LMFDB - Embedded newform 200.2.f.d.149.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [200,2,Mod(149,200)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(200, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("200.149"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$200 = 2^{3} \cdot 5^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	200.f (of order $2$ , degree $1$ , not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$1.59700804043$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{7})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{4} - 3x^{2} + 4$ x^4 - 3*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.4
Root			$1.32288 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	200.149
Dual form			200.2.f.d.149.3

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.32288 + 0.500000i) q^{2} -2.64575 q^{3} +(1.50000 + 1.32288i) q^{4} +(-3.50000 - 1.32288i) q^{6} +4.00000i q^{7} +(1.32288 + 2.50000i) q^{8} +4.00000 q^{9} +2.64575i q^{11} +(-3.96863 - 3.50000i) q^{12} +(-2.00000 + 5.29150i) q^{14} +(0.500000 + 3.96863i) q^{16} -3.00000i q^{17} +(5.29150 + 2.00000i) q^{18} -2.64575i q^{19} -10.5830i q^{21} +(-1.32288 + 3.50000i) q^{22} -4.00000i q^{23} +(-3.50000 - 6.61438i) q^{24} -2.64575 q^{27} +(-5.29150 + 6.00000i) q^{28} +4.00000 q^{31} +(-1.32288 + 5.50000i) q^{32} -7.00000i q^{33} +(1.50000 - 3.96863i) q^{34} +(6.00000 + 5.29150i) q^{36} +10.5830 q^{37} +(1.32288 - 3.50000i) q^{38} -5.00000 q^{41} +(5.29150 - 14.0000i) q^{42} -5.29150 q^{43} +(-3.50000 + 3.96863i) q^{44} +(2.00000 - 5.29150i) q^{46} -8.00000i q^{47} +(-1.32288 - 10.5000i) q^{48} -9.00000 q^{49} +7.93725i q^{51} +10.5830 q^{53} +(-3.50000 - 1.32288i) q^{54} +(-10.0000 + 5.29150i) q^{56} +7.00000i q^{57} -5.29150i q^{59} +10.5830i q^{61} +(5.29150 + 2.00000i) q^{62} +16.0000i q^{63} +(-4.50000 + 6.61438i) q^{64} +(3.50000 - 9.26013i) q^{66} -7.93725 q^{67} +(3.96863 - 4.50000i) q^{68} +10.5830i q^{69} +8.00000 q^{71} +(5.29150 + 10.0000i) q^{72} +7.00000i q^{73} +(14.0000 + 5.29150i) q^{74} +(3.50000 - 3.96863i) q^{76} -10.5830 q^{77} -4.00000 q^{79} -5.00000 q^{81} +(-6.61438 - 2.50000i) q^{82} +7.93725 q^{83} +(14.0000 - 15.8745i) q^{84} +(-7.00000 - 2.64575i) q^{86} +(-6.61438 + 3.50000i) q^{88} +1.00000 q^{89} +(5.29150 - 6.00000i) q^{92} -10.5830 q^{93} +(4.00000 - 10.5830i) q^{94} +(3.50000 - 14.5516i) q^{96} -2.00000i q^{97} +(-11.9059 - 4.50000i) q^{98} +10.5830i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$4 q + 6 q^{4} - 14 q^{6} + 16 q^{9} - 8 q^{14} + 2 q^{16} - 14 q^{24} + 16 q^{31} + 6 q^{34} + 24 q^{36} - 20 q^{41} - 14 q^{44} + 8 q^{46} - 36 q^{49} - 14 q^{54} - 40 q^{56} - 18 q^{64} + 14 q^{66} + 32 q^{71}+ \cdots + 14 q^{96}+O(q^{100})$ 4 * q + 6 * q^4 - 14 * q^6 + 16 * q^9 - 8 * q^14 + 2 * q^16 - 14 * q^24 + 16 * q^31 + 6 * q^34 + 24 * q^36 - 20 * q^41 - 14 * q^44 + 8 * q^46 - 36 * q^49 - 14 * q^54 - 40 * q^56 - 18 * q^64 + 14 * q^66 + 32 * q^71 + 56 * q^74 + 14 * q^76 - 16 * q^79 - 20 * q^81 + 56 * q^84 - 28 * q^86 + 4 * q^89 + 16 * q^94 + 14 * q^96

Character values

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

$n$	$101$	$151$	$177$
$\chi(n)$	$-1$	$1$	$-1$

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

)

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

$2$	1.32288	+	0.500000i	0.935414	+	0.353553i
$2$	1.32288	+	0.500000i	0.935414	+	0.353553i
$3$	−2.64575			−1.52753			−0.763763	−	0.645497i	$-0.776650\pi$
$3$	−2.64575			−1.52753			−0.763763	+	0.645497i	$0.776650\pi$
$4$	1.50000	+	1.32288i	0.750000	+	0.661438i
$5$		0			0
$5$		0			0
$6$	−3.50000	−	1.32288i	−1.42887	−	0.540062i
$7$			4.00000i			1.51186i	0.654654	+	0.755929i	$0.272814\pi$
$7$			4.00000i			1.51186i	−0.654654	+	0.755929i	$0.727186\pi$
$8$	1.32288	+	2.50000i	0.467707	+	0.883883i
$9$	4.00000			1.33333
$10$		0			0
$11$			2.64575i			0.797724i	0.917011	+	0.398862i	$0.130595\pi$
$11$			2.64575i			0.797724i	−0.917011	+	0.398862i	$0.869405\pi$
$12$	−3.96863	−	3.50000i	−1.14564	−	1.01036i
$13$		0			0			−	1.00000i	$-0.5\pi$
$13$		0			0				1.00000i	$0.5\pi$
$14$	−2.00000	+	5.29150i	−0.534522	+	1.41421i
$15$		0			0
$16$	0.500000	+	3.96863i	0.125000	+	0.992157i
$17$		−	3.00000i		−	0.727607i	−0.931476	−	0.363803i	$-0.881478\pi$
$17$		−	3.00000i		−	0.727607i	0.931476	−	0.363803i	$-0.118522\pi$
$18$	5.29150	+	2.00000i	1.24722	+	0.471405i
$19$		−	2.64575i		−	0.606977i	−0.952835	−	0.303488i	$-0.901849\pi$
$19$		−	2.64575i		−	0.606977i	0.952835	−	0.303488i	$-0.0981514\pi$
$20$		0			0
$21$		−	10.5830i		−	2.30940i
$22$	−1.32288	+	3.50000i	−0.282038	+	0.746203i
$23$		−	4.00000i		−	0.834058i	−0.908893	−	0.417029i	$-0.863071\pi$
$23$		−	4.00000i		−	0.834058i	0.908893	−	0.417029i	$-0.136929\pi$
$24$	−3.50000	−	6.61438i	−0.714435	−	1.35015i
$25$		0			0
$26$		0			0
$27$	−2.64575			−0.509175
$28$	−5.29150	+	6.00000i	−1.00000	+	1.13389i
$29$		0			0		1.00000			$0$
$29$		0			0		−1.00000			$\pi$
$30$		0			0
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$	−1.32288	+	5.50000i	−0.233854	+	0.972272i
$33$		−	7.00000i		−	1.21854i
$34$	1.50000	−	3.96863i	0.257248	−	0.680614i
$35$		0			0
$36$	6.00000	+	5.29150i	1.00000	+	0.881917i
$37$	10.5830			1.73984			0.869918	−	0.493197i	$-0.164172\pi$
$37$	10.5830			1.73984			0.869918	+	0.493197i	$0.164172\pi$
$38$	1.32288	−	3.50000i	0.214599	−	0.567775i
$39$		0			0
$40$		0			0
$41$	−5.00000			−0.780869			−0.390434	−	0.920631i	$-0.627675\pi$
$41$	−5.00000			−0.780869			−0.390434	+	0.920631i	$0.627675\pi$
$42$	5.29150	−	14.0000i	0.816497	−	2.16025i
$43$	−5.29150			−0.806947			−0.403473	−	0.914991i	$-0.632197\pi$
$43$	−5.29150			−0.806947			−0.403473	+	0.914991i	$0.632197\pi$
$44$	−3.50000	+	3.96863i	−0.527645	+	0.598293i
$45$		0			0
$46$	2.00000	−	5.29150i	0.294884	−	0.780189i
$47$		−	8.00000i		−	1.16692i	−0.812142	−	0.583460i	$-0.801699\pi$
$47$		−	8.00000i		−	1.16692i	0.812142	−	0.583460i	$-0.198301\pi$
$48$	−1.32288	−	10.5000i	−0.190941	−	1.51554i
$49$	−9.00000			−1.28571
$50$		0			0
$51$			7.93725i			1.11144i
$52$		0			0
$53$	10.5830			1.45369			0.726844	−	0.686803i	$-0.240986\pi$
$53$	10.5830			1.45369			0.726844	+	0.686803i	$0.240986\pi$
$54$	−3.50000	−	1.32288i	−0.476290	−	0.180021i
$55$		0			0
$56$	−10.0000	+	5.29150i	−1.33631	+	0.707107i
$57$			7.00000i			0.927173i
$58$		0			0
$59$		−	5.29150i		−	0.688895i	−0.938806	−	0.344447i	$-0.888066\pi$
$59$		−	5.29150i		−	0.688895i	0.938806	−	0.344447i	$-0.111934\pi$
$60$		0			0
$61$			10.5830i			1.35501i	0.735516	+	0.677507i	$0.236940\pi$
$61$			10.5830i			1.35501i	−0.735516	+	0.677507i	$0.763060\pi$
$62$	5.29150	+	2.00000i	0.672022	+	0.254000i
$63$			16.0000i			2.01581i
$64$	−4.50000	+	6.61438i	−0.562500	+	0.826797i
$65$		0			0
$66$	3.50000	−	9.26013i	0.430820	−	1.13984i
$67$	−7.93725			−0.969690			−0.484845	−	0.874600i	$-0.661124\pi$
$67$	−7.93725			−0.969690			−0.484845	+	0.874600i	$0.661124\pi$
$68$	3.96863	−	4.50000i	0.481267	−	0.545705i
$69$			10.5830i			1.27404i
$70$		0			0
$71$	8.00000			0.949425			0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000			0.949425			0.474713	+	0.880141i	$0.342552\pi$
$72$	5.29150	+	10.0000i	0.623610	+	1.17851i
$73$			7.00000i			0.819288i	0.912245	+	0.409644i	$0.134347\pi$
$73$			7.00000i			0.819288i	−0.912245	+	0.409644i	$0.865653\pi$
$74$	14.0000	+	5.29150i	1.62747	+	0.615125i
$75$		0			0
$76$	3.50000	−	3.96863i	0.401478	−	0.455233i
$77$	−10.5830			−1.20605
$78$		0			0
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$		0			0
$81$	−5.00000			−0.555556
$82$	−6.61438	−	2.50000i	−0.730436	−	0.276079i
$83$	7.93725			0.871227			0.435613	−	0.900134i	$-0.356531\pi$
$83$	7.93725			0.871227			0.435613	+	0.900134i	$0.356531\pi$
$84$	14.0000	−	15.8745i	1.52753	−	1.73205i
$85$		0			0
$86$	−7.00000	−	2.64575i	−0.754829	−	0.285299i
$87$		0			0
$88$	−6.61438	+	3.50000i	−0.705095	+	0.373101i
$89$	1.00000			0.106000			0.0529999	−	0.998595i	$-0.483122\pi$
$89$	1.00000			0.106000			0.0529999	+	0.998595i	$0.483122\pi$
$90$		0			0
$91$		0			0
$92$	5.29150	−	6.00000i	0.551677	−	0.625543i
$93$	−10.5830			−1.09741
$94$	4.00000	−	10.5830i	0.412568	−	1.09155i
$95$		0			0
$96$	3.50000	−	14.5516i	0.357217	−	1.48517i
$97$		−	2.00000i		−	0.203069i	−0.994832	−	0.101535i	$-0.967625\pi$
$97$		−	2.00000i		−	0.203069i	0.994832	−	0.101535i	$-0.0323753\pi$
$98$	−11.9059	−	4.50000i	−1.20268	−	0.454569i
$99$			10.5830i			1.06363i
$100$		0			0
$101$		−	10.5830i		−	1.05305i	−0.850160	−	0.526524i	$-0.823495\pi$
$101$		−	10.5830i		−	1.05305i	0.850160	−	0.526524i	$-0.176505\pi$
$102$	−3.96863	+	10.5000i	−0.392953	+	1.03965i
$103$		−	8.00000i		−	0.788263i	−0.919054	−	0.394132i	$-0.871045\pi$
$103$		−	8.00000i		−	0.788263i	0.919054	−	0.394132i	$-0.128955\pi$
$104$		0			0
$105$		0			0
$106$	14.0000	+	5.29150i	1.35980	+	0.513956i
$107$	2.64575			0.255774			0.127887	−	0.991789i	$-0.459180\pi$
$107$	2.64575			0.255774			0.127887	+	0.991789i	$0.459180\pi$
$108$	−3.96863	−	3.50000i	−0.381881	−	0.336788i
$109$		−	10.5830i		−	1.01367i	−0.862044	−	0.506834i	$-0.830816\pi$
$109$		−	10.5830i		−	1.01367i	0.862044	−	0.506834i	$-0.169184\pi$
$110$		0			0
$111$	−28.0000			−2.65764
$112$	−15.8745	+	2.00000i	−1.50000	+	0.188982i
$113$			15.0000i			1.41108i	0.708669	+	0.705541i	$0.249296\pi$
$113$			15.0000i			1.41108i	−0.708669	+	0.705541i	$0.750704\pi$
$114$	−3.50000	+	9.26013i	−0.327805	+	0.867291i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	2.64575	−	7.00000i	0.243561	−	0.644402i
$119$	12.0000			1.10004
$120$		0			0
$121$	4.00000			0.363636
$122$	−5.29150	+	14.0000i	−0.479070	+	1.26750i
$123$	13.2288			1.19280
$124$	6.00000	+	5.29150i	0.538816	+	0.475191i
$125$		0			0
$126$	−8.00000	+	21.1660i	−0.712697	+	1.88562i
$127$			12.0000i			1.06483i	0.846484	+	0.532414i	$0.178715\pi$
$127$			12.0000i			1.06483i	−0.846484	+	0.532414i	$0.821285\pi$
$128$	−9.26013	+	6.50000i	−0.818488	+	0.574524i
$129$	14.0000			1.23263
$130$		0			0
$131$		−	15.8745i		−	1.38696i	−0.720475	−	0.693481i	$-0.756076\pi$
$131$		−	15.8745i		−	1.38696i	0.720475	−	0.693481i	$-0.243924\pi$
$132$	9.26013	−	10.5000i	0.805991	−	0.913908i
$133$	10.5830			0.917663
$134$	−10.5000	−	3.96863i	−0.907062	−	0.342837i
$135$		0			0
$136$	7.50000	−	3.96863i	0.643120	−	0.340307i
$137$		−	19.0000i		−	1.62328i	−0.584158	−	0.811640i	$-0.698575\pi$
$137$		−	19.0000i		−	1.62328i	0.584158	−	0.811640i	$-0.301425\pi$
$138$	−5.29150	+	14.0000i	−0.450443	+	1.19176i
$139$			18.5203i			1.57087i	0.618945	+	0.785434i	$0.287560\pi$
$139$			18.5203i			1.57087i	−0.618945	+	0.785434i	$0.712440\pi$
$140$		0			0
$141$			21.1660i			1.78250i
$142$	10.5830	+	4.00000i	0.888106	+	0.335673i
$143$		0			0
$144$	2.00000	+	15.8745i	0.166667	+	1.32288i
$145$		0			0
$146$	−3.50000	+	9.26013i	−0.289662	+	0.766374i
$147$	23.8118			1.96396
$148$	15.8745	+	14.0000i	1.30488	+	1.15079i
$149$		0			0		1.00000			$0$
$149$		0			0		−1.00000			$\pi$
$150$		0			0
$151$	4.00000			0.325515			0.162758	−	0.986666i	$-0.447961\pi$
$151$	4.00000			0.325515			0.162758	+	0.986666i	$0.447961\pi$
$152$	6.61438	−	3.50000i	0.536497	−	0.283887i
$153$		−	12.0000i		−	0.970143i
$154$	−14.0000	−	5.29150i	−1.12815	−	0.426401i
$155$		0			0
$156$		0			0
$157$	−10.5830			−0.844616			−0.422308	−	0.906452i	$-0.638780\pi$
$157$	−10.5830			−0.844616			−0.422308	+	0.906452i	$0.638780\pi$
$158$	−5.29150	−	2.00000i	−0.420969	−	0.159111i
$159$	−28.0000			−2.22054
$160$		0			0
$161$	16.0000			1.26098
$162$	−6.61438	−	2.50000i	−0.519675	−	0.196419i
$163$	−13.2288			−1.03616			−0.518078	−	0.855333i	$-0.673352\pi$
$163$	−13.2288			−1.03616			−0.518078	+	0.855333i	$0.673352\pi$
$164$	−7.50000	−	6.61438i	−0.585652	−	0.516496i
$165$		0			0
$166$	10.5000	+	3.96863i	0.814958	+	0.308025i
$167$		0			0		1.00000			$0$
$167$		0			0		−1.00000			$\pi$
$168$	26.4575	−	14.0000i	2.04124	−	1.08012i
$169$	−13.0000			−1.00000
$170$		0			0
$171$		−	10.5830i		−	0.809303i
$172$	−7.93725	−	7.00000i	−0.605210	−	0.533745i
$173$	−21.1660			−1.60922			−0.804611	−	0.593802i	$-0.797626\pi$
$173$	−21.1660			−1.60922			−0.804611	+	0.593802i	$0.797626\pi$
$174$		0			0
$175$		0			0
$176$	−10.5000	+	1.32288i	−0.791467	+	0.0997155i
$177$			14.0000i			1.05230i
$178$	1.32288	+	0.500000i	0.0991537	+	0.0374766i
$179$		−	23.8118i		−	1.77977i	−0.456180	−	0.889887i	$-0.650783\pi$
$179$		−	23.8118i		−	1.77977i	0.456180	−	0.889887i	$-0.349217\pi$
$180$		0			0
$181$			10.5830i			0.786629i	0.919404	+	0.393314i	$0.128672\pi$
$181$			10.5830i			0.786629i	−0.919404	+	0.393314i	$0.871328\pi$
$182$		0			0
$183$		−	28.0000i		−	2.06982i
$184$	10.0000	−	5.29150i	0.737210	−	0.390095i
$185$		0			0
$186$	−14.0000	−	5.29150i	−1.02653	−	0.387992i
$187$	7.93725			0.580429
$188$	10.5830	−	12.0000i	0.771845	−	0.875190i
$189$		−	10.5830i		−	0.769800i
$190$		0			0
$191$	4.00000			0.289430			0.144715	−	0.989473i	$-0.453773\pi$
$191$	4.00000			0.289430			0.144715	+	0.989473i	$0.453773\pi$
$192$	11.9059	−	17.5000i	0.859233	−	1.26295i
$193$		−	5.00000i		−	0.359908i	−0.983675	−	0.179954i	$-0.942405\pi$
$193$		−	5.00000i		−	0.359908i	0.983675	−	0.179954i	$-0.0575949\pi$
$194$	1.00000	−	2.64575i	0.0717958	−	0.189954i
$195$		0			0
$196$	−13.5000	−	11.9059i	−0.964286	−	0.850420i
$197$	−10.5830			−0.754008			−0.377004	−	0.926212i	$-0.623046\pi$
$197$	−10.5830			−0.754008			−0.377004	+	0.926212i	$0.623046\pi$
$198$	−5.29150	+	14.0000i	−0.376051	+	0.994937i
$199$	24.0000			1.70131			0.850657	−	0.525720i	$-0.176204\pi$
$199$	24.0000			1.70131			0.850657	+	0.525720i	$0.176204\pi$
$200$		0			0
$201$	21.0000			1.48123
$202$	5.29150	−	14.0000i	0.372309	−	0.985037i
$203$		0			0
$204$	−10.5000	+	11.9059i	−0.735147	+	0.833578i
$205$		0			0
$206$	4.00000	−	10.5830i	0.278693	−	0.737353i
$207$		−	16.0000i		−	1.11208i
$208$		0			0
$209$	7.00000			0.484200
$210$		0			0
$211$		−	7.93725i		−	0.546423i	−0.961954	−	0.273212i	$-0.911914\pi$
$211$		−	7.93725i		−	0.546423i	0.961954	−	0.273212i	$-0.0880859\pi$
$212$	15.8745	+	14.0000i	1.09027	+	0.961524i
$213$	−21.1660			−1.45027
$214$	3.50000	+	1.32288i	0.239255	+	0.0904299i
$215$		0			0
$216$	−3.50000	−	6.61438i	−0.238145	−	0.450051i
$217$			16.0000i			1.08615i
$218$	5.29150	−	14.0000i	0.358386	−	0.948200i
$219$		−	18.5203i		−	1.25148i
$220$		0			0
$221$		0			0
$222$	−37.0405	−	14.0000i	−2.48600	−	0.939618i
$223$			16.0000i			1.07144i	0.844396	+	0.535720i	$0.179960\pi$
$223$			16.0000i			1.07144i	−0.844396	+	0.535720i	$0.820040\pi$
$224$	−22.0000	−	5.29150i	−1.46994	−	0.353553i
$225$		0			0
$226$	−7.50000	+	19.8431i	−0.498893	+	1.31995i
$227$	−15.8745			−1.05363			−0.526814	−	0.849981i	$-0.676614\pi$
$227$	−15.8745			−1.05363			−0.526814	+	0.849981i	$0.676614\pi$
$228$	−9.26013	+	10.5000i	−0.613267	+	0.695379i
$229$		−	21.1660i		−	1.39869i	−0.714785	−	0.699345i	$-0.753475\pi$
$229$		−	21.1660i		−	1.39869i	0.714785	−	0.699345i	$-0.246525\pi$
$230$		0			0
$231$	28.0000			1.84226
$232$		0			0
$233$		−	6.00000i		−	0.393073i	−0.980497	−	0.196537i	$-0.937031\pi$
$233$		−	6.00000i		−	0.393073i	0.980497	−	0.196537i	$-0.0629694\pi$
$234$		0			0
$235$		0			0
$236$	7.00000	−	7.93725i	0.455661	−	0.516671i
$237$	10.5830			0.687440
$238$	15.8745	+	6.00000i	1.02899	+	0.388922i
$239$	8.00000			0.517477			0.258738	−	0.965947i	$-0.416693\pi$
$239$	8.00000			0.517477			0.258738	+	0.965947i	$0.416693\pi$
$240$		0			0
$241$	−21.0000			−1.35273			−0.676364	−	0.736567i	$-0.736446\pi$
$241$	−21.0000			−1.35273			−0.676364	+	0.736567i	$0.736446\pi$
$242$	5.29150	+	2.00000i	0.340151	+	0.128565i
$243$	21.1660			1.35780
$244$	−14.0000	+	15.8745i	−0.896258	+	1.01626i
$245$		0			0
$246$	17.5000	+	6.61438i	1.11576	+	0.421717i
$247$		0			0
$248$	5.29150	+	10.0000i	0.336011	+	0.635001i
$249$	−21.0000			−1.33082
$250$		0			0
$251$		−	7.93725i		−	0.500995i	−0.968117	−	0.250498i	$-0.919406\pi$
$251$		−	7.93725i		−	0.500995i	0.968117	−	0.250498i	$-0.0805942\pi$
$252$	−21.1660	+	24.0000i	−1.33333	+	1.51186i
$253$	10.5830			0.665348
$254$	−6.00000	+	15.8745i	−0.376473	+	0.996055i
$255$		0			0
$256$	−15.5000	+	3.96863i	−0.968750	+	0.248039i
$257$			14.0000i			0.873296i	0.899632	+	0.436648i	$0.143834\pi$
$257$			14.0000i			0.873296i	−0.899632	+	0.436648i	$0.856166\pi$
$258$	18.5203	+	7.00000i	1.15302	+	0.435801i
$259$			42.3320i			2.63038i
$260$		0			0
$261$		0			0
$262$	7.93725	−	21.0000i	0.490365	−	1.29738i
$263$		−	12.0000i		−	0.739952i	−0.929041	−	0.369976i	$-0.879366\pi$
$263$		−	12.0000i		−	0.739952i	0.929041	−	0.369976i	$-0.120634\pi$
$264$	17.5000	−	9.26013i	1.07705	−	0.569922i
$265$		0			0
$266$	14.0000	+	5.29150i	0.858395	+	0.324443i
$267$	−2.64575			−0.161917
$268$	−11.9059	−	10.5000i	−0.727267	−	0.641390i
$269$			21.1660i			1.29051i	0.763965	+	0.645257i	$0.223250\pi$
$269$			21.1660i			1.29051i	−0.763965	+	0.645257i	$0.776750\pi$
$270$		0			0
$271$	−20.0000			−1.21491			−0.607457	−	0.794353i	$-0.707810\pi$
$271$	−20.0000			−1.21491			−0.607457	+	0.794353i	$0.707810\pi$
$272$	11.9059	−	1.50000i	0.721900	−	0.0909509i
$273$		0			0
$274$	9.50000	−	25.1346i	0.573916	−	1.51844i
$275$		0			0
$276$	−14.0000	+	15.8745i	−0.842701	+	0.955533i
$277$	21.1660			1.27174			0.635871	−	0.771795i	$-0.280641\pi$
$277$	21.1660			1.27174			0.635871	+	0.771795i	$0.280641\pi$
$278$	−9.26013	+	24.5000i	−0.555386	+	1.46941i
$279$	16.0000			0.957895
$280$		0			0
$281$	−22.0000			−1.31241			−0.656205	−	0.754583i	$-0.727839\pi$
$281$	−22.0000			−1.31241			−0.656205	+	0.754583i	$0.727839\pi$
$282$	−10.5830	+	28.0000i	−0.630209	+	1.66738i
$283$	−13.2288			−0.786368			−0.393184	−	0.919460i	$-0.628626\pi$
$283$	−13.2288			−0.786368			−0.393184	+	0.919460i	$0.628626\pi$
$284$	12.0000	+	10.5830i	0.712069	+	0.627986i
$285$		0			0
$286$		0			0
$287$		−	20.0000i		−	1.18056i
$288$	−5.29150	+	22.0000i	−0.311805	+	1.29636i
$289$	8.00000			0.470588
$290$		0			0
$291$			5.29150i			0.310193i
$292$	−9.26013	+	10.5000i	−0.541908	+	0.614466i
$293$	−10.5830			−0.618266			−0.309133	−	0.951019i	$-0.600039\pi$
$293$	−10.5830			−0.618266			−0.309133	+	0.951019i	$0.600039\pi$
$294$	31.5000	+	11.9059i	1.83712	+	0.694365i
$295$		0			0
$296$	14.0000	+	26.4575i	0.813733	+	1.53781i
$297$		−	7.00000i		−	0.406181i
$298$		0			0
$299$		0			0
$300$		0			0
$301$		−	21.1660i		−	1.21999i
$302$	5.29150	+	2.00000i	0.304492	+	0.115087i
$303$			28.0000i			1.60856i
$304$	10.5000	−	1.32288i	0.602216	−	0.0758721i
$305$		0			0
$306$	6.00000	−	15.8745i	0.342997	−	0.907485i
$307$	2.64575			0.151001			0.0755005	−	0.997146i	$-0.475945\pi$
$307$	2.64575			0.151001			0.0755005	+	0.997146i	$0.475945\pi$
$308$	−15.8745	−	14.0000i	−0.904534	−	0.797724i
$309$			21.1660i			1.20409i
$310$		0			0
$311$	−4.00000			−0.226819			−0.113410	−	0.993548i	$-0.536177\pi$
$311$	−4.00000			−0.226819			−0.113410	+	0.993548i	$0.536177\pi$
$312$		0			0
$313$		−	6.00000i		−	0.339140i	−0.985518	−	0.169570i	$-0.945762\pi$
$313$		−	6.00000i		−	0.339140i	0.985518	−	0.169570i	$-0.0542379\pi$
$314$	−14.0000	−	5.29150i	−0.790066	−	0.298617i
$315$		0			0
$316$	−6.00000	−	5.29150i	−0.337526	−	0.297670i
$317$		0			0			−	1.00000i	$-0.5\pi$
$317$		0			0				1.00000i	$0.5\pi$
$318$	−37.0405	−	14.0000i	−2.07713	−	0.785081i
$319$		0			0
$320$		0			0
$321$	−7.00000			−0.390702
$322$	21.1660	+	8.00000i	1.17954	+	0.445823i
$323$	−7.93725			−0.441641
$324$	−7.50000	−	6.61438i	−0.416667	−	0.367465i
$325$		0			0
$326$	−17.5000	−	6.61438i	−0.969235	−	0.366337i
$327$			28.0000i			1.54840i
$328$	−6.61438	−	12.5000i	−0.365218	−	0.690197i
$329$	32.0000			1.76422
$330$		0			0
$331$			2.64575i			0.145424i	0.997353	+	0.0727118i	$0.0231653\pi$
$331$			2.64575i			0.145424i	−0.997353	+	0.0727118i	$0.976835\pi$
$332$	11.9059	+	10.5000i	0.653420	+	0.576262i
$333$	42.3320			2.31978
$334$		0			0
$335$		0			0
$336$	42.0000	−	5.29150i	2.29129	−	0.288675i
$337$		−	15.0000i		−	0.817102i	−0.912735	−	0.408551i	$-0.866034\pi$
$337$		−	15.0000i		−	0.817102i	0.912735	−	0.408551i	$-0.133966\pi$
$338$	−17.1974	−	6.50000i	−0.935414	−	0.353553i
$339$		−	39.6863i		−	2.15546i
$340$		0			0
$341$			10.5830i			0.573102i
$342$	5.29150	−	14.0000i	0.286132	−	0.757033i
$343$		−	8.00000i		−	0.431959i
$344$	−7.00000	−	13.2288i	−0.377415	−	0.713247i
$345$		0			0
$346$	−28.0000	−	10.5830i	−1.50529	−	0.568946i
$347$	2.64575			0.142031			0.0710157	−	0.997475i	$-0.477376\pi$
$347$	2.64575			0.142031			0.0710157	+	0.997475i	$0.477376\pi$
$348$		0			0
$349$			10.5830i			0.566495i	0.959047	+	0.283248i	$0.0914118\pi$
$349$			10.5830i			0.566495i	−0.959047	+	0.283248i	$0.908588\pi$
$350$		0			0
$351$		0			0
$352$	−14.5516	−	3.50000i	−0.775605	−	0.186551i
$353$			18.0000i			0.958043i	0.877803	+	0.479022i	$0.159008\pi$
$353$			18.0000i			0.958043i	−0.877803	+	0.479022i	$0.840992\pi$
$354$	−7.00000	+	18.5203i	−0.372046	+	0.984341i
$355$		0			0
$356$	1.50000	+	1.32288i	0.0794998	+	0.0701123i
$357$	−31.7490			−1.68034
$358$	11.9059	−	31.5000i	0.629245	−	1.66483i
$359$	−36.0000			−1.90001			−0.950004	−	0.312239i	$-0.898921\pi$
$359$	−36.0000			−1.90001			−0.950004	+	0.312239i	$0.898921\pi$
$360$		0			0
$361$	12.0000			0.631579
$362$	−5.29150	+	14.0000i	−0.278115	+	0.735824i
$363$	−10.5830			−0.555464
$364$		0			0
$365$		0			0
$366$	14.0000	−	37.0405i	0.731792	−	1.93614i
$367$		0			0		1.00000			$0$
$367$		0			0		−1.00000			$\pi$
$368$	15.8745	−	2.00000i	0.827516	−	0.104257i
$369$	−20.0000			−1.04116
$370$		0			0
$371$			42.3320i			2.19777i
$372$	−15.8745	−	14.0000i	−0.823055	−	0.725866i
$373$	10.5830			0.547967			0.273984	−	0.961734i	$-0.411659\pi$
$373$	10.5830			0.547967			0.273984	+	0.961734i	$0.411659\pi$
$374$	10.5000	+	3.96863i	0.542942	+	0.205213i
$375$		0			0
$376$	20.0000	−	10.5830i	1.03142	−	0.545777i
$377$		0			0
$378$	5.29150	−	14.0000i	0.272166	−	0.720082i
$379$			7.93725i			0.407709i	0.979001	+	0.203855i	$0.0653470\pi$
$379$			7.93725i			0.407709i	−0.979001	+	0.203855i	$0.934653\pi$
$380$		0			0
$381$		−	31.7490i		−	1.62655i
$382$	5.29150	+	2.00000i	0.270737	+	0.102329i
$383$			36.0000i			1.83951i	0.392488	+	0.919757i	$0.371614\pi$
$383$			36.0000i			1.83951i	−0.392488	+	0.919757i	$0.628386\pi$
$384$	24.5000	−	17.1974i	1.25026	−	0.877600i
$385$		0			0
$386$	2.50000	−	6.61438i	0.127247	−	0.336663i
$387$	−21.1660			−1.07593
$388$	2.64575	−	3.00000i	0.134318	−	0.152302i
$389$		−	10.5830i		−	0.536580i	−0.963338	−	0.268290i	$-0.913542\pi$
$389$		−	10.5830i		−	0.536580i	0.963338	−	0.268290i	$-0.0864585\pi$
$390$		0			0
$391$	−12.0000			−0.606866
$392$	−11.9059	−	22.5000i	−0.601338	−	1.13642i
$393$			42.0000i			2.11862i
$394$	−14.0000	−	5.29150i	−0.705310	−	0.266582i
$395$		0			0
$396$	−14.0000	+	15.8745i	−0.703526	+	0.797724i
$397$	21.1660			1.06229			0.531146	−	0.847280i	$-0.321762\pi$
$397$	21.1660			1.06229			0.531146	+	0.847280i	$0.321762\pi$
$398$	31.7490	+	12.0000i	1.59143	+	0.601506i
$399$	−28.0000			−1.40175
$400$		0			0
$401$	27.0000			1.34832			0.674158	−	0.738587i	$-0.264507\pi$
$401$	27.0000			1.34832			0.674158	+	0.738587i	$0.264507\pi$
$402$	27.7804	+	10.5000i	1.38556	+	0.523692i
$403$		0			0
$404$	14.0000	−	15.8745i	0.696526	−	0.789786i
$405$		0			0
$406$		0			0
$407$			28.0000i			1.38791i
$408$	−19.8431	+	10.5000i	−0.982382	+	0.519827i
$409$	−3.00000			−0.148340			−0.0741702	−	0.997246i	$-0.523631\pi$
$409$	−3.00000			−0.148340			−0.0741702	+	0.997246i	$0.523631\pi$
$410$		0			0
$411$			50.2693i			2.47960i
$412$	10.5830	−	12.0000i	0.521387	−	0.591198i
$413$	21.1660			1.04151
$414$	8.00000	−	21.1660i	0.393179	−	1.04025i
$415$		0			0
$416$		0			0
$417$		−	49.0000i		−	2.39954i
$418$	9.26013	+	3.50000i	0.452928	+	0.171191i
$419$			18.5203i			0.904774i	0.891822	+	0.452387i	$0.149427\pi$
$419$			18.5203i			0.904774i	−0.891822	+	0.452387i	$0.850573\pi$
$420$		0			0
$421$			21.1660i			1.03157i	0.856719	+	0.515784i	$0.172499\pi$
$421$			21.1660i			1.03157i	−0.856719	+	0.515784i	$0.827501\pi$
$422$	3.96863	−	10.5000i	0.193190	−	0.511132i
$423$		−	32.0000i		−	1.55589i
$424$	14.0000	+	26.4575i	0.679900	+	1.28489i
$425$		0			0
$426$	−28.0000	−	10.5830i	−1.35660	−	0.512748i
$427$	−42.3320			−2.04859
$428$	3.96863	+	3.50000i	0.191831	+	0.169179i
$429$		0			0
$430$		0			0
$431$	12.0000			0.578020			0.289010	−	0.957326i	$-0.406674\pi$
$431$	12.0000			0.578020			0.289010	+	0.957326i	$0.406674\pi$
$432$	−1.32288	−	10.5000i	−0.0636469	−	0.505181i
$433$		−	37.0000i		−	1.77811i	−0.457804	−	0.889053i	$-0.651364\pi$
$433$		−	37.0000i		−	1.77811i	0.457804	−	0.889053i	$-0.348636\pi$
$434$	−8.00000	+	21.1660i	−0.384012	+	1.01600i
$435$		0			0
$436$	14.0000	−	15.8745i	0.670478	−	0.760251i
$437$	−10.5830			−0.506254
$438$	9.26013	−	24.5000i	0.442466	−	1.17066i
$439$	−8.00000			−0.381819			−0.190910	−	0.981608i	$-0.561144\pi$
$439$	−8.00000			−0.381819			−0.190910	+	0.981608i	$0.561144\pi$
$440$		0			0
$441$	−36.0000			−1.71429
$442$		0			0
$443$	29.1033			1.38274			0.691369	−	0.722502i	$-0.257008\pi$
$443$	29.1033			1.38274			0.691369	+	0.722502i	$0.257008\pi$
$444$	−42.0000	−	37.0405i	−1.99323	−	1.75787i
$445$		0			0
$446$	−8.00000	+	21.1660i	−0.378811	+	1.00224i
$447$		0			0
$448$	−26.4575	−	18.0000i	−1.25000	−	0.850420i
$449$	−27.0000			−1.27421			−0.637104	−	0.770778i	$-0.719868\pi$
$449$	−27.0000			−1.27421			−0.637104	+	0.770778i	$0.719868\pi$
$450$		0			0
$451$		−	13.2288i		−	0.622918i
$452$	−19.8431	+	22.5000i	−0.933343	+	1.05831i
$453$	−10.5830			−0.497233
$454$	−21.0000	−	7.93725i	−0.985579	−	0.372514i
$455$		0			0
$456$	−17.5000	+	9.26013i	−0.819513	+	0.433645i
$457$		−	27.0000i		−	1.26301i	−0.775373	−	0.631503i	$-0.782438\pi$
$457$		−	27.0000i		−	1.26301i	0.775373	−	0.631503i	$-0.217562\pi$
$458$	10.5830	−	28.0000i	0.494511	−	1.30835i
$459$			7.93725i			0.370479i
$460$		0			0
$461$		−	42.3320i		−	1.97160i	−0.167927	−	0.985799i	$-0.553707\pi$
$461$		−	42.3320i		−	1.97160i	0.167927	−	0.985799i	$-0.446293\pi$
$462$	37.0405	+	14.0000i	1.72328	+	0.651339i
$463$			8.00000i			0.371792i	0.982569	+	0.185896i	$0.0595187\pi$
$463$			8.00000i			0.371792i	−0.982569	+	0.185896i	$0.940481\pi$
$464$		0			0
$465$		0			0
$466$	3.00000	−	7.93725i	0.138972	−	0.367686i
$467$	26.4575			1.22431			0.612154	−	0.790739i	$-0.290303\pi$
$467$	26.4575			1.22431			0.612154	+	0.790739i	$0.290303\pi$
$468$		0			0
$469$		−	31.7490i		−	1.46603i
$470$		0			0
$471$	28.0000			1.29017
$472$	13.2288	−	7.00000i	0.608903	−	0.322201i
$473$		−	14.0000i		−	0.643721i
$474$	14.0000	+	5.29150i	0.643041	+	0.243047i
$475$		0			0
$476$	18.0000	+	15.8745i	0.825029	+	0.727607i
$477$	42.3320			1.93825
$478$	10.5830	+	4.00000i	0.484055	+	0.182956i
$479$	−4.00000			−0.182765			−0.0913823	−	0.995816i	$-0.529129\pi$
$479$	−4.00000			−0.182765			−0.0913823	+	0.995816i	$0.529129\pi$
$480$		0			0
$481$		0			0
$482$	−27.7804	−	10.5000i	−1.26536	−	0.478262i
$483$	−42.3320			−1.92617
$484$	6.00000	+	5.29150i	0.272727	+	0.240523i
$485$		0			0
$486$	28.0000	+	10.5830i	1.27011	+	0.480055i
$487$		−	12.0000i		−	0.543772i	−0.962329	−	0.271886i	$-0.912353\pi$
$487$		−	12.0000i		−	0.543772i	0.962329	−	0.271886i	$-0.0876473\pi$
$488$	−26.4575	+	14.0000i	−1.19768	+	0.633750i
$489$	35.0000			1.58275
$490$		0			0
$491$			5.29150i			0.238802i	0.992846	+	0.119401i	$0.0380974\pi$
$491$			5.29150i			0.238802i	−0.992846	+	0.119401i	$0.961903\pi$
$492$	19.8431	+	17.5000i	0.894598	+	0.788961i
$493$		0			0
$494$		0			0
$495$		0			0
$496$	2.00000	+	15.8745i	0.0898027	+	0.712786i
$497$			32.0000i			1.43540i
$498$	−27.7804	−	10.5000i	−1.24487	−	0.470516i
$499$		−	26.4575i		−	1.18440i	−0.805791	−	0.592200i	$-0.798259\pi$
$499$		−	26.4575i		−	1.18440i	0.805791	−	0.592200i	$-0.201741\pi$
$500$		0			0
$501$		0			0
$502$	3.96863	−	10.5000i	0.177128	−	0.468638i
$503$		0			0		1.00000			$0$
$503$		0			0		−1.00000			$\pi$
$504$	−40.0000	+	21.1660i	−1.78174	+	0.942809i
$505$		0			0
$506$	14.0000	+	5.29150i	0.622376	+	0.235236i
$507$	34.3948			1.52753
$508$	−15.8745	+	18.0000i	−0.704317	+	0.798621i
$509$			31.7490i			1.40725i	0.710571	+	0.703625i	$0.248437\pi$
$509$			31.7490i			1.40725i	−0.710571	+	0.703625i	$0.751563\pi$
$510$		0			0
$511$	−28.0000			−1.23865
$512$	−22.4889	−	2.50000i	−0.993878	−	0.110485i
$513$			7.00000i			0.309058i
$514$	−7.00000	+	18.5203i	−0.308757	+	0.816894i
$515$		0			0
$516$	21.0000	+	18.5203i	0.924473	+	0.815309i
$517$	21.1660			0.930880
$518$	−21.1660	+	56.0000i	−0.929981	+	2.46050i
$519$	56.0000			2.45813
$520$		0			0
$521$	3.00000			0.131432			0.0657162	−	0.997838i	$-0.479067\pi$
$521$	3.00000			0.131432			0.0657162	+	0.997838i	$0.479067\pi$
$522$		0			0
$523$	−2.64575			−0.115691			−0.0578453	−	0.998326i	$-0.518423\pi$
$523$	−2.64575			−0.115691			−0.0578453	+	0.998326i	$0.518423\pi$
$524$	21.0000	−	23.8118i	0.917389	−	1.04022i
$525$		0			0
$526$	6.00000	−	15.8745i	0.261612	−	0.692161i
$527$		−	12.0000i		−	0.522728i
$528$	27.7804	−	3.50000i	1.20899	−	0.152318i
$529$	7.00000			0.304348
$530$		0			0
$531$		−	21.1660i		−	0.918527i
$532$	15.8745	+	14.0000i	0.688247	+	0.606977i
$533$		0			0
$534$	−3.50000	−	1.32288i	−0.151460	−	0.0572464i
$535$		0			0
$536$	−10.5000	−	19.8431i	−0.453531	−	0.857093i
$537$			63.0000i			2.71865i
$538$	−10.5830	+	28.0000i	−0.456266	+	1.20717i
$539$		−	23.8118i		−	1.02565i
$540$		0			0
$541$		−	21.1660i		−	0.909998i	−0.890492	−	0.454999i	$-0.849640\pi$
$541$		−	21.1660i		−	0.909998i	0.890492	−	0.454999i	$-0.150360\pi$
$542$	−26.4575	−	10.0000i	−1.13645	−	0.429537i
$543$		−	28.0000i		−	1.20160i
$544$	16.5000	+	3.96863i	0.707432	+	0.170153i
$545$		0			0
$546$		0			0
$547$	−18.5203			−0.791869			−0.395935	−	0.918279i	$-0.629579\pi$
$547$	−18.5203			−0.791869			−0.395935	+	0.918279i	$0.629579\pi$
$548$	25.1346	−	28.5000i	1.07370	−	1.21746i
$549$			42.3320i			1.80669i
$550$		0			0
$551$		0			0
$552$	−26.4575	+	14.0000i	−1.12611	+	0.595880i
$553$		−	16.0000i		−	0.680389i
$554$	28.0000	+	10.5830i	1.18961	+	0.449629i
$555$		0			0
$556$	−24.5000	+	27.7804i	−1.03903	+	1.17815i
$557$		0			0			−	1.00000i	$-0.5\pi$
$557$		0			0				1.00000i	$0.5\pi$
$558$	21.1660	+	8.00000i	0.896029	+	0.338667i
$559$		0			0
$560$		0			0
$561$	−21.0000			−0.886621
$562$	−29.1033	−	11.0000i	−1.22765	−	0.464007i
$563$	15.8745			0.669031			0.334515	−	0.942390i	$-0.391427\pi$
$563$	15.8745			0.669031			0.334515	+	0.942390i	$0.391427\pi$
$564$	−28.0000	+	31.7490i	−1.17901	+	1.33687i
$565$		0			0
$566$	−17.5000	−	6.61438i	−0.735580	−	0.278023i
$567$		−	20.0000i		−	0.839921i
$568$	10.5830	+	20.0000i	0.444053	+	0.839181i
$569$	−11.0000			−0.461144			−0.230572	−	0.973055i	$-0.574060\pi$
$569$	−11.0000			−0.461144			−0.230572	+	0.973055i	$0.574060\pi$
$570$		0			0
$571$		−	37.0405i		−	1.55010i	−0.631901	−	0.775049i	$-0.717725\pi$
$571$		−	37.0405i		−	1.55010i	0.631901	−	0.775049i	$-0.282275\pi$
$572$		0			0
$573$	−10.5830			−0.442111
$574$	10.0000	−	26.4575i	0.417392	−	1.10432i
$575$		0			0
$576$	−18.0000	+	26.4575i	−0.750000	+	1.10240i
$577$		−	7.00000i		−	0.291414i	−0.989328	−	0.145707i	$-0.953454\pi$
$577$		−	7.00000i		−	0.291414i	0.989328	−	0.145707i	$-0.0465456\pi$
$578$	10.5830	+	4.00000i	0.440195	+	0.166378i
$579$			13.2288i			0.549768i
$580$		0			0
$581$			31.7490i			1.31717i
$582$	−2.64575	+	7.00000i	−0.109670	+	0.290159i
$583$			28.0000i			1.15964i
$584$	−17.5000	+	9.26013i	−0.724155	+	0.383187i
$585$		0			0
$586$	−14.0000	−	5.29150i	−0.578335	−	0.218590i
$587$	−7.93725			−0.327606			−0.163803	−	0.986493i	$-0.552376\pi$
$587$	−7.93725			−0.327606			−0.163803	+	0.986493i	$0.552376\pi$
$588$	35.7176	+	31.5000i	1.47297	+	1.29904i
$589$		−	10.5830i		−	0.436065i
$590$		0			0
$591$	28.0000			1.15177
$592$	5.29150	+	42.0000i	0.217479	+	1.72619i
$593$		−	41.0000i		−	1.68367i	−0.539736	−	0.841834i	$-0.681476\pi$
$593$		−	41.0000i		−	1.68367i	0.539736	−	0.841834i	$-0.318524\pi$
$594$	3.50000	−	9.26013i	0.143607	−	0.379948i
$595$		0			0
$596$		0			0
$597$	−63.4980			−2.59880
$598$		0			0
$599$	12.0000			0.490307			0.245153	−	0.969484i	$-0.421162\pi$
$599$	12.0000			0.490307			0.245153	+	0.969484i	$0.421162\pi$
$600$		0			0
$601$	7.00000			0.285536			0.142768	−	0.989756i	$-0.454400\pi$
$601$	7.00000			0.285536			0.142768	+	0.989756i	$0.454400\pi$
$602$	10.5830	−	28.0000i	0.431331	−	1.14119i
$603$	−31.7490			−1.29292
$604$	6.00000	+	5.29150i	0.244137	+	0.215308i
$605$		0			0
$606$	−14.0000	+	37.0405i	−0.568711	+	1.50467i
$607$		−	8.00000i		−	0.324710i	−0.986732	−	0.162355i	$-0.948091\pi$
$607$		−	8.00000i		−	0.324710i	0.986732	−	0.162355i	$-0.0519090\pi$
$608$	14.5516	+	3.50000i	0.590147	+	0.141944i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	15.8745	−	18.0000i	0.641689	−	0.727607i
$613$	−10.5830			−0.427444			−0.213722	−	0.976895i	$-0.568559\pi$
$613$	−10.5830			−0.427444			−0.213722	+	0.976895i	$0.568559\pi$
$614$	3.50000	+	1.32288i	0.141249	+	0.0533869i
$615$		0			0
$616$	−14.0000	−	26.4575i	−0.564076	−	1.06600i
$617$			6.00000i			0.241551i	0.992680	+	0.120775i	$0.0385381\pi$
$617$			6.00000i			0.241551i	−0.992680	+	0.120775i	$0.961462\pi$
$618$	−10.5830	+	28.0000i	−0.425711	+	1.12633i
$619$		−	5.29150i		−	0.212683i	−0.994330	−	0.106342i	$-0.966086\pi$
$619$		−	5.29150i		−	0.212683i	0.994330	−	0.106342i	$-0.0339137\pi$
$620$		0			0
$621$			10.5830i			0.424681i
$622$	−5.29150	−	2.00000i	−0.212170	−	0.0801927i
$623$			4.00000i			0.160257i
$624$		0			0
$625$		0			0
$626$	3.00000	−	7.93725i	0.119904	−	0.317236i
$627$	−18.5203			−0.739628
$628$	−15.8745	−	14.0000i	−0.633462	−	0.558661i
$629$		−	31.7490i		−	1.26592i
$630$		0			0
$631$	36.0000			1.43314			0.716569	−	0.697517i	$-0.245712\pi$
$631$	36.0000			1.43314			0.716569	+	0.697517i	$0.245712\pi$
$632$	−5.29150	−	10.0000i	−0.210485	−	0.397779i
$633$			21.0000i			0.834675i
$634$		0			0
$635$		0			0
$636$	−42.0000	−	37.0405i	−1.66541	−	1.46875i
$637$		0			0
$638$		0			0
$639$	32.0000			1.26590
$640$		0			0
$641$	2.00000			0.0789953			0.0394976	−	0.999220i	$-0.487424\pi$
$641$	2.00000			0.0789953			0.0394976	+	0.999220i	$0.487424\pi$
$642$	−9.26013	−	3.50000i	−0.365468	−	0.138134i
$643$	15.8745			0.626029			0.313015	−	0.949748i	$-0.398661\pi$
$643$	15.8745			0.626029			0.313015	+	0.949748i	$0.398661\pi$
$644$	24.0000	+	21.1660i	0.945732	+	0.834058i
$645$		0			0
$646$	−10.5000	−	3.96863i	−0.413117	−	0.156144i
$647$		0			0		1.00000			$0$
$647$		0			0		−1.00000			$\pi$
$648$	−6.61438	−	12.5000i	−0.259837	−	0.491046i
$649$	14.0000			0.549548
$650$		0			0
$651$		−	42.3320i		−	1.65912i
$652$	−19.8431	−	17.5000i	−0.777117	−	0.685353i
$653$	−31.7490			−1.24243			−0.621217	−	0.783638i	$-0.713362\pi$
$653$	−31.7490			−1.24243			−0.621217	+	0.783638i	$0.713362\pi$
$654$	−14.0000	+	37.0405i	−0.547443	+	1.44840i
$655$		0			0
$656$	−2.50000	−	19.8431i	−0.0976086	−	0.774744i
$657$			28.0000i			1.09238i
$658$	42.3320	+	16.0000i	1.65027	+	0.623745i
$659$			7.93725i			0.309192i	0.987978	+	0.154596i	$0.0494075\pi$
$659$			7.93725i			0.309192i	−0.987978	+	0.154596i	$0.950592\pi$
$660$		0			0
$661$			21.1660i			0.823262i	0.911351	+	0.411631i	$0.135041\pi$
$661$			21.1660i			0.823262i	−0.911351	+	0.411631i	$0.864959\pi$
$662$	−1.32288	+	3.50000i	−0.0514150	+	0.136031i
$663$		0			0
$664$	10.5000	+	19.8431i	0.407479	+	0.770063i
$665$		0			0
$666$	56.0000	+	21.1660i	2.16996	+	0.820166i
$667$		0			0
$668$		0			0
$669$		−	42.3320i		−	1.63665i
$670$		0			0
$671$	−28.0000			−1.08093
$672$	58.2065	+	14.0000i	2.24537	+	0.540062i
$673$			34.0000i			1.31060i	0.755367	+	0.655302i	$0.227459\pi$
$673$			34.0000i			1.31060i	−0.755367	+	0.655302i	$0.772541\pi$
$674$	7.50000	−	19.8431i	0.288889	−	0.764329i
$675$		0			0
$676$	−19.5000	−	17.1974i	−0.750000	−	0.661438i
$677$	42.3320			1.62695			0.813476	−	0.581599i	$-0.197573\pi$
$677$	42.3320			1.62695			0.813476	+	0.581599i	$0.197573\pi$
$678$	19.8431	−	52.5000i	0.762071	−	2.01625i
$679$	8.00000			0.307012
$680$		0			0
$681$	42.0000			1.60944
$682$	−5.29150	+	14.0000i	−0.202622	+	0.536088i
$683$	−23.8118			−0.911132			−0.455566	−	0.890202i	$-0.650563\pi$
$683$	−23.8118			−0.911132			−0.455566	+	0.890202i	$0.650563\pi$
$684$	14.0000	−	15.8745i	0.535303	−	0.606977i
$685$		0			0
$686$	4.00000	−	10.5830i	0.152721	−	0.404061i
$687$			56.0000i			2.13653i
$688$	−2.64575	−	21.0000i	−0.100868	−	0.800617i
$689$		0			0
$690$		0			0
$691$			23.8118i			0.905842i	0.891551	+	0.452921i	$0.149618\pi$
$691$			23.8118i			0.905842i	−0.891551	+	0.452921i	$0.850382\pi$
$692$	−31.7490	−	28.0000i	−1.20692	−	1.06440i
$693$	−42.3320			−1.60806
$694$	3.50000	+	1.32288i	0.132858	+	0.0502157i
$695$		0			0
$696$		0			0
$697$			15.0000i			0.568166i
$698$	−5.29150	+	14.0000i	−0.200286	+	0.529908i
$699$			15.8745i			0.600429i
$700$		0			0
$701$			21.1660i			0.799429i	0.916640	+	0.399715i	$0.130891\pi$
$701$			21.1660i			0.799429i	−0.916640	+	0.399715i	$0.869109\pi$
$702$		0			0
$703$		−	28.0000i		−	1.05604i
$704$	−17.5000	−	11.9059i	−0.659556	−	0.448720i
$705$		0			0
$706$	−9.00000	+	23.8118i	−0.338719	+	0.896167i
$707$	42.3320			1.59206
$708$	−18.5203	+	21.0000i	−0.696034	+	0.789228i
$709$		−	21.1660i		−	0.794906i	−0.917622	−	0.397453i	$-0.869894\pi$
$709$		−	21.1660i		−	0.794906i	0.917622	−	0.397453i	$-0.130106\pi$
$710$		0			0
$711$	−16.0000			−0.600047
$712$	1.32288	+	2.50000i	0.0495769	+	0.0936915i
$713$		−	16.0000i		−	0.599205i
$714$	−42.0000	−	15.8745i	−1.57181	−	0.594089i
$715$		0			0
$716$	31.5000	−	35.7176i	1.17721	−	1.33483i
$717$	−21.1660			−0.790459
$718$	−47.6235	−	18.0000i	−1.77729	−	0.671754i
$719$	−36.0000			−1.34257			−0.671287	−	0.741198i	$-0.734258\pi$
$719$	−36.0000			−1.34257			−0.671287	+	0.741198i	$0.734258\pi$
$720$		0			0
$721$	32.0000			1.19174
$722$	15.8745	+	6.00000i	0.590788	+	0.223297i
$723$	55.5608			2.06633
$724$	−14.0000	+	15.8745i	−0.520306	+	0.589971i
$725$		0			0
$726$	−14.0000	−	5.29150i	−0.519589	−	0.196386i
$727$		−	16.0000i		−	0.593407i	−0.954970	−	0.296704i	$-0.904113\pi$
$727$		−	16.0000i		−	0.593407i	0.954970	−	0.296704i	$-0.0958873\pi$
$728$		0			0
$729$	−41.0000			−1.51852
$730$		0			0
$731$			15.8745i			0.587140i
$732$	37.0405	−	42.0000i	1.36906	−	1.55236i
$733$		0			0			−	1.00000i	$-0.5\pi$
$733$		0			0				1.00000i	$0.5\pi$
$734$		0			0
$735$		0			0
$736$	22.0000	+	5.29150i	0.810931	+	0.195047i
$737$		−	21.0000i		−	0.773545i
$738$	−26.4575	−	10.0000i	−0.973915	−	0.368105i
$739$			15.8745i			0.583953i	0.956425	+	0.291977i	$0.0943129\pi$
$739$			15.8745i			0.583953i	−0.956425	+	0.291977i	$0.905687\pi$
$740$		0			0
$741$		0			0
$742$	−21.1660	+	56.0000i	−0.777029	+	2.05582i
$743$		−	36.0000i		−	1.32071i	−0.750953	−	0.660356i	$-0.770405\pi$
$743$		−	36.0000i		−	1.32071i	0.750953	−	0.660356i	$-0.229595\pi$
$744$	−14.0000	−	26.4575i	−0.513265	−	0.969979i
$745$		0			0
$746$	14.0000	+	5.29150i	0.512576	+	0.193736i
$747$	31.7490			1.16164
$748$	11.9059	+	10.5000i	0.435322	+	0.383918i
$749$			10.5830i			0.386695i
$750$		0			0
$751$	8.00000			0.291924			0.145962	−	0.989290i	$-0.453372\pi$
$751$	8.00000			0.291924			0.145962	+	0.989290i	$0.453372\pi$
$752$	31.7490	−	4.00000i	1.15777	−	0.145865i
$753$			21.0000i			0.765283i
$754$		0			0
$755$		0			0
$756$	14.0000	−	15.8745i	0.509175	−	0.577350i
$757$	−21.1660			−0.769292			−0.384646	−	0.923064i	$-0.625676\pi$
$757$	−21.1660			−0.769292			−0.384646	+	0.923064i	$0.625676\pi$
$758$	−3.96863	+	10.5000i	−0.144147	+	0.381377i
$759$	−28.0000			−1.01634
$760$		0			0
$761$	−29.0000			−1.05125			−0.525625	−	0.850717i	$-0.676168\pi$
$761$	−29.0000			−1.05125			−0.525625	+	0.850717i	$0.676168\pi$
$762$	15.8745	−	42.0000i	0.575073	−	1.52150i
$763$	42.3320			1.53252
$764$	6.00000	+	5.29150i	0.217072	+	0.191440i
$765$		0			0
$766$	−18.0000	+	47.6235i	−0.650366	+	1.72071i
$767$		0			0
$768$	41.0091	−	10.5000i	1.47979	−	0.378886i
$769$	21.0000			0.757279			0.378640	−	0.925544i	$-0.376392\pi$
$769$	21.0000			0.757279			0.378640	+	0.925544i	$0.376392\pi$
$770$		0			0
$771$		−	37.0405i		−	1.33398i
$772$	6.61438	−	7.50000i	0.238057	−	0.269931i
$773$		0			0			−	1.00000i	$-0.5\pi$
$773$		0			0				1.00000i	$0.5\pi$
$774$	−28.0000	−	10.5830i	−1.00644	−	0.380398i
$775$		0			0
$776$	5.00000	−	2.64575i	0.179490	−	0.0949769i
$777$		−	112.000i		−	4.01798i
$778$	5.29150	−	14.0000i	0.189710	−	0.501924i
$779$			13.2288i			0.473969i
$780$		0			0
$781$			21.1660i			0.757379i
$782$	−15.8745	−	6.00000i	−0.567671	−	0.214560i
$783$		0			0
$784$	−4.50000	−	35.7176i	−0.160714	−	1.27563i
$785$		0			0
$786$	−21.0000	+	55.5608i	−0.749045	+	1.98179i
$787$	26.4575			0.943108			0.471554	−	0.881837i	$-0.343693\pi$
$787$	26.4575			0.943108			0.471554	+	0.881837i	$0.343693\pi$
$788$	−15.8745	−	14.0000i	−0.565506	−	0.498729i
$789$			31.7490i			1.13029i
$790$		0			0
$791$	−60.0000			−2.13335
$792$	−26.4575	+	14.0000i	−0.940127	+	0.497468i
$793$		0			0
$794$	28.0000	+	10.5830i	0.993683	+	0.375577i
$795$		0			0
$796$	36.0000	+	31.7490i	1.27599	+	1.12531i
$797$	−31.7490			−1.12461			−0.562304	−	0.826931i	$-0.690085\pi$
$797$	−31.7490			−1.12461			−0.562304	+	0.826931i	$0.690085\pi$
$798$	−37.0405	−	14.0000i	−1.31122	−	0.495595i
$799$	−24.0000			−0.849059
$800$		0			0
$801$	4.00000			0.141333
$802$	35.7176	+	13.5000i	1.26123	+	0.476702i
$803$	−18.5203			−0.653566
$804$	31.5000	+	27.7804i	1.11092	+	0.979739i
$805$		0			0
$806$		0			0
$807$		−	56.0000i		−	1.97129i
$808$	26.4575	−	14.0000i	0.930772	−	0.492518i
$809$	−10.0000			−0.351581			−0.175791	−	0.984428i	$-0.556248\pi$
$809$	−10.0000			−0.351581			−0.175791	+	0.984428i	$0.556248\pi$
$810$		0			0
$811$			5.29150i			0.185810i	0.995675	+	0.0929049i	$0.0296153\pi$
$811$			5.29150i			0.185810i	−0.995675	+	0.0929049i	$0.970385\pi$
$812$		0			0
$813$	52.9150			1.85581
$814$	−14.0000	+	37.0405i	−0.490700	+	1.29827i
$815$		0			0
$816$	−31.5000	+	3.96863i	−1.10272	+	0.138930i
$817$			14.0000i			0.489798i
$818$	−3.96863	−	1.50000i	−0.138760	−	0.0524463i
$819$		0			0
$820$		0			0
$821$		−	10.5830i		−	0.369349i	−0.982800	−	0.184675i	$-0.940877\pi$
$821$		−	10.5830i		−	0.369349i	0.982800	−	0.184675i	$-0.0591232\pi$
$822$	−25.1346	+	66.5000i	−0.876671	+	2.31945i
$823$			24.0000i			0.836587i	0.908312	+	0.418294i	$0.137372\pi$
$823$			24.0000i			0.836587i	−0.908312	+	0.418294i	$0.862628\pi$
$824$	20.0000	−	10.5830i	0.696733	−	0.368676i
$825$		0			0
$826$	28.0000	+	10.5830i	0.974245	+	0.368230i
$827$	13.2288			0.460009			0.230004	−	0.973190i	$-0.426126\pi$
$827$	13.2288			0.460009			0.230004	+	0.973190i	$0.426126\pi$
$828$	21.1660	−	24.0000i	0.735570	−	0.834058i
$829$			21.1660i			0.735126i	0.929999	+	0.367563i	$0.119808\pi$
$829$			21.1660i			0.735126i	−0.929999	+	0.367563i	$0.880192\pi$
$830$		0			0
$831$	−56.0000			−1.94262
$832$		0			0
$833$			27.0000i			0.935495i
$834$	24.5000	−	64.8209i	0.848366	−	2.24456i
$835$		0			0
$836$	10.5000	+	9.26013i	0.363150	+	0.320268i
$837$	−10.5830			−0.365802
$838$	−9.26013	+	24.5000i	−0.319886	+	0.846338i
$839$	−40.0000			−1.38095			−0.690477	−	0.723355i	$-0.742599\pi$
$839$	−40.0000			−1.38095			−0.690477	+	0.723355i	$0.742599\pi$
$840$		0			0
$841$	29.0000			1.00000
$842$	−10.5830	+	28.0000i	−0.364714	+	0.964944i
$843$	58.2065			2.00474
$844$	10.5000	−	11.9059i	0.361425	−	0.409817i
$845$		0			0
$846$	16.0000	−	42.3320i	0.550091	−	1.45540i
$847$			16.0000i			0.549767i
$848$	5.29150	+	42.0000i	0.181711	+	1.44229i
$849$	35.0000			1.20120
$850$		0			0
$851$		−	42.3320i		−	1.45112i
$852$	−31.7490	−	28.0000i	−1.08770	−	0.959264i
$853$	52.9150			1.81178			0.905888	−	0.423517i	$-0.139205\pi$
$853$	52.9150			1.81178			0.905888	+	0.423517i	$0.139205\pi$
$854$	−56.0000	−	21.1660i	−1.91628	−	0.724286i
$855$		0			0
$856$	3.50000	+	6.61438i	0.119628	+	0.226075i
$857$			21.0000i			0.717346i	0.933463	+	0.358673i	$0.116771\pi$
$857$			21.0000i			0.717346i	−0.933463	+	0.358673i	$0.883229\pi$
$858$		0			0
$859$		−	2.64575i		−	0.0902719i	−0.998981	−	0.0451359i	$-0.985628\pi$
$859$		−	2.64575i		−	0.0902719i	0.998981	−	0.0451359i	$-0.0143721\pi$
$860$		0			0
$861$			52.9150i			1.80334i
$862$	15.8745	+	6.00000i	0.540688	+	0.204361i
$863$		−	24.0000i		−	0.816970i	−0.912765	−	0.408485i	$-0.866057\pi$
$863$		−	24.0000i		−	0.816970i	0.912765	−	0.408485i	$-0.133943\pi$
$864$	3.50000	−	14.5516i	0.119072	−	0.495057i
$865$		0			0
$866$	18.5000	−	48.9464i	0.628656	−	1.66327i
$867$	−21.1660			−0.718835
$868$	−21.1660	+	24.0000i	−0.718421	+	0.814613i
$869$		−	10.5830i		−	0.359004i
$870$		0			0
$871$		0			0
$872$	26.4575	−	14.0000i	0.895964	−	0.474100i
$873$		−	8.00000i		−	0.270759i
$874$	−14.0000	−	5.29150i	−0.473557	−	0.178988i
$875$		0			0
$876$	24.5000	−	27.7804i	0.827778	−	0.938612i
$877$	−42.3320			−1.42945			−0.714725	−	0.699405i	$-0.753448\pi$
$877$	−42.3320			−1.42945			−0.714725	+	0.699405i	$0.753448\pi$
$878$	−10.5830	−	4.00000i	−0.357159	−	0.134993i
$879$	28.0000			0.944417
$880$		0			0
$881$	−30.0000			−1.01073			−0.505363	−	0.862907i	$-0.668641\pi$
$881$	−30.0000			−1.01073			−0.505363	+	0.862907i	$0.668641\pi$
$882$	−47.6235	−	18.0000i	−1.60357	−	0.606092i
$883$	−44.9778			−1.51362			−0.756811	−	0.653633i	$-0.773244\pi$
$883$	−44.9778			−1.51362			−0.756811	+	0.653633i	$0.773244\pi$
$884$		0			0
$885$		0			0
$886$	38.5000	+	14.5516i	1.29343	+	0.488872i
$887$			56.0000i			1.88030i	0.340766	+	0.940148i	$0.389313\pi$
$887$			56.0000i			1.88030i	−0.340766	+	0.940148i	$0.610687\pi$
$888$	−37.0405	−	70.0000i	−1.24300	−	2.34905i
$889$	−48.0000			−1.60987
$890$		0			0
$891$		−	13.2288i		−	0.443180i
$892$	−21.1660	+	24.0000i	−0.708690	+	0.803579i
$893$	−21.1660			−0.708294
$894$		0			0
$895$		0			0
$896$	−26.0000	−	37.0405i	−0.868599	−	1.23744i
$897$		0			0
$898$	−35.7176	−	13.5000i	−1.19191	−	0.450501i
$899$		0			0
$900$		0			0
$901$		−	31.7490i		−	1.05771i
$902$	6.61438	−	17.5000i	0.220235	−	0.582686i
$903$			56.0000i			1.86356i
$904$	−37.5000	+	19.8431i	−1.24723	+	0.659973i
$905$		0			0
$906$	−14.0000	−	5.29150i	−0.465119	−	0.175798i
$907$	5.29150			0.175701			0.0878507	−	0.996134i	$-0.472000\pi$
$907$	5.29150			0.175701			0.0878507	+	0.996134i	$0.472000\pi$
$908$	−23.8118	−	21.0000i	−0.790221	−	0.696909i
$909$		−	42.3320i		−	1.40406i
$910$		0			0
$911$	48.0000			1.59031			0.795155	−	0.606406i	$-0.207389\pi$
$911$	48.0000			1.59031			0.795155	+	0.606406i	$0.207389\pi$
$912$	−27.7804	+	3.50000i	−0.919901	+	0.115897i
$913$			21.0000i			0.694999i
$914$	13.5000	−	35.7176i	0.446540	−	1.18143i
$915$		0			0
$916$	28.0000	−	31.7490i	0.925146	−	1.04902i
$917$	63.4980			2.09689
$918$	−3.96863	+	10.5000i	−0.130984	+	0.346552i
$919$	−4.00000			−0.131948			−0.0659739	−	0.997821i	$-0.521015\pi$
$919$	−4.00000			−0.131948			−0.0659739	+	0.997821i	$0.521015\pi$
$920$		0			0
$921$	−7.00000			−0.230658
$922$	21.1660	−	56.0000i	0.697065	−	1.84426i
$923$		0			0
$924$	42.0000	+	37.0405i	1.38170	+	1.21854i
$925$		0			0
$926$	−4.00000	+	10.5830i	−0.131448	+	0.347779i
$927$		−	32.0000i		−	1.05102i
$928$		0			0
$929$	14.0000			0.459325			0.229663	−	0.973270i	$-0.426238\pi$
$929$	14.0000			0.459325			0.229663	+	0.973270i	$0.426238\pi$
$930$		0			0
$931$			23.8118i			0.780399i
$932$	7.93725	−	9.00000i	0.259993	−	0.294805i
$933$	10.5830			0.346472
$934$	35.0000	+	13.2288i	1.14523	+	0.432858i
$935$		0			0
$936$		0			0
$937$		−	7.00000i		−	0.228680i	−0.993442	−	0.114340i	$-0.963525\pi$
$937$		−	7.00000i		−	0.228680i	0.993442	−	0.114340i	$-0.0364753\pi$
$938$	15.8745	−	42.0000i	0.518321	−	1.37135i
$939$			15.8745i			0.518045i
$940$		0			0
$941$			42.3320i			1.37998i	0.723817	+	0.689992i	$0.242386\pi$
$941$			42.3320i			1.37998i	−0.723817	+	0.689992i	$0.757614\pi$
$942$	37.0405	+	14.0000i	1.20685	+	0.456145i
$943$			20.0000i			0.651290i
$944$	21.0000	−	2.64575i	0.683492	−	0.0861119i
$945$		0			0
$946$	7.00000	−	18.5203i	0.227590	−	0.602146i
$947$	−15.8745			−0.515852			−0.257926	−	0.966165i	$-0.583039\pi$
$947$	−15.8745			−0.515852			−0.257926	+	0.966165i	$0.583039\pi$
$948$	15.8745	+	14.0000i	0.515580	+	0.454699i
$949$		0			0
$950$		0			0
$951$		0			0
$952$	15.8745	+	30.0000i	0.514496	+	0.972306i
$953$		−	5.00000i		−	0.161966i	−0.996715	−	0.0809829i	$-0.974194\pi$
$953$		−	5.00000i		−	0.161966i	0.996715	−	0.0809829i	$-0.0258059\pi$
$954$	56.0000	+	21.1660i	1.81307	+	0.685275i
$955$		0			0
$956$	12.0000	+	10.5830i	0.388108	+	0.342279i
$957$		0			0
$958$	−5.29150	−	2.00000i	−0.170961	−	0.0646171i
$959$	76.0000			2.45417
$960$		0			0
$961$	−15.0000			−0.483871
$962$		0			0
$963$	10.5830			0.341033
$964$	−31.5000	−	27.7804i	−1.01455	−	0.894746i
$965$		0			0
$966$	−56.0000	−	21.1660i	−1.80177	−	0.681005i
$967$			8.00000i			0.257263i	0.991692	+	0.128631i	$0.0410584\pi$
$967$			8.00000i			0.257263i	−0.991692	+	0.128631i	$0.958942\pi$
$968$	5.29150	+	10.0000i	0.170075	+	0.321412i
$969$	21.0000			0.674617
$970$		0			0
$971$			23.8118i			0.764156i	0.924130	+	0.382078i	$0.124791\pi$
$971$			23.8118i			0.764156i	−0.924130	+	0.382078i	$0.875209\pi$
$972$	31.7490	+	28.0000i	1.01835	+	0.898100i
$973$	−74.0810			−2.37493
$974$	6.00000	−	15.8745i	0.192252	−	0.508652i
$975$		0			0
$976$	−42.0000	+	5.29150i	−1.34439	+	0.169377i
$977$			37.0000i			1.18373i	0.806035	+	0.591867i	$0.201609\pi$
$977$			37.0000i			1.18373i	−0.806035	+	0.591867i	$0.798391\pi$
$978$	46.3006	+	17.5000i	1.48053	+	0.559588i
$979$			2.64575i			0.0845586i
$980$		0			0
$981$		−	42.3320i		−	1.35156i
$982$	−2.64575	+	7.00000i	−0.0844293	+	0.223379i
$983$			28.0000i			0.893061i	0.894768	+	0.446531i	$0.147341\pi$
$983$			28.0000i			0.893061i	−0.894768	+	0.446531i	$0.852659\pi$
$984$	17.5000	+	33.0719i	0.557880	+	1.05429i
$985$		0			0
$986$		0			0
$987$	−84.6640			−2.69489
$988$		0			0
$989$			21.1660i			0.673040i
$990$		0			0
$991$	44.0000			1.39771			0.698853	−	0.715265i	$-0.253694\pi$
$991$	44.0000			1.39771			0.698853	+	0.715265i	$0.253694\pi$
$992$	−5.29150	+	22.0000i	−0.168005	+	0.698501i
$993$		−	7.00000i		−	0.222138i
$994$	−16.0000	+	42.3320i	−0.507489	+	1.34269i
$995$		0			0
$996$	−31.5000	−	27.7804i	−0.998116	−	0.880255i
$997$	−42.3320			−1.34067			−0.670334	−	0.742059i	$-0.733849\pi$
$997$	−42.3320			−1.34067			−0.670334	+	0.742059i	$0.733849\pi$
$998$	13.2288	−	35.0000i	0.418749	−	1.10791i
$999$	−28.0000			−0.885881

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.2.f.d.149.4		4
3.2	odd	2		1800.2.d.m.1549.1		4
4.3	odd	2		800.2.f.d.49.3		4
5.2	odd	4		200.2.d.b.101.2	yes	2
5.3	odd	4		200.2.d.c.101.1	yes	2
5.4	even	2	inner	200.2.f.d.149.1		4
8.3	odd	2		800.2.f.d.49.1		4
8.5	even	2	inner	200.2.f.d.149.2		4
12.11	even	2		7200.2.d.m.2449.2		4
15.2	even	4		1800.2.k.f.901.1		2
15.8	even	4		1800.2.k.d.901.2		2
15.14	odd	2		1800.2.d.m.1549.4		4
20.3	even	4		800.2.d.a.401.2		2
20.7	even	4		800.2.d.d.401.1		2
20.19	odd	2		800.2.f.d.49.2		4
24.5	odd	2		1800.2.d.m.1549.3		4
24.11	even	2		7200.2.d.m.2449.1		4
40.3	even	4		800.2.d.a.401.1		2
40.13	odd	4		200.2.d.c.101.2	yes	2
40.19	odd	2		800.2.f.d.49.4		4
40.27	even	4		800.2.d.d.401.2		2
40.29	even	2	inner	200.2.f.d.149.3		4
40.37	odd	4		200.2.d.b.101.1	✓	2
60.23	odd	4		7200.2.k.b.3601.2		2
60.47	odd	4		7200.2.k.i.3601.2		2
60.59	even	2		7200.2.d.m.2449.4		4
80.3	even	4		6400.2.a.cb.1.1		2
80.13	odd	4		6400.2.a.bg.1.2		2
80.27	even	4		6400.2.a.bh.1.1		2
80.37	odd	4		6400.2.a.cc.1.2		2
80.43	even	4		6400.2.a.cb.1.2		2
80.53	odd	4		6400.2.a.bg.1.1		2
80.67	even	4		6400.2.a.bh.1.2		2
80.77	odd	4		6400.2.a.cc.1.1		2
120.29	odd	2		1800.2.d.m.1549.2		4
120.53	even	4		1800.2.k.d.901.1		2
120.59	even	2		7200.2.d.m.2449.3		4
120.77	even	4		1800.2.k.f.901.2		2
120.83	odd	4		7200.2.k.b.3601.1		2
120.107	odd	4		7200.2.k.i.3601.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.d.b.101.1	✓	2	40.37	odd	4
200.2.d.b.101.2	yes	2	5.2	odd	4
200.2.d.c.101.1	yes	2	5.3	odd	4
200.2.d.c.101.2	yes	2	40.13	odd	4
200.2.f.d.149.1		4	5.4	even	2	inner
200.2.f.d.149.2		4	8.5	even	2	inner
200.2.f.d.149.3		4	40.29	even	2	inner
200.2.f.d.149.4		4	1.1	even	1	trivial
800.2.d.a.401.1		2	40.3	even	4
800.2.d.a.401.2		2	20.3	even	4
800.2.d.d.401.1		2	20.7	even	4
800.2.d.d.401.2		2	40.27	even	4
800.2.f.d.49.1		4	8.3	odd	2
800.2.f.d.49.2		4	20.19	odd	2
800.2.f.d.49.3		4	4.3	odd	2
800.2.f.d.49.4		4	40.19	odd	2
1800.2.d.m.1549.1		4	3.2	odd	2
1800.2.d.m.1549.2		4	120.29	odd	2
1800.2.d.m.1549.3		4	24.5	odd	2
1800.2.d.m.1549.4		4	15.14	odd	2
1800.2.k.d.901.1		2	120.53	even	4
1800.2.k.d.901.2		2	15.8	even	4
1800.2.k.f.901.1		2	15.2	even	4
1800.2.k.f.901.2		2	120.77	even	4
6400.2.a.bg.1.1		2	80.53	odd	4
6400.2.a.bg.1.2		2	80.13	odd	4
6400.2.a.bh.1.1		2	80.27	even	4
6400.2.a.bh.1.2		2	80.67	even	4
6400.2.a.cb.1.1		2	80.3	even	4
6400.2.a.cb.1.2		2	80.43	even	4
6400.2.a.cc.1.1		2	80.77	odd	4
6400.2.a.cc.1.2		2	80.37	odd	4
7200.2.d.m.2449.1		4	24.11	even	2
7200.2.d.m.2449.2		4	12.11	even	2
7200.2.d.m.2449.3		4	120.59	even	2
7200.2.d.m.2449.4		4	60.59	even	2
7200.2.k.b.3601.1		2	120.83	odd	4
7200.2.k.b.3601.2		2	60.23	odd	4
7200.2.k.i.3601.1		2	120.107	odd	4
7200.2.k.i.3601.2		2	60.47	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	200.2.f.d.149.4

Level	$200$
Weight	$2$
Character	200.149
Analytic conductor	$1.597$
Analytic rank	$0$
Dimension	$4$
Inner twists	$4$