LMFDB - Embedded newform 350.2.j.a.149.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(149,350)]

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([3, 2]))

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

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

chi := DirichletCharacter("350.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.79476407074$
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 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			149.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	350.149
Dual form			350.2.j.a.249.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-1.73205 + 1.00000i) q^{3} +(0.500000 + 0.866025i) q^{4} -2.00000 q^{6} +(1.73205 + 2.00000i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-1.73205 + 1.00000i) q^{3} +(0.500000 + 0.866025i) q^{4} -2.00000 q^{6} +(1.73205 + 2.00000i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.50000 - 2.59808i) q^{11} +(-1.73205 - 1.00000i) q^{12} +5.00000i q^{13} +(0.500000 + 2.59808i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-5.19615 + 3.00000i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-0.500000 + 0.866025i) q^{19} +(-5.00000 - 1.73205i) q^{21} -3.00000i q^{22} +(-2.59808 - 1.50000i) q^{23} +(-1.00000 - 1.73205i) q^{24} +(-2.50000 + 4.33013i) q^{26} -4.00000i q^{27} +(-0.866025 + 2.50000i) q^{28} +6.00000 q^{29} +(2.00000 + 3.46410i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(5.19615 + 3.00000i) q^{33} -6.00000 q^{34} +1.00000 q^{36} +(9.52628 + 5.50000i) q^{37} +(-0.866025 + 0.500000i) q^{38} +(-5.00000 - 8.66025i) q^{39} +3.00000 q^{41} +(-3.46410 - 4.00000i) q^{42} -10.0000i q^{43} +(1.50000 - 2.59808i) q^{44} +(-1.50000 - 2.59808i) q^{46} +(2.59808 + 1.50000i) q^{47} -2.00000i q^{48} +(-1.00000 + 6.92820i) q^{49} +(6.00000 - 10.3923i) q^{51} +(-4.33013 + 2.50000i) q^{52} +(2.59808 - 1.50000i) q^{53} +(2.00000 - 3.46410i) q^{54} +(-2.00000 + 1.73205i) q^{56} -2.00000i q^{57} +(5.19615 + 3.00000i) q^{58} +(2.00000 - 3.46410i) q^{61} +4.00000i q^{62} +(2.59808 - 0.500000i) q^{63} -1.00000 q^{64} +(3.00000 + 5.19615i) q^{66} +(3.46410 - 2.00000i) q^{67} +(-5.19615 - 3.00000i) q^{68} +6.00000 q^{69} +12.0000 q^{71} +(0.866025 + 0.500000i) q^{72} +(-3.46410 + 2.00000i) q^{73} +(5.50000 + 9.52628i) q^{74} -1.00000 q^{76} +(2.59808 - 7.50000i) q^{77} -10.0000i q^{78} +(-5.00000 + 8.66025i) q^{79} +(5.50000 + 9.52628i) q^{81} +(2.59808 + 1.50000i) q^{82} -12.0000i q^{83} +(-1.00000 - 5.19615i) q^{84} +(5.00000 - 8.66025i) q^{86} +(-10.3923 + 6.00000i) q^{87} +(2.59808 - 1.50000i) q^{88} +(3.00000 - 5.19615i) q^{89} +(-10.0000 + 8.66025i) q^{91} -3.00000i q^{92} +(-6.92820 - 4.00000i) q^{93} +(1.50000 + 2.59808i) q^{94} +(1.00000 - 1.73205i) q^{96} -14.0000i q^{97} +(-4.33013 + 5.50000i) q^{98} -3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} - 8 q^{6} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 - 8 * q^6 + 2 * q^9	$ 4 q + 2 q^{4} - 8 q^{6} + 2 q^{9} - 6 q^{11} + 2 q^{14} - 2 q^{16} - 2 q^{19} - 20 q^{21} - 4 q^{24} - 10 q^{26} + 24 q^{29} + 8 q^{31} - 24 q^{34} + 4 q^{36} - 20 q^{39} + 12 q^{41} + 6 q^{44} - 6 q^{46} - 4 q^{49} + 24 q^{51} + 8 q^{54} - 8 q^{56} + 8 q^{61} - 4 q^{64} + 12 q^{66} + 24 q^{69} + 48 q^{71} + 22 q^{74} - 4 q^{76} - 20 q^{79} + 22 q^{81} - 4 q^{84} + 20 q^{86} + 12 q^{89} - 40 q^{91} + 6 q^{94} + 4 q^{96} - 12 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 - 8 * q^6 + 2 * q^9 - 6 * q^11 + 2 * q^14 - 2 * q^16 - 2 * q^19 - 20 * q^21 - 4 * q^24 - 10 * q^26 + 24 * q^29 + 8 * q^31 - 24 * q^34 + 4 * q^36 - 20 * q^39 + 12 * q^41 + 6 * q^44 - 6 * q^46 - 4 * q^49 + 24 * q^51 + 8 * q^54 - 8 * q^56 + 8 * q^61 - 4 * q^64 + 12 * q^66 + 24 * q^69 + 48 * q^71 + 22 * q^74 - 4 * q^76 - 20 * q^79 + 22 * q^81 - 4 * q^84 + 20 * q^86 + 12 * q^89 - 40 * q^91 + 6 * q^94 + 4 * q^96 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	−1.73205	+	1.00000i	−1.00000	+	0.577350i	−0.908248	−	0.418432i	$-0.862580\pi$
$3$	−1.73205	+	1.00000i	−1.00000	+	0.577350i	−0.0917517	+	0.995782i	$0.529247\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	−2.00000			−0.816497
$7$	1.73205	+	2.00000i	0.654654	+	0.755929i
$7$	1.73205	+	2.00000i	0.654654	+	0.755929i
$8$			1.00000i			0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	0.546259	−	0.837616i	$-0.316051\pi$
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	−0.998526	+	0.0542666i	$0.982718\pi$
$12$	−1.73205	−	1.00000i	−0.500000	−	0.288675i
$13$			5.00000i			1.38675i	0.720577	+	0.693375i	$0.243877\pi$
$13$			5.00000i			1.38675i	−0.720577	+	0.693375i	$0.756123\pi$
$14$	0.500000	+	2.59808i	0.133631	+	0.694365i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−5.19615	+	3.00000i	−1.26025	+	0.727607i	−0.973123	−	0.230285i	$-0.926034\pi$
$17$	−5.19615	+	3.00000i	−1.26025	+	0.727607i	−0.287129	+	0.957892i	$0.592701\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i	0.802955	+	0.596040i	$0.203260\pi$
$20$		0			0
$21$	−5.00000	−	1.73205i	−1.09109	−	0.377964i
$22$		−	3.00000i		−	0.639602i
$23$	−2.59808	−	1.50000i	−0.541736	−	0.312772i	0.204046	−	0.978961i	$-0.434591\pi$
$23$	−2.59808	−	1.50000i	−0.541736	−	0.312772i	−0.745782	+	0.666190i	$0.767924\pi$
$24$	−1.00000	−	1.73205i	−0.204124	−	0.353553i
$25$		0			0
$26$	−2.50000	+	4.33013i	−0.490290	+	0.849208i
$27$		−	4.00000i		−	0.769800i
$28$	−0.866025	+	2.50000i	−0.163663	+	0.472456i
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$		0			0
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	0.987829	−	0.155543i	$-0.0497126\pi$
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	−0.628619	+	0.777714i	$0.716379\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	5.19615	+	3.00000i	0.904534	+	0.522233i
$34$	−6.00000			−1.02899
$35$		0			0
$36$	1.00000			0.166667
$37$	9.52628	+	5.50000i	1.56611	+	0.904194i	0.996616	+	0.0821995i	$0.0261945\pi$
$37$	9.52628	+	5.50000i	1.56611	+	0.904194i	0.569495	+	0.821995i	$0.307139\pi$
$38$	−0.866025	+	0.500000i	−0.140488	+	0.0811107i
$39$	−5.00000	−	8.66025i	−0.800641	−	1.38675i
$40$		0			0
$41$	3.00000			0.468521			0.234261	−	0.972174i	$-0.424733\pi$
$41$	3.00000			0.468521			0.234261	+	0.972174i	$0.424733\pi$
$42$	−3.46410	−	4.00000i	−0.534522	−	0.617213i
$43$		−	10.0000i		−	1.52499i	−0.646997	−	0.762493i	$-0.723975\pi$
$43$		−	10.0000i		−	1.52499i	0.646997	−	0.762493i	$-0.276025\pi$
$44$	1.50000	−	2.59808i	0.226134	−	0.391675i
$45$		0			0
$46$	−1.50000	−	2.59808i	−0.221163	−	0.383065i
$47$	2.59808	+	1.50000i	0.378968	+	0.218797i	0.677369	−	0.735643i	$-0.263120\pi$
$47$	2.59808	+	1.50000i	0.378968	+	0.218797i	−0.298401	+	0.954441i	$0.596453\pi$
$48$		−	2.00000i		−	0.288675i
$49$	−1.00000	+	6.92820i	−0.142857	+	0.989743i
$50$		0			0
$51$	6.00000	−	10.3923i	0.840168	−	1.45521i
$52$	−4.33013	+	2.50000i	−0.600481	+	0.346688i
$53$	2.59808	−	1.50000i	0.356873	−	0.206041i	−0.310835	−	0.950464i	$-0.600609\pi$
$53$	2.59808	−	1.50000i	0.356873	−	0.206041i	0.667708	+	0.744423i	$0.267275\pi$
$54$	2.00000	−	3.46410i	0.272166	−	0.471405i
$55$		0			0
$56$	−2.00000	+	1.73205i	−0.267261	+	0.231455i
$57$		−	2.00000i		−	0.264906i
$58$	5.19615	+	3.00000i	0.682288	+	0.393919i
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$		0			0
$61$	2.00000	−	3.46410i	0.256074	−	0.443533i	−0.709113	−	0.705095i	$-0.750904\pi$
$61$	2.00000	−	3.46410i	0.256074	−	0.443533i	0.965187	+	0.261562i	$0.0842377\pi$
$62$			4.00000i			0.508001i
$63$	2.59808	−	0.500000i	0.327327	−	0.0629941i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	3.00000	+	5.19615i	0.369274	+	0.639602i
$67$	3.46410	−	2.00000i	0.423207	−	0.244339i	−0.273241	−	0.961946i	$-0.588096\pi$
$67$	3.46410	−	2.00000i	0.423207	−	0.244339i	0.696449	+	0.717607i	$0.254762\pi$
$68$	−5.19615	−	3.00000i	−0.630126	−	0.363803i
$69$	6.00000			0.722315
$70$		0			0
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$	−3.46410	+	2.00000i	−0.405442	+	0.234082i	−0.688830	−	0.724923i	$-0.741875\pi$
$73$	−3.46410	+	2.00000i	−0.405442	+	0.234082i	0.283387	+	0.959006i	$0.408542\pi$
$74$	5.50000	+	9.52628i	0.639362	+	1.10741i
$75$		0			0
$76$	−1.00000			−0.114708
$77$	2.59808	−	7.50000i	0.296078	−	0.854704i
$78$		−	10.0000i		−	1.13228i
$79$	−5.00000	+	8.66025i	−0.562544	+	0.974355i	0.434730	+	0.900561i	$0.356844\pi$
$79$	−5.00000	+	8.66025i	−0.562544	+	0.974355i	−0.997274	+	0.0737937i	$0.976489\pi$
$80$		0			0
$81$	5.50000	+	9.52628i	0.611111	+	1.05848i
$82$	2.59808	+	1.50000i	0.286910	+	0.165647i
$83$		−	12.0000i		−	1.31717i	−0.752506	−	0.658586i	$-0.771155\pi$
$83$		−	12.0000i		−	1.31717i	0.752506	−	0.658586i	$-0.228845\pi$
$84$	−1.00000	−	5.19615i	−0.109109	−	0.566947i
$85$		0			0
$86$	5.00000	−	8.66025i	0.539164	−	0.933859i
$87$	−10.3923	+	6.00000i	−1.11417	+	0.643268i
$88$	2.59808	−	1.50000i	0.276956	−	0.159901i
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	−0.662071	−	0.749441i	$-0.730322\pi$
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	0.980071	+	0.198650i	$0.0636557\pi$
$90$		0			0
$91$	−10.0000	+	8.66025i	−1.04828	+	0.907841i
$92$		−	3.00000i		−	0.312772i
$93$	−6.92820	−	4.00000i	−0.718421	−	0.414781i
$94$	1.50000	+	2.59808i	0.154713	+	0.267971i
$95$		0			0
$96$	1.00000	−	1.73205i	0.102062	−	0.176777i
$97$		−	14.0000i		−	1.42148i	−0.703452	−	0.710742i	$-0.748359\pi$
$97$		−	14.0000i		−	1.42148i	0.703452	−	0.710742i	$-0.251641\pi$
$98$	−4.33013	+	5.50000i	−0.437409	+	0.555584i
$99$	−3.00000			−0.301511
$100$		0			0
$101$	6.00000	+	10.3923i	0.597022	+	1.03407i	0.993258	+	0.115924i	$0.0369830\pi$
$101$	6.00000	+	10.3923i	0.597022	+	1.03407i	−0.396236	+	0.918149i	$0.629684\pi$
$102$	10.3923	−	6.00000i	1.02899	−	0.594089i
$103$	3.46410	+	2.00000i	0.341328	+	0.197066i	0.660859	−	0.750510i	$-0.270192\pi$
$103$	3.46410	+	2.00000i	0.341328	+	0.197066i	−0.319531	+	0.947576i	$0.603525\pi$
$104$	−5.00000			−0.490290
$105$		0			0
$106$	3.00000			0.291386
$107$	−10.3923	−	6.00000i	−1.00466	−	0.580042i	−0.0950377	−	0.995474i	$-0.530297\pi$
$107$	−10.3923	−	6.00000i	−1.00466	−	0.580042i	−0.909624	+	0.415432i	$0.863630\pi$
$108$	3.46410	−	2.00000i	0.333333	−	0.192450i
$109$	−2.00000	−	3.46410i	−0.191565	−	0.331801i	0.754204	−	0.656640i	$-0.228023\pi$
$109$	−2.00000	−	3.46410i	−0.191565	−	0.331801i	−0.945769	+	0.324840i	$0.894690\pi$
$110$		0			0
$111$	−22.0000			−2.08815
$112$	−2.59808	+	0.500000i	−0.245495	+	0.0472456i
$113$			12.0000i			1.12887i	0.825479	+	0.564433i	$0.190905\pi$
$113$			12.0000i			1.12887i	−0.825479	+	0.564433i	$0.809095\pi$
$114$	1.00000	−	1.73205i	0.0936586	−	0.162221i
$115$		0			0
$116$	3.00000	+	5.19615i	0.278543	+	0.482451i
$117$	4.33013	+	2.50000i	0.400320	+	0.231125i
$118$		0			0
$119$	−15.0000	−	5.19615i	−1.37505	−	0.476331i
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	3.46410	−	2.00000i	0.313625	−	0.181071i
$123$	−5.19615	+	3.00000i	−0.468521	+	0.270501i
$124$	−2.00000	+	3.46410i	−0.179605	+	0.311086i
$125$		0			0
$126$	2.50000	+	0.866025i	0.222718	+	0.0771517i
$127$			19.0000i			1.68598i	0.537931	+	0.842989i	$0.319206\pi$
$127$			19.0000i			1.68598i	−0.537931	+	0.842989i	$0.680794\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	10.0000	+	17.3205i	0.880451	+	1.52499i
$130$		0			0
$131$	−1.50000	+	2.59808i	−0.131056	+	0.226995i	−0.924084	−	0.382190i	$-0.875170\pi$
$131$	−1.50000	+	2.59808i	−0.131056	+	0.226995i	0.793028	+	0.609185i	$0.208503\pi$
$132$			6.00000i			0.522233i
$133$	−2.59808	+	0.500000i	−0.225282	+	0.0433555i
$134$	4.00000			0.345547
$135$		0			0
$136$	−3.00000	−	5.19615i	−0.257248	−	0.445566i
$137$	−10.3923	+	6.00000i	−0.887875	+	0.512615i	−0.873247	−	0.487278i	$-0.837990\pi$
$137$	−10.3923	+	6.00000i	−0.887875	+	0.512615i	−0.0146279	+	0.999893i	$0.504656\pi$
$138$	5.19615	+	3.00000i	0.442326	+	0.255377i
$139$	4.00000			0.339276			0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000			0.339276			0.169638	+	0.985506i	$0.445740\pi$
$140$		0			0
$141$	−6.00000			−0.505291
$142$	10.3923	+	6.00000i	0.872103	+	0.503509i
$143$	12.9904	−	7.50000i	1.08631	−	0.627182i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$		0			0
$146$	−4.00000			−0.331042
$147$	−5.19615	−	13.0000i	−0.428571	−	1.07222i
$148$			11.0000i			0.904194i
$149$	9.00000	−	15.5885i	0.737309	−	1.27706i	−0.216394	−	0.976306i	$-0.569430\pi$
$149$	9.00000	−	15.5885i	0.737309	−	1.27706i	0.953703	−	0.300750i	$-0.0972370\pi$
$150$		0			0
$151$	−7.00000	−	12.1244i	−0.569652	−	0.986666i	−0.996600	−	0.0823900i	$-0.973745\pi$
$151$	−7.00000	−	12.1244i	−0.569652	−	0.986666i	0.426948	−	0.904276i	$-0.359589\pi$
$152$	−0.866025	−	0.500000i	−0.0702439	−	0.0405554i
$153$			6.00000i			0.485071i
$154$	6.00000	−	5.19615i	0.483494	−	0.418718i
$155$		0			0
$156$	5.00000	−	8.66025i	0.400320	−	0.693375i
$157$	−4.33013	+	2.50000i	−0.345582	+	0.199522i	−0.662738	−	0.748852i	$-0.730606\pi$
$157$	−4.33013	+	2.50000i	−0.345582	+	0.199522i	0.317156	+	0.948373i	$0.397272\pi$
$158$	−8.66025	+	5.00000i	−0.688973	+	0.397779i
$159$	−3.00000	+	5.19615i	−0.237915	+	0.412082i
$160$		0			0
$161$	−1.50000	−	7.79423i	−0.118217	−	0.614271i
$162$			11.0000i			0.864242i
$163$	3.46410	+	2.00000i	0.271329	+	0.156652i	0.629492	−	0.777007i	$-0.283263\pi$
$163$	3.46410	+	2.00000i	0.271329	+	0.156652i	−0.358162	+	0.933659i	$0.616597\pi$
$164$	1.50000	+	2.59808i	0.117130	+	0.202876i
$165$		0			0
$166$	6.00000	−	10.3923i	0.465690	−	0.806599i
$167$		−	9.00000i		−	0.696441i	−0.937413	−	0.348220i	$-0.886786\pi$
$167$		−	9.00000i		−	0.696441i	0.937413	−	0.348220i	$-0.113214\pi$
$168$	1.73205	−	5.00000i	0.133631	−	0.385758i
$169$	−12.0000			−0.923077
$170$		0			0
$171$	0.500000	+	0.866025i	0.0382360	+	0.0662266i
$172$	8.66025	−	5.00000i	0.660338	−	0.381246i
$173$	−2.59808	−	1.50000i	−0.197528	−	0.114043i	0.397974	−	0.917397i	$-0.369713\pi$
$173$	−2.59808	−	1.50000i	−0.197528	−	0.114043i	−0.595502	+	0.803354i	$0.703047\pi$
$174$	−12.0000			−0.909718
$175$		0			0
$176$	3.00000			0.226134
$177$		0			0
$178$	5.19615	−	3.00000i	0.389468	−	0.224860i
$179$	−1.50000	−	2.59808i	−0.112115	−	0.194189i	0.804508	−	0.593942i	$-0.202429\pi$
$179$	−1.50000	−	2.59808i	−0.112115	−	0.194189i	−0.916623	+	0.399753i	$0.869096\pi$
$180$		0			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$	−12.9904	+	2.50000i	−0.962911	+	0.185312i
$183$			8.00000i			0.591377i
$184$	1.50000	−	2.59808i	0.110581	−	0.191533i
$185$		0			0
$186$	−4.00000	−	6.92820i	−0.293294	−	0.508001i
$187$	15.5885	+	9.00000i	1.13994	+	0.658145i
$188$			3.00000i			0.218797i
$189$	8.00000	−	6.92820i	0.581914	−	0.503953i
$190$		0			0
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	−0.997225	−	0.0744412i	$-0.976283\pi$
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	0.563081	+	0.826402i	$0.309616\pi$
$192$	1.73205	−	1.00000i	0.125000	−	0.0721688i
$193$	−3.46410	+	2.00000i	−0.249351	+	0.143963i	−0.619467	−	0.785022i	$-0.712651\pi$
$193$	−3.46410	+	2.00000i	−0.249351	+	0.143963i	0.370116	+	0.928986i	$0.379318\pi$
$194$	7.00000	−	12.1244i	0.502571	−	0.870478i
$195$		0			0
$196$	−6.50000	+	2.59808i	−0.464286	+	0.185577i
$197$			3.00000i			0.213741i	0.994273	+	0.106871i	$0.0340831\pi$
$197$			3.00000i			0.213741i	−0.994273	+	0.106871i	$0.965917\pi$
$198$	−2.59808	−	1.50000i	−0.184637	−	0.106600i
$199$	−2.00000	−	3.46410i	−0.141776	−	0.245564i	0.786389	−	0.617731i	$-0.211948\pi$
$199$	−2.00000	−	3.46410i	−0.141776	−	0.245564i	−0.928166	+	0.372168i	$0.878615\pi$
$200$		0			0
$201$	−4.00000	+	6.92820i	−0.282138	+	0.488678i
$202$			12.0000i			0.844317i
$203$	10.3923	+	12.0000i	0.729397	+	0.842235i
$204$	12.0000			0.840168
$205$		0			0
$206$	2.00000	+	3.46410i	0.139347	+	0.241355i
$207$	−2.59808	+	1.50000i	−0.180579	+	0.104257i
$208$	−4.33013	−	2.50000i	−0.300240	−	0.173344i
$209$	3.00000			0.207514
$210$		0			0
$211$	−1.00000			−0.0688428			−0.0344214	−	0.999407i	$-0.510959\pi$
$211$	−1.00000			−0.0688428			−0.0344214	+	0.999407i	$0.510959\pi$
$212$	2.59808	+	1.50000i	0.178437	+	0.103020i
$213$	−20.7846	+	12.0000i	−1.42414	+	0.822226i
$214$	−6.00000	−	10.3923i	−0.410152	−	0.710403i
$215$		0			0
$216$	4.00000			0.272166
$217$	−3.46410	+	10.0000i	−0.235159	+	0.678844i
$218$		−	4.00000i		−	0.270914i
$219$	4.00000	−	6.92820i	0.270295	−	0.468165i
$220$		0			0
$221$	−15.0000	−	25.9808i	−1.00901	−	1.74766i
$222$	−19.0526	−	11.0000i	−1.27872	−	0.738272i
$223$			8.00000i			0.535720i	0.963458	+	0.267860i	$0.0863164\pi$
$223$			8.00000i			0.535720i	−0.963458	+	0.267860i	$0.913684\pi$
$224$	−2.50000	−	0.866025i	−0.167038	−	0.0578638i
$225$		0			0
$226$	−6.00000	+	10.3923i	−0.399114	+	0.691286i
$227$	20.7846	−	12.0000i	1.37952	−	0.796468i	0.387421	−	0.921903i	$-0.373366\pi$
$227$	20.7846	−	12.0000i	1.37952	−	0.796468i	0.992102	+	0.125435i	$0.0400326\pi$
$228$	1.73205	−	1.00000i	0.114708	−	0.0662266i
$229$	−14.0000	+	24.2487i	−0.925146	+	1.60240i	−0.133820	+	0.991006i	$0.542724\pi$
$229$	−14.0000	+	24.2487i	−0.925146	+	1.60240i	−0.791326	+	0.611394i	$0.790609\pi$
$230$		0			0
$231$	3.00000	+	15.5885i	0.197386	+	1.02565i
$232$			6.00000i			0.393919i
$233$	5.19615	+	3.00000i	0.340411	+	0.196537i	0.660454	−	0.750867i	$-0.270364\pi$
$233$	5.19615	+	3.00000i	0.340411	+	0.196537i	−0.320043	+	0.947403i	$0.603697\pi$
$234$	2.50000	+	4.33013i	0.163430	+	0.283069i
$235$		0			0
$236$		0			0
$237$		−	20.0000i		−	1.29914i
$238$	−10.3923	−	12.0000i	−0.673633	−	0.777844i
$239$	−6.00000			−0.388108			−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000			−0.388108			−0.194054	+	0.980991i	$0.562164\pi$
$240$		0			0
$241$	12.5000	+	21.6506i	0.805196	+	1.39464i	0.916159	+	0.400815i	$0.131273\pi$
$241$	12.5000	+	21.6506i	0.805196	+	1.39464i	−0.110963	+	0.993825i	$0.535394\pi$
$242$	1.73205	−	1.00000i	0.111340	−	0.0642824i
$243$	−8.66025	−	5.00000i	−0.555556	−	0.320750i
$244$	4.00000			0.256074
$245$		0			0
$246$	−6.00000			−0.382546
$247$	−4.33013	−	2.50000i	−0.275519	−	0.159071i
$248$	−3.46410	+	2.00000i	−0.219971	+	0.127000i
$249$	12.0000	+	20.7846i	0.760469	+	1.31717i
$250$		0			0
$251$	−15.0000			−0.946792			−0.473396	−	0.880850i	$-0.656972\pi$
$251$	−15.0000			−0.946792			−0.473396	+	0.880850i	$0.656972\pi$
$252$	1.73205	+	2.00000i	0.109109	+	0.125988i
$253$			9.00000i			0.565825i
$254$	−9.50000	+	16.4545i	−0.596083	+	1.03245i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−10.3923	−	6.00000i	−0.648254	−	0.374270i	0.139533	−	0.990217i	$-0.455440\pi$
$257$	−10.3923	−	6.00000i	−0.648254	−	0.374270i	−0.787787	+	0.615948i	$0.788773\pi$
$258$			20.0000i			1.24515i
$259$	5.50000	+	28.5788i	0.341753	+	1.77580i
$260$		0			0
$261$	3.00000	−	5.19615i	0.185695	−	0.321634i
$262$	−2.59808	+	1.50000i	−0.160510	+	0.0926703i
$263$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$263$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$264$	−3.00000	+	5.19615i	−0.184637	+	0.319801i
$265$		0			0
$266$	−2.50000	−	0.866025i	−0.153285	−	0.0530994i
$267$			12.0000i			0.734388i
$268$	3.46410	+	2.00000i	0.211604	+	0.122169i
$269$	−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
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	−0.513905	−	0.857847i	$-0.671801\pi$
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	0.999870	+	0.0161307i	$0.00513477\pi$
$272$		−	6.00000i		−	0.363803i
$273$	8.66025	−	25.0000i	0.524142	−	1.51307i
$274$	−12.0000			−0.724947
$275$		0			0
$276$	3.00000	+	5.19615i	0.180579	+	0.312772i
$277$	−1.73205	+	1.00000i	−0.104069	+	0.0600842i	−0.551131	−	0.834419i	$-0.685804\pi$
$277$	−1.73205	+	1.00000i	−0.104069	+	0.0600842i	0.447062	+	0.894503i	$0.352470\pi$
$278$	3.46410	+	2.00000i	0.207763	+	0.119952i
$279$	4.00000			0.239474
$280$		0			0
$281$	−3.00000			−0.178965			−0.0894825	−	0.995988i	$-0.528521\pi$
$281$	−3.00000			−0.178965			−0.0894825	+	0.995988i	$0.528521\pi$
$282$	−5.19615	−	3.00000i	−0.309426	−	0.178647i
$283$	22.5167	−	13.0000i	1.33848	−	0.772770i	0.351895	−	0.936039i	$-0.385537\pi$
$283$	22.5167	−	13.0000i	1.33848	−	0.772770i	0.986581	+	0.163270i	$0.0522041\pi$
$284$	6.00000	+	10.3923i	0.356034	+	0.616670i
$285$		0			0
$286$	15.0000			0.886969
$287$	5.19615	+	6.00000i	0.306719	+	0.354169i
$288$			1.00000i			0.0589256i
$289$	9.50000	−	16.4545i	0.558824	−	0.967911i
$290$		0			0
$291$	14.0000	+	24.2487i	0.820695	+	1.42148i
$292$	−3.46410	−	2.00000i	−0.202721	−	0.117041i
$293$		−	27.0000i		−	1.57736i	−0.614806	−	0.788678i	$-0.710766\pi$
$293$		−	27.0000i		−	1.57736i	0.614806	−	0.788678i	$-0.289234\pi$
$294$	2.00000	−	13.8564i	0.116642	−	0.808122i
$295$		0			0
$296$	−5.50000	+	9.52628i	−0.319681	+	0.553704i
$297$	−10.3923	+	6.00000i	−0.603023	+	0.348155i
$298$	15.5885	−	9.00000i	0.903015	−	0.521356i
$299$	7.50000	−	12.9904i	0.433736	−	0.751253i
$300$		0			0
$301$	20.0000	−	17.3205i	1.15278	−	0.998337i
$302$		−	14.0000i		−	0.805609i
$303$	−20.7846	−	12.0000i	−1.19404	−	0.689382i
$304$	−0.500000	−	0.866025i	−0.0286770	−	0.0496700i
$305$		0			0
$306$	−3.00000	+	5.19615i	−0.171499	+	0.297044i
$307$		−	2.00000i		−	0.114146i	−0.998370	−	0.0570730i	$-0.981823\pi$
$307$		−	2.00000i		−	0.114146i	0.998370	−	0.0570730i	$-0.0181768\pi$
$308$	7.79423	−	1.50000i	0.444117	−	0.0854704i
$309$	−8.00000			−0.455104
$310$		0			0
$311$	−6.00000	−	10.3923i	−0.340229	−	0.589294i	0.644246	−	0.764818i	$-0.277171\pi$
$311$	−6.00000	−	10.3923i	−0.340229	−	0.589294i	−0.984475	+	0.175525i	$0.943838\pi$
$312$	8.66025	−	5.00000i	0.490290	−	0.283069i
$313$	−6.92820	−	4.00000i	−0.391605	−	0.226093i	0.291250	−	0.956647i	$-0.405929\pi$
$313$	−6.92820	−	4.00000i	−0.391605	−	0.226093i	−0.682855	+	0.730554i	$0.739262\pi$
$314$	−5.00000			−0.282166
$315$		0			0
$316$	−10.0000			−0.562544
$317$	15.5885	+	9.00000i	0.875535	+	0.505490i	0.869184	−	0.494489i	$-0.164645\pi$
$317$	15.5885	+	9.00000i	0.875535	+	0.505490i	0.00635137	+	0.999980i	$0.497978\pi$
$318$	−5.19615	+	3.00000i	−0.291386	+	0.168232i
$319$	−9.00000	−	15.5885i	−0.503903	−	0.872786i
$320$		0			0
$321$	24.0000			1.33955
$322$	2.59808	−	7.50000i	0.144785	−	0.417959i
$323$		−	6.00000i		−	0.333849i
$324$	−5.50000	+	9.52628i	−0.305556	+	0.529238i
$325$		0			0
$326$	2.00000	+	3.46410i	0.110770	+	0.191859i
$327$	6.92820	+	4.00000i	0.383131	+	0.221201i
$328$			3.00000i			0.165647i
$329$	1.50000	+	7.79423i	0.0826977	+	0.429710i
$330$		0			0
$331$	3.50000	−	6.06218i	0.192377	−	0.333207i	−0.753660	−	0.657264i	$-0.771714\pi$
$331$	3.50000	−	6.06218i	0.192377	−	0.333207i	0.946038	+	0.324057i	$0.105047\pi$
$332$	10.3923	−	6.00000i	0.570352	−	0.329293i
$333$	9.52628	−	5.50000i	0.522037	−	0.301398i
$334$	4.50000	−	7.79423i	0.246229	−	0.426481i
$335$		0			0
$336$	4.00000	−	3.46410i	0.218218	−	0.188982i
$337$		−	14.0000i		−	0.762629i	−0.924445	−	0.381314i	$-0.875472\pi$
$337$		−	14.0000i		−	0.762629i	0.924445	−	0.381314i	$-0.124528\pi$
$338$	−10.3923	−	6.00000i	−0.565267	−	0.326357i
$339$	−12.0000	−	20.7846i	−0.651751	−	1.12887i
$340$		0			0
$341$	6.00000	−	10.3923i	0.324918	−	0.562775i
$342$			1.00000i			0.0540738i
$343$	−15.5885	+	10.0000i	−0.841698	+	0.539949i
$344$	10.0000			0.539164
$345$		0			0
$346$	−1.50000	−	2.59808i	−0.0806405	−	0.139673i
$347$	−20.7846	+	12.0000i	−1.11578	+	0.644194i	−0.940319	−	0.340293i	$-0.889474\pi$
$347$	−20.7846	+	12.0000i	−1.11578	+	0.644194i	−0.175457	+	0.984487i	$0.556140\pi$
$348$	−10.3923	−	6.00000i	−0.557086	−	0.321634i
$349$	10.0000			0.535288			0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000			0.535288			0.267644	+	0.963518i	$0.413755\pi$
$350$		0			0
$351$	20.0000			1.06752
$352$	2.59808	+	1.50000i	0.138478	+	0.0799503i
$353$	10.3923	−	6.00000i	0.553127	−	0.319348i	−0.197256	−	0.980352i	$-0.563203\pi$
$353$	10.3923	−	6.00000i	0.553127	−	0.319348i	0.750382	+	0.661004i	$0.229870\pi$
$354$		0			0
$355$		0			0
$356$	6.00000			0.317999
$357$	31.1769	−	6.00000i	1.65006	−	0.317554i
$358$		−	3.00000i		−	0.158555i
$359$	3.00000	−	5.19615i	0.158334	−	0.274242i	−0.775934	−	0.630814i	$-0.782721\pi$
$359$	3.00000	−	5.19615i	0.158334	−	0.274242i	0.934268	+	0.356572i	$0.116054\pi$
$360$		0			0
$361$	9.00000	+	15.5885i	0.473684	+	0.820445i
$362$	1.73205	+	1.00000i	0.0910346	+	0.0525588i
$363$			4.00000i			0.209946i
$364$	−12.5000	−	4.33013i	−0.655178	−	0.226960i
$365$		0			0
$366$	−4.00000	+	6.92820i	−0.209083	+	0.362143i
$367$	0.866025	−	0.500000i	0.0452062	−	0.0260998i	−0.477227	−	0.878780i	$-0.658358\pi$
$367$	0.866025	−	0.500000i	0.0452062	−	0.0260998i	0.522433	+	0.852680i	$0.325025\pi$
$368$	2.59808	−	1.50000i	0.135434	−	0.0781929i
$369$	1.50000	−	2.59808i	0.0780869	−	0.135250i
$370$		0			0
$371$	7.50000	+	2.59808i	0.389381	+	0.134885i
$372$		−	8.00000i		−	0.414781i
$373$	29.4449	+	17.0000i	1.52460	+	0.880227i	0.999575	+	0.0291379i	$0.00927619\pi$
$373$	29.4449	+	17.0000i	1.52460	+	0.880227i	0.525022	+	0.851089i	$0.324057\pi$
$374$	9.00000	+	15.5885i	0.465379	+	0.806060i
$375$		0			0
$376$	−1.50000	+	2.59808i	−0.0773566	+	0.133986i
$377$			30.0000i			1.54508i
$378$	10.3923	−	2.00000i	0.534522	−	0.102869i
$379$	25.0000			1.28416			0.642082	−	0.766636i	$-0.278071\pi$
$379$	25.0000			1.28416			0.642082	+	0.766636i	$0.278071\pi$
$380$		0			0
$381$	−19.0000	−	32.9090i	−0.973399	−	1.68598i
$382$	−10.3923	+	6.00000i	−0.531717	+	0.306987i
$383$	−12.9904	−	7.50000i	−0.663777	−	0.383232i	0.129937	−	0.991522i	$-0.458522\pi$
$383$	−12.9904	−	7.50000i	−0.663777	−	0.383232i	−0.793715	+	0.608290i	$0.791856\pi$
$384$	2.00000			0.102062
$385$		0			0
$386$	−4.00000			−0.203595
$387$	−8.66025	−	5.00000i	−0.440225	−	0.254164i
$388$	12.1244	−	7.00000i	0.615521	−	0.355371i
$389$	−12.0000	−	20.7846i	−0.608424	−	1.05382i	−0.991500	−	0.130105i	$-0.958469\pi$
$389$	−12.0000	−	20.7846i	−0.608424	−	1.05382i	0.383076	−	0.923717i	$-0.374865\pi$
$390$		0			0
$391$	18.0000			0.910299
$392$	−6.92820	−	1.00000i	−0.349927	−	0.0505076i
$393$		−	6.00000i		−	0.302660i
$394$	−1.50000	+	2.59808i	−0.0755689	+	0.130889i
$395$		0			0
$396$	−1.50000	−	2.59808i	−0.0753778	−	0.130558i
$397$	1.73205	+	1.00000i	0.0869291	+	0.0501886i	0.542834	−	0.839840i	$-0.317351\pi$
$397$	1.73205	+	1.00000i	0.0869291	+	0.0501886i	−0.455905	+	0.890028i	$0.650684\pi$
$398$		−	4.00000i		−	0.200502i
$399$	4.00000	−	3.46410i	0.200250	−	0.173422i
$400$		0			0
$401$	−10.5000	+	18.1865i	−0.524345	+	0.908192i	0.475253	+	0.879849i	$0.342356\pi$
$401$	−10.5000	+	18.1865i	−0.524345	+	0.908192i	−0.999598	+	0.0283431i	$0.990977\pi$
$402$	−6.92820	+	4.00000i	−0.345547	+	0.199502i
$403$	−17.3205	+	10.0000i	−0.862796	+	0.498135i
$404$	−6.00000	+	10.3923i	−0.298511	+	0.517036i
$405$		0			0
$406$	3.00000	+	15.5885i	0.148888	+	0.773642i
$407$		−	33.0000i		−	1.63575i
$408$	10.3923	+	6.00000i	0.514496	+	0.297044i
$409$	−11.0000	−	19.0526i	−0.543915	−	0.942088i	−0.998674	−	0.0514740i	$-0.983608\pi$
$409$	−11.0000	−	19.0526i	−0.543915	−	0.942088i	0.454759	−	0.890614i	$-0.349725\pi$
$410$		0			0
$411$	12.0000	−	20.7846i	0.591916	−	1.02523i
$412$			4.00000i			0.197066i
$413$		0			0
$414$	−3.00000			−0.147442
$415$		0			0
$416$	−2.50000	−	4.33013i	−0.122573	−	0.212302i
$417$	−6.92820	+	4.00000i	−0.339276	+	0.195881i
$418$	2.59808	+	1.50000i	0.127076	+	0.0733674i
$419$	−15.0000			−0.732798			−0.366399	−	0.930458i	$-0.619409\pi$
$419$	−15.0000			−0.732798			−0.366399	+	0.930458i	$0.619409\pi$
$420$		0			0
$421$	−34.0000			−1.65706			−0.828529	−	0.559946i	$-0.810822\pi$
$421$	−34.0000			−1.65706			−0.828529	+	0.559946i	$0.810822\pi$
$422$	−0.866025	−	0.500000i	−0.0421575	−	0.0243396i
$423$	2.59808	−	1.50000i	0.126323	−	0.0729325i
$424$	1.50000	+	2.59808i	0.0728464	+	0.126174i
$425$		0			0
$426$	−24.0000			−1.16280
$427$	10.3923	−	2.00000i	0.502919	−	0.0967868i
$428$		−	12.0000i		−	0.580042i
$429$	−15.0000	+	25.9808i	−0.724207	+	1.25436i
$430$		0			0
$431$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$431$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$432$	3.46410	+	2.00000i	0.166667	+	0.0962250i
$433$		−	16.0000i		−	0.768911i	−0.923144	−	0.384455i	$-0.874389\pi$
$433$		−	16.0000i		−	0.768911i	0.923144	−	0.384455i	$-0.125611\pi$
$434$	−8.00000	+	6.92820i	−0.384012	+	0.332564i
$435$		0			0
$436$	2.00000	−	3.46410i	0.0957826	−	0.165900i
$437$	2.59808	−	1.50000i	0.124283	−	0.0717547i
$438$	6.92820	−	4.00000i	0.331042	−	0.191127i
$439$	−5.00000	+	8.66025i	−0.238637	+	0.413331i	−0.960323	−	0.278889i	$-0.910034\pi$
$439$	−5.00000	+	8.66025i	−0.238637	+	0.413331i	0.721686	+	0.692220i	$0.243367\pi$
$440$		0			0
$441$	5.50000	+	4.33013i	0.261905	+	0.206197i
$442$		−	30.0000i		−	1.42695i
$443$	20.7846	+	12.0000i	0.987507	+	0.570137i	0.904528	−	0.426414i	$-0.140223\pi$
$443$	20.7846	+	12.0000i	0.987507	+	0.570137i	0.0829786	+	0.996551i	$0.473557\pi$
$444$	−11.0000	−	19.0526i	−0.522037	−	0.904194i
$445$		0			0
$446$	−4.00000	+	6.92820i	−0.189405	+	0.328060i
$447$			36.0000i			1.70274i
$448$	−1.73205	−	2.00000i	−0.0818317	−	0.0944911i
$449$	3.00000			0.141579			0.0707894	−	0.997491i	$-0.477448\pi$
$449$	3.00000			0.141579			0.0707894	+	0.997491i	$0.477448\pi$
$450$		0			0
$451$	−4.50000	−	7.79423i	−0.211897	−	0.367016i
$452$	−10.3923	+	6.00000i	−0.488813	+	0.282216i
$453$	24.2487	+	14.0000i	1.13930	+	0.657777i
$454$	24.0000			1.12638
$455$		0			0
$456$	2.00000			0.0936586
$457$	−19.0526	−	11.0000i	−0.891241	−	0.514558i	−0.0168929	−	0.999857i	$-0.505377\pi$
$457$	−19.0526	−	11.0000i	−0.891241	−	0.514558i	−0.874348	+	0.485299i	$0.838711\pi$
$458$	−24.2487	+	14.0000i	−1.13307	+	0.654177i
$459$	12.0000	+	20.7846i	0.560112	+	0.970143i
$460$		0			0
$461$	6.00000			0.279448			0.139724	−	0.990190i	$-0.455378\pi$
$461$	6.00000			0.279448			0.139724	+	0.990190i	$0.455378\pi$
$462$	−5.19615	+	15.0000i	−0.241747	+	0.697863i
$463$		−	19.0000i		−	0.883005i	−0.897260	−	0.441502i	$-0.854446\pi$
$463$		−	19.0000i		−	0.883005i	0.897260	−	0.441502i	$-0.145554\pi$
$464$	−3.00000	+	5.19615i	−0.139272	+	0.241225i
$465$		0			0
$466$	3.00000	+	5.19615i	0.138972	+	0.240707i
$467$	−15.5885	−	9.00000i	−0.721348	−	0.416470i	0.0939008	−	0.995582i	$-0.470066\pi$
$467$	−15.5885	−	9.00000i	−0.721348	−	0.416470i	−0.815249	+	0.579111i	$0.803400\pi$
$468$			5.00000i			0.231125i
$469$	10.0000	+	3.46410i	0.461757	+	0.159957i
$470$		0			0
$471$	5.00000	−	8.66025i	0.230388	−	0.399043i
$472$		0			0
$473$	−25.9808	+	15.0000i	−1.19460	+	0.689701i
$474$	10.0000	−	17.3205i	0.459315	−	0.795557i
$475$		0			0
$476$	−3.00000	−	15.5885i	−0.137505	−	0.714496i
$477$		−	3.00000i		−	0.137361i
$478$	−5.19615	−	3.00000i	−0.237666	−	0.137217i
$479$	12.0000	+	20.7846i	0.548294	+	0.949673i	0.998392	+	0.0566937i	$0.0180558\pi$
$479$	12.0000	+	20.7846i	0.548294	+	0.949673i	−0.450098	+	0.892979i	$0.648611\pi$
$480$		0			0
$481$	−27.5000	+	47.6314i	−1.25389	+	2.17180i
$482$			25.0000i			1.13872i
$483$	10.3923	+	12.0000i	0.472866	+	0.546019i
$484$	2.00000			0.0909091
$485$		0			0
$486$	−5.00000	−	8.66025i	−0.226805	−	0.392837i
$487$	13.8564	−	8.00000i	0.627894	−	0.362515i	−0.152042	−	0.988374i	$-0.548585\pi$
$487$	13.8564	−	8.00000i	0.627894	−	0.362515i	0.779936	+	0.625859i	$0.215252\pi$
$488$	3.46410	+	2.00000i	0.156813	+	0.0905357i
$489$	−8.00000			−0.361773
$490$		0			0
$491$	−12.0000			−0.541552			−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000			−0.541552			−0.270776	+	0.962642i	$0.587280\pi$
$492$	−5.19615	−	3.00000i	−0.234261	−	0.135250i
$493$	−31.1769	+	18.0000i	−1.40414	+	0.810679i
$494$	−2.50000	−	4.33013i	−0.112480	−	0.194822i
$495$		0			0
$496$	−4.00000			−0.179605
$497$	20.7846	+	24.0000i	0.932317	+	1.07655i
$498$			24.0000i			1.07547i
$499$	−14.0000	+	24.2487i	−0.626726	+	1.08552i	0.361478	+	0.932381i	$0.382272\pi$
$499$	−14.0000	+	24.2487i	−0.626726	+	1.08552i	−0.988204	+	0.153141i	$0.951061\pi$
$500$		0			0
$501$	9.00000	+	15.5885i	0.402090	+	0.696441i
$502$	−12.9904	−	7.50000i	−0.579789	−	0.334741i
$503$			24.0000i			1.07011i	0.844818	+	0.535054i	$0.179709\pi$
$503$			24.0000i			1.07011i	−0.844818	+	0.535054i	$0.820291\pi$
$504$	0.500000	+	2.59808i	0.0222718	+	0.115728i
$505$		0			0
$506$	−4.50000	+	7.79423i	−0.200049	+	0.346496i
$507$	20.7846	−	12.0000i	0.923077	−	0.532939i
$508$	−16.4545	+	9.50000i	−0.730050	+	0.421494i
$509$	3.00000	−	5.19615i	0.132973	−	0.230315i	−0.791849	−	0.610718i	$-0.790881\pi$
$509$	3.00000	−	5.19615i	0.132973	−	0.230315i	0.924821	+	0.380402i	$0.124214\pi$
$510$		0			0
$511$	−10.0000	−	3.46410i	−0.442374	−	0.153243i
$512$		−	1.00000i		−	0.0441942i
$513$	3.46410	+	2.00000i	0.152944	+	0.0883022i
$514$	−6.00000	−	10.3923i	−0.264649	−	0.458385i
$515$		0			0
$516$	−10.0000	+	17.3205i	−0.440225	+	0.762493i
$517$		−	9.00000i		−	0.395820i
$518$	−9.52628	+	27.5000i	−0.418561	+	1.20828i
$519$	6.00000			0.263371
$520$		0			0
$521$	−16.5000	−	28.5788i	−0.722878	−	1.25206i	−0.959841	−	0.280543i	$-0.909485\pi$
$521$	−16.5000	−	28.5788i	−0.722878	−	1.25206i	0.236963	−	0.971519i	$-0.423848\pi$
$522$	5.19615	−	3.00000i	0.227429	−	0.131306i
$523$	−17.3205	−	10.0000i	−0.757373	−	0.437269i	0.0709788	−	0.997478i	$-0.477388\pi$
$523$	−17.3205	−	10.0000i	−0.757373	−	0.437269i	−0.828352	+	0.560208i	$0.810721\pi$
$524$	−3.00000			−0.131056
$525$		0			0
$526$		0			0
$527$	−20.7846	−	12.0000i	−0.905392	−	0.522728i
$528$	−5.19615	+	3.00000i	−0.226134	+	0.130558i
$529$	−7.00000	−	12.1244i	−0.304348	−	0.527146i
$530$		0			0
$531$		0			0
$532$	−1.73205	−	2.00000i	−0.0750939	−	0.0867110i
$533$			15.0000i			0.649722i
$534$	−6.00000	+	10.3923i	−0.259645	+	0.449719i
$535$		0			0
$536$	2.00000	+	3.46410i	0.0863868	+	0.149626i
$537$	5.19615	+	3.00000i	0.224231	+	0.129460i
$538$		−	12.0000i		−	0.517357i
$539$	19.5000	−	7.79423i	0.839924	−	0.335721i
$540$		0			0
$541$	−4.00000	+	6.92820i	−0.171973	+	0.297867i	−0.939110	−	0.343617i	$-0.888348\pi$
$541$	−4.00000	+	6.92820i	−0.171973	+	0.297867i	0.767136	+	0.641484i	$0.221681\pi$
$542$	13.8564	−	8.00000i	0.595184	−	0.343629i
$543$	−3.46410	+	2.00000i	−0.148659	+	0.0858282i
$544$	3.00000	−	5.19615i	0.128624	−	0.222783i
$545$		0			0
$546$	20.0000	−	17.3205i	0.855921	−	0.741249i
$547$			28.0000i			1.19719i	0.801050	+	0.598597i	$0.204275\pi$
$547$			28.0000i			1.19719i	−0.801050	+	0.598597i	$0.795725\pi$
$548$	−10.3923	−	6.00000i	−0.443937	−	0.256307i
$549$	−2.00000	−	3.46410i	−0.0853579	−	0.147844i
$550$		0			0
$551$	−3.00000	+	5.19615i	−0.127804	+	0.221364i
$552$			6.00000i			0.255377i
$553$	−25.9808	+	5.00000i	−1.10481	+	0.212622i
$554$	−2.00000			−0.0849719
$555$		0			0
$556$	2.00000	+	3.46410i	0.0848189	+	0.146911i
$557$	23.3827	−	13.5000i	0.990756	−	0.572013i	0.0852559	−	0.996359i	$-0.472829\pi$
$557$	23.3827	−	13.5000i	0.990756	−	0.572013i	0.905500	+	0.424346i	$0.139496\pi$
$558$	3.46410	+	2.00000i	0.146647	+	0.0846668i
$559$	50.0000			2.11477
$560$		0			0
$561$	−36.0000			−1.51992
$562$	−2.59808	−	1.50000i	−0.109593	−	0.0632737i
$563$	−15.5885	+	9.00000i	−0.656975	+	0.379305i	−0.791123	−	0.611656i	$-0.790503\pi$
$563$	−15.5885	+	9.00000i	−0.656975	+	0.379305i	0.134148	+	0.990961i	$0.457170\pi$
$564$	−3.00000	−	5.19615i	−0.126323	−	0.218797i
$565$		0			0
$566$	26.0000			1.09286
$567$	−9.52628	+	27.5000i	−0.400066	+	1.15489i
$568$			12.0000i			0.503509i
$569$	−1.50000	+	2.59808i	−0.0628833	+	0.108917i	−0.895753	−	0.444552i	$-0.853363\pi$
$569$	−1.50000	+	2.59808i	−0.0628833	+	0.108917i	0.832870	+	0.553469i	$0.186696\pi$
$570$		0			0
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	0.577301	−	0.816532i	$-0.304106\pi$
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	−0.995788	+	0.0916910i	$0.970773\pi$
$572$	12.9904	+	7.50000i	0.543155	+	0.313591i
$573$		−	24.0000i		−	1.00261i
$574$	1.50000	+	7.79423i	0.0626088	+	0.325325i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−17.3205	+	10.0000i	−0.721062	+	0.416305i	−0.815144	−	0.579259i	$-0.803342\pi$
$577$	−17.3205	+	10.0000i	−0.721062	+	0.416305i	0.0940813	+	0.995565i	$0.470009\pi$
$578$	16.4545	−	9.50000i	0.684416	−	0.395148i
$579$	4.00000	−	6.92820i	0.166234	−	0.287926i
$580$		0			0
$581$	24.0000	−	20.7846i	0.995688	−	0.862291i
$582$			28.0000i			1.16064i
$583$	−7.79423	−	4.50000i	−0.322804	−	0.186371i
$584$	−2.00000	−	3.46410i	−0.0827606	−	0.143346i
$585$		0			0
$586$	13.5000	−	23.3827i	0.557680	−	0.965930i
$587$		−	12.0000i		−	0.495293i	−0.968850	−	0.247647i	$-0.920343\pi$
$587$		−	12.0000i		−	0.495293i	0.968850	−	0.247647i	$-0.0796572\pi$
$588$	8.66025	−	11.0000i	0.357143	−	0.453632i
$589$	−4.00000			−0.164817
$590$		0			0
$591$	−3.00000	−	5.19615i	−0.123404	−	0.213741i
$592$	−9.52628	+	5.50000i	−0.391528	+	0.226049i
$593$	31.1769	+	18.0000i	1.28028	+	0.739171i	0.976900	−	0.213697i	$-0.0685507\pi$
$593$	31.1769	+	18.0000i	1.28028	+	0.739171i	0.303383	+	0.952869i	$0.401884\pi$
$594$	−12.0000			−0.492366
$595$		0			0
$596$	18.0000			0.737309
$597$	6.92820	+	4.00000i	0.283552	+	0.163709i
$598$	12.9904	−	7.50000i	0.531216	−	0.306698i
$599$	21.0000	+	36.3731i	0.858037	+	1.48616i	0.873799	+	0.486287i	$0.161649\pi$
$599$	21.0000	+	36.3731i	0.858037	+	1.48616i	−0.0157622	+	0.999876i	$0.505017\pi$
$600$		0			0
$601$	2.00000			0.0815817			0.0407909	−	0.999168i	$-0.487012\pi$
$601$	2.00000			0.0815817			0.0407909	+	0.999168i	$0.487012\pi$
$602$	25.9808	−	5.00000i	1.05890	−	0.203785i
$603$		−	4.00000i		−	0.162893i
$604$	7.00000	−	12.1244i	0.284826	−	0.493333i
$605$		0			0
$606$	−12.0000	−	20.7846i	−0.487467	−	0.844317i
$607$	−16.4545	−	9.50000i	−0.667867	−	0.385593i	0.127401	−	0.991851i	$-0.459336\pi$
$607$	−16.4545	−	9.50000i	−0.667867	−	0.385593i	−0.795268	+	0.606258i	$0.792670\pi$
$608$		−	1.00000i		−	0.0405554i
$609$	−30.0000	−	10.3923i	−1.21566	−	0.421117i
$610$		0			0
$611$	−7.50000	+	12.9904i	−0.303418	+	0.525535i
$612$	−5.19615	+	3.00000i	−0.210042	+	0.121268i
$613$	40.7032	−	23.5000i	1.64399	−	0.949156i	0.664590	−	0.747208i	$-0.268606\pi$
$613$	40.7032	−	23.5000i	1.64399	−	0.949156i	0.979396	−	0.201948i	$-0.0647272\pi$
$614$	1.00000	−	1.73205i	0.0403567	−	0.0698999i
$615$		0			0
$616$	7.50000	+	2.59808i	0.302184	+	0.104679i
$617$			6.00000i			0.241551i	0.992680	+	0.120775i	$0.0385381\pi$
$617$			6.00000i			0.241551i	−0.992680	+	0.120775i	$0.961462\pi$
$618$	−6.92820	−	4.00000i	−0.278693	−	0.160904i
$619$	−0.500000	−	0.866025i	−0.0200967	−	0.0348085i	0.855802	−	0.517303i	$-0.173064\pi$
$619$	−0.500000	−	0.866025i	−0.0200967	−	0.0348085i	−0.875899	+	0.482495i	$0.839731\pi$
$620$		0			0
$621$	−6.00000	+	10.3923i	−0.240772	+	0.417029i
$622$		−	12.0000i		−	0.481156i
$623$	15.5885	−	3.00000i	0.624538	−	0.120192i
$624$	10.0000			0.400320
$625$		0			0
$626$	−4.00000	−	6.92820i	−0.159872	−	0.276907i
$627$	−5.19615	+	3.00000i	−0.207514	+	0.119808i
$628$	−4.33013	−	2.50000i	−0.172791	−	0.0997609i
$629$	−66.0000			−2.63159
$630$		0			0
$631$	32.0000			1.27390			0.636950	−	0.770905i	$-0.280196\pi$
$631$	32.0000			1.27390			0.636950	+	0.770905i	$0.280196\pi$
$632$	−8.66025	−	5.00000i	−0.344486	−	0.198889i
$633$	1.73205	−	1.00000i	0.0688428	−	0.0397464i
$634$	9.00000	+	15.5885i	0.357436	+	0.619097i
$635$		0			0
$636$	−6.00000			−0.237915
$637$	−34.6410	−	5.00000i	−1.37253	−	0.198107i
$638$		−	18.0000i		−	0.712627i
$639$	6.00000	−	10.3923i	0.237356	−	0.411113i
$640$		0			0
$641$	22.5000	+	38.9711i	0.888697	+	1.53927i	0.841417	+	0.540386i	$0.181722\pi$
$641$	22.5000	+	38.9711i	0.888697	+	1.53927i	0.0472793	+	0.998882i	$0.484945\pi$
$642$	20.7846	+	12.0000i	0.820303	+	0.473602i
$643$			38.0000i			1.49857i	0.662246	+	0.749287i	$0.269604\pi$
$643$			38.0000i			1.49857i	−0.662246	+	0.749287i	$0.730396\pi$
$644$	6.00000	−	5.19615i	0.236433	−	0.204757i
$645$		0			0
$646$	3.00000	−	5.19615i	0.118033	−	0.204440i
$647$	18.1865	−	10.5000i	0.714986	−	0.412798i	−0.0979182	−	0.995194i	$-0.531218\pi$
$647$	18.1865	−	10.5000i	0.714986	−	0.412798i	0.812905	+	0.582397i	$0.197885\pi$
$648$	−9.52628	+	5.50000i	−0.374228	+	0.216060i
$649$		0			0
$650$		0			0
$651$	−4.00000	−	20.7846i	−0.156772	−	0.814613i
$652$			4.00000i			0.156652i
$653$	−18.1865	−	10.5000i	−0.711694	−	0.410897i	0.0999939	−	0.994988i	$-0.468118\pi$
$653$	−18.1865	−	10.5000i	−0.711694	−	0.410897i	−0.811688	+	0.584091i	$0.801451\pi$
$654$	4.00000	+	6.92820i	0.156412	+	0.270914i
$655$		0			0
$656$	−1.50000	+	2.59808i	−0.0585652	+	0.101438i
$657$			4.00000i			0.156055i
$658$	−2.59808	+	7.50000i	−0.101284	+	0.292380i
$659$	−24.0000			−0.934907			−0.467454	−	0.884018i	$-0.654829\pi$
$659$	−24.0000			−0.934907			−0.467454	+	0.884018i	$0.654829\pi$
$660$		0			0
$661$	−22.0000	−	38.1051i	−0.855701	−	1.48212i	−0.875993	−	0.482323i	$-0.839793\pi$
$661$	−22.0000	−	38.1051i	−0.855701	−	1.48212i	0.0202925	−	0.999794i	$-0.493540\pi$
$662$	6.06218	−	3.50000i	0.235613	−	0.136031i
$663$	51.9615	+	30.0000i	2.01802	+	1.16510i
$664$	12.0000			0.465690
$665$		0			0
$666$	11.0000			0.426241
$667$	−15.5885	−	9.00000i	−0.603587	−	0.348481i
$668$	7.79423	−	4.50000i	0.301568	−	0.174110i
$669$	−8.00000	−	13.8564i	−0.309298	−	0.535720i
$670$		0			0
$671$	−12.0000			−0.463255
$672$	5.19615	−	1.00000i	0.200446	−	0.0385758i
$673$		−	34.0000i		−	1.31060i	−0.755367	−	0.655302i	$-0.772541\pi$
$673$		−	34.0000i		−	1.31060i	0.755367	−	0.655302i	$-0.227459\pi$
$674$	7.00000	−	12.1244i	0.269630	−	0.467013i
$675$		0			0
$676$	−6.00000	−	10.3923i	−0.230769	−	0.399704i
$677$	−2.59808	−	1.50000i	−0.0998522	−	0.0576497i	0.449242	−	0.893410i	$-0.351694\pi$
$677$	−2.59808	−	1.50000i	−0.0998522	−	0.0576497i	−0.549095	+	0.835760i	$0.685027\pi$
$678$		−	24.0000i		−	0.921714i
$679$	28.0000	−	24.2487i	1.07454	−	0.930580i
$680$		0			0
$681$	−24.0000	+	41.5692i	−0.919682	+	1.59294i
$682$	10.3923	−	6.00000i	0.397942	−	0.229752i
$683$	−10.3923	+	6.00000i	−0.397650	+	0.229584i	−0.685470	−	0.728101i	$-0.740403\pi$
$683$	−10.3923	+	6.00000i	−0.397650	+	0.229584i	0.287819	+	0.957685i	$0.407070\pi$
$684$	−0.500000	+	0.866025i	−0.0191180	+	0.0331133i
$685$		0			0
$686$	−18.5000	+	0.866025i	−0.706333	+	0.0330650i
$687$		−	56.0000i		−	2.13653i
$688$	8.66025	+	5.00000i	0.330169	+	0.190623i
$689$	7.50000	+	12.9904i	0.285727	+	0.494894i
$690$		0			0
$691$	−16.0000	+	27.7128i	−0.608669	+	1.05425i	0.382791	+	0.923835i	$0.374963\pi$
$691$	−16.0000	+	27.7128i	−0.608669	+	1.05425i	−0.991460	+	0.130410i	$0.958371\pi$
$692$		−	3.00000i		−	0.114043i
$693$	−5.19615	−	6.00000i	−0.197386	−	0.227921i
$694$	−24.0000			−0.911028
$695$		0			0
$696$	−6.00000	−	10.3923i	−0.227429	−	0.393919i
$697$	−15.5885	+	9.00000i	−0.590455	+	0.340899i
$698$	8.66025	+	5.00000i	0.327795	+	0.189253i
$699$	−12.0000			−0.453882
$700$		0			0
$701$	18.0000			0.679851			0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000			0.679851			0.339925	+	0.940452i	$0.389598\pi$
$702$	17.3205	+	10.0000i	0.653720	+	0.377426i
$703$	−9.52628	+	5.50000i	−0.359290	+	0.207436i
$704$	1.50000	+	2.59808i	0.0565334	+	0.0979187i
$705$		0			0
$706$	12.0000			0.451626
$707$	−10.3923	+	30.0000i	−0.390843	+	1.12827i
$708$		0			0
$709$	7.00000	−	12.1244i	0.262891	−	0.455340i	−0.704118	−	0.710083i	$-0.748658\pi$
$709$	7.00000	−	12.1244i	0.262891	−	0.455340i	0.967009	+	0.254743i	$0.0819909\pi$
$710$		0			0
$711$	5.00000	+	8.66025i	0.187515	+	0.324785i
$712$	5.19615	+	3.00000i	0.194734	+	0.112430i
$713$		−	12.0000i		−	0.449404i
$714$	30.0000	+	10.3923i	1.12272	+	0.388922i
$715$		0			0
$716$	1.50000	−	2.59808i	0.0560576	−	0.0970947i
$717$	10.3923	−	6.00000i	0.388108	−	0.224074i
$718$	5.19615	−	3.00000i	0.193919	−	0.111959i
$719$	−18.0000	+	31.1769i	−0.671287	+	1.16270i	0.306253	+	0.951950i	$0.400925\pi$
$719$	−18.0000	+	31.1769i	−0.671287	+	1.16270i	−0.977539	+	0.210752i	$0.932409\pi$
$720$		0			0
$721$	2.00000	+	10.3923i	0.0744839	+	0.387030i
$722$			18.0000i			0.669891i
$723$	−43.3013	−	25.0000i	−1.61039	−	0.929760i
$724$	1.00000	+	1.73205i	0.0371647	+	0.0643712i
$725$		0			0
$726$	−2.00000	+	3.46410i	−0.0742270	+	0.128565i
$727$		−	29.0000i		−	1.07555i	−0.843088	−	0.537775i	$-0.819265\pi$
$727$		−	29.0000i		−	1.07555i	0.843088	−	0.537775i	$-0.180735\pi$
$728$	−8.66025	−	10.0000i	−0.320970	−	0.370625i
$729$	−13.0000			−0.481481
$730$		0			0
$731$	30.0000	+	51.9615i	1.10959	+	1.92187i
$732$	−6.92820	+	4.00000i	−0.256074	+	0.147844i
$733$	−40.7032	−	23.5000i	−1.50341	−	0.867992i	−0.999992	−	0.00394730i	$-0.998744\pi$
$733$	−40.7032	−	23.5000i	−1.50341	−	0.867992i	−0.503415	−	0.864045i	$-0.667923\pi$
$734$	1.00000			0.0369107
$735$		0			0
$736$	3.00000			0.110581
$737$	−10.3923	−	6.00000i	−0.382805	−	0.221013i
$738$	2.59808	−	1.50000i	0.0956365	−	0.0552158i
$739$	−18.5000	−	32.0429i	−0.680534	−	1.17872i	−0.974818	−	0.223001i	$-0.928415\pi$
$739$	−18.5000	−	32.0429i	−0.680534	−	1.17872i	0.294285	−	0.955718i	$-0.404919\pi$
$740$		0			0
$741$	10.0000			0.367359
$742$	5.19615	+	6.00000i	0.190757	+	0.220267i
$743$			9.00000i			0.330178i	0.986279	+	0.165089i	$0.0527911\pi$
$743$			9.00000i			0.330178i	−0.986279	+	0.165089i	$0.947209\pi$
$744$	4.00000	−	6.92820i	0.146647	−	0.254000i
$745$		0			0
$746$	17.0000	+	29.4449i	0.622414	+	1.07805i
$747$	−10.3923	−	6.00000i	−0.380235	−	0.219529i
$748$			18.0000i			0.658145i
$749$	−6.00000	−	31.1769i	−0.219235	−	1.13918i
$750$		0			0
$751$	−13.0000	+	22.5167i	−0.474377	+	0.821645i	−0.999570	−	0.0293387i	$-0.990660\pi$
$751$	−13.0000	+	22.5167i	−0.474377	+	0.821645i	0.525193	+	0.850983i	$0.323993\pi$
$752$	−2.59808	+	1.50000i	−0.0947421	+	0.0546994i
$753$	25.9808	−	15.0000i	0.946792	−	0.546630i
$754$	−15.0000	+	25.9808i	−0.546268	+	0.946164i
$755$		0			0
$756$	10.0000	+	3.46410i	0.363696	+	0.125988i
$757$		−	26.0000i		−	0.944986i	−0.881334	−	0.472493i	$-0.843354\pi$
$757$		−	26.0000i		−	0.944986i	0.881334	−	0.472493i	$-0.156646\pi$
$758$	21.6506	+	12.5000i	0.786386	+	0.454020i
$759$	−9.00000	−	15.5885i	−0.326679	−	0.565825i
$760$		0			0
$761$	25.5000	−	44.1673i	0.924374	−	1.60106i	0.131810	−	0.991275i	$-0.457921\pi$
$761$	25.5000	−	44.1673i	0.924374	−	1.60106i	0.792564	−	0.609788i	$-0.208745\pi$
$762$		−	38.0000i		−	1.37659i
$763$	3.46410	−	10.0000i	0.125409	−	0.362024i
$764$	−12.0000			−0.434145
$765$		0			0
$766$	−7.50000	−	12.9904i	−0.270986	−	0.469362i
$767$		0			0
$768$	1.73205	+	1.00000i	0.0625000	+	0.0360844i
$769$	49.0000			1.76699			0.883493	−	0.468445i	$-0.155186\pi$
$769$	49.0000			1.76699			0.883493	+	0.468445i	$0.155186\pi$
$770$		0			0
$771$	24.0000			0.864339
$772$	−3.46410	−	2.00000i	−0.124676	−	0.0719816i
$773$	33.7750	−	19.5000i	1.21480	−	0.701366i	0.251000	−	0.967987i	$-0.419240\pi$
$773$	33.7750	−	19.5000i	1.21480	−	0.701366i	0.963802	+	0.266621i	$0.0859071\pi$
$774$	−5.00000	−	8.66025i	−0.179721	−	0.311286i
$775$		0			0
$776$	14.0000			0.502571
$777$	−38.1051	−	44.0000i	−1.36701	−	1.57849i
$778$		−	24.0000i		−	0.860442i
$779$	−1.50000	+	2.59808i	−0.0537431	+	0.0930857i
$780$		0			0
$781$	−18.0000	−	31.1769i	−0.644091	−	1.11560i
$782$	15.5885	+	9.00000i	0.557442	+	0.321839i
$783$		−	24.0000i		−	0.857690i
$784$	−5.50000	−	4.33013i	−0.196429	−	0.154647i
$785$		0			0
$786$	3.00000	−	5.19615i	0.107006	−	0.185341i
$787$	29.4449	−	17.0000i	1.04960	−	0.605985i	0.127060	−	0.991895i	$-0.459446\pi$
$787$	29.4449	−	17.0000i	1.04960	−	0.605985i	0.922536	+	0.385911i	$0.126113\pi$
$788$	−2.59808	+	1.50000i	−0.0925526	+	0.0534353i
$789$		0			0
$790$		0			0
$791$	−24.0000	+	20.7846i	−0.853342	+	0.739016i
$792$		−	3.00000i		−	0.106600i
$793$	17.3205	+	10.0000i	0.615069	+	0.355110i
$794$	1.00000	+	1.73205i	0.0354887	+	0.0614682i
$795$		0			0
$796$	2.00000	−	3.46410i	0.0708881	−	0.122782i
$797$			30.0000i			1.06265i	0.847167	+	0.531327i	$0.178307\pi$
$797$			30.0000i			1.06265i	−0.847167	+	0.531327i	$0.821693\pi$
$798$	5.19615	−	1.00000i	0.183942	−	0.0353996i
$799$	−18.0000			−0.636794
$800$		0			0
$801$	−3.00000	−	5.19615i	−0.106000	−	0.183597i
$802$	−18.1865	+	10.5000i	−0.642189	+	0.370768i
$803$	10.3923	+	6.00000i	0.366736	+	0.211735i
$804$	−8.00000			−0.282138
$805$		0			0
$806$	−20.0000			−0.704470
$807$	20.7846	+	12.0000i	0.731653	+	0.422420i
$808$	−10.3923	+	6.00000i	−0.365600	+	0.211079i
$809$	19.5000	+	33.7750i	0.685583	+	1.18747i	0.973253	+	0.229736i	$0.0737862\pi$
$809$	19.5000	+	33.7750i	0.685583	+	1.18747i	−0.287670	+	0.957730i	$0.592880\pi$
$810$		0			0
$811$	47.0000			1.65039			0.825197	−	0.564846i	$-0.191064\pi$
$811$	47.0000			1.65039			0.825197	+	0.564846i	$0.191064\pi$
$812$	−5.19615	+	15.0000i	−0.182349	+	0.526397i
$813$			32.0000i			1.12229i
$814$	16.5000	−	28.5788i	0.578325	−	1.00169i
$815$		0			0
$816$	6.00000	+	10.3923i	0.210042	+	0.363803i
$817$	8.66025	+	5.00000i	0.302984	+	0.174928i
$818$		−	22.0000i		−	0.769212i
$819$	2.50000	+	12.9904i	0.0873571	+	0.453921i
$820$		0			0
$821$	9.00000	−	15.5885i	0.314102	−	0.544041i	−0.665144	−	0.746715i	$-0.731630\pi$
$821$	9.00000	−	15.5885i	0.314102	−	0.544041i	0.979246	+	0.202674i	$0.0649632\pi$
$822$	20.7846	−	12.0000i	0.724947	−	0.418548i
$823$	38.1051	−	22.0000i	1.32826	−	0.766872i	0.343230	−	0.939251i	$-0.388479\pi$
$823$	38.1051	−	22.0000i	1.32826	−	0.766872i	0.985031	+	0.172379i	$0.0551455\pi$
$824$	−2.00000	+	3.46410i	−0.0696733	+	0.120678i
$825$		0			0
$826$		0			0
$827$			54.0000i			1.87776i	0.344239	+	0.938882i	$0.388137\pi$
$827$			54.0000i			1.87776i	−0.344239	+	0.938882i	$0.611863\pi$
$828$	−2.59808	−	1.50000i	−0.0902894	−	0.0521286i
$829$	7.00000	+	12.1244i	0.243120	+	0.421096i	0.961601	−	0.274450i	$-0.0884958\pi$
$829$	7.00000	+	12.1244i	0.243120	+	0.421096i	−0.718481	+	0.695546i	$0.755162\pi$
$830$		0			0
$831$	2.00000	−	3.46410i	0.0693792	−	0.120168i
$832$		−	5.00000i		−	0.173344i
$833$	−15.5885	−	39.0000i	−0.540108	−	1.35127i
$834$	−8.00000			−0.277017
$835$		0			0
$836$	1.50000	+	2.59808i	0.0518786	+	0.0898563i
$837$	13.8564	−	8.00000i	0.478947	−	0.276520i
$838$	−12.9904	−	7.50000i	−0.448745	−	0.259083i
$839$	6.00000			0.207143			0.103572	−	0.994622i	$-0.466973\pi$
$839$	6.00000			0.207143			0.103572	+	0.994622i	$0.466973\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$	−29.4449	−	17.0000i	−1.01474	−	0.585859i
$843$	5.19615	−	3.00000i	0.178965	−	0.103325i
$844$	−0.500000	−	0.866025i	−0.0172107	−	0.0298098i
$845$		0			0
$846$	3.00000			0.103142
$847$	5.19615	−	1.00000i	0.178542	−	0.0343604i
$848$			3.00000i			0.103020i
$849$	−26.0000	+	45.0333i	−0.892318	+	1.54554i
$850$		0			0
$851$	−16.5000	−	28.5788i	−0.565613	−	0.979670i
$852$	−20.7846	−	12.0000i	−0.712069	−	0.411113i
$853$		−	1.00000i		−	0.0342393i	−0.999853	−	0.0171197i	$-0.994550\pi$
$853$		−	1.00000i		−	0.0342393i	0.999853	−	0.0171197i	$-0.00544963\pi$
$854$	10.0000	+	3.46410i	0.342193	+	0.118539i
$855$		0			0
$856$	6.00000	−	10.3923i	0.205076	−	0.355202i
$857$	15.5885	−	9.00000i	0.532492	−	0.307434i	−0.209539	−	0.977800i	$-0.567196\pi$
$857$	15.5885	−	9.00000i	0.532492	−	0.307434i	0.742030	+	0.670366i	$0.233863\pi$
$858$	−25.9808	+	15.0000i	−0.886969	+	0.512092i
$859$	16.0000	−	27.7128i	0.545913	−	0.945549i	−0.452636	−	0.891695i	$-0.649516\pi$
$859$	16.0000	−	27.7128i	0.545913	−	0.945549i	0.998549	−	0.0538535i	$-0.0171504\pi$
$860$		0			0
$861$	−15.0000	−	5.19615i	−0.511199	−	0.177084i
$862$		0			0
$863$	−33.7750	−	19.5000i	−1.14971	−	0.663788i	−0.200897	−	0.979612i	$-0.564385\pi$
$863$	−33.7750	−	19.5000i	−1.14971	−	0.663788i	−0.948818	+	0.315825i	$0.897719\pi$
$864$	2.00000	+	3.46410i	0.0680414	+	0.117851i
$865$		0			0
$866$	8.00000	−	13.8564i	0.271851	−	0.470860i
$867$			38.0000i			1.29055i
$868$	−10.3923	+	2.00000i	−0.352738	+	0.0678844i
$869$	30.0000			1.01768
$870$		0			0
$871$	10.0000	+	17.3205i	0.338837	+	0.586883i
$872$	3.46410	−	2.00000i	0.117309	−	0.0677285i
$873$	−12.1244	−	7.00000i	−0.410347	−	0.236914i
$874$	3.00000			0.101477
$875$		0			0
$876$	8.00000			0.270295
$877$	−6.06218	−	3.50000i	−0.204705	−	0.118187i	0.394143	−	0.919049i	$-0.371041\pi$
$877$	−6.06218	−	3.50000i	−0.204705	−	0.118187i	−0.598848	+	0.800862i	$0.704375\pi$
$878$	−8.66025	+	5.00000i	−0.292269	+	0.168742i
$879$	27.0000	+	46.7654i	0.910687	+	1.57736i
$880$		0			0
$881$	33.0000			1.11180			0.555899	−	0.831250i	$-0.312374\pi$
$881$	33.0000			1.11180			0.555899	+	0.831250i	$0.312374\pi$
$882$	2.59808	+	6.50000i	0.0874818	+	0.218866i
$883$			8.00000i			0.269221i	0.990899	+	0.134611i	$0.0429784\pi$
$883$			8.00000i			0.269221i	−0.990899	+	0.134611i	$0.957022\pi$
$884$	15.0000	−	25.9808i	0.504505	−	0.873828i
$885$		0			0
$886$	12.0000	+	20.7846i	0.403148	+	0.698273i
$887$	20.7846	+	12.0000i	0.697879	+	0.402921i	0.806557	−	0.591156i	$-0.201328\pi$
$887$	20.7846	+	12.0000i	0.697879	+	0.402921i	−0.108678	+	0.994077i	$0.534662\pi$
$888$		−	22.0000i		−	0.738272i
$889$	−38.0000	+	32.9090i	−1.27448	+	1.10373i
$890$		0			0
$891$	16.5000	−	28.5788i	0.552771	−	0.957427i
$892$	−6.92820	+	4.00000i	−0.231973	+	0.133930i
$893$	−2.59808	+	1.50000i	−0.0869413	+	0.0501956i
$894$	−18.0000	+	31.1769i	−0.602010	+	1.04271i
$895$		0			0
$896$	−0.500000	−	2.59808i	−0.0167038	−	0.0867956i
$897$			30.0000i			1.00167i
$898$	2.59808	+	1.50000i	0.0866989	+	0.0500556i
$899$	12.0000	+	20.7846i	0.400222	+	0.693206i
$900$		0			0
$901$	−9.00000	+	15.5885i	−0.299833	+	0.519327i
$902$		−	9.00000i		−	0.299667i
$903$	−17.3205	+	50.0000i	−0.576390	+	1.66390i
$904$	−12.0000			−0.399114
$905$		0			0
$906$	14.0000	+	24.2487i	0.465119	+	0.805609i
$907$	8.66025	−	5.00000i	0.287559	−	0.166022i	−0.349281	−	0.937018i	$-0.613574\pi$
$907$	8.66025	−	5.00000i	0.287559	−	0.166022i	0.636841	+	0.770996i	$0.280241\pi$
$908$	20.7846	+	12.0000i	0.689761	+	0.398234i
$909$	12.0000			0.398015
$910$		0			0
$911$	−30.0000			−0.993944			−0.496972	−	0.867766i	$-0.665555\pi$
$911$	−30.0000			−0.993944			−0.496972	+	0.867766i	$0.665555\pi$
$912$	1.73205	+	1.00000i	0.0573539	+	0.0331133i
$913$	−31.1769	+	18.0000i	−1.03181	+	0.595713i
$914$	−11.0000	−	19.0526i	−0.363848	−	0.630203i
$915$		0			0
$916$	−28.0000			−0.925146
$917$	−7.79423	+	1.50000i	−0.257388	+	0.0495344i
$918$			24.0000i			0.792118i
$919$	19.0000	−	32.9090i	0.626752	−	1.08557i	−0.361447	−	0.932393i	$-0.617717\pi$
$919$	19.0000	−	32.9090i	0.626752	−	1.08557i	0.988199	−	0.153174i	$-0.0489495\pi$
$920$		0			0
$921$	2.00000	+	3.46410i	0.0659022	+	0.114146i
$922$	5.19615	+	3.00000i	0.171126	+	0.0987997i
$923$			60.0000i			1.97492i
$924$	−12.0000	+	10.3923i	−0.394771	+	0.341882i
$925$		0			0
$926$	9.50000	−	16.4545i	0.312189	−	0.540728i
$927$	3.46410	−	2.00000i	0.113776	−	0.0656886i
$928$	−5.19615	+	3.00000i	−0.170572	+	0.0984798i
$929$	16.5000	−	28.5788i	0.541347	−	0.937641i	−0.457480	−	0.889220i	$-0.651248\pi$
$929$	16.5000	−	28.5788i	0.541347	−	0.937641i	0.998827	−	0.0484211i	$-0.0154190\pi$
$930$		0			0
$931$	−5.50000	−	4.33013i	−0.180255	−	0.141914i
$932$			6.00000i			0.196537i
$933$	20.7846	+	12.0000i	0.680458	+	0.392862i
$934$	−9.00000	−	15.5885i	−0.294489	−	0.510070i
$935$		0			0
$936$	−2.50000	+	4.33013i	−0.0817151	+	0.141535i
$937$		−	2.00000i		−	0.0653372i	−0.999466	−	0.0326686i	$-0.989599\pi$
$937$		−	2.00000i		−	0.0653372i	0.999466	−	0.0326686i	$-0.0104006\pi$
$938$	6.92820	+	8.00000i	0.226214	+	0.261209i
$939$	16.0000			0.522140
$940$		0			0
$941$	−12.0000	−	20.7846i	−0.391189	−	0.677559i	0.601418	−	0.798935i	$-0.294603\pi$
$941$	−12.0000	−	20.7846i	−0.391189	−	0.677559i	−0.992607	+	0.121376i	$0.961269\pi$
$942$	8.66025	−	5.00000i	0.282166	−	0.162909i
$943$	−7.79423	−	4.50000i	−0.253815	−	0.146540i
$944$		0			0
$945$		0			0
$946$	−30.0000			−0.975384
$947$	25.9808	+	15.0000i	0.844261	+	0.487435i	0.858710	−	0.512461i	$-0.171266\pi$
$947$	25.9808	+	15.0000i	0.844261	+	0.487435i	−0.0144491	+	0.999896i	$0.504599\pi$
$948$	17.3205	−	10.0000i	0.562544	−	0.324785i
$949$	−10.0000	−	17.3205i	−0.324614	−	0.562247i
$950$		0			0
$951$	−36.0000			−1.16738
$952$	5.19615	−	15.0000i	0.168408	−	0.486153i
$953$		−	12.0000i		−	0.388718i	−0.980930	−	0.194359i	$-0.937737\pi$
$953$		−	12.0000i		−	0.388718i	0.980930	−	0.194359i	$-0.0622627\pi$
$954$	1.50000	−	2.59808i	0.0485643	−	0.0841158i
$955$		0			0
$956$	−3.00000	−	5.19615i	−0.0970269	−	0.168056i
$957$	31.1769	+	18.0000i	1.00781	+	0.581857i
$958$			24.0000i			0.775405i
$959$	−30.0000	−	10.3923i	−0.968751	−	0.335585i
$960$		0			0
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$	−47.6314	+	27.5000i	−1.53570	+	0.886636i
$963$	−10.3923	+	6.00000i	−0.334887	+	0.193347i
$964$	−12.5000	+	21.6506i	−0.402598	+	0.697320i
$965$		0			0
$966$	3.00000	+	15.5885i	0.0965234	+	0.501550i
$967$		−	32.0000i		−	1.02905i	−0.857475	−	0.514525i	$-0.827968\pi$
$967$		−	32.0000i		−	1.02905i	0.857475	−	0.514525i	$-0.172032\pi$
$968$	1.73205	+	1.00000i	0.0556702	+	0.0321412i
$969$	6.00000	+	10.3923i	0.192748	+	0.333849i
$970$		0			0
$971$	−13.5000	+	23.3827i	−0.433236	+	0.750386i	−0.997150	−	0.0754473i	$-0.975962\pi$
$971$	−13.5000	+	23.3827i	−0.433236	+	0.750386i	0.563914	+	0.825833i	$0.309295\pi$
$972$		−	10.0000i		−	0.320750i
$973$	6.92820	+	8.00000i	0.222108	+	0.256468i
$974$	16.0000			0.512673
$975$		0			0
$976$	2.00000	+	3.46410i	0.0640184	+	0.110883i
$977$	25.9808	−	15.0000i	0.831198	−	0.479893i	−0.0230645	−	0.999734i	$-0.507342\pi$
$977$	25.9808	−	15.0000i	0.831198	−	0.479893i	0.854263	+	0.519841i	$0.174009\pi$
$978$	−6.92820	−	4.00000i	−0.221540	−	0.127906i
$979$	−18.0000			−0.575282
$980$		0			0
$981$	−4.00000			−0.127710
$982$	−10.3923	−	6.00000i	−0.331632	−	0.191468i
$983$	49.3634	−	28.5000i	1.57445	−	0.909009i	0.578836	−	0.815444i	$-0.303507\pi$
$983$	49.3634	−	28.5000i	1.57445	−	0.909009i	0.995613	−	0.0935651i	$-0.0298263\pi$
$984$	−3.00000	−	5.19615i	−0.0956365	−	0.165647i
$985$		0			0
$986$	−36.0000			−1.14647
$987$	−10.3923	−	12.0000i	−0.330791	−	0.381964i
$988$		−	5.00000i		−	0.159071i
$989$	−15.0000	+	25.9808i	−0.476972	+	0.826140i
$990$		0			0
$991$	−10.0000	−	17.3205i	−0.317660	−	0.550204i	0.662339	−	0.749204i	$-0.269564\pi$
$991$	−10.0000	−	17.3205i	−0.317660	−	0.550204i	−0.979999	+	0.199000i	$0.936231\pi$
$992$	−3.46410	−	2.00000i	−0.109985	−	0.0635001i
$993$			14.0000i			0.444277i
$994$	6.00000	+	31.1769i	0.190308	+	0.988872i
$995$		0			0
$996$	−12.0000	+	20.7846i	−0.380235	+	0.658586i
$997$	−12.1244	+	7.00000i	−0.383982	+	0.221692i	−0.679549	−	0.733630i	$-0.737825\pi$
$997$	−12.1244	+	7.00000i	−0.383982	+	0.221692i	0.295567	+	0.955322i	$0.404491\pi$
$998$	−24.2487	+	14.0000i	−0.767580	+	0.443162i
$999$	22.0000	−	38.1051i	0.696049	−	1.20559i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.j.a.149.2		4
5.2	odd	4		70.2.e.b.51.1	yes	2
5.3	odd	4		350.2.e.h.51.1		2
5.4	even	2	inner	350.2.j.a.149.1		4
7.2	even	3		2450.2.c.f.99.1		2
7.4	even	3	inner	350.2.j.a.249.1		4
7.5	odd	6		2450.2.c.p.99.1		2
15.2	even	4		630.2.k.e.541.1		2
20.7	even	4		560.2.q.d.401.1		2
35.2	odd	12		490.2.a.g.1.1		1
35.4	even	6	inner	350.2.j.a.249.2		4
35.9	even	6		2450.2.c.f.99.2		2
35.12	even	12		490.2.a.j.1.1		1
35.17	even	12		490.2.e.a.361.1		2
35.18	odd	12		350.2.e.h.151.1		2
35.19	odd	6		2450.2.c.p.99.2		2
35.23	odd	12		2450.2.a.p.1.1		1
35.27	even	4		490.2.e.a.471.1		2
35.32	odd	12		70.2.e.b.11.1	✓	2
35.33	even	12		2450.2.a.f.1.1		1
105.2	even	12		4410.2.a.m.1.1		1
105.32	even	12		630.2.k.e.361.1		2
105.47	odd	12		4410.2.a.c.1.1		1
140.47	odd	12		3920.2.a.g.1.1		1
140.67	even	12		560.2.q.d.81.1		2
140.107	even	12		3920.2.a.be.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.e.b.11.1	✓	2	35.32	odd	12
70.2.e.b.51.1	yes	2	5.2	odd	4
350.2.e.h.51.1		2	5.3	odd	4
350.2.e.h.151.1		2	35.18	odd	12
350.2.j.a.149.1		4	5.4	even	2	inner
350.2.j.a.149.2		4	1.1	even	1	trivial
350.2.j.a.249.1		4	7.4	even	3	inner
350.2.j.a.249.2		4	35.4	even	6	inner
490.2.a.g.1.1		1	35.2	odd	12
490.2.a.j.1.1		1	35.12	even	12
490.2.e.a.361.1		2	35.17	even	12
490.2.e.a.471.1		2	35.27	even	4
560.2.q.d.81.1		2	140.67	even	12
560.2.q.d.401.1		2	20.7	even	4
630.2.k.e.361.1		2	105.32	even	12
630.2.k.e.541.1		2	15.2	even	4
2450.2.a.f.1.1		1	35.33	even	12
2450.2.a.p.1.1		1	35.23	odd	12
2450.2.c.f.99.1		2	7.2	even	3
2450.2.c.f.99.2		2	35.9	even	6
2450.2.c.p.99.1		2	7.5	odd	6
2450.2.c.p.99.2		2	35.19	odd	6
3920.2.a.g.1.1		1	140.47	odd	12
3920.2.a.be.1.1		1	140.107	even	12
4410.2.a.c.1.1		1	105.47	odd	12
4410.2.a.m.1.1		1	105.2	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-1.73205 + 1.00000i) q^{3} +(0.500000 + 0.866025i) q^{4} -2.00000 q^{6} +(1.73205 + 2.00000i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-1.73205 + 1.00000i) q^{3} +(0.500000 + 0.866025i) q^{4} -2.00000 q^{6} +(1.73205 + 2.00000i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.50000 - 2.59808i) q^{11} +(-1.73205 - 1.00000i) q^{12} +5.00000i q^{13} +(0.500000 + 2.59808i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-5.19615 + 3.00000i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-0.500000 + 0.866025i) q^{19} +(-5.00000 - 1.73205i) q^{21} -3.00000i q^{22} +(-2.59808 - 1.50000i) q^{23} +(-1.00000 - 1.73205i) q^{24} +(-2.50000 + 4.33013i) q^{26} -4.00000i q^{27} +(-0.866025 + 2.50000i) q^{28} +6.00000 q^{29} +(2.00000 + 3.46410i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(5.19615 + 3.00000i) q^{33} -6.00000 q^{34} +1.00000 q^{36} +(9.52628 + 5.50000i) q^{37} +(-0.866025 + 0.500000i) q^{38} +(-5.00000 - 8.66025i) q^{39} +3.00000 q^{41} +(-3.46410 - 4.00000i) q^{42} -10.0000i q^{43} +(1.50000 - 2.59808i) q^{44} +(-1.50000 - 2.59808i) q^{46} +(2.59808 + 1.50000i) q^{47} -2.00000i q^{48} +(-1.00000 + 6.92820i) q^{49} +(6.00000 - 10.3923i) q^{51} +(-4.33013 + 2.50000i) q^{52} +(2.59808 - 1.50000i) q^{53} +(2.00000 - 3.46410i) q^{54} +(-2.00000 + 1.73205i) q^{56} -2.00000i q^{57} +(5.19615 + 3.00000i) q^{58} +(2.00000 - 3.46410i) q^{61} +4.00000i q^{62} +(2.59808 - 0.500000i) q^{63} -1.00000 q^{64} +(3.00000 + 5.19615i) q^{66} +(3.46410 - 2.00000i) q^{67} +(-5.19615 - 3.00000i) q^{68} +6.00000 q^{69} +12.0000 q^{71} +(0.866025 + 0.500000i) q^{72} +(-3.46410 + 2.00000i) q^{73} +(5.50000 + 9.52628i) q^{74} -1.00000 q^{76} +(2.59808 - 7.50000i) q^{77} -10.0000i q^{78} +(-5.00000 + 8.66025i) q^{79} +(5.50000 + 9.52628i) q^{81} +(2.59808 + 1.50000i) q^{82} -12.0000i q^{83} +(-1.00000 - 5.19615i) q^{84} +(5.00000 - 8.66025i) q^{86} +(-10.3923 + 6.00000i) q^{87} +(2.59808 - 1.50000i) q^{88} +(3.00000 - 5.19615i) q^{89} +(-10.0000 + 8.66025i) q^{91} -3.00000i q^{92} +(-6.92820 - 4.00000i) q^{93} +(1.50000 + 2.59808i) q^{94} +(1.00000 - 1.73205i) q^{96} -14.0000i q^{97} +(-4.33013 + 5.50000i) q^{98} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} - 8 q^{6} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 - 8 * q^6 + 2 * q^9	\( 4 q + 2 q^{4} - 8 q^{6} + 2 q^{9} - 6 q^{11} + 2 q^{14} - 2 q^{16} - 2 q^{19} - 20 q^{21} - 4 q^{24} - 10 q^{26} + 24 q^{29} + 8 q^{31} - 24 q^{34} + 4 q^{36} - 20 q^{39} + 12 q^{41} + 6 q^{44} - 6 q^{46} - 4 q^{49} + 24 q^{51} + 8 q^{54} - 8 q^{56} + 8 q^{61} - 4 q^{64} + 12 q^{66} + 24 q^{69} + 48 q^{71} + 22 q^{74} - 4 q^{76} - 20 q^{79} + 22 q^{81} - 4 q^{84} + 20 q^{86} + 12 q^{89} - 40 q^{91} + 6 q^{94} + 4 q^{96} - 12 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 - 8 * q^6 + 2 * q^9 - 6 * q^11 + 2 * q^14 - 2 * q^16 - 2 * q^19 - 20 * q^21 - 4 * q^24 - 10 * q^26 + 24 * q^29 + 8 * q^31 - 24 * q^34 + 4 * q^36 - 20 * q^39 + 12 * q^41 + 6 * q^44 - 6 * q^46 - 4 * q^49 + 24 * q^51 + 8 * q^54 - 8 * q^56 + 8 * q^61 - 4 * q^64 + 12 * q^66 + 24 * q^69 + 48 * q^71 + 22 * q^74 - 4 * q^76 - 20 * q^79 + 22 * q^81 - 4 * q^84 + 20 * q^86 + 12 * q^89 - 40 * q^91 + 6 * q^94 + 4 * q^96 - 12 * q^99

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