LMFDB - Embedded newform 1690.2.l.f.361.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1690,2,Mod(361,1690)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [4,0,0,2,0,0,0,0,6,2,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

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			361.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1690.361
Dual form			1690.2.l.f.1161.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +1.00000i q^{8} +(1.50000 - 2.59808i) q^{9} +(0.500000 + 0.866025i) q^{10} +(-0.500000 - 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{17} +3.00000i q^{18} +(-6.92820 - 4.00000i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(-2.00000 - 3.46410i) q^{23} -1.00000 q^{25} +(1.00000 + 1.73205i) q^{29} +4.00000i q^{31} +(0.866025 + 0.500000i) q^{32} +2.00000i q^{34} +(-1.50000 - 2.59808i) q^{36} +(5.19615 - 3.00000i) q^{37} +8.00000 q^{38} +1.00000 q^{40} +(-8.66025 + 5.00000i) q^{41} +(-2.59808 - 1.50000i) q^{45} +(3.46410 + 2.00000i) q^{46} +8.00000i q^{47} +(-3.50000 - 6.06218i) q^{49} +(0.866025 - 0.500000i) q^{50} +6.00000 q^{53} +(-1.73205 - 1.00000i) q^{58} +(-6.92820 - 4.00000i) q^{59} +(1.00000 - 1.73205i) q^{61} +(-2.00000 - 3.46410i) q^{62} -1.00000 q^{64} +(-3.46410 + 2.00000i) q^{67} +(-1.00000 - 1.73205i) q^{68} +(-10.3923 - 6.00000i) q^{71} +(2.59808 + 1.50000i) q^{72} +10.0000i q^{73} +(-3.00000 + 5.19615i) q^{74} +(-6.92820 + 4.00000i) q^{76} -8.00000 q^{79} +(-0.866025 + 0.500000i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(5.00000 - 8.66025i) q^{82} -12.0000i q^{83} +(-1.73205 - 1.00000i) q^{85} +(8.66025 - 5.00000i) q^{89} +3.00000 q^{90} -4.00000 q^{92} +(-4.00000 - 6.92820i) q^{94} +(-4.00000 + 6.92820i) q^{95} +(-12.1244 - 7.00000i) q^{97} +(6.06218 + 3.50000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 6 q^{9} + 2 q^{10} - 2 q^{16} + 4 q^{17} - 8 q^{23} - 4 q^{25} + 4 q^{29} - 6 q^{36} + 32 q^{38} + 4 q^{40} - 14 q^{49} + 24 q^{53} + 4 q^{61} - 8 q^{62} - 4 q^{64} - 4 q^{68} - 12 q^{74}+ \cdots - 16 q^{95}+O(q^{100}) $ 4 * q + 2 * q^4 + 6 * q^9 + 2 * q^10 - 2 * q^16 + 4 * q^17 - 8 * q^23 - 4 * q^25 + 4 * q^29 - 6 * q^36 + 32 * q^38 + 4 * q^40 - 14 * q^49 + 24 * q^53 + 4 * q^61 - 8 * q^62 - 4 * q^64 - 4 * q^68 - 12 * q^74 - 32 * q^79 - 18 * q^81 + 20 * q^82 + 12 * q^90 - 16 * q^92 - 16 * q^94 - 16 * q^95

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
$3$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$3$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$7$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$8$			1.00000i			0.353553i
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$11$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$12$		0			0
$13$		0			0
$13$		0			0
$14$		0			0
$15$		0			0
$16$	−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	$0.0886875\pi$
$18$			3.00000i			0.707107i
$19$	−6.92820	−	4.00000i	−1.58944	−	0.917663i	−0.993399	−	0.114708i	$-0.963407\pi$
$19$	−6.92820	−	4.00000i	−1.58944	−	0.917663i	−0.596040	−	0.802955i	$-0.703260\pi$
$20$	−0.866025	−	0.500000i	−0.193649	−	0.111803i
$21$		0			0
$22$		0			0
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	0.578610	−	0.815604i	$-0.303595\pi$
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	−0.995639	+	0.0932891i	$0.970262\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.00000	+	1.73205i	0.185695	+	0.321634i	0.943811	−	0.330487i	$-0.107213\pi$
$29$	1.00000	+	1.73205i	0.185695	+	0.321634i	−0.758115	+	0.652121i	$0.773880\pi$
$30$		0			0
$31$			4.00000i			0.718421i	0.933257	+	0.359211i	$0.116954\pi$
$31$			4.00000i			0.718421i	−0.933257	+	0.359211i	$0.883046\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$			2.00000i			0.342997i
$35$		0			0
$36$	−1.50000	−	2.59808i	−0.250000	−	0.433013i
$37$	5.19615	−	3.00000i	0.854242	−	0.493197i	−0.00783774	−	0.999969i	$-0.502495\pi$
$37$	5.19615	−	3.00000i	0.854242	−	0.493197i	0.862080	+	0.506772i	$0.169162\pi$
$38$	8.00000			1.29777
$39$		0			0
$40$	1.00000			0.158114
$41$	−8.66025	+	5.00000i	−1.35250	+	0.780869i	−0.988600	−	0.150567i	$-0.951890\pi$
$41$	−8.66025	+	5.00000i	−1.35250	+	0.780869i	−0.363905	+	0.931436i	$0.618557\pi$
$42$		0			0
$43$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$43$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$44$		0			0
$45$	−2.59808	−	1.50000i	−0.387298	−	0.223607i
$46$	3.46410	+	2.00000i	0.510754	+	0.294884i
$47$			8.00000i			1.16692i	0.812142	+	0.583460i	$0.198301\pi$
$47$			8.00000i			1.16692i	−0.812142	+	0.583460i	$0.801699\pi$
$48$		0			0
$49$	−3.50000	−	6.06218i	−0.500000	−	0.866025i
$50$	0.866025	−	0.500000i	0.122474	−	0.0707107i
$51$		0			0
$52$		0			0
$53$	6.00000			0.824163			0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000			0.824163			0.412082	+	0.911147i	$0.364802\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	−1.73205	−	1.00000i	−0.227429	−	0.131306i
$59$	−6.92820	−	4.00000i	−0.901975	−	0.520756i	−0.0241347	−	0.999709i	$-0.507683\pi$
$59$	−6.92820	−	4.00000i	−0.901975	−	0.520756i	−0.877841	+	0.478953i	$0.841016\pi$
$60$		0			0
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	−0.794879	−	0.606768i	$-0.792466\pi$
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	0.922916	+	0.385002i	$0.125799\pi$
$62$	−2.00000	−	3.46410i	−0.254000	−	0.439941i
$63$		0			0
$64$	−1.00000			−0.125000
$65$		0			0
$66$		0			0
$67$	−3.46410	+	2.00000i	−0.423207	+	0.244339i	−0.696449	−	0.717607i	$-0.745238\pi$
$67$	−3.46410	+	2.00000i	−0.423207	+	0.244339i	0.273241	+	0.961946i	$0.411904\pi$
$68$	−1.00000	−	1.73205i	−0.121268	−	0.210042i
$69$		0			0
$70$		0			0
$71$	−10.3923	−	6.00000i	−1.23334	−	0.712069i	−0.265615	−	0.964079i	$-0.585575\pi$
$71$	−10.3923	−	6.00000i	−1.23334	−	0.712069i	−0.967725	+	0.252010i	$0.918908\pi$
$72$	2.59808	+	1.50000i	0.306186	+	0.176777i
$73$			10.0000i			1.17041i	0.810885	+	0.585206i	$0.198986\pi$
$73$			10.0000i			1.17041i	−0.810885	+	0.585206i	$0.801014\pi$
$74$	−3.00000	+	5.19615i	−0.348743	+	0.604040i
$75$		0			0
$76$	−6.92820	+	4.00000i	−0.794719	+	0.458831i
$77$		0			0
$78$		0			0
$79$	−8.00000			−0.900070			−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000			−0.900070			−0.450035	+	0.893011i	$0.648589\pi$
$80$	−0.866025	+	0.500000i	−0.0968246	+	0.0559017i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	5.00000	−	8.66025i	0.552158	−	0.956365i
$83$		−	12.0000i		−	1.31717i	−0.752506	−	0.658586i	$-0.771155\pi$
$83$		−	12.0000i		−	1.31717i	0.752506	−	0.658586i	$-0.228845\pi$
$84$		0			0
$85$	−1.73205	−	1.00000i	−0.187867	−	0.108465i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	8.66025	−	5.00000i	0.917985	−	0.529999i	0.0349934	−	0.999388i	$-0.488859\pi$
$89$	8.66025	−	5.00000i	0.917985	−	0.529999i	0.882992	+	0.469389i	$0.155526\pi$
$90$	3.00000			0.316228
$91$		0			0
$92$	−4.00000			−0.417029
$93$		0			0
$94$	−4.00000	−	6.92820i	−0.412568	−	0.714590i
$95$	−4.00000	+	6.92820i	−0.410391	+	0.710819i
$96$		0			0
$97$	−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	$0.918307\pi$
$98$	6.06218	+	3.50000i	0.612372	+	0.353553i
$99$		0			0
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	3.00000	+	5.19615i	0.298511	+	0.517036i	0.975796	−	0.218685i	$-0.0701767\pi$
$101$	3.00000	+	5.19615i	0.298511	+	0.517036i	−0.677284	+	0.735721i	$0.736843\pi$
$102$		0			0
$103$	4.00000			0.394132			0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000			0.394132			0.197066	+	0.980390i	$0.436859\pi$
$104$		0			0
$105$		0			0
$106$	−5.19615	+	3.00000i	−0.504695	+	0.291386i
$107$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$107$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$108$		0			0
$109$			2.00000i			0.191565i	0.995402	+	0.0957826i	$0.0305354\pi$
$109$			2.00000i			0.191565i	−0.995402	+	0.0957826i	$0.969465\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	7.00000	−	12.1244i	0.658505	−	1.14056i	−0.322498	−	0.946570i	$-0.604523\pi$
$113$	7.00000	−	12.1244i	0.658505	−	1.14056i	0.981003	−	0.193993i	$-0.0621440\pi$
$114$		0			0
$115$	−3.46410	+	2.00000i	−0.323029	+	0.186501i
$116$	2.00000			0.185695
$117$		0			0
$118$	8.00000			0.736460
$119$		0			0
$120$		0			0
$121$	−5.50000	+	9.52628i	−0.500000	+	0.866025i
$122$			2.00000i			0.181071i
$123$		0			0
$124$	3.46410	+	2.00000i	0.311086	+	0.179605i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$	−10.0000	−	17.3205i	−0.887357	−	1.53695i	−0.842989	−	0.537931i	$-0.819206\pi$
$127$	−10.0000	−	17.3205i	−0.887357	−	1.53695i	−0.0443678	−	0.999015i	$-0.514127\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$		0			0
$131$	4.00000			0.349482			0.174741	−	0.984614i	$-0.444091\pi$
$131$	4.00000			0.349482			0.174741	+	0.984614i	$0.444091\pi$
$132$		0			0
$133$		0			0
$134$	2.00000	−	3.46410i	0.172774	−	0.299253i
$135$		0			0
$136$	1.73205	+	1.00000i	0.148522	+	0.0857493i
$137$	5.19615	+	3.00000i	0.443937	+	0.256307i	0.705266	−	0.708942i	$-0.250827\pi$
$137$	5.19615	+	3.00000i	0.443937	+	0.256307i	−0.261329	+	0.965250i	$0.584161\pi$
$138$		0			0
$139$	−2.00000	+	3.46410i	−0.169638	+	0.293821i	−0.938293	−	0.345843i	$-0.887593\pi$
$139$	−2.00000	+	3.46410i	−0.169638	+	0.293821i	0.768655	+	0.639664i	$0.220926\pi$
$140$		0			0
$141$		0			0
$142$	12.0000			1.00702
$143$		0			0
$144$	−3.00000			−0.250000
$145$	1.73205	−	1.00000i	0.143839	−	0.0830455i
$146$	−5.00000	−	8.66025i	−0.413803	−	0.716728i
$147$		0			0
$148$		−	6.00000i		−	0.493197i
$149$	5.19615	+	3.00000i	0.425685	+	0.245770i	0.697507	−	0.716578i	$-0.254293\pi$
$149$	5.19615	+	3.00000i	0.425685	+	0.245770i	−0.271821	+	0.962348i	$0.587626\pi$
$150$		0			0
$151$		−	20.0000i		−	1.62758i	−0.581161	−	0.813788i	$-0.697401\pi$
$151$		−	20.0000i		−	1.62758i	0.581161	−	0.813788i	$-0.302599\pi$
$152$	4.00000	−	6.92820i	0.324443	−	0.561951i
$153$	−3.00000	−	5.19615i	−0.242536	−	0.420084i
$154$		0			0
$155$	4.00000			0.321288
$156$		0			0
$157$	−18.0000			−1.43656			−0.718278	−	0.695756i	$-0.755069\pi$
$157$	−18.0000			−1.43656			−0.718278	+	0.695756i	$0.755069\pi$
$158$	6.92820	−	4.00000i	0.551178	−	0.318223i
$159$		0			0
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$		0			0
$162$	7.79423	+	4.50000i	0.612372	+	0.353553i
$163$	−17.3205	−	10.0000i	−1.35665	−	0.783260i	−0.367477	−	0.930033i	$-0.619778\pi$
$163$	−17.3205	−	10.0000i	−1.35665	−	0.783260i	−0.989170	+	0.146772i	$0.953112\pi$
$164$			10.0000i			0.780869i
$165$		0			0
$166$	6.00000	+	10.3923i	0.465690	+	0.806599i
$167$	13.8564	−	8.00000i	1.07224	−	0.619059i	0.143448	−	0.989658i	$-0.454181\pi$
$167$	13.8564	−	8.00000i	1.07224	−	0.619059i	0.928793	+	0.370599i	$0.120848\pi$
$168$		0			0
$169$		0			0
$170$	2.00000			0.153393
$171$	−20.7846	+	12.0000i	−1.58944	+	0.917663i
$172$		0			0
$173$	−9.00000	+	15.5885i	−0.684257	+	1.18517i	0.289412	+	0.957205i	$0.406540\pi$
$173$	−9.00000	+	15.5885i	−0.684257	+	1.18517i	−0.973670	+	0.227964i	$0.926793\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	−5.00000	+	8.66025i	−0.374766	+	0.649113i
$179$	2.00000	+	3.46410i	0.149487	+	0.258919i	0.931038	−	0.364922i	$-0.118904\pi$
$179$	2.00000	+	3.46410i	0.149487	+	0.258919i	−0.781551	+	0.623841i	$0.785571\pi$
$180$	−2.59808	+	1.50000i	−0.193649	+	0.111803i
$181$	−22.0000			−1.63525			−0.817624	−	0.575753i	$-0.804709\pi$
$181$	−22.0000			−1.63525			−0.817624	+	0.575753i	$0.804709\pi$
$182$		0			0
$183$		0			0
$184$	3.46410	−	2.00000i	0.255377	−	0.147442i
$185$	−3.00000	−	5.19615i	−0.220564	−	0.382029i
$186$		0			0
$187$		0			0
$188$	6.92820	+	4.00000i	0.505291	+	0.291730i
$189$		0			0
$190$		−	8.00000i		−	0.580381i
$191$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$191$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$192$		0			0
$193$	15.5885	−	9.00000i	1.12208	−	0.647834i	0.180150	−	0.983639i	$-0.442342\pi$
$193$	15.5885	−	9.00000i	1.12208	−	0.647834i	0.941932	+	0.335805i	$0.109008\pi$
$194$	14.0000			1.00514
$195$		0			0
$196$	−7.00000			−0.500000
$197$	22.5167	−	13.0000i	1.60425	−	0.926212i	0.613621	−	0.789601i	$-0.289712\pi$
$197$	22.5167	−	13.0000i	1.60425	−	0.926212i	0.990625	−	0.136611i	$-0.0436210\pi$
$198$		0			0
$199$	12.0000	−	20.7846i	0.850657	−	1.47338i	−0.0299585	−	0.999551i	$-0.509538\pi$
$199$	12.0000	−	20.7846i	0.850657	−	1.47338i	0.880616	−	0.473831i	$-0.157129\pi$
$200$		−	1.00000i		−	0.0707107i
$201$		0			0
$202$	−5.19615	−	3.00000i	−0.365600	−	0.211079i
$203$		0			0
$204$		0			0
$205$	5.00000	+	8.66025i	0.349215	+	0.604858i
$206$	−3.46410	+	2.00000i	−0.241355	+	0.139347i
$207$	−12.0000			−0.834058
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−2.00000	−	3.46410i	−0.137686	−	0.238479i	0.788935	−	0.614477i	$-0.210633\pi$
$211$	−2.00000	−	3.46410i	−0.137686	−	0.238479i	−0.926620	+	0.375999i	$0.877300\pi$
$212$	3.00000	−	5.19615i	0.206041	−	0.356873i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−1.00000	−	1.73205i	−0.0677285	−	0.117309i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	6.92820	−	4.00000i	0.463947	−	0.267860i	−0.249756	−	0.968309i	$-0.580350\pi$
$223$	6.92820	−	4.00000i	0.463947	−	0.267860i	0.713702	+	0.700449i	$0.247017\pi$
$224$		0			0
$225$	−1.50000	+	2.59808i	−0.100000	+	0.173205i
$226$			14.0000i			0.931266i
$227$	17.3205	+	10.0000i	1.14960	+	0.663723i	0.948790	−	0.315906i	$-0.102309\pi$
$227$	17.3205	+	10.0000i	1.14960	+	0.663723i	0.200812	+	0.979630i	$0.435642\pi$
$228$		0			0
$229$		−	10.0000i		−	0.660819i	−0.943838	−	0.330409i	$-0.892813\pi$
$229$		−	10.0000i		−	0.660819i	0.943838	−	0.330409i	$-0.107187\pi$
$230$	2.00000	−	3.46410i	0.131876	−	0.228416i
$231$		0			0
$232$	−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
$235$	8.00000			0.521862
$236$	−6.92820	+	4.00000i	−0.450988	+	0.260378i
$237$		0			0
$238$		0			0
$239$		−	20.0000i		−	1.29369i	−0.762620	−	0.646846i	$-0.776088\pi$
$239$		−	20.0000i		−	1.29369i	0.762620	−	0.646846i	$-0.223912\pi$
$240$		0			0
$241$	−1.73205	−	1.00000i	−0.111571	−	0.0644157i	0.443176	−	0.896435i	$-0.353852\pi$
$241$	−1.73205	−	1.00000i	−0.111571	−	0.0644157i	−0.554747	+	0.832019i	$0.687185\pi$
$242$		−	11.0000i		−	0.707107i
$243$		0			0
$244$	−1.00000	−	1.73205i	−0.0640184	−	0.110883i
$245$	−6.06218	+	3.50000i	−0.387298	+	0.223607i
$246$		0			0
$247$		0			0
$248$	−4.00000			−0.254000
$249$		0			0
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	−14.0000	+	24.2487i	−0.883672	+	1.53057i	−0.0364441	+	0.999336i	$0.511603\pi$
$251$	−14.0000	+	24.2487i	−0.883672	+	1.53057i	−0.847228	+	0.531229i	$0.821730\pi$
$252$		0			0
$253$		0			0
$254$	17.3205	+	10.0000i	1.08679	+	0.627456i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.00000	+	1.73205i	0.0623783	+	0.108042i	0.895528	−	0.445005i	$-0.146798\pi$
$257$	1.00000	+	1.73205i	0.0623783	+	0.108042i	−0.833150	+	0.553047i	$0.813465\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	6.00000			0.371391
$262$	−3.46410	+	2.00000i	−0.214013	+	0.123560i
$263$	14.0000	+	24.2487i	0.863277	+	1.49524i	0.868748	+	0.495255i	$0.164925\pi$
$263$	14.0000	+	24.2487i	0.863277	+	1.49524i	−0.00547092	+	0.999985i	$0.501741\pi$
$264$		0			0
$265$		−	6.00000i		−	0.368577i
$266$		0			0
$267$		0			0
$268$			4.00000i			0.244339i
$269$	9.00000	−	15.5885i	0.548740	−	0.950445i	−0.449622	−	0.893219i	$-0.648441\pi$
$269$	9.00000	−	15.5885i	0.548740	−	0.950445i	0.998361	−	0.0572259i	$-0.0182255\pi$
$270$		0			0
$271$	−24.2487	+	14.0000i	−1.47300	+	0.850439i	−0.999539	−	0.0303728i	$-0.990331\pi$
$271$	−24.2487	+	14.0000i	−1.47300	+	0.850439i	−0.473466	+	0.880812i	$0.656997\pi$
$272$	−2.00000			−0.121268
$273$		0			0
$274$	−6.00000			−0.362473
$275$		0			0
$276$		0			0
$277$	11.0000	−	19.0526i	0.660926	−	1.14476i	−0.319447	−	0.947604i	$-0.603497\pi$
$277$	11.0000	−	19.0526i	0.660926	−	1.14476i	0.980373	−	0.197153i	$-0.0631696\pi$
$278$		−	4.00000i		−	0.239904i
$279$	10.3923	+	6.00000i	0.622171	+	0.359211i
$280$		0			0
$281$		−	22.0000i		−	1.31241i	−0.754583	−	0.656205i	$-0.772161\pi$
$281$		−	22.0000i		−	1.31241i	0.754583	−	0.656205i	$-0.227839\pi$
$282$		0			0
$283$	8.00000	+	13.8564i	0.475551	+	0.823678i	0.999608	−	0.0280052i	$-0.00891551\pi$
$283$	8.00000	+	13.8564i	0.475551	+	0.823678i	−0.524057	+	0.851683i	$0.675582\pi$
$284$	−10.3923	+	6.00000i	−0.616670	+	0.356034i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	2.59808	−	1.50000i	0.153093	−	0.0883883i
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$	−1.00000	+	1.73205i	−0.0587220	+	0.101710i
$291$		0			0
$292$	8.66025	+	5.00000i	0.506803	+	0.292603i
$293$	−5.19615	−	3.00000i	−0.303562	−	0.175262i	0.340480	−	0.940252i	$-0.389411\pi$
$293$	−5.19615	−	3.00000i	−0.303562	−	0.175262i	−0.644042	+	0.764990i	$0.722744\pi$
$294$		0			0
$295$	−4.00000	+	6.92820i	−0.232889	+	0.403376i
$296$	3.00000	+	5.19615i	0.174371	+	0.302020i
$297$		0			0
$298$	−6.00000			−0.347571
$299$		0			0
$300$		0			0
$301$		0			0
$302$	10.0000	+	17.3205i	0.575435	+	0.996683i
$303$		0			0
$304$			8.00000i			0.458831i
$305$	−1.73205	−	1.00000i	−0.0991769	−	0.0572598i
$306$	5.19615	+	3.00000i	0.297044	+	0.171499i
$307$			28.0000i			1.59804i	0.601302	+	0.799022i	$0.294649\pi$
$307$			28.0000i			1.59804i	−0.601302	+	0.799022i	$0.705351\pi$
$308$		0			0
$309$		0			0
$310$	−3.46410	+	2.00000i	−0.196748	+	0.113592i
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$		0			0
$313$	−6.00000			−0.339140			−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000			−0.339140			−0.169570	+	0.985518i	$0.554238\pi$
$314$	15.5885	−	9.00000i	0.879708	−	0.507899i
$315$		0			0
$316$	−4.00000	+	6.92820i	−0.225018	+	0.389742i
$317$			2.00000i			0.112331i	0.998421	+	0.0561656i	$0.0178875\pi$
$317$			2.00000i			0.112331i	−0.998421	+	0.0561656i	$0.982113\pi$
$318$		0			0
$319$		0			0
$320$			1.00000i			0.0559017i
$321$		0			0
$322$		0			0
$323$	−13.8564	+	8.00000i	−0.770991	+	0.445132i
$324$	−9.00000			−0.500000
$325$		0			0
$326$	20.0000			1.10770
$327$		0			0
$328$	−5.00000	−	8.66025i	−0.276079	−	0.478183i
$329$		0			0
$330$		0			0
$331$	−6.92820	−	4.00000i	−0.380808	−	0.219860i	0.297361	−	0.954765i	$-0.403893\pi$
$331$	−6.92820	−	4.00000i	−0.380808	−	0.219860i	−0.678170	+	0.734905i	$0.737227\pi$
$332$	−10.3923	−	6.00000i	−0.570352	−	0.329293i
$333$		−	18.0000i		−	0.986394i
$334$	−8.00000	+	13.8564i	−0.437741	+	0.758189i
$335$	2.00000	+	3.46410i	0.109272	+	0.189264i
$336$		0			0
$337$	−18.0000			−0.980522			−0.490261	−	0.871576i	$-0.663099\pi$
$337$	−18.0000			−0.980522			−0.490261	+	0.871576i	$0.663099\pi$
$338$		0			0
$339$		0			0
$340$	−1.73205	+	1.00000i	−0.0939336	+	0.0542326i
$341$		0			0
$342$	12.0000	−	20.7846i	0.648886	−	1.12390i
$343$		0			0
$344$		0			0
$345$		0			0
$346$		−	18.0000i		−	0.967686i
$347$	−16.0000	+	27.7128i	−0.858925	+	1.48770i	0.0140303	+	0.999902i	$0.495534\pi$
$347$	−16.0000	+	27.7128i	−0.858925	+	1.48770i	−0.872955	+	0.487800i	$0.837799\pi$
$348$		0			0
$349$	12.1244	−	7.00000i	0.649002	−	0.374701i	−0.139072	−	0.990282i	$-0.544412\pi$
$349$	12.1244	−	7.00000i	0.649002	−	0.374701i	0.788074	+	0.615581i	$0.211079\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	25.9808	−	15.0000i	1.38282	−	0.798369i	0.390324	−	0.920677i	$-0.372363\pi$
$353$	25.9808	−	15.0000i	1.38282	−	0.798369i	0.992492	+	0.122308i	$0.0390296\pi$
$354$		0			0
$355$	−6.00000	+	10.3923i	−0.318447	+	0.551566i
$356$		−	10.0000i		−	0.529999i
$357$		0			0
$358$	−3.46410	−	2.00000i	−0.183083	−	0.105703i
$359$			4.00000i			0.211112i	0.994413	+	0.105556i	$0.0336622\pi$
$359$			4.00000i			0.211112i	−0.994413	+	0.105556i	$0.966338\pi$
$360$	1.50000	−	2.59808i	0.0790569	−	0.136931i
$361$	22.5000	+	38.9711i	1.18421	+	2.05111i
$362$	19.0526	−	11.0000i	1.00138	−	0.578147i
$363$		0			0
$364$		0			0
$365$	10.0000			0.523424
$366$		0			0
$367$	6.00000	+	10.3923i	0.313197	+	0.542474i	0.979053	−	0.203607i	$-0.0652665\pi$
$367$	6.00000	+	10.3923i	0.313197	+	0.542474i	−0.665855	+	0.746081i	$0.731933\pi$
$368$	−2.00000	+	3.46410i	−0.104257	+	0.180579i
$369$			30.0000i			1.56174i
$370$	5.19615	+	3.00000i	0.270135	+	0.155963i
$371$		0			0
$372$		0			0
$373$	−3.00000	+	5.19615i	−0.155334	+	0.269047i	−0.933181	−	0.359408i	$-0.882979\pi$
$373$	−3.00000	+	5.19615i	−0.155334	+	0.269047i	0.777847	+	0.628454i	$0.216312\pi$
$374$		0			0
$375$		0			0
$376$	−8.00000			−0.412568
$377$		0			0
$378$		0			0
$379$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$379$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$380$	4.00000	+	6.92820i	0.205196	+	0.355409i
$381$		0			0
$382$		0			0
$383$	6.92820	+	4.00000i	0.354015	+	0.204390i	0.666452	−	0.745548i	$-0.267812\pi$
$383$	6.92820	+	4.00000i	0.354015	+	0.204390i	−0.312437	+	0.949938i	$0.601145\pi$
$384$		0			0
$385$		0			0
$386$	−9.00000	+	15.5885i	−0.458088	+	0.793432i
$387$		0			0
$388$	−12.1244	+	7.00000i	−0.615521	+	0.355371i
$389$	−6.00000			−0.304212			−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000			−0.304212			−0.152106	+	0.988364i	$0.548606\pi$
$390$		0			0
$391$	−8.00000			−0.404577
$392$	6.06218	−	3.50000i	0.306186	−	0.176777i
$393$		0			0
$394$	−13.0000	+	22.5167i	−0.654931	+	1.13437i
$395$			8.00000i			0.402524i
$396$		0			0
$397$	15.5885	+	9.00000i	0.782362	+	0.451697i	0.837267	−	0.546795i	$-0.184152\pi$
$397$	15.5885	+	9.00000i	0.782362	+	0.451697i	−0.0549046	+	0.998492i	$0.517485\pi$
$398$			24.0000i			1.20301i
$399$		0			0
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	−25.9808	+	15.0000i	−1.29742	+	0.749064i	−0.979957	−	0.199207i	$-0.936163\pi$
$401$	−25.9808	+	15.0000i	−1.29742	+	0.749064i	−0.317460	+	0.948272i	$0.602830\pi$
$402$		0			0
$403$		0			0
$404$	6.00000			0.298511
$405$	−7.79423	+	4.50000i	−0.387298	+	0.223607i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	22.5167	+	13.0000i	1.11338	+	0.642809i	0.939702	−	0.341994i	$-0.111102\pi$
$409$	22.5167	+	13.0000i	1.11338	+	0.642809i	0.173675	+	0.984803i	$0.444436\pi$
$410$	−8.66025	−	5.00000i	−0.427699	−	0.246932i
$411$		0			0
$412$	2.00000	−	3.46410i	0.0985329	−	0.170664i
$413$		0			0
$414$	10.3923	−	6.00000i	0.510754	−	0.294884i
$415$	−12.0000			−0.589057
$416$		0			0
$417$		0			0
$418$		0			0
$419$	18.0000	+	31.1769i	0.879358	+	1.52309i	0.852047	+	0.523465i	$0.175361\pi$
$419$	18.0000	+	31.1769i	0.879358	+	1.52309i	0.0273103	+	0.999627i	$0.491306\pi$
$420$		0			0
$421$			26.0000i			1.26716i	0.773676	+	0.633581i	$0.218416\pi$
$421$			26.0000i			1.26716i	−0.773676	+	0.633581i	$0.781584\pi$
$422$	3.46410	+	2.00000i	0.168630	+	0.0973585i
$423$	20.7846	+	12.0000i	1.01058	+	0.583460i
$424$			6.00000i			0.291386i
$425$	−1.00000	+	1.73205i	−0.0485071	+	0.0840168i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−10.3923	+	6.00000i	−0.500580	+	0.289010i	−0.728953	−	0.684564i	$-0.759993\pi$
$431$	−10.3923	+	6.00000i	−0.500580	+	0.289010i	0.228373	+	0.973574i	$0.426659\pi$
$432$		0			0
$433$	17.0000	−	29.4449i	0.816968	−	1.41503i	−0.0909384	−	0.995857i	$-0.528987\pi$
$433$	17.0000	−	29.4449i	0.816968	−	1.41503i	0.907906	−	0.419173i	$-0.137680\pi$
$434$		0			0
$435$		0			0
$436$	1.73205	+	1.00000i	0.0829502	+	0.0478913i
$437$			32.0000i			1.53077i
$438$		0			0
$439$	−12.0000	−	20.7846i	−0.572729	−	0.991995i	−0.996284	−	0.0861252i	$-0.972552\pi$
$439$	−12.0000	−	20.7846i	−0.572729	−	0.991995i	0.423556	−	0.905870i	$-0.360782\pi$
$440$		0			0
$441$	−21.0000			−1.00000
$442$		0			0
$443$	24.0000			1.14027			0.570137	−	0.821549i	$-0.306890\pi$
$443$	24.0000			1.14027			0.570137	+	0.821549i	$0.306890\pi$
$444$		0			0
$445$	−5.00000	−	8.66025i	−0.237023	−	0.410535i
$446$	−4.00000	+	6.92820i	−0.189405	+	0.328060i
$447$		0			0
$448$		0			0
$449$	−15.5885	−	9.00000i	−0.735665	−	0.424736i	0.0848262	−	0.996396i	$-0.472967\pi$
$449$	−15.5885	−	9.00000i	−0.735665	−	0.424736i	−0.820491	+	0.571660i	$0.806300\pi$
$450$		−	3.00000i		−	0.141421i
$451$		0			0
$452$	−7.00000	−	12.1244i	−0.329252	−	0.570282i
$453$		0			0
$454$	−20.0000			−0.938647
$455$		0			0
$456$		0			0
$457$	32.9090	−	19.0000i	1.53942	−	0.888783i	0.540544	−	0.841316i	$-0.318219\pi$
$457$	32.9090	−	19.0000i	1.53942	−	0.888783i	0.998873	−	0.0474665i	$-0.0151147\pi$
$458$	5.00000	+	8.66025i	0.233635	+	0.404667i
$459$		0			0
$460$			4.00000i			0.186501i
$461$	12.1244	+	7.00000i	0.564688	+	0.326023i	0.755025	−	0.655696i	$-0.227625\pi$
$461$	12.1244	+	7.00000i	0.564688	+	0.326023i	−0.190337	+	0.981719i	$0.560958\pi$
$462$		0			0
$463$		−	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
$465$		0			0
$466$	−5.19615	+	3.00000i	−0.240707	+	0.138972i
$467$	16.0000			0.740392			0.370196	−	0.928954i	$-0.379291\pi$
$467$	16.0000			0.740392			0.370196	+	0.928954i	$0.379291\pi$
$468$		0			0
$469$		0			0
$470$	−6.92820	+	4.00000i	−0.319574	+	0.184506i
$471$		0			0
$472$	4.00000	−	6.92820i	0.184115	−	0.318896i
$473$		0			0
$474$		0			0
$475$	6.92820	+	4.00000i	0.317888	+	0.183533i
$476$		0			0
$477$	9.00000	−	15.5885i	0.412082	−	0.713746i
$478$	10.0000	+	17.3205i	0.457389	+	0.792222i
$479$	−3.46410	+	2.00000i	−0.158279	+	0.0913823i	−0.577047	−	0.816711i	$-0.695795\pi$
$479$	−3.46410	+	2.00000i	−0.158279	+	0.0913823i	0.418769	+	0.908093i	$0.362462\pi$
$480$		0			0
$481$		0			0
$482$	2.00000			0.0910975
$483$		0			0
$484$	5.50000	+	9.52628i	0.250000	+	0.433013i
$485$	−7.00000	+	12.1244i	−0.317854	+	0.550539i
$486$		0			0
$487$	−6.92820	−	4.00000i	−0.313947	−	0.181257i	0.334744	−	0.942309i	$-0.391350\pi$
$487$	−6.92820	−	4.00000i	−0.313947	−	0.181257i	−0.648691	+	0.761052i	$0.724683\pi$
$488$	1.73205	+	1.00000i	0.0784063	+	0.0452679i
$489$		0			0
$490$	3.50000	−	6.06218i	0.158114	−	0.273861i
$491$	10.0000	+	17.3205i	0.451294	+	0.781664i	0.998467	−	0.0553560i	$-0.0176294\pi$
$491$	10.0000	+	17.3205i	0.451294	+	0.781664i	−0.547173	+	0.837020i	$0.684296\pi$
$492$		0			0
$493$	4.00000			0.180151
$494$		0			0
$495$		0			0
$496$	3.46410	−	2.00000i	0.155543	−	0.0898027i
$497$		0			0
$498$		0			0
$499$		−	8.00000i		−	0.358129i	−0.983837	−	0.179065i	$-0.942693\pi$
$499$		−	8.00000i		−	0.358129i	0.983837	−	0.179065i	$-0.0573071\pi$
$500$	0.866025	+	0.500000i	0.0387298	+	0.0223607i
$501$		0			0
$502$		−	28.0000i		−	1.24970i
$503$	−10.0000	+	17.3205i	−0.445878	+	0.772283i	−0.998113	−	0.0614052i	$-0.980442\pi$
$503$	−10.0000	+	17.3205i	−0.445878	+	0.772283i	0.552235	+	0.833689i	$0.313775\pi$
$504$		0			0
$505$	5.19615	−	3.00000i	0.231226	−	0.133498i
$506$		0			0
$507$		0			0
$508$	−20.0000			−0.887357
$509$	15.5885	−	9.00000i	0.690946	−	0.398918i	−0.113020	−	0.993593i	$-0.536052\pi$
$509$	15.5885	−	9.00000i	0.690946	−	0.398918i	0.803966	+	0.594675i	$0.202719\pi$
$510$		0			0
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−1.73205	−	1.00000i	−0.0763975	−	0.0441081i
$515$		−	4.00000i		−	0.176261i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	26.0000			1.13908			0.569540	−	0.821963i	$-0.307121\pi$
$521$	26.0000			1.13908			0.569540	+	0.821963i	$0.307121\pi$
$522$	−5.19615	+	3.00000i	−0.227429	+	0.131306i
$523$	4.00000	+	6.92820i	0.174908	+	0.302949i	0.940129	−	0.340818i	$-0.110704\pi$
$523$	4.00000	+	6.92820i	0.174908	+	0.302949i	−0.765222	+	0.643767i	$0.777371\pi$
$524$	2.00000	−	3.46410i	0.0873704	−	0.151330i
$525$		0			0
$526$	−24.2487	−	14.0000i	−1.05729	−	0.610429i
$527$	6.92820	+	4.00000i	0.301797	+	0.174243i
$528$		0			0
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$	3.00000	+	5.19615i	0.130312	+	0.225706i
$531$	−20.7846	+	12.0000i	−0.901975	+	0.520756i
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	−2.00000	−	3.46410i	−0.0863868	−	0.149626i
$537$		0			0
$538$			18.0000i			0.776035i
$539$		0			0
$540$		0			0
$541$		−	2.00000i		−	0.0859867i	−0.999075	−	0.0429934i	$-0.986311\pi$
$541$		−	2.00000i		−	0.0859867i	0.999075	−	0.0429934i	$-0.0136894\pi$
$542$	14.0000	−	24.2487i	0.601351	−	1.04157i
$543$		0			0
$544$	1.73205	−	1.00000i	0.0742611	−	0.0428746i
$545$	2.00000			0.0856706
$546$		0			0
$547$	−40.0000			−1.71028			−0.855138	−	0.518400i	$-0.826528\pi$
$547$	−40.0000			−1.71028			−0.855138	+	0.518400i	$0.826528\pi$
$548$	5.19615	−	3.00000i	0.221969	−	0.128154i
$549$	−3.00000	−	5.19615i	−0.128037	−	0.221766i
$550$		0			0
$551$		−	16.0000i		−	0.681623i
$552$		0			0
$553$		0			0
$554$			22.0000i			0.934690i
$555$		0			0
$556$	2.00000	+	3.46410i	0.0848189	+	0.146911i
$557$	12.1244	−	7.00000i	0.513725	−	0.296600i	−0.220638	−	0.975356i	$-0.570814\pi$
$557$	12.1244	−	7.00000i	0.513725	−	0.296600i	0.734364	+	0.678756i	$0.237481\pi$
$558$	−12.0000			−0.508001
$559$		0			0
$560$		0			0
$561$		0			0
$562$	11.0000	+	19.0526i	0.464007	+	0.803684i
$563$	12.0000	−	20.7846i	0.505740	−	0.875967i	−0.494238	−	0.869326i	$-0.664553\pi$
$563$	12.0000	−	20.7846i	0.505740	−	0.875967i	0.999978	−	0.00664037i	$-0.00211371\pi$
$564$		0			0
$565$	−12.1244	−	7.00000i	−0.510075	−	0.294492i
$566$	−13.8564	−	8.00000i	−0.582428	−	0.336265i
$567$		0			0
$568$	6.00000	−	10.3923i	0.251754	−	0.436051i
$569$	5.00000	+	8.66025i	0.209611	+	0.363057i	0.951592	−	0.307364i	$-0.0994469\pi$
$569$	5.00000	+	8.66025i	0.209611	+	0.363057i	−0.741981	+	0.670421i	$0.766114\pi$
$570$		0			0
$571$	28.0000			1.17176			0.585882	−	0.810397i	$-0.300748\pi$
$571$	28.0000			1.17176			0.585882	+	0.810397i	$0.300748\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	2.00000	+	3.46410i	0.0834058	+	0.144463i
$576$	−1.50000	+	2.59808i	−0.0625000	+	0.108253i
$577$		−	2.00000i		−	0.0832611i	−0.999133	−	0.0416305i	$-0.986745\pi$
$577$		−	2.00000i		−	0.0832611i	0.999133	−	0.0416305i	$-0.0132552\pi$
$578$	−11.2583	−	6.50000i	−0.468285	−	0.270364i
$579$		0			0
$580$		−	2.00000i		−	0.0830455i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−10.0000			−0.413803
$585$		0			0
$586$	6.00000			0.247858
$587$	17.3205	−	10.0000i	0.714894	−	0.412744i	−0.0979766	−	0.995189i	$-0.531237\pi$
$587$	17.3205	−	10.0000i	0.714894	−	0.412744i	0.812870	+	0.582445i	$0.197904\pi$
$588$		0			0
$589$	16.0000	−	27.7128i	0.659269	−	1.14189i
$590$		−	8.00000i		−	0.329355i
$591$		0			0
$592$	−5.19615	−	3.00000i	−0.213561	−	0.123299i
$593$			2.00000i			0.0821302i	0.999156	+	0.0410651i	$0.0130751\pi$
$593$			2.00000i			0.0821302i	−0.999156	+	0.0410651i	$0.986925\pi$
$594$		0			0
$595$		0			0
$596$	5.19615	−	3.00000i	0.212843	−	0.122885i
$597$		0			0
$598$		0			0
$599$	32.0000			1.30748			0.653742	−	0.756717i	$-0.273198\pi$
$599$	32.0000			1.30748			0.653742	+	0.756717i	$0.273198\pi$
$600$		0			0
$601$	−13.0000	−	22.5167i	−0.530281	−	0.918474i	−0.999376	−	0.0353259i	$-0.988753\pi$
$601$	−13.0000	−	22.5167i	−0.530281	−	0.918474i	0.469095	−	0.883148i	$-0.344580\pi$
$602$		0			0
$603$			12.0000i			0.488678i
$604$	−17.3205	−	10.0000i	−0.704761	−	0.406894i
$605$	9.52628	+	5.50000i	0.387298	+	0.223607i
$606$		0			0
$607$	−18.0000	+	31.1769i	−0.730597	+	1.26543i	0.226031	+	0.974120i	$0.427425\pi$
$607$	−18.0000	+	31.1769i	−0.730597	+	1.26543i	−0.956628	+	0.291312i	$0.905908\pi$
$608$	−4.00000	−	6.92820i	−0.162221	−	0.280976i
$609$		0			0
$610$	2.00000			0.0809776
$611$		0			0
$612$	−6.00000			−0.242536
$613$	−32.9090	+	19.0000i	−1.32918	+	0.767403i	−0.985173	−	0.171564i	$-0.945118\pi$
$613$	−32.9090	+	19.0000i	−1.32918	+	0.767403i	−0.344008	+	0.938967i	$0.611785\pi$
$614$	−14.0000	−	24.2487i	−0.564994	−	0.978598i
$615$		0			0
$616$		0			0
$617$	22.5167	+	13.0000i	0.906487	+	0.523360i	0.879299	−	0.476270i	$-0.158012\pi$
$617$	22.5167	+	13.0000i	0.906487	+	0.523360i	0.0271876	+	0.999630i	$0.491345\pi$
$618$		0			0
$619$		−	24.0000i		−	0.964641i	−0.875995	−	0.482321i	$-0.839794\pi$
$619$		−	24.0000i		−	0.964641i	0.875995	−	0.482321i	$-0.160206\pi$
$620$	2.00000	−	3.46410i	0.0803219	−	0.139122i
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	1.00000			0.0400000
$626$	5.19615	−	3.00000i	0.207680	−	0.119904i
$627$		0			0
$628$	−9.00000	+	15.5885i	−0.359139	+	0.622047i
$629$		−	12.0000i		−	0.478471i
$630$		0			0
$631$	−10.3923	−	6.00000i	−0.413711	−	0.238856i	0.278672	−	0.960386i	$-0.410106\pi$
$631$	−10.3923	−	6.00000i	−0.413711	−	0.238856i	−0.692383	+	0.721530i	$0.743439\pi$
$632$		−	8.00000i		−	0.318223i
$633$		0			0
$634$	−1.00000	−	1.73205i	−0.0397151	−	0.0687885i
$635$	−17.3205	+	10.0000i	−0.687343	+	0.396838i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−31.1769	+	18.0000i	−1.23334	+	0.712069i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	−15.0000	+	25.9808i	−0.592464	+	1.02618i	0.401435	+	0.915888i	$0.368512\pi$
$641$	−15.0000	+	25.9808i	−0.592464	+	1.02618i	−0.993899	+	0.110291i	$0.964822\pi$
$642$		0			0
$643$	24.2487	+	14.0000i	0.956276	+	0.552106i	0.895025	−	0.446016i	$-0.147158\pi$
$643$	24.2487	+	14.0000i	0.956276	+	0.552106i	0.0612510	+	0.998122i	$0.480491\pi$
$644$		0			0
$645$		0			0
$646$	8.00000	−	13.8564i	0.314756	−	0.545173i
$647$	−14.0000	−	24.2487i	−0.550397	−	0.953315i	−0.998246	−	0.0592060i	$-0.981143\pi$
$647$	−14.0000	−	24.2487i	−0.550397	−	0.953315i	0.447849	−	0.894109i	$-0.352190\pi$
$648$	7.79423	−	4.50000i	0.306186	−	0.176777i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−17.3205	+	10.0000i	−0.678323	+	0.391630i
$653$	−23.0000	−	39.8372i	−0.900060	−	1.55895i	−0.827415	−	0.561591i	$-0.810189\pi$
$653$	−23.0000	−	39.8372i	−0.900060	−	1.55895i	−0.0726446	−	0.997358i	$-0.523144\pi$
$654$		0			0
$655$		−	4.00000i		−	0.156293i
$656$	8.66025	+	5.00000i	0.338126	+	0.195217i
$657$	25.9808	+	15.0000i	1.01361	+	0.585206i
$658$		0			0
$659$	18.0000	−	31.1769i	0.701180	−	1.21448i	−0.266872	−	0.963732i	$-0.585990\pi$
$659$	18.0000	−	31.1769i	0.701180	−	1.21448i	0.968052	−	0.250748i	$-0.0806766\pi$
$660$		0			0
$661$	19.0526	−	11.0000i	0.741059	−	0.427850i	−0.0813955	−	0.996682i	$-0.525938\pi$
$661$	19.0526	−	11.0000i	0.741059	−	0.427850i	0.822454	+	0.568831i	$0.192604\pi$
$662$	8.00000			0.310929
$663$		0			0
$664$	12.0000			0.465690
$665$		0			0
$666$	9.00000	+	15.5885i	0.348743	+	0.604040i
$667$	4.00000	−	6.92820i	0.154881	−	0.268261i
$668$		−	16.0000i		−	0.619059i
$669$		0			0
$670$	−3.46410	−	2.00000i	−0.133830	−	0.0772667i
$671$		0			0
$672$		0			0
$673$	−7.00000	−	12.1244i	−0.269830	−	0.467360i	0.698988	−	0.715134i	$-0.253634\pi$
$673$	−7.00000	−	12.1244i	−0.269830	−	0.467360i	−0.968818	+	0.247774i	$0.920301\pi$
$674$	15.5885	−	9.00000i	0.600445	−	0.346667i
$675$		0			0
$676$		0			0
$677$	22.0000			0.845529			0.422764	−	0.906240i	$-0.361060\pi$
$677$	22.0000			0.845529			0.422764	+	0.906240i	$0.361060\pi$
$678$		0			0
$679$		0			0
$680$	1.00000	−	1.73205i	0.0383482	−	0.0664211i
$681$		0			0
$682$		0			0
$683$	−24.2487	−	14.0000i	−0.927851	−	0.535695i	−0.0417198	−	0.999129i	$-0.513284\pi$
$683$	−24.2487	−	14.0000i	−0.927851	−	0.535695i	−0.886131	+	0.463434i	$0.846617\pi$
$684$			24.0000i			0.917663i
$685$	3.00000	−	5.19615i	0.114624	−	0.198535i
$686$		0			0
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−27.7128	+	16.0000i	−1.05425	+	0.608669i	−0.923835	−	0.382791i	$-0.874963\pi$
$691$	−27.7128	+	16.0000i	−1.05425	+	0.608669i	−0.130410	+	0.991460i	$0.541629\pi$
$692$	9.00000	+	15.5885i	0.342129	+	0.592584i
$693$		0			0
$694$		−	32.0000i		−	1.21470i
$695$	3.46410	+	2.00000i	0.131401	+	0.0758643i
$696$		0			0
$697$			20.0000i			0.757554i
$698$	−7.00000	+	12.1244i	−0.264954	+	0.458914i
$699$		0			0
$700$		0			0
$701$	34.0000			1.28416			0.642081	−	0.766637i	$-0.278071\pi$
$701$	34.0000			1.28416			0.642081	+	0.766637i	$0.278071\pi$
$702$		0			0
$703$	−48.0000			−1.81035
$704$		0			0
$705$		0			0
$706$	−15.0000	+	25.9808i	−0.564532	+	0.977799i
$707$		0			0
$708$		0			0
$709$	8.66025	+	5.00000i	0.325243	+	0.187779i	0.653727	−	0.756730i	$-0.273204\pi$
$709$	8.66025	+	5.00000i	0.325243	+	0.187779i	−0.328484	+	0.944509i	$0.606538\pi$
$710$		−	12.0000i		−	0.450352i
$711$	−12.0000	+	20.7846i	−0.450035	+	0.779484i
$712$	5.00000	+	8.66025i	0.187383	+	0.324557i
$713$	13.8564	−	8.00000i	0.518927	−	0.299602i
$714$		0			0
$715$		0			0
$716$	4.00000			0.149487
$717$		0			0
$718$	−2.00000	−	3.46410i	−0.0746393	−	0.129279i
$719$	8.00000	−	13.8564i	0.298350	−	0.516757i	−0.677409	−	0.735607i	$-0.736897\pi$
$719$	8.00000	−	13.8564i	0.298350	−	0.516757i	0.975759	+	0.218850i	$0.0702305\pi$
$720$			3.00000i			0.111803i
$721$		0			0
$722$	−38.9711	−	22.5000i	−1.45036	−	0.837363i
$723$		0			0
$724$	−11.0000	+	19.0526i	−0.408812	+	0.708083i
$725$	−1.00000	−	1.73205i	−0.0371391	−	0.0643268i
$726$		0			0
$727$	28.0000			1.03846			0.519231	−	0.854634i	$-0.326218\pi$
$727$	28.0000			1.03846			0.519231	+	0.854634i	$0.326218\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	−8.66025	+	5.00000i	−0.320530	+	0.185058i
$731$		0			0
$732$		0			0
$733$			34.0000i			1.25582i	0.778287	+	0.627909i	$0.216089\pi$
$733$			34.0000i			1.25582i	−0.778287	+	0.627909i	$0.783911\pi$
$734$	−10.3923	−	6.00000i	−0.383587	−	0.221464i
$735$		0			0
$736$		−	4.00000i		−	0.147442i
$737$		0			0
$738$	−15.0000	−	25.9808i	−0.552158	−	0.956365i
$739$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$739$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$740$	−6.00000			−0.220564
$741$		0			0
$742$		0			0
$743$	−13.8564	+	8.00000i	−0.508342	+	0.293492i	−0.732152	−	0.681141i	$-0.761484\pi$
$743$	−13.8564	+	8.00000i	−0.508342	+	0.293492i	0.223810	+	0.974633i	$0.428151\pi$
$744$		0			0
$745$	3.00000	−	5.19615i	0.109911	−	0.190372i
$746$		−	6.00000i		−	0.219676i
$747$	−31.1769	−	18.0000i	−1.14070	−	0.658586i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−20.0000	−	34.6410i	−0.729810	−	1.26407i	−0.956963	−	0.290209i	$-0.906275\pi$
$751$	−20.0000	−	34.6410i	−0.729810	−	1.26407i	0.227153	−	0.973859i	$-0.427058\pi$
$752$	6.92820	−	4.00000i	0.252646	−	0.145865i
$753$		0			0
$754$		0			0
$755$	−20.0000			−0.727875
$756$		0			0
$757$	−11.0000	−	19.0526i	−0.399802	−	0.692477i	0.593899	−	0.804539i	$-0.297588\pi$
$757$	−11.0000	−	19.0526i	−0.399802	−	0.692477i	−0.993701	+	0.112062i	$0.964254\pi$
$758$		0			0
$759$		0			0
$760$	−6.92820	−	4.00000i	−0.251312	−	0.145095i
$761$	5.19615	+	3.00000i	0.188360	+	0.108750i	0.591215	−	0.806514i	$-0.298649\pi$
$761$	5.19615	+	3.00000i	0.188360	+	0.108750i	−0.402854	+	0.915264i	$0.631982\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−5.19615	+	3.00000i	−0.187867	+	0.108465i
$766$	−8.00000			−0.289052
$767$		0			0
$768$		0			0
$769$	12.1244	−	7.00000i	0.437215	−	0.252426i	−0.265200	−	0.964193i	$-0.585438\pi$
$769$	12.1244	−	7.00000i	0.437215	−	0.252426i	0.702416	+	0.711767i	$0.252105\pi$
$770$		0			0
$771$		0			0
$772$		−	18.0000i		−	0.647834i
$773$	−22.5167	−	13.0000i	−0.809868	−	0.467578i	0.0370420	−	0.999314i	$-0.488206\pi$
$773$	−22.5167	−	13.0000i	−0.809868	−	0.467578i	−0.846910	+	0.531736i	$0.821540\pi$
$774$		0			0
$775$		−	4.00000i		−	0.143684i
$776$	7.00000	−	12.1244i	0.251285	−	0.435239i
$777$		0			0
$778$	5.19615	−	3.00000i	0.186291	−	0.107555i
$779$	80.0000			2.86630
$780$		0			0
$781$		0			0
$782$	6.92820	−	4.00000i	0.247752	−	0.143040i
$783$		0			0
$784$	−3.50000	+	6.06218i	−0.125000	+	0.216506i
$785$			18.0000i			0.642448i
$786$		0			0
$787$	3.46410	+	2.00000i	0.123482	+	0.0712923i	0.560469	−	0.828176i	$-0.310621\pi$
$787$	3.46410	+	2.00000i	0.123482	+	0.0712923i	−0.436987	+	0.899468i	$0.643954\pi$
$788$		−	26.0000i		−	0.926212i
$789$		0			0
$790$	−4.00000	−	6.92820i	−0.142314	−	0.246494i
$791$		0			0
$792$		0			0
$793$		0			0
$794$	−18.0000			−0.638796
$795$		0			0
$796$	−12.0000	−	20.7846i	−0.425329	−	0.736691i
$797$	−17.0000	+	29.4449i	−0.602171	+	1.04299i	0.390321	+	0.920679i	$0.372364\pi$
$797$	−17.0000	+	29.4449i	−0.602171	+	1.04299i	−0.992492	+	0.122312i	$0.960969\pi$
$798$		0			0
$799$	13.8564	+	8.00000i	0.490204	+	0.283020i
$800$	−0.866025	−	0.500000i	−0.0306186	−	0.0176777i
$801$		−	30.0000i		−	1.06000i
$802$	15.0000	−	25.9808i	0.529668	−	0.917413i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−5.19615	+	3.00000i	−0.182800	+	0.105540i
$809$	−13.0000	−	22.5167i	−0.457056	−	0.791644i	0.541748	−	0.840541i	$-0.317763\pi$
$809$	−13.0000	−	22.5167i	−0.457056	−	0.791644i	−0.998804	+	0.0488972i	$0.984429\pi$
$810$	4.50000	−	7.79423i	0.158114	−	0.273861i
$811$		−	24.0000i		−	0.842754i	−0.906886	−	0.421377i	$-0.861547\pi$
$811$		−	24.0000i		−	0.842754i	0.906886	−	0.421377i	$-0.138453\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−10.0000	+	17.3205i	−0.350285	+	0.606711i
$816$		0			0
$817$		0			0
$818$	−26.0000			−0.909069
$819$		0			0
$820$	10.0000			0.349215
$821$	36.3731	−	21.0000i	1.26943	−	0.732905i	0.294549	−	0.955636i	$-0.404831\pi$
$821$	36.3731	−	21.0000i	1.26943	−	0.732905i	0.974880	+	0.222731i	$0.0714973\pi$
$822$		0			0
$823$	−2.00000	+	3.46410i	−0.0697156	+	0.120751i	−0.898776	−	0.438408i	$-0.855543\pi$
$823$	−2.00000	+	3.46410i	−0.0697156	+	0.120751i	0.829060	+	0.559159i	$0.188876\pi$
$824$			4.00000i			0.139347i
$825$		0			0
$826$		0			0
$827$			36.0000i			1.25184i	0.779886	+	0.625921i	$0.215277\pi$
$827$			36.0000i			1.25184i	−0.779886	+	0.625921i	$0.784723\pi$
$828$	−6.00000	+	10.3923i	−0.208514	+	0.361158i
$829$	−17.0000	−	29.4449i	−0.590434	−	1.02266i	−0.994174	−	0.107788i	$-0.965623\pi$
$829$	−17.0000	−	29.4449i	−0.590434	−	1.02266i	0.403739	−	0.914874i	$-0.367710\pi$
$830$	10.3923	−	6.00000i	0.360722	−	0.208263i
$831$		0			0
$832$		0			0
$833$	−14.0000			−0.485071
$834$		0			0
$835$	−8.00000	−	13.8564i	−0.276851	−	0.479521i
$836$		0			0
$837$		0			0
$838$	−31.1769	−	18.0000i	−1.07699	−	0.621800i
$839$	−3.46410	−	2.00000i	−0.119594	−	0.0690477i	0.439010	−	0.898482i	$-0.355329\pi$
$839$	−3.46410	−	2.00000i	−0.119594	−	0.0690477i	−0.558604	+	0.829435i	$0.688663\pi$
$840$		0			0
$841$	12.5000	−	21.6506i	0.431034	−	0.746574i
$842$	−13.0000	−	22.5167i	−0.448010	−	0.775975i
$843$		0			0
$844$	−4.00000			−0.137686
$845$		0			0
$846$	−24.0000			−0.825137
$847$		0			0
$848$	−3.00000	−	5.19615i	−0.103020	−	0.178437i
$849$		0			0
$850$		−	2.00000i		−	0.0685994i
$851$	−20.7846	−	12.0000i	−0.712487	−	0.411355i
$852$		0			0
$853$			22.0000i			0.753266i	0.926363	+	0.376633i	$0.122918\pi$
$853$			22.0000i			0.753266i	−0.926363	+	0.376633i	$0.877082\pi$
$854$		0			0
$855$	12.0000	+	20.7846i	0.410391	+	0.710819i
$856$		0			0
$857$	6.00000			0.204956			0.102478	−	0.994735i	$-0.467323\pi$
$857$	6.00000			0.204956			0.102478	+	0.994735i	$0.467323\pi$
$858$		0			0
$859$	−28.0000			−0.955348			−0.477674	−	0.878537i	$-0.658520\pi$
$859$	−28.0000			−0.955348			−0.477674	+	0.878537i	$0.658520\pi$
$860$		0			0
$861$		0			0
$862$	6.00000	−	10.3923i	0.204361	−	0.353963i
$863$		−	40.0000i		−	1.36162i	−0.732462	−	0.680808i	$-0.761629\pi$
$863$		−	40.0000i		−	1.36162i	0.732462	−	0.680808i	$-0.238371\pi$
$864$		0			0
$865$	15.5885	+	9.00000i	0.530023	+	0.306009i
$866$			34.0000i			1.15537i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−2.00000			−0.0677285
$873$	−36.3731	+	21.0000i	−1.23104	+	0.710742i
$874$	−16.0000	−	27.7128i	−0.541208	−	0.937400i
$875$		0			0
$876$		0			0
$877$	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	$0.590708\pi$
$878$	20.7846	+	12.0000i	0.701447	+	0.404980i
$879$		0			0
$880$		0			0
$881$	1.00000	+	1.73205i	0.0336909	+	0.0583543i	0.882379	−	0.470539i	$-0.155941\pi$
$881$	1.00000	+	1.73205i	0.0336909	+	0.0583543i	−0.848688	+	0.528893i	$0.822607\pi$
$882$	18.1865	−	10.5000i	0.612372	−	0.353553i
$883$	8.00000			0.269221			0.134611	−	0.990899i	$-0.457022\pi$
$883$	8.00000			0.269221			0.134611	+	0.990899i	$0.457022\pi$
$884$		0			0
$885$		0			0
$886$	−20.7846	+	12.0000i	−0.698273	+	0.403148i
$887$	−22.0000	−	38.1051i	−0.738688	−	1.27944i	−0.953086	−	0.302698i	$-0.902113\pi$
$887$	−22.0000	−	38.1051i	−0.738688	−	1.27944i	0.214399	−	0.976746i	$-0.431221\pi$
$888$		0			0
$889$		0			0
$890$	8.66025	+	5.00000i	0.290292	+	0.167600i
$891$		0			0
$892$		−	8.00000i		−	0.267860i
$893$	32.0000	−	55.4256i	1.07084	−	1.85475i
$894$		0			0
$895$	3.46410	−	2.00000i	0.115792	−	0.0668526i
$896$		0			0
$897$		0			0
$898$	18.0000			0.600668
$899$	−6.92820	+	4.00000i	−0.231069	+	0.133407i
$900$	1.50000	+	2.59808i	0.0500000	+	0.0866025i
$901$	6.00000	−	10.3923i	0.199889	−	0.346218i
$902$		0			0
$903$		0			0
$904$	12.1244	+	7.00000i	0.403250	+	0.232817i
$905$			22.0000i			0.731305i
$906$		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	$0.790931\pi$
$908$	17.3205	−	10.0000i	0.574801	−	0.331862i
$909$	18.0000			0.597022
$910$		0			0
$911$	48.0000			1.59031			0.795155	−	0.606406i	$-0.207389\pi$
$911$	48.0000			1.59031			0.795155	+	0.606406i	$0.207389\pi$
$912$		0			0
$913$		0			0
$914$	−19.0000	+	32.9090i	−0.628464	+	1.08853i
$915$		0			0
$916$	−8.66025	−	5.00000i	−0.286143	−	0.165205i
$917$		0			0
$918$		0			0
$919$	−16.0000	+	27.7128i	−0.527791	+	0.914161i	0.471684	+	0.881768i	$0.343646\pi$
$919$	−16.0000	+	27.7128i	−0.527791	+	0.914161i	−0.999475	+	0.0323936i	$0.989687\pi$
$920$	−2.00000	−	3.46410i	−0.0659380	−	0.114208i
$921$		0			0
$922$	−14.0000			−0.461065
$923$		0			0
$924$		0			0
$925$	−5.19615	+	3.00000i	−0.170848	+	0.0986394i
$926$	8.00000	+	13.8564i	0.262896	+	0.455350i
$927$	6.00000	−	10.3923i	0.197066	−	0.341328i
$928$			2.00000i			0.0656532i
$929$	−12.1244	−	7.00000i	−0.397787	−	0.229663i	0.287742	−	0.957708i	$-0.407096\pi$
$929$	−12.1244	−	7.00000i	−0.397787	−	0.229663i	−0.685529	+	0.728046i	$0.740429\pi$
$930$		0			0
$931$			56.0000i			1.83533i
$932$	3.00000	−	5.19615i	0.0982683	−	0.170206i
$933$		0			0
$934$	−13.8564	+	8.00000i	−0.453395	+	0.261768i
$935$		0			0
$936$		0			0
$937$	26.0000			0.849383			0.424691	−	0.905338i	$-0.360383\pi$
$937$	26.0000			0.849383			0.424691	+	0.905338i	$0.360383\pi$
$938$		0			0
$939$		0			0
$940$	4.00000	−	6.92820i	0.130466	−	0.225973i
$941$		−	30.0000i		−	0.977972i	−0.872292	−	0.488986i	$-0.837367\pi$
$941$		−	30.0000i		−	0.977972i	0.872292	−	0.488986i	$-0.162633\pi$
$942$		0			0
$943$	34.6410	+	20.0000i	1.12807	+	0.651290i
$944$			8.00000i			0.260378i
$945$		0			0
$946$		0			0
$947$	−3.46410	+	2.00000i	−0.112568	+	0.0649913i	−0.555227	−	0.831699i	$-0.687369\pi$
$947$	−3.46410	+	2.00000i	−0.112568	+	0.0649913i	0.442659	+	0.896690i	$0.354035\pi$
$948$		0			0
$949$		0			0
$950$	−8.00000			−0.259554
$951$		0			0
$952$		0			0
$953$	13.0000	−	22.5167i	0.421111	−	0.729386i	−0.574937	−	0.818198i	$-0.694974\pi$
$953$	13.0000	−	22.5167i	0.421111	−	0.729386i	0.996048	+	0.0888114i	$0.0283068\pi$
$954$			18.0000i			0.582772i
$955$		0			0
$956$	−17.3205	−	10.0000i	−0.560185	−	0.323423i
$957$		0			0
$958$	2.00000	−	3.46410i	0.0646171	−	0.111920i
$959$		0			0
$960$		0			0
$961$	15.0000			0.483871
$962$		0			0
$963$		0			0
$964$	−1.73205	+	1.00000i	−0.0557856	+	0.0322078i
$965$	−9.00000	−	15.5885i	−0.289720	−	0.501810i
$966$		0			0
$967$		−	24.0000i		−	0.771788i	−0.922543	−	0.385894i	$-0.873893\pi$
$967$		−	24.0000i		−	0.771788i	0.922543	−	0.385894i	$-0.126107\pi$
$968$	−9.52628	−	5.50000i	−0.306186	−	0.176777i
$969$		0			0
$970$		−	14.0000i		−	0.449513i
$971$	2.00000	−	3.46410i	0.0641831	−	0.111168i	−0.832148	−	0.554553i	$-0.812889\pi$
$971$	2.00000	−	3.46410i	0.0641831	−	0.111168i	0.896331	+	0.443385i	$0.146223\pi$
$972$		0			0
$973$		0			0
$974$	8.00000			0.256337
$975$		0			0
$976$	−2.00000			−0.0640184
$977$	−15.5885	+	9.00000i	−0.498719	+	0.287936i	−0.728184	−	0.685381i	$-0.759636\pi$
$977$	−15.5885	+	9.00000i	−0.498719	+	0.287936i	0.229465	+	0.973317i	$0.426302\pi$
$978$		0			0
$979$		0			0
$980$			7.00000i			0.223607i
$981$	5.19615	+	3.00000i	0.165900	+	0.0957826i
$982$	−17.3205	−	10.0000i	−0.552720	−	0.319113i
$983$		−	24.0000i		−	0.765481i	−0.923856	−	0.382741i	$-0.874980\pi$
$983$		−	24.0000i		−	0.765481i	0.923856	−	0.382741i	$-0.125020\pi$
$984$		0			0
$985$	−13.0000	−	22.5167i	−0.414214	−	0.717440i
$986$	−3.46410	+	2.00000i	−0.110319	+	0.0636930i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−16.0000	−	27.7128i	−0.508257	−	0.880327i	−0.999954	−	0.00956046i	$-0.996957\pi$
$991$	−16.0000	−	27.7128i	−0.508257	−	0.880327i	0.491698	−	0.870766i	$-0.336377\pi$
$992$	−2.00000	+	3.46410i	−0.0635001	+	0.109985i
$993$		0			0
$994$		0			0
$995$	−20.7846	−	12.0000i	−0.658916	−	0.380426i
$996$		0			0
$997$	−11.0000	+	19.0526i	−0.348373	+	0.603401i	−0.985961	−	0.166978i	$-0.946599\pi$
$997$	−11.0000	+	19.0526i	−0.348373	+	0.603401i	0.637587	+	0.770378i	$0.279933\pi$
$998$	4.00000	+	6.92820i	0.126618	+	0.219308i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1690.2.l.f.361.1		4
13.2	odd	12		1690.2.a.b.1.1		1
13.3	even	3		1690.2.d.d.1351.1		2
13.4	even	6	inner	1690.2.l.f.1161.1		4
13.5	odd	4		1690.2.e.i.991.1		2
13.6	odd	12		1690.2.e.i.191.1		2
13.7	odd	12		1690.2.e.c.191.1		2
13.8	odd	4		1690.2.e.c.991.1		2
13.9	even	3	inner	1690.2.l.f.1161.2		4
13.10	even	6		1690.2.d.d.1351.2		2
13.11	odd	12		130.2.a.b.1.1	✓	1
13.12	even	2	inner	1690.2.l.f.361.2		4
39.11	even	12		1170.2.a.b.1.1		1
52.11	even	12		1040.2.a.e.1.1		1
65.24	odd	12		650.2.a.d.1.1		1
65.37	even	12		650.2.b.e.599.2		2
65.54	odd	12		8450.2.a.r.1.1		1
65.63	even	12		650.2.b.e.599.1		2
91.76	even	12		6370.2.a.r.1.1		1
104.11	even	12		4160.2.a.h.1.1		1
104.37	odd	12		4160.2.a.i.1.1		1
156.11	odd	12		9360.2.a.l.1.1		1
195.89	even	12		5850.2.a.bq.1.1		1
195.128	odd	12		5850.2.e.q.5149.2		2
195.167	odd	12		5850.2.e.q.5149.1		2
260.219	even	12		5200.2.a.r.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.a.b.1.1	✓	1	13.11	odd	12
650.2.a.d.1.1		1	65.24	odd	12
650.2.b.e.599.1		2	65.63	even	12
650.2.b.e.599.2		2	65.37	even	12
1040.2.a.e.1.1		1	52.11	even	12
1170.2.a.b.1.1		1	39.11	even	12
1690.2.a.b.1.1		1	13.2	odd	12
1690.2.d.d.1351.1		2	13.3	even	3
1690.2.d.d.1351.2		2	13.10	even	6
1690.2.e.c.191.1		2	13.7	odd	12
1690.2.e.c.991.1		2	13.8	odd	4
1690.2.e.i.191.1		2	13.6	odd	12
1690.2.e.i.991.1		2	13.5	odd	4
1690.2.l.f.361.1		4	1.1	even	1	trivial
1690.2.l.f.361.2		4	13.12	even	2	inner
1690.2.l.f.1161.1		4	13.4	even	6	inner
1690.2.l.f.1161.2		4	13.9	even	3	inner
4160.2.a.h.1.1		1	104.11	even	12
4160.2.a.i.1.1		1	104.37	odd	12
5200.2.a.r.1.1		1	260.219	even	12
5850.2.a.bq.1.1		1	195.89	even	12
5850.2.e.q.5149.1		2	195.167	odd	12
5850.2.e.q.5149.2		2	195.128	odd	12
6370.2.a.r.1.1		1	91.76	even	12
8450.2.a.r.1.1		1	65.54	odd	12
9360.2.a.l.1.1		1	156.11	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +1.00000i q^{8} +(1.50000 - 2.59808i) q^{9} +(0.500000 + 0.866025i) q^{10} +(-0.500000 - 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{17} +3.00000i q^{18} +(-6.92820 - 4.00000i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(-2.00000 - 3.46410i) q^{23} -1.00000 q^{25} +(1.00000 + 1.73205i) q^{29} +4.00000i q^{31} +(0.866025 + 0.500000i) q^{32} +2.00000i q^{34} +(-1.50000 - 2.59808i) q^{36} +(5.19615 - 3.00000i) q^{37} +8.00000 q^{38} +1.00000 q^{40} +(-8.66025 + 5.00000i) q^{41} +(-2.59808 - 1.50000i) q^{45} +(3.46410 + 2.00000i) q^{46} +8.00000i q^{47} +(-3.50000 - 6.06218i) q^{49} +(0.866025 - 0.500000i) q^{50} +6.00000 q^{53} +(-1.73205 - 1.00000i) q^{58} +(-6.92820 - 4.00000i) q^{59} +(1.00000 - 1.73205i) q^{61} +(-2.00000 - 3.46410i) q^{62} -1.00000 q^{64} +(-3.46410 + 2.00000i) q^{67} +(-1.00000 - 1.73205i) q^{68} +(-10.3923 - 6.00000i) q^{71} +(2.59808 + 1.50000i) q^{72} +10.0000i q^{73} +(-3.00000 + 5.19615i) q^{74} +(-6.92820 + 4.00000i) q^{76} -8.00000 q^{79} +(-0.866025 + 0.500000i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(5.00000 - 8.66025i) q^{82} -12.0000i q^{83} +(-1.73205 - 1.00000i) q^{85} +(8.66025 - 5.00000i) q^{89} +3.00000 q^{90} -4.00000 q^{92} +(-4.00000 - 6.92820i) q^{94} +(-4.00000 + 6.92820i) q^{95} +(-12.1244 - 7.00000i) q^{97} +(6.06218 + 3.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 6 q^{9} + 2 q^{10} - 2 q^{16} + 4 q^{17} - 8 q^{23} - 4 q^{25} + 4 q^{29} - 6 q^{36} + 32 q^{38} + 4 q^{40} - 14 q^{49} + 24 q^{53} + 4 q^{61} - 8 q^{62} - 4 q^{64} - 4 q^{68} - 12 q^{74}+ \cdots - 16 q^{95}+O(q^{100}) \) 4 * q + 2 * q^4 + 6 * q^9 + 2 * q^10 - 2 * q^16 + 4 * q^17 - 8 * q^23 - 4 * q^25 + 4 * q^29 - 6 * q^36 + 32 * q^38 + 4 * q^40 - 14 * q^49 + 24 * q^53 + 4 * q^61 - 8 * q^62 - 4 * q^64 - 4 * q^68 - 12 * q^74 - 32 * q^79 - 18 * q^81 + 20 * q^82 + 12 * q^90 - 16 * q^92 - 16 * q^94 - 16 * q^95

Introduction

L-functions

Modular forms

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Database

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