LMFDB - Embedded newform 1078.2.e.p.177.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1078,2,Mod(67,1078)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1078, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("1078.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1078 = 2 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1078.e (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:	$8.60787333789$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			177.1
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1078.177
Dual form			1078.2.e.p.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.707107 - 1.22474i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.12132 + 3.67423i) q^{5} +1.41421 q^{6} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.12132 - 3.67423i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-0.707107 + 1.22474i) q^{12} +6.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.82843 + 4.89898i) q^{17} +(0.500000 + 0.866025i) q^{18} +4.24264 q^{20} -1.00000 q^{22} +(-3.00000 + 5.19615i) q^{23} +(-0.707107 - 1.22474i) q^{24} +(-6.50000 - 11.2583i) q^{25} -5.65685 q^{27} +2.00000 q^{29} +(-3.00000 + 5.19615i) q^{30} +(0.707107 + 1.22474i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.707107 - 1.22474i) q^{33} -5.65685 q^{34} -1.00000 q^{36} +(5.00000 - 8.66025i) q^{37} +(-2.12132 + 3.67423i) q^{40} -11.3137 q^{41} -8.00000 q^{43} +(0.500000 - 0.866025i) q^{44} +(2.12132 + 3.67423i) q^{45} +(-3.00000 - 5.19615i) q^{46} +(-2.12132 + 3.67423i) q^{47} +1.41421 q^{48} +13.0000 q^{50} +(4.00000 - 6.92820i) q^{51} +(-4.00000 - 6.92820i) q^{53} +(2.82843 - 4.89898i) q^{54} -4.24264 q^{55} +(-1.00000 + 1.73205i) q^{58} +(-0.707107 - 1.22474i) q^{59} +(-3.00000 - 5.19615i) q^{60} +(1.41421 - 2.44949i) q^{61} -1.41421 q^{62} +1.00000 q^{64} +(0.707107 + 1.22474i) q^{66} +(-1.00000 - 1.73205i) q^{67} +(2.82843 - 4.89898i) q^{68} +8.48528 q^{69} -2.00000 q^{71} +(0.500000 - 0.866025i) q^{72} +(-4.24264 - 7.34847i) q^{73} +(5.00000 + 8.66025i) q^{74} +(-9.19239 + 15.9217i) q^{75} +(-8.00000 + 13.8564i) q^{79} +(-2.12132 - 3.67423i) q^{80} +(2.50000 + 4.33013i) q^{81} +(5.65685 - 9.79796i) q^{82} -16.9706 q^{83} -24.0000 q^{85} +(4.00000 - 6.92820i) q^{86} +(-1.41421 - 2.44949i) q^{87} +(0.500000 + 0.866025i) q^{88} +(3.53553 - 6.12372i) q^{89} -4.24264 q^{90} +6.00000 q^{92} +(1.00000 - 1.73205i) q^{93} +(-2.12132 - 3.67423i) q^{94} +(-0.707107 + 1.22474i) q^{96} -9.89949 q^{97} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} + 4 q^{8} + 2 q^{9} + 2 q^{11} + 24 q^{15} - 2 q^{16} + 2 q^{18} - 4 q^{22} - 12 q^{23} - 26 q^{25} + 8 q^{29} - 12 q^{30} - 2 q^{32} - 4 q^{36} + 20 q^{37} - 32 q^{43} + 2 q^{44}+ \cdots + 4 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 + 4 * q^8 + 2 * q^9 + 2 * q^11 + 24 * q^15 - 2 * q^16 + 2 * q^18 - 4 * q^22 - 12 * q^23 - 26 * q^25 + 8 * q^29 - 12 * q^30 - 2 * q^32 - 4 * q^36 + 20 * q^37 - 32 * q^43 + 2 * q^44 - 12 * q^46 + 52 * q^50 + 16 * q^51 - 16 * q^53 - 4 * q^58 - 12 * q^60 + 4 * q^64 - 4 * q^67 - 8 * q^71 + 2 * q^72 + 20 * q^74 - 32 * q^79 + 10 * q^81 - 96 * q^85 + 16 * q^86 + 2 * q^88 + 24 * q^92 + 4 * q^93 + 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times$.

$n$	$199$	$981$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	−0.707107	−	1.22474i	−0.408248	−	0.707107i	0.586445	−	0.809989i	$-0.300527\pi$
$3$	−0.707107	−	1.22474i	−0.408248	−	0.707107i	−0.994694	+	0.102882i	$0.967194\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−2.12132	+	3.67423i	−0.948683	+	1.64317i	−0.200480	+	0.979698i	$0.564250\pi$
$5$	−2.12132	+	3.67423i	−0.948683	+	1.64317i	−0.748203	+	0.663470i	$0.769083\pi$
$6$	1.41421			0.577350
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−2.12132	−	3.67423i	−0.670820	−	1.16190i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	−0.707107	+	1.22474i	−0.204124	+	0.353553i
$13$		0			0			−	1.00000i	$-0.5\pi$
$13$		0			0				1.00000i	$0.5\pi$
$14$		0			0
$15$	6.00000			1.54919
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.82843	+	4.89898i	0.685994	+	1.18818i	0.973123	+	0.230285i	$0.0739659\pi$
$17$	2.82843	+	4.89898i	0.685994	+	1.18818i	−0.287129	+	0.957892i	$0.592701\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$19$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$20$	4.24264			0.948683
$21$		0			0
$22$	−1.00000			−0.213201
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	0.362892	+	0.931831i	$0.381789\pi$
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	−0.988436	+	0.151642i	$0.951544\pi$
$24$	−0.707107	−	1.22474i	−0.144338	−	0.250000i
$25$	−6.50000	−	11.2583i	−1.30000	−	2.25167i
$26$		0			0
$27$	−5.65685			−1.08866
$28$		0			0
$29$	2.00000			0.371391			0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000			0.371391			0.185695	+	0.982607i	$0.440546\pi$
$30$	−3.00000	+	5.19615i	−0.547723	+	0.948683i
$31$	0.707107	+	1.22474i	0.127000	+	0.219971i	0.922513	−	0.385966i	$-0.126132\pi$
$31$	0.707107	+	1.22474i	0.127000	+	0.219971i	−0.795513	+	0.605937i	$0.792798\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	0.707107	−	1.22474i	0.123091	−	0.213201i
$34$	−5.65685			−0.970143
$35$		0			0
$36$	−1.00000			−0.166667
$37$	5.00000	−	8.66025i	0.821995	−	1.42374i	−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	5.00000	−	8.66025i	0.821995	−	1.42374i	0.904194	−	0.427121i	$-0.140472\pi$
$38$		0			0
$39$		0			0
$40$	−2.12132	+	3.67423i	−0.335410	+	0.580948i
$41$	−11.3137			−1.76690			−0.883452	−	0.468521i	$-0.844787\pi$
$41$	−11.3137			−1.76690			−0.883452	+	0.468521i	$0.844787\pi$
$42$		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
$45$	2.12132	+	3.67423i	0.316228	+	0.547723i
$46$	−3.00000	−	5.19615i	−0.442326	−	0.766131i
$47$	−2.12132	+	3.67423i	−0.309426	+	0.535942i	−0.978237	−	0.207491i	$-0.933470\pi$
$47$	−2.12132	+	3.67423i	−0.309426	+	0.535942i	0.668811	+	0.743433i	$0.266804\pi$
$48$	1.41421			0.204124
$49$		0			0
$50$	13.0000			1.83848
$51$	4.00000	−	6.92820i	0.560112	−	0.970143i
$52$		0			0
$53$	−4.00000	−	6.92820i	−0.549442	−	0.951662i	−0.998313	−	0.0580651i	$-0.981507\pi$
$53$	−4.00000	−	6.92820i	−0.549442	−	0.951662i	0.448871	−	0.893597i	$-0.351826\pi$
$54$	2.82843	−	4.89898i	0.384900	−	0.666667i
$55$	−4.24264			−0.572078
$56$		0			0
$57$		0			0
$58$	−1.00000	+	1.73205i	−0.131306	+	0.227429i
$59$	−0.707107	−	1.22474i	−0.0920575	−	0.159448i	0.816319	−	0.577601i	$-0.196011\pi$
$59$	−0.707107	−	1.22474i	−0.0920575	−	0.159448i	−0.908377	+	0.418153i	$0.862678\pi$
$60$	−3.00000	−	5.19615i	−0.387298	−	0.670820i
$61$	1.41421	−	2.44949i	0.181071	−	0.313625i	−0.761174	−	0.648547i	$-0.775377\pi$
$61$	1.41421	−	2.44949i	0.181071	−	0.313625i	0.942246	+	0.334922i	$0.108710\pi$
$62$	−1.41421			−0.179605
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$	0.707107	+	1.22474i	0.0870388	+	0.150756i
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	0.798454	−	0.602056i	$-0.205652\pi$
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	−0.920623	+	0.390453i	$0.872318\pi$
$68$	2.82843	−	4.89898i	0.342997	−	0.594089i
$69$	8.48528			1.02151
$70$		0			0
$71$	−2.00000			−0.237356			−0.118678	−	0.992933i	$-0.537866\pi$
$71$	−2.00000			−0.237356			−0.118678	+	0.992933i	$0.537866\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	−4.24264	−	7.34847i	−0.496564	−	0.860073i	0.503429	−	0.864037i	$-0.332072\pi$
$73$	−4.24264	−	7.34847i	−0.496564	−	0.860073i	−0.999992	+	0.00396356i	$0.998738\pi$
$74$	5.00000	+	8.66025i	0.581238	+	1.00673i
$75$	−9.19239	+	15.9217i	−1.06145	+	1.83848i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−8.00000	+	13.8564i	−0.900070	+	1.55897i	−0.0726692	+	0.997356i	$0.523152\pi$
$79$	−8.00000	+	13.8564i	−0.900070	+	1.55897i	−0.827401	+	0.561611i	$0.810182\pi$
$80$	−2.12132	−	3.67423i	−0.237171	−	0.410792i
$81$	2.50000	+	4.33013i	0.277778	+	0.481125i
$82$	5.65685	−	9.79796i	0.624695	−	1.08200i
$83$	−16.9706			−1.86276			−0.931381	−	0.364047i	$-0.881395\pi$
$83$	−16.9706			−1.86276			−0.931381	+	0.364047i	$0.881395\pi$
$84$		0			0
$85$	−24.0000			−2.60317
$86$	4.00000	−	6.92820i	0.431331	−	0.747087i
$87$	−1.41421	−	2.44949i	−0.151620	−	0.262613i
$88$	0.500000	+	0.866025i	0.0533002	+	0.0923186i
$89$	3.53553	−	6.12372i	0.374766	−	0.649113i	−0.615526	−	0.788116i	$-0.711056\pi$
$89$	3.53553	−	6.12372i	0.374766	−	0.649113i	0.990292	+	0.139003i	$0.0443898\pi$
$90$	−4.24264			−0.447214
$91$		0			0
$92$	6.00000			0.625543
$93$	1.00000	−	1.73205i	0.103695	−	0.179605i
$94$	−2.12132	−	3.67423i	−0.218797	−	0.378968i
$95$		0			0
$96$	−0.707107	+	1.22474i	−0.0721688	+	0.125000i
$97$	−9.89949			−1.00514			−0.502571	−	0.864536i	$-0.667612\pi$
$97$	−9.89949			−1.00514			−0.502571	+	0.864536i	$0.667612\pi$
$98$		0			0
$99$	1.00000			0.100504
$100$	−6.50000	+	11.2583i	−0.650000	+	1.12583i
$101$	−2.82843	−	4.89898i	−0.281439	−	0.487467i	0.690300	−	0.723523i	$-0.257478\pi$
$101$	−2.82843	−	4.89898i	−0.281439	−	0.487467i	−0.971739	+	0.236056i	$0.924145\pi$
$102$	4.00000	+	6.92820i	0.396059	+	0.685994i
$103$	−9.19239	+	15.9217i	−0.905753	+	1.56881i	−0.0858496	+	0.996308i	$0.527360\pi$
$103$	−9.19239	+	15.9217i	−0.905753	+	1.56881i	−0.819903	+	0.572502i	$0.805973\pi$
$104$		0			0
$105$		0			0
$106$	8.00000			0.777029
$107$	−8.00000	+	13.8564i	−0.773389	+	1.33955i	0.162306	+	0.986740i	$0.448107\pi$
$107$	−8.00000	+	13.8564i	−0.773389	+	1.33955i	−0.935695	+	0.352809i	$0.885227\pi$
$108$	2.82843	+	4.89898i	0.272166	+	0.471405i
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	0.909935	−	0.414751i	$-0.136131\pi$
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	−0.814152	+	0.580651i	$0.802798\pi$
$110$	2.12132	−	3.67423i	0.202260	−	0.350325i
$111$	−14.1421			−1.34231
$112$		0			0
$113$	−2.00000			−0.188144			−0.0940721	−	0.995565i	$-0.529988\pi$
$113$	−2.00000			−0.188144			−0.0940721	+	0.995565i	$0.529988\pi$
$114$		0			0
$115$	−12.7279	−	22.0454i	−1.18688	−	2.05574i
$116$	−1.00000	−	1.73205i	−0.0928477	−	0.160817i
$117$		0			0
$118$	1.41421			0.130189
$119$		0			0
$120$	6.00000			0.547723
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	1.41421	+	2.44949i	0.128037	+	0.221766i
$123$	8.00000	+	13.8564i	0.721336	+	1.24939i
$124$	0.707107	−	1.22474i	0.0635001	−	0.109985i
$125$	33.9411			3.03579
$126$		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
$129$	5.65685	+	9.79796i	0.498058	+	0.862662i
$130$		0			0
$131$	9.89949	−	17.1464i	0.864923	−	1.49809i	−0.00220084	−	0.999998i	$-0.500701\pi$
$131$	9.89949	−	17.1464i	0.864923	−	1.49809i	0.867124	−	0.498093i	$-0.165966\pi$
$132$	−1.41421			−0.123091
$133$		0			0
$134$	2.00000			0.172774
$135$	12.0000	−	20.7846i	1.03280	−	1.78885i
$136$	2.82843	+	4.89898i	0.242536	+	0.420084i
$137$	9.00000	+	15.5885i	0.768922	+	1.33181i	0.938148	+	0.346235i	$0.112540\pi$
$137$	9.00000	+	15.5885i	0.768922	+	1.33181i	−0.169226	+	0.985577i	$0.554127\pi$
$138$	−4.24264	+	7.34847i	−0.361158	+	0.625543i
$139$	11.3137			0.959616			0.479808	−	0.877373i	$-0.340706\pi$
$139$	11.3137			0.959616			0.479808	+	0.877373i	$0.340706\pi$
$140$		0			0
$141$	6.00000			0.505291
$142$	1.00000	−	1.73205i	0.0839181	−	0.145350i
$143$		0			0
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	−4.24264	+	7.34847i	−0.352332	+	0.610257i
$146$	8.48528			0.702247
$147$		0			0
$148$	−10.0000			−0.821995
$149$	5.00000	−	8.66025i	0.409616	−	0.709476i	−0.585231	−	0.810867i	$-0.698996\pi$
$149$	5.00000	−	8.66025i	0.409616	−	0.709476i	0.994847	+	0.101391i	$0.0323294\pi$
$150$	−9.19239	−	15.9217i	−0.750555	−	1.30000i
$151$	−2.00000	−	3.46410i	−0.162758	−	0.281905i	0.773099	−	0.634285i	$-0.218706\pi$
$151$	−2.00000	−	3.46410i	−0.162758	−	0.281905i	−0.935857	+	0.352381i	$0.885372\pi$
$152$		0			0
$153$	5.65685			0.457330
$154$		0			0
$155$	−6.00000			−0.481932
$156$		0			0
$157$	−2.12132	−	3.67423i	−0.169300	−	0.293236i	0.768874	−	0.639400i	$-0.220817\pi$
$157$	−2.12132	−	3.67423i	−0.169300	−	0.293236i	−0.938174	+	0.346164i	$0.887484\pi$
$158$	−8.00000	−	13.8564i	−0.636446	−	1.10236i
$159$	−5.65685	+	9.79796i	−0.448618	+	0.777029i
$160$	4.24264			0.335410
$161$		0			0
$162$	−5.00000			−0.392837
$163$	5.00000	−	8.66025i	0.391630	−	0.678323i	−0.601035	−	0.799223i	$-0.705245\pi$
$163$	5.00000	−	8.66025i	0.391630	−	0.678323i	0.992665	+	0.120900i	$0.0385779\pi$
$164$	5.65685	+	9.79796i	0.441726	+	0.765092i
$165$	3.00000	+	5.19615i	0.233550	+	0.404520i
$166$	8.48528	−	14.6969i	0.658586	−	1.14070i
$167$	5.65685			0.437741			0.218870	−	0.975754i	$-0.429763\pi$
$167$	5.65685			0.437741			0.218870	+	0.975754i	$0.429763\pi$
$168$		0			0
$169$	−13.0000			−1.00000
$170$	12.0000	−	20.7846i	0.920358	−	1.59411i
$171$		0			0
$172$	4.00000	+	6.92820i	0.304997	+	0.528271i
$173$	5.65685	−	9.79796i	0.430083	−	0.744925i	−0.566797	−	0.823857i	$-0.691818\pi$
$173$	5.65685	−	9.79796i	0.430083	−	0.744925i	0.996880	+	0.0789322i	$0.0251511\pi$
$174$	2.82843			0.214423
$175$		0			0
$176$	−1.00000			−0.0753778
$177$	−1.00000	+	1.73205i	−0.0751646	+	0.130189i
$178$	3.53553	+	6.12372i	0.264999	+	0.458993i
$179$	−6.00000	−	10.3923i	−0.448461	−	0.776757i	0.549825	−	0.835280i	$-0.314694\pi$
$179$	−6.00000	−	10.3923i	−0.448461	−	0.776757i	−0.998286	+	0.0585225i	$0.981361\pi$
$180$	2.12132	−	3.67423i	0.158114	−	0.273861i
$181$	−7.07107			−0.525588			−0.262794	−	0.964852i	$-0.584644\pi$
$181$	−7.07107			−0.525588			−0.262794	+	0.964852i	$0.584644\pi$
$182$		0			0
$183$	−4.00000			−0.295689
$184$	−3.00000	+	5.19615i	−0.221163	+	0.383065i
$185$	21.2132	+	36.7423i	1.55963	+	2.70135i
$186$	1.00000	+	1.73205i	0.0733236	+	0.127000i
$187$	−2.82843	+	4.89898i	−0.206835	+	0.358249i
$188$	4.24264			0.309426
$189$		0			0
$190$		0			0
$191$	−8.00000	+	13.8564i	−0.578860	+	1.00261i	0.416751	+	0.909021i	$0.363169\pi$
$191$	−8.00000	+	13.8564i	−0.578860	+	1.00261i	−0.995610	+	0.0935936i	$0.970165\pi$
$192$	−0.707107	−	1.22474i	−0.0510310	−	0.0883883i
$193$	3.00000	+	5.19615i	0.215945	+	0.374027i	0.953564	−	0.301189i	$-0.0973836\pi$
$193$	3.00000	+	5.19615i	0.215945	+	0.374027i	−0.737620	+	0.675216i	$0.764050\pi$
$194$	4.94975	−	8.57321i	0.355371	−	0.615521i
$195$		0			0
$196$		0			0
$197$	22.0000			1.56744			0.783718	−	0.621117i	$-0.213321\pi$
$197$	22.0000			1.56744			0.783718	+	0.621117i	$0.213321\pi$
$198$	−0.500000	+	0.866025i	−0.0355335	+	0.0615457i
$199$	0.707107	+	1.22474i	0.0501255	+	0.0868199i	0.889999	−	0.455962i	$-0.150705\pi$
$199$	0.707107	+	1.22474i	0.0501255	+	0.0868199i	−0.839874	+	0.542781i	$0.817371\pi$
$200$	−6.50000	−	11.2583i	−0.459619	−	0.796084i
$201$	−1.41421	+	2.44949i	−0.0997509	+	0.172774i
$202$	5.65685			0.398015
$203$		0			0
$204$	−8.00000			−0.560112
$205$	24.0000	−	41.5692i	1.67623	−	2.90332i
$206$	−9.19239	−	15.9217i	−0.640464	−	1.10932i
$207$	3.00000	+	5.19615i	0.208514	+	0.361158i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	8.00000			0.550743			0.275371	−	0.961338i	$-0.411199\pi$
$211$	8.00000			0.550743			0.275371	+	0.961338i	$0.411199\pi$
$212$	−4.00000	+	6.92820i	−0.274721	+	0.475831i
$213$	1.41421	+	2.44949i	0.0969003	+	0.167836i
$214$	−8.00000	−	13.8564i	−0.546869	−	0.947204i
$215$	16.9706	−	29.3939i	1.15738	−	2.00465i
$216$	−5.65685			−0.384900
$217$		0			0
$218$	−2.00000			−0.135457
$219$	−6.00000	+	10.3923i	−0.405442	+	0.702247i
$220$	2.12132	+	3.67423i	0.143019	+	0.247717i
$221$		0			0
$222$	7.07107	−	12.2474i	0.474579	−	0.821995i
$223$	−21.2132			−1.42054			−0.710271	−	0.703929i	$-0.751427\pi$
$223$	−21.2132			−1.42054			−0.710271	+	0.703929i	$0.751427\pi$
$224$		0			0
$225$	−13.0000			−0.866667
$226$	1.00000	−	1.73205i	0.0665190	−	0.115214i
$227$	7.07107	+	12.2474i	0.469323	+	0.812892i	0.999385	−	0.0350674i	$-0.0111646\pi$
$227$	7.07107	+	12.2474i	0.469323	+	0.812892i	−0.530062	+	0.847959i	$0.677831\pi$
$228$		0			0
$229$	−4.94975	+	8.57321i	−0.327089	+	0.566534i	−0.981933	−	0.189230i	$-0.939401\pi$
$229$	−4.94975	+	8.57321i	−0.327089	+	0.566534i	0.654844	+	0.755764i	$0.272734\pi$
$230$	25.4558			1.67851
$231$		0			0
$232$	2.00000			0.131306
$233$	−7.00000	+	12.1244i	−0.458585	+	0.794293i	−0.998886	−	0.0471787i	$-0.984977\pi$
$233$	−7.00000	+	12.1244i	−0.458585	+	0.794293i	0.540301	+	0.841472i	$0.318310\pi$
$234$		0			0
$235$	−9.00000	−	15.5885i	−0.587095	−	1.01688i
$236$	−0.707107	+	1.22474i	−0.0460287	+	0.0797241i
$237$	22.6274			1.46981
$238$		0			0
$239$	−12.0000			−0.776215			−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000			−0.776215			−0.388108	+	0.921614i	$0.626871\pi$
$240$	−3.00000	+	5.19615i	−0.193649	+	0.335410i
$241$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$241$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$242$	−0.500000	−	0.866025i	−0.0321412	−	0.0556702i
$243$	−4.94975	+	8.57321i	−0.317526	+	0.549972i
$244$	−2.82843			−0.181071
$245$		0			0
$246$	−16.0000			−1.02012
$247$		0			0
$248$	0.707107	+	1.22474i	0.0449013	+	0.0777714i
$249$	12.0000	+	20.7846i	0.760469	+	1.31717i
$250$	−16.9706	+	29.3939i	−1.07331	+	1.85903i
$251$	18.3848			1.16044			0.580218	−	0.814461i	$-0.302967\pi$
$251$	18.3848			1.16044			0.580218	+	0.814461i	$0.302967\pi$
$252$		0			0
$253$	−6.00000			−0.377217
$254$	−8.00000	+	13.8564i	−0.501965	+	0.869428i
$255$	16.9706	+	29.3939i	1.06274	+	1.84072i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−0.707107	+	1.22474i	−0.0441081	+	0.0763975i	−0.887237	−	0.461315i	$-0.847378\pi$
$257$	−0.707107	+	1.22474i	−0.0441081	+	0.0763975i	0.843129	+	0.537712i	$0.180711\pi$
$258$	−11.3137			−0.704361
$259$		0			0
$260$		0			0
$261$	1.00000	−	1.73205i	0.0618984	−	0.107211i
$262$	9.89949	+	17.1464i	0.611593	+	1.05931i
$263$	4.00000	+	6.92820i	0.246651	+	0.427211i	0.962594	−	0.270947i	$-0.0873367\pi$
$263$	4.00000	+	6.92820i	0.246651	+	0.427211i	−0.715944	+	0.698158i	$0.754003\pi$
$264$	0.707107	−	1.22474i	0.0435194	−	0.0753778i
$265$	33.9411			2.08499
$266$		0			0
$267$	−10.0000			−0.611990
$268$	−1.00000	+	1.73205i	−0.0610847	+	0.105802i
$269$	−9.19239	−	15.9217i	−0.560470	−	0.970762i	−0.997455	−	0.0712937i	$-0.977287\pi$
$269$	−9.19239	−	15.9217i	−0.560470	−	0.970762i	0.436986	−	0.899469i	$-0.356046\pi$
$270$	12.0000	+	20.7846i	0.730297	+	1.26491i
$271$	4.24264	−	7.34847i	0.257722	−	0.446388i	−0.707909	−	0.706303i	$-0.750361\pi$
$271$	4.24264	−	7.34847i	0.257722	−	0.446388i	0.965631	+	0.259916i	$0.0836948\pi$
$272$	−5.65685			−0.342997
$273$		0			0
$274$	−18.0000			−1.08742
$275$	6.50000	−	11.2583i	0.391965	−	0.678903i
$276$	−4.24264	−	7.34847i	−0.255377	−	0.442326i
$277$	1.00000	+	1.73205i	0.0600842	+	0.104069i	0.894503	−	0.447062i	$-0.147530\pi$
$277$	1.00000	+	1.73205i	0.0600842	+	0.104069i	−0.834419	+	0.551131i	$0.814196\pi$
$278$	−5.65685	+	9.79796i	−0.339276	+	0.587643i
$279$	1.41421			0.0846668
$280$		0			0
$281$	−14.0000			−0.835170			−0.417585	−	0.908638i	$-0.637123\pi$
$281$	−14.0000			−0.835170			−0.417585	+	0.908638i	$0.637123\pi$
$282$	−3.00000	+	5.19615i	−0.178647	+	0.309426i
$283$	9.89949	+	17.1464i	0.588464	+	1.01925i	0.994434	+	0.105363i	$0.0336004\pi$
$283$	9.89949	+	17.1464i	0.588464	+	1.01925i	−0.405970	+	0.913886i	$0.633066\pi$
$284$	1.00000	+	1.73205i	0.0593391	+	0.102778i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−1.00000			−0.0589256
$289$	−7.50000	+	12.9904i	−0.441176	+	0.764140i
$290$	−4.24264	−	7.34847i	−0.249136	−	0.431517i
$291$	7.00000	+	12.1244i	0.410347	+	0.710742i
$292$	−4.24264	+	7.34847i	−0.248282	+	0.430037i
$293$	−8.48528			−0.495715			−0.247858	−	0.968796i	$-0.579727\pi$
$293$	−8.48528			−0.495715			−0.247858	+	0.968796i	$0.579727\pi$
$294$		0			0
$295$	6.00000			0.349334
$296$	5.00000	−	8.66025i	0.290619	−	0.503367i
$297$	−2.82843	−	4.89898i	−0.164122	−	0.284268i
$298$	5.00000	+	8.66025i	0.289642	+	0.501675i
$299$		0			0
$300$	18.3848			1.06145
$301$		0			0
$302$	4.00000			0.230174
$303$	−4.00000	+	6.92820i	−0.229794	+	0.398015i
$304$		0			0
$305$	6.00000	+	10.3923i	0.343559	+	0.595062i
$306$	−2.82843	+	4.89898i	−0.161690	+	0.280056i
$307$	−25.4558			−1.45284			−0.726421	−	0.687250i	$-0.758818\pi$
$307$	−25.4558			−1.45284			−0.726421	+	0.687250i	$0.758818\pi$
$308$		0			0
$309$	26.0000			1.47909
$310$	3.00000	−	5.19615i	0.170389	−	0.295122i
$311$	−9.19239	−	15.9217i	−0.521253	−	0.902836i	−0.999694	−	0.0247167i	$-0.992132\pi$
$311$	−9.19239	−	15.9217i	−0.521253	−	0.902836i	0.478442	−	0.878119i	$-0.341202\pi$
$312$		0			0
$313$	6.36396	−	11.0227i	0.359712	−	0.623040i	−0.628200	−	0.778052i	$-0.716208\pi$
$313$	6.36396	−	11.0227i	0.359712	−	0.623040i	0.987913	+	0.155012i	$0.0495415\pi$
$314$	4.24264			0.239426
$315$		0			0
$316$	16.0000			0.900070
$317$	−15.0000	+	25.9808i	−0.842484	+	1.45922i	0.0453045	+	0.998973i	$0.485574\pi$
$317$	−15.0000	+	25.9808i	−0.842484	+	1.45922i	−0.887788	+	0.460252i	$0.847759\pi$
$318$	−5.65685	−	9.79796i	−0.317221	−	0.549442i
$319$	1.00000	+	1.73205i	0.0559893	+	0.0969762i
$320$	−2.12132	+	3.67423i	−0.118585	+	0.205396i
$321$	22.6274			1.26294
$322$		0			0
$323$		0			0
$324$	2.50000	−	4.33013i	0.138889	−	0.240563i
$325$		0			0
$326$	5.00000	+	8.66025i	0.276924	+	0.479647i
$327$	1.41421	−	2.44949i	0.0782062	−	0.135457i
$328$	−11.3137			−0.624695
$329$		0			0
$330$	−6.00000			−0.330289
$331$	−10.0000	+	17.3205i	−0.549650	+	0.952021i	0.448649	+	0.893708i	$0.351905\pi$
$331$	−10.0000	+	17.3205i	−0.549650	+	0.952021i	−0.998298	+	0.0583130i	$0.981428\pi$
$332$	8.48528	+	14.6969i	0.465690	+	0.806599i
$333$	−5.00000	−	8.66025i	−0.273998	−	0.474579i
$334$	−2.82843	+	4.89898i	−0.154765	+	0.268060i
$335$	8.48528			0.463600
$336$		0			0
$337$	2.00000			0.108947			0.0544735	−	0.998515i	$-0.482652\pi$
$337$	2.00000			0.108947			0.0544735	+	0.998515i	$0.482652\pi$
$338$	6.50000	−	11.2583i	0.353553	−	0.612372i
$339$	1.41421	+	2.44949i	0.0768095	+	0.133038i
$340$	12.0000	+	20.7846i	0.650791	+	1.12720i
$341$	−0.707107	+	1.22474i	−0.0382920	+	0.0663237i
$342$		0			0
$343$		0			0
$344$	−8.00000			−0.431331
$345$	−18.0000	+	31.1769i	−0.969087	+	1.67851i
$346$	5.65685	+	9.79796i	0.304114	+	0.526742i
$347$	−10.0000	−	17.3205i	−0.536828	−	0.929814i	−0.999072	−	0.0430610i	$-0.986289\pi$
$347$	−10.0000	−	17.3205i	−0.536828	−	0.929814i	0.462244	−	0.886753i	$-0.347044\pi$
$348$	−1.41421	+	2.44949i	−0.0758098	+	0.131306i
$349$	14.1421			0.757011			0.378506	−	0.925599i	$-0.376438\pi$
$349$	14.1421			0.757011			0.378506	+	0.925599i	$0.376438\pi$
$350$		0			0
$351$		0			0
$352$	0.500000	−	0.866025i	0.0266501	−	0.0461593i
$353$	−0.707107	−	1.22474i	−0.0376355	−	0.0651866i	0.846594	−	0.532239i	$-0.178649\pi$
$353$	−0.707107	−	1.22474i	−0.0376355	−	0.0651866i	−0.884230	+	0.467052i	$0.845316\pi$
$354$	−1.00000	−	1.73205i	−0.0531494	−	0.0920575i
$355$	4.24264	−	7.34847i	0.225176	−	0.390016i
$356$	−7.07107			−0.374766
$357$		0			0
$358$	12.0000			0.634220
$359$	6.00000	−	10.3923i	0.316668	−	0.548485i	−0.663123	−	0.748511i	$-0.730769\pi$
$359$	6.00000	−	10.3923i	0.316668	−	0.548485i	0.979791	+	0.200026i	$0.0641026\pi$
$360$	2.12132	+	3.67423i	0.111803	+	0.193649i
$361$	9.50000	+	16.4545i	0.500000	+	0.866025i
$362$	3.53553	−	6.12372i	0.185824	−	0.321856i
$363$	1.41421			0.0742270
$364$		0			0
$365$	36.0000			1.88433
$366$	2.00000	−	3.46410i	0.104542	−	0.181071i
$367$	10.6066	+	18.3712i	0.553660	+	0.958967i	0.998006	+	0.0631123i	$0.0201026\pi$
$367$	10.6066	+	18.3712i	0.553660	+	0.958967i	−0.444346	+	0.895855i	$0.646564\pi$
$368$	−3.00000	−	5.19615i	−0.156386	−	0.270868i
$369$	−5.65685	+	9.79796i	−0.294484	+	0.510061i
$370$	−42.4264			−2.20564
$371$		0			0
$372$	−2.00000			−0.103695
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	−0.707055	−	0.707159i	$-0.749977\pi$
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	0.965945	+	0.258748i	$0.0833099\pi$
$374$	−2.82843	−	4.89898i	−0.146254	−	0.253320i
$375$	−24.0000	−	41.5692i	−1.23935	−	2.14663i
$376$	−2.12132	+	3.67423i	−0.109399	+	0.189484i
$377$		0			0
$378$		0			0
$379$	−6.00000			−0.308199			−0.154100	−	0.988055i	$-0.549248\pi$
$379$	−6.00000			−0.308199			−0.154100	+	0.988055i	$0.549248\pi$
$380$		0			0
$381$	−11.3137	−	19.5959i	−0.579619	−	1.00393i
$382$	−8.00000	−	13.8564i	−0.409316	−	0.708955i
$383$	−7.77817	+	13.4722i	−0.397446	+	0.688397i	−0.993410	−	0.114614i	$-0.963437\pi$
$383$	−7.77817	+	13.4722i	−0.397446	+	0.688397i	0.595964	+	0.803011i	$0.296770\pi$
$384$	1.41421			0.0721688
$385$		0			0
$386$	−6.00000			−0.305392
$387$	−4.00000	+	6.92820i	−0.203331	+	0.352180i
$388$	4.94975	+	8.57321i	0.251285	+	0.435239i
$389$	12.0000	+	20.7846i	0.608424	+	1.05382i	0.991500	+	0.130105i	$0.0415314\pi$
$389$	12.0000	+	20.7846i	0.608424	+	1.05382i	−0.383076	+	0.923717i	$0.625135\pi$
$390$		0			0
$391$	−33.9411			−1.71648
$392$		0			0
$393$	−28.0000			−1.41241
$394$	−11.0000	+	19.0526i	−0.554172	+	0.959854i
$395$	−33.9411	−	58.7878i	−1.70776	−	2.95793i
$396$	−0.500000	−	0.866025i	−0.0251259	−	0.0435194i
$397$	−6.36396	+	11.0227i	−0.319398	+	0.553214i	−0.980363	−	0.197203i	$-0.936814\pi$
$397$	−6.36396	+	11.0227i	−0.319398	+	0.553214i	0.660965	+	0.750417i	$0.270147\pi$
$398$	−1.41421			−0.0708881
$399$		0			0
$400$	13.0000			0.650000
$401$	−6.00000	+	10.3923i	−0.299626	+	0.518967i	−0.976050	−	0.217545i	$-0.930195\pi$
$401$	−6.00000	+	10.3923i	−0.299626	+	0.518967i	0.676425	+	0.736512i	$0.263528\pi$
$402$	−1.41421	−	2.44949i	−0.0705346	−	0.122169i
$403$		0			0
$404$	−2.82843	+	4.89898i	−0.140720	+	0.243733i
$405$	−21.2132			−1.05409
$406$		0			0
$407$	10.0000			0.495682
$408$	4.00000	−	6.92820i	0.198030	−	0.342997i
$409$	1.41421	+	2.44949i	0.0699284	+	0.121119i	0.898870	−	0.438216i	$-0.144390\pi$
$409$	1.41421	+	2.44949i	0.0699284	+	0.121119i	−0.828941	+	0.559336i	$0.811056\pi$
$410$	24.0000	+	41.5692i	1.18528	+	2.05296i
$411$	12.7279	−	22.0454i	0.627822	−	1.08742i
$412$	18.3848			0.905753
$413$		0			0
$414$	−6.00000			−0.294884
$415$	36.0000	−	62.3538i	1.76717	−	3.06083i
$416$		0			0
$417$	−8.00000	−	13.8564i	−0.391762	−	0.678551i
$418$		0			0
$419$	24.0416			1.17451			0.587255	−	0.809402i	$-0.300208\pi$
$419$	24.0416			1.17451			0.587255	+	0.809402i	$0.300208\pi$
$420$		0			0
$421$	−20.0000			−0.974740			−0.487370	−	0.873195i	$-0.662044\pi$
$421$	−20.0000			−0.974740			−0.487370	+	0.873195i	$0.662044\pi$
$422$	−4.00000	+	6.92820i	−0.194717	+	0.337260i
$423$	2.12132	+	3.67423i	0.103142	+	0.178647i
$424$	−4.00000	−	6.92820i	−0.194257	−	0.336463i
$425$	36.7696	−	63.6867i	1.78359	−	3.08926i
$426$	−2.82843			−0.137038
$427$		0			0
$428$	16.0000			0.773389
$429$		0			0
$430$	16.9706	+	29.3939i	0.818393	+	1.41750i
$431$	−16.0000	−	27.7128i	−0.770693	−	1.33488i	−0.937184	−	0.348836i	$-0.886577\pi$
$431$	−16.0000	−	27.7128i	−0.770693	−	1.33488i	0.166491	−	0.986043i	$-0.446756\pi$
$432$	2.82843	−	4.89898i	0.136083	−	0.235702i
$433$	−12.7279			−0.611665			−0.305832	−	0.952085i	$-0.598935\pi$
$433$	−12.7279			−0.611665			−0.305832	+	0.952085i	$0.598935\pi$
$434$		0			0
$435$	12.0000			0.575356
$436$	1.00000	−	1.73205i	0.0478913	−	0.0829502i
$437$		0			0
$438$	−6.00000	−	10.3923i	−0.286691	−	0.496564i
$439$	12.7279	−	22.0454i	0.607471	−	1.05217i	−0.384185	−	0.923256i	$-0.625518\pi$
$439$	12.7279	−	22.0454i	0.607471	−	1.05217i	0.991656	−	0.128914i	$-0.0411491\pi$
$440$	−4.24264			−0.202260
$441$		0			0
$442$		0			0
$443$	−18.0000	+	31.1769i	−0.855206	+	1.48126i	0.0212481	+	0.999774i	$0.493236\pi$
$443$	−18.0000	+	31.1769i	−0.855206	+	1.48126i	−0.876454	+	0.481486i	$0.840097\pi$
$444$	7.07107	+	12.2474i	0.335578	+	0.581238i
$445$	15.0000	+	25.9808i	0.711068	+	1.23161i
$446$	10.6066	−	18.3712i	0.502237	−	0.869900i
$447$	−14.1421			−0.668900
$448$		0			0
$449$	−20.0000			−0.943858			−0.471929	−	0.881636i	$-0.656442\pi$
$449$	−20.0000			−0.943858			−0.471929	+	0.881636i	$0.656442\pi$
$450$	6.50000	−	11.2583i	0.306413	−	0.530723i
$451$	−5.65685	−	9.79796i	−0.266371	−	0.461368i
$452$	1.00000	+	1.73205i	0.0470360	+	0.0814688i
$453$	−2.82843	+	4.89898i	−0.132891	+	0.230174i
$454$	−14.1421			−0.663723
$455$		0			0
$456$		0			0
$457$	−7.00000	+	12.1244i	−0.327446	+	0.567153i	−0.982004	−	0.188858i	$-0.939521\pi$
$457$	−7.00000	+	12.1244i	−0.327446	+	0.567153i	0.654558	+	0.756012i	$0.272855\pi$
$458$	−4.94975	−	8.57321i	−0.231287	−	0.400600i
$459$	−16.0000	−	27.7128i	−0.746816	−	1.29352i
$460$	−12.7279	+	22.0454i	−0.593442	+	1.02787i
$461$	2.82843			0.131733			0.0658665	−	0.997828i	$-0.479019\pi$
$461$	2.82843			0.131733			0.0658665	+	0.997828i	$0.479019\pi$
$462$		0			0
$463$	26.0000			1.20832			0.604161	−	0.796862i	$-0.293508\pi$
$463$	26.0000			1.20832			0.604161	+	0.796862i	$0.293508\pi$
$464$	−1.00000	+	1.73205i	−0.0464238	+	0.0804084i
$465$	4.24264	+	7.34847i	0.196748	+	0.340777i
$466$	−7.00000	−	12.1244i	−0.324269	−	0.561650i
$467$	2.12132	−	3.67423i	0.0981630	−	0.170023i	−0.812761	−	0.582597i	$-0.802037\pi$
$467$	2.12132	−	3.67423i	0.0981630	−	0.170023i	0.910924	+	0.412574i	$0.135370\pi$
$468$		0			0
$469$		0			0
$470$	18.0000			0.830278
$471$	−3.00000	+	5.19615i	−0.138233	+	0.239426i
$472$	−0.707107	−	1.22474i	−0.0325472	−	0.0563735i
$473$	−4.00000	−	6.92820i	−0.183920	−	0.318559i
$474$	−11.3137	+	19.5959i	−0.519656	+	0.900070i
$475$		0			0
$476$		0			0
$477$	−8.00000			−0.366295
$478$	6.00000	−	10.3923i	0.274434	−	0.475333i
$479$	−1.41421	−	2.44949i	−0.0646171	−	0.111920i	0.831907	−	0.554915i	$-0.187249\pi$
$479$	−1.41421	−	2.44949i	−0.0646171	−	0.111920i	−0.896524	+	0.442995i	$0.853916\pi$
$480$	−3.00000	−	5.19615i	−0.136931	−	0.237171i
$481$		0			0
$482$		0			0
$483$		0			0
$484$	1.00000			0.0454545
$485$	21.0000	−	36.3731i	0.953561	−	1.65162i
$486$	−4.94975	−	8.57321i	−0.224525	−	0.388889i
$487$	−1.00000	−	1.73205i	−0.0453143	−	0.0784867i	0.842479	−	0.538730i	$-0.181096\pi$
$487$	−1.00000	−	1.73205i	−0.0453143	−	0.0784867i	−0.887793	+	0.460243i	$0.847762\pi$
$488$	1.41421	−	2.44949i	0.0640184	−	0.110883i
$489$	−14.1421			−0.639529
$490$		0			0
$491$	−12.0000			−0.541552			−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000			−0.541552			−0.270776	+	0.962642i	$0.587280\pi$
$492$	8.00000	−	13.8564i	0.360668	−	0.624695i
$493$	5.65685	+	9.79796i	0.254772	+	0.441278i
$494$		0			0
$495$	−2.12132	+	3.67423i	−0.0953463	+	0.165145i
$496$	−1.41421			−0.0635001
$497$		0			0
$498$	−24.0000			−1.07547
$499$	−3.00000	+	5.19615i	−0.134298	+	0.232612i	−0.925329	−	0.379165i	$-0.876211\pi$
$499$	−3.00000	+	5.19615i	−0.134298	+	0.232612i	0.791031	+	0.611776i	$0.209545\pi$
$500$	−16.9706	−	29.3939i	−0.758947	−	1.31453i
$501$	−4.00000	−	6.92820i	−0.178707	−	0.309529i
$502$	−9.19239	+	15.9217i	−0.410276	+	0.710620i
$503$	31.1127			1.38725			0.693623	−	0.720338i	$-0.256013\pi$
$503$	31.1127			1.38725			0.693623	+	0.720338i	$0.256013\pi$
$504$		0			0
$505$	24.0000			1.06799
$506$	3.00000	−	5.19615i	0.133366	−	0.230997i
$507$	9.19239	+	15.9217i	0.408248	+	0.707107i
$508$	−8.00000	−	13.8564i	−0.354943	−	0.614779i
$509$	−6.36396	+	11.0227i	−0.282078	+	0.488573i	−0.971896	−	0.235409i	$-0.924357\pi$
$509$	−6.36396	+	11.0227i	−0.282078	+	0.488573i	0.689819	+	0.723982i	$0.257690\pi$
$510$	−33.9411			−1.50294
$511$		0			0
$512$	1.00000			0.0441942
$513$		0			0
$514$	−0.707107	−	1.22474i	−0.0311891	−	0.0540212i
$515$	−39.0000	−	67.5500i	−1.71855	−	2.97661i
$516$	5.65685	−	9.79796i	0.249029	−	0.431331i
$517$	−4.24264			−0.186591
$518$		0			0
$519$	−16.0000			−0.702322
$520$		0			0
$521$	−0.707107	−	1.22474i	−0.0309789	−	0.0536570i	0.850120	−	0.526589i	$-0.176529\pi$
$521$	−0.707107	−	1.22474i	−0.0309789	−	0.0536570i	−0.881099	+	0.472931i	$0.843196\pi$
$522$	1.00000	+	1.73205i	0.0437688	+	0.0758098i
$523$	−4.24264	+	7.34847i	−0.185518	+	0.321326i	−0.943751	−	0.330657i	$-0.892730\pi$
$523$	−4.24264	+	7.34847i	−0.185518	+	0.321326i	0.758233	+	0.651984i	$0.226063\pi$
$524$	−19.7990			−0.864923
$525$		0			0
$526$	−8.00000			−0.348817
$527$	−4.00000	+	6.92820i	−0.174243	+	0.301797i
$528$	0.707107	+	1.22474i	0.0307729	+	0.0533002i
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$	−16.9706	+	29.3939i	−0.737154	+	1.27679i
$531$	−1.41421			−0.0613716
$532$		0			0
$533$		0			0
$534$	5.00000	−	8.66025i	0.216371	−	0.374766i
$535$	−33.9411	−	58.7878i	−1.46740	−	2.54162i
$536$	−1.00000	−	1.73205i	−0.0431934	−	0.0748132i
$537$	−8.48528	+	14.6969i	−0.366167	+	0.634220i
$538$	18.3848			0.792624
$539$		0			0
$540$	−24.0000			−1.03280
$541$	15.0000	−	25.9808i	0.644900	−	1.11700i	−0.339424	−	0.940633i	$-0.610232\pi$
$541$	15.0000	−	25.9808i	0.644900	−	1.11700i	0.984325	−	0.176367i	$-0.0564345\pi$
$542$	4.24264	+	7.34847i	0.182237	+	0.315644i
$543$	5.00000	+	8.66025i	0.214571	+	0.371647i
$544$	2.82843	−	4.89898i	0.121268	−	0.210042i
$545$	−8.48528			−0.363470
$546$		0			0
$547$	44.0000			1.88130			0.940652	−	0.339372i	$-0.110215\pi$
$547$	44.0000			1.88130			0.940652	+	0.339372i	$0.110215\pi$
$548$	9.00000	−	15.5885i	0.384461	−	0.665906i
$549$	−1.41421	−	2.44949i	−0.0603572	−	0.104542i
$550$	6.50000	+	11.2583i	0.277161	+	0.480057i
$551$		0			0
$552$	8.48528			0.361158
$553$		0			0
$554$	−2.00000			−0.0849719
$555$	30.0000	−	51.9615i	1.27343	−	2.20564i
$556$	−5.65685	−	9.79796i	−0.239904	−	0.415526i
$557$	15.0000	+	25.9808i	0.635570	+	1.10084i	0.986394	+	0.164399i	$0.0525683\pi$
$557$	15.0000	+	25.9808i	0.635570	+	1.10084i	−0.350824	+	0.936442i	$0.614098\pi$
$558$	−0.707107	+	1.22474i	−0.0299342	+	0.0518476i
$559$		0			0
$560$		0			0
$561$	8.00000			0.337760
$562$	7.00000	−	12.1244i	0.295277	−	0.511435i
$563$	−11.3137	−	19.5959i	−0.476816	−	0.825869i	0.522831	−	0.852436i	$-0.324876\pi$
$563$	−11.3137	−	19.5959i	−0.476816	−	0.825869i	−0.999647	+	0.0265668i	$0.991543\pi$
$564$	−3.00000	−	5.19615i	−0.126323	−	0.218797i
$565$	4.24264	−	7.34847i	0.178489	−	0.309152i
$566$	−19.7990			−0.832214
$567$		0			0
$568$	−2.00000			−0.0839181
$569$	−15.0000	+	25.9808i	−0.628833	+	1.08917i	0.358954	+	0.933355i	$0.383134\pi$
$569$	−15.0000	+	25.9808i	−0.628833	+	1.08917i	−0.987786	+	0.155815i	$0.950200\pi$
$570$		0			0
$571$	−4.00000	−	6.92820i	−0.167395	−	0.289936i	0.770108	−	0.637913i	$-0.220202\pi$
$571$	−4.00000	−	6.92820i	−0.167395	−	0.289936i	−0.937503	+	0.347977i	$0.886869\pi$
$572$		0			0
$573$	22.6274			0.945274
$574$		0			0
$575$	78.0000			3.25282
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	3.53553	+	6.12372i	0.147186	+	0.254934i	0.930186	−	0.367087i	$-0.119645\pi$
$577$	3.53553	+	6.12372i	0.147186	+	0.254934i	−0.783000	+	0.622021i	$0.786312\pi$
$578$	−7.50000	−	12.9904i	−0.311959	−	0.540329i
$579$	4.24264	−	7.34847i	0.176318	−	0.305392i
$580$	8.48528			0.352332
$581$		0			0
$582$	−14.0000			−0.580319
$583$	4.00000	−	6.92820i	0.165663	−	0.286937i
$584$	−4.24264	−	7.34847i	−0.175562	−	0.304082i
$585$		0			0
$586$	4.24264	−	7.34847i	0.175262	−	0.303562i
$587$	−26.8701			−1.10905			−0.554523	−	0.832168i	$-0.687099\pi$
$587$	−26.8701			−1.10905			−0.554523	+	0.832168i	$0.687099\pi$
$588$		0			0
$589$		0			0
$590$	−3.00000	+	5.19615i	−0.123508	+	0.213922i
$591$	−15.5563	−	26.9444i	−0.639903	−	1.10834i
$592$	5.00000	+	8.66025i	0.205499	+	0.355934i
$593$	−21.2132	+	36.7423i	−0.871122	+	1.50883i	−0.0102845	+	0.999947i	$0.503274\pi$
$593$	−21.2132	+	36.7423i	−0.871122	+	1.50883i	−0.860837	+	0.508880i	$0.830060\pi$
$594$	5.65685			0.232104
$595$		0			0
$596$	−10.0000			−0.409616
$597$	1.00000	−	1.73205i	0.0409273	−	0.0708881i
$598$		0			0
$599$	3.00000	+	5.19615i	0.122577	+	0.212309i	0.920783	−	0.390075i	$-0.127551\pi$
$599$	3.00000	+	5.19615i	0.122577	+	0.212309i	−0.798206	+	0.602384i	$0.794218\pi$
$600$	−9.19239	+	15.9217i	−0.375278	+	0.650000i
$601$	5.65685			0.230748			0.115374	−	0.993322i	$-0.463193\pi$
$601$	5.65685			0.230748			0.115374	+	0.993322i	$0.463193\pi$
$602$		0			0
$603$	−2.00000			−0.0814463
$604$	−2.00000	+	3.46410i	−0.0813788	+	0.140952i
$605$	−2.12132	−	3.67423i	−0.0862439	−	0.149379i
$606$	−4.00000	−	6.92820i	−0.162489	−	0.281439i
$607$	−8.48528	+	14.6969i	−0.344407	+	0.596530i	−0.985246	−	0.171145i	$-0.945253\pi$
$607$	−8.48528	+	14.6969i	−0.344407	+	0.596530i	0.640839	+	0.767675i	$0.278587\pi$
$608$		0			0
$609$		0			0
$610$	−12.0000			−0.485866
$611$		0			0
$612$	−2.82843	−	4.89898i	−0.114332	−	0.198030i
$613$	5.00000	+	8.66025i	0.201948	+	0.349784i	0.949156	−	0.314806i	$-0.101939\pi$
$613$	5.00000	+	8.66025i	0.201948	+	0.349784i	−0.747208	+	0.664590i	$0.768606\pi$
$614$	12.7279	−	22.0454i	0.513657	−	0.889680i
$615$	−67.8823			−2.73728
$616$		0			0
$617$	34.0000			1.36879			0.684394	−	0.729112i	$-0.260067\pi$
$617$	34.0000			1.36879			0.684394	+	0.729112i	$0.260067\pi$
$618$	−13.0000	+	22.5167i	−0.522937	+	0.905753i
$619$	−4.94975	−	8.57321i	−0.198947	−	0.344587i	0.749240	−	0.662298i	$-0.230419\pi$
$619$	−4.94975	−	8.57321i	−0.198947	−	0.344587i	−0.948187	+	0.317712i	$0.897086\pi$
$620$	3.00000	+	5.19615i	0.120483	+	0.208683i
$621$	16.9706	−	29.3939i	0.681005	−	1.17954i
$622$	18.3848			0.737162
$623$		0			0
$624$		0			0
$625$	−39.5000	+	68.4160i	−1.58000	+	2.73664i
$626$	6.36396	+	11.0227i	0.254355	+	0.440556i
$627$		0			0
$628$	−2.12132	+	3.67423i	−0.0846499	+	0.146618i
$629$	56.5685			2.25554
$630$		0			0
$631$	24.0000			0.955425			0.477712	−	0.878516i	$-0.341466\pi$
$631$	24.0000			0.955425			0.477712	+	0.878516i	$0.341466\pi$
$632$	−8.00000	+	13.8564i	−0.318223	+	0.551178i
$633$	−5.65685	−	9.79796i	−0.224840	−	0.389434i
$634$	−15.0000	−	25.9808i	−0.595726	−	1.03183i
$635$	−33.9411	+	58.7878i	−1.34691	+	2.33292i
$636$	11.3137			0.448618
$637$		0			0
$638$	−2.00000			−0.0791808
$639$	−1.00000	+	1.73205i	−0.0395594	+	0.0685189i
$640$	−2.12132	−	3.67423i	−0.0838525	−	0.145237i
$641$	17.0000	+	29.4449i	0.671460	+	1.16300i	0.977490	+	0.210981i	$0.0676657\pi$
$641$	17.0000	+	29.4449i	0.671460	+	1.16300i	−0.306031	+	0.952022i	$0.599001\pi$
$642$	−11.3137	+	19.5959i	−0.446516	+	0.773389i
$643$	−38.1838			−1.50582			−0.752910	−	0.658123i	$-0.771351\pi$
$643$	−38.1838			−1.50582			−0.752910	+	0.658123i	$0.771351\pi$
$644$		0			0
$645$	−48.0000			−1.89000
$646$		0			0
$647$	7.77817	+	13.4722i	0.305792	+	0.529647i	0.977437	−	0.211226i	$-0.0677456\pi$
$647$	7.77817	+	13.4722i	0.305792	+	0.529647i	−0.671646	+	0.740873i	$0.734412\pi$
$648$	2.50000	+	4.33013i	0.0982093	+	0.170103i
$649$	0.707107	−	1.22474i	0.0277564	−	0.0480754i
$650$		0			0
$651$		0			0
$652$	−10.0000			−0.391630
$653$	−6.00000	+	10.3923i	−0.234798	+	0.406682i	−0.959214	−	0.282681i	$-0.908776\pi$
$653$	−6.00000	+	10.3923i	−0.234798	+	0.406682i	0.724416	+	0.689363i	$0.242110\pi$
$654$	1.41421	+	2.44949i	0.0553001	+	0.0957826i
$655$	42.0000	+	72.7461i	1.64108	+	2.84243i
$656$	5.65685	−	9.79796i	0.220863	−	0.382546i
$657$	−8.48528			−0.331042
$658$		0			0
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$	3.00000	−	5.19615i	0.116775	−	0.202260i
$661$	−6.36396	−	11.0227i	−0.247529	−	0.428733i	0.715310	−	0.698807i	$-0.246285\pi$
$661$	−6.36396	−	11.0227i	−0.247529	−	0.428733i	−0.962840	+	0.270073i	$0.912952\pi$
$662$	−10.0000	−	17.3205i	−0.388661	−	0.673181i
$663$		0			0
$664$	−16.9706			−0.658586
$665$		0			0
$666$	10.0000			0.387492
$667$	−6.00000	+	10.3923i	−0.232321	+	0.402392i
$668$	−2.82843	−	4.89898i	−0.109435	−	0.189547i
$669$	15.0000	+	25.9808i	0.579934	+	1.00447i
$670$	−4.24264	+	7.34847i	−0.163908	+	0.283896i
$671$	2.82843			0.109190
$672$		0			0
$673$	−22.0000			−0.848038			−0.424019	−	0.905653i	$-0.639381\pi$
$673$	−22.0000			−0.848038			−0.424019	+	0.905653i	$0.639381\pi$
$674$	−1.00000	+	1.73205i	−0.0385186	+	0.0667161i
$675$	36.7696	+	63.6867i	1.41526	+	2.45130i
$676$	6.50000	+	11.2583i	0.250000	+	0.433013i
$677$	19.7990	−	34.2929i	0.760937	−	1.31798i	−0.181431	−	0.983404i	$-0.558073\pi$
$677$	19.7990	−	34.2929i	0.760937	−	1.31798i	0.942368	−	0.334578i	$-0.108594\pi$
$678$	−2.82843			−0.108625
$679$		0			0
$680$	−24.0000			−0.920358
$681$	10.0000	−	17.3205i	0.383201	−	0.663723i
$682$	−0.707107	−	1.22474i	−0.0270765	−	0.0468979i
$683$	14.0000	+	24.2487i	0.535695	+	0.927851i	0.999129	+	0.0417198i	$0.0132837\pi$
$683$	14.0000	+	24.2487i	0.535695	+	0.927851i	−0.463434	+	0.886131i	$0.653383\pi$
$684$		0			0
$685$	−76.3675			−2.91785
$686$		0			0
$687$	14.0000			0.534133
$688$	4.00000	−	6.92820i	0.152499	−	0.264135i
$689$		0			0
$690$	−18.0000	−	31.1769i	−0.685248	−	1.18688i
$691$	−7.77817	+	13.4722i	−0.295896	+	0.512506i	−0.975193	−	0.221357i	$-0.928951\pi$
$691$	−7.77817	+	13.4722i	−0.295896	+	0.512506i	0.679297	+	0.733863i	$0.262285\pi$
$692$	−11.3137			−0.430083
$693$		0			0
$694$	20.0000			0.759190
$695$	−24.0000	+	41.5692i	−0.910372	+	1.57681i
$696$	−1.41421	−	2.44949i	−0.0536056	−	0.0928477i
$697$	−32.0000	−	55.4256i	−1.21209	−	2.09940i
$698$	−7.07107	+	12.2474i	−0.267644	+	0.463573i
$699$	19.7990			0.748867
$700$		0			0
$701$	50.0000			1.88847			0.944237	−	0.329267i	$-0.106802\pi$
$701$	50.0000			1.88847			0.944237	+	0.329267i	$0.106802\pi$
$702$		0			0
$703$		0			0
$704$	0.500000	+	0.866025i	0.0188445	+	0.0326396i
$705$	−12.7279	+	22.0454i	−0.479361	+	0.830278i
$706$	1.41421			0.0532246
$707$		0			0
$708$	2.00000			0.0751646
$709$	10.0000	−	17.3205i	0.375558	−	0.650485i	−0.614852	−	0.788642i	$-0.710784\pi$
$709$	10.0000	−	17.3205i	0.375558	−	0.650485i	0.990410	+	0.138157i	$0.0441178\pi$
$710$	4.24264	+	7.34847i	0.159223	+	0.275783i
$711$	8.00000	+	13.8564i	0.300023	+	0.519656i
$712$	3.53553	−	6.12372i	0.132500	−	0.229496i
$713$	−8.48528			−0.317776
$714$		0			0
$715$		0			0
$716$	−6.00000	+	10.3923i	−0.224231	+	0.388379i
$717$	8.48528	+	14.6969i	0.316889	+	0.548867i
$718$	6.00000	+	10.3923i	0.223918	+	0.387837i
$719$	−9.19239	+	15.9217i	−0.342818	+	0.593779i	−0.984955	−	0.172812i	$-0.944715\pi$
$719$	−9.19239	+	15.9217i	−0.342818	+	0.593779i	0.642137	+	0.766590i	$0.278048\pi$
$720$	−4.24264			−0.158114
$721$		0			0
$722$	−19.0000			−0.707107
$723$		0			0
$724$	3.53553	+	6.12372i	0.131397	+	0.227586i
$725$	−13.0000	−	22.5167i	−0.482808	−	0.836248i
$726$	−0.707107	+	1.22474i	−0.0262432	+	0.0454545i
$727$	12.7279			0.472052			0.236026	−	0.971747i	$-0.424155\pi$
$727$	12.7279			0.472052			0.236026	+	0.971747i	$0.424155\pi$
$728$		0			0
$729$	29.0000			1.07407
$730$	−18.0000	+	31.1769i	−0.666210	+	1.15391i
$731$	−22.6274	−	39.1918i	−0.836905	−	1.44956i
$732$	2.00000	+	3.46410i	0.0739221	+	0.128037i
$733$	−7.07107	+	12.2474i	−0.261176	+	0.452370i	−0.966555	−	0.256461i	$-0.917444\pi$
$733$	−7.07107	+	12.2474i	−0.261176	+	0.452370i	0.705379	+	0.708831i	$0.250777\pi$
$734$	−21.2132			−0.782994
$735$		0			0
$736$	6.00000			0.221163
$737$	1.00000	−	1.73205i	0.0368355	−	0.0638009i
$738$	−5.65685	−	9.79796i	−0.208232	−	0.360668i
$739$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$739$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$740$	21.2132	−	36.7423i	0.779813	−	1.35068i
$741$		0			0
$742$		0			0
$743$	−44.0000			−1.61420			−0.807102	−	0.590412i	$-0.798965\pi$
$743$	−44.0000			−1.61420			−0.807102	+	0.590412i	$0.798965\pi$
$744$	1.00000	−	1.73205i	0.0366618	−	0.0635001i
$745$	21.2132	+	36.7423i	0.777192	+	1.34614i
$746$	5.00000	+	8.66025i	0.183063	+	0.317074i
$747$	−8.48528	+	14.6969i	−0.310460	+	0.537733i
$748$	5.65685			0.206835
$749$		0			0
$750$	48.0000			1.75271
$751$	7.00000	−	12.1244i	0.255434	−	0.442424i	−0.709580	−	0.704625i	$-0.751115\pi$
$751$	7.00000	−	12.1244i	0.255434	−	0.442424i	0.965013	+	0.262201i	$0.0844484\pi$
$752$	−2.12132	−	3.67423i	−0.0773566	−	0.133986i
$753$	−13.0000	−	22.5167i	−0.473746	−	0.820553i
$754$		0			0
$755$	16.9706			0.617622
$756$		0			0
$757$	−8.00000			−0.290765			−0.145382	−	0.989376i	$-0.546441\pi$
$757$	−8.00000			−0.290765			−0.145382	+	0.989376i	$0.546441\pi$
$758$	3.00000	−	5.19615i	0.108965	−	0.188733i
$759$	4.24264	+	7.34847i	0.153998	+	0.266733i
$760$		0			0
$761$	21.2132	−	36.7423i	0.768978	−	1.33191i	−0.169140	−	0.985592i	$-0.554099\pi$
$761$	21.2132	−	36.7423i	0.768978	−	1.33191i	0.938118	−	0.346317i	$-0.112568\pi$
$762$	22.6274			0.819705
$763$		0			0
$764$	16.0000			0.578860
$765$	−12.0000	+	20.7846i	−0.433861	+	0.751469i
$766$	−7.77817	−	13.4722i	−0.281037	−	0.486770i
$767$		0			0
$768$	−0.707107	+	1.22474i	−0.0255155	+	0.0441942i
$769$	19.7990			0.713970			0.356985	−	0.934110i	$-0.383805\pi$
$769$	19.7990			0.713970			0.356985	+	0.934110i	$0.383805\pi$
$770$		0			0
$771$	2.00000			0.0720282
$772$	3.00000	−	5.19615i	0.107972	−	0.187014i
$773$	−0.707107	−	1.22474i	−0.0254329	−	0.0440510i	0.853029	−	0.521864i	$-0.174763\pi$
$773$	−0.707107	−	1.22474i	−0.0254329	−	0.0440510i	−0.878462	+	0.477813i	$0.841430\pi$
$774$	−4.00000	−	6.92820i	−0.143777	−	0.249029i
$775$	9.19239	−	15.9217i	0.330200	−	0.571924i
$776$	−9.89949			−0.355371
$777$		0			0
$778$	−24.0000			−0.860442
$779$		0			0
$780$		0			0
$781$	−1.00000	−	1.73205i	−0.0357828	−	0.0619777i
$782$	16.9706	−	29.3939i	0.606866	−	1.05112i
$783$	−11.3137			−0.404319
$784$		0			0
$785$	18.0000			0.642448
$786$	14.0000	−	24.2487i	0.499363	−	0.864923i
$787$	2.82843	+	4.89898i	0.100823	+	0.174630i	0.912024	−	0.410137i	$-0.134519\pi$
$787$	2.82843	+	4.89898i	0.100823	+	0.174630i	−0.811201	+	0.584767i	$0.801186\pi$
$788$	−11.0000	−	19.0526i	−0.391859	−	0.678719i
$789$	5.65685	−	9.79796i	0.201389	−	0.348817i
$790$	67.8823			2.41514
$791$		0			0
$792$	1.00000			0.0355335
$793$		0			0
$794$	−6.36396	−	11.0227i	−0.225849	−	0.391181i
$795$	−24.0000	−	41.5692i	−0.851192	−	1.47431i
$796$	0.707107	−	1.22474i	0.0250627	−	0.0434099i
$797$	7.07107			0.250470			0.125235	−	0.992127i	$-0.460032\pi$
$797$	7.07107			0.250470			0.125235	+	0.992127i	$0.460032\pi$
$798$		0			0
$799$	−24.0000			−0.849059
$800$	−6.50000	+	11.2583i	−0.229810	+	0.398042i
$801$	−3.53553	−	6.12372i	−0.124922	−	0.216371i
$802$	−6.00000	−	10.3923i	−0.211867	−	0.366965i
$803$	4.24264	−	7.34847i	0.149720	−	0.259322i
$804$	2.82843			0.0997509
$805$		0			0
$806$		0			0
$807$	−13.0000	+	22.5167i	−0.457622	+	0.792624i
$808$	−2.82843	−	4.89898i	−0.0995037	−	0.172345i
$809$	−27.0000	−	46.7654i	−0.949269	−	1.64418i	−0.746968	−	0.664860i	$-0.768491\pi$
$809$	−27.0000	−	46.7654i	−0.949269	−	1.64418i	−0.202301	−	0.979323i	$-0.564842\pi$
$810$	10.6066	−	18.3712i	0.372678	−	0.645497i
$811$	36.7696			1.29115			0.645577	−	0.763695i	$-0.276617\pi$
$811$	36.7696			1.29115			0.645577	+	0.763695i	$0.276617\pi$
$812$		0			0
$813$	−12.0000			−0.420858
$814$	−5.00000	+	8.66025i	−0.175250	+	0.303542i
$815$	21.2132	+	36.7423i	0.743066	+	1.28703i
$816$	4.00000	+	6.92820i	0.140028	+	0.242536i
$817$		0			0
$818$	−2.82843			−0.0988936
$819$		0			0
$820$	−48.0000			−1.67623
$821$	19.0000	−	32.9090i	0.663105	−	1.14853i	−0.316691	−	0.948529i	$-0.602572\pi$
$821$	19.0000	−	32.9090i	0.663105	−	1.14853i	0.979795	−	0.200002i	$-0.0640949\pi$
$822$	12.7279	+	22.0454i	0.443937	+	0.768922i
$823$	−20.0000	−	34.6410i	−0.697156	−	1.20751i	−0.969448	−	0.245295i	$-0.921115\pi$
$823$	−20.0000	−	34.6410i	−0.697156	−	1.20751i	0.272292	−	0.962215i	$-0.412218\pi$
$824$	−9.19239	+	15.9217i	−0.320232	+	0.554658i
$825$	−18.3848			−0.640076
$826$		0			0
$827$	−32.0000			−1.11275			−0.556375	−	0.830932i	$-0.687808\pi$
$827$	−32.0000			−1.11275			−0.556375	+	0.830932i	$0.687808\pi$
$828$	3.00000	−	5.19615i	0.104257	−	0.180579i
$829$	2.12132	+	3.67423i	0.0736765	+	0.127611i	0.900510	−	0.434835i	$-0.143193\pi$
$829$	2.12132	+	3.67423i	0.0736765	+	0.127611i	−0.826833	+	0.562447i	$0.809860\pi$
$830$	36.0000	+	62.3538i	1.24958	+	2.16433i
$831$	1.41421	−	2.44949i	0.0490585	−	0.0849719i
$832$		0			0
$833$		0			0
$834$	16.0000			0.554035
$835$	−12.0000	+	20.7846i	−0.415277	+	0.719281i
$836$		0			0
$837$	−4.00000	−	6.92820i	−0.138260	−	0.239474i
$838$	−12.0208	+	20.8207i	−0.415252	+	0.719238i
$839$	1.41421			0.0488241			0.0244120	−	0.999702i	$-0.492229\pi$
$839$	1.41421			0.0488241			0.0244120	+	0.999702i	$0.492229\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$	10.0000	−	17.3205i	0.344623	−	0.596904i
$843$	9.89949	+	17.1464i	0.340957	+	0.590554i
$844$	−4.00000	−	6.92820i	−0.137686	−	0.238479i
$845$	27.5772	−	47.7650i	0.948683	−	1.64317i
$846$	−4.24264			−0.145865
$847$		0			0
$848$	8.00000			0.274721
$849$	14.0000	−	24.2487i	0.480479	−	0.832214i
$850$	36.7696	+	63.6867i	1.26119	+	2.18444i
$851$	30.0000	+	51.9615i	1.02839	+	1.78122i
$852$	1.41421	−	2.44949i	0.0484502	−	0.0839181i
$853$	28.2843			0.968435			0.484218	−	0.874948i	$-0.339104\pi$
$853$	28.2843			0.968435			0.484218	+	0.874948i	$0.339104\pi$
$854$		0			0
$855$		0			0
$856$	−8.00000	+	13.8564i	−0.273434	+	0.473602i
$857$	12.7279	+	22.0454i	0.434778	+	0.753057i	0.997277	−	0.0737406i	$-0.0234937\pi$
$857$	12.7279	+	22.0454i	0.434778	+	0.753057i	−0.562500	+	0.826797i	$0.690160\pi$
$858$		0			0
$859$	−6.36396	+	11.0227i	−0.217136	+	0.376090i	−0.953931	−	0.300026i	$-0.903005\pi$
$859$	−6.36396	+	11.0227i	−0.217136	+	0.376090i	0.736796	+	0.676116i	$0.236338\pi$
$860$	−33.9411			−1.15738
$861$		0			0
$862$	32.0000			1.08992
$863$	12.0000	−	20.7846i	0.408485	−	0.707516i	−0.586235	−	0.810141i	$-0.699391\pi$
$863$	12.0000	−	20.7846i	0.408485	−	0.707516i	0.994720	+	0.102624i	$0.0327240\pi$
$864$	2.82843	+	4.89898i	0.0962250	+	0.166667i
$865$	24.0000	+	41.5692i	0.816024	+	1.41340i
$866$	6.36396	−	11.0227i	0.216256	−	0.374567i
$867$	21.2132			0.720438
$868$		0			0
$869$	−16.0000			−0.542763
$870$	−6.00000	+	10.3923i	−0.203419	+	0.352332i
$871$		0			0
$872$	1.00000	+	1.73205i	0.0338643	+	0.0586546i
$873$	−4.94975	+	8.57321i	−0.167524	+	0.290159i
$874$		0			0
$875$		0			0
$876$	12.0000			0.405442
$877$	−17.0000	+	29.4449i	−0.574049	+	0.994282i	0.422095	+	0.906552i	$0.361295\pi$
$877$	−17.0000	+	29.4449i	−0.574049	+	0.994282i	−0.996144	+	0.0877308i	$0.972038\pi$
$878$	12.7279	+	22.0454i	0.429547	+	0.743996i
$879$	6.00000	+	10.3923i	0.202375	+	0.350524i
$880$	2.12132	−	3.67423i	0.0715097	−	0.123858i
$881$	−29.6985			−1.00057			−0.500284	−	0.865862i	$-0.666771\pi$
$881$	−29.6985			−1.00057			−0.500284	+	0.865862i	$0.666771\pi$
$882$		0			0
$883$	−36.0000			−1.21150			−0.605748	−	0.795656i	$-0.707126\pi$
$883$	−36.0000			−1.21150			−0.605748	+	0.795656i	$0.707126\pi$
$884$		0			0
$885$	−4.24264	−	7.34847i	−0.142615	−	0.247016i
$886$	−18.0000	−	31.1769i	−0.604722	−	1.04741i
$887$	−18.3848	+	31.8434i	−0.617300	+	1.06920i	0.372676	+	0.927962i	$0.378440\pi$
$887$	−18.3848	+	31.8434i	−0.617300	+	1.06920i	−0.989976	+	0.141234i	$0.954893\pi$
$888$	−14.1421			−0.474579
$889$		0			0
$890$	−30.0000			−1.00560
$891$	−2.50000	+	4.33013i	−0.0837532	+	0.145065i
$892$	10.6066	+	18.3712i	0.355135	+	0.615112i
$893$		0			0
$894$	7.07107	−	12.2474i	0.236492	−	0.409616i
$895$	50.9117			1.70179
$896$		0			0
$897$		0			0
$898$	10.0000	−	17.3205i	0.333704	−	0.577993i
$899$	1.41421	+	2.44949i	0.0471667	+	0.0816951i
$900$	6.50000	+	11.2583i	0.216667	+	0.375278i
$901$	22.6274	−	39.1918i	0.753829	−	1.30567i
$902$	11.3137			0.376705
$903$		0			0
$904$	−2.00000			−0.0665190
$905$	15.0000	−	25.9808i	0.498617	−	0.863630i
$906$	−2.82843	−	4.89898i	−0.0939682	−	0.162758i
$907$	7.00000	+	12.1244i	0.232431	+	0.402583i	0.958523	−	0.285015i	$-0.0919986\pi$
$907$	7.00000	+	12.1244i	0.232431	+	0.402583i	−0.726092	+	0.687598i	$0.758665\pi$
$908$	7.07107	−	12.2474i	0.234662	−	0.406446i
$909$	−5.65685			−0.187626
$910$		0			0
$911$	30.0000			0.993944			0.496972	−	0.867766i	$-0.334445\pi$
$911$	30.0000			0.993944			0.496972	+	0.867766i	$0.334445\pi$
$912$		0			0
$913$	−8.48528	−	14.6969i	−0.280822	−	0.486398i
$914$	−7.00000	−	12.1244i	−0.231539	−	0.401038i
$915$	8.48528	−	14.6969i	0.280515	−	0.485866i
$916$	9.89949			0.327089
$917$		0			0
$918$	32.0000			1.05616
$919$	−4.00000	+	6.92820i	−0.131948	+	0.228540i	−0.924427	−	0.381358i	$-0.875456\pi$
$919$	−4.00000	+	6.92820i	−0.131948	+	0.228540i	0.792480	+	0.609898i	$0.208790\pi$
$920$	−12.7279	−	22.0454i	−0.419627	−	0.726816i
$921$	18.0000	+	31.1769i	0.593120	+	1.02731i
$922$	−1.41421	+	2.44949i	−0.0465746	+	0.0806696i
$923$		0			0
$924$		0			0
$925$	−130.000			−4.27437
$926$	−13.0000	+	22.5167i	−0.427207	+	0.739943i
$927$	9.19239	+	15.9217i	0.301918	+	0.522937i
$928$	−1.00000	−	1.73205i	−0.0328266	−	0.0568574i
$929$	16.2635	−	28.1691i	0.533587	−	0.924199i	−0.465644	−	0.884972i	$-0.654177\pi$
$929$	16.2635	−	28.1691i	0.533587	−	0.924199i	0.999230	−	0.0392269i	$-0.0124895\pi$
$930$	−8.48528			−0.278243
$931$		0			0
$932$	14.0000			0.458585
$933$	−13.0000	+	22.5167i	−0.425601	+	0.737162i
$934$	2.12132	+	3.67423i	0.0694117	+	0.120225i
$935$	−12.0000	−	20.7846i	−0.392442	−	0.679729i
$936$		0			0
$937$	25.4558			0.831606			0.415803	−	0.909455i	$-0.363501\pi$
$937$	25.4558			0.831606			0.415803	+	0.909455i	$0.363501\pi$
$938$		0			0
$939$	−18.0000			−0.587408
$940$	−9.00000	+	15.5885i	−0.293548	+	0.508439i
$941$	−15.5563	−	26.9444i	−0.507122	−	0.878362i	−0.999966	−	0.00824396i	$-0.997376\pi$
$941$	−15.5563	−	26.9444i	−0.507122	−	0.878362i	0.492844	−	0.870118i	$-0.335957\pi$
$942$	−3.00000	−	5.19615i	−0.0977453	−	0.169300i
$943$	33.9411	−	58.7878i	1.10528	−	1.91439i
$944$	1.41421			0.0460287
$945$		0			0
$946$	8.00000			0.260102
$947$	−26.0000	+	45.0333i	−0.844886	+	1.46339i	0.0408333	+	0.999166i	$0.486999\pi$
$947$	−26.0000	+	45.0333i	−0.844886	+	1.46339i	−0.885720	+	0.464220i	$0.846335\pi$
$948$	−11.3137	−	19.5959i	−0.367452	−	0.636446i
$949$		0			0
$950$		0			0
$951$	42.4264			1.37577
$952$		0			0
$953$	14.0000			0.453504			0.226752	−	0.973952i	$-0.427189\pi$
$953$	14.0000			0.453504			0.226752	+	0.973952i	$0.427189\pi$
$954$	4.00000	−	6.92820i	0.129505	−	0.224309i
$955$	−33.9411	−	58.7878i	−1.09831	−	1.90233i
$956$	6.00000	+	10.3923i	0.194054	+	0.336111i
$957$	1.41421	−	2.44949i	0.0457150	−	0.0791808i
$958$	2.82843			0.0913823
$959$		0			0
$960$	6.00000			0.193649
$961$	14.5000	−	25.1147i	0.467742	−	0.810153i
$962$		0			0
$963$	8.00000	+	13.8564i	0.257796	+	0.446516i
$964$		0			0
$965$	−25.4558			−0.819453
$966$		0			0
$967$	8.00000			0.257263			0.128631	−	0.991692i	$-0.458942\pi$
$967$	8.00000			0.257263			0.128631	+	0.991692i	$0.458942\pi$
$968$	−0.500000	+	0.866025i	−0.0160706	+	0.0278351i
$969$		0			0
$970$	21.0000	+	36.3731i	0.674269	+	1.16787i
$971$	−26.1630	+	45.3156i	−0.839609	+	1.45425i	0.0506128	+	0.998718i	$0.483883\pi$
$971$	−26.1630	+	45.3156i	−0.839609	+	1.45425i	−0.890222	+	0.455527i	$0.849451\pi$
$972$	9.89949			0.317526
$973$		0			0
$974$	2.00000			0.0640841
$975$		0			0
$976$	1.41421	+	2.44949i	0.0452679	+	0.0784063i
$977$	−26.0000	−	45.0333i	−0.831814	−	1.44074i	−0.896599	−	0.442844i	$-0.853969\pi$
$977$	−26.0000	−	45.0333i	−0.831814	−	1.44074i	0.0647848	−	0.997899i	$-0.479364\pi$
$978$	7.07107	−	12.2474i	0.226108	−	0.391630i
$979$	7.07107			0.225992
$980$		0			0
$981$	2.00000			0.0638551
$982$	6.00000	−	10.3923i	0.191468	−	0.331632i
$983$	−0.707107	−	1.22474i	−0.0225532	−	0.0390633i	0.854529	−	0.519404i	$-0.173846\pi$
$983$	−0.707107	−	1.22474i	−0.0225532	−	0.0390633i	−0.877082	+	0.480341i	$0.840513\pi$
$984$	8.00000	+	13.8564i	0.255031	+	0.441726i
$985$	−46.6690	+	80.8332i	−1.48700	+	2.57556i
$986$	−11.3137			−0.360302
$987$		0			0
$988$		0			0
$989$	24.0000	−	41.5692i	0.763156	−	1.32182i
$990$	−2.12132	−	3.67423i	−0.0674200	−	0.116775i
$991$	23.0000	+	39.8372i	0.730619	+	1.26547i	0.956619	+	0.291342i	$0.0941018\pi$
$991$	23.0000	+	39.8372i	0.730619	+	1.26547i	−0.226000	+	0.974127i	$0.572565\pi$
$992$	0.707107	−	1.22474i	0.0224507	−	0.0388857i
$993$	28.2843			0.897574
$994$		0			0
$995$	−6.00000			−0.190213
$996$	12.0000	−	20.7846i	0.380235	−	0.658586i
$997$	−8.48528	−	14.6969i	−0.268732	−	0.465457i	0.699803	−	0.714336i	$-0.253271\pi$
$997$	−8.48528	−	14.6969i	−0.268732	−	0.465457i	−0.968535	+	0.248879i	$0.919938\pi$
$998$	−3.00000	−	5.19615i	−0.0949633	−	0.164481i
$999$	−28.2843	+	48.9898i	−0.894875	+	1.54997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1078.2.e.p.177.1		4
7.2	even	3		1078.2.a.u.1.2	yes	2
7.3	odd	6	inner	1078.2.e.p.67.2		4
7.4	even	3	inner	1078.2.e.p.67.1		4
7.5	odd	6		1078.2.a.u.1.1	✓	2
7.6	odd	2	inner	1078.2.e.p.177.2		4
21.2	odd	6		9702.2.a.cp.1.1		2
21.5	even	6		9702.2.a.cp.1.2		2
28.19	even	6		8624.2.a.bs.1.2		2
28.23	odd	6		8624.2.a.bs.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1078.2.a.u.1.1	✓	2	7.5	odd	6
1078.2.a.u.1.2	yes	2	7.2	even	3
1078.2.e.p.67.1		4	7.4	even	3	inner
1078.2.e.p.67.2		4	7.3	odd	6	inner
1078.2.e.p.177.1		4	1.1	even	1	trivial
1078.2.e.p.177.2		4	7.6	odd	2	inner
8624.2.a.bs.1.1		2	28.23	odd	6
8624.2.a.bs.1.2		2	28.19	even	6
9702.2.a.cp.1.1		2	21.2	odd	6
9702.2.a.cp.1.2		2	21.5	even	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:	\( N \)	\(=\)	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1078.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.707107 - 1.22474i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.12132 + 3.67423i) q^{5} +1.41421 q^{6} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.12132 - 3.67423i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-0.707107 + 1.22474i) q^{12} +6.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.82843 + 4.89898i) q^{17} +(0.500000 + 0.866025i) q^{18} +4.24264 q^{20} -1.00000 q^{22} +(-3.00000 + 5.19615i) q^{23} +(-0.707107 - 1.22474i) q^{24} +(-6.50000 - 11.2583i) q^{25} -5.65685 q^{27} +2.00000 q^{29} +(-3.00000 + 5.19615i) q^{30} +(0.707107 + 1.22474i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.707107 - 1.22474i) q^{33} -5.65685 q^{34} -1.00000 q^{36} +(5.00000 - 8.66025i) q^{37} +(-2.12132 + 3.67423i) q^{40} -11.3137 q^{41} -8.00000 q^{43} +(0.500000 - 0.866025i) q^{44} +(2.12132 + 3.67423i) q^{45} +(-3.00000 - 5.19615i) q^{46} +(-2.12132 + 3.67423i) q^{47} +1.41421 q^{48} +13.0000 q^{50} +(4.00000 - 6.92820i) q^{51} +(-4.00000 - 6.92820i) q^{53} +(2.82843 - 4.89898i) q^{54} -4.24264 q^{55} +(-1.00000 + 1.73205i) q^{58} +(-0.707107 - 1.22474i) q^{59} +(-3.00000 - 5.19615i) q^{60} +(1.41421 - 2.44949i) q^{61} -1.41421 q^{62} +1.00000 q^{64} +(0.707107 + 1.22474i) q^{66} +(-1.00000 - 1.73205i) q^{67} +(2.82843 - 4.89898i) q^{68} +8.48528 q^{69} -2.00000 q^{71} +(0.500000 - 0.866025i) q^{72} +(-4.24264 - 7.34847i) q^{73} +(5.00000 + 8.66025i) q^{74} +(-9.19239 + 15.9217i) q^{75} +(-8.00000 + 13.8564i) q^{79} +(-2.12132 - 3.67423i) q^{80} +(2.50000 + 4.33013i) q^{81} +(5.65685 - 9.79796i) q^{82} -16.9706 q^{83} -24.0000 q^{85} +(4.00000 - 6.92820i) q^{86} +(-1.41421 - 2.44949i) q^{87} +(0.500000 + 0.866025i) q^{88} +(3.53553 - 6.12372i) q^{89} -4.24264 q^{90} +6.00000 q^{92} +(1.00000 - 1.73205i) q^{93} +(-2.12132 - 3.67423i) q^{94} +(-0.707107 + 1.22474i) q^{96} -9.89949 q^{97} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} + 4 q^{8} + 2 q^{9} + 2 q^{11} + 24 q^{15} - 2 q^{16} + 2 q^{18} - 4 q^{22} - 12 q^{23} - 26 q^{25} + 8 q^{29} - 12 q^{30} - 2 q^{32} - 4 q^{36} + 20 q^{37} - 32 q^{43} + 2 q^{44}+ \cdots + 4 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 + 4 * q^8 + 2 * q^9 + 2 * q^11 + 24 * q^15 - 2 * q^16 + 2 * q^18 - 4 * q^22 - 12 * q^23 - 26 * q^25 + 8 * q^29 - 12 * q^30 - 2 * q^32 - 4 * q^36 + 20 * q^37 - 32 * q^43 + 2 * q^44 - 12 * q^46 + 52 * q^50 + 16 * q^51 - 16 * q^53 - 4 * q^58 - 12 * q^60 + 4 * q^64 - 4 * q^67 - 8 * q^71 + 2 * q^72 + 20 * q^74 - 32 * q^79 + 10 * q^81 - 96 * q^85 + 16 * q^86 + 2 * q^88 + 24 * q^92 + 4 * q^93 + 4 * q^99

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