LMFDB - Embedded newform 1386.2.k.o.793.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(793,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1386.793");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.k (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.0672657201$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 154)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			793.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1386.793
Dual form			1386.2.k.o.991.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} +(-2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} +(-2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(-1.00000 - 1.73205i) q^{10} +(-0.500000 - 0.866025i) q^{11} -7.00000 q^{13} +(-0.500000 + 2.59808i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} -2.00000 q^{20} -1.00000 q^{22} +(-4.00000 + 6.92820i) q^{23} +(0.500000 + 0.866025i) q^{25} +(-3.50000 + 6.06218i) q^{26} +(2.00000 + 1.73205i) q^{28} +5.00000 q^{29} +(-2.00000 - 3.46410i) q^{31} +(0.500000 + 0.866025i) q^{32} +2.00000 q^{34} +(-1.00000 + 5.19615i) q^{35} +(-2.00000 + 3.46410i) q^{37} +(-1.00000 + 1.73205i) q^{40} -4.00000 q^{41} -8.00000 q^{43} +(-0.500000 + 0.866025i) q^{44} +(4.00000 + 6.92820i) q^{46} +(1.00000 - 1.73205i) q^{47} +(5.50000 - 4.33013i) q^{49} +1.00000 q^{50} +(3.50000 + 6.06218i) q^{52} +(-3.00000 - 5.19615i) q^{53} -2.00000 q^{55} +(2.50000 - 0.866025i) q^{56} +(2.50000 - 4.33013i) q^{58} +(1.50000 + 2.59808i) q^{59} +(-0.500000 + 0.866025i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(-7.00000 + 12.1244i) q^{65} +(-4.50000 - 7.79423i) q^{67} +(1.00000 - 1.73205i) q^{68} +(4.00000 + 3.46410i) q^{70} +2.00000 q^{71} +(-2.00000 - 3.46410i) q^{73} +(2.00000 + 3.46410i) q^{74} +(2.00000 + 1.73205i) q^{77} +(-4.50000 + 7.79423i) q^{79} +(1.00000 + 1.73205i) q^{80} +(-2.00000 + 3.46410i) q^{82} -6.00000 q^{83} +4.00000 q^{85} +(-4.00000 + 6.92820i) q^{86} +(0.500000 + 0.866025i) q^{88} +(3.00000 - 5.19615i) q^{89} +(17.5000 - 6.06218i) q^{91} +8.00000 q^{92} +(-1.00000 - 1.73205i) q^{94} +7.00000 q^{97} +(-1.00000 - 6.92820i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{4} + 2 q^{5} - 5 q^{7} - 2 q^{8}+O(q^{10}) $ 2 * q + q^2 - q^4 + 2 * q^5 - 5 * q^7 - 2 * q^8	$ 2 q + q^{2} - q^{4} + 2 q^{5} - 5 q^{7} - 2 q^{8} - 2 q^{10} - q^{11} - 14 q^{13} - q^{14} - q^{16} + 2 q^{17} - 4 q^{20} - 2 q^{22} - 8 q^{23} + q^{25} - 7 q^{26} + 4 q^{28} + 10 q^{29} - 4 q^{31} + q^{32} + 4 q^{34} - 2 q^{35} - 4 q^{37} - 2 q^{40} - 8 q^{41} - 16 q^{43} - q^{44} + 8 q^{46} + 2 q^{47} + 11 q^{49} + 2 q^{50} + 7 q^{52} - 6 q^{53} - 4 q^{55} + 5 q^{56} + 5 q^{58} + 3 q^{59} - q^{61} - 8 q^{62} + 2 q^{64} - 14 q^{65} - 9 q^{67} + 2 q^{68} + 8 q^{70} + 4 q^{71} - 4 q^{73} + 4 q^{74} + 4 q^{77} - 9 q^{79} + 2 q^{80} - 4 q^{82} - 12 q^{83} + 8 q^{85} - 8 q^{86} + q^{88} + 6 q^{89} + 35 q^{91} + 16 q^{92} - 2 q^{94} + 14 q^{97} - 2 q^{98}+O(q^{100}) $ 2 * q + q^2 - q^4 + 2 * q^5 - 5 * q^7 - 2 * q^8 - 2 * q^10 - q^11 - 14 * q^13 - q^14 - q^16 + 2 * q^17 - 4 * q^20 - 2 * q^22 - 8 * q^23 + q^25 - 7 * q^26 + 4 * q^28 + 10 * q^29 - 4 * q^31 + q^32 + 4 * q^34 - 2 * q^35 - 4 * q^37 - 2 * q^40 - 8 * q^41 - 16 * q^43 - q^44 + 8 * q^46 + 2 * q^47 + 11 * q^49 + 2 * q^50 + 7 * q^52 - 6 * q^53 - 4 * q^55 + 5 * q^56 + 5 * q^58 + 3 * q^59 - q^61 - 8 * q^62 + 2 * q^64 - 14 * q^65 - 9 * q^67 + 2 * q^68 + 8 * q^70 + 4 * q^71 - 4 * q^73 + 4 * q^74 + 4 * q^77 - 9 * q^79 + 2 * q^80 - 4 * q^82 - 12 * q^83 + 8 * q^85 - 8 * q^86 + q^88 + 6 * q^89 + 35 * q^91 + 16 * q^92 - 2 * q^94 + 14 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.00000	−	1.73205i	0.447214	−	0.774597i	−0.550990	−	0.834512i	$-0.685750\pi$
$5$	1.00000	−	1.73205i	0.447214	−	0.774597i	0.998203	+	0.0599153i	$0.0190830\pi$
$6$		0			0
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−1.00000	−	1.73205i	−0.316228	−	0.547723i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$		0			0
$13$	−7.00000			−1.94145			−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−7.00000			−1.94145			−0.970725	+	0.240192i	$0.922790\pi$
$14$	−0.500000	+	2.59808i	−0.133631	+	0.694365i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	0.961436	−	0.275029i	$-0.0886875\pi$
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	−0.718900	+	0.695113i	$0.755354\pi$
$18$		0			0
$19$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$19$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$20$	−2.00000			−0.447214
$21$		0			0
$22$	−1.00000			−0.213201
$23$	−4.00000	+	6.92820i	−0.834058	+	1.44463i	0.0607377	+	0.998154i	$0.480655\pi$
$23$	−4.00000	+	6.92820i	−0.834058	+	1.44463i	−0.894795	+	0.446476i	$0.852679\pi$
$24$		0			0
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−3.50000	+	6.06218i	−0.686406	+	1.18889i
$27$		0			0
$28$	2.00000	+	1.73205i	0.377964	+	0.327327i
$29$	5.00000			0.928477			0.464238	−	0.885710i	$-0.346328\pi$
$29$	5.00000			0.928477			0.464238	+	0.885710i	$0.346328\pi$
$30$		0			0
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	0.628619	−	0.777714i	$-0.283621\pi$
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	−0.987829	+	0.155543i	$0.950287\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	2.00000			0.342997
$35$	−1.00000	+	5.19615i	−0.169031	+	0.878310i
$36$		0			0
$37$	−2.00000	+	3.46410i	−0.328798	+	0.569495i	−0.982274	−	0.187453i	$-0.939977\pi$
$37$	−2.00000	+	3.46410i	−0.328798	+	0.569495i	0.653476	+	0.756948i	$0.273310\pi$
$38$		0			0
$39$		0			0
$40$	−1.00000	+	1.73205i	−0.158114	+	0.273861i
$41$	−4.00000			−0.624695			−0.312348	−	0.949968i	$-0.601115\pi$
$41$	−4.00000			−0.624695			−0.312348	+	0.949968i	$0.601115\pi$
$42$		0			0
$43$	−8.00000			−1.21999			−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000			−1.21999			−0.609994	+	0.792406i	$0.708828\pi$
$44$	−0.500000	+	0.866025i	−0.0753778	+	0.130558i
$45$		0			0
$46$	4.00000	+	6.92820i	0.589768	+	1.02151i
$47$	1.00000	−	1.73205i	0.145865	−	0.252646i	−0.783830	−	0.620975i	$-0.786737\pi$
$47$	1.00000	−	1.73205i	0.145865	−	0.252646i	0.929695	+	0.368329i	$0.120070\pi$
$48$		0			0
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$	1.00000			0.141421
$51$		0			0
$52$	3.50000	+	6.06218i	0.485363	+	0.840673i
$53$	−3.00000	−	5.19615i	−0.412082	−	0.713746i	0.583036	−	0.812447i	$-0.301865\pi$
$53$	−3.00000	−	5.19615i	−0.412082	−	0.713746i	−0.995117	+	0.0987002i	$0.968532\pi$
$54$		0			0
$55$	−2.00000			−0.269680
$56$	2.50000	−	0.866025i	0.334077	−	0.115728i
$57$		0			0
$58$	2.50000	−	4.33013i	0.328266	−	0.568574i
$59$	1.50000	+	2.59808i	0.195283	+	0.338241i	0.946993	−	0.321253i	$-0.104104\pi$
$59$	1.50000	+	2.59808i	0.195283	+	0.338241i	−0.751710	+	0.659494i	$0.770771\pi$
$60$		0			0
$61$	−0.500000	+	0.866025i	−0.0640184	+	0.110883i	−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−0.500000	+	0.866025i	−0.0640184	+	0.110883i	0.832240	+	0.554416i	$0.187058\pi$
$62$	−4.00000			−0.508001
$63$		0			0
$64$	1.00000			0.125000
$65$	−7.00000	+	12.1244i	−0.868243	+	1.50384i
$66$		0			0
$67$	−4.50000	−	7.79423i	−0.549762	−	0.952217i	−0.998290	−	0.0584478i	$-0.981385\pi$
$67$	−4.50000	−	7.79423i	−0.549762	−	0.952217i	0.448528	−	0.893769i	$-0.351948\pi$
$68$	1.00000	−	1.73205i	0.121268	−	0.210042i
$69$		0			0
$70$	4.00000	+	3.46410i	0.478091	+	0.414039i
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$		0			0
$73$	−2.00000	−	3.46410i	−0.234082	−	0.405442i	0.724923	−	0.688830i	$-0.241875\pi$
$73$	−2.00000	−	3.46410i	−0.234082	−	0.405442i	−0.959006	+	0.283387i	$0.908542\pi$
$74$	2.00000	+	3.46410i	0.232495	+	0.402694i
$75$		0			0
$76$		0			0
$77$	2.00000	+	1.73205i	0.227921	+	0.197386i
$78$		0			0
$79$	−4.50000	+	7.79423i	−0.506290	+	0.876919i	0.493684	+	0.869641i	$0.335650\pi$
$79$	−4.50000	+	7.79423i	−0.506290	+	0.876919i	−0.999974	+	0.00727784i	$0.997683\pi$
$80$	1.00000	+	1.73205i	0.111803	+	0.193649i
$81$		0			0
$82$	−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
$85$	4.00000			0.433861
$86$	−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	−0.662071	−	0.749441i	$-0.730322\pi$
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	0.980071	+	0.198650i	$0.0636557\pi$
$90$		0			0
$91$	17.5000	−	6.06218i	1.83450	−	0.635489i
$92$	8.00000			0.834058
$93$		0			0
$94$	−1.00000	−	1.73205i	−0.103142	−	0.178647i
$95$		0			0
$96$		0			0
$97$	7.00000			0.710742			0.355371	−	0.934725i	$-0.384354\pi$
$97$	7.00000			0.710742			0.355371	+	0.934725i	$0.384354\pi$
$98$	−1.00000	−	6.92820i	−0.101015	−	0.699854i
$99$		0			0
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	−4.50000	−	7.79423i	−0.447767	−	0.775555i	0.550474	−	0.834853i	$-0.314447\pi$
$101$	−4.50000	−	7.79423i	−0.447767	−	0.775555i	−0.998240	+	0.0592978i	$0.981114\pi$
$102$		0			0
$103$	−9.00000	+	15.5885i	−0.886796	+	1.53598i	−0.0431555	+	0.999068i	$0.513741\pi$
$103$	−9.00000	+	15.5885i	−0.886796	+	1.53598i	−0.843641	+	0.536908i	$0.819592\pi$
$104$	7.00000			0.686406
$105$		0			0
$106$	−6.00000			−0.582772
$107$	1.00000	−	1.73205i	0.0966736	−	0.167444i	−0.813632	−	0.581380i	$-0.802513\pi$
$107$	1.00000	−	1.73205i	0.0966736	−	0.167444i	0.910306	+	0.413936i	$0.135846\pi$
$108$		0			0
$109$	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	$0.802798\pi$
$110$	−1.00000	+	1.73205i	−0.0953463	+	0.165145i
$111$		0			0
$112$	0.500000	−	2.59808i	0.0472456	−	0.245495i
$113$	−5.00000			−0.470360			−0.235180	−	0.971952i	$-0.575568\pi$
$113$	−5.00000			−0.470360			−0.235180	+	0.971952i	$0.575568\pi$
$114$		0			0
$115$	8.00000	+	13.8564i	0.746004	+	1.29212i
$116$	−2.50000	−	4.33013i	−0.232119	−	0.402042i
$117$		0			0
$118$	3.00000			0.276172
$119$	−4.00000	−	3.46410i	−0.366679	−	0.317554i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	0.500000	+	0.866025i	0.0452679	+	0.0784063i
$123$		0			0
$124$	−2.00000	+	3.46410i	−0.179605	+	0.311086i
$125$	12.0000			1.07331
$126$		0			0
$127$	−19.0000			−1.68598			−0.842989	−	0.537931i	$-0.819206\pi$
$127$	−19.0000			−1.68598			−0.842989	+	0.537931i	$0.819206\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	7.00000	+	12.1244i	0.613941	+	1.06338i
$131$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$131$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$132$		0			0
$133$		0			0
$134$	−9.00000			−0.777482
$135$		0			0
$136$	−1.00000	−	1.73205i	−0.0857493	−	0.148522i
$137$	1.50000	+	2.59808i	0.128154	+	0.221969i	0.922961	−	0.384893i	$-0.125762\pi$
$137$	1.50000	+	2.59808i	0.128154	+	0.221969i	−0.794808	+	0.606861i	$0.792428\pi$
$138$		0			0
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$	5.00000	−	1.73205i	0.422577	−	0.146385i
$141$		0			0
$142$	1.00000	−	1.73205i	0.0839181	−	0.145350i
$143$	3.50000	+	6.06218i	0.292685	+	0.506945i
$144$		0			0
$145$	5.00000	−	8.66025i	0.415227	−	0.719195i
$146$	−4.00000			−0.331042
$147$		0			0
$148$	4.00000			0.328798
$149$	−5.00000	+	8.66025i	−0.409616	+	0.709476i	−0.994847	−	0.101391i	$-0.967671\pi$
$149$	−5.00000	+	8.66025i	−0.409616	+	0.709476i	0.585231	+	0.810867i	$0.301004\pi$
$150$		0			0
$151$	1.50000	+	2.59808i	0.122068	+	0.211428i	0.920583	−	0.390547i	$-0.127714\pi$
$151$	1.50000	+	2.59808i	0.122068	+	0.211428i	−0.798515	+	0.601975i	$0.794381\pi$
$152$		0			0
$153$		0			0
$154$	2.50000	−	0.866025i	0.201456	−	0.0697863i
$155$	−8.00000			−0.642575
$156$		0			0
$157$	−8.00000	−	13.8564i	−0.638470	−	1.10586i	−0.985769	−	0.168107i	$-0.946235\pi$
$157$	−8.00000	−	13.8564i	−0.638470	−	1.10586i	0.347299	−	0.937754i	$-0.387099\pi$
$158$	4.50000	+	7.79423i	0.358001	+	0.620076i
$159$		0			0
$160$	2.00000			0.158114
$161$	4.00000	−	20.7846i	0.315244	−	1.63806i
$162$		0			0
$163$	8.50000	−	14.7224i	0.665771	−	1.15315i	−0.313304	−	0.949653i	$-0.601436\pi$
$163$	8.50000	−	14.7224i	0.665771	−	1.15315i	0.979076	−	0.203497i	$-0.0652307\pi$
$164$	2.00000	+	3.46410i	0.156174	+	0.270501i
$165$		0			0
$166$	−3.00000	+	5.19615i	−0.232845	+	0.403300i
$167$	−19.0000			−1.47026			−0.735132	−	0.677924i	$-0.762880\pi$
$167$	−19.0000			−1.47026			−0.735132	+	0.677924i	$0.762880\pi$
$168$		0			0
$169$	36.0000			2.76923
$170$	2.00000	−	3.46410i	0.153393	−	0.265684i
$171$		0			0
$172$	4.00000	+	6.92820i	0.304997	+	0.528271i
$173$	12.5000	−	21.6506i	0.950357	−	1.64607i	0.205706	−	0.978614i	$-0.434051\pi$
$173$	12.5000	−	21.6506i	0.950357	−	1.64607i	0.744652	−	0.667453i	$-0.232616\pi$
$174$		0			0
$175$	−2.00000	−	1.73205i	−0.151186	−	0.130931i
$176$	1.00000			0.0753778
$177$		0			0
$178$	−3.00000	−	5.19615i	−0.224860	−	0.389468i
$179$	9.50000	+	16.4545i	0.710063	+	1.22987i	0.964833	+	0.262864i	$0.0846670\pi$
$179$	9.50000	+	16.4545i	0.710063	+	1.22987i	−0.254770	+	0.967002i	$0.582000\pi$
$180$		0			0
$181$	−22.0000			−1.63525			−0.817624	−	0.575753i	$-0.804709\pi$
$181$	−22.0000			−1.63525			−0.817624	+	0.575753i	$0.804709\pi$
$182$	3.50000	−	18.1865i	0.259437	−	1.34808i
$183$		0			0
$184$	4.00000	−	6.92820i	0.294884	−	0.510754i
$185$	4.00000	+	6.92820i	0.294086	+	0.509372i
$186$		0			0
$187$	1.00000	−	1.73205i	0.0731272	−	0.126660i
$188$	−2.00000			−0.145865
$189$		0			0
$190$		0			0
$191$	1.00000	−	1.73205i	0.0723575	−	0.125327i	−0.827577	−	0.561353i	$-0.810281\pi$
$191$	1.00000	−	1.73205i	0.0723575	−	0.125327i	0.899934	+	0.436026i	$0.143614\pi$
$192$		0			0
$193$	−4.00000	−	6.92820i	−0.287926	−	0.498703i	0.685388	−	0.728178i	$-0.259632\pi$
$193$	−4.00000	−	6.92820i	−0.287926	−	0.498703i	−0.973315	+	0.229475i	$0.926299\pi$
$194$	3.50000	−	6.06218i	0.251285	−	0.435239i
$195$		0			0
$196$	−6.50000	−	2.59808i	−0.464286	−	0.185577i
$197$	−15.0000			−1.06871			−0.534353	−	0.845262i	$-0.679445\pi$
$197$	−15.0000			−1.06871			−0.534353	+	0.845262i	$0.679445\pi$
$198$		0			0
$199$	−2.00000	−	3.46410i	−0.141776	−	0.245564i	0.786389	−	0.617731i	$-0.211948\pi$
$199$	−2.00000	−	3.46410i	−0.141776	−	0.245564i	−0.928166	+	0.372168i	$0.878615\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$		0			0
$202$	−9.00000			−0.633238
$203$	−12.5000	+	4.33013i	−0.877328	+	0.303915i
$204$		0			0
$205$	−4.00000	+	6.92820i	−0.279372	+	0.483887i
$206$	9.00000	+	15.5885i	0.627060	+	1.08610i
$207$		0			0
$208$	3.50000	−	6.06218i	0.242681	−	0.420336i
$209$		0			0
$210$		0			0
$211$	−20.0000			−1.37686			−0.688428	−	0.725304i	$-0.741699\pi$
$211$	−20.0000			−1.37686			−0.688428	+	0.725304i	$0.741699\pi$
$212$	−3.00000	+	5.19615i	−0.206041	+	0.356873i
$213$		0			0
$214$	−1.00000	−	1.73205i	−0.0683586	−	0.118401i
$215$	−8.00000	+	13.8564i	−0.545595	+	0.944999i
$216$		0			0
$217$	8.00000	+	6.92820i	0.543075	+	0.470317i
$218$	2.00000			0.135457
$219$		0			0
$220$	1.00000	+	1.73205i	0.0674200	+	0.116775i
$221$	−7.00000	−	12.1244i	−0.470871	−	0.815572i
$222$		0			0
$223$	4.00000			0.267860			0.133930	−	0.990991i	$-0.457240\pi$
$223$	4.00000			0.267860			0.133930	+	0.990991i	$0.457240\pi$
$224$	−2.00000	−	1.73205i	−0.133631	−	0.115728i
$225$		0			0
$226$	−2.50000	+	4.33013i	−0.166298	+	0.288036i
$227$	−1.00000	−	1.73205i	−0.0663723	−	0.114960i	0.830930	−	0.556378i	$-0.187809\pi$
$227$	−1.00000	−	1.73205i	−0.0663723	−	0.114960i	−0.897302	+	0.441417i	$0.854476\pi$
$228$		0			0
$229$	14.0000	−	24.2487i	0.925146	−	1.60240i	0.133820	−	0.991006i	$-0.457276\pi$
$229$	14.0000	−	24.2487i	0.925146	−	1.60240i	0.791326	−	0.611394i	$-0.209391\pi$
$230$	16.0000			1.05501
$231$		0			0
$232$	−5.00000			−0.328266
$233$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$233$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$234$		0			0
$235$	−2.00000	−	3.46410i	−0.130466	−	0.225973i
$236$	1.50000	−	2.59808i	0.0976417	−	0.169120i
$237$		0			0
$238$	−5.00000	+	1.73205i	−0.324102	+	0.112272i
$239$	5.00000			0.323423			0.161712	−	0.986838i	$-0.448299\pi$
$239$	5.00000			0.323423			0.161712	+	0.986838i	$0.448299\pi$
$240$		0			0
$241$		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
$243$		0			0
$244$	1.00000			0.0640184
$245$	−2.00000	−	13.8564i	−0.127775	−	0.885253i
$246$		0			0
$247$		0			0
$248$	2.00000	+	3.46410i	0.127000	+	0.219971i
$249$		0			0
$250$	6.00000	−	10.3923i	0.379473	−	0.657267i
$251$	24.0000			1.51487			0.757433	−	0.652913i	$-0.226453\pi$
$251$	24.0000			1.51487			0.757433	+	0.652913i	$0.226453\pi$
$252$		0			0
$253$	8.00000			0.502956
$254$	−9.50000	+	16.4545i	−0.596083	+	1.03245i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	1.50000	−	2.59808i	0.0935674	−	0.162064i	−0.815442	−	0.578838i	$-0.803506\pi$
$257$	1.50000	−	2.59808i	0.0935674	−	0.162064i	0.909010	+	0.416775i	$0.136840\pi$
$258$		0			0
$259$	2.00000	−	10.3923i	0.124274	−	0.645746i
$260$	14.0000			0.868243
$261$		0			0
$262$		0			0
$263$	13.5000	+	23.3827i	0.832446	+	1.44184i	0.896093	+	0.443866i	$0.146393\pi$
$263$	13.5000	+	23.3827i	0.832446	+	1.44184i	−0.0636476	+	0.997972i	$0.520273\pi$
$264$		0			0
$265$	−12.0000			−0.737154
$266$		0			0
$267$		0			0
$268$	−4.50000	+	7.79423i	−0.274881	+	0.476108i
$269$	−12.0000	−	20.7846i	−0.731653	−	1.26726i	−0.956176	−	0.292791i	$-0.905416\pi$
$269$	−12.0000	−	20.7846i	−0.731653	−	1.26726i	0.224523	−	0.974469i	$-0.427917\pi$
$270$		0			0
$271$	5.50000	−	9.52628i	0.334101	−	0.578680i	−0.649211	−	0.760609i	$-0.724901\pi$
$271$	5.50000	−	9.52628i	0.334101	−	0.578680i	0.983312	+	0.181928i	$0.0582339\pi$
$272$	−2.00000			−0.121268
$273$		0			0
$274$	3.00000			0.181237
$275$	0.500000	−	0.866025i	0.0301511	−	0.0522233i
$276$		0			0
$277$	4.50000	+	7.79423i	0.270379	+	0.468310i	0.968959	−	0.247222i	$-0.0795177\pi$
$277$	4.50000	+	7.79423i	0.270379	+	0.468310i	−0.698580	+	0.715532i	$0.746184\pi$
$278$	−2.00000	+	3.46410i	−0.119952	+	0.207763i
$279$		0			0
$280$	1.00000	−	5.19615i	0.0597614	−	0.310530i
$281$	28.0000			1.67034			0.835170	−	0.549992i	$-0.185369\pi$
$281$	28.0000			1.67034			0.835170	+	0.549992i	$0.185369\pi$
$282$		0			0
$283$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$283$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$284$	−1.00000	−	1.73205i	−0.0593391	−	0.102778i
$285$		0			0
$286$	7.00000			0.413919
$287$	10.0000	−	3.46410i	0.590281	−	0.204479i
$288$		0			0
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$	−5.00000	−	8.66025i	−0.293610	−	0.508548i
$291$		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
$295$	6.00000			0.349334
$296$	2.00000	−	3.46410i	0.116248	−	0.201347i
$297$		0			0
$298$	5.00000	+	8.66025i	0.289642	+	0.501675i
$299$	28.0000	−	48.4974i	1.61928	−	2.80468i
$300$		0			0
$301$	20.0000	−	6.92820i	1.15278	−	0.399335i
$302$	3.00000			0.172631
$303$		0			0
$304$		0			0
$305$	1.00000	+	1.73205i	0.0572598	+	0.0991769i
$306$		0			0
$307$	2.00000			0.114146			0.0570730	−	0.998370i	$-0.481823\pi$
$307$	2.00000			0.114146			0.0570730	+	0.998370i	$0.481823\pi$
$308$	0.500000	−	2.59808i	0.0284901	−	0.148039i
$309$		0			0
$310$	−4.00000	+	6.92820i	−0.227185	+	0.393496i
$311$	−5.00000	−	8.66025i	−0.283524	−	0.491078i	0.688726	−	0.725022i	$-0.258170\pi$
$311$	−5.00000	−	8.66025i	−0.283524	−	0.491078i	−0.972250	+	0.233944i	$0.924837\pi$
$312$		0			0
$313$	−0.500000	+	0.866025i	−0.0282617	+	0.0489506i	−0.879810	−	0.475325i	$-0.842331\pi$
$313$	−0.500000	+	0.866025i	−0.0282617	+	0.0489506i	0.851549	+	0.524276i	$0.175664\pi$
$314$	−16.0000			−0.902932
$315$		0			0
$316$	9.00000			0.506290
$317$	−6.00000	+	10.3923i	−0.336994	+	0.583690i	−0.983866	−	0.178908i	$-0.942743\pi$
$317$	−6.00000	+	10.3923i	−0.336994	+	0.583690i	0.646872	+	0.762598i	$0.276077\pi$
$318$		0			0
$319$	−2.50000	−	4.33013i	−0.139973	−	0.242441i
$320$	1.00000	−	1.73205i	0.0559017	−	0.0968246i
$321$		0			0
$322$	−16.0000	−	13.8564i	−0.891645	−	0.772187i
$323$		0			0
$324$		0			0
$325$	−3.50000	−	6.06218i	−0.194145	−	0.336269i
$326$	−8.50000	−	14.7224i	−0.470771	−	0.815400i
$327$		0			0
$328$	4.00000			0.220863
$329$	−1.00000	+	5.19615i	−0.0551318	+	0.286473i
$330$		0			0
$331$	−6.50000	+	11.2583i	−0.357272	+	0.618814i	−0.987504	−	0.157593i	$-0.949627\pi$
$331$	−6.50000	+	11.2583i	−0.357272	+	0.618814i	0.630232	+	0.776407i	$0.282960\pi$
$332$	3.00000	+	5.19615i	0.164646	+	0.285176i
$333$		0			0
$334$	−9.50000	+	16.4545i	−0.519817	+	0.900349i
$335$	−18.0000			−0.983445
$336$		0			0
$337$	−12.0000			−0.653682			−0.326841	−	0.945079i	$-0.605984\pi$
$337$	−12.0000			−0.653682			−0.326841	+	0.945079i	$0.605984\pi$
$338$	18.0000	−	31.1769i	0.979071	−	1.69580i
$339$		0			0
$340$	−2.00000	−	3.46410i	−0.108465	−	0.187867i
$341$	−2.00000	+	3.46410i	−0.108306	+	0.187592i
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$	8.00000			0.431331
$345$		0			0
$346$	−12.5000	−	21.6506i	−0.672004	−	1.16395i
$347$	−11.0000	−	19.0526i	−0.590511	−	1.02279i	−0.994164	−	0.107883i	$-0.965593\pi$
$347$	−11.0000	−	19.0526i	−0.590511	−	1.02279i	0.403653	−	0.914912i	$-0.367740\pi$
$348$		0			0
$349$	2.00000			0.107058			0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000			0.107058			0.0535288	+	0.998566i	$0.482953\pi$
$350$	−2.50000	+	0.866025i	−0.133631	+	0.0462910i
$351$		0			0
$352$	0.500000	−	0.866025i	0.0266501	−	0.0461593i
$353$	−9.00000	−	15.5885i	−0.479022	−	0.829690i	0.520689	−	0.853746i	$-0.325675\pi$
$353$	−9.00000	−	15.5885i	−0.479022	−	0.829690i	−0.999711	+	0.0240566i	$0.992342\pi$
$354$		0			0
$355$	2.00000	−	3.46410i	0.106149	−	0.183855i
$356$	−6.00000			−0.317999
$357$		0			0
$358$	19.0000			1.00418
$359$	−9.50000	+	16.4545i	−0.501391	+	0.868434i	0.498608	+	0.866828i	$0.333845\pi$
$359$	−9.50000	+	16.4545i	−0.501391	+	0.868434i	−0.999999	+	0.00160673i	$0.999489\pi$
$360$		0			0
$361$	9.50000	+	16.4545i	0.500000	+	0.866025i
$362$	−11.0000	+	19.0526i	−0.578147	+	1.00138i
$363$		0			0
$364$	−14.0000	−	12.1244i	−0.733799	−	0.635489i
$365$	−8.00000			−0.418739
$366$		0			0
$367$	−2.00000	−	3.46410i	−0.104399	−	0.180825i	0.809093	−	0.587680i	$-0.199959\pi$
$367$	−2.00000	−	3.46410i	−0.104399	−	0.180825i	−0.913493	+	0.406855i	$0.866625\pi$
$368$	−4.00000	−	6.92820i	−0.208514	−	0.361158i
$369$		0			0
$370$	8.00000			0.415900
$371$	12.0000	+	10.3923i	0.623009	+	0.539542i
$372$		0			0
$373$	−5.50000	+	9.52628i	−0.284779	+	0.493252i	−0.972556	−	0.232671i	$-0.925254\pi$
$373$	−5.50000	+	9.52628i	−0.284779	+	0.493252i	0.687776	+	0.725923i	$0.258587\pi$
$374$	−1.00000	−	1.73205i	−0.0517088	−	0.0895622i
$375$		0			0
$376$	−1.00000	+	1.73205i	−0.0515711	+	0.0893237i
$377$	−35.0000			−1.80259
$378$		0			0
$379$	1.00000			0.0513665			0.0256833	−	0.999670i	$-0.491824\pi$
$379$	1.00000			0.0513665			0.0256833	+	0.999670i	$0.491824\pi$
$380$		0			0
$381$		0			0
$382$	−1.00000	−	1.73205i	−0.0511645	−	0.0886194i
$383$	13.0000	−	22.5167i	0.664269	−	1.15055i	−0.315214	−	0.949021i	$-0.602076\pi$
$383$	13.0000	−	22.5167i	0.664269	−	1.15055i	0.979483	−	0.201527i	$-0.0645904\pi$
$384$		0			0
$385$	5.00000	−	1.73205i	0.254824	−	0.0882735i
$386$	−8.00000			−0.407189
$387$		0			0
$388$	−3.50000	−	6.06218i	−0.177686	−	0.307760i
$389$	9.00000	+	15.5885i	0.456318	+	0.790366i	0.998763	−	0.0497253i	$-0.0158346\pi$
$389$	9.00000	+	15.5885i	0.456318	+	0.790366i	−0.542445	+	0.840091i	$0.682501\pi$
$390$		0			0
$391$	−16.0000			−0.809155
$392$	−5.50000	+	4.33013i	−0.277792	+	0.218704i
$393$		0			0
$394$	−7.50000	+	12.9904i	−0.377845	+	0.654446i
$395$	9.00000	+	15.5885i	0.452839	+	0.784340i
$396$		0			0
$397$	−3.00000	+	5.19615i	−0.150566	+	0.260787i	−0.931436	−	0.363906i	$-0.881443\pi$
$397$	−3.00000	+	5.19615i	−0.150566	+	0.260787i	0.780870	+	0.624694i	$0.214776\pi$
$398$	−4.00000			−0.200502
$399$		0			0
$400$	−1.00000			−0.0500000
$401$	−4.50000	+	7.79423i	−0.224719	+	0.389225i	−0.956235	−	0.292599i	$-0.905480\pi$
$401$	−4.50000	+	7.79423i	−0.224719	+	0.389225i	0.731516	+	0.681824i	$0.238813\pi$
$402$		0			0
$403$	14.0000	+	24.2487i	0.697390	+	1.20791i
$404$	−4.50000	+	7.79423i	−0.223883	+	0.387777i
$405$		0			0
$406$	−2.50000	+	12.9904i	−0.124073	+	0.644702i
$407$	4.00000			0.198273
$408$		0			0
$409$	−11.0000	−	19.0526i	−0.543915	−	0.942088i	−0.998674	−	0.0514740i	$-0.983608\pi$
$409$	−11.0000	−	19.0526i	−0.543915	−	0.942088i	0.454759	−	0.890614i	$-0.349725\pi$
$410$	4.00000	+	6.92820i	0.197546	+	0.342160i
$411$		0			0
$412$	18.0000			0.886796
$413$	−6.00000	−	5.19615i	−0.295241	−	0.255686i
$414$		0			0
$415$	−6.00000	+	10.3923i	−0.294528	+	0.510138i
$416$	−3.50000	−	6.06218i	−0.171602	−	0.297223i
$417$		0			0
$418$		0			0
$419$	−16.0000			−0.781651			−0.390826	−	0.920465i	$-0.627810\pi$
$419$	−16.0000			−0.781651			−0.390826	+	0.920465i	$0.627810\pi$
$420$		0			0
$421$	−20.0000			−0.974740			−0.487370	−	0.873195i	$-0.662044\pi$
$421$	−20.0000			−0.974740			−0.487370	+	0.873195i	$0.662044\pi$
$422$	−10.0000	+	17.3205i	−0.486792	+	0.843149i
$423$		0			0
$424$	3.00000	+	5.19615i	0.145693	+	0.252347i
$425$	−1.00000	+	1.73205i	−0.0485071	+	0.0840168i
$426$		0			0
$427$	0.500000	−	2.59808i	0.0241967	−	0.125730i
$428$	−2.00000			−0.0966736
$429$		0			0
$430$	8.00000	+	13.8564i	0.385794	+	0.668215i
$431$	12.5000	+	21.6506i	0.602104	+	1.04287i	0.992502	+	0.122228i	$0.0390040\pi$
$431$	12.5000	+	21.6506i	0.602104	+	1.04287i	−0.390398	+	0.920646i	$0.627663\pi$
$432$		0			0
$433$	−34.0000			−1.63394			−0.816968	−	0.576683i	$-0.804347\pi$
$433$	−34.0000			−1.63394			−0.816968	+	0.576683i	$0.804347\pi$
$434$	10.0000	−	3.46410i	0.480015	−	0.166282i
$435$		0			0
$436$	1.00000	−	1.73205i	0.0478913	−	0.0829502i
$437$		0			0
$438$		0			0
$439$	2.50000	−	4.33013i	0.119318	−	0.206666i	−0.800179	−	0.599761i	$-0.795262\pi$
$439$	2.50000	−	4.33013i	0.119318	−	0.206666i	0.919498	+	0.393095i	$0.128596\pi$
$440$	2.00000			0.0953463
$441$		0			0
$442$	−14.0000			−0.665912
$443$	18.0000	−	31.1769i	0.855206	−	1.48126i	−0.0212481	−	0.999774i	$-0.506764\pi$
$443$	18.0000	−	31.1769i	0.855206	−	1.48126i	0.876454	−	0.481486i	$-0.159903\pi$
$444$		0			0
$445$	−6.00000	−	10.3923i	−0.284427	−	0.492642i
$446$	2.00000	−	3.46410i	0.0947027	−	0.164030i
$447$		0			0
$448$	−2.50000	+	0.866025i	−0.118114	+	0.0409159i
$449$	6.00000			0.283158			0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000			0.283158			0.141579	+	0.989927i	$0.454782\pi$
$450$		0			0
$451$	2.00000	+	3.46410i	0.0941763	+	0.163118i
$452$	2.50000	+	4.33013i	0.117590	+	0.203672i
$453$		0			0
$454$	−2.00000			−0.0938647
$455$	7.00000	−	36.3731i	0.328165	−	1.70520i
$456$		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	$0.272855\pi$
$458$	−14.0000	−	24.2487i	−0.654177	−	1.13307i
$459$		0			0
$460$	8.00000	−	13.8564i	0.373002	−	0.646058i
$461$	−27.0000			−1.25752			−0.628758	−	0.777601i	$-0.716436\pi$
$461$	−27.0000			−1.25752			−0.628758	+	0.777601i	$0.716436\pi$
$462$		0			0
$463$	−2.00000			−0.0929479			−0.0464739	−	0.998920i	$-0.514798\pi$
$463$	−2.00000			−0.0929479			−0.0464739	+	0.998920i	$0.514798\pi$
$464$	−2.50000	+	4.33013i	−0.116060	+	0.201021i
$465$		0			0
$466$		0			0
$467$	6.00000	−	10.3923i	0.277647	−	0.480899i	−0.693153	−	0.720791i	$-0.743779\pi$
$467$	6.00000	−	10.3923i	0.277647	−	0.480899i	0.970799	+	0.239892i	$0.0771121\pi$
$468$		0			0
$469$	18.0000	+	15.5885i	0.831163	+	0.719808i
$470$	−4.00000			−0.184506
$471$		0			0
$472$	−1.50000	−	2.59808i	−0.0690431	−	0.119586i
$473$	4.00000	+	6.92820i	0.183920	+	0.318559i
$474$		0			0
$475$		0			0
$476$	−1.00000	+	5.19615i	−0.0458349	+	0.238165i
$477$		0			0
$478$	2.50000	−	4.33013i	0.114347	−	0.198055i
$479$	−0.500000	−	0.866025i	−0.0228456	−	0.0395697i	0.854377	−	0.519654i	$-0.173939\pi$
$479$	−0.500000	−	0.866025i	−0.0228456	−	0.0395697i	−0.877222	+	0.480085i	$0.840606\pi$
$480$		0			0
$481$	14.0000	−	24.2487i	0.638345	−	1.10565i
$482$		0			0
$483$		0			0
$484$	1.00000			0.0454545
$485$	7.00000	−	12.1244i	0.317854	−	0.550539i
$486$		0			0
$487$	20.0000	+	34.6410i	0.906287	+	1.56973i	0.819181	+	0.573535i	$0.194428\pi$
$487$	20.0000	+	34.6410i	0.906287	+	1.56973i	0.0871056	+	0.996199i	$0.472238\pi$
$488$	0.500000	−	0.866025i	0.0226339	−	0.0392031i
$489$		0			0
$490$	−13.0000	−	5.19615i	−0.587280	−	0.234738i
$491$	−30.0000			−1.35388			−0.676941	−	0.736038i	$-0.736695\pi$
$491$	−30.0000			−1.35388			−0.676941	+	0.736038i	$0.736695\pi$
$492$		0			0
$493$	5.00000	+	8.66025i	0.225189	+	0.390038i
$494$		0			0
$495$		0			0
$496$	4.00000			0.179605
$497$	−5.00000	+	1.73205i	−0.224281	+	0.0776931i
$498$		0			0
$499$	−10.0000	+	17.3205i	−0.447661	+	0.775372i	−0.998233	−	0.0594153i	$-0.981076\pi$
$499$	−10.0000	+	17.3205i	−0.447661	+	0.775372i	0.550572	+	0.834788i	$0.314410\pi$
$500$	−6.00000	−	10.3923i	−0.268328	−	0.464758i
$501$		0			0
$502$	12.0000	−	20.7846i	0.535586	−	0.927663i
$503$	−3.00000			−0.133763			−0.0668817	−	0.997761i	$-0.521305\pi$
$503$	−3.00000			−0.133763			−0.0668817	+	0.997761i	$0.521305\pi$
$504$		0			0
$505$	−18.0000			−0.800989
$506$	4.00000	−	6.92820i	0.177822	−	0.307996i
$507$		0			0
$508$	9.50000	+	16.4545i	0.421494	+	0.730050i
$509$	−11.0000	+	19.0526i	−0.487566	+	0.844490i	−0.999898	−	0.0142980i	$-0.995449\pi$
$509$	−11.0000	+	19.0526i	−0.487566	+	0.844490i	0.512331	+	0.858788i	$0.328782\pi$
$510$		0			0
$511$	8.00000	+	6.92820i	0.353899	+	0.306486i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−1.50000	−	2.59808i	−0.0661622	−	0.114596i
$515$	18.0000	+	31.1769i	0.793175	+	1.37382i
$516$		0			0
$517$	−2.00000			−0.0879599
$518$	−8.00000	−	6.92820i	−0.351500	−	0.304408i
$519$		0			0
$520$	7.00000	−	12.1244i	0.306970	−	0.531688i
$521$	5.00000	+	8.66025i	0.219054	+	0.379413i	0.954519	−	0.298150i	$-0.0963696\pi$
$521$	5.00000	+	8.66025i	0.219054	+	0.379413i	−0.735465	+	0.677563i	$0.763036\pi$
$522$		0			0
$523$	5.00000	−	8.66025i	0.218635	−	0.378686i	−0.735756	−	0.677247i	$-0.763173\pi$
$523$	5.00000	−	8.66025i	0.218635	−	0.378686i	0.954391	+	0.298560i	$0.0965063\pi$
$524$		0			0
$525$		0			0
$526$	27.0000			1.17726
$527$	4.00000	−	6.92820i	0.174243	−	0.301797i
$528$		0			0
$529$	−20.5000	−	35.5070i	−0.891304	−	1.54378i
$530$	−6.00000	+	10.3923i	−0.260623	+	0.451413i
$531$		0			0
$532$		0			0
$533$	28.0000			1.21281
$534$		0			0
$535$	−2.00000	−	3.46410i	−0.0864675	−	0.149766i
$536$	4.50000	+	7.79423i	0.194370	+	0.336659i
$537$		0			0
$538$	−24.0000			−1.03471
$539$	−6.50000	−	2.59808i	−0.279975	−	0.111907i
$540$		0			0
$541$	−2.50000	+	4.33013i	−0.107483	+	0.186167i	−0.914750	−	0.404020i	$-0.867613\pi$
$541$	−2.50000	+	4.33013i	−0.107483	+	0.186167i	0.807267	+	0.590187i	$0.200946\pi$
$542$	−5.50000	−	9.52628i	−0.236245	−	0.409189i
$543$		0			0
$544$	−1.00000	+	1.73205i	−0.0428746	+	0.0742611i
$545$	4.00000			0.171341
$546$		0			0
$547$	30.0000			1.28271			0.641354	−	0.767245i	$-0.278373\pi$
$547$	30.0000			1.28271			0.641354	+	0.767245i	$0.278373\pi$
$548$	1.50000	−	2.59808i	0.0640768	−	0.110984i
$549$		0			0
$550$	−0.500000	−	0.866025i	−0.0213201	−	0.0369274i
$551$		0			0
$552$		0			0
$553$	4.50000	−	23.3827i	0.191359	−	0.994333i
$554$	9.00000			0.382373
$555$		0			0
$556$	2.00000	+	3.46410i	0.0848189	+	0.146911i
$557$	13.0000	+	22.5167i	0.550828	+	0.954062i	0.998215	+	0.0597213i	$0.0190212\pi$
$557$	13.0000	+	22.5167i	0.550828	+	0.954062i	−0.447387	+	0.894340i	$0.647645\pi$
$558$		0			0
$559$	56.0000			2.36855
$560$	−4.00000	−	3.46410i	−0.169031	−	0.146385i
$561$		0			0
$562$	14.0000	−	24.2487i	0.590554	−	1.02287i
$563$	10.0000	+	17.3205i	0.421450	+	0.729972i	0.996082	−	0.0884397i	$-0.0281881\pi$
$563$	10.0000	+	17.3205i	0.421450	+	0.729972i	−0.574632	+	0.818412i	$0.694855\pi$
$564$		0			0
$565$	−5.00000	+	8.66025i	−0.210352	+	0.364340i
$566$		0			0
$567$		0			0
$568$	−2.00000			−0.0839181
$569$	−6.00000	+	10.3923i	−0.251533	+	0.435668i	−0.963948	−	0.266090i	$-0.914268\pi$
$569$	−6.00000	+	10.3923i	−0.251533	+	0.435668i	0.712415	+	0.701758i	$0.247601\pi$
$570$		0			0
$571$	−11.0000	−	19.0526i	−0.460336	−	0.797325i	0.538642	−	0.842535i	$-0.318938\pi$
$571$	−11.0000	−	19.0526i	−0.460336	−	0.797325i	−0.998978	+	0.0452101i	$0.985604\pi$
$572$	3.50000	−	6.06218i	0.146342	−	0.253472i
$573$		0			0
$574$	2.00000	−	10.3923i	0.0834784	−	0.433766i
$575$	−8.00000			−0.333623
$576$		0			0
$577$	21.5000	+	37.2391i	0.895057	+	1.55028i	0.833734	+	0.552166i	$0.186198\pi$
$577$	21.5000	+	37.2391i	0.895057	+	1.55028i	0.0613223	+	0.998118i	$0.480468\pi$
$578$	−6.50000	−	11.2583i	−0.270364	−	0.468285i
$579$		0			0
$580$	−10.0000			−0.415227
$581$	15.0000	−	5.19615i	0.622305	−	0.215573i
$582$		0			0
$583$	−3.00000	+	5.19615i	−0.124247	+	0.215203i
$584$	2.00000	+	3.46410i	0.0827606	+	0.143346i
$585$		0			0
$586$	9.00000	−	15.5885i	0.371787	−	0.643953i
$587$	−27.0000			−1.11441			−0.557205	−	0.830375i	$-0.688126\pi$
$587$	−27.0000			−1.11441			−0.557205	+	0.830375i	$0.688126\pi$
$588$		0			0
$589$		0			0
$590$	3.00000	−	5.19615i	0.123508	−	0.213922i
$591$		0			0
$592$	−2.00000	−	3.46410i	−0.0821995	−	0.142374i
$593$	3.00000	−	5.19615i	0.123195	−	0.213380i	−0.797831	−	0.602881i	$-0.794019\pi$
$593$	3.00000	−	5.19615i	0.123195	−	0.213380i	0.921026	+	0.389501i	$0.127353\pi$
$594$		0			0
$595$	−10.0000	+	3.46410i	−0.409960	+	0.142014i
$596$	10.0000			0.409616
$597$		0			0
$598$	−28.0000	−	48.4974i	−1.14501	−	1.98321i
$599$	18.0000	+	31.1769i	0.735460	+	1.27385i	0.954521	+	0.298143i	$0.0963673\pi$
$599$	18.0000	+	31.1769i	0.735460	+	1.27385i	−0.219061	+	0.975711i	$0.570299\pi$
$600$		0			0
$601$	26.0000			1.06056			0.530281	−	0.847822i	$-0.322086\pi$
$601$	26.0000			1.06056			0.530281	+	0.847822i	$0.322086\pi$
$602$	4.00000	−	20.7846i	0.163028	−	0.847117i
$603$		0			0
$604$	1.50000	−	2.59808i	0.0610341	−	0.105714i
$605$	1.00000	+	1.73205i	0.0406558	+	0.0704179i
$606$		0			0
$607$	−4.00000	+	6.92820i	−0.162355	+	0.281207i	−0.935713	−	0.352763i	$-0.885242\pi$
$607$	−4.00000	+	6.92820i	−0.162355	+	0.281207i	0.773358	+	0.633970i	$0.218576\pi$
$608$		0			0
$609$		0			0
$610$	2.00000			0.0809776
$611$	−7.00000	+	12.1244i	−0.283190	+	0.490499i
$612$		0			0
$613$	19.0000	+	32.9090i	0.767403	+	1.32918i	0.938967	+	0.344008i	$0.111785\pi$
$613$	19.0000	+	32.9090i	0.767403	+	1.32918i	−0.171564	+	0.985173i	$0.554882\pi$
$614$	1.00000	−	1.73205i	0.0403567	−	0.0698999i
$615$		0			0
$616$	−2.00000	−	1.73205i	−0.0805823	−	0.0697863i
$617$	15.0000			0.603877			0.301939	−	0.953327i	$-0.402366\pi$
$617$	15.0000			0.603877			0.301939	+	0.953327i	$0.402366\pi$
$618$		0			0
$619$	14.0000	+	24.2487i	0.562708	+	0.974638i	0.997259	+	0.0739910i	$0.0235736\pi$
$619$	14.0000	+	24.2487i	0.562708	+	0.974638i	−0.434551	+	0.900647i	$0.643093\pi$
$620$	4.00000	+	6.92820i	0.160644	+	0.278243i
$621$		0			0
$622$	−10.0000			−0.400963
$623$	−3.00000	+	15.5885i	−0.120192	+	0.624538i
$624$		0			0
$625$	9.50000	−	16.4545i	0.380000	−	0.658179i
$626$	0.500000	+	0.866025i	0.0199840	+	0.0346133i
$627$		0			0
$628$	−8.00000	+	13.8564i	−0.319235	+	0.552931i
$629$	−8.00000			−0.318981
$630$		0			0
$631$	−18.0000			−0.716569			−0.358284	−	0.933613i	$-0.616638\pi$
$631$	−18.0000			−0.716569			−0.358284	+	0.933613i	$0.616638\pi$
$632$	4.50000	−	7.79423i	0.179000	−	0.310038i
$633$		0			0
$634$	6.00000	+	10.3923i	0.238290	+	0.412731i
$635$	−19.0000	+	32.9090i	−0.753992	+	1.30595i
$636$		0			0
$637$	−38.5000	+	30.3109i	−1.52543	+	1.20096i
$638$	−5.00000			−0.197952
$639$		0			0
$640$	−1.00000	−	1.73205i	−0.0395285	−	0.0684653i
$641$	−13.5000	−	23.3827i	−0.533218	−	0.923561i	−0.999247	−	0.0387913i	$-0.987649\pi$
$641$	−13.5000	−	23.3827i	−0.533218	−	0.923561i	0.466029	−	0.884769i	$-0.345684\pi$
$642$		0			0
$643$	31.0000			1.22252			0.611260	−	0.791430i	$-0.290663\pi$
$643$	31.0000			1.22252			0.611260	+	0.791430i	$0.290663\pi$
$644$	−20.0000	+	6.92820i	−0.788110	+	0.273009i
$645$		0			0
$646$		0			0
$647$	15.0000	+	25.9808i	0.589711	+	1.02141i	0.994270	+	0.106897i	$0.0340916\pi$
$647$	15.0000	+	25.9808i	0.589711	+	1.02141i	−0.404559	+	0.914512i	$0.632575\pi$
$648$		0			0
$649$	1.50000	−	2.59808i	0.0588802	−	0.101983i
$650$	−7.00000			−0.274563
$651$		0			0
$652$	−17.0000			−0.665771
$653$	20.0000	−	34.6410i	0.782660	−	1.35561i	−0.147726	−	0.989028i	$-0.547195\pi$
$653$	20.0000	−	34.6410i	0.782660	−	1.35561i	0.930387	−	0.366579i	$-0.119471\pi$
$654$		0			0
$655$		0			0
$656$	2.00000	−	3.46410i	0.0780869	−	0.135250i
$657$		0			0
$658$	4.00000	+	3.46410i	0.155936	+	0.135045i
$659$	−28.0000			−1.09073			−0.545363	−	0.838200i	$-0.683608\pi$
$659$	−28.0000			−1.09073			−0.545363	+	0.838200i	$0.683608\pi$
$660$		0			0
$661$	11.0000	+	19.0526i	0.427850	+	0.741059i	0.996682	−	0.0813955i	$-0.0259377\pi$
$661$	11.0000	+	19.0526i	0.427850	+	0.741059i	−0.568831	+	0.822454i	$0.692604\pi$
$662$	6.50000	+	11.2583i	0.252630	+	0.437567i
$663$		0			0
$664$	6.00000			0.232845
$665$		0			0
$666$		0			0
$667$	−20.0000	+	34.6410i	−0.774403	+	1.34131i
$668$	9.50000	+	16.4545i	0.367566	+	0.636643i
$669$		0			0
$670$	−9.00000	+	15.5885i	−0.347700	+	0.602235i
$671$	1.00000			0.0386046
$672$		0			0
$673$	34.0000			1.31060			0.655302	−	0.755367i	$-0.272541\pi$
$673$	34.0000			1.31060			0.655302	+	0.755367i	$0.272541\pi$
$674$	−6.00000	+	10.3923i	−0.231111	+	0.400297i
$675$		0			0
$676$	−18.0000	−	31.1769i	−0.692308	−	1.19911i
$677$	7.00000	−	12.1244i	0.269032	−	0.465977i	−0.699580	−	0.714554i	$-0.746630\pi$
$677$	7.00000	−	12.1244i	0.269032	−	0.465977i	0.968612	+	0.248577i	$0.0799630\pi$
$678$		0			0
$679$	−17.5000	+	6.06218i	−0.671588	+	0.232645i
$680$	−4.00000			−0.153393
$681$		0			0
$682$	2.00000	+	3.46410i	0.0765840	+	0.132647i
$683$	10.5000	+	18.1865i	0.401771	+	0.695888i	0.993940	−	0.109926i	$-0.0350613\pi$
$683$	10.5000	+	18.1865i	0.401771	+	0.695888i	−0.592168	+	0.805814i	$0.701728\pi$
$684$		0			0
$685$	6.00000			0.229248
$686$	8.50000	+	16.4545i	0.324532	+	0.628235i
$687$		0			0
$688$	4.00000	−	6.92820i	0.152499	−	0.264135i
$689$	21.0000	+	36.3731i	0.800036	+	1.38570i
$690$		0			0
$691$	−16.5000	+	28.5788i	−0.627690	+	1.08719i	0.360325	+	0.932827i	$0.382666\pi$
$691$	−16.5000	+	28.5788i	−0.627690	+	1.08719i	−0.988014	+	0.154363i	$0.950667\pi$
$692$	−25.0000			−0.950357
$693$		0			0
$694$	−22.0000			−0.835109
$695$	−4.00000	+	6.92820i	−0.151729	+	0.262802i
$696$		0			0
$697$	−4.00000	−	6.92820i	−0.151511	−	0.262424i
$698$	1.00000	−	1.73205i	0.0378506	−	0.0655591i
$699$		0			0
$700$	−0.500000	+	2.59808i	−0.0188982	+	0.0981981i
$701$	27.0000			1.01978			0.509888	−	0.860241i	$-0.329687\pi$
$701$	27.0000			1.01978			0.509888	+	0.860241i	$0.329687\pi$
$702$		0			0
$703$		0			0
$704$	−0.500000	−	0.866025i	−0.0188445	−	0.0326396i
$705$		0			0
$706$	−18.0000			−0.677439
$707$	18.0000	+	15.5885i	0.676960	+	0.586264i
$708$		0			0
$709$	24.0000	−	41.5692i	0.901339	−	1.56116i	0.0755813	−	0.997140i	$-0.475919\pi$
$709$	24.0000	−	41.5692i	0.901339	−	1.56116i	0.825758	−	0.564025i	$-0.190748\pi$
$710$	−2.00000	−	3.46410i	−0.0750587	−	0.130005i
$711$		0			0
$712$	−3.00000	+	5.19615i	−0.112430	+	0.194734i
$713$	32.0000			1.19841
$714$		0			0
$715$	14.0000			0.523570
$716$	9.50000	−	16.4545i	0.355032	−	0.614933i
$717$		0			0
$718$	9.50000	+	16.4545i	0.354537	+	0.614076i
$719$	−19.0000	+	32.9090i	−0.708580	+	1.22730i	0.256803	+	0.966464i	$0.417331\pi$
$719$	−19.0000	+	32.9090i	−0.708580	+	1.22730i	−0.965384	+	0.260834i	$0.916003\pi$
$720$		0			0
$721$	9.00000	−	46.7654i	0.335178	−	1.74163i
$722$	19.0000			0.707107
$723$		0			0
$724$	11.0000	+	19.0526i	0.408812	+	0.708083i
$725$	2.50000	+	4.33013i	0.0928477	+	0.160817i
$726$		0			0
$727$	−22.0000			−0.815935			−0.407967	−	0.912996i	$-0.633762\pi$
$727$	−22.0000			−0.815935			−0.407967	+	0.912996i	$0.633762\pi$
$728$	−17.5000	+	6.06218i	−0.648593	+	0.224679i
$729$		0			0
$730$	−4.00000	+	6.92820i	−0.148047	+	0.256424i
$731$	−8.00000	−	13.8564i	−0.295891	−	0.512498i
$732$		0			0
$733$	9.50000	−	16.4545i	0.350891	−	0.607760i	−0.635515	−	0.772088i	$-0.719212\pi$
$733$	9.50000	−	16.4545i	0.350891	−	0.607760i	0.986406	+	0.164328i	$0.0525456\pi$
$734$	−4.00000			−0.147643
$735$		0			0
$736$	−8.00000			−0.294884
$737$	−4.50000	+	7.79423i	−0.165760	+	0.287104i
$738$		0			0
$739$	−21.0000	−	36.3731i	−0.772497	−	1.33800i	−0.936190	−	0.351494i	$-0.885674\pi$
$739$	−21.0000	−	36.3731i	−0.772497	−	1.33800i	0.163693	−	0.986511i	$-0.447659\pi$
$740$	4.00000	−	6.92820i	0.147043	−	0.254686i
$741$		0			0
$742$	15.0000	−	5.19615i	0.550667	−	0.190757i
$743$	−12.0000			−0.440237			−0.220119	−	0.975473i	$-0.570644\pi$
$743$	−12.0000			−0.440237			−0.220119	+	0.975473i	$0.570644\pi$
$744$		0			0
$745$	10.0000	+	17.3205i	0.366372	+	0.634574i
$746$	5.50000	+	9.52628i	0.201369	+	0.348782i
$747$		0			0
$748$	−2.00000			−0.0731272
$749$	−1.00000	+	5.19615i	−0.0365392	+	0.189863i
$750$		0			0
$751$	−14.0000	+	24.2487i	−0.510867	+	0.884848i	0.489053	+	0.872254i	$0.337342\pi$
$751$	−14.0000	+	24.2487i	−0.510867	+	0.884848i	−0.999921	+	0.0125942i	$0.995991\pi$
$752$	1.00000	+	1.73205i	0.0364662	+	0.0631614i
$753$		0			0
$754$	−17.5000	+	30.3109i	−0.637312	+	1.10386i
$755$	6.00000			0.218362
$756$		0			0
$757$	−22.0000			−0.799604			−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000			−0.799604			−0.399802	+	0.916602i	$0.630921\pi$
$758$	0.500000	−	0.866025i	0.0181608	−	0.0314555i
$759$		0			0
$760$		0			0
$761$	−3.00000	+	5.19615i	−0.108750	+	0.188360i	−0.915264	−	0.402854i	$-0.868018\pi$
$761$	−3.00000	+	5.19615i	−0.108750	+	0.188360i	0.806514	+	0.591215i	$0.201351\pi$
$762$		0			0
$763$	−4.00000	−	3.46410i	−0.144810	−	0.125409i
$764$	−2.00000			−0.0723575
$765$		0			0
$766$	−13.0000	−	22.5167i	−0.469709	−	0.813560i
$767$	−10.5000	−	18.1865i	−0.379133	−	0.656678i
$768$		0			0
$769$	−14.0000			−0.504853			−0.252426	−	0.967616i	$-0.581229\pi$
$769$	−14.0000			−0.504853			−0.252426	+	0.967616i	$0.581229\pi$
$770$	1.00000	−	5.19615i	0.0360375	−	0.187256i
$771$		0			0
$772$	−4.00000	+	6.92820i	−0.143963	+	0.249351i
$773$	12.0000	+	20.7846i	0.431610	+	0.747570i	0.997012	−	0.0772449i	$-0.0246123\pi$
$773$	12.0000	+	20.7846i	0.431610	+	0.747570i	−0.565402	+	0.824815i	$0.691279\pi$
$774$		0			0
$775$	2.00000	−	3.46410i	0.0718421	−	0.124434i
$776$	−7.00000			−0.251285
$777$		0			0
$778$	18.0000			0.645331
$779$		0			0
$780$		0			0
$781$	−1.00000	−	1.73205i	−0.0357828	−	0.0619777i
$782$	−8.00000	+	13.8564i	−0.286079	+	0.495504i
$783$		0			0
$784$	1.00000	+	6.92820i	0.0357143	+	0.247436i
$785$	−32.0000			−1.14213
$786$		0			0
$787$	20.0000	+	34.6410i	0.712923	+	1.23482i	0.963755	+	0.266788i	$0.0859624\pi$
$787$	20.0000	+	34.6410i	0.712923	+	1.23482i	−0.250832	+	0.968031i	$0.580704\pi$
$788$	7.50000	+	12.9904i	0.267176	+	0.462763i
$789$		0			0
$790$	18.0000			0.640411
$791$	12.5000	−	4.33013i	0.444449	−	0.153962i
$792$		0			0
$793$	3.50000	−	6.06218i	0.124289	−	0.215274i
$794$	3.00000	+	5.19615i	0.106466	+	0.184405i
$795$		0			0
$796$	−2.00000	+	3.46410i	−0.0708881	+	0.122782i
$797$	−50.0000			−1.77109			−0.885545	−	0.464553i	$-0.846215\pi$
$797$	−50.0000			−1.77109			−0.885545	+	0.464553i	$0.846215\pi$
$798$		0			0
$799$	4.00000			0.141510
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$		0			0
$802$	4.50000	+	7.79423i	0.158901	+	0.275224i
$803$	−2.00000	+	3.46410i	−0.0705785	+	0.122245i
$804$		0			0
$805$	−32.0000	−	27.7128i	−1.12785	−	0.976748i
$806$	28.0000			0.986258
$807$		0			0
$808$	4.50000	+	7.79423i	0.158309	+	0.274200i
$809$	6.00000	+	10.3923i	0.210949	+	0.365374i	0.952012	−	0.306062i	$-0.0990113\pi$
$809$	6.00000	+	10.3923i	0.210949	+	0.365374i	−0.741063	+	0.671436i	$0.765678\pi$
$810$		0			0
$811$	8.00000			0.280918			0.140459	−	0.990086i	$-0.455142\pi$
$811$	8.00000			0.280918			0.140459	+	0.990086i	$0.455142\pi$
$812$	10.0000	+	8.66025i	0.350931	+	0.303915i
$813$		0			0
$814$	2.00000	−	3.46410i	0.0701000	−	0.121417i
$815$	−17.0000	−	29.4449i	−0.595484	−	1.03141i
$816$		0			0
$817$		0			0
$818$	−22.0000			−0.769212
$819$		0			0
$820$	8.00000			0.279372
$821$	−22.5000	+	38.9711i	−0.785255	+	1.36010i	0.143591	+	0.989637i	$0.454135\pi$
$821$	−22.5000	+	38.9711i	−0.785255	+	1.36010i	−0.928846	+	0.370465i	$0.879198\pi$
$822$		0			0
$823$	−13.0000	−	22.5167i	−0.453152	−	0.784881i	0.545428	−	0.838157i	$-0.316367\pi$
$823$	−13.0000	−	22.5167i	−0.453152	−	0.784881i	−0.998580	+	0.0532760i	$0.983034\pi$
$824$	9.00000	−	15.5885i	0.313530	−	0.543050i
$825$		0			0
$826$	−7.50000	+	2.59808i	−0.260958	+	0.0903986i
$827$	4.00000			0.139094			0.0695468	−	0.997579i	$-0.477845\pi$
$827$	4.00000			0.139094			0.0695468	+	0.997579i	$0.477845\pi$
$828$		0			0
$829$	1.00000	+	1.73205i	0.0347314	+	0.0601566i	0.882869	−	0.469620i	$-0.155609\pi$
$829$	1.00000	+	1.73205i	0.0347314	+	0.0601566i	−0.848137	+	0.529777i	$0.822276\pi$
$830$	6.00000	+	10.3923i	0.208263	+	0.360722i
$831$		0			0
$832$	−7.00000			−0.242681
$833$	13.0000	+	5.19615i	0.450423	+	0.180036i
$834$		0			0
$835$	−19.0000	+	32.9090i	−0.657522	+	1.13886i
$836$		0			0
$837$		0			0
$838$	−8.00000	+	13.8564i	−0.276355	+	0.478662i
$839$	18.0000			0.621429			0.310715	−	0.950503i	$-0.399432\pi$
$839$	18.0000			0.621429			0.310715	+	0.950503i	$0.399432\pi$
$840$		0			0
$841$	−4.00000			−0.137931
$842$	−10.0000	+	17.3205i	−0.344623	+	0.596904i
$843$		0			0
$844$	10.0000	+	17.3205i	0.344214	+	0.596196i
$845$	36.0000	−	62.3538i	1.23844	−	2.14504i
$846$		0			0
$847$	0.500000	−	2.59808i	0.0171802	−	0.0892710i
$848$	6.00000			0.206041
$849$		0			0
$850$	1.00000	+	1.73205i	0.0342997	+	0.0594089i
$851$	−16.0000	−	27.7128i	−0.548473	−	0.949983i
$852$		0			0
$853$	−10.0000			−0.342393			−0.171197	−	0.985237i	$-0.554763\pi$
$853$	−10.0000			−0.342393			−0.171197	+	0.985237i	$0.554763\pi$
$854$	−2.00000	−	1.73205i	−0.0684386	−	0.0592696i
$855$		0			0
$856$	−1.00000	+	1.73205i	−0.0341793	+	0.0592003i
$857$	22.0000	+	38.1051i	0.751506	+	1.30165i	0.947093	+	0.320960i	$0.104005\pi$
$857$	22.0000	+	38.1051i	0.751506	+	1.30165i	−0.195587	+	0.980686i	$0.562661\pi$
$858$		0			0
$859$	−6.50000	+	11.2583i	−0.221777	+	0.384129i	−0.955348	−	0.295484i	$-0.904519\pi$
$859$	−6.50000	+	11.2583i	−0.221777	+	0.384129i	0.733571	+	0.679613i	$0.237852\pi$
$860$	16.0000			0.545595
$861$		0			0
$862$	25.0000			0.851503
$863$	2.00000	−	3.46410i	0.0680808	−	0.117919i	−0.829976	−	0.557800i	$-0.811646\pi$
$863$	2.00000	−	3.46410i	0.0680808	−	0.117919i	0.898056	+	0.439880i	$0.144979\pi$
$864$		0			0
$865$	−25.0000	−	43.3013i	−0.850026	−	1.47229i
$866$	−17.0000	+	29.4449i	−0.577684	+	1.00058i
$867$		0			0
$868$	2.00000	−	10.3923i	0.0678844	−	0.352738i
$869$	9.00000			0.305304
$870$		0			0
$871$	31.5000	+	54.5596i	1.06734	+	1.84868i
$872$	−1.00000	−	1.73205i	−0.0338643	−	0.0586546i
$873$		0			0
$874$		0			0
$875$	−30.0000	+	10.3923i	−1.01419	+	0.351324i
$876$		0			0
$877$	14.5000	−	25.1147i	0.489630	−	0.848064i	−0.510299	−	0.859997i	$-0.670465\pi$
$877$	14.5000	−	25.1147i	0.489630	−	0.848064i	0.999929	+	0.0119329i	$0.00379845\pi$
$878$	−2.50000	−	4.33013i	−0.0843709	−	0.146135i
$879$		0			0
$880$	1.00000	−	1.73205i	0.0337100	−	0.0583874i
$881$	−21.0000			−0.707508			−0.353754	−	0.935339i	$-0.615095\pi$
$881$	−21.0000			−0.707508			−0.353754	+	0.935339i	$0.615095\pi$
$882$		0			0
$883$	−29.0000			−0.975928			−0.487964	−	0.872864i	$-0.662260\pi$
$883$	−29.0000			−0.975928			−0.487964	+	0.872864i	$0.662260\pi$
$884$	−7.00000	+	12.1244i	−0.235435	+	0.407786i
$885$		0			0
$886$	−18.0000	−	31.1769i	−0.604722	−	1.04741i
$887$	−20.5000	+	35.5070i	−0.688323	+	1.19221i	0.284058	+	0.958807i	$0.408319\pi$
$887$	−20.5000	+	35.5070i	−0.688323	+	1.19221i	−0.972380	+	0.233403i	$0.925014\pi$
$888$		0			0
$889$	47.5000	−	16.4545i	1.59310	−	0.551866i
$890$	−12.0000			−0.402241
$891$		0			0
$892$	−2.00000	−	3.46410i	−0.0669650	−	0.115987i
$893$		0			0
$894$		0			0
$895$	38.0000			1.27020
$896$	−0.500000	+	2.59808i	−0.0167038	+	0.0867956i
$897$		0			0
$898$	3.00000	−	5.19615i	0.100111	−	0.173398i
$899$	−10.0000	−	17.3205i	−0.333519	−	0.577671i
$900$		0			0
$901$	6.00000	−	10.3923i	0.199889	−	0.346218i
$902$	4.00000			0.133185
$903$		0			0
$904$	5.00000			0.166298
$905$	−22.0000	+	38.1051i	−0.731305	+	1.26666i
$906$		0			0
$907$	14.0000	+	24.2487i	0.464862	+	0.805165i	0.999195	−	0.0401089i	$-0.0127705\pi$
$907$	14.0000	+	24.2487i	0.464862	+	0.805165i	−0.534333	+	0.845274i	$0.679437\pi$
$908$	−1.00000	+	1.73205i	−0.0331862	+	0.0574801i
$909$		0			0
$910$	−28.0000	−	24.2487i	−0.928191	−	0.803837i
$911$	−30.0000			−0.993944			−0.496972	−	0.867766i	$-0.665555\pi$
$911$	−30.0000			−0.993944			−0.496972	+	0.867766i	$0.665555\pi$
$912$		0			0
$913$	3.00000	+	5.19615i	0.0992855	+	0.171968i
$914$	7.00000	+	12.1244i	0.231539	+	0.401038i
$915$		0			0
$916$	−28.0000			−0.925146
$917$		0			0
$918$		0			0
$919$	−18.0000	+	31.1769i	−0.593765	+	1.02843i	0.399955	+	0.916535i	$0.369026\pi$
$919$	−18.0000	+	31.1769i	−0.593765	+	1.02843i	−0.993720	+	0.111897i	$0.964307\pi$
$920$	−8.00000	−	13.8564i	−0.263752	−	0.456832i
$921$		0			0
$922$	−13.5000	+	23.3827i	−0.444599	+	0.770068i
$923$	−14.0000			−0.460816
$924$		0			0
$925$	−4.00000			−0.131519
$926$	−1.00000	+	1.73205i	−0.0328620	+	0.0569187i
$927$		0			0
$928$	2.50000	+	4.33013i	0.0820665	+	0.142143i
$929$	7.50000	−	12.9904i	0.246067	−	0.426201i	−0.716364	−	0.697727i	$-0.754195\pi$
$929$	7.50000	−	12.9904i	0.246067	−	0.426201i	0.962431	+	0.271526i	$0.0875283\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	−6.00000	−	10.3923i	−0.196326	−	0.340047i
$935$	−2.00000	−	3.46410i	−0.0654070	−	0.113288i
$936$		0			0
$937$	−30.0000			−0.980057			−0.490029	−	0.871706i	$-0.663014\pi$
$937$	−30.0000			−0.980057			−0.490029	+	0.871706i	$0.663014\pi$
$938$	22.5000	−	7.79423i	0.734651	−	0.254491i
$939$		0			0
$940$	−2.00000	+	3.46410i	−0.0652328	+	0.112987i
$941$	−5.50000	−	9.52628i	−0.179295	−	0.310548i	0.762344	−	0.647172i	$-0.224048\pi$
$941$	−5.50000	−	9.52628i	−0.179295	−	0.310548i	−0.941639	+	0.336624i	$0.890715\pi$
$942$		0			0
$943$	16.0000	−	27.7128i	0.521032	−	0.902453i
$944$	−3.00000			−0.0976417
$945$		0			0
$946$	8.00000			0.260102
$947$	−2.00000	+	3.46410i	−0.0649913	+	0.112568i	−0.896690	−	0.442659i	$-0.854035\pi$
$947$	−2.00000	+	3.46410i	−0.0649913	+	0.112568i	0.831699	+	0.555227i	$0.187369\pi$
$948$		0			0
$949$	14.0000	+	24.2487i	0.454459	+	0.787146i
$950$		0			0
$951$		0			0
$952$	4.00000	+	3.46410i	0.129641	+	0.112272i
$953$	−14.0000			−0.453504			−0.226752	−	0.973952i	$-0.572811\pi$
$953$	−14.0000			−0.453504			−0.226752	+	0.973952i	$0.572811\pi$
$954$		0			0
$955$	−2.00000	−	3.46410i	−0.0647185	−	0.112096i
$956$	−2.50000	−	4.33013i	−0.0808558	−	0.140046i
$957$		0			0
$958$	−1.00000			−0.0323085
$959$	−6.00000	−	5.19615i	−0.193750	−	0.167793i
$960$		0			0
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$	−14.0000	−	24.2487i	−0.451378	−	0.781810i
$963$		0			0
$964$		0			0
$965$	−16.0000			−0.515058
$966$		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
$970$	−7.00000	−	12.1244i	−0.224756	−	0.389290i
$971$	20.5000	−	35.5070i	0.657876	−	1.13948i	−0.323288	−	0.946301i	$-0.604788\pi$
$971$	20.5000	−	35.5070i	0.657876	−	1.13948i	0.981164	−	0.193175i	$-0.0618784\pi$
$972$		0			0
$973$	10.0000	−	3.46410i	0.320585	−	0.111054i
$974$	40.0000			1.28168
$975$		0			0
$976$	−0.500000	−	0.866025i	−0.0160046	−	0.0277208i
$977$	−23.0000	−	39.8372i	−0.735835	−	1.27450i	−0.954356	−	0.298672i	$-0.903456\pi$
$977$	−23.0000	−	39.8372i	−0.735835	−	1.27450i	0.218521	−	0.975832i	$-0.429877\pi$
$978$		0			0
$979$	−6.00000			−0.191761
$980$	−11.0000	+	8.66025i	−0.351382	+	0.276642i
$981$		0			0
$982$	−15.0000	+	25.9808i	−0.478669	+	0.829079i
$983$	−9.00000	−	15.5885i	−0.287055	−	0.497195i	0.686050	−	0.727554i	$-0.259343\pi$
$983$	−9.00000	−	15.5885i	−0.287055	−	0.497195i	−0.973106	+	0.230360i	$0.926010\pi$
$984$		0			0
$985$	−15.0000	+	25.9808i	−0.477940	+	0.827816i
$986$	10.0000			0.318465
$987$		0			0
$988$		0			0
$989$	32.0000	−	55.4256i	1.01754	−	1.76243i
$990$		0			0
$991$	−5.00000	−	8.66025i	−0.158830	−	0.275102i	0.775617	−	0.631204i	$-0.217439\pi$
$991$	−5.00000	−	8.66025i	−0.158830	−	0.275102i	−0.934447	+	0.356102i	$0.884106\pi$
$992$	2.00000	−	3.46410i	0.0635001	−	0.109985i
$993$		0			0
$994$	−1.00000	+	5.19615i	−0.0317181	+	0.164812i
$995$	−8.00000			−0.253617
$996$		0			0
$997$	3.00000	+	5.19615i	0.0950110	+	0.164564i	0.909613	−	0.415456i	$-0.136378\pi$
$997$	3.00000	+	5.19615i	0.0950110	+	0.164564i	−0.814602	+	0.580020i	$0.803045\pi$
$998$	10.0000	+	17.3205i	0.316544	+	0.548271i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.k.o.793.1		2
3.2	odd	2		154.2.e.a.23.1	✓	2
7.2	even	3		9702.2.a.i.1.1		1
7.4	even	3	inner	1386.2.k.o.991.1		2
7.5	odd	6		9702.2.a.y.1.1		1
12.11	even	2		1232.2.q.e.177.1		2
21.2	odd	6		1078.2.a.m.1.1		1
21.5	even	6		1078.2.a.g.1.1		1
21.11	odd	6		154.2.e.a.67.1	yes	2
21.17	even	6		1078.2.e.f.67.1		2
21.20	even	2		1078.2.e.f.177.1		2
84.11	even	6		1232.2.q.e.529.1		2
84.23	even	6		8624.2.a.b.1.1		1
84.47	odd	6		8624.2.a.be.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.e.a.23.1	✓	2	3.2	odd	2
154.2.e.a.67.1	yes	2	21.11	odd	6
1078.2.a.g.1.1		1	21.5	even	6
1078.2.a.m.1.1		1	21.2	odd	6
1078.2.e.f.67.1		2	21.17	even	6
1078.2.e.f.177.1		2	21.20	even	2
1232.2.q.e.177.1		2	12.11	even	2
1232.2.q.e.529.1		2	84.11	even	6
1386.2.k.o.793.1		2	1.1	even	1	trivial
1386.2.k.o.991.1		2	7.4	even	3	inner
8624.2.a.b.1.1		1	84.23	even	6
8624.2.a.be.1.1		1	84.47	odd	6
9702.2.a.i.1.1		1	7.2	even	3
9702.2.a.y.1.1		1	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} +(-2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} +(-2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(-1.00000 - 1.73205i) q^{10} +(-0.500000 - 0.866025i) q^{11} -7.00000 q^{13} +(-0.500000 + 2.59808i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} -2.00000 q^{20} -1.00000 q^{22} +(-4.00000 + 6.92820i) q^{23} +(0.500000 + 0.866025i) q^{25} +(-3.50000 + 6.06218i) q^{26} +(2.00000 + 1.73205i) q^{28} +5.00000 q^{29} +(-2.00000 - 3.46410i) q^{31} +(0.500000 + 0.866025i) q^{32} +2.00000 q^{34} +(-1.00000 + 5.19615i) q^{35} +(-2.00000 + 3.46410i) q^{37} +(-1.00000 + 1.73205i) q^{40} -4.00000 q^{41} -8.00000 q^{43} +(-0.500000 + 0.866025i) q^{44} +(4.00000 + 6.92820i) q^{46} +(1.00000 - 1.73205i) q^{47} +(5.50000 - 4.33013i) q^{49} +1.00000 q^{50} +(3.50000 + 6.06218i) q^{52} +(-3.00000 - 5.19615i) q^{53} -2.00000 q^{55} +(2.50000 - 0.866025i) q^{56} +(2.50000 - 4.33013i) q^{58} +(1.50000 + 2.59808i) q^{59} +(-0.500000 + 0.866025i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(-7.00000 + 12.1244i) q^{65} +(-4.50000 - 7.79423i) q^{67} +(1.00000 - 1.73205i) q^{68} +(4.00000 + 3.46410i) q^{70} +2.00000 q^{71} +(-2.00000 - 3.46410i) q^{73} +(2.00000 + 3.46410i) q^{74} +(2.00000 + 1.73205i) q^{77} +(-4.50000 + 7.79423i) q^{79} +(1.00000 + 1.73205i) q^{80} +(-2.00000 + 3.46410i) q^{82} -6.00000 q^{83} +4.00000 q^{85} +(-4.00000 + 6.92820i) q^{86} +(0.500000 + 0.866025i) q^{88} +(3.00000 - 5.19615i) q^{89} +(17.5000 - 6.06218i) q^{91} +8.00000 q^{92} +(-1.00000 - 1.73205i) q^{94} +7.00000 q^{97} +(-1.00000 - 6.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} + 2 q^{5} - 5 q^{7} - 2 q^{8}+O(q^{10}) \) 2 * q + q^2 - q^4 + 2 * q^5 - 5 * q^7 - 2 * q^8	\( 2 q + q^{2} - q^{4} + 2 q^{5} - 5 q^{7} - 2 q^{8} - 2 q^{10} - q^{11} - 14 q^{13} - q^{14} - q^{16} + 2 q^{17} - 4 q^{20} - 2 q^{22} - 8 q^{23} + q^{25} - 7 q^{26} + 4 q^{28} + 10 q^{29} - 4 q^{31} + q^{32} + 4 q^{34} - 2 q^{35} - 4 q^{37} - 2 q^{40} - 8 q^{41} - 16 q^{43} - q^{44} + 8 q^{46} + 2 q^{47} + 11 q^{49} + 2 q^{50} + 7 q^{52} - 6 q^{53} - 4 q^{55} + 5 q^{56} + 5 q^{58} + 3 q^{59} - q^{61} - 8 q^{62} + 2 q^{64} - 14 q^{65} - 9 q^{67} + 2 q^{68} + 8 q^{70} + 4 q^{71} - 4 q^{73} + 4 q^{74} + 4 q^{77} - 9 q^{79} + 2 q^{80} - 4 q^{82} - 12 q^{83} + 8 q^{85} - 8 q^{86} + q^{88} + 6 q^{89} + 35 q^{91} + 16 q^{92} - 2 q^{94} + 14 q^{97} - 2 q^{98}+O(q^{100}) \) 2 * q + q^2 - q^4 + 2 * q^5 - 5 * q^7 - 2 * q^8 - 2 * q^10 - q^11 - 14 * q^13 - q^14 - q^16 + 2 * q^17 - 4 * q^20 - 2 * q^22 - 8 * q^23 + q^25 - 7 * q^26 + 4 * q^28 + 10 * q^29 - 4 * q^31 + q^32 + 4 * q^34 - 2 * q^35 - 4 * q^37 - 2 * q^40 - 8 * q^41 - 16 * q^43 - q^44 + 8 * q^46 + 2 * q^47 + 11 * q^49 + 2 * q^50 + 7 * q^52 - 6 * q^53 - 4 * q^55 + 5 * q^56 + 5 * q^58 + 3 * q^59 - q^61 - 8 * q^62 + 2 * q^64 - 14 * q^65 - 9 * q^67 + 2 * q^68 + 8 * q^70 + 4 * q^71 - 4 * q^73 + 4 * q^74 + 4 * q^77 - 9 * q^79 + 2 * q^80 - 4 * q^82 - 12 * q^83 + 8 * q^85 - 8 * q^86 + q^88 + 6 * q^89 + 35 * q^91 + 16 * q^92 - 2 * q^94 + 14 * q^97 - 2 * q^98

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