LMFDB - Embedded newform 190.2.e.a.11.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [190,2,Mod(11,190)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(190, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("190.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 190 = 2 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	190.e (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:	$1.51715763840$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			11.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	190.11
Dual form			190.2.e.a.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(0.500000 + 0.866025i) q^{10} +5.00000 q^{11} +(-1.00000 - 1.73205i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} -3.00000 q^{18} +(-0.500000 + 4.33013i) q^{19} -1.00000 q^{20} +(-2.50000 + 4.33013i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(-0.500000 - 0.866025i) q^{25} +2.00000 q^{26} +(-0.500000 - 0.866025i) q^{28} +(-3.00000 - 5.19615i) q^{29} +4.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.500000 - 0.866025i) q^{35} +(1.50000 - 2.59808i) q^{36} -11.0000 q^{37} +(-3.50000 - 2.59808i) q^{38} +(0.500000 - 0.866025i) q^{40} +(4.50000 - 7.79423i) q^{41} +(-3.00000 + 5.19615i) q^{43} +(-2.50000 - 4.33013i) q^{44} +3.00000 q^{45} +1.00000 q^{46} -6.00000 q^{49} +1.00000 q^{50} +(-1.00000 + 1.73205i) q^{52} +(-2.50000 - 4.33013i) q^{53} +(2.50000 - 4.33013i) q^{55} +1.00000 q^{56} +6.00000 q^{58} +(-2.00000 + 3.46410i) q^{62} +(1.50000 + 2.59808i) q^{63} +1.00000 q^{64} -2.00000 q^{65} +(-6.00000 - 10.3923i) q^{67} +(0.500000 + 0.866025i) q^{70} +(-3.00000 + 5.19615i) q^{71} +(1.50000 + 2.59808i) q^{72} +(-7.00000 + 12.1244i) q^{73} +(5.50000 - 9.52628i) q^{74} +(4.00000 - 1.73205i) q^{76} +5.00000 q^{77} +(-5.00000 + 8.66025i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(4.50000 + 7.79423i) q^{82} +14.0000 q^{83} +(-3.00000 - 5.19615i) q^{86} +5.00000 q^{88} +(3.50000 + 6.06218i) q^{89} +(-1.50000 + 2.59808i) q^{90} +(-1.00000 - 1.73205i) q^{91} +(-0.500000 + 0.866025i) q^{92} +(3.50000 + 2.59808i) q^{95} +(1.00000 - 1.73205i) q^{97} +(3.00000 - 5.19615i) q^{98} +(7.50000 + 12.9904i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} + q^{5} + 2 q^{7} + 2 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q - q^2 - q^4 + q^5 + 2 * q^7 + 2 * q^8 + 3 * q^9	$ 2 q - q^{2} - q^{4} + q^{5} + 2 q^{7} + 2 q^{8} + 3 q^{9} + q^{10} + 10 q^{11} - 2 q^{13} - q^{14} - q^{16} - 6 q^{18} - q^{19} - 2 q^{20} - 5 q^{22} - q^{23} - q^{25} + 4 q^{26} - q^{28} - 6 q^{29} + 8 q^{31} - q^{32} + q^{35} + 3 q^{36} - 22 q^{37} - 7 q^{38} + q^{40} + 9 q^{41} - 6 q^{43} - 5 q^{44} + 6 q^{45} + 2 q^{46} - 12 q^{49} + 2 q^{50} - 2 q^{52} - 5 q^{53} + 5 q^{55} + 2 q^{56} + 12 q^{58} - 4 q^{62} + 3 q^{63} + 2 q^{64} - 4 q^{65} - 12 q^{67} + q^{70} - 6 q^{71} + 3 q^{72} - 14 q^{73} + 11 q^{74} + 8 q^{76} + 10 q^{77} - 10 q^{79} + q^{80} - 9 q^{81} + 9 q^{82} + 28 q^{83} - 6 q^{86} + 10 q^{88} + 7 q^{89} - 3 q^{90} - 2 q^{91} - q^{92} + 7 q^{95} + 2 q^{97} + 6 q^{98} + 15 q^{99}+O(q^{100}) $ 2 * q - q^2 - q^4 + q^5 + 2 * q^7 + 2 * q^8 + 3 * q^9 + q^10 + 10 * q^11 - 2 * q^13 - q^14 - q^16 - 6 * q^18 - q^19 - 2 * q^20 - 5 * q^22 - q^23 - q^25 + 4 * q^26 - q^28 - 6 * q^29 + 8 * q^31 - q^32 + q^35 + 3 * q^36 - 22 * q^37 - 7 * q^38 + q^40 + 9 * q^41 - 6 * q^43 - 5 * q^44 + 6 * q^45 + 2 * q^46 - 12 * q^49 + 2 * q^50 - 2 * q^52 - 5 * q^53 + 5 * q^55 + 2 * q^56 + 12 * q^58 - 4 * q^62 + 3 * q^63 + 2 * q^64 - 4 * q^65 - 12 * q^67 + q^70 - 6 * q^71 + 3 * q^72 - 14 * q^73 + 11 * q^74 + 8 * q^76 + 10 * q^77 - 10 * q^79 + q^80 - 9 * q^81 + 9 * q^82 + 28 * q^83 - 6 * q^86 + 10 * q^88 + 7 * q^89 - 3 * q^90 - 2 * q^91 - q^92 + 7 * q^95 + 2 * q^97 + 6 * q^98 + 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/190\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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
$5$	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	$-0.439481\pi$
$7$	1.00000			0.377964			0.188982	+	0.981981i	$0.439481\pi$
$8$	1.00000			0.353553
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	5.00000			1.50756			0.753778	−	0.657129i	$-0.228229\pi$
$11$	5.00000			1.50756			0.753778	+	0.657129i	$0.228229\pi$
$12$		0			0
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	0.693375	−	0.720577i	$-0.256123\pi$
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	−0.970725	+	0.240192i	$0.922790\pi$
$14$	−0.500000	+	0.866025i	−0.133631	+	0.231455i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$	−3.00000			−0.707107
$19$	−0.500000	+	4.33013i	−0.114708	+	0.993399i
$19$	−0.500000	+	4.33013i	−0.114708	+	0.993399i
$20$	−1.00000			−0.223607
$21$		0			0
$22$	−2.50000	+	4.33013i	−0.533002	+	0.923186i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i	0.809177	−	0.587565i	$-0.199913\pi$
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i	−0.913434	+	0.406986i	$0.866580\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	2.00000			0.392232
$27$		0			0
$28$	−0.500000	−	0.866025i	−0.0944911	−	0.163663i
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	−0.997738	−	0.0672232i	$-0.978586\pi$
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	0.440652	−	0.897678i	$-0.354747\pi$
$30$		0			0
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$		0			0
$35$	0.500000	−	0.866025i	0.0845154	−	0.146385i
$36$	1.50000	−	2.59808i	0.250000	−	0.433013i
$37$	−11.0000			−1.80839			−0.904194	−	0.427121i	$-0.859528\pi$
$37$	−11.0000			−1.80839			−0.904194	+	0.427121i	$0.859528\pi$
$38$	−3.50000	−	2.59808i	−0.567775	−	0.421464i
$39$		0			0
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	4.50000	−	7.79423i	0.702782	−	1.21725i	−0.264704	−	0.964330i	$-0.585274\pi$
$41$	4.50000	−	7.79423i	0.702782	−	1.21725i	0.967486	−	0.252924i	$-0.0813924\pi$
$42$		0			0
$43$	−3.00000	+	5.19615i	−0.457496	+	0.792406i	−0.998828	−	0.0484030i	$-0.984587\pi$
$43$	−3.00000	+	5.19615i	−0.457496	+	0.792406i	0.541332	+	0.840809i	$0.317920\pi$
$44$	−2.50000	−	4.33013i	−0.376889	−	0.652791i
$45$	3.00000			0.447214
$46$	1.00000			0.147442
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$		0			0
$49$	−6.00000			−0.857143
$50$	1.00000			0.141421
$51$		0			0
$52$	−1.00000	+	1.73205i	−0.138675	+	0.240192i
$53$	−2.50000	−	4.33013i	−0.343401	−	0.594789i	0.641661	−	0.766989i	$-0.278246\pi$
$53$	−2.50000	−	4.33013i	−0.343401	−	0.594789i	−0.985062	+	0.172200i	$0.944912\pi$
$54$		0			0
$55$	2.50000	−	4.33013i	0.337100	−	0.583874i
$56$	1.00000			0.133631
$57$		0			0
$58$	6.00000			0.787839
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$		0			0
$61$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$61$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$62$	−2.00000	+	3.46410i	−0.254000	+	0.439941i
$63$	1.50000	+	2.59808i	0.188982	+	0.327327i
$64$	1.00000			0.125000
$65$	−2.00000			−0.248069
$66$		0			0
$67$	−6.00000	−	10.3923i	−0.733017	−	1.26962i	−0.955588	−	0.294706i	$-0.904778\pi$
$67$	−6.00000	−	10.3923i	−0.733017	−	1.26962i	0.222571	−	0.974916i	$-0.428555\pi$
$68$		0			0
$69$		0			0
$70$	0.500000	+	0.866025i	0.0597614	+	0.103510i
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	−0.987294	−	0.158901i	$-0.949205\pi$
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	0.631260	+	0.775571i	$0.282538\pi$
$72$	1.50000	+	2.59808i	0.176777	+	0.306186i
$73$	−7.00000	+	12.1244i	−0.819288	+	1.41905i	0.0869195	+	0.996215i	$0.472298\pi$
$73$	−7.00000	+	12.1244i	−0.819288	+	1.41905i	−0.906208	+	0.422833i	$0.861036\pi$
$74$	5.50000	−	9.52628i	0.639362	−	1.10741i
$75$		0			0
$76$	4.00000	−	1.73205i	0.458831	−	0.198680i
$77$	5.00000			0.569803
$78$		0			0
$79$	−5.00000	+	8.66025i	−0.562544	+	0.974355i	0.434730	+	0.900561i	$0.356844\pi$
$79$	−5.00000	+	8.66025i	−0.562544	+	0.974355i	−0.997274	+	0.0737937i	$0.976489\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	4.50000	+	7.79423i	0.496942	+	0.860729i
$83$	14.0000			1.53670			0.768350	−	0.640030i	$-0.221078\pi$
$83$	14.0000			1.53670			0.768350	+	0.640030i	$0.221078\pi$
$84$		0			0
$85$		0			0
$86$	−3.00000	−	5.19615i	−0.323498	−	0.560316i
$87$		0			0
$88$	5.00000			0.533002
$89$	3.50000	+	6.06218i	0.370999	+	0.642590i	0.989720	−	0.143022i	$-0.0456819\pi$
$89$	3.50000	+	6.06218i	0.370999	+	0.642590i	−0.618720	+	0.785611i	$0.712349\pi$
$90$	−1.50000	+	2.59808i	−0.158114	+	0.273861i
$91$	−1.00000	−	1.73205i	−0.104828	−	0.181568i
$92$	−0.500000	+	0.866025i	−0.0521286	+	0.0902894i
$93$		0			0
$94$		0			0
$95$	3.50000	+	2.59808i	0.359092	+	0.266557i
$96$		0			0
$97$	1.00000	−	1.73205i	0.101535	−	0.175863i	−0.810782	−	0.585348i	$-0.800958\pi$
$97$	1.00000	−	1.73205i	0.101535	−	0.175863i	0.912317	+	0.409484i	$0.134291\pi$
$98$	3.00000	−	5.19615i	0.303046	−	0.524891i
$99$	7.50000	+	12.9904i	0.753778	+	1.30558i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−5.00000	−	8.66025i	−0.497519	−	0.861727i	0.502477	−	0.864590i	$-0.332422\pi$
$101$	−5.00000	−	8.66025i	−0.497519	−	0.861727i	−0.999996	+	0.00286291i	$0.999089\pi$
$102$		0			0
$103$	13.0000			1.28093			0.640464	−	0.767988i	$-0.278742\pi$
$103$	13.0000			1.28093			0.640464	+	0.767988i	$0.278742\pi$
$104$	−1.00000	−	1.73205i	−0.0980581	−	0.169842i
$105$		0			0
$106$	5.00000			0.485643
$107$	−4.00000			−0.386695			−0.193347	−	0.981130i	$-0.561934\pi$
$107$	−4.00000			−0.386695			−0.193347	+	0.981130i	$0.561934\pi$
$108$		0			0
$109$	−2.00000	+	3.46410i	−0.191565	+	0.331801i	−0.945769	−	0.324840i	$-0.894690\pi$
$109$	−2.00000	+	3.46410i	−0.191565	+	0.331801i	0.754204	+	0.656640i	$0.228023\pi$
$110$	2.50000	+	4.33013i	0.238366	+	0.412861i
$111$		0			0
$112$	−0.500000	+	0.866025i	−0.0472456	+	0.0818317i
$113$	−12.0000			−1.12887			−0.564433	−	0.825479i	$-0.690905\pi$
$113$	−12.0000			−1.12887			−0.564433	+	0.825479i	$0.690905\pi$
$114$		0			0
$115$	−1.00000			−0.0932505
$116$	−3.00000	+	5.19615i	−0.278543	+	0.482451i
$117$	3.00000	−	5.19615i	0.277350	−	0.480384i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	14.0000			1.27273
$122$		0			0
$123$		0			0
$124$	−2.00000	−	3.46410i	−0.179605	−	0.311086i
$125$	−1.00000			−0.0894427
$126$	−3.00000			−0.267261
$127$	7.50000	+	12.9904i	0.665517	+	1.15271i	0.979145	+	0.203164i	$0.0651224\pi$
$127$	7.50000	+	12.9904i	0.665517	+	1.15271i	−0.313627	+	0.949546i	$0.601544\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	1.00000	−	1.73205i	0.0877058	−	0.151911i
$131$	−0.500000	+	0.866025i	−0.0436852	+	0.0756650i	−0.887041	−	0.461690i	$-0.847243\pi$
$131$	−0.500000	+	0.866025i	−0.0436852	+	0.0756650i	0.843356	+	0.537355i	$0.180577\pi$
$132$		0			0
$133$	−0.500000	+	4.33013i	−0.0433555	+	0.375470i
$134$	12.0000			1.03664
$135$		0			0
$136$		0			0
$137$	−6.00000	−	10.3923i	−0.512615	−	0.887875i	−0.999893	−	0.0146279i	$-0.995344\pi$
$137$	−6.00000	−	10.3923i	−0.512615	−	0.887875i	0.487278	−	0.873247i	$-0.337990\pi$
$138$		0			0
$139$	−8.00000	−	13.8564i	−0.678551	−	1.17529i	−0.975417	−	0.220366i	$-0.929275\pi$
$139$	−8.00000	−	13.8564i	−0.678551	−	1.17529i	0.296866	−	0.954919i	$-0.404058\pi$
$140$	−1.00000			−0.0845154
$141$		0			0
$142$	−3.00000	−	5.19615i	−0.251754	−	0.436051i
$143$	−5.00000	−	8.66025i	−0.418121	−	0.724207i
$144$	−3.00000			−0.250000
$145$	−6.00000			−0.498273
$146$	−7.00000	−	12.1244i	−0.579324	−	1.00342i
$147$		0			0
$148$	5.50000	+	9.52628i	0.452097	+	0.783055i
$149$	2.00000	−	3.46410i	0.163846	−	0.283790i	−0.772399	−	0.635138i	$-0.780943\pi$
$149$	2.00000	−	3.46410i	0.163846	−	0.283790i	0.936245	+	0.351348i	$0.114277\pi$
$150$		0			0
$151$	−16.0000			−1.30206			−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000			−1.30206			−0.651031	+	0.759051i	$0.725663\pi$
$152$	−0.500000	+	4.33013i	−0.0405554	+	0.351220i
$153$		0			0
$154$	−2.50000	+	4.33013i	−0.201456	+	0.348932i
$155$	2.00000	−	3.46410i	0.160644	−	0.278243i
$156$		0			0
$157$	10.5000	−	18.1865i	0.837991	−	1.45144i	−0.0535803	−	0.998564i	$-0.517063\pi$
$157$	10.5000	−	18.1865i	0.837991	−	1.45144i	0.891572	−	0.452880i	$-0.149603\pi$
$158$	−5.00000	−	8.66025i	−0.397779	−	0.688973i
$159$		0			0
$160$	−1.00000			−0.0790569
$161$	−0.500000	−	0.866025i	−0.0394055	−	0.0682524i
$162$	−4.50000	−	7.79423i	−0.353553	−	0.612372i
$163$	10.0000			0.783260			0.391630	−	0.920123i	$-0.371911\pi$
$163$	10.0000			0.783260			0.391630	+	0.920123i	$0.371911\pi$
$164$	−9.00000			−0.702782
$165$		0			0
$166$	−7.00000	+	12.1244i	−0.543305	+	0.941033i
$167$	2.50000	+	4.33013i	0.193456	+	0.335075i	0.946393	−	0.323017i	$-0.104697\pi$
$167$	2.50000	+	4.33013i	0.193456	+	0.335075i	−0.752937	+	0.658092i	$0.771364\pi$
$168$		0			0
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$		0			0
$171$	−12.0000	+	5.19615i	−0.917663	+	0.397360i
$172$	6.00000			0.457496
$173$	−0.500000	+	0.866025i	−0.0380143	+	0.0658427i	−0.884407	−	0.466717i	$-0.845437\pi$
$173$	−0.500000	+	0.866025i	−0.0380143	+	0.0658427i	0.846392	+	0.532560i	$0.178770\pi$
$174$		0			0
$175$	−0.500000	−	0.866025i	−0.0377964	−	0.0654654i
$176$	−2.50000	+	4.33013i	−0.188445	+	0.326396i
$177$		0			0
$178$	−7.00000			−0.524672
$179$	19.0000			1.42013			0.710063	−	0.704138i	$-0.248666\pi$
$179$	19.0000			1.42013			0.710063	+	0.704138i	$0.248666\pi$
$180$	−1.50000	−	2.59808i	−0.111803	−	0.193649i
$181$	−1.00000	−	1.73205i	−0.0743294	−	0.128742i	0.826465	−	0.562988i	$-0.190348\pi$
$181$	−1.00000	−	1.73205i	−0.0743294	−	0.128742i	−0.900794	+	0.434246i	$0.857015\pi$
$182$	2.00000			0.148250
$183$		0			0
$184$	−0.500000	−	0.866025i	−0.0368605	−	0.0638442i
$185$	−5.50000	+	9.52628i	−0.404368	+	0.700386i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$	−4.00000	+	1.73205i	−0.290191	+	0.125656i
$191$	−18.0000			−1.30243			−0.651217	−	0.758891i	$-0.725741\pi$
$191$	−18.0000			−1.30243			−0.651217	+	0.758891i	$0.725741\pi$
$192$		0			0
$193$	−2.00000	+	3.46410i	−0.143963	+	0.249351i	−0.928986	−	0.370116i	$-0.879318\pi$
$193$	−2.00000	+	3.46410i	−0.143963	+	0.249351i	0.785022	+	0.619467i	$0.212651\pi$
$194$	1.00000	+	1.73205i	0.0717958	+	0.124354i
$195$		0			0
$196$	3.00000	+	5.19615i	0.214286	+	0.371154i
$197$	23.0000			1.63868			0.819341	−	0.573306i	$-0.194340\pi$
$197$	23.0000			1.63868			0.819341	+	0.573306i	$0.194340\pi$
$198$	−15.0000			−1.06600
$199$	−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	$-0.490462\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$		0			0
$202$	10.0000			0.703598
$203$	−3.00000	−	5.19615i	−0.210559	−	0.364698i
$204$		0			0
$205$	−4.50000	−	7.79423i	−0.314294	−	0.544373i
$206$	−6.50000	+	11.2583i	−0.452876	+	0.784405i
$207$	1.50000	−	2.59808i	0.104257	−	0.180579i
$208$	2.00000			0.138675
$209$	−2.50000	+	21.6506i	−0.172929	+	1.49761i
$210$		0			0
$211$	−6.50000	+	11.2583i	−0.447478	+	0.775055i	−0.998221	−	0.0596196i	$-0.981011\pi$
$211$	−6.50000	+	11.2583i	−0.447478	+	0.775055i	0.550743	+	0.834675i	$0.314345\pi$
$212$	−2.50000	+	4.33013i	−0.171701	+	0.297394i
$213$		0			0
$214$	2.00000	−	3.46410i	0.136717	−	0.236801i
$215$	3.00000	+	5.19615i	0.204598	+	0.354375i
$216$		0			0
$217$	4.00000			0.271538
$218$	−2.00000	−	3.46410i	−0.135457	−	0.234619i
$219$		0			0
$220$	−5.00000			−0.337100
$221$		0			0
$222$		0			0
$223$	11.5000	−	19.9186i	0.770097	−	1.33385i	−0.167412	−	0.985887i	$-0.553541\pi$
$223$	11.5000	−	19.9186i	0.770097	−	1.33385i	0.937509	−	0.347960i	$-0.113126\pi$
$224$	−0.500000	−	0.866025i	−0.0334077	−	0.0578638i
$225$	1.50000	−	2.59808i	0.100000	−	0.173205i
$226$	6.00000	−	10.3923i	0.399114	−	0.691286i
$227$	−10.0000			−0.663723			−0.331862	−	0.943328i	$-0.607677\pi$
$227$	−10.0000			−0.663723			−0.331862	+	0.943328i	$0.607677\pi$
$228$		0			0
$229$	6.00000			0.396491			0.198246	−	0.980152i	$-0.436476\pi$
$229$	6.00000			0.396491			0.198246	+	0.980152i	$0.436476\pi$
$230$	0.500000	−	0.866025i	0.0329690	−	0.0571040i
$231$		0			0
$232$	−3.00000	−	5.19615i	−0.196960	−	0.341144i
$233$	−5.00000	+	8.66025i	−0.327561	+	0.567352i	−0.982027	−	0.188739i	$-0.939560\pi$
$233$	−5.00000	+	8.66025i	−0.327561	+	0.567352i	0.654466	+	0.756091i	$0.272893\pi$
$234$	3.00000	+	5.19615i	0.196116	+	0.339683i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	16.0000			1.03495			0.517477	−	0.855697i	$-0.326871\pi$
$239$	16.0000			1.03495			0.517477	+	0.855697i	$0.326871\pi$
$240$		0			0
$241$	9.00000	+	15.5885i	0.579741	+	1.00414i	0.995509	+	0.0946700i	$0.0301796\pi$
$241$	9.00000	+	15.5885i	0.579741	+	1.00414i	−0.415768	+	0.909471i	$0.636487\pi$
$242$	−7.00000	+	12.1244i	−0.449977	+	0.779383i
$243$		0			0
$244$		0			0
$245$	−3.00000	+	5.19615i	−0.191663	+	0.331970i
$246$		0			0
$247$	8.00000	−	3.46410i	0.509028	−	0.220416i
$248$	4.00000			0.254000
$249$		0			0
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	6.00000	+	10.3923i	0.378717	+	0.655956i	0.990876	−	0.134778i	$-0.0430322\pi$
$251$	6.00000	+	10.3923i	0.378717	+	0.655956i	−0.612159	+	0.790735i	$0.709699\pi$
$252$	1.50000	−	2.59808i	0.0944911	−	0.163663i
$253$	−2.50000	−	4.33013i	−0.157174	−	0.272233i
$254$	−15.0000			−0.941184
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	7.00000	+	12.1244i	0.436648	+	0.756297i	0.997429	−	0.0716680i	$-0.0228322\pi$
$257$	7.00000	+	12.1244i	0.436648	+	0.756297i	−0.560781	+	0.827964i	$0.689499\pi$
$258$		0			0
$259$	−11.0000			−0.683507
$260$	1.00000	+	1.73205i	0.0620174	+	0.107417i
$261$	9.00000	−	15.5885i	0.557086	−	0.964901i
$262$	−0.500000	−	0.866025i	−0.0308901	−	0.0535032i
$263$	−5.50000	+	9.52628i	−0.339145	+	0.587416i	−0.984272	−	0.176659i	$-0.943471\pi$
$263$	−5.50000	+	9.52628i	−0.339145	+	0.587416i	0.645128	+	0.764075i	$0.276804\pi$
$264$		0			0
$265$	−5.00000			−0.307148
$266$	−3.50000	−	2.59808i	−0.214599	−	0.159298i
$267$		0			0
$268$	−6.00000	+	10.3923i	−0.366508	+	0.634811i
$269$	14.0000	−	24.2487i	0.853595	−	1.47847i	−0.0243472	−	0.999704i	$-0.507751\pi$
$269$	14.0000	−	24.2487i	0.853595	−	1.47847i	0.877942	−	0.478766i	$-0.158916\pi$
$270$		0			0
$271$	3.00000	−	5.19615i	0.182237	−	0.315644i	−0.760405	−	0.649449i	$-0.775000\pi$
$271$	3.00000	−	5.19615i	0.182237	−	0.315644i	0.942642	+	0.333805i	$0.108333\pi$
$272$		0			0
$273$		0			0
$274$	12.0000			0.724947
$275$	−2.50000	−	4.33013i	−0.150756	−	0.261116i
$276$		0			0
$277$	−2.00000			−0.120168			−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000			−0.120168			−0.0600842	+	0.998193i	$0.519137\pi$
$278$	16.0000			0.959616
$279$	6.00000	+	10.3923i	0.359211	+	0.622171i
$280$	0.500000	−	0.866025i	0.0298807	−	0.0517549i
$281$	7.50000	+	12.9904i	0.447412	+	0.774941i	0.998217	−	0.0596933i	$-0.0190123\pi$
$281$	7.50000	+	12.9904i	0.447412	+	0.774941i	−0.550804	+	0.834634i	$0.685679\pi$
$282$		0			0
$283$	7.00000	−	12.1244i	0.416107	−	0.720718i	−0.579437	−	0.815017i	$-0.696728\pi$
$283$	7.00000	−	12.1244i	0.416107	−	0.720718i	0.995544	+	0.0942988i	$0.0300609\pi$
$284$	6.00000			0.356034
$285$		0			0
$286$	10.0000			0.591312
$287$	4.50000	−	7.79423i	0.265627	−	0.460079i
$288$	1.50000	−	2.59808i	0.0883883	−	0.153093i
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$	3.00000	−	5.19615i	0.176166	−	0.305129i
$291$		0			0
$292$	14.0000			0.819288
$293$	−21.0000			−1.22683			−0.613417	−	0.789760i	$-0.710205\pi$
$293$	−21.0000			−1.22683			−0.613417	+	0.789760i	$0.710205\pi$
$294$		0			0
$295$		0			0
$296$	−11.0000			−0.639362
$297$		0			0
$298$	2.00000	+	3.46410i	0.115857	+	0.200670i
$299$	−1.00000	+	1.73205i	−0.0578315	+	0.100167i
$300$		0			0
$301$	−3.00000	+	5.19615i	−0.172917	+	0.299501i
$302$	8.00000	−	13.8564i	0.460348	−	0.797347i
$303$		0			0
$304$	−3.50000	−	2.59808i	−0.200739	−	0.149010i
$305$		0			0
$306$		0			0
$307$	1.00000	−	1.73205i	0.0570730	−	0.0988534i	−0.836077	−	0.548612i	$-0.815157\pi$
$307$	1.00000	−	1.73205i	0.0570730	−	0.0988534i	0.893150	+	0.449758i	$0.148490\pi$
$308$	−2.50000	−	4.33013i	−0.142451	−	0.246732i
$309$		0			0
$310$	2.00000	+	3.46410i	0.113592	+	0.196748i
$311$	4.00000			0.226819			0.113410	−	0.993548i	$-0.463823\pi$
$311$	4.00000			0.226819			0.113410	+	0.993548i	$0.463823\pi$
$312$		0			0
$313$	14.0000	+	24.2487i	0.791327	+	1.37062i	0.925146	+	0.379612i	$0.123943\pi$
$313$	14.0000	+	24.2487i	0.791327	+	1.37062i	−0.133819	+	0.991006i	$0.542724\pi$
$314$	10.5000	+	18.1865i	0.592549	+	1.02633i
$315$	3.00000			0.169031
$316$	10.0000			0.562544
$317$	13.5000	+	23.3827i	0.758236	+	1.31330i	0.943750	+	0.330661i	$0.107272\pi$
$317$	13.5000	+	23.3827i	0.758236	+	1.31330i	−0.185514	+	0.982642i	$0.559395\pi$
$318$		0			0
$319$	−15.0000	−	25.9808i	−0.839839	−	1.45464i
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$		0			0
$322$	1.00000			0.0557278
$323$		0			0
$324$	9.00000			0.500000
$325$	−1.00000	+	1.73205i	−0.0554700	+	0.0960769i
$326$	−5.00000	+	8.66025i	−0.276924	+	0.479647i
$327$		0			0
$328$	4.50000	−	7.79423i	0.248471	−	0.430364i
$329$		0			0
$330$		0			0
$331$	−25.0000			−1.37412			−0.687062	−	0.726599i	$-0.741100\pi$
$331$	−25.0000			−1.37412			−0.687062	+	0.726599i	$0.741100\pi$
$332$	−7.00000	−	12.1244i	−0.384175	−	0.665410i
$333$	−16.5000	−	28.5788i	−0.904194	−	1.56611i
$334$	−5.00000			−0.273588
$335$	−12.0000			−0.655630
$336$		0			0
$337$	−3.00000	+	5.19615i	−0.163420	+	0.283052i	−0.936093	−	0.351752i	$-0.885586\pi$
$337$	−3.00000	+	5.19615i	−0.163420	+	0.283052i	0.772673	+	0.634804i	$0.218919\pi$
$338$	4.50000	+	7.79423i	0.244768	+	0.423950i
$339$		0			0
$340$		0			0
$341$	20.0000			1.08306
$342$	1.50000	−	12.9904i	0.0811107	−	0.702439i
$343$	−13.0000			−0.701934
$344$	−3.00000	+	5.19615i	−0.161749	+	0.280158i
$345$		0			0
$346$	−0.500000	−	0.866025i	−0.0268802	−	0.0465578i
$347$	−9.00000	+	15.5885i	−0.483145	+	0.836832i	−0.999813	−	0.0193540i	$-0.993839\pi$
$347$	−9.00000	+	15.5885i	−0.483145	+	0.836832i	0.516667	+	0.856186i	$0.327172\pi$
$348$		0			0
$349$	−28.0000			−1.49881			−0.749403	−	0.662114i	$-0.769659\pi$
$349$	−28.0000			−1.49881			−0.749403	+	0.662114i	$0.769659\pi$
$350$	1.00000			0.0534522
$351$		0			0
$352$	−2.50000	−	4.33013i	−0.133250	−	0.230797i
$353$	4.00000			0.212899			0.106449	−	0.994318i	$-0.466052\pi$
$353$	4.00000			0.212899			0.106449	+	0.994318i	$0.466052\pi$
$354$		0			0
$355$	3.00000	+	5.19615i	0.159223	+	0.275783i
$356$	3.50000	−	6.06218i	0.185500	−	0.321295i
$357$		0			0
$358$	−9.50000	+	16.4545i	−0.502091	+	0.869646i
$359$	−5.00000	+	8.66025i	−0.263890	+	0.457071i	−0.967272	−	0.253741i	$-0.918339\pi$
$359$	−5.00000	+	8.66025i	−0.263890	+	0.457071i	0.703382	+	0.710812i	$0.251672\pi$
$360$	3.00000			0.158114
$361$	−18.5000	−	4.33013i	−0.973684	−	0.227901i
$362$	2.00000			0.105118
$363$		0			0
$364$	−1.00000	+	1.73205i	−0.0524142	+	0.0907841i
$365$	7.00000	+	12.1244i	0.366397	+	0.634618i
$366$		0			0
$367$	2.00000	+	3.46410i	0.104399	+	0.180825i	0.913493	−	0.406855i	$-0.133375\pi$
$367$	2.00000	+	3.46410i	0.104399	+	0.180825i	−0.809093	+	0.587680i	$0.800041\pi$
$368$	1.00000			0.0521286
$369$	27.0000			1.40556
$370$	−5.50000	−	9.52628i	−0.285931	−	0.495248i
$371$	−2.50000	−	4.33013i	−0.129794	−	0.224809i
$372$		0			0
$373$	31.0000			1.60512			0.802560	−	0.596572i	$-0.203471\pi$
$373$	31.0000			1.60512			0.802560	+	0.596572i	$0.203471\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−6.00000	+	10.3923i	−0.309016	+	0.535231i
$378$		0			0
$379$	−12.0000			−0.616399			−0.308199	−	0.951322i	$-0.599726\pi$
$379$	−12.0000			−0.616399			−0.308199	+	0.951322i	$0.599726\pi$
$380$	0.500000	−	4.33013i	0.0256495	−	0.222131i
$381$		0			0
$382$	9.00000	−	15.5885i	0.460480	−	0.797575i
$383$	−4.00000	+	6.92820i	−0.204390	+	0.354015i	−0.949938	−	0.312437i	$-0.898855\pi$
$383$	−4.00000	+	6.92820i	−0.204390	+	0.354015i	0.745548	+	0.666452i	$0.232188\pi$
$384$		0			0
$385$	2.50000	−	4.33013i	0.127412	−	0.220684i
$386$	−2.00000	−	3.46410i	−0.101797	−	0.176318i
$387$	−18.0000			−0.914991
$388$	−2.00000			−0.101535
$389$	−13.0000	−	22.5167i	−0.659126	−	1.14164i	−0.980842	−	0.194804i	$-0.937593\pi$
$389$	−13.0000	−	22.5167i	−0.659126	−	1.14164i	0.321716	−	0.946836i	$-0.395740\pi$
$390$		0			0
$391$		0			0
$392$	−6.00000			−0.303046
$393$		0			0
$394$	−11.5000	+	19.9186i	−0.579362	+	1.00348i
$395$	5.00000	+	8.66025i	0.251577	+	0.435745i
$396$	7.50000	−	12.9904i	0.376889	−	0.652791i
$397$	−14.5000	+	25.1147i	−0.727734	+	1.26047i	0.230105	+	0.973166i	$0.426093\pi$
$397$	−14.5000	+	25.1147i	−0.727734	+	1.26047i	−0.957839	+	0.287307i	$0.907240\pi$
$398$	24.0000			1.20301
$399$		0			0
$400$	1.00000			0.0500000
$401$	9.00000	−	15.5885i	0.449439	−	0.778450i	−0.548911	−	0.835881i	$-0.684957\pi$
$401$	9.00000	−	15.5885i	0.449439	−	0.778450i	0.998350	+	0.0574304i	$0.0182907\pi$
$402$		0			0
$403$	−4.00000	−	6.92820i	−0.199254	−	0.345118i
$404$	−5.00000	+	8.66025i	−0.248759	+	0.430864i
$405$	4.50000	+	7.79423i	0.223607	+	0.387298i
$406$	6.00000			0.297775
$407$	−55.0000			−2.72625
$408$		0			0
$409$	5.50000	+	9.52628i	0.271957	+	0.471044i	0.969363	−	0.245633i	$-0.0789957\pi$
$409$	5.50000	+	9.52628i	0.271957	+	0.471044i	−0.697406	+	0.716677i	$0.745662\pi$
$410$	9.00000			0.444478
$411$		0			0
$412$	−6.50000	−	11.2583i	−0.320232	−	0.554658i
$413$		0			0
$414$	1.50000	+	2.59808i	0.0737210	+	0.127688i
$415$	7.00000	−	12.1244i	0.343616	−	0.595161i
$416$	−1.00000	+	1.73205i	−0.0490290	+	0.0849208i
$417$		0			0
$418$	−17.5000	−	12.9904i	−0.855953	−	0.635380i
$419$	−7.00000			−0.341972			−0.170986	−	0.985273i	$-0.554695\pi$
$419$	−7.00000			−0.341972			−0.170986	+	0.985273i	$0.554695\pi$
$420$		0			0
$421$	4.00000	−	6.92820i	0.194948	−	0.337660i	−0.751935	−	0.659237i	$-0.770879\pi$
$421$	4.00000	−	6.92820i	0.194948	−	0.337660i	0.946883	+	0.321577i	$0.104213\pi$
$422$	−6.50000	−	11.2583i	−0.316415	−	0.548047i
$423$		0			0
$424$	−2.50000	−	4.33013i	−0.121411	−	0.210290i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	2.00000	+	3.46410i	0.0966736	+	0.167444i
$429$		0			0
$430$	−6.00000			−0.289346
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	0.684564	−	0.728953i	$-0.259993\pi$
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	−0.973574	+	0.228373i	$0.926659\pi$
$432$		0			0
$433$	−1.00000	−	1.73205i	−0.0480569	−	0.0832370i	0.840996	−	0.541041i	$-0.181970\pi$
$433$	−1.00000	−	1.73205i	−0.0480569	−	0.0832370i	−0.889053	+	0.457804i	$0.848636\pi$
$434$	−2.00000	+	3.46410i	−0.0960031	+	0.166282i
$435$		0			0
$436$	4.00000			0.191565
$437$	4.00000	−	1.73205i	0.191346	−	0.0828552i
$438$		0			0
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	−0.945552	−	0.325471i	$-0.894477\pi$
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	0.754642	+	0.656136i	$0.227810\pi$
$440$	2.50000	−	4.33013i	0.119183	−	0.206431i
$441$	−9.00000	−	15.5885i	−0.428571	−	0.742307i
$442$		0			0
$443$	−18.0000	−	31.1769i	−0.855206	−	1.48126i	−0.876454	−	0.481486i	$-0.840097\pi$
$443$	−18.0000	−	31.1769i	−0.855206	−	1.48126i	0.0212481	−	0.999774i	$-0.493236\pi$
$444$		0			0
$445$	7.00000			0.331832
$446$	11.5000	+	19.9186i	0.544541	+	0.943172i
$447$		0			0
$448$	1.00000			0.0472456
$449$	−19.0000			−0.896665			−0.448333	−	0.893867i	$-0.647982\pi$
$449$	−19.0000			−0.896665			−0.448333	+	0.893867i	$0.647982\pi$
$450$	1.50000	+	2.59808i	0.0707107	+	0.122474i
$451$	22.5000	−	38.9711i	1.05948	−	1.83508i
$452$	6.00000	+	10.3923i	0.282216	+	0.488813i
$453$		0			0
$454$	5.00000	−	8.66025i	0.234662	−	0.406446i
$455$	−2.00000			−0.0937614
$456$		0			0
$457$	−32.0000			−1.49690			−0.748448	−	0.663193i	$-0.769201\pi$
$457$	−32.0000			−1.49690			−0.748448	+	0.663193i	$0.769201\pi$
$458$	−3.00000	+	5.19615i	−0.140181	+	0.242800i
$459$		0			0
$460$	0.500000	+	0.866025i	0.0233126	+	0.0403786i
$461$	15.0000	−	25.9808i	0.698620	−	1.21004i	−0.270326	−	0.962769i	$-0.587131\pi$
$461$	15.0000	−	25.9808i	0.698620	−	1.21004i	0.968945	−	0.247276i	$-0.0795353\pi$
$462$		0			0
$463$	37.0000			1.71954			0.859768	−	0.510685i	$-0.170608\pi$
$463$	37.0000			1.71954			0.859768	+	0.510685i	$0.170608\pi$
$464$	6.00000			0.278543
$465$		0			0
$466$	−5.00000	−	8.66025i	−0.231621	−	0.401179i
$467$	34.0000			1.57333			0.786666	−	0.617379i	$-0.211805\pi$
$467$	34.0000			1.57333			0.786666	+	0.617379i	$0.211805\pi$
$468$	−6.00000			−0.277350
$469$	−6.00000	−	10.3923i	−0.277054	−	0.479872i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−15.0000	+	25.9808i	−0.689701	+	1.19460i
$474$		0			0
$475$	4.00000	−	1.73205i	0.183533	−	0.0794719i
$476$		0			0
$477$	7.50000	−	12.9904i	0.343401	−	0.594789i
$478$	−8.00000	+	13.8564i	−0.365911	+	0.633777i
$479$	9.00000	+	15.5885i	0.411220	+	0.712255i	0.995023	−	0.0996406i	$-0.0317693\pi$
$479$	9.00000	+	15.5885i	0.411220	+	0.712255i	−0.583803	+	0.811895i	$0.698436\pi$
$480$		0			0
$481$	11.0000	+	19.0526i	0.501557	+	0.868722i
$482$	−18.0000			−0.819878
$483$		0			0
$484$	−7.00000	−	12.1244i	−0.318182	−	0.551107i
$485$	−1.00000	−	1.73205i	−0.0454077	−	0.0786484i
$486$		0			0
$487$	−23.0000			−1.04223			−0.521115	−	0.853487i	$-0.674484\pi$
$487$	−23.0000			−1.04223			−0.521115	+	0.853487i	$0.674484\pi$
$488$		0			0
$489$		0			0
$490$	−3.00000	−	5.19615i	−0.135526	−	0.234738i
$491$	−13.5000	+	23.3827i	−0.609246	+	1.05525i	0.382118	+	0.924113i	$0.375195\pi$
$491$	−13.5000	+	23.3827i	−0.609246	+	1.05525i	−0.991365	+	0.131132i	$0.958139\pi$
$492$		0			0
$493$		0			0
$494$	−1.00000	+	8.66025i	−0.0449921	+	0.389643i
$495$	15.0000			0.674200
$496$	−2.00000	+	3.46410i	−0.0898027	+	0.155543i
$497$	−3.00000	+	5.19615i	−0.134568	+	0.233079i
$498$		0			0
$499$	19.5000	−	33.7750i	0.872940	−	1.51198i	0.0139987	−	0.999902i	$-0.495544\pi$
$499$	19.5000	−	33.7750i	0.872940	−	1.51198i	0.858941	−	0.512074i	$-0.171123\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$		0			0
$502$	−12.0000			−0.535586
$503$	16.5000	+	28.5788i	0.735699	+	1.27427i	0.954416	+	0.298479i	$0.0964794\pi$
$503$	16.5000	+	28.5788i	0.735699	+	1.27427i	−0.218718	+	0.975788i	$0.570187\pi$
$504$	1.50000	+	2.59808i	0.0668153	+	0.115728i
$505$	−10.0000			−0.444994
$506$	5.00000			0.222277
$507$		0			0
$508$	7.50000	−	12.9904i	0.332759	−	0.576355i
$509$	−7.00000	−	12.1244i	−0.310270	−	0.537403i	0.668151	−	0.744026i	$-0.267086\pi$
$509$	−7.00000	−	12.1244i	−0.310270	−	0.537403i	−0.978421	+	0.206623i	$0.933753\pi$
$510$		0			0
$511$	−7.00000	+	12.1244i	−0.309662	+	0.536350i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−14.0000			−0.617514
$515$	6.50000	−	11.2583i	0.286424	−	0.496101i
$516$		0			0
$517$		0			0
$518$	5.50000	−	9.52628i	0.241656	−	0.418561i
$519$		0			0
$520$	−2.00000			−0.0877058
$521$	18.0000			0.788594			0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000			0.788594			0.394297	+	0.918983i	$0.370988\pi$
$522$	9.00000	+	15.5885i	0.393919	+	0.682288i
$523$	21.0000	+	36.3731i	0.918266	+	1.59048i	0.802048	+	0.597259i	$0.203744\pi$
$523$	21.0000	+	36.3731i	0.918266	+	1.59048i	0.116218	+	0.993224i	$0.462923\pi$
$524$	1.00000			0.0436852
$525$		0			0
$526$	−5.50000	−	9.52628i	−0.239811	−	0.415366i
$527$		0			0
$528$		0			0
$529$	11.0000	−	19.0526i	0.478261	−	0.828372i
$530$	2.50000	−	4.33013i	0.108593	−	0.188089i
$531$		0			0
$532$	4.00000	−	1.73205i	0.173422	−	0.0750939i
$533$	−18.0000			−0.779667
$534$		0			0
$535$	−2.00000	+	3.46410i	−0.0864675	+	0.149766i
$536$	−6.00000	−	10.3923i	−0.259161	−	0.448879i
$537$		0			0
$538$	14.0000	+	24.2487i	0.603583	+	1.04544i
$539$	−30.0000			−1.29219
$540$		0			0
$541$	10.0000	+	17.3205i	0.429934	+	0.744667i	0.996867	−	0.0790969i	$-0.0252036\pi$
$541$	10.0000	+	17.3205i	0.429934	+	0.744667i	−0.566933	+	0.823764i	$0.691870\pi$
$542$	3.00000	+	5.19615i	0.128861	+	0.223194i
$543$		0			0
$544$		0			0
$545$	2.00000	+	3.46410i	0.0856706	+	0.148386i
$546$		0			0
$547$	11.0000	+	19.0526i	0.470326	+	0.814629i	0.999424	−	0.0339321i	$-0.0108030\pi$
$547$	11.0000	+	19.0526i	0.470326	+	0.814629i	−0.529098	+	0.848561i	$0.677470\pi$
$548$	−6.00000	+	10.3923i	−0.256307	+	0.443937i
$549$		0			0
$550$	5.00000			0.213201
$551$	24.0000	−	10.3923i	1.02243	−	0.442727i
$552$		0			0
$553$	−5.00000	+	8.66025i	−0.212622	+	0.368271i
$554$	1.00000	−	1.73205i	0.0424859	−	0.0735878i
$555$		0			0
$556$	−8.00000	+	13.8564i	−0.339276	+	0.587643i
$557$	4.50000	+	7.79423i	0.190671	+	0.330252i	0.945473	−	0.325701i	$-0.105600\pi$
$557$	4.50000	+	7.79423i	0.190671	+	0.330252i	−0.754802	+	0.655953i	$0.772267\pi$
$558$	−12.0000			−0.508001
$559$	12.0000			0.507546
$560$	0.500000	+	0.866025i	0.0211289	+	0.0365963i
$561$		0			0
$562$	−15.0000			−0.632737
$563$	32.0000			1.34864			0.674320	−	0.738440i	$-0.264437\pi$
$563$	32.0000			1.34864			0.674320	+	0.738440i	$0.264437\pi$
$564$		0			0
$565$	−6.00000	+	10.3923i	−0.252422	+	0.437208i
$566$	7.00000	+	12.1244i	0.294232	+	0.509625i
$567$	−4.50000	+	7.79423i	−0.188982	+	0.327327i
$568$	−3.00000	+	5.19615i	−0.125877	+	0.218026i
$569$	45.0000			1.88650			0.943249	−	0.332086i	$-0.107752\pi$
$569$	45.0000			1.88650			0.943249	+	0.332086i	$0.107752\pi$
$570$		0			0
$571$	12.0000			0.502184			0.251092	−	0.967963i	$-0.419210\pi$
$571$	12.0000			0.502184			0.251092	+	0.967963i	$0.419210\pi$
$572$	−5.00000	+	8.66025i	−0.209061	+	0.362103i
$573$		0			0
$574$	4.50000	+	7.79423i	0.187826	+	0.325325i
$575$	−0.500000	+	0.866025i	−0.0208514	+	0.0361158i
$576$	1.50000	+	2.59808i	0.0625000	+	0.108253i
$577$	32.0000			1.33218			0.666089	−	0.745873i	$-0.267967\pi$
$577$	32.0000			1.33218			0.666089	+	0.745873i	$0.267967\pi$
$578$	−17.0000			−0.707107
$579$		0			0
$580$	3.00000	+	5.19615i	0.124568	+	0.215758i
$581$	14.0000			0.580818
$582$		0			0
$583$	−12.5000	−	21.6506i	−0.517697	−	0.896678i
$584$	−7.00000	+	12.1244i	−0.289662	+	0.501709i
$585$	−3.00000	−	5.19615i	−0.124035	−	0.214834i
$586$	10.5000	−	18.1865i	0.433751	−	0.751279i
$587$	−6.00000	+	10.3923i	−0.247647	+	0.428936i	−0.962872	−	0.269957i	$-0.912990\pi$
$587$	−6.00000	+	10.3923i	−0.247647	+	0.428936i	0.715226	+	0.698893i	$0.246324\pi$
$588$		0			0
$589$	−2.00000	+	17.3205i	−0.0824086	+	0.713679i
$590$		0			0
$591$		0			0
$592$	5.50000	−	9.52628i	0.226049	−	0.391528i
$593$	−21.0000	−	36.3731i	−0.862367	−	1.49366i	−0.869638	−	0.493689i	$-0.835648\pi$
$593$	−21.0000	−	36.3731i	−0.862367	−	1.49366i	0.00727173	−	0.999974i	$-0.497685\pi$
$594$		0			0
$595$		0			0
$596$	−4.00000			−0.163846
$597$		0			0
$598$	−1.00000	−	1.73205i	−0.0408930	−	0.0708288i
$599$	22.0000	+	38.1051i	0.898896	+	1.55693i	0.828908	+	0.559385i	$0.188963\pi$
$599$	22.0000	+	38.1051i	0.898896	+	1.55693i	0.0699877	+	0.997548i	$0.477704\pi$
$600$		0			0
$601$	21.0000			0.856608			0.428304	−	0.903635i	$-0.359111\pi$
$601$	21.0000			0.856608			0.428304	+	0.903635i	$0.359111\pi$
$602$	−3.00000	−	5.19615i	−0.122271	−	0.211779i
$603$	18.0000	−	31.1769i	0.733017	−	1.26962i
$604$	8.00000	+	13.8564i	0.325515	+	0.563809i
$605$	7.00000	−	12.1244i	0.284590	−	0.492925i
$606$		0			0
$607$	13.0000			0.527654			0.263827	−	0.964570i	$-0.415015\pi$
$607$	13.0000			0.527654			0.263827	+	0.964570i	$0.415015\pi$
$608$	4.00000	−	1.73205i	0.162221	−	0.0702439i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−12.5000	+	21.6506i	−0.504870	+	0.874461i	0.495114	+	0.868828i	$0.335126\pi$
$613$	−12.5000	+	21.6506i	−0.504870	+	0.874461i	−0.999984	+	0.00563283i	$0.998207\pi$
$614$	1.00000	+	1.73205i	0.0403567	+	0.0698999i
$615$		0			0
$616$	5.00000			0.201456
$617$	−10.0000	−	17.3205i	−0.402585	−	0.697297i	0.591452	−	0.806340i	$-0.298555\pi$
$617$	−10.0000	−	17.3205i	−0.402585	−	0.697297i	−0.994037	+	0.109043i	$0.965221\pi$
$618$		0			0
$619$	−45.0000			−1.80870			−0.904351	−	0.426789i	$-0.859645\pi$
$619$	−45.0000			−1.80870			−0.904351	+	0.426789i	$0.859645\pi$
$620$	−4.00000			−0.160644
$621$		0			0
$622$	−2.00000	+	3.46410i	−0.0801927	+	0.138898i
$623$	3.50000	+	6.06218i	0.140225	+	0.242876i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−28.0000			−1.11911
$627$		0			0
$628$	−21.0000			−0.837991
$629$		0			0
$630$	−1.50000	+	2.59808i	−0.0597614	+	0.103510i
$631$	11.0000	+	19.0526i	0.437903	+	0.758470i	0.997528	−	0.0702759i	$-0.0223880\pi$
$631$	11.0000	+	19.0526i	0.437903	+	0.758470i	−0.559625	+	0.828746i	$0.689055\pi$
$632$	−5.00000	+	8.66025i	−0.198889	+	0.344486i
$633$		0			0
$634$	−27.0000			−1.07231
$635$	15.0000			0.595257
$636$		0			0
$637$	6.00000	+	10.3923i	0.237729	+	0.411758i
$638$	30.0000			1.18771
$639$	−18.0000			−0.712069
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	5.00000	−	8.66025i	0.197488	−	0.342059i	−0.750225	−	0.661182i	$-0.770055\pi$
$641$	5.00000	−	8.66025i	0.197488	−	0.342059i	0.947713	+	0.319123i	$0.103388\pi$
$642$		0			0
$643$	8.00000	−	13.8564i	0.315489	−	0.546443i	−0.664052	−	0.747686i	$-0.731165\pi$
$643$	8.00000	−	13.8564i	0.315489	−	0.546443i	0.979541	+	0.201243i	$0.0644981\pi$
$644$	−0.500000	+	0.866025i	−0.0197028	+	0.0341262i
$645$		0			0
$646$		0			0
$647$	−3.00000			−0.117942			−0.0589711	−	0.998260i	$-0.518782\pi$
$647$	−3.00000			−0.117942			−0.0589711	+	0.998260i	$0.518782\pi$
$648$	−4.50000	+	7.79423i	−0.176777	+	0.306186i
$649$		0			0
$650$	−1.00000	−	1.73205i	−0.0392232	−	0.0679366i
$651$		0			0
$652$	−5.00000	−	8.66025i	−0.195815	−	0.339162i
$653$	−25.0000			−0.978326			−0.489163	−	0.872192i	$-0.662698\pi$
$653$	−25.0000			−0.978326			−0.489163	+	0.872192i	$0.662698\pi$
$654$		0			0
$655$	0.500000	+	0.866025i	0.0195366	+	0.0338384i
$656$	4.50000	+	7.79423i	0.175695	+	0.304314i
$657$	−42.0000			−1.63858
$658$		0			0
$659$	7.50000	+	12.9904i	0.292159	+	0.506033i	0.974320	−	0.225168i	$-0.0722932\pi$
$659$	7.50000	+	12.9904i	0.292159	+	0.506033i	−0.682161	+	0.731202i	$0.738960\pi$
$660$		0			0
$661$	−12.0000	−	20.7846i	−0.466746	−	0.808428i	0.532533	−	0.846410i	$-0.321240\pi$
$661$	−12.0000	−	20.7846i	−0.466746	−	0.808428i	−0.999278	+	0.0379819i	$0.987907\pi$
$662$	12.5000	−	21.6506i	0.485826	−	0.841476i
$663$		0			0
$664$	14.0000			0.543305
$665$	3.50000	+	2.59808i	0.135724	+	0.100749i
$666$	33.0000			1.27872
$667$	−3.00000	+	5.19615i	−0.116160	+	0.201196i
$668$	2.50000	−	4.33013i	0.0967279	−	0.167538i
$669$		0			0
$670$	6.00000	−	10.3923i	0.231800	−	0.401490i
$671$		0			0
$672$		0			0
$673$	16.0000			0.616755			0.308377	−	0.951264i	$-0.400214\pi$
$673$	16.0000			0.616755			0.308377	+	0.951264i	$0.400214\pi$
$674$	−3.00000	−	5.19615i	−0.115556	−	0.200148i
$675$		0			0
$676$	−9.00000			−0.346154
$677$	27.0000			1.03769			0.518847	−	0.854867i	$-0.326361\pi$
$677$	27.0000			1.03769			0.518847	+	0.854867i	$0.326361\pi$
$678$		0			0
$679$	1.00000	−	1.73205i	0.0383765	−	0.0664700i
$680$		0			0
$681$		0			0
$682$	−10.0000	+	17.3205i	−0.382920	+	0.663237i
$683$	−44.0000			−1.68361			−0.841807	−	0.539779i	$-0.818508\pi$
$683$	−44.0000			−1.68361			−0.841807	+	0.539779i	$0.818508\pi$
$684$	10.5000	+	7.79423i	0.401478	+	0.298020i
$685$	−12.0000			−0.458496
$686$	6.50000	−	11.2583i	0.248171	−	0.429845i
$687$		0			0
$688$	−3.00000	−	5.19615i	−0.114374	−	0.198101i
$689$	−5.00000	+	8.66025i	−0.190485	+	0.329929i
$690$		0			0
$691$	−15.0000			−0.570627			−0.285313	−	0.958434i	$-0.592098\pi$
$691$	−15.0000			−0.570627			−0.285313	+	0.958434i	$0.592098\pi$
$692$	1.00000			0.0380143
$693$	7.50000	+	12.9904i	0.284901	+	0.493464i
$694$	−9.00000	−	15.5885i	−0.341635	−	0.591730i
$695$	−16.0000			−0.606915
$696$		0			0
$697$		0			0
$698$	14.0000	−	24.2487i	0.529908	−	0.917827i
$699$		0			0
$700$	−0.500000	+	0.866025i	−0.0188982	+	0.0327327i
$701$	−3.00000	+	5.19615i	−0.113308	+	0.196256i	−0.917102	−	0.398652i	$-0.869478\pi$
$701$	−3.00000	+	5.19615i	−0.113308	+	0.196256i	0.803794	+	0.594908i	$0.202811\pi$
$702$		0			0
$703$	5.50000	−	47.6314i	0.207436	−	1.79645i
$704$	5.00000			0.188445
$705$		0			0
$706$	−2.00000	+	3.46410i	−0.0752710	+	0.130373i
$707$	−5.00000	−	8.66025i	−0.188044	−	0.325702i
$708$		0			0
$709$	−4.00000	−	6.92820i	−0.150223	−	0.260194i	0.781086	−	0.624423i	$-0.214666\pi$
$709$	−4.00000	−	6.92820i	−0.150223	−	0.260194i	−0.931309	+	0.364229i	$0.881333\pi$
$710$	−6.00000			−0.225176
$711$	−30.0000			−1.12509
$712$	3.50000	+	6.06218i	0.131168	+	0.227190i
$713$	−2.00000	−	3.46410i	−0.0749006	−	0.129732i
$714$		0			0
$715$	−10.0000			−0.373979
$716$	−9.50000	−	16.4545i	−0.355032	−	0.614933i
$717$		0			0
$718$	−5.00000	−	8.66025i	−0.186598	−	0.323198i
$719$	24.0000	−	41.5692i	0.895049	−	1.55027i	0.0613050	−	0.998119i	$-0.480474\pi$
$719$	24.0000	−	41.5692i	0.895049	−	1.55027i	0.833744	−	0.552151i	$-0.186193\pi$
$720$	−1.50000	+	2.59808i	−0.0559017	+	0.0968246i
$721$	13.0000			0.484145
$722$	13.0000	−	13.8564i	0.483810	−	0.515682i
$723$		0			0
$724$	−1.00000	+	1.73205i	−0.0371647	+	0.0643712i
$725$	−3.00000	+	5.19615i	−0.111417	+	0.192980i
$726$		0			0
$727$	8.00000	−	13.8564i	0.296704	−	0.513906i	−0.678676	−	0.734438i	$-0.737446\pi$
$727$	8.00000	−	13.8564i	0.296704	−	0.513906i	0.975380	+	0.220532i	$0.0707793\pi$
$728$	−1.00000	−	1.73205i	−0.0370625	−	0.0641941i
$729$	−27.0000			−1.00000
$730$	−14.0000			−0.518163
$731$		0			0
$732$		0			0
$733$	−15.0000			−0.554038			−0.277019	−	0.960864i	$-0.589346\pi$
$733$	−15.0000			−0.554038			−0.277019	+	0.960864i	$0.589346\pi$
$734$	−4.00000			−0.147643
$735$		0			0
$736$	−0.500000	+	0.866025i	−0.0184302	+	0.0319221i
$737$	−30.0000	−	51.9615i	−1.10506	−	1.91403i
$738$	−13.5000	+	23.3827i	−0.496942	+	0.860729i
$739$	15.5000	−	26.8468i	0.570177	−	0.987575i	−0.426371	−	0.904549i	$-0.640208\pi$
$739$	15.5000	−	26.8468i	0.570177	−	0.987575i	0.996547	−	0.0830265i	$-0.0264586\pi$
$740$	11.0000			0.404368
$741$		0			0
$742$	5.00000			0.183556
$743$	7.50000	−	12.9904i	0.275148	−	0.476571i	−0.695024	−	0.718986i	$-0.744606\pi$
$743$	7.50000	−	12.9904i	0.275148	−	0.476571i	0.970173	+	0.242415i	$0.0779397\pi$
$744$		0			0
$745$	−2.00000	−	3.46410i	−0.0732743	−	0.126915i
$746$	−15.5000	+	26.8468i	−0.567495	+	0.982931i
$747$	21.0000	+	36.3731i	0.768350	+	1.33082i
$748$		0			0
$749$	−4.00000			−0.146157
$750$		0			0
$751$	10.0000	+	17.3205i	0.364905	+	0.632034i	0.988761	−	0.149505i	$-0.0477681\pi$
$751$	10.0000	+	17.3205i	0.364905	+	0.632034i	−0.623856	+	0.781540i	$0.714435\pi$
$752$		0			0
$753$		0			0
$754$	−6.00000	−	10.3923i	−0.218507	−	0.378465i
$755$	−8.00000	+	13.8564i	−0.291150	+	0.504286i
$756$		0			0
$757$	7.50000	−	12.9904i	0.272592	−	0.472143i	−0.696933	−	0.717137i	$-0.745452\pi$
$757$	7.50000	−	12.9904i	0.272592	−	0.472143i	0.969525	+	0.244993i	$0.0787857\pi$
$758$	6.00000	−	10.3923i	0.217930	−	0.377466i
$759$		0			0
$760$	3.50000	+	2.59808i	0.126958	+	0.0942421i
$761$	−43.0000			−1.55875			−0.779374	−	0.626559i	$-0.784463\pi$
$761$	−43.0000			−1.55875			−0.779374	+	0.626559i	$0.784463\pi$
$762$		0			0
$763$	−2.00000	+	3.46410i	−0.0724049	+	0.125409i
$764$	9.00000	+	15.5885i	0.325609	+	0.563971i
$765$		0			0
$766$	−4.00000	−	6.92820i	−0.144526	−	0.250326i
$767$		0			0
$768$		0			0
$769$	13.0000	+	22.5167i	0.468792	+	0.811972i	0.999364	−	0.0356685i	$-0.0113561\pi$
$769$	13.0000	+	22.5167i	0.468792	+	0.811972i	−0.530572	+	0.847640i	$0.678023\pi$
$770$	2.50000	+	4.33013i	0.0900937	+	0.156047i
$771$		0			0
$772$	4.00000			0.143963
$773$	−22.5000	−	38.9711i	−0.809269	−	1.40169i	−0.913371	−	0.407128i	$-0.866530\pi$
$773$	−22.5000	−	38.9711i	−0.809269	−	1.40169i	0.104102	−	0.994567i	$-0.466803\pi$
$774$	9.00000	−	15.5885i	0.323498	−	0.560316i
$775$	−2.00000	−	3.46410i	−0.0718421	−	0.124434i
$776$	1.00000	−	1.73205i	0.0358979	−	0.0621770i
$777$		0			0
$778$	26.0000			0.932145
$779$	31.5000	+	23.3827i	1.12860	+	0.837772i
$780$		0			0
$781$	−15.0000	+	25.9808i	−0.536742	+	0.929665i
$782$		0			0
$783$		0			0
$784$	3.00000	−	5.19615i	0.107143	−	0.185577i
$785$	−10.5000	−	18.1865i	−0.374761	−	0.649105i
$786$		0			0
$787$	18.0000			0.641631			0.320815	−	0.947142i	$-0.396043\pi$
$787$	18.0000			0.641631			0.320815	+	0.947142i	$0.396043\pi$
$788$	−11.5000	−	19.9186i	−0.409671	−	0.709570i
$789$		0			0
$790$	−10.0000			−0.355784
$791$	−12.0000			−0.426671
$792$	7.50000	+	12.9904i	0.266501	+	0.461593i
$793$		0			0
$794$	−14.5000	−	25.1147i	−0.514586	−	0.891289i
$795$		0			0
$796$	−12.0000	+	20.7846i	−0.425329	+	0.736691i
$797$	49.0000			1.73567			0.867835	−	0.496853i	$-0.165511\pi$
$797$	49.0000			1.73567			0.867835	+	0.496853i	$0.165511\pi$
$798$		0			0
$799$		0			0
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	−10.5000	+	18.1865i	−0.370999	+	0.642590i
$802$	9.00000	+	15.5885i	0.317801	+	0.550448i
$803$	−35.0000	+	60.6218i	−1.23512	+	2.13930i
$804$		0			0
$805$	−1.00000			−0.0352454
$806$	8.00000			0.281788
$807$		0			0
$808$	−5.00000	−	8.66025i	−0.175899	−	0.304667i
$809$	−2.00000			−0.0703163			−0.0351581	−	0.999382i	$-0.511193\pi$
$809$	−2.00000			−0.0703163			−0.0351581	+	0.999382i	$0.511193\pi$
$810$	−9.00000			−0.316228
$811$	2.50000	+	4.33013i	0.0877869	+	0.152051i	0.906575	−	0.422044i	$-0.138687\pi$
$811$	2.50000	+	4.33013i	0.0877869	+	0.152051i	−0.818788	+	0.574095i	$0.805354\pi$
$812$	−3.00000	+	5.19615i	−0.105279	+	0.182349i
$813$		0			0
$814$	27.5000	−	47.6314i	0.963875	−	1.66948i
$815$	5.00000	−	8.66025i	0.175142	−	0.303355i
$816$		0			0
$817$	−21.0000	−	15.5885i	−0.734697	−	0.545371i
$818$	−11.0000			−0.384606
$819$	3.00000	−	5.19615i	0.104828	−	0.181568i
$820$	−4.50000	+	7.79423i	−0.157147	+	0.272186i
$821$	−25.0000	−	43.3013i	−0.872506	−	1.51122i	−0.859396	−	0.511311i	$-0.829160\pi$
$821$	−25.0000	−	43.3013i	−0.872506	−	1.51122i	−0.0131101	−	0.999914i	$-0.504173\pi$
$822$		0			0
$823$	18.5000	+	32.0429i	0.644869	+	1.11695i	0.984332	+	0.176327i	$0.0564216\pi$
$823$	18.5000	+	32.0429i	0.644869	+	1.11695i	−0.339462	+	0.940620i	$0.610245\pi$
$824$	13.0000			0.452876
$825$		0			0
$826$		0			0
$827$	−3.00000	−	5.19615i	−0.104320	−	0.180688i	0.809140	−	0.587616i	$-0.199933\pi$
$827$	−3.00000	−	5.19615i	−0.104320	−	0.180688i	−0.913460	+	0.406928i	$0.866600\pi$
$828$	−3.00000			−0.104257
$829$	−52.0000			−1.80603			−0.903017	−	0.429604i	$-0.858653\pi$
$829$	−52.0000			−1.80603			−0.903017	+	0.429604i	$0.858653\pi$
$830$	7.00000	+	12.1244i	0.242974	+	0.420843i
$831$		0			0
$832$	−1.00000	−	1.73205i	−0.0346688	−	0.0600481i
$833$		0			0
$834$		0			0
$835$	5.00000			0.173032
$836$	20.0000	−	8.66025i	0.691714	−	0.299521i
$837$		0			0
$838$	3.50000	−	6.06218i	0.120905	−	0.209414i
$839$	−13.0000	+	22.5167i	−0.448810	+	0.777361i	−0.998309	−	0.0581329i	$-0.981485\pi$
$839$	−13.0000	+	22.5167i	−0.448810	+	0.777361i	0.549499	+	0.835494i	$0.314819\pi$
$840$		0			0
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$	4.00000	+	6.92820i	0.137849	+	0.238762i
$843$		0			0
$844$	13.0000			0.447478
$845$	−4.50000	−	7.79423i	−0.154805	−	0.268130i
$846$		0			0
$847$	14.0000			0.481046
$848$	5.00000			0.171701
$849$		0			0
$850$		0			0
$851$	5.50000	+	9.52628i	0.188538	+	0.326557i
$852$		0			0
$853$	−27.0000	+	46.7654i	−0.924462	+	1.60122i	−0.132039	+	0.991245i	$0.542152\pi$
$853$	−27.0000	+	46.7654i	−0.924462	+	1.60122i	−0.792424	+	0.609971i	$0.791181\pi$
$854$		0			0
$855$	−1.50000	+	12.9904i	−0.0512989	+	0.444262i
$856$	−4.00000			−0.136717
$857$	14.0000	−	24.2487i	0.478231	−	0.828320i	−0.521458	−	0.853277i	$-0.674612\pi$
$857$	14.0000	−	24.2487i	0.478231	−	0.828320i	0.999689	+	0.0249570i	$0.00794488\pi$
$858$		0			0
$859$	24.5000	+	42.4352i	0.835929	+	1.44787i	0.893272	+	0.449517i	$0.148404\pi$
$859$	24.5000	+	42.4352i	0.835929	+	1.44787i	−0.0573424	+	0.998355i	$0.518263\pi$
$860$	3.00000	−	5.19615i	0.102299	−	0.177187i
$861$		0			0
$862$	12.0000			0.408722
$863$	17.0000			0.578687			0.289343	−	0.957225i	$-0.406563\pi$
$863$	17.0000			0.578687			0.289343	+	0.957225i	$0.406563\pi$
$864$		0			0
$865$	0.500000	+	0.866025i	0.0170005	+	0.0294457i
$866$	2.00000			0.0679628
$867$		0			0
$868$	−2.00000	−	3.46410i	−0.0678844	−	0.117579i
$869$	−25.0000	+	43.3013i	−0.848067	+	1.46889i
$870$		0			0
$871$	−12.0000	+	20.7846i	−0.406604	+	0.704260i
$872$	−2.00000	+	3.46410i	−0.0677285	+	0.117309i
$873$	6.00000			0.203069
$874$	−0.500000	+	4.33013i	−0.0169128	+	0.146469i
$875$	−1.00000			−0.0338062
$876$		0			0
$877$	−1.50000	+	2.59808i	−0.0506514	+	0.0877308i	−0.890239	−	0.455493i	$-0.849463\pi$
$877$	−1.50000	+	2.59808i	−0.0506514	+	0.0877308i	0.839588	+	0.543224i	$0.182796\pi$
$878$	−4.00000	−	6.92820i	−0.134993	−	0.233816i
$879$		0			0
$880$	2.50000	+	4.33013i	0.0842750	+	0.145969i
$881$	−35.0000			−1.17918			−0.589590	−	0.807703i	$-0.700711\pi$
$881$	−35.0000			−1.17918			−0.589590	+	0.807703i	$0.700711\pi$
$882$	18.0000			0.606092
$883$	18.0000	+	31.1769i	0.605748	+	1.04919i	0.991933	+	0.126765i	$0.0404595\pi$
$883$	18.0000	+	31.1769i	0.605748	+	1.04919i	−0.386185	+	0.922422i	$0.626207\pi$
$884$		0			0
$885$		0			0
$886$	36.0000			1.20944
$887$	−28.0000	−	48.4974i	−0.940148	−	1.62838i	−0.765186	−	0.643809i	$-0.777353\pi$
$887$	−28.0000	−	48.4974i	−0.940148	−	1.62838i	−0.174962	−	0.984575i	$-0.555980\pi$
$888$		0			0
$889$	7.50000	+	12.9904i	0.251542	+	0.435683i
$890$	−3.50000	+	6.06218i	−0.117320	+	0.203205i
$891$	−22.5000	+	38.9711i	−0.753778	+	1.30558i
$892$	−23.0000			−0.770097
$893$		0			0
$894$		0			0
$895$	9.50000	−	16.4545i	0.317550	−	0.550013i
$896$	−0.500000	+	0.866025i	−0.0167038	+	0.0289319i
$897$		0			0
$898$	9.50000	−	16.4545i	0.317019	−	0.549093i
$899$	−12.0000	−	20.7846i	−0.400222	−	0.693206i
$900$	−3.00000			−0.100000
$901$		0			0
$902$	22.5000	+	38.9711i	0.749168	+	1.29760i
$903$		0			0
$904$	−12.0000			−0.399114
$905$	−2.00000			−0.0664822
$906$		0			0
$907$	5.00000	−	8.66025i	0.166022	−	0.287559i	−0.770996	−	0.636841i	$-0.780241\pi$
$907$	5.00000	−	8.66025i	0.166022	−	0.287559i	0.937018	+	0.349281i	$0.113574\pi$
$908$	5.00000	+	8.66025i	0.165931	+	0.287401i
$909$	15.0000	−	25.9808i	0.497519	−	0.861727i
$910$	1.00000	−	1.73205i	0.0331497	−	0.0574169i
$911$	30.0000			0.993944			0.496972	−	0.867766i	$-0.334445\pi$
$911$	30.0000			0.993944			0.496972	+	0.867766i	$0.334445\pi$
$912$		0			0
$913$	70.0000			2.31666
$914$	16.0000	−	27.7128i	0.529233	−	0.916658i
$915$		0			0
$916$	−3.00000	−	5.19615i	−0.0991228	−	0.171686i
$917$	−0.500000	+	0.866025i	−0.0165115	+	0.0285987i
$918$		0			0
$919$	10.0000			0.329870			0.164935	−	0.986304i	$-0.447259\pi$
$919$	10.0000			0.329870			0.164935	+	0.986304i	$0.447259\pi$
$920$	−1.00000			−0.0329690
$921$		0			0
$922$	15.0000	+	25.9808i	0.493999	+	0.855631i
$923$	12.0000			0.394985
$924$		0			0
$925$	5.50000	+	9.52628i	0.180839	+	0.313222i
$926$	−18.5000	+	32.0429i	−0.607948	+	1.05300i
$927$	19.5000	+	33.7750i	0.640464	+	1.10932i
$928$	−3.00000	+	5.19615i	−0.0984798	+	0.170572i
$929$	13.5000	−	23.3827i	0.442921	−	0.767161i	−0.554984	−	0.831861i	$-0.687276\pi$
$929$	13.5000	−	23.3827i	0.442921	−	0.767161i	0.997905	+	0.0646999i	$0.0206090\pi$
$930$		0			0
$931$	3.00000	−	25.9808i	0.0983210	−	0.851485i
$932$	10.0000			0.327561
$933$		0			0
$934$	−17.0000	+	29.4449i	−0.556257	+	0.963465i
$935$		0			0
$936$	3.00000	−	5.19615i	0.0980581	−	0.169842i
$937$	−1.00000	−	1.73205i	−0.0326686	−	0.0565836i	0.849229	−	0.528025i	$-0.177067\pi$
$937$	−1.00000	−	1.73205i	−0.0326686	−	0.0565836i	−0.881897	+	0.471441i	$0.843734\pi$
$938$	12.0000			0.391814
$939$		0			0
$940$		0			0
$941$	9.00000	+	15.5885i	0.293392	+	0.508169i	0.974609	−	0.223912i	$-0.0718827\pi$
$941$	9.00000	+	15.5885i	0.293392	+	0.508169i	−0.681218	+	0.732081i	$0.738549\pi$
$942$		0			0
$943$	−9.00000			−0.293080
$944$		0			0
$945$		0			0
$946$	−15.0000	−	25.9808i	−0.487692	−	0.844707i
$947$	30.0000	−	51.9615i	0.974869	−	1.68852i	0.294502	−	0.955651i	$-0.404846\pi$
$947$	30.0000	−	51.9615i	0.974869	−	1.68852i	0.680367	−	0.732872i	$-0.261821\pi$
$948$		0			0
$949$	28.0000			0.908918
$950$	−0.500000	+	4.33013i	−0.0162221	+	0.140488i
$951$		0			0
$952$		0			0
$953$	18.0000	−	31.1769i	0.583077	−	1.00992i	−0.412035	−	0.911168i	$-0.635182\pi$
$953$	18.0000	−	31.1769i	0.583077	−	1.00992i	0.995112	−	0.0987513i	$-0.0314848\pi$
$954$	7.50000	+	12.9904i	0.242821	+	0.420579i
$955$	−9.00000	+	15.5885i	−0.291233	+	0.504431i
$956$	−8.00000	−	13.8564i	−0.258738	−	0.448148i
$957$		0			0
$958$	−18.0000			−0.581554
$959$	−6.00000	−	10.3923i	−0.193750	−	0.335585i
$960$		0			0
$961$	−15.0000			−0.483871
$962$	−22.0000			−0.709308
$963$	−6.00000	−	10.3923i	−0.193347	−	0.334887i
$964$	9.00000	−	15.5885i	0.289870	−	0.502070i
$965$	2.00000	+	3.46410i	0.0643823	+	0.111513i
$966$		0			0
$967$	4.00000	−	6.92820i	0.128631	−	0.222796i	−0.794515	−	0.607244i	$-0.792275\pi$
$967$	4.00000	−	6.92820i	0.128631	−	0.222796i	0.923147	+	0.384448i	$0.125608\pi$
$968$	14.0000			0.449977
$969$		0			0
$970$	2.00000			0.0642161
$971$	10.0000	−	17.3205i	0.320915	−	0.555842i	−0.659762	−	0.751475i	$-0.729343\pi$
$971$	10.0000	−	17.3205i	0.320915	−	0.555842i	0.980677	+	0.195633i	$0.0626762\pi$
$972$		0			0
$973$	−8.00000	−	13.8564i	−0.256468	−	0.444216i
$974$	11.5000	−	19.9186i	0.368484	−	0.638233i
$975$		0			0
$976$		0			0
$977$	−2.00000			−0.0639857			−0.0319928	−	0.999488i	$-0.510185\pi$
$977$	−2.00000			−0.0639857			−0.0319928	+	0.999488i	$0.510185\pi$
$978$		0			0
$979$	17.5000	+	30.3109i	0.559302	+	0.968740i
$980$	6.00000			0.191663
$981$	−12.0000			−0.383131
$982$	−13.5000	−	23.3827i	−0.430802	−	0.746171i
$983$	−10.5000	+	18.1865i	−0.334898	+	0.580060i	−0.983465	−	0.181097i	$-0.942035\pi$
$983$	−10.5000	+	18.1865i	−0.334898	+	0.580060i	0.648567	+	0.761157i	$0.275369\pi$
$984$		0			0
$985$	11.5000	−	19.9186i	0.366420	−	0.634659i
$986$		0			0
$987$		0			0
$988$	−7.00000	−	5.19615i	−0.222700	−	0.165312i
$989$	6.00000			0.190789
$990$	−7.50000	+	12.9904i	−0.238366	+	0.412861i
$991$	−9.00000	+	15.5885i	−0.285894	+	0.495184i	−0.972826	−	0.231539i	$-0.925624\pi$
$991$	−9.00000	+	15.5885i	−0.285894	+	0.495184i	0.686931	+	0.726722i	$0.258957\pi$
$992$	−2.00000	−	3.46410i	−0.0635001	−	0.109985i
$993$		0			0
$994$	−3.00000	−	5.19615i	−0.0951542	−	0.164812i
$995$	−24.0000			−0.760851
$996$		0			0
$997$	26.5000	+	45.8993i	0.839263	+	1.45365i	0.890511	+	0.454961i	$0.150347\pi$
$997$	26.5000	+	45.8993i	0.839263	+	1.45365i	−0.0512480	+	0.998686i	$0.516320\pi$
$998$	19.5000	+	33.7750i	0.617262	+	1.06913i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	190.2.e.a.11.1	✓	2
3.2	odd	2		1710.2.l.h.1531.1		2
4.3	odd	2		1520.2.q.f.961.1		2
5.2	odd	4		950.2.j.d.49.1		4
5.3	odd	4		950.2.j.d.49.2		4
5.4	even	2		950.2.e.f.201.1		2
19.7	even	3	inner	190.2.e.a.121.1	yes	2
19.8	odd	6		3610.2.a.c.1.1		1
19.11	even	3		3610.2.a.g.1.1		1
57.26	odd	6		1710.2.l.h.1261.1		2
76.7	odd	6		1520.2.q.f.881.1		2
95.7	odd	12		950.2.j.d.349.2		4
95.64	even	6		950.2.e.f.501.1		2
95.83	odd	12		950.2.j.d.349.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.e.a.11.1	✓	2	1.1	even	1	trivial
190.2.e.a.121.1	yes	2	19.7	even	3	inner
950.2.e.f.201.1		2	5.4	even	2
950.2.e.f.501.1		2	95.64	even	6
950.2.j.d.49.1		4	5.2	odd	4
950.2.j.d.49.2		4	5.3	odd	4
950.2.j.d.349.1		4	95.83	odd	12
950.2.j.d.349.2		4	95.7	odd	12
1520.2.q.f.881.1		2	76.7	odd	6
1520.2.q.f.961.1		2	4.3	odd	2
1710.2.l.h.1261.1		2	57.26	odd	6
1710.2.l.h.1531.1		2	3.2	odd	2
3610.2.a.c.1.1		1	19.8	odd	6
3610.2.a.g.1.1		1	19.11	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 190 = 2 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	190.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(0.500000 + 0.866025i) q^{10} +5.00000 q^{11} +(-1.00000 - 1.73205i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} -3.00000 q^{18} +(-0.500000 + 4.33013i) q^{19} -1.00000 q^{20} +(-2.50000 + 4.33013i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(-0.500000 - 0.866025i) q^{25} +2.00000 q^{26} +(-0.500000 - 0.866025i) q^{28} +(-3.00000 - 5.19615i) q^{29} +4.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.500000 - 0.866025i) q^{35} +(1.50000 - 2.59808i) q^{36} -11.0000 q^{37} +(-3.50000 - 2.59808i) q^{38} +(0.500000 - 0.866025i) q^{40} +(4.50000 - 7.79423i) q^{41} +(-3.00000 + 5.19615i) q^{43} +(-2.50000 - 4.33013i) q^{44} +3.00000 q^{45} +1.00000 q^{46} -6.00000 q^{49} +1.00000 q^{50} +(-1.00000 + 1.73205i) q^{52} +(-2.50000 - 4.33013i) q^{53} +(2.50000 - 4.33013i) q^{55} +1.00000 q^{56} +6.00000 q^{58} +(-2.00000 + 3.46410i) q^{62} +(1.50000 + 2.59808i) q^{63} +1.00000 q^{64} -2.00000 q^{65} +(-6.00000 - 10.3923i) q^{67} +(0.500000 + 0.866025i) q^{70} +(-3.00000 + 5.19615i) q^{71} +(1.50000 + 2.59808i) q^{72} +(-7.00000 + 12.1244i) q^{73} +(5.50000 - 9.52628i) q^{74} +(4.00000 - 1.73205i) q^{76} +5.00000 q^{77} +(-5.00000 + 8.66025i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(4.50000 + 7.79423i) q^{82} +14.0000 q^{83} +(-3.00000 - 5.19615i) q^{86} +5.00000 q^{88} +(3.50000 + 6.06218i) q^{89} +(-1.50000 + 2.59808i) q^{90} +(-1.00000 - 1.73205i) q^{91} +(-0.500000 + 0.866025i) q^{92} +(3.50000 + 2.59808i) q^{95} +(1.00000 - 1.73205i) q^{97} +(3.00000 - 5.19615i) q^{98} +(7.50000 + 12.9904i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} + q^{5} + 2 q^{7} + 2 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q - q^2 - q^4 + q^5 + 2 * q^7 + 2 * q^8 + 3 * q^9	\( 2 q - q^{2} - q^{4} + q^{5} + 2 q^{7} + 2 q^{8} + 3 q^{9} + q^{10} + 10 q^{11} - 2 q^{13} - q^{14} - q^{16} - 6 q^{18} - q^{19} - 2 q^{20} - 5 q^{22} - q^{23} - q^{25} + 4 q^{26} - q^{28} - 6 q^{29} + 8 q^{31} - q^{32} + q^{35} + 3 q^{36} - 22 q^{37} - 7 q^{38} + q^{40} + 9 q^{41} - 6 q^{43} - 5 q^{44} + 6 q^{45} + 2 q^{46} - 12 q^{49} + 2 q^{50} - 2 q^{52} - 5 q^{53} + 5 q^{55} + 2 q^{56} + 12 q^{58} - 4 q^{62} + 3 q^{63} + 2 q^{64} - 4 q^{65} - 12 q^{67} + q^{70} - 6 q^{71} + 3 q^{72} - 14 q^{73} + 11 q^{74} + 8 q^{76} + 10 q^{77} - 10 q^{79} + q^{80} - 9 q^{81} + 9 q^{82} + 28 q^{83} - 6 q^{86} + 10 q^{88} + 7 q^{89} - 3 q^{90} - 2 q^{91} - q^{92} + 7 q^{95} + 2 q^{97} + 6 q^{98} + 15 q^{99}+O(q^{100}) \) 2 * q - q^2 - q^4 + q^5 + 2 * q^7 + 2 * q^8 + 3 * q^9 + q^10 + 10 * q^11 - 2 * q^13 - q^14 - q^16 - 6 * q^18 - q^19 - 2 * q^20 - 5 * q^22 - q^23 - q^25 + 4 * q^26 - q^28 - 6 * q^29 + 8 * q^31 - q^32 + q^35 + 3 * q^36 - 22 * q^37 - 7 * q^38 + q^40 + 9 * q^41 - 6 * q^43 - 5 * q^44 + 6 * q^45 + 2 * q^46 - 12 * q^49 + 2 * q^50 - 2 * q^52 - 5 * q^53 + 5 * q^55 + 2 * q^56 + 12 * q^58 - 4 * q^62 + 3 * q^63 + 2 * q^64 - 4 * q^65 - 12 * q^67 + q^70 - 6 * q^71 + 3 * q^72 - 14 * q^73 + 11 * q^74 + 8 * q^76 + 10 * q^77 - 10 * q^79 + q^80 - 9 * q^81 + 9 * q^82 + 28 * q^83 - 6 * q^86 + 10 * q^88 + 7 * q^89 - 3 * q^90 - 2 * q^91 - q^92 + 7 * q^95 + 2 * q^97 + 6 * q^98 + 15 * q^99

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