LMFDB - Embedded newform 1050.2.i.r.751.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(151,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, 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("1050.151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.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:	$8.38429221223$
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			751.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1050.751
Dual form			1050.2.i.r.151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{6} +(-2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{6} +(-2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.00000 + 3.46410i) q^{11} +(0.500000 - 0.866025i) q^{12} +4.00000 q^{13} +(-0.500000 + 2.59808i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-3.00000 + 5.19615i) q^{19} +(-2.00000 - 1.73205i) q^{21} +4.00000 q^{22} +(-3.50000 + 6.06218i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(2.00000 - 3.46410i) q^{26} -1.00000 q^{27} +(2.00000 + 1.73205i) q^{28} +4.00000 q^{29} +(2.50000 + 4.33013i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.00000 + 3.46410i) q^{33} -3.00000 q^{34} +1.00000 q^{36} +(-1.00000 + 1.73205i) q^{37} +(3.00000 + 5.19615i) q^{38} +(2.00000 + 3.46410i) q^{39} +7.00000 q^{41} +(-2.50000 + 0.866025i) q^{42} +2.00000 q^{43} +(2.00000 - 3.46410i) q^{44} +(3.50000 + 6.06218i) q^{46} +(-0.500000 + 0.866025i) q^{47} -1.00000 q^{48} +(5.50000 - 4.33013i) q^{49} +(1.50000 - 2.59808i) q^{51} +(-2.00000 - 3.46410i) q^{52} +(1.00000 + 1.73205i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(2.50000 - 0.866025i) q^{56} -6.00000 q^{57} +(2.00000 - 3.46410i) q^{58} +(7.00000 + 12.1244i) q^{59} +(-6.00000 + 10.3923i) q^{61} +5.00000 q^{62} +(0.500000 - 2.59808i) q^{63} +1.00000 q^{64} +(2.00000 + 3.46410i) q^{66} +(-6.00000 - 10.3923i) q^{67} +(-1.50000 + 2.59808i) q^{68} -7.00000 q^{69} -9.00000 q^{71} +(0.500000 - 0.866025i) q^{72} +(-3.00000 - 5.19615i) q^{73} +(1.00000 + 1.73205i) q^{74} +6.00000 q^{76} +(-8.00000 - 6.92820i) q^{77} +4.00000 q^{78} +(8.50000 - 14.7224i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(3.50000 - 6.06218i) q^{82} -4.00000 q^{83} +(-0.500000 + 2.59808i) q^{84} +(1.00000 - 1.73205i) q^{86} +(2.00000 + 3.46410i) q^{87} +(-2.00000 - 3.46410i) q^{88} +(3.50000 - 6.06218i) q^{89} +(-10.0000 + 3.46410i) q^{91} +7.00000 q^{92} +(-2.50000 + 4.33013i) q^{93} +(0.500000 + 0.866025i) q^{94} +(-0.500000 + 0.866025i) q^{96} -7.00000 q^{97} +(-1.00000 - 6.92820i) q^{98} -4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + q^{3} - q^{4} + 2 q^{6} - 5 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + q^2 + q^3 - q^4 + 2 * q^6 - 5 * q^7 - 2 * q^8 - q^9	$ 2 q + q^{2} + q^{3} - q^{4} + 2 q^{6} - 5 q^{7} - 2 q^{8} - q^{9} + 4 q^{11} + q^{12} + 8 q^{13} - q^{14} - q^{16} - 3 q^{17} + q^{18} - 6 q^{19} - 4 q^{21} + 8 q^{22} - 7 q^{23} - q^{24} + 4 q^{26} - 2 q^{27} + 4 q^{28} + 8 q^{29} + 5 q^{31} + q^{32} - 4 q^{33} - 6 q^{34} + 2 q^{36} - 2 q^{37} + 6 q^{38} + 4 q^{39} + 14 q^{41} - 5 q^{42} + 4 q^{43} + 4 q^{44} + 7 q^{46} - q^{47} - 2 q^{48} + 11 q^{49} + 3 q^{51} - 4 q^{52} + 2 q^{53} - q^{54} + 5 q^{56} - 12 q^{57} + 4 q^{58} + 14 q^{59} - 12 q^{61} + 10 q^{62} + q^{63} + 2 q^{64} + 4 q^{66} - 12 q^{67} - 3 q^{68} - 14 q^{69} - 18 q^{71} + q^{72} - 6 q^{73} + 2 q^{74} + 12 q^{76} - 16 q^{77} + 8 q^{78} + 17 q^{79} - q^{81} + 7 q^{82} - 8 q^{83} - q^{84} + 2 q^{86} + 4 q^{87} - 4 q^{88} + 7 q^{89} - 20 q^{91} + 14 q^{92} - 5 q^{93} + q^{94} - q^{96} - 14 q^{97} - 2 q^{98} - 8 q^{99}+O(q^{100}) $ 2 * q + q^2 + q^3 - q^4 + 2 * q^6 - 5 * q^7 - 2 * q^8 - q^9 + 4 * q^11 + q^12 + 8 * q^13 - q^14 - q^16 - 3 * q^17 + q^18 - 6 * q^19 - 4 * q^21 + 8 * q^22 - 7 * q^23 - q^24 + 4 * q^26 - 2 * q^27 + 4 * q^28 + 8 * q^29 + 5 * q^31 + q^32 - 4 * q^33 - 6 * q^34 + 2 * q^36 - 2 * q^37 + 6 * q^38 + 4 * q^39 + 14 * q^41 - 5 * q^42 + 4 * q^43 + 4 * q^44 + 7 * q^46 - q^47 - 2 * q^48 + 11 * q^49 + 3 * q^51 - 4 * q^52 + 2 * q^53 - q^54 + 5 * q^56 - 12 * q^57 + 4 * q^58 + 14 * q^59 - 12 * q^61 + 10 * q^62 + q^63 + 2 * q^64 + 4 * q^66 - 12 * q^67 - 3 * q^68 - 14 * q^69 - 18 * q^71 + q^72 - 6 * q^73 + 2 * q^74 + 12 * q^76 - 16 * q^77 + 8 * q^78 + 17 * q^79 - q^81 + 7 * q^82 - 8 * q^83 - q^84 + 2 * q^86 + 4 * q^87 - 4 * q^88 + 7 * q^89 - 20 * q^91 + 14 * q^92 - 5 * q^93 + q^94 - q^96 - 14 * q^97 - 2 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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			0
$5$		0			0
$6$	1.00000			0.408248
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	2.00000	+	3.46410i	0.603023	+	1.04447i	0.992361	+	0.123371i	$0.0393705\pi$
$11$	2.00000	+	3.46410i	0.603023	+	1.04447i	−0.389338	+	0.921095i	$0.627296\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	4.00000			1.10940			0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000			1.10940			0.554700	+	0.832050i	$0.312833\pi$
$14$	−0.500000	+	2.59808i	−0.133631	+	0.694365i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	0.624780	−	0.780801i	$-0.285189\pi$
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	−0.988583	+	0.150675i	$0.951855\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	−3.00000	+	5.19615i	−0.688247	+	1.19208i	0.284157	+	0.958778i	$0.408286\pi$
$19$	−3.00000	+	5.19615i	−0.688247	+	1.19208i	−0.972404	+	0.233301i	$0.925047\pi$
$20$		0			0
$21$	−2.00000	−	1.73205i	−0.436436	−	0.377964i
$22$	4.00000			0.852803
$23$	−3.50000	+	6.06218i	−0.729800	+	1.26405i	0.227167	+	0.973856i	$0.427054\pi$
$23$	−3.50000	+	6.06218i	−0.729800	+	1.26405i	−0.956967	+	0.290196i	$0.906280\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$		0			0
$26$	2.00000	−	3.46410i	0.392232	−	0.679366i
$27$	−1.00000			−0.192450
$28$	2.00000	+	1.73205i	0.377964	+	0.327327i
$29$	4.00000			0.742781			0.371391	−	0.928477i	$-0.378881\pi$
$29$	4.00000			0.742781			0.371391	+	0.928477i	$0.378881\pi$
$30$		0			0
$31$	2.50000	+	4.33013i	0.449013	+	0.777714i	0.998322	−	0.0579057i	$-0.0184423\pi$
$31$	2.50000	+	4.33013i	0.449013	+	0.777714i	−0.549309	+	0.835619i	$0.685109\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−2.00000	+	3.46410i	−0.348155	+	0.603023i
$34$	−3.00000			−0.514496
$35$		0			0
$36$	1.00000			0.166667
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	−0.936442	−	0.350823i	$-0.885902\pi$
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	0.772043	+	0.635571i	$0.219235\pi$
$38$	3.00000	+	5.19615i	0.486664	+	0.842927i
$39$	2.00000	+	3.46410i	0.320256	+	0.554700i
$40$		0			0
$41$	7.00000			1.09322			0.546608	−	0.837389i	$-0.315919\pi$
$41$	7.00000			1.09322			0.546608	+	0.837389i	$0.315919\pi$
$42$	−2.50000	+	0.866025i	−0.385758	+	0.133631i
$43$	2.00000			0.304997			0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000			0.304997			0.152499	+	0.988304i	$0.451268\pi$
$44$	2.00000	−	3.46410i	0.301511	−	0.522233i
$45$		0			0
$46$	3.50000	+	6.06218i	0.516047	+	0.893819i
$47$	−0.500000	+	0.866025i	−0.0729325	+	0.126323i	−0.900185	−	0.435507i	$-0.856569\pi$
$47$	−0.500000	+	0.866025i	−0.0729325	+	0.126323i	0.827253	+	0.561830i	$0.189902\pi$
$48$	−1.00000			−0.144338
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$		0			0
$51$	1.50000	−	2.59808i	0.210042	−	0.363803i
$52$	−2.00000	−	3.46410i	−0.277350	−	0.480384i
$53$	1.00000	+	1.73205i	0.137361	+	0.237915i	0.926497	−	0.376303i	$-0.122805\pi$
$53$	1.00000	+	1.73205i	0.137361	+	0.237915i	−0.789136	+	0.614218i	$0.789471\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$		0			0
$56$	2.50000	−	0.866025i	0.334077	−	0.115728i
$57$	−6.00000			−0.794719
$58$	2.00000	−	3.46410i	0.262613	−	0.454859i
$59$	7.00000	+	12.1244i	0.911322	+	1.57846i	0.812198	+	0.583382i	$0.198271\pi$
$59$	7.00000	+	12.1244i	0.911322	+	1.57846i	0.0991242	+	0.995075i	$0.468396\pi$
$60$		0			0
$61$	−6.00000	+	10.3923i	−0.768221	+	1.33060i	0.170305	+	0.985391i	$0.445525\pi$
$61$	−6.00000	+	10.3923i	−0.768221	+	1.33060i	−0.938527	+	0.345207i	$0.887809\pi$
$62$	5.00000			0.635001
$63$	0.500000	−	2.59808i	0.0629941	−	0.327327i
$64$	1.00000			0.125000
$65$		0			0
$66$	2.00000	+	3.46410i	0.246183	+	0.426401i
$67$	−6.00000	−	10.3923i	−0.733017	−	1.26962i	−0.955588	−	0.294706i	$-0.904778\pi$
$67$	−6.00000	−	10.3923i	−0.733017	−	1.26962i	0.222571	−	0.974916i	$-0.428555\pi$
$68$	−1.50000	+	2.59808i	−0.181902	+	0.315063i
$69$	−7.00000			−0.842701
$70$		0			0
$71$	−9.00000			−1.06810			−0.534052	−	0.845452i	$-0.679331\pi$
$71$	−9.00000			−1.06810			−0.534052	+	0.845452i	$0.679331\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	−3.00000	−	5.19615i	−0.351123	−	0.608164i	0.635323	−	0.772246i	$-0.280867\pi$
$73$	−3.00000	−	5.19615i	−0.351123	−	0.608164i	−0.986447	+	0.164083i	$0.947534\pi$
$74$	1.00000	+	1.73205i	0.116248	+	0.201347i
$75$		0			0
$76$	6.00000			0.688247
$77$	−8.00000	−	6.92820i	−0.911685	−	0.789542i
$78$	4.00000			0.452911
$79$	8.50000	−	14.7224i	0.956325	−	1.65640i	0.225018	−	0.974355i	$-0.427756\pi$
$79$	8.50000	−	14.7224i	0.956325	−	1.65640i	0.731307	−	0.682048i	$-0.238911\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	3.50000	−	6.06218i	0.386510	−	0.669456i
$83$	−4.00000			−0.439057			−0.219529	−	0.975606i	$-0.570452\pi$
$83$	−4.00000			−0.439057			−0.219529	+	0.975606i	$0.570452\pi$
$84$	−0.500000	+	2.59808i	−0.0545545	+	0.283473i
$85$		0			0
$86$	1.00000	−	1.73205i	0.107833	−	0.186772i
$87$	2.00000	+	3.46410i	0.214423	+	0.371391i
$88$	−2.00000	−	3.46410i	−0.213201	−	0.369274i
$89$	3.50000	−	6.06218i	0.370999	−	0.642590i	−0.618720	−	0.785611i	$-0.712349\pi$
$89$	3.50000	−	6.06218i	0.370999	−	0.642590i	0.989720	+	0.143022i	$0.0456819\pi$
$90$		0			0
$91$	−10.0000	+	3.46410i	−1.04828	+	0.363137i
$92$	7.00000			0.729800
$93$	−2.50000	+	4.33013i	−0.259238	+	0.449013i
$94$	0.500000	+	0.866025i	0.0515711	+	0.0893237i
$95$		0			0
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	−7.00000			−0.710742			−0.355371	−	0.934725i	$-0.615646\pi$
$97$	−7.00000			−0.710742			−0.355371	+	0.934725i	$0.615646\pi$
$98$	−1.00000	−	6.92820i	−0.101015	−	0.699854i
$99$	−4.00000			−0.402015
$100$		0			0
$101$	9.00000	+	15.5885i	0.895533	+	1.55111i	0.833143	+	0.553058i	$0.186539\pi$
$101$	9.00000	+	15.5885i	0.895533	+	1.55111i	0.0623905	+	0.998052i	$0.480128\pi$
$102$	−1.50000	−	2.59808i	−0.148522	−	0.257248i
$103$	3.50000	−	6.06218i	0.344865	−	0.597324i	−0.640464	−	0.767988i	$-0.721258\pi$
$103$	3.50000	−	6.06218i	0.344865	−	0.597324i	0.985329	+	0.170664i	$0.0545913\pi$
$104$	−4.00000			−0.392232
$105$		0			0
$106$	2.00000			0.194257
$107$	−7.00000	+	12.1244i	−0.676716	+	1.17211i	0.299249	+	0.954175i	$0.403264\pi$
$107$	−7.00000	+	12.1244i	−0.676716	+	1.17211i	−0.975964	+	0.217931i	$0.930069\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	−3.00000	−	5.19615i	−0.287348	−	0.497701i	0.685828	−	0.727764i	$-0.259440\pi$
$109$	−3.00000	−	5.19615i	−0.287348	−	0.497701i	−0.973176	+	0.230063i	$0.926107\pi$
$110$		0			0
$111$	−2.00000			−0.189832
$112$	0.500000	−	2.59808i	0.0472456	−	0.245495i
$113$	−3.00000			−0.282216			−0.141108	−	0.989994i	$-0.545067\pi$
$113$	−3.00000			−0.282216			−0.141108	+	0.989994i	$0.545067\pi$
$114$	−3.00000	+	5.19615i	−0.280976	+	0.486664i
$115$		0			0
$116$	−2.00000	−	3.46410i	−0.185695	−	0.321634i
$117$	−2.00000	+	3.46410i	−0.184900	+	0.320256i
$118$	14.0000			1.28880
$119$	6.00000	+	5.19615i	0.550019	+	0.476331i
$120$		0			0
$121$	−2.50000	+	4.33013i	−0.227273	+	0.393648i
$122$	6.00000	+	10.3923i	0.543214	+	0.940875i
$123$	3.50000	+	6.06218i	0.315584	+	0.546608i
$124$	2.50000	−	4.33013i	0.224507	−	0.388857i
$125$		0			0
$126$	−2.00000	−	1.73205i	−0.178174	−	0.154303i
$127$	16.0000			1.41977			0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000			1.41977			0.709885	+	0.704317i	$0.248747\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	1.00000	+	1.73205i	0.0880451	+	0.152499i
$130$		0			0
$131$	4.00000	−	6.92820i	0.349482	−	0.605320i	−0.636676	−	0.771132i	$-0.719691\pi$
$131$	4.00000	−	6.92820i	0.349482	−	0.605320i	0.986157	+	0.165812i	$0.0530244\pi$
$132$	4.00000			0.348155
$133$	3.00000	−	15.5885i	0.260133	−	1.35169i
$134$	−12.0000			−1.03664
$135$		0			0
$136$	1.50000	+	2.59808i	0.128624	+	0.222783i
$137$	−7.50000	−	12.9904i	−0.640768	−	1.10984i	−0.985262	−	0.171054i	$-0.945283\pi$
$137$	−7.50000	−	12.9904i	−0.640768	−	1.10984i	0.344493	−	0.938789i	$-0.388051\pi$
$138$	−3.50000	+	6.06218i	−0.297940	+	0.516047i
$139$	2.00000			0.169638			0.0848189	−	0.996396i	$-0.472969\pi$
$139$	2.00000			0.169638			0.0848189	+	0.996396i	$0.472969\pi$
$140$		0			0
$141$	−1.00000			−0.0842152
$142$	−4.50000	+	7.79423i	−0.377632	+	0.654077i
$143$	8.00000	+	13.8564i	0.668994	+	1.15873i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$		0			0
$146$	−6.00000			−0.496564
$147$	6.50000	+	2.59808i	0.536111	+	0.214286i
$148$	2.00000			0.164399
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	−0.716578	−	0.697507i	$-0.754293\pi$
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	0.962348	+	0.271821i	$0.0876260\pi$
$150$		0			0
$151$	−12.0000	−	20.7846i	−0.976546	−	1.69143i	−0.674735	−	0.738060i	$-0.735742\pi$
$151$	−12.0000	−	20.7846i	−0.976546	−	1.69143i	−0.301811	−	0.953368i	$-0.597591\pi$
$152$	3.00000	−	5.19615i	0.243332	−	0.421464i
$153$	3.00000			0.242536
$154$	−10.0000	+	3.46410i	−0.805823	+	0.279145i
$155$		0			0
$156$	2.00000	−	3.46410i	0.160128	−	0.277350i
$157$	2.00000	+	3.46410i	0.159617	+	0.276465i	0.934731	−	0.355357i	$-0.115641\pi$
$157$	2.00000	+	3.46410i	0.159617	+	0.276465i	−0.775113	+	0.631822i	$0.782307\pi$
$158$	−8.50000	−	14.7224i	−0.676224	−	1.17125i
$159$	−1.00000	+	1.73205i	−0.0793052	+	0.137361i
$160$		0			0
$161$	3.50000	−	18.1865i	0.275839	−	1.43330i
$162$	−1.00000			−0.0785674
$163$	4.00000	−	6.92820i	0.313304	−	0.542659i	−0.665771	−	0.746156i	$-0.731897\pi$
$163$	4.00000	−	6.92820i	0.313304	−	0.542659i	0.979076	+	0.203497i	$0.0652307\pi$
$164$	−3.50000	−	6.06218i	−0.273304	−	0.473377i
$165$		0			0
$166$	−2.00000	+	3.46410i	−0.155230	+	0.268866i
$167$		0			0			−	1.00000i	$-0.5\pi$
$167$		0			0				1.00000i	$0.5\pi$
$168$	2.00000	+	1.73205i	0.154303	+	0.133631i
$169$	3.00000			0.230769
$170$		0			0
$171$	−3.00000	−	5.19615i	−0.229416	−	0.397360i
$172$	−1.00000	−	1.73205i	−0.0762493	−	0.132068i
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	−0.957241	−	0.289292i	$-0.906580\pi$
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	0.729155	+	0.684349i	$0.239913\pi$
$174$	4.00000			0.303239
$175$		0			0
$176$	−4.00000			−0.301511
$177$	−7.00000	+	12.1244i	−0.526152	+	0.911322i
$178$	−3.50000	−	6.06218i	−0.262336	−	0.454379i
$179$	−1.00000	−	1.73205i	−0.0747435	−	0.129460i	0.826231	−	0.563331i	$-0.190480\pi$
$179$	−1.00000	−	1.73205i	−0.0747435	−	0.129460i	−0.900975	+	0.433872i	$0.857147\pi$
$180$		0			0
$181$	12.0000			0.891953			0.445976	−	0.895045i	$-0.352856\pi$
$181$	12.0000			0.891953			0.445976	+	0.895045i	$0.352856\pi$
$182$	−2.00000	+	10.3923i	−0.148250	+	0.770329i
$183$	−12.0000			−0.887066
$184$	3.50000	−	6.06218i	0.258023	−	0.446910i
$185$		0			0
$186$	2.50000	+	4.33013i	0.183309	+	0.317500i
$187$	6.00000	−	10.3923i	0.438763	−	0.759961i
$188$	1.00000			0.0729325
$189$	2.50000	−	0.866025i	0.181848	−	0.0629941i
$190$		0			0
$191$	−7.50000	+	12.9904i	−0.542681	+	0.939951i	0.456068	+	0.889945i	$0.349257\pi$
$191$	−7.50000	+	12.9904i	−0.542681	+	0.939951i	−0.998749	+	0.0500060i	$0.984076\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−12.5000	−	21.6506i	−0.899770	−	1.55845i	−0.827788	−	0.561041i	$-0.810401\pi$
$193$	−12.5000	−	21.6506i	−0.899770	−	1.55845i	−0.0719816	−	0.997406i	$-0.522932\pi$
$194$	−3.50000	+	6.06218i	−0.251285	+	0.435239i
$195$		0			0
$196$	−6.50000	−	2.59808i	−0.464286	−	0.185577i
$197$	20.0000			1.42494			0.712470	−	0.701702i	$-0.247576\pi$
$197$	20.0000			1.42494			0.712470	+	0.701702i	$0.247576\pi$
$198$	−2.00000	+	3.46410i	−0.142134	+	0.246183i
$199$	−7.50000	−	12.9904i	−0.531661	−	0.920864i	−0.999317	−	0.0369532i	$-0.988235\pi$
$199$	−7.50000	−	12.9904i	−0.531661	−	0.920864i	0.467656	−	0.883911i	$-0.345099\pi$
$200$		0			0
$201$	6.00000	−	10.3923i	0.423207	−	0.733017i
$202$	18.0000			1.26648
$203$	−10.0000	+	3.46410i	−0.701862	+	0.243132i
$204$	−3.00000			−0.210042
$205$		0			0
$206$	−3.50000	−	6.06218i	−0.243857	−	0.422372i
$207$	−3.50000	−	6.06218i	−0.243267	−	0.421350i
$208$	−2.00000	+	3.46410i	−0.138675	+	0.240192i
$209$	−24.0000			−1.66011
$210$		0			0
$211$	−22.0000			−1.51454			−0.757271	−	0.653101i	$-0.773468\pi$
$211$	−22.0000			−1.51454			−0.757271	+	0.653101i	$0.773468\pi$
$212$	1.00000	−	1.73205i	0.0686803	−	0.118958i
$213$	−4.50000	−	7.79423i	−0.308335	−	0.534052i
$214$	7.00000	+	12.1244i	0.478510	+	0.828804i
$215$		0			0
$216$	1.00000			0.0680414
$217$	−10.0000	−	8.66025i	−0.678844	−	0.587896i
$218$	−6.00000			−0.406371
$219$	3.00000	−	5.19615i	0.202721	−	0.351123i
$220$		0			0
$221$	−6.00000	−	10.3923i	−0.403604	−	0.699062i
$222$	−1.00000	+	1.73205i	−0.0671156	+	0.116248i
$223$	9.00000			0.602685			0.301342	−	0.953516i	$-0.402565\pi$
$223$	9.00000			0.602685			0.301342	+	0.953516i	$0.402565\pi$
$224$	−2.00000	−	1.73205i	−0.133631	−	0.115728i
$225$		0			0
$226$	−1.50000	+	2.59808i	−0.0997785	+	0.172821i
$227$	11.0000	+	19.0526i	0.730096	+	1.26456i	0.956842	+	0.290609i	$0.0938578\pi$
$227$	11.0000	+	19.0526i	0.730096	+	1.26456i	−0.226746	+	0.973954i	$0.572809\pi$
$228$	3.00000	+	5.19615i	0.198680	+	0.344124i
$229$	−4.00000	+	6.92820i	−0.264327	+	0.457829i	−0.967387	−	0.253302i	$-0.918483\pi$
$229$	−4.00000	+	6.92820i	−0.264327	+	0.457829i	0.703060	+	0.711131i	$0.251817\pi$
$230$		0			0
$231$	2.00000	−	10.3923i	0.131590	−	0.683763i
$232$	−4.00000			−0.262613
$233$	3.00000	−	5.19615i	0.196537	−	0.340411i	−0.750867	−	0.660454i	$-0.770364\pi$
$233$	3.00000	−	5.19615i	0.196537	−	0.340411i	0.947403	+	0.320043i	$0.103697\pi$
$234$	2.00000	+	3.46410i	0.130744	+	0.226455i
$235$		0			0
$236$	7.00000	−	12.1244i	0.455661	−	0.789228i
$237$	17.0000			1.10427
$238$	7.50000	−	2.59808i	0.486153	−	0.168408i
$239$	3.00000			0.194054			0.0970269	−	0.995282i	$-0.469067\pi$
$239$	3.00000			0.194054			0.0970269	+	0.995282i	$0.469067\pi$
$240$		0			0
$241$	1.00000	+	1.73205i	0.0644157	+	0.111571i	0.896435	−	0.443176i	$-0.146148\pi$
$241$	1.00000	+	1.73205i	0.0644157	+	0.111571i	−0.832019	+	0.554747i	$0.812815\pi$
$242$	2.50000	+	4.33013i	0.160706	+	0.278351i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	12.0000			0.768221
$245$		0			0
$246$	7.00000			0.446304
$247$	−12.0000	+	20.7846i	−0.763542	+	1.32249i
$248$	−2.50000	−	4.33013i	−0.158750	−	0.274963i
$249$	−2.00000	−	3.46410i	−0.126745	−	0.219529i
$250$		0			0
$251$	4.00000			0.252478			0.126239	−	0.992000i	$-0.459709\pi$
$251$	4.00000			0.252478			0.126239	+	0.992000i	$0.459709\pi$
$252$	−2.50000	+	0.866025i	−0.157485	+	0.0545545i
$253$	−28.0000			−1.76034
$254$	8.00000	−	13.8564i	0.501965	−	0.869428i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	1.00000	−	1.73205i	0.0623783	−	0.108042i	−0.833150	−	0.553047i	$-0.813465\pi$
$257$	1.00000	−	1.73205i	0.0623783	−	0.108042i	0.895528	+	0.445005i	$0.146798\pi$
$258$	2.00000			0.124515
$259$	1.00000	−	5.19615i	0.0621370	−	0.322873i
$260$		0			0
$261$	−2.00000	+	3.46410i	−0.123797	+	0.214423i
$262$	−4.00000	−	6.92820i	−0.247121	−	0.428026i
$263$	13.5000	+	23.3827i	0.832446	+	1.44184i	0.896093	+	0.443866i	$0.146393\pi$
$263$	13.5000	+	23.3827i	0.832446	+	1.44184i	−0.0636476	+	0.997972i	$0.520273\pi$
$264$	2.00000	−	3.46410i	0.123091	−	0.213201i
$265$		0			0
$266$	−12.0000	−	10.3923i	−0.735767	−	0.637193i
$267$	7.00000			0.428393
$268$	−6.00000	+	10.3923i	−0.366508	+	0.634811i
$269$	5.00000	+	8.66025i	0.304855	+	0.528025i	0.977229	−	0.212187i	$-0.0680585\pi$
$269$	5.00000	+	8.66025i	0.304855	+	0.528025i	−0.672374	+	0.740212i	$0.734725\pi$
$270$		0			0
$271$	−2.50000	+	4.33013i	−0.151864	+	0.263036i	−0.931913	−	0.362682i	$-0.881861\pi$
$271$	−2.50000	+	4.33013i	−0.151864	+	0.263036i	0.780049	+	0.625719i	$0.215194\pi$
$272$	3.00000			0.181902
$273$	−8.00000	−	6.92820i	−0.484182	−	0.419314i
$274$	−15.0000			−0.906183
$275$		0			0
$276$	3.50000	+	6.06218i	0.210675	+	0.364900i
$277$	8.00000	+	13.8564i	0.480673	+	0.832551i	0.999754	−	0.0221745i	$-0.00705893\pi$
$277$	8.00000	+	13.8564i	0.480673	+	0.832551i	−0.519081	+	0.854725i	$0.673726\pi$
$278$	1.00000	−	1.73205i	0.0599760	−	0.103882i
$279$	−5.00000			−0.299342
$280$		0			0
$281$	17.0000			1.01413			0.507067	−	0.861906i	$-0.330729\pi$
$281$	17.0000			1.01413			0.507067	+	0.861906i	$0.330729\pi$
$282$	−0.500000	+	0.866025i	−0.0297746	+	0.0515711i
$283$	4.00000	+	6.92820i	0.237775	+	0.411839i	0.960076	−	0.279741i	$-0.0902485\pi$
$283$	4.00000	+	6.92820i	0.237775	+	0.411839i	−0.722300	+	0.691580i	$0.756915\pi$
$284$	4.50000	+	7.79423i	0.267026	+	0.462502i
$285$		0			0
$286$	16.0000			0.946100
$287$	−17.5000	+	6.06218i	−1.03299	+	0.357839i
$288$	−1.00000			−0.0589256
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$		0			0
$291$	−3.50000	−	6.06218i	−0.205174	−	0.355371i
$292$	−3.00000	+	5.19615i	−0.175562	+	0.304082i
$293$	−12.0000			−0.701047			−0.350524	−	0.936554i	$-0.613996\pi$
$293$	−12.0000			−0.701047			−0.350524	+	0.936554i	$0.613996\pi$
$294$	5.50000	−	4.33013i	0.320767	−	0.252538i
$295$		0			0
$296$	1.00000	−	1.73205i	0.0581238	−	0.100673i
$297$	−2.00000	−	3.46410i	−0.116052	−	0.201008i
$298$	−3.00000	−	5.19615i	−0.173785	−	0.301005i
$299$	−14.0000	+	24.2487i	−0.809641	+	1.40234i
$300$		0			0
$301$	−5.00000	+	1.73205i	−0.288195	+	0.0998337i
$302$	−24.0000			−1.38104
$303$	−9.00000	+	15.5885i	−0.517036	+	0.895533i
$304$	−3.00000	−	5.19615i	−0.172062	−	0.298020i
$305$		0			0
$306$	1.50000	−	2.59808i	0.0857493	−	0.148522i
$307$	20.0000			1.14146			0.570730	−	0.821138i	$-0.306660\pi$
$307$	20.0000			1.14146			0.570730	+	0.821138i	$0.306660\pi$
$308$	−2.00000	+	10.3923i	−0.113961	+	0.592157i
$309$	7.00000			0.398216
$310$		0			0
$311$	−10.5000	−	18.1865i	−0.595400	−	1.03126i	−0.993490	−	0.113917i	$-0.963660\pi$
$311$	−10.5000	−	18.1865i	−0.595400	−	1.03126i	0.398090	−	0.917346i	$-0.369673\pi$
$312$	−2.00000	−	3.46410i	−0.113228	−	0.196116i
$313$	13.5000	−	23.3827i	0.763065	−	1.32167i	−0.178198	−	0.983995i	$-0.557027\pi$
$313$	13.5000	−	23.3827i	0.763065	−	1.32167i	0.941263	−	0.337673i	$-0.109640\pi$
$314$	4.00000			0.225733
$315$		0			0
$316$	−17.0000			−0.956325
$317$	−9.00000	+	15.5885i	−0.505490	+	0.875535i	0.494489	+	0.869184i	$0.335355\pi$
$317$	−9.00000	+	15.5885i	−0.505490	+	0.875535i	−0.999980	+	0.00635137i	$0.997978\pi$
$318$	1.00000	+	1.73205i	0.0560772	+	0.0971286i
$319$	8.00000	+	13.8564i	0.447914	+	0.775810i
$320$		0			0
$321$	−14.0000			−0.781404
$322$	−14.0000	−	12.1244i	−0.780189	−	0.675664i
$323$	18.0000			1.00155
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$		0			0
$326$	−4.00000	−	6.92820i	−0.221540	−	0.383718i
$327$	3.00000	−	5.19615i	0.165900	−	0.287348i
$328$	−7.00000			−0.386510
$329$	0.500000	−	2.59808i	0.0275659	−	0.143237i
$330$		0			0
$331$	17.0000	−	29.4449i	0.934405	−	1.61844i	0.158712	−	0.987325i	$-0.449266\pi$
$331$	17.0000	−	29.4449i	0.934405	−	1.61844i	0.775692	−	0.631111i	$-0.217401\pi$
$332$	2.00000	+	3.46410i	0.109764	+	0.190117i
$333$	−1.00000	−	1.73205i	−0.0547997	−	0.0949158i
$334$		0			0
$335$		0			0
$336$	2.50000	−	0.866025i	0.136386	−	0.0472456i
$337$	3.00000			0.163420			0.0817102	−	0.996656i	$-0.473962\pi$
$337$	3.00000			0.163420			0.0817102	+	0.996656i	$0.473962\pi$
$338$	1.50000	−	2.59808i	0.0815892	−	0.141317i
$339$	−1.50000	−	2.59808i	−0.0814688	−	0.141108i
$340$		0			0
$341$	−10.0000	+	17.3205i	−0.541530	+	0.937958i
$342$	−6.00000			−0.324443
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$	−2.00000			−0.107833
$345$		0			0
$346$	3.00000	+	5.19615i	0.161281	+	0.279347i
$347$	−16.0000	−	27.7128i	−0.858925	−	1.48770i	−0.872955	−	0.487800i	$-0.837799\pi$
$347$	−16.0000	−	27.7128i	−0.858925	−	1.48770i	0.0140303	−	0.999902i	$-0.495534\pi$
$348$	2.00000	−	3.46410i	0.107211	−	0.185695i
$349$	−18.0000			−0.963518			−0.481759	−	0.876304i	$-0.660002\pi$
$349$	−18.0000			−0.963518			−0.481759	+	0.876304i	$0.660002\pi$
$350$		0			0
$351$	−4.00000			−0.213504
$352$	−2.00000	+	3.46410i	−0.106600	+	0.184637i
$353$	7.50000	+	12.9904i	0.399185	+	0.691408i	0.993626	−	0.112731i	$-0.0359599\pi$
$353$	7.50000	+	12.9904i	0.399185	+	0.691408i	−0.594441	+	0.804139i	$0.702627\pi$
$354$	7.00000	+	12.1244i	0.372046	+	0.644402i
$355$		0			0
$356$	−7.00000			−0.370999
$357$	−1.50000	+	7.79423i	−0.0793884	+	0.412514i
$358$	−2.00000			−0.105703
$359$	−2.00000	+	3.46410i	−0.105556	+	0.182828i	−0.913965	−	0.405793i	$-0.866996\pi$
$359$	−2.00000	+	3.46410i	−0.105556	+	0.182828i	0.808409	+	0.588621i	$0.200329\pi$
$360$		0			0
$361$	−8.50000	−	14.7224i	−0.447368	−	0.774865i
$362$	6.00000	−	10.3923i	0.315353	−	0.546207i
$363$	−5.00000			−0.262432
$364$	8.00000	+	6.92820i	0.419314	+	0.363137i
$365$		0			0
$366$	−6.00000	+	10.3923i	−0.313625	+	0.543214i
$367$	16.0000	+	27.7128i	0.835193	+	1.44660i	0.893873	+	0.448320i	$0.147978\pi$
$367$	16.0000	+	27.7128i	0.835193	+	1.44660i	−0.0586798	+	0.998277i	$0.518689\pi$
$368$	−3.50000	−	6.06218i	−0.182450	−	0.316013i
$369$	−3.50000	+	6.06218i	−0.182203	+	0.315584i
$370$		0			0
$371$	−4.00000	−	3.46410i	−0.207670	−	0.179847i
$372$	5.00000			0.259238
$373$	−6.00000	+	10.3923i	−0.310668	+	0.538093i	−0.978507	−	0.206213i	$-0.933886\pi$
$373$	−6.00000	+	10.3923i	−0.310668	+	0.538093i	0.667839	+	0.744306i	$0.267219\pi$
$374$	−6.00000	−	10.3923i	−0.310253	−	0.537373i
$375$		0			0
$376$	0.500000	−	0.866025i	0.0257855	−	0.0446619i
$377$	16.0000			0.824042
$378$	0.500000	−	2.59808i	0.0257172	−	0.133631i
$379$	20.0000			1.02733			0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000			1.02733			0.513665	+	0.857991i	$0.328287\pi$
$380$		0			0
$381$	8.00000	+	13.8564i	0.409852	+	0.709885i
$382$	7.50000	+	12.9904i	0.383733	+	0.664646i
$383$	15.5000	−	26.8468i	0.792013	−	1.37181i	−0.132706	−	0.991155i	$-0.542367\pi$
$383$	15.5000	−	26.8468i	0.792013	−	1.37181i	0.924719	−	0.380651i	$-0.124300\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	−25.0000			−1.27247
$387$	−1.00000	+	1.73205i	−0.0508329	+	0.0880451i
$388$	3.50000	+	6.06218i	0.177686	+	0.307760i
$389$	−5.00000	−	8.66025i	−0.253510	−	0.439092i	0.710980	−	0.703213i	$-0.248252\pi$
$389$	−5.00000	−	8.66025i	−0.253510	−	0.439092i	−0.964490	+	0.264120i	$0.914918\pi$
$390$		0			0
$391$	21.0000			1.06202
$392$	−5.50000	+	4.33013i	−0.277792	+	0.218704i
$393$	8.00000			0.403547
$394$	10.0000	−	17.3205i	0.503793	−	0.872595i
$395$		0			0
$396$	2.00000	+	3.46410i	0.100504	+	0.174078i
$397$	11.0000	−	19.0526i	0.552074	−	0.956221i	−0.446051	−	0.895008i	$-0.647170\pi$
$397$	11.0000	−	19.0526i	0.552074	−	0.956221i	0.998125	−	0.0612128i	$-0.0194968\pi$
$398$	−15.0000			−0.751882
$399$	15.0000	−	5.19615i	0.750939	−	0.260133i
$400$		0			0
$401$	−17.0000	+	29.4449i	−0.848939	+	1.47041i	0.0332161	+	0.999448i	$0.489425\pi$
$401$	−17.0000	+	29.4449i	−0.848939	+	1.47041i	−0.882156	+	0.470958i	$0.843908\pi$
$402$	−6.00000	−	10.3923i	−0.299253	−	0.518321i
$403$	10.0000	+	17.3205i	0.498135	+	0.862796i
$404$	9.00000	−	15.5885i	0.447767	−	0.775555i
$405$		0			0
$406$	−2.00000	+	10.3923i	−0.0992583	+	0.515761i
$407$	−8.00000			−0.396545
$408$	−1.50000	+	2.59808i	−0.0742611	+	0.128624i
$409$	−14.5000	−	25.1147i	−0.716979	−	1.24184i	−0.962191	−	0.272374i	$-0.912191\pi$
$409$	−14.5000	−	25.1147i	−0.716979	−	1.24184i	0.245212	−	0.969469i	$-0.421142\pi$
$410$		0			0
$411$	7.50000	−	12.9904i	0.369948	−	0.640768i
$412$	−7.00000			−0.344865
$413$	−28.0000	−	24.2487i	−1.37779	−	1.19320i
$414$	−7.00000			−0.344031
$415$		0			0
$416$	2.00000	+	3.46410i	0.0980581	+	0.169842i
$417$	1.00000	+	1.73205i	0.0489702	+	0.0848189i
$418$	−12.0000	+	20.7846i	−0.586939	+	1.01661i
$419$	−26.0000			−1.27018			−0.635092	−	0.772437i	$-0.719038\pi$
$419$	−26.0000			−1.27018			−0.635092	+	0.772437i	$0.719038\pi$
$420$		0			0
$421$	16.0000			0.779792			0.389896	−	0.920859i	$-0.372511\pi$
$421$	16.0000			0.779792			0.389896	+	0.920859i	$0.372511\pi$
$422$	−11.0000	+	19.0526i	−0.535472	+	0.927464i
$423$	−0.500000	−	0.866025i	−0.0243108	−	0.0421076i
$424$	−1.00000	−	1.73205i	−0.0485643	−	0.0841158i
$425$		0			0
$426$	−9.00000			−0.436051
$427$	6.00000	−	31.1769i	0.290360	−	1.50876i
$428$	14.0000			0.676716
$429$	−8.00000	+	13.8564i	−0.386244	+	0.668994i
$430$		0			0
$431$	19.5000	+	33.7750i	0.939282	+	1.62688i	0.766814	+	0.641869i	$0.221841\pi$
$431$	19.5000	+	33.7750i	0.939282	+	1.62688i	0.172468	+	0.985015i	$0.444826\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	37.0000			1.77811			0.889053	−	0.457804i	$-0.151364\pi$
$433$	37.0000			1.77811			0.889053	+	0.457804i	$0.151364\pi$
$434$	−12.5000	+	4.33013i	−0.600019	+	0.207853i
$435$		0			0
$436$	−3.00000	+	5.19615i	−0.143674	+	0.248851i
$437$	−21.0000	−	36.3731i	−1.00457	−	1.73996i
$438$	−3.00000	−	5.19615i	−0.143346	−	0.248282i
$439$	−8.50000	+	14.7224i	−0.405683	+	0.702663i	−0.994401	−	0.105675i	$-0.966300\pi$
$439$	−8.50000	+	14.7224i	−0.405683	+	0.702663i	0.588718	+	0.808339i	$0.299633\pi$
$440$		0			0
$441$	1.00000	+	6.92820i	0.0476190	+	0.329914i
$442$	−12.0000			−0.570782
$443$	13.0000	−	22.5167i	0.617649	−	1.06980i	−0.372265	−	0.928126i	$-0.621419\pi$
$443$	13.0000	−	22.5167i	0.617649	−	1.06980i	0.989914	−	0.141672i	$-0.0452479\pi$
$444$	1.00000	+	1.73205i	0.0474579	+	0.0821995i
$445$		0			0
$446$	4.50000	−	7.79423i	0.213081	−	0.369067i
$447$	6.00000			0.283790
$448$	−2.50000	+	0.866025i	−0.118114	+	0.0409159i
$449$	−13.0000			−0.613508			−0.306754	−	0.951789i	$-0.599243\pi$
$449$	−13.0000			−0.613508			−0.306754	+	0.951789i	$0.599243\pi$
$450$		0			0
$451$	14.0000	+	24.2487i	0.659234	+	1.14183i
$452$	1.50000	+	2.59808i	0.0705541	+	0.122203i
$453$	12.0000	−	20.7846i	0.563809	−	0.976546i
$454$	22.0000			1.03251
$455$		0			0
$456$	6.00000			0.280976
$457$	−9.00000	+	15.5885i	−0.421002	+	0.729197i	−0.996038	−	0.0889312i	$-0.971655\pi$
$457$	−9.00000	+	15.5885i	−0.421002	+	0.729197i	0.575036	+	0.818128i	$0.304988\pi$
$458$	4.00000	+	6.92820i	0.186908	+	0.323734i
$459$	1.50000	+	2.59808i	0.0700140	+	0.121268i
$460$		0			0
$461$	36.0000			1.67669			0.838344	−	0.545142i	$-0.183524\pi$
$461$	36.0000			1.67669			0.838344	+	0.545142i	$0.183524\pi$
$462$	−8.00000	−	6.92820i	−0.372194	−	0.322329i
$463$	−7.00000			−0.325318			−0.162659	−	0.986682i	$-0.552007\pi$
$463$	−7.00000			−0.325318			−0.162659	+	0.986682i	$0.552007\pi$
$464$	−2.00000	+	3.46410i	−0.0928477	+	0.160817i
$465$		0			0
$466$	−3.00000	−	5.19615i	−0.138972	−	0.240707i
$467$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$467$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$468$	4.00000			0.184900
$469$	24.0000	+	20.7846i	1.10822	+	0.959744i
$470$		0			0
$471$	−2.00000	+	3.46410i	−0.0921551	+	0.159617i
$472$	−7.00000	−	12.1244i	−0.322201	−	0.558069i
$473$	4.00000	+	6.92820i	0.183920	+	0.318559i
$474$	8.50000	−	14.7224i	0.390418	−	0.676224i
$475$		0			0
$476$	1.50000	−	7.79423i	0.0687524	−	0.357248i
$477$	−2.00000			−0.0915737
$478$	1.50000	−	2.59808i	0.0686084	−	0.118833i
$479$	−0.500000	−	0.866025i	−0.0228456	−	0.0395697i	0.854377	−	0.519654i	$-0.173939\pi$
$479$	−0.500000	−	0.866025i	−0.0228456	−	0.0395697i	−0.877222	+	0.480085i	$0.840606\pi$
$480$		0			0
$481$	−4.00000	+	6.92820i	−0.182384	+	0.315899i
$482$	2.00000			0.0910975
$483$	17.5000	−	6.06218i	0.796278	−	0.275839i
$484$	5.00000			0.227273
$485$		0			0
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−2.50000	−	4.33013i	−0.113286	−	0.196217i	0.803807	−	0.594890i	$-0.202804\pi$
$487$	−2.50000	−	4.33013i	−0.113286	−	0.196217i	−0.917093	+	0.398673i	$0.869471\pi$
$488$	6.00000	−	10.3923i	0.271607	−	0.470438i
$489$	8.00000			0.361773
$490$		0			0
$491$	38.0000			1.71492			0.857458	−	0.514554i	$-0.172042\pi$
$491$	38.0000			1.71492			0.857458	+	0.514554i	$0.172042\pi$
$492$	3.50000	−	6.06218i	0.157792	−	0.273304i
$493$	−6.00000	−	10.3923i	−0.270226	−	0.468046i
$494$	12.0000	+	20.7846i	0.539906	+	0.935144i
$495$		0			0
$496$	−5.00000			−0.224507
$497$	22.5000	−	7.79423i	1.00926	−	0.349619i
$498$	−4.00000			−0.179244
$499$	−14.0000	+	24.2487i	−0.626726	+	1.08552i	0.361478	+	0.932381i	$0.382272\pi$
$499$	−14.0000	+	24.2487i	−0.626726	+	1.08552i	−0.988204	+	0.153141i	$0.951061\pi$
$500$		0			0
$501$		0			0
$502$	2.00000	−	3.46410i	0.0892644	−	0.154610i
$503$	36.0000			1.60516			0.802580	−	0.596544i	$-0.203460\pi$
$503$	36.0000			1.60516			0.802580	+	0.596544i	$0.203460\pi$
$504$	−0.500000	+	2.59808i	−0.0222718	+	0.115728i
$505$		0			0
$506$	−14.0000	+	24.2487i	−0.622376	+	1.07799i
$507$	1.50000	+	2.59808i	0.0666173	+	0.115385i
$508$	−8.00000	−	13.8564i	−0.354943	−	0.614779i
$509$	8.00000	−	13.8564i	0.354594	−	0.614174i	−0.632455	−	0.774597i	$-0.717953\pi$
$509$	8.00000	−	13.8564i	0.354594	−	0.614174i	0.987048	+	0.160423i	$0.0512858\pi$
$510$		0			0
$511$	12.0000	+	10.3923i	0.530849	+	0.459728i
$512$	−1.00000			−0.0441942
$513$	3.00000	−	5.19615i	0.132453	−	0.229416i
$514$	−1.00000	−	1.73205i	−0.0441081	−	0.0763975i
$515$		0			0
$516$	1.00000	−	1.73205i	0.0440225	−	0.0762493i
$517$	−4.00000			−0.175920
$518$	−4.00000	−	3.46410i	−0.175750	−	0.152204i
$519$	−6.00000			−0.263371
$520$		0			0
$521$	4.50000	+	7.79423i	0.197149	+	0.341471i	0.947603	−	0.319451i	$-0.103499\pi$
$521$	4.50000	+	7.79423i	0.197149	+	0.341471i	−0.750454	+	0.660922i	$0.770165\pi$
$522$	2.00000	+	3.46410i	0.0875376	+	0.151620i
$523$	−22.0000	+	38.1051i	−0.961993	+	1.66622i	−0.244507	+	0.969648i	$0.578626\pi$
$523$	−22.0000	+	38.1051i	−0.961993	+	1.66622i	−0.717486	+	0.696573i	$0.754707\pi$
$524$	−8.00000			−0.349482
$525$		0			0
$526$	27.0000			1.17726
$527$	7.50000	−	12.9904i	0.326705	−	0.565870i
$528$	−2.00000	−	3.46410i	−0.0870388	−	0.150756i
$529$	−13.0000	−	22.5167i	−0.565217	−	0.978985i
$530$		0			0
$531$	−14.0000			−0.607548
$532$	−15.0000	+	5.19615i	−0.650332	+	0.225282i
$533$	28.0000			1.21281
$534$	3.50000	−	6.06218i	0.151460	−	0.262336i
$535$		0			0
$536$	6.00000	+	10.3923i	0.259161	+	0.448879i
$537$	1.00000	−	1.73205i	0.0431532	−	0.0747435i
$538$	10.0000			0.431131
$539$	26.0000	+	10.3923i	1.11990	+	0.447628i
$540$		0			0
$541$	−16.0000	+	27.7128i	−0.687894	+	1.19147i	0.284624	+	0.958639i	$0.408131\pi$
$541$	−16.0000	+	27.7128i	−0.687894	+	1.19147i	−0.972518	+	0.232828i	$0.925202\pi$
$542$	2.50000	+	4.33013i	0.107384	+	0.185995i
$543$	6.00000	+	10.3923i	0.257485	+	0.445976i
$544$	1.50000	−	2.59808i	0.0643120	−	0.111392i
$545$		0			0
$546$	−10.0000	+	3.46410i	−0.427960	+	0.148250i
$547$	22.0000			0.940652			0.470326	−	0.882493i	$-0.344136\pi$
$547$	22.0000			0.940652			0.470326	+	0.882493i	$0.344136\pi$
$548$	−7.50000	+	12.9904i	−0.320384	+	0.554922i
$549$	−6.00000	−	10.3923i	−0.256074	−	0.443533i
$550$		0			0
$551$	−12.0000	+	20.7846i	−0.511217	+	0.885454i
$552$	7.00000			0.297940
$553$	−8.50000	+	44.1673i	−0.361457	+	1.87818i
$554$	16.0000			0.679775
$555$		0			0
$556$	−1.00000	−	1.73205i	−0.0424094	−	0.0734553i
$557$	−15.0000	−	25.9808i	−0.635570	−	1.10084i	−0.986394	−	0.164399i	$-0.947432\pi$
$557$	−15.0000	−	25.9808i	−0.635570	−	1.10084i	0.350824	−	0.936442i	$-0.385902\pi$
$558$	−2.50000	+	4.33013i	−0.105833	+	0.183309i
$559$	8.00000			0.338364
$560$		0			0
$561$	12.0000			0.506640
$562$	8.50000	−	14.7224i	0.358551	−	0.621028i
$563$	1.00000	+	1.73205i	0.0421450	+	0.0729972i	0.886328	−	0.463057i	$-0.153248\pi$
$563$	1.00000	+	1.73205i	0.0421450	+	0.0729972i	−0.844183	+	0.536054i	$0.819914\pi$
$564$	0.500000	+	0.866025i	0.0210538	+	0.0364662i
$565$		0			0
$566$	8.00000			0.336265
$567$	2.00000	+	1.73205i	0.0839921	+	0.0727393i
$568$	9.00000			0.377632
$569$	22.5000	−	38.9711i	0.943249	−	1.63376i	0.184030	−	0.982921i	$-0.441086\pi$
$569$	22.5000	−	38.9711i	0.943249	−	1.63376i	0.759220	−	0.650835i	$-0.225581\pi$
$570$		0			0
$571$	−20.0000	−	34.6410i	−0.836974	−	1.44968i	−0.892413	−	0.451219i	$-0.850989\pi$
$571$	−20.0000	−	34.6410i	−0.836974	−	1.44968i	0.0554391	−	0.998462i	$-0.482344\pi$
$572$	8.00000	−	13.8564i	0.334497	−	0.579365i
$573$	−15.0000			−0.626634
$574$	−3.50000	+	18.1865i	−0.146087	+	0.759091i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	1.00000	+	1.73205i	0.0416305	+	0.0721062i	0.886090	−	0.463513i	$-0.153411\pi$
$577$	1.00000	+	1.73205i	0.0416305	+	0.0721062i	−0.844459	+	0.535620i	$0.820078\pi$
$578$	−4.00000	−	6.92820i	−0.166378	−	0.288175i
$579$	12.5000	−	21.6506i	0.519482	−	0.899770i
$580$		0			0
$581$	10.0000	−	3.46410i	0.414870	−	0.143715i
$582$	−7.00000			−0.290159
$583$	−4.00000	+	6.92820i	−0.165663	+	0.286937i
$584$	3.00000	+	5.19615i	0.124141	+	0.215018i
$585$		0			0
$586$	−6.00000	+	10.3923i	−0.247858	+	0.429302i
$587$	42.0000			1.73353			0.866763	−	0.498721i	$-0.166197\pi$
$587$	42.0000			1.73353			0.866763	+	0.498721i	$0.166197\pi$
$588$	−1.00000	−	6.92820i	−0.0412393	−	0.285714i
$589$	−30.0000			−1.23613
$590$		0			0
$591$	10.0000	+	17.3205i	0.411345	+	0.712470i
$592$	−1.00000	−	1.73205i	−0.0410997	−	0.0711868i
$593$	−6.50000	+	11.2583i	−0.266923	+	0.462324i	−0.968066	−	0.250697i	$-0.919340\pi$
$593$	−6.50000	+	11.2583i	−0.266923	+	0.462324i	0.701143	+	0.713021i	$0.252674\pi$
$594$	−4.00000			−0.164122
$595$		0			0
$596$	−6.00000			−0.245770
$597$	7.50000	−	12.9904i	0.306955	−	0.531661i
$598$	14.0000	+	24.2487i	0.572503	+	0.991604i
$599$	15.5000	+	26.8468i	0.633313	+	1.09693i	0.986870	+	0.161517i	$0.0516387\pi$
$599$	15.5000	+	26.8468i	0.633313	+	1.09693i	−0.353557	+	0.935413i	$0.615028\pi$
$600$		0			0
$601$	46.0000			1.87638			0.938190	−	0.346122i	$-0.112502\pi$
$601$	46.0000			1.87638			0.938190	+	0.346122i	$0.112502\pi$
$602$	−1.00000	+	5.19615i	−0.0407570	+	0.211779i
$603$	12.0000			0.488678
$604$	−12.0000	+	20.7846i	−0.488273	+	0.845714i
$605$		0			0
$606$	9.00000	+	15.5885i	0.365600	+	0.633238i
$607$	−14.5000	+	25.1147i	−0.588537	+	1.01938i	0.405887	+	0.913923i	$0.366962\pi$
$607$	−14.5000	+	25.1147i	−0.588537	+	1.01938i	−0.994424	+	0.105453i	$0.966371\pi$
$608$	−6.00000			−0.243332
$609$	−8.00000	−	6.92820i	−0.324176	−	0.280745i
$610$		0			0
$611$	−2.00000	+	3.46410i	−0.0809113	+	0.140143i
$612$	−1.50000	−	2.59808i	−0.0606339	−	0.105021i
$613$	−2.00000	−	3.46410i	−0.0807792	−	0.139914i	0.822806	−	0.568323i	$-0.192408\pi$
$613$	−2.00000	−	3.46410i	−0.0807792	−	0.139914i	−0.903585	+	0.428409i	$0.859074\pi$
$614$	10.0000	−	17.3205i	0.403567	−	0.698999i
$615$		0			0
$616$	8.00000	+	6.92820i	0.322329	+	0.279145i
$617$	1.00000			0.0402585			0.0201292	−	0.999797i	$-0.493592\pi$
$617$	1.00000			0.0402585			0.0201292	+	0.999797i	$0.493592\pi$
$618$	3.50000	−	6.06218i	0.140791	−	0.243857i
$619$	8.00000	+	13.8564i	0.321547	+	0.556936i	0.980807	−	0.194979i	$-0.0624638\pi$
$619$	8.00000	+	13.8564i	0.321547	+	0.556936i	−0.659260	+	0.751915i	$0.729130\pi$
$620$		0			0
$621$	3.50000	−	6.06218i	0.140450	−	0.243267i
$622$	−21.0000			−0.842023
$623$	−3.50000	+	18.1865i	−0.140225	+	0.728628i
$624$	−4.00000			−0.160128
$625$		0			0
$626$	−13.5000	−	23.3827i	−0.539569	−	0.934560i
$627$	−12.0000	−	20.7846i	−0.479234	−	0.830057i
$628$	2.00000	−	3.46410i	0.0798087	−	0.138233i
$629$	6.00000			0.239236
$630$		0			0
$631$	7.00000			0.278666			0.139333	−	0.990246i	$-0.455504\pi$
$631$	7.00000			0.278666			0.139333	+	0.990246i	$0.455504\pi$
$632$	−8.50000	+	14.7224i	−0.338112	+	0.585627i
$633$	−11.0000	−	19.0526i	−0.437211	−	0.757271i
$634$	9.00000	+	15.5885i	0.357436	+	0.619097i
$635$		0			0
$636$	2.00000			0.0793052
$637$	22.0000	−	17.3205i	0.871672	−	0.686264i
$638$	16.0000			0.633446
$639$	4.50000	−	7.79423i	0.178017	−	0.308335i
$640$		0			0
$641$	4.50000	+	7.79423i	0.177739	+	0.307854i	0.941106	−	0.338112i	$-0.109788\pi$
$641$	4.50000	+	7.79423i	0.177739	+	0.307854i	−0.763367	+	0.645966i	$0.776455\pi$
$642$	−7.00000	+	12.1244i	−0.276268	+	0.478510i
$643$	14.0000			0.552106			0.276053	−	0.961142i	$-0.410973\pi$
$643$	14.0000			0.552106			0.276053	+	0.961142i	$0.410973\pi$
$644$	−17.5000	+	6.06218i	−0.689597	+	0.238883i
$645$		0			0
$646$	9.00000	−	15.5885i	0.354100	−	0.613320i
$647$	16.0000	+	27.7128i	0.629025	+	1.08950i	0.987748	+	0.156059i	$0.0498790\pi$
$647$	16.0000	+	27.7128i	0.629025	+	1.08950i	−0.358723	+	0.933444i	$0.616788\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	−28.0000	+	48.4974i	−1.09910	+	1.90369i
$650$		0			0
$651$	2.50000	−	12.9904i	0.0979827	−	0.509133i
$652$	−8.00000			−0.313304
$653$	−8.00000	+	13.8564i	−0.313064	+	0.542243i	−0.979024	−	0.203744i	$-0.934689\pi$
$653$	−8.00000	+	13.8564i	−0.313064	+	0.542243i	0.665960	+	0.745988i	$0.268022\pi$
$654$	−3.00000	−	5.19615i	−0.117309	−	0.203186i
$655$		0			0
$656$	−3.50000	+	6.06218i	−0.136652	+	0.236688i
$657$	6.00000			0.234082
$658$	−2.00000	−	1.73205i	−0.0779681	−	0.0675224i
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$		0			0
$661$	−15.0000	−	25.9808i	−0.583432	−	1.01053i	−0.995069	−	0.0991864i	$-0.968376\pi$
$661$	−15.0000	−	25.9808i	−0.583432	−	1.01053i	0.411636	−	0.911348i	$-0.364957\pi$
$662$	−17.0000	−	29.4449i	−0.660724	−	1.14441i
$663$	6.00000	−	10.3923i	0.233021	−	0.403604i
$664$	4.00000			0.155230
$665$		0			0
$666$	−2.00000			−0.0774984
$667$	−14.0000	+	24.2487i	−0.542082	+	0.938914i
$668$		0			0
$669$	4.50000	+	7.79423i	0.173980	+	0.301342i
$670$		0			0
$671$	−48.0000			−1.85302
$672$	0.500000	−	2.59808i	0.0192879	−	0.100223i
$673$	−11.0000			−0.424019			−0.212009	−	0.977268i	$-0.568001\pi$
$673$	−11.0000			−0.424019			−0.212009	+	0.977268i	$0.568001\pi$
$674$	1.50000	−	2.59808i	0.0577778	−	0.100074i
$675$		0			0
$676$	−1.50000	−	2.59808i	−0.0576923	−	0.0999260i
$677$	−16.0000	+	27.7128i	−0.614930	+	1.06509i	0.375467	+	0.926836i	$0.377482\pi$
$677$	−16.0000	+	27.7128i	−0.614930	+	1.06509i	−0.990397	+	0.138254i	$0.955851\pi$
$678$	−3.00000			−0.115214
$679$	17.5000	−	6.06218i	0.671588	−	0.232645i
$680$		0			0
$681$	−11.0000	+	19.0526i	−0.421521	+	0.730096i
$682$	10.0000	+	17.3205i	0.382920	+	0.663237i
$683$	−11.0000	−	19.0526i	−0.420903	−	0.729026i	0.575125	−	0.818066i	$-0.304953\pi$
$683$	−11.0000	−	19.0526i	−0.420903	−	0.729026i	−0.996028	+	0.0890398i	$0.971620\pi$
$684$	−3.00000	+	5.19615i	−0.114708	+	0.198680i
$685$		0			0
$686$	8.50000	+	16.4545i	0.324532	+	0.628235i
$687$	−8.00000			−0.305219
$688$	−1.00000	+	1.73205i	−0.0381246	+	0.0660338i
$689$	4.00000	+	6.92820i	0.152388	+	0.263944i
$690$		0			0
$691$	12.0000	−	20.7846i	0.456502	−	0.790684i	−0.542272	−	0.840203i	$-0.682436\pi$
$691$	12.0000	−	20.7846i	0.456502	−	0.790684i	0.998773	+	0.0495194i	$0.0157690\pi$
$692$	6.00000			0.228086
$693$	10.0000	−	3.46410i	0.379869	−	0.131590i
$694$	−32.0000			−1.21470
$695$		0			0
$696$	−2.00000	−	3.46410i	−0.0758098	−	0.131306i
$697$	−10.5000	−	18.1865i	−0.397716	−	0.688864i
$698$	−9.00000	+	15.5885i	−0.340655	+	0.590032i
$699$	6.00000			0.226941
$700$		0			0
$701$	12.0000			0.453234			0.226617	−	0.973984i	$-0.427233\pi$
$701$	12.0000			0.453234			0.226617	+	0.973984i	$0.427233\pi$
$702$	−2.00000	+	3.46410i	−0.0754851	+	0.130744i
$703$	−6.00000	−	10.3923i	−0.226294	−	0.391953i
$704$	2.00000	+	3.46410i	0.0753778	+	0.130558i
$705$		0			0
$706$	15.0000			0.564532
$707$	−36.0000	−	31.1769i	−1.35392	−	1.17253i
$708$	14.0000			0.526152
$709$	−7.00000	+	12.1244i	−0.262891	+	0.455340i	−0.967009	−	0.254743i	$-0.918009\pi$
$709$	−7.00000	+	12.1244i	−0.262891	+	0.455340i	0.704118	+	0.710083i	$0.251342\pi$
$710$		0			0
$711$	8.50000	+	14.7224i	0.318775	+	0.552134i
$712$	−3.50000	+	6.06218i	−0.131168	+	0.227190i
$713$	−35.0000			−1.31076
$714$	6.00000	+	5.19615i	0.224544	+	0.194461i
$715$		0			0
$716$	−1.00000	+	1.73205i	−0.0373718	+	0.0647298i
$717$	1.50000	+	2.59808i	0.0560185	+	0.0970269i
$718$	2.00000	+	3.46410i	0.0746393	+	0.129279i
$719$	3.50000	−	6.06218i	0.130528	−	0.226081i	−0.793352	−	0.608763i	$-0.791666\pi$
$719$	3.50000	−	6.06218i	0.130528	−	0.226081i	0.923880	+	0.382682i	$0.124999\pi$
$720$		0			0
$721$	−3.50000	+	18.1865i	−0.130347	+	0.677302i
$722$	−17.0000			−0.632674
$723$	−1.00000	+	1.73205i	−0.0371904	+	0.0644157i
$724$	−6.00000	−	10.3923i	−0.222988	−	0.386227i
$725$		0			0
$726$	−2.50000	+	4.33013i	−0.0927837	+	0.160706i
$727$	−49.0000			−1.81731			−0.908655	−	0.417548i	$-0.862889\pi$
$727$	−49.0000			−1.81731			−0.908655	+	0.417548i	$0.862889\pi$
$728$	10.0000	−	3.46410i	0.370625	−	0.128388i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−3.00000	−	5.19615i	−0.110959	−	0.192187i
$732$	6.00000	+	10.3923i	0.221766	+	0.384111i
$733$	5.00000	−	8.66025i	0.184679	−	0.319874i	−0.758789	−	0.651336i	$-0.774209\pi$
$733$	5.00000	−	8.66025i	0.184679	−	0.319874i	0.943468	+	0.331463i	$0.107542\pi$
$734$	32.0000			1.18114
$735$		0			0
$736$	−7.00000			−0.258023
$737$	24.0000	−	41.5692i	0.884051	−	1.53122i
$738$	3.50000	+	6.06218i	0.128837	+	0.223152i
$739$	−7.00000	−	12.1244i	−0.257499	−	0.446002i	0.708072	−	0.706140i	$-0.249565\pi$
$739$	−7.00000	−	12.1244i	−0.257499	−	0.446002i	−0.965571	+	0.260138i	$0.916232\pi$
$740$		0			0
$741$	−24.0000			−0.881662
$742$	−5.00000	+	1.73205i	−0.183556	+	0.0635856i
$743$	1.00000			0.0366864			0.0183432	−	0.999832i	$-0.494161\pi$
$743$	1.00000			0.0366864			0.0183432	+	0.999832i	$0.494161\pi$
$744$	2.50000	−	4.33013i	0.0916544	−	0.158750i
$745$		0			0
$746$	6.00000	+	10.3923i	0.219676	+	0.380489i
$747$	2.00000	−	3.46410i	0.0731762	−	0.126745i
$748$	−12.0000			−0.438763
$749$	7.00000	−	36.3731i	0.255774	−	1.32904i
$750$		0			0
$751$	8.00000	−	13.8564i	0.291924	−	0.505627i	−0.682341	−	0.731034i	$-0.739038\pi$
$751$	8.00000	−	13.8564i	0.291924	−	0.505627i	0.974265	+	0.225407i	$0.0723712\pi$
$752$	−0.500000	−	0.866025i	−0.0182331	−	0.0315807i
$753$	2.00000	+	3.46410i	0.0728841	+	0.126239i
$754$	8.00000	−	13.8564i	0.291343	−	0.504621i
$755$		0			0
$756$	−2.00000	−	1.73205i	−0.0727393	−	0.0629941i
$757$	−16.0000			−0.581530			−0.290765	−	0.956795i	$-0.593910\pi$
$757$	−16.0000			−0.581530			−0.290765	+	0.956795i	$0.593910\pi$
$758$	10.0000	−	17.3205i	0.363216	−	0.629109i
$759$	−14.0000	−	24.2487i	−0.508168	−	0.880172i
$760$		0			0
$761$	10.5000	−	18.1865i	0.380625	−	0.659261i	−0.610527	−	0.791995i	$-0.709042\pi$
$761$	10.5000	−	18.1865i	0.380625	−	0.659261i	0.991152	+	0.132734i	$0.0423756\pi$
$762$	16.0000			0.579619
$763$	12.0000	+	10.3923i	0.434429	+	0.376227i
$764$	15.0000			0.542681
$765$		0			0
$766$	−15.5000	−	26.8468i	−0.560038	−	0.970014i
$767$	28.0000	+	48.4974i	1.01102	+	1.75114i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	10.0000			0.360609			0.180305	−	0.983611i	$-0.442292\pi$
$769$	10.0000			0.360609			0.180305	+	0.983611i	$0.442292\pi$
$770$		0			0
$771$	2.00000			0.0720282
$772$	−12.5000	+	21.6506i	−0.449885	+	0.779223i
$773$	9.00000	+	15.5885i	0.323708	+	0.560678i	0.981250	−	0.192740i	$-0.0617373\pi$
$773$	9.00000	+	15.5885i	0.323708	+	0.560678i	−0.657542	+	0.753418i	$0.728404\pi$
$774$	1.00000	+	1.73205i	0.0359443	+	0.0622573i
$775$		0			0
$776$	7.00000			0.251285
$777$	5.00000	−	1.73205i	0.179374	−	0.0621370i
$778$	−10.0000			−0.358517
$779$	−21.0000	+	36.3731i	−0.752403	+	1.30320i
$780$		0			0
$781$	−18.0000	−	31.1769i	−0.644091	−	1.11560i
$782$	10.5000	−	18.1865i	0.375479	−	0.650349i
$783$	−4.00000			−0.142948
$784$	1.00000	+	6.92820i	0.0357143	+	0.247436i
$785$		0			0
$786$	4.00000	−	6.92820i	0.142675	−	0.247121i
$787$	−11.0000	−	19.0526i	−0.392108	−	0.679150i	0.600620	−	0.799535i	$-0.294921\pi$
$787$	−11.0000	−	19.0526i	−0.392108	−	0.679150i	−0.992727	+	0.120384i	$0.961587\pi$
$788$	−10.0000	−	17.3205i	−0.356235	−	0.617018i
$789$	−13.5000	+	23.3827i	−0.480613	+	0.832446i
$790$		0			0
$791$	7.50000	−	2.59808i	0.266669	−	0.0923770i
$792$	4.00000			0.142134
$793$	−24.0000	+	41.5692i	−0.852265	+	1.47617i
$794$	−11.0000	−	19.0526i	−0.390375	−	0.676150i
$795$		0			0
$796$	−7.50000	+	12.9904i	−0.265830	+	0.460432i
$797$	−12.0000			−0.425062			−0.212531	−	0.977154i	$-0.568171\pi$
$797$	−12.0000			−0.425062			−0.212531	+	0.977154i	$0.568171\pi$
$798$	3.00000	−	15.5885i	0.106199	−	0.551825i
$799$	3.00000			0.106132
$800$		0			0
$801$	3.50000	+	6.06218i	0.123666	+	0.214197i
$802$	17.0000	+	29.4449i	0.600291	+	1.03973i
$803$	12.0000	−	20.7846i	0.423471	−	0.733473i
$804$	−12.0000			−0.423207
$805$		0			0
$806$	20.0000			0.704470
$807$	−5.00000	+	8.66025i	−0.176008	+	0.304855i
$808$	−9.00000	−	15.5885i	−0.316619	−	0.548400i
$809$	−27.0000	−	46.7654i	−0.949269	−	1.64418i	−0.746968	−	0.664860i	$-0.768491\pi$
$809$	−27.0000	−	46.7654i	−0.949269	−	1.64418i	−0.202301	−	0.979323i	$-0.564842\pi$
$810$		0			0
$811$		0			0			−	1.00000i	$-0.5\pi$
$811$		0			0				1.00000i	$0.5\pi$
$812$	8.00000	+	6.92820i	0.280745	+	0.243132i
$813$	−5.00000			−0.175358
$814$	−4.00000	+	6.92820i	−0.140200	+	0.242833i
$815$		0			0
$816$	1.50000	+	2.59808i	0.0525105	+	0.0909509i
$817$	−6.00000	+	10.3923i	−0.209913	+	0.363581i
$818$	−29.0000			−1.01396
$819$	2.00000	−	10.3923i	0.0698857	−	0.363137i
$820$		0			0
$821$	−3.00000	+	5.19615i	−0.104701	+	0.181347i	−0.913616	−	0.406578i	$-0.866722\pi$
$821$	−3.00000	+	5.19615i	−0.104701	+	0.181347i	0.808915	+	0.587925i	$0.200055\pi$
$822$	−7.50000	−	12.9904i	−0.261593	−	0.453092i
$823$	12.0000	+	20.7846i	0.418294	+	0.724506i	0.995768	−	0.0919029i	$-0.0292950\pi$
$823$	12.0000	+	20.7846i	0.418294	+	0.724506i	−0.577474	+	0.816409i	$0.695962\pi$
$824$	−3.50000	+	6.06218i	−0.121928	+	0.211186i
$825$		0			0
$826$	−35.0000	+	12.1244i	−1.21781	+	0.421860i
$827$	20.0000			0.695468			0.347734	−	0.937593i	$-0.386951\pi$
$827$	20.0000			0.695468			0.347734	+	0.937593i	$0.386951\pi$
$828$	−3.50000	+	6.06218i	−0.121633	+	0.210675i
$829$	19.0000	+	32.9090i	0.659897	+	1.14298i	0.980642	+	0.195810i	$0.0627335\pi$
$829$	19.0000	+	32.9090i	0.659897	+	1.14298i	−0.320745	+	0.947166i	$0.603933\pi$
$830$		0			0
$831$	−8.00000	+	13.8564i	−0.277517	+	0.480673i
$832$	4.00000			0.138675
$833$	−19.5000	−	7.79423i	−0.675635	−	0.270054i
$834$	2.00000			0.0692543
$835$		0			0
$836$	12.0000	+	20.7846i	0.415029	+	0.718851i
$837$	−2.50000	−	4.33013i	−0.0864126	−	0.149671i
$838$	−13.0000	+	22.5167i	−0.449078	+	0.777825i
$839$	−25.0000			−0.863096			−0.431548	−	0.902090i	$-0.642032\pi$
$839$	−25.0000			−0.863096			−0.431548	+	0.902090i	$0.642032\pi$
$840$		0			0
$841$	−13.0000			−0.448276
$842$	8.00000	−	13.8564i	0.275698	−	0.477523i
$843$	8.50000	+	14.7224i	0.292756	+	0.507067i
$844$	11.0000	+	19.0526i	0.378636	+	0.655816i
$845$		0			0
$846$	−1.00000			−0.0343807
$847$	2.50000	−	12.9904i	0.0859010	−	0.446355i
$848$	−2.00000			−0.0686803
$849$	−4.00000	+	6.92820i	−0.137280	+	0.237775i
$850$		0			0
$851$	−7.00000	−	12.1244i	−0.239957	−	0.415618i
$852$	−4.50000	+	7.79423i	−0.154167	+	0.267026i
$853$	−2.00000			−0.0684787			−0.0342393	−	0.999414i	$-0.510901\pi$
$853$	−2.00000			−0.0684787			−0.0342393	+	0.999414i	$0.510901\pi$
$854$	−24.0000	−	20.7846i	−0.821263	−	0.711235i
$855$		0			0
$856$	7.00000	−	12.1244i	0.239255	−	0.414402i
$857$	13.0000	+	22.5167i	0.444072	+	0.769154i	0.997987	−	0.0634184i	$-0.0202003\pi$
$857$	13.0000	+	22.5167i	0.444072	+	0.769154i	−0.553915	+	0.832573i	$0.686867\pi$
$858$	8.00000	+	13.8564i	0.273115	+	0.473050i
$859$	−12.0000	+	20.7846i	−0.409435	+	0.709162i	−0.994826	−	0.101589i	$-0.967607\pi$
$859$	−12.0000	+	20.7846i	−0.409435	+	0.709162i	0.585392	+	0.810751i	$0.300941\pi$
$860$		0			0
$861$	−14.0000	−	12.1244i	−0.477119	−	0.413197i
$862$	39.0000			1.32835
$863$	5.50000	−	9.52628i	0.187222	−	0.324278i	−0.757101	−	0.653298i	$-0.773385\pi$
$863$	5.50000	−	9.52628i	0.187222	−	0.324278i	0.944323	+	0.329020i	$0.106718\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$		0			0
$866$	18.5000	−	32.0429i	0.628656	−	1.08886i
$867$	8.00000			0.271694
$868$	−2.50000	+	12.9904i	−0.0848555	+	0.440922i
$869$	68.0000			2.30674
$870$		0			0
$871$	−24.0000	−	41.5692i	−0.813209	−	1.40852i
$872$	3.00000	+	5.19615i	0.101593	+	0.175964i
$873$	3.50000	−	6.06218i	0.118457	−	0.205174i
$874$	−42.0000			−1.42067
$875$		0			0
$876$	−6.00000			−0.202721
$877$	−19.0000	+	32.9090i	−0.641584	+	1.11126i	0.343495	+	0.939155i	$0.388389\pi$
$877$	−19.0000	+	32.9090i	−0.641584	+	1.11126i	−0.985079	+	0.172102i	$0.944944\pi$
$878$	8.50000	+	14.7224i	0.286861	+	0.496858i
$879$	−6.00000	−	10.3923i	−0.202375	−	0.350524i
$880$		0			0
$881$	−35.0000			−1.17918			−0.589590	−	0.807703i	$-0.700711\pi$
$881$	−35.0000			−1.17918			−0.589590	+	0.807703i	$0.700711\pi$
$882$	6.50000	+	2.59808i	0.218866	+	0.0874818i
$883$	6.00000			0.201916			0.100958	−	0.994891i	$-0.467809\pi$
$883$	6.00000			0.201916			0.100958	+	0.994891i	$0.467809\pi$
$884$	−6.00000	+	10.3923i	−0.201802	+	0.349531i
$885$		0			0
$886$	−13.0000	−	22.5167i	−0.436744	−	0.756462i
$887$	−28.0000	+	48.4974i	−0.940148	+	1.62838i	−0.174962	+	0.984575i	$0.555980\pi$
$887$	−28.0000	+	48.4974i	−0.940148	+	1.62838i	−0.765186	+	0.643809i	$0.777353\pi$
$888$	2.00000			0.0671156
$889$	−40.0000	+	13.8564i	−1.34156	+	0.464729i
$890$		0			0
$891$	2.00000	−	3.46410i	0.0670025	−	0.116052i
$892$	−4.50000	−	7.79423i	−0.150671	−	0.260970i
$893$	−3.00000	−	5.19615i	−0.100391	−	0.173883i
$894$	3.00000	−	5.19615i	0.100335	−	0.173785i
$895$		0			0
$896$	−0.500000	+	2.59808i	−0.0167038	+	0.0867956i
$897$	−28.0000			−0.934893
$898$	−6.50000	+	11.2583i	−0.216908	+	0.375695i
$899$	10.0000	+	17.3205i	0.333519	+	0.577671i
$900$		0			0
$901$	3.00000	−	5.19615i	0.0999445	−	0.173109i
$902$	28.0000			0.932298
$903$	−4.00000	−	3.46410i	−0.133112	−	0.115278i
$904$	3.00000			0.0997785
$905$		0			0
$906$	−12.0000	−	20.7846i	−0.398673	−	0.690522i
$907$	14.0000	+	24.2487i	0.464862	+	0.805165i	0.999195	−	0.0401089i	$-0.0127705\pi$
$907$	14.0000	+	24.2487i	0.464862	+	0.805165i	−0.534333	+	0.845274i	$0.679437\pi$
$908$	11.0000	−	19.0526i	0.365048	−	0.632281i
$909$	−18.0000			−0.597022
$910$		0			0
$911$	19.0000			0.629498			0.314749	−	0.949175i	$-0.398080\pi$
$911$	19.0000			0.629498			0.314749	+	0.949175i	$0.398080\pi$
$912$	3.00000	−	5.19615i	0.0993399	−	0.172062i
$913$	−8.00000	−	13.8564i	−0.264761	−	0.458580i
$914$	9.00000	+	15.5885i	0.297694	+	0.515620i
$915$		0			0
$916$	8.00000			0.264327
$917$	−4.00000	+	20.7846i	−0.132092	+	0.686368i
$918$	3.00000			0.0990148
$919$	19.5000	−	33.7750i	0.643246	−	1.11413i	−0.341458	−	0.939897i	$-0.610921\pi$
$919$	19.5000	−	33.7750i	0.643246	−	1.11413i	0.984704	−	0.174237i	$-0.0557459\pi$
$920$		0			0
$921$	10.0000	+	17.3205i	0.329511	+	0.570730i
$922$	18.0000	−	31.1769i	0.592798	−	1.02676i
$923$	−36.0000			−1.18495
$924$	−10.0000	+	3.46410i	−0.328976	+	0.113961i
$925$		0			0
$926$	−3.50000	+	6.06218i	−0.115017	+	0.199216i
$927$	3.50000	+	6.06218i	0.114955	+	0.199108i
$928$	2.00000	+	3.46410i	0.0656532	+	0.113715i
$929$	15.0000	−	25.9808i	0.492134	−	0.852401i	−0.507825	−	0.861460i	$-0.669550\pi$
$929$	15.0000	−	25.9808i	0.492134	−	0.852401i	0.999959	+	0.00905914i	$0.00288365\pi$
$930$		0			0
$931$	6.00000	+	41.5692i	0.196642	+	1.36238i
$932$	−6.00000			−0.196537
$933$	10.5000	−	18.1865i	0.343755	−	0.595400i
$934$		0			0
$935$		0			0
$936$	2.00000	−	3.46410i	0.0653720	−	0.113228i
$937$	−6.00000			−0.196011			−0.0980057	−	0.995186i	$-0.531246\pi$
$937$	−6.00000			−0.196011			−0.0980057	+	0.995186i	$0.531246\pi$
$938$	30.0000	−	10.3923i	0.979535	−	0.339321i
$939$	27.0000			0.881112
$940$		0			0
$941$	−21.0000	−	36.3731i	−0.684580	−	1.18573i	−0.973568	−	0.228395i	$-0.926652\pi$
$941$	−21.0000	−	36.3731i	−0.684580	−	1.18573i	0.288988	−	0.957333i	$-0.406681\pi$
$942$	2.00000	+	3.46410i	0.0651635	+	0.112867i
$943$	−24.5000	+	42.4352i	−0.797830	+	1.38188i
$944$	−14.0000			−0.455661
$945$		0			0
$946$	8.00000			0.260102
$947$	16.0000	−	27.7128i	0.519930	−	0.900545i	−0.479801	−	0.877377i	$-0.659291\pi$
$947$	16.0000	−	27.7128i	0.519930	−	0.900545i	0.999732	−	0.0231683i	$-0.00737536\pi$
$948$	−8.50000	−	14.7224i	−0.276067	−	0.478162i
$949$	−12.0000	−	20.7846i	−0.389536	−	0.674697i
$950$		0			0
$951$	−18.0000			−0.583690
$952$	−6.00000	−	5.19615i	−0.194461	−	0.168408i
$953$	−26.0000			−0.842223			−0.421111	−	0.907009i	$-0.638360\pi$
$953$	−26.0000			−0.842223			−0.421111	+	0.907009i	$0.638360\pi$
$954$	−1.00000	+	1.73205i	−0.0323762	+	0.0560772i
$955$		0			0
$956$	−1.50000	−	2.59808i	−0.0485135	−	0.0840278i
$957$	−8.00000	+	13.8564i	−0.258603	+	0.447914i
$958$	−1.00000			−0.0323085
$959$	30.0000	+	25.9808i	0.968751	+	0.838963i
$960$		0			0
$961$	3.00000	−	5.19615i	0.0967742	−	0.167618i
$962$	4.00000	+	6.92820i	0.128965	+	0.223374i
$963$	−7.00000	−	12.1244i	−0.225572	−	0.390702i
$964$	1.00000	−	1.73205i	0.0322078	−	0.0557856i
$965$		0			0
$966$	3.50000	−	18.1865i	0.112611	−	0.585142i
$967$	−29.0000			−0.932577			−0.466289	−	0.884633i	$-0.654409\pi$
$967$	−29.0000			−0.932577			−0.466289	+	0.884633i	$0.654409\pi$
$968$	2.50000	−	4.33013i	0.0803530	−	0.139176i
$969$	9.00000	+	15.5885i	0.289122	+	0.500773i
$970$		0			0
$971$	12.0000	−	20.7846i	0.385098	−	0.667010i	−0.606685	−	0.794943i	$-0.707501\pi$
$971$	12.0000	−	20.7846i	0.385098	−	0.667010i	0.991783	+	0.127933i	$0.0408342\pi$
$972$	−1.00000			−0.0320750
$973$	−5.00000	+	1.73205i	−0.160293	+	0.0555270i
$974$	−5.00000			−0.160210
$975$		0			0
$976$	−6.00000	−	10.3923i	−0.192055	−	0.332650i
$977$	−1.50000	−	2.59808i	−0.0479893	−	0.0831198i	0.841033	−	0.540984i	$-0.181948\pi$
$977$	−1.50000	−	2.59808i	−0.0479893	−	0.0831198i	−0.889022	+	0.457864i	$0.848615\pi$
$978$	4.00000	−	6.92820i	0.127906	−	0.221540i
$979$	28.0000			0.894884
$980$		0			0
$981$	6.00000			0.191565
$982$	19.0000	−	32.9090i	0.606314	−	1.05017i
$983$	−14.0000	−	24.2487i	−0.446531	−	0.773414i	0.551627	−	0.834091i	$-0.314007\pi$
$983$	−14.0000	−	24.2487i	−0.446531	−	0.773414i	−0.998157	+	0.0606773i	$0.980674\pi$
$984$	−3.50000	−	6.06218i	−0.111576	−	0.193255i
$985$		0			0
$986$	−12.0000			−0.382158
$987$	2.50000	−	0.866025i	0.0795759	−	0.0275659i
$988$	24.0000			0.763542
$989$	−7.00000	+	12.1244i	−0.222587	+	0.385532i
$990$		0			0
$991$	−3.50000	−	6.06218i	−0.111181	−	0.192571i	0.805066	−	0.593186i	$-0.202130\pi$
$991$	−3.50000	−	6.06218i	−0.111181	−	0.192571i	−0.916247	+	0.400614i	$0.868797\pi$
$992$	−2.50000	+	4.33013i	−0.0793751	+	0.137482i
$993$	34.0000			1.07896
$994$	4.50000	−	23.3827i	0.142731	−	0.741654i
$995$		0			0
$996$	−2.00000	+	3.46410i	−0.0633724	+	0.109764i
$997$	8.00000	+	13.8564i	0.253363	+	0.438837i	0.964449	−	0.264267i	$-0.0851301\pi$
$997$	8.00000	+	13.8564i	0.253363	+	0.438837i	−0.711087	+	0.703104i	$0.751797\pi$
$998$	14.0000	+	24.2487i	0.443162	+	0.767580i
$999$	1.00000	−	1.73205i	0.0316386	−	0.0547997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.i.r.751.1	yes	2
5.2	odd	4		1050.2.o.l.499.2		4
5.3	odd	4		1050.2.o.l.499.1		4
5.4	even	2		1050.2.i.d.751.1	yes	2
7.2	even	3		7350.2.a.e.1.1		1
7.4	even	3	inner	1050.2.i.r.151.1	yes	2
7.5	odd	6		7350.2.a.v.1.1		1
35.4	even	6		1050.2.i.d.151.1	✓	2
35.9	even	6		7350.2.a.ci.1.1		1
35.18	odd	12		1050.2.o.l.949.2		4
35.19	odd	6		7350.2.a.bs.1.1		1
35.32	odd	12		1050.2.o.l.949.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.2.i.d.151.1	✓	2	35.4	even	6
1050.2.i.d.751.1	yes	2	5.4	even	2
1050.2.i.r.151.1	yes	2	7.4	even	3	inner
1050.2.i.r.751.1	yes	2	1.1	even	1	trivial
1050.2.o.l.499.1		4	5.3	odd	4
1050.2.o.l.499.2		4	5.2	odd	4
1050.2.o.l.949.1		4	35.32	odd	12
1050.2.o.l.949.2		4	35.18	odd	12
7350.2.a.e.1.1		1	7.2	even	3
7350.2.a.v.1.1		1	7.5	odd	6
7350.2.a.bs.1.1		1	35.19	odd	6
7350.2.a.ci.1.1		1	35.9	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{6} +(-2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{6} +(-2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.00000 + 3.46410i) q^{11} +(0.500000 - 0.866025i) q^{12} +4.00000 q^{13} +(-0.500000 + 2.59808i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-3.00000 + 5.19615i) q^{19} +(-2.00000 - 1.73205i) q^{21} +4.00000 q^{22} +(-3.50000 + 6.06218i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(2.00000 - 3.46410i) q^{26} -1.00000 q^{27} +(2.00000 + 1.73205i) q^{28} +4.00000 q^{29} +(2.50000 + 4.33013i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.00000 + 3.46410i) q^{33} -3.00000 q^{34} +1.00000 q^{36} +(-1.00000 + 1.73205i) q^{37} +(3.00000 + 5.19615i) q^{38} +(2.00000 + 3.46410i) q^{39} +7.00000 q^{41} +(-2.50000 + 0.866025i) q^{42} +2.00000 q^{43} +(2.00000 - 3.46410i) q^{44} +(3.50000 + 6.06218i) q^{46} +(-0.500000 + 0.866025i) q^{47} -1.00000 q^{48} +(5.50000 - 4.33013i) q^{49} +(1.50000 - 2.59808i) q^{51} +(-2.00000 - 3.46410i) q^{52} +(1.00000 + 1.73205i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(2.50000 - 0.866025i) q^{56} -6.00000 q^{57} +(2.00000 - 3.46410i) q^{58} +(7.00000 + 12.1244i) q^{59} +(-6.00000 + 10.3923i) q^{61} +5.00000 q^{62} +(0.500000 - 2.59808i) q^{63} +1.00000 q^{64} +(2.00000 + 3.46410i) q^{66} +(-6.00000 - 10.3923i) q^{67} +(-1.50000 + 2.59808i) q^{68} -7.00000 q^{69} -9.00000 q^{71} +(0.500000 - 0.866025i) q^{72} +(-3.00000 - 5.19615i) q^{73} +(1.00000 + 1.73205i) q^{74} +6.00000 q^{76} +(-8.00000 - 6.92820i) q^{77} +4.00000 q^{78} +(8.50000 - 14.7224i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(3.50000 - 6.06218i) q^{82} -4.00000 q^{83} +(-0.500000 + 2.59808i) q^{84} +(1.00000 - 1.73205i) q^{86} +(2.00000 + 3.46410i) q^{87} +(-2.00000 - 3.46410i) q^{88} +(3.50000 - 6.06218i) q^{89} +(-10.0000 + 3.46410i) q^{91} +7.00000 q^{92} +(-2.50000 + 4.33013i) q^{93} +(0.500000 + 0.866025i) q^{94} +(-0.500000 + 0.866025i) q^{96} -7.00000 q^{97} +(-1.00000 - 6.92820i) q^{98} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + q^{3} - q^{4} + 2 q^{6} - 5 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 + q^3 - q^4 + 2 * q^6 - 5 * q^7 - 2 * q^8 - q^9	\( 2 q + q^{2} + q^{3} - q^{4} + 2 q^{6} - 5 q^{7} - 2 q^{8} - q^{9} + 4 q^{11} + q^{12} + 8 q^{13} - q^{14} - q^{16} - 3 q^{17} + q^{18} - 6 q^{19} - 4 q^{21} + 8 q^{22} - 7 q^{23} - q^{24} + 4 q^{26} - 2 q^{27} + 4 q^{28} + 8 q^{29} + 5 q^{31} + q^{32} - 4 q^{33} - 6 q^{34} + 2 q^{36} - 2 q^{37} + 6 q^{38} + 4 q^{39} + 14 q^{41} - 5 q^{42} + 4 q^{43} + 4 q^{44} + 7 q^{46} - q^{47} - 2 q^{48} + 11 q^{49} + 3 q^{51} - 4 q^{52} + 2 q^{53} - q^{54} + 5 q^{56} - 12 q^{57} + 4 q^{58} + 14 q^{59} - 12 q^{61} + 10 q^{62} + q^{63} + 2 q^{64} + 4 q^{66} - 12 q^{67} - 3 q^{68} - 14 q^{69} - 18 q^{71} + q^{72} - 6 q^{73} + 2 q^{74} + 12 q^{76} - 16 q^{77} + 8 q^{78} + 17 q^{79} - q^{81} + 7 q^{82} - 8 q^{83} - q^{84} + 2 q^{86} + 4 q^{87} - 4 q^{88} + 7 q^{89} - 20 q^{91} + 14 q^{92} - 5 q^{93} + q^{94} - q^{96} - 14 q^{97} - 2 q^{98} - 8 q^{99}+O(q^{100}) \) 2 * q + q^2 + q^3 - q^4 + 2 * q^6 - 5 * q^7 - 2 * q^8 - q^9 + 4 * q^11 + q^12 + 8 * q^13 - q^14 - q^16 - 3 * q^17 + q^18 - 6 * q^19 - 4 * q^21 + 8 * q^22 - 7 * q^23 - q^24 + 4 * q^26 - 2 * q^27 + 4 * q^28 + 8 * q^29 + 5 * q^31 + q^32 - 4 * q^33 - 6 * q^34 + 2 * q^36 - 2 * q^37 + 6 * q^38 + 4 * q^39 + 14 * q^41 - 5 * q^42 + 4 * q^43 + 4 * q^44 + 7 * q^46 - q^47 - 2 * q^48 + 11 * q^49 + 3 * q^51 - 4 * q^52 + 2 * q^53 - q^54 + 5 * q^56 - 12 * q^57 + 4 * q^58 + 14 * q^59 - 12 * q^61 + 10 * q^62 + q^63 + 2 * q^64 + 4 * q^66 - 12 * q^67 - 3 * q^68 - 14 * q^69 - 18 * q^71 + q^72 - 6 * q^73 + 2 * q^74 + 12 * q^76 - 16 * q^77 + 8 * q^78 + 17 * q^79 - q^81 + 7 * q^82 - 8 * q^83 - q^84 + 2 * q^86 + 4 * q^87 - 4 * q^88 + 7 * q^89 - 20 * q^91 + 14 * q^92 - 5 * q^93 + q^94 - q^96 - 14 * q^97 - 2 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more