LMFDB - Embedded newform 1690.2.l.a.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1690,2,Mod(361,1690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1690, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("1690.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1690 = 2 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1690.l (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.4947179416$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1690.361
Dual form			1690.2.l.a.1161.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(-1.73205 - 1.00000i) q^{6} +(-3.46410 - 2.00000i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(-1.73205 - 1.00000i) q^{6} +(-3.46410 - 2.00000i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(1.73205 - 1.00000i) q^{11} -2.00000 q^{12} -4.00000 q^{14} +(-1.73205 + 1.00000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{17} +1.00000i q^{18} +(-5.19615 - 3.00000i) q^{19} +(-0.866025 - 0.500000i) q^{20} +8.00000i q^{21} +(1.00000 - 1.73205i) q^{22} +(3.00000 + 5.19615i) q^{23} +(-1.73205 + 1.00000i) q^{24} -1.00000 q^{25} -4.00000 q^{27} +(-3.46410 + 2.00000i) q^{28} +(-1.00000 - 1.73205i) q^{29} +(-1.00000 + 1.73205i) q^{30} -6.00000i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-3.46410 - 2.00000i) q^{33} -2.00000i q^{34} +(-2.00000 + 3.46410i) q^{35} +(0.500000 + 0.866025i) q^{36} +(1.73205 - 1.00000i) q^{37} -6.00000 q^{38} -1.00000 q^{40} +(8.66025 - 5.00000i) q^{41} +(4.00000 + 6.92820i) q^{42} +(-5.00000 + 8.66025i) q^{43} -2.00000i q^{44} +(0.866025 + 0.500000i) q^{45} +(5.19615 + 3.00000i) q^{46} +12.0000i q^{47} +(-1.00000 + 1.73205i) q^{48} +(4.50000 + 7.79423i) q^{49} +(-0.866025 + 0.500000i) q^{50} -4.00000 q^{51} +2.00000 q^{53} +(-3.46410 + 2.00000i) q^{54} +(-1.00000 - 1.73205i) q^{55} +(-2.00000 + 3.46410i) q^{56} +12.0000i q^{57} +(-1.73205 - 1.00000i) q^{58} +(8.66025 + 5.00000i) q^{59} +2.00000i q^{60} +(-1.00000 + 1.73205i) q^{61} +(-3.00000 - 5.19615i) q^{62} +(3.46410 - 2.00000i) q^{63} -1.00000 q^{64} -4.00000 q^{66} +(-10.3923 + 6.00000i) q^{67} +(-1.00000 - 1.73205i) q^{68} +(6.00000 - 10.3923i) q^{69} +4.00000i q^{70} +(-8.66025 - 5.00000i) q^{71} +(0.866025 + 0.500000i) q^{72} -10.0000i q^{73} +(1.00000 - 1.73205i) q^{74} +(1.00000 + 1.73205i) q^{75} +(-5.19615 + 3.00000i) q^{76} -8.00000 q^{77} -4.00000 q^{79} +(-0.866025 + 0.500000i) q^{80} +(5.50000 + 9.52628i) q^{81} +(5.00000 - 8.66025i) q^{82} +(6.92820 + 4.00000i) q^{84} +(-1.73205 - 1.00000i) q^{85} +10.0000i q^{86} +(-2.00000 + 3.46410i) q^{87} +(-1.00000 - 1.73205i) q^{88} +(12.1244 - 7.00000i) q^{89} +1.00000 q^{90} +6.00000 q^{92} +(-10.3923 + 6.00000i) q^{93} +(6.00000 + 10.3923i) q^{94} +(-3.00000 + 5.19615i) q^{95} +2.00000i q^{96} +(-12.1244 - 7.00000i) q^{97} +(7.79423 + 4.50000i) q^{98} +2.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} + 2 q^{4} - 2 q^{9}+O(q^{10}) $ 4 * q - 4 * q^3 + 2 * q^4 - 2 * q^9	$ 4 q - 4 q^{3} + 2 q^{4} - 2 q^{9} - 2 q^{10} - 8 q^{12} - 16 q^{14} - 2 q^{16} + 4 q^{17} + 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{27} - 4 q^{29} - 4 q^{30} - 8 q^{35} + 2 q^{36} - 24 q^{38} - 4 q^{40} + 16 q^{42} - 20 q^{43} - 4 q^{48} + 18 q^{49} - 16 q^{51} + 8 q^{53} - 4 q^{55} - 8 q^{56} - 4 q^{61} - 12 q^{62} - 4 q^{64} - 16 q^{66} - 4 q^{68} + 24 q^{69} + 4 q^{74} + 4 q^{75} - 32 q^{77} - 16 q^{79} + 22 q^{81} + 20 q^{82} - 8 q^{87} - 4 q^{88} + 4 q^{90} + 24 q^{92} + 24 q^{94} - 12 q^{95}+O(q^{100}) $ 4 * q - 4 * q^3 + 2 * q^4 - 2 * q^9 - 2 * q^10 - 8 * q^12 - 16 * q^14 - 2 * q^16 + 4 * q^17 + 4 * q^22 + 12 * q^23 - 4 * q^25 - 16 * q^27 - 4 * q^29 - 4 * q^30 - 8 * q^35 + 2 * q^36 - 24 * q^38 - 4 * q^40 + 16 * q^42 - 20 * q^43 - 4 * q^48 + 18 * q^49 - 16 * q^51 + 8 * q^53 - 4 * q^55 - 8 * q^56 - 4 * q^61 - 12 * q^62 - 4 * q^64 - 16 * q^66 - 4 * q^68 + 24 * q^69 + 4 * q^74 + 4 * q^75 - 32 * q^77 - 16 * q^79 + 22 * q^81 + 20 * q^82 - 8 * q^87 - 4 * q^88 + 4 * q^90 + 24 * q^92 + 24 * q^94 - 12 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1690\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−1.00000	−	1.73205i	−0.577350	−	1.00000i	−0.995782	−	0.0917517i	$-0.970753\pi$
$3$	−1.00000	−	1.73205i	−0.577350	−	1.00000i	0.418432	−	0.908248i	$-0.362580\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−1.73205	−	1.00000i	−0.707107	−	0.408248i
$7$	−3.46410	−	2.00000i	−1.30931	−	0.755929i	−0.327327	−	0.944911i	$-0.606148\pi$
$7$	−3.46410	−	2.00000i	−1.30931	−	0.755929i	−0.981981	+	0.188982i	$0.939481\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	1.73205	−	1.00000i	0.522233	−	0.301511i	−0.215615	−	0.976478i	$-0.569176\pi$
$11$	1.73205	−	1.00000i	0.522233	−	0.301511i	0.737848	+	0.674967i	$0.235842\pi$
$12$	−2.00000			−0.577350
$13$		0			0
$13$		0			0
$14$	−4.00000			−1.06904
$15$	−1.73205	+	1.00000i	−0.447214	+	0.258199i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	−0.718900	−	0.695113i	$-0.755354\pi$
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	0.961436	+	0.275029i	$0.0886875\pi$
$18$			1.00000i			0.235702i
$19$	−5.19615	−	3.00000i	−1.19208	−	0.688247i	−0.233301	−	0.972404i	$-0.574953\pi$
$19$	−5.19615	−	3.00000i	−1.19208	−	0.688247i	−0.958778	+	0.284157i	$0.908286\pi$
$20$	−0.866025	−	0.500000i	−0.193649	−	0.111803i
$21$			8.00000i			1.74574i
$22$	1.00000	−	1.73205i	0.213201	−	0.369274i
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	0.988436	+	0.151642i	$0.0484560\pi$
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	−0.362892	+	0.931831i	$0.618211\pi$
$24$	−1.73205	+	1.00000i	−0.353553	+	0.204124i
$25$	−1.00000			−0.200000
$26$		0			0
$27$	−4.00000			−0.769800
$28$	−3.46410	+	2.00000i	−0.654654	+	0.377964i
$29$	−1.00000	−	1.73205i	−0.185695	−	0.321634i	0.758115	−	0.652121i	$-0.226120\pi$
$29$	−1.00000	−	1.73205i	−0.185695	−	0.321634i	−0.943811	+	0.330487i	$0.892787\pi$
$30$	−1.00000	+	1.73205i	−0.182574	+	0.316228i
$31$		−	6.00000i		−	1.07763i	−0.842424	−	0.538816i	$-0.818872\pi$
$31$		−	6.00000i		−	1.07763i	0.842424	−	0.538816i	$-0.181128\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−3.46410	−	2.00000i	−0.603023	−	0.348155i
$34$		−	2.00000i		−	0.342997i
$35$	−2.00000	+	3.46410i	−0.338062	+	0.585540i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	1.73205	−	1.00000i	0.284747	−	0.164399i	−0.350823	−	0.936442i	$-0.614098\pi$
$37$	1.73205	−	1.00000i	0.284747	−	0.164399i	0.635571	+	0.772043i	$0.280765\pi$
$38$	−6.00000			−0.973329
$39$		0			0
$40$	−1.00000			−0.158114
$41$	8.66025	−	5.00000i	1.35250	−	0.780869i	0.363905	−	0.931436i	$-0.381443\pi$
$41$	8.66025	−	5.00000i	1.35250	−	0.780869i	0.988600	+	0.150567i	$0.0481100\pi$
$42$	4.00000	+	6.92820i	0.617213	+	1.06904i
$43$	−5.00000	+	8.66025i	−0.762493	+	1.32068i	0.179069	+	0.983836i	$0.442691\pi$
$43$	−5.00000	+	8.66025i	−0.762493	+	1.32068i	−0.941562	+	0.336840i	$0.890642\pi$
$44$		−	2.00000i		−	0.301511i
$45$	0.866025	+	0.500000i	0.129099	+	0.0745356i
$46$	5.19615	+	3.00000i	0.766131	+	0.442326i
$47$			12.0000i			1.75038i	0.483779	+	0.875190i	$0.339264\pi$
$47$			12.0000i			1.75038i	−0.483779	+	0.875190i	$0.660736\pi$
$48$	−1.00000	+	1.73205i	−0.144338	+	0.250000i
$49$	4.50000	+	7.79423i	0.642857	+	1.11346i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$	−4.00000			−0.560112
$52$		0			0
$53$	2.00000			0.274721			0.137361	−	0.990521i	$-0.456138\pi$
$53$	2.00000			0.274721			0.137361	+	0.990521i	$0.456138\pi$
$54$	−3.46410	+	2.00000i	−0.471405	+	0.272166i
$55$	−1.00000	−	1.73205i	−0.134840	−	0.233550i
$56$	−2.00000	+	3.46410i	−0.267261	+	0.462910i
$57$			12.0000i			1.58944i
$58$	−1.73205	−	1.00000i	−0.227429	−	0.131306i
$59$	8.66025	+	5.00000i	1.12747	+	0.650945i	0.943297	−	0.331949i	$-0.107706\pi$
$59$	8.66025	+	5.00000i	1.12747	+	0.650945i	0.184172	+	0.982894i	$0.441040\pi$
$60$			2.00000i			0.258199i
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	−0.922916	−	0.385002i	$-0.874201\pi$
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	0.794879	+	0.606768i	$0.207534\pi$
$62$	−3.00000	−	5.19615i	−0.381000	−	0.659912i
$63$	3.46410	−	2.00000i	0.436436	−	0.251976i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−4.00000			−0.492366
$67$	−10.3923	+	6.00000i	−1.26962	+	0.733017i	−0.974916	−	0.222571i	$-0.928555\pi$
$67$	−10.3923	+	6.00000i	−1.26962	+	0.733017i	−0.294706	+	0.955588i	$0.595222\pi$
$68$	−1.00000	−	1.73205i	−0.121268	−	0.210042i
$69$	6.00000	−	10.3923i	0.722315	−	1.25109i
$70$			4.00000i			0.478091i
$71$	−8.66025	−	5.00000i	−1.02778	−	0.593391i	−0.111434	−	0.993772i	$-0.535544\pi$
$71$	−8.66025	−	5.00000i	−1.02778	−	0.593391i	−0.916349	+	0.400381i	$0.868878\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$		−	10.0000i		−	1.17041i	−0.810885	−	0.585206i	$-0.801014\pi$
$73$		−	10.0000i		−	1.17041i	0.810885	−	0.585206i	$-0.198986\pi$
$74$	1.00000	−	1.73205i	0.116248	−	0.201347i
$75$	1.00000	+	1.73205i	0.115470	+	0.200000i
$76$	−5.19615	+	3.00000i	−0.596040	+	0.344124i
$77$	−8.00000			−0.911685
$78$		0			0
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$	−0.866025	+	0.500000i	−0.0968246	+	0.0559017i
$81$	5.50000	+	9.52628i	0.611111	+	1.05848i
$82$	5.00000	−	8.66025i	0.552158	−	0.956365i
$83$		0			0		1.00000			$0$
$83$		0			0		−1.00000			$\pi$
$84$	6.92820	+	4.00000i	0.755929	+	0.436436i
$85$	−1.73205	−	1.00000i	−0.187867	−	0.108465i
$86$			10.0000i			1.07833i
$87$	−2.00000	+	3.46410i	−0.214423	+	0.371391i
$88$	−1.00000	−	1.73205i	−0.106600	−	0.184637i
$89$	12.1244	−	7.00000i	1.28518	−	0.741999i	0.307389	−	0.951584i	$-0.400545\pi$
$89$	12.1244	−	7.00000i	1.28518	−	0.741999i	0.977790	+	0.209585i	$0.0672115\pi$
$90$	1.00000			0.105409
$91$		0			0
$92$	6.00000			0.625543
$93$	−10.3923	+	6.00000i	−1.07763	+	0.622171i
$94$	6.00000	+	10.3923i	0.618853	+	1.07188i
$95$	−3.00000	+	5.19615i	−0.307794	+	0.533114i
$96$			2.00000i			0.204124i
$97$	−12.1244	−	7.00000i	−1.23104	−	0.710742i	−0.263795	−	0.964579i	$-0.584974\pi$
$97$	−12.1244	−	7.00000i	−1.23104	−	0.710742i	−0.967247	+	0.253837i	$0.918307\pi$
$98$	7.79423	+	4.50000i	0.787336	+	0.454569i
$99$			2.00000i			0.201008i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	7.00000	+	12.1244i	0.696526	+	1.20642i	0.969664	+	0.244443i	$0.0786053\pi$
$101$	7.00000	+	12.1244i	0.696526	+	1.20642i	−0.273138	+	0.961975i	$0.588061\pi$
$102$	−3.46410	+	2.00000i	−0.342997	+	0.198030i
$103$	18.0000			1.77359			0.886796	−	0.462160i	$-0.152926\pi$
$103$	18.0000			1.77359			0.886796	+	0.462160i	$0.152926\pi$
$104$		0			0
$105$	8.00000			0.780720
$106$	1.73205	−	1.00000i	0.168232	−	0.0971286i
$107$	−3.00000	−	5.19615i	−0.290021	−	0.502331i	0.683793	−	0.729676i	$-0.260329\pi$
$107$	−3.00000	−	5.19615i	−0.290021	−	0.502331i	−0.973814	+	0.227345i	$0.926996\pi$
$108$	−2.00000	+	3.46410i	−0.192450	+	0.333333i
$109$		−	6.00000i		−	0.574696i	−0.957826	−	0.287348i	$-0.907226\pi$
$109$		−	6.00000i		−	0.574696i	0.957826	−	0.287348i	$-0.0927736\pi$
$110$	−1.73205	−	1.00000i	−0.165145	−	0.0953463i
$111$	−3.46410	−	2.00000i	−0.328798	−	0.189832i
$112$			4.00000i			0.377964i
$113$	−1.00000	+	1.73205i	−0.0940721	+	0.162938i	−0.909221	−	0.416314i	$-0.863322\pi$
$113$	−1.00000	+	1.73205i	−0.0940721	+	0.162938i	0.815149	+	0.579252i	$0.196655\pi$
$114$	6.00000	+	10.3923i	0.561951	+	0.973329i
$115$	5.19615	−	3.00000i	0.484544	−	0.279751i
$116$	−2.00000			−0.185695
$117$		0			0
$118$	10.0000			0.920575
$119$	−6.92820	+	4.00000i	−0.635107	+	0.366679i
$120$	1.00000	+	1.73205i	0.0912871	+	0.158114i
$121$	−3.50000	+	6.06218i	−0.318182	+	0.551107i
$122$			2.00000i			0.181071i
$123$	−17.3205	−	10.0000i	−1.56174	−	0.901670i
$124$	−5.19615	−	3.00000i	−0.466628	−	0.269408i
$125$			1.00000i			0.0894427i
$126$	2.00000	−	3.46410i	0.178174	−	0.308607i
$127$	−7.00000	−	12.1244i	−0.621150	−	1.07586i	−0.989272	−	0.146085i	$-0.953333\pi$
$127$	−7.00000	−	12.1244i	−0.621150	−	1.07586i	0.368122	−	0.929777i	$-0.380001\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	20.0000			1.76090
$130$		0			0
$131$	4.00000			0.349482			0.174741	−	0.984614i	$-0.444091\pi$
$131$	4.00000			0.349482			0.174741	+	0.984614i	$0.444091\pi$
$132$	−3.46410	+	2.00000i	−0.301511	+	0.174078i
$133$	12.0000	+	20.7846i	1.04053	+	1.80225i
$134$	−6.00000	+	10.3923i	−0.518321	+	0.897758i
$135$			4.00000i			0.344265i
$136$	−1.73205	−	1.00000i	−0.148522	−	0.0857493i
$137$	−15.5885	−	9.00000i	−1.33181	−	0.768922i	−0.346235	−	0.938148i	$-0.612540\pi$
$137$	−15.5885	−	9.00000i	−1.33181	−	0.768922i	−0.985577	+	0.169226i	$0.945873\pi$
$138$		−	12.0000i		−	1.02151i
$139$	4.00000	−	6.92820i	0.339276	−	0.587643i	−0.645021	−	0.764165i	$-0.723151\pi$
$139$	4.00000	−	6.92820i	0.339276	−	0.587643i	0.984297	+	0.176522i	$0.0564848\pi$
$140$	2.00000	+	3.46410i	0.169031	+	0.292770i
$141$	20.7846	−	12.0000i	1.75038	−	1.01058i
$142$	−10.0000			−0.839181
$143$		0			0
$144$	1.00000			0.0833333
$145$	−1.73205	+	1.00000i	−0.143839	+	0.0830455i
$146$	−5.00000	−	8.66025i	−0.413803	−	0.716728i
$147$	9.00000	−	15.5885i	0.742307	−	1.28571i
$148$		−	2.00000i		−	0.164399i
$149$	−1.73205	−	1.00000i	−0.141895	−	0.0819232i	0.427372	−	0.904076i	$-0.359440\pi$
$149$	−1.73205	−	1.00000i	−0.141895	−	0.0819232i	−0.569267	+	0.822153i	$0.692773\pi$
$150$	1.73205	+	1.00000i	0.141421	+	0.0816497i
$151$		−	6.00000i		−	0.488273i	−0.969741	−	0.244137i	$-0.921495\pi$
$151$		−	6.00000i		−	0.488273i	0.969741	−	0.244137i	$-0.0785045\pi$
$152$	−3.00000	+	5.19615i	−0.243332	+	0.421464i
$153$	1.00000	+	1.73205i	0.0808452	+	0.140028i
$154$	−6.92820	+	4.00000i	−0.558291	+	0.322329i
$155$	−6.00000			−0.481932
$156$		0			0
$157$	10.0000			0.798087			0.399043	−	0.916932i	$-0.369342\pi$
$157$	10.0000			0.798087			0.399043	+	0.916932i	$0.369342\pi$
$158$	−3.46410	+	2.00000i	−0.275589	+	0.159111i
$159$	−2.00000	−	3.46410i	−0.158610	−	0.274721i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$		−	24.0000i		−	1.89146i
$162$	9.52628	+	5.50000i	0.748455	+	0.432121i
$163$	−3.46410	−	2.00000i	−0.271329	−	0.156652i	0.358162	−	0.933659i	$-0.383403\pi$
$163$	−3.46410	−	2.00000i	−0.271329	−	0.156652i	−0.629492	+	0.777007i	$0.716737\pi$
$164$		−	10.0000i		−	0.780869i
$165$	−2.00000	+	3.46410i	−0.155700	+	0.269680i
$166$		0			0
$167$	−17.3205	+	10.0000i	−1.34030	+	0.773823i	−0.986851	−	0.161630i	$-0.948325\pi$
$167$	−17.3205	+	10.0000i	−1.34030	+	0.773823i	−0.353450	+	0.935454i	$0.614991\pi$
$168$	8.00000			0.617213
$169$		0			0
$170$	−2.00000			−0.153393
$171$	5.19615	−	3.00000i	0.397360	−	0.229416i
$172$	5.00000	+	8.66025i	0.381246	+	0.660338i
$173$	5.00000	−	8.66025i	0.380143	−	0.658427i	−0.610939	−	0.791677i	$-0.709208\pi$
$173$	5.00000	−	8.66025i	0.380143	−	0.658427i	0.991082	+	0.133250i	$0.0425415\pi$
$174$			4.00000i			0.303239i
$175$	3.46410	+	2.00000i	0.261861	+	0.151186i
$176$	−1.73205	−	1.00000i	−0.130558	−	0.0753778i
$177$		−	20.0000i		−	1.50329i
$178$	7.00000	−	12.1244i	0.524672	−	0.908759i
$179$	−2.00000	−	3.46410i	−0.149487	−	0.258919i	0.781551	−	0.623841i	$-0.214429\pi$
$179$	−2.00000	−	3.46410i	−0.149487	−	0.258919i	−0.931038	+	0.364922i	$0.881096\pi$
$180$	0.866025	−	0.500000i	0.0645497	−	0.0372678i
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$		0			0
$183$	4.00000			0.295689
$184$	5.19615	−	3.00000i	0.383065	−	0.221163i
$185$	−1.00000	−	1.73205i	−0.0735215	−	0.127343i
$186$	−6.00000	+	10.3923i	−0.439941	+	0.762001i
$187$		−	4.00000i		−	0.292509i
$188$	10.3923	+	6.00000i	0.757937	+	0.437595i
$189$	13.8564	+	8.00000i	1.00791	+	0.581914i
$190$			6.00000i			0.435286i
$191$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$191$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$192$	1.00000	+	1.73205i	0.0721688	+	0.125000i
$193$	−12.1244	+	7.00000i	−0.872730	+	0.503871i	−0.868255	−	0.496119i	$-0.834758\pi$
$193$	−12.1244	+	7.00000i	−0.872730	+	0.503871i	−0.00447566	+	0.999990i	$0.501425\pi$
$194$	−14.0000			−1.00514
$195$		0			0
$196$	9.00000			0.642857
$197$	−5.19615	+	3.00000i	−0.370211	+	0.213741i	−0.673550	−	0.739141i	$-0.735232\pi$
$197$	−5.19615	+	3.00000i	−0.370211	+	0.213741i	0.303340	+	0.952882i	$0.401898\pi$
$198$	1.00000	+	1.73205i	0.0710669	+	0.123091i
$199$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$199$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$200$			1.00000i			0.0707107i
$201$	20.7846	+	12.0000i	1.46603	+	0.846415i
$202$	12.1244	+	7.00000i	0.853067	+	0.492518i
$203$			8.00000i			0.561490i
$204$	−2.00000	+	3.46410i	−0.140028	+	0.242536i
$205$	−5.00000	−	8.66025i	−0.349215	−	0.604858i
$206$	15.5885	−	9.00000i	1.08610	−	0.627060i
$207$	−6.00000			−0.417029
$208$		0			0
$209$	−12.0000			−0.830057
$210$	6.92820	−	4.00000i	0.478091	−	0.276026i
$211$	−14.0000	−	24.2487i	−0.963800	−	1.66935i	−0.712806	−	0.701361i	$-0.752576\pi$
$211$	−14.0000	−	24.2487i	−0.963800	−	1.66935i	−0.250994	−	0.967989i	$-0.580757\pi$
$212$	1.00000	−	1.73205i	0.0686803	−	0.118958i
$213$			20.0000i			1.37038i
$214$	−5.19615	−	3.00000i	−0.355202	−	0.205076i
$215$	8.66025	+	5.00000i	0.590624	+	0.340997i
$216$			4.00000i			0.272166i
$217$	−12.0000	+	20.7846i	−0.814613	+	1.41095i
$218$	−3.00000	−	5.19615i	−0.203186	−	0.351928i
$219$	−17.3205	+	10.0000i	−1.17041	+	0.675737i
$220$	−2.00000			−0.134840
$221$		0			0
$222$	−4.00000			−0.268462
$223$	3.46410	−	2.00000i	0.231973	−	0.133930i	−0.379509	−	0.925188i	$-0.623907\pi$
$223$	3.46410	−	2.00000i	0.231973	−	0.133930i	0.611482	+	0.791258i	$0.290574\pi$
$224$	2.00000	+	3.46410i	0.133631	+	0.231455i
$225$	0.500000	−	0.866025i	0.0333333	−	0.0577350i
$226$			2.00000i			0.133038i
$227$	3.46410	+	2.00000i	0.229920	+	0.132745i	0.610535	−	0.791989i	$-0.290954\pi$
$227$	3.46410	+	2.00000i	0.229920	+	0.132745i	−0.380615	+	0.924734i	$0.624288\pi$
$228$	10.3923	+	6.00000i	0.688247	+	0.397360i
$229$		−	10.0000i		−	0.660819i	−0.943838	−	0.330409i	$-0.892813\pi$
$229$		−	10.0000i		−	0.660819i	0.943838	−	0.330409i	$-0.107187\pi$
$230$	3.00000	−	5.19615i	0.197814	−	0.342624i
$231$	8.00000	+	13.8564i	0.526361	+	0.911685i
$232$	−1.73205	+	1.00000i	−0.113715	+	0.0656532i
$233$	6.00000			0.393073			0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000			0.393073			0.196537	+	0.980497i	$0.437031\pi$
$234$		0			0
$235$	12.0000			0.782794
$236$	8.66025	−	5.00000i	0.563735	−	0.325472i
$237$	4.00000	+	6.92820i	0.259828	+	0.450035i
$238$	−4.00000	+	6.92820i	−0.259281	+	0.449089i
$239$		−	26.0000i		−	1.68180i	−0.541190	−	0.840900i	$-0.682026\pi$
$239$		−	26.0000i		−	1.68180i	0.541190	−	0.840900i	$-0.317974\pi$
$240$	1.73205	+	1.00000i	0.111803	+	0.0645497i
$241$	−19.0526	−	11.0000i	−1.22728	−	0.708572i	−0.260822	−	0.965387i	$-0.583994\pi$
$241$	−19.0526	−	11.0000i	−1.22728	−	0.708572i	−0.966461	+	0.256814i	$0.917327\pi$
$242$			7.00000i			0.449977i
$243$	5.00000	−	8.66025i	0.320750	−	0.555556i
$244$	1.00000	+	1.73205i	0.0640184	+	0.110883i
$245$	7.79423	−	4.50000i	0.497955	−	0.287494i
$246$	−20.0000			−1.27515
$247$		0			0
$248$	−6.00000			−0.381000
$249$		0			0
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$251$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$252$		−	4.00000i		−	0.251976i
$253$	10.3923	+	6.00000i	0.653359	+	0.377217i
$254$	−12.1244	−	7.00000i	−0.760750	−	0.439219i
$255$			4.00000i			0.250490i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−15.0000	−	25.9808i	−0.935674	−	1.62064i	−0.773427	−	0.633885i	$-0.781459\pi$
$257$	−15.0000	−	25.9808i	−0.935674	−	1.62064i	−0.162247	−	0.986750i	$-0.551874\pi$
$258$	17.3205	−	10.0000i	1.07833	−	0.622573i
$259$	−8.00000			−0.497096
$260$		0			0
$261$	2.00000			0.123797
$262$	3.46410	−	2.00000i	0.214013	−	0.123560i
$263$	−1.00000	−	1.73205i	−0.0616626	−	0.106803i	0.833546	−	0.552450i	$-0.186307\pi$
$263$	−1.00000	−	1.73205i	−0.0616626	−	0.106803i	−0.895209	+	0.445647i	$0.852974\pi$
$264$	−2.00000	+	3.46410i	−0.123091	+	0.213201i
$265$		−	2.00000i		−	0.122859i
$266$	20.7846	+	12.0000i	1.27439	+	0.735767i
$267$	−24.2487	−	14.0000i	−1.48400	−	0.856786i
$268$			12.0000i			0.733017i
$269$	−3.00000	+	5.19615i	−0.182913	+	0.316815i	−0.942871	−	0.333157i	$-0.891886\pi$
$269$	−3.00000	+	5.19615i	−0.182913	+	0.316815i	0.759958	+	0.649972i	$0.225219\pi$
$270$	2.00000	+	3.46410i	0.121716	+	0.210819i
$271$	1.73205	−	1.00000i	0.105215	−	0.0607457i	−0.446469	−	0.894799i	$-0.647319\pi$
$271$	1.73205	−	1.00000i	0.105215	−	0.0607457i	0.551684	+	0.834053i	$0.313985\pi$
$272$	−2.00000			−0.121268
$273$		0			0
$274$	−18.0000			−1.08742
$275$	−1.73205	+	1.00000i	−0.104447	+	0.0603023i
$276$	−6.00000	−	10.3923i	−0.361158	−	0.625543i
$277$	1.00000	−	1.73205i	0.0600842	−	0.104069i	−0.834419	−	0.551131i	$-0.814196\pi$
$277$	1.00000	−	1.73205i	0.0600842	−	0.104069i	0.894503	+	0.447062i	$0.147530\pi$
$278$		−	8.00000i		−	0.479808i
$279$	5.19615	+	3.00000i	0.311086	+	0.179605i
$280$	3.46410	+	2.00000i	0.207020	+	0.119523i
$281$			6.00000i			0.357930i	0.983855	+	0.178965i	$0.0572749\pi$
$281$			6.00000i			0.357930i	−0.983855	+	0.178965i	$0.942725\pi$
$282$	12.0000	−	20.7846i	0.714590	−	1.23771i
$283$	7.00000	+	12.1244i	0.416107	+	0.720718i	0.995544	−	0.0942988i	$-0.0300609\pi$
$283$	7.00000	+	12.1244i	0.416107	+	0.720718i	−0.579437	+	0.815017i	$0.696728\pi$
$284$	−8.66025	+	5.00000i	−0.513892	+	0.296695i
$285$	12.0000			0.710819
$286$		0			0
$287$	−40.0000			−2.36113
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$	−1.00000	+	1.73205i	−0.0587220	+	0.101710i
$291$			28.0000i			1.64139i
$292$	−8.66025	−	5.00000i	−0.506803	−	0.292603i
$293$	19.0526	+	11.0000i	1.11306	+	0.642627i	0.939621	−	0.342217i	$-0.111178\pi$
$293$	19.0526	+	11.0000i	1.11306	+	0.642627i	0.173442	+	0.984844i	$0.444511\pi$
$294$		−	18.0000i		−	1.04978i
$295$	5.00000	−	8.66025i	0.291111	−	0.504219i
$296$	−1.00000	−	1.73205i	−0.0581238	−	0.100673i
$297$	−6.92820	+	4.00000i	−0.402015	+	0.232104i
$298$	−2.00000			−0.115857
$299$		0			0
$300$	2.00000			0.115470
$301$	34.6410	−	20.0000i	1.99667	−	1.15278i
$302$	−3.00000	−	5.19615i	−0.172631	−	0.299005i
$303$	14.0000	−	24.2487i	0.804279	−	1.39305i
$304$			6.00000i			0.344124i
$305$	1.73205	+	1.00000i	0.0991769	+	0.0572598i
$306$	1.73205	+	1.00000i	0.0990148	+	0.0571662i
$307$		−	24.0000i		−	1.36975i	−0.728659	−	0.684876i	$-0.759856\pi$
$307$		−	24.0000i		−	1.36975i	0.728659	−	0.684876i	$-0.240144\pi$
$308$	−4.00000	+	6.92820i	−0.227921	+	0.394771i
$309$	−18.0000	−	31.1769i	−1.02398	−	1.77359i
$310$	−5.19615	+	3.00000i	−0.295122	+	0.170389i
$311$	12.0000			0.680458			0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000			0.680458			0.340229	+	0.940343i	$0.389495\pi$
$312$		0			0
$313$	−6.00000			−0.339140			−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000			−0.339140			−0.169570	+	0.985518i	$0.554238\pi$
$314$	8.66025	−	5.00000i	0.488726	−	0.282166i
$315$	−2.00000	−	3.46410i	−0.112687	−	0.195180i
$316$	−2.00000	+	3.46410i	−0.112509	+	0.194871i
$317$		−	18.0000i		−	1.01098i	−0.862832	−	0.505490i	$-0.831312\pi$
$317$		−	18.0000i		−	1.01098i	0.862832	−	0.505490i	$-0.168688\pi$
$318$	−3.46410	−	2.00000i	−0.194257	−	0.112154i
$319$	−3.46410	−	2.00000i	−0.193952	−	0.111979i
$320$			1.00000i			0.0559017i
$321$	−6.00000	+	10.3923i	−0.334887	+	0.580042i
$322$	−12.0000	−	20.7846i	−0.668734	−	1.15828i
$323$	−10.3923	+	6.00000i	−0.578243	+	0.333849i
$324$	11.0000			0.611111
$325$		0			0
$326$	−4.00000			−0.221540
$327$	−10.3923	+	6.00000i	−0.574696	+	0.331801i
$328$	−5.00000	−	8.66025i	−0.276079	−	0.478183i
$329$	24.0000	−	41.5692i	1.32316	−	2.29179i
$330$			4.00000i			0.220193i
$331$	12.1244	+	7.00000i	0.666415	+	0.384755i	0.794717	−	0.606980i	$-0.207619\pi$
$331$	12.1244	+	7.00000i	0.666415	+	0.384755i	−0.128302	+	0.991735i	$0.540953\pi$
$332$		0			0
$333$			2.00000i			0.109599i
$334$	−10.0000	+	17.3205i	−0.547176	+	0.947736i
$335$	6.00000	+	10.3923i	0.327815	+	0.567792i
$336$	6.92820	−	4.00000i	0.377964	−	0.218218i
$337$	22.0000			1.19842			0.599208	−	0.800593i	$-0.295482\pi$
$337$	22.0000			1.19842			0.599208	+	0.800593i	$0.295482\pi$
$338$		0			0
$339$	4.00000			0.217250
$340$	−1.73205	+	1.00000i	−0.0939336	+	0.0542326i
$341$	−6.00000	−	10.3923i	−0.324918	−	0.562775i
$342$	3.00000	−	5.19615i	0.162221	−	0.280976i
$343$		−	8.00000i		−	0.431959i
$344$	8.66025	+	5.00000i	0.466930	+	0.269582i
$345$	−10.3923	−	6.00000i	−0.559503	−	0.323029i
$346$		−	10.0000i		−	0.537603i
$347$	−3.00000	+	5.19615i	−0.161048	+	0.278944i	−0.935245	−	0.354001i	$-0.884821\pi$
$347$	−3.00000	+	5.19615i	−0.161048	+	0.278944i	0.774197	+	0.632945i	$0.218154\pi$
$348$	2.00000	+	3.46410i	0.107211	+	0.185695i
$349$	−1.73205	+	1.00000i	−0.0927146	+	0.0535288i	−0.545640	−	0.838019i	$-0.683714\pi$
$349$	−1.73205	+	1.00000i	−0.0927146	+	0.0535288i	0.452926	+	0.891548i	$0.350380\pi$
$350$	4.00000			0.213809
$351$		0			0
$352$	−2.00000			−0.106600
$353$	29.4449	−	17.0000i	1.56719	−	0.904819i	0.570697	−	0.821160i	$-0.306673\pi$
$353$	29.4449	−	17.0000i	1.56719	−	0.904819i	0.996495	−	0.0836583i	$-0.0266604\pi$
$354$	−10.0000	−	17.3205i	−0.531494	−	0.920575i
$355$	−5.00000	+	8.66025i	−0.265372	+	0.459639i
$356$		−	14.0000i		−	0.741999i
$357$	13.8564	+	8.00000i	0.733359	+	0.423405i
$358$	−3.46410	−	2.00000i	−0.183083	−	0.105703i
$359$			6.00000i			0.316668i	0.987386	+	0.158334i	$0.0506123\pi$
$359$			6.00000i			0.316668i	−0.987386	+	0.158334i	$0.949388\pi$
$360$	0.500000	−	0.866025i	0.0263523	−	0.0456435i
$361$	8.50000	+	14.7224i	0.447368	+	0.774865i
$362$	−8.66025	+	5.00000i	−0.455173	+	0.262794i
$363$	14.0000			0.734809
$364$		0			0
$365$	−10.0000			−0.523424
$366$	3.46410	−	2.00000i	0.181071	−	0.104542i
$367$	−15.0000	−	25.9808i	−0.782994	−	1.35618i	−0.930190	−	0.367078i	$-0.880358\pi$
$367$	−15.0000	−	25.9808i	−0.782994	−	1.35618i	0.147197	−	0.989107i	$-0.452975\pi$
$368$	3.00000	−	5.19615i	0.156386	−	0.270868i
$369$			10.0000i			0.520579i
$370$	−1.73205	−	1.00000i	−0.0900450	−	0.0519875i
$371$	−6.92820	−	4.00000i	−0.359694	−	0.207670i
$372$			12.0000i			0.622171i
$373$	7.00000	−	12.1244i	0.362446	−	0.627775i	−0.625917	−	0.779890i	$-0.715275\pi$
$373$	7.00000	−	12.1244i	0.362446	−	0.627775i	0.988363	+	0.152115i	$0.0486083\pi$
$374$	−2.00000	−	3.46410i	−0.103418	−	0.179124i
$375$	1.73205	−	1.00000i	0.0894427	−	0.0516398i
$376$	12.0000			0.618853
$377$		0			0
$378$	16.0000			0.822951
$379$	5.19615	−	3.00000i	0.266908	−	0.154100i	−0.360573	−	0.932731i	$-0.617419\pi$
$379$	5.19615	−	3.00000i	0.266908	−	0.154100i	0.627482	+	0.778631i	$0.284086\pi$
$380$	3.00000	+	5.19615i	0.153897	+	0.266557i
$381$	−14.0000	+	24.2487i	−0.717242	+	1.24230i
$382$		0			0
$383$	−10.3923	−	6.00000i	−0.531022	−	0.306586i	0.210411	−	0.977613i	$-0.432520\pi$
$383$	−10.3923	−	6.00000i	−0.531022	−	0.306586i	−0.741433	+	0.671027i	$0.765853\pi$
$384$	1.73205	+	1.00000i	0.0883883	+	0.0510310i
$385$			8.00000i			0.407718i
$386$	−7.00000	+	12.1244i	−0.356291	+	0.617113i
$387$	−5.00000	−	8.66025i	−0.254164	−	0.440225i
$388$	−12.1244	+	7.00000i	−0.615521	+	0.355371i
$389$	10.0000			0.507020			0.253510	−	0.967333i	$-0.418415\pi$
$389$	10.0000			0.507020			0.253510	+	0.967333i	$0.418415\pi$
$390$		0			0
$391$	12.0000			0.606866
$392$	7.79423	−	4.50000i	0.393668	−	0.227284i
$393$	−4.00000	−	6.92820i	−0.201773	−	0.349482i
$394$	−3.00000	+	5.19615i	−0.151138	+	0.261778i
$395$			4.00000i			0.201262i
$396$	1.73205	+	1.00000i	0.0870388	+	0.0502519i
$397$	32.9090	+	19.0000i	1.65165	+	0.953583i	0.976392	+	0.216004i	$0.0693024\pi$
$397$	32.9090	+	19.0000i	1.65165	+	0.953583i	0.675261	+	0.737579i	$0.264031\pi$
$398$		0			0
$399$	24.0000	−	41.5692i	1.20150	−	2.08106i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	5.19615	−	3.00000i	0.259483	−	0.149813i	−0.364615	−	0.931158i	$-0.618800\pi$
$401$	5.19615	−	3.00000i	0.259483	−	0.149813i	0.624099	+	0.781345i	$0.285466\pi$
$402$	24.0000			1.19701
$403$		0			0
$404$	14.0000			0.696526
$405$	9.52628	−	5.50000i	0.473365	−	0.273297i
$406$	4.00000	+	6.92820i	0.198517	+	0.343841i
$407$	2.00000	−	3.46410i	0.0991363	−	0.171709i
$408$			4.00000i			0.198030i
$409$	−29.4449	−	17.0000i	−1.45595	−	0.840596i	−0.457146	−	0.889392i	$-0.651128\pi$
$409$	−29.4449	−	17.0000i	−1.45595	−	0.840596i	−0.998809	+	0.0487958i	$0.984462\pi$
$410$	−8.66025	−	5.00000i	−0.427699	−	0.246932i
$411$			36.0000i			1.77575i
$412$	9.00000	−	15.5885i	0.443398	−	0.767988i
$413$	−20.0000	−	34.6410i	−0.984136	−	1.70457i
$414$	−5.19615	+	3.00000i	−0.255377	+	0.147442i
$415$		0			0
$416$		0			0
$417$	−16.0000			−0.783523
$418$	−10.3923	+	6.00000i	−0.508304	+	0.293470i
$419$	−8.00000	−	13.8564i	−0.390826	−	0.676930i	0.601733	−	0.798697i	$-0.294477\pi$
$419$	−8.00000	−	13.8564i	−0.390826	−	0.676930i	−0.992559	+	0.121768i	$0.961144\pi$
$420$	4.00000	−	6.92820i	0.195180	−	0.338062i
$421$			10.0000i			0.487370i	0.969854	+	0.243685i	$0.0783563\pi$
$421$			10.0000i			0.487370i	−0.969854	+	0.243685i	$0.921644\pi$
$422$	−24.2487	−	14.0000i	−1.18041	−	0.681509i
$423$	−10.3923	−	6.00000i	−0.505291	−	0.291730i
$424$		−	2.00000i		−	0.0971286i
$425$	−1.00000	+	1.73205i	−0.0485071	+	0.0840168i
$426$	10.0000	+	17.3205i	0.484502	+	0.839181i
$427$	6.92820	−	4.00000i	0.335279	−	0.193574i
$428$	−6.00000			−0.290021
$429$		0			0
$430$	10.0000			0.482243
$431$	15.5885	−	9.00000i	0.750870	−	0.433515i	−0.0751385	−	0.997173i	$-0.523940\pi$
$431$	15.5885	−	9.00000i	0.750870	−	0.433515i	0.826008	+	0.563658i	$0.190607\pi$
$432$	2.00000	+	3.46410i	0.0962250	+	0.166667i
$433$	−19.0000	+	32.9090i	−0.913082	+	1.58150i	−0.103396	+	0.994640i	$0.532971\pi$
$433$	−19.0000	+	32.9090i	−0.913082	+	1.58150i	−0.809686	+	0.586864i	$0.800362\pi$
$434$			24.0000i			1.15204i
$435$	3.46410	+	2.00000i	0.166091	+	0.0958927i
$436$	−5.19615	−	3.00000i	−0.248851	−	0.143674i
$437$		−	36.0000i		−	1.72211i
$438$	−10.0000	+	17.3205i	−0.477818	+	0.827606i
$439$	−16.0000	−	27.7128i	−0.763638	−	1.32266i	−0.940963	−	0.338508i	$-0.890078\pi$
$439$	−16.0000	−	27.7128i	−0.763638	−	1.32266i	0.177325	−	0.984152i	$-0.443256\pi$
$440$	−1.73205	+	1.00000i	−0.0825723	+	0.0476731i
$441$	−9.00000			−0.428571
$442$		0			0
$443$	−14.0000			−0.665160			−0.332580	−	0.943075i	$-0.607919\pi$
$443$	−14.0000			−0.665160			−0.332580	+	0.943075i	$0.607919\pi$
$444$	−3.46410	+	2.00000i	−0.164399	+	0.0949158i
$445$	−7.00000	−	12.1244i	−0.331832	−	0.574750i
$446$	2.00000	−	3.46410i	0.0947027	−	0.164030i
$447$			4.00000i			0.189194i
$448$	3.46410	+	2.00000i	0.163663	+	0.0944911i
$449$	−5.19615	−	3.00000i	−0.245222	−	0.141579i	0.372353	−	0.928091i	$-0.378551\pi$
$449$	−5.19615	−	3.00000i	−0.245222	−	0.141579i	−0.617574	+	0.786513i	$0.711885\pi$
$450$		−	1.00000i		−	0.0471405i
$451$	10.0000	−	17.3205i	0.470882	−	0.815591i
$452$	1.00000	+	1.73205i	0.0470360	+	0.0814688i
$453$	−10.3923	+	6.00000i	−0.488273	+	0.281905i
$454$	4.00000			0.187729
$455$		0			0
$456$	12.0000			0.561951
$457$	−8.66025	+	5.00000i	−0.405110	+	0.233890i	−0.688686	−	0.725059i	$-0.741812\pi$
$457$	−8.66025	+	5.00000i	−0.405110	+	0.233890i	0.283577	+	0.958950i	$0.408479\pi$
$458$	−5.00000	−	8.66025i	−0.233635	−	0.404667i
$459$	−4.00000	+	6.92820i	−0.186704	+	0.323381i
$460$		−	6.00000i		−	0.279751i
$461$	5.19615	+	3.00000i	0.242009	+	0.139724i	0.616100	−	0.787668i	$-0.288712\pi$
$461$	5.19615	+	3.00000i	0.242009	+	0.139724i	−0.374091	+	0.927392i	$0.622045\pi$
$462$	13.8564	+	8.00000i	0.644658	+	0.372194i
$463$		−	16.0000i		−	0.743583i	−0.928316	−	0.371792i	$-0.878744\pi$
$463$		−	16.0000i		−	0.743583i	0.928316	−	0.371792i	$-0.121256\pi$
$464$	−1.00000	+	1.73205i	−0.0464238	+	0.0804084i
$465$	6.00000	+	10.3923i	0.278243	+	0.481932i
$466$	5.19615	−	3.00000i	0.240707	−	0.138972i
$467$	−10.0000			−0.462745			−0.231372	−	0.972865i	$-0.574322\pi$
$467$	−10.0000			−0.462745			−0.231372	+	0.972865i	$0.574322\pi$
$468$		0			0
$469$	48.0000			2.21643
$470$	10.3923	−	6.00000i	0.479361	−	0.276759i
$471$	−10.0000	−	17.3205i	−0.460776	−	0.798087i
$472$	5.00000	−	8.66025i	0.230144	−	0.398621i
$473$			20.0000i			0.919601i
$474$	6.92820	+	4.00000i	0.318223	+	0.183726i
$475$	5.19615	+	3.00000i	0.238416	+	0.137649i
$476$			8.00000i			0.366679i
$477$	−1.00000	+	1.73205i	−0.0457869	+	0.0793052i
$478$	−13.0000	−	22.5167i	−0.594606	−	1.02989i
$479$	−1.73205	+	1.00000i	−0.0791394	+	0.0456912i	−0.539048	−	0.842275i	$-0.681216\pi$
$479$	−1.73205	+	1.00000i	−0.0791394	+	0.0456912i	0.459908	+	0.887967i	$0.347882\pi$
$480$	2.00000			0.0912871
$481$		0			0
$482$	−22.0000			−1.00207
$483$	−41.5692	+	24.0000i	−1.89146	+	1.09204i
$484$	3.50000	+	6.06218i	0.159091	+	0.275554i
$485$	−7.00000	+	12.1244i	−0.317854	+	0.550539i
$486$		−	10.0000i		−	0.453609i
$487$	13.8564	+	8.00000i	0.627894	+	0.362515i	0.779936	−	0.625859i	$-0.215252\pi$
$487$	13.8564	+	8.00000i	0.627894	+	0.362515i	−0.152042	+	0.988374i	$0.548585\pi$
$488$	1.73205	+	1.00000i	0.0784063	+	0.0452679i
$489$			8.00000i			0.361773i
$490$	4.50000	−	7.79423i	0.203289	−	0.352107i
$491$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$491$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$492$	−17.3205	+	10.0000i	−0.780869	+	0.450835i
$493$	−4.00000			−0.180151
$494$		0			0
$495$	2.00000			0.0898933
$496$	−5.19615	+	3.00000i	−0.233314	+	0.134704i
$497$	20.0000	+	34.6410i	0.897123	+	1.55386i
$498$		0			0
$499$			38.0000i			1.70111i	0.525883	+	0.850557i	$0.323735\pi$
$499$			38.0000i			1.70111i	−0.525883	+	0.850557i	$0.676265\pi$
$500$	0.866025	+	0.500000i	0.0387298	+	0.0223607i
$501$	34.6410	+	20.0000i	1.54765	+	0.893534i
$502$		0			0
$503$	7.00000	−	12.1244i	0.312115	−	0.540598i	−0.666705	−	0.745321i	$-0.732296\pi$
$503$	7.00000	−	12.1244i	0.312115	−	0.540598i	0.978820	+	0.204723i	$0.0656294\pi$
$504$	−2.00000	−	3.46410i	−0.0890871	−	0.154303i
$505$	12.1244	−	7.00000i	0.539527	−	0.311496i
$506$	12.0000			0.533465
$507$		0			0
$508$	−14.0000			−0.621150
$509$	−5.19615	+	3.00000i	−0.230315	+	0.132973i	−0.610718	−	0.791849i	$-0.709119\pi$
$509$	−5.19615	+	3.00000i	−0.230315	+	0.132973i	0.380402	+	0.924821i	$0.375786\pi$
$510$	2.00000	+	3.46410i	0.0885615	+	0.153393i
$511$	−20.0000	+	34.6410i	−0.884748	+	1.53243i
$512$			1.00000i			0.0441942i
$513$	20.7846	+	12.0000i	0.917663	+	0.529813i
$514$	−25.9808	−	15.0000i	−1.14596	−	0.661622i
$515$		−	18.0000i		−	0.793175i
$516$	10.0000	−	17.3205i	0.440225	−	0.762493i
$517$	12.0000	+	20.7846i	0.527759	+	0.914106i
$518$	−6.92820	+	4.00000i	−0.304408	+	0.175750i
$519$	−20.0000			−0.877903
$520$		0			0
$521$	−26.0000			−1.13908			−0.569540	−	0.821963i	$-0.692879\pi$
$521$	−26.0000			−1.13908			−0.569540	+	0.821963i	$0.692879\pi$
$522$	1.73205	−	1.00000i	0.0758098	−	0.0437688i
$523$	3.00000	+	5.19615i	0.131181	+	0.227212i	0.924132	−	0.382073i	$-0.124790\pi$
$523$	3.00000	+	5.19615i	0.131181	+	0.227212i	−0.792951	+	0.609285i	$0.791456\pi$
$524$	2.00000	−	3.46410i	0.0873704	−	0.151330i
$525$		−	8.00000i		−	0.349149i
$526$	−1.73205	−	1.00000i	−0.0755210	−	0.0436021i
$527$	−10.3923	−	6.00000i	−0.452696	−	0.261364i
$528$			4.00000i			0.174078i
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$	−1.00000	−	1.73205i	−0.0434372	−	0.0752355i
$531$	−8.66025	+	5.00000i	−0.375823	+	0.216982i
$532$	24.0000			1.04053
$533$		0			0
$534$	−28.0000			−1.21168
$535$	−5.19615	+	3.00000i	−0.224649	+	0.129701i
$536$	6.00000	+	10.3923i	0.259161	+	0.448879i
$537$	−4.00000	+	6.92820i	−0.172613	+	0.298974i
$538$			6.00000i			0.258678i
$539$	15.5885	+	9.00000i	0.671442	+	0.387657i
$540$	3.46410	+	2.00000i	0.149071	+	0.0860663i
$541$			38.0000i			1.63375i	0.576816	+	0.816874i	$0.304295\pi$
$541$			38.0000i			1.63375i	−0.576816	+	0.816874i	$0.695705\pi$
$542$	1.00000	−	1.73205i	0.0429537	−	0.0743980i
$543$	10.0000	+	17.3205i	0.429141	+	0.743294i
$544$	−1.73205	+	1.00000i	−0.0742611	+	0.0428746i
$545$	−6.00000			−0.257012
$546$		0			0
$547$	22.0000			0.940652			0.470326	−	0.882493i	$-0.344136\pi$
$547$	22.0000			0.940652			0.470326	+	0.882493i	$0.344136\pi$
$548$	−15.5885	+	9.00000i	−0.665906	+	0.384461i
$549$	−1.00000	−	1.73205i	−0.0426790	−	0.0739221i
$550$	−1.00000	+	1.73205i	−0.0426401	+	0.0738549i
$551$			12.0000i			0.511217i
$552$	−10.3923	−	6.00000i	−0.442326	−	0.255377i
$553$	13.8564	+	8.00000i	0.589234	+	0.340195i
$554$		−	2.00000i		−	0.0849719i
$555$	−2.00000	+	3.46410i	−0.0848953	+	0.147043i
$556$	−4.00000	−	6.92820i	−0.169638	−	0.293821i
$557$	−32.9090	+	19.0000i	−1.39440	+	0.805056i	−0.993798	−	0.111198i	$-0.964531\pi$
$557$	−32.9090	+	19.0000i	−1.39440	+	0.805056i	−0.400599	+	0.916253i	$0.631198\pi$
$558$	6.00000			0.254000
$559$		0			0
$560$	4.00000			0.169031
$561$	−6.92820	+	4.00000i	−0.292509	+	0.168880i
$562$	3.00000	+	5.19615i	0.126547	+	0.219186i
$563$	3.00000	−	5.19615i	0.126435	−	0.218992i	−0.795858	−	0.605483i	$-0.792980\pi$
$563$	3.00000	−	5.19615i	0.126435	−	0.218992i	0.922293	+	0.386492i	$0.126313\pi$
$564$		−	24.0000i		−	1.01058i
$565$	1.73205	+	1.00000i	0.0728679	+	0.0420703i
$566$	12.1244	+	7.00000i	0.509625	+	0.294232i
$567$		−	44.0000i		−	1.84783i
$568$	−5.00000	+	8.66025i	−0.209795	+	0.363376i
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	0.922032	−	0.387113i	$-0.126528\pi$
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	−0.796266	+	0.604947i	$0.793194\pi$
$570$	10.3923	−	6.00000i	0.435286	−	0.251312i
$571$	32.0000			1.33916			0.669579	−	0.742741i	$-0.266474\pi$
$571$	32.0000			1.33916			0.669579	+	0.742741i	$0.266474\pi$
$572$		0			0
$573$		0			0
$574$	−34.6410	+	20.0000i	−1.44589	+	0.834784i
$575$	−3.00000	−	5.19615i	−0.125109	−	0.216695i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$			18.0000i			0.749350i	0.927156	+	0.374675i	$0.122246\pi$
$577$			18.0000i			0.749350i	−0.927156	+	0.374675i	$0.877754\pi$
$578$	11.2583	+	6.50000i	0.468285	+	0.270364i
$579$	24.2487	+	14.0000i	1.00774	+	0.581820i
$580$			2.00000i			0.0830455i
$581$		0			0
$582$	14.0000	+	24.2487i	0.580319	+	1.00514i
$583$	3.46410	−	2.00000i	0.143468	−	0.0828315i
$584$	−10.0000			−0.413803
$585$		0			0
$586$	22.0000			0.908812
$587$	10.3923	−	6.00000i	0.428936	−	0.247647i	−0.269957	−	0.962872i	$-0.587010\pi$
$587$	10.3923	−	6.00000i	0.428936	−	0.247647i	0.698893	+	0.715226i	$0.253676\pi$
$588$	−9.00000	−	15.5885i	−0.371154	−	0.642857i
$589$	−18.0000	+	31.1769i	−0.741677	+	1.28462i
$590$		−	10.0000i		−	0.411693i
$591$	10.3923	+	6.00000i	0.427482	+	0.246807i
$592$	−1.73205	−	1.00000i	−0.0711868	−	0.0410997i
$593$			2.00000i			0.0821302i	0.999156	+	0.0410651i	$0.0130751\pi$
$593$			2.00000i			0.0821302i	−0.999156	+	0.0410651i	$0.986925\pi$
$594$	−4.00000	+	6.92820i	−0.164122	+	0.284268i
$595$	4.00000	+	6.92820i	0.163984	+	0.284029i
$596$	−1.73205	+	1.00000i	−0.0709476	+	0.0409616i
$597$		0			0
$598$		0			0
$599$	−12.0000			−0.490307			−0.245153	−	0.969484i	$-0.578838\pi$
$599$	−12.0000			−0.490307			−0.245153	+	0.969484i	$0.578838\pi$
$600$	1.73205	−	1.00000i	0.0707107	−	0.0408248i
$601$	−5.00000	−	8.66025i	−0.203954	−	0.353259i	0.745845	−	0.666120i	$-0.232046\pi$
$601$	−5.00000	−	8.66025i	−0.203954	−	0.353259i	−0.949799	+	0.312861i	$0.898713\pi$
$602$	20.0000	−	34.6410i	0.815139	−	1.41186i
$603$		−	12.0000i		−	0.488678i
$604$	−5.19615	−	3.00000i	−0.211428	−	0.122068i
$605$	6.06218	+	3.50000i	0.246463	+	0.142295i
$606$		−	28.0000i		−	1.13742i
$607$	17.0000	−	29.4449i	0.690009	−	1.19513i	−0.281826	−	0.959466i	$-0.590940\pi$
$607$	17.0000	−	29.4449i	0.690009	−	1.19513i	0.971834	−	0.235665i	$-0.0757267\pi$
$608$	3.00000	+	5.19615i	0.121666	+	0.210732i
$609$	13.8564	−	8.00000i	0.561490	−	0.324176i
$610$	2.00000			0.0809776
$611$		0			0
$612$	2.00000			0.0808452
$613$	22.5167	−	13.0000i	0.909439	−	0.525065i	0.0291886	−	0.999574i	$-0.490708\pi$
$613$	22.5167	−	13.0000i	0.909439	−	0.525065i	0.880251	+	0.474509i	$0.157374\pi$
$614$	−12.0000	−	20.7846i	−0.484281	−	0.838799i
$615$	−10.0000	+	17.3205i	−0.403239	+	0.698430i
$616$			8.00000i			0.322329i
$617$	−5.19615	−	3.00000i	−0.209189	−	0.120775i	0.391745	−	0.920074i	$-0.371871\pi$
$617$	−5.19615	−	3.00000i	−0.209189	−	0.120775i	−0.600935	+	0.799298i	$0.705205\pi$
$618$	−31.1769	−	18.0000i	−1.25412	−	0.724066i
$619$			46.0000i			1.84890i	0.381308	+	0.924448i	$0.375474\pi$
$619$			46.0000i			1.84890i	−0.381308	+	0.924448i	$0.624526\pi$
$620$	−3.00000	+	5.19615i	−0.120483	+	0.208683i
$621$	−12.0000	−	20.7846i	−0.481543	−	0.834058i
$622$	10.3923	−	6.00000i	0.416693	−	0.240578i
$623$	−56.0000			−2.24359
$624$		0			0
$625$	1.00000			0.0400000
$626$	−5.19615	+	3.00000i	−0.207680	+	0.119904i
$627$	12.0000	+	20.7846i	0.479234	+	0.830057i
$628$	5.00000	−	8.66025i	0.199522	−	0.345582i
$629$		−	4.00000i		−	0.159490i
$630$	−3.46410	−	2.00000i	−0.138013	−	0.0796819i
$631$	25.9808	+	15.0000i	1.03428	+	0.597141i	0.918207	−	0.396100i	$-0.129637\pi$
$631$	25.9808	+	15.0000i	1.03428	+	0.597141i	0.116071	+	0.993241i	$0.462970\pi$
$632$			4.00000i			0.159111i
$633$	−28.0000	+	48.4974i	−1.11290	+	1.92760i
$634$	−9.00000	−	15.5885i	−0.357436	−	0.619097i
$635$	−12.1244	+	7.00000i	−0.481140	+	0.277787i
$636$	−4.00000			−0.158610
$637$		0			0
$638$	−4.00000			−0.158362
$639$	8.66025	−	5.00000i	0.342594	−	0.197797i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	9.00000	−	15.5885i	0.355479	−	0.615707i	−0.631721	−	0.775196i	$-0.717651\pi$
$641$	9.00000	−	15.5885i	0.355479	−	0.615707i	0.987200	+	0.159489i	$0.0509845\pi$
$642$			12.0000i			0.473602i
$643$	13.8564	+	8.00000i	0.546443	+	0.315489i	0.747686	−	0.664052i	$-0.231165\pi$
$643$	13.8564	+	8.00000i	0.546443	+	0.315489i	−0.201243	+	0.979541i	$0.564498\pi$
$644$	−20.7846	−	12.0000i	−0.819028	−	0.472866i
$645$		−	20.0000i		−	0.787499i
$646$	−6.00000	+	10.3923i	−0.236067	+	0.408880i
$647$	21.0000	+	36.3731i	0.825595	+	1.42997i	0.901464	+	0.432855i	$0.142494\pi$
$647$	21.0000	+	36.3731i	0.825595	+	1.42997i	−0.0758684	+	0.997118i	$0.524173\pi$
$648$	9.52628	−	5.50000i	0.374228	−	0.216060i
$649$	20.0000			0.785069
$650$		0			0
$651$	48.0000			1.88127
$652$	−3.46410	+	2.00000i	−0.135665	+	0.0783260i
$653$	3.00000	+	5.19615i	0.117399	+	0.203341i	0.918736	−	0.394872i	$-0.129211\pi$
$653$	3.00000	+	5.19615i	0.117399	+	0.203341i	−0.801337	+	0.598213i	$0.795878\pi$
$654$	−6.00000	+	10.3923i	−0.234619	+	0.406371i
$655$		−	4.00000i		−	0.156293i
$656$	−8.66025	−	5.00000i	−0.338126	−	0.195217i
$657$	8.66025	+	5.00000i	0.337869	+	0.195069i
$658$		−	48.0000i		−	1.87123i
$659$	−4.00000	+	6.92820i	−0.155818	+	0.269884i	−0.933357	−	0.358951i	$-0.883135\pi$
$659$	−4.00000	+	6.92820i	−0.155818	+	0.269884i	0.777539	+	0.628835i	$0.216468\pi$
$660$	2.00000	+	3.46410i	0.0778499	+	0.134840i
$661$	25.9808	−	15.0000i	1.01053	−	0.583432i	0.0991864	−	0.995069i	$-0.468376\pi$
$661$	25.9808	−	15.0000i	1.01053	−	0.583432i	0.911348	+	0.411636i	$0.135043\pi$
$662$	14.0000			0.544125
$663$		0			0
$664$		0			0
$665$	20.7846	−	12.0000i	0.805993	−	0.465340i
$666$	1.00000	+	1.73205i	0.0387492	+	0.0671156i
$667$	6.00000	−	10.3923i	0.232321	−	0.402392i
$668$			20.0000i			0.773823i
$669$	−6.92820	−	4.00000i	−0.267860	−	0.154649i
$670$	10.3923	+	6.00000i	0.401490	+	0.231800i
$671$			4.00000i			0.154418i
$672$	4.00000	−	6.92820i	0.154303	−	0.267261i
$673$	1.00000	+	1.73205i	0.0385472	+	0.0667657i	0.884655	−	0.466246i	$-0.154394\pi$
$673$	1.00000	+	1.73205i	0.0385472	+	0.0667657i	−0.846108	+	0.533011i	$0.821060\pi$
$674$	19.0526	−	11.0000i	0.733877	−	0.423704i
$675$	4.00000			0.153960
$676$		0			0
$677$	−6.00000			−0.230599			−0.115299	−	0.993331i	$-0.536783\pi$
$677$	−6.00000			−0.230599			−0.115299	+	0.993331i	$0.536783\pi$
$678$	3.46410	−	2.00000i	0.133038	−	0.0768095i
$679$	28.0000	+	48.4974i	1.07454	+	1.86116i
$680$	−1.00000	+	1.73205i	−0.0383482	+	0.0664211i
$681$		−	8.00000i		−	0.306561i
$682$	−10.3923	−	6.00000i	−0.397942	−	0.229752i
$683$	−38.1051	−	22.0000i	−1.45805	−	0.841807i	−0.459136	−	0.888366i	$-0.651841\pi$
$683$	−38.1051	−	22.0000i	−1.45805	−	0.841807i	−0.998916	+	0.0465592i	$0.985174\pi$
$684$		−	6.00000i		−	0.229416i
$685$	−9.00000	+	15.5885i	−0.343872	+	0.595604i
$686$	−4.00000	−	6.92820i	−0.152721	−	0.264520i
$687$	−17.3205	+	10.0000i	−0.660819	+	0.381524i
$688$	10.0000			0.381246
$689$		0			0
$690$	−12.0000			−0.456832
$691$	−32.9090	+	19.0000i	−1.25192	+	0.722794i	−0.971490	−	0.237082i	$-0.923809\pi$
$691$	−32.9090	+	19.0000i	−1.25192	+	0.722794i	−0.280426	+	0.959876i	$0.590476\pi$
$692$	−5.00000	−	8.66025i	−0.190071	−	0.329213i
$693$	4.00000	−	6.92820i	0.151947	−	0.263181i
$694$			6.00000i			0.227757i
$695$	−6.92820	−	4.00000i	−0.262802	−	0.151729i
$696$	3.46410	+	2.00000i	0.131306	+	0.0758098i
$697$		−	20.0000i		−	0.757554i
$698$	−1.00000	+	1.73205i	−0.0378506	+	0.0655591i
$699$	−6.00000	−	10.3923i	−0.226941	−	0.393073i
$700$	3.46410	−	2.00000i	0.130931	−	0.0755929i
$701$	−38.0000			−1.43524			−0.717620	−	0.696435i	$-0.754769\pi$
$701$	−38.0000			−1.43524			−0.717620	+	0.696435i	$0.754769\pi$
$702$		0			0
$703$	−12.0000			−0.452589
$704$	−1.73205	+	1.00000i	−0.0652791	+	0.0376889i
$705$	−12.0000	−	20.7846i	−0.451946	−	0.782794i
$706$	17.0000	−	29.4449i	0.639803	−	1.10817i
$707$		−	56.0000i		−	2.10610i
$708$	−17.3205	−	10.0000i	−0.650945	−	0.375823i
$709$	−19.0526	−	11.0000i	−0.715534	−	0.413114i	0.0975728	−	0.995228i	$-0.468892\pi$
$709$	−19.0526	−	11.0000i	−0.715534	−	0.413114i	−0.813107	+	0.582115i	$0.802225\pi$
$710$			10.0000i			0.375293i
$711$	2.00000	−	3.46410i	0.0750059	−	0.129914i
$712$	−7.00000	−	12.1244i	−0.262336	−	0.454379i
$713$	31.1769	−	18.0000i	1.16758	−	0.674105i
$714$	16.0000			0.598785
$715$		0			0
$716$	−4.00000			−0.149487
$717$	−45.0333	+	26.0000i	−1.68180	+	0.970988i
$718$	3.00000	+	5.19615i	0.111959	+	0.193919i
$719$	24.0000	−	41.5692i	0.895049	−	1.55027i	0.0613050	−	0.998119i	$-0.480474\pi$
$719$	24.0000	−	41.5692i	0.895049	−	1.55027i	0.833744	−	0.552151i	$-0.186193\pi$
$720$		−	1.00000i		−	0.0372678i
$721$	−62.3538	−	36.0000i	−2.32218	−	1.34071i
$722$	14.7224	+	8.50000i	0.547912	+	0.316337i
$723$			44.0000i			1.63638i
$724$	−5.00000	+	8.66025i	−0.185824	+	0.321856i
$725$	1.00000	+	1.73205i	0.0371391	+	0.0643268i
$726$	12.1244	−	7.00000i	0.449977	−	0.259794i
$727$	14.0000			0.519231			0.259616	−	0.965712i	$-0.416404\pi$
$727$	14.0000			0.519231			0.259616	+	0.965712i	$0.416404\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$	−8.66025	+	5.00000i	−0.320530	+	0.185058i
$731$	10.0000	+	17.3205i	0.369863	+	0.640622i
$732$	2.00000	−	3.46410i	0.0739221	−	0.128037i
$733$			2.00000i			0.0738717i	0.999318	+	0.0369358i	$0.0117597\pi$
$733$			2.00000i			0.0738717i	−0.999318	+	0.0369358i	$0.988240\pi$
$734$	−25.9808	−	15.0000i	−0.958967	−	0.553660i
$735$	−15.5885	−	9.00000i	−0.574989	−	0.331970i
$736$		−	6.00000i		−	0.221163i
$737$	−12.0000	+	20.7846i	−0.442026	+	0.765611i
$738$	5.00000	+	8.66025i	0.184053	+	0.318788i
$739$	−36.3731	+	21.0000i	−1.33800	+	0.772497i	−0.986511	−	0.163693i	$-0.947659\pi$
$739$	−36.3731	+	21.0000i	−1.33800	+	0.772497i	−0.351494	+	0.936190i	$0.614326\pi$
$740$	−2.00000			−0.0735215
$741$		0			0
$742$	−8.00000			−0.293689
$743$	−10.3923	+	6.00000i	−0.381257	+	0.220119i	−0.678365	−	0.734725i	$-0.737311\pi$
$743$	−10.3923	+	6.00000i	−0.381257	+	0.220119i	0.297108	+	0.954844i	$0.403978\pi$
$744$	6.00000	+	10.3923i	0.219971	+	0.381000i
$745$	−1.00000	+	1.73205i	−0.0366372	+	0.0634574i
$746$		−	14.0000i		−	0.512576i
$747$		0			0
$748$	−3.46410	−	2.00000i	−0.126660	−	0.0731272i
$749$			24.0000i			0.876941i
$750$	1.00000	−	1.73205i	0.0365148	−	0.0632456i
$751$	22.0000	+	38.1051i	0.802791	+	1.39048i	0.917772	+	0.397108i	$0.129986\pi$
$751$	22.0000	+	38.1051i	0.802791	+	1.39048i	−0.114981	+	0.993368i	$0.536681\pi$
$752$	10.3923	−	6.00000i	0.378968	−	0.218797i
$753$		0			0
$754$		0			0
$755$	−6.00000			−0.218362
$756$	13.8564	−	8.00000i	0.503953	−	0.290957i
$757$	−9.00000	−	15.5885i	−0.327111	−	0.566572i	0.654827	−	0.755779i	$-0.272742\pi$
$757$	−9.00000	−	15.5885i	−0.327111	−	0.566572i	−0.981937	+	0.189207i	$0.939408\pi$
$758$	3.00000	−	5.19615i	0.108965	−	0.188733i
$759$		−	24.0000i		−	0.871145i
$760$	5.19615	+	3.00000i	0.188484	+	0.108821i
$761$	−12.1244	−	7.00000i	−0.439508	−	0.253750i	0.263881	−	0.964555i	$-0.414997\pi$
$761$	−12.1244	−	7.00000i	−0.439508	−	0.253750i	−0.703389	+	0.710805i	$0.748331\pi$
$762$			28.0000i			1.01433i
$763$	−12.0000	+	20.7846i	−0.434429	+	0.752453i
$764$		0			0
$765$	1.73205	−	1.00000i	0.0626224	−	0.0361551i
$766$	−12.0000			−0.433578
$767$		0			0
$768$	2.00000			0.0721688
$769$	8.66025	−	5.00000i	0.312297	−	0.180305i	−0.335657	−	0.941984i	$-0.608958\pi$
$769$	8.66025	−	5.00000i	0.312297	−	0.180305i	0.647954	+	0.761680i	$0.275625\pi$
$770$	4.00000	+	6.92820i	0.144150	+	0.249675i
$771$	−30.0000	+	51.9615i	−1.08042	+	1.87135i
$772$			14.0000i			0.503871i
$773$	29.4449	+	17.0000i	1.05906	+	0.611448i	0.925172	−	0.379549i	$-0.123921\pi$
$773$	29.4449	+	17.0000i	1.05906	+	0.611448i	0.133887	+	0.990997i	$0.457254\pi$
$774$	−8.66025	−	5.00000i	−0.311286	−	0.179721i
$775$			6.00000i			0.215526i
$776$	−7.00000	+	12.1244i	−0.251285	+	0.435239i
$777$	8.00000	+	13.8564i	0.286998	+	0.497096i
$778$	8.66025	−	5.00000i	0.310485	−	0.179259i
$779$	−60.0000			−2.14972
$780$		0			0
$781$	−20.0000			−0.715656
$782$	10.3923	−	6.00000i	0.371628	−	0.214560i
$783$	4.00000	+	6.92820i	0.142948	+	0.247594i
$784$	4.50000	−	7.79423i	0.160714	−	0.278365i
$785$		−	10.0000i		−	0.356915i
$786$	−6.92820	−	4.00000i	−0.247121	−	0.142675i
$787$	−6.92820	−	4.00000i	−0.246964	−	0.142585i	0.371409	−	0.928469i	$-0.378875\pi$
$787$	−6.92820	−	4.00000i	−0.246964	−	0.142585i	−0.618373	+	0.785885i	$0.712208\pi$
$788$			6.00000i			0.213741i
$789$	−2.00000	+	3.46410i	−0.0712019	+	0.123325i
$790$	2.00000	+	3.46410i	0.0711568	+	0.123247i
$791$	6.92820	−	4.00000i	0.246339	−	0.142224i
$792$	2.00000			0.0710669
$793$		0			0
$794$	38.0000			1.34857
$795$	−3.46410	+	2.00000i	−0.122859	+	0.0709327i
$796$		0			0
$797$	−11.0000	+	19.0526i	−0.389640	+	0.674876i	−0.992401	−	0.123045i	$-0.960734\pi$
$797$	−11.0000	+	19.0526i	−0.389640	+	0.674876i	0.602761	+	0.797922i	$0.294067\pi$
$798$		−	48.0000i		−	1.69918i
$799$	20.7846	+	12.0000i	0.735307	+	0.424529i
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$			14.0000i			0.494666i
$802$	3.00000	−	5.19615i	0.105934	−	0.183483i
$803$	−10.0000	−	17.3205i	−0.352892	−	0.611227i
$804$	20.7846	−	12.0000i	0.733017	−	0.423207i
$805$	−24.0000			−0.845889
$806$		0			0
$807$	12.0000			0.422420
$808$	12.1244	−	7.00000i	0.426533	−	0.246259i
$809$	17.0000	+	29.4449i	0.597688	+	1.03523i	0.993161	+	0.116749i	$0.0372472\pi$
$809$	17.0000	+	29.4449i	0.597688	+	1.03523i	−0.395473	+	0.918477i	$0.629419\pi$
$810$	5.50000	−	9.52628i	0.193250	−	0.334719i
$811$		−	38.0000i		−	1.33436i	−0.744896	−	0.667180i	$-0.767501\pi$
$811$		−	38.0000i		−	1.33436i	0.744896	−	0.667180i	$-0.232499\pi$
$812$	6.92820	+	4.00000i	0.243132	+	0.140372i
$813$	−3.46410	−	2.00000i	−0.121491	−	0.0701431i
$814$		−	4.00000i		−	0.140200i
$815$	−2.00000	+	3.46410i	−0.0700569	+	0.121342i
$816$	2.00000	+	3.46410i	0.0700140	+	0.121268i
$817$	51.9615	−	30.0000i	1.81790	−	1.04957i
$818$	−34.0000			−1.18878
$819$		0			0
$820$	−10.0000			−0.349215
$821$	43.3013	−	25.0000i	1.51122	−	0.872506i	0.511311	−	0.859396i	$-0.329160\pi$
$821$	43.3013	−	25.0000i	1.51122	−	0.872506i	0.999914	−	0.0131101i	$-0.00417319\pi$
$822$	18.0000	+	31.1769i	0.627822	+	1.08742i
$823$	7.00000	−	12.1244i	0.244005	−	0.422628i	−0.717847	−	0.696201i	$-0.754872\pi$
$823$	7.00000	−	12.1244i	0.244005	−	0.422628i	0.961851	+	0.273573i	$0.0882054\pi$
$824$		−	18.0000i		−	0.627060i
$825$	3.46410	+	2.00000i	0.120605	+	0.0696311i
$826$	−34.6410	−	20.0000i	−1.20532	−	0.695889i
$827$		0			0		1.00000			$0$
$827$		0			0		−1.00000			$\pi$
$828$	−3.00000	+	5.19615i	−0.104257	+	0.180579i
$829$	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	$0.822276\pi$
$830$		0			0
$831$	−4.00000			−0.138758
$832$		0			0
$833$	18.0000			0.623663
$834$	−13.8564	+	8.00000i	−0.479808	+	0.277017i
$835$	10.0000	+	17.3205i	0.346064	+	0.599401i
$836$	−6.00000	+	10.3923i	−0.207514	+	0.359425i
$837$			24.0000i			0.829561i
$838$	−13.8564	−	8.00000i	−0.478662	−	0.276355i
$839$	22.5167	+	13.0000i	0.777361	+	0.448810i	0.835494	−	0.549499i	$-0.185181\pi$
$839$	22.5167	+	13.0000i	0.777361	+	0.448810i	−0.0581329	+	0.998309i	$0.518515\pi$
$840$		−	8.00000i		−	0.276026i
$841$	12.5000	−	21.6506i	0.431034	−	0.746574i
$842$	5.00000	+	8.66025i	0.172311	+	0.298452i
$843$	10.3923	−	6.00000i	0.357930	−	0.206651i
$844$	−28.0000			−0.963800
$845$		0			0
$846$	−12.0000			−0.412568
$847$	24.2487	−	14.0000i	0.833196	−	0.481046i
$848$	−1.00000	−	1.73205i	−0.0343401	−	0.0594789i
$849$	14.0000	−	24.2487i	0.480479	−	0.832214i
$850$			2.00000i			0.0685994i
$851$	10.3923	+	6.00000i	0.356244	+	0.205677i
$852$	17.3205	+	10.0000i	0.593391	+	0.342594i
$853$			26.0000i			0.890223i	0.895475	+	0.445112i	$0.146836\pi$
$853$			26.0000i			0.890223i	−0.895475	+	0.445112i	$0.853164\pi$
$854$	4.00000	−	6.92820i	0.136877	−	0.237078i
$855$	−3.00000	−	5.19615i	−0.102598	−	0.177705i
$856$	−5.19615	+	3.00000i	−0.177601	+	0.102538i
$857$	14.0000			0.478231			0.239115	−	0.970991i	$-0.423143\pi$
$857$	14.0000			0.478231			0.239115	+	0.970991i	$0.423143\pi$
$858$		0			0
$859$		0			0			−	1.00000i	$-0.5\pi$
$859$		0			0				1.00000i	$0.5\pi$
$860$	8.66025	−	5.00000i	0.295312	−	0.170499i
$861$	40.0000	+	69.2820i	1.36320	+	2.36113i
$862$	9.00000	−	15.5885i	0.306541	−	0.530945i
$863$		−	36.0000i		−	1.22545i	−0.790295	−	0.612727i	$-0.790072\pi$
$863$		−	36.0000i		−	1.22545i	0.790295	−	0.612727i	$-0.209928\pi$
$864$	3.46410	+	2.00000i	0.117851	+	0.0680414i
$865$	−8.66025	−	5.00000i	−0.294457	−	0.170005i
$866$			38.0000i			1.29129i
$867$	13.0000	−	22.5167i	0.441503	−	0.764706i
$868$	12.0000	+	20.7846i	0.407307	+	0.705476i
$869$	−6.92820	+	4.00000i	−0.235023	+	0.135691i
$870$	4.00000			0.135613
$871$		0			0
$872$	−6.00000			−0.203186
$873$	12.1244	−	7.00000i	0.410347	−	0.236914i
$874$	−18.0000	−	31.1769i	−0.608859	−	1.05457i
$875$	2.00000	−	3.46410i	0.0676123	−	0.117108i
$876$			20.0000i			0.675737i
$877$	12.1244	+	7.00000i	0.409410	+	0.236373i	0.690536	−	0.723298i	$-0.257375\pi$
$877$	12.1244	+	7.00000i	0.409410	+	0.236373i	−0.281126	+	0.959671i	$0.590708\pi$
$878$	−27.7128	−	16.0000i	−0.935262	−	0.539974i
$879$		−	44.0000i		−	1.48408i
$880$	−1.00000	+	1.73205i	−0.0337100	+	0.0583874i
$881$	3.00000	+	5.19615i	0.101073	+	0.175063i	0.912127	−	0.409908i	$-0.134439\pi$
$881$	3.00000	+	5.19615i	0.101073	+	0.175063i	−0.811054	+	0.584971i	$0.801106\pi$
$882$	−7.79423	+	4.50000i	−0.262445	+	0.151523i
$883$	−38.0000			−1.27880			−0.639401	−	0.768874i	$-0.720818\pi$
$883$	−38.0000			−1.27880			−0.639401	+	0.768874i	$0.720818\pi$
$884$		0			0
$885$	−20.0000			−0.672293
$886$	−12.1244	+	7.00000i	−0.407326	+	0.235170i
$887$	−11.0000	−	19.0526i	−0.369344	−	0.639722i	0.620119	−	0.784508i	$-0.287084\pi$
$887$	−11.0000	−	19.0526i	−0.369344	−	0.639722i	−0.989463	+	0.144785i	$0.953751\pi$
$888$	−2.00000	+	3.46410i	−0.0671156	+	0.116248i
$889$			56.0000i			1.87818i
$890$	−12.1244	−	7.00000i	−0.406409	−	0.234641i
$891$	19.0526	+	11.0000i	0.638285	+	0.368514i
$892$		−	4.00000i		−	0.133930i
$893$	36.0000	−	62.3538i	1.20469	−	2.08659i
$894$	2.00000	+	3.46410i	0.0668900	+	0.115857i
$895$	−3.46410	+	2.00000i	−0.115792	+	0.0668526i
$896$	4.00000			0.133631
$897$		0			0
$898$	−6.00000			−0.200223
$899$	−10.3923	+	6.00000i	−0.346603	+	0.200111i
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	2.00000	−	3.46410i	0.0666297	−	0.115406i
$902$		−	20.0000i		−	0.665927i
$903$	−69.2820	−	40.0000i	−2.30556	−	1.33112i
$904$	1.73205	+	1.00000i	0.0576072	+	0.0332595i
$905$			10.0000i			0.332411i
$906$	−6.00000	+	10.3923i	−0.199337	+	0.345261i
$907$	−7.00000	−	12.1244i	−0.232431	−	0.402583i	0.726092	−	0.687598i	$-0.241335\pi$
$907$	−7.00000	−	12.1244i	−0.232431	−	0.402583i	−0.958523	+	0.285015i	$0.908001\pi$
$908$	3.46410	−	2.00000i	0.114960	−	0.0663723i
$909$	−14.0000			−0.464351
$910$		0			0
$911$	16.0000			0.530104			0.265052	−	0.964234i	$-0.414611\pi$
$911$	16.0000			0.530104			0.265052	+	0.964234i	$0.414611\pi$
$912$	10.3923	−	6.00000i	0.344124	−	0.198680i
$913$		0			0
$914$	−5.00000	+	8.66025i	−0.165385	+	0.286456i
$915$		−	4.00000i		−	0.132236i
$916$	−8.66025	−	5.00000i	−0.286143	−	0.165205i
$917$	−13.8564	−	8.00000i	−0.457579	−	0.264183i
$918$			8.00000i			0.264039i
$919$	−2.00000	+	3.46410i	−0.0659739	+	0.114270i	−0.897126	−	0.441776i	$-0.854349\pi$
$919$	−2.00000	+	3.46410i	−0.0659739	+	0.114270i	0.831152	+	0.556046i	$0.187682\pi$
$920$	−3.00000	−	5.19615i	−0.0989071	−	0.171312i
$921$	−41.5692	+	24.0000i	−1.36975	+	0.790827i
$922$	6.00000			0.197599
$923$		0			0
$924$	16.0000			0.526361
$925$	−1.73205	+	1.00000i	−0.0569495	+	0.0328798i
$926$	−8.00000	−	13.8564i	−0.262896	−	0.455350i
$927$	−9.00000	+	15.5885i	−0.295599	+	0.511992i
$928$			2.00000i			0.0656532i
$929$	5.19615	+	3.00000i	0.170480	+	0.0984268i	0.582812	−	0.812607i	$-0.301952\pi$
$929$	5.19615	+	3.00000i	0.170480	+	0.0984268i	−0.412332	+	0.911034i	$0.635286\pi$
$930$	10.3923	+	6.00000i	0.340777	+	0.196748i
$931$		−	54.0000i		−	1.76978i
$932$	3.00000	−	5.19615i	0.0982683	−	0.170206i
$933$	−12.0000	−	20.7846i	−0.392862	−	0.680458i
$934$	−8.66025	+	5.00000i	−0.283372	+	0.163605i
$935$	−4.00000			−0.130814
$936$		0			0
$937$	18.0000			0.588034			0.294017	−	0.955800i	$-0.405008\pi$
$937$	18.0000			0.588034			0.294017	+	0.955800i	$0.405008\pi$
$938$	41.5692	−	24.0000i	1.35728	−	0.783628i
$939$	6.00000	+	10.3923i	0.195803	+	0.339140i
$940$	6.00000	−	10.3923i	0.195698	−	0.338960i
$941$			50.0000i			1.62995i	0.579494	+	0.814977i	$0.303250\pi$
$941$			50.0000i			1.62995i	−0.579494	+	0.814977i	$0.696750\pi$
$942$	−17.3205	−	10.0000i	−0.564333	−	0.325818i
$943$	51.9615	+	30.0000i	1.69210	+	0.976934i
$944$		−	10.0000i		−	0.325472i
$945$	8.00000	−	13.8564i	0.260240	−	0.450749i
$946$	10.0000	+	17.3205i	0.325128	+	0.563138i
$947$	6.92820	−	4.00000i	0.225136	−	0.129983i	−0.383190	−	0.923670i	$-0.625175\pi$
$947$	6.92820	−	4.00000i	0.225136	−	0.129983i	0.608326	+	0.793687i	$0.291841\pi$
$948$	8.00000			0.259828
$949$		0			0
$950$	6.00000			0.194666
$951$	−31.1769	+	18.0000i	−1.01098	+	0.583690i
$952$	4.00000	+	6.92820i	0.129641	+	0.224544i
$953$	9.00000	−	15.5885i	0.291539	−	0.504960i	−0.682635	−	0.730759i	$-0.739166\pi$
$953$	9.00000	−	15.5885i	0.291539	−	0.504960i	0.974174	+	0.225800i	$0.0724995\pi$
$954$			2.00000i			0.0647524i
$955$		0			0
$956$	−22.5167	−	13.0000i	−0.728241	−	0.420450i
$957$			8.00000i			0.258603i
$958$	−1.00000	+	1.73205i	−0.0323085	+	0.0559600i
$959$	36.0000	+	62.3538i	1.16250	+	2.01351i
$960$	1.73205	−	1.00000i	0.0559017	−	0.0322749i
$961$	−5.00000			−0.161290
$962$		0			0
$963$	6.00000			0.193347
$964$	−19.0526	+	11.0000i	−0.613642	+	0.354286i
$965$	7.00000	+	12.1244i	0.225338	+	0.390297i
$966$	−24.0000	+	41.5692i	−0.772187	+	1.33747i
$967$		−	32.0000i		−	1.02905i	−0.857475	−	0.514525i	$-0.827968\pi$
$967$		−	32.0000i		−	1.02905i	0.857475	−	0.514525i	$-0.172032\pi$
$968$	6.06218	+	3.50000i	0.194846	+	0.112494i
$969$	20.7846	+	12.0000i	0.667698	+	0.385496i
$970$			14.0000i			0.449513i
$971$	−10.0000	+	17.3205i	−0.320915	+	0.555842i	−0.980677	−	0.195633i	$-0.937324\pi$
$971$	−10.0000	+	17.3205i	−0.320915	+	0.555842i	0.659762	+	0.751475i	$0.270657\pi$
$972$	−5.00000	−	8.66025i	−0.160375	−	0.277778i
$973$	−27.7128	+	16.0000i	−0.888432	+	0.512936i
$974$	16.0000			0.512673
$975$		0			0
$976$	2.00000			0.0640184
$977$	−25.9808	+	15.0000i	−0.831198	+	0.479893i	−0.854263	−	0.519841i	$-0.825991\pi$
$977$	−25.9808	+	15.0000i	−0.831198	+	0.479893i	0.0230645	+	0.999734i	$0.492658\pi$
$978$	4.00000	+	6.92820i	0.127906	+	0.221540i
$979$	14.0000	−	24.2487i	0.447442	−	0.774992i
$980$		−	9.00000i		−	0.287494i
$981$	5.19615	+	3.00000i	0.165900	+	0.0957826i
$982$		0			0
$983$			16.0000i			0.510321i	0.966899	+	0.255160i	$0.0821283\pi$
$983$			16.0000i			0.510321i	−0.966899	+	0.255160i	$0.917872\pi$
$984$	−10.0000	+	17.3205i	−0.318788	+	0.552158i
$985$	3.00000	+	5.19615i	0.0955879	+	0.165563i
$986$	−3.46410	+	2.00000i	−0.110319	+	0.0636930i
$987$	−96.0000			−3.05571
$988$		0			0
$989$	−60.0000			−1.90789
$990$	1.73205	−	1.00000i	0.0550482	−	0.0317821i
$991$		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
$993$		−	28.0000i		−	0.888553i
$994$	34.6410	+	20.0000i	1.09875	+	0.634361i
$995$		0			0
$996$		0			0
$997$	−5.00000	+	8.66025i	−0.158352	+	0.274273i	−0.934274	−	0.356555i	$-0.883951\pi$
$997$	−5.00000	+	8.66025i	−0.158352	+	0.274273i	0.775923	+	0.630828i	$0.217285\pi$
$998$	19.0000	+	32.9090i	0.601434	+	1.04172i
$999$	−6.92820	+	4.00000i	−0.219199	+	0.126554i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1690.2.l.a.361.2		4
13.2	odd	12		130.2.a.c.1.1	✓	1
13.3	even	3		1690.2.d.e.1351.2		2
13.4	even	6	inner	1690.2.l.a.1161.2		4
13.5	odd	4		1690.2.e.a.991.1		2
13.6	odd	12		1690.2.e.a.191.1		2
13.7	odd	12		1690.2.e.g.191.1		2
13.8	odd	4		1690.2.e.g.991.1		2
13.9	even	3	inner	1690.2.l.a.1161.1		4
13.10	even	6		1690.2.d.e.1351.1		2
13.11	odd	12		1690.2.a.e.1.1		1
13.12	even	2	inner	1690.2.l.a.361.1		4
39.2	even	12		1170.2.a.d.1.1		1
52.15	even	12		1040.2.a.b.1.1		1
65.2	even	12		650.2.b.g.599.2		2
65.24	odd	12		8450.2.a.n.1.1		1
65.28	even	12		650.2.b.g.599.1		2
65.54	odd	12		650.2.a.c.1.1		1
91.41	even	12		6370.2.a.l.1.1		1
104.67	even	12		4160.2.a.t.1.1		1
104.93	odd	12		4160.2.a.c.1.1		1
156.119	odd	12		9360.2.a.by.1.1		1
195.2	odd	12		5850.2.e.u.5149.1		2
195.119	even	12		5850.2.a.cb.1.1		1
195.158	odd	12		5850.2.e.u.5149.2		2
260.119	even	12		5200.2.a.bd.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.a.c.1.1	✓	1	13.2	odd	12
650.2.a.c.1.1		1	65.54	odd	12
650.2.b.g.599.1		2	65.28	even	12
650.2.b.g.599.2		2	65.2	even	12
1040.2.a.b.1.1		1	52.15	even	12
1170.2.a.d.1.1		1	39.2	even	12
1690.2.a.e.1.1		1	13.11	odd	12
1690.2.d.e.1351.1		2	13.10	even	6
1690.2.d.e.1351.2		2	13.3	even	3
1690.2.e.a.191.1		2	13.6	odd	12
1690.2.e.a.991.1		2	13.5	odd	4
1690.2.e.g.191.1		2	13.7	odd	12
1690.2.e.g.991.1		2	13.8	odd	4
1690.2.l.a.361.1		4	13.12	even	2	inner
1690.2.l.a.361.2		4	1.1	even	1	trivial
1690.2.l.a.1161.1		4	13.9	even	3	inner
1690.2.l.a.1161.2		4	13.4	even	6	inner
4160.2.a.c.1.1		1	104.93	odd	12
4160.2.a.t.1.1		1	104.67	even	12
5200.2.a.bd.1.1		1	260.119	even	12
5850.2.a.cb.1.1		1	195.119	even	12
5850.2.e.u.5149.1		2	195.2	odd	12
5850.2.e.u.5149.2		2	195.158	odd	12
6370.2.a.l.1.1		1	91.41	even	12
8450.2.a.n.1.1		1	65.24	odd	12
9360.2.a.by.1.1		1	156.119	odd	12

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:	\( N \)	\(=\)	\( 1690 = 2 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1690.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(-1.73205 - 1.00000i) q^{6} +(-3.46410 - 2.00000i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(-1.73205 - 1.00000i) q^{6} +(-3.46410 - 2.00000i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(1.73205 - 1.00000i) q^{11} -2.00000 q^{12} -4.00000 q^{14} +(-1.73205 + 1.00000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{17} +1.00000i q^{18} +(-5.19615 - 3.00000i) q^{19} +(-0.866025 - 0.500000i) q^{20} +8.00000i q^{21} +(1.00000 - 1.73205i) q^{22} +(3.00000 + 5.19615i) q^{23} +(-1.73205 + 1.00000i) q^{24} -1.00000 q^{25} -4.00000 q^{27} +(-3.46410 + 2.00000i) q^{28} +(-1.00000 - 1.73205i) q^{29} +(-1.00000 + 1.73205i) q^{30} -6.00000i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-3.46410 - 2.00000i) q^{33} -2.00000i q^{34} +(-2.00000 + 3.46410i) q^{35} +(0.500000 + 0.866025i) q^{36} +(1.73205 - 1.00000i) q^{37} -6.00000 q^{38} -1.00000 q^{40} +(8.66025 - 5.00000i) q^{41} +(4.00000 + 6.92820i) q^{42} +(-5.00000 + 8.66025i) q^{43} -2.00000i q^{44} +(0.866025 + 0.500000i) q^{45} +(5.19615 + 3.00000i) q^{46} +12.0000i q^{47} +(-1.00000 + 1.73205i) q^{48} +(4.50000 + 7.79423i) q^{49} +(-0.866025 + 0.500000i) q^{50} -4.00000 q^{51} +2.00000 q^{53} +(-3.46410 + 2.00000i) q^{54} +(-1.00000 - 1.73205i) q^{55} +(-2.00000 + 3.46410i) q^{56} +12.0000i q^{57} +(-1.73205 - 1.00000i) q^{58} +(8.66025 + 5.00000i) q^{59} +2.00000i q^{60} +(-1.00000 + 1.73205i) q^{61} +(-3.00000 - 5.19615i) q^{62} +(3.46410 - 2.00000i) q^{63} -1.00000 q^{64} -4.00000 q^{66} +(-10.3923 + 6.00000i) q^{67} +(-1.00000 - 1.73205i) q^{68} +(6.00000 - 10.3923i) q^{69} +4.00000i q^{70} +(-8.66025 - 5.00000i) q^{71} +(0.866025 + 0.500000i) q^{72} -10.0000i q^{73} +(1.00000 - 1.73205i) q^{74} +(1.00000 + 1.73205i) q^{75} +(-5.19615 + 3.00000i) q^{76} -8.00000 q^{77} -4.00000 q^{79} +(-0.866025 + 0.500000i) q^{80} +(5.50000 + 9.52628i) q^{81} +(5.00000 - 8.66025i) q^{82} +(6.92820 + 4.00000i) q^{84} +(-1.73205 - 1.00000i) q^{85} +10.0000i q^{86} +(-2.00000 + 3.46410i) q^{87} +(-1.00000 - 1.73205i) q^{88} +(12.1244 - 7.00000i) q^{89} +1.00000 q^{90} +6.00000 q^{92} +(-10.3923 + 6.00000i) q^{93} +(6.00000 + 10.3923i) q^{94} +(-3.00000 + 5.19615i) q^{95} +2.00000i q^{96} +(-12.1244 - 7.00000i) q^{97} +(7.79423 + 4.50000i) q^{98} +2.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} + 2 q^{4} - 2 q^{9}+O(q^{10}) \) 4 * q - 4 * q^3 + 2 * q^4 - 2 * q^9	\( 4 q - 4 q^{3} + 2 q^{4} - 2 q^{9} - 2 q^{10} - 8 q^{12} - 16 q^{14} - 2 q^{16} + 4 q^{17} + 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{27} - 4 q^{29} - 4 q^{30} - 8 q^{35} + 2 q^{36} - 24 q^{38} - 4 q^{40} + 16 q^{42} - 20 q^{43} - 4 q^{48} + 18 q^{49} - 16 q^{51} + 8 q^{53} - 4 q^{55} - 8 q^{56} - 4 q^{61} - 12 q^{62} - 4 q^{64} - 16 q^{66} - 4 q^{68} + 24 q^{69} + 4 q^{74} + 4 q^{75} - 32 q^{77} - 16 q^{79} + 22 q^{81} + 20 q^{82} - 8 q^{87} - 4 q^{88} + 4 q^{90} + 24 q^{92} + 24 q^{94} - 12 q^{95}+O(q^{100}) \) 4 * q - 4 * q^3 + 2 * q^4 - 2 * q^9 - 2 * q^10 - 8 * q^12 - 16 * q^14 - 2 * q^16 + 4 * q^17 + 4 * q^22 + 12 * q^23 - 4 * q^25 - 16 * q^27 - 4 * q^29 - 4 * q^30 - 8 * q^35 + 2 * q^36 - 24 * q^38 - 4 * q^40 + 16 * q^42 - 20 * q^43 - 4 * q^48 + 18 * q^49 - 16 * q^51 + 8 * q^53 - 4 * q^55 - 8 * q^56 - 4 * q^61 - 12 * q^62 - 4 * q^64 - 16 * q^66 - 4 * q^68 + 24 * q^69 + 4 * q^74 + 4 * q^75 - 32 * q^77 - 16 * q^79 + 22 * q^81 + 20 * q^82 - 8 * q^87 - 4 * q^88 + 4 * q^90 + 24 * q^92 + 24 * q^94 - 12 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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