LMFDB - Embedded newform 513.2.g.a.505.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [513,2,Mod(64,513)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("513.64"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(513, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 513 = 3^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	513.g (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,-1,0,1,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$4.09632562369$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 171)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			505.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	513.505
Dual form			513.2.g.a.64.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} -3.00000 q^{5} +(-0.500000 + 0.866025i) q^{7} -3.00000 q^{8} +(1.50000 + 2.59808i) q^{10} +(2.50000 - 4.33013i) q^{11} +(-1.00000 + 1.73205i) q^{13} +1.00000 q^{14} +(0.500000 + 0.866025i) q^{16} +(-2.50000 + 4.33013i) q^{17} +(-4.00000 + 1.73205i) q^{19} +(-1.50000 + 2.59808i) q^{20} -5.00000 q^{22} +(-4.00000 + 6.92820i) q^{23} +4.00000 q^{25} +2.00000 q^{26} +(0.500000 + 0.866025i) q^{28} +1.00000 q^{29} +(-1.50000 - 2.59808i) q^{31} +(-2.50000 + 4.33013i) q^{32} +5.00000 q^{34} +(1.50000 - 2.59808i) q^{35} -6.00000 q^{37} +(3.50000 + 2.59808i) q^{38} +9.00000 q^{40} +9.00000 q^{41} +(-4.00000 - 6.92820i) q^{43} +(-2.50000 - 4.33013i) q^{44} +8.00000 q^{46} -3.00000 q^{47} +(3.00000 + 5.19615i) q^{49} +(-2.00000 - 3.46410i) q^{50} +(1.00000 + 1.73205i) q^{52} +(-0.500000 - 0.866025i) q^{53} +(-7.50000 + 12.9904i) q^{55} +(1.50000 - 2.59808i) q^{56} +(-0.500000 - 0.866025i) q^{58} -5.00000 q^{59} -13.0000 q^{61} +(-1.50000 + 2.59808i) q^{62} +7.00000 q^{64} +(3.00000 - 5.19615i) q^{65} +(2.00000 - 3.46410i) q^{67} +(2.50000 + 4.33013i) q^{68} -3.00000 q^{70} +(1.50000 - 2.59808i) q^{71} +(2.50000 - 4.33013i) q^{73} +(3.00000 + 5.19615i) q^{74} +(-0.500000 + 4.33013i) q^{76} +(2.50000 + 4.33013i) q^{77} +(-2.00000 - 3.46410i) q^{79} +(-1.50000 - 2.59808i) q^{80} +(-4.50000 - 7.79423i) q^{82} +(4.50000 - 7.79423i) q^{83} +(7.50000 - 12.9904i) q^{85} +(-4.00000 + 6.92820i) q^{86} +(-7.50000 + 12.9904i) q^{88} +(-4.50000 - 7.79423i) q^{89} +(-1.00000 - 1.73205i) q^{91} +(4.00000 + 6.92820i) q^{92} +(1.50000 + 2.59808i) q^{94} +(12.0000 - 5.19615i) q^{95} +(5.00000 + 8.66025i) q^{97} +(3.00000 - 5.19615i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + q^{4} - 6 q^{5} - q^{7} - 6 q^{8} + 3 q^{10} + 5 q^{11} - 2 q^{13} + 2 q^{14} + q^{16} - 5 q^{17} - 8 q^{19} - 3 q^{20} - 10 q^{22} - 8 q^{23} + 8 q^{25} + 4 q^{26} + q^{28} + 2 q^{29}+ \cdots + 6 q^{98}+O(q^{100}) $ 2 * q - q^2 + q^4 - 6 * q^5 - q^7 - 6 * q^8 + 3 * q^10 + 5 * q^11 - 2 * q^13 + 2 * q^14 + q^16 - 5 * q^17 - 8 * q^19 - 3 * q^20 - 10 * q^22 - 8 * q^23 + 8 * q^25 + 4 * q^26 + q^28 + 2 * q^29 - 3 * q^31 - 5 * q^32 + 10 * q^34 + 3 * q^35 - 12 * q^37 + 7 * q^38 + 18 * q^40 + 18 * q^41 - 8 * q^43 - 5 * q^44 + 16 * q^46 - 6 * q^47 + 6 * q^49 - 4 * q^50 + 2 * q^52 - q^53 - 15 * q^55 + 3 * q^56 - q^58 - 10 * q^59 - 26 * q^61 - 3 * q^62 + 14 * q^64 + 6 * q^65 + 4 * q^67 + 5 * q^68 - 6 * q^70 + 3 * q^71 + 5 * q^73 + 6 * q^74 - q^76 + 5 * q^77 - 4 * q^79 - 3 * q^80 - 9 * q^82 + 9 * q^83 + 15 * q^85 - 8 * q^86 - 15 * q^88 - 9 * q^89 - 2 * q^91 + 8 * q^92 + 3 * q^94 + 24 * q^95 + 10 * q^97 + 6 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/513\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i	0.633316	−	0.773893i	$-0.281693\pi$
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i	−0.986869	+	0.161521i	$0.948360\pi$
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−3.00000			−1.34164			−0.670820	−	0.741620i	$-0.734058\pi$
$5$	−3.00000			−1.34164			−0.670820	+	0.741620i	$0.734058\pi$
$6$		0			0
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i	−0.944911	−	0.327327i	$-0.893852\pi$
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i	0.755929	+	0.654654i	$0.227186\pi$
$8$	−3.00000			−1.06066
$9$		0			0
$10$	1.50000	+	2.59808i	0.474342	+	0.821584i
$11$	2.50000	−	4.33013i	0.753778	−	1.30558i	−0.192201	−	0.981356i	$-0.561563\pi$
$11$	2.50000	−	4.33013i	0.753778	−	1.30558i	0.945979	−	0.324227i	$-0.105104\pi$
$12$		0			0
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	0.693375	+	0.720577i	$0.256123\pi$
$14$	1.00000			0.267261
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−2.50000	+	4.33013i	−0.606339	+	1.05021i	0.385499	+	0.922708i	$0.374029\pi$
$17$	−2.50000	+	4.33013i	−0.606339	+	1.05021i	−0.991838	+	0.127502i	$0.959304\pi$
$18$		0			0
$19$	−4.00000	+	1.73205i	−0.917663	+	0.397360i
$19$	−4.00000	+	1.73205i	−0.917663	+	0.397360i
$20$	−1.50000	+	2.59808i	−0.335410	+	0.580948i
$21$		0			0
$22$	−5.00000			−1.06600
$23$	−4.00000	+	6.92820i	−0.834058	+	1.44463i	0.0607377	+	0.998154i	$0.480655\pi$
$23$	−4.00000	+	6.92820i	−0.834058	+	1.44463i	−0.894795	+	0.446476i	$0.852679\pi$
$24$		0			0
$25$	4.00000			0.800000
$26$	2.00000			0.392232
$27$		0			0
$28$	0.500000	+	0.866025i	0.0944911	+	0.163663i
$29$	1.00000			0.185695			0.0928477	−	0.995680i	$-0.470403\pi$
$29$	1.00000			0.185695			0.0928477	+	0.995680i	$0.470403\pi$
$30$		0			0
$31$	−1.50000	−	2.59808i	−0.269408	−	0.466628i	0.699301	−	0.714827i	$-0.253495\pi$
$31$	−1.50000	−	2.59808i	−0.269408	−	0.466628i	−0.968709	+	0.248199i	$0.920161\pi$
$32$	−2.50000	+	4.33013i	−0.441942	+	0.765466i
$33$		0			0
$34$	5.00000			0.857493
$35$	1.50000	−	2.59808i	0.253546	−	0.439155i
$36$		0			0
$37$	−6.00000			−0.986394			−0.493197	−	0.869918i	$-0.664172\pi$
$37$	−6.00000			−0.986394			−0.493197	+	0.869918i	$0.664172\pi$
$38$	3.50000	+	2.59808i	0.567775	+	0.421464i
$39$		0			0
$40$	9.00000			1.42302
$41$	9.00000			1.40556			0.702782	−	0.711405i	$-0.251941\pi$
$41$	9.00000			1.40556			0.702782	+	0.711405i	$0.251941\pi$
$42$		0			0
$43$	−4.00000	−	6.92820i	−0.609994	−	1.05654i	−0.991241	−	0.132068i	$-0.957838\pi$
$43$	−4.00000	−	6.92820i	−0.609994	−	1.05654i	0.381246	−	0.924473i	$-0.375495\pi$
$44$	−2.50000	−	4.33013i	−0.376889	−	0.652791i
$45$		0			0
$46$	8.00000			1.17954
$47$	−3.00000			−0.437595			−0.218797	−	0.975770i	$-0.570213\pi$
$47$	−3.00000			−0.437595			−0.218797	+	0.975770i	$0.570213\pi$
$48$		0			0
$49$	3.00000	+	5.19615i	0.428571	+	0.742307i
$50$	−2.00000	−	3.46410i	−0.282843	−	0.489898i
$51$		0			0
$52$	1.00000	+	1.73205i	0.138675	+	0.240192i
$53$	−0.500000	−	0.866025i	−0.0686803	−	0.118958i	0.829640	−	0.558298i	$-0.188546\pi$
$53$	−0.500000	−	0.866025i	−0.0686803	−	0.118958i	−0.898321	+	0.439340i	$0.855212\pi$
$54$		0			0
$55$	−7.50000	+	12.9904i	−1.01130	+	1.75162i
$56$	1.50000	−	2.59808i	0.200446	−	0.347183i
$57$		0			0
$58$	−0.500000	−	0.866025i	−0.0656532	−	0.113715i
$59$	−5.00000			−0.650945			−0.325472	−	0.945552i	$-0.605523\pi$
$59$	−5.00000			−0.650945			−0.325472	+	0.945552i	$0.605523\pi$
$60$		0			0
$61$	−13.0000			−1.66448			−0.832240	−	0.554416i	$-0.812942\pi$
$61$	−13.0000			−1.66448			−0.832240	+	0.554416i	$0.812942\pi$
$62$	−1.50000	+	2.59808i	−0.190500	+	0.329956i
$63$		0			0
$64$	7.00000			0.875000
$65$	3.00000	−	5.19615i	0.372104	−	0.644503i
$66$		0			0
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	−0.717607	−	0.696449i	$-0.754762\pi$
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	0.961946	+	0.273241i	$0.0880957\pi$
$68$	2.50000	+	4.33013i	0.303170	+	0.525105i
$69$		0			0
$70$	−3.00000			−0.358569
$71$	1.50000	−	2.59808i	0.178017	−	0.308335i	−0.763184	−	0.646181i	$-0.776365\pi$
$71$	1.50000	−	2.59808i	0.178017	−	0.308335i	0.941201	+	0.337846i	$0.109698\pi$
$72$		0			0
$73$	2.50000	−	4.33013i	0.292603	−	0.506803i	−0.681822	−	0.731519i	$-0.738812\pi$
$73$	2.50000	−	4.33013i	0.292603	−	0.506803i	0.974424	+	0.224716i	$0.0721453\pi$
$74$	3.00000	+	5.19615i	0.348743	+	0.604040i
$75$		0			0
$76$	−0.500000	+	4.33013i	−0.0573539	+	0.496700i
$77$	2.50000	+	4.33013i	0.284901	+	0.493464i
$78$		0			0
$79$	−2.00000	−	3.46410i	−0.225018	−	0.389742i	0.731307	−	0.682048i	$-0.238911\pi$
$79$	−2.00000	−	3.46410i	−0.225018	−	0.389742i	−0.956325	+	0.292306i	$0.905577\pi$
$80$	−1.50000	−	2.59808i	−0.167705	−	0.290474i
$81$		0			0
$82$	−4.50000	−	7.79423i	−0.496942	−	0.860729i
$83$	4.50000	−	7.79423i	0.493939	−	0.855528i	−0.506036	−	0.862512i	$-0.668890\pi$
$83$	4.50000	−	7.79423i	0.493939	−	0.855528i	0.999976	+	0.00698436i	$0.00222321\pi$
$84$		0			0
$85$	7.50000	−	12.9904i	0.813489	−	1.40900i
$86$	−4.00000	+	6.92820i	−0.431331	+	0.747087i
$87$		0			0
$88$	−7.50000	+	12.9904i	−0.799503	+	1.38478i
$89$	−4.50000	−	7.79423i	−0.476999	−	0.826187i	0.522654	−	0.852545i	$-0.324942\pi$
$89$	−4.50000	−	7.79423i	−0.476999	−	0.826187i	−0.999653	+	0.0263586i	$0.991609\pi$
$90$		0			0
$91$	−1.00000	−	1.73205i	−0.104828	−	0.181568i
$92$	4.00000	+	6.92820i	0.417029	+	0.722315i
$93$		0			0
$94$	1.50000	+	2.59808i	0.154713	+	0.267971i
$95$	12.0000	−	5.19615i	1.23117	−	0.533114i
$96$		0			0
$97$	5.00000	+	8.66025i	0.507673	+	0.879316i	0.999961	+	0.00888289i	$0.00282755\pi$
$97$	5.00000	+	8.66025i	0.507673	+	0.879316i	−0.492287	+	0.870433i	$0.663839\pi$
$98$	3.00000	−	5.19615i	0.303046	−	0.524891i
$99$		0			0
$100$	2.00000	−	3.46410i	0.200000	−	0.346410i
$101$	−7.00000			−0.696526			−0.348263	−	0.937397i	$-0.613228\pi$
$101$	−7.00000			−0.696526			−0.348263	+	0.937397i	$0.613228\pi$
$102$		0			0
$103$	2.50000	+	4.33013i	0.246332	+	0.426660i	0.962505	−	0.271263i	$-0.0874412\pi$
$103$	2.50000	+	4.33013i	0.246332	+	0.426660i	−0.716173	+	0.697923i	$0.754108\pi$
$104$	3.00000	−	5.19615i	0.294174	−	0.509525i
$105$		0			0
$106$	−0.500000	+	0.866025i	−0.0485643	+	0.0841158i
$107$	−12.0000			−1.16008			−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000			−1.16008			−0.580042	+	0.814587i	$0.696964\pi$
$108$		0			0
$109$	2.50000	−	4.33013i	0.239457	−	0.414751i	−0.721102	−	0.692829i	$-0.756364\pi$
$109$	2.50000	−	4.33013i	0.239457	−	0.414751i	0.960558	+	0.278078i	$0.0896974\pi$
$110$	15.0000			1.43019
$111$		0			0
$112$	−1.00000			−0.0944911
$113$	−8.50000	−	14.7224i	−0.799613	−	1.38497i	−0.919868	−	0.392227i	$-0.871705\pi$
$113$	−8.50000	−	14.7224i	−0.799613	−	1.38497i	0.120256	−	0.992743i	$-0.461629\pi$
$114$		0			0
$115$	12.0000	−	20.7846i	1.11901	−	1.93817i
$116$	0.500000	−	0.866025i	0.0464238	−	0.0804084i
$117$		0			0
$118$	2.50000	+	4.33013i	0.230144	+	0.398621i
$119$	−2.50000	−	4.33013i	−0.229175	−	0.396942i
$120$		0			0
$121$	−7.00000	−	12.1244i	−0.636364	−	1.10221i
$122$	6.50000	+	11.2583i	0.588482	+	1.01928i
$123$		0			0
$124$	−3.00000			−0.269408
$125$	3.00000			0.268328
$126$		0			0
$127$	−6.50000	−	11.2583i	−0.576782	−	0.999015i	−0.995846	−	0.0910585i	$-0.970975\pi$
$127$	−6.50000	−	11.2583i	−0.576782	−	0.999015i	0.419064	−	0.907957i	$-0.362358\pi$
$128$	1.50000	+	2.59808i	0.132583	+	0.229640i
$129$		0			0
$130$	−6.00000			−0.526235
$131$	7.00000			0.611593			0.305796	−	0.952097i	$-0.401077\pi$
$131$	7.00000			0.611593			0.305796	+	0.952097i	$0.401077\pi$
$132$		0			0
$133$	0.500000	−	4.33013i	0.0433555	−	0.375470i
$134$	−4.00000			−0.345547
$135$		0			0
$136$	7.50000	−	12.9904i	0.643120	−	1.11392i
$137$	−3.00000			−0.256307			−0.128154	−	0.991754i	$-0.540905\pi$
$137$	−3.00000			−0.256307			−0.128154	+	0.991754i	$0.540905\pi$
$138$		0			0
$139$	−10.0000	+	17.3205i	−0.848189	+	1.46911i	0.0346338	+	0.999400i	$0.488974\pi$
$139$	−10.0000	+	17.3205i	−0.848189	+	1.46911i	−0.882823	+	0.469706i	$0.844360\pi$
$140$	−1.50000	−	2.59808i	−0.126773	−	0.219578i
$141$		0			0
$142$	−3.00000			−0.251754
$143$	5.00000	+	8.66025i	0.418121	+	0.724207i
$144$		0			0
$145$	−3.00000			−0.249136
$146$	−5.00000			−0.413803
$147$		0			0
$148$	−3.00000	+	5.19615i	−0.246598	+	0.427121i
$149$	−15.0000			−1.22885			−0.614424	−	0.788976i	$-0.710612\pi$
$149$	−15.0000			−1.22885			−0.614424	+	0.788976i	$0.710612\pi$
$150$		0			0
$151$	7.50000	−	12.9904i	0.610341	−	1.05714i	−0.380841	−	0.924640i	$-0.624366\pi$
$151$	7.50000	−	12.9904i	0.610341	−	1.05714i	0.991183	−	0.132502i	$-0.0423010\pi$
$152$	12.0000	−	5.19615i	0.973329	−	0.421464i
$153$		0			0
$154$	2.50000	−	4.33013i	0.201456	−	0.348932i
$155$	4.50000	+	7.79423i	0.361449	+	0.626048i
$156$		0			0
$157$	3.00000			0.239426			0.119713	−	0.992809i	$-0.461803\pi$
$157$	3.00000			0.239426			0.119713	+	0.992809i	$0.461803\pi$
$158$	−2.00000	+	3.46410i	−0.159111	+	0.275589i
$159$		0			0
$160$	7.50000	−	12.9904i	0.592927	−	1.02698i
$161$	−4.00000	−	6.92820i	−0.315244	−	0.546019i
$162$		0			0
$163$	12.0000			0.939913			0.469956	−	0.882690i	$-0.344270\pi$
$163$	12.0000			0.939913			0.469956	+	0.882690i	$0.344270\pi$
$164$	4.50000	−	7.79423i	0.351391	−	0.608627i
$165$		0			0
$166$	−9.00000			−0.698535
$167$	−2.00000	+	3.46410i	−0.154765	+	0.268060i	−0.932973	−	0.359946i	$-0.882795\pi$
$167$	−2.00000	+	3.46410i	−0.154765	+	0.268060i	0.778209	+	0.628006i	$0.216129\pi$
$168$		0			0
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$	−15.0000			−1.15045
$171$		0			0
$172$	−8.00000			−0.609994
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	0.729155	−	0.684349i	$-0.239913\pi$
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	−0.957241	+	0.289292i	$0.906580\pi$
$174$		0			0
$175$	−2.00000	+	3.46410i	−0.151186	+	0.261861i
$176$	5.00000			0.376889
$177$		0			0
$178$	−4.50000	+	7.79423i	−0.337289	+	0.584202i
$179$	12.0000			0.896922			0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000			0.896922			0.448461	+	0.893802i	$0.351972\pi$
$180$		0			0
$181$	−3.50000	−	6.06218i	−0.260153	−	0.450598i	0.706129	−	0.708083i	$-0.250440\pi$
$181$	−3.50000	−	6.06218i	−0.260153	−	0.450598i	−0.966282	+	0.257485i	$0.917106\pi$
$182$	−1.00000	+	1.73205i	−0.0741249	+	0.128388i
$183$		0			0
$184$	12.0000	−	20.7846i	0.884652	−	1.53226i
$185$	18.0000			1.32339
$186$		0			0
$187$	12.5000	+	21.6506i	0.914091	+	1.58325i
$188$	−1.50000	+	2.59808i	−0.109399	+	0.189484i
$189$		0			0
$190$	−10.5000	−	7.79423i	−0.761750	−	0.565453i
$191$	−1.50000	+	2.59808i	−0.108536	+	0.187990i	−0.915177	−	0.403051i	$-0.867950\pi$
$191$	−1.50000	+	2.59808i	−0.108536	+	0.187990i	0.806641	+	0.591041i	$0.201283\pi$
$192$		0			0
$193$	−17.0000			−1.22369			−0.611843	−	0.790979i	$-0.709572\pi$
$193$	−17.0000			−1.22369			−0.611843	+	0.790979i	$0.709572\pi$
$194$	5.00000	−	8.66025i	0.358979	−	0.621770i
$195$		0			0
$196$	6.00000			0.428571
$197$	−2.00000			−0.142494			−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000			−0.142494			−0.0712470	+	0.997459i	$0.522698\pi$
$198$		0			0
$199$	1.50000	+	2.59808i	0.106332	+	0.184173i	0.914282	−	0.405079i	$-0.132756\pi$
$199$	1.50000	+	2.59808i	0.106332	+	0.184173i	−0.807950	+	0.589252i	$0.799423\pi$
$200$	−12.0000			−0.848528
$201$		0			0
$202$	3.50000	+	6.06218i	0.246259	+	0.426533i
$203$	−0.500000	+	0.866025i	−0.0350931	+	0.0607831i
$204$		0			0
$205$	−27.0000			−1.88576
$206$	2.50000	−	4.33013i	0.174183	−	0.301694i
$207$		0			0
$208$	−2.00000			−0.138675
$209$	−2.50000	+	21.6506i	−0.172929	+	1.49761i
$210$		0			0
$211$	−15.0000			−1.03264			−0.516321	−	0.856395i	$-0.672699\pi$
$211$	−15.0000			−1.03264			−0.516321	+	0.856395i	$0.672699\pi$
$212$	−1.00000			−0.0686803
$213$		0			0
$214$	6.00000	+	10.3923i	0.410152	+	0.710403i
$215$	12.0000	+	20.7846i	0.818393	+	1.41750i
$216$		0			0
$217$	3.00000			0.203653
$218$	−5.00000			−0.338643
$219$		0			0
$220$	7.50000	+	12.9904i	0.505650	+	0.875811i
$221$	−5.00000	−	8.66025i	−0.336336	−	0.582552i
$222$		0			0
$223$	12.0000	+	20.7846i	0.803579	+	1.39184i	0.917246	+	0.398321i	$0.130407\pi$
$223$	12.0000	+	20.7846i	0.803579	+	1.39184i	−0.113666	+	0.993519i	$0.536260\pi$
$224$	−2.50000	−	4.33013i	−0.167038	−	0.289319i
$225$		0			0
$226$	−8.50000	+	14.7224i	−0.565412	+	0.979322i
$227$	10.5000	−	18.1865i	0.696909	−	1.20708i	−0.272623	−	0.962121i	$-0.587891\pi$
$227$	10.5000	−	18.1865i	0.696909	−	1.20708i	0.969533	−	0.244962i	$-0.0787754\pi$
$228$		0			0
$229$	8.50000	+	14.7224i	0.561696	+	0.972886i	0.997349	+	0.0727709i	$0.0231842\pi$
$229$	8.50000	+	14.7224i	0.561696	+	0.972886i	−0.435653	+	0.900115i	$0.643482\pi$
$230$	−24.0000			−1.58251
$231$		0			0
$232$	−3.00000			−0.196960
$233$	−4.50000	+	7.79423i	−0.294805	+	0.510617i	−0.974939	−	0.222470i	$-0.928588\pi$
$233$	−4.50000	+	7.79423i	−0.294805	+	0.510617i	0.680135	+	0.733087i	$0.261921\pi$
$234$		0			0
$235$	9.00000			0.587095
$236$	−2.50000	+	4.33013i	−0.162736	+	0.281867i
$237$		0			0
$238$	−2.50000	+	4.33013i	−0.162051	+	0.280680i
$239$	7.50000	+	12.9904i	0.485135	+	0.840278i	0.999854	−	0.0170808i	$-0.00543724\pi$
$239$	7.50000	+	12.9904i	0.485135	+	0.840278i	−0.514719	+	0.857359i	$0.672104\pi$
$240$		0			0
$241$	−1.00000			−0.0644157			−0.0322078	−	0.999481i	$-0.510254\pi$
$241$	−1.00000			−0.0644157			−0.0322078	+	0.999481i	$0.510254\pi$
$242$	−7.00000	+	12.1244i	−0.449977	+	0.779383i
$243$		0			0
$244$	−6.50000	+	11.2583i	−0.416120	+	0.720741i
$245$	−9.00000	−	15.5885i	−0.574989	−	0.995910i
$246$		0			0
$247$	1.00000	−	8.66025i	0.0636285	−	0.551039i
$248$	4.50000	+	7.79423i	0.285750	+	0.494934i
$249$		0			0
$250$	−1.50000	−	2.59808i	−0.0948683	−	0.164317i
$251$	2.50000	+	4.33013i	0.157799	+	0.273315i	0.934075	−	0.357078i	$-0.116227\pi$
$251$	2.50000	+	4.33013i	0.157799	+	0.273315i	−0.776276	+	0.630393i	$0.782894\pi$
$252$		0			0
$253$	20.0000	+	34.6410i	1.25739	+	2.17786i
$254$	−6.50000	+	11.2583i	−0.407846	+	0.706410i
$255$		0			0
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	−5.00000	+	8.66025i	−0.311891	+	0.540212i	−0.978772	−	0.204953i	$-0.934296\pi$
$257$	−5.00000	+	8.66025i	−0.311891	+	0.540212i	0.666880	+	0.745165i	$0.267629\pi$
$258$		0			0
$259$	3.00000	−	5.19615i	0.186411	−	0.322873i
$260$	−3.00000	−	5.19615i	−0.186052	−	0.322252i
$261$		0			0
$262$	−3.50000	−	6.06218i	−0.216231	−	0.374523i
$263$	−4.00000	−	6.92820i	−0.246651	−	0.427211i	0.715944	−	0.698158i	$-0.245997\pi$
$263$	−4.00000	−	6.92820i	−0.246651	−	0.427211i	−0.962594	+	0.270947i	$0.912663\pi$
$264$		0			0
$265$	1.50000	+	2.59808i	0.0921443	+	0.159599i
$266$	−4.00000	+	1.73205i	−0.245256	+	0.106199i
$267$		0			0
$268$	−2.00000	−	3.46410i	−0.122169	−	0.211604i
$269$	−12.5000	+	21.6506i	−0.762138	+	1.32006i	0.179608	+	0.983738i	$0.442517\pi$
$269$	−12.5000	+	21.6506i	−0.762138	+	1.32006i	−0.941746	+	0.336324i	$0.890816\pi$
$270$		0			0
$271$	−13.5000	+	23.3827i	−0.820067	+	1.42040i	0.0855654	+	0.996333i	$0.472730\pi$
$271$	−13.5000	+	23.3827i	−0.820067	+	1.42040i	−0.905632	+	0.424064i	$0.860603\pi$
$272$	−5.00000			−0.303170
$273$		0			0
$274$	1.50000	+	2.59808i	0.0906183	+	0.156956i
$275$	10.0000	−	17.3205i	0.603023	−	1.04447i
$276$		0			0
$277$	−3.50000	+	6.06218i	−0.210295	+	0.364241i	−0.951807	−	0.306699i	$-0.900776\pi$
$277$	−3.50000	+	6.06218i	−0.210295	+	0.364241i	0.741512	+	0.670940i	$0.234109\pi$
$278$	20.0000			1.19952
$279$		0			0
$280$	−4.50000	+	7.79423i	−0.268926	+	0.465794i
$281$	−11.0000			−0.656205			−0.328102	−	0.944642i	$-0.606409\pi$
$281$	−11.0000			−0.656205			−0.328102	+	0.944642i	$0.606409\pi$
$282$		0			0
$283$	29.0000			1.72387			0.861936	−	0.507018i	$-0.169252\pi$
$283$	29.0000			1.72387			0.861936	+	0.507018i	$0.169252\pi$
$284$	−1.50000	−	2.59808i	−0.0890086	−	0.154167i
$285$		0			0
$286$	5.00000	−	8.66025i	0.295656	−	0.512092i
$287$	−4.50000	+	7.79423i	−0.265627	+	0.460079i
$288$		0			0
$289$	−4.00000	−	6.92820i	−0.235294	−	0.407541i
$290$	1.50000	+	2.59808i	0.0880830	+	0.152564i
$291$		0			0
$292$	−2.50000	−	4.33013i	−0.146301	−	0.253402i
$293$	−2.50000	−	4.33013i	−0.146052	−	0.252969i	0.783713	−	0.621123i	$-0.213323\pi$
$293$	−2.50000	−	4.33013i	−0.146052	−	0.252969i	−0.929765	+	0.368154i	$0.879990\pi$
$294$		0			0
$295$	15.0000			0.873334
$296$	18.0000			1.04623
$297$		0			0
$298$	7.50000	+	12.9904i	0.434463	+	0.752513i
$299$	−8.00000	−	13.8564i	−0.462652	−	0.801337i
$300$		0			0
$301$	8.00000			0.461112
$302$	−15.0000			−0.863153
$303$		0			0
$304$	−3.50000	−	2.59808i	−0.200739	−	0.149010i
$305$	39.0000			2.23313
$306$		0			0
$307$	16.5000	−	28.5788i	0.941705	−	1.63108i	0.179486	−	0.983760i	$-0.442556\pi$
$307$	16.5000	−	28.5788i	0.941705	−	1.63108i	0.762218	−	0.647320i	$-0.224110\pi$
$308$	5.00000			0.284901
$309$		0			0
$310$	4.50000	−	7.79423i	0.255583	−	0.442682i
$311$	−10.5000	−	18.1865i	−0.595400	−	1.03126i	−0.993490	−	0.113917i	$-0.963660\pi$
$311$	−10.5000	−	18.1865i	−0.595400	−	1.03126i	0.398090	−	0.917346i	$-0.369673\pi$
$312$		0			0
$313$	−17.0000			−0.960897			−0.480448	−	0.877023i	$-0.659526\pi$
$313$	−17.0000			−0.960897			−0.480448	+	0.877023i	$0.659526\pi$
$314$	−1.50000	−	2.59808i	−0.0846499	−	0.146618i
$315$		0			0
$316$	−4.00000			−0.225018
$317$	17.0000			0.954815			0.477408	−	0.878682i	$-0.341577\pi$
$317$	17.0000			0.954815			0.477408	+	0.878682i	$0.341577\pi$
$318$		0			0
$319$	2.50000	−	4.33013i	0.139973	−	0.242441i
$320$	−21.0000			−1.17394
$321$		0			0
$322$	−4.00000	+	6.92820i	−0.222911	+	0.386094i
$323$	2.50000	−	21.6506i	0.139104	−	1.20467i
$324$		0			0
$325$	−4.00000	+	6.92820i	−0.221880	+	0.384308i
$326$	−6.00000	−	10.3923i	−0.332309	−	0.575577i
$327$		0			0
$328$	−27.0000			−1.49083
$329$	1.50000	−	2.59808i	0.0826977	−	0.143237i
$330$		0			0
$331$	9.50000	−	16.4545i	0.522167	−	0.904420i	−0.477500	−	0.878632i	$-0.658457\pi$
$331$	9.50000	−	16.4545i	0.522167	−	0.904420i	0.999667	−	0.0257885i	$-0.00820965\pi$
$332$	−4.50000	−	7.79423i	−0.246970	−	0.427764i
$333$		0			0
$334$	4.00000			0.218870
$335$	−6.00000	+	10.3923i	−0.327815	+	0.567792i
$336$		0			0
$337$	−5.00000			−0.272367			−0.136184	−	0.990684i	$-0.543484\pi$
$337$	−5.00000			−0.272367			−0.136184	+	0.990684i	$0.543484\pi$
$338$	4.50000	−	7.79423i	0.244768	−	0.423950i
$339$		0			0
$340$	−7.50000	−	12.9904i	−0.406745	−	0.704502i
$341$	−15.0000			−0.812296
$342$		0			0
$343$	−13.0000			−0.701934
$344$	12.0000	+	20.7846i	0.646997	+	1.12063i
$345$		0			0
$346$	−3.00000	+	5.19615i	−0.161281	+	0.279347i
$347$	−1.00000			−0.0536828			−0.0268414	−	0.999640i	$-0.508545\pi$
$347$	−1.00000			−0.0536828			−0.0268414	+	0.999640i	$0.508545\pi$
$348$		0			0
$349$	−7.50000	+	12.9904i	−0.401466	+	0.695359i	−0.993903	−	0.110257i	$-0.964832\pi$
$349$	−7.50000	+	12.9904i	−0.401466	+	0.695359i	0.592437	+	0.805617i	$0.298166\pi$
$350$	4.00000			0.213809
$351$		0			0
$352$	12.5000	+	21.6506i	0.666252	+	1.15398i
$353$	−18.5000	+	32.0429i	−0.984656	+	1.70547i	−0.341199	+	0.939991i	$0.610833\pi$
$353$	−18.5000	+	32.0429i	−0.984656	+	1.70547i	−0.643457	+	0.765482i	$0.722500\pi$
$354$		0			0
$355$	−4.50000	+	7.79423i	−0.238835	+	0.413675i
$356$	−9.00000			−0.476999
$357$		0			0
$358$	−6.00000	−	10.3923i	−0.317110	−	0.549250i
$359$	−6.50000	+	11.2583i	−0.343057	+	0.594192i	−0.984999	−	0.172561i	$-0.944796\pi$
$359$	−6.50000	+	11.2583i	−0.343057	+	0.594192i	0.641942	+	0.766753i	$0.278129\pi$
$360$		0			0
$361$	13.0000	−	13.8564i	0.684211	−	0.729285i
$362$	−3.50000	+	6.06218i	−0.183956	+	0.318621i
$363$		0			0
$364$	−2.00000			−0.104828
$365$	−7.50000	+	12.9904i	−0.392568	+	0.679948i
$366$		0			0
$367$	−5.00000			−0.260998			−0.130499	−	0.991448i	$-0.541658\pi$
$367$	−5.00000			−0.260998			−0.130499	+	0.991448i	$0.541658\pi$
$368$	−8.00000			−0.417029
$369$		0			0
$370$	−9.00000	−	15.5885i	−0.467888	−	0.810405i
$371$	1.00000			0.0519174
$372$		0			0
$373$	2.50000	+	4.33013i	0.129445	+	0.224205i	0.923462	−	0.383691i	$-0.125347\pi$
$373$	2.50000	+	4.33013i	0.129445	+	0.224205i	−0.794017	+	0.607896i	$0.792014\pi$
$374$	12.5000	−	21.6506i	0.646360	−	1.11953i
$375$		0			0
$376$	9.00000			0.464140
$377$	−1.00000	+	1.73205i	−0.0515026	+	0.0892052i
$378$		0			0
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$	1.50000	−	12.9904i	0.0769484	−	0.666392i
$381$		0			0
$382$	3.00000			0.153493
$383$	23.0000			1.17525			0.587623	−	0.809135i	$-0.300064\pi$
$383$	23.0000			1.17525			0.587623	+	0.809135i	$0.300064\pi$
$384$		0			0
$385$	−7.50000	−	12.9904i	−0.382235	−	0.662051i
$386$	8.50000	+	14.7224i	0.432639	+	0.749352i
$387$		0			0
$388$	10.0000			0.507673
$389$	−3.00000			−0.152106			−0.0760530	−	0.997104i	$-0.524232\pi$
$389$	−3.00000			−0.152106			−0.0760530	+	0.997104i	$0.524232\pi$
$390$		0			0
$391$	−20.0000	−	34.6410i	−1.01144	−	1.75187i
$392$	−9.00000	−	15.5885i	−0.454569	−	0.787336i
$393$		0			0
$394$	1.00000	+	1.73205i	0.0503793	+	0.0872595i
$395$	6.00000	+	10.3923i	0.301893	+	0.522894i
$396$		0			0
$397$	−3.50000	+	6.06218i	−0.175660	+	0.304252i	−0.940389	−	0.340099i	$-0.889539\pi$
$397$	−3.50000	+	6.06218i	−0.175660	+	0.304252i	0.764730	+	0.644351i	$0.222873\pi$
$398$	1.50000	−	2.59808i	0.0751882	−	0.130230i
$399$		0			0
$400$	2.00000	+	3.46410i	0.100000	+	0.173205i
$401$	33.0000			1.64794			0.823971	−	0.566632i	$-0.191754\pi$
$401$	33.0000			1.64794			0.823971	+	0.566632i	$0.191754\pi$
$402$		0			0
$403$	6.00000			0.298881
$404$	−3.50000	+	6.06218i	−0.174132	+	0.301605i
$405$		0			0
$406$	1.00000			0.0496292
$407$	−15.0000	+	25.9808i	−0.743522	+	1.28782i
$408$		0			0
$409$	−5.00000	+	8.66025i	−0.247234	+	0.428222i	−0.962757	−	0.270367i	$-0.912855\pi$
$409$	−5.00000	+	8.66025i	−0.247234	+	0.428222i	0.715523	+	0.698589i	$0.246188\pi$
$410$	13.5000	+	23.3827i	0.666717	+	1.15479i
$411$		0			0
$412$	5.00000			0.246332
$413$	2.50000	−	4.33013i	0.123017	−	0.213072i
$414$		0			0
$415$	−13.5000	+	23.3827i	−0.662689	+	1.14781i
$416$	−5.00000	−	8.66025i	−0.245145	−	0.424604i
$417$		0			0
$418$	20.0000	−	8.66025i	0.978232	−	0.423587i
$419$	−0.500000	−	0.866025i	−0.0244266	−	0.0423081i	0.853554	−	0.521005i	$-0.174443\pi$
$419$	−0.500000	−	0.866025i	−0.0244266	−	0.0423081i	−0.877980	+	0.478697i	$0.841109\pi$
$420$		0			0
$421$	−13.0000	−	22.5167i	−0.633581	−	1.09739i	−0.986814	−	0.161859i	$-0.948251\pi$
$421$	−13.0000	−	22.5167i	−0.633581	−	1.09739i	0.353233	−	0.935536i	$-0.385082\pi$
$422$	7.50000	+	12.9904i	0.365094	+	0.632362i
$423$		0			0
$424$	1.50000	+	2.59808i	0.0728464	+	0.126174i
$425$	−10.0000	+	17.3205i	−0.485071	+	0.840168i
$426$		0			0
$427$	6.50000	−	11.2583i	0.314557	−	0.544829i
$428$	−6.00000	+	10.3923i	−0.290021	+	0.502331i
$429$		0			0
$430$	12.0000	−	20.7846i	0.578691	−	1.00232i
$431$	0.500000	+	0.866025i	0.0240842	+	0.0417150i	0.877816	−	0.478997i	$-0.159000\pi$
$431$	0.500000	+	0.866025i	0.0240842	+	0.0417150i	−0.853732	+	0.520712i	$0.825666\pi$
$432$		0			0
$433$	−13.5000	−	23.3827i	−0.648769	−	1.12370i	−0.983417	−	0.181357i	$-0.941951\pi$
$433$	−13.5000	−	23.3827i	−0.648769	−	1.12370i	0.334649	−	0.942343i	$-0.391382\pi$
$434$	−1.50000	−	2.59808i	−0.0720023	−	0.124712i
$435$		0			0
$436$	−2.50000	−	4.33013i	−0.119728	−	0.207375i
$437$	4.00000	−	34.6410i	0.191346	−	1.65710i
$438$		0			0
$439$	8.00000	+	13.8564i	0.381819	+	0.661330i	0.991322	−	0.131453i	$-0.0419644\pi$
$439$	8.00000	+	13.8564i	0.381819	+	0.661330i	−0.609503	+	0.792784i	$0.708631\pi$
$440$	22.5000	−	38.9711i	1.07265	−	1.85788i
$441$		0			0
$442$	−5.00000	+	8.66025i	−0.237826	+	0.411926i
$443$	25.0000			1.18779			0.593893	−	0.804544i	$-0.297590\pi$
$443$	25.0000			1.18779			0.593893	+	0.804544i	$0.297590\pi$
$444$		0			0
$445$	13.5000	+	23.3827i	0.639961	+	1.10845i
$446$	12.0000	−	20.7846i	0.568216	−	0.984180i
$447$		0			0
$448$	−3.50000	+	6.06218i	−0.165359	+	0.286411i
$449$	−30.0000			−1.41579			−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000			−1.41579			−0.707894	+	0.706319i	$0.750354\pi$
$450$		0			0
$451$	22.5000	−	38.9711i	1.05948	−	1.83508i
$452$	−17.0000			−0.799613
$453$		0			0
$454$	−21.0000			−0.985579
$455$	3.00000	+	5.19615i	0.140642	+	0.243599i
$456$		0			0
$457$	−9.50000	+	16.4545i	−0.444391	+	0.769708i	−0.998010	−	0.0630623i	$-0.979913\pi$
$457$	−9.50000	+	16.4545i	−0.444391	+	0.769708i	0.553618	+	0.832771i	$0.313247\pi$
$458$	8.50000	−	14.7224i	0.397179	−	0.687934i
$459$		0			0
$460$	−12.0000	−	20.7846i	−0.559503	−	0.969087i
$461$	−15.0000	−	25.9808i	−0.698620	−	1.21004i	−0.968945	−	0.247276i	$-0.920465\pi$
$461$	−15.0000	−	25.9808i	−0.698620	−	1.21004i	0.270326	−	0.962769i	$-0.412869\pi$
$462$		0			0
$463$	0.500000	+	0.866025i	0.0232370	+	0.0402476i	0.877410	−	0.479741i	$-0.159269\pi$
$463$	0.500000	+	0.866025i	0.0232370	+	0.0402476i	−0.854173	+	0.519989i	$0.825936\pi$
$464$	0.500000	+	0.866025i	0.0232119	+	0.0402042i
$465$		0			0
$466$	9.00000			0.416917
$467$	−8.00000			−0.370196			−0.185098	−	0.982720i	$-0.559260\pi$
$467$	−8.00000			−0.370196			−0.185098	+	0.982720i	$0.559260\pi$
$468$		0			0
$469$	2.00000	+	3.46410i	0.0923514	+	0.159957i
$470$	−4.50000	−	7.79423i	−0.207570	−	0.359521i
$471$		0			0
$472$	15.0000			0.690431
$473$	−40.0000			−1.83920
$474$		0			0
$475$	−16.0000	+	6.92820i	−0.734130	+	0.317888i
$476$	−5.00000			−0.229175
$477$		0			0
$478$	7.50000	−	12.9904i	0.343042	−	0.594166i
$479$	5.00000			0.228456			0.114228	−	0.993455i	$-0.463561\pi$
$479$	5.00000			0.228456			0.114228	+	0.993455i	$0.463561\pi$
$480$		0			0
$481$	6.00000	−	10.3923i	0.273576	−	0.473848i
$482$	0.500000	+	0.866025i	0.0227744	+	0.0394464i
$483$		0			0
$484$	−14.0000			−0.636364
$485$	−15.0000	−	25.9808i	−0.681115	−	1.17973i
$486$		0			0
$487$	32.0000			1.45006			0.725029	−	0.688718i	$-0.241826\pi$
$487$	32.0000			1.45006			0.725029	+	0.688718i	$0.241826\pi$
$488$	39.0000			1.76545
$489$		0			0
$490$	−9.00000	+	15.5885i	−0.406579	+	0.704215i
$491$	27.0000			1.21849			0.609246	−	0.792981i	$-0.291472\pi$
$491$	27.0000			1.21849			0.609246	+	0.792981i	$0.291472\pi$
$492$		0			0
$493$	−2.50000	+	4.33013i	−0.112594	+	0.195019i
$494$	−8.00000	+	3.46410i	−0.359937	+	0.155857i
$495$		0			0
$496$	1.50000	−	2.59808i	0.0673520	−	0.116657i
$497$	1.50000	+	2.59808i	0.0672842	+	0.116540i
$498$		0			0
$499$	29.0000			1.29822			0.649109	−	0.760695i	$-0.275142\pi$
$499$	29.0000			1.29822			0.649109	+	0.760695i	$0.275142\pi$
$500$	1.50000	−	2.59808i	0.0670820	−	0.116190i
$501$		0			0
$502$	2.50000	−	4.33013i	0.111580	−	0.193263i
$503$	14.5000	+	25.1147i	0.646523	+	1.11981i	0.983948	+	0.178458i	$0.0571109\pi$
$503$	14.5000	+	25.1147i	0.646523	+	1.11981i	−0.337424	+	0.941353i	$0.609556\pi$
$504$		0			0
$505$	21.0000			0.934488
$506$	20.0000	−	34.6410i	0.889108	−	1.53998i
$507$		0			0
$508$	−13.0000			−0.576782
$509$	9.00000	−	15.5885i	0.398918	−	0.690946i	−0.594675	−	0.803966i	$-0.702719\pi$
$509$	9.00000	−	15.5885i	0.398918	−	0.690946i	0.993593	+	0.113020i	$0.0360525\pi$
$510$		0			0
$511$	2.50000	+	4.33013i	0.110593	+	0.191554i
$512$	−11.0000			−0.486136
$513$		0			0
$514$	10.0000			0.441081
$515$	−7.50000	−	12.9904i	−0.330489	−	0.572425i
$516$		0			0
$517$	−7.50000	+	12.9904i	−0.329850	+	0.571316i
$518$	−6.00000			−0.263625
$519$		0			0
$520$	−9.00000	+	15.5885i	−0.394676	+	0.683599i
$521$	42.0000			1.84005			0.920027	−	0.391856i	$-0.128167\pi$
$521$	42.0000			1.84005			0.920027	+	0.391856i	$0.128167\pi$
$522$		0			0
$523$	−14.5000	−	25.1147i	−0.634041	−	1.09819i	−0.986718	−	0.162446i	$-0.948062\pi$
$523$	−14.5000	−	25.1147i	−0.634041	−	1.09819i	0.352677	−	0.935745i	$-0.385272\pi$
$524$	3.50000	−	6.06218i	0.152898	−	0.264827i
$525$		0			0
$526$	−4.00000	+	6.92820i	−0.174408	+	0.302084i
$527$	15.0000			0.653410
$528$		0			0
$529$	−20.5000	−	35.5070i	−0.891304	−	1.54378i
$530$	1.50000	−	2.59808i	0.0651558	−	0.112853i
$531$		0			0
$532$	−3.50000	−	2.59808i	−0.151744	−	0.112641i
$533$	−9.00000	+	15.5885i	−0.389833	+	0.675211i
$534$		0			0
$535$	36.0000			1.55642
$536$	−6.00000	+	10.3923i	−0.259161	+	0.448879i
$537$		0			0
$538$	25.0000			1.07783
$539$	30.0000			1.29219
$540$		0			0
$541$	−1.50000	−	2.59808i	−0.0644900	−	0.111700i	0.831978	−	0.554809i	$-0.187209\pi$
$541$	−1.50000	−	2.59808i	−0.0644900	−	0.111700i	−0.896468	+	0.443109i	$0.853875\pi$
$542$	27.0000			1.15975
$543$		0			0
$544$	−12.5000	−	21.6506i	−0.535933	−	0.928263i
$545$	−7.50000	+	12.9904i	−0.321265	+	0.556447i
$546$		0			0
$547$	−5.00000			−0.213785			−0.106892	−	0.994271i	$-0.534090\pi$
$547$	−5.00000			−0.213785			−0.106892	+	0.994271i	$0.534090\pi$
$548$	−1.50000	+	2.59808i	−0.0640768	+	0.110984i
$549$		0			0
$550$	−20.0000			−0.852803
$551$	−4.00000	+	1.73205i	−0.170406	+	0.0737878i
$552$		0			0
$553$	4.00000			0.170097
$554$	7.00000			0.297402
$555$		0			0
$556$	10.0000	+	17.3205i	0.424094	+	0.734553i
$557$	−6.50000	−	11.2583i	−0.275414	−	0.477031i	0.694826	−	0.719178i	$-0.255482\pi$
$557$	−6.50000	−	11.2583i	−0.275414	−	0.477031i	−0.970239	+	0.242147i	$0.922148\pi$
$558$		0			0
$559$	16.0000			0.676728
$560$	3.00000			0.126773
$561$		0			0
$562$	5.50000	+	9.52628i	0.232003	+	0.401842i
$563$	13.5000	+	23.3827i	0.568957	+	0.985463i	0.996669	+	0.0815478i	$0.0259863\pi$
$563$	13.5000	+	23.3827i	0.568957	+	0.985463i	−0.427712	+	0.903915i	$0.640680\pi$
$564$		0			0
$565$	25.5000	+	44.1673i	1.07279	+	1.85813i
$566$	−14.5000	−	25.1147i	−0.609480	−	1.05565i
$567$		0			0
$568$	−4.50000	+	7.79423i	−0.188816	+	0.327039i
$569$	−4.50000	+	7.79423i	−0.188650	+	0.326751i	−0.944800	−	0.327647i	$-0.893744\pi$
$569$	−4.50000	+	7.79423i	−0.188650	+	0.326751i	0.756151	+	0.654398i	$0.227078\pi$
$570$		0			0
$571$	10.5000	+	18.1865i	0.439411	+	0.761083i	0.997644	−	0.0686016i	$-0.0218537\pi$
$571$	10.5000	+	18.1865i	0.439411	+	0.761083i	−0.558233	+	0.829684i	$0.688520\pi$
$572$	10.0000			0.418121
$573$		0			0
$574$	9.00000			0.375653
$575$	−16.0000	+	27.7128i	−0.667246	+	1.15570i
$576$		0			0
$577$	−42.0000			−1.74848			−0.874241	−	0.485491i	$-0.838641\pi$
$577$	−42.0000			−1.74848			−0.874241	+	0.485491i	$0.838641\pi$
$578$	−4.00000	+	6.92820i	−0.166378	+	0.288175i
$579$		0			0
$580$	−1.50000	+	2.59808i	−0.0622841	+	0.107879i
$581$	4.50000	+	7.79423i	0.186691	+	0.323359i
$582$		0			0
$583$	−5.00000			−0.207079
$584$	−7.50000	+	12.9904i	−0.310352	+	0.537546i
$585$		0			0
$586$	−2.50000	+	4.33013i	−0.103274	+	0.178876i
$587$	−2.00000	−	3.46410i	−0.0825488	−	0.142979i	0.821795	−	0.569783i	$-0.192973\pi$
$587$	−2.00000	−	3.46410i	−0.0825488	−	0.142979i	−0.904344	+	0.426804i	$0.859639\pi$
$588$		0			0
$589$	10.5000	+	7.79423i	0.432645	+	0.321156i
$590$	−7.50000	−	12.9904i	−0.308770	−	0.534806i
$591$		0			0
$592$	−3.00000	−	5.19615i	−0.123299	−	0.213561i
$593$	−4.50000	−	7.79423i	−0.184793	−	0.320071i	0.758714	−	0.651424i	$-0.225828\pi$
$593$	−4.50000	−	7.79423i	−0.184793	−	0.320071i	−0.943507	+	0.331353i	$0.892495\pi$
$594$		0			0
$595$	7.50000	+	12.9904i	0.307470	+	0.532554i
$596$	−7.50000	+	12.9904i	−0.307212	+	0.532107i
$597$		0			0
$598$	−8.00000	+	13.8564i	−0.327144	+	0.566631i
$599$	−6.00000	+	10.3923i	−0.245153	+	0.424618i	−0.962175	−	0.272433i	$-0.912172\pi$
$599$	−6.00000	+	10.3923i	−0.245153	+	0.424618i	0.717021	+	0.697051i	$0.245505\pi$
$600$		0			0
$601$	−1.50000	+	2.59808i	−0.0611863	+	0.105978i	−0.894996	−	0.446074i	$-0.852822\pi$
$601$	−1.50000	+	2.59808i	−0.0611863	+	0.105978i	0.833810	+	0.552052i	$0.186155\pi$
$602$	−4.00000	−	6.92820i	−0.163028	−	0.282372i
$603$		0			0
$604$	−7.50000	−	12.9904i	−0.305171	−	0.528571i
$605$	21.0000	+	36.3731i	0.853771	+	1.47878i
$606$		0			0
$607$	−11.5000	−	19.9186i	−0.466771	−	0.808470i	0.532509	−	0.846424i	$-0.321249\pi$
$607$	−11.5000	−	19.9186i	−0.466771	−	0.808470i	−0.999279	+	0.0379540i	$0.987916\pi$
$608$	2.50000	−	21.6506i	0.101388	−	0.878049i
$609$		0			0
$610$	−19.5000	−	33.7750i	−0.789532	−	1.36751i
$611$	3.00000	−	5.19615i	0.121367	−	0.210214i
$612$		0			0
$613$	4.50000	−	7.79423i	0.181753	−	0.314806i	−0.760724	−	0.649075i	$-0.775156\pi$
$613$	4.50000	−	7.79423i	0.181753	−	0.314806i	0.942478	+	0.334269i	$0.108489\pi$
$614$	−33.0000			−1.33177
$615$		0			0
$616$	−7.50000	−	12.9904i	−0.302184	−	0.523397i
$617$	15.0000	−	25.9808i	0.603877	−	1.04595i	−0.388351	−	0.921512i	$-0.626955\pi$
$617$	15.0000	−	25.9808i	0.603877	−	1.04595i	0.992228	−	0.124434i	$-0.0397116\pi$
$618$		0			0
$619$	5.50000	−	9.52628i	0.221064	−	0.382893i	−0.734068	−	0.679076i	$-0.762380\pi$
$619$	5.50000	−	9.52628i	0.221064	−	0.382893i	0.955131	+	0.296183i	$0.0957138\pi$
$620$	9.00000			0.361449
$621$		0			0
$622$	−10.5000	+	18.1865i	−0.421012	+	0.729214i
$623$	9.00000			0.360577
$624$		0			0
$625$	−29.0000			−1.16000
$626$	8.50000	+	14.7224i	0.339728	+	0.588427i
$627$		0			0
$628$	1.50000	−	2.59808i	0.0598565	−	0.103675i
$629$	15.0000	−	25.9808i	0.598089	−	1.03592i
$630$		0			0
$631$	19.5000	+	33.7750i	0.776283	+	1.34456i	0.934071	+	0.357088i	$0.116230\pi$
$631$	19.5000	+	33.7750i	0.776283	+	1.34456i	−0.157788	+	0.987473i	$0.550436\pi$
$632$	6.00000	+	10.3923i	0.238667	+	0.413384i
$633$		0			0
$634$	−8.50000	−	14.7224i	−0.337578	−	0.584702i
$635$	19.5000	+	33.7750i	0.773834	+	1.34032i
$636$		0			0
$637$	−12.0000			−0.475457
$638$	−5.00000			−0.197952
$639$		0			0
$640$	−4.50000	−	7.79423i	−0.177878	−	0.308094i
$641$	−15.0000	−	25.9808i	−0.592464	−	1.02618i	−0.993899	−	0.110291i	$-0.964822\pi$
$641$	−15.0000	−	25.9808i	−0.592464	−	1.02618i	0.401435	−	0.915888i	$-0.368512\pi$
$642$		0			0
$643$	−7.00000			−0.276053			−0.138027	−	0.990429i	$-0.544076\pi$
$643$	−7.00000			−0.276053			−0.138027	+	0.990429i	$0.544076\pi$
$644$	−8.00000			−0.315244
$645$		0			0
$646$	−20.0000	+	8.66025i	−0.786889	+	0.340733i
$647$	−48.0000			−1.88707			−0.943537	−	0.331266i	$-0.892524\pi$
$647$	−48.0000			−1.88707			−0.943537	+	0.331266i	$0.892524\pi$
$648$		0			0
$649$	−12.5000	+	21.6506i	−0.490668	+	0.849862i
$650$	8.00000			0.313786
$651$		0			0
$652$	6.00000	−	10.3923i	0.234978	−	0.406994i
$653$	−4.50000	−	7.79423i	−0.176099	−	0.305012i	0.764442	−	0.644692i	$-0.223014\pi$
$653$	−4.50000	−	7.79423i	−0.176099	−	0.305012i	−0.940541	+	0.339680i	$0.889681\pi$
$654$		0			0
$655$	−21.0000			−0.820538
$656$	4.50000	+	7.79423i	0.175695	+	0.304314i
$657$		0			0
$658$	−3.00000			−0.116952
$659$	−23.0000			−0.895953			−0.447976	−	0.894045i	$-0.647855\pi$
$659$	−23.0000			−0.895953			−0.447976	+	0.894045i	$0.647855\pi$
$660$		0			0
$661$	15.0000	−	25.9808i	0.583432	−	1.01053i	−0.411636	−	0.911348i	$-0.635043\pi$
$661$	15.0000	−	25.9808i	0.583432	−	1.01053i	0.995069	−	0.0991864i	$-0.0316240\pi$
$662$	−19.0000			−0.738456
$663$		0			0
$664$	−13.5000	+	23.3827i	−0.523902	+	0.907424i
$665$	−1.50000	+	12.9904i	−0.0581675	+	0.503745i
$666$		0			0
$667$	−4.00000	+	6.92820i	−0.154881	+	0.268261i
$668$	2.00000	+	3.46410i	0.0773823	+	0.134030i
$669$		0			0
$670$	12.0000			0.463600
$671$	−32.5000	+	56.2917i	−1.25465	+	2.17312i
$672$		0			0
$673$	4.50000	−	7.79423i	0.173462	−	0.300445i	−0.766166	−	0.642643i	$-0.777838\pi$
$673$	4.50000	−	7.79423i	0.173462	−	0.300445i	0.939628	+	0.342198i	$0.111171\pi$
$674$	2.50000	+	4.33013i	0.0962964	+	0.166790i
$675$		0			0
$676$	9.00000			0.346154
$677$	−18.5000	+	32.0429i	−0.711013	+	1.23151i	0.253465	+	0.967345i	$0.418430\pi$
$677$	−18.5000	+	32.0429i	−0.711013	+	1.23151i	−0.964477	+	0.264166i	$0.914903\pi$
$678$		0			0
$679$	−10.0000			−0.383765
$680$	−22.5000	+	38.9711i	−0.862836	+	1.49448i
$681$		0			0
$682$	7.50000	+	12.9904i	0.287190	+	0.497427i
$683$	−36.0000			−1.37750			−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000			−1.37750			−0.688751	+	0.724998i	$0.741841\pi$
$684$		0			0
$685$	9.00000			0.343872
$686$	6.50000	+	11.2583i	0.248171	+	0.429845i
$687$		0			0
$688$	4.00000	−	6.92820i	0.152499	−	0.264135i
$689$	2.00000			0.0761939
$690$		0			0
$691$	9.50000	−	16.4545i	0.361397	−	0.625958i	−0.626794	−	0.779185i	$-0.715633\pi$
$691$	9.50000	−	16.4545i	0.361397	−	0.625958i	0.988191	+	0.153227i	$0.0489666\pi$
$692$	−6.00000			−0.228086
$693$		0			0
$694$	0.500000	+	0.866025i	0.0189797	+	0.0328739i
$695$	30.0000	−	51.9615i	1.13796	−	1.97101i
$696$		0			0
$697$	−22.5000	+	38.9711i	−0.852248	+	1.47614i
$698$	15.0000			0.567758
$699$		0			0
$700$	2.00000	+	3.46410i	0.0755929	+	0.130931i
$701$	9.50000	−	16.4545i	0.358810	−	0.621477i	−0.628952	−	0.777444i	$-0.716516\pi$
$701$	9.50000	−	16.4545i	0.358810	−	0.621477i	0.987762	+	0.155967i	$0.0498493\pi$
$702$		0			0
$703$	24.0000	−	10.3923i	0.905177	−	0.391953i
$704$	17.5000	−	30.3109i	0.659556	−	1.14238i
$705$		0			0
$706$	37.0000			1.39251
$707$	3.50000	−	6.06218i	0.131631	−	0.227992i
$708$		0			0
$709$	39.0000			1.46468			0.732338	−	0.680941i	$-0.238429\pi$
$709$	39.0000			1.46468			0.732338	+	0.680941i	$0.238429\pi$
$710$	9.00000			0.337764
$711$		0			0
$712$	13.5000	+	23.3827i	0.505934	+	0.876303i
$713$	24.0000			0.898807
$714$		0			0
$715$	−15.0000	−	25.9808i	−0.560968	−	0.971625i
$716$	6.00000	−	10.3923i	0.224231	−	0.388379i
$717$		0			0
$718$	13.0000			0.485156
$719$	1.50000	−	2.59808i	0.0559406	−	0.0968919i	−0.836699	−	0.547663i	$-0.815518\pi$
$719$	1.50000	−	2.59808i	0.0559406	−	0.0968919i	0.892640	+	0.450771i	$0.148851\pi$
$720$		0			0
$721$	−5.00000			−0.186210
$722$	−18.5000	−	4.33013i	−0.688499	−	0.161151i
$723$		0			0
$724$	−7.00000			−0.260153
$725$	4.00000			0.148556
$726$		0			0
$727$	4.00000	+	6.92820i	0.148352	+	0.256953i	0.930618	−	0.365991i	$-0.119270\pi$
$727$	4.00000	+	6.92820i	0.148352	+	0.256953i	−0.782267	+	0.622944i	$0.785937\pi$
$728$	3.00000	+	5.19615i	0.111187	+	0.192582i
$729$		0			0
$730$	15.0000			0.555175
$731$	40.0000			1.47945
$732$		0			0
$733$	−9.50000	−	16.4545i	−0.350891	−	0.607760i	0.635515	−	0.772088i	$-0.280788\pi$
$733$	−9.50000	−	16.4545i	−0.350891	−	0.607760i	−0.986406	+	0.164328i	$0.947454\pi$
$734$	2.50000	+	4.33013i	0.0922767	+	0.159828i
$735$		0			0
$736$	−20.0000	−	34.6410i	−0.737210	−	1.27688i
$737$	−10.0000	−	17.3205i	−0.368355	−	0.638009i
$738$		0			0
$739$	−9.50000	+	16.4545i	−0.349463	+	0.605288i	−0.986154	−	0.165831i	$-0.946969\pi$
$739$	−9.50000	+	16.4545i	−0.349463	+	0.605288i	0.636691	+	0.771119i	$0.280303\pi$
$740$	9.00000	−	15.5885i	0.330847	−	0.573043i
$741$		0			0
$742$	−0.500000	−	0.866025i	−0.0183556	−	0.0317928i
$743$	−41.0000			−1.50414			−0.752072	−	0.659081i	$-0.770945\pi$
$743$	−41.0000			−1.50414			−0.752072	+	0.659081i	$0.770945\pi$
$744$		0			0
$745$	45.0000			1.64867
$746$	2.50000	−	4.33013i	0.0915315	−	0.158537i
$747$		0			0
$748$	25.0000			0.914091
$749$	6.00000	−	10.3923i	0.219235	−	0.379727i
$750$		0			0
$751$	−12.0000	+	20.7846i	−0.437886	+	0.758441i	−0.997526	−	0.0702946i	$-0.977606\pi$
$751$	−12.0000	+	20.7846i	−0.437886	+	0.758441i	0.559640	+	0.828736i	$0.310939\pi$
$752$	−1.50000	−	2.59808i	−0.0546994	−	0.0947421i
$753$		0			0
$754$	2.00000			0.0728357
$755$	−22.5000	+	38.9711i	−0.818859	+	1.41831i
$756$		0			0
$757$	−15.5000	+	26.8468i	−0.563357	+	0.975763i	0.433843	+	0.900988i	$0.357157\pi$
$757$	−15.5000	+	26.8468i	−0.563357	+	0.975763i	−0.997200	+	0.0747748i	$0.976176\pi$
$758$	10.0000	+	17.3205i	0.363216	+	0.629109i
$759$		0			0
$760$	−36.0000	+	15.5885i	−1.30586	+	0.565453i
$761$	−4.50000	−	7.79423i	−0.163125	−	0.282541i	0.772863	−	0.634573i	$-0.218824\pi$
$761$	−4.50000	−	7.79423i	−0.163125	−	0.282541i	−0.935988	+	0.352032i	$0.885491\pi$
$762$		0			0
$763$	2.50000	+	4.33013i	0.0905061	+	0.156761i
$764$	1.50000	+	2.59808i	0.0542681	+	0.0939951i
$765$		0			0
$766$	−11.5000	−	19.9186i	−0.415512	−	0.719688i
$767$	5.00000	−	8.66025i	0.180540	−	0.312704i
$768$		0			0
$769$	−7.00000	+	12.1244i	−0.252426	+	0.437215i	−0.964193	−	0.265200i	$-0.914562\pi$
$769$	−7.00000	+	12.1244i	−0.252426	+	0.437215i	0.711767	+	0.702416i	$0.247895\pi$
$770$	−7.50000	+	12.9904i	−0.270281	+	0.468141i
$771$		0			0
$772$	−8.50000	+	14.7224i	−0.305922	+	0.529872i
$773$	−8.50000	−	14.7224i	−0.305724	−	0.529529i	0.671698	−	0.740825i	$-0.265565\pi$
$773$	−8.50000	−	14.7224i	−0.305724	−	0.529529i	−0.977422	+	0.211296i	$0.932232\pi$
$774$		0			0
$775$	−6.00000	−	10.3923i	−0.215526	−	0.373303i
$776$	−15.0000	−	25.9808i	−0.538469	−	0.932655i
$777$		0			0
$778$	1.50000	+	2.59808i	0.0537776	+	0.0931455i
$779$	−36.0000	+	15.5885i	−1.28983	+	0.558514i
$780$		0			0
$781$	−7.50000	−	12.9904i	−0.268371	−	0.464832i
$782$	−20.0000	+	34.6410i	−0.715199	+	1.23876i
$783$		0			0
$784$	−3.00000	+	5.19615i	−0.107143	+	0.185577i
$785$	−9.00000			−0.321224
$786$		0			0
$787$	−3.50000	−	6.06218i	−0.124762	−	0.216093i	0.796878	−	0.604140i	$-0.206483\pi$
$787$	−3.50000	−	6.06218i	−0.124762	−	0.216093i	−0.921640	+	0.388047i	$0.873150\pi$
$788$	−1.00000	+	1.73205i	−0.0356235	+	0.0617018i
$789$		0			0
$790$	6.00000	−	10.3923i	0.213470	−	0.369742i
$791$	17.0000			0.604450
$792$		0			0
$793$	13.0000	−	22.5167i	0.461644	−	0.799590i
$794$	7.00000			0.248421
$795$		0			0
$796$	3.00000			0.106332
$797$	5.50000	+	9.52628i	0.194820	+	0.337438i	0.946841	−	0.321700i	$-0.104254\pi$
$797$	5.50000	+	9.52628i	0.194820	+	0.337438i	−0.752022	+	0.659139i	$0.770921\pi$
$798$		0			0
$799$	7.50000	−	12.9904i	0.265331	−	0.459567i
$800$	−10.0000	+	17.3205i	−0.353553	+	0.612372i
$801$		0			0
$802$	−16.5000	−	28.5788i	−0.582635	−	1.00915i
$803$	−12.5000	−	21.6506i	−0.441115	−	0.764034i
$804$		0			0
$805$	12.0000	+	20.7846i	0.422944	+	0.732561i
$806$	−3.00000	−	5.19615i	−0.105670	−	0.183027i
$807$		0			0
$808$	21.0000			0.738777
$809$	2.00000			0.0703163			0.0351581	−	0.999382i	$-0.488807\pi$
$809$	2.00000			0.0703163			0.0351581	+	0.999382i	$0.488807\pi$
$810$		0			0
$811$	−12.5000	−	21.6506i	−0.438934	−	0.760257i	0.558673	−	0.829388i	$-0.311311\pi$
$811$	−12.5000	−	21.6506i	−0.438934	−	0.760257i	−0.997608	+	0.0691313i	$0.977977\pi$
$812$	0.500000	+	0.866025i	0.0175466	+	0.0303915i
$813$		0			0
$814$	30.0000			1.05150
$815$	−36.0000			−1.26102
$816$		0			0
$817$	28.0000	+	20.7846i	0.979596	+	0.727161i
$818$	10.0000			0.349642
$819$		0			0
$820$	−13.5000	+	23.3827i	−0.471440	+	0.816559i
$821$	−15.0000			−0.523504			−0.261752	−	0.965135i	$-0.584300\pi$
$821$	−15.0000			−0.523504			−0.261752	+	0.965135i	$0.584300\pi$
$822$		0			0
$823$	−20.0000	+	34.6410i	−0.697156	+	1.20751i	0.272292	+	0.962215i	$0.412218\pi$
$823$	−20.0000	+	34.6410i	−0.697156	+	1.20751i	−0.969448	+	0.245295i	$0.921115\pi$
$824$	−7.50000	−	12.9904i	−0.261275	−	0.452541i
$825$		0			0
$826$	−5.00000			−0.173972
$827$	4.50000	+	7.79423i	0.156480	+	0.271032i	0.933597	−	0.358325i	$-0.116652\pi$
$827$	4.50000	+	7.79423i	0.156480	+	0.271032i	−0.777117	+	0.629356i	$0.783319\pi$
$828$		0			0
$829$	−38.0000			−1.31979			−0.659897	−	0.751356i	$-0.729400\pi$
$829$	−38.0000			−1.31979			−0.659897	+	0.751356i	$0.729400\pi$
$830$	27.0000			0.937184
$831$		0			0
$832$	−7.00000	+	12.1244i	−0.242681	+	0.420336i
$833$	−30.0000			−1.03944
$834$		0			0
$835$	6.00000	−	10.3923i	0.207639	−	0.359641i
$836$	17.5000	+	12.9904i	0.605250	+	0.449282i
$837$		0			0
$838$	−0.500000	+	0.866025i	−0.0172722	+	0.0299164i
$839$	−12.0000	−	20.7846i	−0.414286	−	0.717564i	0.581067	−	0.813856i	$-0.302635\pi$
$839$	−12.0000	−	20.7846i	−0.414286	−	0.717564i	−0.995353	+	0.0962912i	$0.969302\pi$
$840$		0			0
$841$	−28.0000			−0.965517
$842$	−13.0000	+	22.5167i	−0.448010	+	0.775975i
$843$		0			0
$844$	−7.50000	+	12.9904i	−0.258161	+	0.447147i
$845$	−13.5000	−	23.3827i	−0.464414	−	0.804389i
$846$		0			0
$847$	14.0000			0.481046
$848$	0.500000	−	0.866025i	0.0171701	−	0.0297394i
$849$		0			0
$850$	20.0000			0.685994
$851$	24.0000	−	41.5692i	0.822709	−	1.42497i
$852$		0			0
$853$	19.0000	+	32.9090i	0.650548	+	1.12678i	0.982990	+	0.183658i	$0.0587939\pi$
$853$	19.0000	+	32.9090i	0.650548	+	1.12678i	−0.332443	+	0.943123i	$0.607873\pi$
$854$	−13.0000			−0.444851
$855$		0			0
$856$	36.0000			1.23045
$857$	7.00000	+	12.1244i	0.239115	+	0.414160i	0.960461	−	0.278416i	$-0.0898092\pi$
$857$	7.00000	+	12.1244i	0.239115	+	0.414160i	−0.721345	+	0.692576i	$0.756476\pi$
$858$		0			0
$859$	6.00000	−	10.3923i	0.204717	−	0.354581i	−0.745325	−	0.666701i	$-0.767706\pi$
$859$	6.00000	−	10.3923i	0.204717	−	0.354581i	0.950043	+	0.312120i	$0.101039\pi$
$860$	24.0000			0.818393
$861$		0			0
$862$	0.500000	−	0.866025i	0.0170301	−	0.0294969i
$863$	16.0000			0.544646			0.272323	−	0.962206i	$-0.412208\pi$
$863$	16.0000			0.544646			0.272323	+	0.962206i	$0.412208\pi$
$864$		0			0
$865$	9.00000	+	15.5885i	0.306009	+	0.530023i
$866$	−13.5000	+	23.3827i	−0.458749	+	0.794576i
$867$		0			0
$868$	1.50000	−	2.59808i	0.0509133	−	0.0881845i
$869$	−20.0000			−0.678454
$870$		0			0
$871$	4.00000	+	6.92820i	0.135535	+	0.234753i
$872$	−7.50000	+	12.9904i	−0.253982	+	0.439910i
$873$		0			0
$874$	−32.0000	+	13.8564i	−1.08242	+	0.468700i
$875$	−1.50000	+	2.59808i	−0.0507093	+	0.0878310i
$876$		0			0
$877$	39.0000			1.31694			0.658468	−	0.752609i	$-0.271205\pi$
$877$	39.0000			1.31694			0.658468	+	0.752609i	$0.271205\pi$
$878$	8.00000	−	13.8564i	0.269987	−	0.467631i
$879$		0			0
$880$	−15.0000			−0.505650
$881$	2.00000			0.0673817			0.0336909	−	0.999432i	$-0.489274\pi$
$881$	2.00000			0.0673817			0.0336909	+	0.999432i	$0.489274\pi$
$882$		0			0
$883$	−14.5000	−	25.1147i	−0.487964	−	0.845178i	0.511940	−	0.859021i	$-0.328927\pi$
$883$	−14.5000	−	25.1147i	−0.487964	−	0.845178i	−0.999904	+	0.0138428i	$0.995594\pi$
$884$	−10.0000			−0.336336
$885$		0			0
$886$	−12.5000	−	21.6506i	−0.419946	−	0.727367i
$887$	−12.0000	+	20.7846i	−0.402921	+	0.697879i	−0.994077	−	0.108678i	$-0.965338\pi$
$887$	−12.0000	+	20.7846i	−0.402921	+	0.697879i	0.591156	+	0.806557i	$0.298672\pi$
$888$		0			0
$889$	13.0000			0.436006
$890$	13.5000	−	23.3827i	0.452521	−	0.783789i
$891$		0			0
$892$	24.0000			0.803579
$893$	12.0000	−	5.19615i	0.401565	−	0.173883i
$894$		0			0
$895$	−36.0000			−1.20335
$896$	−3.00000			−0.100223
$897$		0			0
$898$	15.0000	+	25.9808i	0.500556	+	0.866989i
$899$	−1.50000	−	2.59808i	−0.0500278	−	0.0866507i
$900$		0			0
$901$	5.00000			0.166574
$902$	−45.0000			−1.49834
$903$		0			0
$904$	25.5000	+	44.1673i	0.848117	+	1.46898i
$905$	10.5000	+	18.1865i	0.349032	+	0.604541i
$906$		0			0
$907$	−8.00000	−	13.8564i	−0.265636	−	0.460094i	0.702094	−	0.712084i	$-0.252248\pi$
$907$	−8.00000	−	13.8564i	−0.265636	−	0.460094i	−0.967730	+	0.251990i	$0.918915\pi$
$908$	−10.5000	−	18.1865i	−0.348455	−	0.603541i
$909$		0			0
$910$	3.00000	−	5.19615i	0.0994490	−	0.172251i
$911$	22.5000	−	38.9711i	0.745458	−	1.29117i	−0.204522	−	0.978862i	$-0.565564\pi$
$911$	22.5000	−	38.9711i	0.745458	−	1.29117i	0.949980	−	0.312310i	$-0.101103\pi$
$912$		0			0
$913$	−22.5000	−	38.9711i	−0.744641	−	1.28976i
$914$	19.0000			0.628464
$915$		0			0
$916$	17.0000			0.561696
$917$	−3.50000	+	6.06218i	−0.115580	+	0.200191i
$918$		0			0
$919$	20.0000			0.659739			0.329870	−	0.944027i	$-0.392995\pi$
$919$	20.0000			0.659739			0.329870	+	0.944027i	$0.392995\pi$
$920$	−36.0000	+	62.3538i	−1.18688	+	2.05574i
$921$		0			0
$922$	−15.0000	+	25.9808i	−0.493999	+	0.855631i
$923$	3.00000	+	5.19615i	0.0987462	+	0.171033i
$924$		0			0
$925$	−24.0000			−0.789115
$926$	0.500000	−	0.866025i	0.0164310	−	0.0284594i
$927$		0			0
$928$	−2.50000	+	4.33013i	−0.0820665	+	0.142143i
$929$	25.0000	+	43.3013i	0.820223	+	1.42067i	0.905516	+	0.424313i	$0.139484\pi$
$929$	25.0000	+	43.3013i	0.820223	+	1.42067i	−0.0852924	+	0.996356i	$0.527182\pi$
$930$		0			0
$931$	−21.0000	−	15.5885i	−0.688247	−	0.510891i
$932$	4.50000	+	7.79423i	0.147402	+	0.255308i
$933$		0			0
$934$	4.00000	+	6.92820i	0.130884	+	0.226698i
$935$	−37.5000	−	64.9519i	−1.22638	−	2.12415i
$936$		0			0
$937$	4.50000	+	7.79423i	0.147009	+	0.254626i	0.930121	−	0.367254i	$-0.119702\pi$
$937$	4.50000	+	7.79423i	0.147009	+	0.254626i	−0.783112	+	0.621881i	$0.786369\pi$
$938$	2.00000	−	3.46410i	0.0653023	−	0.113107i
$939$		0			0
$940$	4.50000	−	7.79423i	0.146774	−	0.254220i
$941$	9.00000	−	15.5885i	0.293392	−	0.508169i	−0.681218	−	0.732081i	$-0.738549\pi$
$941$	9.00000	−	15.5885i	0.293392	−	0.508169i	0.974609	+	0.223912i	$0.0718827\pi$
$942$		0			0
$943$	−36.0000	+	62.3538i	−1.17232	+	2.03052i
$944$	−2.50000	−	4.33013i	−0.0813681	−	0.140934i
$945$		0			0
$946$	20.0000	+	34.6410i	0.650256	+	1.12628i
$947$	14.0000	+	24.2487i	0.454939	+	0.787977i	0.998685	−	0.0512727i	$-0.0163278\pi$
$947$	14.0000	+	24.2487i	0.454939	+	0.787977i	−0.543746	+	0.839250i	$0.682994\pi$
$948$		0			0
$949$	5.00000	+	8.66025i	0.162307	+	0.281124i
$950$	14.0000	+	10.3923i	0.454220	+	0.337171i
$951$		0			0
$952$	7.50000	+	12.9904i	0.243076	+	0.421021i
$953$	11.5000	−	19.9186i	0.372522	−	0.645226i	−0.617431	−	0.786625i	$-0.711827\pi$
$953$	11.5000	−	19.9186i	0.372522	−	0.645226i	0.989953	+	0.141399i	$0.0451599\pi$
$954$		0			0
$955$	4.50000	−	7.79423i	0.145617	−	0.252215i
$956$	15.0000			0.485135
$957$		0			0
$958$	−2.50000	−	4.33013i	−0.0807713	−	0.139900i
$959$	1.50000	−	2.59808i	0.0484375	−	0.0838963i
$960$		0			0
$961$	11.0000	−	19.0526i	0.354839	−	0.614599i
$962$	−12.0000			−0.386896
$963$		0			0
$964$	−0.500000	+	0.866025i	−0.0161039	+	0.0278928i
$965$	51.0000			1.64175
$966$		0			0
$967$	37.0000			1.18984			0.594920	−	0.803785i	$-0.297184\pi$
$967$	37.0000			1.18984			0.594920	+	0.803785i	$0.297184\pi$
$968$	21.0000	+	36.3731i	0.674966	+	1.16907i
$969$		0			0
$970$	−15.0000	+	25.9808i	−0.481621	+	0.834192i
$971$	−10.5000	+	18.1865i	−0.336961	+	0.583634i	−0.983860	−	0.178942i	$-0.942732\pi$
$971$	−10.5000	+	18.1865i	−0.336961	+	0.583634i	0.646899	+	0.762576i	$0.276066\pi$
$972$		0			0
$973$	−10.0000	−	17.3205i	−0.320585	−	0.555270i
$974$	−16.0000	−	27.7128i	−0.512673	−	0.887976i
$975$		0			0
$976$	−6.50000	−	11.2583i	−0.208060	−	0.360370i
$977$	−10.5000	−	18.1865i	−0.335925	−	0.581839i	0.647737	−	0.761864i	$-0.275715\pi$
$977$	−10.5000	−	18.1865i	−0.335925	−	0.581839i	−0.983662	+	0.180025i	$0.942382\pi$
$978$		0			0
$979$	−45.0000			−1.43821
$980$	−18.0000			−0.574989
$981$		0			0
$982$	−13.5000	−	23.3827i	−0.430802	−	0.746171i
$983$	4.00000	+	6.92820i	0.127580	+	0.220975i	0.922739	−	0.385426i	$-0.125946\pi$
$983$	4.00000	+	6.92820i	0.127580	+	0.220975i	−0.795158	+	0.606402i	$0.792612\pi$
$984$		0			0
$985$	6.00000			0.191176
$986$	5.00000			0.159232
$987$		0			0
$988$	−7.00000	−	5.19615i	−0.222700	−	0.165312i
$989$	64.0000			2.03508
$990$		0			0
$991$	−11.5000	+	19.9186i	−0.365310	+	0.632735i	−0.988826	−	0.149076i	$-0.952370\pi$
$991$	−11.5000	+	19.9186i	−0.365310	+	0.632735i	0.623516	+	0.781810i	$0.285704\pi$
$992$	15.0000			0.476250
$993$		0			0
$994$	1.50000	−	2.59808i	0.0475771	−	0.0824060i
$995$	−4.50000	−	7.79423i	−0.142660	−	0.247094i
$996$		0			0
$997$	−5.00000			−0.158352			−0.0791758	−	0.996861i	$-0.525229\pi$
$997$	−5.00000			−0.158352			−0.0791758	+	0.996861i	$0.525229\pi$
$998$	−14.5000	−	25.1147i	−0.458989	−	0.794993i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	513.2.g.a.505.1		2
3.2	odd	2		171.2.g.a.106.1	✓	2
9.4	even	3		513.2.h.b.334.1		2
9.5	odd	6		171.2.h.a.49.1	yes	2
19.7	even	3		513.2.h.b.235.1		2
57.26	odd	6		171.2.h.a.7.1	yes	2
171.121	even	3	inner	513.2.g.a.64.1		2
171.140	odd	6		171.2.g.a.121.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.g.a.106.1	✓	2	3.2	odd	2
171.2.g.a.121.1	yes	2	171.140	odd	6
171.2.h.a.7.1	yes	2	57.26	odd	6
171.2.h.a.49.1	yes	2	9.5	odd	6
513.2.g.a.64.1		2	171.121	even	3	inner
513.2.g.a.505.1		2	1.1	even	1	trivial
513.2.h.b.235.1		2	19.7	even	3
513.2.h.b.334.1		2	9.4	even	3

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

Level:	\( N \)	\(=\)	\( 513 = 3^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	513.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} -3.00000 q^{5} +(-0.500000 + 0.866025i) q^{7} -3.00000 q^{8} +(1.50000 + 2.59808i) q^{10} +(2.50000 - 4.33013i) q^{11} +(-1.00000 + 1.73205i) q^{13} +1.00000 q^{14} +(0.500000 + 0.866025i) q^{16} +(-2.50000 + 4.33013i) q^{17} +(-4.00000 + 1.73205i) q^{19} +(-1.50000 + 2.59808i) q^{20} -5.00000 q^{22} +(-4.00000 + 6.92820i) q^{23} +4.00000 q^{25} +2.00000 q^{26} +(0.500000 + 0.866025i) q^{28} +1.00000 q^{29} +(-1.50000 - 2.59808i) q^{31} +(-2.50000 + 4.33013i) q^{32} +5.00000 q^{34} +(1.50000 - 2.59808i) q^{35} -6.00000 q^{37} +(3.50000 + 2.59808i) q^{38} +9.00000 q^{40} +9.00000 q^{41} +(-4.00000 - 6.92820i) q^{43} +(-2.50000 - 4.33013i) q^{44} +8.00000 q^{46} -3.00000 q^{47} +(3.00000 + 5.19615i) q^{49} +(-2.00000 - 3.46410i) q^{50} +(1.00000 + 1.73205i) q^{52} +(-0.500000 - 0.866025i) q^{53} +(-7.50000 + 12.9904i) q^{55} +(1.50000 - 2.59808i) q^{56} +(-0.500000 - 0.866025i) q^{58} -5.00000 q^{59} -13.0000 q^{61} +(-1.50000 + 2.59808i) q^{62} +7.00000 q^{64} +(3.00000 - 5.19615i) q^{65} +(2.00000 - 3.46410i) q^{67} +(2.50000 + 4.33013i) q^{68} -3.00000 q^{70} +(1.50000 - 2.59808i) q^{71} +(2.50000 - 4.33013i) q^{73} +(3.00000 + 5.19615i) q^{74} +(-0.500000 + 4.33013i) q^{76} +(2.50000 + 4.33013i) q^{77} +(-2.00000 - 3.46410i) q^{79} +(-1.50000 - 2.59808i) q^{80} +(-4.50000 - 7.79423i) q^{82} +(4.50000 - 7.79423i) q^{83} +(7.50000 - 12.9904i) q^{85} +(-4.00000 + 6.92820i) q^{86} +(-7.50000 + 12.9904i) q^{88} +(-4.50000 - 7.79423i) q^{89} +(-1.00000 - 1.73205i) q^{91} +(4.00000 + 6.92820i) q^{92} +(1.50000 + 2.59808i) q^{94} +(12.0000 - 5.19615i) q^{95} +(5.00000 + 8.66025i) q^{97} +(3.00000 - 5.19615i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + q^{4} - 6 q^{5} - q^{7} - 6 q^{8} + 3 q^{10} + 5 q^{11} - 2 q^{13} + 2 q^{14} + q^{16} - 5 q^{17} - 8 q^{19} - 3 q^{20} - 10 q^{22} - 8 q^{23} + 8 q^{25} + 4 q^{26} + q^{28} + 2 q^{29}+ \cdots + 6 q^{98}+O(q^{100}) \) 2 * q - q^2 + q^4 - 6 * q^5 - q^7 - 6 * q^8 + 3 * q^10 + 5 * q^11 - 2 * q^13 + 2 * q^14 + q^16 - 5 * q^17 - 8 * q^19 - 3 * q^20 - 10 * q^22 - 8 * q^23 + 8 * q^25 + 4 * q^26 + q^28 + 2 * q^29 - 3 * q^31 - 5 * q^32 + 10 * q^34 + 3 * q^35 - 12 * q^37 + 7 * q^38 + 18 * q^40 + 18 * q^41 - 8 * q^43 - 5 * q^44 + 16 * q^46 - 6 * q^47 + 6 * q^49 - 4 * q^50 + 2 * q^52 - q^53 - 15 * q^55 + 3 * q^56 - q^58 - 10 * q^59 - 26 * q^61 - 3 * q^62 + 14 * q^64 + 6 * q^65 + 4 * q^67 + 5 * q^68 - 6 * q^70 + 3 * q^71 + 5 * q^73 + 6 * q^74 - q^76 + 5 * q^77 - 4 * q^79 - 3 * q^80 - 9 * q^82 + 9 * q^83 + 15 * q^85 - 8 * q^86 - 15 * q^88 - 9 * q^89 - 2 * q^91 + 8 * q^92 + 3 * q^94 + 24 * q^95 + 10 * q^97 + 6 * q^98

Introduction

L-functions

Modular forms

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Database

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