LMFDB - Embedded newform 405.3.s.a.118.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [405,3,Mod(37,405)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("405.37"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(405, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([28, 9])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	405.s (of order $36$, degree $12$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$11.0354507066$
Analytic rank:	$0$
Dimension:	$408$
Relative dimension:	$34$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			118.17
Character	$\chi$	$=$	405.118
Dual form			405.3.s.a.127.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.00242499 - 0.0277177i) q^{2} +(3.93847 + 0.694458i) q^{4} +(-2.37496 + 4.39995i) q^{5} +(-3.04016 - 2.12874i) q^{7} +(0.0576046 - 0.214983i) q^{8} +(0.116197 + 0.0764983i) q^{10} +(-3.20314 - 1.16585i) q^{11} +(1.03393 + 11.8179i) q^{13} +(-0.0663761 + 0.0791040i) q^{14} +(15.0264 + 5.46915i) q^{16} +(7.97341 + 29.7572i) q^{17} +(2.81936 - 1.62776i) q^{19} +(-12.4093 + 15.6798i) q^{20} +(-0.0400822 + 0.0859566i) q^{22} +(-13.0837 + 9.16134i) q^{23} +(-13.7191 - 20.8994i) q^{25} +0.330073 q^{26} +(-10.4952 - 10.4952i) q^{28} +(-27.8129 - 33.1461i) q^{29} +(-8.79682 + 49.8892i) q^{31} +(0.564275 - 1.21009i) q^{32} +(0.844136 - 0.148844i) q^{34} +(16.5866 - 8.32085i) q^{35} +(3.64899 + 13.6182i) q^{37} +(-0.0382809 - 0.0820936i) q^{38} +(0.809107 + 0.764035i) q^{40} +(-9.67690 - 8.11988i) q^{41} +(32.4393 + 69.5664i) q^{43} +(-11.8058 - 6.81610i) q^{44} +(0.222203 + 0.384868i) q^{46} +(38.7099 + 27.1050i) q^{47} +(-12.0480 - 33.1015i) q^{49} +(-0.612553 + 0.329582i) q^{50} +(-4.13494 + 47.2625i) q^{52} +(-15.4300 - 15.4300i) q^{53} +(12.7370 - 11.3248i) q^{55} +(-0.632771 + 0.530958i) q^{56} +(-0.986180 + 0.690531i) q^{58} +(9.94222 + 27.3160i) q^{59} +(-3.58125 - 20.3103i) q^{61} +(1.36148 + 0.364808i) q^{62} +(55.3613 + 31.9628i) q^{64} +(-54.4538 - 23.5179i) q^{65} +(7.35361 - 0.643358i) q^{67} +(10.7379 + 122.735i) q^{68} +(-0.190413 - 0.479921i) q^{70} +(44.8146 - 77.6212i) q^{71} +(3.90769 - 14.5837i) q^{73} +(0.386314 - 0.0681177i) q^{74} +(12.2344 - 4.45295i) q^{76} +(7.25626 + 10.3630i) q^{77} +(62.7357 + 74.7655i) q^{79} +(-59.7510 + 53.1262i) q^{80} +(-0.248531 + 0.248531i) q^{82} +(-67.6198 - 5.91597i) q^{83} +(-149.867 - 35.5895i) q^{85} +(2.00689 - 0.730447i) q^{86} +(-0.435154 + 0.621464i) q^{88} +(65.5625 - 37.8526i) q^{89} +(22.0140 - 38.1293i) q^{91} +(-57.8921 + 26.9955i) q^{92} +(0.845159 - 1.00722i) q^{94} +(0.466183 + 16.2709i) q^{95} +(78.7818 - 36.7366i) q^{97} +(-0.946715 + 0.253672i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 408 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 6 q^{8} - 6 q^{10} + 60 q^{11} - 12 q^{13} - 24 q^{16} + 6 q^{17} + 300 q^{20} - 12 q^{22} + 156 q^{23} + 6 q^{25} + 48 q^{26} - 24 q^{28} - 24 q^{31} - 72 q^{32}+ \cdots + 1032 q^{98}+O(q^{100}) $ 408 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 6 * q^8 - 6 * q^10 + 60 * q^11 - 12 * q^13 - 24 * q^16 + 6 * q^17 + 300 * q^20 - 12 * q^22 + 156 * q^23 + 6 * q^25 + 48 * q^26 - 24 * q^28 - 24 * q^31 - 72 * q^32 - 156 * q^35 - 6 * q^37 + 252 * q^38 - 108 * q^40 + 384 * q^41 - 12 * q^43 - 12 * q^46 + 210 * q^47 - 276 * q^50 - 60 * q^52 - 516 * q^53 - 24 * q^55 - 912 * q^56 - 12 * q^58 - 312 * q^61 + 6 * q^62 - 420 * q^65 - 480 * q^67 + 540 * q^68 - 12 * q^70 + 12 * q^71 - 6 * q^73 - 216 * q^76 + 876 * q^77 + 1644 * q^80 - 24 * q^82 + 372 * q^83 - 12 * q^85 - 516 * q^86 + 348 * q^88 - 12 * q^91 - 2082 * q^92 - 198 * q^95 + 600 * q^97 + 1032 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{7}{9}\right)$

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 $

$2$	0.00242499	−	0.0277177i	0.00121249	−	0.0138589i	−0.995564	−	0.0940831i	$-0.970008\pi$
$2$	0.00242499	−	0.0277177i	0.00121249	−	0.0138589i	0.996777	+	0.0802242i	$0.0255636\pi$
$3$		0			0
$3$		0			0
$4$	3.93847	+	0.694458i	0.984617	+	0.173615i
$5$	−2.37496	+	4.39995i	−0.474992	+	0.879990i
$5$	−2.37496	+	4.39995i	−0.474992	+	0.879990i
$6$		0			0
$7$	−3.04016	−	2.12874i	−0.434308	−	0.304106i	0.335901	−	0.941897i	$-0.390959\pi$
$7$	−3.04016	−	2.12874i	−0.434308	−	0.304106i	−0.770209	+	0.637792i	$0.779848\pi$
$8$	0.0576046	−	0.214983i	0.00720058	−	0.0268729i
$9$		0			0
$10$	0.116197	+	0.0764983i	0.0116197	+	0.00764983i
$11$	−3.20314	−	1.16585i	−0.291195	−	0.105986i	0.192292	−	0.981338i	$-0.438408\pi$
$11$	−3.20314	−	1.16585i	−0.291195	−	0.105986i	−0.483487	+	0.875351i	$0.660630\pi$
$12$		0			0
$13$	1.03393	+	11.8179i	0.0795334	+	0.909071i	0.926221	+	0.376981i	$0.123038\pi$
$13$	1.03393	+	11.8179i	0.0795334	+	0.909071i	−0.846688	+	0.532090i	$0.821407\pi$
$14$	−0.0663761	+	0.0791040i	−0.00474115	+	0.00565028i
$15$		0			0
$16$	15.0264	+	5.46915i	0.939147	+	0.341822i
$17$	7.97341	+	29.7572i	0.469024	+	1.75042i	0.643191	+	0.765706i	$0.277610\pi$
$17$	7.97341	+	29.7572i	0.469024	+	1.75042i	−0.174167	+	0.984716i	$0.555723\pi$
$18$		0			0
$19$	2.81936	−	1.62776i	0.148387	−	0.0856715i	−0.423968	−	0.905677i	$-0.639363\pi$
$19$	2.81936	−	1.62776i	0.148387	−	0.0856715i	0.572355	+	0.820006i	$0.306030\pi$
$20$	−12.4093	+	15.6798i	−0.620465	+	0.783988i
$21$		0			0
$22$	−0.0400822	+	0.0859566i	−0.00182192	+	0.00390712i
$23$	−13.0837	+	9.16134i	−0.568858	+	0.398319i	−0.822319	−	0.569027i	$-0.807320\pi$
$23$	−13.0837	+	9.16134i	−0.568858	+	0.398319i	0.253461	+	0.967346i	$0.418431\pi$
$24$		0			0
$25$	−13.7191	−	20.8994i	−0.548765	−	0.835977i
$26$	0.330073			0.0126951
$27$		0			0
$28$	−10.4952	−	10.4952i	−0.374830	−	0.374830i
$29$	−27.8129	−	33.1461i	−0.959065	−	1.14297i	−0.989659	−	0.143438i	$-0.954184\pi$
$29$	−27.8129	−	33.1461i	−0.959065	−	1.14297i	0.0305940	−	0.999532i	$-0.490260\pi$
$30$		0			0
$31$	−8.79682	+	49.8892i	−0.283768	+	1.60933i	0.425884	+	0.904778i	$0.359963\pi$
$31$	−8.79682	+	49.8892i	−0.283768	+	1.60933i	−0.709652	+	0.704552i	$0.751148\pi$
$32$	0.564275	−	1.21009i	0.0176336	−	0.0378153i
$33$		0			0
$34$	0.844136	−	0.148844i	0.0248275	−	0.00437776i
$35$	16.5866	−	8.32085i	0.473903	−	0.237739i
$36$		0			0
$37$	3.64899	+	13.6182i	0.0986213	+	0.368060i	0.997544	−	0.0700483i	$-0.0223153\pi$
$37$	3.64899	+	13.6182i	0.0986213	+	0.368060i	−0.898922	+	0.438108i	$0.855649\pi$
$38$	−0.0382809	−	0.0820936i	−0.00100739	−	0.00216036i
$39$		0			0
$40$	0.809107	+	0.764035i	0.0202277	+	0.0191009i
$41$	−9.67690	−	8.11988i	−0.236022	−	0.198046i	0.517103	−	0.855923i	$-0.327010\pi$
$41$	−9.67690	−	8.11988i	−0.236022	−	0.198046i	−0.753125	+	0.657877i	$0.771455\pi$
$42$		0			0
$43$	32.4393	+	69.5664i	0.754403	+	1.61782i	0.785927	+	0.618319i	$0.212186\pi$
$43$	32.4393	+	69.5664i	0.754403	+	1.61782i	−0.0315239	+	0.999503i	$0.510036\pi$
$44$	−11.8058	−	6.81610i	−0.268315	−	0.154911i
$45$		0			0
$46$	0.222203	+	0.384868i	0.00483051	+	0.00836669i
$47$	38.7099	+	27.1050i	0.823615	+	0.576701i	0.907634	−	0.419763i	$-0.137887\pi$
$47$	38.7099	+	27.1050i	0.823615	+	0.576701i	−0.0840189	+	0.996464i	$0.526776\pi$
$48$		0			0
$49$	−12.0480	−	33.1015i	−0.245877	−	0.675542i
$50$	−0.612553	+	0.329582i	−0.0122511	+	0.00659163i
$51$		0			0
$52$	−4.13494	+	47.2625i	−0.0795180	+	0.908895i
$53$	−15.4300	−	15.4300i	−0.291131	−	0.291131i	0.546396	−	0.837527i	$-0.315999\pi$
$53$	−15.4300	−	15.4300i	−0.291131	−	0.291131i	−0.837527	+	0.546396i	$0.815999\pi$
$54$		0			0
$55$	12.7370	−	11.3248i	0.231582	−	0.205906i
$56$	−0.632771	+	0.530958i	−0.0112995	+	0.00948139i
$57$		0			0
$58$	−0.986180	+	0.690531i	−0.0170031	+	0.0119057i
$59$	9.94222	+	27.3160i	0.168512	+	0.462983i	0.994989	−	0.0999878i	$-0.0318804\pi$
$59$	9.94222	+	27.3160i	0.168512	+	0.462983i	−0.826476	+	0.562971i	$0.809658\pi$
$60$		0			0
$61$	−3.58125	−	20.3103i	−0.0587089	−	0.332955i	0.941280	−	0.337627i	$-0.109624\pi$
$61$	−3.58125	−	20.3103i	−0.0587089	−	0.332955i	−0.999989	+	0.00467160i	$0.998513\pi$
$62$	1.36148	+	0.364808i	0.0219594	+	0.00588400i
$63$		0			0
$64$	55.3613	+	31.9628i	0.865020	+	0.499419i
$65$	−54.4538	−	23.5179i	−0.837751	−	0.361813i
$66$		0			0
$67$	7.35361	−	0.643358i	0.109755	−	0.00960235i	−0.0321457	−	0.999483i	$-0.510234\pi$
$67$	7.35361	−	0.643358i	0.109755	−	0.00960235i	0.141901	+	0.989881i	$0.454679\pi$
$68$	10.7379	+	122.735i	0.157910	+	1.80492i
$69$		0			0
$70$	−0.190413	−	0.479921i	−0.00272018	−	0.00685601i
$71$	44.8146	−	77.6212i	0.631192	−	1.09326i	−0.356117	−	0.934441i	$-0.615899\pi$
$71$	44.8146	−	77.6212i	0.631192	−	1.09326i	0.987308	−	0.158815i	$-0.0507672\pi$
$72$		0			0
$73$	3.90769	−	14.5837i	0.0535300	−	0.199777i	−0.933982	−	0.357320i	$-0.883691\pi$
$73$	3.90769	−	14.5837i	0.0535300	−	0.199777i	0.987512	+	0.157543i	$0.0503573\pi$
$74$	0.386314	−	0.0681177i	0.00522047	−	0.000920509i
$75$		0			0
$76$	12.2344	−	4.45295i	0.160979	−	0.0585914i
$77$	7.25626	+	10.3630i	0.0942371	+	0.134585i
$78$		0			0
$79$	62.7357	+	74.7655i	0.794123	+	0.946399i	0.999479	−	0.0322886i	$-0.0102796\pi$
$79$	62.7357	+	74.7655i	0.794123	+	0.946399i	−0.205356	+	0.978687i	$0.565835\pi$
$80$	−59.7510	+	53.1262i	−0.746887	+	0.664077i
$81$		0			0
$82$	−0.248531	+	0.248531i	−0.00303087	+	0.00303087i
$83$	−67.6198	−	5.91597i	−0.814697	−	0.0712767i	−0.327812	−	0.944743i	$-0.606311\pi$
$83$	−67.6198	−	5.91597i	−0.814697	−	0.0712767i	−0.486885	+	0.873466i	$0.661867\pi$
$84$		0			0
$85$	−149.867	−	35.5895i	−1.76314	−	0.418700i
$86$	2.00689	−	0.730447i	0.0233359	−	0.00849356i
$87$		0			0
$88$	−0.435154	+	0.621464i	−0.00494493	+	0.00706209i
$89$	65.5625	−	37.8526i	0.736658	−	0.425310i	−0.0841951	−	0.996449i	$-0.526832\pi$
$89$	65.5625	−	37.8526i	0.736658	−	0.425310i	0.820853	+	0.571140i	$0.193499\pi$
$90$		0			0
$91$	22.0140	−	38.1293i	0.241912	−	0.419003i
$92$	−57.8921	+	26.9955i	−0.629262	+	0.293430i
$93$		0			0
$94$	0.845159	−	1.00722i	0.00899105	−	0.0107151i
$95$	0.466183	+	16.2709i	0.00490719	+	0.171273i
$96$		0			0
$97$	78.7818	−	36.7366i	0.812184	−	0.378727i	0.0282724	−	0.999600i	$-0.490999\pi$
$97$	78.7818	−	36.7366i	0.812184	−	0.378727i	0.783911	+	0.620873i	$0.213222\pi$
$98$	−0.946715	+	0.253672i	−0.00966036	+	0.00258849i
$99$		0			0
$100$	−39.5185	−	91.8391i	−0.395185	−	0.918391i
$101$	13.5497	+	76.8441i	0.134155	+	0.760832i	0.975444	+	0.220247i	$0.0706862\pi$
$101$	13.5497	+	76.8441i	0.134155	+	0.760832i	−0.841289	+	0.540586i	$0.818203\pi$
$102$		0			0
$103$	−117.501	−	54.7918i	−1.14079	−	0.531959i	−0.241972	−	0.970283i	$-0.577794\pi$
$103$	−117.501	−	54.7918i	−1.14079	−	0.531959i	−0.898817	+	0.438324i	$0.855572\pi$
$104$	2.60022	+	0.458488i	0.0250021	+	0.00440854i
$105$		0			0
$106$	−0.465101	+	0.390266i	−0.00438774	+	0.00368175i
$107$	101.087	−	101.087i	0.944741	−	0.944741i	−0.0538098	−	0.998551i	$-0.517136\pi$
$107$	101.087	−	101.087i	0.944741	−	0.944741i	0.998551	+	0.0538098i	$0.0171365\pi$
$108$		0			0
$109$		−	187.977i		−	1.72456i	−0.506433	−	0.862280i	$-0.669036\pi$
$109$		−	187.977i		−	1.72456i	0.506433	−	0.862280i	$-0.330964\pi$
$110$	−0.283011	−	0.380503i	−0.00257283	−	0.00345912i
$111$		0			0
$112$	−34.0401	−	48.6142i	−0.303929	−	0.434056i
$113$	129.461	+	60.3689i	1.14568	+	0.534238i	0.900334	−	0.435199i	$-0.143322\pi$
$113$	129.461	+	60.3689i	1.14568	+	0.534238i	0.245342	+	0.969437i	$0.421100\pi$
$114$		0			0
$115$	−9.23603	−	79.3256i	−0.0803133	−	0.689788i
$116$	−86.5216	−	149.860i	−0.745876	−	1.29190i
$117$		0			0
$118$	0.781247	−	0.209335i	0.00662074	−	0.00177402i
$119$	39.1049	−	107.440i	0.328612	−	0.902855i
$120$		0			0
$121$	−83.7905	−	70.3085i	−0.692483	−	0.581062i
$122$	−0.571638	+	0.0500119i	−0.00468556	+	0.000409933i
$123$		0			0
$124$	−69.2920	+	190.378i	−0.558806	+	1.53531i
$125$	124.539	−	10.7281i	0.996310	−	0.0858246i
$126$		0			0
$127$	−19.2524	−	5.15868i	−0.151594	−	0.0406195i	0.182224	−	0.983257i	$-0.441670\pi$
$127$	−19.2524	−	5.15868i	−0.151594	−	0.0406195i	−0.333818	+	0.942638i	$0.608337\pi$
$128$	4.08352	−	5.83187i	0.0319025	−	0.0455614i
$129$		0			0
$130$	−0.783911	+	1.45230i	−0.00603008	+	0.0111716i
$131$	6.20196	−	35.1730i	0.0473432	−	0.268497i	−0.951943	−	0.306275i	$-0.900917\pi$
$131$	6.20196	−	35.1730i	0.0473432	−	0.268497i	0.999286	+	0.0377789i	$0.0120283\pi$
$132$		0			0
$133$	−12.0364	−	1.05305i	−0.0904990	−	0.00791764i
$134$		−	0.205385i		−	0.00153273i
$135$		0			0
$136$	6.85660			0.0504162
$137$	8.26760	−	94.4991i	0.0603474	−	0.689774i	−0.904415	−	0.426653i	$-0.859693\pi$
$137$	8.26760	−	94.4991i	0.0603474	−	0.689774i	0.964763	−	0.263121i	$-0.0847519\pi$
$138$		0			0
$139$	152.945	+	26.9683i	1.10032	+	0.194017i	0.694186	−	0.719796i	$-0.255765\pi$
$139$	152.945	+	26.9683i	1.10032	+	0.194017i	0.406137	+	0.913812i	$0.366876\pi$
$140$	71.1043	−	21.2527i	0.507888	−	0.151805i
$141$		0			0
$142$	−2.04281	−	1.43039i	−0.0143860	−	0.0100732i
$143$	10.4661	−	39.0599i	0.0731893	−	0.273146i
$144$		0			0
$145$	211.896	−	43.6546i	1.46135	−	0.301066i
$146$	−0.394750	−	0.143677i	−0.00270377	−	0.000984092i
$147$		0			0
$148$	4.91415	+	56.1690i	0.0332037	+	0.379520i
$149$	11.5658	−	13.7835i	0.0776225	−	0.0925070i	−0.725836	−	0.687868i	$-0.758547\pi$
$149$	11.5658	−	13.7835i	0.0776225	−	0.0925070i	0.803458	+	0.595361i	$0.202991\pi$
$150$		0			0
$151$	−13.4319	−	4.88880i	−0.0889528	−	0.0323762i	0.297160	−	0.954828i	$-0.403960\pi$
$151$	−13.4319	−	4.88880i	−0.0889528	−	0.0323762i	−0.386113	+	0.922451i	$0.626183\pi$
$152$	−0.187533	−	0.699882i	−0.00123377	−	0.00460449i
$153$		0			0
$154$	0.304835	−	0.175997i	0.00197945	−	0.00114284i
$155$	−198.618	−	157.191i	−1.28141	−	1.01413i
$156$		0			0
$157$	−30.1378	+	64.6307i	−0.191960	+	0.411661i	−0.978606	−	0.205745i	$-0.934038\pi$
$157$	−30.1378	+	64.6307i	−0.191960	+	0.411661i	0.786645	+	0.617405i	$0.211816\pi$
$158$	2.22446	−	1.55759i	0.0140789	−	0.00985813i
$159$		0			0
$160$	3.98421	+	5.35670i	0.0249013	+	0.0334794i
$161$	59.2787			0.368191
$162$		0			0
$163$	−135.434	−	135.434i	−0.830886	−	0.830886i	0.156752	−	0.987638i	$-0.449898\pi$
$163$	−135.434	−	135.434i	−0.830886	−	0.830886i	−0.987638	+	0.156752i	$0.949898\pi$
$164$	−32.4732	−	38.7001i	−0.198008	−	0.235976i
$165$		0			0
$166$	−0.327954	+	1.85992i	−0.00197563	+	0.0112043i
$167$	34.4311	−	73.8378i	0.206174	−	0.442143i	−0.775845	−	0.630924i	$-0.782676\pi$
$167$	34.4311	−	73.8378i	0.206174	−	0.442143i	0.982019	+	0.188781i	$0.0604538\pi$
$168$		0			0
$169$	27.8383	−	4.90864i	0.164723	−	0.0290452i
$170$	−1.34988	+	4.06765i	−0.00794050	+	0.0239274i
$171$		0			0
$172$	79.4503	+	296.513i	0.461921	+	1.72391i
$173$	40.9591	+	87.8371i	0.236758	+	0.507729i	0.988406	−	0.151836i	$-0.0485184\pi$
$173$	40.9591	+	87.8371i	0.236758	+	0.507729i	−0.751648	+	0.659565i	$0.770741\pi$
$174$		0			0
$175$	−2.78119	+	92.7419i	−0.0158925	+	0.529954i
$176$	−41.7553	−	35.0369i	−0.237246	−	0.199073i
$177$		0			0
$178$	−0.890198	−	1.90904i	−0.00500111	−	0.0107249i
$179$	184.581	+	106.568i	1.03118	+	0.595350i	0.917321	−	0.398147i	$-0.130347\pi$
$179$	184.581	+	106.568i	1.03118	+	0.595350i	0.113855	+	0.993497i	$0.463680\pi$
$180$		0			0
$181$	−111.535	−	193.184i	−0.616214	−	1.06731i	−0.990170	−	0.139867i	$-0.955332\pi$
$181$	−111.535	−	193.184i	−0.616214	−	1.06731i	0.373956	−	0.927446i	$-0.378001\pi$
$182$	−1.00347	−	0.702640i	−0.00551359	−	0.00386066i
$183$		0			0
$184$	1.21585	+	3.34052i	0.00660789	+	0.0181550i
$185$	−68.5857	−	16.2874i	−0.370733	−	0.0880398i
$186$		0			0
$187$	9.15238	−	104.612i	0.0489432	−	0.559424i
$188$	133.634	+	133.634i	0.710822	+	0.710822i
$189$		0			0
$190$	0.452123	+	0.0265352i	0.00237960	+	0.000139659i
$191$	−119.862	+	100.576i	−0.627549	+	0.526576i	−0.900166	−	0.435546i	$-0.856555\pi$
$191$	−119.862	+	100.576i	−0.627549	+	0.526576i	0.272617	+	0.962123i	$0.412111\pi$
$192$		0			0
$193$	−188.322	+	131.865i	−0.975763	+	0.683237i	−0.948628	−	0.316395i	$-0.897528\pi$
$193$	−188.322	+	131.865i	−0.975763	+	0.683237i	−0.0271359	+	0.999632i	$0.508639\pi$
$194$	−0.827209	−	2.27274i	−0.00426396	−	0.0117151i
$195$		0			0
$196$	−24.4629	−	138.736i	−0.124811	−	0.707838i
$197$	65.4230	+	17.5300i	0.332096	+	0.0889849i	0.421014	−	0.907054i	$-0.361674\pi$
$197$	65.4230	+	17.5300i	0.332096	+	0.0889849i	−0.0889180	+	0.996039i	$0.528341\pi$
$198$		0			0
$199$	30.0472	+	17.3478i	0.150991	+	0.0871747i	0.573592	−	0.819141i	$-0.305550\pi$
$199$	30.0472	+	17.3478i	0.150991	+	0.0871747i	−0.422601	+	0.906316i	$0.638883\pi$
$200$	−5.28331	+	1.74548i	−0.0264166	+	0.00872739i
$201$		0			0
$202$	2.16280	−	0.189220i	0.0107069	−	0.000936735i
$203$	13.9961	+	159.976i	0.0689461	+	0.788058i
$204$		0			0
$205$	58.7093	−	23.2935i	0.286387	−	0.113627i
$206$	−1.80364	+	3.12400i	−0.00875554	+	0.0151650i
$207$		0			0
$208$	−49.0977	+	183.235i	−0.236046	+	0.880937i
$209$	−10.9285	+	1.92700i	−0.0522896	+	0.00922007i
$210$		0			0
$211$	−23.7166	+	8.63213i	−0.112401	+	0.0409106i	−0.397608	−	0.917555i	$-0.630160\pi$
$211$	−23.7166	+	8.63213i	−0.112401	+	0.0409106i	0.285207	+	0.958466i	$0.407937\pi$
$212$	−50.0550	−	71.4859i	−0.236108	−	0.337198i
$213$		0			0
$214$	−2.55677	−	3.04704i	−0.0119475	−	0.0142385i
$215$	−383.131	−	22.4860i	−1.78200	−	0.104586i
$216$		0			0
$217$	132.945	−	132.945i	0.612649	−	0.612649i
$218$	−5.21029	−	0.455841i	−0.0239004	−	0.00209102i
$219$		0			0
$220$	58.0289	−	35.7571i	0.263768	−	0.162532i
$221$	−343.424	+	124.996i	−1.55395	+	0.565593i
$222$		0			0
$223$	−193.818	+	276.801i	−0.869140	+	1.24126i	0.100059	+	0.994981i	$0.468097\pi$
$223$	−193.818	+	276.801i	−0.869140	+	1.24126i	−0.969199	+	0.246279i	$0.920792\pi$
$224$	−4.29145	+	2.47767i	−0.0191583	+	0.0110610i
$225$		0			0
$226$	1.98723	−	3.44198i	0.00879305	−	0.0152300i
$227$	314.339	−	146.579i	1.38475	−	0.645721i	0.419673	−	0.907675i	$-0.362145\pi$
$227$	314.339	−	146.579i	1.38475	−	0.645721i	0.965080	+	0.261954i	$0.0843669\pi$
$228$		0			0
$229$	188.298	−	224.405i	0.822263	−	0.979935i	−0.177729	−	0.984080i	$-0.556875\pi$
$229$	188.298	−	224.405i	0.822263	−	0.979935i	0.999991	+	0.00414481i	$0.00131934\pi$
$230$	−2.22112	+	0.0636380i	−0.00965705	+	0.000276687i
$231$		0			0
$232$	−8.72802	+	4.06994i	−0.0376208	+	0.0175428i
$233$	−288.534	+	77.3125i	−1.23834	+	0.331813i	−0.817823	−	0.575469i	$-0.804819\pi$
$233$	−288.534	+	77.3125i	−1.23834	+	0.331813i	−0.420521	+	0.907283i	$0.638153\pi$
$234$		0			0
$235$	−211.195	+	105.948i	−0.898702	+	0.450844i
$236$	20.1873	+	114.488i	0.0855393	+	0.485118i
$237$		0			0
$238$	−2.88315	−	1.34444i	−0.0121141	−	0.00564890i
$239$	187.530	+	33.0665i	0.784643	+	0.138354i	0.551596	−	0.834112i	$-0.314019\pi$
$239$	187.530	+	33.0665i	0.784643	+	0.138354i	0.233047	+	0.972465i	$0.425130\pi$
$240$		0			0
$241$	180.472	−	151.434i	0.748845	−	0.628356i	−0.186352	−	0.982483i	$-0.559667\pi$
$241$	180.472	−	151.434i	0.748845	−	0.628356i	0.935197	+	0.354127i	$0.115222\pi$
$242$	−2.15198	+	2.15198i	−0.00889249	+	0.00889249i
$243$		0			0
$244$		−	82.4783i		−	0.338026i
$245$	174.259	+	25.6044i	0.711260	+	0.104508i
$246$		0			0
$247$	22.1518	+	31.6360i	0.0896833	+	0.128081i
$248$	10.2186	+	4.76502i	0.0412041	+	0.0192138i
$249$		0			0
$250$	0.00464688	−	3.47795i	1.85875e−5	−	0.0139118i
$251$	171.937	+	297.803i	0.685007	+	1.18647i	0.973435	+	0.228966i	$0.0735343\pi$
$251$	171.937	+	297.803i	0.685007	+	1.18647i	−0.288427	+	0.957502i	$0.593132\pi$
$252$		0			0
$253$	52.5898	−	14.0914i	0.207865	−	0.0556972i
$254$	−0.189674	+	0.521124i	−0.000746747	+	0.00205167i
$255$		0			0
$256$	195.728	+	164.235i	0.764562	+	0.641544i
$257$	−132.871	+	11.6247i	−0.517007	+	0.0452323i	−0.342674	−	0.939454i	$-0.611333\pi$
$257$	−132.871	+	11.6247i	−0.517007	+	0.0452323i	−0.174333	+	0.984687i	$0.555777\pi$
$258$		0			0
$259$	17.8961	−	49.1692i	0.0690971	−	0.189843i
$260$	−198.132	−	130.440i	−0.762048	−	0.501693i
$261$		0			0
$262$	−0.959877	−	0.257198i	−0.00366365	−	0.000981672i
$263$	69.8930	−	99.8176i	0.265753	−	0.379535i	−0.663991	−	0.747740i	$-0.731139\pi$
$263$	69.8930	−	99.8176i	0.265753	−	0.379535i	0.929744	+	0.368206i	$0.120028\pi$
$264$		0			0
$265$	104.537	−	31.2455i	0.394478	−	0.117908i
$266$	−0.0583761	+	0.331067i	−0.000219459	+	0.00124461i
$267$		0			0
$268$	29.4087	+	2.57293i	0.109734	+	0.00960049i
$269$		−	95.8193i		−	0.356206i	−0.984012	−	0.178103i	$-0.943004\pi$
$269$		−	95.8193i		−	0.356206i	0.984012	−	0.178103i	$-0.0569960\pi$
$270$		0			0
$271$	113.483			0.418755			0.209378	−	0.977835i	$-0.432856\pi$
$271$	113.483			0.418755			0.209378	+	0.977835i	$0.432856\pi$
$272$	−42.9350	+	490.749i	−0.157849	+	1.80423i
$273$		0			0
$274$	−2.59925	−	0.458318i	−0.00948631	−	0.00167269i
$275$	19.5787	+	82.9382i	0.0711953	+	0.301593i
$276$		0			0
$277$	332.818	+	233.042i	1.20151	+	0.841306i	0.990679	−	0.136217i	$-0.0434945\pi$
$277$	332.818	+	233.042i	1.20151	+	0.841306i	0.210830	+	0.977523i	$0.432383\pi$
$278$	1.11839	−	4.17388i	0.00402298	−	0.0150140i
$279$		0			0
$280$	−0.833381	−	4.04516i	−0.00297636	−	0.0144470i
$281$	−103.770	−	37.7692i	−0.369288	−	0.134410i	0.150708	−	0.988578i	$-0.451845\pi$
$281$	−103.770	−	37.7692i	−0.369288	−	0.134410i	−0.519997	+	0.854168i	$0.674067\pi$
$282$		0			0
$283$	8.27217	+	94.5514i	0.0292303	+	0.334104i	0.996704	+	0.0811303i	$0.0258530\pi$
$283$	8.27217	+	94.5514i	0.0292303	+	0.334104i	−0.967473	+	0.252974i	$0.918591\pi$
$284$	230.406	−	274.587i	0.811287	−	0.966855i
$285$		0			0
$286$	−1.05727	−	0.384815i	−0.00369675	−	0.00134551i
$287$	12.1342	+	45.2853i	0.0422793	+	0.157789i
$288$		0			0
$289$	−571.632	+	330.032i	−1.97797	+	1.14198i
$290$	−0.696161	−	5.97913i	−0.00240055	−	0.0206177i
$291$		0			0
$292$	25.5181	−	54.7237i	0.0873907	−	0.187410i
$293$	−143.570	+	100.529i	−0.490001	+	0.343103i	−0.792321	−	0.610104i	$-0.791128\pi$
$293$	−143.570	+	100.529i	−0.490001	+	0.343103i	0.302320	+	0.953206i	$0.402239\pi$
$294$		0			0
$295$	−143.802	−	21.1292i	−0.487463	−	0.0716246i
$296$	3.13789			0.0106010
$297$		0			0
$298$	−0.354001	−	0.354001i	−0.00118792	−	0.00118792i
$299$	−121.796	−	145.150i	−0.407343	−	0.485453i
$300$		0			0
$301$	49.4681	−	280.547i	0.164346	−	0.932051i
$302$	−0.168078	+	0.360445i	−0.000556551	+	0.00119353i
$303$		0			0
$304$	51.2672	−	9.03979i	0.168642	−	0.0297361i
$305$	97.8694	+	32.4788i	0.320883	+	0.106488i
$306$		0			0
$307$	114.100	+	425.826i	0.371660	+	1.38706i	0.858163	+	0.513377i	$0.171606\pi$
$307$	114.100	+	425.826i	0.371660	+	1.38706i	−0.486503	+	0.873679i	$0.661728\pi$
$308$	21.3819	+	45.8536i	0.0694217	+	0.148875i
$309$		0			0
$310$	−4.83861	+	5.12405i	−0.0156084	+	0.0165292i
$311$	−150.000	−	125.865i	−0.482315	−	0.404710i	0.368948	−	0.929450i	$-0.379718\pi$
$311$	−150.000	−	125.865i	−0.482315	−	0.404710i	−0.851263	+	0.524740i	$0.824163\pi$
$312$		0			0
$313$	−175.366	−	376.073i	−0.560274	−	1.20151i	−0.958728	−	0.284324i	$-0.908231\pi$
$313$	−175.366	−	376.073i	−0.560274	−	1.20151i	0.398454	−	0.917188i	$-0.369547\pi$
$314$	1.71833	+	0.992079i	0.00547239	+	0.00315949i
$315$		0			0
$316$	195.161	+	338.029i	0.617598	+	1.06971i
$317$	−63.5215	−	44.4782i	−0.200383	−	0.140310i	0.469078	−	0.883157i	$-0.344586\pi$
$317$	−63.5215	−	44.4782i	−0.200383	−	0.140310i	−0.669461	+	0.742847i	$0.733475\pi$
$318$		0			0
$319$	50.4453	+	138.597i	0.158136	+	0.434474i
$320$	−272.116	+	167.676i	−0.850362	+	0.523988i
$321$		0			0
$322$	0.143750	−	1.64307i	0.000446429	−	0.00510270i
$323$	70.9174	+	70.9174i	0.219559	+	0.219559i
$324$		0			0
$325$	232.803	−	183.740i	0.716317	−	0.565354i
$326$	−4.08236	+	3.42551i	−0.0125226	+	0.0105077i
$327$		0			0
$328$	−2.30307	+	1.61263i	−0.00702157	+	0.00491655i
$329$	−59.9847	−	164.807i	−0.182324	−	0.500932i
$330$		0			0
$331$	68.7150	+	389.702i	0.207598	+	1.17735i	0.893299	+	0.449464i	$0.148385\pi$
$331$	68.7150	+	389.702i	0.207598	+	1.17735i	−0.685701	+	0.727884i	$0.740504\pi$
$332$	−262.210	−	70.2590i	−0.789790	−	0.211623i
$333$		0			0
$334$	−1.96312	−	1.13341i	−0.00587760	−	0.00339344i
$335$	−14.6338	+	33.8835i	−0.0436830	+	0.101145i
$336$		0			0
$337$	−459.782	+	40.2257i	−1.36434	+	0.119364i	−0.745684	−	0.666300i	$-0.767877\pi$
$337$	−459.782	+	40.2257i	−1.36434	+	0.119364i	−0.618653	+	0.785664i	$0.712321\pi$
$338$	−0.0685488	−	0.783517i	−0.000202807	−	0.00231810i
$339$		0			0
$340$	−565.529	−	244.244i	−1.66332	−	0.718366i
$341$	86.3407	−	149.546i	0.253199	−	0.438553i
$342$		0			0
$343$	−80.9046	+	301.940i	−0.235873	+	0.880292i
$344$	16.8243	−	2.96657i	0.0489078	−	0.00862376i
$345$		0			0
$346$	2.53397	−	0.922290i	0.00732361	−	0.00266558i
$347$	220.327	+	314.659i	0.634947	+	0.906799i	0.999705	−	0.0243038i	$-0.00773691\pi$
$347$	220.327	+	314.659i	0.634947	+	0.906799i	−0.364757	+	0.931103i	$0.618848\pi$
$348$		0			0
$349$	266.611	+	317.734i	0.763928	+	0.910414i	0.998090	−	0.0617837i	$-0.0196789\pi$
$349$	266.611	+	317.734i	0.763928	+	0.910414i	−0.234162	+	0.972198i	$0.575234\pi$
$350$	2.56385	+	0.301986i	0.00732528	+	0.000862818i
$351$		0			0
$352$	−3.21823	+	3.21823i	−0.00914271	+	0.00914271i
$353$	509.636	+	44.5873i	1.44373	+	0.126310i	0.781927	−	0.623370i	$-0.214237\pi$
$353$	509.636	+	44.5873i	1.44373	+	0.126310i	0.661800	+	0.749680i	$0.269793\pi$
$354$		0			0
$355$	235.096	+	381.529i	0.662243	+	1.07473i
$356$	284.503	−	103.551i	0.799166	−	0.290873i
$357$		0			0
$358$	3.40142	−	4.85773i	0.00950116	−	0.0135691i
$359$	−569.064	+	328.549i	−1.58514	+	0.915179i	−0.591044	+	0.806639i	$0.701284\pi$
$359$	−569.064	+	328.549i	−1.58514	+	0.915179i	−0.994092	+	0.108539i	$0.965383\pi$
$360$		0			0
$361$	−175.201	+	303.457i	−0.485321	+	0.840600i
$362$	−5.62508	+	2.62302i	−0.0155389	+	0.00724591i
$363$		0			0
$364$	113.180	−	134.883i	0.310935	−	0.370558i
$365$	54.8869	+	51.8293i	0.150375	+	0.141998i
$366$		0			0
$367$	233.762	−	109.005i	0.636952	−	0.297016i	−0.0771898	−	0.997016i	$-0.524595\pi$
$367$	233.762	−	109.005i	0.636952	−	0.297016i	0.714142	+	0.700001i	$0.246817\pi$
$368$	−246.706	+	66.1046i	−0.670396	+	0.179632i
$369$		0			0
$370$	−0.617768	+	1.86154i	−0.00166964	+	0.00503119i
$371$	14.0631	+	79.7559i	0.0379060	+	0.214975i
$372$		0			0
$373$	596.261	+	278.041i	1.59855	+	0.745418i	0.998511	−	0.0545499i	$-0.0173724\pi$
$373$	596.261	+	278.041i	1.59855	+	0.745418i	0.600043	+	0.799968i	$0.295150\pi$
$374$	−2.87742	−	0.507366i	−0.00769363	−	0.00135659i
$375$		0			0
$376$	8.05699	−	6.76061i	0.0214282	−	0.0179804i
$377$	362.962	−	362.962i	0.962763	−	0.962763i
$378$		0			0
$379$		−	513.424i		−	1.35468i	−0.735670	−	0.677340i	$-0.763133\pi$
$379$		−	513.424i		−	1.35468i	0.735670	−	0.677340i	$-0.236867\pi$
$380$	−9.46343	+	64.4062i	−0.0249038	+	0.169490i
$381$		0			0
$382$	2.49707	+	3.56619i	0.00653684	+	0.00933558i
$383$	−413.568	−	192.850i	−1.07981	−	0.503524i	−0.200462	−	0.979701i	$-0.564244\pi$
$383$	−413.568	−	192.850i	−1.07981	−	0.503524i	−0.879349	+	0.476177i	$0.842022\pi$
$384$		0			0
$385$	−62.8301	+	7.31542i	−0.163195	+	0.0190011i
$386$	3.19831	+	5.53963i	0.00828578	+	0.0143514i
$387$		0			0
$388$	335.792	−	89.9751i	0.865443	−	0.231895i
$389$	−199.989	+	549.466i	−0.514111	+	1.41251i	0.362806	+	0.931865i	$0.381819\pi$
$389$	−199.989	+	549.466i	−0.514111	+	1.41251i	−0.876916	+	0.480643i	$0.840403\pi$
$390$		0			0
$391$	−376.937	−	316.288i	−0.964034	−	0.808921i
$392$	−7.81030	+	0.683313i	−0.0199242	+	0.00174314i
$393$		0			0
$394$	0.644542	−	1.77087i	0.00163589	−	0.00449458i
$395$	−477.959	+	98.4688i	−1.21002	+	0.249288i
$396$		0			0
$397$	−462.051	−	123.806i	−1.16386	−	0.311854i	−0.375352	−	0.926883i	$-0.622478\pi$
$397$	−462.051	−	123.806i	−1.16386	−	0.311854i	−0.788505	+	0.615028i	$0.789145\pi$
$398$	0.553704	−	0.790772i	0.00139122	−	0.00198686i
$399$		0			0
$400$	−91.8463	−	389.074i	−0.229616	−	0.972685i
$401$	106.695	−	605.096i	0.266072	−	1.50897i	−0.499894	−	0.866087i	$-0.666628\pi$
$401$	106.695	−	605.096i	0.266072	−	1.50897i	0.765966	−	0.642882i	$-0.222261\pi$
$402$		0			0
$403$	−598.682	−	52.3779i	−1.48556	−	0.129970i
$404$			312.058i			0.772420i
$405$		0			0
$406$	4.46810			0.0110052
$407$	4.18854	−	47.8752i	0.0102913	−	0.117630i
$408$		0			0
$409$	426.780	+	75.2529i	1.04347	+	0.183992i	0.669013	−	0.743251i	$-0.266717\pi$
$409$	426.780	+	75.2529i	1.04347	+	0.183992i	0.374460	+	0.927243i	$0.377828\pi$
$410$	−0.503272	−	1.68378i	−0.00122749	−	0.00410677i
$411$		0			0
$412$	−424.725	−	297.395i	−1.03088	−	0.721833i
$413$	27.9228	−	104.209i	0.0676097	−	0.252323i
$414$		0			0
$415$	186.624	−	283.474i	0.449697	−	0.683069i
$416$	14.8842	+	5.41740i	0.0357793	+	0.0130226i
$417$		0			0
$418$	0.0269104	+	0.307587i	6.43789e−5	+	0.000735854i
$419$	440.574	−	525.056i	1.05149	−	1.25312i	0.0850087	−	0.996380i	$-0.472908\pi$
$419$	440.574	−	525.056i	1.05149	−	1.25312i	0.966481	−	0.256737i	$-0.0826473\pi$
$420$		0			0
$421$	23.5432	+	8.56902i	0.0559221	+	0.0203540i	0.369830	−	0.929100i	$-0.379416\pi$
$421$	23.5432	+	8.56902i	0.0559221	+	0.0203540i	−0.313908	+	0.949454i	$0.601638\pi$
$422$	0.181750	+	0.678302i	0.000430688	+	0.00160735i
$423$		0			0
$424$	−4.20602	+	2.42835i	−0.00991986	+	0.00572724i
$425$	512.520	−	574.882i	1.20593	−	1.35266i
$426$		0			0
$427$	−32.3477	+	69.3699i	−0.0757557	+	0.162459i
$428$	468.330	−	327.928i	1.09423	−	0.766188i
$429$		0			0
$430$	−1.55235	+	10.5650i	−0.00361011	+	0.0245697i
$431$	−127.076			−0.294840			−0.147420	−	0.989074i	$-0.547097\pi$
$431$	−127.076			−0.294840			−0.147420	+	0.989074i	$0.547097\pi$
$432$		0			0
$433$	207.828	+	207.828i	0.479973	+	0.479973i	0.905123	−	0.425150i	$-0.139779\pi$
$433$	207.828	+	207.828i	0.479973	+	0.479973i	−0.425150	+	0.905123i	$0.639779\pi$
$434$	−3.36254	−	4.00732i	−0.00774778	−	0.00923345i
$435$		0			0
$436$	130.542	−	740.341i	0.299409	−	1.69803i
$437$	−21.9754	+	47.1263i	−0.0502869	+	0.107841i
$438$		0			0
$439$	−220.046	+	38.8000i	−0.501243	+	0.0883826i	−0.418552	−	0.908193i	$-0.637462\pi$
$439$	−220.046	+	38.8000i	−0.501243	+	0.0883826i	−0.0826904	+	0.996575i	$0.526351\pi$
$440$	−1.70094	−	3.39061i	−0.00386576	−	0.00770593i
$441$		0			0
$442$	2.63181	+	9.82204i	0.00595432	+	0.0222218i
$443$	8.77681	+	18.8219i	0.0198122	+	0.0424874i	0.915965	−	0.401258i	$-0.131427\pi$
$443$	8.77681	+	18.8219i	0.0198122	+	0.0424874i	−0.896153	+	0.443746i	$0.853649\pi$
$444$		0			0
$445$	10.8408	+	378.370i	0.0243613	+	0.850270i
$446$	7.20228	+	6.04343i	0.0161486	+	0.0135503i
$447$		0			0
$448$	−100.266	−	215.022i	−0.223809	−	0.479959i
$449$	650.041	+	375.302i	1.44775	+	0.835861i	0.998347	−	0.0574664i	$-0.0183022\pi$
$449$	650.041	+	375.302i	1.44775	+	0.835861i	0.449406	+	0.893327i	$0.351636\pi$
$450$		0			0
$451$	21.5299	+	37.2909i	0.0477382	+	0.0826850i
$452$	467.956	+	327.667i	1.03530	+	0.724926i
$453$		0			0
$454$	−3.30056	−	9.06821i	−0.00726995	−	0.0199740i
$455$	115.485	+	187.416i	0.253812	+	0.411903i
$456$		0			0
$457$	45.5034	−	520.107i	0.0995699	−	1.13809i	−0.767890	−	0.640582i	$-0.778693\pi$
$457$	45.5034	−	520.107i	0.0995699	−	1.13809i	0.867460	−	0.497507i	$-0.165751\pi$
$458$	−5.76337	−	5.76337i	−0.0125838	−	0.0125838i
$459$		0			0
$460$	18.7125	−	318.836i	0.0406794	−	0.693121i
$461$	498.139	−	417.988i	1.08056	−	0.906699i	0.0845942	−	0.996415i	$-0.473041\pi$
$461$	498.139	−	417.988i	1.08056	−	0.906699i	0.995967	+	0.0897167i	$0.0285962\pi$
$462$		0			0
$463$	165.786	−	116.084i	0.358068	−	0.250722i	−0.380675	−	0.924709i	$-0.624308\pi$
$463$	165.786	−	116.084i	0.358068	−	0.250722i	0.738743	+	0.673987i	$0.235420\pi$
$464$	−236.645	−	650.178i	−0.510012	−	1.40125i
$465$		0			0
$466$	1.44323	+	8.18499i	0.00309707	+	0.0175644i
$467$	−33.9068	−	9.08531i	−0.0726056	−	0.0194546i	0.222333	−	0.974971i	$-0.428633\pi$
$467$	−33.9068	−	9.08531i	−0.0726056	−	0.0194546i	−0.294939	+	0.955516i	$0.595299\pi$
$468$		0			0
$469$	−23.7257	−	13.6980i	−0.0505878	−	0.0292069i
$470$	2.42450	+	6.11077i	0.00515851	+	0.0130016i
$471$		0			0
$472$	6.44521	−	0.563883i	0.0136551	−	0.00119467i
$473$	−22.8039	−	260.650i	−0.0482113	−	0.551058i
$474$		0			0
$475$	−72.6984	−	36.5916i	−0.153049	−	0.0770350i
$476$	228.626	−	395.991i	0.480306	−	0.831914i
$477$		0			0
$478$	1.37129	−	5.11771i	0.00286880	−	0.0107065i
$479$	−797.108	+	140.552i	−1.66411	+	0.293427i	−0.924946	−	0.380099i	$-0.875890\pi$
$479$	−797.108	+	140.552i	−1.66411	+	0.293427i	−0.739163	+	0.673526i	$0.764779\pi$
$480$		0			0
$481$	−157.166	+	57.2038i	−0.326749	+	0.118927i
$482$	−3.75976	−	5.36949i	−0.00780032	−	0.0111400i
$483$		0			0
$484$	−281.180	−	335.097i	−0.580950	−	0.692349i
$485$	−25.4648	+	433.884i	−0.0525047	+	0.894606i
$486$		0			0
$487$	75.7890	−	75.7890i	0.155624	−	0.155624i	−0.625000	−	0.780625i	$-0.714901\pi$
$487$	75.7890	−	75.7890i	0.155624	−	0.155624i	0.780625	+	0.625000i	$0.214901\pi$
$488$	−4.57266	−	0.400056i	−0.00937021	−	0.000819787i
$489$		0			0
$490$	1.13227	−	4.76796i	0.00231076	−	0.00973053i
$491$	−340.188	+	123.818i	−0.692848	+	0.252176i	−0.664354	−	0.747418i	$-0.731293\pi$
$491$	−340.188	+	123.818i	−0.692848	+	0.252176i	−0.0284938	+	0.999594i	$0.509071\pi$
$492$		0			0
$493$	764.571	−	1091.92i	1.55085	−	2.21485i
$494$	0.930595	−	0.537279i	0.00188380	−	0.00108761i
$495$		0			0
$496$	−405.035	+	701.542i	−0.816604	+	1.41440i
$497$	−301.479	+	140.582i	−0.606597	+	0.282861i
$498$		0			0
$499$	152.789	−	182.086i	0.306190	−	0.364903i	−0.590905	−	0.806741i	$-0.701229\pi$
$499$	152.789	−	182.086i	0.306190	−	0.364903i	0.897095	+	0.441839i	$0.145674\pi$
$500$	497.942	+	44.2348i	0.995885	+	0.0884696i
$501$		0			0
$502$	8.67137	−	4.04353i	0.0172736	−	0.00805483i
$503$	−316.975	+	84.9331i	−0.630168	+	0.168853i	−0.559746	−	0.828664i	$-0.689101\pi$
$503$	−316.975	+	84.9331i	−0.630168	+	0.168853i	−0.0704222	+	0.997517i	$0.522435\pi$
$504$		0			0
$505$	−370.290	−	122.884i	−0.733248	−	0.243334i
$506$	−0.263052	−	1.49184i	−0.000519865	−	0.00294830i
$507$		0			0
$508$	−72.2427	−	33.6873i	−0.142210	−	0.0663136i
$509$	−261.364	−	46.0856i	−0.513486	−	0.0905414i	−0.0890997	−	0.996023i	$-0.528399\pi$
$509$	−261.364	−	46.0856i	−0.513486	−	0.0905414i	−0.424386	+	0.905481i	$0.639510\pi$
$510$		0			0
$511$	−42.9249	+	36.0182i	−0.0840017	+	0.0704858i
$512$	25.1635	−	25.1635i	0.0491476	−	0.0491476i
$513$		0			0
$514$			3.71107i			0.00721997i
$515$	520.142	−	386.871i	1.00998	−	0.751207i
$516$		0			0
$517$	−92.3930	−	131.951i	−0.178710	−	0.255224i
$518$	−1.31946	−	0.615275i	−0.00254722	−	0.00118779i
$519$		0			0
$520$	−8.19274	+	10.3519i	−0.0157553	+	0.0199076i
$521$	378.245	+	655.139i	0.725997	+	1.25746i	0.958562	+	0.284883i	$0.0919548\pi$
$521$	378.245	+	655.139i	0.725997	+	1.25746i	−0.232565	+	0.972581i	$0.574712\pi$
$522$		0			0
$523$	580.072	−	155.430i	1.10912	−	0.297189i	0.342649	−	0.939463i	$-0.388676\pi$
$523$	580.072	−	155.430i	1.10912	−	0.297189i	0.766475	+	0.642275i	$0.222009\pi$
$524$	48.8524	−	134.221i	0.0932298	−	0.256147i
$525$		0			0
$526$	−2.59723	−	2.17933i	−0.00493769	−	0.00414321i
$527$	−1554.70	+	136.019i	−2.95010	+	0.258100i
$528$		0			0
$529$	−93.6744	+	257.368i	−0.177078	+	0.486518i
$530$	−0.612554	−	2.97329i	−0.00115576	−	0.00560997i
$531$		0			0
$532$	−46.6736	−	12.5061i	−0.0877323	−	0.0235078i
$533$	85.9549	−	122.756i	0.161266	−	0.230312i
$534$		0			0
$535$	204.701	+	684.858i	0.382618	+	1.28011i
$536$	0.285291	−	1.61796i	0.000532259	−	0.00301859i
$537$		0			0
$538$	−2.65589	−	0.232361i	−0.00493660	−	0.000431897i
$539$			120.075i			0.222774i
$540$		0			0
$541$	−870.344			−1.60877			−0.804384	−	0.594109i	$-0.797505\pi$
$541$	−870.344			−1.60877			−0.804384	+	0.594109i	$0.797505\pi$
$542$	0.275194	−	3.14548i	0.000507738	−	0.00580347i
$543$		0			0
$544$	40.5081	+	7.14267i	0.0744634	+	0.0131299i
$545$	827.089	+	446.438i	1.51759	+	0.819152i
$546$		0			0
$547$	17.2226	+	12.0594i	0.0314855	+	0.0220464i	0.589213	−	0.807978i	$-0.299438\pi$
$547$	17.2226	+	12.0594i	0.0314855	+	0.0220464i	−0.557728	+	0.830024i	$0.688327\pi$
$548$	98.1873	−	366.440i	0.179174	−	0.668686i
$549$		0			0
$550$	2.34634	−	0.341553i	0.00426606	−	0.000621006i
$551$	−132.369	−	48.1782i	−0.240233	−	0.0874378i
$552$		0			0
$553$	−31.5700	−	360.847i	−0.0570886	−	0.652526i
$554$	7.26646	−	8.65983i	0.0131164	−	0.0156315i
$555$		0			0
$556$	583.640	+	212.428i	1.04971	+	0.382064i
$557$	−205.862	−	768.287i	−0.369590	−	1.37933i	−0.861090	−	0.508452i	$-0.830218\pi$
$557$	−205.862	−	768.287i	−0.369590	−	1.37933i	0.491500	−	0.870878i	$-0.336449\pi$
$558$		0			0
$559$	−788.590	+	455.292i	−1.41071	+	0.814477i
$560$	294.744	−	34.3176i	0.526329	−	0.0612814i
$561$		0			0
$562$	−1.29852	+	2.78468i	−0.00231053	+	0.00495494i
$563$	−293.859	+	205.762i	−0.521952	+	0.365474i	−0.804664	−	0.593730i	$-0.797655\pi$
$563$	−293.859	+	205.762i	−0.521952	+	0.365474i	0.282713	+	0.959205i	$0.408766\pi$
$564$		0			0
$565$	−573.086	+	426.250i	−1.01431	+	0.754425i
$566$	2.64081			0.00466574
$567$		0			0
$568$	−14.1057	−	14.1057i	−0.0248340	−	0.0248340i
$569$	−229.931	−	274.021i	−0.404096	−	0.481583i	0.525168	−	0.850998i	$-0.324002\pi$
$569$	−229.931	−	274.021i	−0.404096	−	0.481583i	−0.929264	+	0.369415i	$0.879558\pi$
$570$		0			0
$571$	−92.1257	+	522.471i	−0.161341	+	0.915010i	0.791416	+	0.611278i	$0.209344\pi$
$571$	−92.1257	+	522.471i	−0.161341	+	0.915010i	−0.952757	+	0.303733i	$0.901767\pi$
$572$	68.3457	−	146.568i	0.119486	−	0.256238i
$573$		0			0
$574$	1.28463	−	0.226515i	0.00223803	−	0.000394625i
$575$	370.964	+	147.757i	0.645155	+	0.256969i
$576$		0			0
$577$	−31.8850	−	118.997i	−0.0552600	−	0.206233i	0.932776	−	0.360457i	$-0.117379\pi$
$577$	−31.8850	−	118.997i	−0.0552600	−	0.206233i	−0.988036	+	0.154223i	$0.950712\pi$
$578$	7.76154	+	16.6447i	0.0134283	+	0.0287970i
$579$		0			0
$580$	864.861	−	24.7794i	1.49114	−	0.0427231i
$581$	192.981	+	161.930i	0.332154	+	0.278710i
$582$		0			0
$583$	31.4354	+	67.4133i	0.0539200	+	0.115632i
$584$	−2.91015	−	1.68018i	−0.00498313	−	0.00287701i
$585$		0			0
$586$	2.43828	+	4.22322i	0.00416089	+	0.00720687i
$587$	245.325	+	171.778i	0.417930	+	0.292638i	0.763564	−	0.645732i	$-0.223447\pi$
$587$	245.325	+	171.778i	0.417930	+	0.292638i	−0.345635	+	0.938369i	$0.612336\pi$
$588$		0			0
$589$	56.4062	+	154.975i	0.0957661	+	0.263115i
$590$	−0.934371	+	3.93461i	−0.00158368	+	0.00666883i
$591$		0			0
$592$	−19.6490	+	224.589i	−0.0331909	+	0.379373i
$593$	39.9297	+	39.9297i	0.0673351	+	0.0673351i	0.739972	−	0.672637i	$-0.234839\pi$
$593$	39.9297	+	39.9297i	0.0673351	+	0.0673351i	−0.672637	+	0.739972i	$0.734839\pi$
$594$		0			0
$595$	379.857	+	427.225i	0.638415	+	0.718025i
$596$	55.1235	−	46.2541i	0.0924890	−	0.0776075i
$597$		0			0
$598$	−4.31859	+	3.02391i	−0.00722172	+	0.00505671i
$599$	348.730	+	958.128i	0.582187	+	1.59955i	0.784435	+	0.620212i	$0.212953\pi$
$599$	348.730	+	958.128i	0.582187	+	1.59955i	−0.202247	+	0.979334i	$0.564825\pi$
$600$		0			0
$601$	−45.2302	−	256.513i	−0.0752582	−	0.426810i	−0.999037	−	0.0438830i	$-0.986027\pi$
$601$	−45.2302	−	256.513i	−0.0752582	−	0.426810i	0.923779	−	0.382927i	$-0.125084\pi$
$602$	−7.65617	−	2.05147i	−0.0127179	−	0.00340775i
$603$		0			0
$604$	−49.5059	−	28.5823i	−0.0819635	−	0.0473216i
$605$	508.353	−	201.694i	0.840253	−	0.333378i
$606$		0			0
$607$	105.011	−	9.18728i	0.173000	−	0.0151356i	−0.000326450	−	1.00000i	$-0.500104\pi$
$607$	105.011	−	9.18728i	0.173000	−	0.0151356i	0.173327	+	0.984864i	$0.444548\pi$
$608$	−0.378842	−	4.33019i	−0.000623096	−	0.00712202i
$609$		0			0
$610$	1.13757	−	2.63396i	0.00186487	−	0.00431796i
$611$	−280.301	+	485.495i	−0.458758	+	0.794591i
$612$		0			0
$613$	137.987	−	514.974i	0.225101	−	0.840087i	−0.757263	−	0.653110i	$-0.773464\pi$
$613$	137.987	−	514.974i	0.225101	−	0.840087i	0.982364	−	0.186978i	$-0.0598693\pi$
$614$	12.0796	−	2.12996i	0.0196736	−	0.00346899i
$615$		0			0
$616$	2.64587	−	0.963018i	0.00429524	−	0.00156334i
$617$	−379.147	−	541.478i	−0.614501	−	0.877598i	0.384462	−	0.923141i	$-0.374387\pi$
$617$	−379.147	−	541.478i	−0.614501	−	0.877598i	−0.998962	+	0.0455428i	$0.985498\pi$
$618$		0			0
$619$	316.843	+	377.599i	0.511862	+	0.610014i	0.958637	−	0.284633i	$-0.0918717\pi$
$619$	316.843	+	377.599i	0.511862	+	0.610014i	−0.446774	+	0.894647i	$0.647427\pi$
$620$	−673.088	−	757.022i	−1.08563	−	1.22100i
$621$		0			0
$622$	−3.85244	+	3.85244i	−0.00619363	+	0.00619363i
$623$	−279.899	−	24.4879i	−0.449275	−	0.0393065i
$624$		0			0
$625$	−248.572	+	573.443i	−0.397715	+	0.917509i
$626$	−10.8492	+	3.94877i	−0.0173309	+	0.00630794i
$627$		0			0
$628$	−163.580	+	233.617i	−0.260478	+	0.372001i
$629$	−376.145	+	217.167i	−0.598004	+	0.345258i
$630$		0			0
$631$	22.9586	−	39.7654i	0.0363844	−	0.0630197i	−0.847260	−	0.531179i	$-0.821749\pi$
$631$	22.9586	−	39.7654i	0.0363844	−	0.0630197i	0.883644	+	0.468159i	$0.155083\pi$
$632$	19.6872	−	9.18030i	0.0311506	−	0.0145258i
$633$		0			0
$634$	−1.38687	+	1.65281i	−0.00218750	+	0.00260696i
$635$	68.4217	−	72.4581i	0.107751	−	0.114107i
$636$		0			0
$637$	378.735	−	176.607i	0.594560	−	0.277248i
$638$	3.96393	−	1.06213i	0.00621306	−	0.00166478i
$639$		0			0
$640$	15.9617	+	31.8177i	0.0249402	+	0.0497152i
$641$	33.0604	+	187.495i	0.0515763	+	0.292504i	0.999676	−	0.0254707i	$-0.00810844\pi$
$641$	33.0604	+	187.495i	0.0515763	+	0.292504i	−0.948099	+	0.317975i	$0.896997\pi$
$642$		0			0
$643$	−690.791	−	322.121i	−1.07432	−	0.500966i	−0.196774	−	0.980449i	$-0.563046\pi$
$643$	−690.791	−	322.121i	−1.07432	−	0.500966i	−0.877551	+	0.479483i	$0.840824\pi$
$644$	233.467	+	41.1666i	0.362527	+	0.0639233i
$645$		0			0
$646$	2.13764	−	1.79370i	0.00330904	−	0.00277662i
$647$	157.925	−	157.925i	0.244088	−	0.244088i	−0.574451	−	0.818539i	$-0.694784\pi$
$647$	157.925	−	157.925i	0.244088	−	0.244088i	0.818539	+	0.574451i	$0.194784\pi$
$648$		0			0
$649$		−	99.0882i		−	0.152678i
$650$	−4.52831	−	6.89834i	−0.00696663	−	0.0106128i
$651$		0			0
$652$	−439.351	−	627.458i	−0.673851	−	0.962359i
$653$	−678.708	−	316.487i	−1.03937	−	0.484665i	−0.173446	−	0.984843i	$-0.555490\pi$
$653$	−678.708	−	316.487i	−1.03937	−	0.484665i	−0.865923	+	0.500178i	$0.833268\pi$
$654$		0			0
$655$	140.030	+	110.823i	0.213787	+	0.169195i
$656$	−101.000	−	174.937i	−0.153963	−	0.266672i
$657$		0			0
$658$	−4.71352	+	1.26299i	−0.00716341	+	0.00191943i
$659$	−80.1439	+	220.194i	−0.121614	+	0.334133i	−0.985529	−	0.169505i	$-0.945783\pi$
$659$	−80.1439	+	220.194i	−0.121614	+	0.334133i	0.863915	+	0.503638i	$0.168005\pi$
$660$		0			0
$661$	−544.613	−	456.985i	−0.823923	−	0.691354i	0.129964	−	0.991519i	$-0.458514\pi$
$661$	−544.613	−	456.985i	−0.823923	−	0.691354i	−0.953887	+	0.300165i	$0.902958\pi$
$662$	10.9683	−	0.959600i	0.0165684	−	0.00144955i
$663$		0			0
$664$	−5.16705	+	14.1964i	−0.00778170	+	0.0213800i
$665$	33.2193	−	50.4585i	0.0499538	−	0.0758774i
$666$		0			0
$667$	667.560	+	178.872i	1.00084	+	0.268174i
$668$	186.883	−	266.897i	0.279765	−	0.399546i
$669$		0			0
$670$	0.903685	+	0.487782i	0.00134878	+	0.000728033i
$671$	−12.2074	+	69.2318i	−0.0181929	+	0.103177i
$672$		0			0
$673$	609.916	+	53.3607i	0.906265	+	0.0792879i	0.530750	−	0.847529i	$-0.321910\pi$
$673$	609.916	+	53.3607i	0.906265	+	0.0792879i	0.375515	+	0.926816i	$0.377466\pi$
$674$			12.8416i			0.0190529i
$675$		0			0
$676$	113.049			0.167232
$677$	−18.3088	+	209.271i	−0.0270441	+	0.309115i	0.970610	+	0.240658i	$0.0773632\pi$
$677$	−18.3088	+	209.271i	−0.0270441	+	0.309115i	−0.997654	+	0.0684572i	$0.978192\pi$
$678$		0			0
$679$	−317.712	−	56.0211i	−0.467911	−	0.0825053i
$680$	−16.2842	+	30.1687i	−0.0239473	+	0.0443657i
$681$		0			0
$682$	−3.93571	−	2.75581i	−0.00577084	−	0.00404078i
$683$	281.554	−	1050.77i	0.412232	−	1.53847i	−0.378085	−	0.925771i	$-0.623417\pi$
$683$	281.554	−	1050.77i	0.412232	−	1.53847i	0.790317	−	0.612699i	$-0.209916\pi$
$684$		0			0
$685$	396.156	+	260.809i	0.578330	+	0.380743i
$686$	8.17290	+	2.97469i	0.0119138	+	0.00433628i
$687$		0			0
$688$	106.976	+	1222.74i	0.155489	+	1.77724i
$689$	166.397	−	198.304i	0.241504	−	0.287814i
$690$		0			0
$691$	1047.01	+	381.079i	1.51520	+	0.551489i	0.959945	−	0.280189i	$-0.0903971\pi$
$691$	1047.01	+	381.079i	1.51520	+	0.551489i	0.555258	+	0.831678i	$0.312619\pi$
$692$	100.317	+	374.388i	0.144967	+	0.541023i
$693$		0			0
$694$	9.25592	−	5.34391i	0.0133371	−	0.00770016i
$695$	−481.897	+	608.901i	−0.693377	+	0.876116i
$696$		0			0
$697$	164.467	−	352.700i	0.235964	−	0.506026i
$698$	9.45340	−	6.61934i	0.0135436	−	0.00948330i
$699$		0			0
$700$	−75.3590	+	363.330i	−0.107656	+	0.519042i
$701$	598.694			0.854056			0.427028	−	0.904238i	$-0.359560\pi$
$701$	598.694			0.854056			0.427028	+	0.904238i	$0.359560\pi$
$702$		0			0
$703$	32.4550	+	32.4550i	0.0461664	+	0.0461664i
$704$	−140.066	−	166.924i	−0.198958	−	0.237108i
$705$		0			0
$706$	2.47172	−	14.0178i	0.00350102	−	0.0198553i
$707$	122.388	−	262.462i	0.173109	−	0.371233i
$708$		0			0
$709$	−277.380	+	48.9096i	−0.391227	+	0.0689839i	−0.365802	−	0.930693i	$-0.619205\pi$
$709$	−277.380	+	48.9096i	−0.391227	+	0.0689839i	−0.0254256	+	0.999677i	$0.508094\pi$
$710$	11.1452	−	5.59113i	0.0156975	−	0.00787483i
$711$		0			0
$712$	−4.36096	−	16.2753i	−0.00612495	−	0.0228586i
$713$	−341.957	−	733.328i	−0.479603	−	1.02851i
$714$		0			0
$715$	147.005	+	138.816i	0.205601	+	0.194148i
$716$	652.958	+	547.897i	0.911953	+	0.765219i
$717$		0			0
$718$	7.72666	+	16.5699i	0.0107614	+	0.0230778i
$719$	836.274	+	482.823i	1.16311	+	0.671520i	0.952047	−	0.305953i	$-0.0989750\pi$
$719$	836.274	+	482.823i	1.16311	+	0.671520i	0.211060	+	0.977473i	$0.432308\pi$
$720$		0			0
$721$	240.585	+	416.705i	0.333682	+	0.577954i
$722$	7.98627	+	5.59204i	0.0110613	+	0.00774521i
$723$		0			0
$724$	−305.118	−	838.304i	−0.421434	−	1.15788i
$725$	−311.166	+	1036.01i	−0.429195	+	1.42898i
$726$		0			0
$727$	22.6711	−	259.132i	0.0311845	−	0.356441i	−0.964531	−	0.263970i	$-0.914968\pi$
$727$	22.6711	−	259.132i	0.0311845	−	0.356441i	0.995715	−	0.0924706i	$-0.0294764\pi$
$728$	−6.92906	−	6.92906i	−0.00951794	−	0.00951794i
$729$		0			0
$730$	1.56969	−	1.39565i	0.00215026	−	0.00191185i
$731$	−1811.45	+	1519.98i	−2.47804	+	2.07932i
$732$		0			0
$733$	−272.467	+	190.784i	−0.371715	+	0.260278i	−0.744475	−	0.667650i	$-0.767300\pi$
$733$	−272.467	+	190.784i	−0.371715	+	0.260278i	0.372760	+	0.927928i	$0.378411\pi$
$734$	−2.45450	−	6.74367i	−0.00334400	−	0.00918756i
$735$		0			0
$736$	3.70322	+	21.0020i	0.00503156	+	0.0285354i
$737$	−24.3047	−	6.51243i	−0.0329779	−	0.00883640i
$738$		0			0
$739$	−955.178	−	551.472i	−1.29253	−	0.746241i	−0.313426	−	0.949613i	$-0.601477\pi$
$739$	−955.178	−	551.472i	−1.29253	−	0.746241i	−0.979102	+	0.203372i	$0.934810\pi$
$740$	−258.812	−	111.777i	−0.349745	−	0.151050i
$741$		0			0
$742$	2.24475	−	0.196390i	0.00302527	−	0.000264677i
$743$	111.043	+	1269.23i	0.149453	+	1.70825i	0.587436	+	0.809270i	$0.300137\pi$
$743$	111.043	+	1269.23i	0.149453	+	1.70825i	−0.437984	+	0.898983i	$0.644307\pi$
$744$		0			0
$745$	33.1786	+	83.6241i	0.0445351	+	0.112247i
$746$	9.15258	−	15.8527i	0.0122689	−	0.0212503i
$747$		0			0
$748$	108.695	−	405.656i	0.145314	−	0.542321i
$749$	−522.510	+	92.1326i	−0.697610	+	0.123007i
$750$		0			0
$751$	315.133	−	114.699i	0.419618	−	0.152728i	−0.123577	−	0.992335i	$-0.539437\pi$
$751$	315.133	−	114.699i	0.419618	−	0.152728i	0.543195	+	0.839607i	$0.317214\pi$
$752$	433.428	+	618.999i	0.576367	+	0.823137i
$753$		0			0
$754$	−9.18029	−	10.9406i	−0.0121754	−	0.0145101i
$755$	53.4106	−	47.4888i	0.0707426	−	0.0628991i
$756$		0			0
$757$	218.550	−	218.550i	0.288705	−	0.288705i	−0.547863	−	0.836568i	$-0.684559\pi$
$757$	218.550	−	218.550i	0.288705	−	0.288705i	0.836568	+	0.547863i	$0.184559\pi$
$758$	−14.2309	−	1.24505i	−0.0187743	−	0.00164254i
$759$		0			0
$760$	3.52483	+	0.837058i	0.00463794	+	0.00110139i
$761$	−586.465	+	213.456i	−0.770651	+	0.280494i	−0.697269	−	0.716810i	$-0.745601\pi$
$761$	−586.465	+	213.456i	−0.770651	+	0.280494i	−0.0733821	+	0.997304i	$0.523379\pi$
$762$		0			0
$763$	−400.154	+	571.479i	−0.524448	+	0.748990i
$764$	−541.918	+	312.877i	−0.709317	+	0.409524i
$765$		0			0
$766$	−6.34825	+	10.9955i	−0.00828754	+	0.0143544i
$767$	−312.539	+	145.739i	−0.407482	+	0.190012i
$768$		0			0
$769$	−267.715	+	319.050i	−0.348134	+	0.414890i	−0.911489	−	0.411325i	$-0.865066\pi$
$769$	−267.715	+	319.050i	−0.348134	+	0.414890i	0.563355	+	0.826215i	$0.309510\pi$
$770$	0.0504047	+	1.75925i	6.54606e−5	+	0.00228473i
$771$		0			0
$772$	−833.276	+	388.563i	−1.07937	+	0.503320i
$773$	−258.350	+	69.2246i	−0.334217	+	0.0895531i	−0.422025	−	0.906584i	$-0.638680\pi$
$773$	−258.350	+	69.2246i	−0.334217	+	0.0895531i	0.0878080	+	0.996137i	$0.472014\pi$
$774$		0			0
$775$	1163.34	−	500.588i	1.50108	−	0.645919i
$776$	−3.35955	−	19.0530i	−0.00432932	−	0.0245528i
$777$		0			0
$778$	14.7450	+	6.87569i	0.0189524	+	0.00883764i
$779$	−40.4999	−	7.14122i	−0.0519896	−	0.00916717i
$780$		0			0
$781$	−234.042	+	196.385i	−0.299670	+	0.251453i
$782$	−9.68085	+	9.68085i	−0.0123796	+	0.0123796i
$783$		0			0
$784$		−	563.288i		−	0.718479i
$785$	−212.796	−	286.100i	−0.271077	−	0.364459i
$786$		0			0
$787$	−78.7629	−	112.485i	−0.100080	−	0.142929i	0.765989	−	0.642854i	$-0.222250\pi$
$787$	−78.7629	−	112.485i	−0.100080	−	0.142929i	−0.866069	+	0.499925i	$0.833361\pi$
$788$	245.492	+	114.475i	0.311539	+	0.145273i
$789$		0			0
$790$	1.57028	+	13.4867i	0.00198770	+	0.0170718i
$791$	−265.073	−	459.121i	−0.335112	−	0.580430i
$792$		0			0
$793$	236.322	−	63.3223i	0.298010	−	0.0798516i
$794$	−4.55209	+	12.5068i	−0.00573311	+	0.0157516i
$795$		0			0
$796$	106.293	+	89.1901i	0.133533	+	0.112048i
$797$	−275.890	+	24.1372i	−0.346160	+	0.0302851i	−0.258910	−	0.965901i	$-0.583363\pi$
$797$	−275.890	+	24.1372i	−0.346160	+	0.0302851i	−0.0872500	+	0.996186i	$0.527808\pi$
$798$		0			0
$799$	−497.917	+	1368.02i	−0.623175	+	1.71216i
$800$	−33.0316	+	4.80836i	−0.0412894	+	0.00601045i
$801$		0			0
$802$	−16.5132	−	4.42469i	−0.0205900	−	0.00551706i
$803$	−29.5192	+	42.1579i	−0.0367612	+	0.0525004i
$804$		0			0
$805$	−140.785	+	260.823i	−0.174888	+	0.324004i
$806$	−2.90359	+	16.4671i	−0.00360247	+	0.0204306i
$807$		0			0
$808$	17.3007	+	1.51362i	0.0214118	+	0.00187329i
$809$			977.734i			1.20857i	0.796768	+	0.604286i	$0.206541\pi$
$809$			977.734i			1.20857i	−0.796768	+	0.604286i	$0.793459\pi$
$810$		0			0
$811$	601.353			0.741496			0.370748	−	0.928734i	$-0.379101\pi$
$811$	601.353			0.741496			0.370748	+	0.928734i	$0.379101\pi$
$812$	−55.9734	+	639.779i	−0.0689328	+	0.787905i
$813$		0			0
$814$	−1.31683	−	0.232193i	−0.00161773	−	0.000285250i
$815$	917.556	−	274.253i	1.12584	−	0.336507i
$816$		0			0
$817$	204.696	+	143.329i	0.250545	+	0.175434i
$818$	3.12077	−	11.6469i	0.00381513	−	0.0142382i
$819$		0			0
$820$	247.401	−	50.9694i	0.301709	−	0.0621578i
$821$	1124.15	+	409.157i	1.36924	+	0.498364i	0.918900	−	0.394490i	$-0.129079\pi$
$821$	1124.15	+	409.157i	1.36924	+	0.498364i	0.450345	+	0.892855i	$0.351301\pi$
$822$		0			0
$823$	−28.7895	−	329.066i	−0.0349812	−	0.399837i	−0.993419	−	0.114536i	$-0.963462\pi$
$823$	−28.7895	−	329.066i	−0.0349812	−	0.399837i	0.958438	−	0.285301i	$-0.0920936\pi$
$824$	−18.5479	+	22.1046i	−0.0225096	+	0.0268259i
$825$		0			0
$826$	−2.82073	−	1.02666i	−0.00341493	−	0.00124293i
$827$	−24.5489	−	91.6177i	−0.0296843	−	0.110783i	0.949494	−	0.313785i	$-0.101597\pi$
$827$	−24.5489	−	91.6177i	−0.0296843	−	0.110783i	−0.979178	+	0.203002i	$0.934930\pi$
$828$		0			0
$829$	964.314	−	556.747i	1.16323	−	0.671589i	0.211151	−	0.977454i	$-0.432279\pi$
$829$	964.314	−	556.747i	1.16323	−	0.671589i	0.952075	+	0.305865i	$0.0989456\pi$
$830$	−7.40468	−	5.86022i	−0.00892130	−	0.00706051i
$831$		0			0
$832$	−320.494	+	687.303i	−0.385210	+	0.826085i
$833$	888.945	−	622.446i	1.06716	−	0.747234i
$834$		0			0
$835$	243.110	+	326.857i	0.291150	+	0.391446i
$836$	−44.3799			−0.0530860
$837$		0			0
$838$	−13.4850	−	13.4850i	−0.0160918	−	0.0160918i
$839$	−148.555	−	177.041i	−0.177062	−	0.211015i	0.670213	−	0.742169i	$-0.266203\pi$
$839$	−148.555	−	177.041i	−0.177062	−	0.211015i	−0.847275	+	0.531154i	$0.821758\pi$
$840$		0			0
$841$	−179.070	+	1015.56i	−0.212925	+	1.20756i
$842$	0.294606	−	0.631784i	0.000349888	−	0.000750337i
$843$		0			0
$844$	−99.4016	+	17.5272i	−0.117774	+	0.0207668i
$845$	−44.5171	+	134.145i	−0.0526829	+	0.158751i
$846$		0			0
$847$	105.067	+	392.117i	0.124047	+	0.462948i
$848$	−147.467	−	316.245i	−0.173900	−	0.372930i
$849$		0			0
$850$	−14.6916	−	15.5999i	−0.0172842	−	0.0183529i
$851$	−172.503	−	144.748i	−0.202707	−	0.170091i
$852$		0			0
$853$	207.570	+	445.135i	0.243341	+	0.521847i	0.989607	−	0.143802i	$-0.0459328\pi$
$853$	207.570	+	445.135i	0.243341	+	0.521847i	−0.746265	+	0.665649i	$0.768155\pi$
$854$	1.84433	+	1.06483i	0.00215964	+	0.00124687i
$855$		0			0
$856$	−15.9090	−	27.5552i	−0.0185853	−	0.0321906i
$857$	−422.738	−	296.004i	−0.493276	−	0.345396i	0.300322	−	0.953838i	$-0.402906\pi$
$857$	−422.738	−	296.004i	−0.493276	−	0.345396i	−0.793598	+	0.608442i	$0.791795\pi$
$858$		0			0
$859$	−269.812	−	741.302i	−0.314100	−	0.862982i	−0.991818	−	0.127660i	$-0.959253\pi$
$859$	−269.812	−	741.302i	−0.314100	−	0.862982i	0.677718	−	0.735322i	$-0.262969\pi$
$860$	−1493.33	−	354.629i	−1.73643	−	0.412359i
$861$		0			0
$862$	−0.308158	+	3.52226i	−0.000357492	+	0.00408615i
$863$	−956.689	−	956.689i	−1.10856	−	1.10856i	−0.993340	−	0.115222i	$-0.963242\pi$
$863$	−956.689	−	956.689i	−1.10856	−	1.10856i	−0.115222	−	0.993340i	$-0.536758\pi$
$864$		0			0
$865$	−483.755	−	28.3917i	−0.559255	−	0.0328228i
$866$	6.26450	−	5.25654i	0.00723384	−	0.00606991i
$867$		0			0
$868$	615.924	−	431.274i	0.709590	−	0.496860i
$869$	−113.786	−	312.625i	−0.130939	−	0.359752i
$870$		0			0
$871$	15.2063	+	86.2392i	0.0174584	+	0.0990117i
$872$	−40.4119	−	10.8283i	−0.0463439	−	0.0124178i
$873$		0			0
$874$	1.25294	+	0.723387i	0.00143357	+	0.000827674i
$875$	−401.455	−	232.496i	−0.458805	−	0.265709i
$876$		0			0
$877$	−849.409	+	74.3137i	−0.968539	+	0.0847362i	−0.560434	−	0.828199i	$-0.689366\pi$
$877$	−849.409	+	74.3137i	−0.968539	+	0.0847362i	−0.408105	+	0.912935i	$0.633810\pi$
$878$	0.541839	+	6.19325i	0.000617129	+	0.00705382i
$879$		0			0
$880$	253.328	−	100.510i	0.287873	−	0.114216i
$881$	529.633	−	917.351i	0.601172	−	1.04126i	−0.391472	−	0.920190i	$-0.628034\pi$
$881$	529.633	−	917.351i	0.601172	−	1.04126i	0.992644	−	0.121071i	$-0.0386328\pi$
$882$		0			0
$883$	199.854	−	745.867i	0.226336	−	0.844696i	−0.755529	−	0.655115i	$-0.772620\pi$
$883$	199.854	−	745.867i	0.226336	−	0.844696i	0.981865	−	0.189581i	$-0.0607131\pi$
$884$	−1439.37	+	253.800i	−1.62825	+	0.287104i
$885$		0			0
$886$	0.542984	−	0.197630i	0.000612849	−	0.000223059i
$887$	590.142	+	842.810i	0.665323	+	0.950180i	0.999969	+	0.00783619i	$0.00249436\pi$
$887$	590.142	+	842.810i	0.665323	+	0.950180i	−0.334646	+	0.942344i	$0.608617\pi$
$888$		0			0
$889$	47.5489	+	56.6666i	0.0534859	+	0.0637420i
$890$	10.5138	+	0.617060i	0.0118133	+	0.000693326i
$891$		0			0
$892$	−955.573	+	955.573i	−1.07127	+	1.07127i
$893$	153.258	+	13.4083i	0.171621	+	0.0150149i
$894$		0			0
$895$	−907.264	+	559.051i	−1.01370	+	0.624638i
$896$	−24.8290	+	9.03703i	−0.0277110	+	0.0100860i
$897$		0			0
$898$	11.9788	−	17.1076i	0.0133395	−	0.0190507i
$899$	1898.30	−	1095.98i	2.11157	−	1.21911i
$900$		0			0
$901$	336.123	−	582.181i	0.373055	−	0.646150i
$902$	1.08583	−	0.506330i	0.00120380	−	0.000561342i
$903$		0			0
$904$	20.4359	−	24.3545i	0.0226061	−	0.0269409i
$905$	1114.89	−	31.9430i	1.23192	−	0.0352962i
$906$		0			0
$907$	1212.97	−	565.619i	1.33735	−	0.623615i	0.383398	−	0.923583i	$-0.374754\pi$
$907$	1212.97	−	565.619i	1.33735	−	0.623615i	0.953949	+	0.299968i	$0.0969760\pi$
$908$	1339.81	−	359.000i	1.47556	−	0.395375i
$909$		0			0
$910$	5.47479	−	2.74649i	0.00601625	−	0.00301812i
$911$	24.1338	+	136.870i	0.0264916	+	0.150241i	0.995184	−	0.0980217i	$-0.0312514\pi$
$911$	24.1338	+	136.870i	0.0264916	+	0.150241i	−0.968693	+	0.248263i	$0.920140\pi$
$912$		0			0
$913$	209.699	+	97.7841i	0.229681	+	0.107102i
$914$	−14.3058	−	2.52250i	−0.0156519	−	0.00275985i
$915$		0			0
$916$	897.447	−	753.047i	0.979745	−	0.822104i
$917$	−93.7292	+	93.7292i	−0.102213	+	0.102213i
$918$		0			0
$919$			995.456i			1.08319i	0.840638	+	0.541597i	$0.182180\pi$
$919$			995.456i			1.08319i	−0.840638	+	0.541597i	$0.817820\pi$
$920$	−17.5857	−	2.58393i	−0.0191149	−	0.00280862i
$921$		0			0
$922$	−10.3777	−	14.8209i	−0.0112556	−	0.0160747i
$923$	963.656	+	449.360i	1.04405	+	0.486848i
$924$		0			0
$925$	234.552	−	263.092i	0.253570	−	0.284423i
$926$	−2.81556	−	4.87670i	−0.00304056	−	0.00526641i
$927$		0			0
$928$	−55.8039	+	14.9526i	−0.0601335	+	0.0161127i
$929$	475.730	−	1307.06i	0.512089	−	1.40695i	−0.366968	−	0.930234i	$-0.619604\pi$
$929$	475.730	−	1307.06i	0.512089	−	1.40695i	0.879056	−	0.476718i	$-0.158174\pi$
$930$		0			0
$931$	−87.8489	−	73.7140i	−0.0943598	−	0.0791772i
$932$	−1190.07	+	104.118i	−1.27690	+	0.111715i
$933$		0			0
$934$	−0.334048	+	0.917788i	−0.000357653	+	0.000982642i
$935$	438.552	+	288.720i	0.469039	+	0.308791i
$936$		0			0
$937$	−84.0579	−	22.5232i	−0.0897096	−	0.0240376i	0.213685	−	0.976903i	$-0.431453\pi$
$937$	−84.0579	−	22.5232i	−0.0897096	−	0.0240376i	−0.303395	+	0.952865i	$0.598120\pi$
$938$	−0.437212	+	0.624403i	−0.000466111	+	0.000665675i
$939$		0			0
$940$	−905.362	+	270.608i	−0.963151	+	0.287881i
$941$	233.836	−	1326.15i	0.248498	−	1.40930i	−0.563729	−	0.825959i	$-0.690634\pi$
$941$	233.836	−	1326.15i	0.248498	−	1.40930i	0.812227	−	0.583341i	$-0.198255\pi$
$942$		0			0
$943$	200.999	+	17.5851i	0.213149	+	0.0186481i
$944$			464.836i			0.492411i
$945$		0			0
$946$	−7.27993			−0.00769548
$947$	116.040	−	1326.35i	0.122535	−	1.40058i	−0.647252	−	0.762276i	$-0.724082\pi$
$947$	116.040	−	1326.35i	0.122535	−	1.40058i	0.769787	−	0.638301i	$-0.220363\pi$
$948$		0			0
$949$	176.389	+	31.1022i	0.185868	+	0.0327736i
$950$	−1.19053	+	1.92630i	−0.00125319	+	0.00202768i
$951$		0			0
$952$	−20.8451	−	14.5959i	−0.0218961	−	0.0153318i
$953$	47.5657	−	177.518i	0.0499115	−	0.186272i	−0.936469	−	0.350749i	$-0.885927\pi$
$953$	47.5657	−	177.518i	0.0499115	−	0.186272i	0.986381	+	0.164477i	$0.0525936\pi$
$954$		0			0
$955$	−157.862	−	766.250i	−0.165301	−	0.802356i
$956$	715.616	+	260.463i	0.748553	+	0.272451i
$957$		0			0
$958$	1.96280	+	22.4349i	0.00204885	+	0.0234184i
$959$	−226.299	+	269.692i	−0.235974	+	0.281222i
$960$		0			0
$961$	−1508.51	−	549.051i	−1.56972	−	0.571333i
$962$	1.20443	+	4.49501i	0.00125201	+	0.00467256i
$963$		0			0
$964$	815.946	−	471.087i	0.846417	−	0.488679i
$965$	−132.940	−	1141.78i	−0.137761	−	1.18319i
$966$		0			0
$967$	80.4459	−	172.517i	0.0831913	−	0.178404i	−0.860312	−	0.509768i	$-0.829731\pi$
$967$	80.4459	−	172.517i	0.0831913	−	0.178404i	0.943503	+	0.331364i	$0.107509\pi$
$968$	−19.9419	+	13.9635i	−0.0206011	+	0.0144251i
$969$		0			0
$970$	11.9645	+	1.75799i	0.0123346	+	0.00181236i
$971$	544.835			0.561107			0.280554	−	0.959838i	$-0.409482\pi$
$971$	544.835			0.561107			0.280554	+	0.959838i	$0.409482\pi$
$972$		0			0
$973$	−407.568	−	407.568i	−0.418877	−	0.418877i
$974$	−1.91691	−	2.28449i	−0.00196808	−	0.00234547i
$975$		0			0
$976$	57.2667	−	324.775i	0.0586749	−	0.332762i
$977$	321.165	−	688.740i	0.328726	−	0.704954i	−0.670595	−	0.741824i	$-0.733961\pi$
$977$	321.165	−	688.740i	0.328726	−	0.704954i	0.999320	+	0.0368699i	$0.0117387\pi$
$978$		0			0
$979$	−254.136	+	44.8111i	−0.259588	+	0.0457723i
$980$	668.531	+	221.857i	0.682174	+	0.226385i
$981$		0			0
$982$	2.60701	+	9.72950i	0.00265480	+	0.00990784i
$983$	132.243	+	283.595i	0.134530	+	0.288499i	0.962019	−	0.272981i	$-0.0880097\pi$
$983$	132.243	+	283.595i	0.134530	+	0.288499i	−0.827490	+	0.561481i	$0.810232\pi$
$984$		0			0
$985$	−232.508	+	246.225i	−0.236049	+	0.249974i
$986$	−28.4115	−	23.8401i	−0.0288149	−	0.0241786i
$987$		0			0
$988$	65.2742	+	139.981i	0.0660670	+	0.141681i
$989$	−1061.75	−	613.001i	−1.07356	−	0.619819i
$990$		0			0
$991$	−633.858	−	1097.87i	−0.639614	−	1.10784i	−0.985517	−	0.169574i	$-0.945761\pi$
$991$	−633.858	−	1097.87i	−0.639614	−	1.10784i	0.345903	−	0.938270i	$-0.387573\pi$
$992$	55.4067	+	38.7962i	0.0558535	+	0.0391090i
$993$		0			0
$994$	3.16552	+	8.69721i	0.00318463	+	0.00874971i
$995$	−147.690	+	91.0059i	−0.148432	+	0.0914632i
$996$		0			0
$997$	69.9231	−	799.225i	0.0701335	−	0.801630i	−0.876937	−	0.480605i	$-0.840417\pi$
$997$	69.9231	−	799.225i	0.0701335	−	0.801630i	0.947071	−	0.321025i	$-0.104027\pi$
$998$	−4.67651	−	4.67651i	−0.00468588	−	0.00468588i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.s.a.118.17		408
3.2	odd	2		135.3.r.a.103.18	yes	408
5.2	odd	4	inner	405.3.s.a.37.17		408
15.2	even	4		135.3.r.a.22.18	✓	408
27.11	odd	18		135.3.r.a.43.18	yes	408
27.16	even	9	inner	405.3.s.a.208.17		408
135.92	even	36		135.3.r.a.97.18	yes	408
135.97	odd	36	inner	405.3.s.a.127.17		408

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.3.r.a.22.18	✓	408	15.2	even	4
135.3.r.a.43.18	yes	408	27.11	odd	18
135.3.r.a.97.18	yes	408	135.92	even	36
135.3.r.a.103.18	yes	408	3.2	odd	2
405.3.s.a.37.17		408	5.2	odd	4	inner
405.3.s.a.118.17		408	1.1	even	1	trivial
405.3.s.a.127.17		408	135.97	odd	36	inner
405.3.s.a.208.17		408	27.16	even	9	inner

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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	405.s (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.00242499 - 0.0277177i) q^{2} +(3.93847 + 0.694458i) q^{4} +(-2.37496 + 4.39995i) q^{5} +(-3.04016 - 2.12874i) q^{7} +(0.0576046 - 0.214983i) q^{8} +(0.116197 + 0.0764983i) q^{10} +(-3.20314 - 1.16585i) q^{11} +(1.03393 + 11.8179i) q^{13} +(-0.0663761 + 0.0791040i) q^{14} +(15.0264 + 5.46915i) q^{16} +(7.97341 + 29.7572i) q^{17} +(2.81936 - 1.62776i) q^{19} +(-12.4093 + 15.6798i) q^{20} +(-0.0400822 + 0.0859566i) q^{22} +(-13.0837 + 9.16134i) q^{23} +(-13.7191 - 20.8994i) q^{25} +0.330073 q^{26} +(-10.4952 - 10.4952i) q^{28} +(-27.8129 - 33.1461i) q^{29} +(-8.79682 + 49.8892i) q^{31} +(0.564275 - 1.21009i) q^{32} +(0.844136 - 0.148844i) q^{34} +(16.5866 - 8.32085i) q^{35} +(3.64899 + 13.6182i) q^{37} +(-0.0382809 - 0.0820936i) q^{38} +(0.809107 + 0.764035i) q^{40} +(-9.67690 - 8.11988i) q^{41} +(32.4393 + 69.5664i) q^{43} +(-11.8058 - 6.81610i) q^{44} +(0.222203 + 0.384868i) q^{46} +(38.7099 + 27.1050i) q^{47} +(-12.0480 - 33.1015i) q^{49} +(-0.612553 + 0.329582i) q^{50} +(-4.13494 + 47.2625i) q^{52} +(-15.4300 - 15.4300i) q^{53} +(12.7370 - 11.3248i) q^{55} +(-0.632771 + 0.530958i) q^{56} +(-0.986180 + 0.690531i) q^{58} +(9.94222 + 27.3160i) q^{59} +(-3.58125 - 20.3103i) q^{61} +(1.36148 + 0.364808i) q^{62} +(55.3613 + 31.9628i) q^{64} +(-54.4538 - 23.5179i) q^{65} +(7.35361 - 0.643358i) q^{67} +(10.7379 + 122.735i) q^{68} +(-0.190413 - 0.479921i) q^{70} +(44.8146 - 77.6212i) q^{71} +(3.90769 - 14.5837i) q^{73} +(0.386314 - 0.0681177i) q^{74} +(12.2344 - 4.45295i) q^{76} +(7.25626 + 10.3630i) q^{77} +(62.7357 + 74.7655i) q^{79} +(-59.7510 + 53.1262i) q^{80} +(-0.248531 + 0.248531i) q^{82} +(-67.6198 - 5.91597i) q^{83} +(-149.867 - 35.5895i) q^{85} +(2.00689 - 0.730447i) q^{86} +(-0.435154 + 0.621464i) q^{88} +(65.5625 - 37.8526i) q^{89} +(22.0140 - 38.1293i) q^{91} +(-57.8921 + 26.9955i) q^{92} +(0.845159 - 1.00722i) q^{94} +(0.466183 + 16.2709i) q^{95} +(78.7818 - 36.7366i) q^{97} +(-0.946715 + 0.253672i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 408 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 6 q^{8} - 6 q^{10} + 60 q^{11} - 12 q^{13} - 24 q^{16} + 6 q^{17} + 300 q^{20} - 12 q^{22} + 156 q^{23} + 6 q^{25} + 48 q^{26} - 24 q^{28} - 24 q^{31} - 72 q^{32}+ \cdots + 1032 q^{98}+O(q^{100}) \) 408 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 6 * q^8 - 6 * q^10 + 60 * q^11 - 12 * q^13 - 24 * q^16 + 6 * q^17 + 300 * q^20 - 12 * q^22 + 156 * q^23 + 6 * q^25 + 48 * q^26 - 24 * q^28 - 24 * q^31 - 72 * q^32 - 156 * q^35 - 6 * q^37 + 252 * q^38 - 108 * q^40 + 384 * q^41 - 12 * q^43 - 12 * q^46 + 210 * q^47 - 276 * q^50 - 60 * q^52 - 516 * q^53 - 24 * q^55 - 912 * q^56 - 12 * q^58 - 312 * q^61 + 6 * q^62 - 420 * q^65 - 480 * q^67 + 540 * q^68 - 12 * q^70 + 12 * q^71 - 6 * q^73 - 216 * q^76 + 876 * q^77 + 1644 * q^80 - 24 * q^82 + 372 * q^83 - 12 * q^85 - 516 * q^86 + 348 * q^88 - 12 * q^91 - 2082 * q^92 - 198 * q^95 + 600 * q^97 + 1032 * q^98

Introduction

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