LMFDB - Embedded newform 238.2.j.a.67.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [238,2,Mod(67,238)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(238, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("238.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 238 = 2 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	238.j (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.90043956811$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			67.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	238.67
Dual form			238.2.j.a.135.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(2.59808 + 1.50000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.00000i q^{6} +(-1.73205 - 2.00000i) q^{7} -1.00000 q^{8} +(3.00000 + 5.19615i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(2.59808 + 1.50000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.00000i q^{6} +(-1.73205 - 2.00000i) q^{7} -1.00000 q^{8} +(3.00000 + 5.19615i) q^{9} +(-2.59808 - 1.50000i) q^{11} +(-2.59808 + 1.50000i) q^{12} +5.00000 q^{13} +(0.866025 - 2.50000i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.96410 - 1.13397i) q^{17} +(-3.00000 + 5.19615i) q^{18} +(-2.00000 - 3.46410i) q^{19} +(-1.50000 - 7.79423i) q^{21} -3.00000i q^{22} +(3.46410 - 2.00000i) q^{23} +(-2.59808 - 1.50000i) q^{24} +(-2.50000 + 4.33013i) q^{25} +(2.50000 + 4.33013i) q^{26} +9.00000i q^{27} +(2.59808 - 0.500000i) q^{28} -4.00000i q^{29} +(3.46410 + 2.00000i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-4.50000 - 7.79423i) q^{33} +(-1.00000 - 4.00000i) q^{34} -6.00000 q^{36} +(-6.92820 + 4.00000i) q^{37} +(2.00000 - 3.46410i) q^{38} +(12.9904 + 7.50000i) q^{39} +4.00000i q^{41} +(6.00000 - 5.19615i) q^{42} +8.00000 q^{43} +(2.59808 - 1.50000i) q^{44} +(3.46410 + 2.00000i) q^{46} +(-2.00000 - 3.46410i) q^{47} -3.00000i q^{48} +(-1.00000 + 6.92820i) q^{49} -5.00000 q^{50} +(-8.59808 - 8.89230i) q^{51} +(-2.50000 + 4.33013i) q^{52} +(0.500000 - 0.866025i) q^{53} +(-7.79423 + 4.50000i) q^{54} +(1.73205 + 2.00000i) q^{56} -12.0000i q^{57} +(3.46410 - 2.00000i) q^{58} +(-6.00000 + 10.3923i) q^{59} +4.00000i q^{62} +(5.19615 - 15.0000i) q^{63} +1.00000 q^{64} +(4.50000 - 7.79423i) q^{66} +(8.00000 - 13.8564i) q^{67} +(2.96410 - 2.86603i) q^{68} +12.0000 q^{69} +1.00000i q^{71} +(-3.00000 - 5.19615i) q^{72} +(-6.92820 - 4.00000i) q^{73} +(-6.92820 - 4.00000i) q^{74} +(-12.9904 + 7.50000i) q^{75} +4.00000 q^{76} +(1.50000 + 7.79423i) q^{77} +15.0000i q^{78} +(6.06218 - 3.50000i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-3.46410 + 2.00000i) q^{82} -16.0000 q^{83} +(7.50000 + 2.59808i) q^{84} +(4.00000 + 6.92820i) q^{86} +(6.00000 - 10.3923i) q^{87} +(2.59808 + 1.50000i) q^{88} +(-4.50000 - 7.79423i) q^{89} +(-8.66025 - 10.0000i) q^{91} +4.00000i q^{92} +(6.00000 + 10.3923i) q^{93} +(2.00000 - 3.46410i) q^{94} +(2.59808 - 1.50000i) q^{96} +8.00000i q^{97} +(-6.50000 + 2.59808i) q^{98} -18.0000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} - 4 q^{8} + 12 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 + 12 * q^9	$ 4 q + 2 q^{2} - 2 q^{4} - 4 q^{8} + 12 q^{9} + 20 q^{13} - 2 q^{16} - 2 q^{17} - 12 q^{18} - 8 q^{19} - 6 q^{21} - 10 q^{25} + 10 q^{26} + 2 q^{32} - 18 q^{33} - 4 q^{34} - 24 q^{36} + 8 q^{38} + 24 q^{42} + 32 q^{43} - 8 q^{47} - 4 q^{49} - 20 q^{50} - 24 q^{51} - 10 q^{52} + 2 q^{53} - 24 q^{59} + 4 q^{64} + 18 q^{66} + 32 q^{67} - 2 q^{68} + 48 q^{69} - 12 q^{72} + 16 q^{76} + 6 q^{77} - 18 q^{81} - 64 q^{83} + 30 q^{84} + 16 q^{86} + 24 q^{87} - 18 q^{89} + 24 q^{93} + 8 q^{94} - 26 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 + 12 * q^9 + 20 * q^13 - 2 * q^16 - 2 * q^17 - 12 * q^18 - 8 * q^19 - 6 * q^21 - 10 * q^25 + 10 * q^26 + 2 * q^32 - 18 * q^33 - 4 * q^34 - 24 * q^36 + 8 * q^38 + 24 * q^42 + 32 * q^43 - 8 * q^47 - 4 * q^49 - 20 * q^50 - 24 * q^51 - 10 * q^52 + 2 * q^53 - 24 * q^59 + 4 * q^64 + 18 * q^66 + 32 * q^67 - 2 * q^68 + 48 * q^69 - 12 * q^72 + 16 * q^76 + 6 * q^77 - 18 * q^81 - 64 * q^83 + 30 * q^84 + 16 * q^86 + 24 * q^87 - 18 * q^89 + 24 * q^93 + 8 * q^94 - 26 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/238\mathbb{Z}\right)^\times$.

$n$	$71$	$171$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	2.59808	+	1.50000i	1.50000	+	0.866025i	1.00000			$0$
$3$	2.59808	+	1.50000i	1.50000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$5$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$6$			3.00000i			1.22474i
$7$	−1.73205	−	2.00000i	−0.654654	−	0.755929i
$7$	−1.73205	−	2.00000i	−0.654654	−	0.755929i
$8$	−1.00000			−0.353553
$9$	3.00000	+	5.19615i	1.00000	+	1.73205i
$10$		0			0
$11$	−2.59808	−	1.50000i	−0.783349	−	0.452267i	0.0542666	−	0.998526i	$-0.482718\pi$
$11$	−2.59808	−	1.50000i	−0.783349	−	0.452267i	−0.837616	+	0.546259i	$0.816051\pi$
$12$	−2.59808	+	1.50000i	−0.750000	+	0.433013i
$13$	5.00000			1.38675			0.693375	−	0.720577i	$-0.256123\pi$
$13$	5.00000			1.38675			0.693375	+	0.720577i	$0.256123\pi$
$14$	0.866025	−	2.50000i	0.231455	−	0.668153i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.96410	−	1.13397i	−0.961436	−	0.275029i
$17$	−3.96410	−	1.13397i	−0.961436	−	0.275029i
$18$	−3.00000	+	5.19615i	−0.707107	+	1.22474i
$19$	−2.00000	−	3.46410i	−0.458831	−	0.794719i	0.540068	−	0.841621i	$-0.318398\pi$
$19$	−2.00000	−	3.46410i	−0.458831	−	0.794719i	−0.998899	+	0.0469020i	$0.985065\pi$
$20$		0			0
$21$	−1.50000	−	7.79423i	−0.327327	−	1.70084i
$22$		−	3.00000i		−	0.639602i
$23$	3.46410	−	2.00000i	0.722315	−	0.417029i	−0.0932891	−	0.995639i	$-0.529738\pi$
$23$	3.46410	−	2.00000i	0.722315	−	0.417029i	0.815604	+	0.578610i	$0.196405\pi$
$24$	−2.59808	−	1.50000i	−0.530330	−	0.306186i
$25$	−2.50000	+	4.33013i	−0.500000	+	0.866025i
$26$	2.50000	+	4.33013i	0.490290	+	0.849208i
$27$			9.00000i			1.73205i
$28$	2.59808	−	0.500000i	0.490990	−	0.0944911i
$29$		−	4.00000i		−	0.742781i	−0.928477	−	0.371391i	$-0.878881\pi$
$29$		−	4.00000i		−	0.742781i	0.928477	−	0.371391i	$-0.121119\pi$
$30$		0			0
$31$	3.46410	+	2.00000i	0.622171	+	0.359211i	0.777714	−	0.628619i	$-0.216379\pi$
$31$	3.46410	+	2.00000i	0.622171	+	0.359211i	−0.155543	+	0.987829i	$0.549713\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−4.50000	−	7.79423i	−0.783349	−	1.35680i
$34$	−1.00000	−	4.00000i	−0.171499	−	0.685994i
$35$		0			0
$36$	−6.00000			−1.00000
$37$	−6.92820	+	4.00000i	−1.13899	+	0.657596i	−0.946180	−	0.323640i	$-0.895093\pi$
$37$	−6.92820	+	4.00000i	−1.13899	+	0.657596i	−0.192809	+	0.981236i	$0.561760\pi$
$38$	2.00000	−	3.46410i	0.324443	−	0.561951i
$39$	12.9904	+	7.50000i	2.08013	+	1.20096i
$40$		0			0
$41$			4.00000i			0.624695i	0.949968	+	0.312348i	$0.101115\pi$
$41$			4.00000i			0.624695i	−0.949968	+	0.312348i	$0.898885\pi$
$42$	6.00000	−	5.19615i	0.925820	−	0.801784i
$43$	8.00000			1.21999			0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000			1.21999			0.609994	+	0.792406i	$0.291172\pi$
$44$	2.59808	−	1.50000i	0.391675	−	0.226134i
$45$		0			0
$46$	3.46410	+	2.00000i	0.510754	+	0.294884i
$47$	−2.00000	−	3.46410i	−0.291730	−	0.505291i	0.682489	−	0.730896i	$-0.260898\pi$
$47$	−2.00000	−	3.46410i	−0.291730	−	0.505291i	−0.974219	+	0.225605i	$0.927564\pi$
$48$		−	3.00000i		−	0.433013i
$49$	−1.00000	+	6.92820i	−0.142857	+	0.989743i
$50$	−5.00000			−0.707107
$51$	−8.59808	−	8.89230i	−1.20397	−	1.24517i
$52$	−2.50000	+	4.33013i	−0.346688	+	0.600481i
$53$	0.500000	−	0.866025i	0.0686803	−	0.118958i	−0.829640	−	0.558298i	$-0.811454\pi$
$53$	0.500000	−	0.866025i	0.0686803	−	0.118958i	0.898321	+	0.439340i	$0.144788\pi$
$54$	−7.79423	+	4.50000i	−1.06066	+	0.612372i
$55$		0			0
$56$	1.73205	+	2.00000i	0.231455	+	0.267261i
$57$		−	12.0000i		−	1.58944i
$58$	3.46410	−	2.00000i	0.454859	−	0.262613i
$59$	−6.00000	+	10.3923i	−0.781133	+	1.35296i	0.150148	+	0.988663i	$0.452025\pi$
$59$	−6.00000	+	10.3923i	−0.781133	+	1.35296i	−0.931282	+	0.364299i	$0.881308\pi$
$60$		0			0
$61$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$61$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$62$			4.00000i			0.508001i
$63$	5.19615	−	15.0000i	0.654654	−	1.88982i
$64$	1.00000			0.125000
$65$		0			0
$66$	4.50000	−	7.79423i	0.553912	−	0.959403i
$67$	8.00000	−	13.8564i	0.977356	−	1.69283i	0.305424	−	0.952217i	$-0.401202\pi$
$67$	8.00000	−	13.8564i	0.977356	−	1.69283i	0.671932	−	0.740613i	$-0.265465\pi$
$68$	2.96410	−	2.86603i	0.359450	−	0.347557i
$69$	12.0000			1.44463
$70$		0			0
$71$			1.00000i			0.118678i	0.998238	+	0.0593391i	$0.0188993\pi$
$71$			1.00000i			0.118678i	−0.998238	+	0.0593391i	$0.981101\pi$
$72$	−3.00000	−	5.19615i	−0.353553	−	0.612372i
$73$	−6.92820	−	4.00000i	−0.810885	−	0.468165i	0.0363782	−	0.999338i	$-0.488418\pi$
$73$	−6.92820	−	4.00000i	−0.810885	−	0.468165i	−0.847263	+	0.531174i	$0.821751\pi$
$74$	−6.92820	−	4.00000i	−0.805387	−	0.464991i
$75$	−12.9904	+	7.50000i	−1.50000	+	0.866025i
$76$	4.00000			0.458831
$77$	1.50000	+	7.79423i	0.170941	+	0.888235i
$78$			15.0000i			1.69842i
$79$	6.06218	−	3.50000i	0.682048	−	0.393781i	−0.118578	−	0.992945i	$-0.537834\pi$
$79$	6.06218	−	3.50000i	0.682048	−	0.393781i	0.800626	+	0.599164i	$0.204500\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	−3.46410	+	2.00000i	−0.382546	+	0.220863i
$83$	−16.0000			−1.75623			−0.878114	−	0.478451i	$-0.841198\pi$
$83$	−16.0000			−1.75623			−0.878114	+	0.478451i	$0.841198\pi$
$84$	7.50000	+	2.59808i	0.818317	+	0.283473i
$85$		0			0
$86$	4.00000	+	6.92820i	0.431331	+	0.747087i
$87$	6.00000	−	10.3923i	0.643268	−	1.11417i
$88$	2.59808	+	1.50000i	0.276956	+	0.159901i
$89$	−4.50000	−	7.79423i	−0.476999	−	0.826187i	0.522654	−	0.852545i	$-0.324942\pi$
$89$	−4.50000	−	7.79423i	−0.476999	−	0.826187i	−0.999653	+	0.0263586i	$0.991609\pi$
$90$		0			0
$91$	−8.66025	−	10.0000i	−0.907841	−	1.04828i
$92$			4.00000i			0.417029i
$93$	6.00000	+	10.3923i	0.622171	+	1.07763i
$94$	2.00000	−	3.46410i	0.206284	−	0.357295i
$95$		0			0
$96$	2.59808	−	1.50000i	0.265165	−	0.153093i
$97$			8.00000i			0.812277i	0.913812	+	0.406138i	$0.133125\pi$
$97$			8.00000i			0.812277i	−0.913812	+	0.406138i	$0.866875\pi$
$98$	−6.50000	+	2.59808i	−0.656599	+	0.262445i
$99$		−	18.0000i		−	1.80907i
$100$	−2.50000	−	4.33013i	−0.250000	−	0.433013i
$101$	−5.00000	+	8.66025i	−0.497519	+	0.861727i	−0.999996	−	0.00286291i	$-0.999089\pi$
$101$	−5.00000	+	8.66025i	−0.497519	+	0.861727i	0.502477	+	0.864590i	$0.332422\pi$
$102$	3.40192	−	11.8923i	0.336841	−	1.17751i
$103$	4.00000	+	6.92820i	0.394132	+	0.682656i	0.992990	−	0.118199i	$-0.0377120\pi$
$103$	4.00000	+	6.92820i	0.394132	+	0.682656i	−0.598858	+	0.800855i	$0.704379\pi$
$104$	−5.00000			−0.490290
$105$		0			0
$106$	1.00000			0.0971286
$107$	−2.59808	+	1.50000i	−0.251166	+	0.145010i	−0.620298	−	0.784366i	$-0.712988\pi$
$107$	−2.59808	+	1.50000i	−0.251166	+	0.145010i	0.369132	+	0.929377i	$0.379655\pi$
$108$	−7.79423	−	4.50000i	−0.750000	−	0.433013i
$109$	17.3205	+	10.0000i	1.65900	+	0.957826i	0.973176	+	0.230063i	$0.0738931\pi$
$109$	17.3205	+	10.0000i	1.65900	+	0.957826i	0.685828	+	0.727764i	$0.259440\pi$
$110$		0			0
$111$	−24.0000			−2.27798
$112$	−0.866025	+	2.50000i	−0.0818317	+	0.236228i
$113$			12.0000i			1.12887i	0.825479	+	0.564433i	$0.190905\pi$
$113$			12.0000i			1.12887i	−0.825479	+	0.564433i	$0.809095\pi$
$114$	10.3923	−	6.00000i	0.973329	−	0.561951i
$115$		0			0
$116$	3.46410	+	2.00000i	0.321634	+	0.185695i
$117$	15.0000	+	25.9808i	1.38675	+	2.40192i
$118$	−12.0000			−1.10469
$119$	4.59808	+	9.89230i	0.421505	+	0.906826i
$120$		0			0
$121$	−1.00000	−	1.73205i	−0.0909091	−	0.157459i
$122$		0			0
$123$	−6.00000	+	10.3923i	−0.541002	+	0.937043i
$124$	−3.46410	+	2.00000i	−0.311086	+	0.179605i
$125$		0			0
$126$	15.5885	−	3.00000i	1.38873	−	0.267261i
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	20.7846	+	12.0000i	1.82998	+	1.05654i
$130$		0			0
$131$	−6.92820	+	4.00000i	−0.605320	+	0.349482i	−0.771132	−	0.636676i	$-0.780309\pi$
$131$	−6.92820	+	4.00000i	−0.605320	+	0.349482i	0.165812	+	0.986157i	$0.446976\pi$
$132$	9.00000			0.783349
$133$	−3.46410	+	10.0000i	−0.300376	+	0.867110i
$134$	16.0000			1.38219
$135$		0			0
$136$	3.96410	+	1.13397i	0.339919	+	0.0972375i
$137$	−4.50000	+	7.79423i	−0.384461	+	0.665906i	−0.991694	−	0.128618i	$-0.958946\pi$
$137$	−4.50000	+	7.79423i	−0.384461	+	0.665906i	0.607233	+	0.794524i	$0.292279\pi$
$138$	6.00000	+	10.3923i	0.510754	+	0.884652i
$139$			11.0000i			0.933008i	0.884519	+	0.466504i	$0.154487\pi$
$139$			11.0000i			0.933008i	−0.884519	+	0.466504i	$0.845513\pi$
$140$		0			0
$141$		−	12.0000i		−	1.01058i
$142$	−0.866025	+	0.500000i	−0.0726752	+	0.0419591i
$143$	−12.9904	−	7.50000i	−1.08631	−	0.627182i
$144$	3.00000	−	5.19615i	0.250000	−	0.433013i
$145$		0			0
$146$		−	8.00000i		−	0.662085i
$147$	−12.9904	+	16.5000i	−1.07143	+	1.36090i
$148$		−	8.00000i		−	0.657596i
$149$	−5.50000	−	9.52628i	−0.450578	−	0.780423i	0.547844	−	0.836580i	$-0.315449\pi$
$149$	−5.50000	−	9.52628i	−0.450578	−	0.780423i	−0.998422	+	0.0561570i	$0.982115\pi$
$150$	−12.9904	−	7.50000i	−1.06066	−	0.612372i
$151$	6.00000	−	10.3923i	0.488273	−	0.845714i	−0.511636	−	0.859202i	$-0.670960\pi$
$151$	6.00000	−	10.3923i	0.488273	−	0.845714i	0.999909	+	0.0134886i	$0.00429367\pi$
$152$	2.00000	+	3.46410i	0.162221	+	0.280976i
$153$	−6.00000	−	24.0000i	−0.485071	−	1.94029i
$154$	−6.00000	+	5.19615i	−0.483494	+	0.418718i
$155$		0			0
$156$	−12.9904	+	7.50000i	−1.04006	+	0.600481i
$157$	−1.50000	+	2.59808i	−0.119713	+	0.207349i	−0.919654	−	0.392730i	$-0.871531\pi$
$157$	−1.50000	+	2.59808i	−0.119713	+	0.207349i	0.799941	+	0.600079i	$0.204864\pi$
$158$	6.06218	+	3.50000i	0.482281	+	0.278445i
$159$	2.59808	−	1.50000i	0.206041	−	0.118958i
$160$		0			0
$161$	−10.0000	−	3.46410i	−0.788110	−	0.273009i
$162$	−9.00000			−0.707107
$163$	−13.8564	+	8.00000i	−1.08532	+	0.626608i	−0.932326	−	0.361619i	$-0.882224\pi$
$163$	−13.8564	+	8.00000i	−1.08532	+	0.626608i	−0.152992	+	0.988227i	$0.548891\pi$
$164$	−3.46410	−	2.00000i	−0.270501	−	0.156174i
$165$		0			0
$166$	−8.00000	−	13.8564i	−0.620920	−	1.07547i
$167$		−	25.0000i		−	1.93456i	−0.253715	−	0.967279i	$-0.581653\pi$
$167$		−	25.0000i		−	1.93456i	0.253715	−	0.967279i	$-0.418347\pi$
$168$	1.50000	+	7.79423i	0.115728	+	0.601338i
$169$	12.0000			0.923077
$170$		0			0
$171$	12.0000	−	20.7846i	0.917663	−	1.58944i
$172$	−4.00000	+	6.92820i	−0.304997	+	0.528271i
$173$	−3.46410	+	2.00000i	−0.263371	+	0.152057i	−0.625871	−	0.779926i	$-0.715256\pi$
$173$	−3.46410	+	2.00000i	−0.263371	+	0.152057i	0.362500	+	0.931984i	$0.381923\pi$
$174$	12.0000			0.909718
$175$	12.9904	−	2.50000i	0.981981	−	0.188982i
$176$			3.00000i			0.226134i
$177$	−31.1769	+	18.0000i	−2.34340	+	1.35296i
$178$	4.50000	−	7.79423i	0.337289	−	0.584202i
$179$	8.00000	−	13.8564i	0.597948	−	1.03568i	−0.395175	−	0.918606i	$-0.629316\pi$
$179$	8.00000	−	13.8564i	0.597948	−	1.03568i	0.993124	−	0.117071i	$-0.0373504\pi$
$180$		0			0
$181$			4.00000i			0.297318i	0.988889	+	0.148659i	$0.0474956\pi$
$181$			4.00000i			0.297318i	−0.988889	+	0.148659i	$0.952504\pi$
$182$	4.33013	−	12.5000i	0.320970	−	0.926562i
$183$		0			0
$184$	−3.46410	+	2.00000i	−0.255377	+	0.147442i
$185$		0			0
$186$	−6.00000	+	10.3923i	−0.439941	+	0.762001i
$187$	8.59808	+	8.89230i	0.628754	+	0.650270i
$188$	4.00000			0.291730
$189$	18.0000	−	15.5885i	1.30931	−	1.13389i
$190$		0			0
$191$	6.00000	+	10.3923i	0.434145	+	0.751961i	0.997225	−	0.0744412i	$-0.0237173\pi$
$191$	6.00000	+	10.3923i	0.434145	+	0.751961i	−0.563081	+	0.826402i	$0.690384\pi$
$192$	2.59808	+	1.50000i	0.187500	+	0.108253i
$193$	3.46410	+	2.00000i	0.249351	+	0.143963i	0.619467	−	0.785022i	$-0.287349\pi$
$193$	3.46410	+	2.00000i	0.249351	+	0.143963i	−0.370116	+	0.928986i	$0.620682\pi$
$194$	−6.92820	+	4.00000i	−0.497416	+	0.287183i
$195$		0			0
$196$	−5.50000	−	4.33013i	−0.392857	−	0.309295i
$197$			16.0000i			1.13995i	0.821661	+	0.569976i	$0.193048\pi$
$197$			16.0000i			1.13995i	−0.821661	+	0.569976i	$0.806952\pi$
$198$	15.5885	−	9.00000i	1.10782	−	0.639602i
$199$	−2.59808	−	1.50000i	−0.184173	−	0.106332i	0.405079	−	0.914282i	$-0.367244\pi$
$199$	−2.59808	−	1.50000i	−0.184173	−	0.106332i	−0.589252	+	0.807950i	$0.700577\pi$
$200$	2.50000	−	4.33013i	0.176777	−	0.306186i
$201$	41.5692	−	24.0000i	2.93207	−	1.69283i
$202$	−10.0000			−0.703598
$203$	−8.00000	+	6.92820i	−0.561490	+	0.486265i
$204$	12.0000	−	3.00000i	0.840168	−	0.210042i
$205$		0			0
$206$	−4.00000	+	6.92820i	−0.278693	+	0.482711i
$207$	20.7846	+	12.0000i	1.44463	+	0.834058i
$208$	−2.50000	−	4.33013i	−0.173344	−	0.300240i
$209$			12.0000i			0.830057i
$210$		0			0
$211$		−	24.0000i		−	1.65223i	−0.563503	−	0.826114i	$-0.690547\pi$
$211$		−	24.0000i		−	1.65223i	0.563503	−	0.826114i	$-0.309453\pi$
$212$	0.500000	+	0.866025i	0.0343401	+	0.0594789i
$213$	−1.50000	+	2.59808i	−0.102778	+	0.178017i
$214$	−2.59808	−	1.50000i	−0.177601	−	0.102538i
$215$		0			0
$216$		−	9.00000i		−	0.612372i
$217$	−2.00000	−	10.3923i	−0.135769	−	0.705476i
$218$			20.0000i			1.35457i
$219$	−12.0000	−	20.7846i	−0.810885	−	1.40449i
$220$		0			0
$221$	−19.8205	−	5.66987i	−1.33327	−	0.381397i
$222$	−12.0000	−	20.7846i	−0.805387	−	1.39497i
$223$	12.0000			0.803579			0.401790	−	0.915732i	$-0.368388\pi$
$223$	12.0000			0.803579			0.401790	+	0.915732i	$0.368388\pi$
$224$	−2.59808	+	0.500000i	−0.173591	+	0.0334077i
$225$	−30.0000			−2.00000
$226$	−10.3923	+	6.00000i	−0.691286	+	0.399114i
$227$	18.1865	+	10.5000i	1.20708	+	0.696909i	0.962121	−	0.272623i	$-0.0878913\pi$
$227$	18.1865	+	10.5000i	1.20708	+	0.696909i	0.244962	+	0.969533i	$0.421225\pi$
$228$	10.3923	+	6.00000i	0.688247	+	0.397360i
$229$	−13.0000	−	22.5167i	−0.859064	−	1.48794i	−0.872823	−	0.488037i	$-0.837713\pi$
$229$	−13.0000	−	22.5167i	−0.859064	−	1.48794i	0.0137585	−	0.999905i	$-0.495620\pi$
$230$		0			0
$231$	−7.79423	+	22.5000i	−0.512823	+	1.48039i
$232$			4.00000i			0.262613i
$233$	13.8564	−	8.00000i	0.907763	−	0.524097i	0.0280525	−	0.999606i	$-0.491069\pi$
$233$	13.8564	−	8.00000i	0.907763	−	0.524097i	0.879711	+	0.475509i	$0.157736\pi$
$234$	−15.0000	+	25.9808i	−0.980581	+	1.69842i
$235$		0			0
$236$	−6.00000	−	10.3923i	−0.390567	−	0.676481i
$237$	21.0000			1.36410
$238$	−6.26795	+	8.92820i	−0.406291	+	0.578729i
$239$	−16.0000			−1.03495			−0.517477	−	0.855697i	$-0.673129\pi$
$239$	−16.0000			−1.03495			−0.517477	+	0.855697i	$0.673129\pi$
$240$		0			0
$241$	10.3923	+	6.00000i	0.669427	+	0.386494i	0.795860	−	0.605481i	$-0.207019\pi$
$241$	10.3923	+	6.00000i	0.669427	+	0.386494i	−0.126432	+	0.991975i	$0.540353\pi$
$242$	1.00000	−	1.73205i	0.0642824	−	0.111340i
$243$		0			0
$244$		0			0
$245$		0			0
$246$	−12.0000			−0.765092
$247$	−10.0000	−	17.3205i	−0.636285	−	1.10208i
$248$	−3.46410	−	2.00000i	−0.219971	−	0.127000i
$249$	−41.5692	−	24.0000i	−2.63434	−	1.52094i
$250$		0			0
$251$	16.0000			1.00991			0.504956	−	0.863145i	$-0.331509\pi$
$251$	16.0000			1.00991			0.504956	+	0.863145i	$0.331509\pi$
$252$	10.3923	+	12.0000i	0.654654	+	0.755929i
$253$	−12.0000			−0.754434
$254$	4.00000	+	6.92820i	0.250982	+	0.434714i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	3.50000	+	6.06218i	0.218324	+	0.378148i	0.954296	−	0.298864i	$-0.0966077\pi$
$257$	3.50000	+	6.06218i	0.218324	+	0.378148i	−0.735972	+	0.677012i	$0.763274\pi$
$258$			24.0000i			1.49417i
$259$	20.0000	+	6.92820i	1.24274	+	0.430498i
$260$		0			0
$261$	20.7846	−	12.0000i	1.28654	−	0.742781i
$262$	−6.92820	−	4.00000i	−0.428026	−	0.247121i
$263$	−2.00000	+	3.46410i	−0.123325	+	0.213606i	−0.921077	−	0.389380i	$-0.872689\pi$
$263$	−2.00000	+	3.46410i	−0.123325	+	0.213606i	0.797752	+	0.602986i	$0.206023\pi$
$264$	4.50000	+	7.79423i	0.276956	+	0.479702i
$265$		0			0
$266$	−10.3923	+	2.00000i	−0.637193	+	0.122628i
$267$		−	27.0000i		−	1.65237i
$268$	8.00000	+	13.8564i	0.488678	+	0.846415i
$269$	3.46410	+	2.00000i	0.211210	+	0.121942i	0.601874	−	0.798591i	$-0.294421\pi$
$269$	3.46410	+	2.00000i	0.211210	+	0.121942i	−0.390664	+	0.920534i	$0.627754\pi$
$270$		0			0
$271$	−6.00000	−	10.3923i	−0.364474	−	0.631288i	0.624218	−	0.781251i	$-0.285418\pi$
$271$	−6.00000	−	10.3923i	−0.364474	−	0.631288i	−0.988692	+	0.149963i	$0.952085\pi$
$272$	1.00000	+	4.00000i	0.0606339	+	0.242536i
$273$	−7.50000	−	38.9711i	−0.453921	−	2.35864i
$274$	−9.00000			−0.543710
$275$	12.9904	−	7.50000i	0.783349	−	0.452267i
$276$	−6.00000	+	10.3923i	−0.361158	+	0.625543i
$277$	−3.46410	−	2.00000i	−0.208138	−	0.120168i	0.392308	−	0.919834i	$-0.371677\pi$
$277$	−3.46410	−	2.00000i	−0.208138	−	0.120168i	−0.600446	+	0.799666i	$0.705010\pi$
$278$	−9.52628	+	5.50000i	−0.571348	+	0.329868i
$279$			24.0000i			1.43684i
$280$		0			0
$281$	7.00000			0.417585			0.208792	−	0.977960i	$-0.433047\pi$
$281$	7.00000			0.417585			0.208792	+	0.977960i	$0.433047\pi$
$282$	10.3923	−	6.00000i	0.618853	−	0.357295i
$283$	9.52628	+	5.50000i	0.566279	+	0.326941i	0.755662	−	0.654962i	$-0.227315\pi$
$283$	9.52628	+	5.50000i	0.566279	+	0.326941i	−0.189383	+	0.981903i	$0.560649\pi$
$284$	−0.866025	−	0.500000i	−0.0513892	−	0.0296695i
$285$		0			0
$286$		−	15.0000i		−	0.886969i
$287$	8.00000	−	6.92820i	0.472225	−	0.408959i
$288$	6.00000			0.353553
$289$	14.4282	+	8.99038i	0.848718	+	0.528846i
$290$		0			0
$291$	−12.0000	+	20.7846i	−0.703452	+	1.21842i
$292$	6.92820	−	4.00000i	0.405442	−	0.234082i
$293$	23.0000			1.34367			0.671837	−	0.740699i	$-0.265505\pi$
$293$	23.0000			1.34367			0.671837	+	0.740699i	$0.265505\pi$
$294$	−20.7846	−	3.00000i	−1.21218	−	0.174964i
$295$		0			0
$296$	6.92820	−	4.00000i	0.402694	−	0.232495i
$297$	13.5000	−	23.3827i	0.783349	−	1.35680i
$298$	5.50000	−	9.52628i	0.318606	−	0.551843i
$299$	17.3205	−	10.0000i	1.00167	−	0.578315i
$300$		−	15.0000i		−	0.866025i
$301$	−13.8564	−	16.0000i	−0.798670	−	0.922225i
$302$	12.0000			0.690522
$303$	−25.9808	+	15.0000i	−1.49256	+	0.861727i
$304$	−2.00000	+	3.46410i	−0.114708	+	0.198680i
$305$		0			0
$306$	17.7846	−	17.1962i	1.01668	−	0.983039i
$307$	−16.0000			−0.913168			−0.456584	−	0.889680i	$-0.650927\pi$
$307$	−16.0000			−0.913168			−0.456584	+	0.889680i	$0.650927\pi$
$308$	−7.50000	−	2.59808i	−0.427352	−	0.148039i
$309$			24.0000i			1.36531i
$310$		0			0
$311$	−18.1865	−	10.5000i	−1.03126	−	0.595400i	−0.113917	−	0.993490i	$-0.536340\pi$
$311$	−18.1865	−	10.5000i	−1.03126	−	0.595400i	−0.917346	+	0.398090i	$0.869673\pi$
$312$	−12.9904	−	7.50000i	−0.735436	−	0.424604i
$313$	−17.3205	+	10.0000i	−0.979013	+	0.565233i	−0.901972	−	0.431795i	$-0.857881\pi$
$313$	−17.3205	+	10.0000i	−0.979013	+	0.565233i	−0.0770410	+	0.997028i	$0.524547\pi$
$314$	−3.00000			−0.169300
$315$		0			0
$316$			7.00000i			0.393781i
$317$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$317$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$318$	2.59808	+	1.50000i	0.145693	+	0.0841158i
$319$	−6.00000	+	10.3923i	−0.335936	+	0.581857i
$320$		0			0
$321$	−9.00000			−0.502331
$322$	−2.00000	−	10.3923i	−0.111456	−	0.579141i
$323$	4.00000	+	16.0000i	0.222566	+	0.890264i
$324$	−4.50000	−	7.79423i	−0.250000	−	0.433013i
$325$	−12.5000	+	21.6506i	−0.693375	+	1.20096i
$326$	−13.8564	−	8.00000i	−0.767435	−	0.443079i
$327$	30.0000	+	51.9615i	1.65900	+	2.87348i
$328$		−	4.00000i		−	0.220863i
$329$	−3.46410	+	10.0000i	−0.190982	+	0.551318i
$330$		0			0
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	0.915742	−	0.401768i	$-0.131604\pi$
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	−0.805812	+	0.592172i	$0.798271\pi$
$332$	8.00000	−	13.8564i	0.439057	−	0.760469i
$333$	−41.5692	−	24.0000i	−2.27798	−	1.31519i
$334$	21.6506	−	12.5000i	1.18467	−	0.683970i
$335$		0			0
$336$	−6.00000	+	5.19615i	−0.327327	+	0.283473i
$337$		−	8.00000i		−	0.435788i	−0.975972	−	0.217894i	$-0.930081\pi$
$337$		−	8.00000i		−	0.435788i	0.975972	−	0.217894i	$-0.0699187\pi$
$338$	6.00000	+	10.3923i	0.326357	+	0.565267i
$339$	−18.0000	+	31.1769i	−0.977626	+	1.69330i
$340$		0			0
$341$	−6.00000	−	10.3923i	−0.324918	−	0.562775i
$342$	24.0000			1.29777
$343$	15.5885	−	10.0000i	0.841698	−	0.539949i
$344$	−8.00000			−0.431331
$345$		0			0
$346$	−3.46410	−	2.00000i	−0.186231	−	0.107521i
$347$	27.7128	+	16.0000i	1.48770	+	0.858925i	0.999902	−	0.0140303i	$-0.00446613\pi$
$347$	27.7128	+	16.0000i	1.48770	+	0.858925i	0.487800	+	0.872955i	$0.337799\pi$
$348$	6.00000	+	10.3923i	0.321634	+	0.557086i
$349$	30.0000			1.60586			0.802932	−	0.596071i	$-0.203272\pi$
$349$	30.0000			1.60586			0.802932	+	0.596071i	$0.203272\pi$
$350$	8.66025	+	10.0000i	0.462910	+	0.534522i
$351$			45.0000i			2.40192i
$352$	−2.59808	+	1.50000i	−0.138478	+	0.0799503i
$353$	10.5000	−	18.1865i	0.558859	−	0.967972i	−0.438733	−	0.898617i	$-0.644573\pi$
$353$	10.5000	−	18.1865i	0.558859	−	0.967972i	0.997592	−	0.0693543i	$-0.0220939\pi$
$354$	−31.1769	−	18.0000i	−1.65703	−	0.956689i
$355$		0			0
$356$	9.00000			0.476999
$357$	−2.89230	+	32.5981i	−0.153077	+	1.72527i
$358$	16.0000			0.845626
$359$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$359$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$360$		0			0
$361$	1.50000	−	2.59808i	0.0789474	−	0.136741i
$362$	−3.46410	+	2.00000i	−0.182069	+	0.105118i
$363$		−	6.00000i		−	0.314918i
$364$	12.9904	−	2.50000i	0.680881	−	0.131036i
$365$		0			0
$366$		0			0
$367$	−6.06218	−	3.50000i	−0.316443	−	0.182699i	0.333363	−	0.942799i	$-0.391817\pi$
$367$	−6.06218	−	3.50000i	−0.316443	−	0.182699i	−0.649806	+	0.760100i	$0.725150\pi$
$368$	−3.46410	−	2.00000i	−0.180579	−	0.104257i
$369$	−20.7846	+	12.0000i	−1.08200	+	0.624695i
$370$		0			0
$371$	−2.59808	+	0.500000i	−0.134885	+	0.0259587i
$372$	−12.0000			−0.622171
$373$	9.50000	+	16.4545i	0.491891	+	0.851981i	0.999956	−	0.00933789i	$-0.00297238\pi$
$373$	9.50000	+	16.4545i	0.491891	+	0.851981i	−0.508065	+	0.861319i	$0.669639\pi$
$374$	−3.40192	+	11.8923i	−0.175909	+	0.614936i
$375$		0			0
$376$	2.00000	+	3.46410i	0.103142	+	0.178647i
$377$		−	20.0000i		−	1.03005i
$378$	22.5000	+	7.79423i	1.15728	+	0.400892i
$379$			1.00000i			0.0513665i	0.999670	+	0.0256833i	$0.00817614\pi$
$379$			1.00000i			0.0513665i	−0.999670	+	0.0256833i	$0.991824\pi$
$380$		0			0
$381$	20.7846	+	12.0000i	1.06483	+	0.614779i
$382$	−6.00000	+	10.3923i	−0.306987	+	0.531717i
$383$	−12.0000	−	20.7846i	−0.613171	−	1.06204i	−0.990702	−	0.136047i	$-0.956560\pi$
$383$	−12.0000	−	20.7846i	−0.613171	−	1.06204i	0.377531	−	0.925997i	$-0.376773\pi$
$384$			3.00000i			0.153093i
$385$		0			0
$386$			4.00000i			0.203595i
$387$	24.0000	+	41.5692i	1.21999	+	2.11308i
$388$	−6.92820	−	4.00000i	−0.351726	−	0.203069i
$389$	7.50000	−	12.9904i	0.380265	−	0.658638i	−0.610835	−	0.791758i	$-0.709166\pi$
$389$	7.50000	−	12.9904i	0.380265	−	0.658638i	0.991100	+	0.133120i	$0.0424994\pi$
$390$		0			0
$391$	−16.0000	+	4.00000i	−0.809155	+	0.202289i
$392$	1.00000	−	6.92820i	0.0505076	−	0.349927i
$393$	−24.0000			−1.21064
$394$	−13.8564	+	8.00000i	−0.698076	+	0.403034i
$395$		0			0
$396$	15.5885	+	9.00000i	0.783349	+	0.452267i
$397$	27.7128	−	16.0000i	1.39087	−	0.803017i	0.397455	−	0.917622i	$-0.369893\pi$
$397$	27.7128	−	16.0000i	1.39087	−	0.803017i	0.993411	+	0.114605i	$0.0365601\pi$
$398$		−	3.00000i		−	0.150376i
$399$	−24.0000	+	20.7846i	−1.20150	+	1.04053i
$400$	5.00000			0.250000
$401$	17.3205	−	10.0000i	0.864945	−	0.499376i	−0.000720188	−	1.00000i	$-0.500229\pi$
$401$	17.3205	−	10.0000i	0.864945	−	0.499376i	0.865665	+	0.500624i	$0.166896\pi$
$402$	41.5692	+	24.0000i	2.07328	+	1.19701i
$403$	17.3205	+	10.0000i	0.862796	+	0.498135i
$404$	−5.00000	−	8.66025i	−0.248759	−	0.430864i
$405$		0			0
$406$	−10.0000	−	3.46410i	−0.496292	−	0.171920i
$407$	24.0000			1.18964
$408$	8.59808	+	8.89230i	0.425668	+	0.440235i
$409$	−9.50000	+	16.4545i	−0.469745	+	0.813622i	−0.999402	−	0.0345902i	$-0.988987\pi$
$409$	−9.50000	+	16.4545i	−0.469745	+	0.813622i	0.529657	+	0.848212i	$0.322321\pi$
$410$		0			0
$411$	−23.3827	+	13.5000i	−1.15338	+	0.665906i
$412$	−8.00000			−0.394132
$413$	31.1769	−	6.00000i	1.53412	−	0.295241i
$414$			24.0000i			1.17954i
$415$		0			0
$416$	2.50000	−	4.33013i	0.122573	−	0.212302i
$417$	−16.5000	+	28.5788i	−0.808008	+	1.39951i
$418$	−10.3923	+	6.00000i	−0.508304	+	0.293470i
$419$		−	5.00000i		−	0.244266i	−0.992514	−	0.122133i	$-0.961027\pi$
$419$		−	5.00000i		−	0.244266i	0.992514	−	0.122133i	$-0.0389734\pi$
$420$		0			0
$421$	10.0000			0.487370			0.243685	−	0.969854i	$-0.421644\pi$
$421$	10.0000			0.487370			0.243685	+	0.969854i	$0.421644\pi$
$422$	20.7846	−	12.0000i	1.01178	−	0.584151i
$423$	12.0000	−	20.7846i	0.583460	−	1.01058i
$424$	−0.500000	+	0.866025i	−0.0242821	+	0.0420579i
$425$	14.8205	−	14.3301i	0.718900	−	0.695113i
$426$	−3.00000			−0.145350
$427$		0			0
$428$		−	3.00000i		−	0.145010i
$429$	−22.5000	−	38.9711i	−1.08631	−	1.88154i
$430$		0			0
$431$	−18.1865	−	10.5000i	−0.876014	−	0.505767i	−0.00667224	−	0.999978i	$-0.502124\pi$
$431$	−18.1865	−	10.5000i	−0.876014	−	0.505767i	−0.869342	+	0.494211i	$0.835457\pi$
$432$	7.79423	−	4.50000i	0.375000	−	0.216506i
$433$	−34.0000			−1.63394			−0.816968	−	0.576683i	$-0.804347\pi$
$433$	−34.0000			−1.63394			−0.816968	+	0.576683i	$0.804347\pi$
$434$	8.00000	−	6.92820i	0.384012	−	0.332564i
$435$		0			0
$436$	−17.3205	+	10.0000i	−0.829502	+	0.478913i
$437$	−13.8564	−	8.00000i	−0.662842	−	0.382692i
$438$	12.0000	−	20.7846i	0.573382	−	0.993127i
$439$	0.866025	−	0.500000i	0.0413331	−	0.0238637i	−0.479191	−	0.877711i	$-0.659070\pi$
$439$	0.866025	−	0.500000i	0.0413331	−	0.0238637i	0.520524	+	0.853847i	$0.325737\pi$
$440$		0			0
$441$	−39.0000	+	15.5885i	−1.85714	+	0.742307i
$442$	−5.00000	−	20.0000i	−0.237826	−	0.951303i
$443$	8.00000	+	13.8564i	0.380091	+	0.658338i	0.991075	−	0.133306i	$-0.0425592\pi$
$443$	8.00000	+	13.8564i	0.380091	+	0.658338i	−0.610984	+	0.791643i	$0.709226\pi$
$444$	12.0000	−	20.7846i	0.569495	−	0.986394i
$445$		0			0
$446$	6.00000	+	10.3923i	0.284108	+	0.492090i
$447$		−	33.0000i		−	1.56085i
$448$	−1.73205	−	2.00000i	−0.0818317	−	0.0944911i
$449$			4.00000i			0.188772i	0.995536	+	0.0943858i	$0.0300887\pi$
$449$			4.00000i			0.188772i	−0.995536	+	0.0943858i	$0.969911\pi$
$450$	−15.0000	−	25.9808i	−0.707107	−	1.22474i
$451$	6.00000	−	10.3923i	0.282529	−	0.489355i
$452$	−10.3923	−	6.00000i	−0.488813	−	0.282216i
$453$	31.1769	−	18.0000i	1.46482	−	0.845714i
$454$			21.0000i			0.985579i
$455$		0			0
$456$			12.0000i			0.561951i
$457$	5.00000	+	8.66025i	0.233890	+	0.405110i	0.958950	−	0.283577i	$-0.0915211\pi$
$457$	5.00000	+	8.66025i	0.233890	+	0.405110i	−0.725059	+	0.688686i	$0.758188\pi$
$458$	13.0000	−	22.5167i	0.607450	−	1.05213i
$459$	10.2058	−	35.6769i	0.476365	−	1.66526i
$460$		0			0
$461$	−1.00000			−0.0465746			−0.0232873	−	0.999729i	$-0.507413\pi$
$461$	−1.00000			−0.0465746			−0.0232873	+	0.999729i	$0.507413\pi$
$462$	−23.3827	+	4.50000i	−1.08786	+	0.209359i
$463$	20.0000			0.929479			0.464739	−	0.885448i	$-0.346148\pi$
$463$	20.0000			0.929479			0.464739	+	0.885448i	$0.346148\pi$
$464$	−3.46410	+	2.00000i	−0.160817	+	0.0928477i
$465$		0			0
$466$	13.8564	+	8.00000i	0.641886	+	0.370593i
$467$	12.0000	+	20.7846i	0.555294	+	0.961797i	0.997881	+	0.0650714i	$0.0207275\pi$
$467$	12.0000	+	20.7846i	0.555294	+	0.961797i	−0.442587	+	0.896726i	$0.645939\pi$
$468$	−30.0000			−1.38675
$469$	−41.5692	+	8.00000i	−1.91949	+	0.369406i
$470$		0			0
$471$	−7.79423	+	4.50000i	−0.359139	+	0.207349i
$472$	6.00000	−	10.3923i	0.276172	−	0.478345i
$473$	−20.7846	−	12.0000i	−0.955677	−	0.551761i
$474$	10.5000	+	18.1865i	0.482281	+	0.835335i
$475$	20.0000			0.917663
$476$	−10.8660	−	0.964102i	−0.498043	−	0.0441895i
$477$	6.00000			0.274721
$478$	−8.00000	−	13.8564i	−0.365911	−	0.633777i
$479$	−31.1769	−	18.0000i	−1.42451	−	0.822441i	−0.427830	−	0.903859i	$-0.640722\pi$
$479$	−31.1769	−	18.0000i	−1.42451	−	0.822441i	−0.996680	+	0.0814184i	$0.974055\pi$
$480$		0			0
$481$	−34.6410	+	20.0000i	−1.57949	+	0.911922i
$482$			12.0000i			0.546585i
$483$	−20.7846	−	24.0000i	−0.945732	−	1.09204i
$484$	2.00000			0.0909091
$485$		0			0
$486$		0			0
$487$	−16.4545	−	9.50000i	−0.745624	−	0.430486i	0.0784867	−	0.996915i	$-0.474991\pi$
$487$	−16.4545	−	9.50000i	−0.745624	−	0.430486i	−0.824110	+	0.566429i	$0.808325\pi$
$488$		0			0
$489$	−48.0000			−2.17064
$490$		0			0
$491$	−36.0000			−1.62466			−0.812329	−	0.583200i	$-0.801800\pi$
$491$	−36.0000			−1.62466			−0.812329	+	0.583200i	$0.801800\pi$
$492$	−6.00000	−	10.3923i	−0.270501	−	0.468521i
$493$	−4.53590	+	15.8564i	−0.204287	+	0.714137i
$494$	10.0000	−	17.3205i	0.449921	−	0.779287i
$495$		0			0
$496$		−	4.00000i		−	0.179605i
$497$	2.00000	−	1.73205i	0.0897123	−	0.0776931i
$498$		−	48.0000i		−	2.15093i
$499$	21.6506	−	12.5000i	0.969216	−	0.559577i	0.0702185	−	0.997532i	$-0.477630\pi$
$499$	21.6506	−	12.5000i	0.969216	−	0.559577i	0.898997	+	0.437955i	$0.144297\pi$
$500$		0			0
$501$	37.5000	−	64.9519i	1.67538	−	2.90184i
$502$	8.00000	+	13.8564i	0.357057	+	0.618442i
$503$			1.00000i			0.0445878i	0.999751	+	0.0222939i	$0.00709696\pi$
$503$			1.00000i			0.0445878i	−0.999751	+	0.0222939i	$0.992903\pi$
$504$	−5.19615	+	15.0000i	−0.231455	+	0.668153i
$505$		0			0
$506$	−6.00000	−	10.3923i	−0.266733	−	0.461994i
$507$	31.1769	+	18.0000i	1.38462	+	0.799408i
$508$	−4.00000	+	6.92820i	−0.177471	+	0.307389i
$509$	−15.0000	−	25.9808i	−0.664863	−	1.15158i	−0.979322	−	0.202306i	$-0.935156\pi$
$509$	−15.0000	−	25.9808i	−0.664863	−	1.15158i	0.314459	−	0.949271i	$-0.398177\pi$
$510$		0			0
$511$	4.00000	+	20.7846i	0.176950	+	0.919457i
$512$	−1.00000			−0.0441942
$513$	31.1769	−	18.0000i	1.37649	−	0.794719i
$514$	−3.50000	+	6.06218i	−0.154378	+	0.267391i
$515$		0			0
$516$	−20.7846	+	12.0000i	−0.914991	+	0.528271i
$517$			12.0000i			0.527759i
$518$	4.00000	+	20.7846i	0.175750	+	0.913223i
$519$	−12.0000			−0.526742
$520$		0			0
$521$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$521$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$522$	20.7846	+	12.0000i	0.909718	+	0.525226i
$523$	−10.0000	−	17.3205i	−0.437269	−	0.757373i	0.560208	−	0.828352i	$-0.310721\pi$
$523$	−10.0000	−	17.3205i	−0.437269	−	0.757373i	−0.997478	+	0.0709788i	$0.977388\pi$
$524$		−	8.00000i		−	0.349482i
$525$	37.5000	+	12.9904i	1.63663	+	0.566947i
$526$	−4.00000			−0.174408
$527$	−11.4641	−	11.8564i	−0.499384	−	0.516473i
$528$	−4.50000	+	7.79423i	−0.195837	+	0.339200i
$529$	−3.50000	+	6.06218i	−0.152174	+	0.263573i
$530$		0			0
$531$	−72.0000			−3.12453
$532$	−6.92820	−	8.00000i	−0.300376	−	0.346844i
$533$			20.0000i			0.866296i
$534$	23.3827	−	13.5000i	1.01187	−	0.584202i
$535$		0			0
$536$	−8.00000	+	13.8564i	−0.345547	+	0.598506i
$537$	41.5692	−	24.0000i	1.79384	−	1.03568i
$538$			4.00000i			0.172452i
$539$	12.9904	−	16.5000i	0.559535	−	0.710705i
$540$		0			0
$541$	27.7128	−	16.0000i	1.19147	−	0.687894i	0.232828	−	0.972518i	$-0.425202\pi$
$541$	27.7128	−	16.0000i	1.19147	−	0.687894i	0.958639	+	0.284624i	$0.0918688\pi$
$542$	6.00000	−	10.3923i	0.257722	−	0.446388i
$543$	−6.00000	+	10.3923i	−0.257485	+	0.445976i
$544$	−2.96410	+	2.86603i	−0.127085	+	0.122880i
$545$		0			0
$546$	30.0000	−	25.9808i	1.28388	−	1.11187i
$547$		−	9.00000i		−	0.384812i	−0.981315	−	0.192406i	$-0.938371\pi$
$547$		−	9.00000i		−	0.384812i	0.981315	−	0.192406i	$-0.0616291\pi$
$548$	−4.50000	−	7.79423i	−0.192230	−	0.332953i
$549$		0			0
$550$	12.9904	+	7.50000i	0.553912	+	0.319801i
$551$	−13.8564	+	8.00000i	−0.590303	+	0.340811i
$552$	−12.0000			−0.510754
$553$	−17.5000	−	6.06218i	−0.744176	−	0.257790i
$554$		−	4.00000i		−	0.169944i
$555$		0			0
$556$	−9.52628	−	5.50000i	−0.404004	−	0.233252i
$557$	19.5000	−	33.7750i	0.826242	−	1.43109i	−0.0747252	−	0.997204i	$-0.523808\pi$
$557$	19.5000	−	33.7750i	0.826242	−	1.43109i	0.900967	−	0.433888i	$-0.142859\pi$
$558$	−20.7846	+	12.0000i	−0.879883	+	0.508001i
$559$	40.0000			1.69182
$560$		0			0
$561$	9.00000	+	36.0000i	0.379980	+	1.51992i
$562$	3.50000	+	6.06218i	0.147639	+	0.255718i
$563$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$563$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$564$	10.3923	+	6.00000i	0.437595	+	0.252646i
$565$		0			0
$566$			11.0000i			0.462364i
$567$	23.3827	−	4.50000i	0.981981	−	0.188982i
$568$		−	1.00000i		−	0.0419591i
$569$	−7.50000	−	12.9904i	−0.314416	−	0.544585i	0.664897	−	0.746935i	$-0.268475\pi$
$569$	−7.50000	−	12.9904i	−0.314416	−	0.544585i	−0.979313	+	0.202350i	$0.935142\pi$
$570$		0			0
$571$	−13.8564	−	8.00000i	−0.579873	−	0.334790i	0.181210	−	0.983444i	$-0.441999\pi$
$571$	−13.8564	−	8.00000i	−0.579873	−	0.334790i	−0.761083	+	0.648655i	$0.775332\pi$
$572$	12.9904	−	7.50000i	0.543155	−	0.313591i
$573$			36.0000i			1.50392i
$574$	10.0000	+	3.46410i	0.417392	+	0.144589i
$575$			20.0000i			0.834058i
$576$	3.00000	+	5.19615i	0.125000	+	0.216506i
$577$	−8.50000	+	14.7224i	−0.353860	+	0.612903i	−0.986922	−	0.161198i	$-0.948464\pi$
$577$	−8.50000	+	14.7224i	−0.353860	+	0.612903i	0.633062	+	0.774101i	$0.281798\pi$
$578$	−0.571797	+	16.9904i	−0.0237836	+	0.706707i
$579$	6.00000	+	10.3923i	0.249351	+	0.431889i
$580$		0			0
$581$	27.7128	+	32.0000i	1.14972	+	1.32758i
$582$	−24.0000			−0.994832
$583$	−2.59808	+	1.50000i	−0.107601	+	0.0621237i
$584$	6.92820	+	4.00000i	0.286691	+	0.165521i
$585$		0			0
$586$	11.5000	+	19.9186i	0.475061	+	0.822829i
$587$	8.00000			0.330195			0.165098	−	0.986277i	$-0.447206\pi$
$587$	8.00000			0.330195			0.165098	+	0.986277i	$0.447206\pi$
$588$	−7.79423	−	19.5000i	−0.321429	−	0.804166i
$589$		−	16.0000i		−	0.659269i
$590$		0			0
$591$	−24.0000	+	41.5692i	−0.987228	+	1.70993i
$592$	6.92820	+	4.00000i	0.284747	+	0.164399i
$593$	4.50000	+	7.79423i	0.184793	+	0.320071i	0.943507	−	0.331353i	$-0.107505\pi$
$593$	4.50000	+	7.79423i	0.184793	+	0.320071i	−0.758714	+	0.651424i	$0.774172\pi$
$594$	27.0000			1.10782
$595$		0			0
$596$	11.0000			0.450578
$597$	−4.50000	−	7.79423i	−0.184173	−	0.318997i
$598$	17.3205	+	10.0000i	0.708288	+	0.408930i
$599$	20.0000	−	34.6410i	0.817178	−	1.41539i	−0.0905757	−	0.995890i	$-0.528871\pi$
$599$	20.0000	−	34.6410i	0.817178	−	1.41539i	0.907754	−	0.419504i	$-0.137796\pi$
$600$	12.9904	−	7.50000i	0.530330	−	0.306186i
$601$		−	8.00000i		−	0.326327i	−0.986599	−	0.163163i	$-0.947830\pi$
$601$		−	8.00000i		−	0.326327i	0.986599	−	0.163163i	$-0.0521698\pi$
$602$	6.92820	−	20.0000i	0.282372	−	0.815139i
$603$	96.0000			3.90942
$604$	6.00000	+	10.3923i	0.244137	+	0.422857i
$605$		0			0
$606$	−25.9808	−	15.0000i	−1.05540	−	0.609333i
$607$	−32.0429	+	18.5000i	−1.30058	+	0.750892i	−0.980504	−	0.196499i	$-0.937043\pi$
$607$	−32.0429	+	18.5000i	−1.30058	+	0.750892i	−0.320079	+	0.947391i	$0.603709\pi$
$608$	−4.00000			−0.162221
$609$	−31.1769	+	6.00000i	−1.26335	+	0.243132i
$610$		0			0
$611$	−10.0000	−	17.3205i	−0.404557	−	0.700713i
$612$	23.7846	+	6.80385i	0.961436	+	0.275029i
$613$	−13.5000	+	23.3827i	−0.545260	+	0.944418i	0.453331	+	0.891342i	$0.350236\pi$
$613$	−13.5000	+	23.3827i	−0.545260	+	0.944418i	−0.998591	+	0.0530754i	$0.983098\pi$
$614$	−8.00000	−	13.8564i	−0.322854	−	0.559199i
$615$		0			0
$616$	−1.50000	−	7.79423i	−0.0604367	−	0.314038i
$617$			48.0000i			1.93241i	0.257780	+	0.966204i	$0.417009\pi$
$617$			48.0000i			1.93241i	−0.257780	+	0.966204i	$0.582991\pi$
$618$	−20.7846	+	12.0000i	−0.836080	+	0.482711i
$619$	6.06218	+	3.50000i	0.243659	+	0.140677i	0.616858	−	0.787075i	$-0.288405\pi$
$619$	6.06218	+	3.50000i	0.243659	+	0.140677i	−0.373198	+	0.927752i	$0.621739\pi$
$620$		0			0
$621$	18.0000	+	31.1769i	0.722315	+	1.25109i
$622$		−	21.0000i		−	0.842023i
$623$	−7.79423	+	22.5000i	−0.312269	+	0.901443i
$624$		−	15.0000i		−	0.600481i
$625$	−12.5000	−	21.6506i	−0.500000	−	0.866025i
$626$	−17.3205	−	10.0000i	−0.692267	−	0.399680i
$627$	−18.0000	+	31.1769i	−0.718851	+	1.24509i
$628$	−1.50000	−	2.59808i	−0.0598565	−	0.103675i
$629$	32.0000	−	8.00000i	1.27592	−	0.318981i
$630$		0			0
$631$	−36.0000			−1.43314			−0.716569	−	0.697517i	$-0.754288\pi$
$631$	−36.0000			−1.43314			−0.716569	+	0.697517i	$0.754288\pi$
$632$	−6.06218	+	3.50000i	−0.241140	+	0.139223i
$633$	36.0000	−	62.3538i	1.43087	−	2.47834i
$634$		0			0
$635$		0			0
$636$			3.00000i			0.118958i
$637$	−5.00000	+	34.6410i	−0.198107	+	1.37253i
$638$	−12.0000			−0.475085
$639$	−5.19615	+	3.00000i	−0.205557	+	0.118678i
$640$		0			0
$641$	10.3923	+	6.00000i	0.410471	+	0.236986i	0.690992	−	0.722862i	$-0.257174\pi$
$641$	10.3923	+	6.00000i	0.410471	+	0.236986i	−0.280521	+	0.959848i	$0.590507\pi$
$642$	−4.50000	−	7.79423i	−0.177601	−	0.307614i
$643$			43.0000i			1.69575i	0.530193	+	0.847877i	$0.322120\pi$
$643$			43.0000i			1.69575i	−0.530193	+	0.847877i	$0.677880\pi$
$644$	8.00000	−	6.92820i	0.315244	−	0.273009i
$645$		0			0
$646$	−11.8564	+	11.4641i	−0.466484	+	0.451049i
$647$	−6.00000	+	10.3923i	−0.235884	+	0.408564i	−0.959529	−	0.281609i	$-0.909132\pi$
$647$	−6.00000	+	10.3923i	−0.235884	+	0.408564i	0.723645	+	0.690172i	$0.242465\pi$
$648$	4.50000	−	7.79423i	0.176777	−	0.306186i
$649$	31.1769	−	18.0000i	1.22380	−	0.706562i
$650$	−25.0000			−0.980581
$651$	10.3923	−	30.0000i	0.407307	−	1.17579i
$652$		−	16.0000i		−	0.626608i
$653$	−31.1769	+	18.0000i	−1.22005	+	0.704394i	−0.964928	−	0.262515i	$-0.915448\pi$
$653$	−31.1769	+	18.0000i	−1.22005	+	0.704394i	−0.255119	+	0.966910i	$0.582115\pi$
$654$	−30.0000	+	51.9615i	−1.17309	+	2.03186i
$655$		0			0
$656$	3.46410	−	2.00000i	0.135250	−	0.0780869i
$657$		−	48.0000i		−	1.87266i
$658$	−10.3923	+	2.00000i	−0.405134	+	0.0779681i
$659$	−4.00000			−0.155818			−0.0779089	−	0.996960i	$-0.524824\pi$
$659$	−4.00000			−0.155818			−0.0779089	+	0.996960i	$0.524824\pi$
$660$		0			0
$661$	−11.0000	+	19.0526i	−0.427850	+	0.741059i	−0.996682	−	0.0813955i	$-0.974062\pi$
$661$	−11.0000	+	19.0526i	−0.427850	+	0.741059i	0.568831	+	0.822454i	$0.307396\pi$
$662$	−2.00000	+	3.46410i	−0.0777322	+	0.134636i
$663$	−42.9904	−	44.4615i	−1.66961	−	1.72674i
$664$	16.0000			0.620920
$665$		0			0
$666$		−	48.0000i		−	1.85996i
$667$	−8.00000	−	13.8564i	−0.309761	−	0.536522i
$668$	21.6506	+	12.5000i	0.837688	+	0.483640i
$669$	31.1769	+	18.0000i	1.20537	+	0.695920i
$670$		0			0
$671$		0			0
$672$	−7.50000	−	2.59808i	−0.289319	−	0.100223i
$673$		−	4.00000i		−	0.154189i	−0.997024	−	0.0770943i	$-0.975436\pi$
$673$		−	4.00000i		−	0.154189i	0.997024	−	0.0770943i	$-0.0245643\pi$
$674$	6.92820	−	4.00000i	0.266864	−	0.154074i
$675$	−38.9711	−	22.5000i	−1.50000	−	0.866025i
$676$	−6.00000	+	10.3923i	−0.230769	+	0.399704i
$677$	−17.3205	+	10.0000i	−0.665681	+	0.384331i	−0.794438	−	0.607345i	$-0.792235\pi$
$677$	−17.3205	+	10.0000i	−0.665681	+	0.384331i	0.128757	+	0.991676i	$0.458901\pi$
$678$	−36.0000			−1.38257
$679$	16.0000	−	13.8564i	0.614024	−	0.531760i
$680$		0			0
$681$	31.5000	+	54.5596i	1.20708	+	2.09073i
$682$	6.00000	−	10.3923i	0.229752	−	0.397942i
$683$	7.79423	+	4.50000i	0.298238	+	0.172188i	0.641651	−	0.766997i	$-0.278250\pi$
$683$	7.79423	+	4.50000i	0.298238	+	0.172188i	−0.343413	+	0.939184i	$0.611583\pi$
$684$	12.0000	+	20.7846i	0.458831	+	0.794719i
$685$		0			0
$686$	16.4545	+	8.50000i	0.628235	+	0.324532i
$687$		−	78.0000i		−	2.97589i
$688$	−4.00000	−	6.92820i	−0.152499	−	0.264135i
$689$	2.50000	−	4.33013i	0.0952424	−	0.164965i
$690$		0			0
$691$	−6.92820	+	4.00000i	−0.263561	+	0.152167i	−0.625958	−	0.779857i	$-0.715292\pi$
$691$	−6.92820	+	4.00000i	−0.263561	+	0.152167i	0.362397	+	0.932024i	$0.381959\pi$
$692$		−	4.00000i		−	0.152057i
$693$	−36.0000	+	31.1769i	−1.36753	+	1.18431i
$694$			32.0000i			1.21470i
$695$		0			0
$696$	−6.00000	+	10.3923i	−0.227429	+	0.393919i
$697$	4.53590	−	15.8564i	0.171809	−	0.600604i
$698$	15.0000	+	25.9808i	0.567758	+	0.983386i
$699$	48.0000			1.81553
$700$	−4.33013	+	12.5000i	−0.163663	+	0.472456i
$701$	1.00000			0.0377695			0.0188847	−	0.999822i	$-0.493988\pi$
$701$	1.00000			0.0377695			0.0188847	+	0.999822i	$0.493988\pi$
$702$	−38.9711	+	22.5000i	−1.47087	+	0.849208i
$703$	27.7128	+	16.0000i	1.04521	+	0.603451i
$704$	−2.59808	−	1.50000i	−0.0979187	−	0.0565334i
$705$		0			0
$706$	21.0000			0.790345
$707$	25.9808	−	5.00000i	0.977107	−	0.188044i
$708$		−	36.0000i		−	1.35296i
$709$	−41.5692	+	24.0000i	−1.56116	+	0.901339i	−0.564025	+	0.825758i	$0.690748\pi$
$709$	−41.5692	+	24.0000i	−1.56116	+	0.901339i	−0.997140	+	0.0755813i	$0.975919\pi$
$710$		0			0
$711$	36.3731	+	21.0000i	1.36410	+	0.787562i
$712$	4.50000	+	7.79423i	0.168645	+	0.292101i
$713$	16.0000			0.599205
$714$	−29.6769	+	13.7942i	−1.11063	+	0.516236i
$715$		0			0
$716$	8.00000	+	13.8564i	0.298974	+	0.517838i
$717$	−41.5692	−	24.0000i	−1.55243	−	0.896296i
$718$		0			0
$719$	−7.79423	+	4.50000i	−0.290676	+	0.167822i	−0.638247	−	0.769832i	$-0.720340\pi$
$719$	−7.79423	+	4.50000i	−0.290676	+	0.167822i	0.347571	+	0.937654i	$0.387007\pi$
$720$		0			0
$721$	6.92820	−	20.0000i	0.258020	−	0.744839i
$722$	3.00000			0.111648
$723$	18.0000	+	31.1769i	0.669427	+	1.15948i
$724$	−3.46410	−	2.00000i	−0.128742	−	0.0743294i
$725$	17.3205	+	10.0000i	0.643268	+	0.371391i
$726$	5.19615	−	3.00000i	0.192847	−	0.111340i
$727$	8.00000			0.296704			0.148352	−	0.988935i	$-0.452603\pi$
$727$	8.00000			0.296704			0.148352	+	0.988935i	$0.452603\pi$
$728$	8.66025	+	10.0000i	0.320970	+	0.370625i
$729$	27.0000			1.00000
$730$		0			0
$731$	−31.7128	−	9.07180i	−1.17294	−	0.335533i
$732$		0			0
$733$	14.5000	+	25.1147i	0.535570	+	0.927634i	0.999136	+	0.0415715i	$0.0132364\pi$
$733$	14.5000	+	25.1147i	0.535570	+	0.927634i	−0.463566	+	0.886062i	$0.653430\pi$
$734$		−	7.00000i		−	0.258375i
$735$		0			0
$736$		−	4.00000i		−	0.147442i
$737$	−41.5692	+	24.0000i	−1.53122	+	0.884051i
$738$	−20.7846	−	12.0000i	−0.765092	−	0.441726i
$739$	−10.0000	+	17.3205i	−0.367856	+	0.637145i	−0.989230	−	0.146369i	$-0.953241\pi$
$739$	−10.0000	+	17.3205i	−0.367856	+	0.637145i	0.621374	+	0.783514i	$0.286575\pi$
$740$		0			0
$741$		−	60.0000i		−	2.20416i
$742$	−1.73205	−	2.00000i	−0.0635856	−	0.0734223i
$743$		−	33.0000i		−	1.21065i	−0.795977	−	0.605326i	$-0.793043\pi$
$743$		−	33.0000i		−	1.21065i	0.795977	−	0.605326i	$-0.206957\pi$
$744$	−6.00000	−	10.3923i	−0.219971	−	0.381000i
$745$		0			0
$746$	−9.50000	+	16.4545i	−0.347820	+	0.602441i
$747$	−48.0000	−	83.1384i	−1.75623	−	3.04188i
$748$	−12.0000	+	3.00000i	−0.438763	+	0.109691i
$749$	7.50000	+	2.59808i	0.274044	+	0.0949316i
$750$		0			0
$751$	11.2583	−	6.50000i	0.410822	−	0.237188i	−0.280321	−	0.959906i	$-0.590441\pi$
$751$	11.2583	−	6.50000i	0.410822	−	0.237188i	0.691143	+	0.722718i	$0.257107\pi$
$752$	−2.00000	+	3.46410i	−0.0729325	+	0.126323i
$753$	41.5692	+	24.0000i	1.51487	+	0.874609i
$754$	17.3205	−	10.0000i	0.630776	−	0.364179i
$755$		0			0
$756$	4.50000	+	23.3827i	0.163663	+	0.850420i
$757$	−39.0000			−1.41748			−0.708740	−	0.705470i	$-0.750736\pi$
$757$	−39.0000			−1.41748			−0.708740	+	0.705470i	$0.750736\pi$
$758$	−0.866025	+	0.500000i	−0.0314555	+	0.0181608i
$759$	−31.1769	−	18.0000i	−1.13165	−	0.653359i
$760$		0			0
$761$	7.50000	+	12.9904i	0.271875	+	0.470901i	0.969342	−	0.245716i	$-0.0790230\pi$
$761$	7.50000	+	12.9904i	0.271875	+	0.470901i	−0.697467	+	0.716617i	$0.745690\pi$
$762$			24.0000i			0.869428i
$763$	−10.0000	−	51.9615i	−0.362024	−	1.88113i
$764$	−12.0000			−0.434145
$765$		0			0
$766$	12.0000	−	20.7846i	0.433578	−	0.750978i
$767$	−30.0000	+	51.9615i	−1.08324	+	1.87622i
$768$	−2.59808	+	1.50000i	−0.0937500	+	0.0541266i
$769$	−35.0000			−1.26213			−0.631066	−	0.775729i	$-0.717382\pi$
$769$	−35.0000			−1.26213			−0.631066	+	0.775729i	$0.717382\pi$
$770$		0			0
$771$			21.0000i			0.756297i
$772$	−3.46410	+	2.00000i	−0.124676	+	0.0719816i
$773$	−0.500000	+	0.866025i	−0.0179838	+	0.0311488i	−0.874877	−	0.484345i	$-0.839058\pi$
$773$	−0.500000	+	0.866025i	−0.0179838	+	0.0311488i	0.856893	+	0.515494i	$0.172391\pi$
$774$	−24.0000	+	41.5692i	−0.862662	+	1.49417i
$775$	−17.3205	+	10.0000i	−0.622171	+	0.359211i
$776$		−	8.00000i		−	0.287183i
$777$	41.5692	+	48.0000i	1.49129	+	1.72199i
$778$	15.0000			0.537776
$779$	13.8564	−	8.00000i	0.496457	−	0.286630i
$780$		0			0
$781$	1.50000	−	2.59808i	0.0536742	−	0.0929665i
$782$	−11.4641	−	11.8564i	−0.409955	−	0.423984i
$783$	36.0000			1.28654
$784$	6.50000	−	2.59808i	0.232143	−	0.0927884i
$785$		0			0
$786$	−12.0000	−	20.7846i	−0.428026	−	0.741362i
$787$	−20.7846	−	12.0000i	−0.740891	−	0.427754i	0.0815020	−	0.996673i	$-0.474028\pi$
$787$	−20.7846	−	12.0000i	−0.740891	−	0.427754i	−0.822393	+	0.568919i	$0.807362\pi$
$788$	−13.8564	−	8.00000i	−0.493614	−	0.284988i
$789$	−10.3923	+	6.00000i	−0.369976	+	0.213606i
$790$		0			0
$791$	24.0000	−	20.7846i	0.853342	−	0.739016i
$792$			18.0000i			0.639602i
$793$		0			0
$794$	27.7128	+	16.0000i	0.983491	+	0.567819i
$795$		0			0
$796$	2.59808	−	1.50000i	0.0920864	−	0.0531661i
$797$	−9.00000			−0.318796			−0.159398	−	0.987214i	$-0.550955\pi$
$797$	−9.00000			−0.318796			−0.159398	+	0.987214i	$0.550955\pi$
$798$	−30.0000	−	10.3923i	−1.06199	−	0.367884i
$799$	4.00000	+	16.0000i	0.141510	+	0.566039i
$800$	2.50000	+	4.33013i	0.0883883	+	0.153093i
$801$	27.0000	−	46.7654i	0.953998	−	1.65237i
$802$	17.3205	+	10.0000i	0.611608	+	0.353112i
$803$	12.0000	+	20.7846i	0.423471	+	0.733473i
$804$			48.0000i			1.69283i
$805$		0			0
$806$			20.0000i			0.704470i
$807$	6.00000	+	10.3923i	0.211210	+	0.365826i
$808$	5.00000	−	8.66025i	0.175899	−	0.304667i
$809$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$809$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$810$		0			0
$811$			33.0000i			1.15879i	0.815048	+	0.579393i	$0.196710\pi$
$811$			33.0000i			1.15879i	−0.815048	+	0.579393i	$0.803290\pi$
$812$	−2.00000	−	10.3923i	−0.0701862	−	0.364698i
$813$		−	36.0000i		−	1.26258i
$814$	12.0000	+	20.7846i	0.420600	+	0.728500i
$815$		0			0
$816$	−3.40192	+	11.8923i	−0.119091	+	0.416314i
$817$	−16.0000	−	27.7128i	−0.559769	−	0.969549i
$818$	−19.0000			−0.664319
$819$	25.9808	−	75.0000i	0.907841	−	2.62071i
$820$		0			0
$821$	41.5692	−	24.0000i	1.45078	−	0.837606i	0.452250	−	0.891891i	$-0.350621\pi$
$821$	41.5692	−	24.0000i	1.45078	−	0.837606i	0.998525	+	0.0542853i	$0.0172880\pi$
$822$	−23.3827	−	13.5000i	−0.815565	−	0.470867i
$823$	12.9904	+	7.50000i	0.452816	+	0.261434i	0.709019	−	0.705190i	$-0.249138\pi$
$823$	12.9904	+	7.50000i	0.452816	+	0.261434i	−0.256203	+	0.966623i	$0.582471\pi$
$824$	−4.00000	−	6.92820i	−0.139347	−	0.241355i
$825$	45.0000			1.56670
$826$	20.7846	+	24.0000i	0.723189	+	0.835067i
$827$			43.0000i			1.49526i	0.664117	+	0.747628i	$0.268807\pi$
$827$			43.0000i			1.49526i	−0.664117	+	0.747628i	$0.731193\pi$
$828$	−20.7846	+	12.0000i	−0.722315	+	0.417029i
$829$	−3.50000	+	6.06218i	−0.121560	+	0.210548i	−0.920383	−	0.391018i	$-0.872123\pi$
$829$	−3.50000	+	6.06218i	−0.121560	+	0.210548i	0.798823	+	0.601566i	$0.205456\pi$
$830$		0			0
$831$	−6.00000	−	10.3923i	−0.208138	−	0.360505i
$832$	5.00000			0.173344
$833$	11.8205	−	26.3301i	0.409556	−	0.912285i
$834$	−33.0000			−1.14270
$835$		0			0
$836$	−10.3923	−	6.00000i	−0.359425	−	0.207514i
$837$	−18.0000	+	31.1769i	−0.622171	+	1.07763i
$838$	4.33013	−	2.50000i	0.149582	−	0.0863611i
$839$			12.0000i			0.414286i	0.978311	+	0.207143i	$0.0664165\pi$
$839$			12.0000i			0.414286i	−0.978311	+	0.207143i	$0.933583\pi$
$840$		0			0
$841$	13.0000			0.448276
$842$	5.00000	+	8.66025i	0.172311	+	0.298452i
$843$	18.1865	+	10.5000i	0.626377	+	0.361639i
$844$	20.7846	+	12.0000i	0.715436	+	0.413057i
$845$		0			0
$846$	24.0000			0.825137
$847$	−1.73205	+	5.00000i	−0.0595140	+	0.171802i
$848$	−1.00000			−0.0343401
$849$	16.5000	+	28.5788i	0.566279	+	0.980823i
$850$	19.8205	+	5.66987i	0.679838	+	0.194475i
$851$	−16.0000	+	27.7128i	−0.548473	+	0.949983i
$852$	−1.50000	−	2.59808i	−0.0513892	−	0.0890086i
$853$		−	4.00000i		−	0.136957i	−0.997653	−	0.0684787i	$-0.978185\pi$
$853$		−	4.00000i		−	0.136957i	0.997653	−	0.0684787i	$-0.0218145\pi$
$854$		0			0
$855$		0			0
$856$	2.59808	−	1.50000i	0.0888004	−	0.0512689i
$857$	−20.7846	−	12.0000i	−0.709989	−	0.409912i	0.101068	−	0.994880i	$-0.467774\pi$
$857$	−20.7846	−	12.0000i	−0.709989	−	0.409912i	−0.811057	+	0.584967i	$0.801107\pi$
$858$	22.5000	−	38.9711i	0.768137	−	1.33045i
$859$	6.00000	+	10.3923i	0.204717	+	0.354581i	0.950043	−	0.312120i	$-0.101039\pi$
$859$	6.00000	+	10.3923i	0.204717	+	0.354581i	−0.745325	+	0.666701i	$0.767706\pi$
$860$		0			0
$861$	31.1769	−	6.00000i	1.06251	−	0.204479i
$862$		−	21.0000i		−	0.715263i
$863$	18.0000	+	31.1769i	0.612727	+	1.06127i	0.990779	+	0.135490i	$0.0432609\pi$
$863$	18.0000	+	31.1769i	0.612727	+	1.06127i	−0.378052	+	0.925785i	$0.623406\pi$
$864$	7.79423	+	4.50000i	0.265165	+	0.153093i
$865$		0			0
$866$	−17.0000	−	29.4449i	−0.577684	−	1.00058i
$867$	24.0000	+	45.0000i	0.815083	+	1.52828i
$868$	10.0000	+	3.46410i	0.339422	+	0.117579i
$869$	−21.0000			−0.712376
$870$		0			0
$871$	40.0000	−	69.2820i	1.35535	−	2.34753i
$872$	−17.3205	−	10.0000i	−0.586546	−	0.338643i
$873$	−41.5692	+	24.0000i	−1.40690	+	0.812277i
$874$		−	16.0000i		−	0.541208i
$875$		0			0
$876$	24.0000			0.810885
$877$	−10.3923	+	6.00000i	−0.350923	+	0.202606i	−0.665092	−	0.746762i	$-0.731608\pi$
$877$	−10.3923	+	6.00000i	−0.350923	+	0.202606i	0.314169	+	0.949367i	$0.398274\pi$
$878$	0.866025	+	0.500000i	0.0292269	+	0.0168742i
$879$	59.7558	+	34.5000i	2.01551	+	1.16366i
$880$		0			0
$881$		−	12.0000i		−	0.404290i	−0.979356	−	0.202145i	$-0.935209\pi$
$881$		−	12.0000i		−	0.404290i	0.979356	−	0.202145i	$-0.0647913\pi$
$882$	−33.0000	−	25.9808i	−1.11117	−	0.874818i
$883$	−40.0000			−1.34611			−0.673054	−	0.739594i	$-0.735018\pi$
$883$	−40.0000			−1.34611			−0.673054	+	0.739594i	$0.735018\pi$
$884$	14.8205	−	14.3301i	0.498468	−	0.481974i
$885$		0			0
$886$	−8.00000	+	13.8564i	−0.268765	+	0.465515i
$887$	−11.2583	+	6.50000i	−0.378018	+	0.218249i	−0.676955	−	0.736024i	$-0.736701\pi$
$887$	−11.2583	+	6.50000i	−0.378018	+	0.218249i	0.298938	+	0.954273i	$0.403368\pi$
$888$	24.0000			0.805387
$889$	−13.8564	−	16.0000i	−0.464729	−	0.536623i
$890$		0			0
$891$	23.3827	−	13.5000i	0.783349	−	0.452267i
$892$	−6.00000	+	10.3923i	−0.200895	+	0.347960i
$893$	−8.00000	+	13.8564i	−0.267710	+	0.463687i
$894$	28.5788	−	16.5000i	0.955819	−	0.551843i
$895$		0			0
$896$	0.866025	−	2.50000i	0.0289319	−	0.0835191i
$897$	60.0000			2.00334
$898$	−3.46410	+	2.00000i	−0.115599	+	0.0667409i
$899$	8.00000	−	13.8564i	0.266815	−	0.462137i
$900$	15.0000	−	25.9808i	0.500000	−	0.866025i
$901$	−2.96410	+	2.86603i	−0.0987485	+	0.0954811i
$902$	12.0000			0.399556
$903$	−12.0000	−	62.3538i	−0.399335	−	2.07501i
$904$		−	12.0000i		−	0.399114i
$905$		0			0
$906$	31.1769	+	18.0000i	1.03578	+	0.598010i
$907$	6.92820	+	4.00000i	0.230047	+	0.132818i	0.610594	−	0.791944i	$-0.290931\pi$
$907$	6.92820	+	4.00000i	0.230047	+	0.132818i	−0.380547	+	0.924762i	$0.624264\pi$
$908$	−18.1865	+	10.5000i	−0.603541	+	0.348455i
$909$	−60.0000			−1.99007
$910$		0			0
$911$		−	36.0000i		−	1.19273i	−0.802712	−	0.596367i	$-0.796610\pi$
$911$		−	36.0000i		−	1.19273i	0.802712	−	0.596367i	$-0.203390\pi$
$912$	−10.3923	+	6.00000i	−0.344124	+	0.198680i
$913$	41.5692	+	24.0000i	1.37574	+	0.794284i
$914$	−5.00000	+	8.66025i	−0.165385	+	0.286456i
$915$		0			0
$916$	26.0000			0.859064
$917$	20.0000	+	6.92820i	0.660458	+	0.228789i
$918$	36.0000	−	9.00000i	1.18818	−	0.297044i
$919$	−22.0000	−	38.1051i	−0.725713	−	1.25697i	−0.958680	−	0.284487i	$-0.908177\pi$
$919$	−22.0000	−	38.1051i	−0.725713	−	1.25697i	0.232967	−	0.972485i	$-0.425157\pi$
$920$		0			0
$921$	−41.5692	−	24.0000i	−1.36975	−	0.790827i
$922$	−0.500000	−	0.866025i	−0.0164666	−	0.0285210i
$923$			5.00000i			0.164577i
$924$	−15.5885	−	18.0000i	−0.512823	−	0.592157i
$925$		−	40.0000i		−	1.31519i
$926$	10.0000	+	17.3205i	0.328620	+	0.569187i
$927$	−24.0000	+	41.5692i	−0.788263	+	1.36531i
$928$	−3.46410	−	2.00000i	−0.113715	−	0.0656532i
$929$	−34.6410	+	20.0000i	−1.13653	+	0.656179i	−0.945570	−	0.325418i	$-0.894495\pi$
$929$	−34.6410	+	20.0000i	−1.13653	+	0.656179i	−0.190965	+	0.981597i	$0.561162\pi$
$930$		0			0
$931$	26.0000	−	10.3923i	0.852116	−	0.340594i
$932$			16.0000i			0.524097i
$933$	−31.5000	−	54.5596i	−1.03126	−	1.78620i
$934$	−12.0000	+	20.7846i	−0.392652	+	0.680093i
$935$		0			0
$936$	−15.0000	−	25.9808i	−0.490290	−	0.849208i
$937$	−38.0000			−1.24141			−0.620703	−	0.784046i	$-0.713153\pi$
$937$	−38.0000			−1.24141			−0.620703	+	0.784046i	$0.713153\pi$
$938$	−27.7128	−	32.0000i	−0.904855	−	1.04484i
$939$	−60.0000			−1.95803
$940$		0			0
$941$	−51.9615	−	30.0000i	−1.69390	−	0.977972i	−0.951317	−	0.308215i	$-0.900268\pi$
$941$	−51.9615	−	30.0000i	−1.69390	−	0.977972i	−0.742581	−	0.669757i	$-0.766398\pi$
$942$	−7.79423	−	4.50000i	−0.253950	−	0.146618i
$943$	8.00000	+	13.8564i	0.260516	+	0.451227i
$944$	12.0000			0.390567
$945$		0			0
$946$		−	24.0000i		−	0.780307i
$947$	0.866025	−	0.500000i	0.0281420	−	0.0162478i	−0.485863	−	0.874035i	$-0.661495\pi$
$947$	0.866025	−	0.500000i	0.0281420	−	0.0162478i	0.514005	+	0.857787i	$0.328161\pi$
$948$	−10.5000	+	18.1865i	−0.341024	+	0.590671i
$949$	−34.6410	−	20.0000i	−1.12449	−	0.649227i
$950$	10.0000	+	17.3205i	0.324443	+	0.561951i
$951$		0			0
$952$	−4.59808	−	9.89230i	−0.149025	−	0.320611i
$953$	−27.0000			−0.874616			−0.437308	−	0.899312i	$-0.644068\pi$
$953$	−27.0000			−0.874616			−0.437308	+	0.899312i	$0.644068\pi$
$954$	3.00000	+	5.19615i	0.0971286	+	0.168232i
$955$		0			0
$956$	8.00000	−	13.8564i	0.258738	−	0.448148i
$957$	−31.1769	+	18.0000i	−1.00781	+	0.581857i
$958$		−	36.0000i		−	1.16311i
$959$	23.3827	−	4.50000i	0.755066	−	0.145313i
$960$		0			0
$961$	−7.50000	−	12.9904i	−0.241935	−	0.419045i
$962$	−34.6410	−	20.0000i	−1.11687	−	0.644826i
$963$	−15.5885	−	9.00000i	−0.502331	−	0.290021i
$964$	−10.3923	+	6.00000i	−0.334714	+	0.193247i
$965$		0			0
$966$	10.3923	−	30.0000i	0.334367	−	0.965234i
$967$	−4.00000			−0.128631			−0.0643157	−	0.997930i	$-0.520486\pi$
$967$	−4.00000			−0.128631			−0.0643157	+	0.997930i	$0.520486\pi$
$968$	1.00000	+	1.73205i	0.0321412	+	0.0556702i
$969$	−13.6077	+	47.5692i	−0.437142	+	1.52814i
$970$		0			0
$971$	2.00000	+	3.46410i	0.0641831	+	0.111168i	0.896331	−	0.443385i	$-0.146223\pi$
$971$	2.00000	+	3.46410i	0.0641831	+	0.111168i	−0.832148	+	0.554553i	$0.812889\pi$
$972$		0			0
$973$	22.0000	−	19.0526i	0.705288	−	0.610797i
$974$		−	19.0000i		−	0.608799i
$975$	−64.9519	+	37.5000i	−2.08013	+	1.20096i
$976$		0			0
$977$	15.0000	−	25.9808i	0.479893	−	0.831198i	−0.519841	−	0.854263i	$-0.674009\pi$
$977$	15.0000	−	25.9808i	0.479893	−	0.831198i	0.999734	+	0.0230645i	$0.00734232\pi$
$978$	−24.0000	−	41.5692i	−0.767435	−	1.32924i
$979$			27.0000i			0.862924i
$980$		0			0
$981$			120.000i			3.83131i
$982$	−18.0000	−	31.1769i	−0.574403	−	0.994895i
$983$	19.9186	+	11.5000i	0.635304	+	0.366793i	0.782803	−	0.622269i	$-0.213789\pi$
$983$	19.9186	+	11.5000i	0.635304	+	0.366793i	−0.147499	+	0.989062i	$0.547122\pi$
$984$	6.00000	−	10.3923i	0.191273	−	0.331295i
$985$		0			0
$986$	−16.0000	+	4.00000i	−0.509544	+	0.127386i
$987$	−24.0000	+	20.7846i	−0.763928	+	0.661581i
$988$	20.0000			0.636285
$989$	27.7128	−	16.0000i	0.881216	−	0.508770i
$990$		0			0
$991$	−40.7032	−	23.5000i	−1.29298	−	0.746502i	−0.313798	−	0.949490i	$-0.601602\pi$
$991$	−40.7032	−	23.5000i	−1.29298	−	0.746502i	−0.979181	+	0.202988i	$0.934935\pi$
$992$	3.46410	−	2.00000i	0.109985	−	0.0635001i
$993$			12.0000i			0.380808i
$994$	2.50000	+	0.866025i	0.0792952	+	0.0274687i
$995$		0			0
$996$	41.5692	−	24.0000i	1.31717	−	0.760469i
$997$	13.8564	+	8.00000i	0.438837	+	0.253363i	0.703104	−	0.711087i	$-0.251797\pi$
$997$	13.8564	+	8.00000i	0.438837	+	0.253363i	−0.264267	+	0.964449i	$0.585130\pi$
$998$	21.6506	+	12.5000i	0.685339	+	0.395681i
$999$	−36.0000	−	62.3538i	−1.13899	−	1.97279i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	238.2.j.a.67.2	yes	4
7.2	even	3	inner	238.2.j.a.135.1	yes	4
7.3	odd	6		1666.2.b.a.883.2		2
7.4	even	3		1666.2.b.b.883.1		2
17.16	even	2	inner	238.2.j.a.67.1	✓	4
119.16	even	6	inner	238.2.j.a.135.2	yes	4
119.67	even	6		1666.2.b.b.883.2		2
119.101	odd	6		1666.2.b.a.883.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
238.2.j.a.67.1	✓	4	17.16	even	2	inner
238.2.j.a.67.2	yes	4	1.1	even	1	trivial
238.2.j.a.135.1	yes	4	7.2	even	3	inner
238.2.j.a.135.2	yes	4	119.16	even	6	inner
1666.2.b.a.883.1		2	119.101	odd	6
1666.2.b.a.883.2		2	7.3	odd	6
1666.2.b.b.883.1		2	7.4	even	3
1666.2.b.b.883.2		2	119.67	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 238 = 2 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	238.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(2.59808 + 1.50000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.00000i q^{6} +(-1.73205 - 2.00000i) q^{7} -1.00000 q^{8} +(3.00000 + 5.19615i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(2.59808 + 1.50000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.00000i q^{6} +(-1.73205 - 2.00000i) q^{7} -1.00000 q^{8} +(3.00000 + 5.19615i) q^{9} +(-2.59808 - 1.50000i) q^{11} +(-2.59808 + 1.50000i) q^{12} +5.00000 q^{13} +(0.866025 - 2.50000i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.96410 - 1.13397i) q^{17} +(-3.00000 + 5.19615i) q^{18} +(-2.00000 - 3.46410i) q^{19} +(-1.50000 - 7.79423i) q^{21} -3.00000i q^{22} +(3.46410 - 2.00000i) q^{23} +(-2.59808 - 1.50000i) q^{24} +(-2.50000 + 4.33013i) q^{25} +(2.50000 + 4.33013i) q^{26} +9.00000i q^{27} +(2.59808 - 0.500000i) q^{28} -4.00000i q^{29} +(3.46410 + 2.00000i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-4.50000 - 7.79423i) q^{33} +(-1.00000 - 4.00000i) q^{34} -6.00000 q^{36} +(-6.92820 + 4.00000i) q^{37} +(2.00000 - 3.46410i) q^{38} +(12.9904 + 7.50000i) q^{39} +4.00000i q^{41} +(6.00000 - 5.19615i) q^{42} +8.00000 q^{43} +(2.59808 - 1.50000i) q^{44} +(3.46410 + 2.00000i) q^{46} +(-2.00000 - 3.46410i) q^{47} -3.00000i q^{48} +(-1.00000 + 6.92820i) q^{49} -5.00000 q^{50} +(-8.59808 - 8.89230i) q^{51} +(-2.50000 + 4.33013i) q^{52} +(0.500000 - 0.866025i) q^{53} +(-7.79423 + 4.50000i) q^{54} +(1.73205 + 2.00000i) q^{56} -12.0000i q^{57} +(3.46410 - 2.00000i) q^{58} +(-6.00000 + 10.3923i) q^{59} +4.00000i q^{62} +(5.19615 - 15.0000i) q^{63} +1.00000 q^{64} +(4.50000 - 7.79423i) q^{66} +(8.00000 - 13.8564i) q^{67} +(2.96410 - 2.86603i) q^{68} +12.0000 q^{69} +1.00000i q^{71} +(-3.00000 - 5.19615i) q^{72} +(-6.92820 - 4.00000i) q^{73} +(-6.92820 - 4.00000i) q^{74} +(-12.9904 + 7.50000i) q^{75} +4.00000 q^{76} +(1.50000 + 7.79423i) q^{77} +15.0000i q^{78} +(6.06218 - 3.50000i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-3.46410 + 2.00000i) q^{82} -16.0000 q^{83} +(7.50000 + 2.59808i) q^{84} +(4.00000 + 6.92820i) q^{86} +(6.00000 - 10.3923i) q^{87} +(2.59808 + 1.50000i) q^{88} +(-4.50000 - 7.79423i) q^{89} +(-8.66025 - 10.0000i) q^{91} +4.00000i q^{92} +(6.00000 + 10.3923i) q^{93} +(2.00000 - 3.46410i) q^{94} +(2.59808 - 1.50000i) q^{96} +8.00000i q^{97} +(-6.50000 + 2.59808i) q^{98} -18.0000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{8} + 12 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 + 12 * q^9	\( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{8} + 12 q^{9} + 20 q^{13} - 2 q^{16} - 2 q^{17} - 12 q^{18} - 8 q^{19} - 6 q^{21} - 10 q^{25} + 10 q^{26} + 2 q^{32} - 18 q^{33} - 4 q^{34} - 24 q^{36} + 8 q^{38} + 24 q^{42} + 32 q^{43} - 8 q^{47} - 4 q^{49} - 20 q^{50} - 24 q^{51} - 10 q^{52} + 2 q^{53} - 24 q^{59} + 4 q^{64} + 18 q^{66} + 32 q^{67} - 2 q^{68} + 48 q^{69} - 12 q^{72} + 16 q^{76} + 6 q^{77} - 18 q^{81} - 64 q^{83} + 30 q^{84} + 16 q^{86} + 24 q^{87} - 18 q^{89} + 24 q^{93} + 8 q^{94} - 26 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 + 12 * q^9 + 20 * q^13 - 2 * q^16 - 2 * q^17 - 12 * q^18 - 8 * q^19 - 6 * q^21 - 10 * q^25 + 10 * q^26 + 2 * q^32 - 18 * q^33 - 4 * q^34 - 24 * q^36 + 8 * q^38 + 24 * q^42 + 32 * q^43 - 8 * q^47 - 4 * q^49 - 20 * q^50 - 24 * q^51 - 10 * q^52 + 2 * q^53 - 24 * q^59 + 4 * q^64 + 18 * q^66 + 32 * q^67 - 2 * q^68 + 48 * q^69 - 12 * q^72 + 16 * q^76 + 6 * q^77 - 18 * q^81 - 64 * q^83 + 30 * q^84 + 16 * q^86 + 24 * q^87 - 18 * q^89 + 24 * q^93 + 8 * q^94 - 26 * q^98

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