LMFDB - Embedded newform 1950.2.bc.b.901.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(751,1950)]

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, 0, 5]))

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

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

chi := DirichletCharacter("1950.751");

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.bc (of order $6$, 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:	$15.5708283941$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			901.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1950.901
Dual form			1950.2.bc.b.751.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−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
$6$	0.866025	−	0.500000i	0.353553	−	0.204124i
$7$	−1.73205	+	1.00000i	−0.654654	+	0.377964i	−0.790237	−	0.612801i	$-0.790043\pi$
$7$	−1.73205	+	1.00000i	−0.654654	+	0.377964i	0.135583	+	0.990766i	$0.456709\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−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	$0.644378\pi$
$12$	−1.00000			−0.288675
$13$	−1.00000	+	3.46410i	−0.277350	+	0.960769i
$13$	−1.00000	+	3.46410i	−0.277350	+	0.960769i
$14$	2.00000			0.534522
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.00000	−	3.46410i	−0.485071	−	0.840168i	0.514782	−	0.857321i	$-0.327873\pi$
$17$	−2.00000	−	3.46410i	−0.485071	−	0.840168i	−0.999853	+	0.0171533i	$0.994540\pi$
$18$			1.00000i			0.235702i
$19$	−0.464102	+	0.267949i	−0.106472	+	0.0614718i	−0.552291	−	0.833652i	$-0.686246\pi$
$19$	−0.464102	+	0.267949i	−0.106472	+	0.0614718i	0.445818	+	0.895123i	$0.352913\pi$
$20$		0			0
$21$		−	2.00000i		−	0.436436i
$22$	−0.232051	−	0.401924i	−0.0494734	−	0.0856904i
$23$	0.133975	−	0.232051i	0.0279356	−	0.0483859i	−0.851720	−	0.523998i	$-0.824440\pi$
$23$	0.133975	−	0.232051i	0.0279356	−	0.0483859i	0.879655	+	0.475612i	$0.157773\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$		0			0
$26$	2.59808	−	2.50000i	0.509525	−	0.490290i
$27$	1.00000			0.192450
$28$	−1.73205	−	1.00000i	−0.327327	−	0.188982i
$29$	−1.86603	+	3.23205i	−0.346512	+	0.600177i	−0.985627	−	0.168934i	$-0.945967\pi$
$29$	−1.86603	+	3.23205i	−0.346512	+	0.600177i	0.639115	+	0.769111i	$0.279301\pi$
$30$		0			0
$31$		−	1.73205i		−	0.311086i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$		−	1.73205i		−	0.311086i	0.987829	−	0.155543i	$-0.0497126\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−0.401924	+	0.232051i	−0.0699660	+	0.0403949i
$34$			4.00000i			0.685994i
$35$		0			0
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−1.03590	−	0.598076i	−0.170301	−	0.0983231i	0.412427	−	0.910991i	$-0.364681\pi$
$37$	−1.03590	−	0.598076i	−0.170301	−	0.0983231i	−0.582728	+	0.812668i	$0.698015\pi$
$38$	0.535898			0.0869342
$39$	−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	$0.716583\pi$
$42$	−1.00000	+	1.73205i	−0.154303	+	0.267261i
$43$	−0.964102	−	1.66987i	−0.147024	−	0.254653i	0.783102	−	0.621893i	$-0.213636\pi$
$43$	−0.964102	−	1.66987i	−0.147024	−	0.254653i	−0.930126	+	0.367240i	$0.880303\pi$
$44$			0.464102i			0.0699660i
$45$		0			0
$46$	−0.232051	+	0.133975i	−0.0342140	+	0.0197535i
$47$		−	10.4641i		−	1.52635i	−0.646194	−	0.763173i	$-0.723640\pi$
$47$		−	10.4641i		−	1.52635i	0.646194	−	0.763173i	$-0.276360\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	−1.50000	+	2.59808i	−0.214286	+	0.371154i
$50$		0			0
$51$	4.00000			0.560112
$52$	−3.50000	+	0.866025i	−0.485363	+	0.120096i
$53$	12.9282			1.77583			0.887913	−	0.460012i	$-0.152155\pi$
$53$	12.9282			1.77583			0.887913	+	0.460012i	$0.152155\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$		0			0
$56$	1.00000	+	1.73205i	0.133631	+	0.231455i
$57$		−	0.535898i		−	0.0709815i
$58$	3.23205	−	1.86603i	0.424389	−	0.245021i
$59$	−1.33013	+	0.767949i	−0.173168	+	0.0999785i	−0.584079	−	0.811697i	$-0.698544\pi$
$59$	−1.33013	+	0.767949i	−0.173168	+	0.0999785i	0.410911	+	0.911676i	$0.365211\pi$
$60$		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	$-0.398363\pi$
$62$	−0.866025	+	1.50000i	−0.109985	+	0.190500i
$63$	1.73205	+	1.00000i	0.218218	+	0.125988i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	0.464102			0.0571270
$67$	−3.92820	−	2.26795i	−0.479906	−	0.277074i	0.240471	−	0.970656i	$-0.422698\pi$
$67$	−3.92820	−	2.26795i	−0.479906	−	0.277074i	−0.720377	+	0.693582i	$0.756031\pi$
$68$	2.00000	−	3.46410i	0.242536	−	0.420084i
$69$	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	$0.499262\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$			2.00000i			0.234082i	0.993127	+	0.117041i	$0.0373409\pi$
$73$			2.00000i			0.234082i	−0.993127	+	0.117041i	$0.962659\pi$
$74$	0.598076	+	1.03590i	0.0695249	+	0.120421i
$75$		0			0
$76$	−0.464102	−	0.267949i	−0.0532361	−	0.0307359i
$77$	−0.928203			−0.105779
$78$	0.866025	+	3.50000i	0.0980581	+	0.396297i
$79$	−0.0717968			−0.00807777			−0.00403888	−	0.999992i	$-0.501286\pi$
$79$	−0.0717968			−0.00807777			−0.00403888	+	0.999992i	$0.501286\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	1.00000	+	1.73205i	0.110432	+	0.191273i
$83$		−	4.92820i		−	0.540941i	−0.962728	−	0.270470i	$-0.912821\pi$
$83$		−	4.92820i		−	0.540941i	0.962728	−	0.270470i	$-0.0871792\pi$
$84$	1.73205	−	1.00000i	0.188982	−	0.109109i
$85$		0			0
$86$			1.92820i			0.207924i
$87$	−1.86603	−	3.23205i	−0.200059	−	0.346512i
$88$	0.232051	−	0.401924i	0.0247367	−	0.0428452i
$89$	6.46410	+	3.73205i	0.685193	+	0.395597i	0.801809	−	0.597581i	$-0.203871\pi$
$89$	6.46410	+	3.73205i	0.685193	+	0.395597i	−0.116615	+	0.993177i	$0.537205\pi$
$90$		0			0
$91$	−1.73205	−	7.00000i	−0.181568	−	0.733799i
$92$	0.267949			0.0279356
$93$	1.50000	+	0.866025i	0.155543	+	0.0898027i
$94$	−5.23205	+	9.06218i	−0.539645	+	0.934692i
$95$		0			0
$96$			1.00000i			0.102062i
$97$	6.46410	−	3.73205i	0.656330	−	0.378932i	−0.134547	−	0.990907i	$-0.542958\pi$
$97$	6.46410	−	3.73205i	0.656330	−	0.378932i	0.790877	+	0.611975i	$0.209625\pi$
$98$	2.59808	−	1.50000i	0.262445	−	0.151523i
$99$		−	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	$-0.0163098\pi$
$102$	−3.46410	−	2.00000i	−0.342997	−	0.198030i
$103$	−15.8564			−1.56238			−0.781189	−	0.624295i	$-0.785387\pi$
$103$	−15.8564			−1.56238			−0.781189	+	0.624295i	$0.785387\pi$
$104$	3.46410	+	1.00000i	0.339683	+	0.0980581i
$105$		0			0
$106$	−11.1962	−	6.46410i	−1.08747	−	0.627849i
$107$	9.92820	−	17.1962i	0.959796	−	1.66241i	0.236805	−	0.971557i	$-0.423900\pi$
$107$	9.92820	−	17.1962i	0.959796	−	1.66241i	0.722991	−	0.690858i	$-0.242767\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$		−	11.8564i		−	1.13564i	−0.823154	−	0.567819i	$-0.807787\pi$
$109$		−	11.8564i		−	1.13564i	0.823154	−	0.567819i	$-0.192213\pi$
$110$		0			0
$111$	1.03590	−	0.598076i	0.0983231	−	0.0567669i
$112$		−	2.00000i		−	0.188982i
$113$	5.59808	+	9.69615i	0.526623	+	0.912137i	0.999519	+	0.0310191i	$0.00987527\pi$
$113$	5.59808	+	9.69615i	0.526623	+	0.912137i	−0.472896	+	0.881118i	$0.656791\pi$
$114$	−0.267949	+	0.464102i	−0.0250957	+	0.0434671i
$115$		0			0
$116$	−3.73205			−0.346512
$117$	3.50000	−	0.866025i	0.323575	−	0.0800641i
$118$	1.53590			0.141391
$119$	6.92820	+	4.00000i	0.635107	+	0.366679i
$120$		0			0
$121$	−5.39230	−	9.33975i	−0.490210	−	0.849068i
$122$			10.3923i			0.940875i
$123$	1.73205	−	1.00000i	0.156174	−	0.0901670i
$124$	1.50000	−	0.866025i	0.134704	−	0.0777714i
$125$		0			0
$126$	−1.00000	−	1.73205i	−0.0890871	−	0.154303i
$127$	4.46410	−	7.73205i	0.396125	−	0.686109i	−0.597119	−	0.802153i	$-0.703688\pi$
$127$	4.46410	−	7.73205i	0.396125	−	0.686109i	0.993244	+	0.116044i	$0.0370214\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	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	$0.518640\pi$
$132$	−0.401924	−	0.232051i	−0.0349830	−	0.0201974i
$133$	0.535898	−	0.928203i	0.0464683	−	0.0804854i
$134$	2.26795	+	3.92820i	0.195921	+	0.339345i
$135$		0			0
$136$	−3.46410	+	2.00000i	−0.297044	+	0.171499i
$137$	3.86603	−	2.23205i	0.330297	−	0.190697i	−0.325676	−	0.945481i	$-0.605592\pi$
$137$	3.86603	−	2.23205i	0.330297	−	0.190697i	0.655973	+	0.754784i	$0.272259\pi$
$138$		−	0.267949i		−	0.0228093i
$139$	−0.464102	−	0.803848i	−0.0393646	−	0.0681815i	0.845672	−	0.533703i	$-0.179200\pi$
$139$	−0.464102	−	0.803848i	−0.0393646	−	0.0681815i	−0.885036	+	0.465522i	$0.845867\pi$
$140$		0			0
$141$	9.06218	+	5.23205i	0.763173	+	0.440618i
$142$	8.39230			0.704267
$143$	−1.20577	+	1.16025i	−0.100832	+	0.0970253i
$144$	1.00000			0.0833333
$145$		0			0
$146$	1.00000	−	1.73205i	0.0827606	−	0.143346i
$147$	−1.50000	−	2.59808i	−0.123718	−	0.214286i
$148$		−	1.19615i		−	0.0983231i
$149$	17.7224	−	10.2321i	1.45188	−	0.838242i	0.453290	−	0.891363i	$-0.350250\pi$
$149$	17.7224	−	10.2321i	1.45188	−	0.838242i	0.998588	+	0.0531208i	$0.0169168\pi$
$150$		0			0
$151$		−	10.3923i		−	0.845714i	−0.906196	−	0.422857i	$-0.861027\pi$
$151$		−	10.3923i		−	0.845714i	0.906196	−	0.422857i	$-0.138973\pi$
$152$	0.267949	+	0.464102i	0.0217335	+	0.0376436i
$153$	−2.00000	+	3.46410i	−0.161690	+	0.280056i
$154$	0.803848	+	0.464102i	0.0647759	+	0.0373984i
$155$		0			0
$156$	1.00000	−	3.46410i	0.0800641	−	0.277350i
$157$	5.00000			0.399043			0.199522	−	0.979893i	$-0.436061\pi$
$157$	5.00000			0.399043			0.199522	+	0.979893i	$0.436061\pi$
$158$	0.0621778	+	0.0358984i	0.00494660	+	0.00285592i
$159$	−6.46410	+	11.1962i	−0.512637	+	0.887913i
$160$		0			0
$161$			0.535898i			0.0422347i
$162$	0.866025	−	0.500000i	0.0680414	−	0.0392837i
$163$	−19.9641	+	11.5263i	−1.56371	+	0.902808i	−0.566833	+	0.823833i	$0.691831\pi$
$163$	−19.9641	+	11.5263i	−1.56371	+	0.902808i	−0.996877	+	0.0789748i	$0.974835\pi$
$164$		−	2.00000i		−	0.156174i
$165$		0			0
$166$	−2.46410	+	4.26795i	−0.191251	+	0.331257i
$167$	−15.8660	−	9.16025i	−1.22775	−	0.708842i	−0.261191	−	0.965287i	$-0.584115\pi$
$167$	−15.8660	−	9.16025i	−1.22775	−	0.708842i	−0.966559	+	0.256445i	$0.917449\pi$
$168$	−2.00000			−0.154303
$169$	−11.0000	−	6.92820i	−0.846154	−	0.532939i
$170$		0			0
$171$	0.464102	+	0.267949i	0.0354907	+	0.0204906i
$172$	0.964102	−	1.66987i	0.0735121	−	0.127327i
$173$	−1.46410	−	2.53590i	−0.111314	−	0.192801i	0.804987	−	0.593293i	$-0.202172\pi$
$173$	−1.46410	−	2.53590i	−0.111314	−	0.192801i	−0.916300	+	0.400492i	$0.868839\pi$
$174$			3.73205i			0.282926i
$175$		0			0
$176$	−0.401924	+	0.232051i	−0.0302961	+	0.0174915i
$177$		−	1.53590i		−	0.115445i
$178$	−3.73205	−	6.46410i	−0.279729	−	0.484505i
$179$	8.13397	−	14.0885i	0.607962	−	1.05302i	−0.383614	−	0.923494i	$-0.625321\pi$
$179$	8.13397	−	14.0885i	0.607962	−	1.05302i	0.991576	−	0.129527i	$-0.0413460\pi$
$180$		0			0
$181$	10.9282			0.812287			0.406143	−	0.913809i	$-0.366873\pi$
$181$	10.9282			0.812287			0.406143	+	0.913809i	$0.366873\pi$
$182$	−2.00000	+	6.92820i	−0.148250	+	0.513553i
$183$	10.3923			0.768221
$184$	−0.232051	−	0.133975i	−0.0171070	−	0.00987674i
$185$		0			0
$186$	−0.866025	−	1.50000i	−0.0635001	−	0.109985i
$187$		−	1.85641i		−	0.135754i
$188$	9.06218	−	5.23205i	0.660927	−	0.381587i
$189$	−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	$-0.342934\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−20.1962	−	11.6603i	−1.45375	−	0.839323i	−0.455059	−	0.890461i	$-0.650382\pi$
$193$	−20.1962	−	11.6603i	−1.45375	−	0.839323i	−0.998692	+	0.0511377i	$0.983715\pi$
$194$	−7.46410			−0.535891
$195$		0			0
$196$	−3.00000			−0.214286
$197$	−14.1962	−	8.19615i	−1.01143	−	0.583952i	−0.0998228	−	0.995005i	$-0.531828\pi$
$197$	−14.1962	−	8.19615i	−1.01143	−	0.583952i	−0.911611	+	0.411054i	$0.865161\pi$
$198$	−0.232051	+	0.401924i	−0.0164911	+	0.0285635i
$199$	9.46410	+	16.3923i	0.670892	+	1.16202i	0.977651	+	0.210232i	$0.0674221\pi$
$199$	9.46410	+	16.3923i	0.670892	+	1.16202i	−0.306759	+	0.951787i	$0.599245\pi$
$200$		0			0
$201$	3.92820	−	2.26795i	0.277074	−	0.159969i
$202$	−9.46410	+	5.46410i	−0.665892	+	0.384453i
$203$		−	7.46410i		−	0.523877i
$204$	2.00000	+	3.46410i	0.140028	+	0.242536i
$205$		0			0
$206$	13.7321	+	7.92820i	0.956757	+	0.552384i
$207$	−0.267949			−0.0186238
$208$	−2.50000	−	2.59808i	−0.173344	−	0.180144i
$209$	−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	$0.870049\pi$
$212$	6.46410	+	11.1962i	0.443956	+	0.768955i
$213$		−	8.39230i		−	0.575031i
$214$	−17.1962	+	9.92820i	−1.17550	+	0.678678i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	1.73205	+	3.00000i	0.117579	+	0.203653i
$218$	−5.92820	+	10.2679i	−0.401509	+	0.695433i
$219$	−1.73205	−	1.00000i	−0.117041	−	0.0675737i
$220$		0			0
$221$	14.0000	−	3.46410i	0.941742	−	0.233021i
$222$	−1.19615			−0.0802805
$223$	−23.7846	−	13.7321i	−1.59274	−	0.919566i	−0.992835	−	0.119491i	$-0.961874\pi$
$223$	−23.7846	−	13.7321i	−1.59274	−	0.919566i	−0.599900	−	0.800075i	$-0.704793\pi$
$224$	−1.00000	+	1.73205i	−0.0668153	+	0.115728i
$225$		0			0
$226$		−	11.1962i		−	0.744757i
$227$	3.80385	−	2.19615i	0.252470	−	0.145764i	−0.368425	−	0.929658i	$-0.620103\pi$
$227$	3.80385	−	2.19615i	0.252470	−	0.145764i	0.620895	+	0.783894i	$0.286769\pi$
$228$	0.464102	−	0.267949i	0.0307359	−	0.0177454i
$229$		−	19.8564i		−	1.31215i	−0.754696	−	0.656074i	$-0.772216\pi$
$229$		−	19.8564i		−	1.31215i	0.754696	−	0.656074i	$-0.227784\pi$
$230$		0			0
$231$	0.464102	−	0.803848i	0.0305356	−	0.0528893i
$232$	3.23205	+	1.86603i	0.212195	+	0.122511i
$233$	18.1244			1.18737			0.593683	−	0.804699i	$-0.297673\pi$
$233$	18.1244			1.18737			0.593683	+	0.804699i	$0.297673\pi$
$234$	−3.46410	−	1.00000i	−0.226455	−	0.0653720i
$235$		0			0
$236$	−1.33013	−	0.767949i	−0.0865839	−	0.0499892i
$237$	0.0358984	−	0.0621778i	0.00233185	−	0.00403888i
$238$	−4.00000	−	6.92820i	−0.259281	−	0.449089i
$239$		−	4.39230i		−	0.284115i	−0.989858	−	0.142057i	$-0.954628\pi$
$239$		−	4.39230i		−	0.284115i	0.989858	−	0.142057i	$-0.0453717\pi$
$240$		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	$0.485319\pi$
$242$			10.7846i			0.693261i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	5.19615	−	9.00000i	0.332650	−	0.576166i
$245$		0			0
$246$	−2.00000			−0.127515
$247$	−0.464102	−	1.87564i	−0.0295301	−	0.119344i
$248$	−1.73205			−0.109985
$249$	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	$0.959882\pi$
$252$			2.00000i			0.125988i
$253$	0.107695	−	0.0621778i	0.00677074	−	0.00390909i
$254$	−7.73205	+	4.46410i	−0.485152	+	0.280103i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−11.3301	+	19.6244i	−0.706754	+	1.22413i	0.259301	+	0.965797i	$0.416508\pi$
$257$	−11.3301	+	19.6244i	−0.706754	+	1.22413i	−0.966055	+	0.258337i	$0.916825\pi$
$258$	−1.66987	−	0.964102i	−0.103962	−	0.0600223i
$259$	2.39230			0.148651
$260$		0			0
$261$	3.73205			0.231008
$262$	1.16025	+	0.669873i	0.0716807	+	0.0413849i
$263$	−9.06218	+	15.6962i	−0.558798	+	0.967866i	0.438799	+	0.898585i	$0.355404\pi$
$263$	−9.06218	+	15.6962i	−0.558798	+	0.967866i	−0.997597	+	0.0692812i	$0.977929\pi$
$264$	0.232051	+	0.401924i	0.0142817	+	0.0247367i
$265$		0			0
$266$	−0.928203	+	0.535898i	−0.0569118	+	0.0328580i
$267$	−6.46410	+	3.73205i	−0.395597	+	0.228398i
$268$		−	4.53590i		−	0.277074i
$269$	−6.00000	−	10.3923i	−0.365826	−	0.633630i	0.623082	−	0.782157i	$-0.285880\pi$
$269$	−6.00000	−	10.3923i	−0.365826	−	0.633630i	−0.988908	+	0.148527i	$0.952547\pi$
$270$		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	$0.576560\pi$
$272$	4.00000			0.242536
$273$	6.92820	+	2.00000i	0.419314	+	0.121046i
$274$	−4.46410			−0.269686
$275$		0			0
$276$	−0.133975	+	0.232051i	−0.00806432	+	0.0139678i
$277$	4.96410	+	8.59808i	0.298264	+	0.516608i	0.975739	−	0.218938i	$-0.0702591\pi$
$277$	4.96410	+	8.59808i	0.298264	+	0.516608i	−0.677475	+	0.735546i	$0.736926\pi$
$278$			0.928203i			0.0556699i
$279$	−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	$-0.0469604\pi$
$282$	−5.23205	−	9.06218i	−0.311564	−	0.539645i
$283$	1.96410	−	3.40192i	0.116754	−	0.202223i	−0.801726	−	0.597692i	$-0.796085\pi$
$283$	1.96410	−	3.40192i	0.116754	−	0.202223i	0.918479	+	0.395469i	$0.129418\pi$
$284$	−7.26795	−	4.19615i	−0.431273	−	0.248996i
$285$		0			0
$286$	1.62436	−	0.401924i	0.0960502	−	0.0237663i
$287$	4.00000			0.236113
$288$	−0.866025	−	0.500000i	−0.0510310	−	0.0294628i
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$		0			0
$291$			7.46410i			0.437553i
$292$	−1.73205	+	1.00000i	−0.101361	+	0.0585206i
$293$	−3.58846	+	2.07180i	−0.209640	+	0.121036i	−0.601144	−	0.799141i	$-0.705288\pi$
$293$	−3.58846	+	2.07180i	−0.209640	+	0.121036i	0.391504	+	0.920176i	$0.371955\pi$
$294$			3.00000i			0.174964i
$295$		0			0
$296$	−0.598076	+	1.03590i	−0.0347625	+	0.0602104i
$297$	0.401924	+	0.232051i	0.0233220	+	0.0134650i
$298$	−20.4641			−1.18545
$299$	0.669873	+	0.696152i	0.0387398	+	0.0402595i
$300$		0			0
$301$	3.33975	+	1.92820i	0.192500	+	0.111140i
$302$	−5.19615	+	9.00000i	−0.299005	+	0.517892i
$303$	5.46410	+	9.46410i	0.313904	+	0.543698i
$304$		−	0.535898i		−	0.0307359i
$305$		0			0
$306$	3.46410	−	2.00000i	0.198030	−	0.114332i
$307$			12.5359i			0.715462i	0.933825	+	0.357731i	$0.116449\pi$
$307$			12.5359i			0.715462i	−0.933825	+	0.357731i	$0.883551\pi$
$308$	−0.464102	−	0.803848i	−0.0264446	−	0.0458035i
$309$	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	$0.569202\pi$
$312$	−2.59808	+	2.50000i	−0.147087	+	0.141535i
$313$	28.0000			1.58265			0.791327	−	0.611393i	$-0.209391\pi$
$313$	28.0000			1.58265			0.791327	+	0.611393i	$0.209391\pi$
$314$	−4.33013	−	2.50000i	−0.244363	−	0.141083i
$315$		0			0
$316$	−0.0358984	−	0.0621778i	−0.00201944	−	0.00349778i
$317$			21.4641i			1.20554i	0.797913	+	0.602772i	$0.205937\pi$
$317$			21.4641i			1.20554i	−0.797913	+	0.602772i	$0.794063\pi$
$318$	11.1962	−	6.46410i	0.627849	−	0.362489i
$319$	−1.50000	+	0.866025i	−0.0839839	+	0.0484881i
$320$		0			0
$321$	9.92820	+	17.1962i	0.554138	+	0.959796i
$322$	0.267949	−	0.464102i	0.0149322	−	0.0258634i
$323$	1.85641	+	1.07180i	0.103293	+	0.0596364i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	23.0526			1.27676
$327$	10.2679	+	5.92820i	0.567819	+	0.327830i
$328$	−1.00000	+	1.73205i	−0.0552158	+	0.0956365i
$329$	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	$0.571850\pi$
$332$	4.26795	−	2.46410i	0.234234	−	0.135235i
$333$			1.19615i			0.0655487i
$334$	9.16025	+	15.8660i	0.501227	+	0.868150i
$335$		0			0
$336$	1.73205	+	1.00000i	0.0944911	+	0.0545545i
$337$	25.3205			1.37930			0.689648	−	0.724145i	$-0.257765\pi$
$337$	25.3205			1.37930			0.689648	+	0.724145i	$0.257765\pi$
$338$	6.06218	+	11.5000i	0.329739	+	0.625518i
$339$	−11.1962			−0.608092
$340$		0			0
$341$	0.401924	−	0.696152i	0.0217654	−	0.0376988i
$342$	−0.267949	−	0.464102i	−0.0144890	−	0.0250957i
$343$		−	20.0000i		−	1.07990i
$344$	−1.66987	+	0.964102i	−0.0900335	+	0.0519809i
$345$		0			0
$346$			2.92820i			0.157421i
$347$	11.1962	+	19.3923i	0.601041	+	1.04103i	0.992664	+	0.120908i	$0.0385805\pi$
$347$	11.1962	+	19.3923i	0.601041	+	1.04103i	−0.391623	+	0.920126i	$0.628086\pi$
$348$	1.86603	−	3.23205i	0.100029	−	0.173256i
$349$	−12.5885	−	7.26795i	−0.673845	−	0.389044i	0.123687	−	0.992321i	$-0.460528\pi$
$349$	−12.5885	−	7.26795i	−0.673845	−	0.389044i	−0.797532	+	0.603277i	$0.793861\pi$
$350$		0			0
$351$	−1.00000	+	3.46410i	−0.0533761	+	0.184900i
$352$	0.464102			0.0247367
$353$	1.73205	+	1.00000i	0.0921878	+	0.0532246i	0.545385	−	0.838186i	$-0.316383\pi$
$353$	1.73205	+	1.00000i	0.0921878	+	0.0532246i	−0.453197	+	0.891410i	$0.649717\pi$
$354$	−0.767949	+	1.33013i	−0.0408160	+	0.0706955i
$355$		0			0
$356$			7.46410i			0.395597i
$357$	−6.92820	+	4.00000i	−0.366679	+	0.211702i
$358$	−14.0885	+	8.13397i	−0.744598	+	0.429894i
$359$		−	18.9282i		−	0.998992i	−0.866316	−	0.499496i	$-0.833518\pi$
$359$		−	18.9282i		−	0.998992i	0.866316	−	0.499496i	$-0.166482\pi$
$360$		0			0
$361$	−9.35641	+	16.2058i	−0.492442	+	0.852935i
$362$	−9.46410	−	5.46410i	−0.497422	−	0.287187i
$363$	10.7846			0.566045
$364$	5.19615	−	5.00000i	0.272352	−	0.262071i
$365$		0			0
$366$	−9.00000	−	5.19615i	−0.470438	−	0.271607i
$367$	18.1962	−	31.5167i	0.949831	−	1.64516i	0.204056	−	0.978959i	$-0.434588\pi$
$367$	18.1962	−	31.5167i	0.949831	−	1.64516i	0.745776	−	0.666197i	$-0.232079\pi$
$368$	0.133975	+	0.232051i	0.00698391	+	0.0120965i
$369$			2.00000i			0.104116i
$370$		0			0
$371$	−22.3923	+	12.9282i	−1.16255	+	0.671199i
$372$			1.73205i			0.0898027i
$373$	12.8923	+	22.3301i	0.667538	+	1.15621i	0.978590	+	0.205817i	$0.0659853\pi$
$373$	12.8923	+	22.3301i	0.667538	+	1.15621i	−0.311052	+	0.950393i	$0.600681\pi$
$374$	−0.928203	+	1.60770i	−0.0479962	+	0.0831319i
$375$		0			0
$376$	−10.4641			−0.539645
$377$	−9.33013	−	9.69615i	−0.480526	−	0.499377i
$378$	2.00000			0.102869
$379$	−0.124356	−	0.0717968i	−0.00638772	−	0.00368795i	0.496803	−	0.867863i	$-0.334507\pi$
$379$	−0.124356	−	0.0717968i	−0.00638772	−	0.00368795i	−0.503190	+	0.864176i	$0.667841\pi$
$380$		0			0
$381$	4.46410	+	7.73205i	0.228703	+	0.396125i
$382$			14.5359i			0.743721i
$383$	3.99038	−	2.30385i	0.203899	−	0.117721i	−0.394574	−	0.918864i	$-0.629108\pi$
$383$	3.99038	−	2.30385i	0.203899	−	0.117721i	0.598473	+	0.801143i	$0.295774\pi$
$384$	−0.866025	+	0.500000i	−0.0441942	+	0.0255155i
$385$		0			0
$386$	11.6603	+	20.1962i	0.593491	+	1.02796i
$387$	−0.964102	+	1.66987i	−0.0490080	+	0.0848844i
$388$	6.46410	+	3.73205i	0.328165	+	0.189466i
$389$	−20.2679			−1.02763			−0.513813	−	0.857902i	$-0.671767\pi$
$389$	−20.2679			−1.02763			−0.513813	+	0.857902i	$0.671767\pi$
$390$		0			0
$391$	−1.07180			−0.0542031
$392$	2.59808	+	1.50000i	0.131223	+	0.0757614i
$393$	0.669873	−	1.16025i	0.0337906	−	0.0585271i
$394$	8.19615	+	14.1962i	0.412916	+	0.715192i
$395$		0			0
$396$	0.401924	−	0.232051i	0.0201974	−	0.0116610i
$397$	−10.5000	+	6.06218i	−0.526980	+	0.304252i	−0.739786	−	0.672843i	$-0.765073\pi$
$397$	−10.5000	+	6.06218i	−0.526980	+	0.304252i	0.212806	+	0.977095i	$0.431740\pi$
$398$		−	18.9282i		−	0.948785i
$399$	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	$0.372028\pi$
$402$	−4.53590			−0.226230
$403$	6.00000	+	1.73205i	0.298881	+	0.0862796i
$404$	10.9282			0.543698
$405$		0			0
$406$	−3.73205	+	6.46410i	−0.185219	+	0.320808i
$407$	−0.277568	−	0.480762i	−0.0137585	−	0.0238305i
$408$		−	4.00000i		−	0.198030i
$409$	−3.46410	+	2.00000i	−0.171289	+	0.0988936i	−0.583193	−	0.812333i	$-0.698197\pi$
$409$	−3.46410	+	2.00000i	−0.171289	+	0.0988936i	0.411905	+	0.911227i	$0.364864\pi$
$410$		0			0
$411$			4.46410i			0.220198i
$412$	−7.92820	−	13.7321i	−0.390595	−	0.676530i
$413$	1.53590	−	2.66025i	0.0755766	−	0.130903i
$414$	0.232051	+	0.133975i	0.0114047	+	0.00658449i
$415$		0			0
$416$	0.866025	+	3.50000i	0.0424604	+	0.171602i
$417$	0.928203			0.0454543
$418$	0.215390	+	0.124356i	0.0105351	+	0.00608243i
$419$	−0.803848	+	1.39230i	−0.0392705	+	0.0680185i	−0.884993	−	0.465605i	$-0.845837\pi$
$419$	−0.803848	+	1.39230i	−0.0392705	+	0.0680185i	0.845722	+	0.533624i	$0.179170\pi$
$420$		0			0
$421$			16.3923i			0.798912i	0.916752	+	0.399456i	$0.130801\pi$
$421$			16.3923i			0.798912i	−0.916752	+	0.399456i	$0.869199\pi$
$422$	20.1962	−	11.6603i	0.983133	−	0.567612i
$423$	−9.06218	+	5.23205i	−0.440618	+	0.254391i
$424$		−	12.9282i		−	0.627849i
$425$		0			0
$426$	−4.19615	+	7.26795i	−0.203304	+	0.352133i
$427$	18.0000	+	10.3923i	0.871081	+	0.502919i
$428$	19.8564			0.959796
$429$	−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	$0.725320\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	−7.66025	−	13.2679i	−0.368128	−	0.637617i	0.621145	−	0.783696i	$-0.286668\pi$
$433$	−7.66025	−	13.2679i	−0.368128	−	0.637617i	−0.989273	+	0.146079i	$0.953335\pi$
$434$		−	3.46410i		−	0.166282i
$435$		0			0
$436$	10.2679	−	5.92820i	0.491746	−	0.283909i
$437$			0.143594i			0.00686901i
$438$	1.00000	+	1.73205i	0.0477818	+	0.0827606i
$439$	−4.92820	+	8.53590i	−0.235210	+	0.407396i	−0.959334	−	0.282274i	$-0.908911\pi$
$439$	−4.92820	+	8.53590i	−0.235210	+	0.407396i	0.724123	+	0.689670i	$0.242245\pi$
$440$		0			0
$441$	3.00000			0.142857
$442$	−13.8564	−	4.00000i	−0.659082	−	0.190261i
$443$	4.39230			0.208685			0.104342	−	0.994541i	$-0.466726\pi$
$443$	4.39230			0.208685			0.104342	+	0.994541i	$0.466726\pi$
$444$	1.03590	+	0.598076i	0.0491616	+	0.0283834i
$445$		0			0
$446$	13.7321	+	23.7846i	0.650231	+	1.12623i
$447$			20.4641i			0.967919i
$448$	1.73205	−	1.00000i	0.0818317	−	0.0472456i
$449$	−34.3923	+	19.8564i	−1.62307	+	0.937082i	−0.636982	+	0.770879i	$0.719817\pi$
$449$	−34.3923	+	19.8564i	−1.62307	+	0.937082i	−0.986092	+	0.166203i	$0.946849\pi$
$450$		0			0
$451$	−0.464102	−	0.803848i	−0.0218537	−	0.0378517i
$452$	−5.59808	+	9.69615i	−0.263311	+	0.456069i
$453$	9.00000	+	5.19615i	0.422857	+	0.244137i
$454$	−4.39230			−0.206141
$455$		0			0
$456$	−0.535898			−0.0250957
$457$	27.2487	+	15.7321i	1.27464	+	0.735914i	0.975858	−	0.218407i	$-0.0700859\pi$
$457$	27.2487	+	15.7321i	1.27464	+	0.735914i	0.298783	+	0.954321i	$0.403419\pi$
$458$	−9.92820	+	17.1962i	−0.463914	+	0.803523i
$459$	−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	$0.285235\pi$
$462$	−0.803848	+	0.464102i	−0.0373984	+	0.0215920i
$463$			20.9282i			0.972616i	0.873787	+	0.486308i	$0.161657\pi$
$463$			20.9282i			0.972616i	−0.873787	+	0.486308i	$0.838343\pi$
$464$	−1.86603	−	3.23205i	−0.0866281	−	0.150044i
$465$		0			0
$466$	−15.6962	−	9.06218i	−0.727110	−	0.419797i
$467$	−11.8564			−0.548649			−0.274325	−	0.961637i	$-0.588454\pi$
$467$	−11.8564			−0.548649			−0.274325	+	0.961637i	$0.588454\pi$
$468$	2.50000	+	2.59808i	0.115563	+	0.120096i
$469$	9.07180			0.418897
$470$		0			0
$471$	−2.50000	+	4.33013i	−0.115194	+	0.199522i
$472$	0.767949	+	1.33013i	0.0353477	+	0.0612241i
$473$		−	0.894882i		−	0.0411467i
$474$	−0.0621778	+	0.0358984i	−0.00285592	+	0.00164887i
$475$		0			0
$476$			8.00000i			0.366679i
$477$	−6.46410	−	11.1962i	−0.295971	−	0.512637i
$478$	−2.19615	+	3.80385i	−0.100450	+	0.173984i
$479$	1.26795	+	0.732051i	0.0579341	+	0.0334483i	0.528687	−	0.848817i	$-0.322684\pi$
$479$	1.26795	+	0.732051i	0.0579341	+	0.0334483i	−0.470753	+	0.882265i	$0.656018\pi$
$480$		0			0
$481$	3.10770	−	2.99038i	0.141699	−	0.136350i
$482$	14.2679			0.649887
$483$	−0.464102	−	0.267949i	−0.0211174	−	0.0121921i
$484$	5.39230	−	9.33975i	0.245105	−	0.424534i
$485$		0			0
$486$			1.00000i			0.0453609i
$487$	−33.9282	+	19.5885i	−1.53743	+	0.887638i	−0.538446	+	0.842660i	$0.680988\pi$
$487$	−33.9282	+	19.5885i	−1.53743	+	0.887638i	−0.998988	+	0.0449775i	$0.985678\pi$
$488$	−9.00000	+	5.19615i	−0.407411	+	0.235219i
$489$		−	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	$0.294479\pi$
$492$	1.73205	+	1.00000i	0.0780869	+	0.0450835i
$493$	14.9282			0.672332
$494$	−0.535898	+	1.85641i	−0.0241112	+	0.0835237i
$495$		0			0
$496$	1.50000	+	0.866025i	0.0673520	+	0.0388857i
$497$	8.39230	−	14.5359i	0.376446	−	0.652024i
$498$	−2.46410	−	4.26795i	−0.110419	−	0.191251i
$499$		−	13.4641i		−	0.602736i	−0.953508	−	0.301368i	$-0.902557\pi$
$499$		−	13.4641i		−	0.602736i	0.953508	−	0.301368i	$-0.0974433\pi$
$500$		0			0
$501$	15.8660	−	9.16025i	0.708842	−	0.409250i
$502$			12.2679i			0.547545i
$503$	15.5885	+	27.0000i	0.695055	+	1.20387i	0.970162	+	0.242457i	$0.0779533\pi$
$503$	15.5885	+	27.0000i	0.695055	+	1.20387i	−0.275107	+	0.961414i	$0.588713\pi$
$504$	1.00000	−	1.73205i	0.0445435	−	0.0771517i
$505$		0			0
$506$	−0.124356			−0.00552828
$507$	11.5000	−	6.06218i	0.510733	−	0.269231i
$508$	8.92820			0.396125
$509$	16.7942	+	9.69615i	0.744391	+	0.429774i	0.823664	−	0.567079i	$-0.191926\pi$
$509$	16.7942	+	9.69615i	0.744391	+	0.429774i	−0.0792726	+	0.996853i	$0.525260\pi$
$510$		0			0
$511$	−2.00000	−	3.46410i	−0.0884748	−	0.153243i
$512$			1.00000i			0.0441942i
$513$	−0.464102	+	0.267949i	−0.0204906	+	0.0118302i
$514$	19.6244	−	11.3301i	0.865593	−	0.499750i
$515$		0			0
$516$	0.964102	+	1.66987i	0.0424422	+	0.0735121i
$517$	2.42820	−	4.20577i	0.106792	−	0.184970i
$518$	−2.07180	−	1.19615i	−0.0910295	−	0.0525559i
$519$	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	$0.376126\pi$
$522$	−3.23205	−	1.86603i	−0.141463	−	0.0816737i
$523$	−14.8923	+	25.7942i	−0.651195	+	1.12790i	0.331638	+	0.943407i	$0.392399\pi$
$523$	−14.8923	+	25.7942i	−0.651195	+	1.12790i	−0.982833	+	0.184496i	$0.940935\pi$
$524$	−0.669873	−	1.16025i	−0.0292635	−	0.0506859i
$525$		0			0
$526$	15.6962	−	9.06218i	0.684385	−	0.395130i
$527$	−6.00000	+	3.46410i	−0.261364	+	0.150899i
$528$		−	0.464102i		−	0.0201974i
$529$	11.4641	+	19.8564i	0.498439	+	0.863322i
$530$		0			0
$531$	1.33013	+	0.767949i	0.0577226	+	0.0333262i
$532$	1.07180			0.0464683
$533$	5.19615	−	5.00000i	0.225070	−	0.216574i
$534$	7.46410			0.323003
$535$		0			0
$536$	−2.26795	+	3.92820i	−0.0979605	+	0.169673i
$537$	8.13397	+	14.0885i	0.351007	+	0.607962i
$538$			12.0000i			0.517357i
$539$	−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	$-0.0906662\pi$
$542$	−4.59808	−	7.96410i	−0.197504	−	0.342087i
$543$	−5.46410	+	9.46410i	−0.234487	+	0.406143i
$544$	−3.46410	−	2.00000i	−0.148522	−	0.0857493i
$545$		0			0
$546$	−5.00000	−	5.19615i	−0.213980	−	0.222375i
$547$	−9.07180			−0.387882			−0.193941	−	0.981013i	$-0.562127\pi$
$547$	−9.07180			−0.387882			−0.193941	+	0.981013i	$0.562127\pi$
$548$	3.86603	+	2.23205i	0.165148	+	0.0953485i
$549$	−5.19615	+	9.00000i	−0.221766	+	0.384111i
$550$		0			0
$551$		−	2.00000i		−	0.0852029i
$552$	0.232051	−	0.133975i	0.00987674	−	0.00570234i
$553$	0.124356	−	0.0717968i	0.00528814	−	0.00305311i
$554$		−	9.92820i		−	0.421809i
$555$		0			0
$556$	0.464102	−	0.803848i	0.0196823	−	0.0340907i
$557$	−32.6603	−	18.8564i	−1.38386	−	0.798972i	−0.391245	−	0.920286i	$-0.627956\pi$
$557$	−32.6603	−	18.8564i	−1.38386	−	0.798972i	−0.992614	+	0.121315i	$0.961289\pi$
$558$	1.73205			0.0733236
$559$	6.74871	−	1.66987i	0.285440	−	0.0706281i
$560$		0			0
$561$	1.60770	+	0.928203i	0.0678769	+	0.0391888i
$562$	−2.46410	+	4.26795i	−0.103942	+	0.180033i
$563$	−19.6603	−	34.0526i	−0.828581	−	1.43514i	−0.899152	−	0.437637i	$-0.855815\pi$
$563$	−19.6603	−	34.0526i	−0.828581	−	1.43514i	0.0705706	−	0.997507i	$-0.477518\pi$
$564$			10.4641i			0.440618i
$565$		0			0
$566$	−3.40192	+	1.96410i	−0.142994	+	0.0825573i
$567$		−	2.00000i		−	0.0839921i
$568$	4.19615	+	7.26795i	0.176067	+	0.304956i
$569$	2.66025	−	4.60770i	0.111524	−	0.193165i	−0.804861	−	0.593463i	$-0.797760\pi$
$569$	2.66025	−	4.60770i	0.111524	−	0.193165i	0.916385	+	0.400299i	$0.131094\pi$
$570$		0			0
$571$	45.1769			1.89060			0.945298	−	0.326209i	$-0.105771\pi$
$571$	45.1769			1.89060			0.945298	+	0.326209i	$0.105771\pi$
$572$	−1.60770	−	0.464102i	−0.0672211	−	0.0194051i
$573$	14.5359			0.607246
$574$	−3.46410	−	2.00000i	−0.144589	−	0.0834784i
$575$		0			0
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$		−	10.0000i		−	0.416305i	−0.978096	−	0.208153i	$-0.933255\pi$
$577$		−	10.0000i		−	0.416305i	0.978096	−	0.208153i	$-0.0667451\pi$
$578$	−0.866025	+	0.500000i	−0.0360219	+	0.0207973i
$579$	20.1962	−	11.6603i	0.839323	−	0.484584i
$580$		0			0
$581$	4.92820	+	8.53590i	0.204456	+	0.354129i
$582$	3.73205	−	6.46410i	0.154698	−	0.267946i
$583$	5.19615	+	3.00000i	0.215203	+	0.124247i
$584$	2.00000			0.0827606
$585$		0			0
$586$	4.14359			0.171170
$587$	15.9282	+	9.19615i	0.657427	+	0.379566i	0.791296	−	0.611433i	$-0.209407\pi$
$587$	15.9282	+	9.19615i	0.657427	+	0.379566i	−0.133869	+	0.990999i	$0.542740\pi$
$588$	1.50000	−	2.59808i	0.0618590	−	0.107143i
$589$	0.464102	+	0.803848i	0.0191230	+	0.0331220i
$590$		0			0
$591$	14.1962	−	8.19615i	0.583952	−	0.337145i
$592$	1.03590	−	0.598076i	0.0425752	−	0.0245808i
$593$		−	31.1051i		−	1.27733i	−0.769483	−	0.638667i	$-0.779486\pi$
$593$		−	31.1051i		−	1.27733i	0.769483	−	0.638667i	$-0.220514\pi$
$594$	−0.232051	−	0.401924i	−0.00952116	−	0.0164911i
$595$		0			0
$596$	17.7224	+	10.2321i	0.725939	+	0.419121i
$597$	−18.9282			−0.774680
$598$	−0.232051	−	0.937822i	−0.00948926	−	0.0383504i
$599$	10.3923			0.424618			0.212309	−	0.977203i	$-0.431902\pi$
$599$	10.3923			0.424618			0.212309	+	0.977203i	$0.431902\pi$
$600$		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	$0.313216\pi$
$602$	−1.92820	−	3.33975i	−0.0785877	−	0.136118i
$603$			4.53590i			0.184716i
$604$	9.00000	−	5.19615i	0.366205	−	0.211428i
$605$		0			0
$606$		−	10.9282i		−	0.443928i
$607$	21.5885	+	37.3923i	0.876248	+	1.51771i	0.855427	+	0.517924i	$0.173295\pi$
$607$	21.5885	+	37.3923i	0.876248	+	1.51771i	0.0208216	+	0.999783i	$0.493372\pi$
$608$	−0.267949	+	0.464102i	−0.0108668	+	0.0188218i
$609$	6.46410	+	3.73205i	0.261939	+	0.151230i
$610$		0			0
$611$	36.2487	+	10.4641i	1.46647	+	0.423332i
$612$	−4.00000			−0.161690
$613$	−0.820508	−	0.473721i	−0.0331400	−	0.0191334i	0.483338	−	0.875434i	$-0.339424\pi$
$613$	−0.820508	−	0.473721i	−0.0331400	−	0.0191334i	−0.516478	+	0.856300i	$0.672757\pi$
$614$	6.26795	−	10.8564i	0.252954	−	0.438129i
$615$		0			0
$616$			0.928203i			0.0373984i
$617$	−13.4545	+	7.76795i	−0.541657	+	0.312726i	−0.745750	−	0.666226i	$-0.767909\pi$
$617$	−13.4545	+	7.76795i	−0.541657	+	0.312726i	0.204093	+	0.978951i	$0.434575\pi$
$618$	−13.7321	+	7.92820i	−0.552384	+	0.318919i
$619$		−	24.2487i		−	0.974638i	−0.873224	−	0.487319i	$-0.837975\pi$
$619$		−	24.2487i		−	0.974638i	0.873224	−	0.487319i	$-0.162025\pi$
$620$		0			0
$621$	0.133975	−	0.232051i	0.00537622	−	0.00931188i
$622$	6.58846	+	3.80385i	0.264173	+	0.152520i
$623$	−14.9282			−0.598086
$624$	3.50000	−	0.866025i	0.140112	−	0.0346688i
$625$		0			0
$626$	−24.2487	−	14.0000i	−0.969173	−	0.559553i
$627$	0.124356	−	0.215390i	0.00496629	−	0.00860186i
$628$	2.50000	+	4.33013i	0.0997609	+	0.172791i
$629$			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	$0.495745\pi$
$632$			0.0717968i			0.00285592i
$633$	−11.6603	−	20.1962i	−0.463453	−	0.802725i
$634$	10.7321	−	18.5885i	0.426224	−	0.738242i
$635$		0			0
$636$	−12.9282			−0.512637
$637$	−7.50000	−	7.79423i	−0.297161	−	0.308819i
$638$	1.73205			0.0685725
$639$	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	$-0.352089\pi$
$642$		−	19.8564i		−	0.783670i
$643$	−23.7846	+	13.7321i	−0.937973	+	0.541539i	−0.889324	−	0.457277i	$-0.848825\pi$
$643$	−23.7846	+	13.7321i	−0.937973	+	0.541539i	−0.0486490	+	0.998816i	$0.515492\pi$
$644$	−0.464102	+	0.267949i	−0.0182882	+	0.0105587i
$645$		0			0
$646$	−1.07180	−	1.85641i	−0.0421693	−	0.0730393i
$647$	10.6603	−	18.4641i	0.419098	−	0.725899i	−0.576751	−	0.816920i	$-0.695680\pi$
$647$	10.6603	−	18.4641i	0.419098	−	0.725899i	0.995849	+	0.0910212i	$0.0290131\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	−0.712813			−0.0279804
$650$		0			0
$651$	−3.46410			−0.135769
$652$	−19.9641	−	11.5263i	−0.781855	−	0.451404i
$653$	−22.1244	+	38.3205i	−0.865793	+	1.49960i	0.000464739		1.00000i	$0.499852\pi$
$653$	−22.1244	+	38.3205i	−0.865793	+	1.49960i	−0.866258	+	0.499597i	$0.833481\pi$
$654$	−5.92820	−	10.2679i	−0.231811	−	0.401509i
$655$		0			0
$656$	1.73205	−	1.00000i	0.0676252	−	0.0390434i
$657$	1.73205	−	1.00000i	0.0675737	−	0.0390137i
$658$		−	20.9282i		−	0.815866i
$659$	1.86603	+	3.23205i	0.0726900	+	0.125903i	0.900079	−	0.435726i	$-0.143508\pi$
$659$	1.86603	+	3.23205i	0.0726900	+	0.125903i	−0.827389	+	0.561629i	$0.810175\pi$
$660$		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	$0.347758\pi$
$662$	24.7846			0.963281
$663$	−4.00000	+	13.8564i	−0.155347	+	0.538138i
$664$	−4.92820			−0.191251
$665$		0			0
$666$	0.598076	−	1.03590i	0.0231750	−	0.0401402i
$667$	0.500000	+	0.866025i	0.0193601	+	0.0335326i
$668$		−	18.3205i		−	0.708842i
$669$	23.7846	−	13.7321i	0.919566	−	0.530912i
$670$		0			0
$671$		−	4.82309i		−	0.186193i
$672$	−1.00000	−	1.73205i	−0.0385758	−	0.0668153i
$673$	16.0000	−	27.7128i	0.616755	−	1.06825i	−0.373319	−	0.927703i	$-0.621780\pi$
$673$	16.0000	−	27.7128i	0.616755	−	1.06825i	0.990074	−	0.140548i	$-0.0448863\pi$
$674$	−21.9282	−	12.6603i	−0.844643	−	0.487655i
$675$		0			0
$676$	0.500000	−	12.9904i	0.0192308	−	0.499630i
$677$	−11.6077			−0.446120			−0.223060	−	0.974805i	$-0.571605\pi$
$677$	−11.6077			−0.446120			−0.223060	+	0.974805i	$0.571605\pi$
$678$	9.69615	+	5.59808i	0.372378	+	0.214993i
$679$	−7.46410	+	12.9282i	−0.286446	+	0.496139i
$680$		0			0
$681$			4.39230i			0.168313i
$682$	−0.696152	+	0.401924i	−0.0266571	+	0.0153905i
$683$	0.679492	−	0.392305i	0.0260000	−	0.0150111i	−0.486944	−	0.873433i	$-0.661888\pi$
$683$	0.679492	−	0.392305i	0.0260000	−	0.0150111i	0.512944	+	0.858422i	$0.328555\pi$
$684$			0.535898i			0.0204906i
$685$		0			0
$686$	−10.0000	+	17.3205i	−0.381802	+	0.661300i
$687$	17.1962	+	9.92820i	0.656074	+	0.378785i
$688$	1.92820			0.0735121
$689$	−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	$0.899985\pi$
$692$	1.46410	−	2.53590i	0.0556568	−	0.0964004i
$693$	0.464102	+	0.803848i	0.0176298	+	0.0305356i
$694$		−	22.3923i		−	0.850000i
$695$		0			0
$696$	−3.23205	+	1.86603i	−0.122511	+	0.0707315i
$697$			8.00000i			0.303022i
$698$	7.26795	+	12.5885i	0.275096	+	0.476480i
$699$	−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	$0.522453\pi$
$702$	2.59808	−	2.50000i	0.0980581	−	0.0943564i
$703$	0.641016			0.0241764
$704$	−0.401924	−	0.232051i	−0.0151481	−	0.00874574i
$705$		0			0
$706$	−1.00000	−	1.73205i	−0.0376355	−	0.0651866i
$707$			21.8564i			0.821995i
$708$	1.33013	−	0.767949i	0.0499892	−	0.0288613i
$709$	7.85641	−	4.53590i	0.295054	−	0.170349i	−0.345165	−	0.938542i	$-0.612177\pi$
$709$	7.85641	−	4.53590i	0.295054	−	0.170349i	0.640219	+	0.768193i	$0.278844\pi$
$710$		0			0
$711$	0.0358984	+	0.0621778i	0.00134629	+	0.00233185i
$712$	3.73205	−	6.46410i	0.139865	−	0.242252i
$713$	−0.401924	−	0.232051i	−0.0150522	−	0.00869037i
$714$	8.00000			0.299392
$715$		0			0
$716$	16.2679			0.607962
$717$	3.80385	+	2.19615i	0.142057	+	0.0820168i
$718$	−9.46410	+	16.3923i	−0.353197	+	0.611755i
$719$	−17.3205	−	30.0000i	−0.645946	−	1.11881i	−0.984082	−	0.177714i	$-0.943130\pi$
$719$	−17.3205	−	30.0000i	−0.645946	−	1.11881i	0.338136	−	0.941097i	$-0.390204\pi$
$720$		0			0
$721$	27.4641	−	15.8564i	1.02282	−	0.590523i
$722$	16.2058	−	9.35641i	0.603116	−	0.348209i
$723$		−	14.2679i		−	0.530631i
$724$	5.46410	+	9.46410i	0.203072	+	0.351731i
$725$		0			0
$726$	−9.33975	−	5.39230i	−0.346630	−	0.200127i
$727$	−23.7128			−0.879460			−0.439730	−	0.898130i	$-0.644926\pi$
$727$	−23.7128			−0.879460			−0.439730	+	0.898130i	$0.644926\pi$
$728$	−7.00000	+	1.73205i	−0.259437	+	0.0641941i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−3.85641	+	6.67949i	−0.142634	+	0.247050i
$732$	5.19615	+	9.00000i	0.192055	+	0.332650i
$733$		−	37.0718i		−	1.36928i	−0.728882	−	0.684639i	$-0.759960\pi$
$733$		−	37.0718i		−	1.36928i	0.728882	−	0.684639i	$-0.240040\pi$
$734$	−31.5167	+	18.1962i	−1.16330	+	0.671632i
$735$		0			0
$736$		−	0.267949i		−	0.00987674i
$737$	−1.05256	−	1.82309i	−0.0387715	−	0.0671542i
$738$	1.00000	−	1.73205i	0.0368105	−	0.0637577i
$739$	−13.2679	−	7.66025i	−0.488069	−	0.281787i	0.235704	−	0.971825i	$-0.424260\pi$
$739$	−13.2679	−	7.66025i	−0.488069	−	0.281787i	−0.723773	+	0.690038i	$0.757594\pi$
$740$		0			0
$741$	1.85641	+	0.535898i	0.0681968	+	0.0196867i
$742$	25.8564			0.949219
$743$	−29.0429	−	16.7679i	−1.06548	−	0.615156i	−0.138539	−	0.990357i	$-0.544240\pi$
$743$	−29.0429	−	16.7679i	−1.06548	−	0.615156i	−0.926944	+	0.375201i	$0.877574\pi$
$744$	0.866025	−	1.50000i	0.0317500	−	0.0549927i
$745$		0			0
$746$		−	25.7846i		−	0.944042i
$747$	−4.26795	+	2.46410i	−0.156156	+	0.0901568i
$748$	1.60770	−	0.928203i	0.0587832	−	0.0339385i
$749$			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	$0.996476\pi$
$752$	9.06218	+	5.23205i	0.330464	+	0.190793i
$753$	12.2679			0.447069
$754$	3.23205	+	13.0622i	0.117704	+	0.475696i
$755$		0			0
$756$	−1.73205	−	1.00000i	−0.0629941	−	0.0363696i
$757$	−9.00000	+	15.5885i	−0.327111	+	0.566572i	−0.981937	−	0.189207i	$-0.939408\pi$
$757$	−9.00000	+	15.5885i	−0.327111	+	0.566572i	0.654827	+	0.755779i	$0.272742\pi$
$758$	0.0717968	+	0.124356i	0.00260778	+	0.00451680i
$759$			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	$0.444801\pi$
$762$		−	8.92820i		−	0.323435i
$763$	11.8564	+	20.5359i	0.429231	+	0.743449i
$764$	7.26795	−	12.5885i	0.262945	−	0.455434i
$765$		0			0
$766$	−4.60770			−0.166483
$767$	−1.33013	−	5.37564i	−0.0480281	−	0.194103i
$768$	1.00000			0.0360844
$769$	−16.9641	−	9.79423i	−0.611741	−	0.353189i	0.161905	−	0.986806i	$-0.448236\pi$
$769$	−16.9641	−	9.79423i	−0.611741	−	0.353189i	−0.773647	+	0.633617i	$0.781569\pi$
$770$		0			0
$771$	−11.3301	−	19.6244i	−0.408045	−	0.706754i
$772$		−	23.3205i		−	0.839323i
$773$	−24.0000	+	13.8564i	−0.863220	+	0.498380i	−0.865089	−	0.501618i	$-0.832738\pi$
$773$	−24.0000	+	13.8564i	−0.863220	+	0.498380i	0.00186926	+	0.999998i	$0.499405\pi$
$774$	1.66987	−	0.964102i	0.0600223	−	0.0346539i
$775$		0			0
$776$	−3.73205	−	6.46410i	−0.133973	−	0.232048i
$777$	−1.19615	+	2.07180i	−0.0429117	+	0.0743253i
$778$	17.5526	+	10.1340i	0.629290	+	0.363321i
$779$	1.07180			0.0384011
$780$		0			0
$781$	−3.89488			−0.139370
$782$	0.928203	+	0.535898i	0.0331925	+	0.0191637i
$783$	−1.86603	+	3.23205i	−0.0666863	+	0.115504i
$784$	−1.50000	−	2.59808i	−0.0535714	−	0.0927884i
$785$		0			0
$786$	−1.16025	+	0.669873i	−0.0413849	+	0.0238936i
$787$	−1.50000	+	0.866025i	−0.0534692	+	0.0308705i	−0.526496	−	0.850177i	$-0.676495\pi$
$787$	−1.50000	+	0.866025i	−0.0534692	+	0.0308705i	0.473027	+	0.881048i	$0.343161\pi$
$788$		−	16.3923i		−	0.583952i
$789$	−9.06218	−	15.6962i	−0.322622	−	0.558798i
$790$		0			0
$791$	−19.3923	−	11.1962i	−0.689511	−	0.398089i
$792$	−0.464102			−0.0164911
$793$	36.3731	−	9.00000i	1.29165	−	0.319599i
$794$	12.1244			0.430277
$795$		0			0
$796$	−9.46410	+	16.3923i	−0.335446	+	0.581010i
$797$	−18.9282	−	32.7846i	−0.670471	−	1.16129i	−0.977771	−	0.209678i	$-0.932759\pi$
$797$	−18.9282	−	32.7846i	−0.670471	−	1.16129i	0.307299	−	0.951613i	$-0.400575\pi$
$798$		−	1.07180i		−	0.0379412i
$799$	−36.2487	+	20.9282i	−1.28239	+	0.740387i
$800$		0			0
$801$		−	7.46410i		−	0.263731i
$802$	−16.0000	−	27.7128i	−0.564980	−	0.978573i
$803$	−0.464102	+	0.803848i	−0.0163778	+	0.0283672i
$804$	3.92820	+	2.26795i	0.138537	+	0.0799844i
$805$		0			0
$806$	−4.33013	−	4.50000i	−0.152522	−	0.158506i
$807$	12.0000			0.422420
$808$	−9.46410	−	5.46410i	−0.332946	−	0.192226i
$809$	0.607695	−	1.05256i	0.0213654	−	0.0370060i	−0.855145	−	0.518389i	$-0.826532\pi$
$809$	0.607695	−	1.05256i	0.0213654	−	0.0370060i	0.876510	+	0.481383i	$0.159865\pi$
$810$		0			0
$811$			0.784610i			0.0275514i	0.999905	+	0.0137757i	$0.00438508\pi$
$811$			0.784610i			0.0275514i	−0.999905	+	0.0137757i	$0.995615\pi$
$812$	6.46410	−	3.73205i	0.226845	−	0.130969i
$813$	−7.96410	+	4.59808i	−0.279313	+	0.161262i
$814$			0.555136i			0.0194575i
$815$		0			0
$816$	−2.00000	+	3.46410i	−0.0700140	+	0.121268i
$817$	0.894882	+	0.516660i	0.0313080	+	0.0180757i
$818$	4.00000			0.139857
$819$	−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	$0.878562\pi$
$822$	2.23205	−	3.86603i	0.0778517	−	0.134843i
$823$	−11.5885	−	20.0718i	−0.403948	−	0.699659i	0.590250	−	0.807220i	$-0.299029\pi$
$823$	−11.5885	−	20.0718i	−0.403948	−	0.699659i	−0.994198	+	0.107561i	$0.965696\pi$
$824$			15.8564i			0.552384i
$825$		0			0
$826$	−2.66025	+	1.53590i	−0.0925621	+	0.0534407i
$827$		−	17.3205i		−	0.602293i	−0.953578	−	0.301147i	$-0.902631\pi$
$827$		−	17.3205i		−	0.602293i	0.953578	−	0.301147i	$-0.0973693\pi$
$828$	−0.133975	−	0.232051i	−0.00465594	−	0.00806432i
$829$	−11.7321	+	20.3205i	−0.407471	+	0.705760i	−0.994606	−	0.103729i	$-0.966923\pi$
$829$	−11.7321	+	20.3205i	−0.407471	+	0.705760i	0.587135	+	0.809489i	$0.300256\pi$
$830$		0			0
$831$	−9.92820			−0.344406
$832$	1.00000	−	3.46410i	0.0346688	−	0.120096i
$833$	12.0000			0.415775
$834$	−0.803848	−	0.464102i	−0.0278350	−	0.0160705i
$835$		0			0
$836$	−0.124356	−	0.215390i	−0.00430093	−	0.00744943i
$837$		−	1.73205i		−	0.0598684i
$838$	1.39230	−	0.803848i	0.0480964	−	0.0277685i
$839$	−34.2679	+	19.7846i	−1.18306	+	0.683041i	−0.956721	−	0.291008i	$-0.906009\pi$
$839$	−34.2679	+	19.7846i	−1.18306	+	0.683041i	−0.226340	+	0.974048i	$0.572676\pi$
$840$		0			0
$841$	7.53590	+	13.0526i	0.259859	+	0.450088i
$842$	8.19615	−	14.1962i	0.282458	−	0.489232i
$843$	4.26795	+	2.46410i	0.146996	+	0.0848682i
$844$	−23.3205			−0.802725
$845$		0			0
$846$	10.4641			0.359763
$847$	18.6795	+	10.7846i	0.641835	+	0.370564i
$848$	−6.46410	+	11.1962i	−0.221978	+	0.384477i
$849$	1.96410	+	3.40192i	0.0674078	+	0.116754i
$850$		0			0
$851$	−0.277568	+	0.160254i	−0.00951491	+	0.00549344i
$852$	7.26795	−	4.19615i	0.248996	−	0.143758i
$853$		−	35.8372i		−	1.22704i	−0.789679	−	0.613521i	$-0.789753\pi$
$853$		−	35.8372i		−	1.22704i	0.789679	−	0.613521i	$-0.210247\pi$
$854$	−10.3923	−	18.0000i	−0.355617	−	0.615947i
$855$		0			0
$856$	−17.1962	−	9.92820i	−0.587752	−	0.339339i
$857$	20.5167			0.700836			0.350418	−	0.936593i	$-0.386040\pi$
$857$	20.5167			0.700836			0.350418	+	0.936593i	$0.386040\pi$
$858$	−0.464102	+	1.60770i	−0.0158442	+	0.0548858i
$859$	27.1769			0.927264			0.463632	−	0.886028i	$-0.346546\pi$
$859$	27.1769			0.927264			0.463632	+	0.886028i	$0.346546\pi$
$860$		0			0
$861$	−2.00000	+	3.46410i	−0.0681598	+	0.118056i
$862$	3.80385	+	6.58846i	0.129560	+	0.224404i
$863$			42.4641i			1.44549i	0.691112	+	0.722747i	$0.257121\pi$
$863$			42.4641i			1.44549i	−0.691112	+	0.722747i	$0.742879\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$		0			0
$866$			15.3205i			0.520612i
$867$	0.500000	+	0.866025i	0.0169809	+	0.0294118i
$868$	−1.73205	+	3.00000i	−0.0587896	+	0.101827i
$869$	−0.0288568	−	0.0166605i	−0.000978901	−	0.000565169i
$870$		0			0
$871$	11.7846	−	11.3397i	0.399306	−	0.384233i
$872$	−11.8564			−0.401509
$873$	−6.46410	−	3.73205i	−0.218777	−	0.126311i
$874$	0.0717968	−	0.124356i	0.00242856	−	0.00420639i
$875$		0			0
$876$		−	2.00000i		−	0.0675737i
$877$	−24.3564	+	14.0622i	−0.822457	+	0.474846i	−0.851263	−	0.524739i	$-0.824163\pi$
$877$	−24.3564	+	14.0622i	−0.822457	+	0.474846i	0.0288057	+	0.999585i	$0.490830\pi$
$878$	8.53590	−	4.92820i	0.288073	−	0.166319i
$879$		−	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	$0.0908839\pi$
$882$	−2.59808	−	1.50000i	−0.0874818	−	0.0505076i
$883$	−16.0718			−0.540859			−0.270430	−	0.962740i	$-0.587166\pi$
$883$	−16.0718			−0.540859			−0.270430	+	0.962740i	$0.587166\pi$
$884$	10.0000	+	10.3923i	0.336336	+	0.349531i
$885$		0			0
$886$	−3.80385	−	2.19615i	−0.127793	−	0.0737812i
$887$	−5.06218	+	8.76795i	−0.169971	+	0.294399i	−0.938410	−	0.345525i	$-0.887701\pi$
$887$	−5.06218	+	8.76795i	−0.169971	+	0.294399i	0.768438	+	0.639924i	$0.221034\pi$
$888$	−0.598076	−	1.03590i	−0.0200701	−	0.0347625i
$889$			17.8564i			0.598885i
$890$		0			0
$891$	−0.401924	+	0.232051i	−0.0134650	+	0.00777399i
$892$		−	27.4641i		−	0.919566i
$893$	2.80385	+	4.85641i	0.0938272	+	0.162513i
$894$	10.2321	−	17.7224i	0.342211	−	0.592727i
$895$		0			0
$896$	−2.00000			−0.0668153
$897$	−0.937822	+	0.232051i	−0.0313130	+	0.00774795i
$898$	39.7128			1.32523
$899$	5.59808	+	3.23205i	0.186706	+	0.107795i
$900$		0			0
$901$	−25.8564	−	44.7846i	−0.861402	−	1.49199i
$902$			0.928203i			0.0309058i
$903$	−3.33975	+	1.92820i	−0.111140	+	0.0641666i
$904$	9.69615	−	5.59808i	0.322489	−	0.186189i
$905$		0			0
$906$	−5.19615	−	9.00000i	−0.172631	−	0.299005i
$907$	3.42820	−	5.93782i	0.113832	−	0.197162i	−0.803480	−	0.595331i	$-0.797021\pi$
$907$	3.42820	−	5.93782i	0.113832	−	0.197162i	0.917312	+	0.398169i	$0.130354\pi$
$908$	3.80385	+	2.19615i	0.126235	+	0.0728819i
$909$	−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	$0.631580\pi$
$912$	0.464102	+	0.267949i	0.0153679	+	0.00887268i
$913$	1.14359	−	1.98076i	0.0378474	−	0.0655537i
$914$	−15.7321	−	27.2487i	−0.520370	−	0.901307i
$915$		0			0
$916$	17.1962	−	9.92820i	0.568177	−	0.328037i
$917$	2.32051	−	1.33975i	0.0766299	−	0.0442423i
$918$			4.00000i			0.132020i
$919$	27.3205	+	47.3205i	0.901220	+	1.56096i	0.825912	+	0.563799i	$0.190661\pi$
$919$	27.3205	+	47.3205i	0.901220	+	1.56096i	0.0753085	+	0.997160i	$0.476006\pi$
$920$		0			0
$921$	−10.8564	−	6.26795i	−0.357731	−	0.206536i
$922$	−6.46410			−0.212884
$923$	−7.26795	−	29.3731i	−0.239227	−	0.966826i
$924$	0.928203			0.0305356
$925$		0			0
$926$	10.4641	−	18.1244i	0.343872	−	0.595603i
$927$	7.92820	+	13.7321i	0.260396	+	0.451020i
$928$			3.73205i			0.122511i
$929$	29.3205	−	16.9282i	0.961975	−	0.555396i	0.0651944	−	0.997873i	$-0.479233\pi$
$929$	29.3205	−	16.9282i	0.961975	−	0.555396i	0.896780	+	0.442476i	$0.145900\pi$
$930$		0			0
$931$		−	1.60770i		−	0.0526901i
$932$	9.06218	+	15.6962i	0.296842	+	0.514145i
$933$	3.80385	−	6.58846i	0.124532	−	0.215696i
$934$	10.2679	+	5.92820i	0.335978	+	0.193977i
$935$		0			0
$936$	−0.866025	−	3.50000i	−0.0283069	−	0.114401i
$937$	−44.6410			−1.45836			−0.729179	−	0.684323i	$-0.760098\pi$
$937$	−44.6410			−1.45836			−0.729179	+	0.684323i	$0.760098\pi$
$938$	−7.85641	−	4.53590i	−0.256521	−	0.148102i
$939$	−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	$-0.143809\pi$
$942$	4.33013	−	2.50000i	0.141083	−	0.0814544i
$943$	−0.464102	+	0.267949i	−0.0151132	+	0.00872563i
$944$		−	1.53590i		−	0.0499892i
$945$		0			0
$946$	−0.447441	+	0.774991i	−0.0145476	+	0.0251971i
$947$	2.19615	+	1.26795i	0.0713654	+	0.0412028i	0.535258	−	0.844689i	$-0.320214\pi$
$947$	2.19615	+	1.26795i	0.0713654	+	0.0412028i	−0.463893	+	0.885891i	$0.653548\pi$
$948$	0.0717968			0.00233185
$949$	−6.92820	−	2.00000i	−0.224899	−	0.0649227i
$950$		0			0
$951$	−18.5885	−	10.7321i	−0.602772	−	0.348011i
$952$	4.00000	−	6.92820i	0.129641	−	0.224544i
$953$	−7.86603	−	13.6244i	−0.254806	−	0.441336i	0.710037	−	0.704164i	$-0.248678\pi$
$953$	−7.86603	−	13.6244i	−0.254806	−	0.441336i	−0.964843	+	0.262828i	$0.915345\pi$
$954$			12.9282i			0.418566i
$955$		0			0
$956$	3.80385	−	2.19615i	0.123025	−	0.0710286i
$957$		−	1.73205i		−	0.0559893i
$958$	−0.732051	−	1.26795i	−0.0236515	−	0.0409656i
$959$	−4.46410	+	7.73205i	−0.144153	+	0.249681i
$960$		0			0
$961$	28.0000			0.903226
$962$	−4.18653	+	1.03590i	−0.134979	+	0.0333987i
$963$	−19.8564			−0.639864
$964$	−12.3564	−	7.13397i	−0.397973	−	0.229770i
$965$		0			0
$966$	0.267949	+	0.464102i	0.00862112	+	0.0149322i
$967$		−	34.5359i		−	1.11060i	−0.831650	−	0.555300i	$-0.812604\pi$
$967$		−	34.5359i		−	1.11060i	0.831650	−	0.555300i	$-0.187396\pi$
$968$	−9.33975	+	5.39230i	−0.300191	+	0.173315i
$969$	−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	$0.892222\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	1.60770	+	0.928203i	0.0515403	+	0.0297568i
$974$	39.1769			1.25531
$975$		0			0
$976$	10.3923			0.332650
$977$	28.9186	+	16.6962i	0.925187	+	0.534157i	0.885286	−	0.465046i	$-0.153962\pi$
$977$	28.9186	+	16.6962i	0.925187	+	0.534157i	0.0399012	+	0.999204i	$0.487296\pi$
$978$	−11.5263	+	19.9641i	−0.368570	+	0.638382i
$979$	1.73205	+	3.00000i	0.0553566	+	0.0958804i
$980$		0			0
$981$	−10.2679	+	5.92820i	−0.327830	+	0.189273i
$982$	15.0000	−	8.66025i	0.478669	−	0.276360i
$983$		−	57.3923i		−	1.83053i	−0.402852	−	0.915265i	$-0.631981\pi$
$983$		−	57.3923i		−	1.83053i	0.402852	−	0.915265i	$-0.368019\pi$
$984$	−1.00000	−	1.73205i	−0.0318788	−	0.0552158i
$985$		0			0
$986$	−12.9282	−	7.46410i	−0.411718	−	0.237705i
$987$	−20.9282			−0.666152
$988$	1.39230	−	1.33975i	0.0442951	−	0.0426230i
$989$	−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	$0.0359003\pi$
$992$	−0.866025	−	1.50000i	−0.0274963	−	0.0476250i
$993$		−	24.7846i		−	0.786516i
$994$	−14.5359	+	8.39230i	−0.461051	+	0.266188i
$995$		0			0
$996$			4.92820i			0.156156i
$997$	−23.7846	−	41.1962i	−0.753266	−	1.30470i	−0.946232	−	0.323490i	$-0.895144\pi$
$997$	−23.7846	−	41.1962i	−0.753266	−	1.30470i	0.192966	−	0.981206i	$-0.438189\pi$
$998$	−6.73205	+	11.6603i	−0.213099	+	0.369099i
$999$	−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.bc.b.901.1		4
5.2	odd	4		1950.2.y.f.199.2		4
5.3	odd	4		1950.2.y.c.199.1		4
5.4	even	2		390.2.bb.b.121.2	✓	4
13.10	even	6	inner	1950.2.bc.b.751.1		4
15.14	odd	2		1170.2.bs.e.901.1		4
65.4	even	6		5070.2.b.o.1351.4		4
65.9	even	6		5070.2.b.o.1351.1		4
65.19	odd	12		5070.2.a.y.1.2		2
65.23	odd	12		1950.2.y.f.49.2		4
65.49	even	6		390.2.bb.b.361.2	yes	4
65.59	odd	12		5070.2.a.bg.1.1		2
65.62	odd	12		1950.2.y.c.49.1		4
195.179	odd	6		1170.2.bs.e.361.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bb.b.121.2	✓	4	5.4	even	2
390.2.bb.b.361.2	yes	4	65.49	even	6
1170.2.bs.e.361.1		4	195.179	odd	6
1170.2.bs.e.901.1		4	15.14	odd	2
1950.2.y.c.49.1		4	65.62	odd	12
1950.2.y.c.199.1		4	5.3	odd	4
1950.2.y.f.49.2		4	65.23	odd	12
1950.2.y.f.199.2		4	5.2	odd	4
1950.2.bc.b.751.1		4	13.10	even	6	inner
1950.2.bc.b.901.1		4	1.1	even	1	trivial
5070.2.a.y.1.2		2	65.19	odd	12
5070.2.a.bg.1.1		2	65.59	odd	12
5070.2.b.o.1351.1		4	65.9	even	6
5070.2.b.o.1351.4		4	65.4	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.bc (of order \(6\), degree \(2\), minimal)

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

Introduction

L-functions

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