LMFDB - Embedded newform 507.2.q.b.16.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(16,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("507.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.q (of order $39$, degree $24$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$16$ over $\Q(\zeta_{39})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{39}]$

Embedding invariants

Embedding label			16.11
Character	$\chi$	$=$	507.16
Dual form			507.2.q.b.412.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.910598 + 0.0735111i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(-1.15032 - 0.186944i) q^{4} +(3.23408 + 2.86515i) q^{5} +(-0.730339 - 0.548814i) q^{6} +(-1.27940 + 1.33200i) q^{7} +(-2.80776 - 0.692051i) q^{8} +(0.428693 + 0.903450i) q^{9} +(2.73433 + 2.84674i) q^{10} +(0.424127 - 0.893828i) q^{11} +(0.872320 + 0.772808i) q^{12} +(-0.603766 + 3.55464i) q^{13} +(-1.26294 + 1.11886i) q^{14} +(-1.20209 - 4.15010i) q^{15} +(-0.295006 - 0.0984874i) q^{16} +(-2.25266 + 2.34527i) q^{17} +(0.323953 + 0.854194i) q^{18} +(-1.52309 + 2.63806i) q^{19} +(-3.18459 - 3.90041i) q^{20} +(1.79324 - 0.441995i) q^{21} +(0.451915 - 0.782740i) q^{22} +(-0.353527 - 0.612328i) q^{23} +(2.00321 + 2.08557i) q^{24} +(1.64754 + 13.5687i) q^{25} +(-0.811094 + 3.19246i) q^{26} +(0.120537 - 0.992709i) q^{27} +(1.72072 - 1.29304i) q^{28} +(7.23593 + 0.584145i) q^{29} +(-0.789543 - 3.86744i) q^{30} +(0.0198237 - 0.163263i) q^{31} +(5.05938 + 2.15560i) q^{32} +(-0.836189 + 0.528774i) q^{33} +(-2.22367 + 1.97000i) q^{34} +(-7.95405 + 0.642117i) q^{35} +(-0.324237 - 1.11939i) q^{36} +(6.37129 - 2.71455i) q^{37} +(-1.58085 + 2.29025i) q^{38} +(2.41013 - 2.68165i) q^{39} +(-7.09770 - 10.2828i) q^{40} +(-1.39615 - 0.882871i) q^{41} +(1.66542 - 0.270656i) q^{42} +(-0.668250 - 0.284715i) q^{43} +(-0.654976 + 0.948897i) q^{44} +(-1.20209 + 4.15010i) q^{45} +(-0.276909 - 0.583572i) q^{46} +(1.35726 - 3.57879i) q^{47} +(0.196698 + 0.240911i) q^{48} +(0.144511 + 3.58601i) q^{49} +(0.502795 + 12.4767i) q^{50} +(3.15739 - 0.778227i) q^{51} +(1.35904 - 3.97609i) q^{52} +(-4.44435 - 1.09543i) q^{53} +(0.182736 - 0.895098i) q^{54} +(3.93261 - 1.67553i) q^{55} +(4.51406 - 2.85452i) q^{56} +(2.69725 - 1.41563i) q^{57} +(6.54608 + 1.06384i) q^{58} +(1.63503 - 0.545855i) q^{59} +(0.606946 + 4.99865i) q^{60} +(3.00944 - 10.3898i) q^{61} +(0.0300530 - 0.147209i) q^{62} +(-1.75186 - 0.584858i) q^{63} +(4.99938 + 2.62388i) q^{64} +(-12.1372 + 9.76612i) q^{65} +(-0.800302 + 0.420031i) q^{66} +(-7.46708 + 1.21352i) q^{67} +(3.02970 - 2.27668i) q^{68} +(-0.0284702 + 0.706481i) q^{69} -7.29015 q^{70} +(-0.573933 + 14.2420i) q^{71} +(-0.578432 - 2.83335i) q^{72} +(-5.45049 - 7.89640i) q^{73} +(6.00123 - 2.00351i) q^{74} +(5.85951 - 12.3487i) q^{75} +(2.24520 - 2.74987i) q^{76} +(0.647949 + 1.70850i) q^{77} +(2.39179 - 2.26474i) q^{78} +(6.20589 - 16.3636i) q^{79} +(-0.671892 - 1.16375i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(-1.20643 - 0.906573i) q^{82} +(-5.66638 - 2.97395i) q^{83} +(-2.14542 + 0.173197i) q^{84} +(-14.0048 + 1.13059i) q^{85} +(-0.587578 - 0.308385i) q^{86} +(-5.80353 - 4.36107i) q^{87} +(-1.80942 + 2.21614i) q^{88} +(2.69063 + 4.66031i) q^{89} +(-1.39970 + 3.69070i) q^{90} +(-3.96231 - 5.35202i) q^{91} +(0.292197 + 0.770460i) q^{92} +(-0.104013 + 0.127393i) q^{93} +(1.49899 - 3.15906i) q^{94} +(-12.4842 + 4.16784i) q^{95} +(-3.12405 - 4.52596i) q^{96} +(-3.25260 - 15.9323i) q^{97} +(-0.132020 + 3.27603i) q^{98} +0.989350 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9} + 3 q^{10} - 4 q^{11} - 34 q^{12} - 15 q^{13} + 24 q^{14} - 3 q^{15} + 11 q^{16} - 3 q^{17} - 2 q^{18} + 6 q^{19}+ \cdots - 18 q^{99}+O(q^{100}) $ 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9 + 3 * q^10 - 4 * q^11 - 34 * q^12 - 15 * q^13 + 24 * q^14 - 3 * q^15 + 11 * q^16 - 3 * q^17 - 2 * q^18 + 6 * q^19 + q^20 + 6 * q^21 - 86 * q^22 - 52 * q^23 + 9 * q^24 - 74 * q^25 - 64 * q^26 - 32 * q^27 - 16 * q^28 - 44 * q^29 + 3 * q^30 - 28 * q^31 + 74 * q^32 - 17 * q^33 - 83 * q^34 + 70 * q^35 + 17 * q^36 + 11 * q^37 - 29 * q^38 + q^39 - 5 * q^40 + q^41 + 118 * q^42 - 79 * q^43 - 19 * q^44 - 3 * q^45 + 314 * q^46 + 11 * q^48 - 69 * q^49 - 76 * q^50 + 6 * q^51 - 37 * q^52 - 102 * q^53 + q^54 - 73 * q^55 - 36 * q^56 + 14 * q^57 - 51 * q^58 + 194 * q^59 + 76 * q^60 + 4 * q^61 - 89 * q^62 - 3 * q^63 - 184 * q^64 - 49 * q^65 - 36 * q^66 - 73 * q^67 + 4 * q^68 - 100 * q^70 + 106 * q^71 + 9 * q^72 - 132 * q^73 - 45 * q^74 + 11 * q^75 + 24 * q^76 - 54 * q^77 - 39 * q^78 - 2 * q^79 + 177 * q^80 + 16 * q^81 - 76 * q^82 - 58 * q^83 - 16 * q^84 - 123 * q^85 - 157 * q^86 - 57 * q^87 + 476 * q^88 + 18 * q^89 - 6 * q^90 + 233 * q^91 - 12 * q^92 + q^93 - 111 * q^94 + 64 * q^95 - 83 * q^96 - 143 * q^97 - 79 * q^98 - 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{39}\right)$

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 $

$2$	0.910598	+	0.0735111i	0.643890	+	0.0519802i	0.398099	−	0.917343i	$-0.369670\pi$
$2$	0.910598	+	0.0735111i	0.643890	+	0.0519802i	0.245791	+	0.969323i	$0.420952\pi$
$3$	−0.845190	−	0.534466i	−0.487971	−	0.308574i
$3$	−0.845190	−	0.534466i	−0.487971	−	0.308574i
$4$	−1.15032	−	0.186944i	−0.575158	−	0.0934722i
$5$	3.23408	+	2.86515i	1.44632	+	1.28133i	0.894273	+	0.447523i	$0.147694\pi$
$5$	3.23408	+	2.86515i	1.44632	+	1.28133i	0.552052	+	0.833810i	$0.313845\pi$
$6$	−0.730339	−	0.548814i	−0.298160	−	0.224053i
$7$	−1.27940	+	1.33200i	−0.483568	+	0.503448i	−0.917630	−	0.397435i	$-0.869900\pi$
$7$	−1.27940	+	1.33200i	−0.483568	+	0.503448i	0.434062	+	0.900883i	$0.357080\pi$
$8$	−2.80776	−	0.692051i	−0.992693	−	0.244677i
$9$	0.428693	+	0.903450i	0.142898	+	0.301150i
$10$	2.73433	+	2.84674i	0.864670	+	0.900217i
$11$	0.424127	−	0.893828i	0.127879	−	0.269499i	−0.829405	−	0.558647i	$-0.811321\pi$
$11$	0.424127	−	0.893828i	0.127879	−	0.269499i	0.957284	+	0.289148i	$0.0933719\pi$
$12$	0.872320	+	0.772808i	0.251817	+	0.223090i
$13$	−0.603766	+	3.55464i	−0.167455	+	0.985880i
$13$	−0.603766	+	3.55464i	−0.167455	+	0.985880i
$14$	−1.26294	+	1.11886i	−0.337534	+	0.299029i
$15$	−1.20209	−	4.15010i	−0.310378	−	1.07155i
$16$	−0.295006	−	0.0984874i	−0.0737514	−	0.0246218i
$17$	−2.25266	+	2.34527i	−0.546350	+	0.568811i	−0.935932	−	0.352181i	$-0.885440\pi$
$17$	−2.25266	+	2.34527i	−0.546350	+	0.568811i	0.389582	+	0.920992i	$0.372620\pi$
$18$	0.323953	+	0.854194i	0.0763565	+	0.201335i
$19$	−1.52309	+	2.63806i	−0.349420	+	0.605213i	−0.986146	−	0.165877i	$-0.946955\pi$
$19$	−1.52309	+	2.63806i	−0.349420	+	0.605213i	0.636727	+	0.771090i	$0.280288\pi$
$20$	−3.18459	−	3.90041i	−0.712096	−	0.872159i
$21$	1.79324	−	0.441995i	0.391318	−	0.0964512i
$22$	0.451915	−	0.782740i	0.0963487	−	0.166881i
$23$	−0.353527	−	0.612328i	−0.0737156	−	0.127679i	0.826811	−	0.562479i	$-0.190152\pi$
$23$	−0.353527	−	0.612328i	−0.0737156	−	0.127679i	−0.900527	+	0.434800i	$0.856819\pi$
$24$	2.00321	+	2.08557i	0.408904	+	0.425715i
$25$	1.64754	+	13.5687i	0.329507	+	2.71374i
$26$	−0.811094	+	3.19246i	−0.159069	+	0.626094i
$27$	0.120537	−	0.992709i	0.0231973	−	0.191047i
$28$	1.72072	−	1.29304i	0.325186	−	0.244362i
$29$	7.23593	+	0.584145i	1.34368	+	0.108473i	0.731280	−	0.682077i	$-0.238923\pi$
$29$	7.23593	+	0.584145i	1.34368	+	0.108473i	0.612398	+	0.790550i	$0.290205\pi$
$30$	−0.789543	−	3.86744i	−0.144150	−	0.706094i
$31$	0.0198237	−	0.163263i	0.00356044	−	0.0293228i	−0.990820	−	0.135185i	$-0.956837\pi$
$31$	0.0198237	−	0.163263i	0.00356044	−	0.0293228i	0.994381	+	0.105862i	$0.0337602\pi$
$32$	5.05938	+	2.15560i	0.894381	+	0.381060i
$33$	−0.836189	+	0.528774i	−0.145562	+	0.0920477i
$34$	−2.22367	+	1.97000i	−0.381356	+	0.337852i
$35$	−7.95405	+	0.642117i	−1.34448	+	0.108538i
$36$	−0.324237	−	1.11939i	−0.0540394	−	0.186566i
$37$	6.37129	−	2.71455i	1.04743	−	0.446270i	0.201461	−	0.979497i	$-0.435431\pi$
$37$	6.37129	−	2.71455i	1.04743	−	0.446270i	0.845972	+	0.533227i	$0.179021\pi$
$38$	−1.58085	+	2.29025i	−0.256447	+	0.371528i
$39$	2.41013	−	2.68165i	0.385930	−	0.429408i
$40$	−7.09770	−	10.2828i	−1.12224	−	1.62585i
$41$	−1.39615	−	0.882871i	−0.218042	−	0.137881i	0.420980	−	0.907070i	$-0.361686\pi$
$41$	−1.39615	−	0.882871i	−0.218042	−	0.137881i	−0.639022	+	0.769189i	$0.720661\pi$
$42$	1.66542	−	0.270656i	0.256979	−	0.0417632i
$43$	−0.668250	−	0.284715i	−0.101907	−	0.0434186i	0.340411	−	0.940277i	$-0.389434\pi$
$43$	−0.668250	−	0.284715i	−0.101907	−	0.0434186i	−0.442319	+	0.896858i	$0.645844\pi$
$44$	−0.654976	+	0.948897i	−0.0987413	+	0.143052i
$45$	−1.20209	+	4.15010i	−0.179197	+	0.618660i
$46$	−0.276909	−	0.583572i	−0.0408279	−	0.0860431i
$47$	1.35726	−	3.57879i	0.197976	−	0.522020i	−0.798859	−	0.601518i	$-0.794563\pi$
$47$	1.35726	−	3.57879i	0.197976	−	0.522020i	0.996835	+	0.0794985i	$0.0253319\pi$
$48$	0.196698	+	0.240911i	0.0283909	+	0.0347725i
$49$	0.144511	+	3.58601i	0.0206444	+	0.512287i
$50$	0.502795	+	12.4767i	0.0711059	+	1.76448i
$51$	3.15739	−	0.778227i	0.442123	−	0.108974i
$52$	1.35904	−	3.97609i	0.188465	−	0.551384i
$53$	−4.44435	−	1.09543i	−0.610478	−	0.150469i	−0.0780569	−	0.996949i	$-0.524872\pi$
$53$	−4.44435	−	1.09543i	−0.610478	−	0.150469i	−0.532421	+	0.846480i	$0.678718\pi$
$54$	0.182736	−	0.895098i	0.0248672	−	0.121807i
$55$	3.93261	−	1.67553i	0.530273	−	0.225928i
$56$	4.51406	−	2.85452i	0.603217	−	0.381451i
$57$	2.69725	−	1.41563i	0.357260	−	0.187504i
$58$	6.54608	+	1.06384i	0.859543	+	0.139689i
$59$	1.63503	−	0.545855i	0.212863	−	0.0710642i	−0.208237	−	0.978078i	$-0.566772\pi$
$59$	1.63503	−	0.545855i	0.212863	−	0.0710642i	0.421100	+	0.907014i	$0.361644\pi$
$60$	0.606946	+	4.99865i	0.0783563	+	0.645323i
$61$	3.00944	−	10.3898i	0.385320	−	1.33028i	−0.500294	−	0.865856i	$-0.666775\pi$
$61$	3.00944	−	10.3898i	0.385320	−	1.33028i	0.885614	−	0.464423i	$-0.153738\pi$
$62$	0.0300530	−	0.147209i	0.00381674	−	0.0186956i
$63$	−1.75186	−	0.584858i	−0.220714	−	0.0736852i
$64$	4.99938	+	2.62388i	0.624922	+	0.327985i
$65$	−12.1372	+	9.76612i	−1.50543	+	1.21134i
$66$	−0.800302	+	0.420031i	−0.0985104	+	0.0517023i
$67$	−7.46708	+	1.21352i	−0.912249	+	0.148255i	−0.598381	−	0.801212i	$-0.704189\pi$
$67$	−7.46708	+	1.21352i	−0.912249	+	0.148255i	−0.313868	+	0.949467i	$0.601625\pi$
$68$	3.02970	−	2.27668i	0.367406	−	0.276087i
$69$	−0.0284702	+	0.706481i	−0.00342741	+	0.0850504i
$70$	−7.29015			−0.871339
$71$	−0.573933	+	14.2420i	−0.0681134	+	1.69022i	0.499020	+	0.866590i	$0.333693\pi$
$71$	−0.573933	+	14.2420i	−0.0681134	+	1.69022i	−0.567134	+	0.823626i	$0.691948\pi$
$72$	−0.578432	−	2.83335i	−0.0681689	−	0.333913i
$73$	−5.45049	−	7.89640i	−0.637932	−	0.924204i	0.362037	−	0.932164i	$-0.382082\pi$
$73$	−5.45049	−	7.89640i	−0.637932	−	0.924204i	−0.999968	+	0.00796017i	$0.997466\pi$
$74$	6.00123	−	2.00351i	0.697629	−	0.232903i
$75$	5.85951	−	12.3487i	0.676598	−	1.42590i
$76$	2.24520	−	2.74987i	0.257542	−	0.315432i
$77$	0.647949	+	1.70850i	0.0738406	+	0.194702i
$78$	2.39179	−	2.26474i	0.270817	−	0.256431i
$79$	6.20589	−	16.3636i	0.698217	−	1.84105i	0.185121	−	0.982716i	$-0.440732\pi$
$79$	6.20589	−	16.3636i	0.698217	−	1.84105i	0.513096	−	0.858331i	$-0.328498\pi$
$80$	−0.671892	−	1.16375i	−0.0751198	−	0.130111i
$81$	−0.632445	+	0.774605i	−0.0702717	+	0.0860672i
$82$	−1.20643	−	0.906573i	−0.133228	−	0.100114i
$83$	−5.66638	−	2.97395i	−0.621966	−	0.326433i	0.124135	−	0.992265i	$-0.460384\pi$
$83$	−5.66638	−	2.97395i	−0.621966	−	0.326433i	−0.746102	+	0.665832i	$0.768077\pi$
$84$	−2.14542	+	0.173197i	−0.234085	+	0.0188973i
$85$	−14.0048	+	1.13059i	−1.51904	+	0.122629i
$86$	−0.587578	−	0.308385i	−0.0633601	−	0.0332540i
$87$	−5.80353	−	4.36107i	−0.622204	−	0.467556i
$88$	−1.80942	+	2.21614i	−0.192885	+	0.236241i
$89$	2.69063	+	4.66031i	0.285207	+	0.493992i	0.972659	−	0.232237i	$-0.0746045\pi$
$89$	2.69063	+	4.66031i	0.285207	+	0.493992i	−0.687453	+	0.726229i	$0.741271\pi$
$90$	−1.39970	+	3.69070i	−0.147541	+	0.389034i
$91$	−3.96231	−	5.35202i	−0.415363	−	0.561045i
$92$	0.292197	+	0.770460i	0.0304636	+	0.0803260i
$93$	−0.104013	+	0.127393i	−0.0107857	+	0.0132100i
$94$	1.49899	−	3.15906i	0.154609	−	0.325833i
$95$	−12.4842	+	4.16784i	−1.28085	+	0.427612i
$96$	−3.12405	−	4.52596i	−0.318847	−	0.461929i
$97$	−3.25260	−	15.9323i	−0.330252	−	1.61768i	−0.718088	−	0.695952i	$-0.754983\pi$
$97$	−3.25260	−	15.9323i	−0.330252	−	1.61768i	0.387837	−	0.921728i	$-0.373222\pi$
$98$	−0.132020	+	3.27603i	−0.0133360	+	0.330929i
$99$	0.989350			0.0994334
$100$	0.641403	−	15.9163i	0.0641403	−	1.59163i
$101$	10.9031	−	8.19314i	1.08490	−	0.815247i	0.101162	−	0.994870i	$-0.467744\pi$
$101$	10.9031	−	8.19314i	1.08490	−	0.815247i	0.983736	+	0.179622i	$0.0574876\pi$
$102$	2.93232	−	0.476549i	0.290343	−	0.0471854i
$103$	5.61628	−	2.94765i	0.553389	−	0.290441i	−0.164756	−	0.986334i	$-0.552684\pi$
$103$	5.61628	−	2.94765i	0.553389	−	0.290441i	0.718145	+	0.695893i	$0.244991\pi$
$104$	4.15522	−	9.56274i	0.407453	−	0.937704i
$105$	7.06588	+	3.70846i	0.689559	+	0.361908i
$106$	−3.96649	−	1.32421i	−0.385259	−	0.128618i
$107$	2.38072	−	11.6615i	0.230153	−	1.12736i	−0.686330	−	0.727290i	$-0.740779\pi$
$107$	2.38072	−	11.6615i	0.230153	−	1.12736i	0.916483	−	0.400074i	$-0.131015\pi$
$108$	−0.324237	+	1.11939i	−0.0311997	+	0.107714i
$109$	0.610598	+	5.02872i	0.0584847	+	0.481664i	0.992295	+	0.123896i	$0.0395391\pi$
$109$	0.610598	+	5.02872i	0.0584847	+	0.481664i	−0.933810	+	0.357768i	$0.883538\pi$
$110$	3.70420	−	1.23664i	0.353181	−	0.117909i
$111$	−6.83578	−	1.11092i	−0.648824	−	0.105444i
$112$	0.508615	−	0.266942i	0.0480596	−	0.0252236i
$113$	−15.3790	+	9.72512i	−1.44674	+	0.914862i	−0.446945	+	0.894561i	$0.647488\pi$
$113$	−15.3790	+	9.72512i	−1.44674	+	0.914862i	−0.999794	+	0.0203010i	$0.993538\pi$
$114$	2.56018	−	1.09079i	0.239782	−	0.102162i
$115$	0.611071	−	2.99322i	0.0569827	−	0.279120i
$116$	−8.21440	−	2.02467i	−0.762688	−	0.187986i
$117$	−3.47027	+	0.978375i	−0.320827	+	0.0904508i
$118$	1.52899	−	0.376861i	0.140755	−	0.0346929i
$119$	−0.241835	−	6.00107i	−0.0221690	−	0.550118i
$120$	0.503104	+	12.4844i	0.0459269	+	1.13966i
$121$	6.33785	+	7.76246i	0.576168	+	0.705678i
$122$	3.50416	−	9.23971i	0.317252	−	0.836524i
$123$	0.708147	+	1.49239i	0.0638514	+	0.134564i
$124$	−0.0533245	+	0.184098i	−0.00478868	+	0.0165325i
$125$	−21.2758	+	30.8234i	−1.90297	+	2.75693i
$126$	−1.55225	−	0.661352i	−0.138285	−	0.0589179i
$127$	18.5556	−	3.01558i	1.64654	−	0.267590i	0.734781	−	0.678305i	$-0.237285\pi$
$127$	18.5556	−	3.01558i	1.64654	−	0.267590i	0.911764	+	0.410715i	$0.134721\pi$
$128$	−4.93663	−	3.12173i	−0.436340	−	0.275925i
$129$	0.412628	+	0.597795i	0.0363299	+	0.0526329i
$130$	−11.7700	+	8.00079i	−1.03230	+	0.701716i
$131$	6.04426	−	8.75662i	0.528089	−	0.765070i	−0.464632	−	0.885504i	$-0.653813\pi$
$131$	6.04426	−	8.75662i	0.528089	−	0.765070i	0.992721	+	0.120434i	$0.0384287\pi$
$132$	1.06073	−	0.451936i	0.0923249	−	0.0393360i
$133$	−1.56525	−	5.40388i	−0.135725	−	0.468576i
$134$	−6.88872	+	0.556115i	−0.595095	+	0.0480410i
$135$	3.23408	−	2.86515i	0.278345	−	0.246592i
$136$	7.94797	−	5.02599i	0.681533	−	0.430976i
$137$	20.5260	+	8.74529i	1.75365	+	0.747161i	0.995466	+	0.0951209i	$0.0303238\pi$
$137$	20.5260	+	8.74529i	1.75365	+	0.747161i	0.758185	+	0.652040i	$0.226086\pi$
$138$	−0.0778592	+	0.641228i	−0.00662781	+	0.0545849i
$139$	2.04627	+	10.0233i	0.173563	+	0.850166i	0.969558	+	0.244863i	$0.0787429\pi$
$139$	2.04627	+	10.0233i	0.173563	+	0.850166i	−0.795995	+	0.605303i	$0.793052\pi$
$140$	9.26971	+	0.748328i	0.783433	+	0.0632453i
$141$	−3.05988	+	2.29935i	−0.257688	+	0.193640i
$142$	−1.56957	+	12.9266i	−0.131715	+	1.08477i
$143$	2.92116	+	2.04728i	0.244280	+	0.171202i
$144$	−0.0374883	−	0.308744i	−0.00312402	−	0.0257287i
$145$	21.7279	+	22.6212i	1.80441	+	1.87858i
$146$	−4.38273	−	7.59112i	−0.362718	−	0.628245i
$147$	1.79446	−	3.10809i	0.148004	−	0.256351i
$148$	−7.83646	+	1.93151i	−0.644153	+	0.158769i
$149$	3.98787	+	4.88426i	0.326699	+	0.400134i	0.911672	−	0.410919i	$-0.134792\pi$
$149$	3.98787	+	4.88426i	0.326699	+	0.400134i	−0.584972	+	0.811053i	$0.698895\pi$
$150$	6.24343	−	10.8139i	0.509774	−	0.882954i
$151$	4.08664	+	10.7756i	0.332566	+	0.876906i	0.992125	+	0.125252i	$0.0399740\pi$
$151$	4.08664	+	10.7756i	0.332566	+	0.876906i	−0.659558	+	0.751653i	$0.729257\pi$
$152$	6.10213	−	6.35299i	0.494948	−	0.515296i
$153$	−3.08453	−	1.02977i	−0.249370	−	0.0832518i
$154$	0.464427	+	1.60339i	0.0374246	+	0.129205i
$155$	0.531883	−	0.471207i	0.0427218	−	0.0378482i
$156$	−3.27373	+	2.63419i	−0.262108	+	0.210904i
$157$	6.17724	+	5.47256i	0.492998	+	0.436758i	0.872632	−	0.488379i	$-0.162412\pi$
$157$	6.17724	+	5.47256i	0.492998	+	0.436758i	−0.379634	+	0.925137i	$0.623950\pi$
$158$	6.85397	−	14.4444i	0.545273	−	1.14914i
$159$	3.17085	+	3.30120i	0.251465	+	0.261802i
$160$	10.1863	+	21.4673i	0.805301	+	1.69714i
$161$	1.26792	+	0.312515i	0.0999262	+	0.0246296i
$162$	−0.632846	+	0.658862i	−0.0497210	+	0.0517651i
$163$	10.3341	+	7.76555i	0.809427	+	0.608245i	0.922788	−	0.385309i	$-0.125905\pi$
$163$	10.3341	+	7.76555i	0.809427	+	0.608245i	−0.113361	+	0.993554i	$0.536162\pi$
$164$	1.44096	+	1.27658i	0.112520	+	0.0996844i
$165$	−4.21931	−	0.685705i	−0.328473	−	0.0533821i
$166$	−4.94118	−	3.12461i	−0.383510	−	0.242517i
$167$	1.48103	+	0.119561i	0.114605	+	0.00925190i	0.137636	−	0.990483i	$-0.456050\pi$
$167$	1.48103	+	0.119561i	0.114605	+	0.00925190i	−0.0230308	+	0.999735i	$0.507332\pi$
$168$	−5.34088			−0.412058
$169$	−12.2709	−	4.29234i	−0.943918	−	0.330180i
$170$	−12.8359			−0.984466
$171$	−3.03629	−	0.245115i	−0.232191	−	0.0187444i
$172$	0.715473	+	0.452438i	0.0545543	+	0.0344980i
$173$	−11.2364	−	1.82608i	−0.854284	−	0.138835i	−0.282529	−	0.959259i	$-0.591173\pi$
$173$	−11.2364	−	1.82608i	−0.854284	−	0.138835i	−0.571755	+	0.820424i	$0.693737\pi$
$174$	−4.96410	−	4.39781i	−0.376327	−	0.333397i
$175$	−20.1813	−	15.1653i	−1.52556	−	1.14639i
$176$	−0.213151	+	0.221913i	−0.0160668	+	0.0167273i
$177$	−1.67366	−	0.412519i	−0.125800	−	0.0310068i
$178$	2.10750	+	4.44146i	0.157964	+	0.332902i
$179$	−0.665775	−	0.693145i	−0.0497624	−	0.0518081i	0.695856	−	0.718181i	$-0.255025\pi$
$179$	−0.665775	−	0.693145i	−0.0497624	−	0.0518081i	−0.745618	+	0.666373i	$0.767846\pi$
$180$	2.15862	−	4.54920i	0.160894	−	0.339077i
$181$	3.31123	+	2.93349i	0.246122	+	0.218045i	0.777160	−	0.629303i	$-0.216660\pi$
$181$	3.31123	+	2.93349i	0.246122	+	0.218045i	−0.531038	+	0.847348i	$0.678198\pi$
$182$	−3.21464	−	5.16482i	−0.238285	−	0.382842i
$183$	−8.09655	+	7.17292i	−0.598514	+	0.530237i
$184$	0.568859	+	1.96393i	0.0419368	+	0.144783i
$185$	28.3828	+	9.47559i	2.08675	+	0.696659i
$186$	−0.104079	+	0.108358i	−0.00763143	+	0.00794517i
$187$	1.14085	+	3.00818i	0.0834274	+	0.219980i
$188$	−2.23031	+	3.86300i	−0.162662	+	0.281739i
$189$	1.16807	+	1.43063i	0.0849647	+	0.104063i
$190$	−11.6745	+	2.87750i	−0.846956	+	0.208756i
$191$	−8.11351	+	14.0530i	−0.587073	+	1.01684i	0.407541	+	0.913187i	$0.366386\pi$
$191$	−8.11351	+	14.0530i	−0.587073	+	1.01684i	−0.994614	+	0.103653i	$0.966947\pi$
$192$	−2.82305	−	4.88967i	−0.203736	−	0.352882i
$193$	−9.14311	−	9.51899i	−0.658135	−	0.685192i	0.305567	−	0.952171i	$-0.401154\pi$
$193$	−9.14311	−	9.51899i	−0.658135	−	0.685192i	−0.963702	+	0.266979i	$0.913975\pi$
$194$	−1.79061	−	14.7470i	−0.128559	−	1.05877i
$195$	15.4779	−	1.76731i	1.10839	−	0.126560i
$196$	0.504151	−	4.15205i	0.0360108	−	0.296575i
$197$	−0.970140	+	0.729013i	−0.0691196	+	0.0519400i	−0.634740	−	0.772725i	$-0.718893\pi$
$197$	−0.970140	+	0.729013i	−0.0691196	+	0.0519400i	0.565621	+	0.824665i	$0.308637\pi$
$198$	0.900900	+	0.0727282i	0.0640242	+	0.00516857i
$199$	−4.02326	−	19.7072i	−0.285201	−	1.39701i	−0.829683	−	0.558235i	$-0.811479\pi$
$199$	−4.02326	−	19.7072i	−0.285201	−	1.39701i	0.544482	−	0.838773i	$-0.316726\pi$
$200$	4.76433	−	39.2378i	0.336889	−	2.77453i
$201$	6.95969	+	2.96525i	0.490899	+	0.209152i
$202$	10.5306	−	6.65916i	0.740931	−	0.468537i
$203$	−10.0357	+	8.89088i	−0.704370	+	0.624018i
$204$	−3.77748	+	0.304950i	−0.264477	+	0.0213508i
$205$	−1.98570	−	6.85545i	−0.138688	−	0.478805i
$206$	5.33086	−	2.27127i	0.371419	−	0.158247i
$207$	0.401653	−	0.581895i	0.0279168	−	0.0404445i
$208$	0.528202	−	0.989176i	0.0366242	−	0.0685870i
$209$	1.71199	+	2.48025i	0.118421	+	0.171562i
$210$	6.16156	+	3.89633i	0.425188	+	0.268873i
$211$	20.0174	−	3.25314i	1.37805	−	0.223955i	0.574166	−	0.818739i	$-0.305326\pi$
$211$	20.0174	−	3.25314i	1.37805	−	0.223955i	0.803886	+	0.594784i	$0.202762\pi$
$212$	4.90762	+	2.09094i	0.337057	+	0.143606i
$213$	8.09695	−	11.7305i	0.554794	−	0.803758i
$214$	3.02513	−	10.4440i	0.206794	−	0.713935i
$215$	−1.34543	−	2.83543i	−0.0917573	−	0.193374i
$216$	−1.02544	+	2.70387i	−0.0697726	+	0.183975i
$217$	0.192103	+	0.235283i	0.0130408	+	0.0159721i
$218$	0.186342	+	4.62403i	0.0126207	+	0.313179i
$219$	0.386345	+	9.58706i	0.0261068	+	0.647834i
$220$	−4.83697	+	1.19221i	−0.326109	+	0.0803785i
$221$	−6.97650	−	9.42339i	−0.469290	−	0.633886i
$222$	−6.14299	−	1.51411i	−0.412290	−	0.101620i
$223$	−4.90653	+	24.0338i	−0.328566	+	1.60942i	0.394673	+	0.918822i	$0.370858\pi$
$223$	−4.90653	+	24.0338i	−0.328566	+	1.60942i	−0.723238	+	0.690599i	$0.757347\pi$
$224$	−9.34424	+	3.98121i	−0.624338	+	0.266006i
$225$	−11.5523	+	7.30526i	−0.770156	+	0.487017i
$226$	−14.7190	+	7.72515i	−0.979096	+	0.513869i
$227$	0.819910	+	0.133248i	0.0544193	+	0.00884400i	0.187560	−	0.982253i	$-0.439942\pi$
$227$	0.819910	+	0.133248i	0.0544193	+	0.00884400i	−0.133141	+	0.991097i	$0.542506\pi$
$228$	−3.36733	+	1.12418i	−0.223007	+	0.0744507i
$229$	−1.56342	−	12.8760i	−0.103314	−	0.850867i	−0.948583	−	0.316527i	$-0.897483\pi$
$229$	−1.56342	−	12.8760i	−0.103314	−	0.850867i	0.845269	−	0.534340i	$-0.179440\pi$
$230$	0.776475	−	2.68070i	0.0511993	−	0.176760i
$231$	0.365495	−	1.79031i	0.0240478	−	0.117794i
$232$	−19.9125	−	6.64777i	−1.30732	−	0.436447i
$233$	13.4292	+	7.04818i	0.879775	+	0.461742i	0.843207	−	0.537590i	$-0.180665\pi$
$233$	13.4292	+	7.04818i	0.879775	+	0.461742i	0.0365685	+	0.999331i	$0.488357\pi$
$234$	−3.23194	+	0.635803i	−0.211279	+	0.0415637i
$235$	14.6432	−	7.68536i	0.955218	−	0.501337i
$236$	−1.98285	+	0.322244i	−0.129073	+	0.0209763i
$237$	−13.9909	+	10.5135i	−0.908809	+	0.682925i
$238$	0.220931	−	5.48234i	0.0143208	−	0.355368i
$239$	−8.77444			−0.567572			−0.283786	−	0.958888i	$-0.591590\pi$
$239$	−8.77444			−0.567572			−0.283786	+	0.958888i	$0.591590\pi$
$240$	−0.0541087	+	1.34269i	−0.00349270	+	0.0866705i
$241$	1.88824	+	9.24923i	0.121632	+	0.595795i	0.994222	+	0.107341i	$0.0342337\pi$
$241$	1.88824	+	9.24923i	0.121632	+	0.595795i	−0.872590	+	0.488454i	$0.837561\pi$
$242$	5.20061	+	7.53438i	0.334308	+	0.484329i
$243$	0.948536	−	0.316668i	0.0608486	−	0.0203143i
$244$	−5.40413	+	11.3890i	−0.345964	+	0.729103i
$245$	−9.80707	+	12.0115i	−0.626551	+	0.767385i
$246$	0.535130	+	1.41102i	0.0341186	+	0.0899635i
$247$	−8.45777	−	7.00679i	−0.538155	−	0.445832i
$248$	−0.168646	+	0.444683i	−0.0107090	+	0.0282374i
$249$	3.19970	+	5.54204i	0.202773	+	0.351212i
$250$	−21.6396	+	26.5037i	−1.36861	+	1.67624i
$251$	−21.9002	−	16.4570i	−1.38233	−	1.03875i	−0.993057	−	0.117632i	$-0.962470\pi$
$251$	−21.9002	−	16.4570i	−1.38233	−	1.03875i	−0.389273	−	0.921122i	$-0.627274\pi$
$252$	1.90586	+	1.00027i	0.120058	+	0.0630112i
$253$	−0.697256	+	0.0562883i	−0.0438361	+	0.00353882i
$254$	17.1184	−	1.38194i	1.07410	−	0.0867106i
$255$	12.4410	+	6.52954i	0.779085	+	0.408895i
$256$	−13.2933	−	9.98925i	−0.830830	−	0.624328i
$257$	−2.39828	+	2.93736i	−0.149600	+	0.183227i	−0.843968	−	0.536393i	$-0.819787\pi$
$257$	−2.39828	+	2.93736i	−0.149600	+	0.183227i	0.694368	+	0.719620i	$0.255684\pi$
$258$	0.331794	+	0.574684i	0.0206566	+	0.0357783i
$259$	−4.53565	+	11.9595i	−0.281832	+	0.743129i
$260$	15.7873	−	8.96513i	0.979088	−	0.555994i
$261$	2.57424	+	6.78772i	0.159342	+	0.420149i
$262$	6.14760	−	7.52944i	0.379800	−	0.465171i
$263$	−12.0876	+	25.4740i	−0.745352	+	1.57080i	0.0738353	+	0.997270i	$0.476476\pi$
$263$	−12.0876	+	25.4740i	−0.745352	+	1.57080i	−0.819187	+	0.573526i	$0.805575\pi$
$264$	2.71376	−	0.905985i	0.167020	−	0.0557595i
$265$	−11.2348	−	16.2764i	−0.690149	−	0.999853i
$266$	−1.02807	−	5.03583i	−0.0630351	−	0.308767i
$267$	0.216682	−	5.37690i	0.0132607	−	0.329061i
$268$	8.81636			0.538545
$269$	0.502221	−	12.4625i	0.0306210	−	0.759852i	−0.908830	−	0.417167i	$-0.863023\pi$
$269$	0.502221	−	12.4625i	0.0306210	−	0.759852i	0.939451	−	0.342684i	$-0.111336\pi$
$270$	3.15557	−	2.37126i	0.192042	−	0.144310i
$271$	19.4176	−	3.15566i	1.17953	−	0.191693i	0.461138	−	0.887328i	$-0.347441\pi$
$271$	19.4176	−	3.15566i	1.17953	−	0.191693i	0.718395	+	0.695636i	$0.244877\pi$
$272$	0.895527	−	0.470009i	0.0542993	−	0.0284985i
$273$	0.488433	+	6.64120i	0.0295613	+	0.401944i
$274$	18.0480	+	9.47233i	1.09032	+	0.572244i
$275$	12.8268	+	4.28223i	0.773487	+	0.258228i
$276$	0.164823	−	0.807354i	0.00992115	−	0.0485970i
$277$	3.19462	−	11.0291i	0.191946	−	0.662675i	−0.805587	−	0.592478i	$-0.798150\pi$
$277$	3.19462	−	11.0291i	0.191946	−	0.662675i	0.997533	−	0.0701975i	$-0.0223630\pi$
$278$	1.12651	+	9.27763i	0.0675635	+	0.556435i
$279$	0.155998	−	0.0520798i	0.00933935	−	0.00311793i
$280$	22.7775	+	3.70170i	1.36121	+	0.221219i
$281$	4.46023	−	2.34091i	0.266075	−	0.139647i	−0.326410	−	0.945228i	$-0.605839\pi$
$281$	4.46023	−	2.34091i	0.266075	−	0.139647i	0.592485	+	0.805581i	$0.298147\pi$
$282$	−2.95535	+	1.86885i	−0.175988	+	0.111288i
$283$	−3.02684	+	1.28961i	−0.179927	+	0.0766596i	−0.480051	−	0.877240i	$-0.659382\pi$
$283$	−3.02684	+	1.28961i	−0.179927	+	0.0766596i	0.300125	+	0.953900i	$0.402972\pi$
$284$	3.32267	−	16.2755i	0.197164	−	0.965774i
$285$	12.7791	+	3.14977i	0.756969	+	0.186576i
$286$	2.50951	+	2.07899i	0.148390	+	0.122933i
$287$	2.96222	−	0.730121i	0.174854	−	0.0430977i
$288$	0.221441	+	5.49499i	0.0130485	+	0.323796i
$289$	0.258718	+	6.42003i	0.0152187	+	0.377649i
$290$	18.1225	+	22.1960i	1.06419	+	1.30340i
$291$	−5.76620	+	15.2042i	−0.338021	+	0.891288i
$292$	4.79360	+	10.1023i	0.280524	+	0.591192i
$293$	−6.02984	+	20.8174i	−0.352267	+	1.21617i	0.567392	+	0.823448i	$0.307953\pi$
$293$	−6.02984	+	20.8174i	−0.352267	+	1.21617i	−0.919659	+	0.392719i	$0.871535\pi$
$294$	1.86251	−	2.69831i	0.108624	−	0.157369i
$295$	6.85179	+	2.91927i	0.398926	+	0.169967i
$296$	−19.7677	+	3.21256i	−1.14897	+	0.186726i
$297$	−0.836189	−	0.528774i	−0.0485206	−	0.0306826i
$298$	3.27230	+	4.74075i	0.189559	+	0.274624i
$299$	2.39005	−	0.886960i	0.138220	−	0.0512942i
$300$	−9.04881	+	13.1095i	−0.522433	+	0.756875i
$301$	1.23420	−	0.525843i	0.0711381	−	0.0303091i
$302$	2.92917	+	10.1127i	0.168555	+	0.581918i
$303$	−13.5941	+	1.09743i	−0.780962	+	0.0630458i
$304$	0.709135	−	0.628238i	0.0406717	−	0.0360319i
$305$	39.5011	−	24.9790i	2.26183	−	1.43029i
$306$	−2.73307	−	1.16445i	−0.156239	−	0.0665673i
$307$	−0.637766	+	5.25248i	−0.0363992	+	0.299775i	0.963128	+	0.269042i	$0.0867071\pi$
$307$	−0.637766	+	5.25248i	−0.0363992	+	0.299775i	−0.999528	+	0.0307325i	$0.990216\pi$
$308$	−0.425951	−	2.08645i	−0.0242708	−	0.118886i
$309$	−6.32225	−	0.510385i	−0.359660	−	0.0290348i
$310$	0.518970	−	0.389981i	0.0294755	−	0.0221494i
$311$	0.937823	−	7.72367i	0.0531791	−	0.437969i	−0.941665	−	0.336552i	$-0.890739\pi$
$311$	0.937823	−	7.72367i	0.0531791	−	0.437969i	0.994844	−	0.101417i	$-0.0323377\pi$
$312$	−8.62291	+	5.86151i	−0.488176	+	0.331843i
$313$	−2.65988	−	21.9061i	−0.150345	−	1.23820i	−0.851178	−	0.524878i	$-0.824111\pi$
$313$	−2.65988	−	21.9061i	−0.150345	−	1.23820i	0.700833	−	0.713326i	$-0.252812\pi$
$314$	5.22269	+	5.43740i	0.294734	+	0.306850i
$315$	−3.98996	−	6.91082i	−0.224809	−	0.389381i
$316$	−10.1978	+	17.6631i	−0.573672	+	0.993629i
$317$	−0.898314	+	0.221414i	−0.0504543	+	0.0124359i	−0.264462	−	0.964396i	$-0.585194\pi$
$317$	−0.898314	+	0.221414i	−0.0504543	+	0.0124359i	0.214008	+	0.976832i	$0.431348\pi$
$318$	2.64469	+	3.23916i	0.148307	+	0.181643i
$319$	3.59108	−	6.21993i	0.201062	−	0.348249i
$320$	8.65061	+	22.8098i	0.483584	+	1.27511i
$321$	−8.24486	+	8.58381i	−0.460183	+	0.479101i
$322$	1.13159	+	0.377782i	0.0630613	+	0.0210529i
$323$	−2.75597	−	9.51470i	−0.153346	−	0.529412i
$324$	0.872320	−	0.772808i	0.0484622	−	0.0429338i
$325$	−49.2265	−	2.33591i	−2.73059	−	0.129573i
$326$	8.83933	+	7.83096i	0.489565	+	0.433717i
$327$	2.17161	−	4.57657i	0.120090	−	0.253085i
$328$	3.30906	+	3.44510i	0.182712	+	0.190224i
$329$	3.03046	+	6.38656i	0.167075	+	0.352103i
$330$	−3.79169	−	0.934568i	−0.208726	−	0.0514463i
$331$	1.54129	−	1.60465i	0.0847169	−	0.0881996i	−0.677494	−	0.735528i	$-0.736934\pi$
$331$	1.54129	−	1.60465i	0.0847169	−	0.0881996i	0.762211	+	0.647328i	$0.224114\pi$
$332$	5.96217	+	4.48028i	0.327216	+	0.245887i
$333$	5.18379	+	4.59243i	0.284070	+	0.251664i
$334$	1.33983	+	0.217744i	0.0733123	+	0.0119144i
$335$	−27.6261	−	17.4697i	−1.50937	−	0.954469i
$336$	−0.572548	−	0.0462209i	−0.0312351	−	0.00252155i
$337$	20.0357			1.09141			0.545707	−	0.837976i	$-0.316261\pi$
$337$	20.0357			1.09141			0.545707	+	0.837976i	$0.316261\pi$
$338$	−10.8584	−	4.81065i	−0.590617	−	0.261665i
$339$	18.1960			0.988269
$340$	16.3213	+	1.31759i	0.885148	+	0.0714565i
$341$	−0.137521	−	0.0869630i	−0.00744718	−	0.00470931i
$342$	−2.74682	−	0.446402i	−0.148531	−	0.0241387i
$343$	−14.6385	−	12.9686i	−0.790403	−	0.700236i
$344$	1.67925	+	1.26187i	0.0905391	+	0.0680357i
$345$	−2.11625	+	2.20325i	−0.113935	+	0.118619i
$346$	−10.0976	−	2.48883i	−0.542848	−	0.133800i
$347$	12.2909	+	25.9024i	0.659808	+	1.39052i	0.906826	+	0.421504i	$0.138498\pi$
$347$	12.2909	+	25.9024i	0.659808	+	1.39052i	−0.247019	+	0.969011i	$0.579451\pi$
$348$	5.86061	+	6.10154i	0.314162	+	0.327077i
$349$	2.86708	−	6.04225i	0.153472	−	0.323434i	−0.812123	−	0.583486i	$-0.801688\pi$
$349$	2.86708	−	6.04225i	0.153472	−	0.323434i	0.965595	+	0.260052i	$0.0837396\pi$
$350$	−17.2622	−	15.2930i	−0.922706	−	0.817446i
$351$	3.45595	+	1.02783i	0.184465	+	0.0548614i
$352$	4.07256	−	3.60797i	0.217068	−	0.192306i
$353$	−5.67044	−	19.5766i	−0.301807	−	1.04196i	−0.957858	−	0.287242i	$-0.907261\pi$
$353$	−5.67044	−	19.5766i	−0.301807	−	1.04196i	0.656051	−	0.754717i	$-0.272226\pi$
$354$	−1.49370	−	0.498671i	−0.0793894	−	0.0265041i
$355$	−42.6616	+	44.4154i	−2.26424	+	2.35733i
$356$	−2.22386	−	5.86383i	−0.117864	−	0.310782i
$357$	−3.00297	+	5.20130i	−0.158934	+	0.275282i
$358$	−0.555300	−	0.680118i	−0.0293485	−	0.0359454i
$359$	30.2268	−	7.45025i	1.59531	−	0.393209i	0.661205	−	0.750205i	$-0.270045\pi$
$359$	30.2268	−	7.45025i	1.59531	−	0.393209i	0.934106	+	0.356996i	$0.116199\pi$
$360$	6.24726	−	10.8206i	0.329260	−	0.570294i
$361$	4.86042	+	8.41850i	0.255812	+	0.443079i
$362$	2.79955	+	2.91465i	0.147141	+	0.153190i
$363$	−1.20792	−	9.94812i	−0.0633994	−	0.522141i
$364$	3.55738	+	6.89725i	0.186457	+	0.361514i
$365$	4.99701	−	41.1540i	0.261555	−	2.15410i
$366$	−7.89999	+	5.93646i	−0.412939	+	0.310304i
$367$	−24.8734	−	2.00799i	−1.29838	−	0.104816i	−0.588131	−	0.808765i	$-0.700136\pi$
$367$	−24.8734	−	2.00799i	−1.29838	−	0.104816i	−0.710250	+	0.703949i	$0.751418\pi$
$368$	0.0439861	+	0.215458i	0.00229293	+	0.0112315i
$369$	0.199112	−	1.63983i	0.0103653	−	0.0853662i
$370$	25.1488	+	10.7149i	1.30742	+	0.557041i
$371$	7.14522	−	4.51836i	0.370961	−	0.234582i
$372$	0.143463	−	0.127097i	0.00743822	−	0.00658969i
$373$	5.50463	−	0.444379i	0.285019	−	0.0230091i	0.0628694	−	0.998022i	$-0.479975\pi$
$373$	5.50463	−	0.444379i	0.285019	−	0.0230091i	0.222149	+	0.975013i	$0.428693\pi$
$374$	0.817724	+	2.82311i	0.0422835	+	0.145980i
$375$	34.4562	−	14.6804i	1.77931	−	0.758092i
$376$	−6.28755	+	9.10909i	−0.324256	+	0.469766i
$377$	−6.44523	+	25.3684i	−0.331946	+	1.30654i
$378$	0.958476	+	1.38859i	0.0492987	+	0.0714215i
$379$	6.38021	+	4.03460i	0.327729	+	0.207244i	0.688189	−	0.725531i	$-0.258406\pi$
$379$	6.38021	+	4.03460i	0.327729	+	0.207244i	−0.360460	+	0.932775i	$0.617380\pi$
$380$	15.1399	−	2.46048i	0.776662	−	0.126220i
$381$	−17.2947	−	7.36860i	−0.886037	−	0.377505i
$382$	−8.42119	+	12.2002i	−0.430866	+	0.624217i
$383$	3.90511	−	13.4820i	0.199542	−	0.688899i	−0.796861	−	0.604162i	$-0.793508\pi$
$383$	3.90511	−	13.4820i	0.199542	−	0.688899i	0.996403	−	0.0847368i	$-0.0270049\pi$
$384$	2.50393	+	5.27692i	0.127778	+	0.269287i
$385$	−2.79958	+	7.38190i	−0.142680	+	0.376216i
$386$	−7.62595	−	9.34009i	−0.388150	−	0.475398i
$387$	−0.0292482	−	0.725786i	−0.00148677	−	0.0368938i
$388$	0.763064	+	18.9352i	0.0387387	+	0.961291i
$389$	−27.3996	+	6.75339i	−1.38921	+	0.342411i	−0.861822	−	0.507211i	$-0.830677\pi$
$389$	−27.3996	+	6.75339i	−1.38921	+	0.342411i	−0.527393	+	0.849622i	$0.676830\pi$
$390$	14.2241	−	0.471513i	0.720263	−	0.0238760i
$391$	2.23245	+	0.550249i	0.112900	+	0.0278273i
$392$	2.07595	−	10.1687i	0.104851	−	0.513595i
$393$	−9.78866	+	4.17056i	−0.493773	+	0.210377i
$394$	−0.936998	+	0.592522i	−0.0472053	+	0.0298508i
$395$	66.9544	−	35.1404i	3.36884	−	1.76810i
$396$	−1.13806	−	0.184953i	−0.0571899	−	0.00929426i
$397$	−0.130962	+	0.0437214i	−0.00657277	+	0.00219431i	−0.319952	−	0.947434i	$-0.603667\pi$
$397$	−0.130962	+	0.0437214i	−0.00657277	+	0.00219431i	0.313380	+	0.949628i	$0.398539\pi$
$398$	−2.21487	−	18.2411i	−0.111021	−	0.914344i
$399$	−1.56525	+	5.40388i	−0.0783607	+	0.270533i
$400$	0.850311	−	4.16510i	0.0425156	−	0.208255i
$401$	−16.7021	−	5.57598i	−0.834063	−	0.278451i	−0.132611	−	0.991168i	$-0.542336\pi$
$401$	−16.7021	−	5.57598i	−0.834063	−	0.278451i	−0.701452	+	0.712717i	$0.747464\pi$
$402$	6.11950	+	3.21176i	0.305213	+	0.160188i
$403$	0.568371	+	0.169038i	0.0283126	+	0.00842041i
$404$	−14.0736	+	7.38642i	−0.700190	+	0.367488i
$405$	−4.26474	+	0.693087i	−0.211916	+	0.0344398i
$406$	−9.79210	+	7.35828i	−0.485974	+	0.365185i
$407$	0.275890	−	6.84615i	0.0136754	−	0.339351i
$408$	−9.40377			−0.465556
$409$	0.642718	−	15.9489i	0.0317803	−	0.788621i	−0.902205	−	0.431309i	$-0.858052\pi$
$409$	0.642718	−	15.9489i	0.0317803	−	0.788621i	0.933985	−	0.357313i	$-0.116307\pi$
$410$	−1.30423	−	6.38853i	−0.0644112	−	0.315507i
$411$	−12.6743	−	18.3619i	−0.625176	−	0.905723i
$412$	−7.01155	+	2.34080i	−0.345434	+	0.115323i
$413$	−1.36479	+	2.87623i	−0.0671568	+	0.141530i
$414$	0.408520	−	0.500346i	0.0200777	−	0.0245907i
$415$	−9.80475	−	25.8530i	−0.481296	−	1.26907i
$416$	−10.7171	+	16.6828i	−0.525448	+	0.817942i
$417$	3.62763	−	9.56526i	0.177646	−	0.468413i
$418$	1.37661	+	2.38436i	0.0673323	+	0.116623i
$419$	−7.47882	+	9.15989i	−0.365364	+	0.447490i	−0.924269	−	0.381742i	$-0.875324\pi$
$419$	−7.47882	+	9.15989i	−0.365364	+	0.447490i	0.558905	+	0.829232i	$0.311222\pi$
$420$	−7.43471	−	5.58682i	−0.362777	−	0.272609i
$421$	17.5901	+	9.23199i	0.857289	+	0.449940i	0.835284	−	0.549818i	$-0.185303\pi$
$421$	17.5901	+	9.23199i	0.857289	+	0.449940i	0.0220043	+	0.999758i	$0.492995\pi$
$422$	18.4669	−	1.49080i	0.898955	−	0.0725711i
$423$	3.81510	−	0.307987i	0.185497	−	0.0149748i
$424$	11.7206	+	6.15143i	0.569201	+	0.298740i
$425$	−35.5335	−	26.7017i	−1.72363	−	1.29522i
$426$	8.23539	−	10.0865i	0.399006	−	0.488693i
$427$	9.98891	+	17.3013i	0.483397	+	0.837269i
$428$	−4.91864	+	12.9694i	−0.237752	+	0.626899i
$429$	−1.37474	−	3.29161i	−0.0663730	−	0.158920i
$430$	−1.01671	−	2.68084i	−0.0490300	−	0.129281i
$431$	−12.6198	+	15.4564i	−0.607872	+	0.744509i	−0.983230	−	0.182372i	$-0.941623\pi$
$431$	−12.6198	+	15.4564i	−0.607872	+	0.744509i	0.375357	+	0.926880i	$0.377520\pi$
$432$	−0.133328	+	0.280983i	−0.00641476	+	0.0135188i
$433$	2.26656	−	0.756688i	0.108924	−	0.0363641i	−0.261684	−	0.965154i	$-0.584278\pi$
$433$	2.26656	−	0.756688i	0.108924	−	0.0363641i	0.370607	+	0.928790i	$0.379150\pi$
$434$	0.157633	+	0.228370i	0.00756661	+	0.0109621i
$435$	−6.27398	−	30.7320i	−0.300815	−	1.47349i
$436$	0.237712	−	5.89877i	0.0113844	−	0.282500i
$437$	2.15381			0.103031
$438$	−0.352950	+	8.75836i	−0.0168646	+	0.418491i
$439$	14.3420	−	10.7773i	0.684506	−	0.514373i	−0.200653	−	0.979662i	$-0.564306\pi$
$439$	14.3420	−	10.7773i	0.684506	−	0.514373i	0.885158	+	0.465290i	$0.154050\pi$
$440$	−12.2014	+	1.98292i	−0.581678	+	0.0945318i
$441$	−3.17783	+	1.66785i	−0.151325	+	0.0794216i
$442$	−5.66007	−	9.09377i	−0.269222	−	0.432547i
$443$	−31.4302	−	16.4958i	−1.49329	−	0.783740i	−0.496835	−	0.867845i	$-0.665505\pi$
$443$	−31.4302	−	16.4958i	−1.49329	−	0.783740i	−0.996457	+	0.0841046i	$0.973197\pi$
$444$	7.65563	+	2.55582i	0.363320	+	0.121294i
$445$	−4.65075	+	22.7809i	−0.220467	+	1.07992i
$446$	−6.23463	+	21.5244i	−0.295218	+	1.01921i
$447$	−0.760042	−	6.25951i	−0.0359488	−	0.296065i
$448$	−9.89121	+	3.30217i	−0.467316	+	0.156013i
$449$	33.5380	+	5.45045i	1.58275	+	0.257223i	0.887247	−	0.461296i	$-0.152615\pi$
$449$	33.5380	+	5.45045i	1.58275	+	0.257223i	0.695508	+	0.718518i	$0.255179\pi$
$450$	−11.0566	+	5.80293i	−0.521211	+	0.273553i
$451$	−1.38128	+	0.873468i	−0.0650419	+	0.0411300i
$452$	19.5088	−	8.31193i	0.917617	−	0.390960i
$453$	2.30520	−	11.2916i	0.108308	−	0.530526i
$454$	0.736813	+	0.181608i	0.0345804	+	0.00852329i
$455$	2.51989	−	28.6615i	0.118134	−	1.34367i
$456$	−8.55292	+	2.10811i	−0.400527	+	0.0987211i
$457$	−0.691358	−	17.1559i	−0.0323404	−	0.802518i	−0.931249	−	0.364383i	$-0.881280\pi$
$457$	−0.691358	−	17.1559i	−0.0323404	−	0.802518i	0.898909	−	0.438136i	$-0.144361\pi$
$458$	−0.477126	−	11.8398i	−0.0222946	−	0.553235i
$459$	2.05664	+	2.51893i	0.0959957	+	0.117573i
$460$	−1.26249	+	3.32892i	−0.0588640	+	0.155212i
$461$	1.01736	+	2.14403i	0.0473830	+	0.0998575i	0.925761	−	0.378109i	$-0.123425\pi$
$461$	1.01736	+	2.14403i	0.0473830	+	0.0998575i	−0.878378	+	0.477966i	$0.841374\pi$
$462$	0.464427	−	1.60339i	0.0216071	−	0.0745964i
$463$	−3.22684	+	4.67489i	−0.149964	+	0.217260i	−0.890765	−	0.454464i	$-0.849831\pi$
$463$	−3.22684	+	4.67489i	−0.149964	+	0.217260i	0.740801	+	0.671725i	$0.234446\pi$
$464$	−2.07711	−	0.884974i	−0.0964274	−	0.0410839i
$465$	−0.701386	+	0.113986i	−0.0325260	+	0.00528599i
$466$	11.7105	+	7.40525i	0.542477	+	0.343042i
$467$	6.06388	+	8.78504i	0.280603	+	0.406523i	0.937789	−	0.347205i	$-0.112869\pi$
$467$	6.06388	+	8.78504i	0.280603	+	0.406523i	−0.657187	+	0.753728i	$0.728254\pi$
$468$	4.17481	−	0.476692i	0.192981	−	0.0220351i
$469$	7.93699	−	11.4987i	0.366496	−	0.530961i
$470$	13.8990	−	5.92183i	0.641115	−	0.273154i
$471$	−2.29605	−	7.92688i	−0.105796	−	0.365251i
$472$	−4.96854	+	0.401102i	−0.228696	+	0.0184622i
$473$	−0.537909	+	0.476546i	−0.0247331	+	0.0219116i
$474$	−13.5130	+	8.54509i	−0.620671	+	0.392489i
$475$	−38.3044	−	16.3200i	−1.75752	−	0.748811i
$476$	−0.843681	+	6.94834i	−0.0386701	+	0.318477i
$477$	−0.915589	−	4.48485i	−0.0419219	−	0.205347i
$478$	−7.98999	−	0.645019i	−0.365454	−	0.0295025i
$479$	−28.1691	+	21.1677i	−1.28708	+	0.967175i	−0.287120	+	0.957895i	$0.592698\pi$
$479$	−28.1691	+	21.1677i	−1.28708	+	0.967175i	−0.999957	+	0.00928084i	$0.997046\pi$
$480$	2.86412	−	23.5882i	0.130729	−	1.07665i
$481$	5.80249	+	24.2866i	0.264571	+	1.10737i
$482$	1.03951	+	8.56113i	0.0473484	+	0.389949i
$483$	−0.904607	−	0.941795i	−0.0411610	−	0.0428532i
$484$	−5.83938	−	10.1141i	−0.265426	−	0.459732i
$485$	35.1292	−	60.8455i	1.59513	−	2.76285i
$486$	0.887014	−	0.218629i	0.0402358	−	0.00991723i
$487$	12.2102	+	14.9547i	0.553295	+	0.677663i	0.973215	−	0.229898i	$-0.0738393\pi$
$487$	12.2102	+	14.9547i	0.553295	+	0.677663i	−0.419920	+	0.907561i	$0.637942\pi$
$488$	−15.6401	+	27.0894i	−0.707993	+	1.22628i
$489$	−4.58383	−	12.0866i	−0.207288	−	0.546574i
$490$	−9.81327	+	10.2167i	−0.443319	+	0.461544i
$491$	−3.71239	−	1.23938i	−0.167538	−	0.0559324i	0.231662	−	0.972796i	$-0.425584\pi$
$491$	−3.71239	−	1.23938i	−0.167538	−	0.0559324i	−0.399200	+	0.916864i	$0.630712\pi$
$492$	−0.535599	−	1.84910i	−0.0241466	−	0.0833639i
$493$	−17.6701	+	15.6543i	−0.795820	+	0.705035i
$494$	−7.18655	−	7.00211i	−0.323338	−	0.315040i
$495$	3.19964	+	2.83463i	0.143813	+	0.127407i
$496$	−0.0219274	+	0.0462110i	−0.000984570	+	0.00207494i
$497$	−18.2360	−	18.9857i	−0.817998	−	0.851626i
$498$	2.50624	+	5.28178i	0.112307	+	0.236682i
$499$	−7.90760	−	1.94905i	−0.353993	−	0.0872514i	0.0583093	−	0.998299i	$-0.481429\pi$
$499$	−7.90760	−	1.94905i	−0.353993	−	0.0872514i	−0.412302	+	0.911047i	$0.635275\pi$
$500$	30.2362	−	31.4792i	1.35220	−	1.40779i
$501$	−1.18785	−	0.892610i	−0.0530691	−	0.0398789i
$502$	−18.7325	−	16.5956i	−0.836074	−	0.740697i
$503$	−28.9625	−	4.70686i	−1.29137	−	0.209869i	−0.524359	−	0.851498i	$-0.675695\pi$
$503$	−28.9625	−	4.70686i	−1.29137	−	0.209869i	−0.767015	+	0.641629i	$0.778259\pi$
$504$	4.51406	+	2.85452i	0.201072	+	0.127150i
$505$	58.7360	+	4.74166i	2.61372	+	0.211001i
$506$	−0.639058			−0.0284096
$507$	8.07716	+	10.1862i	0.358719	+	0.452387i
$508$	−21.9086			−0.972035
$509$	−7.75895	−	0.626367i	−0.343909	−	0.0277632i	−0.0926946	−	0.995695i	$-0.529548\pi$
$509$	−7.75895	−	0.626367i	−0.343909	−	0.0277632i	−0.251215	+	0.967931i	$0.580830\pi$
$510$	10.8488	+	6.86033i	0.480391	+	0.303781i
$511$	17.4913	+	2.84262i	0.773772	+	0.125750i
$512$	−2.62664	−	2.32700i	−0.116082	−	0.102840i
$513$	2.43524	+	1.82996i	0.107518	+	0.0807949i
$514$	−2.39980	+	2.49845i	−0.105850	+	0.110202i
$515$	26.6090	+	6.55852i	1.17253	+	0.289003i
$516$	−0.362898	−	0.764792i	−0.0159757	−	0.0336681i
$517$	−2.62317	−	2.73101i	−0.115367	−	0.120110i
$518$	−5.00932	+	10.5569i	−0.220097	+	0.463844i
$519$	8.52087	+	7.54883i	0.374025	+	0.331357i
$520$	40.8370	−	19.0214i	1.79082	−	0.834142i
$521$	4.43135	−	3.92584i	0.194141	−	0.171994i	−0.560452	−	0.828187i	$-0.689373\pi$
$521$	4.43135	−	3.92584i	0.194141	−	0.171994i	0.754593	+	0.656193i	$0.227834\pi$
$522$	1.84513	+	6.37012i	0.0807591	+	0.278813i
$523$	37.5938	+	12.5506i	1.64386	+	0.548801i	0.979990	−	0.199046i	$-0.0637844\pi$
$523$	37.5938	+	12.5506i	1.64386	+	0.548801i	0.663870	+	0.747848i	$0.268913\pi$
$524$	−8.58981	+	8.94294i	−0.375247	+	0.390674i
$525$	8.95172	+	23.6038i	0.390685	+	1.03015i
$526$	−12.8796	+	22.3080i	−0.561575	+	0.972677i
$527$	0.338239	+	0.414267i	0.0147339	+	0.0180458i
$528$	0.298758	−	0.0736372i	0.0130018	−	0.00320465i
$529$	11.2500	−	19.4856i	0.489132	−	0.847202i
$530$	−9.03389	−	15.6472i	−0.392407	−	0.679669i
$531$	1.19408	+	1.24317i	0.0518186	+	0.0539489i
$532$	0.790310	+	6.50879i	0.0342643	+	0.282192i
$533$	3.98124	−	4.42976i	0.172446	−	0.191874i
$534$	0.592572	−	4.88027i	0.0256431	−	0.211190i
$535$	41.1115	−	30.8933i	1.77740	−	1.33563i
$536$	21.8056	+	1.76033i	0.941858	+	0.0760347i
$537$	0.192244	+	0.941673i	0.00829594	+	0.0406362i
$538$	1.37345	−	11.3114i	0.0592138	−	0.487669i
$539$	3.26657	+	1.39175i	0.140701	+	0.0599471i
$540$	−4.25584	+	2.69123i	−0.183142	+	0.115812i
$541$	20.6453	−	18.2902i	0.887612	−	0.786356i	−0.0901813	−	0.995925i	$-0.528745\pi$
$541$	20.6453	−	18.2902i	0.887612	−	0.786356i	0.977794	+	0.209569i	$0.0672062\pi$
$542$	17.9136	−	1.44613i	0.769454	−	0.0621167i
$543$	−1.23077	−	4.24910i	−0.0528172	−	0.182346i
$544$	−16.4525	+	7.00977i	−0.705397	+	0.300541i
$545$	−12.4333	+	18.0128i	−0.532584	+	0.771582i
$546$	−0.0434357	+	6.08337i	−0.00185888	+	0.260344i
$547$	13.0431	+	18.8961i	0.557681	+	0.807941i	0.995856	−	0.0909493i	$-0.0289901\pi$
$547$	13.0431	+	18.8961i	0.557681	+	0.807941i	−0.438174	+	0.898890i	$0.644375\pi$
$548$	−21.9764	−	13.8971i	−0.938787	−	0.593653i
$549$	10.6768	−	1.73515i	0.455675	−	0.0740544i
$550$	11.3653	+	4.84230i	0.484618	+	0.206476i
$551$	−12.5619	+	18.1991i	−0.535157	+	0.775309i
$552$	0.568859	−	1.96393i	0.0242122	−	0.0835903i
$553$	13.8564	+	29.2018i	0.589235	+	1.24179i
$554$	3.71978	−	9.80825i	0.158038	−	0.416713i
$555$	−18.9245	−	23.1783i	−0.803301	−	0.983865i
$556$	−0.480057	−	11.9125i	−0.0203590	−	0.505203i
$557$	−0.759074	−	18.8362i	−0.0321630	−	0.798117i	−0.932122	−	0.362143i	$-0.882045\pi$
$557$	−0.759074	−	18.8362i	−0.0321630	−	0.798117i	0.899959	−	0.435974i	$-0.143596\pi$
$558$	0.145880	−	0.0359562i	0.00617559	−	0.00152215i
$559$	1.41553	−	2.20349i	0.0598704	−	0.0931976i
$560$	2.40973	+	0.593945i	0.101830	+	0.0250988i
$561$	0.643533	−	3.15223i	0.0271700	−	0.133087i
$562$	4.23356	−	1.80375i	0.178582	−	0.0760866i
$563$	12.1900	−	7.70850i	0.513748	−	0.324875i	−0.252309	−	0.967647i	$-0.581190\pi$
$563$	12.1900	−	7.70850i	0.513748	−	0.324875i	0.766058	+	0.642772i	$0.222216\pi$
$564$	3.94968	−	2.07295i	0.166311	−	0.0872869i
$565$	−77.6010	−	12.6114i	−3.26470	−	0.530565i
$566$	−2.85103	+	0.951814i	−0.119838	+	0.0400077i
$567$	−0.222621	−	1.83345i	−0.00934919	−	0.0769975i
$568$	11.4677	−	39.5910i	0.481173	−	1.66120i
$569$	−1.66698	+	8.16541i	−0.0698835	+	0.342312i	−0.999667	−	0.0257941i	$-0.991789\pi$
$569$	−1.66698	+	8.16541i	−0.0698835	+	0.342312i	0.929784	+	0.368106i	$0.119994\pi$
$570$	11.4051	+	3.80758i	0.477706	+	0.159482i
$571$	−30.0577	−	15.7755i	−1.25787	−	0.660184i	−0.301818	−	0.953366i	$-0.597594\pi$
$571$	−30.0577	−	15.7755i	−1.25787	−	0.660184i	−0.956057	+	0.293182i	$0.905286\pi$
$572$	−2.97753	−	2.90112i	−0.124497	−	0.121302i
$573$	14.3683	−	7.54107i	0.600245	−	0.315033i
$574$	2.75106	−	0.447091i	0.114827	−	0.0186612i
$575$	7.72603	−	5.80573i	0.322198	−	0.242116i
$576$	−0.227346	+	5.64153i	−0.00947274	+	0.235064i
$577$	−41.1334			−1.71240			−0.856202	−	0.516641i	$-0.827182\pi$
$577$	−41.1334			−1.71240			−0.856202	+	0.516641i	$0.827182\pi$
$578$	−0.236355	+	5.86509i	−0.00983107	+	0.243955i
$579$	2.64009	+	12.9320i	0.109719	+	0.537437i
$580$	−20.7651	−	30.0834i	−0.862222	−	1.24914i
$581$	11.2109	−	3.74274i	0.465105	−	0.155275i
$582$	−6.36837	+	13.4211i	−0.263978	+	0.556321i
$583$	−2.86410	+	3.50788i	−0.118619	+	0.145282i
$584$	9.83897	+	25.9432i	0.407139	+	1.07354i
$585$	−14.0263	−	6.77869i	−0.579917	−	0.280264i
$586$	−7.02107	+	18.5130i	−0.290038	+	0.764767i
$587$	−0.922987	−	1.59866i	−0.0380957	−	0.0659837i	0.846349	−	0.532629i	$-0.178796\pi$
$587$	−0.922987	−	1.59866i	−0.0380957	−	0.0659837i	−0.884445	+	0.466645i	$0.845463\pi$
$588$	−2.64523	+	3.23982i	−0.109088	+	0.133608i
$589$	0.400504	+	0.300959i	0.0165025	+	0.0124008i
$590$	6.02462	+	3.16197i	0.248030	+	0.130176i
$591$	1.20958	−	0.0976478i	0.0497557	−	0.00401669i
$592$	−2.14692	+	0.173317i	−0.0882377	+	0.00712328i
$593$	−8.90236	−	4.67232i	−0.365576	−	0.191869i	0.271925	−	0.962318i	$-0.412340\pi$
$593$	−8.90236	−	4.67232i	−0.365576	−	0.191869i	−0.637501	+	0.770449i	$0.720032\pi$
$594$	−0.722561	−	0.542969i	−0.0296470	−	0.0222783i
$595$	16.4118	−	20.1009i	0.672820	−	0.824055i
$596$	−3.67423	−	6.36395i	−0.150502	−	0.260678i
$597$	−7.13242	+	18.8066i	−0.291910	+	0.769704i
$598$	2.24158	−	0.631969i	0.0916649	−	0.0258431i
$599$	−16.3950	−	43.2301i	−0.669883	−	1.76634i	−0.641975	−	0.766725i	$-0.721885\pi$
$599$	−16.3950	−	43.2301i	−0.669883	−	1.76634i	−0.0279074	−	0.999611i	$-0.508884\pi$
$600$	−24.9980	+	30.6170i	−1.02054	+	1.24993i
$601$	−1.66084	+	3.50014i	−0.0677470	+	0.142774i	−0.934499	−	0.355965i	$-0.884152\pi$
$601$	−1.66084	+	3.50014i	−0.0677470	+	0.142774i	0.866752	+	0.498739i	$0.166203\pi$
$602$	1.16251	−	0.388105i	0.0473806	−	0.0158180i
$603$	−4.29744	−	6.22591i	−0.175005	−	0.253539i
$604$	−2.68649	−	13.1593i	−0.109312	−	0.535445i
$605$	−1.74345	+	43.2633i	−0.0708814	+	1.75890i
$606$	−12.4595			−0.506131
$607$	1.57877	−	39.1767i	0.0640802	−	1.59013i	−0.573144	−	0.819455i	$-0.694276\pi$
$607$	1.57877	−	39.1767i	0.0640802	−	1.59013i	0.637224	−	0.770679i	$-0.280083\pi$
$608$	−13.3925	+	10.0638i	−0.543137	+	0.408141i
$609$	13.2340	−	2.15073i	0.536268	−	0.0871520i
$610$	37.8059	−	19.8420i	1.53071	−	0.803381i
$611$	11.9018	+	6.98531i	0.481497	+	0.282595i
$612$	3.35568	+	1.76119i	0.135645	+	0.0711921i
$613$	−6.91404	−	2.30825i	−0.279255	−	0.0932292i	0.173591	−	0.984818i	$-0.444463\pi$
$613$	−6.91404	−	2.30825i	−0.279255	−	0.0932292i	−0.452846	+	0.891589i	$0.649591\pi$
$614$	−0.966864	+	4.73601i	−0.0390194	+	0.191130i
$615$	−1.98570	+	6.85545i	−0.0800713	+	0.276438i
$616$	−0.636916	−	5.24547i	−0.0256621	−	0.211346i
$617$	−14.2128	+	4.74492i	−0.572184	+	0.191023i	−0.588013	−	0.808852i	$-0.700090\pi$
$617$	−14.2128	+	4.74492i	−0.572184	+	0.191023i	0.0158288	+	0.999875i	$0.494961\pi$
$618$	−5.71951	−	0.929510i	−0.230072	−	0.0373904i
$619$	6.00738	−	3.15291i	0.241457	−	0.126726i	−0.339655	−	0.940550i	$-0.610310\pi$
$619$	6.00738	−	3.15291i	0.241457	−	0.126726i	0.581112	+	0.813824i	$0.302618\pi$
$620$	−0.699922	+	0.442604i	−0.0281096	+	0.0177754i
$621$	−0.650476	+	0.277142i	−0.0261027	+	0.0111213i
$622$	1.42175	−	6.96422i	0.0570072	−	0.279240i
$623$	−9.64992	−	2.37849i	−0.386616	−	0.0952923i
$624$	−0.975111	+	0.553736i	−0.0390357	+	0.0221672i
$625$	−90.7654	+	22.3717i	−3.63061	+	0.894866i
$626$	−0.811741	−	20.1431i	−0.0324437	−	0.805082i
$627$	−0.121351	−	3.01128i	−0.00484628	−	0.120259i
$628$	−6.08271	−	7.44997i	−0.242727	−	0.297286i
$629$	−7.98599	+	21.0573i	−0.318422	+	0.839611i
$630$	−3.12523	−	6.58629i	−0.124512	−	0.262404i
$631$	11.8135	−	40.7848i	0.470286	−	1.62362i	−0.278239	−	0.960512i	$-0.589751\pi$
$631$	11.8135	−	40.7848i	0.470286	−	1.62362i	0.748526	−	0.663106i	$-0.230762\pi$
$632$	−28.7491	+	41.6502i	−1.14358	+	1.65676i
$633$	−18.6572	−	7.94907i	−0.741555	−	0.315947i
$634$	−0.834279	+	0.135584i	−0.0331335	+	0.00538471i
$635$	68.6504	+	43.4119i	2.72431	+	1.72275i
$636$	−3.03033	−	4.39020i	−0.120161	−	0.174083i
$637$	−12.8342	−	1.65142i	−0.508510	−	0.0654318i
$638$	3.72726	−	5.39987i	0.147564	−	0.213783i
$639$	−13.1130	+	5.58692i	−0.518742	+	0.221015i
$640$	−7.02123	−	24.2401i	−0.277538	−	0.958174i
$641$	11.7775	−	0.950780i	0.465184	−	0.0375536i	0.154347	−	0.988017i	$-0.450673\pi$
$641$	11.7775	−	0.950780i	0.465184	−	0.0375536i	0.310837	+	0.950463i	$0.399391\pi$
$642$	−8.13876	+	7.21031i	−0.321211	+	0.284568i
$643$	−4.94585	+	3.12757i	−0.195045	+	0.123339i	−0.628419	−	0.777875i	$-0.716298\pi$
$643$	−4.94585	+	3.12757i	−0.195045	+	0.123339i	0.433373	+	0.901214i	$0.357323\pi$
$644$	−1.40009	−	0.596521i	−0.0551712	−	0.0235062i
$645$	−0.378297	+	3.11556i	−0.0148954	+	0.122675i
$646$	−1.81014	−	8.86666i	−0.0712191	−	0.348854i
$647$	18.4215	+	1.48713i	0.724223	+	0.0584653i	0.437080	−	0.899423i	$-0.356013\pi$
$647$	18.4215	+	1.48713i	0.724223	+	0.0584653i	0.287142	+	0.957888i	$0.407295\pi$
$648$	2.31182	−	1.73722i	0.0908169	−	0.0682445i
$649$	0.205562	−	1.69295i	0.00806900	−	0.0664542i
$650$	−44.6538	−	5.74577i	−1.75147	−	0.225368i
$651$	−0.0366126	−	0.301532i	−0.00143496	−	0.0118180i
$652$	−10.4357	−	10.8647i	−0.408694	−	0.425496i
$653$	−21.7401	−	37.6550i	−0.850757	−	1.47356i	−0.880526	−	0.473998i	$-0.842810\pi$
$653$	−21.7401	−	37.6550i	−0.850757	−	1.47356i	0.0297682	−	0.999557i	$-0.490523\pi$
$654$	2.31389	−	4.00778i	0.0904804	−	0.156717i
$655$	44.6366	−	11.0019i	1.74410	−	0.429881i
$656$	0.324920	+	0.397955i	0.0126860	+	0.0155375i
$657$	4.79742	−	8.30938i	0.187165	−	0.324180i
$658$	2.29005	+	6.03837i	0.0892755	+	0.235400i
$659$	−15.7284	+	16.3750i	−0.612693	+	0.637881i	−0.953193	−	0.302364i	$-0.902224\pi$
$659$	−15.7284	+	16.3750i	−0.612693	+	0.637881i	0.340500	+	0.940245i	$0.389404\pi$
$660$	4.72535	+	1.57756i	0.183934	+	0.0614062i
$661$	5.26452	+	18.1752i	0.204766	+	0.706934i	0.995499	+	0.0947728i	$0.0302125\pi$
$661$	5.26452	+	18.1752i	0.204766	+	0.706934i	−0.790733	+	0.612161i	$0.790300\pi$
$662$	1.52145	−	1.34789i	0.0591330	−	0.0523873i
$663$	0.859991	+	11.6933i	0.0333993	+	0.454128i
$664$	13.8517	+	12.2716i	0.537551	+	0.476229i
$665$	10.4208	−	21.9613i	0.404100	−	0.851622i
$666$	4.38275	+	4.56293i	0.169828	+	0.176810i
$667$	−2.20041	−	4.63727i	−0.0852003	−	0.179556i
$668$	−1.68130	−	0.414402i	−0.0650513	−	0.0160337i
$669$	16.9922	−	17.6907i	0.656956	−	0.683963i
$670$	−23.8720	−	17.9387i	−0.922256	−	0.693031i
$671$	−8.01032	−	7.09652i	−0.309235	−	0.273958i
$672$	10.0255	+	1.62930i	0.386741	+	0.0628516i
$673$	−16.1609	−	10.2196i	−0.622959	−	0.393935i	0.185368	−	0.982669i	$-0.440652\pi$
$673$	−16.1609	−	10.2196i	−0.622959	−	0.393935i	−0.808327	+	0.588734i	$0.799627\pi$
$674$	18.2445	+	1.47285i	0.702751	+	0.0567319i
$675$	13.6683			0.526095
$676$	13.3130	+	7.23153i	0.512039	+	0.278136i
$677$	31.2914			1.20263			0.601314	−	0.799013i	$-0.294644\pi$
$677$	31.2914			1.20263			0.601314	+	0.799013i	$0.294644\pi$
$678$	16.5692	+	1.33760i	0.636337	+	0.0513704i
$679$	25.3832	+	16.0513i	0.974116	+	0.615994i
$680$	40.1046	+	6.51763i	1.53794	+	0.249940i
$681$	−0.621763	−	0.550834i	−0.0238260	−	0.0211080i
$682$	−0.118834	−	0.0892977i	−0.00455038	−	0.00341939i
$683$	−29.7985	+	31.0235i	−1.14021	+	1.18708i	−0.160419	+	0.987049i	$0.551284\pi$
$683$	−29.7985	+	31.0235i	−1.14021	+	1.18708i	−0.979789	+	0.200033i	$0.935895\pi$
$684$	3.44687	+	0.849578i	0.131794	+	0.0324844i
$685$	41.3261	+	87.0928i	1.57899	+	3.32765i
$686$	−12.3764	−	12.8852i	−0.472534	−	0.491960i
$687$	−5.56037	+	11.7182i	−0.212141	+	0.447078i
$688$	0.169097	+	0.149807i	0.00644676	+	0.00571133i
$689$	6.57722	−	15.1367i	0.250572	−	0.576661i
$690$	−2.08901	+	1.85070i	−0.0795274	+	0.0704551i
$691$	−4.48223	−	15.4744i	−0.170512	−	0.588675i	−0.999565	−	0.0295050i	$-0.990607\pi$
$691$	−4.48223	−	15.4744i	−0.170512	−	0.588675i	0.829053	−	0.559170i	$-0.188880\pi$
$692$	12.5840	+	4.20115i	0.478371	+	0.159704i
$693$	−1.26577	+	1.31781i	−0.0480828	+	0.0500595i
$694$	9.28791	+	24.4902i	0.352564	+	0.929636i
$695$	−22.1004	+	38.2790i	−0.838317	+	1.45201i
$696$	13.2768	+	16.2612i	0.503257	+	0.616378i
$697$	5.21562	−	1.28553i	0.197556	−	0.0486931i
$698$	3.05493	−	5.29130i	0.115631	−	0.200279i
$699$	−7.58320	−	13.1345i	−0.286823	−	0.496792i
$700$	20.3798	+	21.2176i	0.770284	+	0.801951i
$701$	0.739404	+	6.08954i	0.0279269	+	0.229999i	0.999989	−	0.00472578i	$-0.00150427\pi$
$701$	0.739404	+	6.08954i	0.0279269	+	0.229999i	−0.972062	+	0.234725i	$0.924581\pi$
$702$	3.07142	+	1.18999i	0.115923	+	0.0449132i
$703$	−2.54286	+	20.9423i	−0.0959058	+	0.789855i
$704$	4.46567	−	3.35573i	0.168306	−	0.126474i
$705$	−16.4839	−	1.33072i	−0.620818	−	0.0501176i
$706$	−3.72439	−	18.2433i	−0.140169	−	0.686595i
$707$	−3.03618	+	25.0052i	−0.114187	+	0.940417i
$708$	1.84811	+	0.787408i	0.0694564	+	0.0295926i
$709$	9.90239	−	6.26189i	0.371892	−	0.235170i	−0.335425	−	0.942067i	$-0.608880\pi$
$709$	9.90239	−	6.26189i	0.371892	−	0.235170i	0.707317	+	0.706897i	$0.249905\pi$
$710$	−42.1126	+	37.3085i	−1.58046	+	1.40016i
$711$	17.4441	−	1.40823i	0.654205	−	0.0528129i
$712$	−4.32948	−	14.9471i	−0.162254	−	0.560166i
$713$	−0.106978	+	0.0455792i	−0.00400637	+	0.00170696i
$714$	−3.11685	+	4.51554i	−0.116645	+	0.168990i
$715$	3.58152	+	14.9906i	0.133941	+	0.560618i
$716$	0.636272	+	0.921798i	0.0237786	+	0.0344492i
$717$	7.41607	+	4.68964i	0.276958	+	0.175138i
$718$	28.0722	−	4.56217i	1.04764	−	0.170259i
$719$	11.4433	+	4.87555i	0.426765	+	0.181827i	0.594660	−	0.803977i	$-0.297287\pi$
$719$	11.4433	+	4.87555i	0.426765	+	0.181827i	−0.167895	+	0.985805i	$0.553697\pi$
$720$	0.763356	−	1.10591i	0.0284486	−	0.0412149i
$721$	−3.25921	+	11.2521i	−0.121379	+	0.419050i
$722$	3.80704	+	8.02316i	0.141683	+	0.298591i
$723$	3.34747	−	8.82655i	0.124494	−	0.328263i
$724$	−3.26056	−	3.99346i	−0.121178	−	0.148416i
$725$	3.99538	+	99.1444i	0.148385	+	3.68213i
$726$	−0.368633	−	9.14754i	−0.0136813	−	0.339497i
$727$	−38.0016	+	9.36656i	−1.40940	+	0.347387i	−0.869330	−	0.494232i	$-0.835449\pi$
$727$	−38.0016	+	9.36656i	−1.40940	+	0.347387i	−0.540073	+	0.841618i	$0.681603\pi$
$728$	7.42135	+	17.7693i	0.275054	+	0.658575i
$729$	−0.970942	−	0.239316i	−0.0359608	−	0.00886354i
$730$	7.57554	−	37.1075i	0.280383	−	1.37341i
$731$	2.17307	−	0.925860i	0.0803740	−	0.0342442i
$732$	10.6545	−	6.73751i	0.393803	−	0.249026i
$733$	−3.72124	+	1.95306i	−0.137447	+	0.0721377i	−0.532045	−	0.846716i	$-0.678576\pi$
$733$	−3.72124	+	1.95306i	−0.137447	+	0.0721377i	0.394598	+	0.918854i	$0.370884\pi$
$734$	−22.5021	−	3.65694i	−0.830567	−	0.134980i
$735$	14.7086	−	4.91044i	0.542533	−	0.181124i
$736$	−0.468697	−	3.86007i	−0.0172764	−	0.142284i
$737$	−2.08231	+	7.18898i	−0.0767030	+	0.264809i
$738$	0.301856	−	1.47859i	0.0111115	−	0.0544277i
$739$	13.7572	+	4.59282i	0.506066	+	0.168950i	0.558226	−	0.829689i	$-0.311482\pi$
$739$	13.7572	+	4.59282i	0.506066	+	0.168950i	−0.0521598	+	0.998639i	$0.516611\pi$
$740$	−30.8778	−	16.2059i	−1.13509	−	0.595742i
$741$	3.40353	+	10.4425i	0.125032	+	0.383613i
$742$	6.83857	−	3.58916i	0.251052	−	0.131762i
$743$	9.81382	−	1.59490i	0.360034	−	0.0585112i	0.0222961	−	0.999751i	$-0.492902\pi$
$743$	9.81382	−	1.59490i	0.360034	−	0.0585112i	0.337738	+	0.941240i	$0.390338\pi$
$744$	0.380206	−	0.285706i	0.0139390	−	0.0104745i
$745$	−1.09701	+	27.2219i	−0.0401912	+	0.997334i
$746$	5.04517			0.184717
$747$	0.257678	−	6.39421i	0.00942793	−	0.233952i
$748$	−0.749978	−	3.67364i	−0.0274219	−	0.134321i
$749$	12.4872	+	18.0909i	0.456274	+	0.661027i
$750$	32.4549	−	10.8350i	1.18508	−	0.395639i
$751$	0.550196	−	1.15951i	0.0200769	−	0.0423112i	−0.893164	−	0.449731i	$-0.851520\pi$
$751$	0.550196	−	1.15951i	0.0200769	−	0.0423112i	0.913241	+	0.407419i	$0.133571\pi$
$752$	−0.752864	+	0.922090i	−0.0274541	+	0.0336252i
$753$	9.71418	+	25.6142i	0.354004	+	0.933433i
$754$	−7.73388	+	22.6267i	−0.281651	+	0.824014i
$755$	−17.6571	+	46.5580i	−0.642608	+	1.69442i
$756$	−1.07620	−	1.86404i	−0.0391411	−	0.0677944i
$757$	−9.98369	+	12.2278i	−0.362864	+	0.444427i	−0.923479	−	0.383649i	$-0.874667\pi$
$757$	−9.98369	+	12.2278i	−0.362864	+	0.444427i	0.560615	+	0.828076i	$0.310565\pi$
$758$	5.51322	+	4.14292i	0.200249	+	0.150477i
$759$	0.619398	+	0.325085i	0.0224827	+	0.0117998i
$760$	37.9370	−	3.06259i	1.37612	−	0.111092i
$761$	8.62945	−	0.696641i	0.312817	−	0.0252532i	0.0769389	−	0.997036i	$-0.475485\pi$
$761$	8.62945	−	0.696641i	0.312817	−	0.0252532i	0.235878	+	0.971783i	$0.424203\pi$
$762$	−15.2069	−	7.98119i	−0.550887	−	0.289128i
$763$	−7.47945	−	5.62044i	−0.270774	−	0.203474i
$764$	11.9602	−	14.6486i	0.432706	−	0.529968i
$765$	−7.02519	−	12.1680i	−0.253996	−	0.439934i
$766$	4.54707	−	11.9896i	0.164292	−	0.433203i
$767$	0.953138	+	6.14153i	0.0344158	+	0.221758i
$768$	5.89643	+	15.5476i	0.212769	+	0.561026i
$769$	19.6086	−	24.0162i	0.707104

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.q (of order \(39\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.910598 + 0.0735111i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(-1.15032 - 0.186944i) q^{4} +(3.23408 + 2.86515i) q^{5} +(-0.730339 - 0.548814i) q^{6} +(-1.27940 + 1.33200i) q^{7} +(-2.80776 - 0.692051i) q^{8} +(0.428693 + 0.903450i) q^{9} +(2.73433 + 2.84674i) q^{10} +(0.424127 - 0.893828i) q^{11} +(0.872320 + 0.772808i) q^{12} +(-0.603766 + 3.55464i) q^{13} +(-1.26294 + 1.11886i) q^{14} +(-1.20209 - 4.15010i) q^{15} +(-0.295006 - 0.0984874i) q^{16} +(-2.25266 + 2.34527i) q^{17} +(0.323953 + 0.854194i) q^{18} +(-1.52309 + 2.63806i) q^{19} +(-3.18459 - 3.90041i) q^{20} +(1.79324 - 0.441995i) q^{21} +(0.451915 - 0.782740i) q^{22} +(-0.353527 - 0.612328i) q^{23} +(2.00321 + 2.08557i) q^{24} +(1.64754 + 13.5687i) q^{25} +(-0.811094 + 3.19246i) q^{26} +(0.120537 - 0.992709i) q^{27} +(1.72072 - 1.29304i) q^{28} +(7.23593 + 0.584145i) q^{29} +(-0.789543 - 3.86744i) q^{30} +(0.0198237 - 0.163263i) q^{31} +(5.05938 + 2.15560i) q^{32} +(-0.836189 + 0.528774i) q^{33} +(-2.22367 + 1.97000i) q^{34} +(-7.95405 + 0.642117i) q^{35} +(-0.324237 - 1.11939i) q^{36} +(6.37129 - 2.71455i) q^{37} +(-1.58085 + 2.29025i) q^{38} +(2.41013 - 2.68165i) q^{39} +(-7.09770 - 10.2828i) q^{40} +(-1.39615 - 0.882871i) q^{41} +(1.66542 - 0.270656i) q^{42} +(-0.668250 - 0.284715i) q^{43} +(-0.654976 + 0.948897i) q^{44} +(-1.20209 + 4.15010i) q^{45} +(-0.276909 - 0.583572i) q^{46} +(1.35726 - 3.57879i) q^{47} +(0.196698 + 0.240911i) q^{48} +(0.144511 + 3.58601i) q^{49} +(0.502795 + 12.4767i) q^{50} +(3.15739 - 0.778227i) q^{51} +(1.35904 - 3.97609i) q^{52} +(-4.44435 - 1.09543i) q^{53} +(0.182736 - 0.895098i) q^{54} +(3.93261 - 1.67553i) q^{55} +(4.51406 - 2.85452i) q^{56} +(2.69725 - 1.41563i) q^{57} +(6.54608 + 1.06384i) q^{58} +(1.63503 - 0.545855i) q^{59} +(0.606946 + 4.99865i) q^{60} +(3.00944 - 10.3898i) q^{61} +(0.0300530 - 0.147209i) q^{62} +(-1.75186 - 0.584858i) q^{63} +(4.99938 + 2.62388i) q^{64} +(-12.1372 + 9.76612i) q^{65} +(-0.800302 + 0.420031i) q^{66} +(-7.46708 + 1.21352i) q^{67} +(3.02970 - 2.27668i) q^{68} +(-0.0284702 + 0.706481i) q^{69} -7.29015 q^{70} +(-0.573933 + 14.2420i) q^{71} +(-0.578432 - 2.83335i) q^{72} +(-5.45049 - 7.89640i) q^{73} +(6.00123 - 2.00351i) q^{74} +(5.85951 - 12.3487i) q^{75} +(2.24520 - 2.74987i) q^{76} +(0.647949 + 1.70850i) q^{77} +(2.39179 - 2.26474i) q^{78} +(6.20589 - 16.3636i) q^{79} +(-0.671892 - 1.16375i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(-1.20643 - 0.906573i) q^{82} +(-5.66638 - 2.97395i) q^{83} +(-2.14542 + 0.173197i) q^{84} +(-14.0048 + 1.13059i) q^{85} +(-0.587578 - 0.308385i) q^{86} +(-5.80353 - 4.36107i) q^{87} +(-1.80942 + 2.21614i) q^{88} +(2.69063 + 4.66031i) q^{89} +(-1.39970 + 3.69070i) q^{90} +(-3.96231 - 5.35202i) q^{91} +(0.292197 + 0.770460i) q^{92} +(-0.104013 + 0.127393i) q^{93} +(1.49899 - 3.15906i) q^{94} +(-12.4842 + 4.16784i) q^{95} +(-3.12405 - 4.52596i) q^{96} +(-3.25260 - 15.9323i) q^{97} +(-0.132020 + 3.27603i) q^{98} +0.989350 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9} + 3 q^{10} - 4 q^{11} - 34 q^{12} - 15 q^{13} + 24 q^{14} - 3 q^{15} + 11 q^{16} - 3 q^{17} - 2 q^{18} + 6 q^{19}+ \cdots - 18 q^{99}+O(q^{100}) \) 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9 + 3 * q^10 - 4 * q^11 - 34 * q^12 - 15 * q^13 + 24 * q^14 - 3 * q^15 + 11 * q^16 - 3 * q^17 - 2 * q^18 + 6 * q^19 + q^20 + 6 * q^21 - 86 * q^22 - 52 * q^23 + 9 * q^24 - 74 * q^25 - 64 * q^26 - 32 * q^27 - 16 * q^28 - 44 * q^29 + 3 * q^30 - 28 * q^31 + 74 * q^32 - 17 * q^33 - 83 * q^34 + 70 * q^35 + 17 * q^36 + 11 * q^37 - 29 * q^38 + q^39 - 5 * q^40 + q^41 + 118 * q^42 - 79 * q^43 - 19 * q^44 - 3 * q^45 + 314 * q^46 + 11 * q^48 - 69 * q^49 - 76 * q^50 + 6 * q^51 - 37 * q^52 - 102 * q^53 + q^54 - 73 * q^55 - 36 * q^56 + 14 * q^57 - 51 * q^58 + 194 * q^59 + 76 * q^60 + 4 * q^61 - 89 * q^62 - 3 * q^63 - 184 * q^64 - 49 * q^65 - 36 * q^66 - 73 * q^67 + 4 * q^68 - 100 * q^70 + 106 * q^71 + 9 * q^72 - 132 * q^73 - 45 * q^74 + 11 * q^75 + 24 * q^76 - 54 * q^77 - 39 * q^78 - 2 * q^79 + 177 * q^80 + 16 * q^81 - 76 * q^82 - 58 * q^83 - 16 * q^84 - 123 * q^85 - 157 * q^86 - 57 * q^87 + 476 * q^88 + 18 * q^89 - 6 * q^90 + 233 * q^91 - 12 * q^92 + q^93 - 111 * q^94 + 64 * q^95 - 83 * q^96 - 143 * q^97 - 79 * q^98 - 18 * q^99

Introduction

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