LMFDB - Embedded newform 1050.2.i.a.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.a.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} +1.00000 q^{13} +(2.00000 - 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.00000 - 1.73205i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-0.500000 + 0.866025i) q^{19} +(0.500000 + 2.59808i) q^{21} -4.00000 q^{22} +(1.00000 - 1.73205i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{26} +1.00000 q^{27} +(0.500000 + 2.59808i) q^{28} +4.00000 q^{29} +(-0.500000 - 0.866025i) q^{32} +(2.00000 - 3.46410i) q^{33} +2.00000 q^{34} +1.00000 q^{36} +(-1.50000 + 2.59808i) q^{37} +(-0.500000 - 0.866025i) q^{38} +(-0.500000 - 0.866025i) q^{39} +12.0000 q^{41} +(-2.50000 - 0.866025i) q^{42} +8.00000 q^{43} +(2.00000 - 3.46410i) q^{44} +(1.00000 + 1.73205i) q^{46} +(3.00000 - 5.19615i) q^{47} +1.00000 q^{48} +(5.50000 + 4.33013i) q^{49} +(-1.00000 + 1.73205i) q^{51} +(-0.500000 - 0.866025i) q^{52} +(-1.00000 - 1.73205i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-2.50000 - 0.866025i) q^{56} +1.00000 q^{57} +(-2.00000 + 3.46410i) q^{58} +(-3.00000 - 5.19615i) q^{59} +(6.50000 - 11.2583i) q^{61} +(2.00000 - 1.73205i) q^{63} +1.00000 q^{64} +(2.00000 + 3.46410i) q^{66} +(-1.50000 - 2.59808i) q^{67} +(-1.00000 + 1.73205i) q^{68} -2.00000 q^{69} +16.0000 q^{71} +(-0.500000 + 0.866025i) q^{72} +(5.50000 + 9.52628i) q^{73} +(-1.50000 - 2.59808i) q^{74} +1.00000 q^{76} +(-2.00000 - 10.3923i) q^{77} +1.00000 q^{78} +(-6.50000 + 11.2583i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(-6.00000 + 10.3923i) q^{82} -6.00000 q^{83} +(2.00000 - 1.73205i) q^{84} +(-4.00000 + 6.92820i) q^{86} +(-2.00000 - 3.46410i) q^{87} +(2.00000 + 3.46410i) q^{88} +(1.00000 - 1.73205i) q^{89} +(-2.50000 - 0.866025i) q^{91} -2.00000 q^{92} +(3.00000 + 5.19615i) q^{94} +(-0.500000 + 0.866025i) q^{96} +17.0000 q^{97} +(-6.50000 + 2.59808i) 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} + 2 q^{13} + 4 q^{14} - q^{16} - 2 q^{17} - q^{18} - q^{19} + q^{21} - 8 q^{22} + 2 q^{23} - q^{24} - q^{26} + 2 q^{27} + q^{28} + 8 q^{29} - q^{32} + 4 q^{33} + 4 q^{34} + 2 q^{36} - 3 q^{37} - q^{38} - q^{39} + 24 q^{41} - 5 q^{42} + 16 q^{43} + 4 q^{44} + 2 q^{46} + 6 q^{47} + 2 q^{48} + 11 q^{49} - 2 q^{51} - q^{52} - 2 q^{53} - q^{54} - 5 q^{56} + 2 q^{57} - 4 q^{58} - 6 q^{59} + 13 q^{61} + 4 q^{63} + 2 q^{64} + 4 q^{66} - 3 q^{67} - 2 q^{68} - 4 q^{69} + 32 q^{71} - q^{72} + 11 q^{73} - 3 q^{74} + 2 q^{76} - 4 q^{77} + 2 q^{78} - 13 q^{79} - q^{81} - 12 q^{82} - 12 q^{83} + 4 q^{84} - 8 q^{86} - 4 q^{87} + 4 q^{88} + 2 q^{89} - 5 q^{91} - 4 q^{92} + 6 q^{94} - q^{96} + 34 q^{97} - 13 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 + 2 * q^13 + 4 * q^14 - q^16 - 2 * q^17 - q^18 - q^19 + q^21 - 8 * q^22 + 2 * q^23 - q^24 - q^26 + 2 * q^27 + q^28 + 8 * q^29 - q^32 + 4 * q^33 + 4 * q^34 + 2 * q^36 - 3 * q^37 - q^38 - q^39 + 24 * q^41 - 5 * q^42 + 16 * q^43 + 4 * q^44 + 2 * q^46 + 6 * q^47 + 2 * q^48 + 11 * q^49 - 2 * q^51 - q^52 - 2 * q^53 - q^54 - 5 * q^56 + 2 * q^57 - 4 * q^58 - 6 * q^59 + 13 * q^61 + 4 * q^63 + 2 * q^64 + 4 * q^66 - 3 * q^67 - 2 * q^68 - 4 * q^69 + 32 * q^71 - q^72 + 11 * q^73 - 3 * q^74 + 2 * q^76 - 4 * q^77 + 2 * q^78 - 13 * q^79 - q^81 - 12 * q^82 - 12 * q^83 + 4 * q^84 - 8 * q^86 - 4 * q^87 + 4 * q^88 + 2 * q^89 - 5 * q^91 - 4 * q^92 + 6 * q^94 - q^96 + 34 * q^97 - 13 * 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
$13$	1.00000			0.277350			0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000			0.277350			0.138675	+	0.990338i	$0.455716\pi$
$14$	2.00000	−	1.73205i	0.534522	−	0.462910i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	0.718900	−	0.695113i	$-0.244646\pi$
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	−0.961436	+	0.275029i	$0.911312\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i	0.802955	+	0.596040i	$0.203260\pi$
$20$		0			0
$21$	0.500000	+	2.59808i	0.109109	+	0.566947i
$22$	−4.00000			−0.852803
$23$	1.00000	−	1.73205i	0.208514	−	0.361158i	−0.742732	−	0.669588i	$-0.766471\pi$
$23$	1.00000	−	1.73205i	0.208514	−	0.361158i	0.951247	+	0.308431i	$0.0998038\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$		0			0
$26$	−0.500000	+	0.866025i	−0.0980581	+	0.169842i
$27$	1.00000			0.192450
$28$	0.500000	+	2.59808i	0.0944911	+	0.490990i
$29$	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
$31$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$31$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	2.00000	−	3.46410i	0.348155	−	0.603023i
$34$	2.00000			0.342997
$35$		0			0
$36$	1.00000			0.166667
$37$	−1.50000	+	2.59808i	−0.246598	+	0.427121i	−0.962580	−	0.270998i	$-0.912646\pi$
$37$	−1.50000	+	2.59808i	−0.246598	+	0.427121i	0.715981	+	0.698119i	$0.245980\pi$
$38$	−0.500000	−	0.866025i	−0.0811107	−	0.140488i
$39$	−0.500000	−	0.866025i	−0.0800641	−	0.138675i
$40$		0			0
$41$	12.0000			1.87409			0.937043	−	0.349215i	$-0.113552\pi$
$41$	12.0000			1.87409			0.937043	+	0.349215i	$0.113552\pi$
$42$	−2.50000	−	0.866025i	−0.385758	−	0.133631i
$43$	8.00000			1.21999			0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000			1.21999			0.609994	+	0.792406i	$0.291172\pi$
$44$	2.00000	−	3.46410i	0.301511	−	0.522233i
$45$		0			0
$46$	1.00000	+	1.73205i	0.147442	+	0.255377i
$47$	3.00000	−	5.19615i	0.437595	−	0.757937i	−0.559908	−	0.828554i	$-0.689164\pi$
$47$	3.00000	−	5.19615i	0.437595	−	0.757937i	0.997503	+	0.0706177i	$0.0224970\pi$
$48$	1.00000			0.144338
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$		0			0
$51$	−1.00000	+	1.73205i	−0.140028	+	0.242536i
$52$	−0.500000	−	0.866025i	−0.0693375	−	0.120096i
$53$	−1.00000	−	1.73205i	−0.137361	−	0.237915i	0.789136	−	0.614218i	$-0.210529\pi$
$53$	−1.00000	−	1.73205i	−0.137361	−	0.237915i	−0.926497	+	0.376303i	$0.877195\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$		0			0
$56$	−2.50000	−	0.866025i	−0.334077	−	0.115728i
$57$	1.00000			0.132453
$58$	−2.00000	+	3.46410i	−0.262613	+	0.454859i
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	0.601958	−	0.798528i	$-0.294388\pi$
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	−0.992524	+	0.122047i	$0.961054\pi$
$60$		0			0
$61$	6.50000	−	11.2583i	0.832240	−	1.44148i	−0.0640184	−	0.997949i	$-0.520392\pi$
$61$	6.50000	−	11.2583i	0.832240	−	1.44148i	0.896258	−	0.443533i	$-0.146275\pi$
$62$		0			0
$63$	2.00000	−	1.73205i	0.251976	−	0.218218i
$64$	1.00000			0.125000
$65$		0			0
$66$	2.00000	+	3.46410i	0.246183	+	0.426401i
$67$	−1.50000	−	2.59808i	−0.183254	−	0.317406i	0.759733	−	0.650236i	$-0.225330\pi$
$67$	−1.50000	−	2.59808i	−0.183254	−	0.317406i	−0.942987	+	0.332830i	$0.891996\pi$
$68$	−1.00000	+	1.73205i	−0.121268	+	0.210042i
$69$	−2.00000			−0.240772
$70$		0			0
$71$	16.0000			1.89885			0.949425	−	0.313993i	$-0.101667\pi$
$71$	16.0000			1.89885			0.949425	+	0.313993i	$0.101667\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	5.50000	+	9.52628i	0.643726	+	1.11497i	0.984594	+	0.174855i	$0.0559458\pi$
$73$	5.50000	+	9.52628i	0.643726	+	1.11497i	−0.340868	+	0.940111i	$0.610721\pi$
$74$	−1.50000	−	2.59808i	−0.174371	−	0.302020i
$75$		0			0
$76$	1.00000			0.114708
$77$	−2.00000	−	10.3923i	−0.227921	−	1.18431i
$78$	1.00000			0.113228
$79$	−6.50000	+	11.2583i	−0.731307	+	1.26666i	0.225018	+	0.974355i	$0.427756\pi$
$79$	−6.50000	+	11.2583i	−0.731307	+	1.26666i	−0.956325	+	0.292306i	$0.905577\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−6.00000	+	10.3923i	−0.662589	+	1.14764i
$83$	−6.00000			−0.658586			−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000			−0.658586			−0.329293	+	0.944228i	$0.606810\pi$
$84$	2.00000	−	1.73205i	0.218218	−	0.188982i
$85$		0			0
$86$	−4.00000	+	6.92820i	−0.431331	+	0.747087i
$87$	−2.00000	−	3.46410i	−0.214423	−	0.371391i
$88$	2.00000	+	3.46410i	0.213201	+	0.369274i
$89$	1.00000	−	1.73205i	0.106000	−	0.183597i	−0.808146	−	0.588982i	$-0.799529\pi$
$89$	1.00000	−	1.73205i	0.106000	−	0.183597i	0.914146	+	0.405385i	$0.132862\pi$
$90$		0			0
$91$	−2.50000	−	0.866025i	−0.262071	−	0.0907841i
$92$	−2.00000			−0.208514
$93$		0			0
$94$	3.00000	+	5.19615i	0.309426	+	0.535942i
$95$		0			0
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	17.0000			1.72609			0.863044	−	0.505128i	$-0.168555\pi$
$97$	17.0000			1.72609			0.863044	+	0.505128i	$0.168555\pi$
$98$	−6.50000	+	2.59808i	−0.656599	+	0.262445i
$99$	−4.00000			−0.402015
$100$		0			0
$101$	−6.00000	−	10.3923i	−0.597022	−	1.03407i	−0.993258	−	0.115924i	$-0.963017\pi$
$101$	−6.00000	−	10.3923i	−0.597022	−	1.03407i	0.396236	−	0.918149i	$-0.370316\pi$
$102$	−1.00000	−	1.73205i	−0.0990148	−	0.171499i
$103$	−3.50000	+	6.06218i	−0.344865	+	0.597324i	−0.985329	−	0.170664i	$-0.945409\pi$
$103$	−3.50000	+	6.06218i	−0.344865	+	0.597324i	0.640464	+	0.767988i	$0.278742\pi$
$104$	1.00000			0.0980581
$105$		0			0
$106$	2.00000			0.194257
$107$	−3.00000	+	5.19615i	−0.290021	+	0.502331i	−0.973814	−	0.227345i	$-0.926996\pi$
$107$	−3.00000	+	5.19615i	−0.290021	+	0.502331i	0.683793	+	0.729676i	$0.260329\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	9.50000	+	16.4545i	0.909935	+	1.57605i	0.814152	+	0.580651i	$0.197202\pi$
$109$	9.50000	+	16.4545i	0.909935	+	1.57605i	0.0957826	+	0.995402i	$0.469465\pi$
$110$		0			0
$111$	3.00000			0.284747
$112$	2.00000	−	1.73205i	0.188982	−	0.163663i
$113$	18.0000			1.69330			0.846649	−	0.532152i	$-0.178617\pi$
$113$	18.0000			1.69330			0.846649	+	0.532152i	$0.178617\pi$
$114$	−0.500000	+	0.866025i	−0.0468293	+	0.0811107i
$115$		0			0
$116$	−2.00000	−	3.46410i	−0.185695	−	0.321634i
$117$	−0.500000	+	0.866025i	−0.0462250	+	0.0800641i
$118$	6.00000			0.552345
$119$	1.00000	+	5.19615i	0.0916698	+	0.476331i
$120$		0			0
$121$	−2.50000	+	4.33013i	−0.227273	+	0.393648i
$122$	6.50000	+	11.2583i	0.588482	+	1.01928i
$123$	−6.00000	−	10.3923i	−0.541002	−	0.937043i
$124$		0			0
$125$		0			0
$126$	0.500000	+	2.59808i	0.0445435	+	0.231455i
$127$	−1.00000			−0.0887357			−0.0443678	−	0.999015i	$-0.514127\pi$
$127$	−1.00000			−0.0887357			−0.0443678	+	0.999015i	$0.514127\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−4.00000	−	6.92820i	−0.352180	−	0.609994i
$130$		0			0
$131$	−1.00000	+	1.73205i	−0.0873704	+	0.151330i	−0.906399	−	0.422423i	$-0.861180\pi$
$131$	−1.00000	+	1.73205i	−0.0873704	+	0.151330i	0.819028	+	0.573753i	$0.194513\pi$
$132$	−4.00000			−0.348155
$133$	2.00000	−	1.73205i	0.173422	−	0.150188i
$134$	3.00000			0.259161
$135$		0			0
$136$	−1.00000	−	1.73205i	−0.0857493	−	0.148522i
$137$	−5.00000	−	8.66025i	−0.427179	−	0.739895i	0.569442	−	0.822031i	$-0.307159\pi$
$137$	−5.00000	−	8.66025i	−0.427179	−	0.739895i	−0.996621	+	0.0821359i	$0.973826\pi$
$138$	1.00000	−	1.73205i	0.0851257	−	0.147442i
$139$	−13.0000			−1.10265			−0.551323	−	0.834292i	$-0.685877\pi$
$139$	−13.0000			−1.10265			−0.551323	+	0.834292i	$0.685877\pi$
$140$		0			0
$141$	−6.00000			−0.505291
$142$	−8.00000	+	13.8564i	−0.671345	+	1.16280i
$143$	2.00000	+	3.46410i	0.167248	+	0.289683i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$		0			0
$146$	−11.0000			−0.910366
$147$	1.00000	−	6.92820i	0.0824786	−	0.571429i
$148$	3.00000			0.246598
$149$	8.00000	−	13.8564i	0.655386	−	1.13516i	−0.326411	−	0.945228i	$-0.605840\pi$
$149$	8.00000	−	13.8564i	0.655386	−	1.13516i	0.981797	−	0.189933i	$-0.0608272\pi$
$150$		0			0
$151$	−9.50000	−	16.4545i	−0.773099	−	1.33905i	−0.935857	−	0.352381i	$-0.885372\pi$
$151$	−9.50000	−	16.4545i	−0.773099	−	1.33905i	0.162758	−	0.986666i	$-0.447961\pi$
$152$	−0.500000	+	0.866025i	−0.0405554	+	0.0702439i
$153$	2.00000			0.161690
$154$	10.0000	+	3.46410i	0.805823	+	0.279145i
$155$		0			0
$156$	−0.500000	+	0.866025i	−0.0400320	+	0.0693375i
$157$	10.5000	+	18.1865i	0.837991	+	1.45144i	0.891572	+	0.452880i	$0.149603\pi$
$157$	10.5000	+	18.1865i	0.837991	+	1.45144i	−0.0535803	+	0.998564i	$0.517063\pi$
$158$	−6.50000	−	11.2583i	−0.517112	−	0.895665i
$159$	−1.00000	+	1.73205i	−0.0793052	+	0.137361i
$160$		0			0
$161$	−4.00000	+	3.46410i	−0.315244	+	0.273009i
$162$	1.00000			0.0785674
$163$	−11.5000	+	19.9186i	−0.900750	+	1.56014i	−0.0742262	+	0.997241i	$0.523649\pi$
$163$	−11.5000	+	19.9186i	−0.900750	+	1.56014i	−0.826523	+	0.562902i	$0.809685\pi$
$164$	−6.00000	−	10.3923i	−0.468521	−	0.811503i
$165$		0			0
$166$	3.00000	−	5.19615i	0.232845	−	0.403300i
$167$	10.0000			0.773823			0.386912	−	0.922117i	$-0.373542\pi$
$167$	10.0000			0.773823			0.386912	+	0.922117i	$0.373542\pi$
$168$	0.500000	+	2.59808i	0.0385758	+	0.200446i
$169$	−12.0000			−0.923077
$170$		0			0
$171$	−0.500000	−	0.866025i	−0.0382360	−	0.0662266i
$172$	−4.00000	−	6.92820i	−0.304997	−	0.528271i
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	−0.729155	−	0.684349i	$-0.760087\pi$
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	0.957241	+	0.289292i	$0.0934200\pi$
$174$	4.00000			0.303239
$175$		0			0
$176$	−4.00000			−0.301511
$177$	−3.00000	+	5.19615i	−0.225494	+	0.390567i
$178$	1.00000	+	1.73205i	0.0749532	+	0.129823i
$179$	4.00000	+	6.92820i	0.298974	+	0.517838i	0.975901	−	0.218212i	$-0.0700223\pi$
$179$	4.00000	+	6.92820i	0.298974	+	0.517838i	−0.676927	+	0.736050i	$0.736689\pi$
$180$		0			0
$181$	−18.0000			−1.33793			−0.668965	−	0.743294i	$-0.733262\pi$
$181$	−18.0000			−1.33793			−0.668965	+	0.743294i	$0.733262\pi$
$182$	2.00000	−	1.73205i	0.148250	−	0.128388i
$183$	−13.0000			−0.960988
$184$	1.00000	−	1.73205i	0.0737210	−	0.127688i
$185$		0			0
$186$		0			0
$187$	4.00000	−	6.92820i	0.292509	−	0.506640i
$188$	−6.00000			−0.437595
$189$	−2.50000	−	0.866025i	−0.181848	−	0.0629941i
$190$		0			0
$191$	−10.0000	+	17.3205i	−0.723575	+	1.25327i	0.235983	+	0.971757i	$0.424169\pi$
$191$	−10.0000	+	17.3205i	−0.723575	+	1.25327i	−0.959558	+	0.281511i	$0.909164\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	5.00000	+	8.66025i	0.359908	+	0.623379i	0.987945	−	0.154805i	$-0.0494748\pi$
$193$	5.00000	+	8.66025i	0.359908	+	0.623379i	−0.628037	+	0.778183i	$0.716141\pi$
$194$	−8.50000	+	14.7224i	−0.610264	+	1.05701i
$195$		0			0
$196$	1.00000	−	6.92820i	0.0714286	−	0.494872i
$197$		0			0			−	1.00000i	$-0.5\pi$
$197$		0			0				1.00000i	$0.5\pi$
$198$	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
$201$	−1.50000	+	2.59808i	−0.105802	+	0.183254i
$202$	12.0000			0.844317
$203$	−10.0000	−	3.46410i	−0.701862	−	0.243132i
$204$	2.00000			0.140028
$205$		0			0
$206$	−3.50000	−	6.06218i	−0.243857	−	0.422372i
$207$	1.00000	+	1.73205i	0.0695048	+	0.120386i
$208$	−0.500000	+	0.866025i	−0.0346688	+	0.0600481i
$209$	−4.00000			−0.276686
$210$		0			0
$211$	3.00000			0.206529			0.103264	−	0.994654i	$-0.467071\pi$
$211$	3.00000			0.206529			0.103264	+	0.994654i	$0.467071\pi$
$212$	−1.00000	+	1.73205i	−0.0686803	+	0.118958i
$213$	−8.00000	−	13.8564i	−0.548151	−	0.949425i
$214$	−3.00000	−	5.19615i	−0.205076	−	0.355202i
$215$		0			0
$216$	1.00000			0.0680414
$217$		0			0
$218$	−19.0000			−1.28684
$219$	5.50000	−	9.52628i	0.371656	−	0.643726i
$220$		0			0
$221$	−1.00000	−	1.73205i	−0.0672673	−	0.116510i
$222$	−1.50000	+	2.59808i	−0.100673	+	0.174371i
$223$	−19.0000			−1.27233			−0.636167	−	0.771551i	$-0.719481\pi$
$223$	−19.0000			−1.27233			−0.636167	+	0.771551i	$0.719481\pi$
$224$	0.500000	+	2.59808i	0.0334077	+	0.173591i
$225$		0			0
$226$	−9.00000	+	15.5885i	−0.598671	+	1.03693i
$227$	4.00000	+	6.92820i	0.265489	+	0.459841i	0.967692	−	0.252136i	$-0.0811332\pi$
$227$	4.00000	+	6.92820i	0.265489	+	0.459841i	−0.702202	+	0.711977i	$0.747800\pi$
$228$	−0.500000	−	0.866025i	−0.0331133	−	0.0573539i
$229$	3.50000	−	6.06218i	0.231287	−	0.400600i	−0.726900	−	0.686743i	$-0.759040\pi$
$229$	3.50000	−	6.06218i	0.231287	−	0.400600i	0.958187	+	0.286143i	$0.0923732\pi$
$230$		0			0
$231$	−8.00000	+	6.92820i	−0.526361	+	0.455842i
$232$	4.00000			0.262613
$233$	2.00000	−	3.46410i	0.131024	−	0.226941i	−0.793047	−	0.609160i	$-0.791507\pi$
$233$	2.00000	−	3.46410i	0.131024	−	0.226941i	0.924072	+	0.382219i	$0.124840\pi$
$234$	−0.500000	−	0.866025i	−0.0326860	−	0.0566139i
$235$		0			0
$236$	−3.00000	+	5.19615i	−0.195283	+	0.338241i
$237$	13.0000			0.844441
$238$	−5.00000	−	1.73205i	−0.324102	−	0.112272i
$239$	−12.0000			−0.776215			−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000			−0.776215			−0.388108	+	0.921614i	$0.626871\pi$
$240$		0			0
$241$	−6.50000	−	11.2583i	−0.418702	−	0.725213i	0.577107	−	0.816668i	$-0.304181\pi$
$241$	−6.50000	−	11.2583i	−0.418702	−	0.725213i	−0.995809	+	0.0914555i	$0.970848\pi$
$242$	−2.50000	−	4.33013i	−0.160706	−	0.278351i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−13.0000			−0.832240
$245$		0			0
$246$	12.0000			0.765092
$247$	−0.500000	+	0.866025i	−0.0318142	+	0.0551039i
$248$		0			0
$249$	3.00000	+	5.19615i	0.190117	+	0.329293i
$250$		0			0
$251$	24.0000			1.51487			0.757433	−	0.652913i	$-0.226453\pi$
$251$	24.0000			1.51487			0.757433	+	0.652913i	$0.226453\pi$
$252$	−2.50000	−	0.866025i	−0.157485	−	0.0545545i
$253$	8.00000			0.502956
$254$	0.500000	−	0.866025i	0.0313728	−	0.0543393i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	4.00000	−	6.92820i	0.249513	−	0.432169i	−0.713878	−	0.700270i	$-0.753063\pi$
$257$	4.00000	−	6.92820i	0.249513	−	0.432169i	0.963391	+	0.268101i	$0.0863961\pi$
$258$	8.00000			0.498058
$259$	6.00000	−	5.19615i	0.372822	−	0.322873i
$260$		0			0
$261$	−2.00000	+	3.46410i	−0.123797	+	0.214423i
$262$	−1.00000	−	1.73205i	−0.0617802	−	0.107006i
$263$	−16.0000	−	27.7128i	−0.986602	−	1.70885i	−0.634588	−	0.772851i	$-0.718830\pi$
$263$	−16.0000	−	27.7128i	−0.986602	−	1.70885i	−0.352014	−	0.935995i	$-0.614503\pi$
$264$	2.00000	−	3.46410i	0.123091	−	0.213201i
$265$		0			0
$266$	0.500000	+	2.59808i	0.0306570	+	0.159298i
$267$	−2.00000			−0.122398
$268$	−1.50000	+	2.59808i	−0.0916271	+	0.158703i
$269$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$269$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$270$		0			0
$271$	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	$-0.0411435\pi$
$272$	2.00000			0.121268
$273$	0.500000	+	2.59808i	0.0302614	+	0.157243i
$274$	10.0000			0.604122
$275$		0			0
$276$	1.00000	+	1.73205i	0.0601929	+	0.104257i
$277$	−0.500000	−	0.866025i	−0.0300421	−	0.0520344i	0.850613	−	0.525792i	$-0.176231\pi$
$277$	−0.500000	−	0.866025i	−0.0300421	−	0.0520344i	−0.880656	+	0.473757i	$0.842897\pi$
$278$	6.50000	−	11.2583i	0.389844	−	0.675230i
$279$		0			0
$280$		0			0
$281$	−18.0000			−1.07379			−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000			−1.07379			−0.536895	+	0.843649i	$0.680403\pi$
$282$	3.00000	−	5.19615i	0.178647	−	0.309426i
$283$	−6.50000	−	11.2583i	−0.386385	−	0.669238i	0.605575	−	0.795788i	$-0.292943\pi$
$283$	−6.50000	−	11.2583i	−0.386385	−	0.669238i	−0.991960	+	0.126550i	$0.959610\pi$
$284$	−8.00000	−	13.8564i	−0.474713	−	0.822226i
$285$		0			0
$286$	−4.00000			−0.236525
$287$	−30.0000	−	10.3923i	−1.77084	−	0.613438i
$288$	1.00000			0.0589256
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$		0			0
$291$	−8.50000	−	14.7224i	−0.498279	−	0.863044i
$292$	5.50000	−	9.52628i	0.321863	−	0.557483i
$293$	12.0000			0.701047			0.350524	−	0.936554i	$-0.386004\pi$
$293$	12.0000			0.701047			0.350524	+	0.936554i	$0.386004\pi$
$294$	5.50000	+	4.33013i	0.320767	+	0.252538i
$295$		0			0
$296$	−1.50000	+	2.59808i	−0.0871857	+	0.151010i
$297$	2.00000	+	3.46410i	0.116052	+	0.201008i
$298$	8.00000	+	13.8564i	0.463428	+	0.802680i
$299$	1.00000	−	1.73205i	0.0578315	−	0.100167i
$300$		0			0
$301$	−20.0000	−	6.92820i	−1.15278	−	0.399335i
$302$	19.0000			1.09333
$303$	−6.00000	+	10.3923i	−0.344691	+	0.597022i
$304$	−0.500000	−	0.866025i	−0.0286770	−	0.0496700i
$305$		0			0
$306$	−1.00000	+	1.73205i	−0.0571662	+	0.0990148i
$307$	20.0000			1.14146			0.570730	−	0.821138i	$-0.306660\pi$
$307$	20.0000			1.14146			0.570730	+	0.821138i	$0.306660\pi$
$308$	−8.00000	+	6.92820i	−0.455842	+	0.394771i
$309$	7.00000			0.398216
$310$		0			0
$311$	7.00000	+	12.1244i	0.396934	+	0.687509i	0.993346	−	0.115169i	$-0.0367410\pi$
$311$	7.00000	+	12.1244i	0.396934	+	0.687509i	−0.596412	+	0.802678i	$0.703408\pi$
$312$	−0.500000	−	0.866025i	−0.0283069	−	0.0490290i
$313$	9.00000	−	15.5885i	0.508710	−	0.881112i	−0.491239	−	0.871025i	$-0.663456\pi$
$313$	9.00000	−	15.5885i	0.508710	−	0.881112i	0.999949	−	0.0100869i	$-0.00321082\pi$
$314$	−21.0000			−1.18510
$315$		0			0
$316$	13.0000			0.731307
$317$	−11.0000	+	19.0526i	−0.617822	+	1.07010i	0.372061	+	0.928208i	$0.378651\pi$
$317$	−11.0000	+	19.0526i	−0.617822	+	1.07010i	−0.989882	+	0.141890i	$0.954682\pi$
$318$	−1.00000	−	1.73205i	−0.0560772	−	0.0971286i
$319$	8.00000	+	13.8564i	0.447914	+	0.775810i
$320$		0			0
$321$	6.00000			0.334887
$322$	−1.00000	−	5.19615i	−0.0557278	−	0.289570i
$323$	2.00000			0.111283
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$		0			0
$326$	−11.5000	−	19.9186i	−0.636926	−	1.10319i
$327$	9.50000	−	16.4545i	0.525351	−	0.909935i
$328$	12.0000			0.662589
$329$	−12.0000	+	10.3923i	−0.661581	+	0.572946i
$330$		0			0
$331$	−10.5000	+	18.1865i	−0.577132	+	0.999622i	0.418674	+	0.908137i	$0.362495\pi$
$331$	−10.5000	+	18.1865i	−0.577132	+	0.999622i	−0.995806	+	0.0914858i	$0.970838\pi$
$332$	3.00000	+	5.19615i	0.164646	+	0.285176i
$333$	−1.50000	−	2.59808i	−0.0821995	−	0.142374i
$334$	−5.00000	+	8.66025i	−0.273588	+	0.473868i
$335$		0			0
$336$	−2.50000	−	0.866025i	−0.136386	−	0.0472456i
$337$	−18.0000			−0.980522			−0.490261	−	0.871576i	$-0.663099\pi$
$337$	−18.0000			−0.980522			−0.490261	+	0.871576i	$0.663099\pi$
$338$	6.00000	−	10.3923i	0.326357	−	0.565267i
$339$	−9.00000	−	15.5885i	−0.488813	−	0.846649i
$340$		0			0
$341$		0			0
$342$	1.00000			0.0540738
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$	8.00000			0.431331
$345$		0			0
$346$	3.00000	+	5.19615i	0.161281	+	0.279347i
$347$	11.0000	+	19.0526i	0.590511	+	1.02279i	0.994164	+	0.107883i	$0.0344071\pi$
$347$	11.0000	+	19.0526i	0.590511	+	1.02279i	−0.403653	+	0.914912i	$0.632260\pi$
$348$	−2.00000	+	3.46410i	−0.107211	+	0.185695i
$349$	2.00000			0.107058			0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000			0.107058			0.0535288	+	0.998566i	$0.482953\pi$
$350$		0			0
$351$	1.00000			0.0533761
$352$	2.00000	−	3.46410i	0.106600	−	0.184637i
$353$	10.0000	+	17.3205i	0.532246	+	0.921878i	0.999291	+	0.0376440i	$0.0119853\pi$
$353$	10.0000	+	17.3205i	0.532246	+	0.921878i	−0.467045	+	0.884234i	$0.654681\pi$
$354$	−3.00000	−	5.19615i	−0.159448	−	0.276172i
$355$		0			0
$356$	−2.00000			−0.106000
$357$	4.00000	−	3.46410i	0.211702	−	0.183340i
$358$	−8.00000			−0.422813
$359$	3.00000	−	5.19615i	0.158334	−	0.274242i	−0.775934	−	0.630814i	$-0.782721\pi$
$359$	3.00000	−	5.19615i	0.158334	−	0.274242i	0.934268	+	0.356572i	$0.116054\pi$
$360$		0			0
$361$	9.00000	+	15.5885i	0.473684	+	0.820445i
$362$	9.00000	−	15.5885i	0.473029	−	0.819311i
$363$	5.00000			0.262432
$364$	0.500000	+	2.59808i	0.0262071	+	0.136176i
$365$		0			0
$366$	6.50000	−	11.2583i	0.339760	−	0.588482i
$367$	4.00000	+	6.92820i	0.208798	+	0.361649i	0.951336	−	0.308155i	$-0.0997115\pi$
$367$	4.00000	+	6.92820i	0.208798	+	0.361649i	−0.742538	+	0.669804i	$0.766378\pi$
$368$	1.00000	+	1.73205i	0.0521286	+	0.0902894i
$369$	−6.00000	+	10.3923i	−0.312348	+	0.541002i
$370$		0			0
$371$	1.00000	+	5.19615i	0.0519174	+	0.269771i
$372$		0			0
$373$	−11.5000	+	19.9186i	−0.595447	+	1.03135i	0.398036	+	0.917370i	$0.369692\pi$
$373$	−11.5000	+	19.9186i	−0.595447	+	1.03135i	−0.993484	+	0.113975i	$0.963641\pi$
$374$	4.00000	+	6.92820i	0.206835	+	0.358249i
$375$		0			0
$376$	3.00000	−	5.19615i	0.154713	−	0.267971i
$377$	4.00000			0.206010
$378$	2.00000	−	1.73205i	0.102869	−	0.0890871i
$379$	−5.00000			−0.256833			−0.128416	−	0.991720i	$-0.540989\pi$
$379$	−5.00000			−0.256833			−0.128416	+	0.991720i	$0.540989\pi$
$380$		0			0
$381$	0.500000	+	0.866025i	0.0256158	+	0.0443678i
$382$	−10.0000	−	17.3205i	−0.511645	−	0.886194i
$383$	7.00000	−	12.1244i	0.357683	−	0.619526i	−0.629890	−	0.776684i	$-0.716900\pi$
$383$	7.00000	−	12.1244i	0.357683	−	0.619526i	0.987573	+	0.157159i	$0.0502334\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	−10.0000			−0.508987
$387$	−4.00000	+	6.92820i	−0.203331	+	0.352180i
$388$	−8.50000	−	14.7224i	−0.431522	−	0.747418i
$389$	10.0000	+	17.3205i	0.507020	+	0.878185i	0.999967	+	0.00812520i	$0.00258636\pi$
$389$	10.0000	+	17.3205i	0.507020	+	0.878185i	−0.492947	+	0.870059i	$0.664080\pi$
$390$		0			0
$391$	−4.00000			−0.202289
$392$	5.50000	+	4.33013i	0.277792	+	0.218704i
$393$	2.00000			0.100887
$394$		0			0
$395$		0			0
$396$	2.00000	+	3.46410i	0.100504	+	0.174078i
$397$	9.00000	−	15.5885i	0.451697	−	0.782362i	−0.546795	−	0.837267i	$-0.684152\pi$
$397$	9.00000	−	15.5885i	0.451697	−	0.782362i	0.998492	+	0.0549046i	$0.0174855\pi$
$398$	15.0000			0.751882
$399$	−2.50000	−	0.866025i	−0.125157	−	0.0433555i
$400$		0			0
$401$	−2.00000	+	3.46410i	−0.0998752	+	0.172989i	−0.911633	−	0.411005i	$-0.865178\pi$
$401$	−2.00000	+	3.46410i	−0.0998752	+	0.172989i	0.811758	+	0.583994i	$0.198511\pi$
$402$	−1.50000	−	2.59808i	−0.0748132	−	0.129580i
$403$		0			0
$404$	−6.00000	+	10.3923i	−0.298511	+	0.517036i
$405$		0			0
$406$	8.00000	−	6.92820i	0.397033	−	0.343841i
$407$	−12.0000			−0.594818
$408$	−1.00000	+	1.73205i	−0.0495074	+	0.0857493i
$409$	5.50000	+	9.52628i	0.271957	+	0.471044i	0.969363	−	0.245633i	$-0.0789957\pi$
$409$	5.50000	+	9.52628i	0.271957	+	0.471044i	−0.697406	+	0.716677i	$0.745662\pi$
$410$		0			0
$411$	−5.00000	+	8.66025i	−0.246632	+	0.427179i
$412$	7.00000			0.344865
$413$	3.00000	+	15.5885i	0.147620	+	0.767058i
$414$	−2.00000			−0.0982946
$415$		0			0
$416$	−0.500000	−	0.866025i	−0.0245145	−	0.0424604i
$417$	6.50000	+	11.2583i	0.318306	+	0.551323i
$418$	2.00000	−	3.46410i	0.0978232	−	0.169435i
$419$	−16.0000			−0.781651			−0.390826	−	0.920465i	$-0.627810\pi$
$419$	−16.0000			−0.781651			−0.390826	+	0.920465i	$0.627810\pi$
$420$		0			0
$421$	1.00000			0.0487370			0.0243685	−	0.999703i	$-0.492242\pi$
$421$	1.00000			0.0487370			0.0243685	+	0.999703i	$0.492242\pi$
$422$	−1.50000	+	2.59808i	−0.0730189	+	0.126472i
$423$	3.00000	+	5.19615i	0.145865	+	0.252646i
$424$	−1.00000	−	1.73205i	−0.0485643	−	0.0841158i
$425$		0			0
$426$	16.0000			0.775203
$427$	−26.0000	+	22.5167i	−1.25823	+	1.08966i
$428$	6.00000			0.290021
$429$	2.00000	−	3.46410i	0.0965609	−	0.167248i
$430$		0			0
$431$	−3.00000	−	5.19615i	−0.144505	−	0.250290i	0.784683	−	0.619897i	$-0.212826\pi$
$431$	−3.00000	−	5.19615i	−0.144505	−	0.250290i	−0.929188	+	0.369607i	$0.879492\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	−2.00000			−0.0961139			−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000			−0.0961139			−0.0480569	+	0.998845i	$0.515303\pi$
$434$		0			0
$435$		0			0
$436$	9.50000	−	16.4545i	0.454967	−	0.788027i
$437$	1.00000	+	1.73205i	0.0478365	+	0.0828552i
$438$	5.50000	+	9.52628i	0.262800	+	0.455183i
$439$	11.5000	−	19.9186i	0.548865	−	0.950662i	−0.449488	−	0.893287i	$-0.648393\pi$
$439$	11.5000	−	19.9186i	0.548865	−	0.950662i	0.998353	−	0.0573756i	$-0.0182733\pi$
$440$		0			0
$441$	−6.50000	+	2.59808i	−0.309524	+	0.123718i
$442$	2.00000			0.0951303
$443$	−3.00000	+	5.19615i	−0.142534	+	0.246877i	−0.928450	−	0.371457i	$-0.878858\pi$
$443$	−3.00000	+	5.19615i	−0.142534	+	0.246877i	0.785916	+	0.618333i	$0.212192\pi$
$444$	−1.50000	−	2.59808i	−0.0711868	−	0.123299i
$445$		0			0
$446$	9.50000	−	16.4545i	0.449838	−	0.779142i
$447$	−16.0000			−0.756774
$448$	−2.50000	−	0.866025i	−0.118114	−	0.0409159i
$449$	2.00000			0.0943858			0.0471929	−	0.998886i	$-0.484972\pi$
$449$	2.00000			0.0943858			0.0471929	+	0.998886i	$0.484972\pi$
$450$		0			0
$451$	24.0000	+	41.5692i	1.13012	+	1.95742i
$452$	−9.00000	−	15.5885i	−0.423324	−	0.733219i
$453$	−9.50000	+	16.4545i	−0.446349	+	0.773099i
$454$	−8.00000			−0.375459
$455$		0			0
$456$	1.00000			0.0468293
$457$	−18.5000	+	32.0429i	−0.865393	+	1.49891i	0.00126243	+	0.999999i	$0.499598\pi$
$457$	−18.5000	+	32.0429i	−0.865393	+	1.49891i	−0.866656	+	0.498906i	$0.833735\pi$
$458$	3.50000	+	6.06218i	0.163544	+	0.283267i
$459$	−1.00000	−	1.73205i	−0.0466760	−	0.0808452i
$460$		0			0
$461$	26.0000			1.21094			0.605470	−	0.795868i	$-0.292985\pi$
$461$	26.0000			1.21094			0.605470	+	0.795868i	$0.292985\pi$
$462$	−2.00000	−	10.3923i	−0.0930484	−	0.483494i
$463$	−3.00000			−0.139422			−0.0697109	−	0.997567i	$-0.522208\pi$
$463$	−3.00000			−0.139422			−0.0697109	+	0.997567i	$0.522208\pi$
$464$	−2.00000	+	3.46410i	−0.0928477	+	0.160817i
$465$		0			0
$466$	2.00000	+	3.46410i	0.0926482	+	0.160471i
$467$	−15.0000	+	25.9808i	−0.694117	+	1.20225i	0.276360	+	0.961054i	$0.410872\pi$
$467$	−15.0000	+	25.9808i	−0.694117	+	1.20225i	−0.970477	+	0.241192i	$0.922462\pi$
$468$	1.00000			0.0462250
$469$	1.50000	+	7.79423i	0.0692636	+	0.359904i
$470$		0			0
$471$	10.5000	−	18.1865i	0.483814	−	0.837991i
$472$	−3.00000	−	5.19615i	−0.138086	−	0.239172i
$473$	16.0000	+	27.7128i	0.735681	+	1.27424i
$474$	−6.50000	+	11.2583i	−0.298555	+	0.517112i
$475$		0			0
$476$	4.00000	−	3.46410i	0.183340	−	0.158777i
$477$	2.00000			0.0915737
$478$	6.00000	−	10.3923i	0.274434	−	0.475333i
$479$	17.0000	+	29.4449i	0.776750	+	1.34537i	0.933806	+	0.357780i	$0.116466\pi$
$479$	17.0000	+	29.4449i	0.776750	+	1.34537i	−0.157056	+	0.987590i	$0.550200\pi$
$480$		0			0
$481$	−1.50000	+	2.59808i	−0.0683941	+	0.118462i
$482$	13.0000			0.592134
$483$	5.00000	+	1.73205i	0.227508	+	0.0788110i
$484$	5.00000			0.227273
$485$		0			0
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−20.0000	−	34.6410i	−0.906287	−	1.56973i	−0.819181	−	0.573535i	$-0.805572\pi$
$487$	−20.0000	−	34.6410i	−0.906287	−	1.56973i	−0.0871056	−	0.996199i	$-0.527762\pi$
$488$	6.50000	−	11.2583i	0.294241	−	0.509641i
$489$	23.0000			1.04010
$490$		0			0
$491$	18.0000			0.812329			0.406164	−	0.913800i	$-0.366866\pi$
$491$	18.0000			0.812329			0.406164	+	0.913800i	$0.366866\pi$
$492$	−6.00000	+	10.3923i	−0.270501	+	0.468521i
$493$	−4.00000	−	6.92820i	−0.180151	−	0.312031i
$494$	−0.500000	−	0.866025i	−0.0224961	−	0.0389643i
$495$		0			0
$496$		0			0
$497$	−40.0000	−	13.8564i	−1.79425	−	0.621545i
$498$	−6.00000			−0.268866
$499$	13.5000	−	23.3827i	0.604343	−	1.04675i	−0.387812	−	0.921739i	$-0.626769\pi$
$499$	13.5000	−	23.3827i	0.604343	−	1.04675i	0.992155	−	0.125014i	$-0.0398977\pi$
$500$		0			0
$501$	−5.00000	−	8.66025i	−0.223384	−	0.386912i
$502$	−12.0000	+	20.7846i	−0.535586	+	0.927663i
$503$	4.00000			0.178351			0.0891756	−	0.996016i	$-0.471577\pi$
$503$	4.00000			0.178351			0.0891756	+	0.996016i	$0.471577\pi$
$504$	2.00000	−	1.73205i	0.0890871	−	0.0771517i
$505$		0			0
$506$	−4.00000	+	6.92820i	−0.177822	+	0.307996i
$507$	6.00000	+	10.3923i	0.266469	+	0.461538i
$508$	0.500000	+	0.866025i	0.0221839	+	0.0384237i
$509$	18.0000	−	31.1769i	0.797836	−	1.38189i	−0.123187	−	0.992384i	$-0.539311\pi$
$509$	18.0000	−	31.1769i	0.797836	−	1.38189i	0.921023	−	0.389509i	$-0.127355\pi$
$510$		0			0
$511$	−5.50000	−	28.5788i	−0.243306	−	1.26425i
$512$	1.00000			0.0441942
$513$	−0.500000	+	0.866025i	−0.0220755	+	0.0382360i
$514$	4.00000	+	6.92820i	0.176432	+	0.305590i
$515$		0			0
$516$	−4.00000	+	6.92820i	−0.176090	+	0.304997i
$517$	24.0000			1.05552
$518$	1.50000	+	7.79423i	0.0659062	+	0.342459i
$519$	−6.00000			−0.263371
$520$		0			0
$521$	−3.00000	−	5.19615i	−0.131432	−	0.227648i	0.792797	−	0.609486i	$-0.208624\pi$
$521$	−3.00000	−	5.19615i	−0.131432	−	0.227648i	−0.924229	+	0.381839i	$0.875291\pi$
$522$	−2.00000	−	3.46410i	−0.0875376	−	0.151620i
$523$	−8.00000	+	13.8564i	−0.349816	+	0.605898i	−0.986216	−	0.165460i	$-0.947089\pi$
$523$	−8.00000	+	13.8564i	−0.349816	+	0.605898i	0.636401	+	0.771358i	$0.280422\pi$
$524$	2.00000			0.0873704
$525$		0			0
$526$	32.0000			1.39527
$527$		0			0
$528$	2.00000	+	3.46410i	0.0870388	+	0.150756i
$529$	9.50000	+	16.4545i	0.413043	+	0.715412i
$530$		0			0
$531$	6.00000			0.260378
$532$	−2.50000	−	0.866025i	−0.108389	−	0.0375470i
$533$	12.0000			0.519778
$534$	1.00000	−	1.73205i	0.0432742	−	0.0749532i
$535$		0			0
$536$	−1.50000	−	2.59808i	−0.0647901	−	0.112220i
$537$	4.00000	−	6.92820i	0.172613	−	0.298974i
$538$		0			0
$539$	−4.00000	+	27.7128i	−0.172292	+	1.19368i
$540$		0			0
$541$	−8.50000	+	14.7224i	−0.365444	+	0.632967i	−0.988847	−	0.148933i	$-0.952416\pi$
$541$	−8.50000	+	14.7224i	−0.365444	+	0.632967i	0.623404	+	0.781900i	$0.285749\pi$
$542$	10.0000	+	17.3205i	0.429537	+	0.743980i
$543$	9.00000	+	15.5885i	0.386227	+	0.668965i
$544$	−1.00000	+	1.73205i	−0.0428746	+	0.0742611i
$545$		0			0
$546$	−2.50000	−	0.866025i	−0.106990	−	0.0370625i
$547$	−12.0000			−0.513083			−0.256541	−	0.966533i	$-0.582583\pi$
$547$	−12.0000			−0.513083			−0.256541	+	0.966533i	$0.582583\pi$
$548$	−5.00000	+	8.66025i	−0.213589	+	0.369948i
$549$	6.50000	+	11.2583i	0.277413	+	0.480494i
$550$		0			0
$551$	−2.00000	+	3.46410i	−0.0852029	+	0.147576i
$552$	−2.00000			−0.0851257
$553$	26.0000	−	22.5167i	1.10563	−	0.957506i
$554$	1.00000			0.0424859
$555$		0			0
$556$	6.50000	+	11.2583i	0.275661	+	0.477460i
$557$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$557$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$558$		0			0
$559$	8.00000			0.338364
$560$		0			0
$561$	−8.00000			−0.337760
$562$	9.00000	−	15.5885i	0.379642	−	0.657559i
$563$	14.0000	+	24.2487i	0.590030	+	1.02196i	0.994228	+	0.107290i	$0.0342173\pi$
$563$	14.0000	+	24.2487i	0.590030	+	1.02196i	−0.404198	+	0.914671i	$0.632449\pi$
$564$	3.00000	+	5.19615i	0.126323	+	0.218797i
$565$		0			0
$566$	13.0000			0.546431
$567$	0.500000	+	2.59808i	0.0209980	+	0.109109i
$568$	16.0000			0.671345
$569$	20.0000	−	34.6410i	0.838444	−	1.45223i	−0.0527519	−	0.998608i	$-0.516799\pi$
$569$	20.0000	−	34.6410i	0.838444	−	1.45223i	0.891196	−	0.453619i	$-0.149867\pi$
$570$		0			0
$571$	17.5000	+	30.3109i	0.732352	+	1.26847i	0.955875	+	0.293773i	$0.0949108\pi$
$571$	17.5000	+	30.3109i	0.732352	+	1.26847i	−0.223523	+	0.974699i	$0.571756\pi$
$572$	2.00000	−	3.46410i	0.0836242	−	0.144841i
$573$	20.0000			0.835512
$574$	24.0000	−	20.7846i	1.00174	−	0.867533i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−11.0000	−	19.0526i	−0.457936	−	0.793168i	0.540916	−	0.841077i	$-0.318078\pi$
$577$	−11.0000	−	19.0526i	−0.457936	−	0.793168i	−0.998852	+	0.0479084i	$0.984744\pi$
$578$	6.50000	+	11.2583i	0.270364	+	0.468285i
$579$	5.00000	−	8.66025i	0.207793	−	0.359908i
$580$		0			0
$581$	15.0000	+	5.19615i	0.622305	+	0.215573i
$582$	17.0000			0.704673
$583$	4.00000	−	6.92820i	0.165663	−	0.286937i
$584$	5.50000	+	9.52628i	0.227592	+	0.394200i
$585$		0			0
$586$	−6.00000	+	10.3923i	−0.247858	+	0.429302i
$587$	−42.0000			−1.73353			−0.866763	−	0.498721i	$-0.833803\pi$
$587$	−42.0000			−1.73353			−0.866763	+	0.498721i	$0.833803\pi$
$588$	−6.50000	+	2.59808i	−0.268055	+	0.107143i
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−1.50000	−	2.59808i	−0.0616496	−	0.106780i
$593$	−21.0000	+	36.3731i	−0.862367	+	1.49366i	0.00727173	+	0.999974i	$0.497685\pi$
$593$	−21.0000	+	36.3731i	−0.862367	+	1.49366i	−0.869638	+	0.493689i	$0.835648\pi$
$594$	−4.00000			−0.164122
$595$		0			0
$596$	−16.0000			−0.655386
$597$	−7.50000	+	12.9904i	−0.306955	+	0.531661i
$598$	1.00000	+	1.73205i	0.0408930	+	0.0708288i
$599$	3.00000	+	5.19615i	0.122577	+	0.212309i	0.920783	−	0.390075i	$-0.127551\pi$
$599$	3.00000	+	5.19615i	0.122577	+	0.212309i	−0.798206	+	0.602384i	$0.794218\pi$
$600$		0			0
$601$	−29.0000			−1.18293			−0.591467	−	0.806329i	$-0.701451\pi$
$601$	−29.0000			−1.18293			−0.591467	+	0.806329i	$0.701451\pi$
$602$	16.0000	−	13.8564i	0.652111	−	0.564745i
$603$	3.00000			0.122169
$604$	−9.50000	+	16.4545i	−0.386550	+	0.669523i
$605$		0			0
$606$	−6.00000	−	10.3923i	−0.243733	−	0.422159i
$607$	−0.500000	+	0.866025i	−0.0202944	+	0.0351509i	−0.875994	−	0.482322i	$-0.839794\pi$
$607$	−0.500000	+	0.866025i	−0.0202944	+	0.0351509i	0.855700	+	0.517472i	$0.173127\pi$
$608$	1.00000			0.0405554
$609$	2.00000	+	10.3923i	0.0810441	+	0.421117i
$610$		0			0
$611$	3.00000	−	5.19615i	0.121367	−	0.210214i
$612$	−1.00000	−	1.73205i	−0.0404226	−	0.0700140i
$613$	−3.00000	−	5.19615i	−0.121169	−	0.209871i	0.799060	−	0.601251i	$-0.205331\pi$
$613$	−3.00000	−	5.19615i	−0.121169	−	0.209871i	−0.920229	+	0.391381i	$0.871998\pi$
$614$	−10.0000	+	17.3205i	−0.403567	+	0.698999i
$615$		0			0
$616$	−2.00000	−	10.3923i	−0.0805823	−	0.418718i
$617$	44.0000			1.77137			0.885687	−	0.464283i	$-0.153688\pi$
$617$	44.0000			1.77137			0.885687	+	0.464283i	$0.153688\pi$
$618$	−3.50000	+	6.06218i	−0.140791	+	0.243857i
$619$	−22.0000	−	38.1051i	−0.884255	−	1.53157i	−0.846566	−	0.532284i	$-0.821334\pi$
$619$	−22.0000	−	38.1051i	−0.884255	−	1.53157i	−0.0376891	−	0.999290i	$-0.512000\pi$
$620$		0			0
$621$	1.00000	−	1.73205i	0.0401286	−	0.0695048i
$622$	−14.0000			−0.561349
$623$	−4.00000	+	3.46410i	−0.160257	+	0.138786i
$624$	1.00000			0.0400320
$625$		0			0
$626$	9.00000	+	15.5885i	0.359712	+	0.623040i
$627$	2.00000	+	3.46410i	0.0798723	+	0.138343i
$628$	10.5000	−	18.1865i	0.418996	−	0.725722i
$629$	6.00000			0.239236
$630$		0			0
$631$	17.0000			0.676759			0.338380	−	0.941010i	$-0.390121\pi$
$631$	17.0000			0.676759			0.338380	+	0.941010i	$0.390121\pi$
$632$	−6.50000	+	11.2583i	−0.258556	+	0.447832i
$633$	−1.50000	−	2.59808i	−0.0596196	−	0.103264i
$634$	−11.0000	−	19.0526i	−0.436866	−	0.756674i
$635$		0			0
$636$	2.00000			0.0793052
$637$	5.50000	+	4.33013i	0.217918	+	0.171566i
$638$	−16.0000			−0.633446
$639$	−8.00000	+	13.8564i	−0.316475	+	0.548151i
$640$		0			0
$641$	−8.00000	−	13.8564i	−0.315981	−	0.547295i	0.663665	−	0.748030i	$-0.269000\pi$
$641$	−8.00000	−	13.8564i	−0.315981	−	0.547295i	−0.979646	+	0.200735i	$0.935667\pi$
$642$	−3.00000	+	5.19615i	−0.118401	+	0.205076i
$643$	11.0000			0.433798			0.216899	−	0.976194i	$-0.430406\pi$
$643$	11.0000			0.433798			0.216899	+	0.976194i	$0.430406\pi$
$644$	5.00000	+	1.73205i	0.197028	+	0.0682524i
$645$		0			0
$646$	−1.00000	+	1.73205i	−0.0393445	+	0.0681466i
$647$	−6.00000	−	10.3923i	−0.235884	−	0.408564i	0.723645	−	0.690172i	$-0.242465\pi$
$647$	−6.00000	−	10.3923i	−0.235884	−	0.408564i	−0.959529	+	0.281609i	$0.909132\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	12.0000	−	20.7846i	0.471041	−	0.815867i
$650$		0			0
$651$		0			0
$652$	23.0000			0.900750
$653$	8.00000	−	13.8564i	0.313064	−	0.542243i	−0.665960	−	0.745988i	$-0.731978\pi$
$653$	8.00000	−	13.8564i	0.313064	−	0.542243i	0.979024	+	0.203744i	$0.0653112\pi$
$654$	9.50000	+	16.4545i	0.371479	+	0.643421i
$655$		0			0
$656$	−6.00000	+	10.3923i	−0.234261	+	0.405751i
$657$	−11.0000			−0.429151
$658$	−3.00000	−	15.5885i	−0.116952	−	0.607701i
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$		0			0
$661$	12.5000	+	21.6506i	0.486194	+	0.842112i	0.999874	−	0.0158695i	$-0.00505163\pi$
$661$	12.5000	+	21.6506i	0.486194	+	0.842112i	−0.513680	+	0.857982i	$0.671718\pi$
$662$	−10.5000	−	18.1865i	−0.408094	−	0.706840i
$663$	−1.00000	+	1.73205i	−0.0388368	+	0.0672673i
$664$	−6.00000			−0.232845
$665$		0			0
$666$	3.00000			0.116248
$667$	4.00000	−	6.92820i	0.154881	−	0.268261i
$668$	−5.00000	−	8.66025i	−0.193456	−	0.335075i
$669$	9.50000	+	16.4545i	0.367291	+	0.636167i
$670$		0			0
$671$	52.0000			2.00744
$672$	2.00000	−	1.73205i	0.0771517	−	0.0668153i
$673$	−9.00000			−0.346925			−0.173462	−	0.984841i	$-0.555495\pi$
$673$	−9.00000			−0.346925			−0.173462	+	0.984841i	$0.555495\pi$
$674$	9.00000	−	15.5885i	0.346667	−	0.600445i
$675$		0			0
$676$	6.00000	+	10.3923i	0.230769	+	0.399704i
$677$	1.00000	−	1.73205i	0.0384331	−	0.0665681i	−0.846169	−	0.532915i	$-0.821097\pi$
$677$	1.00000	−	1.73205i	0.0384331	−	0.0665681i	0.884602	+	0.466347i	$0.154430\pi$
$678$	18.0000			0.691286
$679$	−42.5000	−	14.7224i	−1.63100	−	0.564995i
$680$		0			0
$681$	4.00000	−	6.92820i	0.153280	−	0.265489i
$682$		0			0
$683$	−24.0000	−	41.5692i	−0.918334	−	1.59060i	−0.801945	−	0.597398i	$-0.796201\pi$
$683$	−24.0000	−	41.5692i	−0.918334	−	1.59060i	−0.116390	−	0.993204i	$-0.537132\pi$
$684$	−0.500000	+	0.866025i	−0.0191180	+	0.0331133i
$685$		0			0
$686$	18.5000	−	0.866025i	0.706333	−	0.0330650i
$687$	−7.00000			−0.267067
$688$	−4.00000	+	6.92820i	−0.152499	+	0.264135i
$689$	−1.00000	−	1.73205i	−0.0380970	−	0.0659859i
$690$		0			0
$691$	19.5000	−	33.7750i	0.741815	−	1.28486i	−0.209853	−	0.977733i	$-0.567299\pi$
$691$	19.5000	−	33.7750i	0.741815	−	1.28486i	0.951668	−	0.307128i	$-0.0993681\pi$
$692$	−6.00000			−0.228086
$693$	10.0000	+	3.46410i	0.379869	+	0.131590i
$694$	−22.0000			−0.835109
$695$		0			0
$696$	−2.00000	−	3.46410i	−0.0758098	−	0.131306i
$697$	−12.0000	−	20.7846i	−0.454532	−	0.787273i
$698$	−1.00000	+	1.73205i	−0.0378506	+	0.0655591i
$699$	−4.00000			−0.151294
$700$		0			0
$701$	−18.0000			−0.679851			−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000			−0.679851			−0.339925	+	0.940452i	$0.610402\pi$
$702$	−0.500000	+	0.866025i	−0.0188713	+	0.0326860i
$703$	−1.50000	−	2.59808i	−0.0565736	−	0.0979883i
$704$	2.00000	+	3.46410i	0.0753778	+	0.130558i
$705$		0			0
$706$	−20.0000			−0.752710
$707$	6.00000	+	31.1769i	0.225653	+	1.17253i
$708$	6.00000			0.225494
$709$	5.50000	−	9.52628i	0.206557	−	0.357767i	−0.744071	−	0.668101i	$-0.767108\pi$
$709$	5.50000	−	9.52628i	0.206557	−	0.357767i	0.950628	+	0.310334i	$0.100441\pi$
$710$		0			0
$711$	−6.50000	−	11.2583i	−0.243769	−	0.422220i
$712$	1.00000	−	1.73205i	0.0374766	−	0.0649113i
$713$		0			0
$714$	1.00000	+	5.19615i	0.0374241	+	0.194461i
$715$		0			0
$716$	4.00000	−	6.92820i	0.149487	−	0.258919i
$717$	6.00000	+	10.3923i	0.224074	+	0.388108i
$718$	3.00000	+	5.19615i	0.111959	+	0.193919i
$719$	−4.00000	+	6.92820i	−0.149175	+	0.258378i	−0.930923	−	0.365216i	$-0.880995\pi$
$719$	−4.00000	+	6.92820i	−0.149175	+	0.258378i	0.781748	+	0.623595i	$0.214328\pi$
$720$		0			0
$721$	14.0000	−	12.1244i	0.521387	−	0.451535i
$722$	−18.0000			−0.669891
$723$	−6.50000	+	11.2583i	−0.241738	+	0.418702i
$724$	9.00000	+	15.5885i	0.334482	+	0.579340i
$725$		0			0
$726$	−2.50000	+	4.33013i	−0.0927837	+	0.160706i
$727$	−1.00000			−0.0370879			−0.0185440	−	0.999828i	$-0.505903\pi$
$727$	−1.00000			−0.0370879			−0.0185440	+	0.999828i	$0.505903\pi$
$728$	−2.50000	−	0.866025i	−0.0926562	−	0.0320970i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−8.00000	−	13.8564i	−0.295891	−	0.512498i
$732$	6.50000	+	11.2583i	0.240247	+	0.416120i
$733$	17.5000	−	30.3109i	0.646377	−	1.11956i	−0.337604	−	0.941288i	$-0.609617\pi$
$733$	17.5000	−	30.3109i	0.646377	−	1.11956i	0.983982	−	0.178270i	$-0.0570501\pi$
$734$	−8.00000			−0.295285
$735$		0			0
$736$	−2.00000			−0.0737210
$737$	6.00000	−	10.3923i	0.221013	−	0.382805i
$738$	−6.00000	−	10.3923i	−0.220863	−	0.382546i
$739$	0.500000	+	0.866025i	0.0183928	+	0.0318573i	0.875075	−	0.483987i	$-0.160812\pi$
$739$	0.500000	+	0.866025i	0.0183928	+	0.0318573i	−0.856683	+	0.515844i	$0.827478\pi$
$740$		0			0
$741$	1.00000			0.0367359
$742$	−5.00000	−	1.73205i	−0.183556	−	0.0635856i
$743$	−6.00000			−0.220119			−0.110059	−	0.993925i	$-0.535104\pi$
$743$	−6.00000			−0.220119			−0.110059	+	0.993925i	$0.535104\pi$
$744$		0			0
$745$		0			0
$746$	−11.5000	−	19.9186i	−0.421045	−	0.729271i
$747$	3.00000	−	5.19615i	0.109764	−	0.190117i
$748$	−8.00000			−0.292509
$749$	12.0000	−	10.3923i	0.438470	−	0.379727i
$750$		0			0
$751$	−9.50000	+	16.4545i	−0.346660	+	0.600433i	−0.985654	−	0.168779i	$-0.946018\pi$
$751$	−9.50000	+	16.4545i	−0.346660	+	0.600433i	0.638994	+	0.769212i	$0.279351\pi$
$752$	3.00000	+	5.19615i	0.109399	+	0.189484i
$753$	−12.0000	−	20.7846i	−0.437304	−	0.757433i
$754$	−2.00000	+	3.46410i	−0.0728357	+	0.126155i
$755$		0			0
$756$	0.500000	+	2.59808i	0.0181848	+	0.0944911i
$757$	1.00000			0.0363456			0.0181728	−	0.999835i	$-0.494215\pi$
$757$	1.00000			0.0363456			0.0181728	+	0.999835i	$0.494215\pi$
$758$	2.50000	−	4.33013i	0.0908041	−	0.157277i
$759$	−4.00000	−	6.92820i	−0.145191	−	0.251478i
$760$		0			0
$761$	−17.0000	+	29.4449i	−0.616250	+	1.06738i	0.373914	+	0.927463i	$0.378015\pi$
$761$	−17.0000	+	29.4449i	−0.616250	+	1.06738i	−0.990164	+	0.139912i	$0.955318\pi$
$762$	−1.00000			−0.0362262
$763$	−9.50000	−	49.3634i	−0.343923	−	1.78708i
$764$	20.0000			0.723575
$765$		0			0
$766$	7.00000	+	12.1244i	0.252920	+	0.438071i
$767$	−3.00000	−	5.19615i	−0.108324	−	0.187622i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	−50.0000			−1.80305			−0.901523	−	0.432731i	$-0.857550\pi$
$769$	−50.0000			−1.80305			−0.901523	+	0.432731i	$0.857550\pi$
$770$		0			0
$771$	−8.00000			−0.288113
$772$	5.00000	−	8.66025i	0.179954	−	0.311689i
$773$	16.0000	+	27.7128i	0.575480	+	0.996761i	0.995989	+	0.0894724i	$0.0285181\pi$
$773$	16.0000	+	27.7128i	0.575480	+	0.996761i	−0.420509	+	0.907288i	$0.638149\pi$
$774$	−4.00000	−	6.92820i	−0.143777	−	0.249029i
$775$		0			0
$776$	17.0000			0.610264
$777$	−7.50000	−	2.59808i	−0.269061	−	0.0932055i
$778$	−20.0000			−0.717035
$779$	−6.00000	+	10.3923i	−0.214972	+	0.372343i
$780$		0			0
$781$	32.0000	+	55.4256i	1.14505	+	1.98328i
$782$	2.00000	−	3.46410i	0.0715199	−	0.123876i
$783$	4.00000			0.142948
$784$	−6.50000	+	2.59808i	−0.232143	+	0.0927884i
$785$		0			0
$786$	−1.00000	+	1.73205i	−0.0356688	+	0.0617802i
$787$	−11.5000	−	19.9186i	−0.409931	−	0.710021i	0.584951	−	0.811069i	$-0.301114\pi$
$787$	−11.5000	−	19.9186i	−0.409931	−	0.710021i	−0.994882	+	0.101048i	$0.967780\pi$
$788$		0			0
$789$	−16.0000	+	27.7128i	−0.569615	+	0.986602i
$790$		0			0
$791$	−45.0000	−	15.5885i	−1.60002	−	0.554262i
$792$	−4.00000			−0.142134
$793$	6.50000	−	11.2583i	0.230822	−	0.399795i
$794$	9.00000	+	15.5885i	0.319398	+	0.553214i
$795$		0			0
$796$	−7.50000	+	12.9904i	−0.265830	+	0.460432i
$797$	42.0000			1.48772			0.743858	−	0.668338i	$-0.232994\pi$
$797$	42.0000			1.48772			0.743858	+	0.668338i	$0.232994\pi$
$798$	2.00000	−	1.73205i	0.0707992	−	0.0613139i
$799$	−12.0000			−0.424529
$800$		0			0
$801$	1.00000	+	1.73205i	0.0353333	+	0.0611990i
$802$	−2.00000	−	3.46410i	−0.0706225	−	0.122322i
$803$	−22.0000	+	38.1051i	−0.776363	+	1.34470i
$804$	3.00000			0.105802
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−6.00000	−	10.3923i	−0.211079	−	0.365600i
$809$	−7.00000	−	12.1244i	−0.246107	−	0.426270i	0.716335	−	0.697756i	$-0.245818\pi$
$809$	−7.00000	−	12.1244i	−0.246107	−	0.426270i	−0.962442	+	0.271487i	$0.912485\pi$
$810$		0			0
$811$	−5.00000			−0.175574			−0.0877869	−	0.996139i	$-0.527979\pi$
$811$	−5.00000			−0.175574			−0.0877869	+	0.996139i	$0.527979\pi$
$812$	2.00000	+	10.3923i	0.0701862	+	0.364698i
$813$	−20.0000			−0.701431
$814$	6.00000	−	10.3923i	0.210300	−	0.364250i
$815$		0			0
$816$	−1.00000	−	1.73205i	−0.0350070	−	0.0606339i
$817$	−4.00000	+	6.92820i	−0.139942	+	0.242387i
$818$	−11.0000			−0.384606
$819$	2.00000	−	1.73205i	0.0698857	−	0.0605228i
$820$		0			0
$821$	22.0000	−	38.1051i	0.767805	−	1.32988i	−0.170945	−	0.985281i	$-0.554682\pi$
$821$	22.0000	−	38.1051i	0.767805	−	1.32988i	0.938751	−	0.344597i	$-0.111985\pi$
$822$	−5.00000	−	8.66025i	−0.174395	−	0.302061i
$823$	−4.50000	−	7.79423i	−0.156860	−	0.271690i	0.776875	−	0.629655i	$-0.216804\pi$
$823$	−4.50000	−	7.79423i	−0.156860	−	0.271690i	−0.933735	+	0.357966i	$0.883471\pi$
$824$	−3.50000	+	6.06218i	−0.121928	+	0.211186i
$825$		0			0
$826$	−15.0000	−	5.19615i	−0.521917	−	0.180797i
$827$	40.0000			1.39094			0.695468	−	0.718557i	$-0.255197\pi$
$827$	40.0000			1.39094			0.695468	+	0.718557i	$0.255197\pi$
$828$	1.00000	−	1.73205i	0.0347524	−	0.0601929i
$829$	1.50000	+	2.59808i	0.0520972	+	0.0902349i	0.890898	−	0.454204i	$-0.150076\pi$
$829$	1.50000	+	2.59808i	0.0520972	+	0.0902349i	−0.838801	+	0.544438i	$0.816743\pi$
$830$		0			0
$831$	−0.500000	+	0.866025i	−0.0173448	+	0.0300421i
$832$	1.00000			0.0346688
$833$	2.00000	−	13.8564i	0.0692959	−	0.480096i
$834$	−13.0000			−0.450153
$835$		0			0
$836$	2.00000	+	3.46410i	0.0691714	+	0.119808i
$837$		0			0
$838$	8.00000	−	13.8564i	0.276355	−	0.478662i
$839$	50.0000			1.72619			0.863096	−	0.505040i	$-0.168522\pi$
$839$	50.0000			1.72619			0.863096	+	0.505040i	$0.168522\pi$
$840$		0			0
$841$	−13.0000			−0.448276
$842$	−0.500000	+	0.866025i	−0.0172311	+	0.0298452i
$843$	9.00000	+	15.5885i	0.309976	+	0.536895i
$844$	−1.50000	−	2.59808i	−0.0516321	−	0.0894295i
$845$		0			0
$846$	−6.00000			−0.206284
$847$	10.0000	−	8.66025i	0.343604	−	0.297570i
$848$	2.00000			0.0686803
$849$	−6.50000	+	11.2583i	−0.223079	+	0.386385i
$850$		0			0
$851$	3.00000	+	5.19615i	0.102839	+	0.178122i
$852$	−8.00000	+	13.8564i	−0.274075	+	0.474713i
$853$	−38.0000			−1.30110			−0.650548	−	0.759465i	$-0.725461\pi$
$853$	−38.0000			−1.30110			−0.650548	+	0.759465i	$0.725461\pi$
$854$	−6.50000	−	33.7750i	−0.222425	−	1.15576i
$855$		0			0
$856$	−3.00000	+	5.19615i	−0.102538	+	0.177601i
$857$	−13.0000	−	22.5167i	−0.444072	−	0.769154i	0.553915	−	0.832573i	$-0.313133\pi$
$857$	−13.0000	−	22.5167i	−0.444072	−	0.769154i	−0.997987	+	0.0634184i	$0.979800\pi$
$858$	2.00000	+	3.46410i	0.0682789	+	0.118262i
$859$	−2.00000	+	3.46410i	−0.0682391	+	0.118194i	−0.898126	−	0.439738i	$-0.855071\pi$
$859$	−2.00000	+	3.46410i	−0.0682391	+	0.118194i	0.829887	+	0.557931i	$0.188405\pi$
$860$		0			0
$861$	6.00000	+	31.1769i	0.204479	+	1.06251i
$862$	6.00000			0.204361
$863$	17.0000	−	29.4449i	0.578687	−	1.00231i	−0.416944	−	0.908932i	$-0.636899\pi$
$863$	17.0000	−	29.4449i	0.578687	−	1.00231i	0.995630	−	0.0933825i	$-0.0297679\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$		0			0
$866$	1.00000	−	1.73205i	0.0339814	−	0.0588575i
$867$	−13.0000			−0.441503
$868$		0			0
$869$	−52.0000			−1.76398
$870$		0			0
$871$	−1.50000	−	2.59808i	−0.0508256	−	0.0880325i
$872$	9.50000	+	16.4545i	0.321711	+	0.557219i
$873$	−8.50000	+	14.7224i	−0.287681	+	0.498279i
$874$	−2.00000			−0.0676510
$875$		0			0
$876$	−11.0000			−0.371656
$877$	6.50000	−	11.2583i	0.219489	−	0.380167i	−0.735163	−	0.677891i	$-0.762894\pi$
$877$	6.50000	−	11.2583i	0.219489	−	0.380167i	0.954652	+	0.297724i	$0.0962275\pi$
$878$	11.5000	+	19.9186i	0.388106	+	0.672220i
$879$	−6.00000	−	10.3923i	−0.202375	−	0.350524i
$880$		0			0
$881$	−40.0000			−1.34763			−0.673817	−	0.738898i	$-0.735346\pi$
$881$	−40.0000			−1.34763			−0.673817	+	0.738898i	$0.735346\pi$
$882$	1.00000	−	6.92820i	0.0336718	−	0.233285i
$883$	−1.00000			−0.0336527			−0.0168263	−	0.999858i	$-0.505356\pi$
$883$	−1.00000			−0.0336527			−0.0168263	+	0.999858i	$0.505356\pi$
$884$	−1.00000	+	1.73205i	−0.0336336	+	0.0582552i
$885$		0			0
$886$	−3.00000	−	5.19615i	−0.100787	−	0.174568i
$887$	23.0000	−	39.8372i	0.772264	−	1.33760i	−0.164055	−	0.986451i	$-0.552457\pi$
$887$	23.0000	−	39.8372i	0.772264	−	1.33760i	0.936319	−	0.351150i	$-0.114209\pi$
$888$	3.00000			0.100673
$889$	2.50000	+	0.866025i	0.0838473	+	0.0290456i
$890$		0			0
$891$	2.00000	−	3.46410i	0.0670025	−	0.116052i
$892$	9.50000	+	16.4545i	0.318084	+	0.550937i
$893$	3.00000	+	5.19615i	0.100391	+	0.173883i
$894$	8.00000	−	13.8564i	0.267560	−	0.463428i
$895$		0			0
$896$	2.00000	−	1.73205i	0.0668153	−	0.0578638i
$897$	−2.00000			−0.0667781
$898$	−1.00000	+	1.73205i	−0.0333704	+	0.0577993i
$899$		0			0
$900$		0			0
$901$	−2.00000	+	3.46410i	−0.0666297	+	0.115406i
$902$	−48.0000			−1.59823
$903$	4.00000	+	20.7846i	0.133112	+	0.691669i
$904$	18.0000			0.598671
$905$		0			0
$906$	−9.50000	−	16.4545i	−0.315616	−	0.546664i
$907$	23.5000	+	40.7032i	0.780305	+	1.35153i	0.931764	+	0.363064i	$0.118269\pi$
$907$	23.5000	+	40.7032i	0.780305	+	1.35153i	−0.151460	+	0.988463i	$0.548397\pi$
$908$	4.00000	−	6.92820i	0.132745	−	0.229920i
$909$	12.0000			0.398015
$910$		0			0
$911$	−46.0000			−1.52405			−0.762024	−	0.647549i	$-0.775794\pi$
$911$	−46.0000			−1.52405			−0.762024	+	0.647549i	$0.775794\pi$
$912$	−0.500000	+	0.866025i	−0.0165567	+	0.0286770i
$913$	−12.0000	−	20.7846i	−0.397142	−	0.687870i
$914$	−18.5000	−	32.0429i	−0.611926	−	1.05989i
$915$		0			0
$916$	−7.00000			−0.231287
$917$	4.00000	−	3.46410i	0.132092	−	0.114395i
$918$	2.00000			0.0660098
$919$	−8.00000	+	13.8564i	−0.263896	+	0.457081i	−0.967274	−	0.253735i	$-0.918341\pi$
$919$	−8.00000	+	13.8564i	−0.263896	+	0.457081i	0.703378	+	0.710816i	$0.251674\pi$
$920$		0			0
$921$	−10.0000	−	17.3205i	−0.329511	−	0.570730i
$922$	−13.0000	+	22.5167i	−0.428132	+	0.741547i
$923$	16.0000			0.526646
$924$	10.0000	+	3.46410i	0.328976	+	0.113961i
$925$		0			0
$926$	1.50000	−	2.59808i	0.0492931	−	0.0853781i
$927$	−3.50000	−	6.06218i	−0.114955	−	0.199108i
$928$	−2.00000	−	3.46410i	−0.0656532	−	0.113715i
$929$	10.0000	−	17.3205i	0.328089	−	0.568267i	−0.654043	−	0.756457i	$-0.726929\pi$
$929$	10.0000	−	17.3205i	0.328089	−	0.568267i	0.982133	+	0.188190i	$0.0602620\pi$
$930$		0			0
$931$	−6.50000	+	2.59808i	−0.213029	+	0.0851485i
$932$	−4.00000			−0.131024
$933$	7.00000	−	12.1244i	0.229170	−	0.396934i
$934$	−15.0000	−	25.9808i	−0.490815	−	0.850117i
$935$		0			0
$936$	−0.500000	+	0.866025i	−0.0163430	+	0.0283069i
$937$	46.0000			1.50275			0.751377	−	0.659873i	$-0.229390\pi$
$937$	46.0000			1.50275			0.751377	+	0.659873i	$0.229390\pi$
$938$	−7.50000	−	2.59808i	−0.244884	−	0.0848302i
$939$	−18.0000			−0.587408
$940$		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	$-0.406681\pi$
$942$	10.5000	+	18.1865i	0.342108	+	0.592549i
$943$	12.0000	−	20.7846i	0.390774	−	0.676840i
$944$	6.00000			0.195283
$945$		0			0
$946$	−32.0000			−1.04041
$947$	19.0000	−	32.9090i	0.617417	−	1.06940i	−0.372538	−	0.928017i	$-0.621512\pi$
$947$	19.0000	−	32.9090i	0.617417	−	1.06940i	0.989955	−	0.141381i	$-0.0451542\pi$
$948$	−6.50000	−	11.2583i	−0.211110	−	0.365654i
$949$	5.50000	+	9.52628i	0.178538	+	0.309236i
$950$		0			0
$951$	22.0000			0.713399
$952$	1.00000	+	5.19615i	0.0324102	+	0.168408i
$953$	−4.00000			−0.129573			−0.0647864	−	0.997899i	$-0.520637\pi$
$953$	−4.00000			−0.129573			−0.0647864	+	0.997899i	$0.520637\pi$
$954$	−1.00000	+	1.73205i	−0.0323762	+	0.0560772i
$955$		0			0
$956$	6.00000	+	10.3923i	0.194054	+	0.336111i
$957$	8.00000	−	13.8564i	0.258603	−	0.447914i
$958$	−34.0000			−1.09849
$959$	5.00000	+	25.9808i	0.161458	+	0.838963i
$960$		0			0
$961$	15.5000	−	26.8468i	0.500000	−	0.866025i
$962$	−1.50000	−	2.59808i	−0.0483619	−	0.0837653i
$963$	−3.00000	−	5.19615i	−0.0966736	−	0.167444i
$964$	−6.50000	+	11.2583i	−0.209351	+	0.362606i
$965$		0			0
$966$	−4.00000	+	3.46410i	−0.128698	+	0.111456i
$967$	−11.0000			−0.353736			−0.176868	−	0.984235i	$-0.556597\pi$
$967$	−11.0000			−0.353736			−0.176868	+	0.984235i	$0.556597\pi$
$968$	−2.50000	+	4.33013i	−0.0803530	+	0.139176i
$969$	−1.00000	−	1.73205i	−0.0321246	−	0.0556415i
$970$		0			0
$971$	−8.00000	+	13.8564i	−0.256732	+	0.444673i	−0.965365	−	0.260905i	$-0.915979\pi$
$971$	−8.00000	+	13.8564i	−0.256732	+	0.444673i	0.708632	+	0.705578i	$0.249313\pi$
$972$	1.00000			0.0320750
$973$	32.5000	+	11.2583i	1.04190	+	0.360925i
$974$	40.0000			1.28168
$975$		0			0
$976$	6.50000	+	11.2583i	0.208060	+	0.360370i
$977$	24.0000	+	41.5692i	0.767828	+	1.32992i	0.938738	+	0.344631i	$0.111996\pi$
$977$	24.0000	+	41.5692i	0.767828	+	1.32992i	−0.170910	+	0.985287i	$0.554671\pi$
$978$	−11.5000	+	19.9186i	−0.367729	+	0.636926i
$979$	8.00000			0.255681
$980$		0			0
$981$	−19.0000			−0.606623
$982$	−9.00000	+	15.5885i	−0.287202	+	0.497448i
$983$	−21.0000	−	36.3731i	−0.669796	−	1.16012i	−0.977961	−	0.208788i	$-0.933048\pi$
$983$	−21.0000	−	36.3731i	−0.669796	−	1.16012i	0.308165	−	0.951333i	$-0.400285\pi$
$984$	−6.00000	−	10.3923i	−0.191273	−	0.331295i
$985$		0			0
$986$	8.00000			0.254772
$987$	15.0000	+	5.19615i	0.477455	+	0.165395i
$988$	1.00000			0.0318142
$989$	8.00000	−	13.8564i	0.254385	−	0.440608i
$990$		0			0
$991$	4.00000	+	6.92820i	0.127064	+	0.220082i	0.922538	−	0.385906i	$-0.126111\pi$
$991$	4.00000	+	6.92820i	0.127064	+	0.220082i	−0.795474	+	0.605988i	$0.792778\pi$
$992$		0			0
$993$	21.0000			0.666415
$994$	32.0000	−	27.7128i	1.01498	−	0.878997i
$995$		0			0
$996$	3.00000	−	5.19615i	0.0950586	−	0.164646i
$997$	−15.5000	−	26.8468i	−0.490890	−	0.850246i	0.509055	−	0.860734i	$-0.329995\pi$
$997$	−15.5000	−	26.8468i	−0.490890	−	0.850246i	−0.999945	+	0.0104877i	$0.996662\pi$
$998$	13.5000	+	23.3827i	0.427335	+	0.740166i
$999$	−1.50000	+	2.59808i	−0.0474579	+	0.0821995i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.i.a.751.1	yes	2
5.2	odd	4		1050.2.o.k.499.1		4
5.3	odd	4		1050.2.o.k.499.2		4
5.4	even	2		1050.2.i.t.751.1	yes	2
7.2	even	3		7350.2.a.cl.1.1		1
7.4	even	3	inner	1050.2.i.a.151.1	✓	2
7.5	odd	6		7350.2.a.bp.1.1		1
35.4	even	6		1050.2.i.t.151.1	yes	2
35.9	even	6		7350.2.a.c.1.1		1
35.18	odd	12		1050.2.o.k.949.1		4
35.19	odd	6		7350.2.a.y.1.1		1
35.32	odd	12		1050.2.o.k.949.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.2.i.a.151.1	✓	2	7.4	even	3	inner
1050.2.i.a.751.1	yes	2	1.1	even	1	trivial
1050.2.i.t.151.1	yes	2	35.4	even	6
1050.2.i.t.751.1	yes	2	5.4	even	2
1050.2.o.k.499.1		4	5.2	odd	4
1050.2.o.k.499.2		4	5.3	odd	4
1050.2.o.k.949.1		4	35.18	odd	12
1050.2.o.k.949.2		4	35.32	odd	12
7350.2.a.c.1.1		1	35.9	even	6
7350.2.a.y.1.1		1	35.19	odd	6
7350.2.a.bp.1.1		1	7.5	odd	6
7350.2.a.cl.1.1		1	7.2	even	3

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} +1.00000 q^{13} +(2.00000 - 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.00000 - 1.73205i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-0.500000 + 0.866025i) q^{19} +(0.500000 + 2.59808i) q^{21} -4.00000 q^{22} +(1.00000 - 1.73205i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{26} +1.00000 q^{27} +(0.500000 + 2.59808i) q^{28} +4.00000 q^{29} +(-0.500000 - 0.866025i) q^{32} +(2.00000 - 3.46410i) q^{33} +2.00000 q^{34} +1.00000 q^{36} +(-1.50000 + 2.59808i) q^{37} +(-0.500000 - 0.866025i) q^{38} +(-0.500000 - 0.866025i) q^{39} +12.0000 q^{41} +(-2.50000 - 0.866025i) q^{42} +8.00000 q^{43} +(2.00000 - 3.46410i) q^{44} +(1.00000 + 1.73205i) q^{46} +(3.00000 - 5.19615i) q^{47} +1.00000 q^{48} +(5.50000 + 4.33013i) q^{49} +(-1.00000 + 1.73205i) q^{51} +(-0.500000 - 0.866025i) q^{52} +(-1.00000 - 1.73205i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-2.50000 - 0.866025i) q^{56} +1.00000 q^{57} +(-2.00000 + 3.46410i) q^{58} +(-3.00000 - 5.19615i) q^{59} +(6.50000 - 11.2583i) q^{61} +(2.00000 - 1.73205i) q^{63} +1.00000 q^{64} +(2.00000 + 3.46410i) q^{66} +(-1.50000 - 2.59808i) q^{67} +(-1.00000 + 1.73205i) q^{68} -2.00000 q^{69} +16.0000 q^{71} +(-0.500000 + 0.866025i) q^{72} +(5.50000 + 9.52628i) q^{73} +(-1.50000 - 2.59808i) q^{74} +1.00000 q^{76} +(-2.00000 - 10.3923i) q^{77} +1.00000 q^{78} +(-6.50000 + 11.2583i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(-6.00000 + 10.3923i) q^{82} -6.00000 q^{83} +(2.00000 - 1.73205i) q^{84} +(-4.00000 + 6.92820i) q^{86} +(-2.00000 - 3.46410i) q^{87} +(2.00000 + 3.46410i) q^{88} +(1.00000 - 1.73205i) q^{89} +(-2.50000 - 0.866025i) q^{91} -2.00000 q^{92} +(3.00000 + 5.19615i) q^{94} +(-0.500000 + 0.866025i) q^{96} +17.0000 q^{97} +(-6.50000 + 2.59808i) 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	\( 2 q - q^{2} - q^{3} - q^{4} + 2 q^{6} - 5 q^{7} + 2 q^{8} - q^{9} + 4 q^{11} - q^{12} + 2 q^{13} + 4 q^{14} - q^{16} - 2 q^{17} - q^{18} - q^{19} + q^{21} - 8 q^{22} + 2 q^{23} - q^{24} - q^{26} + 2 q^{27} + q^{28} + 8 q^{29} - q^{32} + 4 q^{33} + 4 q^{34} + 2 q^{36} - 3 q^{37} - q^{38} - q^{39} + 24 q^{41} - 5 q^{42} + 16 q^{43} + 4 q^{44} + 2 q^{46} + 6 q^{47} + 2 q^{48} + 11 q^{49} - 2 q^{51} - q^{52} - 2 q^{53} - q^{54} - 5 q^{56} + 2 q^{57} - 4 q^{58} - 6 q^{59} + 13 q^{61} + 4 q^{63} + 2 q^{64} + 4 q^{66} - 3 q^{67} - 2 q^{68} - 4 q^{69} + 32 q^{71} - q^{72} + 11 q^{73} - 3 q^{74} + 2 q^{76} - 4 q^{77} + 2 q^{78} - 13 q^{79} - q^{81} - 12 q^{82} - 12 q^{83} + 4 q^{84} - 8 q^{86} - 4 q^{87} + 4 q^{88} + 2 q^{89} - 5 q^{91} - 4 q^{92} + 6 q^{94} - q^{96} + 34 q^{97} - 13 q^{98} - 8 q^{99}+O(q^{100}) \) 2 * q - q^2 - q^3 - q^4 + 2 * q^6 - 5 * q^7 + 2 * q^8 - q^9 + 4 * q^11 - q^12 + 2 * q^13 + 4 * q^14 - q^16 - 2 * q^17 - q^18 - q^19 + q^21 - 8 * q^22 + 2 * q^23 - q^24 - q^26 + 2 * q^27 + q^28 + 8 * q^29 - q^32 + 4 * q^33 + 4 * q^34 + 2 * q^36 - 3 * q^37 - q^38 - q^39 + 24 * q^41 - 5 * q^42 + 16 * q^43 + 4 * q^44 + 2 * q^46 + 6 * q^47 + 2 * q^48 + 11 * q^49 - 2 * q^51 - q^52 - 2 * q^53 - q^54 - 5 * q^56 + 2 * q^57 - 4 * q^58 - 6 * q^59 + 13 * q^61 + 4 * q^63 + 2 * q^64 + 4 * q^66 - 3 * q^67 - 2 * q^68 - 4 * q^69 + 32 * q^71 - q^72 + 11 * q^73 - 3 * q^74 + 2 * q^76 - 4 * q^77 + 2 * q^78 - 13 * q^79 - q^81 - 12 * q^82 - 12 * q^83 + 4 * q^84 - 8 * q^86 - 4 * q^87 + 4 * q^88 + 2 * q^89 - 5 * q^91 - 4 * q^92 + 6 * q^94 - q^96 + 34 * q^97 - 13 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more