LMFDB - Embedded newform 8007.2.a.f.1.45

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$1$
Dimension:	$48$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.45
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.45513 q^{2} -1.00000 q^{3} +4.02764 q^{4} +0.940315 q^{5} -2.45513 q^{6} -2.20409 q^{7} +4.97812 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.45513 q^{2} -1.00000 q^{3} +4.02764 q^{4} +0.940315 q^{5} -2.45513 q^{6} -2.20409 q^{7} +4.97812 q^{8} +1.00000 q^{9} +2.30859 q^{10} -2.19163 q^{11} -4.02764 q^{12} +1.05565 q^{13} -5.41133 q^{14} -0.940315 q^{15} +4.16662 q^{16} -1.00000 q^{17} +2.45513 q^{18} +2.34063 q^{19} +3.78725 q^{20} +2.20409 q^{21} -5.38072 q^{22} -4.57089 q^{23} -4.97812 q^{24} -4.11581 q^{25} +2.59176 q^{26} -1.00000 q^{27} -8.87730 q^{28} -0.413086 q^{29} -2.30859 q^{30} -5.18661 q^{31} +0.273335 q^{32} +2.19163 q^{33} -2.45513 q^{34} -2.07254 q^{35} +4.02764 q^{36} -4.26539 q^{37} +5.74653 q^{38} -1.05565 q^{39} +4.68100 q^{40} -1.99957 q^{41} +5.41133 q^{42} +5.39509 q^{43} -8.82710 q^{44} +0.940315 q^{45} -11.2221 q^{46} +0.440846 q^{47} -4.16662 q^{48} -2.14197 q^{49} -10.1048 q^{50} +1.00000 q^{51} +4.25179 q^{52} +2.47520 q^{53} -2.45513 q^{54} -2.06082 q^{55} -10.9722 q^{56} -2.34063 q^{57} -1.01418 q^{58} -6.59905 q^{59} -3.78725 q^{60} -7.41297 q^{61} -12.7338 q^{62} -2.20409 q^{63} -7.66216 q^{64} +0.992646 q^{65} +5.38072 q^{66} +12.6240 q^{67} -4.02764 q^{68} +4.57089 q^{69} -5.08835 q^{70} -4.61020 q^{71} +4.97812 q^{72} -16.5399 q^{73} -10.4721 q^{74} +4.11581 q^{75} +9.42721 q^{76} +4.83056 q^{77} -2.59176 q^{78} +2.07978 q^{79} +3.91793 q^{80} +1.00000 q^{81} -4.90918 q^{82} +5.79676 q^{83} +8.87730 q^{84} -0.940315 q^{85} +13.2456 q^{86} +0.413086 q^{87} -10.9102 q^{88} -0.0466153 q^{89} +2.30859 q^{90} -2.32676 q^{91} -18.4099 q^{92} +5.18661 q^{93} +1.08233 q^{94} +2.20093 q^{95} -0.273335 q^{96} +15.6767 q^{97} -5.25880 q^{98} -2.19163 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - q^{2} - 48 q^{3} + 45 q^{4} + q^{5} + q^{6} - 13 q^{7} - 6 q^{8} + 48 q^{9}+O(q^{10}) $ 48 * q - q^2 - 48 * q^3 + 45 * q^4 + q^5 + q^6 - 13 * q^7 - 6 * q^8 + 48 * q^9	\( 48 q - q^{2} - 48 q^{3} + 45 q^{4} + q^{5} + q^{6} - 13 q^{7} - 6 q^{8} + 48 q^{9} - 20 q^{10} + 5 q^{11} - 45 q^{12} - 8 q^{13} + 4 q^{14} - q^{15} + 39 q^{16} - 48 q^{17} - q^{18} - 6 q^{19} + 6 q^{20} + 13 q^{21} - 35 q^{22} - 8 q^{23} + 6 q^{24} + 13 q^{25} + 17 q^{26} - 48 q^{27} - 38 q^{28} + q^{29} + 20 q^{30} - 21 q^{31} - 3 q^{32} - 5 q^{33} + q^{34} + 19 q^{35} + 45 q^{36} - 58 q^{37} - 14 q^{38} + 8 q^{39} - 54 q^{40} - 3 q^{41} - 4 q^{42} - 33 q^{43} + 2 q^{44} + q^{45} - 26 q^{46} + 9 q^{47} - 39 q^{48} + 11 q^{49} + 4 q^{50} + 48 q^{51} - 31 q^{52} - 33 q^{53} + q^{54} - 21 q^{55} + 6 q^{57} - 55 q^{58} + 77 q^{59} - 6 q^{60} - 29 q^{61} - 46 q^{62} - 13 q^{63} + 24 q^{64} - 49 q^{65} + 35 q^{66} - 44 q^{67} - 45 q^{68} + 8 q^{69} + 4 q^{70} + 22 q^{71} - 6 q^{72} - 63 q^{73} - 16 q^{74} - 13 q^{75} - 46 q^{76} - 30 q^{77} - 17 q^{78} - 46 q^{79} - 14 q^{80} + 48 q^{81} - 75 q^{82} + 11 q^{83} + 38 q^{84} - q^{85} + 8 q^{86} - q^{87} - 116 q^{88} + 10 q^{89} - 20 q^{90} - 67 q^{91} - 64 q^{92} + 21 q^{93} - 16 q^{94} - 8 q^{95} + 3 q^{96} - 96 q^{97} - 46 q^{98} + 5 q^{99}+O(q^{100}) \) 48 * q - q^2 - 48 * q^3 + 45 * q^4 + q^5 + q^6 - 13 * q^7 - 6 * q^8 + 48 * q^9 - 20 * q^10 + 5 * q^11 - 45 * q^12 - 8 * q^13 + 4 * q^14 - q^15 + 39 * q^16 - 48 * q^17 - q^18 - 6 * q^19 + 6 * q^20 + 13 * q^21 - 35 * q^22 - 8 * q^23 + 6 * q^24 + 13 * q^25 + 17 * q^26 - 48 * q^27 - 38 * q^28 + q^29 + 20 * q^30 - 21 * q^31 - 3 * q^32 - 5 * q^33 + q^34 + 19 * q^35 + 45 * q^36 - 58 * q^37 - 14 * q^38 + 8 * q^39 - 54 * q^40 - 3 * q^41 - 4 * q^42 - 33 * q^43 + 2 * q^44 + q^45 - 26 * q^46 + 9 * q^47 - 39 * q^48 + 11 * q^49 + 4 * q^50 + 48 * q^51 - 31 * q^52 - 33 * q^53 + q^54 - 21 * q^55 + 6 * q^57 - 55 * q^58 + 77 * q^59 - 6 * q^60 - 29 * q^61 - 46 * q^62 - 13 * q^63 + 24 * q^64 - 49 * q^65 + 35 * q^66 - 44 * q^67 - 45 * q^68 + 8 * q^69 + 4 * q^70 + 22 * q^71 - 6 * q^72 - 63 * q^73 - 16 * q^74 - 13 * q^75 - 46 * q^76 - 30 * q^77 - 17 * q^78 - 46 * q^79 - 14 * q^80 + 48 * q^81 - 75 * q^82 + 11 * q^83 + 38 * q^84 - q^85 + 8 * q^86 - q^87 - 116 * q^88 + 10 * q^89 - 20 * q^90 - 67 * q^91 - 64 * q^92 + 21 * q^93 - 16 * q^94 - 8 * q^95 + 3 * q^96 - 96 * q^97 - 46 * q^98 + 5 * 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 $

$2$	2.45513	1.73604	0.868018	−	0.496533i	$-0.165394\pi$
$2$	2.45513	1.73604	0.868018	+	0.496533i	$0.165394\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.02764	2.01382
$5$	0.940315	0.420522	0.210261	−	0.977645i	$-0.432569\pi$
$5$	0.940315	0.420522	0.210261	+	0.977645i	$0.432569\pi$
$6$	−2.45513	−1.00230
$7$	−2.20409	−0.833069	−0.416535	−	0.909120i	$-0.636756\pi$
$7$	−2.20409	−0.833069	−0.416535	+	0.909120i	$0.636756\pi$
$8$	4.97812	1.76003
$9$	1.00000	0.333333
$10$	2.30859	0.730041
$11$	−2.19163	−0.660801	−0.330400	−	0.943841i	$-0.607184\pi$
$11$	−2.19163	−0.660801	−0.330400	+	0.943841i	$0.607184\pi$
$12$	−4.02764	−1.16268
$13$	1.05565	0.292785	0.146393	−	0.989227i	$-0.453234\pi$
$13$	1.05565	0.292785	0.146393	+	0.989227i	$0.453234\pi$
$14$	−5.41133	−1.44624
$15$	−0.940315	−0.242788
$16$	4.16662	1.04165
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	2.45513	0.578679
$19$	2.34063	0.536977	0.268488	−	0.963283i	$-0.413476\pi$
$19$	2.34063	0.536977	0.268488	+	0.963283i	$0.413476\pi$
$20$	3.78725	0.846856
$21$	2.20409	0.480973
$22$	−5.38072	−1.14717
$23$	−4.57089	−0.953097	−0.476548	−	0.879148i	$-0.658112\pi$
$23$	−4.57089	−0.953097	−0.476548	+	0.879148i	$0.658112\pi$
$24$	−4.97812	−1.01615
$25$	−4.11581	−0.823161
$26$	2.59176	0.508286
$27$	−1.00000	−0.192450
$28$	−8.87730	−1.67765
$29$	−0.413086	−0.0767081	−0.0383540	−	0.999264i	$-0.512211\pi$
$29$	−0.413086	−0.0767081	−0.0383540	+	0.999264i	$0.512211\pi$
$30$	−2.30859	−0.421489
$31$	−5.18661	−0.931543	−0.465772	−	0.884905i	$-0.654223\pi$
$31$	−5.18661	−0.931543	−0.465772	+	0.884905i	$0.654223\pi$
$32$	0.273335	0.0483193
$33$	2.19163	0.381514
$34$	−2.45513	−0.421051
$35$	−2.07254	−0.350324
$36$	4.02764	0.671274
$37$	−4.26539	−0.701227	−0.350613	−	0.936520i	$-0.614027\pi$
$37$	−4.26539	−0.701227	−0.350613	+	0.936520i	$0.614027\pi$
$38$	5.74653	0.932211
$39$	−1.05565	−0.169040
$40$	4.68100	0.740131
$41$	−1.99957	−0.312280	−0.156140	−	0.987735i	$-0.549905\pi$
$41$	−1.99957	−0.312280	−0.156140	+	0.987735i	$0.549905\pi$
$42$	5.41133	0.834986
$43$	5.39509	0.822744	0.411372	−	0.911468i	$-0.365050\pi$
$43$	5.39509	0.822744	0.411372	+	0.911468i	$0.365050\pi$
$44$	−8.82710	−1.33073
$45$	0.940315	0.140174
$46$	−11.2221	−1.65461
$47$	0.440846	0.0643040	0.0321520	−	0.999483i	$-0.489764\pi$
$47$	0.440846	0.0643040	0.0321520	+	0.999483i	$0.489764\pi$
$48$	−4.16662	−0.601399
$49$	−2.14197	−0.305995
$50$	−10.1048	−1.42904
$51$	1.00000	0.140028
$52$	4.25179	0.589617
$53$	2.47520	0.339994	0.169997	−	0.985445i	$-0.445624\pi$
$53$	2.47520	0.339994	0.169997	+	0.985445i	$0.445624\pi$
$54$	−2.45513	−0.334100
$55$	−2.06082	−0.277881
$56$	−10.9722	−1.46623
$57$	−2.34063	−0.310024
$58$	−1.01418	−0.133168
$59$	−6.59905	−0.859123	−0.429562	−	0.903038i	$-0.641332\pi$
$59$	−6.59905	−0.859123	−0.429562	+	0.903038i	$0.641332\pi$
$60$	−3.78725	−0.488932
$61$	−7.41297	−0.949134	−0.474567	−	0.880220i	$-0.657395\pi$
$61$	−7.41297	−0.949134	−0.474567	+	0.880220i	$0.657395\pi$
$62$	−12.7338	−1.61719
$63$	−2.20409	−0.277690
$64$	−7.66216	−0.957770
$65$	0.992646	0.123123
$66$	5.38072	0.662321
$67$	12.6240	1.54226	0.771131	−	0.636676i	$-0.219691\pi$
$67$	12.6240	1.54226	0.771131	+	0.636676i	$0.219691\pi$
$68$	−4.02764	−0.488423
$69$	4.57089	0.550271
$70$	−5.08835	−0.608175
$71$	−4.61020	−0.547130	−0.273565	−	0.961854i	$-0.588203\pi$
$71$	−4.61020	−0.547130	−0.273565	+	0.961854i	$0.588203\pi$
$72$	4.97812	0.586677
$73$	−16.5399	−1.93585	−0.967926	−	0.251234i	$-0.919164\pi$
$73$	−16.5399	−1.93585	−0.967926	+	0.251234i	$0.919164\pi$
$74$	−10.4721	−1.21735
$75$	4.11581	0.475252
$76$	9.42721	1.08137
$77$	4.83056	0.550493
$78$	−2.59176	−0.293459
$79$	2.07978	0.233993	0.116997	−	0.993132i	$-0.462673\pi$
$79$	2.07978	0.233993	0.116997	+	0.993132i	$0.462673\pi$
$80$	3.91793	0.438038
$81$	1.00000	0.111111
$82$	−4.90918	−0.542129
$83$	5.79676	0.636277	0.318138	−	0.948044i	$-0.396942\pi$
$83$	5.79676	0.636277	0.318138	+	0.948044i	$0.396942\pi$
$84$	8.87730	0.968593
$85$	−0.940315	−0.101992
$86$	13.2456	1.42831
$87$	0.413086	0.0442874
$88$	−10.9102	−1.16303
$89$	−0.0466153	−0.00494122	−0.00247061	−	0.999997i	$-0.500786\pi$
$89$	−0.0466153	−0.00494122	−0.00247061	+	0.999997i	$0.500786\pi$
$90$	2.30859	0.243347
$91$	−2.32676	−0.243911
$92$	−18.4099	−1.91937
$93$	5.18661	0.537827
$94$	1.08233	0.111634
$95$	2.20093	0.225810
$96$	−0.273335	−0.0278971
$97$	15.6767	1.59173	0.795863	−	0.605477i	$-0.207017\pi$
$97$	15.6767	1.59173	0.795863	+	0.605477i	$0.207017\pi$
$98$	−5.25880	−0.531219
$99$	−2.19163	−0.220267
$100$	−16.5770	−1.65770
$101$	−13.9930	−1.39236	−0.696178	−	0.717869i	$-0.745118\pi$
$101$	−13.9930	−1.39236	−0.696178	+	0.717869i	$0.745118\pi$
$102$	2.45513	0.243094
$103$	5.35560	0.527703	0.263851	−	0.964563i	$-0.415007\pi$
$103$	5.35560	0.527703	0.263851	+	0.964563i	$0.415007\pi$
$104$	5.25516	0.515311
$105$	2.07254	0.202260
$106$	6.07692	0.590243
$107$	−4.13977	−0.400207	−0.200103	−	0.979775i	$-0.564128\pi$
$107$	−4.13977	−0.400207	−0.200103	+	0.979775i	$0.564128\pi$
$108$	−4.02764	−0.387560
$109$	2.64234	0.253091	0.126545	−	0.991961i	$-0.459611\pi$
$109$	2.64234	0.253091	0.126545	+	0.991961i	$0.459611\pi$
$110$	−5.05958	−0.482412
$111$	4.26539	0.404853
$112$	−9.18362	−0.867770
$113$	17.6980	1.66489	0.832446	−	0.554107i	$-0.186940\pi$
$113$	17.6980	1.66489	0.832446	+	0.554107i	$0.186940\pi$
$114$	−5.74653	−0.538212
$115$	−4.29808	−0.400798
$116$	−1.66376	−0.154476
$117$	1.05565	0.0975951
$118$	−16.2015	−1.49147
$119$	2.20409	0.202049
$120$	−4.68100	−0.427315
$121$	−6.19676	−0.563342
$122$	−18.1998	−1.64773
$123$	1.99957	0.180295
$124$	−20.8898	−1.87596
$125$	−8.57173	−0.766679
$126$	−5.41133	−0.482079
$127$	−4.61078	−0.409141	−0.204570	−	0.978852i	$-0.565580\pi$
$127$	−4.61078	−0.409141	−0.204570	+	0.978852i	$0.565580\pi$
$128$	−19.3582	−1.71104
$129$	−5.39509	−0.475011
$130$	2.43707	0.213745
$131$	2.20540	0.192687	0.0963434	−	0.995348i	$-0.469285\pi$
$131$	2.20540	0.192687	0.0963434	+	0.995348i	$0.469285\pi$
$132$	8.82710	0.768300
$133$	−5.15896	−0.447339
$134$	30.9934	2.67742
$135$	−0.940315	−0.0809295
$136$	−4.97812	−0.426870
$137$	−18.0456	−1.54174	−0.770870	−	0.636992i	$-0.780178\pi$
$137$	−18.0456	−1.54174	−0.770870	+	0.636992i	$0.780178\pi$
$138$	11.2221	0.955290
$139$	−6.19172	−0.525175	−0.262588	−	0.964908i	$-0.584576\pi$
$139$	−6.19172	−0.525175	−0.262588	+	0.964908i	$0.584576\pi$
$140$	−8.34746	−0.705489
$141$	−0.440846	−0.0371259
$142$	−11.3186	−0.949837
$143$	−2.31360	−0.193473
$144$	4.16662	0.347218
$145$	−0.388431	−0.0322574
$146$	−40.6076	−3.36071
$147$	2.14197	0.176667
$148$	−17.1795	−1.41214
$149$	10.0318	0.821835	0.410917	−	0.911673i	$-0.365208\pi$
$149$	10.0318	0.821835	0.410917	+	0.911673i	$0.365208\pi$
$150$	10.1048	0.825055
$151$	1.64782	0.134098	0.0670489	−	0.997750i	$-0.478642\pi$
$151$	1.64782	0.134098	0.0670489	+	0.997750i	$0.478642\pi$
$152$	11.6519	0.945095
$153$	−1.00000	−0.0808452
$154$	11.8596	0.955676
$155$	−4.87705	−0.391734
$156$	−4.25179	−0.340416
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	5.10612	0.406221
$159$	−2.47520	−0.196296
$160$	0.257021	0.0203193
$161$	10.0747	0.793996
$162$	2.45513	0.192893
$163$	−18.3450	−1.43689	−0.718447	−	0.695582i	$-0.755147\pi$
$163$	−18.3450	−1.43689	−0.718447	+	0.695582i	$0.755147\pi$
$164$	−8.05353	−0.628875
$165$	2.06082	0.160435
$166$	14.2318	1.10460
$167$	4.40543	0.340902	0.170451	−	0.985366i	$-0.445477\pi$
$167$	4.40543	0.340902	0.170451	+	0.985366i	$0.445477\pi$
$168$	10.9722	0.846527
$169$	−11.8856	−0.914277
$170$	−2.30859	−0.177061
$171$	2.34063	0.178992
$172$	21.7295	1.65686
$173$	−5.98786	−0.455248	−0.227624	−	0.973749i	$-0.573096\pi$
$173$	−5.98786	−0.455248	−0.227624	+	0.973749i	$0.573096\pi$
$174$	1.01418	0.0768846
$175$	9.07163	0.685751
$176$	−9.13168	−0.688326
$177$	6.59905	0.496015
$178$	−0.114447	−0.00857813
$179$	5.98666	0.447464	0.223732	−	0.974651i	$-0.428176\pi$
$179$	5.98666	0.447464	0.223732	+	0.974651i	$0.428176\pi$
$180$	3.78725	0.282285
$181$	−17.1545	−1.27508	−0.637542	−	0.770416i	$-0.720049\pi$
$181$	−17.1545	−1.27508	−0.637542	+	0.770416i	$0.720049\pi$
$182$	−5.71248	−0.423437
$183$	7.41297	0.547982
$184$	−22.7544	−1.67748
$185$	−4.01082	−0.294881
$186$	12.7338	0.933687
$187$	2.19163	0.160268
$188$	1.77557	0.129497
$189$	2.20409	0.160324
$190$	5.40355	0.392015
$191$	11.7739	0.851926	0.425963	−	0.904741i	$-0.359935\pi$
$191$	11.7739	0.851926	0.425963	+	0.904741i	$0.359935\pi$
$192$	7.66216	0.552969
$193$	−10.4745	−0.753968	−0.376984	−	0.926220i	$-0.623039\pi$
$193$	−10.4745	−0.753968	−0.376984	+	0.926220i	$0.623039\pi$
$194$	38.4882	2.76329
$195$	−0.992646	−0.0710849
$196$	−8.62708	−0.616220
$197$	−15.6245	−1.11320	−0.556599	−	0.830781i	$-0.687894\pi$
$197$	−15.6245	−1.11320	−0.556599	+	0.830781i	$0.687894\pi$
$198$	−5.38072	−0.382391
$199$	13.0676	0.926338	0.463169	−	0.886270i	$-0.346712\pi$
$199$	13.0676	0.926338	0.463169	+	0.886270i	$0.346712\pi$
$200$	−20.4890	−1.44879
$201$	−12.6240	−0.890425
$202$	−34.3546	−2.41718
$203$	0.910480	0.0639031
$204$	4.02764	0.281991
$205$	−1.88022	−0.131320
$206$	13.1487	0.916111
$207$	−4.57089	−0.317699
$208$	4.39850	0.304981
$209$	−5.12978	−0.354835
$210$	5.08835	0.351130
$211$	5.69321	0.391937	0.195969	−	0.980610i	$-0.437215\pi$
$211$	5.69321	0.391937	0.195969	+	0.980610i	$0.437215\pi$
$212$	9.96921	0.684688
$213$	4.61020	0.315885
$214$	−10.1637	−0.694773
$215$	5.07309	0.345982
$216$	−4.97812	−0.338718
$217$	11.4318	0.776040
$218$	6.48729	0.439374
$219$	16.5399	1.11767
$220$	−8.30025	−0.559603
$221$	−1.05565	−0.0710109
$222$	10.4721	0.702840
$223$	−0.272673	−0.0182596	−0.00912978	−	0.999958i	$-0.502906\pi$
$223$	−0.272673	−0.0182596	−0.00912978	+	0.999958i	$0.502906\pi$
$224$	−0.602456	−0.0402533
$225$	−4.11581	−0.274387
$226$	43.4509	2.89031
$227$	28.5750	1.89659	0.948296	−	0.317387i	$-0.102805\pi$
$227$	28.5750	1.89659	0.948296	+	0.317387i	$0.102805\pi$
$228$	−9.42721	−0.624332
$229$	−20.5559	−1.35837	−0.679187	−	0.733965i	$-0.737667\pi$
$229$	−20.5559	−1.35837	−0.679187	+	0.733965i	$0.737667\pi$
$230$	−10.5523	−0.695800
$231$	−4.83056	−0.317827
$232$	−2.05639	−0.135008
$233$	4.92520	0.322661	0.161330	−	0.986900i	$-0.448422\pi$
$233$	4.92520	0.322661	0.161330	+	0.986900i	$0.448422\pi$
$234$	2.59176	0.169429
$235$	0.414534	0.0270412
$236$	−26.5786	−1.73012
$237$	−2.07978	−0.135096
$238$	5.41133	0.350764
$239$	8.12516	0.525573	0.262786	−	0.964854i	$-0.415359\pi$
$239$	8.12516	0.525573	0.262786	+	0.964854i	$0.415359\pi$
$240$	−3.91793	−0.252902
$241$	−10.8644	−0.699836	−0.349918	−	0.936780i	$-0.613791\pi$
$241$	−10.8644	−0.699836	−0.349918	+	0.936780i	$0.613791\pi$
$242$	−15.2138	−0.977982
$243$	−1.00000	−0.0641500
$244$	−29.8568	−1.91139
$245$	−2.01413	−0.128678
$246$	4.90918	0.312998
$247$	2.47089	0.157219
$248$	−25.8196	−1.63954
$249$	−5.79676	−0.367355
$250$	−21.0447	−1.33098
$251$	−27.2575	−1.72048	−0.860240	−	0.509889i	$-0.829687\pi$
$251$	−27.2575	−1.72048	−0.860240	+	0.509889i	$0.829687\pi$
$252$	−8.87730	−0.559218
$253$	10.0177	0.629807
$254$	−11.3200	−0.710283
$255$	0.940315	0.0588848
$256$	−32.2026	−2.01266
$257$	12.7933	0.798025	0.399013	−	0.916945i	$-0.369353\pi$
$257$	12.7933	0.798025	0.399013	+	0.916945i	$0.369353\pi$
$258$	−13.2456	−0.824637
$259$	9.40133	0.584170
$260$	3.99802	0.247947
$261$	−0.413086	−0.0255694
$262$	5.41453	0.334511
$263$	−20.8358	−1.28479	−0.642396	−	0.766373i	$-0.722059\pi$
$263$	−20.8358	−1.28479	−0.642396	+	0.766373i	$0.722059\pi$
$264$	10.9102	0.671475
$265$	2.32747	0.142975
$266$	−12.6659	−0.776596
$267$	0.0466153	0.00285281
$268$	50.8448	3.10584
$269$	11.1293	0.678567	0.339283	−	0.940684i	$-0.389815\pi$
$269$	11.1293	0.678567	0.339283	+	0.940684i	$0.389815\pi$
$270$	−2.30859	−0.140496
$271$	24.8663	1.51052	0.755260	−	0.655426i	$-0.227511\pi$
$271$	24.8663	1.51052	0.755260	+	0.655426i	$0.227511\pi$
$272$	−4.16662	−0.252638
$273$	2.32676	0.140822
$274$	−44.3043	−2.67652
$275$	9.02032	0.543946
$276$	18.4099	1.10815
$277$	−13.4048	−0.805418	−0.402709	−	0.915328i	$-0.631931\pi$
$277$	−13.4048	−0.805418	−0.402709	+	0.915328i	$0.631931\pi$
$278$	−15.2015	−0.911723
$279$	−5.18661	−0.310514
$280$	−10.3174	−0.616580
$281$	6.36966	0.379982	0.189991	−	0.981786i	$-0.439154\pi$
$281$	6.36966	0.379982	0.189991	+	0.981786i	$0.439154\pi$
$282$	−1.08233	−0.0644520
$283$	2.44477	0.145326	0.0726631	−	0.997357i	$-0.476850\pi$
$283$	2.44477	0.145326	0.0726631	+	0.997357i	$0.476850\pi$
$284$	−18.5682	−1.10182
$285$	−2.20093	−0.130372
$286$	−5.68018	−0.335876
$287$	4.40723	0.260151
$288$	0.273335	0.0161064
$289$	1.00000	0.0588235
$290$	−0.953646	−0.0560000
$291$	−15.6767	−0.918984
$292$	−66.6169	−3.89846
$293$	22.5516	1.31748	0.658739	−	0.752371i	$-0.271090\pi$
$293$	22.5516	1.31748	0.658739	+	0.752371i	$0.271090\pi$
$294$	5.25880	0.306699
$295$	−6.20519	−0.361280
$296$	−21.2336	−1.23418
$297$	2.19163	0.127171
$298$	24.6293	1.42673
$299$	−4.82527	−0.279053
$300$	16.5770	0.957073
$301$	−11.8913	−0.685403
$302$	4.04561	0.232799
$303$	13.9930	0.803877
$304$	9.75249	0.559344
$305$	−6.97053	−0.399131
$306$	−2.45513	−0.140350
$307$	−11.3143	−0.645741	−0.322871	−	0.946443i	$-0.604648\pi$
$307$	−11.3143	−0.645741	−0.322871	+	0.946443i	$0.604648\pi$
$308$	19.4558	1.10859
$309$	−5.35560	−0.304669
$310$	−11.9738	−0.680065
$311$	−6.53583	−0.370613	−0.185306	−	0.982681i	$-0.559328\pi$
$311$	−6.53583	−0.370613	−0.185306	+	0.982681i	$0.559328\pi$
$312$	−5.25516	−0.297515
$313$	23.2867	1.31624	0.658121	−	0.752912i	$-0.271352\pi$
$313$	23.2867	1.31624	0.658121	+	0.752912i	$0.271352\pi$
$314$	−2.45513	−0.138551
$315$	−2.07254	−0.116775
$316$	8.37661	0.471221
$317$	−12.3194	−0.691924	−0.345962	−	0.938249i	$-0.612447\pi$
$317$	−12.3194	−0.691924	−0.345962	+	0.938249i	$0.612447\pi$
$318$	−6.07692	−0.340777
$319$	0.905330	0.0506888
$320$	−7.20485	−0.402763
$321$	4.13977	0.231059
$322$	24.7346	1.37841
$323$	−2.34063	−0.130236
$324$	4.02764	0.223758
$325$	−4.34486	−0.241010
$326$	−45.0393	−2.49450
$327$	−2.64234	−0.146122
$328$	−9.95407	−0.549621
$329$	−0.971667	−0.0535697
$330$	5.05958	0.278521
$331$	−11.0849	−0.609280	−0.304640	−	0.952468i	$-0.598536\pi$
$331$	−11.0849	−0.609280	−0.304640	+	0.952468i	$0.598536\pi$
$332$	23.3473	1.28135
$333$	−4.26539	−0.233742
$334$	10.8159	0.591819
$335$	11.8705	0.648555
$336$	9.18362	0.501007
$337$	6.03457	0.328724	0.164362	−	0.986400i	$-0.447443\pi$
$337$	6.03457	0.328724	0.164362	+	0.986400i	$0.447443\pi$
$338$	−29.1806	−1.58722
$339$	−17.6980	−0.961226
$340$	−3.78725	−0.205393
$341$	11.3671	0.615565
$342$	5.74653	0.310737
$343$	20.1498	1.08798
$344$	26.8574	1.44805
$345$	4.29808	0.231401
$346$	−14.7009	−0.790328
$347$	−31.7272	−1.70320	−0.851602	−	0.524188i	$-0.824369\pi$
$347$	−31.7272	−1.70320	−0.851602	+	0.524188i	$0.824369\pi$
$348$	1.66376	0.0891869
$349$	23.7228	1.26985	0.634925	−	0.772574i	$-0.281031\pi$
$349$	23.7228	1.26985	0.634925	+	0.772574i	$0.281031\pi$
$350$	22.2720	1.19049
$351$	−1.05565	−0.0563466
$352$	−0.599049	−0.0319294
$353$	−12.5431	−0.667601	−0.333801	−	0.942644i	$-0.608331\pi$
$353$	−12.5431	−0.667601	−0.333801	+	0.942644i	$0.608331\pi$
$354$	16.2015	0.861100
$355$	−4.33504	−0.230080
$356$	−0.187750	−0.00995072
$357$	−2.20409	−0.116653
$358$	14.6980	0.776814
$359$	0.542532	0.0286338	0.0143169	−	0.999898i	$-0.495443\pi$
$359$	0.542532	0.0286338	0.0143169	+	0.999898i	$0.495443\pi$
$360$	4.68100	0.246710
$361$	−13.5215	−0.711656
$362$	−42.1164	−2.21359
$363$	6.19676	0.325246
$364$	−9.37135	−0.491192
$365$	−15.5528	−0.814068
$366$	18.1998	0.951317
$367$	21.7498	1.13533	0.567665	−	0.823260i	$-0.307847\pi$
$367$	21.7498	1.13533	0.567665	+	0.823260i	$0.307847\pi$
$368$	−19.0452	−0.992797
$369$	−1.99957	−0.104093
$370$	−9.84706	−0.511924
$371$	−5.45557	−0.283239
$372$	20.8898	1.08309
$373$	10.6254	0.550161	0.275080	−	0.961421i	$-0.411296\pi$
$373$	10.6254	0.550161	0.275080	+	0.961421i	$0.411296\pi$
$374$	5.38072	0.278231
$375$	8.57173	0.442642
$376$	2.19458	0.113177
$377$	−0.436075	−0.0224590
$378$	5.41133	0.278329
$379$	−0.111443	−0.00572445	−0.00286222	−	0.999996i	$-0.500911\pi$
$379$	−0.111443	−0.00572445	−0.00286222	+	0.999996i	$0.500911\pi$
$380$	8.86455	0.454742
$381$	4.61078	0.236218
$382$	28.9063	1.47897
$383$	−2.38124	−0.121676	−0.0608379	−	0.998148i	$-0.519377\pi$
$383$	−2.38124	−0.121676	−0.0608379	+	0.998148i	$0.519377\pi$
$384$	19.3582	0.987871
$385$	4.54225	0.231494
$386$	−25.7161	−1.30891
$387$	5.39509	0.274248
$388$	63.1401	3.20545
$389$	10.7283	0.543945	0.271973	−	0.962305i	$-0.412324\pi$
$389$	10.7283	0.543945	0.271973	+	0.962305i	$0.412324\pi$
$390$	−2.43707	−0.123406
$391$	4.57089	0.231160
$392$	−10.6630	−0.538561
$393$	−2.20540	−0.111248
$394$	−38.3600	−1.93255
$395$	1.95565	0.0983993
$396$	−8.82710	−0.443578
$397$	−12.8204	−0.643438	−0.321719	−	0.946835i	$-0.604261\pi$
$397$	−12.8204	−0.643438	−0.321719	+	0.946835i	$0.604261\pi$
$398$	32.0826	1.60816
$399$	5.15896	0.258271
$400$	−17.1490	−0.857450
$401$	−30.0760	−1.50193	−0.750963	−	0.660345i	$-0.770410\pi$
$401$	−30.0760	−1.50193	−0.750963	+	0.660345i	$0.770410\pi$
$402$	−30.9934	−1.54581
$403$	−5.47526	−0.272742
$404$	−56.3588	−2.80396
$405$	0.940315	0.0467246
$406$	2.23534	0.110938
$407$	9.34816	0.463371
$408$	4.97812	0.246453
$409$	−10.7624	−0.532169	−0.266084	−	0.963950i	$-0.585730\pi$
$409$	−10.7624	−0.532169	−0.266084	+	0.963950i	$0.585730\pi$
$410$	−4.61618	−0.227977
$411$	18.0456	0.890124
$412$	21.5704	1.06270
$413$	14.5449	0.715709
$414$	−11.2221	−0.551537
$415$	5.45078	0.267568
$416$	0.288547	0.0141472
$417$	6.19172	0.303210
$418$	−12.5943	−0.616006
$419$	10.5383	0.514830	0.257415	−	0.966301i	$-0.417129\pi$
$419$	10.5383	0.514830	0.257415	+	0.966301i	$0.417129\pi$
$420$	8.34746	0.407315
$421$	25.9671	1.26556	0.632780	−	0.774332i	$-0.281914\pi$
$421$	25.9671	1.26556	0.632780	+	0.774332i	$0.281914\pi$
$422$	13.9776	0.680417
$423$	0.440846	0.0214347
$424$	12.3218	0.598400
$425$	4.11581	0.199646
$426$	11.3186	0.548389
$427$	16.3389	0.790694
$428$	−16.6735	−0.805945
$429$	2.31360	0.111702
$430$	12.4551	0.600637
$431$	21.4917	1.03522	0.517610	−	0.855616i	$-0.326822\pi$
$431$	21.4917	1.03522	0.517610	+	0.855616i	$0.326822\pi$
$432$	−4.16662	−0.200466
$433$	0.277977	0.0133587	0.00667936	−	0.999978i	$-0.497874\pi$
$433$	0.277977	0.0133587	0.00667936	+	0.999978i	$0.497874\pi$
$434$	28.0665	1.34723
$435$	0.388431	0.0186238
$436$	10.6424	0.509679
$437$	−10.6988	−0.511791
$438$	40.6076	1.94031
$439$	−8.46535	−0.404029	−0.202015	−	0.979382i	$-0.564749\pi$
$439$	−8.46535	−0.404029	−0.202015	+	0.979382i	$0.564749\pi$
$440$	−10.2590	−0.489079
$441$	−2.14197	−0.101998
$442$	−2.59176	−0.123277
$443$	1.49565	0.0710606	0.0355303	−	0.999369i	$-0.488688\pi$
$443$	1.49565	0.0710606	0.0355303	+	0.999369i	$0.488688\pi$
$444$	17.1795	0.815302
$445$	−0.0438331	−0.00207789
$446$	−0.669447	−0.0316992
$447$	−10.0318	−0.474487
$448$	16.8881	0.797889
$449$	32.2081	1.51999	0.759997	−	0.649927i	$-0.225200\pi$
$449$	32.2081	1.51999	0.759997	+	0.649927i	$0.225200\pi$
$450$	−10.1048	−0.476346
$451$	4.38230	0.206355
$452$	71.2814	3.35279
$453$	−1.64782	−0.0774214
$454$	70.1553	3.29255
$455$	−2.18789	−0.102570
$456$	−11.6519	−0.545651
$457$	−0.271547	−0.0127024	−0.00635121	−	0.999980i	$-0.502022\pi$
$457$	−0.271547	−0.0127024	−0.00635121	+	0.999980i	$0.502022\pi$
$458$	−50.4674	−2.35819
$459$	1.00000	0.0466760
$460$	−17.3111	−0.807135
$461$	9.14111	0.425744	0.212872	−	0.977080i	$-0.431718\pi$
$461$	9.14111	0.425744	0.212872	+	0.977080i	$0.431718\pi$
$462$	−11.8596	−0.551760
$463$	22.6359	1.05198	0.525989	−	0.850491i	$-0.323695\pi$
$463$	22.6359	1.05198	0.525989	+	0.850491i	$0.323695\pi$
$464$	−1.72117	−0.0799033
$465$	4.87705	0.226168
$466$	12.0920	0.560150
$467$	22.0765	1.02158	0.510789	−	0.859706i	$-0.329353\pi$
$467$	22.0765	1.02158	0.510789	+	0.859706i	$0.329353\pi$
$468$	4.25179	0.196539
$469$	−27.8244	−1.28481
$470$	1.01773	0.0469446
$471$	1.00000	0.0460776
$472$	−32.8508	−1.51208
$473$	−11.8240	−0.543670
$474$	−5.10612	−0.234532
$475$	−9.63357	−0.442018
$476$	8.87730	0.406891
$477$	2.47520	0.113331
$478$	19.9483	0.912413
$479$	26.8567	1.22712	0.613558	−	0.789650i	$-0.289738\pi$
$479$	26.8567	1.22712	0.613558	+	0.789650i	$0.289738\pi$
$480$	−0.257021	−0.0117314
$481$	−4.50278	−0.205309
$482$	−26.6734	−1.21494
$483$	−10.0747	−0.458414
$484$	−24.9583	−1.13447
$485$	14.7410	0.669356
$486$	−2.45513	−0.111367
$487$	14.8888	0.674676	0.337338	−	0.941384i	$-0.390473\pi$
$487$	14.8888	0.674676	0.337338	+	0.941384i	$0.390473\pi$
$488$	−36.9026	−1.67050
$489$	18.3450	0.829591
$490$	−4.94493	−0.223389
$491$	−30.6936	−1.38518	−0.692592	−	0.721329i	$-0.743531\pi$
$491$	−30.6936	−1.38518	−0.692592	+	0.721329i	$0.743531\pi$
$492$	8.05353	0.363081
$493$	0.413086	0.0186044
$494$	6.06634	0.272938
$495$	−2.06082	−0.0926271
$496$	−21.6106	−0.970346
$497$	10.1613	0.455797
$498$	−14.2318	−0.637741
$499$	33.9673	1.52059	0.760293	−	0.649580i	$-0.225055\pi$
$499$	33.9673	1.52059	0.760293	+	0.649580i	$0.225055\pi$
$500$	−34.5239	−1.54395
$501$	−4.40543	−0.196820
$502$	−66.9207	−2.98682
$503$	−32.9640	−1.46979	−0.734895	−	0.678180i	$-0.762769\pi$
$503$	−32.9640	−1.46979	−0.734895	+	0.678180i	$0.762769\pi$
$504$	−10.9722	−0.488742
$505$	−13.1578	−0.585516
$506$	24.5947	1.09337
$507$	11.8856	0.527858
$508$	−18.5706	−0.823936
$509$	−20.3173	−0.900549	−0.450275	−	0.892890i	$-0.648674\pi$
$509$	−20.3173	−0.900549	−0.450275	+	0.892890i	$0.648674\pi$
$510$	2.30859	0.102226
$511$	36.4556	1.61270
$512$	−40.3449	−1.78301
$513$	−2.34063	−0.103341
$514$	31.4092	1.38540
$515$	5.03595	0.221910
$516$	−21.7295	−0.956588
$517$	−0.966171	−0.0424922
$518$	23.0815	1.01414
$519$	5.98786	0.262838
$520$	4.94151	0.216699
$521$	−2.83585	−0.124241	−0.0621205	−	0.998069i	$-0.519786\pi$
$521$	−2.83585	−0.124241	−0.0621205	+	0.998069i	$0.519786\pi$
$522$	−1.01418	−0.0443893
$523$	28.2833	1.23674	0.618370	−	0.785887i	$-0.287793\pi$
$523$	28.2833	1.23674	0.618370	+	0.785887i	$0.287793\pi$
$524$	8.88256	0.388037
$525$	−9.07163	−0.395918
$526$	−51.1546	−2.23044
$527$	5.18661	0.225932
$528$	9.13168	0.397405
$529$	−2.10695	−0.0916065
$530$	5.71422	0.248210
$531$	−6.59905	−0.286374
$532$	−20.7785	−0.900860
$533$	−2.11085	−0.0914309
$534$	0.114447	0.00495258
$535$	−3.89269	−0.168296
$536$	62.8435	2.71443
$537$	−5.98666	−0.258344
$538$	27.3239	1.17802
$539$	4.69440	0.202202
$540$	−3.78725	−0.162977
$541$	−37.3445	−1.60557	−0.802784	−	0.596270i	$-0.796649\pi$
$541$	−37.3445	−1.60557	−0.802784	+	0.596270i	$0.796649\pi$
$542$	61.0499	2.62232
$543$	17.1545	0.736170
$544$	−0.273335	−0.0117191
$545$	2.48464	0.106430
$546$	5.71248	0.244472
$547$	4.93348	0.210940	0.105470	−	0.994422i	$-0.466365\pi$
$547$	4.93348	0.210940	0.105470	+	0.994422i	$0.466365\pi$
$548$	−72.6813	−3.10479
$549$	−7.41297	−0.316378
$550$	22.1460	0.944310
$551$	−0.966879	−0.0411904
$552$	22.7544	0.968493
$553$	−4.58403	−0.194933
$554$	−32.9105	−1.39823
$555$	4.01082	0.170250
$556$	−24.9380	−1.05761
$557$	−3.32177	−0.140748	−0.0703740	−	0.997521i	$-0.522419\pi$
$557$	−3.32177	−0.140748	−0.0703740	+	0.997521i	$0.522419\pi$
$558$	−12.7338	−0.539064
$559$	5.69534	0.240887
$560$	−8.63549	−0.364916
$561$	−2.19163	−0.0925306
$562$	15.6383	0.659662
$563$	17.6284	0.742950	0.371475	−	0.928443i	$-0.378852\pi$
$563$	17.6284	0.742950	0.371475	+	0.928443i	$0.378852\pi$
$564$	−1.77557	−0.0747650
$565$	16.6417	0.700123
$566$	6.00221	0.252292
$567$	−2.20409	−0.0925633
$568$	−22.9501	−0.962964
$569$	−25.1519	−1.05442	−0.527212	−	0.849734i	$-0.676763\pi$
$569$	−25.1519	−1.05442	−0.527212	+	0.849734i	$0.676763\pi$
$570$	−5.40355	−0.226330
$571$	16.2381	0.679542	0.339771	−	0.940508i	$-0.389651\pi$
$571$	16.2381	0.679542	0.339771	+	0.940508i	$0.389651\pi$
$572$	−9.31835	−0.389620
$573$	−11.7739	−0.491860
$574$	10.8203	0.451631
$575$	18.8129	0.784553
$576$	−7.66216	−0.319257
$577$	−12.6123	−0.525055	−0.262527	−	0.964925i	$-0.584556\pi$
$577$	−12.6123	−0.525055	−0.262527	+	0.964925i	$0.584556\pi$
$578$	2.45513	0.102120
$579$	10.4745	0.435303
$580$	−1.56446	−0.0649607
$581$	−12.7766	−0.530063
$582$	−38.4882	−1.59539
$583$	−5.42471	−0.224669
$584$	−82.3377	−3.40716
$585$	0.992646	0.0410409
$586$	55.3670	2.28719
$587$	−17.7162	−0.731225	−0.365612	−	0.930767i	$-0.619140\pi$
$587$	−17.7162	−0.731225	−0.365612	+	0.930767i	$0.619140\pi$
$588$	8.62708	0.355775
$589$	−12.1399	−0.500217
$590$	−15.2345	−0.627195
$591$	15.6245	0.642705
$592$	−17.7723	−0.730436
$593$	21.2406	0.872248	0.436124	−	0.899886i	$-0.356351\pi$
$593$	21.2406	0.872248	0.436124	+	0.899886i	$0.356351\pi$
$594$	5.38072	0.220774
$595$	2.07254	0.0849660
$596$	40.4044	1.65503
$597$	−13.0676	−0.534822
$598$	−11.8467	−0.484446
$599$	11.0157	0.450089	0.225044	−	0.974349i	$-0.427747\pi$
$599$	11.0157	0.450089	0.225044	+	0.974349i	$0.427747\pi$
$600$	20.4890	0.836459
$601$	−30.0304	−1.22496	−0.612482	−	0.790484i	$-0.709829\pi$
$601$	−30.0304	−1.22496	−0.612482	+	0.790484i	$0.709829\pi$
$602$	−29.1946	−1.18988
$603$	12.6240	0.514087
$604$	6.63683	0.270049
$605$	−5.82691	−0.236898
$606$	34.3546	1.39556
$607$	−3.91891	−0.159064	−0.0795318	−	0.996832i	$-0.525343\pi$
$607$	−3.91891	−0.159064	−0.0795318	+	0.996832i	$0.525343\pi$
$608$	0.639775	0.0259463
$609$	−0.910480	−0.0368945
$610$	−17.1135	−0.692906
$611$	0.465380	0.0188273
$612$	−4.02764	−0.162808
$613$	−29.3736	−1.18639	−0.593193	−	0.805060i	$-0.702133\pi$
$613$	−29.3736	−1.18639	−0.593193	+	0.805060i	$0.702133\pi$
$614$	−27.7780	−1.12103
$615$	1.88022	0.0758179
$616$	24.0471	0.968884
$617$	34.7312	1.39823	0.699113	−	0.715012i	$-0.253579\pi$
$617$	34.7312	1.39823	0.699113	+	0.715012i	$0.253579\pi$
$618$	−13.1487	−0.528917
$619$	13.9980	0.562626	0.281313	−	0.959616i	$-0.409230\pi$
$619$	13.9980	0.562626	0.281313	+	0.959616i	$0.409230\pi$
$620$	−19.6430	−0.788883
$621$	4.57089	0.183424
$622$	−16.0463	−0.643397
$623$	0.102745	0.00411638
$624$	−4.39850	−0.176081
$625$	12.5189	0.500756
$626$	57.1718	2.28504
$627$	5.12978	0.204864
$628$	−4.02764	−0.160720
$629$	4.26539	0.170072
$630$	−5.08835	−0.202725
$631$	15.9550	0.635157	0.317579	−	0.948232i	$-0.397130\pi$
$631$	15.9550	0.635157	0.317579	+	0.948232i	$0.397130\pi$
$632$	10.3534	0.411835
$633$	−5.69321	−0.226285
$634$	−30.2456	−1.20120
$635$	−4.33559	−0.172053
$636$	−9.96921	−0.395305
$637$	−2.26117	−0.0895910
$638$	2.22270	0.0879975
$639$	−4.61020	−0.182377
$640$	−18.2028	−0.719531
$641$	−10.7062	−0.422870	−0.211435	−	0.977392i	$-0.567814\pi$
$641$	−10.7062	−0.422870	−0.211435	+	0.977392i	$0.567814\pi$
$642$	10.1637	0.401128
$643$	−42.8102	−1.68827	−0.844135	−	0.536131i	$-0.819885\pi$
$643$	−42.8102	−1.68827	−0.844135	+	0.536131i	$0.819885\pi$
$644$	40.5772	1.59897
$645$	−5.07309	−0.199753
$646$	−5.74653	−0.226094
$647$	32.9112	1.29387	0.646936	−	0.762544i	$-0.276050\pi$
$647$	32.9112	1.29387	0.646936	+	0.762544i	$0.276050\pi$
$648$	4.97812	0.195559
$649$	14.4627	0.567709
$650$	−10.6672	−0.418401
$651$	−11.4318	−0.448047
$652$	−73.8872	−2.89365
$653$	−2.30507	−0.0902043	−0.0451021	−	0.998982i	$-0.514361\pi$
$653$	−2.30507	−0.0902043	−0.0451021	+	0.998982i	$0.514361\pi$
$654$	−6.48729	−0.253673
$655$	2.07377	0.0810290
$656$	−8.33142	−0.325287
$657$	−16.5399	−0.645284
$658$	−2.38556	−0.0929990
$659$	1.57036	0.0611727	0.0305863	−	0.999532i	$-0.490263\pi$
$659$	1.57036	0.0611727	0.0305863	+	0.999532i	$0.490263\pi$
$660$	8.30025	0.323087
$661$	−7.67753	−0.298621	−0.149311	−	0.988790i	$-0.547705\pi$
$661$	−7.67753	−0.298621	−0.149311	+	0.988790i	$0.547705\pi$
$662$	−27.2148	−1.05773
$663$	1.05565	0.0409982
$664$	28.8569	1.11987
$665$	−4.85105	−0.188116
$666$	−10.4721	−0.405785
$667$	1.88817	0.0731102
$668$	17.7435	0.686517
$669$	0.272673	0.0105422
$670$	29.1436	1.12591
$671$	16.2465	0.627188
$672$	0.602456	0.0232403
$673$	44.2322	1.70503	0.852514	−	0.522705i	$-0.175077\pi$
$673$	44.2322	1.70503	0.852514	+	0.522705i	$0.175077\pi$
$674$	14.8156	0.570677
$675$	4.11581	0.158417
$676$	−47.8709	−1.84119
$677$	−26.8378	−1.03146	−0.515731	−	0.856751i	$-0.672480\pi$
$677$	−26.8378	−1.03146	−0.515731	+	0.856751i	$0.672480\pi$
$678$	−43.4509	−1.66872
$679$	−34.5529	−1.32602
$680$	−4.68100	−0.179508
$681$	−28.5750	−1.09500
$682$	27.9077	1.06864
$683$	−37.9479	−1.45204	−0.726018	−	0.687676i	$-0.758631\pi$
$683$	−37.9479	−1.45204	−0.726018	+	0.687676i	$0.758631\pi$
$684$	9.42721	0.360458
$685$	−16.9686	−0.648336
$686$	49.4702	1.88878
$687$	20.5559	0.784258
$688$	22.4793	0.857015
$689$	2.61295	0.0995454
$690$	10.5523	0.401720
$691$	−6.97120	−0.265197	−0.132599	−	0.991170i	$-0.542332\pi$
$691$	−6.97120	−0.265197	−0.132599	+	0.991170i	$0.542332\pi$
$692$	−24.1170	−0.916789
$693$	4.83056	0.183498
$694$	−77.8942	−2.95682
$695$	−5.82217	−0.220848
$696$	2.05639	0.0779472
$697$	1.99957	0.0757389
$698$	58.2423	2.20451
$699$	−4.92520	−0.186288
$700$	36.5373	1.38098
$701$	8.07668	0.305052	0.152526	−	0.988299i	$-0.451259\pi$
$701$	8.07668	0.305052	0.152526	+	0.988299i	$0.451259\pi$
$702$	−2.59176	−0.0978197
$703$	−9.98370	−0.376542
$704$	16.7926	0.632895
$705$	−0.414534	−0.0156123
$706$	−30.7949	−1.15898
$707$	30.8419	1.15993
$708$	26.5786	0.998886
$709$	9.25735	0.347667	0.173833	−	0.984775i	$-0.444385\pi$
$709$	9.25735	0.347667	0.173833	+	0.984775i	$0.444385\pi$
$710$	−10.6431	−0.399427
$711$	2.07978	0.0779978
$712$	−0.232057	−0.00869669
$713$	23.7075	0.887851
$714$	−5.41133	−0.202514
$715$	−2.17551	−0.0813595
$716$	24.1121	0.901113
$717$	−8.12516	−0.303440
$718$	1.33198	0.0497092
$719$	47.6922	1.77862	0.889309	−	0.457308i	$-0.151186\pi$
$719$	47.6922	1.77862	0.889309	+	0.457308i	$0.151186\pi$
$720$	3.91793	0.146013
$721$	−11.8042	−0.439613
$722$	−33.1969	−1.23546
$723$	10.8644	0.404050
$724$	−69.0922	−2.56779
$725$	1.70018	0.0631431
$726$	15.2138	0.564638
$727$	17.2580	0.640065	0.320032	−	0.947407i	$-0.396306\pi$
$727$	17.2580	0.640065	0.320032	+	0.947407i	$0.396306\pi$
$728$	−11.5829	−0.429290
$729$	1.00000	0.0370370
$730$	−38.1840	−1.41325
$731$	−5.39509	−0.199545
$732$	29.8568	1.10354
$733$	17.3699	0.641571	0.320786	−	0.947152i	$-0.396053\pi$
$733$	17.3699	0.641571	0.320786	+	0.947152i	$0.396053\pi$
$734$	53.3984	1.97097
$735$	2.01413	0.0742921
$736$	−1.24939	−0.0460530
$737$	−27.6670	−1.01913
$738$	−4.90918	−0.180710
$739$	22.2670	0.819105	0.409553	−	0.912286i	$-0.365685\pi$
$739$	22.2670	0.819105	0.409553	+	0.912286i	$0.365685\pi$
$740$	−16.1541	−0.593838
$741$	−2.47089	−0.0907704
$742$	−13.3941	−0.491713
$743$	27.5352	1.01017	0.505085	−	0.863070i	$-0.331461\pi$
$743$	27.5352	1.01017	0.505085	+	0.863070i	$0.331461\pi$
$744$	25.8196	0.946591
$745$	9.43303	0.345599
$746$	26.0866	0.955099
$747$	5.79676	0.212092
$748$	8.82710	0.322751
$749$	9.12444	0.333400
$750$	21.0447	0.768443
$751$	−32.9541	−1.20251	−0.601256	−	0.799056i	$-0.705333\pi$
$751$	−32.9541	−1.20251	−0.601256	+	0.799056i	$0.705333\pi$
$752$	1.83684	0.0669826
$753$	27.2575	0.993320
$754$	−1.07062	−0.0389896
$755$	1.54947	0.0563910
$756$	8.87730	0.322864
$757$	9.13239	0.331922	0.165961	−	0.986132i	$-0.446927\pi$
$757$	9.13239	0.331922	0.165961	+	0.986132i	$0.446927\pi$
$758$	−0.273607	−0.00993785
$759$	−10.0177	−0.363619
$760$	10.9565	0.397433
$761$	29.3151	1.06267	0.531336	−	0.847161i	$-0.321690\pi$
$761$	29.3151	1.06267	0.531336	+	0.847161i	$0.321690\pi$
$762$	11.3200	0.410082
$763$	−5.82398	−0.210842
$764$	47.4209	1.71563
$765$	−0.940315	−0.0339972
$766$	−5.84625	−0.211234
$767$	−6.96631	−0.251539
$768$	32.2026	1.16201
$769$	−40.9760	−1.47763	−0.738816	−	0.673908i	$-0.764615\pi$
$769$	−40.9760	−1.47763	−0.738816	+	0.673908i	$0.764615\pi$
$770$	11.1518	0.401882
$771$	−12.7933	−0.460740
$772$	−42.1873	−1.51836
$773$	−26.6535	−0.958661	−0.479331	−	0.877634i	$-0.659120\pi$
$773$	−26.6535	−0.958661	−0.479331	+	0.877634i	$0.659120\pi$
$774$	13.2456	0.476104
$775$	21.3471	0.766811
$776$	78.0404	2.80149
$777$	−9.40133	−0.337271
$778$	26.3393	0.944309
$779$	−4.68023	−0.167687
$780$	−3.99802	−0.143152
$781$	10.1038	0.361544
$782$	11.2221	0.401302
$783$	0.413086	0.0147625
$784$	−8.92476	−0.318741
$785$	−0.940315	−0.0335613
$786$	−5.41453	−0.193130
$787$	−37.8563	−1.34943	−0.674716	−	0.738078i	$-0.735734\pi$
$787$	−37.8563	−1.34943	−0.674716	+	0.738078i	$0.735734\pi$
$788$	−62.9298	−2.24178
$789$	20.8358	0.741775
$790$	4.80136	0.170825
$791$	−39.0081	−1.38697
$792$	−10.9102	−0.387676
$793$	−7.82552	−0.277892
$794$	−31.4757	−1.11703
$795$	−2.32747	−0.0825467
$796$	52.6316	1.86548
$797$	−35.6581	−1.26307	−0.631537	−	0.775346i	$-0.717575\pi$
$797$	−35.6581	−1.26307	−0.631537	+	0.775346i	$0.717575\pi$
$798$	12.6659	0.448368
$799$	−0.440846	−0.0155960
$800$	−1.12499	−0.0397746
$801$	−0.0466153	−0.00164707
$802$	−73.8404	−2.60740
$803$	36.2494	1.27921
$804$	−50.8448	−1.79316
$805$	9.47337	0.333892
$806$	−13.4425	−0.473490
$807$	−11.1293	−0.391771
$808$	−69.6588	−2.45059
$809$	41.6208	1.46331	0.731654	−	0.681676i	$-0.238749\pi$
$809$	41.6208	1.46331	0.731654	+	0.681676i	$0.238749\pi$
$810$	2.30859	0.0811157
$811$	34.3205	1.20516	0.602578	−	0.798060i	$-0.294140\pi$
$811$	34.3205	1.20516	0.602578	+	0.798060i	$0.294140\pi$
$812$	3.66709	0.128689
$813$	−24.8663	−0.872099
$814$	22.9509	0.804429
$815$	−17.2501	−0.604245
$816$	4.16662	0.145861
$817$	12.6279	0.441794
$818$	−26.4231	−0.923864
$819$	−2.32676	−0.0813035
$820$	−7.57286	−0.264456
$821$	29.5872	1.03260	0.516300	−	0.856408i	$-0.327309\pi$
$821$	29.5872	1.03260	0.516300	+	0.856408i	$0.327309\pi$
$822$	44.3043	1.54529
$823$	12.3456	0.430340	0.215170	−	0.976577i	$-0.430969\pi$
$823$	12.3456	0.430340	0.215170	+	0.976577i	$0.430969\pi$
$824$	26.6608	0.928772
$825$	−9.02032	−0.314047
$826$	35.7096	1.24250
$827$	−35.6508	−1.23970	−0.619851	−	0.784720i	$-0.712807\pi$
$827$	−35.6508	−1.23970	−0.619851	+	0.784720i	$0.712807\pi$
$828$	−18.4099	−0.639789
$829$	2.45389	0.0852271	0.0426136	−	0.999092i	$-0.486432\pi$
$829$	2.45389	0.0852271	0.0426136	+	0.999092i	$0.486432\pi$
$830$	13.3824	0.464508
$831$	13.4048	0.465008
$832$	−8.08858	−0.280421
$833$	2.14197	0.0742148
$834$	15.2015	0.526383
$835$	4.14249	0.143357
$836$	−20.6609	−0.714573
$837$	5.18661	0.179276
$838$	25.8729	0.893763
$839$	−35.8108	−1.23632	−0.618162	−	0.786050i	$-0.712123\pi$
$839$	−35.8108	−1.23632	−0.618162	+	0.786050i	$0.712123\pi$
$840$	10.3174	0.355983
$841$	−28.8294	−0.994116
$842$	63.7525	2.19706
$843$	−6.36966	−0.219383
$844$	22.9302	0.789291
$845$	−11.1762	−0.384473
$846$	1.08233	0.0372114
$847$	13.6583	0.469303
$848$	10.3132	0.354157
$849$	−2.44477	−0.0839042
$850$	10.1048	0.346593
$851$	19.4967	0.668337
$852$	18.5682	0.636137
$853$	24.0542	0.823600	0.411800	−	0.911274i	$-0.364900\pi$
$853$	24.0542	0.823600	0.411800	+	0.911274i	$0.364900\pi$
$854$	40.1140	1.37267
$855$	2.20093	0.0752701
$856$	−20.6083	−0.704376
$857$	13.5708	0.463571	0.231785	−	0.972767i	$-0.425543\pi$
$857$	13.5708	0.463571	0.231785	+	0.972767i	$0.425543\pi$
$858$	5.68018	0.193918
$859$	14.9012	0.508422	0.254211	−	0.967149i	$-0.418184\pi$
$859$	14.9012	0.508422	0.254211	+	0.967149i	$0.418184\pi$
$860$	20.4326	0.696745
$861$	−4.40723	−0.150198
$862$	52.7649	1.79718
$863$	14.1870	0.482932	0.241466	−	0.970409i	$-0.422372\pi$
$863$	14.1870	0.482932	0.241466	+	0.970409i	$0.422372\pi$
$864$	−0.273335	−0.00929905
$865$	−5.63047	−0.191442
$866$	0.682468	0.0231912
$867$	−1.00000	−0.0339618
$868$	46.0431	1.56281
$869$	−4.55810	−0.154623
$870$	0.953646	0.0323316
$871$	13.3265	0.451552
$872$	13.1539	0.445447
$873$	15.6767	0.530575
$874$	−26.2668	−0.888487
$875$	18.8929	0.638697
$876$	66.6169	2.25078
$877$	−23.5753	−0.796082	−0.398041	−	0.917368i	$-0.630310\pi$
$877$	−23.5753	−0.796082	−0.398041	+	0.917368i	$0.630310\pi$
$878$	−20.7835	−0.701409
$879$	−22.5516	−0.760647
$880$	−8.58666	−0.289456
$881$	18.5366	0.624515	0.312257	−	0.949998i	$-0.398915\pi$
$881$	18.5366	0.624515	0.312257	+	0.949998i	$0.398915\pi$
$882$	−5.25880	−0.177073
$883$	−8.96129	−0.301571	−0.150786	−	0.988566i	$-0.548180\pi$
$883$	−8.96129	−0.301571	−0.150786	+	0.988566i	$0.548180\pi$
$884$	−4.25179	−0.143003
$885$	6.20519	0.208585
$886$	3.67202	0.123364
$887$	−29.7260	−0.998103	−0.499052	−	0.866572i	$-0.666318\pi$
$887$	−29.7260	−0.998103	−0.499052	+	0.866572i	$0.666318\pi$
$888$	21.2336	0.712554
$889$	10.1626	0.340843
$890$	−0.107616	−0.00360729
$891$	−2.19163	−0.0734223
$892$	−1.09823	−0.0367715
$893$	1.03186	0.0345298
$894$	−24.6293	−0.823726
$895$	5.62935	0.188168
$896$	42.6674	1.42542
$897$	4.82527	0.161111
$898$	79.0749	2.63876
$899$	2.14252	0.0714569
$900$	−16.5770	−0.552567
$901$	−2.47520	−0.0824608
$902$	10.7591	0.358239
$903$	11.8913	0.395717
$904$	88.1029	2.93026
$905$	−16.1306	−0.536200
$906$	−4.04561	−0.134406
$907$	−18.2268	−0.605212	−0.302606	−	0.953116i	$-0.597857\pi$
$907$	−18.2268	−0.605212	−0.302606	+	0.953116i	$0.597857\pi$
$908$	115.090	3.81940
$909$	−13.9930	−0.464119
$910$	−5.37154	−0.178065
$911$	12.9167	0.427949	0.213975	−	0.976839i	$-0.431359\pi$
$911$	12.9167	0.427949	0.213975	+	0.976839i	$0.431359\pi$
$912$	−9.75249	−0.322937
$913$	−12.7043	−0.420452
$914$	−0.666682	−0.0220519
$915$	6.97053	0.230439
$916$	−82.7919	−2.73552
$917$	−4.86091	−0.160521
$918$	2.45513	0.0810312
$919$	45.8151	1.51130	0.755650	−	0.654976i	$-0.227321\pi$
$919$	45.8151	1.51130	0.755650	+	0.654976i	$0.227321\pi$
$920$	−21.3963	−0.705416
$921$	11.3143	0.372819
$922$	22.4426	0.739106
$923$	−4.86677	−0.160192
$924$	−19.4558	−0.640047
$925$	17.5555	0.577223
$926$	55.5739	1.82627
$927$	5.35560	0.175901
$928$	−0.112911	−0.00370648
$929$	18.0085	0.590841	0.295421	−	0.955367i	$-0.404540\pi$
$929$	18.0085	0.590841	0.295421	+	0.955367i	$0.404540\pi$
$930$	11.9738	0.392636
$931$	−5.01355	−0.164312
$932$	19.8369	0.649781
$933$	6.53583	0.213973
$934$	54.2005	1.77350
$935$	2.06082	0.0673961
$936$	5.25516	0.171770
$937$	17.5437	0.573126	0.286563	−	0.958061i	$-0.407487\pi$
$937$	17.5437	0.573126	0.286563	+	0.958061i	$0.407487\pi$
$938$	−68.3124	−2.23048
$939$	−23.2867	−0.759933
$940$	1.66960	0.0544562
$941$	14.1592	0.461578	0.230789	−	0.973004i	$-0.425869\pi$
$941$	14.1592	0.461578	0.230789	+	0.973004i	$0.425869\pi$
$942$	2.45513	0.0799923
$943$	9.13980	0.297633
$944$	−27.4957	−0.894909
$945$	2.07254	0.0674198
$946$	−29.0295	−0.943831
$947$	40.7207	1.32325	0.661623	−	0.749837i	$-0.269868\pi$
$947$	40.7207	1.32325	0.661623	+	0.749837i	$0.269868\pi$
$948$	−8.37661	−0.272060
$949$	−17.4604	−0.566789
$950$	−23.6516	−0.767360
$951$	12.3194	0.399482
$952$	10.9722	0.355612
$953$	−28.9513	−0.937825	−0.468913	−	0.883245i	$-0.655354\pi$
$953$	−28.9513	−0.937825	−0.468913	+	0.883245i	$0.655354\pi$
$954$	6.07692	0.196748
$955$	11.0711	0.358253
$956$	32.7252	1.05841
$957$	−0.905330	−0.0292652
$958$	65.9367	2.13032
$959$	39.7742	1.28438
$960$	7.20485	0.232535
$961$	−4.09903	−0.132227
$962$	−11.0549	−0.356424
$963$	−4.13977	−0.133402
$964$	−43.7578	−1.40934
$965$	−9.84929	−0.317060
$966$	−24.7346	−0.795823
$967$	−57.9945	−1.86498	−0.932489	−	0.361199i	$-0.882367\pi$
$967$	−57.9945	−1.86498	−0.932489	+	0.361199i	$0.882367\pi$
$968$	−30.8482	−0.991499
$969$	2.34063	0.0751918
$970$	36.1911	1.16203
$971$	−11.5844	−0.371761	−0.185881	−	0.982572i	$-0.559514\pi$
$971$	−11.5844	−0.371761	−0.185881	+	0.982572i	$0.559514\pi$
$972$	−4.02764	−0.129187
$973$	13.6471	0.437507
$974$	36.5539	1.17126
$975$	4.34486	0.139147
$976$	−30.8870	−0.988669
$977$	−41.6869	−1.33368	−0.666841	−	0.745200i	$-0.732354\pi$
$977$	−41.6869	−1.33368	−0.666841	+	0.745200i	$0.732354\pi$
$978$	45.0393	1.44020
$979$	0.102164	0.00326516
$980$	−8.11218	−0.259134
$981$	2.64234	0.0843635
$982$	−75.3567	−2.40473
$983$	−42.3156	−1.34966	−0.674829	−	0.737974i	$-0.735783\pi$
$983$	−42.3156	−1.34966	−0.674829	+	0.737974i	$0.735783\pi$
$984$	9.95407	0.317324
$985$	−14.6919	−0.468124
$986$	1.01418	0.0322980
$987$	0.971667	0.0309285
$988$	9.95185	0.316611
$989$	−24.6604	−0.784155
$990$	−5.05958	−0.160804
$991$	−53.5139	−1.69993	−0.849963	−	0.526842i	$-0.823376\pi$
$991$	−53.5139	−1.69993	−0.849963	+	0.526842i	$0.823376\pi$
$992$	−1.41768	−0.0450115
$993$	11.0849	0.351768
$994$	24.9473	0.791280
$995$	12.2877	0.389545
$996$	−23.3473	−0.739787
$997$	20.8459	0.660197	0.330098	−	0.943947i	$-0.392918\pi$
$997$	20.8459	0.660197	0.330098	+	0.943947i	$0.392918\pi$
$998$	83.3941	2.63979
$999$	4.26539	0.134951

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.f.1.45	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.f.1.45	✓	48	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q+2.45513 q^{2} -1.00000 q^{3} +4.02764 q^{4} +0.940315 q^{5} -2.45513 q^{6} -2.20409 q^{7} +4.97812 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.45513 q^{2} -1.00000 q^{3} +4.02764 q^{4} +0.940315 q^{5} -2.45513 q^{6} -2.20409 q^{7} +4.97812 q^{8} +1.00000 q^{9} +2.30859 q^{10} -2.19163 q^{11} -4.02764 q^{12} +1.05565 q^{13} -5.41133 q^{14} -0.940315 q^{15} +4.16662 q^{16} -1.00000 q^{17} +2.45513 q^{18} +2.34063 q^{19} +3.78725 q^{20} +2.20409 q^{21} -5.38072 q^{22} -4.57089 q^{23} -4.97812 q^{24} -4.11581 q^{25} +2.59176 q^{26} -1.00000 q^{27} -8.87730 q^{28} -0.413086 q^{29} -2.30859 q^{30} -5.18661 q^{31} +0.273335 q^{32} +2.19163 q^{33} -2.45513 q^{34} -2.07254 q^{35} +4.02764 q^{36} -4.26539 q^{37} +5.74653 q^{38} -1.05565 q^{39} +4.68100 q^{40} -1.99957 q^{41} +5.41133 q^{42} +5.39509 q^{43} -8.82710 q^{44} +0.940315 q^{45} -11.2221 q^{46} +0.440846 q^{47} -4.16662 q^{48} -2.14197 q^{49} -10.1048 q^{50} +1.00000 q^{51} +4.25179 q^{52} +2.47520 q^{53} -2.45513 q^{54} -2.06082 q^{55} -10.9722 q^{56} -2.34063 q^{57} -1.01418 q^{58} -6.59905 q^{59} -3.78725 q^{60} -7.41297 q^{61} -12.7338 q^{62} -2.20409 q^{63} -7.66216 q^{64} +0.992646 q^{65} +5.38072 q^{66} +12.6240 q^{67} -4.02764 q^{68} +4.57089 q^{69} -5.08835 q^{70} -4.61020 q^{71} +4.97812 q^{72} -16.5399 q^{73} -10.4721 q^{74} +4.11581 q^{75} +9.42721 q^{76} +4.83056 q^{77} -2.59176 q^{78} +2.07978 q^{79} +3.91793 q^{80} +1.00000 q^{81} -4.90918 q^{82} +5.79676 q^{83} +8.87730 q^{84} -0.940315 q^{85} +13.2456 q^{86} +0.413086 q^{87} -10.9102 q^{88} -0.0466153 q^{89} +2.30859 q^{90} -2.32676 q^{91} -18.4099 q^{92} +5.18661 q^{93} +1.08233 q^{94} +2.20093 q^{95} -0.273335 q^{96} +15.6767 q^{97} -5.25880 q^{98} -2.19163 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - q^{2} - 48 q^{3} + 45 q^{4} + q^{5} + q^{6} - 13 q^{7} - 6 q^{8} + 48 q^{9}+O(q^{10}) \) 48 * q - q^2 - 48 * q^3 + 45 * q^4 + q^5 + q^6 - 13 * q^7 - 6 * q^8 + 48 * q^9	\( 48 q - q^{2} - 48 q^{3} + 45 q^{4} + q^{5} + q^{6} - 13 q^{7} - 6 q^{8} + 48 q^{9} - 20 q^{10} + 5 q^{11} - 45 q^{12} - 8 q^{13} + 4 q^{14} - q^{15} + 39 q^{16} - 48 q^{17} - q^{18} - 6 q^{19} + 6 q^{20} + 13 q^{21} - 35 q^{22} - 8 q^{23} + 6 q^{24} + 13 q^{25} + 17 q^{26} - 48 q^{27} - 38 q^{28} + q^{29} + 20 q^{30} - 21 q^{31} - 3 q^{32} - 5 q^{33} + q^{34} + 19 q^{35} + 45 q^{36} - 58 q^{37} - 14 q^{38} + 8 q^{39} - 54 q^{40} - 3 q^{41} - 4 q^{42} - 33 q^{43} + 2 q^{44} + q^{45} - 26 q^{46} + 9 q^{47} - 39 q^{48} + 11 q^{49} + 4 q^{50} + 48 q^{51} - 31 q^{52} - 33 q^{53} + q^{54} - 21 q^{55} + 6 q^{57} - 55 q^{58} + 77 q^{59} - 6 q^{60} - 29 q^{61} - 46 q^{62} - 13 q^{63} + 24 q^{64} - 49 q^{65} + 35 q^{66} - 44 q^{67} - 45 q^{68} + 8 q^{69} + 4 q^{70} + 22 q^{71} - 6 q^{72} - 63 q^{73} - 16 q^{74} - 13 q^{75} - 46 q^{76} - 30 q^{77} - 17 q^{78} - 46 q^{79} - 14 q^{80} + 48 q^{81} - 75 q^{82} + 11 q^{83} + 38 q^{84} - q^{85} + 8 q^{86} - q^{87} - 116 q^{88} + 10 q^{89} - 20 q^{90} - 67 q^{91} - 64 q^{92} + 21 q^{93} - 16 q^{94} - 8 q^{95} + 3 q^{96} - 96 q^{97} - 46 q^{98} + 5 q^{99}+O(q^{100}) \) 48 * q - q^2 - 48 * q^3 + 45 * q^4 + q^5 + q^6 - 13 * q^7 - 6 * q^8 + 48 * q^9 - 20 * q^10 + 5 * q^11 - 45 * q^12 - 8 * q^13 + 4 * q^14 - q^15 + 39 * q^16 - 48 * q^17 - q^18 - 6 * q^19 + 6 * q^20 + 13 * q^21 - 35 * q^22 - 8 * q^23 + 6 * q^24 + 13 * q^25 + 17 * q^26 - 48 * q^27 - 38 * q^28 + q^29 + 20 * q^30 - 21 * q^31 - 3 * q^32 - 5 * q^33 + q^34 + 19 * q^35 + 45 * q^36 - 58 * q^37 - 14 * q^38 + 8 * q^39 - 54 * q^40 - 3 * q^41 - 4 * q^42 - 33 * q^43 + 2 * q^44 + q^45 - 26 * q^46 + 9 * q^47 - 39 * q^48 + 11 * q^49 + 4 * q^50 + 48 * q^51 - 31 * q^52 - 33 * q^53 + q^54 - 21 * q^55 + 6 * q^57 - 55 * q^58 + 77 * q^59 - 6 * q^60 - 29 * q^61 - 46 * q^62 - 13 * q^63 + 24 * q^64 - 49 * q^65 + 35 * q^66 - 44 * q^67 - 45 * q^68 + 8 * q^69 + 4 * q^70 + 22 * q^71 - 6 * q^72 - 63 * q^73 - 16 * q^74 - 13 * q^75 - 46 * q^76 - 30 * q^77 - 17 * q^78 - 46 * q^79 - 14 * q^80 + 48 * q^81 - 75 * q^82 + 11 * q^83 + 38 * q^84 - q^85 + 8 * q^86 - q^87 - 116 * q^88 + 10 * q^89 - 20 * q^90 - 67 * q^91 - 64 * q^92 + 21 * q^93 - 16 * q^94 - 8 * q^95 + 3 * q^96 - 96 * q^97 - 46 * q^98 + 5 * q^99

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