LMFDB - Embedded newform 1274.2.f.f.1145.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1274,2,Mod(79,1274)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1274, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("1274.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1274 = 2 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1274.f (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.1729412175$
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 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1145.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1274.1145
Dual form			1274.2.f.f.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{5} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{5} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-1.00000 + 1.73205i) q^{10} +(-2.00000 + 3.46410i) q^{11} -1.00000 q^{13} +(-0.500000 - 0.866025i) q^{16} +(3.00000 - 5.19615i) q^{17} +(1.50000 - 2.59808i) q^{18} +2.00000 q^{20} +4.00000 q^{22} +(-4.00000 - 6.92820i) q^{23} +(0.500000 - 0.866025i) q^{25} +(0.500000 + 0.866025i) q^{26} -10.0000 q^{29} +(4.00000 - 6.92820i) q^{31} +(-0.500000 + 0.866025i) q^{32} -6.00000 q^{34} -3.00000 q^{36} +(-3.00000 - 5.19615i) q^{37} +(-1.00000 - 1.73205i) q^{40} -6.00000 q^{41} +4.00000 q^{43} +(-2.00000 - 3.46410i) q^{44} +(3.00000 - 5.19615i) q^{45} +(-4.00000 + 6.92820i) q^{46} +(4.00000 + 6.92820i) q^{47} -1.00000 q^{50} +(0.500000 - 0.866025i) q^{52} +(-3.00000 + 5.19615i) q^{53} +8.00000 q^{55} +(5.00000 + 8.66025i) q^{58} +(-4.00000 + 6.92820i) q^{59} +(-5.00000 - 8.66025i) q^{61} -8.00000 q^{62} +1.00000 q^{64} +(1.00000 + 1.73205i) q^{65} +(-2.00000 + 3.46410i) q^{67} +(3.00000 + 5.19615i) q^{68} -8.00000 q^{71} +(1.50000 + 2.59808i) q^{72} +(-1.00000 + 1.73205i) q^{73} +(-3.00000 + 5.19615i) q^{74} +(-4.00000 - 6.92820i) q^{79} +(-1.00000 + 1.73205i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(3.00000 + 5.19615i) q^{82} -12.0000 q^{85} +(-2.00000 - 3.46410i) q^{86} +(-2.00000 + 3.46410i) q^{88} +(-9.00000 - 15.5885i) q^{89} -6.00000 q^{90} +8.00000 q^{92} +(4.00000 - 6.92820i) q^{94} +2.00000 q^{97} -12.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} - 2 q^{5} + 2 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q - q^2 - q^4 - 2 * q^5 + 2 * q^8 + 3 * q^9	$ 2 q - q^{2} - q^{4} - 2 q^{5} + 2 q^{8} + 3 q^{9} - 2 q^{10} - 4 q^{11} - 2 q^{13} - q^{16} + 6 q^{17} + 3 q^{18} + 4 q^{20} + 8 q^{22} - 8 q^{23} + q^{25} + q^{26} - 20 q^{29} + 8 q^{31} - q^{32} - 12 q^{34} - 6 q^{36} - 6 q^{37} - 2 q^{40} - 12 q^{41} + 8 q^{43} - 4 q^{44} + 6 q^{45} - 8 q^{46} + 8 q^{47} - 2 q^{50} + q^{52} - 6 q^{53} + 16 q^{55} + 10 q^{58} - 8 q^{59} - 10 q^{61} - 16 q^{62} + 2 q^{64} + 2 q^{65} - 4 q^{67} + 6 q^{68} - 16 q^{71} + 3 q^{72} - 2 q^{73} - 6 q^{74} - 8 q^{79} - 2 q^{80} - 9 q^{81} + 6 q^{82} - 24 q^{85} - 4 q^{86} - 4 q^{88} - 18 q^{89} - 12 q^{90} + 16 q^{92} + 8 q^{94} + 4 q^{97} - 24 q^{99}+O(q^{100}) $ 2 * q - q^2 - q^4 - 2 * q^5 + 2 * q^8 + 3 * q^9 - 2 * q^10 - 4 * q^11 - 2 * q^13 - q^16 + 6 * q^17 + 3 * q^18 + 4 * q^20 + 8 * q^22 - 8 * q^23 + q^25 + q^26 - 20 * q^29 + 8 * q^31 - q^32 - 12 * q^34 - 6 * q^36 - 6 * q^37 - 2 * q^40 - 12 * q^41 + 8 * q^43 - 4 * q^44 + 6 * q^45 - 8 * q^46 + 8 * q^47 - 2 * q^50 + q^52 - 6 * q^53 + 16 * q^55 + 10 * q^58 - 8 * q^59 - 10 * q^61 - 16 * q^62 + 2 * q^64 + 2 * q^65 - 4 * q^67 + 6 * q^68 - 16 * q^71 + 3 * q^72 - 2 * q^73 - 6 * q^74 - 8 * q^79 - 2 * q^80 - 9 * q^81 + 6 * q^82 - 24 * q^85 - 4 * q^86 - 4 * q^88 - 18 * q^89 - 12 * q^90 + 16 * q^92 + 8 * q^94 + 4 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times$.

$n$	$197$	$885$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$3$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.00000	−	1.73205i	−0.447214	−	0.774597i	0.550990	−	0.834512i	$-0.314250\pi$
$5$	−1.00000	−	1.73205i	−0.447214	−	0.774597i	−0.998203	+	0.0599153i	$0.980917\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	−1.00000	+	1.73205i	−0.316228	+	0.547723i
$11$	−2.00000	+	3.46410i	−0.603023	+	1.04447i	0.389338	+	0.921095i	$0.372704\pi$
$11$	−2.00000	+	3.46410i	−0.603023	+	1.04447i	−0.992361	+	0.123371i	$0.960630\pi$
$12$		0			0
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$		0			0
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	−0.230285	−	0.973123i	$-0.573966\pi$
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	0.957892	−	0.287129i	$-0.0927008\pi$
$18$	1.50000	−	2.59808i	0.353553	−	0.612372i
$19$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$19$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$20$	2.00000			0.447214
$21$		0			0
$22$	4.00000			0.852803
$23$	−4.00000	−	6.92820i	−0.834058	−	1.44463i	−0.894795	−	0.446476i	$-0.852679\pi$
$23$	−4.00000	−	6.92820i	−0.834058	−	1.44463i	0.0607377	−	0.998154i	$-0.480655\pi$
$24$		0			0
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	0.500000	+	0.866025i	0.0980581	+	0.169842i
$27$		0			0
$28$		0			0
$29$	−10.0000			−1.85695			−0.928477	−	0.371391i	$-0.878881\pi$
$29$	−10.0000			−1.85695			−0.928477	+	0.371391i	$0.878881\pi$
$30$		0			0
$31$	4.00000	−	6.92820i	0.718421	−	1.24434i	−0.243204	−	0.969975i	$-0.578198\pi$
$31$	4.00000	−	6.92820i	0.718421	−	1.24434i	0.961625	−	0.274367i	$-0.0884683\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−6.00000			−1.02899
$35$		0			0
$36$	−3.00000			−0.500000
$37$	−3.00000	−	5.19615i	−0.493197	−	0.854242i	0.506772	−	0.862080i	$-0.330838\pi$
$37$	−3.00000	−	5.19615i	−0.493197	−	0.854242i	−0.999969	+	0.00783774i	$0.997505\pi$
$38$		0			0
$39$		0			0
$40$	−1.00000	−	1.73205i	−0.158114	−	0.273861i
$41$	−6.00000			−0.937043			−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000			−0.937043			−0.468521	+	0.883452i	$0.655213\pi$
$42$		0			0
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$	−2.00000	−	3.46410i	−0.301511	−	0.522233i
$45$	3.00000	−	5.19615i	0.447214	−	0.774597i
$46$	−4.00000	+	6.92820i	−0.589768	+	1.02151i
$47$	4.00000	+	6.92820i	0.583460	+	1.01058i	0.995066	+	0.0992202i	$0.0316348\pi$
$47$	4.00000	+	6.92820i	0.583460	+	1.01058i	−0.411606	+	0.911362i	$0.635032\pi$
$48$		0			0
$49$		0			0
$50$	−1.00000			−0.141421
$51$		0			0
$52$	0.500000	−	0.866025i	0.0693375	−	0.120096i
$53$	−3.00000	+	5.19615i	−0.412082	+	0.713746i	−0.995117	−	0.0987002i	$-0.968532\pi$
$53$	−3.00000	+	5.19615i	−0.412082	+	0.713746i	0.583036	+	0.812447i	$0.301865\pi$
$54$		0			0
$55$	8.00000			1.07872
$56$		0			0
$57$		0			0
$58$	5.00000	+	8.66025i	0.656532	+	1.13715i
$59$	−4.00000	+	6.92820i	−0.520756	+	0.901975i	0.478953	+	0.877841i	$0.341016\pi$
$59$	−4.00000	+	6.92820i	−0.520756	+	0.901975i	−0.999709	+	0.0241347i	$0.992317\pi$
$60$		0			0
$61$	−5.00000	−	8.66025i	−0.640184	−	1.10883i	−0.985391	−	0.170305i	$-0.945525\pi$
$61$	−5.00000	−	8.66025i	−0.640184	−	1.10883i	0.345207	−	0.938527i	$-0.387809\pi$
$62$	−8.00000			−1.01600
$63$		0			0
$64$	1.00000			0.125000
$65$	1.00000	+	1.73205i	0.124035	+	0.214834i
$66$		0			0
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	−0.961946	−	0.273241i	$-0.911904\pi$
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	0.717607	+	0.696449i	$0.245238\pi$
$68$	3.00000	+	5.19615i	0.363803	+	0.630126i
$69$		0			0
$70$		0			0
$71$	−8.00000			−0.949425			−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000			−0.949425			−0.474713	+	0.880141i	$0.657448\pi$
$72$	1.50000	+	2.59808i	0.176777	+	0.306186i
$73$	−1.00000	+	1.73205i	−0.117041	+	0.202721i	−0.918594	−	0.395203i	$-0.870674\pi$
$73$	−1.00000	+	1.73205i	−0.117041	+	0.202721i	0.801553	+	0.597924i	$0.204008\pi$
$74$	−3.00000	+	5.19615i	−0.348743	+	0.604040i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	0.548352	−	0.836247i	$-0.315255\pi$
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	−0.998388	+	0.0567635i	$0.981922\pi$
$80$	−1.00000	+	1.73205i	−0.111803	+	0.193649i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	3.00000	+	5.19615i	0.331295	+	0.573819i
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$		0			0
$85$	−12.0000			−1.30158
$86$	−2.00000	−	3.46410i	−0.215666	−	0.373544i
$87$		0			0
$88$	−2.00000	+	3.46410i	−0.213201	+	0.369274i
$89$	−9.00000	−	15.5885i	−0.953998	−	1.65237i	−0.736644	−	0.676280i	$-0.763591\pi$
$89$	−9.00000	−	15.5885i	−0.953998	−	1.65237i	−0.217354	−	0.976093i	$-0.569742\pi$
$90$	−6.00000			−0.632456
$91$		0			0
$92$	8.00000			0.834058
$93$		0			0
$94$	4.00000	−	6.92820i	0.412568	−	0.714590i
$95$		0			0
$96$		0			0
$97$	2.00000			0.203069			0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000			0.203069			0.101535	+	0.994832i	$0.467625\pi$
$98$		0			0
$99$	−12.0000			−1.20605
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	7.00000	−	12.1244i	0.696526	−	1.20642i	−0.273138	−	0.961975i	$-0.588061\pi$
$101$	7.00000	−	12.1244i	0.696526	−	1.20642i	0.969664	−	0.244443i	$-0.0786053\pi$
$102$		0			0
$103$	−8.00000	−	13.8564i	−0.788263	−	1.36531i	−0.927030	−	0.374987i	$-0.877647\pi$
$103$	−8.00000	−	13.8564i	−0.788263	−	1.36531i	0.138767	−	0.990325i	$-0.455686\pi$
$104$	−1.00000			−0.0980581
$105$		0			0
$106$	6.00000			0.582772
$107$	2.00000	+	3.46410i	0.193347	+	0.334887i	0.946357	−	0.323122i	$-0.104732\pi$
$107$	2.00000	+	3.46410i	0.193347	+	0.334887i	−0.753010	+	0.658009i	$0.771399\pi$
$108$		0			0
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	−0.814152	−	0.580651i	$-0.802798\pi$
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	0.909935	+	0.414751i	$0.136131\pi$
$110$	−4.00000	−	6.92820i	−0.381385	−	0.660578i
$111$		0			0
$112$		0			0
$113$	2.00000			0.188144			0.0940721	−	0.995565i	$-0.470012\pi$
$113$	2.00000			0.188144			0.0940721	+	0.995565i	$0.470012\pi$
$114$		0			0
$115$	−8.00000	+	13.8564i	−0.746004	+	1.29212i
$116$	5.00000	−	8.66025i	0.464238	−	0.804084i
$117$	−1.50000	−	2.59808i	−0.138675	−	0.240192i
$118$	8.00000			0.736460
$119$		0			0
$120$		0			0
$121$	−2.50000	−	4.33013i	−0.227273	−	0.393648i
$122$	−5.00000	+	8.66025i	−0.452679	+	0.784063i
$123$		0			0
$124$	4.00000	+	6.92820i	0.359211	+	0.622171i
$125$	−12.0000			−1.07331
$126$		0			0
$127$	16.0000			1.41977			0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000			1.41977			0.709885	+	0.704317i	$0.248747\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	1.00000	−	1.73205i	0.0877058	−	0.151911i
$131$	−4.00000	−	6.92820i	−0.349482	−	0.605320i	0.636676	−	0.771132i	$-0.280309\pi$
$131$	−4.00000	−	6.92820i	−0.349482	−	0.605320i	−0.986157	+	0.165812i	$0.946976\pi$
$132$		0			0
$133$		0			0
$134$	4.00000			0.345547
$135$		0			0
$136$	3.00000	−	5.19615i	0.257248	−	0.445566i
$137$	3.00000	−	5.19615i	0.256307	−	0.443937i	−0.708942	−	0.705266i	$-0.750827\pi$
$137$	3.00000	−	5.19615i	0.256307	−	0.443937i	0.965250	+	0.261329i	$0.0841608\pi$
$138$		0			0
$139$	−8.00000			−0.678551			−0.339276	−	0.940687i	$-0.610182\pi$
$139$	−8.00000			−0.678551			−0.339276	+	0.940687i	$0.610182\pi$
$140$		0			0
$141$		0			0
$142$	4.00000	+	6.92820i	0.335673	+	0.581402i
$143$	2.00000	−	3.46410i	0.167248	−	0.289683i
$144$	1.50000	−	2.59808i	0.125000	−	0.216506i
$145$	10.0000	+	17.3205i	0.830455	+	1.43839i
$146$	2.00000			0.165521
$147$		0			0
$148$	6.00000			0.493197
$149$	9.00000	+	15.5885i	0.737309	+	1.27706i	0.953703	+	0.300750i	$0.0972370\pi$
$149$	9.00000	+	15.5885i	0.737309	+	1.27706i	−0.216394	+	0.976306i	$0.569430\pi$
$150$		0			0
$151$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$151$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$152$		0			0
$153$	18.0000			1.45521
$154$		0			0
$155$	−16.0000			−1.28515
$156$		0			0
$157$	−1.00000	+	1.73205i	−0.0798087	+	0.138233i	−0.903167	−	0.429289i	$-0.858764\pi$
$157$	−1.00000	+	1.73205i	−0.0798087	+	0.138233i	0.823359	+	0.567521i	$0.192098\pi$
$158$	−4.00000	+	6.92820i	−0.318223	+	0.551178i
$159$		0			0
$160$	2.00000			0.158114
$161$		0			0
$162$	9.00000			0.707107
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	0.933659	−	0.358162i	$-0.116597\pi$
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	−0.777007	+	0.629492i	$0.783263\pi$
$164$	3.00000	−	5.19615i	0.234261	−	0.405751i
$165$		0			0
$166$		0			0
$167$		0			0			−	1.00000i	$-0.5\pi$
$167$		0			0				1.00000i	$0.5\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	6.00000	+	10.3923i	0.460179	+	0.797053i
$171$		0			0
$172$	−2.00000	+	3.46410i	−0.152499	+	0.264135i
$173$	−1.00000	−	1.73205i	−0.0760286	−	0.131685i	0.825505	−	0.564396i	$-0.190891\pi$
$173$	−1.00000	−	1.73205i	−0.0760286	−	0.131685i	−0.901533	+	0.432710i	$0.857557\pi$
$174$		0			0
$175$		0			0
$176$	4.00000			0.301511
$177$		0			0
$178$	−9.00000	+	15.5885i	−0.674579	+	1.16840i
$179$	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	$0.0186389\pi$
$180$	3.00000	+	5.19615i	0.223607	+	0.387298i
$181$	−6.00000			−0.445976			−0.222988	−	0.974821i	$-0.571581\pi$
$181$	−6.00000			−0.445976			−0.222988	+	0.974821i	$0.571581\pi$
$182$		0			0
$183$		0			0
$184$	−4.00000	−	6.92820i	−0.294884	−	0.510754i
$185$	−6.00000	+	10.3923i	−0.441129	+	0.764057i
$186$		0			0
$187$	12.0000	+	20.7846i	0.877527	+	1.51992i
$188$	−8.00000			−0.583460
$189$		0			0
$190$		0			0
$191$	4.00000	+	6.92820i	0.289430	+	0.501307i	0.973674	−	0.227946i	$-0.0732010\pi$
$191$	4.00000	+	6.92820i	0.289430	+	0.501307i	−0.684244	+	0.729253i	$0.739868\pi$
$192$		0			0
$193$	−1.00000	+	1.73205i	−0.0719816	+	0.124676i	−0.899770	−	0.436365i	$-0.856266\pi$
$193$	−1.00000	+	1.73205i	−0.0719816	+	0.124676i	0.827788	+	0.561041i	$0.189599\pi$
$194$	−1.00000	−	1.73205i	−0.0717958	−	0.124354i
$195$		0			0
$196$		0			0
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$	6.00000	+	10.3923i	0.426401	+	0.738549i
$199$	8.00000	−	13.8564i	0.567105	−	0.982255i	−0.429745	−	0.902950i	$-0.641397\pi$
$199$	8.00000	−	13.8564i	0.567105	−	0.982255i	0.996850	−	0.0793045i	$-0.0252700\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$		0			0
$202$	−14.0000			−0.985037
$203$		0			0
$204$		0			0
$205$	6.00000	+	10.3923i	0.419058	+	0.725830i
$206$	−8.00000	+	13.8564i	−0.557386	+	0.965422i
$207$	12.0000	−	20.7846i	0.834058	−	1.44463i
$208$	0.500000	+	0.866025i	0.0346688	+	0.0600481i
$209$		0			0
$210$		0			0
$211$	20.0000			1.37686			0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000			1.37686			0.688428	+	0.725304i	$0.258301\pi$
$212$	−3.00000	−	5.19615i	−0.206041	−	0.356873i
$213$		0			0
$214$	2.00000	−	3.46410i	0.136717	−	0.236801i
$215$	−4.00000	−	6.92820i	−0.272798	−	0.472500i
$216$		0			0
$217$		0			0
$218$	−2.00000			−0.135457
$219$		0			0
$220$	−4.00000	+	6.92820i	−0.269680	+	0.467099i
$221$	−3.00000	+	5.19615i	−0.201802	+	0.349531i
$222$		0			0
$223$		0			0			−	1.00000i	$-0.5\pi$
$223$		0			0				1.00000i	$0.5\pi$
$224$		0			0
$225$	3.00000			0.200000
$226$	−1.00000	−	1.73205i	−0.0665190	−	0.115214i
$227$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$227$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$228$		0			0
$229$	3.00000	+	5.19615i	0.198246	+	0.343371i	0.947960	−	0.318390i	$-0.103142\pi$
$229$	3.00000	+	5.19615i	0.198246	+	0.343371i	−0.749714	+	0.661762i	$0.769809\pi$
$230$	16.0000			1.05501
$231$		0			0
$232$	−10.0000			−0.656532
$233$	−5.00000	−	8.66025i	−0.327561	−	0.567352i	0.654466	−	0.756091i	$-0.272893\pi$
$233$	−5.00000	−	8.66025i	−0.327561	−	0.567352i	−0.982027	+	0.188739i	$0.939560\pi$
$234$	−1.50000	+	2.59808i	−0.0980581	+	0.169842i
$235$	8.00000	−	13.8564i	0.521862	−	0.903892i
$236$	−4.00000	−	6.92820i	−0.260378	−	0.450988i
$237$		0			0
$238$		0			0
$239$	−24.0000			−1.55243			−0.776215	−	0.630468i	$-0.782863\pi$
$239$	−24.0000			−1.55243			−0.776215	+	0.630468i	$0.782863\pi$
$240$		0			0
$241$	−9.00000	+	15.5885i	−0.579741	+	1.00414i	0.415768	+	0.909471i	$0.363513\pi$
$241$	−9.00000	+	15.5885i	−0.579741	+	1.00414i	−0.995509	+	0.0946700i	$0.969820\pi$
$242$	−2.50000	+	4.33013i	−0.160706	+	0.278351i
$243$		0			0
$244$	10.0000			0.640184
$245$		0			0
$246$		0			0
$247$		0			0
$248$	4.00000	−	6.92820i	0.254000	−	0.439941i
$249$		0			0
$250$	6.00000	+	10.3923i	0.379473	+	0.657267i
$251$	24.0000			1.51487			0.757433	−	0.652913i	$-0.226453\pi$
$251$	24.0000			1.51487			0.757433	+	0.652913i	$0.226453\pi$
$252$		0			0
$253$	32.0000			2.01182
$254$	−8.00000	−	13.8564i	−0.501965	−	0.869428i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−9.00000	−	15.5885i	−0.561405	−	0.972381i	−0.997374	−	0.0724199i	$-0.976928\pi$
$257$	−9.00000	−	15.5885i	−0.561405	−	0.972381i	0.435970	−	0.899961i	$-0.356405\pi$
$258$		0			0
$259$		0			0
$260$	−2.00000			−0.124035
$261$	−15.0000	−	25.9808i	−0.928477	−	1.60817i
$262$	−4.00000	+	6.92820i	−0.247121	+	0.428026i
$263$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$263$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$264$		0			0
$265$	12.0000			0.737154
$266$		0			0
$267$		0			0
$268$	−2.00000	−	3.46410i	−0.122169	−	0.211604i
$269$	15.0000	−	25.9808i	0.914566	−	1.58408i	0.107031	−	0.994256i	$-0.465866\pi$
$269$	15.0000	−	25.9808i	0.914566	−	1.58408i	0.807535	−	0.589819i	$-0.200801\pi$
$270$		0			0
$271$	16.0000	+	27.7128i	0.971931	+	1.68343i	0.689713	+	0.724083i	$0.257737\pi$
$271$	16.0000	+	27.7128i	0.971931	+	1.68343i	0.282218	+	0.959350i	$0.408930\pi$
$272$	−6.00000			−0.363803
$273$		0			0
$274$	−6.00000			−0.362473
$275$	2.00000	+	3.46410i	0.120605	+	0.208893i
$276$		0			0
$277$	−3.00000	+	5.19615i	−0.180253	+	0.312207i	−0.941966	−	0.335707i	$-0.891025\pi$
$277$	−3.00000	+	5.19615i	−0.180253	+	0.312207i	0.761714	+	0.647913i	$0.224358\pi$
$278$	4.00000	+	6.92820i	0.239904	+	0.415526i
$279$	24.0000			1.43684
$280$		0			0
$281$	10.0000			0.596550			0.298275	−	0.954480i	$-0.403589\pi$
$281$	10.0000			0.596550			0.298275	+	0.954480i	$0.403589\pi$
$282$		0			0
$283$	−8.00000	+	13.8564i	−0.475551	+	0.823678i	−0.999608	−	0.0280052i	$-0.991084\pi$
$283$	−8.00000	+	13.8564i	−0.475551	+	0.823678i	0.524057	+	0.851683i	$0.324418\pi$
$284$	4.00000	−	6.92820i	0.237356	−	0.411113i
$285$		0			0
$286$	−4.00000			−0.236525
$287$		0			0
$288$	−3.00000			−0.176777
$289$	−9.50000	−	16.4545i	−0.558824	−	0.967911i
$290$	10.0000	−	17.3205i	0.587220	−	1.01710i
$291$		0			0
$292$	−1.00000	−	1.73205i	−0.0585206	−	0.101361i
$293$	−14.0000			−0.817889			−0.408944	−	0.912559i	$-0.634103\pi$
$293$	−14.0000			−0.817889			−0.408944	+	0.912559i	$0.634103\pi$
$294$		0			0
$295$	16.0000			0.931556
$296$	−3.00000	−	5.19615i	−0.174371	−	0.302020i
$297$		0			0
$298$	9.00000	−	15.5885i	0.521356	−	0.903015i
$299$	4.00000	+	6.92820i	0.231326	+	0.400668i
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−10.0000	+	17.3205i	−0.572598	+	0.991769i
$306$	−9.00000	−	15.5885i	−0.514496	−	0.891133i
$307$	32.0000			1.82634			0.913168	−	0.407583i	$-0.133628\pi$
$307$	32.0000			1.82634			0.913168	+	0.407583i	$0.133628\pi$
$308$		0			0
$309$		0			0
$310$	8.00000	+	13.8564i	0.454369	+	0.786991i
$311$	−12.0000	+	20.7846i	−0.680458	+	1.17859i	0.294384	+	0.955687i	$0.404886\pi$
$311$	−12.0000	+	20.7846i	−0.680458	+	1.17859i	−0.974841	+	0.222900i	$0.928448\pi$
$312$		0			0
$313$	−1.00000	−	1.73205i	−0.0565233	−	0.0979013i	0.836379	−	0.548151i	$-0.184668\pi$
$313$	−1.00000	−	1.73205i	−0.0565233	−	0.0979013i	−0.892903	+	0.450250i	$0.851335\pi$
$314$	2.00000			0.112867
$315$		0			0
$316$	8.00000			0.450035
$317$	−3.00000	−	5.19615i	−0.168497	−	0.291845i	0.769395	−	0.638774i	$-0.220558\pi$
$317$	−3.00000	−	5.19615i	−0.168497	−	0.291845i	−0.937892	+	0.346929i	$0.887225\pi$
$318$		0			0
$319$	20.0000	−	34.6410i	1.11979	−	1.93952i
$320$	−1.00000	−	1.73205i	−0.0559017	−	0.0968246i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−4.50000	−	7.79423i	−0.250000	−	0.433013i
$325$	−0.500000	+	0.866025i	−0.0277350	+	0.0480384i
$326$	2.00000	−	3.46410i	0.110770	−	0.191859i
$327$		0			0
$328$	−6.00000			−0.331295
$329$		0			0
$330$		0			0
$331$	14.0000	+	24.2487i	0.769510	+	1.33283i	0.937829	+	0.347097i	$0.112833\pi$
$331$	14.0000	+	24.2487i	0.769510	+	1.33283i	−0.168320	+	0.985732i	$0.553834\pi$
$332$		0			0
$333$	9.00000	−	15.5885i	0.493197	−	0.854242i
$334$		0			0
$335$	8.00000			0.437087
$336$		0			0
$337$	2.00000			0.108947			0.0544735	−	0.998515i	$-0.482652\pi$
$337$	2.00000			0.108947			0.0544735	+	0.998515i	$0.482652\pi$
$338$	−0.500000	−	0.866025i	−0.0271964	−	0.0471056i
$339$		0			0
$340$	6.00000	−	10.3923i	0.325396	−	0.563602i
$341$	16.0000	+	27.7128i	0.866449	+	1.50073i
$342$		0			0
$343$		0			0
$344$	4.00000			0.215666
$345$		0			0
$346$	−1.00000	+	1.73205i	−0.0537603	+	0.0931156i
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	−0.658824	−	0.752297i	$-0.728946\pi$
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	0.980921	+	0.194409i	$0.0622790\pi$
$348$		0			0
$349$	−14.0000			−0.749403			−0.374701	−	0.927146i	$-0.622255\pi$
$349$	−14.0000			−0.749403			−0.374701	+	0.927146i	$0.622255\pi$
$350$		0			0
$351$		0			0
$352$	−2.00000	−	3.46410i	−0.106600	−	0.184637i
$353$	−5.00000	+	8.66025i	−0.266123	+	0.460939i	−0.967857	−	0.251500i	$-0.919076\pi$
$353$	−5.00000	+	8.66025i	−0.266123	+	0.460939i	0.701734	+	0.712439i	$0.252409\pi$
$354$		0			0
$355$	8.00000	+	13.8564i	0.424596	+	0.735422i
$356$	18.0000			0.953998
$357$		0			0
$358$	−12.0000			−0.634220
$359$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$359$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$360$	3.00000	−	5.19615i	0.158114	−	0.273861i
$361$	9.50000	−	16.4545i	0.500000	−	0.866025i
$362$	3.00000	+	5.19615i	0.157676	+	0.273104i
$363$		0			0
$364$		0			0
$365$	4.00000			0.209370
$366$		0			0
$367$	8.00000	−	13.8564i	0.417597	−	0.723299i	−0.578101	−	0.815966i	$-0.696206\pi$
$367$	8.00000	−	13.8564i	0.417597	−	0.723299i	0.995697	+	0.0926670i	$0.0295392\pi$
$368$	−4.00000	+	6.92820i	−0.208514	+	0.361158i
$369$	−9.00000	−	15.5885i	−0.468521	−	0.811503i
$370$	12.0000			0.623850
$371$		0			0
$372$		0			0
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	0.965945	−	0.258748i	$-0.0833099\pi$
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	−0.707055	+	0.707159i	$0.749977\pi$
$374$	12.0000	−	20.7846i	0.620505	−	1.07475i
$375$		0			0
$376$	4.00000	+	6.92820i	0.206284	+	0.357295i
$377$	10.0000			0.515026
$378$		0			0
$379$	4.00000			0.205466			0.102733	−	0.994709i	$-0.467241\pi$
$379$	4.00000			0.205466			0.102733	+	0.994709i	$0.467241\pi$
$380$		0			0
$381$		0			0
$382$	4.00000	−	6.92820i	0.204658	−	0.354478i
$383$	−12.0000	−	20.7846i	−0.613171	−	1.06204i	−0.990702	−	0.136047i	$-0.956560\pi$
$383$	−12.0000	−	20.7846i	−0.613171	−	1.06204i	0.377531	−	0.925997i	$-0.376773\pi$
$384$		0			0
$385$		0			0
$386$	2.00000			0.101797
$387$	6.00000	+	10.3923i	0.304997	+	0.528271i
$388$	−1.00000	+	1.73205i	−0.0507673	+	0.0879316i
$389$	−15.0000	+	25.9808i	−0.760530	+	1.31728i	0.182047	+	0.983290i	$0.441728\pi$
$389$	−15.0000	+	25.9808i	−0.760530	+	1.31728i	−0.942578	+	0.333987i	$0.891606\pi$
$390$		0			0
$391$	−48.0000			−2.42746
$392$		0			0
$393$		0			0
$394$	9.00000	+	15.5885i	0.453413	+	0.785335i
$395$	−8.00000	+	13.8564i	−0.402524	+	0.697191i
$396$	6.00000	−	10.3923i	0.301511	−	0.522233i
$397$	−1.00000	−	1.73205i	−0.0501886	−	0.0869291i	0.839840	−	0.542834i	$-0.182649\pi$
$397$	−1.00000	−	1.73205i	−0.0501886	−	0.0869291i	−0.890028	+	0.455905i	$0.849316\pi$
$398$	−16.0000			−0.802008
$399$		0			0
$400$	−1.00000			−0.0500000
$401$	−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
$403$	−4.00000	+	6.92820i	−0.199254	+	0.345118i
$404$	7.00000	+	12.1244i	0.348263	+	0.603209i
$405$	18.0000			0.894427
$406$		0			0
$407$	24.0000			1.18964
$408$		0			0
$409$	19.0000	−	32.9090i	0.939490	−	1.62724i	0.173064	−	0.984911i	$-0.444633\pi$
$409$	19.0000	−	32.9090i	0.939490	−	1.62724i	0.766426	−	0.642333i	$-0.222033\pi$
$410$	6.00000	−	10.3923i	0.296319	−	0.513239i
$411$		0			0
$412$	16.0000			0.788263
$413$		0			0
$414$	−24.0000			−1.17954
$415$		0			0
$416$	0.500000	−	0.866025i	0.0245145	−	0.0424604i
$417$		0			0
$418$		0			0
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	−2.00000			−0.0974740			−0.0487370	−	0.998812i	$-0.515520\pi$
$421$	−2.00000			−0.0974740			−0.0487370	+	0.998812i	$0.515520\pi$
$422$	−10.0000	−	17.3205i	−0.486792	−	0.843149i
$423$	−12.0000	+	20.7846i	−0.583460	+	1.01058i
$424$	−3.00000	+	5.19615i	−0.145693	+	0.252347i
$425$	−3.00000	−	5.19615i	−0.145521	−	0.252050i
$426$		0			0
$427$		0			0
$428$	−4.00000			−0.193347
$429$		0			0
$430$	−4.00000	+	6.92820i	−0.192897	+	0.334108i
$431$	12.0000	−	20.7846i	0.578020	−	1.00116i	−0.417687	−	0.908591i	$-0.637159\pi$
$431$	12.0000	−	20.7846i	0.578020	−	1.00116i	0.995706	−	0.0925683i	$-0.0295076\pi$
$432$		0			0
$433$	−38.0000			−1.82616			−0.913082	−	0.407777i	$-0.866304\pi$
$433$	−38.0000			−1.82616			−0.913082	+	0.407777i	$0.866304\pi$
$434$		0			0
$435$		0			0
$436$	1.00000	+	1.73205i	0.0478913	+	0.0829502i
$437$		0			0
$438$		0			0
$439$	−4.00000	−	6.92820i	−0.190910	−	0.330665i	0.754642	−	0.656136i	$-0.227810\pi$
$439$	−4.00000	−	6.92820i	−0.190910	−	0.330665i	−0.945552	+	0.325471i	$0.894477\pi$
$440$	8.00000			0.381385
$441$		0			0
$442$	6.00000			0.285391
$443$	18.0000	+	31.1769i	0.855206	+	1.48126i	0.876454	+	0.481486i	$0.159903\pi$
$443$	18.0000	+	31.1769i	0.855206	+	1.48126i	−0.0212481	+	0.999774i	$0.506764\pi$
$444$		0			0
$445$	−18.0000	+	31.1769i	−0.853282	+	1.47793i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−14.0000			−0.660701			−0.330350	−	0.943858i	$-0.607167\pi$
$449$	−14.0000			−0.660701			−0.330350	+	0.943858i	$0.607167\pi$
$450$	−1.50000	−	2.59808i	−0.0707107	−	0.122474i
$451$	12.0000	−	20.7846i	0.565058	−	0.978709i
$452$	−1.00000	+	1.73205i	−0.0470360	+	0.0814688i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−5.00000	−	8.66025i	−0.233890	−	0.405110i	0.725059	−	0.688686i	$-0.241812\pi$
$457$	−5.00000	−	8.66025i	−0.233890	−	0.405110i	−0.958950	+	0.283577i	$0.908479\pi$
$458$	3.00000	−	5.19615i	0.140181	−	0.242800i
$459$		0			0
$460$	−8.00000	−	13.8564i	−0.373002	−	0.646058i
$461$	18.0000			0.838344			0.419172	−	0.907907i	$-0.362320\pi$
$461$	18.0000			0.838344			0.419172	+	0.907907i	$0.362320\pi$
$462$		0			0
$463$	16.0000			0.743583			0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000			0.743583			0.371792	+	0.928316i	$0.378744\pi$
$464$	5.00000	+	8.66025i	0.232119	+	0.402042i
$465$		0			0
$466$	−5.00000	+	8.66025i	−0.231621	+	0.401179i
$467$	−4.00000	−	6.92820i	−0.185098	−	0.320599i	0.758512	−	0.651660i	$-0.225927\pi$
$467$	−4.00000	−	6.92820i	−0.185098	−	0.320599i	−0.943610	+	0.331061i	$0.892594\pi$
$468$	3.00000			0.138675
$469$		0			0
$470$	−16.0000			−0.738025
$471$		0			0
$472$	−4.00000	+	6.92820i	−0.184115	+	0.318896i
$473$	−8.00000	+	13.8564i	−0.367840	+	0.637118i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−18.0000			−0.824163
$478$	12.0000	+	20.7846i	0.548867	+	0.950666i
$479$	−12.0000	+	20.7846i	−0.548294	+	0.949673i	0.450098	+	0.892979i	$0.351389\pi$
$479$	−12.0000	+	20.7846i	−0.548294	+	0.949673i	−0.998392	+	0.0566937i	$0.981944\pi$
$480$		0			0
$481$	3.00000	+	5.19615i	0.136788	+	0.236924i
$482$	18.0000			0.819878
$483$		0			0
$484$	5.00000			0.227273
$485$	−2.00000	−	3.46410i	−0.0908153	−	0.157297i
$486$		0			0
$487$	8.00000	−	13.8564i	0.362515	−	0.627894i	−0.625859	−	0.779936i	$-0.715252\pi$
$487$	8.00000	−	13.8564i	0.362515	−	0.627894i	0.988374	+	0.152042i	$0.0485850\pi$
$488$	−5.00000	−	8.66025i	−0.226339	−	0.392031i
$489$		0			0
$490$		0			0
$491$	28.0000			1.26362			0.631811	−	0.775122i	$-0.282312\pi$
$491$	28.0000			1.26362			0.631811	+	0.775122i	$0.282312\pi$
$492$		0			0
$493$	−30.0000	+	51.9615i	−1.35113	+	2.34023i
$494$		0			0
$495$	12.0000	+	20.7846i	0.539360	+	0.934199i
$496$	−8.00000			−0.359211
$497$		0			0
$498$		0			0
$499$	−2.00000	−	3.46410i	−0.0895323	−	0.155074i	0.817781	−	0.575529i	$-0.195204\pi$
$499$	−2.00000	−	3.46410i	−0.0895323	−	0.155074i	−0.907314	+	0.420455i	$0.861871\pi$
$500$	6.00000	−	10.3923i	0.268328	−	0.464758i
$501$		0			0
$502$	−12.0000	−	20.7846i	−0.535586	−	0.927663i
$503$	−8.00000			−0.356702			−0.178351	−	0.983967i	$-0.557076\pi$
$503$	−8.00000			−0.356702			−0.178351	+	0.983967i	$0.557076\pi$
$504$		0			0
$505$	−28.0000			−1.24598
$506$	−16.0000	−	27.7128i	−0.711287	−	1.23198i
$507$		0			0
$508$	−8.00000	+	13.8564i	−0.354943	+	0.614779i
$509$	7.00000	+	12.1244i	0.310270	+	0.537403i	0.978421	−	0.206623i	$-0.0662474\pi$
$509$	7.00000	+	12.1244i	0.310270	+	0.537403i	−0.668151	+	0.744026i	$0.732914\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			0.0441942
$513$		0			0
$514$	−9.00000	+	15.5885i	−0.396973	+	0.687577i
$515$	−16.0000	+	27.7128i	−0.705044	+	1.22117i
$516$		0			0
$517$	−32.0000			−1.40736
$518$		0			0
$519$		0			0
$520$	1.00000	+	1.73205i	0.0438529	+	0.0759555i
$521$	15.0000	−	25.9808i	0.657162	−	1.13824i	−0.324185	−	0.945994i	$-0.605090\pi$
$521$	15.0000	−	25.9808i	0.657162	−	1.13824i	0.981347	−	0.192244i	$-0.0615766\pi$
$522$	−15.0000	+	25.9808i	−0.656532	+	1.13715i
$523$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$523$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$524$	8.00000			0.349482
$525$		0			0
$526$		0			0
$527$	−24.0000	−	41.5692i	−1.04546	−	1.81078i
$528$		0			0
$529$	−20.5000	+	35.5070i	−0.891304	+	1.54378i
$530$	−6.00000	−	10.3923i	−0.260623	−	0.451413i
$531$	−24.0000			−1.04151
$532$		0			0
$533$	6.00000			0.259889
$534$		0			0
$535$	4.00000	−	6.92820i	0.172935	−	0.299532i
$536$	−2.00000	+	3.46410i	−0.0863868	+	0.149626i
$537$		0			0
$538$	−30.0000			−1.29339
$539$		0			0
$540$		0			0
$541$	5.00000	+	8.66025i	0.214967	+	0.372333i	0.953262	−	0.302144i	$-0.0977023\pi$
$541$	5.00000	+	8.66025i	0.214967	+	0.372333i	−0.738296	+	0.674477i	$0.764369\pi$
$542$	16.0000	−	27.7128i	0.687259	−	1.19037i
$543$		0			0
$544$	3.00000	+	5.19615i	0.128624	+	0.222783i
$545$	−4.00000			−0.171341
$546$		0			0
$547$	28.0000			1.19719			0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000			1.19719			0.598597	+	0.801050i	$0.295725\pi$
$548$	3.00000	+	5.19615i	0.128154	+	0.221969i
$549$	15.0000	−	25.9808i	0.640184	−	1.10883i
$550$	2.00000	−	3.46410i	0.0852803	−	0.147710i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	6.00000			0.254916
$555$		0			0
$556$	4.00000	−	6.92820i	0.169638	−	0.293821i
$557$	21.0000	−	36.3731i	0.889799	−	1.54118i	0.0496855	−	0.998765i	$-0.484178\pi$
$557$	21.0000	−	36.3731i	0.889799	−	1.54118i	0.840113	−	0.542411i	$-0.182489\pi$
$558$	−12.0000	−	20.7846i	−0.508001	−	0.879883i
$559$	−4.00000			−0.169182
$560$		0			0
$561$		0			0
$562$	−5.00000	−	8.66025i	−0.210912	−	0.365311i
$563$	8.00000	−	13.8564i	0.337160	−	0.583978i	−0.646737	−	0.762713i	$-0.723867\pi$
$563$	8.00000	−	13.8564i	0.337160	−	0.583978i	0.983897	+	0.178735i	$0.0572004\pi$
$564$		0			0
$565$	−2.00000	−	3.46410i	−0.0841406	−	0.145736i
$566$	16.0000			0.672530
$567$		0			0
$568$	−8.00000			−0.335673
$569$	19.0000	+	32.9090i	0.796521	+	1.37962i	0.921869	+	0.387503i	$0.126662\pi$
$569$	19.0000	+	32.9090i	0.796521	+	1.37962i	−0.125347	+	0.992113i	$0.540004\pi$
$570$		0			0
$571$	6.00000	−	10.3923i	0.251092	−	0.434904i	−0.712735	−	0.701434i	$-0.752544\pi$
$571$	6.00000	−	10.3923i	0.251092	−	0.434904i	0.963827	+	0.266529i	$0.0858769\pi$
$572$	2.00000	+	3.46410i	0.0836242	+	0.144841i
$573$		0			0
$574$		0			0
$575$	−8.00000			−0.333623
$576$	1.50000	+	2.59808i	0.0625000	+	0.108253i
$577$	−21.0000	+	36.3731i	−0.874241	+	1.51423i	−0.0166728	+	0.999861i	$0.505307\pi$
$577$	−21.0000	+	36.3731i	−0.874241	+	1.51423i	−0.857569	+	0.514370i	$0.828026\pi$
$578$	−9.50000	+	16.4545i	−0.395148	+	0.684416i
$579$		0			0
$580$	−20.0000			−0.830455
$581$		0			0
$582$		0			0
$583$	−12.0000	−	20.7846i	−0.496989	−	0.860811i
$584$	−1.00000	+	1.73205i	−0.0413803	+	0.0716728i
$585$	−3.00000	+	5.19615i	−0.124035	+	0.214834i
$586$	7.00000	+	12.1244i	0.289167	+	0.500853i
$587$	−16.0000			−0.660391			−0.330195	−	0.943913i	$-0.607115\pi$
$587$	−16.0000			−0.660391			−0.330195	+	0.943913i	$0.607115\pi$
$588$		0			0
$589$		0			0
$590$	−8.00000	−	13.8564i	−0.329355	−	0.570459i
$591$		0			0
$592$	−3.00000	+	5.19615i	−0.123299	+	0.213561i
$593$	11.0000	+	19.0526i	0.451716	+	0.782395i	0.998493	−	0.0548835i	$-0.0174787\pi$
$593$	11.0000	+	19.0526i	0.451716	+	0.782395i	−0.546777	+	0.837278i	$0.684145\pi$
$594$		0			0
$595$		0			0
$596$	−18.0000			−0.737309
$597$		0			0
$598$	4.00000	−	6.92820i	0.163572	−	0.283315i
$599$	−8.00000	+	13.8564i	−0.326871	+	0.566157i	−0.981889	−	0.189456i	$-0.939328\pi$
$599$	−8.00000	+	13.8564i	−0.326871	+	0.566157i	0.655018	+	0.755613i	$0.272661\pi$
$600$		0			0
$601$	10.0000			0.407909			0.203954	−	0.978980i	$-0.434621\pi$
$601$	10.0000			0.407909			0.203954	+	0.978980i	$0.434621\pi$
$602$		0			0
$603$	−12.0000			−0.488678
$604$		0			0
$605$	−5.00000	+	8.66025i	−0.203279	+	0.352089i
$606$		0			0
$607$	24.0000	+	41.5692i	0.974130	+	1.68724i	0.682777	+	0.730627i	$0.260772\pi$
$607$	24.0000	+	41.5692i	0.974130	+	1.68724i	0.291353	+	0.956616i	$0.405895\pi$
$608$		0			0
$609$		0			0
$610$	20.0000			0.809776
$611$	−4.00000	−	6.92820i	−0.161823	−	0.280285i
$612$	−9.00000	+	15.5885i	−0.363803	+	0.630126i
$613$	−19.0000	+	32.9090i	−0.767403	+	1.32918i	0.171564	+	0.985173i	$0.445118\pi$
$613$	−19.0000	+	32.9090i	−0.767403	+	1.32918i	−0.938967	+	0.344008i	$0.888215\pi$
$614$	−16.0000	−	27.7128i	−0.645707	−	1.11840i
$615$		0			0
$616$		0			0
$617$	10.0000			0.402585			0.201292	−	0.979531i	$-0.435486\pi$
$617$	10.0000			0.402585			0.201292	+	0.979531i	$0.435486\pi$
$618$		0			0
$619$	−20.0000	+	34.6410i	−0.803868	+	1.39234i	0.113185	+	0.993574i	$0.463895\pi$
$619$	−20.0000	+	34.6410i	−0.803868	+	1.39234i	−0.917053	+	0.398766i	$0.869439\pi$
$620$	8.00000	−	13.8564i	0.321288	−	0.556487i
$621$		0			0
$622$	24.0000			0.962312
$623$		0			0
$624$		0			0
$625$	9.50000	+	16.4545i	0.380000	+	0.658179i
$626$	−1.00000	+	1.73205i	−0.0399680	+	0.0692267i
$627$		0			0
$628$	−1.00000	−	1.73205i	−0.0399043	−	0.0691164i
$629$	−36.0000			−1.43541
$630$		0			0
$631$	−8.00000			−0.318475			−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000			−0.318475			−0.159237	+	0.987240i	$0.550904\pi$
$632$	−4.00000	−	6.92820i	−0.159111	−	0.275589i
$633$		0			0
$634$	−3.00000	+	5.19615i	−0.119145	+	0.206366i
$635$	−16.0000	−	27.7128i	−0.634941	−	1.09975i
$636$		0			0
$637$		0			0
$638$	−40.0000			−1.58362
$639$	−12.0000	−	20.7846i	−0.474713	−	0.822226i
$640$	−1.00000	+	1.73205i	−0.0395285	+	0.0684653i
$641$	−17.0000	+	29.4449i	−0.671460	+	1.16300i	0.306031	+	0.952022i	$0.400999\pi$
$641$	−17.0000	+	29.4449i	−0.671460	+	1.16300i	−0.977490	+	0.210981i	$0.932334\pi$
$642$		0			0
$643$	8.00000			0.315489			0.157745	−	0.987480i	$-0.449578\pi$
$643$	8.00000			0.315489			0.157745	+	0.987480i	$0.449578\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	16.0000	−	27.7128i	0.629025	−	1.08950i	−0.358723	−	0.933444i	$-0.616788\pi$
$647$	16.0000	−	27.7128i	0.629025	−	1.08950i	0.987748	−	0.156059i	$-0.0498790\pi$
$648$	−4.50000	+	7.79423i	−0.176777	+	0.306186i
$649$	−16.0000	−	27.7128i	−0.628055	−	1.08782i
$650$	1.00000			0.0392232
$651$		0			0
$652$	−4.00000			−0.156652
$653$	21.0000	+	36.3731i	0.821794	+	1.42339i	0.904345	+	0.426801i	$0.140360\pi$
$653$	21.0000	+	36.3731i	0.821794	+	1.42339i	−0.0825519	+	0.996587i	$0.526307\pi$
$654$		0			0
$655$	−8.00000	+	13.8564i	−0.312586	+	0.541415i
$656$	3.00000	+	5.19615i	0.117130	+	0.202876i
$657$	−6.00000			−0.234082
$658$		0			0
$659$	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
$661$	−1.00000	+	1.73205i	−0.0388955	+	0.0673690i	−0.884818	−	0.465937i	$-0.845717\pi$
$661$	−1.00000	+	1.73205i	−0.0388955	+	0.0673690i	0.845922	+	0.533306i	$0.179051\pi$
$662$	14.0000	−	24.2487i	0.544125	−	0.942453i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−18.0000			−0.697486
$667$	40.0000	+	69.2820i	1.54881	+	2.68261i
$668$		0			0
$669$		0			0
$670$	−4.00000	−	6.92820i	−0.154533	−	0.267660i
$671$	40.0000			1.54418
$672$		0			0
$673$	−14.0000			−0.539660			−0.269830	−	0.962908i	$-0.586968\pi$
$673$	−14.0000			−0.539660			−0.269830	+	0.962908i	$0.586968\pi$
$674$	−1.00000	−	1.73205i	−0.0385186	−	0.0667161i
$675$		0			0
$676$	−0.500000	+	0.866025i	−0.0192308	+	0.0333087i
$677$	−21.0000	−	36.3731i	−0.807096	−	1.39793i	−0.914867	−	0.403755i	$-0.867705\pi$
$677$	−21.0000	−	36.3731i	−0.807096	−	1.39793i	0.107772	−	0.994176i	$-0.465628\pi$
$678$		0			0
$679$		0			0
$680$	−12.0000			−0.460179
$681$		0			0
$682$	16.0000	−	27.7128i	0.612672	−	1.06118i
$683$	−14.0000	+	24.2487i	−0.535695	+	0.927851i	0.463434	+	0.886131i	$0.346617\pi$
$683$	−14.0000	+	24.2487i	−0.535695	+	0.927851i	−0.999129	+	0.0417198i	$0.986716\pi$
$684$		0			0
$685$	−12.0000			−0.458496
$686$		0			0
$687$		0			0
$688$	−2.00000	−	3.46410i	−0.0762493	−	0.132068i
$689$	3.00000	−	5.19615i	0.114291	−	0.197958i
$690$		0			0
$691$	−8.00000	−	13.8564i	−0.304334	−	0.527123i	0.672779	−	0.739844i	$-0.265101\pi$
$691$	−8.00000	−	13.8564i	−0.304334	−	0.527123i	−0.977113	+	0.212721i	$0.931767\pi$
$692$	2.00000			0.0760286
$693$		0			0
$694$	−12.0000			−0.455514
$695$	8.00000	+	13.8564i	0.303457	+	0.525603i
$696$		0			0
$697$	−18.0000	+	31.1769i	−0.681799	+	1.18091i
$698$	7.00000	+	12.1244i	0.264954	+	0.458914i
$699$		0			0
$700$		0			0
$701$	−42.0000			−1.58632			−0.793159	−	0.609015i	$-0.791565\pi$
$701$	−42.0000			−1.58632			−0.793159	+	0.609015i	$0.791565\pi$
$702$		0			0
$703$		0			0
$704$	−2.00000	+	3.46410i	−0.0753778	+	0.130558i
$705$		0			0
$706$	10.0000			0.376355
$707$		0			0
$708$		0			0
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	0.944509	−	0.328484i	$-0.106538\pi$
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	−0.756730	+	0.653727i	$0.773204\pi$
$710$	8.00000	−	13.8564i	0.300235	−	0.520022i
$711$	12.0000	−	20.7846i	0.450035	−	0.779484i
$712$	−9.00000	−	15.5885i	−0.337289	−	0.584202i
$713$	−64.0000			−2.39682
$714$		0			0
$715$	−8.00000			−0.299183
$716$	6.00000	+	10.3923i	0.224231	+	0.388379i
$717$		0			0
$718$		0			0
$719$	−4.00000	−	6.92820i	−0.149175	−	0.258378i	0.781748	−	0.623595i	$-0.214328\pi$
$719$	−4.00000	−	6.92820i	−0.149175	−	0.258378i	−0.930923	+	0.365216i	$0.880995\pi$
$720$	−6.00000			−0.223607
$721$		0			0
$722$	−19.0000			−0.707107
$723$		0			0
$724$	3.00000	−	5.19615i	0.111494	−	0.193113i
$725$	−5.00000	+	8.66025i	−0.185695	+	0.321634i
$726$		0			0
$727$	16.0000			0.593407			0.296704	−	0.954970i	$-0.404113\pi$
$727$	16.0000			0.593407			0.296704	+	0.954970i	$0.404113\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	−2.00000	−	3.46410i	−0.0740233	−	0.128212i
$731$	12.0000	−	20.7846i	0.443836	−	0.768747i
$732$		0			0
$733$	−13.0000	−	22.5167i	−0.480166	−	0.831672i	0.519575	−	0.854425i	$-0.326090\pi$
$733$	−13.0000	−	22.5167i	−0.480166	−	0.831672i	−0.999741	+	0.0227529i	$0.992757\pi$
$734$	−16.0000			−0.590571
$735$		0			0
$736$	8.00000			0.294884
$737$	−8.00000	−	13.8564i	−0.294684	−	0.510407i
$738$	−9.00000	+	15.5885i	−0.331295	+	0.573819i
$739$	18.0000	−	31.1769i	0.662141	−	1.14686i	−0.317911	−	0.948120i	$-0.602981\pi$
$739$	18.0000	−	31.1769i	0.662141	−	1.14686i	0.980052	−	0.198741i	$-0.0636852\pi$
$740$	−6.00000	−	10.3923i	−0.220564	−	0.382029i
$741$		0			0
$742$		0			0
$743$	16.0000			0.586983			0.293492	−	0.955962i	$-0.405183\pi$
$743$	16.0000			0.586983			0.293492	+	0.955962i	$0.405183\pi$
$744$		0			0
$745$	18.0000	−	31.1769i	0.659469	−	1.14223i
$746$	5.00000	−	8.66025i	0.183063	−	0.317074i
$747$		0			0
$748$	−24.0000			−0.877527
$749$		0			0
$750$		0			0
$751$	−24.0000	−	41.5692i	−0.875772	−	1.51688i	−0.855938	−	0.517079i	$-0.827019\pi$
$751$	−24.0000	−	41.5692i	−0.875772	−	1.51688i	−0.0198348	−	0.999803i	$-0.506314\pi$
$752$	4.00000	−	6.92820i	0.145865	−	0.252646i
$753$		0			0
$754$	−5.00000	−	8.66025i	−0.182089	−	0.315388i
$755$		0			0
$756$		0			0
$757$	30.0000			1.09037			0.545184	−	0.838316i	$-0.316460\pi$
$757$	30.0000			1.09037			0.545184	+	0.838316i	$0.316460\pi$
$758$	−2.00000	−	3.46410i	−0.0726433	−	0.125822i
$759$		0			0
$760$		0			0
$761$	3.00000	+	5.19615i	0.108750	+	0.188360i	0.915264	−	0.402854i	$-0.131982\pi$
$761$	3.00000	+	5.19615i	0.108750	+	0.188360i	−0.806514	+	0.591215i	$0.798649\pi$
$762$		0			0
$763$		0			0
$764$	−8.00000			−0.289430
$765$	−18.0000	−	31.1769i	−0.650791	−	1.12720i
$766$	−12.0000	+	20.7846i	−0.433578	+	0.750978i
$767$	4.00000	−	6.92820i	0.144432	−	0.250163i
$768$		0			0
$769$	−30.0000			−1.08183			−0.540914	−	0.841078i	$-0.681921\pi$
$769$	−30.0000			−1.08183			−0.540914	+	0.841078i	$0.681921\pi$
$770$		0			0
$771$		0			0
$772$	−1.00000	−	1.73205i	−0.0359908	−	0.0623379i
$773$	23.0000	−	39.8372i	0.827253	−	1.43284i	−0.0729331	−	0.997337i	$-0.523236\pi$
$773$	23.0000	−	39.8372i	0.827253	−	1.43284i	0.900186	−	0.435507i	$-0.143431\pi$
$774$	6.00000	−	10.3923i	0.215666	−	0.373544i
$775$	−4.00000	−	6.92820i	−0.143684	−	0.248868i
$776$	2.00000			0.0717958
$777$		0			0
$778$	30.0000			1.07555
$779$		0			0
$780$		0			0
$781$	16.0000	−	27.7128i	0.572525	−	0.991642i
$782$	24.0000	+	41.5692i	0.858238	+	1.48651i
$783$		0			0
$784$		0			0
$785$	4.00000			0.142766
$786$		0			0
$787$	−16.0000	+	27.7128i	−0.570338	+	0.987855i	0.426193	+	0.904632i	$0.359855\pi$
$787$	−16.0000	+	27.7128i	−0.570338	+	0.987855i	−0.996531	+	0.0832226i	$0.973479\pi$
$788$	9.00000	−	15.5885i	0.320612	−	0.555316i
$789$		0			0
$790$	16.0000			0.569254
$791$		0			0
$792$	−12.0000			−0.426401
$793$	5.00000	+	8.66025i	0.177555	+	0.307535i
$794$	−1.00000	+	1.73205i	−0.0354887	+	0.0614682i
$795$		0			0
$796$	8.00000	+	13.8564i	0.283552	+	0.491127i
$797$	18.0000			0.637593			0.318796	−	0.947823i	$-0.396721\pi$
$797$	18.0000			0.637593			0.318796	+	0.947823i	$0.396721\pi$
$798$		0			0
$799$	48.0000			1.69812
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	27.0000	−	46.7654i	0.953998	−	1.65237i
$802$	−9.00000	+	15.5885i	−0.317801	+	0.550448i
$803$	−4.00000	−	6.92820i	−0.141157	−	0.244491i
$804$		0			0
$805$		0			0
$806$	8.00000			0.281788
$807$		0			0
$808$	7.00000	−	12.1244i	0.246259	−	0.426533i
$809$	3.00000	−	5.19615i	0.105474	−	0.182687i	−0.808458	−	0.588555i	$-0.799697\pi$
$809$	3.00000	−	5.19615i	0.105474	−	0.182687i	0.913932	+	0.405868i	$0.133031\pi$
$810$	−9.00000	−	15.5885i	−0.316228	−	0.547723i
$811$	8.00000			0.280918			0.140459	−	0.990086i	$-0.455142\pi$
$811$	8.00000			0.280918			0.140459	+	0.990086i	$0.455142\pi$
$812$		0			0
$813$		0			0
$814$	−12.0000	−	20.7846i	−0.420600	−	0.728500i
$815$	4.00000	−	6.92820i	0.140114	−	0.242684i
$816$		0			0
$817$		0			0
$818$	−38.0000			−1.32864
$819$		0			0
$820$	−12.0000			−0.419058
$821$	−7.00000	−	12.1244i	−0.244302	−	0.423143i	0.717633	−	0.696421i	$-0.245225\pi$
$821$	−7.00000	−	12.1244i	−0.244302	−	0.423143i	−0.961935	+	0.273278i	$0.911892\pi$
$822$		0			0
$823$	−24.0000	+	41.5692i	−0.836587	+	1.44901i	0.0561440	+	0.998423i	$0.482119\pi$
$823$	−24.0000	+	41.5692i	−0.836587	+	1.44901i	−0.892731	+	0.450589i	$0.851214\pi$
$824$	−8.00000	−	13.8564i	−0.278693	−	0.482711i
$825$		0			0
$826$		0			0
$827$	−36.0000			−1.25184			−0.625921	−	0.779886i	$-0.715277\pi$
$827$	−36.0000			−1.25184			−0.625921	+	0.779886i	$0.715277\pi$
$828$	12.0000	+	20.7846i	0.417029	+	0.722315i
$829$	−5.00000	+	8.66025i	−0.173657	+	0.300783i	−0.939696	−	0.342012i	$-0.888892\pi$
$829$	−5.00000	+	8.66025i	−0.173657	+	0.300783i	0.766039	+	0.642795i	$0.222225\pi$
$830$		0			0
$831$		0			0
$832$	−1.00000			−0.0346688
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$	32.0000			1.10476			0.552381	−	0.833592i	$-0.313719\pi$
$839$	32.0000			1.10476			0.552381	+	0.833592i	$0.313719\pi$
$840$		0			0
$841$	71.0000			2.44828
$842$	1.00000	+	1.73205i	0.0344623	+	0.0596904i
$843$		0			0
$844$	−10.0000	+	17.3205i	−0.344214	+	0.596196i
$845$	−1.00000	−	1.73205i	−0.0344010	−	0.0595844i
$846$	24.0000			0.825137
$847$		0			0
$848$	6.00000			0.206041
$849$		0			0
$850$	−3.00000	+	5.19615i	−0.102899	+	0.178227i
$851$	−24.0000	+	41.5692i	−0.822709	+	1.42497i
$852$		0			0
$853$	10.0000			0.342393			0.171197	−	0.985237i	$-0.445237\pi$
$853$	10.0000			0.342393			0.171197	+	0.985237i	$0.445237\pi$
$854$		0			0
$855$		0			0
$856$	2.00000	+	3.46410i	0.0683586	+	0.118401i
$857$	−17.0000	+	29.4449i	−0.580709	+	1.00582i	0.414687	+	0.909964i	$0.363891\pi$
$857$	−17.0000	+	29.4449i	−0.580709	+	1.00582i	−0.995395	+	0.0958531i	$0.969442\pi$
$858$		0			0
$859$	−4.00000	−	6.92820i	−0.136478	−	0.236387i	0.789683	−	0.613515i	$-0.210245\pi$
$859$	−4.00000	−	6.92820i	−0.136478	−	0.236387i	−0.926161	+	0.377128i	$0.876912\pi$
$860$	8.00000			0.272798
$861$		0			0
$862$	−24.0000			−0.817443
$863$	16.0000	+	27.7128i	0.544646	+	0.943355i	0.998629	+	0.0523446i	$0.0166694\pi$
$863$	16.0000	+	27.7128i	0.544646	+	0.943355i	−0.453983	+	0.891010i	$0.649997\pi$
$864$		0			0
$865$	−2.00000	+	3.46410i	−0.0680020	+	0.117783i
$866$	19.0000	+	32.9090i	0.645646	+	1.11829i
$867$		0			0
$868$		0			0
$869$	32.0000			1.08553
$870$		0			0
$871$	2.00000	−	3.46410i	0.0677674	−	0.117377i
$872$	1.00000	−	1.73205i	0.0338643	−	0.0586546i
$873$	3.00000	+	5.19615i	0.101535	+	0.175863i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−15.0000	−	25.9808i	−0.506514	−	0.877308i	−0.999972	−	0.00753813i	$-0.997601\pi$
$877$	−15.0000	−	25.9808i	−0.506514	−	0.877308i	0.493458	−	0.869770i	$-0.335733\pi$
$878$	−4.00000	+	6.92820i	−0.134993	+	0.233816i
$879$		0			0
$880$	−4.00000	−	6.92820i	−0.134840	−	0.233550i
$881$	−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
$883$	−44.0000			−1.48072			−0.740359	−	0.672212i	$-0.765344\pi$
$883$	−44.0000			−1.48072			−0.740359	+	0.672212i	$0.765344\pi$
$884$	−3.00000	−	5.19615i	−0.100901	−	0.174766i
$885$		0			0
$886$	18.0000	−	31.1769i	0.604722	−	1.04741i
$887$	16.0000	+	27.7128i	0.537227	+	0.930505i	0.999052	+	0.0435339i	$0.0138616\pi$
$887$	16.0000	+	27.7128i	0.537227	+	0.930505i	−0.461825	+	0.886971i	$0.652805\pi$
$888$		0			0
$889$		0			0
$890$	36.0000			1.20672
$891$	−18.0000	−	31.1769i	−0.603023	−	1.04447i
$892$		0			0
$893$		0			0
$894$		0			0
$895$	−24.0000			−0.802232
$896$		0			0
$897$		0			0
$898$	7.00000	+	12.1244i	0.233593	+	0.404595i
$899$	−40.0000	+	69.2820i	−1.33407	+	2.31069i
$900$	−1.50000	+	2.59808i	−0.0500000	+	0.0866025i
$901$	18.0000	+	31.1769i	0.599667	+	1.03865i
$902$	−24.0000			−0.799113
$903$		0			0
$904$	2.00000			0.0665190
$905$	6.00000	+	10.3923i	0.199447	+	0.345452i
$906$		0			0
$907$	−6.00000	+	10.3923i	−0.199227	+	0.345071i	−0.948278	−	0.317441i	$-0.897176\pi$
$907$	−6.00000	+	10.3923i	−0.199227	+	0.345071i	0.749051	+	0.662512i	$0.230510\pi$
$908$		0			0
$909$	42.0000			1.39305
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$		0			0
$913$		0			0
$914$	−5.00000	+	8.66025i	−0.165385	+	0.286456i
$915$		0			0
$916$	−6.00000			−0.198246
$917$		0			0
$918$		0			0
$919$	−24.0000	−	41.5692i	−0.791687	−	1.37124i	−0.924922	−	0.380158i	$-0.875870\pi$
$919$	−24.0000	−	41.5692i	−0.791687	−	1.37124i	0.133235	−	0.991084i	$-0.457464\pi$
$920$	−8.00000	+	13.8564i	−0.263752	+	0.456832i
$921$		0			0
$922$	−9.00000	−	15.5885i	−0.296399	−	0.513378i
$923$	8.00000			0.263323
$924$		0			0
$925$	−6.00000			−0.197279
$926$	−8.00000	−	13.8564i	−0.262896	−	0.455350i
$927$	24.0000	−	41.5692i	0.788263	−	1.36531i
$928$	5.00000	−	8.66025i	0.164133	−	0.284287i
$929$	15.0000	+	25.9808i	0.492134	+	0.852401i	0.999959	−	0.00905914i	$-0.00288365\pi$
$929$	15.0000	+	25.9808i	0.492134	+	0.852401i	−0.507825	+	0.861460i	$0.669550\pi$
$930$		0			0
$931$		0			0
$932$	10.0000			0.327561
$933$		0			0
$934$	−4.00000	+	6.92820i	−0.130884	+	0.226698i
$935$	24.0000	−	41.5692i	0.784884	−	1.35946i
$936$	−1.50000	−	2.59808i	−0.0490290	−	0.0849208i
$937$	42.0000			1.37208			0.686040	−	0.727564i	$-0.259347\pi$
$937$	42.0000			1.37208			0.686040	+	0.727564i	$0.259347\pi$
$938$		0			0
$939$		0			0
$940$	8.00000	+	13.8564i	0.260931	+	0.451946i
$941$	−5.00000	+	8.66025i	−0.162995	+	0.282316i	−0.935942	−	0.352155i	$-0.885449\pi$
$941$	−5.00000	+	8.66025i	−0.162995	+	0.282316i	0.772946	+	0.634472i	$0.218782\pi$
$942$		0			0
$943$	24.0000	+	41.5692i	0.781548	+	1.35368i
$944$	8.00000			0.260378
$945$		0			0
$946$	16.0000			0.520205
$947$	−6.00000	−	10.3923i	−0.194974	−	0.337705i	0.751918	−	0.659256i	$-0.229129\pi$
$947$	−6.00000	−	10.3923i	−0.194974	−	0.337705i	−0.946892	+	0.321552i	$0.895796\pi$
$948$		0			0
$949$	1.00000	−	1.73205i	0.0324614	−	0.0562247i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	26.0000			0.842223			0.421111	−	0.907009i	$-0.361640\pi$
$953$	26.0000			0.842223			0.421111	+	0.907009i	$0.361640\pi$
$954$	9.00000	+	15.5885i	0.291386	+	0.504695i
$955$	8.00000	−	13.8564i	0.258874	−	0.448383i
$956$	12.0000	−	20.7846i	0.388108	−	0.672222i
$957$		0			0
$958$	24.0000			0.775405
$959$		0			0
$960$		0			0
$961$	−16.5000	−	28.5788i	−0.532258	−	0.921898i
$962$	3.00000	−	5.19615i	0.0967239	−	0.167531i
$963$	−6.00000	+	10.3923i	−0.193347	+	0.334887i
$964$	−9.00000	−	15.5885i	−0.289870	−	0.502070i
$965$	4.00000			0.128765
$966$		0			0
$967$	32.0000			1.02905			0.514525	−	0.857475i	$-0.327968\pi$
$967$	32.0000			1.02905			0.514525	+	0.857475i	$0.327968\pi$
$968$	−2.50000	−	4.33013i	−0.0803530	−	0.139176i
$969$		0			0
$970$	−2.00000	+	3.46410i	−0.0642161	+	0.111226i
$971$	−24.0000	−	41.5692i	−0.770197	−	1.33402i	−0.937455	−	0.348107i	$-0.886825\pi$
$971$	−24.0000	−	41.5692i	−0.770197	−	1.33402i	0.167258	−	0.985913i	$-0.446509\pi$
$972$		0			0
$973$		0			0
$974$	−16.0000			−0.512673
$975$		0			0
$976$	−5.00000	+	8.66025i	−0.160046	+	0.277208i
$977$	15.0000	−	25.9808i	0.479893	−	0.831198i	−0.519841	−	0.854263i	$-0.674009\pi$
$977$	15.0000	−	25.9808i	0.479893	−	0.831198i	0.999734	+	0.0230645i	$0.00734232\pi$
$978$		0			0
$979$	72.0000			2.30113
$980$		0			0
$981$	6.00000			0.191565
$982$	−14.0000	−	24.2487i	−0.446758	−	0.773807i
$983$	−16.0000	+	27.7128i	−0.510321	+	0.883901i	0.489608	+	0.871943i	$0.337140\pi$
$983$	−16.0000	+	27.7128i	−0.510321	+	0.883901i	−0.999928	+	0.0119587i	$0.996193\pi$
$984$		0			0
$985$	18.0000	+	31.1769i	0.573528	+	0.993379i
$986$	60.0000			1.91079
$987$		0			0
$988$		0			0
$989$	−16.0000	−	27.7128i	−0.508770	−	0.881216i
$990$	12.0000	−	20.7846i	0.381385	−	0.660578i
$991$	−12.0000	+	20.7846i	−0.381193	+	0.660245i	−0.991233	−	0.132125i	$-0.957820\pi$
$991$	−12.0000	+	20.7846i	−0.381193	+	0.660245i	0.610040	+	0.792370i	$0.291153\pi$
$992$	4.00000	+	6.92820i	0.127000	+	0.219971i
$993$		0			0
$994$		0			0
$995$	−32.0000			−1.01447
$996$		0			0
$997$	−1.00000	+	1.73205i	−0.0316703	+	0.0548546i	−0.881426	−	0.472322i	$-0.843416\pi$
$997$	−1.00000	+	1.73205i	−0.0316703	+	0.0548546i	0.849756	+	0.527176i	$0.176749\pi$
$998$	−2.00000	+	3.46410i	−0.0633089	+	0.109654i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1274.2.f.f.1145.1		2
7.2	even	3	inner	1274.2.f.f.79.1		2
7.3	odd	6		1274.2.a.l.1.1		1
7.4	even	3		182.2.a.c.1.1	✓	1
7.5	odd	6		1274.2.f.g.79.1		2
7.6	odd	2		1274.2.f.g.1145.1		2
21.11	odd	6		1638.2.a.c.1.1		1
28.11	odd	6		1456.2.a.i.1.1		1
35.4	even	6		4550.2.a.g.1.1		1
56.11	odd	6		5824.2.a.m.1.1		1
56.53	even	6		5824.2.a.l.1.1		1
91.18	odd	12		2366.2.d.d.337.1		2
91.25	even	6		2366.2.a.d.1.1		1
91.60	odd	12		2366.2.d.d.337.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.a.c.1.1	✓	1	7.4	even	3
1274.2.a.l.1.1		1	7.3	odd	6
1274.2.f.f.79.1		2	7.2	even	3	inner
1274.2.f.f.1145.1		2	1.1	even	1	trivial
1274.2.f.g.79.1		2	7.5	odd	6
1274.2.f.g.1145.1		2	7.6	odd	2
1456.2.a.i.1.1		1	28.11	odd	6
1638.2.a.c.1.1		1	21.11	odd	6
2366.2.a.d.1.1		1	91.25	even	6
2366.2.d.d.337.1		2	91.18	odd	12
2366.2.d.d.337.2		2	91.60	odd	12
4550.2.a.g.1.1		1	35.4	even	6
5824.2.a.l.1.1		1	56.53	even	6
5824.2.a.m.1.1		1	56.11	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:	\( N \)	\(=\)	\( 1274 = 2 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1274.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{5} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{5} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-1.00000 + 1.73205i) q^{10} +(-2.00000 + 3.46410i) q^{11} -1.00000 q^{13} +(-0.500000 - 0.866025i) q^{16} +(3.00000 - 5.19615i) q^{17} +(1.50000 - 2.59808i) q^{18} +2.00000 q^{20} +4.00000 q^{22} +(-4.00000 - 6.92820i) q^{23} +(0.500000 - 0.866025i) q^{25} +(0.500000 + 0.866025i) q^{26} -10.0000 q^{29} +(4.00000 - 6.92820i) q^{31} +(-0.500000 + 0.866025i) q^{32} -6.00000 q^{34} -3.00000 q^{36} +(-3.00000 - 5.19615i) q^{37} +(-1.00000 - 1.73205i) q^{40} -6.00000 q^{41} +4.00000 q^{43} +(-2.00000 - 3.46410i) q^{44} +(3.00000 - 5.19615i) q^{45} +(-4.00000 + 6.92820i) q^{46} +(4.00000 + 6.92820i) q^{47} -1.00000 q^{50} +(0.500000 - 0.866025i) q^{52} +(-3.00000 + 5.19615i) q^{53} +8.00000 q^{55} +(5.00000 + 8.66025i) q^{58} +(-4.00000 + 6.92820i) q^{59} +(-5.00000 - 8.66025i) q^{61} -8.00000 q^{62} +1.00000 q^{64} +(1.00000 + 1.73205i) q^{65} +(-2.00000 + 3.46410i) q^{67} +(3.00000 + 5.19615i) q^{68} -8.00000 q^{71} +(1.50000 + 2.59808i) q^{72} +(-1.00000 + 1.73205i) q^{73} +(-3.00000 + 5.19615i) q^{74} +(-4.00000 - 6.92820i) q^{79} +(-1.00000 + 1.73205i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(3.00000 + 5.19615i) q^{82} -12.0000 q^{85} +(-2.00000 - 3.46410i) q^{86} +(-2.00000 + 3.46410i) q^{88} +(-9.00000 - 15.5885i) q^{89} -6.00000 q^{90} +8.00000 q^{92} +(4.00000 - 6.92820i) q^{94} +2.00000 q^{97} -12.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} - 2 q^{5} + 2 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q - q^2 - q^4 - 2 * q^5 + 2 * q^8 + 3 * q^9	\( 2 q - q^{2} - q^{4} - 2 q^{5} + 2 q^{8} + 3 q^{9} - 2 q^{10} - 4 q^{11} - 2 q^{13} - q^{16} + 6 q^{17} + 3 q^{18} + 4 q^{20} + 8 q^{22} - 8 q^{23} + q^{25} + q^{26} - 20 q^{29} + 8 q^{31} - q^{32} - 12 q^{34} - 6 q^{36} - 6 q^{37} - 2 q^{40} - 12 q^{41} + 8 q^{43} - 4 q^{44} + 6 q^{45} - 8 q^{46} + 8 q^{47} - 2 q^{50} + q^{52} - 6 q^{53} + 16 q^{55} + 10 q^{58} - 8 q^{59} - 10 q^{61} - 16 q^{62} + 2 q^{64} + 2 q^{65} - 4 q^{67} + 6 q^{68} - 16 q^{71} + 3 q^{72} - 2 q^{73} - 6 q^{74} - 8 q^{79} - 2 q^{80} - 9 q^{81} + 6 q^{82} - 24 q^{85} - 4 q^{86} - 4 q^{88} - 18 q^{89} - 12 q^{90} + 16 q^{92} + 8 q^{94} + 4 q^{97} - 24 q^{99}+O(q^{100}) \) 2 * q - q^2 - q^4 - 2 * q^5 + 2 * q^8 + 3 * q^9 - 2 * q^10 - 4 * q^11 - 2 * q^13 - q^16 + 6 * q^17 + 3 * q^18 + 4 * q^20 + 8 * q^22 - 8 * q^23 + q^25 + q^26 - 20 * q^29 + 8 * q^31 - q^32 - 12 * q^34 - 6 * q^36 - 6 * q^37 - 2 * q^40 - 12 * q^41 + 8 * q^43 - 4 * q^44 + 6 * q^45 - 8 * q^46 + 8 * q^47 - 2 * q^50 + q^52 - 6 * q^53 + 16 * q^55 + 10 * q^58 - 8 * q^59 - 10 * q^61 - 16 * q^62 + 2 * q^64 + 2 * q^65 - 4 * q^67 + 6 * q^68 - 16 * q^71 + 3 * q^72 - 2 * q^73 - 6 * q^74 - 8 * q^79 - 2 * q^80 - 9 * q^81 + 6 * q^82 - 24 * q^85 - 4 * q^86 - 4 * q^88 - 18 * q^89 - 12 * q^90 + 16 * q^92 + 8 * q^94 + 4 * q^97 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more