LMFDB - Embedded newform 1110.2.i.g.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(121,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1110.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1110.121
Dual form			1110.2.i.g.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +1.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +1.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +1.00000 q^{10} -3.00000 q^{11} +(0.500000 - 0.866025i) q^{12} +(2.50000 + 4.33013i) q^{13} +(-0.500000 + 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} +(0.500000 + 0.866025i) q^{18} +(2.50000 + 4.33013i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-1.50000 + 2.59808i) q^{22} +5.00000 q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +5.00000 q^{26} -1.00000 q^{27} +6.00000 q^{29} +(0.500000 + 0.866025i) q^{30} -6.00000 q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.50000 - 2.59808i) q^{33} +(1.00000 + 1.73205i) q^{34} +1.00000 q^{36} +(0.500000 + 6.06218i) q^{37} +5.00000 q^{38} +(-2.50000 + 4.33013i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-1.00000 - 1.73205i) q^{41} +4.00000 q^{43} +(1.50000 + 2.59808i) q^{44} -1.00000 q^{45} +(2.50000 - 4.33013i) q^{46} -3.00000 q^{47} -1.00000 q^{48} +(3.50000 - 6.06218i) q^{49} +(0.500000 + 0.866025i) q^{50} -2.00000 q^{51} +(2.50000 - 4.33013i) q^{52} +(-1.00000 + 1.73205i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-1.50000 - 2.59808i) q^{55} +(-2.50000 + 4.33013i) q^{57} +(3.00000 - 5.19615i) q^{58} +(-5.50000 + 9.52628i) q^{59} +1.00000 q^{60} +(3.00000 + 5.19615i) q^{61} +(-3.00000 + 5.19615i) q^{62} +1.00000 q^{64} +(-2.50000 + 4.33013i) q^{65} -3.00000 q^{66} +(1.00000 + 1.73205i) q^{67} +2.00000 q^{68} +(2.50000 + 4.33013i) q^{69} +(-2.00000 - 3.46410i) q^{71} +(0.500000 - 0.866025i) q^{72} -4.00000 q^{73} +(5.50000 + 2.59808i) q^{74} -1.00000 q^{75} +(2.50000 - 4.33013i) q^{76} +(2.50000 + 4.33013i) q^{78} +(1.00000 + 1.73205i) q^{79} -1.00000 q^{80} +(-0.500000 - 0.866025i) q^{81} -2.00000 q^{82} +(7.00000 - 12.1244i) q^{83} -2.00000 q^{85} +(2.00000 - 3.46410i) q^{86} +(3.00000 + 5.19615i) q^{87} +3.00000 q^{88} +(2.50000 - 4.33013i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(-2.50000 - 4.33013i) q^{92} +(-3.00000 - 5.19615i) q^{93} +(-1.50000 + 2.59808i) q^{94} +(-2.50000 + 4.33013i) q^{95} +(-0.500000 + 0.866025i) q^{96} +16.0000 q^{97} +(-3.50000 - 6.06218i) q^{98} +(1.50000 - 2.59808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + q^{3} - q^{4} + q^{5} + 2 q^{6} - 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + q^2 + q^3 - q^4 + q^5 + 2 * q^6 - 2 * q^8 - q^9	$ 2 q + q^{2} + q^{3} - q^{4} + q^{5} + 2 q^{6} - 2 q^{8} - q^{9} + 2 q^{10} - 6 q^{11} + q^{12} + 5 q^{13} - q^{15} - q^{16} - 2 q^{17} + q^{18} + 5 q^{19} + q^{20} - 3 q^{22} + 10 q^{23} - q^{24} - q^{25} + 10 q^{26} - 2 q^{27} + 12 q^{29} + q^{30} - 12 q^{31} + q^{32} - 3 q^{33} + 2 q^{34} + 2 q^{36} + q^{37} + 10 q^{38} - 5 q^{39} - q^{40} - 2 q^{41} + 8 q^{43} + 3 q^{44} - 2 q^{45} + 5 q^{46} - 6 q^{47} - 2 q^{48} + 7 q^{49} + q^{50} - 4 q^{51} + 5 q^{52} - 2 q^{53} - q^{54} - 3 q^{55} - 5 q^{57} + 6 q^{58} - 11 q^{59} + 2 q^{60} + 6 q^{61} - 6 q^{62} + 2 q^{64} - 5 q^{65} - 6 q^{66} + 2 q^{67} + 4 q^{68} + 5 q^{69} - 4 q^{71} + q^{72} - 8 q^{73} + 11 q^{74} - 2 q^{75} + 5 q^{76} + 5 q^{78} + 2 q^{79} - 2 q^{80} - q^{81} - 4 q^{82} + 14 q^{83} - 4 q^{85} + 4 q^{86} + 6 q^{87} + 6 q^{88} + 5 q^{89} - q^{90} - 5 q^{92} - 6 q^{93} - 3 q^{94} - 5 q^{95} - q^{96} + 32 q^{97} - 7 q^{98} + 3 q^{99}+O(q^{100}) $ 2 * q + q^2 + q^3 - q^4 + q^5 + 2 * q^6 - 2 * q^8 - q^9 + 2 * q^10 - 6 * q^11 + q^12 + 5 * q^13 - q^15 - q^16 - 2 * q^17 + q^18 + 5 * q^19 + q^20 - 3 * q^22 + 10 * q^23 - q^24 - q^25 + 10 * q^26 - 2 * q^27 + 12 * q^29 + q^30 - 12 * q^31 + q^32 - 3 * q^33 + 2 * q^34 + 2 * q^36 + q^37 + 10 * q^38 - 5 * q^39 - q^40 - 2 * q^41 + 8 * q^43 + 3 * q^44 - 2 * q^45 + 5 * q^46 - 6 * q^47 - 2 * q^48 + 7 * q^49 + q^50 - 4 * q^51 + 5 * q^52 - 2 * q^53 - q^54 - 3 * q^55 - 5 * q^57 + 6 * q^58 - 11 * q^59 + 2 * q^60 + 6 * q^61 - 6 * q^62 + 2 * q^64 - 5 * q^65 - 6 * q^66 + 2 * q^67 + 4 * q^68 + 5 * q^69 - 4 * q^71 + q^72 - 8 * q^73 + 11 * q^74 - 2 * q^75 + 5 * q^76 + 5 * q^78 + 2 * q^79 - 2 * q^80 - q^81 - 4 * q^82 + 14 * q^83 - 4 * q^85 + 4 * q^86 + 6 * q^87 + 6 * q^88 + 5 * q^89 - q^90 - 5 * q^92 - 6 * q^93 - 3 * q^94 - 5 * q^95 - q^96 + 32 * q^97 - 7 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	1.00000			0.408248
$7$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$7$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.00000			0.316228
$11$	−3.00000			−0.904534			−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000			−0.904534			−0.452267	+	0.891883i	$0.649385\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	2.50000	+	4.33013i	0.693375	+	1.20096i	0.970725	+	0.240192i	$0.0772105\pi$
$13$	2.50000	+	4.33013i	0.693375	+	1.20096i	−0.277350	+	0.960769i	$0.589456\pi$
$14$		0			0
$15$	−0.500000	+	0.866025i	−0.129099	+	0.223607i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	−0.961436	−	0.275029i	$-0.911312\pi$
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	0.718900	+	0.695113i	$0.244646\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	0.996199	+	0.0871106i	$0.0277634\pi$
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	−0.422659	+	0.906289i	$0.638903\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$		0			0
$22$	−1.50000	+	2.59808i	−0.319801	+	0.553912i
$23$	5.00000			1.04257			0.521286	−	0.853382i	$-0.325452\pi$
$23$	5.00000			1.04257			0.521286	+	0.853382i	$0.325452\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	5.00000			0.980581
$27$	−1.00000			−0.192450
$28$		0			0
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$	0.500000	+	0.866025i	0.0912871	+	0.158114i
$31$	−6.00000			−1.07763			−0.538816	−	0.842424i	$-0.681128\pi$
$31$	−6.00000			−1.07763			−0.538816	+	0.842424i	$0.681128\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−1.50000	−	2.59808i	−0.261116	−	0.452267i
$34$	1.00000	+	1.73205i	0.171499	+	0.297044i
$35$		0			0
$36$	1.00000			0.166667
$37$	0.500000	+	6.06218i	0.0821995	+	0.996616i
$37$	0.500000	+	6.06218i	0.0821995	+	0.996616i
$38$	5.00000			0.811107
$39$	−2.50000	+	4.33013i	−0.400320	+	0.693375i
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	−1.00000	−	1.73205i	−0.156174	−	0.270501i	0.777312	−	0.629115i	$-0.216583\pi$
$41$	−1.00000	−	1.73205i	−0.156174	−	0.270501i	−0.933486	+	0.358614i	$0.883249\pi$
$42$		0			0
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$	1.50000	+	2.59808i	0.226134	+	0.391675i
$45$	−1.00000			−0.149071
$46$	2.50000	−	4.33013i	0.368605	−	0.638442i
$47$	−3.00000			−0.437595			−0.218797	−	0.975770i	$-0.570213\pi$
$47$	−3.00000			−0.437595			−0.218797	+	0.975770i	$0.570213\pi$
$48$	−1.00000			−0.144338
$49$	3.50000	−	6.06218i	0.500000	−	0.866025i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	−2.00000			−0.280056
$52$	2.50000	−	4.33013i	0.346688	−	0.600481i
$53$	−1.00000	+	1.73205i	−0.137361	+	0.237915i	−0.926497	−	0.376303i	$-0.877195\pi$
$53$	−1.00000	+	1.73205i	−0.137361	+	0.237915i	0.789136	+	0.614218i	$0.210529\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	−1.50000	−	2.59808i	−0.202260	−	0.350325i
$56$		0			0
$57$	−2.50000	+	4.33013i	−0.331133	+	0.573539i
$58$	3.00000	−	5.19615i	0.393919	−	0.682288i
$59$	−5.50000	+	9.52628i	−0.716039	+	1.24022i	0.246518	+	0.969138i	$0.420713\pi$
$59$	−5.50000	+	9.52628i	−0.716039	+	1.24022i	−0.962557	+	0.271078i	$0.912620\pi$
$60$	1.00000			0.129099
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	0.991645	−	0.128994i	$-0.0411748\pi$
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	−0.607535	+	0.794293i	$0.707841\pi$
$62$	−3.00000	+	5.19615i	−0.381000	+	0.659912i
$63$		0			0
$64$	1.00000			0.125000
$65$	−2.50000	+	4.33013i	−0.310087	+	0.537086i
$66$	−3.00000			−0.369274
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	0.920623	−	0.390453i	$-0.127682\pi$
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	−0.798454	+	0.602056i	$0.794348\pi$
$68$	2.00000			0.242536
$69$	2.50000	+	4.33013i	0.300965	+	0.521286i
$70$		0			0
$71$	−2.00000	−	3.46410i	−0.237356	−	0.411113i	0.722599	−	0.691268i	$-0.242948\pi$
$71$	−2.00000	−	3.46410i	−0.237356	−	0.411113i	−0.959955	+	0.280155i	$0.909614\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	−4.00000			−0.468165			−0.234082	−	0.972217i	$-0.575209\pi$
$73$	−4.00000			−0.468165			−0.234082	+	0.972217i	$0.575209\pi$
$74$	5.50000	+	2.59808i	0.639362	+	0.302020i
$75$	−1.00000			−0.115470
$76$	2.50000	−	4.33013i	0.286770	−	0.496700i
$77$		0			0
$78$	2.50000	+	4.33013i	0.283069	+	0.490290i
$79$	1.00000	+	1.73205i	0.112509	+	0.194871i	0.916781	−	0.399390i	$-0.130778\pi$
$79$	1.00000	+	1.73205i	0.112509	+	0.194871i	−0.804272	+	0.594261i	$0.797445\pi$
$80$	−1.00000			−0.111803
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−2.00000			−0.220863
$83$	7.00000	−	12.1244i	0.768350	−	1.33082i	−0.170107	−	0.985426i	$-0.554411\pi$
$83$	7.00000	−	12.1244i	0.768350	−	1.33082i	0.938457	−	0.345395i	$-0.112255\pi$
$84$		0			0
$85$	−2.00000			−0.216930
$86$	2.00000	−	3.46410i	0.215666	−	0.373544i
$87$	3.00000	+	5.19615i	0.321634	+	0.557086i
$88$	3.00000			0.319801
$89$	2.50000	−	4.33013i	0.264999	−	0.458993i	−0.702564	−	0.711621i	$-0.747962\pi$
$89$	2.50000	−	4.33013i	0.264999	−	0.458993i	0.967563	+	0.252628i	$0.0812949\pi$
$90$	−0.500000	+	0.866025i	−0.0527046	+	0.0912871i
$91$		0			0
$92$	−2.50000	−	4.33013i	−0.260643	−	0.451447i
$93$	−3.00000	−	5.19615i	−0.311086	−	0.538816i
$94$	−1.50000	+	2.59808i	−0.154713	+	0.267971i
$95$	−2.50000	+	4.33013i	−0.256495	+	0.444262i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	16.0000			1.62455			0.812277	−	0.583272i	$-0.198228\pi$
$97$	16.0000			1.62455			0.812277	+	0.583272i	$0.198228\pi$
$98$	−3.50000	−	6.06218i	−0.353553	−	0.612372i
$99$	1.50000	−	2.59808i	0.150756	−	0.261116i
$100$	1.00000			0.100000
$101$	8.00000			0.796030			0.398015	−	0.917379i	$-0.369699\pi$
$101$	8.00000			0.796030			0.398015	+	0.917379i	$0.369699\pi$
$102$	−1.00000	+	1.73205i	−0.0990148	+	0.171499i
$103$	−7.00000			−0.689730			−0.344865	−	0.938652i	$-0.612075\pi$
$103$	−7.00000			−0.689730			−0.344865	+	0.938652i	$0.612075\pi$
$104$	−2.50000	−	4.33013i	−0.245145	−	0.424604i
$105$		0			0
$106$	1.00000	+	1.73205i	0.0971286	+	0.168232i
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	−0.995474	−	0.0950377i	$-0.969703\pi$
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	0.415432	−	0.909624i	$-0.363630\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	−8.00000	+	13.8564i	−0.766261	+	1.32720i	0.173316	+	0.984866i	$0.444552\pi$
$109$	−8.00000	+	13.8564i	−0.766261	+	1.32720i	−0.939577	+	0.342337i	$0.888782\pi$
$110$	−3.00000			−0.286039
$111$	−5.00000	+	3.46410i	−0.474579	+	0.328798i
$112$		0			0
$113$	4.00000	−	6.92820i	0.376288	−	0.651751i	−0.614231	−	0.789127i	$-0.710534\pi$
$113$	4.00000	−	6.92820i	0.376288	−	0.651751i	0.990519	+	0.137376i	$0.0438669\pi$
$114$	2.50000	+	4.33013i	0.234146	+	0.405554i
$115$	2.50000	+	4.33013i	0.233126	+	0.403786i
$116$	−3.00000	−	5.19615i	−0.278543	−	0.482451i
$117$	−5.00000			−0.462250
$118$	5.50000	+	9.52628i	0.506316	+	0.876965i
$119$		0			0
$120$	0.500000	−	0.866025i	0.0456435	−	0.0790569i
$121$	−2.00000			−0.181818
$122$	6.00000			0.543214
$123$	1.00000	−	1.73205i	0.0901670	−	0.156174i
$124$	3.00000	+	5.19615i	0.269408	+	0.466628i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	7.50000	−	12.9904i	0.665517	−	1.15271i	−0.313627	−	0.949546i	$-0.601544\pi$
$127$	7.50000	−	12.9904i	0.665517	−	1.15271i	0.979145	−	0.203164i	$-0.0651224\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	2.00000	+	3.46410i	0.176090	+	0.304997i
$130$	2.50000	+	4.33013i	0.219265	+	0.379777i
$131$	6.00000	−	10.3923i	0.524222	−	0.907980i	−0.475380	−	0.879781i	$-0.657689\pi$
$131$	6.00000	−	10.3923i	0.524222	−	0.907980i	0.999602	−	0.0281993i	$-0.00897729\pi$
$132$	−1.50000	+	2.59808i	−0.130558	+	0.226134i
$133$		0			0
$134$	2.00000			0.172774
$135$	−0.500000	−	0.866025i	−0.0430331	−	0.0745356i
$136$	1.00000	−	1.73205i	0.0857493	−	0.148522i
$137$	−18.0000			−1.53784			−0.768922	−	0.639343i	$-0.779207\pi$
$137$	−18.0000			−1.53784			−0.768922	+	0.639343i	$0.779207\pi$
$138$	5.00000			0.425628
$139$	1.50000	−	2.59808i	0.127228	−	0.220366i	−0.795373	−	0.606120i	$-0.792725\pi$
$139$	1.50000	−	2.59808i	0.127228	−	0.220366i	0.922602	+	0.385754i	$0.126059\pi$
$140$		0			0
$141$	−1.50000	−	2.59808i	−0.126323	−	0.218797i
$142$	−4.00000			−0.335673
$143$	−7.50000	−	12.9904i	−0.627182	−	1.08631i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	3.00000	+	5.19615i	0.249136	+	0.431517i
$146$	−2.00000	+	3.46410i	−0.165521	+	0.286691i
$147$	7.00000			0.577350
$148$	5.00000	−	3.46410i	0.410997	−	0.284747i
$149$		0			0			−	1.00000i	$-0.5\pi$
$149$		0			0				1.00000i	$0.5\pi$
$150$	−0.500000	+	0.866025i	−0.0408248	+	0.0707107i
$151$	−2.00000	−	3.46410i	−0.162758	−	0.281905i	0.773099	−	0.634285i	$-0.218706\pi$
$151$	−2.00000	−	3.46410i	−0.162758	−	0.281905i	−0.935857	+	0.352381i	$0.885372\pi$
$152$	−2.50000	−	4.33013i	−0.202777	−	0.351220i
$153$	−1.00000	−	1.73205i	−0.0808452	−	0.140028i
$154$		0			0
$155$	−3.00000	−	5.19615i	−0.240966	−	0.417365i
$156$	5.00000			0.400320
$157$	−3.50000	+	6.06218i	−0.279330	+	0.483814i	−0.971219	−	0.238190i	$-0.923446\pi$
$157$	−3.50000	+	6.06218i	−0.279330	+	0.483814i	0.691888	+	0.722005i	$0.256779\pi$
$158$	2.00000			0.159111
$159$	−2.00000			−0.158610
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$		0			0
$162$	−1.00000			−0.0785674
$163$	−9.00000	+	15.5885i	−0.704934	+	1.22098i	0.261781	+	0.965127i	$0.415690\pi$
$163$	−9.00000	+	15.5885i	−0.704934	+	1.22098i	−0.966715	+	0.255855i	$0.917643\pi$
$164$	−1.00000	+	1.73205i	−0.0780869	+	0.135250i
$165$	1.50000	−	2.59808i	0.116775	−	0.202260i
$166$	−7.00000	−	12.1244i	−0.543305	−	0.941033i
$167$	−4.00000	−	6.92820i	−0.309529	−	0.536120i	0.668730	−	0.743505i	$-0.266838\pi$
$167$	−4.00000	−	6.92820i	−0.309529	−	0.536120i	−0.978259	+	0.207385i	$0.933505\pi$
$168$		0			0
$169$	−6.00000	+	10.3923i	−0.461538	+	0.799408i
$170$	−1.00000	+	1.73205i	−0.0766965	+	0.132842i
$171$	−5.00000			−0.382360
$172$	−2.00000	−	3.46410i	−0.152499	−	0.264135i
$173$	12.5000	−	21.6506i	0.950357	−	1.64607i	0.205706	−	0.978614i	$-0.434051\pi$
$173$	12.5000	−	21.6506i	0.950357	−	1.64607i	0.744652	−	0.667453i	$-0.232616\pi$
$174$	6.00000			0.454859
$175$		0			0
$176$	1.50000	−	2.59808i	0.113067	−	0.195837i
$177$	−11.0000			−0.826811
$178$	−2.50000	−	4.33013i	−0.187383	−	0.324557i
$179$	−7.00000			−0.523205			−0.261602	−	0.965176i	$-0.584251\pi$
$179$	−7.00000			−0.523205			−0.261602	+	0.965176i	$0.584251\pi$
$180$	0.500000	+	0.866025i	0.0372678	+	0.0645497i
$181$	−8.00000	−	13.8564i	−0.594635	−	1.02994i	−0.993598	−	0.112972i	$-0.963963\pi$
$181$	−8.00000	−	13.8564i	−0.594635	−	1.02994i	0.398963	−	0.916967i	$-0.369370\pi$
$182$		0			0
$183$	−3.00000	+	5.19615i	−0.221766	+	0.384111i
$184$	−5.00000			−0.368605
$185$	−5.00000	+	3.46410i	−0.367607	+	0.254686i
$186$	−6.00000			−0.439941
$187$	3.00000	−	5.19615i	0.219382	−	0.379980i
$188$	1.50000	+	2.59808i	0.109399	+	0.189484i
$189$		0			0
$190$	2.50000	+	4.33013i	0.181369	+	0.314140i
$191$	14.0000			1.01300			0.506502	−	0.862239i	$-0.330938\pi$
$191$	14.0000			1.01300			0.506502	+	0.862239i	$0.330938\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	4.00000			0.287926			0.143963	−	0.989583i	$-0.454015\pi$
$193$	4.00000			0.287926			0.143963	+	0.989583i	$0.454015\pi$
$194$	8.00000	−	13.8564i	0.574367	−	0.994832i
$195$	−5.00000			−0.358057
$196$	−7.00000			−0.500000
$197$	−3.00000	+	5.19615i	−0.213741	+	0.370211i	−0.952882	−	0.303340i	$-0.901898\pi$
$197$	−3.00000	+	5.19615i	−0.213741	+	0.370211i	0.739141	+	0.673550i	$0.235232\pi$
$198$	−1.50000	−	2.59808i	−0.106600	−	0.184637i
$199$	4.00000			0.283552			0.141776	−	0.989899i	$-0.454719\pi$
$199$	4.00000			0.283552			0.141776	+	0.989899i	$0.454719\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$	−1.00000	+	1.73205i	−0.0705346	+	0.122169i
$202$	4.00000	−	6.92820i	0.281439	−	0.487467i
$203$		0			0
$204$	1.00000	+	1.73205i	0.0700140	+	0.121268i
$205$	1.00000	−	1.73205i	0.0698430	−	0.120972i
$206$	−3.50000	+	6.06218i	−0.243857	+	0.422372i
$207$	−2.50000	+	4.33013i	−0.173762	+	0.300965i
$208$	−5.00000			−0.346688
$209$	−7.50000	−	12.9904i	−0.518786	−	0.898563i
$210$		0			0
$211$	13.0000			0.894957			0.447478	−	0.894295i	$-0.352322\pi$
$211$	13.0000			0.894957			0.447478	+	0.894295i	$0.352322\pi$
$212$	2.00000			0.137361
$213$	2.00000	−	3.46410i	0.137038	−	0.237356i
$214$	−12.0000			−0.820303
$215$	2.00000	+	3.46410i	0.136399	+	0.236250i
$216$	1.00000			0.0680414
$217$		0			0
$218$	8.00000	+	13.8564i	0.541828	+	0.938474i
$219$	−2.00000	−	3.46410i	−0.135147	−	0.234082i
$220$	−1.50000	+	2.59808i	−0.101130	+	0.175162i
$221$	−10.0000			−0.672673
$222$	0.500000	+	6.06218i	0.0335578	+	0.406867i
$223$	7.00000			0.468755			0.234377	−	0.972146i	$-0.424695\pi$
$223$	7.00000			0.468755			0.234377	+	0.972146i	$0.424695\pi$
$224$		0			0
$225$	−0.500000	−	0.866025i	−0.0333333	−	0.0577350i
$226$	−4.00000	−	6.92820i	−0.266076	−	0.460857i
$227$	−15.0000	−	25.9808i	−0.995585	−	1.72440i	−0.579082	−	0.815270i	$-0.696589\pi$
$227$	−15.0000	−	25.9808i	−0.995585	−	1.72440i	−0.416503	−	0.909134i	$-0.636745\pi$
$228$	5.00000			0.331133
$229$	2.00000	+	3.46410i	0.132164	+	0.228914i	0.924510	−	0.381157i	$-0.124474\pi$
$229$	2.00000	+	3.46410i	0.132164	+	0.228914i	−0.792347	+	0.610071i	$0.791141\pi$
$230$	5.00000			0.329690
$231$		0			0
$232$	−6.00000			−0.393919
$233$	−8.00000			−0.524097			−0.262049	−	0.965055i	$-0.584398\pi$
$233$	−8.00000			−0.524097			−0.262049	+	0.965055i	$0.584398\pi$
$234$	−2.50000	+	4.33013i	−0.163430	+	0.283069i
$235$	−1.50000	−	2.59808i	−0.0978492	−	0.169480i
$236$	11.0000			0.716039
$237$	−1.00000	+	1.73205i	−0.0649570	+	0.112509i
$238$		0			0
$239$	−4.00000	+	6.92820i	−0.258738	+	0.448148i	−0.965904	−	0.258900i	$-0.916640\pi$
$239$	−4.00000	+	6.92820i	−0.258738	+	0.448148i	0.707166	+	0.707048i	$0.249973\pi$
$240$	−0.500000	−	0.866025i	−0.0322749	−	0.0559017i
$241$	8.50000	+	14.7224i	0.547533	+	0.948355i	0.998443	+	0.0557856i	$0.0177663\pi$
$241$	8.50000	+	14.7224i	0.547533	+	0.948355i	−0.450910	+	0.892570i	$0.648900\pi$
$242$	−1.00000	+	1.73205i	−0.0642824	+	0.111340i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	3.00000	−	5.19615i	0.192055	−	0.332650i
$245$	7.00000			0.447214
$246$	−1.00000	−	1.73205i	−0.0637577	−	0.110432i
$247$	−12.5000	+	21.6506i	−0.795356	+	1.37760i
$248$	6.00000			0.381000
$249$	14.0000			0.887214
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	−1.00000			−0.0631194			−0.0315597	−	0.999502i	$-0.510047\pi$
$251$	−1.00000			−0.0631194			−0.0315597	+	0.999502i	$0.510047\pi$
$252$		0			0
$253$	−15.0000			−0.943042
$254$	−7.50000	−	12.9904i	−0.470592	−	0.815089i
$255$	−1.00000	−	1.73205i	−0.0626224	−	0.108465i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−1.00000	+	1.73205i	−0.0623783	+	0.108042i	−0.895528	−	0.445005i	$-0.853202\pi$
$257$	−1.00000	+	1.73205i	−0.0623783	+	0.108042i	0.833150	+	0.553047i	$0.186535\pi$
$258$	4.00000			0.249029
$259$		0			0
$260$	5.00000			0.310087
$261$	−3.00000	+	5.19615i	−0.185695	+	0.321634i
$262$	−6.00000	−	10.3923i	−0.370681	−	0.642039i
$263$	−7.50000	−	12.9904i	−0.462470	−	0.801021i	0.536614	−	0.843828i	$-0.319703\pi$
$263$	−7.50000	−	12.9904i	−0.462470	−	0.801021i	−0.999083	+	0.0428069i	$0.986370\pi$
$264$	1.50000	+	2.59808i	0.0923186	+	0.159901i
$265$	−2.00000			−0.122859
$266$		0			0
$267$	5.00000			0.305995
$268$	1.00000	−	1.73205i	0.0610847	−	0.105802i
$269$	10.0000			0.609711			0.304855	−	0.952399i	$-0.401392\pi$
$269$	10.0000			0.609711			0.304855	+	0.952399i	$0.401392\pi$
$270$	−1.00000			−0.0608581
$271$	10.0000	−	17.3205i	0.607457	−	1.05215i	−0.384201	−	0.923249i	$-0.625523\pi$
$271$	10.0000	−	17.3205i	0.607457	−	1.05215i	0.991658	−	0.128897i	$-0.0411435\pi$
$272$	−1.00000	−	1.73205i	−0.0606339	−	0.105021i
$273$		0			0
$274$	−9.00000	+	15.5885i	−0.543710	+	0.941733i
$275$	1.50000	−	2.59808i	0.0904534	−	0.156670i
$276$	2.50000	−	4.33013i	0.150482	−	0.260643i
$277$	13.0000	+	22.5167i	0.781094	+	1.35290i	0.931305	+	0.364241i	$0.118672\pi$
$277$	13.0000	+	22.5167i	0.781094	+	1.35290i	−0.150210	+	0.988654i	$0.547995\pi$
$278$	−1.50000	−	2.59808i	−0.0899640	−	0.155822i
$279$	3.00000	−	5.19615i	0.179605	−	0.311086i
$280$		0			0
$281$	−13.5000	+	23.3827i	−0.805342	+	1.39489i	0.110717	+	0.993852i	$0.464685\pi$
$281$	−13.5000	+	23.3827i	−0.805342	+	1.39489i	−0.916060	+	0.401042i	$0.868648\pi$
$282$	−3.00000			−0.178647
$283$	−13.0000	−	22.5167i	−0.772770	−	1.33848i	−0.936039	−	0.351895i	$-0.885537\pi$
$283$	−13.0000	−	22.5167i	−0.772770	−	1.33848i	0.163270	−	0.986581i	$-0.447796\pi$
$284$	−2.00000	+	3.46410i	−0.118678	+	0.205557i
$285$	−5.00000			−0.296174
$286$	−15.0000			−0.886969
$287$		0			0
$288$	−1.00000			−0.0589256
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$	6.00000			0.352332
$291$	8.00000	+	13.8564i	0.468968	+	0.812277i
$292$	2.00000	+	3.46410i	0.117041	+	0.202721i
$293$	−4.50000	−	7.79423i	−0.262893	−	0.455344i	0.704117	−	0.710084i	$-0.251343\pi$
$293$	−4.50000	−	7.79423i	−0.262893	−	0.455344i	−0.967009	+	0.254741i	$0.918010\pi$
$294$	3.50000	−	6.06218i	0.204124	−	0.353553i
$295$	−11.0000			−0.640445
$296$	−0.500000	−	6.06218i	−0.0290619	−	0.352357i
$297$	3.00000			0.174078
$298$		0			0
$299$	12.5000	+	21.6506i	0.722894	+	1.25209i
$300$	0.500000	+	0.866025i	0.0288675	+	0.0500000i
$301$		0			0
$302$	−4.00000			−0.230174
$303$	4.00000	+	6.92820i	0.229794	+	0.398015i
$304$	−5.00000			−0.286770
$305$	−3.00000	+	5.19615i	−0.171780	+	0.297531i
$306$	−2.00000			−0.114332
$307$	18.0000			1.02731			0.513657	−	0.857996i	$-0.328290\pi$
$307$	18.0000			1.02731			0.513657	+	0.857996i	$0.328290\pi$
$308$		0			0
$309$	−3.50000	−	6.06218i	−0.199108	−	0.344865i
$310$	−6.00000			−0.340777
$311$	2.00000	−	3.46410i	0.113410	−	0.196431i	−0.803733	−	0.594990i	$-0.797156\pi$
$311$	2.00000	−	3.46410i	0.113410	−	0.196431i	0.917143	+	0.398559i	$0.130489\pi$
$312$	2.50000	−	4.33013i	0.141535	−	0.245145i
$313$	10.0000	−	17.3205i	0.565233	−	0.979013i	−0.431795	−	0.901972i	$-0.642119\pi$
$313$	10.0000	−	17.3205i	0.565233	−	0.979013i	0.997028	−	0.0770410i	$-0.0245472\pi$
$314$	3.50000	+	6.06218i	0.197516	+	0.342108i
$315$		0			0
$316$	1.00000	−	1.73205i	0.0562544	−	0.0974355i
$317$	6.50000	−	11.2583i	0.365076	−	0.632331i	−0.623712	−	0.781654i	$-0.714376\pi$
$317$	6.50000	−	11.2583i	0.365076	−	0.632331i	0.988788	+	0.149323i	$0.0477095\pi$
$318$	−1.00000	+	1.73205i	−0.0560772	+	0.0971286i
$319$	−18.0000			−1.00781
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$	6.00000	−	10.3923i	0.334887	−	0.580042i
$322$		0			0
$323$	−10.0000			−0.556415
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−5.00000			−0.277350
$326$	9.00000	+	15.5885i	0.498464	+	0.863365i
$327$	−16.0000			−0.884802
$328$	1.00000	+	1.73205i	0.0552158	+	0.0956365i
$329$		0			0
$330$	−1.50000	−	2.59808i	−0.0825723	−	0.143019i
$331$	−8.50000	+	14.7224i	−0.467202	+	0.809218i	−0.999298	−	0.0374662i	$-0.988071\pi$
$331$	−8.50000	+	14.7224i	−0.467202	+	0.809218i	0.532096	+	0.846684i	$0.321405\pi$
$332$	−14.0000			−0.768350
$333$	−5.50000	−	2.59808i	−0.301398	−	0.142374i
$334$	−8.00000			−0.437741
$335$	−1.00000	+	1.73205i	−0.0546358	+	0.0946320i
$336$		0			0
$337$	−8.00000	−	13.8564i	−0.435788	−	0.754807i	0.561572	−	0.827428i	$-0.310197\pi$
$337$	−8.00000	−	13.8564i	−0.435788	−	0.754807i	−0.997360	+	0.0726214i	$0.976864\pi$
$338$	6.00000	+	10.3923i	0.326357	+	0.565267i
$339$	8.00000			0.434500
$340$	1.00000	+	1.73205i	0.0542326	+	0.0939336i
$341$	18.0000			0.974755
$342$	−2.50000	+	4.33013i	−0.135185	+	0.234146i
$343$		0			0
$344$	−4.00000			−0.215666
$345$	−2.50000	+	4.33013i	−0.134595	+	0.233126i
$346$	−12.5000	−	21.6506i	−0.672004	−	1.16395i
$347$	18.0000			0.966291			0.483145	−	0.875540i	$-0.339494\pi$
$347$	18.0000			0.966291			0.483145	+	0.875540i	$0.339494\pi$
$348$	3.00000	−	5.19615i	0.160817	−	0.278543i
$349$	−10.0000	+	17.3205i	−0.535288	+	0.927146i	0.463862	+	0.885908i	$0.346463\pi$
$349$	−10.0000	+	17.3205i	−0.535288	+	0.927146i	−0.999149	+	0.0412379i	$0.986870\pi$
$350$		0			0
$351$	−2.50000	−	4.33013i	−0.133440	−	0.231125i
$352$	−1.50000	−	2.59808i	−0.0799503	−	0.138478i
$353$	5.00000	−	8.66025i	0.266123	−	0.460939i	−0.701734	−	0.712439i	$-0.747591\pi$
$353$	5.00000	−	8.66025i	0.266123	−	0.460939i	0.967857	+	0.251500i	$0.0809239\pi$
$354$	−5.50000	+	9.52628i	−0.292322	+	0.506316i
$355$	2.00000	−	3.46410i	0.106149	−	0.183855i
$356$	−5.00000			−0.264999
$357$		0			0
$358$	−3.50000	+	6.06218i	−0.184981	+	0.320396i
$359$	−18.0000			−0.950004			−0.475002	−	0.879985i	$-0.657553\pi$
$359$	−18.0000			−0.950004			−0.475002	+	0.879985i	$0.657553\pi$
$360$	1.00000			0.0527046
$361$	−3.00000	+	5.19615i	−0.157895	+	0.273482i
$362$	−16.0000			−0.840941
$363$	−1.00000	−	1.73205i	−0.0524864	−	0.0909091i
$364$		0			0
$365$	−2.00000	−	3.46410i	−0.104685	−	0.181319i
$366$	3.00000	+	5.19615i	0.156813	+	0.271607i
$367$	−13.5000	−	23.3827i	−0.704694	−	1.22057i	−0.966802	−	0.255528i	$-0.917751\pi$
$367$	−13.5000	−	23.3827i	−0.704694	−	1.22057i	0.262108	−	0.965039i	$-0.415582\pi$
$368$	−2.50000	+	4.33013i	−0.130322	+	0.225723i
$369$	2.00000			0.104116
$370$	0.500000	+	6.06218i	0.0259938	+	0.315158i
$371$		0			0
$372$	−3.00000	+	5.19615i	−0.155543	+	0.269408i
$373$	−1.50000	−	2.59808i	−0.0776671	−	0.134523i	0.824576	−	0.565751i	$-0.191414\pi$
$373$	−1.50000	−	2.59808i	−0.0776671	−	0.134523i	−0.902243	+	0.431228i	$0.858080\pi$
$374$	−3.00000	−	5.19615i	−0.155126	−	0.268687i
$375$	−0.500000	−	0.866025i	−0.0258199	−	0.0447214i
$376$	3.00000			0.154713
$377$	15.0000	+	25.9808i	0.772539	+	1.33808i
$378$		0			0
$379$	−6.00000	+	10.3923i	−0.308199	+	0.533817i	−0.977969	−	0.208752i	$-0.933060\pi$
$379$	−6.00000	+	10.3923i	−0.308199	+	0.533817i	0.669769	+	0.742569i	$0.266393\pi$
$380$	5.00000			0.256495
$381$	15.0000			0.768473
$382$	7.00000	−	12.1244i	0.358151	−	0.620336i
$383$	−10.5000	−	18.1865i	−0.536525	−	0.929288i	−0.999088	−	0.0427020i	$-0.986403\pi$
$383$	−10.5000	−	18.1865i	−0.536525	−	0.929288i	0.462563	−	0.886586i	$-0.346930\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	2.00000	−	3.46410i	0.101797	−	0.176318i
$387$	−2.00000	+	3.46410i	−0.101666	+	0.176090i
$388$	−8.00000	−	13.8564i	−0.406138	−	0.703452i
$389$	3.00000	+	5.19615i	0.152106	+	0.263455i	0.932002	−	0.362454i	$-0.118061\pi$
$389$	3.00000	+	5.19615i	0.152106	+	0.263455i	−0.779895	+	0.625910i	$0.784728\pi$
$390$	−2.50000	+	4.33013i	−0.126592	+	0.219265i
$391$	−5.00000	+	8.66025i	−0.252861	+	0.437968i
$392$	−3.50000	+	6.06218i	−0.176777	+	0.306186i
$393$	12.0000			0.605320
$394$	3.00000	+	5.19615i	0.151138	+	0.261778i
$395$	−1.00000	+	1.73205i	−0.0503155	+	0.0871489i
$396$	−3.00000			−0.150756
$397$	33.0000			1.65622			0.828111	−	0.560564i	$-0.189416\pi$
$397$	33.0000			1.65622			0.828111	+	0.560564i	$0.189416\pi$
$398$	2.00000	−	3.46410i	0.100251	−	0.173640i
$399$		0			0
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	15.0000			0.749064			0.374532	−	0.927214i	$-0.377803\pi$
$401$	15.0000			0.749064			0.374532	+	0.927214i	$0.377803\pi$
$402$	1.00000	+	1.73205i	0.0498755	+	0.0863868i
$403$	−15.0000	−	25.9808i	−0.747203	−	1.29419i
$404$	−4.00000	−	6.92820i	−0.199007	−	0.344691i
$405$	0.500000	−	0.866025i	0.0248452	−	0.0430331i
$406$		0			0
$407$	−1.50000	−	18.1865i	−0.0743522	−	0.901473i
$408$	2.00000			0.0990148
$409$	−19.0000	+	32.9090i	−0.939490	+	1.62724i	−0.173064	+	0.984911i	$0.555367\pi$
$409$	−19.0000	+	32.9090i	−0.939490	+	1.62724i	−0.766426	+	0.642333i	$0.777967\pi$
$410$	−1.00000	−	1.73205i	−0.0493865	−	0.0855399i
$411$	−9.00000	−	15.5885i	−0.443937	−	0.768922i
$412$	3.50000	+	6.06218i	0.172433	+	0.298662i
$413$		0			0
$414$	2.50000	+	4.33013i	0.122868	+	0.212814i
$415$	14.0000			0.687233
$416$	−2.50000	+	4.33013i	−0.122573	+	0.212302i
$417$	3.00000			0.146911
$418$	−15.0000			−0.733674
$419$	−9.50000	+	16.4545i	−0.464105	+	0.803854i	−0.999161	−	0.0409630i	$-0.986957\pi$
$419$	−9.50000	+	16.4545i	−0.464105	+	0.803854i	0.535055	+	0.844817i	$0.320291\pi$
$420$		0			0
$421$	32.0000			1.55958			0.779792	−	0.626038i	$-0.215325\pi$
$421$	32.0000			1.55958			0.779792	+	0.626038i	$0.215325\pi$
$422$	6.50000	−	11.2583i	0.316415	−	0.548047i
$423$	1.50000	−	2.59808i	0.0729325	−	0.126323i
$424$	1.00000	−	1.73205i	0.0485643	−	0.0841158i
$425$	−1.00000	−	1.73205i	−0.0485071	−	0.0840168i
$426$	−2.00000	−	3.46410i	−0.0969003	−	0.167836i
$427$		0			0
$428$	−6.00000	+	10.3923i	−0.290021	+	0.502331i
$429$	7.50000	−	12.9904i	0.362103	−	0.627182i
$430$	4.00000			0.192897
$431$	14.0000	+	24.2487i	0.674356	+	1.16802i	0.976657	+	0.214807i	$0.0689121\pi$
$431$	14.0000	+	24.2487i	0.674356	+	1.16802i	−0.302300	+	0.953213i	$0.597755\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	18.0000			0.865025			0.432512	−	0.901628i	$-0.357627\pi$
$433$	18.0000			0.865025			0.432512	+	0.901628i	$0.357627\pi$
$434$		0			0
$435$	−3.00000	+	5.19615i	−0.143839	+	0.249136i
$436$	16.0000			0.766261
$437$	12.5000	+	21.6506i	0.597956	+	1.03569i
$438$	−4.00000			−0.191127
$439$	−6.00000	−	10.3923i	−0.286364	−	0.495998i	0.686575	−	0.727059i	$-0.259113\pi$
$439$	−6.00000	−	10.3923i	−0.286364	−	0.495998i	−0.972939	+	0.231062i	$0.925780\pi$
$440$	1.50000	+	2.59808i	0.0715097	+	0.123858i
$441$	3.50000	+	6.06218i	0.166667	+	0.288675i
$442$	−5.00000	+	8.66025i	−0.237826	+	0.411926i
$443$	−28.0000			−1.33032			−0.665160	−	0.746701i	$-0.731637\pi$
$443$	−28.0000			−1.33032			−0.665160	+	0.746701i	$0.731637\pi$
$444$	5.50000	+	2.59808i	0.261018	+	0.123299i
$445$	5.00000			0.237023
$446$	3.50000	−	6.06218i	0.165730	−	0.287052i
$447$		0			0
$448$		0			0
$449$	5.00000	+	8.66025i	0.235965	+	0.408703i	0.959553	−	0.281529i	$-0.0908417\pi$
$449$	5.00000	+	8.66025i	0.235965	+	0.408703i	−0.723588	+	0.690232i	$0.757508\pi$
$450$	−1.00000			−0.0471405
$451$	3.00000	+	5.19615i	0.141264	+	0.244677i
$452$	−8.00000			−0.376288
$453$	2.00000	−	3.46410i	0.0939682	−	0.162758i
$454$	−30.0000			−1.40797
$455$		0			0
$456$	2.50000	−	4.33013i	0.117073	−	0.202777i
$457$	4.00000	+	6.92820i	0.187112	+	0.324088i	0.944286	−	0.329125i	$-0.106754\pi$
$457$	4.00000	+	6.92820i	0.187112	+	0.324088i	−0.757174	+	0.653213i	$0.773421\pi$
$458$	4.00000			0.186908
$459$	1.00000	−	1.73205i	0.0466760	−	0.0808452i
$460$	2.50000	−	4.33013i	0.116563	−	0.201893i
$461$	20.0000	−	34.6410i	0.931493	−	1.61339i	0.150721	−	0.988576i	$-0.451840\pi$
$461$	20.0000	−	34.6410i	0.931493	−	1.61339i	0.780771	−	0.624817i	$-0.214826\pi$
$462$		0			0
$463$	−14.0000	−	24.2487i	−0.650635	−	1.12693i	−0.982969	−	0.183771i	$-0.941169\pi$
$463$	−14.0000	−	24.2487i	−0.650635	−	1.12693i	0.332334	−	0.943162i	$-0.392164\pi$
$464$	−3.00000	+	5.19615i	−0.139272	+	0.241225i
$465$	3.00000	−	5.19615i	0.139122	−	0.240966i
$466$	−4.00000	+	6.92820i	−0.185296	+	0.320943i
$467$	−6.00000			−0.277647			−0.138823	−	0.990317i	$-0.544332\pi$
$467$	−6.00000			−0.277647			−0.138823	+	0.990317i	$0.544332\pi$
$468$	2.50000	+	4.33013i	0.115563	+	0.200160i
$469$		0			0
$470$	−3.00000			−0.138380
$471$	−7.00000			−0.322543
$472$	5.50000	−	9.52628i	0.253158	−	0.438483i
$473$	−12.0000			−0.551761
$474$	1.00000	+	1.73205i	0.0459315	+	0.0795557i
$475$	−5.00000			−0.229416
$476$		0			0
$477$	−1.00000	−	1.73205i	−0.0457869	−	0.0793052i
$478$	4.00000	+	6.92820i	0.182956	+	0.316889i
$479$	4.00000	−	6.92820i	0.182765	−	0.316558i	−0.760056	−	0.649857i	$-0.774829\pi$
$479$	4.00000	−	6.92820i	0.182765	−	0.316558i	0.942821	+	0.333300i	$0.108162\pi$
$480$	−1.00000			−0.0456435
$481$	−25.0000	+	17.3205i	−1.13990	+	0.789747i
$482$	17.0000			0.774329
$483$		0			0
$484$	1.00000	+	1.73205i	0.0454545	+	0.0787296i
$485$	8.00000	+	13.8564i	0.363261	+	0.629187i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	28.0000			1.26880			0.634401	−	0.773004i	$-0.281247\pi$
$487$	28.0000			1.26880			0.634401	+	0.773004i	$0.281247\pi$
$488$	−3.00000	−	5.19615i	−0.135804	−	0.235219i
$489$	−18.0000			−0.813988
$490$	3.50000	−	6.06218i	0.158114	−	0.273861i
$491$	−9.00000			−0.406164			−0.203082	−	0.979162i	$-0.565096\pi$
$491$	−9.00000			−0.406164			−0.203082	+	0.979162i	$0.565096\pi$
$492$	−2.00000			−0.0901670
$493$	−6.00000	+	10.3923i	−0.270226	+	0.468046i
$494$	12.5000	+	21.6506i	0.562402	+	0.974108i
$495$	3.00000			0.134840
$496$	3.00000	−	5.19615i	0.134704	−	0.233314i
$497$		0			0
$498$	7.00000	−	12.1244i	0.313678	−	0.543305i
$499$	−2.00000	−	3.46410i	−0.0895323	−	0.155074i	0.817781	−	0.575529i	$-0.195204\pi$
$499$	−2.00000	−	3.46410i	−0.0895323	−	0.155074i	−0.907314	+	0.420455i	$0.861871\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$	4.00000	−	6.92820i	0.178707	−	0.309529i
$502$	−0.500000	+	0.866025i	−0.0223161	+	0.0386526i
$503$	4.00000	−	6.92820i	0.178351	−	0.308913i	−0.762965	−	0.646440i	$-0.776257\pi$
$503$	4.00000	−	6.92820i	0.178351	−	0.308913i	0.941316	+	0.337527i	$0.109590\pi$
$504$		0			0
$505$	4.00000	+	6.92820i	0.177998	+	0.308301i
$506$	−7.50000	+	12.9904i	−0.333416	+	0.577493i
$507$	−12.0000			−0.532939
$508$	−15.0000			−0.665517
$509$	12.0000	−	20.7846i	0.531891	−	0.921262i	−0.467416	−	0.884037i	$-0.654815\pi$
$509$	12.0000	−	20.7846i	0.531891	−	0.921262i	0.999307	−	0.0372243i	$-0.0118516\pi$
$510$	−2.00000			−0.0885615
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	−2.50000	−	4.33013i	−0.110378	−	0.191180i
$514$	1.00000	+	1.73205i	0.0441081	+	0.0763975i
$515$	−3.50000	−	6.06218i	−0.154228	−	0.267131i
$516$	2.00000	−	3.46410i	0.0880451	−	0.152499i
$517$	9.00000			0.395820
$518$		0			0
$519$	25.0000			1.09738
$520$	2.50000	−	4.33013i	0.109632	−	0.189889i
$521$	20.5000	+	35.5070i	0.898121	+	1.55559i	0.829893	+	0.557922i	$0.188401\pi$
$521$	20.5000	+	35.5070i	0.898121	+	1.55559i	0.0682279	+	0.997670i	$0.478266\pi$
$522$	3.00000	+	5.19615i	0.131306	+	0.227429i
$523$	14.0000	+	24.2487i	0.612177	+	1.06032i	0.990873	+	0.134801i	$0.0430394\pi$
$523$	14.0000	+	24.2487i	0.612177	+	1.06032i	−0.378695	+	0.925521i	$0.623627\pi$
$524$	−12.0000			−0.524222
$525$		0			0
$526$	−15.0000			−0.654031
$527$	6.00000	−	10.3923i	0.261364	−	0.452696i
$528$	3.00000			0.130558
$529$	2.00000			0.0869565
$530$	−1.00000	+	1.73205i	−0.0434372	+	0.0752355i
$531$	−5.50000	−	9.52628i	−0.238680	−	0.413405i
$532$		0			0
$533$	5.00000	−	8.66025i	0.216574	−	0.375117i
$534$	2.50000	−	4.33013i	0.108186	−	0.187383i
$535$	6.00000	−	10.3923i	0.259403	−	0.449299i
$536$	−1.00000	−	1.73205i	−0.0431934	−	0.0748132i
$537$	−3.50000	−	6.06218i	−0.151036	−	0.261602i
$538$	5.00000	−	8.66025i	0.215565	−	0.373370i
$539$	−10.5000	+	18.1865i	−0.452267	+	0.783349i
$540$	−0.500000	+	0.866025i	−0.0215166	+	0.0372678i
$541$	−2.00000			−0.0859867			−0.0429934	−	0.999075i	$-0.513689\pi$
$541$	−2.00000			−0.0859867			−0.0429934	+	0.999075i	$0.513689\pi$
$542$	−10.0000	−	17.3205i	−0.429537	−	0.743980i
$543$	8.00000	−	13.8564i	0.343313	−	0.594635i
$544$	−2.00000			−0.0857493
$545$	−16.0000			−0.685365
$546$		0			0
$547$	30.0000			1.28271			0.641354	−	0.767245i	$-0.278373\pi$
$547$	30.0000			1.28271			0.641354	+	0.767245i	$0.278373\pi$
$548$	9.00000	+	15.5885i	0.384461	+	0.665906i
$549$	−6.00000			−0.256074
$550$	−1.50000	−	2.59808i	−0.0639602	−	0.110782i
$551$	15.0000	+	25.9808i	0.639021	+	1.10682i
$552$	−2.50000	−	4.33013i	−0.106407	−	0.184302i
$553$		0			0
$554$	26.0000			1.10463
$555$	−5.50000	−	2.59808i	−0.233462	−	0.110282i
$556$	−3.00000			−0.127228
$557$	5.50000	−	9.52628i	0.233042	−	0.403641i	−0.725660	−	0.688054i	$-0.758465\pi$
$557$	5.50000	−	9.52628i	0.233042	−	0.403641i	0.958702	+	0.284413i	$0.0917985\pi$
$558$	−3.00000	−	5.19615i	−0.127000	−	0.219971i
$559$	10.0000	+	17.3205i	0.422955	+	0.732579i
$560$		0			0
$561$	6.00000			0.253320
$562$	13.5000	+	23.3827i	0.569463	+	0.986339i
$563$	24.0000			1.01148			0.505740	−	0.862686i	$-0.331220\pi$
$563$	24.0000			1.01148			0.505740	+	0.862686i	$0.331220\pi$
$564$	−1.50000	+	2.59808i	−0.0631614	+	0.109399i
$565$	8.00000			0.336563
$566$	−26.0000			−1.09286
$567$		0			0
$568$	2.00000	+	3.46410i	0.0839181	+	0.145350i
$569$	27.0000			1.13190			0.565949	−	0.824440i	$-0.308510\pi$
$569$	27.0000			1.13190			0.565949	+	0.824440i	$0.308510\pi$
$570$	−2.50000	+	4.33013i	−0.104713	+	0.181369i
$571$	4.50000	−	7.79423i	0.188319	−	0.326178i	−0.756371	−	0.654143i	$-0.773029\pi$
$571$	4.50000	−	7.79423i	0.188319	−	0.326178i	0.944690	+	0.327965i	$0.106363\pi$
$572$	−7.50000	+	12.9904i	−0.313591	+	0.543155i
$573$	7.00000	+	12.1244i	0.292429	+	0.506502i
$574$		0			0
$575$	−2.50000	+	4.33013i	−0.104257	+	0.180579i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	12.0000	−	20.7846i	0.499567	−	0.865275i	−0.500433	−	0.865775i	$-0.666826\pi$
$577$	12.0000	−	20.7846i	0.499567	−	0.865275i	1.00000		0.000500448i	$0.000159298\pi$
$578$	13.0000			0.540729
$579$	2.00000	+	3.46410i	0.0831172	+	0.143963i
$580$	3.00000	−	5.19615i	0.124568	−	0.215758i
$581$		0			0
$582$	16.0000			0.663221
$583$	3.00000	−	5.19615i	0.124247	−	0.215203i
$584$	4.00000			0.165521
$585$	−2.50000	−	4.33013i	−0.103362	−	0.179029i
$586$	−9.00000			−0.371787
$587$	14.0000	+	24.2487i	0.577842	+	1.00085i	0.995726	+	0.0923513i	$0.0294383\pi$
$587$	14.0000	+	24.2487i	0.577842	+	1.00085i	−0.417885	+	0.908500i	$0.637228\pi$
$588$	−3.50000	−	6.06218i	−0.144338	−	0.250000i
$589$	−15.0000	−	25.9808i	−0.618064	−	1.07052i
$590$	−5.50000	+	9.52628i	−0.226431	+	0.392191i
$591$	−6.00000			−0.246807
$592$	−5.50000	−	2.59808i	−0.226049	−	0.106780i
$593$	48.0000			1.97112			0.985562	−	0.169316i	$-0.0541557\pi$
$593$	48.0000			1.97112			0.985562	+	0.169316i	$0.0541557\pi$
$594$	1.50000	−	2.59808i	0.0615457	−	0.106600i
$595$		0			0
$596$		0			0
$597$	2.00000	+	3.46410i	0.0818546	+	0.141776i
$598$	25.0000			1.02233
$599$	16.0000	+	27.7128i	0.653742	+	1.13231i	0.982208	+	0.187799i	$0.0601353\pi$
$599$	16.0000	+	27.7128i	0.653742	+	1.13231i	−0.328465	+	0.944516i	$0.606531\pi$
$600$	1.00000			0.0408248
$601$	−14.5000	+	25.1147i	−0.591467	+	1.02445i	0.402568	+	0.915390i	$0.368118\pi$
$601$	−14.5000	+	25.1147i	−0.591467	+	1.02445i	−0.994035	+	0.109061i	$0.965216\pi$
$602$		0			0
$603$	−2.00000			−0.0814463
$604$	−2.00000	+	3.46410i	−0.0813788	+	0.140952i
$605$	−1.00000	−	1.73205i	−0.0406558	−	0.0704179i
$606$	8.00000			0.324978
$607$	8.00000	−	13.8564i	0.324710	−	0.562414i	−0.656744	−	0.754114i	$-0.728067\pi$
$607$	8.00000	−	13.8564i	0.324710	−	0.562414i	0.981454	+	0.191700i	$0.0614000\pi$
$608$	−2.50000	+	4.33013i	−0.101388	+	0.175610i
$609$		0			0
$610$	3.00000	+	5.19615i	0.121466	+	0.210386i
$611$	−7.50000	−	12.9904i	−0.303418	−	0.525535i
$612$	−1.00000	+	1.73205i	−0.0404226	+	0.0700140i
$613$	−2.50000	+	4.33013i	−0.100974	+	0.174892i	−0.912086	−	0.409998i	$-0.865529\pi$
$613$	−2.50000	+	4.33013i	−0.100974	+	0.174892i	0.811112	+	0.584891i	$0.198863\pi$
$614$	9.00000	−	15.5885i	0.363210	−	0.629099i
$615$	2.00000			0.0806478
$616$		0			0
$617$	−10.0000	+	17.3205i	−0.402585	+	0.697297i	−0.994037	−	0.109043i	$-0.965221\pi$
$617$	−10.0000	+	17.3205i	−0.402585	+	0.697297i	0.591452	+	0.806340i	$0.298555\pi$
$618$	−7.00000			−0.281581
$619$	16.0000			0.643094			0.321547	−	0.946894i	$-0.395797\pi$
$619$	16.0000			0.643094			0.321547	+	0.946894i	$0.395797\pi$
$620$	−3.00000	+	5.19615i	−0.120483	+	0.208683i
$621$	−5.00000			−0.200643
$622$	−2.00000	−	3.46410i	−0.0801927	−	0.138898i
$623$		0			0
$624$	−2.50000	−	4.33013i	−0.100080	−	0.173344i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−10.0000	−	17.3205i	−0.399680	−	0.692267i
$627$	7.50000	−	12.9904i	0.299521	−	0.518786i
$628$	7.00000			0.279330
$629$	−11.0000	−	5.19615i	−0.438599	−	0.207184i
$630$		0			0
$631$	14.0000	−	24.2487i	0.557331	−	0.965326i	−0.440387	−	0.897808i	$-0.645159\pi$
$631$	14.0000	−	24.2487i	0.557331	−	0.965326i	0.997718	−	0.0675178i	$-0.0215080\pi$
$632$	−1.00000	−	1.73205i	−0.0397779	−	0.0688973i
$633$	6.50000	+	11.2583i	0.258352	+	0.447478i
$634$	−6.50000	−	11.2583i	−0.258148	−	0.447125i
$635$	15.0000			0.595257
$636$	1.00000	+	1.73205i	0.0396526	+	0.0686803i
$637$	35.0000			1.38675
$638$	−9.00000	+	15.5885i	−0.356313	+	0.617153i
$639$	4.00000			0.158238
$640$	1.00000			0.0395285
$641$	11.5000	−	19.9186i	0.454223	−	0.786737i	−0.544420	−	0.838812i	$-0.683250\pi$
$641$	11.5000	−	19.9186i	0.454223	−	0.786737i	0.998643	+	0.0520757i	$0.0165837\pi$
$642$	−6.00000	−	10.3923i	−0.236801	−	0.410152i
$643$	−14.0000			−0.552106			−0.276053	−	0.961142i	$-0.589027\pi$
$643$	−14.0000			−0.552106			−0.276053	+	0.961142i	$0.589027\pi$
$644$		0			0
$645$	−2.00000	+	3.46410i	−0.0787499	+	0.136399i
$646$	−5.00000	+	8.66025i	−0.196722	+	0.340733i
$647$	4.50000	+	7.79423i	0.176913	+	0.306423i	0.940822	−	0.338902i	$-0.110055\pi$
$647$	4.50000	+	7.79423i	0.176913	+	0.306423i	−0.763908	+	0.645325i	$0.776722\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	16.5000	−	28.5788i	0.647682	−	1.12182i
$650$	−2.50000	+	4.33013i	−0.0980581	+	0.169842i
$651$		0			0
$652$	18.0000			0.704934
$653$	3.50000	+	6.06218i	0.136966	+	0.237231i	0.926347	−	0.376672i	$-0.122932\pi$
$653$	3.50000	+	6.06218i	0.136966	+	0.237231i	−0.789381	+	0.613904i	$0.789598\pi$
$654$	−8.00000	+	13.8564i	−0.312825	+	0.541828i
$655$	12.0000			0.468879
$656$	2.00000			0.0780869
$657$	2.00000	−	3.46410i	0.0780274	−	0.135147i
$658$		0			0
$659$	16.5000	+	28.5788i	0.642749	+	1.11327i	0.984817	+	0.173598i	$0.0555394\pi$
$659$	16.5000	+	28.5788i	0.642749	+	1.11327i	−0.342068	+	0.939675i	$0.611127\pi$
$660$	−3.00000			−0.116775
$661$	−6.00000	−	10.3923i	−0.233373	−	0.404214i	0.725426	−	0.688301i	$-0.241643\pi$
$661$	−6.00000	−	10.3923i	−0.233373	−	0.404214i	−0.958799	+	0.284087i	$0.908310\pi$
$662$	8.50000	+	14.7224i	0.330362	+	0.572204i
$663$	−5.00000	−	8.66025i	−0.194184	−	0.336336i
$664$	−7.00000	+	12.1244i	−0.271653	+	0.470516i
$665$		0			0
$666$	−5.00000	+	3.46410i	−0.193746	+	0.134231i
$667$	30.0000			1.16160
$668$	−4.00000	+	6.92820i	−0.154765	+	0.268060i
$669$	3.50000	+	6.06218i	0.135318	+	0.234377i
$670$	1.00000	+	1.73205i	0.0386334	+	0.0669150i
$671$	−9.00000	−	15.5885i	−0.347441	−	0.601786i
$672$		0			0
$673$	24.0000	+	41.5692i	0.925132	+	1.60238i	0.791349	+	0.611365i	$0.209379\pi$
$673$	24.0000	+	41.5692i	0.925132	+	1.60238i	0.133783	+	0.991011i	$0.457287\pi$
$674$	−16.0000			−0.616297
$675$	0.500000	−	0.866025i	0.0192450	−	0.0333333i
$676$	12.0000			0.461538
$677$	−31.0000			−1.19143			−0.595713	−	0.803197i	$-0.703131\pi$
$677$	−31.0000			−1.19143			−0.595713	+	0.803197i	$0.703131\pi$
$678$	4.00000	−	6.92820i	0.153619	−	0.266076i
$679$		0			0
$680$	2.00000			0.0766965
$681$	15.0000	−	25.9808i	0.574801	−	0.995585i
$682$	9.00000	−	15.5885i	0.344628	−	0.596913i
$683$	−23.0000	+	39.8372i	−0.880071	+	1.52433i	−0.0288092	+	0.999585i	$0.509172\pi$
$683$	−23.0000	+	39.8372i	−0.880071	+	1.52433i	−0.851261	+	0.524742i	$0.824162\pi$
$684$	2.50000	+	4.33013i	0.0955899	+	0.165567i
$685$	−9.00000	−	15.5885i	−0.343872	−	0.595604i
$686$		0			0
$687$	−2.00000	+	3.46410i	−0.0763048	+	0.132164i
$688$	−2.00000	+	3.46410i	−0.0762493	+	0.132068i
$689$	−10.0000			−0.380970
$690$	2.50000	+	4.33013i	0.0951734	+	0.164845i
$691$	20.0000	−	34.6410i	0.760836	−	1.31781i	−0.181584	−	0.983375i	$-0.558123\pi$
$691$	20.0000	−	34.6410i	0.760836	−	1.31781i	0.942420	−	0.334431i	$-0.108544\pi$
$692$	−25.0000			−0.950357
$693$		0			0
$694$	9.00000	−	15.5885i	0.341635	−	0.591730i
$695$	3.00000			0.113796
$696$	−3.00000	−	5.19615i	−0.113715	−	0.196960i
$697$	4.00000			0.151511
$698$	10.0000	+	17.3205i	0.378506	+	0.655591i
$699$	−4.00000	−	6.92820i	−0.151294	−	0.262049i
$700$		0			0
$701$	10.0000	−	17.3205i	0.377695	−	0.654187i	−0.613032	−	0.790058i	$-0.710050\pi$
$701$	10.0000	−	17.3205i	0.377695	−	0.654187i	0.990726	+	0.135872i	$0.0433835\pi$
$702$	−5.00000			−0.188713
$703$	−25.0000	+	17.3205i	−0.942893	+	0.653255i
$704$	−3.00000			−0.113067
$705$	1.50000	−	2.59808i	0.0564933	−	0.0978492i
$706$	−5.00000	−	8.66025i	−0.188177	−	0.325933i
$707$		0			0
$708$	5.50000	+	9.52628i	0.206703	+	0.358020i
$709$	−22.0000			−0.826227			−0.413114	−	0.910679i	$-0.635559\pi$
$709$	−22.0000			−0.826227			−0.413114	+	0.910679i	$0.635559\pi$
$710$	−2.00000	−	3.46410i	−0.0750587	−	0.130005i
$711$	−2.00000			−0.0750059
$712$	−2.50000	+	4.33013i	−0.0936915	+	0.162278i
$713$	−30.0000			−1.12351
$714$		0			0
$715$	7.50000	−	12.9904i	0.280484	−	0.485813i
$716$	3.50000	+	6.06218i	0.130801	+	0.226554i
$717$	−8.00000			−0.298765
$718$	−9.00000	+	15.5885i	−0.335877	+	0.581756i
$719$	−1.00000	+	1.73205i	−0.0372937	+	0.0645946i	−0.884070	−	0.467355i	$-0.845207\pi$
$719$	−1.00000	+	1.73205i	−0.0372937	+	0.0645946i	0.846776	+	0.531949i	$0.178540\pi$
$720$	0.500000	−	0.866025i	0.0186339	−	0.0322749i
$721$		0			0
$722$	3.00000	+	5.19615i	0.111648	+	0.193381i
$723$	−8.50000	+	14.7224i	−0.316118	+	0.547533i
$724$	−8.00000	+	13.8564i	−0.297318	+	0.514969i
$725$	−3.00000	+	5.19615i	−0.111417	+	0.192980i
$726$	−2.00000			−0.0742270
$727$	7.50000	+	12.9904i	0.278160	+	0.481787i	0.970927	−	0.239374i	$-0.0769423\pi$
$727$	7.50000	+	12.9904i	0.278160	+	0.481787i	−0.692768	+	0.721161i	$0.743609\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−4.00000			−0.148047
$731$	−4.00000	+	6.92820i	−0.147945	+	0.256249i
$732$	6.00000			0.221766
$733$	−2.50000	−	4.33013i	−0.0923396	−	0.159937i	0.816156	−	0.577832i	$-0.196101\pi$
$733$	−2.50000	−	4.33013i	−0.0923396	−	0.159937i	−0.908495	+	0.417895i	$0.862768\pi$
$734$	−27.0000			−0.996588
$735$	3.50000	+	6.06218i	0.129099	+	0.223607i
$736$	2.50000	+	4.33013i	0.0921512	+	0.159611i
$737$	−3.00000	−	5.19615i	−0.110506	−	0.191403i
$738$	1.00000	−	1.73205i	0.0368105	−	0.0637577i
$739$	−23.0000			−0.846069			−0.423034	−	0.906114i	$-0.639035\pi$
$739$	−23.0000			−0.846069			−0.423034	+	0.906114i	$0.639035\pi$
$740$	5.50000	+	2.59808i	0.202184	+	0.0955072i
$741$	−25.0000			−0.918398
$742$		0			0
$743$	−14.5000	−	25.1147i	−0.531953	−	0.921370i	−0.999304	−	0.0372984i	$-0.988125\pi$
$743$	−14.5000	−	25.1147i	−0.531953	−	0.921370i	0.467351	−	0.884072i	$-0.345209\pi$
$744$	3.00000	+	5.19615i	0.109985	+	0.190500i
$745$		0			0
$746$	−3.00000			−0.109838
$747$	7.00000	+	12.1244i	0.256117	+	0.443607i
$748$	−6.00000			−0.219382
$749$		0			0
$750$	−1.00000			−0.0365148
$751$	−16.0000			−0.583848			−0.291924	−	0.956441i	$-0.594295\pi$
$751$	−16.0000			−0.583848			−0.291924	+	0.956441i	$0.594295\pi$
$752$	1.50000	−	2.59808i	0.0546994	−	0.0947421i
$753$	−0.500000	−	0.866025i	−0.0182210	−	0.0315597i
$754$	30.0000			1.09254
$755$	2.00000	−	3.46410i	0.0727875	−	0.126072i
$756$		0			0
$757$	−8.50000	+	14.7224i	−0.308938	+	0.535096i	−0.978130	−	0.207993i	$-0.933307\pi$
$757$	−8.50000	+	14.7224i	−0.308938	+	0.535096i	0.669193	+	0.743089i	$0.266640\pi$
$758$	6.00000	+	10.3923i	0.217930	+	0.377466i
$759$	−7.50000	−	12.9904i	−0.272233	−	0.471521i
$760$	2.50000	−	4.33013i	0.0906845	−	0.157070i
$761$	−21.5000	+	37.2391i	−0.779374	+	1.34992i	0.152928	+	0.988237i	$0.451130\pi$
$761$	−21.5000	+	37.2391i	−0.779374	+	1.34992i	−0.932303	+	0.361679i	$0.882204\pi$
$762$	7.50000	−	12.9904i	0.271696	−	0.470592i
$763$		0			0
$764$	−7.00000	−	12.1244i	−0.253251	−	0.438644i
$765$	1.00000	−	1.73205i	0.0361551	−	0.0626224i
$766$	−21.0000			−0.758761
$767$	−55.0000			−1.98593
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	−26.0000			−0.937584			−0.468792	−	0.883309i	$-0.655311\pi$
$769$	−26.0000			−0.937584			−0.468792	+	0.883309i	$0.655311\pi$
$770$		0			0
$771$	−2.00000			−0.0720282
$772$	−2.00000	−	3.46410i	−0.0719816	−	0.124676i
$773$	−3.50000	−	6.06218i	−0.125886	−	0.218041i	0.796193	−	0.605043i	$-0.206844\pi$
$773$	−3.50000	−	6.06218i	−0.125886	−	0.218041i	−0.922079	+	0.387002i	$0.873511\pi$
$774$	2.00000	+	3.46410i	0.0718885	+	0.124515i
$775$	3.00000	−	5.19615i	0.107763	−	0.186651i
$776$	−16.0000			−0.574367
$777$		0			0
$778$	6.00000			0.215110
$779$	5.00000	−	8.66025i	0.179144	−	0.310286i
$780$	2.50000	+	4.33013i	0.0895144	+	0.155043i
$781$	6.00000	+	10.3923i	0.214697	+	0.371866i
$782$	5.00000	+	8.66025i	0.178800	+	0.309690i
$783$	−6.00000			−0.214423
$784$	3.50000	+	6.06218i	0.125000	+	0.216506i
$785$	−7.00000			−0.249841
$786$	6.00000	−	10.3923i	0.214013	−	0.370681i
$787$	−20.0000			−0.712923			−0.356462	−	0.934310i	$-0.616017\pi$
$787$	−20.0000			−0.712923			−0.356462	+	0.934310i	$0.616017\pi$
$788$	6.00000			0.213741
$789$	7.50000	−	12.9904i	0.267007	−	0.462470i
$790$	1.00000	+	1.73205i	0.0355784	+	0.0616236i
$791$		0			0
$792$	−1.50000	+	2.59808i	−0.0533002	+	0.0923186i
$793$	−15.0000	+	25.9808i	−0.532666	+	0.922604i
$794$	16.5000	−	28.5788i	0.585563	−	1.01423i
$795$	−1.00000	−	1.73205i	−0.0354663	−	0.0614295i
$796$	−2.00000	−	3.46410i	−0.0708881	−	0.122782i
$797$	−25.5000	+	44.1673i	−0.903256	+	1.56449i	−0.0800155	+	0.996794i	$0.525497\pi$
$797$	−25.5000	+	44.1673i	−0.903256	+	1.56449i	−0.823241	+	0.567692i	$0.807836\pi$
$798$		0			0
$799$	3.00000	−	5.19615i	0.106132	−	0.183827i
$800$	−1.00000			−0.0353553
$801$	2.50000	+	4.33013i	0.0883332	+	0.152998i
$802$	7.50000	−	12.9904i	0.264834	−	0.458706i
$803$	12.0000			0.423471
$804$	2.00000			0.0705346
$805$		0			0
$806$	−30.0000			−1.05670
$807$	5.00000	+	8.66025i	0.176008	+	0.304855i
$808$	−8.00000			−0.281439
$809$	−18.5000	−	32.0429i	−0.650425	−	1.12657i	−0.983020	−	0.183500i	$-0.941257\pi$
$809$	−18.5000	−	32.0429i	−0.650425	−	1.12657i	0.332594	−	0.943070i	$-0.392076\pi$
$810$	−0.500000	−	0.866025i	−0.0175682	−	0.0304290i
$811$	17.5000	+	30.3109i	0.614508	+	1.06436i	0.990471	+	0.137724i	$0.0439788\pi$
$811$	17.5000	+	30.3109i	0.614508	+	1.06436i	−0.375962	+	0.926635i	$0.622688\pi$
$812$		0			0
$813$	20.0000			0.701431
$814$	−16.5000	−	7.79423i	−0.578325	−	0.273188i
$815$	−18.0000			−0.630512
$816$	1.00000	−	1.73205i	0.0350070	−	0.0606339i
$817$	10.0000	+	17.3205i	0.349856	+	0.605968i
$818$	19.0000	+	32.9090i	0.664319	+	1.15063i
$819$		0			0
$820$	−2.00000			−0.0698430
$821$	10.0000	+	17.3205i	0.349002	+	0.604490i	0.986073	−	0.166316i	$-0.0531872\pi$
$821$	10.0000	+	17.3205i	0.349002	+	0.604490i	−0.637070	+	0.770806i	$0.719854\pi$
$822$	−18.0000			−0.627822
$823$	12.0000	−	20.7846i	0.418294	−	0.724506i	−0.577474	−	0.816409i	$-0.695962\pi$
$823$	12.0000	−	20.7846i	0.418294	−	0.724506i	0.995768	+	0.0919029i	$0.0292950\pi$
$824$	7.00000			0.243857
$825$	3.00000			0.104447
$826$		0			0
$827$	5.00000	+	8.66025i	0.173867	+	0.301147i	0.939769	−	0.341811i	$-0.111040\pi$
$827$	5.00000	+	8.66025i	0.173867	+	0.301147i	−0.765902	+	0.642958i	$0.777707\pi$
$828$	5.00000			0.173762
$829$	25.0000	−	43.3013i	0.868286	−	1.50392i	0.00453881	−	0.999990i	$-0.498555\pi$
$829$	25.0000	−	43.3013i	0.868286	−	1.50392i	0.863747	−	0.503926i	$-0.168111\pi$
$830$	7.00000	−	12.1244i	0.242974	−	0.420843i
$831$	−13.0000	+	22.5167i	−0.450965	+	0.781094i
$832$	2.50000	+	4.33013i	0.0866719	+	0.150120i
$833$	7.00000	+	12.1244i	0.242536	+	0.420084i
$834$	1.50000	−	2.59808i	0.0519408	−	0.0899640i
$835$	4.00000	−	6.92820i	0.138426	−	0.239760i
$836$	−7.50000	+	12.9904i	−0.259393	+	0.449282i
$837$	6.00000			0.207390
$838$	9.50000	+	16.4545i	0.328172	+	0.568411i
$839$	−12.0000	+	20.7846i	−0.414286	+	0.717564i	−0.995353	−	0.0962912i	$-0.969302\pi$
$839$	−12.0000	+	20.7846i	−0.414286	+	0.717564i	0.581067	+	0.813856i	$0.302635\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$	16.0000	−	27.7128i	0.551396	−	0.955047i
$843$	−27.0000			−0.929929
$844$	−6.50000	−	11.2583i	−0.223739	−	0.387528i
$845$	−12.0000			−0.412813
$846$	−1.50000	−	2.59808i	−0.0515711	−	0.0893237i
$847$		0			0
$848$	−1.00000	−	1.73205i	−0.0343401	−	0.0594789i
$849$	13.0000	−	22.5167i	0.446159	−	0.772770i
$850$	−2.00000			−0.0685994
$851$	2.50000	+	30.3109i	0.0856989	+	1.03904i
$852$	−4.00000			−0.137038
$853$	−14.5000	+	25.1147i	−0.496471	+	0.859912i	−0.999992	−	0.00407068i	$-0.998704\pi$
$853$	−14.5000	+	25.1147i	−0.496471	+	0.859912i	0.503521	+	0.863983i	$0.332038\pi$
$854$		0			0
$855$	−2.50000	−	4.33013i	−0.0854982	−	0.148087i
$856$	6.00000	+	10.3923i	0.205076	+	0.355202i
$857$	24.0000			0.819824			0.409912	−	0.912125i	$-0.365559\pi$
$857$	24.0000			0.819824			0.409912	+	0.912125i	$0.365559\pi$
$858$	−7.50000	−	12.9904i	−0.256046	−	0.443484i
$859$	21.0000			0.716511			0.358255	−	0.933624i	$-0.383372\pi$
$859$	21.0000			0.716511			0.358255	+	0.933624i	$0.383372\pi$
$860$	2.00000	−	3.46410i	0.0681994	−	0.118125i
$861$		0			0
$862$	28.0000			0.953684
$863$	−22.5000	+	38.9711i	−0.765909	+	1.32659i	0.173856	+	0.984771i	$0.444377\pi$
$863$	−22.5000	+	38.9711i	−0.765909	+	1.32659i	−0.939765	+	0.341822i	$0.888956\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	25.0000			0.850026
$866$	9.00000	−	15.5885i	0.305832	−	0.529717i
$867$	−6.50000	+	11.2583i	−0.220752	+	0.382353i
$868$		0			0
$869$	−3.00000	−	5.19615i	−0.101768	−	0.176267i
$870$	3.00000	+	5.19615i	0.101710	+	0.176166i
$871$	−5.00000	+	8.66025i	−0.169419	+	0.293442i
$872$	8.00000	−	13.8564i	0.270914	−	0.469237i
$873$	−8.00000	+	13.8564i	−0.270759	+	0.468968i
$874$	25.0000			0.845638
$875$		0			0
$876$	−2.00000	+	3.46410i	−0.0675737	+	0.117041i
$877$	27.0000			0.911725			0.455863	−	0.890050i	$-0.349331\pi$
$877$	27.0000			0.911725			0.455863	+	0.890050i	$0.349331\pi$
$878$	−12.0000			−0.404980
$879$	4.50000	−	7.79423i	0.151781	−	0.262893i
$880$	3.00000			0.101130
$881$	16.5000	+	28.5788i	0.555899	+	0.962846i	0.997833	+	0.0657979i	$0.0209593\pi$
$881$	16.5000	+	28.5788i	0.555899	+	0.962846i	−0.441934	+	0.897048i	$0.645707\pi$
$882$	7.00000			0.235702
$883$	−19.0000	−	32.9090i	−0.639401	−	1.10747i	−0.985564	−	0.169301i	$-0.945849\pi$
$883$	−19.0000	−	32.9090i	−0.639401	−	1.10747i	0.346164	−	0.938174i	$-0.387484\pi$
$884$	5.00000	+	8.66025i	0.168168	+	0.291276i
$885$	−5.50000	−	9.52628i	−0.184880	−	0.320222i
$886$	−14.0000	+	24.2487i	−0.470339	+	0.814651i
$887$	−40.0000			−1.34307			−0.671534	−	0.740973i	$-0.734364\pi$
$887$	−40.0000			−1.34307			−0.671534	+	0.740973i	$0.734364\pi$
$888$	5.00000	−	3.46410i	0.167789	−	0.116248i
$889$		0			0
$890$	2.50000	−	4.33013i	0.0838002	−	0.145146i
$891$	1.50000	+	2.59808i	0.0502519	+	0.0870388i
$892$	−3.50000	−	6.06218i	−0.117189	−	0.202977i
$893$	−7.50000	−	12.9904i	−0.250978	−	0.434707i
$894$		0			0
$895$	−3.50000	−	6.06218i	−0.116992	−	0.202636i
$896$		0			0
$897$	−12.5000	+	21.6506i	−0.417363	+	0.722894i
$898$	10.0000			0.333704
$899$	−36.0000			−1.20067
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	−2.00000	−	3.46410i	−0.0666297	−	0.115406i
$902$	6.00000			0.199778
$903$		0			0
$904$	−4.00000	+	6.92820i	−0.133038	+	0.230429i
$905$	8.00000	−	13.8564i	0.265929	−	0.460603i
$906$	−2.00000	−	3.46410i	−0.0664455	−	0.115087i
$907$	−29.0000	−	50.2295i	−0.962929	−	1.66784i	−0.715079	−	0.699044i	$-0.753609\pi$
$907$	−29.0000	−	50.2295i	−0.962929	−	1.66784i	−0.247851	−	0.968798i	$-0.579724\pi$
$908$	−15.0000	+	25.9808i	−0.497792	+	0.862202i
$909$	−4.00000	+	6.92820i	−0.132672	+	0.229794i
$910$		0			0
$911$	−22.0000			−0.728893			−0.364446	−	0.931224i	$-0.618742\pi$
$911$	−22.0000			−0.728893			−0.364446	+	0.931224i	$0.618742\pi$
$912$	−2.50000	−	4.33013i	−0.0827833	−	0.143385i
$913$	−21.0000	+	36.3731i	−0.694999	+	1.20377i
$914$	8.00000			0.264616
$915$	−6.00000			−0.198354
$916$	2.00000	−	3.46410i	0.0660819	−	0.114457i
$917$		0			0
$918$	−1.00000	−	1.73205i	−0.0330049	−	0.0571662i
$919$	−42.0000			−1.38545			−0.692726	−	0.721201i	$-0.743591\pi$
$919$	−42.0000			−1.38545			−0.692726	+	0.721201i	$0.743591\pi$
$920$	−2.50000	−	4.33013i	−0.0824226	−	0.142760i
$921$	9.00000	+	15.5885i	0.296560	+	0.513657i
$922$	−20.0000	−	34.6410i	−0.658665	−	1.14084i
$923$	10.0000	−	17.3205i	0.329154	−	0.570111i
$924$		0			0
$925$	−5.50000	−	2.59808i	−0.180839	−	0.0854242i
$926$	−28.0000			−0.920137
$927$	3.50000	−	6.06218i	0.114955	−	0.199108i
$928$	3.00000	+	5.19615i	0.0984798	+	0.170572i
$929$	−3.50000	−	6.06218i	−0.114831	−	0.198894i	0.802881	−	0.596139i	$-0.203299\pi$
$929$	−3.50000	−	6.06218i	−0.114831	−	0.198894i	−0.917712	+	0.397246i	$0.869966\pi$
$930$	−3.00000	−	5.19615i	−0.0983739	−	0.170389i
$931$	35.0000			1.14708
$932$	4.00000	+	6.92820i	0.131024	+	0.226941i
$933$	4.00000			0.130954
$934$	−3.00000	+	5.19615i	−0.0981630	+	0.170023i
$935$	6.00000			0.196221
$936$	5.00000			0.163430
$937$	−14.0000	+	24.2487i	−0.457360	+	0.792171i	−0.998820	−	0.0485554i	$-0.984538\pi$
$937$	−14.0000	+	24.2487i	−0.457360	+	0.792171i	0.541460	+	0.840726i	$0.317872\pi$
$938$		0			0
$939$	20.0000			0.652675
$940$	−1.50000	+	2.59808i	−0.0489246	+	0.0847399i
$941$	15.0000	−	25.9808i	0.488986	−	0.846949i	−0.510934	−	0.859620i	$-0.670700\pi$
$941$	15.0000	−	25.9808i	0.488986	−	0.846949i	0.999920	+	0.0126715i	$0.00403357\pi$
$942$	−3.50000	+	6.06218i	−0.114036	+	0.197516i
$943$	−5.00000	−	8.66025i	−0.162822	−	0.282017i
$944$	−5.50000	−	9.52628i	−0.179010	−	0.310054i
$945$		0			0
$946$	−6.00000	+	10.3923i	−0.195077	+	0.337883i
$947$	11.0000	−	19.0526i	0.357452	−	0.619125i	−0.630082	−	0.776528i	$-0.716979\pi$
$947$	11.0000	−	19.0526i	0.357452	−	0.619125i	0.987534	+	0.157403i	$0.0503122\pi$
$948$	2.00000			0.0649570
$949$	−10.0000	−	17.3205i	−0.324614	−	0.562247i
$950$	−2.50000	+	4.33013i	−0.0811107	+	0.140488i
$951$	13.0000			0.421554
$952$		0			0
$953$	24.0000	−	41.5692i	0.777436	−	1.34656i	−0.155979	−	0.987760i	$-0.549853\pi$
$953$	24.0000	−	41.5692i	0.777436	−	1.34656i	0.933415	−	0.358799i	$-0.116814\pi$
$954$	−2.00000			−0.0647524
$955$	7.00000	+	12.1244i	0.226515	+	0.392335i
$956$	8.00000			0.258738
$957$	−9.00000	−	15.5885i	−0.290929	−	0.503903i
$958$	−4.00000	−	6.92820i	−0.129234	−	0.223840i
$959$		0			0
$960$	−0.500000	+	0.866025i	−0.0161374	+	0.0279508i
$961$	5.00000			0.161290
$962$	2.50000	+	30.3109i	0.0806032	+	0.977262i
$963$	12.0000			0.386695
$964$	8.50000	−	14.7224i	0.273767	−	0.474178i
$965$	2.00000	+	3.46410i	0.0643823	+	0.111513i
$966$		0			0
$967$	−15.5000	−	26.8468i	−0.498446	−	0.863334i	0.501552	−	0.865128i	$-0.332763\pi$
$967$	−15.5000	−	26.8468i	−0.498446	−	0.863334i	−0.999998	+	0.00179302i	$0.999429\pi$
$968$	2.00000			0.0642824
$969$	−5.00000	−	8.66025i	−0.160623	−	0.278207i
$970$	16.0000			0.513729
$971$	3.50000	−	6.06218i	0.112320	−	0.194545i	−0.804385	−	0.594108i	$-0.797505\pi$
$971$	3.50000	−	6.06218i	0.112320	−	0.194545i	0.916705	+	0.399564i	$0.130838\pi$
$972$	−1.00000			−0.0320750
$973$		0			0
$974$	14.0000	−	24.2487i	0.448589	−	0.776979i
$975$	−2.50000	−	4.33013i	−0.0800641	−	0.138675i
$976$	−6.00000			−0.192055
$977$	−6.00000	+	10.3923i	−0.191957	+	0.332479i	−0.945899	−	0.324462i	$-0.894817\pi$
$977$	−6.00000	+	10.3923i	−0.191957	+	0.332479i	0.753942	+	0.656941i	$0.228150\pi$
$978$	−9.00000	+	15.5885i	−0.287788	+	0.498464i
$979$	−7.50000	+	12.9904i	−0.239701	+	0.415174i
$980$	−3.50000	−	6.06218i	−0.111803	−	0.193649i
$981$	−8.00000	−	13.8564i	−0.255420	−	0.442401i
$982$	−4.50000	+	7.79423i	−0.143601	+	0.248724i
$983$	4.50000	−	7.79423i	0.143528	−	0.248597i	−0.785295	−	0.619122i	$-0.787489\pi$
$983$	4.50000	−	7.79423i	0.143528	−	0.248597i	0.928823	+	0.370525i	$0.120822\pi$
$984$	−1.00000	+	1.73205i	−0.0318788	+	0.0552158i
$985$	−6.00000			−0.191176
$986$	6.00000	+	10.3923i	0.191079	+	0.330958i
$987$		0			0
$988$	25.0000			0.795356
$989$	20.0000			0.635963
$990$	1.50000	−	2.59808i	0.0476731	−	0.0825723i
$991$	−56.0000			−1.77890			−0.889449	−	0.457034i	$-0.848912\pi$
$991$	−56.0000			−1.77890			−0.889449	+	0.457034i	$0.848912\pi$
$992$	−3.00000	−	5.19615i	−0.0952501	−	0.164978i
$993$	−17.0000			−0.539479
$994$		0			0
$995$	2.00000	+	3.46410i	0.0634043	+	0.109819i
$996$	−7.00000	−	12.1244i	−0.221803	−	0.384175i
$997$	−1.50000	+	2.59808i	−0.0475055	+	0.0822819i	−0.888800	−	0.458295i	$-0.848460\pi$
$997$	−1.50000	+	2.59808i	−0.0475055	+	0.0822819i	0.841295	+	0.540576i	$0.181794\pi$
$998$	−4.00000			−0.126618
$999$	−0.500000	−	6.06218i	−0.0158193	−	0.191799i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.i.g.121.1	✓	2
37.26	even	3	inner	1110.2.i.g.211.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.i.g.121.1	✓	2	1.1	even	1	trivial
1110.2.i.g.211.1	yes	2	37.26	even	3	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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +1.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +1.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +1.00000 q^{10} -3.00000 q^{11} +(0.500000 - 0.866025i) q^{12} +(2.50000 + 4.33013i) q^{13} +(-0.500000 + 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} +(0.500000 + 0.866025i) q^{18} +(2.50000 + 4.33013i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-1.50000 + 2.59808i) q^{22} +5.00000 q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +5.00000 q^{26} -1.00000 q^{27} +6.00000 q^{29} +(0.500000 + 0.866025i) q^{30} -6.00000 q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.50000 - 2.59808i) q^{33} +(1.00000 + 1.73205i) q^{34} +1.00000 q^{36} +(0.500000 + 6.06218i) q^{37} +5.00000 q^{38} +(-2.50000 + 4.33013i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-1.00000 - 1.73205i) q^{41} +4.00000 q^{43} +(1.50000 + 2.59808i) q^{44} -1.00000 q^{45} +(2.50000 - 4.33013i) q^{46} -3.00000 q^{47} -1.00000 q^{48} +(3.50000 - 6.06218i) q^{49} +(0.500000 + 0.866025i) q^{50} -2.00000 q^{51} +(2.50000 - 4.33013i) q^{52} +(-1.00000 + 1.73205i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-1.50000 - 2.59808i) q^{55} +(-2.50000 + 4.33013i) q^{57} +(3.00000 - 5.19615i) q^{58} +(-5.50000 + 9.52628i) q^{59} +1.00000 q^{60} +(3.00000 + 5.19615i) q^{61} +(-3.00000 + 5.19615i) q^{62} +1.00000 q^{64} +(-2.50000 + 4.33013i) q^{65} -3.00000 q^{66} +(1.00000 + 1.73205i) q^{67} +2.00000 q^{68} +(2.50000 + 4.33013i) q^{69} +(-2.00000 - 3.46410i) q^{71} +(0.500000 - 0.866025i) q^{72} -4.00000 q^{73} +(5.50000 + 2.59808i) q^{74} -1.00000 q^{75} +(2.50000 - 4.33013i) q^{76} +(2.50000 + 4.33013i) q^{78} +(1.00000 + 1.73205i) q^{79} -1.00000 q^{80} +(-0.500000 - 0.866025i) q^{81} -2.00000 q^{82} +(7.00000 - 12.1244i) q^{83} -2.00000 q^{85} +(2.00000 - 3.46410i) q^{86} +(3.00000 + 5.19615i) q^{87} +3.00000 q^{88} +(2.50000 - 4.33013i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(-2.50000 - 4.33013i) q^{92} +(-3.00000 - 5.19615i) q^{93} +(-1.50000 + 2.59808i) q^{94} +(-2.50000 + 4.33013i) q^{95} +(-0.500000 + 0.866025i) q^{96} +16.0000 q^{97} +(-3.50000 - 6.06218i) q^{98} +(1.50000 - 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + q^{3} - q^{4} + q^{5} + 2 q^{6} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 + q^3 - q^4 + q^5 + 2 * q^6 - 2 * q^8 - q^9	\( 2 q + q^{2} + q^{3} - q^{4} + q^{5} + 2 q^{6} - 2 q^{8} - q^{9} + 2 q^{10} - 6 q^{11} + q^{12} + 5 q^{13} - q^{15} - q^{16} - 2 q^{17} + q^{18} + 5 q^{19} + q^{20} - 3 q^{22} + 10 q^{23} - q^{24} - q^{25} + 10 q^{26} - 2 q^{27} + 12 q^{29} + q^{30} - 12 q^{31} + q^{32} - 3 q^{33} + 2 q^{34} + 2 q^{36} + q^{37} + 10 q^{38} - 5 q^{39} - q^{40} - 2 q^{41} + 8 q^{43} + 3 q^{44} - 2 q^{45} + 5 q^{46} - 6 q^{47} - 2 q^{48} + 7 q^{49} + q^{50} - 4 q^{51} + 5 q^{52} - 2 q^{53} - q^{54} - 3 q^{55} - 5 q^{57} + 6 q^{58} - 11 q^{59} + 2 q^{60} + 6 q^{61} - 6 q^{62} + 2 q^{64} - 5 q^{65} - 6 q^{66} + 2 q^{67} + 4 q^{68} + 5 q^{69} - 4 q^{71} + q^{72} - 8 q^{73} + 11 q^{74} - 2 q^{75} + 5 q^{76} + 5 q^{78} + 2 q^{79} - 2 q^{80} - q^{81} - 4 q^{82} + 14 q^{83} - 4 q^{85} + 4 q^{86} + 6 q^{87} + 6 q^{88} + 5 q^{89} - q^{90} - 5 q^{92} - 6 q^{93} - 3 q^{94} - 5 q^{95} - q^{96} + 32 q^{97} - 7 q^{98} + 3 q^{99}+O(q^{100}) \) 2 * q + q^2 + q^3 - q^4 + q^5 + 2 * q^6 - 2 * q^8 - q^9 + 2 * q^10 - 6 * q^11 + q^12 + 5 * q^13 - q^15 - q^16 - 2 * q^17 + q^18 + 5 * q^19 + q^20 - 3 * q^22 + 10 * q^23 - q^24 - q^25 + 10 * q^26 - 2 * q^27 + 12 * q^29 + q^30 - 12 * q^31 + q^32 - 3 * q^33 + 2 * q^34 + 2 * q^36 + q^37 + 10 * q^38 - 5 * q^39 - q^40 - 2 * q^41 + 8 * q^43 + 3 * q^44 - 2 * q^45 + 5 * q^46 - 6 * q^47 - 2 * q^48 + 7 * q^49 + q^50 - 4 * q^51 + 5 * q^52 - 2 * q^53 - q^54 - 3 * q^55 - 5 * q^57 + 6 * q^58 - 11 * q^59 + 2 * q^60 + 6 * q^61 - 6 * q^62 + 2 * q^64 - 5 * q^65 - 6 * q^66 + 2 * q^67 + 4 * q^68 + 5 * q^69 - 4 * q^71 + q^72 - 8 * q^73 + 11 * q^74 - 2 * q^75 + 5 * q^76 + 5 * q^78 + 2 * q^79 - 2 * q^80 - q^81 - 4 * q^82 + 14 * q^83 - 4 * q^85 + 4 * q^86 + 6 * q^87 + 6 * q^88 + 5 * q^89 - q^90 - 5 * q^92 - 6 * q^93 - 3 * q^94 - 5 * q^95 - q^96 + 32 * q^97 - 7 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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