LMFDB - Embedded newform 966.2.l.a.185.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(47,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("966.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.l (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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			185.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	966.185
Dual form			966.2.l.a.47.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 1.50000i) q^{5} -1.73205i q^{6} +(0.500000 - 2.59808i) q^{7} +1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 1.50000i) q^{5} -1.73205i q^{6} +(0.500000 - 2.59808i) q^{7} +1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-1.50000 - 0.866025i) q^{10} +(0.866025 + 1.50000i) q^{12} +1.73205i q^{13} +(0.866025 + 2.50000i) q^{14} -3.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.59808 - 4.50000i) q^{17} +(2.59808 + 1.50000i) q^{18} +(3.00000 - 1.73205i) q^{19} +1.73205 q^{20} +(3.46410 + 3.00000i) q^{21} +(-0.866025 + 0.500000i) q^{23} +(-1.50000 - 0.866025i) q^{24} +(1.00000 - 1.73205i) q^{25} +(-0.866025 - 1.50000i) q^{26} +5.19615 q^{27} +(-2.00000 - 1.73205i) q^{28} -6.00000i q^{29} +(2.59808 - 1.50000i) q^{30} +(3.00000 + 1.73205i) q^{31} +(0.866025 + 0.500000i) q^{32} +5.19615i q^{34} +(4.33013 - 1.50000i) q^{35} -3.00000 q^{36} +(-2.00000 - 3.46410i) q^{37} +(-1.73205 + 3.00000i) q^{38} +(-2.59808 - 1.50000i) q^{39} +(-1.50000 + 0.866025i) q^{40} +(-4.50000 - 0.866025i) q^{42} +4.00000 q^{43} +(2.59808 - 4.50000i) q^{45} +(0.500000 - 0.866025i) q^{46} +(-2.59808 - 4.50000i) q^{47} +1.73205 q^{48} +(-6.50000 - 2.59808i) q^{49} +2.00000i q^{50} +(4.50000 + 7.79423i) q^{51} +(1.50000 + 0.866025i) q^{52} +(7.79423 + 4.50000i) q^{53} +(-4.50000 + 2.59808i) q^{54} +(2.59808 + 0.500000i) q^{56} +6.00000i q^{57} +(3.00000 + 5.19615i) q^{58} +(-5.19615 + 9.00000i) q^{59} +(-1.50000 + 2.59808i) q^{60} +(12.0000 - 6.92820i) q^{61} -3.46410 q^{62} +(-7.50000 + 2.59808i) q^{63} -1.00000 q^{64} +(-2.59808 + 1.50000i) q^{65} +(-2.50000 + 4.33013i) q^{67} +(-2.59808 - 4.50000i) q^{68} -1.73205i q^{69} +(-3.00000 + 3.46410i) q^{70} +15.0000i q^{71} +(2.59808 - 1.50000i) q^{72} +(10.5000 + 6.06218i) q^{73} +(3.46410 + 2.00000i) q^{74} +(1.73205 + 3.00000i) q^{75} -3.46410i q^{76} +3.00000 q^{78} +(-4.00000 - 6.92820i) q^{79} +(0.866025 - 1.50000i) q^{80} +(-4.50000 + 7.79423i) q^{81} +6.92820 q^{83} +(4.33013 - 1.50000i) q^{84} +9.00000 q^{85} +(-3.46410 + 2.00000i) q^{86} +(9.00000 + 5.19615i) q^{87} +(-3.46410 - 6.00000i) q^{89} +5.19615i q^{90} +(4.50000 + 0.866025i) q^{91} +1.00000i q^{92} +(-5.19615 + 3.00000i) q^{93} +(4.50000 + 2.59808i) q^{94} +(5.19615 + 3.00000i) q^{95} +(-1.50000 + 0.866025i) q^{96} +10.3923i q^{97} +(6.92820 - 1.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 2 q^{7} - 6 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 + 2 * q^7 - 6 * q^9	$ 4 q + 2 q^{4} + 2 q^{7} - 6 q^{9} - 6 q^{10} - 12 q^{15} - 2 q^{16} + 12 q^{19} - 6 q^{24} + 4 q^{25} - 8 q^{28} + 12 q^{31} - 12 q^{36} - 8 q^{37} - 6 q^{40} - 18 q^{42} + 16 q^{43} + 2 q^{46} - 26 q^{49} + 18 q^{51} + 6 q^{52} - 18 q^{54} + 12 q^{58} - 6 q^{60} + 48 q^{61} - 30 q^{63} - 4 q^{64} - 10 q^{67} - 12 q^{70} + 42 q^{73} + 12 q^{78} - 16 q^{79} - 18 q^{81} + 36 q^{85} + 36 q^{87} + 18 q^{91} + 18 q^{94} - 6 q^{96}+O(q^{100}) $ 4 * q + 2 * q^4 + 2 * q^7 - 6 * q^9 - 6 * q^10 - 12 * q^15 - 2 * q^16 + 12 * q^19 - 6 * q^24 + 4 * q^25 - 8 * q^28 + 12 * q^31 - 12 * q^36 - 8 * q^37 - 6 * q^40 - 18 * q^42 + 16 * q^43 + 2 * q^46 - 26 * q^49 + 18 * q^51 + 6 * q^52 - 18 * q^54 + 12 * q^58 - 6 * q^60 + 48 * q^61 - 30 * q^63 - 4 * q^64 - 10 * q^67 - 12 * q^70 + 42 * q^73 + 12 * q^78 - 16 * q^79 - 18 * q^81 + 36 * q^85 + 36 * q^87 + 18 * q^91 + 18 * q^94 - 6 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−0.866025	+	1.50000i	−0.500000	+	0.866025i
$3$	−0.866025	+	1.50000i	−0.500000	+	0.866025i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.866025	+	1.50000i	0.387298	+	0.670820i	0.992085	−	0.125567i	$-0.0400750\pi$
$5$	0.866025	+	1.50000i	0.387298	+	0.670820i	−0.604787	+	0.796387i	$0.706742\pi$
$6$		−	1.73205i		−	0.707107i
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$8$			1.00000i			0.353553i
$9$	−1.50000	−	2.59808i	−0.500000	−	0.866025i
$10$	−1.50000	−	0.866025i	−0.474342	−	0.273861i
$11$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$11$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$12$	0.866025	+	1.50000i	0.250000	+	0.433013i
$13$			1.73205i			0.480384i	0.970725	+	0.240192i	$0.0772105\pi$
$13$			1.73205i			0.480384i	−0.970725	+	0.240192i	$0.922790\pi$
$14$	0.866025	+	2.50000i	0.231455	+	0.668153i
$15$	−3.00000			−0.774597
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.59808	−	4.50000i	0.630126	−	1.09141i	−0.357400	−	0.933952i	$-0.616337\pi$
$17$	2.59808	−	4.50000i	0.630126	−	1.09141i	0.987526	−	0.157459i	$-0.0503301\pi$
$18$	2.59808	+	1.50000i	0.612372	+	0.353553i
$19$	3.00000	−	1.73205i	0.688247	−	0.397360i	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	3.00000	−	1.73205i	0.688247	−	0.397360i	0.802955	+	0.596040i	$0.203260\pi$
$20$	1.73205			0.387298
$21$	3.46410	+	3.00000i	0.755929	+	0.654654i
$22$		0			0
$23$	−0.866025	+	0.500000i	−0.180579	+	0.104257i
$23$	−0.866025	+	0.500000i	−0.180579	+	0.104257i
$24$	−1.50000	−	0.866025i	−0.306186	−	0.176777i
$25$	1.00000	−	1.73205i	0.200000	−	0.346410i
$26$	−0.866025	−	1.50000i	−0.169842	−	0.294174i
$27$	5.19615			1.00000
$28$	−2.00000	−	1.73205i	−0.377964	−	0.327327i
$29$		−	6.00000i		−	1.11417i	−0.830455	−	0.557086i	$-0.811919\pi$
$29$		−	6.00000i		−	1.11417i	0.830455	−	0.557086i	$-0.188081\pi$
$30$	2.59808	−	1.50000i	0.474342	−	0.273861i
$31$	3.00000	+	1.73205i	0.538816	+	0.311086i	0.744599	−	0.667512i	$-0.232641\pi$
$31$	3.00000	+	1.73205i	0.538816	+	0.311086i	−0.205783	+	0.978598i	$0.565974\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$			5.19615i			0.891133i
$35$	4.33013	−	1.50000i	0.731925	−	0.253546i
$36$	−3.00000			−0.500000
$37$	−2.00000	−	3.46410i	−0.328798	−	0.569495i	0.653476	−	0.756948i	$-0.273310\pi$
$37$	−2.00000	−	3.46410i	−0.328798	−	0.569495i	−0.982274	+	0.187453i	$0.939977\pi$
$38$	−1.73205	+	3.00000i	−0.280976	+	0.486664i
$39$	−2.59808	−	1.50000i	−0.416025	−	0.240192i
$40$	−1.50000	+	0.866025i	−0.237171	+	0.136931i
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$	−4.50000	−	0.866025i	−0.694365	−	0.133631i
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$		0			0
$45$	2.59808	−	4.50000i	0.387298	−	0.670820i
$46$	0.500000	−	0.866025i	0.0737210	−	0.127688i
$47$	−2.59808	−	4.50000i	−0.378968	−	0.656392i	0.611944	−	0.790901i	$-0.290388\pi$
$47$	−2.59808	−	4.50000i	−0.378968	−	0.656392i	−0.990912	+	0.134509i	$0.957054\pi$
$48$	1.73205			0.250000
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$			2.00000i			0.282843i
$51$	4.50000	+	7.79423i	0.630126	+	1.09141i
$52$	1.50000	+	0.866025i	0.208013	+	0.120096i
$53$	7.79423	+	4.50000i	1.07062	+	0.618123i	0.928351	−	0.371706i	$-0.121227\pi$
$53$	7.79423	+	4.50000i	1.07062	+	0.618123i	0.142269	+	0.989828i	$0.454560\pi$
$54$	−4.50000	+	2.59808i	−0.612372	+	0.353553i
$55$		0			0
$56$	2.59808	+	0.500000i	0.347183	+	0.0668153i
$57$			6.00000i			0.794719i
$58$	3.00000	+	5.19615i	0.393919	+	0.682288i
$59$	−5.19615	+	9.00000i	−0.676481	+	1.17170i	0.299552	+	0.954080i	$0.403163\pi$
$59$	−5.19615	+	9.00000i	−0.676481	+	1.17170i	−0.976034	+	0.217620i	$0.930171\pi$
$60$	−1.50000	+	2.59808i	−0.193649	+	0.335410i
$61$	12.0000	−	6.92820i	1.53644	−	0.887066i	0.537400	−	0.843328i	$-0.319407\pi$
$61$	12.0000	−	6.92820i	1.53644	−	0.887066i	0.999043	−	0.0437377i	$-0.0139266\pi$
$62$	−3.46410			−0.439941
$63$	−7.50000	+	2.59808i	−0.944911	+	0.327327i
$64$	−1.00000			−0.125000
$65$	−2.59808	+	1.50000i	−0.322252	+	0.186052i
$66$		0			0
$67$	−2.50000	+	4.33013i	−0.305424	+	0.529009i	−0.977356	−	0.211604i	$-0.932131\pi$
$67$	−2.50000	+	4.33013i	−0.305424	+	0.529009i	0.671932	+	0.740613i	$0.265465\pi$
$68$	−2.59808	−	4.50000i	−0.315063	−	0.545705i
$69$		−	1.73205i		−	0.208514i
$70$	−3.00000	+	3.46410i	−0.358569	+	0.414039i
$71$			15.0000i			1.78017i	0.455792	+	0.890086i	$0.349356\pi$
$71$			15.0000i			1.78017i	−0.455792	+	0.890086i	$0.650644\pi$
$72$	2.59808	−	1.50000i	0.306186	−	0.176777i
$73$	10.5000	+	6.06218i	1.22893	+	0.709524i	0.966807	−	0.255510i	$-0.0822432\pi$
$73$	10.5000	+	6.06218i	1.22893	+	0.709524i	0.262126	+	0.965034i	$0.415577\pi$
$74$	3.46410	+	2.00000i	0.402694	+	0.232495i
$75$	1.73205	+	3.00000i	0.200000	+	0.346410i
$76$		−	3.46410i		−	0.397360i
$77$		0			0
$78$	3.00000			0.339683
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	0.548352	−	0.836247i	$-0.315255\pi$
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	−0.998388	+	0.0567635i	$0.981922\pi$
$80$	0.866025	−	1.50000i	0.0968246	−	0.167705i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$		0			0
$83$	6.92820			0.760469			0.380235	−	0.924890i	$-0.375843\pi$
$83$	6.92820			0.760469			0.380235	+	0.924890i	$0.375843\pi$
$84$	4.33013	−	1.50000i	0.472456	−	0.163663i
$85$	9.00000			0.976187
$86$	−3.46410	+	2.00000i	−0.373544	+	0.215666i
$87$	9.00000	+	5.19615i	0.964901	+	0.557086i
$88$		0			0
$89$	−3.46410	−	6.00000i	−0.367194	−	0.635999i	0.621932	−	0.783072i	$-0.286348\pi$
$89$	−3.46410	−	6.00000i	−0.367194	−	0.635999i	−0.989126	+	0.147073i	$0.953015\pi$
$90$			5.19615i			0.547723i
$91$	4.50000	+	0.866025i	0.471728	+	0.0907841i
$92$			1.00000i			0.104257i
$93$	−5.19615	+	3.00000i	−0.538816	+	0.311086i
$94$	4.50000	+	2.59808i	0.464140	+	0.267971i
$95$	5.19615	+	3.00000i	0.533114	+	0.307794i
$96$	−1.50000	+	0.866025i	−0.153093	+	0.0883883i
$97$			10.3923i			1.05518i	0.849500	+	0.527589i	$0.176904\pi$
$97$			10.3923i			1.05518i	−0.849500	+	0.527589i	$0.823096\pi$
$98$	6.92820	−	1.00000i	0.699854	−	0.101015i
$99$		0			0
$100$	−1.00000	−	1.73205i	−0.100000	−	0.173205i
$101$	5.19615	−	9.00000i	0.517036	−	0.895533i	−0.482768	−	0.875748i	$-0.660368\pi$
$101$	5.19615	−	9.00000i	0.517036	−	0.895533i	0.999804	−	0.0197851i	$-0.00629819\pi$
$102$	−7.79423	−	4.50000i	−0.771744	−	0.445566i
$103$	4.50000	−	2.59808i	0.443398	−	0.255996i	−0.261640	−	0.965166i	$-0.584263\pi$
$103$	4.50000	−	2.59808i	0.443398	−	0.255996i	0.705038	+	0.709170i	$0.250930\pi$
$104$	−1.73205			−0.169842
$105$	−1.50000	+	7.79423i	−0.146385	+	0.760639i
$106$	−9.00000			−0.874157
$107$	−5.19615	+	3.00000i	−0.502331	+	0.290021i	−0.729676	−	0.683793i	$-0.760329\pi$
$107$	−5.19615	+	3.00000i	−0.502331	+	0.290021i	0.227345	+	0.973814i	$0.426996\pi$
$108$	2.59808	−	4.50000i	0.250000	−	0.433013i
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	−0.814152	−	0.580651i	$-0.802798\pi$
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	0.909935	+	0.414751i	$0.136131\pi$
$110$		0			0
$111$	6.92820			0.657596
$112$	−2.50000	+	0.866025i	−0.236228	+	0.0818317i
$113$			9.00000i			0.846649i	0.905978	+	0.423324i	$0.139137\pi$
$113$			9.00000i			0.846649i	−0.905978	+	0.423324i	$0.860863\pi$
$114$	−3.00000	−	5.19615i	−0.280976	−	0.486664i
$115$	−1.50000	−	0.866025i	−0.139876	−	0.0807573i
$116$	−5.19615	−	3.00000i	−0.482451	−	0.278543i
$117$	4.50000	−	2.59808i	0.416025	−	0.240192i
$118$		−	10.3923i		−	0.956689i
$119$	−10.3923	−	9.00000i	−0.952661	−	0.825029i
$120$		−	3.00000i		−	0.273861i
$121$	−5.50000	−	9.52628i	−0.500000	−	0.866025i
$122$	−6.92820	+	12.0000i	−0.627250	+	1.08643i
$123$		0			0
$124$	3.00000	−	1.73205i	0.269408	−	0.155543i
$125$	12.1244			1.08444
$126$	5.19615	−	6.00000i	0.462910	−	0.534522i
$127$	14.0000			1.24230			0.621150	−	0.783692i	$-0.286666\pi$
$127$	14.0000			1.24230			0.621150	+	0.783692i	$0.286666\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−3.46410	+	6.00000i	−0.304997	+	0.528271i
$130$	1.50000	−	2.59808i	0.131559	−	0.227866i
$131$	−11.2583	−	19.5000i	−0.983645	−	1.70372i	−0.647810	−	0.761802i	$-0.724315\pi$
$131$	−11.2583	−	19.5000i	−0.983645	−	1.70372i	−0.335835	−	0.941921i	$-0.609018\pi$
$132$		0			0
$133$	−3.00000	−	8.66025i	−0.260133	−	0.750939i
$134$		−	5.00000i		−	0.431934i
$135$	4.50000	+	7.79423i	0.387298	+	0.670820i
$136$	4.50000	+	2.59808i	0.385872	+	0.222783i
$137$	7.79423	+	4.50000i	0.665906	+	0.384461i	0.794524	−	0.607233i	$-0.207721\pi$
$137$	7.79423	+	4.50000i	0.665906	+	0.384461i	−0.128618	+	0.991694i	$0.541054\pi$
$138$	0.866025	+	1.50000i	0.0737210	+	0.127688i
$139$		0			0		1.00000			$0$
$139$		0			0		−1.00000			$\pi$
$140$	0.866025	−	4.50000i	0.0731925	−	0.380319i
$141$	9.00000			0.757937
$142$	−7.50000	−	12.9904i	−0.629386	−	1.09013i
$143$		0			0
$144$	−1.50000	+	2.59808i	−0.125000	+	0.216506i
$145$	9.00000	−	5.19615i	0.747409	−	0.431517i
$146$	−12.1244			−1.00342
$147$	9.52628	−	7.50000i	0.785714	−	0.618590i
$148$	−4.00000			−0.328798
$149$	−2.59808	+	1.50000i	−0.212843	+	0.122885i	−0.602632	−	0.798019i	$-0.705881\pi$
$149$	−2.59808	+	1.50000i	−0.212843	+	0.122885i	0.389789	+	0.920904i	$0.372548\pi$
$150$	−3.00000	−	1.73205i	−0.244949	−	0.141421i
$151$	−11.0000	+	19.0526i	−0.895167	+	1.55048i	−0.0615699	+	0.998103i	$0.519611\pi$
$151$	−11.0000	+	19.0526i	−0.895167	+	1.55048i	−0.833597	+	0.552372i	$0.813723\pi$
$152$	1.73205	+	3.00000i	0.140488	+	0.243332i
$153$	−15.5885			−1.26025
$154$		0			0
$155$			6.00000i			0.481932i
$156$	−2.59808	+	1.50000i	−0.208013	+	0.120096i
$157$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$157$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$158$	6.92820	+	4.00000i	0.551178	+	0.318223i
$159$	−13.5000	+	7.79423i	−1.07062	+	0.618123i
$160$			1.73205i			0.136931i
$161$	0.866025	+	2.50000i	0.0682524	+	0.197028i
$162$		−	9.00000i		−	0.707107i
$163$	5.00000	+	8.66025i	0.391630	+	0.678323i	0.992665	−	0.120900i	$-0.0385779\pi$
$163$	5.00000	+	8.66025i	0.391630	+	0.678323i	−0.601035	+	0.799223i	$0.705245\pi$
$164$		0			0
$165$		0			0
$166$	−6.00000	+	3.46410i	−0.465690	+	0.268866i
$167$	−12.1244			−0.938211			−0.469105	−	0.883142i	$-0.655424\pi$
$167$	−12.1244			−0.938211			−0.469105	+	0.883142i	$0.655424\pi$
$168$	−3.00000	+	3.46410i	−0.231455	+	0.267261i
$169$	10.0000			0.769231
$170$	−7.79423	+	4.50000i	−0.597790	+	0.345134i
$171$	−9.00000	−	5.19615i	−0.688247	−	0.397360i
$172$	2.00000	−	3.46410i	0.152499	−	0.264135i
$173$	1.73205	+	3.00000i	0.131685	+	0.228086i	0.924326	−	0.381603i	$-0.124628\pi$
$173$	1.73205	+	3.00000i	0.131685	+	0.228086i	−0.792641	+	0.609689i	$0.791294\pi$
$174$	−10.3923			−0.787839
$175$	−4.00000	−	3.46410i	−0.302372	−	0.261861i
$176$		0			0
$177$	−9.00000	−	15.5885i	−0.676481	−	1.17170i
$178$	6.00000	+	3.46410i	0.449719	+	0.259645i
$179$	−12.9904	−	7.50000i	−0.970947	−	0.560576i	−0.0714220	−	0.997446i	$-0.522754\pi$
$179$	−12.9904	−	7.50000i	−0.970947	−	0.560576i	−0.899525	+	0.436870i	$0.856087\pi$
$180$	−2.59808	−	4.50000i	−0.193649	−	0.335410i
$181$		−	3.46410i		−	0.257485i	−0.991678	−	0.128742i	$-0.958906\pi$
$181$		−	3.46410i		−	0.257485i	0.991678	−	0.128742i	$-0.0410940\pi$
$182$	−4.33013	+	1.50000i	−0.320970	+	0.111187i
$183$			24.0000i			1.77413i
$184$	−0.500000	−	0.866025i	−0.0368605	−	0.0638442i
$185$	3.46410	−	6.00000i	0.254686	−	0.441129i
$186$	3.00000	−	5.19615i	0.219971	−	0.381000i
$187$		0			0
$188$	−5.19615			−0.378968
$189$	2.59808	−	13.5000i	0.188982	−	0.981981i
$190$	−6.00000			−0.435286
$191$	−5.19615	+	3.00000i	−0.375980	+	0.217072i	−0.676068	−	0.736839i	$-0.736317\pi$
$191$	−5.19615	+	3.00000i	−0.375980	+	0.217072i	0.300088	+	0.953912i	$0.402984\pi$
$192$	0.866025	−	1.50000i	0.0625000	−	0.108253i
$193$	8.50000	−	14.7224i	0.611843	−	1.05974i	−0.379086	−	0.925361i	$-0.623762\pi$
$193$	8.50000	−	14.7224i	0.611843	−	1.05974i	0.990930	−	0.134382i	$-0.0429051\pi$
$194$	−5.19615	−	9.00000i	−0.373062	−	0.646162i
$195$		−	5.19615i		−	0.372104i
$196$	−5.50000	+	4.33013i	−0.392857	+	0.309295i
$197$		−	12.0000i		−	0.854965i	−0.904024	−	0.427482i	$-0.859401\pi$
$197$		−	12.0000i		−	0.854965i	0.904024	−	0.427482i	$-0.140599\pi$
$198$		0			0
$199$	−21.0000	−	12.1244i	−1.48865	−	0.859473i	−0.488735	−	0.872433i	$-0.662541\pi$
$199$	−21.0000	−	12.1244i	−1.48865	−	0.859473i	−0.999916	+	0.0129598i	$0.995875\pi$
$200$	1.73205	+	1.00000i	0.122474	+	0.0707107i
$201$	−4.33013	−	7.50000i	−0.305424	−	0.529009i
$202$			10.3923i			0.731200i
$203$	−15.5885	−	3.00000i	−1.09410	−	0.210559i
$204$	9.00000			0.630126
$205$		0			0
$206$	−2.59808	+	4.50000i	−0.181017	+	0.313530i
$207$	2.59808	+	1.50000i	0.180579	+	0.104257i
$208$	1.50000	−	0.866025i	0.104006	−	0.0600481i
$209$		0			0
$210$	−2.59808	−	7.50000i	−0.179284	−	0.517549i
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$	7.79423	−	4.50000i	0.535310	−	0.309061i
$213$	−22.5000	−	12.9904i	−1.54167	−	0.890086i
$214$	3.00000	−	5.19615i	0.205076	−	0.355202i
$215$	3.46410	+	6.00000i	0.236250	+	0.409197i
$216$			5.19615i			0.353553i
$217$	6.00000	−	6.92820i	0.407307	−	0.470317i
$218$			2.00000i			0.135457i
$219$	−18.1865	+	10.5000i	−1.22893	+	0.709524i
$220$		0			0
$221$	7.79423	+	4.50000i	0.524297	+	0.302703i
$222$	−6.00000	+	3.46410i	−0.402694	+	0.232495i
$223$			6.92820i			0.463947i	0.972722	+	0.231973i	$0.0745182\pi$
$223$			6.92820i			0.463947i	−0.972722	+	0.231973i	$0.925482\pi$
$224$	1.73205	−	2.00000i	0.115728	−	0.133631i
$225$	−6.00000			−0.400000
$226$	−4.50000	−	7.79423i	−0.299336	−	0.518464i
$227$	10.3923	−	18.0000i	0.689761	−	1.19470i	−0.282153	−	0.959369i	$-0.591049\pi$
$227$	10.3923	−	18.0000i	0.689761	−	1.19470i	0.971915	−	0.235333i	$-0.0756180\pi$
$228$	5.19615	+	3.00000i	0.344124	+	0.198680i
$229$	21.0000	−	12.1244i	1.38772	−	0.801200i	0.394661	−	0.918827i	$-0.370862\pi$
$229$	21.0000	−	12.1244i	1.38772	−	0.801200i	0.993058	+	0.117627i	$0.0375286\pi$
$230$	1.73205			0.114208
$231$		0			0
$232$	6.00000			0.393919
$233$	−5.19615	+	3.00000i	−0.340411	+	0.196537i	−0.660454	−	0.750867i	$-0.729636\pi$
$233$	−5.19615	+	3.00000i	−0.340411	+	0.196537i	0.320043	+	0.947403i	$0.396303\pi$
$234$	−2.59808	+	4.50000i	−0.169842	+	0.294174i
$235$	4.50000	−	7.79423i	0.293548	−	0.508439i
$236$	5.19615	+	9.00000i	0.338241	+	0.585850i
$237$	13.8564			0.900070
$238$	13.5000	+	2.59808i	0.875075	+	0.168408i
$239$		−	12.0000i		−	0.776215i	−0.921614	−	0.388108i	$-0.873129\pi$
$239$		−	12.0000i		−	0.776215i	0.921614	−	0.388108i	$-0.126871\pi$
$240$	1.50000	+	2.59808i	0.0968246	+	0.167705i
$241$	−3.00000	−	1.73205i	−0.193247	−	0.111571i	0.400255	−	0.916404i	$-0.368922\pi$
$241$	−3.00000	−	1.73205i	−0.193247	−	0.111571i	−0.593502	+	0.804833i	$0.702255\pi$
$242$	9.52628	+	5.50000i	0.612372	+	0.353553i
$243$	−7.79423	−	13.5000i	−0.500000	−	0.866025i
$244$		−	13.8564i		−	0.887066i
$245$	−1.73205	−	12.0000i	−0.110657	−	0.766652i
$246$		0			0
$247$	3.00000	+	5.19615i	0.190885	+	0.330623i
$248$	−1.73205	+	3.00000i	−0.109985	+	0.190500i
$249$	−6.00000	+	10.3923i	−0.380235	+	0.658586i
$250$	−10.5000	+	6.06218i	−0.664078	+	0.383406i
$251$	24.2487			1.53057			0.765283	−	0.643695i	$-0.222599\pi$
$251$	24.2487			1.53057			0.765283	+	0.643695i	$0.222599\pi$
$252$	−1.50000	+	7.79423i	−0.0944911	+	0.490990i
$253$		0			0
$254$	−12.1244	+	7.00000i	−0.760750	+	0.439219i
$255$	−7.79423	+	13.5000i	−0.488094	+	0.845403i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−12.1244	−	21.0000i	−0.756297	−	1.30994i	−0.944727	−	0.327858i	$-0.893673\pi$
$257$	−12.1244	−	21.0000i	−0.756297	−	1.30994i	0.188431	−	0.982086i	$-0.439660\pi$
$258$		−	6.92820i		−	0.431331i
$259$	−10.0000	+	3.46410i	−0.621370	+	0.215249i
$260$			3.00000i			0.186052i
$261$	−15.5885	+	9.00000i	−0.964901	+	0.557086i
$262$	19.5000	+	11.2583i	1.20471	+	0.695542i
$263$	−15.5885	−	9.00000i	−0.961225	−	0.554964i	−0.0646755	−	0.997906i	$-0.520601\pi$
$263$	−15.5885	−	9.00000i	−0.961225	−	0.554964i	−0.896550	+	0.442943i	$0.853935\pi$
$264$		0			0
$265$			15.5885i			0.957591i
$266$	6.92820	+	6.00000i	0.424795	+	0.367884i
$267$	12.0000			0.734388
$268$	2.50000	+	4.33013i	0.152712	+	0.264505i
$269$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$269$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$270$	−7.79423	−	4.50000i	−0.474342	−	0.273861i
$271$	−21.0000	+	12.1244i	−1.27566	+	0.736502i	−0.976047	−	0.217559i	$-0.930191\pi$
$271$	−21.0000	+	12.1244i	−1.27566	+	0.736502i	−0.299612	+	0.954061i	$0.596857\pi$
$272$	−5.19615			−0.315063
$273$	−5.19615	+	6.00000i	−0.314485	+	0.363137i
$274$	−9.00000			−0.543710
$275$		0			0
$276$	−1.50000	−	0.866025i	−0.0902894	−	0.0521286i
$277$	3.50000	−	6.06218i	0.210295	−	0.364241i	−0.741512	−	0.670940i	$-0.765891\pi$
$277$	3.50000	−	6.06218i	0.210295	−	0.364241i	0.951807	+	0.306699i	$0.0992243\pi$
$278$		0			0
$279$		−	10.3923i		−	0.622171i
$280$	1.50000	+	4.33013i	0.0896421	+	0.258775i
$281$		−	9.00000i		−	0.536895i	−0.963294	−	0.268447i	$-0.913489\pi$
$281$		−	9.00000i		−	0.536895i	0.963294	−	0.268447i	$-0.0865106\pi$
$282$	−7.79423	+	4.50000i	−0.464140	+	0.267971i
$283$	7.50000	+	4.33013i	0.445829	+	0.257399i	0.706067	−	0.708145i	$-0.250468\pi$
$283$	7.50000	+	4.33013i	0.445829	+	0.257399i	−0.260238	+	0.965544i	$0.583801\pi$
$284$	12.9904	+	7.50000i	0.770837	+	0.445043i
$285$	−9.00000	+	5.19615i	−0.533114	+	0.307794i
$286$		0			0
$287$		0			0
$288$		−	3.00000i		−	0.176777i
$289$	−5.00000	−	8.66025i	−0.294118	−	0.509427i
$290$	−5.19615	+	9.00000i	−0.305129	+	0.528498i
$291$	−15.5885	−	9.00000i	−0.913812	−	0.527589i
$292$	10.5000	−	6.06218i	0.614466	−	0.354762i
$293$	−1.73205			−0.101187			−0.0505937	−	0.998719i	$-0.516111\pi$
$293$	−1.73205			−0.101187			−0.0505937	+	0.998719i	$0.516111\pi$
$294$	−4.50000	+	11.2583i	−0.262445	+	0.656599i
$295$	−18.0000			−1.04800
$296$	3.46410	−	2.00000i	0.201347	−	0.116248i
$297$		0			0
$298$	1.50000	−	2.59808i	0.0868927	−	0.150503i
$299$	−0.866025	−	1.50000i	−0.0500835	−	0.0867472i
$300$	3.46410			0.200000
$301$	2.00000	−	10.3923i	0.115278	−	0.599002i
$302$		−	22.0000i		−	1.26596i
$303$	9.00000	+	15.5885i	0.517036	+	0.895533i
$304$	−3.00000	−	1.73205i	−0.172062	−	0.0993399i
$305$	20.7846	+	12.0000i	1.19012	+	0.687118i
$306$	13.5000	−	7.79423i	0.771744	−	0.445566i
$307$			20.7846i			1.18624i	0.805114	+	0.593120i	$0.202104\pi$
$307$			20.7846i			1.18624i	−0.805114	+	0.593120i	$0.797896\pi$
$308$		0			0
$309$			9.00000i			0.511992i
$310$	−3.00000	−	5.19615i	−0.170389	−	0.295122i
$311$	−0.866025	+	1.50000i	−0.0491078	+	0.0850572i	−0.889534	−	0.456868i	$-0.848971\pi$
$311$	−0.866025	+	1.50000i	−0.0491078	+	0.0850572i	0.840427	+	0.541925i	$0.182304\pi$
$312$	1.50000	−	2.59808i	0.0849208	−	0.147087i
$313$	3.00000	−	1.73205i	0.169570	−	0.0979013i	−0.412813	−	0.910816i	$-0.635454\pi$
$313$	3.00000	−	1.73205i	0.169570	−	0.0979013i	0.582383	+	0.812914i	$0.302120\pi$
$314$		0			0
$315$	−10.3923	−	9.00000i	−0.585540	−	0.507093i
$316$	−8.00000			−0.450035
$317$	−10.3923	+	6.00000i	−0.583690	+	0.336994i	−0.762598	−	0.646872i	$-0.776077\pi$
$317$	−10.3923	+	6.00000i	−0.583690	+	0.336994i	0.178908	+	0.983866i	$0.442743\pi$
$318$	7.79423	−	13.5000i	0.437079	−	0.757042i
$319$		0			0
$320$	−0.866025	−	1.50000i	−0.0484123	−	0.0838525i
$321$		−	10.3923i		−	0.580042i
$322$	−2.00000	−	1.73205i	−0.111456	−	0.0965234i
$323$		−	18.0000i		−	1.00155i
$324$	4.50000	+	7.79423i	0.250000	+	0.433013i
$325$	3.00000	+	1.73205i	0.166410	+	0.0960769i
$326$	−8.66025	−	5.00000i	−0.479647	−	0.276924i
$327$	1.73205	+	3.00000i	0.0957826	+	0.165900i
$328$		0			0
$329$	−12.9904	+	4.50000i	−0.716183	+	0.248093i
$330$		0			0
$331$	1.00000	+	1.73205i	0.0549650	+	0.0952021i	0.892199	−	0.451643i	$-0.149162\pi$
$331$	1.00000	+	1.73205i	0.0549650	+	0.0952021i	−0.837234	+	0.546845i	$0.815829\pi$
$332$	3.46410	−	6.00000i	0.190117	−	0.329293i
$333$	−6.00000	+	10.3923i	−0.328798	+	0.569495i
$334$	10.5000	−	6.06218i	0.574534	−	0.331708i
$335$	−8.66025			−0.473160
$336$	0.866025	−	4.50000i	0.0472456	−	0.245495i
$337$	10.0000			0.544735			0.272367	−	0.962193i	$-0.412193\pi$
$337$	10.0000			0.544735			0.272367	+	0.962193i	$0.412193\pi$
$338$	−8.66025	+	5.00000i	−0.471056	+	0.271964i
$339$	−13.5000	−	7.79423i	−0.733219	−	0.423324i
$340$	4.50000	−	7.79423i	0.244047	−	0.422701i
$341$		0			0
$342$	10.3923			0.561951
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$			4.00000i			0.215666i
$345$	2.59808	−	1.50000i	0.139876	−	0.0807573i
$346$	−3.00000	−	1.73205i	−0.161281	−	0.0931156i
$347$	23.3827	+	13.5000i	1.25525	+	0.724718i	0.972147	−	0.234372i	$-0.0753034\pi$
$347$	23.3827	+	13.5000i	1.25525	+	0.724718i	0.283101	+	0.959090i	$0.408637\pi$
$348$	9.00000	−	5.19615i	0.482451	−	0.278543i
$349$		−	19.0526i		−	1.01986i	−0.860216	−	0.509930i	$-0.829671\pi$
$349$		−	19.0526i		−	1.01986i	0.860216	−	0.509930i	$-0.170329\pi$
$350$	5.19615	+	1.00000i	0.277746	+	0.0534522i
$351$			9.00000i			0.480384i
$352$		0			0
$353$	1.73205	−	3.00000i	0.0921878	−	0.159674i	−0.816244	−	0.577708i	$-0.803947\pi$
$353$	1.73205	−	3.00000i	0.0921878	−	0.159674i	0.908431	+	0.418034i	$0.137281\pi$
$354$	15.5885	+	9.00000i	0.828517	+	0.478345i
$355$	−22.5000	+	12.9904i	−1.19418	+	0.689458i
$356$	−6.92820			−0.367194
$357$	22.5000	−	7.79423i	1.19083	−	0.412514i
$358$	15.0000			0.792775
$359$	−5.19615	+	3.00000i	−0.274242	+	0.158334i	−0.630814	−	0.775934i	$-0.717279\pi$
$359$	−5.19615	+	3.00000i	−0.274242	+	0.158334i	0.356572	+	0.934268i	$0.383946\pi$
$360$	4.50000	+	2.59808i	0.237171	+	0.136931i
$361$	−3.50000	+	6.06218i	−0.184211	+	0.319062i
$362$	1.73205	+	3.00000i	0.0910346	+	0.157676i
$363$	19.0526			1.00000
$364$	3.00000	−	3.46410i	0.157243	−	0.181568i
$365$			21.0000i			1.09919i
$366$	−12.0000	−	20.7846i	−0.627250	−	1.08643i
$367$	7.50000	+	4.33013i	0.391497	+	0.226031i	0.682808	−	0.730597i	$-0.260758\pi$
$367$	7.50000	+	4.33013i	0.391497	+	0.226031i	−0.291312	+	0.956628i	$0.594092\pi$
$368$	0.866025	+	0.500000i	0.0451447	+	0.0260643i
$369$		0			0
$370$			6.92820i			0.360180i
$371$	15.5885	−	18.0000i	0.809312	−	0.934513i
$372$			6.00000i			0.311086i
$373$	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
$375$	−10.5000	+	18.1865i	−0.542218	+	0.939149i
$376$	4.50000	−	2.59808i	0.232070	−	0.133986i
$377$	10.3923			0.535231
$378$	4.50000	+	12.9904i	0.231455	+	0.668153i
$379$	−5.00000			−0.256833			−0.128416	−	0.991720i	$-0.540989\pi$
$379$	−5.00000			−0.256833			−0.128416	+	0.991720i	$0.540989\pi$
$380$	5.19615	−	3.00000i	0.266557	−	0.153897i
$381$	−12.1244	+	21.0000i	−0.621150	+	1.07586i
$382$	3.00000	−	5.19615i	0.153493	−	0.265858i
$383$	−13.8564	−	24.0000i	−0.708029	−	1.22634i	−0.965587	−	0.260080i	$-0.916251\pi$
$383$	−13.8564	−	24.0000i	−0.708029	−	1.22634i	0.257558	−	0.966263i	$-0.417082\pi$
$384$			1.73205i			0.0883883i
$385$		0			0
$386$			17.0000i			0.865277i
$387$	−6.00000	−	10.3923i	−0.304997	−	0.528271i
$388$	9.00000	+	5.19615i	0.456906	+	0.263795i
$389$	25.9808	+	15.0000i	1.31728	+	0.760530i	0.983290	−	0.182047i	$-0.0582724\pi$
$389$	25.9808	+	15.0000i	1.31728	+	0.760530i	0.333987	+	0.942578i	$0.391606\pi$
$390$	2.59808	+	4.50000i	0.131559	+	0.227866i
$391$			5.19615i			0.262781i
$392$	2.59808	−	6.50000i	0.131223	−	0.328300i
$393$	39.0000			1.96729
$394$	6.00000	+	10.3923i	0.302276	+	0.523557i
$395$	6.92820	−	12.0000i	0.348596	−	0.603786i
$396$		0			0
$397$	−22.5000	+	12.9904i	−1.12924	+	0.651969i	−0.943744	−	0.330676i	$-0.892723\pi$
$397$	−22.5000	+	12.9904i	−1.12924	+	0.651969i	−0.185498	+	0.982645i	$0.559390\pi$
$398$	24.2487			1.21548
$399$	15.5885	+	3.00000i	0.780399	+	0.150188i
$400$	−2.00000			−0.100000
$401$	−2.59808	+	1.50000i	−0.129742	+	0.0749064i	−0.563466	−	0.826139i	$-0.690532\pi$
$401$	−2.59808	+	1.50000i	−0.129742	+	0.0749064i	0.433724	+	0.901046i	$0.357199\pi$
$402$	7.50000	+	4.33013i	0.374066	+	0.215967i
$403$	−3.00000	+	5.19615i	−0.149441	+	0.258839i
$404$	−5.19615	−	9.00000i	−0.258518	−	0.447767i
$405$	−15.5885			−0.774597
$406$	15.0000	−	5.19615i	0.744438	−	0.257881i
$407$		0			0
$408$	−7.79423	+	4.50000i	−0.385872	+	0.222783i
$409$	−16.5000	−	9.52628i	−0.815872	−	0.471044i	0.0331186	−	0.999451i	$-0.489456\pi$
$409$	−16.5000	−	9.52628i	−0.815872	−	0.471044i	−0.848991	+	0.528407i	$0.822789\pi$
$410$		0			0
$411$	−13.5000	+	7.79423i	−0.665906	+	0.384461i
$412$		−	5.19615i		−	0.255996i
$413$	20.7846	+	18.0000i	1.02274	+	0.885722i
$414$	−3.00000			−0.147442
$415$	6.00000	+	10.3923i	0.294528	+	0.510138i
$416$	−0.866025	+	1.50000i	−0.0424604	+	0.0735436i
$417$		0			0
$418$		0			0
$419$	10.3923			0.507697			0.253849	−	0.967244i	$-0.418303\pi$
$419$	10.3923			0.507697			0.253849	+	0.967244i	$0.418303\pi$
$420$	6.00000	+	5.19615i	0.292770	+	0.253546i
$421$	−34.0000			−1.65706			−0.828529	−	0.559946i	$-0.810822\pi$
$421$	−34.0000			−1.65706			−0.828529	+	0.559946i	$0.810822\pi$
$422$	−3.46410	+	2.00000i	−0.168630	+	0.0973585i
$423$	−7.79423	+	13.5000i	−0.378968	+	0.656392i
$424$	−4.50000	+	7.79423i	−0.218539	+	0.378521i
$425$	−5.19615	−	9.00000i	−0.252050	−	0.436564i
$426$	25.9808			1.25877
$427$	−12.0000	−	34.6410i	−0.580721	−	1.67640i
$428$			6.00000i			0.290021i
$429$		0			0
$430$	−6.00000	−	3.46410i	−0.289346	−	0.167054i
$431$	25.9808	+	15.0000i	1.25145	+	0.722525i	0.971397	−	0.237460i	$-0.0763149\pi$
$431$	25.9808	+	15.0000i	1.25145	+	0.722525i	0.280052	+	0.959985i	$0.409648\pi$
$432$	−2.59808	−	4.50000i	−0.125000	−	0.216506i
$433$			20.7846i			0.998845i	0.866359	+	0.499422i	$0.166454\pi$
$433$			20.7846i			0.998845i	−0.866359	+	0.499422i	$0.833546\pi$
$434$	−1.73205	+	9.00000i	−0.0831411	+	0.432014i
$435$			18.0000i			0.863034i
$436$	−1.00000	−	1.73205i	−0.0478913	−	0.0829502i
$437$	−1.73205	+	3.00000i	−0.0828552	+	0.143509i
$438$	10.5000	−	18.1865i	0.501709	−	0.868986i
$439$	−12.0000	+	6.92820i	−0.572729	+	0.330665i	−0.758238	−	0.651977i	$-0.773940\pi$
$439$	−12.0000	+	6.92820i	−0.572729	+	0.330665i	0.185510	+	0.982642i	$0.440606\pi$
$440$		0			0
$441$	3.00000	+	20.7846i	0.142857	+	0.989743i
$442$	−9.00000			−0.428086
$443$	7.79423	−	4.50000i	0.370315	−	0.213801i	−0.303281	−	0.952901i	$-0.598082\pi$
$443$	7.79423	−	4.50000i	0.370315	−	0.213801i	0.673596	+	0.739100i	$0.264749\pi$
$444$	3.46410	−	6.00000i	0.164399	−	0.284747i
$445$	6.00000	−	10.3923i	0.284427	−	0.492642i
$446$	−3.46410	−	6.00000i	−0.164030	−	0.284108i
$447$		−	5.19615i		−	0.245770i
$448$	−0.500000	+	2.59808i	−0.0236228	+	0.122748i
$449$			6.00000i			0.283158i	0.989927	+	0.141579i	$0.0452178\pi$
$449$			6.00000i			0.283158i	−0.989927	+	0.141579i	$0.954782\pi$
$450$	5.19615	−	3.00000i	0.244949	−	0.141421i
$451$		0			0
$452$	7.79423	+	4.50000i	0.366610	+	0.211662i
$453$	−19.0526	−	33.0000i	−0.895167	−	1.55048i
$454$			20.7846i			0.975470i
$455$	2.59808	+	7.50000i	0.121800	+	0.351605i
$456$	−6.00000			−0.280976
$457$	7.00000	+	12.1244i	0.327446	+	0.567153i	0.982004	−	0.188858i	$-0.0604787\pi$
$457$	7.00000	+	12.1244i	0.327446	+	0.567153i	−0.654558	+	0.756012i	$0.727145\pi$
$458$	−12.1244	+	21.0000i	−0.566534	+	0.981266i
$459$	13.5000	−	23.3827i	0.630126	−	1.09141i
$460$	−1.50000	+	0.866025i	−0.0699379	+	0.0403786i
$461$	−27.7128			−1.29071			−0.645357	−	0.763881i	$-0.723291\pi$
$461$	−27.7128			−1.29071			−0.645357	+	0.763881i	$0.723291\pi$
$462$		0			0
$463$	14.0000			0.650635			0.325318	−	0.945605i	$-0.394529\pi$
$463$	14.0000			0.650635			0.325318	+	0.945605i	$0.394529\pi$
$464$	−5.19615	+	3.00000i	−0.241225	+	0.139272i
$465$	−9.00000	−	5.19615i	−0.417365	−	0.240966i
$466$	3.00000	−	5.19615i	0.138972	−	0.240707i
$467$	3.46410	+	6.00000i	0.160300	+	0.277647i	0.934976	−	0.354711i	$-0.115421\pi$
$467$	3.46410	+	6.00000i	0.160300	+	0.277647i	−0.774677	+	0.632358i	$0.782087\pi$
$468$		−	5.19615i		−	0.240192i
$469$	10.0000	+	8.66025i	0.461757	+	0.399893i
$470$			9.00000i			0.415139i
$471$		0			0
$472$	−9.00000	−	5.19615i	−0.414259	−	0.239172i
$473$		0			0
$474$	−12.0000	+	6.92820i	−0.551178	+	0.318223i
$475$		−	6.92820i		−	0.317888i
$476$	−12.9904	+	4.50000i	−0.595413	+	0.206257i
$477$		−	27.0000i		−	1.23625i
$478$	6.00000	+	10.3923i	0.274434	+	0.475333i
$479$	−5.19615	+	9.00000i	−0.237418	+	0.411220i	−0.959973	−	0.280094i	$-0.909635\pi$
$479$	−5.19615	+	9.00000i	−0.237418	+	0.411220i	0.722554	+	0.691314i	$0.242968\pi$
$480$	−2.59808	−	1.50000i	−0.118585	−	0.0684653i
$481$	6.00000	−	3.46410i	0.273576	−	0.157949i
$482$	3.46410			0.157786
$483$	−4.50000	−	0.866025i	−0.204757	−	0.0394055i
$484$	−11.0000			−0.500000
$485$	−15.5885	+	9.00000i	−0.707835	+	0.408669i
$486$	13.5000	+	7.79423i	0.612372	+	0.353553i
$487$	−2.00000	+	3.46410i	−0.0906287	+	0.156973i	−0.907776	−	0.419456i	$-0.862221\pi$
$487$	−2.00000	+	3.46410i	−0.0906287	+	0.156973i	0.817147	+	0.576429i	$0.195554\pi$
$488$	6.92820	+	12.0000i	0.313625	+	0.543214i
$489$	−17.3205			−0.783260
$490$	7.50000	+	9.52628i	0.338815	+	0.430353i
$491$		−	15.0000i		−	0.676941i	−0.940977	−	0.338470i	$-0.890091\pi$
$491$		−	15.0000i		−	0.676941i	0.940977	−	0.338470i	$-0.109909\pi$
$492$		0			0
$493$	−27.0000	−	15.5885i	−1.21602	−	0.702069i
$494$	−5.19615	−	3.00000i	−0.233786	−	0.134976i
$495$		0			0
$496$		−	3.46410i		−	0.155543i
$497$	38.9711	+	7.50000i	1.74809	+	0.336421i
$498$		−	12.0000i		−	0.537733i
$499$	16.0000	+	27.7128i	0.716258	+	1.24060i	0.962472	+	0.271380i	$0.0874801\pi$
$499$	16.0000	+	27.7128i	0.716258	+	1.24060i	−0.246214	+	0.969216i	$0.579187\pi$
$500$	6.06218	−	10.5000i	0.271109	−	0.469574i
$501$	10.5000	−	18.1865i	0.469105	−	0.812514i
$502$	−21.0000	+	12.1244i	−0.937276	+	0.541136i
$503$	24.2487			1.08120			0.540598	−	0.841281i	$-0.318198\pi$
$503$	24.2487			1.08120			0.540598	+	0.841281i	$0.318198\pi$
$504$	−2.59808	−	7.50000i	−0.115728	−	0.334077i
$505$	18.0000			0.800989
$506$		0			0
$507$	−8.66025	+	15.0000i	−0.384615	+	0.666173i
$508$	7.00000	−	12.1244i	0.310575	−	0.537931i
$509$	15.5885	+	27.0000i	0.690946	+	1.19675i	0.971528	+	0.236924i	$0.0761392\pi$
$509$	15.5885	+	27.0000i	0.690946	+	1.19675i	−0.280582	+	0.959830i	$0.590527\pi$
$510$		−	15.5885i		−	0.690268i
$511$	21.0000	−	24.2487i	0.928985	−	1.07270i
$512$		−	1.00000i		−	0.0441942i
$513$	15.5885	−	9.00000i	0.688247	−	0.397360i
$514$	21.0000	+	12.1244i	0.926270	+	0.534782i
$515$	7.79423	+	4.50000i	0.343455	+	0.198294i
$516$	3.46410	+	6.00000i	0.152499	+	0.264135i
$517$		0			0
$518$	6.92820	−	8.00000i	0.304408	−	0.351500i
$519$	−6.00000			−0.263371
$520$	−1.50000	−	2.59808i	−0.0657794	−	0.113933i
$521$	−4.33013	+	7.50000i	−0.189706	+	0.328581i	−0.945152	−	0.326630i	$-0.894087\pi$
$521$	−4.33013	+	7.50000i	−0.189706	+	0.328581i	0.755446	+	0.655211i	$0.227420\pi$
$522$	9.00000	−	15.5885i	0.393919	−	0.682288i
$523$	25.5000	−	14.7224i	1.11504	−	0.643767i	0.174908	−	0.984585i	$-0.444037\pi$
$523$	25.5000	−	14.7224i	1.11504	−	0.643767i	0.940129	+	0.340818i	$0.110704\pi$
$524$	−22.5167			−0.983645
$525$	8.66025	−	3.00000i	0.377964	−	0.130931i
$526$	18.0000			0.784837
$527$	15.5885	−	9.00000i	0.679044	−	0.392046i
$528$		0			0
$529$	0.500000	−	0.866025i	0.0217391	−	0.0376533i
$530$	−7.79423	−	13.5000i	−0.338560	−	0.586403i
$531$	31.1769			1.35296
$532$	−9.00000	−	1.73205i	−0.390199	−	0.0750939i
$533$		0			0
$534$	−10.3923	+	6.00000i	−0.449719	+	0.259645i
$535$	−9.00000	−	5.19615i	−0.389104	−	0.224649i
$536$	−4.33013	−	2.50000i	−0.187033	−	0.107984i
$537$	22.5000	−	12.9904i	0.970947	−	0.560576i
$538$		0			0
$539$		0			0
$540$	9.00000			0.387298
$541$	−14.5000	−	25.1147i	−0.623404	−	1.07977i	−0.988847	−	0.148933i	$-0.952416\pi$
$541$	−14.5000	−	25.1147i	−0.623404	−	1.07977i	0.365444	−	0.930834i	$-0.380917\pi$
$542$	12.1244	−	21.0000i	0.520786	−	0.902027i
$543$	5.19615	+	3.00000i	0.222988	+	0.128742i
$544$	4.50000	−	2.59808i	0.192936	−	0.111392i
$545$	3.46410			0.148386
$546$	1.50000	−	7.79423i	0.0641941	−	0.333562i
$547$	−46.0000			−1.96682			−0.983409	−	0.181402i	$-0.941936\pi$
$547$	−46.0000			−1.96682			−0.983409	+	0.181402i	$0.941936\pi$
$548$	7.79423	−	4.50000i	0.332953	−	0.192230i
$549$	−36.0000	−	20.7846i	−1.53644	−	0.887066i
$550$		0			0
$551$	−10.3923	−	18.0000i	−0.442727	−	0.766826i
$552$	1.73205			0.0737210
$553$	−20.0000	+	6.92820i	−0.850487	+	0.294617i
$554$			7.00000i			0.297402i
$555$	6.00000	+	10.3923i	0.254686	+	0.441129i
$556$		0			0
$557$	15.5885	+	9.00000i	0.660504	+	0.381342i	0.792469	−	0.609912i	$-0.208795\pi$
$557$	15.5885	+	9.00000i	0.660504	+	0.381342i	−0.131965	+	0.991254i	$0.542129\pi$
$558$	5.19615	+	9.00000i	0.219971	+	0.381000i
$559$			6.92820i			0.293032i
$560$	−3.46410	−	3.00000i	−0.146385	−	0.126773i
$561$		0			0
$562$	4.50000	+	7.79423i	0.189821	+	0.328780i
$563$	−6.92820	+	12.0000i	−0.291989	+	0.505740i	−0.974280	−	0.225341i	$-0.927650\pi$
$563$	−6.92820	+	12.0000i	−0.291989	+	0.505740i	0.682291	+	0.731081i	$0.260984\pi$
$564$	4.50000	−	7.79423i	0.189484	−	0.328196i
$565$	−13.5000	+	7.79423i	−0.567949	+	0.327906i
$566$	−8.66025			−0.364018
$567$	18.0000	+	15.5885i	0.755929	+	0.654654i
$568$	−15.0000			−0.629386
$569$	−23.3827	+	13.5000i	−0.980253	+	0.565949i	−0.902347	−	0.431011i	$-0.858157\pi$
$569$	−23.3827	+	13.5000i	−0.980253	+	0.565949i	−0.0779066	+	0.996961i	$0.524824\pi$
$570$	5.19615	−	9.00000i	0.217643	−	0.376969i
$571$	−20.5000	+	35.5070i	−0.857898	+	1.48592i	0.0160316	+	0.999871i	$0.494897\pi$
$571$	−20.5000	+	35.5070i	−0.857898	+	1.48592i	−0.873930	+	0.486052i	$0.838437\pi$
$572$		0			0
$573$		−	10.3923i		−	0.434145i
$574$		0			0
$575$			2.00000i			0.0834058i
$576$	1.50000	+	2.59808i	0.0625000	+	0.108253i
$577$	30.0000	+	17.3205i	1.24892	+	0.721062i	0.970893	−	0.239512i	$-0.0769875\pi$
$577$	30.0000	+	17.3205i	1.24892	+	0.721062i	0.278023	+	0.960574i	$0.410321\pi$
$578$	8.66025	+	5.00000i	0.360219	+	0.207973i
$579$	14.7224	+	25.5000i	0.611843	+	1.05974i
$580$		−	10.3923i		−	0.431517i
$581$	3.46410	−	18.0000i	0.143715	−	0.746766i
$582$	18.0000			0.746124
$583$		0			0
$584$	−6.06218	+	10.5000i	−0.250855	+	0.434493i
$585$	7.79423	+	4.50000i	0.322252	+	0.186052i
$586$	1.50000	−	0.866025i	0.0619644	−	0.0357752i
$587$	19.0526			0.786383			0.393192	−	0.919457i	$-0.371371\pi$
$587$	19.0526			0.786383			0.393192	+	0.919457i	$0.371371\pi$
$588$	−1.73205	−	12.0000i	−0.0714286	−	0.494872i
$589$	12.0000			0.494451
$590$	15.5885	−	9.00000i	0.641767	−	0.370524i
$591$	18.0000	+	10.3923i	0.740421	+	0.427482i
$592$	−2.00000	+	3.46410i	−0.0821995	+	0.142374i
$593$	−6.92820	−	12.0000i	−0.284507	−	0.492781i	0.687982	−	0.725727i	$-0.258497\pi$
$593$	−6.92820	−	12.0000i	−0.284507	−	0.492781i	−0.972490	+	0.232946i	$0.925163\pi$
$594$		0			0
$595$	4.50000	−	23.3827i	0.184482	−	0.958597i
$596$			3.00000i			0.122885i
$597$	36.3731	−	21.0000i	1.48865	−	0.859473i
$598$	1.50000	+	0.866025i	0.0613396	+	0.0354144i
$599$	−2.59808	−	1.50000i	−0.106155	−	0.0612883i	0.445983	−	0.895042i	$-0.352854\pi$
$599$	−2.59808	−	1.50000i	−0.106155	−	0.0612883i	−0.552137	+	0.833753i	$0.686188\pi$
$600$	−3.00000	+	1.73205i	−0.122474	+	0.0707107i
$601$			20.7846i			0.847822i	0.905704	+	0.423911i	$0.139343\pi$
$601$			20.7846i			0.847822i	−0.905704	+	0.423911i	$0.860657\pi$
$602$	3.46410	+	10.0000i	0.141186	+	0.407570i
$603$	15.0000			0.610847
$604$	11.0000	+	19.0526i	0.447584	+	0.775238i
$605$	9.52628	−	16.5000i	0.387298	−	0.670820i
$606$	−15.5885	−	9.00000i	−0.633238	−	0.365600i
$607$	27.0000	−	15.5885i	1.09590	−	0.632716i	0.160756	−	0.986994i	$-0.448607\pi$
$607$	27.0000	−	15.5885i	1.09590	−	0.632716i	0.935140	+	0.354278i	$0.115273\pi$
$608$	3.46410			0.140488
$609$	18.0000	−	20.7846i	0.729397	−	0.842235i
$610$	−24.0000			−0.971732
$611$	7.79423	−	4.50000i	0.315321	−	0.182051i
$612$	−7.79423	+	13.5000i	−0.315063	+	0.545705i
$613$	−10.0000	+	17.3205i	−0.403896	+	0.699569i	−0.994192	−	0.107618i	$-0.965678\pi$
$613$	−10.0000	+	17.3205i	−0.403896	+	0.699569i	0.590296	+	0.807187i	$0.299011\pi$
$614$	−10.3923	−	18.0000i	−0.419399	−	0.726421i
$615$		0			0
$616$		0			0
$617$		−	9.00000i		−	0.362326i	−0.983453	−	0.181163i	$-0.942014\pi$
$617$		−	9.00000i		−	0.362326i	0.983453	−	0.181163i	$-0.0579862\pi$
$618$	−4.50000	−	7.79423i	−0.181017	−	0.313530i
$619$	−28.5000	−	16.4545i	−1.14551	−	0.661361i	−0.197722	−	0.980258i	$-0.563354\pi$
$619$	−28.5000	−	16.4545i	−1.14551	−	0.661361i	−0.947790	+	0.318897i	$0.896688\pi$
$620$	5.19615	+	3.00000i	0.208683	+	0.120483i
$621$	−4.50000	+	2.59808i	−0.180579	+	0.104257i
$622$		−	1.73205i		−	0.0694489i
$623$	−17.3205	+	6.00000i	−0.693932	+	0.240385i
$624$			3.00000i			0.120096i
$625$	5.50000	+	9.52628i	0.220000	+	0.381051i
$626$	−1.73205	+	3.00000i	−0.0692267	+	0.119904i
$627$		0			0
$628$		0			0
$629$	−20.7846			−0.828737
$630$	13.5000	+	2.59808i	0.537853	+	0.103510i
$631$	−43.0000			−1.71180			−0.855901	−	0.517139i	$-0.826997\pi$
$631$	−43.0000			−1.71180			−0.855901	+	0.517139i	$0.826997\pi$
$632$	6.92820	−	4.00000i	0.275589	−	0.159111i
$633$	−3.46410	+	6.00000i	−0.137686	+	0.238479i
$634$	6.00000	−	10.3923i	0.238290	−	0.412731i
$635$	12.1244	+	21.0000i	0.481140	+	0.833360i
$636$			15.5885i			0.618123i
$637$	4.50000	−	11.2583i	0.178296	−	0.446071i
$638$		0			0
$639$	38.9711	−	22.5000i	1.54167	−	0.890086i
$640$	1.50000	+	0.866025i	0.0592927	+	0.0342327i
$641$	−18.1865	−	10.5000i	−0.718325	−	0.414725i	0.0958109	−	0.995400i	$-0.469456\pi$
$641$	−18.1865	−	10.5000i	−0.718325	−	0.414725i	−0.814136	+	0.580674i	$0.802789\pi$
$642$	5.19615	+	9.00000i	0.205076	+	0.355202i
$643$			38.1051i			1.50272i	0.659893	+	0.751360i	$0.270602\pi$
$643$			38.1051i			1.50272i	−0.659893	+	0.751360i	$0.729398\pi$
$644$	2.59808	+	0.500000i	0.102379	+	0.0197028i
$645$	−12.0000			−0.472500
$646$	9.00000	+	15.5885i	0.354100	+	0.613320i
$647$	1.73205	−	3.00000i	0.0680939	−	0.117942i	−0.829968	−	0.557811i	$-0.811642\pi$
$647$	1.73205	−	3.00000i	0.0680939	−	0.117942i	0.898062	+	0.439868i	$0.144975\pi$
$648$	−7.79423	−	4.50000i	−0.306186	−	0.176777i
$649$		0			0
$650$	−3.46410			−0.135873
$651$	5.19615	+	15.0000i	0.203653	+	0.587896i
$652$	10.0000			0.391630
$653$	−15.5885	+	9.00000i	−0.610023	+	0.352197i	−0.772975	−	0.634437i	$-0.781232\pi$
$653$	−15.5885	+	9.00000i	−0.610023	+	0.352197i	0.162951	+	0.986634i	$0.447899\pi$
$654$	−3.00000	−	1.73205i	−0.117309	−	0.0677285i
$655$	19.5000	−	33.7750i	0.761928	−	1.31970i
$656$		0			0
$657$		−	36.3731i		−	1.41905i
$658$	9.00000	−	10.3923i	0.350857	−	0.405134i
$659$			12.0000i			0.467454i	0.972302	+	0.233727i	$0.0750921\pi$
$659$			12.0000i			0.467454i	−0.972302	+	0.233727i	$0.924908\pi$
$660$		0			0
$661$	−33.0000	−	19.0526i	−1.28355	−	0.741059i	−0.306055	−	0.952014i	$-0.599009\pi$
$661$	−33.0000	−	19.0526i	−1.28355	−	0.741059i	−0.977496	+	0.210955i	$0.932343\pi$
$662$	−1.73205	−	1.00000i	−0.0673181	−	0.0388661i
$663$	−13.5000	+	7.79423i	−0.524297	+	0.302703i
$664$			6.92820i			0.268866i
$665$	10.3923	−	12.0000i	0.402996	−	0.465340i
$666$		−	12.0000i		−	0.464991i
$667$	3.00000	+	5.19615i	0.116160	+	0.201196i
$668$	−6.06218	+	10.5000i	−0.234553	+	0.406257i
$669$	−10.3923	−	6.00000i	−0.401790	−	0.231973i
$670$	7.50000	−	4.33013i	0.289750	−	0.167287i
$671$		0			0
$672$	1.50000	+	4.33013i	0.0578638	+	0.167038i
$673$	−26.0000			−1.00223			−0.501113	−	0.865382i	$-0.667076\pi$
$673$	−26.0000			−1.00223			−0.501113	+	0.865382i	$0.667076\pi$
$674$	−8.66025	+	5.00000i	−0.333581	+	0.192593i
$675$	5.19615	−	9.00000i	0.200000	−	0.346410i
$676$	5.00000	−	8.66025i	0.192308	−	0.333087i
$677$	−0.866025	−	1.50000i	−0.0332841	−	0.0576497i	0.848904	−	0.528548i	$-0.177263\pi$
$677$	−0.866025	−	1.50000i	−0.0332841	−	0.0576497i	−0.882188	+	0.470898i	$0.843930\pi$
$678$	15.5885			0.598671
$679$	27.0000	+	5.19615i	1.03616	+	0.199410i
$680$			9.00000i			0.345134i
$681$	18.0000	+	31.1769i	0.689761	+	1.19470i
$682$		0			0
$683$	−18.1865	−	10.5000i	−0.695888	−	0.401771i	0.109926	−	0.993940i	$-0.464939\pi$
$683$	−18.1865	−	10.5000i	−0.695888	−	0.401771i	−0.805814	+	0.592168i	$0.798272\pi$
$684$	−9.00000	+	5.19615i	−0.344124	+	0.198680i
$685$			15.5885i			0.595604i
$686$	0.866025	−	18.5000i	0.0330650	−	0.706333i
$687$			42.0000i			1.60240i
$688$	−2.00000	−	3.46410i	−0.0762493	−	0.132068i
$689$	−7.79423	+	13.5000i	−0.296936	+	0.514309i
$690$	−1.50000	+	2.59808i	−0.0571040	+	0.0989071i
$691$	−18.0000	+	10.3923i	−0.684752	+	0.395342i	−0.801643	−	0.597803i	$-0.796041\pi$
$691$	−18.0000	+	10.3923i	−0.684752	+	0.395342i	0.116891	+	0.993145i	$0.462707\pi$
$692$	3.46410			0.131685
$693$		0			0
$694$	−27.0000			−1.02491
$695$		0			0
$696$	−5.19615	+	9.00000i	−0.196960	+	0.341144i
$697$		0			0
$698$	9.52628	+	16.5000i	0.360575	+	0.624534i
$699$		−	10.3923i		−	0.393073i
$700$	−5.00000	+	1.73205i	−0.188982	+	0.0654654i
$701$			45.0000i			1.69963i	0.527084	+	0.849813i	$0.323285\pi$
$701$			45.0000i			1.69963i	−0.527084	+	0.849813i	$0.676715\pi$
$702$	−4.50000	−	7.79423i	−0.169842	−	0.294174i
$703$	−12.0000	−	6.92820i	−0.452589	−	0.261302i
$704$		0			0
$705$	7.79423	+	13.5000i	0.293548	+	0.508439i
$706$			3.46410i			0.130373i
$707$	−20.7846	−	18.0000i	−0.781686	−	0.676960i
$708$	−18.0000			−0.676481
$709$	−14.0000	−	24.2487i	−0.525781	−	0.910679i	−0.999549	−	0.0300298i	$-0.990440\pi$
$709$	−14.0000	−	24.2487i	−0.525781	−	0.910679i	0.473768	−	0.880650i	$-0.342894\pi$
$710$	12.9904	−	22.5000i	0.487520	−	0.844410i
$711$	−12.0000	+	20.7846i	−0.450035	+	0.779484i
$712$	6.00000	−	3.46410i	0.224860	−	0.129823i
$713$	−3.46410			−0.129732
$714$	−15.5885	+	18.0000i	−0.583383	+	0.673633i
$715$		0			0
$716$	−12.9904	+	7.50000i	−0.485473	+	0.280288i
$717$	18.0000	+	10.3923i	0.672222	+	0.388108i
$718$	3.00000	−	5.19615i	0.111959	−	0.193919i
$719$	4.33013	+	7.50000i	0.161486	+	0.279703i	0.935402	−	0.353586i	$-0.115038\pi$
$719$	4.33013	+	7.50000i	0.161486	+	0.279703i	−0.773916	+	0.633289i	$0.781705\pi$
$720$	−5.19615			−0.193649
$721$	−4.50000	−	12.9904i	−0.167589	−	0.483787i
$722$		−	7.00000i		−	0.260513i
$723$	5.19615	−	3.00000i	0.193247	−	0.111571i
$724$	−3.00000	−	1.73205i	−0.111494	−	0.0643712i
$725$	−10.3923	−	6.00000i	−0.385961	−	0.222834i
$726$	−16.5000	+	9.52628i	−0.612372	+	0.353553i
$727$			3.46410i			0.128476i	0.997935	+	0.0642382i	$0.0204617\pi$
$727$			3.46410i			0.128476i	−0.997935	+	0.0642382i	$0.979538\pi$
$728$	−0.866025	+	4.50000i	−0.0320970	+	0.166781i
$729$	27.0000			1.00000
$730$	−10.5000	−	18.1865i	−0.388622	−	0.673114i
$731$	10.3923	−	18.0000i	0.384373	−	0.665754i
$732$	20.7846	+	12.0000i	0.768221	+	0.443533i
$733$	9.00000	−	5.19615i	0.332423	−	0.191924i	−0.324494	−	0.945888i	$-0.605194\pi$
$733$	9.00000	−	5.19615i	0.332423	−	0.191924i	0.656916	+	0.753964i	$0.271861\pi$
$734$	−8.66025			−0.319656
$735$	19.5000	+	7.79423i	0.719268	+	0.287494i
$736$	−1.00000			−0.0368605
$737$		0			0
$738$		0			0
$739$	−16.0000	+	27.7128i	−0.588570	+	1.01943i	0.405851	+	0.913939i	$0.366975\pi$
$739$	−16.0000	+	27.7128i	−0.588570	+	1.01943i	−0.994420	+	0.105493i	$0.966358\pi$
$740$	−3.46410	−	6.00000i	−0.127343	−	0.220564i
$741$	−10.3923			−0.381771
$742$	−4.50000	+	23.3827i	−0.165200	+	0.858405i
$743$			42.0000i			1.54083i	0.637542	+	0.770415i	$0.279951\pi$
$743$			42.0000i			1.54083i	−0.637542	+	0.770415i	$0.720049\pi$
$744$	−3.00000	−	5.19615i	−0.109985	−	0.190500i
$745$	−4.50000	−	2.59808i	−0.164867	−	0.0951861i
$746$	−3.46410	−	2.00000i	−0.126830	−	0.0732252i
$747$	−10.3923	−	18.0000i	−0.380235	−	0.658586i
$748$		0			0
$749$	5.19615	+	15.0000i	0.189863	+	0.548088i
$750$		−	21.0000i		−	0.766812i
$751$	16.0000	+	27.7128i	0.583848	+	1.01125i	0.995018	+	0.0996961i	$0.0317870\pi$
$751$	16.0000	+	27.7128i	0.583848	+	1.01125i	−0.411170	+	0.911559i	$0.634880\pi$
$752$	−2.59808	+	4.50000i	−0.0947421	+	0.164098i
$753$	−21.0000	+	36.3731i	−0.765283	+	1.32551i
$754$	−9.00000	+	5.19615i	−0.327761	+	0.189233i
$755$	−38.1051			−1.38679
$756$	−10.3923	−	9.00000i	−0.377964	−	0.327327i
$757$	−50.0000			−1.81728			−0.908640	−	0.417579i	$-0.862879\pi$
$757$	−50.0000			−1.81728			−0.908640	+	0.417579i	$0.862879\pi$
$758$	4.33013	−	2.50000i	0.157277	−	0.0908041i
$759$		0			0
$760$	−3.00000	+	5.19615i	−0.108821	+	0.188484i
$761$	−8.66025	−	15.0000i	−0.313934	−	0.543750i	0.665276	−	0.746597i	$-0.268314\pi$
$761$	−8.66025	−	15.0000i	−0.313934	−	0.543750i	−0.979210	+	0.202848i	$0.934980\pi$
$762$		−	24.2487i		−	0.878438i
$763$	−4.00000	−	3.46410i	−0.144810	−	0.125409i
$764$			6.00000i			0.217072i
$765$	−13.5000	−	23.3827i	−0.488094	−	0.845403i
$766$	24.0000	+	13.8564i	0.867155	+	0.500652i
$767$	−15.5885	−	9.00000i	−0.562867	−	0.324971i
$768$	−0.866025	−	1.50000i	−0.0312500	−	0.0541266i
$769$			10.3923i			0.374756i	0.982288	+	0.187378i	$0.0599989\pi$
$769$			10.3923i			0.374756i	−0.982288	+	0.187378i	$0.940001\pi$
$770$		0			0
$771$	42.0000			1.51259
$772$	−8.50000	−	14.7224i	−0.305922	−	0.529872i
$773$	0.866025	−	1.50000i	0.0311488	−	0.0539513i	−0.850031	−	0.526733i	$-0.823417\pi$
$773$	0.866025	−	1.50000i	0.0311488	−	0.0539513i	0.881180	+	0.472782i	$0.156750\pi$
$774$	10.3923	+	6.00000i	0.373544	+	0.215666i
$775$	6.00000	−	3.46410i	0.215526	−	0.124434i
$776$	−10.3923			−0.373062
$777$	3.46410	−	18.0000i	0.124274	−	0.645746i
$778$	−30.0000			−1.07555
$779$		0			0
$780$	−4.50000	−	2.59808i	−0.161126	−	0.0930261i
$781$		0			0
$782$	−2.59808	−	4.50000i	−0.0929070	−	0.160920i
$783$		−	31.1769i		−	1.11417i
$784$	1.00000	+	6.92820i	0.0357143	+	0.247436i
$785$		0			0
$786$	−33.7750	+	19.5000i	−1.20471	+	0.695542i
$787$	31.5000	+	18.1865i	1.12285	+	0.648280i	0.942128	−	0.335254i	$-0.108822\pi$
$787$	31.5000	+	18.1865i	1.12285	+	0.648280i	0.180726	+	0.983534i	$0.442155\pi$
$788$	−10.3923	−	6.00000i	−0.370211	−	0.213741i
$789$	27.0000	−	15.5885i	0.961225	−	0.554964i
$790$			13.8564i			0.492989i
$791$	23.3827	+	4.50000i	0.831393	+	0.160002i
$792$		0			0
$793$	12.0000	+	20.7846i	0.426132	+	0.738083i
$794$	12.9904	−	22.5000i	0.461011	−	0.798495i
$795$	−23.3827	−	13.5000i	−0.829298	−	0.478796i
$796$	−21.0000	+	12.1244i	−0.744325	+	0.429736i
$797$	−5.19615			−0.184057			−0.0920286	−	0.995756i	$-0.529335\pi$
$797$	−5.19615			−0.184057			−0.0920286	+	0.995756i	$0.529335\pi$
$798$	−15.0000	+	5.19615i	−0.530994	+	0.183942i
$799$	−27.0000			−0.955191
$800$	1.73205	−	1.00000i	0.0612372	−	0.0353553i
$801$	−10.3923	+	18.0000i	−0.367194	+	0.635999i
$802$	1.50000	−	2.59808i	0.0529668	−	0.0917413i
$803$		0			0
$804$	−8.66025			−0.305424
$805$	−3.00000	+	3.46410i	−0.105736	+	0.122094i
$806$		−	6.00000i		−	0.211341i
$807$		0			0
$808$	9.00000	+	5.19615i	0.316619	+	0.182800i
$809$	−5.19615	−	3.00000i	−0.182687	−	0.105474i	0.405868	−	0.913932i	$-0.366969\pi$
$809$	−5.19615	−	3.00000i	−0.182687	−	0.105474i	−0.588555	+	0.808458i	$0.700303\pi$
$810$	13.5000	−	7.79423i	0.474342	−	0.273861i
$811$			34.6410i			1.21641i	0.793780	+	0.608205i	$0.208110\pi$
$811$			34.6410i			1.21641i	−0.793780	+	0.608205i	$0.791890\pi$
$812$	−10.3923	+	12.0000i	−0.364698	+	0.421117i
$813$		−	42.0000i		−	1.47300i
$814$		0			0
$815$	−8.66025	+	15.0000i	−0.303355	+	0.525427i
$816$	4.50000	−	7.79423i	0.157532	−	0.272853i
$817$	12.0000	−	6.92820i	0.419827	−	0.242387i
$818$	19.0526			0.666157
$819$	−4.50000	−	12.9904i	−0.157243	−	0.453921i
$820$		0			0
$821$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$821$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$822$	7.79423	−	13.5000i	0.271855	−	0.470867i
$823$	20.0000	−	34.6410i	0.697156	−	1.20751i	−0.272292	−	0.962215i	$-0.587782\pi$
$823$	20.0000	−	34.6410i	0.697156	−	1.20751i	0.969448	−	0.245295i	$-0.0788849\pi$
$824$	2.59808	+	4.50000i	0.0905083	+	0.156765i
$825$		0			0
$826$	−27.0000	−	5.19615i	−0.939450	−	0.180797i
$827$		−	24.0000i		−	0.834562i	−0.908778	−	0.417281i	$-0.862983\pi$
$827$		−	24.0000i		−	0.834562i	0.908778	−	0.417281i	$-0.137017\pi$
$828$	2.59808	−	1.50000i	0.0902894	−	0.0521286i
$829$	25.5000	+	14.7224i	0.885652	+	0.511331i	0.872518	−	0.488583i	$-0.162486\pi$
$829$	25.5000	+	14.7224i	0.885652	+	0.511331i	0.0131339	+	0.999914i	$0.495819\pi$
$830$	−10.3923	−	6.00000i	−0.360722	−	0.208263i
$831$	6.06218	+	10.5000i	0.210295	+	0.364241i
$832$		−	1.73205i		−	0.0600481i
$833$	−28.5788	+	22.5000i	−0.990198	+	0.779579i
$834$		0			0
$835$	−10.5000	−	18.1865i	−0.363367	−	0.629371i
$836$		0			0
$837$	15.5885	+	9.00000i	0.538816	+	0.311086i
$838$	−9.00000	+	5.19615i	−0.310900	+	0.179498i
$839$	−41.5692			−1.43513			−0.717564	−	0.696492i	$-0.754743\pi$
$839$	−41.5692			−1.43513			−0.717564	+	0.696492i	$0.754743\pi$
$840$	−7.79423	−	1.50000i	−0.268926	−	0.0517549i
$841$	−7.00000			−0.241379
$842$	29.4449	−	17.0000i	1.01474	−	0.585859i
$843$	13.5000	+	7.79423i	0.464965	+	0.268447i
$844$	2.00000	−	3.46410i	0.0688428	−	0.119239i
$845$	8.66025	+	15.0000i	0.297922	+	0.516016i
$846$		−	15.5885i		−	0.535942i
$847$	−27.5000	+	9.52628i	−0.944911	+	0.327327i
$848$		−	9.00000i		−	0.309061i
$849$	−12.9904	+	7.50000i	−0.445829	+	0.257399i
$850$	9.00000	+	5.19615i	0.308697	+	0.178227i
$851$	3.46410	+	2.00000i	0.118748	+	0.0685591i
$852$	−22.5000	+	12.9904i	−0.770837	+	0.445043i
$853$		−	41.5692i		−	1.42330i	−0.702533	−	0.711651i	$-0.747948\pi$
$853$		−	41.5692i		−	1.42330i	0.702533	−	0.711651i	$-0.252052\pi$
$854$	27.7128	+	24.0000i	0.948313	+	0.821263i
$855$		−	18.0000i		−	0.615587i
$856$	−3.00000	−	5.19615i	−0.102538	−	0.177601i
$857$	5.19615	−	9.00000i	0.177497	−	0.307434i	−0.763525	−	0.645778i	$-0.776533\pi$
$857$	5.19615	−	9.00000i	0.177497	−	0.307434i	0.941023	+	0.338344i	$0.109867\pi$
$858$		0			0
$859$	30.0000	−	17.3205i	1.02359	−	0.590968i	0.108446	−	0.994102i	$-0.465413\pi$
$859$	30.0000	−	17.3205i	1.02359	−	0.590968i	0.915141	+	0.403134i	$0.132079\pi$
$860$	6.92820			0.236250
$861$		0			0
$862$	−30.0000			−1.02180
$863$	−49.3634	+	28.5000i	−1.68035	+	0.970151i	−0.718925	+	0.695087i	$0.755366\pi$
$863$	−49.3634	+	28.5000i	−1.68035	+	0.970151i	−0.961426	+	0.275064i	$0.911301\pi$
$864$	4.50000	+	2.59808i	0.153093	+	0.0883883i
$865$	−3.00000	+	5.19615i	−0.102003	+	0.176674i
$866$	−10.3923	−	18.0000i	−0.353145	−	0.611665i
$867$	17.3205			0.588235
$868$	−3.00000	−	8.66025i	−0.101827	−	0.293948i
$869$		0			0
$870$	−9.00000	−	15.5885i	−0.305129	−	0.528498i
$871$	−7.50000	−	4.33013i	−0.254128	−	0.146721i
$872$	1.73205	+	1.00000i	0.0586546	+	0.0338643i
$873$	27.0000	−	15.5885i	0.913812	−	0.527589i
$874$		−	3.46410i		−	0.117175i
$875$	6.06218	−	31.5000i	0.204939	−	1.06489i
$876$			21.0000i			0.709524i
$877$	6.50000	+	11.2583i	0.219489	+	0.380167i	0.954652	−	0.297724i	$-0.0962275\pi$
$877$	6.50000	+	11.2583i	0.219489	+	0.380167i	−0.735163	+	0.677891i	$0.762894\pi$
$878$	6.92820	−	12.0000i	0.233816	−	0.404980i
$879$	1.50000	−	2.59808i	0.0505937	−	0.0876309i
$880$		0			0
$881$	−19.0526			−0.641897			−0.320949	−	0.947097i	$-0.604002\pi$
$881$	−19.0526			−0.641897			−0.320949	+	0.947097i	$0.604002\pi$
$882$	−12.9904	−	16.5000i	−0.437409	−	0.555584i
$883$	34.0000			1.14419			0.572096	−	0.820187i	$-0.306131\pi$
$883$	34.0000			1.14419			0.572096	+	0.820187i	$0.306131\pi$
$884$	7.79423	−	4.50000i	0.262148	−	0.151351i
$885$	15.5885	−	27.0000i	0.524000	−	0.907595i
$886$	−4.50000	+	7.79423i	−0.151180	+	0.261852i
$887$	−19.0526	−	33.0000i	−0.639722	−	1.10803i	−0.985494	−	0.169713i	$-0.945716\pi$
$887$	−19.0526	−	33.0000i	−0.639722	−	1.10803i	0.345771	−	0.938319i	$-0.387617\pi$
$888$			6.92820i			0.232495i
$889$	7.00000	−	36.3731i	0.234772	−	1.21991i
$890$			12.0000i			0.402241i
$891$		0			0
$892$	6.00000	+	3.46410i	0.200895	+	0.115987i
$893$	−15.5885	−	9.00000i	−0.521648	−	0.301174i
$894$	2.59808	+	4.50000i	0.0868927	+	0.150503i
$895$		−	25.9808i		−	0.868441i
$896$	−0.866025	−	2.50000i	−0.0289319	−	0.0835191i
$897$	3.00000			0.100167
$898$	−3.00000	−	5.19615i	−0.100111	−	0.173398i
$899$	10.3923	−	18.0000i	0.346603	−	0.600334i
$900$	−3.00000	+	5.19615i	−0.100000	+	0.173205i
$901$	40.5000	−	23.3827i	1.34925	−	0.778990i
$902$		0			0
$903$	13.8564	+	12.0000i	0.461112	+	0.399335i
$904$	−9.00000			−0.299336
$905$	5.19615	−	3.00000i	0.172726	−	0.0997234i
$906$	33.0000	+	19.0526i	1.09635	+	0.632979i
$907$	−21.5000	+	37.2391i	−0.713896	+	1.23650i	0.249488	+	0.968378i	$0.419738\pi$
$907$	−21.5000	+	37.2391i	−0.713896	+	1.23650i	−0.963384	+	0.268126i	$0.913596\pi$
$908$	−10.3923	−	18.0000i	−0.344881	−	0.597351i
$909$	−31.1769			−1.03407
$910$	−6.00000	−	5.19615i	−0.198898	−	0.172251i
$911$		−	36.0000i		−	1.19273i	−0.802712	−	0.596367i	$-0.796610\pi$
$911$		−	36.0000i		−	1.19273i	0.802712	−	0.596367i	$-0.203390\pi$
$912$	5.19615	−	3.00000i	0.172062	−	0.0993399i
$913$		0			0
$914$	−12.1244	−	7.00000i	−0.401038	−	0.231539i
$915$	−36.0000	+	20.7846i	−1.19012	+	0.687118i
$916$		−	24.2487i		−	0.801200i
$917$	−56.2917	+	19.5000i	−1.85891	+	0.643947i
$918$			27.0000i			0.891133i
$919$	2.50000	+	4.33013i	0.0824674	+	0.142838i	0.904309	−	0.426878i	$-0.140387\pi$
$919$	2.50000	+	4.33013i	0.0824674	+	0.142838i	−0.821842	+	0.569716i	$0.807053\pi$
$920$	0.866025	−	1.50000i	0.0285520	−	0.0494535i
$921$	−31.1769	−	18.0000i	−1.02731	−	0.593120i
$922$	24.0000	−	13.8564i	0.790398	−	0.456336i
$923$	−25.9808			−0.855167
$924$		0			0
$925$	−8.00000			−0.263038
$926$	−12.1244	+	7.00000i	−0.398431	+	0.230034i
$927$	−13.5000	−	7.79423i	−0.443398	−	0.255996i
$928$	3.00000	−	5.19615i	0.0984798	−	0.170572i
$929$	8.66025	+	15.0000i	0.284134	+	0.492134i	0.972399	−	0.233325i	$-0.0749607\pi$
$929$	8.66025	+	15.0000i	0.284134	+	0.492134i	−0.688265	+	0.725459i	$0.741627\pi$
$930$	10.3923			0.340777
$931$	−24.0000	+	3.46410i	−0.786568	+	0.113531i
$932$			6.00000i			0.196537i
$933$	−1.50000	−	2.59808i	−0.0491078	−	0.0850572i
$934$	−6.00000	−	3.46410i	−0.196326	−	0.113349i
$935$		0			0
$936$	2.59808	+	4.50000i	0.0849208	+	0.147087i
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$	−12.9904	−	2.50000i	−0.424151	−	0.0816279i
$939$			6.00000i			0.195803i
$940$	−4.50000	−	7.79423i	−0.146774	−	0.254220i
$941$	27.7128	−	48.0000i	0.903412	−	1.56476i	0.0803769	−	0.996765i	$-0.474388\pi$
$941$	27.7128	−	48.0000i	0.903412	−	1.56476i	0.823035	−	0.567991i	$-0.192279\pi$
$942$		0			0
$943$		0			0
$944$	10.3923			0.338241
$945$	22.5000	−	7.79423i	0.731925	−	0.253546i
$946$		0			0
$947$	23.3827	−	13.5000i	0.759835	−	0.438691i	−0.0694014	−	0.997589i	$-0.522109\pi$
$947$	23.3827	−	13.5000i	0.759835	−	0.438691i	0.829237	+	0.558898i	$0.188776\pi$
$948$	6.92820	−	12.0000i	0.225018	−	0.389742i
$949$	−10.5000	+	18.1865i	−0.340844	+	0.590360i
$950$	3.46410	+	6.00000i	0.112390	+	0.194666i
$951$		−	20.7846i		−	0.673987i
$952$	9.00000	−	10.3923i	0.291692	−	0.336817i
$953$		−	30.0000i		−	0.971795i	−0.874016	−	0.485898i	$-0.838493\pi$
$953$		−	30.0000i		−	0.971795i	0.874016	−	0.485898i	$-0.161507\pi$
$954$	13.5000	+	23.3827i	0.437079	+	0.757042i
$955$	−9.00000	−	5.19615i	−0.291233	−	0.168144i
$956$	−10.3923	−	6.00000i	−0.336111	−	0.194054i
$957$		0			0
$958$		−	10.3923i		−	0.335760i
$959$	15.5885	−	18.0000i	0.503378	−	0.581250i
$960$	3.00000			0.0968246
$961$	−9.50000	−	16.4545i	−0.306452	−	0.530790i
$962$	−3.46410	+	6.00000i	−0.111687	+	0.193448i
$963$	15.5885	+	9.00000i	0.502331	+	0.290021i
$964$	−3.00000	+	1.73205i	−0.0966235	+	0.0557856i
$965$	29.4449			0.947864
$966$	4.33013	−	1.50000i	0.139320	−	0.0482617i
$967$	44.0000			1.41494			0.707472	−	0.706741i	$-0.249835\pi$
$967$	44.0000			1.41494			0.707472	+	0.706741i	$0.249835\pi$
$968$	9.52628	−	5.50000i	0.306186	−	0.176777i
$969$	27.0000	+	15.5885i	0.867365	+	0.500773i
$970$	9.00000	−	15.5885i	0.288973	−	0.500515i
$971$	19.0526	+	33.0000i	0.611426	+	1.05902i	0.991000	+	0.133859i	$0.0427370\pi$
$971$	19.0526	+	33.0000i	0.611426	+	1.05902i	−0.379575	+	0.925161i	$0.623930\pi$
$972$	−15.5885			−0.500000
$973$		0			0
$974$		−	4.00000i		−	0.128168i
$975$	−5.19615	+	3.00000i	−0.166410	+	0.0960769i
$976$	−12.0000	−	6.92820i	−0.384111	−	0.221766i
$977$	−18.1865	−	10.5000i	−0.581839	−	0.335925i	0.180025	−	0.983662i	$-0.442382\pi$
$977$	−18.1865	−	10.5000i	−0.581839	−	0.335925i	−0.761864	+	0.647737i	$0.775715\pi$
$978$	15.0000	−	8.66025i	0.479647	−	0.276924i
$979$		0			0
$980$	−11.2583	−	4.50000i	−0.359634	−	0.143747i
$981$	−6.00000			−0.191565
$982$	7.50000	+	12.9904i	0.239335	+	0.414540i
$983$	−10.3923	+	18.0000i	−0.331463	+	0.574111i	−0.982799	−	0.184679i	$-0.940876\pi$
$983$	−10.3923	+	18.0000i	−0.331463	+	0.574111i	0.651336	+	0.758790i	$0.274209\pi$
$984$		0			0
$985$	18.0000	−	10.3923i	0.573528	−	0.331126i
$986$	31.1769			0.992875
$987$	4.50000	−	23.3827i	0.143237	−	0.744279i
$988$	6.00000			0.190885
$989$	−3.46410	+	2.00000i	−0.110152	+	0.0635963i
$990$		0			0
$991$	19.0000	−	32.9090i	0.603555	−	1.04539i	−0.388723	−	0.921355i	$-0.627084\pi$
$991$	19.0000	−	32.9090i	0.603555	−	1.04539i	0.992278	−	0.124033i	$-0.0395829\pi$
$992$	1.73205	+	3.00000i	0.0549927	+	0.0952501i
$993$	−3.46410			−0.109930
$994$	−37.5000	+	12.9904i	−1.18943	+	0.412030i
$995$		−	42.0000i		−	1.33149i
$996$	6.00000	+	10.3923i	0.190117	+	0.329293i
$997$	12.0000	+	6.92820i	0.380044	+	0.219418i	0.677837	−	0.735212i	$-0.262917\pi$
$997$	12.0000	+	6.92820i	0.380044	+	0.219418i	−0.297794	+	0.954630i	$0.596251\pi$
$998$	−27.7128	−	16.0000i	−0.877234	−	0.506471i
$999$	−10.3923	−	18.0000i	−0.328798	−	0.569495i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.l.a.185.1	yes	4
3.2	odd	2	inner	966.2.l.a.185.2	yes	4
7.5	odd	6	inner	966.2.l.a.47.2	yes	4
21.5	even	6	inner	966.2.l.a.47.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.l.a.47.1	✓	4	21.5	even	6	inner
966.2.l.a.47.2	yes	4	7.5	odd	6	inner
966.2.l.a.185.1	yes	4	1.1	even	1	trivial
966.2.l.a.185.2	yes	4	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 1.50000i) q^{5} -1.73205i q^{6} +(0.500000 - 2.59808i) q^{7} +1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 1.50000i) q^{5} -1.73205i q^{6} +(0.500000 - 2.59808i) q^{7} +1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-1.50000 - 0.866025i) q^{10} +(0.866025 + 1.50000i) q^{12} +1.73205i q^{13} +(0.866025 + 2.50000i) q^{14} -3.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.59808 - 4.50000i) q^{17} +(2.59808 + 1.50000i) q^{18} +(3.00000 - 1.73205i) q^{19} +1.73205 q^{20} +(3.46410 + 3.00000i) q^{21} +(-0.866025 + 0.500000i) q^{23} +(-1.50000 - 0.866025i) q^{24} +(1.00000 - 1.73205i) q^{25} +(-0.866025 - 1.50000i) q^{26} +5.19615 q^{27} +(-2.00000 - 1.73205i) q^{28} -6.00000i q^{29} +(2.59808 - 1.50000i) q^{30} +(3.00000 + 1.73205i) q^{31} +(0.866025 + 0.500000i) q^{32} +5.19615i q^{34} +(4.33013 - 1.50000i) q^{35} -3.00000 q^{36} +(-2.00000 - 3.46410i) q^{37} +(-1.73205 + 3.00000i) q^{38} +(-2.59808 - 1.50000i) q^{39} +(-1.50000 + 0.866025i) q^{40} +(-4.50000 - 0.866025i) q^{42} +4.00000 q^{43} +(2.59808 - 4.50000i) q^{45} +(0.500000 - 0.866025i) q^{46} +(-2.59808 - 4.50000i) q^{47} +1.73205 q^{48} +(-6.50000 - 2.59808i) q^{49} +2.00000i q^{50} +(4.50000 + 7.79423i) q^{51} +(1.50000 + 0.866025i) q^{52} +(7.79423 + 4.50000i) q^{53} +(-4.50000 + 2.59808i) q^{54} +(2.59808 + 0.500000i) q^{56} +6.00000i q^{57} +(3.00000 + 5.19615i) q^{58} +(-5.19615 + 9.00000i) q^{59} +(-1.50000 + 2.59808i) q^{60} +(12.0000 - 6.92820i) q^{61} -3.46410 q^{62} +(-7.50000 + 2.59808i) q^{63} -1.00000 q^{64} +(-2.59808 + 1.50000i) q^{65} +(-2.50000 + 4.33013i) q^{67} +(-2.59808 - 4.50000i) q^{68} -1.73205i q^{69} +(-3.00000 + 3.46410i) q^{70} +15.0000i q^{71} +(2.59808 - 1.50000i) q^{72} +(10.5000 + 6.06218i) q^{73} +(3.46410 + 2.00000i) q^{74} +(1.73205 + 3.00000i) q^{75} -3.46410i q^{76} +3.00000 q^{78} +(-4.00000 - 6.92820i) q^{79} +(0.866025 - 1.50000i) q^{80} +(-4.50000 + 7.79423i) q^{81} +6.92820 q^{83} +(4.33013 - 1.50000i) q^{84} +9.00000 q^{85} +(-3.46410 + 2.00000i) q^{86} +(9.00000 + 5.19615i) q^{87} +(-3.46410 - 6.00000i) q^{89} +5.19615i q^{90} +(4.50000 + 0.866025i) q^{91} +1.00000i q^{92} +(-5.19615 + 3.00000i) q^{93} +(4.50000 + 2.59808i) q^{94} +(5.19615 + 3.00000i) q^{95} +(-1.50000 + 0.866025i) q^{96} +10.3923i q^{97} +(6.92820 - 1.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 2 q^{7} - 6 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 + 2 * q^7 - 6 * q^9	\( 4 q + 2 q^{4} + 2 q^{7} - 6 q^{9} - 6 q^{10} - 12 q^{15} - 2 q^{16} + 12 q^{19} - 6 q^{24} + 4 q^{25} - 8 q^{28} + 12 q^{31} - 12 q^{36} - 8 q^{37} - 6 q^{40} - 18 q^{42} + 16 q^{43} + 2 q^{46} - 26 q^{49} + 18 q^{51} + 6 q^{52} - 18 q^{54} + 12 q^{58} - 6 q^{60} + 48 q^{61} - 30 q^{63} - 4 q^{64} - 10 q^{67} - 12 q^{70} + 42 q^{73} + 12 q^{78} - 16 q^{79} - 18 q^{81} + 36 q^{85} + 36 q^{87} + 18 q^{91} + 18 q^{94} - 6 q^{96}+O(q^{100}) \) 4 * q + 2 * q^4 + 2 * q^7 - 6 * q^9 - 6 * q^10 - 12 * q^15 - 2 * q^16 + 12 * q^19 - 6 * q^24 + 4 * q^25 - 8 * q^28 + 12 * q^31 - 12 * q^36 - 8 * q^37 - 6 * q^40 - 18 * q^42 + 16 * q^43 + 2 * q^46 - 26 * q^49 + 18 * q^51 + 6 * q^52 - 18 * q^54 + 12 * q^58 - 6 * q^60 + 48 * q^61 - 30 * q^63 - 4 * q^64 - 10 * q^67 - 12 * q^70 + 42 * q^73 + 12 * q^78 - 16 * q^79 - 18 * q^81 + 36 * q^85 + 36 * q^87 + 18 * q^91 + 18 * q^94 - 6 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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