LMFDB - Embedded newform 8006.2.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8006,2,Mod(1,8006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8006, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8006 = 2 \cdot 4003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8006.a (trivial)

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:	yes
Analytic conductor:	$63.9282318582$
Analytic rank:	$0$
Dimension:	$98$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	8006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.30357 q^{3} +1.00000 q^{4} -2.71504 q^{5} -3.30357 q^{6} +0.802195 q^{7} +1.00000 q^{8} +7.91355 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.30357 q^{3} +1.00000 q^{4} -2.71504 q^{5} -3.30357 q^{6} +0.802195 q^{7} +1.00000 q^{8} +7.91355 q^{9} -2.71504 q^{10} -2.03790 q^{11} -3.30357 q^{12} -5.68972 q^{13} +0.802195 q^{14} +8.96932 q^{15} +1.00000 q^{16} -3.06731 q^{17} +7.91355 q^{18} -3.54177 q^{19} -2.71504 q^{20} -2.65011 q^{21} -2.03790 q^{22} -3.69022 q^{23} -3.30357 q^{24} +2.37146 q^{25} -5.68972 q^{26} -16.2322 q^{27} +0.802195 q^{28} +6.21167 q^{29} +8.96932 q^{30} -5.35567 q^{31} +1.00000 q^{32} +6.73234 q^{33} -3.06731 q^{34} -2.17799 q^{35} +7.91355 q^{36} -6.25812 q^{37} -3.54177 q^{38} +18.7964 q^{39} -2.71504 q^{40} +0.393636 q^{41} -2.65011 q^{42} +6.10303 q^{43} -2.03790 q^{44} -21.4856 q^{45} -3.69022 q^{46} +10.0197 q^{47} -3.30357 q^{48} -6.35648 q^{49} +2.37146 q^{50} +10.1331 q^{51} -5.68972 q^{52} -0.795708 q^{53} -16.2322 q^{54} +5.53299 q^{55} +0.802195 q^{56} +11.7005 q^{57} +6.21167 q^{58} -8.38303 q^{59} +8.96932 q^{60} -6.87941 q^{61} -5.35567 q^{62} +6.34821 q^{63} +1.00000 q^{64} +15.4478 q^{65} +6.73234 q^{66} -11.2311 q^{67} -3.06731 q^{68} +12.1909 q^{69} -2.17799 q^{70} -2.93379 q^{71} +7.91355 q^{72} -2.52647 q^{73} -6.25812 q^{74} -7.83426 q^{75} -3.54177 q^{76} -1.63479 q^{77} +18.7964 q^{78} +2.76018 q^{79} -2.71504 q^{80} +29.8836 q^{81} +0.393636 q^{82} -1.81395 q^{83} -2.65011 q^{84} +8.32788 q^{85} +6.10303 q^{86} -20.5207 q^{87} -2.03790 q^{88} -10.7986 q^{89} -21.4856 q^{90} -4.56427 q^{91} -3.69022 q^{92} +17.6928 q^{93} +10.0197 q^{94} +9.61606 q^{95} -3.30357 q^{96} -2.29394 q^{97} -6.35648 q^{98} -16.1270 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 98 q + 98 q^{2} + 16 q^{3} + 98 q^{4} + 4 q^{5} + 16 q^{6} + 29 q^{7} + 98 q^{8} + 130 q^{9}+O(q^{10}) $ 98 * q + 98 * q^2 + 16 * q^3 + 98 * q^4 + 4 * q^5 + 16 * q^6 + 29 * q^7 + 98 * q^8 + 130 * q^9	\( 98 q + 98 q^{2} + 16 q^{3} + 98 q^{4} + 4 q^{5} + 16 q^{6} + 29 q^{7} + 98 q^{8} + 130 q^{9} + 4 q^{10} + 51 q^{11} + 16 q^{12} + 31 q^{13} + 29 q^{14} + 57 q^{15} + 98 q^{16} + 35 q^{17} + 130 q^{18} + 77 q^{19} + 4 q^{20} + 46 q^{21} + 51 q^{22} + 73 q^{23} + 16 q^{24} + 150 q^{25} + 31 q^{26} + 52 q^{27} + 29 q^{28} + 20 q^{29} + 57 q^{30} + 59 q^{31} + 98 q^{32} + 27 q^{33} + 35 q^{34} + 48 q^{35} + 130 q^{36} + 41 q^{37} + 77 q^{38} + 64 q^{39} + 4 q^{40} + 29 q^{41} + 46 q^{42} + 94 q^{43} + 51 q^{44} - 3 q^{45} + 73 q^{46} + 58 q^{47} + 16 q^{48} + 149 q^{49} + 150 q^{50} + 58 q^{51} + 31 q^{52} - 11 q^{53} + 52 q^{54} + 56 q^{55} + 29 q^{56} + 64 q^{57} + 20 q^{58} + 45 q^{59} + 57 q^{60} + 73 q^{61} + 59 q^{62} + 53 q^{63} + 98 q^{64} + 39 q^{65} + 27 q^{66} + 133 q^{67} + 35 q^{68} + 13 q^{69} + 48 q^{70} + 67 q^{71} + 130 q^{72} + 42 q^{73} + 41 q^{74} + 36 q^{75} + 77 q^{76} - 25 q^{77} + 64 q^{78} + 154 q^{79} + 4 q^{80} + 198 q^{81} + 29 q^{82} + 69 q^{83} + 46 q^{84} + 81 q^{85} + 94 q^{86} + 25 q^{87} + 51 q^{88} + 32 q^{89} - 3 q^{90} + 95 q^{91} + 73 q^{92} - 23 q^{93} + 58 q^{94} + 50 q^{95} + 16 q^{96} + 76 q^{97} + 149 q^{98} + 149 q^{99}+O(q^{100}) \) 98 * q + 98 * q^2 + 16 * q^3 + 98 * q^4 + 4 * q^5 + 16 * q^6 + 29 * q^7 + 98 * q^8 + 130 * q^9 + 4 * q^10 + 51 * q^11 + 16 * q^12 + 31 * q^13 + 29 * q^14 + 57 * q^15 + 98 * q^16 + 35 * q^17 + 130 * q^18 + 77 * q^19 + 4 * q^20 + 46 * q^21 + 51 * q^22 + 73 * q^23 + 16 * q^24 + 150 * q^25 + 31 * q^26 + 52 * q^27 + 29 * q^28 + 20 * q^29 + 57 * q^30 + 59 * q^31 + 98 * q^32 + 27 * q^33 + 35 * q^34 + 48 * q^35 + 130 * q^36 + 41 * q^37 + 77 * q^38 + 64 * q^39 + 4 * q^40 + 29 * q^41 + 46 * q^42 + 94 * q^43 + 51 * q^44 - 3 * q^45 + 73 * q^46 + 58 * q^47 + 16 * q^48 + 149 * q^49 + 150 * q^50 + 58 * q^51 + 31 * q^52 - 11 * q^53 + 52 * q^54 + 56 * q^55 + 29 * q^56 + 64 * q^57 + 20 * q^58 + 45 * q^59 + 57 * q^60 + 73 * q^61 + 59 * q^62 + 53 * q^63 + 98 * q^64 + 39 * q^65 + 27 * q^66 + 133 * q^67 + 35 * q^68 + 13 * q^69 + 48 * q^70 + 67 * q^71 + 130 * q^72 + 42 * q^73 + 41 * q^74 + 36 * q^75 + 77 * q^76 - 25 * q^77 + 64 * q^78 + 154 * q^79 + 4 * q^80 + 198 * q^81 + 29 * q^82 + 69 * q^83 + 46 * q^84 + 81 * q^85 + 94 * q^86 + 25 * q^87 + 51 * q^88 + 32 * q^89 - 3 * q^90 + 95 * q^91 + 73 * q^92 - 23 * q^93 + 58 * q^94 + 50 * q^95 + 16 * q^96 + 76 * q^97 + 149 * q^98 + 149 * q^99

Display 100 coefficients 10 coefficients

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	0.707107
$2$	1.00000	0.707107
$3$	−3.30357	−1.90731	−0.953657	−	0.300895i	$-0.902715\pi$
$3$	−3.30357	−1.90731	−0.953657	+	0.300895i	$0.902715\pi$
$4$	1.00000	0.500000
$5$	−2.71504	−1.21420	−0.607102	−	0.794624i	$-0.707668\pi$
$5$	−2.71504	−1.21420	−0.607102	+	0.794624i	$0.707668\pi$
$6$	−3.30357	−1.34868
$7$	0.802195	0.303201	0.151601	−	0.988442i	$-0.451557\pi$
$7$	0.802195	0.303201	0.151601	+	0.988442i	$0.451557\pi$
$8$	1.00000	0.353553
$9$	7.91355	2.63785
$10$	−2.71504	−0.858572
$11$	−2.03790	−0.614450	−0.307225	−	0.951637i	$-0.599400\pi$
$11$	−2.03790	−0.614450	−0.307225	+	0.951637i	$0.599400\pi$
$12$	−3.30357	−0.953657
$13$	−5.68972	−1.57804	−0.789022	−	0.614364i	$-0.789412\pi$
$13$	−5.68972	−1.57804	−0.789022	+	0.614364i	$0.789412\pi$
$14$	0.802195	0.214396
$15$	8.96932	2.31587
$16$	1.00000	0.250000
$17$	−3.06731	−0.743932	−0.371966	−	0.928246i	$-0.621316\pi$
$17$	−3.06731	−0.743932	−0.371966	+	0.928246i	$0.621316\pi$
$18$	7.91355	1.86524
$19$	−3.54177	−0.812538	−0.406269	−	0.913753i	$-0.633170\pi$
$19$	−3.54177	−0.812538	−0.406269	+	0.913753i	$0.633170\pi$
$20$	−2.71504	−0.607102
$21$	−2.65011	−0.578300
$22$	−2.03790	−0.434482
$23$	−3.69022	−0.769465	−0.384732	−	0.923028i	$-0.625706\pi$
$23$	−3.69022	−0.769465	−0.384732	+	0.923028i	$0.625706\pi$
$24$	−3.30357	−0.674338
$25$	2.37146	0.474291
$26$	−5.68972	−1.11585
$27$	−16.2322	−3.12389
$28$	0.802195	0.151601
$29$	6.21167	1.15348	0.576739	−	0.816928i	$-0.304325\pi$
$29$	6.21167	1.15348	0.576739	+	0.816928i	$0.304325\pi$
$30$	8.96932	1.63757
$31$	−5.35567	−0.961906	−0.480953	−	0.876746i	$-0.659709\pi$
$31$	−5.35567	−0.961906	−0.480953	+	0.876746i	$0.659709\pi$
$32$	1.00000	0.176777
$33$	6.73234	1.17195
$34$	−3.06731	−0.526039
$35$	−2.17799	−0.368148
$36$	7.91355	1.31892
$37$	−6.25812	−1.02883	−0.514415	−	0.857542i	$-0.671991\pi$
$37$	−6.25812	−1.02883	−0.514415	+	0.857542i	$0.671991\pi$
$38$	−3.54177	−0.574551
$39$	18.7964	3.00983
$40$	−2.71504	−0.429286
$41$	0.393636	0.0614757	0.0307378	−	0.999527i	$-0.490214\pi$
$41$	0.393636	0.0614757	0.0307378	+	0.999527i	$0.490214\pi$
$42$	−2.65011	−0.408920
$43$	6.10303	0.930704	0.465352	−	0.885126i	$-0.345928\pi$
$43$	6.10303	0.930704	0.465352	+	0.885126i	$0.345928\pi$
$44$	−2.03790	−0.307225
$45$	−21.4856	−3.20289
$46$	−3.69022	−0.544094
$47$	10.0197	1.46152	0.730760	−	0.682634i	$-0.239166\pi$
$47$	10.0197	1.46152	0.730760	+	0.682634i	$0.239166\pi$
$48$	−3.30357	−0.476829
$49$	−6.35648	−0.908069
$50$	2.37146	0.335375
$51$	10.1331	1.41891
$52$	−5.68972	−0.789022
$53$	−0.795708	−0.109299	−0.0546495	−	0.998506i	$-0.517404\pi$
$53$	−0.795708	−0.109299	−0.0546495	+	0.998506i	$0.517404\pi$
$54$	−16.2322	−2.20893
$55$	5.53299	0.746068
$56$	0.802195	0.107198
$57$	11.7005	1.54977
$58$	6.21167	0.815632
$59$	−8.38303	−1.09138	−0.545689	−	0.837988i	$-0.683732\pi$
$59$	−8.38303	−1.09138	−0.545689	+	0.837988i	$0.683732\pi$
$60$	8.96932	1.15793
$61$	−6.87941	−0.880818	−0.440409	−	0.897797i	$-0.645166\pi$
$61$	−6.87941	−0.880818	−0.440409	+	0.897797i	$0.645166\pi$
$62$	−5.35567	−0.680170
$63$	6.34821	0.799799
$64$	1.00000	0.125000
$65$	15.4478	1.91607
$66$	6.73234	0.828693
$67$	−11.2311	−1.37209	−0.686046	−	0.727558i	$-0.740655\pi$
$67$	−11.2311	−1.37209	−0.686046	+	0.727558i	$0.740655\pi$
$68$	−3.06731	−0.371966
$69$	12.1909	1.46761
$70$	−2.17799	−0.260320
$71$	−2.93379	−0.348176	−0.174088	−	0.984730i	$-0.555698\pi$
$71$	−2.93379	−0.348176	−0.174088	+	0.984730i	$0.555698\pi$
$72$	7.91355	0.932620
$73$	−2.52647	−0.295702	−0.147851	−	0.989010i	$-0.547236\pi$
$73$	−2.52647	−0.295702	−0.147851	+	0.989010i	$0.547236\pi$
$74$	−6.25812	−0.727492
$75$	−7.83426	−0.904623
$76$	−3.54177	−0.406269
$77$	−1.63479	−0.186302
$78$	18.7964	2.12827
$79$	2.76018	0.310545	0.155272	−	0.987872i	$-0.450374\pi$
$79$	2.76018	0.310545	0.155272	+	0.987872i	$0.450374\pi$
$80$	−2.71504	−0.303551
$81$	29.8836	3.32040
$82$	0.393636	0.0434699
$83$	−1.81395	−0.199107	−0.0995533	−	0.995032i	$-0.531741\pi$
$83$	−1.81395	−0.199107	−0.0995533	+	0.995032i	$0.531741\pi$
$84$	−2.65011	−0.289150
$85$	8.32788	0.903285
$86$	6.10303	0.658107
$87$	−20.5207	−2.20005
$88$	−2.03790	−0.217241
$89$	−10.7986	−1.14465	−0.572325	−	0.820027i	$-0.693959\pi$
$89$	−10.7986	−1.14465	−0.572325	+	0.820027i	$0.693959\pi$
$90$	−21.4856	−2.26478
$91$	−4.56427	−0.478465
$92$	−3.69022	−0.384732
$93$	17.6928	1.83466
$94$	10.0197	1.03345
$95$	9.61606	0.986587
$96$	−3.30357	−0.337169
$97$	−2.29394	−0.232914	−0.116457	−	0.993196i	$-0.537154\pi$
$97$	−2.29394	−0.232914	−0.116457	+	0.993196i	$0.537154\pi$
$98$	−6.35648	−0.642102
$99$	−16.1270	−1.62083
$100$	2.37146	0.237146
$101$	−12.7360	−1.26727	−0.633637	−	0.773630i	$-0.718439\pi$
$101$	−12.7360	−1.26727	−0.633637	+	0.773630i	$0.718439\pi$
$102$	10.1331	1.00332
$103$	−1.59977	−0.157630	−0.0788152	−	0.996889i	$-0.525114\pi$
$103$	−1.59977	−0.157630	−0.0788152	+	0.996889i	$0.525114\pi$
$104$	−5.68972	−0.557923
$105$	7.19515	0.702175
$106$	−0.795708	−0.0772860
$107$	−9.26062	−0.895258	−0.447629	−	0.894219i	$-0.647731\pi$
$107$	−9.26062	−0.895258	−0.447629	+	0.894219i	$0.647731\pi$
$108$	−16.2322	−1.56195
$109$	−7.57323	−0.725384	−0.362692	−	0.931909i	$-0.618142\pi$
$109$	−7.57323	−0.725384	−0.362692	+	0.931909i	$0.618142\pi$
$110$	5.53299	0.527549
$111$	20.6741	1.96230
$112$	0.802195	0.0758003
$113$	−8.50524	−0.800105	−0.400053	−	0.916492i	$-0.631008\pi$
$113$	−8.50524	−0.800105	−0.400053	+	0.916492i	$0.631008\pi$
$114$	11.7005	1.09585
$115$	10.0191	0.934287
$116$	6.21167	0.576739
$117$	−45.0259	−4.16264
$118$	−8.38303	−0.771720
$119$	−2.46058	−0.225561
$120$	8.96932	0.818783
$121$	−6.84696	−0.622451
$122$	−6.87941	−0.622832
$123$	−1.30040	−0.117253
$124$	−5.35567	−0.480953
$125$	7.13661	0.638318
$126$	6.34821	0.565544
$127$	10.2253	0.907353	0.453676	−	0.891167i	$-0.350112\pi$
$127$	10.2253	0.907353	0.453676	+	0.891167i	$0.350112\pi$
$128$	1.00000	0.0883883
$129$	−20.1618	−1.77515
$130$	15.4478	1.35486
$131$	3.70415	0.323633	0.161817	−	0.986821i	$-0.448265\pi$
$131$	3.70415	0.323633	0.161817	+	0.986821i	$0.448265\pi$
$132$	6.73234	0.585975
$133$	−2.84119	−0.246363
$134$	−11.2311	−0.970216
$135$	44.0712	3.79304
$136$	−3.06731	−0.263020
$137$	−6.58047	−0.562208	−0.281104	−	0.959677i	$-0.590701\pi$
$137$	−6.58047	−0.562208	−0.281104	+	0.959677i	$0.590701\pi$
$138$	12.1909	1.03776
$139$	−18.0450	−1.53055	−0.765277	−	0.643701i	$-0.777398\pi$
$139$	−18.0450	−1.53055	−0.765277	+	0.643701i	$0.777398\pi$
$140$	−2.17799	−0.184074
$141$	−33.1007	−2.78758
$142$	−2.93379	−0.246198
$143$	11.5951	0.969630
$144$	7.91355	0.659462
$145$	−16.8649	−1.40056
$146$	−2.52647	−0.209093
$147$	20.9991	1.73197
$148$	−6.25812	−0.514415
$149$	12.2636	1.00467	0.502336	−	0.864673i	$-0.332474\pi$
$149$	12.2636	1.00467	0.502336	+	0.864673i	$0.332474\pi$
$150$	−7.83426	−0.639665
$151$	16.6007	1.35094	0.675472	−	0.737386i	$-0.263940\pi$
$151$	16.6007	1.35094	0.675472	+	0.737386i	$0.263940\pi$
$152$	−3.54177	−0.287276
$153$	−24.2733	−1.96238
$154$	−1.63479	−0.131735
$155$	14.5409	1.16795
$156$	18.7964	1.50491
$157$	4.92680	0.393202	0.196601	−	0.980484i	$-0.437010\pi$
$157$	4.92680	0.393202	0.196601	+	0.980484i	$0.437010\pi$
$158$	2.76018	0.219588
$159$	2.62867	0.208467
$160$	−2.71504	−0.214643
$161$	−2.96028	−0.233303
$162$	29.8836	2.34788
$163$	−11.3159	−0.886328	−0.443164	−	0.896440i	$-0.646144\pi$
$163$	−11.3159	−0.886328	−0.443164	+	0.896440i	$0.646144\pi$
$164$	0.393636	0.0307378
$165$	−18.2786	−1.42299
$166$	−1.81395	−0.140790
$167$	1.02908	0.0796329	0.0398164	−	0.999207i	$-0.487323\pi$
$167$	1.02908	0.0796329	0.0398164	+	0.999207i	$0.487323\pi$
$168$	−2.65011	−0.204460
$169$	19.3729	1.49023
$170$	8.32788	0.638719
$171$	−28.0280	−2.14335
$172$	6.10303	0.465352
$173$	9.31102	0.707903	0.353952	−	0.935264i	$-0.384838\pi$
$173$	9.31102	0.707903	0.353952	+	0.935264i	$0.384838\pi$
$174$	−20.5207	−1.55567
$175$	1.90237	0.143806
$176$	−2.03790	−0.153613
$177$	27.6939	2.08160
$178$	−10.7986	−0.809390
$179$	−7.00262	−0.523401	−0.261700	−	0.965149i	$-0.584283\pi$
$179$	−7.00262	−0.523401	−0.261700	+	0.965149i	$0.584283\pi$
$180$	−21.4856	−1.60144
$181$	1.46196	0.108667	0.0543333	−	0.998523i	$-0.482697\pi$
$181$	1.46196	0.108667	0.0543333	+	0.998523i	$0.482697\pi$
$182$	−4.56427	−0.338326
$183$	22.7266	1.68000
$184$	−3.69022	−0.272047
$185$	16.9911	1.24921
$186$	17.6928	1.29730
$187$	6.25087	0.457109
$188$	10.0197	0.730760
$189$	−13.0214	−0.947169
$190$	9.61606	0.697623
$191$	15.3705	1.11217	0.556087	−	0.831124i	$-0.312302\pi$
$191$	15.3705	1.11217	0.556087	+	0.831124i	$0.312302\pi$
$192$	−3.30357	−0.238414
$193$	−3.30237	−0.237710	−0.118855	−	0.992912i	$-0.537922\pi$
$193$	−3.30237	−0.237710	−0.118855	+	0.992912i	$0.537922\pi$
$194$	−2.29394	−0.164695
$195$	−51.0329	−3.65454
$196$	−6.35648	−0.454034
$197$	−18.1421	−1.29257	−0.646287	−	0.763094i	$-0.723679\pi$
$197$	−18.1421	−1.29257	−0.646287	+	0.763094i	$0.723679\pi$
$198$	−16.1270	−1.14610
$199$	−3.94076	−0.279353	−0.139676	−	0.990197i	$-0.544606\pi$
$199$	−3.94076	−0.279353	−0.139676	+	0.990197i	$0.544606\pi$
$200$	2.37146	0.167687
$201$	37.1025	2.61701
$202$	−12.7360	−0.896099
$203$	4.98297	0.349736
$204$	10.1331	0.709456
$205$	−1.06874	−0.0746440
$206$	−1.59977	−0.111462
$207$	−29.2028	−2.02973
$208$	−5.68972	−0.394511
$209$	7.21778	0.499264
$210$	7.19515	0.496512
$211$	3.18182	0.219046	0.109523	−	0.993984i	$-0.465068\pi$
$211$	3.18182	0.219046	0.109523	+	0.993984i	$0.465068\pi$
$212$	−0.795708	−0.0546495
$213$	9.69196	0.664082
$214$	−9.26062	−0.633043
$215$	−16.5700	−1.13006
$216$	−16.2322	−1.10446
$217$	−4.29629	−0.291651
$218$	−7.57323	−0.512924
$219$	8.34638	0.563996
$220$	5.53299	0.373034
$221$	17.4521	1.17396
$222$	20.6741	1.38756
$223$	18.3866	1.23126	0.615628	−	0.788037i	$-0.288902\pi$
$223$	18.3866	1.23126	0.615628	+	0.788037i	$0.288902\pi$
$224$	0.802195	0.0535989
$225$	18.7666	1.25111
$226$	−8.50524	−0.565760
$227$	−8.09494	−0.537280	−0.268640	−	0.963241i	$-0.586574\pi$
$227$	−8.09494	−0.537280	−0.268640	+	0.963241i	$0.586574\pi$
$228$	11.7005	0.774883
$229$	17.5685	1.16096	0.580478	−	0.814276i	$-0.302866\pi$
$229$	17.5685	1.16096	0.580478	+	0.814276i	$0.302866\pi$
$230$	10.0191	0.660641
$231$	5.40065	0.355337
$232$	6.21167	0.407816
$233$	−8.67272	−0.568169	−0.284084	−	0.958799i	$-0.591690\pi$
$233$	−8.67272	−0.568169	−0.284084	+	0.958799i	$0.591690\pi$
$234$	−45.0259	−2.94343
$235$	−27.2039	−1.77458
$236$	−8.38303	−0.545689
$237$	−9.11845	−0.592307
$238$	−2.46058	−0.159496
$239$	1.78190	0.115261	0.0576307	−	0.998338i	$-0.481645\pi$
$239$	1.78190	0.115261	0.0576307	+	0.998338i	$0.481645\pi$
$240$	8.96932	0.578967
$241$	22.2547	1.43355	0.716776	−	0.697303i	$-0.245617\pi$
$241$	22.2547	1.43355	0.716776	+	0.697303i	$0.245617\pi$
$242$	−6.84696	−0.440139
$243$	−50.0257	−3.20915
$244$	−6.87941	−0.440409
$245$	17.2581	1.10258
$246$	−1.30040	−0.0829107
$247$	20.1517	1.28222
$248$	−5.35567	−0.340085
$249$	5.99250	0.379759
$250$	7.13661	0.451359
$251$	9.52002	0.600898	0.300449	−	0.953798i	$-0.402863\pi$
$251$	9.52002	0.600898	0.300449	+	0.953798i	$0.402863\pi$
$252$	6.34821	0.399900
$253$	7.52031	0.472798
$254$	10.2253	0.641595
$255$	−27.5117	−1.72285
$256$	1.00000	0.0625000
$257$	2.17813	0.135868	0.0679341	−	0.997690i	$-0.478359\pi$
$257$	2.17813	0.135868	0.0679341	+	0.997690i	$0.478359\pi$
$258$	−20.1618	−1.25522
$259$	−5.02024	−0.311942
$260$	15.4478	0.958034
$261$	49.1563	3.04270
$262$	3.70415	0.228843
$263$	−9.95711	−0.613982	−0.306991	−	0.951712i	$-0.599322\pi$
$263$	−9.95711	−0.613982	−0.306991	+	0.951712i	$0.599322\pi$
$264$	6.73234	0.414347
$265$	2.16038	0.132711
$266$	−2.84119	−0.174205
$267$	35.6739	2.18321
$268$	−11.2311	−0.686046
$269$	3.75095	0.228700	0.114350	−	0.993441i	$-0.463522\pi$
$269$	3.75095	0.228700	0.114350	+	0.993441i	$0.463522\pi$
$270$	44.0712	2.68209
$271$	5.62372	0.341617	0.170808	−	0.985304i	$-0.445362\pi$
$271$	5.62372	0.341617	0.170808	+	0.985304i	$0.445362\pi$
$272$	−3.06731	−0.185983
$273$	15.0784	0.912584
$274$	−6.58047	−0.397541
$275$	−4.83279	−0.291428
$276$	12.1909	0.733806
$277$	−1.25407	−0.0753495	−0.0376748	−	0.999290i	$-0.511995\pi$
$277$	−1.25407	−0.0753495	−0.0376748	+	0.999290i	$0.511995\pi$
$278$	−18.0450	−1.08227
$279$	−42.3823	−2.53736
$280$	−2.17799	−0.130160
$281$	23.4452	1.39862	0.699312	−	0.714816i	$-0.253490\pi$
$281$	23.4452	1.39862	0.699312	+	0.714816i	$0.253490\pi$
$282$	−33.1007	−1.97112
$283$	22.6472	1.34624	0.673119	−	0.739534i	$-0.264954\pi$
$283$	22.6472	1.34624	0.673119	+	0.739534i	$0.264954\pi$
$284$	−2.93379	−0.174088
$285$	−31.7673	−1.88173
$286$	11.5951	0.685632
$287$	0.315773	0.0186395
$288$	7.91355	0.466310
$289$	−7.59160	−0.446565
$290$	−16.8649	−0.990344
$291$	7.57819	0.444241
$292$	−2.52647	−0.147851
$293$	−10.1089	−0.590567	−0.295284	−	0.955410i	$-0.595414\pi$
$293$	−10.1089	−0.590567	−0.295284	+	0.955410i	$0.595414\pi$
$294$	20.9991	1.22469
$295$	22.7603	1.32515
$296$	−6.25812	−0.363746
$297$	33.0797	1.91948
$298$	12.2636	0.710410
$299$	20.9963	1.21425
$300$	−7.83426	−0.452311
$301$	4.89583	0.282191
$302$	16.6007	0.955262
$303$	42.0741	2.41709
$304$	−3.54177	−0.203135
$305$	18.6779	1.06949
$306$	−24.2733	−1.38761
$307$	19.2511	1.09872	0.549359	−	0.835586i	$-0.314872\pi$
$307$	19.2511	1.09872	0.549359	+	0.835586i	$0.314872\pi$
$308$	−1.63479	−0.0931510
$309$	5.28496	0.300651
$310$	14.5409	0.825866
$311$	−6.90552	−0.391576	−0.195788	−	0.980646i	$-0.562726\pi$
$311$	−6.90552	−0.391576	−0.195788	+	0.980646i	$0.562726\pi$
$312$	18.7964	1.06413
$313$	19.6532	1.11086	0.555432	−	0.831562i	$-0.312553\pi$
$313$	19.6532	1.11086	0.555432	+	0.831562i	$0.312553\pi$
$314$	4.92680	0.278035
$315$	−17.2357	−0.971120
$316$	2.76018	0.155272
$317$	−34.8062	−1.95491	−0.977457	−	0.211137i	$-0.932283\pi$
$317$	−34.8062	−1.95491	−0.977457	+	0.211137i	$0.932283\pi$
$318$	2.62867	0.147409
$319$	−12.6588	−0.708755
$320$	−2.71504	−0.151775
$321$	30.5931	1.70754
$322$	−2.96028	−0.164970
$323$	10.8637	0.604473
$324$	29.8836	1.66020
$325$	−13.4929	−0.748453
$326$	−11.3159	−0.626729
$327$	25.0187	1.38353
$328$	0.393636	0.0217349
$329$	8.03774	0.443135
$330$	−18.2786	−1.00620
$331$	18.3964	1.01116	0.505579	−	0.862780i	$-0.331279\pi$
$331$	18.3964	1.01116	0.505579	+	0.862780i	$0.331279\pi$
$332$	−1.81395	−0.0995533
$333$	−49.5239	−2.71390
$334$	1.02908	0.0563090
$335$	30.4928	1.66600
$336$	−2.65011	−0.144575
$337$	4.72241	0.257246	0.128623	−	0.991694i	$-0.458944\pi$
$337$	4.72241	0.257246	0.128623	+	0.991694i	$0.458944\pi$
$338$	19.3729	1.05375
$339$	28.0976	1.52605
$340$	8.32788	0.451643
$341$	10.9143	0.591043
$342$	−28.0280	−1.51558
$343$	−10.7145	−0.578529
$344$	6.10303	0.329054
$345$	−33.0988	−1.78198
$346$	9.31102	0.500563
$347$	−3.05314	−0.163901	−0.0819504	−	0.996636i	$-0.526115\pi$
$347$	−3.05314	−0.163901	−0.0819504	+	0.996636i	$0.526115\pi$
$348$	−20.5207	−1.10002
$349$	35.2075	1.88461	0.942307	−	0.334751i	$-0.108652\pi$
$349$	35.2075	1.88461	0.942307	+	0.334751i	$0.108652\pi$
$350$	1.90237	0.101686
$351$	92.3568	4.92964
$352$	−2.03790	−0.108620
$353$	−18.9182	−1.00692	−0.503458	−	0.864020i	$-0.667939\pi$
$353$	−18.9182	−1.00692	−0.503458	+	0.864020i	$0.667939\pi$
$354$	27.6939	1.47191
$355$	7.96535	0.422757
$356$	−10.7986	−0.572325
$357$	8.12870	0.430216
$358$	−7.00262	−0.370100
$359$	12.1022	0.638730	0.319365	−	0.947632i	$-0.396530\pi$
$359$	12.1022	0.638730	0.319365	+	0.947632i	$0.396530\pi$
$360$	−21.4856	−1.13239
$361$	−6.45585	−0.339781
$362$	1.46196	0.0768389
$363$	22.6194	1.18721
$364$	−4.56427	−0.239233
$365$	6.85949	0.359042
$366$	22.7266	1.18794
$367$	14.7420	0.769527	0.384764	−	0.923015i	$-0.374283\pi$
$367$	14.7420	0.769527	0.384764	+	0.923015i	$0.374283\pi$
$368$	−3.69022	−0.192366
$369$	3.11506	0.162164
$370$	16.9911	0.883324
$371$	−0.638313	−0.0331396
$372$	17.6928	0.917329
$373$	20.7253	1.07312	0.536559	−	0.843863i	$-0.319724\pi$
$373$	20.7253	1.07312	0.536559	+	0.843863i	$0.319724\pi$
$374$	6.25087	0.323225
$375$	−23.5763	−1.21747
$376$	10.0197	0.516726
$377$	−35.3427	−1.82024
$378$	−13.0214	−0.669749
$379$	23.0820	1.18564	0.592822	−	0.805333i	$-0.298014\pi$
$379$	23.0820	1.18564	0.592822	+	0.805333i	$0.298014\pi$
$380$	9.61606	0.493294
$381$	−33.7801	−1.73061
$382$	15.3705	0.786425
$383$	−15.1150	−0.772342	−0.386171	−	0.922427i	$-0.626202\pi$
$383$	−15.1150	−0.772342	−0.386171	+	0.922427i	$0.626202\pi$
$384$	−3.30357	−0.168584
$385$	4.43854	0.226209
$386$	−3.30237	−0.168086
$387$	48.2966	2.45506
$388$	−2.29394	−0.116457
$389$	1.46744	0.0744021	0.0372011	−	0.999308i	$-0.488156\pi$
$389$	1.46744	0.0744021	0.0372011	+	0.999308i	$0.488156\pi$
$390$	−51.0329	−2.58415
$391$	11.3191	0.572430
$392$	−6.35648	−0.321051
$393$	−12.2369	−0.617270
$394$	−18.1421	−0.913988
$395$	−7.49402	−0.377065
$396$	−16.1270	−0.810413
$397$	−22.8139	−1.14500	−0.572498	−	0.819906i	$-0.694026\pi$
$397$	−22.8139	−1.14500	−0.572498	+	0.819906i	$0.694026\pi$
$398$	−3.94076	−0.197532
$399$	9.38607	0.469891
$400$	2.37146	0.118573
$401$	19.8849	0.993007	0.496503	−	0.868035i	$-0.334617\pi$
$401$	19.8849	0.993007	0.496503	+	0.868035i	$0.334617\pi$
$402$	37.1025	1.85051
$403$	30.4723	1.51793
$404$	−12.7360	−0.633637
$405$	−81.1352	−4.03164
$406$	4.98297	0.247301
$407$	12.7534	0.632164
$408$	10.1331	0.501661
$409$	5.92764	0.293103	0.146551	−	0.989203i	$-0.453183\pi$
$409$	5.92764	0.293103	0.146551	+	0.989203i	$0.453183\pi$
$410$	−1.06874	−0.0527813
$411$	21.7390	1.07231
$412$	−1.59977	−0.0788152
$413$	−6.72483	−0.330907
$414$	−29.2028	−1.43524
$415$	4.92495	0.241756
$416$	−5.68972	−0.278962
$417$	59.6128	2.91925
$418$	7.21778	0.353033
$419$	−22.4945	−1.09893	−0.549463	−	0.835518i	$-0.685168\pi$
$419$	−22.4945	−1.09893	−0.549463	+	0.835518i	$0.685168\pi$
$420$	7.19515	0.351087
$421$	5.38600	0.262497	0.131249	−	0.991349i	$-0.458101\pi$
$421$	5.38600	0.262497	0.131249	+	0.991349i	$0.458101\pi$
$422$	3.18182	0.154889
$423$	79.2912	3.85527
$424$	−0.795708	−0.0386430
$425$	−7.27399	−0.352841
$426$	9.69196	0.469577
$427$	−5.51863	−0.267065
$428$	−9.26062	−0.447629
$429$	−38.3051	−1.84939
$430$	−16.5700	−0.799076
$431$	24.8015	1.19465	0.597323	−	0.802001i	$-0.296231\pi$
$431$	24.8015	1.19465	0.597323	+	0.802001i	$0.296231\pi$
$432$	−16.2322	−0.780973
$433$	−29.6778	−1.42622	−0.713111	−	0.701051i	$-0.752715\pi$
$433$	−29.6778	−1.42622	−0.713111	+	0.701051i	$0.752715\pi$
$434$	−4.29629	−0.206229
$435$	55.7145	2.67130
$436$	−7.57323	−0.362692
$437$	13.0699	0.625220
$438$	8.34638	0.398805
$439$	13.0697	0.623785	0.311893	−	0.950117i	$-0.399037\pi$
$439$	13.0697	0.623785	0.311893	+	0.950117i	$0.399037\pi$
$440$	5.53299	0.263775
$441$	−50.3023	−2.39535
$442$	17.4521	0.830114
$443$	−35.2313	−1.67389	−0.836945	−	0.547287i	$-0.815660\pi$
$443$	−35.2313	−1.67389	−0.836945	+	0.547287i	$0.815660\pi$
$444$	20.6741	0.981150
$445$	29.3187	1.38984
$446$	18.3866	0.870630
$447$	−40.5135	−1.91622
$448$	0.802195	0.0379002
$449$	2.35663	0.111216	0.0556082	−	0.998453i	$-0.482290\pi$
$449$	2.35663	0.111216	0.0556082	+	0.998453i	$0.482290\pi$
$450$	18.7666	0.884667
$451$	−0.802192	−0.0377737
$452$	−8.50524	−0.400053
$453$	−54.8414	−2.57668
$454$	−8.09494	−0.379915
$455$	12.3922	0.580955
$456$	11.7005	0.547925
$457$	−30.1750	−1.41153	−0.705764	−	0.708447i	$-0.749396\pi$
$457$	−30.1750	−1.41153	−0.705764	+	0.708447i	$0.749396\pi$
$458$	17.5685	0.820920
$459$	49.7893	2.32396
$460$	10.0191	0.467144
$461$	14.0557	0.654640	0.327320	−	0.944914i	$-0.393854\pi$
$461$	14.0557	0.654640	0.327320	+	0.944914i	$0.393854\pi$
$462$	5.40065	0.251261
$463$	−24.9074	−1.15754	−0.578772	−	0.815489i	$-0.696468\pi$
$463$	−24.9074	−1.15754	−0.578772	+	0.815489i	$0.696468\pi$
$464$	6.21167	0.288370
$465$	−48.0367	−2.22765
$466$	−8.67272	−0.401756
$467$	3.51254	0.162541	0.0812704	−	0.996692i	$-0.474102\pi$
$467$	3.51254	0.162541	0.0812704	+	0.996692i	$0.474102\pi$
$468$	−45.0259	−2.08132
$469$	−9.00950	−0.416020
$470$	−27.2039	−1.25482
$471$	−16.2760	−0.749959
$472$	−8.38303	−0.385860
$473$	−12.4374	−0.571871
$474$	−9.11845	−0.418824
$475$	−8.39916	−0.385380
$476$	−2.46058	−0.112781
$477$	−6.29687	−0.288314
$478$	1.78190	0.0815022
$479$	−34.3107	−1.56770	−0.783848	−	0.620952i	$-0.786746\pi$
$479$	−34.3107	−1.56770	−0.783848	+	0.620952i	$0.786746\pi$
$480$	8.96932	0.409392
$481$	35.6070	1.62354
$482$	22.2547	1.01367
$483$	9.77948	0.444982
$484$	−6.84696	−0.311226
$485$	6.22815	0.282806
$486$	−50.0257	−2.26921
$487$	8.81729	0.399549	0.199775	−	0.979842i	$-0.435979\pi$
$487$	8.81729	0.399549	0.199775	+	0.979842i	$0.435979\pi$
$488$	−6.87941	−0.311416
$489$	37.3828	1.69051
$490$	17.2581	0.779642
$491$	15.2638	0.688848	0.344424	−	0.938814i	$-0.388074\pi$
$491$	15.2638	0.688848	0.344424	+	0.938814i	$0.388074\pi$
$492$	−1.30040	−0.0586267
$493$	−19.0531	−0.858110
$494$	20.1517	0.906668
$495$	43.7855	1.96801
$496$	−5.35567	−0.240477
$497$	−2.35347	−0.105568
$498$	5.99250	0.268530
$499$	34.5992	1.54887	0.774435	−	0.632653i	$-0.218034\pi$
$499$	34.5992	1.54887	0.774435	+	0.632653i	$0.218034\pi$
$500$	7.13661	0.319159
$501$	−3.39965	−0.151885
$502$	9.52002	0.424899
$503$	1.69920	0.0757638	0.0378819	−	0.999282i	$-0.487939\pi$
$503$	1.69920	0.0757638	0.0378819	+	0.999282i	$0.487939\pi$
$504$	6.34821	0.282772
$505$	34.5787	1.53873
$506$	7.52031	0.334318
$507$	−63.9998	−2.84233
$508$	10.2253	0.453676
$509$	−6.68839	−0.296458	−0.148229	−	0.988953i	$-0.547357\pi$
$509$	−6.68839	−0.296458	−0.148229	+	0.988953i	$0.547357\pi$
$510$	−27.5117	−1.21824
$511$	−2.02673	−0.0896571
$512$	1.00000	0.0441942
$513$	57.4909	2.53828
$514$	2.17813	0.0960733
$515$	4.34345	0.191395
$516$	−20.1618	−0.887573
$517$	−20.4191	−0.898032
$518$	−5.02024	−0.220577
$519$	−30.7596	−1.35019
$520$	15.4478	0.677432
$521$	−22.2362	−0.974184	−0.487092	−	0.873351i	$-0.661942\pi$
$521$	−22.2362	−0.974184	−0.487092	+	0.873351i	$0.661942\pi$
$522$	49.1563	2.15151
$523$	−8.37182	−0.366074	−0.183037	−	0.983106i	$-0.558593\pi$
$523$	−8.37182	−0.366074	−0.183037	+	0.983106i	$0.558593\pi$
$524$	3.70415	0.161817
$525$	−6.28461	−0.274283
$526$	−9.95711	−0.434151
$527$	16.4275	0.715593
$528$	6.73234	0.292987
$529$	−9.38225	−0.407924
$530$	2.16038	0.0938410
$531$	−66.3395	−2.87889
$532$	−2.84119	−0.123181
$533$	−2.23968	−0.0970114
$534$	35.6739	1.54376
$535$	25.1430	1.08703
$536$	−11.2311	−0.485108
$537$	23.1336	0.998290
$538$	3.75095	0.161715
$539$	12.9539	0.557963
$540$	44.0712	1.89652
$541$	7.04306	0.302805	0.151402	−	0.988472i	$-0.451621\pi$
$541$	7.04306	0.302805	0.151402	+	0.988472i	$0.451621\pi$
$542$	5.62372	0.241560
$543$	−4.82968	−0.207261
$544$	−3.06731	−0.131510
$545$	20.5616	0.880764
$546$	15.0784	0.645294
$547$	0.454380	0.0194279	0.00971394	−	0.999953i	$-0.496908\pi$
$547$	0.454380	0.0194279	0.00971394	+	0.999953i	$0.496908\pi$
$548$	−6.58047	−0.281104
$549$	−54.4405	−2.32346
$550$	−4.83279	−0.206071
$551$	−22.0003	−0.937245
$552$	12.1909	0.518879
$553$	2.21421	0.0941577
$554$	−1.25407	−0.0532802
$555$	−56.1311	−2.38263
$556$	−18.0450	−0.765277
$557$	30.0780	1.27445	0.637223	−	0.770679i	$-0.280083\pi$
$557$	30.0780	1.27445	0.637223	+	0.770679i	$0.280083\pi$
$558$	−42.3823	−1.79419
$559$	−34.7246	−1.46869
$560$	−2.17799	−0.0920371
$561$	−20.6502	−0.871851
$562$	23.4452	0.988977
$563$	−4.79697	−0.202168	−0.101084	−	0.994878i	$-0.532231\pi$
$563$	−4.79697	−0.202168	−0.101084	+	0.994878i	$0.532231\pi$
$564$	−33.1007	−1.39379
$565$	23.0921	0.971491
$566$	22.6472	0.951935
$567$	23.9725	1.00675
$568$	−2.93379	−0.123099
$569$	−28.2703	−1.18515	−0.592577	−	0.805514i	$-0.701889\pi$
$569$	−28.2703	−1.18515	−0.592577	+	0.805514i	$0.701889\pi$
$570$	−31.7673	−1.33059
$571$	1.70380	0.0713018	0.0356509	−	0.999364i	$-0.488650\pi$
$571$	1.70380	0.0713018	0.0356509	+	0.999364i	$0.488650\pi$
$572$	11.5951	0.484815
$573$	−50.7776	−2.12126
$574$	0.315773	0.0131801
$575$	−8.75121	−0.364950
$576$	7.91355	0.329731
$577$	−39.1395	−1.62940	−0.814699	−	0.579884i	$-0.803098\pi$
$577$	−39.1395	−1.62940	−0.814699	+	0.579884i	$0.803098\pi$
$578$	−7.59160	−0.315769
$579$	10.9096	0.453387
$580$	−16.8649	−0.700279
$581$	−1.45514	−0.0603694
$582$	7.57819	0.314126
$583$	1.62157	0.0671587
$584$	−2.52647	−0.104546
$585$	122.247	5.05430
$586$	−10.1089	−0.417594
$587$	18.7330	0.773192	0.386596	−	0.922249i	$-0.373651\pi$
$587$	18.7330	0.773192	0.386596	+	0.922249i	$0.373651\pi$
$588$	20.9991	0.865987
$589$	18.9686	0.781586
$590$	22.7603	0.937026
$591$	59.9338	2.46535
$592$	−6.25812	−0.257207
$593$	0.759426	0.0311859	0.0155929	−	0.999878i	$-0.495036\pi$
$593$	0.759426	0.0311859	0.0155929	+	0.999878i	$0.495036\pi$
$594$	33.0797	1.35727
$595$	6.68059	0.273877
$596$	12.2636	0.502336
$597$	13.0186	0.532814
$598$	20.9963	0.858605
$599$	14.3253	0.585316	0.292658	−	0.956217i	$-0.405460\pi$
$599$	14.3253	0.585316	0.292658	+	0.956217i	$0.405460\pi$
$600$	−7.83426	−0.319832
$601$	24.9742	1.01872	0.509358	−	0.860554i	$-0.329883\pi$
$601$	24.9742	1.01872	0.509358	+	0.860554i	$0.329883\pi$
$602$	4.89583	0.199539
$603$	−88.8775	−3.61937
$604$	16.6007	0.675472
$605$	18.5898	0.755783
$606$	42.0741	1.70914
$607$	26.3529	1.06963	0.534815	−	0.844969i	$-0.320381\pi$
$607$	26.3529	1.06963	0.534815	+	0.844969i	$0.320381\pi$
$608$	−3.54177	−0.143638
$609$	−16.4616	−0.667057
$610$	18.6779	0.756245
$611$	−57.0092	−2.30635
$612$	−24.2733	−0.981190
$613$	−25.6847	−1.03740	−0.518698	−	0.854957i	$-0.673583\pi$
$613$	−25.6847	−1.03740	−0.518698	+	0.854957i	$0.673583\pi$
$614$	19.2511	0.776912
$615$	3.53065	0.142370
$616$	−1.63479	−0.0658677
$617$	−25.6061	−1.03086	−0.515432	−	0.856930i	$-0.672369\pi$
$617$	−25.6061	−1.03086	−0.515432	+	0.856930i	$0.672369\pi$
$618$	5.28496	0.212592
$619$	−11.9430	−0.480029	−0.240015	−	0.970769i	$-0.577152\pi$
$619$	−11.9430	−0.480029	−0.240015	+	0.970769i	$0.577152\pi$
$620$	14.5409	0.583975
$621$	59.9005	2.40373
$622$	−6.90552	−0.276886
$623$	−8.66260	−0.347060
$624$	18.7964	0.752457
$625$	−31.2335	−1.24934
$626$	19.6532	0.785500
$627$	−23.8444	−0.952254
$628$	4.92680	0.196601
$629$	19.1956	0.765379
$630$	−17.2357	−0.686685
$631$	49.3725	1.96549	0.982744	−	0.184969i	$-0.0592186\pi$
$631$	49.3725	1.96549	0.982744	+	0.184969i	$0.0592186\pi$
$632$	2.76018	0.109794
$633$	−10.5114	−0.417789
$634$	−34.8062	−1.38233
$635$	−27.7622	−1.10171
$636$	2.62867	0.104234
$637$	36.1666	1.43297
$638$	−12.6588	−0.501165
$639$	−23.2167	−0.918437
$640$	−2.71504	−0.107321
$641$	43.0307	1.69961	0.849806	−	0.527095i	$-0.176719\pi$
$641$	43.0307	1.69961	0.849806	+	0.527095i	$0.176719\pi$
$642$	30.5931	1.20741
$643$	25.1798	0.992993	0.496497	−	0.868039i	$-0.334620\pi$
$643$	25.1798	0.992993	0.496497	+	0.868039i	$0.334620\pi$
$644$	−2.96028	−0.116651
$645$	54.7401	2.15539
$646$	10.8637	0.427427
$647$	19.6562	0.772764	0.386382	−	0.922339i	$-0.373725\pi$
$647$	19.6562	0.772764	0.386382	+	0.922339i	$0.373725\pi$
$648$	29.8836	1.17394
$649$	17.0838	0.670597
$650$	−13.4929	−0.529236
$651$	14.1931	0.556271
$652$	−11.3159	−0.443164
$653$	−21.2339	−0.830946	−0.415473	−	0.909606i	$-0.636384\pi$
$653$	−21.2339	−0.830946	−0.415473	+	0.909606i	$0.636384\pi$
$654$	25.0187	0.978307
$655$	−10.0569	−0.392956
$656$	0.393636	0.0153689
$657$	−19.9934	−0.780016
$658$	8.03774	0.313344
$659$	−0.928806	−0.0361811	−0.0180906	−	0.999836i	$-0.505759\pi$
$659$	−0.928806	−0.0361811	−0.0180906	+	0.999836i	$0.505759\pi$
$660$	−18.2786	−0.711493
$661$	−1.58349	−0.0615906	−0.0307953	−	0.999526i	$-0.509804\pi$
$661$	−1.58349	−0.0615906	−0.0307953	+	0.999526i	$0.509804\pi$
$662$	18.3964	0.714996
$663$	−57.6543	−2.23911
$664$	−1.81395	−0.0703948
$665$	7.71396	0.299135
$666$	−49.5239	−1.91901
$667$	−22.9225	−0.887561
$668$	1.02908	0.0398164
$669$	−60.7413	−2.34839
$670$	30.4928	1.17804
$671$	14.0195	0.541218
$672$	−2.65011	−0.102230
$673$	17.1138	0.659688	0.329844	−	0.944035i	$-0.393004\pi$
$673$	17.1138	0.659688	0.329844	+	0.944035i	$0.393004\pi$
$674$	4.72241	0.181901
$675$	−38.4940	−1.48164
$676$	19.3729	0.745113
$677$	33.3070	1.28009	0.640046	−	0.768337i	$-0.278915\pi$
$677$	33.3070	1.28009	0.640046	+	0.768337i	$0.278915\pi$
$678$	28.0976	1.07908
$679$	−1.84019	−0.0706200
$680$	8.32788	0.319360
$681$	26.7422	1.02476
$682$	10.9143	0.417931
$683$	22.4996	0.860922	0.430461	−	0.902609i	$-0.358351\pi$
$683$	22.4996	0.860922	0.430461	+	0.902609i	$0.358351\pi$
$684$	−28.0280	−1.07168
$685$	17.8663	0.682635
$686$	−10.7145	−0.409082
$687$	−58.0386	−2.21431
$688$	6.10303	0.232676
$689$	4.52736	0.172479
$690$	−33.0988	−1.26005
$691$	0.0665300	0.00253092	0.00126546	−	0.999999i	$-0.499597\pi$
$691$	0.0665300	0.00253092	0.00126546	+	0.999999i	$0.499597\pi$
$692$	9.31102	0.353952
$693$	−12.9370	−0.491437
$694$	−3.05314	−0.115895
$695$	48.9929	1.85841
$696$	−20.5207	−0.777834
$697$	−1.20741	−0.0457337
$698$	35.2075	1.33262
$699$	28.6509	1.08368
$700$	1.90237	0.0719029
$701$	−10.8702	−0.410561	−0.205280	−	0.978703i	$-0.565811\pi$
$701$	−10.8702	−0.410561	−0.205280	+	0.978703i	$0.565811\pi$
$702$	92.3568	3.48578
$703$	22.1648	0.835963
$704$	−2.03790	−0.0768063
$705$	89.8698	3.38469
$706$	−18.9182	−0.711998
$707$	−10.2167	−0.384240
$708$	27.6939	1.04080
$709$	7.80530	0.293134	0.146567	−	0.989201i	$-0.453178\pi$
$709$	7.80530	0.293134	0.146567	+	0.989201i	$0.453178\pi$
$710$	7.96535	0.298934
$711$	21.8428	0.819171
$712$	−10.7986	−0.404695
$713$	19.7636	0.740153
$714$	8.12870	0.304209
$715$	−31.4811	−1.17733
$716$	−7.00262	−0.261700
$717$	−5.88662	−0.219840
$718$	12.1022	0.451650
$719$	7.20822	0.268821	0.134411	−	0.990926i	$-0.457086\pi$
$719$	7.20822	0.268821	0.134411	+	0.990926i	$0.457086\pi$
$720$	−21.4856	−0.800722
$721$	−1.28333	−0.0477938
$722$	−6.45585	−0.240262
$723$	−73.5199	−2.73423
$724$	1.46196	0.0543333
$725$	14.7307	0.547085
$726$	22.6194	0.839484
$727$	36.2439	1.34421	0.672106	−	0.740455i	$-0.265390\pi$
$727$	36.2439	1.34421	0.672106	+	0.740455i	$0.265390\pi$
$728$	−4.56427	−0.169163
$729$	75.6124	2.80046
$730$	6.85949	0.253881
$731$	−18.7199	−0.692381
$732$	22.7266	0.839998
$733$	−37.5551	−1.38713	−0.693564	−	0.720395i	$-0.743961\pi$
$733$	−37.5551	−1.38713	−0.693564	+	0.720395i	$0.743961\pi$
$734$	14.7420	0.544138
$735$	−57.0133	−2.10297
$736$	−3.69022	−0.136023
$737$	22.8878	0.843082
$738$	3.11506	0.114667
$739$	−6.93566	−0.255132	−0.127566	−	0.991830i	$-0.540717\pi$
$739$	−6.93566	−0.255132	−0.127566	+	0.991830i	$0.540717\pi$
$740$	16.9911	0.624604
$741$	−66.5725	−2.44560
$742$	−0.638313	−0.0234332
$743$	−28.1212	−1.03167	−0.515833	−	0.856689i	$-0.672518\pi$
$743$	−28.1212	−1.03167	−0.515833	+	0.856689i	$0.672518\pi$
$744$	17.6928	0.648649
$745$	−33.2961	−1.21988
$746$	20.7253	0.758808
$747$	−14.3548	−0.525213
$748$	6.25087	0.228555
$749$	−7.42883	−0.271443
$750$	−23.5763	−0.860883
$751$	−15.2825	−0.557666	−0.278833	−	0.960340i	$-0.589948\pi$
$751$	−15.2825	−0.557666	−0.278833	+	0.960340i	$0.589948\pi$
$752$	10.0197	0.365380
$753$	−31.4500	−1.14610
$754$	−35.3427	−1.28710
$755$	−45.0716	−1.64032
$756$	−13.0214	−0.473584
$757$	25.8003	0.937727	0.468863	−	0.883271i	$-0.344664\pi$
$757$	25.8003	0.937727	0.468863	+	0.883271i	$0.344664\pi$
$758$	23.0820	0.838377
$759$	−24.8438	−0.901774
$760$	9.61606	0.348811
$761$	25.2690	0.916000	0.458000	−	0.888952i	$-0.348566\pi$
$761$	25.2690	0.916000	0.458000	+	0.888952i	$0.348566\pi$
$762$	−33.7801	−1.22372
$763$	−6.07521	−0.219937
$764$	15.3705	0.556087
$765$	65.9031	2.38273
$766$	−15.1150	−0.546128
$767$	47.6971	1.72224
$768$	−3.30357	−0.119207
$769$	3.76201	0.135662	0.0678308	−	0.997697i	$-0.478392\pi$
$769$	3.76201	0.135662	0.0678308	+	0.997697i	$0.478392\pi$
$770$	4.43854	0.159954
$771$	−7.19560	−0.259143
$772$	−3.30237	−0.118855
$773$	12.7469	0.458473	0.229236	−	0.973371i	$-0.426377\pi$
$773$	12.7469	0.458473	0.229236	+	0.973371i	$0.426377\pi$
$774$	48.2966	1.73599
$775$	−12.7007	−0.456224
$776$	−2.29394	−0.0823477
$777$	16.5847	0.594972
$778$	1.46744	0.0526103
$779$	−1.39417	−0.0499513
$780$	−51.0329	−1.82727
$781$	5.97876	0.213937
$782$	11.3191	0.404769
$783$	−100.829	−3.60334
$784$	−6.35648	−0.227017
$785$	−13.3765	−0.477427
$786$	−12.2369	−0.436476
$787$	47.3846	1.68908	0.844539	−	0.535493i	$-0.179874\pi$
$787$	47.3846	1.68908	0.844539	+	0.535493i	$0.179874\pi$
$788$	−18.1421	−0.646287
$789$	32.8940	1.17106
$790$	−7.49402	−0.266625
$791$	−6.82286	−0.242593
$792$	−16.1270	−0.573049
$793$	39.1419	1.38997
$794$	−22.8139	−0.809634
$795$	−7.13696	−0.253122
$796$	−3.94076	−0.139676
$797$	−36.9325	−1.30822	−0.654108	−	0.756401i	$-0.726956\pi$
$797$	−36.9325	−1.30822	−0.654108	+	0.756401i	$0.726956\pi$
$798$	9.38607	0.332263
$799$	−30.7335	−1.08727
$800$	2.37146	0.0838436
$801$	−85.4553	−3.01942
$802$	19.8849	0.702162
$803$	5.14870	0.181694
$804$	37.1025	1.30851
$805$	8.03729	0.283277
$806$	30.4723	1.07334
$807$	−12.3915	−0.436202
$808$	−12.7360	−0.448049
$809$	17.1379	0.602537	0.301269	−	0.953539i	$-0.402590\pi$
$809$	17.1379	0.602537	0.301269	+	0.953539i	$0.402590\pi$
$810$	−81.1352	−2.85080
$811$	1.62295	0.0569894	0.0284947	−	0.999594i	$-0.490929\pi$
$811$	1.62295	0.0569894	0.0284947	+	0.999594i	$0.490929\pi$
$812$	4.98297	0.174868
$813$	−18.5783	−0.651571
$814$	12.7534	0.447007
$815$	30.7231	1.07618
$816$	10.1331	0.354728
$817$	−21.6156	−0.756233
$818$	5.92764	0.207255
$819$	−36.1196	−1.26212
$820$	−1.06874	−0.0373220
$821$	−25.3757	−0.885619	−0.442810	−	0.896616i	$-0.646018\pi$
$821$	−25.3757	−0.885619	−0.442810	+	0.896616i	$0.646018\pi$
$822$	21.7390	0.758235
$823$	3.19778	0.111468	0.0557338	−	0.998446i	$-0.482250\pi$
$823$	3.19778	0.111468	0.0557338	+	0.998446i	$0.482250\pi$
$824$	−1.59977	−0.0557308
$825$	15.9654	0.555845
$826$	−6.72483	−0.233987
$827$	−27.7146	−0.963730	−0.481865	−	0.876245i	$-0.660041\pi$
$827$	−27.7146	−0.963730	−0.481865	+	0.876245i	$0.660041\pi$
$828$	−29.2028	−1.01487
$829$	40.9202	1.42122	0.710609	−	0.703587i	$-0.248420\pi$
$829$	40.9202	1.42122	0.710609	+	0.703587i	$0.248420\pi$
$830$	4.92495	0.170947
$831$	4.14289	0.143715
$832$	−5.68972	−0.197256
$833$	19.4973	0.675542
$834$	59.6128	2.06422
$835$	−2.79401	−0.0966906
$836$	7.21778	0.249632
$837$	86.9344	3.00489
$838$	−22.4945	−0.777058
$839$	−40.0073	−1.38120	−0.690602	−	0.723235i	$-0.742655\pi$
$839$	−40.0073	−1.38120	−0.690602	+	0.723235i	$0.742655\pi$
$840$	7.19515	0.248256
$841$	9.58485	0.330512
$842$	5.38600	0.185614
$843$	−77.4528	−2.66762
$844$	3.18182	0.109523
$845$	−52.5983	−1.80944
$846$	79.2912	2.72609
$847$	−5.49260	−0.188728
$848$	−0.795708	−0.0273247
$849$	−74.8167	−2.56770
$850$	−7.27399	−0.249496
$851$	23.0939	0.791648
$852$	9.69196	0.332041
$853$	−43.8326	−1.50080	−0.750400	−	0.660984i	$-0.770139\pi$
$853$	−43.8326	−1.50080	−0.750400	+	0.660984i	$0.770139\pi$
$854$	−5.51863	−0.188844
$855$	76.0972	2.60247
$856$	−9.26062	−0.316521
$857$	−54.5306	−1.86273	−0.931364	−	0.364088i	$-0.881381\pi$
$857$	−54.5306	−1.86273	−0.931364	+	0.364088i	$0.881381\pi$
$858$	−38.3051	−1.30772
$859$	34.2644	1.16909	0.584543	−	0.811363i	$-0.301274\pi$
$859$	34.2644	1.16909	0.584543	+	0.811363i	$0.301274\pi$
$860$	−16.5700	−0.565032
$861$	−1.04318	−0.0355514
$862$	24.8015	0.844742
$863$	−37.4005	−1.27313	−0.636564	−	0.771224i	$-0.719645\pi$
$863$	−37.4005	−1.27313	−0.636564	+	0.771224i	$0.719645\pi$
$864$	−16.2322	−0.552231
$865$	−25.2798	−0.859539
$866$	−29.6778	−1.00849
$867$	25.0794	0.851740
$868$	−4.29629	−0.145826
$869$	−5.62498	−0.190814
$870$	55.7145	1.88890
$871$	63.9016	2.16522
$872$	−7.57323	−0.256462
$873$	−18.1532	−0.614393
$874$	13.0699	0.442097
$875$	5.72495	0.193539
$876$	8.34638	0.281998
$877$	−58.3437	−1.97013	−0.985063	−	0.172192i	$-0.944915\pi$
$877$	−58.3437	−1.97013	−0.985063	+	0.172192i	$0.944915\pi$
$878$	13.0697	0.441083
$879$	33.3954	1.12640
$880$	5.53299	0.186517
$881$	−8.80205	−0.296549	−0.148274	−	0.988946i	$-0.547372\pi$
$881$	−8.80205	−0.296549	−0.148274	+	0.988946i	$0.547372\pi$
$882$	−50.3023	−1.69377
$883$	6.30182	0.212073	0.106037	−	0.994362i	$-0.466184\pi$
$883$	6.30182	0.212073	0.106037	+	0.994362i	$0.466184\pi$
$884$	17.4521	0.586979
$885$	−75.1901	−2.52749
$886$	−35.2313	−1.18362
$887$	−41.9197	−1.40752	−0.703762	−	0.710435i	$-0.748498\pi$
$887$	−41.9197	−1.40752	−0.703762	+	0.710435i	$0.748498\pi$
$888$	20.6741	0.693778
$889$	8.20273	0.275111
$890$	29.3187	0.982765
$891$	−60.8998	−2.04022
$892$	18.3866	0.615628
$893$	−35.4874	−1.18754
$894$	−40.5135	−1.35497
$895$	19.0124	0.635515
$896$	0.802195	0.0267995
$897$	−69.3628	−2.31596
$898$	2.35663	0.0786419
$899$	−33.2676	−1.10954
$900$	18.7666	0.625554
$901$	2.44068	0.0813110
$902$	−0.802192	−0.0267101
$903$	−16.1737	−0.538227
$904$	−8.50524	−0.282880
$905$	−3.96928	−0.131943
$906$	−54.8414	−1.82198
$907$	3.47323	0.115327	0.0576634	−	0.998336i	$-0.481635\pi$
$907$	3.47323	0.115327	0.0576634	+	0.998336i	$0.481635\pi$
$908$	−8.09494	−0.268640
$909$	−100.787	−3.34288
$910$	12.3922	0.410797
$911$	27.1804	0.900527	0.450264	−	0.892896i	$-0.351330\pi$
$911$	27.1804	0.900527	0.450264	+	0.892896i	$0.351330\pi$
$912$	11.7005	0.387442
$913$	3.69665	0.122341
$914$	−30.1750	−0.998101
$915$	−61.7036	−2.03986
$916$	17.5685	0.580478
$917$	2.97145	0.0981260
$918$	49.7893	1.64329
$919$	−55.2038	−1.82101	−0.910503	−	0.413503i	$-0.864305\pi$
$919$	−55.2038	−1.82101	−0.910503	+	0.413503i	$0.864305\pi$
$920$	10.0191	0.330320
$921$	−63.5973	−2.09560
$922$	14.0557	0.462901
$923$	16.6924	0.549438
$924$	5.40065	0.177668
$925$	−14.8409	−0.487965
$926$	−24.9074	−0.818508
$927$	−12.6599	−0.415805
$928$	6.21167	0.203908
$929$	27.7072	0.909044	0.454522	−	0.890735i	$-0.349810\pi$
$929$	27.7072	0.909044	0.454522	+	0.890735i	$0.349810\pi$
$930$	−48.0367	−1.57519
$931$	22.5132	0.737841
$932$	−8.67272	−0.284084
$933$	22.8128	0.746858
$934$	3.51254	0.114934
$935$	−16.9714	−0.555024
$936$	−45.0259	−1.47172
$937$	12.3693	0.404087	0.202044	−	0.979377i	$-0.435242\pi$
$937$	12.3693	0.404087	0.202044	+	0.979377i	$0.435242\pi$
$938$	−9.00950	−0.294171
$939$	−64.9256	−2.11877
$940$	−27.2039	−0.887292
$941$	−31.4127	−1.02402	−0.512012	−	0.858978i	$-0.671100\pi$
$941$	−31.4127	−1.02402	−0.512012	+	0.858978i	$0.671100\pi$
$942$	−16.2760	−0.530301
$943$	−1.45261	−0.0473034
$944$	−8.38303	−0.272844
$945$	35.3537	1.15006
$946$	−12.4374	−0.404374
$947$	13.5968	0.441836	0.220918	−	0.975292i	$-0.429095\pi$
$947$	13.5968	0.441836	0.220918	+	0.975292i	$0.429095\pi$
$948$	−9.11845	−0.296154
$949$	14.3749	0.466630
$950$	−8.39916	−0.272505
$951$	114.985	3.72863
$952$	−2.46058	−0.0797479
$953$	−54.3359	−1.76011	−0.880057	−	0.474869i	$-0.842496\pi$
$953$	−54.3359	−1.76011	−0.880057	+	0.474869i	$0.842496\pi$
$954$	−6.29687	−0.203869
$955$	−41.7317	−1.35041
$956$	1.78190	0.0576307
$957$	41.8191	1.35182
$958$	−34.3107	−1.10853
$959$	−5.27882	−0.170462
$960$	8.96932	0.289484
$961$	−2.31683	−0.0747365
$962$	35.6070	1.14802
$963$	−73.2843	−2.36156
$964$	22.2547	0.716776
$965$	8.96607	0.288628
$966$	9.77948	0.314650
$967$	−50.5113	−1.62433	−0.812167	−	0.583424i	$-0.801712\pi$
$967$	−50.5113	−1.62433	−0.812167	+	0.583424i	$0.801712\pi$
$968$	−6.84696	−0.220070
$969$	−35.8890	−1.15292
$970$	6.22815	0.199974
$971$	53.6009	1.72013	0.860067	−	0.510182i	$-0.170422\pi$
$971$	53.6009	1.72013	0.860067	+	0.510182i	$0.170422\pi$
$972$	−50.0257	−1.60457
$973$	−14.4756	−0.464066
$974$	8.81729	0.282524
$975$	44.5748	1.42754
$976$	−6.87941	−0.220204
$977$	−40.3502	−1.29092	−0.645459	−	0.763795i	$-0.723334\pi$
$977$	−40.3502	−1.29092	−0.645459	+	0.763795i	$0.723334\pi$
$978$	37.3828	1.19537
$979$	22.0065	0.703331
$980$	17.2581	0.551290
$981$	−59.9311	−1.91345
$982$	15.2638	0.487089
$983$	25.8746	0.825273	0.412636	−	0.910896i	$-0.364608\pi$
$983$	25.8746	0.825273	0.412636	+	0.910896i	$0.364608\pi$
$984$	−1.30040	−0.0414554
$985$	49.2567	1.56945
$986$	−19.0531	−0.606775
$987$	−26.5532	−0.845198
$988$	20.1517	0.641111
$989$	−22.5216	−0.716144
$990$	43.7855	1.39160
$991$	37.4445	1.18946	0.594731	−	0.803925i	$-0.297259\pi$
$991$	37.4445	1.18946	0.594731	+	0.803925i	$0.297259\pi$
$992$	−5.35567	−0.170043
$993$	−60.7737	−1.92860
$994$	−2.35347	−0.0746475
$995$	10.6993	0.339191
$996$	5.99250	0.189880
$997$	−43.2310	−1.36914	−0.684570	−	0.728947i	$-0.740010\pi$
$997$	−43.2310	−1.36914	−0.684570	+	0.728947i	$0.740010\pi$
$998$	34.5992	1.09522
$999$	101.583	3.21395

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8006.2.a.d.1.2	✓	98

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8006.2.a.d.1.2	✓	98	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:	\( N \)	\(=\)	\( 8006 = 2 \cdot 4003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8006.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.30357 q^{3} +1.00000 q^{4} -2.71504 q^{5} -3.30357 q^{6} +0.802195 q^{7} +1.00000 q^{8} +7.91355 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.30357 q^{3} +1.00000 q^{4} -2.71504 q^{5} -3.30357 q^{6} +0.802195 q^{7} +1.00000 q^{8} +7.91355 q^{9} -2.71504 q^{10} -2.03790 q^{11} -3.30357 q^{12} -5.68972 q^{13} +0.802195 q^{14} +8.96932 q^{15} +1.00000 q^{16} -3.06731 q^{17} +7.91355 q^{18} -3.54177 q^{19} -2.71504 q^{20} -2.65011 q^{21} -2.03790 q^{22} -3.69022 q^{23} -3.30357 q^{24} +2.37146 q^{25} -5.68972 q^{26} -16.2322 q^{27} +0.802195 q^{28} +6.21167 q^{29} +8.96932 q^{30} -5.35567 q^{31} +1.00000 q^{32} +6.73234 q^{33} -3.06731 q^{34} -2.17799 q^{35} +7.91355 q^{36} -6.25812 q^{37} -3.54177 q^{38} +18.7964 q^{39} -2.71504 q^{40} +0.393636 q^{41} -2.65011 q^{42} +6.10303 q^{43} -2.03790 q^{44} -21.4856 q^{45} -3.69022 q^{46} +10.0197 q^{47} -3.30357 q^{48} -6.35648 q^{49} +2.37146 q^{50} +10.1331 q^{51} -5.68972 q^{52} -0.795708 q^{53} -16.2322 q^{54} +5.53299 q^{55} +0.802195 q^{56} +11.7005 q^{57} +6.21167 q^{58} -8.38303 q^{59} +8.96932 q^{60} -6.87941 q^{61} -5.35567 q^{62} +6.34821 q^{63} +1.00000 q^{64} +15.4478 q^{65} +6.73234 q^{66} -11.2311 q^{67} -3.06731 q^{68} +12.1909 q^{69} -2.17799 q^{70} -2.93379 q^{71} +7.91355 q^{72} -2.52647 q^{73} -6.25812 q^{74} -7.83426 q^{75} -3.54177 q^{76} -1.63479 q^{77} +18.7964 q^{78} +2.76018 q^{79} -2.71504 q^{80} +29.8836 q^{81} +0.393636 q^{82} -1.81395 q^{83} -2.65011 q^{84} +8.32788 q^{85} +6.10303 q^{86} -20.5207 q^{87} -2.03790 q^{88} -10.7986 q^{89} -21.4856 q^{90} -4.56427 q^{91} -3.69022 q^{92} +17.6928 q^{93} +10.0197 q^{94} +9.61606 q^{95} -3.30357 q^{96} -2.29394 q^{97} -6.35648 q^{98} -16.1270 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 98 q + 98 q^{2} + 16 q^{3} + 98 q^{4} + 4 q^{5} + 16 q^{6} + 29 q^{7} + 98 q^{8} + 130 q^{9}+O(q^{10}) \) 98 * q + 98 * q^2 + 16 * q^3 + 98 * q^4 + 4 * q^5 + 16 * q^6 + 29 * q^7 + 98 * q^8 + 130 * q^9	\( 98 q + 98 q^{2} + 16 q^{3} + 98 q^{4} + 4 q^{5} + 16 q^{6} + 29 q^{7} + 98 q^{8} + 130 q^{9} + 4 q^{10} + 51 q^{11} + 16 q^{12} + 31 q^{13} + 29 q^{14} + 57 q^{15} + 98 q^{16} + 35 q^{17} + 130 q^{18} + 77 q^{19} + 4 q^{20} + 46 q^{21} + 51 q^{22} + 73 q^{23} + 16 q^{24} + 150 q^{25} + 31 q^{26} + 52 q^{27} + 29 q^{28} + 20 q^{29} + 57 q^{30} + 59 q^{31} + 98 q^{32} + 27 q^{33} + 35 q^{34} + 48 q^{35} + 130 q^{36} + 41 q^{37} + 77 q^{38} + 64 q^{39} + 4 q^{40} + 29 q^{41} + 46 q^{42} + 94 q^{43} + 51 q^{44} - 3 q^{45} + 73 q^{46} + 58 q^{47} + 16 q^{48} + 149 q^{49} + 150 q^{50} + 58 q^{51} + 31 q^{52} - 11 q^{53} + 52 q^{54} + 56 q^{55} + 29 q^{56} + 64 q^{57} + 20 q^{58} + 45 q^{59} + 57 q^{60} + 73 q^{61} + 59 q^{62} + 53 q^{63} + 98 q^{64} + 39 q^{65} + 27 q^{66} + 133 q^{67} + 35 q^{68} + 13 q^{69} + 48 q^{70} + 67 q^{71} + 130 q^{72} + 42 q^{73} + 41 q^{74} + 36 q^{75} + 77 q^{76} - 25 q^{77} + 64 q^{78} + 154 q^{79} + 4 q^{80} + 198 q^{81} + 29 q^{82} + 69 q^{83} + 46 q^{84} + 81 q^{85} + 94 q^{86} + 25 q^{87} + 51 q^{88} + 32 q^{89} - 3 q^{90} + 95 q^{91} + 73 q^{92} - 23 q^{93} + 58 q^{94} + 50 q^{95} + 16 q^{96} + 76 q^{97} + 149 q^{98} + 149 q^{99}+O(q^{100}) \) 98 * q + 98 * q^2 + 16 * q^3 + 98 * q^4 + 4 * q^5 + 16 * q^6 + 29 * q^7 + 98 * q^8 + 130 * q^9 + 4 * q^10 + 51 * q^11 + 16 * q^12 + 31 * q^13 + 29 * q^14 + 57 * q^15 + 98 * q^16 + 35 * q^17 + 130 * q^18 + 77 * q^19 + 4 * q^20 + 46 * q^21 + 51 * q^22 + 73 * q^23 + 16 * q^24 + 150 * q^25 + 31 * q^26 + 52 * q^27 + 29 * q^28 + 20 * q^29 + 57 * q^30 + 59 * q^31 + 98 * q^32 + 27 * q^33 + 35 * q^34 + 48 * q^35 + 130 * q^36 + 41 * q^37 + 77 * q^38 + 64 * q^39 + 4 * q^40 + 29 * q^41 + 46 * q^42 + 94 * q^43 + 51 * q^44 - 3 * q^45 + 73 * q^46 + 58 * q^47 + 16 * q^48 + 149 * q^49 + 150 * q^50 + 58 * q^51 + 31 * q^52 - 11 * q^53 + 52 * q^54 + 56 * q^55 + 29 * q^56 + 64 * q^57 + 20 * q^58 + 45 * q^59 + 57 * q^60 + 73 * q^61 + 59 * q^62 + 53 * q^63 + 98 * q^64 + 39 * q^65 + 27 * q^66 + 133 * q^67 + 35 * q^68 + 13 * q^69 + 48 * q^70 + 67 * q^71 + 130 * q^72 + 42 * q^73 + 41 * q^74 + 36 * q^75 + 77 * q^76 - 25 * q^77 + 64 * q^78 + 154 * q^79 + 4 * q^80 + 198 * q^81 + 29 * q^82 + 69 * q^83 + 46 * q^84 + 81 * q^85 + 94 * q^86 + 25 * q^87 + 51 * q^88 + 32 * q^89 - 3 * q^90 + 95 * q^91 + 73 * q^92 - 23 * q^93 + 58 * q^94 + 50 * q^95 + 16 * q^96 + 76 * q^97 + 149 * q^98 + 149 * q^99

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