LMFDB - Embedded newform 1386.2.k.f.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:	$0$
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 462)
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.f.991.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{11} +4.00000 q^{13} +(-2.50000 + 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.500000 - 0.866025i) q^{17} +(1.50000 - 2.59808i) q^{19} +1.00000 q^{22} +(-0.500000 + 0.866025i) q^{23} +(2.50000 + 4.33013i) q^{25} +(-2.00000 + 3.46410i) q^{26} +(0.500000 - 2.59808i) q^{28} +1.00000 q^{29} +(-3.00000 - 5.19615i) q^{31} +(-0.500000 - 0.866025i) q^{32} +1.00000 q^{34} +(1.50000 - 2.59808i) q^{37} +(1.50000 + 2.59808i) q^{38} +6.00000 q^{41} +1.00000 q^{43} +(-0.500000 + 0.866025i) q^{44} +(-0.500000 - 0.866025i) q^{46} +(-0.500000 + 0.866025i) q^{47} +(1.00000 + 6.92820i) q^{49} -5.00000 q^{50} +(-2.00000 - 3.46410i) q^{52} +(2.00000 + 1.73205i) q^{56} +(-0.500000 + 0.866025i) q^{58} +(3.50000 + 6.06218i) q^{59} +(-3.00000 + 5.19615i) q^{61} +6.00000 q^{62} +1.00000 q^{64} +(2.00000 + 3.46410i) q^{67} +(-0.500000 + 0.866025i) q^{68} +15.0000 q^{71} +(-6.00000 - 10.3923i) q^{73} +(1.50000 + 2.59808i) q^{74} -3.00000 q^{76} +(0.500000 - 2.59808i) q^{77} +(-3.00000 + 5.19615i) q^{82} +16.0000 q^{83} +(-0.500000 + 0.866025i) q^{86} +(-0.500000 - 0.866025i) q^{88} +(-4.00000 + 6.92820i) q^{89} +(8.00000 + 6.92820i) q^{91} +1.00000 q^{92} +(-0.500000 - 0.866025i) q^{94} +7.00000 q^{97} +(-6.50000 - 2.59808i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} + 4 q^{7} + 2 q^{8}+O(q^{10}) $ 2 * q - q^2 - q^4 + 4 * q^7 + 2 * q^8	$ 2 q - q^{2} - q^{4} + 4 q^{7} + 2 q^{8} - q^{11} + 8 q^{13} - 5 q^{14} - q^{16} - q^{17} + 3 q^{19} + 2 q^{22} - q^{23} + 5 q^{25} - 4 q^{26} + q^{28} + 2 q^{29} - 6 q^{31} - q^{32} + 2 q^{34} + 3 q^{37} + 3 q^{38} + 12 q^{41} + 2 q^{43} - q^{44} - q^{46} - q^{47} + 2 q^{49} - 10 q^{50} - 4 q^{52} + 4 q^{56} - q^{58} + 7 q^{59} - 6 q^{61} + 12 q^{62} + 2 q^{64} + 4 q^{67} - q^{68} + 30 q^{71} - 12 q^{73} + 3 q^{74} - 6 q^{76} + q^{77} - 6 q^{82} + 32 q^{83} - q^{86} - q^{88} - 8 q^{89} + 16 q^{91} + 2 q^{92} - q^{94} + 14 q^{97} - 13 q^{98}+O(q^{100}) $ 2 * q - q^2 - q^4 + 4 * q^7 + 2 * q^8 - q^11 + 8 * q^13 - 5 * q^14 - q^16 - q^17 + 3 * q^19 + 2 * q^22 - q^23 + 5 * q^25 - 4 * q^26 + q^28 + 2 * q^29 - 6 * q^31 - q^32 + 2 * q^34 + 3 * q^37 + 3 * q^38 + 12 * q^41 + 2 * q^43 - q^44 - q^46 - q^47 + 2 * q^49 - 10 * q^50 - 4 * q^52 + 4 * q^56 - q^58 + 7 * q^59 - 6 * q^61 + 12 * q^62 + 2 * q^64 + 4 * q^67 - q^68 + 30 * q^71 - 12 * q^73 + 3 * q^74 - 6 * q^76 + q^77 - 6 * q^82 + 32 * q^83 - q^86 - q^88 - 8 * q^89 + 16 * q^91 + 2 * q^92 - q^94 + 14 * q^97 - 13 * 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
$5$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$5$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$6$		0			0
$7$	2.00000	+	1.73205i	0.755929	+	0.654654i
$7$	2.00000	+	1.73205i	0.755929	+	0.654654i
$8$	1.00000			0.353553
$9$		0			0
$10$		0			0
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$		0			0
$13$	4.00000			1.10940			0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000			1.10940			0.554700	+	0.832050i	$0.312833\pi$
$14$	−2.50000	+	0.866025i	−0.668153	+	0.231455i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i	0.799000	−	0.601331i	$-0.205363\pi$
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i	−0.920268	+	0.391289i	$0.872029\pi$
$18$		0			0
$19$	1.50000	−	2.59808i	0.344124	−	0.596040i	−0.641071	−	0.767482i	$-0.721509\pi$
$19$	1.50000	−	2.59808i	0.344124	−	0.596040i	0.985194	+	0.171442i	$0.0548427\pi$
$20$		0			0
$21$		0			0
$22$	1.00000			0.213201
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i	−0.913434	−	0.406986i	$-0.866580\pi$
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i	0.809177	+	0.587565i	$0.199913\pi$
$24$		0			0
$25$	2.50000	+	4.33013i	0.500000	+	0.866025i
$26$	−2.00000	+	3.46410i	−0.392232	+	0.679366i
$27$		0			0
$28$	0.500000	−	2.59808i	0.0944911	−	0.490990i
$29$	1.00000			0.185695			0.0928477	−	0.995680i	$-0.470403\pi$
$29$	1.00000			0.185695			0.0928477	+	0.995680i	$0.470403\pi$
$30$		0			0
$31$	−3.00000	−	5.19615i	−0.538816	−	0.933257i	−0.998968	−	0.0454165i	$-0.985539\pi$
$31$	−3.00000	−	5.19615i	−0.538816	−	0.933257i	0.460152	−	0.887840i	$-0.347795\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	1.00000			0.171499
$35$		0			0
$36$		0			0
$37$	1.50000	−	2.59808i	0.246598	−	0.427121i	−0.715981	−	0.698119i	$-0.754020\pi$
$37$	1.50000	−	2.59808i	0.246598	−	0.427121i	0.962580	+	0.270998i	$0.0873538\pi$
$38$	1.50000	+	2.59808i	0.243332	+	0.421464i
$39$		0			0
$40$		0			0
$41$	6.00000			0.937043			0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000			0.937043			0.468521	+	0.883452i	$0.344787\pi$
$42$		0			0
$43$	1.00000			0.152499			0.0762493	−	0.997089i	$-0.475706\pi$
$43$	1.00000			0.152499			0.0762493	+	0.997089i	$0.475706\pi$
$44$	−0.500000	+	0.866025i	−0.0753778	+	0.130558i
$45$		0			0
$46$	−0.500000	−	0.866025i	−0.0737210	−	0.127688i
$47$	−0.500000	+	0.866025i	−0.0729325	+	0.126323i	−0.900185	−	0.435507i	$-0.856569\pi$
$47$	−0.500000	+	0.866025i	−0.0729325	+	0.126323i	0.827253	+	0.561830i	$0.189902\pi$
$48$		0			0
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$	−5.00000			−0.707107
$51$		0			0
$52$	−2.00000	−	3.46410i	−0.277350	−	0.480384i
$53$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$53$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$54$		0			0
$55$		0			0
$56$	2.00000	+	1.73205i	0.267261	+	0.231455i
$57$		0			0
$58$	−0.500000	+	0.866025i	−0.0656532	+	0.113715i
$59$	3.50000	+	6.06218i	0.455661	+	0.789228i	0.998726	−	0.0504625i	$-0.0160695\pi$
$59$	3.50000	+	6.06218i	0.455661	+	0.789228i	−0.543065	+	0.839691i	$0.682736\pi$
$60$		0			0
$61$	−3.00000	+	5.19615i	−0.384111	+	0.665299i	−0.991645	−	0.128994i	$-0.958825\pi$
$61$	−3.00000	+	5.19615i	−0.384111	+	0.665299i	0.607535	+	0.794293i	$0.292159\pi$
$62$	6.00000			0.762001
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	0.961946	−	0.273241i	$-0.0880957\pi$
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	−0.717607	+	0.696449i	$0.754762\pi$
$68$	−0.500000	+	0.866025i	−0.0606339	+	0.105021i
$69$		0			0
$70$		0			0
$71$	15.0000			1.78017			0.890086	−	0.455792i	$-0.150644\pi$
$71$	15.0000			1.78017			0.890086	+	0.455792i	$0.150644\pi$
$72$		0			0
$73$	−6.00000	−	10.3923i	−0.702247	−	1.21633i	−0.967676	−	0.252197i	$-0.918847\pi$
$73$	−6.00000	−	10.3923i	−0.702247	−	1.21633i	0.265429	−	0.964130i	$-0.414486\pi$
$74$	1.50000	+	2.59808i	0.174371	+	0.302020i
$75$		0			0
$76$	−3.00000			−0.344124
$77$	0.500000	−	2.59808i	0.0569803	−	0.296078i
$78$		0			0
$79$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$79$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$80$		0			0
$81$		0			0
$82$	−3.00000	+	5.19615i	−0.331295	+	0.573819i
$83$	16.0000			1.75623			0.878114	−	0.478451i	$-0.158802\pi$
$83$	16.0000			1.75623			0.878114	+	0.478451i	$0.158802\pi$
$84$		0			0
$85$		0			0
$86$	−0.500000	+	0.866025i	−0.0539164	+	0.0933859i
$87$		0			0
$88$	−0.500000	−	0.866025i	−0.0533002	−	0.0923186i
$89$	−4.00000	+	6.92820i	−0.423999	+	0.734388i	−0.996326	−	0.0856373i	$-0.972707\pi$
$89$	−4.00000	+	6.92820i	−0.423999	+	0.734388i	0.572327	+	0.820025i	$0.306041\pi$
$90$		0			0
$91$	8.00000	+	6.92820i	0.838628	+	0.726273i
$92$	1.00000			0.104257
$93$		0			0
$94$	−0.500000	−	0.866025i	−0.0515711	−	0.0893237i
$95$		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	$0.384354\pi$
$98$	−6.50000	−	2.59808i	−0.656599	−	0.262445i
$99$		0			0
$100$	2.50000	−	4.33013i	0.250000	−	0.433013i
$101$	7.50000	+	12.9904i	0.746278	+	1.29259i	0.949595	+	0.313478i	$0.101494\pi$
$101$	7.50000	+	12.9904i	0.746278	+	1.29259i	−0.203317	+	0.979113i	$0.565172\pi$
$102$		0			0
$103$	−2.00000	+	3.46410i	−0.197066	+	0.341328i	−0.947576	−	0.319531i	$-0.896475\pi$
$103$	−2.00000	+	3.46410i	−0.197066	+	0.341328i	0.750510	+	0.660859i	$0.229808\pi$
$104$	4.00000			0.392232
$105$		0			0
$106$		0			0
$107$	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
$109$	9.00000	+	15.5885i	0.862044	+	1.49310i	0.869953	+	0.493135i	$0.164149\pi$
$109$	9.00000	+	15.5885i	0.862044	+	1.49310i	−0.00790932	+	0.999969i	$0.502518\pi$
$110$		0			0
$111$		0			0
$112$	−2.50000	+	0.866025i	−0.236228	+	0.0818317i
$113$	−4.00000			−0.376288			−0.188144	−	0.982141i	$-0.560247\pi$
$113$	−4.00000			−0.376288			−0.188144	+	0.982141i	$0.560247\pi$
$114$		0			0
$115$		0			0
$116$	−0.500000	−	0.866025i	−0.0464238	−	0.0804084i
$117$		0			0
$118$	−7.00000			−0.644402
$119$	0.500000	−	2.59808i	0.0458349	−	0.238165i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−3.00000	−	5.19615i	−0.271607	−	0.470438i
$123$		0			0
$124$	−3.00000	+	5.19615i	−0.269408	+	0.466628i
$125$		0			0
$126$		0			0
$127$	−7.00000			−0.621150			−0.310575	−	0.950549i	$-0.600522\pi$
$127$	−7.00000			−0.621150			−0.310575	+	0.950549i	$0.600522\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$		0			0
$131$	−1.00000	+	1.73205i	−0.0873704	+	0.151330i	−0.906399	−	0.422423i	$-0.861180\pi$
$131$	−1.00000	+	1.73205i	−0.0873704	+	0.151330i	0.819028	+	0.573753i	$0.194513\pi$
$132$		0			0
$133$	7.50000	−	2.59808i	0.650332	−	0.225282i
$134$	−4.00000			−0.345547
$135$		0			0
$136$	−0.500000	−	0.866025i	−0.0428746	−	0.0742611i
$137$	−2.00000	−	3.46410i	−0.170872	−	0.295958i	0.767853	−	0.640626i	$-0.221325\pi$
$137$	−2.00000	−	3.46410i	−0.170872	−	0.295958i	−0.938725	+	0.344668i	$0.887992\pi$
$138$		0			0
$139$	−17.0000			−1.44192			−0.720961	−	0.692976i	$-0.756299\pi$
$139$	−17.0000			−1.44192			−0.720961	+	0.692976i	$0.756299\pi$
$140$		0			0
$141$		0			0
$142$	−7.50000	+	12.9904i	−0.629386	+	1.09013i
$143$	−2.00000	−	3.46410i	−0.167248	−	0.289683i
$144$		0			0
$145$		0			0
$146$	12.0000			0.993127
$147$		0			0
$148$	−3.00000			−0.246598
$149$	0.500000	−	0.866025i	0.0409616	−	0.0709476i	−0.844818	−	0.535054i	$-0.820291\pi$
$149$	0.500000	−	0.866025i	0.0409616	−	0.0709476i	0.885779	+	0.464107i	$0.153625\pi$
$150$		0			0
$151$	−5.50000	−	9.52628i	−0.447584	−	0.775238i	0.550645	−	0.834740i	$-0.314382\pi$
$151$	−5.50000	−	9.52628i	−0.447584	−	0.775238i	−0.998228	+	0.0595022i	$0.981049\pi$
$152$	1.50000	−	2.59808i	0.121666	−	0.210732i
$153$		0			0
$154$	2.00000	+	1.73205i	0.161165	+	0.139573i
$155$		0			0
$156$		0			0
$157$	4.50000	+	7.79423i	0.359139	+	0.622047i	0.987817	−	0.155618i	$-0.0497370\pi$
$157$	4.50000	+	7.79423i	0.359139	+	0.622047i	−0.628678	+	0.777666i	$0.716404\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−2.50000	+	0.866025i	−0.197028	+	0.0682524i
$162$		0			0
$163$	9.00000	−	15.5885i	0.704934	−	1.22098i	−0.261781	−	0.965127i	$-0.584310\pi$
$163$	9.00000	−	15.5885i	0.704934	−	1.22098i	0.966715	−	0.255855i	$-0.0823569\pi$
$164$	−3.00000	−	5.19615i	−0.234261	−	0.405751i
$165$		0			0
$166$	−8.00000	+	13.8564i	−0.620920	+	1.07547i
$167$	12.0000			0.928588			0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000			0.928588			0.464294	+	0.885681i	$0.346308\pi$
$168$		0			0
$169$	3.00000			0.230769
$170$		0			0
$171$		0			0
$172$	−0.500000	−	0.866025i	−0.0381246	−	0.0660338i
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	−0.957241	−	0.289292i	$-0.906580\pi$
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	0.729155	+	0.684349i	$0.239913\pi$
$174$		0			0
$175$	−2.50000	+	12.9904i	−0.188982	+	0.981981i
$176$	1.00000			0.0753778
$177$		0			0
$178$	−4.00000	−	6.92820i	−0.299813	−	0.519291i
$179$	−12.5000	−	21.6506i	−0.934294	−	1.61824i	−0.775888	−	0.630870i	$-0.782698\pi$
$179$	−12.5000	−	21.6506i	−0.934294	−	1.61824i	−0.158406	−	0.987374i	$-0.550635\pi$
$180$		0			0
$181$	22.0000			1.63525			0.817624	−	0.575753i	$-0.195291\pi$
$181$	22.0000			1.63525			0.817624	+	0.575753i	$0.195291\pi$
$182$	−10.0000	+	3.46410i	−0.741249	+	0.256776i
$183$		0			0
$184$	−0.500000	+	0.866025i	−0.0368605	+	0.0638442i
$185$		0			0
$186$		0			0
$187$	−0.500000	+	0.866025i	−0.0365636	+	0.0633300i
$188$	1.00000			0.0729325
$189$		0			0
$190$		0			0
$191$	−12.0000	+	20.7846i	−0.868290	+	1.50392i	−0.00454614	+	0.999990i	$0.501447\pi$
$191$	−12.0000	+	20.7846i	−0.868290	+	1.50392i	−0.863743	+	0.503932i	$0.831886\pi$
$192$		0			0
$193$	−7.00000	−	12.1244i	−0.503871	−	0.872730i	−0.999990	−	0.00447566i	$-0.998575\pi$
$193$	−7.00000	−	12.1244i	−0.503871	−	0.872730i	0.496119	−	0.868255i	$-0.334758\pi$
$194$	−3.50000	+	6.06218i	−0.251285	+	0.435239i
$195$		0			0
$196$	5.50000	−	4.33013i	0.392857	−	0.309295i
$197$	−27.0000			−1.92367			−0.961835	−	0.273629i	$-0.911776\pi$
$197$	−27.0000			−1.92367			−0.961835	+	0.273629i	$0.911776\pi$
$198$		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	$0.878615\pi$
$200$	2.50000	+	4.33013i	0.176777	+	0.306186i
$201$		0			0
$202$	−15.0000			−1.05540
$203$	2.00000	+	1.73205i	0.140372	+	0.121566i
$204$		0			0
$205$		0			0
$206$	−2.00000	−	3.46410i	−0.139347	−	0.241355i
$207$		0			0
$208$	−2.00000	+	3.46410i	−0.138675	+	0.240192i
$209$	−3.00000			−0.207514
$210$		0			0
$211$	−20.0000			−1.37686			−0.688428	−	0.725304i	$-0.741699\pi$
$211$	−20.0000			−1.37686			−0.688428	+	0.725304i	$0.741699\pi$
$212$		0			0
$213$		0			0
$214$	1.00000	+	1.73205i	0.0683586	+	0.118401i
$215$		0			0
$216$		0			0
$217$	3.00000	−	15.5885i	0.203653	−	1.05821i
$218$	−18.0000			−1.21911
$219$		0			0
$220$		0			0
$221$	−2.00000	−	3.46410i	−0.134535	−	0.233021i
$222$		0			0
$223$	16.0000			1.07144			0.535720	−	0.844396i	$-0.320040\pi$
$223$	16.0000			1.07144			0.535720	+	0.844396i	$0.320040\pi$
$224$	0.500000	−	2.59808i	0.0334077	−	0.173591i
$225$		0			0
$226$	2.00000	−	3.46410i	0.133038	−	0.230429i
$227$	−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
$229$	3.00000	−	5.19615i	0.198246	−	0.343371i	−0.749714	−	0.661762i	$-0.769809\pi$
$229$	3.00000	−	5.19615i	0.198246	−	0.343371i	0.947960	+	0.318390i	$0.103142\pi$
$230$		0			0
$231$		0			0
$232$	1.00000			0.0656532
$233$	−5.50000	+	9.52628i	−0.360317	+	0.624087i	−0.988013	−	0.154371i	$-0.950665\pi$
$233$	−5.50000	+	9.52628i	−0.360317	+	0.624087i	0.627696	+	0.778459i	$0.283998\pi$
$234$		0			0
$235$		0			0
$236$	3.50000	−	6.06218i	0.227831	−	0.394614i
$237$		0			0
$238$	2.00000	+	1.73205i	0.129641	+	0.112272i
$239$	−16.0000			−1.03495			−0.517477	−	0.855697i	$-0.673129\pi$
$239$	−16.0000			−1.03495			−0.517477	+	0.855697i	$0.673129\pi$
$240$		0			0
$241$	2.00000	+	3.46410i	0.128831	+	0.223142i	0.923224	−	0.384262i	$-0.125544\pi$
$241$	2.00000	+	3.46410i	0.128831	+	0.223142i	−0.794393	+	0.607404i	$0.792211\pi$
$242$	−0.500000	−	0.866025i	−0.0321412	−	0.0556702i
$243$		0			0
$244$	6.00000			0.384111
$245$		0			0
$246$		0			0
$247$	6.00000	−	10.3923i	0.381771	−	0.661247i
$248$	−3.00000	−	5.19615i	−0.190500	−	0.329956i
$249$		0			0
$250$		0			0
$251$	7.00000			0.441836			0.220918	−	0.975292i	$-0.429095\pi$
$251$	7.00000			0.441836			0.220918	+	0.975292i	$0.429095\pi$
$252$		0			0
$253$	1.00000			0.0628695
$254$	3.50000	−	6.06218i	0.219610	−	0.380375i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−6.00000	+	10.3923i	−0.374270	+	0.648254i	−0.990217	−	0.139533i	$-0.955440\pi$
$257$	−6.00000	+	10.3923i	−0.374270	+	0.648254i	0.615948	+	0.787787i	$0.288773\pi$
$258$		0			0
$259$	7.50000	−	2.59808i	0.466027	−	0.161437i
$260$		0			0
$261$		0			0
$262$	−1.00000	−	1.73205i	−0.0617802	−	0.107006i
$263$	−7.00000	−	12.1244i	−0.431638	−	0.747620i	0.565376	−	0.824833i	$-0.308731\pi$
$263$	−7.00000	−	12.1244i	−0.431638	−	0.747620i	−0.997015	+	0.0772134i	$0.975398\pi$
$264$		0			0
$265$		0			0
$266$	−1.50000	+	7.79423i	−0.0919709	+	0.477895i
$267$		0			0
$268$	2.00000	−	3.46410i	0.122169	−	0.211604i
$269$	−9.00000	−	15.5885i	−0.548740	−	0.950445i	−0.998361	−	0.0572259i	$-0.981774\pi$
$269$	−9.00000	−	15.5885i	−0.548740	−	0.950445i	0.449622	−	0.893219i	$-0.351559\pi$
$270$		0			0
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	−0.513905	−	0.857847i	$-0.671801\pi$
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	0.999870	+	0.0161307i	$0.00513477\pi$
$272$	1.00000			0.0606339
$273$		0			0
$274$	4.00000			0.241649
$275$	2.50000	−	4.33013i	0.150756	−	0.261116i
$276$		0			0
$277$	8.00000	+	13.8564i	0.480673	+	0.832551i	0.999754	−	0.0221745i	$-0.00705893\pi$
$277$	8.00000	+	13.8564i	0.480673	+	0.832551i	−0.519081	+	0.854725i	$0.673726\pi$
$278$	8.50000	−	14.7224i	0.509796	−	0.882993i
$279$		0			0
$280$		0			0
$281$	27.0000			1.61068			0.805342	−	0.592810i	$-0.201981\pi$
$281$	27.0000			1.61068			0.805342	+	0.592810i	$0.201981\pi$
$282$		0			0
$283$	−10.0000	−	17.3205i	−0.594438	−	1.02960i	−0.993626	−	0.112728i	$-0.964041\pi$
$283$	−10.0000	−	17.3205i	−0.594438	−	1.02960i	0.399188	−	0.916869i	$-0.369292\pi$
$284$	−7.50000	−	12.9904i	−0.445043	−	0.770837i
$285$		0			0
$286$	4.00000			0.236525
$287$	12.0000	+	10.3923i	0.708338	+	0.613438i
$288$		0			0
$289$	8.00000	−	13.8564i	0.470588	−	0.815083i
$290$		0			0
$291$		0			0
$292$	−6.00000	+	10.3923i	−0.351123	+	0.608164i
$293$	15.0000			0.876309			0.438155	−	0.898900i	$-0.355632\pi$
$293$	15.0000			0.876309			0.438155	+	0.898900i	$0.355632\pi$
$294$		0			0
$295$		0			0
$296$	1.50000	−	2.59808i	0.0871857	−	0.151010i
$297$		0			0
$298$	0.500000	+	0.866025i	0.0289642	+	0.0501675i
$299$	−2.00000	+	3.46410i	−0.115663	+	0.200334i
$300$		0			0
$301$	2.00000	+	1.73205i	0.115278	+	0.0998337i
$302$	11.0000			0.632979
$303$		0			0
$304$	1.50000	+	2.59808i	0.0860309	+	0.149010i
$305$		0			0
$306$		0			0
$307$	−20.0000			−1.14146			−0.570730	−	0.821138i	$-0.693340\pi$
$307$	−20.0000			−1.14146			−0.570730	+	0.821138i	$0.693340\pi$
$308$	−2.50000	+	0.866025i	−0.142451	+	0.0493464i
$309$		0			0
$310$		0			0
$311$	−15.5000	−	26.8468i	−0.878924	−	1.52234i	−0.852523	−	0.522690i	$-0.824928\pi$
$311$	−15.5000	−	26.8468i	−0.878924	−	1.52234i	−0.0264017	−	0.999651i	$-0.508405\pi$
$312$		0			0
$313$	16.5000	−	28.5788i	0.932635	−	1.61537i	0.153838	−	0.988096i	$-0.450837\pi$
$313$	16.5000	−	28.5788i	0.932635	−	1.61537i	0.778798	−	0.627275i	$-0.215830\pi$
$314$	−9.00000			−0.507899
$315$		0			0
$316$		0			0
$317$	6.00000	−	10.3923i	0.336994	−	0.583690i	−0.646872	−	0.762598i	$-0.723923\pi$
$317$	6.00000	−	10.3923i	0.336994	−	0.583690i	0.983866	+	0.178908i	$0.0572566\pi$
$318$		0			0
$319$	−0.500000	−	0.866025i	−0.0279946	−	0.0484881i
$320$		0			0
$321$		0			0
$322$	0.500000	−	2.59808i	0.0278639	−	0.144785i
$323$	−3.00000			−0.166924
$324$		0			0
$325$	10.0000	+	17.3205i	0.554700	+	0.960769i
$326$	9.00000	+	15.5885i	0.498464	+	0.863365i
$327$		0			0
$328$	6.00000			0.331295
$329$	−2.50000	+	0.866025i	−0.137829	+	0.0477455i
$330$		0			0
$331$	−5.00000	+	8.66025i	−0.274825	+	0.476011i	−0.970091	−	0.242742i	$-0.921953\pi$
$331$	−5.00000	+	8.66025i	−0.274825	+	0.476011i	0.695266	+	0.718752i	$0.255287\pi$
$332$	−8.00000	−	13.8564i	−0.439057	−	0.760469i
$333$		0			0
$334$	−6.00000	+	10.3923i	−0.328305	+	0.568642i
$335$		0			0
$336$		0			0
$337$	−26.0000			−1.41631			−0.708155	−	0.706057i	$-0.750472\pi$
$337$	−26.0000			−1.41631			−0.708155	+	0.706057i	$0.750472\pi$
$338$	−1.50000	+	2.59808i	−0.0815892	+	0.141317i
$339$		0			0
$340$		0			0
$341$	−3.00000	+	5.19615i	−0.162459	+	0.281387i
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$	1.00000			0.0539164
$345$		0			0
$346$	−3.00000	−	5.19615i	−0.161281	−	0.279347i
$347$	−10.0000	−	17.3205i	−0.536828	−	0.929814i	−0.999072	−	0.0430610i	$-0.986289\pi$
$347$	−10.0000	−	17.3205i	−0.536828	−	0.929814i	0.462244	−	0.886753i	$-0.347044\pi$
$348$		0			0
$349$	32.0000			1.71292			0.856460	−	0.516213i	$-0.172659\pi$
$349$	32.0000			1.71292			0.856460	+	0.516213i	$0.172659\pi$
$350$	−10.0000	−	8.66025i	−0.534522	−	0.462910i
$351$		0			0
$352$	−0.500000	+	0.866025i	−0.0266501	+	0.0461593i
$353$	−4.00000	−	6.92820i	−0.212899	−	0.368751i	0.739722	−	0.672913i	$-0.234957\pi$
$353$	−4.00000	−	6.92820i	−0.212899	−	0.368751i	−0.952620	+	0.304162i	$0.901624\pi$
$354$		0			0
$355$		0			0
$356$	8.00000			0.423999
$357$		0			0
$358$	25.0000			1.32129
$359$	1.00000	−	1.73205i	0.0527780	−	0.0914141i	−0.838429	−	0.545010i	$-0.816526\pi$
$359$	1.00000	−	1.73205i	0.0527780	−	0.0914141i	0.891207	+	0.453596i	$0.149859\pi$
$360$		0			0
$361$	5.00000	+	8.66025i	0.263158	+	0.455803i
$362$	−11.0000	+	19.0526i	−0.578147	+	1.00138i
$363$		0			0
$364$	2.00000	−	10.3923i	0.104828	−	0.544705i
$365$		0			0
$366$		0			0
$367$	−10.0000	−	17.3205i	−0.521996	−	0.904123i	−0.999673	−	0.0255875i	$-0.991854\pi$
$367$	−10.0000	−	17.3205i	−0.521996	−	0.904123i	0.477677	−	0.878536i	$-0.341479\pi$
$368$	−0.500000	−	0.866025i	−0.0260643	−	0.0451447i
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−17.0000	+	29.4449i	−0.880227	+	1.52460i	−0.0291379	+	0.999575i	$0.509276\pi$
$373$	−17.0000	+	29.4449i	−0.880227	+	1.52460i	−0.851089	+	0.525022i	$0.824057\pi$
$374$	−0.500000	−	0.866025i	−0.0258544	−	0.0447811i
$375$		0			0
$376$	−0.500000	+	0.866025i	−0.0257855	+	0.0446619i
$377$	4.00000			0.206010
$378$		0			0
$379$	−22.0000			−1.13006			−0.565032	−	0.825069i	$-0.691136\pi$
$379$	−22.0000			−1.13006			−0.565032	+	0.825069i	$0.691136\pi$
$380$		0			0
$381$		0			0
$382$	−12.0000	−	20.7846i	−0.613973	−	1.06343i
$383$	14.5000	−	25.1147i	0.740915	−	1.28330i	−0.211164	−	0.977451i	$-0.567725\pi$
$383$	14.5000	−	25.1147i	0.740915	−	1.28330i	0.952079	−	0.305852i	$-0.0989414\pi$
$384$		0			0
$385$		0			0
$386$	14.0000			0.712581
$387$		0			0
$388$	−3.50000	−	6.06218i	−0.177686	−	0.307760i
$389$	−14.0000	−	24.2487i	−0.709828	−	1.22946i	−0.964921	−	0.262542i	$-0.915439\pi$
$389$	−14.0000	−	24.2487i	−0.709828	−	1.22946i	0.255092	−	0.966917i	$-0.417894\pi$
$390$		0			0
$391$	1.00000			0.0505722
$392$	1.00000	+	6.92820i	0.0505076	+	0.349927i
$393$		0			0
$394$	13.5000	−	23.3827i	0.680120	−	1.17800i
$395$		0			0
$396$		0			0
$397$	−11.5000	+	19.9186i	−0.577168	+	0.999685i	0.418634	+	0.908155i	$0.362509\pi$
$397$	−11.5000	+	19.9186i	−0.577168	+	0.999685i	−0.995802	+	0.0915300i	$0.970824\pi$
$398$	4.00000			0.200502
$399$		0			0
$400$	−5.00000			−0.250000
$401$	1.00000	−	1.73205i	0.0499376	−	0.0864945i	−0.839976	−	0.542623i	$-0.817431\pi$
$401$	1.00000	−	1.73205i	0.0499376	−	0.0864945i	0.889914	+	0.456129i	$0.150764\pi$
$402$		0			0
$403$	−12.0000	−	20.7846i	−0.597763	−	1.03536i
$404$	7.50000	−	12.9904i	0.373139	−	0.646296i
$405$		0			0
$406$	−2.50000	+	0.866025i	−0.124073	+	0.0429801i
$407$	−3.00000			−0.148704
$408$		0			0
$409$	−3.00000	−	5.19615i	−0.148340	−	0.256933i	0.782274	−	0.622935i	$-0.214060\pi$
$409$	−3.00000	−	5.19615i	−0.148340	−	0.256933i	−0.930614	+	0.366002i	$0.880726\pi$
$410$		0			0
$411$		0			0
$412$	4.00000			0.197066
$413$	−3.50000	+	18.1865i	−0.172224	+	0.894901i
$414$		0			0
$415$		0			0
$416$	−2.00000	−	3.46410i	−0.0980581	−	0.169842i
$417$		0			0
$418$	1.50000	−	2.59808i	0.0733674	−	0.127076i
$419$	17.0000			0.830504			0.415252	−	0.909706i	$-0.363693\pi$
$419$	17.0000			0.830504			0.415252	+	0.909706i	$0.363693\pi$
$420$		0			0
$421$	−3.00000			−0.146211			−0.0731055	−	0.997324i	$-0.523291\pi$
$421$	−3.00000			−0.146211			−0.0731055	+	0.997324i	$0.523291\pi$
$422$	10.0000	−	17.3205i	0.486792	−	0.843149i
$423$		0			0
$424$		0			0
$425$	2.50000	−	4.33013i	0.121268	−	0.210042i
$426$		0			0
$427$	−15.0000	+	5.19615i	−0.725901	+	0.251459i
$428$	−2.00000			−0.0966736
$429$		0			0
$430$		0			0
$431$	−14.0000	−	24.2487i	−0.674356	−	1.16802i	−0.976657	−	0.214807i	$-0.931088\pi$
$431$	−14.0000	−	24.2487i	−0.674356	−	1.16802i	0.302300	−	0.953213i	$-0.402245\pi$
$432$		0			0
$433$	−19.0000			−0.913082			−0.456541	−	0.889702i	$-0.650912\pi$
$433$	−19.0000			−0.913082			−0.456541	+	0.889702i	$0.650912\pi$
$434$	12.0000	+	10.3923i	0.576018	+	0.498847i
$435$		0			0
$436$	9.00000	−	15.5885i	0.431022	−	0.746552i
$437$	1.50000	+	2.59808i	0.0717547	+	0.124283i
$438$		0			0
$439$	5.50000	−	9.52628i	0.262501	−	0.454665i	−0.704405	−	0.709798i	$-0.748786\pi$
$439$	5.50000	−	9.52628i	0.262501	−	0.454665i	0.966906	+	0.255134i	$0.0821195\pi$
$440$		0			0
$441$		0			0
$442$	4.00000			0.190261
$443$	−1.50000	+	2.59808i	−0.0712672	+	0.123438i	−0.899457	−	0.437009i	$-0.856038\pi$
$443$	−1.50000	+	2.59808i	−0.0712672	+	0.123438i	0.828190	+	0.560448i	$0.189371\pi$
$444$		0			0
$445$		0			0
$446$	−8.00000	+	13.8564i	−0.378811	+	0.656120i
$447$		0			0
$448$	2.00000	+	1.73205i	0.0944911	+	0.0818317i
$449$	8.00000			0.377543			0.188772	−	0.982021i	$-0.439549\pi$
$449$	8.00000			0.377543			0.188772	+	0.982021i	$0.439549\pi$
$450$		0			0
$451$	−3.00000	−	5.19615i	−0.141264	−	0.244677i
$452$	2.00000	+	3.46410i	0.0940721	+	0.162938i
$453$		0			0
$454$	2.00000			0.0938647
$455$		0			0
$456$		0			0
$457$	−9.00000	+	15.5885i	−0.421002	+	0.729197i	−0.996038	−	0.0889312i	$-0.971655\pi$
$457$	−9.00000	+	15.5885i	−0.421002	+	0.729197i	0.575036	+	0.818128i	$0.304988\pi$
$458$	3.00000	+	5.19615i	0.140181	+	0.242800i
$459$		0			0
$460$		0			0
$461$	−21.0000			−0.978068			−0.489034	−	0.872265i	$-0.662651\pi$
$461$	−21.0000			−0.978068			−0.489034	+	0.872265i	$0.662651\pi$
$462$		0			0
$463$	−32.0000			−1.48717			−0.743583	−	0.668644i	$-0.766875\pi$
$463$	−32.0000			−1.48717			−0.743583	+	0.668644i	$0.766875\pi$
$464$	−0.500000	+	0.866025i	−0.0232119	+	0.0402042i
$465$		0			0
$466$	−5.50000	−	9.52628i	−0.254783	−	0.441296i
$467$	−11.5000	+	19.9186i	−0.532157	+	0.921722i	0.467139	+	0.884184i	$0.345285\pi$
$467$	−11.5000	+	19.9186i	−0.532157	+	0.921722i	−0.999295	+	0.0375381i	$0.988048\pi$
$468$		0			0
$469$	−2.00000	+	10.3923i	−0.0923514	+	0.479872i
$470$		0			0
$471$		0			0
$472$	3.50000	+	6.06218i	0.161101	+	0.279034i
$473$	−0.500000	−	0.866025i	−0.0229900	−	0.0398199i
$474$		0			0
$475$	15.0000			0.688247
$476$	−2.50000	+	0.866025i	−0.114587	+	0.0396942i
$477$		0			0
$478$	8.00000	−	13.8564i	0.365911	−	0.633777i
$479$	5.00000	+	8.66025i	0.228456	+	0.395697i	0.957351	−	0.288929i	$-0.0932990\pi$
$479$	5.00000	+	8.66025i	0.228456	+	0.395697i	−0.728895	+	0.684626i	$0.759966\pi$
$480$		0			0
$481$	6.00000	−	10.3923i	0.273576	−	0.473848i
$482$	−4.00000			−0.182195
$483$		0			0
$484$	1.00000			0.0454545
$485$		0			0
$486$		0			0
$487$	−10.0000	−	17.3205i	−0.453143	−	0.784867i	0.545436	−	0.838152i	$-0.316364\pi$
$487$	−10.0000	−	17.3205i	−0.453143	−	0.784867i	−0.998579	+	0.0532853i	$0.983031\pi$
$488$	−3.00000	+	5.19615i	−0.135804	+	0.235219i
$489$		0			0
$490$		0			0
$491$	−12.0000			−0.541552			−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000			−0.541552			−0.270776	+	0.962642i	$0.587280\pi$
$492$		0			0
$493$	−0.500000	−	0.866025i	−0.0225189	−	0.0390038i
$494$	6.00000	+	10.3923i	0.269953	+	0.467572i
$495$		0			0
$496$	6.00000			0.269408
$497$	30.0000	+	25.9808i	1.34568	+	1.16540i
$498$		0			0
$499$	−5.00000	+	8.66025i	−0.223831	+	0.387686i	−0.955968	−	0.293471i	$-0.905190\pi$
$499$	−5.00000	+	8.66025i	−0.223831	+	0.387686i	0.732137	+	0.681157i	$0.238523\pi$
$500$		0			0
$501$		0			0
$502$	−3.50000	+	6.06218i	−0.156213	+	0.270568i
$503$	−2.00000			−0.0891756			−0.0445878	−	0.999005i	$-0.514197\pi$
$503$	−2.00000			−0.0891756			−0.0445878	+	0.999005i	$0.514197\pi$
$504$		0			0
$505$		0			0
$506$	−0.500000	+	0.866025i	−0.0222277	+	0.0384995i
$507$		0			0
$508$	3.50000	+	6.06218i	0.155287	+	0.268966i
$509$	2.00000	−	3.46410i	0.0886484	−	0.153544i	−0.818292	−	0.574803i	$-0.805079\pi$
$509$	2.00000	−	3.46410i	0.0886484	−	0.153544i	0.906940	+	0.421260i	$0.138412\pi$
$510$		0			0
$511$	6.00000	−	31.1769i	0.265424	−	1.37919i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−6.00000	−	10.3923i	−0.264649	−	0.458385i
$515$		0			0
$516$		0			0
$517$	1.00000			0.0439799
$518$	−1.50000	+	7.79423i	−0.0659062	+	0.342459i
$519$		0			0
$520$		0			0
$521$	9.00000	+	15.5885i	0.394297	+	0.682943i	0.993011	−	0.118020i	$-0.0376547\pi$
$521$	9.00000	+	15.5885i	0.394297	+	0.682943i	−0.598714	+	0.800963i	$0.704321\pi$
$522$		0			0
$523$	−22.0000	+	38.1051i	−0.961993	+	1.66622i	−0.244507	+	0.969648i	$0.578626\pi$
$523$	−22.0000	+	38.1051i	−0.961993	+	1.66622i	−0.717486	+	0.696573i	$0.754707\pi$
$524$	2.00000			0.0873704
$525$		0			0
$526$	14.0000			0.610429
$527$	−3.00000	+	5.19615i	−0.130682	+	0.226348i
$528$		0			0
$529$	11.0000	+	19.0526i	0.478261	+	0.828372i
$530$		0			0
$531$		0			0
$532$	−6.00000	−	5.19615i	−0.260133	−	0.225282i
$533$	24.0000			1.03956
$534$		0			0
$535$		0			0
$536$	2.00000	+	3.46410i	0.0863868	+	0.149626i
$537$		0			0
$538$	18.0000			0.776035
$539$	5.50000	−	4.33013i	0.236902	−	0.186512i
$540$		0			0
$541$	−10.0000	+	17.3205i	−0.429934	+	0.744667i	−0.996867	−	0.0790969i	$-0.974796\pi$
$541$	−10.0000	+	17.3205i	−0.429934	+	0.744667i	0.566933	+	0.823764i	$0.308130\pi$
$542$	8.00000	+	13.8564i	0.343629	+	0.595184i
$543$		0			0
$544$	−0.500000	+	0.866025i	−0.0214373	+	0.0371305i
$545$		0			0
$546$		0			0
$547$	7.00000			0.299298			0.149649	−	0.988739i	$-0.452186\pi$
$547$	7.00000			0.299298			0.149649	+	0.988739i	$0.452186\pi$
$548$	−2.00000	+	3.46410i	−0.0854358	+	0.147979i
$549$		0			0
$550$	2.50000	+	4.33013i	0.106600	+	0.184637i
$551$	1.50000	−	2.59808i	0.0639021	−	0.110682i
$552$		0			0
$553$		0			0
$554$	−16.0000			−0.679775
$555$		0			0
$556$	8.50000	+	14.7224i	0.360480	+	0.624370i
$557$	−1.50000	−	2.59808i	−0.0635570	−	0.110084i	0.832496	−	0.554031i	$-0.186911\pi$
$557$	−1.50000	−	2.59808i	−0.0635570	−	0.110084i	−0.896053	+	0.443947i	$0.853578\pi$
$558$		0			0
$559$	4.00000			0.169182
$560$		0			0
$561$		0			0
$562$	−13.5000	+	23.3827i	−0.569463	+	0.986339i
$563$	6.00000	+	10.3923i	0.252870	+	0.437983i	0.964315	−	0.264758i	$-0.0852922\pi$
$563$	6.00000	+	10.3923i	0.252870	+	0.437983i	−0.711445	+	0.702742i	$0.751959\pi$
$564$		0			0
$565$		0			0
$566$	20.0000			0.840663
$567$		0			0
$568$	15.0000			0.629386
$569$	19.5000	−	33.7750i	0.817483	−	1.41592i	−0.0900490	−	0.995937i	$-0.528702\pi$
$569$	19.5000	−	33.7750i	0.817483	−	1.41592i	0.907532	−	0.419984i	$-0.137964\pi$
$570$		0			0
$571$	−3.50000	−	6.06218i	−0.146470	−	0.253694i	0.783450	−	0.621455i	$-0.213458\pi$
$571$	−3.50000	−	6.06218i	−0.146470	−	0.253694i	−0.929921	+	0.367760i	$0.880125\pi$
$572$	−2.00000	+	3.46410i	−0.0836242	+	0.144841i
$573$		0			0
$574$	−15.0000	+	5.19615i	−0.626088	+	0.216883i
$575$	−5.00000			−0.208514
$576$		0			0
$577$	11.0000	+	19.0526i	0.457936	+	0.793168i	0.998852	−	0.0479084i	$-0.0152556\pi$
$577$	11.0000	+	19.0526i	0.457936	+	0.793168i	−0.540916	+	0.841077i	$0.681922\pi$
$578$	8.00000	+	13.8564i	0.332756	+	0.576351i
$579$		0			0
$580$		0			0
$581$	32.0000	+	27.7128i	1.32758	+	1.14972i
$582$		0			0
$583$		0			0
$584$	−6.00000	−	10.3923i	−0.248282	−	0.430037i
$585$		0			0
$586$	−7.50000	+	12.9904i	−0.309822	+	0.536628i
$587$	−4.00000			−0.165098			−0.0825488	−	0.996587i	$-0.526306\pi$
$587$	−4.00000			−0.165098			−0.0825488	+	0.996587i	$0.526306\pi$
$588$		0			0
$589$	−18.0000			−0.741677
$590$		0			0
$591$		0			0
$592$	1.50000	+	2.59808i	0.0616496	+	0.106780i
$593$	−9.50000	+	16.4545i	−0.390118	+	0.675705i	−0.992465	−	0.122530i	$-0.960899\pi$
$593$	−9.50000	+	16.4545i	−0.390118	+	0.675705i	0.602347	+	0.798235i	$0.294233\pi$
$594$		0			0
$595$		0			0
$596$	−1.00000			−0.0409616
$597$		0			0
$598$	−2.00000	−	3.46410i	−0.0817861	−	0.141658i
$599$	−20.0000	−	34.6410i	−0.817178	−	1.41539i	−0.907754	−	0.419504i	$-0.862204\pi$
$599$	−20.0000	−	34.6410i	−0.817178	−	1.41539i	0.0905757	−	0.995890i	$-0.471129\pi$
$600$		0			0
$601$	22.0000			0.897399			0.448699	−	0.893683i	$-0.351887\pi$
$601$	22.0000			0.897399			0.448699	+	0.893683i	$0.351887\pi$
$602$	−2.50000	+	0.866025i	−0.101892	+	0.0352966i
$603$		0			0
$604$	−5.50000	+	9.52628i	−0.223792	+	0.387619i
$605$		0			0
$606$		0			0
$607$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$607$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$608$	−3.00000			−0.121666
$609$		0			0
$610$		0			0
$611$	−2.00000	+	3.46410i	−0.0809113	+	0.140143i
$612$		0			0
$613$	−20.0000	−	34.6410i	−0.807792	−	1.39914i	−0.914390	−	0.404835i	$-0.867329\pi$
$613$	−20.0000	−	34.6410i	−0.807792	−	1.39914i	0.106597	−	0.994302i	$-0.466004\pi$
$614$	10.0000	−	17.3205i	0.403567	−	0.698999i
$615$		0			0
$616$	0.500000	−	2.59808i	0.0201456	−	0.104679i
$617$	−26.0000			−1.04672			−0.523360	−	0.852111i	$-0.675322\pi$
$617$	−26.0000			−1.04672			−0.523360	+	0.852111i	$0.675322\pi$
$618$		0			0
$619$	15.0000	+	25.9808i	0.602901	+	1.04425i	0.992379	+	0.123219i	$0.0393219\pi$
$619$	15.0000	+	25.9808i	0.602901	+	1.04425i	−0.389479	+	0.921036i	$0.627345\pi$
$620$		0			0
$621$		0			0
$622$	31.0000			1.24299
$623$	−20.0000	+	6.92820i	−0.801283	+	0.277573i
$624$		0			0
$625$	−12.5000	+	21.6506i	−0.500000	+	0.866025i
$626$	16.5000	+	28.5788i	0.659473	+	1.14224i
$627$		0			0
$628$	4.50000	−	7.79423i	0.179570	−	0.311024i
$629$	−3.00000			−0.119618
$630$		0			0
$631$	40.0000			1.59237			0.796187	−	0.605050i	$-0.206847\pi$
$631$	40.0000			1.59237			0.796187	+	0.605050i	$0.206847\pi$
$632$		0			0
$633$		0			0
$634$	6.00000	+	10.3923i	0.238290	+	0.412731i
$635$		0			0
$636$		0			0
$637$	4.00000	+	27.7128i	0.158486	+	1.09802i
$638$	1.00000			0.0395904
$639$		0			0
$640$		0			0
$641$	17.0000	+	29.4449i	0.671460	+	1.16300i	0.977490	+	0.210981i	$0.0676657\pi$
$641$	17.0000	+	29.4449i	0.671460	+	1.16300i	−0.306031	+	0.952022i	$0.599001\pi$
$642$		0			0
$643$	−10.0000			−0.394362			−0.197181	−	0.980367i	$-0.563179\pi$
$643$	−10.0000			−0.394362			−0.197181	+	0.980367i	$0.563179\pi$
$644$	2.00000	+	1.73205i	0.0788110	+	0.0682524i
$645$		0			0
$646$	1.50000	−	2.59808i	0.0590167	−	0.102220i
$647$	4.00000	+	6.92820i	0.157256	+	0.272376i	0.933878	−	0.357591i	$-0.116402\pi$
$647$	4.00000	+	6.92820i	0.157256	+	0.272376i	−0.776622	+	0.629967i	$0.783068\pi$
$648$		0			0
$649$	3.50000	−	6.06218i	0.137387	−	0.237961i
$650$	−20.0000			−0.784465
$651$		0			0
$652$	−18.0000			−0.704934
$653$	24.0000	−	41.5692i	0.939193	−	1.62673i	0.172211	−	0.985060i	$-0.444909\pi$
$653$	24.0000	−	41.5692i	0.939193	−	1.62673i	0.766982	−	0.641669i	$-0.221758\pi$
$654$		0			0
$655$		0			0
$656$	−3.00000	+	5.19615i	−0.117130	+	0.202876i
$657$		0			0
$658$	0.500000	−	2.59808i	0.0194920	−	0.101284i
$659$	−50.0000			−1.94772			−0.973862	−	0.227142i	$-0.927062\pi$
$659$	−50.0000			−1.94772			−0.973862	+	0.227142i	$0.927062\pi$
$660$		0			0
$661$	20.5000	+	35.5070i	0.797358	+	1.38106i	0.921331	+	0.388778i	$0.127103\pi$
$661$	20.5000	+	35.5070i	0.797358	+	1.38106i	−0.123974	+	0.992286i	$0.539564\pi$
$662$	−5.00000	−	8.66025i	−0.194331	−	0.336590i
$663$		0			0
$664$	16.0000			0.620920
$665$		0			0
$666$		0			0
$667$	−0.500000	+	0.866025i	−0.0193601	+	0.0335326i
$668$	−6.00000	−	10.3923i	−0.232147	−	0.402090i
$669$		0			0
$670$		0			0
$671$	6.00000			0.231627
$672$		0			0
$673$	−28.0000			−1.07932			−0.539660	−	0.841883i	$-0.681447\pi$
$673$	−28.0000			−1.07932			−0.539660	+	0.841883i	$0.681447\pi$
$674$	13.0000	−	22.5167i	0.500741	−	0.867309i
$675$		0			0
$676$	−1.50000	−	2.59808i	−0.0576923	−	0.0999260i
$677$	−4.50000	+	7.79423i	−0.172949	+	0.299557i	−0.939450	−	0.342687i	$-0.888663\pi$
$677$	−4.50000	+	7.79423i	−0.172949	+	0.299557i	0.766501	+	0.642244i	$0.221996\pi$
$678$		0			0
$679$	14.0000	+	12.1244i	0.537271	+	0.465290i
$680$		0			0
$681$		0			0
$682$	−3.00000	−	5.19615i	−0.114876	−	0.198971i
$683$	19.5000	+	33.7750i	0.746147	+	1.29236i	0.949657	+	0.313291i	$0.101432\pi$
$683$	19.5000	+	33.7750i	0.746147	+	1.29236i	−0.203510	+	0.979073i	$0.565235\pi$
$684$		0			0
$685$		0			0
$686$	−8.50000	−	16.4545i	−0.324532	−	0.628235i
$687$		0			0
$688$	−0.500000	+	0.866025i	−0.0190623	+	0.0330169i
$689$		0			0
$690$		0			0
$691$	17.0000	−	29.4449i	0.646710	−	1.12014i	−0.337193	−	0.941435i	$-0.609478\pi$
$691$	17.0000	−	29.4449i	0.646710	−	1.12014i	0.983904	−	0.178700i	$-0.0571891\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$	20.0000			0.759190
$695$		0			0
$696$		0			0
$697$	−3.00000	−	5.19615i	−0.113633	−	0.196818i
$698$	−16.0000	+	27.7128i	−0.605609	+	1.04895i
$699$		0			0
$700$	12.5000	−	4.33013i	0.472456	−	0.163663i
$701$	−29.0000			−1.09531			−0.547657	−	0.836703i	$-0.684480\pi$
$701$	−29.0000			−1.09531			−0.547657	+	0.836703i	$0.684480\pi$
$702$		0			0
$703$	−4.50000	−	7.79423i	−0.169721	−	0.293965i
$704$	−0.500000	−	0.866025i	−0.0188445	−	0.0326396i
$705$		0			0
$706$	8.00000			0.301084
$707$	−7.50000	+	38.9711i	−0.282067	+	1.46566i
$708$		0			0
$709$	4.50000	−	7.79423i	0.169001	−	0.292718i	−0.769068	−	0.639167i	$-0.779279\pi$
$709$	4.50000	−	7.79423i	0.169001	−	0.292718i	0.938069	+	0.346449i	$0.112613\pi$
$710$		0			0
$711$		0			0
$712$	−4.00000	+	6.92820i	−0.149906	+	0.259645i
$713$	6.00000			0.224702
$714$		0			0
$715$		0			0
$716$	−12.5000	+	21.6506i	−0.467147	+	0.809122i
$717$		0			0
$718$	1.00000	+	1.73205i	0.0373197	+	0.0646396i
$719$	−18.5000	+	32.0429i	−0.689934	+	1.19500i	0.281925	+	0.959436i	$0.409027\pi$
$719$	−18.5000	+	32.0429i	−0.689934	+	1.19500i	−0.971859	+	0.235564i	$0.924306\pi$
$720$		0			0
$721$	−10.0000	+	3.46410i	−0.372419	+	0.129010i
$722$	−10.0000			−0.372161
$723$		0			0
$724$	−11.0000	−	19.0526i	−0.408812	−	0.708083i
$725$	2.50000	+	4.33013i	0.0928477	+	0.160817i
$726$		0			0
$727$	14.0000			0.519231			0.259616	−	0.965712i	$-0.416404\pi$
$727$	14.0000			0.519231			0.259616	+	0.965712i	$0.416404\pi$
$728$	8.00000	+	6.92820i	0.296500	+	0.256776i
$729$		0			0
$730$		0			0
$731$	−0.500000	−	0.866025i	−0.0184932	−	0.0320311i
$732$		0			0
$733$	5.00000	−	8.66025i	0.184679	−	0.319874i	−0.758789	−	0.651336i	$-0.774209\pi$
$733$	5.00000	−	8.66025i	0.184679	−	0.319874i	0.943468	+	0.331463i	$0.107542\pi$
$734$	20.0000			0.738213
$735$		0			0
$736$	1.00000			0.0368605
$737$	2.00000	−	3.46410i	0.0736709	−	0.127602i
$738$		0			0
$739$	10.0000	+	17.3205i	0.367856	+	0.637145i	0.989230	−	0.146369i	$-0.0467586\pi$
$739$	10.0000	+	17.3205i	0.367856	+	0.637145i	−0.621374	+	0.783514i	$0.713425\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	6.00000			0.220119			0.110059	−	0.993925i	$-0.464896\pi$
$743$	6.00000			0.220119			0.110059	+	0.993925i	$0.464896\pi$
$744$		0			0
$745$		0			0
$746$	−17.0000	−	29.4449i	−0.622414	−	1.07805i
$747$		0			0
$748$	1.00000			0.0365636
$749$	5.00000	−	1.73205i	0.182696	−	0.0632878i
$750$		0			0
$751$	17.0000	−	29.4449i	0.620339	−	1.07446i	−0.369084	−	0.929396i	$-0.620328\pi$
$751$	17.0000	−	29.4449i	0.620339	−	1.07446i	0.989423	−	0.145062i	$-0.0463382\pi$
$752$	−0.500000	−	0.866025i	−0.0182331	−	0.0315807i
$753$		0			0
$754$	−2.00000	+	3.46410i	−0.0728357	+	0.126155i
$755$		0			0
$756$		0			0
$757$	29.0000			1.05402			0.527011	−	0.849858i	$-0.323312\pi$
$757$	29.0000			1.05402			0.527011	+	0.849858i	$0.323312\pi$
$758$	11.0000	−	19.0526i	0.399538	−	0.692020i
$759$		0			0
$760$		0			0
$761$	−9.00000	+	15.5885i	−0.326250	+	0.565081i	−0.981764	−	0.190101i	$-0.939118\pi$
$761$	−9.00000	+	15.5885i	−0.326250	+	0.565081i	0.655515	+	0.755182i	$0.272452\pi$
$762$		0			0
$763$	−9.00000	+	46.7654i	−0.325822	+	1.69302i
$764$	24.0000			0.868290
$765$		0			0
$766$	14.5000	+	25.1147i	0.523906	+	0.907432i
$767$	14.0000	+	24.2487i	0.505511	+	0.875570i
$768$		0			0
$769$	−22.0000			−0.793340			−0.396670	−	0.917961i	$-0.629834\pi$
$769$	−22.0000			−0.793340			−0.396670	+	0.917961i	$0.629834\pi$
$770$		0			0
$771$		0			0
$772$	−7.00000	+	12.1244i	−0.251936	+	0.436365i
$773$	7.00000	+	12.1244i	0.251773	+	0.436083i	0.964014	−	0.265852i	$-0.0856532\pi$
$773$	7.00000	+	12.1244i	0.251773	+	0.436083i	−0.712241	+	0.701935i	$0.752320\pi$
$774$		0			0
$775$	15.0000	−	25.9808i	0.538816	−	0.933257i
$776$	7.00000			0.251285
$777$		0			0
$778$	28.0000			1.00385
$779$	9.00000	−	15.5885i	0.322458	−	0.558514i
$780$		0			0
$781$	−7.50000	−	12.9904i	−0.268371	−	0.464832i
$782$	−0.500000	+	0.866025i	−0.0178800	+	0.0309690i
$783$		0			0
$784$	−6.50000	−	2.59808i	−0.232143	−	0.0927884i
$785$		0			0
$786$		0			0
$787$	5.50000	+	9.52628i	0.196054	+	0.339575i	0.947245	−	0.320509i	$-0.103854\pi$
$787$	5.50000	+	9.52628i	0.196054	+	0.339575i	−0.751192	+	0.660084i	$0.770521\pi$
$788$	13.5000	+	23.3827i	0.480918	+	0.832974i
$789$		0			0
$790$		0			0
$791$	−8.00000	−	6.92820i	−0.284447	−	0.246339i
$792$		0			0
$793$	−12.0000	+	20.7846i	−0.426132	+	0.738083i
$794$	−11.5000	−	19.9186i	−0.408120	−	0.706884i
$795$		0			0
$796$	−2.00000	+	3.46410i	−0.0708881	+	0.122782i
$797$	−42.0000			−1.48772			−0.743858	−	0.668338i	$-0.767006\pi$
$797$	−42.0000			−1.48772			−0.743858	+	0.668338i	$0.767006\pi$
$798$		0			0
$799$	1.00000			0.0353775
$800$	2.50000	−	4.33013i	0.0883883	−	0.153093i
$801$		0			0
$802$	1.00000	+	1.73205i	0.0353112	+	0.0611608i
$803$	−6.00000	+	10.3923i	−0.211735	+	0.366736i
$804$		0			0
$805$		0			0
$806$	24.0000			0.845364
$807$		0			0
$808$	7.50000	+	12.9904i	0.263849	+	0.457000i
$809$	21.0000	+	36.3731i	0.738321	+	1.27881i	0.953251	+	0.302180i	$0.0977142\pi$
$809$	21.0000	+	36.3731i	0.738321	+	1.27881i	−0.214930	+	0.976629i	$0.568952\pi$
$810$		0			0
$811$	20.0000			0.702295			0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000			0.702295			0.351147	+	0.936320i	$0.385792\pi$
$812$	0.500000	−	2.59808i	0.0175466	−	0.0911746i
$813$		0			0
$814$	1.50000	−	2.59808i	0.0525750	−	0.0910625i
$815$		0			0
$816$		0			0
$817$	1.50000	−	2.59808i	0.0524784	−	0.0908952i
$818$	6.00000			0.209785
$819$		0			0
$820$		0			0
$821$	5.00000	−	8.66025i	0.174501	−	0.302245i	−0.765487	−	0.643451i	$-0.777502\pi$
$821$	5.00000	−	8.66025i	0.174501	−	0.302245i	0.939989	+	0.341206i	$0.110835\pi$
$822$		0			0
$823$	−25.0000	−	43.3013i	−0.871445	−	1.50939i	−0.860502	−	0.509447i	$-0.829850\pi$
$823$	−25.0000	−	43.3013i	−0.871445	−	1.50939i	−0.0109433	−	0.999940i	$-0.503483\pi$
$824$	−2.00000	+	3.46410i	−0.0696733	+	0.120678i
$825$		0			0
$826$	−14.0000	−	12.1244i	−0.487122	−	0.421860i
$827$	−30.0000			−1.04320			−0.521601	−	0.853189i	$-0.674665\pi$
$827$	−30.0000			−1.04320			−0.521601	+	0.853189i	$0.674665\pi$
$828$		0			0
$829$	3.50000	+	6.06218i	0.121560	+	0.210548i	0.920383	−	0.391018i	$-0.127877\pi$
$829$	3.50000	+	6.06218i	0.121560	+	0.210548i	−0.798823	+	0.601566i	$0.794544\pi$
$830$		0			0
$831$		0			0
$832$	4.00000			0.138675
$833$	5.50000	−	4.33013i	0.190564	−	0.150030i
$834$		0			0
$835$		0			0
$836$	1.50000	+	2.59808i	0.0518786	+	0.0898563i
$837$		0			0
$838$	−8.50000	+	14.7224i	−0.293628	+	0.508578i
$839$	4.00000			0.138095			0.0690477	−	0.997613i	$-0.478004\pi$
$839$	4.00000			0.138095			0.0690477	+	0.997613i	$0.478004\pi$
$840$		0			0
$841$	−28.0000			−0.965517
$842$	1.50000	−	2.59808i	0.0516934	−	0.0895356i
$843$		0			0
$844$	10.0000	+	17.3205i	0.344214	+	0.596196i
$845$		0			0
$846$		0			0
$847$	−2.50000	+	0.866025i	−0.0859010	+	0.0297570i
$848$		0			0
$849$		0			0
$850$	2.50000	+	4.33013i	0.0857493	+	0.148522i
$851$	1.50000	+	2.59808i	0.0514193	+	0.0890609i
$852$		0			0
$853$	−36.0000			−1.23262			−0.616308	−	0.787505i	$-0.711372\pi$
$853$	−36.0000			−1.23262			−0.616308	+	0.787505i	$0.711372\pi$
$854$	3.00000	−	15.5885i	0.102658	−	0.533426i
$855$		0			0
$856$	1.00000	−	1.73205i	0.0341793	−	0.0592003i
$857$	25.5000	+	44.1673i	0.871063	+	1.50873i	0.860898	+	0.508778i	$0.169903\pi$
$857$	25.5000	+	44.1673i	0.871063	+	1.50873i	0.0101655	+	0.999948i	$0.496764\pi$
$858$		0			0
$859$	−4.00000	+	6.92820i	−0.136478	+	0.236387i	−0.926161	−	0.377128i	$-0.876912\pi$
$859$	−4.00000	+	6.92820i	−0.136478	+	0.236387i	0.789683	+	0.613515i	$0.210245\pi$
$860$		0			0
$861$		0			0
$862$	28.0000			0.953684
$863$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$863$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$864$		0			0
$865$		0			0
$866$	9.50000	−	16.4545i	0.322823	−	0.559146i
$867$		0			0
$868$	−15.0000	+	5.19615i	−0.509133	+	0.176369i
$869$		0			0
$870$		0			0
$871$	8.00000	+	13.8564i	0.271070	+	0.469506i
$872$	9.00000	+	15.5885i	0.304778	+	0.527892i
$873$		0			0
$874$	−3.00000			−0.101477
$875$		0			0
$876$		0			0
$877$	−16.0000	+	27.7128i	−0.540282	+	0.935795i	0.458606	+	0.888640i	$0.348349\pi$
$877$	−16.0000	+	27.7128i	−0.540282	+	0.935795i	−0.998888	+	0.0471555i	$0.984984\pi$
$878$	5.50000	+	9.52628i	0.185616	+	0.321496i
$879$		0			0
$880$		0			0
$881$	12.0000			0.404290			0.202145	−	0.979356i	$-0.435209\pi$
$881$	12.0000			0.404290			0.202145	+	0.979356i	$0.435209\pi$
$882$		0			0
$883$	14.0000			0.471138			0.235569	−	0.971858i	$-0.424305\pi$
$883$	14.0000			0.471138			0.235569	+	0.971858i	$0.424305\pi$
$884$	−2.00000	+	3.46410i	−0.0672673	+	0.116510i
$885$		0			0
$886$	−1.50000	−	2.59808i	−0.0503935	−	0.0872841i
$887$	4.00000	−	6.92820i	0.134307	−	0.232626i	−0.791026	−	0.611783i	$-0.790453\pi$
$887$	4.00000	−	6.92820i	0.134307	−	0.232626i	0.925332	+	0.379157i	$0.123786\pi$
$888$		0			0
$889$	−14.0000	−	12.1244i	−0.469545	−	0.406638i
$890$		0			0
$891$		0			0
$892$	−8.00000	−	13.8564i	−0.267860	−	0.463947i
$893$	1.50000	+	2.59808i	0.0501956	+	0.0869413i
$894$		0			0
$895$		0			0
$896$	−2.50000	+	0.866025i	−0.0835191	+	0.0289319i
$897$		0			0
$898$	−4.00000	+	6.92820i	−0.133482	+	0.231197i
$899$	−3.00000	−	5.19615i	−0.100056	−	0.173301i
$900$		0			0
$901$		0			0
$902$	6.00000			0.199778
$903$		0			0
$904$	−4.00000			−0.133038
$905$		0			0
$906$		0			0
$907$	4.00000	+	6.92820i	0.132818	+	0.230047i	0.924762	−	0.380547i	$-0.124264\pi$
$907$	4.00000	+	6.92820i	0.132818	+	0.230047i	−0.791944	+	0.610594i	$0.790931\pi$
$908$	−1.00000	+	1.73205i	−0.0331862	+	0.0574801i
$909$		0			0
$910$		0			0
$911$	21.0000			0.695761			0.347881	−	0.937539i	$-0.386901\pi$
$911$	21.0000			0.695761			0.347881	+	0.937539i	$0.386901\pi$
$912$		0			0
$913$	−8.00000	−	13.8564i	−0.264761	−	0.458580i
$914$	−9.00000	−	15.5885i	−0.297694	−	0.515620i
$915$		0			0
$916$	−6.00000			−0.198246
$917$	−5.00000	+	1.73205i	−0.165115	+	0.0571974i
$918$		0			0
$919$	16.5000	−	28.5788i	0.544285	−	0.942729i	−0.454367	−	0.890815i	$-0.650134\pi$
$919$	16.5000	−	28.5788i	0.544285	−	0.942729i	0.998652	−	0.0519142i	$-0.0165322\pi$
$920$		0			0
$921$		0			0
$922$	10.5000	−	18.1865i	0.345799	−	0.598942i
$923$	60.0000			1.97492
$924$		0			0
$925$	15.0000			0.493197
$926$	16.0000	−	27.7128i	0.525793	−	0.910700i
$927$		0			0
$928$	−0.500000	−	0.866025i	−0.0164133	−	0.0284287i
$929$	27.0000	−	46.7654i	0.885841	−	1.53432i	0.0410949	−	0.999155i	$-0.486915\pi$
$929$	27.0000	−	46.7654i	0.885841	−	1.53432i	0.844746	−	0.535167i	$-0.179751\pi$
$930$		0			0
$931$	19.5000	+	7.79423i	0.639087	+	0.255446i
$932$	11.0000			0.360317
$933$		0			0
$934$	−11.5000	−	19.9186i	−0.376291	−	0.651756i
$935$		0			0
$936$		0			0
$937$	8.00000			0.261349			0.130674	−	0.991425i	$-0.458286\pi$
$937$	8.00000			0.261349			0.130674	+	0.991425i	$0.458286\pi$
$938$	−8.00000	−	6.92820i	−0.261209	−	0.226214i
$939$		0			0
$940$		0			0
$941$	−22.5000	−	38.9711i	−0.733479	−	1.27042i	−0.955387	−	0.295355i	$-0.904562\pi$
$941$	−22.5000	−	38.9711i	−0.733479	−	1.27042i	0.221908	−	0.975068i	$-0.428771\pi$
$942$		0			0
$943$	−3.00000	+	5.19615i	−0.0976934	+	0.169210i
$944$	−7.00000			−0.227831
$945$		0			0
$946$	1.00000			0.0325128
$947$	−25.5000	+	44.1673i	−0.828639	+	1.43524i	0.0704677	+	0.997514i	$0.477551\pi$
$947$	−25.5000	+	44.1673i	−0.828639	+	1.43524i	−0.899106	+	0.437730i	$0.855783\pi$
$948$		0			0
$949$	−24.0000	−	41.5692i	−0.779073	−	1.34939i
$950$	−7.50000	+	12.9904i	−0.243332	+	0.421464i
$951$		0			0
$952$	0.500000	−	2.59808i	0.0162051	−	0.0842041i
$953$	−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
$955$		0			0
$956$	8.00000	+	13.8564i	0.258738	+	0.448148i
$957$		0			0
$958$	−10.0000			−0.323085
$959$	2.00000	−	10.3923i	0.0645834	−	0.335585i
$960$		0			0
$961$	−2.50000	+	4.33013i	−0.0806452	+	0.139682i
$962$	6.00000	+	10.3923i	0.193448	+	0.335061i
$963$		0			0
$964$	2.00000	−	3.46410i	0.0644157	−	0.111571i
$965$		0			0
$966$		0			0
$967$	−35.0000			−1.12552			−0.562762	−	0.826619i	$-0.690261\pi$
$967$	−35.0000			−1.12552			−0.562762	+	0.826619i	$0.690261\pi$
$968$	−0.500000	+	0.866025i	−0.0160706	+	0.0278351i
$969$		0			0
$970$		0			0
$971$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$971$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$972$		0			0
$973$	−34.0000	−	29.4449i	−1.08999	−	0.943959i
$974$	20.0000			0.640841
$975$		0			0
$976$	−3.00000	−	5.19615i	−0.0960277	−	0.166325i
$977$	6.00000	+	10.3923i	0.191957	+	0.332479i	0.945899	−	0.324462i	$-0.105183\pi$
$977$	6.00000	+	10.3923i	0.191957	+	0.332479i	−0.753942	+	0.656941i	$0.771850\pi$
$978$		0			0
$979$	8.00000			0.255681
$980$		0			0
$981$		0			0
$982$	6.00000	−	10.3923i	0.191468	−	0.331632i
$983$	9.50000	+	16.4545i	0.303003	+	0.524816i	0.976815	−	0.214087i	$-0.0686775\pi$
$983$	9.50000	+	16.4545i	0.303003	+	0.524816i	−0.673812	+	0.738903i	$0.735344\pi$
$984$		0			0
$985$		0			0
$986$	1.00000			0.0318465
$987$		0			0
$988$	−12.0000			−0.381771
$989$	−0.500000	+	0.866025i	−0.0158991	+	0.0275380i
$990$		0			0
$991$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$991$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$992$	−3.00000	+	5.19615i	−0.0952501	+	0.164978i
$993$		0			0
$994$	−37.5000	+	12.9904i	−1.18943	+	0.412030i
$995$		0			0
$996$		0			0
$997$	22.0000	+	38.1051i	0.696747	+	1.20680i	0.969588	+	0.244742i	$0.0787033\pi$
$997$	22.0000	+	38.1051i	0.696747	+	1.20680i	−0.272841	+	0.962059i	$0.587963\pi$
$998$	−5.00000	−	8.66025i	−0.158272	−	0.274136i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.k.f.793.1		2
3.2	odd	2		462.2.i.d.331.1	yes	2
7.2	even	3		9702.2.a.bv.1.1		1
7.4	even	3	inner	1386.2.k.f.991.1		2
7.5	odd	6		9702.2.a.bq.1.1		1
21.2	odd	6		3234.2.a.c.1.1		1
21.5	even	6		3234.2.a.j.1.1		1
21.11	odd	6		462.2.i.d.67.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.i.d.67.1	✓	2	21.11	odd	6
462.2.i.d.331.1	yes	2	3.2	odd	2
1386.2.k.f.793.1		2	1.1	even	1	trivial
1386.2.k.f.991.1		2	7.4	even	3	inner
3234.2.a.c.1.1		1	21.2	odd	6
3234.2.a.j.1.1		1	21.5	even	6
9702.2.a.bq.1.1		1	7.5	odd	6
9702.2.a.bv.1.1		1	7.2	even	3

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)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{11} +4.00000 q^{13} +(-2.50000 + 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.500000 - 0.866025i) q^{17} +(1.50000 - 2.59808i) q^{19} +1.00000 q^{22} +(-0.500000 + 0.866025i) q^{23} +(2.50000 + 4.33013i) q^{25} +(-2.00000 + 3.46410i) q^{26} +(0.500000 - 2.59808i) q^{28} +1.00000 q^{29} +(-3.00000 - 5.19615i) q^{31} +(-0.500000 - 0.866025i) q^{32} +1.00000 q^{34} +(1.50000 - 2.59808i) q^{37} +(1.50000 + 2.59808i) q^{38} +6.00000 q^{41} +1.00000 q^{43} +(-0.500000 + 0.866025i) q^{44} +(-0.500000 - 0.866025i) q^{46} +(-0.500000 + 0.866025i) q^{47} +(1.00000 + 6.92820i) q^{49} -5.00000 q^{50} +(-2.00000 - 3.46410i) q^{52} +(2.00000 + 1.73205i) q^{56} +(-0.500000 + 0.866025i) q^{58} +(3.50000 + 6.06218i) q^{59} +(-3.00000 + 5.19615i) q^{61} +6.00000 q^{62} +1.00000 q^{64} +(2.00000 + 3.46410i) q^{67} +(-0.500000 + 0.866025i) q^{68} +15.0000 q^{71} +(-6.00000 - 10.3923i) q^{73} +(1.50000 + 2.59808i) q^{74} -3.00000 q^{76} +(0.500000 - 2.59808i) q^{77} +(-3.00000 + 5.19615i) q^{82} +16.0000 q^{83} +(-0.500000 + 0.866025i) q^{86} +(-0.500000 - 0.866025i) q^{88} +(-4.00000 + 6.92820i) q^{89} +(8.00000 + 6.92820i) q^{91} +1.00000 q^{92} +(-0.500000 - 0.866025i) q^{94} +7.00000 q^{97} +(-6.50000 - 2.59808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} + 4 q^{7} + 2 q^{8}+O(q^{10}) \) 2 * q - q^2 - q^4 + 4 * q^7 + 2 * q^8	\( 2 q - q^{2} - q^{4} + 4 q^{7} + 2 q^{8} - q^{11} + 8 q^{13} - 5 q^{14} - q^{16} - q^{17} + 3 q^{19} + 2 q^{22} - q^{23} + 5 q^{25} - 4 q^{26} + q^{28} + 2 q^{29} - 6 q^{31} - q^{32} + 2 q^{34} + 3 q^{37} + 3 q^{38} + 12 q^{41} + 2 q^{43} - q^{44} - q^{46} - q^{47} + 2 q^{49} - 10 q^{50} - 4 q^{52} + 4 q^{56} - q^{58} + 7 q^{59} - 6 q^{61} + 12 q^{62} + 2 q^{64} + 4 q^{67} - q^{68} + 30 q^{71} - 12 q^{73} + 3 q^{74} - 6 q^{76} + q^{77} - 6 q^{82} + 32 q^{83} - q^{86} - q^{88} - 8 q^{89} + 16 q^{91} + 2 q^{92} - q^{94} + 14 q^{97} - 13 q^{98}+O(q^{100}) \) 2 * q - q^2 - q^4 + 4 * q^7 + 2 * q^8 - q^11 + 8 * q^13 - 5 * q^14 - q^16 - q^17 + 3 * q^19 + 2 * q^22 - q^23 + 5 * q^25 - 4 * q^26 + q^28 + 2 * q^29 - 6 * q^31 - q^32 + 2 * q^34 + 3 * q^37 + 3 * q^38 + 12 * q^41 + 2 * q^43 - q^44 - q^46 - q^47 + 2 * q^49 - 10 * q^50 - 4 * q^52 + 4 * q^56 - q^58 + 7 * q^59 - 6 * q^61 + 12 * q^62 + 2 * q^64 + 4 * q^67 - q^68 + 30 * q^71 - 12 * q^73 + 3 * q^74 - 6 * q^76 + q^77 - 6 * q^82 + 32 * q^83 - q^86 - q^88 - 8 * q^89 + 16 * q^91 + 2 * q^92 - q^94 + 14 * q^97 - 13 * q^98

Introduction

L-functions

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