LMFDB - Embedded newform 1638.2.j.h.235.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(235,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("1638.235");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.j (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$13.0794958511$
Analytic rank:	$0$
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 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			235.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1638.235
Dual form			1638.2.j.h.1171.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 - 2.59808i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 - 2.59808i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{10} +(-0.500000 + 0.866025i) q^{11} -1.00000 q^{13} +(2.00000 - 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.00000 + 5.19615i) q^{17} +(2.00000 + 3.46410i) q^{19} +1.00000 q^{20} -1.00000 q^{22} +(-3.00000 - 5.19615i) q^{23} +(2.00000 - 3.46410i) q^{25} +(-0.500000 - 0.866025i) q^{26} +(2.50000 + 0.866025i) q^{28} -3.00000 q^{29} +(5.50000 - 9.52628i) q^{31} +(0.500000 - 0.866025i) q^{32} -6.00000 q^{34} +(-2.00000 + 1.73205i) q^{35} +(-2.00000 - 3.46410i) q^{37} +(-2.00000 + 3.46410i) q^{38} +(0.500000 + 0.866025i) q^{40} -12.0000 q^{41} -8.00000 q^{43} +(-0.500000 - 0.866025i) q^{44} +(3.00000 - 5.19615i) q^{46} +(-4.00000 - 6.92820i) q^{47} +(-6.50000 + 2.59808i) q^{49} +4.00000 q^{50} +(0.500000 - 0.866025i) q^{52} +(-2.50000 + 4.33013i) q^{53} +1.00000 q^{55} +(0.500000 + 2.59808i) q^{56} +(-1.50000 - 2.59808i) q^{58} +(-2.50000 + 4.33013i) q^{59} +(-6.00000 - 10.3923i) q^{61} +11.0000 q^{62} +1.00000 q^{64} +(0.500000 + 0.866025i) q^{65} +(-8.00000 + 13.8564i) q^{67} +(-3.00000 - 5.19615i) q^{68} +(-2.50000 - 0.866025i) q^{70} -6.00000 q^{71} +(5.00000 - 8.66025i) q^{73} +(2.00000 - 3.46410i) q^{74} -4.00000 q^{76} +(2.50000 + 0.866025i) q^{77} +(-3.50000 - 6.06218i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-6.00000 - 10.3923i) q^{82} +17.0000 q^{83} +6.00000 q^{85} +(-4.00000 - 6.92820i) q^{86} +(0.500000 - 0.866025i) q^{88} +(-6.00000 - 10.3923i) q^{89} +(0.500000 + 2.59808i) q^{91} +6.00000 q^{92} +(4.00000 - 6.92820i) q^{94} +(2.00000 - 3.46410i) q^{95} +13.0000 q^{97} +(-5.50000 - 4.33013i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{4} - q^{5} - q^{7} - 2 q^{8}+O(q^{10}) $ 2 * q + q^2 - q^4 - q^5 - q^7 - 2 * q^8	$ 2 q + q^{2} - q^{4} - q^{5} - q^{7} - 2 q^{8} + q^{10} - q^{11} - 2 q^{13} + 4 q^{14} - q^{16} - 6 q^{17} + 4 q^{19} + 2 q^{20} - 2 q^{22} - 6 q^{23} + 4 q^{25} - q^{26} + 5 q^{28} - 6 q^{29} + 11 q^{31} + q^{32} - 12 q^{34} - 4 q^{35} - 4 q^{37} - 4 q^{38} + q^{40} - 24 q^{41} - 16 q^{43} - q^{44} + 6 q^{46} - 8 q^{47} - 13 q^{49} + 8 q^{50} + q^{52} - 5 q^{53} + 2 q^{55} + q^{56} - 3 q^{58} - 5 q^{59} - 12 q^{61} + 22 q^{62} + 2 q^{64} + q^{65} - 16 q^{67} - 6 q^{68} - 5 q^{70} - 12 q^{71} + 10 q^{73} + 4 q^{74} - 8 q^{76} + 5 q^{77} - 7 q^{79} - q^{80} - 12 q^{82} + 34 q^{83} + 12 q^{85} - 8 q^{86} + q^{88} - 12 q^{89} + q^{91} + 12 q^{92} + 8 q^{94} + 4 q^{95} + 26 q^{97} - 11 q^{98}+O(q^{100}) $ 2 * q + q^2 - q^4 - q^5 - q^7 - 2 * q^8 + q^10 - q^11 - 2 * q^13 + 4 * q^14 - q^16 - 6 * q^17 + 4 * q^19 + 2 * q^20 - 2 * q^22 - 6 * q^23 + 4 * q^25 - q^26 + 5 * q^28 - 6 * q^29 + 11 * q^31 + q^32 - 12 * q^34 - 4 * q^35 - 4 * q^37 - 4 * q^38 + q^40 - 24 * q^41 - 16 * q^43 - q^44 + 6 * q^46 - 8 * q^47 - 13 * q^49 + 8 * q^50 + q^52 - 5 * q^53 + 2 * q^55 + q^56 - 3 * q^58 - 5 * q^59 - 12 * q^61 + 22 * q^62 + 2 * q^64 + q^65 - 16 * q^67 - 6 * q^68 - 5 * q^70 - 12 * q^71 + 10 * q^73 + 4 * q^74 - 8 * q^76 + 5 * q^77 - 7 * q^79 - q^80 - 12 * q^82 + 34 * q^83 + 12 * q^85 - 8 * q^86 + q^88 - 12 * q^89 + q^91 + 12 * q^92 + 8 * q^94 + 4 * q^95 + 26 * q^97 - 11 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	0.732294	−	0.680989i	$-0.238450\pi$
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	−0.955901	+	0.293691i	$0.905116\pi$
$6$		0			0
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i	−0.931505	−	0.363727i	$-0.881504\pi$
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i	0.780750	+	0.624844i	$0.214837\pi$
$12$		0			0
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	2.00000	−	1.73205i	0.534522	−	0.462910i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.00000	+	5.19615i	−0.727607	+	1.26025i	0.230285	+	0.973123i	$0.426034\pi$
$17$	−3.00000	+	5.19615i	−0.727607	+	1.26025i	−0.957892	+	0.287129i	$0.907299\pi$
$18$		0			0
$19$	2.00000	+	3.46410i	0.458831	+	0.794719i	0.998899	−	0.0469020i	$-0.0149348\pi$
$19$	2.00000	+	3.46410i	0.458831	+	0.794719i	−0.540068	+	0.841621i	$0.681602\pi$
$20$	1.00000			0.223607
$21$		0			0
$22$	−1.00000			−0.213201
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	−0.988436	−	0.151642i	$-0.951544\pi$
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	0.362892	−	0.931831i	$-0.381789\pi$
$24$		0			0
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$	−0.500000	−	0.866025i	−0.0980581	−	0.169842i
$27$		0			0
$28$	2.50000	+	0.866025i	0.472456	+	0.163663i
$29$	−3.00000			−0.557086			−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000			−0.557086			−0.278543	+	0.960424i	$0.589851\pi$
$30$		0			0
$31$	5.50000	−	9.52628i	0.987829	−	1.71097i	0.359211	−	0.933257i	$-0.383046\pi$
$31$	5.50000	−	9.52628i	0.987829	−	1.71097i	0.628619	−	0.777714i	$-0.283621\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	−6.00000			−1.02899
$35$	−2.00000	+	1.73205i	−0.338062	+	0.292770i
$36$		0			0
$37$	−2.00000	−	3.46410i	−0.328798	−	0.569495i	0.653476	−	0.756948i	$-0.273310\pi$
$37$	−2.00000	−	3.46410i	−0.328798	−	0.569495i	−0.982274	+	0.187453i	$0.939977\pi$
$38$	−2.00000	+	3.46410i	−0.324443	+	0.561951i
$39$		0			0
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	−12.0000			−1.87409			−0.937043	−	0.349215i	$-0.886448\pi$
$41$	−12.0000			−1.87409			−0.937043	+	0.349215i	$0.886448\pi$
$42$		0			0
$43$	−8.00000			−1.21999			−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000			−1.21999			−0.609994	+	0.792406i	$0.708828\pi$
$44$	−0.500000	−	0.866025i	−0.0753778	−	0.130558i
$45$		0			0
$46$	3.00000	−	5.19615i	0.442326	−	0.766131i
$47$	−4.00000	−	6.92820i	−0.583460	−	1.01058i	−0.995066	−	0.0992202i	$-0.968365\pi$
$47$	−4.00000	−	6.92820i	−0.583460	−	1.01058i	0.411606	−	0.911362i	$-0.364968\pi$
$48$		0			0
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$	4.00000			0.565685
$51$		0			0
$52$	0.500000	−	0.866025i	0.0693375	−	0.120096i
$53$	−2.50000	+	4.33013i	−0.343401	+	0.594789i	−0.985062	−	0.172200i	$-0.944912\pi$
$53$	−2.50000	+	4.33013i	−0.343401	+	0.594789i	0.641661	+	0.766989i	$0.278246\pi$
$54$		0			0
$55$	1.00000			0.134840
$56$	0.500000	+	2.59808i	0.0668153	+	0.347183i
$57$		0			0
$58$	−1.50000	−	2.59808i	−0.196960	−	0.341144i
$59$	−2.50000	+	4.33013i	−0.325472	+	0.563735i	−0.981608	−	0.190909i	$-0.938857\pi$
$59$	−2.50000	+	4.33013i	−0.325472	+	0.563735i	0.656136	+	0.754643i	$0.272190\pi$
$60$		0			0
$61$	−6.00000	−	10.3923i	−0.768221	−	1.33060i	−0.938527	−	0.345207i	$-0.887809\pi$
$61$	−6.00000	−	10.3923i	−0.768221	−	1.33060i	0.170305	−	0.985391i	$-0.445525\pi$
$62$	11.0000			1.39700
$63$		0			0
$64$	1.00000			0.125000
$65$	0.500000	+	0.866025i	0.0620174	+	0.107417i
$66$		0			0
$67$	−8.00000	+	13.8564i	−0.977356	+	1.69283i	−0.305424	+	0.952217i	$0.598798\pi$
$67$	−8.00000	+	13.8564i	−0.977356	+	1.69283i	−0.671932	+	0.740613i	$0.734535\pi$
$68$	−3.00000	−	5.19615i	−0.363803	−	0.630126i
$69$		0			0
$70$	−2.50000	−	0.866025i	−0.298807	−	0.103510i
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$		0			0
$73$	5.00000	−	8.66025i	0.585206	−	1.01361i	−0.409644	−	0.912245i	$-0.634347\pi$
$73$	5.00000	−	8.66025i	0.585206	−	1.01361i	0.994850	−	0.101361i	$-0.0323196\pi$
$74$	2.00000	−	3.46410i	0.232495	−	0.402694i
$75$		0			0
$76$	−4.00000			−0.458831
$77$	2.50000	+	0.866025i	0.284901	+	0.0986928i
$78$		0			0
$79$	−3.50000	−	6.06218i	−0.393781	−	0.682048i	0.599164	−	0.800626i	$-0.295500\pi$
$79$	−3.50000	−	6.06218i	−0.393781	−	0.682048i	−0.992945	+	0.118578i	$0.962166\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$		0			0
$82$	−6.00000	−	10.3923i	−0.662589	−	1.14764i
$83$	17.0000			1.86599			0.932996	−	0.359886i	$-0.117184\pi$
$83$	17.0000			1.86599			0.932996	+	0.359886i	$0.117184\pi$
$84$		0			0
$85$	6.00000			0.650791
$86$	−4.00000	−	6.92820i	−0.431331	−	0.747087i
$87$		0			0
$88$	0.500000	−	0.866025i	0.0533002	−	0.0923186i
$89$	−6.00000	−	10.3923i	−0.635999	−	1.10158i	−0.986303	−	0.164946i	$-0.947255\pi$
$89$	−6.00000	−	10.3923i	−0.635999	−	1.10158i	0.350304	−	0.936636i	$-0.386078\pi$
$90$		0			0
$91$	0.500000	+	2.59808i	0.0524142	+	0.272352i
$92$	6.00000			0.625543
$93$		0			0
$94$	4.00000	−	6.92820i	0.412568	−	0.714590i
$95$	2.00000	−	3.46410i	0.205196	−	0.355409i
$96$		0			0
$97$	13.0000			1.31995			0.659975	−	0.751288i	$-0.270567\pi$
$97$	13.0000			1.31995			0.659975	+	0.751288i	$0.270567\pi$
$98$	−5.50000	−	4.33013i	−0.555584	−	0.437409i
$99$		0			0
$100$	2.00000	+	3.46410i	0.200000	+	0.346410i
$101$	5.00000	−	8.66025i	0.497519	−	0.861727i	−0.502477	−	0.864590i	$-0.667578\pi$
$101$	5.00000	−	8.66025i	0.497519	−	0.861727i	0.999996	+	0.00286291i	$0.000911295\pi$
$102$		0			0
$103$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$103$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$104$	1.00000			0.0980581
$105$		0			0
$106$	−5.00000			−0.485643
$107$	3.50000	+	6.06218i	0.338358	+	0.586053i	0.984124	−	0.177482i	$-0.0567953\pi$
$107$	3.50000	+	6.06218i	0.338358	+	0.586053i	−0.645766	+	0.763535i	$0.723462\pi$
$108$		0			0
$109$	−6.00000	+	10.3923i	−0.574696	+	0.995402i	0.421379	+	0.906885i	$0.361546\pi$
$109$	−6.00000	+	10.3923i	−0.574696	+	0.995402i	−0.996075	+	0.0885176i	$0.971787\pi$
$110$	0.500000	+	0.866025i	0.0476731	+	0.0825723i
$111$		0			0
$112$	−2.00000	+	1.73205i	−0.188982	+	0.163663i
$113$	4.00000			0.376288			0.188144	−	0.982141i	$-0.439753\pi$
$113$	4.00000			0.376288			0.188144	+	0.982141i	$0.439753\pi$
$114$		0			0
$115$	−3.00000	+	5.19615i	−0.279751	+	0.484544i
$116$	1.50000	−	2.59808i	0.139272	−	0.241225i
$117$		0			0
$118$	−5.00000			−0.460287
$119$	15.0000	+	5.19615i	1.37505	+	0.476331i
$120$		0			0
$121$	5.00000	+	8.66025i	0.454545	+	0.787296i
$122$	6.00000	−	10.3923i	0.543214	−	0.940875i
$123$		0			0
$124$	5.50000	+	9.52628i	0.493915	+	0.855485i
$125$	−9.00000			−0.804984
$126$		0			0
$127$	−7.00000			−0.621150			−0.310575	−	0.950549i	$-0.600522\pi$
$127$	−7.00000			−0.621150			−0.310575	+	0.950549i	$0.600522\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−0.500000	+	0.866025i	−0.0438529	+	0.0759555i
$131$	0.500000	+	0.866025i	0.0436852	+	0.0756650i	0.887041	−	0.461690i	$-0.152757\pi$
$131$	0.500000	+	0.866025i	0.0436852	+	0.0756650i	−0.843356	+	0.537355i	$0.819423\pi$
$132$		0			0
$133$	8.00000	−	6.92820i	0.693688	−	0.600751i
$134$	−16.0000			−1.38219
$135$		0			0
$136$	3.00000	−	5.19615i	0.257248	−	0.445566i
$137$	−4.00000	+	6.92820i	−0.341743	+	0.591916i	−0.984757	−	0.173939i	$-0.944351\pi$
$137$	−4.00000	+	6.92820i	−0.341743	+	0.591916i	0.643013	+	0.765855i	$0.277684\pi$
$138$		0			0
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$	−0.500000	−	2.59808i	−0.0422577	−	0.219578i
$141$		0			0
$142$	−3.00000	−	5.19615i	−0.251754	−	0.436051i
$143$	0.500000	−	0.866025i	0.0418121	−	0.0724207i
$144$		0			0
$145$	1.50000	+	2.59808i	0.124568	+	0.215758i
$146$	10.0000			0.827606
$147$		0			0
$148$	4.00000			0.328798
$149$	−5.00000	−	8.66025i	−0.409616	−	0.709476i	0.585231	−	0.810867i	$-0.301004\pi$
$149$	−5.00000	−	8.66025i	−0.409616	−	0.709476i	−0.994847	+	0.101391i	$0.967671\pi$
$150$		0			0
$151$	−6.50000	+	11.2583i	−0.528962	+	0.916190i	0.470467	+	0.882418i	$0.344085\pi$
$151$	−6.50000	+	11.2583i	−0.528962	+	0.916190i	−0.999430	+	0.0337724i	$0.989248\pi$
$152$	−2.00000	−	3.46410i	−0.162221	−	0.280976i
$153$		0			0
$154$	0.500000	+	2.59808i	0.0402911	+	0.209359i
$155$	−11.0000			−0.883541
$156$		0			0
$157$	9.00000	−	15.5885i	0.718278	−	1.24409i	−0.243403	−	0.969925i	$-0.578264\pi$
$157$	9.00000	−	15.5885i	0.718278	−	1.24409i	0.961681	−	0.274169i	$-0.0884028\pi$
$158$	3.50000	−	6.06218i	0.278445	−	0.482281i
$159$		0			0
$160$	−1.00000			−0.0790569
$161$	−12.0000	+	10.3923i	−0.945732	+	0.819028i
$162$		0			0
$163$	4.00000	+	6.92820i	0.313304	+	0.542659i	0.979076	−	0.203497i	$-0.0652307\pi$
$163$	4.00000	+	6.92820i	0.313304	+	0.542659i	−0.665771	+	0.746156i	$0.731897\pi$
$164$	6.00000	−	10.3923i	0.468521	−	0.811503i
$165$		0			0
$166$	8.50000	+	14.7224i	0.659728	+	1.14268i
$167$	24.0000			1.85718			0.928588	−	0.371113i	$-0.121024\pi$
$167$	24.0000			1.85718			0.928588	+	0.371113i	$0.121024\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	3.00000	+	5.19615i	0.230089	+	0.398527i
$171$		0			0
$172$	4.00000	−	6.92820i	0.304997	−	0.528271i
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	0.957241	−	0.289292i	$-0.0934200\pi$
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	−0.729155	+	0.684349i	$0.760087\pi$
$174$		0			0
$175$	−10.0000	−	3.46410i	−0.755929	−	0.261861i
$176$	1.00000			0.0753778
$177$		0			0
$178$	6.00000	−	10.3923i	0.449719	−	0.778936i
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	−0.549825	−	0.835280i	$-0.685306\pi$
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	0.998286	+	0.0585225i	$0.0186389\pi$
$180$		0			0
$181$	−16.0000			−1.18927			−0.594635	−	0.803996i	$-0.702704\pi$
$181$	−16.0000			−1.18927			−0.594635	+	0.803996i	$0.702704\pi$
$182$	−2.00000	+	1.73205i	−0.148250	+	0.128388i
$183$		0			0
$184$	3.00000	+	5.19615i	0.221163	+	0.383065i
$185$	−2.00000	+	3.46410i	−0.147043	+	0.254686i
$186$		0			0
$187$	−3.00000	−	5.19615i	−0.219382	−	0.379980i
$188$	8.00000			0.583460
$189$		0			0
$190$	4.00000			0.290191
$191$	−3.00000	−	5.19615i	−0.217072	−	0.375980i	0.736839	−	0.676068i	$-0.236317\pi$
$191$	−3.00000	−	5.19615i	−0.217072	−	0.375980i	−0.953912	+	0.300088i	$0.902984\pi$
$192$		0			0
$193$	−7.50000	+	12.9904i	−0.539862	+	0.935068i	0.459049	+	0.888411i	$0.348190\pi$
$193$	−7.50000	+	12.9904i	−0.539862	+	0.935068i	−0.998911	+	0.0466572i	$0.985143\pi$
$194$	6.50000	+	11.2583i	0.466673	+	0.808301i
$195$		0			0
$196$	1.00000	−	6.92820i	0.0714286	−	0.494872i
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$		0			0
$199$	−4.00000	+	6.92820i	−0.283552	+	0.491127i	−0.972257	−	0.233915i	$-0.924846\pi$
$199$	−4.00000	+	6.92820i	−0.283552	+	0.491127i	0.688705	+	0.725042i	$0.258180\pi$
$200$	−2.00000	+	3.46410i	−0.141421	+	0.244949i
$201$		0			0
$202$	10.0000			0.703598
$203$	1.50000	+	7.79423i	0.105279	+	0.547048i
$204$		0			0
$205$	6.00000	+	10.3923i	0.419058	+	0.725830i
$206$		0			0
$207$		0			0
$208$	0.500000	+	0.866025i	0.0346688	+	0.0600481i
$209$	−4.00000			−0.276686
$210$		0			0
$211$	12.0000			0.826114			0.413057	−	0.910705i	$-0.364461\pi$
$211$	12.0000			0.826114			0.413057	+	0.910705i	$0.364461\pi$
$212$	−2.50000	−	4.33013i	−0.171701	−	0.297394i
$213$		0			0
$214$	−3.50000	+	6.06218i	−0.239255	+	0.414402i
$215$	4.00000	+	6.92820i	0.272798	+	0.472500i
$216$		0			0
$217$	−27.5000	−	9.52628i	−1.86682	−	0.646686i
$218$	−12.0000			−0.812743
$219$		0			0
$220$	−0.500000	+	0.866025i	−0.0337100	+	0.0583874i
$221$	3.00000	−	5.19615i	0.201802	−	0.349531i
$222$		0			0
$223$	7.00000			0.468755			0.234377	−	0.972146i	$-0.424695\pi$
$223$	7.00000			0.468755			0.234377	+	0.972146i	$0.424695\pi$
$224$	−2.50000	−	0.866025i	−0.167038	−	0.0578638i
$225$		0			0
$226$	2.00000	+	3.46410i	0.133038	+	0.230429i
$227$	−7.50000	+	12.9904i	−0.497792	+	0.862202i	−0.999997	−	0.00254715i	$-0.999189\pi$
$227$	−7.50000	+	12.9904i	−0.497792	+	0.862202i	0.502204	+	0.864749i	$0.332523\pi$
$228$		0			0
$229$	−3.00000	−	5.19615i	−0.198246	−	0.343371i	0.749714	−	0.661762i	$-0.230191\pi$
$229$	−3.00000	−	5.19615i	−0.198246	−	0.343371i	−0.947960	+	0.318390i	$0.896858\pi$
$230$	−6.00000			−0.395628
$231$		0			0
$232$	3.00000			0.196960
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	0.947403	−	0.320043i	$-0.103697\pi$
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	−0.750867	+	0.660454i	$0.770364\pi$
$234$		0			0
$235$	−4.00000	+	6.92820i	−0.260931	+	0.451946i
$236$	−2.50000	−	4.33013i	−0.162736	−	0.281867i
$237$		0			0
$238$	3.00000	+	15.5885i	0.194461	+	1.01045i
$239$	6.00000			0.388108			0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000			0.388108			0.194054	+	0.980991i	$0.437836\pi$
$240$		0			0
$241$	7.50000	−	12.9904i	0.483117	−	0.836784i	−0.516695	−	0.856170i	$-0.672838\pi$
$241$	7.50000	−	12.9904i	0.483117	−	0.836784i	0.999812	+	0.0193858i	$0.00617107\pi$
$242$	−5.00000	+	8.66025i	−0.321412	+	0.556702i
$243$		0			0
$244$	12.0000			0.768221
$245$	5.50000	+	4.33013i	0.351382	+	0.276642i
$246$		0			0
$247$	−2.00000	−	3.46410i	−0.127257	−	0.220416i
$248$	−5.50000	+	9.52628i	−0.349250	+	0.604919i
$249$		0			0
$250$	−4.50000	−	7.79423i	−0.284605	−	0.492950i
$251$	−17.0000			−1.07303			−0.536515	−	0.843891i	$-0.680260\pi$
$251$	−17.0000			−1.07303			−0.536515	+	0.843891i	$0.680260\pi$
$252$		0			0
$253$	6.00000			0.377217
$254$	−3.50000	−	6.06218i	−0.219610	−	0.380375i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.00000	−	5.19615i	−0.187135	−	0.324127i	0.757159	−	0.653231i	$-0.226587\pi$
$257$	−3.00000	−	5.19615i	−0.187135	−	0.324127i	−0.944294	+	0.329104i	$0.893253\pi$
$258$		0			0
$259$	−8.00000	+	6.92820i	−0.497096	+	0.430498i
$260$	−1.00000			−0.0620174
$261$		0			0
$262$	−0.500000	+	0.866025i	−0.0308901	+	0.0535032i
$263$	−9.00000	+	15.5885i	−0.554964	+	0.961225i	0.442943	+	0.896550i	$0.353935\pi$
$263$	−9.00000	+	15.5885i	−0.554964	+	0.961225i	−0.997906	+	0.0646755i	$0.979399\pi$
$264$		0			0
$265$	5.00000			0.307148
$266$	10.0000	+	3.46410i	0.613139	+	0.212398i
$267$		0			0
$268$	−8.00000	−	13.8564i	−0.488678	−	0.846415i
$269$	−4.50000	+	7.79423i	−0.274370	+	0.475223i	−0.969976	−	0.243201i	$-0.921803\pi$
$269$	−4.50000	+	7.79423i	−0.274370	+	0.475223i	0.695606	+	0.718423i	$0.255136\pi$
$270$		0			0
$271$	3.50000	+	6.06218i	0.212610	+	0.368251i	0.952531	−	0.304443i	$-0.0984703\pi$
$271$	3.50000	+	6.06218i	0.212610	+	0.368251i	−0.739921	+	0.672694i	$0.765137\pi$
$272$	6.00000			0.363803
$273$		0			0
$274$	−8.00000			−0.483298
$275$	2.00000	+	3.46410i	0.120605	+	0.208893i
$276$		0			0
$277$	5.00000	−	8.66025i	0.300421	−	0.520344i	−0.675810	−	0.737075i	$-0.736206\pi$
$277$	5.00000	−	8.66025i	0.300421	−	0.520344i	0.976231	+	0.216731i	$0.0695395\pi$
$278$		0			0
$279$		0			0
$280$	2.00000	−	1.73205i	0.119523	−	0.103510i
$281$	−4.00000			−0.238620			−0.119310	−	0.992857i	$-0.538068\pi$
$281$	−4.00000			−0.238620			−0.119310	+	0.992857i	$0.538068\pi$
$282$		0			0
$283$	−5.00000	+	8.66025i	−0.297219	+	0.514799i	−0.975499	−	0.220005i	$-0.929393\pi$
$283$	−5.00000	+	8.66025i	−0.297219	+	0.514799i	0.678280	+	0.734804i	$0.262726\pi$
$284$	3.00000	−	5.19615i	0.178017	−	0.308335i
$285$		0			0
$286$	1.00000			0.0591312
$287$	6.00000	+	31.1769i	0.354169	+	1.84032i
$288$		0			0
$289$	−9.50000	−	16.4545i	−0.558824	−	0.967911i
$290$	−1.50000	+	2.59808i	−0.0880830	+	0.152564i
$291$		0			0
$292$	5.00000	+	8.66025i	0.292603	+	0.506803i
$293$	7.00000			0.408944			0.204472	−	0.978872i	$-0.434452\pi$
$293$	7.00000			0.408944			0.204472	+	0.978872i	$0.434452\pi$
$294$		0			0
$295$	5.00000			0.291111
$296$	2.00000	+	3.46410i	0.116248	+	0.201347i
$297$		0			0
$298$	5.00000	−	8.66025i	0.289642	−	0.501675i
$299$	3.00000	+	5.19615i	0.173494	+	0.300501i
$300$		0			0
$301$	4.00000	+	20.7846i	0.230556	+	1.19800i
$302$	−13.0000			−0.748066
$303$		0			0
$304$	2.00000	−	3.46410i	0.114708	−	0.198680i
$305$	−6.00000	+	10.3923i	−0.343559	+	0.595062i
$306$		0			0
$307$	6.00000			0.342438			0.171219	−	0.985233i	$-0.445229\pi$
$307$	6.00000			0.342438			0.171219	+	0.985233i	$0.445229\pi$
$308$	−2.00000	+	1.73205i	−0.113961	+	0.0986928i
$309$		0			0
$310$	−5.50000	−	9.52628i	−0.312379	−	0.541056i
$311$	1.00000	−	1.73205i	0.0567048	−	0.0982156i	−0.836280	−	0.548303i	$-0.815274\pi$
$311$	1.00000	−	1.73205i	0.0567048	−	0.0982156i	0.892984	+	0.450088i	$0.148607\pi$
$312$		0			0
$313$	−6.50000	−	11.2583i	−0.367402	−	0.636358i	0.621757	−	0.783210i	$-0.286419\pi$
$313$	−6.50000	−	11.2583i	−0.367402	−	0.636358i	−0.989158	+	0.146852i	$0.953086\pi$
$314$	18.0000			1.01580
$315$		0			0
$316$	7.00000			0.393781
$317$	−1.50000	−	2.59808i	−0.0842484	−	0.145922i	0.820822	−	0.571184i	$-0.193516\pi$
$317$	−1.50000	−	2.59808i	−0.0842484	−	0.145922i	−0.905071	+	0.425261i	$0.860182\pi$
$318$		0			0
$319$	1.50000	−	2.59808i	0.0839839	−	0.145464i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$		0			0
$322$	−15.0000	−	5.19615i	−0.835917	−	0.289570i
$323$	−24.0000			−1.33540
$324$		0			0
$325$	−2.00000	+	3.46410i	−0.110940	+	0.192154i
$326$	−4.00000	+	6.92820i	−0.221540	+	0.383718i
$327$		0			0
$328$	12.0000			0.662589
$329$	−16.0000	+	13.8564i	−0.882109	+	0.763928i
$330$		0			0
$331$	4.00000	+	6.92820i	0.219860	+	0.380808i	0.954765	−	0.297361i	$-0.0961066\pi$
$331$	4.00000	+	6.92820i	0.219860	+	0.380808i	−0.734905	+	0.678170i	$0.762773\pi$
$332$	−8.50000	+	14.7224i	−0.466498	+	0.807998i
$333$		0			0
$334$	12.0000	+	20.7846i	0.656611	+	1.13728i
$335$	16.0000			0.874173
$336$		0			0
$337$	25.0000			1.36184			0.680918	−	0.732359i	$-0.261581\pi$
$337$	25.0000			1.36184			0.680918	+	0.732359i	$0.261581\pi$
$338$	0.500000	+	0.866025i	0.0271964	+	0.0471056i
$339$		0			0
$340$	−3.00000	+	5.19615i	−0.162698	+	0.281801i
$341$	5.50000	+	9.52628i	0.297842	+	0.515877i
$342$		0			0
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	8.00000			0.431331
$345$		0			0
$346$	−3.00000	+	5.19615i	−0.161281	+	0.279347i
$347$	10.0000	−	17.3205i	0.536828	−	0.929814i	−0.462244	−	0.886753i	$-0.652956\pi$
$347$	10.0000	−	17.3205i	0.536828	−	0.929814i	0.999072	−	0.0430610i	$-0.0137110\pi$
$348$		0			0
$349$	14.0000			0.749403			0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000			0.749403			0.374701	+	0.927146i	$0.377745\pi$
$350$	−2.00000	−	10.3923i	−0.106904	−	0.555492i
$351$		0			0
$352$	0.500000	+	0.866025i	0.0266501	+	0.0461593i
$353$	15.0000	−	25.9808i	0.798369	−	1.38282i	−0.122308	−	0.992492i	$-0.539030\pi$
$353$	15.0000	−	25.9808i	0.798369	−	1.38282i	0.920677	−	0.390324i	$-0.127637\pi$
$354$		0			0
$355$	3.00000	+	5.19615i	0.159223	+	0.275783i
$356$	12.0000			0.635999
$357$		0			0
$358$	12.0000			0.634220
$359$	−11.0000	−	19.0526i	−0.580558	−	1.00556i	−0.995413	−	0.0956683i	$-0.969501\pi$
$359$	−11.0000	−	19.0526i	−0.580558	−	1.00556i	0.414855	−	0.909887i	$-0.363832\pi$
$360$		0			0
$361$	1.50000	−	2.59808i	0.0789474	−	0.136741i
$362$	−8.00000	−	13.8564i	−0.420471	−	0.728277i
$363$		0			0
$364$	−2.50000	−	0.866025i	−0.131036	−	0.0453921i
$365$	−10.0000			−0.523424
$366$		0			0
$367$	3.50000	−	6.06218i	0.182699	−	0.316443i	−0.760100	−	0.649806i	$-0.774850\pi$
$367$	3.50000	−	6.06218i	0.182699	−	0.316443i	0.942799	+	0.333363i	$0.108183\pi$
$368$	−3.00000	+	5.19615i	−0.156386	+	0.270868i
$369$		0			0
$370$	−4.00000			−0.207950
$371$	12.5000	+	4.33013i	0.648968	+	0.224809i
$372$		0			0
$373$	−13.0000	−	22.5167i	−0.673114	−	1.16587i	−0.977016	−	0.213165i	$-0.931623\pi$
$373$	−13.0000	−	22.5167i	−0.673114	−	1.16587i	0.303902	−	0.952703i	$-0.401711\pi$
$374$	3.00000	−	5.19615i	0.155126	−	0.268687i
$375$		0			0
$376$	4.00000	+	6.92820i	0.206284	+	0.357295i
$377$	3.00000			0.154508
$378$		0			0
$379$	16.0000			0.821865			0.410932	−	0.911666i	$-0.365203\pi$
$379$	16.0000			0.821865			0.410932	+	0.911666i	$0.365203\pi$
$380$	2.00000	+	3.46410i	0.102598	+	0.177705i
$381$		0			0
$382$	3.00000	−	5.19615i	0.153493	−	0.265858i
$383$	−7.00000	−	12.1244i	−0.357683	−	0.619526i	0.629890	−	0.776684i	$-0.283100\pi$
$383$	−7.00000	−	12.1244i	−0.357683	−	0.619526i	−0.987573	+	0.157159i	$0.949767\pi$
$384$		0			0
$385$	−0.500000	−	2.59808i	−0.0254824	−	0.132410i
$386$	−15.0000			−0.763480
$387$		0			0
$388$	−6.50000	+	11.2583i	−0.329988	+	0.571555i
$389$	11.0000	−	19.0526i	0.557722	−	0.966003i	−0.439964	−	0.898015i	$-0.645009\pi$
$389$	11.0000	−	19.0526i	0.557722	−	0.966003i	0.997686	−	0.0679877i	$-0.0216579\pi$
$390$		0			0
$391$	36.0000			1.82060
$392$	6.50000	−	2.59808i	0.328300	−	0.131223i
$393$		0			0
$394$	9.00000	+	15.5885i	0.453413	+	0.785335i
$395$	−3.50000	+	6.06218i	−0.176104	+	0.305021i
$396$		0			0
$397$	9.00000	+	15.5885i	0.451697	+	0.782362i	0.998492	−	0.0549046i	$-0.0174855\pi$
$397$	9.00000	+	15.5885i	0.451697	+	0.782362i	−0.546795	+	0.837267i	$0.684152\pi$
$398$	−8.00000			−0.401004
$399$		0			0
$400$	−4.00000			−0.200000
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	0.548911	−	0.835881i	$-0.315043\pi$
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	−0.998350	+	0.0574304i	$0.981709\pi$
$402$		0			0
$403$	−5.50000	+	9.52628i	−0.273975	+	0.474538i
$404$	5.00000	+	8.66025i	0.248759	+	0.430864i
$405$		0			0
$406$	−6.00000	+	5.19615i	−0.297775	+	0.257881i
$407$	4.00000			0.198273
$408$		0			0
$409$	−12.5000	+	21.6506i	−0.618085	+	1.07056i	0.371750	+	0.928333i	$0.378758\pi$
$409$	−12.5000	+	21.6506i	−0.618085	+	1.07056i	−0.989835	+	0.142222i	$0.954575\pi$
$410$	−6.00000	+	10.3923i	−0.296319	+	0.513239i
$411$		0			0
$412$		0			0
$413$	12.5000	+	4.33013i	0.615085	+	0.213072i
$414$		0			0
$415$	−8.50000	−	14.7224i	−0.417249	−	0.722696i
$416$	−0.500000	+	0.866025i	−0.0245145	+	0.0424604i
$417$		0			0
$418$	−2.00000	−	3.46410i	−0.0978232	−	0.169435i
$419$	−16.0000			−0.781651			−0.390826	−	0.920465i	$-0.627810\pi$
$419$	−16.0000			−0.781651			−0.390826	+	0.920465i	$0.627810\pi$
$420$		0			0
$421$	−36.0000			−1.75453			−0.877266	−	0.480004i	$-0.840635\pi$
$421$	−36.0000			−1.75453			−0.877266	+	0.480004i	$0.840635\pi$
$422$	6.00000	+	10.3923i	0.292075	+	0.505889i
$423$		0			0
$424$	2.50000	−	4.33013i	0.121411	−	0.210290i
$425$	12.0000	+	20.7846i	0.582086	+	1.00820i
$426$		0			0
$427$	−24.0000	+	20.7846i	−1.16144	+	1.00584i
$428$	−7.00000			−0.338358
$429$		0			0
$430$	−4.00000	+	6.92820i	−0.192897	+	0.334108i
$431$	−19.0000	+	32.9090i	−0.915198	+	1.58517i	−0.108586	+	0.994087i	$0.534632\pi$
$431$	−19.0000	+	32.9090i	−0.915198	+	1.58517i	−0.806611	+	0.591082i	$0.798701\pi$
$432$		0			0
$433$	−14.0000			−0.672797			−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000			−0.672797			−0.336399	+	0.941720i	$0.609209\pi$
$434$	−5.50000	−	28.5788i	−0.264008	−	1.37183i
$435$		0			0
$436$	−6.00000	−	10.3923i	−0.287348	−	0.497701i
$437$	12.0000	−	20.7846i	0.574038	−	0.994263i
$438$		0			0
$439$	8.50000	+	14.7224i	0.405683	+	0.702663i	0.994401	−	0.105675i	$-0.0337004\pi$
$439$	8.50000	+	14.7224i	0.405683	+	0.702663i	−0.588718	+	0.808339i	$0.700367\pi$
$440$	−1.00000			−0.0476731
$441$		0			0
$442$	6.00000			0.285391
$443$	−19.5000	−	33.7750i	−0.926473	−	1.60470i	−0.789175	−	0.614168i	$-0.789492\pi$
$443$	−19.5000	−	33.7750i	−0.926473	−	1.60470i	−0.137298	−	0.990530i	$-0.543842\pi$
$444$		0			0
$445$	−6.00000	+	10.3923i	−0.284427	+	0.492642i
$446$	3.50000	+	6.06218i	0.165730	+	0.287052i
$447$		0			0
$448$	−0.500000	−	2.59808i	−0.0236228	−	0.122748i
$449$	−20.0000			−0.943858			−0.471929	−	0.881636i	$-0.656442\pi$
$449$	−20.0000			−0.943858			−0.471929	+	0.881636i	$0.656442\pi$
$450$		0			0
$451$	6.00000	−	10.3923i	0.282529	−	0.489355i
$452$	−2.00000	+	3.46410i	−0.0940721	+	0.162938i
$453$		0			0
$454$	−15.0000			−0.703985
$455$	2.00000	−	1.73205i	0.0937614	−	0.0811998i
$456$		0			0
$457$	5.50000	+	9.52628i	0.257279	+	0.445621i	0.965512	−	0.260358i	$-0.0838407\pi$
$457$	5.50000	+	9.52628i	0.257279	+	0.445621i	−0.708233	+	0.705979i	$0.750507\pi$
$458$	3.00000	−	5.19615i	0.140181	−	0.242800i
$459$		0			0
$460$	−3.00000	−	5.19615i	−0.139876	−	0.242272i
$461$	−34.0000			−1.58354			−0.791769	−	0.610821i	$-0.790840\pi$
$461$	−34.0000			−1.58354			−0.791769	+	0.610821i	$0.790840\pi$
$462$		0			0
$463$	−24.0000			−1.11537			−0.557687	−	0.830051i	$-0.688311\pi$
$463$	−24.0000			−1.11537			−0.557687	+	0.830051i	$0.688311\pi$
$464$	1.50000	+	2.59808i	0.0696358	+	0.120613i
$465$		0			0
$466$	−3.00000	+	5.19615i	−0.138972	+	0.240707i
$467$	6.00000	+	10.3923i	0.277647	+	0.480899i	0.970799	−	0.239892i	$-0.0771121\pi$
$467$	6.00000	+	10.3923i	0.277647	+	0.480899i	−0.693153	+	0.720791i	$0.743779\pi$
$468$		0			0
$469$	40.0000	+	13.8564i	1.84703	+	0.639829i
$470$	−8.00000			−0.369012
$471$		0			0
$472$	2.50000	−	4.33013i	0.115072	−	0.199310i
$473$	4.00000	−	6.92820i	0.183920	−	0.318559i
$474$		0			0
$475$	16.0000			0.734130
$476$	−12.0000	+	10.3923i	−0.550019	+	0.476331i
$477$		0			0
$478$	3.00000	+	5.19615i	0.137217	+	0.237666i
$479$	7.00000	−	12.1244i	0.319838	−	0.553976i	−0.660616	−	0.750724i	$-0.729705\pi$
$479$	7.00000	−	12.1244i	0.319838	−	0.553976i	0.980454	+	0.196748i	$0.0630381\pi$
$480$		0			0
$481$	2.00000	+	3.46410i	0.0911922	+	0.157949i
$482$	15.0000			0.683231
$483$		0			0
$484$	−10.0000			−0.454545
$485$	−6.50000	−	11.2583i	−0.295150	−	0.511214i
$486$		0			0
$487$	−11.5000	+	19.9186i	−0.521115	+	0.902597i	0.478584	+	0.878042i	$0.341150\pi$
$487$	−11.5000	+	19.9186i	−0.521115	+	0.902597i	−0.999698	+	0.0245553i	$0.992183\pi$
$488$	6.00000	+	10.3923i	0.271607	+	0.470438i
$489$		0			0
$490$	−1.00000	+	6.92820i	−0.0451754	+	0.312984i
$491$	35.0000			1.57953			0.789764	−	0.613411i	$-0.210203\pi$
$491$	35.0000			1.57953			0.789764	+	0.613411i	$0.210203\pi$
$492$		0			0
$493$	9.00000	−	15.5885i	0.405340	−	0.702069i
$494$	2.00000	−	3.46410i	0.0899843	−	0.155857i
$495$		0			0
$496$	−11.0000			−0.493915
$497$	3.00000	+	15.5885i	0.134568	+	0.699238i
$498$		0			0
$499$	14.0000	+	24.2487i	0.626726	+	1.08552i	0.988204	+	0.153141i	$0.0489388\pi$
$499$	14.0000	+	24.2487i	0.626726	+	1.08552i	−0.361478	+	0.932381i	$0.617728\pi$
$500$	4.50000	−	7.79423i	0.201246	−	0.348569i
$501$		0			0
$502$	−8.50000	−	14.7224i	−0.379374	−	0.657094i
$503$	6.00000			0.267527			0.133763	−	0.991013i	$-0.457294\pi$
$503$	6.00000			0.267527			0.133763	+	0.991013i	$0.457294\pi$
$504$		0			0
$505$	−10.0000			−0.444994
$506$	3.00000	+	5.19615i	0.133366	+	0.230997i
$507$		0			0
$508$	3.50000	−	6.06218i	0.155287	−	0.268966i
$509$	6.50000	+	11.2583i	0.288107	+	0.499017i	0.973358	−	0.229291i	$-0.0736406\pi$
$509$	6.50000	+	11.2583i	0.288107	+	0.499017i	−0.685251	+	0.728307i	$0.740307\pi$
$510$		0			0
$511$	−25.0000	−	8.66025i	−1.10593	−	0.383107i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	3.00000	−	5.19615i	0.132324	−	0.229192i
$515$		0			0
$516$		0			0
$517$	8.00000			0.351840
$518$	−10.0000	−	3.46410i	−0.439375	−	0.152204i
$519$		0			0
$520$	−0.500000	−	0.866025i	−0.0219265	−	0.0379777i
$521$	14.0000	−	24.2487i	0.613351	−	1.06236i	−0.377320	−	0.926083i	$-0.623154\pi$
$521$	14.0000	−	24.2487i	0.613351	−	1.06236i	0.990671	−	0.136272i	$-0.0435123\pi$
$522$		0			0
$523$	−8.00000	−	13.8564i	−0.349816	−	0.605898i	0.636401	−	0.771358i	$-0.280422\pi$
$523$	−8.00000	−	13.8564i	−0.349816	−	0.605898i	−0.986216	+	0.165460i	$0.947089\pi$
$524$	−1.00000			−0.0436852
$525$		0			0
$526$	−18.0000			−0.784837
$527$	33.0000	+	57.1577i	1.43750	+	2.48983i
$528$		0			0
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$	2.50000	+	4.33013i	0.108593	+	0.188089i
$531$		0			0
$532$	2.00000	+	10.3923i	0.0867110	+	0.450564i
$533$	12.0000			0.519778
$534$		0			0
$535$	3.50000	−	6.06218i	0.151318	−	0.262091i
$536$	8.00000	−	13.8564i	0.345547	−	0.598506i
$537$		0			0
$538$	−9.00000			−0.388018
$539$	1.00000	−	6.92820i	0.0430730	−	0.298419i
$540$		0			0
$541$	−16.0000	−	27.7128i	−0.687894	−	1.19147i	−0.972518	−	0.232828i	$-0.925202\pi$
$541$	−16.0000	−	27.7128i	−0.687894	−	1.19147i	0.284624	−	0.958639i	$-0.408131\pi$
$542$	−3.50000	+	6.06218i	−0.150338	+	0.260393i
$543$		0			0
$544$	3.00000	+	5.19615i	0.128624	+	0.222783i
$545$	12.0000			0.514024
$546$		0			0
$547$	36.0000			1.53925			0.769624	−	0.638497i	$-0.220443\pi$
$547$	36.0000			1.53925			0.769624	+	0.638497i	$0.220443\pi$
$548$	−4.00000	−	6.92820i	−0.170872	−	0.295958i
$549$		0			0
$550$	−2.00000	+	3.46410i	−0.0852803	+	0.147710i
$551$	−6.00000	−	10.3923i	−0.255609	−	0.442727i
$552$		0			0
$553$	−14.0000	+	12.1244i	−0.595341	+	0.515580i
$554$	10.0000			0.424859
$555$		0			0
$556$		0			0
$557$	−8.50000	+	14.7224i	−0.360157	+	0.623809i	−0.987986	−	0.154541i	$-0.950610\pi$
$557$	−8.50000	+	14.7224i	−0.360157	+	0.623809i	0.627830	+	0.778351i	$0.283943\pi$
$558$		0			0
$559$	8.00000			0.338364
$560$	2.50000	+	0.866025i	0.105644	+	0.0365963i
$561$		0			0
$562$	−2.00000	−	3.46410i	−0.0843649	−	0.146124i
$563$	10.5000	−	18.1865i	0.442522	−	0.766471i	−0.555354	−	0.831614i	$-0.687417\pi$
$563$	10.5000	−	18.1865i	0.442522	−	0.766471i	0.997876	+	0.0651433i	$0.0207504\pi$
$564$		0			0
$565$	−2.00000	−	3.46410i	−0.0841406	−	0.145736i
$566$	−10.0000			−0.420331
$567$		0			0
$568$	6.00000			0.251754
$569$	−2.00000	−	3.46410i	−0.0838444	−	0.145223i	0.821054	−	0.570851i	$-0.193387\pi$
$569$	−2.00000	−	3.46410i	−0.0838444	−	0.145223i	−0.904898	+	0.425628i	$0.860053\pi$
$570$		0			0
$571$	−14.0000	+	24.2487i	−0.585882	+	1.01478i	0.408883	+	0.912587i	$0.365918\pi$
$571$	−14.0000	+	24.2487i	−0.585882	+	1.01478i	−0.994765	+	0.102190i	$0.967415\pi$
$572$	0.500000	+	0.866025i	0.0209061	+	0.0362103i
$573$		0			0
$574$	−24.0000	+	20.7846i	−1.00174	+	0.867533i
$575$	−24.0000			−1.00087
$576$		0			0
$577$	−0.500000	+	0.866025i	−0.0208153	+	0.0360531i	−0.876245	−	0.481865i	$-0.839960\pi$
$577$	−0.500000	+	0.866025i	−0.0208153	+	0.0360531i	0.855430	+	0.517918i	$0.173293\pi$
$578$	9.50000	−	16.4545i	0.395148	−	0.684416i
$579$		0			0
$580$	−3.00000			−0.124568
$581$	−8.50000	−	44.1673i	−0.352639	−	1.83237i
$582$		0			0
$583$	−2.50000	−	4.33013i	−0.103539	−	0.179336i
$584$	−5.00000	+	8.66025i	−0.206901	+	0.358364i
$585$		0			0
$586$	3.50000	+	6.06218i	0.144584	+	0.250426i
$587$	−5.00000			−0.206372			−0.103186	−	0.994662i	$-0.532904\pi$
$587$	−5.00000			−0.206372			−0.103186	+	0.994662i	$0.532904\pi$
$588$		0			0
$589$	44.0000			1.81299
$590$	2.50000	+	4.33013i	0.102923	+	0.178269i
$591$		0			0
$592$	−2.00000	+	3.46410i	−0.0821995	+	0.142374i
$593$	−18.0000	−	31.1769i	−0.739171	−	1.28028i	−0.952869	−	0.303383i	$-0.901884\pi$
$593$	−18.0000	−	31.1769i	−0.739171	−	1.28028i	0.213697	−	0.976900i	$-0.431449\pi$
$594$		0			0
$595$	−3.00000	−	15.5885i	−0.122988	−	0.639064i
$596$	10.0000			0.409616
$597$		0			0
$598$	−3.00000	+	5.19615i	−0.122679	+	0.212486i
$599$	−5.00000	+	8.66025i	−0.204294	+	0.353848i	−0.949908	−	0.312531i	$-0.898823\pi$
$599$	−5.00000	+	8.66025i	−0.204294	+	0.353848i	0.745613	+	0.666379i	$0.232157\pi$
$600$		0			0
$601$	11.0000			0.448699			0.224350	−	0.974509i	$-0.427974\pi$
$601$	11.0000			0.448699			0.224350	+	0.974509i	$0.427974\pi$
$602$	−16.0000	+	13.8564i	−0.652111	+	0.564745i
$603$		0			0
$604$	−6.50000	−	11.2583i	−0.264481	−	0.458095i
$605$	5.00000	−	8.66025i	0.203279	−	0.352089i
$606$		0			0
$607$	−14.5000	−	25.1147i	−0.588537	−	1.01938i	−0.994424	−	0.105453i	$-0.966371\pi$
$607$	−14.5000	−	25.1147i	−0.588537	−	1.01938i	0.405887	−	0.913923i	$-0.366962\pi$
$608$	4.00000			0.162221
$609$		0			0
$610$	−12.0000			−0.485866
$611$	4.00000	+	6.92820i	0.161823	+	0.280285i
$612$		0			0
$613$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$613$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$614$	3.00000	+	5.19615i	0.121070	+	0.209700i
$615$		0			0
$616$	−2.50000	−	0.866025i	−0.100728	−	0.0348932i
$617$	36.0000			1.44931			0.724653	−	0.689114i	$-0.242000\pi$
$617$	36.0000			1.44931			0.724653	+	0.689114i	$0.242000\pi$
$618$		0			0
$619$	4.00000	−	6.92820i	0.160774	−	0.278468i	−0.774373	−	0.632730i	$-0.781934\pi$
$619$	4.00000	−	6.92820i	0.160774	−	0.278468i	0.935146	+	0.354262i	$0.115268\pi$
$620$	5.50000	−	9.52628i	0.220885	−	0.382585i
$621$		0			0
$622$	2.00000			0.0801927
$623$	−24.0000	+	20.7846i	−0.961540	+	0.832718i
$624$		0			0
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$	6.50000	−	11.2583i	0.259792	−	0.449973i
$627$		0			0
$628$	9.00000	+	15.5885i	0.359139	+	0.622047i
$629$	24.0000			0.956943
$630$		0			0
$631$	−29.0000			−1.15447			−0.577236	−	0.816577i	$-0.695869\pi$
$631$	−29.0000			−1.15447			−0.577236	+	0.816577i	$0.695869\pi$
$632$	3.50000	+	6.06218i	0.139223	+	0.241140i
$633$		0			0
$634$	1.50000	−	2.59808i	0.0595726	−	0.103183i
$635$	3.50000	+	6.06218i	0.138893	+	0.240570i
$636$		0			0
$637$	6.50000	−	2.59808i	0.257539	−	0.102940i
$638$	3.00000			0.118771
$639$		0			0
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	−6.00000	+	10.3923i	−0.236986	+	0.410471i	−0.959848	−	0.280521i	$-0.909493\pi$
$641$	−6.00000	+	10.3923i	−0.236986	+	0.410471i	0.722862	+	0.690992i	$0.242826\pi$
$642$		0			0
$643$	20.0000			0.788723			0.394362	−	0.918955i	$-0.370966\pi$
$643$	20.0000			0.788723			0.394362	+	0.918955i	$0.370966\pi$
$644$	−3.00000	−	15.5885i	−0.118217	−	0.614271i
$645$		0			0
$646$	−12.0000	−	20.7846i	−0.472134	−	0.817760i
$647$	−2.00000	+	3.46410i	−0.0786281	+	0.136188i	−0.902658	−	0.430358i	$-0.858387\pi$
$647$	−2.00000	+	3.46410i	−0.0786281	+	0.136188i	0.824030	+	0.566546i	$0.191721\pi$
$648$		0			0
$649$	−2.50000	−	4.33013i	−0.0981336	−	0.169972i
$650$	−4.00000			−0.156893
$651$		0			0
$652$	−8.00000			−0.313304
$653$	−5.50000	−	9.52628i	−0.215232	−	0.372792i	0.738113	−	0.674678i	$-0.235717\pi$
$653$	−5.50000	−	9.52628i	−0.215232	−	0.372792i	−0.953344	+	0.301885i	$0.902384\pi$
$654$		0			0
$655$	0.500000	−	0.866025i	0.0195366	−	0.0338384i
$656$	6.00000	+	10.3923i	0.234261	+	0.405751i
$657$		0			0
$658$	−20.0000	−	6.92820i	−0.779681	−	0.270089i
$659$	12.0000			0.467454			0.233727	−	0.972302i	$-0.424908\pi$
$659$	12.0000			0.467454			0.233727	+	0.972302i	$0.424908\pi$
$660$		0			0
$661$	−11.0000	+	19.0526i	−0.427850	+	0.741059i	−0.996682	−	0.0813955i	$-0.974062\pi$
$661$	−11.0000	+	19.0526i	−0.427850	+	0.741059i	0.568831	+	0.822454i	$0.307396\pi$
$662$	−4.00000	+	6.92820i	−0.155464	+	0.269272i
$663$		0			0
$664$	−17.0000			−0.659728
$665$	−10.0000	−	3.46410i	−0.387783	−	0.134332i
$666$		0			0
$667$	9.00000	+	15.5885i	0.348481	+	0.603587i
$668$	−12.0000	+	20.7846i	−0.464294	+	0.804181i
$669$		0			0
$670$	8.00000	+	13.8564i	0.309067	+	0.535320i
$671$	12.0000			0.463255
$672$		0			0
$673$	−39.0000			−1.50334			−0.751670	−	0.659540i	$-0.770751\pi$
$673$	−39.0000			−1.50334			−0.751670	+	0.659540i	$0.770751\pi$
$674$	12.5000	+	21.6506i	0.481482	+	0.833951i
$675$		0			0
$676$	−0.500000	+	0.866025i	−0.0192308	+	0.0333087i
$677$	−17.5000	−	30.3109i	−0.672580	−	1.16494i	−0.977170	−	0.212459i	$-0.931853\pi$
$677$	−17.5000	−	30.3109i	−0.672580	−	1.16494i	0.304590	−	0.952483i	$-0.401480\pi$
$678$		0			0
$679$	−6.50000	−	33.7750i	−0.249447	−	1.29617i
$680$	−6.00000			−0.230089
$681$		0			0
$682$	−5.50000	+	9.52628i	−0.210606	+	0.364780i
$683$	−13.5000	+	23.3827i	−0.516563	+	0.894714i	0.483252	+	0.875481i	$0.339456\pi$
$683$	−13.5000	+	23.3827i	−0.516563	+	0.894714i	−0.999815	+	0.0192323i	$0.993878\pi$
$684$		0			0
$685$	8.00000			0.305664
$686$	−8.50000	+	16.4545i	−0.324532	+	0.628235i
$687$		0			0
$688$	4.00000	+	6.92820i	0.152499	+	0.264135i
$689$	2.50000	−	4.33013i	0.0952424	−	0.164965i
$690$		0			0
$691$	20.0000	+	34.6410i	0.760836	+	1.31781i	0.942420	+	0.334431i	$0.108544\pi$
$691$	20.0000	+	34.6410i	0.760836	+	1.31781i	−0.181584	+	0.983375i	$0.558123\pi$
$692$	−6.00000			−0.228086
$693$		0			0
$694$	20.0000			0.759190
$695$		0			0
$696$		0			0
$697$	36.0000	−	62.3538i	1.36360	−	2.36182i
$698$	7.00000	+	12.1244i	0.264954	+	0.458914i
$699$		0			0
$700$	8.00000	−	6.92820i	0.302372	−	0.261861i
$701$	13.0000			0.491003			0.245502	−	0.969396i	$-0.421047\pi$
$701$	13.0000			0.491003			0.245502	+	0.969396i	$0.421047\pi$
$702$		0			0
$703$	8.00000	−	13.8564i	0.301726	−	0.522604i
$704$	−0.500000	+	0.866025i	−0.0188445	+	0.0326396i
$705$		0			0
$706$	30.0000			1.12906
$707$	−25.0000	−	8.66025i	−0.940222	−	0.325702i
$708$		0			0
$709$	−3.00000	−	5.19615i	−0.112667	−	0.195146i	0.804178	−	0.594389i	$-0.202606\pi$
$709$	−3.00000	−	5.19615i	−0.112667	−	0.195146i	−0.916845	+	0.399244i	$0.869273\pi$
$710$	−3.00000	+	5.19615i	−0.112588	+	0.195008i
$711$		0			0
$712$	6.00000	+	10.3923i	0.224860	+	0.389468i
$713$	−66.0000			−2.47172
$714$		0			0
$715$	−1.00000			−0.0373979
$716$	6.00000	+	10.3923i	0.224231	+	0.388379i
$717$		0			0
$718$	11.0000	−	19.0526i	0.410516	−	0.711035i
$719$	23.0000	+	39.8372i	0.857755	+	1.48568i	0.874065	+	0.485809i	$0.161475\pi$
$719$	23.0000	+	39.8372i	0.857755	+	1.48568i	−0.0163099	+	0.999867i	$0.505192\pi$
$720$		0			0
$721$		0			0
$722$	3.00000			0.111648
$723$		0			0
$724$	8.00000	−	13.8564i	0.297318	−	0.514969i
$725$	−6.00000	+	10.3923i	−0.222834	+	0.385961i
$726$		0			0
$727$	19.0000			0.704671			0.352335	−	0.935874i	$-0.385388\pi$
$727$	19.0000			0.704671			0.352335	+	0.935874i	$0.385388\pi$
$728$	−0.500000	−	2.59808i	−0.0185312	−	0.0962911i
$729$		0			0
$730$	−5.00000	−	8.66025i	−0.185058	−	0.320530i
$731$	24.0000	−	41.5692i	0.887672	−	1.53749i
$732$		0			0
$733$	−1.00000	−	1.73205i	−0.0369358	−	0.0639748i	0.846967	−	0.531646i	$-0.178426\pi$
$733$	−1.00000	−	1.73205i	−0.0369358	−	0.0639748i	−0.883902	+	0.467671i	$0.845093\pi$
$734$	7.00000			0.258375
$735$		0			0
$736$	−6.00000			−0.221163
$737$	−8.00000	−	13.8564i	−0.294684	−	0.510407i
$738$		0			0
$739$	13.0000	−	22.5167i	0.478213	−	0.828289i	−0.521475	−	0.853266i	$-0.674618\pi$
$739$	13.0000	−	22.5167i	0.478213	−	0.828289i	0.999688	+	0.0249776i	$0.00795146\pi$
$740$	−2.00000	−	3.46410i	−0.0735215	−	0.127343i
$741$		0			0
$742$	2.50000	+	12.9904i	0.0917779	+	0.476892i
$743$	32.0000			1.17397			0.586983	−	0.809599i	$-0.300316\pi$
$743$	32.0000			1.17397			0.586983	+	0.809599i	$0.300316\pi$
$744$		0			0
$745$	−5.00000	+	8.66025i	−0.183186	+	0.317287i
$746$	13.0000	−	22.5167i	0.475964	−	0.824394i
$747$		0			0
$748$	6.00000			0.219382
$749$	14.0000	−	12.1244i	0.511549	−	0.443014i
$750$		0			0
$751$	−12.5000	−	21.6506i	−0.456131	−	0.790043i	0.542621	−	0.839978i	$-0.317432\pi$
$751$	−12.5000	−	21.6506i	−0.456131	−	0.790043i	−0.998752	+	0.0499348i	$0.984099\pi$
$752$	−4.00000	+	6.92820i	−0.145865	+	0.252646i
$753$		0			0
$754$	1.50000	+	2.59808i	0.0546268	+	0.0946164i
$755$	13.0000			0.473118
$756$		0			0
$757$	−38.0000			−1.38113			−0.690567	−	0.723269i	$-0.742639\pi$
$757$	−38.0000			−1.38113			−0.690567	+	0.723269i	$0.742639\pi$
$758$	8.00000	+	13.8564i	0.290573	+	0.503287i
$759$		0			0
$760$	−2.00000	+	3.46410i	−0.0725476	+	0.125656i
$761$	−14.0000	−	24.2487i	−0.507500	−	0.879015i	−0.999962	−	0.00868155i	$-0.997237\pi$
$761$	−14.0000	−	24.2487i	−0.507500	−	0.879015i	0.492463	−	0.870334i	$-0.336097\pi$
$762$		0			0
$763$	30.0000	+	10.3923i	1.08607	+	0.376227i
$764$	6.00000			0.217072
$765$		0			0
$766$	7.00000	−	12.1244i	0.252920	−	0.438071i
$767$	2.50000	−	4.33013i	0.0902698	−	0.156352i
$768$		0			0
$769$	31.0000			1.11789			0.558944	−	0.829205i	$-0.311207\pi$
$769$	31.0000			1.11789			0.558944	+	0.829205i	$0.311207\pi$
$770$	2.00000	−	1.73205i	0.0720750	−	0.0624188i
$771$		0			0
$772$	−7.50000	−	12.9904i	−0.269931	−	0.467534i
$773$	−21.0000	+	36.3731i	−0.755318	+	1.30825i	0.189899	+	0.981804i	$0.439184\pi$
$773$	−21.0000	+	36.3731i	−0.755318	+	1.30825i	−0.945216	+	0.326445i	$0.894149\pi$
$774$		0			0
$775$	−22.0000	−	38.1051i	−0.790263	−	1.36878i
$776$	−13.0000			−0.466673
$777$		0			0
$778$	22.0000			0.788738
$779$	−24.0000	−	41.5692i	−0.859889	−	1.48937i
$780$		0			0
$781$	3.00000	−	5.19615i	0.107348	−	0.185933i
$782$	18.0000	+	31.1769i	0.643679	+	1.11488i
$783$		0			0
$784$	5.50000	+	4.33013i	0.196429	+	0.154647i
$785$	−18.0000			−0.642448
$786$		0			0
$787$	6.00000	−	10.3923i	0.213877	−	0.370446i	−0.739048	−	0.673653i	$-0.764724\pi$
$787$	6.00000	−	10.3923i	0.213877	−	0.370446i	0.952925	+	0.303207i	$0.0980575\pi$
$788$	−9.00000	+	15.5885i	−0.320612	+	0.555316i
$789$		0			0
$790$	−7.00000			−0.249049
$791$	−2.00000	−	10.3923i	−0.0711118	−	0.369508i
$792$		0			0
$793$	6.00000	+	10.3923i	0.213066	+	0.369042i
$794$	−9.00000	+	15.5885i	−0.319398	+	0.553214i
$795$		0			0
$796$	−4.00000	−	6.92820i	−0.141776	−	0.245564i
$797$	3.00000			0.106265			0.0531327	−	0.998587i	$-0.483079\pi$
$797$	3.00000			0.106265			0.0531327	+	0.998587i	$0.483079\pi$
$798$		0			0
$799$	48.0000			1.69812
$800$	−2.00000	−	3.46410i	−0.0707107	−	0.122474i
$801$		0			0
$802$	9.00000	−	15.5885i	0.317801	−	0.550448i
$803$	5.00000	+	8.66025i	0.176446	+	0.305614i
$804$		0			0
$805$	15.0000	+	5.19615i	0.528681	+	0.183140i
$806$	−11.0000			−0.387458
$807$		0			0
$808$	−5.00000	+	8.66025i	−0.175899	+	0.304667i
$809$	6.00000	−	10.3923i	0.210949	−	0.365374i	−0.741063	−	0.671436i	$-0.765678\pi$
$809$	6.00000	−	10.3923i	0.210949	−	0.365374i	0.952012	+	0.306062i	$0.0990113\pi$
$810$		0			0
$811$	−40.0000			−1.40459			−0.702295	−	0.711886i	$-0.747841\pi$
$811$	−40.0000			−1.40459			−0.702295	+	0.711886i	$0.747841\pi$
$812$	−7.50000	−	2.59808i	−0.263198	−	0.0911746i
$813$		0			0
$814$	2.00000	+	3.46410i	0.0701000	+	0.121417i
$815$	4.00000	−	6.92820i	0.140114	−	0.242684i
$816$		0			0
$817$	−16.0000	−	27.7128i	−0.559769	−	0.969549i
$818$	−25.0000			−0.874105
$819$		0			0
$820$	−12.0000			−0.419058
$821$	−5.50000	−	9.52628i	−0.191951	−	0.332469i	0.753946	−	0.656937i	$-0.228148\pi$
$821$	−5.50000	−	9.52628i	−0.191951	−	0.332469i	−0.945897	+	0.324468i	$0.894815\pi$
$822$		0			0
$823$	−22.0000	+	38.1051i	−0.766872	+	1.32826i	0.172379	+	0.985031i	$0.444854\pi$
$823$	−22.0000	+	38.1051i	−0.766872	+	1.32826i	−0.939251	+	0.343230i	$0.888479\pi$
$824$		0			0
$825$		0			0
$826$	2.50000	+	12.9904i	0.0869861	+	0.451993i
$827$	25.0000			0.869335			0.434668	−	0.900591i	$-0.356866\pi$
$827$	25.0000			0.869335			0.434668	+	0.900591i	$0.356866\pi$
$828$		0			0
$829$	1.00000	−	1.73205i	0.0347314	−	0.0601566i	−0.848137	−	0.529777i	$-0.822276\pi$
$829$	1.00000	−	1.73205i	0.0347314	−	0.0601566i	0.882869	+	0.469620i	$0.155609\pi$
$830$	8.50000	−	14.7224i	0.295039	−	0.511023i
$831$		0			0
$832$	−1.00000			−0.0346688
$833$	6.00000	−	41.5692i	0.207888	−	1.44029i
$834$		0			0
$835$	−12.0000	−	20.7846i	−0.415277	−	0.719281i
$836$	2.00000	−	3.46410i	0.0691714	−	0.119808i
$837$		0			0
$838$	−8.00000	−	13.8564i	−0.276355	−	0.478662i
$839$	16.0000			0.552381			0.276191	−	0.961103i	$-0.410928\pi$
$839$	16.0000			0.552381			0.276191	+	0.961103i	$0.410928\pi$
$840$		0			0
$841$	−20.0000			−0.689655
$842$	−18.0000	−	31.1769i	−0.620321	−	1.07443i
$843$		0			0
$844$	−6.00000	+	10.3923i	−0.206529	+	0.357718i
$845$	−0.500000	−	0.866025i	−0.0172005	−	0.0297922i
$846$		0			0
$847$	20.0000	−	17.3205i	0.687208	−	0.595140i
$848$	5.00000			0.171701
$849$		0			0
$850$	−12.0000	+	20.7846i	−0.411597	+	0.712906i
$851$	−12.0000	+	20.7846i	−0.411355	+	0.712487i
$852$		0			0
$853$	26.0000			0.890223			0.445112	−	0.895475i	$-0.353164\pi$
$853$	26.0000			0.890223			0.445112	+	0.895475i	$0.353164\pi$
$854$	−30.0000	−	10.3923i	−1.02658	−	0.355617i
$855$		0			0
$856$	−3.50000	−	6.06218i	−0.119628	−	0.207201i
$857$	27.0000	−	46.7654i	0.922302	−	1.59747i	0.126459	−	0.991972i	$-0.459639\pi$
$857$	27.0000	−	46.7654i	0.922302	−	1.59747i	0.795843	−	0.605503i	$-0.207028\pi$
$858$		0			0
$859$	4.00000	+	6.92820i	0.136478	+	0.236387i	0.926161	−	0.377128i	$-0.123088\pi$
$859$	4.00000	+	6.92820i	0.136478	+	0.236387i	−0.789683	+	0.613515i	$0.789755\pi$
$860$	−8.00000			−0.272798
$861$		0			0
$862$	−38.0000			−1.29429
$863$	−2.00000	−	3.46410i	−0.0680808	−	0.117919i	0.829976	−	0.557800i	$-0.188354\pi$
$863$	−2.00000	−	3.46410i	−0.0680808	−	0.117919i	−0.898056	+	0.439880i	$0.855021\pi$
$864$		0			0
$865$	3.00000	−	5.19615i	0.102003	−	0.176674i
$866$	−7.00000	−	12.1244i	−0.237870	−	0.412002i
$867$		0			0
$868$	22.0000	−	19.0526i	0.746729	−	0.646686i
$869$	7.00000			0.237459
$870$		0			0
$871$	8.00000	−	13.8564i	0.271070	−	0.469506i
$872$	6.00000	−	10.3923i	0.203186	−	0.351928i
$873$		0			0
$874$	24.0000			0.811812
$875$	4.50000	+	23.3827i	0.152128	+	0.790479i
$876$		0			0
$877$	−9.00000	−	15.5885i	−0.303908	−	0.526385i	0.673109	−	0.739543i	$-0.264958\pi$
$877$	−9.00000	−	15.5885i	−0.303908	−	0.526385i	−0.977018	+	0.213158i	$0.931625\pi$
$878$	−8.50000	+	14.7224i	−0.286861	+	0.496858i
$879$		0			0
$880$	−0.500000	−	0.866025i	−0.0168550	−	0.0291937i
$881$	−30.0000			−1.01073			−0.505363	−	0.862907i	$-0.668641\pi$
$881$	−30.0000			−1.01073			−0.505363	+	0.862907i	$0.668641\pi$
$882$		0			0
$883$	30.0000			1.00958			0.504790	−	0.863242i	$-0.331570\pi$
$883$	30.0000			1.00958			0.504790	+	0.863242i	$0.331570\pi$
$884$	3.00000	+	5.19615i	0.100901	+	0.174766i
$885$		0			0
$886$	19.5000	−	33.7750i	0.655115	−	1.13469i
$887$	18.0000	+	31.1769i	0.604381	+	1.04682i	0.992149	+	0.125061i	$0.0399128\pi$
$887$	18.0000	+	31.1769i	0.604381	+	1.04682i	−0.387768	+	0.921757i	$0.626754\pi$
$888$		0			0
$889$	3.50000	+	18.1865i	0.117386	+	0.609957i
$890$	−12.0000			−0.402241
$891$		0			0
$892$	−3.50000	+	6.06218i	−0.117189	+	0.202977i
$893$	16.0000	−	27.7128i	0.535420	−	0.927374i
$894$		0			0
$895$	−12.0000			−0.401116
$896$	2.00000	−	1.73205i	0.0668153	−	0.0578638i
$897$		0			0
$898$	−10.0000	−	17.3205i	−0.333704	−	0.577993i
$899$	−16.5000	+	28.5788i	−0.550306	+	0.953158i
$900$		0			0
$901$	−15.0000	−	25.9808i	−0.499722	−	0.865545i
$902$	12.0000			0.399556
$903$		0			0
$904$	−4.00000			−0.133038
$905$	8.00000	+	13.8564i	0.265929	+	0.460603i
$906$		0			0
$907$	18.0000	−	31.1769i	0.597680	−	1.03521i	−0.395482	−	0.918474i	$-0.629423\pi$
$907$	18.0000	−	31.1769i	0.597680	−	1.03521i	0.993163	−	0.116739i	$-0.0372441\pi$
$908$	−7.50000	−	12.9904i	−0.248896	−	0.431101i
$909$		0			0
$910$	2.50000	+	0.866025i	0.0828742	+	0.0287085i
$911$	10.0000			0.331315			0.165657	−	0.986183i	$-0.447025\pi$
$911$	10.0000			0.331315			0.165657	+	0.986183i	$0.447025\pi$
$912$		0			0
$913$	−8.50000	+	14.7224i	−0.281309	+	0.487241i
$914$	−5.50000	+	9.52628i	−0.181924	+	0.315101i
$915$		0			0
$916$	6.00000			0.198246
$917$	2.00000	−	1.73205i	0.0660458	−	0.0571974i
$918$		0			0
$919$	−16.0000	−	27.7128i	−0.527791	−	0.914161i	−0.999475	−	0.0323936i	$-0.989687\pi$
$919$	−16.0000	−	27.7128i	−0.527791	−	0.914161i	0.471684	−	0.881768i	$-0.343646\pi$
$920$	3.00000	−	5.19615i	0.0989071	−	0.171312i
$921$		0			0
$922$	−17.0000	−	29.4449i	−0.559865	−	0.969715i
$923$	6.00000			0.197492
$924$		0			0
$925$	−16.0000			−0.526077
$926$	−12.0000	−	20.7846i	−0.394344	−	0.683025i
$927$		0			0
$928$	−1.50000	+	2.59808i	−0.0492399	+	0.0852860i
$929$	−10.0000	−	17.3205i	−0.328089	−	0.568267i	0.654043	−	0.756457i	$-0.273071\pi$
$929$	−10.0000	−	17.3205i	−0.328089	−	0.568267i	−0.982133	+	0.188190i	$0.939738\pi$
$930$		0			0
$931$	−22.0000	−	17.3205i	−0.721021	−	0.567657i
$932$	−6.00000			−0.196537
$933$		0			0
$934$	−6.00000	+	10.3923i	−0.196326	+	0.340047i
$935$	−3.00000	+	5.19615i	−0.0981105	+	0.169932i
$936$		0			0
$937$	−13.0000			−0.424691			−0.212346	−	0.977195i	$-0.568110\pi$
$937$	−13.0000			−0.424691			−0.212346	+	0.977195i	$0.568110\pi$
$938$	8.00000	+	41.5692i	0.261209	+	1.35728i
$939$		0			0
$940$	−4.00000	−	6.92820i	−0.130466	−	0.225973i
$941$	7.50000	−	12.9904i	0.244493	−	0.423474i	−0.717496	−	0.696563i	$-0.754712\pi$
$941$	7.50000	−	12.9904i	0.244493	−	0.423474i	0.961989	+	0.273088i	$0.0880451\pi$
$942$		0			0
$943$	36.0000	+	62.3538i	1.17232	+	2.03052i
$944$	5.00000			0.162736
$945$		0			0
$946$	8.00000			0.260102
$947$	18.0000	+	31.1769i	0.584921	+	1.01311i	0.994885	+	0.101012i	$0.0322080\pi$
$947$	18.0000	+	31.1769i	0.584921	+	1.01311i	−0.409964	+	0.912102i	$0.634459\pi$
$948$		0			0
$949$	−5.00000	+	8.66025i	−0.162307	+	0.281124i
$950$	8.00000	+	13.8564i	0.259554	+	0.449561i
$951$		0			0
$952$	−15.0000	−	5.19615i	−0.486153	−	0.168408i
$953$	44.0000			1.42530			0.712650	−	0.701520i	$-0.247495\pi$
$953$	44.0000			1.42530			0.712650	+	0.701520i	$0.247495\pi$
$954$		0			0
$955$	−3.00000	+	5.19615i	−0.0970777	+	0.168144i
$956$	−3.00000	+	5.19615i	−0.0970269	+	0.168056i
$957$		0			0
$958$	14.0000			0.452319
$959$	20.0000	+	6.92820i	0.645834	+	0.223723i
$960$		0			0
$961$	−45.0000	−	77.9423i	−1.45161	−	2.51427i
$962$	−2.00000	+	3.46410i	−0.0644826	+	0.111687i
$963$		0			0
$964$	7.50000	+	12.9904i	0.241559	+	0.418392i
$965$	15.0000			0.482867
$966$		0			0
$967$	−11.0000			−0.353736			−0.176868	−	0.984235i	$-0.556597\pi$
$967$	−11.0000			−0.353736			−0.176868	+	0.984235i	$0.556597\pi$
$968$	−5.00000	−	8.66025i	−0.160706	−	0.278351i
$969$		0			0
$970$	6.50000	−	11.2583i	0.208702	−	0.361483i
$971$	−14.5000	−	25.1147i	−0.465327	−	0.805970i	0.533889	−	0.845555i	$-0.320730\pi$
$971$	−14.5000	−	25.1147i	−0.465327	−	0.805970i	−0.999216	+	0.0395843i	$0.987397\pi$
$972$		0			0
$973$		0			0
$974$	−23.0000			−0.736968
$975$		0			0
$976$	−6.00000	+	10.3923i	−0.192055	+	0.332650i
$977$	21.0000	−	36.3731i	0.671850	−	1.16368i	−0.305530	−	0.952183i	$-0.598833\pi$
$977$	21.0000	−	36.3731i	0.671850	−	1.16368i	0.977379	−	0.211495i	$-0.0678332\pi$
$978$		0			0
$979$	12.0000			0.383522
$980$	−6.50000	+	2.59808i	−0.207635	+	0.0829925i
$981$		0			0
$982$	17.5000	+	30.3109i	0.558447	+	0.967259i
$983$	−13.0000	+	22.5167i	−0.414636	+	0.718170i	−0.995390	−	0.0959088i	$-0.969424\pi$
$983$	−13.0000	+	22.5167i	−0.414636	+	0.718170i	0.580755	+	0.814079i	$0.302758\pi$
$984$		0			0
$985$	−9.00000	−	15.5885i	−0.286764	−	0.496690i
$986$	18.0000			0.573237
$987$		0			0
$988$	4.00000			0.127257
$989$	24.0000	+	41.5692i	0.763156	+	1.32182i
$990$		0			0
$991$	2.50000	−	4.33013i	0.0794151	−	0.137551i	−0.823583	−	0.567196i	$-0.808028\pi$
$991$	2.50000	−	4.33013i	0.0794151	−	0.137551i	0.902998	+	0.429645i	$0.141361\pi$
$992$	−5.50000	−	9.52628i	−0.174625	−	0.302460i
$993$		0			0
$994$	−12.0000	+	10.3923i	−0.380617	+	0.329624i
$995$	8.00000			0.253617
$996$		0			0
$997$	14.0000	−	24.2487i	0.443384	−	0.767964i	−0.554554	−	0.832148i	$-0.687111\pi$
$997$	14.0000	−	24.2487i	0.443384	−	0.767964i	0.997938	+	0.0641836i	$0.0204443\pi$
$998$	−14.0000	+	24.2487i	−0.443162	+	0.767580i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.j.h.235.1		2
3.2	odd	2		546.2.i.b.235.1	yes	2
7.2	even	3	inner	1638.2.j.h.1171.1		2
21.2	odd	6		546.2.i.b.79.1	✓	2
21.11	odd	6		3822.2.a.be.1.1		1
21.17	even	6		3822.2.a.v.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.i.b.79.1	✓	2	21.2	odd	6
546.2.i.b.235.1	yes	2	3.2	odd	2
1638.2.j.h.235.1		2	1.1	even	1	trivial
1638.2.j.h.1171.1		2	7.2	even	3	inner
3822.2.a.v.1.1		1	21.17	even	6
3822.2.a.be.1.1		1	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 - 2.59808i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 - 2.59808i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{10} +(-0.500000 + 0.866025i) q^{11} -1.00000 q^{13} +(2.00000 - 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.00000 + 5.19615i) q^{17} +(2.00000 + 3.46410i) q^{19} +1.00000 q^{20} -1.00000 q^{22} +(-3.00000 - 5.19615i) q^{23} +(2.00000 - 3.46410i) q^{25} +(-0.500000 - 0.866025i) q^{26} +(2.50000 + 0.866025i) q^{28} -3.00000 q^{29} +(5.50000 - 9.52628i) q^{31} +(0.500000 - 0.866025i) q^{32} -6.00000 q^{34} +(-2.00000 + 1.73205i) q^{35} +(-2.00000 - 3.46410i) q^{37} +(-2.00000 + 3.46410i) q^{38} +(0.500000 + 0.866025i) q^{40} -12.0000 q^{41} -8.00000 q^{43} +(-0.500000 - 0.866025i) q^{44} +(3.00000 - 5.19615i) q^{46} +(-4.00000 - 6.92820i) q^{47} +(-6.50000 + 2.59808i) q^{49} +4.00000 q^{50} +(0.500000 - 0.866025i) q^{52} +(-2.50000 + 4.33013i) q^{53} +1.00000 q^{55} +(0.500000 + 2.59808i) q^{56} +(-1.50000 - 2.59808i) q^{58} +(-2.50000 + 4.33013i) q^{59} +(-6.00000 - 10.3923i) q^{61} +11.0000 q^{62} +1.00000 q^{64} +(0.500000 + 0.866025i) q^{65} +(-8.00000 + 13.8564i) q^{67} +(-3.00000 - 5.19615i) q^{68} +(-2.50000 - 0.866025i) q^{70} -6.00000 q^{71} +(5.00000 - 8.66025i) q^{73} +(2.00000 - 3.46410i) q^{74} -4.00000 q^{76} +(2.50000 + 0.866025i) q^{77} +(-3.50000 - 6.06218i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-6.00000 - 10.3923i) q^{82} +17.0000 q^{83} +6.00000 q^{85} +(-4.00000 - 6.92820i) q^{86} +(0.500000 - 0.866025i) q^{88} +(-6.00000 - 10.3923i) q^{89} +(0.500000 + 2.59808i) q^{91} +6.00000 q^{92} +(4.00000 - 6.92820i) q^{94} +(2.00000 - 3.46410i) q^{95} +13.0000 q^{97} +(-5.50000 - 4.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} - q^{5} - q^{7} - 2 q^{8}+O(q^{10}) \) 2 * q + q^2 - q^4 - q^5 - q^7 - 2 * q^8	\( 2 q + q^{2} - q^{4} - q^{5} - q^{7} - 2 q^{8} + q^{10} - q^{11} - 2 q^{13} + 4 q^{14} - q^{16} - 6 q^{17} + 4 q^{19} + 2 q^{20} - 2 q^{22} - 6 q^{23} + 4 q^{25} - q^{26} + 5 q^{28} - 6 q^{29} + 11 q^{31} + q^{32} - 12 q^{34} - 4 q^{35} - 4 q^{37} - 4 q^{38} + q^{40} - 24 q^{41} - 16 q^{43} - q^{44} + 6 q^{46} - 8 q^{47} - 13 q^{49} + 8 q^{50} + q^{52} - 5 q^{53} + 2 q^{55} + q^{56} - 3 q^{58} - 5 q^{59} - 12 q^{61} + 22 q^{62} + 2 q^{64} + q^{65} - 16 q^{67} - 6 q^{68} - 5 q^{70} - 12 q^{71} + 10 q^{73} + 4 q^{74} - 8 q^{76} + 5 q^{77} - 7 q^{79} - q^{80} - 12 q^{82} + 34 q^{83} + 12 q^{85} - 8 q^{86} + q^{88} - 12 q^{89} + q^{91} + 12 q^{92} + 8 q^{94} + 4 q^{95} + 26 q^{97} - 11 q^{98}+O(q^{100}) \) 2 * q + q^2 - q^4 - q^5 - q^7 - 2 * q^8 + q^10 - q^11 - 2 * q^13 + 4 * q^14 - q^16 - 6 * q^17 + 4 * q^19 + 2 * q^20 - 2 * q^22 - 6 * q^23 + 4 * q^25 - q^26 + 5 * q^28 - 6 * q^29 + 11 * q^31 + q^32 - 12 * q^34 - 4 * q^35 - 4 * q^37 - 4 * q^38 + q^40 - 24 * q^41 - 16 * q^43 - q^44 + 6 * q^46 - 8 * q^47 - 13 * q^49 + 8 * q^50 + q^52 - 5 * q^53 + 2 * q^55 + q^56 - 3 * q^58 - 5 * q^59 - 12 * q^61 + 22 * q^62 + 2 * q^64 + q^65 - 16 * q^67 - 6 * q^68 - 5 * q^70 - 12 * q^71 + 10 * q^73 + 4 * q^74 - 8 * q^76 + 5 * q^77 - 7 * q^79 - q^80 - 12 * q^82 + 34 * q^83 + 12 * q^85 - 8 * q^86 + q^88 - 12 * q^89 + q^91 + 12 * q^92 + 8 * q^94 + 4 * q^95 + 26 * q^97 - 11 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more