	0.591497i
$873$	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	0.540092	−	0.841606i	$-0.318390\pi$
$877$	14.2844	+	4.64130i	0.482351	+	0.156725i	−0.0577404	+	0.998332i	$0.518390\pi$
$878$	5.77683	−	39.6711i	0.194958	−	1.33883i
$879$	−14.4387	−	10.4903i	−0.487004	−	0.353829i
$880$		0			0
$881$	37.8296	−	27.4848i	1.27451	−	0.925986i	0.275138	−	0.961405i	$-0.411277\pi$
$881$	37.8296	−	27.4848i	1.27451	−	0.925986i	0.999373	+	0.0354189i	$0.0112766\pi$
$882$	0.330940	+	0.629949i	0.0111433	+	0.0212115i
$883$	−19.8395	−	27.3068i	−0.667653	−	0.918946i	0.332051	−	0.943261i	$-0.392259\pi$
$883$	−19.8395	−	27.3068i	−0.667653	−	0.918946i	−0.999704	+	0.0243155i	$0.992259\pi$
$884$	−2.49566	+	8.38748i	−0.0839380	+	0.282101i
$885$		0			0
$886$	6.14856	+	35.9142i	0.206565	+	1.20656i
$887$	−1.28737	−	3.96211i	−0.0432256	−	0.133035i	0.927115	−	0.374778i	$-0.122281\pi$
$887$	−1.28737	−	3.96211i	−0.0432256	−	0.133035i	−0.970340	+	0.241743i	$0.922281\pi$
$888$	−6.11814	−	31.0559i	−0.205311	−	1.04217i
$889$	18.2824	−	56.2675i	0.613172	−	1.88715i
$890$		0			0
$891$	−45.0976	+	14.6531i	−1.51083	+	0.490897i
$892$	0.111327	+	4.46001i	0.00372749	+	0.149332i
$893$		−	13.9234i		−	0.465928i
$894$	10.0493	+	4.96340i	0.336098	+	0.166001i
$895$		0			0
$896$	−18.7452	+	46.4067i	−0.626235	+	1.55034i
$897$	−5.64075	−	4.09824i	−0.188339	−	0.136836i
$898$	−6.38484	+	1.09309i	−0.213065	+	0.0364770i
$899$			5.37148i			0.179149i
$900$		0			0
$901$		−	26.5827i		−	0.885597i
$902$	3.11277	+	18.1819i	0.103644	+	0.605392i
$903$	−40.9590	−	29.7585i	−1.36303	−	0.990299i
$904$	−11.2126	−	10.4031i	−0.372927	−	0.346002i
$905$		0			0
$906$	−1.89825	+	3.84333i	−0.0630650	+	0.127686i
$907$		−	44.9685i		−	1.49315i	−0.665299	−	0.746577i	$-0.731696\pi$
$907$		−	44.9685i		−	1.49315i	0.665299	−	0.746577i	$-0.268304\pi$
$908$	13.3169	−	0.332404i	0.441937	−	0.0110312i
$909$	−0.148573	+	0.0482742i	−0.00492784	+	0.00160115i
$910$		0			0
$911$	−3.92631	+	12.0839i	−0.130085	+	0.400359i	−0.994793	−	0.101915i	$-0.967503\pi$
$911$	−3.92631	+	12.0839i	−0.130085	+	0.400359i	0.864709	+	0.502274i	$0.167503\pi$
$912$	9.27735	−	7.47512i	0.307204	−	0.247526i
$913$	11.2187	+	34.5277i	0.371286	+	1.14270i
$914$	14.5570	−	2.49218i	0.481504	−	0.0824341i
$915$		0			0
$916$	−6.26847	+	21.0673i	−0.207116	+	0.696082i
$917$	−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	−0.239537	−	0.970887i	$-0.576996\pi$
$919$	18.4864	−	13.4312i	0.609810	−	0.443053i	0.849347	+	0.527834i	$0.176996\pi$
$920$		0			0
$921$	4.23591	+	3.07757i	0.139578	+	0.101409i
$922$	44.1296	+	6.42606i	1.45333	+	0.211631i
$923$	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
$928$	−2.53777	−	11.3770i	−0.0833064	−	0.373467i
$929$	24.2098	+	17.5894i	0.794297	+	0.577090i	0.909236	−	0.416282i	$-0.136667\pi$
$929$	24.2098	+	17.5894i	0.794297	+	0.577090i	−0.114939	+	0.993373i	$0.536667\pi$
$930$		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
$934$	19.5028	+	19.0220i	0.638151	+	0.622420i
$935$		0			0
$936$	0.0789605	+	0.0365772i	0.00258090	+	0.00119556i
$937$	14.6065	+	44.9541i	0.477172	+	1.46859i	0.843005	+	0.537905i	$0.180784\pi$
$937$	14.6065	+	44.9541i	0.477172	+	1.46859i	−0.365833	+	0.930681i	$0.619216\pi$
$938$	28.3926	+	27.6927i	0.927051	+	0.904200i
$939$	−0.195185	−	0.0634195i	−0.00636963	−	0.00206962i
$940$		0			0
$941$	20.6937	−	6.72379i	0.674595	−	0.219189i	0.0483677	−	0.998830i	$-0.484598\pi$
$941$	20.6937	−	6.72379i	0.674595	−	0.219189i	0.626228	+	0.779640i	$0.284598\pi$
$942$	9.45974	+	4.67223i	0.308215	+	0.152229i
$943$	12.8770			0.419333
$944$	2.36433	−	3.62131i	0.0769524	−	0.117864i
$945$		0			0
$946$	−7.24007	+	49.7196i	−0.235395	+	1.61652i
$947$	−31.9125	+	43.9238i	−1.03702	+	1.42733i	−0.137472	+	0.990506i	$0.543898\pi$
$947$	−31.9125	+	43.9238i	−1.03702	+	1.42733i	−0.899546	+	0.436827i	$0.856102\pi$
$948$	21.1770	−	16.2086i	0.687798	−	0.526430i
$949$			4.43220i			0.143875i
$950$		0			0
$951$	50.5237			1.63834
$952$	29.9397	−	64.6319i	0.970352	−	2.09473i
$953$	36.3305	+	26.3956i	1.17686	+	0.855039i	0.991814	−	0.127691i	$-0.0407566\pi$
$953$	36.3305	+	26.3956i	1.17686	+	0.855039i	0.185046	+	0.982730i	$0.440757\pi$
$954$	−0.261586	−	0.0380916i	−0.00846915	−	0.00123326i
$955$		0			0
$956$	0.538841	+	21.5873i	0.0174274	+	0.698182i
$957$		−	18.9346i		−	0.612068i
$958$	25.5213	+	12.6052i	0.824557	+	0.407254i
$959$	29.5751	+	91.0227i	0.955029	+	2.93928i
$960$		0			0
$961$	−7.47972	+	23.0202i	−0.241281	+	0.742588i
$962$	−4.93671	+	5.06148i	−0.159166	+	0.163189i
$963$	−0.465068	+	0.151110i	−0.0149866	+	0.00486944i
$964$	−11.7596	−	15.3643i	−0.378752	−	0.494852i
$965$		0			0
$966$	40.6279	+	39.6265i	1.30718	+	1.27496i
$967$	2.39657	−	1.74121i	0.0770686	−	0.0559936i	−0.548584	−	0.836096i	$-0.684833\pi$
$967$	2.39657	−	1.74121i	0.0770686	−	0.0559936i	0.625652	+	0.780102i	$0.284833\pi$
$968$	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	$-0.936394\pi$
$971$	−15.2206	+	20.9493i	−0.488451	+	0.672295i	0.491650	+	0.870793i	$0.336394\pi$
$972$	−0.276746	−	0.784556i	−0.00887662	−	0.0251647i
$973$	−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	0.597107	+	0.802161i	$0.296317\pi$
$977$	−11.1732	+	34.3875i	−0.357461	+	1.10015i	−0.954569	+	0.297991i	$0.903683\pi$
$978$	−2.53231	+	17.3901i	−0.0809742	+	0.556073i
$979$	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	$-0.512839\pi$
$983$	28.1391	−	20.4443i	0.897499	−	0.652071i	0.937822	+	0.347115i	$0.112839\pi$
$984$	11.6601	−	2.29709i	0.371710	−	0.0732285i
$985$		0			0
$986$	2.79940	+	16.3515i	0.0891510	+	0.520738i
$987$	58.2146	−	18.9151i	1.85299	−	0.602073i
$988$	−2.55076	−	0.758968i	−0.0811506	−	0.0241460i
$989$	33.3574	+	10.8385i	1.06070	+	0.344643i
$990$		0			0
$991$	−1.42805	−	4.39510i	−0.0453636	−	0.139615i	0.925809	−	0.377991i	$-0.123385\pi$
$991$	−1.42805	−	4.39510i	−0.0453636	−	0.139615i	−0.971173	+	0.238376i	$0.923385\pi$
$992$	−1.39421	+	14.6799i	−0.0442662	+	0.466088i
$993$	57.7546			1.83279
$994$	−3.27825	−	1.61915i	−0.103980	−	0.0513562i
$995$		0			0
$996$	22.0573	−	7.78054i	0.698913	−	0.246536i
$997$	21.5409	−	29.6486i	0.682209	−	0.938979i	−0.317749	−	0.948175i	$-0.602927\pi$
$997$	21.5409	−	29.6486i	0.682209	−	0.938979i	0.999958	+	0.00919532i	$0.00292700\pi$
$998$	6.34801	+	37.0792i	0.200943	+	1.17372i
$999$	34.0208			1.07637

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.29.8	✓	112	40.13	odd	4
200.2.o.a.29.14	yes	112	5.3	odd	4
200.2.o.a.69.8	yes	112	25.17	odd	20
200.2.o.a.69.14	yes	112	200.117	odd	20
800.2.be.a.369.7		112	100.67	even	20
800.2.be.a.369.22		112	200.67	even	20
800.2.be.a.529.7		112	40.3	even	4
800.2.be.a.529.22		112	20.3	even	4
1000.2.o.a.149.15		112	5.2	odd	4
1000.2.o.a.149.21		112	40.37	odd	4
1000.2.o.a.349.15		112	200.133	odd	20
1000.2.o.a.349.21		112	25.8	odd	20
1000.2.t.b.101.4		224	5.4	even	2	inner
1000.2.t.b.101.16		224	8.5	even	2	inner
1000.2.t.b.101.41		224	40.29	even	2	inner
1000.2.t.b.101.53		224	1.1	even	1	trivial
1000.2.t.b.901.4		224	200.69	even	10	inner
1000.2.t.b.901.16		224	25.6	even	5	inner
1000.2.t.b.901.41		224	25.19	even	10	inner
1000.2.t.b.901.53		224	200.181	even	10	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)

\(f(q)\)	\(=\)	\(q+(1.39393 - 0.238643i) q^{2} +(-1.01126 + 1.39188i) q^{3} +(1.88610 - 0.665306i) q^{4} +(-1.07746 + 2.18152i) q^{6} -4.42380 q^{7} +(2.47032 - 1.37750i) q^{8} +(0.0123697 + 0.0380700i) q^{9} +O(q^{10})\)	\(q+(1.39393 - 0.238643i) q^{2} +(-1.01126 + 1.39188i) q^{3} +(1.88610 - 0.665306i) q^{4} +(-1.07746 + 2.18152i) q^{6} -4.42380 q^{7} +(2.47032 - 1.37750i) q^{8} +(0.0123697 + 0.0380700i) q^{9} +(-5.07953 - 1.65044i) q^{11} +(-0.981310 + 3.29802i) q^{12} +(0.730985 - 0.237511i) q^{13} +(-6.16649 + 1.05571i) q^{14} +(3.11474 - 2.50966i) 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} +(-7.47439 - 1.08841i) 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} +(-8.34373 + 2.94318i) 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} +(-5.62125 + 5.76331i) q^{34} +(0.0486587 + 0.0635742i) q^{36} +(-6.18628 + 2.01004i) q^{37} +(-1.75271 - 1.70951i) q^{38} +(-0.408628 + 1.25763i) q^{39} +(-0.754681 - 2.32267i) q^{41} +(4.76649 - 9.65060i) q^{42} -6.65200i q^{43} +(-10.6785 + 0.266548i) q^{44} +(-1.07450 + 7.37890i) q^{46} +(6.50644 + 4.72720i) q^{47} +(0.343341 + 6.87326i) q^{48} +12.5700 q^{49} -9.79409i q^{51} +(1.22069 - 0.934298i) q^{52} +(-2.74471 + 3.77778i) q^{53} +(-7.31948 - 1.06585i) q^{54} +(-10.9282 + 6.09377i) q^{56} +2.97854 q^{57} +(1.29049 - 2.61282i) q^{58} +(1.02828 - 0.334110i) q^{59} +(6.86954 + 2.23205i) q^{61} +(-2.57402 + 2.63907i) q^{62} +(-0.0547211 - 0.168414i) q^{63} +(4.20501 - 6.80573i) q^{64} +(9.07347 - 9.30278i) 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} +(0.0829985 + 0.0770061i) 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} +(-0.269476 + 1.85057i) 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} +(4.34112 - 14.5898i) q^{84} +(-1.58745 - 9.27244i) q^{86} +(1.09552 + 3.37167i) q^{87} +(-14.8216 + 2.91991i) q^{88} +(-3.89405 + 11.9847i) q^{89} +(-3.23373 + 1.05070i) q^{91} +(0.263143 + 10.5421i) q^{92} -4.48479i q^{93} +(10.1977 + 5.03669i) q^{94} +(2.11885 + 9.49892i) q^{96} +(-2.62786 - 1.90925i) q^{97} +(17.5218 - 2.99975i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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