LMFDB - Embedded newform 1710.2.l.f.1261.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(1261,1710)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1710.1261");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1710.l (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.6544187456$
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 570)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1261.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1710.1261
Dual form			1710.2.l.f.1531.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.00000 q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.00000 q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{10} -2.00000 q^{11} +(1.50000 - 2.59808i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.00000 + 3.46410i) q^{17} +(4.00000 + 1.73205i) q^{19} +1.00000 q^{20} +(-1.00000 - 1.73205i) q^{22} +(-3.00000 + 5.19615i) q^{23} +(-0.500000 + 0.866025i) q^{25} +3.00000 q^{26} +(0.500000 - 0.866025i) q^{28} +(-5.00000 + 8.66025i) q^{29} +1.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-2.00000 + 3.46410i) q^{34} +(0.500000 + 0.866025i) q^{35} -5.00000 q^{37} +(0.500000 + 4.33013i) q^{38} +(0.500000 + 0.866025i) q^{40} +(1.00000 + 1.73205i) q^{41} +(2.50000 + 4.33013i) q^{43} +(1.00000 - 1.73205i) q^{44} -6.00000 q^{46} -6.00000 q^{49} -1.00000 q^{50} +(1.50000 + 2.59808i) q^{52} +(-6.00000 + 10.3923i) q^{53} +(1.00000 + 1.73205i) q^{55} +1.00000 q^{56} -10.0000 q^{58} +(-1.00000 - 1.73205i) q^{59} +(-2.50000 + 4.33013i) q^{61} +(0.500000 + 0.866025i) q^{62} +1.00000 q^{64} -3.00000 q^{65} +(2.50000 - 4.33013i) q^{67} -4.00000 q^{68} +(-0.500000 + 0.866025i) q^{70} +(-5.50000 - 9.52628i) q^{73} +(-2.50000 - 4.33013i) q^{74} +(-3.50000 + 2.59808i) q^{76} +2.00000 q^{77} +(5.50000 + 9.52628i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-1.00000 + 1.73205i) q^{82} -2.00000 q^{83} +(2.00000 - 3.46410i) q^{85} +(-2.50000 + 4.33013i) q^{86} +2.00000 q^{88} +(-1.50000 + 2.59808i) q^{91} +(-3.00000 - 5.19615i) q^{92} +(-0.500000 - 4.33013i) q^{95} +(1.00000 + 1.73205i) q^{97} +(-3.00000 - 5.19615i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{4} - q^{5} - 2 q^{7} - 2 q^{8}+O(q^{10}) $ 2 * q + q^2 - q^4 - q^5 - 2 * q^7 - 2 * q^8	$ 2 q + q^{2} - q^{4} - q^{5} - 2 q^{7} - 2 q^{8} + q^{10} - 4 q^{11} + 3 q^{13} - q^{14} - q^{16} + 4 q^{17} + 8 q^{19} + 2 q^{20} - 2 q^{22} - 6 q^{23} - q^{25} + 6 q^{26} + q^{28} - 10 q^{29} + 2 q^{31} + q^{32} - 4 q^{34} + q^{35} - 10 q^{37} + q^{38} + q^{40} + 2 q^{41} + 5 q^{43} + 2 q^{44} - 12 q^{46} - 12 q^{49} - 2 q^{50} + 3 q^{52} - 12 q^{53} + 2 q^{55} + 2 q^{56} - 20 q^{58} - 2 q^{59} - 5 q^{61} + q^{62} + 2 q^{64} - 6 q^{65} + 5 q^{67} - 8 q^{68} - q^{70} - 11 q^{73} - 5 q^{74} - 7 q^{76} + 4 q^{77} + 11 q^{79} - q^{80} - 2 q^{82} - 4 q^{83} + 4 q^{85} - 5 q^{86} + 4 q^{88} - 3 q^{91} - 6 q^{92} - q^{95} + 2 q^{97} - 6 q^{98}+O(q^{100}) $ 2 * q + q^2 - q^4 - q^5 - 2 * q^7 - 2 * q^8 + q^10 - 4 * q^11 + 3 * q^13 - q^14 - q^16 + 4 * q^17 + 8 * q^19 + 2 * q^20 - 2 * q^22 - 6 * q^23 - q^25 + 6 * q^26 + q^28 - 10 * q^29 + 2 * q^31 + q^32 - 4 * q^34 + q^35 - 10 * q^37 + q^38 + q^40 + 2 * q^41 + 5 * q^43 + 2 * q^44 - 12 * q^46 - 12 * q^49 - 2 * q^50 + 3 * q^52 - 12 * q^53 + 2 * q^55 + 2 * q^56 - 20 * q^58 - 2 * q^59 - 5 * q^61 + q^62 + 2 * q^64 - 6 * q^65 + 5 * q^67 - 8 * q^68 - q^70 - 11 * q^73 - 5 * q^74 - 7 * q^76 + 4 * q^77 + 11 * q^79 - q^80 - 2 * q^82 - 4 * q^83 + 4 * q^85 - 5 * q^86 + 4 * q^88 - 3 * q^91 - 6 * q^92 - q^95 + 2 * q^97 - 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$.

$n$	$191$	$1027$	$1351$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	−1.00000			−0.377964			−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000			−0.377964			−0.188982	+	0.981981i	$0.560519\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	−2.00000			−0.603023			−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000			−0.603023			−0.301511	+	0.953463i	$0.597491\pi$
$12$		0			0
$13$	1.50000	−	2.59808i	0.416025	−	0.720577i	−0.579510	−	0.814965i	$-0.696756\pi$
$13$	1.50000	−	2.59808i	0.416025	−	0.720577i	0.995535	+	0.0943882i	$0.0300895\pi$
$14$	−0.500000	−	0.866025i	−0.133631	−	0.231455i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.00000	+	3.46410i	0.485071	+	0.840168i	0.999853	−	0.0171533i	$-0.00546033\pi$
$17$	2.00000	+	3.46410i	0.485071	+	0.840168i	−0.514782	+	0.857321i	$0.672127\pi$
$18$		0			0
$19$	4.00000	+	1.73205i	0.917663	+	0.397360i
$19$	4.00000	+	1.73205i	0.917663	+	0.397360i
$20$	1.00000			0.223607
$21$		0			0
$22$	−1.00000	−	1.73205i	−0.213201	−	0.369274i
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	0.362892	+	0.931831i	$0.381789\pi$
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	−0.988436	+	0.151642i	$0.951544\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	3.00000			0.588348
$27$		0			0
$28$	0.500000	−	0.866025i	0.0944911	−	0.163663i
$29$	−5.00000	+	8.66025i	−0.928477	+	1.60817i	−0.142605	+	0.989780i	$0.545548\pi$
$29$	−5.00000	+	8.66025i	−0.928477	+	1.60817i	−0.785872	+	0.618389i	$0.787786\pi$
$30$		0			0
$31$	1.00000			0.179605			0.0898027	−	0.995960i	$-0.471376\pi$
$31$	1.00000			0.179605			0.0898027	+	0.995960i	$0.471376\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	−2.00000	+	3.46410i	−0.342997	+	0.594089i
$35$	0.500000	+	0.866025i	0.0845154	+	0.146385i
$36$		0			0
$37$	−5.00000			−0.821995			−0.410997	−	0.911636i	$-0.634819\pi$
$37$	−5.00000			−0.821995			−0.410997	+	0.911636i	$0.634819\pi$
$38$	0.500000	+	4.33013i	0.0811107	+	0.702439i
$39$		0			0
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	1.00000	+	1.73205i	0.156174	+	0.270501i	0.933486	−	0.358614i	$-0.116751\pi$
$41$	1.00000	+	1.73205i	0.156174	+	0.270501i	−0.777312	+	0.629115i	$0.783417\pi$
$42$		0			0
$43$	2.50000	+	4.33013i	0.381246	+	0.660338i	0.991241	−	0.132068i	$-0.0421616\pi$
$43$	2.50000	+	4.33013i	0.381246	+	0.660338i	−0.609994	+	0.792406i	$0.708828\pi$
$44$	1.00000	−	1.73205i	0.150756	−	0.261116i
$45$		0			0
$46$	−6.00000			−0.884652
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$		0			0
$49$	−6.00000			−0.857143
$50$	−1.00000			−0.141421
$51$		0			0
$52$	1.50000	+	2.59808i	0.208013	+	0.360288i
$53$	−6.00000	+	10.3923i	−0.824163	+	1.42749i	0.0783936	+	0.996922i	$0.475021\pi$
$53$	−6.00000	+	10.3923i	−0.824163	+	1.42749i	−0.902557	+	0.430570i	$0.858312\pi$
$54$		0			0
$55$	1.00000	+	1.73205i	0.134840	+	0.233550i
$56$	1.00000			0.133631
$57$		0			0
$58$	−10.0000			−1.31306
$59$	−1.00000	−	1.73205i	−0.130189	−	0.225494i	0.793560	−	0.608492i	$-0.208225\pi$
$59$	−1.00000	−	1.73205i	−0.130189	−	0.225494i	−0.923749	+	0.382998i	$0.874892\pi$
$60$		0			0
$61$	−2.50000	+	4.33013i	−0.320092	+	0.554416i	−0.980507	−	0.196485i	$-0.937047\pi$
$61$	−2.50000	+	4.33013i	−0.320092	+	0.554416i	0.660415	+	0.750901i	$0.270381\pi$
$62$	0.500000	+	0.866025i	0.0635001	+	0.109985i
$63$		0			0
$64$	1.00000			0.125000
$65$	−3.00000			−0.372104
$66$		0			0
$67$	2.50000	−	4.33013i	0.305424	−	0.529009i	−0.671932	−	0.740613i	$-0.734535\pi$
$67$	2.50000	−	4.33013i	0.305424	−	0.529009i	0.977356	+	0.211604i	$0.0678686\pi$
$68$	−4.00000			−0.485071
$69$		0			0
$70$	−0.500000	+	0.866025i	−0.0597614	+	0.103510i
$71$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$71$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$72$		0			0
$73$	−5.50000	−	9.52628i	−0.643726	−	1.11497i	−0.984594	−	0.174855i	$-0.944054\pi$
$73$	−5.50000	−	9.52628i	−0.643726	−	1.11497i	0.340868	−	0.940111i	$-0.389279\pi$
$74$	−2.50000	−	4.33013i	−0.290619	−	0.503367i
$75$		0			0
$76$	−3.50000	+	2.59808i	−0.401478	+	0.298020i
$77$	2.00000			0.227921
$78$		0			0
$79$	5.50000	+	9.52628i	0.618798	+	1.07179i	0.989705	+	0.143120i	$0.0457135\pi$
$79$	5.50000	+	9.52628i	0.618798	+	1.07179i	−0.370907	+	0.928670i	$0.620953\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$		0			0
$82$	−1.00000	+	1.73205i	−0.110432	+	0.191273i
$83$	−2.00000			−0.219529			−0.109764	−	0.993958i	$-0.535010\pi$
$83$	−2.00000			−0.219529			−0.109764	+	0.993958i	$0.535010\pi$
$84$		0			0
$85$	2.00000	−	3.46410i	0.216930	−	0.375735i
$86$	−2.50000	+	4.33013i	−0.269582	+	0.466930i
$87$		0			0
$88$	2.00000			0.213201
$89$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$89$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$90$		0			0
$91$	−1.50000	+	2.59808i	−0.157243	+	0.272352i
$92$	−3.00000	−	5.19615i	−0.312772	−	0.541736i
$93$		0			0
$94$		0			0
$95$	−0.500000	−	4.33013i	−0.0512989	−	0.444262i
$96$		0			0
$97$	1.00000	+	1.73205i	0.101535	+	0.175863i	0.912317	−	0.409484i	$-0.134291\pi$
$97$	1.00000	+	1.73205i	0.101535	+	0.175863i	−0.810782	+	0.585348i	$0.800958\pi$
$98$	−3.00000	−	5.19615i	−0.303046	−	0.524891i
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	−0.677284	−	0.735721i	$-0.736843\pi$
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	0.975796	+	0.218685i	$0.0701767\pi$
$102$		0			0
$103$	19.0000			1.87213			0.936063	−	0.351833i	$-0.114441\pi$
$103$	19.0000			1.87213			0.936063	+	0.351833i	$0.114441\pi$
$104$	−1.50000	+	2.59808i	−0.147087	+	0.254762i
$105$		0			0
$106$	−12.0000			−1.16554
$107$	4.00000			0.386695			0.193347	−	0.981130i	$-0.438066\pi$
$107$	4.00000			0.386695			0.193347	+	0.981130i	$0.438066\pi$
$108$		0			0
$109$	9.00000	+	15.5885i	0.862044	+	1.49310i	0.869953	+	0.493135i	$0.164149\pi$
$109$	9.00000	+	15.5885i	0.862044	+	1.49310i	−0.00790932	+	0.999969i	$0.502518\pi$
$110$	−1.00000	+	1.73205i	−0.0953463	+	0.165145i
$111$		0			0
$112$	0.500000	+	0.866025i	0.0472456	+	0.0818317i
$113$	−14.0000			−1.31701			−0.658505	−	0.752577i	$-0.728811\pi$
$113$	−14.0000			−1.31701			−0.658505	+	0.752577i	$0.728811\pi$
$114$		0			0
$115$	6.00000			0.559503
$116$	−5.00000	−	8.66025i	−0.464238	−	0.804084i
$117$		0			0
$118$	1.00000	−	1.73205i	0.0920575	−	0.159448i
$119$	−2.00000	−	3.46410i	−0.183340	−	0.317554i
$120$		0			0
$121$	−7.00000			−0.636364
$122$	−5.00000			−0.452679
$123$		0			0
$124$	−0.500000	+	0.866025i	−0.0449013	+	0.0777714i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−8.00000	+	13.8564i	−0.709885	+	1.22956i	0.255014	+	0.966937i	$0.417920\pi$
$127$	−8.00000	+	13.8564i	−0.709885	+	1.22956i	−0.964899	+	0.262620i	$0.915413\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−1.50000	−	2.59808i	−0.131559	−	0.227866i
$131$	−3.00000	−	5.19615i	−0.262111	−	0.453990i	0.704692	−	0.709514i	$-0.251085\pi$
$131$	−3.00000	−	5.19615i	−0.262111	−	0.453990i	−0.966803	+	0.255524i	$0.917752\pi$
$132$		0			0
$133$	−4.00000	−	1.73205i	−0.346844	−	0.150188i
$134$	5.00000			0.431934
$135$		0			0
$136$	−2.00000	−	3.46410i	−0.171499	−	0.297044i
$137$	−1.00000	+	1.73205i	−0.0854358	+	0.147979i	−0.905577	−	0.424182i	$-0.860562\pi$
$137$	−1.00000	+	1.73205i	−0.0854358	+	0.147979i	0.820141	+	0.572161i	$0.193895\pi$
$138$		0			0
$139$	4.50000	−	7.79423i	0.381685	−	0.661098i	−0.609618	−	0.792695i	$-0.708677\pi$
$139$	4.50000	−	7.79423i	0.381685	−	0.661098i	0.991303	+	0.131597i	$0.0420106\pi$
$140$	−1.00000			−0.0845154
$141$		0			0
$142$		0			0
$143$	−3.00000	+	5.19615i	−0.250873	+	0.434524i
$144$		0			0
$145$	10.0000			0.830455
$146$	5.50000	−	9.52628i	0.455183	−	0.788400i
$147$		0			0
$148$	2.50000	−	4.33013i	0.205499	−	0.355934i
$149$	9.00000	+	15.5885i	0.737309	+	1.27706i	0.953703	+	0.300750i	$0.0972370\pi$
$149$	9.00000	+	15.5885i	0.737309	+	1.27706i	−0.216394	+	0.976306i	$0.569430\pi$
$150$		0			0
$151$		0			0			−	1.00000i	$-0.5\pi$
$151$		0			0				1.00000i	$0.5\pi$
$152$	−4.00000	−	1.73205i	−0.324443	−	0.140488i
$153$		0			0
$154$	1.00000	+	1.73205i	0.0805823	+	0.139573i
$155$	−0.500000	−	0.866025i	−0.0401610	−	0.0695608i
$156$		0			0
$157$	6.50000	+	11.2583i	0.518756	+	0.898513i	0.999762	+	0.0217953i	$0.00693820\pi$
$157$	6.50000	+	11.2583i	0.518756	+	0.898513i	−0.481006	+	0.876717i	$0.659728\pi$
$158$	−5.50000	+	9.52628i	−0.437557	+	0.757870i
$159$		0			0
$160$	−1.00000			−0.0790569
$161$	3.00000	−	5.19615i	0.236433	−	0.409514i
$162$		0			0
$163$	−17.0000			−1.33154			−0.665771	−	0.746156i	$-0.731897\pi$
$163$	−17.0000			−1.33154			−0.665771	+	0.746156i	$0.731897\pi$
$164$	−2.00000			−0.156174
$165$		0			0
$166$	−1.00000	−	1.73205i	−0.0776151	−	0.134433i
$167$	7.00000	−	12.1244i	0.541676	−	0.938211i	−0.457132	−	0.889399i	$-0.651123\pi$
$167$	7.00000	−	12.1244i	0.541676	−	0.938211i	0.998808	−	0.0488118i	$-0.0155435\pi$
$168$		0			0
$169$	2.00000	+	3.46410i	0.153846	+	0.266469i
$170$	4.00000			0.306786
$171$		0			0
$172$	−5.00000			−0.381246
$173$	−13.0000	−	22.5167i	−0.988372	−	1.71191i	−0.625871	−	0.779926i	$-0.715256\pi$
$173$	−13.0000	−	22.5167i	−0.988372	−	1.71191i	−0.362500	−	0.931984i	$-0.618077\pi$
$174$		0			0
$175$	0.500000	−	0.866025i	0.0377964	−	0.0654654i
$176$	1.00000	+	1.73205i	0.0753778	+	0.130558i
$177$		0			0
$178$		0			0
$179$	10.0000			0.747435			0.373718	−	0.927543i	$-0.378083\pi$
$179$	10.0000			0.747435			0.373718	+	0.927543i	$0.378083\pi$
$180$		0			0
$181$	3.00000	−	5.19615i	0.222988	−	0.386227i	−0.732726	−	0.680524i	$-0.761752\pi$
$181$	3.00000	−	5.19615i	0.222988	−	0.386227i	0.955714	+	0.294297i	$0.0950855\pi$
$182$	−3.00000			−0.222375
$183$		0			0
$184$	3.00000	−	5.19615i	0.221163	−	0.383065i
$185$	2.50000	+	4.33013i	0.183804	+	0.318357i
$186$		0			0
$187$	−4.00000	−	6.92820i	−0.292509	−	0.506640i
$188$		0			0
$189$		0			0
$190$	3.50000	−	2.59808i	0.253917	−	0.188484i
$191$	−16.0000			−1.15772			−0.578860	−	0.815427i	$-0.696502\pi$
$191$	−16.0000			−1.15772			−0.578860	+	0.815427i	$0.696502\pi$
$192$		0			0
$193$	−12.5000	−	21.6506i	−0.899770	−	1.55845i	−0.827788	−	0.561041i	$-0.810401\pi$
$193$	−12.5000	−	21.6506i	−0.899770	−	1.55845i	−0.0719816	−	0.997406i	$-0.522932\pi$
$194$	−1.00000	+	1.73205i	−0.0717958	+	0.124354i
$195$		0			0
$196$	3.00000	−	5.19615i	0.214286	−	0.371154i
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$		0			0
$199$	−2.50000	+	4.33013i	−0.177220	+	0.306955i	−0.940927	−	0.338608i	$-0.890044\pi$
$199$	−2.50000	+	4.33013i	−0.177220	+	0.306955i	0.763707	+	0.645563i	$0.223377\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$		0			0
$202$	6.00000			0.422159
$203$	5.00000	−	8.66025i	0.350931	−	0.607831i
$204$		0			0
$205$	1.00000	−	1.73205i	0.0698430	−	0.120972i
$206$	9.50000	+	16.4545i	0.661896	+	1.14644i
$207$		0			0
$208$	−3.00000			−0.208013
$209$	−8.00000	−	3.46410i	−0.553372	−	0.239617i
$210$		0			0
$211$	2.50000	+	4.33013i	0.172107	+	0.298098i	0.939156	−	0.343490i	$-0.111609\pi$
$211$	2.50000	+	4.33013i	0.172107	+	0.298098i	−0.767049	+	0.641588i	$0.778276\pi$
$212$	−6.00000	−	10.3923i	−0.412082	−	0.713746i
$213$		0			0
$214$	2.00000	+	3.46410i	0.136717	+	0.236801i
$215$	2.50000	−	4.33013i	0.170499	−	0.295312i
$216$		0			0
$217$	−1.00000			−0.0678844
$218$	−9.00000	+	15.5885i	−0.609557	+	1.05578i
$219$		0			0
$220$	−2.00000			−0.134840
$221$	12.0000			0.807207
$222$		0			0
$223$	0.500000	+	0.866025i	0.0334825	+	0.0579934i	0.882281	−	0.470723i	$-0.156007\pi$
$223$	0.500000	+	0.866025i	0.0334825	+	0.0579934i	−0.848799	+	0.528716i	$0.822674\pi$
$224$	−0.500000	+	0.866025i	−0.0334077	+	0.0578638i
$225$		0			0
$226$	−7.00000	−	12.1244i	−0.465633	−	0.806500i
$227$	18.0000			1.19470			0.597351	−	0.801980i	$-0.296220\pi$
$227$	18.0000			1.19470			0.597351	+	0.801980i	$0.296220\pi$
$228$		0			0
$229$	−5.00000			−0.330409			−0.165205	−	0.986259i	$-0.552828\pi$
$229$	−5.00000			−0.330409			−0.165205	+	0.986259i	$0.552828\pi$
$230$	3.00000	+	5.19615i	0.197814	+	0.342624i
$231$		0			0
$232$	5.00000	−	8.66025i	0.328266	−	0.568574i
$233$	−2.00000	−	3.46410i	−0.131024	−	0.226941i	0.793047	−	0.609160i	$-0.208493\pi$
$233$	−2.00000	−	3.46410i	−0.131024	−	0.226941i	−0.924072	+	0.382219i	$0.875160\pi$
$234$		0			0
$235$		0			0
$236$	2.00000			0.130189
$237$		0			0
$238$	2.00000	−	3.46410i	0.129641	−	0.224544i
$239$	18.0000			1.16432			0.582162	−	0.813073i	$-0.302207\pi$
$239$	18.0000			1.16432			0.582162	+	0.813073i	$0.302207\pi$
$240$		0			0
$241$	−2.50000	+	4.33013i	−0.161039	+	0.278928i	−0.935242	−	0.354010i	$-0.884818\pi$
$241$	−2.50000	+	4.33013i	−0.161039	+	0.278928i	0.774202	+	0.632938i	$0.218151\pi$
$242$	−3.50000	−	6.06218i	−0.224989	−	0.389692i
$243$		0			0
$244$	−2.50000	−	4.33013i	−0.160046	−	0.277208i
$245$	3.00000	+	5.19615i	0.191663	+	0.331970i
$246$		0			0
$247$	10.5000	−	7.79423i	0.668099	−	0.495935i
$248$	−1.00000			−0.0635001
$249$		0			0
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	−1.00000	+	1.73205i	−0.0631194	+	0.109326i	−0.895858	−	0.444340i	$-0.853438\pi$
$251$	−1.00000	+	1.73205i	−0.0631194	+	0.109326i	0.832739	+	0.553666i	$0.186772\pi$
$252$		0			0
$253$	6.00000	−	10.3923i	0.377217	−	0.653359i
$254$	−16.0000			−1.00393
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	−0.944294	−	0.329104i	$-0.893253\pi$
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	0.757159	+	0.653231i	$0.226587\pi$
$258$		0			0
$259$	5.00000			0.310685
$260$	1.50000	−	2.59808i	0.0930261	−	0.161126i
$261$		0			0
$262$	3.00000	−	5.19615i	0.185341	−	0.321019i
$263$	−5.00000	−	8.66025i	−0.308313	−	0.534014i	0.669680	−	0.742650i	$-0.266431\pi$
$263$	−5.00000	−	8.66025i	−0.308313	−	0.534014i	−0.977993	+	0.208635i	$0.933098\pi$
$264$		0			0
$265$	12.0000			0.737154
$266$	−0.500000	−	4.33013i	−0.0306570	−	0.265497i
$267$		0			0
$268$	2.50000	+	4.33013i	0.152712	+	0.264505i
$269$	5.00000	+	8.66025i	0.304855	+	0.528025i	0.977229	−	0.212187i	$-0.0680585\pi$
$269$	5.00000	+	8.66025i	0.304855	+	0.528025i	−0.672374	+	0.740212i	$0.734725\pi$
$270$		0			0
$271$	4.00000	+	6.92820i	0.242983	+	0.420858i	0.961563	−	0.274586i	$-0.0885408\pi$
$271$	4.00000	+	6.92820i	0.242983	+	0.420858i	−0.718580	+	0.695444i	$0.755208\pi$
$272$	2.00000	−	3.46410i	0.121268	−	0.210042i
$273$		0			0
$274$	−2.00000			−0.120824
$275$	1.00000	−	1.73205i	0.0603023	−	0.104447i
$276$		0			0
$277$	−10.0000			−0.600842			−0.300421	−	0.953807i	$-0.597127\pi$
$277$	−10.0000			−0.600842			−0.300421	+	0.953807i	$0.597127\pi$
$278$	9.00000			0.539784
$279$		0			0
$280$	−0.500000	−	0.866025i	−0.0298807	−	0.0517549i
$281$	−15.0000	+	25.9808i	−0.894825	+	1.54988i	−0.0608039	+	0.998150i	$0.519366\pi$
$281$	−15.0000	+	25.9808i	−0.894825	+	1.54988i	−0.834021	+	0.551733i	$0.813967\pi$
$282$		0			0
$283$	−4.00000	−	6.92820i	−0.237775	−	0.411839i	0.722300	−	0.691580i	$-0.243085\pi$
$283$	−4.00000	−	6.92820i	−0.237775	−	0.411839i	−0.960076	+	0.279741i	$0.909752\pi$
$284$		0			0
$285$		0			0
$286$	−6.00000			−0.354787
$287$	−1.00000	−	1.73205i	−0.0590281	−	0.102240i
$288$		0			0
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$	5.00000	+	8.66025i	0.293610	+	0.508548i
$291$		0			0
$292$	11.0000			0.643726
$293$	26.0000			1.51894			0.759468	−	0.650545i	$-0.225459\pi$
$293$	26.0000			1.51894			0.759468	+	0.650545i	$0.225459\pi$
$294$		0			0
$295$	−1.00000	+	1.73205i	−0.0582223	+	0.100844i
$296$	5.00000			0.290619
$297$		0			0
$298$	−9.00000	+	15.5885i	−0.521356	+	0.903015i
$299$	9.00000	+	15.5885i	0.520483	+	0.901504i
$300$		0			0
$301$	−2.50000	−	4.33013i	−0.144098	−	0.249584i
$302$		0			0
$303$		0			0
$304$	−0.500000	−	4.33013i	−0.0286770	−	0.248350i
$305$	5.00000			0.286299
$306$		0			0
$307$	−2.00000	−	3.46410i	−0.114146	−	0.197707i	0.803292	−	0.595585i	$-0.203080\pi$
$307$	−2.00000	−	3.46410i	−0.114146	−	0.197707i	−0.917438	+	0.397879i	$0.869747\pi$
$308$	−1.00000	+	1.73205i	−0.0569803	+	0.0986928i
$309$		0			0
$310$	0.500000	−	0.866025i	0.0283981	−	0.0491869i
$311$	10.0000			0.567048			0.283524	−	0.958965i	$-0.408496\pi$
$311$	10.0000			0.567048			0.283524	+	0.958965i	$0.408496\pi$
$312$		0			0
$313$	−9.00000	+	15.5885i	−0.508710	+	0.881112i	0.491239	+	0.871025i	$0.336544\pi$
$313$	−9.00000	+	15.5885i	−0.508710	+	0.881112i	−0.999949	+	0.0100869i	$0.996789\pi$
$314$	−6.50000	+	11.2583i	−0.366816	+	0.635344i
$315$		0			0
$316$	−11.0000			−0.618798
$317$	15.0000	−	25.9808i	0.842484	−	1.45922i	−0.0453045	−	0.998973i	$-0.514426\pi$
$317$	15.0000	−	25.9808i	0.842484	−	1.45922i	0.887788	−	0.460252i	$-0.152241\pi$
$318$		0			0
$319$	10.0000	−	17.3205i	0.559893	−	0.969762i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$		0			0
$322$	6.00000			0.334367
$323$	2.00000	+	17.3205i	0.111283	+	0.963739i
$324$		0			0
$325$	1.50000	+	2.59808i	0.0832050	+	0.144115i
$326$	−8.50000	−	14.7224i	−0.470771	−	0.815400i
$327$		0			0
$328$	−1.00000	−	1.73205i	−0.0552158	−	0.0956365i
$329$		0			0
$330$		0			0
$331$	5.00000			0.274825			0.137412	−	0.990514i	$-0.456121\pi$
$331$	5.00000			0.274825			0.137412	+	0.990514i	$0.456121\pi$
$332$	1.00000	−	1.73205i	0.0548821	−	0.0950586i
$333$		0			0
$334$	14.0000			0.766046
$335$	−5.00000			−0.273179
$336$		0			0
$337$	−11.5000	−	19.9186i	−0.626445	−	1.08503i	−0.988260	−	0.152784i	$-0.951176\pi$
$337$	−11.5000	−	19.9186i	−0.626445	−	1.08503i	0.361815	−	0.932250i	$-0.382157\pi$
$338$	−2.00000	+	3.46410i	−0.108786	+	0.188422i
$339$		0			0
$340$	2.00000	+	3.46410i	0.108465	+	0.187867i
$341$	−2.00000			−0.108306
$342$		0			0
$343$	13.0000			0.701934
$344$	−2.50000	−	4.33013i	−0.134791	−	0.233465i
$345$		0			0
$346$	13.0000	−	22.5167i	0.698884	−	1.21050i
$347$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$347$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$348$		0			0
$349$	17.0000			0.909989			0.454995	−	0.890494i	$-0.349641\pi$
$349$	17.0000			0.909989			0.454995	+	0.890494i	$0.349641\pi$
$350$	1.00000			0.0534522
$351$		0			0
$352$	−1.00000	+	1.73205i	−0.0533002	+	0.0923186i
$353$	6.00000			0.319348			0.159674	−	0.987170i	$-0.448956\pi$
$353$	6.00000			0.319348			0.159674	+	0.987170i	$0.448956\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	5.00000	+	8.66025i	0.264258	+	0.457709i
$359$	−1.00000	−	1.73205i	−0.0527780	−	0.0914141i	0.838429	−	0.545010i	$-0.183474\pi$
$359$	−1.00000	−	1.73205i	−0.0527780	−	0.0914141i	−0.891207	+	0.453596i	$0.850141\pi$
$360$		0			0
$361$	13.0000	+	13.8564i	0.684211	+	0.729285i
$362$	6.00000			0.315353
$363$		0			0
$364$	−1.50000	−	2.59808i	−0.0786214	−	0.136176i
$365$	−5.50000	+	9.52628i	−0.287883	+	0.498628i
$366$		0			0
$367$	3.50000	−	6.06218i	0.182699	−	0.316443i	−0.760100	−	0.649806i	$-0.774850\pi$
$367$	3.50000	−	6.06218i	0.182699	−	0.316443i	0.942799	+	0.333363i	$0.108183\pi$
$368$	6.00000			0.312772
$369$		0			0
$370$	−2.50000	+	4.33013i	−0.129969	+	0.225113i
$371$	6.00000	−	10.3923i	0.311504	−	0.539542i
$372$		0			0
$373$	−22.0000			−1.13912			−0.569558	−	0.821951i	$-0.692886\pi$
$373$	−22.0000			−1.13912			−0.569558	+	0.821951i	$0.692886\pi$
$374$	4.00000	−	6.92820i	0.206835	−	0.358249i
$375$		0			0
$376$		0			0
$377$	15.0000	+	25.9808i	0.772539	+	1.33808i
$378$		0			0
$379$	−11.0000			−0.565032			−0.282516	−	0.959263i	$-0.591169\pi$
$379$	−11.0000			−0.565032			−0.282516	+	0.959263i	$0.591169\pi$
$380$	4.00000	+	1.73205i	0.205196	+	0.0888523i
$381$		0			0
$382$	−8.00000	−	13.8564i	−0.409316	−	0.708955i
$383$	−18.0000	−	31.1769i	−0.919757	−	1.59307i	−0.799783	−	0.600289i	$-0.795052\pi$
$383$	−18.0000	−	31.1769i	−0.919757	−	1.59307i	−0.119974	−	0.992777i	$-0.538281\pi$
$384$		0			0
$385$	−1.00000	−	1.73205i	−0.0509647	−	0.0882735i
$386$	12.5000	−	21.6506i	0.636233	−	1.10199i
$387$		0			0
$388$	−2.00000			−0.101535
$389$	−5.00000	+	8.66025i	−0.253510	+	0.439092i	−0.964490	−	0.264120i	$-0.914918\pi$
$389$	−5.00000	+	8.66025i	−0.253510	+	0.439092i	0.710980	+	0.703213i	$0.248252\pi$
$390$		0			0
$391$	−24.0000			−1.21373
$392$	6.00000			0.303046
$393$		0			0
$394$	9.00000	+	15.5885i	0.453413	+	0.785335i
$395$	5.50000	−	9.52628i	0.276735	−	0.479319i
$396$		0			0
$397$	0.500000	+	0.866025i	0.0250943	+	0.0434646i	0.878300	−	0.478110i	$-0.158678\pi$
$397$	0.500000	+	0.866025i	0.0250943	+	0.0434646i	−0.853206	+	0.521575i	$0.825345\pi$
$398$	−5.00000			−0.250627
$399$		0			0
$400$	1.00000			0.0500000
$401$	−19.0000	−	32.9090i	−0.948815	−	1.64340i	−0.747927	−	0.663781i	$-0.768951\pi$
$401$	−19.0000	−	32.9090i	−0.948815	−	1.64340i	−0.200888	−	0.979614i	$-0.564383\pi$
$402$		0			0
$403$	1.50000	−	2.59808i	0.0747203	−	0.129419i
$404$	3.00000	+	5.19615i	0.149256	+	0.258518i
$405$		0			0
$406$	10.0000			0.496292
$407$	10.0000			0.495682
$408$		0			0
$409$	15.0000	−	25.9808i	0.741702	−	1.28467i	−0.210017	−	0.977698i	$-0.567352\pi$
$409$	15.0000	−	25.9808i	0.741702	−	1.28467i	0.951720	−	0.306968i	$-0.0993146\pi$
$410$	2.00000			0.0987730
$411$		0			0
$412$	−9.50000	+	16.4545i	−0.468031	+	0.810654i
$413$	1.00000	+	1.73205i	0.0492068	+	0.0852286i
$414$		0			0
$415$	1.00000	+	1.73205i	0.0490881	+	0.0850230i
$416$	−1.50000	−	2.59808i	−0.0735436	−	0.127381i
$417$		0			0
$418$	−1.00000	−	8.66025i	−0.0489116	−	0.423587i
$419$	24.0000			1.17248			0.586238	−	0.810139i	$-0.300608\pi$
$419$	24.0000			1.17248			0.586238	+	0.810139i	$0.300608\pi$
$420$		0			0
$421$	7.00000	+	12.1244i	0.341159	+	0.590905i	0.984648	−	0.174550i	$-0.0558472\pi$
$421$	7.00000	+	12.1244i	0.341159	+	0.590905i	−0.643489	+	0.765455i	$0.722514\pi$
$422$	−2.50000	+	4.33013i	−0.121698	+	0.210787i
$423$		0			0
$424$	6.00000	−	10.3923i	0.291386	−	0.504695i
$425$	−4.00000			−0.194029
$426$		0			0
$427$	2.50000	−	4.33013i	0.120983	−	0.209550i
$428$	−2.00000	+	3.46410i	−0.0966736	+	0.167444i
$429$		0			0
$430$	5.00000			0.241121
$431$	−10.0000	+	17.3205i	−0.481683	+	0.834300i	−0.999779	−	0.0210230i	$-0.993308\pi$
$431$	−10.0000	+	17.3205i	−0.481683	+	0.834300i	0.518096	+	0.855323i	$0.326641\pi$
$432$		0			0
$433$	−14.5000	+	25.1147i	−0.696826	+	1.20694i	0.272736	+	0.962089i	$0.412071\pi$
$433$	−14.5000	+	25.1147i	−0.696826	+	1.20694i	−0.969561	+	0.244848i	$0.921262\pi$
$434$	−0.500000	−	0.866025i	−0.0240008	−	0.0415705i
$435$		0			0
$436$	−18.0000			−0.862044
$437$	−21.0000	+	15.5885i	−1.00457	+	0.745697i
$438$		0			0
$439$	20.5000	+	35.5070i	0.978412	+	1.69466i	0.668184	+	0.743996i	$0.267072\pi$
$439$	20.5000	+	35.5070i	0.978412	+	1.69466i	0.310228	+	0.950662i	$0.399595\pi$
$440$	−1.00000	−	1.73205i	−0.0476731	−	0.0825723i
$441$		0			0
$442$	6.00000	+	10.3923i	0.285391	+	0.494312i
$443$	6.00000	−	10.3923i	0.285069	−	0.493753i	−0.687557	−	0.726130i	$-0.741317\pi$
$443$	6.00000	−	10.3923i	0.285069	−	0.493753i	0.972626	+	0.232377i	$0.0746503\pi$
$444$		0			0
$445$		0			0
$446$	−0.500000	+	0.866025i	−0.0236757	+	0.0410075i
$447$		0			0
$448$	−1.00000			−0.0472456
$449$	−28.0000			−1.32140			−0.660701	−	0.750649i	$-0.729741\pi$
$449$	−28.0000			−1.32140			−0.660701	+	0.750649i	$0.729741\pi$
$450$		0			0
$451$	−2.00000	−	3.46410i	−0.0941763	−	0.163118i
$452$	7.00000	−	12.1244i	0.329252	−	0.570282i
$453$		0			0
$454$	9.00000	+	15.5885i	0.422391	+	0.731603i
$455$	3.00000			0.140642
$456$		0			0
$457$	23.0000			1.07589			0.537947	−	0.842978i	$-0.319200\pi$
$457$	23.0000			1.07589			0.537947	+	0.842978i	$0.319200\pi$
$458$	−2.50000	−	4.33013i	−0.116817	−	0.202334i
$459$		0			0
$460$	−3.00000	+	5.19615i	−0.139876	+	0.242272i
$461$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$461$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$462$		0			0
$463$	1.00000			0.0464739			0.0232370	−	0.999730i	$-0.492603\pi$
$463$	1.00000			0.0464739			0.0232370	+	0.999730i	$0.492603\pi$
$464$	10.0000			0.464238
$465$		0			0
$466$	2.00000	−	3.46410i	0.0926482	−	0.160471i
$467$	−30.0000			−1.38823			−0.694117	−	0.719862i	$-0.744205\pi$
$467$	−30.0000			−1.38823			−0.694117	+	0.719862i	$0.744205\pi$
$468$		0			0
$469$	−2.50000	+	4.33013i	−0.115439	+	0.199947i
$470$		0			0
$471$		0			0
$472$	1.00000	+	1.73205i	0.0460287	+	0.0797241i
$473$	−5.00000	−	8.66025i	−0.229900	−	0.398199i
$474$		0			0
$475$	−3.50000	+	2.59808i	−0.160591	+	0.119208i
$476$	4.00000			0.183340
$477$		0			0
$478$	9.00000	+	15.5885i	0.411650	+	0.712999i
$479$	21.0000	−	36.3731i	0.959514	−	1.66193i	0.235833	−	0.971794i	$-0.424218\pi$
$479$	21.0000	−	36.3731i	0.959514	−	1.66193i	0.723681	−	0.690134i	$-0.242449\pi$
$480$		0			0
$481$	−7.50000	+	12.9904i	−0.341971	+	0.592310i
$482$	−5.00000			−0.227744
$483$		0			0
$484$	3.50000	−	6.06218i	0.159091	−	0.275554i
$485$	1.00000	−	1.73205i	0.0454077	−	0.0786484i
$486$		0			0
$487$	16.0000			0.725029			0.362515	−	0.931978i	$-0.381918\pi$
$487$	16.0000			0.725029			0.362515	+	0.931978i	$0.381918\pi$
$488$	2.50000	−	4.33013i	0.113170	−	0.196016i
$489$		0			0
$490$	−3.00000	+	5.19615i	−0.135526	+	0.234738i
$491$	14.0000	+	24.2487i	0.631811	+	1.09433i	0.987181	+	0.159603i	$0.0510215\pi$
$491$	14.0000	+	24.2487i	0.631811	+	1.09433i	−0.355370	+	0.934726i	$0.615645\pi$
$492$		0			0
$493$	−40.0000			−1.80151
$494$	12.0000	+	5.19615i	0.539906	+	0.233786i
$495$		0			0
$496$	−0.500000	−	0.866025i	−0.0224507	−	0.0388857i
$497$		0			0
$498$		0			0
$499$	12.5000	+	21.6506i	0.559577	+	0.969216i	0.997532	+	0.0702185i	$0.0223697\pi$
$499$	12.5000	+	21.6506i	0.559577	+	0.969216i	−0.437955	+	0.898997i	$0.644297\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$		0			0
$502$	−2.00000			−0.0892644
$503$	22.0000	−	38.1051i	0.980932	−	1.69902i	0.322151	−	0.946688i	$-0.395594\pi$
$503$	22.0000	−	38.1051i	0.980932	−	1.69902i	0.658781	−	0.752335i	$-0.271072\pi$
$504$		0			0
$505$	−6.00000			−0.266996
$506$	12.0000			0.533465
$507$		0			0
$508$	−8.00000	−	13.8564i	−0.354943	−	0.614779i
$509$	−4.00000	+	6.92820i	−0.177297	+	0.307087i	−0.940954	−	0.338535i	$-0.890069\pi$
$509$	−4.00000	+	6.92820i	−0.177297	+	0.307087i	0.763657	+	0.645622i	$0.223402\pi$
$510$		0			0
$511$	5.50000	+	9.52628i	0.243306	+	0.421418i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−6.00000			−0.264649
$515$	−9.50000	−	16.4545i	−0.418620	−	0.725071i
$516$		0			0
$517$		0			0
$518$	2.50000	+	4.33013i	0.109844	+	0.190255i
$519$		0			0
$520$	3.00000			0.131559
$521$	−8.00000			−0.350486			−0.175243	−	0.984525i	$-0.556071\pi$
$521$	−8.00000			−0.350486			−0.175243	+	0.984525i	$0.556071\pi$
$522$		0			0
$523$	5.50000	−	9.52628i	0.240498	−	0.416555i	−0.720358	−	0.693602i	$-0.756023\pi$
$523$	5.50000	−	9.52628i	0.240498	−	0.416555i	0.960856	+	0.277047i	$0.0893559\pi$
$524$	6.00000			0.262111
$525$		0			0
$526$	5.00000	−	8.66025i	0.218010	−	0.377605i
$527$	2.00000	+	3.46410i	0.0871214	+	0.150899i
$528$		0			0
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$	6.00000	+	10.3923i	0.260623	+	0.451413i
$531$		0			0
$532$	3.50000	−	2.59808i	0.151744	−	0.112641i
$533$	6.00000			0.259889
$534$		0			0
$535$	−2.00000	−	3.46410i	−0.0864675	−	0.149766i
$536$	−2.50000	+	4.33013i	−0.107984	+	0.187033i
$537$		0			0
$538$	−5.00000	+	8.66025i	−0.215565	+	0.373370i
$539$	12.0000			0.516877
$540$		0			0
$541$	4.50000	−	7.79423i	0.193470	−	0.335100i	−0.752928	−	0.658103i	$-0.771359\pi$
$541$	4.50000	−	7.79423i	0.193470	−	0.335100i	0.946398	+	0.323003i	$0.104692\pi$
$542$	−4.00000	+	6.92820i	−0.171815	+	0.297592i
$543$		0			0
$544$	4.00000			0.171499
$545$	9.00000	−	15.5885i	0.385518	−	0.667736i
$546$		0			0
$547$	4.50000	−	7.79423i	0.192406	−	0.333257i	−0.753641	−	0.657286i	$-0.771704\pi$
$547$	4.50000	−	7.79423i	0.192406	−	0.333257i	0.946047	+	0.324029i	$0.105038\pi$
$548$	−1.00000	−	1.73205i	−0.0427179	−	0.0739895i
$549$		0			0
$550$	2.00000			0.0852803
$551$	−35.0000	+	25.9808i	−1.49105	+	1.10682i
$552$		0			0
$553$	−5.50000	−	9.52628i	−0.233884	−	0.405099i
$554$	−5.00000	−	8.66025i	−0.212430	−	0.367939i
$555$		0			0
$556$	4.50000	+	7.79423i	0.190843	+	0.330549i
$557$	−6.00000	+	10.3923i	−0.254228	+	0.440336i	−0.964686	−	0.263404i	$-0.915155\pi$
$557$	−6.00000	+	10.3923i	−0.254228	+	0.440336i	0.710457	+	0.703740i	$0.248488\pi$
$558$		0			0
$559$	15.0000			0.634432
$560$	0.500000	−	0.866025i	0.0211289	−	0.0365963i
$561$		0			0
$562$	−30.0000			−1.26547
$563$	−22.0000			−0.927189			−0.463595	−	0.886047i	$-0.653441\pi$
$563$	−22.0000			−0.927189			−0.463595	+	0.886047i	$0.653441\pi$
$564$		0			0
$565$	7.00000	+	12.1244i	0.294492	+	0.510075i
$566$	4.00000	−	6.92820i	0.168133	−	0.291214i
$567$		0			0
$568$		0			0
$569$		0			0			−	1.00000i	$-0.5\pi$
$569$		0			0				1.00000i	$0.5\pi$
$570$		0			0
$571$	39.0000			1.63210			0.816050	−	0.577982i	$-0.196160\pi$
$571$	39.0000			1.63210			0.816050	+	0.577982i	$0.196160\pi$
$572$	−3.00000	−	5.19615i	−0.125436	−	0.217262i
$573$		0			0
$574$	1.00000	−	1.73205i	0.0417392	−	0.0722944i
$575$	−3.00000	−	5.19615i	−0.125109	−	0.216695i
$576$		0			0
$577$	−18.0000			−0.749350			−0.374675	−	0.927156i	$-0.622246\pi$
$577$	−18.0000			−0.749350			−0.374675	+	0.927156i	$0.622246\pi$
$578$	1.00000			0.0415945
$579$		0			0
$580$	−5.00000	+	8.66025i	−0.207614	+	0.359597i
$581$	2.00000			0.0829740
$582$		0			0
$583$	12.0000	−	20.7846i	0.496989	−	0.860811i
$584$	5.50000	+	9.52628i	0.227592	+	0.394200i
$585$		0			0
$586$	13.0000	+	22.5167i	0.537025	+	0.930155i
$587$	9.00000	+	15.5885i	0.371470	+	0.643404i	0.989792	−	0.142520i	$-0.0455206\pi$
$587$	9.00000	+	15.5885i	0.371470	+	0.643404i	−0.618322	+	0.785925i	$0.712187\pi$
$588$		0			0
$589$	4.00000	+	1.73205i	0.164817	+	0.0713679i
$590$	−2.00000			−0.0823387
$591$		0			0
$592$	2.50000	+	4.33013i	0.102749	+	0.177967i
$593$	14.0000	−	24.2487i	0.574911	−	0.995775i	−0.421140	−	0.906996i	$-0.638370\pi$
$593$	14.0000	−	24.2487i	0.574911	−	0.995775i	0.996051	−	0.0887797i	$-0.0282967\pi$
$594$		0			0
$595$	−2.00000	+	3.46410i	−0.0819920	+	0.142014i
$596$	−18.0000			−0.737309
$597$		0			0
$598$	−9.00000	+	15.5885i	−0.368037	+	0.637459i
$599$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$599$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$600$		0			0
$601$	7.00000			0.285536			0.142768	−	0.989756i	$-0.454400\pi$
$601$	7.00000			0.285536			0.142768	+	0.989756i	$0.454400\pi$
$602$	2.50000	−	4.33013i	0.101892	−	0.176483i
$603$		0			0
$604$		0			0
$605$	3.50000	+	6.06218i	0.142295	+	0.246463i
$606$		0			0
$607$	−9.00000			−0.365299			−0.182649	−	0.983178i	$-0.558467\pi$
$607$	−9.00000			−0.365299			−0.182649	+	0.983178i	$0.558467\pi$
$608$	3.50000	−	2.59808i	0.141944	−	0.105366i
$609$		0			0
$610$	2.50000	+	4.33013i	0.101222	+	0.175322i
$611$		0			0
$612$		0			0
$613$	11.0000	+	19.0526i	0.444286	+	0.769526i	0.998002	−	0.0631797i	$-0.0201241\pi$
$613$	11.0000	+	19.0526i	0.444286	+	0.769526i	−0.553716	+	0.832705i	$0.686791\pi$
$614$	2.00000	−	3.46410i	0.0807134	−	0.139800i
$615$		0			0
$616$	−2.00000			−0.0805823
$617$	12.0000	−	20.7846i	0.483102	−	0.836757i	−0.516710	−	0.856161i	$-0.672843\pi$
$617$	12.0000	−	20.7846i	0.483102	−	0.836757i	0.999812	+	0.0194037i	$0.00617676\pi$
$618$		0			0
$619$	−29.0000			−1.16561			−0.582804	−	0.812613i	$-0.698045\pi$
$619$	−29.0000			−1.16561			−0.582804	+	0.812613i	$0.698045\pi$
$620$	1.00000			0.0401610
$621$		0			0
$622$	5.00000	+	8.66025i	0.200482	+	0.347245i
$623$		0			0
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−18.0000			−0.719425
$627$		0			0
$628$	−13.0000			−0.518756
$629$	−10.0000	−	17.3205i	−0.398726	−	0.690614i
$630$		0			0
$631$	21.5000	−	37.2391i	0.855901	−	1.48246i	−0.0199047	−	0.999802i	$-0.506336\pi$
$631$	21.5000	−	37.2391i	0.855901	−	1.48246i	0.875806	−	0.482663i	$-0.160330\pi$
$632$	−5.50000	−	9.52628i	−0.218778	−	0.378935i
$633$		0			0
$634$	30.0000			1.19145
$635$	16.0000			0.634941
$636$		0			0
$637$	−9.00000	+	15.5885i	−0.356593	+	0.617637i
$638$	20.0000			0.791808
$639$		0			0
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	12.0000	+	20.7846i	0.473972	+	0.820943i	0.999556	−	0.0297987i	$-0.00948663\pi$
$641$	12.0000	+	20.7846i	0.473972	+	0.820943i	−0.525584	+	0.850741i	$0.676153\pi$
$642$		0			0
$643$	−20.5000	−	35.5070i	−0.808441	−	1.40026i	−0.913943	−	0.405842i	$-0.866978\pi$
$643$	−20.5000	−	35.5070i	−0.808441	−	1.40026i	0.105502	−	0.994419i	$-0.466355\pi$
$644$	3.00000	+	5.19615i	0.118217	+	0.204757i
$645$		0			0
$646$	−14.0000	+	10.3923i	−0.550823	+	0.408880i
$647$	−46.0000			−1.80845			−0.904223	−	0.427060i	$-0.859549\pi$
$647$	−46.0000			−1.80845			−0.904223	+	0.427060i	$0.859549\pi$
$648$		0			0
$649$	2.00000	+	3.46410i	0.0785069	+	0.135978i
$650$	−1.50000	+	2.59808i	−0.0588348	+	0.101905i
$651$		0			0
$652$	8.50000	−	14.7224i	0.332886	−	0.576575i
$653$		0			0			−	1.00000i	$-0.5\pi$
$653$		0			0				1.00000i	$0.5\pi$
$654$		0			0
$655$	−3.00000	+	5.19615i	−0.117220	+	0.203030i
$656$	1.00000	−	1.73205i	0.0390434	−	0.0676252i
$657$		0			0
$658$		0			0
$659$	9.00000	−	15.5885i	0.350590	−	0.607240i	−0.635763	−	0.771885i	$-0.719314\pi$
$659$	9.00000	−	15.5885i	0.350590	−	0.607240i	0.986353	+	0.164644i	$0.0526477\pi$
$660$		0			0
$661$	−23.0000	+	39.8372i	−0.894596	+	1.54949i	−0.0602929	+	0.998181i	$0.519203\pi$
$661$	−23.0000	+	39.8372i	−0.894596	+	1.54949i	−0.834303	+	0.551306i	$0.814130\pi$
$662$	2.50000	+	4.33013i	0.0971653	+	0.168295i
$663$		0			0
$664$	2.00000			0.0776151
$665$	0.500000	+	4.33013i	0.0193892	+	0.167915i
$666$		0			0
$667$	−30.0000	−	51.9615i	−1.16160	−	2.01196i
$668$	7.00000	+	12.1244i	0.270838	+	0.469105i
$669$		0			0
$670$	−2.50000	−	4.33013i	−0.0965834	−	0.167287i
$671$	5.00000	−	8.66025i	0.193023	−	0.334325i
$672$		0			0
$673$	−23.0000			−0.886585			−0.443292	−	0.896377i	$-0.646190\pi$
$673$	−23.0000			−0.886585			−0.443292	+	0.896377i	$0.646190\pi$
$674$	11.5000	−	19.9186i	0.442963	−	0.767235i
$675$		0			0
$676$	−4.00000			−0.153846
$677$	−48.0000			−1.84479			−0.922395	−	0.386248i	$-0.873771\pi$
$677$	−48.0000			−1.84479			−0.922395	+	0.386248i	$0.873771\pi$
$678$		0			0
$679$	−1.00000	−	1.73205i	−0.0383765	−	0.0664700i
$680$	−2.00000	+	3.46410i	−0.0766965	+	0.132842i
$681$		0			0
$682$	−1.00000	−	1.73205i	−0.0382920	−	0.0663237i
$683$		0			0			−	1.00000i	$-0.5\pi$
$683$		0			0				1.00000i	$0.5\pi$
$684$		0			0
$685$	2.00000			0.0764161
$686$	6.50000	+	11.2583i	0.248171	+	0.429845i
$687$		0			0
$688$	2.50000	−	4.33013i	0.0953116	−	0.165085i
$689$	18.0000	+	31.1769i	0.685745	+	1.18775i
$690$		0			0
$691$	4.00000			0.152167			0.0760836	−	0.997101i	$-0.475758\pi$
$691$	4.00000			0.152167			0.0760836	+	0.997101i	$0.475758\pi$
$692$	26.0000			0.988372
$693$		0			0
$694$		0			0
$695$	−9.00000			−0.341389
$696$		0			0
$697$	−4.00000	+	6.92820i	−0.151511	+	0.262424i
$698$	8.50000	+	14.7224i	0.321730	+	0.557252i
$699$		0			0
$700$	0.500000	+	0.866025i	0.0188982	+	0.0327327i
$701$	14.0000	+	24.2487i	0.528773	+	0.915861i	0.999437	+	0.0335489i	$0.0106809\pi$
$701$	14.0000	+	24.2487i	0.528773	+	0.915861i	−0.470664	+	0.882312i	$0.655986\pi$
$702$		0			0
$703$	−20.0000	−	8.66025i	−0.754314	−	0.326628i
$704$	−2.00000			−0.0753778
$705$		0			0
$706$	3.00000	+	5.19615i	0.112906	+	0.195560i
$707$	−3.00000	+	5.19615i	−0.112827	+	0.195421i
$708$		0			0
$709$	−9.50000	+	16.4545i	−0.356780	+	0.617961i	−0.987421	−	0.158114i	$-0.949459\pi$
$709$	−9.50000	+	16.4545i	−0.356780	+	0.617961i	0.630641	+	0.776075i	$0.282792\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−3.00000	+	5.19615i	−0.112351	+	0.194597i
$714$		0			0
$715$	6.00000			0.224387
$716$	−5.00000	+	8.66025i	−0.186859	+	0.323649i
$717$		0			0
$718$	1.00000	−	1.73205i	0.0373197	−	0.0646396i
$719$	13.0000	+	22.5167i	0.484818	+	0.839730i	0.999848	−	0.0174426i	$-0.00555244\pi$
$719$	13.0000	+	22.5167i	0.484818	+	0.839730i	−0.515030	+	0.857172i	$0.672219\pi$
$720$		0			0
$721$	−19.0000			−0.707597
$722$	−5.50000	+	18.1865i	−0.204689	+	0.676833i
$723$		0			0
$724$	3.00000	+	5.19615i	0.111494	+	0.193113i
$725$	−5.00000	−	8.66025i	−0.185695	−	0.321634i
$726$		0			0
$727$	22.5000	+	38.9711i	0.834479	+	1.44536i	0.894454	+	0.447160i	$0.147564\pi$
$727$	22.5000	+	38.9711i	0.834479	+	1.44536i	−0.0599753	+	0.998200i	$0.519102\pi$
$728$	1.50000	−	2.59808i	0.0555937	−	0.0962911i
$729$		0			0
$730$	−11.0000			−0.407128
$731$	−10.0000	+	17.3205i	−0.369863	+	0.640622i
$732$		0			0
$733$	−34.0000			−1.25582			−0.627909	−	0.778287i	$-0.716089\pi$
$733$	−34.0000			−1.25582			−0.627909	+	0.778287i	$0.716089\pi$
$734$	7.00000			0.258375
$735$		0			0
$736$	3.00000	+	5.19615i	0.110581	+	0.191533i
$737$	−5.00000	+	8.66025i	−0.184177	+	0.319005i
$738$		0			0
$739$	−0.500000	−	0.866025i	−0.0183928	−	0.0318573i	0.856683	−	0.515844i	$-0.172522\pi$
$739$	−0.500000	−	0.866025i	−0.0183928	−	0.0318573i	−0.875075	+	0.483987i	$0.839188\pi$
$740$	−5.00000			−0.183804
$741$		0			0
$742$	12.0000			0.440534
$743$	3.00000	+	5.19615i	0.110059	+	0.190628i	0.915794	−	0.401648i	$-0.131563\pi$
$743$	3.00000	+	5.19615i	0.110059	+	0.190628i	−0.805735	+	0.592277i	$0.798229\pi$
$744$		0			0
$745$	9.00000	−	15.5885i	0.329734	−	0.571117i
$746$	−11.0000	−	19.0526i	−0.402739	−	0.697564i
$747$		0			0
$748$	8.00000			0.292509
$749$	−4.00000			−0.146157
$750$		0			0
$751$	23.5000	−	40.7032i	0.857527	−	1.48528i	−0.0167534	−	0.999860i	$-0.505333\pi$
$751$	23.5000	−	40.7032i	0.857527	−	1.48528i	0.874281	−	0.485421i	$-0.161334\pi$
$752$		0			0
$753$		0			0
$754$	−15.0000	+	25.9808i	−0.546268	+	0.946164i
$755$		0			0
$756$		0			0
$757$	3.50000	+	6.06218i	0.127210	+	0.220334i	0.922595	−	0.385771i	$-0.126065\pi$
$757$	3.50000	+	6.06218i	0.127210	+	0.220334i	−0.795385	+	0.606105i	$0.792731\pi$
$758$	−5.50000	−	9.52628i	−0.199769	−	0.346010i
$759$		0			0
$760$	0.500000	+	4.33013i	0.0181369	+	0.157070i
$761$	−10.0000			−0.362500			−0.181250	−	0.983437i	$-0.558014\pi$
$761$	−10.0000			−0.362500			−0.181250	+	0.983437i	$0.558014\pi$
$762$		0			0
$763$	−9.00000	−	15.5885i	−0.325822	−	0.564340i
$764$	8.00000	−	13.8564i	0.289430	−	0.501307i
$765$		0			0
$766$	18.0000	−	31.1769i	0.650366	−	1.12647i
$767$	−6.00000			−0.216647
$768$		0			0
$769$	16.5000	−	28.5788i	0.595005	−	1.03058i	−0.398541	−	0.917151i	$-0.630483\pi$
$769$	16.5000	−	28.5788i	0.595005	−	1.03058i	0.993546	−	0.113429i	$-0.0361834\pi$
$770$	1.00000	−	1.73205i	0.0360375	−	0.0624188i
$771$		0			0
$772$	25.0000			0.899770
$773$	−3.00000	+	5.19615i	−0.107903	+	0.186893i	−0.914920	−	0.403634i	$-0.867747\pi$
$773$	−3.00000	+	5.19615i	−0.107903	+	0.186893i	0.807018	+	0.590527i	$0.201080\pi$
$774$		0			0
$775$	−0.500000	+	0.866025i	−0.0179605	+	0.0311086i
$776$	−1.00000	−	1.73205i	−0.0358979	−	0.0621770i
$777$		0			0
$778$	−10.0000			−0.358517
$779$	1.00000	+	8.66025i	0.0358287	+	0.310286i
$780$		0			0
$781$		0			0
$782$	−12.0000	−	20.7846i	−0.429119	−	0.743256i
$783$		0			0
$784$	3.00000	+	5.19615i	0.107143	+	0.185577i
$785$	6.50000	−	11.2583i	0.231995	−	0.401827i
$786$		0			0
$787$	−23.0000			−0.819861			−0.409931	−	0.912117i	$-0.634447\pi$
$787$	−23.0000			−0.819861			−0.409931	+	0.912117i	$0.634447\pi$
$788$	−9.00000	+	15.5885i	−0.320612	+	0.555316i
$789$		0			0
$790$	11.0000			0.391362
$791$	14.0000			0.497783
$792$		0			0
$793$	7.50000	+	12.9904i	0.266333	+	0.461302i
$794$	−0.500000	+	0.866025i	−0.0177443	+	0.0307341i
$795$		0			0
$796$	−2.50000	−	4.33013i	−0.0886102	−	0.153477i
$797$	−2.00000			−0.0708436			−0.0354218	−	0.999372i	$-0.511277\pi$
$797$	−2.00000			−0.0708436			−0.0354218	+	0.999372i	$0.511277\pi$
$798$		0			0
$799$		0			0
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$		0			0
$802$	19.0000	−	32.9090i	0.670913	−	1.16206i
$803$	11.0000	+	19.0526i	0.388182	+	0.672350i
$804$		0			0
$805$	−6.00000			−0.211472
$806$	3.00000			0.105670
$807$		0			0
$808$	−3.00000	+	5.19615i	−0.105540	+	0.182800i
$809$	−50.0000			−1.75791			−0.878953	−	0.476908i	$-0.841757\pi$
$809$	−50.0000			−1.75791			−0.878953	+	0.476908i	$0.841757\pi$
$810$		0			0
$811$	14.0000	−	24.2487i	0.491606	−	0.851487i	−0.508347	−	0.861152i	$-0.669743\pi$
$811$	14.0000	−	24.2487i	0.491606	−	0.851487i	0.999953	+	0.00966502i	$0.00307652\pi$
$812$	5.00000	+	8.66025i	0.175466	+	0.303915i
$813$		0			0
$814$	5.00000	+	8.66025i	0.175250	+	0.303542i
$815$	8.50000	+	14.7224i	0.297742	+	0.515704i
$816$		0			0
$817$	2.50000	+	21.6506i	0.0874639	+	0.757460i
$818$	30.0000			1.04893
$819$		0			0
$820$	1.00000	+	1.73205i	0.0349215	+	0.0604858i
$821$	−5.00000	+	8.66025i	−0.174501	+	0.302245i	−0.939989	−	0.341206i	$-0.889165\pi$
$821$	−5.00000	+	8.66025i	−0.174501	+	0.302245i	0.765487	+	0.643451i	$0.222498\pi$
$822$		0			0
$823$	22.0000	−	38.1051i	0.766872	−	1.32826i	−0.172379	−	0.985031i	$-0.555146\pi$
$823$	22.0000	−	38.1051i	0.766872	−	1.32826i	0.939251	−	0.343230i	$-0.111521\pi$
$824$	−19.0000			−0.661896
$825$		0			0
$826$	−1.00000	+	1.73205i	−0.0347945	+	0.0602658i
$827$	−11.0000	+	19.0526i	−0.382507	+	0.662522i	−0.991420	−	0.130715i	$-0.958273\pi$
$827$	−11.0000	+	19.0526i	−0.382507	+	0.662522i	0.608913	+	0.793237i	$0.291606\pi$
$828$		0			0
$829$	23.0000			0.798823			0.399412	−	0.916772i	$-0.369214\pi$
$829$	23.0000			0.798823			0.399412	+	0.916772i	$0.369214\pi$
$830$	−1.00000	+	1.73205i	−0.0347105	+	0.0601204i
$831$		0			0
$832$	1.50000	−	2.59808i	0.0520031	−	0.0900721i
$833$	−12.0000	−	20.7846i	−0.415775	−	0.720144i
$834$		0			0
$835$	−14.0000			−0.484490
$836$	7.00000	−	5.19615i	0.242100	−	0.179713i
$837$		0			0
$838$	12.0000	+	20.7846i	0.414533	+	0.717992i
$839$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$839$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$840$		0			0
$841$	−35.5000	−	61.4878i	−1.22414	−	2.12027i
$842$	−7.00000	+	12.1244i	−0.241236	+	0.417833i
$843$		0			0
$844$	−5.00000			−0.172107
$845$	2.00000	−	3.46410i	0.0688021	−	0.119169i
$846$		0			0
$847$	7.00000			0.240523
$848$	12.0000			0.412082
$849$		0			0
$850$	−2.00000	−	3.46410i	−0.0685994	−	0.118818i
$851$	15.0000	−	25.9808i	0.514193	−	0.890609i
$852$		0			0
$853$	8.50000	+	14.7224i	0.291034	+	0.504086i	0.974055	−	0.226313i	$-0.0726672\pi$
$853$	8.50000	+	14.7224i	0.291034	+	0.504086i	−0.683020	+	0.730400i	$0.739334\pi$
$854$	5.00000			0.171096
$855$		0			0
$856$	−4.00000			−0.136717
$857$	12.0000	+	20.7846i	0.409912	+	0.709989i	0.994880	−	0.101068i	$-0.0322260\pi$
$857$	12.0000	+	20.7846i	0.409912	+	0.709989i	−0.584967	+	0.811057i	$0.698893\pi$
$858$		0			0
$859$	−18.5000	+	32.0429i	−0.631212	+	1.09329i	0.356092	+	0.934451i	$0.384109\pi$
$859$	−18.5000	+	32.0429i	−0.631212	+	1.09329i	−0.987304	+	0.158840i	$0.949225\pi$
$860$	2.50000	+	4.33013i	0.0852493	+	0.147656i
$861$		0			0
$862$	−20.0000			−0.681203
$863$	−46.0000			−1.56586			−0.782929	−	0.622111i	$-0.786275\pi$
$863$	−46.0000			−1.56586			−0.782929	+	0.622111i	$0.786275\pi$
$864$		0			0
$865$	−13.0000	+	22.5167i	−0.442013	+	0.765589i
$866$	−29.0000			−0.985460
$867$		0			0
$868$	0.500000	−	0.866025i	0.0169711	−	0.0293948i
$869$	−11.0000	−	19.0526i	−0.373149	−	0.646314i
$870$		0			0
$871$	−7.50000	−	12.9904i	−0.254128	−	0.440162i
$872$	−9.00000	−	15.5885i	−0.304778	−	0.527892i
$873$		0			0
$874$	−24.0000	−	10.3923i	−0.811812	−	0.351525i
$875$	−1.00000			−0.0338062
$876$		0			0
$877$	−7.50000	−	12.9904i	−0.253257	−	0.438654i	0.711164	−	0.703027i	$-0.248168\pi$
$877$	−7.50000	−	12.9904i	−0.253257	−	0.438654i	−0.964421	+	0.264373i	$0.914835\pi$
$878$	−20.5000	+	35.5070i	−0.691841	+	1.19830i
$879$		0			0
$880$	1.00000	−	1.73205i	0.0337100	−	0.0583874i
$881$	−34.0000			−1.14549			−0.572745	−	0.819734i	$-0.694121\pi$
$881$	−34.0000			−1.14549			−0.572745	+	0.819734i	$0.694121\pi$
$882$		0			0
$883$	−15.5000	+	26.8468i	−0.521617	+	0.903466i	0.478067	+	0.878323i	$0.341337\pi$
$883$	−15.5000	+	26.8468i	−0.521617	+	0.903466i	−0.999684	+	0.0251431i	$0.991996\pi$
$884$	−6.00000	+	10.3923i	−0.201802	+	0.349531i
$885$		0			0
$886$	12.0000			0.403148
$887$	−12.0000	+	20.7846i	−0.402921	+	0.697879i	−0.994077	−	0.108678i	$-0.965338\pi$
$887$	−12.0000	+	20.7846i	−0.402921	+	0.697879i	0.591156	+	0.806557i	$0.298672\pi$
$888$		0			0
$889$	8.00000	−	13.8564i	0.268311	−	0.464729i
$890$		0			0
$891$		0			0
$892$	−1.00000			−0.0334825
$893$		0			0
$894$		0			0
$895$	−5.00000	−	8.66025i	−0.167132	−	0.289480i
$896$	−0.500000	−	0.866025i	−0.0167038	−	0.0289319i
$897$		0			0
$898$	−14.0000	−	24.2487i	−0.467186	−	0.809190i
$899$	−5.00000	+	8.66025i	−0.166759	+	0.288836i
$900$		0			0
$901$	−48.0000			−1.59911
$902$	2.00000	−	3.46410i	0.0665927	−	0.115342i
$903$		0			0
$904$	14.0000			0.465633
$905$	−6.00000			−0.199447
$906$		0			0
$907$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$907$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$908$	−9.00000	+	15.5885i	−0.298675	+	0.517321i
$909$		0			0
$910$	1.50000	+	2.59808i	0.0497245	+	0.0861254i
$911$	−30.0000			−0.993944			−0.496972	−	0.867766i	$-0.665555\pi$
$911$	−30.0000			−0.993944			−0.496972	+	0.867766i	$0.665555\pi$
$912$		0			0
$913$	4.00000			0.132381
$914$	11.5000	+	19.9186i	0.380386	+	0.658848i
$915$		0			0
$916$	2.50000	−	4.33013i	0.0826023	−	0.143071i
$917$	3.00000	+	5.19615i	0.0990687	+	0.171592i
$918$		0			0
$919$	43.0000			1.41844			0.709220	−	0.704988i	$-0.249047\pi$
$919$	43.0000			1.41844			0.709220	+	0.704988i	$0.249047\pi$
$920$	−6.00000			−0.197814
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	2.50000	−	4.33013i	0.0821995	−	0.142374i
$926$	0.500000	+	0.866025i	0.0164310	+	0.0284594i
$927$		0			0
$928$	5.00000	+	8.66025i	0.164133	+	0.284287i
$929$	−24.0000	−	41.5692i	−0.787414	−	1.36384i	−0.927546	−	0.373709i	$-0.878086\pi$
$929$	−24.0000	−	41.5692i	−0.787414	−	1.36384i	0.140132	−	0.990133i	$-0.455247\pi$
$930$		0			0
$931$	−24.0000	−	10.3923i	−0.786568	−	0.340594i
$932$	4.00000			0.131024
$933$		0			0
$934$	−15.0000	−	25.9808i	−0.490815	−	0.850117i
$935$	−4.00000	+	6.92820i	−0.130814	+	0.226576i
$936$		0			0
$937$	−10.5000	+	18.1865i	−0.343020	+	0.594128i	−0.984992	−	0.172600i	$-0.944783\pi$
$937$	−10.5000	+	18.1865i	−0.343020	+	0.594128i	0.641972	+	0.766728i	$0.278117\pi$
$938$	−5.00000			−0.163256
$939$		0			0
$940$		0			0
$941$	−17.0000	+	29.4449i	−0.554184	+	0.959875i	0.443782	+	0.896135i	$0.353636\pi$
$941$	−17.0000	+	29.4449i	−0.554184	+	0.959875i	−0.997967	+	0.0637405i	$0.979697\pi$
$942$		0			0
$943$	−12.0000			−0.390774
$944$	−1.00000	+	1.73205i	−0.0325472	+	0.0563735i
$945$		0			0
$946$	5.00000	−	8.66025i	0.162564	−	0.281569i
$947$	−11.0000	−	19.0526i	−0.357452	−	0.619125i	0.630082	−	0.776528i	$-0.283021\pi$
$947$	−11.0000	−	19.0526i	−0.357452	−	0.619125i	−0.987534	+	0.157403i	$0.949688\pi$
$948$		0			0
$949$	−33.0000			−1.07123
$950$	−4.00000	−	1.73205i	−0.129777	−	0.0561951i
$951$		0			0
$952$	2.00000	+	3.46410i	0.0648204	+	0.112272i
$953$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$953$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$954$		0			0
$955$	8.00000	+	13.8564i	0.258874	+	0.448383i
$956$	−9.00000	+	15.5885i	−0.291081	+	0.504167i
$957$		0			0
$958$	42.0000			1.35696
$959$	1.00000	−	1.73205i	0.0322917	−	0.0559308i
$960$		0			0
$961$	−30.0000			−0.967742
$962$	−15.0000			−0.483619
$963$		0			0
$964$	−2.50000	−	4.33013i	−0.0805196	−	0.139464i
$965$	−12.5000	+	21.6506i	−0.402389	+	0.696959i
$966$		0			0
$967$	−14.5000	−	25.1147i	−0.466289	−	0.807635i	0.532970	−	0.846134i	$-0.321076\pi$
$967$	−14.5000	−	25.1147i	−0.466289	−	0.807635i	−0.999259	+	0.0384986i	$0.987742\pi$
$968$	7.00000			0.224989
$969$		0			0
$970$	2.00000			0.0642161
$971$	−4.00000	−	6.92820i	−0.128366	−	0.222337i	0.794678	−	0.607032i	$-0.207640\pi$
$971$	−4.00000	−	6.92820i	−0.128366	−	0.222337i	−0.923044	+	0.384695i	$0.874307\pi$
$972$		0			0
$973$	−4.50000	+	7.79423i	−0.144263	+	0.249871i
$974$	8.00000	+	13.8564i	0.256337	+	0.443988i
$975$		0			0
$976$	5.00000			0.160046
$977$	34.0000			1.08776			0.543878	−	0.839164i	$-0.316955\pi$
$977$	34.0000			1.08776			0.543878	+	0.839164i	$0.316955\pi$
$978$		0			0
$979$		0			0
$980$	−6.00000			−0.191663
$981$		0			0
$982$	−14.0000	+	24.2487i	−0.446758	+	0.773807i
$983$	12.0000	+	20.7846i	0.382741	+	0.662926i	0.991453	−	0.130465i	$-0.0416470\pi$
$983$	12.0000	+	20.7846i	0.382741	+	0.662926i	−0.608712	+	0.793391i	$0.708314\pi$
$984$		0			0
$985$	−9.00000	−	15.5885i	−0.286764	−	0.496690i
$986$	−20.0000	−	34.6410i	−0.636930	−	1.10319i
$987$		0			0
$988$	1.50000	+	12.9904i	0.0477214	+	0.413279i
$989$	−30.0000			−0.953945
$990$		0			0
$991$	−11.5000	−	19.9186i	−0.365310	−	0.632735i	0.623516	−	0.781810i	$-0.285704\pi$
$991$	−11.5000	−	19.9186i	−0.365310	−	0.632735i	−0.988826	+	0.149076i	$0.952370\pi$
$992$	0.500000	−	0.866025i	0.0158750	−	0.0274963i
$993$		0			0
$994$		0			0
$995$	5.00000			0.158511
$996$		0			0
$997$	−5.50000	+	9.52628i	−0.174187	+	0.301700i	−0.939880	−	0.341506i	$-0.889063\pi$
$997$	−5.50000	+	9.52628i	−0.174187	+	0.301700i	0.765693	+	0.643206i	$0.222396\pi$
$998$	−12.5000	+	21.6506i	−0.395681	+	0.685339i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.l.f.1261.1		2
3.2	odd	2		570.2.i.b.121.1	✓	2
19.11	even	3	inner	1710.2.l.f.1531.1		2
57.11	odd	6		570.2.i.b.391.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.i.b.121.1	✓	2	3.2	odd	2
570.2.i.b.391.1	yes	2	57.11	odd	6
1710.2.l.f.1261.1		2	1.1	even	1	trivial
1710.2.l.f.1531.1		2	19.11	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.00000 q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.00000 q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{10} -2.00000 q^{11} +(1.50000 - 2.59808i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.00000 + 3.46410i) q^{17} +(4.00000 + 1.73205i) q^{19} +1.00000 q^{20} +(-1.00000 - 1.73205i) q^{22} +(-3.00000 + 5.19615i) q^{23} +(-0.500000 + 0.866025i) q^{25} +3.00000 q^{26} +(0.500000 - 0.866025i) q^{28} +(-5.00000 + 8.66025i) q^{29} +1.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-2.00000 + 3.46410i) q^{34} +(0.500000 + 0.866025i) q^{35} -5.00000 q^{37} +(0.500000 + 4.33013i) q^{38} +(0.500000 + 0.866025i) q^{40} +(1.00000 + 1.73205i) q^{41} +(2.50000 + 4.33013i) q^{43} +(1.00000 - 1.73205i) q^{44} -6.00000 q^{46} -6.00000 q^{49} -1.00000 q^{50} +(1.50000 + 2.59808i) q^{52} +(-6.00000 + 10.3923i) q^{53} +(1.00000 + 1.73205i) q^{55} +1.00000 q^{56} -10.0000 q^{58} +(-1.00000 - 1.73205i) q^{59} +(-2.50000 + 4.33013i) q^{61} +(0.500000 + 0.866025i) q^{62} +1.00000 q^{64} -3.00000 q^{65} +(2.50000 - 4.33013i) q^{67} -4.00000 q^{68} +(-0.500000 + 0.866025i) q^{70} +(-5.50000 - 9.52628i) q^{73} +(-2.50000 - 4.33013i) q^{74} +(-3.50000 + 2.59808i) q^{76} +2.00000 q^{77} +(5.50000 + 9.52628i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-1.00000 + 1.73205i) q^{82} -2.00000 q^{83} +(2.00000 - 3.46410i) q^{85} +(-2.50000 + 4.33013i) q^{86} +2.00000 q^{88} +(-1.50000 + 2.59808i) q^{91} +(-3.00000 - 5.19615i) q^{92} +(-0.500000 - 4.33013i) q^{95} +(1.00000 + 1.73205i) q^{97} +(-3.00000 - 5.19615i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} - q^{5} - 2 q^{7} - 2 q^{8}+O(q^{10}) \) 2 * q + q^2 - q^4 - q^5 - 2 * q^7 - 2 * q^8	\( 2 q + q^{2} - q^{4} - q^{5} - 2 q^{7} - 2 q^{8} + q^{10} - 4 q^{11} + 3 q^{13} - q^{14} - q^{16} + 4 q^{17} + 8 q^{19} + 2 q^{20} - 2 q^{22} - 6 q^{23} - q^{25} + 6 q^{26} + q^{28} - 10 q^{29} + 2 q^{31} + q^{32} - 4 q^{34} + q^{35} - 10 q^{37} + q^{38} + q^{40} + 2 q^{41} + 5 q^{43} + 2 q^{44} - 12 q^{46} - 12 q^{49} - 2 q^{50} + 3 q^{52} - 12 q^{53} + 2 q^{55} + 2 q^{56} - 20 q^{58} - 2 q^{59} - 5 q^{61} + q^{62} + 2 q^{64} - 6 q^{65} + 5 q^{67} - 8 q^{68} - q^{70} - 11 q^{73} - 5 q^{74} - 7 q^{76} + 4 q^{77} + 11 q^{79} - q^{80} - 2 q^{82} - 4 q^{83} + 4 q^{85} - 5 q^{86} + 4 q^{88} - 3 q^{91} - 6 q^{92} - q^{95} + 2 q^{97} - 6 q^{98}+O(q^{100}) \) 2 * q + q^2 - q^4 - q^5 - 2 * q^7 - 2 * q^8 + q^10 - 4 * q^11 + 3 * q^13 - q^14 - q^16 + 4 * q^17 + 8 * q^19 + 2 * q^20 - 2 * q^22 - 6 * q^23 - q^25 + 6 * q^26 + q^28 - 10 * q^29 + 2 * q^31 + q^32 - 4 * q^34 + q^35 - 10 * q^37 + q^38 + q^40 + 2 * q^41 + 5 * q^43 + 2 * q^44 - 12 * q^46 - 12 * q^49 - 2 * q^50 + 3 * q^52 - 12 * q^53 + 2 * q^55 + 2 * q^56 - 20 * q^58 - 2 * q^59 - 5 * q^61 + q^62 + 2 * q^64 - 6 * q^65 + 5 * q^67 - 8 * q^68 - q^70 - 11 * q^73 - 5 * q^74 - 7 * q^76 + 4 * q^77 + 11 * q^79 - q^80 - 2 * q^82 - 4 * q^83 + 4 * q^85 - 5 * q^86 + 4 * q^88 - 3 * q^91 - 6 * q^92 - q^95 + 2 * q^97 - 6 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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