LMFDB - Embedded newform 171.2.f.a.64.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,2,Mod(64,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("171.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	171.f (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:	$1.36544187456$
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 57)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			64.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	171.64
Dual form			171.2.f.a.163.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.00000 q^{7} +3.00000 q^{8} +2.00000 q^{11} +(-2.50000 + 4.33013i) q^{13} +(0.500000 + 0.866025i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-2.00000 - 3.46410i) q^{17} +(-4.00000 - 1.73205i) q^{19} +(1.00000 + 1.73205i) q^{22} +(-2.00000 + 3.46410i) q^{23} +(2.50000 - 4.33013i) q^{25} -5.00000 q^{26} +(0.500000 - 0.866025i) q^{28} +(-4.00000 + 6.92820i) q^{29} -3.00000 q^{31} +(2.50000 - 4.33013i) q^{32} +(2.00000 - 3.46410i) q^{34} +3.00000 q^{37} +(-0.500000 - 4.33013i) q^{38} +(-6.00000 - 10.3923i) q^{41} +(0.500000 + 0.866025i) q^{43} +(1.00000 - 1.73205i) q^{44} -4.00000 q^{46} +(-3.00000 + 5.19615i) q^{47} -6.00000 q^{49} +5.00000 q^{50} +(2.50000 + 4.33013i) q^{52} +(2.00000 - 3.46410i) q^{53} +3.00000 q^{56} -8.00000 q^{58} +(5.00000 + 8.66025i) q^{59} +(6.50000 - 11.2583i) q^{61} +(-1.50000 - 2.59808i) q^{62} +7.00000 q^{64} +(-5.50000 + 9.52628i) q^{67} -4.00000 q^{68} +(3.00000 + 5.19615i) q^{71} +(5.50000 + 9.52628i) q^{73} +(1.50000 + 2.59808i) q^{74} +(-3.50000 + 2.59808i) q^{76} +2.00000 q^{77} +(-0.500000 - 0.866025i) q^{79} +(6.00000 - 10.3923i) q^{82} +(-0.500000 + 0.866025i) q^{86} +6.00000 q^{88} +(-3.00000 + 5.19615i) q^{89} +(-2.50000 + 4.33013i) q^{91} +(2.00000 + 3.46410i) q^{92} -6.00000 q^{94} +(-1.00000 - 1.73205i) q^{97} +(-3.00000 - 5.19615i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + q^{4} + 2 q^{7} + 6 q^{8} + 4 q^{11} - 5 q^{13} + q^{14} + q^{16} - 4 q^{17} - 8 q^{19} + 2 q^{22} - 4 q^{23} + 5 q^{25} - 10 q^{26} + q^{28} - 8 q^{29} - 6 q^{31} + 5 q^{32} + 4 q^{34}+ \cdots - 6 q^{98}+O(q^{100}) $ 2 * q + q^2 + q^4 + 2 * q^7 + 6 * q^8 + 4 * q^11 - 5 * q^13 + q^14 + q^16 - 4 * q^17 - 8 * q^19 + 2 * q^22 - 4 * q^23 + 5 * q^25 - 10 * q^26 + q^28 - 8 * q^29 - 6 * q^31 + 5 * q^32 + 4 * q^34 + 6 * q^37 - q^38 - 12 * q^41 + q^43 + 2 * q^44 - 8 * q^46 - 6 * q^47 - 12 * q^49 + 10 * q^50 + 5 * q^52 + 4 * q^53 + 6 * q^56 - 16 * q^58 + 10 * q^59 + 13 * q^61 - 3 * q^62 + 14 * q^64 - 11 * q^67 - 8 * q^68 + 6 * q^71 + 11 * q^73 + 3 * q^74 - 7 * q^76 + 4 * q^77 - q^79 + 12 * q^82 - q^86 + 12 * q^88 - 6 * q^89 - 5 * q^91 + 4 * q^92 - 12 * q^94 - 2 * q^97 - 6 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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	0.986869	−	0.161521i	$-0.0516399\pi$
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i	−0.633316	+	0.773893i	$0.718307\pi$
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$5$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$6$		0			0
$7$	1.00000			0.377964			0.188982	−	0.981981i	$-0.439481\pi$
$7$	1.00000			0.377964			0.188982	+	0.981981i	$0.439481\pi$
$8$	3.00000			1.06066
$9$		0			0
$10$		0			0
$11$	2.00000			0.603023			0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000			0.603023			0.301511	+	0.953463i	$0.402509\pi$
$12$		0			0
$13$	−2.50000	+	4.33013i	−0.693375	+	1.20096i	0.277350	+	0.960769i	$0.410544\pi$
$13$	−2.50000	+	4.33013i	−0.693375	+	1.20096i	−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
$17$	−2.00000	−	3.46410i	−0.485071	−	0.840168i	0.514782	−	0.857321i	$-0.327873\pi$
$17$	−2.00000	−	3.46410i	−0.485071	−	0.840168i	−0.999853	+	0.0171533i	$0.994540\pi$
$18$		0			0
$19$	−4.00000	−	1.73205i	−0.917663	−	0.397360i
$19$	−4.00000	−	1.73205i	−0.917663	−	0.397360i
$20$		0			0
$21$		0			0
$22$	1.00000	+	1.73205i	0.213201	+	0.369274i
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	−0.995639	−	0.0932891i	$-0.970262\pi$
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	0.578610	+	0.815604i	$0.303595\pi$
$24$		0			0
$25$	2.50000	−	4.33013i	0.500000	−	0.866025i
$26$	−5.00000			−0.980581
$27$		0			0
$28$	0.500000	−	0.866025i	0.0944911	−	0.163663i
$29$	−4.00000	+	6.92820i	−0.742781	+	1.28654i	0.208443	+	0.978035i	$0.433160\pi$
$29$	−4.00000	+	6.92820i	−0.742781	+	1.28654i	−0.951224	+	0.308500i	$0.900173\pi$
$30$		0			0
$31$	−3.00000			−0.538816			−0.269408	−	0.963026i	$-0.586828\pi$
$31$	−3.00000			−0.538816			−0.269408	+	0.963026i	$0.586828\pi$
$32$	2.50000	−	4.33013i	0.441942	−	0.765466i
$33$		0			0
$34$	2.00000	−	3.46410i	0.342997	−	0.594089i
$35$		0			0
$36$		0			0
$37$	3.00000			0.493197			0.246598	−	0.969118i	$-0.420687\pi$
$37$	3.00000			0.493197			0.246598	+	0.969118i	$0.420687\pi$
$38$	−0.500000	−	4.33013i	−0.0811107	−	0.702439i
$39$		0			0
$40$		0			0
$41$	−6.00000	−	10.3923i	−0.937043	−	1.62301i	−0.770950	−	0.636895i	$-0.780218\pi$
$41$	−6.00000	−	10.3923i	−0.937043	−	1.62301i	−0.166092	−	0.986110i	$-0.553115\pi$
$42$		0			0
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	0.901629	−	0.432511i	$-0.142372\pi$
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	−0.825380	+	0.564578i	$0.809039\pi$
$44$	1.00000	−	1.73205i	0.150756	−	0.261116i
$45$		0			0
$46$	−4.00000			−0.589768
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	−0.997503	−	0.0706177i	$-0.977503\pi$
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	0.559908	+	0.828554i	$0.310836\pi$
$48$		0			0
$49$	−6.00000			−0.857143
$50$	5.00000			0.707107
$51$		0			0
$52$	2.50000	+	4.33013i	0.346688	+	0.600481i
$53$	2.00000	−	3.46410i	0.274721	−	0.475831i	−0.695344	−	0.718677i	$-0.744748\pi$
$53$	2.00000	−	3.46410i	0.274721	−	0.475831i	0.970065	+	0.242846i	$0.0780811\pi$
$54$		0			0
$55$		0			0
$56$	3.00000			0.400892
$57$		0			0
$58$	−8.00000			−1.05045
$59$	5.00000	+	8.66025i	0.650945	+	1.12747i	0.982894	+	0.184172i	$0.0589603\pi$
$59$	5.00000	+	8.66025i	0.650945	+	1.12747i	−0.331949	+	0.943297i	$0.607706\pi$
$60$		0			0
$61$	6.50000	−	11.2583i	0.832240	−	1.44148i	−0.0640184	−	0.997949i	$-0.520392\pi$
$61$	6.50000	−	11.2583i	0.832240	−	1.44148i	0.896258	−	0.443533i	$-0.146275\pi$
$62$	−1.50000	−	2.59808i	−0.190500	−	0.329956i
$63$		0			0
$64$	7.00000			0.875000
$65$		0			0
$66$		0			0
$67$	−5.50000	+	9.52628i	−0.671932	+	1.16382i	0.305424	+	0.952217i	$0.401202\pi$
$67$	−5.50000	+	9.52628i	−0.671932	+	1.16382i	−0.977356	+	0.211604i	$0.932131\pi$
$68$	−4.00000			−0.485071
$69$		0			0
$70$		0			0
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	0.987294	−	0.158901i	$-0.0507952\pi$
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	−0.631260	+	0.775571i	$0.717462\pi$
$72$		0			0
$73$	5.50000	+	9.52628i	0.643726	+	1.11497i	0.984594	+	0.174855i	$0.0559458\pi$
$73$	5.50000	+	9.52628i	0.643726	+	1.11497i	−0.340868	+	0.940111i	$0.610721\pi$
$74$	1.50000	+	2.59808i	0.174371	+	0.302020i
$75$		0			0
$76$	−3.50000	+	2.59808i	−0.401478	+	0.298020i
$77$	2.00000			0.227921
$78$		0			0
$79$	−0.500000	−	0.866025i	−0.0562544	−	0.0974355i	0.836527	−	0.547926i	$-0.184582\pi$
$79$	−0.500000	−	0.866025i	−0.0562544	−	0.0974355i	−0.892781	+	0.450490i	$0.851249\pi$
$80$		0			0
$81$		0			0
$82$	6.00000	−	10.3923i	0.662589	−	1.14764i
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$		0			0
$85$		0			0
$86$	−0.500000	+	0.866025i	−0.0539164	+	0.0933859i
$87$		0			0
$88$	6.00000			0.639602
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	−0.980071	−	0.198650i	$-0.936344\pi$
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	0.662071	+	0.749441i	$0.269678\pi$
$90$		0			0
$91$	−2.50000	+	4.33013i	−0.262071	+	0.453921i
$92$	2.00000	+	3.46410i	0.208514	+	0.361158i
$93$		0			0
$94$	−6.00000			−0.618853
$95$		0			0
$96$		0			0
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	0.810782	−	0.585348i	$-0.199042\pi$
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	−0.912317	+	0.409484i	$0.865709\pi$
$98$	−3.00000	−	5.19615i	−0.303046	−	0.524891i
$99$		0			0
$100$	−2.50000	−	4.33013i	−0.250000	−	0.433013i
$101$	7.00000	−	12.1244i	0.696526	−	1.20642i	−0.273138	−	0.961975i	$-0.588061\pi$
$101$	7.00000	−	12.1244i	0.696526	−	1.20642i	0.969664	−	0.244443i	$-0.0786053\pi$
$102$		0			0
$103$	13.0000			1.28093			0.640464	−	0.767988i	$-0.278742\pi$
$103$	13.0000			1.28093			0.640464	+	0.767988i	$0.278742\pi$
$104$	−7.50000	+	12.9904i	−0.735436	+	1.27381i
$105$		0			0
$106$	4.00000			0.388514
$107$	18.0000			1.74013			0.870063	−	0.492941i	$-0.164078\pi$
$107$	18.0000			1.74013			0.870063	+	0.492941i	$0.164078\pi$
$108$		0			0
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	0.909935	−	0.414751i	$-0.136131\pi$
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	−0.814152	+	0.580651i	$0.802798\pi$
$110$		0			0
$111$		0			0
$112$	0.500000	+	0.866025i	0.0472456	+	0.0818317i
$113$	−2.00000			−0.188144			−0.0940721	−	0.995565i	$-0.529988\pi$
$113$	−2.00000			−0.188144			−0.0940721	+	0.995565i	$0.529988\pi$
$114$		0			0
$115$		0			0
$116$	4.00000	+	6.92820i	0.371391	+	0.643268i
$117$		0			0
$118$	−5.00000	+	8.66025i	−0.460287	+	0.797241i
$119$	−2.00000	−	3.46410i	−0.183340	−	0.317554i
$120$		0			0
$121$	−7.00000			−0.636364
$122$	13.0000			1.17696
$123$		0			0
$124$	−1.50000	+	2.59808i	−0.134704	+	0.233314i
$125$		0			0
$126$		0			0
$127$	4.00000	−	6.92820i	0.354943	−	0.614779i	−0.632166	−	0.774833i	$-0.717834\pi$
$127$	4.00000	−	6.92820i	0.354943	−	0.614779i	0.987108	+	0.160055i	$0.0511671\pi$
$128$	−1.50000	−	2.59808i	−0.132583	−	0.229640i
$129$		0			0
$130$		0			0
$131$	−7.00000	−	12.1244i	−0.611593	−	1.05931i	−0.990972	−	0.134069i	$-0.957196\pi$
$131$	−7.00000	−	12.1244i	−0.611593	−	1.05931i	0.379379	−	0.925241i	$-0.376138\pi$
$132$		0			0
$133$	−4.00000	−	1.73205i	−0.346844	−	0.150188i
$134$	−11.0000			−0.950255
$135$		0			0
$136$	−6.00000	−	10.3923i	−0.514496	−	0.891133i
$137$	9.00000	−	15.5885i	0.768922	−	1.33181i	−0.169226	−	0.985577i	$-0.554127\pi$
$137$	9.00000	−	15.5885i	0.768922	−	1.33181i	0.938148	−	0.346235i	$-0.112540\pi$
$138$		0			0
$139$	−2.50000	+	4.33013i	−0.212047	+	0.367277i	−0.952355	−	0.304991i	$-0.901346\pi$
$139$	−2.50000	+	4.33013i	−0.212047	+	0.367277i	0.740308	+	0.672268i	$0.234680\pi$
$140$		0			0
$141$		0			0
$142$	−3.00000	+	5.19615i	−0.251754	+	0.436051i
$143$	−5.00000	+	8.66025i	−0.418121	+	0.724207i
$144$		0			0
$145$		0			0
$146$	−5.50000	+	9.52628i	−0.455183	+	0.788400i
$147$		0			0
$148$	1.50000	−	2.59808i	0.123299	−	0.213561i
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	0.716578	−	0.697507i	$-0.245707\pi$
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	−0.962348	+	0.271821i	$0.912374\pi$
$150$		0			0
$151$	12.0000			0.976546			0.488273	−	0.872691i	$-0.337627\pi$
$151$	12.0000			0.976546			0.488273	+	0.872691i	$0.337627\pi$
$152$	−12.0000	−	5.19615i	−0.973329	−	0.421464i
$153$		0			0
$154$	1.00000	+	1.73205i	0.0805823	+	0.139573i
$155$		0			0
$156$		0			0
$157$	−1.50000	−	2.59808i	−0.119713	−	0.207349i	0.799941	−	0.600079i	$-0.204864\pi$
$157$	−1.50000	−	2.59808i	−0.119713	−	0.207349i	−0.919654	+	0.392730i	$0.871531\pi$
$158$	0.500000	−	0.866025i	0.0397779	−	0.0688973i
$159$		0			0
$160$		0			0
$161$	−2.00000	+	3.46410i	−0.157622	+	0.273009i
$162$		0			0
$163$	3.00000			0.234978			0.117489	−	0.993074i	$-0.462515\pi$
$163$	3.00000			0.234978			0.117489	+	0.993074i	$0.462515\pi$
$164$	−12.0000			−0.937043
$165$		0			0
$166$		0			0
$167$	−1.00000	+	1.73205i	−0.0773823	+	0.134030i	−0.902120	−	0.431486i	$-0.857990\pi$
$167$	−1.00000	+	1.73205i	−0.0773823	+	0.134030i	0.824737	+	0.565516i	$0.191323\pi$
$168$		0			0
$169$	−6.00000	−	10.3923i	−0.461538	−	0.799408i
$170$		0			0
$171$		0			0
$172$	1.00000			0.0762493
$173$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$173$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$174$		0			0
$175$	2.50000	−	4.33013i	0.188982	−	0.327327i
$176$	1.00000	+	1.73205i	0.0753778	+	0.130558i
$177$		0			0
$178$	−6.00000			−0.449719
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$		0			0
$181$	1.00000	−	1.73205i	0.0743294	−	0.128742i	−0.826465	−	0.562988i	$-0.809652\pi$
$181$	1.00000	−	1.73205i	0.0743294	−	0.128742i	0.900794	+	0.434246i	$0.142985\pi$
$182$	−5.00000			−0.370625
$183$		0			0
$184$	−6.00000	+	10.3923i	−0.442326	+	0.766131i
$185$		0			0
$186$		0			0
$187$	−4.00000	−	6.92820i	−0.292509	−	0.506640i
$188$	3.00000	+	5.19615i	0.218797	+	0.378968i
$189$		0			0
$190$		0			0
$191$	−24.0000			−1.73658			−0.868290	−	0.496058i	$-0.834780\pi$
$191$	−24.0000			−1.73658			−0.868290	+	0.496058i	$0.834780\pi$
$192$		0			0
$193$	−9.50000	−	16.4545i	−0.683825	−	1.18442i	−0.973805	−	0.227387i	$-0.926982\pi$
$193$	−9.50000	−	16.4545i	−0.683825	−	1.18442i	0.289980	−	0.957033i	$-0.406351\pi$
$194$	1.00000	−	1.73205i	0.0717958	−	0.124354i
$195$		0			0
$196$	−3.00000	+	5.19615i	−0.214286	+	0.371154i
$197$	26.0000			1.85242			0.926212	−	0.377004i	$-0.123046\pi$
$197$	26.0000			1.85242			0.926212	+	0.377004i	$0.123046\pi$
$198$		0			0
$199$	−10.5000	+	18.1865i	−0.744325	+	1.28921i	0.206184	+	0.978513i	$0.433895\pi$
$199$	−10.5000	+	18.1865i	−0.744325	+	1.28921i	−0.950509	+	0.310696i	$0.899438\pi$
$200$	7.50000	−	12.9904i	0.530330	−	0.918559i
$201$		0			0
$202$	14.0000			0.985037
$203$	−4.00000	+	6.92820i	−0.280745	+	0.486265i
$204$		0			0
$205$		0			0
$206$	6.50000	+	11.2583i	0.452876	+	0.784405i
$207$		0			0
$208$	−5.00000			−0.346688
$209$	−8.00000	−	3.46410i	−0.553372	−	0.239617i
$210$		0			0
$211$	7.50000	+	12.9904i	0.516321	+	0.894295i	0.999820	+	0.0189499i	$0.00603229\pi$
$211$	7.50000	+	12.9904i	0.516321	+	0.894295i	−0.483499	+	0.875345i	$0.660634\pi$
$212$	−2.00000	−	3.46410i	−0.137361	−	0.237915i
$213$		0			0
$214$	9.00000	+	15.5885i	0.615227	+	1.06561i
$215$		0			0
$216$		0			0
$217$	−3.00000			−0.203653
$218$	−1.00000	+	1.73205i	−0.0677285	+	0.117309i
$219$		0			0
$220$		0			0
$221$	20.0000			1.34535
$222$		0			0
$223$	−4.50000	−	7.79423i	−0.301342	−	0.521940i	0.675098	−	0.737728i	$-0.264101\pi$
$223$	−4.50000	−	7.79423i	−0.301342	−	0.521940i	−0.976440	+	0.215788i	$0.930768\pi$
$224$	2.50000	−	4.33013i	0.167038	−	0.289319i
$225$		0			0
$226$	−1.00000	−	1.73205i	−0.0665190	−	0.115214i
$227$	24.0000			1.59294			0.796468	−	0.604681i	$-0.206699\pi$
$227$	24.0000			1.59294			0.796468	+	0.604681i	$0.206699\pi$
$228$		0			0
$229$	13.0000			0.859064			0.429532	−	0.903052i	$-0.358679\pi$
$229$	13.0000			0.859064			0.429532	+	0.903052i	$0.358679\pi$
$230$		0			0
$231$		0			0
$232$	−12.0000	+	20.7846i	−0.787839	+	1.36458i
$233$	−3.00000	−	5.19615i	−0.196537	−	0.340411i	0.750867	−	0.660454i	$-0.229636\pi$
$233$	−3.00000	−	5.19615i	−0.196537	−	0.340411i	−0.947403	+	0.320043i	$0.896303\pi$
$234$		0			0
$235$		0			0
$236$	10.0000			0.650945
$237$		0			0
$238$	2.00000	−	3.46410i	0.129641	−	0.224544i
$239$	12.0000			0.776215			0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000			0.776215			0.388108	+	0.921614i	$0.373129\pi$
$240$		0			0
$241$	3.50000	−	6.06218i	0.225455	−	0.390499i	−0.731001	−	0.682376i	$-0.760947\pi$
$241$	3.50000	−	6.06218i	0.225455	−	0.390499i	0.956456	+	0.291877i	$0.0942799\pi$
$242$	−3.50000	−	6.06218i	−0.224989	−	0.389692i
$243$		0			0
$244$	−6.50000	−	11.2583i	−0.416120	−	0.720741i
$245$		0			0
$246$		0			0
$247$	17.5000	−	12.9904i	1.11350	−	0.826558i
$248$	−9.00000			−0.571501
$249$		0			0
$250$		0			0
$251$	−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
$253$	−4.00000	+	6.92820i	−0.251478	+	0.435572i
$254$	8.00000			0.501965
$255$		0			0
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	−10.0000	+	17.3205i	−0.623783	+	1.08042i	0.364992	+	0.931011i	$0.381072\pi$
$257$	−10.0000	+	17.3205i	−0.623783	+	1.08042i	−0.988775	+	0.149413i	$0.952262\pi$
$258$		0			0
$259$	3.00000			0.186411
$260$		0			0
$261$		0			0
$262$	7.00000	−	12.1244i	0.432461	−	0.749045i
$263$	13.0000	+	22.5167i	0.801614	+	1.38844i	0.918553	+	0.395298i	$0.129359\pi$
$263$	13.0000	+	22.5167i	0.801614	+	1.38844i	−0.116939	+	0.993139i	$0.537308\pi$
$264$		0			0
$265$		0			0
$266$	−0.500000	−	4.33013i	−0.0306570	−	0.265497i
$267$		0			0
$268$	5.50000	+	9.52628i	0.335966	+	0.581910i
$269$	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
$271$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$271$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$272$	2.00000	−	3.46410i	0.121268	−	0.210042i
$273$		0			0
$274$	18.0000			1.08742
$275$	5.00000	−	8.66025i	0.301511	−	0.522233i
$276$		0			0
$277$	−2.00000			−0.120168			−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000			−0.120168			−0.0600842	+	0.998193i	$0.519137\pi$
$278$	−5.00000			−0.299880
$279$		0			0
$280$		0			0
$281$	−4.00000	+	6.92820i	−0.238620	+	0.413302i	−0.960319	−	0.278906i	$-0.910028\pi$
$281$	−4.00000	+	6.92820i	−0.238620	+	0.413302i	0.721699	+	0.692207i	$0.243362\pi$
$282$		0			0
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	0.919327	−	0.393494i	$-0.128734\pi$
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	−0.800439	+	0.599414i	$0.795400\pi$
$284$	6.00000			0.356034
$285$		0			0
$286$	−10.0000			−0.591312
$287$	−6.00000	−	10.3923i	−0.354169	−	0.613438i
$288$		0			0
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$		0			0
$291$		0			0
$292$	11.0000			0.643726
$293$	−14.0000			−0.817889			−0.408944	−	0.912559i	$-0.634103\pi$
$293$	−14.0000			−0.817889			−0.408944	+	0.912559i	$0.634103\pi$
$294$		0			0
$295$		0			0
$296$	9.00000			0.523114
$297$		0			0
$298$	3.00000	−	5.19615i	0.173785	−	0.301005i
$299$	−10.0000	−	17.3205i	−0.578315	−	1.00167i
$300$		0			0
$301$	0.500000	+	0.866025i	0.0288195	+	0.0499169i
$302$	6.00000	+	10.3923i	0.345261	+	0.598010i
$303$		0			0
$304$	−0.500000	−	4.33013i	−0.0286770	−	0.248350i
$305$		0			0
$306$		0			0
$307$	6.00000	+	10.3923i	0.342438	+	0.593120i	0.984885	−	0.173210i	$-0.0554140\pi$
$307$	6.00000	+	10.3923i	0.342438	+	0.593120i	−0.642447	+	0.766330i	$0.722081\pi$
$308$	1.00000	−	1.73205i	0.0569803	−	0.0986928i
$309$		0			0
$310$		0			0
$311$	−18.0000			−1.02069			−0.510343	−	0.859971i	$-0.670482\pi$
$311$	−18.0000			−1.02069			−0.510343	+	0.859971i	$0.670482\pi$
$312$		0			0
$313$	−11.0000	+	19.0526i	−0.621757	+	1.07691i	0.367402	+	0.930062i	$0.380247\pi$
$313$	−11.0000	+	19.0526i	−0.621757	+	1.07691i	−0.989158	+	0.146852i	$0.953086\pi$
$314$	1.50000	−	2.59808i	0.0846499	−	0.146618i
$315$		0			0
$316$	−1.00000			−0.0562544
$317$	−2.00000	+	3.46410i	−0.112331	+	0.194563i	−0.916710	−	0.399554i	$-0.869165\pi$
$317$	−2.00000	+	3.46410i	−0.112331	+	0.194563i	0.804379	+	0.594117i	$0.202498\pi$
$318$		0			0
$319$	−8.00000	+	13.8564i	−0.447914	+	0.775810i
$320$		0			0
$321$		0			0
$322$	−4.00000			−0.222911
$323$	2.00000	+	17.3205i	0.111283	+	0.963739i
$324$		0			0
$325$	12.5000	+	21.6506i	0.693375	+	1.20096i
$326$	1.50000	+	2.59808i	0.0830773	+	0.143894i
$327$		0			0
$328$	−18.0000	−	31.1769i	−0.993884	−	1.72146i
$329$	−3.00000	+	5.19615i	−0.165395	+	0.286473i
$330$		0			0
$331$	−25.0000			−1.37412			−0.687062	−	0.726599i	$-0.741100\pi$
$331$	−25.0000			−1.37412			−0.687062	+	0.726599i	$0.741100\pi$
$332$		0			0
$333$		0			0
$334$	−2.00000			−0.109435
$335$		0			0
$336$		0			0
$337$	−6.50000	−	11.2583i	−0.354078	−	0.613280i	0.632882	−	0.774248i	$-0.281872\pi$
$337$	−6.50000	−	11.2583i	−0.354078	−	0.613280i	−0.986960	+	0.160968i	$0.948538\pi$
$338$	6.00000	−	10.3923i	0.326357	−	0.565267i
$339$		0			0
$340$		0			0
$341$	−6.00000			−0.324918
$342$		0			0
$343$	−13.0000			−0.701934
$344$	1.50000	+	2.59808i	0.0808746	+	0.140079i
$345$		0			0
$346$		0			0
$347$	−8.00000	−	13.8564i	−0.429463	−	0.743851i	0.567363	−	0.823468i	$-0.307964\pi$
$347$	−8.00000	−	13.8564i	−0.429463	−	0.743851i	−0.996826	+	0.0796169i	$0.974630\pi$
$348$		0			0
$349$	−21.0000			−1.12410			−0.562052	−	0.827102i	$-0.689988\pi$
$349$	−21.0000			−1.12410			−0.562052	+	0.827102i	$0.689988\pi$
$350$	5.00000			0.267261
$351$		0			0
$352$	5.00000	−	8.66025i	0.266501	−	0.461593i
$353$	−4.00000			−0.212899			−0.106449	−	0.994318i	$-0.533948\pi$
$353$	−4.00000			−0.212899			−0.106449	+	0.994318i	$0.533948\pi$
$354$		0			0
$355$		0			0
$356$	3.00000	+	5.19615i	0.159000	+	0.275396i
$357$		0			0
$358$	−6.00000	−	10.3923i	−0.317110	−	0.549250i
$359$	−10.0000	−	17.3205i	−0.527780	−	0.914141i	−0.999476	−	0.0323801i	$-0.989691\pi$
$359$	−10.0000	−	17.3205i	−0.527780	−	0.914141i	0.471696	−	0.881761i	$-0.343642\pi$
$360$		0			0
$361$	13.0000	+	13.8564i	0.684211	+	0.729285i
$362$	2.00000			0.105118
$363$		0			0
$364$	2.50000	+	4.33013i	0.131036	+	0.226960i
$365$		0			0
$366$		0			0
$367$	−3.50000	+	6.06218i	−0.182699	+	0.316443i	−0.942799	−	0.333363i	$-0.891817\pi$
$367$	−3.50000	+	6.06218i	−0.182699	+	0.316443i	0.760100	+	0.649806i	$0.225150\pi$
$368$	−4.00000			−0.208514
$369$		0			0
$370$		0			0
$371$	2.00000	−	3.46410i	0.103835	−	0.179847i
$372$		0			0
$373$	10.0000			0.517780			0.258890	−	0.965907i	$-0.416643\pi$
$373$	10.0000			0.517780			0.258890	+	0.965907i	$0.416643\pi$
$374$	4.00000	−	6.92820i	0.206835	−	0.358249i
$375$		0			0
$376$	−9.00000	+	15.5885i	−0.464140	+	0.803913i
$377$	−20.0000	−	34.6410i	−1.03005	−	1.78410i
$378$		0			0
$379$	−5.00000			−0.256833			−0.128416	−	0.991720i	$-0.540989\pi$
$379$	−5.00000			−0.256833			−0.128416	+	0.991720i	$0.540989\pi$
$380$		0			0
$381$		0			0
$382$	−12.0000	−	20.7846i	−0.613973	−	1.06343i
$383$	7.00000	+	12.1244i	0.357683	+	0.619526i	0.987573	−	0.157159i	$-0.0502334\pi$
$383$	7.00000	+	12.1244i	0.357683	+	0.619526i	−0.629890	+	0.776684i	$0.716900\pi$
$384$		0			0
$385$		0			0
$386$	9.50000	−	16.4545i	0.483537	−	0.837511i
$387$		0			0
$388$	−2.00000			−0.101535
$389$	−12.0000	+	20.7846i	−0.608424	+	1.05382i	0.383076	+	0.923717i	$0.374865\pi$
$389$	−12.0000	+	20.7846i	−0.608424	+	1.05382i	−0.991500	+	0.130105i	$0.958469\pi$
$390$		0			0
$391$	16.0000			0.809155
$392$	−18.0000			−0.909137
$393$		0			0
$394$	13.0000	+	22.5167i	0.654931	+	1.13437i
$395$		0			0
$396$		0			0
$397$	−3.50000	−	6.06218i	−0.175660	−	0.304252i	0.764730	−	0.644351i	$-0.222873\pi$
$397$	−3.50000	−	6.06218i	−0.175660	−	0.304252i	−0.940389	+	0.340099i	$0.889539\pi$
$398$	−21.0000			−1.05263
$399$		0			0
$400$	5.00000			0.250000
$401$	−3.00000	−	5.19615i	−0.149813	−	0.259483i	0.781345	−	0.624099i	$-0.214534\pi$
$401$	−3.00000	−	5.19615i	−0.149813	−	0.259483i	−0.931158	+	0.364615i	$0.881200\pi$
$402$		0			0
$403$	7.50000	−	12.9904i	0.373602	−	0.647097i
$404$	−7.00000	−	12.1244i	−0.348263	−	0.603209i
$405$		0			0
$406$	−8.00000			−0.397033
$407$	6.00000			0.297409
$408$		0			0
$409$	7.00000	−	12.1244i	0.346128	−	0.599511i	−0.639430	−	0.768849i	$-0.720830\pi$
$409$	7.00000	−	12.1244i	0.346128	−	0.599511i	0.985558	+	0.169338i	$0.0541630\pi$
$410$		0			0
$411$		0			0
$412$	6.50000	−	11.2583i	0.320232	−	0.554658i
$413$	5.00000	+	8.66025i	0.246034	+	0.426143i
$414$		0			0
$415$		0			0
$416$	12.5000	+	21.6506i	0.612863	+	1.06151i
$417$		0			0
$418$	−1.00000	−	8.66025i	−0.0489116	−	0.423587i
$419$	14.0000			0.683945			0.341972	−	0.939710i	$-0.388905\pi$
$419$	14.0000			0.683945			0.341972	+	0.939710i	$0.388905\pi$
$420$		0			0
$421$	11.0000	+	19.0526i	0.536107	+	0.928565i	0.999109	+	0.0422075i	$0.0134391\pi$
$421$	11.0000	+	19.0526i	0.536107	+	0.928565i	−0.463002	+	0.886357i	$0.653228\pi$
$422$	−7.50000	+	12.9904i	−0.365094	+	0.632362i
$423$		0			0
$424$	6.00000	−	10.3923i	0.291386	−	0.504695i
$425$	−20.0000			−0.970143
$426$		0			0
$427$	6.50000	−	11.2583i	0.314557	−	0.544829i
$428$	9.00000	−	15.5885i	0.435031	−	0.753497i
$429$		0			0
$430$		0			0
$431$	−5.00000	+	8.66025i	−0.240842	+	0.417150i	−0.960954	−	0.276707i	$-0.910757\pi$
$431$	−5.00000	+	8.66025i	−0.240842	+	0.417150i	0.720113	+	0.693857i	$0.244090\pi$
$432$		0			0
$433$	4.50000	−	7.79423i	0.216256	−	0.374567i	−0.737404	−	0.675452i	$-0.763949\pi$
$433$	4.50000	−	7.79423i	0.216256	−	0.374567i	0.953660	+	0.300885i	$0.0972820\pi$
$434$	−1.50000	−	2.59808i	−0.0720023	−	0.124712i
$435$		0			0
$436$	2.00000			0.0957826
$437$	14.0000	−	10.3923i	0.669711	−	0.497131i
$438$		0			0
$439$	−17.5000	−	30.3109i	−0.835229	−	1.44666i	−0.893843	−	0.448379i	$-0.852001\pi$
$439$	−17.5000	−	30.3109i	−0.835229	−	1.44666i	0.0586141	−	0.998281i	$-0.481332\pi$
$440$		0			0
$441$		0			0
$442$	10.0000	+	17.3205i	0.475651	+	0.823853i
$443$	−16.0000	+	27.7128i	−0.760183	+	1.31668i	0.182573	+	0.983192i	$0.441557\pi$
$443$	−16.0000	+	27.7128i	−0.760183	+	1.31668i	−0.942756	+	0.333483i	$0.891776\pi$
$444$		0			0
$445$		0			0
$446$	4.50000	−	7.79423i	0.213081	−	0.369067i
$447$		0			0
$448$	7.00000			0.330719
$449$	12.0000			0.566315			0.283158	−	0.959073i	$-0.408618\pi$
$449$	12.0000			0.566315			0.283158	+	0.959073i	$0.408618\pi$
$450$		0			0
$451$	−12.0000	−	20.7846i	−0.565058	−	0.978709i
$452$	−1.00000	+	1.73205i	−0.0470360	+	0.0814688i
$453$		0			0
$454$	12.0000	+	20.7846i	0.563188	+	0.975470i
$455$		0			0
$456$		0			0
$457$	−11.0000			−0.514558			−0.257279	−	0.966337i	$-0.582826\pi$
$457$	−11.0000			−0.514558			−0.257279	+	0.966337i	$0.582826\pi$
$458$	6.50000	+	11.2583i	0.303725	+	0.526067i
$459$		0			0
$460$		0			0
$461$	15.0000	+	25.9808i	0.698620	+	1.21004i	0.968945	+	0.247276i	$0.0795353\pi$
$461$	15.0000	+	25.9808i	0.698620	+	1.21004i	−0.270326	+	0.962769i	$0.587131\pi$
$462$		0			0
$463$	23.0000			1.06890			0.534450	−	0.845200i	$-0.320519\pi$
$463$	23.0000			1.06890			0.534450	+	0.845200i	$0.320519\pi$
$464$	−8.00000			−0.371391
$465$		0			0
$466$	3.00000	−	5.19615i	0.138972	−	0.240707i
$467$	8.00000			0.370196			0.185098	−	0.982720i	$-0.440740\pi$
$467$	8.00000			0.370196			0.185098	+	0.982720i	$0.440740\pi$
$468$		0			0
$469$	−5.50000	+	9.52628i	−0.253966	+	0.439883i
$470$		0			0
$471$		0			0
$472$	15.0000	+	25.9808i	0.690431	+	1.19586i
$473$	1.00000	+	1.73205i	0.0459800	+	0.0796398i
$474$		0			0
$475$	−17.5000	+	12.9904i	−0.802955	+	0.596040i
$476$	−4.00000			−0.183340
$477$		0			0
$478$	6.00000	+	10.3923i	0.274434	+	0.475333i
$479$	7.00000	−	12.1244i	0.319838	−	0.553976i	−0.660616	−	0.750724i	$-0.729705\pi$
$479$	7.00000	−	12.1244i	0.319838	−	0.553976i	0.980454	+	0.196748i	$0.0630381\pi$
$480$		0			0
$481$	−7.50000	+	12.9904i	−0.341971	+	0.592310i
$482$	7.00000			0.318841
$483$		0			0
$484$	−3.50000	+	6.06218i	−0.159091	+	0.275554i
$485$		0			0
$486$		0			0
$487$	−16.0000			−0.725029			−0.362515	−	0.931978i	$-0.618082\pi$
$487$	−16.0000			−0.725029			−0.362515	+	0.931978i	$0.618082\pi$
$488$	19.5000	−	33.7750i	0.882724	−	1.52892i
$489$		0			0
$490$		0			0
$491$	3.00000	+	5.19615i	0.135388	+	0.234499i	0.925746	−	0.378147i	$-0.123439\pi$
$491$	3.00000	+	5.19615i	0.135388	+	0.234499i	−0.790358	+	0.612646i	$0.790105\pi$
$492$		0			0
$493$	32.0000			1.44121
$494$	20.0000	+	8.66025i	0.899843	+	0.389643i
$495$		0			0
$496$	−1.50000	−	2.59808i	−0.0673520	−	0.116657i
$497$	3.00000	+	5.19615i	0.134568	+	0.233079i
$498$		0			0
$499$	−14.5000	−	25.1147i	−0.649109	−	1.12429i	−0.983336	−	0.181797i	$-0.941809\pi$
$499$	−14.5000	−	25.1147i	−0.649109	−	1.12429i	0.334227	−	0.942493i	$-0.391525\pi$
$500$		0			0
$501$		0			0
$502$	−2.00000			−0.0892644
$503$	20.0000	−	34.6410i	0.891756	−	1.54457i	0.0539870	−	0.998542i	$-0.482807\pi$
$503$	20.0000	−	34.6410i	0.891756	−	1.54457i	0.837769	−	0.546025i	$-0.183860\pi$
$504$		0			0
$505$		0			0
$506$	−8.00000			−0.355643
$507$		0			0
$508$	−4.00000	−	6.92820i	−0.177471	−	0.307389i
$509$	−3.00000	+	5.19615i	−0.132973	+	0.230315i	−0.924821	−	0.380402i	$-0.875786\pi$
$509$	−3.00000	+	5.19615i	−0.132973	+	0.230315i	0.791849	+	0.610718i	$0.209119\pi$
$510$		0			0
$511$	5.50000	+	9.52628i	0.243306	+	0.421418i
$512$	11.0000			0.486136
$513$		0			0
$514$	−20.0000			−0.882162
$515$		0			0
$516$		0			0
$517$	−6.00000	+	10.3923i	−0.263880	+	0.457053i
$518$	1.50000	+	2.59808i	0.0659062	+	0.114153i
$519$		0			0
$520$		0			0
$521$	−18.0000			−0.788594			−0.394297	−	0.918983i	$-0.629012\pi$
$521$	−18.0000			−0.788594			−0.394297	+	0.918983i	$0.629012\pi$
$522$		0			0
$523$	−14.5000	+	25.1147i	−0.634041	+	1.09819i	0.352677	+	0.935745i	$0.385272\pi$
$523$	−14.5000	+	25.1147i	−0.634041	+	1.09819i	−0.986718	+	0.162446i	$0.948062\pi$
$524$	−14.0000			−0.611593
$525$		0			0
$526$	−13.0000	+	22.5167i	−0.566827	+	0.981773i
$527$	6.00000	+	10.3923i	0.261364	+	0.452696i
$528$		0			0
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$		0			0
$531$		0			0
$532$	−3.50000	+	2.59808i	−0.151744	+	0.112641i
$533$	60.0000			2.59889
$534$		0			0
$535$		0			0
$536$	−16.5000	+	28.5788i	−0.712691	+	1.23442i
$537$		0			0
$538$	−5.00000	+	8.66025i	−0.215565	+	0.373370i
$539$	−12.0000			−0.516877
$540$		0			0
$541$	19.5000	−	33.7750i	0.838370	−	1.45210i	−0.0528859	−	0.998601i	$-0.516842\pi$
$541$	19.5000	−	33.7750i	0.838370	−	1.45210i	0.891256	−	0.453500i	$-0.149825\pi$
$542$		0			0
$543$		0			0
$544$	−20.0000			−0.857493
$545$		0			0
$546$		0			0
$547$	14.5000	−	25.1147i	0.619975	−	1.07383i	−0.369514	−	0.929225i	$-0.620476\pi$
$547$	14.5000	−	25.1147i	0.619975	−	1.07383i	0.989490	−	0.144604i	$-0.0461907\pi$
$548$	−9.00000	−	15.5885i	−0.384461	−	0.665906i
$549$		0			0
$550$	10.0000			0.426401
$551$	28.0000	−	20.7846i	1.19284	−	0.885454i
$552$		0			0
$553$	−0.500000	−	0.866025i	−0.0212622	−	0.0368271i
$554$	−1.00000	−	1.73205i	−0.0424859	−	0.0735878i
$555$		0			0
$556$	2.50000	+	4.33013i	0.106024	+	0.183638i
$557$	−19.0000	+	32.9090i	−0.805056	+	1.39440i	0.111198	+	0.993798i	$0.464531\pi$
$557$	−19.0000	+	32.9090i	−0.805056	+	1.39440i	−0.916253	+	0.400599i	$0.868802\pi$
$558$		0			0
$559$	−5.00000			−0.211477
$560$		0			0
$561$		0			0
$562$	−8.00000			−0.337460
$563$	−18.0000			−0.758610			−0.379305	−	0.925272i	$-0.623837\pi$
$563$	−18.0000			−0.758610			−0.379305	+	0.925272i	$0.623837\pi$
$564$		0			0
$565$		0			0
$566$	−2.00000	+	3.46410i	−0.0840663	+	0.145607i
$567$		0			0
$568$	9.00000	+	15.5885i	0.377632	+	0.654077i
$569$	−24.0000			−1.00613			−0.503066	−	0.864248i	$-0.667795\pi$
$569$	−24.0000			−1.00613			−0.503066	+	0.864248i	$0.667795\pi$
$570$		0			0
$571$	33.0000			1.38101			0.690504	−	0.723329i	$-0.257389\pi$
$571$	33.0000			1.38101			0.690504	+	0.723329i	$0.257389\pi$
$572$	5.00000	+	8.66025i	0.209061	+	0.362103i
$573$		0			0
$574$	6.00000	−	10.3923i	0.250435	−	0.433766i
$575$	10.0000	+	17.3205i	0.417029	+	0.722315i
$576$		0			0
$577$	18.0000			0.749350			0.374675	−	0.927156i	$-0.377754\pi$
$577$	18.0000			0.749350			0.374675	+	0.927156i	$0.377754\pi$
$578$	1.00000			0.0415945
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	4.00000	−	6.92820i	0.165663	−	0.286937i
$584$	16.5000	+	28.5788i	0.682775	+	1.18260i
$585$		0			0
$586$	−7.00000	−	12.1244i	−0.289167	−	0.500853i
$587$	−13.0000	−	22.5167i	−0.536567	−	0.929362i	−0.999086	−	0.0427523i	$-0.986387\pi$
$587$	−13.0000	−	22.5167i	−0.536567	−	0.929362i	0.462518	−	0.886610i	$-0.346946\pi$
$588$		0			0
$589$	12.0000	+	5.19615i	0.494451	+	0.214104i
$590$		0			0
$591$		0			0
$592$	1.50000	+	2.59808i	0.0616496	+	0.106780i
$593$	−3.00000	+	5.19615i	−0.123195	+	0.213380i	−0.921026	−	0.389501i	$-0.872647\pi$
$593$	−3.00000	+	5.19615i	−0.123195	+	0.213380i	0.797831	+	0.602881i	$0.205981\pi$
$594$		0			0
$595$		0			0
$596$	−6.00000			−0.245770
$597$		0			0
$598$	10.0000	−	17.3205i	0.408930	−	0.708288i
$599$	9.00000	−	15.5885i	0.367730	−	0.636927i	−0.621480	−	0.783430i	$-0.713468\pi$
$599$	9.00000	−	15.5885i	0.367730	−	0.636927i	0.989210	+	0.146503i	$0.0468017\pi$
$600$		0			0
$601$	−21.0000			−0.856608			−0.428304	−	0.903635i	$-0.640889\pi$
$601$	−21.0000			−0.856608			−0.428304	+	0.903635i	$0.640889\pi$
$602$	−0.500000	+	0.866025i	−0.0203785	+	0.0352966i
$603$		0			0
$604$	6.00000	−	10.3923i	0.244137	−	0.422857i
$605$		0			0
$606$		0			0
$607$	−43.0000			−1.74532			−0.872658	−	0.488332i	$-0.837606\pi$
$607$	−43.0000			−1.74532			−0.872658	+	0.488332i	$0.837606\pi$
$608$	−17.5000	+	12.9904i	−0.709719	+	0.526830i
$609$		0			0
$610$		0			0
$611$	−15.0000	−	25.9808i	−0.606835	−	1.05107i
$612$		0			0
$613$	15.0000	+	25.9808i	0.605844	+	1.04935i	0.991917	+	0.126885i	$0.0404979\pi$
$613$	15.0000	+	25.9808i	0.605844	+	1.04935i	−0.386073	+	0.922468i	$0.626169\pi$
$614$	−6.00000	+	10.3923i	−0.242140	+	0.419399i
$615$		0			0
$616$	6.00000			0.241747
$617$	3.00000	−	5.19615i	0.120775	−	0.209189i	−0.799298	−	0.600935i	$-0.794795\pi$
$617$	3.00000	−	5.19615i	0.120775	−	0.209189i	0.920074	+	0.391745i	$0.128129\pi$
$618$		0			0
$619$	25.0000			1.00483			0.502417	−	0.864625i	$-0.332444\pi$
$619$	25.0000			1.00483			0.502417	+	0.864625i	$0.332444\pi$
$620$		0			0
$621$		0			0
$622$	−9.00000	−	15.5885i	−0.360867	−	0.625040i
$623$	−3.00000	+	5.19615i	−0.120192	+	0.208179i
$624$		0			0
$625$	−12.5000	−	21.6506i	−0.500000	−	0.866025i
$626$	−22.0000			−0.879297
$627$		0			0
$628$	−3.00000			−0.119713
$629$	−6.00000	−	10.3923i	−0.239236	−	0.414368i
$630$		0			0
$631$	7.50000	−	12.9904i	0.298570	−	0.517139i	−0.677239	−	0.735763i	$-0.736824\pi$
$631$	7.50000	−	12.9904i	0.298570	−	0.517139i	0.975809	+	0.218624i	$0.0701569\pi$
$632$	−1.50000	−	2.59808i	−0.0596668	−	0.103346i
$633$		0			0
$634$	−4.00000			−0.158860
$635$		0			0
$636$		0			0
$637$	15.0000	−	25.9808i	0.594322	−	1.02940i
$638$	−16.0000			−0.633446
$639$		0			0
$640$		0			0
$641$	−15.0000	−	25.9808i	−0.592464	−	1.02618i	−0.993899	−	0.110291i	$-0.964822\pi$
$641$	−15.0000	−	25.9808i	−0.592464	−	1.02618i	0.401435	−	0.915888i	$-0.368512\pi$
$642$		0			0
$643$	9.50000	+	16.4545i	0.374643	+	0.648901i	0.990274	−	0.139134i	$-0.0444318\pi$
$643$	9.50000	+	16.4545i	0.374643	+	0.648901i	−0.615630	+	0.788035i	$0.711098\pi$
$644$	2.00000	+	3.46410i	0.0788110	+	0.136505i
$645$		0			0
$646$	−14.0000	+	10.3923i	−0.550823	+	0.408880i
$647$	24.0000			0.943537			0.471769	−	0.881722i	$-0.343616\pi$
$647$	24.0000			0.943537			0.471769	+	0.881722i	$0.343616\pi$
$648$		0			0
$649$	10.0000	+	17.3205i	0.392534	+	0.679889i
$650$	−12.5000	+	21.6506i	−0.490290	+	0.849208i
$651$		0			0
$652$	1.50000	−	2.59808i	0.0587445	−	0.101749i
$653$	18.0000			0.704394			0.352197	−	0.935926i	$-0.385435\pi$
$653$	18.0000			0.704394			0.352197	+	0.935926i	$0.385435\pi$
$654$		0			0
$655$		0			0
$656$	6.00000	−	10.3923i	0.234261	−	0.405751i
$657$		0			0
$658$	−6.00000			−0.233904
$659$	17.0000	−	29.4449i	0.662226	−	1.14701i	−0.317803	−	0.948157i	$-0.602945\pi$
$659$	17.0000	−	29.4449i	0.662226	−	1.14701i	0.980029	−	0.198852i	$-0.0637214\pi$
$660$		0			0
$661$	−21.0000	+	36.3731i	−0.816805	+	1.41475i	0.0912190	+	0.995831i	$0.470924\pi$
$661$	−21.0000	+	36.3731i	−0.816805	+	1.41475i	−0.908024	+	0.418917i	$0.862410\pi$
$662$	−12.5000	−	21.6506i	−0.485826	−	0.841476i
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−16.0000	−	27.7128i	−0.619522	−	1.07304i
$668$	1.00000	+	1.73205i	0.0386912	+	0.0670151i
$669$		0			0
$670$		0			0
$671$	13.0000	−	22.5167i	0.501859	−	0.869246i
$672$		0			0
$673$	−33.0000			−1.27206			−0.636028	−	0.771666i	$-0.719424\pi$
$673$	−33.0000			−1.27206			−0.636028	+	0.771666i	$0.719424\pi$
$674$	6.50000	−	11.2583i	0.250371	−	0.433655i
$675$		0			0
$676$	−12.0000			−0.461538
$677$	−34.0000			−1.30673			−0.653363	−	0.757045i	$-0.726642\pi$
$677$	−34.0000			−1.30673			−0.653363	+	0.757045i	$0.726642\pi$
$678$		0			0
$679$	−1.00000	−	1.73205i	−0.0383765	−	0.0664700i
$680$		0			0
$681$		0			0
$682$	−3.00000	−	5.19615i	−0.114876	−	0.198971i
$683$	−12.0000			−0.459167			−0.229584	−	0.973289i	$-0.573736\pi$
$683$	−12.0000			−0.459167			−0.229584	+	0.973289i	$0.573736\pi$
$684$		0			0
$685$		0			0
$686$	−6.50000	−	11.2583i	−0.248171	−	0.429845i
$687$		0			0
$688$	−0.500000	+	0.866025i	−0.0190623	+	0.0330169i
$689$	10.0000	+	17.3205i	0.380970	+	0.659859i
$690$		0			0
$691$	20.0000			0.760836			0.380418	−	0.924815i	$-0.375780\pi$
$691$	20.0000			0.760836			0.380418	+	0.924815i	$0.375780\pi$
$692$		0			0
$693$		0			0
$694$	8.00000	−	13.8564i	0.303676	−	0.525982i
$695$		0			0
$696$		0			0
$697$	−24.0000	+	41.5692i	−0.909065	+	1.57455i
$698$	−10.5000	−	18.1865i	−0.397431	−	0.688370i
$699$		0			0
$700$	−2.50000	−	4.33013i	−0.0944911	−	0.163663i
$701$	10.0000	+	17.3205i	0.377695	+	0.654187i	0.990726	−	0.135872i	$-0.0433835\pi$
$701$	10.0000	+	17.3205i	0.377695	+	0.654187i	−0.613032	+	0.790058i	$0.710050\pi$
$702$		0			0
$703$	−12.0000	−	5.19615i	−0.452589	−	0.195977i
$704$	14.0000			0.527645
$705$		0			0
$706$	−2.00000	−	3.46410i	−0.0752710	−	0.130373i
$707$	7.00000	−	12.1244i	0.263262	−	0.455983i
$708$		0			0
$709$	19.5000	−	33.7750i	0.732338	−	1.26845i	−0.223544	−	0.974694i	$-0.571763\pi$
$709$	19.5000	−	33.7750i	0.732338	−	1.26845i	0.955882	−	0.293752i	$-0.0949041\pi$
$710$		0			0
$711$		0			0
$712$	−9.00000	+	15.5885i	−0.337289	+	0.584202i
$713$	6.00000	−	10.3923i	0.224702	−	0.389195i
$714$		0			0
$715$		0			0
$716$	−6.00000	+	10.3923i	−0.224231	+	0.388379i
$717$		0			0
$718$	10.0000	−	17.3205i	0.373197	−	0.646396i
$719$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$719$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$720$		0			0
$721$	13.0000			0.484145
$722$	−5.50000	+	18.1865i	−0.204689	+	0.676833i
$723$		0			0
$724$	−1.00000	−	1.73205i	−0.0371647	−	0.0643712i
$725$	20.0000	+	34.6410i	0.742781	+	1.28654i
$726$		0			0
$727$	23.5000	+	40.7032i	0.871567	+	1.50960i	0.860376	+	0.509661i	$0.170229\pi$
$727$	23.5000	+	40.7032i	0.871567	+	1.50960i	0.0111912	+	0.999937i	$0.496438\pi$
$728$	−7.50000	+	12.9904i	−0.277968	+	0.481456i
$729$		0			0
$730$		0			0
$731$	2.00000	−	3.46410i	0.0739727	−	0.128124i
$732$		0			0
$733$	−50.0000			−1.84679			−0.923396	−	0.383849i	$-0.874598\pi$
$733$	−50.0000			−1.84679			−0.923396	+	0.383849i	$0.874598\pi$
$734$	−7.00000			−0.258375
$735$		0			0
$736$	10.0000	+	17.3205i	0.368605	+	0.638442i
$737$	−11.0000	+	19.0526i	−0.405190	+	0.701810i
$738$		0			0
$739$	−9.50000	−	16.4545i	−0.349463	−	0.605288i	0.636691	−	0.771119i	$-0.280303\pi$
$739$	−9.50000	−	16.4545i	−0.349463	−	0.605288i	−0.986154	+	0.165831i	$0.946969\pi$
$740$		0			0
$741$		0			0
$742$	4.00000			0.146845
$743$	−25.0000	−	43.3013i	−0.917161	−	1.58857i	−0.803706	−	0.595026i	$-0.797142\pi$
$743$	−25.0000	−	43.3013i	−0.917161	−	1.58857i	−0.113455	−	0.993543i	$-0.536192\pi$
$744$		0			0
$745$		0			0
$746$	5.00000	+	8.66025i	0.183063	+	0.317074i
$747$		0			0
$748$	−8.00000			−0.292509
$749$	18.0000			0.657706
$750$		0			0
$751$	−22.5000	+	38.9711i	−0.821037	+	1.42208i	0.0838743	+	0.996476i	$0.473271\pi$
$751$	−22.5000	+	38.9711i	−0.821037	+	1.42208i	−0.904911	+	0.425601i	$0.860063\pi$
$752$	−6.00000			−0.218797
$753$		0			0
$754$	20.0000	−	34.6410i	0.728357	−	1.26155i
$755$		0			0
$756$		0			0
$757$	−6.50000	−	11.2583i	−0.236247	−	0.409191i	0.723388	−	0.690442i	$-0.242584\pi$
$757$	−6.50000	−	11.2583i	−0.236247	−	0.409191i	−0.959634	+	0.281251i	$0.909251\pi$
$758$	−2.50000	−	4.33013i	−0.0908041	−	0.157277i
$759$		0			0
$760$		0			0
$761$	−6.00000			−0.217500			−0.108750	−	0.994069i	$-0.534685\pi$
$761$	−6.00000			−0.217500			−0.108750	+	0.994069i	$0.534685\pi$
$762$		0			0
$763$	1.00000	+	1.73205i	0.0362024	+	0.0627044i
$764$	−12.0000	+	20.7846i	−0.434145	+	0.751961i
$765$		0			0
$766$	−7.00000	+	12.1244i	−0.252920	+	0.438071i
$767$	−50.0000			−1.80540
$768$		0			0
$769$	18.5000	−	32.0429i	0.667127	−	1.15550i	−0.311577	−	0.950221i	$-0.600857\pi$
$769$	18.5000	−	32.0429i	0.667127	−	1.15550i	0.978704	−	0.205277i	$-0.0658095\pi$
$770$		0			0
$771$		0			0
$772$	−19.0000			−0.683825
$773$	7.00000	−	12.1244i	0.251773	−	0.436083i	−0.712241	−	0.701935i	$-0.752320\pi$
$773$	7.00000	−	12.1244i	0.251773	−	0.436083i	0.964014	+	0.265852i	$0.0856532\pi$
$774$		0			0
$775$	−7.50000	+	12.9904i	−0.269408	+	0.466628i
$776$	−3.00000	−	5.19615i	−0.107694	−	0.186531i
$777$		0			0
$778$	−24.0000			−0.860442
$779$	6.00000	+	51.9615i	0.214972	+	1.86171i
$780$		0			0
$781$	6.00000	+	10.3923i	0.214697	+	0.371866i
$782$	8.00000	+	13.8564i	0.286079	+	0.495504i
$783$		0			0
$784$	−3.00000	−	5.19615i	−0.107143	−	0.185577i
$785$		0			0
$786$		0			0
$787$	25.0000			0.891154			0.445577	−	0.895244i	$-0.352999\pi$
$787$	25.0000			0.891154			0.445577	+	0.895244i	$0.352999\pi$
$788$	13.0000	−	22.5167i	0.463106	−	0.802123i
$789$		0			0
$790$		0			0
$791$	−2.00000			−0.0711118
$792$		0			0
$793$	32.5000	+	56.2917i	1.15411	+	1.99898i
$794$	3.50000	−	6.06218i	0.124210	−	0.215139i
$795$		0			0
$796$	10.5000	+	18.1865i	0.372163	+	0.644605i
$797$	14.0000			0.495905			0.247953	−	0.968772i	$-0.420242\pi$
$797$	14.0000			0.495905			0.247953	+	0.968772i	$0.420242\pi$
$798$		0			0
$799$	24.0000			0.849059
$800$	−12.5000	−	21.6506i	−0.441942	−	0.765466i
$801$		0			0
$802$	3.00000	−	5.19615i	0.105934	−	0.183483i
$803$	11.0000	+	19.0526i	0.388182	+	0.672350i
$804$		0			0
$805$		0			0
$806$	15.0000			0.528352
$807$		0			0
$808$	21.0000	−	36.3731i	0.738777	−	1.27960i
$809$	16.0000			0.562530			0.281265	−	0.959630i	$-0.409246\pi$
$809$	16.0000			0.562530			0.281265	+	0.959630i	$0.409246\pi$
$810$		0			0
$811$	22.0000	−	38.1051i	0.772524	−	1.33805i	−0.163651	−	0.986518i	$-0.552327\pi$
$811$	22.0000	−	38.1051i	0.772524	−	1.33805i	0.936175	−	0.351533i	$-0.114340\pi$
$812$	4.00000	+	6.92820i	0.140372	+	0.243132i
$813$		0			0
$814$	3.00000	+	5.19615i	0.105150	+	0.182125i
$815$		0			0
$816$		0			0
$817$	−0.500000	−	4.33013i	−0.0174928	−	0.151492i
$818$	14.0000			0.489499
$819$		0			0
$820$		0			0
$821$	12.0000	−	20.7846i	0.418803	−	0.725388i	−0.577016	−	0.816733i	$-0.695783\pi$
$821$	12.0000	−	20.7846i	0.418803	−	0.725388i	0.995819	+	0.0913446i	$0.0291165\pi$
$822$		0			0
$823$	−2.00000	+	3.46410i	−0.0697156	+	0.120751i	−0.898776	−	0.438408i	$-0.855543\pi$
$823$	−2.00000	+	3.46410i	−0.0697156	+	0.120751i	0.829060	+	0.559159i	$0.188876\pi$
$824$	39.0000			1.35863
$825$		0			0
$826$	−5.00000	+	8.66025i	−0.173972	+	0.301329i
$827$	−18.0000	+	31.1769i	−0.625921	+	1.08413i	0.362441	+	0.932007i	$0.381944\pi$
$827$	−18.0000	+	31.1769i	−0.625921	+	1.08413i	−0.988362	+	0.152121i	$0.951390\pi$
$828$		0			0
$829$	25.0000			0.868286			0.434143	−	0.900844i	$-0.357051\pi$
$829$	25.0000			0.868286			0.434143	+	0.900844i	$0.357051\pi$
$830$		0			0
$831$		0			0
$832$	−17.5000	+	30.3109i	−0.606703	+	1.05084i
$833$	12.0000	+	20.7846i	0.415775	+	0.720144i
$834$		0			0
$835$		0			0
$836$	−7.00000	+	5.19615i	−0.242100	+	0.179713i
$837$		0			0
$838$	7.00000	+	12.1244i	0.241811	+	0.418829i
$839$	−6.00000	−	10.3923i	−0.207143	−	0.358782i	0.743670	−	0.668546i	$-0.233083\pi$
$839$	−6.00000	−	10.3923i	−0.207143	−	0.358782i	−0.950813	+	0.309764i	$0.899750\pi$
$840$		0			0
$841$	−17.5000	−	30.3109i	−0.603448	−	1.04520i
$842$	−11.0000	+	19.0526i	−0.379085	+	0.656595i
$843$		0			0
$844$	15.0000			0.516321
$845$		0			0
$846$		0			0
$847$	−7.00000			−0.240523
$848$	4.00000			0.137361
$849$		0			0
$850$	−10.0000	−	17.3205i	−0.342997	−	0.594089i
$851$	−6.00000	+	10.3923i	−0.205677	+	0.356244i
$852$		0			0
$853$	2.50000	+	4.33013i	0.0855984	+	0.148261i	0.905646	−	0.424034i	$-0.139386\pi$
$853$	2.50000	+	4.33013i	0.0855984	+	0.148261i	−0.820048	+	0.572295i	$0.806053\pi$
$854$	13.0000			0.444851
$855$		0			0
$856$	54.0000			1.84568
$857$	5.00000	+	8.66025i	0.170797	+	0.295829i	0.938699	−	0.344739i	$-0.112033\pi$
$857$	5.00000	+	8.66025i	0.170797	+	0.295829i	−0.767902	+	0.640567i	$0.778699\pi$
$858$		0			0
$859$	−7.50000	+	12.9904i	−0.255897	+	0.443226i	−0.965139	−	0.261739i	$-0.915704\pi$
$859$	−7.50000	+	12.9904i	−0.255897	+	0.443226i	0.709242	+	0.704965i	$0.249037\pi$
$860$		0			0
$861$		0			0
$862$	−10.0000			−0.340601
$863$	−10.0000			−0.340404			−0.170202	−	0.985409i	$-0.554442\pi$
$863$	−10.0000			−0.340404			−0.170202	+	0.985409i	$0.554442\pi$
$864$		0			0
$865$		0			0
$866$	9.00000			0.305832
$867$		0			0
$868$	−1.50000	+	2.59808i	−0.0509133	+	0.0881845i
$869$	−1.00000	−	1.73205i	−0.0339227	−	0.0587558i
$870$		0			0
$871$	−27.5000	−	47.6314i	−0.931802	−	1.61393i
$872$	3.00000	+	5.19615i	0.101593	+	0.175964i
$873$		0			0
$874$	16.0000	+	6.92820i	0.541208	+	0.234350i
$875$		0			0
$876$		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	$0.914835\pi$
$878$	17.5000	−	30.3109i	0.590596	−	1.02294i
$879$		0			0
$880$		0			0
$881$	28.0000			0.943344			0.471672	−	0.881774i	$-0.343651\pi$
$881$	28.0000			0.943344			0.471672	+	0.881774i	$0.343651\pi$
$882$		0			0
$883$	0.500000	−	0.866025i	0.0168263	−	0.0291441i	−0.857490	−	0.514501i	$-0.827977\pi$
$883$	0.500000	−	0.866025i	0.0168263	−	0.0291441i	0.874316	+	0.485357i	$0.161310\pi$
$884$	10.0000	−	17.3205i	0.336336	−	0.582552i
$885$		0			0
$886$	−32.0000			−1.07506
$887$	−3.00000	+	5.19615i	−0.100730	+	0.174470i	−0.911986	−	0.410222i	$-0.865451\pi$
$887$	−3.00000	+	5.19615i	−0.100730	+	0.174470i	0.811256	+	0.584692i	$0.198785\pi$
$888$		0			0
$889$	4.00000	−	6.92820i	0.134156	−	0.232364i
$890$		0			0
$891$		0			0
$892$	−9.00000			−0.301342
$893$	21.0000	−	15.5885i	0.702738	−	0.521648i
$894$		0			0
$895$		0			0
$896$	−1.50000	−	2.59808i	−0.0501115	−	0.0867956i
$897$		0			0
$898$	6.00000	+	10.3923i	0.200223	+	0.346796i
$899$	12.0000	−	20.7846i	0.400222	−	0.693206i
$900$		0			0
$901$	−16.0000			−0.533037
$902$	12.0000	−	20.7846i	0.399556	−	0.692052i
$903$		0			0
$904$	−6.00000			−0.199557
$905$		0			0
$906$		0			0
$907$	22.0000	+	38.1051i	0.730498	+	1.26526i	0.956671	+	0.291172i	$0.0940453\pi$
$907$	22.0000	+	38.1051i	0.730498	+	1.26526i	−0.226173	+	0.974087i	$0.572621\pi$
$908$	12.0000	−	20.7846i	0.398234	−	0.689761i
$909$		0			0
$910$		0			0
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$		0			0
$913$		0			0
$914$	−5.50000	−	9.52628i	−0.181924	−	0.315101i
$915$		0			0
$916$	6.50000	−	11.2583i	0.214766	−	0.371986i
$917$	−7.00000	−	12.1244i	−0.231160	−	0.400381i
$918$		0			0
$919$	−25.0000			−0.824674			−0.412337	−	0.911031i	$-0.635287\pi$
$919$	−25.0000			−0.824674			−0.412337	+	0.911031i	$0.635287\pi$
$920$		0			0
$921$		0			0
$922$	−15.0000	+	25.9808i	−0.493999	+	0.855631i
$923$	−30.0000			−0.987462
$924$		0			0
$925$	7.50000	−	12.9904i	0.246598	−	0.427121i
$926$	11.5000	+	19.9186i	0.377913	+	0.654565i
$927$		0			0
$928$	20.0000	+	34.6410i	0.656532	+	1.13715i
$929$	14.0000	+	24.2487i	0.459325	+	0.795574i	0.998925	−	0.0463469i	$-0.0147580\pi$
$929$	14.0000	+	24.2487i	0.459325	+	0.795574i	−0.539600	+	0.841921i	$0.681425\pi$
$930$		0			0
$931$	24.0000	+	10.3923i	0.786568	+	0.340594i
$932$	−6.00000			−0.196537
$933$		0			0
$934$	4.00000	+	6.92820i	0.130884	+	0.226698i
$935$		0			0
$936$		0			0
$937$	4.50000	−	7.79423i	0.147009	−	0.254626i	−0.783112	−	0.621881i	$-0.786369\pi$
$937$	4.50000	−	7.79423i	0.147009	−	0.254626i	0.930121	+	0.367254i	$0.119702\pi$
$938$	−11.0000			−0.359163
$939$		0			0
$940$		0			0
$941$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$941$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$942$		0			0
$943$	48.0000			1.56310
$944$	−5.00000	+	8.66025i	−0.162736	+	0.281867i
$945$		0			0
$946$	−1.00000	+	1.73205i	−0.0325128	+	0.0563138i
$947$	25.0000	+	43.3013i	0.812391	+	1.40710i	0.911186	+	0.411994i	$0.135168\pi$
$947$	25.0000	+	43.3013i	0.812391	+	1.40710i	−0.0987955	+	0.995108i	$0.531499\pi$
$948$		0			0
$949$	−55.0000			−1.78538
$950$	−20.0000	−	8.66025i	−0.648886	−	0.280976i
$951$		0			0
$952$	−6.00000	−	10.3923i	−0.194461	−	0.336817i
$953$	17.0000	+	29.4449i	0.550684	+	0.953813i	0.998225	+	0.0595495i	$0.0189664\pi$
$953$	17.0000	+	29.4449i	0.550684	+	0.953813i	−0.447541	+	0.894263i	$0.647700\pi$
$954$		0			0
$955$		0			0
$956$	6.00000	−	10.3923i	0.194054	−	0.336111i
$957$		0			0
$958$	14.0000			0.452319
$959$	9.00000	−	15.5885i	0.290625	−	0.503378i
$960$		0			0
$961$	−22.0000			−0.709677
$962$	−15.0000			−0.483619
$963$		0			0
$964$	−3.50000	−	6.06218i	−0.112727	−	0.195250i
$965$		0			0
$966$		0			0
$967$	14.5000	+	25.1147i	0.466289	+	0.807635i	0.999259	−	0.0384986i	$-0.0122575\pi$
$967$	14.5000	+	25.1147i	0.466289	+	0.807635i	−0.532970	+	0.846134i	$0.678924\pi$
$968$	−21.0000			−0.674966
$969$		0			0
$970$		0			0
$971$	−21.0000	−	36.3731i	−0.673922	−	1.16727i	−0.976783	−	0.214232i	$-0.931275\pi$
$971$	−21.0000	−	36.3731i	−0.673922	−	1.16727i	0.302861	−	0.953035i	$-0.402058\pi$
$972$		0			0
$973$	−2.50000	+	4.33013i	−0.0801463	+	0.138817i
$974$	−8.00000	−	13.8564i	−0.256337	−	0.443988i
$975$		0			0
$976$	13.0000			0.416120
$977$	−54.0000			−1.72761			−0.863807	−	0.503824i	$-0.831926\pi$
$977$	−54.0000			−1.72761			−0.863807	+	0.503824i	$0.831926\pi$
$978$		0			0
$979$	−6.00000	+	10.3923i	−0.191761	+	0.332140i
$980$		0			0
$981$		0			0
$982$	−3.00000	+	5.19615i	−0.0957338	+	0.165816i
$983$	5.00000	+	8.66025i	0.159475	+	0.276219i	0.934680	−	0.355491i	$-0.115686\pi$
$983$	5.00000	+	8.66025i	0.159475	+	0.276219i	−0.775204	+	0.631711i	$0.782353\pi$
$984$		0			0
$985$		0			0
$986$	16.0000	+	27.7128i	0.509544	+	0.882556i
$987$		0			0
$988$	−2.50000	−	21.6506i	−0.0795356	−	0.688798i
$989$	−4.00000			−0.127193
$990$		0			0
$991$	−23.5000	−	40.7032i	−0.746502	−	1.29298i	−0.949490	−	0.313798i	$-0.898398\pi$
$991$	−23.5000	−	40.7032i	−0.746502	−	1.29298i	0.202988	−	0.979181i	$-0.434935\pi$
$992$	−7.50000	+	12.9904i	−0.238125	+	0.412445i
$993$		0			0
$994$	−3.00000	+	5.19615i	−0.0951542	+	0.164812i
$995$		0			0
$996$		0			0
$997$	−3.50000	+	6.06218i	−0.110846	+	0.191991i	−0.916112	−	0.400923i	$-0.868689\pi$
$997$	−3.50000	+	6.06218i	−0.110846	+	0.191991i	0.805266	+	0.592914i	$0.202023\pi$
$998$	14.5000	−	25.1147i	0.458989	−	0.794993i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.2.f.a.64.1		2
3.2	odd	2		57.2.e.a.7.1	✓	2
4.3	odd	2		2736.2.s.j.577.1		2
12.11	even	2		912.2.q.a.577.1		2
19.7	even	3		3249.2.a.c.1.1		1
19.11	even	3	inner	171.2.f.a.163.1		2
19.12	odd	6		3249.2.a.f.1.1		1
57.11	odd	6		57.2.e.a.49.1	yes	2
57.26	odd	6		1083.2.a.c.1.1		1
57.50	even	6		1083.2.a.b.1.1		1
76.11	odd	6		2736.2.s.j.1873.1		2
228.11	even	6		912.2.q.a.49.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.2.e.a.7.1	✓	2	3.2	odd	2
57.2.e.a.49.1	yes	2	57.11	odd	6
171.2.f.a.64.1		2	1.1	even	1	trivial
171.2.f.a.163.1		2	19.11	even	3	inner
912.2.q.a.49.1		2	228.11	even	6
912.2.q.a.577.1		2	12.11	even	2
1083.2.a.b.1.1		1	57.50	even	6
1083.2.a.c.1.1		1	57.26	odd	6
2736.2.s.j.577.1		2	4.3	odd	2
2736.2.s.j.1873.1		2	76.11	odd	6
3249.2.a.c.1.1		1	19.7	even	3
3249.2.a.f.1.1		1	19.12	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	171.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.00000 q^{7} +3.00000 q^{8} +2.00000 q^{11} +(-2.50000 + 4.33013i) q^{13} +(0.500000 + 0.866025i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-2.00000 - 3.46410i) q^{17} +(-4.00000 - 1.73205i) q^{19} +(1.00000 + 1.73205i) q^{22} +(-2.00000 + 3.46410i) q^{23} +(2.50000 - 4.33013i) q^{25} -5.00000 q^{26} +(0.500000 - 0.866025i) q^{28} +(-4.00000 + 6.92820i) q^{29} -3.00000 q^{31} +(2.50000 - 4.33013i) q^{32} +(2.00000 - 3.46410i) q^{34} +3.00000 q^{37} +(-0.500000 - 4.33013i) q^{38} +(-6.00000 - 10.3923i) q^{41} +(0.500000 + 0.866025i) q^{43} +(1.00000 - 1.73205i) q^{44} -4.00000 q^{46} +(-3.00000 + 5.19615i) q^{47} -6.00000 q^{49} +5.00000 q^{50} +(2.50000 + 4.33013i) q^{52} +(2.00000 - 3.46410i) q^{53} +3.00000 q^{56} -8.00000 q^{58} +(5.00000 + 8.66025i) q^{59} +(6.50000 - 11.2583i) q^{61} +(-1.50000 - 2.59808i) q^{62} +7.00000 q^{64} +(-5.50000 + 9.52628i) q^{67} -4.00000 q^{68} +(3.00000 + 5.19615i) q^{71} +(5.50000 + 9.52628i) q^{73} +(1.50000 + 2.59808i) q^{74} +(-3.50000 + 2.59808i) q^{76} +2.00000 q^{77} +(-0.500000 - 0.866025i) q^{79} +(6.00000 - 10.3923i) q^{82} +(-0.500000 + 0.866025i) q^{86} +6.00000 q^{88} +(-3.00000 + 5.19615i) q^{89} +(-2.50000 + 4.33013i) q^{91} +(2.00000 + 3.46410i) q^{92} -6.00000 q^{94} +(-1.00000 - 1.73205i) q^{97} +(-3.00000 - 5.19615i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + q^{4} + 2 q^{7} + 6 q^{8} + 4 q^{11} - 5 q^{13} + q^{14} + q^{16} - 4 q^{17} - 8 q^{19} + 2 q^{22} - 4 q^{23} + 5 q^{25} - 10 q^{26} + q^{28} - 8 q^{29} - 6 q^{31} + 5 q^{32} + 4 q^{34}+ \cdots - 6 q^{98}+O(q^{100}) \) 2 * q + q^2 + q^4 + 2 * q^7 + 6 * q^8 + 4 * q^11 - 5 * q^13 + q^14 + q^16 - 4 * q^17 - 8 * q^19 + 2 * q^22 - 4 * q^23 + 5 * q^25 - 10 * q^26 + q^28 - 8 * q^29 - 6 * q^31 + 5 * q^32 + 4 * q^34 + 6 * q^37 - q^38 - 12 * q^41 + q^43 + 2 * q^44 - 8 * q^46 - 6 * q^47 - 12 * q^49 + 10 * q^50 + 5 * q^52 + 4 * q^53 + 6 * q^56 - 16 * q^58 + 10 * q^59 + 13 * q^61 - 3 * q^62 + 14 * q^64 - 11 * q^67 - 8 * q^68 + 6 * q^71 + 11 * q^73 + 3 * q^74 - 7 * q^76 + 4 * q^77 - q^79 + 12 * q^82 - q^86 + 12 * q^88 - 6 * q^89 - 5 * q^91 + 4 * q^92 - 12 * q^94 - 2 * q^97 - 6 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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