LMFDB - Embedded newform 338.2.e.c.147.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [338,2,Mod(23,338)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(338, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("338.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 338 = 2 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	338.e (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:	$2.69894358832$
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 26)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			147.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	338.147
Dual form			338.2.e.c.23.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -3.00000i q^{5} +(-0.866025 + 0.500000i) q^{6} +(2.59808 - 1.50000i) q^{7} -1.00000i q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -3.00000i q^{5} +(-0.866025 + 0.500000i) q^{6} +(2.59808 - 1.50000i) q^{7} -1.00000i q^{8} +(1.00000 + 1.73205i) q^{9} +(-1.50000 + 2.59808i) q^{10} +1.00000 q^{12} -3.00000 q^{14} +(-2.59808 - 1.50000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} -2.00000i q^{18} +(-5.19615 + 3.00000i) q^{19} +(2.59808 - 1.50000i) q^{20} -3.00000i q^{21} +(3.00000 - 5.19615i) q^{23} +(-0.866025 - 0.500000i) q^{24} -4.00000 q^{25} +5.00000 q^{27} +(2.59808 + 1.50000i) q^{28} +(1.50000 + 2.59808i) q^{30} +(0.866025 - 0.500000i) q^{32} +3.00000i q^{34} +(-4.50000 - 7.79423i) q^{35} +(-1.00000 + 1.73205i) q^{36} +(-2.59808 - 1.50000i) q^{37} +6.00000 q^{38} -3.00000 q^{40} +(-1.50000 + 2.59808i) q^{42} +(0.500000 + 0.866025i) q^{43} +(5.19615 - 3.00000i) q^{45} +(-5.19615 + 3.00000i) q^{46} +3.00000i q^{47} +(0.500000 + 0.866025i) q^{48} +(1.00000 - 1.73205i) q^{49} +(3.46410 + 2.00000i) q^{50} -3.00000 q^{51} -6.00000 q^{53} +(-4.33013 - 2.50000i) q^{54} +(-1.50000 - 2.59808i) q^{56} +6.00000i q^{57} +(-5.19615 + 3.00000i) q^{59} -3.00000i q^{60} +(4.00000 + 6.92820i) q^{61} +(5.19615 + 3.00000i) q^{63} -1.00000 q^{64} +(10.3923 + 6.00000i) q^{67} +(1.50000 - 2.59808i) q^{68} +(-3.00000 - 5.19615i) q^{69} +9.00000i q^{70} +(12.9904 - 7.50000i) q^{71} +(1.73205 - 1.00000i) q^{72} +6.00000i q^{73} +(1.50000 + 2.59808i) q^{74} +(-2.00000 + 3.46410i) q^{75} +(-5.19615 - 3.00000i) q^{76} +10.0000 q^{79} +(2.59808 + 1.50000i) q^{80} +(-0.500000 + 0.866025i) q^{81} +6.00000i q^{83} +(2.59808 - 1.50000i) q^{84} +(-7.79423 + 4.50000i) q^{85} -1.00000i q^{86} +(5.19615 + 3.00000i) q^{89} -6.00000 q^{90} +6.00000 q^{92} +(1.50000 - 2.59808i) q^{94} +(9.00000 + 15.5885i) q^{95} -1.00000i q^{96} +(-10.3923 + 6.00000i) q^{97} +(-1.73205 + 1.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 2 q^{4} + 4 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 + 2 * q^4 + 4 * q^9	$ 4 q + 2 q^{3} + 2 q^{4} + 4 q^{9} - 6 q^{10} + 4 q^{12} - 12 q^{14} - 2 q^{16} - 6 q^{17} + 12 q^{23} - 16 q^{25} + 20 q^{27} + 6 q^{30} - 18 q^{35} - 4 q^{36} + 24 q^{38} - 12 q^{40} - 6 q^{42} + 2 q^{43} + 2 q^{48} + 4 q^{49} - 12 q^{51} - 24 q^{53} - 6 q^{56} + 16 q^{61} - 4 q^{64} + 6 q^{68} - 12 q^{69} + 6 q^{74} - 8 q^{75} + 40 q^{79} - 2 q^{81} - 24 q^{90} + 24 q^{92} + 6 q^{94} + 36 q^{95}+O(q^{100}) $ 4 * q + 2 * q^3 + 2 * q^4 + 4 * q^9 - 6 * q^10 + 4 * q^12 - 12 * q^14 - 2 * q^16 - 6 * q^17 + 12 * q^23 - 16 * q^25 + 20 * q^27 + 6 * q^30 - 18 * q^35 - 4 * q^36 + 24 * q^38 - 12 * q^40 - 6 * q^42 + 2 * q^43 + 2 * q^48 + 4 * q^49 - 12 * q^51 - 24 * q^53 - 6 * q^56 + 16 * q^61 - 4 * q^64 + 6 * q^68 - 12 * q^69 + 6 * q^74 - 8 * q^75 + 40 * q^79 - 2 * q^81 - 24 * q^90 + 24 * q^92 + 6 * q^94 + 36 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/338\mathbb{Z}\right)^\times$.

$n$	$171$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i	−0.684819	−	0.728714i	$-0.740119\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i	0.973494	+	0.228714i	$0.0734519\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		−	3.00000i		−	1.34164i	−0.741620	−	0.670820i	$-0.765942\pi$
$5$		−	3.00000i		−	1.34164i	0.741620	−	0.670820i	$-0.234058\pi$
$6$	−0.866025	+	0.500000i	−0.353553	+	0.204124i
$7$	2.59808	−	1.50000i	0.981981	−	0.566947i	0.0791130	−	0.996866i	$-0.474791\pi$
$7$	2.59808	−	1.50000i	0.981981	−	0.566947i	0.902867	+	0.429919i	$0.141458\pi$
$8$		−	1.00000i		−	0.353553i
$9$	1.00000	+	1.73205i	0.333333	+	0.577350i
$10$	−1.50000	+	2.59808i	−0.474342	+	0.821584i
$11$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$11$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$12$	1.00000			0.288675
$13$		0			0
$13$		0			0
$14$	−3.00000			−0.801784
$15$	−2.59808	−	1.50000i	−0.670820	−	0.387298i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	0.624780	−	0.780801i	$-0.285189\pi$
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	−0.988583	+	0.150675i	$0.951855\pi$
$18$		−	2.00000i		−	0.471405i
$19$	−5.19615	+	3.00000i	−1.19208	+	0.688247i	−0.958778	−	0.284157i	$-0.908286\pi$
$19$	−5.19615	+	3.00000i	−1.19208	+	0.688247i	−0.233301	+	0.972404i	$0.574953\pi$
$20$	2.59808	−	1.50000i	0.580948	−	0.335410i
$21$		−	3.00000i		−	0.654654i
$22$		0			0
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	−0.362892	−	0.931831i	$-0.618211\pi$
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	0.988436	−	0.151642i	$-0.0484560\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$	−4.00000			−0.800000
$26$		0			0
$27$	5.00000			0.962250
$28$	2.59808	+	1.50000i	0.490990	+	0.283473i
$29$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$29$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$30$	1.50000	+	2.59808i	0.273861	+	0.474342i
$31$		0			0		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$			3.00000i			0.514496i
$35$	−4.50000	−	7.79423i	−0.760639	−	1.31747i
$36$	−1.00000	+	1.73205i	−0.166667	+	0.288675i
$37$	−2.59808	−	1.50000i	−0.427121	−	0.246598i	0.270998	−	0.962580i	$-0.412646\pi$
$37$	−2.59808	−	1.50000i	−0.427121	−	0.246598i	−0.698119	+	0.715981i	$0.745980\pi$
$38$	6.00000			0.973329
$39$		0			0
$40$	−3.00000			−0.474342
$41$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$41$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$42$	−1.50000	+	2.59808i	−0.231455	+	0.400892i
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	0.901629	−	0.432511i	$-0.142372\pi$
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	−0.825380	+	0.564578i	$0.809039\pi$
$44$		0			0
$45$	5.19615	−	3.00000i	0.774597	−	0.447214i
$46$	−5.19615	+	3.00000i	−0.766131	+	0.442326i
$47$			3.00000i			0.437595i	0.975770	+	0.218797i	$0.0702134\pi$
$47$			3.00000i			0.437595i	−0.975770	+	0.218797i	$0.929787\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	1.00000	−	1.73205i	0.142857	−	0.247436i
$50$	3.46410	+	2.00000i	0.489898	+	0.282843i
$51$	−3.00000			−0.420084
$52$		0			0
$53$	−6.00000			−0.824163			−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000			−0.824163			−0.412082	+	0.911147i	$0.635198\pi$
$54$	−4.33013	−	2.50000i	−0.589256	−	0.340207i
$55$		0			0
$56$	−1.50000	−	2.59808i	−0.200446	−	0.347183i
$57$			6.00000i			0.794719i
$58$		0			0
$59$	−5.19615	+	3.00000i	−0.676481	+	0.390567i	−0.798528	−	0.601958i	$-0.794388\pi$
$59$	−5.19615	+	3.00000i	−0.676481	+	0.390567i	0.122047	+	0.992524i	$0.461054\pi$
$60$		−	3.00000i		−	0.387298i
$61$	4.00000	+	6.92820i	0.512148	+	0.887066i	0.999901	+	0.0140840i	$0.00448323\pi$
$61$	4.00000	+	6.92820i	0.512148	+	0.887066i	−0.487753	+	0.872982i	$0.662183\pi$
$62$		0			0
$63$	5.19615	+	3.00000i	0.654654	+	0.377964i
$64$	−1.00000			−0.125000
$65$		0			0
$66$		0			0
$67$	10.3923	+	6.00000i	1.26962	+	0.733017i	0.974916	−	0.222571i	$-0.0714450\pi$
$67$	10.3923	+	6.00000i	1.26962	+	0.733017i	0.294706	+	0.955588i	$0.404778\pi$
$68$	1.50000	−	2.59808i	0.181902	−	0.315063i
$69$	−3.00000	−	5.19615i	−0.361158	−	0.625543i
$70$			9.00000i			1.07571i
$71$	12.9904	−	7.50000i	1.54167	−	0.890086i	0.542941	−	0.839771i	$-0.317311\pi$
$71$	12.9904	−	7.50000i	1.54167	−	0.890086i	0.998733	−	0.0503155i	$-0.0160227\pi$
$72$	1.73205	−	1.00000i	0.204124	−	0.117851i
$73$			6.00000i			0.702247i	0.936329	+	0.351123i	$0.114200\pi$
$73$			6.00000i			0.702247i	−0.936329	+	0.351123i	$0.885800\pi$
$74$	1.50000	+	2.59808i	0.174371	+	0.302020i
$75$	−2.00000	+	3.46410i	−0.230940	+	0.400000i
$76$	−5.19615	−	3.00000i	−0.596040	−	0.344124i
$77$		0			0
$78$		0			0
$79$	10.0000			1.12509			0.562544	−	0.826767i	$-0.309823\pi$
$79$	10.0000			1.12509			0.562544	+	0.826767i	$0.309823\pi$
$80$	2.59808	+	1.50000i	0.290474	+	0.167705i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$			6.00000i			0.658586i	0.944228	+	0.329293i	$0.106810\pi$
$83$			6.00000i			0.658586i	−0.944228	+	0.329293i	$0.893190\pi$
$84$	2.59808	−	1.50000i	0.283473	−	0.163663i
$85$	−7.79423	+	4.50000i	−0.845403	+	0.488094i
$86$		−	1.00000i		−	0.107833i
$87$		0			0
$88$		0			0
$89$	5.19615	+	3.00000i	0.550791	+	0.317999i	0.749441	−	0.662071i	$-0.230322\pi$
$89$	5.19615	+	3.00000i	0.550791	+	0.317999i	−0.198650	+	0.980071i	$0.563656\pi$
$90$	−6.00000			−0.632456
$91$		0			0
$92$	6.00000			0.625543
$93$		0			0
$94$	1.50000	−	2.59808i	0.154713	−	0.267971i
$95$	9.00000	+	15.5885i	0.923381	+	1.59934i
$96$		−	1.00000i		−	0.102062i
$97$	−10.3923	+	6.00000i	−1.05518	+	0.609208i	−0.924095	−	0.382164i	$-0.875179\pi$
$97$	−10.3923	+	6.00000i	−1.05518	+	0.609208i	−0.131084	+	0.991371i	$0.541846\pi$
$98$	−1.73205	+	1.00000i	−0.174964	+	0.101015i
$99$		0			0
$100$	−2.00000	−	3.46410i	−0.200000	−	0.346410i
$101$	−6.00000	+	10.3923i	−0.597022	+	1.03407i	0.396236	+	0.918149i	$0.370316\pi$
$101$	−6.00000	+	10.3923i	−0.597022	+	1.03407i	−0.993258	+	0.115924i	$0.963017\pi$
$102$	2.59808	+	1.50000i	0.257248	+	0.148522i
$103$	14.0000			1.37946			0.689730	−	0.724066i	$-0.257729\pi$
$103$	14.0000			1.37946			0.689730	+	0.724066i	$0.257729\pi$
$104$		0			0
$105$	−9.00000			−0.878310
$106$	5.19615	+	3.00000i	0.504695	+	0.291386i
$107$	6.00000	−	10.3923i	0.580042	−	1.00466i	−0.415432	−	0.909624i	$-0.636370\pi$
$107$	6.00000	−	10.3923i	0.580042	−	1.00466i	0.995474	−	0.0950377i	$-0.0302972\pi$
$108$	2.50000	+	4.33013i	0.240563	+	0.416667i
$109$			9.00000i			0.862044i	0.902342	+	0.431022i	$0.141847\pi$
$109$			9.00000i			0.862044i	−0.902342	+	0.431022i	$0.858153\pi$
$110$		0			0
$111$	−2.59808	+	1.50000i	−0.246598	+	0.142374i
$112$			3.00000i			0.283473i
$113$	3.00000	+	5.19615i	0.282216	+	0.488813i	0.971930	−	0.235269i	$-0.0755971\pi$
$113$	3.00000	+	5.19615i	0.282216	+	0.488813i	−0.689714	+	0.724082i	$0.742264\pi$
$114$	3.00000	−	5.19615i	0.280976	−	0.486664i
$115$	−15.5885	−	9.00000i	−1.45363	−	0.839254i
$116$		0			0
$117$		0			0
$118$	6.00000			0.552345
$119$	−7.79423	−	4.50000i	−0.714496	−	0.412514i
$120$	−1.50000	+	2.59808i	−0.136931	+	0.237171i
$121$	−5.50000	−	9.52628i	−0.500000	−	0.866025i
$122$		−	8.00000i		−	0.724286i
$123$		0			0
$124$		0			0
$125$		−	3.00000i		−	0.268328i
$126$	−3.00000	−	5.19615i	−0.267261	−	0.462910i
$127$	1.00000	−	1.73205i	0.0887357	−	0.153695i	−0.818241	−	0.574875i	$-0.805051\pi$
$127$	1.00000	−	1.73205i	0.0887357	−	0.153695i	0.906977	+	0.421180i	$0.138384\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	1.00000			0.0880451
$130$		0			0
$131$	−3.00000			−0.262111			−0.131056	−	0.991375i	$-0.541837\pi$
$131$	−3.00000			−0.262111			−0.131056	+	0.991375i	$0.541837\pi$
$132$		0			0
$133$	−9.00000	+	15.5885i	−0.780399	+	1.35169i
$134$	−6.00000	−	10.3923i	−0.518321	−	0.897758i
$135$		−	15.0000i		−	1.29099i
$136$	−2.59808	+	1.50000i	−0.222783	+	0.128624i
$137$	15.5885	−	9.00000i	1.33181	−	0.768922i	0.346235	−	0.938148i	$-0.387460\pi$
$137$	15.5885	−	9.00000i	1.33181	−	0.768922i	0.985577	+	0.169226i	$0.0541268\pi$
$138$			6.00000i			0.510754i
$139$	−2.50000	−	4.33013i	−0.212047	−	0.367277i	0.740308	−	0.672268i	$-0.234680\pi$
$139$	−2.50000	−	4.33013i	−0.212047	−	0.367277i	−0.952355	+	0.304991i	$0.901346\pi$
$140$	4.50000	−	7.79423i	0.380319	−	0.658733i
$141$	2.59808	+	1.50000i	0.218797	+	0.126323i
$142$	−15.0000			−1.25877
$143$		0			0
$144$	−2.00000			−0.166667
$145$		0			0
$146$	3.00000	−	5.19615i	0.248282	−	0.430037i
$147$	−1.00000	−	1.73205i	−0.0824786	−	0.142857i
$148$		−	3.00000i		−	0.246598i
$149$	−5.19615	+	3.00000i	−0.425685	+	0.245770i	−0.697507	−	0.716578i	$-0.745707\pi$
$149$	−5.19615	+	3.00000i	−0.425685	+	0.245770i	0.271821	+	0.962348i	$0.412374\pi$
$150$	3.46410	−	2.00000i	0.282843	−	0.163299i
$151$		−	15.0000i		−	1.22068i	−0.792139	−	0.610341i	$-0.791032\pi$
$151$		−	15.0000i		−	1.22068i	0.792139	−	0.610341i	$-0.208968\pi$
$152$	3.00000	+	5.19615i	0.243332	+	0.421464i
$153$	3.00000	−	5.19615i	0.242536	−	0.420084i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−22.0000			−1.75579			−0.877896	−	0.478852i	$-0.841053\pi$
$157$	−22.0000			−1.75579			−0.877896	+	0.478852i	$0.841053\pi$
$158$	−8.66025	−	5.00000i	−0.688973	−	0.397779i
$159$	−3.00000	+	5.19615i	−0.237915	+	0.412082i
$160$	−1.50000	−	2.59808i	−0.118585	−	0.205396i
$161$		−	18.0000i		−	1.41860i
$162$	0.866025	−	0.500000i	0.0680414	−	0.0392837i
$163$	5.19615	−	3.00000i	0.406994	−	0.234978i	−0.282503	−	0.959266i	$-0.591165\pi$
$163$	5.19615	−	3.00000i	0.406994	−	0.234978i	0.689497	+	0.724288i	$0.257831\pi$
$164$		0			0
$165$		0			0
$166$	3.00000	−	5.19615i	0.232845	−	0.403300i
$167$	10.3923	+	6.00000i	0.804181	+	0.464294i	0.844931	−	0.534875i	$-0.179641\pi$
$167$	10.3923	+	6.00000i	0.804181	+	0.464294i	−0.0407502	+	0.999169i	$0.512975\pi$
$168$	−3.00000			−0.231455
$169$		0			0
$170$	9.00000			0.690268
$171$	−10.3923	−	6.00000i	−0.794719	−	0.458831i
$172$	−0.500000	+	0.866025i	−0.0381246	+	0.0660338i
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	0.957241	−	0.289292i	$-0.0934200\pi$
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	−0.729155	+	0.684349i	$0.760087\pi$
$174$		0			0
$175$	−10.3923	+	6.00000i	−0.785584	+	0.453557i
$176$		0			0
$177$			6.00000i			0.450988i
$178$	−3.00000	−	5.19615i	−0.224860	−	0.389468i
$179$	−7.50000	+	12.9904i	−0.560576	+	0.970947i	0.436870	+	0.899525i	$0.356087\pi$
$179$	−7.50000	+	12.9904i	−0.560576	+	0.970947i	−0.997446	+	0.0714220i	$0.977246\pi$
$180$	5.19615	+	3.00000i	0.387298	+	0.223607i
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$		0			0
$183$	8.00000			0.591377
$184$	−5.19615	−	3.00000i	−0.383065	−	0.221163i
$185$	−4.50000	+	7.79423i	−0.330847	+	0.573043i
$186$		0			0
$187$		0			0
$188$	−2.59808	+	1.50000i	−0.189484	+	0.109399i
$189$	12.9904	−	7.50000i	0.944911	−	0.545545i
$190$		−	18.0000i		−	1.30586i
$191$	−6.00000	−	10.3923i	−0.434145	−	0.751961i	0.563081	−	0.826402i	$-0.309616\pi$
$191$	−6.00000	−	10.3923i	−0.434145	−	0.751961i	−0.997225	+	0.0744412i	$0.976283\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−5.19615	−	3.00000i	−0.374027	−	0.215945i	0.301189	−	0.953564i	$-0.402616\pi$
$193$	−5.19615	−	3.00000i	−0.374027	−	0.215945i	−0.675216	+	0.737620i	$0.735950\pi$
$194$	12.0000			0.861550
$195$		0			0
$196$	2.00000			0.142857
$197$	−2.59808	−	1.50000i	−0.185105	−	0.106871i	0.404584	−	0.914501i	$-0.367416\pi$
$197$	−2.59808	−	1.50000i	−0.185105	−	0.106871i	−0.589689	+	0.807630i	$0.700750\pi$
$198$		0			0
$199$	10.0000	+	17.3205i	0.708881	+	1.22782i	0.965272	+	0.261245i	$0.0841331\pi$
$199$	10.0000	+	17.3205i	0.708881	+	1.22782i	−0.256391	+	0.966573i	$0.582534\pi$
$200$			4.00000i			0.282843i
$201$	10.3923	−	6.00000i	0.733017	−	0.423207i
$202$	10.3923	−	6.00000i	0.731200	−	0.422159i
$203$		0			0
$204$	−1.50000	−	2.59808i	−0.105021	−	0.181902i
$205$		0			0
$206$	−12.1244	−	7.00000i	−0.844744	−	0.487713i
$207$	12.0000			0.834058
$208$		0			0
$209$		0			0
$210$	7.79423	+	4.50000i	0.537853	+	0.310530i
$211$	11.5000	−	19.9186i	0.791693	−	1.37125i	−0.133226	−	0.991086i	$-0.542533\pi$
$211$	11.5000	−	19.9186i	0.791693	−	1.37125i	0.924918	−	0.380166i	$-0.124133\pi$
$212$	−3.00000	−	5.19615i	−0.206041	−	0.356873i
$213$		−	15.0000i		−	1.02778i
$214$	−10.3923	+	6.00000i	−0.710403	+	0.410152i
$215$	2.59808	−	1.50000i	0.177187	−	0.102299i
$216$		−	5.00000i		−	0.340207i
$217$		0			0
$218$	4.50000	−	7.79423i	0.304778	−	0.527892i
$219$	5.19615	+	3.00000i	0.351123	+	0.202721i
$220$		0			0
$221$		0			0
$222$	3.00000			0.201347
$223$	7.79423	+	4.50000i	0.521940	+	0.301342i	0.737728	−	0.675098i	$-0.235899\pi$
$223$	7.79423	+	4.50000i	0.521940	+	0.301342i	−0.215788	+	0.976440i	$0.569232\pi$
$224$	1.50000	−	2.59808i	0.100223	−	0.173591i
$225$	−4.00000	−	6.92820i	−0.266667	−	0.461880i
$226$		−	6.00000i		−	0.399114i
$227$	−10.3923	+	6.00000i	−0.689761	+	0.398234i	−0.803523	−	0.595274i	$-0.797043\pi$
$227$	−10.3923	+	6.00000i	−0.689761	+	0.398234i	0.113761	+	0.993508i	$0.463710\pi$
$228$	−5.19615	+	3.00000i	−0.344124	+	0.198680i
$229$			9.00000i			0.594737i	0.954763	+	0.297368i	$0.0961089\pi$
$229$			9.00000i			0.594737i	−0.954763	+	0.297368i	$0.903891\pi$
$230$	9.00000	+	15.5885i	0.593442	+	1.02787i
$231$		0			0
$232$		0			0
$233$	−21.0000			−1.37576			−0.687878	−	0.725826i	$-0.741458\pi$
$233$	−21.0000			−1.37576			−0.687878	+	0.725826i	$0.741458\pi$
$234$		0			0
$235$	9.00000			0.587095
$236$	−5.19615	−	3.00000i	−0.338241	−	0.195283i
$237$	5.00000	−	8.66025i	0.324785	−	0.562544i
$238$	4.50000	+	7.79423i	0.291692	+	0.505225i
$239$			9.00000i			0.582162i	0.956698	+	0.291081i	$0.0940149\pi$
$239$			9.00000i			0.582162i	−0.956698	+	0.291081i	$0.905985\pi$
$240$	2.59808	−	1.50000i	0.167705	−	0.0968246i
$241$	−25.9808	+	15.0000i	−1.67357	+	0.966235i	−0.707953	+	0.706260i	$0.750381\pi$
$241$	−25.9808	+	15.0000i	−1.67357	+	0.966235i	−0.965615	+	0.259975i	$0.916286\pi$
$242$			11.0000i			0.707107i
$243$	8.00000	+	13.8564i	0.513200	+	0.888889i
$244$	−4.00000	+	6.92820i	−0.256074	+	0.443533i
$245$	−5.19615	−	3.00000i	−0.331970	−	0.191663i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	5.19615	+	3.00000i	0.329293	+	0.190117i
$250$	−1.50000	+	2.59808i	−0.0948683	+	0.164317i
$251$	−6.00000	−	10.3923i	−0.378717	−	0.655956i	0.612159	−	0.790735i	$-0.290301\pi$
$251$	−6.00000	−	10.3923i	−0.378717	−	0.655956i	−0.990876	+	0.134778i	$0.956968\pi$
$252$			6.00000i			0.377964i
$253$		0			0
$254$	−1.73205	+	1.00000i	−0.108679	+	0.0627456i
$255$			9.00000i			0.563602i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−1.50000	+	2.59808i	−0.0935674	+	0.162064i	−0.909010	−	0.416775i	$-0.863160\pi$
$257$	−1.50000	+	2.59808i	−0.0935674	+	0.162064i	0.815442	+	0.578838i	$0.196494\pi$
$258$	−0.866025	−	0.500000i	−0.0539164	−	0.0311286i
$259$	−9.00000			−0.559233
$260$		0			0
$261$		0			0
$262$	2.59808	+	1.50000i	0.160510	+	0.0926703i
$263$	−12.0000	+	20.7846i	−0.739952	+	1.28163i	0.212565	+	0.977147i	$0.431818\pi$
$263$	−12.0000	+	20.7846i	−0.739952	+	1.28163i	−0.952517	+	0.304487i	$0.901515\pi$
$264$		0			0
$265$			18.0000i			1.10573i
$266$	15.5885	−	9.00000i	0.955790	−	0.551825i
$267$	5.19615	−	3.00000i	0.317999	−	0.183597i
$268$			12.0000i			0.733017i
$269$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$269$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$270$	−7.50000	+	12.9904i	−0.456435	+	0.790569i
$271$	−12.9904	−	7.50000i	−0.789109	−	0.455593i	0.0505395	−	0.998722i	$-0.483906\pi$
$271$	−12.9904	−	7.50000i	−0.789109	−	0.455593i	−0.839649	+	0.543130i	$0.817239\pi$
$272$	3.00000			0.181902
$273$		0			0
$274$	−18.0000			−1.08742
$275$		0			0
$276$	3.00000	−	5.19615i	0.180579	−	0.312772i
$277$	−4.00000	−	6.92820i	−0.240337	−	0.416275i	0.720473	−	0.693482i	$-0.243925\pi$
$277$	−4.00000	−	6.92820i	−0.240337	−	0.416275i	−0.960810	+	0.277207i	$0.910591\pi$
$278$			5.00000i			0.299880i
$279$		0			0
$280$	−7.79423	+	4.50000i	−0.465794	+	0.268926i
$281$		−	30.0000i		−	1.78965i	−0.446417	−	0.894825i	$-0.647300\pi$
$281$		−	30.0000i		−	1.78965i	0.446417	−	0.894825i	$-0.352700\pi$
$282$	−1.50000	−	2.59808i	−0.0893237	−	0.154713i
$283$	−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	$0.204600\pi$
$284$	12.9904	+	7.50000i	0.770837	+	0.445043i
$285$	18.0000			1.06623
$286$		0			0
$287$		0			0
$288$	1.73205	+	1.00000i	0.102062	+	0.0589256i
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$		0			0
$291$			12.0000i			0.703452i
$292$	−5.19615	+	3.00000i	−0.304082	+	0.175562i
$293$	−7.79423	+	4.50000i	−0.455344	+	0.262893i	−0.710084	−	0.704117i	$-0.751343\pi$
$293$	−7.79423	+	4.50000i	−0.455344	+	0.262893i	0.254741	+	0.967009i	$0.418010\pi$
$294$			2.00000i			0.116642i
$295$	9.00000	+	15.5885i	0.524000	+	0.907595i
$296$	−1.50000	+	2.59808i	−0.0871857	+	0.151010i
$297$		0			0
$298$	6.00000			0.347571
$299$		0			0
$300$	−4.00000			−0.230940
$301$	2.59808	+	1.50000i	0.149751	+	0.0864586i
$302$	−7.50000	+	12.9904i	−0.431577	+	0.747512i
$303$	6.00000	+	10.3923i	0.344691	+	0.597022i
$304$		−	6.00000i		−	0.344124i
$305$	20.7846	−	12.0000i	1.19012	−	0.687118i
$306$	−5.19615	+	3.00000i	−0.297044	+	0.171499i
$307$			18.0000i			1.02731i	0.857996	+	0.513657i	$0.171710\pi$
$307$			18.0000i			1.02731i	−0.857996	+	0.513657i	$0.828290\pi$
$308$		0			0
$309$	7.00000	−	12.1244i	0.398216	−	0.689730i
$310$		0			0
$311$	−18.0000			−1.02069			−0.510343	−	0.859971i	$-0.670482\pi$
$311$	−18.0000			−1.02069			−0.510343	+	0.859971i	$0.670482\pi$
$312$		0			0
$313$	19.0000			1.07394			0.536972	−	0.843600i	$-0.319568\pi$
$313$	19.0000			1.07394			0.536972	+	0.843600i	$0.319568\pi$
$314$	19.0526	+	11.0000i	1.07520	+	0.620766i
$315$	9.00000	−	15.5885i	0.507093	−	0.878310i
$316$	5.00000	+	8.66025i	0.281272	+	0.487177i
$317$			18.0000i			1.01098i	0.862832	+	0.505490i	$0.168688\pi$
$317$			18.0000i			1.01098i	−0.862832	+	0.505490i	$0.831312\pi$
$318$	5.19615	−	3.00000i	0.291386	−	0.168232i
$319$		0			0
$320$			3.00000i			0.167705i
$321$	−6.00000	−	10.3923i	−0.334887	−	0.580042i
$322$	−9.00000	+	15.5885i	−0.501550	+	0.868711i
$323$	15.5885	+	9.00000i	0.867365	+	0.500773i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−6.00000			−0.332309
$327$	7.79423	+	4.50000i	0.431022	+	0.248851i
$328$		0			0
$329$	4.50000	+	7.79423i	0.248093	+	0.429710i
$330$		0			0
$331$	25.9808	−	15.0000i	1.42803	−	0.824475i	0.431066	−	0.902320i	$-0.358137\pi$
$331$	25.9808	−	15.0000i	1.42803	−	0.824475i	0.996965	+	0.0778456i	$0.0248041\pi$
$332$	−5.19615	+	3.00000i	−0.285176	+	0.164646i
$333$		−	6.00000i		−	0.328798i
$334$	−6.00000	−	10.3923i	−0.328305	−	0.568642i
$335$	18.0000	−	31.1769i	0.983445	−	1.70338i
$336$	2.59808	+	1.50000i	0.141737	+	0.0818317i
$337$	13.0000			0.708155			0.354078	−	0.935216i	$-0.384795\pi$
$337$	13.0000			0.708155			0.354078	+	0.935216i	$0.384795\pi$
$338$		0			0
$339$	6.00000			0.325875
$340$	−7.79423	−	4.50000i	−0.422701	−	0.244047i
$341$		0			0
$342$	6.00000	+	10.3923i	0.324443	+	0.561951i
$343$			15.0000i			0.809924i
$344$	0.866025	−	0.500000i	0.0466930	−	0.0269582i
$345$	−15.5885	+	9.00000i	−0.839254	+	0.484544i
$346$		−	6.00000i		−	0.322562i
$347$	−16.5000	−	28.5788i	−0.885766	−	1.53419i	−0.844833	−	0.535031i	$-0.820300\pi$
$347$	−16.5000	−	28.5788i	−0.885766	−	1.53419i	−0.0409337	−	0.999162i	$-0.513033\pi$
$348$		0			0
$349$	18.1865	+	10.5000i	0.973503	+	0.562052i	0.900302	−	0.435265i	$-0.143345\pi$
$349$	18.1865	+	10.5000i	0.973503	+	0.562052i	0.0732005	+	0.997317i	$0.476679\pi$
$350$	12.0000			0.641427
$351$		0			0
$352$		0			0
$353$	−5.19615	−	3.00000i	−0.276563	−	0.159674i	0.355303	−	0.934751i	$-0.384378\pi$
$353$	−5.19615	−	3.00000i	−0.276563	−	0.159674i	−0.631867	+	0.775077i	$0.717711\pi$
$354$	3.00000	−	5.19615i	0.159448	−	0.276172i
$355$	−22.5000	−	38.9711i	−1.19418	−	2.06837i
$356$			6.00000i			0.317999i
$357$	−7.79423	+	4.50000i	−0.412514	+	0.238165i
$358$	12.9904	−	7.50000i	0.686563	−	0.396387i
$359$			24.0000i			1.26667i	0.773877	+	0.633336i	$0.218315\pi$
$359$			24.0000i			1.26667i	−0.773877	+	0.633336i	$0.781685\pi$
$360$	−3.00000	−	5.19615i	−0.158114	−	0.273861i
$361$	8.50000	−	14.7224i	0.447368	−	0.774865i
$362$	−1.73205	−	1.00000i	−0.0910346	−	0.0525588i
$363$	−11.0000			−0.577350
$364$		0			0
$365$	18.0000			0.942163
$366$	−6.92820	−	4.00000i	−0.362143	−	0.209083i
$367$	−4.00000	+	6.92820i	−0.208798	+	0.361649i	−0.951336	−	0.308155i	$-0.900289\pi$
$367$	−4.00000	+	6.92820i	−0.208798	+	0.361649i	0.742538	+	0.669804i	$0.233622\pi$
$368$	3.00000	+	5.19615i	0.156386	+	0.270868i
$369$		0			0
$370$	7.79423	−	4.50000i	0.405203	−	0.233944i
$371$	−15.5885	+	9.00000i	−0.809312	+	0.467257i
$372$		0			0
$373$	−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	$0.866355\pi$
$374$		0			0
$375$	−2.59808	−	1.50000i	−0.134164	−	0.0774597i
$376$	3.00000			0.154713
$377$		0			0
$378$	−15.0000			−0.771517
$379$	5.19615	+	3.00000i	0.266908	+	0.154100i	0.627482	−	0.778631i	$-0.284086\pi$
$379$	5.19615	+	3.00000i	0.266908	+	0.154100i	−0.360573	+	0.932731i	$0.617419\pi$
$380$	−9.00000	+	15.5885i	−0.461690	+	0.799671i
$381$	−1.00000	−	1.73205i	−0.0512316	−	0.0887357i
$382$			12.0000i			0.613973i
$383$	−7.79423	+	4.50000i	−0.398266	+	0.229939i	−0.685736	−	0.727851i	$-0.740519\pi$
$383$	−7.79423	+	4.50000i	−0.398266	+	0.229939i	0.287469	+	0.957790i	$0.407186\pi$
$384$	0.866025	−	0.500000i	0.0441942	−	0.0255155i
$385$		0			0
$386$	3.00000	+	5.19615i	0.152696	+	0.264477i
$387$	−1.00000	+	1.73205i	−0.0508329	+	0.0880451i
$388$	−10.3923	−	6.00000i	−0.527589	−	0.304604i
$389$	−30.0000			−1.52106			−0.760530	−	0.649303i	$-0.775061\pi$
$389$	−30.0000			−1.52106			−0.760530	+	0.649303i	$0.775061\pi$
$390$		0			0
$391$	−18.0000			−0.910299
$392$	−1.73205	−	1.00000i	−0.0874818	−	0.0505076i
$393$	−1.50000	+	2.59808i	−0.0756650	+	0.131056i
$394$	1.50000	+	2.59808i	0.0755689	+	0.130889i
$395$		−	30.0000i		−	1.50946i
$396$		0			0
$397$	15.5885	−	9.00000i	0.782362	−	0.451697i	−0.0549046	−	0.998492i	$-0.517485\pi$
$397$	15.5885	−	9.00000i	0.782362	−	0.451697i	0.837267	+	0.546795i	$0.184152\pi$
$398$		−	20.0000i		−	1.00251i
$399$	9.00000	+	15.5885i	0.450564	+	0.780399i
$400$	2.00000	−	3.46410i	0.100000	−	0.173205i
$401$	−25.9808	−	15.0000i	−1.29742	−	0.749064i	−0.317460	−	0.948272i	$-0.602830\pi$
$401$	−25.9808	−	15.0000i	−1.29742	−	0.749064i	−0.979957	+	0.199207i	$0.936163\pi$
$402$	−12.0000			−0.598506
$403$		0			0
$404$	−12.0000			−0.597022
$405$	2.59808	+	1.50000i	0.129099	+	0.0745356i
$406$		0			0
$407$		0			0
$408$			3.00000i			0.148522i
$409$	−5.19615	+	3.00000i	−0.256933	+	0.148340i	−0.622935	−	0.782274i	$-0.714060\pi$
$409$	−5.19615	+	3.00000i	−0.256933	+	0.148340i	0.366002	+	0.930614i	$0.380726\pi$
$410$		0			0
$411$		−	18.0000i		−	0.887875i
$412$	7.00000	+	12.1244i	0.344865	+	0.597324i
$413$	−9.00000	+	15.5885i	−0.442861	+	0.767058i
$414$	−10.3923	−	6.00000i	−0.510754	−	0.294884i
$415$	18.0000			0.883585
$416$		0			0
$417$	−5.00000			−0.244851
$418$		0			0
$419$	−7.50000	+	12.9904i	−0.366399	+	0.634622i	−0.989000	−	0.147918i	$-0.952743\pi$
$419$	−7.50000	+	12.9904i	−0.366399	+	0.634622i	0.622601	+	0.782540i	$0.286076\pi$
$420$	−4.50000	−	7.79423i	−0.219578	−	0.380319i
$421$		−	15.0000i		−	0.731055i	−0.930800	−	0.365528i	$-0.880889\pi$
$421$		−	15.0000i		−	0.731055i	0.930800	−	0.365528i	$-0.119111\pi$
$422$	−19.9186	+	11.5000i	−0.969622	+	0.559811i
$423$	−5.19615	+	3.00000i	−0.252646	+	0.145865i
$424$			6.00000i			0.291386i
$425$	6.00000	+	10.3923i	0.291043	+	0.504101i
$426$	−7.50000	+	12.9904i	−0.363376	+	0.629386i
$427$	20.7846	+	12.0000i	1.00584	+	0.580721i
$428$	12.0000			0.580042
$429$		0			0
$430$	−3.00000			−0.144673
$431$	12.9904	+	7.50000i	0.625725	+	0.361262i	0.779094	−	0.626907i	$-0.215679\pi$
$431$	12.9904	+	7.50000i	0.625725	+	0.361262i	−0.153370	+	0.988169i	$0.549013\pi$
$432$	−2.50000	+	4.33013i	−0.120281	+	0.208333i
$433$	5.50000	+	9.52628i	0.264313	+	0.457804i	0.967383	−	0.253317i	$-0.0815214\pi$
$433$	5.50000	+	9.52628i	0.264313	+	0.457804i	−0.703070	+	0.711120i	$0.748188\pi$
$434$		0			0
$435$		0			0
$436$	−7.79423	+	4.50000i	−0.373276	+	0.215511i
$437$			36.0000i			1.72211i
$438$	−3.00000	−	5.19615i	−0.143346	−	0.248282i
$439$	5.00000	−	8.66025i	0.238637	−	0.413331i	−0.721686	−	0.692220i	$-0.756633\pi$
$439$	5.00000	−	8.66025i	0.238637	−	0.413331i	0.960323	+	0.278889i	$0.0899661\pi$
$440$		0			0
$441$	4.00000			0.190476
$442$		0			0
$443$	−21.0000			−0.997740			−0.498870	−	0.866677i	$-0.666252\pi$
$443$	−21.0000			−0.997740			−0.498870	+	0.866677i	$0.666252\pi$
$444$	−2.59808	−	1.50000i	−0.123299	−	0.0711868i
$445$	9.00000	−	15.5885i	0.426641	−	0.738964i
$446$	−4.50000	−	7.79423i	−0.213081	−	0.369067i
$447$			6.00000i			0.283790i
$448$	−2.59808	+	1.50000i	−0.122748	+	0.0708683i
$449$	20.7846	−	12.0000i	0.980886	−	0.566315i	0.0783487	−	0.996926i	$-0.475035\pi$
$449$	20.7846	−	12.0000i	0.980886	−	0.566315i	0.902538	+	0.430611i	$0.141702\pi$
$450$			8.00000i			0.377124i
$451$		0			0
$452$	−3.00000	+	5.19615i	−0.141108	+	0.244406i
$453$	−12.9904	−	7.50000i	−0.610341	−	0.352381i
$454$	12.0000			0.563188
$455$		0			0
$456$	6.00000			0.280976
$457$	−15.5885	−	9.00000i	−0.729197	−	0.421002i	0.0889312	−	0.996038i	$-0.471655\pi$
$457$	−15.5885	−	9.00000i	−0.729197	−	0.421002i	−0.818128	+	0.575036i	$0.804988\pi$
$458$	4.50000	−	7.79423i	0.210271	−	0.364200i
$459$	−7.50000	−	12.9904i	−0.350070	−	0.606339i
$460$		−	18.0000i		−	0.839254i
$461$	−12.9904	+	7.50000i	−0.605022	+	0.349310i	−0.771015	−	0.636817i	$-0.780251\pi$
$461$	−12.9904	+	7.50000i	−0.605022	+	0.349310i	0.165992	+	0.986127i	$0.446917\pi$
$462$		0			0
$463$		−	24.0000i		−	1.11537i	−0.830051	−	0.557687i	$-0.811689\pi$
$463$		−	24.0000i		−	1.11537i	0.830051	−	0.557687i	$-0.188311\pi$
$464$		0			0
$465$		0			0
$466$	18.1865	+	10.5000i	0.842475	+	0.486403i
$467$	−12.0000			−0.555294			−0.277647	−	0.960683i	$-0.589555\pi$
$467$	−12.0000			−0.555294			−0.277647	+	0.960683i	$0.589555\pi$
$468$		0			0
$469$	36.0000			1.66233
$470$	−7.79423	−	4.50000i	−0.359521	−	0.207570i
$471$	−11.0000	+	19.0526i	−0.506853	+	0.877896i
$472$	3.00000	+	5.19615i	0.138086	+	0.239172i
$473$		0			0
$474$	−8.66025	+	5.00000i	−0.397779	+	0.229658i
$475$	20.7846	−	12.0000i	0.953663	−	0.550598i
$476$		−	9.00000i		−	0.412514i
$477$	−6.00000	−	10.3923i	−0.274721	−	0.475831i
$478$	4.50000	−	7.79423i	0.205825	−	0.356500i
$479$	−33.7750	−	19.5000i	−1.54322	−	0.890978i	−0.998633	−	0.0522726i	$-0.983354\pi$
$479$	−33.7750	−	19.5000i	−1.54322	−	0.890978i	−0.544586	−	0.838705i	$-0.683313\pi$
$480$	−3.00000			−0.136931
$481$		0			0
$482$	30.0000			1.36646
$483$	−15.5885	−	9.00000i	−0.709299	−	0.409514i
$484$	5.50000	−	9.52628i	0.250000	−	0.433013i
$485$	18.0000	+	31.1769i	0.817338	+	1.41567i
$486$		−	16.0000i		−	0.725775i
$487$	−10.3923	+	6.00000i	−0.470920	+	0.271886i	−0.716625	−	0.697459i	$-0.754314\pi$
$487$	−10.3923	+	6.00000i	−0.470920	+	0.271886i	0.245705	+	0.969345i	$0.420981\pi$
$488$	6.92820	−	4.00000i	0.313625	−	0.181071i
$489$		−	6.00000i		−	0.271329i
$490$	3.00000	+	5.19615i	0.135526	+	0.234738i
$491$	−13.5000	+	23.3827i	−0.609246	+	1.05525i	0.382118	+	0.924113i	$0.375195\pi$
$491$	−13.5000	+	23.3827i	−0.609246	+	1.05525i	−0.991365	+	0.131132i	$0.958139\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	22.5000	−	38.9711i	1.00926	−	1.74809i
$498$	−3.00000	−	5.19615i	−0.134433	−	0.232845i
$499$		−	36.0000i		−	1.61158i	−0.592200	−	0.805791i	$-0.701741\pi$
$499$		−	36.0000i		−	1.61158i	0.592200	−	0.805791i	$-0.298259\pi$
$500$	2.59808	−	1.50000i	0.116190	−	0.0670820i
$501$	10.3923	−	6.00000i	0.464294	−	0.268060i
$502$			12.0000i			0.535586i
$503$	3.00000	+	5.19615i	0.133763	+	0.231685i	0.925124	−	0.379664i	$-0.123960\pi$
$503$	3.00000	+	5.19615i	0.133763	+	0.231685i	−0.791361	+	0.611349i	$0.790627\pi$
$504$	3.00000	−	5.19615i	0.133631	−	0.231455i
$505$	31.1769	+	18.0000i	1.38735	+	0.800989i
$506$		0			0
$507$		0			0
$508$	2.00000			0.0887357
$509$	5.19615	+	3.00000i	0.230315	+	0.132973i	0.610718	−	0.791849i	$-0.290881\pi$
$509$	5.19615	+	3.00000i	0.230315	+	0.132973i	−0.380402	+	0.924821i	$0.624214\pi$
$510$	4.50000	−	7.79423i	0.199263	−	0.345134i
$511$	9.00000	+	15.5885i	0.398137	+	0.689593i
$512$			1.00000i			0.0441942i
$513$	−25.9808	+	15.0000i	−1.14708	+	0.662266i
$514$	2.59808	−	1.50000i	0.114596	−	0.0661622i
$515$		−	42.0000i		−	1.85074i
$516$	0.500000	+	0.866025i	0.0220113	+	0.0381246i
$517$		0			0
$518$	7.79423	+	4.50000i	0.342459	+	0.197719i
$519$	6.00000			0.263371
$520$		0			0
$521$	27.0000			1.18289			0.591446	−	0.806345i	$-0.298557\pi$
$521$	27.0000			1.18289			0.591446	+	0.806345i	$0.298557\pi$
$522$		0			0
$523$	8.00000	−	13.8564i	0.349816	−	0.605898i	−0.636401	−	0.771358i	$-0.719578\pi$
$523$	8.00000	−	13.8564i	0.349816	−	0.605898i	0.986216	+	0.165460i	$0.0529109\pi$
$524$	−1.50000	−	2.59808i	−0.0655278	−	0.113497i
$525$			12.0000i			0.523723i
$526$	20.7846	−	12.0000i	0.906252	−	0.523225i
$527$		0			0
$528$		0			0
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$	9.00000	−	15.5885i	0.390935	−	0.677119i
$531$	−10.3923	−	6.00000i	−0.450988	−	0.260378i
$532$	−18.0000			−0.780399
$533$		0			0
$534$	−6.00000			−0.259645
$535$	−31.1769	−	18.0000i	−1.34790	−	0.778208i
$536$	6.00000	−	10.3923i	0.259161	−	0.448879i
$537$	7.50000	+	12.9904i	0.323649	+	0.560576i
$538$		0			0
$539$		0			0
$540$	12.9904	−	7.50000i	0.559017	−	0.322749i
$541$		−	15.0000i		−	0.644900i	−0.946586	−	0.322450i	$-0.895494\pi$
$541$		−	15.0000i		−	0.644900i	0.946586	−	0.322450i	$-0.104506\pi$
$542$	7.50000	+	12.9904i	0.322153	+	0.557985i
$543$	1.00000	−	1.73205i	0.0429141	−	0.0743294i
$544$	−2.59808	−	1.50000i	−0.111392	−	0.0643120i
$545$	27.0000			1.15655
$546$		0			0
$547$	−37.0000			−1.58201			−0.791003	−	0.611812i	$-0.790441\pi$
$547$	−37.0000			−1.58201			−0.791003	+	0.611812i	$0.790441\pi$
$548$	15.5885	+	9.00000i	0.665906	+	0.384461i
$549$	−8.00000	+	13.8564i	−0.341432	+	0.591377i
$550$		0			0
$551$		0			0
$552$	−5.19615	+	3.00000i	−0.221163	+	0.127688i
$553$	25.9808	−	15.0000i	1.10481	−	0.637865i
$554$			8.00000i			0.339887i
$555$	4.50000	+	7.79423i	0.191014	+	0.330847i
$556$	2.50000	−	4.33013i	0.106024	−	0.183638i
$557$	23.3827	+	13.5000i	0.990756	+	0.572013i	0.905500	−	0.424346i	$-0.139496\pi$
$557$	23.3827	+	13.5000i	0.990756	+	0.572013i	0.0852559	+	0.996359i	$0.472829\pi$
$558$		0			0
$559$		0			0
$560$	9.00000			0.380319
$561$		0			0
$562$	−15.0000	+	25.9808i	−0.632737	+	1.09593i
$563$	−19.5000	−	33.7750i	−0.821827	−	1.42345i	−0.904320	−	0.426855i	$-0.859622\pi$
$563$	−19.5000	−	33.7750i	−0.821827	−	1.42345i	0.0824933	−	0.996592i	$-0.473712\pi$
$564$			3.00000i			0.126323i
$565$	15.5885	−	9.00000i	0.655811	−	0.378633i
$566$	3.46410	−	2.00000i	0.145607	−	0.0840663i
$567$			3.00000i			0.125988i
$568$	−7.50000	−	12.9904i	−0.314693	−	0.545064i
$569$	−22.5000	+	38.9711i	−0.943249	+	1.63376i	−0.184030	+	0.982921i	$0.558914\pi$
$569$	−22.5000	+	38.9711i	−0.943249	+	1.63376i	−0.759220	+	0.650835i	$0.774419\pi$
$570$	−15.5885	−	9.00000i	−0.652929	−	0.376969i
$571$	−23.0000			−0.962520			−0.481260	−	0.876578i	$-0.659821\pi$
$571$	−23.0000			−0.962520			−0.481260	+	0.876578i	$0.659821\pi$
$572$		0			0
$573$	−12.0000			−0.501307
$574$		0			0
$575$	−12.0000	+	20.7846i	−0.500435	+	0.866778i
$576$	−1.00000	−	1.73205i	−0.0416667	−	0.0721688i
$577$		−	42.0000i		−	1.74848i	−0.485491	−	0.874241i	$-0.661359\pi$
$577$		−	42.0000i		−	1.74848i	0.485491	−	0.874241i	$-0.338641\pi$
$578$	−6.92820	+	4.00000i	−0.288175	+	0.166378i
$579$	−5.19615	+	3.00000i	−0.215945	+	0.124676i
$580$		0			0
$581$	9.00000	+	15.5885i	0.373383	+	0.646718i
$582$	6.00000	−	10.3923i	0.248708	−	0.430775i
$583$		0			0
$584$	6.00000			0.248282
$585$		0			0
$586$	9.00000			0.371787
$587$	−15.5885	−	9.00000i	−0.643404	−	0.371470i	0.142520	−	0.989792i	$-0.454479\pi$
$587$	−15.5885	−	9.00000i	−0.643404	−	0.371470i	−0.785925	+	0.618322i	$0.787813\pi$
$588$	1.00000	−	1.73205i	0.0412393	−	0.0714286i
$589$		0			0
$590$		−	18.0000i		−	0.741048i
$591$	−2.59808	+	1.50000i	−0.106871	+	0.0617018i
$592$	2.59808	−	1.50000i	0.106780	−	0.0616496i
$593$			36.0000i			1.47834i	0.673517	+	0.739171i	$0.264783\pi$
$593$			36.0000i			1.47834i	−0.673517	+	0.739171i	$0.735217\pi$
$594$		0			0
$595$	−13.5000	+	23.3827i	−0.553446	+	0.958597i
$596$	−5.19615	−	3.00000i	−0.212843	−	0.122885i
$597$	20.0000			0.818546
$598$		0			0
$599$	−30.0000			−1.22577			−0.612883	−	0.790173i	$-0.709990\pi$
$599$	−30.0000			−1.22577			−0.612883	+	0.790173i	$0.709990\pi$
$600$	3.46410	+	2.00000i	0.141421	+	0.0816497i
$601$	−18.5000	+	32.0429i	−0.754631	+	1.30706i	0.190927	+	0.981604i	$0.438851\pi$
$601$	−18.5000	+	32.0429i	−0.754631	+	1.30706i	−0.945558	+	0.325455i	$0.894483\pi$
$602$	−1.50000	−	2.59808i	−0.0611354	−	0.105890i
$603$			24.0000i			0.977356i
$604$	12.9904	−	7.50000i	0.528571	−	0.305171i
$605$	−28.5788	+	16.5000i	−1.16190	+	0.670820i
$606$		−	12.0000i		−	0.487467i
$607$	11.0000	+	19.0526i	0.446476	+	0.773320i	0.998154	−	0.0607380i	$-0.0193454\pi$
$607$	11.0000	+	19.0526i	0.446476	+	0.773320i	−0.551678	+	0.834058i	$0.686012\pi$
$608$	−3.00000	+	5.19615i	−0.121666	+	0.210732i
$609$		0			0
$610$	−24.0000			−0.971732
$611$		0			0
$612$	6.00000			0.242536
$613$	−5.19615	−	3.00000i	−0.209871	−	0.121169i	0.391381	−	0.920229i	$-0.371998\pi$
$613$	−5.19615	−	3.00000i	−0.209871	−	0.121169i	−0.601251	+	0.799060i	$0.705331\pi$
$614$	9.00000	−	15.5885i	0.363210	−	0.629099i
$615$		0			0
$616$		0			0
$617$	−10.3923	+	6.00000i	−0.418378	+	0.241551i	−0.694383	−	0.719605i	$-0.744323\pi$
$617$	−10.3923	+	6.00000i	−0.418378	+	0.241551i	0.276005	+	0.961156i	$0.410989\pi$
$618$	−12.1244	+	7.00000i	−0.487713	+	0.281581i
$619$			24.0000i			0.964641i	0.875995	+	0.482321i	$0.160206\pi$
$619$			24.0000i			0.964641i	−0.875995	+	0.482321i	$0.839794\pi$
$620$		0			0
$621$	15.0000	−	25.9808i	0.601929	−	1.04257i
$622$	15.5885	+	9.00000i	0.625040	+	0.360867i
$623$	18.0000			0.721155
$624$		0			0
$625$	−29.0000			−1.16000
$626$	−16.4545	−	9.50000i	−0.657653	−	0.379696i
$627$		0			0
$628$	−11.0000	−	19.0526i	−0.438948	−	0.760280i
$629$			9.00000i			0.358854i
$630$	−15.5885	+	9.00000i	−0.621059	+	0.358569i
$631$	−12.9904	+	7.50000i	−0.517139	+	0.298570i	−0.735763	−	0.677239i	$-0.763176\pi$
$631$	−12.9904	+	7.50000i	−0.517139	+	0.298570i	0.218624	+	0.975809i	$0.429843\pi$
$632$		−	10.0000i		−	0.397779i
$633$	−11.5000	−	19.9186i	−0.457084	−	0.791693i
$634$	9.00000	−	15.5885i	0.357436	−	0.619097i
$635$	−5.19615	−	3.00000i	−0.206203	−	0.119051i
$636$	−6.00000			−0.237915
$637$		0			0
$638$		0			0
$639$	25.9808	+	15.0000i	1.02778	+	0.593391i
$640$	1.50000	−	2.59808i	0.0592927	−	0.102698i
$641$	9.00000	+	15.5885i	0.355479	+	0.615707i	0.987200	−	0.159489i	$-0.0509845\pi$
$641$	9.00000	+	15.5885i	0.355479	+	0.615707i	−0.631721	+	0.775196i	$0.717651\pi$
$642$			12.0000i			0.473602i
$643$	31.1769	−	18.0000i	1.22950	−	0.709851i	0.262573	−	0.964912i	$-0.415429\pi$
$643$	31.1769	−	18.0000i	1.22950	−	0.709851i	0.966925	+	0.255062i	$0.0820957\pi$
$644$	15.5885	−	9.00000i	0.614271	−	0.354650i
$645$		−	3.00000i		−	0.118125i
$646$	−9.00000	−	15.5885i	−0.354100	−	0.613320i
$647$	21.0000	−	36.3731i	0.825595	−	1.42997i	−0.0758684	−	0.997118i	$-0.524173\pi$
$647$	21.0000	−	36.3731i	0.825595	−	1.42997i	0.901464	−	0.432855i	$-0.142494\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	5.19615	+	3.00000i	0.203497	+	0.117489i
$653$	18.0000	−	31.1769i	0.704394	−	1.22005i	−0.262515	−	0.964928i	$-0.584552\pi$
$653$	18.0000	−	31.1769i	0.704394	−	1.22005i	0.966910	−	0.255119i	$-0.0821147\pi$
$654$	−4.50000	−	7.79423i	−0.175964	−	0.304778i
$655$			9.00000i			0.351659i
$656$		0			0
$657$	−10.3923	+	6.00000i	−0.405442	+	0.234082i
$658$		−	9.00000i		−	0.350857i
$659$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$659$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$660$		0			0
$661$	−25.9808	−	15.0000i	−1.01053	−	0.583432i	−0.0991864	−	0.995069i	$-0.531624\pi$
$661$	−25.9808	−	15.0000i	−1.01053	−	0.583432i	−0.911348	+	0.411636i	$0.864957\pi$
$662$	−30.0000			−1.16598
$663$		0			0
$664$	6.00000			0.232845
$665$	46.7654	+	27.0000i	1.81348	+	1.04702i
$666$	−3.00000	+	5.19615i	−0.116248	+	0.201347i
$667$		0			0
$668$			12.0000i			0.464294i
$669$	7.79423	−	4.50000i	0.301342	−	0.173980i
$670$	−31.1769	+	18.0000i	−1.20447	+	0.695401i
$671$		0			0
$672$	−1.50000	−	2.59808i	−0.0578638	−	0.100223i
$673$	0.500000	−	0.866025i	0.0192736	−	0.0333828i	−0.856228	−	0.516599i	$-0.827198\pi$
$673$	0.500000	−	0.866025i	0.0192736	−	0.0333828i	0.875501	+	0.483216i	$0.160531\pi$
$674$	−11.2583	−	6.50000i	−0.433655	−	0.250371i
$675$	−20.0000			−0.769800
$676$		0			0
$677$	18.0000			0.691796			0.345898	−	0.938272i	$-0.387574\pi$
$677$	18.0000			0.691796			0.345898	+	0.938272i	$0.387574\pi$
$678$	−5.19615	−	3.00000i	−0.199557	−	0.115214i
$679$	−18.0000	+	31.1769i	−0.690777	+	1.19646i
$680$	4.50000	+	7.79423i	0.172567	+	0.298895i
$681$			12.0000i			0.459841i
$682$		0			0
$683$	5.19615	−	3.00000i	0.198825	−	0.114792i	−0.397282	−	0.917697i	$-0.630047\pi$
$683$	5.19615	−	3.00000i	0.198825	−	0.114792i	0.596107	+	0.802905i	$0.296713\pi$
$684$		−	12.0000i		−	0.458831i
$685$	−27.0000	−	46.7654i	−1.03162	−	1.78681i
$686$	7.50000	−	12.9904i	0.286351	−	0.495975i
$687$	7.79423	+	4.50000i	0.297368	+	0.171686i
$688$	−1.00000			−0.0381246
$689$		0			0
$690$	18.0000			0.685248
$691$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$691$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$692$	−3.00000	+	5.19615i	−0.114043	+	0.197528i
$693$		0			0
$694$			33.0000i			1.25266i
$695$	−12.9904	+	7.50000i	−0.492753	+	0.284491i
$696$		0			0
$697$		0			0
$698$	−10.5000	−	18.1865i	−0.397431	−	0.688370i
$699$	−10.5000	+	18.1865i	−0.397146	+	0.687878i
$700$	−10.3923	−	6.00000i	−0.392792	−	0.226779i
$701$	42.0000			1.58632			0.793159	−	0.609015i	$-0.208435\pi$
$701$	42.0000			1.58632			0.793159	+	0.609015i	$0.208435\pi$
$702$		0			0
$703$	18.0000			0.678883
$704$		0			0
$705$	4.50000	−	7.79423i	0.169480	−	0.293548i
$706$	3.00000	+	5.19615i	0.112906	+	0.195560i
$707$			36.0000i			1.35392i
$708$	−5.19615	+	3.00000i	−0.195283	+	0.112747i
$709$	−5.19615	+	3.00000i	−0.195146	+	0.112667i	−0.594389	−	0.804178i	$-0.702606\pi$
$709$	−5.19615	+	3.00000i	−0.195146	+	0.112667i	0.399244	+	0.916845i	$0.369273\pi$
$710$			45.0000i			1.68882i
$711$	10.0000	+	17.3205i	0.375029	+	0.649570i
$712$	3.00000	−	5.19615i	0.112430	−	0.194734i
$713$		0			0
$714$	9.00000			0.336817
$715$		0			0
$716$	−15.0000			−0.560576
$717$	7.79423	+	4.50000i	0.291081	+	0.168056i
$718$	12.0000	−	20.7846i	0.447836	−	0.775675i
$719$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$719$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$720$			6.00000i			0.223607i
$721$	36.3731	−	21.0000i	1.35460	−	0.782081i
$722$	−14.7224	+	8.50000i	−0.547912	+	0.316337i
$723$			30.0000i			1.11571i
$724$	1.00000	+	1.73205i	0.0371647	+	0.0643712i
$725$		0			0
$726$	9.52628	+	5.50000i	0.353553	+	0.204124i
$727$	28.0000			1.03846			0.519231	−	0.854634i	$-0.326218\pi$
$727$	28.0000			1.03846			0.519231	+	0.854634i	$0.326218\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$	−15.5885	−	9.00000i	−0.576955	−	0.333105i
$731$	1.50000	−	2.59808i	0.0554795	−	0.0960933i
$732$	4.00000	+	6.92820i	0.147844	+	0.256074i
$733$		−	9.00000i		−	0.332423i	−0.986090	−	0.166211i	$-0.946847\pi$
$733$		−	9.00000i		−	0.332423i	0.986090	−	0.166211i	$-0.0531534\pi$
$734$	6.92820	−	4.00000i	0.255725	−	0.147643i
$735$	−5.19615	+	3.00000i	−0.191663	+	0.110657i
$736$		−	6.00000i		−	0.221163i
$737$		0			0
$738$		0			0
$739$	31.1769	+	18.0000i	1.14686	+	0.662141i	0.948120	−	0.317911i	$-0.102981\pi$
$739$	31.1769	+	18.0000i	1.14686	+	0.662141i	0.198741	+	0.980052i	$0.436315\pi$
$740$	−9.00000			−0.330847
$741$		0			0
$742$	18.0000			0.660801
$743$	33.7750	+	19.5000i	1.23908	+	0.715386i	0.968907	−	0.247425i	$-0.0795844\pi$
$743$	33.7750	+	19.5000i	1.23908	+	0.715386i	0.270177	+	0.962811i	$0.412918\pi$
$744$		0			0
$745$	9.00000	+	15.5885i	0.329734	+	0.571117i
$746$			4.00000i			0.146450i
$747$	−10.3923	+	6.00000i	−0.380235	+	0.219529i
$748$		0			0
$749$		−	36.0000i		−	1.31541i
$750$	1.50000	+	2.59808i	0.0547723	+	0.0948683i
$751$	−16.0000	+	27.7128i	−0.583848	+	1.01125i	0.411170	+	0.911559i	$0.365120\pi$
$751$	−16.0000	+	27.7128i	−0.583848	+	1.01125i	−0.995018	+	0.0996961i	$0.968213\pi$
$752$	−2.59808	−	1.50000i	−0.0947421	−	0.0546994i
$753$	−12.0000			−0.437304
$754$		0			0
$755$	−45.0000			−1.63772
$756$	12.9904	+	7.50000i	0.472456	+	0.272772i
$757$	1.00000	−	1.73205i	0.0363456	−	0.0629525i	−0.847280	−	0.531146i	$-0.821762\pi$
$757$	1.00000	−	1.73205i	0.0363456	−	0.0629525i	0.883626	+	0.468193i	$0.155095\pi$
$758$	−3.00000	−	5.19615i	−0.108965	−	0.188733i
$759$		0			0
$760$	15.5885	−	9.00000i	0.565453	−	0.326464i
$761$	−25.9808	+	15.0000i	−0.941802	+	0.543750i	−0.890525	−	0.454935i	$-0.849663\pi$
$761$	−25.9808	+	15.0000i	−0.941802	+	0.543750i	−0.0512772	+	0.998684i	$0.516329\pi$
$762$			2.00000i			0.0724524i
$763$	13.5000	+	23.3827i	0.488733	+	0.846510i
$764$	6.00000	−	10.3923i	0.217072	−	0.375980i
$765$	−15.5885	−	9.00000i	−0.563602	−	0.325396i
$766$	9.00000			0.325183
$767$		0			0
$768$	−1.00000			−0.0360844
$769$	−20.7846	−	12.0000i	−0.749512	−	0.432731i	0.0760054	−	0.997107i	$-0.475783\pi$
$769$	−20.7846	−	12.0000i	−0.749512	−	0.432731i	−0.825518	+	0.564376i	$0.809117\pi$
$770$		0			0
$771$	1.50000	+	2.59808i	0.0540212	+	0.0935674i
$772$		−	6.00000i		−	0.215945i
$773$	18.1865	−	10.5000i	0.654124	−	0.377659i	−0.135910	−	0.990721i	$-0.543396\pi$
$773$	18.1865	−	10.5000i	0.654124	−	0.377659i	0.790034	+	0.613062i	$0.210063\pi$
$774$	1.73205	−	1.00000i	0.0622573	−	0.0359443i
$775$		0			0
$776$	6.00000	+	10.3923i	0.215387	+	0.373062i
$777$	−4.50000	+	7.79423i	−0.161437	+	0.279616i
$778$	25.9808	+	15.0000i	0.931455	+	0.537776i
$779$		0			0
$780$		0			0
$781$		0			0
$782$	15.5885	+	9.00000i	0.557442	+	0.321839i
$783$		0			0
$784$	1.00000	+	1.73205i	0.0357143	+	0.0618590i
$785$			66.0000i			2.35564i
$786$	2.59808	−	1.50000i	0.0926703	−	0.0535032i
$787$	−10.3923	+	6.00000i	−0.370446	+	0.213877i	−0.673653	−	0.739048i	$-0.735276\pi$
$787$	−10.3923	+	6.00000i	−0.370446	+	0.213877i	0.303207	+	0.952925i	$0.401942\pi$
$788$		−	3.00000i		−	0.106871i
$789$	12.0000	+	20.7846i	0.427211	+	0.739952i
$790$	−15.0000	+	25.9808i	−0.533676	+	0.924354i
$791$	15.5885	+	9.00000i	0.554262	+	0.320003i
$792$		0			0
$793$		0			0
$794$	−18.0000			−0.638796
$795$	15.5885	+	9.00000i	0.552866	+	0.319197i
$796$	−10.0000	+	17.3205i	−0.354441	+	0.613909i
$797$	−9.00000	−	15.5885i	−0.318796	−	0.552171i	0.661441	−	0.749997i	$-0.269945\pi$
$797$	−9.00000	−	15.5885i	−0.318796	−	0.552171i	−0.980237	+	0.197826i	$0.936612\pi$
$798$		−	18.0000i		−	0.637193i
$799$	7.79423	−	4.50000i	0.275740	−	0.159199i
$800$	−3.46410	+	2.00000i	−0.122474	+	0.0707107i
$801$			12.0000i			0.423999i
$802$	15.0000	+	25.9808i	0.529668	+	0.917413i
$803$		0			0
$804$	10.3923	+	6.00000i	0.366508	+	0.211604i
$805$	−54.0000			−1.90325
$806$		0			0
$807$		0			0
$808$	10.3923	+	6.00000i	0.365600	+	0.211079i
$809$	−7.50000	+	12.9904i	−0.263686	+	0.456717i	−0.967219	−	0.253946i	$-0.918272\pi$
$809$	−7.50000	+	12.9904i	−0.263686	+	0.456717i	0.703533	+	0.710663i	$0.251605\pi$
$810$	−1.50000	−	2.59808i	−0.0527046	−	0.0912871i
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$		0			0
$813$	−12.9904	+	7.50000i	−0.455593	+	0.263036i
$814$		0			0
$815$	−9.00000	−	15.5885i	−0.315256	−	0.546040i
$816$	1.50000	−	2.59808i	0.0525105	−	0.0909509i
$817$	−5.19615	−	3.00000i	−0.181790	−	0.104957i
$818$	6.00000			0.209785
$819$		0			0
$820$		0			0
$821$	−38.9711	−	22.5000i	−1.36010	−	0.785255i	−0.370465	−	0.928846i	$-0.620802\pi$
$821$	−38.9711	−	22.5000i	−1.36010	−	0.785255i	−0.989637	+	0.143591i	$0.954135\pi$
$822$	−9.00000	+	15.5885i	−0.313911	+	0.543710i
$823$	−7.00000	−	12.1244i	−0.244005	−	0.422628i	0.717847	−	0.696201i	$-0.245128\pi$
$823$	−7.00000	−	12.1244i	−0.244005	−	0.422628i	−0.961851	+	0.273573i	$0.911795\pi$
$824$		−	14.0000i		−	0.487713i
$825$		0			0
$826$	15.5885	−	9.00000i	0.542392	−	0.313150i
$827$			18.0000i			0.625921i	0.949766	+	0.312961i	$0.101321\pi$
$827$			18.0000i			0.625921i	−0.949766	+	0.312961i	$0.898679\pi$
$828$	6.00000	+	10.3923i	0.208514	+	0.361158i
$829$	10.0000	−	17.3205i	0.347314	−	0.601566i	−0.638457	−	0.769657i	$-0.720427\pi$
$829$	10.0000	−	17.3205i	0.347314	−	0.601566i	0.985771	+	0.168091i	$0.0537604\pi$
$830$	−15.5885	−	9.00000i	−0.541083	−	0.312395i
$831$	−8.00000			−0.277517
$832$		0			0
$833$	−6.00000			−0.207888
$834$	4.33013	+	2.50000i	0.149940	+	0.0865679i
$835$	18.0000	−	31.1769i	0.622916	−	1.07892i
$836$		0			0
$837$		0			0
$838$	12.9904	−	7.50000i	0.448745	−	0.259083i
$839$	20.7846	−	12.0000i	0.717564	−	0.414286i	−0.0962912	−	0.995353i	$-0.530698\pi$
$839$	20.7846	−	12.0000i	0.717564	−	0.414286i	0.813856	+	0.581067i	$0.197365\pi$
$840$			9.00000i			0.310530i
$841$	14.5000	+	25.1147i	0.500000	+	0.866025i
$842$	−7.50000	+	12.9904i	−0.258467	+	0.447678i
$843$	−25.9808	−	15.0000i	−0.894825	−	0.516627i
$844$	23.0000			0.791693
$845$		0			0
$846$	6.00000			0.206284
$847$	−28.5788	−	16.5000i	−0.981981	−	0.566947i
$848$	3.00000	−	5.19615i	0.103020	−	0.178437i
$849$	2.00000	+	3.46410i	0.0686398	+	0.118888i
$850$		−	12.0000i		−	0.411597i
$851$	−15.5885	+	9.00000i	−0.534365	+	0.308516i
$852$	12.9904	−	7.50000i	0.445043	−	0.256946i
$853$		−	39.0000i		−	1.33533i	−0.744460	−	0.667667i	$-0.767293\pi$
$853$		−	39.0000i		−	1.33533i	0.744460	−	0.667667i	$-0.232707\pi$
$854$	−12.0000	−	20.7846i	−0.410632	−	0.711235i
$855$	−18.0000	+	31.1769i	−0.615587	+	1.06623i
$856$	−10.3923	−	6.00000i	−0.355202	−	0.205076i
$857$	18.0000			0.614868			0.307434	−	0.951569i	$-0.400530\pi$
$857$	18.0000			0.614868			0.307434	+	0.951569i	$0.400530\pi$
$858$		0			0
$859$	40.0000			1.36478			0.682391	−	0.730987i	$-0.260940\pi$
$859$	40.0000			1.36478			0.682391	+	0.730987i	$0.260940\pi$
$860$	2.59808	+	1.50000i	0.0885937	+	0.0511496i
$861$		0			0
$862$	−7.50000	−	12.9904i	−0.255451	−	0.442454i
$863$		−	39.0000i		−	1.32758i	−0.747921	−	0.663788i	$-0.768948\pi$
$863$		−	39.0000i		−	1.32758i	0.747921	−	0.663788i	$-0.231052\pi$
$864$	4.33013	−	2.50000i	0.147314	−	0.0850517i
$865$	15.5885	−	9.00000i	0.530023	−	0.306009i
$866$		−	11.0000i		−	0.373795i
$867$	−4.00000	−	6.92820i	−0.135847	−	0.235294i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	9.00000			0.304778
$873$	−20.7846	−	12.0000i	−0.703452	−	0.406138i
$874$	18.0000	−	31.1769i	0.608859	−	1.05457i
$875$	−4.50000	−	7.79423i	−0.152128	−	0.263493i
$876$			6.00000i			0.202721i
$877$	2.59808	−	1.50000i	0.0877308	−	0.0506514i	−0.455493	−	0.890239i	$-0.650537\pi$
$877$	2.59808	−	1.50000i	0.0877308	−	0.0506514i	0.543224	+	0.839588i	$0.317204\pi$
$878$	−8.66025	+	5.00000i	−0.292269	+	0.168742i
$879$			9.00000i			0.303562i
$880$		0			0
$881$	16.5000	−	28.5788i	0.555899	−	0.962846i	−0.441934	−	0.897048i	$-0.645707\pi$
$881$	16.5000	−	28.5788i	0.555899	−	0.962846i	0.997833	−	0.0657979i	$-0.0209593\pi$
$882$	−3.46410	−	2.00000i	−0.116642	−	0.0673435i
$883$	−11.0000			−0.370179			−0.185090	−	0.982722i	$-0.559258\pi$
$883$	−11.0000			−0.370179			−0.185090	+	0.982722i	$0.559258\pi$
$884$		0			0
$885$	18.0000			0.605063
$886$	18.1865	+	10.5000i	0.610989	+	0.352754i
$887$	6.00000	−	10.3923i	0.201460	−	0.348939i	−0.747539	−	0.664218i	$-0.768765\pi$
$887$	6.00000	−	10.3923i	0.201460	−	0.348939i	0.948999	+	0.315279i	$0.102098\pi$
$888$	1.50000	+	2.59808i	0.0503367	+	0.0871857i
$889$		−	6.00000i		−	0.201234i
$890$	−15.5885	+	9.00000i	−0.522526	+	0.301681i
$891$		0			0
$892$			9.00000i			0.301342i
$893$	−9.00000	−	15.5885i	−0.301174	−	0.521648i
$894$	3.00000	−	5.19615i	0.100335	−	0.173785i
$895$	38.9711	+	22.5000i	1.30266	+	0.752092i
$896$	3.00000			0.100223
$897$		0			0
$898$	−24.0000			−0.800890
$899$		0			0
$900$	4.00000	−	6.92820i	0.133333	−	0.230940i
$901$	9.00000	+	15.5885i	0.299833	+	0.519327i
$902$		0			0
$903$	2.59808	−	1.50000i	0.0864586	−	0.0499169i
$904$	5.19615	−	3.00000i	0.172821	−	0.0997785i
$905$		−	6.00000i		−	0.199447i
$906$	7.50000	+	12.9904i	0.249171	+	0.431577i
$907$	8.50000	−	14.7224i	0.282238	−	0.488850i	−0.689698	−	0.724097i	$-0.742257\pi$
$907$	8.50000	−	14.7224i	0.282238	−	0.488850i	0.971936	+	0.235247i	$0.0755899\pi$
$908$	−10.3923	−	6.00000i	−0.344881	−	0.199117i
$909$	−24.0000			−0.796030
$910$		0			0
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$	−5.19615	−	3.00000i	−0.172062	−	0.0993399i
$913$		0			0
$914$	9.00000	+	15.5885i	0.297694	+	0.515620i
$915$		−	24.0000i		−	0.793416i
$916$	−7.79423	+	4.50000i	−0.257529	+	0.148684i
$917$	−7.79423	+	4.50000i	−0.257388	+	0.148603i
$918$			15.0000i			0.495074i
$919$	10.0000	+	17.3205i	0.329870	+	0.571351i	0.982486	−	0.186338i	$-0.0596619\pi$
$919$	10.0000	+	17.3205i	0.329870	+	0.571351i	−0.652616	+	0.757689i	$0.726329\pi$
$920$	−9.00000	+	15.5885i	−0.296721	+	0.513936i
$921$	15.5885	+	9.00000i	0.513657	+	0.296560i
$922$	15.0000			0.493999
$923$		0			0
$924$		0			0
$925$	10.3923	+	6.00000i	0.341697	+	0.197279i
$926$	−12.0000	+	20.7846i	−0.394344	+	0.683025i
$927$	14.0000	+	24.2487i	0.459820	+	0.796432i
$928$		0			0
$929$	−31.1769	+	18.0000i	−1.02288	+	0.590561i	−0.914937	−	0.403596i	$-0.867760\pi$
$929$	−31.1769	+	18.0000i	−1.02288	+	0.590561i	−0.107944	+	0.994157i	$0.534427\pi$
$930$		0			0
$931$			12.0000i			0.393284i
$932$	−10.5000	−	18.1865i	−0.343939	−	0.595720i
$933$	−9.00000	+	15.5885i	−0.294647	+	0.510343i
$934$	10.3923	+	6.00000i	0.340047	+	0.196326i
$935$		0			0
$936$		0			0
$937$	−2.00000			−0.0653372			−0.0326686	−	0.999466i	$-0.510401\pi$
$937$	−2.00000			−0.0653372			−0.0326686	+	0.999466i	$0.510401\pi$
$938$	−31.1769	−	18.0000i	−1.01796	−	0.587721i
$939$	9.50000	−	16.4545i	0.310021	−	0.536972i
$940$	4.50000	+	7.79423i	0.146774	+	0.254220i
$941$		−	45.0000i		−	1.46696i	−0.679712	−	0.733479i	$-0.737895\pi$
$941$		−	45.0000i		−	1.46696i	0.679712	−	0.733479i	$-0.262105\pi$
$942$	19.0526	−	11.0000i	0.620766	−	0.358399i
$943$		0			0
$944$		−	6.00000i		−	0.195283i
$945$	−22.5000	−	38.9711i	−0.731925	−	1.26773i
$946$		0			0
$947$	−41.5692	−	24.0000i	−1.35082	−	0.779895i	−0.362454	−	0.932002i	$-0.618061\pi$
$947$	−41.5692	−	24.0000i	−1.35082	−	0.779895i	−0.988364	+	0.152106i	$0.951394\pi$
$948$	10.0000			0.324785
$949$		0			0
$950$	−24.0000			−0.778663
$951$	15.5885	+	9.00000i	0.505490	+	0.291845i
$952$	−4.50000	+	7.79423i	−0.145846	+	0.252612i
$953$	−4.50000	−	7.79423i	−0.145769	−	0.252480i	0.783890	−	0.620899i	$-0.213232\pi$
$953$	−4.50000	−	7.79423i	−0.145769	−	0.252480i	−0.929660	+	0.368419i	$0.879899\pi$
$954$			12.0000i			0.388514i
$955$	−31.1769	+	18.0000i	−1.00886	+	0.582466i
$956$	−7.79423	+	4.50000i	−0.252083	+	0.145540i
$957$		0			0
$958$	19.5000	+	33.7750i	0.630016	+	1.09122i
$959$	27.0000	−	46.7654i	0.871875	−	1.51013i
$960$	2.59808	+	1.50000i	0.0838525	+	0.0484123i
$961$	31.0000			1.00000
$962$		0			0
$963$	24.0000			0.773389
$964$	−25.9808	−	15.0000i	−0.836784	−	0.483117i
$965$	−9.00000	+	15.5885i	−0.289720	+	0.501810i
$966$	9.00000	+	15.5885i	0.289570	+	0.501550i
$967$			3.00000i			0.0964735i	0.998836	+	0.0482367i	$0.0153602\pi$
$967$			3.00000i			0.0964735i	−0.998836	+	0.0482367i	$0.984640\pi$
$968$	−9.52628	+	5.50000i	−0.306186	+	0.176777i
$969$	15.5885	−	9.00000i	0.500773	−	0.289122i
$970$		−	36.0000i		−	1.15589i
$971$	−13.5000	−	23.3827i	−0.433236	−	0.750386i	0.563914	−	0.825833i	$-0.309295\pi$
$971$	−13.5000	−	23.3827i	−0.433236	−	0.750386i	−0.997150	+	0.0754473i	$0.975962\pi$
$972$	−8.00000	+	13.8564i	−0.256600	+	0.444444i
$973$	−12.9904	−	7.50000i	−0.416452	−	0.240439i
$974$	12.0000			0.384505
$975$		0			0
$976$	−8.00000			−0.256074
$977$	10.3923	+	6.00000i	0.332479	+	0.191957i	0.656941	−	0.753942i	$-0.271850\pi$
$977$	10.3923	+	6.00000i	0.332479	+	0.191957i	−0.324462	+	0.945899i	$0.605183\pi$
$978$	−3.00000	+	5.19615i	−0.0959294	+	0.166155i
$979$		0			0
$980$		−	6.00000i		−	0.191663i
$981$	−15.5885	+	9.00000i	−0.497701	+	0.287348i
$982$	23.3827	−	13.5000i	0.746171	−	0.430802i
$983$		−	9.00000i		−	0.287055i	−0.989646	−	0.143528i	$-0.954155\pi$
$983$		−	9.00000i		−	0.287055i	0.989646	−	0.143528i	$-0.0458446\pi$
$984$		0			0
$985$	−4.50000	+	7.79423i	−0.143382	+	0.248345i
$986$		0			0
$987$	9.00000			0.286473
$988$		0			0
$989$	6.00000			0.190789
$990$		0			0
$991$	−1.00000	+	1.73205i	−0.0317660	+	0.0550204i	−0.881471	−	0.472237i	$-0.843446\pi$
$991$	−1.00000	+	1.73205i	−0.0317660	+	0.0550204i	0.849705	+	0.527258i	$0.176780\pi$
$992$		0			0
$993$		−	30.0000i		−	0.952021i
$994$	−38.9711	+	22.5000i	−1.23609	+	0.713657i
$995$	51.9615	−	30.0000i	1.64729	−	0.951064i
$996$			6.00000i			0.190117i
$997$	−4.00000	−	6.92820i	−0.126681	−	0.219418i	0.795708	−	0.605681i	$-0.207099\pi$
$997$	−4.00000	−	6.92820i	−0.126681	−	0.219418i	−0.922389	+	0.386263i	$0.873766\pi$
$998$	−18.0000	+	31.1769i	−0.569780	+	0.986888i
$999$	−12.9904	−	7.50000i	−0.410997	−	0.237289i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.2.e.c.147.1		4
13.2	odd	12		338.2.c.b.315.1		2
13.3	even	3	inner	338.2.e.c.23.2		4
13.4	even	6		26.2.b.a.25.1	✓	2
13.5	odd	4		338.2.c.b.191.1		2
13.6	odd	12		338.2.a.d.1.1		1
13.7	odd	12		338.2.a.b.1.1		1
13.8	odd	4		338.2.c.f.191.1		2
13.9	even	3		26.2.b.a.25.2	yes	2
13.10	even	6	inner	338.2.e.c.23.1		4
13.11	odd	12		338.2.c.f.315.1		2
13.12	even	2	inner	338.2.e.c.147.2		4
39.17	odd	6		234.2.b.b.181.2		2
39.20	even	12		3042.2.a.j.1.1		1
39.32	even	12		3042.2.a.g.1.1		1
39.35	odd	6		234.2.b.b.181.1		2
52.7	even	12		2704.2.a.k.1.1		1
52.19	even	12		2704.2.a.j.1.1		1
52.35	odd	6		208.2.f.a.129.1		2
52.43	odd	6		208.2.f.a.129.2		2
65.4	even	6		650.2.d.b.51.2		2
65.9	even	6		650.2.d.b.51.1		2
65.17	odd	12		650.2.c.d.649.2		2
65.19	odd	12		8450.2.a.h.1.1		1
65.22	odd	12		650.2.c.a.649.2		2
65.43	odd	12		650.2.c.a.649.1		2
65.48	odd	12		650.2.c.d.649.1		2
65.59	odd	12		8450.2.a.u.1.1		1
91.4	even	6		1274.2.n.d.961.2		4
91.9	even	3		1274.2.n.d.753.2		4
91.17	odd	6		1274.2.n.c.961.2		4
91.30	even	6		1274.2.n.d.753.1		4
91.48	odd	6		1274.2.d.c.883.2		2
91.61	odd	6		1274.2.n.c.753.2		4
91.69	odd	6		1274.2.d.c.883.1		2
91.74	even	3		1274.2.n.d.961.1		4
91.82	odd	6		1274.2.n.c.753.1		4
91.87	odd	6		1274.2.n.c.961.1		4
104.35	odd	6		832.2.f.b.129.2		2
104.43	odd	6		832.2.f.b.129.1		2
104.61	even	6		832.2.f.d.129.2		2
104.69	even	6		832.2.f.d.129.1		2
156.35	even	6		1872.2.c.f.1585.2		2
156.95	even	6		1872.2.c.f.1585.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.2.b.a.25.1	✓	2	13.4	even	6
26.2.b.a.25.2	yes	2	13.9	even	3
208.2.f.a.129.1		2	52.35	odd	6
208.2.f.a.129.2		2	52.43	odd	6
234.2.b.b.181.1		2	39.35	odd	6
234.2.b.b.181.2		2	39.17	odd	6
338.2.a.b.1.1		1	13.7	odd	12
338.2.a.d.1.1		1	13.6	odd	12
338.2.c.b.191.1		2	13.5	odd	4
338.2.c.b.315.1		2	13.2	odd	12
338.2.c.f.191.1		2	13.8	odd	4
338.2.c.f.315.1		2	13.11	odd	12
338.2.e.c.23.1		4	13.10	even	6	inner
338.2.e.c.23.2		4	13.3	even	3	inner
338.2.e.c.147.1		4	1.1	even	1	trivial
338.2.e.c.147.2		4	13.12	even	2	inner
650.2.c.a.649.1		2	65.43	odd	12
650.2.c.a.649.2		2	65.22	odd	12
650.2.c.d.649.1		2	65.48	odd	12
650.2.c.d.649.2		2	65.17	odd	12
650.2.d.b.51.1		2	65.9	even	6
650.2.d.b.51.2		2	65.4	even	6
832.2.f.b.129.1		2	104.43	odd	6
832.2.f.b.129.2		2	104.35	odd	6
832.2.f.d.129.1		2	104.69	even	6
832.2.f.d.129.2		2	104.61	even	6
1274.2.d.c.883.1		2	91.69	odd	6
1274.2.d.c.883.2		2	91.48	odd	6
1274.2.n.c.753.1		4	91.82	odd	6
1274.2.n.c.753.2		4	91.61	odd	6
1274.2.n.c.961.1		4	91.87	odd	6
1274.2.n.c.961.2		4	91.17	odd	6
1274.2.n.d.753.1		4	91.30	even	6
1274.2.n.d.753.2		4	91.9	even	3
1274.2.n.d.961.1		4	91.74	even	3
1274.2.n.d.961.2		4	91.4	even	6
1872.2.c.f.1585.1		2	156.95	even	6
1872.2.c.f.1585.2		2	156.35	even	6
2704.2.a.j.1.1		1	52.19	even	12
2704.2.a.k.1.1		1	52.7	even	12
3042.2.a.g.1.1		1	39.32	even	12
3042.2.a.j.1.1		1	39.20	even	12
8450.2.a.h.1.1		1	65.19	odd	12
8450.2.a.u.1.1		1	65.59	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	338.e (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -3.00000i q^{5} +(-0.866025 + 0.500000i) q^{6} +(2.59808 - 1.50000i) q^{7} -1.00000i q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -3.00000i q^{5} +(-0.866025 + 0.500000i) q^{6} +(2.59808 - 1.50000i) q^{7} -1.00000i q^{8} +(1.00000 + 1.73205i) q^{9} +(-1.50000 + 2.59808i) q^{10} +1.00000 q^{12} -3.00000 q^{14} +(-2.59808 - 1.50000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} -2.00000i q^{18} +(-5.19615 + 3.00000i) q^{19} +(2.59808 - 1.50000i) q^{20} -3.00000i q^{21} +(3.00000 - 5.19615i) q^{23} +(-0.866025 - 0.500000i) q^{24} -4.00000 q^{25} +5.00000 q^{27} +(2.59808 + 1.50000i) q^{28} +(1.50000 + 2.59808i) q^{30} +(0.866025 - 0.500000i) q^{32} +3.00000i q^{34} +(-4.50000 - 7.79423i) q^{35} +(-1.00000 + 1.73205i) q^{36} +(-2.59808 - 1.50000i) q^{37} +6.00000 q^{38} -3.00000 q^{40} +(-1.50000 + 2.59808i) q^{42} +(0.500000 + 0.866025i) q^{43} +(5.19615 - 3.00000i) q^{45} +(-5.19615 + 3.00000i) q^{46} +3.00000i q^{47} +(0.500000 + 0.866025i) q^{48} +(1.00000 - 1.73205i) q^{49} +(3.46410 + 2.00000i) q^{50} -3.00000 q^{51} -6.00000 q^{53} +(-4.33013 - 2.50000i) q^{54} +(-1.50000 - 2.59808i) q^{56} +6.00000i q^{57} +(-5.19615 + 3.00000i) q^{59} -3.00000i q^{60} +(4.00000 + 6.92820i) q^{61} +(5.19615 + 3.00000i) q^{63} -1.00000 q^{64} +(10.3923 + 6.00000i) q^{67} +(1.50000 - 2.59808i) q^{68} +(-3.00000 - 5.19615i) q^{69} +9.00000i q^{70} +(12.9904 - 7.50000i) q^{71} +(1.73205 - 1.00000i) q^{72} +6.00000i q^{73} +(1.50000 + 2.59808i) q^{74} +(-2.00000 + 3.46410i) q^{75} +(-5.19615 - 3.00000i) q^{76} +10.0000 q^{79} +(2.59808 + 1.50000i) q^{80} +(-0.500000 + 0.866025i) q^{81} +6.00000i q^{83} +(2.59808 - 1.50000i) q^{84} +(-7.79423 + 4.50000i) q^{85} -1.00000i q^{86} +(5.19615 + 3.00000i) q^{89} -6.00000 q^{90} +6.00000 q^{92} +(1.50000 - 2.59808i) q^{94} +(9.00000 + 15.5885i) q^{95} -1.00000i q^{96} +(-10.3923 + 6.00000i) q^{97} +(-1.73205 + 1.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 2 q^{4} + 4 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 + 2 * q^4 + 4 * q^9	\( 4 q + 2 q^{3} + 2 q^{4} + 4 q^{9} - 6 q^{10} + 4 q^{12} - 12 q^{14} - 2 q^{16} - 6 q^{17} + 12 q^{23} - 16 q^{25} + 20 q^{27} + 6 q^{30} - 18 q^{35} - 4 q^{36} + 24 q^{38} - 12 q^{40} - 6 q^{42} + 2 q^{43} + 2 q^{48} + 4 q^{49} - 12 q^{51} - 24 q^{53} - 6 q^{56} + 16 q^{61} - 4 q^{64} + 6 q^{68} - 12 q^{69} + 6 q^{74} - 8 q^{75} + 40 q^{79} - 2 q^{81} - 24 q^{90} + 24 q^{92} + 6 q^{94} + 36 q^{95}+O(q^{100}) \) 4 * q + 2 * q^3 + 2 * q^4 + 4 * q^9 - 6 * q^10 + 4 * q^12 - 12 * q^14 - 2 * q^16 - 6 * q^17 + 12 * q^23 - 16 * q^25 + 20 * q^27 + 6 * q^30 - 18 * q^35 - 4 * q^36 + 24 * q^38 - 12 * q^40 - 6 * q^42 + 2 * q^43 + 2 * q^48 + 4 * q^49 - 12 * q^51 - 24 * q^53 - 6 * q^56 + 16 * q^61 - 4 * q^64 + 6 * q^68 - 12 * q^69 + 6 * q^74 - 8 * q^75 + 40 * q^79 - 2 * q^81 - 24 * q^90 + 24 * q^92 + 6 * q^94 + 36 * q^95

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