LMFDB - Embedded newform 350.2.e.l.151.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(51,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("350.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	350.151
Dual form			350.2.e.l.51.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.00000 q^{6} +(-0.500000 - 2.59808i) q^{7} -1.00000 q^{8} +(-3.00000 - 5.19615i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.00000 q^{6} +(-0.500000 - 2.59808i) q^{7} -1.00000 q^{8} +(-3.00000 - 5.19615i) q^{9} +(1.00000 - 1.73205i) q^{11} +(1.50000 + 2.59808i) q^{12} +(2.00000 - 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.00000 + 3.46410i) q^{17} +(3.00000 - 5.19615i) q^{18} +(3.00000 + 5.19615i) q^{19} +(-7.50000 - 2.59808i) q^{21} +2.00000 q^{22} +(1.50000 + 2.59808i) q^{23} +(-1.50000 + 2.59808i) q^{24} -9.00000 q^{27} +(2.50000 + 0.866025i) q^{28} +9.00000 q^{29} +(2.00000 - 3.46410i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-3.00000 - 5.19615i) q^{33} -4.00000 q^{34} +6.00000 q^{36} +(-2.00000 - 3.46410i) q^{37} +(-3.00000 + 5.19615i) q^{38} -7.00000 q^{41} +(-1.50000 - 7.79423i) q^{42} +5.00000 q^{43} +(1.00000 + 1.73205i) q^{44} +(-1.50000 + 2.59808i) q^{46} +(4.00000 + 6.92820i) q^{47} -3.00000 q^{48} +(-6.50000 + 2.59808i) q^{49} +(6.00000 + 10.3923i) q^{51} +(-1.00000 + 1.73205i) q^{53} +(-4.50000 - 7.79423i) q^{54} +(0.500000 + 2.59808i) q^{56} +18.0000 q^{57} +(4.50000 + 7.79423i) q^{58} +(-5.00000 + 8.66025i) q^{59} +(-0.500000 - 0.866025i) q^{61} +4.00000 q^{62} +(-12.0000 + 10.3923i) q^{63} +1.00000 q^{64} +(3.00000 - 5.19615i) q^{66} +(-4.50000 + 7.79423i) q^{67} +(-2.00000 - 3.46410i) q^{68} +9.00000 q^{69} +2.00000 q^{71} +(3.00000 + 5.19615i) q^{72} +(-2.00000 + 3.46410i) q^{73} +(2.00000 - 3.46410i) q^{74} -6.00000 q^{76} +(-5.00000 - 1.73205i) q^{77} +(-5.00000 - 8.66025i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-3.50000 - 6.06218i) q^{82} +7.00000 q^{83} +(6.00000 - 5.19615i) q^{84} +(2.50000 + 4.33013i) q^{86} +(13.5000 - 23.3827i) q^{87} +(-1.00000 + 1.73205i) q^{88} +(-0.500000 - 0.866025i) q^{89} -3.00000 q^{92} +(-6.00000 - 10.3923i) q^{93} +(-4.00000 + 6.92820i) q^{94} +(-1.50000 - 2.59808i) q^{96} -14.0000 q^{97} +(-5.50000 - 4.33013i) q^{98} -12.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + 3 q^{3} - q^{4} + 6 q^{6} - q^{7} - 2 q^{8} - 6 q^{9}+O(q^{10}) $ 2 * q + q^2 + 3 * q^3 - q^4 + 6 * q^6 - q^7 - 2 * q^8 - 6 * q^9	$ 2 q + q^{2} + 3 q^{3} - q^{4} + 6 q^{6} - q^{7} - 2 q^{8} - 6 q^{9} + 2 q^{11} + 3 q^{12} + 4 q^{14} - q^{16} - 4 q^{17} + 6 q^{18} + 6 q^{19} - 15 q^{21} + 4 q^{22} + 3 q^{23} - 3 q^{24} - 18 q^{27} + 5 q^{28} + 18 q^{29} + 4 q^{31} + q^{32} - 6 q^{33} - 8 q^{34} + 12 q^{36} - 4 q^{37} - 6 q^{38} - 14 q^{41} - 3 q^{42} + 10 q^{43} + 2 q^{44} - 3 q^{46} + 8 q^{47} - 6 q^{48} - 13 q^{49} + 12 q^{51} - 2 q^{53} - 9 q^{54} + q^{56} + 36 q^{57} + 9 q^{58} - 10 q^{59} - q^{61} + 8 q^{62} - 24 q^{63} + 2 q^{64} + 6 q^{66} - 9 q^{67} - 4 q^{68} + 18 q^{69} + 4 q^{71} + 6 q^{72} - 4 q^{73} + 4 q^{74} - 12 q^{76} - 10 q^{77} - 10 q^{79} - 9 q^{81} - 7 q^{82} + 14 q^{83} + 12 q^{84} + 5 q^{86} + 27 q^{87} - 2 q^{88} - q^{89} - 6 q^{92} - 12 q^{93} - 8 q^{94} - 3 q^{96} - 28 q^{97} - 11 q^{98} - 24 q^{99}+O(q^{100}) $ 2 * q + q^2 + 3 * q^3 - q^4 + 6 * q^6 - q^7 - 2 * q^8 - 6 * q^9 + 2 * q^11 + 3 * q^12 + 4 * q^14 - q^16 - 4 * q^17 + 6 * q^18 + 6 * q^19 - 15 * q^21 + 4 * q^22 + 3 * q^23 - 3 * q^24 - 18 * q^27 + 5 * q^28 + 18 * q^29 + 4 * q^31 + q^32 - 6 * q^33 - 8 * q^34 + 12 * q^36 - 4 * q^37 - 6 * q^38 - 14 * q^41 - 3 * q^42 + 10 * q^43 + 2 * q^44 - 3 * q^46 + 8 * q^47 - 6 * q^48 - 13 * q^49 + 12 * q^51 - 2 * q^53 - 9 * q^54 + q^56 + 36 * q^57 + 9 * q^58 - 10 * q^59 - q^61 + 8 * q^62 - 24 * q^63 + 2 * q^64 + 6 * q^66 - 9 * q^67 - 4 * q^68 + 18 * q^69 + 4 * q^71 + 6 * q^72 - 4 * q^73 + 4 * q^74 - 12 * q^76 - 10 * q^77 - 10 * q^79 - 9 * q^81 - 7 * q^82 + 14 * q^83 + 12 * q^84 + 5 * q^86 + 27 * q^87 - 2 * q^88 - q^89 - 6 * q^92 - 12 * q^93 - 8 * q^94 - 3 * q^96 - 28 * q^97 - 11 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	1.50000	−	2.59808i	0.866025	−	1.50000i		−	1.00000i	$-0.5\pi$
$3$	1.50000	−	2.59808i	0.866025	−	1.50000i	0.866025	−	0.500000i	$-0.166667\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	3.00000			1.22474
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$8$	−1.00000			−0.353553
$9$	−3.00000	−	5.19615i	−1.00000	−	1.73205i
$10$		0			0
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	−0.674967	−	0.737848i	$-0.735842\pi$
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	0.976478	+	0.215615i	$0.0691756\pi$
$12$	1.50000	+	2.59808i	0.433013	+	0.750000i
$13$		0			0			−	1.00000i	$-0.5\pi$
$13$		0			0				1.00000i	$0.5\pi$
$14$	2.00000	−	1.73205i	0.534522	−	0.462910i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.00000	+	3.46410i	−0.485071	+	0.840168i	−0.999853	−	0.0171533i	$-0.994540\pi$
$17$	−2.00000	+	3.46410i	−0.485071	+	0.840168i	0.514782	+	0.857321i	$0.327873\pi$
$18$	3.00000	−	5.19615i	0.707107	−	1.22474i
$19$	3.00000	+	5.19615i	0.688247	+	1.19208i	0.972404	+	0.233301i	$0.0749529\pi$
$19$	3.00000	+	5.19615i	0.688247	+	1.19208i	−0.284157	+	0.958778i	$0.591714\pi$
$20$		0			0
$21$	−7.50000	−	2.59808i	−1.63663	−	0.566947i
$22$	2.00000			0.426401
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	0.978961	−	0.204046i	$-0.0654092\pi$
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	−0.666190	+	0.745782i	$0.732076\pi$
$24$	−1.50000	+	2.59808i	−0.306186	+	0.530330i
$25$		0			0
$26$		0			0
$27$	−9.00000			−1.73205
$28$	2.50000	+	0.866025i	0.472456	+	0.163663i
$29$	9.00000			1.67126			0.835629	−	0.549294i	$-0.185103\pi$
$29$	9.00000			1.67126			0.835629	+	0.549294i	$0.185103\pi$
$30$		0			0
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	0.987829	+	0.155543i	$0.0497126\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−3.00000	−	5.19615i	−0.522233	−	0.904534i
$34$	−4.00000			−0.685994
$35$		0			0
$36$	6.00000			1.00000
$37$	−2.00000	−	3.46410i	−0.328798	−	0.569495i	0.653476	−	0.756948i	$-0.273310\pi$
$37$	−2.00000	−	3.46410i	−0.328798	−	0.569495i	−0.982274	+	0.187453i	$0.939977\pi$
$38$	−3.00000	+	5.19615i	−0.486664	+	0.842927i
$39$		0			0
$40$		0			0
$41$	−7.00000			−1.09322			−0.546608	−	0.837389i	$-0.684081\pi$
$41$	−7.00000			−1.09322			−0.546608	+	0.837389i	$0.684081\pi$
$42$	−1.50000	−	7.79423i	−0.231455	−	1.20268i
$43$	5.00000			0.762493			0.381246	−	0.924473i	$-0.375495\pi$
$43$	5.00000			0.762493			0.381246	+	0.924473i	$0.375495\pi$
$44$	1.00000	+	1.73205i	0.150756	+	0.261116i
$45$		0			0
$46$	−1.50000	+	2.59808i	−0.221163	+	0.383065i
$47$	4.00000	+	6.92820i	0.583460	+	1.01058i	0.995066	+	0.0992202i	$0.0316348\pi$
$47$	4.00000	+	6.92820i	0.583460	+	1.01058i	−0.411606	+	0.911362i	$0.635032\pi$
$48$	−3.00000			−0.433013
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$		0			0
$51$	6.00000	+	10.3923i	0.840168	+	1.45521i
$52$		0			0
$53$	−1.00000	+	1.73205i	−0.137361	+	0.237915i	−0.926497	−	0.376303i	$-0.877195\pi$
$53$	−1.00000	+	1.73205i	−0.137361	+	0.237915i	0.789136	+	0.614218i	$0.210529\pi$
$54$	−4.50000	−	7.79423i	−0.612372	−	1.06066i
$55$		0			0
$56$	0.500000	+	2.59808i	0.0668153	+	0.347183i
$57$	18.0000			2.38416
$58$	4.50000	+	7.79423i	0.590879	+	1.02343i
$59$	−5.00000	+	8.66025i	−0.650945	+	1.12747i	0.331949	+	0.943297i	$0.392294\pi$
$59$	−5.00000	+	8.66025i	−0.650945	+	1.12747i	−0.982894	+	0.184172i	$0.941040\pi$
$60$		0			0
$61$	−0.500000	−	0.866025i	−0.0640184	−	0.110883i	0.832240	−	0.554416i	$-0.187058\pi$
$61$	−0.500000	−	0.866025i	−0.0640184	−	0.110883i	−0.896258	+	0.443533i	$0.853725\pi$
$62$	4.00000			0.508001
$63$	−12.0000	+	10.3923i	−1.51186	+	1.30931i
$64$	1.00000			0.125000
$65$		0			0
$66$	3.00000	−	5.19615i	0.369274	−	0.639602i
$67$	−4.50000	+	7.79423i	−0.549762	+	0.952217i	0.448528	+	0.893769i	$0.351948\pi$
$67$	−4.50000	+	7.79423i	−0.549762	+	0.952217i	−0.998290	+	0.0584478i	$0.981385\pi$
$68$	−2.00000	−	3.46410i	−0.242536	−	0.420084i
$69$	9.00000			1.08347
$70$		0			0
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$	3.00000	+	5.19615i	0.353553	+	0.612372i
$73$	−2.00000	+	3.46410i	−0.234082	+	0.405442i	−0.959006	−	0.283387i	$-0.908542\pi$
$73$	−2.00000	+	3.46410i	−0.234082	+	0.405442i	0.724923	+	0.688830i	$0.241875\pi$
$74$	2.00000	−	3.46410i	0.232495	−	0.402694i
$75$		0			0
$76$	−6.00000			−0.688247
$77$	−5.00000	−	1.73205i	−0.569803	−	0.197386i
$78$		0			0
$79$	−5.00000	−	8.66025i	−0.562544	−	0.974355i	−0.997274	−	0.0737937i	$-0.976489\pi$
$79$	−5.00000	−	8.66025i	−0.562544	−	0.974355i	0.434730	−	0.900561i	$-0.356844\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	−3.50000	−	6.06218i	−0.386510	−	0.669456i
$83$	7.00000			0.768350			0.384175	−	0.923260i	$-0.374486\pi$
$83$	7.00000			0.768350			0.384175	+	0.923260i	$0.374486\pi$
$84$	6.00000	−	5.19615i	0.654654	−	0.566947i
$85$		0			0
$86$	2.50000	+	4.33013i	0.269582	+	0.466930i
$87$	13.5000	−	23.3827i	1.44735	−	2.50689i
$88$	−1.00000	+	1.73205i	−0.106600	+	0.184637i
$89$	−0.500000	−	0.866025i	−0.0529999	−	0.0917985i	0.838308	−	0.545197i	$-0.183545\pi$
$89$	−0.500000	−	0.866025i	−0.0529999	−	0.0917985i	−0.891308	+	0.453398i	$0.850212\pi$
$90$		0			0
$91$		0			0
$92$	−3.00000			−0.312772
$93$	−6.00000	−	10.3923i	−0.622171	−	1.07763i
$94$	−4.00000	+	6.92820i	−0.412568	+	0.714590i
$95$		0			0
$96$	−1.50000	−	2.59808i	−0.153093	−	0.265165i
$97$	−14.0000			−1.42148			−0.710742	−	0.703452i	$-0.751641\pi$
$97$	−14.0000			−1.42148			−0.710742	+	0.703452i	$0.751641\pi$
$98$	−5.50000	−	4.33013i	−0.555584	−	0.437409i
$99$	−12.0000			−1.20605
$100$		0			0
$101$	−1.50000	+	2.59808i	−0.149256	+	0.258518i	−0.930953	−	0.365140i	$-0.881021\pi$
$101$	−1.50000	+	2.59808i	−0.149256	+	0.258518i	0.781697	+	0.623658i	$0.214354\pi$
$102$	−6.00000	+	10.3923i	−0.594089	+	1.02899i
$103$	0.500000	+	0.866025i	0.0492665	+	0.0853320i	0.889607	−	0.456727i	$-0.150978\pi$
$103$	0.500000	+	0.866025i	0.0492665	+	0.0853320i	−0.840341	+	0.542059i	$0.817645\pi$
$104$		0			0
$105$		0			0
$106$	−2.00000			−0.194257
$107$	1.50000	+	2.59808i	0.145010	+	0.251166i	0.929377	−	0.369132i	$-0.120345\pi$
$107$	1.50000	+	2.59808i	0.145010	+	0.251166i	−0.784366	+	0.620298i	$0.787012\pi$
$108$	4.50000	−	7.79423i	0.433013	−	0.750000i
$109$	4.50000	−	7.79423i	0.431022	−	0.746552i	−0.565940	−	0.824447i	$-0.691487\pi$
$109$	4.50000	−	7.79423i	0.431022	−	0.746552i	0.996962	+	0.0778949i	$0.0248199\pi$
$110$		0			0
$111$	−12.0000			−1.13899
$112$	−2.00000	+	1.73205i	−0.188982	+	0.163663i
$113$	−2.00000			−0.188144			−0.0940721	−	0.995565i	$-0.529988\pi$
$113$	−2.00000			−0.188144			−0.0940721	+	0.995565i	$0.529988\pi$
$114$	9.00000	+	15.5885i	0.842927	+	1.45999i
$115$		0			0
$116$	−4.50000	+	7.79423i	−0.417815	+	0.723676i
$117$		0			0
$118$	−10.0000			−0.920575
$119$	10.0000	+	3.46410i	0.916698	+	0.317554i
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	0.500000	−	0.866025i	0.0452679	−	0.0784063i
$123$	−10.5000	+	18.1865i	−0.946753	+	1.63982i
$124$	2.00000	+	3.46410i	0.179605	+	0.311086i
$125$		0			0
$126$	−15.0000	−	5.19615i	−1.33631	−	0.462910i
$127$	−16.0000			−1.41977			−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000			−1.41977			−0.709885	+	0.704317i	$0.751253\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	7.50000	−	12.9904i	0.660338	−	1.14374i
$130$		0			0
$131$	−4.00000	−	6.92820i	−0.349482	−	0.605320i	0.636676	−	0.771132i	$-0.280309\pi$
$131$	−4.00000	−	6.92820i	−0.349482	−	0.605320i	−0.986157	+	0.165812i	$0.946976\pi$
$132$	6.00000			0.522233
$133$	12.0000	−	10.3923i	1.04053	−	0.901127i
$134$	−9.00000			−0.777482
$135$		0			0
$136$	2.00000	−	3.46410i	0.171499	−	0.297044i
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	−0.487278	−	0.873247i	$-0.662010\pi$
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	0.999893	−	0.0146279i	$-0.00465636\pi$
$138$	4.50000	+	7.79423i	0.383065	+	0.663489i
$139$	−14.0000			−1.18746			−0.593732	−	0.804663i	$-0.702346\pi$
$139$	−14.0000			−1.18746			−0.593732	+	0.804663i	$0.702346\pi$
$140$		0			0
$141$	24.0000			2.02116
$142$	1.00000	+	1.73205i	0.0839181	+	0.145350i
$143$		0			0
$144$	−3.00000	+	5.19615i	−0.250000	+	0.433013i
$145$		0			0
$146$	−4.00000			−0.331042
$147$	−3.00000	+	20.7846i	−0.247436	+	1.71429i
$148$	4.00000			0.328798
$149$	−1.50000	−	2.59808i	−0.122885	−	0.212843i	0.798019	−	0.602632i	$-0.205881\pi$
$149$	−1.50000	−	2.59808i	−0.122885	−	0.212843i	−0.920904	+	0.389789i	$0.872548\pi$
$150$		0			0
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	−0.331842	−	0.943335i	$-0.607670\pi$
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	0.982873	−	0.184284i	$-0.0589965\pi$
$152$	−3.00000	−	5.19615i	−0.243332	−	0.421464i
$153$	24.0000			1.94029
$154$	−1.00000	−	5.19615i	−0.0805823	−	0.418718i
$155$		0			0
$156$		0			0
$157$	5.00000	−	8.66025i	0.399043	−	0.691164i	−0.594565	−	0.804048i	$-0.702676\pi$
$157$	5.00000	−	8.66025i	0.399043	−	0.691164i	0.993608	+	0.112884i	$0.0360089\pi$
$158$	5.00000	−	8.66025i	0.397779	−	0.688973i
$159$	3.00000	+	5.19615i	0.237915	+	0.412082i
$160$		0			0
$161$	6.00000	−	5.19615i	0.472866	−	0.409514i
$162$	−9.00000			−0.707107
$163$	−2.00000	−	3.46410i	−0.156652	−	0.271329i	0.777007	−	0.629492i	$-0.216737\pi$
$163$	−2.00000	−	3.46410i	−0.156652	−	0.271329i	−0.933659	+	0.358162i	$0.883403\pi$
$164$	3.50000	−	6.06218i	0.273304	−	0.473377i
$165$		0			0
$166$	3.50000	+	6.06218i	0.271653	+	0.470516i
$167$	21.0000			1.62503			0.812514	−	0.582941i	$-0.198098\pi$
$167$	21.0000			1.62503			0.812514	+	0.582941i	$0.198098\pi$
$168$	7.50000	+	2.59808i	0.578638	+	0.200446i
$169$	−13.0000			−1.00000
$170$		0			0
$171$	18.0000	−	31.1769i	1.37649	−	2.38416i
$172$	−2.50000	+	4.33013i	−0.190623	+	0.330169i
$173$	4.00000	+	6.92820i	0.304114	+	0.526742i	0.977064	−	0.212947i	$-0.0683062\pi$
$173$	4.00000	+	6.92820i	0.304114	+	0.526742i	−0.672949	+	0.739689i	$0.734973\pi$
$174$	27.0000			2.04686
$175$		0			0
$176$	−2.00000			−0.150756
$177$	15.0000	+	25.9808i	1.12747	+	1.95283i
$178$	0.500000	−	0.866025i	0.0374766	−	0.0649113i
$179$	−6.00000	+	10.3923i	−0.448461	+	0.776757i	−0.998286	−	0.0585225i	$-0.981361\pi$
$179$	−6.00000	+	10.3923i	−0.448461	+	0.776757i	0.549825	+	0.835280i	$0.314694\pi$
$180$		0			0
$181$	7.00000			0.520306			0.260153	−	0.965567i	$-0.416227\pi$
$181$	7.00000			0.520306			0.260153	+	0.965567i	$0.416227\pi$
$182$		0			0
$183$	−3.00000			−0.221766
$184$	−1.50000	−	2.59808i	−0.110581	−	0.191533i
$185$		0			0
$186$	6.00000	−	10.3923i	0.439941	−	0.762001i
$187$	4.00000	+	6.92820i	0.292509	+	0.506640i
$188$	−8.00000			−0.583460
$189$	4.50000	+	23.3827i	0.327327	+	1.70084i
$190$		0			0
$191$	9.00000	+	15.5885i	0.651217	+	1.12794i	0.982828	+	0.184525i	$0.0590746\pi$
$191$	9.00000	+	15.5885i	0.651217	+	1.12794i	−0.331611	+	0.943416i	$0.607592\pi$
$192$	1.50000	−	2.59808i	0.108253	−	0.187500i
$193$	13.0000	−	22.5167i	0.935760	−	1.62078i	0.162488	−	0.986710i	$-0.448048\pi$
$193$	13.0000	−	22.5167i	0.935760	−	1.62078i	0.773272	−	0.634074i	$-0.218619\pi$
$194$	−7.00000	−	12.1244i	−0.502571	−	0.870478i
$195$		0			0
$196$	1.00000	−	6.92820i	0.0714286	−	0.494872i
$197$	−2.00000			−0.142494			−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000			−0.142494			−0.0712470	+	0.997459i	$0.522698\pi$
$198$	−6.00000	−	10.3923i	−0.426401	−	0.738549i
$199$	2.00000	−	3.46410i	0.141776	−	0.245564i	−0.786389	−	0.617731i	$-0.788052\pi$
$199$	2.00000	−	3.46410i	0.141776	−	0.245564i	0.928166	+	0.372168i	$0.121385\pi$
$200$		0			0
$201$	13.5000	+	23.3827i	0.952217	+	1.64929i
$202$	−3.00000			−0.211079
$203$	−4.50000	−	23.3827i	−0.315838	−	1.64114i
$204$	−12.0000			−0.840168
$205$		0			0
$206$	−0.500000	+	0.866025i	−0.0348367	+	0.0603388i
$207$	9.00000	−	15.5885i	0.625543	−	1.08347i
$208$		0			0
$209$	12.0000			0.830057
$210$		0			0
$211$	−26.0000			−1.78991			−0.894957	−	0.446153i	$-0.852794\pi$
$211$	−26.0000			−1.78991			−0.894957	+	0.446153i	$0.852794\pi$
$212$	−1.00000	−	1.73205i	−0.0686803	−	0.118958i
$213$	3.00000	−	5.19615i	0.205557	−	0.356034i
$214$	−1.50000	+	2.59808i	−0.102538	+	0.177601i
$215$		0			0
$216$	9.00000			0.612372
$217$	−10.0000	−	3.46410i	−0.678844	−	0.235159i
$218$	9.00000			0.609557
$219$	6.00000	+	10.3923i	0.405442	+	0.702247i
$220$		0			0
$221$		0			0
$222$	−6.00000	−	10.3923i	−0.402694	−	0.697486i
$223$	−28.0000			−1.87502			−0.937509	−	0.347960i	$-0.886874\pi$
$223$	−28.0000			−1.87502			−0.937509	+	0.347960i	$0.886874\pi$
$224$	−2.50000	−	0.866025i	−0.167038	−	0.0578638i
$225$		0			0
$226$	−1.00000	−	1.73205i	−0.0665190	−	0.115214i
$227$	−2.00000	+	3.46410i	−0.132745	+	0.229920i	−0.924734	−	0.380615i	$-0.875712\pi$
$227$	−2.00000	+	3.46410i	−0.132745	+	0.229920i	0.791989	+	0.610535i	$0.209046\pi$
$228$	−9.00000	+	15.5885i	−0.596040	+	1.03237i
$229$	−11.0000	−	19.0526i	−0.726900	−	1.25903i	−0.958187	−	0.286143i	$-0.907627\pi$
$229$	−11.0000	−	19.0526i	−0.726900	−	1.25903i	0.231287	−	0.972886i	$-0.425707\pi$
$230$		0			0
$231$	−12.0000	+	10.3923i	−0.789542	+	0.683763i
$232$	−9.00000			−0.590879
$233$	12.0000	+	20.7846i	0.786146	+	1.36165i	0.928312	+	0.371802i	$0.121260\pi$
$233$	12.0000	+	20.7846i	0.786146	+	1.36165i	−0.142166	+	0.989843i	$0.545407\pi$
$234$		0			0
$235$		0			0
$236$	−5.00000	−	8.66025i	−0.325472	−	0.563735i
$237$	−30.0000			−1.94871
$238$	2.00000	+	10.3923i	0.129641	+	0.673633i
$239$	16.0000			1.03495			0.517477	−	0.855697i	$-0.326871\pi$
$239$	16.0000			1.03495			0.517477	+	0.855697i	$0.326871\pi$
$240$		0			0
$241$	−5.00000	+	8.66025i	−0.322078	+	0.557856i	−0.980917	−	0.194429i	$-0.937715\pi$
$241$	−5.00000	+	8.66025i	−0.322078	+	0.557856i	0.658838	+	0.752285i	$0.271048\pi$
$242$	−3.50000	+	6.06218i	−0.224989	+	0.389692i
$243$		0			0
$244$	1.00000			0.0640184
$245$		0			0
$246$	−21.0000			−1.33891
$247$		0			0
$248$	−2.00000	+	3.46410i	−0.127000	+	0.219971i
$249$	10.5000	−	18.1865i	0.665410	−	1.15252i
$250$		0			0
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$	−3.00000	−	15.5885i	−0.188982	−	0.981981i
$253$	6.00000			0.377217
$254$	−8.00000	−	13.8564i	−0.501965	−	0.869428i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.00000	+	6.92820i	0.249513	+	0.432169i	0.963391	−	0.268101i	$-0.0863961\pi$
$257$	4.00000	+	6.92820i	0.249513	+	0.432169i	−0.713878	+	0.700270i	$0.753063\pi$
$258$	15.0000			0.933859
$259$	−8.00000	+	6.92820i	−0.497096	+	0.430498i
$260$		0			0
$261$	−27.0000	−	46.7654i	−1.67126	−	2.89470i
$262$	4.00000	−	6.92820i	0.247121	−	0.428026i
$263$	2.50000	−	4.33013i	0.154157	−	0.267007i	−0.778595	−	0.627527i	$-0.784067\pi$
$263$	2.50000	−	4.33013i	0.154157	−	0.267007i	0.932752	+	0.360520i	$0.117401\pi$
$264$	3.00000	+	5.19615i	0.184637	+	0.319801i
$265$		0			0
$266$	15.0000	+	5.19615i	0.919709	+	0.318597i
$267$	−3.00000			−0.183597
$268$	−4.50000	−	7.79423i	−0.274881	−	0.476108i
$269$	−1.50000	+	2.59808i	−0.0914566	+	0.158408i	−0.908124	−	0.418701i	$-0.862486\pi$
$269$	−1.50000	+	2.59808i	−0.0914566	+	0.158408i	0.816668	+	0.577108i	$0.195819\pi$
$270$		0			0
$271$	3.00000	+	5.19615i	0.182237	+	0.315644i	0.942642	−	0.333805i	$-0.108333\pi$
$271$	3.00000	+	5.19615i	0.182237	+	0.315644i	−0.760405	+	0.649449i	$0.775000\pi$
$272$	4.00000			0.242536
$273$		0			0
$274$	12.0000			0.724947
$275$		0			0
$276$	−4.50000	+	7.79423i	−0.270868	+	0.469157i
$277$	6.00000	−	10.3923i	0.360505	−	0.624413i	−0.627539	−	0.778585i	$-0.715938\pi$
$277$	6.00000	−	10.3923i	0.360505	−	0.624413i	0.988044	+	0.154172i	$0.0492710\pi$
$278$	−7.00000	−	12.1244i	−0.419832	−	0.727171i
$279$	−24.0000			−1.43684
$280$		0			0
$281$	2.00000			0.119310			0.0596550	−	0.998219i	$-0.481000\pi$
$281$	2.00000			0.119310			0.0596550	+	0.998219i	$0.481000\pi$
$282$	12.0000	+	20.7846i	0.714590	+	1.23771i
$283$	−2.00000	+	3.46410i	−0.118888	+	0.205919i	−0.919327	−	0.393494i	$-0.871266\pi$
$283$	−2.00000	+	3.46410i	−0.118888	+	0.205919i	0.800439	+	0.599414i	$0.204600\pi$
$284$	−1.00000	+	1.73205i	−0.0593391	+	0.102778i
$285$		0			0
$286$		0			0
$287$	3.50000	+	18.1865i	0.206598	+	1.07352i
$288$	−6.00000			−0.353553
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$		0			0
$291$	−21.0000	+	36.3731i	−1.23104	+	2.13223i
$292$	−2.00000	−	3.46410i	−0.117041	−	0.202721i
$293$	−28.0000			−1.63578			−0.817889	−	0.575376i	$-0.804856\pi$
$293$	−28.0000			−1.63578			−0.817889	+	0.575376i	$0.804856\pi$
$294$	−19.5000	+	7.79423i	−1.13726	+	0.454569i
$295$		0			0
$296$	2.00000	+	3.46410i	0.116248	+	0.201347i
$297$	−9.00000	+	15.5885i	−0.522233	+	0.904534i
$298$	1.50000	−	2.59808i	0.0868927	−	0.150503i
$299$		0			0
$300$		0			0
$301$	−2.50000	−	12.9904i	−0.144098	−	0.748753i
$302$	16.0000			0.920697
$303$	4.50000	+	7.79423i	0.258518	+	0.447767i
$304$	3.00000	−	5.19615i	0.172062	−	0.298020i
$305$		0			0
$306$	12.0000	+	20.7846i	0.685994	+	1.18818i
$307$	−7.00000			−0.399511			−0.199756	−	0.979846i	$-0.564015\pi$
$307$	−7.00000			−0.399511			−0.199756	+	0.979846i	$0.564015\pi$
$308$	4.00000	−	3.46410i	0.227921	−	0.197386i
$309$	3.00000			0.170664
$310$		0			0
$311$	9.00000	−	15.5885i	0.510343	−	0.883940i	−0.489585	−	0.871956i	$-0.662852\pi$
$311$	9.00000	−	15.5885i	0.510343	−	0.883940i	0.999928	−	0.0119847i	$-0.00381495\pi$
$312$		0			0
$313$	4.00000	+	6.92820i	0.226093	+	0.391605i	0.956647	−	0.291250i	$-0.0940712\pi$
$313$	4.00000	+	6.92820i	0.226093	+	0.391605i	−0.730554	+	0.682855i	$0.760738\pi$
$314$	10.0000			0.564333
$315$		0			0
$316$	10.0000			0.562544
$317$	−16.0000	−	27.7128i	−0.898650	−	1.55651i	−0.829222	−	0.558920i	$-0.811216\pi$
$317$	−16.0000	−	27.7128i	−0.898650	−	1.55651i	−0.0694277	−	0.997587i	$-0.522117\pi$
$318$	−3.00000	+	5.19615i	−0.168232	+	0.291386i
$319$	9.00000	−	15.5885i	0.503903	−	0.872786i
$320$		0			0
$321$	9.00000			0.502331
$322$	7.50000	+	2.59808i	0.417959	+	0.144785i
$323$	−24.0000			−1.33540
$324$	−4.50000	−	7.79423i	−0.250000	−	0.433013i
$325$		0			0
$326$	2.00000	−	3.46410i	0.110770	−	0.191859i
$327$	−13.5000	−	23.3827i	−0.746552	−	1.29307i
$328$	7.00000			0.386510
$329$	16.0000	−	13.8564i	0.882109	−	0.763928i
$330$		0			0
$331$	16.0000	+	27.7128i	0.879440	+	1.52323i	0.851957	+	0.523612i	$0.175416\pi$
$331$	16.0000	+	27.7128i	0.879440	+	1.52323i	0.0274825	+	0.999622i	$0.491251\pi$
$332$	−3.50000	+	6.06218i	−0.192087	+	0.332705i
$333$	−12.0000	+	20.7846i	−0.657596	+	1.13899i
$334$	10.5000	+	18.1865i	0.574534	+	0.995123i
$335$		0			0
$336$	1.50000	+	7.79423i	0.0818317	+	0.425210i
$337$	26.0000			1.41631			0.708155	−	0.706057i	$-0.249528\pi$
$337$	26.0000			1.41631			0.708155	+	0.706057i	$0.249528\pi$
$338$	−6.50000	−	11.2583i	−0.353553	−	0.612372i
$339$	−3.00000	+	5.19615i	−0.162938	+	0.282216i
$340$		0			0
$341$	−4.00000	−	6.92820i	−0.216612	−	0.375183i
$342$	36.0000			1.94666
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	−5.00000			−0.269582
$345$		0			0
$346$	−4.00000	+	6.92820i	−0.215041	+	0.372463i
$347$	9.50000	−	16.4545i	0.509987	−	0.883323i	−0.489946	−	0.871753i	$-0.662984\pi$
$347$	9.50000	−	16.4545i	0.509987	−	0.883323i	0.999933	−	0.0115703i	$-0.00368303\pi$
$348$	13.5000	+	23.3827i	0.723676	+	1.25344i
$349$	−35.0000			−1.87351			−0.936754	−	0.349990i	$-0.886185\pi$
$349$	−35.0000			−1.87351			−0.936754	+	0.349990i	$0.886185\pi$
$350$		0			0
$351$		0			0
$352$	−1.00000	−	1.73205i	−0.0533002	−	0.0923186i
$353$	−9.00000	+	15.5885i	−0.479022	+	0.829690i	−0.999711	−	0.0240566i	$-0.992342\pi$
$353$	−9.00000	+	15.5885i	−0.479022	+	0.829690i	0.520689	+	0.853746i	$0.325675\pi$
$354$	−15.0000	+	25.9808i	−0.797241	+	1.38086i
$355$		0			0
$356$	1.00000			0.0529999
$357$	24.0000	−	20.7846i	1.27021	−	1.10004i
$358$	−12.0000			−0.634220
$359$	2.00000	+	3.46410i	0.105556	+	0.182828i	0.913965	−	0.405793i	$-0.133004\pi$
$359$	2.00000	+	3.46410i	0.105556	+	0.182828i	−0.808409	+	0.588621i	$0.799671\pi$
$360$		0			0
$361$	−8.50000	+	14.7224i	−0.447368	+	0.774865i
$362$	3.50000	+	6.06218i	0.183956	+	0.318621i
$363$	21.0000			1.10221
$364$		0			0
$365$		0			0
$366$	−1.50000	−	2.59808i	−0.0784063	−	0.135804i
$367$	−5.50000	+	9.52628i	−0.287098	+	0.497268i	−0.973116	−	0.230317i	$-0.926024\pi$
$367$	−5.50000	+	9.52628i	−0.287098	+	0.497268i	0.686018	+	0.727585i	$0.259357\pi$
$368$	1.50000	−	2.59808i	0.0781929	−	0.135434i
$369$	21.0000	+	36.3731i	1.09322	+	1.89351i
$370$		0			0
$371$	5.00000	+	1.73205i	0.259587	+	0.0899236i
$372$	12.0000			0.622171
$373$	−2.00000	−	3.46410i	−0.103556	−	0.179364i	0.809591	−	0.586994i	$-0.199689\pi$
$373$	−2.00000	−	3.46410i	−0.103556	−	0.179364i	−0.913147	+	0.407630i	$0.866355\pi$
$374$	−4.00000	+	6.92820i	−0.206835	+	0.358249i
$375$		0			0
$376$	−4.00000	−	6.92820i	−0.206284	−	0.357295i
$377$		0			0
$378$	−18.0000	+	15.5885i	−0.925820	+	0.801784i
$379$	30.0000			1.54100			0.770498	−	0.637442i	$-0.220007\pi$
$379$	30.0000			1.54100			0.770498	+	0.637442i	$0.220007\pi$
$380$		0			0
$381$	−24.0000	+	41.5692i	−1.22956	+	2.12966i
$382$	−9.00000	+	15.5885i	−0.460480	+	0.797575i
$383$	7.50000	+	12.9904i	0.383232	+	0.663777i	0.991522	−	0.129937i	$-0.0414776\pi$
$383$	7.50000	+	12.9904i	0.383232	+	0.663777i	−0.608290	+	0.793715i	$0.708144\pi$
$384$	3.00000			0.153093
$385$		0			0
$386$	26.0000			1.32337
$387$	−15.0000	−	25.9808i	−0.762493	−	1.32068i
$388$	7.00000	−	12.1244i	0.355371	−	0.615521i
$389$	−13.0000	+	22.5167i	−0.659126	+	1.14164i	0.321716	+	0.946836i	$0.395740\pi$
$389$	−13.0000	+	22.5167i	−0.659126	+	1.14164i	−0.980842	+	0.194804i	$0.937593\pi$
$390$		0			0
$391$	−12.0000			−0.606866
$392$	6.50000	−	2.59808i	0.328300	−	0.131223i
$393$	−24.0000			−1.21064
$394$	−1.00000	−	1.73205i	−0.0503793	−	0.0872595i
$395$		0			0
$396$	6.00000	−	10.3923i	0.301511	−	0.522233i
$397$	11.0000	+	19.0526i	0.552074	+	0.956221i	0.998125	+	0.0612128i	$0.0194968\pi$
$397$	11.0000	+	19.0526i	0.552074	+	0.956221i	−0.446051	+	0.895008i	$0.647170\pi$
$398$	4.00000			0.200502
$399$	−9.00000	−	46.7654i	−0.450564	−	2.34120i
$400$		0			0
$401$	−15.5000	−	26.8468i	−0.774033	−	1.34066i	−0.935336	−	0.353760i	$-0.884903\pi$
$401$	−15.5000	−	26.8468i	−0.774033	−	1.34066i	0.161303	−	0.986905i	$-0.448430\pi$
$402$	−13.5000	+	23.3827i	−0.673319	+	1.16622i
$403$		0			0
$404$	−1.50000	−	2.59808i	−0.0746278	−	0.129259i
$405$		0			0
$406$	18.0000	−	15.5885i	0.893325	−	0.773642i
$407$	−8.00000			−0.396545
$408$	−6.00000	−	10.3923i	−0.297044	−	0.514496i
$409$	−1.50000	+	2.59808i	−0.0741702	+	0.128467i	−0.900725	−	0.434389i	$-0.856964\pi$
$409$	−1.50000	+	2.59808i	−0.0741702	+	0.128467i	0.826555	+	0.562856i	$0.190297\pi$
$410$		0			0
$411$	−18.0000	−	31.1769i	−0.887875	−	1.53784i
$412$	−1.00000			−0.0492665
$413$	25.0000	+	8.66025i	1.23017	+	0.426143i
$414$	18.0000			0.884652
$415$		0			0
$416$		0			0
$417$	−21.0000	+	36.3731i	−1.02837	+	1.78120i
$418$	6.00000	+	10.3923i	0.293470	+	0.508304i
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	−19.0000			−0.926003			−0.463002	−	0.886357i	$-0.653228\pi$
$421$	−19.0000			−0.926003			−0.463002	+	0.886357i	$0.653228\pi$
$422$	−13.0000	−	22.5167i	−0.632830	−	1.09609i
$423$	24.0000	−	41.5692i	1.16692	−	2.02116i
$424$	1.00000	−	1.73205i	0.0485643	−	0.0841158i
$425$		0			0
$426$	6.00000			0.290701
$427$	−2.00000	+	1.73205i	−0.0967868	+	0.0838198i
$428$	−3.00000			−0.145010
$429$		0			0
$430$		0			0
$431$	15.0000	−	25.9808i	0.722525	−	1.25145i	−0.237460	−	0.971397i	$-0.576315\pi$
$431$	15.0000	−	25.9808i	0.722525	−	1.25145i	0.959985	−	0.280052i	$-0.0903517\pi$
$432$	4.50000	+	7.79423i	0.216506	+	0.375000i
$433$	−14.0000			−0.672797			−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000			−0.672797			−0.336399	+	0.941720i	$0.609209\pi$
$434$	−2.00000	−	10.3923i	−0.0960031	−	0.498847i
$435$		0			0
$436$	4.50000	+	7.79423i	0.215511	+	0.373276i
$437$	−9.00000	+	15.5885i	−0.430528	+	0.745697i
$438$	−6.00000	+	10.3923i	−0.286691	+	0.496564i
$439$	10.0000	+	17.3205i	0.477274	+	0.826663i	0.999661	−	0.0260459i	$-0.00829161\pi$
$439$	10.0000	+	17.3205i	0.477274	+	0.826663i	−0.522387	+	0.852709i	$0.674958\pi$
$440$		0			0
$441$	33.0000	+	25.9808i	1.57143	+	1.23718i
$442$		0			0
$443$	15.5000	+	26.8468i	0.736427	+	1.27553i	0.954094	+	0.299506i	$0.0968220\pi$
$443$	15.5000	+	26.8468i	0.736427	+	1.27553i	−0.217667	+	0.976023i	$0.569845\pi$
$444$	6.00000	−	10.3923i	0.284747	−	0.493197i
$445$		0			0
$446$	−14.0000	−	24.2487i	−0.662919	−	1.14821i
$447$	−9.00000			−0.425685
$448$	−0.500000	−	2.59808i	−0.0236228	−	0.122748i
$449$	−33.0000			−1.55737			−0.778683	−	0.627417i	$-0.784112\pi$
$449$	−33.0000			−1.55737			−0.778683	+	0.627417i	$0.784112\pi$
$450$		0			0
$451$	−7.00000	+	12.1244i	−0.329617	+	0.570914i
$452$	1.00000	−	1.73205i	0.0470360	−	0.0814688i
$453$	−24.0000	−	41.5692i	−1.12762	−	1.95309i
$454$	−4.00000			−0.187729
$455$		0			0
$456$	−18.0000			−0.842927
$457$	−16.0000	−	27.7128i	−0.748448	−	1.29635i	−0.948566	−	0.316579i	$-0.897466\pi$
$457$	−16.0000	−	27.7128i	−0.748448	−	1.29635i	0.200118	−	0.979772i	$-0.435868\pi$
$458$	11.0000	−	19.0526i	0.513996	−	0.890268i
$459$	18.0000	−	31.1769i	0.840168	−	1.45521i
$460$		0			0
$461$	−14.0000			−0.652045			−0.326023	−	0.945362i	$-0.605709\pi$
$461$	−14.0000			−0.652045			−0.326023	+	0.945362i	$0.605709\pi$
$462$	−15.0000	−	5.19615i	−0.697863	−	0.241747i
$463$	19.0000			0.883005			0.441502	−	0.897260i	$-0.354446\pi$
$463$	19.0000			0.883005			0.441502	+	0.897260i	$0.354446\pi$
$464$	−4.50000	−	7.79423i	−0.208907	−	0.361838i
$465$		0			0
$466$	−12.0000	+	20.7846i	−0.555889	+	0.962828i
$467$	−6.50000	−	11.2583i	−0.300784	−	0.520973i	0.675530	−	0.737333i	$-0.263915\pi$
$467$	−6.50000	−	11.2583i	−0.300784	−	0.520973i	−0.976314	+	0.216359i	$0.930582\pi$
$468$		0			0
$469$	22.5000	+	7.79423i	1.03895	+	0.359904i
$470$		0			0
$471$	−15.0000	−	25.9808i	−0.691164	−	1.19713i
$472$	5.00000	−	8.66025i	0.230144	−	0.398621i
$473$	5.00000	−	8.66025i	0.229900	−	0.398199i
$474$	−15.0000	−	25.9808i	−0.688973	−	1.19334i
$475$		0			0
$476$	−8.00000	+	6.92820i	−0.366679	+	0.317554i
$477$	12.0000			0.549442
$478$	8.00000	+	13.8564i	0.365911	+	0.633777i
$479$	−12.0000	+	20.7846i	−0.548294	+	0.949673i	0.450098	+	0.892979i	$0.351389\pi$
$479$	−12.0000	+	20.7846i	−0.548294	+	0.949673i	−0.998392	+	0.0566937i	$0.981944\pi$
$480$		0			0
$481$		0			0
$482$	−10.0000			−0.455488
$483$	−4.50000	−	23.3827i	−0.204757	−	1.06395i
$484$	−7.00000			−0.318182
$485$		0			0
$486$		0			0
$487$	−8.00000	+	13.8564i	−0.362515	+	0.627894i	−0.988374	−	0.152042i	$-0.951415\pi$
$487$	−8.00000	+	13.8564i	−0.362515	+	0.627894i	0.625859	+	0.779936i	$0.284748\pi$
$488$	0.500000	+	0.866025i	0.0226339	+	0.0392031i
$489$	−12.0000			−0.542659
$490$		0			0
$491$	−12.0000			−0.541552			−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000			−0.541552			−0.270776	+	0.962642i	$0.587280\pi$
$492$	−10.5000	−	18.1865i	−0.473377	−	0.819912i
$493$	−18.0000	+	31.1769i	−0.810679	+	1.40414i
$494$		0			0
$495$		0			0
$496$	−4.00000			−0.179605
$497$	−1.00000	−	5.19615i	−0.0448561	−	0.233079i
$498$	21.0000			0.941033
$499$	9.00000	+	15.5885i	0.402895	+	0.697835i	0.994074	−	0.108705i	$-0.0346705\pi$
$499$	9.00000	+	15.5885i	0.402895	+	0.697835i	−0.591179	+	0.806541i	$0.701337\pi$
$500$		0			0
$501$	31.5000	−	54.5596i	1.40732	−	2.43754i
$502$		0			0
$503$	21.0000			0.936344			0.468172	−	0.883637i	$-0.344913\pi$
$503$	21.0000			0.936344			0.468172	+	0.883637i	$0.344913\pi$
$504$	12.0000	−	10.3923i	0.534522	−	0.462910i
$505$		0			0
$506$	3.00000	+	5.19615i	0.133366	+	0.230997i
$507$	−19.5000	+	33.7750i	−0.866025	+	1.50000i
$508$	8.00000	−	13.8564i	0.354943	−	0.614779i
$509$	−0.500000	−	0.866025i	−0.0221621	−	0.0383859i	0.854732	−	0.519070i	$-0.173722\pi$
$509$	−0.500000	−	0.866025i	−0.0221621	−	0.0383859i	−0.876894	+	0.480684i	$0.840388\pi$
$510$		0			0
$511$	10.0000	+	3.46410i	0.442374	+	0.153243i
$512$	−1.00000			−0.0441942
$513$	−27.0000	−	46.7654i	−1.19208	−	2.06474i
$514$	−4.00000	+	6.92820i	−0.176432	+	0.305590i
$515$		0			0
$516$	7.50000	+	12.9904i	0.330169	+	0.571870i
$517$	16.0000			0.703679
$518$	−10.0000	−	3.46410i	−0.439375	−	0.152204i
$519$	24.0000			1.05348
$520$		0			0
$521$	−19.0000	+	32.9090i	−0.832405	+	1.44177i	0.0637207	+	0.997968i	$0.479703\pi$
$521$	−19.0000	+	32.9090i	−0.832405	+	1.44177i	−0.896126	+	0.443800i	$0.853630\pi$
$522$	27.0000	−	46.7654i	1.18176	−	2.04686i
$523$	−10.0000	−	17.3205i	−0.437269	−	0.757373i	0.560208	−	0.828352i	$-0.310721\pi$
$523$	−10.0000	−	17.3205i	−0.437269	−	0.757373i	−0.997478	+	0.0709788i	$0.977388\pi$
$524$	8.00000			0.349482
$525$		0			0
$526$	5.00000			0.218010
$527$	8.00000	+	13.8564i	0.348485	+	0.603595i
$528$	−3.00000	+	5.19615i	−0.130558	+	0.226134i
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$		0			0
$531$	60.0000			2.60378
$532$	3.00000	+	15.5885i	0.130066	+	0.675845i
$533$		0			0
$534$	−1.50000	−	2.59808i	−0.0649113	−	0.112430i
$535$		0			0
$536$	4.50000	−	7.79423i	0.194370	−	0.336659i
$537$	18.0000	+	31.1769i	0.776757	+	1.34538i
$538$	−3.00000			−0.129339
$539$	−2.00000	+	13.8564i	−0.0861461	+	0.596838i
$540$		0			0
$541$	−1.50000	−	2.59808i	−0.0644900	−	0.111700i	0.831978	−	0.554809i	$-0.187209\pi$
$541$	−1.50000	−	2.59808i	−0.0644900	−	0.111700i	−0.896468	+	0.443109i	$0.853875\pi$
$542$	−3.00000	+	5.19615i	−0.128861	+	0.223194i
$543$	10.5000	−	18.1865i	0.450598	−	0.780459i
$544$	2.00000	+	3.46410i	0.0857493	+	0.148522i
$545$		0			0
$546$		0			0
$547$	33.0000			1.41098			0.705489	−	0.708721i	$-0.250727\pi$
$547$	33.0000			1.41098			0.705489	+	0.708721i	$0.250727\pi$
$548$	6.00000	+	10.3923i	0.256307	+	0.443937i
$549$	−3.00000	+	5.19615i	−0.128037	+	0.221766i
$550$		0			0
$551$	27.0000	+	46.7654i	1.15024	+	1.99227i
$552$	−9.00000			−0.383065
$553$	−20.0000	+	17.3205i	−0.850487	+	0.736543i
$554$	12.0000			0.509831
$555$		0			0
$556$	7.00000	−	12.1244i	0.296866	−	0.514187i
$557$	−1.00000	+	1.73205i	−0.0423714	+	0.0733893i	−0.886433	−	0.462856i	$-0.846825\pi$
$557$	−1.00000	+	1.73205i	−0.0423714	+	0.0733893i	0.844062	+	0.536246i	$0.180158\pi$
$558$	−12.0000	−	20.7846i	−0.508001	−	0.879883i
$559$		0			0
$560$		0			0
$561$	24.0000			1.01328
$562$	1.00000	+	1.73205i	0.0421825	+	0.0730622i
$563$	8.50000	−	14.7224i	0.358232	−	0.620477i	−0.629433	−	0.777055i	$-0.716713\pi$
$563$	8.50000	−	14.7224i	0.358232	−	0.620477i	0.987666	+	0.156578i	$0.0500463\pi$
$564$	−12.0000	+	20.7846i	−0.505291	+	0.875190i
$565$		0			0
$566$	−4.00000			−0.168133
$567$	22.5000	+	7.79423i	0.944911	+	0.327327i
$568$	−2.00000			−0.0839181
$569$	9.00000	+	15.5885i	0.377300	+	0.653502i	0.990668	−	0.136295i	$-0.0435194\pi$
$569$	9.00000	+	15.5885i	0.377300	+	0.653502i	−0.613369	+	0.789797i	$0.710186\pi$
$570$		0			0
$571$	15.0000	−	25.9808i	0.627730	−	1.08726i	−0.360276	−	0.932846i	$-0.617317\pi$
$571$	15.0000	−	25.9808i	0.627730	−	1.08726i	0.988006	−	0.154415i	$-0.0493493\pi$
$572$		0			0
$573$	54.0000			2.25588
$574$	−14.0000	+	12.1244i	−0.584349	+	0.506061i
$575$		0			0
$576$	−3.00000	−	5.19615i	−0.125000	−	0.216506i
$577$	5.00000	−	8.66025i	0.208153	−	0.360531i	−0.742980	−	0.669314i	$-0.766588\pi$
$577$	5.00000	−	8.66025i	0.208153	−	0.360531i	0.951133	+	0.308783i	$0.0999216\pi$
$578$	−0.500000	+	0.866025i	−0.0207973	+	0.0360219i
$579$	−39.0000	−	67.5500i	−1.62078	−	2.80728i
$580$		0			0
$581$	−3.50000	−	18.1865i	−0.145204	−	0.754505i
$582$	−42.0000			−1.74096
$583$	2.00000	+	3.46410i	0.0828315	+	0.143468i
$584$	2.00000	−	3.46410i	0.0827606	−	0.143346i
$585$		0			0
$586$	−14.0000	−	24.2487i	−0.578335	−	1.00171i
$587$	28.0000			1.15568			0.577842	−	0.816149i	$-0.303895\pi$
$587$	28.0000			1.15568			0.577842	+	0.816149i	$0.303895\pi$
$588$	−16.5000	−	12.9904i	−0.680449	−	0.535714i
$589$	24.0000			0.988903
$590$		0			0
$591$	−3.00000	+	5.19615i	−0.123404	+	0.213741i
$592$	−2.00000	+	3.46410i	−0.0821995	+	0.142374i
$593$	−3.00000	−	5.19615i	−0.123195	−	0.213380i	0.797831	−	0.602881i	$-0.205981\pi$
$593$	−3.00000	−	5.19615i	−0.123195	−	0.213380i	−0.921026	+	0.389501i	$0.872647\pi$
$594$	−18.0000			−0.738549
$595$		0			0
$596$	3.00000			0.122885
$597$	−6.00000	−	10.3923i	−0.245564	−	0.425329i
$598$		0			0
$599$	−6.00000	+	10.3923i	−0.245153	+	0.424618i	−0.962175	−	0.272433i	$-0.912172\pi$
$599$	−6.00000	+	10.3923i	−0.245153	+	0.424618i	0.717021	+	0.697051i	$0.245505\pi$
$600$		0			0
$601$	42.0000			1.71322			0.856608	−	0.515968i	$-0.172568\pi$
$601$	42.0000			1.71322			0.856608	+	0.515968i	$0.172568\pi$
$602$	10.0000	−	8.66025i	0.407570	−	0.352966i
$603$	54.0000			2.19905
$604$	8.00000	+	13.8564i	0.325515	+	0.563809i
$605$		0			0
$606$	−4.50000	+	7.79423i	−0.182800	+	0.316619i
$607$	0.500000	+	0.866025i	0.0202944	+	0.0351509i	0.875994	−	0.482322i	$-0.160206\pi$
$607$	0.500000	+	0.866025i	0.0202944	+	0.0351509i	−0.855700	+	0.517472i	$0.826873\pi$
$608$	6.00000			0.243332
$609$	−67.5000	−	23.3827i	−2.73524	−	0.947514i
$610$		0			0
$611$		0			0
$612$	−12.0000	+	20.7846i	−0.485071	+	0.840168i
$613$	6.00000	−	10.3923i	0.242338	−	0.419741i	−0.719042	−	0.694967i	$-0.755419\pi$
$613$	6.00000	−	10.3923i	0.242338	−	0.419741i	0.961380	+	0.275225i	$0.0887525\pi$
$614$	−3.50000	−	6.06218i	−0.141249	−	0.244650i
$615$		0			0
$616$	5.00000	+	1.73205i	0.201456	+	0.0697863i
$617$	−44.0000			−1.77137			−0.885687	−	0.464283i	$-0.846312\pi$
$617$	−44.0000			−1.77137			−0.885687	+	0.464283i	$0.846312\pi$
$618$	1.50000	+	2.59808i	0.0603388	+	0.104510i
$619$	23.0000	−	39.8372i	0.924448	−	1.60119i	0.132002	−	0.991250i	$-0.457860\pi$
$619$	23.0000	−	39.8372i	0.924448	−	1.60119i	0.792446	−	0.609941i	$-0.208807\pi$
$620$		0			0
$621$	−13.5000	−	23.3827i	−0.541736	−	0.938315i
$622$	18.0000			0.721734
$623$	−2.00000	+	1.73205i	−0.0801283	+	0.0693932i
$624$		0			0
$625$		0			0
$626$	−4.00000	+	6.92820i	−0.159872	+	0.276907i
$627$	18.0000	−	31.1769i	0.718851	−	1.24509i
$628$	5.00000	+	8.66025i	0.199522	+	0.345582i
$629$	16.0000			0.637962
$630$		0			0
$631$	2.00000			0.0796187			0.0398094	−	0.999207i	$-0.487325\pi$
$631$	2.00000			0.0796187			0.0398094	+	0.999207i	$0.487325\pi$
$632$	5.00000	+	8.66025i	0.198889	+	0.344486i
$633$	−39.0000	+	67.5500i	−1.55011	+	2.68487i
$634$	16.0000	−	27.7128i	0.635441	−	1.10062i
$635$		0			0
$636$	−6.00000			−0.237915
$637$		0			0
$638$	18.0000			0.712627
$639$	−6.00000	−	10.3923i	−0.237356	−	0.411113i
$640$		0			0
$641$	−2.50000	+	4.33013i	−0.0987441	+	0.171030i	−0.911165	−	0.412042i	$-0.864816\pi$
$641$	−2.50000	+	4.33013i	−0.0987441	+	0.171030i	0.812421	+	0.583071i	$0.198149\pi$
$642$	4.50000	+	7.79423i	0.177601	+	0.307614i
$643$	−28.0000			−1.10421			−0.552106	−	0.833774i	$-0.686176\pi$
$643$	−28.0000			−1.10421			−0.552106	+	0.833774i	$0.686176\pi$
$644$	1.50000	+	7.79423i	0.0591083	+	0.307136i
$645$		0			0
$646$	−12.0000	−	20.7846i	−0.472134	−	0.817760i
$647$	−5.50000	+	9.52628i	−0.216227	+	0.374517i	−0.953652	−	0.300913i	$-0.902709\pi$
$647$	−5.50000	+	9.52628i	−0.216227	+	0.374517i	0.737424	+	0.675430i	$0.236042\pi$
$648$	4.50000	−	7.79423i	0.176777	−	0.306186i
$649$	10.0000	+	17.3205i	0.392534	+	0.679889i
$650$		0			0
$651$	−24.0000	+	20.7846i	−0.940634	+	0.814613i
$652$	4.00000			0.156652
$653$	−2.00000	−	3.46410i	−0.0782660	−	0.135561i	0.824236	−	0.566247i	$-0.191605\pi$
$653$	−2.00000	−	3.46410i	−0.0782660	−	0.135561i	−0.902502	+	0.430686i	$0.858272\pi$
$654$	13.5000	−	23.3827i	0.527892	−	0.914335i
$655$		0			0
$656$	3.50000	+	6.06218i	0.136652	+	0.236688i
$657$	24.0000			0.936329
$658$	20.0000	+	6.92820i	0.779681	+	0.270089i
$659$	−26.0000			−1.01282			−0.506408	−	0.862294i	$-0.669027\pi$
$659$	−26.0000			−1.01282			−0.506408	+	0.862294i	$0.669027\pi$
$660$		0			0
$661$	5.50000	−	9.52628i	0.213925	−	0.370529i	−0.739014	−	0.673690i	$-0.764708\pi$
$661$	5.50000	−	9.52628i	0.213925	−	0.370529i	0.952940	+	0.303160i	$0.0980418\pi$
$662$	−16.0000	+	27.7128i	−0.621858	+	1.07709i
$663$		0			0
$664$	−7.00000			−0.271653
$665$		0			0
$666$	−24.0000			−0.929981
$667$	13.5000	+	23.3827i	0.522722	+	0.905381i
$668$	−10.5000	+	18.1865i	−0.406257	+	0.703658i
$669$	−42.0000	+	72.7461i	−1.62381	+	2.81253i
$670$		0			0
$671$	−2.00000			−0.0772091
$672$	−6.00000	+	5.19615i	−0.231455	+	0.200446i
$673$	−16.0000			−0.616755			−0.308377	−	0.951264i	$-0.599786\pi$
$673$	−16.0000			−0.616755			−0.308377	+	0.951264i	$0.599786\pi$
$674$	13.0000	+	22.5167i	0.500741	+	0.867309i
$675$		0			0
$676$	6.50000	−	11.2583i	0.250000	−	0.433013i
$677$	−24.0000	−	41.5692i	−0.922395	−	1.59763i	−0.795698	−	0.605693i	$-0.792896\pi$
$677$	−24.0000	−	41.5692i	−0.922395	−	1.59763i	−0.126697	−	0.991941i	$-0.540438\pi$
$678$	−6.00000			−0.230429
$679$	7.00000	+	36.3731i	0.268635	+	1.39587i
$680$		0			0
$681$	6.00000	+	10.3923i	0.229920	+	0.398234i
$682$	4.00000	−	6.92820i	0.153168	−	0.265295i
$683$	−18.5000	+	32.0429i	−0.707883	+	1.22609i	0.257758	+	0.966209i	$0.417016\pi$
$683$	−18.5000	+	32.0429i	−0.707883	+	1.22609i	−0.965641	+	0.259880i	$0.916317\pi$
$684$	18.0000	+	31.1769i	0.688247	+	1.19208i
$685$		0			0
$686$	−8.50000	+	16.4545i	−0.324532	+	0.628235i
$687$	−66.0000			−2.51806
$688$	−2.50000	−	4.33013i	−0.0953116	−	0.165085i
$689$		0			0
$690$		0			0
$691$	−11.0000	−	19.0526i	−0.418460	−	0.724793i	0.577325	−	0.816514i	$-0.304097\pi$
$691$	−11.0000	−	19.0526i	−0.418460	−	0.724793i	−0.995785	+	0.0917209i	$0.970763\pi$
$692$	−8.00000			−0.304114
$693$	6.00000	+	31.1769i	0.227921	+	1.18431i
$694$	19.0000			0.721230
$695$		0			0
$696$	−13.5000	+	23.3827i	−0.511716	+	0.886318i
$697$	14.0000	−	24.2487i	0.530288	−	0.918485i
$698$	−17.5000	−	30.3109i	−0.662385	−	1.14728i
$699$	72.0000			2.72329
$700$		0			0
$701$	−47.0000			−1.77517			−0.887583	−	0.460648i	$-0.847617\pi$
$701$	−47.0000			−1.77517			−0.887583	+	0.460648i	$0.847617\pi$
$702$		0			0
$703$	12.0000	−	20.7846i	0.452589	−	0.783906i
$704$	1.00000	−	1.73205i	0.0376889	−	0.0652791i
$705$		0			0
$706$	−18.0000			−0.677439
$707$	7.50000	+	2.59808i	0.282067	+	0.0977107i
$708$	−30.0000			−1.12747
$709$	5.50000	+	9.52628i	0.206557	+	0.357767i	0.950628	−	0.310334i	$-0.100441\pi$
$709$	5.50000	+	9.52628i	0.206557	+	0.357767i	−0.744071	+	0.668101i	$0.767108\pi$
$710$		0			0
$711$	−30.0000	+	51.9615i	−1.12509	+	1.94871i
$712$	0.500000	+	0.866025i	0.0187383	+	0.0324557i
$713$	12.0000			0.449404
$714$	30.0000	+	10.3923i	1.12272	+	0.388922i
$715$		0			0
$716$	−6.00000	−	10.3923i	−0.224231	−	0.388379i
$717$	24.0000	−	41.5692i	0.896296	−	1.55243i
$718$	−2.00000	+	3.46410i	−0.0746393	+	0.129279i
$719$	3.00000	+	5.19615i	0.111881	+	0.193784i	0.916529	−	0.399969i	$-0.130979\pi$
$719$	3.00000	+	5.19615i	0.111881	+	0.193784i	−0.804648	+	0.593753i	$0.797646\pi$
$720$		0			0
$721$	2.00000	−	1.73205i	0.0744839	−	0.0645049i
$722$	−17.0000			−0.632674
$723$	15.0000	+	25.9808i	0.557856	+	0.966235i
$724$	−3.50000	+	6.06218i	−0.130076	+	0.225299i
$725$		0			0
$726$	10.5000	+	18.1865i	0.389692	+	0.674966i
$727$	21.0000			0.778847			0.389423	−	0.921059i	$-0.372674\pi$
$727$	21.0000			0.778847			0.389423	+	0.921059i	$0.372674\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−10.0000	+	17.3205i	−0.369863	+	0.640622i
$732$	1.50000	−	2.59808i	0.0554416	−	0.0960277i
$733$	11.0000	+	19.0526i	0.406294	+	0.703722i	0.994471	−	0.105010i	$-0.0334875\pi$
$733$	11.0000	+	19.0526i	0.406294	+	0.703722i	−0.588177	+	0.808732i	$0.700154\pi$
$734$	−11.0000			−0.406017
$735$		0			0
$736$	3.00000			0.110581
$737$	9.00000	+	15.5885i	0.331519	+	0.574208i
$738$	−21.0000	+	36.3731i	−0.773021	+	1.33891i
$739$	1.00000	−	1.73205i	0.0367856	−	0.0637145i	−0.847046	−	0.531519i	$-0.821621\pi$
$739$	1.00000	−	1.73205i	0.0367856	−	0.0637145i	0.883832	+	0.467804i	$0.154955\pi$
$740$		0			0
$741$		0			0
$742$	1.00000	+	5.19615i	0.0367112	+	0.190757i
$743$	−9.00000			−0.330178			−0.165089	−	0.986279i	$-0.552791\pi$
$743$	−9.00000			−0.330178			−0.165089	+	0.986279i	$0.552791\pi$
$744$	6.00000	+	10.3923i	0.219971	+	0.381000i
$745$		0			0
$746$	2.00000	−	3.46410i	0.0732252	−	0.126830i
$747$	−21.0000	−	36.3731i	−0.768350	−	1.33082i
$748$	−8.00000			−0.292509
$749$	6.00000	−	5.19615i	0.219235	−	0.189863i
$750$		0			0
$751$	2.00000	+	3.46410i	0.0729810	+	0.126407i	0.900207	−	0.435463i	$-0.143415\pi$
$751$	2.00000	+	3.46410i	0.0729810	+	0.126407i	−0.827225	+	0.561870i	$0.810082\pi$
$752$	4.00000	−	6.92820i	0.145865	−	0.252646i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	−22.5000	−	7.79423i	−0.818317	−	0.283473i
$757$	−16.0000			−0.581530			−0.290765	−	0.956795i	$-0.593910\pi$
$757$	−16.0000			−0.581530			−0.290765	+	0.956795i	$0.593910\pi$
$758$	15.0000	+	25.9808i	0.544825	+	0.943664i
$759$	9.00000	−	15.5885i	0.326679	−	0.565825i
$760$		0			0
$761$	3.00000	+	5.19615i	0.108750	+	0.188360i	0.915264	−	0.402854i	$-0.131982\pi$
$761$	3.00000	+	5.19615i	0.108750	+	0.188360i	−0.806514	+	0.591215i	$0.798649\pi$
$762$	−48.0000			−1.73886
$763$	−22.5000	−	7.79423i	−0.814555	−	0.282170i
$764$	−18.0000			−0.651217
$765$		0			0
$766$	−7.50000	+	12.9904i	−0.270986	+	0.469362i
$767$		0			0
$768$	1.50000	+	2.59808i	0.0541266	+	0.0937500i
$769$	−14.0000			−0.504853			−0.252426	−	0.967616i	$-0.581229\pi$
$769$	−14.0000			−0.504853			−0.252426	+	0.967616i	$0.581229\pi$
$770$		0			0
$771$	24.0000			0.864339
$772$	13.0000	+	22.5167i	0.467880	+	0.810392i
$773$	12.0000	−	20.7846i	0.431610	−	0.747570i	−0.565402	−	0.824815i	$-0.691279\pi$
$773$	12.0000	−	20.7846i	0.431610	−	0.747570i	0.997012	+	0.0772449i	$0.0246123\pi$
$774$	15.0000	−	25.9808i	0.539164	−	0.933859i
$775$		0			0
$776$	14.0000			0.502571
$777$	6.00000	+	31.1769i	0.215249	+	1.11847i
$778$	−26.0000			−0.932145
$779$	−21.0000	−	36.3731i	−0.752403	−	1.30320i
$780$		0			0
$781$	2.00000	−	3.46410i	0.0715656	−	0.123955i
$782$	−6.00000	−	10.3923i	−0.214560	−	0.371628i
$783$	−81.0000			−2.89470
$784$	5.50000	+	4.33013i	0.196429	+	0.154647i
$785$		0			0
$786$	−12.0000	−	20.7846i	−0.428026	−	0.741362i
$787$	15.5000	−	26.8468i	0.552515	−	0.956985i	−0.445577	−	0.895244i	$-0.647001\pi$
$787$	15.5000	−	26.8468i	0.552515	−	0.956985i	0.998092	−	0.0617409i	$-0.0196653\pi$
$788$	1.00000	−	1.73205i	0.0356235	−	0.0617018i
$789$	−7.50000	−	12.9904i	−0.267007	−	0.462470i
$790$		0			0
$791$	1.00000	+	5.19615i	0.0355559	+	0.184754i
$792$	12.0000			0.426401
$793$		0			0
$794$	−11.0000	+	19.0526i	−0.390375	+	0.676150i
$795$		0			0
$796$	2.00000	+	3.46410i	0.0708881	+	0.122782i
$797$		0			0			−	1.00000i	$-0.5\pi$
$797$		0			0				1.00000i	$0.5\pi$
$798$	36.0000	−	31.1769i	1.27439	−	1.10365i
$799$	−32.0000			−1.13208
$800$		0			0
$801$	−3.00000	+	5.19615i	−0.106000	+	0.183597i
$802$	15.5000	−	26.8468i	0.547324	−	0.947993i
$803$	4.00000	+	6.92820i	0.141157	+	0.244491i
$804$	−27.0000			−0.952217
$805$		0			0
$806$		0			0
$807$	4.50000	+	7.79423i	0.158408	+	0.274370i
$808$	1.50000	−	2.59808i	0.0527698	−	0.0914000i
$809$	25.5000	−	44.1673i	0.896532	−	1.55284i	0.0646355	−	0.997909i	$-0.479412\pi$
$809$	25.5000	−	44.1673i	0.896532	−	1.55284i	0.831897	−	0.554930i	$-0.187255\pi$
$810$		0			0
$811$	−28.0000			−0.983213			−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000			−0.983213			−0.491606	+	0.870817i	$0.663590\pi$
$812$	22.5000	+	7.79423i	0.789595	+	0.273524i
$813$	18.0000			0.631288
$814$	−4.00000	−	6.92820i	−0.140200	−	0.242833i
$815$		0			0
$816$	6.00000	−	10.3923i	0.210042	−	0.363803i
$817$	15.0000	+	25.9808i	0.524784	+	0.908952i
$818$	−3.00000			−0.104893
$819$		0			0
$820$		0			0
$821$	9.00000	+	15.5885i	0.314102	+	0.544041i	0.979246	−	0.202674i	$-0.0649632\pi$
$821$	9.00000	+	15.5885i	0.314102	+	0.544041i	−0.665144	+	0.746715i	$0.731630\pi$
$822$	18.0000	−	31.1769i	0.627822	−	1.08742i
$823$	9.50000	−	16.4545i	0.331149	−	0.573567i	−0.651588	−	0.758573i	$-0.725897\pi$
$823$	9.50000	−	16.4545i	0.331149	−	0.573567i	0.982737	+	0.185006i	$0.0592303\pi$
$824$	−0.500000	−	0.866025i	−0.0174183	−	0.0301694i
$825$		0			0
$826$	5.00000	+	25.9808i	0.173972	+	0.903986i
$827$	19.0000			0.660695			0.330347	−	0.943859i	$-0.392834\pi$
$827$	19.0000			0.660695			0.330347	+	0.943859i	$0.392834\pi$
$828$	9.00000	+	15.5885i	0.312772	+	0.541736i
$829$	23.0000	−	39.8372i	0.798823	−	1.38360i	−0.121560	−	0.992584i	$-0.538790\pi$
$829$	23.0000	−	39.8372i	0.798823	−	1.38360i	0.920383	−	0.391018i	$-0.127877\pi$
$830$		0			0
$831$	−18.0000	−	31.1769i	−0.624413	−	1.08152i
$832$		0			0
$833$	4.00000	−	27.7128i	0.138592	−	0.960192i
$834$	−42.0000			−1.45434
$835$		0			0
$836$	−6.00000	+	10.3923i	−0.207514	+	0.359425i
$837$	−18.0000	+	31.1769i	−0.622171	+	1.07763i
$838$		0			0
$839$	14.0000			0.483334			0.241667	−	0.970359i	$-0.422306\pi$
$839$	14.0000			0.483334			0.241667	+	0.970359i	$0.422306\pi$
$840$		0			0
$841$	52.0000			1.79310
$842$	−9.50000	−	16.4545i	−0.327392	−	0.567059i
$843$	3.00000	−	5.19615i	0.103325	−	0.178965i
$844$	13.0000	−	22.5167i	0.447478	−	0.775055i
$845$		0			0
$846$	48.0000			1.65027
$847$	14.0000	−	12.1244i	0.481046	−	0.416598i
$848$	2.00000			0.0686803
$849$	6.00000	+	10.3923i	0.205919	+	0.356663i
$850$		0			0
$851$	6.00000	−	10.3923i	0.205677	−	0.356244i
$852$	3.00000	+	5.19615i	0.102778	+	0.178017i
$853$	−14.0000			−0.479351			−0.239675	−	0.970853i	$-0.577041\pi$
$853$	−14.0000			−0.479351			−0.239675	+	0.970853i	$0.577041\pi$
$854$	−2.50000	−	0.866025i	−0.0855482	−	0.0296348i
$855$		0			0
$856$	−1.50000	−	2.59808i	−0.0512689	−	0.0888004i
$857$	−9.00000	+	15.5885i	−0.307434	+	0.532492i	−0.977800	−	0.209539i	$-0.932804\pi$
$857$	−9.00000	+	15.5885i	−0.307434	+	0.532492i	0.670366	+	0.742030i	$0.266137\pi$
$858$		0			0
$859$	24.0000	+	41.5692i	0.818869	+	1.41832i	0.906516	+	0.422172i	$0.138732\pi$
$859$	24.0000	+	41.5692i	0.818869	+	1.41832i	−0.0876464	+	0.996152i	$0.527935\pi$
$860$		0			0
$861$	52.5000	+	18.1865i	1.78920	+	0.619795i
$862$	30.0000			1.02180
$863$	−5.50000	−	9.52628i	−0.187222	−	0.324278i	0.757101	−	0.653298i	$-0.226615\pi$
$863$	−5.50000	−	9.52628i	−0.187222	−	0.324278i	−0.944323	+	0.329020i	$0.893282\pi$
$864$	−4.50000	+	7.79423i	−0.153093	+	0.265165i
$865$		0			0
$866$	−7.00000	−	12.1244i	−0.237870	−	0.412002i
$867$	3.00000			0.101885
$868$	8.00000	−	6.92820i	0.271538	−	0.235159i
$869$	−20.0000			−0.678454
$870$		0			0
$871$		0			0
$872$	−4.50000	+	7.79423i	−0.152389	+	0.263946i
$873$	42.0000	+	72.7461i	1.42148	+	2.46208i
$874$	−18.0000			−0.608859
$875$		0			0
$876$	−12.0000			−0.405442
$877$	19.0000	+	32.9090i	0.641584	+	1.11126i	0.985079	+	0.172102i	$0.0550559\pi$
$877$	19.0000	+	32.9090i	0.641584	+	1.11126i	−0.343495	+	0.939155i	$0.611611\pi$
$878$	−10.0000	+	17.3205i	−0.337484	+	0.584539i
$879$	−42.0000	+	72.7461i	−1.41662	+	2.45367i
$880$		0			0
$881$	−7.00000			−0.235836			−0.117918	−	0.993023i	$-0.537622\pi$
$881$	−7.00000			−0.235836			−0.117918	+	0.993023i	$0.537622\pi$
$882$	−6.00000	+	41.5692i	−0.202031	+	1.39971i
$883$	12.0000			0.403832			0.201916	−	0.979403i	$-0.435283\pi$
$883$	12.0000			0.403832			0.201916	+	0.979403i	$0.435283\pi$
$884$		0			0
$885$		0			0
$886$	−15.5000	+	26.8468i	−0.520733	+	0.901935i
$887$	14.5000	+	25.1147i	0.486862	+	0.843270i	0.999886	−	0.0151042i	$-0.00480800\pi$
$887$	14.5000	+	25.1147i	0.486862	+	0.843270i	−0.513024	+	0.858375i	$0.671475\pi$
$888$	12.0000			0.402694
$889$	8.00000	+	41.5692i	0.268311	+	1.39419i
$890$		0			0
$891$	9.00000	+	15.5885i	0.301511	+	0.522233i
$892$	14.0000	−	24.2487i	0.468755	−	0.811907i
$893$	−24.0000	+	41.5692i	−0.803129	+	1.39106i
$894$	−4.50000	−	7.79423i	−0.150503	−	0.260678i
$895$		0			0
$896$	2.00000	−	1.73205i	0.0668153	−	0.0578638i
$897$		0			0
$898$	−16.5000	−	28.5788i	−0.550612	−	0.953688i
$899$	18.0000	−	31.1769i	0.600334	−	1.03981i
$900$		0			0
$901$	−4.00000	−	6.92820i	−0.133259	−	0.230812i
$902$	−14.0000			−0.466149
$903$	−37.5000	−	12.9904i	−1.24792	−	0.432293i
$904$	2.00000			0.0665190
$905$		0			0
$906$	24.0000	−	41.5692i	0.797347	−	1.38104i
$907$	2.50000	−	4.33013i	0.0830111	−	0.143780i	−0.821531	−	0.570164i	$-0.806880\pi$
$907$	2.50000	−	4.33013i	0.0830111	−	0.143780i	0.904542	+	0.426385i	$0.140213\pi$
$908$	−2.00000	−	3.46410i	−0.0663723	−	0.114960i
$909$	18.0000			0.597022
$910$		0			0
$911$	30.0000			0.993944			0.496972	−	0.867766i	$-0.334445\pi$
$911$	30.0000			0.993944			0.496972	+	0.867766i	$0.334445\pi$
$912$	−9.00000	−	15.5885i	−0.298020	−	0.516185i
$913$	7.00000	−	12.1244i	0.231666	−	0.401258i
$914$	16.0000	−	27.7128i	0.529233	−	0.916658i
$915$		0			0
$916$	22.0000			0.726900
$917$	−16.0000	+	13.8564i	−0.528367	+	0.457579i
$918$	36.0000			1.18818
$919$	−19.0000	−	32.9090i	−0.626752	−	1.08557i	−0.988199	−	0.153174i	$-0.951051\pi$
$919$	−19.0000	−	32.9090i	−0.626752	−	1.08557i	0.361447	−	0.932393i	$-0.382283\pi$
$920$		0			0
$921$	−10.5000	+	18.1865i	−0.345987	+	0.599267i
$922$	−7.00000	−	12.1244i	−0.230533	−	0.399294i
$923$		0			0
$924$	−3.00000	−	15.5885i	−0.0986928	−	0.512823i
$925$		0			0
$926$	9.50000	+	16.4545i	0.312189	+	0.540728i
$927$	3.00000	−	5.19615i	0.0985329	−	0.170664i
$928$	4.50000	−	7.79423i	0.147720	−	0.255858i
$929$	−21.5000	−	37.2391i	−0.705392	−	1.22177i	−0.966550	−	0.256479i	$-0.917438\pi$
$929$	−21.5000	−	37.2391i	−0.705392	−	1.22177i	0.261158	−	0.965296i	$-0.415896\pi$
$930$		0			0
$931$	−33.0000	−	25.9808i	−1.08153	−	0.851485i
$932$	−24.0000			−0.786146
$933$	−27.0000	−	46.7654i	−0.883940	−	1.53103i
$934$	6.50000	−	11.2583i	0.212686	−	0.368384i
$935$		0			0
$936$		0			0
$937$	28.0000			0.914720			0.457360	−	0.889282i	$-0.348795\pi$
$937$	28.0000			0.914720			0.457360	+	0.889282i	$0.348795\pi$
$938$	4.50000	+	23.3827i	0.146930	+	0.763472i
$939$	24.0000			0.783210
$940$		0			0
$941$	23.0000	−	39.8372i	0.749779	−	1.29865i	−0.198150	−	0.980172i	$-0.563493\pi$
$941$	23.0000	−	39.8372i	0.749779	−	1.29865i	0.947929	−	0.318483i	$-0.103173\pi$
$942$	15.0000	−	25.9808i	0.488726	−	0.846499i
$943$	−10.5000	−	18.1865i	−0.341927	−	0.592235i
$944$	10.0000			0.325472
$945$		0			0
$946$	10.0000			0.325128
$947$	−12.5000	−	21.6506i	−0.406195	−	0.703551i	0.588264	−	0.808669i	$-0.299811\pi$
$947$	−12.5000	−	21.6506i	−0.406195	−	0.703551i	−0.994460	+	0.105118i	$0.966478\pi$
$948$	15.0000	−	25.9808i	0.487177	−	0.843816i
$949$		0			0
$950$		0			0
$951$	−96.0000			−3.11301
$952$	−10.0000	−	3.46410i	−0.324102	−	0.112272i
$953$	12.0000			0.388718			0.194359	−	0.980930i	$-0.437737\pi$
$953$	12.0000			0.388718			0.194359	+	0.980930i	$0.437737\pi$
$954$	6.00000	+	10.3923i	0.194257	+	0.336463i
$955$		0			0
$956$	−8.00000	+	13.8564i	−0.258738	+	0.448148i
$957$	−27.0000	−	46.7654i	−0.872786	−	1.51171i
$958$	−24.0000			−0.775405
$959$	−30.0000	−	10.3923i	−0.968751	−	0.335585i
$960$		0			0
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$		0			0
$963$	9.00000	−	15.5885i	0.290021	−	0.502331i
$964$	−5.00000	−	8.66025i	−0.161039	−	0.278928i
$965$		0			0
$966$	18.0000	−	15.5885i	0.579141	−	0.501550i
$967$	−37.0000			−1.18984			−0.594920	−	0.803785i	$-0.702816\pi$
$967$	−37.0000			−1.18984			−0.594920	+	0.803785i	$0.702816\pi$
$968$	−3.50000	−	6.06218i	−0.112494	−	0.194846i
$969$	−36.0000	+	62.3538i	−1.15649	+	2.00309i
$970$		0			0
$971$	24.0000	+	41.5692i	0.770197	+	1.33402i	0.937455	+	0.348107i	$0.113175\pi$
$971$	24.0000	+	41.5692i	0.770197	+	1.33402i	−0.167258	+	0.985913i	$0.553491\pi$
$972$		0			0
$973$	7.00000	+	36.3731i	0.224410	+	1.16607i
$974$	−16.0000			−0.512673
$975$		0			0
$976$	−0.500000	+	0.866025i	−0.0160046	+	0.0277208i
$977$	−15.0000	+	25.9808i	−0.479893	+	0.831198i	−0.999734	−	0.0230645i	$-0.992658\pi$
$977$	−15.0000	+	25.9808i	−0.479893	+	0.831198i	0.519841	+	0.854263i	$0.325991\pi$
$978$	−6.00000	−	10.3923i	−0.191859	−	0.332309i
$979$	−2.00000			−0.0639203
$980$		0			0
$981$	−54.0000			−1.72409
$982$	−6.00000	−	10.3923i	−0.191468	−	0.331632i
$983$	8.50000	−	14.7224i	0.271108	−	0.469573i	−0.698038	−	0.716061i	$-0.745943\pi$
$983$	8.50000	−	14.7224i	0.271108	−	0.469573i	0.969146	+	0.246488i	$0.0792766\pi$
$984$	10.5000	−	18.1865i	0.334728	−	0.579766i
$985$		0			0
$986$	−36.0000			−1.14647
$987$	−12.0000	−	62.3538i	−0.381964	−	1.98474i
$988$		0			0
$989$	7.50000	+	12.9904i	0.238486	+	0.413070i
$990$		0			0
$991$	−20.0000	+	34.6410i	−0.635321	+	1.10041i	0.351126	+	0.936328i	$0.385799\pi$
$991$	−20.0000	+	34.6410i	−0.635321	+	1.10041i	−0.986447	+	0.164080i	$0.947534\pi$
$992$	−2.00000	−	3.46410i	−0.0635001	−	0.109985i
$993$	96.0000			3.04647
$994$	4.00000	−	3.46410i	0.126872	−	0.109875i
$995$		0			0
$996$	10.5000	+	18.1865i	0.332705	+	0.576262i
$997$	−23.0000	+	39.8372i	−0.728417	+	1.26166i	0.229135	+	0.973395i	$0.426410\pi$
$997$	−23.0000	+	39.8372i	−0.728417	+	1.26166i	−0.957552	+	0.288261i	$0.906923\pi$
$998$	−9.00000	+	15.5885i	−0.284890	+	0.493444i
$999$	18.0000	+	31.1769i	0.569495	+	0.986394i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.e.l.151.1		2
5.2	odd	4		350.2.j.f.249.1		4
5.3	odd	4		350.2.j.f.249.2		4
5.4	even	2		70.2.e.a.11.1	✓	2
7.2	even	3	inner	350.2.e.l.51.1		2
7.3	odd	6		2450.2.a.q.1.1		1
7.4	even	3		2450.2.a.b.1.1		1
15.14	odd	2		630.2.k.f.361.1		2
20.19	odd	2		560.2.q.i.81.1		2
35.2	odd	12		350.2.j.f.149.2		4
35.3	even	12		2450.2.c.a.99.2		2
35.4	even	6		490.2.a.k.1.1		1
35.9	even	6		70.2.e.a.51.1	yes	2
35.17	even	12		2450.2.c.a.99.1		2
35.18	odd	12		2450.2.c.s.99.2		2
35.19	odd	6		490.2.e.f.471.1		2
35.23	odd	12		350.2.j.f.149.1		4
35.24	odd	6		490.2.a.e.1.1		1
35.32	odd	12		2450.2.c.s.99.1		2
35.34	odd	2		490.2.e.f.361.1		2
105.44	odd	6		630.2.k.f.541.1		2
105.59	even	6		4410.2.a.h.1.1		1
105.74	odd	6		4410.2.a.r.1.1		1
140.39	odd	6		3920.2.a.b.1.1		1
140.59	even	6		3920.2.a.bk.1.1		1
140.79	odd	6		560.2.q.i.401.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.e.a.11.1	✓	2	5.4	even	2
70.2.e.a.51.1	yes	2	35.9	even	6
350.2.e.l.51.1		2	7.2	even	3	inner
350.2.e.l.151.1		2	1.1	even	1	trivial
350.2.j.f.149.1		4	35.23	odd	12
350.2.j.f.149.2		4	35.2	odd	12
350.2.j.f.249.1		4	5.2	odd	4
350.2.j.f.249.2		4	5.3	odd	4
490.2.a.e.1.1		1	35.24	odd	6
490.2.a.k.1.1		1	35.4	even	6
490.2.e.f.361.1		2	35.34	odd	2
490.2.e.f.471.1		2	35.19	odd	6
560.2.q.i.81.1		2	20.19	odd	2
560.2.q.i.401.1		2	140.79	odd	6
630.2.k.f.361.1		2	15.14	odd	2
630.2.k.f.541.1		2	105.44	odd	6
2450.2.a.b.1.1		1	7.4	even	3
2450.2.a.q.1.1		1	7.3	odd	6
2450.2.c.a.99.1		2	35.17	even	12
2450.2.c.a.99.2		2	35.3	even	12
2450.2.c.s.99.1		2	35.32	odd	12
2450.2.c.s.99.2		2	35.18	odd	12
3920.2.a.b.1.1		1	140.39	odd	6
3920.2.a.bk.1.1		1	140.59	even	6
4410.2.a.h.1.1		1	105.59	even	6
4410.2.a.r.1.1		1	105.74	odd	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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.00000 q^{6} +(-0.500000 - 2.59808i) q^{7} -1.00000 q^{8} +(-3.00000 - 5.19615i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.00000 q^{6} +(-0.500000 - 2.59808i) q^{7} -1.00000 q^{8} +(-3.00000 - 5.19615i) q^{9} +(1.00000 - 1.73205i) q^{11} +(1.50000 + 2.59808i) q^{12} +(2.00000 - 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.00000 + 3.46410i) q^{17} +(3.00000 - 5.19615i) q^{18} +(3.00000 + 5.19615i) q^{19} +(-7.50000 - 2.59808i) q^{21} +2.00000 q^{22} +(1.50000 + 2.59808i) q^{23} +(-1.50000 + 2.59808i) q^{24} -9.00000 q^{27} +(2.50000 + 0.866025i) q^{28} +9.00000 q^{29} +(2.00000 - 3.46410i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-3.00000 - 5.19615i) q^{33} -4.00000 q^{34} +6.00000 q^{36} +(-2.00000 - 3.46410i) q^{37} +(-3.00000 + 5.19615i) q^{38} -7.00000 q^{41} +(-1.50000 - 7.79423i) q^{42} +5.00000 q^{43} +(1.00000 + 1.73205i) q^{44} +(-1.50000 + 2.59808i) q^{46} +(4.00000 + 6.92820i) q^{47} -3.00000 q^{48} +(-6.50000 + 2.59808i) q^{49} +(6.00000 + 10.3923i) q^{51} +(-1.00000 + 1.73205i) q^{53} +(-4.50000 - 7.79423i) q^{54} +(0.500000 + 2.59808i) q^{56} +18.0000 q^{57} +(4.50000 + 7.79423i) q^{58} +(-5.00000 + 8.66025i) q^{59} +(-0.500000 - 0.866025i) q^{61} +4.00000 q^{62} +(-12.0000 + 10.3923i) q^{63} +1.00000 q^{64} +(3.00000 - 5.19615i) q^{66} +(-4.50000 + 7.79423i) q^{67} +(-2.00000 - 3.46410i) q^{68} +9.00000 q^{69} +2.00000 q^{71} +(3.00000 + 5.19615i) q^{72} +(-2.00000 + 3.46410i) q^{73} +(2.00000 - 3.46410i) q^{74} -6.00000 q^{76} +(-5.00000 - 1.73205i) q^{77} +(-5.00000 - 8.66025i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-3.50000 - 6.06218i) q^{82} +7.00000 q^{83} +(6.00000 - 5.19615i) q^{84} +(2.50000 + 4.33013i) q^{86} +(13.5000 - 23.3827i) q^{87} +(-1.00000 + 1.73205i) q^{88} +(-0.500000 - 0.866025i) q^{89} -3.00000 q^{92} +(-6.00000 - 10.3923i) q^{93} +(-4.00000 + 6.92820i) q^{94} +(-1.50000 - 2.59808i) q^{96} -14.0000 q^{97} +(-5.50000 - 4.33013i) q^{98} -12.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 3 q^{3} - q^{4} + 6 q^{6} - q^{7} - 2 q^{8} - 6 q^{9}+O(q^{10}) \) 2 * q + q^2 + 3 * q^3 - q^4 + 6 * q^6 - q^7 - 2 * q^8 - 6 * q^9	\( 2 q + q^{2} + 3 q^{3} - q^{4} + 6 q^{6} - q^{7} - 2 q^{8} - 6 q^{9} + 2 q^{11} + 3 q^{12} + 4 q^{14} - q^{16} - 4 q^{17} + 6 q^{18} + 6 q^{19} - 15 q^{21} + 4 q^{22} + 3 q^{23} - 3 q^{24} - 18 q^{27} + 5 q^{28} + 18 q^{29} + 4 q^{31} + q^{32} - 6 q^{33} - 8 q^{34} + 12 q^{36} - 4 q^{37} - 6 q^{38} - 14 q^{41} - 3 q^{42} + 10 q^{43} + 2 q^{44} - 3 q^{46} + 8 q^{47} - 6 q^{48} - 13 q^{49} + 12 q^{51} - 2 q^{53} - 9 q^{54} + q^{56} + 36 q^{57} + 9 q^{58} - 10 q^{59} - q^{61} + 8 q^{62} - 24 q^{63} + 2 q^{64} + 6 q^{66} - 9 q^{67} - 4 q^{68} + 18 q^{69} + 4 q^{71} + 6 q^{72} - 4 q^{73} + 4 q^{74} - 12 q^{76} - 10 q^{77} - 10 q^{79} - 9 q^{81} - 7 q^{82} + 14 q^{83} + 12 q^{84} + 5 q^{86} + 27 q^{87} - 2 q^{88} - q^{89} - 6 q^{92} - 12 q^{93} - 8 q^{94} - 3 q^{96} - 28 q^{97} - 11 q^{98} - 24 q^{99}+O(q^{100}) \) 2 * q + q^2 + 3 * q^3 - q^4 + 6 * q^6 - q^7 - 2 * q^8 - 6 * q^9 + 2 * q^11 + 3 * q^12 + 4 * q^14 - q^16 - 4 * q^17 + 6 * q^18 + 6 * q^19 - 15 * q^21 + 4 * q^22 + 3 * q^23 - 3 * q^24 - 18 * q^27 + 5 * q^28 + 18 * q^29 + 4 * q^31 + q^32 - 6 * q^33 - 8 * q^34 + 12 * q^36 - 4 * q^37 - 6 * q^38 - 14 * q^41 - 3 * q^42 + 10 * q^43 + 2 * q^44 - 3 * q^46 + 8 * q^47 - 6 * q^48 - 13 * q^49 + 12 * q^51 - 2 * q^53 - 9 * q^54 + q^56 + 36 * q^57 + 9 * q^58 - 10 * q^59 - q^61 + 8 * q^62 - 24 * q^63 + 2 * q^64 + 6 * q^66 - 9 * q^67 - 4 * q^68 + 18 * q^69 + 4 * q^71 + 6 * q^72 - 4 * q^73 + 4 * q^74 - 12 * q^76 - 10 * q^77 - 10 * q^79 - 9 * q^81 - 7 * q^82 + 14 * q^83 + 12 * q^84 + 5 * q^86 + 27 * q^87 - 2 * q^88 - q^89 - 6 * q^92 - 12 * q^93 - 8 * q^94 - 3 * q^96 - 28 * q^97 - 11 * q^98 - 24 * q^99

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