LMFDB - Embedded newform 1078.2.e.j.67.1

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:	$2$
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 154)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1078.67
Dual form			1078.2.e.j.177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.00000 + 3.46410i) q^{5} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.00000 + 3.46410i) q^{5} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-2.00000 + 3.46410i) q^{10} +(0.500000 - 0.866025i) q^{11} +2.00000 q^{13} +(-0.500000 - 0.866025i) q^{16} +(2.00000 - 3.46410i) q^{17} +(-1.50000 + 2.59808i) q^{18} +(3.00000 + 5.19615i) q^{19} -4.00000 q^{20} +1.00000 q^{22} +(-2.00000 - 3.46410i) q^{23} +(-5.50000 + 9.52628i) q^{25} +(1.00000 + 1.73205i) q^{26} -2.00000 q^{29} +(1.00000 - 1.73205i) q^{31} +(0.500000 - 0.866025i) q^{32} +4.00000 q^{34} -3.00000 q^{36} +(-5.00000 - 8.66025i) q^{37} +(-3.00000 + 5.19615i) q^{38} +(-2.00000 - 3.46410i) q^{40} +4.00000 q^{41} -8.00000 q^{43} +(0.500000 + 0.866025i) q^{44} +(-6.00000 + 10.3923i) q^{45} +(2.00000 - 3.46410i) q^{46} +(-1.00000 - 1.73205i) q^{47} -11.0000 q^{50} +(-1.00000 + 1.73205i) q^{52} +(-3.00000 + 5.19615i) q^{53} +4.00000 q^{55} +(-1.00000 - 1.73205i) q^{58} +(6.00000 - 10.3923i) q^{59} +(7.00000 + 12.1244i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(4.00000 + 6.92820i) q^{65} +(6.00000 - 10.3923i) q^{67} +(2.00000 + 3.46410i) q^{68} -8.00000 q^{71} +(-1.50000 - 2.59808i) q^{72} +(-2.00000 + 3.46410i) q^{73} +(5.00000 - 8.66025i) q^{74} -6.00000 q^{76} +(2.00000 - 3.46410i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(2.00000 + 3.46410i) q^{82} -6.00000 q^{83} +16.0000 q^{85} +(-4.00000 - 6.92820i) q^{86} +(-0.500000 + 0.866025i) q^{88} +(3.00000 + 5.19615i) q^{89} -12.0000 q^{90} +4.00000 q^{92} +(1.00000 - 1.73205i) q^{94} +(-12.0000 + 20.7846i) q^{95} -14.0000 q^{97} +3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{4} + 4 q^{5} - 2 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q + q^2 - q^4 + 4 * q^5 - 2 * q^8 + 3 * q^9	$ 2 q + q^{2} - q^{4} + 4 q^{5} - 2 q^{8} + 3 q^{9} - 4 q^{10} + q^{11} + 4 q^{13} - q^{16} + 4 q^{17} - 3 q^{18} + 6 q^{19} - 8 q^{20} + 2 q^{22} - 4 q^{23} - 11 q^{25} + 2 q^{26} - 4 q^{29} + 2 q^{31} + q^{32} + 8 q^{34} - 6 q^{36} - 10 q^{37} - 6 q^{38} - 4 q^{40} + 8 q^{41} - 16 q^{43} + q^{44} - 12 q^{45} + 4 q^{46} - 2 q^{47} - 22 q^{50} - 2 q^{52} - 6 q^{53} + 8 q^{55} - 2 q^{58} + 12 q^{59} + 14 q^{61} + 4 q^{62} + 2 q^{64} + 8 q^{65} + 12 q^{67} + 4 q^{68} - 16 q^{71} - 3 q^{72} - 4 q^{73} + 10 q^{74} - 12 q^{76} + 4 q^{80} - 9 q^{81} + 4 q^{82} - 12 q^{83} + 32 q^{85} - 8 q^{86} - q^{88} + 6 q^{89} - 24 q^{90} + 8 q^{92} + 2 q^{94} - 24 q^{95} - 28 q^{97} + 6 q^{99}+O(q^{100}) $ 2 * q + q^2 - q^4 + 4 * q^5 - 2 * q^8 + 3 * q^9 - 4 * q^10 + q^11 + 4 * q^13 - q^16 + 4 * q^17 - 3 * q^18 + 6 * q^19 - 8 * q^20 + 2 * q^22 - 4 * q^23 - 11 * q^25 + 2 * q^26 - 4 * q^29 + 2 * q^31 + q^32 + 8 * q^34 - 6 * q^36 - 10 * q^37 - 6 * q^38 - 4 * q^40 + 8 * q^41 - 16 * q^43 + q^44 - 12 * q^45 + 4 * q^46 - 2 * q^47 - 22 * q^50 - 2 * q^52 - 6 * q^53 + 8 * q^55 - 2 * q^58 + 12 * q^59 + 14 * q^61 + 4 * q^62 + 2 * q^64 + 8 * q^65 + 12 * q^67 + 4 * q^68 - 16 * q^71 - 3 * q^72 - 4 * q^73 + 10 * q^74 - 12 * q^76 + 4 * q^80 - 9 * q^81 + 4 * q^82 - 12 * q^83 + 32 * q^85 - 8 * q^86 - q^88 + 6 * q^89 - 24 * q^90 + 8 * q^92 + 2 * q^94 - 24 * q^95 - 28 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$981$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0		−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
$5$	2.00000	+	3.46410i	0.894427	+	1.54919i	0.834512	+	0.550990i	$0.185750\pi$
$5$	2.00000	+	3.46410i	0.894427	+	1.54919i	0.0599153	+	0.998203i	$0.480917\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	−2.00000	+	3.46410i	−0.632456	+	1.09545i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$		0			0
$13$	2.00000			0.554700			0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000			0.554700			0.277350	+	0.960769i	$0.410544\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.00000	−	3.46410i	0.485071	−	0.840168i	−0.514782	−	0.857321i	$-0.672127\pi$
$17$	2.00000	−	3.46410i	0.485071	−	0.840168i	0.999853	+	0.0171533i	$0.00546033\pi$
$18$	−1.50000	+	2.59808i	−0.353553	+	0.612372i
$19$	3.00000	+	5.19615i	0.688247	+	1.19208i	0.972404	+	0.233301i	$0.0749529\pi$
$19$	3.00000	+	5.19615i	0.688247	+	1.19208i	−0.284157	+	0.958778i	$0.591714\pi$
$20$	−4.00000			−0.894427
$21$		0			0
$22$	1.00000			0.213201
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	0.578610	−	0.815604i	$-0.303595\pi$
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	−0.995639	+	0.0932891i	$0.970262\pi$
$24$		0			0
$25$	−5.50000	+	9.52628i	−1.10000	+	1.90526i
$26$	1.00000	+	1.73205i	0.196116	+	0.339683i
$27$		0			0
$28$		0			0
$29$	−2.00000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$		0			0
$31$	1.00000	−	1.73205i	0.179605	−	0.311086i	−0.762140	−	0.647412i	$-0.775851\pi$
$31$	1.00000	−	1.73205i	0.179605	−	0.311086i	0.941745	+	0.336327i	$0.109185\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	4.00000			0.685994
$35$		0			0
$36$	−3.00000			−0.500000
$37$	−5.00000	−	8.66025i	−0.821995	−	1.42374i	−0.904194	−	0.427121i	$-0.859528\pi$
$37$	−5.00000	−	8.66025i	−0.821995	−	1.42374i	0.0821995	−	0.996616i	$-0.473806\pi$
$38$	−3.00000	+	5.19615i	−0.486664	+	0.842927i
$39$		0			0
$40$	−2.00000	−	3.46410i	−0.316228	−	0.547723i
$41$	4.00000			0.624695			0.312348	−	0.949968i	$-0.398885\pi$
$41$	4.00000			0.624695			0.312348	+	0.949968i	$0.398885\pi$
$42$		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
$45$	−6.00000	+	10.3923i	−0.894427	+	1.54919i
$46$	2.00000	−	3.46410i	0.294884	−	0.510754i
$47$	−1.00000	−	1.73205i	−0.145865	−	0.252646i	0.783830	−	0.620975i	$-0.213263\pi$
$47$	−1.00000	−	1.73205i	−0.145865	−	0.252646i	−0.929695	+	0.368329i	$0.879930\pi$
$48$		0			0
$49$		0			0
$50$	−11.0000			−1.55563
$51$		0			0
$52$	−1.00000	+	1.73205i	−0.138675	+	0.240192i
$53$	−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
$55$	4.00000			0.539360
$56$		0			0
$57$		0			0
$58$	−1.00000	−	1.73205i	−0.131306	−	0.227429i
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	−0.150148	−	0.988663i	$-0.547975\pi$
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	0.931282	−	0.364299i	$-0.118692\pi$
$60$		0			0
$61$	7.00000	+	12.1244i	0.896258	+	1.55236i	0.832240	+	0.554416i	$0.187058\pi$
$61$	7.00000	+	12.1244i	0.896258	+	1.55236i	0.0640184	+	0.997949i	$0.479608\pi$
$62$	2.00000			0.254000
$63$		0			0
$64$	1.00000			0.125000
$65$	4.00000	+	6.92820i	0.496139	+	0.859338i
$66$		0			0
$67$	6.00000	−	10.3923i	0.733017	−	1.26962i	−0.222571	−	0.974916i	$-0.571445\pi$
$67$	6.00000	−	10.3923i	0.733017	−	1.26962i	0.955588	−	0.294706i	$-0.0952216\pi$
$68$	2.00000	+	3.46410i	0.242536	+	0.420084i
$69$		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
$73$	−2.00000	+	3.46410i	−0.234082	+	0.405442i	−0.959006	−	0.283387i	$-0.908542\pi$
$73$	−2.00000	+	3.46410i	−0.234082	+	0.405442i	0.724923	+	0.688830i	$0.241875\pi$
$74$	5.00000	−	8.66025i	0.581238	−	1.00673i
$75$		0			0
$76$	−6.00000			−0.688247
$77$		0			0
$78$		0			0
$79$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$79$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$80$	2.00000	−	3.46410i	0.223607	−	0.387298i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	2.00000	+	3.46410i	0.220863	+	0.382546i
$83$	−6.00000			−0.658586			−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000			−0.658586			−0.329293	+	0.944228i	$0.606810\pi$
$84$		0			0
$85$	16.0000			1.73544
$86$	−4.00000	−	6.92820i	−0.431331	−	0.747087i
$87$		0			0
$88$	−0.500000	+	0.866025i	−0.0533002	+	0.0923186i
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	0.980071	−	0.198650i	$-0.0636557\pi$
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	−0.662071	+	0.749441i	$0.730322\pi$
$90$	−12.0000			−1.26491
$91$		0			0
$92$	4.00000			0.417029
$93$		0			0
$94$	1.00000	−	1.73205i	0.103142	−	0.178647i
$95$	−12.0000	+	20.7846i	−1.23117	+	2.13246i
$96$		0			0
$97$	−14.0000			−1.42148			−0.710742	−	0.703452i	$-0.751641\pi$
$97$	−14.0000			−1.42148			−0.710742	+	0.703452i	$0.751641\pi$
$98$		0			0
$99$	3.00000			0.301511
$100$	−5.50000	−	9.52628i	−0.550000	−	0.952628i
$101$	−3.00000	+	5.19615i	−0.298511	+	0.517036i	−0.975796	−	0.218685i	$-0.929823\pi$
$101$	−3.00000	+	5.19615i	−0.298511	+	0.517036i	0.677284	+	0.735721i	$0.263157\pi$
$102$		0			0
$103$	−9.00000	−	15.5885i	−0.886796	−	1.53598i	−0.843641	−	0.536908i	$-0.819592\pi$
$103$	−9.00000	−	15.5885i	−0.886796	−	1.53598i	−0.0431555	−	0.999068i	$-0.513741\pi$
$104$	−2.00000			−0.196116
$105$		0			0
$106$	−6.00000			−0.582772
$107$	8.00000	+	13.8564i	0.773389	+	1.33955i	0.935695	+	0.352809i	$0.114773\pi$
$107$	8.00000	+	13.8564i	0.773389	+	1.33955i	−0.162306	+	0.986740i	$0.551893\pi$
$108$		0			0
$109$	7.00000	−	12.1244i	0.670478	−	1.16130i	−0.307290	−	0.951616i	$-0.599422\pi$
$109$	7.00000	−	12.1244i	0.670478	−	1.16130i	0.977769	−	0.209687i	$-0.0672444\pi$
$110$	2.00000	+	3.46410i	0.190693	+	0.330289i
$111$		0			0
$112$		0			0
$113$	14.0000			1.31701			0.658505	−	0.752577i	$-0.271189\pi$
$113$	14.0000			1.31701			0.658505	+	0.752577i	$0.271189\pi$
$114$		0			0
$115$	8.00000	−	13.8564i	0.746004	−	1.29212i
$116$	1.00000	−	1.73205i	0.0928477	−	0.160817i
$117$	3.00000	+	5.19615i	0.277350	+	0.480384i
$118$	12.0000			1.10469
$119$		0			0
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−7.00000	+	12.1244i	−0.633750	+	1.09769i
$123$		0			0
$124$	1.00000	+	1.73205i	0.0898027	+	0.155543i
$125$	−24.0000			−2.14663
$126$		0			0
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−4.00000	+	6.92820i	−0.350823	+	0.607644i
$131$	−3.00000	−	5.19615i	−0.262111	−	0.453990i	0.704692	−	0.709514i	$-0.251085\pi$
$131$	−3.00000	−	5.19615i	−0.262111	−	0.453990i	−0.966803	+	0.255524i	$0.917752\pi$
$132$		0			0
$133$		0			0
$134$	12.0000			1.03664
$135$		0			0
$136$	−2.00000	+	3.46410i	−0.171499	+	0.297044i
$137$	−3.00000	+	5.19615i	−0.256307	+	0.443937i	−0.965250	−	0.261329i	$-0.915839\pi$
$137$	−3.00000	+	5.19615i	−0.256307	+	0.443937i	0.708942	+	0.705266i	$0.249173\pi$
$138$		0			0
$139$	14.0000			1.18746			0.593732	−	0.804663i	$-0.297654\pi$
$139$	14.0000			1.18746			0.593732	+	0.804663i	$0.297654\pi$
$140$		0			0
$141$		0			0
$142$	−4.00000	−	6.92820i	−0.335673	−	0.581402i
$143$	1.00000	−	1.73205i	0.0836242	−	0.144841i
$144$	1.50000	−	2.59808i	0.125000	−	0.216506i
$145$	−4.00000	−	6.92820i	−0.332182	−	0.575356i
$146$	−4.00000			−0.331042
$147$		0			0
$148$	10.0000			0.821995
$149$	−1.00000	−	1.73205i	−0.0819232	−	0.141895i	0.822153	−	0.569267i	$-0.192773\pi$
$149$	−1.00000	−	1.73205i	−0.0819232	−	0.141895i	−0.904076	+	0.427372i	$0.859440\pi$
$150$		0			0
$151$	12.0000	−	20.7846i	0.976546	−	1.69143i	0.301811	−	0.953368i	$-0.402409\pi$
$151$	12.0000	−	20.7846i	0.976546	−	1.69143i	0.674735	−	0.738060i	$-0.264258\pi$
$152$	−3.00000	−	5.19615i	−0.243332	−	0.421464i
$153$	12.0000			0.970143
$154$		0			0
$155$	8.00000			0.642575
$156$		0			0
$157$	4.00000	−	6.92820i	0.319235	−	0.552931i	−0.661094	−	0.750303i	$-0.729907\pi$
$157$	4.00000	−	6.92820i	0.319235	−	0.552931i	0.980329	+	0.197372i	$0.0632408\pi$
$158$		0			0
$159$		0			0
$160$	4.00000			0.316228
$161$		0			0
$162$	−9.00000			−0.707107
$163$	−2.00000	−	3.46410i	−0.156652	−	0.271329i	0.777007	−	0.629492i	$-0.216737\pi$
$163$	−2.00000	−	3.46410i	−0.156652	−	0.271329i	−0.933659	+	0.358162i	$0.883403\pi$
$164$	−2.00000	+	3.46410i	−0.156174	+	0.270501i
$165$		0			0
$166$	−3.00000	−	5.19615i	−0.232845	−	0.403300i
$167$	4.00000			0.309529			0.154765	−	0.987951i	$-0.450538\pi$
$167$	4.00000			0.309529			0.154765	+	0.987951i	$0.450538\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$	8.00000	+	13.8564i	0.613572	+	1.06274i
$171$	−9.00000	+	15.5885i	−0.688247	+	1.19208i
$172$	4.00000	−	6.92820i	0.304997	−	0.528271i
$173$	7.00000	+	12.1244i	0.532200	+	0.921798i	0.999293	+	0.0375896i	$0.0119679\pi$
$173$	7.00000	+	12.1244i	0.532200	+	0.921798i	−0.467093	+	0.884208i	$0.654699\pi$
$174$		0			0
$175$		0			0
$176$	−1.00000			−0.0753778
$177$		0			0
$178$	−3.00000	+	5.19615i	−0.224860	+	0.389468i
$179$	−2.00000	+	3.46410i	−0.149487	+	0.258919i	−0.931038	−	0.364922i	$-0.881096\pi$
$179$	−2.00000	+	3.46410i	−0.149487	+	0.258919i	0.781551	+	0.623841i	$0.214429\pi$
$180$	−6.00000	−	10.3923i	−0.447214	−	0.774597i
$181$	20.0000			1.48659			0.743294	−	0.668965i	$-0.233262\pi$
$181$	20.0000			1.48659			0.743294	+	0.668965i	$0.233262\pi$
$182$		0			0
$183$		0			0
$184$	2.00000	+	3.46410i	0.147442	+	0.255377i
$185$	20.0000	−	34.6410i	1.47043	−	2.54686i
$186$		0			0
$187$	−2.00000	−	3.46410i	−0.146254	−	0.253320i
$188$	2.00000			0.145865
$189$		0			0
$190$	−24.0000			−1.74114
$191$	2.00000	+	3.46410i	0.144715	+	0.250654i	0.929267	−	0.369410i	$-0.120440\pi$
$191$	2.00000	+	3.46410i	0.144715	+	0.250654i	−0.784552	+	0.620063i	$0.787107\pi$
$192$		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	$0.189599\pi$
$194$	−7.00000	−	12.1244i	−0.502571	−	0.870478i
$195$		0			0
$196$		0			0
$197$	6.00000			0.427482			0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000			0.427482			0.213741	+	0.976890i	$0.431435\pi$
$198$	1.50000	+	2.59808i	0.106600	+	0.184637i
$199$	7.00000	−	12.1244i	0.496217	−	0.859473i	−0.503774	−	0.863836i	$-0.668055\pi$
$199$	7.00000	−	12.1244i	0.496217	−	0.859473i	0.999990	+	0.00436292i	$0.00138876\pi$
$200$	5.50000	−	9.52628i	0.388909	−	0.673610i
$201$		0			0
$202$	−6.00000			−0.422159
$203$		0			0
$204$		0			0
$205$	8.00000	+	13.8564i	0.558744	+	0.967773i
$206$	9.00000	−	15.5885i	0.627060	−	1.08610i
$207$	6.00000	−	10.3923i	0.417029	−	0.722315i
$208$	−1.00000	−	1.73205i	−0.0693375	−	0.120096i
$209$	6.00000			0.415029
$210$		0			0
$211$	−8.00000			−0.550743			−0.275371	−	0.961338i	$-0.588801\pi$
$211$	−8.00000			−0.550743			−0.275371	+	0.961338i	$0.588801\pi$
$212$	−3.00000	−	5.19615i	−0.206041	−	0.356873i
$213$		0			0
$214$	−8.00000	+	13.8564i	−0.546869	+	0.947204i
$215$	−16.0000	−	27.7128i	−1.09119	−	1.89000i
$216$		0			0
$217$		0			0
$218$	14.0000			0.948200
$219$		0			0
$220$	−2.00000	+	3.46410i	−0.134840	+	0.233550i
$221$	4.00000	−	6.92820i	0.269069	−	0.466041i
$222$		0			0
$223$	−2.00000			−0.133930			−0.0669650	−	0.997755i	$-0.521332\pi$
$223$	−2.00000			−0.133930			−0.0669650	+	0.997755i	$0.521332\pi$
$224$		0			0
$225$	−33.0000			−2.20000
$226$	7.00000	+	12.1244i	0.465633	+	0.806500i
$227$	1.00000	−	1.73205i	0.0663723	−	0.114960i	−0.830930	−	0.556378i	$-0.812191\pi$
$227$	1.00000	−	1.73205i	0.0663723	−	0.114960i	0.897302	+	0.441417i	$0.145524\pi$
$228$		0			0
$229$	−10.0000	−	17.3205i	−0.660819	−	1.14457i	−0.980401	−	0.197013i	$-0.936876\pi$
$229$	−10.0000	−	17.3205i	−0.660819	−	1.14457i	0.319582	−	0.947559i	$-0.396457\pi$
$230$	16.0000			1.05501
$231$		0			0
$232$	2.00000			0.131306
$233$	−15.0000	−	25.9808i	−0.982683	−	1.70206i	−0.651813	−	0.758380i	$-0.725991\pi$
$233$	−15.0000	−	25.9808i	−0.982683	−	1.70206i	−0.330870	−	0.943676i	$-0.607342\pi$
$234$	−3.00000	+	5.19615i	−0.196116	+	0.339683i
$235$	4.00000	−	6.92820i	0.260931	−	0.451946i
$236$	6.00000	+	10.3923i	0.390567	+	0.676481i
$237$		0			0
$238$		0			0
$239$	16.0000			1.03495			0.517477	−	0.855697i	$-0.326871\pi$
$239$	16.0000			1.03495			0.517477	+	0.855697i	$0.326871\pi$
$240$		0			0
$241$	−6.00000	+	10.3923i	−0.386494	+	0.669427i	−0.991975	−	0.126432i	$-0.959647\pi$
$241$	−6.00000	+	10.3923i	−0.386494	+	0.669427i	0.605481	+	0.795860i	$0.292981\pi$
$242$	0.500000	−	0.866025i	0.0321412	−	0.0556702i
$243$		0			0
$244$	−14.0000			−0.896258
$245$		0			0
$246$		0			0
$247$	6.00000	+	10.3923i	0.381771	+	0.661247i
$248$	−1.00000	+	1.73205i	−0.0635001	+	0.109985i
$249$		0			0
$250$	−12.0000	−	20.7846i	−0.758947	−	1.31453i
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$		0			0
$253$	−4.00000			−0.251478
$254$	4.00000	+	6.92820i	0.250982	+	0.434714i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	3.00000	+	5.19615i	0.187135	+	0.324127i	0.944294	−	0.329104i	$-0.106747\pi$
$257$	3.00000	+	5.19615i	0.187135	+	0.324127i	−0.757159	+	0.653231i	$0.773413\pi$
$258$		0			0
$259$		0			0
$260$	−8.00000			−0.496139
$261$	−3.00000	−	5.19615i	−0.185695	−	0.321634i
$262$	3.00000	−	5.19615i	0.185341	−	0.321019i
$263$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$263$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$264$		0			0
$265$	−24.0000			−1.47431
$266$		0			0
$267$		0			0
$268$	6.00000	+	10.3923i	0.366508	+	0.634811i
$269$	−6.00000	+	10.3923i	−0.365826	+	0.633630i	−0.988908	−	0.148527i	$-0.952547\pi$
$269$	−6.00000	+	10.3923i	−0.365826	+	0.633630i	0.623082	+	0.782157i	$0.285880\pi$
$270$		0			0
$271$	10.0000	+	17.3205i	0.607457	+	1.05215i	0.991658	+	0.128897i	$0.0411435\pi$
$271$	10.0000	+	17.3205i	0.607457	+	1.05215i	−0.384201	+	0.923249i	$0.625523\pi$
$272$	−4.00000			−0.242536
$273$		0			0
$274$	−6.00000			−0.362473
$275$	5.50000	+	9.52628i	0.331662	+	0.574456i
$276$		0			0
$277$	15.0000	−	25.9808i	0.901263	−	1.56103i	0.0754058	−	0.997153i	$-0.475975\pi$
$277$	15.0000	−	25.9808i	0.901263	−	1.56103i	0.825857	−	0.563880i	$-0.190692\pi$
$278$	7.00000	+	12.1244i	0.419832	+	0.727171i
$279$	6.00000			0.359211
$280$		0			0
$281$	−10.0000			−0.596550			−0.298275	−	0.954480i	$-0.596411\pi$
$281$	−10.0000			−0.596550			−0.298275	+	0.954480i	$0.596411\pi$
$282$		0			0
$283$	−3.00000	+	5.19615i	−0.178331	+	0.308879i	−0.941309	−	0.337546i	$-0.890403\pi$
$283$	−3.00000	+	5.19615i	−0.178331	+	0.308879i	0.762978	+	0.646425i	$0.223737\pi$
$284$	4.00000	−	6.92820i	0.237356	−	0.411113i
$285$		0			0
$286$	2.00000			0.118262
$287$		0			0
$288$	3.00000			0.176777
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$	4.00000	−	6.92820i	0.234888	−	0.406838i
$291$		0			0
$292$	−2.00000	−	3.46410i	−0.117041	−	0.202721i
$293$	18.0000			1.05157			0.525786	−	0.850617i	$-0.323771\pi$
$293$	18.0000			1.05157			0.525786	+	0.850617i	$0.323771\pi$
$294$		0			0
$295$	48.0000			2.79467
$296$	5.00000	+	8.66025i	0.290619	+	0.503367i
$297$		0			0
$298$	1.00000	−	1.73205i	0.0579284	−	0.100335i
$299$	−4.00000	−	6.92820i	−0.231326	−	0.400668i
$300$		0			0
$301$		0			0
$302$	24.0000			1.38104
$303$		0			0
$304$	3.00000	−	5.19615i	0.172062	−	0.298020i
$305$	−28.0000	+	48.4974i	−1.60328	+	2.77695i
$306$	6.00000	+	10.3923i	0.342997	+	0.594089i
$307$	−10.0000			−0.570730			−0.285365	−	0.958419i	$-0.592115\pi$
$307$	−10.0000			−0.570730			−0.285365	+	0.958419i	$0.592115\pi$
$308$		0			0
$309$		0			0
$310$	4.00000	+	6.92820i	0.227185	+	0.393496i
$311$	−7.00000	+	12.1244i	−0.396934	+	0.687509i	−0.993346	−	0.115169i	$-0.963259\pi$
$311$	−7.00000	+	12.1244i	−0.396934	+	0.687509i	0.596412	+	0.802678i	$0.296592\pi$
$312$		0			0
$313$	1.00000	+	1.73205i	0.0565233	+	0.0979013i	0.892903	−	0.450250i	$-0.148665\pi$
$313$	1.00000	+	1.73205i	0.0565233	+	0.0979013i	−0.836379	+	0.548151i	$0.815332\pi$
$314$	8.00000			0.451466
$315$		0			0
$316$		0			0
$317$	−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
$319$	−1.00000	+	1.73205i	−0.0559893	+	0.0969762i
$320$	2.00000	+	3.46410i	0.111803	+	0.193649i
$321$		0			0
$322$		0			0
$323$	24.0000			1.33540
$324$	−4.50000	−	7.79423i	−0.250000	−	0.433013i
$325$	−11.0000	+	19.0526i	−0.610170	+	1.05685i
$326$	2.00000	−	3.46410i	0.110770	−	0.191859i
$327$		0			0
$328$	−4.00000			−0.220863
$329$		0			0
$330$		0			0
$331$	10.0000	+	17.3205i	0.549650	+	0.952021i	0.998298	+	0.0583130i	$0.0185721\pi$
$331$	10.0000	+	17.3205i	0.549650	+	0.952021i	−0.448649	+	0.893708i	$0.648095\pi$
$332$	3.00000	−	5.19615i	0.164646	−	0.285176i
$333$	15.0000	−	25.9808i	0.821995	−	1.42374i
$334$	2.00000	+	3.46410i	0.109435	+	0.189547i
$335$	48.0000			2.62252
$336$		0			0
$337$	−18.0000			−0.980522			−0.490261	−	0.871576i	$-0.663099\pi$
$337$	−18.0000			−0.980522			−0.490261	+	0.871576i	$0.663099\pi$
$338$	−4.50000	−	7.79423i	−0.244768	−	0.423950i
$339$		0			0
$340$	−8.00000	+	13.8564i	−0.433861	+	0.751469i
$341$	−1.00000	−	1.73205i	−0.0541530	−	0.0937958i
$342$	−18.0000			−0.973329
$343$		0			0
$344$	8.00000			0.431331
$345$		0			0
$346$	−7.00000	+	12.1244i	−0.376322	+	0.651809i
$347$	−4.00000	+	6.92820i	−0.214731	+	0.371925i	−0.953189	−	0.302374i	$-0.902221\pi$
$347$	−4.00000	+	6.92820i	−0.214731	+	0.371925i	0.738458	+	0.674299i	$0.235554\pi$
$348$		0			0
$349$	−10.0000			−0.535288			−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000			−0.535288			−0.267644	+	0.963518i	$0.586245\pi$
$350$		0			0
$351$		0			0
$352$	−0.500000	−	0.866025i	−0.0266501	−	0.0461593i
$353$	3.00000	−	5.19615i	0.159674	−	0.276563i	−0.775077	−	0.631867i	$-0.782289\pi$
$353$	3.00000	−	5.19615i	0.159674	−	0.276563i	0.934751	+	0.355303i	$0.115622\pi$
$354$		0			0
$355$	−16.0000	−	27.7128i	−0.849192	−	1.47084i
$356$	−6.00000			−0.317999
$357$		0			0
$358$	−4.00000			−0.211407
$359$	8.00000	+	13.8564i	0.422224	+	0.731313i	0.996157	−	0.0875892i	$-0.0279163\pi$
$359$	8.00000	+	13.8564i	0.422224	+	0.731313i	−0.573933	+	0.818902i	$0.694583\pi$
$360$	6.00000	−	10.3923i	0.316228	−	0.547723i
$361$	−8.50000	+	14.7224i	−0.447368	+	0.774865i
$362$	10.0000	+	17.3205i	0.525588	+	0.910346i
$363$		0			0
$364$		0			0
$365$	−16.0000			−0.837478
$366$		0			0
$367$	−11.0000	+	19.0526i	−0.574195	+	0.994535i	0.421933	+	0.906627i	$0.361352\pi$
$367$	−11.0000	+	19.0526i	−0.574195	+	0.994535i	−0.996129	+	0.0879086i	$0.971982\pi$
$368$	−2.00000	+	3.46410i	−0.104257	+	0.180579i
$369$	6.00000	+	10.3923i	0.312348	+	0.541002i
$370$	40.0000			2.07950
$371$		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	$0.749977\pi$
$374$	2.00000	−	3.46410i	0.103418	−	0.179124i
$375$		0			0
$376$	1.00000	+	1.73205i	0.0515711	+	0.0893237i
$377$	−4.00000			−0.206010
$378$		0			0
$379$	4.00000			0.205466			0.102733	−	0.994709i	$-0.467241\pi$
$379$	4.00000			0.205466			0.102733	+	0.994709i	$0.467241\pi$
$380$	−12.0000	−	20.7846i	−0.615587	−	1.06623i
$381$		0			0
$382$	−2.00000	+	3.46410i	−0.102329	+	0.177239i
$383$	5.00000	+	8.66025i	0.255488	+	0.442518i	0.965028	−	0.262147i	$-0.0844305\pi$
$383$	5.00000	+	8.66025i	0.255488	+	0.442518i	−0.709540	+	0.704665i	$0.751097\pi$
$384$		0			0
$385$		0			0
$386$	−2.00000			−0.101797
$387$	−12.0000	−	20.7846i	−0.609994	−	1.05654i
$388$	7.00000	−	12.1244i	0.355371	−	0.615521i
$389$	15.0000	−	25.9808i	0.760530	−	1.31728i	−0.182047	−	0.983290i	$-0.558272\pi$
$389$	15.0000	−	25.9808i	0.760530	−	1.31728i	0.942578	−	0.333987i	$-0.108394\pi$
$390$		0			0
$391$	−16.0000			−0.809155
$392$		0			0
$393$		0			0
$394$	3.00000	+	5.19615i	0.151138	+	0.261778i
$395$		0			0
$396$	−1.50000	+	2.59808i	−0.0753778	+	0.130558i
$397$	−12.0000	−	20.7846i	−0.602263	−	1.04315i	−0.992478	−	0.122426i	$-0.960933\pi$
$397$	−12.0000	−	20.7846i	−0.602263	−	1.04315i	0.390215	−	0.920724i	$-0.372401\pi$
$398$	14.0000			0.701757
$399$		0			0
$400$	11.0000			0.550000
$401$	9.00000	+	15.5885i	0.449439	+	0.778450i	0.998350	−	0.0574304i	$-0.0182907\pi$
$401$	9.00000	+	15.5885i	0.449439	+	0.778450i	−0.548911	+	0.835881i	$0.684957\pi$
$402$		0			0
$403$	2.00000	−	3.46410i	0.0996271	−	0.172559i
$404$	−3.00000	−	5.19615i	−0.149256	−	0.258518i
$405$	−36.0000			−1.78885
$406$		0			0
$407$	−10.0000			−0.495682
$408$		0			0
$409$	−8.00000	+	13.8564i	−0.395575	+	0.685155i	−0.993174	−	0.116639i	$-0.962788\pi$
$409$	−8.00000	+	13.8564i	−0.395575	+	0.685155i	0.597600	+	0.801795i	$0.296121\pi$
$410$	−8.00000	+	13.8564i	−0.395092	+	0.684319i
$411$		0			0
$412$	18.0000			0.886796
$413$		0			0
$414$	12.0000			0.589768
$415$	−12.0000	−	20.7846i	−0.589057	−	1.02028i
$416$	1.00000	−	1.73205i	0.0490290	−	0.0849208i
$417$		0			0
$418$	3.00000	+	5.19615i	0.146735	+	0.254152i
$419$	−32.0000			−1.56330			−0.781651	−	0.623716i	$-0.785622\pi$
$419$	−32.0000			−1.56330			−0.781651	+	0.623716i	$0.785622\pi$
$420$		0			0
$421$	−2.00000			−0.0974740			−0.0487370	−	0.998812i	$-0.515520\pi$
$421$	−2.00000			−0.0974740			−0.0487370	+	0.998812i	$0.515520\pi$
$422$	−4.00000	−	6.92820i	−0.194717	−	0.337260i
$423$	3.00000	−	5.19615i	0.145865	−	0.252646i
$424$	3.00000	−	5.19615i	0.145693	−	0.252347i
$425$	22.0000	+	38.1051i	1.06716	+	1.84837i
$426$		0			0
$427$		0			0
$428$	−16.0000			−0.773389
$429$		0			0
$430$	16.0000	−	27.7128i	0.771589	−	1.33643i
$431$	−8.00000	+	13.8564i	−0.385346	+	0.667440i	−0.991817	−	0.127666i	$-0.959251\pi$
$431$	−8.00000	+	13.8564i	−0.385346	+	0.667440i	0.606471	+	0.795106i	$0.292585\pi$
$432$		0			0
$433$	2.00000			0.0961139			0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000			0.0961139			0.0480569	+	0.998845i	$0.484697\pi$
$434$		0			0
$435$		0			0
$436$	7.00000	+	12.1244i	0.335239	+	0.580651i
$437$	12.0000	−	20.7846i	0.574038	−	0.994263i
$438$		0			0
$439$	−14.0000	−	24.2487i	−0.668184	−	1.15733i	−0.978412	−	0.206666i	$-0.933739\pi$
$439$	−14.0000	−	24.2487i	−0.668184	−	1.15733i	0.310228	−	0.950662i	$-0.399595\pi$
$440$	−4.00000			−0.190693
$441$		0			0
$442$	8.00000			0.380521
$443$	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
$445$	−12.0000	+	20.7846i	−0.568855	+	0.985285i
$446$	−1.00000	−	1.73205i	−0.0473514	−	0.0820150i
$447$		0			0
$448$		0			0
$449$	−18.0000			−0.849473			−0.424736	−	0.905317i	$-0.639633\pi$
$449$	−18.0000			−0.849473			−0.424736	+	0.905317i	$0.639633\pi$
$450$	−16.5000	−	28.5788i	−0.777817	−	1.34722i
$451$	2.00000	−	3.46410i	0.0941763	−	0.163118i
$452$	−7.00000	+	12.1244i	−0.329252	+	0.570282i
$453$		0			0
$454$	2.00000			0.0938647
$455$		0			0
$456$		0			0
$457$	−1.00000	−	1.73205i	−0.0467780	−	0.0810219i	0.841688	−	0.539964i	$-0.181562\pi$
$457$	−1.00000	−	1.73205i	−0.0467780	−	0.0810219i	−0.888466	+	0.458942i	$0.848229\pi$
$458$	10.0000	−	17.3205i	0.467269	−	0.809334i
$459$		0			0
$460$	8.00000	+	13.8564i	0.373002	+	0.646058i
$461$	30.0000			1.39724			0.698620	−	0.715493i	$-0.253798\pi$
$461$	30.0000			1.39724			0.698620	+	0.715493i	$0.253798\pi$
$462$		0			0
$463$	−32.0000			−1.48717			−0.743583	−	0.668644i	$-0.766875\pi$
$463$	−32.0000			−1.48717			−0.743583	+	0.668644i	$0.766875\pi$
$464$	1.00000	+	1.73205i	0.0464238	+	0.0804084i
$465$		0			0
$466$	15.0000	−	25.9808i	0.694862	−	1.20354i
$467$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$467$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$468$	−6.00000			−0.277350
$469$		0			0
$470$	8.00000			0.369012
$471$		0			0
$472$	−6.00000	+	10.3923i	−0.276172	+	0.478345i
$473$	−4.00000	+	6.92820i	−0.183920	+	0.318559i
$474$		0			0
$475$	−66.0000			−3.02829
$476$		0			0
$477$	−18.0000			−0.824163
$478$	8.00000	+	13.8564i	0.365911	+	0.633777i
$479$	8.00000	−	13.8564i	0.365529	−	0.633115i	−0.623332	−	0.781958i	$-0.714221\pi$
$479$	8.00000	−	13.8564i	0.365529	−	0.633115i	0.988861	+	0.148842i	$0.0475547\pi$
$480$		0			0
$481$	−10.0000	−	17.3205i	−0.455961	−	0.789747i
$482$	−12.0000			−0.546585
$483$		0			0
$484$	1.00000			0.0454545
$485$	−28.0000	−	48.4974i	−1.27141	−	2.20215i
$486$		0			0
$487$	14.0000	−	24.2487i	0.634401	−	1.09881i	−0.352241	−	0.935909i	$-0.614580\pi$
$487$	14.0000	−	24.2487i	0.634401	−	1.09881i	0.986642	−	0.162905i	$-0.0520863\pi$
$488$	−7.00000	−	12.1244i	−0.316875	−	0.548844i
$489$		0			0
$490$		0			0
$491$	−36.0000			−1.62466			−0.812329	−	0.583200i	$-0.801800\pi$
$491$	−36.0000			−1.62466			−0.812329	+	0.583200i	$0.801800\pi$
$492$		0			0
$493$	−4.00000	+	6.92820i	−0.180151	+	0.312031i
$494$	−6.00000	+	10.3923i	−0.269953	+	0.467572i
$495$	6.00000	+	10.3923i	0.269680	+	0.467099i
$496$	−2.00000			−0.0898027
$497$		0			0
$498$		0			0
$499$	−22.0000	−	38.1051i	−0.984855	−	1.70582i	−0.642578	−	0.766220i	$-0.722135\pi$
$499$	−22.0000	−	38.1051i	−0.984855	−	1.70582i	−0.342277	−	0.939599i	$-0.611198\pi$
$500$	12.0000	−	20.7846i	0.536656	−	0.929516i
$501$		0			0
$502$	6.00000	+	10.3923i	0.267793	+	0.463831i
$503$	−36.0000			−1.60516			−0.802580	−	0.596544i	$-0.796540\pi$
$503$	−36.0000			−1.60516			−0.802580	+	0.596544i	$0.796540\pi$
$504$		0			0
$505$	−24.0000			−1.06799
$506$	−2.00000	−	3.46410i	−0.0889108	−	0.153998i
$507$		0			0
$508$	−4.00000	+	6.92820i	−0.177471	+	0.307389i
$509$	14.0000	+	24.2487i	0.620539	+	1.07481i	0.989385	+	0.145315i	$0.0464195\pi$
$509$	14.0000	+	24.2487i	0.620539	+	1.07481i	−0.368846	+	0.929490i	$0.620247\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−3.00000	+	5.19615i	−0.132324	+	0.229192i
$515$	36.0000	−	62.3538i	1.58635	−	2.74764i
$516$		0			0
$517$	−2.00000			−0.0879599
$518$		0			0
$519$		0			0
$520$	−4.00000	−	6.92820i	−0.175412	−	0.303822i
$521$	−5.00000	+	8.66025i	−0.219054	+	0.379413i	−0.954519	−	0.298150i	$-0.903630\pi$
$521$	−5.00000	+	8.66025i	−0.219054	+	0.379413i	0.735465	+	0.677563i	$0.236964\pi$
$522$	3.00000	−	5.19615i	0.131306	−	0.227429i
$523$	17.0000	+	29.4449i	0.743358	+	1.28753i	0.950958	+	0.309320i	$0.100101\pi$
$523$	17.0000	+	29.4449i	0.743358	+	1.28753i	−0.207600	+	0.978214i	$0.566565\pi$
$524$	6.00000			0.262111
$525$		0			0
$526$		0			0
$527$	−4.00000	−	6.92820i	−0.174243	−	0.301797i
$528$		0			0
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$	−12.0000	−	20.7846i	−0.521247	−	0.902826i
$531$	36.0000			1.56227
$532$		0			0
$533$	8.00000			0.346518
$534$		0			0
$535$	−32.0000	+	55.4256i	−1.38348	+	2.39626i
$536$	−6.00000	+	10.3923i	−0.259161	+	0.448879i
$537$		0			0
$538$	−12.0000			−0.517357
$539$		0			0
$540$		0			0
$541$	−7.00000	−	12.1244i	−0.300954	−	0.521267i	0.675399	−	0.737453i	$-0.263972\pi$
$541$	−7.00000	−	12.1244i	−0.300954	−	0.521267i	−0.976352	+	0.216186i	$0.930638\pi$
$542$	−10.0000	+	17.3205i	−0.429537	+	0.743980i
$543$		0			0
$544$	−2.00000	−	3.46410i	−0.0857493	−	0.148522i
$545$	56.0000			2.39878
$546$		0			0
$547$	−12.0000			−0.513083			−0.256541	−	0.966533i	$-0.582583\pi$
$547$	−12.0000			−0.513083			−0.256541	+	0.966533i	$0.582583\pi$
$548$	−3.00000	−	5.19615i	−0.128154	−	0.221969i
$549$	−21.0000	+	36.3731i	−0.896258	+	1.55236i
$550$	−5.50000	+	9.52628i	−0.234521	+	0.406202i
$551$	−6.00000	−	10.3923i	−0.255609	−	0.442727i
$552$		0			0
$553$		0			0
$554$	30.0000			1.27458
$555$		0			0
$556$	−7.00000	+	12.1244i	−0.296866	+	0.514187i
$557$	−7.00000	+	12.1244i	−0.296600	+	0.513725i	−0.975356	−	0.220638i	$-0.929186\pi$
$557$	−7.00000	+	12.1244i	−0.296600	+	0.513725i	0.678756	+	0.734364i	$0.262519\pi$
$558$	3.00000	+	5.19615i	0.127000	+	0.219971i
$559$	−16.0000			−0.676728
$560$		0			0
$561$		0			0
$562$	−5.00000	−	8.66025i	−0.210912	−	0.365311i
$563$	17.0000	−	29.4449i	0.716465	−	1.24095i	−0.245927	−	0.969288i	$-0.579092\pi$
$563$	17.0000	−	29.4449i	0.716465	−	1.24095i	0.962392	−	0.271665i	$-0.0875742\pi$
$564$		0			0
$565$	28.0000	+	48.4974i	1.17797	+	2.04030i
$566$	−6.00000			−0.252199
$567$		0			0
$568$	8.00000			0.335673
$569$	−3.00000	−	5.19615i	−0.125767	−	0.217834i	0.796266	−	0.604947i	$-0.206806\pi$
$569$	−3.00000	−	5.19615i	−0.125767	−	0.217834i	−0.922032	+	0.387113i	$0.873472\pi$
$570$		0			0
$571$	−14.0000	+	24.2487i	−0.585882	+	1.01478i	0.408883	+	0.912587i	$0.365918\pi$
$571$	−14.0000	+	24.2487i	−0.585882	+	1.01478i	−0.994765	+	0.102190i	$0.967415\pi$
$572$	1.00000	+	1.73205i	0.0418121	+	0.0724207i
$573$		0			0
$574$		0			0
$575$	44.0000			1.83493
$576$	1.50000	+	2.59808i	0.0625000	+	0.108253i
$577$	−7.00000	+	12.1244i	−0.291414	+	0.504744i	−0.974144	−	0.225927i	$-0.927459\pi$
$577$	−7.00000	+	12.1244i	−0.291414	+	0.504744i	0.682730	+	0.730670i	$0.260792\pi$
$578$	−0.500000	+	0.866025i	−0.0207973	+	0.0360219i
$579$		0			0
$580$	8.00000			0.332182
$581$		0			0
$582$		0			0
$583$	3.00000	+	5.19615i	0.124247	+	0.215203i
$584$	2.00000	−	3.46410i	0.0827606	−	0.143346i
$585$	−12.0000	+	20.7846i	−0.496139	+	0.859338i
$586$	9.00000	+	15.5885i	0.371787	+	0.643953i
$587$	−12.0000			−0.495293			−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000			−0.495293			−0.247647	+	0.968850i	$0.579657\pi$
$588$		0			0
$589$	12.0000			0.494451
$590$	24.0000	+	41.5692i	0.988064	+	1.71138i
$591$		0			0
$592$	−5.00000	+	8.66025i	−0.205499	+	0.355934i
$593$	6.00000	+	10.3923i	0.246390	+	0.426761i	0.962522	−	0.271205i	$-0.0874221\pi$
$593$	6.00000	+	10.3923i	0.246390	+	0.426761i	−0.716131	+	0.697966i	$0.754089\pi$
$594$		0			0
$595$		0			0
$596$	2.00000			0.0819232
$597$		0			0
$598$	4.00000	−	6.92820i	0.163572	−	0.283315i
$599$	−12.0000	+	20.7846i	−0.490307	+	0.849236i	−0.999938	−	0.0111569i	$-0.996449\pi$
$599$	−12.0000	+	20.7846i	−0.490307	+	0.849236i	0.509631	+	0.860393i	$0.329782\pi$
$600$		0			0
$601$	8.00000			0.326327			0.163163	−	0.986599i	$-0.447830\pi$
$601$	8.00000			0.326327			0.163163	+	0.986599i	$0.447830\pi$
$602$		0			0
$603$	36.0000			1.46603
$604$	12.0000	+	20.7846i	0.488273	+	0.845714i
$605$	2.00000	−	3.46410i	0.0813116	−	0.140836i
$606$		0			0
$607$	−4.00000	−	6.92820i	−0.162355	−	0.281207i	0.773358	−	0.633970i	$-0.218576\pi$
$607$	−4.00000	−	6.92820i	−0.162355	−	0.281207i	−0.935713	+	0.352763i	$0.885242\pi$
$608$	6.00000			0.243332
$609$		0			0
$610$	−56.0000			−2.26737
$611$	−2.00000	−	3.46410i	−0.0809113	−	0.140143i
$612$	−6.00000	+	10.3923i	−0.242536	+	0.420084i
$613$	−23.0000	+	39.8372i	−0.928961	+	1.60901i	−0.143898	+	0.989593i	$0.545964\pi$
$613$	−23.0000	+	39.8372i	−0.928961	+	1.60901i	−0.785063	+	0.619416i	$0.787370\pi$
$614$	−5.00000	−	8.66025i	−0.201784	−	0.349499i
$615$		0			0
$616$		0			0
$617$	18.0000			0.724653			0.362326	−	0.932051i	$-0.381983\pi$
$617$	18.0000			0.724653			0.362326	+	0.932051i	$0.381983\pi$
$618$		0			0
$619$	−4.00000	+	6.92820i	−0.160774	+	0.278468i	−0.935146	−	0.354262i	$-0.884732\pi$
$619$	−4.00000	+	6.92820i	−0.160774	+	0.278468i	0.774373	+	0.632730i	$0.218066\pi$
$620$	−4.00000	+	6.92820i	−0.160644	+	0.278243i
$621$		0			0
$622$	−14.0000			−0.561349
$623$		0			0
$624$		0			0
$625$	−20.5000	−	35.5070i	−0.820000	−	1.42028i
$626$	−1.00000	+	1.73205i	−0.0399680	+	0.0692267i
$627$		0			0
$628$	4.00000	+	6.92820i	0.159617	+	0.276465i
$629$	−40.0000			−1.59490
$630$		0			0
$631$	−12.0000			−0.477712			−0.238856	−	0.971055i	$-0.576772\pi$
$631$	−12.0000			−0.477712			−0.238856	+	0.971055i	$0.576772\pi$
$632$		0			0
$633$		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
$638$	−2.00000			−0.0791808
$639$	−12.0000	−	20.7846i	−0.474713	−	0.822226i
$640$	−2.00000	+	3.46410i	−0.0790569	+	0.136931i
$641$	3.00000	−	5.19615i	0.118493	−	0.205236i	−0.800678	−	0.599095i	$-0.795527\pi$
$641$	3.00000	−	5.19615i	0.118493	−	0.205236i	0.919171	+	0.393860i	$0.128860\pi$
$642$		0			0
$643$	4.00000			0.157745			0.0788723	−	0.996885i	$-0.474868\pi$
$643$	4.00000			0.157745			0.0788723	+	0.996885i	$0.474868\pi$
$644$		0			0
$645$		0			0
$646$	12.0000	+	20.7846i	0.472134	+	0.817760i
$647$	−3.00000	+	5.19615i	−0.117942	+	0.204282i	−0.918952	−	0.394369i	$-0.870963\pi$
$647$	−3.00000	+	5.19615i	−0.117942	+	0.204282i	0.801010	+	0.598651i	$0.204296\pi$
$648$	4.50000	−	7.79423i	0.176777	−	0.306186i
$649$	−6.00000	−	10.3923i	−0.235521	−	0.407934i
$650$	−22.0000			−0.862911
$651$		0			0
$652$	4.00000			0.156652
$653$	−5.00000	−	8.66025i	−0.195665	−	0.338902i	0.751453	−	0.659786i	$-0.229353\pi$
$653$	−5.00000	−	8.66025i	−0.195665	−	0.338902i	−0.947118	+	0.320884i	$0.896020\pi$
$654$		0			0
$655$	12.0000	−	20.7846i	0.468879	−	0.812122i
$656$	−2.00000	−	3.46410i	−0.0780869	−	0.135250i
$657$	−12.0000			−0.468165
$658$		0			0
$659$	−8.00000			−0.311636			−0.155818	−	0.987786i	$-0.549801\pi$
$659$	−8.00000			−0.311636			−0.155818	+	0.987786i	$0.549801\pi$
$660$		0			0
$661$	−10.0000	+	17.3205i	−0.388955	+	0.673690i	−0.992309	−	0.123784i	$-0.960497\pi$
$661$	−10.0000	+	17.3205i	−0.388955	+	0.673690i	0.603354	+	0.797473i	$0.293830\pi$
$662$	−10.0000	+	17.3205i	−0.388661	+	0.673181i
$663$		0			0
$664$	6.00000			0.232845
$665$		0			0
$666$	30.0000			1.16248
$667$	4.00000	+	6.92820i	0.154881	+	0.268261i
$668$	−2.00000	+	3.46410i	−0.0773823	+	0.134030i
$669$		0			0
$670$	24.0000	+	41.5692i	0.927201	+	1.60596i
$671$	14.0000			0.540464
$672$		0			0
$673$	22.0000			0.848038			0.424019	−	0.905653i	$-0.360619\pi$
$673$	22.0000			0.848038			0.424019	+	0.905653i	$0.360619\pi$
$674$	−9.00000	−	15.5885i	−0.346667	−	0.600445i
$675$		0			0
$676$	4.50000	−	7.79423i	0.173077	−	0.299778i
$677$	−13.0000	−	22.5167i	−0.499631	−	0.865386i	0.500369	−	0.865812i	$-0.333198\pi$
$677$	−13.0000	−	22.5167i	−0.499631	−	0.865386i	−1.00000		0.000426509i	$0.999864\pi$
$678$		0			0
$679$		0			0
$680$	−16.0000			−0.613572
$681$		0			0
$682$	1.00000	−	1.73205i	0.0382920	−	0.0663237i
$683$	−18.0000	+	31.1769i	−0.688751	+	1.19295i	0.283491	+	0.958975i	$0.408507\pi$
$683$	−18.0000	+	31.1769i	−0.688751	+	1.19295i	−0.972242	+	0.233977i	$0.924826\pi$
$684$	−9.00000	−	15.5885i	−0.344124	−	0.596040i
$685$	−24.0000			−0.916993
$686$		0			0
$687$		0			0
$688$	4.00000	+	6.92820i	0.152499	+	0.264135i
$689$	−6.00000	+	10.3923i	−0.228582	+	0.395915i
$690$		0			0
$691$	−18.0000	−	31.1769i	−0.684752	−	1.18603i	−0.973515	−	0.228625i	$-0.926577\pi$
$691$	−18.0000	−	31.1769i	−0.684752	−	1.18603i	0.288762	−	0.957401i	$-0.406756\pi$
$692$	−14.0000			−0.532200
$693$		0			0
$694$	−8.00000			−0.303676
$695$	28.0000	+	48.4974i	1.06210	+	1.83961i
$696$		0			0
$697$	8.00000	−	13.8564i	0.303022	−	0.524849i
$698$	−5.00000	−	8.66025i	−0.189253	−	0.327795i
$699$		0			0
$700$		0			0
$701$	−30.0000			−1.13308			−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000			−1.13308			−0.566542	+	0.824033i	$0.691719\pi$
$702$		0			0
$703$	30.0000	−	51.9615i	1.13147	−	1.95977i
$704$	0.500000	−	0.866025i	0.0188445	−	0.0326396i
$705$		0			0
$706$	6.00000			0.225813
$707$		0			0
$708$		0			0
$709$	−9.00000	−	15.5885i	−0.338002	−	0.585437i	0.646055	−	0.763291i	$-0.276418\pi$
$709$	−9.00000	−	15.5885i	−0.338002	−	0.585437i	−0.984057	+	0.177854i	$0.943084\pi$
$710$	16.0000	−	27.7128i	0.600469	−	1.04004i
$711$		0			0
$712$	−3.00000	−	5.19615i	−0.112430	−	0.194734i
$713$	−8.00000			−0.299602
$714$		0			0
$715$	8.00000			0.299183
$716$	−2.00000	−	3.46410i	−0.0747435	−	0.129460i
$717$		0			0
$718$	−8.00000	+	13.8564i	−0.298557	+	0.517116i
$719$	13.0000	+	22.5167i	0.484818	+	0.839730i	0.999848	−	0.0174426i	$-0.00555244\pi$
$719$	13.0000	+	22.5167i	0.484818	+	0.839730i	−0.515030	+	0.857172i	$0.672219\pi$
$720$	12.0000			0.447214
$721$		0			0
$722$	−17.0000			−0.632674
$723$		0			0
$724$	−10.0000	+	17.3205i	−0.371647	+	0.643712i
$725$	11.0000	−	19.0526i	0.408530	−	0.707594i
$726$		0			0
$727$	−10.0000			−0.370879			−0.185440	−	0.982656i	$-0.559371\pi$
$727$	−10.0000			−0.370879			−0.185440	+	0.982656i	$0.559371\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	−8.00000	−	13.8564i	−0.296093	−	0.512849i
$731$	−16.0000	+	27.7128i	−0.591781	+	1.02500i
$732$		0			0
$733$	11.0000	+	19.0526i	0.406294	+	0.703722i	0.994471	−	0.105010i	$-0.0334875\pi$
$733$	11.0000	+	19.0526i	0.406294	+	0.703722i	−0.588177	+	0.808732i	$0.700154\pi$
$734$	−22.0000			−0.812035
$735$		0			0
$736$	−4.00000			−0.147442
$737$	−6.00000	−	10.3923i	−0.221013	−	0.382805i
$738$	−6.00000	+	10.3923i	−0.220863	+	0.382546i
$739$	6.00000	−	10.3923i	0.220714	−	0.382287i	−0.734311	−	0.678813i	$-0.762495\pi$
$739$	6.00000	−	10.3923i	0.220714	−	0.382287i	0.955025	+	0.296526i	$0.0958281\pi$
$740$	20.0000	+	34.6410i	0.735215	+	1.27343i
$741$		0			0
$742$		0			0
$743$	−24.0000			−0.880475			−0.440237	−	0.897881i	$-0.645106\pi$
$743$	−24.0000			−0.880475			−0.440237	+	0.897881i	$0.645106\pi$
$744$		0			0
$745$	4.00000	−	6.92820i	0.146549	−	0.253830i
$746$	−5.00000	+	8.66025i	−0.183063	+	0.317074i
$747$	−9.00000	−	15.5885i	−0.329293	−	0.570352i
$748$	4.00000			0.146254
$749$		0			0
$750$		0			0
$751$	−14.0000	−	24.2487i	−0.510867	−	0.884848i	−0.999921	−	0.0125942i	$-0.995991\pi$
$751$	−14.0000	−	24.2487i	−0.510867	−	0.884848i	0.489053	−	0.872254i	$-0.337342\pi$
$752$	−1.00000	+	1.73205i	−0.0364662	+	0.0631614i
$753$		0			0
$754$	−2.00000	−	3.46410i	−0.0728357	−	0.126155i
$755$	96.0000			3.49380
$756$		0			0
$757$	26.0000			0.944986			0.472493	−	0.881334i	$-0.343354\pi$
$757$	26.0000			0.944986			0.472493	+	0.881334i	$0.343354\pi$
$758$	2.00000	+	3.46410i	0.0726433	+	0.125822i
$759$		0			0
$760$	12.0000	−	20.7846i	0.435286	−	0.753937i
$761$	24.0000	+	41.5692i	0.869999	+	1.50688i	0.861996	+	0.506915i	$0.169214\pi$
$761$	24.0000	+	41.5692i	0.869999	+	1.50688i	0.00800331	+	0.999968i	$0.497452\pi$
$762$		0			0
$763$		0			0
$764$	−4.00000			−0.144715
$765$	24.0000	+	41.5692i	0.867722	+	1.50294i
$766$	−5.00000	+	8.66025i	−0.180657	+	0.312908i
$767$	12.0000	−	20.7846i	0.433295	−	0.750489i
$768$		0			0
$769$	16.0000			0.576975			0.288487	−	0.957484i	$-0.406848\pi$
$769$	16.0000			0.576975			0.288487	+	0.957484i	$0.406848\pi$
$770$		0			0
$771$		0			0
$772$	−1.00000	−	1.73205i	−0.0359908	−	0.0623379i
$773$	24.0000	−	41.5692i	0.863220	−	1.49514i	−0.00558380	−	0.999984i	$-0.501777\pi$
$773$	24.0000	−	41.5692i	0.863220	−	1.49514i	0.868804	−	0.495156i	$-0.164889\pi$
$774$	12.0000	−	20.7846i	0.431331	−	0.747087i
$775$	11.0000	+	19.0526i	0.395132	+	0.684388i
$776$	14.0000			0.502571
$777$		0			0
$778$	30.0000			1.07555
$779$	12.0000	+	20.7846i	0.429945	+	0.744686i
$780$		0			0
$781$	−4.00000	+	6.92820i	−0.143131	+	0.247911i
$782$	−8.00000	−	13.8564i	−0.286079	−	0.495504i
$783$		0			0
$784$		0			0
$785$	32.0000			1.14213
$786$		0			0
$787$	11.0000	−	19.0526i	0.392108	−	0.679150i	−0.600620	−	0.799535i	$-0.705079\pi$
$787$	11.0000	−	19.0526i	0.392108	−	0.679150i	0.992727	+	0.120384i	$0.0384127\pi$
$788$	−3.00000	+	5.19615i	−0.106871	+	0.185105i
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−3.00000			−0.106600
$793$	14.0000	+	24.2487i	0.497155	+	0.861097i
$794$	12.0000	−	20.7846i	0.425864	−	0.737618i
$795$		0			0
$796$	7.00000	+	12.1244i	0.248108	+	0.429736i
$797$	−16.0000			−0.566749			−0.283375	−	0.959009i	$-0.591454\pi$
$797$	−16.0000			−0.566749			−0.283375	+	0.959009i	$0.591454\pi$
$798$		0			0
$799$	−8.00000			−0.283020
$800$	5.50000	+	9.52628i	0.194454	+	0.336805i
$801$	−9.00000	+	15.5885i	−0.317999	+	0.550791i
$802$	−9.00000	+	15.5885i	−0.317801	+	0.550448i
$803$	2.00000	+	3.46410i	0.0705785	+	0.122245i
$804$		0			0
$805$		0			0
$806$	4.00000			0.140894
$807$		0			0
$808$	3.00000	−	5.19615i	0.105540	−	0.182800i
$809$	15.0000	−	25.9808i	0.527372	−	0.913435i	−0.472119	−	0.881535i	$-0.656511\pi$
$809$	15.0000	−	25.9808i	0.527372	−	0.913435i	0.999491	−	0.0319002i	$-0.0101559\pi$
$810$	−18.0000	−	31.1769i	−0.632456	−	1.09545i
$811$	38.0000			1.33436			0.667180	−	0.744896i	$-0.267501\pi$
$811$	38.0000			1.33436			0.667180	+	0.744896i	$0.267501\pi$
$812$		0			0
$813$		0			0
$814$	−5.00000	−	8.66025i	−0.175250	−	0.303542i
$815$	8.00000	−	13.8564i	0.280228	−	0.485369i
$816$		0			0
$817$	−24.0000	−	41.5692i	−0.839654	−	1.45432i
$818$	−16.0000			−0.559427
$819$		0			0
$820$	−16.0000			−0.558744
$821$	−9.00000	−	15.5885i	−0.314102	−	0.544041i	0.665144	−	0.746715i	$-0.268370\pi$
$821$	−9.00000	−	15.5885i	−0.314102	−	0.544041i	−0.979246	+	0.202674i	$0.935037\pi$
$822$		0			0
$823$	2.00000	−	3.46410i	0.0697156	−	0.120751i	−0.829060	−	0.559159i	$-0.811124\pi$
$823$	2.00000	−	3.46410i	0.0697156	−	0.120751i	0.898776	+	0.438408i	$0.144457\pi$
$824$	9.00000	+	15.5885i	0.313530	+	0.543050i
$825$		0			0
$826$		0			0
$827$	20.0000			0.695468			0.347734	−	0.937593i	$-0.386951\pi$
$827$	20.0000			0.695468			0.347734	+	0.937593i	$0.386951\pi$
$828$	6.00000	+	10.3923i	0.208514	+	0.361158i
$829$	10.0000	−	17.3205i	0.347314	−	0.601566i	−0.638457	−	0.769657i	$-0.720427\pi$
$829$	10.0000	−	17.3205i	0.347314	−	0.601566i	0.985771	+	0.168091i	$0.0537604\pi$
$830$	12.0000	−	20.7846i	0.416526	−	0.721444i
$831$		0			0
$832$	2.00000			0.0693375
$833$		0			0
$834$		0			0
$835$	8.00000	+	13.8564i	0.276851	+	0.479521i
$836$	−3.00000	+	5.19615i	−0.103757	+	0.179713i
$837$		0			0
$838$	−16.0000	−	27.7128i	−0.552711	−	0.957323i
$839$	30.0000			1.03572			0.517858	−	0.855467i	$-0.326730\pi$
$839$	30.0000			1.03572			0.517858	+	0.855467i	$0.326730\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$	−1.00000	−	1.73205i	−0.0344623	−	0.0596904i
$843$		0			0
$844$	4.00000	−	6.92820i	0.137686	−	0.238479i
$845$	−18.0000	−	31.1769i	−0.619219	−	1.07252i
$846$	6.00000			0.206284
$847$		0			0
$848$	6.00000			0.206041
$849$		0			0
$850$	−22.0000	+	38.1051i	−0.754594	+	1.30699i
$851$	−20.0000	+	34.6410i	−0.685591	+	1.18748i
$852$		0			0
$853$	2.00000			0.0684787			0.0342393	−	0.999414i	$-0.489099\pi$
$853$	2.00000			0.0684787			0.0342393	+	0.999414i	$0.489099\pi$
$854$		0			0
$855$	−72.0000			−2.46235
$856$	−8.00000	−	13.8564i	−0.273434	−	0.473602i
$857$	−16.0000	+	27.7128i	−0.546550	+	0.946652i	0.451958	+	0.892039i	$0.350726\pi$
$857$	−16.0000	+	27.7128i	−0.546550	+	0.946652i	−0.998508	+	0.0546125i	$0.982608\pi$
$858$		0			0
$859$	−14.0000	−	24.2487i	−0.477674	−	0.827355i	0.521999	−	0.852946i	$-0.325187\pi$
$859$	−14.0000	−	24.2487i	−0.477674	−	0.827355i	−0.999672	+	0.0255910i	$0.991853\pi$
$860$	32.0000			1.09119
$861$		0			0
$862$	−16.0000			−0.544962
$863$	22.0000	+	38.1051i	0.748889	+	1.29711i	0.948356	+	0.317209i	$0.102746\pi$
$863$	22.0000	+	38.1051i	0.748889	+	1.29711i	−0.199467	+	0.979905i	$0.563921\pi$
$864$		0			0
$865$	−28.0000	+	48.4974i	−0.952029	+	1.64896i
$866$	1.00000	+	1.73205i	0.0339814	+	0.0588575i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$	12.0000	−	20.7846i	0.406604	−	0.704260i
$872$	−7.00000	+	12.1244i	−0.237050	+	0.410582i
$873$	−21.0000	−	36.3731i	−0.710742	−	1.23104i
$874$	24.0000			0.811812
$875$		0			0
$876$		0			0
$877$	−17.0000	−	29.4449i	−0.574049	−	0.994282i	−0.996144	−	0.0877308i	$-0.972038\pi$
$877$	−17.0000	−	29.4449i	−0.574049	−	0.994282i	0.422095	−	0.906552i	$-0.361295\pi$
$878$	14.0000	−	24.2487i	0.472477	−	0.818354i
$879$		0			0
$880$	−2.00000	−	3.46410i	−0.0674200	−	0.116775i
$881$	30.0000			1.01073			0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000			1.01073			0.505363	+	0.862907i	$0.331359\pi$
$882$		0			0
$883$	−44.0000			−1.48072			−0.740359	−	0.672212i	$-0.765344\pi$
$883$	−44.0000			−1.48072			−0.740359	+	0.672212i	$0.765344\pi$
$884$	4.00000	+	6.92820i	0.134535	+	0.233021i
$885$		0			0
$886$	−18.0000	+	31.1769i	−0.604722	+	1.04741i
$887$	−8.00000	−	13.8564i	−0.268614	−	0.465253i	0.699890	−	0.714250i	$-0.253232\pi$
$887$	−8.00000	−	13.8564i	−0.268614	−	0.465253i	−0.968504	+	0.248998i	$0.919899\pi$
$888$		0			0
$889$		0			0
$890$	−24.0000			−0.804482
$891$	4.50000	+	7.79423i	0.150756	+	0.261116i
$892$	1.00000	−	1.73205i	0.0334825	−	0.0579934i
$893$	6.00000	−	10.3923i	0.200782	−	0.347765i
$894$		0			0
$895$	−16.0000			−0.534821
$896$		0			0
$897$		0			0
$898$	−9.00000	−	15.5885i	−0.300334	−	0.520194i
$899$	−2.00000	+	3.46410i	−0.0667037	+	0.115534i
$900$	16.5000	−	28.5788i	0.550000	−	0.952628i
$901$	12.0000	+	20.7846i	0.399778	+	0.692436i
$902$	4.00000			0.133185
$903$		0			0
$904$	−14.0000			−0.465633
$905$	40.0000	+	69.2820i	1.32964	+	2.30301i
$906$		0			0
$907$	26.0000	−	45.0333i	0.863316	−	1.49531i	−0.00539395	−	0.999985i	$-0.501717\pi$
$907$	26.0000	−	45.0333i	0.863316	−	1.49531i	0.868710	−	0.495321i	$-0.164950\pi$
$908$	1.00000	+	1.73205i	0.0331862	+	0.0574801i
$909$	−18.0000			−0.597022
$910$		0			0
$911$	−36.0000			−1.19273			−0.596367	−	0.802712i	$-0.703390\pi$
$911$	−36.0000			−1.19273			−0.596367	+	0.802712i	$0.703390\pi$
$912$		0			0
$913$	−3.00000	+	5.19615i	−0.0992855	+	0.171968i
$914$	1.00000	−	1.73205i	0.0330771	−	0.0572911i
$915$		0			0
$916$	20.0000			0.660819
$917$		0			0
$918$		0			0
$919$	−12.0000	−	20.7846i	−0.395843	−	0.685621i	0.597365	−	0.801970i	$-0.296214\pi$
$919$	−12.0000	−	20.7846i	−0.395843	−	0.685621i	−0.993208	+	0.116348i	$0.962881\pi$
$920$	−8.00000	+	13.8564i	−0.263752	+	0.456832i
$921$		0			0
$922$	15.0000	+	25.9808i	0.493999	+	0.855631i
$923$	−16.0000			−0.526646
$924$		0			0
$925$	110.000			3.61678
$926$	−16.0000	−	27.7128i	−0.525793	−	0.910700i
$927$	27.0000	−	46.7654i	0.886796	−	1.53598i
$928$	−1.00000	+	1.73205i	−0.0328266	+	0.0568574i
$929$	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
$932$	30.0000			0.982683
$933$		0			0
$934$		0			0
$935$	8.00000	−	13.8564i	0.261628	−	0.453153i
$936$	−3.00000	−	5.19615i	−0.0980581	−	0.169842i
$937$	12.0000			0.392023			0.196011	−	0.980602i	$-0.437201\pi$
$937$	12.0000			0.392023			0.196011	+	0.980602i	$0.437201\pi$
$938$		0			0
$939$		0			0
$940$	4.00000	+	6.92820i	0.130466	+	0.225973i
$941$	7.00000	−	12.1244i	0.228193	−	0.395243i	−0.729079	−	0.684429i	$-0.760051\pi$
$941$	7.00000	−	12.1244i	0.228193	−	0.395243i	0.957273	+	0.289187i	$0.0933848\pi$
$942$		0			0
$943$	−8.00000	−	13.8564i	−0.260516	−	0.451227i
$944$	−12.0000			−0.390567
$945$		0			0
$946$	−8.00000			−0.260102
$947$	2.00000	+	3.46410i	0.0649913	+	0.112568i	0.896690	−	0.442659i	$-0.145965\pi$
$947$	2.00000	+	3.46410i	0.0649913	+	0.112568i	−0.831699	+	0.555227i	$0.812631\pi$
$948$		0			0
$949$	−4.00000	+	6.92820i	−0.129845	+	0.224899i
$950$	−33.0000	−	57.1577i	−1.07066	−	1.85444i
$951$		0			0
$952$		0			0
$953$	−22.0000			−0.712650			−0.356325	−	0.934362i	$-0.615970\pi$
$953$	−22.0000			−0.712650			−0.356325	+	0.934362i	$0.615970\pi$
$954$	−9.00000	−	15.5885i	−0.291386	−	0.504695i
$955$	−8.00000	+	13.8564i	−0.258874	+	0.448383i
$956$	−8.00000	+	13.8564i	−0.258738	+	0.448148i
$957$		0			0
$958$	16.0000			0.516937
$959$		0			0
$960$		0			0
$961$	13.5000	+	23.3827i	0.435484	+	0.754280i
$962$	10.0000	−	17.3205i	0.322413	−	0.558436i
$963$	−24.0000	+	41.5692i	−0.773389	+	1.33955i
$964$	−6.00000	−	10.3923i	−0.193247	−	0.334714i
$965$	−8.00000			−0.257529
$966$		0			0
$967$	32.0000			1.02905			0.514525	−	0.857475i	$-0.327968\pi$
$967$	32.0000			1.02905			0.514525	+	0.857475i	$0.327968\pi$
$968$	0.500000	+	0.866025i	0.0160706	+	0.0278351i
$969$		0			0
$970$	28.0000	−	48.4974i	0.899026	−	1.55716i
$971$	−28.0000	−	48.4974i	−0.898563	−	1.55636i	−0.829332	−	0.558756i	$-0.811279\pi$
$971$	−28.0000	−	48.4974i	−0.898563	−	1.55636i	−0.0692304	−	0.997601i	$-0.522054\pi$
$972$		0			0
$973$		0			0
$974$	28.0000			0.897178
$975$		0			0
$976$	7.00000	−	12.1244i	0.224065	−	0.388091i
$977$	−1.00000	+	1.73205i	−0.0319928	+	0.0554132i	−0.881579	−	0.472037i	$-0.843519\pi$
$977$	−1.00000	+	1.73205i	−0.0319928	+	0.0554132i	0.849586	+	0.527451i	$0.176852\pi$
$978$		0			0
$979$	6.00000			0.191761
$980$		0			0
$981$	42.0000			1.34096
$982$	−18.0000	−	31.1769i	−0.574403	−	0.994895i
$983$	−9.00000	+	15.5885i	−0.287055	+	0.497195i	−0.973106	−	0.230360i	$-0.926010\pi$
$983$	−9.00000	+	15.5885i	−0.287055	+	0.497195i	0.686050	+	0.727554i	$0.259343\pi$
$984$		0			0
$985$	12.0000	+	20.7846i	0.382352	+	0.662253i
$986$	−8.00000			−0.254772
$987$		0			0
$988$	−12.0000			−0.381771
$989$	16.0000	+	27.7128i	0.508770	+	0.881216i
$990$	−6.00000	+	10.3923i	−0.190693	+	0.330289i
$991$	−8.00000	+	13.8564i	−0.254128	+	0.440163i	−0.964658	−	0.263504i	$-0.915122\pi$
$991$	−8.00000	+	13.8564i	−0.254128	+	0.440163i	0.710530	+	0.703667i	$0.248455\pi$
$992$	−1.00000	−	1.73205i	−0.0317500	−	0.0549927i
$993$		0			0
$994$		0			0
$995$	56.0000			1.77532
$996$		0			0
$997$	21.0000	−	36.3731i	0.665077	−	1.15195i	−0.314188	−	0.949361i	$-0.601732\pi$
$997$	21.0000	−	36.3731i	0.665077	−	1.15195i	0.979265	−	0.202586i	$-0.0649345\pi$
$998$	22.0000	−	38.1051i	0.696398	−	1.20620i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1078.2.e.j.67.1		2
7.2	even	3	inner	1078.2.e.j.177.1		2
7.3	odd	6		1078.2.a.d.1.1		1
7.4	even	3		154.2.a.a.1.1	✓	1
7.5	odd	6		1078.2.e.i.177.1		2
7.6	odd	2		1078.2.e.i.67.1		2
21.11	odd	6		1386.2.a.l.1.1		1
21.17	even	6		9702.2.a.ba.1.1		1
28.3	even	6		8624.2.a.r.1.1		1
28.11	odd	6		1232.2.a.e.1.1		1
35.4	even	6		3850.2.a.u.1.1		1
35.18	odd	12		3850.2.c.j.1849.2		2
35.32	odd	12		3850.2.c.j.1849.1		2
56.11	odd	6		4928.2.a.w.1.1		1
56.53	even	6		4928.2.a.v.1.1		1
77.32	odd	6		1694.2.a.g.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.a.a.1.1	✓	1	7.4	even	3
1078.2.a.d.1.1		1	7.3	odd	6
1078.2.e.i.67.1		2	7.6	odd	2
1078.2.e.i.177.1		2	7.5	odd	6
1078.2.e.j.67.1		2	1.1	even	1	trivial
1078.2.e.j.177.1		2	7.2	even	3	inner
1232.2.a.e.1.1		1	28.11	odd	6
1386.2.a.l.1.1		1	21.11	odd	6
1694.2.a.g.1.1		1	77.32	odd	6
3850.2.a.u.1.1		1	35.4	even	6
3850.2.c.j.1849.1		2	35.32	odd	12
3850.2.c.j.1849.2		2	35.18	odd	12
4928.2.a.v.1.1		1	56.53	even	6
4928.2.a.w.1.1		1	56.11	odd	6
8624.2.a.r.1.1		1	28.3	even	6
9702.2.a.ba.1.1		1	21.17	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)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.00000 + 3.46410i) q^{5} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.00000 + 3.46410i) q^{5} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-2.00000 + 3.46410i) q^{10} +(0.500000 - 0.866025i) q^{11} +2.00000 q^{13} +(-0.500000 - 0.866025i) q^{16} +(2.00000 - 3.46410i) q^{17} +(-1.50000 + 2.59808i) q^{18} +(3.00000 + 5.19615i) q^{19} -4.00000 q^{20} +1.00000 q^{22} +(-2.00000 - 3.46410i) q^{23} +(-5.50000 + 9.52628i) q^{25} +(1.00000 + 1.73205i) q^{26} -2.00000 q^{29} +(1.00000 - 1.73205i) q^{31} +(0.500000 - 0.866025i) q^{32} +4.00000 q^{34} -3.00000 q^{36} +(-5.00000 - 8.66025i) q^{37} +(-3.00000 + 5.19615i) q^{38} +(-2.00000 - 3.46410i) q^{40} +4.00000 q^{41} -8.00000 q^{43} +(0.500000 + 0.866025i) q^{44} +(-6.00000 + 10.3923i) q^{45} +(2.00000 - 3.46410i) q^{46} +(-1.00000 - 1.73205i) q^{47} -11.0000 q^{50} +(-1.00000 + 1.73205i) q^{52} +(-3.00000 + 5.19615i) q^{53} +4.00000 q^{55} +(-1.00000 - 1.73205i) q^{58} +(6.00000 - 10.3923i) q^{59} +(7.00000 + 12.1244i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(4.00000 + 6.92820i) q^{65} +(6.00000 - 10.3923i) q^{67} +(2.00000 + 3.46410i) q^{68} -8.00000 q^{71} +(-1.50000 - 2.59808i) q^{72} +(-2.00000 + 3.46410i) q^{73} +(5.00000 - 8.66025i) q^{74} -6.00000 q^{76} +(2.00000 - 3.46410i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(2.00000 + 3.46410i) q^{82} -6.00000 q^{83} +16.0000 q^{85} +(-4.00000 - 6.92820i) q^{86} +(-0.500000 + 0.866025i) q^{88} +(3.00000 + 5.19615i) q^{89} -12.0000 q^{90} +4.00000 q^{92} +(1.00000 - 1.73205i) q^{94} +(-12.0000 + 20.7846i) q^{95} -14.0000 q^{97} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} + 4 q^{5} - 2 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q + q^2 - q^4 + 4 * q^5 - 2 * q^8 + 3 * q^9	\( 2 q + q^{2} - q^{4} + 4 q^{5} - 2 q^{8} + 3 q^{9} - 4 q^{10} + q^{11} + 4 q^{13} - q^{16} + 4 q^{17} - 3 q^{18} + 6 q^{19} - 8 q^{20} + 2 q^{22} - 4 q^{23} - 11 q^{25} + 2 q^{26} - 4 q^{29} + 2 q^{31} + q^{32} + 8 q^{34} - 6 q^{36} - 10 q^{37} - 6 q^{38} - 4 q^{40} + 8 q^{41} - 16 q^{43} + q^{44} - 12 q^{45} + 4 q^{46} - 2 q^{47} - 22 q^{50} - 2 q^{52} - 6 q^{53} + 8 q^{55} - 2 q^{58} + 12 q^{59} + 14 q^{61} + 4 q^{62} + 2 q^{64} + 8 q^{65} + 12 q^{67} + 4 q^{68} - 16 q^{71} - 3 q^{72} - 4 q^{73} + 10 q^{74} - 12 q^{76} + 4 q^{80} - 9 q^{81} + 4 q^{82} - 12 q^{83} + 32 q^{85} - 8 q^{86} - q^{88} + 6 q^{89} - 24 q^{90} + 8 q^{92} + 2 q^{94} - 24 q^{95} - 28 q^{97} + 6 q^{99}+O(q^{100}) \) 2 * q + q^2 - q^4 + 4 * q^5 - 2 * q^8 + 3 * q^9 - 4 * q^10 + q^11 + 4 * q^13 - q^16 + 4 * q^17 - 3 * q^18 + 6 * q^19 - 8 * q^20 + 2 * q^22 - 4 * q^23 - 11 * q^25 + 2 * q^26 - 4 * q^29 + 2 * q^31 + q^32 + 8 * q^34 - 6 * q^36 - 10 * q^37 - 6 * q^38 - 4 * q^40 + 8 * q^41 - 16 * q^43 + q^44 - 12 * q^45 + 4 * q^46 - 2 * q^47 - 22 * q^50 - 2 * q^52 - 6 * q^53 + 8 * q^55 - 2 * q^58 + 12 * q^59 + 14 * q^61 + 4 * q^62 + 2 * q^64 + 8 * q^65 + 12 * q^67 + 4 * q^68 - 16 * q^71 - 3 * q^72 - 4 * q^73 + 10 * q^74 - 12 * q^76 + 4 * q^80 - 9 * q^81 + 4 * q^82 - 12 * q^83 + 32 * q^85 - 8 * q^86 - q^88 + 6 * q^89 - 24 * q^90 + 8 * q^92 + 2 * q^94 - 24 * q^95 - 28 * q^97 + 6 * q^99

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