LMFDB - Embedded newform 1950.2.y.c.199.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(49,1950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1950, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1950.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1950.y (of order $6$, degree $2$, not 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:	$15.5708283941$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1950.199
Dual form			1950.2.y.c.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(0.401924 + 0.232051i) q^{11} +1.00000i q^{12} +(-3.46410 - 1.00000i) q^{13} -2.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.46410 + 2.00000i) q^{17} -1.00000 q^{18} +(0.464102 - 0.267949i) q^{19} -2.00000i q^{21} +(-0.401924 + 0.232051i) q^{22} +(0.232051 + 0.133975i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(2.59808 - 2.50000i) q^{26} -1.00000i q^{27} +(1.00000 - 1.73205i) q^{28} +(1.86603 - 3.23205i) q^{29} -1.73205i q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.232051 - 0.401924i) q^{33} -4.00000i q^{34} +(0.500000 - 0.866025i) q^{36} +(-0.598076 + 1.03590i) q^{37} +0.535898i q^{38} +(2.50000 + 2.59808i) q^{39} +(-1.73205 - 1.00000i) q^{41} +(1.73205 + 1.00000i) q^{42} +(1.66987 - 0.964102i) q^{43} -0.464102i q^{44} +(-0.232051 + 0.133975i) q^{46} -10.4641 q^{47} +(0.866025 - 0.500000i) q^{48} +(1.50000 - 2.59808i) q^{49} +4.00000 q^{51} +(0.866025 + 3.50000i) q^{52} +12.9282i q^{53} +(0.866025 + 0.500000i) q^{54} +(1.00000 + 1.73205i) q^{56} -0.535898 q^{57} +(1.86603 + 3.23205i) q^{58} +(1.33013 - 0.767949i) q^{59} +(-5.19615 - 9.00000i) q^{61} +(1.50000 + 0.866025i) q^{62} +(-1.00000 + 1.73205i) q^{63} +1.00000 q^{64} +0.464102 q^{66} +(-2.26795 + 3.92820i) q^{67} +(3.46410 + 2.00000i) q^{68} +(-0.133975 - 0.232051i) q^{69} +(-7.26795 + 4.19615i) q^{71} +(0.500000 + 0.866025i) q^{72} -2.00000 q^{73} +(-0.598076 - 1.03590i) q^{74} +(-0.464102 - 0.267949i) q^{76} +0.928203i q^{77} +(-3.50000 + 0.866025i) q^{78} +0.0717968 q^{79} +(-0.500000 + 0.866025i) q^{81} +(1.73205 - 1.00000i) q^{82} +4.92820 q^{83} +(-1.73205 + 1.00000i) q^{84} +1.92820i q^{86} +(-3.23205 + 1.86603i) q^{87} +(0.401924 + 0.232051i) q^{88} +(-6.46410 - 3.73205i) q^{89} +(-1.73205 - 7.00000i) q^{91} -0.267949i q^{92} +(-0.866025 + 1.50000i) q^{93} +(5.23205 - 9.06218i) q^{94} +1.00000i q^{96} +(-3.73205 - 6.46410i) q^{97} +(1.50000 + 2.59808i) q^{98} +0.464102i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} + 4 q^{7} + 4 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^4 + 4 * q^7 + 4 * q^8 + 2 * q^9	$ 4 q - 2 q^{2} - 2 q^{4} + 4 q^{7} + 4 q^{8} + 2 q^{9} + 12 q^{11} - 8 q^{14} - 2 q^{16} - 4 q^{18} - 12 q^{19} - 12 q^{22} - 6 q^{23} + 4 q^{28} + 4 q^{29} - 2 q^{32} + 6 q^{33} + 2 q^{36} + 8 q^{37} + 10 q^{39} + 24 q^{43} + 6 q^{46} - 28 q^{47} + 6 q^{49} + 16 q^{51} + 4 q^{56} - 16 q^{57} + 4 q^{58} - 12 q^{59} + 6 q^{62} - 4 q^{63} + 4 q^{64} - 12 q^{66} - 16 q^{67} - 4 q^{69} - 36 q^{71} + 2 q^{72} - 8 q^{73} + 8 q^{74} + 12 q^{76} - 14 q^{78} + 28 q^{79} - 2 q^{81} - 8 q^{83} - 6 q^{87} + 12 q^{88} - 12 q^{89} + 14 q^{94} - 8 q^{97} + 6 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 + 4 * q^7 + 4 * q^8 + 2 * q^9 + 12 * q^11 - 8 * q^14 - 2 * q^16 - 4 * q^18 - 12 * q^19 - 12 * q^22 - 6 * q^23 + 4 * q^28 + 4 * q^29 - 2 * q^32 + 6 * q^33 + 2 * q^36 + 8 * q^37 + 10 * q^39 + 24 * q^43 + 6 * q^46 - 28 * q^47 + 6 * q^49 + 16 * q^51 + 4 * q^56 - 16 * q^57 + 4 * q^58 - 12 * q^59 + 6 * q^62 - 4 * q^63 + 4 * q^64 - 12 * q^66 - 16 * q^67 - 4 * q^69 - 36 * q^71 + 2 * q^72 - 8 * q^73 + 8 * q^74 + 12 * q^76 - 14 * q^78 + 28 * q^79 - 2 * q^81 - 8 * q^83 - 6 * q^87 + 12 * q^88 - 12 * q^89 + 14 * q^94 - 8 * q^97 + 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$.

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

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
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	0.866025	−	0.500000i	0.353553	−	0.204124i
$7$	1.00000	+	1.73205i	0.377964	+	0.654654i	0.990766	−	0.135583i	$-0.0432908\pi$
$7$	1.00000	+	1.73205i	0.377964	+	0.654654i	−0.612801	+	0.790237i	$0.709957\pi$
$8$	1.00000			0.353553
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	0.401924	+	0.232051i	0.121185	+	0.0699660i	0.559367	−	0.828920i	$-0.311044\pi$
$11$	0.401924	+	0.232051i	0.121185	+	0.0699660i	−0.438182	+	0.898886i	$0.644378\pi$
$12$			1.00000i			0.288675i
$13$	−3.46410	−	1.00000i	−0.960769	−	0.277350i
$13$	−3.46410	−	1.00000i	−0.960769	−	0.277350i
$14$	−2.00000			−0.534522
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.46410	+	2.00000i	−0.840168	+	0.485071i	−0.857321	−	0.514782i	$-0.827873\pi$
$17$	−3.46410	+	2.00000i	−0.840168	+	0.485071i	0.0171533	+	0.999853i	$0.494540\pi$
$18$	−1.00000			−0.235702
$19$	0.464102	−	0.267949i	0.106472	−	0.0614718i	−0.445818	−	0.895123i	$-0.647087\pi$
$19$	0.464102	−	0.267949i	0.106472	−	0.0614718i	0.552291	+	0.833652i	$0.313754\pi$
$20$		0			0
$21$		−	2.00000i		−	0.436436i
$22$	−0.401924	+	0.232051i	−0.0856904	+	0.0494734i
$23$	0.232051	+	0.133975i	0.0483859	+	0.0279356i	0.523998	−	0.851720i	$-0.324440\pi$
$23$	0.232051	+	0.133975i	0.0483859	+	0.0279356i	−0.475612	+	0.879655i	$0.657773\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$		0			0
$26$	2.59808	−	2.50000i	0.509525	−	0.490290i
$27$		−	1.00000i		−	0.192450i
$28$	1.00000	−	1.73205i	0.188982	−	0.327327i
$29$	1.86603	−	3.23205i	0.346512	−	0.600177i	−0.639115	−	0.769111i	$-0.720699\pi$
$29$	1.86603	−	3.23205i	0.346512	−	0.600177i	0.985627	+	0.168934i	$0.0540326\pi$
$30$		0			0
$31$		−	1.73205i		−	0.311086i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$		−	1.73205i		−	0.311086i	0.987829	−	0.155543i	$-0.0497126\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−0.232051	−	0.401924i	−0.0403949	−	0.0699660i
$34$		−	4.00000i		−	0.685994i
$35$		0			0
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−0.598076	+	1.03590i	−0.0983231	+	0.170301i	−0.910991	−	0.412427i	$-0.864681\pi$
$37$	−0.598076	+	1.03590i	−0.0983231	+	0.170301i	0.812668	+	0.582728i	$0.198015\pi$
$38$			0.535898i			0.0869342i
$39$	2.50000	+	2.59808i	0.400320	+	0.416025i
$40$		0			0
$41$	−1.73205	−	1.00000i	−0.270501	−	0.156174i	0.358614	−	0.933486i	$-0.383249\pi$
$41$	−1.73205	−	1.00000i	−0.270501	−	0.156174i	−0.629115	+	0.777312i	$0.716583\pi$
$42$	1.73205	+	1.00000i	0.267261	+	0.154303i
$43$	1.66987	−	0.964102i	0.254653	−	0.147024i	−0.367240	−	0.930126i	$-0.619697\pi$
$43$	1.66987	−	0.964102i	0.254653	−	0.147024i	0.621893	+	0.783102i	$0.286364\pi$
$44$		−	0.464102i		−	0.0699660i
$45$		0			0
$46$	−0.232051	+	0.133975i	−0.0342140	+	0.0197535i
$47$	−10.4641			−1.52635			−0.763173	−	0.646194i	$-0.776360\pi$
$47$	−10.4641			−1.52635			−0.763173	+	0.646194i	$0.776360\pi$
$48$	0.866025	−	0.500000i	0.125000	−	0.0721688i
$49$	1.50000	−	2.59808i	0.214286	−	0.371154i
$50$		0			0
$51$	4.00000			0.560112
$52$	0.866025	+	3.50000i	0.120096	+	0.485363i
$53$			12.9282i			1.77583i	0.460012	+	0.887913i	$0.347845\pi$
$53$			12.9282i			1.77583i	−0.460012	+	0.887913i	$0.652155\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$		0			0
$56$	1.00000	+	1.73205i	0.133631	+	0.231455i
$57$	−0.535898			−0.0709815
$58$	1.86603	+	3.23205i	0.245021	+	0.424389i
$59$	1.33013	−	0.767949i	0.173168	−	0.0999785i	−0.410911	−	0.911676i	$-0.634789\pi$
$59$	1.33013	−	0.767949i	0.173168	−	0.0999785i	0.584079	+	0.811697i	$0.301456\pi$
$60$		0			0
$61$	−5.19615	−	9.00000i	−0.665299	−	1.15233i	−0.979204	−	0.202878i	$-0.934971\pi$
$61$	−5.19615	−	9.00000i	−0.665299	−	1.15233i	0.313905	−	0.949454i	$-0.398363\pi$
$62$	1.50000	+	0.866025i	0.190500	+	0.109985i
$63$	−1.00000	+	1.73205i	−0.125988	+	0.218218i
$64$	1.00000			0.125000
$65$		0			0
$66$	0.464102			0.0571270
$67$	−2.26795	+	3.92820i	−0.277074	+	0.479906i	−0.970656	−	0.240471i	$-0.922698\pi$
$67$	−2.26795	+	3.92820i	−0.277074	+	0.479906i	0.693582	+	0.720377i	$0.256031\pi$
$68$	3.46410	+	2.00000i	0.420084	+	0.242536i
$69$	−0.133975	−	0.232051i	−0.0161286	−	0.0279356i
$70$		0			0
$71$	−7.26795	+	4.19615i	−0.862547	+	0.497992i	−0.864864	−	0.502006i	$-0.832596\pi$
$71$	−7.26795	+	4.19615i	−0.862547	+	0.497992i	0.00231747	+	0.999997i	$0.499262\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	−2.00000			−0.234082			−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000			−0.234082			−0.117041	+	0.993127i	$0.537341\pi$
$74$	−0.598076	−	1.03590i	−0.0695249	−	0.120421i
$75$		0			0
$76$	−0.464102	−	0.267949i	−0.0532361	−	0.0307359i
$77$			0.928203i			0.105779i
$78$	−3.50000	+	0.866025i	−0.396297	+	0.0980581i
$79$	0.0717968			0.00807777			0.00403888	−	0.999992i	$-0.498714\pi$
$79$	0.0717968			0.00807777			0.00403888	+	0.999992i	$0.498714\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	1.73205	−	1.00000i	0.191273	−	0.110432i
$83$	4.92820			0.540941			0.270470	−	0.962728i	$-0.412821\pi$
$83$	4.92820			0.540941			0.270470	+	0.962728i	$0.412821\pi$
$84$	−1.73205	+	1.00000i	−0.188982	+	0.109109i
$85$		0			0
$86$			1.92820i			0.207924i
$87$	−3.23205	+	1.86603i	−0.346512	+	0.200059i
$88$	0.401924	+	0.232051i	0.0428452	+	0.0247367i
$89$	−6.46410	−	3.73205i	−0.685193	−	0.395597i	0.116615	−	0.993177i	$-0.462795\pi$
$89$	−6.46410	−	3.73205i	−0.685193	−	0.395597i	−0.801809	+	0.597581i	$0.796129\pi$
$90$		0			0
$91$	−1.73205	−	7.00000i	−0.181568	−	0.733799i
$92$		−	0.267949i		−	0.0279356i
$93$	−0.866025	+	1.50000i	−0.0898027	+	0.155543i
$94$	5.23205	−	9.06218i	0.539645	−	0.934692i
$95$		0			0
$96$			1.00000i			0.102062i
$97$	−3.73205	−	6.46410i	−0.378932	−	0.656330i	0.611975	−	0.790877i	$-0.290375\pi$
$97$	−3.73205	−	6.46410i	−0.378932	−	0.656330i	−0.990907	+	0.134547i	$0.957042\pi$
$98$	1.50000	+	2.59808i	0.151523	+	0.262445i
$99$			0.464102i			0.0466440i
$100$		0			0
$101$	5.46410	−	9.46410i	0.543698	−	0.941713i	−0.454989	−	0.890497i	$-0.650357\pi$
$101$	5.46410	−	9.46410i	0.543698	−	0.941713i	0.998688	−	0.0512163i	$-0.0163098\pi$
$102$	−2.00000	+	3.46410i	−0.198030	+	0.342997i
$103$		−	15.8564i		−	1.56238i	−0.624295	−	0.781189i	$-0.714613\pi$
$103$		−	15.8564i		−	1.56238i	0.624295	−	0.781189i	$-0.285387\pi$
$104$	−3.46410	−	1.00000i	−0.339683	−	0.0980581i
$105$		0			0
$106$	−11.1962	−	6.46410i	−1.08747	−	0.627849i
$107$	−17.1962	−	9.92820i	−1.66241	−	0.959796i	−0.971557	−	0.236805i	$-0.923900\pi$
$107$	−17.1962	−	9.92820i	−1.66241	−	0.959796i	−0.690858	−	0.722991i	$-0.742767\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$			11.8564i			1.13564i	0.823154	+	0.567819i	$0.192213\pi$
$109$			11.8564i			1.13564i	−0.823154	+	0.567819i	$0.807787\pi$
$110$		0			0
$111$	1.03590	−	0.598076i	0.0983231	−	0.0567669i
$112$	−2.00000			−0.188982
$113$	−9.69615	+	5.59808i	−0.912137	+	0.526623i	−0.881118	−	0.472896i	$-0.843209\pi$
$113$	−9.69615	+	5.59808i	−0.912137	+	0.526623i	−0.0310191	+	0.999519i	$0.509875\pi$
$114$	0.267949	−	0.464102i	0.0250957	−	0.0434671i
$115$		0			0
$116$	−3.73205			−0.346512
$117$	−0.866025	−	3.50000i	−0.0800641	−	0.323575i
$118$			1.53590i			0.141391i
$119$	−6.92820	−	4.00000i	−0.635107	−	0.366679i
$120$		0			0
$121$	−5.39230	−	9.33975i	−0.490210	−	0.849068i
$122$	10.3923			0.940875
$123$	1.00000	+	1.73205i	0.0901670	+	0.156174i
$124$	−1.50000	+	0.866025i	−0.134704	+	0.0777714i
$125$		0			0
$126$	−1.00000	−	1.73205i	−0.0890871	−	0.154303i
$127$	−7.73205	−	4.46410i	−0.686109	−	0.396125i	0.116044	−	0.993244i	$-0.462979\pi$
$127$	−7.73205	−	4.46410i	−0.686109	−	0.396125i	−0.802153	+	0.597119i	$0.796312\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−1.92820			−0.169769
$130$		0			0
$131$	−1.33975			−0.117054			−0.0585271	−	0.998286i	$-0.518640\pi$
$131$	−1.33975			−0.117054			−0.0585271	+	0.998286i	$0.518640\pi$
$132$	−0.232051	+	0.401924i	−0.0201974	+	0.0349830i
$133$	0.928203	+	0.535898i	0.0804854	+	0.0464683i
$134$	−2.26795	−	3.92820i	−0.195921	−	0.339345i
$135$		0			0
$136$	−3.46410	+	2.00000i	−0.297044	+	0.171499i
$137$	−2.23205	−	3.86603i	−0.190697	−	0.330297i	0.754784	−	0.655973i	$-0.227741\pi$
$137$	−2.23205	−	3.86603i	−0.190697	−	0.330297i	−0.945481	+	0.325676i	$0.894408\pi$
$138$	0.267949			0.0228093
$139$	0.464102	+	0.803848i	0.0393646	+	0.0681815i	0.885036	−	0.465522i	$-0.154133\pi$
$139$	0.464102	+	0.803848i	0.0393646	+	0.0681815i	−0.845672	+	0.533703i	$0.820800\pi$
$140$		0			0
$141$	9.06218	+	5.23205i	0.763173	+	0.440618i
$142$		−	8.39230i		−	0.704267i
$143$	−1.16025	−	1.20577i	−0.0970253	−	0.100832i
$144$	−1.00000			−0.0833333
$145$		0			0
$146$	1.00000	−	1.73205i	0.0827606	−	0.143346i
$147$	−2.59808	+	1.50000i	−0.214286	+	0.123718i
$148$	1.19615			0.0983231
$149$	−17.7224	+	10.2321i	−1.45188	+	0.838242i	−0.998588	−	0.0531208i	$-0.983083\pi$
$149$	−17.7224	+	10.2321i	−1.45188	+	0.838242i	−0.453290	+	0.891363i	$0.649750\pi$
$150$		0			0
$151$		−	10.3923i		−	0.845714i	−0.906196	−	0.422857i	$-0.861027\pi$
$151$		−	10.3923i		−	0.845714i	0.906196	−	0.422857i	$-0.138973\pi$
$152$	0.464102	−	0.267949i	0.0376436	−	0.0217335i
$153$	−3.46410	−	2.00000i	−0.280056	−	0.161690i
$154$	−0.803848	−	0.464102i	−0.0647759	−	0.0373984i
$155$		0			0
$156$	1.00000	−	3.46410i	0.0800641	−	0.277350i
$157$		−	5.00000i		−	0.399043i	−0.979893	−	0.199522i	$-0.936061\pi$
$157$		−	5.00000i		−	0.399043i	0.979893	−	0.199522i	$-0.0639388\pi$
$158$	−0.0358984	+	0.0621778i	−0.00285592	+	0.00494660i
$159$	6.46410	−	11.1962i	0.512637	−	0.887913i
$160$		0			0
$161$			0.535898i			0.0422347i
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	−11.5263	−	19.9641i	−0.902808	−	1.56371i	−0.823833	−	0.566833i	$-0.808169\pi$
$163$	−11.5263	−	19.9641i	−0.902808	−	1.56371i	−0.0789748	−	0.996877i	$-0.525165\pi$
$164$			2.00000i			0.156174i
$165$		0			0
$166$	−2.46410	+	4.26795i	−0.191251	+	0.331257i
$167$	−9.16025	+	15.8660i	−0.708842	+	1.22775i	0.256445	+	0.966559i	$0.417449\pi$
$167$	−9.16025	+	15.8660i	−0.708842	+	1.22775i	−0.965287	+	0.261191i	$0.915885\pi$
$168$		−	2.00000i		−	0.154303i
$169$	11.0000	+	6.92820i	0.846154	+	0.532939i
$170$		0			0
$171$	0.464102	+	0.267949i	0.0354907	+	0.0204906i
$172$	−1.66987	−	0.964102i	−0.127327	−	0.0735121i
$173$	2.53590	−	1.46410i	0.192801	−	0.111314i	−0.400492	−	0.916300i	$-0.631161\pi$
$173$	2.53590	−	1.46410i	0.192801	−	0.111314i	0.593293	+	0.804987i	$0.297828\pi$
$174$		−	3.73205i		−	0.282926i
$175$		0			0
$176$	−0.401924	+	0.232051i	−0.0302961	+	0.0174915i
$177$	−1.53590			−0.115445
$178$	6.46410	−	3.73205i	0.484505	−	0.279729i
$179$	−8.13397	+	14.0885i	−0.607962	+	1.05302i	0.383614	+	0.923494i	$0.374679\pi$
$179$	−8.13397	+	14.0885i	−0.607962	+	1.05302i	−0.991576	+	0.129527i	$0.958654\pi$
$180$		0			0
$181$	10.9282			0.812287			0.406143	−	0.913809i	$-0.366873\pi$
$181$	10.9282			0.812287			0.406143	+	0.913809i	$0.366873\pi$
$182$	6.92820	+	2.00000i	0.513553	+	0.148250i
$183$			10.3923i			0.768221i
$184$	0.232051	+	0.133975i	0.0171070	+	0.00987674i
$185$		0			0
$186$	−0.866025	−	1.50000i	−0.0635001	−	0.109985i
$187$	−1.85641			−0.135754
$188$	5.23205	+	9.06218i	0.381587	+	0.660927i
$189$	1.73205	−	1.00000i	0.125988	−	0.0727393i
$190$		0			0
$191$	−7.26795	−	12.5885i	−0.525890	−	0.910869i	−0.999545	−	0.0301582i	$-0.990399\pi$
$191$	−7.26795	−	12.5885i	−0.525890	−	0.910869i	0.473655	−	0.880711i	$-0.342934\pi$
$192$	−0.866025	−	0.500000i	−0.0625000	−	0.0360844i
$193$	11.6603	−	20.1962i	0.839323	−	1.45375i	−0.0511377	−	0.998692i	$-0.516285\pi$
$193$	11.6603	−	20.1962i	0.839323	−	1.45375i	0.890461	−	0.455059i	$-0.150382\pi$
$194$	7.46410			0.535891
$195$		0			0
$196$	−3.00000			−0.214286
$197$	−8.19615	+	14.1962i	−0.583952	+	1.01143i	0.411054	+	0.911611i	$0.365161\pi$
$197$	−8.19615	+	14.1962i	−0.583952	+	1.01143i	−0.995005	+	0.0998228i	$0.968172\pi$
$198$	−0.401924	−	0.232051i	−0.0285635	−	0.0164911i
$199$	−9.46410	−	16.3923i	−0.670892	−	1.16202i	−0.977651	−	0.210232i	$-0.932578\pi$
$199$	−9.46410	−	16.3923i	−0.670892	−	1.16202i	0.306759	−	0.951787i	$-0.400755\pi$
$200$		0			0
$201$	3.92820	−	2.26795i	0.277074	−	0.159969i
$202$	5.46410	+	9.46410i	0.384453	+	0.665892i
$203$	7.46410			0.523877
$204$	−2.00000	−	3.46410i	−0.140028	−	0.242536i
$205$		0			0
$206$	13.7321	+	7.92820i	0.956757	+	0.552384i
$207$			0.267949i			0.0186238i
$208$	2.59808	−	2.50000i	0.180144	−	0.173344i
$209$	0.248711			0.0172037
$210$		0			0
$211$	−11.6603	+	20.1962i	−0.802725	+	1.39036i	0.115091	+	0.993355i	$0.463284\pi$
$211$	−11.6603	+	20.1962i	−0.802725	+	1.39036i	−0.917816	+	0.397006i	$0.870049\pi$
$212$	11.1962	−	6.46410i	0.768955	−	0.443956i
$213$	8.39230			0.575031
$214$	17.1962	−	9.92820i	1.17550	−	0.678678i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	3.00000	−	1.73205i	0.203653	−	0.117579i
$218$	−10.2679	−	5.92820i	−0.695433	−	0.401509i
$219$	1.73205	+	1.00000i	0.117041	+	0.0675737i
$220$		0			0
$221$	14.0000	−	3.46410i	0.941742	−	0.233021i
$222$			1.19615i			0.0802805i
$223$	13.7321	−	23.7846i	0.919566	−	1.59274i	0.119491	−	0.992835i	$-0.461874\pi$
$223$	13.7321	−	23.7846i	0.919566	−	1.59274i	0.800075	−	0.599900i	$-0.204793\pi$
$224$	1.00000	−	1.73205i	0.0668153	−	0.115728i
$225$		0			0
$226$		−	11.1962i		−	0.744757i
$227$	−2.19615	−	3.80385i	−0.145764	−	0.252470i	0.783894	−	0.620895i	$-0.213231\pi$
$227$	−2.19615	−	3.80385i	−0.145764	−	0.252470i	−0.929658	+	0.368425i	$0.879897\pi$
$228$	0.267949	+	0.464102i	0.0177454	+	0.0307359i
$229$			19.8564i			1.31215i	0.754696	+	0.656074i	$0.227784\pi$
$229$			19.8564i			1.31215i	−0.754696	+	0.656074i	$0.772216\pi$
$230$		0			0
$231$	0.464102	−	0.803848i	0.0305356	−	0.0528893i
$232$	1.86603	−	3.23205i	0.122511	−	0.212195i
$233$			18.1244i			1.18737i	0.804699	+	0.593683i	$0.202327\pi$
$233$			18.1244i			1.18737i	−0.804699	+	0.593683i	$0.797673\pi$
$234$	3.46410	+	1.00000i	0.226455	+	0.0653720i
$235$		0			0
$236$	−1.33013	−	0.767949i	−0.0865839	−	0.0499892i
$237$	−0.0621778	−	0.0358984i	−0.00403888	−	0.00233185i
$238$	6.92820	−	4.00000i	0.449089	−	0.259281i
$239$			4.39230i			0.284115i	0.989858	+	0.142057i	$0.0453717\pi$
$239$			4.39230i			0.284115i	−0.989858	+	0.142057i	$0.954628\pi$
$240$		0			0
$241$	−12.3564	+	7.13397i	−0.795946	+	0.459540i	−0.842052	−	0.539397i	$-0.818652\pi$
$241$	−12.3564	+	7.13397i	−0.795946	+	0.459540i	0.0461056	+	0.998937i	$0.485319\pi$
$242$	10.7846			0.693261
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−5.19615	+	9.00000i	−0.332650	+	0.576166i
$245$		0			0
$246$	−2.00000			−0.127515
$247$	−1.87564	+	0.464102i	−0.119344	+	0.0295301i
$248$		−	1.73205i		−	0.109985i
$249$	−4.26795	−	2.46410i	−0.270470	−	0.156156i
$250$		0			0
$251$	−6.13397	−	10.6244i	−0.387173	−	0.670603i	0.604895	−	0.796305i	$-0.293215\pi$
$251$	−6.13397	−	10.6244i	−0.387173	−	0.670603i	−0.992068	+	0.125702i	$0.959882\pi$
$252$	2.00000			0.125988
$253$	0.0621778	+	0.107695i	0.00390909	+	0.00677074i
$254$	7.73205	−	4.46410i	0.485152	−	0.280103i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	19.6244	+	11.3301i	1.22413	+	0.706754i	0.965797	−	0.259301i	$-0.0834921\pi$
$257$	19.6244	+	11.3301i	1.22413	+	0.706754i	0.258337	+	0.966055i	$0.416825\pi$
$258$	0.964102	−	1.66987i	0.0600223	−	0.103962i
$259$	−2.39230			−0.148651
$260$		0			0
$261$	3.73205			0.231008
$262$	0.669873	−	1.16025i	0.0413849	−	0.0716807i
$263$	−15.6962	−	9.06218i	−0.967866	−	0.558798i	−0.0692812	−	0.997597i	$-0.522071\pi$
$263$	−15.6962	−	9.06218i	−0.967866	−	0.558798i	−0.898585	+	0.438799i	$0.855404\pi$
$264$	−0.232051	−	0.401924i	−0.0142817	−	0.0247367i
$265$		0			0
$266$	−0.928203	+	0.535898i	−0.0569118	+	0.0328580i
$267$	3.73205	+	6.46410i	0.228398	+	0.395597i
$268$	4.53590			0.277074
$269$	6.00000	+	10.3923i	0.365826	+	0.633630i	0.988908	−	0.148527i	$-0.0474530\pi$
$269$	6.00000	+	10.3923i	0.365826	+	0.633630i	−0.623082	+	0.782157i	$0.714120\pi$
$270$		0			0
$271$	7.96410	+	4.59808i	0.483785	+	0.279313i	0.721992	−	0.691901i	$-0.243227\pi$
$271$	7.96410	+	4.59808i	0.483785	+	0.279313i	−0.238208	+	0.971214i	$0.576560\pi$
$272$		−	4.00000i		−	0.242536i
$273$	−2.00000	+	6.92820i	−0.121046	+	0.419314i
$274$	4.46410			0.269686
$275$		0			0
$276$	−0.133975	+	0.232051i	−0.00806432	+	0.0139678i
$277$	8.59808	−	4.96410i	0.516608	−	0.298264i	−0.218938	−	0.975739i	$-0.570259\pi$
$277$	8.59808	−	4.96410i	0.516608	−	0.298264i	0.735546	+	0.677475i	$0.236926\pi$
$278$	−0.928203			−0.0556699
$279$	1.50000	−	0.866025i	0.0898027	−	0.0518476i
$280$		0			0
$281$		−	4.92820i		−	0.293992i	−0.989137	−	0.146996i	$-0.953040\pi$
$281$		−	4.92820i		−	0.293992i	0.989137	−	0.146996i	$-0.0469604\pi$
$282$	−9.06218	+	5.23205i	−0.539645	+	0.311564i
$283$	3.40192	+	1.96410i	0.202223	+	0.116754i	0.597692	−	0.801726i	$-0.296085\pi$
$283$	3.40192	+	1.96410i	0.202223	+	0.116754i	−0.395469	+	0.918479i	$0.629418\pi$
$284$	7.26795	+	4.19615i	0.431273	+	0.248996i
$285$		0			0
$286$	1.62436	−	0.401924i	0.0960502	−	0.0237663i
$287$		−	4.00000i		−	0.236113i
$288$	0.500000	−	0.866025i	0.0294628	−	0.0510310i
$289$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i
$290$		0			0
$291$			7.46410i			0.437553i
$292$	1.00000	+	1.73205i	0.0585206	+	0.101361i
$293$	−2.07180	−	3.58846i	−0.121036	−	0.209640i	0.799141	−	0.601144i	$-0.205288\pi$
$293$	−2.07180	−	3.58846i	−0.121036	−	0.209640i	−0.920176	+	0.391504i	$0.871955\pi$
$294$		−	3.00000i		−	0.174964i
$295$		0			0
$296$	−0.598076	+	1.03590i	−0.0347625	+	0.0602104i
$297$	0.232051	−	0.401924i	0.0134650	−	0.0233220i
$298$		−	20.4641i		−	1.18545i
$299$	−0.669873	−	0.696152i	−0.0387398	−	0.0402595i
$300$		0			0
$301$	3.33975	+	1.92820i	0.192500	+	0.111140i
$302$	9.00000	+	5.19615i	0.517892	+	0.299005i
$303$	−9.46410	+	5.46410i	−0.543698	+	0.313904i
$304$			0.535898i			0.0307359i
$305$		0			0
$306$	3.46410	−	2.00000i	0.198030	−	0.114332i
$307$	12.5359			0.715462			0.357731	−	0.933825i	$-0.383551\pi$
$307$	12.5359			0.715462			0.357731	+	0.933825i	$0.383551\pi$
$308$	0.803848	−	0.464102i	0.0458035	−	0.0264446i
$309$	−7.92820	+	13.7321i	−0.451020	+	0.781189i
$310$		0			0
$311$	−7.60770			−0.431393			−0.215696	−	0.976460i	$-0.569202\pi$
$311$	−7.60770			−0.431393			−0.215696	+	0.976460i	$0.569202\pi$
$312$	2.50000	+	2.59808i	0.141535	+	0.147087i
$313$			28.0000i			1.58265i	0.611393	+	0.791327i	$0.290609\pi$
$313$			28.0000i			1.58265i	−0.611393	+	0.791327i	$0.709391\pi$
$314$	4.33013	+	2.50000i	0.244363	+	0.141083i
$315$		0			0
$316$	−0.0358984	−	0.0621778i	−0.00201944	−	0.00349778i
$317$	21.4641			1.20554			0.602772	−	0.797913i	$-0.294063\pi$
$317$	21.4641			1.20554			0.602772	+	0.797913i	$0.294063\pi$
$318$	6.46410	+	11.1962i	0.362489	+	0.627849i
$319$	1.50000	−	0.866025i	0.0839839	−	0.0484881i
$320$		0			0
$321$	9.92820	+	17.1962i	0.554138	+	0.959796i
$322$	−0.464102	−	0.267949i	−0.0258634	−	0.0149322i
$323$	−1.07180	+	1.85641i	−0.0596364	+	0.103293i
$324$	1.00000			0.0555556
$325$		0			0
$326$	23.0526			1.27676
$327$	5.92820	−	10.2679i	0.327830	−	0.567819i
$328$	−1.73205	−	1.00000i	−0.0956365	−	0.0552158i
$329$	−10.4641	−	18.1244i	−0.576905	−	0.999228i
$330$		0			0
$331$	−21.4641	+	12.3923i	−1.17977	+	0.681143i	−0.955962	−	0.293490i	$-0.905183\pi$
$331$	−21.4641	+	12.3923i	−1.17977	+	0.681143i	−0.223812	+	0.974632i	$0.571850\pi$
$332$	−2.46410	−	4.26795i	−0.135235	−	0.234234i
$333$	−1.19615			−0.0655487
$334$	−9.16025	−	15.8660i	−0.501227	−	0.868150i
$335$		0			0
$336$	1.73205	+	1.00000i	0.0944911	+	0.0545545i
$337$		−	25.3205i		−	1.37930i	−0.724145	−	0.689648i	$-0.757765\pi$
$337$		−	25.3205i		−	1.37930i	0.724145	−	0.689648i	$-0.242235\pi$
$338$	−11.5000	+	6.06218i	−0.625518	+	0.329739i
$339$	11.1962			0.608092
$340$		0			0
$341$	0.401924	−	0.696152i	0.0217654	−	0.0376988i
$342$	−0.464102	+	0.267949i	−0.0250957	+	0.0144890i
$343$	20.0000			1.07990
$344$	1.66987	−	0.964102i	0.0900335	−	0.0519809i
$345$		0			0
$346$			2.92820i			0.157421i
$347$	19.3923	−	11.1962i	1.04103	−	0.601041i	0.120908	−	0.992664i	$-0.461420\pi$
$347$	19.3923	−	11.1962i	1.04103	−	0.601041i	0.920126	+	0.391623i	$0.128086\pi$
$348$	3.23205	+	1.86603i	0.173256	+	0.100029i
$349$	12.5885	+	7.26795i	0.673845	+	0.389044i	0.797532	−	0.603277i	$-0.206139\pi$
$349$	12.5885	+	7.26795i	0.673845	+	0.389044i	−0.123687	+	0.992321i	$0.539472\pi$
$350$		0			0
$351$	−1.00000	+	3.46410i	−0.0533761	+	0.184900i
$352$		−	0.464102i		−	0.0247367i
$353$	−1.00000	+	1.73205i	−0.0532246	+	0.0921878i	−0.891410	−	0.453197i	$-0.850283\pi$
$353$	−1.00000	+	1.73205i	−0.0532246	+	0.0921878i	0.838186	+	0.545385i	$0.183617\pi$
$354$	0.767949	−	1.33013i	0.0408160	−	0.0706955i
$355$		0			0
$356$			7.46410i			0.395597i
$357$	4.00000	+	6.92820i	0.211702	+	0.366679i
$358$	−8.13397	−	14.0885i	−0.429894	−	0.744598i
$359$			18.9282i			0.998992i	0.866316	+	0.499496i	$0.166482\pi$
$359$			18.9282i			0.998992i	−0.866316	+	0.499496i	$0.833518\pi$
$360$		0			0
$361$	−9.35641	+	16.2058i	−0.492442	+	0.852935i
$362$	−5.46410	+	9.46410i	−0.287187	+	0.497422i
$363$			10.7846i			0.566045i
$364$	−5.19615	+	5.00000i	−0.272352	+	0.262071i
$365$		0			0
$366$	−9.00000	−	5.19615i	−0.470438	−	0.271607i
$367$	−31.5167	−	18.1962i	−1.64516	−	0.949831i	−0.978959	−	0.204056i	$-0.934588\pi$
$367$	−31.5167	−	18.1962i	−1.64516	−	0.949831i	−0.666197	−	0.745776i	$-0.732079\pi$
$368$	−0.232051	+	0.133975i	−0.0120965	+	0.00698391i
$369$		−	2.00000i		−	0.104116i
$370$		0			0
$371$	−22.3923	+	12.9282i	−1.16255	+	0.671199i
$372$	1.73205			0.0898027
$373$	−22.3301	+	12.8923i	−1.15621	+	0.667538i	−0.950393	−	0.311052i	$-0.899319\pi$
$373$	−22.3301	+	12.8923i	−1.15621	+	0.667538i	−0.205817	+	0.978590i	$0.565985\pi$
$374$	0.928203	−	1.60770i	0.0479962	−	0.0831319i
$375$		0			0
$376$	−10.4641			−0.539645
$377$	−9.69615	+	9.33013i	−0.499377	+	0.480526i
$378$			2.00000i			0.102869i
$379$	0.124356	+	0.0717968i	0.00638772	+	0.00368795i	0.503190	−	0.864176i	$-0.332159\pi$
$379$	0.124356	+	0.0717968i	0.00638772	+	0.00368795i	−0.496803	+	0.867863i	$0.665493\pi$
$380$		0			0
$381$	4.46410	+	7.73205i	0.228703	+	0.396125i
$382$	14.5359			0.743721
$383$	2.30385	+	3.99038i	0.117721	+	0.203899i	0.918864	−	0.394574i	$-0.129108\pi$
$383$	2.30385	+	3.99038i	0.117721	+	0.203899i	−0.801143	+	0.598473i	$0.795774\pi$
$384$	0.866025	−	0.500000i	0.0441942	−	0.0255155i
$385$		0			0
$386$	11.6603	+	20.1962i	0.593491	+	1.02796i
$387$	1.66987	+	0.964102i	0.0848844	+	0.0490080i
$388$	−3.73205	+	6.46410i	−0.189466	+	0.328165i
$389$	20.2679			1.02763			0.513813	−	0.857902i	$-0.328233\pi$
$389$	20.2679			1.02763			0.513813	+	0.857902i	$0.328233\pi$
$390$		0			0
$391$	−1.07180			−0.0542031
$392$	1.50000	−	2.59808i	0.0757614	−	0.131223i
$393$	1.16025	+	0.669873i	0.0585271	+	0.0337906i
$394$	−8.19615	−	14.1962i	−0.412916	−	0.715192i
$395$		0			0
$396$	0.401924	−	0.232051i	0.0201974	−	0.0116610i
$397$	6.06218	+	10.5000i	0.304252	+	0.526980i	0.977095	−	0.212806i	$-0.0682602\pi$
$397$	6.06218	+	10.5000i	0.304252	+	0.526980i	−0.672843	+	0.739786i	$0.734927\pi$
$398$	18.9282			0.948785
$399$	−0.535898	−	0.928203i	−0.0268285	−	0.0464683i
$400$		0			0
$401$	27.7128	+	16.0000i	1.38391	+	0.799002i	0.992620	−	0.121265i	$-0.0386950\pi$
$401$	27.7128	+	16.0000i	1.38391	+	0.799002i	0.391292	+	0.920267i	$0.372028\pi$
$402$			4.53590i			0.226230i
$403$	−1.73205	+	6.00000i	−0.0862796	+	0.298881i
$404$	−10.9282			−0.543698
$405$		0			0
$406$	−3.73205	+	6.46410i	−0.185219	+	0.320808i
$407$	−0.480762	+	0.277568i	−0.0238305	+	0.0137585i
$408$	4.00000			0.198030
$409$	3.46410	−	2.00000i	0.171289	−	0.0988936i	−0.411905	−	0.911227i	$-0.635136\pi$
$409$	3.46410	−	2.00000i	0.171289	−	0.0988936i	0.583193	+	0.812333i	$0.301803\pi$
$410$		0			0
$411$			4.46410i			0.220198i
$412$	−13.7321	+	7.92820i	−0.676530	+	0.390595i
$413$	2.66025	+	1.53590i	0.130903	+	0.0755766i
$414$	−0.232051	−	0.133975i	−0.0114047	−	0.00658449i
$415$		0			0
$416$	0.866025	+	3.50000i	0.0424604	+	0.171602i
$417$		−	0.928203i		−	0.0454543i
$418$	−0.124356	+	0.215390i	−0.00608243	+	0.0105351i
$419$	0.803848	−	1.39230i	0.0392705	−	0.0680185i	−0.845722	−	0.533624i	$-0.820830\pi$
$419$	0.803848	−	1.39230i	0.0392705	−	0.0680185i	0.884993	+	0.465605i	$0.154163\pi$
$420$		0			0
$421$			16.3923i			0.798912i	0.916752	+	0.399456i	$0.130801\pi$
$421$			16.3923i			0.798912i	−0.916752	+	0.399456i	$0.869199\pi$
$422$	−11.6603	−	20.1962i	−0.567612	−	0.983133i
$423$	−5.23205	−	9.06218i	−0.254391	−	0.440618i
$424$			12.9282i			0.627849i
$425$		0			0
$426$	−4.19615	+	7.26795i	−0.203304	+	0.352133i
$427$	10.3923	−	18.0000i	0.502919	−	0.871081i
$428$			19.8564i			0.959796i
$429$	0.401924	+	1.62436i	0.0194051	+	0.0784246i
$430$		0			0
$431$	−6.58846	−	3.80385i	−0.317355	−	0.183225i	0.332858	−	0.942977i	$-0.391987\pi$
$431$	−6.58846	−	3.80385i	−0.317355	−	0.183225i	−0.650213	+	0.759752i	$0.725320\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$	13.2679	−	7.66025i	0.637617	−	0.368128i	−0.146079	−	0.989273i	$-0.546665\pi$
$433$	13.2679	−	7.66025i	0.637617	−	0.368128i	0.783696	+	0.621145i	$0.213332\pi$
$434$			3.46410i			0.166282i
$435$		0			0
$436$	10.2679	−	5.92820i	0.491746	−	0.283909i
$437$	0.143594			0.00686901
$438$	−1.73205	+	1.00000i	−0.0827606	+	0.0477818i
$439$	4.92820	−	8.53590i	0.235210	−	0.407396i	−0.724123	−	0.689670i	$-0.757755\pi$
$439$	4.92820	−	8.53590i	0.235210	−	0.407396i	0.959334	+	0.282274i	$0.0910888\pi$
$440$		0			0
$441$	3.00000			0.142857
$442$	−4.00000	+	13.8564i	−0.190261	+	0.659082i
$443$			4.39230i			0.208685i	0.994541	+	0.104342i	$0.0332738\pi$
$443$			4.39230i			0.208685i	−0.994541	+	0.104342i	$0.966726\pi$
$444$	−1.03590	−	0.598076i	−0.0491616	−	0.0283834i
$445$		0			0
$446$	13.7321	+	23.7846i	0.650231	+	1.12623i
$447$	20.4641			0.967919
$448$	1.00000	+	1.73205i	0.0472456	+	0.0818317i
$449$	34.3923	−	19.8564i	1.62307	−	0.937082i	0.636982	−	0.770879i	$-0.280183\pi$
$449$	34.3923	−	19.8564i	1.62307	−	0.937082i	0.986092	−	0.166203i	$-0.0531506\pi$
$450$		0			0
$451$	−0.464102	−	0.803848i	−0.0218537	−	0.0378517i
$452$	9.69615	+	5.59808i	0.456069	+	0.263311i
$453$	−5.19615	+	9.00000i	−0.244137	+	0.422857i
$454$	4.39230			0.206141
$455$		0			0
$456$	−0.535898			−0.0250957
$457$	15.7321	−	27.2487i	0.735914	−	1.27464i	−0.218407	−	0.975858i	$-0.570086\pi$
$457$	15.7321	−	27.2487i	0.735914	−	1.27464i	0.954321	−	0.298783i	$-0.0965807\pi$
$458$	−17.1962	−	9.92820i	−0.803523	−	0.463914i
$459$	2.00000	+	3.46410i	0.0933520	+	0.161690i
$460$		0			0
$461$	5.59808	−	3.23205i	0.260728	−	0.150532i	−0.363938	−	0.931423i	$-0.618568\pi$
$461$	5.59808	−	3.23205i	0.260728	−	0.150532i	0.624667	+	0.780891i	$0.285235\pi$
$462$	0.464102	+	0.803848i	0.0215920	+	0.0373984i
$463$	−20.9282			−0.972616			−0.486308	−	0.873787i	$-0.661657\pi$
$463$	−20.9282			−0.972616			−0.486308	+	0.873787i	$0.661657\pi$
$464$	1.86603	+	3.23205i	0.0866281	+	0.150044i
$465$		0			0
$466$	−15.6962	−	9.06218i	−0.727110	−	0.419797i
$467$			11.8564i			0.548649i	0.961637	+	0.274325i	$0.0884542\pi$
$467$			11.8564i			0.548649i	−0.961637	+	0.274325i	$0.911546\pi$
$468$	−2.59808	+	2.50000i	−0.120096	+	0.115563i
$469$	−9.07180			−0.418897
$470$		0			0
$471$	−2.50000	+	4.33013i	−0.115194	+	0.199522i
$472$	1.33013	−	0.767949i	0.0612241	−	0.0353477i
$473$	0.894882			0.0411467
$474$	0.0621778	−	0.0358984i	0.00285592	−	0.00164887i
$475$		0			0
$476$			8.00000i			0.366679i
$477$	−11.1962	+	6.46410i	−0.512637	+	0.295971i
$478$	−3.80385	−	2.19615i	−0.173984	−	0.100450i
$479$	−1.26795	−	0.732051i	−0.0579341	−	0.0334483i	0.470753	−	0.882265i	$-0.343982\pi$
$479$	−1.26795	−	0.732051i	−0.0579341	−	0.0334483i	−0.528687	+	0.848817i	$0.677316\pi$
$480$		0			0
$481$	3.10770	−	2.99038i	0.141699	−	0.136350i
$482$		−	14.2679i		−	0.649887i
$483$	0.267949	−	0.464102i	0.0121921	−	0.0211174i
$484$	−5.39230	+	9.33975i	−0.245105	+	0.424534i
$485$		0			0
$486$			1.00000i			0.0453609i
$487$	19.5885	+	33.9282i	0.887638	+	1.53743i	0.842660	+	0.538446i	$0.180988\pi$
$487$	19.5885	+	33.9282i	0.887638	+	1.53743i	0.0449775	+	0.998988i	$0.485678\pi$
$488$	−5.19615	−	9.00000i	−0.235219	−	0.407411i
$489$			23.0526i			1.04247i
$490$		0			0
$491$	−8.66025	+	15.0000i	−0.390832	+	0.676941i	−0.992559	−	0.121761i	$-0.961146\pi$
$491$	−8.66025	+	15.0000i	−0.390832	+	0.676941i	0.601728	+	0.798701i	$0.294479\pi$
$492$	1.00000	−	1.73205i	0.0450835	−	0.0780869i
$493$			14.9282i			0.672332i
$494$	0.535898	−	1.85641i	0.0241112	−	0.0835237i
$495$		0			0
$496$	1.50000	+	0.866025i	0.0673520	+	0.0388857i
$497$	−14.5359	−	8.39230i	−0.652024	−	0.376446i
$498$	4.26795	−	2.46410i	0.191251	−	0.110419i
$499$			13.4641i			0.602736i	0.953508	+	0.301368i	$0.0974433\pi$
$499$			13.4641i			0.602736i	−0.953508	+	0.301368i	$0.902557\pi$
$500$		0			0
$501$	15.8660	−	9.16025i	0.708842	−	0.409250i
$502$	12.2679			0.547545
$503$	−27.0000	+	15.5885i	−1.20387	+	0.695055i	−0.961414	−	0.275107i	$-0.911287\pi$
$503$	−27.0000	+	15.5885i	−1.20387	+	0.695055i	−0.242457	+	0.970162i	$0.577953\pi$
$504$	−1.00000	+	1.73205i	−0.0445435	+	0.0771517i
$505$		0			0
$506$	−0.124356			−0.00552828
$507$	−6.06218	−	11.5000i	−0.269231	−	0.510733i
$508$			8.92820i			0.396125i
$509$	−16.7942	−	9.69615i	−0.744391	−	0.429774i	0.0792726	−	0.996853i	$-0.474740\pi$
$509$	−16.7942	−	9.69615i	−0.744391	−	0.429774i	−0.823664	+	0.567079i	$0.808074\pi$
$510$		0			0
$511$	−2.00000	−	3.46410i	−0.0884748	−	0.153243i
$512$	1.00000			0.0441942
$513$	−0.267949	−	0.464102i	−0.0118302	−	0.0204906i
$514$	−19.6244	+	11.3301i	−0.865593	+	0.499750i
$515$		0			0
$516$	0.964102	+	1.66987i	0.0424422	+	0.0735121i
$517$	−4.20577	−	2.42820i	−0.184970	−	0.106792i
$518$	1.19615	−	2.07180i	0.0525559	−	0.0910295i
$519$	−2.92820			−0.128534
$520$		0			0
$521$	17.3205			0.758825			0.379413	−	0.925228i	$-0.376126\pi$
$521$	17.3205			0.758825			0.379413	+	0.925228i	$0.376126\pi$
$522$	−1.86603	+	3.23205i	−0.0816737	+	0.141463i
$523$	−25.7942	−	14.8923i	−1.12790	−	0.651195i	−0.184496	−	0.982833i	$-0.559065\pi$
$523$	−25.7942	−	14.8923i	−1.12790	−	0.651195i	−0.943407	+	0.331638i	$0.892399\pi$
$524$	0.669873	+	1.16025i	0.0292635	+	0.0506859i
$525$		0			0
$526$	15.6962	−	9.06218i	0.684385	−	0.395130i
$527$	3.46410	+	6.00000i	0.150899	+	0.261364i
$528$	0.464102			0.0201974
$529$	−11.4641	−	19.8564i	−0.498439	−	0.863322i
$530$		0			0
$531$	1.33013	+	0.767949i	0.0577226	+	0.0333262i
$532$		−	1.07180i		−	0.0464683i
$533$	5.00000	+	5.19615i	0.216574	+	0.225070i
$534$	−7.46410			−0.323003
$535$		0			0
$536$	−2.26795	+	3.92820i	−0.0979605	+	0.169673i
$537$	14.0885	−	8.13397i	0.607962	−	0.351007i
$538$	−12.0000			−0.517357
$539$	1.20577	−	0.696152i	0.0519362	−	0.0299854i
$540$		0			0
$541$		−	13.0718i		−	0.562000i	−0.959708	−	0.281000i	$-0.909334\pi$
$541$		−	13.0718i		−	0.562000i	0.959708	−	0.281000i	$-0.0906662\pi$
$542$	−7.96410	+	4.59808i	−0.342087	+	0.197504i
$543$	−9.46410	−	5.46410i	−0.406143	−	0.234487i
$544$	3.46410	+	2.00000i	0.148522	+	0.0857493i
$545$		0			0
$546$	−5.00000	−	5.19615i	−0.213980	−	0.222375i
$547$			9.07180i			0.387882i	0.981013	+	0.193941i	$0.0621270\pi$
$547$			9.07180i			0.387882i	−0.981013	+	0.193941i	$0.937873\pi$
$548$	−2.23205	+	3.86603i	−0.0953485	+	0.165148i
$549$	5.19615	−	9.00000i	0.221766	−	0.384111i
$550$		0			0
$551$		−	2.00000i		−	0.0852029i
$552$	−0.133975	−	0.232051i	−0.00570234	−	0.00987674i
$553$	0.0717968	+	0.124356i	0.00305311	+	0.00528814i
$554$			9.92820i			0.421809i
$555$		0			0
$556$	0.464102	−	0.803848i	0.0196823	−	0.0340907i
$557$	−18.8564	+	32.6603i	−0.798972	+	1.38386i	0.121315	+	0.992614i	$0.461289\pi$
$557$	−18.8564	+	32.6603i	−0.798972	+	1.38386i	−0.920286	+	0.391245i	$0.872044\pi$
$558$			1.73205i			0.0733236i
$559$	−6.74871	+	1.66987i	−0.285440	+	0.0706281i
$560$		0			0
$561$	1.60770	+	0.928203i	0.0678769	+	0.0391888i
$562$	4.26795	+	2.46410i	0.180033	+	0.103942i
$563$	34.0526	−	19.6603i	1.43514	−	0.828581i	0.437637	−	0.899152i	$-0.355815\pi$
$563$	34.0526	−	19.6603i	1.43514	−	0.828581i	0.997507	+	0.0705706i	$0.0224820\pi$
$564$		−	10.4641i		−	0.440618i
$565$		0			0
$566$	−3.40192	+	1.96410i	−0.142994	+	0.0825573i
$567$	−2.00000			−0.0839921
$568$	−7.26795	+	4.19615i	−0.304956	+	0.176067i
$569$	−2.66025	+	4.60770i	−0.111524	+	0.193165i	−0.916385	−	0.400299i	$-0.868906\pi$
$569$	−2.66025	+	4.60770i	−0.111524	+	0.193165i	0.804861	+	0.593463i	$0.202240\pi$
$570$		0			0
$571$	45.1769			1.89060			0.945298	−	0.326209i	$-0.105771\pi$
$571$	45.1769			1.89060			0.945298	+	0.326209i	$0.105771\pi$
$572$	−0.464102	+	1.60770i	−0.0194051	+	0.0672211i
$573$			14.5359i			0.607246i
$574$	3.46410	+	2.00000i	0.144589	+	0.0834784i
$575$		0			0
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	−10.0000			−0.416305			−0.208153	−	0.978096i	$-0.566745\pi$
$577$	−10.0000			−0.416305			−0.208153	+	0.978096i	$0.566745\pi$
$578$	−0.500000	−	0.866025i	−0.0207973	−	0.0360219i
$579$	−20.1962	+	11.6603i	−0.839323	+	0.484584i
$580$		0			0
$581$	4.92820	+	8.53590i	0.204456	+	0.354129i
$582$	−6.46410	−	3.73205i	−0.267946	−	0.154698i
$583$	−3.00000	+	5.19615i	−0.124247	+	0.215203i
$584$	−2.00000			−0.0827606
$585$		0			0
$586$	4.14359			0.171170
$587$	9.19615	−	15.9282i	0.379566	−	0.657427i	−0.611433	−	0.791296i	$-0.709407\pi$
$587$	9.19615	−	15.9282i	0.379566	−	0.657427i	0.990999	+	0.133869i	$0.0427400\pi$
$588$	2.59808	+	1.50000i	0.107143	+	0.0618590i
$589$	−0.464102	−	0.803848i	−0.0191230	−	0.0331220i
$590$		0			0
$591$	14.1962	−	8.19615i	0.583952	−	0.337145i
$592$	−0.598076	−	1.03590i	−0.0245808	−	0.0425752i
$593$	31.1051			1.27733			0.638667	−	0.769483i	$-0.279486\pi$
$593$	31.1051			1.27733			0.638667	+	0.769483i	$0.279486\pi$
$594$	0.232051	+	0.401924i	0.00952116	+	0.0164911i
$595$		0			0
$596$	17.7224	+	10.2321i	0.725939	+	0.419121i
$597$			18.9282i			0.774680i
$598$	0.937822	−	0.232051i	0.0383504	−	0.00948926i
$599$	−10.3923			−0.424618			−0.212309	−	0.977203i	$-0.568098\pi$
$599$	−10.3923			−0.424618			−0.212309	+	0.977203i	$0.568098\pi$
$600$		0			0
$601$	−10.8923	+	18.8660i	−0.444306	+	0.769561i	−0.998004	−	0.0631568i	$-0.979883\pi$
$601$	−10.8923	+	18.8660i	−0.444306	+	0.769561i	0.553697	+	0.832718i	$0.313216\pi$
$602$	−3.33975	+	1.92820i	−0.136118	+	0.0785877i
$603$	−4.53590			−0.184716
$604$	−9.00000	+	5.19615i	−0.366205	+	0.211428i
$605$		0			0
$606$		−	10.9282i		−	0.443928i
$607$	37.3923	−	21.5885i	1.51771	−	0.876248i	0.517924	−	0.855427i	$-0.326705\pi$
$607$	37.3923	−	21.5885i	1.51771	−	0.876248i	0.999783	−	0.0208216i	$-0.00662820\pi$
$608$	−0.464102	−	0.267949i	−0.0188218	−	0.0108668i
$609$	−6.46410	−	3.73205i	−0.261939	−	0.151230i
$610$		0			0
$611$	36.2487	+	10.4641i	1.46647	+	0.423332i
$612$			4.00000i			0.161690i
$613$	0.473721	−	0.820508i	0.0191334	−	0.0331400i	−0.856300	−	0.516478i	$-0.827243\pi$
$613$	0.473721	−	0.820508i	0.0191334	−	0.0331400i	0.875434	+	0.483338i	$0.160576\pi$
$614$	−6.26795	+	10.8564i	−0.252954	+	0.438129i
$615$		0			0
$616$			0.928203i			0.0373984i
$617$	7.76795	+	13.4545i	0.312726	+	0.541657i	0.978951	−	0.204093i	$-0.0654246\pi$
$617$	7.76795	+	13.4545i	0.312726	+	0.541657i	−0.666226	+	0.745750i	$0.732091\pi$
$618$	−7.92820	−	13.7321i	−0.318919	−	0.552384i
$619$			24.2487i			0.974638i	0.873224	+	0.487319i	$0.162025\pi$
$619$			24.2487i			0.974638i	−0.873224	+	0.487319i	$0.837975\pi$
$620$		0			0
$621$	0.133975	−	0.232051i	0.00537622	−	0.00931188i
$622$	3.80385	−	6.58846i	0.152520	−	0.264173i
$623$		−	14.9282i		−	0.598086i
$624$	−3.50000	+	0.866025i	−0.140112	+	0.0346688i
$625$		0			0
$626$	−24.2487	−	14.0000i	−0.969173	−	0.559553i
$627$	−0.215390	−	0.124356i	−0.00860186	−	0.00496629i
$628$	−4.33013	+	2.50000i	−0.172791	+	0.0997609i
$629$		−	4.78461i		−	0.190775i
$630$		0			0
$631$	−21.2487	+	12.2679i	−0.845898	+	0.488379i	−0.859265	−	0.511531i	$-0.829078\pi$
$631$	−21.2487	+	12.2679i	−0.845898	+	0.488379i	0.0133668	+	0.999911i	$0.495745\pi$
$632$	0.0717968			0.00285592
$633$	20.1962	−	11.6603i	0.802725	−	0.463453i
$634$	−10.7321	+	18.5885i	−0.426224	+	0.738242i
$635$		0			0
$636$	−12.9282			−0.512637
$637$	−7.79423	+	7.50000i	−0.308819	+	0.297161i
$638$			1.73205i			0.0685725i
$639$	−7.26795	−	4.19615i	−0.287516	−	0.165997i
$640$		0			0
$641$	−13.9282	−	24.1244i	−0.550131	−	0.952855i	−0.998265	−	0.0588882i	$-0.981244\pi$
$641$	−13.9282	−	24.1244i	−0.550131	−	0.952855i	0.448134	−	0.893967i	$-0.352089\pi$
$642$	−19.8564			−0.783670
$643$	−13.7321	−	23.7846i	−0.541539	−	0.937973i	−0.998816	−	0.0486490i	$-0.984508\pi$
$643$	−13.7321	−	23.7846i	−0.541539	−	0.937973i	0.457277	−	0.889324i	$-0.348825\pi$
$644$	0.464102	−	0.267949i	0.0182882	−	0.0105587i
$645$		0			0
$646$	−1.07180	−	1.85641i	−0.0421693	−	0.0730393i
$647$	−18.4641	−	10.6603i	−0.725899	−	0.419098i	0.0910212	−	0.995849i	$-0.470987\pi$
$647$	−18.4641	−	10.6603i	−0.725899	−	0.419098i	−0.816920	+	0.576751i	$0.804320\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	0.712813			0.0279804
$650$		0			0
$651$	−3.46410			−0.135769
$652$	−11.5263	+	19.9641i	−0.451404	+	0.781855i
$653$	−38.3205	−	22.1244i	−1.49960	−	0.865793i	−0.499597	−	0.866258i	$-0.666519\pi$
$653$	−38.3205	−	22.1244i	−1.49960	−	0.865793i	−1.00000		0.000464739i	$0.999852\pi$
$654$	5.92820	+	10.2679i	0.231811	+	0.401509i
$655$		0			0
$656$	1.73205	−	1.00000i	0.0676252	−	0.0390434i
$657$	−1.00000	−	1.73205i	−0.0390137	−	0.0675737i
$658$	20.9282			0.815866
$659$	−1.86603	−	3.23205i	−0.0726900	−	0.125903i	0.827389	−	0.561629i	$-0.189825\pi$
$659$	−1.86603	−	3.23205i	−0.0726900	−	0.125903i	−0.900079	+	0.435726i	$0.856492\pi$
$660$		0			0
$661$	37.5167	+	21.6603i	1.45923	+	0.842486i	0.998973	−	0.0453002i	$-0.0144244\pi$
$661$	37.5167	+	21.6603i	1.45923	+	0.842486i	0.460256	+	0.887786i	$0.347758\pi$
$662$		−	24.7846i		−	0.963281i
$663$	−13.8564	−	4.00000i	−0.538138	−	0.155347i
$664$	4.92820			0.191251
$665$		0			0
$666$	0.598076	−	1.03590i	0.0231750	−	0.0401402i
$667$	0.866025	−	0.500000i	0.0335326	−	0.0193601i
$668$	18.3205			0.708842
$669$	−23.7846	+	13.7321i	−0.919566	+	0.530912i
$670$		0			0
$671$		−	4.82309i		−	0.186193i
$672$	−1.73205	+	1.00000i	−0.0668153	+	0.0385758i
$673$	27.7128	+	16.0000i	1.06825	+	0.616755i	0.927703	−	0.373319i	$-0.121780\pi$
$673$	27.7128	+	16.0000i	1.06825	+	0.616755i	0.140548	+	0.990074i	$0.455114\pi$
$674$	21.9282	+	12.6603i	0.844643	+	0.487655i
$675$		0			0
$676$	0.500000	−	12.9904i	0.0192308	−	0.499630i
$677$			11.6077i			0.446120i	0.974805	+	0.223060i	$0.0716046\pi$
$677$			11.6077i			0.446120i	−0.974805	+	0.223060i	$0.928395\pi$
$678$	−5.59808	+	9.69615i	−0.214993	+	0.372378i
$679$	7.46410	−	12.9282i	0.286446	−	0.496139i
$680$		0			0
$681$			4.39230i			0.168313i
$682$	0.401924	+	0.696152i	0.0153905	+	0.0266571i
$683$	0.392305	+	0.679492i	0.0150111	+	0.0260000i	0.873433	−	0.486944i	$-0.161888\pi$
$683$	0.392305	+	0.679492i	0.0150111	+	0.0260000i	−0.858422	+	0.512944i	$0.828555\pi$
$684$		−	0.535898i		−	0.0204906i
$685$		0			0
$686$	−10.0000	+	17.3205i	−0.381802	+	0.661300i
$687$	9.92820	−	17.1962i	0.378785	−	0.656074i
$688$			1.92820i			0.0735121i
$689$	12.9282	−	44.7846i	0.492525	−	1.70616i
$690$		0			0
$691$	−30.4641	−	17.5885i	−1.15891	−	0.669096i	−0.207867	−	0.978157i	$-0.566652\pi$
$691$	−30.4641	−	17.5885i	−1.15891	−	0.669096i	−0.951042	+	0.309061i	$0.899985\pi$
$692$	−2.53590	−	1.46410i	−0.0964004	−	0.0556568i
$693$	−0.803848	+	0.464102i	−0.0305356	+	0.0176298i
$694$			22.3923i			0.850000i
$695$		0			0
$696$	−3.23205	+	1.86603i	−0.122511	+	0.0707315i
$697$	8.00000			0.303022
$698$	−12.5885	+	7.26795i	−0.476480	+	0.275096i
$699$	9.06218	−	15.6962i	0.342763	−	0.593683i
$700$		0			0
$701$	−3.73205			−0.140958			−0.0704788	−	0.997513i	$-0.522453\pi$
$701$	−3.73205			−0.140958			−0.0704788	+	0.997513i	$0.522453\pi$
$702$	−2.50000	−	2.59808i	−0.0943564	−	0.0980581i
$703$			0.641016i			0.0241764i
$704$	0.401924	+	0.232051i	0.0151481	+	0.00874574i
$705$		0			0
$706$	−1.00000	−	1.73205i	−0.0376355	−	0.0651866i
$707$	21.8564			0.821995
$708$	0.767949	+	1.33013i	0.0288613	+	0.0499892i
$709$	−7.85641	+	4.53590i	−0.295054	+	0.170349i	−0.640219	−	0.768193i	$-0.721156\pi$
$709$	−7.85641	+	4.53590i	−0.295054	+	0.170349i	0.345165	+	0.938542i	$0.387823\pi$
$710$		0			0
$711$	0.0358984	+	0.0621778i	0.00134629	+	0.00233185i
$712$	−6.46410	−	3.73205i	−0.242252	−	0.139865i
$713$	0.232051	−	0.401924i	0.00869037	−	0.0150522i
$714$	−8.00000			−0.299392
$715$		0			0
$716$	16.2679			0.607962
$717$	2.19615	−	3.80385i	0.0820168	−	0.142057i
$718$	−16.3923	−	9.46410i	−0.611755	−	0.353197i
$719$	17.3205	+	30.0000i	0.645946	+	1.11881i	0.984082	+	0.177714i	$0.0568702\pi$
$719$	17.3205	+	30.0000i	0.645946	+	1.11881i	−0.338136	+	0.941097i	$0.609796\pi$
$720$		0			0
$721$	27.4641	−	15.8564i	1.02282	−	0.590523i
$722$	−9.35641	−	16.2058i	−0.348209	−	0.603116i
$723$	14.2679			0.530631
$724$	−5.46410	−	9.46410i	−0.203072	−	0.351731i
$725$		0			0
$726$	−9.33975	−	5.39230i	−0.346630	−	0.200127i
$727$			23.7128i			0.879460i	0.898130	+	0.439730i	$0.144926\pi$
$727$			23.7128i			0.879460i	−0.898130	+	0.439730i	$0.855074\pi$
$728$	−1.73205	−	7.00000i	−0.0641941	−	0.259437i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−3.85641	+	6.67949i	−0.142634	+	0.247050i
$732$	9.00000	−	5.19615i	0.332650	−	0.192055i
$733$	37.0718			1.36928			0.684639	−	0.728882i	$-0.259960\pi$
$733$	37.0718			1.36928			0.684639	+	0.728882i	$0.259960\pi$
$734$	31.5167	−	18.1962i	1.16330	−	0.671632i
$735$		0			0
$736$		−	0.267949i		−	0.00987674i
$737$	−1.82309	+	1.05256i	−0.0671542	+	0.0387715i
$738$	1.73205	+	1.00000i	0.0637577	+	0.0368105i
$739$	13.2679	+	7.66025i	0.488069	+	0.281787i	0.723773	−	0.690038i	$-0.242406\pi$
$739$	13.2679	+	7.66025i	0.488069	+	0.281787i	−0.235704	+	0.971825i	$0.575740\pi$
$740$		0			0
$741$	1.85641	+	0.535898i	0.0681968	+	0.0196867i
$742$		−	25.8564i		−	0.949219i
$743$	16.7679	−	29.0429i	0.615156	−	1.06548i	−0.375201	−	0.926944i	$-0.622426\pi$
$743$	16.7679	−	29.0429i	0.615156	−	1.06548i	0.990357	−	0.138539i	$-0.0442405\pi$
$744$	−0.866025	+	1.50000i	−0.0317500	+	0.0549927i
$745$		0			0
$746$		−	25.7846i		−	0.944042i
$747$	2.46410	+	4.26795i	0.0901568	+	0.156156i
$748$	0.928203	+	1.60770i	0.0339385	+	0.0587832i
$749$		−	39.7128i		−	1.45107i
$750$		0			0
$751$	−13.9641	+	24.1865i	−0.509557	+	0.882579i	0.490381	+	0.871508i	$0.336857\pi$
$751$	−13.9641	+	24.1865i	−0.509557	+	0.882579i	−0.999939	+	0.0110712i	$0.996476\pi$
$752$	5.23205	−	9.06218i	0.190793	−	0.330464i
$753$			12.2679i			0.447069i
$754$	−3.23205	−	13.0622i	−0.117704	−	0.475696i
$755$		0			0
$756$	−1.73205	−	1.00000i	−0.0629941	−	0.0363696i
$757$	15.5885	+	9.00000i	0.566572	+	0.327111i	0.755779	−	0.654827i	$-0.227258\pi$
$757$	15.5885	+	9.00000i	0.566572	+	0.327111i	−0.189207	+	0.981937i	$0.560592\pi$
$758$	−0.124356	+	0.0717968i	−0.00451680	+	0.00260778i
$759$		−	0.124356i		−	0.00451382i
$760$		0			0
$761$	−16.3923	+	9.46410i	−0.594221	+	0.343073i	−0.766765	−	0.641928i	$-0.778135\pi$
$761$	−16.3923	+	9.46410i	−0.594221	+	0.343073i	0.172544	+	0.985002i	$0.444801\pi$
$762$	−8.92820			−0.323435
$763$	−20.5359	+	11.8564i	−0.743449	+	0.429231i
$764$	−7.26795	+	12.5885i	−0.262945	+	0.455434i
$765$		0			0
$766$	−4.60770			−0.166483
$767$	−5.37564	+	1.33013i	−0.194103	+	0.0480281i
$768$			1.00000i			0.0360844i
$769$	16.9641	+	9.79423i	0.611741	+	0.353189i	0.773647	−	0.633617i	$-0.218431\pi$
$769$	16.9641	+	9.79423i	0.611741	+	0.353189i	−0.161905	+	0.986806i	$0.551764\pi$
$770$		0			0
$771$	−11.3301	−	19.6244i	−0.408045	−	0.706754i
$772$	−23.3205			−0.839323
$773$	−13.8564	−	24.0000i	−0.498380	−	0.863220i	0.501618	−	0.865089i	$-0.332738\pi$
$773$	−13.8564	−	24.0000i	−0.498380	−	0.863220i	−0.999998	+	0.00186926i	$0.999405\pi$
$774$	−1.66987	+	0.964102i	−0.0600223	+	0.0346539i
$775$		0			0
$776$	−3.73205	−	6.46410i	−0.133973	−	0.232048i
$777$	2.07180	+	1.19615i	0.0743253	+	0.0429117i
$778$	−10.1340	+	17.5526i	−0.363321	+	0.629290i
$779$	−1.07180			−0.0384011
$780$		0			0
$781$	−3.89488			−0.139370
$782$	0.535898	−	0.928203i	0.0191637	−	0.0331925i
$783$	−3.23205	−	1.86603i	−0.115504	−	0.0666863i
$784$	1.50000	+	2.59808i	0.0535714	+	0.0927884i
$785$		0			0
$786$	−1.16025	+	0.669873i	−0.0413849	+	0.0238936i
$787$	0.866025	+	1.50000i	0.0308705	+	0.0534692i	0.881048	−	0.473027i	$-0.156839\pi$
$787$	0.866025	+	1.50000i	0.0308705	+	0.0534692i	−0.850177	+	0.526496i	$0.823505\pi$
$788$	16.3923			0.583952
$789$	9.06218	+	15.6962i	0.322622	+	0.558798i
$790$		0			0
$791$	−19.3923	−	11.1962i	−0.689511	−	0.398089i
$792$			0.464102i			0.0164911i
$793$	9.00000	+	36.3731i	0.319599	+	1.29165i
$794$	−12.1244			−0.430277
$795$		0			0
$796$	−9.46410	+	16.3923i	−0.335446	+	0.581010i
$797$	−32.7846	+	18.9282i	−1.16129	+	0.670471i	−0.951613	−	0.307299i	$-0.900575\pi$
$797$	−32.7846	+	18.9282i	−1.16129	+	0.670471i	−0.209678	+	0.977771i	$0.567241\pi$
$798$	1.07180			0.0379412
$799$	36.2487	−	20.9282i	1.28239	−	0.740387i
$800$		0			0
$801$		−	7.46410i		−	0.263731i
$802$	−27.7128	+	16.0000i	−0.978573	+	0.564980i
$803$	−0.803848	−	0.464102i	−0.0283672	−	0.0163778i
$804$	−3.92820	−	2.26795i	−0.138537	−	0.0799844i
$805$		0			0
$806$	−4.33013	−	4.50000i	−0.152522	−	0.158506i
$807$		−	12.0000i		−	0.422420i
$808$	5.46410	−	9.46410i	0.192226	−	0.332946i
$809$	−0.607695	+	1.05256i	−0.0213654	+	0.0370060i	−0.876510	−	0.481383i	$-0.840135\pi$
$809$	−0.607695	+	1.05256i	−0.0213654	+	0.0370060i	0.855145	+	0.518389i	$0.173468\pi$
$810$		0			0
$811$			0.784610i			0.0275514i	0.999905	+	0.0137757i	$0.00438508\pi$
$811$			0.784610i			0.0275514i	−0.999905	+	0.0137757i	$0.995615\pi$
$812$	−3.73205	−	6.46410i	−0.130969	−	0.226845i
$813$	−4.59808	−	7.96410i	−0.161262	−	0.279313i
$814$		−	0.555136i		−	0.0194575i
$815$		0			0
$816$	−2.00000	+	3.46410i	−0.0700140	+	0.121268i
$817$	0.516660	−	0.894882i	0.0180757	−	0.0313080i
$818$			4.00000i			0.139857i
$819$	5.19615	−	5.00000i	0.181568	−	0.174714i
$820$		0			0
$821$	−30.6506	−	17.6962i	−1.06971	−	0.617600i	−0.141611	−	0.989922i	$-0.545228\pi$
$821$	−30.6506	−	17.6962i	−1.06971	−	0.617600i	−0.928103	+	0.372322i	$0.878562\pi$
$822$	−3.86603	−	2.23205i	−0.134843	−	0.0778517i
$823$	20.0718	−	11.5885i	0.699659	−	0.403948i	−0.107561	−	0.994198i	$-0.534304\pi$
$823$	20.0718	−	11.5885i	0.699659	−	0.403948i	0.807220	+	0.590250i	$0.200971\pi$
$824$		−	15.8564i		−	0.552384i
$825$		0			0
$826$	−2.66025	+	1.53590i	−0.0925621	+	0.0534407i
$827$	−17.3205			−0.602293			−0.301147	−	0.953578i	$-0.597369\pi$
$827$	−17.3205			−0.602293			−0.301147	+	0.953578i	$0.597369\pi$
$828$	0.232051	−	0.133975i	0.00806432	−	0.00465594i
$829$	11.7321	−	20.3205i	0.407471	−	0.705760i	−0.587135	−	0.809489i	$-0.699744\pi$
$829$	11.7321	−	20.3205i	0.407471	−	0.705760i	0.994606	+	0.103729i	$0.0330774\pi$
$830$		0			0
$831$	−9.92820			−0.344406
$832$	−3.46410	−	1.00000i	−0.120096	−	0.0346688i
$833$			12.0000i			0.415775i
$834$	0.803848	+	0.464102i	0.0278350	+	0.0160705i
$835$		0			0
$836$	−0.124356	−	0.215390i	−0.00430093	−	0.00744943i
$837$	−1.73205			−0.0598684
$838$	0.803848	+	1.39230i	0.0277685	+	0.0480964i
$839$	34.2679	−	19.7846i	1.18306	−	0.683041i	0.226340	−	0.974048i	$-0.427324\pi$
$839$	34.2679	−	19.7846i	1.18306	−	0.683041i	0.956721	+	0.291008i	$0.0939905\pi$
$840$		0			0
$841$	7.53590	+	13.0526i	0.259859	+	0.450088i
$842$	−14.1962	−	8.19615i	−0.489232	−	0.282458i
$843$	−2.46410	+	4.26795i	−0.0848682	+	0.146996i
$844$	23.3205			0.802725
$845$		0			0
$846$	10.4641			0.359763
$847$	10.7846	−	18.6795i	0.370564	−	0.641835i
$848$	−11.1962	−	6.46410i	−0.384477	−	0.221978i
$849$	−1.96410	−	3.40192i	−0.0674078	−	0.116754i
$850$		0			0
$851$	−0.277568	+	0.160254i	−0.00951491	+	0.00549344i
$852$	−4.19615	−	7.26795i	−0.143758	−	0.248996i
$853$	35.8372			1.22704			0.613521	−	0.789679i	$-0.289753\pi$
$853$	35.8372			1.22704			0.613521	+	0.789679i	$0.289753\pi$
$854$	10.3923	+	18.0000i	0.355617	+	0.615947i
$855$		0			0
$856$	−17.1962	−	9.92820i	−0.587752	−	0.339339i
$857$		−	20.5167i		−	0.700836i	−0.936593	−	0.350418i	$-0.886040\pi$
$857$		−	20.5167i		−	0.700836i	0.936593	−	0.350418i	$-0.113960\pi$
$858$	−1.60770	−	0.464102i	−0.0548858	−	0.0158442i
$859$	−27.1769			−0.927264			−0.463632	−	0.886028i	$-0.653454\pi$
$859$	−27.1769			−0.927264			−0.463632	+	0.886028i	$0.653454\pi$
$860$		0			0
$861$	−2.00000	+	3.46410i	−0.0681598	+	0.118056i
$862$	6.58846	−	3.80385i	0.224404	−	0.129560i
$863$	−42.4641			−1.44549			−0.722747	−	0.691112i	$-0.757121\pi$
$863$	−42.4641			−1.44549			−0.722747	+	0.691112i	$0.757121\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$		0			0
$866$			15.3205i			0.520612i
$867$	0.866025	−	0.500000i	0.0294118	−	0.0169809i
$868$	−3.00000	−	1.73205i	−0.101827	−	0.0587896i
$869$	0.0288568	+	0.0166605i	0.000978901	+	0.000565169i
$870$		0			0
$871$	11.7846	−	11.3397i	0.399306	−	0.384233i
$872$			11.8564i			0.401509i
$873$	3.73205	−	6.46410i	0.126311	−	0.218777i
$874$	−0.0717968	+	0.124356i	−0.00242856	+	0.00420639i
$875$		0			0
$876$		−	2.00000i		−	0.0675737i
$877$	14.0622	+	24.3564i	0.474846	+	0.822457i	0.999585	−	0.0288057i	$-0.00917042\pi$
$877$	14.0622	+	24.3564i	0.474846	+	0.822457i	−0.524739	+	0.851263i	$0.675837\pi$
$878$	4.92820	+	8.53590i	0.166319	+	0.288073i
$879$			4.14359i			0.139760i
$880$		0			0
$881$	7.00000	−	12.1244i	0.235836	−	0.408480i	−0.723679	−	0.690136i	$-0.757551\pi$
$881$	7.00000	−	12.1244i	0.235836	−	0.408480i	0.959515	+	0.281656i	$0.0908839\pi$
$882$	−1.50000	+	2.59808i	−0.0505076	+	0.0874818i
$883$		−	16.0718i		−	0.540859i	−0.962740	−	0.270430i	$-0.912834\pi$
$883$		−	16.0718i		−	0.540859i	0.962740	−	0.270430i	$-0.0871657\pi$
$884$	−10.0000	−	10.3923i	−0.336336	−	0.349531i
$885$		0			0
$886$	−3.80385	−	2.19615i	−0.127793	−	0.0737812i
$887$	8.76795	+	5.06218i	0.294399	+	0.169971i	0.639924	−	0.768438i	$-0.278966\pi$
$887$	8.76795	+	5.06218i	0.294399	+	0.169971i	−0.345525	+	0.938410i	$0.612299\pi$
$888$	1.03590	−	0.598076i	0.0347625	−	0.0200701i
$889$		−	17.8564i		−	0.598885i
$890$		0			0
$891$	−0.401924	+	0.232051i	−0.0134650	+	0.00777399i
$892$	−27.4641			−0.919566
$893$	−4.85641	+	2.80385i	−0.162513	+	0.0938272i
$894$	−10.2321	+	17.7224i	−0.342211	+	0.592727i
$895$		0			0
$896$	−2.00000			−0.0668153
$897$	0.232051	+	0.937822i	0.00774795	+	0.0313130i
$898$			39.7128i			1.32523i
$899$	−5.59808	−	3.23205i	−0.186706	−	0.107795i
$900$		0			0
$901$	−25.8564	−	44.7846i	−0.861402	−	1.49199i
$902$	0.928203			0.0309058
$903$	−1.92820	−	3.33975i	−0.0641666	−	0.111140i
$904$	−9.69615	+	5.59808i	−0.322489	+	0.186189i
$905$		0			0
$906$	−5.19615	−	9.00000i	−0.172631	−	0.299005i
$907$	−5.93782	−	3.42820i	−0.197162	−	0.113832i	0.398169	−	0.917312i	$-0.369646\pi$
$907$	−5.93782	−	3.42820i	−0.197162	−	0.113832i	−0.595331	+	0.803480i	$0.702979\pi$
$908$	−2.19615	+	3.80385i	−0.0728819	+	0.126235i
$909$	10.9282			0.362466
$910$		0			0
$911$	−24.2487			−0.803396			−0.401698	−	0.915772i	$-0.631580\pi$
$911$	−24.2487			−0.803396			−0.401698	+	0.915772i	$0.631580\pi$
$912$	0.267949	−	0.464102i	0.00887268	−	0.0153679i
$913$	1.98076	+	1.14359i	0.0655537	+	0.0378474i
$914$	15.7321	+	27.2487i	0.520370	+	0.901307i
$915$		0			0
$916$	17.1962	−	9.92820i	0.568177	−	0.328037i
$917$	−1.33975	−	2.32051i	−0.0442423	−	0.0766299i
$918$	−4.00000			−0.132020
$919$	−27.3205	−	47.3205i	−0.901220	−	1.56096i	−0.825912	−	0.563799i	$-0.809339\pi$
$919$	−27.3205	−	47.3205i	−0.901220	−	1.56096i	−0.0753085	−	0.997160i	$-0.523994\pi$
$920$		0			0
$921$	−10.8564	−	6.26795i	−0.357731	−	0.206536i
$922$			6.46410i			0.212884i
$923$	29.3731	−	7.26795i	0.966826	−	0.239227i
$924$	−0.928203			−0.0305356
$925$		0			0
$926$	10.4641	−	18.1244i	0.343872	−	0.595603i
$927$	13.7321	−	7.92820i	0.451020	−	0.260396i
$928$	−3.73205			−0.122511
$929$	−29.3205	+	16.9282i	−0.961975	+	0.555396i	−0.896780	−	0.442476i	$-0.854100\pi$
$929$	−29.3205	+	16.9282i	−0.961975	+	0.555396i	−0.0651944	+	0.997873i	$0.520767\pi$
$930$		0			0
$931$		−	1.60770i		−	0.0526901i
$932$	15.6962	−	9.06218i	0.514145	−	0.296842i
$933$	6.58846	+	3.80385i	0.215696	+	0.124532i
$934$	−10.2679	−	5.92820i	−0.335978	−	0.193977i
$935$		0			0
$936$	−0.866025	−	3.50000i	−0.0283069	−	0.114401i
$937$			44.6410i			1.45836i	0.684323	+	0.729179i	$0.260098\pi$
$937$			44.6410i			1.45836i	−0.684323	+	0.729179i	$0.739902\pi$
$938$	4.53590	−	7.85641i	0.148102	−	0.256521i
$939$	14.0000	−	24.2487i	0.456873	−	0.791327i
$940$		0			0
$941$		−	26.7846i		−	0.873153i	−0.899667	−	0.436577i	$-0.856191\pi$
$941$		−	26.7846i		−	0.873153i	0.899667	−	0.436577i	$-0.143809\pi$
$942$	−2.50000	−	4.33013i	−0.0814544	−	0.141083i
$943$	−0.267949	−	0.464102i	−0.00872563	−	0.0151132i
$944$			1.53590i			0.0499892i
$945$		0			0
$946$	−0.447441	+	0.774991i	−0.0145476	+	0.0251971i
$947$	1.26795	−	2.19615i	0.0412028	−	0.0713654i	−0.844689	−	0.535258i	$-0.820214\pi$
$947$	1.26795	−	2.19615i	0.0412028	−	0.0713654i	0.885891	+	0.463893i	$0.153548\pi$
$948$			0.0717968i			0.00233185i
$949$	6.92820	+	2.00000i	0.224899	+	0.0649227i
$950$		0			0
$951$	−18.5885	−	10.7321i	−0.602772	−	0.348011i
$952$	−6.92820	−	4.00000i	−0.224544	−	0.129641i
$953$	13.6244	−	7.86603i	0.441336	−	0.254806i	−0.262828	−	0.964843i	$-0.584655\pi$
$953$	13.6244	−	7.86603i	0.441336	−	0.254806i	0.704164	+	0.710037i	$0.251322\pi$
$954$		−	12.9282i		−	0.418566i
$955$		0			0
$956$	3.80385	−	2.19615i	0.123025	−	0.0710286i
$957$	−1.73205			−0.0559893
$958$	1.26795	−	0.732051i	0.0409656	−	0.0236515i
$959$	4.46410	−	7.73205i	0.144153	−	0.249681i
$960$		0			0
$961$	28.0000			0.903226
$962$	1.03590	+	4.18653i	0.0333987	+	0.134979i
$963$		−	19.8564i		−	0.639864i
$964$	12.3564	+	7.13397i	0.397973	+	0.229770i
$965$		0			0
$966$	0.267949	+	0.464102i	0.00862112	+	0.0149322i
$967$	−34.5359			−1.11060			−0.555300	−	0.831650i	$-0.687396\pi$
$967$	−34.5359			−1.11060			−0.555300	+	0.831650i	$0.687396\pi$
$968$	−5.39230	−	9.33975i	−0.173315	−	0.300191i
$969$	1.85641	−	1.07180i	0.0596364	−	0.0344311i
$970$		0			0
$971$	−5.73205	−	9.92820i	−0.183950	−	0.318611i	0.759272	−	0.650773i	$-0.225555\pi$
$971$	−5.73205	−	9.92820i	−0.183950	−	0.318611i	−0.943222	+	0.332162i	$0.892222\pi$
$972$	−0.866025	−	0.500000i	−0.0277778	−	0.0160375i
$973$	−0.928203	+	1.60770i	−0.0297568	+	0.0515403i
$974$	−39.1769			−1.25531
$975$		0			0
$976$	10.3923			0.332650
$977$	16.6962	−	28.9186i	0.534157	−	0.925187i	−0.465046	−	0.885286i	$-0.653962\pi$
$977$	16.6962	−	28.9186i	0.534157	−	0.925187i	0.999204	−	0.0399012i	$-0.0127043\pi$
$978$	−19.9641	−	11.5263i	−0.638382	−	0.368570i
$979$	−1.73205	−	3.00000i	−0.0553566	−	0.0958804i
$980$		0			0
$981$	−10.2679	+	5.92820i	−0.327830	+	0.189273i
$982$	−8.66025	−	15.0000i	−0.276360	−	0.478669i
$983$	57.3923			1.83053			0.915265	−	0.402852i	$-0.131981\pi$
$983$	57.3923			1.83053			0.915265	+	0.402852i	$0.131981\pi$
$984$	1.00000	+	1.73205i	0.0318788	+	0.0552158i
$985$		0			0
$986$	−12.9282	−	7.46410i	−0.411718	−	0.237705i
$987$			20.9282i			0.666152i
$988$	1.33975	+	1.39230i	0.0426230	+	0.0442951i
$989$	0.516660			0.0164288
$990$		0			0
$991$	12.5718	−	21.7750i	0.399356	−	0.691705i	−0.594290	−	0.804251i	$-0.702567\pi$
$991$	12.5718	−	21.7750i	0.399356	−	0.691705i	0.993647	+	0.112545i	$0.0359003\pi$
$992$	−1.50000	+	0.866025i	−0.0476250	+	0.0274963i
$993$	24.7846			0.786516
$994$	14.5359	−	8.39230i	0.461051	−	0.266188i
$995$		0			0
$996$			4.92820i			0.156156i
$997$	−41.1962	+	23.7846i	−1.30470	+	0.753266i	−0.981206	−	0.192966i	$-0.938189\pi$
$997$	−41.1962	+	23.7846i	−1.30470	+	0.753266i	−0.323490	+	0.946232i	$0.604856\pi$
$998$	−11.6603	−	6.73205i	−0.369099	−	0.213099i
$999$	1.03590	+	0.598076i	0.0327744	+	0.0189223i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.y.c.199.1		4
5.2	odd	4		1950.2.bc.b.901.1		4
5.3	odd	4		390.2.bb.b.121.2	✓	4
5.4	even	2		1950.2.y.f.199.2		4
13.10	even	6		1950.2.y.f.49.2		4
15.8	even	4		1170.2.bs.e.901.1		4
65.23	odd	12		390.2.bb.b.361.2	yes	4
65.33	even	12		5070.2.a.bg.1.1		2
65.43	odd	12		5070.2.b.o.1351.4		4
65.48	odd	12		5070.2.b.o.1351.1		4
65.49	even	6	inner	1950.2.y.c.49.1		4
65.58	even	12		5070.2.a.y.1.2		2
65.62	odd	12		1950.2.bc.b.751.1		4
195.23	even	12		1170.2.bs.e.361.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bb.b.121.2	✓	4	5.3	odd	4
390.2.bb.b.361.2	yes	4	65.23	odd	12
1170.2.bs.e.361.1		4	195.23	even	12
1170.2.bs.e.901.1		4	15.8	even	4
1950.2.y.c.49.1		4	65.49	even	6	inner
1950.2.y.c.199.1		4	1.1	even	1	trivial
1950.2.y.f.49.2		4	13.10	even	6
1950.2.y.f.199.2		4	5.4	even	2
1950.2.bc.b.751.1		4	65.62	odd	12
1950.2.bc.b.901.1		4	5.2	odd	4
5070.2.a.y.1.2		2	65.58	even	12
5070.2.a.bg.1.1		2	65.33	even	12
5070.2.b.o.1351.1		4	65.48	odd	12
5070.2.b.o.1351.4		4	65.43	odd	12

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:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.y (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(0.401924 + 0.232051i) q^{11} +1.00000i q^{12} +(-3.46410 - 1.00000i) q^{13} -2.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.46410 + 2.00000i) q^{17} -1.00000 q^{18} +(0.464102 - 0.267949i) q^{19} -2.00000i q^{21} +(-0.401924 + 0.232051i) q^{22} +(0.232051 + 0.133975i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(2.59808 - 2.50000i) q^{26} -1.00000i q^{27} +(1.00000 - 1.73205i) q^{28} +(1.86603 - 3.23205i) q^{29} -1.73205i q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.232051 - 0.401924i) q^{33} -4.00000i q^{34} +(0.500000 - 0.866025i) q^{36} +(-0.598076 + 1.03590i) q^{37} +0.535898i q^{38} +(2.50000 + 2.59808i) q^{39} +(-1.73205 - 1.00000i) q^{41} +(1.73205 + 1.00000i) q^{42} +(1.66987 - 0.964102i) q^{43} -0.464102i q^{44} +(-0.232051 + 0.133975i) q^{46} -10.4641 q^{47} +(0.866025 - 0.500000i) q^{48} +(1.50000 - 2.59808i) q^{49} +4.00000 q^{51} +(0.866025 + 3.50000i) q^{52} +12.9282i q^{53} +(0.866025 + 0.500000i) q^{54} +(1.00000 + 1.73205i) q^{56} -0.535898 q^{57} +(1.86603 + 3.23205i) q^{58} +(1.33013 - 0.767949i) q^{59} +(-5.19615 - 9.00000i) q^{61} +(1.50000 + 0.866025i) q^{62} +(-1.00000 + 1.73205i) q^{63} +1.00000 q^{64} +0.464102 q^{66} +(-2.26795 + 3.92820i) q^{67} +(3.46410 + 2.00000i) q^{68} +(-0.133975 - 0.232051i) q^{69} +(-7.26795 + 4.19615i) q^{71} +(0.500000 + 0.866025i) q^{72} -2.00000 q^{73} +(-0.598076 - 1.03590i) q^{74} +(-0.464102 - 0.267949i) q^{76} +0.928203i q^{77} +(-3.50000 + 0.866025i) q^{78} +0.0717968 q^{79} +(-0.500000 + 0.866025i) q^{81} +(1.73205 - 1.00000i) q^{82} +4.92820 q^{83} +(-1.73205 + 1.00000i) q^{84} +1.92820i q^{86} +(-3.23205 + 1.86603i) q^{87} +(0.401924 + 0.232051i) q^{88} +(-6.46410 - 3.73205i) q^{89} +(-1.73205 - 7.00000i) q^{91} -0.267949i q^{92} +(-0.866025 + 1.50000i) q^{93} +(5.23205 - 9.06218i) q^{94} +1.00000i q^{96} +(-3.73205 - 6.46410i) q^{97} +(1.50000 + 2.59808i) q^{98} +0.464102i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} + 4 q^{7} + 4 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^4 + 4 * q^7 + 4 * q^8 + 2 * q^9	\( 4 q - 2 q^{2} - 2 q^{4} + 4 q^{7} + 4 q^{8} + 2 q^{9} + 12 q^{11} - 8 q^{14} - 2 q^{16} - 4 q^{18} - 12 q^{19} - 12 q^{22} - 6 q^{23} + 4 q^{28} + 4 q^{29} - 2 q^{32} + 6 q^{33} + 2 q^{36} + 8 q^{37} + 10 q^{39} + 24 q^{43} + 6 q^{46} - 28 q^{47} + 6 q^{49} + 16 q^{51} + 4 q^{56} - 16 q^{57} + 4 q^{58} - 12 q^{59} + 6 q^{62} - 4 q^{63} + 4 q^{64} - 12 q^{66} - 16 q^{67} - 4 q^{69} - 36 q^{71} + 2 q^{72} - 8 q^{73} + 8 q^{74} + 12 q^{76} - 14 q^{78} + 28 q^{79} - 2 q^{81} - 8 q^{83} - 6 q^{87} + 12 q^{88} - 12 q^{89} + 14 q^{94} - 8 q^{97} + 6 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 + 4 * q^7 + 4 * q^8 + 2 * q^9 + 12 * q^11 - 8 * q^14 - 2 * q^16 - 4 * q^18 - 12 * q^19 - 12 * q^22 - 6 * q^23 + 4 * q^28 + 4 * q^29 - 2 * q^32 + 6 * q^33 + 2 * q^36 + 8 * q^37 + 10 * q^39 + 24 * q^43 + 6 * q^46 - 28 * q^47 + 6 * q^49 + 16 * q^51 + 4 * q^56 - 16 * q^57 + 4 * q^58 - 12 * q^59 + 6 * q^62 - 4 * q^63 + 4 * q^64 - 12 * q^66 - 16 * q^67 - 4 * q^69 - 36 * q^71 + 2 * q^72 - 8 * q^73 + 8 * q^74 + 12 * q^76 - 14 * q^78 + 28 * q^79 - 2 * q^81 - 8 * q^83 - 6 * q^87 + 12 * q^88 - 12 * q^89 + 14 * q^94 - 8 * q^97 + 6 * q^98

Introduction

L-functions

Modular forms

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Database

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