LMFDB - Embedded newform 538.3.c.b.351.4

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			351.4
Character	$\chi$	$=$	538.351
Dual form			538.3.c.b.187.4

$q$-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 $\left(\mathbb{Z}/538\mathbb{Z}\right)^\times$.

$n$	$271$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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	−0.999792	−	0.0204112i	$-0.993502\pi$
$3$	−2.93814	+	2.93814i	−0.979380	+	0.979380i	0.0204112	+	0.999792i	$0.493502\pi$
$4$		−	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	0.680479	−	0.732768i	$-0.261772\pi$
$7$	−0.366019	−	0.366019i	−0.0522884	−	0.0522884i	−0.732768	+	0.680479i	$0.761772\pi$
$8$	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	$0.145279\pi$
$11$			9.69599i			0.881453i	−0.897641	+	0.440727i	$0.854721\pi$
$12$	5.87628	+	5.87628i	0.489690	+	0.489690i
$13$			22.1669i			1.70514i	0.522610	+	0.852572i	$0.324958\pi$
$13$			22.1669i			1.70514i	−0.522610	+	0.852572i	$0.675042\pi$
$14$	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	−0.870218	−	0.492667i	$-0.836022\pi$
$17$	−6.41838	+	6.41838i	−0.377551	+	0.377551i	0.492667	+	0.870218i	$0.336022\pi$
$18$	8.26535	+	8.26535i	0.459186	+	0.459186i
$19$	−20.9838	−	20.9838i	−1.10441	−	1.10441i	−0.993872	−	0.110537i	$-0.964743\pi$
$19$	−20.9838	−	20.9838i	−1.10441	−	1.10441i	−0.110537	−	0.993872i	$-0.535257\pi$
$20$			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	0.0433954	−	0.999058i	$-0.486182\pi$
$29$	−27.7142	−	27.7142i	−0.955663	−	0.955663i	−0.999058	+	0.0433954i	$0.986182\pi$
$30$			2.36322i			0.0787739i
$31$	22.8932	+	22.8932i	0.738491	+	0.738491i	0.972286	−	0.233795i	$-0.0751144\pi$
$31$	22.8932	+	22.8932i	0.738491	+	0.738491i	−0.233795	+	0.972286i	$0.575114\pi$
$32$	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	$0.276499\pi$
$43$			65.6572i			1.52691i	−0.645860	+	0.763456i	$0.723501\pi$
$44$	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	−0.995040	−	0.0994736i	$-0.968284\pi$
$59$	−64.5763	−	64.5763i	−1.09451	−	1.09451i	−0.0994736	−	0.995040i	$-0.531716\pi$
$60$	−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	0.447741	−	0.894163i	$-0.352229\pi$
$71$	−31.6960	−	31.6960i	−0.446422	−	0.446422i	−0.894163	+	0.447741i	$0.852229\pi$
$72$	16.5307	−	16.5307i	0.229593	−	0.229593i
$73$		−	59.8307i		−	0.819599i	−0.912176	−	0.409800i	$-0.865599\pi$
$73$		−	59.8307i		−	0.819599i	0.912176	−	0.409800i	$-0.134401\pi$
$74$	−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	$-0.917851\pi$
$79$		−	40.3254i		−	0.510449i	0.966882	−	0.255224i	$-0.0821493\pi$
$80$	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	−0.990408	−	0.138175i	$-0.955876\pi$
$83$	−93.6724	−	93.6724i	−1.12858	−	1.12858i	−0.138175	−	0.990408i	$-0.544124\pi$
$84$		−	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	$0.130572\pi$
$89$			70.9859i			0.797595i	−0.917039	+	0.398797i	$0.869428\pi$
$90$	−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	$-0.980586\pi$
$97$		−	11.8247i		−	0.121904i	0.998141	−	0.0609519i	$-0.0194136\pi$
$98$	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	−0.377456	−	0.926027i	$-0.623201\pi$
$101$	55.4057	−	55.4057i	0.548571	−	0.548571i	0.926027	+	0.377456i	$0.123201\pi$
$102$	37.7162	+	37.7162i	0.369767	+	0.369767i
$103$		−	190.350i		−	1.84806i	−0.382317	−	0.924031i	$-0.624874\pi$
$103$		−	190.350i		−	1.84806i	0.382317	−	0.924031i	$-0.375126\pi$
$104$	−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	0.0162829	−	0.999867i	$-0.494817\pi$
$107$	−105.244	−	105.244i	−0.983584	−	0.983584i	−0.999867	+	0.0162829i	$0.994817\pi$
$108$	−4.31702	+	4.31702i	−0.0399724	+	0.0399724i
$109$	124.845	+	124.845i	1.14537	+	1.14537i	0.987453	+	0.157916i	$0.0504775\pi$
$109$	124.845	+	124.845i	1.14537	+	1.14537i	0.157916	+	0.987453i	$0.449522\pi$
$110$	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	0.797102	−	0.603844i	$-0.206365\pi$
$113$	21.8381	+	21.8381i	0.193258	+	0.193258i	−0.603844	+	0.797102i	$0.706365\pi$
$114$	−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	$0.125357\pi$
$127$			97.4646i			0.767437i	−0.923450	+	0.383719i	$0.874643\pi$
$128$	−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	0.211395	−	0.977401i	$-0.432199\pi$
$137$	−104.943	−	104.943i	−0.766005	−	0.766005i	−0.977401	+	0.211395i	$0.932199\pi$
$138$		−	7.69841i		−	0.0557856i
$139$	−167.297	+	167.297i	−1.20358	+	1.20358i	−0.230504	+	0.973071i	$0.574037\pi$
$139$	−167.297	+	167.297i	−1.20358	+	1.20358i	−0.973071	+	0.230504i	$0.925963\pi$
$140$	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	$-0.741137\pi$
$149$		−	216.502i		−	1.45304i	0.687148	−	0.726518i	$-0.258863\pi$
$150$			145.957i			0.973044i
$151$		−	208.990i		−	1.38404i	−0.721877	−	0.692021i	$-0.756721\pi$
$151$		−	208.990i		−	1.38404i	0.721877	−	0.692021i	$-0.243279\pi$
$152$		−	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	−0.987674	−	0.156528i	$-0.949970\pi$
$157$	−130.490	+	130.490i	−0.831146	+	0.831146i	0.156528	+	0.987674i	$0.449970\pi$
$158$	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	0.924940	+	0.380114i	$0.124115\pi$
$163$	212.724	+	212.724i	1.30505	+	1.30505i	0.380114	+	0.924940i	$0.375885\pi$
$164$		−	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	−0.368006	−	0.929823i	$-0.619959\pi$
$167$	93.8235	−	93.8235i	0.561817	−	0.561817i	0.929823	+	0.368006i	$0.119959\pi$
$168$	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	−0.994515	−	0.104591i	$-0.966647\pi$
$179$	−159.297	+	159.297i	−0.889925	+	0.889925i	0.104591	+	0.994515i	$0.466647\pi$
$180$	6.64802			0.0369334
$181$	−84.4401	−	84.4401i	−0.466520	−	0.466520i	0.434265	−	0.900785i	$-0.357008\pi$
$181$	−84.4401	−	84.4401i	−0.466520	−	0.466520i	−0.900785	+	0.434265i	$0.857008\pi$
$182$			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	$0.110530\pi$
$191$			129.997i			0.680610i	−0.940315	+	0.340305i	$0.889470\pi$
$192$	−23.5051	−	23.5051i	−0.122423	−	0.122423i
$193$	129.219	+	129.219i	0.669528	+	0.669528i	0.957607	−	0.288078i	$-0.0930164\pi$
$193$	129.219	+	129.219i	0.669528	+	0.669528i	−0.288078	+	0.957607i	$0.593016\pi$
$194$	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	0.962780	−	0.270285i	$-0.0871179\pi$
$197$	136.422	+	136.422i	0.692496	+	0.692496i	−0.270285	+	0.962780i	$0.587118\pi$
$198$	−80.1407	+	80.1407i	−0.404751	+	0.404751i
$199$			19.3603i			0.0972881i	0.998816	+	0.0486441i	$0.0154900\pi$
$199$			19.3603i			0.0972881i	−0.998816	+	0.0486441i	$0.984510\pi$
$200$	−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	$0.160088\pi$
$211$			203.403i			0.963994i	−0.876173	+	0.481997i	$0.839912\pi$
$212$		−	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	0.944517	−	0.328462i	$-0.106530\pi$
$223$	137.380	+	137.380i	0.616056	+	0.616056i	−0.328462	+	0.944517i	$0.606530\pi$
$224$	−2.92815			−0.0130721
$225$			205.297i			0.912431i
$226$	−43.6763			−0.193258
$227$	−221.821	−	221.821i	−0.977185	−	0.977185i	0.0225608	−	0.999745i	$-0.492818\pi$
$227$	−221.821	−	221.821i	−0.977185	−	0.977185i	−0.999745	+	0.0225608i	$0.992818\pi$
$228$		−	246.613i		−	1.08164i
$229$	−271.374	+	271.374i	−1.18504	+	1.18504i	−0.206620	+	0.978421i	$0.566246\pi$
$229$	−271.374	+	271.374i	−1.18504	+	1.18504i	−0.978421	+	0.206620i	$0.933754\pi$
$230$	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	$-0.915241\pi$
$233$		−	122.625i		−	0.526288i	0.964757	−	0.263144i	$-0.0847594\pi$
$234$	−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	0.221955	−	0.975057i	$-0.428756\pi$
$241$	−181.498	−	181.498i	−0.753102	−	0.753102i	−0.975057	+	0.221955i	$0.928756\pi$
$242$	−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	−0.907446	−	0.420168i	$-0.861971\pi$
$251$	−122.307	+	122.307i	−0.487279	+	0.487279i	0.420168	+	0.907446i	$0.361971\pi$
$252$	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	−0.960581	−	0.277999i	$-0.910329\pi$
$257$	−175.424	+	175.424i	−0.682582	+	0.682582i	0.277999	+	0.960581i	$0.410329\pi$
$258$	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	−0.671507	−	0.740998i	$-0.734353\pi$
$271$	18.8319	−	18.8319i	0.0694904	−	0.0694904i	0.740998	+	0.671507i	$0.234353\pi$
$272$	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	0.921819	−	0.387621i	$-0.126703\pi$
$277$	147.973	+	147.973i	0.534198	+	0.534198i	−0.387621	+	0.921819i	$0.626703\pi$
$278$		−	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	0.990706	−	0.136018i	$-0.0434306\pi$
$281$	240.167	+	240.167i	0.854688	+	0.854688i	−0.136018	+	0.990706i	$0.543431\pi$
$282$		−	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	−0.102714	+	0.994711i	$0.532753\pi$
$311$	−341.299	+	341.299i	−1.09742	+	1.09742i	−0.994711	+	0.102714i	$0.967247\pi$
$312$		−	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	−0.814037	−	0.580813i	$-0.802735\pi$
$317$	−73.9318	+	73.9318i	−0.233223	+	0.233223i	0.580813	+	0.814037i	$0.302735\pi$
$318$		−	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	0.297153	−	0.954830i	$-0.403963\pi$
$337$	−221.637	−	221.637i	−0.657676	−	0.657676i	−0.954830	+	0.297153i	$0.903963\pi$
$338$	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	$-0.648667\pi$
$353$		−	630.388i		−	1.78580i	0.450254	−	0.892900i	$-0.351333\pi$
$354$	−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	0.114058	−	0.993474i	$-0.463615\pi$
$359$	−315.711	−	315.711i	−0.879416	−	0.879416i	−0.993474	+	0.114058i	$0.963615\pi$
$360$	−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	0.340979	−	0.940071i	$-0.389242\pi$
$367$	−219.867	−	219.867i	−0.599092	−	0.599092i	−0.940071	+	0.340979i	$0.889242\pi$
$368$	−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	−0.899947	−	0.436000i	$-0.856395\pi$
$373$	−173.052	+	173.052i	−0.463947	+	0.463947i	0.436000	+	0.899947i	$0.356395\pi$
$374$	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	0.581224	−	0.813743i	$-0.302574\pi$
$379$	−88.1247	−	88.1247i	−0.232519	−	0.232519i	−0.813743	+	0.581224i	$0.802574\pi$
$380$	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	−0.904878	−	0.425670i	$-0.860038\pi$
$383$	−183.537	+	183.537i	−0.479208	+	0.479208i	0.425670	+	0.904878i	$0.360038\pi$
$384$	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	0.751391	−	0.659858i	$-0.229383\pi$
$397$	36.3386	+	36.3386i	0.0915330	+	0.0915330i	−0.659858	+	0.751391i	$0.729383\pi$
$398$	−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	−0.0345424	+	0.999403i	$0.510997\pi$
$401$	−414.612	+	414.612i	−1.03395	+	1.03395i	−0.999403	+	0.0345424i	$0.989003\pi$
$402$			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	−0.450741	−	0.892655i	$-0.648840\pi$
$409$	180.743	−	180.743i	0.441914	−	0.441914i	0.892655	+	0.450741i	$0.148840\pi$
$410$	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	$-0.848978\pi$
$419$		−	382.839i		−	0.913697i	0.889544	−	0.456849i	$-0.151022\pi$
$420$			1.72996i			0.00411896i
$421$		−	503.393i		−	1.19571i	−0.801605	−	0.597854i	$-0.796020\pi$
$421$		−	503.393i		−	1.19571i	0.801605	−	0.597854i	$-0.203980\pi$
$422$	−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	−0.811967	−	0.583703i	$-0.801603\pi$
$431$	−98.3821	+	98.3821i	−0.228265	+	0.228265i	0.583703	+	0.811967i	$0.301603\pi$
$432$	8.63403	+	8.63403i	0.0199862	+	0.0199862i
$433$		−	5.30339i		−	0.0122480i	−0.999981	−	0.00612401i	$-0.998051\pi$
$433$		−	5.30339i		−	0.0122480i	0.999981	−	0.00612401i	$-0.00194935\pi$
$434$	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	$0.205845\pi$
$439$			529.030i			1.20508i	−0.798088	+	0.602540i	$0.794155\pi$
$440$	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	−0.0993432	−	0.995053i	$-0.531674\pi$
$443$	396.800	−	396.800i	0.895710	−	0.895710i	0.995053	+	0.0993432i	$0.0316742\pi$
$444$	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	$0.104138\pi$
$457$			293.719i			0.642710i	−0.946959	+	0.321355i	$0.895862\pi$
$458$		−	542.749i		−	1.18504i
$459$	27.7082			0.0603665
$460$			1.05373i			0.00229072i
$461$	52.9283	+	52.9283i	0.114812	+	0.114812i	0.762179	−	0.647367i	$-0.224130\pi$
$461$	52.9283	+	52.9283i	0.114812	+	0.114812i	−0.647367	+	0.762179i	$0.724130\pi$
$462$	−20.8544	−	20.8544i	−0.0451395	−	0.0451395i
$463$	−237.363	−	237.363i	−0.512663	−	0.512663i	0.402679	−	0.915341i	$-0.368079\pi$
$463$	−237.363	−	237.363i	−0.512663	−	0.512663i	−0.915341	+	0.402679i	$0.868079\pi$
$464$	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	−0.869069	−	0.494692i	$-0.835281\pi$
$467$	−174.834	+	174.834i	−0.374377	+	0.374377i	0.494692	+	0.869069i	$0.335281\pi$
$468$		−	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	−0.396545	−	0.918015i	$-0.629791\pi$
$479$	249.784	−	249.784i	0.521470	−	0.521470i	0.918015	+	0.396545i	$0.129791\pi$
$480$		−	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	$-0.786199\pi$
$491$		−	611.098i		−	1.24460i	0.782780	−	0.622299i	$-0.213801\pi$
$492$	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	−0.524600	−	0.851349i	$-0.675785\pi$
$499$	163.048	−	163.048i	0.326749	−	0.326749i	0.851349	+	0.524600i	$0.175785\pi$
$500$		−	40.0861i		−	0.0801722i
$501$			551.333i			1.10047i
$502$		−	244.614i		−	0.487279i
$503$	193.054	−	193.054i	0.383806	−	0.383806i	−0.488665	−	0.872471i	$-0.662516\pi$
$503$	193.054	−	193.054i	0.383806	−	0.383806i	0.872471	+	0.488665i	$0.162516\pi$
$504$	−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	−0.826582	−	0.562816i	$-0.809718\pi$
$509$	−134.257	+	134.257i	−0.263767	+	0.263767i	0.562816	+	0.826582i	$0.309718\pi$
$510$	−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	0.314187	−	0.949361i	$-0.398268\pi$
$521$	−330.926	−	330.926i	−0.635174	−	0.635174i	−0.949361	+	0.314187i	$0.898268\pi$
$522$		−	458.135i		−	0.877654i
$523$	262.398	+	262.398i	0.501716	+	0.501716i	0.911971	−	0.410255i	$-0.134560\pi$
$523$	262.398	+	262.398i	0.501716	+	0.501716i	−0.410255	+	0.911971i	$0.634560\pi$
$524$			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	−0.905884	−	0.423525i	$-0.860793\pi$
$541$	−260.956	+	260.956i	−0.482359	+	0.482359i	0.423525	+	0.905884i	$0.360793\pi$
$542$			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	$0.160570\pi$
$547$			528.756i			0.966647i	−0.875442	+	0.483323i	$0.839430\pi$
$548$	−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	0.757137	−	0.653257i	$-0.226598\pi$
$557$	57.8611	+	57.8611i	0.103880	+	0.103880i	−0.653257	+	0.757137i	$0.726598\pi$
$558$			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	0.644313	−	0.764762i	$-0.277143\pi$
$569$	−68.5356	−	68.5356i	−0.120449	−	0.120449i	−0.764762	+	0.644313i	$0.777143\pi$
$570$	49.5892	−	49.5892i	0.0869986	−	0.0869986i
$571$	−179.419	−	179.419i	−0.314219	−	0.314219i	0.532323	−	0.846541i	$-0.321319\pi$
$571$	−179.419	−	179.419i	−0.314219	−	0.314219i	−0.846541	+	0.532323i	$0.821319\pi$
$572$			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	0.0459758	−	0.998943i	$-0.485360\pi$
$577$	−549.862	−	549.862i	−0.952967	−	0.952967i	−0.998943	+	0.0459758i	$0.985360\pi$
$578$	−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	$0.0698414\pi$
$587$			255.529i			0.435314i	−0.976025	+	0.217657i	$0.930159\pi$
$588$	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	$-0.791773\pi$
$593$		−	721.678i		−	1.21699i	0.793556	−	0.608497i	$-0.208227\pi$
$594$			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	−0.785422	−	0.618960i	$-0.787554\pi$
$601$	−100.044	+	100.044i	−0.166462	+	0.166462i	0.618960	+	0.785422i	$0.287554\pi$
$602$			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	−0.979048	−	0.203631i	$-0.934726\pi$
$607$	−470.678	+	470.678i	−0.775417	+	0.775417i	0.203631	+	0.979048i	$0.434726\pi$
$608$	−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	−0.950468	−	0.310821i	$-0.899396\pi$
$613$	−392.104	+	392.104i	−0.639647	+	0.639647i	0.310821	+	0.950468i	$0.399396\pi$
$614$	−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	$0.288338\pi$
$617$			971.089i			1.57389i	−0.617024	+	0.786944i	$0.711662\pi$
$618$	−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	$0.0379119\pi$
$641$			152.330i			0.237645i	−0.992916	+	0.118822i	$0.962088\pi$
$642$	−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	0.573586	−	0.819145i	$-0.305552\pi$
$647$	−158.877	−	158.877i	−0.245559	−	0.245559i	−0.819145	+	0.573586i	$0.805552\pi$
$648$	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	−0.907456	−	0.420148i	$-0.861978\pi$
$661$	−322.111	+	322.111i	−0.487308	+	0.487308i	0.420148	+	0.907456i	$0.361978\pi$
$662$	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	0.931850	−	0.362844i	$-0.118194\pi$
$673$	382.941	+	382.941i	0.569006	+	0.569006i	−0.362844	+	0.931850i	$0.618194\pi$
$674$	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	−0.975641	−	0.219372i	$-0.929599\pi$
$677$	−511.994	+	511.994i	−0.756269	+	0.756269i	0.219372	+	0.975641i	$0.429599\pi$
$678$	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	0.523218	−	0.852199i	$-0.324732\pi$
$683$	−224.694	−	224.694i	−0.328982	−	0.328982i	−0.852199	+	0.523218i	$0.824732\pi$
$684$	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	0.172265	−	0.985051i	$-0.444892\pi$
$691$	−561.635	−	561.635i	−0.812786	−	0.812786i	−0.985051	+	0.172265i	$0.944892\pi$
$692$		−	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	0.968989	−	0.247106i	$-0.0794795\pi$
$701$	506.040	+	506.040i	0.721883	+	0.721883i	−0.247106	+	0.968989i	$0.579480\pi$
$702$			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	−0.577548	−	0.816357i	$-0.695990\pi$
$709$	169.316	−	169.316i	0.238809	−	0.238809i	0.816357	+	0.577548i	$0.195990\pi$
$710$	−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	0.270511	−	0.962717i	$-0.412807\pi$
$719$	−497.696	−	497.696i	−0.692206	−	0.692206i	−0.962717	+	0.270511i	$0.912807\pi$
$720$		−	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	$0.205498\pi$
$727$			874.830i			1.20334i	−0.798744	+	0.601671i	$0.794502\pi$
$728$	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	0.592895	−	0.805280i	$-0.297985\pi$
$733$	−155.678	−	155.678i	−0.212385	−	0.212385i	−0.805280	+	0.592895i	$0.797985\pi$
$734$	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	−0.644114	−	0.764929i	$-0.722774\pi$
$739$	89.2820	−	89.2820i	0.120815	−	0.120815i	0.764929	+	0.644114i	$0.222774\pi$
$740$			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	0.0512104	−	0.998688i	$-0.483692\pi$
$757$	−717.240	−	717.240i	−0.947478	−	0.947478i	−0.998688	+	0.0512104i	$0.983692\pi$
$758$	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	0.431027	−	0.902339i	$-0.358151\pi$
$761$	−358.668	−	358.668i	−0.471312	−	0.471312i	−0.902339	+	0.431027i	$0.858151\pi$
$762$	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	$0.341034\pi$
$769$			1350.16i			1.75573i	−0.478905	+	0.877867i	$0.658966\pi$
$770$		−	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	0.593182	−	0.805069i	$-0.297872\pi$
$797$	−168.874	−	168.874i	−0.211887	−	0.211887i	−0.805069	+	0.593182i	$0.797872\pi$
$798$	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	0.101105	−	0.994876i	$-0.467762\pi$
$809$	886.649	−	886.649i	1.09598	−	1.09598i	0.994876	−	0.101105i	$-0.0322379\pi$
$810$	35.0171	−	35.0171i	0.0432310	−	0.0432310i
$811$		−	906.558i		−	1.11783i	−0.829226	−	0.558914i	$-0.811218\pi$
$811$		−	906.558i		−	1.11783i	0.829226	−	0.558914i	$-0.188782\pi$
$812$	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	$-0.979549\pi$
$827$		−	106.193i		−	0.128407i	0.997937	−	0.0642036i	$-0.0204507\pi$
$828$	−21.6566			−0.0261553
$829$	−381.228	−	381.228i	−0.459864	−	0.459864i	0.438746	−	0.898611i	$-0.355423\pi$
$829$	−381.228	−	381.228i	−0.459864	−	0.459864i	−0.898611	+	0.438746i	$0.855423\pi$
$830$	−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	−0.200598	+	0.979674i	$0.564288\pi$
$839$	−990.248	+	990.248i	−1.18027	+	1.18027i	−0.979674	+	0.200598i	$0.935712\pi$
$840$	−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	−0.564495	−	0.825436i	$-0.690929\pi$
$853$	222.583	−	222.583i	0.260941	−	0.260941i	0.825436	+	0.564495i	$0.190929\pi$
$854$	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	−0.658926	−	0.752208i	$-0.728989\pi$
$857$	79.9429	−	79.9429i	0.0932823	−	0.0932823i	0.752208	+	0.658926i	$0.228989\pi$
$858$			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	$0.334473\pi$
$863$			1497.84i			1.73562i	−0.496896	+	0.867810i	$0.665527\pi$
$864$	−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	−0.00498636	−	0.999988i	$-0.501587\pi$
$881$	876.596	−	876.596i	0.995001	−	0.995001i	0.999988	+	0.00498636i	$0.00158721\pi$
$882$	402.787	−	402.787i	0.456675	−	0.456675i
$883$	−544.138	+	544.138i	−0.616237	+	0.616237i	−0.944564	−	0.328327i	$-0.893515\pi$
$883$	−544.138	+	544.138i	−0.616237	+	0.616237i	0.328327	+	0.944564i	$0.393515\pi$
$884$	−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	$0.203057\pi$
$907$			1080.29i			1.19106i	−0.803334	+	0.595528i	$0.796943\pi$
$908$	−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	−0.00775260	−	0.999970i	$-0.502468\pi$
$911$	903.910	−	903.910i	0.992217	−	0.992217i	0.999970	+	0.00775260i	$0.00246775\pi$
$912$	−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	0.378504	−	0.925600i	$-0.376439\pi$
$919$	−502.782	−	502.782i	−0.547096	−	0.547096i	−0.925600	+	0.378504i	$0.876439\pi$
$920$	−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	−0.0874557	−	0.996168i	$-0.527874\pi$
$929$	844.194	−	844.194i	0.908713	−	0.908713i	0.996168	+	0.0874557i	$0.0278736\pi$
$930$	−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	0.130233	−	0.991483i	$-0.458428\pi$
$937$	−806.992	−	806.992i	−0.861251	−	0.861251i	−0.991483	+	0.130233i	$0.958428\pi$
$938$	−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	−0.985916	−	0.167243i	$-0.946514\pi$
$941$	−770.371	+	770.371i	−0.818673	+	0.818673i	0.167243	+	0.985916i	$0.446514\pi$
$942$	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	−0.0262220	−	0.999656i	$-0.508348\pi$
$947$	921.842	−	921.842i	0.973434	−	0.973434i	0.999656	+	0.0262220i	$0.00834767\pi$
$948$	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	0.766971	−	0.641682i	$-0.221763\pi$
$953$	119.401	+	119.401i	0.125289	+	0.125289i	−0.641682	+	0.766971i	$0.721763\pi$
$954$	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	−0.985271	−	0.171001i	$-0.945300\pi$
$967$	−787.398	+	787.398i	−0.814269	+	0.814269i	0.171001	+	0.985271i	$0.445300\pi$
$968$	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	$0.211116\pi$
$971$			1195.64i			1.23135i	−0.788002	+	0.615673i	$0.788884\pi$
$972$	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	$0.197194\pi$
$977$			1134.55i			1.16126i	−0.814168	+	0.580630i	$0.802806\pi$
$978$	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	$-0.637394\pi$
$983$		−	1785.68i		−	1.81656i	0.418358	−	0.908282i	$-0.362606\pi$
$984$	−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	−0.907635	−	0.419761i	$-0.862114\pi$
$991$	−1315.45	−	1315.45i	−1.32740	−	1.32740i	−0.419761	−	0.907635i	$-0.637886\pi$
$992$	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.351.4	yes	46
269.187	odd	4	inner	538.3.c.b.187.4	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
538.3.c.b.187.4	✓	46	269.187	odd	4	inner
538.3.c.b.351.4	yes	46	1.1	even	1	trivial

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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more