LMFDB - Embedded newform 475.2.p.d.407.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [475,2,Mod(107,475)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(475, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([3, 10])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("475.107"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.p (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,6,6,0,0,12,8,0,0,0,-20,0,0,0,0,8,4,0,0,0,24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(21)] == traces)

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

Self dual:	no
Analytic conductor:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$4$
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:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			407.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	475.407
Dual form			475.2.p.d.468.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.633975 + 2.36603i) q^{2} +(2.36603 - 0.633975i) q^{3} +(-3.46410 + 2.00000i) q^{4} +(3.00000 + 5.19615i) q^{6} +(2.00000 + 2.00000i) q^{7} +(-3.46410 - 3.46410i) q^{8} +(2.59808 - 1.50000i) q^{9} -5.00000 q^{11} +(-6.92820 + 6.92820i) q^{12} +(-3.46410 + 6.00000i) q^{14} +(2.00000 - 3.46410i) q^{16} +(2.73205 - 0.732051i) q^{17} +(5.19615 + 5.19615i) q^{18} +(4.33013 - 0.500000i) q^{19} +(6.00000 + 3.46410i) q^{21} +(-3.16987 - 11.8301i) q^{22} +(4.09808 + 1.09808i) q^{23} +(-10.3923 - 6.00000i) q^{24} +(-10.9282 - 2.92820i) q^{28} +(-0.866025 - 1.50000i) q^{29} -5.19615i q^{31} +(-11.8301 + 3.16987i) q^{33} +(3.46410 + 6.00000i) q^{34} +(-6.00000 + 10.3923i) q^{36} +(-1.73205 + 1.73205i) q^{37} +(3.92820 + 9.92820i) q^{38} +(-3.00000 - 1.73205i) q^{41} +(-4.39230 + 16.3923i) q^{42} +(-2.56218 - 9.56218i) q^{43} +(17.3205 - 10.0000i) q^{44} +10.3923i q^{46} +(2.19615 - 8.19615i) q^{47} +(2.53590 - 9.46410i) q^{48} +1.00000i q^{49} +(6.00000 - 3.46410i) q^{51} +(1.90192 - 7.09808i) q^{53} -13.8564i q^{56} +(9.92820 - 3.92820i) q^{57} +(3.00000 - 3.00000i) q^{58} +(-2.59808 + 4.50000i) q^{59} +(2.50000 + 4.33013i) q^{61} +(12.2942 - 3.29423i) q^{62} +(8.19615 + 2.19615i) q^{63} -8.00000i q^{64} +(-15.0000 - 25.9808i) q^{66} +(9.46410 + 2.53590i) q^{67} +(-8.00000 + 8.00000i) q^{68} +10.3923 q^{69} +(-4.50000 - 2.59808i) q^{71} +(-14.1962 - 3.80385i) q^{72} +(0.366025 + 1.36603i) q^{73} +(-5.19615 - 3.00000i) q^{74} +(-14.0000 + 10.3923i) q^{76} +(-10.0000 - 10.0000i) q^{77} +(-0.866025 + 1.50000i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(2.19615 - 8.19615i) q^{82} +(-5.00000 + 5.00000i) q^{83} -27.7128 q^{84} +(21.0000 - 12.1244i) q^{86} +(-3.00000 - 3.00000i) q^{87} +(17.3205 + 17.3205i) q^{88} +(-2.59808 - 4.50000i) q^{89} +(-16.3923 + 4.39230i) q^{92} +(-3.29423 - 12.2942i) q^{93} +20.7846 q^{94} +(1.90192 + 7.09808i) q^{97} +(-2.36603 + 0.633975i) q^{98} +(-12.9904 + 7.50000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{2} + 6 q^{3} + 12 q^{6} + 8 q^{7} - 20 q^{11} + 8 q^{16} + 4 q^{17} + 24 q^{21} - 30 q^{22} + 6 q^{23} - 16 q^{28} - 30 q^{33} - 24 q^{36} - 12 q^{38} - 12 q^{41} + 24 q^{42} + 14 q^{43} - 12 q^{47}+ \cdots - 6 q^{98}+O(q^{100}) $ 4 * q + 6 * q^2 + 6 * q^3 + 12 * q^6 + 8 * q^7 - 20 * q^11 + 8 * q^16 + 4 * q^17 + 24 * q^21 - 30 * q^22 + 6 * q^23 - 16 * q^28 - 30 * q^33 - 24 * q^36 - 12 * q^38 - 12 * q^41 + 24 * q^42 + 14 * q^43 - 12 * q^47 + 24 * q^48 + 24 * q^51 + 18 * q^53 + 12 * q^57 + 12 * q^58 + 10 * q^61 + 18 * q^62 + 12 * q^63 - 60 * q^66 + 24 * q^67 - 32 * q^68 - 18 * q^71 - 36 * q^72 - 2 * q^73 - 56 * q^76 - 40 * q^77 - 18 * q^81 - 12 * q^82 - 20 * q^83 + 84 * q^86 - 12 * q^87 - 24 * q^92 + 18 * q^93 + 18 * q^97 - 6 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.633975	+	2.36603i	0.448288	+	1.67303i	0.707107	+	0.707107i	$0.250000\pi$
$2$	0.633975	+	2.36603i	0.448288	+	1.67303i	−0.258819	+	0.965926i	$0.583333\pi$
$3$	2.36603	−	0.633975i	1.36603	−	0.366025i	0.500000	−	0.866025i	$-0.333333\pi$
$3$	2.36603	−	0.633975i	1.36603	−	0.366025i	0.866025	+	0.500000i	$0.166667\pi$
$4$	−3.46410	+	2.00000i	−1.73205	+	1.00000i
$5$		0			0
$5$		0			0
$6$	3.00000	+	5.19615i	1.22474	+	2.12132i
$7$	2.00000	+	2.00000i	0.755929	+	0.755929i	0.975579	−	0.219650i	$-0.0704915\pi$
$7$	2.00000	+	2.00000i	0.755929	+	0.755929i	−0.219650	+	0.975579i	$0.570491\pi$
$8$	−3.46410	−	3.46410i	−1.22474	−	1.22474i
$9$	2.59808	−	1.50000i	0.866025	−	0.500000i
$10$		0			0
$11$	−5.00000			−1.50756			−0.753778	−	0.657129i	$-0.771771\pi$
$11$	−5.00000			−1.50756			−0.753778	+	0.657129i	$0.771771\pi$
$12$	−6.92820	+	6.92820i	−2.00000	+	2.00000i
$13$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$13$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$14$	−3.46410	+	6.00000i	−0.925820	+	1.60357i
$15$		0			0
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	2.73205	−	0.732051i	0.662620	−	0.177548i	0.0881917	−	0.996104i	$-0.471891\pi$
$17$	2.73205	−	0.732051i	0.662620	−	0.177548i	0.574428	+	0.818555i	$0.305225\pi$
$18$	5.19615	+	5.19615i	1.22474	+	1.22474i
$19$	4.33013	−	0.500000i	0.993399	−	0.114708i
$19$	4.33013	−	0.500000i	0.993399	−	0.114708i
$20$		0			0
$21$	6.00000	+	3.46410i	1.30931	+	0.755929i
$22$	−3.16987	−	11.8301i	−0.675819	−	2.52219i
$23$	4.09808	+	1.09808i	0.854508	+	0.228965i	0.659377	−	0.751812i	$-0.270820\pi$
$23$	4.09808	+	1.09808i	0.854508	+	0.228965i	0.195131	+	0.980777i	$0.437487\pi$
$24$	−10.3923	−	6.00000i	−2.12132	−	1.22474i
$25$		0			0
$26$		0			0
$27$		0			0
$28$	−10.9282	−	2.92820i	−2.06524	−	0.553378i
$29$	−0.866025	−	1.50000i	−0.160817	−	0.278543i	0.774345	−	0.632764i	$-0.218080\pi$
$29$	−0.866025	−	1.50000i	−0.160817	−	0.278543i	−0.935162	+	0.354221i	$0.884746\pi$
$30$		0			0
$31$		−	5.19615i		−	0.933257i	−0.884454	−	0.466628i	$-0.845469\pi$
$31$		−	5.19615i		−	0.933257i	0.884454	−	0.466628i	$-0.154531\pi$
$32$		0			0
$33$	−11.8301	+	3.16987i	−2.05936	+	0.551804i
$34$	3.46410	+	6.00000i	0.594089	+	1.02899i
$35$		0			0
$36$	−6.00000	+	10.3923i	−1.00000	+	1.73205i
$37$	−1.73205	+	1.73205i	−0.284747	+	0.284747i	−0.834999	−	0.550252i	$-0.814532\pi$
$37$	−1.73205	+	1.73205i	−0.284747	+	0.284747i	0.550252	+	0.834999i	$0.314532\pi$
$38$	3.92820	+	9.92820i	0.637239	+	1.61057i
$39$		0			0
$40$		0			0
$41$	−3.00000	−	1.73205i	−0.468521	−	0.270501i	0.247099	−	0.968990i	$-0.420523\pi$
$41$	−3.00000	−	1.73205i	−0.468521	−	0.270501i	−0.715621	+	0.698489i	$0.753856\pi$
$42$	−4.39230	+	16.3923i	−0.677747	+	2.52939i
$43$	−2.56218	−	9.56218i	−0.390728	−	1.45822i	−0.828935	−	0.559344i	$-0.811053\pi$
$43$	−2.56218	−	9.56218i	−0.390728	−	1.45822i	0.438207	−	0.898874i	$-0.355614\pi$
$44$	17.3205	−	10.0000i	2.61116	−	1.50756i
$45$		0			0
$46$			10.3923i			1.53226i
$47$	2.19615	−	8.19615i	0.320342	−	1.19553i	−0.598571	−	0.801070i	$-0.704264\pi$
$47$	2.19615	−	8.19615i	0.320342	−	1.19553i	0.918912	−	0.394462i	$-0.129069\pi$
$48$	2.53590	−	9.46410i	0.366025	−	1.36603i
$49$			1.00000i			0.142857i
$50$		0			0
$51$	6.00000	−	3.46410i	0.840168	−	0.485071i
$52$		0			0
$53$	1.90192	−	7.09808i	0.261249	−	0.974996i	−0.703257	−	0.710936i	$-0.748272\pi$
$53$	1.90192	−	7.09808i	0.261249	−	0.974996i	0.964506	−	0.264060i	$-0.0850617\pi$
$54$		0			0
$55$		0			0
$56$		−	13.8564i		−	1.85164i
$57$	9.92820	−	3.92820i	1.31502	−	0.520303i
$58$	3.00000	−	3.00000i	0.393919	−	0.393919i
$59$	−2.59808	+	4.50000i	−0.338241	+	0.585850i	−0.984102	−	0.177605i	$-0.943165\pi$
$59$	−2.59808	+	4.50000i	−0.338241	+	0.585850i	0.645861	+	0.763455i	$0.276498\pi$
$60$		0			0
$61$	2.50000	+	4.33013i	0.320092	+	0.554416i	0.980507	−	0.196485i	$-0.0629528\pi$
$61$	2.50000	+	4.33013i	0.320092	+	0.554416i	−0.660415	+	0.750901i	$0.729619\pi$
$62$	12.2942	−	3.29423i	1.56137	−	0.418367i
$63$	8.19615	+	2.19615i	1.03262	+	0.276689i
$64$		−	8.00000i		−	1.00000i
$65$		0			0
$66$	−15.0000	−	25.9808i	−1.84637	−	3.19801i
$67$	9.46410	+	2.53590i	1.15622	+	0.309809i	0.785457	−	0.618917i	$-0.212428\pi$
$67$	9.46410	+	2.53590i	1.15622	+	0.309809i	0.370767	+	0.928726i	$0.379095\pi$
$68$	−8.00000	+	8.00000i	−0.970143	+	0.970143i
$69$	10.3923			1.25109
$70$		0			0
$71$	−4.50000	−	2.59808i	−0.534052	−	0.308335i	0.208613	−	0.977998i	$-0.433105\pi$
$71$	−4.50000	−	2.59808i	−0.534052	−	0.308335i	−0.742665	+	0.669663i	$0.766438\pi$
$72$	−14.1962	−	3.80385i	−1.67303	−	0.448288i
$73$	0.366025	+	1.36603i	0.0428400	+	0.159881i	0.984032	−	0.177991i	$-0.0569597\pi$
$73$	0.366025	+	1.36603i	0.0428400	+	0.159881i	−0.941192	+	0.337872i	$0.890293\pi$
$74$	−5.19615	−	3.00000i	−0.604040	−	0.348743i
$75$		0			0
$76$	−14.0000	+	10.3923i	−1.60591	+	1.19208i
$77$	−10.0000	−	10.0000i	−1.13961	−	1.13961i
$78$		0			0
$79$	−0.866025	+	1.50000i	−0.0974355	+	0.168763i	−0.910622	−	0.413239i	$-0.864397\pi$
$79$	−0.866025	+	1.50000i	−0.0974355	+	0.168763i	0.813187	+	0.582003i	$0.197731\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	2.19615	−	8.19615i	0.242524	−	0.905114i
$83$	−5.00000	+	5.00000i	−0.548821	+	0.548821i	−0.926100	−	0.377279i	$-0.876860\pi$
$83$	−5.00000	+	5.00000i	−0.548821	+	0.548821i	0.377279	+	0.926100i	$0.376860\pi$
$84$	−27.7128			−3.02372
$85$		0			0
$86$	21.0000	−	12.1244i	2.26449	−	1.30740i
$87$	−3.00000	−	3.00000i	−0.321634	−	0.321634i
$88$	17.3205	+	17.3205i	1.84637	+	1.84637i
$89$	−2.59808	−	4.50000i	−0.275396	−	0.476999i	0.694839	−	0.719165i	$-0.255475\pi$
$89$	−2.59808	−	4.50000i	−0.275396	−	0.476999i	−0.970235	+	0.242166i	$0.922142\pi$
$90$		0			0
$91$		0			0
$92$	−16.3923	+	4.39230i	−1.70902	+	0.457929i
$93$	−3.29423	−	12.2942i	−0.341596	−	1.27485i
$94$	20.7846			2.14377
$95$		0			0
$96$		0			0
$97$	1.90192	+	7.09808i	0.193111	+	0.720700i	0.992748	+	0.120216i	$0.0383588\pi$
$97$	1.90192	+	7.09808i	0.193111	+	0.720700i	−0.799637	+	0.600484i	$0.794975\pi$
$98$	−2.36603	+	0.633975i	−0.239005	+	0.0640411i
$99$	−12.9904	+	7.50000i	−1.30558	+	0.753778i
$100$		0			0
$101$	−2.50000	−	4.33013i	−0.248759	−	0.430864i	0.714423	−	0.699715i	$-0.246689\pi$
$101$	−2.50000	−	4.33013i	−0.248759	−	0.430864i	−0.963182	+	0.268851i	$0.913356\pi$
$102$	12.0000	+	12.0000i	1.18818	+	1.18818i
$103$	6.92820	+	6.92820i	0.682656	+	0.682656i	0.960598	−	0.277942i	$-0.0896522\pi$
$103$	6.92820	+	6.92820i	0.682656	+	0.682656i	−0.277942	+	0.960598i	$0.589652\pi$
$104$		0			0
$105$		0			0
$106$	18.0000			1.74831
$107$	−1.73205	+	1.73205i	−0.167444	+	0.167444i	−0.785855	−	0.618411i	$-0.787777\pi$
$107$	−1.73205	+	1.73205i	−0.167444	+	0.167444i	0.618411	+	0.785855i	$0.287777\pi$
$108$		0			0
$109$	−0.866025	+	1.50000i	−0.0829502	+	0.143674i	−0.904516	−	0.426440i	$-0.859768\pi$
$109$	−0.866025	+	1.50000i	−0.0829502	+	0.143674i	0.821566	+	0.570114i	$0.193101\pi$
$110$		0			0
$111$	−3.00000	+	5.19615i	−0.284747	+	0.493197i
$112$	10.9282	−	2.92820i	1.03262	−	0.276689i
$113$	−1.73205	−	1.73205i	−0.162938	−	0.162938i	0.620929	−	0.783867i	$-0.286755\pi$
$113$	−1.73205	−	1.73205i	−0.162938	−	0.162938i	−0.783867	+	0.620929i	$0.786755\pi$
$114$	15.5885	+	21.0000i	1.45999	+	1.96683i
$115$		0			0
$116$	6.00000	+	3.46410i	0.557086	+	0.321634i
$117$		0			0
$118$	−12.2942	−	3.29423i	−1.13178	−	0.303258i
$119$	6.92820	+	4.00000i	0.635107	+	0.366679i
$120$		0			0
$121$	14.0000			1.27273
$122$	−8.66025	+	8.66025i	−0.784063	+	0.784063i
$123$	−8.19615	−	2.19615i	−0.739022	−	0.198020i
$124$	10.3923	+	18.0000i	0.933257	+	1.61645i
$125$		0			0
$126$			20.7846i			1.85164i
$127$	9.46410	+	2.53590i	0.839803	+	0.225025i	0.652986	−	0.757370i	$-0.273516\pi$
$127$	9.46410	+	2.53590i	0.839803	+	0.225025i	0.186817	+	0.982395i	$0.440183\pi$
$128$	18.9282	−	5.07180i	1.67303	−	0.448288i
$129$	−12.1244	−	21.0000i	−1.06749	−	1.84895i
$130$		0			0
$131$	−5.00000	+	8.66025i	−0.436852	+	0.756650i	−0.997445	−	0.0714417i	$-0.977240\pi$
$131$	−5.00000	+	8.66025i	−0.436852	+	0.756650i	0.560593	+	0.828092i	$0.310573\pi$
$132$	34.6410	−	34.6410i	3.01511	−	3.01511i
$133$	9.66025	+	7.66025i	0.837650	+	0.664228i
$134$			24.0000i			2.07328i
$135$		0			0
$136$	−12.0000	−	6.92820i	−1.02899	−	0.594089i
$137$	−2.92820	+	10.9282i	−0.250173	+	0.933659i	0.720539	+	0.693414i	$0.243894\pi$
$137$	−2.92820	+	10.9282i	−0.250173	+	0.933659i	−0.970712	+	0.240245i	$0.922772\pi$
$138$	6.58846	+	24.5885i	0.560847	+	2.09311i
$139$	−15.5885	+	9.00000i	−1.32220	+	0.763370i	−0.984079	−	0.177734i	$-0.943123\pi$
$139$	−15.5885	+	9.00000i	−1.32220	+	0.763370i	−0.338117	+	0.941104i	$0.609790\pi$
$140$		0			0
$141$		−	20.7846i		−	1.75038i
$142$	3.29423	−	12.2942i	0.276446	−	1.03171i
$143$		0			0
$144$		−	12.0000i		−	1.00000i
$145$		0			0
$146$	−3.00000	+	1.73205i	−0.248282	+	0.143346i
$147$	0.633975	+	2.36603i	0.0522893	+	0.195146i
$148$	2.53590	−	9.46410i	0.208450	−	0.777944i
$149$	−16.4545	−	9.50000i	−1.34800	−	0.778270i	−0.360037	−	0.932938i	$-0.617236\pi$
$149$	−16.4545	−	9.50000i	−1.34800	−	0.778270i	−0.987967	+	0.154668i	$0.950569\pi$
$150$		0			0
$151$			15.5885i			1.26857i	0.773099	+	0.634285i	$0.218706\pi$
$151$			15.5885i			1.26857i	−0.773099	+	0.634285i	$0.781294\pi$
$152$	−16.7321	−	13.2679i	−1.35715	−	1.07617i
$153$	6.00000	−	6.00000i	0.485071	−	0.485071i
$154$	17.3205	−	30.0000i	1.39573	−	2.41747i
$155$		0			0
$156$		0			0
$157$	−9.56218	+	2.56218i	−0.763145	+	0.204484i	−0.619341	−	0.785122i	$-0.712600\pi$
$157$	−9.56218	+	2.56218i	−0.763145	+	0.204484i	−0.143804	+	0.989606i	$0.545933\pi$
$158$	−4.09808	−	1.09808i	−0.326025	−	0.0873583i
$159$		−	18.0000i		−	1.42749i
$160$		0			0
$161$	6.00000	+	10.3923i	0.472866	+	0.819028i
$162$	−21.2942	−	5.70577i	−1.67303	−	0.448288i
$163$	11.0000	−	11.0000i	0.861586	−	0.861586i	−0.129936	−	0.991522i	$-0.541477\pi$
$163$	11.0000	−	11.0000i	0.861586	−	0.861586i	0.991522	+	0.129936i	$0.0414772\pi$
$164$	13.8564			1.08200
$165$		0			0
$166$	−15.0000	−	8.66025i	−1.16423	−	0.672166i
$167$	−18.9282	−	5.07180i	−1.46471	−	0.392467i	−0.563595	−	0.826051i	$-0.690582\pi$
$167$	−18.9282	−	5.07180i	−1.46471	−	0.392467i	−0.901113	+	0.433584i	$0.857249\pi$
$168$	−8.78461	−	32.7846i	−0.677747	−	2.52939i
$169$	11.2583	+	6.50000i	0.866025	+	0.500000i
$170$		0			0
$171$	10.5000	−	7.79423i	0.802955	−	0.596040i
$172$	28.0000	+	28.0000i	2.13498	+	2.13498i
$173$	−4.73205	+	1.26795i	−0.359771	+	0.0964004i	−0.434177	−	0.900828i	$-0.642961\pi$
$173$	−4.73205	+	1.26795i	−0.359771	+	0.0964004i	0.0744057	+	0.997228i	$0.476294\pi$
$174$	5.19615	−	9.00000i	0.393919	−	0.682288i
$175$		0			0
$176$	−10.0000	+	17.3205i	−0.753778	+	1.30558i
$177$	−3.29423	+	12.2942i	−0.247609	+	0.924091i
$178$	9.00000	−	9.00000i	0.674579	−	0.674579i
$179$	19.0526			1.42406			0.712028	−	0.702152i	$-0.247777\pi$
$179$	19.0526			1.42406			0.712028	+	0.702152i	$0.247777\pi$
$180$		0			0
$181$	6.00000	−	3.46410i	0.445976	−	0.257485i	−0.260153	−	0.965567i	$-0.583773\pi$
$181$	6.00000	−	3.46410i	0.445976	−	0.257485i	0.706129	+	0.708083i	$0.250440\pi$
$182$		0			0
$183$	8.66025	+	8.66025i	0.640184	+	0.640184i
$184$	−10.3923	−	18.0000i	−0.766131	−	1.32698i
$185$		0			0
$186$	27.0000	−	15.5885i	1.97974	−	1.14300i
$187$	−13.6603	+	3.66025i	−0.998937	+	0.267664i
$188$	8.78461	+	32.7846i	0.640684	+	2.39106i
$189$		0			0
$190$		0			0
$191$	−7.00000			−0.506502			−0.253251	−	0.967401i	$-0.581500\pi$
$191$	−7.00000			−0.506502			−0.253251	+	0.967401i	$0.581500\pi$
$192$	−5.07180	−	18.9282i	−0.366025	−	1.36603i
$193$	9.46410	−	2.53590i	0.681241	−	0.182538i	0.0984278	−	0.995144i	$-0.468619\pi$
$193$	9.46410	−	2.53590i	0.681241	−	0.182538i	0.582813	+	0.812606i	$0.301952\pi$
$194$	−15.5885	+	9.00000i	−1.11919	+	0.646162i
$195$		0			0
$196$	−2.00000	−	3.46410i	−0.142857	−	0.247436i
$197$	6.00000	+	6.00000i	0.427482	+	0.427482i	0.887770	−	0.460288i	$-0.152254\pi$
$197$	6.00000	+	6.00000i	0.427482	+	0.427482i	−0.460288	+	0.887770i	$0.652254\pi$
$198$	−25.9808	−	25.9808i	−1.84637	−	1.84637i
$199$	12.9904	−	7.50000i	0.920864	−	0.531661i	0.0369532	−	0.999317i	$-0.488235\pi$
$199$	12.9904	−	7.50000i	0.920864	−	0.531661i	0.883911	+	0.467656i	$0.154901\pi$
$200$		0			0
$201$	24.0000			1.69283
$202$	8.66025	−	8.66025i	0.609333	−	0.609333i
$203$	1.26795	−	4.73205i	0.0889926	−	0.332125i
$204$	−13.8564	+	24.0000i	−0.970143	+	1.68034i
$205$		0			0
$206$	−12.0000	+	20.7846i	−0.836080	+	1.44813i
$207$	12.2942	−	3.29423i	0.854508	−	0.228965i
$208$		0			0
$209$	−21.6506	+	2.50000i	−1.49761	+	0.172929i
$210$		0			0
$211$	−22.5000	−	12.9904i	−1.54896	−	0.894295i	−0.998221	−	0.0596196i	$-0.981011\pi$
$211$	−22.5000	−	12.9904i	−1.54896	−	0.894295i	−0.550743	−	0.834675i	$-0.685655\pi$
$212$	7.60770	+	28.3923i	0.522499	+	1.94999i
$213$	−12.2942	−	3.29423i	−0.842387	−	0.225717i
$214$	−5.19615	−	3.00000i	−0.355202	−	0.205076i
$215$		0			0
$216$		0			0
$217$	10.3923	−	10.3923i	0.705476	−	0.705476i
$218$	−4.09808	−	1.09808i	−0.277557	−	0.0743711i
$219$	1.73205	+	3.00000i	0.117041	+	0.202721i
$220$		0			0
$221$		0			0
$222$	−14.1962	−	3.80385i	−0.952783	−	0.255298i
$223$	−26.0263	+	6.97372i	−1.74285	+	0.466995i	−0.983077	−	0.183195i	$-0.941356\pi$
$223$	−26.0263	+	6.97372i	−1.74285	+	0.466995i	−0.759772	+	0.650190i	$0.774689\pi$
$224$		0			0
$225$		0			0
$226$	3.00000	−	5.19615i	0.199557	−	0.345643i
$227$	−8.66025	+	8.66025i	−0.574801	+	0.574801i	−0.933466	−	0.358665i	$-0.883232\pi$
$227$	−8.66025	+	8.66025i	−0.574801	+	0.574801i	0.358665	+	0.933466i	$0.383232\pi$
$228$	−26.5359	+	33.4641i	−1.75738	+	2.21621i
$229$			9.00000i			0.594737i	0.954763	+	0.297368i	$0.0961089\pi$
$229$			9.00000i			0.594737i	−0.954763	+	0.297368i	$0.903891\pi$
$230$		0			0
$231$	−30.0000	−	17.3205i	−1.97386	−	1.13961i
$232$	−2.19615	+	8.19615i	−0.144184	+	0.538104i
$233$	3.29423	+	12.2942i	0.215812	+	0.805422i	0.985879	+	0.167459i	$0.0535561\pi$
$233$	3.29423	+	12.2942i	0.215812	+	0.805422i	−0.770067	+	0.637963i	$0.779777\pi$
$234$		0			0
$235$		0			0
$236$		−	20.7846i		−	1.35296i
$237$	−1.09808	+	4.09808i	−0.0713277	+	0.266199i
$238$	−5.07180	+	18.9282i	−0.328756	+	1.22693i
$239$		−	11.0000i		−	0.711531i	−0.934575	−	0.355765i	$-0.884220\pi$
$239$		−	11.0000i		−	0.711531i	0.934575	−	0.355765i	$-0.115780\pi$
$240$		0			0
$241$	−10.5000	+	6.06218i	−0.676364	+	0.390499i	−0.798484	−	0.602016i	$-0.794364\pi$
$241$	−10.5000	+	6.06218i	−0.676364	+	0.390499i	0.122119	+	0.992515i	$0.461031\pi$
$242$	8.87564	+	33.1244i	0.570548	+	2.12931i
$243$	−5.70577	+	21.2942i	−0.366025	+	1.36603i
$244$	−17.3205	−	10.0000i	−1.10883	−	0.640184i
$245$		0			0
$246$		−	20.7846i		−	1.32518i
$247$		0			0
$248$	−18.0000	+	18.0000i	−1.14300	+	1.14300i
$249$	−8.66025	+	15.0000i	−0.548821	+	0.950586i
$250$		0			0
$251$	2.50000	+	4.33013i	0.157799	+	0.273315i	0.934075	−	0.357078i	$-0.116227\pi$
$251$	2.50000	+	4.33013i	0.157799	+	0.273315i	−0.776276	+	0.630393i	$0.782894\pi$
$252$	−32.7846	+	8.78461i	−2.06524	+	0.553378i
$253$	−20.4904	−	5.49038i	−1.28822	−	0.345177i
$254$			24.0000i			1.50589i
$255$		0			0
$256$	16.0000	+	27.7128i	1.00000	+	1.73205i
$257$	23.6603	+	6.33975i	1.47589	+	0.395462i	0.904945	−	0.425529i	$-0.139912\pi$
$257$	23.6603	+	6.33975i	1.47589	+	0.395462i	0.570941	+	0.820991i	$0.306578\pi$
$258$	42.0000	−	42.0000i	2.61481	−	2.61481i
$259$	−6.92820			−0.430498
$260$		0			0
$261$	−4.50000	−	2.59808i	−0.278543	−	0.160817i
$262$	−23.6603	−	6.33975i	−1.46174	−	0.391671i
$263$	−4.75833	−	17.7583i	−0.293411	−	1.09503i	−0.942471	−	0.334288i	$-0.891504\pi$
$263$	−4.75833	−	17.7583i	−0.293411	−	1.09503i	0.649060	−	0.760737i	$-0.275163\pi$
$264$	51.9615	+	30.0000i	3.19801	+	1.84637i
$265$		0			0
$266$	−12.0000	+	27.7128i	−0.735767	+	1.69918i
$267$	−9.00000	−	9.00000i	−0.550791	−	0.550791i
$268$	−37.8564	+	10.1436i	−2.31245	+	0.619619i
$269$	−0.866025	+	1.50000i	−0.0528025	+	0.0914566i	−0.891219	−	0.453574i	$-0.850149\pi$
$269$	−0.866025	+	1.50000i	−0.0528025	+	0.0914566i	0.838416	+	0.545031i	$0.183482\pi$
$270$		0			0
$271$	7.50000	−	12.9904i	0.455593	−	0.789109i	−0.543130	−	0.839649i	$-0.682761\pi$
$271$	7.50000	−	12.9904i	0.455593	−	0.789109i	0.998722	+	0.0505395i	$0.0160941\pi$
$272$	2.92820	−	10.9282i	0.177548	−	0.662620i
$273$		0			0
$274$	−27.7128			−1.67419
$275$		0			0
$276$	−36.0000	+	20.7846i	−2.16695	+	1.25109i
$277$	−4.00000	−	4.00000i	−0.240337	−	0.240337i	0.576653	−	0.816989i	$-0.304359\pi$
$277$	−4.00000	−	4.00000i	−0.240337	−	0.240337i	−0.816989	+	0.576653i	$0.804359\pi$
$278$	−31.1769	−	31.1769i	−1.86987	−	1.86987i
$279$	−7.79423	−	13.5000i	−0.466628	−	0.808224i
$280$		0			0
$281$	−3.00000	+	1.73205i	−0.178965	+	0.103325i	−0.586806	−	0.809727i	$-0.699615\pi$
$281$	−3.00000	+	1.73205i	−0.178965	+	0.103325i	0.407841	+	0.913053i	$0.366282\pi$
$282$	49.1769	−	13.1769i	2.92844	−	0.784674i
$283$	−1.46410	−	5.46410i	−0.0870318	−	0.324807i	0.908659	−	0.417538i	$-0.137107\pi$
$283$	−1.46410	−	5.46410i	−0.0870318	−	0.324807i	−0.995691	+	0.0927310i	$0.970440\pi$
$284$	20.7846			1.23334
$285$		0			0
$286$		0			0
$287$	−2.53590	−	9.46410i	−0.149689	−	0.558648i
$288$		0			0
$289$	−7.79423	+	4.50000i	−0.458484	+	0.264706i
$290$		0			0
$291$	9.00000	+	15.5885i	0.527589	+	0.913812i
$292$	−4.00000	−	4.00000i	−0.234082	−	0.234082i
$293$	−6.92820	−	6.92820i	−0.404750	−	0.404750i	0.475153	−	0.879903i	$-0.342393\pi$
$293$	−6.92820	−	6.92820i	−0.404750	−	0.404750i	−0.879903	+	0.475153i	$0.842393\pi$
$294$	−5.19615	+	3.00000i	−0.303046	+	0.174964i
$295$		0			0
$296$	12.0000			0.697486
$297$		0			0
$298$	12.0455	−	44.9545i	0.697778	−	2.60414i
$299$		0			0
$300$		0			0
$301$	14.0000	−	24.2487i	0.806947	−	1.39767i
$302$	−36.8827	+	9.88269i	−2.12236	+	0.568685i
$303$	−8.66025	−	8.66025i	−0.497519	−	0.497519i
$304$	6.92820	−	16.0000i	0.397360	−	0.917663i
$305$		0			0
$306$	18.0000	+	10.3923i	1.02899	+	0.594089i
$307$	−3.16987	−	11.8301i	−0.180914	−	0.675181i	−0.995468	−	0.0950935i	$-0.969685\pi$
$307$	−3.16987	−	11.8301i	−0.180914	−	0.675181i	0.814554	−	0.580088i	$-0.196982\pi$
$308$	54.6410	+	14.6410i	3.11346	+	0.834249i
$309$	20.7846	+	12.0000i	1.18240	+	0.682656i
$310$		0			0
$311$	−20.0000			−1.13410			−0.567048	−	0.823685i	$-0.691915\pi$
$311$	−20.0000			−1.13410			−0.567048	+	0.823685i	$0.691915\pi$
$312$		0			0
$313$	27.3205	+	7.32051i	1.54425	+	0.413780i	0.927635	−	0.373488i	$-0.121838\pi$
$313$	27.3205	+	7.32051i	1.54425	+	0.413780i	0.616611	+	0.787268i	$0.288505\pi$
$314$	−12.1244	−	21.0000i	−0.684217	−	1.18510i
$315$		0			0
$316$		−	6.92820i		−	0.389742i
$317$	−21.2942	−	5.70577i	−1.19600	−	0.320468i	−0.394747	−	0.918790i	$-0.629168\pi$
$317$	−21.2942	−	5.70577i	−1.19600	−	0.320468i	−0.801256	+	0.598322i	$0.795834\pi$
$318$	42.5885	−	11.4115i	2.38824	−	0.639928i
$319$	4.33013	+	7.50000i	0.242441	+	0.419919i
$320$		0			0
$321$	−3.00000	+	5.19615i	−0.167444	+	0.290021i
$322$	−20.7846	+	20.7846i	−1.15828	+	1.15828i
$323$	11.4641	−	4.53590i	0.637880	−	0.252384i
$324$		−	36.0000i		−	2.00000i
$325$		0			0
$326$	33.0000	+	19.0526i	1.82770	+	1.05522i
$327$	−1.09808	+	4.09808i	−0.0607238	+	0.226624i
$328$	4.39230	+	16.3923i	0.242524	+	0.905114i
$329$	20.7846	−	12.0000i	1.14589	−	0.661581i
$330$		0			0
$331$		0			0		1.00000			$0$
$331$		0			0		−1.00000			$\pi$
$332$	7.32051	−	27.3205i	0.401765	−	1.49941i
$333$	−1.90192	+	7.09808i	−0.104225	+	0.388972i
$334$		−	48.0000i		−	2.62644i
$335$		0			0
$336$	24.0000	−	13.8564i	1.30931	−	0.755929i
$337$	4.43782	+	16.5622i	0.241744	+	0.902199i	0.974992	+	0.222239i	$0.0713364\pi$
$337$	4.43782	+	16.5622i	0.241744	+	0.902199i	−0.733249	+	0.679961i	$0.761997\pi$
$338$	−8.24167	+	30.7583i	−0.448288	+	1.67303i
$339$	−5.19615	−	3.00000i	−0.282216	−	0.162938i
$340$		0			0
$341$			25.9808i			1.40694i
$342$	25.0981	+	19.9019i	1.35715	+	1.07617i
$343$	12.0000	−	12.0000i	0.647939	−	0.647939i
$344$	−24.2487	+	42.0000i	−1.30740	+	2.26449i
$345$		0			0
$346$	−6.00000	−	10.3923i	−0.322562	−	0.558694i
$347$	10.9282	−	2.92820i	0.586657	−	0.157194i	0.0467319	−	0.998907i	$-0.485119\pi$
$347$	10.9282	−	2.92820i	0.586657	−	0.157194i	0.539925	+	0.841713i	$0.318453\pi$
$348$	16.3923	+	4.39230i	0.878720	+	0.235452i
$349$			18.0000i			0.963518i	0.876304	+	0.481759i	$0.160002\pi$
$349$			18.0000i			0.963518i	−0.876304	+	0.481759i	$0.839998\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−6.00000	+	6.00000i	−0.319348	+	0.319348i	−0.848517	−	0.529169i	$-0.822504\pi$
$353$	−6.00000	+	6.00000i	−0.319348	+	0.319348i	0.529169	+	0.848517i	$0.322504\pi$
$354$	−31.1769			−1.65703
$355$		0			0
$356$	18.0000	+	10.3923i	0.953998	+	0.550791i
$357$	18.9282	+	5.07180i	1.00179	+	0.268428i
$358$	12.0788	+	45.0788i	0.638386	+	2.38249i
$359$	29.4449	+	17.0000i	1.55404	+	0.897226i	0.997806	+	0.0662000i	$0.0210875\pi$
$359$	29.4449	+	17.0000i	1.55404	+	0.897226i	0.556234	+	0.831026i	$0.312246\pi$
$360$		0			0
$361$	18.5000	−	4.33013i	0.973684	−	0.227901i
$362$	12.0000	+	12.0000i	0.630706	+	0.630706i
$363$	33.1244	−	8.87564i	1.73858	−	0.465851i
$364$		0			0
$365$		0			0
$366$	−15.0000	+	25.9808i	−0.784063	+	1.35804i
$367$	8.05256	−	30.0526i	0.420340	−	1.56873i	−0.353553	−	0.935415i	$-0.615027\pi$
$367$	8.05256	−	30.0526i	0.420340	−	1.56873i	0.773893	−	0.633316i	$-0.218307\pi$
$368$	12.0000	−	12.0000i	0.625543	−	0.625543i
$369$	−10.3923			−0.541002
$370$		0			0
$371$	18.0000	−	10.3923i	0.934513	−	0.539542i
$372$	36.0000	+	36.0000i	1.86651	+	1.86651i
$373$	6.92820	+	6.92820i	0.358729	+	0.358729i	0.863344	−	0.504615i	$-0.168366\pi$
$373$	6.92820	+	6.92820i	0.358729	+	0.358729i	−0.504615	+	0.863344i	$0.668366\pi$
$374$	−17.3205	−	30.0000i	−0.895622	−	1.55126i
$375$		0			0
$376$	−36.0000	+	20.7846i	−1.85656	+	1.07188i
$377$		0			0
$378$		0			0
$379$	−32.9090			−1.69042			−0.845210	−	0.534434i	$-0.820525\pi$
$379$	−32.9090			−1.69042			−0.845210	+	0.534434i	$0.820525\pi$
$380$		0			0
$381$	24.0000			1.22956
$382$	−4.43782	−	16.5622i	−0.227059	−	0.847395i
$383$	−28.3923	+	7.60770i	−1.45078	+	0.388735i	−0.896295	−	0.443459i	$-0.853751\pi$
$383$	−28.3923	+	7.60770i	−1.45078	+	0.388735i	−0.554484	+	0.832194i	$0.687084\pi$
$384$	41.5692	−	24.0000i	2.12132	−	1.22474i
$385$		0			0
$386$	12.0000	+	20.7846i	0.610784	+	1.05791i
$387$	−21.0000	−	21.0000i	−1.06749	−	1.06749i
$388$	−20.7846	−	20.7846i	−1.05518	−	1.05518i
$389$	−19.9186	+	11.5000i	−1.00991	+	0.583073i	−0.911166	−	0.412039i	$-0.864817\pi$
$389$	−19.9186	+	11.5000i	−1.00991	+	0.583073i	−0.0987463	+	0.995113i	$0.531483\pi$
$390$		0			0
$391$	12.0000			0.606866
$392$	3.46410	−	3.46410i	0.174964	−	0.174964i
$393$	−6.33975	+	23.6603i	−0.319798	+	1.19350i
$394$	−10.3923	+	18.0000i	−0.523557	+	0.906827i
$395$		0			0
$396$	30.0000	−	51.9615i	1.50756	−	2.61116i
$397$	5.46410	−	1.46410i	0.274235	−	0.0734812i	−0.119080	−	0.992885i	$-0.537995\pi$
$397$	5.46410	−	1.46410i	0.274235	−	0.0734812i	0.393316	+	0.919403i	$0.371328\pi$
$398$	25.9808	+	25.9808i	1.30230	+	1.30230i
$399$	27.7128	+	12.0000i	1.38738	+	0.600751i
$400$		0			0
$401$	−31.5000	−	18.1865i	−1.57303	−	0.908192i	−0.995794	−	0.0916181i	$-0.970796\pi$
$401$	−31.5000	−	18.1865i	−1.57303	−	0.908192i	−0.577241	−	0.816574i	$-0.695871\pi$
$402$	15.2154	+	56.7846i	0.758875	+	2.83216i
$403$		0			0
$404$	17.3205	+	10.0000i	0.861727	+	0.497519i
$405$		0			0
$406$	12.0000			0.595550
$407$	8.66025	−	8.66025i	0.429273	−	0.429273i
$408$	−32.7846	−	8.78461i	−1.62308	−	0.434903i
$409$	16.4545	+	28.5000i	0.813622	+	1.40923i	0.910313	+	0.413920i	$0.135841\pi$
$409$	16.4545	+	28.5000i	0.813622	+	1.40923i	−0.0966915	+	0.995314i	$0.530826\pi$
$410$		0			0
$411$			27.7128i			1.36697i
$412$	−37.8564	−	10.1436i	−1.86505	−	0.499739i
$413$	−14.1962	+	3.80385i	−0.698547	+	0.187175i
$414$	15.5885	+	27.0000i	0.766131	+	1.32698i
$415$		0			0
$416$		0			0
$417$	−31.1769	+	31.1769i	−1.52674	+	1.52674i
$418$	−19.6410	−	49.6410i	−0.960674	−	2.42802i
$419$		−	31.0000i		−	1.51445i	−0.653155	−	0.757225i	$-0.726555\pi$
$419$		−	31.0000i		−	1.51445i	0.653155	−	0.757225i	$-0.273445\pi$
$420$		0			0
$421$	−10.5000	−	6.06218i	−0.511739	−	0.295452i	0.221809	−	0.975090i	$-0.428804\pi$
$421$	−10.5000	−	6.06218i	−0.511739	−	0.295452i	−0.733548	+	0.679638i	$0.762137\pi$
$422$	16.4711	−	61.4711i	0.801803	−	2.99237i
$423$	−6.58846	−	24.5885i	−0.320342	−	1.19553i
$424$	−31.1769	+	18.0000i	−1.51408	+	0.874157i
$425$		0			0
$426$		−	31.1769i		−	1.51053i
$427$	−3.66025	+	13.6603i	−0.177132	+	0.661066i
$428$	2.53590	−	9.46410i	0.122577	−	0.457465i
$429$		0			0
$430$		0			0
$431$	19.5000	−	11.2583i	0.939282	−	0.542295i	0.0495468	−	0.998772i	$-0.484222\pi$
$431$	19.5000	−	11.2583i	0.939282	−	0.542295i	0.889735	+	0.456477i	$0.150889\pi$
$432$		0			0
$433$	2.53590	−	9.46410i	0.121867	−	0.454816i	−0.877841	−	0.478952i	$-0.841017\pi$
$433$	2.53590	−	9.46410i	0.121867	−	0.454816i	0.999709	+	0.0241361i	$0.00768352\pi$
$434$	31.1769	+	18.0000i	1.49654	+	0.864028i
$435$		0			0
$436$		−	6.92820i		−	0.331801i
$437$	18.2942	+	2.70577i	0.875132	+	0.129435i
$438$	−6.00000	+	6.00000i	−0.286691	+	0.286691i
$439$	14.7224	−	25.5000i	0.702663	−	1.21705i	−0.264865	−	0.964286i	$-0.585327\pi$
$439$	14.7224	−	25.5000i	0.702663	−	1.21705i	0.967528	−	0.252763i	$-0.0813393\pi$
$440$		0			0
$441$	1.50000	+	2.59808i	0.0714286	+	0.123718i
$442$		0			0
$443$	8.19615	+	2.19615i	0.389411	+	0.104342i	0.448212	−	0.893927i	$-0.352061\pi$
$443$	8.19615	+	2.19615i	0.389411	+	0.104342i	−0.0588009	+	0.998270i	$0.518728\pi$
$444$		−	24.0000i		−	1.13899i
$445$		0			0
$446$	−33.0000	−	57.1577i	−1.56260	−	2.70649i
$447$	−44.9545	−	12.0455i	−2.12627	−	0.569733i
$448$	16.0000	−	16.0000i	0.755929	−	0.755929i
$449$	15.5885			0.735665			0.367832	−	0.929892i	$-0.380100\pi$
$449$	15.5885			0.735665			0.367832	+	0.929892i	$0.380100\pi$
$450$		0			0
$451$	15.0000	+	8.66025i	0.706322	+	0.407795i
$452$	9.46410	+	2.53590i	0.445154	+	0.119279i
$453$	9.88269	+	36.8827i	0.464329	+	1.73290i
$454$	−25.9808	−	15.0000i	−1.21934	−	0.703985i
$455$		0			0
$456$	−48.0000	−	20.7846i	−2.24781	−	0.973329i
$457$	10.0000	+	10.0000i	0.467780	+	0.467780i	0.901195	−	0.433414i	$-0.142691\pi$
$457$	10.0000	+	10.0000i	0.467780	+	0.467780i	−0.433414	+	0.901195i	$0.642691\pi$
$458$	−21.2942	+	5.70577i	−0.995014	+	0.266613i
$459$		0			0
$460$		0			0
$461$	2.50000	−	4.33013i	0.116437	−	0.201674i	−0.801917	−	0.597436i	$-0.796186\pi$
$461$	2.50000	−	4.33013i	0.116437	−	0.201674i	0.918353	+	0.395762i	$0.129519\pi$
$462$	21.9615	−	81.9615i	1.02174	−	3.81320i
$463$	−8.00000	+	8.00000i	−0.371792	+	0.371792i	−0.868129	−	0.496338i	$-0.834678\pi$
$463$	−8.00000	+	8.00000i	−0.371792	+	0.371792i	0.496338	+	0.868129i	$0.334678\pi$
$464$	−6.92820			−0.321634
$465$		0			0
$466$	−27.0000	+	15.5885i	−1.25075	+	0.722121i
$467$	−9.00000	−	9.00000i	−0.416470	−	0.416470i	0.467515	−	0.883985i	$-0.345149\pi$
$467$	−9.00000	−	9.00000i	−0.416470	−	0.416470i	−0.883985	+	0.467515i	$0.845149\pi$
$468$		0			0
$469$	13.8564	+	24.0000i	0.639829	+	1.10822i
$470$		0			0
$471$	−21.0000	+	12.1244i	−0.967629	+	0.558661i
$472$	24.5885	−	6.58846i	1.13178	−	0.303258i
$473$	12.8109	+	47.8109i	0.589045	+	2.19835i
$474$	−10.3923			−0.477334
$475$		0			0
$476$	−32.0000			−1.46672
$477$	−5.70577	−	21.2942i	−0.261249	−	0.974996i
$478$	26.0263	−	6.97372i	1.19041	−	0.318971i
$479$	11.2583	−	6.50000i	0.514406	−	0.296993i	−0.220237	−	0.975446i	$-0.570683\pi$
$479$	11.2583	−	6.50000i	0.514406	−	0.296993i	0.734643	+	0.678454i	$0.237350\pi$
$480$		0			0
$481$		0			0
$482$	−21.0000	−	21.0000i	−0.956524	−	0.956524i
$483$	20.7846	+	20.7846i	0.945732	+	0.945732i
$484$	−48.4974	+	28.0000i	−2.20443	+	1.27273i
$485$		0			0
$486$	−54.0000			−2.44949
$487$	−6.92820	+	6.92820i	−0.313947	+	0.313947i	−0.846437	−	0.532490i	$-0.821257\pi$
$487$	−6.92820	+	6.92820i	−0.313947	+	0.313947i	0.532490	+	0.846437i	$0.321257\pi$
$488$	6.33975	−	23.6603i	0.286987	−	1.07105i
$489$	19.0526	−	33.0000i	0.861586	−	1.49231i
$490$		0			0
$491$	−18.5000	+	32.0429i	−0.834893	+	1.44608i	0.0592240	+	0.998245i	$0.481137\pi$
$491$	−18.5000	+	32.0429i	−0.834893	+	1.44608i	−0.894117	+	0.447833i	$0.852196\pi$
$492$	32.7846	−	8.78461i	1.47804	−	0.396041i
$493$	−3.46410	−	3.46410i	−0.156015	−	0.156015i
$494$		0			0
$495$		0			0
$496$	−18.0000	−	10.3923i	−0.808224	−	0.466628i
$497$	−3.80385	−	14.1962i	−0.170626	−	0.636784i
$498$	−40.9808	−	10.9808i	−1.83639	−	0.492060i
$499$	−5.19615	−	3.00000i	−0.232612	−	0.134298i	0.379165	−	0.925329i	$-0.376211\pi$
$499$	−5.19615	−	3.00000i	−0.232612	−	0.134298i	−0.611776	+	0.791031i	$0.709545\pi$
$500$		0			0
$501$	−48.0000			−2.14448
$502$	−8.66025	+	8.66025i	−0.386526	+	0.386526i
$503$	−13.6603	−	3.66025i	−0.609081	−	0.163203i	−0.0589217	−	0.998263i	$-0.518766\pi$
$503$	−13.6603	−	3.66025i	−0.609081	−	0.163203i	−0.550159	+	0.835060i	$0.685433\pi$
$504$	−20.7846	−	36.0000i	−0.925820	−	1.60357i
$505$		0			0
$506$		−	51.9615i		−	2.30997i
$507$	30.7583	+	8.24167i	1.36603	+	0.366025i
$508$	−37.8564	+	10.1436i	−1.67961	+	0.450049i
$509$	15.5885	+	27.0000i	0.690946	+	1.19675i	0.971528	+	0.236924i	$0.0761392\pi$
$509$	15.5885	+	27.0000i	0.690946	+	1.19675i	−0.280582	+	0.959830i	$0.590527\pi$
$510$		0			0
$511$	−2.00000	+	3.46410i	−0.0884748	+	0.153243i
$512$	−27.7128	+	27.7128i	−1.22474	+	1.22474i
$513$		0			0
$514$			60.0000i			2.64649i
$515$		0			0
$516$	84.0000	+	48.4974i	3.69789	+	2.13498i
$517$	−10.9808	+	40.9808i	−0.482933	+	1.80233i
$518$	−4.39230	−	16.3923i	−0.192987	−	0.720237i
$519$	−10.3923	+	6.00000i	−0.456172	+	0.263371i
$520$		0			0
$521$			1.73205i			0.0758825i	0.999280	+	0.0379413i	$0.0120800\pi$
$521$			1.73205i			0.0758825i	−0.999280	+	0.0379413i	$0.987920\pi$
$522$	3.29423	−	12.2942i	0.144184	−	0.538104i
$523$	3.16987	−	11.8301i	0.138609	−	0.517295i	−0.861348	−	0.508015i	$-0.830379\pi$
$523$	3.16987	−	11.8301i	0.138609	−	0.517295i	0.999957	−	0.00928008i	$-0.00295398\pi$
$524$		−	40.0000i		−	1.74741i
$525$		0			0
$526$	39.0000	−	22.5167i	1.70048	−	0.981773i
$527$	−3.80385	−	14.1962i	−0.165698	−	0.618394i
$528$	−12.6795	+	47.3205i	−0.551804	+	2.05936i
$529$	−4.33013	−	2.50000i	−0.188266	−	0.108696i
$530$		0			0
$531$			15.5885i			0.676481i
$532$	−48.7846	−	7.21539i	−2.11508	−	0.312827i
$533$		0			0
$534$	15.5885	−	27.0000i	0.674579	−	1.16840i
$535$		0			0
$536$	−24.0000	−	41.5692i	−1.03664	−	1.79552i
$537$	45.0788	−	12.0788i	1.94530	−	0.521240i
$538$	−4.09808	−	1.09808i	−0.176681	−	0.0473414i
$539$		−	5.00000i		−	0.215365i
$540$		0			0
$541$	16.5000	+	28.5788i	0.709390	+	1.22870i	0.965084	+	0.261942i	$0.0843630\pi$
$541$	16.5000	+	28.5788i	0.709390	+	1.22870i	−0.255693	+	0.966758i	$0.582304\pi$
$542$	35.4904	+	9.50962i	1.52444	+	0.408473i
$543$	12.0000	−	12.0000i	0.514969	−	0.514969i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	35.4904	+	9.50962i	1.51746	+	0.406602i	0.918905	−	0.394480i	$-0.129075\pi$
$547$	35.4904	+	9.50962i	1.51746	+	0.406602i	0.598555	+	0.801082i	$0.295742\pi$
$548$	−11.7128	−	43.7128i	−0.500347	−	1.86732i
$549$	12.9904	+	7.50000i	0.554416	+	0.320092i
$550$		0			0
$551$	−4.50000	−	6.06218i	−0.191706	−	0.258257i
$552$	−36.0000	−	36.0000i	−1.53226	−	1.53226i
$553$	−4.73205	+	1.26795i	−0.201227	+	0.0539187i
$554$	6.92820	−	12.0000i	0.294351	−	0.509831i
$555$		0			0
$556$	36.0000	−	62.3538i	1.52674	−	2.64439i
$557$	−12.0788	+	45.0788i	−0.511797	+	1.91005i	−0.111198	+	0.993798i	$0.535469\pi$
$557$	−12.0788	+	45.0788i	−0.511797	+	1.91005i	−0.400599	+	0.916253i	$0.631198\pi$
$558$	27.0000	−	27.0000i	1.14300	−	1.14300i
$559$		0			0
$560$		0			0
$561$	−30.0000	+	17.3205i	−1.26660	+	0.731272i
$562$	−6.00000	−	6.00000i	−0.253095	−	0.253095i
$563$	19.0526	+	19.0526i	0.802970	+	0.802970i	0.983559	−	0.180589i	$-0.0578004\pi$
$563$	19.0526	+	19.0526i	0.802970	+	0.802970i	−0.180589	+	0.983559i	$0.557800\pi$
$564$	41.5692	+	72.0000i	1.75038	+	3.03175i
$565$		0			0
$566$	12.0000	−	6.92820i	0.504398	−	0.291214i
$567$	−24.5885	+	6.58846i	−1.03262	+	0.276689i
$568$	6.58846	+	24.5885i	0.276446	+	1.03171i
$569$	1.73205			0.0726113			0.0363057	−	0.999341i	$-0.488441\pi$
$569$	1.73205			0.0726113			0.0363057	+	0.999341i	$0.488441\pi$
$570$		0			0
$571$	9.00000			0.376638			0.188319	−	0.982108i	$-0.439696\pi$
$571$	9.00000			0.376638			0.188319	+	0.982108i	$0.439696\pi$
$572$		0			0
$573$	−16.5622	+	4.43782i	−0.691895	+	0.185393i
$574$	20.7846	−	12.0000i	0.867533	−	0.500870i
$575$		0			0
$576$	−12.0000	−	20.7846i	−0.500000	−	0.866025i
$577$	7.00000	+	7.00000i	0.291414	+	0.291414i	0.837639	−	0.546225i	$-0.183936\pi$
$577$	7.00000	+	7.00000i	0.291414	+	0.291414i	−0.546225	+	0.837639i	$0.683936\pi$
$578$	−15.5885	−	15.5885i	−0.648394	−	0.648394i
$579$	20.7846	−	12.0000i	0.863779	−	0.498703i
$580$		0			0
$581$	−20.0000			−0.829740
$582$	−31.1769	+	31.1769i	−1.29232	+	1.29232i
$583$	−9.50962	+	35.4904i	−0.393848	+	1.46986i
$584$	3.46410	−	6.00000i	0.143346	−	0.248282i
$585$		0			0
$586$	12.0000	−	20.7846i	0.495715	−	0.858604i
$587$	24.5885	−	6.58846i	1.01487	−	0.271935i	0.287210	−	0.957868i	$-0.407272\pi$
$587$	24.5885	−	6.58846i	1.01487	−	0.271935i	0.727665	+	0.685933i	$0.240606\pi$
$588$	−6.92820	−	6.92820i	−0.285714	−	0.285714i
$589$	−2.59808	−	22.5000i	−0.107052	−	0.927096i
$590$		0			0
$591$	18.0000	+	10.3923i	0.740421	+	0.427482i
$592$	2.53590	+	9.46410i	0.104225	+	0.388972i
$593$	38.2487	+	10.2487i	1.57069	+	0.420864i	0.936027	−	0.351928i	$-0.114474\pi$
$593$	38.2487	+	10.2487i	1.57069	+	0.420864i	0.634659	+	0.772792i	$0.281140\pi$
$594$		0			0
$595$		0			0
$596$	76.0000			3.11308
$597$	25.9808	−	25.9808i	1.06332	−	1.06332i
$598$		0			0
$599$	−13.8564	−	24.0000i	−0.566157	−	0.980613i	−0.996941	−	0.0781581i	$-0.975096\pi$
$599$	−13.8564	−	24.0000i	−0.566157	−	0.980613i	0.430784	−	0.902455i	$-0.358237\pi$
$600$		0			0
$601$			22.5167i			0.918474i	0.888314	+	0.459237i	$0.151877\pi$
$601$			22.5167i			0.918474i	−0.888314	+	0.459237i	$0.848123\pi$
$602$	66.2487	+	17.7513i	2.70010	+	0.723489i
$603$	28.3923	−	7.60770i	1.15622	−	0.309809i
$604$	−31.1769	−	54.0000i	−1.26857	−	2.19723i
$605$		0			0
$606$	15.0000	−	25.9808i	0.609333	−	1.05540i
$607$	3.46410	−	3.46410i	0.140604	−	0.140604i	−0.633302	−	0.773905i	$-0.718301\pi$
$607$	3.46410	−	3.46410i	0.140604	−	0.140604i	0.773905	+	0.633302i	$0.218301\pi$
$608$		0			0
$609$		−	12.0000i		−	0.486265i
$610$		0			0
$611$		0			0
$612$	−8.78461	+	32.7846i	−0.355097	+	1.32524i
$613$	−4.02628	−	15.0263i	−0.162620	−	0.606906i	−0.998332	−	0.0577376i	$-0.981611\pi$
$613$	−4.02628	−	15.0263i	−0.162620	−	0.606906i	0.835712	−	0.549168i	$-0.185055\pi$
$614$	25.9808	−	15.0000i	1.04850	−	0.605351i
$615$		0			0
$616$			69.2820i			2.79145i
$617$	1.83013	−	6.83013i	0.0736781	−	0.274971i	−0.919252	−	0.393669i	$-0.871206\pi$
$617$	1.83013	−	6.83013i	0.0736781	−	0.274971i	0.992930	+	0.118699i	$0.0378722\pi$
$618$	−15.2154	+	56.7846i	−0.612053	+	2.28421i
$619$			30.0000i			1.20580i	0.797816	+	0.602901i	$0.205989\pi$
$619$			30.0000i			1.20580i	−0.797816	+	0.602901i	$0.794011\pi$
$620$		0			0
$621$		0			0
$622$	−12.6795	−	47.3205i	−0.508401	−	1.89738i
$623$	3.80385	−	14.1962i	0.152398	−	0.568757i
$624$		0			0
$625$		0			0
$626$			69.2820i			2.76907i
$627$	−49.6410	+	19.6410i	−1.98247	+	0.784387i
$628$	28.0000	−	28.0000i	1.11732	−	1.11732i
$629$	−3.46410	+	6.00000i	−0.138123	+	0.239236i
$630$		0			0
$631$	−20.5000	−	35.5070i	−0.816092	−	1.41351i	−0.908541	−	0.417796i	$-0.862803\pi$
$631$	−20.5000	−	35.5070i	−0.816092	−	1.41351i	0.0924489	−	0.995717i	$-0.470531\pi$
$632$	8.19615	−	2.19615i	0.326025	−	0.0873583i
$633$	−61.4711	−	16.4711i	−2.44326	−	0.654669i
$634$		−	54.0000i		−	2.14461i
$635$		0			0
$636$	36.0000	+	62.3538i	1.42749	+	2.47249i
$637$		0			0
$638$	−15.0000	+	15.0000i	−0.593856	+	0.593856i
$639$	−15.5885			−0.616670
$640$		0			0
$641$	−7.50000	−	4.33013i	−0.296232	−	0.171030i	0.344517	−	0.938780i	$-0.388043\pi$
$641$	−7.50000	−	4.33013i	−0.296232	−	0.171030i	−0.640749	+	0.767750i	$0.721376\pi$
$642$	−14.1962	−	3.80385i	−0.560277	−	0.150126i
$643$	−7.32051	−	27.3205i	−0.288693	−	1.07742i	−0.946099	−	0.323879i	$-0.895013\pi$
$643$	−7.32051	−	27.3205i	−0.288693	−	1.07742i	0.657406	−	0.753537i	$-0.271654\pi$
$644$	−41.5692	−	24.0000i	−1.63806	−	0.945732i
$645$		0			0
$646$	18.0000	+	24.2487i	0.708201	+	0.954053i
$647$	−10.0000	−	10.0000i	−0.393141	−	0.393141i	0.482665	−	0.875805i	$-0.339669\pi$
$647$	−10.0000	−	10.0000i	−0.393141	−	0.393141i	−0.875805	+	0.482665i	$0.839669\pi$
$648$	42.5885	−	11.4115i	1.67303	−	0.448288i
$649$	12.9904	−	22.5000i	0.509917	−	0.883202i
$650$		0			0
$651$	18.0000	−	31.1769i	0.705476	−	1.22192i
$652$	−16.1051	+	60.1051i	−0.630725	+	2.35390i
$653$	23.0000	−	23.0000i	0.900060	−	0.900060i	−0.0953813	−	0.995441i	$-0.530407\pi$
$653$	23.0000	−	23.0000i	0.900060	−	0.900060i	0.995441	+	0.0953813i	$0.0304070\pi$
$654$	−10.3923			−0.406371
$655$		0			0
$656$	−12.0000	+	6.92820i	−0.468521	+	0.270501i
$657$	3.00000	+	3.00000i	0.117041	+	0.117041i
$658$	41.5692	+	41.5692i	1.62054	+	1.62054i
$659$	−1.73205	−	3.00000i	−0.0674711	−	0.116863i	0.830316	−	0.557292i	$-0.188160\pi$
$659$	−1.73205	−	3.00000i	−0.0674711	−	0.116863i	−0.897787	+	0.440429i	$0.854826\pi$
$660$		0			0
$661$	25.5000	−	14.7224i	0.991835	−	0.572636i	0.0860127	−	0.996294i	$-0.472587\pi$
$661$	25.5000	−	14.7224i	0.991835	−	0.572636i	0.905822	+	0.423658i	$0.139254\pi$
$662$		0			0
$663$		0			0
$664$	34.6410			1.34433
$665$		0			0
$666$	−18.0000			−0.697486
$667$	−1.90192	−	7.09808i	−0.0736428	−	0.274839i
$668$	75.7128	−	20.2872i	2.92942	−	0.784935i
$669$	−57.1577	+	33.0000i	−2.20984	+	1.27585i
$670$		0			0
$671$	−12.5000	−	21.6506i	−0.482557	−	0.835813i
$672$		0			0
$673$	−13.8564	−	13.8564i	−0.534125	−	0.534125i	0.387672	−	0.921797i	$-0.373279\pi$
$673$	−13.8564	−	13.8564i	−0.534125	−	0.534125i	−0.921797	+	0.387672i	$0.873279\pi$
$674$	−36.3731	+	21.0000i	−1.40104	+	0.808890i
$675$		0			0
$676$	−52.0000			−2.00000
$677$	31.1769	−	31.1769i	1.19823	−	1.19823i	0.223529	−	0.974697i	$-0.428242\pi$
$677$	31.1769	−	31.1769i	1.19823	−	1.19823i	0.974697	−	0.223529i	$-0.0717577\pi$
$678$	3.80385	−	14.1962i	0.146086	−	0.545200i
$679$	−10.3923	+	18.0000i	−0.398820	+	0.690777i
$680$		0			0
$681$	−15.0000	+	25.9808i	−0.574801	+	0.995585i
$682$	−61.4711	+	16.4711i	−2.35385	+	0.630713i
$683$	27.7128	+	27.7128i	1.06040	+	1.06040i	0.998055	+	0.0623468i	$0.0198585\pi$
$683$	27.7128	+	27.7128i	1.06040	+	1.06040i	0.0623468	+	0.998055i	$0.480142\pi$
$684$	−20.7846	+	48.0000i	−0.794719	+	1.83533i
$685$		0			0
$686$	36.0000	+	20.7846i	1.37449	+	0.793560i
$687$	5.70577	+	21.2942i	0.217689	+	0.812425i
$688$	−38.2487	−	10.2487i	−1.45822	−	0.390728i
$689$		0			0
$690$		0			0
$691$	15.0000			0.570627			0.285313	−	0.958434i	$-0.407902\pi$
$691$	15.0000			0.570627			0.285313	+	0.958434i	$0.407902\pi$
$692$	13.8564	−	13.8564i	0.526742	−	0.526742i
$693$	−40.9808	−	10.9808i	−1.55673	−	0.417125i
$694$	13.8564	+	24.0000i	0.525982	+	0.911028i
$695$		0			0
$696$			20.7846i			0.787839i
$697$	−9.46410	−	2.53590i	−0.358478	−	0.0960540i
$698$	−42.5885	+	11.4115i	−1.61200	+	0.431933i
$699$	15.5885	+	27.0000i	0.589610	+	1.02123i
$700$		0			0
$701$	11.0000	−	19.0526i	0.415464	−	0.719605i	−0.580013	−	0.814607i	$-0.696952\pi$
$701$	11.0000	−	19.0526i	0.415464	−	0.719605i	0.995477	+	0.0950021i	$0.0302858\pi$
$702$		0			0
$703$	−6.63397	+	8.36603i	−0.250205	+	0.315531i
$704$			40.0000i			1.50756i
$705$		0			0
$706$	−18.0000	−	10.3923i	−0.677439	−	0.391120i
$707$	3.66025	−	13.6603i	0.137658	−	0.513747i
$708$	−13.1769	−	49.1769i	−0.495219	−	1.84818i
$709$	12.9904	−	7.50000i	0.487864	−	0.281668i	−0.235824	−	0.971796i	$-0.575779\pi$
$709$	12.9904	−	7.50000i	0.487864	−	0.281668i	0.723688	+	0.690127i	$0.242446\pi$
$710$		0			0
$711$			5.19615i			0.194871i
$712$	−6.58846	+	24.5885i	−0.246913	+	0.921491i
$713$	5.70577	−	21.2942i	0.213683	−	0.797475i
$714$			48.0000i			1.79635i
$715$		0			0
$716$	−66.0000	+	38.1051i	−2.46654	+	1.42406i
$717$	−6.97372	−	26.0263i	−0.260438	−	0.971969i
$718$	−21.5551	+	80.4449i	−0.804431	+	3.00218i
$719$	−6.06218	−	3.50000i	−0.226081	−	0.130528i	0.382682	−	0.923880i	$-0.375001\pi$
$719$	−6.06218	−	3.50000i	−0.226081	−	0.130528i	−0.608763	+	0.793352i	$0.708334\pi$
$720$		0			0
$721$			27.7128i			1.03208i
$722$	21.9737	+	41.0263i	0.817777	+	1.52684i
$723$	−21.0000	+	21.0000i	−0.780998	+	0.780998i
$724$	−13.8564	+	24.0000i	−0.514969	+	0.891953i
$725$		0			0
$726$	42.0000	+	72.7461i	1.55877	+	2.69986i
$727$	25.9545	−	6.95448i	0.962598	−	0.257927i	0.256899	−	0.966438i	$-0.417299\pi$
$727$	25.9545	−	6.95448i	0.962598	−	0.257927i	0.705700	+	0.708511i	$0.250633\pi$
$728$		0			0
$729$			27.0000i			1.00000i
$730$		0			0
$731$	−14.0000	−	24.2487i	−0.517809	−	0.896871i
$732$	−47.3205	−	12.6795i	−1.74902	−	0.468648i
$733$	−19.0000	+	19.0000i	−0.701781	+	0.701781i	−0.964793	−	0.263012i	$-0.915284\pi$
$733$	−19.0000	+	19.0000i	−0.701781	+	0.701781i	0.263012	+	0.964793i	$0.415284\pi$
$734$	76.2102			2.81297
$735$		0			0
$736$		0			0
$737$	−47.3205	−	12.6795i	−1.74307	−	0.467055i
$738$	−6.58846	−	24.5885i	−0.242524	−	0.905114i
$739$	−16.4545	−	9.50000i	−0.605288	−	0.349463i	0.165831	−	0.986154i	$-0.446969\pi$
$739$	−16.4545	−	9.50000i	−0.605288	−	0.349463i	−0.771119	+	0.636691i	$0.780303\pi$
$740$		0			0
$741$		0			0
$742$	36.0000	+	36.0000i	1.32160	+	1.32160i
$743$	21.2942	−	5.70577i	0.781209	−	0.209324i	0.153892	−	0.988088i	$-0.450819\pi$
$743$	21.2942	−	5.70577i	0.781209	−	0.209324i	0.627318	+	0.778763i	$0.284153\pi$
$744$	−31.1769	+	54.0000i	−1.14300	+	1.97974i
$745$		0			0
$746$	−12.0000	+	20.7846i	−0.439351	+	0.760979i
$747$	−5.49038	+	20.4904i	−0.200883	+	0.749704i
$748$	40.0000	−	40.0000i	1.46254	−	1.46254i
$749$	−6.92820			−0.253151
$750$		0			0
$751$	7.50000	−	4.33013i	0.273679	−	0.158009i	−0.356879	−	0.934150i	$-0.616159\pi$
$751$	7.50000	−	4.33013i	0.273679	−	0.158009i	0.630558	+	0.776142i	$0.282826\pi$
$752$	−24.0000	−	24.0000i	−0.875190	−	0.875190i
$753$	8.66025	+	8.66025i	0.315597	+	0.315597i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	19.1244	−	5.12436i	0.695087	−	0.186248i	0.106058	−	0.994360i	$-0.466177\pi$
$757$	19.1244	−	5.12436i	0.695087	−	0.186248i	0.589029	+	0.808112i	$0.299510\pi$
$758$	−20.8634	−	77.8634i	−0.757795	−	2.82813i
$759$	−51.9615			−1.88608
$760$		0			0
$761$	34.0000			1.23250			0.616250	−	0.787551i	$-0.288651\pi$
$761$	34.0000			1.23250			0.616250	+	0.787551i	$0.288651\pi$
$762$	15.2154	+	56.7846i	0.551195	+	2.05709i
$763$	−4.73205	+	1.26795i	−0.171312	+	0.0459028i
$764$	24.2487	−	14.0000i	0.877288	−	0.506502i
$765$		0			0
$766$	−36.0000	−	62.3538i	−1.30073	−	2.25294i
$767$		0			0
$768$	55.4256	+	55.4256i	2.00000	+	2.00000i
$769$	18.1865	−	10.5000i	0.655823	−	0.378640i	−0.134860	−	0.990865i	$-0.543059\pi$
$769$	18.1865	−	10.5000i	0.655823	−	0.378640i	0.790684	+	0.612225i	$0.209725\pi$
$770$		0			0
$771$	60.0000			2.16085
$772$	−27.7128	+	27.7128i	−0.997406	+	0.997406i
$773$	−2.53590	+	9.46410i	−0.0912099	+	0.340400i	−0.996418	−	0.0845694i	$-0.973049\pi$
$773$	−2.53590	+	9.46410i	−0.0912099	+	0.340400i	0.905208	+	0.424970i	$0.139715\pi$
$774$	36.3731	−	63.0000i	1.30740	−	2.26449i
$775$		0			0
$776$	18.0000	−	31.1769i	0.646162	−	1.11919i
$777$	−16.3923	+	4.39230i	−0.588071	+	0.157573i
$778$	−39.8372	−	39.8372i	−1.42823	−	1.42823i
$779$	−13.8564	−	6.00000i	−0.496457	−	0.214972i
$780$		0			0
$781$	22.5000	+	12.9904i	0.805113	+	0.464832i
$782$	7.60770	+	28.3923i	0.272051	+	1.01531i
$783$		0			0
$784$	3.46410	+	2.00000i	0.123718	+	0.0714286i
$785$		0			0
$786$	−60.0000			−2.14013
$787$	−24.2487	+	24.2487i	−0.864373	+	0.864373i	−0.991843	−	0.127469i	$-0.959315\pi$
$787$	−24.2487	+	24.2487i	−0.864373	+	0.864373i	0.127469	+	0.991843i	$0.459315\pi$
$788$	−32.7846	−	8.78461i	−1.16790	−	0.312939i
$789$	−22.5167	−	39.0000i	−0.801614	−	1.38844i
$790$		0			0
$791$		−	6.92820i		−	0.246339i
$792$	70.9808	+	19.0192i	2.52219	+	0.675819i
$793$		0			0
$794$	6.92820	+	12.0000i	0.245873	+	0.425864i
$795$		0			0
$796$	−30.0000	+	51.9615i	−1.06332	+	1.84173i
$797$	1.73205	−	1.73205i	0.0613524	−	0.0613524i	−0.675765	−	0.737117i	$-0.736187\pi$
$797$	1.73205	−	1.73205i	0.0613524	−	0.0613524i	0.737117	+	0.675765i	$0.236187\pi$
$798$	−10.8231	+	73.1769i	−0.383133	+	2.59043i
$799$		−	24.0000i		−	0.849059i
$800$		0			0
$801$	−13.5000	−	7.79423i	−0.476999	−	0.275396i
$802$	23.0596	−	86.0596i	0.814263	−	3.03887i
$803$	−1.83013	−	6.83013i	−0.0645838	−	0.241030i
$804$	−83.1384	+	48.0000i	−2.93207	+	1.69283i
$805$		0			0
$806$		0			0
$807$	−1.09808	+	4.09808i	−0.0386541	+	0.144259i
$808$	−6.33975	+	23.6603i	−0.223031	+	0.832365i
$809$			35.0000i			1.23053i	0.788319	+	0.615267i	$0.210952\pi$
$809$			35.0000i			1.23053i	−0.788319	+	0.615267i	$0.789048\pi$
$810$		0			0
$811$	−34.5000	+	19.9186i	−1.21146	+	0.699436i	−0.963077	−	0.269226i	$-0.913232\pi$
$811$	−34.5000	+	19.9186i	−1.21146	+	0.699436i	−0.248382	+	0.968662i	$0.579899\pi$
$812$	5.07180	+	18.9282i	0.177985	+	0.664250i
$813$	9.50962	−	35.4904i	0.333517	−	1.24470i
$814$	25.9808	+	15.0000i	0.910625	+	0.525750i
$815$		0			0
$816$		−	27.7128i		−	0.970143i
$817$	−15.8756	−	40.1244i	−0.555418	−	1.40377i
$818$	−57.0000	+	57.0000i	−1.99296	+	1.99296i
$819$		0			0
$820$		0			0
$821$	14.5000	+	25.1147i	0.506053	+	0.876510i	0.999975	+	0.00700413i	$0.00222950\pi$
$821$	14.5000	+	25.1147i	0.506053	+	0.876510i	−0.493922	+	0.869506i	$0.664437\pi$
$822$	−65.5692	+	17.5692i	−2.28699	+	0.612797i
$823$	−2.73205	−	0.732051i	−0.0952333	−	0.0255177i	0.210888	−	0.977510i	$-0.432365\pi$
$823$	−2.73205	−	0.732051i	−0.0952333	−	0.0255177i	−0.306121	+	0.951993i	$0.599031\pi$
$824$		−	48.0000i		−	1.67216i
$825$		0			0
$826$	−18.0000	−	31.1769i	−0.626300	−	1.08478i
$827$	−23.6603	−	6.33975i	−0.822748	−	0.220455i	−0.177200	−	0.984175i	$-0.556704\pi$
$827$	−23.6603	−	6.33975i	−0.822748	−	0.220455i	−0.645547	+	0.763720i	$0.723371\pi$
$828$	−36.0000	+	36.0000i	−1.25109	+	1.25109i
$829$	−17.3205			−0.601566			−0.300783	−	0.953693i	$-0.597248\pi$
$829$	−17.3205			−0.601566			−0.300783	+	0.953693i	$0.597248\pi$
$830$		0			0
$831$	−12.0000	−	6.92820i	−0.416275	−	0.240337i
$832$		0			0
$833$	0.732051	+	2.73205i	0.0253641	+	0.0946600i
$834$	−93.5307	−	54.0000i	−3.23870	−	1.86987i
$835$		0			0
$836$	70.0000	−	51.9615i	2.42100	−	1.79713i
$837$		0			0
$838$	73.3468	−	19.6532i	2.53372	−	0.678909i
$839$	−13.8564	+	24.0000i	−0.478376	+	0.828572i	−0.999693	−	0.0247915i	$-0.992108\pi$
$839$	−13.8564	+	24.0000i	−0.478376	+	0.828572i	0.521316	+	0.853363i	$0.325441\pi$
$840$		0			0
$841$	13.0000	−	22.5167i	0.448276	−	0.776437i
$842$	7.68653	−	28.6865i	0.264895	−	0.988603i
$843$	−6.00000	+	6.00000i	−0.206651	+	0.206651i
$844$	103.923			3.57718
$845$		0			0
$846$	54.0000	−	31.1769i	1.85656	−	1.07188i
$847$	28.0000	+	28.0000i	0.962091	+	0.962091i
$848$	−20.7846	−	20.7846i	−0.713746	−	0.713746i
$849$	−6.92820	−	12.0000i	−0.237775	−	0.411839i
$850$		0			0
$851$	−9.00000	+	5.19615i	−0.308516	+	0.178122i
$852$	49.1769	−	13.1769i	1.68477	−	0.451434i
$853$	−6.22243	−	23.2224i	−0.213052	−	0.795121i	−0.986843	−	0.161680i	$-0.948309\pi$
$853$	−6.22243	−	23.2224i	−0.213052	−	0.795121i	0.773791	−	0.633441i	$-0.218358\pi$
$854$	−34.6410			−1.18539
$855$		0			0
$856$	12.0000			0.410152
$857$	14.5814	+	54.4186i	0.498092	+	1.85890i	0.511976	+	0.859000i	$0.328914\pi$
$857$	14.5814	+	54.4186i	0.498092	+	1.85890i	−0.0138842	+	0.999904i	$0.504420\pi$
$858$		0			0
$859$	45.8993	−	26.5000i	1.56607	−	0.904168i	0.569445	−	0.822030i	$-0.307158\pi$
$859$	45.8993	−	26.5000i	1.56607	−	0.904168i	0.996621	−	0.0821386i	$-0.0261750\pi$
$860$		0			0
$861$	−12.0000	−	20.7846i	−0.408959	−	0.708338i
$862$	39.0000	+	39.0000i	1.32835	+	1.32835i
$863$	−22.5167	−	22.5167i	−0.766476	−	0.766476i	0.211008	−	0.977484i	$-0.432325\pi$
$863$	−22.5167	−	22.5167i	−0.766476	−	0.766476i	−0.977484	+	0.211008i	$0.932325\pi$
$864$		0			0
$865$		0			0
$866$	24.0000			0.815553
$867$	−15.5885	+	15.5885i	−0.529412	+	0.529412i
$868$	−15.2154	+	56.7846i	−0.516444	+	1.92740i
$869$	4.33013	−	7.50000i	0.146889	−	0.254420i
$870$		0			0
$871$		0			0
$872$	8.19615	−	2.19615i	0.277557	−	0.0743711i
$873$	15.5885	+	15.5885i	0.527589	+	0.527589i
$874$	5.19615	+	45.0000i	0.175762	+	1.52215i
$875$		0			0
$876$	−12.0000	−	6.92820i	−0.405442	−	0.234082i
$877$	−1.90192	−	7.09808i	−0.0642234	−	0.239685i	0.926351	−	0.376662i	$-0.122928\pi$
$877$	−1.90192	−	7.09808i	−0.0642234	−	0.239685i	−0.990574	+	0.136977i	$0.956261\pi$
$878$	69.6673	+	18.6673i	2.35116	+	0.629991i
$879$	−20.7846	−	12.0000i	−0.701047	−	0.404750i
$880$		0			0
$881$	47.0000			1.58347			0.791735	−	0.610865i	$-0.209178\pi$
$881$	47.0000			1.58347			0.791735	+	0.610865i	$0.209178\pi$
$882$	−5.19615	+	5.19615i	−0.174964	+	0.174964i
$883$	19.1244	+	5.12436i	0.643586	+	0.172448i	0.565827	−	0.824524i	$-0.308557\pi$
$883$	19.1244	+	5.12436i	0.643586	+	0.172448i	0.0777587	+	0.996972i	$0.475224\pi$
$884$		0			0
$885$		0			0
$886$			20.7846i			0.698273i
$887$	−42.5885	−	11.4115i	−1.42998	−	0.383162i	−0.540967	−	0.841044i	$-0.681942\pi$
$887$	−42.5885	−	11.4115i	−1.42998	−	0.383162i	−0.889013	+	0.457882i	$0.848608\pi$
$888$	28.3923	−	7.60770i	0.952783	−	0.255298i
$889$	13.8564	+	24.0000i	0.464729	+	0.804934i
$890$		0			0
$891$	22.5000	−	38.9711i	0.753778	−	1.30558i
$892$	76.2102	−	76.2102i	2.55171	−	2.55171i
$893$	5.41154	−	36.5885i	0.181090	−	1.22439i
$894$		−	114.000i		−	3.81273i
$895$		0			0
$896$	48.0000	+	27.7128i	1.60357	+	0.925820i
$897$		0			0
$898$	9.88269	+	36.8827i	0.329789	+	1.23079i
$899$	−7.79423	+	4.50000i	−0.259952	+	0.150083i
$900$		0			0
$901$		−	20.7846i		−	0.692436i
$902$	−10.9808	+	40.9808i	−0.365619	+	1.36451i
$903$	17.7513	−	66.2487i	0.590726	−	2.20462i
$904$			12.0000i			0.399114i
$905$		0			0
$906$	−81.0000	+	46.7654i	−2.69104	+	1.55368i
$907$	1.26795	+	4.73205i	0.0421016	+	0.157125i	0.983776	−	0.179399i	$-0.0574153\pi$
$907$	1.26795	+	4.73205i	0.0421016	+	0.157125i	−0.941675	+	0.336524i	$0.890749\pi$
$908$	12.6795	−	47.3205i	0.420784	−	1.57039i
$909$	−12.9904	−	7.50000i	−0.430864	−	0.248759i
$910$		0			0
$911$		−	29.4449i		−	0.975552i	−0.872969	−	0.487776i	$-0.837808\pi$
$911$		−	29.4449i		−	0.975552i	0.872969	−	0.487776i	$-0.162192\pi$
$912$	6.24871	−	42.2487i	0.206916	−	1.39899i
$913$	25.0000	−	25.0000i	0.827379	−	0.827379i
$914$	−17.3205	+	30.0000i	−0.572911	+	0.992312i
$915$		0			0
$916$	−18.0000	−	31.1769i	−0.594737	−	1.03011i
$917$	−27.3205	+	7.32051i	−0.902203	+	0.241744i
$918$		0			0
$919$		−	22.0000i		−	0.725713i	−0.931845	−	0.362857i	$-0.881802\pi$
$919$		−	22.0000i		−	0.725713i	0.931845	−	0.362857i	$-0.118198\pi$
$920$		0			0
$921$	−15.0000	−	25.9808i	−0.494267	−	0.856095i
$922$	11.8301	+	3.16987i	0.389604	+	0.104394i
$923$		0			0
$924$	138.564			4.55842
$925$		0			0
$926$	−24.0000	−	13.8564i	−0.788689	−	0.455350i
$927$	28.3923	+	7.60770i	0.932526	+	0.249869i
$928$		0			0
$929$	−6.06218	−	3.50000i	−0.198894	−	0.114831i	0.397246	−	0.917712i	$-0.369966\pi$
$929$	−6.06218	−	3.50000i	−0.198894	−	0.114831i	−0.596139	+	0.802881i	$0.703299\pi$
$930$		0			0
$931$	0.500000	+	4.33013i	0.0163868	+	0.141914i
$932$	−36.0000	−	36.0000i	−1.17922	−	1.17922i
$933$	−47.3205	+	12.6795i	−1.54920	+	0.415108i
$934$	15.5885	−	27.0000i	0.510070	−	0.883467i
$935$		0			0
$936$		0			0
$937$	−6.22243	+	23.2224i	−0.203278	+	0.758644i	0.786690	+	0.617349i	$0.211793\pi$
$937$	−6.22243	+	23.2224i	−0.203278	+	0.758644i	−0.989968	+	0.141295i	$0.954873\pi$
$938$	−48.0000	+	48.0000i	−1.56726	+	1.56726i
$939$	69.2820			2.26093
$940$		0			0
$941$	−28.5000	+	16.4545i	−0.929073	+	0.536401i	−0.886518	−	0.462693i	$-0.846883\pi$
$941$	−28.5000	+	16.4545i	−0.929073	+	0.536401i	−0.0425550	+	0.999094i	$0.513550\pi$
$942$	−42.0000	−	42.0000i	−1.36843	−	1.36843i
$943$	−10.3923	−	10.3923i	−0.338420	−	0.338420i
$944$	10.3923	+	18.0000i	0.338241	+	0.585850i
$945$		0			0
$946$	−105.000	+	60.6218i	−3.41384	+	1.97098i
$947$	−5.46410	+	1.46410i	−0.177559	+	0.0475769i	−0.346503	−	0.938049i	$-0.612631\pi$
$947$	−5.46410	+	1.46410i	−0.177559	+	0.0475769i	0.168944	+	0.985626i	$0.445964\pi$
$948$	−4.39230	−	16.3923i	−0.142655	−	0.532397i
$949$		0			0
$950$		0			0
$951$	−54.0000			−1.75107
$952$	−10.1436	−	37.8564i	−0.328756	−	1.22693i
$953$	33.1244	−	8.87564i	1.07300	−	0.287510i	0.321277	−	0.946985i	$-0.395888\pi$
$953$	33.1244	−	8.87564i	1.07300	−	0.287510i	0.751726	+	0.659475i	$0.229221\pi$
$954$	46.7654	−	27.0000i	1.51408	−	0.874157i
$955$		0			0
$956$	22.0000	+	38.1051i	0.711531	+	1.23241i
$957$	15.0000	+	15.0000i	0.484881	+	0.484881i
$958$	22.5167	+	22.5167i	0.727480	+	0.727480i
$959$	−27.7128	+	16.0000i	−0.894893	+	0.516667i
$960$		0			0
$961$	4.00000			0.129032
$962$		0			0
$963$	−1.90192	+	7.09808i	−0.0612886	+	0.228732i
$964$	24.2487	−	42.0000i	0.780998	−	1.35273i
$965$		0			0
$966$	−36.0000	+	62.3538i	−1.15828	+	2.00620i
$967$	34.1506	−	9.15064i	1.09821	−	0.294265i	0.336175	−	0.941800i	$-0.390867\pi$
$967$	34.1506	−	9.15064i	1.09821	−	0.294265i	0.762036	+	0.647535i	$0.224200\pi$
$968$	−48.4974	−	48.4974i	−1.55877	−	1.55877i
$969$	24.2487	−	18.0000i	0.778981	−	0.578243i
$970$		0			0
$971$	−45.0000	−	25.9808i	−1.44412	−	0.833762i	−0.445998	−	0.895034i	$-0.647151\pi$
$971$	−45.0000	−	25.9808i	−1.44412	−	0.833762i	−0.998121	+	0.0612718i	$0.980484\pi$
$972$	−22.8231	−	85.1769i	−0.732051	−	2.73205i
$973$	−49.1769	−	13.1769i	−1.57654	−	0.422432i
$974$	−20.7846	−	12.0000i	−0.665982	−	0.384505i
$975$		0			0
$976$	20.0000			0.640184
$977$	31.1769	−	31.1769i	0.997438	−	0.997438i	−0.00255886	−	0.999997i	$-0.500815\pi$
$977$	31.1769	−	31.1769i	0.997438	−	0.997438i	0.999997	+	0.00255886i	$0.000814512\pi$
$978$	90.1577	+	24.1577i	2.88292	+	0.772477i
$979$	12.9904	+	22.5000i	0.415174	+	0.719103i
$980$		0			0
$981$			5.19615i			0.165900i
$982$	−87.5429	−	23.4571i	−2.79361	−	0.748545i
$983$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$983$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$984$	20.7846	+	36.0000i	0.662589	+	1.14764i
$985$		0			0
$986$	6.00000	−	10.3923i	0.191079	−	0.330958i
$987$	41.5692	−	41.5692i	1.32316	−	1.32316i
$988$		0			0
$989$		−	42.0000i		−	1.33552i
$990$		0			0
$991$	−18.0000	−	10.3923i	−0.571789	−	0.330122i	0.186075	−	0.982536i	$-0.440423\pi$
$991$	−18.0000	−	10.3923i	−0.571789	−	0.330122i	−0.757863	+	0.652413i	$0.773757\pi$
$992$		0			0
$993$		0			0
$994$	31.1769	−	18.0000i	0.988872	−	0.570925i
$995$		0			0
$996$		−	69.2820i		−	2.19529i
$997$	2.92820	−	10.9282i	0.0927371	−	0.346100i	−0.903930	−	0.427681i	$-0.859331\pi$
$997$	2.92820	−	10.9282i	0.0927371	−	0.346100i	0.996667	+	0.0815818i	$0.0259972\pi$
$998$	3.80385	−	14.1962i	0.120409	−	0.449371i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.p.d.407.1		4
5.2	odd	4		95.2.l.a.8.1	✓	4
5.3	odd	4	inner	475.2.p.d.293.1		4
5.4	even	2		95.2.l.a.27.1	yes	4
15.2	even	4		855.2.cj.d.388.1		4
15.14	odd	2		855.2.cj.d.217.1		4
19.12	odd	6	inner	475.2.p.d.107.1		4
95.12	even	12		95.2.l.a.88.1	yes	4
95.69	odd	6		95.2.l.a.12.1	yes	4
95.88	even	12	inner	475.2.p.d.468.1		4
285.107	odd	12		855.2.cj.d.658.1		4
285.164	even	6		855.2.cj.d.487.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.l.a.8.1	✓	4	5.2	odd	4
95.2.l.a.12.1	yes	4	95.69	odd	6
95.2.l.a.27.1	yes	4	5.4	even	2
95.2.l.a.88.1	yes	4	95.12	even	12
475.2.p.d.107.1		4	19.12	odd	6	inner
475.2.p.d.293.1		4	5.3	odd	4	inner
475.2.p.d.407.1		4	1.1	even	1	trivial
475.2.p.d.468.1		4	95.88	even	12	inner
855.2.cj.d.217.1		4	15.14	odd	2
855.2.cj.d.388.1		4	15.2	even	4
855.2.cj.d.487.1		4	285.164	even	6
855.2.cj.d.658.1		4	285.107	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.p (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.633975 + 2.36603i) q^{2} +(2.36603 - 0.633975i) q^{3} +(-3.46410 + 2.00000i) q^{4} +(3.00000 + 5.19615i) q^{6} +(2.00000 + 2.00000i) q^{7} +(-3.46410 - 3.46410i) q^{8} +(2.59808 - 1.50000i) q^{9} -5.00000 q^{11} +(-6.92820 + 6.92820i) q^{12} +(-3.46410 + 6.00000i) q^{14} +(2.00000 - 3.46410i) q^{16} +(2.73205 - 0.732051i) q^{17} +(5.19615 + 5.19615i) q^{18} +(4.33013 - 0.500000i) q^{19} +(6.00000 + 3.46410i) q^{21} +(-3.16987 - 11.8301i) q^{22} +(4.09808 + 1.09808i) q^{23} +(-10.3923 - 6.00000i) q^{24} +(-10.9282 - 2.92820i) q^{28} +(-0.866025 - 1.50000i) q^{29} -5.19615i q^{31} +(-11.8301 + 3.16987i) q^{33} +(3.46410 + 6.00000i) q^{34} +(-6.00000 + 10.3923i) q^{36} +(-1.73205 + 1.73205i) q^{37} +(3.92820 + 9.92820i) q^{38} +(-3.00000 - 1.73205i) q^{41} +(-4.39230 + 16.3923i) q^{42} +(-2.56218 - 9.56218i) q^{43} +(17.3205 - 10.0000i) q^{44} +10.3923i q^{46} +(2.19615 - 8.19615i) q^{47} +(2.53590 - 9.46410i) q^{48} +1.00000i q^{49} +(6.00000 - 3.46410i) q^{51} +(1.90192 - 7.09808i) q^{53} -13.8564i q^{56} +(9.92820 - 3.92820i) q^{57} +(3.00000 - 3.00000i) q^{58} +(-2.59808 + 4.50000i) q^{59} +(2.50000 + 4.33013i) q^{61} +(12.2942 - 3.29423i) q^{62} +(8.19615 + 2.19615i) q^{63} -8.00000i q^{64} +(-15.0000 - 25.9808i) q^{66} +(9.46410 + 2.53590i) q^{67} +(-8.00000 + 8.00000i) q^{68} +10.3923 q^{69} +(-4.50000 - 2.59808i) q^{71} +(-14.1962 - 3.80385i) q^{72} +(0.366025 + 1.36603i) q^{73} +(-5.19615 - 3.00000i) q^{74} +(-14.0000 + 10.3923i) q^{76} +(-10.0000 - 10.0000i) q^{77} +(-0.866025 + 1.50000i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(2.19615 - 8.19615i) q^{82} +(-5.00000 + 5.00000i) q^{83} -27.7128 q^{84} +(21.0000 - 12.1244i) q^{86} +(-3.00000 - 3.00000i) q^{87} +(17.3205 + 17.3205i) q^{88} +(-2.59808 - 4.50000i) q^{89} +(-16.3923 + 4.39230i) q^{92} +(-3.29423 - 12.2942i) q^{93} +20.7846 q^{94} +(1.90192 + 7.09808i) q^{97} +(-2.36603 + 0.633975i) q^{98} +(-12.9904 + 7.50000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{2} + 6 q^{3} + 12 q^{6} + 8 q^{7} - 20 q^{11} + 8 q^{16} + 4 q^{17} + 24 q^{21} - 30 q^{22} + 6 q^{23} - 16 q^{28} - 30 q^{33} - 24 q^{36} - 12 q^{38} - 12 q^{41} + 24 q^{42} + 14 q^{43} - 12 q^{47}+ \cdots - 6 q^{98}+O(q^{100}) \) 4 * q + 6 * q^2 + 6 * q^3 + 12 * q^6 + 8 * q^7 - 20 * q^11 + 8 * q^16 + 4 * q^17 + 24 * q^21 - 30 * q^22 + 6 * q^23 - 16 * q^28 - 30 * q^33 - 24 * q^36 - 12 * q^38 - 12 * q^41 + 24 * q^42 + 14 * q^43 - 12 * q^47 + 24 * q^48 + 24 * q^51 + 18 * q^53 + 12 * q^57 + 12 * q^58 + 10 * q^61 + 18 * q^62 + 12 * q^63 - 60 * q^66 + 24 * q^67 - 32 * q^68 - 18 * q^71 - 36 * q^72 - 2 * q^73 - 56 * q^76 - 40 * q^77 - 18 * q^81 - 12 * q^82 - 20 * q^83 + 84 * q^86 - 12 * q^87 - 24 * q^92 + 18 * q^93 + 18 * q^97 - 6 * q^98

Introduction

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