LMFDB - Embedded newform 315.2.bl.g.146.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(41,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("315.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bl (of order $6$, 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:	$2.51528766367$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			146.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	315.146
Dual form			315.2.bl.g.41.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.50000 + 0.866025i) q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.50000 + 0.866025i) q^{7} +(1.50000 - 2.59808i) q^{9} +(-3.00000 - 1.73205i) q^{11} +(-3.00000 - 1.73205i) q^{12} +(4.50000 - 2.59808i) q^{13} +(-1.50000 - 0.866025i) q^{15} +(-2.00000 + 3.46410i) q^{16} +3.00000 q^{17} -3.46410i q^{19} +(-1.00000 + 1.73205i) q^{20} +(-3.00000 + 3.46410i) q^{21} +(-6.00000 + 3.46410i) q^{23} +(-0.500000 + 0.866025i) q^{25} -5.19615i q^{27} +(4.00000 + 3.46410i) q^{28} +(1.50000 + 0.866025i) q^{29} +(3.00000 - 1.73205i) q^{31} -6.00000 q^{33} +(2.00000 + 1.73205i) q^{35} -6.00000 q^{36} +10.0000 q^{37} +(4.50000 - 7.79423i) q^{39} +(6.00000 + 10.3923i) q^{41} +(4.00000 - 6.92820i) q^{43} +6.92820i q^{44} -3.00000 q^{45} +6.92820i q^{48} +(5.50000 - 4.33013i) q^{49} +(4.50000 - 2.59808i) q^{51} +(-9.00000 - 5.19615i) q^{52} -3.46410i q^{53} +3.46410i q^{55} +(-3.00000 - 5.19615i) q^{57} +3.46410i q^{60} +(-6.00000 - 3.46410i) q^{61} +(-1.50000 + 7.79423i) q^{63} +8.00000 q^{64} +(-4.50000 - 2.59808i) q^{65} +(5.00000 + 8.66025i) q^{67} +(-3.00000 - 5.19615i) q^{68} +(-6.00000 + 10.3923i) q^{69} +12.1244i q^{71} -1.73205i q^{73} +1.73205i q^{75} +(-6.00000 + 3.46410i) q^{76} +(9.00000 + 1.73205i) q^{77} +(-4.00000 + 6.92820i) q^{79} +4.00000 q^{80} +(-4.50000 - 7.79423i) q^{81} +(4.50000 - 7.79423i) q^{83} +(9.00000 + 1.73205i) q^{84} +(-1.50000 - 2.59808i) q^{85} +3.00000 q^{87} -6.00000 q^{89} +(-9.00000 + 10.3923i) q^{91} +(12.0000 + 6.92820i) q^{92} +(3.00000 - 5.19615i) q^{93} +(-3.00000 + 1.73205i) q^{95} +(6.00000 + 3.46410i) q^{97} +(-9.00000 + 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{3} - 2 q^{4} - q^{5} - 5 q^{7} + 3 q^{9}+O(q^{10}) $ 2 * q + 3 * q^3 - 2 * q^4 - q^5 - 5 * q^7 + 3 * q^9	$ 2 q + 3 q^{3} - 2 q^{4} - q^{5} - 5 q^{7} + 3 q^{9} - 6 q^{11} - 6 q^{12} + 9 q^{13} - 3 q^{15} - 4 q^{16} + 6 q^{17} - 2 q^{20} - 6 q^{21} - 12 q^{23} - q^{25} + 8 q^{28} + 3 q^{29} + 6 q^{31} - 12 q^{33} + 4 q^{35} - 12 q^{36} + 20 q^{37} + 9 q^{39} + 12 q^{41} + 8 q^{43} - 6 q^{45} + 11 q^{49} + 9 q^{51} - 18 q^{52} - 6 q^{57} - 12 q^{61} - 3 q^{63} + 16 q^{64} - 9 q^{65} + 10 q^{67} - 6 q^{68} - 12 q^{69} - 12 q^{76} + 18 q^{77} - 8 q^{79} + 8 q^{80} - 9 q^{81} + 9 q^{83} + 18 q^{84} - 3 q^{85} + 6 q^{87} - 12 q^{89} - 18 q^{91} + 24 q^{92} + 6 q^{93} - 6 q^{95} + 12 q^{97} - 18 q^{99}+O(q^{100}) $ 2 * q + 3 * q^3 - 2 * q^4 - q^5 - 5 * q^7 + 3 * q^9 - 6 * q^11 - 6 * q^12 + 9 * q^13 - 3 * q^15 - 4 * q^16 + 6 * q^17 - 2 * q^20 - 6 * q^21 - 12 * q^23 - q^25 + 8 * q^28 + 3 * q^29 + 6 * q^31 - 12 * q^33 + 4 * q^35 - 12 * q^36 + 20 * q^37 + 9 * q^39 + 12 * q^41 + 8 * q^43 - 6 * q^45 + 11 * q^49 + 9 * q^51 - 18 * q^52 - 6 * q^57 - 12 * q^61 - 3 * q^63 + 16 * q^64 - 9 * q^65 + 10 * q^67 - 6 * q^68 - 12 * q^69 - 12 * q^76 + 18 * q^77 - 8 * q^79 + 8 * q^80 - 9 * q^81 + 9 * q^83 + 18 * q^84 - 3 * q^85 + 6 * q^87 - 12 * q^89 - 18 * q^91 + 24 * q^92 + 6 * q^93 - 6 * q^95 + 12 * q^97 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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			0		0.500000	−	0.866025i	$-0.333333\pi$
$2$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$3$	1.50000	−	0.866025i	0.866025	−	0.500000i
$3$	1.50000	−	0.866025i	0.866025	−	0.500000i
$4$	−1.00000	−	1.73205i	−0.500000	−	0.866025i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$8$		0			0
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$		0			0
$11$	−3.00000	−	1.73205i	−0.904534	−	0.522233i	−0.0258656	−	0.999665i	$-0.508234\pi$
$11$	−3.00000	−	1.73205i	−0.904534	−	0.522233i	−0.878668	+	0.477432i	$0.841568\pi$
$12$	−3.00000	−	1.73205i	−0.866025	−	0.500000i
$13$	4.50000	−	2.59808i	1.24808	−	0.720577i	0.277350	−	0.960769i	$-0.410544\pi$
$13$	4.50000	−	2.59808i	1.24808	−	0.720577i	0.970725	+	0.240192i	$0.0772105\pi$
$14$		0			0
$15$	−1.50000	−	0.866025i	−0.387298	−	0.223607i
$16$	−2.00000	+	3.46410i	−0.500000	+	0.866025i
$17$	3.00000			0.727607			0.363803	−	0.931476i	$-0.381478\pi$
$17$	3.00000			0.727607			0.363803	+	0.931476i	$0.381478\pi$
$18$		0			0
$19$		−	3.46410i		−	0.794719i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$		−	3.46410i		−	0.794719i	0.917663	−	0.397360i	$-0.130073\pi$
$20$	−1.00000	+	1.73205i	−0.223607	+	0.387298i
$21$	−3.00000	+	3.46410i	−0.654654	+	0.755929i
$22$		0			0
$23$	−6.00000	+	3.46410i	−1.25109	+	0.722315i	−0.971325	−	0.237754i	$-0.923589\pi$
$23$	−6.00000	+	3.46410i	−1.25109	+	0.722315i	−0.279761	+	0.960070i	$0.590255\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$		−	5.19615i		−	1.00000i
$28$	4.00000	+	3.46410i	0.755929	+	0.654654i
$29$	1.50000	+	0.866025i	0.278543	+	0.160817i	0.632764	−	0.774345i	$-0.281920\pi$
$29$	1.50000	+	0.866025i	0.278543	+	0.160817i	−0.354221	+	0.935162i	$0.615254\pi$
$30$		0			0
$31$	3.00000	−	1.73205i	0.538816	−	0.311086i	−0.205783	−	0.978598i	$-0.565974\pi$
$31$	3.00000	−	1.73205i	0.538816	−	0.311086i	0.744599	+	0.667512i	$0.232641\pi$
$32$		0			0
$33$	−6.00000			−1.04447
$34$		0			0
$35$	2.00000	+	1.73205i	0.338062	+	0.292770i
$36$	−6.00000			−1.00000
$37$	10.0000			1.64399			0.821995	−	0.569495i	$-0.192861\pi$
$37$	10.0000			1.64399			0.821995	+	0.569495i	$0.192861\pi$
$38$		0			0
$39$	4.50000	−	7.79423i	0.720577	−	1.24808i
$40$		0			0
$41$	6.00000	+	10.3923i	0.937043	+	1.62301i	0.770950	+	0.636895i	$0.219782\pi$
$41$	6.00000	+	10.3923i	0.937043	+	1.62301i	0.166092	+	0.986110i	$0.446885\pi$
$42$		0			0
$43$	4.00000	−	6.92820i	0.609994	−	1.05654i	−0.381246	−	0.924473i	$-0.624505\pi$
$43$	4.00000	−	6.92820i	0.609994	−	1.05654i	0.991241	−	0.132068i	$-0.0421616\pi$
$44$			6.92820i			1.04447i
$45$	−3.00000			−0.447214
$46$		0			0
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$			6.92820i			1.00000i
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$		0			0
$51$	4.50000	−	2.59808i	0.630126	−	0.363803i
$52$	−9.00000	−	5.19615i	−1.24808	−	0.720577i
$53$		−	3.46410i		−	0.475831i	−0.971286	−	0.237915i	$-0.923536\pi$
$53$		−	3.46410i		−	0.475831i	0.971286	−	0.237915i	$-0.0764641\pi$
$54$		0			0
$55$			3.46410i			0.467099i
$56$		0			0
$57$	−3.00000	−	5.19615i	−0.397360	−	0.688247i
$58$		0			0
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$			3.46410i			0.447214i
$61$	−6.00000	−	3.46410i	−0.768221	−	0.443533i	0.0640184	−	0.997949i	$-0.479608\pi$
$61$	−6.00000	−	3.46410i	−0.768221	−	0.443533i	−0.832240	+	0.554416i	$0.812942\pi$
$62$		0			0
$63$	−1.50000	+	7.79423i	−0.188982	+	0.981981i
$64$	8.00000			1.00000
$65$	−4.50000	−	2.59808i	−0.558156	−	0.322252i
$66$		0			0
$67$	5.00000	+	8.66025i	0.610847	+	1.05802i	0.991098	+	0.133135i	$0.0425044\pi$
$67$	5.00000	+	8.66025i	0.610847	+	1.05802i	−0.380251	+	0.924883i	$0.624162\pi$
$68$	−3.00000	−	5.19615i	−0.363803	−	0.630126i
$69$	−6.00000	+	10.3923i	−0.722315	+	1.25109i
$70$		0			0
$71$			12.1244i			1.43890i	0.694546	+	0.719448i	$0.255605\pi$
$71$			12.1244i			1.43890i	−0.694546	+	0.719448i	$0.744395\pi$
$72$		0			0
$73$		−	1.73205i		−	0.202721i	−0.994850	−	0.101361i	$-0.967680\pi$
$73$		−	1.73205i		−	0.202721i	0.994850	−	0.101361i	$-0.0323196\pi$
$74$		0			0
$75$			1.73205i			0.200000i
$76$	−6.00000	+	3.46410i	−0.688247	+	0.397360i
$77$	9.00000	+	1.73205i	1.02565	+	0.197386i
$78$		0			0
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	−0.998388	−	0.0567635i	$-0.981922\pi$
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	0.548352	+	0.836247i	$0.315255\pi$
$80$	4.00000			0.447214
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$		0			0
$83$	4.50000	−	7.79423i	0.493939	−	0.855528i	−0.506036	−	0.862512i	$-0.668890\pi$
$83$	4.50000	−	7.79423i	0.493939	−	0.855528i	0.999976	+	0.00698436i	$0.00222321\pi$
$84$	9.00000	+	1.73205i	0.981981	+	0.188982i
$85$	−1.50000	−	2.59808i	−0.162698	−	0.281801i
$86$		0			0
$87$	3.00000			0.321634
$88$		0			0
$89$	−6.00000			−0.635999			−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000			−0.635999			−0.317999	+	0.948091i	$0.603011\pi$
$90$		0			0
$91$	−9.00000	+	10.3923i	−0.943456	+	1.08941i
$92$	12.0000	+	6.92820i	1.25109	+	0.722315i
$93$	3.00000	−	5.19615i	0.311086	−	0.538816i
$94$		0			0
$95$	−3.00000	+	1.73205i	−0.307794	+	0.177705i
$96$		0			0
$97$	6.00000	+	3.46410i	0.609208	+	0.351726i	0.772655	−	0.634826i	$-0.218928\pi$
$97$	6.00000	+	3.46410i	0.609208	+	0.351726i	−0.163448	+	0.986552i	$0.552261\pi$
$98$		0			0
$99$	−9.00000	+	5.19615i	−0.904534	+	0.522233i
$100$	2.00000			0.200000
$101$	−9.00000	+	15.5885i	−0.895533	+	1.55111i	−0.0623905	+	0.998052i	$0.519872\pi$
$101$	−9.00000	+	15.5885i	−0.895533	+	1.55111i	−0.833143	+	0.553058i	$0.813461\pi$
$102$		0			0
$103$	7.50000	−	4.33013i	0.738997	−	0.426660i	−0.0827075	−	0.996574i	$-0.526357\pi$
$103$	7.50000	−	4.33013i	0.738997	−	0.426660i	0.821705	+	0.569914i	$0.193023\pi$
$104$		0			0
$105$	4.50000	+	0.866025i	0.439155	+	0.0845154i
$106$		0			0
$107$		−	17.3205i		−	1.67444i	−0.546869	−	0.837218i	$-0.684180\pi$
$107$		−	17.3205i		−	1.67444i	0.546869	−	0.837218i	$-0.315820\pi$
$108$	−9.00000	+	5.19615i	−0.866025	+	0.500000i
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$		0			0
$111$	15.0000	−	8.66025i	1.42374	−	0.821995i
$112$	2.00000	−	10.3923i	0.188982	−	0.981981i
$113$	−9.00000	+	5.19615i	−0.846649	+	0.488813i	−0.859519	−	0.511104i	$-0.829237\pi$
$113$	−9.00000	+	5.19615i	−0.846649	+	0.488813i	0.0128699	+	0.999917i	$0.495903\pi$
$114$		0			0
$115$	6.00000	+	3.46410i	0.559503	+	0.323029i
$116$		−	3.46410i		−	0.321634i
$117$		−	15.5885i		−	1.44115i
$118$		0			0
$119$	−7.50000	+	2.59808i	−0.687524	+	0.238165i
$120$		0			0
$121$	0.500000	+	0.866025i	0.0454545	+	0.0787296i
$122$		0			0
$123$	18.0000	+	10.3923i	1.62301	+	0.937043i
$124$	−6.00000	−	3.46410i	−0.538816	−	0.311086i
$125$	1.00000			0.0894427
$126$		0			0
$127$	2.00000			0.177471			0.0887357	−	0.996055i	$-0.471717\pi$
$127$	2.00000			0.177471			0.0887357	+	0.996055i	$0.471717\pi$
$128$		0			0
$129$		−	13.8564i		−	1.21999i
$130$		0			0
$131$	−3.00000	−	5.19615i	−0.262111	−	0.453990i	0.704692	−	0.709514i	$-0.251085\pi$
$131$	−3.00000	−	5.19615i	−0.262111	−	0.453990i	−0.966803	+	0.255524i	$0.917752\pi$
$132$	6.00000	+	10.3923i	0.522233	+	0.904534i
$133$	3.00000	+	8.66025i	0.260133	+	0.750939i
$134$		0			0
$135$	−4.50000	+	2.59808i	−0.387298	+	0.223607i
$136$		0			0
$137$	−3.00000	−	1.73205i	−0.256307	−	0.147979i	0.366342	−	0.930480i	$-0.380610\pi$
$137$	−3.00000	−	1.73205i	−0.256307	−	0.147979i	−0.622649	+	0.782501i	$0.713943\pi$
$138$		0			0
$139$	−6.00000	+	3.46410i	−0.508913	+	0.293821i	−0.732387	−	0.680889i	$-0.761594\pi$
$139$	−6.00000	+	3.46410i	−0.508913	+	0.293821i	0.223474	+	0.974710i	$0.428260\pi$
$140$	1.00000	−	5.19615i	0.0845154	−	0.439155i
$141$		0			0
$142$		0			0
$143$	−18.0000			−1.50524
$144$	6.00000	+	10.3923i	0.500000	+	0.866025i
$145$		−	1.73205i		−	0.143839i
$146$		0			0
$147$	4.50000	−	11.2583i	0.371154	−	0.928571i
$148$	−10.0000	−	17.3205i	−0.821995	−	1.42374i
$149$	4.50000	−	2.59808i	0.368654	−	0.212843i	−0.304216	−	0.952603i	$-0.598394\pi$
$149$	4.50000	−	2.59808i	0.368654	−	0.212843i	0.672870	+	0.739760i	$0.265061\pi$
$150$		0			0
$151$	−9.50000	+	16.4545i	−0.773099	+	1.33905i	0.162758	+	0.986666i	$0.447961\pi$
$151$	−9.50000	+	16.4545i	−0.773099	+	1.33905i	−0.935857	+	0.352381i	$0.885372\pi$
$152$		0			0
$153$	4.50000	−	7.79423i	0.363803	−	0.630126i
$154$		0			0
$155$	−3.00000	−	1.73205i	−0.240966	−	0.139122i
$156$	−18.0000			−1.44115
$157$	−7.50000	+	4.33013i	−0.598565	+	0.345582i	−0.768477	−	0.639878i	$-0.778985\pi$
$157$	−7.50000	+	4.33013i	−0.598565	+	0.345582i	0.169912	+	0.985459i	$0.445652\pi$
$158$		0			0
$159$	−3.00000	−	5.19615i	−0.237915	−	0.412082i
$160$		0			0
$161$	12.0000	−	13.8564i	0.945732	−	1.09204i
$162$		0			0
$163$	−4.00000			−0.313304			−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000			−0.313304			−0.156652	+	0.987654i	$0.550070\pi$
$164$	12.0000	−	20.7846i	0.937043	−	1.62301i
$165$	3.00000	+	5.19615i	0.233550	+	0.404520i
$166$		0			0
$167$	−4.50000	−	7.79423i	−0.348220	−	0.603136i	0.637713	−	0.770274i	$-0.279881\pi$
$167$	−4.50000	−	7.79423i	−0.348220	−	0.603136i	−0.985933	+	0.167139i	$0.946547\pi$
$168$		0			0
$169$	7.00000	−	12.1244i	0.538462	−	0.932643i
$170$		0			0
$171$	−9.00000	−	5.19615i	−0.688247	−	0.397360i
$172$	−16.0000			−1.21999
$173$	10.5000	−	18.1865i	0.798300	−	1.38270i	−0.122422	−	0.992478i	$-0.539066\pi$
$173$	10.5000	−	18.1865i	0.798300	−	1.38270i	0.920722	−	0.390218i	$-0.127601\pi$
$174$		0			0
$175$	0.500000	−	2.59808i	0.0377964	−	0.196396i
$176$	12.0000	−	6.92820i	0.904534	−	0.522233i
$177$		0			0
$178$		0			0
$179$		−	15.5885i		−	1.16514i	−0.812782	−	0.582568i	$-0.802048\pi$
$179$		−	15.5885i		−	1.16514i	0.812782	−	0.582568i	$-0.197952\pi$
$180$	3.00000	+	5.19615i	0.223607	+	0.387298i
$181$		−	10.3923i		−	0.772454i	−0.922404	−	0.386227i	$-0.873778\pi$
$181$		−	10.3923i		−	0.772454i	0.922404	−	0.386227i	$-0.126222\pi$
$182$		0			0
$183$	−12.0000			−0.887066
$184$		0			0
$185$	−5.00000	−	8.66025i	−0.367607	−	0.636715i
$186$		0			0
$187$	−9.00000	−	5.19615i	−0.658145	−	0.379980i
$188$		0			0
$189$	4.50000	+	12.9904i	0.327327	+	0.944911i
$190$		0			0
$191$	10.5000	+	6.06218i	0.759753	+	0.438644i	0.829207	−	0.558941i	$-0.188792\pi$
$191$	10.5000	+	6.06218i	0.759753	+	0.438644i	−0.0694538	+	0.997585i	$0.522126\pi$
$192$	12.0000	−	6.92820i	0.866025	−	0.500000i
$193$	−2.00000	−	3.46410i	−0.143963	−	0.249351i	0.785022	−	0.619467i	$-0.212651\pi$
$193$	−2.00000	−	3.46410i	−0.143963	−	0.249351i	−0.928986	+	0.370116i	$0.879318\pi$
$194$		0			0
$195$	−9.00000			−0.644503
$196$	−13.0000	−	5.19615i	−0.928571	−	0.371154i
$197$			24.2487i			1.72765i	0.503793	+	0.863825i	$0.331938\pi$
$197$			24.2487i			1.72765i	−0.503793	+	0.863825i	$0.668062\pi$
$198$		0			0
$199$			10.3923i			0.736691i	0.929689	+	0.368345i	$0.120076\pi$
$199$			10.3923i			0.736691i	−0.929689	+	0.368345i	$0.879924\pi$
$200$		0			0
$201$	15.0000	+	8.66025i	1.05802	+	0.610847i
$202$		0			0
$203$	−4.50000	−	0.866025i	−0.315838	−	0.0607831i
$204$	−9.00000	−	5.19615i	−0.630126	−	0.363803i
$205$	6.00000	−	10.3923i	0.419058	−	0.725830i
$206$		0			0
$207$			20.7846i			1.44463i
$208$			20.7846i			1.44115i
$209$	−6.00000	+	10.3923i	−0.415029	+	0.718851i
$210$		0			0
$211$	4.00000	+	6.92820i	0.275371	+	0.476957i	0.970229	−	0.242190i	$-0.0778659\pi$
$211$	4.00000	+	6.92820i	0.275371	+	0.476957i	−0.694857	+	0.719148i	$0.744533\pi$
$212$	−6.00000	+	3.46410i	−0.412082	+	0.237915i
$213$	10.5000	+	18.1865i	0.719448	+	1.24612i
$214$		0			0
$215$	−8.00000			−0.545595
$216$		0			0
$217$	−6.00000	+	6.92820i	−0.407307	+	0.470317i
$218$		0			0
$219$	−1.50000	−	2.59808i	−0.101361	−	0.175562i
$220$	6.00000	−	3.46410i	0.404520	−	0.233550i
$221$	13.5000	−	7.79423i	0.908108	−	0.524297i
$222$		0			0
$223$	16.5000	+	9.52628i	1.10492	+	0.637927i	0.937509	−	0.347960i	$-0.113126\pi$
$223$	16.5000	+	9.52628i	1.10492	+	0.637927i	0.167412	+	0.985887i	$0.446459\pi$
$224$		0			0
$225$	1.50000	+	2.59808i	0.100000	+	0.173205i
$226$		0			0
$227$	1.50000	−	2.59808i	0.0995585	−	0.172440i	−0.811943	−	0.583736i	$-0.801590\pi$
$227$	1.50000	−	2.59808i	0.0995585	−	0.172440i	0.911502	+	0.411296i	$0.134924\pi$
$228$	−6.00000	+	10.3923i	−0.397360	+	0.688247i
$229$	−3.00000	+	1.73205i	−0.198246	+	0.114457i	−0.595837	−	0.803105i	$-0.703180\pi$
$229$	−3.00000	+	1.73205i	−0.198246	+	0.114457i	0.397591	+	0.917563i	$0.369846\pi$
$230$		0			0
$231$	15.0000	−	5.19615i	0.986928	−	0.341882i
$232$		0			0
$233$			6.92820i			0.453882i	0.973909	+	0.226941i	$0.0728724\pi$
$233$			6.92820i			0.453882i	−0.973909	+	0.226941i	$0.927128\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$			13.8564i			0.900070i
$238$		0			0
$239$	1.50000	−	0.866025i	0.0970269	−	0.0560185i	−0.450701	−	0.892675i	$-0.648826\pi$
$239$	1.50000	−	0.866025i	0.0970269	−	0.0560185i	0.547728	+	0.836656i	$0.315493\pi$
$240$	6.00000	−	3.46410i	0.387298	−	0.223607i
$241$	−9.00000	−	5.19615i	−0.579741	−	0.334714i	0.181289	−	0.983430i	$-0.441973\pi$
$241$	−9.00000	−	5.19615i	−0.579741	−	0.334714i	−0.761030	+	0.648716i	$0.775306\pi$
$242$		0			0
$243$	−13.5000	−	7.79423i	−0.866025	−	0.500000i
$244$			13.8564i			0.887066i
$245$	−6.50000	−	2.59808i	−0.415270	−	0.165985i
$246$		0			0
$247$	−9.00000	−	15.5885i	−0.572656	−	0.991870i
$248$		0			0
$249$		−	15.5885i		−	0.987878i
$250$		0			0
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$	15.0000	−	5.19615i	0.944911	−	0.327327i
$253$	24.0000			1.50887
$254$		0			0
$255$	−4.50000	−	2.59808i	−0.281801	−	0.162698i
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	7.50000	+	12.9904i	0.467837	+	0.810318i	0.999325	−	0.0367485i	$-0.0117000\pi$
$257$	7.50000	+	12.9904i	0.467837	+	0.810318i	−0.531487	+	0.847066i	$0.678367\pi$
$258$		0			0
$259$	−25.0000	+	8.66025i	−1.55342	+	0.538122i
$260$			10.3923i			0.644503i
$261$	4.50000	−	2.59808i	0.278543	−	0.160817i
$262$		0			0
$263$	−3.00000	−	1.73205i	−0.184988	−	0.106803i	0.404646	−	0.914473i	$-0.367395\pi$
$263$	−3.00000	−	1.73205i	−0.184988	−	0.106803i	−0.589634	+	0.807671i	$0.700728\pi$
$264$		0			0
$265$	−3.00000	+	1.73205i	−0.184289	+	0.106399i
$266$		0			0
$267$	−9.00000	+	5.19615i	−0.550791	+	0.317999i
$268$	10.0000	−	17.3205i	0.610847	−	1.05802i
$269$	24.0000			1.46331			0.731653	−	0.681677i	$-0.238749\pi$
$269$	24.0000			1.46331			0.731653	+	0.681677i	$0.238749\pi$
$270$		0			0
$271$		−	3.46410i		−	0.210429i	−0.994450	−	0.105215i	$-0.966447\pi$
$271$		−	3.46410i		−	0.210429i	0.994450	−	0.105215i	$-0.0335529\pi$
$272$	−6.00000	+	10.3923i	−0.363803	+	0.630126i
$273$	−4.50000	+	23.3827i	−0.272352	+	1.41518i
$274$		0			0
$275$	3.00000	−	1.73205i	0.180907	−	0.104447i
$276$	24.0000			1.44463
$277$	−13.0000	+	22.5167i	−0.781094	+	1.35290i	0.150210	+	0.988654i	$0.452005\pi$
$277$	−13.0000	+	22.5167i	−0.781094	+	1.35290i	−0.931305	+	0.364241i	$0.881328\pi$
$278$		0			0
$279$		−	10.3923i		−	0.622171i
$280$		0			0
$281$	12.0000	+	6.92820i	0.715860	+	0.413302i	0.813227	−	0.581947i	$-0.197709\pi$
$281$	12.0000	+	6.92820i	0.715860	+	0.413302i	−0.0973670	+	0.995249i	$0.531042\pi$
$282$		0			0
$283$	3.00000	−	1.73205i	0.178331	−	0.102960i	−0.408177	−	0.912903i	$-0.633835\pi$
$283$	3.00000	−	1.73205i	0.178331	−	0.102960i	0.586509	+	0.809943i	$0.300502\pi$
$284$	21.0000	−	12.1244i	1.24612	−	0.719448i
$285$	−3.00000	+	5.19615i	−0.177705	+	0.307794i
$286$		0			0
$287$	−24.0000	−	20.7846i	−1.41668	−	1.22688i
$288$		0			0
$289$	−8.00000			−0.470588
$290$		0			0
$291$	12.0000			0.703452
$292$	−3.00000	+	1.73205i	−0.175562	+	0.101361i
$293$	−4.50000	−	7.79423i	−0.262893	−	0.455344i	0.704117	−	0.710084i	$-0.251343\pi$
$293$	−4.50000	−	7.79423i	−0.262893	−	0.455344i	−0.967009	+	0.254741i	$0.918010\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−9.00000	+	15.5885i	−0.522233	+	0.904534i
$298$		0			0
$299$	−18.0000	+	31.1769i	−1.04097	+	1.80301i
$300$	3.00000	−	1.73205i	0.173205	−	0.100000i
$301$	−4.00000	+	20.7846i	−0.230556	+	1.19800i
$302$		0			0
$303$			31.1769i			1.79107i
$304$	12.0000	+	6.92820i	0.688247	+	0.397360i
$305$			6.92820i			0.396708i
$306$		0			0
$307$		−	22.5167i		−	1.28509i	−0.766246	−	0.642547i	$-0.777878\pi$
$307$		−	22.5167i		−	1.28509i	0.766246	−	0.642547i	$-0.222122\pi$
$308$	−6.00000	−	17.3205i	−0.341882	−	0.986928i
$309$	7.50000	−	12.9904i	0.426660	−	0.738997i
$310$		0			0
$311$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$311$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$312$		0			0
$313$	4.50000	+	2.59808i	0.254355	+	0.146852i	0.621757	−	0.783210i	$-0.286419\pi$
$313$	4.50000	+	2.59808i	0.254355	+	0.146852i	−0.367402	+	0.930062i	$0.619753\pi$
$314$		0			0
$315$	7.50000	−	2.59808i	0.422577	−	0.146385i
$316$	16.0000			0.900070
$317$	21.0000	+	12.1244i	1.17948	+	0.680972i	0.955894	−	0.293713i	$-0.0948910\pi$
$317$	21.0000	+	12.1244i	1.17948	+	0.680972i	0.223584	+	0.974685i	$0.428224\pi$
$318$		0			0
$319$	−3.00000	−	5.19615i	−0.167968	−	0.290929i
$320$	−4.00000	−	6.92820i	−0.223607	−	0.387298i
$321$	−15.0000	−	25.9808i	−0.837218	−	1.45010i
$322$		0			0
$323$		−	10.3923i		−	0.578243i
$324$	−9.00000	+	15.5885i	−0.500000	+	0.866025i
$325$			5.19615i			0.288231i
$326$		0			0
$327$	−3.00000	+	1.73205i	−0.165900	+	0.0957826i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−0.500000	+	0.866025i	−0.0274825	+	0.0476011i	−0.879440	−	0.476011i	$-0.842082\pi$
$331$	−0.500000	+	0.866025i	−0.0274825	+	0.0476011i	0.851957	+	0.523612i	$0.175416\pi$
$332$	−18.0000			−0.987878
$333$	15.0000	−	25.9808i	0.821995	−	1.42374i
$334$		0			0
$335$	5.00000	−	8.66025i	0.273179	−	0.473160i
$336$	−6.00000	−	17.3205i	−0.327327	−	0.944911i
$337$	4.00000	+	6.92820i	0.217894	+	0.377403i	0.954164	−	0.299285i	$-0.0967480\pi$
$337$	4.00000	+	6.92820i	0.217894	+	0.377403i	−0.736270	+	0.676688i	$0.763415\pi$
$338$		0			0
$339$	−9.00000	+	15.5885i	−0.488813	+	0.846649i
$340$	−3.00000	+	5.19615i	−0.162698	+	0.281801i
$341$	−12.0000			−0.649836
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$		0			0
$345$	12.0000			0.646058
$346$		0			0
$347$	−21.0000	+	12.1244i	−1.12734	+	0.650870i	−0.943264	−	0.332043i	$-0.892262\pi$
$347$	−21.0000	+	12.1244i	−1.12734	+	0.650870i	−0.184075	+	0.982912i	$0.558929\pi$
$348$	−3.00000	−	5.19615i	−0.160817	−	0.278543i
$349$	6.00000	+	3.46410i	0.321173	+	0.185429i	0.651915	−	0.758292i	$-0.273966\pi$
$349$	6.00000	+	3.46410i	0.321173	+	0.185429i	−0.330743	+	0.943721i	$0.607299\pi$
$350$		0			0
$351$	−13.5000	−	23.3827i	−0.720577	−	1.24808i
$352$		0			0
$353$	1.50000	−	2.59808i	0.0798369	−	0.138282i	−0.823343	−	0.567545i	$-0.807893\pi$
$353$	1.50000	−	2.59808i	0.0798369	−	0.138282i	0.903179	+	0.429263i	$0.141227\pi$
$354$		0			0
$355$	10.5000	−	6.06218i	0.557282	−	0.321747i
$356$	6.00000	+	10.3923i	0.317999	+	0.550791i
$357$	−9.00000	+	10.3923i	−0.476331	+	0.550019i
$358$		0			0
$359$			31.1769i			1.64545i	0.568436	+	0.822727i	$0.307549\pi$
$359$			31.1769i			1.64545i	−0.568436	+	0.822727i	$0.692451\pi$
$360$		0			0
$361$	7.00000			0.368421
$362$		0			0
$363$	1.50000	+	0.866025i	0.0787296	+	0.0454545i
$364$	27.0000	+	5.19615i	1.41518	+	0.272352i
$365$	−1.50000	+	0.866025i	−0.0785136	+	0.0453298i
$366$		0			0
$367$	22.5000	+	12.9904i	1.17449	+	0.678092i	0.954734	−	0.297462i	$-0.0961403\pi$
$367$	22.5000	+	12.9904i	1.17449	+	0.678092i	0.219757	+	0.975555i	$0.429474\pi$
$368$		−	27.7128i		−	1.44463i
$369$	36.0000			1.87409
$370$		0			0
$371$	3.00000	+	8.66025i	0.155752	+	0.449618i
$372$	−12.0000			−0.622171
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	0.913147	−	0.407630i	$-0.133645\pi$
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	−0.809591	+	0.586994i	$0.800311\pi$
$374$		0			0
$375$	1.50000	−	0.866025i	0.0774597	−	0.0447214i
$376$		0			0
$377$	9.00000			0.463524
$378$		0			0
$379$	−5.00000			−0.256833			−0.128416	−	0.991720i	$-0.540989\pi$
$379$	−5.00000			−0.256833			−0.128416	+	0.991720i	$0.540989\pi$
$380$	6.00000	+	3.46410i	0.307794	+	0.177705i
$381$	3.00000	−	1.73205i	0.153695	−	0.0887357i
$382$		0			0
$383$	7.50000	+	12.9904i	0.383232	+	0.663777i	0.991522	−	0.129937i	$-0.0414776\pi$
$383$	7.50000	+	12.9904i	0.383232	+	0.663777i	−0.608290	+	0.793715i	$0.708144\pi$
$384$		0			0
$385$	−3.00000	−	8.66025i	−0.152894	−	0.441367i
$386$		0			0
$387$	−12.0000	−	20.7846i	−0.609994	−	1.05654i
$388$		−	13.8564i		−	0.703452i
$389$	−24.0000	−	13.8564i	−1.21685	−	0.702548i	−0.252606	−	0.967569i	$-0.581288\pi$
$389$	−24.0000	−	13.8564i	−1.21685	−	0.702548i	−0.964242	+	0.265022i	$0.914621\pi$
$390$		0			0
$391$	−18.0000	+	10.3923i	−0.910299	+	0.525561i
$392$		0			0
$393$	−9.00000	−	5.19615i	−0.453990	−	0.262111i
$394$		0			0
$395$	8.00000			0.402524
$396$	18.0000	+	10.3923i	0.904534	+	0.522233i
$397$			32.9090i			1.65165i	0.563924	+	0.825827i	$0.309291\pi$
$397$			32.9090i			1.65165i	−0.563924	+	0.825827i	$0.690709\pi$
$398$		0			0
$399$	12.0000	+	10.3923i	0.600751	+	0.520266i
$400$	−2.00000	−	3.46410i	−0.100000	−	0.173205i
$401$	4.50000	−	2.59808i	0.224719	−	0.129742i	−0.383414	−	0.923576i	$-0.625252\pi$
$401$	4.50000	−	2.59808i	0.224719	−	0.129742i	0.608134	+	0.793835i	$0.291919\pi$
$402$		0			0
$403$	9.00000	−	15.5885i	0.448322	−	0.776516i
$404$	36.0000			1.79107
$405$	−4.50000	+	7.79423i	−0.223607	+	0.387298i
$406$		0			0
$407$	−30.0000	−	17.3205i	−1.48704	−	0.858546i
$408$		0			0
$409$	−18.0000	+	10.3923i	−0.890043	+	0.513866i	−0.873956	−	0.486004i	$-0.838454\pi$
$409$	−18.0000	+	10.3923i	−0.890043	+	0.513866i	−0.0160862	+	0.999871i	$0.505121\pi$
$410$		0			0
$411$	−6.00000			−0.295958
$412$	−15.0000	−	8.66025i	−0.738997	−	0.426660i
$413$		0			0
$414$		0			0
$415$	−9.00000			−0.441793
$416$		0			0
$417$	−6.00000	+	10.3923i	−0.293821	+	0.508913i
$418$		0			0
$419$	−15.0000	−	25.9808i	−0.732798	−	1.26924i	−0.955683	−	0.294398i	$-0.904881\pi$
$419$	−15.0000	−	25.9808i	−0.732798	−	1.26924i	0.222885	−	0.974845i	$-0.428453\pi$
$420$	−3.00000	−	8.66025i	−0.146385	−	0.422577i
$421$	11.0000	−	19.0526i	0.536107	−	0.928565i	−0.463002	−	0.886357i	$-0.653228\pi$
$421$	11.0000	−	19.0526i	0.536107	−	0.928565i	0.999109	−	0.0422075i	$-0.0134391\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−1.50000	+	2.59808i	−0.0727607	+	0.126025i
$426$		0			0
$427$	18.0000	+	3.46410i	0.871081	+	0.167640i
$428$	−30.0000	+	17.3205i	−1.45010	+	0.837218i
$429$	−27.0000	+	15.5885i	−1.30357	+	0.752618i
$430$		0			0
$431$		−	15.5885i		−	0.750870i	−0.926849	−	0.375435i	$-0.877493\pi$
$431$		−	15.5885i		−	0.750870i	0.926849	−	0.375435i	$-0.122507\pi$
$432$	18.0000	+	10.3923i	0.866025	+	0.500000i
$433$		−	34.6410i		−	1.66474i	−0.554220	−	0.832370i	$-0.686983\pi$
$433$		−	34.6410i		−	1.66474i	0.554220	−	0.832370i	$-0.313017\pi$
$434$		0			0
$435$	−1.50000	−	2.59808i	−0.0719195	−	0.124568i
$436$	2.00000	+	3.46410i	0.0957826	+	0.165900i
$437$	12.0000	+	20.7846i	0.574038	+	0.994263i
$438$		0			0
$439$	−6.00000	−	3.46410i	−0.286364	−	0.165333i	0.349937	−	0.936773i	$-0.386203\pi$
$439$	−6.00000	−	3.46410i	−0.286364	−	0.165333i	−0.636301	+	0.771441i	$0.719536\pi$
$440$		0			0
$441$	−3.00000	−	20.7846i	−0.142857	−	0.989743i
$442$		0			0
$443$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$443$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$444$	−30.0000	−	17.3205i	−1.42374	−	0.821995i
$445$	3.00000	+	5.19615i	0.142214	+	0.246321i
$446$		0			0
$447$	4.50000	−	7.79423i	0.212843	−	0.368654i
$448$	−20.0000	+	6.92820i	−0.944911	+	0.327327i
$449$			36.3731i			1.71655i	0.513189	+	0.858276i	$0.328464\pi$
$449$			36.3731i			1.71655i	−0.513189	+	0.858276i	$0.671536\pi$
$450$		0			0
$451$		−	41.5692i		−	1.95742i
$452$	18.0000	+	10.3923i	0.846649	+	0.488813i
$453$			32.9090i			1.54620i
$454$		0			0
$455$	13.5000	+	2.59808i	0.632890	+	0.121800i
$456$		0			0
$457$	10.0000	−	17.3205i	0.467780	−	0.810219i	−0.531542	−	0.847032i	$-0.678387\pi$
$457$	10.0000	−	17.3205i	0.467780	−	0.810219i	0.999322	+	0.0368128i	$0.0117205\pi$
$458$		0			0
$459$		−	15.5885i		−	0.727607i
$460$		−	13.8564i		−	0.646058i
$461$	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
$463$	11.0000	+	19.0526i	0.511213	+	0.885448i	0.999916	+	0.0129968i	$0.00413714\pi$
$463$	11.0000	+	19.0526i	0.511213	+	0.885448i	−0.488702	+	0.872451i	$0.662530\pi$
$464$	−6.00000	+	3.46410i	−0.278543	+	0.160817i
$465$	−6.00000			−0.278243
$466$		0			0
$467$	36.0000			1.66588			0.832941	−	0.553362i	$-0.186655\pi$
$467$	36.0000			1.66588			0.832941	+	0.553362i	$0.186655\pi$
$468$	−27.0000	+	15.5885i	−1.24808	+	0.720577i
$469$	−20.0000	−	17.3205i	−0.923514	−	0.799787i
$470$		0			0
$471$	−7.50000	+	12.9904i	−0.345582	+	0.598565i
$472$		0			0
$473$	−24.0000	+	13.8564i	−1.10352	+	0.637118i
$474$		0			0
$475$	3.00000	+	1.73205i	0.137649	+	0.0794719i
$476$	12.0000	+	10.3923i	0.550019	+	0.476331i
$477$	−9.00000	−	5.19615i	−0.412082	−	0.237915i
$478$		0			0
$479$	−9.00000	+	15.5885i	−0.411220	+	0.712255i	−0.995023	−	0.0996406i	$-0.968231\pi$
$479$	−9.00000	+	15.5885i	−0.411220	+	0.712255i	0.583803	+	0.811895i	$0.301564\pi$
$480$		0			0
$481$	45.0000	−	25.9808i	2.05182	−	1.18462i
$482$		0			0
$483$	6.00000	−	31.1769i	0.273009	−	1.41860i
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$		−	6.92820i		−	0.314594i
$486$		0			0
$487$	−2.00000			−0.0906287			−0.0453143	−	0.998973i	$-0.514429\pi$
$487$	−2.00000			−0.0906287			−0.0453143	+	0.998973i	$0.514429\pi$
$488$		0			0
$489$	−6.00000	+	3.46410i	−0.271329	+	0.156652i
$490$		0			0
$491$	−19.5000	+	11.2583i	−0.880023	+	0.508081i	−0.870666	−	0.491875i	$-0.836312\pi$
$491$	−19.5000	+	11.2583i	−0.880023	+	0.508081i	−0.00935679	+	0.999956i	$0.502978\pi$
$492$		−	41.5692i		−	1.87409i
$493$	4.50000	+	2.59808i	0.202670	+	0.117011i
$494$		0			0
$495$	9.00000	+	5.19615i	0.404520	+	0.233550i
$496$			13.8564i			0.622171i
$497$	−10.5000	−	30.3109i	−0.470989	−	1.35963i
$498$		0			0
$499$	5.50000	+	9.52628i	0.246214	+	0.426455i	0.962472	−	0.271380i	$-0.0874801\pi$
$499$	5.50000	+	9.52628i	0.246214	+	0.426455i	−0.716258	+	0.697835i	$0.754147\pi$
$500$	−1.00000	−	1.73205i	−0.0447214	−	0.0774597i
$501$	−13.5000	−	7.79423i	−0.603136	−	0.348220i
$502$		0			0
$503$	−21.0000			−0.936344			−0.468172	−	0.883637i	$-0.655087\pi$
$503$	−21.0000			−0.936344			−0.468172	+	0.883637i	$0.655087\pi$
$504$		0			0
$505$	18.0000			0.800989
$506$		0			0
$507$		−	24.2487i		−	1.07692i
$508$	−2.00000	−	3.46410i	−0.0887357	−	0.153695i
$509$	−3.00000	−	5.19615i	−0.132973	−	0.230315i	0.791849	−	0.610718i	$-0.209119\pi$
$509$	−3.00000	−	5.19615i	−0.132973	−	0.230315i	−0.924821	+	0.380402i	$0.875786\pi$
$510$		0			0
$511$	1.50000	+	4.33013i	0.0663561	+	0.191554i
$512$		0			0
$513$	−18.0000			−0.794719
$514$		0			0
$515$	−7.50000	−	4.33013i	−0.330489	−	0.190808i
$516$	−24.0000	+	13.8564i	−1.05654	+	0.609994i
$517$		0			0
$518$		0			0
$519$		−	36.3731i		−	1.59660i
$520$		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
$523$			8.66025i			0.378686i	0.981911	+	0.189343i	$0.0606359\pi$
$523$			8.66025i			0.378686i	−0.981911	+	0.189343i	$0.939364\pi$
$524$	−6.00000	+	10.3923i	−0.262111	+	0.453990i
$525$	−1.50000	−	4.33013i	−0.0654654	−	0.188982i
$526$		0			0
$527$	9.00000	−	5.19615i	0.392046	−	0.226348i
$528$	12.0000	−	20.7846i	0.522233	−	0.904534i
$529$	12.5000	−	21.6506i	0.543478	−	0.941332i
$530$		0			0
$531$		0			0
$532$	12.0000	−	13.8564i	0.520266	−	0.600751i
$533$	54.0000	+	31.1769i	2.33900	+	1.35042i
$534$		0			0
$535$	−15.0000	+	8.66025i	−0.648507	+	0.374415i
$536$		0			0
$537$	−13.5000	−	23.3827i	−0.582568	−	1.00904i
$538$		0			0
$539$	−24.0000	+	3.46410i	−1.03375	+	0.149209i
$540$	9.00000	+	5.19615i	0.387298	+	0.223607i
$541$	17.0000			0.730887			0.365444	−	0.930834i	$-0.380917\pi$
$541$	17.0000			0.730887			0.365444	+	0.930834i	$0.380917\pi$
$542$		0			0
$543$	−9.00000	−	15.5885i	−0.386227	−	0.668965i
$544$		0			0
$545$	1.00000	+	1.73205i	0.0428353	+	0.0741929i
$546$		0			0
$547$	11.0000	−	19.0526i	0.470326	−	0.814629i	−0.529098	−	0.848561i	$-0.677470\pi$
$547$	11.0000	−	19.0526i	0.470326	−	0.814629i	0.999424	+	0.0339321i	$0.0108030\pi$
$548$			6.92820i			0.295958i
$549$	−18.0000	+	10.3923i	−0.768221	+	0.443533i
$550$		0			0
$551$	3.00000	−	5.19615i	0.127804	−	0.221364i
$552$		0			0
$553$	4.00000	−	20.7846i	0.170097	−	0.883852i
$554$		0			0
$555$	−15.0000	−	8.66025i	−0.636715	−	0.367607i
$556$	12.0000	+	6.92820i	0.508913	+	0.293821i
$557$			20.7846i			0.880672i	0.897833	+	0.440336i	$0.145141\pi$
$557$			20.7846i			0.880672i	−0.897833	+	0.440336i	$0.854859\pi$
$558$		0			0
$559$		−	41.5692i		−	1.75819i
$560$	−10.0000	+	3.46410i	−0.422577	+	0.146385i
$561$	−18.0000			−0.759961
$562$		0			0
$563$	10.5000	+	18.1865i	0.442522	+	0.766471i	0.997876	−	0.0651433i	$-0.0207504\pi$
$563$	10.5000	+	18.1865i	0.442522	+	0.766471i	−0.555354	+	0.831614i	$0.687417\pi$
$564$		0			0
$565$	9.00000	+	5.19615i	0.378633	+	0.218604i
$566$		0			0
$567$	18.0000	+	15.5885i	0.755929	+	0.654654i
$568$		0			0
$569$	−31.5000	−	18.1865i	−1.32055	−	0.762419i	−0.336733	−	0.941600i	$-0.609322\pi$
$569$	−31.5000	−	18.1865i	−1.32055	−	0.762419i	−0.983816	+	0.179181i	$0.942655\pi$
$570$		0			0
$571$	15.5000	+	26.8468i	0.648655	+	1.12350i	0.983444	+	0.181210i	$0.0580014\pi$
$571$	15.5000	+	26.8468i	0.648655	+	1.12350i	−0.334790	+	0.942293i	$0.608665\pi$
$572$	18.0000	+	31.1769i	0.752618	+	1.30357i
$573$	21.0000			0.877288
$574$		0			0
$575$		−	6.92820i		−	0.288926i
$576$	12.0000	−	20.7846i	0.500000	−	0.866025i
$577$		−	13.8564i		−	0.576850i	−0.957503	−	0.288425i	$-0.906868\pi$
$577$		−	13.8564i		−	0.576850i	0.957503	−	0.288425i	$-0.0931316\pi$
$578$		0			0
$579$	−6.00000	−	3.46410i	−0.249351	−	0.143963i
$580$	−3.00000	+	1.73205i	−0.124568	+	0.0719195i
$581$	−4.50000	+	23.3827i	−0.186691	+	0.970077i
$582$		0			0
$583$	−6.00000	+	10.3923i	−0.248495	+	0.430405i
$584$		0			0
$585$	−13.5000	+	7.79423i	−0.558156	+	0.322252i
$586$		0			0
$587$	−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	$0.246324\pi$
$588$	−24.0000	+	3.46410i	−0.989743	+	0.142857i
$589$	−6.00000	−	10.3923i	−0.247226	−	0.428207i
$590$		0			0
$591$	21.0000	+	36.3731i	0.863825	+	1.49619i
$592$	−20.0000	+	34.6410i	−0.821995	+	1.42374i
$593$	15.0000			0.615976			0.307988	−	0.951390i	$-0.400344\pi$
$593$	15.0000			0.615976			0.307988	+	0.951390i	$0.400344\pi$
$594$		0			0
$595$	6.00000	+	5.19615i	0.245976	+	0.213021i
$596$	−9.00000	−	5.19615i	−0.368654	−	0.212843i
$597$	9.00000	+	15.5885i	0.368345	+	0.637993i
$598$		0			0
$599$	31.5000	−	18.1865i	1.28706	−	0.743082i	0.308927	−	0.951086i	$-0.400030\pi$
$599$	31.5000	−	18.1865i	1.28706	−	0.743082i	0.978128	+	0.208004i	$0.0666967\pi$
$600$		0			0
$601$	−15.0000	−	8.66025i	−0.611863	−	0.353259i	0.161831	−	0.986818i	$-0.448260\pi$
$601$	−15.0000	−	8.66025i	−0.611863	−	0.353259i	−0.773694	+	0.633559i	$0.781593\pi$
$602$		0			0
$603$	30.0000			1.22169
$604$	38.0000			1.54620
$605$	0.500000	−	0.866025i	0.0203279	−	0.0352089i
$606$		0			0
$607$	−34.5000	+	19.9186i	−1.40031	+	0.808470i	−0.994424	−	0.105453i	$-0.966371\pi$
$607$	−34.5000	+	19.9186i	−1.40031	+	0.808470i	−0.405887	+	0.913923i	$0.633038\pi$
$608$		0			0
$609$	−7.50000	+	2.59808i	−0.303915	+	0.105279i
$610$		0			0
$611$		0			0
$612$	−18.0000			−0.727607
$613$	−16.0000			−0.646234			−0.323117	−	0.946359i	$-0.604731\pi$
$613$	−16.0000			−0.646234			−0.323117	+	0.946359i	$0.604731\pi$
$614$		0			0
$615$		−	20.7846i		−	0.838116i
$616$		0			0
$617$	12.0000	−	6.92820i	0.483102	−	0.278919i	−0.238606	−	0.971116i	$-0.576691\pi$
$617$	12.0000	−	6.92820i	0.483102	−	0.278919i	0.721708	+	0.692197i	$0.243357\pi$
$618$		0			0
$619$	33.0000	+	19.0526i	1.32638	+	0.765787i	0.984738	−	0.174042i	$-0.0556830\pi$
$619$	33.0000	+	19.0526i	1.32638	+	0.765787i	0.341644	+	0.939829i	$0.389016\pi$
$620$			6.92820i			0.278243i
$621$	18.0000	+	31.1769i	0.722315	+	1.25109i
$622$		0			0
$623$	15.0000	−	5.19615i	0.600962	−	0.208179i
$624$	18.0000	+	31.1769i	0.720577	+	1.24808i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$			20.7846i			0.830057i
$628$	15.0000	+	8.66025i	0.598565	+	0.345582i
$629$	30.0000			1.19618
$630$		0			0
$631$	−40.0000			−1.59237			−0.796187	−	0.605050i	$-0.793153\pi$
$631$	−40.0000			−1.59237			−0.796187	+	0.605050i	$0.793153\pi$
$632$		0			0
$633$	12.0000	+	6.92820i	0.476957	+	0.275371i
$634$		0			0
$635$	−1.00000	−	1.73205i	−0.0396838	−	0.0687343i
$636$	−6.00000	+	10.3923i	−0.237915	+	0.412082i
$637$	13.5000	−	33.7750i	0.534889	−	1.33821i
$638$		0			0
$639$	31.5000	+	18.1865i	1.24612	+	0.719448i
$640$		0			0
$641$	18.0000	+	10.3923i	0.710957	+	0.410471i	0.811415	−	0.584470i	$-0.198698\pi$
$641$	18.0000	+	10.3923i	0.710957	+	0.410471i	−0.100458	+	0.994941i	$0.532031\pi$
$642$		0			0
$643$	−27.0000	+	15.5885i	−1.06478	+	0.614749i	−0.926750	−	0.375680i	$-0.877409\pi$
$643$	−27.0000	+	15.5885i	−1.06478	+	0.614749i	−0.138027	+	0.990429i	$0.544076\pi$
$644$	−36.0000	−	6.92820i	−1.41860	−	0.273009i
$645$	−12.0000	+	6.92820i	−0.472500	+	0.272798i
$646$		0			0
$647$	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
$649$		0			0
$650$		0			0
$651$	−3.00000	+	15.5885i	−0.117579	+	0.610960i
$652$	4.00000	+	6.92820i	0.156652	+	0.271329i
$653$	−6.00000	+	3.46410i	−0.234798	+	0.135561i	−0.612784	−	0.790251i	$-0.709950\pi$
$653$	−6.00000	+	3.46410i	−0.234798	+	0.135561i	0.377985	+	0.925812i	$0.376617\pi$
$654$		0			0
$655$	−3.00000	+	5.19615i	−0.117220	+	0.203030i
$656$	−48.0000			−1.87409
$657$	−4.50000	−	2.59808i	−0.175562	−	0.101361i
$658$		0			0
$659$	1.50000	+	0.866025i	0.0584317	+	0.0337356i	0.528931	−	0.848665i	$-0.322593\pi$
$659$	1.50000	+	0.866025i	0.0584317	+	0.0337356i	−0.470500	+	0.882400i	$0.655926\pi$
$660$	6.00000	−	10.3923i	0.233550	−	0.404520i
$661$	−39.0000	+	22.5167i	−1.51692	+	0.875797i	−0.517122	+	0.855912i	$0.672997\pi$
$661$	−39.0000	+	22.5167i	−1.51692	+	0.875797i	−0.999802	+	0.0198848i	$0.993670\pi$
$662$		0			0
$663$	13.5000	−	23.3827i	0.524297	−	0.908108i
$664$		0			0
$665$	6.00000	−	6.92820i	0.232670	−	0.268664i
$666$		0			0
$667$	−12.0000			−0.464642
$668$	−9.00000	+	15.5885i	−0.348220	+	0.603136i
$669$	33.0000			1.27585
$670$		0			0
$671$	12.0000	+	20.7846i	0.463255	+	0.802381i
$672$		0			0
$673$	4.00000	−	6.92820i	0.154189	−	0.267063i	−0.778575	−	0.627552i	$-0.784057\pi$
$673$	4.00000	−	6.92820i	0.154189	−	0.267063i	0.932763	+	0.360489i	$0.117390\pi$
$674$		0			0
$675$	4.50000	+	2.59808i	0.173205	+	0.100000i
$676$	−28.0000			−1.07692
$677$	10.5000	−	18.1865i	0.403548	−	0.698965i	−0.590603	−	0.806962i	$-0.701110\pi$
$677$	10.5000	−	18.1865i	0.403548	−	0.698965i	0.994151	+	0.107997i	$0.0344436\pi$
$678$		0			0
$679$	−18.0000	−	3.46410i	−0.690777	−	0.132940i
$680$		0			0
$681$		−	5.19615i		−	0.199117i
$682$		0			0
$683$		−	3.46410i		−	0.132550i	−0.997801	−	0.0662751i	$-0.978889\pi$
$683$		−	3.46410i		−	0.132550i	0.997801	−	0.0662751i	$-0.0211115\pi$
$684$			20.7846i			0.794719i
$685$			3.46410i			0.132357i
$686$		0			0
$687$	−3.00000	+	5.19615i	−0.114457	+	0.198246i
$688$	16.0000	+	27.7128i	0.609994	+	1.05654i
$689$	−9.00000	−	15.5885i	−0.342873	−	0.593873i
$690$		0			0
$691$	36.0000	+	20.7846i	1.36950	+	0.790684i	0.990865	−	0.134860i	$-0.0430585\pi$
$691$	36.0000	+	20.7846i	1.36950	+	0.790684i	0.378640	+	0.925544i	$0.376392\pi$
$692$	−42.0000			−1.59660
$693$	18.0000	−	20.7846i	0.683763	−	0.789542i
$694$		0			0
$695$	6.00000	+	3.46410i	0.227593	+	0.131401i
$696$		0			0
$697$	18.0000	+	31.1769i	0.681799	+	1.18091i
$698$		0			0
$699$	6.00000	+	10.3923i	0.226941	+	0.393073i
$700$	−5.00000	+	1.73205i	−0.188982	+	0.0654654i
$701$		−	12.1244i		−	0.457931i	−0.973435	−	0.228965i	$-0.926466\pi$
$701$		−	12.1244i		−	0.457931i	0.973435	−	0.228965i	$-0.0735342\pi$
$702$		0			0
$703$		−	34.6410i		−	1.30651i
$704$	−24.0000	−	13.8564i	−0.904534	−	0.522233i
$705$		0			0
$706$		0			0
$707$	9.00000	−	46.7654i	0.338480	−	1.75879i
$708$		0			0
$709$	−0.500000	+	0.866025i	−0.0187779	+	0.0325243i	−0.875262	−	0.483650i	$-0.839311\pi$
$709$	−0.500000	+	0.866025i	−0.0187779	+	0.0325243i	0.856484	+	0.516174i	$0.172644\pi$
$710$		0			0
$711$	12.0000	+	20.7846i	0.450035	+	0.779484i
$712$		0			0
$713$	−12.0000	+	20.7846i	−0.449404	+	0.778390i
$714$		0			0
$715$	9.00000	+	15.5885i	0.336581	+	0.582975i
$716$	−27.0000	+	15.5885i	−1.00904	+	0.582568i
$717$	1.50000	−	2.59808i	0.0560185	−	0.0970269i
$718$		0			0
$719$	−6.00000			−0.223762			−0.111881	−	0.993722i	$-0.535688\pi$
$719$	−6.00000			−0.223762			−0.111881	+	0.993722i	$0.535688\pi$
$720$	6.00000	−	10.3923i	0.223607	−	0.387298i
$721$	−15.0000	+	17.3205i	−0.558629	+	0.645049i
$722$		0			0
$723$	−18.0000			−0.669427
$724$	−18.0000	+	10.3923i	−0.668965	+	0.386227i
$725$	−1.50000	+	0.866025i	−0.0557086	+	0.0321634i
$726$		0			0
$727$	37.5000	+	21.6506i	1.39080	+	0.802978i	0.993404	−	0.114670i	$-0.0365812\pi$
$727$	37.5000	+	21.6506i	1.39080	+	0.802978i	0.397394	+	0.917648i	$0.369914\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	12.0000	−	20.7846i	0.443836	−	0.768747i
$732$	12.0000	+	20.7846i	0.443533	+	0.768221i
$733$	−13.5000	+	7.79423i	−0.498634	+	0.287886i	−0.728149	−	0.685419i	$-0.759619\pi$
$733$	−13.5000	+	7.79423i	−0.498634	+	0.287886i	0.229515	+	0.973305i	$0.426286\pi$
$734$		0			0
$735$	−12.0000	+	1.73205i	−0.442627	+	0.0638877i
$736$		0			0
$737$		−	34.6410i		−	1.27602i
$738$		0			0
$739$	5.00000			0.183928			0.0919640	−	0.995762i	$-0.470686\pi$
$739$	5.00000			0.183928			0.0919640	+	0.995762i	$0.470686\pi$
$740$	−10.0000	+	17.3205i	−0.367607	+	0.636715i
$741$	−27.0000	−	15.5885i	−0.991870	−	0.572656i
$742$		0			0
$743$	12.0000	−	6.92820i	0.440237	−	0.254171i	−0.263461	−	0.964670i	$-0.584864\pi$
$743$	12.0000	−	6.92820i	0.440237	−	0.254171i	0.703698	+	0.710499i	$0.251531\pi$
$744$		0			0
$745$	−4.50000	−	2.59808i	−0.164867	−	0.0951861i
$746$		0			0
$747$	−13.5000	−	23.3827i	−0.493939	−	0.855528i
$748$			20.7846i			0.759961i
$749$	15.0000	+	43.3013i	0.548088	+	1.58219i
$750$		0			0
$751$	−15.5000	−	26.8468i	−0.565603	−	0.979653i	−0.996993	−	0.0774878i	$-0.975310\pi$
$751$	−15.5000	−	26.8468i	−0.565603	−	0.979653i	0.431390	−	0.902165i	$-0.358023\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	19.0000			0.691481
$756$	18.0000	−	20.7846i	0.654654	−	0.755929i
$757$	16.0000			0.581530			0.290765	−	0.956795i	$-0.406090\pi$
$757$	16.0000			0.581530			0.290765	+	0.956795i	$0.406090\pi$
$758$		0			0
$759$	36.0000	−	20.7846i	1.30672	−	0.754434i
$760$		0			0
$761$	−3.00000	−	5.19615i	−0.108750	−	0.188360i	0.806514	−	0.591215i	$-0.201351\pi$
$761$	−3.00000	−	5.19615i	−0.108750	−	0.188360i	−0.915264	+	0.402854i	$0.868018\pi$
$762$		0			0
$763$	5.00000	−	1.73205i	0.181012	−	0.0627044i
$764$		−	24.2487i		−	0.877288i
$765$	−9.00000			−0.325396
$766$		0			0
$767$		0			0
$768$	−24.0000	−	13.8564i	−0.866025	−	0.500000i
$769$	36.0000	−	20.7846i	1.29819	−	0.749512i	0.318101	−	0.948057i	$-0.396955\pi$
$769$	36.0000	−	20.7846i	1.29819	−	0.749512i	0.980092	+	0.198545i	$0.0636214\pi$
$770$		0			0
$771$	22.5000	+	12.9904i	0.810318	+	0.467837i
$772$	−4.00000	+	6.92820i	−0.143963	+	0.249351i
$773$	−18.0000			−0.647415			−0.323708	−	0.946157i	$-0.604929\pi$
$773$	−18.0000			−0.647415			−0.323708	+	0.946157i	$0.604929\pi$
$774$		0			0
$775$			3.46410i			0.124434i
$776$		0			0
$777$	−30.0000	+	34.6410i	−1.07624	+	1.24274i
$778$		0			0
$779$	36.0000	−	20.7846i	1.28983	−	0.744686i
$780$	9.00000	+	15.5885i	0.322252	+	0.558156i
$781$	21.0000	−	36.3731i	0.751439	−	1.30153i
$782$		0			0
$783$	4.50000	−	7.79423i	0.160817	−	0.278543i
$784$	4.00000	+	27.7128i	0.142857	+	0.989743i
$785$	7.50000	+	4.33013i	0.267686	+	0.154549i
$786$		0			0
$787$	−28.5000	+	16.4545i	−1.01592	+	0.586539i	−0.912918	−	0.408143i	$-0.866177\pi$
$787$	−28.5000	+	16.4545i	−1.01592	+	0.586539i	−0.102997	+	0.994682i	$0.532843\pi$
$788$	42.0000	−	24.2487i	1.49619	−	0.863825i
$789$	−6.00000			−0.213606
$790$		0			0
$791$	18.0000	−	20.7846i	0.640006	−	0.739016i
$792$		0			0
$793$	−36.0000			−1.27840
$794$		0			0
$795$	−3.00000	+	5.19615i	−0.106399	+	0.184289i
$796$	18.0000	−	10.3923i	0.637993	−	0.368345i
$797$	−25.5000	−	44.1673i	−0.903256	−	1.56449i	−0.823241	−	0.567692i	$-0.807836\pi$
$797$	−25.5000	−	44.1673i	−0.903256	−	1.56449i	−0.0800155	−	0.996794i	$-0.525497\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	−9.00000	+	15.5885i	−0.317999	+	0.550791i
$802$		0			0
$803$	−3.00000	+	5.19615i	−0.105868	+	0.183368i
$804$		−	34.6410i		−	1.22169i
$805$	−18.0000	−	3.46410i	−0.634417	−	0.122094i
$806$		0			0
$807$	36.0000	−	20.7846i	1.26726	−	0.731653i
$808$		0			0
$809$			32.9090i			1.15702i	0.815676	+	0.578509i	$0.196365\pi$
$809$			32.9090i			1.15702i	−0.815676	+	0.578509i	$0.803635\pi$
$810$		0			0
$811$			38.1051i			1.33805i	0.743239	+	0.669026i	$0.233288\pi$
$811$			38.1051i			1.33805i	−0.743239	+	0.669026i	$0.766712\pi$
$812$	3.00000	+	8.66025i	0.105279	+	0.303915i
$813$	−3.00000	−	5.19615i	−0.105215	−	0.182237i
$814$		0			0
$815$	2.00000	+	3.46410i	0.0700569	+	0.121342i
$816$			20.7846i			0.727607i
$817$	−24.0000	−	13.8564i	−0.839654	−	0.484774i
$818$		0			0
$819$	13.5000	+	38.9711i	0.471728	+	1.36176i
$820$	−24.0000			−0.838116
$821$	−10.5000	−	6.06218i	−0.366453	−	0.211571i	0.305455	−	0.952207i	$-0.401191\pi$
$821$	−10.5000	−	6.06218i	−0.366453	−	0.211571i	−0.671908	+	0.740635i	$0.734525\pi$
$822$		0			0
$823$	5.00000	+	8.66025i	0.174289	+	0.301877i	0.939915	−	0.341409i	$-0.110904\pi$
$823$	5.00000	+	8.66025i	0.174289	+	0.301877i	−0.765626	+	0.643286i	$0.777571\pi$
$824$		0			0
$825$	3.00000	−	5.19615i	0.104447	−	0.180907i
$826$		0			0
$827$			24.2487i			0.843210i	0.906780	+	0.421605i	$0.138533\pi$
$827$			24.2487i			0.843210i	−0.906780	+	0.421605i	$0.861467\pi$
$828$	36.0000	−	20.7846i	1.25109	−	0.722315i
$829$		−	13.8564i		−	0.481253i	−0.970618	−	0.240626i	$-0.922647\pi$
$829$		−	13.8564i		−	0.481253i	0.970618	−	0.240626i	$-0.0773529\pi$
$830$		0			0
$831$			45.0333i			1.56219i
$832$	36.0000	−	20.7846i	1.24808	−	0.720577i
$833$	16.5000	−	12.9904i	0.571691	−	0.450090i
$834$		0			0
$835$	−4.50000	+	7.79423i	−0.155729	+	0.269730i
$836$	24.0000			0.830057
$837$	−9.00000	−	15.5885i	−0.311086	−	0.538816i
$838$		0			0
$839$	15.0000	−	25.9808i	0.517858	−	0.896956i	−0.481927	−	0.876211i	$-0.660063\pi$
$839$	15.0000	−	25.9808i	0.517858	−	0.896956i	0.999785	−	0.0207443i	$-0.00660359\pi$
$840$		0			0
$841$	−13.0000	−	22.5167i	−0.448276	−	0.776437i
$842$		0			0
$843$	24.0000			0.826604
$844$	8.00000	−	13.8564i	0.275371	−	0.476957i
$845$	−14.0000			−0.481615
$846$		0			0
$847$	−2.00000	−	1.73205i	−0.0687208	−	0.0595140i
$848$	12.0000	+	6.92820i	0.412082	+	0.237915i
$849$	3.00000	−	5.19615i	0.102960	−	0.178331i
$850$		0			0
$851$	−60.0000	+	34.6410i	−2.05677	+	1.18748i
$852$	21.0000	−	36.3731i	0.719448	−	1.24612i
$853$	−36.0000	−	20.7846i	−1.23262	−	0.711651i	−0.265042	−	0.964237i	$-0.585386\pi$
$853$	−36.0000	−	20.7846i	−1.23262	−	0.711651i	−0.967575	+	0.252585i	$0.918719\pi$
$854$		0			0
$855$			10.3923i			0.355409i
$856$		0			0
$857$	1.50000	−	2.59808i	0.0512390	−	0.0887486i	−0.839268	−	0.543718i	$-0.817016\pi$
$857$	1.50000	−	2.59808i	0.0512390	−	0.0887486i	0.890507	+	0.454969i	$0.150350\pi$
$858$		0			0
$859$	−3.00000	+	1.73205i	−0.102359	+	0.0590968i	−0.550305	−	0.834963i	$-0.685489\pi$
$859$	−3.00000	+	1.73205i	−0.102359	+	0.0590968i	0.447947	+	0.894060i	$0.352155\pi$
$860$	8.00000	+	13.8564i	0.272798	+	0.472500i
$861$	−54.0000	−	10.3923i	−1.84032	−	0.354169i
$862$		0			0
$863$		−	17.3205i		−	0.589597i	−0.955559	−	0.294798i	$-0.904747\pi$
$863$		−	17.3205i		−	0.589597i	0.955559	−	0.294798i	$-0.0952525\pi$
$864$		0			0
$865$	−21.0000			−0.714021
$866$		0			0
$867$	−12.0000	+	6.92820i	−0.407541	+	0.235294i
$868$	18.0000	+	3.46410i	0.610960	+	0.117579i
$869$	24.0000	−	13.8564i	0.814144	−	0.470046i
$870$		0			0
$871$	45.0000	+	25.9808i	1.52477	+	0.880325i
$872$		0			0
$873$	18.0000	−	10.3923i	0.609208	−	0.351726i
$874$		0			0
$875$	−2.50000	+	0.866025i	−0.0845154	+	0.0292770i
$876$	−3.00000	+	5.19615i	−0.101361	+	0.175562i
$877$	2.00000	+	3.46410i	0.0675352	+	0.116974i	0.897816	−	0.440371i	$-0.145153\pi$
$877$	2.00000	+	3.46410i	0.0675352	+	0.116974i	−0.830281	+	0.557346i	$0.811820\pi$
$878$		0			0
$879$	−13.5000	−	7.79423i	−0.455344	−	0.262893i
$880$	−12.0000	−	6.92820i	−0.404520	−	0.233550i
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$		0			0
$883$	−26.0000			−0.874970			−0.437485	−	0.899226i	$-0.644131\pi$
$883$	−26.0000			−0.874970			−0.437485	+	0.899226i	$0.644131\pi$
$884$	−27.0000	−	15.5885i	−0.908108	−	0.524297i
$885$		0			0
$886$		0			0
$887$	−24.0000	−	41.5692i	−0.805841	−	1.39576i	−0.915722	−	0.401813i	$-0.868380\pi$
$887$	−24.0000	−	41.5692i	−0.805841	−	1.39576i	0.109881	−	0.993945i	$-0.464953\pi$
$888$		0			0
$889$	−5.00000	+	1.73205i	−0.167695	+	0.0580911i
$890$		0			0
$891$			31.1769i			1.04447i
$892$		−	38.1051i		−	1.27585i
$893$		0			0
$894$		0			0
$895$	−13.5000	+	7.79423i	−0.451255	+	0.260532i
$896$		0			0
$897$			62.3538i			2.08193i
$898$		0			0
$899$	6.00000			0.200111
$900$	3.00000	−	5.19615i	0.100000	−	0.173205i
$901$		−	10.3923i		−	0.346218i
$902$		0			0
$903$	12.0000	+	34.6410i	0.399335	+	1.15278i
$904$		0			0
$905$	−9.00000	+	5.19615i	−0.299170	+	0.172726i
$906$		0			0
$907$	22.0000	−	38.1051i	0.730498	−	1.26526i	−0.226173	−	0.974087i	$-0.572621\pi$
$907$	22.0000	−	38.1051i	0.730498	−	1.26526i	0.956671	−	0.291172i	$-0.0940453\pi$
$908$	−6.00000			−0.199117
$909$	27.0000	+	46.7654i	0.895533	+	1.55111i
$910$		0			0
$911$	−19.5000	−	11.2583i	−0.646064	−	0.373005i	0.140883	−	0.990026i	$-0.455006\pi$
$911$	−19.5000	−	11.2583i	−0.646064	−	0.373005i	−0.786947	+	0.617021i	$0.788339\pi$
$912$	24.0000			0.794719
$913$	−27.0000	+	15.5885i	−0.893570	+	0.515903i
$914$		0			0
$915$	6.00000	+	10.3923i	0.198354	+	0.343559i
$916$	6.00000	+	3.46410i	0.198246	+	0.114457i
$917$	12.0000	+	10.3923i	0.396275	+	0.343184i
$918$		0			0
$919$	−53.0000			−1.74831			−0.874154	−	0.485648i	$-0.838584\pi$
$919$	−53.0000			−1.74831			−0.874154	+	0.485648i	$0.838584\pi$
$920$		0			0
$921$	−19.5000	−	33.7750i	−0.642547	−	1.11292i
$922$		0			0
$923$	31.5000	+	54.5596i	1.03684	+	1.79585i
$924$	−24.0000	−	20.7846i	−0.789542	−	0.683763i
$925$	−5.00000	+	8.66025i	−0.164399	+	0.284747i
$926$		0			0
$927$		−	25.9808i		−	0.853320i
$928$		0			0
$929$	21.0000	−	36.3731i	0.688988	−	1.19336i	−0.283178	−	0.959067i	$-0.591389\pi$
$929$	21.0000	−	36.3731i	0.688988	−	1.19336i	0.972166	−	0.234294i	$-0.0752779\pi$
$930$		0			0
$931$	−15.0000	−	19.0526i	−0.491605	−	0.624422i
$932$	12.0000	−	6.92820i	0.393073	−	0.226941i
$933$		0			0
$934$		0			0
$935$			10.3923i			0.339865i
$936$		0			0
$937$			1.73205i			0.0565836i	0.999600	+	0.0282918i	$0.00900677\pi$
$937$			1.73205i			0.0565836i	−0.999600	+	0.0282918i	$0.990993\pi$
$938$		0			0
$939$	9.00000			0.293704
$940$		0			0
$941$	−21.0000	−	36.3731i	−0.684580	−	1.18573i	−0.973568	−	0.228395i	$-0.926652\pi$
$941$	−21.0000	−	36.3731i	−0.684580	−	1.18573i	0.288988	−	0.957333i	$-0.406681\pi$
$942$		0			0
$943$	−72.0000	−	41.5692i	−2.34464	−	1.35368i
$944$		0			0
$945$	9.00000	−	10.3923i	0.292770	−	0.338062i
$946$		0			0
$947$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$947$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$948$	24.0000	−	13.8564i	0.779484	−	0.450035i
$949$	−4.50000	−	7.79423i	−0.146076	−	0.253011i
$950$		0			0
$951$	42.0000			1.36194
$952$		0			0
$953$		−	48.4974i		−	1.57099i	−0.618871	−	0.785493i	$-0.712410\pi$
$953$		−	48.4974i		−	1.57099i	0.618871	−	0.785493i	$-0.287590\pi$
$954$		0			0
$955$		−	12.1244i		−	0.392335i
$956$	−3.00000	−	1.73205i	−0.0970269	−	0.0560185i
$957$	−9.00000	−	5.19615i	−0.290929	−	0.167968i
$958$		0			0
$959$	9.00000	+	1.73205i	0.290625	+	0.0559308i
$960$	−12.0000	−	6.92820i	−0.387298	−	0.223607i
$961$	−9.50000	+	16.4545i	−0.306452	+	0.530790i
$962$		0			0
$963$	−45.0000	−	25.9808i	−1.45010	−	0.837218i
$964$			20.7846i			0.669427i
$965$	−2.00000	+	3.46410i	−0.0643823	+	0.111513i
$966$		0			0
$967$	−10.0000	−	17.3205i	−0.321578	−	0.556990i	0.659236	−	0.751936i	$-0.270880\pi$
$967$	−10.0000	−	17.3205i	−0.321578	−	0.556990i	−0.980814	+	0.194946i	$0.937547\pi$
$968$		0			0
$969$	−9.00000	−	15.5885i	−0.289122	−	0.500773i
$970$		0			0
$971$	−48.0000			−1.54039			−0.770197	−	0.637806i	$-0.779842\pi$
$971$	−48.0000			−1.54039			−0.770197	+	0.637806i	$0.779842\pi$
$972$			31.1769i			1.00000i
$973$	12.0000	−	13.8564i	0.384702	−	0.444216i
$974$		0			0
$975$	4.50000	+	7.79423i	0.144115	+	0.249615i
$976$	24.0000	−	13.8564i	0.768221	−	0.443533i
$977$	−21.0000	+	12.1244i	−0.671850	+	0.387893i	−0.796777	−	0.604273i	$-0.793463\pi$
$977$	−21.0000	+	12.1244i	−0.671850	+	0.387893i	0.124928	+	0.992166i	$0.460130\pi$
$978$		0			0
$979$	18.0000	+	10.3923i	0.575282	+	0.332140i
$980$	2.00000	+	13.8564i	0.0638877	+	0.442627i
$981$	−3.00000	+	5.19615i	−0.0957826	+	0.165900i
$982$		0			0
$983$	12.0000	−	20.7846i	0.382741	−	0.662926i	−0.608712	−	0.793391i	$-0.708314\pi$
$983$	12.0000	−	20.7846i	0.382741	−	0.662926i	0.991453	+	0.130465i	$0.0416470\pi$
$984$		0			0
$985$	21.0000	−	12.1244i	0.669116	−	0.386314i
$986$		0			0
$987$		0			0
$988$	−18.0000	+	31.1769i	−0.572656	+	0.991870i
$989$			55.4256i			1.76243i
$990$		0			0
$991$	19.0000			0.603555			0.301777	−	0.953378i	$-0.402420\pi$
$991$	19.0000			0.603555			0.301777	+	0.953378i	$0.402420\pi$
$992$		0			0
$993$			1.73205i			0.0549650i
$994$		0			0
$995$	9.00000	−	5.19615i	0.285319	−	0.164729i
$996$	−27.0000	+	15.5885i	−0.855528	+	0.493939i
$997$	22.5000	+	12.9904i	0.712582	+	0.411409i	0.812016	−	0.583635i	$-0.198370\pi$
$997$	22.5000	+	12.9904i	0.712582	+	0.411409i	−0.0994342	+	0.995044i	$0.531703\pi$
$998$		0			0
$999$		−	51.9615i		−	1.64399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bl.g.146.1	yes	2
3.2	odd	2		945.2.bl.d.251.1		2
7.6	odd	2		315.2.bl.f.146.1	yes	2
9.4	even	3		945.2.bl.b.881.1		2
9.5	odd	6		315.2.bl.f.41.1	✓	2
21.20	even	2		945.2.bl.b.251.1		2
63.13	odd	6		945.2.bl.d.881.1		2
63.41	even	6	inner	315.2.bl.g.41.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bl.f.41.1	✓	2	9.5	odd	6
315.2.bl.f.146.1	yes	2	7.6	odd	2
315.2.bl.g.41.1	yes	2	63.41	even	6	inner
315.2.bl.g.146.1	yes	2	1.1	even	1	trivial
945.2.bl.b.251.1		2	21.20	even	2
945.2.bl.b.881.1		2	9.4	even	3
945.2.bl.d.251.1		2	3.2	odd	2
945.2.bl.d.881.1		2	63.13	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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bl (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.50000 + 0.866025i) q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.50000 + 0.866025i) q^{7} +(1.50000 - 2.59808i) q^{9} +(-3.00000 - 1.73205i) q^{11} +(-3.00000 - 1.73205i) q^{12} +(4.50000 - 2.59808i) q^{13} +(-1.50000 - 0.866025i) q^{15} +(-2.00000 + 3.46410i) q^{16} +3.00000 q^{17} -3.46410i q^{19} +(-1.00000 + 1.73205i) q^{20} +(-3.00000 + 3.46410i) q^{21} +(-6.00000 + 3.46410i) q^{23} +(-0.500000 + 0.866025i) q^{25} -5.19615i q^{27} +(4.00000 + 3.46410i) q^{28} +(1.50000 + 0.866025i) q^{29} +(3.00000 - 1.73205i) q^{31} -6.00000 q^{33} +(2.00000 + 1.73205i) q^{35} -6.00000 q^{36} +10.0000 q^{37} +(4.50000 - 7.79423i) q^{39} +(6.00000 + 10.3923i) q^{41} +(4.00000 - 6.92820i) q^{43} +6.92820i q^{44} -3.00000 q^{45} +6.92820i q^{48} +(5.50000 - 4.33013i) q^{49} +(4.50000 - 2.59808i) q^{51} +(-9.00000 - 5.19615i) q^{52} -3.46410i q^{53} +3.46410i q^{55} +(-3.00000 - 5.19615i) q^{57} +3.46410i q^{60} +(-6.00000 - 3.46410i) q^{61} +(-1.50000 + 7.79423i) q^{63} +8.00000 q^{64} +(-4.50000 - 2.59808i) q^{65} +(5.00000 + 8.66025i) q^{67} +(-3.00000 - 5.19615i) q^{68} +(-6.00000 + 10.3923i) q^{69} +12.1244i q^{71} -1.73205i q^{73} +1.73205i q^{75} +(-6.00000 + 3.46410i) q^{76} +(9.00000 + 1.73205i) q^{77} +(-4.00000 + 6.92820i) q^{79} +4.00000 q^{80} +(-4.50000 - 7.79423i) q^{81} +(4.50000 - 7.79423i) q^{83} +(9.00000 + 1.73205i) q^{84} +(-1.50000 - 2.59808i) q^{85} +3.00000 q^{87} -6.00000 q^{89} +(-9.00000 + 10.3923i) q^{91} +(12.0000 + 6.92820i) q^{92} +(3.00000 - 5.19615i) q^{93} +(-3.00000 + 1.73205i) q^{95} +(6.00000 + 3.46410i) q^{97} +(-9.00000 + 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{3} - 2 q^{4} - q^{5} - 5 q^{7} + 3 q^{9}+O(q^{10}) \) 2 * q + 3 * q^3 - 2 * q^4 - q^5 - 5 * q^7 + 3 * q^9	\( 2 q + 3 q^{3} - 2 q^{4} - q^{5} - 5 q^{7} + 3 q^{9} - 6 q^{11} - 6 q^{12} + 9 q^{13} - 3 q^{15} - 4 q^{16} + 6 q^{17} - 2 q^{20} - 6 q^{21} - 12 q^{23} - q^{25} + 8 q^{28} + 3 q^{29} + 6 q^{31} - 12 q^{33} + 4 q^{35} - 12 q^{36} + 20 q^{37} + 9 q^{39} + 12 q^{41} + 8 q^{43} - 6 q^{45} + 11 q^{49} + 9 q^{51} - 18 q^{52} - 6 q^{57} - 12 q^{61} - 3 q^{63} + 16 q^{64} - 9 q^{65} + 10 q^{67} - 6 q^{68} - 12 q^{69} - 12 q^{76} + 18 q^{77} - 8 q^{79} + 8 q^{80} - 9 q^{81} + 9 q^{83} + 18 q^{84} - 3 q^{85} + 6 q^{87} - 12 q^{89} - 18 q^{91} + 24 q^{92} + 6 q^{93} - 6 q^{95} + 12 q^{97} - 18 q^{99}+O(q^{100}) \) 2 * q + 3 * q^3 - 2 * q^4 - q^5 - 5 * q^7 + 3 * q^9 - 6 * q^11 - 6 * q^12 + 9 * q^13 - 3 * q^15 - 4 * q^16 + 6 * q^17 - 2 * q^20 - 6 * q^21 - 12 * q^23 - q^25 + 8 * q^28 + 3 * q^29 + 6 * q^31 - 12 * q^33 + 4 * q^35 - 12 * q^36 + 20 * q^37 + 9 * q^39 + 12 * q^41 + 8 * q^43 - 6 * q^45 + 11 * q^49 + 9 * q^51 - 18 * q^52 - 6 * q^57 - 12 * q^61 - 3 * q^63 + 16 * q^64 - 9 * q^65 + 10 * q^67 - 6 * q^68 - 12 * q^69 - 12 * q^76 + 18 * q^77 - 8 * q^79 + 8 * q^80 - 9 * q^81 + 9 * q^83 + 18 * q^84 - 3 * q^85 + 6 * q^87 - 12 * q^89 - 18 * q^91 + 24 * q^92 + 6 * q^93 - 6 * q^95 + 12 * q^97 - 18 * q^99

Introduction

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