LMFDB - Embedded newform 930.2.i.a.811.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(211,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("930.211");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.42608738798$
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:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			811.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	930.811
Dual form			930.2.i.a.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(1.50000 + 2.59808i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-1.00000 - 1.73205i) q^{13} +(-0.500000 + 0.866025i) q^{14} -1.00000 q^{15} +1.00000 q^{16} +(-3.00000 + 5.19615i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-1.00000 + 1.73205i) q^{19} +(0.500000 + 0.866025i) q^{20} +(0.500000 + 0.866025i) q^{21} +(-1.50000 - 2.59808i) q^{22} +6.00000 q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.00000 + 1.73205i) q^{26} +1.00000 q^{27} +(0.500000 - 0.866025i) q^{28} +9.00000 q^{29} +1.00000 q^{30} +(-3.50000 - 4.33013i) q^{31} -1.00000 q^{32} -3.00000 q^{33} +(3.00000 - 5.19615i) q^{34} +1.00000 q^{35} +(-0.500000 - 0.866025i) q^{36} +(-4.00000 + 6.92820i) q^{37} +(1.00000 - 1.73205i) q^{38} +2.00000 q^{39} +(-0.500000 - 0.866025i) q^{40} +(-0.500000 - 0.866025i) q^{42} +(-4.00000 + 6.92820i) q^{43} +(1.50000 + 2.59808i) q^{44} +(0.500000 - 0.866025i) q^{45} -6.00000 q^{46} -6.00000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(3.00000 + 5.19615i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-3.00000 - 5.19615i) q^{51} +(-1.00000 - 1.73205i) q^{52} +(-1.50000 - 2.59808i) q^{53} -1.00000 q^{54} +(-1.50000 + 2.59808i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(-1.00000 - 1.73205i) q^{57} -9.00000 q^{58} +(-7.50000 + 12.9904i) q^{59} -1.00000 q^{60} +14.0000 q^{61} +(3.50000 + 4.33013i) q^{62} -1.00000 q^{63} +1.00000 q^{64} +(1.00000 - 1.73205i) q^{65} +3.00000 q^{66} +(-4.00000 - 6.92820i) q^{67} +(-3.00000 + 5.19615i) q^{68} +(-3.00000 + 5.19615i) q^{69} -1.00000 q^{70} +(6.00000 + 10.3923i) q^{71} +(0.500000 + 0.866025i) q^{72} +(-7.00000 - 12.1244i) q^{73} +(4.00000 - 6.92820i) q^{74} +(-0.500000 - 0.866025i) q^{75} +(-1.00000 + 1.73205i) q^{76} +3.00000 q^{77} -2.00000 q^{78} +(-4.00000 + 6.92820i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.50000 + 7.79423i) q^{83} +(0.500000 + 0.866025i) q^{84} -6.00000 q^{85} +(4.00000 - 6.92820i) q^{86} +(-4.50000 + 7.79423i) q^{87} +(-1.50000 - 2.59808i) q^{88} +(-0.500000 + 0.866025i) q^{90} -2.00000 q^{91} +6.00000 q^{92} +(5.50000 - 0.866025i) q^{93} +6.00000 q^{94} -2.00000 q^{95} +(0.500000 - 0.866025i) q^{96} -19.0000 q^{97} +(-3.00000 - 5.19615i) q^{98} +(1.50000 - 2.59808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - q^{3} + 2 q^{4} + q^{5} + q^{6} + q^{7} - 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - q^3 + 2 * q^4 + q^5 + q^6 + q^7 - 2 * q^8 - q^9	$ 2 q - 2 q^{2} - q^{3} + 2 q^{4} + q^{5} + q^{6} + q^{7} - 2 q^{8} - q^{9} - q^{10} + 3 q^{11} - q^{12} - 2 q^{13} - q^{14} - 2 q^{15} + 2 q^{16} - 6 q^{17} + q^{18} - 2 q^{19} + q^{20} + q^{21} - 3 q^{22} + 12 q^{23} + q^{24} - q^{25} + 2 q^{26} + 2 q^{27} + q^{28} + 18 q^{29} + 2 q^{30} - 7 q^{31} - 2 q^{32} - 6 q^{33} + 6 q^{34} + 2 q^{35} - q^{36} - 8 q^{37} + 2 q^{38} + 4 q^{39} - q^{40} - q^{42} - 8 q^{43} + 3 q^{44} + q^{45} - 12 q^{46} - 12 q^{47} - q^{48} + 6 q^{49} + q^{50} - 6 q^{51} - 2 q^{52} - 3 q^{53} - 2 q^{54} - 3 q^{55} - q^{56} - 2 q^{57} - 18 q^{58} - 15 q^{59} - 2 q^{60} + 28 q^{61} + 7 q^{62} - 2 q^{63} + 2 q^{64} + 2 q^{65} + 6 q^{66} - 8 q^{67} - 6 q^{68} - 6 q^{69} - 2 q^{70} + 12 q^{71} + q^{72} - 14 q^{73} + 8 q^{74} - q^{75} - 2 q^{76} + 6 q^{77} - 4 q^{78} - 8 q^{79} + q^{80} - q^{81} + 9 q^{83} + q^{84} - 12 q^{85} + 8 q^{86} - 9 q^{87} - 3 q^{88} - q^{90} - 4 q^{91} + 12 q^{92} + 11 q^{93} + 12 q^{94} - 4 q^{95} + q^{96} - 38 q^{97} - 6 q^{98} + 3 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - q^3 + 2 * q^4 + q^5 + q^6 + q^7 - 2 * q^8 - q^9 - q^10 + 3 * q^11 - q^12 - 2 * q^13 - q^14 - 2 * q^15 + 2 * q^16 - 6 * q^17 + q^18 - 2 * q^19 + q^20 + q^21 - 3 * q^22 + 12 * q^23 + q^24 - q^25 + 2 * q^26 + 2 * q^27 + q^28 + 18 * q^29 + 2 * q^30 - 7 * q^31 - 2 * q^32 - 6 * q^33 + 6 * q^34 + 2 * q^35 - q^36 - 8 * q^37 + 2 * q^38 + 4 * q^39 - q^40 - q^42 - 8 * q^43 + 3 * q^44 + q^45 - 12 * q^46 - 12 * q^47 - q^48 + 6 * q^49 + q^50 - 6 * q^51 - 2 * q^52 - 3 * q^53 - 2 * q^54 - 3 * q^55 - q^56 - 2 * q^57 - 18 * q^58 - 15 * q^59 - 2 * q^60 + 28 * q^61 + 7 * q^62 - 2 * q^63 + 2 * q^64 + 2 * q^65 + 6 * q^66 - 8 * q^67 - 6 * q^68 - 6 * q^69 - 2 * q^70 + 12 * q^71 + q^72 - 14 * q^73 + 8 * q^74 - q^75 - 2 * q^76 + 6 * q^77 - 4 * q^78 - 8 * q^79 + q^80 - q^81 + 9 * q^83 + q^84 - 12 * q^85 + 8 * q^86 - 9 * q^87 - 3 * q^88 - q^90 - 4 * q^91 + 12 * q^92 + 11 * q^93 + 12 * q^94 - 4 * q^95 + q^96 - 38 * q^97 - 6 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	1.00000			0.500000
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i	−0.755929	−	0.654654i	$-0.772814\pi$
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i	0.944911	+	0.327327i	$0.106148\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	0.998526	−	0.0542666i	$-0.0172821\pi$
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	−0.546259	+	0.837616i	$0.683949\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	0.693375	−	0.720577i	$-0.256123\pi$
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	−0.970725	+	0.240192i	$0.922790\pi$
$14$	−0.500000	+	0.866025i	−0.133631	+	0.231455i
$15$	−1.00000			−0.258199
$16$	1.00000			0.250000
$17$	−3.00000	+	5.19615i	−0.727607	+	1.26025i	0.230285	+	0.973123i	$0.426034\pi$
$17$	−3.00000	+	5.19615i	−0.727607	+	1.26025i	−0.957892	+	0.287129i	$0.907299\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	−0.957635	−	0.287984i	$-0.907015\pi$
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	0.728219	+	0.685344i	$0.240348\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	0.500000	+	0.866025i	0.109109	+	0.188982i
$22$	−1.50000	−	2.59808i	−0.319801	−	0.553912i
$23$	6.00000			1.25109			0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000			1.25109			0.625543	+	0.780189i	$0.284877\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	1.00000	+	1.73205i	0.196116	+	0.339683i
$27$	1.00000			0.192450
$28$	0.500000	−	0.866025i	0.0944911	−	0.163663i
$29$	9.00000			1.67126			0.835629	−	0.549294i	$-0.185103\pi$
$29$	9.00000			1.67126			0.835629	+	0.549294i	$0.185103\pi$
$30$	1.00000			0.182574
$31$	−3.50000	−	4.33013i	−0.628619	−	0.777714i
$31$	−3.50000	−	4.33013i	−0.628619	−	0.777714i
$32$	−1.00000			−0.176777
$33$	−3.00000			−0.522233
$34$	3.00000	−	5.19615i	0.514496	−	0.891133i
$35$	1.00000			0.169031
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−4.00000	+	6.92820i	−0.657596	+	1.13899i	0.323640	+	0.946180i	$0.395093\pi$
$37$	−4.00000	+	6.92820i	−0.657596	+	1.13899i	−0.981236	+	0.192809i	$0.938240\pi$
$38$	1.00000	−	1.73205i	0.162221	−	0.280976i
$39$	2.00000			0.320256
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$41$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$42$	−0.500000	−	0.866025i	−0.0771517	−	0.133631i
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	0.381246	+	0.924473i	$0.375495\pi$
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	−0.991241	+	0.132068i	$0.957838\pi$
$44$	1.50000	+	2.59808i	0.226134	+	0.391675i
$45$	0.500000	−	0.866025i	0.0745356	−	0.129099i
$46$	−6.00000			−0.884652
$47$	−6.00000			−0.875190			−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000			−0.875190			−0.437595	+	0.899172i	$0.644170\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	3.00000	+	5.19615i	0.428571	+	0.742307i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	−3.00000	−	5.19615i	−0.420084	−	0.727607i
$52$	−1.00000	−	1.73205i	−0.138675	−	0.240192i
$53$	−1.50000	−	2.59808i	−0.206041	−	0.356873i	0.744423	−	0.667708i	$-0.232725\pi$
$53$	−1.50000	−	2.59808i	−0.206041	−	0.356873i	−0.950464	+	0.310835i	$0.899391\pi$
$54$	−1.00000			−0.136083
$55$	−1.50000	+	2.59808i	−0.202260	+	0.350325i
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$	−1.00000	−	1.73205i	−0.132453	−	0.229416i
$58$	−9.00000			−1.18176
$59$	−7.50000	+	12.9904i	−0.976417	+	1.69120i	−0.301239	+	0.953549i	$0.597400\pi$
$59$	−7.50000	+	12.9904i	−0.976417	+	1.69120i	−0.675178	+	0.737655i	$0.735933\pi$
$60$	−1.00000			−0.129099
$61$	14.0000			1.79252			0.896258	−	0.443533i	$-0.146275\pi$
$61$	14.0000			1.79252			0.896258	+	0.443533i	$0.146275\pi$
$62$	3.50000	+	4.33013i	0.444500	+	0.549927i
$63$	−1.00000			−0.125988
$64$	1.00000			0.125000
$65$	1.00000	−	1.73205i	0.124035	−	0.214834i
$66$	3.00000			0.369274
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	0.511237	−	0.859440i	$-0.329187\pi$
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	−0.999915	+	0.0130248i	$0.995854\pi$
$68$	−3.00000	+	5.19615i	−0.363803	+	0.630126i
$69$	−3.00000	+	5.19615i	−0.361158	+	0.625543i
$70$	−1.00000			−0.119523
$71$	6.00000	+	10.3923i	0.712069	+	1.23334i	0.964079	+	0.265615i	$0.0855750\pi$
$71$	6.00000	+	10.3923i	0.712069	+	1.23334i	−0.252010	+	0.967725i	$0.581092\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	−7.00000	−	12.1244i	−0.819288	−	1.41905i	−0.906208	−	0.422833i	$-0.861036\pi$
$73$	−7.00000	−	12.1244i	−0.819288	−	1.41905i	0.0869195	−	0.996215i	$-0.472298\pi$
$74$	4.00000	−	6.92820i	0.464991	−	0.805387i
$75$	−0.500000	−	0.866025i	−0.0577350	−	0.100000i
$76$	−1.00000	+	1.73205i	−0.114708	+	0.198680i
$77$	3.00000			0.341882
$78$	−2.00000			−0.226455
$79$	−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	$0.315255\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	4.50000	+	7.79423i	0.493939	+	0.855528i	0.999976	−	0.00698436i	$-0.00222321\pi$
$83$	4.50000	+	7.79423i	0.493939	+	0.855528i	−0.506036	+	0.862512i	$0.668890\pi$
$84$	0.500000	+	0.866025i	0.0545545	+	0.0944911i
$85$	−6.00000			−0.650791
$86$	4.00000	−	6.92820i	0.431331	−	0.747087i
$87$	−4.50000	+	7.79423i	−0.482451	+	0.835629i
$88$	−1.50000	−	2.59808i	−0.159901	−	0.276956i
$89$		0			0			−	1.00000i	$-0.5\pi$
$89$		0			0				1.00000i	$0.5\pi$
$90$	−0.500000	+	0.866025i	−0.0527046	+	0.0912871i
$91$	−2.00000			−0.209657
$92$	6.00000			0.625543
$93$	5.50000	−	0.866025i	0.570323	−	0.0898027i
$94$	6.00000			0.618853
$95$	−2.00000			−0.205196
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	−19.0000			−1.92916			−0.964579	−	0.263795i	$-0.915026\pi$
$97$	−19.0000			−1.92916			−0.964579	+	0.263795i	$0.915026\pi$
$98$	−3.00000	−	5.19615i	−0.303046	−	0.524891i
$99$	1.50000	−	2.59808i	0.150756	−	0.261116i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−3.00000			−0.298511			−0.149256	−	0.988799i	$-0.547688\pi$
$101$	−3.00000			−0.298511			−0.149256	+	0.988799i	$0.547688\pi$
$102$	3.00000	+	5.19615i	0.297044	+	0.514496i
$103$	6.50000	+	11.2583i	0.640464	+	1.10932i	0.985329	+	0.170664i	$0.0545913\pi$
$103$	6.50000	+	11.2583i	0.640464	+	1.10932i	−0.344865	+	0.938652i	$0.612075\pi$
$104$	1.00000	+	1.73205i	0.0980581	+	0.169842i
$105$	−0.500000	+	0.866025i	−0.0487950	+	0.0845154i
$106$	1.50000	+	2.59808i	0.145693	+	0.252347i
$107$	−7.50000	+	12.9904i	−0.725052	+	1.25583i	0.233900	+	0.972261i	$0.424851\pi$
$107$	−7.50000	+	12.9904i	−0.725052	+	1.25583i	−0.958952	+	0.283567i	$0.908482\pi$
$108$	1.00000			0.0962250
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$	1.50000	−	2.59808i	0.143019	−	0.247717i
$111$	−4.00000	−	6.92820i	−0.379663	−	0.657596i
$112$	0.500000	−	0.866025i	0.0472456	−	0.0818317i
$113$	9.00000	+	15.5885i	0.846649	+	1.46644i	0.884182	+	0.467143i	$0.154717\pi$
$113$	9.00000	+	15.5885i	0.846649	+	1.46644i	−0.0375328	+	0.999295i	$0.511950\pi$
$114$	1.00000	+	1.73205i	0.0936586	+	0.162221i
$115$	3.00000	+	5.19615i	0.279751	+	0.484544i
$116$	9.00000			0.835629
$117$	−1.00000	+	1.73205i	−0.0924500	+	0.160128i
$118$	7.50000	−	12.9904i	0.690431	−	1.19586i
$119$	3.00000	+	5.19615i	0.275010	+	0.476331i
$120$	1.00000			0.0912871
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	−14.0000			−1.26750
$123$		0			0
$124$	−3.50000	−	4.33013i	−0.314309	−	0.388857i
$125$	−1.00000			−0.0894427
$126$	1.00000			0.0890871
$127$	3.50000	−	6.06218i	0.310575	−	0.537931i	−0.667912	−	0.744240i	$-0.732812\pi$
$127$	3.50000	−	6.06218i	0.310575	−	0.537931i	0.978487	+	0.206309i	$0.0661452\pi$
$128$	−1.00000			−0.0883883
$129$	−4.00000	−	6.92820i	−0.352180	−	0.609994i
$130$	−1.00000	+	1.73205i	−0.0877058	+	0.151911i
$131$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$131$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$132$	−3.00000			−0.261116
$133$	1.00000	+	1.73205i	0.0867110	+	0.150188i
$134$	4.00000	+	6.92820i	0.345547	+	0.598506i
$135$	0.500000	+	0.866025i	0.0430331	+	0.0745356i
$136$	3.00000	−	5.19615i	0.257248	−	0.445566i
$137$	−6.00000	−	10.3923i	−0.512615	−	0.887875i	−0.999893	−	0.0146279i	$-0.995344\pi$
$137$	−6.00000	−	10.3923i	−0.512615	−	0.887875i	0.487278	−	0.873247i	$-0.337990\pi$
$138$	3.00000	−	5.19615i	0.255377	−	0.442326i
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$	1.00000			0.0845154
$141$	3.00000	−	5.19615i	0.252646	−	0.437595i
$142$	−6.00000	−	10.3923i	−0.503509	−	0.872103i
$143$	3.00000	−	5.19615i	0.250873	−	0.434524i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	4.50000	+	7.79423i	0.373705	+	0.647275i
$146$	7.00000	+	12.1244i	0.579324	+	1.00342i
$147$	−6.00000			−0.494872
$148$	−4.00000	+	6.92820i	−0.328798	+	0.569495i
$149$	4.50000	−	7.79423i	0.368654	−	0.638528i	−0.620701	−	0.784047i	$-0.713152\pi$
$149$	4.50000	−	7.79423i	0.368654	−	0.638528i	0.989355	+	0.145519i	$0.0464853\pi$
$150$	0.500000	+	0.866025i	0.0408248	+	0.0707107i
$151$	5.00000			0.406894			0.203447	−	0.979086i	$-0.434786\pi$
$151$	5.00000			0.406894			0.203447	+	0.979086i	$0.434786\pi$
$152$	1.00000	−	1.73205i	0.0811107	−	0.140488i
$153$	6.00000			0.485071
$154$	−3.00000			−0.241747
$155$	2.00000	−	5.19615i	0.160644	−	0.417365i
$156$	2.00000			0.160128
$157$	14.0000			1.11732			0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000			1.11732			0.558661	+	0.829396i	$0.311315\pi$
$158$	4.00000	−	6.92820i	0.318223	−	0.551178i
$159$	3.00000			0.237915
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	3.00000	−	5.19615i	0.236433	−	0.409514i
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	14.0000			1.09656			0.548282	−	0.836293i	$-0.315282\pi$
$163$	14.0000			1.09656			0.548282	+	0.836293i	$0.315282\pi$
$164$		0			0
$165$	−1.50000	−	2.59808i	−0.116775	−	0.202260i
$166$	−4.50000	−	7.79423i	−0.349268	−	0.604949i
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	−0.999169	−	0.0407502i	$-0.987025\pi$
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	0.534875	+	0.844931i	$0.320359\pi$
$168$	−0.500000	−	0.866025i	−0.0385758	−	0.0668153i
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$	6.00000			0.460179
$171$	2.00000			0.152944
$172$	−4.00000	+	6.92820i	−0.304997	+	0.528271i
$173$	−10.5000	−	18.1865i	−0.798300	−	1.38270i	−0.920722	−	0.390218i	$-0.872399\pi$
$173$	−10.5000	−	18.1865i	−0.798300	−	1.38270i	0.122422	−	0.992478i	$-0.460934\pi$
$174$	4.50000	−	7.79423i	0.341144	−	0.590879i
$175$	0.500000	+	0.866025i	0.0377964	+	0.0654654i
$176$	1.50000	+	2.59808i	0.113067	+	0.195837i
$177$	−7.50000	−	12.9904i	−0.563735	−	0.976417i
$178$		0			0
$179$	10.5000	−	18.1865i	0.784807	−	1.35933i	−0.144308	−	0.989533i	$-0.546095\pi$
$179$	10.5000	−	18.1865i	0.784807	−	1.35933i	0.929114	−	0.369792i	$-0.120571\pi$
$180$	0.500000	−	0.866025i	0.0372678	−	0.0645497i
$181$	2.00000	+	3.46410i	0.148659	+	0.257485i	0.930732	−	0.365702i	$-0.119171\pi$
$181$	2.00000	+	3.46410i	0.148659	+	0.257485i	−0.782073	+	0.623187i	$0.785838\pi$
$182$	2.00000			0.148250
$183$	−7.00000	+	12.1244i	−0.517455	+	0.896258i
$184$	−6.00000			−0.442326
$185$	−8.00000			−0.588172
$186$	−5.50000	+	0.866025i	−0.403280	+	0.0635001i
$187$	−18.0000			−1.31629
$188$	−6.00000			−0.437595
$189$	0.500000	−	0.866025i	0.0363696	−	0.0629941i
$190$	2.00000			0.145095
$191$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$191$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	12.5000	−	21.6506i	0.899770	−	1.55845i	0.0719816	−	0.997406i	$-0.477068\pi$
$193$	12.5000	−	21.6506i	0.899770	−	1.55845i	0.827788	−	0.561041i	$-0.189599\pi$
$194$	19.0000			1.36412
$195$	1.00000	+	1.73205i	0.0716115	+	0.124035i
$196$	3.00000	+	5.19615i	0.214286	+	0.371154i
$197$	−3.00000	−	5.19615i	−0.213741	−	0.370211i	0.739141	−	0.673550i	$-0.235232\pi$
$197$	−3.00000	−	5.19615i	−0.213741	−	0.370211i	−0.952882	+	0.303340i	$0.901898\pi$
$198$	−1.50000	+	2.59808i	−0.106600	+	0.184637i
$199$	−8.50000	−	14.7224i	−0.602549	−	1.04365i	−0.992434	−	0.122782i	$-0.960818\pi$
$199$	−8.50000	−	14.7224i	−0.602549	−	1.04365i	0.389885	−	0.920864i	$-0.372515\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$	8.00000			0.564276
$202$	3.00000			0.211079
$203$	4.50000	−	7.79423i	0.315838	−	0.547048i
$204$	−3.00000	−	5.19615i	−0.210042	−	0.363803i
$205$		0			0
$206$	−6.50000	−	11.2583i	−0.452876	−	0.784405i
$207$	−3.00000	−	5.19615i	−0.208514	−	0.361158i
$208$	−1.00000	−	1.73205i	−0.0693375	−	0.120096i
$209$	−6.00000			−0.415029
$210$	0.500000	−	0.866025i	0.0345033	−	0.0597614i
$211$	−7.00000	+	12.1244i	−0.481900	+	0.834675i	−0.999784	−	0.0207756i	$-0.993386\pi$
$211$	−7.00000	+	12.1244i	−0.481900	+	0.834675i	0.517884	+	0.855451i	$0.326720\pi$
$212$	−1.50000	−	2.59808i	−0.103020	−	0.178437i
$213$	−12.0000			−0.822226
$214$	7.50000	−	12.9904i	0.512689	−	0.888004i
$215$	−8.00000			−0.545595
$216$	−1.00000			−0.0680414
$217$	−5.50000	+	0.866025i	−0.373364	+	0.0587896i
$218$	−2.00000			−0.135457
$219$	14.0000			0.946032
$220$	−1.50000	+	2.59808i	−0.101130	+	0.175162i
$221$	12.0000			0.807207
$222$	4.00000	+	6.92820i	0.268462	+	0.464991i
$223$	0.500000	−	0.866025i	0.0334825	−	0.0579934i	−0.848799	−	0.528716i	$-0.822674\pi$
$223$	0.500000	−	0.866025i	0.0334825	−	0.0579934i	0.882281	+	0.470723i	$0.156007\pi$
$224$	−0.500000	+	0.866025i	−0.0334077	+	0.0578638i
$225$	1.00000			0.0666667
$226$	−9.00000	−	15.5885i	−0.598671	−	1.03693i
$227$	4.50000	+	7.79423i	0.298675	+	0.517321i	0.975833	−	0.218517i	$-0.0701218\pi$
$227$	4.50000	+	7.79423i	0.298675	+	0.517321i	−0.677158	+	0.735838i	$0.736789\pi$
$228$	−1.00000	−	1.73205i	−0.0662266	−	0.114708i
$229$	8.00000	−	13.8564i	0.528655	−	0.915657i	−0.470787	−	0.882247i	$-0.656030\pi$
$229$	8.00000	−	13.8564i	0.528655	−	0.915657i	0.999442	−	0.0334101i	$-0.0106368\pi$
$230$	−3.00000	−	5.19615i	−0.197814	−	0.342624i
$231$	−1.50000	+	2.59808i	−0.0986928	+	0.170941i
$232$	−9.00000			−0.590879
$233$	24.0000			1.57229			0.786146	−	0.618041i	$-0.212073\pi$
$233$	24.0000			1.57229			0.786146	+	0.618041i	$0.212073\pi$
$234$	1.00000	−	1.73205i	0.0653720	−	0.113228i
$235$	−3.00000	−	5.19615i	−0.195698	−	0.338960i
$236$	−7.50000	+	12.9904i	−0.488208	+	0.845602i
$237$	−4.00000	−	6.92820i	−0.259828	−	0.450035i
$238$	−3.00000	−	5.19615i	−0.194461	−	0.336817i
$239$	3.00000	+	5.19615i	0.194054	+	0.336111i	0.946590	−	0.322440i	$-0.104503\pi$
$239$	3.00000	+	5.19615i	0.194054	+	0.336111i	−0.752536	+	0.658551i	$0.771170\pi$
$240$	−1.00000			−0.0645497
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	−0.849472	−	0.527633i	$-0.823079\pi$
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	0.881680	+	0.471848i	$0.156413\pi$
$242$	−1.00000	+	1.73205i	−0.0642824	+	0.111340i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	14.0000			0.896258
$245$	−3.00000	+	5.19615i	−0.191663	+	0.331970i
$246$		0			0
$247$	4.00000			0.254514
$248$	3.50000	+	4.33013i	0.222250	+	0.274963i
$249$	−9.00000			−0.570352
$250$	1.00000			0.0632456
$251$	12.0000	−	20.7846i	0.757433	−	1.31191i	−0.186722	−	0.982413i	$-0.559786\pi$
$251$	12.0000	−	20.7846i	0.757433	−	1.31191i	0.944156	−	0.329500i	$-0.106880\pi$
$252$	−1.00000			−0.0629941
$253$	9.00000	+	15.5885i	0.565825	+	0.980038i
$254$	−3.50000	+	6.06218i	−0.219610	+	0.380375i
$255$	3.00000	−	5.19615i	0.187867	−	0.325396i
$256$	1.00000			0.0625000
$257$	9.00000	+	15.5885i	0.561405	+	0.972381i	0.997374	+	0.0724199i	$0.0230722\pi$
$257$	9.00000	+	15.5885i	0.561405	+	0.972381i	−0.435970	+	0.899961i	$0.643595\pi$
$258$	4.00000	+	6.92820i	0.249029	+	0.431331i
$259$	4.00000	+	6.92820i	0.248548	+	0.430498i
$260$	1.00000	−	1.73205i	0.0620174	−	0.107417i
$261$	−4.50000	−	7.79423i	−0.278543	−	0.482451i
$262$		0			0
$263$	−6.00000			−0.369976			−0.184988	−	0.982741i	$-0.559225\pi$
$263$	−6.00000			−0.369976			−0.184988	+	0.982741i	$0.559225\pi$
$264$	3.00000			0.184637
$265$	1.50000	−	2.59808i	0.0921443	−	0.159599i
$266$	−1.00000	−	1.73205i	−0.0613139	−	0.106199i
$267$		0			0
$268$	−4.00000	−	6.92820i	−0.244339	−	0.423207i
$269$	−9.00000	−	15.5885i	−0.548740	−	0.950445i	−0.998361	−	0.0572259i	$-0.981774\pi$
$269$	−9.00000	−	15.5885i	−0.548740	−	0.950445i	0.449622	−	0.893219i	$-0.351559\pi$
$270$	−0.500000	−	0.866025i	−0.0304290	−	0.0527046i
$271$	−7.00000			−0.425220			−0.212610	−	0.977137i	$-0.568196\pi$
$271$	−7.00000			−0.425220			−0.212610	+	0.977137i	$0.568196\pi$
$272$	−3.00000	+	5.19615i	−0.181902	+	0.315063i
$273$	1.00000	−	1.73205i	0.0605228	−	0.104828i
$274$	6.00000	+	10.3923i	0.362473	+	0.627822i
$275$	−3.00000			−0.180907
$276$	−3.00000	+	5.19615i	−0.180579	+	0.312772i
$277$	26.0000			1.56219			0.781094	−	0.624413i	$-0.214662\pi$
$277$	26.0000			1.56219			0.781094	+	0.624413i	$0.214662\pi$
$278$	4.00000			0.239904
$279$	−2.00000	+	5.19615i	−0.119737	+	0.311086i
$280$	−1.00000			−0.0597614
$281$		0			0			−	1.00000i	$-0.5\pi$
$281$		0			0				1.00000i	$0.5\pi$
$282$	−3.00000	+	5.19615i	−0.178647	+	0.309426i
$283$	14.0000			0.832214			0.416107	−	0.909316i	$-0.363394\pi$
$283$	14.0000			0.832214			0.416107	+	0.909316i	$0.363394\pi$
$284$	6.00000	+	10.3923i	0.356034	+	0.616670i
$285$	1.00000	−	1.73205i	0.0592349	−	0.102598i
$286$	−3.00000	+	5.19615i	−0.177394	+	0.307255i
$287$		0			0
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	−9.50000	−	16.4545i	−0.558824	−	0.967911i
$290$	−4.50000	−	7.79423i	−0.264249	−	0.457693i
$291$	9.50000	−	16.4545i	0.556900	−	0.964579i
$292$	−7.00000	−	12.1244i	−0.409644	−	0.709524i
$293$	10.5000	−	18.1865i	0.613417	−	1.06247i	−0.377244	−	0.926114i	$-0.623128\pi$
$293$	10.5000	−	18.1865i	0.613417	−	1.06247i	0.990660	−	0.136355i	$-0.0435386\pi$
$294$	6.00000			0.349927
$295$	−15.0000			−0.873334
$296$	4.00000	−	6.92820i	0.232495	−	0.402694i
$297$	1.50000	+	2.59808i	0.0870388	+	0.150756i
$298$	−4.50000	+	7.79423i	−0.260678	+	0.451508i
$299$	−6.00000	−	10.3923i	−0.346989	−	0.601003i
$300$	−0.500000	−	0.866025i	−0.0288675	−	0.0500000i
$301$	4.00000	+	6.92820i	0.230556	+	0.399335i
$302$	−5.00000			−0.287718
$303$	1.50000	−	2.59808i	0.0861727	−	0.149256i
$304$	−1.00000	+	1.73205i	−0.0573539	+	0.0993399i
$305$	7.00000	+	12.1244i	0.400819	+	0.694239i
$306$	−6.00000			−0.342997
$307$	8.00000	−	13.8564i	0.456584	−	0.790827i	−0.542194	−	0.840254i	$-0.682406\pi$
$307$	8.00000	−	13.8564i	0.456584	−	0.790827i	0.998778	+	0.0494267i	$0.0157394\pi$
$308$	3.00000			0.170941
$309$	−13.0000			−0.739544
$310$	−2.00000	+	5.19615i	−0.113592	+	0.295122i
$311$	−30.0000			−1.70114			−0.850572	−	0.525859i	$-0.823744\pi$
$311$	−30.0000			−1.70114			−0.850572	+	0.525859i	$0.823744\pi$
$312$	−2.00000			−0.113228
$313$	0.500000	−	0.866025i	0.0282617	−	0.0489506i	−0.851549	−	0.524276i	$-0.824336\pi$
$313$	0.500000	−	0.866025i	0.0282617	−	0.0489506i	0.879810	+	0.475325i	$0.157669\pi$
$314$	−14.0000			−0.790066
$315$	−0.500000	−	0.866025i	−0.0281718	−	0.0487950i
$316$	−4.00000	+	6.92820i	−0.225018	+	0.389742i
$317$	−13.5000	+	23.3827i	−0.758236	+	1.31330i	0.185514	+	0.982642i	$0.440605\pi$
$317$	−13.5000	+	23.3827i	−0.758236	+	1.31330i	−0.943750	+	0.330661i	$0.892728\pi$
$318$	−3.00000			−0.168232
$319$	13.5000	+	23.3827i	0.755855	+	1.30918i
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$	−7.50000	−	12.9904i	−0.418609	−	0.725052i
$322$	−3.00000	+	5.19615i	−0.167183	+	0.289570i
$323$	−6.00000	−	10.3923i	−0.333849	−	0.578243i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	2.00000			0.110940
$326$	−14.0000			−0.775388
$327$	−1.00000	+	1.73205i	−0.0553001	+	0.0957826i
$328$		0			0
$329$	−3.00000	+	5.19615i	−0.165395	+	0.286473i
$330$	1.50000	+	2.59808i	0.0825723	+	0.143019i
$331$	5.00000	+	8.66025i	0.274825	+	0.476011i	0.970091	−	0.242742i	$-0.0780468\pi$
$331$	5.00000	+	8.66025i	0.274825	+	0.476011i	−0.695266	+	0.718752i	$0.744713\pi$
$332$	4.50000	+	7.79423i	0.246970	+	0.427764i
$333$	8.00000			0.438397
$334$	6.00000	−	10.3923i	0.328305	−	0.568642i
$335$	4.00000	−	6.92820i	0.218543	−	0.378528i
$336$	0.500000	+	0.866025i	0.0272772	+	0.0472456i
$337$	−13.0000			−0.708155			−0.354078	−	0.935216i	$-0.615205\pi$
$337$	−13.0000			−0.708155			−0.354078	+	0.935216i	$0.615205\pi$
$338$	−4.50000	+	7.79423i	−0.244768	+	0.423950i
$339$	−18.0000			−0.977626
$340$	−6.00000			−0.325396
$341$	6.00000	−	15.5885i	0.324918	−	0.844162i
$342$	−2.00000			−0.108148
$343$	13.0000			0.701934
$344$	4.00000	−	6.92820i	0.215666	−	0.373544i
$345$	−6.00000			−0.323029
$346$	10.5000	+	18.1865i	0.564483	+	0.977714i
$347$	−10.5000	+	18.1865i	−0.563670	+	0.976304i	0.433503	+	0.901152i	$0.357278\pi$
$347$	−10.5000	+	18.1865i	−0.563670	+	0.976304i	−0.997172	+	0.0751519i	$0.976056\pi$
$348$	−4.50000	+	7.79423i	−0.241225	+	0.417815i
$349$	14.0000			0.749403			0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000			0.749403			0.374701	+	0.927146i	$0.377745\pi$
$350$	−0.500000	−	0.866025i	−0.0267261	−	0.0462910i
$351$	−1.00000	−	1.73205i	−0.0533761	−	0.0924500i
$352$	−1.50000	−	2.59808i	−0.0799503	−	0.138478i
$353$	15.0000	−	25.9808i	0.798369	−	1.38282i	−0.122308	−	0.992492i	$-0.539030\pi$
$353$	15.0000	−	25.9808i	0.798369	−	1.38282i	0.920677	−	0.390324i	$-0.127637\pi$
$354$	7.50000	+	12.9904i	0.398621	+	0.690431i
$355$	−6.00000	+	10.3923i	−0.318447	+	0.551566i
$356$		0			0
$357$	−6.00000			−0.317554
$358$	−10.5000	+	18.1865i	−0.554942	+	0.961188i
$359$	3.00000	+	5.19615i	0.158334	+	0.274242i	0.934268	−	0.356572i	$-0.116054\pi$
$359$	3.00000	+	5.19615i	0.158334	+	0.274242i	−0.775934	+	0.630814i	$0.782721\pi$
$360$	−0.500000	+	0.866025i	−0.0263523	+	0.0456435i
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	−2.00000	−	3.46410i	−0.105118	−	0.182069i
$363$	1.00000	+	1.73205i	0.0524864	+	0.0909091i
$364$	−2.00000			−0.104828
$365$	7.00000	−	12.1244i	0.366397	−	0.634618i
$366$	7.00000	−	12.1244i	0.365896	−	0.633750i
$367$	−4.00000	−	6.92820i	−0.208798	−	0.361649i	0.742538	−	0.669804i	$-0.233622\pi$
$367$	−4.00000	−	6.92820i	−0.208798	−	0.361649i	−0.951336	+	0.308155i	$0.900289\pi$
$368$	6.00000			0.312772
$369$		0			0
$370$	8.00000			0.415900
$371$	−3.00000			−0.155752
$372$	5.50000	−	0.866025i	0.285162	−	0.0449013i
$373$	14.0000			0.724893			0.362446	−	0.932005i	$-0.381942\pi$
$373$	14.0000			0.724893			0.362446	+	0.932005i	$0.381942\pi$
$374$	18.0000			0.930758
$375$	0.500000	−	0.866025i	0.0258199	−	0.0447214i
$376$	6.00000			0.309426
$377$	−9.00000	−	15.5885i	−0.463524	−	0.802846i
$378$	−0.500000	+	0.866025i	−0.0257172	+	0.0445435i
$379$	8.00000	−	13.8564i	0.410932	−	0.711756i	−0.584060	−	0.811711i	$-0.698537\pi$
$379$	8.00000	−	13.8564i	0.410932	−	0.711756i	0.994992	+	0.0999550i	$0.0318699\pi$
$380$	−2.00000			−0.102598
$381$	3.50000	+	6.06218i	0.179310	+	0.310575i
$382$		0			0
$383$	6.00000	+	10.3923i	0.306586	+	0.531022i	0.977613	−	0.210411i	$-0.0674801\pi$
$383$	6.00000	+	10.3923i	0.306586	+	0.531022i	−0.671027	+	0.741433i	$0.734147\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$	1.50000	+	2.59808i	0.0764471	+	0.132410i
$386$	−12.5000	+	21.6506i	−0.636233	+	1.10199i
$387$	8.00000			0.406663
$388$	−19.0000			−0.964579
$389$	−3.00000	+	5.19615i	−0.152106	+	0.263455i	−0.932002	−	0.362454i	$-0.881939\pi$
$389$	−3.00000	+	5.19615i	−0.152106	+	0.263455i	0.779895	+	0.625910i	$0.215272\pi$
$390$	−1.00000	−	1.73205i	−0.0506370	−	0.0877058i
$391$	−18.0000	+	31.1769i	−0.910299	+	1.57668i
$392$	−3.00000	−	5.19615i	−0.151523	−	0.262445i
$393$		0			0
$394$	3.00000	+	5.19615i	0.151138	+	0.261778i
$395$	−8.00000			−0.402524
$396$	1.50000	−	2.59808i	0.0753778	−	0.130558i
$397$	14.0000	−	24.2487i	0.702640	−	1.21701i	−0.264897	−	0.964277i	$-0.585338\pi$
$397$	14.0000	−	24.2487i	0.702640	−	1.21701i	0.967537	−	0.252731i	$-0.0813288\pi$
$398$	8.50000	+	14.7224i	0.426067	+	0.737969i
$399$	−2.00000			−0.100125
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−30.0000			−1.49813			−0.749064	−	0.662497i	$-0.769497\pi$
$401$	−30.0000			−1.49813			−0.749064	+	0.662497i	$0.769497\pi$
$402$	−8.00000			−0.399004
$403$	−4.00000	+	10.3923i	−0.199254	+	0.517678i
$404$	−3.00000			−0.149256
$405$	−1.00000			−0.0496904
$406$	−4.50000	+	7.79423i	−0.223331	+	0.386821i
$407$	−24.0000			−1.18964
$408$	3.00000	+	5.19615i	0.148522	+	0.257248i
$409$	−17.5000	+	30.3109i	−0.865319	+	1.49878i	0.00141047	+	0.999999i	$0.499551\pi$
$409$	−17.5000	+	30.3109i	−0.865319	+	1.49878i	−0.866730	+	0.498778i	$0.833782\pi$
$410$		0			0
$411$	12.0000			0.591916
$412$	6.50000	+	11.2583i	0.320232	+	0.554658i
$413$	7.50000	+	12.9904i	0.369051	+	0.639215i
$414$	3.00000	+	5.19615i	0.147442	+	0.255377i
$415$	−4.50000	+	7.79423i	−0.220896	+	0.382604i
$416$	1.00000	+	1.73205i	0.0490290	+	0.0849208i
$417$	2.00000	−	3.46410i	0.0979404	−	0.169638i
$418$	6.00000			0.293470
$419$	9.00000			0.439679			0.219839	−	0.975536i	$-0.429447\pi$
$419$	9.00000			0.439679			0.219839	+	0.975536i	$0.429447\pi$
$420$	−0.500000	+	0.866025i	−0.0243975	+	0.0422577i
$421$	5.00000	+	8.66025i	0.243685	+	0.422075i	0.961761	−	0.273890i	$-0.0883103\pi$
$421$	5.00000	+	8.66025i	0.243685	+	0.422075i	−0.718076	+	0.695965i	$0.754977\pi$
$422$	7.00000	−	12.1244i	0.340755	−	0.590204i
$423$	3.00000	+	5.19615i	0.145865	+	0.252646i
$424$	1.50000	+	2.59808i	0.0728464	+	0.126174i
$425$	−3.00000	−	5.19615i	−0.145521	−	0.252050i
$426$	12.0000			0.581402
$427$	7.00000	−	12.1244i	0.338754	−	0.586739i
$428$	−7.50000	+	12.9904i	−0.362526	+	0.627914i
$429$	3.00000	+	5.19615i	0.144841	+	0.250873i
$430$	8.00000			0.385794
$431$	−6.00000	+	10.3923i	−0.289010	+	0.500580i	−0.973574	−	0.228373i	$-0.926659\pi$
$431$	−6.00000	+	10.3923i	−0.289010	+	0.500580i	0.684564	+	0.728953i	$0.259993\pi$
$432$	1.00000			0.0481125
$433$	2.00000			0.0961139			0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000			0.0961139			0.0480569	+	0.998845i	$0.484697\pi$
$434$	5.50000	−	0.866025i	0.264008	−	0.0415705i
$435$	−9.00000			−0.431517
$436$	2.00000			0.0957826
$437$	−6.00000	+	10.3923i	−0.287019	+	0.497131i
$438$	−14.0000			−0.668946
$439$	3.50000	+	6.06218i	0.167046	+	0.289332i	0.937380	−	0.348309i	$-0.113244\pi$
$439$	3.50000	+	6.06218i	0.167046	+	0.289332i	−0.770334	+	0.637641i	$0.779911\pi$
$440$	1.50000	−	2.59808i	0.0715097	−	0.123858i
$441$	3.00000	−	5.19615i	0.142857	−	0.247436i
$442$	−12.0000			−0.570782
$443$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$443$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$444$	−4.00000	−	6.92820i	−0.189832	−	0.328798i
$445$		0			0
$446$	−0.500000	+	0.866025i	−0.0236757	+	0.0410075i
$447$	4.50000	+	7.79423i	0.212843	+	0.368654i
$448$	0.500000	−	0.866025i	0.0236228	−	0.0409159i
$449$	−12.0000			−0.566315			−0.283158	−	0.959073i	$-0.591382\pi$
$449$	−12.0000			−0.566315			−0.283158	+	0.959073i	$0.591382\pi$
$450$	−1.00000			−0.0471405
$451$		0			0
$452$	9.00000	+	15.5885i	0.423324	+	0.733219i
$453$	−2.50000	+	4.33013i	−0.117460	+	0.203447i
$454$	−4.50000	−	7.79423i	−0.211195	−	0.365801i
$455$	−1.00000	−	1.73205i	−0.0468807	−	0.0811998i
$456$	1.00000	+	1.73205i	0.0468293	+	0.0811107i
$457$	38.0000			1.77757			0.888783	−	0.458329i	$-0.151552\pi$
$457$	38.0000			1.77757			0.888783	+	0.458329i	$0.151552\pi$
$458$	−8.00000	+	13.8564i	−0.373815	+	0.647467i
$459$	−3.00000	+	5.19615i	−0.140028	+	0.242536i
$460$	3.00000	+	5.19615i	0.139876	+	0.242272i
$461$	15.0000			0.698620			0.349310	−	0.937007i	$-0.386416\pi$
$461$	15.0000			0.698620			0.349310	+	0.937007i	$0.386416\pi$
$462$	1.50000	−	2.59808i	0.0697863	−	0.120873i
$463$	−31.0000			−1.44069			−0.720346	−	0.693615i	$-0.756017\pi$
$463$	−31.0000			−1.44069			−0.720346	+	0.693615i	$0.756017\pi$
$464$	9.00000			0.417815
$465$	3.50000	+	4.33013i	0.162309	+	0.200805i
$466$	−24.0000			−1.11178
$467$	3.00000			0.138823			0.0694117	−	0.997588i	$-0.477888\pi$
$467$	3.00000			0.138823			0.0694117	+	0.997588i	$0.477888\pi$
$468$	−1.00000	+	1.73205i	−0.0462250	+	0.0800641i
$469$	−8.00000			−0.369406
$470$	3.00000	+	5.19615i	0.138380	+	0.239681i
$471$	−7.00000	+	12.1244i	−0.322543	+	0.558661i
$472$	7.50000	−	12.9904i	0.345215	−	0.597931i
$473$	−24.0000			−1.10352
$474$	4.00000	+	6.92820i	0.183726	+	0.318223i
$475$	−1.00000	−	1.73205i	−0.0458831	−	0.0794719i
$476$	3.00000	+	5.19615i	0.137505	+	0.238165i
$477$	−1.50000	+	2.59808i	−0.0686803	+	0.118958i
$478$	−3.00000	−	5.19615i	−0.137217	−	0.237666i
$479$	3.00000	−	5.19615i	0.137073	−	0.237418i	−0.789314	−	0.613990i	$-0.789564\pi$
$479$	3.00000	−	5.19615i	0.137073	−	0.237418i	0.926388	+	0.376571i	$0.122897\pi$
$480$	1.00000			0.0456435
$481$	16.0000			0.729537
$482$	−0.500000	+	0.866025i	−0.0227744	+	0.0394464i
$483$	3.00000	+	5.19615i	0.136505	+	0.236433i
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$	−9.50000	−	16.4545i	−0.431373	−	0.747160i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−5.50000	−	9.52628i	−0.249229	−	0.431677i	0.714083	−	0.700061i	$-0.246844\pi$
$487$	−5.50000	−	9.52628i	−0.249229	−	0.431677i	−0.963312	+	0.268384i	$0.913510\pi$
$488$	−14.0000			−0.633750
$489$	−7.00000	+	12.1244i	−0.316551	+	0.548282i
$490$	3.00000	−	5.19615i	0.135526	−	0.234738i
$491$	7.50000	+	12.9904i	0.338470	+	0.586248i	0.984145	−	0.177365i	$-0.0567572\pi$
$491$	7.50000	+	12.9904i	0.338470	+	0.586248i	−0.645675	+	0.763612i	$0.723424\pi$
$492$		0			0
$493$	−27.0000	+	46.7654i	−1.21602	+	2.10621i
$494$	−4.00000			−0.179969
$495$	3.00000			0.134840
$496$	−3.50000	−	4.33013i	−0.157155	−	0.194428i
$497$	12.0000			0.538274
$498$	9.00000			0.403300
$499$	2.00000	−	3.46410i	0.0895323	−	0.155074i	−0.817781	−	0.575529i	$-0.804796\pi$
$499$	2.00000	−	3.46410i	0.0895323	−	0.155074i	0.907314	+	0.420455i	$0.138129\pi$
$500$	−1.00000			−0.0447214
$501$	−6.00000	−	10.3923i	−0.268060	−	0.464294i
$502$	−12.0000	+	20.7846i	−0.535586	+	0.927663i
$503$	18.0000	−	31.1769i	0.802580	−	1.39011i	−0.115332	−	0.993327i	$-0.536793\pi$
$503$	18.0000	−	31.1769i	0.802580	−	1.39011i	0.917912	−	0.396783i	$-0.129873\pi$
$504$	1.00000			0.0445435
$505$	−1.50000	−	2.59808i	−0.0667491	−	0.115613i
$506$	−9.00000	−	15.5885i	−0.400099	−	0.692991i
$507$	4.50000	+	7.79423i	0.199852	+	0.346154i
$508$	3.50000	−	6.06218i	0.155287	−	0.268966i
$509$	−4.50000	−	7.79423i	−0.199459	−	0.345473i	0.748894	−	0.662690i	$-0.230585\pi$
$509$	−4.50000	−	7.79423i	−0.199459	−	0.345473i	−0.948353	+	0.317217i	$0.897252\pi$
$510$	−3.00000	+	5.19615i	−0.132842	+	0.230089i
$511$	−14.0000			−0.619324
$512$	−1.00000			−0.0441942
$513$	−1.00000	+	1.73205i	−0.0441511	+	0.0764719i
$514$	−9.00000	−	15.5885i	−0.396973	−	0.687577i
$515$	−6.50000	+	11.2583i	−0.286424	+	0.496101i
$516$	−4.00000	−	6.92820i	−0.176090	−	0.304997i
$517$	−9.00000	−	15.5885i	−0.395820	−	0.685580i
$518$	−4.00000	−	6.92820i	−0.175750	−	0.304408i
$519$	21.0000			0.921798
$520$	−1.00000	+	1.73205i	−0.0438529	+	0.0759555i
$521$	15.0000	−	25.9808i	0.657162	−	1.13824i	−0.324185	−	0.945994i	$-0.605090\pi$
$521$	15.0000	−	25.9808i	0.657162	−	1.13824i	0.981347	−	0.192244i	$-0.0615766\pi$
$522$	4.50000	+	7.79423i	0.196960	+	0.341144i
$523$	44.0000			1.92399			0.961993	−	0.273075i	$-0.0880406\pi$
$523$	44.0000			1.92399			0.961993	+	0.273075i	$0.0880406\pi$
$524$		0			0
$525$	−1.00000			−0.0436436
$526$	6.00000			0.261612
$527$	33.0000	−	5.19615i	1.43750	−	0.226348i
$528$	−3.00000			−0.130558
$529$	13.0000			0.565217
$530$	−1.50000	+	2.59808i	−0.0651558	+	0.112853i
$531$	15.0000			0.650945
$532$	1.00000	+	1.73205i	0.0433555	+	0.0750939i
$533$		0			0
$534$		0			0
$535$	−15.0000			−0.648507
$536$	4.00000	+	6.92820i	0.172774	+	0.299253i
$537$	10.5000	+	18.1865i	0.453108	+	0.784807i
$538$	9.00000	+	15.5885i	0.388018	+	0.672066i
$539$	−9.00000	+	15.5885i	−0.387657	+	0.671442i
$540$	0.500000	+	0.866025i	0.0215166	+	0.0372678i
$541$	−7.00000	+	12.1244i	−0.300954	+	0.521267i	−0.976352	−	0.216186i	$-0.930638\pi$
$541$	−7.00000	+	12.1244i	−0.300954	+	0.521267i	0.675399	+	0.737453i	$0.263972\pi$
$542$	7.00000			0.300676
$543$	−4.00000			−0.171656
$544$	3.00000	−	5.19615i	0.128624	−	0.222783i
$545$	1.00000	+	1.73205i	0.0428353	+	0.0741929i
$546$	−1.00000	+	1.73205i	−0.0427960	+	0.0741249i
$547$	−4.00000	−	6.92820i	−0.171028	−	0.296229i	0.767752	−	0.640747i	$-0.221375\pi$
$547$	−4.00000	−	6.92820i	−0.171028	−	0.296229i	−0.938779	+	0.344519i	$0.888042\pi$
$548$	−6.00000	−	10.3923i	−0.256307	−	0.443937i
$549$	−7.00000	−	12.1244i	−0.298753	−	0.517455i
$550$	3.00000			0.127920
$551$	−9.00000	+	15.5885i	−0.383413	+	0.664091i
$552$	3.00000	−	5.19615i	0.127688	−	0.221163i
$553$	4.00000	+	6.92820i	0.170097	+	0.294617i
$554$	−26.0000			−1.10463
$555$	4.00000	−	6.92820i	0.169791	−	0.294086i
$556$	−4.00000			−0.169638
$557$	−27.0000			−1.14403			−0.572013	−	0.820244i	$-0.693837\pi$
$557$	−27.0000			−1.14403			−0.572013	+	0.820244i	$0.693837\pi$
$558$	2.00000	−	5.19615i	0.0846668	−	0.219971i
$559$	16.0000			0.676728
$560$	1.00000			0.0422577
$561$	9.00000	−	15.5885i	0.379980	−	0.658145i
$562$		0			0
$563$	−4.50000	−	7.79423i	−0.189652	−	0.328488i	0.755482	−	0.655169i	$-0.227403\pi$
$563$	−4.50000	−	7.79423i	−0.189652	−	0.328488i	−0.945134	+	0.326682i	$0.894069\pi$
$564$	3.00000	−	5.19615i	0.126323	−	0.218797i
$565$	−9.00000	+	15.5885i	−0.378633	+	0.655811i
$566$	−14.0000			−0.588464
$567$	0.500000	+	0.866025i	0.0209980	+	0.0363696i
$568$	−6.00000	−	10.3923i	−0.251754	−	0.436051i
$569$	−3.00000	−	5.19615i	−0.125767	−	0.217834i	0.796266	−	0.604947i	$-0.206806\pi$
$569$	−3.00000	−	5.19615i	−0.125767	−	0.217834i	−0.922032	+	0.387113i	$0.873472\pi$
$570$	−1.00000	+	1.73205i	−0.0418854	+	0.0725476i
$571$	−16.0000	−	27.7128i	−0.669579	−	1.15975i	−0.978022	−	0.208502i	$-0.933141\pi$
$571$	−16.0000	−	27.7128i	−0.669579	−	1.15975i	0.308443	−	0.951243i	$-0.400192\pi$
$572$	3.00000	−	5.19615i	0.125436	−	0.217262i
$573$		0			0
$574$		0			0
$575$	−3.00000	+	5.19615i	−0.125109	+	0.216695i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−13.0000	+	22.5167i	−0.541197	+	0.937381i	0.457639	+	0.889138i	$0.348695\pi$
$577$	−13.0000	+	22.5167i	−0.541197	+	0.937381i	−0.998836	+	0.0482425i	$0.984638\pi$
$578$	9.50000	+	16.4545i	0.395148	+	0.684416i
$579$	12.5000	+	21.6506i	0.519482	+	0.899770i
$580$	4.50000	+	7.79423i	0.186852	+	0.323638i
$581$	9.00000			0.373383
$582$	−9.50000	+	16.4545i	−0.393788	+	0.682060i
$583$	4.50000	−	7.79423i	0.186371	−	0.322804i
$584$	7.00000	+	12.1244i	0.289662	+	0.501709i
$585$	−2.00000			−0.0826898
$586$	−10.5000	+	18.1865i	−0.433751	+	0.751279i
$587$	33.0000			1.36206			0.681028	−	0.732257i	$-0.261533\pi$
$587$	33.0000			1.36206			0.681028	+	0.732257i	$0.261533\pi$
$588$	−6.00000			−0.247436
$589$	11.0000	−	1.73205i	0.453247	−	0.0713679i
$590$	15.0000			0.617540
$591$	6.00000			0.246807
$592$	−4.00000	+	6.92820i	−0.164399	+	0.284747i
$593$	12.0000			0.492781			0.246390	−	0.969171i	$-0.420755\pi$
$593$	12.0000			0.492781			0.246390	+	0.969171i	$0.420755\pi$
$594$	−1.50000	−	2.59808i	−0.0615457	−	0.106600i
$595$	−3.00000	+	5.19615i	−0.122988	+	0.213021i
$596$	4.50000	−	7.79423i	0.184327	−	0.319264i
$597$	17.0000			0.695764
$598$	6.00000	+	10.3923i	0.245358	+	0.424973i
$599$	6.00000	+	10.3923i	0.245153	+	0.424618i	0.962175	−	0.272433i	$-0.0878284\pi$
$599$	6.00000	+	10.3923i	0.245153	+	0.424618i	−0.717021	+	0.697051i	$0.754495\pi$
$600$	0.500000	+	0.866025i	0.0204124	+	0.0353553i
$601$	−19.0000	+	32.9090i	−0.775026	+	1.34238i	0.159754	+	0.987157i	$0.448930\pi$
$601$	−19.0000	+	32.9090i	−0.775026	+	1.34238i	−0.934780	+	0.355228i	$0.884403\pi$
$602$	−4.00000	−	6.92820i	−0.163028	−	0.282372i
$603$	−4.00000	+	6.92820i	−0.162893	+	0.282138i
$604$	5.00000			0.203447
$605$	2.00000			0.0813116
$606$	−1.50000	+	2.59808i	−0.0609333	+	0.105540i
$607$	−10.0000	−	17.3205i	−0.405887	−	0.703018i	0.588537	−	0.808470i	$-0.299704\pi$
$607$	−10.0000	−	17.3205i	−0.405887	−	0.703018i	−0.994424	+	0.105453i	$0.966371\pi$
$608$	1.00000	−	1.73205i	0.0405554	−	0.0702439i
$609$	4.50000	+	7.79423i	0.182349	+	0.315838i
$610$	−7.00000	−	12.1244i	−0.283422	−	0.490901i
$611$	6.00000	+	10.3923i	0.242734	+	0.420428i
$612$	6.00000			0.242536
$613$	8.00000	−	13.8564i	0.323117	−	0.559655i	−0.658012	−	0.753007i	$-0.728603\pi$
$613$	8.00000	−	13.8564i	0.323117	−	0.559655i	0.981129	+	0.193352i	$0.0619359\pi$
$614$	−8.00000	+	13.8564i	−0.322854	+	0.559199i
$615$		0			0
$616$	−3.00000			−0.120873
$617$	−15.0000	+	25.9808i	−0.603877	+	1.04595i	0.388351	+	0.921512i	$0.373045\pi$
$617$	−15.0000	+	25.9808i	−0.603877	+	1.04595i	−0.992228	+	0.124434i	$0.960288\pi$
$618$	13.0000			0.522937
$619$	−28.0000			−1.12542			−0.562708	−	0.826656i	$-0.690240\pi$
$619$	−28.0000			−1.12542			−0.562708	+	0.826656i	$0.690240\pi$
$620$	2.00000	−	5.19615i	0.0803219	−	0.208683i
$621$	6.00000			0.240772
$622$	30.0000			1.20289
$623$		0			0
$624$	2.00000			0.0800641
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−0.500000	+	0.866025i	−0.0199840	+	0.0346133i
$627$	3.00000	−	5.19615i	0.119808	−	0.207514i
$628$	14.0000			0.558661
$629$	−24.0000	−	41.5692i	−0.956943	−	1.65747i
$630$	0.500000	+	0.866025i	0.0199205	+	0.0345033i
$631$	3.50000	+	6.06218i	0.139333	+	0.241331i	0.927244	−	0.374457i	$-0.122171\pi$
$631$	3.50000	+	6.06218i	0.139333	+	0.241331i	−0.787911	+	0.615789i	$0.788838\pi$
$632$	4.00000	−	6.92820i	0.159111	−	0.275589i
$633$	−7.00000	−	12.1244i	−0.278225	−	0.481900i
$634$	13.5000	−	23.3827i	0.536153	−	0.928645i
$635$	7.00000			0.277787
$636$	3.00000			0.118958
$637$	6.00000	−	10.3923i	0.237729	−	0.411758i
$638$	−13.5000	−	23.3827i	−0.534470	−	0.925729i
$639$	6.00000	−	10.3923i	0.237356	−	0.411113i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	−21.0000	−	36.3731i	−0.829450	−	1.43665i	−0.898470	−	0.439034i	$-0.855321\pi$
$641$	−21.0000	−	36.3731i	−0.829450	−	1.43665i	0.0690201	−	0.997615i	$-0.478013\pi$
$642$	7.50000	+	12.9904i	0.296001	+	0.512689i
$643$	2.00000			0.0788723			0.0394362	−	0.999222i	$-0.487444\pi$
$643$	2.00000			0.0788723			0.0394362	+	0.999222i	$0.487444\pi$
$644$	3.00000	−	5.19615i	0.118217	−	0.204757i
$645$	4.00000	−	6.92820i	0.157500	−	0.272798i
$646$	6.00000	+	10.3923i	0.236067	+	0.408880i
$647$	−18.0000			−0.707653			−0.353827	−	0.935311i	$-0.615120\pi$
$647$	−18.0000			−0.707653			−0.353827	+	0.935311i	$0.615120\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	−45.0000			−1.76640
$650$	−2.00000			−0.0784465
$651$	2.00000	−	5.19615i	0.0783862	−	0.203653i
$652$	14.0000			0.548282
$653$	−39.0000			−1.52619			−0.763094	−	0.646288i	$-0.776321\pi$
$653$	−39.0000			−1.52619			−0.763094	+	0.646288i	$0.776321\pi$
$654$	1.00000	−	1.73205i	0.0391031	−	0.0677285i
$655$		0			0
$656$		0			0
$657$	−7.00000	+	12.1244i	−0.273096	+	0.473016i
$658$	3.00000	−	5.19615i	0.116952	−	0.202567i
$659$	−21.0000			−0.818044			−0.409022	−	0.912525i	$-0.634130\pi$
$659$	−21.0000			−0.818044			−0.409022	+	0.912525i	$0.634130\pi$
$660$	−1.50000	−	2.59808i	−0.0583874	−	0.101130i
$661$	−7.00000	−	12.1244i	−0.272268	−	0.471583i	0.697174	−	0.716902i	$-0.254441\pi$
$661$	−7.00000	−	12.1244i	−0.272268	−	0.471583i	−0.969442	+	0.245319i	$0.921107\pi$
$662$	−5.00000	−	8.66025i	−0.194331	−	0.336590i
$663$	−6.00000	+	10.3923i	−0.233021	+	0.403604i
$664$	−4.50000	−	7.79423i	−0.174634	−	0.302475i
$665$	−1.00000	+	1.73205i	−0.0387783	+	0.0671660i
$666$	−8.00000			−0.309994
$667$	54.0000			2.09089
$668$	−6.00000	+	10.3923i	−0.232147	+	0.402090i
$669$	0.500000	+	0.866025i	0.0193311	+	0.0334825i
$670$	−4.00000	+	6.92820i	−0.154533	+	0.267660i
$671$	21.0000	+	36.3731i	0.810696	+	1.40417i
$672$	−0.500000	−	0.866025i	−0.0192879	−	0.0334077i
$673$	0.500000	+	0.866025i	0.0192736	+	0.0333828i	0.875501	−	0.483216i	$-0.160531\pi$
$673$	0.500000	+	0.866025i	0.0192736	+	0.0333828i	−0.856228	+	0.516599i	$0.827198\pi$
$674$	13.0000			0.500741
$675$	−0.500000	+	0.866025i	−0.0192450	+	0.0333333i
$676$	4.50000	−	7.79423i	0.173077	−	0.299778i
$677$	1.50000	+	2.59808i	0.0576497	+	0.0998522i	0.893410	−	0.449242i	$-0.148306\pi$
$677$	1.50000	+	2.59808i	0.0576497	+	0.0998522i	−0.835760	+	0.549095i	$0.814973\pi$
$678$	18.0000			0.691286
$679$	−9.50000	+	16.4545i	−0.364577	+	0.631465i
$680$	6.00000			0.230089
$681$	−9.00000			−0.344881
$682$	−6.00000	+	15.5885i	−0.229752	+	0.596913i
$683$	−27.0000			−1.03313			−0.516563	−	0.856249i	$-0.672789\pi$
$683$	−27.0000			−1.03313			−0.516563	+	0.856249i	$0.672789\pi$
$684$	2.00000			0.0764719
$685$	6.00000	−	10.3923i	0.229248	−	0.397070i
$686$	−13.0000			−0.496342
$687$	8.00000	+	13.8564i	0.305219	+	0.528655i
$688$	−4.00000	+	6.92820i	−0.152499	+	0.264135i
$689$	−3.00000	+	5.19615i	−0.114291	+	0.197958i
$690$	6.00000			0.228416
$691$	14.0000	+	24.2487i	0.532585	+	0.922464i	0.999276	+	0.0380440i	$0.0121127\pi$
$691$	14.0000	+	24.2487i	0.532585	+	0.922464i	−0.466691	+	0.884420i	$0.654554\pi$
$692$	−10.5000	−	18.1865i	−0.399150	−	0.691348i
$693$	−1.50000	−	2.59808i	−0.0569803	−	0.0986928i
$694$	10.5000	−	18.1865i	0.398575	−	0.690351i
$695$	−2.00000	−	3.46410i	−0.0758643	−	0.131401i
$696$	4.50000	−	7.79423i	0.170572	−	0.295439i
$697$		0			0
$698$	−14.0000			−0.529908
$699$	−12.0000	+	20.7846i	−0.453882	+	0.786146i
$700$	0.500000	+	0.866025i	0.0188982	+	0.0327327i
$701$	19.5000	−	33.7750i	0.736505	−	1.27566i	−0.217555	−	0.976048i	$-0.569808\pi$
$701$	19.5000	−	33.7750i	0.736505	−	1.27566i	0.954060	−	0.299616i	$-0.0968585\pi$
$702$	1.00000	+	1.73205i	0.0377426	+	0.0653720i
$703$	−8.00000	−	13.8564i	−0.301726	−	0.522604i
$704$	1.50000	+	2.59808i	0.0565334	+	0.0979187i
$705$	6.00000			0.225973
$706$	−15.0000	+	25.9808i	−0.564532	+	0.977799i
$707$	−1.50000	+	2.59808i	−0.0564133	+	0.0977107i
$708$	−7.50000	−	12.9904i	−0.281867	−	0.488208i
$709$	8.00000			0.300446			0.150223	−	0.988652i	$-0.452001\pi$
$709$	8.00000			0.300446			0.150223	+	0.988652i	$0.452001\pi$
$710$	6.00000	−	10.3923i	0.225176	−	0.390016i
$711$	8.00000			0.300023
$712$		0			0
$713$	−21.0000	−	25.9808i	−0.786456	−	0.972987i
$714$	6.00000			0.224544
$715$	6.00000			0.224387
$716$	10.5000	−	18.1865i	0.392403	−	0.679663i
$717$	−6.00000			−0.224074
$718$	−3.00000	−	5.19615i	−0.111959	−	0.193919i
$719$	−12.0000	+	20.7846i	−0.447524	+	0.775135i	−0.998224	−	0.0595683i	$-0.981028\pi$
$719$	−12.0000	+	20.7846i	−0.447524	+	0.775135i	0.550700	+	0.834703i	$0.314361\pi$
$720$	0.500000	−	0.866025i	0.0186339	−	0.0322749i
$721$	13.0000			0.484145
$722$	−7.50000	−	12.9904i	−0.279121	−	0.483452i
$723$	0.500000	+	0.866025i	0.0185952	+	0.0322078i
$724$	2.00000	+	3.46410i	0.0743294	+	0.128742i
$725$	−4.50000	+	7.79423i	−0.167126	+	0.289470i
$726$	−1.00000	−	1.73205i	−0.0371135	−	0.0642824i
$727$	3.50000	−	6.06218i	0.129808	−	0.224834i	−0.793794	−	0.608186i	$-0.791897\pi$
$727$	3.50000	−	6.06218i	0.129808	−	0.224834i	0.923602	+	0.383353i	$0.125231\pi$
$728$	2.00000			0.0741249
$729$	1.00000			0.0370370
$730$	−7.00000	+	12.1244i	−0.259082	+	0.448743i
$731$	−24.0000	−	41.5692i	−0.887672	−	1.53749i
$732$	−7.00000	+	12.1244i	−0.258727	+	0.448129i
$733$	−13.0000	−	22.5167i	−0.480166	−	0.831672i	0.519575	−	0.854425i	$-0.326090\pi$
$733$	−13.0000	−	22.5167i	−0.480166	−	0.831672i	−0.999741	+	0.0227529i	$0.992757\pi$
$734$	4.00000	+	6.92820i	0.147643	+	0.255725i
$735$	−3.00000	−	5.19615i	−0.110657	−	0.191663i
$736$	−6.00000			−0.221163
$737$	12.0000	−	20.7846i	0.442026	−	0.765611i
$738$		0			0
$739$	−16.0000	−	27.7128i	−0.588570	−	1.01943i	−0.994420	−	0.105493i	$-0.966358\pi$
$739$	−16.0000	−	27.7128i	−0.588570	−	1.01943i	0.405851	−	0.913939i	$-0.366975\pi$
$740$	−8.00000			−0.294086
$741$	−2.00000	+	3.46410i	−0.0734718	+	0.127257i
$742$	3.00000			0.110133
$743$	−12.0000			−0.440237			−0.220119	−	0.975473i	$-0.570644\pi$
$743$	−12.0000			−0.440237			−0.220119	+	0.975473i	$0.570644\pi$
$744$	−5.50000	+	0.866025i	−0.201640	+	0.0317500i
$745$	9.00000			0.329734
$746$	−14.0000			−0.512576
$747$	4.50000	−	7.79423i	0.164646	−	0.285176i
$748$	−18.0000			−0.658145
$749$	7.50000	+	12.9904i	0.274044	+	0.474658i
$750$	−0.500000	+	0.866025i	−0.0182574	+	0.0316228i
$751$	3.50000	−	6.06218i	0.127717	−	0.221212i	−0.795075	−	0.606511i	$-0.792568\pi$
$751$	3.50000	−	6.06218i	0.127717	−	0.221212i	0.922792	+	0.385299i	$0.125902\pi$
$752$	−6.00000			−0.218797
$753$	12.0000	+	20.7846i	0.437304	+	0.757433i
$754$	9.00000	+	15.5885i	0.327761	+	0.567698i
$755$	2.50000	+	4.33013i	0.0909843	+	0.157589i
$756$	0.500000	−	0.866025i	0.0181848	−	0.0314970i
$757$	−22.0000	−	38.1051i	−0.799604	−	1.38495i	−0.919874	−	0.392213i	$-0.871710\pi$
$757$	−22.0000	−	38.1051i	−0.799604	−	1.38495i	0.120271	−	0.992741i	$-0.461624\pi$
$758$	−8.00000	+	13.8564i	−0.290573	+	0.503287i
$759$	−18.0000			−0.653359
$760$	2.00000			0.0725476
$761$	6.00000	−	10.3923i	0.217500	−	0.376721i	−0.736543	−	0.676391i	$-0.763543\pi$
$761$	6.00000	−	10.3923i	0.217500	−	0.376721i	0.954043	+	0.299670i	$0.0968765\pi$
$762$	−3.50000	−	6.06218i	−0.126792	−	0.219610i
$763$	1.00000	−	1.73205i	0.0362024	−	0.0627044i
$764$		0			0
$765$	3.00000	+	5.19615i	0.108465	+	0.187867i
$766$	−6.00000	−	10.3923i	−0.216789	−	0.375489i
$767$	30.0000			1.08324
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	−14.5000	+	25.1147i	−0.522883	+	0.905661i	0.476762	+	0.879032i	$0.341810\pi$
$769$	−14.5000	+	25.1147i	−0.522883	+	0.905661i	−0.999645	+	0.0266282i	$0.991523\pi$
$770$	−1.50000	−	2.59808i	−0.0540562	−	0.0936282i
$771$	−18.0000			−0.648254
$772$	12.5000	−	21.6506i	0.449885	−	0.779223i
$773$	−6.00000			−0.215805			−0.107903	−	0.994161i

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(1.50000 + 2.59808i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-1.00000 - 1.73205i) q^{13} +(-0.500000 + 0.866025i) q^{14} -1.00000 q^{15} +1.00000 q^{16} +(-3.00000 + 5.19615i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-1.00000 + 1.73205i) q^{19} +(0.500000 + 0.866025i) q^{20} +(0.500000 + 0.866025i) q^{21} +(-1.50000 - 2.59808i) q^{22} +6.00000 q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.00000 + 1.73205i) q^{26} +1.00000 q^{27} +(0.500000 - 0.866025i) q^{28} +9.00000 q^{29} +1.00000 q^{30} +(-3.50000 - 4.33013i) q^{31} -1.00000 q^{32} -3.00000 q^{33} +(3.00000 - 5.19615i) q^{34} +1.00000 q^{35} +(-0.500000 - 0.866025i) q^{36} +(-4.00000 + 6.92820i) q^{37} +(1.00000 - 1.73205i) q^{38} +2.00000 q^{39} +(-0.500000 - 0.866025i) q^{40} +(-0.500000 - 0.866025i) q^{42} +(-4.00000 + 6.92820i) q^{43} +(1.50000 + 2.59808i) q^{44} +(0.500000 - 0.866025i) q^{45} -6.00000 q^{46} -6.00000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(3.00000 + 5.19615i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-3.00000 - 5.19615i) q^{51} +(-1.00000 - 1.73205i) q^{52} +(-1.50000 - 2.59808i) q^{53} -1.00000 q^{54} +(-1.50000 + 2.59808i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(-1.00000 - 1.73205i) q^{57} -9.00000 q^{58} +(-7.50000 + 12.9904i) q^{59} -1.00000 q^{60} +14.0000 q^{61} +(3.50000 + 4.33013i) q^{62} -1.00000 q^{63} +1.00000 q^{64} +(1.00000 - 1.73205i) q^{65} +3.00000 q^{66} +(-4.00000 - 6.92820i) q^{67} +(-3.00000 + 5.19615i) q^{68} +(-3.00000 + 5.19615i) q^{69} -1.00000 q^{70} +(6.00000 + 10.3923i) q^{71} +(0.500000 + 0.866025i) q^{72} +(-7.00000 - 12.1244i) q^{73} +(4.00000 - 6.92820i) q^{74} +(-0.500000 - 0.866025i) q^{75} +(-1.00000 + 1.73205i) q^{76} +3.00000 q^{77} -2.00000 q^{78} +(-4.00000 + 6.92820i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.50000 + 7.79423i) q^{83} +(0.500000 + 0.866025i) q^{84} -6.00000 q^{85} +(4.00000 - 6.92820i) q^{86} +(-4.50000 + 7.79423i) q^{87} +(-1.50000 - 2.59808i) q^{88} +(-0.500000 + 0.866025i) q^{90} -2.00000 q^{91} +6.00000 q^{92} +(5.50000 - 0.866025i) q^{93} +6.00000 q^{94} -2.00000 q^{95} +(0.500000 - 0.866025i) q^{96} -19.0000 q^{97} +(-3.00000 - 5.19615i) q^{98} +(1.50000 - 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - q^{3} + 2 q^{4} + q^{5} + q^{6} + q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - q^3 + 2 * q^4 + q^5 + q^6 + q^7 - 2 * q^8 - q^9	\( 2 q - 2 q^{2} - q^{3} + 2 q^{4} + q^{5} + q^{6} + q^{7} - 2 q^{8} - q^{9} - q^{10} + 3 q^{11} - q^{12} - 2 q^{13} - q^{14} - 2 q^{15} + 2 q^{16} - 6 q^{17} + q^{18} - 2 q^{19} + q^{20} + q^{21} - 3 q^{22} + 12 q^{23} + q^{24} - q^{25} + 2 q^{26} + 2 q^{27} + q^{28} + 18 q^{29} + 2 q^{30} - 7 q^{31} - 2 q^{32} - 6 q^{33} + 6 q^{34} + 2 q^{35} - q^{36} - 8 q^{37} + 2 q^{38} + 4 q^{39} - q^{40} - q^{42} - 8 q^{43} + 3 q^{44} + q^{45} - 12 q^{46} - 12 q^{47} - q^{48} + 6 q^{49} + q^{50} - 6 q^{51} - 2 q^{52} - 3 q^{53} - 2 q^{54} - 3 q^{55} - q^{56} - 2 q^{57} - 18 q^{58} - 15 q^{59} - 2 q^{60} + 28 q^{61} + 7 q^{62} - 2 q^{63} + 2 q^{64} + 2 q^{65} + 6 q^{66} - 8 q^{67} - 6 q^{68} - 6 q^{69} - 2 q^{70} + 12 q^{71} + q^{72} - 14 q^{73} + 8 q^{74} - q^{75} - 2 q^{76} + 6 q^{77} - 4 q^{78} - 8 q^{79} + q^{80} - q^{81} + 9 q^{83} + q^{84} - 12 q^{85} + 8 q^{86} - 9 q^{87} - 3 q^{88} - q^{90} - 4 q^{91} + 12 q^{92} + 11 q^{93} + 12 q^{94} - 4 q^{95} + q^{96} - 38 q^{97} - 6 q^{98} + 3 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - q^3 + 2 * q^4 + q^5 + q^6 + q^7 - 2 * q^8 - q^9 - q^10 + 3 * q^11 - q^12 - 2 * q^13 - q^14 - 2 * q^15 + 2 * q^16 - 6 * q^17 + q^18 - 2 * q^19 + q^20 + q^21 - 3 * q^22 + 12 * q^23 + q^24 - q^25 + 2 * q^26 + 2 * q^27 + q^28 + 18 * q^29 + 2 * q^30 - 7 * q^31 - 2 * q^32 - 6 * q^33 + 6 * q^34 + 2 * q^35 - q^36 - 8 * q^37 + 2 * q^38 + 4 * q^39 - q^40 - q^42 - 8 * q^43 + 3 * q^44 + q^45 - 12 * q^46 - 12 * q^47 - q^48 + 6 * q^49 + q^50 - 6 * q^51 - 2 * q^52 - 3 * q^53 - 2 * q^54 - 3 * q^55 - q^56 - 2 * q^57 - 18 * q^58 - 15 * q^59 - 2 * q^60 + 28 * q^61 + 7 * q^62 - 2 * q^63 + 2 * q^64 + 2 * q^65 + 6 * q^66 - 8 * q^67 - 6 * q^68 - 6 * q^69 - 2 * q^70 + 12 * q^71 + q^72 - 14 * q^73 + 8 * q^74 - q^75 - 2 * q^76 + 6 * q^77 - 4 * q^78 - 8 * q^79 + q^80 - q^81 + 9 * q^83 + q^84 - 12 * q^85 + 8 * q^86 - 9 * q^87 - 3 * q^88 - q^90 - 4 * q^91 + 12 * q^92 + 11 * q^93 + 12 * q^94 - 4 * q^95 + q^96 - 38 * q^97 - 6 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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