LMFDB - Embedded newform 538.3.c.b.187.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [538,3,Mod(187,538)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(538, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("538.187");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 538 = 2 \cdot 269 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	538.c (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.6594382226$
Analytic rank:	$0$
Dimension:	$46$
Relative dimension:	$23$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			187.4
Character	$\chi$	$=$	538.187
Dual form			538.3.c.b.351.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 - 1.00000i) q^{2} +(-2.93814 - 2.93814i) q^{3} +2.00000i q^{4} -0.402162 q^{5} +5.87628i q^{6} +(-0.366019 + 0.366019i) q^{7} +(2.00000 - 2.00000i) q^{8} +8.26535i q^{9} +(0.402162 + 0.402162i) q^{10} -9.69599i q^{11} +(5.87628 - 5.87628i) q^{12} -22.1669i q^{13} +0.732038 q^{14} +(1.18161 + 1.18161i) q^{15} -4.00000 q^{16} +(-6.41838 - 6.41838i) q^{17} +(8.26535 - 8.26535i) q^{18} +(-20.9838 + 20.9838i) q^{19} -0.804324i q^{20} +2.15083 q^{21} +(-9.69599 + 9.69599i) q^{22} +1.31008 q^{23} -11.7526 q^{24} -24.8383 q^{25} +(-22.1669 + 22.1669i) q^{26} +(-2.15851 + 2.15851i) q^{27} +(-0.732038 - 0.732038i) q^{28} +(-27.7142 + 27.7142i) q^{29} -2.36322i q^{30} +(22.8932 - 22.8932i) q^{31} +(4.00000 + 4.00000i) q^{32} +(-28.4882 + 28.4882i) q^{33} +12.8368i q^{34} +(0.147199 - 0.147199i) q^{35} -16.5307 q^{36} +42.5097 q^{37} +41.9676 q^{38} +(-65.1294 + 65.1294i) q^{39} +(-0.804324 + 0.804324i) q^{40} +34.9325 q^{41} +(-2.15083 - 2.15083i) q^{42} -65.6572i q^{43} +19.3920 q^{44} -3.32401i q^{45} +(-1.31008 - 1.31008i) q^{46} +41.6093 q^{47} +(11.7526 + 11.7526i) q^{48} +48.7321i q^{49} +(24.8383 + 24.8383i) q^{50} +37.7162i q^{51} +44.3337 q^{52} +27.5045 q^{53} +4.31702 q^{54} +3.89936i q^{55} +1.46408i q^{56} +123.307 q^{57} +55.4284 q^{58} +(-64.5763 + 64.5763i) q^{59} +(-2.36322 + 2.36322i) q^{60} +34.4764 q^{61} -45.7864 q^{62} +(-3.02528 - 3.02528i) q^{63} -8.00000i q^{64} +8.91467i q^{65} +56.9764 q^{66} -102.668 q^{67} +(12.8368 - 12.8368i) q^{68} +(-3.84920 - 3.84920i) q^{69} -0.294398 q^{70} +(-31.6960 + 31.6960i) q^{71} +(16.5307 + 16.5307i) q^{72} +59.8307i q^{73} +(-42.5097 - 42.5097i) q^{74} +(72.9783 + 72.9783i) q^{75} +(-41.9676 - 41.9676i) q^{76} +(3.54892 + 3.54892i) q^{77} +130.259 q^{78} +40.3254i q^{79} +1.60865 q^{80} +87.0721 q^{81} +(-34.9325 - 34.9325i) q^{82} +(-93.6724 + 93.6724i) q^{83} +4.30166i q^{84} +(2.58123 + 2.58123i) q^{85} +(-65.6572 + 65.6572i) q^{86} +162.857 q^{87} +(-19.3920 - 19.3920i) q^{88} -70.9859i q^{89} +(-3.32401 + 3.32401i) q^{90} +(8.11349 + 8.11349i) q^{91} +2.62016i q^{92} -134.527 q^{93} +(-41.6093 - 41.6093i) q^{94} +(8.43888 - 8.43888i) q^{95} -23.5051i q^{96} +11.8247i q^{97} +(48.7321 - 48.7321i) q^{98} +80.1407 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 46 q^{2} - 6 q^{3} - 32 q^{5} + 4 q^{7} + 92 q^{8} + 32 q^{10} + 12 q^{12} - 8 q^{14} - 10 q^{15} - 184 q^{16} - 50 q^{17} + 118 q^{18} + 10 q^{19} + 16 q^{21} + 8 q^{22} - 124 q^{23} - 24 q^{24}+ \cdots + 508 q^{99}+O(q^{100}) $ 46 * q - 46 * q^2 - 6 * q^3 - 32 * q^5 + 4 * q^7 + 92 * q^8 + 32 * q^10 + 12 * q^12 - 8 * q^14 - 10 * q^15 - 184 * q^16 - 50 * q^17 + 118 * q^18 + 10 * q^19 + 16 * q^21 + 8 * q^22 - 124 * q^23 - 24 * q^24 + 178 * q^25 + 4 * q^26 + 90 * q^27 + 8 * q^28 + 40 * q^29 + 40 * q^31 + 184 * q^32 - 64 * q^33 - 14 * q^35 - 236 * q^36 - 32 * q^37 - 20 * q^38 - 54 * q^39 - 64 * q^40 - 132 * q^41 - 16 * q^42 - 16 * q^44 + 124 * q^46 - 60 * q^47 + 24 * q^48 - 178 * q^50 - 8 * q^52 - 188 * q^53 - 180 * q^54 - 40 * q^57 - 80 * q^58 + 190 * q^59 + 20 * q^60 - 80 * q^62 - 266 * q^63 + 128 * q^66 - 164 * q^67 + 100 * q^68 + 170 * q^69 + 28 * q^70 - 92 * q^71 + 236 * q^72 + 32 * q^74 - 190 * q^75 + 20 * q^76 + 20 * q^77 + 108 * q^78 + 128 * q^80 - 298 * q^81 + 132 * q^82 + 190 * q^83 + 298 * q^85 + 228 * q^86 - 92 * q^87 + 16 * q^88 - 528 * q^90 + 2 * q^91 + 232 * q^93 + 60 * q^94 - 280 * q^95 - 226 * q^98 + 508 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/538\mathbb{Z}\right)^\times$.

$n$	$271$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$3$	−2.93814	−	2.93814i	−0.979380	−	0.979380i	0.0204112	−	0.999792i	$-0.493502\pi$
$3$	−2.93814	−	2.93814i	−0.979380	−	0.979380i	−0.999792	+	0.0204112i	$0.993502\pi$
$4$			2.00000i			0.500000i
$5$	−0.402162			−0.0804324			−0.0402162	−	0.999191i	$-0.512805\pi$
$5$	−0.402162			−0.0804324			−0.0402162	+	0.999191i	$0.512805\pi$
$6$			5.87628i			0.979380i
$7$	−0.366019	+	0.366019i	−0.0522884	+	0.0522884i	−0.732768	−	0.680479i	$-0.761772\pi$
$7$	−0.366019	+	0.366019i	−0.0522884	+	0.0522884i	0.680479	+	0.732768i	$0.261772\pi$
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$			8.26535i			0.918372i
$10$	0.402162	+	0.402162i	0.0402162	+	0.0402162i
$11$		−	9.69599i		−	0.881453i	−0.897641	−	0.440727i	$-0.854721\pi$
$11$		−	9.69599i		−	0.881453i	0.897641	−	0.440727i	$-0.145279\pi$
$12$	5.87628	−	5.87628i	0.489690	−	0.489690i
$13$		−	22.1669i		−	1.70514i	−0.522610	−	0.852572i	$-0.675042\pi$
$13$		−	22.1669i		−	1.70514i	0.522610	−	0.852572i	$-0.324958\pi$
$14$	0.732038			0.0522884
$15$	1.18161	+	1.18161i	0.0787739	+	0.0787739i
$16$	−4.00000			−0.250000
$17$	−6.41838	−	6.41838i	−0.377551	−	0.377551i	0.492667	−	0.870218i	$-0.336022\pi$
$17$	−6.41838	−	6.41838i	−0.377551	−	0.377551i	−0.870218	+	0.492667i	$0.836022\pi$
$18$	8.26535	−	8.26535i	0.459186	−	0.459186i
$19$	−20.9838	+	20.9838i	−1.10441	+	1.10441i	−0.110537	+	0.993872i	$0.535257\pi$
$19$	−20.9838	+	20.9838i	−1.10441	+	1.10441i	−0.993872	+	0.110537i	$0.964743\pi$
$20$		−	0.804324i		−	0.0402162i
$21$	2.15083			0.102421
$22$	−9.69599	+	9.69599i	−0.440727	+	0.440727i
$23$	1.31008			0.0569601			0.0284800	−	0.999594i	$-0.490933\pi$
$23$	1.31008			0.0569601			0.0284800	+	0.999594i	$0.490933\pi$
$24$	−11.7526			−0.489690
$25$	−24.8383			−0.993531
$26$	−22.1669	+	22.1669i	−0.852572	+	0.852572i
$27$	−2.15851	+	2.15851i	−0.0799447	+	0.0799447i
$28$	−0.732038	−	0.732038i	−0.0261442	−	0.0261442i
$29$	−27.7142	+	27.7142i	−0.955663	+	0.955663i	−0.999058	−	0.0433954i	$-0.986182\pi$
$29$	−27.7142	+	27.7142i	−0.955663	+	0.955663i	0.0433954	+	0.999058i	$0.486182\pi$
$30$		−	2.36322i		−	0.0787739i
$31$	22.8932	−	22.8932i	0.738491	−	0.738491i	−0.233795	−	0.972286i	$-0.575114\pi$
$31$	22.8932	−	22.8932i	0.738491	−	0.738491i	0.972286	+	0.233795i	$0.0751144\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	−28.4882	+	28.4882i	−0.863278	+	0.863278i
$34$			12.8368i			0.377551i
$35$	0.147199	−	0.147199i	0.00420568	−	0.00420568i
$36$	−16.5307			−0.459186
$37$	42.5097			1.14891			0.574456	−	0.818536i	$-0.305214\pi$
$37$	42.5097			1.14891			0.574456	+	0.818536i	$0.305214\pi$
$38$	41.9676			1.10441
$39$	−65.1294	+	65.1294i	−1.66998	+	1.66998i
$40$	−0.804324	+	0.804324i	−0.0201081	+	0.0201081i
$41$	34.9325			0.852013			0.426007	−	0.904720i	$-0.359920\pi$
$41$	34.9325			0.852013			0.426007	+	0.904720i	$0.359920\pi$
$42$	−2.15083	−	2.15083i	−0.0512103	−	0.0512103i
$43$		−	65.6572i		−	1.52691i	−0.645860	−	0.763456i	$-0.723501\pi$
$43$		−	65.6572i		−	1.52691i	0.645860	−	0.763456i	$-0.276499\pi$
$44$	19.3920			0.440727
$45$		−	3.32401i		−	0.0738669i
$46$	−1.31008	−	1.31008i	−0.0284800	−	0.0284800i
$47$	41.6093			0.885305			0.442653	−	0.896693i	$-0.354037\pi$
$47$	41.6093			0.885305			0.442653	+	0.896693i	$0.354037\pi$
$48$	11.7526	+	11.7526i	0.244845	+	0.244845i
$49$			48.7321i			0.994532i
$50$	24.8383	+	24.8383i	0.496765	+	0.496765i
$51$			37.7162i			0.739533i
$52$	44.3337			0.852572
$53$	27.5045			0.518953			0.259477	−	0.965749i	$-0.416450\pi$
$53$	27.5045			0.518953			0.259477	+	0.965749i	$0.416450\pi$
$54$	4.31702			0.0799447
$55$			3.89936i			0.0708974i
$56$			1.46408i			0.0261442i
$57$	123.307			2.16327
$58$	55.4284			0.955663
$59$	−64.5763	+	64.5763i	−1.09451	+	1.09451i	−0.0994736	+	0.995040i	$0.531716\pi$
$59$	−64.5763	+	64.5763i	−1.09451	+	1.09451i	−0.995040	+	0.0994736i	$0.968284\pi$
$60$	−2.36322	+	2.36322i	−0.0393869	+	0.0393869i
$61$	34.4764			0.565186			0.282593	−	0.959240i	$-0.408805\pi$
$61$	34.4764			0.565186			0.282593	+	0.959240i	$0.408805\pi$
$62$	−45.7864			−0.738491
$63$	−3.02528	−	3.02528i	−0.0480202	−	0.0480202i
$64$		−	8.00000i		−	0.125000i
$65$			8.91467i			0.137149i
$66$	56.9764			0.863278
$67$	−102.668			−1.53236			−0.766180	−	0.642626i	$-0.777845\pi$
$67$	−102.668			−1.53236			−0.766180	+	0.642626i	$0.777845\pi$
$68$	12.8368	−	12.8368i	0.188776	−	0.188776i
$69$	−3.84920	−	3.84920i	−0.0557856	−	0.0557856i
$70$	−0.294398			−0.00420568
$71$	−31.6960	+	31.6960i	−0.446422	+	0.446422i	−0.894163	−	0.447741i	$-0.852229\pi$
$71$	−31.6960	+	31.6960i	−0.446422	+	0.446422i	0.447741	+	0.894163i	$0.352229\pi$
$72$	16.5307	+	16.5307i	0.229593	+	0.229593i
$73$			59.8307i			0.819599i	0.912176	+	0.409800i	$0.134401\pi$
$73$			59.8307i			0.819599i	−0.912176	+	0.409800i	$0.865599\pi$
$74$	−42.5097	−	42.5097i	−0.574456	−	0.574456i
$75$	72.9783	+	72.9783i	0.973044	+	0.973044i
$76$	−41.9676	−	41.9676i	−0.552205	−	0.552205i
$77$	3.54892	+	3.54892i	0.0460898	+	0.0460898i
$78$	130.259			1.66998
$79$			40.3254i			0.510449i	0.966882	+	0.255224i	$0.0821493\pi$
$79$			40.3254i			0.510449i	−0.966882	+	0.255224i	$0.917851\pi$
$80$	1.60865			0.0201081
$81$	87.0721			1.07496
$82$	−34.9325	−	34.9325i	−0.426007	−	0.426007i
$83$	−93.6724	+	93.6724i	−1.12858	+	1.12858i	−0.138175	+	0.990408i	$0.544124\pi$
$83$	−93.6724	+	93.6724i	−1.12858	+	1.12858i	−0.990408	+	0.138175i	$0.955876\pi$
$84$			4.30166i			0.0512103i
$85$	2.58123	+	2.58123i	0.0303674	+	0.0303674i
$86$	−65.6572	+	65.6572i	−0.763456	+	0.763456i
$87$	162.857			1.87191
$88$	−19.3920	−	19.3920i	−0.220363	−	0.220363i
$89$		−	70.9859i		−	0.797595i	−0.917039	−	0.398797i	$-0.869428\pi$
$89$		−	70.9859i		−	0.797595i	0.917039	−	0.398797i	$-0.130572\pi$
$90$	−3.32401	+	3.32401i	−0.0369334	+	0.0369334i
$91$	8.11349	+	8.11349i	0.0891593	+	0.0891593i
$92$			2.62016i			0.0284800i
$93$	−134.527			−1.44653
$94$	−41.6093	−	41.6093i	−0.442653	−	0.442653i
$95$	8.43888	−	8.43888i	0.0888303	−	0.0888303i
$96$		−	23.5051i		−	0.244845i
$97$			11.8247i			0.121904i	0.998141	+	0.0609519i	$0.0194136\pi$
$97$			11.8247i			0.121904i	−0.998141	+	0.0609519i	$0.980586\pi$
$98$	48.7321	−	48.7321i	0.497266	−	0.497266i
$99$	80.1407			0.809502
$100$		−	49.6765i		−	0.496765i
$101$	55.4057	+	55.4057i	0.548571	+	0.548571i	0.926027	−	0.377456i	$-0.123201\pi$
$101$	55.4057	+	55.4057i	0.548571	+	0.548571i	−0.377456	+	0.926027i	$0.623201\pi$
$102$	37.7162	−	37.7162i	0.369767	−	0.369767i
$103$			190.350i			1.84806i	0.382317	+	0.924031i	$0.375126\pi$
$103$			190.350i			1.84806i	−0.382317	+	0.924031i	$0.624874\pi$
$104$	−44.3337	−	44.3337i	−0.426286	−	0.426286i
$105$	−0.864982			−0.00823793
$106$	−27.5045	−	27.5045i	−0.259477	−	0.259477i
$107$	−105.244	+	105.244i	−0.983584	+	0.983584i	−0.999867	−	0.0162829i	$-0.994817\pi$
$107$	−105.244	+	105.244i	−0.983584	+	0.983584i	0.0162829	+	0.999867i	$0.494817\pi$
$108$	−4.31702	−	4.31702i	−0.0399724	−	0.0399724i
$109$	124.845	−	124.845i	1.14537	−	1.14537i	0.157916	−	0.987453i	$-0.449522\pi$
$109$	124.845	−	124.845i	1.14537	−	1.14537i	0.987453	−	0.157916i	$-0.0504775\pi$
$110$	3.89936	−	3.89936i	0.0354487	−	0.0354487i
$111$	−124.900	−	124.900i	−1.12522	−	1.12522i
$112$	1.46408	−	1.46408i	0.0130721	−	0.0130721i
$113$	21.8381	−	21.8381i	0.193258	−	0.193258i	−0.603844	−	0.797102i	$-0.706365\pi$
$113$	21.8381	−	21.8381i	0.193258	−	0.193258i	0.797102	+	0.603844i	$0.206365\pi$
$114$	−123.307	−	123.307i	−1.08164	−	1.08164i
$115$	−0.526865			−0.00458143
$116$	−55.4284	−	55.4284i	−0.477831	−	0.477831i
$117$	183.217			1.56596
$118$	129.153			1.09451
$119$	4.69850			0.0394832
$120$	4.72643			0.0393869
$121$	26.9878			0.223040
$122$	−34.4764	−	34.4764i	−0.282593	−	0.282593i
$123$	−102.637	−	102.637i	−0.834445	−	0.834445i
$124$	45.7864	+	45.7864i	0.369245	+	0.369245i
$125$	20.0431			0.160344
$126$			6.05055i			0.0480202i
$127$		−	97.4646i		−	0.767437i	−0.923450	−	0.383719i	$-0.874643\pi$
$127$		−	97.4646i		−	0.767437i	0.923450	−	0.383719i	$-0.125357\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$	−192.910	+	192.910i	−1.49543	+	1.49543i
$130$	8.91467	−	8.91467i	0.0685744	−	0.0685744i
$131$	−167.978			−1.28228			−0.641139	−	0.767425i	$-0.721538\pi$
$131$	−167.978			−1.28228			−0.641139	+	0.767425i	$0.721538\pi$
$132$	−56.9764	−	56.9764i	−0.431639	−	0.431639i
$133$		−	15.3609i		−	0.115496i
$134$	102.668	+	102.668i	0.766180	+	0.766180i
$135$	0.868070	−	0.868070i	0.00643015	−	0.00643015i
$136$	−25.6735			−0.188776
$137$	−104.943	+	104.943i	−0.766005	+	0.766005i	−0.977401	−	0.211395i	$-0.932199\pi$
$137$	−104.943	+	104.943i	−0.766005	+	0.766005i	0.211395	+	0.977401i	$0.432199\pi$
$138$			7.69841i			0.0557856i
$139$	−167.297	−	167.297i	−1.20358	−	1.20358i	−0.973071	−	0.230504i	$-0.925963\pi$
$139$	−167.297	−	167.297i	−1.20358	−	1.20358i	−0.230504	−	0.973071i	$-0.574037\pi$
$140$	0.294398	+	0.294398i	0.00210284	+	0.00210284i
$141$	−122.254	−	122.254i	−0.867051	−	0.867051i
$142$	63.3919			0.446422
$143$	−214.930			−1.50300
$144$		−	33.0614i		−	0.229593i
$145$	11.1456	−	11.1456i	0.0768662	−	0.0768662i
$146$	59.8307	−	59.8307i	0.409800	−	0.409800i
$147$	143.182	−	143.182i	0.974025	−	0.974025i
$148$			85.0195i			0.574456i
$149$			216.502i			1.45304i	0.687148	+	0.726518i	$0.258863\pi$
$149$			216.502i			1.45304i	−0.687148	+	0.726518i	$0.741137\pi$
$150$		−	145.957i		−	0.973044i
$151$			208.990i			1.38404i	0.721877	+	0.692021i	$0.243279\pi$
$151$			208.990i			1.38404i	−0.721877	+	0.692021i	$0.756721\pi$
$152$			83.9351i			0.552205i
$153$	53.0501	−	53.0501i	0.346733	−	0.346733i
$154$		−	7.09783i		−	0.0460898i
$155$	−9.20678	+	9.20678i	−0.0593986	+	0.0593986i
$156$	−130.259	−	130.259i	−0.834992	−	0.834992i
$157$	−130.490	−	130.490i	−0.831146	−	0.831146i	0.156528	−	0.987674i	$-0.449970\pi$
$157$	−130.490	−	130.490i	−0.831146	−	0.831146i	−0.987674	+	0.156528i	$0.949970\pi$
$158$	40.3254	−	40.3254i	0.255224	−	0.255224i
$159$	−80.8122	−	80.8122i	−0.508253	−	0.508253i
$160$	−1.60865	−	1.60865i	−0.0100540	−	0.0100540i
$161$	−0.479515	+	0.479515i	−0.00297835	+	0.00297835i
$162$	−87.0721	−	87.0721i	−0.537482	−	0.537482i
$163$	212.724	−	212.724i	1.30505	−	1.30505i	0.380114	−	0.924940i	$-0.375885\pi$
$163$	212.724	−	212.724i	1.30505	−	1.30505i	0.924940	−	0.380114i	$-0.124115\pi$
$164$			69.8651i			0.426007i
$165$	11.4569	−	11.4569i	0.0694355	−	0.0694355i
$166$	187.345			1.12858
$167$	93.8235	+	93.8235i	0.561817	+	0.561817i	0.929823	−	0.368006i	$-0.119959\pi$
$167$	93.8235	+	93.8235i	0.561817	+	0.561817i	−0.368006	+	0.929823i	$0.619959\pi$
$168$	4.30166	−	4.30166i	0.0256051	−	0.0256051i
$169$	−322.370			−1.90751
$170$		−	5.16245i		−	0.0303674i
$171$	−173.438	−	173.438i	−1.01426	−	1.01426i
$172$	131.314			0.763456
$173$	163.957			0.947730			0.473865	−	0.880598i	$-0.342859\pi$
$173$	163.957			0.947730			0.473865	+	0.880598i	$0.342859\pi$
$174$	−162.857	−	162.857i	−0.935957	−	0.935957i
$175$	9.09128	−	9.09128i	0.0519502	−	0.0519502i
$176$			38.7840i			0.220363i
$177$	379.469			2.14389
$178$	−70.9859	+	70.9859i	−0.398797	+	0.398797i
$179$	−159.297	−	159.297i	−0.889925	−	0.889925i	0.104591	−	0.994515i	$-0.466647\pi$
$179$	−159.297	−	159.297i	−0.889925	−	0.889925i	−0.994515	+	0.104591i	$0.966647\pi$
$180$	6.64802			0.0369334
$181$	−84.4401	+	84.4401i	−0.466520	+	0.466520i	−0.900785	−	0.434265i	$-0.857008\pi$
$181$	−84.4401	+	84.4401i	−0.466520	+	0.466520i	0.434265	+	0.900785i	$0.357008\pi$
$182$		−	16.2270i		−	0.0891593i
$183$	−101.296	−	101.296i	−0.553532	−	0.553532i
$184$	2.62016	−	2.62016i	0.0142400	−	0.0142400i
$185$	−17.0958			−0.0924097
$186$	134.527	+	134.527i	0.723264	+	0.723264i
$187$	−62.2325	+	62.2325i	−0.332794	+	0.332794i
$188$			83.2187i			0.442653i
$189$		−	1.58011i		−	0.00836037i
$190$	−16.8778			−0.0888303
$191$		−	129.997i		−	0.680610i	−0.940315	−	0.340305i	$-0.889470\pi$
$191$		−	129.997i		−	0.680610i	0.940315	−	0.340305i	$-0.110530\pi$
$192$	−23.5051	+	23.5051i	−0.122423	+	0.122423i
$193$	129.219	−	129.219i	0.669528	−	0.669528i	−0.288078	−	0.957607i	$-0.593016\pi$
$193$	129.219	−	129.219i	0.669528	−	0.669528i	0.957607	+	0.288078i	$0.0930164\pi$
$194$	11.8247	−	11.8247i	0.0609519	−	0.0609519i
$195$	26.1926	−	26.1926i	0.134321	−	0.134321i
$196$	−97.4641			−0.497266
$197$	136.422	−	136.422i	0.692496	−	0.692496i	−0.270285	−	0.962780i	$-0.587118\pi$
$197$	136.422	−	136.422i	0.692496	−	0.692496i	0.962780	+	0.270285i	$0.0871179\pi$
$198$	−80.1407	−	80.1407i	−0.404751	−	0.404751i
$199$		−	19.3603i		−	0.0972881i	−0.998816	−	0.0486441i	$-0.984510\pi$
$199$		−	19.3603i		−	0.0972881i	0.998816	−	0.0486441i	$-0.0154900\pi$
$200$	−49.6765	+	49.6765i	−0.248383	+	0.248383i
$201$	301.653	+	301.653i	1.50076	+	1.50076i
$202$		−	110.811i		−	0.548571i
$203$		−	20.2879i		−	0.0999402i
$204$	−75.4324			−0.369767
$205$	−14.0485			−0.0685294
$206$	190.350	−	190.350i	0.924031	−	0.924031i
$207$			10.8283i			0.0523105i
$208$			88.6675i			0.426286i
$209$	203.458	+	203.458i	0.973486	+	0.973486i
$210$	0.864982	+	0.864982i	0.00411896	+	0.00411896i
$211$		−	203.403i		−	0.963994i	−0.876173	−	0.481997i	$-0.839912\pi$
$211$		−	203.403i		−	0.963994i	0.876173	−	0.481997i	$-0.160088\pi$
$212$			55.0090i			0.259477i
$213$	186.254			0.874434
$214$	210.487			0.983584
$215$			26.4048i			0.122813i
$216$			8.63403i			0.0399724i
$217$			16.7587i			0.0772291i
$218$	−249.690			−1.14537
$219$	175.791	−	175.791i	0.802699	−	0.802699i
$220$	−7.79871			−0.0354487
$221$	−142.275	+	142.275i	−0.643779	+	0.643779i
$222$			249.799i			1.12522i
$223$	137.380	−	137.380i	0.616056	−	0.616056i	−0.328462	−	0.944517i	$-0.606530\pi$
$223$	137.380	−	137.380i	0.616056	−	0.616056i	0.944517	+	0.328462i	$0.106530\pi$
$224$	−2.92815			−0.0130721
$225$		−	205.297i		−	0.912431i
$226$	−43.6763			−0.193258
$227$	−221.821	+	221.821i	−0.977185	+	0.977185i	−0.999745	−	0.0225608i	$-0.992818\pi$
$227$	−221.821	+	221.821i	−0.977185	+	0.977185i	0.0225608	+	0.999745i	$0.492818\pi$
$228$			246.613i			1.08164i
$229$	−271.374	−	271.374i	−1.18504	−	1.18504i	−0.978421	−	0.206620i	$-0.933754\pi$
$229$	−271.374	−	271.374i	−1.18504	−	1.18504i	−0.206620	−	0.978421i	$-0.566246\pi$
$230$	0.526865	+	0.526865i	0.00229072	+	0.00229072i
$231$		−	20.8544i		−	0.0902789i
$232$			110.857i			0.477831i
$233$			122.625i			0.526288i	0.964757	+	0.263144i	$0.0847594\pi$
$233$			122.625i			0.526288i	−0.964757	+	0.263144i	$0.915241\pi$
$234$	−183.217	−	183.217i	−0.782978	−	0.782978i
$235$	−16.7337			−0.0712072
$236$	−129.153	−	129.153i	−0.547257	−	0.547257i
$237$	118.482	−	118.482i	0.499923	−	0.499923i
$238$	−4.69850	−	4.69850i	−0.0197416	−	0.0197416i
$239$	−241.191			−1.00917			−0.504583	−	0.863363i	$-0.668354\pi$
$239$	−241.191			−1.00917			−0.504583	+	0.863363i	$0.668354\pi$
$240$	−4.72643	−	4.72643i	−0.0196935	−	0.0196935i
$241$	−181.498	+	181.498i	−0.753102	+	0.753102i	−0.975057	−	0.221955i	$-0.928756\pi$
$241$	−181.498	+	181.498i	−0.753102	+	0.753102i	0.221955	+	0.975057i	$0.428756\pi$
$242$	−26.9878	−	26.9878i	−0.111520	−	0.111520i
$243$	−236.404	−	236.404i	−0.972855	−	0.972855i
$244$			68.9527i			0.282593i
$245$		−	19.5982i		−	0.0799926i
$246$			205.273i			0.834445i
$247$	465.145	+	465.145i	1.88318	+	1.88318i
$248$		−	91.5729i		−	0.369245i
$249$	550.445			2.21062
$250$	−20.0431	−	20.0431i	−0.0801722	−	0.0801722i
$251$	−122.307	−	122.307i	−0.487279	−	0.487279i	0.420168	−	0.907446i	$-0.361971\pi$
$251$	−122.307	−	122.307i	−0.487279	−	0.487279i	−0.907446	+	0.420168i	$0.861971\pi$
$252$	6.05055	−	6.05055i	0.0240101	−	0.0240101i
$253$		−	12.7025i		−	0.0502076i
$254$	−97.4646	+	97.4646i	−0.383719	+	0.383719i
$255$		−	15.1680i		−	0.0594824i
$256$	16.0000			0.0625000
$257$	−175.424	−	175.424i	−0.682582	−	0.682582i	0.277999	−	0.960581i	$-0.410329\pi$
$257$	−175.424	−	175.424i	−0.682582	−	0.682582i	−0.960581	+	0.277999i	$0.910329\pi$
$258$	385.820			1.49543
$259$	−15.5594	+	15.5594i	−0.0600748	+	0.0600748i
$260$	−17.8293			−0.0685744
$261$	−229.068	−	229.068i	−0.877654	−	0.877654i
$262$	167.978	+	167.978i	0.641139	+	0.641139i
$263$	−129.955			−0.494125			−0.247062	−	0.969000i	$-0.579465\pi$
$263$	−129.955			−0.494125			−0.247062	+	0.969000i	$0.579465\pi$
$264$			113.953i			0.431639i
$265$	−11.0613			−0.0417406
$266$	−15.3609	+	15.3609i	−0.0577478	+	0.0577478i
$267$	−208.567	+	208.567i	−0.781149	+	0.781149i
$268$		−	205.336i		−	0.766180i
$269$	−264.098	+	51.1190i	−0.981778	+	0.190033i
$269$	−264.098	+	51.1190i	−0.981778	+	0.190033i
$270$	−1.73614			−0.00643015
$271$	18.8319	+	18.8319i	0.0694904	+	0.0694904i	0.740998	−	0.671507i	$-0.234353\pi$
$271$	18.8319	+	18.8319i	0.0694904	+	0.0694904i	−0.671507	+	0.740998i	$0.734353\pi$
$272$	25.6735	+	25.6735i	0.0943879	+	0.0943879i
$273$		−	47.6772i		−	0.174642i
$274$	209.885			0.766005
$275$			240.832i			0.875751i
$276$	7.69841	−	7.69841i	0.0278928	−	0.0278928i
$277$	147.973	−	147.973i	0.534198	−	0.534198i	−0.387621	−	0.921819i	$-0.626703\pi$
$277$	147.973	−	147.973i	0.534198	−	0.534198i	0.921819	+	0.387621i	$0.126703\pi$
$278$			334.594i			1.20358i
$279$	189.220	+	189.220i	0.678210	+	0.678210i
$280$		−	0.588796i		−	0.00210284i
$281$	240.167	−	240.167i	0.854688	−	0.854688i	−0.136018	−	0.990706i	$-0.543431\pi$
$281$	240.167	−	240.167i	0.854688	−	0.854688i	0.990706	+	0.136018i	$0.0434306\pi$
$282$			244.508i			0.867051i
$283$	163.475			0.577650			0.288825	−	0.957382i	$-0.406735\pi$
$283$	163.475			0.577650			0.288825	+	0.957382i	$0.406735\pi$
$284$	−63.3919	−	63.3919i	−0.223211	−	0.223211i
$285$	−49.5892			−0.173997
$286$	214.930	+	214.930i	0.751502	+	0.751502i
$287$	−12.7860	+	12.7860i	−0.0445504	+	0.0445504i
$288$	−33.0614	+	33.0614i	−0.114797	+	0.114797i
$289$		−	206.609i		−	0.714910i
$290$	−22.2912			−0.0768662
$291$	34.7426	−	34.7426i	0.119390	−	0.119390i
$292$	−119.661			−0.409800
$293$	−369.575			−1.26135			−0.630673	−	0.776048i	$-0.717221\pi$
$293$	−369.575			−1.26135			−0.630673	+	0.776048i	$0.717221\pi$
$294$	−286.363			−0.974025
$295$	25.9701	−	25.9701i	0.0880343	−	0.0880343i
$296$	85.0195	−	85.0195i	0.287228	−	0.287228i
$297$	20.9289	+	20.9289i	0.0704676	+	0.0704676i
$298$	216.502	−	216.502i	0.726518	−	0.726518i
$299$		−	29.0404i		−	0.0971251i
$300$	−145.957	+	145.957i	−0.486522	+	0.486522i
$301$	24.0318	+	24.0318i	0.0798398	+	0.0798398i
$302$	208.990	−	208.990i	0.692021	−	0.692021i
$303$		−	325.579i		−	1.07452i
$304$	83.9351	−	83.9351i	0.276102	−	0.276102i
$305$	−13.8651			−0.0454593
$306$	−106.100			−0.346733
$307$	556.329			1.81215			0.906073	−	0.423122i	$-0.139066\pi$
$307$	556.329			1.81215			0.906073	+	0.423122i	$0.139066\pi$
$308$	−7.09783	+	7.09783i	−0.0230449	+	0.0230449i
$309$	559.276	−	559.276i	1.80996	−	1.80996i
$310$	18.4136			0.0593986
$311$	−341.299	−	341.299i	−1.09742	−	1.09742i	−0.994711	−	0.102714i	$-0.967247\pi$
$311$	−341.299	−	341.299i	−1.09742	−	1.09742i	−0.102714	−	0.994711i	$-0.532753\pi$
$312$			260.518i			0.834992i
$313$	180.420			0.576422			0.288211	−	0.957567i	$-0.406940\pi$
$313$	180.420			0.576422			0.288211	+	0.957567i	$0.406940\pi$
$314$			260.980i			0.831146i
$315$	1.21665	+	1.21665i	0.00386238	+	0.00386238i
$316$	−80.6509			−0.255224
$317$	−73.9318	−	73.9318i	−0.233223	−	0.233223i	0.580813	−	0.814037i	$-0.302735\pi$
$317$	−73.9318	−	73.9318i	−0.233223	−	0.233223i	−0.814037	+	0.580813i	$0.802735\pi$
$318$			161.624i			0.508253i
$319$	268.717	+	268.717i	0.842372	+	0.842372i
$320$			3.21730i			0.0100540i
$321$	618.441			1.92661
$322$	0.959029			0.00297835
$323$	269.364			0.833943
$324$			174.144i			0.537482i
$325$			550.586i			1.69411i
$326$	−425.448			−1.30505
$327$	−733.626			−2.24350
$328$	69.8651	−	69.8651i	0.213003	−	0.213003i
$329$	−15.2298	+	15.2298i	−0.0462912	+	0.0462912i
$330$	−22.9137			−0.0694355
$331$	−287.956			−0.869957			−0.434979	−	0.900441i	$-0.643244\pi$
$331$	−287.956			−0.869957			−0.434979	+	0.900441i	$0.643244\pi$
$332$	−187.345	−	187.345i	−0.564292	−	0.564292i
$333$			351.358i			1.05513i
$334$		−	187.647i		−	0.561817i
$335$	41.2892			0.123251
$336$	−8.60333			−0.0256051
$337$	−221.637	+	221.637i	−0.657676	+	0.657676i	−0.954830	−	0.297153i	$-0.903963\pi$
$337$	−221.637	+	221.637i	−0.657676	+	0.657676i	0.297153	+	0.954830i	$0.403963\pi$
$338$	322.370	+	322.370i	0.953757	+	0.953757i
$339$	−128.327			−0.378546
$340$	−5.16245	+	5.16245i	−0.0151837	+	0.0151837i
$341$	−221.972	−	221.972i	−0.650945	−	0.650945i
$342$			346.877i			1.01426i
$343$	−35.7718	−	35.7718i	−0.104291	−	0.104291i
$344$	−131.314	−	131.314i	−0.381728	−	0.381728i
$345$	1.54800	+	1.54800i	0.00448697	+	0.00448697i
$346$	−163.957	−	163.957i	−0.473865	−	0.473865i
$347$	158.820			0.457693			0.228847	−	0.973462i	$-0.426505\pi$
$347$	158.820			0.457693			0.228847	+	0.973462i	$0.426505\pi$
$348$			325.713i			0.935957i
$349$	−27.7738			−0.0795811			−0.0397905	−	0.999208i	$-0.512669\pi$
$349$	−27.7738			−0.0795811			−0.0397905	+	0.999208i	$0.512669\pi$
$350$	−18.1826			−0.0519502
$351$	47.8474	+	47.8474i	0.136317	+	0.136317i
$352$	38.7840	−	38.7840i	0.110182	−	0.110182i
$353$			630.388i			1.78580i	0.450254	+	0.892900i	$0.351333\pi$
$353$			630.388i			1.78580i	−0.450254	+	0.892900i	$0.648667\pi$
$354$	−379.469	−	379.469i	−1.07195	−	1.07195i
$355$	12.7469	−	12.7469i	0.0359068	−	0.0359068i
$356$	141.972			0.398797
$357$	−13.8048	−	13.8048i	−0.0386690	−	0.0386690i
$358$			318.593i			0.889925i
$359$	−315.711	+	315.711i	−0.879416	+	0.879416i	−0.993474	−	0.114058i	$-0.963615\pi$
$359$	−315.711	+	315.711i	−0.879416	+	0.879416i	0.114058	+	0.993474i	$0.463615\pi$
$360$	−6.64802	−	6.64802i	−0.0184667	−	0.0184667i
$361$		−	519.638i		−	1.43944i
$362$	168.880			0.466520
$363$	−79.2940	−	79.2940i	−0.218441	−	0.218441i
$364$	−16.2270	+	16.2270i	−0.0445796	+	0.0445796i
$365$		−	24.0616i		−	0.0659223i
$366$			202.593i			0.553532i
$367$	−219.867	+	219.867i	−0.599092	+	0.599092i	−0.940071	−	0.340979i	$-0.889242\pi$
$367$	−219.867	+	219.867i	−0.599092	+	0.599092i	0.340979	+	0.940071i	$0.389242\pi$
$368$	−5.24032			−0.0142400
$369$			288.730i			0.782465i
$370$	17.0958	+	17.0958i	0.0462048	+	0.0462048i
$371$	−10.0672	+	10.0672i	−0.0271353	+	0.0271353i
$372$		−	269.054i		−	0.723264i
$373$	−173.052	−	173.052i	−0.463947	−	0.463947i	0.436000	−	0.899947i	$-0.356395\pi$
$373$	−173.052	−	173.052i	−0.463947	−	0.463947i	−0.899947	+	0.436000i	$0.856395\pi$
$374$	124.465			0.332794
$375$	−58.8893	−	58.8893i	−0.157038	−	0.157038i
$376$	83.2187	−	83.2187i	0.221326	−	0.221326i
$377$	614.337	+	614.337i	1.62954	+	1.62954i
$378$	−1.58011	+	1.58011i	−0.00418019	+	0.00418019i
$379$	−88.1247	+	88.1247i	−0.232519	+	0.232519i	−0.813743	−	0.581224i	$-0.802574\pi$
$379$	−88.1247	+	88.1247i	−0.232519	+	0.232519i	0.581224	+	0.813743i	$0.302574\pi$
$380$	16.8778	+	16.8778i	0.0444151	+	0.0444151i
$381$	−286.365	+	286.365i	−0.751613	+	0.751613i
$382$	−129.997	+	129.997i	−0.340305	+	0.340305i
$383$	−183.537	−	183.537i	−0.479208	−	0.479208i	0.425670	−	0.904878i	$-0.360038\pi$
$383$	−183.537	−	183.537i	−0.479208	−	0.479208i	−0.904878	+	0.425670i	$0.860038\pi$
$384$	47.0103			0.122423
$385$	−1.42724	−	1.42724i	−0.00370711	−	0.00370711i
$386$	−258.438			−0.669528
$387$	542.680			1.40227
$388$	−23.6493			−0.0609519
$389$	650.190			1.67144			0.835720	−	0.549155i	$-0.185050\pi$
$389$	650.190			1.67144			0.835720	+	0.549155i	$0.185050\pi$
$390$	−52.3851			−0.134321
$391$	−8.40859	−	8.40859i	−0.0215054	−	0.0215054i
$392$	97.4641	+	97.4641i	0.248633	+	0.248633i
$393$	493.544	+	493.544i	1.25584	+	1.25584i
$394$	−272.843			−0.692496
$395$		−	16.2174i		−	0.0410566i
$396$			160.281i			0.404751i
$397$	36.3386	−	36.3386i	0.0915330	−	0.0915330i	−0.659858	−	0.751391i	$-0.729383\pi$
$397$	36.3386	−	36.3386i	0.0915330	−	0.0915330i	0.751391	+	0.659858i	$0.229383\pi$
$398$	−19.3603	+	19.3603i	−0.0486441	+	0.0486441i
$399$	−45.1326	+	45.1326i	−0.113114	+	0.113114i
$400$	99.3531			0.248383
$401$	−414.612	−	414.612i	−1.03395	−	1.03395i	−0.999403	−	0.0345424i	$-0.989003\pi$
$401$	−414.612	−	414.612i	−1.03395	−	1.03395i	−0.0345424	−	0.999403i	$-0.510997\pi$
$402$		−	603.307i		−	1.50076i
$403$	−507.471	−	507.471i	−1.25923	−	1.25923i
$404$	−110.811	+	110.811i	−0.274285	+	0.274285i
$405$	−35.0171			−0.0864620
$406$	−20.2879	+	20.2879i	−0.0499701	+	0.0499701i
$407$		−	412.174i		−	1.01271i
$408$	75.4324	+	75.4324i	0.184883	+	0.184883i
$409$	180.743	+	180.743i	0.441914	+	0.441914i	0.892655	−	0.450741i	$-0.148840\pi$
$409$	180.743	+	180.743i	0.441914	+	0.441914i	−0.450741	+	0.892655i	$0.648840\pi$
$410$	14.0485	+	14.0485i	0.0342647	+	0.0342647i
$411$	616.673			1.50042
$412$	−380.701			−0.924031
$413$		−	47.2723i		−	0.114461i
$414$	10.8283	−	10.8283i	0.0261553	−	0.0261553i
$415$	37.6715	−	37.6715i	0.0907746	−	0.0907746i
$416$	88.6675	−	88.6675i	0.213143	−	0.213143i
$417$			983.084i			2.35752i
$418$		−	406.917i		−	0.973486i
$419$			382.839i			0.913697i	0.889544	+	0.456849i	$0.151022\pi$
$419$			382.839i			0.913697i	−0.889544	+	0.456849i	$0.848978\pi$
$420$		−	1.72996i		−	0.00411896i
$421$			503.393i			1.19571i	0.801605	+	0.597854i	$0.203980\pi$
$421$			503.393i			1.19571i	−0.801605	+	0.597854i	$0.796020\pi$
$422$	−203.403	+	203.403i	−0.481997	+	0.481997i
$423$			343.916i			0.813040i
$424$	55.0090	−	55.0090i	0.129738	−	0.129738i
$425$	159.421	+	159.421i	0.375109	+	0.375109i
$426$	−186.254	−	186.254i	−0.437217	−	0.437217i
$427$	−12.6190	+	12.6190i	−0.0295527	+	0.0295527i
$428$	−210.487	−	210.487i	−0.491792	−	0.491792i
$429$	631.494	+	631.494i	1.47201	+	1.47201i
$430$	26.4048	−	26.4048i	0.0614066	−	0.0614066i
$431$	−98.3821	−	98.3821i	−0.228265	−	0.228265i	0.583703	−	0.811967i	$-0.301603\pi$
$431$	−98.3821	−	98.3821i	−0.228265	−	0.228265i	−0.811967	+	0.583703i	$0.801603\pi$
$432$	8.63403	−	8.63403i	0.0199862	−	0.0199862i
$433$			5.30339i			0.0122480i	0.999981	+	0.00612401i	$0.00194935\pi$
$433$			5.30339i			0.0122480i	−0.999981	+	0.00612401i	$0.998051\pi$
$434$	16.7587	−	16.7587i	0.0386145	−	0.0386145i
$435$	−65.4947			−0.150563
$436$	249.690	+	249.690i	0.572684	+	0.572684i
$437$	−27.4905	+	27.4905i	−0.0629072	+	0.0629072i
$438$	−351.582			−0.802699
$439$		−	529.030i		−	1.20508i	−0.798088	−	0.602540i	$-0.794155\pi$
$439$		−	529.030i		−	1.20508i	0.798088	−	0.602540i	$-0.205845\pi$
$440$	7.79871	+	7.79871i	0.0177243	+	0.0177243i
$441$	−402.787			−0.913350
$442$	284.550			0.643779
$443$	396.800	+	396.800i	0.895710	+	0.895710i	0.995053	−	0.0993432i	$-0.0316742\pi$
$443$	396.800	+	396.800i	0.895710	+	0.895710i	−0.0993432	+	0.995053i	$0.531674\pi$
$444$	249.799	−	249.799i	0.562611	−	0.562611i
$445$			28.5478i			0.0641524i
$446$	−274.761			−0.616056
$447$	636.114	−	636.114i	1.42307	−	1.42307i
$448$	2.92815	+	2.92815i	0.00653605	+	0.00653605i
$449$	−298.673			−0.665195			−0.332598	−	0.943069i	$-0.607925\pi$
$449$	−298.673			−0.665195			−0.332598	+	0.943069i	$0.607925\pi$
$450$	−205.297	+	205.297i	−0.456215	+	0.456215i
$451$		−	338.705i		−	0.751010i
$452$	43.6763	+	43.6763i	0.0966289	+	0.0966289i
$453$	614.043	−	614.043i	1.35550	−	1.35550i
$454$	443.642			0.977185
$455$	−3.26294	−	3.26294i	−0.00717129	−	0.00717129i
$456$	246.613	−	246.613i	0.540819	−	0.540819i
$457$		−	293.719i		−	0.642710i	−0.946959	−	0.321355i	$-0.895862\pi$
$457$		−	293.719i		−	0.642710i	0.946959	−	0.321355i	$-0.104138\pi$
$458$			542.749i			1.18504i
$459$	27.7082			0.0603665
$460$		−	1.05373i		−	0.00229072i
$461$	52.9283	−	52.9283i	0.114812	−	0.114812i	−0.647367	−	0.762179i	$-0.724130\pi$
$461$	52.9283	−	52.9283i	0.114812	−	0.114812i	0.762179	+	0.647367i	$0.224130\pi$
$462$	−20.8544	+	20.8544i	−0.0451395	+	0.0451395i
$463$	−237.363	+	237.363i	−0.512663	+	0.512663i	−0.915341	−	0.402679i	$-0.868079\pi$
$463$	−237.363	+	237.363i	−0.512663	+	0.512663i	0.402679	+	0.915341i	$0.368079\pi$
$464$	110.857	−	110.857i	0.238916	−	0.238916i
$465$	54.1016			0.116348
$466$	122.625	−	122.625i	0.263144	−	0.263144i
$467$	−174.834	−	174.834i	−0.374377	−	0.374377i	0.494692	−	0.869069i	$-0.335281\pi$
$467$	−174.834	−	174.834i	−0.374377	−	0.374377i	−0.869069	+	0.494692i	$0.835281\pi$
$468$			366.434i			0.782978i
$469$	37.5785	−	37.5785i	0.0801247	−	0.0801247i
$470$	16.7337	+	16.7337i	0.0356036	+	0.0356036i
$471$			766.796i			1.62802i
$472$			258.305i			0.547257i
$473$	−636.612			−1.34590
$474$	−236.964			−0.499923
$475$	521.201	−	521.201i	1.09726	−	1.09726i
$476$			9.39699i			0.0197416i
$477$			227.334i			0.476592i
$478$	241.191	+	241.191i	0.504583	+	0.504583i
$479$	249.784	+	249.784i	0.521470	+	0.521470i	0.918015	−	0.396545i	$-0.129791\pi$
$479$	249.784	+	249.784i	0.521470	+	0.521470i	−0.396545	+	0.918015i	$0.629791\pi$
$480$			9.45287i			0.0196935i
$481$		−	942.307i		−	1.95906i
$482$	362.995			0.753102
$483$	2.81776			0.00583388
$484$			53.9756i			0.111520i
$485$		−	4.75543i		−	0.00980501i
$486$			472.807i			0.972855i
$487$	486.669			0.999321			0.499660	−	0.866221i	$-0.333458\pi$
$487$	486.669			0.999321			0.499660	+	0.866221i	$0.333458\pi$
$488$	68.9527	−	68.9527i	0.141297	−	0.141297i
$489$	−1250.03			−2.55629
$490$	−19.5982	+	19.5982i	−0.0399963	+	0.0399963i
$491$			611.098i			1.24460i	0.782780	+	0.622299i	$0.213801\pi$
$491$			611.098i			1.24460i	−0.782780	+	0.622299i	$0.786199\pi$
$492$	205.273	−	205.273i	0.417222	−	0.417222i
$493$	355.760			0.721624
$494$		−	930.289i		−	1.88318i
$495$	−32.2295			−0.0651102
$496$	−91.5729	+	91.5729i	−0.184623	+	0.184623i
$497$		−	23.2027i		−	0.0466854i
$498$	−550.445	−	550.445i	−1.10531	−	1.10531i
$499$	163.048	+	163.048i	0.326749	+	0.326749i	0.851349	−	0.524600i	$-0.175785\pi$
$499$	163.048	+	163.048i	0.326749	+	0.326749i	−0.524600	+	0.851349i	$0.675785\pi$
$500$			40.0861i			0.0801722i
$501$		−	551.333i		−	1.10047i
$502$			244.614i			0.487279i
$503$	193.054	+	193.054i	0.383806	+	0.383806i	0.872471	−	0.488665i	$-0.162516\pi$
$503$	193.054	+	193.054i	0.383806	+	0.383806i	−0.488665	+	0.872471i	$0.662516\pi$
$504$	−12.1011			−0.0240101
$505$	−22.2820	−	22.2820i	−0.0441229	−	0.0441229i
$506$	−12.7025	+	12.7025i	−0.0251038	+	0.0251038i
$507$	947.168	+	947.168i	1.86818	+	1.86818i
$508$	194.929			0.383719
$509$	−134.257	−	134.257i	−0.263767	−	0.263767i	0.562816	−	0.826582i	$-0.309718\pi$
$509$	−134.257	−	134.257i	−0.263767	−	0.263767i	−0.826582	+	0.562816i	$0.809718\pi$
$510$	−15.1680	+	15.1680i	−0.0297412	+	0.0297412i
$511$	−21.8992	−	21.8992i	−0.0428556	−	0.0428556i
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$		−	90.5873i		−	0.176583i
$514$			350.847i			0.682582i
$515$		−	76.5517i		−	0.148644i
$516$	−385.820	−	385.820i	−0.747714	−	0.747714i
$517$		−	403.444i		−	0.780355i
$518$	31.1187			0.0600748
$519$	−481.730	−	481.730i	−0.928188	−	0.928188i
$520$	17.8293	+	17.8293i	0.0342872	+	0.0342872i
$521$	−330.926	+	330.926i	−0.635174	+	0.635174i	−0.949361	−	0.314187i	$-0.898268\pi$
$521$	−330.926	+	330.926i	−0.635174	+	0.635174i	0.314187	+	0.949361i	$0.398268\pi$
$522$			458.135i			0.877654i
$523$	262.398	−	262.398i	0.501716	−	0.501716i	−0.410255	−	0.911971i	$-0.634560\pi$
$523$	262.398	−	262.398i	0.501716	−	0.501716i	0.911971	+	0.410255i	$0.134560\pi$
$524$		−	335.957i		−	0.641139i
$525$	−53.4229			−0.101758
$526$	129.955	+	129.955i	0.247062	+	0.247062i
$527$	−293.875			−0.557637
$528$	113.953	−	113.953i	0.215820	−	0.215820i
$529$	−527.284			−0.996756
$530$	11.0613	+	11.0613i	0.0208703	+	0.0208703i
$531$	−533.746	−	533.746i	−1.00517	−	1.00517i
$532$	30.7219			0.0577478
$533$		−	774.345i		−	1.45280i
$534$	417.133			0.781149
$535$	42.3249	−	42.3249i	0.0791120	−	0.0791120i
$536$	−205.336	+	205.336i	−0.383090	+	0.383090i
$537$			936.071i			1.74315i
$538$	315.217	+	212.979i	0.585906	+	0.395872i
$539$	472.505			0.876634
$540$	1.73614	+	1.73614i	0.00321507	+	0.00321507i
$541$	−260.956	−	260.956i	−0.482359	−	0.482359i	0.423525	−	0.905884i	$-0.360793\pi$
$541$	−260.956	−	260.956i	−0.482359	−	0.482359i	−0.905884	+	0.423525i	$0.860793\pi$
$542$		−	37.6638i		−	0.0694904i
$543$	496.194			0.913801
$544$		−	51.3470i		−	0.0943879i
$545$	−50.2080	+	50.2080i	−0.0921247	+	0.0921247i
$546$	−47.6772	+	47.6772i	−0.0873209	+	0.0873209i
$547$		−	528.756i		−	0.966647i	−0.875442	−	0.483323i	$-0.839430\pi$
$547$		−	528.756i		−	0.966647i	0.875442	−	0.483323i	$-0.160570\pi$
$548$	−209.885	−	209.885i	−0.383003	−	0.383003i
$549$			284.959i			0.519051i
$550$	240.832	−	240.832i	0.437876	−	0.437876i
$551$		−	1163.10i		−	2.11089i
$552$	−15.3968			−0.0278928
$553$	−14.7599	−	14.7599i	−0.0266906	−	0.0266906i
$554$	−295.946			−0.534198
$555$	50.2299	+	50.2299i	0.0905042	+	0.0905042i
$556$	334.594	−	334.594i	0.601788	−	0.601788i
$557$	57.8611	−	57.8611i	0.103880	−	0.103880i	−0.653257	−	0.757137i	$-0.726598\pi$
$557$	57.8611	−	57.8611i	0.103880	−	0.103880i	0.757137	+	0.653257i	$0.226598\pi$
$558$		−	378.441i		−	0.678210i
$559$	−1455.41			−2.60360
$560$	−0.588796	+	0.588796i	−0.00105142	+	0.00105142i
$561$	365.696			0.651864
$562$	−480.335			−0.854688
$563$	−118.024			−0.209633			−0.104817	−	0.994492i	$-0.533426\pi$
$563$	−118.024			−0.209633			−0.104817	+	0.994492i	$0.533426\pi$
$564$	244.508	−	244.508i	0.433525	−	0.433525i
$565$	−8.78247	+	8.78247i	−0.0155442	+	0.0155442i
$566$	−163.475	−	163.475i	−0.288825	−	0.288825i
$567$	−31.8701	+	31.8701i	−0.0562082	+	0.0562082i
$568$			126.784i			0.223211i
$569$	−68.5356	+	68.5356i	−0.120449	+	0.120449i	−0.764762	−	0.644313i	$-0.777143\pi$
$569$	−68.5356	+	68.5356i	−0.120449	+	0.120449i	0.644313	+	0.764762i	$0.277143\pi$
$570$	49.5892	+	49.5892i	0.0869986	+	0.0869986i
$571$	−179.419	+	179.419i	−0.314219	+	0.314219i	−0.846541	−	0.532323i	$-0.821319\pi$
$571$	−179.419	+	179.419i	−0.314219	+	0.314219i	0.532323	+	0.846541i	$0.321319\pi$
$572$		−	429.859i		−	0.751502i
$573$	−381.948	+	381.948i	−0.666576	+	0.666576i
$574$	25.5719			0.0445504
$575$	−32.5401			−0.0565916
$576$	66.1228			0.114797
$577$	−549.862	+	549.862i	−0.952967	+	0.952967i	−0.998943	−	0.0459758i	$-0.985360\pi$
$577$	−549.862	+	549.862i	−0.952967	+	0.952967i	0.0459758	+	0.998943i	$0.485360\pi$
$578$	−206.609	+	206.609i	−0.357455	+	0.357455i
$579$	−759.327			−1.31145
$580$	22.2912	+	22.2912i	0.0384331	+	0.0384331i
$581$		−	68.5718i		−	0.118024i
$582$	−69.4851			−0.119390
$583$		−	266.684i		−	0.457433i
$584$	119.661	+	119.661i	0.204900	+	0.204900i
$585$	−73.6828			−0.125954
$586$	369.575	+	369.575i	0.630673	+	0.630673i
$587$		−	255.529i		−	0.435314i	−0.976025	−	0.217657i	$-0.930159\pi$
$587$		−	255.529i		−	0.435314i	0.976025	−	0.217657i	$-0.0698414\pi$
$588$	286.363	+	286.363i	0.487013	+	0.487013i
$589$			960.773i			1.63119i
$590$	−51.9403			−0.0880343
$591$	−801.652			−1.35643
$592$	−170.039			−0.287228
$593$			721.678i			1.21699i	0.793556	+	0.608497i	$0.208227\pi$
$593$			721.678i			1.21699i	−0.793556	+	0.608497i	$0.791773\pi$
$594$		−	41.8577i		−	0.0704676i
$595$	−1.88956			−0.00317572
$596$	−433.005			−0.726518
$597$	−56.8834	+	56.8834i	−0.0952821	+	0.0952821i
$598$	−29.0404	+	29.0404i	−0.0485625	+	0.0485625i
$599$	−1018.77			−1.70078			−0.850391	−	0.526151i	$-0.823635\pi$
$599$	−1018.77			−1.70078			−0.850391	+	0.526151i	$0.823635\pi$
$600$	291.913			0.486522
$601$	−100.044	−	100.044i	−0.166462	−	0.166462i	0.618960	−	0.785422i	$-0.287554\pi$
$601$	−100.044	−	100.044i	−0.166462	−	0.166462i	−0.785422	+	0.618960i	$0.787554\pi$
$602$		−	48.0636i		−	0.0798398i
$603$		−	848.588i		−	1.40728i
$604$	−417.981			−0.692021
$605$	−10.8535			−0.0179396
$606$	−325.579	+	325.579i	−0.537260	+	0.537260i
$607$	−470.678	−	470.678i	−0.775417	−	0.775417i	0.203631	−	0.979048i	$-0.434726\pi$
$607$	−470.678	−	470.678i	−0.775417	−	0.775417i	−0.979048	+	0.203631i	$0.934726\pi$
$608$	−167.870			−0.276102
$609$	−59.6086	+	59.6086i	−0.0978795	+	0.0978795i
$610$	13.8651	+	13.8651i	0.0227296	+	0.0227296i
$611$		−	922.349i		−	1.50957i
$612$	106.100	+	106.100i	0.173366	+	0.173366i
$613$	−392.104	−	392.104i	−0.639647	−	0.639647i	0.310821	−	0.950468i	$-0.399396\pi$
$613$	−392.104	−	392.104i	−0.639647	−	0.639647i	−0.950468	+	0.310821i	$0.899396\pi$
$614$	−556.329	−	556.329i	−0.906073	−	0.906073i
$615$	41.2766	+	41.2766i	0.0671164	+	0.0671164i
$616$	14.1957			0.0230449
$617$		−	971.089i		−	1.57389i	−0.617024	−	0.786944i	$-0.711662\pi$
$617$		−	971.089i		−	1.57389i	0.617024	−	0.786944i	$-0.288338\pi$
$618$	−1118.55			−1.80996
$619$	568.239			0.917995			0.458997	−	0.888438i	$-0.348209\pi$
$619$	568.239			0.917995			0.458997	+	0.888438i	$0.348209\pi$
$620$	−18.4136	−	18.4136i	−0.0296993	−	0.0296993i
$621$	−2.82782	+	2.82782i	−0.00455366	+	0.00455366i
$622$			682.598i			1.09742i
$623$	25.9822	+	25.9822i	0.0417050	+	0.0417050i
$624$	260.518	−	260.518i	0.417496	−	0.417496i
$625$	612.896			0.980634
$626$	−180.420	−	180.420i	−0.288211	−	0.288211i
$627$		−	1195.58i		−	1.90683i
$628$	260.980	−	260.980i	0.415573	−	0.415573i
$629$	−272.843	−	272.843i	−0.433773	−	0.433773i
$630$		−	2.43330i		−	0.00386238i
$631$	814.489			1.29079			0.645396	−	0.763849i	$-0.276693\pi$
$631$	814.489			1.29079			0.645396	+	0.763849i	$0.276693\pi$
$632$	80.6509	+	80.6509i	0.127612	+	0.127612i
$633$	−597.626	+	597.626i	−0.944117	+	0.944117i
$634$			147.864i			0.233223i
$635$			39.1965i			0.0617268i
$636$	161.624	−	161.624i	0.254126	−	0.254126i
$637$	1080.24			1.69582
$638$		−	537.433i		−	0.842372i
$639$	−261.978	−	261.978i	−0.409982	−	0.409982i
$640$	3.21730	−	3.21730i	0.00502702	−	0.00502702i
$641$		−	152.330i		−	0.237645i	−0.992916	−	0.118822i	$-0.962088\pi$
$641$		−	152.330i		−	0.237645i	0.992916	−	0.118822i	$-0.0379119\pi$
$642$	−618.441	−	618.441i	−0.963303	−	0.963303i
$643$	235.446			0.366167			0.183084	−	0.983097i	$-0.441392\pi$
$643$	235.446			0.366167			0.183084	+	0.983097i	$0.441392\pi$
$644$	−0.959029	−	0.959029i	−0.00148918	−	0.00148918i
$645$	77.5811	−	77.5811i	0.120281	−	0.120281i
$646$	−269.364	−	269.364i	−0.416971	−	0.416971i
$647$	−158.877	+	158.877i	−0.245559	+	0.245559i	−0.819145	−	0.573586i	$-0.805552\pi$
$647$	−158.877	+	158.877i	−0.245559	+	0.245559i	0.573586	+	0.819145i	$0.305552\pi$
$648$	174.144	−	174.144i	0.268741	−	0.268741i
$649$	626.131	+	626.131i	0.964763	+	0.964763i
$650$	550.586	−	550.586i	0.847056	−	0.847056i
$651$	49.2395	−	49.2395i	0.0756366	−	0.0756366i
$652$	425.448	+	425.448i	0.652527	+	0.652527i
$653$	−115.607			−0.177040			−0.0885202	−	0.996074i	$-0.528214\pi$
$653$	−115.607			−0.177040			−0.0885202	+	0.996074i	$0.528214\pi$
$654$	733.626	+	733.626i	1.12175	+	1.12175i
$655$	67.5545			0.103137
$656$	−139.730			−0.213003
$657$	−494.522			−0.752697
$658$	30.4596			0.0462912
$659$	529.980			0.804219			0.402109	−	0.915592i	$-0.368277\pi$
$659$	529.980			0.804219			0.402109	+	0.915592i	$0.368277\pi$
$660$	22.9137	+	22.9137i	0.0347178	+	0.0347178i
$661$	−322.111	−	322.111i	−0.487308	−	0.487308i	0.420148	−	0.907456i	$-0.361978\pi$
$661$	−322.111	−	322.111i	−0.487308	−	0.487308i	−0.907456	+	0.420148i	$0.861978\pi$
$662$	287.956	+	287.956i	0.434979	+	0.434979i
$663$	836.050			1.26101
$664$			374.690i			0.564292i
$665$			6.17758i			0.00928959i
$666$	351.358	−	351.358i	0.527564	−	0.527564i
$667$	−36.3079	+	36.3079i	−0.0544346	+	0.0544346i
$668$	−187.647	+	187.647i	−0.280909	+	0.280909i
$669$	−807.286			−1.20671
$670$	−41.2892	−	41.2892i	−0.0616257	−	0.0616257i
$671$		−	334.282i		−	0.498185i
$672$	8.60333	+	8.60333i	0.0128026	+	0.0128026i
$673$	382.941	−	382.941i	0.569006	−	0.569006i	−0.362844	−	0.931850i	$-0.618194\pi$
$673$	382.941	−	382.941i	0.569006	−	0.569006i	0.931850	+	0.362844i	$0.118194\pi$
$674$	443.274			0.657676
$675$	53.6136	−	53.6136i	0.0794275	−	0.0794275i
$676$		−	644.740i		−	0.953757i
$677$	−511.994	−	511.994i	−0.756269	−	0.756269i	0.219372	−	0.975641i	$-0.429599\pi$
$677$	−511.994	−	511.994i	−0.756269	−	0.756269i	−0.975641	+	0.219372i	$0.929599\pi$
$678$	128.327	+	128.327i	0.189273	+	0.189273i
$679$	−4.32806	−	4.32806i	−0.00637416	−	0.00637416i
$680$	10.3249			0.0151837
$681$	1303.48			1.91407
$682$			443.945i			0.650945i
$683$	−224.694	+	224.694i	−0.328982	+	0.328982i	−0.852199	−	0.523218i	$-0.824732\pi$
$683$	−224.694	+	224.694i	−0.328982	+	0.328982i	0.523218	+	0.852199i	$0.324732\pi$
$684$	346.877	−	346.877i	0.507129	−	0.507129i
$685$	42.2040	−	42.2040i	0.0616116	−	0.0616116i
$686$			71.5436i			0.104291i
$687$			1594.67i			2.32121i
$688$			262.629i			0.381728i
$689$		−	609.689i		−	0.884890i
$690$		−	3.09601i		−	0.00448697i
$691$	−561.635	+	561.635i	−0.812786	+	0.812786i	−0.985051	−	0.172265i	$-0.944892\pi$
$691$	−561.635	+	561.635i	−0.812786	+	0.812786i	0.172265	+	0.985051i	$0.444892\pi$
$692$			327.915i			0.473865i
$693$	−29.3330	+	29.3330i	−0.0423276	+	0.0423276i
$694$	−158.820	−	158.820i	−0.228847	−	0.228847i
$695$	67.2805	+	67.2805i	0.0968064	+	0.0968064i
$696$	325.713	−	325.713i	0.467979	−	0.467979i
$697$	−224.210	−	224.210i	−0.321679	−	0.321679i
$698$	27.7738	+	27.7738i	0.0397905	+	0.0397905i
$699$	360.290	−	360.290i	0.515436	−	0.515436i
$700$	18.1826	+	18.1826i	0.0259751	+	0.0259751i
$701$	506.040	−	506.040i	0.721883	−	0.721883i	−0.247106	−	0.968989i	$-0.579480\pi$
$701$	506.040	−	506.040i	0.721883	−	0.721883i	0.968989	+	0.247106i	$0.0794795\pi$
$702$		−	95.6947i		−	0.136317i
$703$	−892.015	+	892.015i	−1.26887	+	1.26887i
$704$	−77.5679			−0.110182
$705$	49.1660	+	49.1660i	0.0697389	+	0.0697389i
$706$	630.388	−	630.388i	0.892900	−	0.892900i
$707$	−40.5591			−0.0573678
$708$			758.937i			1.07195i
$709$	169.316	+	169.316i	0.238809	+	0.238809i	0.816357	−	0.577548i	$-0.195990\pi$
$709$	169.316	+	169.316i	0.238809	+	0.238809i	−0.577548	+	0.816357i	$0.695990\pi$
$710$	−25.4938			−0.0359068
$711$	−333.304			−0.468782
$712$	−141.972	−	141.972i	−0.199399	−	0.199399i
$713$	29.9920	−	29.9920i	0.0420645	−	0.0420645i
$714$			27.6097i			0.0386690i
$715$	86.4365			0.120890
$716$	318.593	−	318.593i	0.444962	−	0.444962i
$717$	708.652	+	708.652i	0.988357	+	0.988357i
$718$	631.421			0.879416
$719$	−497.696	+	497.696i	−0.692206	+	0.692206i	−0.962717	−	0.270511i	$-0.912807\pi$
$719$	−497.696	+	497.696i	−0.692206	+	0.692206i	0.270511	+	0.962717i	$0.412807\pi$
$720$			13.2960i			0.0184667i
$721$	−69.6719	−	69.6719i	−0.0966323	−	0.0966323i
$722$	−519.638	+	519.638i	−0.719720	+	0.719720i
$723$	1066.53			1.47515
$724$	−168.880	−	168.880i	−0.233260	−	0.233260i
$725$	688.373	−	688.373i	0.949480	−	0.949480i
$726$			158.588i			0.218441i
$727$		−	874.830i		−	1.20334i	−0.798744	−	0.601671i	$-0.794502\pi$
$727$		−	874.830i		−	1.20334i	0.798744	−	0.601671i	$-0.205498\pi$
$728$	32.4540			0.0445796
$729$			605.526i			0.830625i
$730$	−24.0616	+	24.0616i	−0.0329611	+	0.0329611i
$731$	−421.413	+	421.413i	−0.576488	+	0.576488i
$732$	202.593	−	202.593i	0.276766	−	0.276766i
$733$	−155.678	+	155.678i	−0.212385	+	0.212385i	−0.805280	−	0.592895i	$-0.797985\pi$
$733$	−155.678	+	155.678i	−0.212385	+	0.212385i	0.592895	+	0.805280i	$0.297985\pi$
$734$	439.734			0.599092
$735$	−57.5822	+	57.5822i	−0.0783431	+	0.0783431i
$736$	5.24032	+	5.24032i	0.00712001	+	0.00712001i
$737$			995.469i			1.35070i
$738$	288.730	−	288.730i	0.391233	−	0.391233i
$739$	89.2820	+	89.2820i	0.120815	+	0.120815i	0.764929	−	0.644114i	$-0.222774\pi$
$739$	89.2820	+	89.2820i	0.120815	+	0.120815i	−0.644114	+	0.764929i	$0.722774\pi$
$740$		−	34.1916i		−	0.0462048i
$741$		−	2733.32i		−	3.68869i
$742$	20.1344			0.0271353
$743$	1165.35			1.56844			0.784221	−	0.620482i	$-0.213063\pi$
$743$	1165.35			1.56844			0.784221	+	0.620482i	$0.213063\pi$
$744$	−269.054	+	269.054i	−0.361632	+	0.361632i
$745$		−	87.0690i		−	0.116871i
$746$			346.104i			0.463947i
$747$	−774.235	−	774.235i	−1.03646	−	1.03646i
$748$	−124.465	−	124.465i	−0.166397	−	0.166397i
$749$		−	77.0423i		−	0.102860i
$750$			117.779i			0.157038i
$751$	181.913			0.242228			0.121114	−	0.992639i	$-0.461353\pi$
$751$	181.913			0.242228			0.121114	+	0.992639i	$0.461353\pi$
$752$	−166.437			−0.221326
$753$			718.710i			0.954462i
$754$		−	1228.67i		−	1.62954i
$755$		−	84.0479i		−	0.111322i
$756$	3.16022			0.00418019
$757$	−717.240	+	717.240i	−0.947478	+	0.947478i	−0.998688	−	0.0512104i	$-0.983692\pi$
$757$	−717.240	+	717.240i	−0.947478	+	0.947478i	0.0512104	+	0.998688i	$0.483692\pi$
$758$	176.249			0.232519
$759$	−37.3218	+	37.3218i	−0.0491724	+	0.0491724i
$760$		−	33.7555i		−	0.0444151i
$761$	−358.668	+	358.668i	−0.471312	+	0.471312i	−0.902339	−	0.431027i	$-0.858151\pi$
$761$	−358.668	+	358.668i	−0.471312	+	0.471312i	0.431027	+	0.902339i	$0.358151\pi$
$762$	572.729			0.751613
$763$			91.3914i			0.119779i
$764$	259.993			0.340305
$765$	−21.3347	+	21.3347i	−0.0278885	+	0.0278885i
$766$			367.073i			0.479208i
$767$	1431.45	+	1431.45i	1.86630	+	1.86630i
$768$	−47.0103	−	47.0103i	−0.0612113	−	0.0612113i
$769$		−	1350.16i		−	1.75573i	−0.478905	−	0.877867i	$-0.658966\pi$
$769$		−	1350.16i		−	1.75573i	0.478905	−	0.877867i	$-0.341034\pi$
$770$			2.85448i			0.00370711i
$771$			1030.84i			1.33702i
$772$	258.438	+	258.438i	0.334764	+	0.334764i
$773$	−324.515			−0.419813			−0.209906	−	0.977721i	$-0.567316\pi$
$773$	−324.515			−0.419813			−0.209906	+	0.977721i	$0.567316\pi$
$774$	−542.680	−	542.680i	−0.701137	−	0.701137i
$775$	−568.628	+	568.628i	−0.733713	+	0.733713i
$776$	23.6493	+	23.6493i	0.0304760	+	0.0304760i
$777$	91.4313			0.117672
$778$	−650.190	−	650.190i	−0.835720	−	0.835720i
$779$	−733.017	+	733.017i	−0.940971	+	0.940971i
$780$	52.3851	+	52.3851i	0.0671604	+	0.0671604i
$781$	307.324	+	307.324i	0.393500	+	0.393500i
$782$			16.8172i			0.0215054i
$783$		−	119.643i		−	0.152800i
$784$		−	194.928i		−	0.248633i
$785$	52.4781	+	52.4781i	0.0668510	+	0.0668510i
$786$		−	987.088i		−	1.25584i
$787$	−1465.98			−1.86274			−0.931371	−	0.364071i	$-0.881387\pi$
$787$	−1465.98			−1.86274			−0.931371	+	0.364071i	$0.881387\pi$
$788$	272.843	+	272.843i	0.346248	+	0.346248i
$789$	381.826	+	381.826i	0.483936	+	0.483936i
$790$	−16.2174	+	16.2174i	−0.0205283	+	0.0205283i
$791$			15.9863i			0.0202103i
$792$	160.281	−	160.281i	0.202376	−	0.202376i
$793$		−	764.233i		−	0.963723i
$794$	−72.6772			−0.0915330
$795$	32.4996	+	32.4996i	0.0408800	+	0.0408800i
$796$	38.7207			0.0486441
$797$	−168.874	+	168.874i	−0.211887	+	0.211887i	−0.805069	−	0.593182i	$-0.797872\pi$
$797$	−168.874	+	168.874i	−0.211887	+	0.211887i	0.593182	+	0.805069i	$0.297872\pi$
$798$	90.2651			0.113114
$799$	−267.064	−	267.064i	−0.334248	−	0.334248i
$800$	−99.3531	−	99.3531i	−0.124191	−	0.124191i
$801$	586.723			0.732489
$802$			829.224i			1.03395i
$803$	580.118			0.722438
$804$	−603.307	+	603.307i	−0.750382	+	0.750382i
$805$	0.192843	−	0.192843i	0.000239556	−	0.000239556i
$806$			1014.94i			1.25923i
$807$	926.153	+	625.763i	1.14765	+	0.775419i
$808$	221.623			0.274285
$809$	886.649	+	886.649i	1.09598	+	1.09598i	0.994876	+	0.101105i	$0.0322379\pi$
$809$	886.649	+	886.649i	1.09598	+	1.09598i	0.101105	+	0.994876i	$0.467762\pi$
$810$	35.0171	+	35.0171i	0.0432310	+	0.0432310i
$811$			906.558i			1.11783i	0.829226	+	0.558914i	$0.188782\pi$
$811$			906.558i			1.11783i	−0.829226	+	0.558914i	$0.811218\pi$
$812$	40.5757			0.0499701
$813$		−	110.661i		−	0.136115i
$814$	−412.174	+	412.174i	−0.506356	+	0.506356i
$815$	−85.5494	+	85.5494i	−0.104969	+	0.104969i
$816$		−	150.865i		−	0.184883i
$817$	1377.74	+	1377.74i	1.68634	+	1.68634i
$818$		−	361.486i		−	0.441914i
$819$	−67.0609	+	67.0609i	−0.0818814	+	0.0818814i
$820$		−	28.0971i		−	0.0342647i
$821$	−264.710			−0.322424			−0.161212	−	0.986920i	$-0.551540\pi$
$821$	−264.710			−0.322424			−0.161212	+	0.986920i	$0.551540\pi$
$822$	−616.673	−	616.673i	−0.750211	−	0.750211i
$823$	−24.7558			−0.0300799			−0.0150400	−	0.999887i	$-0.504788\pi$
$823$	−24.7558			−0.0300799			−0.0150400	+	0.999887i	$0.504788\pi$
$824$	380.701	+	380.701i	0.462016	+	0.462016i
$825$	707.597	−	707.597i	0.857693	−	0.857693i
$826$	−47.2723	+	47.2723i	−0.0572304	+	0.0572304i
$827$			106.193i			0.128407i	0.997937	+	0.0642036i	$0.0204507\pi$
$827$			106.193i			0.128407i	−0.997937	+	0.0642036i	$0.979549\pi$
$828$	−21.6566			−0.0261553
$829$	−381.228	+	381.228i	−0.459864	+	0.459864i	−0.898611	−	0.438746i	$-0.855423\pi$
$829$	−381.228	+	381.228i	−0.459864	+	0.459864i	0.438746	+	0.898611i	$0.355423\pi$
$830$	−75.3429			−0.0907746
$831$	−869.530			−1.04637
$832$	−177.335			−0.213143
$833$	312.781	−	312.781i	0.375487	−	0.375487i
$834$	983.084	−	983.084i	1.17876	−	1.17876i
$835$	−37.7322	−	37.7322i	−0.0451883	−	0.0451883i
$836$	−406.917	+	406.917i	−0.486743	+	0.486743i
$837$			98.8304i			0.118077i
$838$	382.839	−	382.839i	0.456849	−	0.456849i
$839$	−990.248	−	990.248i	−1.18027	−	1.18027i	−0.979674	−	0.200598i	$-0.935712\pi$
$839$	−990.248	−	990.248i	−1.18027	−	1.18027i	−0.200598	−	0.979674i	$-0.564288\pi$
$840$	−1.72996	+	1.72996i	−0.00205948	+	0.00205948i
$841$		−	695.155i		−	0.826582i
$842$	503.393	−	503.393i	0.597854	−	0.597854i
$843$	−1411.29			−1.67413
$844$	406.806			0.481997
$845$	129.645			0.153426
$846$	343.916	−	343.916i	0.406520	−	0.406520i
$847$	−9.87805	+	9.87805i	−0.0116624	+	0.0116624i
$848$	−110.018			−0.129738
$849$	−480.313	−	480.313i	−0.565740	−	0.565740i
$850$		−	318.843i		−	0.375109i
$851$	55.6912			0.0654421
$852$			372.509i			0.437217i
$853$	222.583	+	222.583i	0.260941	+	0.260941i	0.825436	−	0.564495i	$-0.190929\pi$
$853$	222.583	+	222.583i	0.260941	+	0.260941i	−0.564495	+	0.825436i	$0.690929\pi$
$854$	25.2380			0.0295527
$855$	69.7503	+	69.7503i	0.0815793	+	0.0815793i
$856$			420.974i			0.491792i
$857$	79.9429	+	79.9429i	0.0932823	+	0.0932823i	0.752208	−	0.658926i	$-0.228989\pi$
$857$	79.9429	+	79.9429i	0.0932823	+	0.0932823i	−0.658926	+	0.752208i	$0.728989\pi$
$858$		−	1262.99i		−	1.47201i
$859$	1384.49			1.61175			0.805873	−	0.592089i	$-0.201697\pi$
$859$	1384.49			1.61175			0.805873	+	0.592089i	$0.201697\pi$
$860$	−52.8097			−0.0614066
$861$	75.1340			0.0872636
$862$			196.764i			0.228265i
$863$		−	1497.84i		−	1.73562i	−0.496896	−	0.867810i	$-0.665527\pi$
$863$		−	1497.84i		−	1.73562i	0.496896	−	0.867810i	$-0.334473\pi$
$864$	−17.2681			−0.0199862
$865$	−65.9374			−0.0762282
$866$	5.30339	−	5.30339i	0.00612401	−	0.00612401i
$867$	−607.046	+	607.046i	−0.700169	+	0.700169i
$868$	−33.5174			−0.0386145
$869$	390.995			0.449937
$870$	65.4947	+	65.4947i	0.0752813	+	0.0752813i
$871$			2275.83i			2.61289i
$872$		−	499.381i		−	0.572684i
$873$	−97.7350			−0.111953
$874$	54.9809			0.0629072
$875$	−7.33614	+	7.33614i	−0.00838416	+	0.00838416i
$876$	351.582	+	351.582i	0.401350	+	0.401350i
$877$	−497.170			−0.566899			−0.283449	−	0.958987i	$-0.591479\pi$
$877$	−497.170			−0.566899			−0.283449	+	0.958987i	$0.591479\pi$
$878$	−529.030	+	529.030i	−0.602540	+	0.602540i
$879$	1085.86	+	1085.86i	1.23534	+	1.23534i
$880$		−	15.5974i		−	0.0177243i
$881$	876.596	+	876.596i	0.995001	+	0.995001i	0.999988	−	0.00498636i	$-0.00158721\pi$
$881$	876.596	+	876.596i	0.995001	+	0.995001i	−0.00498636	+	0.999988i	$0.501587\pi$
$882$	402.787	+	402.787i	0.456675	+	0.456675i
$883$	−544.138	−	544.138i	−0.616237	−	0.616237i	0.328327	−	0.944564i	$-0.393515\pi$
$883$	−544.138	−	544.138i	−0.616237	−	0.616237i	−0.944564	+	0.328327i	$0.893515\pi$
$884$	−284.550	−	284.550i	−0.321890	−	0.321890i
$885$	−152.608			−0.172438
$886$		−	793.599i		−	0.895710i
$887$	−779.500			−0.878805			−0.439402	−	0.898290i	$-0.644810\pi$
$887$	−779.500			−0.878805			−0.439402	+	0.898290i	$0.644810\pi$
$888$	−499.598			−0.562611
$889$	35.6739	+	35.6739i	0.0401281	+	0.0401281i
$890$	28.5478	−	28.5478i	0.0320762	−	0.0320762i
$891$		−	844.250i		−	0.947531i
$892$	274.761	+	274.761i	0.308028	+	0.308028i
$893$	−873.121	+	873.121i	−0.977739	+	0.977739i
$894$	−1272.23			−1.42307
$895$	64.0630	+	64.0630i	0.0715788	+	0.0715788i
$896$		−	5.85630i		−	0.00653605i
$897$	−85.3248	+	85.3248i	−0.0951224	+	0.0951224i
$898$	298.673	+	298.673i	0.332598	+	0.332598i
$899$			1268.94i			1.41150i
$900$	410.594			0.456215
$901$	−176.534	−	176.534i	−0.195932	−	0.195932i
$902$	−338.705	+	338.705i	−0.375505	+	0.375505i
$903$		−	141.218i		−	0.156387i
$904$		−	87.3525i		−	0.0966289i
$905$	33.9586	−	33.9586i	0.0375233	−	0.0375233i
$906$	−1228.09			−1.35550
$907$		−	1080.29i		−	1.19106i	−0.803334	−	0.595528i	$-0.796943\pi$
$907$		−	1080.29i		−	1.19106i	0.803334	−	0.595528i	$-0.203057\pi$
$908$	−443.642	−	443.642i	−0.488592	−	0.488592i
$909$	−457.947	+	457.947i	−0.503792	+	0.503792i
$910$			6.52588i			0.00717129i
$911$	903.910	+	903.910i	0.992217	+	0.992217i	0.999970	−	0.00775260i	$-0.00246775\pi$
$911$	903.910	+	903.910i	0.992217	+	0.992217i	−0.00775260	+	0.999970i	$0.502468\pi$
$912$	−493.226			−0.540819
$913$	908.246	+	908.246i	0.994793	+	0.994793i
$914$	−293.719	+	293.719i	−0.321355	+	0.321355i
$915$	40.7376	+	40.7376i	0.0445219	+	0.0445219i
$916$	542.749	−	542.749i	0.592521	−	0.592521i
$917$	61.4833	−	61.4833i	0.0670483	−	0.0670483i
$918$	−27.7082	−	27.7082i	−0.0301833	−	0.0301833i
$919$	−502.782	+	502.782i	−0.547096	+	0.547096i	−0.925600	−	0.378504i	$-0.876439\pi$
$919$	−502.782	+	502.782i	−0.547096	+	0.547096i	0.378504	+	0.925600i	$0.376439\pi$
$920$	−1.05373	+	1.05373i	−0.00114536	+	0.00114536i
$921$	−1634.57	−	1634.57i	−1.77478	−	1.77478i
$922$	−105.857			−0.114812
$923$	702.600	+	702.600i	0.761214	+	0.761214i
$924$	41.7089			0.0451395
$925$	−1055.87			−1.14148
$926$	474.726			0.512663
$927$	−1573.31			−1.69721
$928$	−221.714			−0.238916
$929$	844.194	+	844.194i	0.908713	+	0.908713i	0.996168	−	0.0874557i	$-0.0278736\pi$
$929$	844.194	+	844.194i	0.908713	+	0.908713i	−0.0874557	+	0.996168i	$0.527874\pi$
$930$	−54.1016	−	54.1016i	−0.0581738	−	0.0581738i
$931$	−1022.58	−	1022.58i	−1.09837	−	1.09837i
$932$	−245.250			−0.263144
$933$			2005.57i			2.14959i
$934$			349.668i			0.374377i
$935$	25.0275	−	25.0275i	0.0267674	−	0.0267674i
$936$	366.434	−	366.434i	0.391489	−	0.391489i
$937$	−806.992	+	806.992i	−0.861251	+	0.861251i	−0.991483	−	0.130233i	$-0.958428\pi$
$937$	−806.992	+	806.992i	−0.861251	+	0.861251i	0.130233	+	0.991483i	$0.458428\pi$
$938$	−75.1570			−0.0801247
$939$	−530.100	−	530.100i	−0.564537	−	0.564537i
$940$		−	33.4674i		−	0.0356036i
$941$	−770.371	−	770.371i	−0.818673	−	0.818673i	0.167243	−	0.985916i	$-0.446514\pi$
$941$	−770.371	−	770.371i	−0.818673	−	0.818673i	−0.985916	+	0.167243i	$0.946514\pi$
$942$	766.796	−	766.796i	0.814008	−	0.814008i
$943$	45.7645			0.0485307
$944$	258.305	−	258.305i	0.273628	−	0.273628i
$945$			0.635460i			0.000672444i
$946$	636.612	+	636.612i	0.672951	+	0.672951i
$947$	921.842	+	921.842i	0.973434	+	0.973434i	0.999656	−	0.0262220i	$-0.00834767\pi$
$947$	921.842	+	921.842i	0.973434	+	0.973434i	−0.0262220	+	0.999656i	$0.508348\pi$
$948$	236.964	+	236.964i	0.249962	+	0.249962i
$949$	1326.26			1.39753
$950$	−1042.40			−1.09726
$951$			434.444i			0.456829i
$952$	9.39699	−	9.39699i	0.00987079	−	0.00987079i
$953$	119.401	−	119.401i	0.125289	−	0.125289i	−0.641682	−	0.766971i	$-0.721763\pi$
$953$	119.401	−	119.401i	0.125289	−	0.125289i	0.766971	+	0.641682i	$0.221763\pi$
$954$	227.334	−	227.334i	0.238296	−	0.238296i
$955$			52.2797i			0.0547431i
$956$		−	482.381i		−	0.504583i
$957$		−	1579.06i		−	1.65001i
$958$		−	499.568i		−	0.521470i
$959$		−	76.8221i		−	0.0801064i
$960$	9.45287	−	9.45287i	0.00984674	−	0.00984674i
$961$		−	87.1990i		−	0.0907378i
$962$	−942.307	+	942.307i	−0.979529	+	0.979529i
$963$	−869.875	−	869.875i	−0.903297	−	0.903297i
$964$	−362.995	−	362.995i	−0.376551	−	0.376551i
$965$	−51.9669	+	51.9669i	−0.0538518	+	0.0538518i
$966$	−2.81776	−	2.81776i	−0.00291694	−	0.00291694i
$967$	−787.398	−	787.398i	−0.814269	−	0.814269i	0.171001	−	0.985271i	$-0.445300\pi$
$967$	−787.398	−	787.398i	−0.814269	−	0.814269i	−0.985271	+	0.171001i	$0.945300\pi$
$968$	53.9756	−	53.9756i	0.0557599	−	0.0557599i
$969$	−791.428	−	791.428i	−0.816747	−	0.816747i
$970$	−4.75543	+	4.75543i	−0.00490251	+	0.00490251i
$971$		−	1195.64i		−	1.23135i	−0.788002	−	0.615673i	$-0.788884\pi$
$971$		−	1195.64i		−	1.23135i	0.788002	−	0.615673i	$-0.211116\pi$
$972$	472.807	−	472.807i	0.486427	−	0.486427i
$973$	122.468			0.125866
$974$	−486.669	−	486.669i	−0.499660	−	0.499660i
$975$	1617.70	−	1617.70i	1.65918	−	1.65918i
$976$	−137.905			−0.141297
$977$		−	1134.55i		−	1.16126i	−0.814168	−	0.580630i	$-0.802806\pi$
$977$		−	1134.55i		−	1.16126i	0.814168	−	0.580630i	$-0.197194\pi$
$978$	1250.03	+	1250.03i	1.27814	+	1.27814i
$979$	−688.279			−0.703043
$980$	39.1964			0.0399963
$981$	1031.89	+	1031.89i	1.05187	+	1.05187i
$982$	611.098	−	611.098i	0.622299	−	0.622299i
$983$			1785.68i			1.81656i	0.418358	+	0.908282i	$0.362606\pi$
$983$			1785.68i			1.81656i	−0.418358	+	0.908282i	$0.637394\pi$
$984$	−410.547			−0.417222
$985$	−54.8636	+	54.8636i	−0.0556991	+	0.0556991i
$986$	−355.760	−	355.760i	−0.360812	−	0.360812i
$987$	89.4947			0.0906734
$988$	−930.289	+	930.289i	−0.941588	+	0.941588i
$989$		−	86.0163i		−	0.0869730i
$990$	32.2295	+	32.2295i	0.0325551	+	0.0325551i
$991$	−1315.45	+	1315.45i	−1.32740	+	1.32740i	−0.419761	+	0.907635i	$0.637886\pi$
$991$	−1315.45	+	1315.45i	−1.32740	+	1.32740i	−0.907635	+	0.419761i	$0.862114\pi$
$992$	183.146			0.184623
$993$	846.055	+	846.055i	0.852019	+	0.852019i
$994$	−23.2027	+	23.2027i	−0.0233427	+	0.0233427i
$995$			7.78599i			0.00782511i
$996$			1100.89i			1.10531i
$997$	−1258.16			−1.26195			−0.630975	−	0.775803i	$-0.717345\pi$
$997$	−1258.16			−1.26195			−0.630975	+	0.775803i	$0.717345\pi$
$998$		−	326.095i		−	0.326749i
$999$	−91.7576	+	91.7576i	−0.0918494	+	0.0918494i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	538.3.c.b.187.4	✓	46
269.82	odd	4	inner	538.3.c.b.351.4	yes	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
538.3.c.b.187.4	✓	46	1.1	even	1	trivial
538.3.c.b.351.4	yes	46	269.82	odd	4	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 538 = 2 \cdot 269 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	538.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-2.93814 - 2.93814i) q^{3} +2.00000i q^{4} -0.402162 q^{5} +5.87628i q^{6} +(-0.366019 + 0.366019i) q^{7} +(2.00000 - 2.00000i) q^{8} +8.26535i q^{9} +(0.402162 + 0.402162i) q^{10} -9.69599i q^{11} +(5.87628 - 5.87628i) q^{12} -22.1669i q^{13} +0.732038 q^{14} +(1.18161 + 1.18161i) q^{15} -4.00000 q^{16} +(-6.41838 - 6.41838i) q^{17} +(8.26535 - 8.26535i) q^{18} +(-20.9838 + 20.9838i) q^{19} -0.804324i q^{20} +2.15083 q^{21} +(-9.69599 + 9.69599i) q^{22} +1.31008 q^{23} -11.7526 q^{24} -24.8383 q^{25} +(-22.1669 + 22.1669i) q^{26} +(-2.15851 + 2.15851i) q^{27} +(-0.732038 - 0.732038i) q^{28} +(-27.7142 + 27.7142i) q^{29} -2.36322i q^{30} +(22.8932 - 22.8932i) q^{31} +(4.00000 + 4.00000i) q^{32} +(-28.4882 + 28.4882i) q^{33} +12.8368i q^{34} +(0.147199 - 0.147199i) q^{35} -16.5307 q^{36} +42.5097 q^{37} +41.9676 q^{38} +(-65.1294 + 65.1294i) q^{39} +(-0.804324 + 0.804324i) q^{40} +34.9325 q^{41} +(-2.15083 - 2.15083i) q^{42} -65.6572i q^{43} +19.3920 q^{44} -3.32401i q^{45} +(-1.31008 - 1.31008i) q^{46} +41.6093 q^{47} +(11.7526 + 11.7526i) q^{48} +48.7321i q^{49} +(24.8383 + 24.8383i) q^{50} +37.7162i q^{51} +44.3337 q^{52} +27.5045 q^{53} +4.31702 q^{54} +3.89936i q^{55} +1.46408i q^{56} +123.307 q^{57} +55.4284 q^{58} +(-64.5763 + 64.5763i) q^{59} +(-2.36322 + 2.36322i) q^{60} +34.4764 q^{61} -45.7864 q^{62} +(-3.02528 - 3.02528i) q^{63} -8.00000i q^{64} +8.91467i q^{65} +56.9764 q^{66} -102.668 q^{67} +(12.8368 - 12.8368i) q^{68} +(-3.84920 - 3.84920i) q^{69} -0.294398 q^{70} +(-31.6960 + 31.6960i) q^{71} +(16.5307 + 16.5307i) q^{72} +59.8307i q^{73} +(-42.5097 - 42.5097i) q^{74} +(72.9783 + 72.9783i) q^{75} +(-41.9676 - 41.9676i) q^{76} +(3.54892 + 3.54892i) q^{77} +130.259 q^{78} +40.3254i q^{79} +1.60865 q^{80} +87.0721 q^{81} +(-34.9325 - 34.9325i) q^{82} +(-93.6724 + 93.6724i) q^{83} +4.30166i q^{84} +(2.58123 + 2.58123i) q^{85} +(-65.6572 + 65.6572i) q^{86} +162.857 q^{87} +(-19.3920 - 19.3920i) q^{88} -70.9859i q^{89} +(-3.32401 + 3.32401i) q^{90} +(8.11349 + 8.11349i) q^{91} +2.62016i q^{92} -134.527 q^{93} +(-41.6093 - 41.6093i) q^{94} +(8.43888 - 8.43888i) q^{95} -23.5051i q^{96} +11.8247i q^{97} +(48.7321 - 48.7321i) q^{98} +80.1407 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 46 q^{2} - 6 q^{3} - 32 q^{5} + 4 q^{7} + 92 q^{8} + 32 q^{10} + 12 q^{12} - 8 q^{14} - 10 q^{15} - 184 q^{16} - 50 q^{17} + 118 q^{18} + 10 q^{19} + 16 q^{21} + 8 q^{22} - 124 q^{23} - 24 q^{24}+ \cdots + 508 q^{99}+O(q^{100}) \) 46 * q - 46 * q^2 - 6 * q^3 - 32 * q^5 + 4 * q^7 + 92 * q^8 + 32 * q^10 + 12 * q^12 - 8 * q^14 - 10 * q^15 - 184 * q^16 - 50 * q^17 + 118 * q^18 + 10 * q^19 + 16 * q^21 + 8 * q^22 - 124 * q^23 - 24 * q^24 + 178 * q^25 + 4 * q^26 + 90 * q^27 + 8 * q^28 + 40 * q^29 + 40 * q^31 + 184 * q^32 - 64 * q^33 - 14 * q^35 - 236 * q^36 - 32 * q^37 - 20 * q^38 - 54 * q^39 - 64 * q^40 - 132 * q^41 - 16 * q^42 - 16 * q^44 + 124 * q^46 - 60 * q^47 + 24 * q^48 - 178 * q^50 - 8 * q^52 - 188 * q^53 - 180 * q^54 - 40 * q^57 - 80 * q^58 + 190 * q^59 + 20 * q^60 - 80 * q^62 - 266 * q^63 + 128 * q^66 - 164 * q^67 + 100 * q^68 + 170 * q^69 + 28 * q^70 - 92 * q^71 + 236 * q^72 + 32 * q^74 - 190 * q^75 + 20 * q^76 + 20 * q^77 + 108 * q^78 + 128 * q^80 - 298 * q^81 + 132 * q^82 + 190 * q^83 + 298 * q^85 + 228 * q^86 - 92 * q^87 + 16 * q^88 - 528 * q^90 + 2 * q^91 + 232 * q^93 + 60 * q^94 - 280 * q^95 - 226 * q^98 + 508 * q^99

Introduction

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