LMFDB - Embedded newform 1690.2.e.c.191.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1690,2,Mod(191,1690)] 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, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1690.191"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1690 = 2 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1690.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,-1,0,-1,2,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$13.4947179416$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			191.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1690.191
Dual form			1690.2.e.c.991.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-0.500000 + 0.866025i) q^{16} +(-1.00000 - 1.73205i) q^{17} -3.00000 q^{18} +(4.00000 + 6.92820i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(2.00000 - 3.46410i) q^{23} +1.00000 q^{25} +(1.00000 - 1.73205i) q^{29} -4.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +2.00000 q^{34} +(1.50000 - 2.59808i) q^{36} +(-3.00000 + 5.19615i) q^{37} -8.00000 q^{38} +1.00000 q^{40} +(-5.00000 + 8.66025i) q^{41} +(1.50000 + 2.59808i) q^{45} +(2.00000 + 3.46410i) q^{46} +8.00000 q^{47} +(3.50000 - 6.06218i) q^{49} +(-0.500000 + 0.866025i) q^{50} +6.00000 q^{53} +(1.00000 + 1.73205i) q^{58} +(-4.00000 - 6.92820i) q^{59} +(1.00000 + 1.73205i) q^{61} +(2.00000 - 3.46410i) q^{62} +1.00000 q^{64} +(-2.00000 + 3.46410i) q^{67} +(-1.00000 + 1.73205i) q^{68} +(6.00000 + 10.3923i) q^{71} +(1.50000 + 2.59808i) q^{72} +10.0000 q^{73} +(-3.00000 - 5.19615i) q^{74} +(4.00000 - 6.92820i) q^{76} -8.00000 q^{79} +(-0.500000 + 0.866025i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-5.00000 - 8.66025i) q^{82} +12.0000 q^{83} +(-1.00000 - 1.73205i) q^{85} +(-5.00000 + 8.66025i) q^{89} -3.00000 q^{90} -4.00000 q^{92} +(-4.00000 + 6.92820i) q^{94} +(4.00000 + 6.92820i) q^{95} +(7.00000 + 12.1244i) q^{97} +(3.50000 + 6.06218i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} + 2 q^{5} + 2 q^{8} + 3 q^{9} - q^{10} - q^{16} - 2 q^{17} - 6 q^{18} + 8 q^{19} - q^{20} + 4 q^{23} + 2 q^{25} + 2 q^{29} - 8 q^{31} - q^{32} + 4 q^{34} + 3 q^{36} - 6 q^{37}+ \cdots + 7 q^{98}+O(q^{100}) $ 2 * q - q^2 - q^4 + 2 * q^5 + 2 * q^8 + 3 * q^9 - q^10 - q^16 - 2 * q^17 - 6 * q^18 + 8 * q^19 - q^20 + 4 * q^23 + 2 * q^25 + 2 * q^29 - 8 * q^31 - q^32 + 4 * q^34 + 3 * q^36 - 6 * q^37 - 16 * q^38 + 2 * q^40 - 10 * q^41 + 3 * q^45 + 4 * q^46 + 16 * q^47 + 7 * q^49 - q^50 + 12 * q^53 + 2 * q^58 - 8 * q^59 + 2 * q^61 + 4 * q^62 + 2 * q^64 - 4 * q^67 - 2 * q^68 + 12 * q^71 + 3 * q^72 + 20 * q^73 - 6 * q^74 + 8 * q^76 - 16 * q^79 - q^80 - 9 * q^81 - 10 * q^82 + 24 * q^83 - 2 * q^85 - 10 * q^89 - 6 * q^90 - 8 * q^92 - 8 * q^94 + 8 * q^95 + 14 * q^97 + 7 * q^98

Character values

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

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$3$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$7$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$8$	1.00000			0.353553
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$11$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$12$		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	$-0.244646\pi$
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	−0.961436	+	0.275029i	$0.911312\pi$
$18$	−3.00000			−0.707107
$19$	4.00000	+	6.92820i	0.917663	+	1.58944i	0.802955	+	0.596040i	$0.203260\pi$
$19$	4.00000	+	6.92820i	0.917663	+	1.58944i	0.114708	+	0.993399i	$0.463407\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$		0			0
$22$		0			0
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	−0.578610	−	0.815604i	$-0.696405\pi$
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	0.995639	+	0.0932891i	$0.0297381\pi$
$24$		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	−0.758115	−	0.652121i	$-0.773880\pi$
$29$	1.00000	−	1.73205i	0.185695	−	0.321634i	0.943811	+	0.330487i	$0.107213\pi$
$30$		0			0
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	2.00000			0.342997
$35$		0			0
$36$	1.50000	−	2.59808i	0.250000	−	0.433013i
$37$	−3.00000	+	5.19615i	−0.493197	+	0.854242i	−0.999969	−	0.00783774i	$-0.997505\pi$
$37$	−3.00000	+	5.19615i	−0.493197	+	0.854242i	0.506772	+	0.862080i	$0.330838\pi$
$38$	−8.00000			−1.29777
$39$		0			0
$40$	1.00000			0.158114
$41$	−5.00000	+	8.66025i	−0.780869	+	1.35250i	0.150567	+	0.988600i	$0.451890\pi$
$41$	−5.00000	+	8.66025i	−0.780869	+	1.35250i	−0.931436	+	0.363905i	$0.881443\pi$
$42$		0			0
$43$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$43$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$44$		0			0
$45$	1.50000	+	2.59808i	0.223607	+	0.387298i
$46$	2.00000	+	3.46410i	0.294884	+	0.510754i
$47$	8.00000			1.16692			0.583460	−	0.812142i	$-0.301699\pi$
$47$	8.00000			1.16692			0.583460	+	0.812142i	$0.301699\pi$
$48$		0			0
$49$	3.50000	−	6.06218i	0.500000	−	0.866025i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$		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
$58$	1.00000	+	1.73205i	0.131306	+	0.227429i
$59$	−4.00000	−	6.92820i	−0.520756	−	0.901975i	−0.999709	−	0.0241347i	$-0.992317\pi$
$59$	−4.00000	−	6.92820i	−0.520756	−	0.901975i	0.478953	−	0.877841i	$-0.341016\pi$
$60$		0			0
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	0.922916	−	0.385002i	$-0.125799\pi$
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	−0.794879	+	0.606768i	$0.792466\pi$
$62$	2.00000	−	3.46410i	0.254000	−	0.439941i
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	−0.961946	−	0.273241i	$-0.911904\pi$
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	0.717607	+	0.696449i	$0.245238\pi$
$68$	−1.00000	+	1.73205i	−0.121268	+	0.210042i
$69$		0			0
$70$		0			0
$71$	6.00000	+	10.3923i	0.712069	+	1.23334i	0.964079	+	0.265615i	$0.0855750\pi$
$71$	6.00000	+	10.3923i	0.712069	+	1.23334i	−0.252010	+	0.967725i	$0.581092\pi$
$72$	1.50000	+	2.59808i	0.176777	+	0.306186i
$73$	10.0000			1.17041			0.585206	−	0.810885i	$-0.301014\pi$
$73$	10.0000			1.17041			0.585206	+	0.810885i	$0.301014\pi$
$74$	−3.00000	−	5.19615i	−0.348743	−	0.604040i
$75$		0			0
$76$	4.00000	−	6.92820i	0.458831	−	0.794719i
$77$		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	$0.648589\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	−5.00000	−	8.66025i	−0.552158	−	0.956365i
$83$	12.0000			1.31717			0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000			1.31717			0.658586	+	0.752506i	$0.271155\pi$
$84$		0			0
$85$	−1.00000	−	1.73205i	−0.108465	−	0.187867i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−5.00000	+	8.66025i	−0.529999	+	0.917985i	0.469389	+	0.882992i	$0.344474\pi$
$89$	−5.00000	+	8.66025i	−0.529999	+	0.917985i	−0.999388	+	0.0349934i	$0.988859\pi$
$90$	−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
$97$	7.00000	+	12.1244i	0.710742	+	1.23104i	0.964579	+	0.263795i	$0.0849741\pi$
$97$	7.00000	+	12.1244i	0.710742	+	1.23104i	−0.253837	+	0.967247i	$0.581693\pi$
$98$	3.50000	+	6.06218i	0.353553	+	0.612372i
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−3.00000	+	5.19615i	−0.298511	+	0.517036i	−0.975796	−	0.218685i	$-0.929823\pi$
$101$	−3.00000	+	5.19615i	−0.298511	+	0.517036i	0.677284	+	0.735721i	$0.263157\pi$
$102$		0			0
$103$	−4.00000			−0.394132			−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000			−0.394132			−0.197066	+	0.980390i	$0.563141\pi$
$104$		0			0
$105$		0			0
$106$	−3.00000	+	5.19615i	−0.291386	+	0.504695i
$107$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$107$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$108$		0			0
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	7.00000	+	12.1244i	0.658505	+	1.14056i	0.981003	+	0.193993i	$0.0621440\pi$
$113$	7.00000	+	12.1244i	0.658505	+	1.14056i	−0.322498	+	0.946570i	$0.604523\pi$
$114$		0			0
$115$	2.00000	−	3.46410i	0.186501	−	0.323029i
$116$	−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
$122$	−2.00000			−0.181071
$123$		0			0
$124$	2.00000	+	3.46410i	0.179605	+	0.311086i
$125$	1.00000			0.0894427
$126$		0			0
$127$	10.0000	−	17.3205i	0.887357	−	1.53695i	0.0443678	−	0.999015i	$-0.485873\pi$
$127$	10.0000	−	17.3205i	0.887357	−	1.53695i	0.842989	−	0.537931i	$-0.180794\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		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
$136$	−1.00000	−	1.73205i	−0.0857493	−	0.148522i
$137$	3.00000	+	5.19615i	0.256307	+	0.443937i	0.965250	−	0.261329i	$-0.0841608\pi$
$137$	3.00000	+	5.19615i	0.256307	+	0.443937i	−0.708942	+	0.705266i	$0.750827\pi$
$138$		0			0
$139$	−2.00000	−	3.46410i	−0.169638	−	0.293821i	0.768655	−	0.639664i	$-0.220926\pi$
$139$	−2.00000	−	3.46410i	−0.169638	−	0.293821i	−0.938293	+	0.345843i	$0.887593\pi$
$140$		0			0
$141$		0			0
$142$	−12.0000			−1.00702
$143$		0			0
$144$	−3.00000			−0.250000
$145$	1.00000	−	1.73205i	0.0830455	−	0.143839i
$146$	−5.00000	+	8.66025i	−0.413803	+	0.716728i
$147$		0			0
$148$	6.00000			0.493197
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	0.716578	−	0.697507i	$-0.245707\pi$
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	−0.962348	+	0.271821i	$0.912374\pi$
$150$		0			0
$151$	−20.0000			−1.62758			−0.813788	−	0.581161i	$-0.802599\pi$
$151$	−20.0000			−1.62758			−0.813788	+	0.581161i	$0.802599\pi$
$152$	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	$0.755069\pi$
$158$	4.00000	−	6.92820i	0.318223	−	0.551178i
$159$		0			0
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$		0			0
$162$	−4.50000	−	7.79423i	−0.353553	−	0.612372i
$163$	−10.0000	−	17.3205i	−0.783260	−	1.35665i	−0.930033	−	0.367477i	$-0.880222\pi$
$163$	−10.0000	−	17.3205i	−0.783260	−	1.35665i	0.146772	−	0.989170i	$-0.453112\pi$
$164$	10.0000			0.780869
$165$		0			0
$166$	−6.00000	+	10.3923i	−0.465690	+	0.806599i
$167$	−8.00000	+	13.8564i	−0.619059	+	1.07224i	0.370599	+	0.928793i	$0.379152\pi$
$167$	−8.00000	+	13.8564i	−0.619059	+	1.07224i	−0.989658	+	0.143448i	$0.954181\pi$
$168$		0			0
$169$		0			0
$170$	2.00000			0.153393
$171$	−12.0000	+	20.7846i	−0.917663	+	1.58944i
$172$		0			0
$173$	9.00000	+	15.5885i	0.684257	+	1.18517i	0.973670	+	0.227964i	$0.0732068\pi$
$173$	9.00000	+	15.5885i	0.684257	+	1.18517i	−0.289412	+	0.957205i	$0.593460\pi$
$174$		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	$-0.881096\pi$
$179$	−2.00000	+	3.46410i	−0.149487	+	0.258919i	0.781551	+	0.623841i	$0.214429\pi$
$180$	1.50000	−	2.59808i	0.111803	−	0.193649i
$181$	22.0000			1.63525			0.817624	−	0.575753i	$-0.195291\pi$
$181$	22.0000			1.63525			0.817624	+	0.575753i	$0.195291\pi$
$182$		0			0
$183$		0			0
$184$	2.00000	−	3.46410i	0.147442	−	0.255377i
$185$	−3.00000	+	5.19615i	−0.220564	+	0.382029i
$186$		0			0
$187$		0			0
$188$	−4.00000	−	6.92820i	−0.291730	−	0.505291i
$189$		0			0
$190$	−8.00000			−0.580381
$191$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$191$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$192$		0			0
$193$	−9.00000	+	15.5885i	−0.647834	+	1.12208i	0.335805	+	0.941932i	$0.390992\pi$
$193$	−9.00000	+	15.5885i	−0.647834	+	1.12208i	−0.983639	+	0.180150i	$0.942342\pi$
$194$	−14.0000			−1.00514
$195$		0			0
$196$	−7.00000			−0.500000
$197$	13.0000	−	22.5167i	0.926212	−	1.60425i	0.136611	−	0.990625i	$-0.456379\pi$
$197$	13.0000	−	22.5167i	0.926212	−	1.60425i	0.789601	−	0.613621i	$-0.210288\pi$
$198$		0			0
$199$	−12.0000	−	20.7846i	−0.850657	−	1.47338i	−0.880616	−	0.473831i	$-0.842871\pi$
$199$	−12.0000	−	20.7846i	−0.850657	−	1.47338i	0.0299585	−	0.999551i	$-0.490462\pi$
$200$	1.00000			0.0707107
$201$		0			0
$202$	−3.00000	−	5.19615i	−0.211079	−	0.365600i
$203$		0			0
$204$		0			0
$205$	−5.00000	+	8.66025i	−0.349215	+	0.604858i
$206$	2.00000	−	3.46410i	0.139347	−	0.241355i
$207$	12.0000			0.834058
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−2.00000	+	3.46410i	−0.137686	+	0.238479i	−0.926620	−	0.375999i	$-0.877300\pi$
$211$	−2.00000	+	3.46410i	−0.137686	+	0.238479i	0.788935	+	0.614477i	$0.210633\pi$
$212$	−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
$223$	4.00000	−	6.92820i	0.267860	−	0.463947i	−0.700449	−	0.713702i	$-0.747017\pi$
$223$	4.00000	−	6.92820i	0.267860	−	0.463947i	0.968309	+	0.249756i	$0.0803503\pi$
$224$		0			0
$225$	1.50000	+	2.59808i	0.100000	+	0.173205i
$226$	−14.0000			−0.931266
$227$	−10.0000	−	17.3205i	−0.663723	−	1.14960i	−0.979630	−	0.200812i	$-0.935642\pi$
$227$	−10.0000	−	17.3205i	−0.663723	−	1.14960i	0.315906	−	0.948790i	$-0.397691\pi$
$228$		0			0
$229$	−10.0000			−0.660819			−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000			−0.660819			−0.330409	+	0.943838i	$0.607187\pi$
$230$	2.00000	+	3.46410i	0.131876	+	0.228416i
$231$		0			0
$232$	1.00000	−	1.73205i	0.0656532	−	0.113715i
$233$	−6.00000			−0.393073			−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000			−0.393073			−0.196537	+	0.980497i	$0.562969\pi$
$234$		0			0
$235$	8.00000			0.521862
$236$	−4.00000	+	6.92820i	−0.260378	+	0.450988i
$237$		0			0
$238$		0			0
$239$	20.0000			1.29369			0.646846	−	0.762620i	$-0.276088\pi$
$239$	20.0000			1.29369			0.646846	+	0.762620i	$0.276088\pi$
$240$		0			0
$241$	−1.00000	−	1.73205i	−0.0644157	−	0.111571i	0.832019	−	0.554747i	$-0.187185\pi$
$241$	−1.00000	−	1.73205i	−0.0644157	−	0.111571i	−0.896435	+	0.443176i	$0.853852\pi$
$242$	−11.0000			−0.707107
$243$		0			0
$244$	1.00000	−	1.73205i	0.0640184	−	0.110883i
$245$	3.50000	−	6.06218i	0.223607	−	0.387298i
$246$		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	0.847228	+	0.531229i	$0.178270\pi$
$251$	14.0000	+	24.2487i	0.883672	+	1.53057i	0.0364441	+	0.999336i	$0.488397\pi$
$252$		0			0
$253$		0			0
$254$	10.0000	+	17.3205i	0.627456	+	1.08679i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−1.00000	+	1.73205i	−0.0623783	+	0.108042i	−0.895528	−	0.445005i	$-0.853202\pi$
$257$	−1.00000	+	1.73205i	−0.0623783	+	0.108042i	0.833150	+	0.553047i	$0.186535\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	6.00000			0.371391
$262$	−2.00000	+	3.46410i	−0.123560	+	0.214013i
$263$	14.0000	−	24.2487i	0.863277	−	1.49524i	−0.00547092	−	0.999985i	$-0.501741\pi$
$263$	14.0000	−	24.2487i	0.863277	−	1.49524i	0.868748	−	0.495255i	$-0.164925\pi$
$264$		0			0
$265$	6.00000			0.368577
$266$		0			0
$267$		0			0
$268$	4.00000			0.244339
$269$	9.00000	+	15.5885i	0.548740	+	0.950445i	0.998361	+	0.0572259i	$0.0182255\pi$
$269$	9.00000	+	15.5885i	0.548740	+	0.950445i	−0.449622	+	0.893219i	$0.648441\pi$
$270$		0			0
$271$	14.0000	−	24.2487i	0.850439	−	1.47300i	−0.0303728	−	0.999539i	$-0.509669\pi$
$271$	14.0000	−	24.2487i	0.850439	−	1.47300i	0.880812	−	0.473466i	$-0.156997\pi$
$272$	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	−0.980373	−	0.197153i	$-0.936830\pi$
$277$	−11.0000	−	19.0526i	−0.660926	−	1.14476i	0.319447	−	0.947604i	$-0.396503\pi$
$278$	4.00000			0.239904
$279$	−6.00000	−	10.3923i	−0.359211	−	0.622171i
$280$		0			0
$281$	−22.0000			−1.31241			−0.656205	−	0.754583i	$-0.727839\pi$
$281$	−22.0000			−1.31241			−0.656205	+	0.754583i	$0.727839\pi$
$282$		0			0
$283$	−8.00000	+	13.8564i	−0.475551	+	0.823678i	−0.999608	−	0.0280052i	$-0.991084\pi$
$283$	−8.00000	+	13.8564i	−0.475551	+	0.823678i	0.524057	+	0.851683i	$0.324418\pi$
$284$	6.00000	−	10.3923i	0.356034	−	0.616670i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	1.50000	−	2.59808i	0.0883883	−	0.153093i
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$	1.00000	+	1.73205i	0.0587220	+	0.101710i
$291$		0			0
$292$	−5.00000	−	8.66025i	−0.292603	−	0.506803i
$293$	−3.00000	−	5.19615i	−0.175262	−	0.303562i	0.764990	−	0.644042i	$-0.222744\pi$
$293$	−3.00000	−	5.19615i	−0.175262	−	0.303562i	−0.940252	+	0.340480i	$0.889411\pi$
$294$		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
$304$	−8.00000			−0.458831
$305$	1.00000	+	1.73205i	0.0572598	+	0.0991769i
$306$	3.00000	+	5.19615i	0.171499	+	0.297044i
$307$	28.0000			1.59804			0.799022	−	0.601302i	$-0.205351\pi$
$307$	28.0000			1.59804			0.799022	+	0.601302i	$0.205351\pi$
$308$		0			0
$309$		0			0
$310$	2.00000	−	3.46410i	0.113592	−	0.196748i
$311$		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	$0.554238\pi$
$314$	9.00000	−	15.5885i	0.507899	−	0.879708i
$315$		0			0
$316$	4.00000	+	6.92820i	0.225018	+	0.389742i
$317$	−2.00000			−0.112331			−0.0561656	−	0.998421i	$-0.517887\pi$
$317$	−2.00000			−0.112331			−0.0561656	+	0.998421i	$0.517887\pi$
$318$		0			0
$319$		0			0
$320$	1.00000			0.0559017
$321$		0			0
$322$		0			0
$323$	8.00000	−	13.8564i	0.445132	−	0.770991i
$324$	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
$331$	4.00000	+	6.92820i	0.219860	+	0.380808i	0.954765	−	0.297361i	$-0.0961066\pi$
$331$	4.00000	+	6.92820i	0.219860	+	0.380808i	−0.734905	+	0.678170i	$0.762773\pi$
$332$	−6.00000	−	10.3923i	−0.329293	−	0.570352i
$333$	−18.0000			−0.986394
$334$	−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	$-0.336901\pi$
$337$	18.0000			0.980522			0.490261	+	0.871576i	$0.336901\pi$
$338$		0			0
$339$		0			0
$340$	−1.00000	+	1.73205i	−0.0542326	+	0.0939336i
$341$		0			0
$342$	−12.0000	−	20.7846i	−0.648886	−	1.12390i
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−18.0000			−0.967686
$347$	−16.0000	−	27.7128i	−0.858925	−	1.48770i	−0.872955	−	0.487800i	$-0.837799\pi$
$347$	−16.0000	−	27.7128i	−0.858925	−	1.48770i	0.0140303	−	0.999902i	$-0.495534\pi$
$348$		0			0
$349$	−7.00000	+	12.1244i	−0.374701	+	0.649002i	−0.990282	−	0.139072i	$-0.955588\pi$
$349$	−7.00000	+	12.1244i	−0.374701	+	0.649002i	0.615581	+	0.788074i	$0.288921\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	15.0000	−	25.9808i	0.798369	−	1.38282i	−0.122308	−	0.992492i	$-0.539030\pi$
$353$	15.0000	−	25.9808i	0.798369	−	1.38282i	0.920677	−	0.390324i	$-0.127637\pi$
$354$		0			0
$355$	6.00000	+	10.3923i	0.318447	+	0.551566i
$356$	10.0000			0.529999
$357$		0			0
$358$	−2.00000	−	3.46410i	−0.105703	−	0.183083i
$359$	4.00000			0.211112			0.105556	−	0.994413i	$-0.466338\pi$
$359$	4.00000			0.211112			0.105556	+	0.994413i	$0.466338\pi$
$360$	1.50000	+	2.59808i	0.0790569	+	0.136931i
$361$	−22.5000	+	38.9711i	−1.18421	+	2.05111i
$362$	−11.0000	+	19.0526i	−0.578147	+	1.00138i
$363$		0			0
$364$		0			0
$365$	10.0000			0.523424
$366$		0			0
$367$	6.00000	−	10.3923i	0.313197	−	0.542474i	−0.665855	−	0.746081i	$-0.731933\pi$
$367$	6.00000	−	10.3923i	0.313197	−	0.542474i	0.979053	+	0.203607i	$0.0652665\pi$
$368$	2.00000	+	3.46410i	0.104257	+	0.180579i
$369$	−30.0000			−1.56174
$370$	−3.00000	−	5.19615i	−0.155963	−	0.270135i
$371$		0			0
$372$		0			0
$373$	−3.00000	−	5.19615i	−0.155334	−	0.269047i	0.777847	−	0.628454i	$-0.216312\pi$
$373$	−3.00000	−	5.19615i	−0.155334	−	0.269047i	−0.933181	+	0.359408i	$0.882979\pi$
$374$		0			0
$375$		0			0
$376$	8.00000			0.412568
$377$		0			0
$378$		0			0
$379$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$379$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$380$	4.00000	−	6.92820i	0.205196	−	0.355409i
$381$		0			0
$382$		0			0
$383$	−4.00000	−	6.92820i	−0.204390	−	0.354015i	0.745548	−	0.666452i	$-0.232188\pi$
$383$	−4.00000	−	6.92820i	−0.204390	−	0.354015i	−0.949938	+	0.312437i	$0.898855\pi$
$384$		0			0
$385$		0			0
$386$	−9.00000	−	15.5885i	−0.458088	−	0.793432i
$387$		0			0
$388$	7.00000	−	12.1244i	0.355371	−	0.615521i
$389$	6.00000			0.304212			0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000			0.304212			0.152106	+	0.988364i	$0.451394\pi$
$390$		0			0
$391$	−8.00000			−0.404577
$392$	3.50000	−	6.06218i	0.176777	−	0.306186i
$393$		0			0
$394$	13.0000	+	22.5167i	0.654931	+	1.13437i
$395$	−8.00000			−0.402524
$396$		0			0
$397$	9.00000	+	15.5885i	0.451697	+	0.782362i	0.998492	−	0.0549046i	$-0.0174855\pi$
$397$	9.00000	+	15.5885i	0.451697	+	0.782362i	−0.546795	+	0.837267i	$0.684152\pi$
$398$	24.0000			1.20301
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	15.0000	−	25.9808i	0.749064	−	1.29742i	−0.199207	−	0.979957i	$-0.563837\pi$
$401$	15.0000	−	25.9808i	0.749064	−	1.29742i	0.948272	−	0.317460i	$-0.102830\pi$
$402$		0			0
$403$		0			0
$404$	6.00000			0.298511
$405$	−4.50000	+	7.79423i	−0.223607	+	0.387298i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−13.0000	−	22.5167i	−0.642809	−	1.11338i	−0.984803	−	0.173675i	$-0.944436\pi$
$409$	−13.0000	−	22.5167i	−0.642809	−	1.11338i	0.341994	−	0.939702i	$-0.388898\pi$
$410$	−5.00000	−	8.66025i	−0.246932	−	0.427699i
$411$		0			0
$412$	2.00000	+	3.46410i	0.0985329	+	0.170664i
$413$		0			0
$414$	−6.00000	+	10.3923i	−0.294884	+	0.510754i
$415$	12.0000			0.589057
$416$		0			0
$417$		0			0
$418$		0			0
$419$	18.0000	−	31.1769i	0.879358	−	1.52309i	0.0273103	−	0.999627i	$-0.491306\pi$
$419$	18.0000	−	31.1769i	0.879358	−	1.52309i	0.852047	−	0.523465i	$-0.175361\pi$
$420$		0			0
$421$	−26.0000			−1.26716			−0.633581	−	0.773676i	$-0.718416\pi$
$421$	−26.0000			−1.26716			−0.633581	+	0.773676i	$0.718416\pi$
$422$	−2.00000	−	3.46410i	−0.0973585	−	0.168630i
$423$	12.0000	+	20.7846i	0.583460	+	1.01058i
$424$	6.00000			0.291386
$425$	−1.00000	−	1.73205i	−0.0485071	−	0.0840168i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−6.00000	+	10.3923i	−0.289010	+	0.500580i	−0.973574	−	0.228373i	$-0.926659\pi$
$431$	−6.00000	+	10.3923i	−0.289010	+	0.500580i	0.684564	+	0.728953i	$0.259993\pi$
$432$		0			0
$433$	−17.0000	−	29.4449i	−0.816968	−	1.41503i	−0.907906	−	0.419173i	$-0.862320\pi$
$433$	−17.0000	−	29.4449i	−0.816968	−	1.41503i	0.0909384	−	0.995857i	$-0.471013\pi$
$434$		0			0
$435$		0			0
$436$	1.00000	+	1.73205i	0.0478913	+	0.0829502i
$437$	32.0000			1.53077
$438$		0			0
$439$	12.0000	−	20.7846i	0.572729	−	0.991995i	−0.423556	−	0.905870i	$-0.639218\pi$
$439$	12.0000	−	20.7846i	0.572729	−	0.991995i	0.996284	−	0.0861252i	$-0.0274485\pi$
$440$		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
$449$	−9.00000	−	15.5885i	−0.424736	−	0.735665i	0.571660	−	0.820491i	$-0.306300\pi$
$449$	−9.00000	−	15.5885i	−0.424736	−	0.735665i	−0.996396	+	0.0848262i	$0.972967\pi$
$450$	−3.00000			−0.141421
$451$		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
$457$	19.0000	−	32.9090i	0.888783	−	1.53942i	0.0474665	−	0.998873i	$-0.484885\pi$
$457$	19.0000	−	32.9090i	0.888783	−	1.53942i	0.841316	−	0.540544i	$-0.181781\pi$
$458$	5.00000	−	8.66025i	0.233635	−	0.404667i
$459$		0			0
$460$	−4.00000			−0.186501
$461$	−7.00000	−	12.1244i	−0.326023	−	0.564688i	0.655696	−	0.755025i	$-0.272375\pi$
$461$	−7.00000	−	12.1244i	−0.326023	−	0.564688i	−0.981719	+	0.190337i	$0.939042\pi$
$462$		0			0
$463$	−16.0000			−0.743583			−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000			−0.743583			−0.371792	+	0.928316i	$0.621256\pi$
$464$	1.00000	+	1.73205i	0.0464238	+	0.0804084i
$465$		0			0
$466$	3.00000	−	5.19615i	0.138972	−	0.240707i
$467$	−16.0000			−0.740392			−0.370196	−	0.928954i	$-0.620709\pi$
$467$	−16.0000			−0.740392			−0.370196	+	0.928954i	$0.620709\pi$
$468$		0			0
$469$		0			0
$470$	−4.00000	+	6.92820i	−0.184506	+	0.319574i
$471$		0			0
$472$	−4.00000	−	6.92820i	−0.184115	−	0.318896i
$473$		0			0
$474$		0			0
$475$	4.00000	+	6.92820i	0.183533	+	0.317888i
$476$		0			0
$477$	9.00000	+	15.5885i	0.412082	+	0.713746i
$478$	−10.0000	+	17.3205i	−0.457389	+	0.792222i
$479$	2.00000	−	3.46410i	0.0913823	−	0.158279i	−0.816711	−	0.577047i	$-0.804205\pi$
$479$	2.00000	−	3.46410i	0.0913823	−	0.158279i	0.908093	+	0.418769i	$0.137538\pi$
$480$		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
$487$	4.00000	+	6.92820i	0.181257	+	0.313947i	0.942309	−	0.334744i	$-0.108650\pi$
$487$	4.00000	+	6.92820i	0.181257	+	0.313947i	−0.761052	+	0.648691i	$0.775317\pi$
$488$	1.00000	+	1.73205i	0.0452679	+	0.0784063i
$489$		0			0
$490$	3.50000	+	6.06218i	0.158114	+	0.273861i
$491$	−10.0000	+	17.3205i	−0.451294	+	0.781664i	−0.998467	−	0.0553560i	$-0.982371\pi$
$491$	−10.0000	+	17.3205i	−0.451294	+	0.781664i	0.547173	+	0.837020i	$0.315704\pi$
$492$		0			0
$493$	−4.00000			−0.180151
$494$		0			0
$495$		0			0
$496$	2.00000	−	3.46410i	0.0898027	−	0.155543i
$497$		0			0
$498$		0			0
$499$	8.00000			0.358129			0.179065	−	0.983837i	$-0.442693\pi$
$499$	8.00000			0.358129			0.179065	+	0.983837i	$0.442693\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$		0			0
$502$	−28.0000			−1.24970
$503$	−10.0000	−	17.3205i	−0.445878	−	0.772283i	0.552235	−	0.833689i	$-0.313775\pi$
$503$	−10.0000	−	17.3205i	−0.445878	−	0.772283i	−0.998113	+	0.0614052i	$0.980442\pi$
$504$		0			0
$505$	−3.00000	+	5.19615i	−0.133498	+	0.231226i
$506$		0			0
$507$		0			0
$508$	−20.0000			−0.887357
$509$	9.00000	−	15.5885i	0.398918	−	0.690946i	−0.594675	−	0.803966i	$-0.702719\pi$
$509$	9.00000	−	15.5885i	0.398918	−	0.690946i	0.993593	+	0.113020i	$0.0360525\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			0.0441942
$513$		0			0
$514$	−1.00000	−	1.73205i	−0.0441081	−	0.0763975i
$515$	−4.00000			−0.176261
$516$		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	$0.307121\pi$
$522$	−3.00000	+	5.19615i	−0.131306	+	0.227429i
$523$	4.00000	−	6.92820i	0.174908	−	0.302949i	−0.765222	−	0.643767i	$-0.777371\pi$
$523$	4.00000	−	6.92820i	0.174908	−	0.302949i	0.940129	+	0.340818i	$0.110704\pi$
$524$	−2.00000	−	3.46410i	−0.0873704	−	0.151330i
$525$		0			0
$526$	14.0000	+	24.2487i	0.610429	+	1.05729i
$527$	4.00000	+	6.92820i	0.174243	+	0.301797i
$528$		0			0
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$	−3.00000	+	5.19615i	−0.130312	+	0.225706i
$531$	12.0000	−	20.7846i	0.520756	−	0.901975i
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	−2.00000	+	3.46410i	−0.0863868	+	0.149626i
$537$		0			0
$538$	−18.0000			−0.776035
$539$		0			0
$540$		0			0
$541$	−2.00000			−0.0859867			−0.0429934	−	0.999075i	$-0.513689\pi$
$541$	−2.00000			−0.0859867			−0.0429934	+	0.999075i	$0.513689\pi$
$542$	14.0000	+	24.2487i	0.601351	+	1.04157i
$543$		0			0
$544$	−1.00000	+	1.73205i	−0.0428746	+	0.0742611i
$545$	−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	$0.826528\pi$
$548$	3.00000	−	5.19615i	0.128154	−	0.221969i
$549$	−3.00000	+	5.19615i	−0.128037	+	0.221766i
$550$		0			0
$551$	16.0000			0.681623
$552$		0			0
$553$		0			0
$554$	22.0000			0.934690
$555$		0			0
$556$	−2.00000	+	3.46410i	−0.0848189	+	0.146911i
$557$	−7.00000	+	12.1244i	−0.296600	+	0.513725i	−0.975356	−	0.220638i	$-0.929186\pi$
$557$	−7.00000	+	12.1244i	−0.296600	+	0.513725i	0.678756	+	0.734364i	$0.262519\pi$
$558$	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	−0.999978	−	0.00664037i	$-0.997886\pi$
$563$	−12.0000	−	20.7846i	−0.505740	−	0.875967i	0.494238	−	0.869326i	$-0.335447\pi$
$564$		0			0
$565$	7.00000	+	12.1244i	0.294492	+	0.510075i
$566$	−8.00000	−	13.8564i	−0.336265	−	0.582428i
$567$		0			0
$568$	6.00000	+	10.3923i	0.251754	+	0.436051i
$569$	−5.00000	+	8.66025i	−0.209611	+	0.363057i	−0.951592	−	0.307364i	$-0.900553\pi$
$569$	−5.00000	+	8.66025i	−0.209611	+	0.363057i	0.741981	+	0.670421i	$0.233886\pi$
$570$		0			0
$571$	−28.0000			−1.17176			−0.585882	−	0.810397i	$-0.699252\pi$
$571$	−28.0000			−1.17176			−0.585882	+	0.810397i	$0.699252\pi$
$572$		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
$577$	2.00000			0.0832611			0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000			0.0832611			0.0416305	+	0.999133i	$0.486745\pi$
$578$	6.50000	+	11.2583i	0.270364	+	0.468285i
$579$		0			0
$580$	−2.00000			−0.0830455
$581$		0			0
$582$		0			0
$583$		0			0
$584$	10.0000			0.413803
$585$		0			0
$586$	6.00000			0.247858
$587$	10.0000	−	17.3205i	0.412744	−	0.714894i	−0.582445	−	0.812870i	$-0.697904\pi$
$587$	10.0000	−	17.3205i	0.412744	−	0.714894i	0.995189	+	0.0979766i	$0.0312370\pi$
$588$		0			0
$589$	−16.0000	−	27.7128i	−0.659269	−	1.14189i
$590$	8.00000			0.329355
$591$		0			0
$592$	−3.00000	−	5.19615i	−0.123299	−	0.213561i
$593$	2.00000			0.0821302			0.0410651	−	0.999156i	$-0.486925\pi$
$593$	2.00000			0.0821302			0.0410651	+	0.999156i	$0.486925\pi$
$594$		0			0
$595$		0			0
$596$	−3.00000	+	5.19615i	−0.122885	+	0.212843i
$597$		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	0.469095	+	0.883148i	$0.344580\pi$
$601$	−13.0000	+	22.5167i	−0.530281	+	0.918474i	−0.999376	+	0.0353259i	$0.988753\pi$
$602$		0			0
$603$	−12.0000			−0.488678
$604$	10.0000	+	17.3205i	0.406894	+	0.704761i
$605$	5.50000	+	9.52628i	0.223607	+	0.387298i
$606$		0			0
$607$	−18.0000	−	31.1769i	−0.730597	−	1.26543i	−0.956628	−	0.291312i	$-0.905908\pi$
$607$	−18.0000	−	31.1769i	−0.730597	−	1.26543i	0.226031	−	0.974120i	$-0.427425\pi$
$608$	4.00000	−	6.92820i	0.162221	−	0.280976i
$609$		0			0
$610$	−2.00000			−0.0809776
$611$		0			0
$612$	−6.00000			−0.242536
$613$	−19.0000	+	32.9090i	−0.767403	+	1.32918i	0.171564	+	0.985173i	$0.445118\pi$
$613$	−19.0000	+	32.9090i	−0.767403	+	1.32918i	−0.938967	+	0.344008i	$0.888215\pi$
$614$	−14.0000	+	24.2487i	−0.564994	+	0.978598i
$615$		0			0
$616$		0			0
$617$	−13.0000	−	22.5167i	−0.523360	−	0.906487i	−0.999630	−	0.0271876i	$-0.991345\pi$
$617$	−13.0000	−	22.5167i	−0.523360	−	0.906487i	0.476270	−	0.879299i	$-0.341988\pi$
$618$		0			0
$619$	−24.0000			−0.964641			−0.482321	−	0.875995i	$-0.660206\pi$
$619$	−24.0000			−0.964641			−0.482321	+	0.875995i	$0.660206\pi$
$620$	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
$626$	3.00000	−	5.19615i	0.119904	−	0.207680i
$627$		0			0
$628$	9.00000	+	15.5885i	0.359139	+	0.622047i
$629$	12.0000			0.478471
$630$		0			0
$631$	−6.00000	−	10.3923i	−0.238856	−	0.413711i	0.721530	−	0.692383i	$-0.243439\pi$
$631$	−6.00000	−	10.3923i	−0.238856	−	0.413711i	−0.960386	+	0.278672i	$0.910106\pi$
$632$	−8.00000			−0.318223
$633$		0			0
$634$	1.00000	−	1.73205i	0.0397151	−	0.0687885i
$635$	10.0000	−	17.3205i	0.396838	−	0.687343i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−18.0000	+	31.1769i	−0.712069	+	1.23334i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	15.0000	+	25.9808i	0.592464	+	1.02618i	0.993899	+	0.110291i	$0.0351782\pi$
$641$	15.0000	+	25.9808i	0.592464	+	1.02618i	−0.401435	+	0.915888i	$0.631488\pi$
$642$		0			0
$643$	−14.0000	−	24.2487i	−0.552106	−	0.956276i	−0.998122	−	0.0612510i	$-0.980491\pi$
$643$	−14.0000	−	24.2487i	−0.552106	−	0.956276i	0.446016	−	0.895025i	$-0.352842\pi$
$644$		0			0
$645$		0			0
$646$	8.00000	+	13.8564i	0.314756	+	0.545173i
$647$	14.0000	−	24.2487i	0.550397	−	0.953315i	−0.447849	−	0.894109i	$-0.647810\pi$
$647$	14.0000	−	24.2487i	0.550397	−	0.953315i	0.998246	−	0.0592060i	$-0.0188569\pi$
$648$	−4.50000	+	7.79423i	−0.176777	+	0.306186i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−10.0000	+	17.3205i	−0.391630	+	0.678323i
$653$	−23.0000	+	39.8372i	−0.900060	+	1.55895i	−0.0726446	+	0.997358i	$0.523144\pi$
$653$	−23.0000	+	39.8372i	−0.900060	+	1.55895i	−0.827415	+	0.561591i	$0.810189\pi$
$654$		0			0
$655$	4.00000			0.156293
$656$	−5.00000	−	8.66025i	−0.195217	−	0.338126i
$657$	15.0000	+	25.9808i	0.585206	+	1.01361i
$658$		0			0
$659$	18.0000	+	31.1769i	0.701180	+	1.21448i	0.968052	+	0.250748i	$0.0806766\pi$
$659$	18.0000	+	31.1769i	0.701180	+	1.21448i	−0.266872	+	0.963732i	$0.585990\pi$
$660$		0			0
$661$	−11.0000	+	19.0526i	−0.427850	+	0.741059i	−0.996682	−	0.0813955i	$-0.974062\pi$
$661$	−11.0000	+	19.0526i	−0.427850	+	0.741059i	0.568831	+	0.822454i	$0.307396\pi$
$662$	−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
$668$	16.0000			0.619059
$669$		0			0
$670$	−2.00000	−	3.46410i	−0.0772667	−	0.133830i
$671$		0			0
$672$		0			0
$673$	7.00000	−	12.1244i	0.269830	−	0.467360i	−0.698988	−	0.715134i	$-0.746366\pi$
$673$	7.00000	−	12.1244i	0.269830	−	0.467360i	0.968818	+	0.247774i	$0.0796991\pi$
$674$	−9.00000	+	15.5885i	−0.346667	+	0.600445i
$675$		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
$683$	−14.0000	−	24.2487i	−0.535695	−	0.927851i	−0.999129	−	0.0417198i	$-0.986716\pi$
$683$	−14.0000	−	24.2487i	−0.535695	−	0.927851i	0.463434	−	0.886131i	$-0.346617\pi$
$684$	24.0000			0.917663
$685$	3.00000	+	5.19615i	0.114624	+	0.198535i
$686$		0			0
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−16.0000	+	27.7128i	−0.608669	+	1.05425i	0.382791	+	0.923835i	$0.374963\pi$
$691$	−16.0000	+	27.7128i	−0.608669	+	1.05425i	−0.991460	+	0.130410i	$0.958371\pi$
$692$	9.00000	−	15.5885i	0.342129	−	0.592584i
$693$		0			0
$694$	32.0000			1.21470
$695$	−2.00000	−	3.46410i	−0.0758643	−	0.131401i
$696$		0			0
$697$	20.0000			0.757554
$698$	−7.00000	−	12.1244i	−0.264954	−	0.458914i
$699$		0			0
$700$		0			0
$701$	−34.0000			−1.28416			−0.642081	−	0.766637i	$-0.721929\pi$
$701$	−34.0000			−1.28416			−0.642081	+	0.766637i	$0.721929\pi$
$702$		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
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	0.944509	−	0.328484i	$-0.106538\pi$
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	−0.756730	+	0.653727i	$0.773204\pi$
$710$	−12.0000			−0.450352
$711$	−12.0000	−	20.7846i	−0.450035	−	0.779484i
$712$	−5.00000	+	8.66025i	−0.187383	+	0.324557i
$713$	−8.00000	+	13.8564i	−0.299602	+	0.518927i
$714$		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	$-0.263103\pi$
$719$	−8.00000	−	13.8564i	−0.298350	−	0.516757i	−0.975759	+	0.218850i	$0.929769\pi$
$720$	−3.00000			−0.111803
$721$		0			0
$722$	−22.5000	−	38.9711i	−0.837363	−	1.45036i
$723$		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	$-0.673782\pi$
$727$	−28.0000			−1.03846			−0.519231	+	0.854634i	$0.673782\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	−5.00000	+	8.66025i	−0.185058	+	0.320530i
$731$		0			0
$732$		0			0
$733$	−34.0000			−1.25582			−0.627909	−	0.778287i	$-0.716089\pi$
$733$	−34.0000			−1.25582			−0.627909	+	0.778287i	$0.716089\pi$
$734$	6.00000	+	10.3923i	0.221464	+	0.383587i
$735$		0			0
$736$	−4.00000			−0.147442
$737$		0			0
$738$	15.0000	−	25.9808i	0.552158	−	0.956365i
$739$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$739$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$740$	6.00000			0.220564
$741$		0			0
$742$		0			0
$743$	−8.00000	+	13.8564i	−0.293492	+	0.508342i	−0.974633	−	0.223810i	$-0.928151\pi$
$743$	−8.00000	+	13.8564i	−0.293492	+	0.508342i	0.681141	+	0.732152i	$0.261484\pi$
$744$		0			0
$745$	−3.00000	−	5.19615i	−0.109911	−	0.190372i
$746$	6.00000			0.219676
$747$	18.0000	+	31.1769i	0.658586	+	1.14070i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	20.0000	−	34.6410i	0.729810	−	1.26407i	−0.227153	−	0.973859i	$-0.572942\pi$
$751$	20.0000	−	34.6410i	0.729810	−	1.26407i	0.956963	−	0.290209i	$-0.0937250\pi$
$752$	−4.00000	+	6.92820i	−0.145865	+	0.252646i
$753$		0			0
$754$		0			0
$755$	−20.0000			−0.727875
$756$		0			0
$757$	−11.0000	+	19.0526i	−0.399802	+	0.692477i	−0.993701	−	0.112062i	$-0.964254\pi$
$757$	−11.0000	+	19.0526i	−0.399802	+	0.692477i	0.593899	+	0.804539i	$0.297588\pi$
$758$		0			0
$759$		0			0
$760$	4.00000	+	6.92820i	0.145095	+	0.251312i
$761$	3.00000	+	5.19615i	0.108750	+	0.188360i	0.915264	−	0.402854i	$-0.131982\pi$
$761$	3.00000	+	5.19615i	0.108750	+	0.188360i	−0.806514	+	0.591215i	$0.798649\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	3.00000	−	5.19615i	0.108465	−	0.187867i
$766$	8.00000			0.289052
$767$		0			0
$768$		0			0
$769$	7.00000	−	12.1244i	0.252426	−	0.437215i	−0.711767	−	0.702416i	$-0.752105\pi$
$769$	7.00000	−	12.1244i	0.252426	−	0.437215i	0.964193	+	0.265200i	$0.0854381\pi$
$770$		0			0
$771$		0			0
$772$	18.0000			0.647834
$773$	13.0000	+	22.5167i	0.467578	+	0.809868i	0.999314	−	0.0370420i	$-0.0117935\pi$
$773$	13.0000	+	22.5167i	0.467578	+	0.809868i	−0.531736	+	0.846910i	$0.678460\pi$
$774$		0			0
$775$	−4.00000			−0.143684
$776$	7.00000	+	12.1244i	0.251285	+	0.435239i
$777$		0			0
$778$	−3.00000	+	5.19615i	−0.107555	+	0.186291i
$779$	−80.0000			−2.86630
$780$		0			0
$781$		0			0
$782$	4.00000	−	6.92820i	0.143040	−	0.247752i
$783$		0			0
$784$	3.50000	+	6.06218i	0.125000	+	0.216506i
$785$	−18.0000			−0.642448
$786$		0			0
$787$	2.00000	+	3.46410i	0.0712923	+	0.123482i	0.899468	−	0.436987i	$-0.143954\pi$
$787$	2.00000	+	3.46410i	0.0712923	+	0.123482i	−0.828176	+	0.560469i	$0.810621\pi$
$788$	−26.0000			−0.926212
$789$		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	0.992492	+	0.122312i	$0.0390308\pi$
$797$	17.0000	+	29.4449i	0.602171	+	1.04299i	−0.390321	+	0.920679i	$0.627636\pi$
$798$		0			0
$799$	−8.00000	−	13.8564i	−0.283020	−	0.490204i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	−30.0000			−1.06000
$802$	15.0000	+	25.9808i	0.529668	+	0.917413i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−3.00000	+	5.19615i	−0.105540	+	0.182800i
$809$	−13.0000	+	22.5167i	−0.457056	+	0.791644i	−0.998804	−	0.0488972i	$-0.984429\pi$
$809$	−13.0000	+	22.5167i	−0.457056	+	0.791644i	0.541748	+	0.840541i	$0.317763\pi$
$810$	−4.50000	−	7.79423i	−0.158114	−	0.273861i
$811$	24.0000			0.842754			0.421377	−	0.906886i	$-0.361547\pi$
$811$	24.0000			0.842754			0.421377	+	0.906886i	$0.361547\pi$
$812$		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
$821$	21.0000	−	36.3731i	0.732905	−	1.26943i	−0.222731	−	0.974880i	$-0.571497\pi$
$821$	21.0000	−	36.3731i	0.732905	−	1.26943i	0.955636	−	0.294549i	$-0.0951694\pi$
$822$		0			0
$823$	2.00000	+	3.46410i	0.0697156	+	0.120751i	0.898776	−	0.438408i	$-0.144457\pi$
$823$	2.00000	+	3.46410i	0.0697156	+	0.120751i	−0.829060	+	0.559159i	$0.811124\pi$
$824$	−4.00000			−0.139347
$825$		0			0
$826$		0			0
$827$	36.0000			1.25184			0.625921	−	0.779886i	$-0.284723\pi$
$827$	36.0000			1.25184			0.625921	+	0.779886i	$0.284723\pi$
$828$	−6.00000	−	10.3923i	−0.208514	−	0.361158i
$829$	17.0000	−	29.4449i	0.590434	−	1.02266i	−0.403739	−	0.914874i	$-0.632290\pi$
$829$	17.0000	−	29.4449i	0.590434	−	1.02266i	0.994174	−	0.107788i	$-0.0343769\pi$
$830$	−6.00000	+	10.3923i	−0.208263	+	0.360722i
$831$		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
$838$	18.0000	+	31.1769i	0.621800	+	1.07699i
$839$	−2.00000	−	3.46410i	−0.0690477	−	0.119594i	0.829435	−	0.558604i	$-0.188663\pi$
$839$	−2.00000	−	3.46410i	−0.0690477	−	0.119594i	−0.898482	+	0.439010i	$0.855329\pi$
$840$		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
$850$	2.00000			0.0685994
$851$	12.0000	+	20.7846i	0.411355	+	0.712487i
$852$		0			0
$853$	22.0000			0.753266			0.376633	−	0.926363i	$-0.377082\pi$
$853$	22.0000			0.753266			0.376633	+	0.926363i	$0.377082\pi$
$854$		0			0
$855$	−12.0000	+	20.7846i	−0.410391	+	0.710819i
$856$		0			0
$857$	−6.00000			−0.204956			−0.102478	−	0.994735i	$-0.532677\pi$
$857$	−6.00000			−0.204956			−0.102478	+	0.994735i	$0.532677\pi$
$858$		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
$863$	40.0000			1.36162			0.680808	−	0.732462i	$-0.261629\pi$
$863$	40.0000			1.36162			0.680808	+	0.732462i	$0.261629\pi$
$864$		0			0
$865$	9.00000	+	15.5885i	0.306009	+	0.530023i
$866$	34.0000			1.15537
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−2.00000			−0.0677285
$873$	−21.0000	+	36.3731i	−0.710742	+	1.23104i
$874$	−16.0000	+	27.7128i	−0.541208	+	0.937400i
$875$		0			0
$876$		0			0
$877$	−7.00000	−	12.1244i	−0.236373	−	0.409410i	0.723298	−	0.690536i	$-0.242625\pi$
$877$	−7.00000	−	12.1244i	−0.236373	−	0.409410i	−0.959671	+	0.281126i	$0.909292\pi$
$878$	12.0000	+	20.7846i	0.404980	+	0.701447i
$879$		0			0
$880$		0			0
$881$	−1.00000	+	1.73205i	−0.0336909	+	0.0583543i	−0.882379	−	0.470539i	$-0.844059\pi$
$881$	−1.00000	+	1.73205i	−0.0336909	+	0.0583543i	0.848688	+	0.528893i	$0.177393\pi$
$882$	−10.5000	+	18.1865i	−0.353553	+	0.612372i
$883$	−8.00000			−0.269221			−0.134611	−	0.990899i	$-0.542978\pi$
$883$	−8.00000			−0.269221			−0.134611	+	0.990899i	$0.542978\pi$
$884$		0			0
$885$		0			0
$886$	−12.0000	+	20.7846i	−0.403148	+	0.698273i
$887$	−22.0000	+	38.1051i	−0.738688	+	1.27944i	0.214399	+	0.976746i	$0.431221\pi$
$887$	−22.0000	+	38.1051i	−0.738688	+	1.27944i	−0.953086	+	0.302698i	$0.902113\pi$
$888$		0			0
$889$		0			0
$890$	−5.00000	−	8.66025i	−0.167600	−	0.290292i
$891$		0			0
$892$	−8.00000			−0.267860
$893$	32.0000	+	55.4256i	1.07084	+	1.85475i
$894$		0			0
$895$	−2.00000	+	3.46410i	−0.0668526	+	0.115792i
$896$		0			0
$897$		0			0
$898$	18.0000			0.600668
$899$	−4.00000	+	6.92820i	−0.133407	+	0.231069i
$900$	1.50000	−	2.59808i	0.0500000	−	0.0866025i
$901$	−6.00000	−	10.3923i	−0.199889	−	0.346218i
$902$		0			0
$903$		0			0
$904$	7.00000	+	12.1244i	0.232817	+	0.403250i
$905$	22.0000			0.731305
$906$		0			0
$907$	−4.00000	+	6.92820i	−0.132818	+	0.230047i	−0.924762	−	0.380547i	$-0.875736\pi$
$907$	−4.00000	+	6.92820i	−0.132818	+	0.230047i	0.791944	+	0.610594i	$0.209069\pi$
$908$	−10.0000	+	17.3205i	−0.331862	+	0.574801i
$909$	−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
$916$	5.00000	+	8.66025i	0.165205	+	0.286143i
$917$		0			0
$918$		0			0
$919$	−16.0000	−	27.7128i	−0.527791	−	0.914161i	−0.999475	−	0.0323936i	$-0.989687\pi$
$919$	−16.0000	−	27.7128i	−0.527791	−	0.914161i	0.471684	−	0.881768i	$-0.343646\pi$
$920$	2.00000	−	3.46410i	0.0659380	−	0.114208i
$921$		0			0
$922$	14.0000			0.461065
$923$		0			0
$924$		0			0
$925$	−3.00000	+	5.19615i	−0.0986394	+	0.170848i
$926$	8.00000	−	13.8564i	0.262896	−	0.455350i
$927$	−6.00000	−	10.3923i	−0.197066	−	0.341328i
$928$	−2.00000			−0.0656532
$929$	7.00000	+	12.1244i	0.229663	+	0.397787i	0.957708	−	0.287742i	$-0.0929044\pi$
$929$	7.00000	+	12.1244i	0.229663	+	0.397787i	−0.728046	+	0.685529i	$0.759571\pi$
$930$		0			0
$931$	56.0000			1.83533
$932$	3.00000	+	5.19615i	0.0982683	+	0.170206i
$933$		0			0
$934$	8.00000	−	13.8564i	0.261768	−	0.453395i
$935$		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
$941$	30.0000			0.977972			0.488986	−	0.872292i	$-0.337367\pi$
$941$	30.0000			0.977972			0.488986	+	0.872292i	$0.337367\pi$
$942$		0			0
$943$	20.0000	+	34.6410i	0.651290	+	1.12807i
$944$	8.00000			0.260378
$945$		0			0
$946$		0			0
$947$	2.00000	−	3.46410i	0.0649913	−	0.112568i	−0.831699	−	0.555227i	$-0.812631\pi$
$947$	2.00000	−	3.46410i	0.0649913	−	0.112568i	0.896690	+	0.442659i	$0.145965\pi$
$948$		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	$-0.305026\pi$
$953$	−13.0000	−	22.5167i	−0.421111	−	0.729386i	−0.996048	+	0.0888114i	$0.971693\pi$
$954$	−18.0000			−0.582772
$955$		0			0
$956$	−10.0000	−	17.3205i	−0.323423	−	0.560185i
$957$		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
$964$	−1.00000	+	1.73205i	−0.0322078	+	0.0557856i
$965$	−9.00000	+	15.5885i	−0.289720	+	0.501810i
$966$		0			0
$967$	24.0000			0.771788			0.385894	−	0.922543i	$-0.373893\pi$
$967$	24.0000			0.771788			0.385894	+	0.922543i	$0.373893\pi$
$968$	5.50000	+	9.52628i	0.176777	+	0.306186i
$969$		0			0
$970$	−14.0000			−0.449513
$971$	2.00000	+	3.46410i	0.0641831	+	0.111168i	0.896331	−	0.443385i	$-0.146223\pi$
$971$	2.00000	+	3.46410i	0.0641831	+	0.111168i	−0.832148	+	0.554553i	$0.812889\pi$
$972$		0			0
$973$		0			0
$974$	−8.00000			−0.256337
$975$		0			0
$976$	−2.00000			−0.0640184
$977$	−9.00000	+	15.5885i	−0.287936	+	0.498719i	−0.973317	−	0.229465i	$-0.926302\pi$
$977$	−9.00000	+	15.5885i	−0.287936	+	0.498719i	0.685381	+	0.728184i	$0.259636\pi$
$978$		0			0
$979$		0			0
$980$	−7.00000			−0.223607
$981$	−3.00000	−	5.19615i	−0.0957826	−	0.165900i
$982$	−10.0000	−	17.3205i	−0.319113	−	0.552720i
$983$	−24.0000			−0.765481			−0.382741	−	0.923856i	$-0.625020\pi$
$983$	−24.0000			−0.765481			−0.382741	+	0.923856i	$0.625020\pi$
$984$		0			0
$985$	13.0000	−	22.5167i	0.414214	−	0.717440i
$986$	2.00000	−	3.46410i	0.0636930	−	0.110319i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−16.0000	+	27.7128i	−0.508257	+	0.880327i	0.491698	+	0.870766i	$0.336377\pi$
$991$	−16.0000	+	27.7128i	−0.508257	+	0.880327i	−0.999954	+	0.00956046i	$0.996957\pi$
$992$	2.00000	+	3.46410i	0.0635001	+	0.109985i
$993$		0			0
$994$		0			0
$995$	−12.0000	−	20.7846i	−0.380426	−	0.658916i
$996$		0			0
$997$	−11.0000	−	19.0526i	−0.348373	−	0.603401i	0.637587	−	0.770378i	$-0.279933\pi$
$997$	−11.0000	−	19.0526i	−0.348373	−	0.603401i	−0.985961	+	0.166978i	$0.946599\pi$
$998$	−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.e.c.191.1		2
13.2	odd	12		1690.2.l.f.361.1		4
13.3	even	3	inner	1690.2.e.c.991.1		2
13.4	even	6		1690.2.a.b.1.1		1
13.5	odd	4		1690.2.l.f.1161.2		4
13.6	odd	12		1690.2.d.d.1351.1		2
13.7	odd	12		1690.2.d.d.1351.2		2
13.8	odd	4		1690.2.l.f.1161.1		4
13.9	even	3		130.2.a.b.1.1	✓	1
13.10	even	6		1690.2.e.i.991.1		2
13.11	odd	12		1690.2.l.f.361.2		4
13.12	even	2		1690.2.e.i.191.1		2
39.35	odd	6		1170.2.a.b.1.1		1
52.35	odd	6		1040.2.a.e.1.1		1
65.4	even	6		8450.2.a.r.1.1		1
65.9	even	6		650.2.a.d.1.1		1
65.22	odd	12		650.2.b.e.599.2		2
65.48	odd	12		650.2.b.e.599.1		2
91.48	odd	6		6370.2.a.r.1.1		1
104.35	odd	6		4160.2.a.h.1.1		1
104.61	even	6		4160.2.a.i.1.1		1
156.35	even	6		9360.2.a.l.1.1		1
195.74	odd	6		5850.2.a.bq.1.1		1
195.113	even	12		5850.2.e.q.5149.2		2
195.152	even	12		5850.2.e.q.5149.1		2
260.139	odd	6		5200.2.a.r.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.a.b.1.1	✓	1	13.9	even	3
650.2.a.d.1.1		1	65.9	even	6
650.2.b.e.599.1		2	65.48	odd	12
650.2.b.e.599.2		2	65.22	odd	12
1040.2.a.e.1.1		1	52.35	odd	6
1170.2.a.b.1.1		1	39.35	odd	6
1690.2.a.b.1.1		1	13.4	even	6
1690.2.d.d.1351.1		2	13.6	odd	12
1690.2.d.d.1351.2		2	13.7	odd	12
1690.2.e.c.191.1		2	1.1	even	1	trivial
1690.2.e.c.991.1		2	13.3	even	3	inner
1690.2.e.i.191.1		2	13.12	even	2
1690.2.e.i.991.1		2	13.10	even	6
1690.2.l.f.361.1		4	13.2	odd	12
1690.2.l.f.361.2		4	13.11	odd	12
1690.2.l.f.1161.1		4	13.8	odd	4
1690.2.l.f.1161.2		4	13.5	odd	4
4160.2.a.h.1.1		1	104.35	odd	6
4160.2.a.i.1.1		1	104.61	even	6
5200.2.a.r.1.1		1	260.139	odd	6
5850.2.a.bq.1.1		1	195.74	odd	6
5850.2.e.q.5149.1		2	195.152	even	12
5850.2.e.q.5149.2		2	195.113	even	12
6370.2.a.r.1.1		1	91.48	odd	6
8450.2.a.r.1.1		1	65.4	even	6
9360.2.a.l.1.1		1	156.35	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1690 = 2 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1690.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-0.500000 + 0.866025i) q^{16} +(-1.00000 - 1.73205i) q^{17} -3.00000 q^{18} +(4.00000 + 6.92820i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(2.00000 - 3.46410i) q^{23} +1.00000 q^{25} +(1.00000 - 1.73205i) q^{29} -4.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +2.00000 q^{34} +(1.50000 - 2.59808i) q^{36} +(-3.00000 + 5.19615i) q^{37} -8.00000 q^{38} +1.00000 q^{40} +(-5.00000 + 8.66025i) q^{41} +(1.50000 + 2.59808i) q^{45} +(2.00000 + 3.46410i) q^{46} +8.00000 q^{47} +(3.50000 - 6.06218i) q^{49} +(-0.500000 + 0.866025i) q^{50} +6.00000 q^{53} +(1.00000 + 1.73205i) q^{58} +(-4.00000 - 6.92820i) q^{59} +(1.00000 + 1.73205i) q^{61} +(2.00000 - 3.46410i) q^{62} +1.00000 q^{64} +(-2.00000 + 3.46410i) q^{67} +(-1.00000 + 1.73205i) q^{68} +(6.00000 + 10.3923i) q^{71} +(1.50000 + 2.59808i) q^{72} +10.0000 q^{73} +(-3.00000 - 5.19615i) q^{74} +(4.00000 - 6.92820i) q^{76} -8.00000 q^{79} +(-0.500000 + 0.866025i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-5.00000 - 8.66025i) q^{82} +12.0000 q^{83} +(-1.00000 - 1.73205i) q^{85} +(-5.00000 + 8.66025i) q^{89} -3.00000 q^{90} -4.00000 q^{92} +(-4.00000 + 6.92820i) q^{94} +(4.00000 + 6.92820i) q^{95} +(7.00000 + 12.1244i) q^{97} +(3.50000 + 6.06218i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} + 2 q^{5} + 2 q^{8} + 3 q^{9} - q^{10} - q^{16} - 2 q^{17} - 6 q^{18} + 8 q^{19} - q^{20} + 4 q^{23} + 2 q^{25} + 2 q^{29} - 8 q^{31} - q^{32} + 4 q^{34} + 3 q^{36} - 6 q^{37}+ \cdots + 7 q^{98}+O(q^{100}) \) 2 * q - q^2 - q^4 + 2 * q^5 + 2 * q^8 + 3 * q^9 - q^10 - q^16 - 2 * q^17 - 6 * q^18 + 8 * q^19 - q^20 + 4 * q^23 + 2 * q^25 + 2 * q^29 - 8 * q^31 - q^32 + 4 * q^34 + 3 * q^36 - 6 * q^37 - 16 * q^38 + 2 * q^40 - 10 * q^41 + 3 * q^45 + 4 * q^46 + 16 * q^47 + 7 * q^49 - q^50 + 12 * q^53 + 2 * q^58 - 8 * q^59 + 2 * q^61 + 4 * q^62 + 2 * q^64 - 4 * q^67 - 2 * q^68 + 12 * q^71 + 3 * q^72 + 20 * q^73 - 6 * q^74 + 8 * q^76 - 16 * q^79 - q^80 - 9 * q^81 - 10 * q^82 + 24 * q^83 - 2 * q^85 - 10 * q^89 - 6 * q^90 - 8 * q^92 - 8 * q^94 + 8 * q^95 + 14 * q^97 + 7 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more