LMFDB - Embedded newform 475.2.p.d.293.1

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			293.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	475.293
Dual form			475.2.p.d.107.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.36603 - 0.633975i) q^{2} +(0.633975 + 2.36603i) q^{3} +(3.46410 - 2.00000i) q^{4} +(3.00000 + 5.19615i) q^{6} +(2.00000 - 2.00000i) q^{7} +(3.46410 - 3.46410i) q^{8} +(-2.59808 + 1.50000i) q^{9} -5.00000 q^{11} +(6.92820 + 6.92820i) q^{12} +(3.46410 - 6.00000i) q^{14} +(2.00000 - 3.46410i) q^{16} +(-0.732051 - 2.73205i) q^{17} +(-5.19615 + 5.19615i) q^{18} +(-4.33013 + 0.500000i) q^{19} +(6.00000 + 3.46410i) q^{21} +(-11.8301 + 3.16987i) q^{22} +(-1.09808 + 4.09808i) q^{23} +(10.3923 + 6.00000i) q^{24} +(2.92820 - 10.9282i) q^{28} +(0.866025 + 1.50000i) q^{29} -5.19615i q^{31} +(-3.16987 - 11.8301i) q^{33} +(-3.46410 - 6.00000i) q^{34} +(-6.00000 + 10.3923i) q^{36} +(1.73205 + 1.73205i) q^{37} +(-9.92820 + 3.92820i) q^{38} +(-3.00000 - 1.73205i) q^{41} +(16.3923 + 4.39230i) q^{42} +(9.56218 - 2.56218i) q^{43} +(-17.3205 + 10.0000i) q^{44} +10.3923i q^{46} +(-8.19615 - 2.19615i) q^{47} +(9.46410 + 2.53590i) q^{48} -1.00000i q^{49} +(6.00000 - 3.46410i) q^{51} +(7.09808 + 1.90192i) q^{53} -13.8564i q^{56} +(-3.92820 - 9.92820i) q^{57} +(3.00000 + 3.00000i) q^{58} +(2.59808 - 4.50000i) q^{59} +(2.50000 + 4.33013i) q^{61} +(-3.29423 - 12.2942i) q^{62} +(-2.19615 + 8.19615i) q^{63} +8.00000i q^{64} +(-15.0000 - 25.9808i) q^{66} +(2.53590 - 9.46410i) q^{67} +(-8.00000 - 8.00000i) q^{68} -10.3923 q^{69} +(-4.50000 - 2.59808i) q^{71} +(-3.80385 + 14.1962i) q^{72} +(-1.36603 + 0.366025i) q^{73} +(5.19615 + 3.00000i) q^{74} +(-14.0000 + 10.3923i) q^{76} +(-10.0000 + 10.0000i) q^{77} +(0.866025 - 1.50000i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-8.19615 - 2.19615i) q^{82} +(-5.00000 - 5.00000i) q^{83} +27.7128 q^{84} +(21.0000 - 12.1244i) q^{86} +(-3.00000 + 3.00000i) q^{87} +(-17.3205 + 17.3205i) q^{88} +(2.59808 + 4.50000i) q^{89} +(4.39230 + 16.3923i) q^{92} +(12.2942 - 3.29423i) q^{93} -20.7846 q^{94} +(7.09808 - 1.90192i) q^{97} +(-0.633975 - 2.36603i) q^{98} +(12.9904 - 7.50000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	2.36603	−	0.633975i	1.67303	−	0.448288i	0.707107	−	0.707107i	$-0.250000\pi$
$2$	2.36603	−	0.633975i	1.67303	−	0.448288i	0.965926	+	0.258819i	$0.0833333\pi$
$3$	0.633975	+	2.36603i	0.366025	+	1.36603i	0.866025	+	0.500000i	$0.166667\pi$
$3$	0.633975	+	2.36603i	0.366025	+	1.36603i	−0.500000	+	0.866025i	$0.666667\pi$
$4$	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	−0.219650	−	0.975579i	$-0.570491\pi$
$7$	2.00000	−	2.00000i	0.755929	−	0.755929i	0.975579	+	0.219650i	$0.0704915\pi$
$8$	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		0.258819	−	0.965926i	$-0.416667\pi$
$13$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$14$	3.46410	−	6.00000i	0.925820	−	1.60357i
$15$		0			0
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	−0.732051	−	2.73205i	−0.177548	−	0.662620i	−0.996104	−	0.0881917i	$-0.971891\pi$
$17$	−0.732051	−	2.73205i	−0.177548	−	0.662620i	0.818555	−	0.574428i	$-0.194775\pi$
$18$	−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
$22$	−11.8301	+	3.16987i	−2.52219	+	0.675819i
$23$	−1.09808	+	4.09808i	−0.228965	+	0.854508i	0.751812	+	0.659377i	$0.229180\pi$
$23$	−1.09808	+	4.09808i	−0.228965	+	0.854508i	−0.980777	+	0.195131i	$0.937487\pi$
$24$	10.3923	+	6.00000i	2.12132	+	1.22474i
$25$		0			0
$26$		0			0
$27$		0			0
$28$	2.92820	−	10.9282i	0.553378	−	2.06524i
$29$	0.866025	+	1.50000i	0.160817	+	0.278543i	0.935162	−	0.354221i	$-0.115254\pi$
$29$	0.866025	+	1.50000i	0.160817	+	0.278543i	−0.774345	+	0.632764i	$0.781920\pi$
$30$		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
$33$	−3.16987	−	11.8301i	−0.551804	−	2.05936i
$34$	−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	$-0.185468\pi$
$37$	1.73205	+	1.73205i	0.284747	+	0.284747i	−0.550252	+	0.834999i	$0.685468\pi$
$38$	−9.92820	+	3.92820i	−1.61057	+	0.637239i
$39$		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	$0.753856\pi$
$42$	16.3923	+	4.39230i	2.52939	+	0.677747i
$43$	9.56218	−	2.56218i	1.45822	−	0.390728i	0.559344	−	0.828935i	$-0.311053\pi$
$43$	9.56218	−	2.56218i	1.45822	−	0.390728i	0.898874	+	0.438207i	$0.144386\pi$
$44$	−17.3205	+	10.0000i	−2.61116	+	1.50756i
$45$		0			0
$46$			10.3923i			1.53226i
$47$	−8.19615	−	2.19615i	−1.19553	−	0.320342i	−0.394462	−	0.918912i	$-0.629069\pi$
$47$	−8.19615	−	2.19615i	−1.19553	−	0.320342i	−0.801070	+	0.598571i	$0.795736\pi$
$48$	9.46410	+	2.53590i	1.36603	+	0.366025i
$49$		−	1.00000i		−	0.142857i
$50$		0			0
$51$	6.00000	−	3.46410i	0.840168	−	0.485071i
$52$		0			0
$53$	7.09808	+	1.90192i	0.974996	+	0.261249i	0.710936	−	0.703257i	$-0.248272\pi$
$53$	7.09808	+	1.90192i	0.974996	+	0.261249i	0.264060	+	0.964506i	$0.414938\pi$
$54$		0			0
$55$		0			0
$56$		−	13.8564i		−	1.85164i
$57$	−3.92820	−	9.92820i	−0.520303	−	1.31502i
$58$	3.00000	+	3.00000i	0.393919	+	0.393919i
$59$	2.59808	−	4.50000i	0.338241	−	0.585850i	−0.645861	−	0.763455i	$-0.723502\pi$
$59$	2.59808	−	4.50000i	0.338241	−	0.585850i	0.984102	+	0.177605i	$0.0568349\pi$
$60$		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	$0.729619\pi$
$62$	−3.29423	−	12.2942i	−0.418367	−	1.56137i
$63$	−2.19615	+	8.19615i	−0.276689	+	1.03262i
$64$			8.00000i			1.00000i
$65$		0			0
$66$	−15.0000	−	25.9808i	−1.84637	−	3.19801i
$67$	2.53590	−	9.46410i	0.309809	−	1.15622i	−0.618917	−	0.785457i	$-0.712428\pi$
$67$	2.53590	−	9.46410i	0.309809	−	1.15622i	0.928726	−	0.370767i	$-0.120905\pi$
$68$	−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	$0.766438\pi$
$72$	−3.80385	+	14.1962i	−0.448288	+	1.67303i
$73$	−1.36603	+	0.366025i	−0.159881	+	0.0428400i	−0.337872	−	0.941192i	$-0.609707\pi$
$73$	−1.36603	+	0.366025i	−0.159881	+	0.0428400i	0.177991	+	0.984032i	$0.443040\pi$
$74$	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	−0.813187	−	0.582003i	$-0.802269\pi$
$79$	0.866025	−	1.50000i	0.0974355	−	0.168763i	0.910622	+	0.413239i	$0.135603\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	−8.19615	−	2.19615i	−0.905114	−	0.242524i
$83$	−5.00000	−	5.00000i	−0.548821	−	0.548821i	0.377279	−	0.926100i	$-0.376860\pi$
$83$	−5.00000	−	5.00000i	−0.548821	−	0.548821i	−0.926100	+	0.377279i	$0.876860\pi$
$84$	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	0.970235	−	0.242166i	$-0.0778579\pi$
$89$	2.59808	+	4.50000i	0.275396	+	0.476999i	−0.694839	+	0.719165i	$0.744525\pi$
$90$		0			0
$91$		0			0
$92$	4.39230	+	16.3923i	0.457929	+	1.70902i
$93$	12.2942	−	3.29423i	1.27485	−	0.341596i
$94$	−20.7846			−2.14377
$95$		0			0
$96$		0			0
$97$	7.09808	−	1.90192i	0.720700	−	0.193111i	0.120216	−	0.992748i	$-0.461641\pi$
$97$	7.09808	−	1.90192i	0.720700	−	0.193111i	0.600484	+	0.799637i	$0.294975\pi$
$98$	−0.633975	−	2.36603i	−0.0640411	−	0.239005i
$99$	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	$-0.910348\pi$
$103$	−6.92820	+	6.92820i	−0.682656	+	0.682656i	0.277942	+	0.960598i	$0.410348\pi$
$104$		0			0
$105$		0			0
$106$	18.0000			1.74831
$107$	1.73205	+	1.73205i	0.167444	+	0.167444i	0.785855	−	0.618411i	$-0.212223\pi$
$107$	1.73205	+	1.73205i	0.167444	+	0.167444i	−0.618411	+	0.785855i	$0.712223\pi$
$108$		0			0
$109$	0.866025	−	1.50000i	0.0829502	−	0.143674i	−0.821566	−	0.570114i	$-0.806899\pi$
$109$	0.866025	−	1.50000i	0.0829502	−	0.143674i	0.904516	+	0.426440i	$0.140232\pi$
$110$		0			0
$111$	−3.00000	+	5.19615i	−0.284747	+	0.493197i
$112$	−2.92820	−	10.9282i	−0.276689	−	1.03262i
$113$	1.73205	−	1.73205i	0.162938	−	0.162938i	−0.620929	−	0.783867i	$-0.713245\pi$
$113$	1.73205	−	1.73205i	0.162938	−	0.162938i	0.783867	+	0.620929i	$0.213245\pi$
$114$	−15.5885	−	21.0000i	−1.45999	−	1.96683i
$115$		0			0
$116$	6.00000	+	3.46410i	0.557086	+	0.321634i
$117$		0			0
$118$	3.29423	−	12.2942i	0.303258	−	1.13178i
$119$	−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
$123$	2.19615	−	8.19615i	0.198020	−	0.739022i
$124$	−10.3923	−	18.0000i	−0.933257	−	1.61645i
$125$		0			0
$126$			20.7846i			1.85164i
$127$	2.53590	−	9.46410i	0.225025	−	0.839803i	−0.757370	−	0.652986i	$-0.773516\pi$
$127$	2.53590	−	9.46410i	0.225025	−	0.839803i	0.982395	−	0.186817i	$-0.0598173\pi$
$128$	5.07180	+	18.9282i	0.448288	+	1.67303i
$129$	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
$133$	−7.66025	+	9.66025i	−0.664228	+	0.837650i
$134$		−	24.0000i		−	2.07328i
$135$		0			0
$136$	−12.0000	−	6.92820i	−1.02899	−	0.594089i
$137$	10.9282	+	2.92820i	0.933659	+	0.250173i	0.693414	−	0.720539i	$-0.256106\pi$
$137$	10.9282	+	2.92820i	0.933659	+	0.250173i	0.240245	+	0.970712i	$0.422772\pi$
$138$	−24.5885	+	6.58846i	−2.09311	+	0.560847i
$139$	15.5885	−	9.00000i	1.32220	−	0.763370i	0.338117	−	0.941104i	$-0.390210\pi$
$139$	15.5885	−	9.00000i	1.32220	−	0.763370i	0.984079	+	0.177734i	$0.0568767\pi$
$140$		0			0
$141$		−	20.7846i		−	1.75038i
$142$	−12.2942	−	3.29423i	−1.03171	−	0.276446i
$143$		0			0
$144$			12.0000i			1.00000i
$145$		0			0
$146$	−3.00000	+	1.73205i	−0.248282	+	0.143346i
$147$	2.36603	−	0.633975i	0.195146	−	0.0522893i
$148$	9.46410	+	2.53590i	0.777944	+	0.208450i
$149$	16.4545	+	9.50000i	1.34800	+	0.778270i	0.987967	−	0.154668i	$-0.0494307\pi$
$149$	16.4545	+	9.50000i	1.34800	+	0.778270i	0.360037	+	0.932938i	$0.382764\pi$
$150$		0			0
$151$			15.5885i			1.26857i	0.773099	+	0.634285i	$0.218706\pi$
$151$			15.5885i			1.26857i	−0.773099	+	0.634285i	$0.781294\pi$
$152$	−13.2679	+	16.7321i	−1.07617	+	1.35715i
$153$	6.00000	+	6.00000i	0.485071	+	0.485071i
$154$	−17.3205	+	30.0000i	−1.39573	+	2.41747i
$155$		0			0
$156$		0			0
$157$	2.56218	+	9.56218i	0.204484	+	0.763145i	0.989606	+	0.143804i	$0.0459335\pi$
$157$	2.56218	+	9.56218i	0.204484	+	0.763145i	−0.785122	+	0.619341i	$0.787400\pi$
$158$	1.09808	−	4.09808i	0.0873583	−	0.326025i
$159$			18.0000i			1.42749i
$160$		0			0
$161$	6.00000	+	10.3923i	0.472866	+	0.819028i
$162$	−5.70577	+	21.2942i	−0.448288	+	1.67303i
$163$	11.0000	+	11.0000i	0.861586	+	0.861586i	0.991522	−	0.129936i	$-0.0414772\pi$
$163$	11.0000	+	11.0000i	0.861586	+	0.861586i	−0.129936	+	0.991522i	$0.541477\pi$
$164$	−13.8564			−1.08200
$165$		0			0
$166$	−15.0000	−	8.66025i	−1.16423	−	0.672166i
$167$	−5.07180	+	18.9282i	−0.392467	+	1.46471i	0.433584	+	0.901113i	$0.357249\pi$
$167$	−5.07180	+	18.9282i	−0.392467	+	1.46471i	−0.826051	+	0.563595i	$0.809418\pi$
$168$	32.7846	−	8.78461i	2.52939	−	0.677747i
$169$	−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
$173$	−1.26795	−	4.73205i	−0.0964004	−	0.359771i	0.900828	−	0.434177i	$-0.142961\pi$
$173$	−1.26795	−	4.73205i	−0.0964004	−	0.359771i	−0.997228	+	0.0744057i	$0.976294\pi$
$174$	−5.19615	+	9.00000i	−0.393919	+	0.682288i
$175$		0			0
$176$	−10.0000	+	17.3205i	−0.753778	+	1.30558i
$177$	12.2942	+	3.29423i	0.924091	+	0.247609i
$178$	9.00000	+	9.00000i	0.674579	+	0.674579i
$179$	−19.0526			−1.42406			−0.712028	−	0.702152i	$-0.752223\pi$
$179$	−19.0526			−1.42406			−0.712028	+	0.702152i	$0.752223\pi$
$180$		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
$187$	3.66025	+	13.6603i	0.267664	+	0.998937i
$188$	−32.7846	+	8.78461i	−2.39106	+	0.640684i
$189$		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	$0.581500\pi$
$192$	−18.9282	+	5.07180i	−1.36603	+	0.366025i
$193$	2.53590	+	9.46410i	0.182538	+	0.681241i	0.995144	+	0.0984278i	$0.0313814\pi$
$193$	2.53590	+	9.46410i	0.182538	+	0.681241i	−0.812606	+	0.582813i	$0.801952\pi$
$194$	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	−0.460288	−	0.887770i	$-0.652254\pi$
$197$	6.00000	−	6.00000i	0.427482	−	0.427482i	0.887770	+	0.460288i	$0.152254\pi$
$198$	25.9808	−	25.9808i	1.84637	−	1.84637i
$199$	−12.9904	+	7.50000i	−0.920864	+	0.531661i	−0.883911	−	0.467656i	$-0.845099\pi$
$199$	−12.9904	+	7.50000i	−0.920864	+	0.531661i	−0.0369532	+	0.999317i	$0.511765\pi$
$200$		0			0
$201$	24.0000			1.69283
$202$	−8.66025	−	8.66025i	−0.609333	−	0.609333i
$203$	4.73205	+	1.26795i	0.332125	+	0.0889926i
$204$	13.8564	−	24.0000i	0.970143	−	1.68034i
$205$		0			0
$206$	−12.0000	+	20.7846i	−0.836080	+	1.44813i
$207$	−3.29423	−	12.2942i	−0.228965	−	0.854508i
$208$		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	$-0.685655\pi$
$212$	28.3923	−	7.60770i	1.94999	−	0.522499i
$213$	3.29423	−	12.2942i	0.225717	−	0.842387i
$214$	5.19615	+	3.00000i	0.355202	+	0.205076i
$215$		0			0
$216$		0			0
$217$	−10.3923	−	10.3923i	−0.705476	−	0.705476i
$218$	1.09808	−	4.09808i	0.0743711	−	0.277557i
$219$	−1.73205	−	3.00000i	−0.117041	−	0.202721i
$220$		0			0
$221$		0			0
$222$	−3.80385	+	14.1962i	−0.255298	+	0.952783i
$223$	−6.97372	−	26.0263i	−0.466995	−	1.74285i	−0.650190	−	0.759772i	$-0.725311\pi$
$223$	−6.97372	−	26.0263i	−0.466995	−	1.74285i	0.183195	−	0.983077i	$-0.441356\pi$
$224$		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	$-0.116768\pi$
$227$	8.66025	+	8.66025i	0.574801	+	0.574801i	−0.358665	+	0.933466i	$0.616768\pi$
$228$	−33.4641	−	26.5359i	−2.21621	−	1.75738i
$229$		−	9.00000i		−	0.594737i	−0.954763	−	0.297368i	$-0.903891\pi$
$229$		−	9.00000i		−	0.594737i	0.954763	−	0.297368i	$-0.0961089\pi$
$230$		0			0
$231$	−30.0000	−	17.3205i	−1.97386	−	1.13961i
$232$	8.19615	+	2.19615i	0.538104	+	0.144184i
$233$	−12.2942	+	3.29423i	−0.805422	+	0.215812i	−0.637963	−	0.770067i	$-0.720223\pi$
$233$	−12.2942	+	3.29423i	−0.805422	+	0.215812i	−0.167459	+	0.985879i	$0.553556\pi$
$234$		0			0
$235$		0			0
$236$		−	20.7846i		−	1.35296i
$237$	4.09808	+	1.09808i	0.266199	+	0.0713277i
$238$	−18.9282	−	5.07180i	−1.22693	−	0.328756i
$239$			11.0000i			0.711531i	0.934575	+	0.355765i	$0.115780\pi$
$239$			11.0000i			0.711531i	−0.934575	+	0.355765i	$0.884220\pi$
$240$		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	$0.461031\pi$
$242$	33.1244	−	8.87564i	2.12931	−	0.570548i
$243$	−21.2942	−	5.70577i	−1.36603	−	0.366025i
$244$	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	$0.782894\pi$
$252$	8.78461	+	32.7846i	0.553378	+	2.06524i
$253$	5.49038	−	20.4904i	0.345177	−	1.28822i
$254$		−	24.0000i		−	1.50589i
$255$		0			0
$256$	16.0000	+	27.7128i	1.00000	+	1.73205i
$257$	6.33975	−	23.6603i	0.395462	−	1.47589i	−0.425529	−	0.904945i	$-0.639912\pi$
$257$	6.33975	−	23.6603i	0.395462	−	1.47589i	0.820991	−	0.570941i	$-0.193422\pi$
$258$	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
$262$	−6.33975	+	23.6603i	−0.391671	+	1.46174i
$263$	17.7583	−	4.75833i	1.09503	−	0.293411i	0.334288	−	0.942471i	$-0.391504\pi$
$263$	17.7583	−	4.75833i	1.09503	−	0.293411i	0.760737	+	0.649060i	$0.224837\pi$
$264$	−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
$268$	−10.1436	−	37.8564i	−0.619619	−	2.31245i
$269$	0.866025	−	1.50000i	0.0528025	−	0.0914566i	−0.838416	−	0.545031i	$-0.816518\pi$
$269$	0.866025	−	1.50000i	0.0528025	−	0.0914566i	0.891219	+	0.453574i	$0.149851\pi$
$270$		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	$0.0160941\pi$
$272$	−10.9282	−	2.92820i	−0.662620	−	0.177548i
$273$		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	−0.816989	−	0.576653i	$-0.804359\pi$
$277$	−4.00000	+	4.00000i	−0.240337	+	0.240337i	0.576653	+	0.816989i	$0.304359\pi$
$278$	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	$0.366282\pi$
$282$	−13.1769	−	49.1769i	−0.784674	−	2.92844i
$283$	5.46410	−	1.46410i	0.324807	−	0.0870318i	−0.0927310	−	0.995691i	$-0.529560\pi$
$283$	5.46410	−	1.46410i	0.324807	−	0.0870318i	0.417538	+	0.908659i	$0.362893\pi$
$284$	−20.7846			−1.23334
$285$		0			0
$286$		0			0
$287$	−9.46410	+	2.53590i	−0.558648	+	0.149689i
$288$		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	$-0.657607\pi$
$293$	6.92820	−	6.92820i	0.404750	−	0.404750i	0.879903	+	0.475153i	$0.157607\pi$
$294$	5.19615	−	3.00000i	0.303046	−	0.174964i
$295$		0			0
$296$	12.0000			0.697486
$297$		0			0
$298$	44.9545	+	12.0455i	2.60414	+	0.697778i
$299$		0			0
$300$		0			0
$301$	14.0000	−	24.2487i	0.806947	−	1.39767i
$302$	9.88269	+	36.8827i	0.568685	+	2.12236i
$303$	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
$307$	−11.8301	+	3.16987i	−0.675181	+	0.180914i	−0.580088	−	0.814554i	$-0.696982\pi$
$307$	−11.8301	+	3.16987i	−0.675181	+	0.180914i	−0.0950935	+	0.995468i	$0.530315\pi$
$308$	−14.6410	+	54.6410i	−0.834249	+	3.11346i
$309$	−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
$313$	−7.32051	+	27.3205i	−0.413780	+	1.54425i	0.373488	+	0.927635i	$0.378162\pi$
$313$	−7.32051	+	27.3205i	−0.413780	+	1.54425i	−0.787268	+	0.616611i	$0.788505\pi$
$314$	12.1244	+	21.0000i	0.684217	+	1.18510i
$315$		0			0
$316$		−	6.92820i		−	0.389742i
$317$	−5.70577	+	21.2942i	−0.320468	+	1.19600i	0.598322	+	0.801256i	$0.295834\pi$
$317$	−5.70577	+	21.2942i	−0.320468	+	1.19600i	−0.918790	+	0.394747i	$0.870832\pi$
$318$	11.4115	+	42.5885i	0.639928	+	2.38824i
$319$	−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
$323$	4.53590	+	11.4641i	0.252384	+	0.637880i
$324$			36.0000i			2.00000i
$325$		0			0
$326$	33.0000	+	19.0526i	1.82770	+	1.05522i
$327$	4.09808	+	1.09808i	0.226624	+	0.0607238i
$328$	−16.3923	+	4.39230i	−0.905114	+	0.242524i
$329$	−20.7846	+	12.0000i	−1.14589	+	0.661581i
$330$		0			0
$331$		0			0		1.00000			$0$
$331$		0			0		−1.00000			$\pi$
$332$	−27.3205	−	7.32051i	−1.49941	−	0.401765i
$333$	−7.09808	−	1.90192i	−0.388972	−	0.104225i
$334$			48.0000i			2.62644i
$335$		0			0
$336$	24.0000	−	13.8564i	1.30931	−	0.755929i
$337$	16.5622	−	4.43782i	0.902199	−	0.241744i	0.222239	−	0.974992i	$-0.428664\pi$
$337$	16.5622	−	4.43782i	0.902199	−	0.241744i	0.679961	+	0.733249i	$0.261997\pi$
$338$	−30.7583	−	8.24167i	−1.67303	−	0.448288i
$339$	5.19615	+	3.00000i	0.282216	+	0.162938i
$340$		0			0
$341$			25.9808i			1.40694i
$342$	19.9019	−	25.0981i	1.07617	−	1.35715i
$343$	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
$347$	−2.92820	−	10.9282i	−0.157194	−	0.586657i	−0.998907	−	0.0467319i	$-0.985119\pi$
$347$	−2.92820	−	10.9282i	−0.157194	−	0.586657i	0.841713	−	0.539925i	$-0.181547\pi$
$348$	−4.39230	+	16.3923i	−0.235452	+	0.878720i
$349$		−	18.0000i		−	0.963518i	−0.876304	−	0.481759i	$-0.839998\pi$
$349$		−	18.0000i		−	0.963518i	0.876304	−	0.481759i	$-0.160002\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−6.00000	−	6.00000i	−0.319348	−	0.319348i	0.529169	−	0.848517i	$-0.322504\pi$
$353$	−6.00000	−	6.00000i	−0.319348	−	0.319348i	−0.848517	+	0.529169i	$0.822504\pi$
$354$	31.1769			1.65703
$355$		0			0
$356$	18.0000	+	10.3923i	0.953998	+	0.550791i
$357$	5.07180	−	18.9282i	0.268428	−	1.00179i
$358$	−45.0788	+	12.0788i	−2.38249	+	0.638386i
$359$	−29.4449	−	17.0000i	−1.55404	−	0.897226i	−0.997806	−	0.0662000i	$-0.978912\pi$
$359$	−29.4449	−	17.0000i	−1.55404	−	0.897226i	−0.556234	−	0.831026i	$-0.687754\pi$
$360$		0			0
$361$	18.5000	−	4.33013i	0.973684	−	0.227901i
$362$	12.0000	−	12.0000i	0.630706	−	0.630706i
$363$	8.87564	+	33.1244i	0.465851	+	1.73858i
$364$		0			0
$365$		0			0
$366$	−15.0000	+	25.9808i	−0.784063	+	1.35804i
$367$	−30.0526	−	8.05256i	−1.56873	−	0.420340i	−0.633316	−	0.773893i	$-0.718307\pi$
$367$	−30.0526	−	8.05256i	−1.56873	−	0.420340i	−0.935415	+	0.353553i	$0.884973\pi$
$368$	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	$-0.831634\pi$
$373$	−6.92820	+	6.92820i	−0.358729	+	0.358729i	0.504615	+	0.863344i	$0.331634\pi$
$374$	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	$-0.179475\pi$
$379$	32.9090			1.69042			0.845210	+	0.534434i	$0.179475\pi$
$380$		0			0
$381$	24.0000			1.22956
$382$	−16.5622	+	4.43782i	−0.847395	+	0.227059i
$383$	−7.60770	−	28.3923i	−0.388735	−	1.45078i	−0.832194	−	0.554484i	$-0.812916\pi$
$383$	−7.60770	−	28.3923i	−0.388735	−	1.45078i	0.443459	−	0.896295i	$-0.353751\pi$
$384$	−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	0.0987463	−	0.995113i	$-0.468517\pi$
$389$	19.9186	−	11.5000i	1.00991	−	0.583073i	0.911166	+	0.412039i	$0.135183\pi$
$390$		0			0
$391$	12.0000			0.606866
$392$	−3.46410	−	3.46410i	−0.174964	−	0.174964i
$393$	−23.6603	−	6.33975i	−1.19350	−	0.319798i
$394$	10.3923	−	18.0000i	0.523557	−	0.906827i
$395$		0			0
$396$	30.0000	−	51.9615i	1.50756	−	2.61116i
$397$	−1.46410	−	5.46410i	−0.0734812	−	0.274235i	0.919403	−	0.393316i	$-0.128672\pi$
$397$	−1.46410	−	5.46410i	−0.0734812	−	0.274235i	−0.992885	+	0.119080i	$0.962005\pi$
$398$	−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	$-0.695871\pi$
$402$	56.7846	−	15.2154i	2.83216	−	0.758875i
$403$		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
$408$	8.78461	−	32.7846i	0.434903	−	1.62308i
$409$	−16.4545	−	28.5000i	−0.813622	−	1.40923i	−0.910313	−	0.413920i	$-0.864159\pi$
$409$	−16.4545	−	28.5000i	−0.813622	−	1.40923i	0.0966915	−	0.995314i	$-0.469174\pi$
$410$		0			0
$411$			27.7128i			1.36697i
$412$	−10.1436	+	37.8564i	−0.499739	+	1.86505i
$413$	−3.80385	−	14.1962i	−0.187175	−	0.698547i
$414$	−15.5885	−	27.0000i	−0.766131	−	1.32698i
$415$		0			0
$416$		0			0
$417$	31.1769	+	31.1769i	1.52674	+	1.52674i
$418$	49.6410	−	19.6410i	2.42802	−	0.960674i
$419$			31.0000i			1.51445i	0.653155	+	0.757225i	$0.273445\pi$
$419$			31.0000i			1.51445i	−0.653155	+	0.757225i	$0.726555\pi$
$420$		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	$0.762137\pi$
$422$	−61.4711	−	16.4711i	−2.99237	−	0.801803i
$423$	24.5885	−	6.58846i	1.19553	−	0.320342i
$424$	31.1769	−	18.0000i	1.51408	−	0.874157i
$425$		0			0
$426$		−	31.1769i		−	1.51053i
$427$	13.6603	+	3.66025i	0.661066	+	0.177132i
$428$	9.46410	+	2.53590i	0.457465	+	0.122577i
$429$		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
$433$	9.46410	+	2.53590i	0.454816	+	0.121867i	0.478952	−	0.877841i	$-0.341017\pi$
$433$	9.46410	+	2.53590i	0.454816	+	0.121867i	−0.0241361	+	0.999709i	$0.507684\pi$
$434$	−31.1769	−	18.0000i	−1.49654	−	0.864028i
$435$		0			0
$436$		−	6.92820i		−	0.331801i
$437$	2.70577	−	18.2942i	0.129435	−	0.875132i
$438$	−6.00000	−	6.00000i	−0.286691	−	0.286691i
$439$	−14.7224	+	25.5000i	−0.702663	+	1.21705i	0.264865	+	0.964286i	$0.414673\pi$
$439$	−14.7224	+	25.5000i	−0.702663	+	1.21705i	−0.967528	+	0.252763i	$0.918661\pi$
$440$		0			0
$441$	1.50000	+	2.59808i	0.0714286	+	0.123718i
$442$		0			0
$443$	−2.19615	+	8.19615i	−0.104342	+	0.389411i	−0.998270	−	0.0588009i	$-0.981272\pi$
$443$	−2.19615	+	8.19615i	−0.104342	+	0.389411i	0.893927	+	0.448212i	$0.147939\pi$
$444$			24.0000i			1.13899i
$445$		0			0
$446$	−33.0000	−	57.1577i	−1.56260	−	2.70649i
$447$	−12.0455	+	44.9545i	−0.569733	+	2.12627i
$448$	16.0000	+	16.0000i	0.755929	+	0.755929i
$449$	−15.5885			−0.735665			−0.367832	−	0.929892i	$-0.619900\pi$
$449$	−15.5885			−0.735665			−0.367832	+	0.929892i	$0.619900\pi$
$450$		0			0
$451$	15.0000	+	8.66025i	0.706322	+	0.407795i
$452$	2.53590	−	9.46410i	0.119279	−	0.445154i
$453$	−36.8827	+	9.88269i	−1.73290	+	0.464329i
$454$	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	−0.433414	−	0.901195i	$-0.642691\pi$
$457$	10.0000	−	10.0000i	0.467780	−	0.467780i	0.901195	+	0.433414i	$0.142691\pi$
$458$	−5.70577	−	21.2942i	−0.266613	−	0.995014i
$459$		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	$0.129519\pi$
$462$	−81.9615	−	21.9615i	−3.81320	−	1.02174i
$463$	−8.00000	−	8.00000i	−0.371792	−	0.371792i	0.496338	−	0.868129i	$-0.334678\pi$
$463$	−8.00000	−	8.00000i	−0.371792	−	0.371792i	−0.868129	+	0.496338i	$0.834678\pi$
$464$	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	−0.883985	−	0.467515i	$-0.845149\pi$
$467$	−9.00000	+	9.00000i	−0.416470	+	0.416470i	0.467515	+	0.883985i	$0.345149\pi$
$468$		0			0
$469$	−13.8564	−	24.0000i	−0.639829	−	1.10822i
$470$		0			0
$471$	−21.0000	+	12.1244i	−0.967629	+	0.558661i
$472$	−6.58846	−	24.5885i	−0.303258	−	1.13178i
$473$	−47.8109	+	12.8109i	−2.19835	+	0.589045i
$474$	10.3923			0.477334
$475$		0			0
$476$	−32.0000			−1.46672
$477$	−21.2942	+	5.70577i	−0.974996	+	0.261249i
$478$	6.97372	+	26.0263i	0.318971	+	1.19041i
$479$	−11.2583	+	6.50000i	−0.514406	+	0.296993i	−0.734643	−	0.678454i	$-0.762650\pi$
$479$	−11.2583	+	6.50000i	−0.514406	+	0.296993i	0.220237	+	0.975446i	$0.429317\pi$
$480$		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	$-0.178743\pi$
$487$	6.92820	+	6.92820i	0.313947	+	0.313947i	−0.532490	+	0.846437i	$0.678743\pi$
$488$	23.6603	+	6.33975i	1.07105	+	0.286987i
$489$	−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	$0.852196\pi$
$492$	−8.78461	−	32.7846i	−0.396041	−	1.47804i
$493$	3.46410	−	3.46410i	0.156015	−	0.156015i
$494$		0			0
$495$		0			0
$496$	−18.0000	−	10.3923i	−0.808224	−	0.466628i
$497$	−14.1962	+	3.80385i	−0.636784	+	0.170626i
$498$	10.9808	−	40.9808i	0.492060	−	1.83639i
$499$	5.19615	+	3.00000i	0.232612	+	0.134298i	0.611776	−	0.791031i	$-0.290455\pi$
$499$	5.19615	+	3.00000i	0.232612	+	0.134298i	−0.379165	+	0.925329i	$0.623789\pi$
$500$		0			0
$501$	−48.0000			−2.14448
$502$	8.66025	+	8.66025i	0.386526	+	0.386526i
$503$	3.66025	−	13.6603i	0.163203	−	0.609081i	−0.835060	−	0.550159i	$-0.814567\pi$
$503$	3.66025	−	13.6603i	0.163203	−	0.609081i	0.998263	−	0.0589217i	$-0.0187662\pi$
$504$	20.7846	+	36.0000i	0.925820	+	1.60357i
$505$		0			0
$506$		−	51.9615i		−	2.30997i
$507$	8.24167	−	30.7583i	0.366025	−	1.36603i
$508$	−10.1436	−	37.8564i	−0.450049	−	1.67961i
$509$	−15.5885	−	27.0000i	−0.690946	−	1.19675i	−0.971528	−	0.236924i	$-0.923861\pi$
$509$	−15.5885	−	27.0000i	−0.690946	−	1.19675i	0.280582	−	0.959830i	$-0.409473\pi$
$510$		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
$517$	40.9808	+	10.9808i	1.80233	+	0.482933i
$518$	16.3923	−	4.39230i	0.720237	−	0.192987i
$519$	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	$0.987920\pi$
$522$	−12.2942	−	3.29423i	−0.538104	−	0.144184i
$523$	11.8301	+	3.16987i	0.517295	+	0.138609i	0.508015	−	0.861348i	$-0.330379\pi$
$523$	11.8301	+	3.16987i	0.517295	+	0.138609i	0.00928008	+	0.999957i	$0.497046\pi$
$524$			40.0000i			1.74741i
$525$		0			0
$526$	39.0000	−	22.5167i	1.70048	−	0.981773i
$527$	−14.1962	+	3.80385i	−0.618394	+	0.165698i
$528$	−47.3205	−	12.6795i	−2.05936	−	0.551804i
$529$	4.33013	+	2.50000i	0.188266	+	0.108696i
$530$		0			0
$531$			15.5885i			0.676481i
$532$	−7.21539	+	48.7846i	−0.312827	+	2.11508i
$533$		0			0
$534$	−15.5885	+	27.0000i	−0.674579	+	1.16840i
$535$		0			0
$536$	−24.0000	−	41.5692i	−1.03664	−	1.79552i
$537$	−12.0788	−	45.0788i	−0.521240	−	1.94530i
$538$	1.09808	−	4.09808i	0.0473414	−	0.176681i
$539$			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	$0.582304\pi$
$542$	9.50962	−	35.4904i	0.408473	−	1.52444i
$543$	12.0000	+	12.0000i	0.514969	+	0.514969i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	9.50962	−	35.4904i	0.406602	−	1.51746i	−0.394480	−	0.918905i	$-0.629075\pi$
$547$	9.50962	−	35.4904i	0.406602	−	1.51746i	0.801082	−	0.598555i	$-0.204258\pi$
$548$	43.7128	−	11.7128i	1.86732	−	0.500347i
$549$	−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
$553$	−1.26795	−	4.73205i	−0.0539187	−	0.201227i
$554$	−6.92820	+	12.0000i	−0.294351	+	0.509831i
$555$		0			0
$556$	36.0000	−	62.3538i	1.52674	−	2.64439i
$557$	45.0788	+	12.0788i	1.91005	+	0.511797i	0.993798	+	0.111198i	$0.0354686\pi$
$557$	45.0788	+	12.0788i	1.91005	+	0.511797i	0.916253	+	0.400599i	$0.131198\pi$
$558$	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	$-0.942200\pi$
$563$	−19.0526	+	19.0526i	−0.802970	+	0.802970i	0.180589	+	0.983559i	$0.442200\pi$
$564$	−41.5692	−	72.0000i	−1.75038	−	3.03175i
$565$		0			0
$566$	12.0000	−	6.92820i	0.504398	−	0.291214i
$567$	6.58846	+	24.5885i	0.276689	+	1.03262i
$568$	−24.5885	+	6.58846i	−1.03171	+	0.276446i
$569$	−1.73205			−0.0726113			−0.0363057	−	0.999341i	$-0.511559\pi$
$569$	−1.73205			−0.0726113			−0.0363057	+	0.999341i	$0.511559\pi$
$570$		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
$573$	−4.43782	−	16.5622i	−0.185393	−	0.691895i
$574$	−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	−0.546225	−	0.837639i	$-0.683936\pi$
$577$	7.00000	−	7.00000i	0.291414	−	0.291414i	0.837639	+	0.546225i	$0.183936\pi$
$578$	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
$583$	−35.4904	−	9.50962i	−1.46986	−	0.393848i
$584$	−3.46410	+	6.00000i	−0.143346	+	0.248282i
$585$		0			0
$586$	12.0000	−	20.7846i	0.495715	−	0.858604i
$587$	−6.58846	−	24.5885i	−0.271935	−	1.01487i	−0.957868	−	0.287210i	$-0.907272\pi$
$587$	−6.58846	−	24.5885i	−0.271935	−	1.01487i	0.685933	−	0.727665i	$-0.259394\pi$
$588$	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
$592$	9.46410	−	2.53590i	0.388972	−	0.104225i
$593$	−10.2487	+	38.2487i	−0.420864	+	1.57069i	0.351928	+	0.936027i	$0.385526\pi$
$593$	−10.2487	+	38.2487i	−0.420864	+	1.57069i	−0.772792	+	0.634659i	$0.781140\pi$
$594$		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	$0.0249039\pi$
$599$	13.8564	+	24.0000i	0.566157	+	0.980613i	−0.430784	+	0.902455i	$0.641763\pi$
$600$		0			0
$601$			22.5167i			0.918474i	0.888314	+	0.459237i	$0.151877\pi$
$601$			22.5167i			0.918474i	−0.888314	+	0.459237i	$0.848123\pi$
$602$	17.7513	−	66.2487i	0.723489	−	2.70010i
$603$	7.60770	+	28.3923i	0.309809	+	1.15622i
$604$	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	$-0.281699\pi$
$607$	−3.46410	−	3.46410i	−0.140604	−	0.140604i	−0.773905	+	0.633302i	$0.781699\pi$
$608$		0			0
$609$			12.0000i			0.486265i
$610$		0			0
$611$		0			0
$612$	32.7846	+	8.78461i	1.32524	+	0.355097i
$613$	15.0263	−	4.02628i	0.606906	−	0.162620i	0.0577376	−	0.998332i	$-0.481611\pi$
$613$	15.0263	−	4.02628i	0.606906	−	0.162620i	0.549168	+	0.835712i	$0.314945\pi$
$614$	−25.9808	+	15.0000i	−1.04850	+	0.605351i
$615$		0			0
$616$			69.2820i			2.79145i
$617$	−6.83013	−	1.83013i	−0.274971	−	0.0736781i	0.118699	−	0.992930i	$-0.462128\pi$
$617$	−6.83013	−	1.83013i	−0.274971	−	0.0736781i	−0.393669	+	0.919252i	$0.628794\pi$
$618$	−56.7846	−	15.2154i	−2.28421	−	0.612053i
$619$		−	30.0000i		−	1.20580i	−0.797816	−	0.602901i	$-0.794011\pi$
$619$		−	30.0000i		−	1.20580i	0.797816	−	0.602901i	$-0.205989\pi$
$620$		0			0
$621$		0			0
$622$	−47.3205	+	12.6795i	−1.89738	+	0.508401i
$623$	14.1962	+	3.80385i	0.568757	+	0.152398i
$624$		0			0
$625$		0			0
$626$			69.2820i			2.76907i
$627$	19.6410	+	49.6410i	0.784387	+	1.98247i
$628$	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	$-0.470531\pi$
$632$	−2.19615	−	8.19615i	−0.0873583	−	0.326025i
$633$	16.4711	−	61.4711i	0.654669	−	2.44326i
$634$			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	$0.721376\pi$
$642$	−3.80385	+	14.1962i	−0.150126	+	0.560277i
$643$	27.3205	−	7.32051i	1.07742	−	0.288693i	0.323879	−	0.946099i	$-0.395013\pi$
$643$	27.3205	−	7.32051i	1.07742	−	0.288693i	0.753537	+	0.657406i	$0.228346\pi$
$644$	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	−0.875805	−	0.482665i	$-0.839669\pi$
$647$	−10.0000	+	10.0000i	−0.393141	+	0.393141i	0.482665	+	0.875805i	$0.339669\pi$
$648$	11.4115	+	42.5885i	0.448288	+	1.67303i
$649$	−12.9904	+	22.5000i	−0.509917	+	0.883202i
$650$		0			0
$651$	18.0000	−	31.1769i	0.705476	−	1.22192i
$652$	60.1051	+	16.1051i	2.35390	+	0.630725i
$653$	23.0000	+	23.0000i	0.900060	+	0.900060i	0.995441	−	0.0953813i	$-0.0304070\pi$
$653$	23.0000	+	23.0000i	0.900060	+	0.900060i	−0.0953813	+	0.995441i	$0.530407\pi$
$654$	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	0.897787	−	0.440429i	$-0.145174\pi$
$659$	1.73205	+	3.00000i	0.0674711	+	0.116863i	−0.830316	+	0.557292i	$0.811840\pi$
$660$		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
$667$	−7.09808	+	1.90192i	−0.274839	+	0.0736428i
$668$	20.2872	+	75.7128i	0.784935	+	2.92942i
$669$	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	$-0.626721\pi$
$673$	13.8564	−	13.8564i	0.534125	−	0.534125i	0.921797	+	0.387672i	$0.126721\pi$
$674$	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	−0.974697	−	0.223529i	$-0.928242\pi$
$677$	−31.1769	−	31.1769i	−1.19823	−	1.19823i	−0.223529	−	0.974697i	$-0.571758\pi$
$678$	14.1962	+	3.80385i	0.545200	+	0.146086i
$679$	10.3923	−	18.0000i	0.398820	−	0.690777i
$680$		0			0
$681$	−15.0000	+	25.9808i	−0.574801	+	0.995585i
$682$	16.4711	+	61.4711i	0.630713	+	2.35385i
$683$	−27.7128	+	27.7128i	−1.06040	+	1.06040i	−0.0623468	+	0.998055i	$0.519858\pi$
$683$	−27.7128	+	27.7128i	−1.06040	+	1.06040i	−0.998055	+	0.0623468i	$0.980142\pi$
$684$	20.7846	−	48.0000i	0.794719	−	1.83533i
$685$		0			0
$686$	36.0000	+	20.7846i	1.37449	+	0.793560i
$687$	21.2942	−	5.70577i	0.812425	−	0.217689i
$688$	10.2487	−	38.2487i	0.390728	−	1.45822i
$689$		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
$693$	10.9808	−	40.9808i	0.417125	−	1.55673i
$694$	−13.8564	−	24.0000i	−0.525982	−	0.911028i
$695$		0			0
$696$			20.7846i			0.787839i
$697$	−2.53590	+	9.46410i	−0.0960540	+	0.358478i
$698$	−11.4115	−	42.5885i	−0.431933	−	1.61200i
$699$	−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
$703$	−8.36603	−	6.63397i	−0.315531	−	0.250205i
$704$		−	40.0000i		−	1.50756i
$705$		0			0
$706$	−18.0000	−	10.3923i	−0.677439	−	0.391120i
$707$	−13.6603	−	3.66025i	−0.513747	−	0.137658i
$708$	49.1769	−	13.1769i	1.84818	−	0.495219i
$709$	−12.9904	+	7.50000i	−0.487864	+	0.281668i	−0.723688	−	0.690127i	$-0.757554\pi$
$709$	−12.9904	+	7.50000i	−0.487864	+	0.281668i	0.235824	+	0.971796i	$0.424221\pi$
$710$		0			0
$711$			5.19615i			0.194871i
$712$	24.5885	+	6.58846i	0.921491	+	0.246913i
$713$	21.2942	+	5.70577i	0.797475	+	0.213683i
$714$		−	48.0000i		−	1.79635i
$715$		0			0
$716$	−66.0000	+	38.1051i	−2.46654	+	1.42406i
$717$	−26.0263	+	6.97372i	−0.971969	+	0.260438i
$718$	−80.4449	−	21.5551i	−3.00218	−	0.804431i
$719$	6.06218	+	3.50000i	0.226081	+	0.130528i	0.608763	−	0.793352i	$-0.291666\pi$
$719$	6.06218	+	3.50000i	0.226081	+	0.130528i	−0.382682	+	0.923880i	$0.624999\pi$
$720$		0			0
$721$			27.7128i			1.03208i
$722$	41.0263	−	21.9737i	1.52684	−	0.817777i
$723$	−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
$727$	−6.95448	−	25.9545i	−0.257927	−	0.962598i	−0.966438	−	0.256899i	$-0.917299\pi$
$727$	−6.95448	−	25.9545i	−0.257927	−	0.962598i	0.708511	−	0.705700i	$-0.249367\pi$
$728$		0			0
$729$		−	27.0000i		−	1.00000i
$730$		0			0
$731$	−14.0000	−	24.2487i	−0.517809	−	0.896871i
$732$	−12.6795	+	47.3205i	−0.468648	+	1.74902i
$733$	−19.0000	−	19.0000i	−0.701781	−	0.701781i	0.263012	−	0.964793i	$-0.415284\pi$
$733$	−19.0000	−	19.0000i	−0.701781	−	0.701781i	−0.964793	+	0.263012i	$0.915284\pi$
$734$	−76.2102			−2.81297
$735$		0			0
$736$		0			0
$737$	−12.6795	+	47.3205i	−0.467055	+	1.74307i
$738$	24.5885	−	6.58846i	0.905114	−	0.242524i
$739$	16.4545	+	9.50000i	0.605288	+	0.349463i	0.771119	−	0.636691i	$-0.219697\pi$
$739$	16.4545	+	9.50000i	0.605288	+	0.349463i	−0.165831	+	0.986154i	$0.553031\pi$
$740$		0			0
$741$		0			0
$742$	36.0000	−	36.0000i	1.32160	−	1.32160i
$743$	5.70577	+	21.2942i	0.209324	+	0.781209i	0.988088	+	0.153892i	$0.0491807\pi$
$743$	5.70577	+	21.2942i	0.209324	+	0.781209i	−0.778763	+	0.627318i	$0.784153\pi$
$744$	31.1769	−	54.0000i	1.14300	−	1.97974i
$745$		0			0
$746$	−12.0000	+	20.7846i	−0.439351	+	0.760979i
$747$	20.4904	+	5.49038i	0.749704	+	0.200883i
$748$	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
$757$	−5.12436	−	19.1244i	−0.186248	−	0.695087i	−0.994360	−	0.106058i	$-0.966177\pi$
$757$	−5.12436	−	19.1244i	−0.186248	−	0.695087i	0.808112	−	0.589029i	$-0.200490\pi$
$758$	77.8634	−	20.8634i	2.82813	−	0.757795i
$759$	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	$0.288651\pi$
$762$	56.7846	−	15.2154i	2.05709	−	0.551195i
$763$	−1.26795	−	4.73205i	−0.0459028	−	0.171312i
$764$	−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	−0.790684	−	0.612225i	$-0.790275\pi$
$769$	−18.1865	+	10.5000i	−0.655823	+	0.378640i	0.134860	+	0.990865i	$0.456941\pi$
$770$		0			0
$771$	60.0000			2.16085
$772$	27.7128	+	27.7128i	0.997406	+	0.997406i
$773$	−9.46410	−	2.53590i	−0.340400	−	0.0912099i	0.0845694	−	0.996418i	$-0.473049\pi$
$773$	−9.46410	−	2.53590i	−0.340400	−	0.0912099i	−0.424970	+	0.905208i	$0.639715\pi$
$774$	−36.3731	+	63.0000i	−1.30740	+	2.26449i
$775$		0			0
$776$	18.0000	−	31.1769i	0.646162	−	1.11919i
$777$	4.39230	+	16.3923i	0.157573	+	0.588071i
$778$	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
$782$	28.3923	−	7.60770i	1.01531	−	0.272051i
$783$		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	$-0.0406854\pi$
$787$	24.2487	+	24.2487i	0.864373	+	0.864373i	−0.127469	+	0.991843i	$0.540685\pi$
$788$	8.78461	−	32.7846i	0.312939	−	1.16790i
$789$	22.5167	+	39.0000i	0.801614	+	1.38844i
$790$		0			0
$791$		−	6.92820i		−	0.246339i
$792$	19.0192	−	70.9808i	0.675819	−	2.52219i
$793$		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	$-0.263813\pi$
$797$	−1.73205	−	1.73205i	−0.0613524	−	0.0613524i	−0.737117	+	0.675765i	$0.763813\pi$
$798$	−73.1769	−	10.8231i	−2.59043	−	0.383133i
$799$			24.0000i			0.849059i
$800$		0			0
$801$	−13.5000	−	7.79423i	−0.476999	−	0.275396i
$802$	−86.0596	−	23.0596i	−3.03887	−	0.814263i
$803$	6.83013	−	1.83013i	0.241030	−	0.0645838i
$804$	83.1384	−	48.0000i	2.93207	−	1.69283i
$805$		0			0
$806$		0			0
$807$	4.09808	+	1.09808i	0.144259	+	0.0386541i
$808$	−23.6603	−	6.33975i	−0.832365	−	0.223031i
$809$		−	35.0000i		−	1.23053i	−0.788319	−	0.615267i	$-0.789048\pi$
$809$		−	35.0000i		−	1.23053i	0.788319	−	0.615267i	$-0.210952\pi$
$810$		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	$0.579899\pi$
$812$	18.9282	−	5.07180i	0.664250	−	0.177985i
$813$	35.4904	+	9.50962i	1.24470	+	0.333517i
$814$	−25.9808	−	15.0000i	−0.910625	−	0.525750i
$815$		0			0
$816$		−	27.7128i		−	0.970143i
$817$	−40.1244	+	15.8756i	−1.40377	+	0.555418i
$818$	−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	$0.664437\pi$
$822$	17.5692	+	65.5692i	0.612797	+	2.28699i
$823$	0.732051	−	2.73205i	0.0255177	−	0.0952333i	−0.951993	−	0.306121i	$-0.900969\pi$
$823$	0.732051	−	2.73205i	0.0255177	−	0.0952333i	0.977510	+	0.210888i	$0.0676354\pi$
$824$			48.0000i			1.67216i
$825$		0			0
$826$	−18.0000	−	31.1769i	−0.626300	−	1.08478i
$827$	−6.33975	+	23.6603i	−0.220455	+	0.822748i	0.763720	+	0.645547i	$0.223371\pi$
$827$	−6.33975	+	23.6603i	−0.220455	+	0.822748i	−0.984175	+	0.177200i	$0.943296\pi$
$828$	−36.0000	−	36.0000i	−1.25109	−	1.25109i
$829$	17.3205			0.601566			0.300783	−	0.953693i	$-0.402752\pi$
$829$	17.3205			0.601566			0.300783	+	0.953693i	$0.402752\pi$
$830$		0			0
$831$	−12.0000	−	6.92820i	−0.416275	−	0.240337i
$832$		0			0
$833$	−2.73205	+	0.732051i	−0.0946600	+	0.0253641i
$834$	93.5307	+	54.0000i	3.23870	+	1.86987i
$835$		0			0
$836$	70.0000	−	51.9615i	2.42100	−	1.79713i
$837$		0			0
$838$	19.6532	+	73.3468i	0.678909	+	2.53372i
$839$	13.8564	−	24.0000i	0.478376	−	0.828572i	−0.521316	−	0.853363i	$-0.674559\pi$
$839$	13.8564	−	24.0000i	0.478376	−	0.828572i	0.999693	+	0.0247915i	$0.00789218\pi$
$840$		0			0
$841$	13.0000	−	22.5167i	0.448276	−	0.776437i
$842$	−28.6865	−	7.68653i	−0.988603	−	0.264895i
$843$	−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
$852$	−13.1769	−	49.1769i	−0.451434	−	1.68477i
$853$	23.2224	−	6.22243i	0.795121	−	0.213052i	0.161680	−	0.986843i	$-0.448309\pi$
$853$	23.2224	−	6.22243i	0.795121	−	0.213052i	0.633441	+	0.773791i	$0.281642\pi$
$854$	34.6410			1.18539
$855$		0			0
$856$	12.0000			0.410152
$857$	54.4186	−	14.5814i	1.85890	−	0.498092i	0.859000	−	0.511976i	$-0.171086\pi$
$857$	54.4186	−	14.5814i	1.85890	−	0.498092i	0.999904	+	0.0138842i	$0.00441963\pi$
$858$		0			0
$859$	−45.8993	+	26.5000i	−1.56607	+	0.904168i	−0.569445	+	0.822030i	$0.692842\pi$
$859$	−45.8993	+	26.5000i	−1.56607	+	0.904168i	−0.996621	+	0.0821386i	$0.973825\pi$
$860$		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	$-0.567675\pi$
$863$	22.5167	−	22.5167i	0.766476	−	0.766476i	0.977484	+	0.211008i	$0.0676747\pi$
$864$		0			0
$865$		0			0
$866$	24.0000			0.815553
$867$	15.5885	+	15.5885i	0.529412	+	0.529412i
$868$	−56.7846	−	15.2154i	−1.92740	−	0.516444i
$869$	−4.33013	+	7.50000i	−0.146889	+	0.254420i
$870$		0			0
$871$		0			0
$872$	−2.19615	−	8.19615i	−0.0743711	−	0.277557i
$873$	−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
$877$	−7.09808	+	1.90192i	−0.239685	+	0.0642234i	−0.376662	−	0.926351i	$-0.622928\pi$
$877$	−7.09808	+	1.90192i	−0.239685	+	0.0642234i	0.136977	+	0.990574i	$0.456261\pi$
$878$	−18.6673	+	69.6673i	−0.629991	+	2.35116i
$879$	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
$883$	−5.12436	+	19.1244i	−0.172448	+	0.643586i	0.824524	+	0.565827i	$0.191443\pi$
$883$	−5.12436	+	19.1244i	−0.172448	+	0.643586i	−0.996972	+	0.0777587i	$0.975224\pi$
$884$		0			0
$885$		0			0
$886$			20.7846i			0.698273i
$887$	−11.4115	+	42.5885i	−0.383162	+	1.42998i	0.457882	+	0.889013i	$0.348608\pi$
$887$	−11.4115	+	42.5885i	−0.383162	+	1.42998i	−0.841044	+	0.540967i	$0.818058\pi$
$888$	7.60770	+	28.3923i	0.255298	+	0.952783i
$889$	−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
$893$	36.5885	+	5.41154i	1.22439	+	0.181090i
$894$			114.000i			3.81273i
$895$		0			0
$896$	48.0000	+	27.7128i	1.60357	+	0.925820i
$897$		0			0
$898$	−36.8827	+	9.88269i	−1.23079	+	0.329789i
$899$	7.79423	−	4.50000i	0.259952	−	0.150083i
$900$		0			0
$901$		−	20.7846i		−	0.692436i
$902$	40.9808	+	10.9808i	1.36451	+	0.365619i
$903$	66.2487	+	17.7513i	2.20462	+	0.590726i
$904$		−	12.0000i		−	0.399114i
$905$		0			0
$906$	−81.0000	+	46.7654i	−2.69104	+	1.55368i
$907$	4.73205	−	1.26795i	0.157125	−	0.0421016i	−0.179399	−	0.983776i	$-0.557415\pi$
$907$	4.73205	−	1.26795i	0.157125	−	0.0421016i	0.336524	+	0.941675i	$0.390749\pi$
$908$	47.3205	+	12.6795i	1.57039	+	0.420784i
$909$	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	$-0.162192\pi$
$912$	−42.2487	−	6.24871i	−1.39899	−	0.206916i
$913$	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
$917$	7.32051	+	27.3205i	0.241744	+	0.902203i
$918$		0			0
$919$			22.0000i			0.725713i	0.931845	+	0.362857i	$0.118198\pi$
$919$			22.0000i			0.725713i	−0.931845	+	0.362857i	$0.881802\pi$
$920$		0			0
$921$	−15.0000	−	25.9808i	−0.494267	−	0.856095i
$922$	3.16987	−	11.8301i	0.104394	−	0.389604i
$923$		0			0
$924$	−138.564			−4.55842
$925$		0			0
$926$	−24.0000	−	13.8564i	−0.788689	−	0.455350i
$927$	7.60770	−	28.3923i	0.249869	−	0.932526i
$928$		0			0
$929$	6.06218	+	3.50000i	0.198894	+	0.114831i	0.596139	−	0.802881i	$-0.296701\pi$
$929$	6.06218	+	3.50000i	0.198894	+	0.114831i	−0.397246	+	0.917712i	$0.630034\pi$
$930$		0			0
$931$	0.500000	+	4.33013i	0.0163868	+	0.141914i
$932$	−36.0000	+	36.0000i	−1.17922	+	1.17922i
$933$	−12.6795	−	47.3205i	−0.415108	−	1.54920i
$934$	−15.5885	+	27.0000i	−0.510070	+	0.883467i
$935$		0			0
$936$		0			0
$937$	23.2224	+	6.22243i	0.758644	+	0.203278i	0.617349	−	0.786690i	$-0.288207\pi$
$937$	23.2224	+	6.22243i	0.758644	+	0.203278i	0.141295	+	0.989968i	$0.454873\pi$
$938$	−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
$947$	1.46410	+	5.46410i	0.0475769	+	0.177559i	0.985626	−	0.168944i	$-0.0540356\pi$
$947$	1.46410	+	5.46410i	0.0475769	+	0.177559i	−0.938049	+	0.346503i	$0.887369\pi$
$948$	16.3923	−	4.39230i	0.532397	−	0.142655i
$949$		0			0
$950$		0			0
$951$	−54.0000			−1.75107
$952$	−37.8564	+	10.1436i	−1.22693	+	0.328756i
$953$	8.87564	+	33.1244i	0.287510	+	1.07300i	0.946985	+	0.321277i	$0.104112\pi$
$953$	8.87564	+	33.1244i	0.287510	+	1.07300i	−0.659475	+	0.751726i	$0.729221\pi$
$954$	−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
$963$	−7.09808	−	1.90192i	−0.228732	−	0.0612886i
$964$	−24.2487	+	42.0000i	−0.780998	+	1.35273i
$965$		0			0
$966$	−36.0000	+	62.3538i	−1.15828	+	2.00620i
$967$	−9.15064	−	34.1506i	−0.294265	−	1.09821i	−0.941800	−	0.336175i	$-0.890867\pi$
$967$	−9.15064	−	34.1506i	−0.294265	−	1.09821i	0.647535	−	0.762036i	$-0.275800\pi$
$968$	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	$0.980484\pi$
$972$	−85.1769	+	22.8231i	−2.73205	+	0.732051i
$973$	13.1769	−	49.1769i	0.422432	−	1.57654i
$974$	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	$-0.499185\pi$
$977$	−31.1769	−	31.1769i	−0.997438	−	0.997438i	−0.999997	+	0.00255886i	$0.999185\pi$
$978$	−24.1577	+	90.1577i	−0.772477	+	2.88292i
$979$	−12.9904	−	22.5000i	−0.415174	−	0.719103i
$980$		0			0
$981$			5.19615i			0.165900i
$982$	−23.4571	+	87.5429i	−0.748545	+	2.79361i
$983$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$983$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$984$	−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
$997$	−10.9282	−	2.92820i	−0.346100	−	0.0927371i	0.0815818	−	0.996667i	$-0.474003\pi$
$997$	−10.9282	−	2.92820i	−0.346100	−	0.0927371i	−0.427681	+	0.903930i	$0.640669\pi$
$998$	14.1962	+	3.80385i	0.449371	+	0.120409i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.l.a.8.1	✓	4	5.4	even	2
95.2.l.a.12.1	yes	4	95.88	even	12
95.2.l.a.27.1	yes	4	5.3	odd	4
95.2.l.a.88.1	yes	4	95.69	odd	6
475.2.p.d.107.1		4	95.12	even	12	inner
475.2.p.d.293.1		4	1.1	even	1	trivial
475.2.p.d.407.1		4	5.2	odd	4	inner
475.2.p.d.468.1		4	19.12	odd	6	inner
855.2.cj.d.217.1		4	15.8	even	4
855.2.cj.d.388.1		4	15.14	odd	2
855.2.cj.d.487.1		4	285.278	odd	12
855.2.cj.d.658.1		4	285.164	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 $\F_{q}$
Belyi maps

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

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