LMFDB - Embedded newform 8015.2.a.k.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, 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("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$1$
Dimension:	$49$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.56783 q^{2} +2.04149 q^{3} +0.458083 q^{4} -1.00000 q^{5} -3.20071 q^{6} -1.00000 q^{7} +2.41746 q^{8} +1.16770 q^{9} +O(q^{10})$	\(q-1.56783 q^{2} +2.04149 q^{3} +0.458083 q^{4} -1.00000 q^{5} -3.20071 q^{6} -1.00000 q^{7} +2.41746 q^{8} +1.16770 q^{9} +1.56783 q^{10} +0.485158 q^{11} +0.935174 q^{12} -4.20380 q^{13} +1.56783 q^{14} -2.04149 q^{15} -4.70633 q^{16} +1.01070 q^{17} -1.83075 q^{18} +3.38518 q^{19} -0.458083 q^{20} -2.04149 q^{21} -0.760645 q^{22} -0.531688 q^{23} +4.93523 q^{24} +1.00000 q^{25} +6.59083 q^{26} -3.74063 q^{27} -0.458083 q^{28} +6.97528 q^{29} +3.20071 q^{30} +6.52458 q^{31} +2.54379 q^{32} +0.990448 q^{33} -1.58461 q^{34} +1.00000 q^{35} +0.534904 q^{36} -6.79667 q^{37} -5.30739 q^{38} -8.58203 q^{39} -2.41746 q^{40} +3.44338 q^{41} +3.20071 q^{42} -3.61440 q^{43} +0.222243 q^{44} -1.16770 q^{45} +0.833595 q^{46} -11.2023 q^{47} -9.60794 q^{48} +1.00000 q^{49} -1.56783 q^{50} +2.06334 q^{51} -1.92569 q^{52} -2.64755 q^{53} +5.86466 q^{54} -0.485158 q^{55} -2.41746 q^{56} +6.91084 q^{57} -10.9360 q^{58} +0.439164 q^{59} -0.935174 q^{60} -2.39868 q^{61} -10.2294 q^{62} -1.16770 q^{63} +5.42443 q^{64} +4.20380 q^{65} -1.55285 q^{66} +8.51509 q^{67} +0.462985 q^{68} -1.08544 q^{69} -1.56783 q^{70} +11.3155 q^{71} +2.82287 q^{72} +2.88524 q^{73} +10.6560 q^{74} +2.04149 q^{75} +1.55070 q^{76} -0.485158 q^{77} +13.4551 q^{78} +10.4801 q^{79} +4.70633 q^{80} -11.1396 q^{81} -5.39862 q^{82} -11.7213 q^{83} -0.935174 q^{84} -1.01070 q^{85} +5.66676 q^{86} +14.2400 q^{87} +1.17285 q^{88} -10.2237 q^{89} +1.83075 q^{90} +4.20380 q^{91} -0.243557 q^{92} +13.3199 q^{93} +17.5633 q^{94} -3.38518 q^{95} +5.19313 q^{96} +18.2484 q^{97} -1.56783 q^{98} +0.566519 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9}+O(q^{10}) $ 49 * q - 3 * q^2 - 10 * q^3 + 49 * q^4 - 49 * q^5 + 10 * q^6 - 49 * q^7 - 6 * q^8 + 39 * q^9	\( 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9} + 3 q^{10} + 16 q^{11} - 26 q^{12} - 31 q^{13} + 3 q^{14} + 10 q^{15} + 49 q^{16} - 18 q^{17} + 4 q^{18} - 16 q^{19} - 49 q^{20} + 10 q^{21} + 10 q^{22} + 10 q^{23} + 2 q^{24} + 49 q^{25} - 22 q^{26} - 58 q^{27} - 49 q^{28} + 31 q^{29} - 10 q^{30} - 35 q^{31} - 5 q^{32} - 82 q^{33} - 41 q^{34} + 49 q^{35} + 49 q^{36} - 24 q^{37} - 20 q^{38} + 41 q^{39} + 6 q^{40} + 30 q^{41} - 10 q^{42} - 19 q^{43} + 27 q^{44} - 39 q^{45} + 15 q^{46} - 39 q^{47} - 51 q^{48} + 49 q^{49} - 3 q^{50} + 46 q^{51} - 94 q^{52} - 17 q^{53} + 9 q^{54} - 16 q^{55} + 6 q^{56} - 23 q^{57} - 46 q^{58} + 11 q^{59} + 26 q^{60} - 9 q^{61} - 49 q^{62} - 39 q^{63} + 10 q^{64} + 31 q^{65} - 10 q^{66} - 2 q^{67} - 73 q^{68} - 47 q^{69} - 3 q^{70} + 26 q^{71} - 39 q^{72} - 100 q^{73} + 8 q^{74} - 10 q^{75} - 71 q^{76} - 16 q^{77} - 51 q^{78} + 50 q^{79} - 49 q^{80} + 61 q^{81} - 36 q^{82} - 67 q^{83} + 26 q^{84} + 18 q^{85} + 33 q^{86} - 45 q^{87} - q^{88} - 19 q^{89} - 4 q^{90} + 31 q^{91} + 7 q^{92} + 9 q^{93} - 33 q^{94} + 16 q^{95} - 8 q^{96} - 85 q^{97} - 3 q^{98} + 27 q^{99}+O(q^{100}) \) 49 * q - 3 * q^2 - 10 * q^3 + 49 * q^4 - 49 * q^5 + 10 * q^6 - 49 * q^7 - 6 * q^8 + 39 * q^9 + 3 * q^10 + 16 * q^11 - 26 * q^12 - 31 * q^13 + 3 * q^14 + 10 * q^15 + 49 * q^16 - 18 * q^17 + 4 * q^18 - 16 * q^19 - 49 * q^20 + 10 * q^21 + 10 * q^22 + 10 * q^23 + 2 * q^24 + 49 * q^25 - 22 * q^26 - 58 * q^27 - 49 * q^28 + 31 * q^29 - 10 * q^30 - 35 * q^31 - 5 * q^32 - 82 * q^33 - 41 * q^34 + 49 * q^35 + 49 * q^36 - 24 * q^37 - 20 * q^38 + 41 * q^39 + 6 * q^40 + 30 * q^41 - 10 * q^42 - 19 * q^43 + 27 * q^44 - 39 * q^45 + 15 * q^46 - 39 * q^47 - 51 * q^48 + 49 * q^49 - 3 * q^50 + 46 * q^51 - 94 * q^52 - 17 * q^53 + 9 * q^54 - 16 * q^55 + 6 * q^56 - 23 * q^57 - 46 * q^58 + 11 * q^59 + 26 * q^60 - 9 * q^61 - 49 * q^62 - 39 * q^63 + 10 * q^64 + 31 * q^65 - 10 * q^66 - 2 * q^67 - 73 * q^68 - 47 * q^69 - 3 * q^70 + 26 * q^71 - 39 * q^72 - 100 * q^73 + 8 * q^74 - 10 * q^75 - 71 * q^76 - 16 * q^77 - 51 * q^78 + 50 * q^79 - 49 * q^80 + 61 * q^81 - 36 * q^82 - 67 * q^83 + 26 * q^84 + 18 * q^85 + 33 * q^86 - 45 * q^87 - q^88 - 19 * q^89 - 4 * q^90 + 31 * q^91 + 7 * q^92 + 9 * q^93 - 33 * q^94 + 16 * q^95 - 8 * q^96 - 85 * q^97 - 3 * q^98 + 27 * 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 $

$2$	−1.56783	−1.10862	−0.554311	−	0.832310i	$-0.687018\pi$
$2$	−1.56783	−1.10862	−0.554311	+	0.832310i	$0.687018\pi$
$3$	2.04149	1.17866	0.589329	−	0.807893i	$-0.299392\pi$
$3$	2.04149	1.17866	0.589329	+	0.807893i	$0.299392\pi$
$4$	0.458083	0.229042
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−3.20071	−1.30668
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.41746	0.854701
$9$	1.16770	0.389233
$10$	1.56783	0.495791
$11$	0.485158	0.146281	0.0731404	−	0.997322i	$-0.476698\pi$
$11$	0.485158	0.146281	0.0731404	+	0.997322i	$0.476698\pi$
$12$	0.935174	0.269962
$13$	−4.20380	−1.16592	−0.582962	−	0.812500i	$-0.698106\pi$
$13$	−4.20380	−1.16592	−0.582962	+	0.812500i	$0.698106\pi$
$14$	1.56783	0.419020
$15$	−2.04149	−0.527112
$16$	−4.70633	−1.17658
$17$	1.01070	0.245131	0.122566	−	0.992460i	$-0.460888\pi$
$17$	1.01070	0.245131	0.122566	+	0.992460i	$0.460888\pi$
$18$	−1.83075	−0.431512
$19$	3.38518	0.776615	0.388307	−	0.921530i	$-0.373060\pi$
$19$	3.38518	0.776615	0.388307	+	0.921530i	$0.373060\pi$
$20$	−0.458083	−0.102431
$21$	−2.04149	−0.445491
$22$	−0.760645	−0.162170
$23$	−0.531688	−0.110865	−0.0554323	−	0.998462i	$-0.517654\pi$
$23$	−0.531688	−0.110865	−0.0554323	+	0.998462i	$0.517654\pi$
$24$	4.93523	1.00740
$25$	1.00000	0.200000
$26$	6.59083	1.29257
$27$	−3.74063	−0.719885
$28$	−0.458083	−0.0865696
$29$	6.97528	1.29528	0.647639	−	0.761947i	$-0.275757\pi$
$29$	6.97528	1.29528	0.647639	+	0.761947i	$0.275757\pi$
$30$	3.20071	0.584367
$31$	6.52458	1.17185	0.585925	−	0.810366i	$-0.300731\pi$
$31$	6.52458	1.17185	0.585925	+	0.810366i	$0.300731\pi$
$32$	2.54379	0.449683
$33$	0.990448	0.172415
$34$	−1.58461	−0.271758
$35$	1.00000	0.169031
$36$	0.534904	0.0891506
$37$	−6.79667	−1.11737	−0.558683	−	0.829382i	$-0.688693\pi$
$37$	−6.79667	−1.11737	−0.558683	+	0.829382i	$0.688693\pi$
$38$	−5.30739	−0.860972
$39$	−8.58203	−1.37422
$40$	−2.41746	−0.382234
$41$	3.44338	0.537765	0.268883	−	0.963173i	$-0.413346\pi$
$41$	3.44338	0.537765	0.268883	+	0.963173i	$0.413346\pi$
$42$	3.20071	0.493880
$43$	−3.61440	−0.551191	−0.275595	−	0.961274i	$-0.588875\pi$
$43$	−3.61440	−0.551191	−0.275595	+	0.961274i	$0.588875\pi$
$44$	0.222243	0.0335044
$45$	−1.16770	−0.174070
$46$	0.833595	0.122907
$47$	−11.2023	−1.63402	−0.817011	−	0.576622i	$-0.804370\pi$
$47$	−11.2023	−1.63402	−0.817011	+	0.576622i	$0.804370\pi$
$48$	−9.60794	−1.38679
$49$	1.00000	0.142857
$50$	−1.56783	−0.221724
$51$	2.06334	0.288926
$52$	−1.92569	−0.267045
$53$	−2.64755	−0.363669	−0.181834	−	0.983329i	$-0.558203\pi$
$53$	−2.64755	−0.363669	−0.181834	+	0.983329i	$0.558203\pi$
$54$	5.86466	0.798080
$55$	−0.485158	−0.0654187
$56$	−2.41746	−0.323047
$57$	6.91084	0.915362
$58$	−10.9360	−1.43597
$59$	0.439164	0.0571743	0.0285872	−	0.999591i	$-0.490899\pi$
$59$	0.439164	0.0571743	0.0285872	+	0.999591i	$0.490899\pi$
$60$	−0.935174	−0.120731
$61$	−2.39868	−0.307119	−0.153559	−	0.988139i	$-0.549074\pi$
$61$	−2.39868	−0.307119	−0.153559	+	0.988139i	$0.549074\pi$
$62$	−10.2294	−1.29914
$63$	−1.16770	−0.147116
$64$	5.42443	0.678054
$65$	4.20380	0.521417
$66$	−1.55285	−0.191143
$67$	8.51509	1.04028	0.520142	−	0.854080i	$-0.325879\pi$
$67$	8.51509	1.04028	0.520142	+	0.854080i	$0.325879\pi$
$68$	0.462985	0.0561452
$69$	−1.08544	−0.130671
$70$	−1.56783	−0.187391
$71$	11.3155	1.34290	0.671452	−	0.741048i	$-0.265671\pi$
$71$	11.3155	1.34290	0.671452	+	0.741048i	$0.265671\pi$
$72$	2.82287	0.332678
$73$	2.88524	0.337691	0.168846	−	0.985643i	$-0.445996\pi$
$73$	2.88524	0.337691	0.168846	+	0.985643i	$0.445996\pi$
$74$	10.6560	1.23874
$75$	2.04149	0.235731
$76$	1.55070	0.177877
$77$	−0.485158	−0.0552889
$78$	13.4551	1.52349
$79$	10.4801	1.17910	0.589552	−	0.807730i	$-0.299304\pi$
$79$	10.4801	1.17910	0.589552	+	0.807730i	$0.299304\pi$
$80$	4.70633	0.526183
$81$	−11.1396	−1.23773
$82$	−5.39862	−0.596178
$83$	−11.7213	−1.28658	−0.643289	−	0.765623i	$-0.722431\pi$
$83$	−11.7213	−1.28658	−0.643289	+	0.765623i	$0.722431\pi$
$84$	−0.935174	−0.102036
$85$	−1.01070	−0.109626
$86$	5.66676	0.611062
$87$	14.2400	1.52669
$88$	1.17285	0.125026
$89$	−10.2237	−1.08371	−0.541855	−	0.840472i	$-0.682278\pi$
$89$	−10.2237	−1.08371	−0.541855	+	0.840472i	$0.682278\pi$
$90$	1.83075	0.192978
$91$	4.20380	0.440677
$92$	−0.243557	−0.0253926
$93$	13.3199	1.38121
$94$	17.5633	1.81151
$95$	−3.38518	−0.347313
$96$	5.19313	0.530022
$97$	18.2484	1.85285	0.926425	−	0.376480i	$-0.122866\pi$
$97$	18.2484	1.85285	0.926425	+	0.376480i	$0.122866\pi$
$98$	−1.56783	−0.158374
$99$	0.566519	0.0569373
$100$	0.458083	0.0458083
$101$	−10.0661	−1.00162	−0.500808	−	0.865558i	$-0.666964\pi$
$101$	−10.0661	−1.00162	−0.500808	+	0.865558i	$0.666964\pi$
$102$	−3.23496	−0.320309
$103$	−2.83657	−0.279495	−0.139748	−	0.990187i	$-0.544629\pi$
$103$	−2.83657	−0.279495	−0.139748	+	0.990187i	$0.544629\pi$
$104$	−10.1625	−0.996516
$105$	2.04149	0.199229
$106$	4.15090	0.403171
$107$	−14.6258	−1.41393	−0.706966	−	0.707248i	$-0.749936\pi$
$107$	−14.6258	−1.41393	−0.706966	+	0.707248i	$0.749936\pi$
$108$	−1.71352	−0.164884
$109$	5.93355	0.568331	0.284166	−	0.958775i	$-0.408283\pi$
$109$	5.93355	0.568331	0.284166	+	0.958775i	$0.408283\pi$
$110$	0.760645	0.0725246
$111$	−13.8754	−1.31699
$112$	4.70633	0.444706
$113$	4.89834	0.460797	0.230398	−	0.973096i	$-0.425997\pi$
$113$	4.89834	0.460797	0.230398	+	0.973096i	$0.425997\pi$
$114$	−10.8350	−1.01479
$115$	0.531688	0.0495802
$116$	3.19526	0.296672
$117$	−4.90877	−0.453816
$118$	−0.688534	−0.0633847
$119$	−1.01070	−0.0926509
$120$	−4.93523	−0.450523
$121$	−10.7646	−0.978602
$122$	3.76071	0.340479
$123$	7.02964	0.633841
$124$	2.98880	0.268402
$125$	−1.00000	−0.0894427
$126$	1.83075	0.163096
$127$	−4.07483	−0.361583	−0.180791	−	0.983521i	$-0.557866\pi$
$127$	−4.07483	−0.361583	−0.180791	+	0.983521i	$0.557866\pi$
$128$	−13.5921	−1.20139
$129$	−7.37878	−0.649665
$130$	−6.59083	−0.578054
$131$	−2.49224	−0.217748	−0.108874	−	0.994056i	$-0.534725\pi$
$131$	−2.49224	−0.217748	−0.108874	+	0.994056i	$0.534725\pi$
$132$	0.453708	0.0394902
$133$	−3.38518	−0.293533
$134$	−13.3502	−1.15328
$135$	3.74063	0.321942
$136$	2.44333	0.209514
$137$	−6.48873	−0.554369	−0.277185	−	0.960817i	$-0.589401\pi$
$137$	−6.48873	−0.554369	−0.277185	+	0.960817i	$0.589401\pi$
$138$	1.70178	0.144865
$139$	11.4438	0.970651	0.485326	−	0.874333i	$-0.338701\pi$
$139$	11.4438	0.970651	0.485326	+	0.874333i	$0.338701\pi$
$140$	0.458083	0.0387151
$141$	−22.8694	−1.92595
$142$	−17.7408	−1.48877
$143$	−2.03951	−0.170552
$144$	−5.49558	−0.457965
$145$	−6.97528	−0.579266
$146$	−4.52355	−0.374372
$147$	2.04149	0.168380
$148$	−3.11344	−0.255923
$149$	−4.49453	−0.368207	−0.184103	−	0.982907i	$-0.558938\pi$
$149$	−4.49453	−0.368207	−0.184103	+	0.982907i	$0.558938\pi$
$150$	−3.20071	−0.261337
$151$	−10.0634	−0.818951	−0.409475	−	0.912321i	$-0.634288\pi$
$151$	−10.0634	−0.818951	−0.409475	+	0.912321i	$0.634288\pi$
$152$	8.18355	0.663773
$153$	1.18020	0.0954132
$154$	0.760645	0.0612945
$155$	−6.52458	−0.524067
$156$	−3.93128	−0.314754
$157$	13.4839	1.07613	0.538067	−	0.842902i	$-0.319155\pi$
$157$	13.4839	1.07613	0.538067	+	0.842902i	$0.319155\pi$
$158$	−16.4310	−1.30718
$159$	−5.40496	−0.428641
$160$	−2.54379	−0.201104
$161$	0.531688	0.0419029
$162$	17.4649	1.37217
$163$	−15.2171	−1.19190	−0.595949	−	0.803022i	$-0.703224\pi$
$163$	−15.2171	−1.19190	−0.595949	+	0.803022i	$0.703224\pi$
$164$	1.57735	0.123171
$165$	−0.990448	−0.0771063
$166$	18.3770	1.42633
$167$	6.49055	0.502254	0.251127	−	0.967954i	$-0.419199\pi$
$167$	6.49055	0.502254	0.251127	+	0.967954i	$0.419199\pi$
$168$	−4.93523	−0.380761
$169$	4.67190	0.359377
$170$	1.58461	0.121534
$171$	3.95288	0.302284
$172$	−1.65570	−0.126246
$173$	−9.95548	−0.756901	−0.378450	−	0.925622i	$-0.623543\pi$
$173$	−9.95548	−0.756901	−0.378450	+	0.925622i	$0.623543\pi$
$174$	−22.3259	−1.69252
$175$	−1.00000	−0.0755929
$176$	−2.28331	−0.172111
$177$	0.896552	0.0673890
$178$	16.0290	1.20142
$179$	1.15409	0.0862606	0.0431303	−	0.999069i	$-0.486267\pi$
$179$	1.15409	0.0862606	0.0431303	+	0.999069i	$0.486267\pi$
$180$	−0.534904	−0.0398694
$181$	−9.96926	−0.741009	−0.370504	−	0.928831i	$-0.620815\pi$
$181$	−9.96926	−0.741009	−0.370504	+	0.928831i	$0.620815\pi$
$182$	−6.59083	−0.488545
$183$	−4.89688	−0.361988
$184$	−1.28533	−0.0947561
$185$	6.79667	0.499701
$186$	−20.8833	−1.53124
$187$	0.490350	0.0358580
$188$	−5.13158	−0.374259
$189$	3.74063	0.272091
$190$	5.30739	0.385038
$191$	11.3080	0.818216	0.409108	−	0.912486i	$-0.365840\pi$
$191$	11.3080	0.818216	0.409108	+	0.912486i	$0.365840\pi$
$192$	11.0739	0.799193
$193$	−24.2215	−1.74350	−0.871749	−	0.489952i	$-0.837014\pi$
$193$	−24.2215	−1.74350	−0.871749	+	0.489952i	$0.837014\pi$
$194$	−28.6104	−2.05411
$195$	8.58203	0.614572
$196$	0.458083	0.0327202
$197$	13.1653	0.937987	0.468994	−	0.883202i	$-0.344617\pi$
$197$	13.1653	0.937987	0.468994	+	0.883202i	$0.344617\pi$
$198$	−0.888205	−0.0631220
$199$	−2.18877	−0.155158	−0.0775788	−	0.996986i	$-0.524719\pi$
$199$	−2.18877	−0.155158	−0.0775788	+	0.996986i	$0.524719\pi$
$200$	2.41746	0.170940
$201$	17.3835	1.22614
$202$	15.7819	1.11041
$203$	−6.97528	−0.489569
$204$	0.945182	0.0661760
$205$	−3.44338	−0.240496
$206$	4.44725	0.309854
$207$	−0.620852	−0.0431522
$208$	19.7844	1.37180
$209$	1.64235	0.113604
$210$	−3.20071	−0.220870
$211$	−10.0553	−0.692236	−0.346118	−	0.938191i	$-0.612500\pi$
$211$	−10.0553	−0.692236	−0.346118	+	0.938191i	$0.612500\pi$
$212$	−1.21280	−0.0832953
$213$	23.1006	1.58282
$214$	22.9308	1.56751
$215$	3.61440	0.246500
$216$	−9.04282	−0.615286
$217$	−6.52458	−0.442917
$218$	−9.30279	−0.630064
$219$	5.89019	0.398022
$220$	−0.222243	−0.0149836
$221$	−4.24878	−0.285804
$222$	21.7542	1.46004
$223$	−14.9318	−0.999907	−0.499954	−	0.866052i	$-0.666650\pi$
$223$	−14.9318	−0.999907	−0.499954	+	0.866052i	$0.666650\pi$
$224$	−2.54379	−0.169964
$225$	1.16770	0.0778467
$226$	−7.67975	−0.510849
$227$	8.63005	0.572796	0.286398	−	0.958111i	$-0.407542\pi$
$227$	8.63005	0.572796	0.286398	+	0.958111i	$0.407542\pi$
$228$	3.16574	0.209656
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	−0.833595	−0.0549656
$231$	−0.990448	−0.0651667
$232$	16.8625	1.10708
$233$	−8.14435	−0.533554	−0.266777	−	0.963758i	$-0.585959\pi$
$233$	−8.14435	−0.533554	−0.266777	+	0.963758i	$0.585959\pi$
$234$	7.69611	0.503110
$235$	11.2023	0.730757
$236$	0.201174	0.0130953
$237$	21.3951	1.38976
$238$	1.58461	0.102715
$239$	14.5148	0.938882	0.469441	−	0.882964i	$-0.344455\pi$
$239$	14.5148	0.938882	0.469441	+	0.882964i	$0.344455\pi$
$240$	9.60794	0.620190
$241$	−24.2207	−1.56019	−0.780096	−	0.625660i	$-0.784830\pi$
$241$	−24.2207	−1.56019	−0.780096	+	0.625660i	$0.784830\pi$
$242$	16.8771	1.08490
$243$	−11.5195	−0.738976
$244$	−1.09879	−0.0703430
$245$	−1.00000	−0.0638877
$246$	−11.0213	−0.702690
$247$	−14.2306	−0.905473
$248$	15.7729	1.00158
$249$	−23.9289	−1.51644
$250$	1.56783	0.0991581
$251$	−19.8821	−1.25495	−0.627474	−	0.778638i	$-0.715911\pi$
$251$	−19.8821	−1.25495	−0.627474	+	0.778638i	$0.715911\pi$
$252$	−0.534904	−0.0336958
$253$	−0.257953	−0.0162174
$254$	6.38864	0.400859
$255$	−2.06334	−0.129211
$256$	10.4613	0.653830
$257$	−11.6440	−0.726334	−0.363167	−	0.931724i	$-0.618305\pi$
$257$	−11.6440	−0.726334	−0.363167	+	0.931724i	$0.618305\pi$
$258$	11.5686	0.720233
$259$	6.79667	0.422324
$260$	1.92569	0.119426
$261$	8.14504	0.504165
$262$	3.90741	0.241400
$263$	12.8775	0.794058	0.397029	−	0.917806i	$-0.370041\pi$
$263$	12.8775	0.794058	0.397029	+	0.917806i	$0.370041\pi$
$264$	2.39437	0.147363
$265$	2.64755	0.162638
$266$	5.30739	0.325417
$267$	−20.8716	−1.27732
$268$	3.90062	0.238268
$269$	3.61739	0.220556	0.110278	−	0.993901i	$-0.464826\pi$
$269$	3.61739	0.220556	0.110278	+	0.993901i	$0.464826\pi$
$270$	−5.86466	−0.356912
$271$	−6.71319	−0.407797	−0.203899	−	0.978992i	$-0.565361\pi$
$271$	−6.71319	−0.407797	−0.203899	+	0.978992i	$0.565361\pi$
$272$	−4.75669	−0.288417
$273$	8.58203	0.519408
$274$	10.1732	0.614586
$275$	0.485158	0.0292561
$276$	−0.497221	−0.0299292
$277$	16.8846	1.01449	0.507247	−	0.861801i	$-0.330663\pi$
$277$	16.8846	1.01449	0.507247	+	0.861801i	$0.330663\pi$
$278$	−17.9419	−1.07608
$279$	7.61875	0.456123
$280$	2.41746	0.144471
$281$	−13.1112	−0.782151	−0.391075	−	0.920359i	$-0.627897\pi$
$281$	−13.1112	−0.782151	−0.391075	+	0.920359i	$0.627897\pi$
$282$	35.8553	2.13515
$283$	−10.4717	−0.622477	−0.311238	−	0.950332i	$-0.600744\pi$
$283$	−10.4717	−0.622477	−0.311238	+	0.950332i	$0.600744\pi$
$284$	5.18345	0.307581
$285$	−6.91084	−0.409363
$286$	3.19759	0.189078
$287$	−3.44338	−0.203256
$288$	2.97038	0.175031
$289$	−15.9785	−0.939911
$290$	10.9360	0.642186
$291$	37.2541	2.18387
$292$	1.32168	0.0773454
$293$	−6.19984	−0.362199	−0.181099	−	0.983465i	$-0.557966\pi$
$293$	−6.19984	−0.362199	−0.181099	+	0.983465i	$0.557966\pi$
$294$	−3.20071	−0.186669
$295$	−0.439164	−0.0255691
$296$	−16.4307	−0.955013
$297$	−1.81480	−0.105305
$298$	7.04665	0.408202
$299$	2.23511	0.129260
$300$	0.935174	0.0539923
$301$	3.61440	0.208331
$302$	15.7777	0.907906
$303$	−20.5499	−1.18056
$304$	−15.9318	−0.913750
$305$	2.39868	0.137348
$306$	−1.85034	−0.105777
$307$	−28.9005	−1.64944	−0.824719	−	0.565543i	$-0.808667\pi$
$307$	−28.9005	−1.64944	−0.824719	+	0.565543i	$0.808667\pi$
$308$	−0.222243	−0.0126635
$309$	−5.79084	−0.329429
$310$	10.2294	0.580992
$311$	13.1739	0.747026	0.373513	−	0.927625i	$-0.378153\pi$
$311$	13.1739	0.747026	0.373513	+	0.927625i	$0.378153\pi$
$312$	−20.7467	−1.17455
$313$	−1.32928	−0.0751354	−0.0375677	−	0.999294i	$-0.511961\pi$
$313$	−1.32928	−0.0751354	−0.0375677	+	0.999294i	$0.511961\pi$
$314$	−21.1405	−1.19303
$315$	1.16770	0.0657924
$316$	4.80076	0.270064
$317$	28.8070	1.61796	0.808981	−	0.587835i	$-0.200019\pi$
$317$	28.8070	1.61796	0.808981	+	0.587835i	$0.200019\pi$
$318$	8.47404	0.475201
$319$	3.38412	0.189474
$320$	−5.42443	−0.303235
$321$	−29.8585	−1.66654
$322$	−0.833595	−0.0464544
$323$	3.42141	0.190372
$324$	−5.10285	−0.283492
$325$	−4.20380	−0.233185
$326$	23.8578	1.32136
$327$	12.1133	0.669868
$328$	8.32423	0.459629
$329$	11.2023	0.617602
$330$	1.55285	0.0854817
$331$	−17.6905	−0.972359	−0.486180	−	0.873859i	$-0.661610\pi$
$331$	−17.6905	−0.972359	−0.486180	+	0.873859i	$0.661610\pi$
$332$	−5.36933	−0.294680
$333$	−7.93647	−0.434916
$334$	−10.1761	−0.556810
$335$	−8.51509	−0.465229
$336$	9.60794	0.524156
$337$	−15.6388	−0.851900	−0.425950	−	0.904747i	$-0.640060\pi$
$337$	−15.6388	−0.851900	−0.425950	+	0.904747i	$0.640060\pi$
$338$	−7.32473	−0.398413
$339$	9.99993	0.543122
$340$	−0.462985	−0.0251089
$341$	3.16545	0.171419
$342$	−6.19743	−0.335119
$343$	−1.00000	−0.0539949
$344$	−8.73766	−0.471103
$345$	1.08544	0.0584380
$346$	15.6085	0.839117
$347$	−8.13055	−0.436471	−0.218235	−	0.975896i	$-0.570030\pi$
$347$	−8.13055	−0.436471	−0.218235	+	0.975896i	$0.570030\pi$
$348$	6.52311	0.349675
$349$	14.5529	0.778998	0.389499	−	0.921027i	$-0.372648\pi$
$349$	14.5529	0.778998	0.389499	+	0.921027i	$0.372648\pi$
$350$	1.56783	0.0838039
$351$	15.7248	0.839330
$352$	1.23414	0.0657799
$353$	−30.9556	−1.64760	−0.823799	−	0.566882i	$-0.808150\pi$
$353$	−30.9556	−1.64760	−0.823799	+	0.566882i	$0.808150\pi$
$354$	−1.40564	−0.0747088
$355$	−11.3155	−0.600565
$356$	−4.68331	−0.248215
$357$	−2.06334	−0.109204
$358$	−1.80941	−0.0956304
$359$	−4.84944	−0.255943	−0.127972	−	0.991778i	$-0.540847\pi$
$359$	−4.84944	−0.255943	−0.127972	+	0.991778i	$0.540847\pi$
$360$	−2.82287	−0.148778
$361$	−7.54053	−0.396870
$362$	15.6301	0.821498
$363$	−21.9759	−1.15344
$364$	1.92569	0.100933
$365$	−2.88524	−0.151020
$366$	7.67747	0.401308
$367$	0.111263	0.00580786	0.00290393	−	0.999996i	$-0.499076\pi$
$367$	0.111263	0.00580786	0.00290393	+	0.999996i	$0.499076\pi$
$368$	2.50230	0.130441
$369$	4.02083	0.209316
$370$	−10.6560	−0.553979
$371$	2.64755	0.137454
$372$	6.10162	0.316354
$373$	−0.962881	−0.0498561	−0.0249281	−	0.999689i	$-0.507936\pi$
$373$	−0.962881	−0.0498561	−0.0249281	+	0.999689i	$0.507936\pi$
$374$	−0.768785	−0.0397529
$375$	−2.04149	−0.105422
$376$	−27.0811	−1.39660
$377$	−29.3227	−1.51019
$378$	−5.86466	−0.301646
$379$	−18.5874	−0.954771	−0.477385	−	0.878694i	$-0.658415\pi$
$379$	−18.5874	−0.954771	−0.477385	+	0.878694i	$0.658415\pi$
$380$	−1.55070	−0.0795490
$381$	−8.31875	−0.426182
$382$	−17.7290	−0.907092
$383$	31.1695	1.59269	0.796344	−	0.604844i	$-0.206764\pi$
$383$	31.1695	1.59269	0.796344	+	0.604844i	$0.206764\pi$
$384$	−27.7483	−1.41602
$385$	0.485158	0.0247260
$386$	37.9751	1.93288
$387$	−4.22053	−0.214542
$388$	8.35931	0.424380
$389$	13.5858	0.688827	0.344413	−	0.938818i	$-0.388078\pi$
$389$	13.5858	0.688827	0.344413	+	0.938818i	$0.388078\pi$
$390$	−13.4551	−0.681327
$391$	−0.537378	−0.0271764
$392$	2.41746	0.122100
$393$	−5.08790	−0.256651
$394$	−20.6409	−1.03987
$395$	−10.4801	−0.527312
$396$	0.259513	0.0130410
$397$	−24.2835	−1.21875	−0.609376	−	0.792881i	$-0.708580\pi$
$397$	−24.2835	−1.21875	−0.609376	+	0.792881i	$0.708580\pi$
$398$	3.43161	0.172011
$399$	−6.91084	−0.345975
$400$	−4.70633	−0.235316
$401$	−9.48475	−0.473646	−0.236823	−	0.971553i	$-0.576106\pi$
$401$	−9.48475	−0.473646	−0.236823	+	0.971553i	$0.576106\pi$
$402$	−27.2544	−1.35932
$403$	−27.4280	−1.36629
$404$	−4.61112	−0.229412
$405$	11.1396	0.553530
$406$	10.9360	0.542747
$407$	−3.29746	−0.163449
$408$	4.98805	0.246945
$409$	−0.438667	−0.0216907	−0.0108453	−	0.999941i	$-0.503452\pi$
$409$	−0.438667	−0.0216907	−0.0108453	+	0.999941i	$0.503452\pi$
$410$	5.39862	0.266619
$411$	−13.2467	−0.653411
$412$	−1.29938	−0.0640160
$413$	−0.439164	−0.0216099
$414$	0.973389	0.0478395
$415$	11.7213	0.575375
$416$	−10.6936	−0.524295
$417$	23.3625	1.14407
$418$	−2.57492	−0.125944
$419$	−14.8333	−0.724654	−0.362327	−	0.932051i	$-0.618018\pi$
$419$	−14.8333	−0.724654	−0.362327	+	0.932051i	$0.618018\pi$
$420$	0.935174	0.0456318
$421$	27.6751	1.34880	0.674401	−	0.738366i	$-0.264402\pi$
$421$	27.6751	1.34880	0.674401	+	0.738366i	$0.264402\pi$
$422$	15.7650	0.767427
$423$	−13.0809	−0.636016
$424$	−6.40034	−0.310828
$425$	1.01070	0.0490262
$426$	−36.2177	−1.75475
$427$	2.39868	0.116080
$428$	−6.69984	−0.323849
$429$	−4.16364	−0.201022
$430$	−5.66676	−0.273275
$431$	−9.75752	−0.470003	−0.235002	−	0.971995i	$-0.575510\pi$
$431$	−9.75752	−0.470003	−0.235002	+	0.971995i	$0.575510\pi$
$432$	17.6046	0.847003
$433$	−13.3673	−0.642390	−0.321195	−	0.947013i	$-0.604085\pi$
$433$	−13.3673	−0.642390	−0.321195	+	0.947013i	$0.604085\pi$
$434$	10.2294	0.491028
$435$	−14.2400	−0.682756
$436$	2.71806	0.130171
$437$	−1.79986	−0.0860991
$438$	−9.23481	−0.441256
$439$	2.78889	0.133107	0.0665533	−	0.997783i	$-0.478800\pi$
$439$	2.78889	0.133107	0.0665533	+	0.997783i	$0.478800\pi$
$440$	−1.17285	−0.0559135
$441$	1.16770	0.0556048
$442$	6.66136	0.316848
$443$	7.22852	0.343437	0.171719	−	0.985146i	$-0.445068\pi$
$443$	7.22852	0.343437	0.171719	+	0.985146i	$0.445068\pi$
$444$	−6.35607	−0.301646
$445$	10.2237	0.484650
$446$	23.4105	1.10852
$447$	−9.17557	−0.433989
$448$	−5.42443	−0.256280
$449$	36.6399	1.72914	0.864572	−	0.502509i	$-0.167590\pi$
$449$	36.6399	1.72914	0.864572	+	0.502509i	$0.167590\pi$
$450$	−1.83075	−0.0863025
$451$	1.67058	0.0786647
$452$	2.24385	0.105542
$453$	−20.5444	−0.965262
$454$	−13.5304	−0.635014
$455$	−4.20380	−0.197077
$456$	16.7067	0.782361
$457$	−17.2427	−0.806579	−0.403290	−	0.915072i	$-0.632133\pi$
$457$	−17.2427	−0.806579	−0.403290	+	0.915072i	$0.632133\pi$
$458$	1.56783	0.0732598
$459$	−3.78066	−0.176466
$460$	0.243557	0.0113559
$461$	6.51157	0.303274	0.151637	−	0.988436i	$-0.451546\pi$
$461$	6.51157	0.303274	0.151637	+	0.988436i	$0.451546\pi$
$462$	1.55285	0.0722452
$463$	−6.06605	−0.281913	−0.140957	−	0.990016i	$-0.545018\pi$
$463$	−6.06605	−0.281913	−0.140957	+	0.990016i	$0.545018\pi$
$464$	−32.8280	−1.52400
$465$	−13.3199	−0.617695
$466$	12.7689	0.591510
$467$	26.6825	1.23472	0.617360	−	0.786681i	$-0.288202\pi$
$467$	26.6825	1.23472	0.617360	+	0.786681i	$0.288202\pi$
$468$	−2.24863	−0.103943
$469$	−8.51509	−0.393190
$470$	−17.5633	−0.810133
$471$	27.5274	1.26839
$472$	1.06166	0.0488670
$473$	−1.75356	−0.0806286
$474$	−33.5438	−1.54072
$475$	3.38518	0.155323
$476$	−0.462985	−0.0212209
$477$	−3.09154	−0.141552
$478$	−22.7566	−1.04086
$479$	−0.125562	−0.00573706	−0.00286853	−	0.999996i	$-0.500913\pi$
$479$	−0.125562	−0.00573706	−0.00286853	+	0.999996i	$0.500913\pi$
$480$	−5.19313	−0.237033
$481$	28.5718	1.30276
$482$	37.9738	1.72966
$483$	1.08544	0.0493892
$484$	−4.93109	−0.224141
$485$	−18.2484	−0.828619
$486$	18.0606	0.819245
$487$	−34.6972	−1.57228	−0.786141	−	0.618047i	$-0.787924\pi$
$487$	−34.6972	−1.57228	−0.786141	+	0.618047i	$0.787924\pi$
$488$	−5.79870	−0.262495
$489$	−31.0657	−1.40484
$490$	1.56783	0.0708272
$491$	−7.21307	−0.325521	−0.162761	−	0.986666i	$-0.552040\pi$
$491$	−7.21307	−0.325521	−0.162761	+	0.986666i	$0.552040\pi$
$492$	3.22016	0.145176
$493$	7.04993	0.317513
$494$	22.3112	1.00383
$495$	−0.566519	−0.0254631
$496$	−30.7068	−1.37878
$497$	−11.3155	−0.507570
$498$	37.5165	1.68115
$499$	−29.5254	−1.32174	−0.660869	−	0.750502i	$-0.729812\pi$
$499$	−29.5254	−1.32174	−0.660869	+	0.750502i	$0.729812\pi$
$500$	−0.458083	−0.0204861
$501$	13.2504	0.591986
$502$	31.1717	1.39126
$503$	−32.3507	−1.44244	−0.721222	−	0.692704i	$-0.756419\pi$
$503$	−32.3507	−1.44244	−0.721222	+	0.692704i	$0.756419\pi$
$504$	−2.82287	−0.125741
$505$	10.0661	0.447937
$506$	0.404426	0.0179789
$507$	9.53765	0.423582
$508$	−1.86661	−0.0828175
$509$	13.3805	0.593079	0.296539	−	0.955021i	$-0.404167\pi$
$509$	13.3805	0.593079	0.296539	+	0.955021i	$0.404167\pi$
$510$	3.23496	0.143247
$511$	−2.88524	−0.127635
$512$	10.7828	0.476537
$513$	−12.6627	−0.559073
$514$	18.2558	0.805230
$515$	2.83657	0.124994
$516$	−3.38009	−0.148800
$517$	−5.43488	−0.239026
$518$	−10.6560	−0.468198
$519$	−20.3241	−0.892127
$520$	10.1625	0.445655
$521$	−40.3448	−1.76754	−0.883770	−	0.467922i	$-0.845003\pi$
$521$	−40.3448	−1.76754	−0.883770	+	0.467922i	$0.845003\pi$
$522$	−12.7700	−0.558928
$523$	−15.4935	−0.677482	−0.338741	−	0.940880i	$-0.610001\pi$
$523$	−15.4935	−0.677482	−0.338741	+	0.940880i	$0.610001\pi$
$524$	−1.14165	−0.0498734
$525$	−2.04149	−0.0890981
$526$	−20.1896	−0.880309
$527$	6.59440	0.287257
$528$	−4.66137	−0.202860
$529$	−22.7173	−0.987709
$530$	−4.15090	−0.180304
$531$	0.512812	0.0222542
$532$	−1.55070	−0.0672312
$533$	−14.4753	−0.626993
$534$	32.7231	1.41607
$535$	14.6258	0.632329
$536$	20.5849	0.889132
$537$	2.35607	0.101672
$538$	−5.67145	−0.244513
$539$	0.485158	0.0208972
$540$	1.71352	0.0737382
$541$	22.0471	0.947881	0.473940	−	0.880557i	$-0.342831\pi$
$541$	22.0471	0.947881	0.473940	+	0.880557i	$0.342831\pi$
$542$	10.5251	0.452093
$543$	−20.3522	−0.873396
$544$	2.57101	0.110231
$545$	−5.93355	−0.254165
$546$	−13.4551	−0.575827
$547$	1.64795	0.0704612	0.0352306	−	0.999379i	$-0.488783\pi$
$547$	1.64795	0.0704612	0.0352306	+	0.999379i	$0.488783\pi$
$548$	−2.97238	−0.126974
$549$	−2.80093	−0.119541
$550$	−0.760645	−0.0324340
$551$	23.6126	1.00593
$552$	−2.62400	−0.111685
$553$	−10.4801	−0.445660
$554$	−26.4721	−1.12469
$555$	13.8754	0.588976
$556$	5.24222	0.222320
$557$	33.3560	1.41334	0.706668	−	0.707545i	$-0.250197\pi$
$557$	33.3560	1.41334	0.706668	+	0.707545i	$0.250197\pi$
$558$	−11.9449	−0.505667
$559$	15.1942	0.642646
$560$	−4.70633	−0.198879
$561$	1.00105	0.0422643
$562$	20.5562	0.867109
$563$	14.5694	0.614028	0.307014	−	0.951705i	$-0.400670\pi$
$563$	14.5694	0.614028	0.307014	+	0.951705i	$0.400670\pi$
$564$	−10.4761	−0.441123
$565$	−4.89834	−0.206075
$566$	16.4178	0.690091
$567$	11.1396	0.467818
$568$	27.3548	1.14778
$569$	10.6347	0.445831	0.222916	−	0.974838i	$-0.428443\pi$
$569$	10.6347	0.445831	0.222916	+	0.974838i	$0.428443\pi$
$570$	10.8350	0.453828
$571$	9.33318	0.390581	0.195291	−	0.980745i	$-0.437435\pi$
$571$	9.33318	0.390581	0.195291	+	0.980745i	$0.437435\pi$
$572$	−0.934264	−0.0390635
$573$	23.0852	0.964397
$574$	5.39862	0.225334
$575$	−0.531688	−0.0221729
$576$	6.33411	0.263921
$577$	24.6951	1.02807	0.514036	−	0.857769i	$-0.328150\pi$
$577$	24.6951	1.02807	0.514036	+	0.857769i	$0.328150\pi$
$578$	25.0515	1.04201
$579$	−49.4480	−2.05499
$580$	−3.19526	−0.132676
$581$	11.7213	0.486281
$582$	−58.4080	−2.42109
$583$	−1.28448	−0.0531977
$584$	6.97494	0.288625
$585$	4.90877	0.202953
$586$	9.72028	0.401541
$587$	−22.1419	−0.913896	−0.456948	−	0.889493i	$-0.651057\pi$
$587$	−22.1419	−0.913896	−0.456948	+	0.889493i	$0.651057\pi$
$588$	0.935174	0.0385659
$589$	22.0869	0.910075
$590$	0.688534	0.0283465
$591$	26.8768	1.10557
$592$	31.9873	1.31467
$593$	−6.03864	−0.247977	−0.123989	−	0.992284i	$-0.539569\pi$
$593$	−6.03864	−0.247977	−0.123989	+	0.992284i	$0.539569\pi$
$594$	2.84529	0.116744
$595$	1.01070	0.0414347
$596$	−2.05887	−0.0843346
$597$	−4.46836	−0.182878
$598$	−3.50426	−0.143300
$599$	−23.1189	−0.944612	−0.472306	−	0.881435i	$-0.656578\pi$
$599$	−23.1189	−0.944612	−0.472306	+	0.881435i	$0.656578\pi$
$600$	4.93523	0.201480
$601$	21.1000	0.860688	0.430344	−	0.902665i	$-0.358392\pi$
$601$	21.1000	0.860688	0.430344	+	0.902665i	$0.358392\pi$
$602$	−5.66676	−0.230960
$603$	9.94307	0.404913
$604$	−4.60989	−0.187574
$605$	10.7646	0.437644
$606$	32.2188	1.30880
$607$	−14.4345	−0.585878	−0.292939	−	0.956131i	$-0.594633\pi$
$607$	−14.4345	−0.585878	−0.292939	+	0.956131i	$0.594633\pi$
$608$	8.61119	0.349230
$609$	−14.2400	−0.577034
$610$	−3.76071	−0.152267
$611$	47.0921	1.90514
$612$	0.540628	0.0218536
$613$	−28.2316	−1.14026	−0.570131	−	0.821554i	$-0.693108\pi$
$613$	−28.2316	−1.14026	−0.570131	+	0.821554i	$0.693108\pi$
$614$	45.3110	1.82860
$615$	−7.02964	−0.283462
$616$	−1.17285	−0.0472555
$617$	−30.8031	−1.24008	−0.620042	−	0.784568i	$-0.712885\pi$
$617$	−30.8031	−1.24008	−0.620042	+	0.784568i	$0.712885\pi$
$618$	9.07903	0.365212
$619$	−35.7650	−1.43752	−0.718758	−	0.695260i	$-0.755289\pi$
$619$	−35.7650	−1.43752	−0.718758	+	0.695260i	$0.755289\pi$
$620$	−2.98880	−0.120033
$621$	1.98885	0.0798098
$622$	−20.6545	−0.828169
$623$	10.2237	0.409604
$624$	40.3898	1.61689
$625$	1.00000	0.0400000
$626$	2.08408	0.0832968
$627$	3.35285	0.133900
$628$	6.17676	0.246480
$629$	−6.86940	−0.273901
$630$	−1.83075	−0.0729389
$631$	−21.4178	−0.852629	−0.426315	−	0.904575i	$-0.640188\pi$
$631$	−21.4178	−0.852629	−0.426315	+	0.904575i	$0.640188\pi$
$632$	25.3353	1.00778
$633$	−20.5278	−0.815909
$634$	−45.1644	−1.79371
$635$	4.07483	0.161705
$636$	−2.47592	−0.0981766
$637$	−4.20380	−0.166560
$638$	−5.30571	−0.210055
$639$	13.2131	0.522703
$640$	13.5921	0.537277
$641$	18.9158	0.747131	0.373566	−	0.927604i	$-0.378135\pi$
$641$	18.9158	0.747131	0.373566	+	0.927604i	$0.378135\pi$
$642$	46.8130	1.84756
$643$	29.3478	1.15736	0.578681	−	0.815554i	$-0.303568\pi$
$643$	29.3478	1.15736	0.578681	+	0.815554i	$0.303568\pi$
$644$	0.243557	0.00959751
$645$	7.37878	0.290539
$646$	−5.36418	−0.211051
$647$	−18.0269	−0.708709	−0.354354	−	0.935111i	$-0.615299\pi$
$647$	−18.0269	−0.708709	−0.354354	+	0.935111i	$0.615299\pi$
$648$	−26.9295	−1.05789
$649$	0.213064	0.00836350
$650$	6.59083	0.258513
$651$	−13.3199	−0.522048
$652$	−6.97071	−0.272994
$653$	31.5094	1.23306	0.616529	−	0.787332i	$-0.288538\pi$
$653$	31.5094	1.23306	0.616529	+	0.787332i	$0.288538\pi$
$654$	−18.9916	−0.742630
$655$	2.49224	0.0973800
$656$	−16.2057	−0.632725
$657$	3.36909	0.131441
$658$	−17.5633	−0.684687
$659$	−40.0066	−1.55844	−0.779218	−	0.626752i	$-0.784384\pi$
$659$	−40.0066	−1.55844	−0.779218	+	0.626752i	$0.784384\pi$
$660$	−0.453708	−0.0176605
$661$	41.1572	1.60083	0.800415	−	0.599446i	$-0.204613\pi$
$661$	41.1572	1.60083	0.800415	+	0.599446i	$0.204613\pi$
$662$	27.7357	1.07798
$663$	−8.67387	−0.336865
$664$	−28.3357	−1.09964
$665$	3.38518	0.131272
$666$	12.4430	0.482157
$667$	−3.70868	−0.143600
$668$	2.97321	0.115037
$669$	−30.4832	−1.17855
$670$	13.3502	0.515763
$671$	−1.16374	−0.0449256
$672$	−5.19313	−0.200329
$673$	23.4365	0.903412	0.451706	−	0.892167i	$-0.350816\pi$
$673$	23.4365	0.903412	0.451706	+	0.892167i	$0.350816\pi$
$674$	24.5189	0.944434
$675$	−3.74063	−0.143977
$676$	2.14012	0.0823122
$677$	−11.6171	−0.446482	−0.223241	−	0.974763i	$-0.571664\pi$
$677$	−11.6171	−0.446482	−0.223241	+	0.974763i	$0.571664\pi$
$678$	−15.6782	−0.602116
$679$	−18.2484	−0.700311
$680$	−2.44333	−0.0936974
$681$	17.6182	0.675131
$682$	−4.96289	−0.190039
$683$	46.1728	1.76675	0.883376	−	0.468665i	$-0.155265\pi$
$683$	46.1728	1.76675	0.883376	+	0.468665i	$0.155265\pi$
$684$	1.81075	0.0692357
$685$	6.48873	0.247921
$686$	1.56783	0.0598599
$687$	−2.04149	−0.0778879
$688$	17.0105	0.648521
$689$	11.1298	0.424010
$690$	−1.70178	−0.0647857
$691$	25.9175	0.985947	0.492974	−	0.870044i	$-0.335910\pi$
$691$	25.9175	0.985947	0.492974	+	0.870044i	$0.335910\pi$
$692$	−4.56044	−0.173362
$693$	−0.566519	−0.0215203
$694$	12.7473	0.483881
$695$	−11.4438	−0.434088
$696$	34.4246	1.30486
$697$	3.48023	0.131823
$698$	−22.8164	−0.863614
$699$	−16.6266	−0.628878
$700$	−0.458083	−0.0173139
$701$	−44.4774	−1.67989	−0.839944	−	0.542673i	$-0.817412\pi$
$701$	−44.4774	−1.67989	−0.839944	+	0.542673i	$0.817412\pi$
$702$	−24.6538	−0.930499
$703$	−23.0080	−0.867762
$704$	2.63171	0.0991862
$705$	22.8694	0.861312
$706$	48.5330	1.82656
$707$	10.0661	0.378576
$708$	0.410695	0.0154349
$709$	13.6499	0.512634	0.256317	−	0.966593i	$-0.417491\pi$
$709$	13.6499	0.512634	0.256317	+	0.966593i	$0.417491\pi$
$710$	17.7408	0.665800
$711$	12.2376	0.458947
$712$	−24.7154	−0.926248
$713$	−3.46904	−0.129917
$714$	3.23496	0.121065
$715$	2.03951	0.0762732
$716$	0.528669	0.0197573
$717$	29.6318	1.10662
$718$	7.60308	0.283744
$719$	−40.7592	−1.52006	−0.760030	−	0.649888i	$-0.774816\pi$
$719$	−40.7592	−1.52006	−0.760030	+	0.649888i	$0.774816\pi$
$720$	5.49558	0.204808
$721$	2.83657	0.105639
$722$	11.8222	0.439978
$723$	−49.4464	−1.83893
$724$	−4.56675	−0.169722
$725$	6.97528	0.259056
$726$	34.4544	1.27872
$727$	23.0545	0.855044	0.427522	−	0.904005i	$-0.359387\pi$
$727$	23.0545	0.855044	0.427522	+	0.904005i	$0.359387\pi$
$728$	10.1625	0.376648
$729$	9.90175	0.366731
$730$	4.52355	0.167424
$731$	−3.65308	−0.135114
$732$	−2.24318	−0.0829103
$733$	−19.9706	−0.737631	−0.368816	−	0.929503i	$-0.620237\pi$
$733$	−19.9706	−0.737631	−0.368816	+	0.929503i	$0.620237\pi$
$734$	−0.174441	−0.00643872
$735$	−2.04149	−0.0753017
$736$	−1.35250	−0.0498539
$737$	4.13117	0.152174
$738$	−6.30397	−0.232052
$739$	21.0494	0.774316	0.387158	−	0.922013i	$-0.373457\pi$
$739$	21.0494	0.774316	0.387158	+	0.922013i	$0.373457\pi$
$740$	3.11344	0.114452
$741$	−29.0517	−1.06724
$742$	−4.15090	−0.152384
$743$	−7.67671	−0.281631	−0.140816	−	0.990036i	$-0.544972\pi$
$743$	−7.67671	−0.281631	−0.140816	+	0.990036i	$0.544972\pi$
$744$	32.2003	1.18052
$745$	4.49453	0.164667
$746$	1.50963	0.0552715
$747$	−13.6869	−0.500779
$748$	0.224621	0.00821297
$749$	14.6258	0.534416
$750$	3.20071	0.116873
$751$	−16.1972	−0.591045	−0.295523	−	0.955336i	$-0.595494\pi$
$751$	−16.1972	−0.591045	−0.295523	+	0.955336i	$0.595494\pi$
$752$	52.7216	1.92256
$753$	−40.5892	−1.47915
$754$	45.9729	1.67423
$755$	10.0634	0.366246
$756$	1.71352	0.0623201
$757$	−15.1804	−0.551741	−0.275870	−	0.961195i	$-0.588966\pi$
$757$	−15.1804	−0.551741	−0.275870	+	0.961195i	$0.588966\pi$
$758$	29.1418	1.05848
$759$	−0.526609	−0.0191147
$760$	−8.18355	−0.296848
$761$	21.1838	0.767910	0.383955	−	0.923352i	$-0.374562\pi$
$761$	21.1838	0.767910	0.383955	+	0.923352i	$0.374562\pi$
$762$	13.0424	0.472475
$763$	−5.93355	−0.214809
$764$	5.17999	0.187406
$765$	−1.18020	−0.0426701
$766$	−48.8684	−1.76569
$767$	−1.84616	−0.0666609
$768$	21.3567	0.770642
$769$	−16.8431	−0.607379	−0.303690	−	0.952771i	$-0.598219\pi$
$769$	−16.8431	−0.607379	−0.303690	+	0.952771i	$0.598219\pi$
$770$	−0.760645	−0.0274117
$771$	−23.7712	−0.856099
$772$	−11.0954	−0.399334
$773$	−31.2574	−1.12425	−0.562125	−	0.827052i	$-0.690016\pi$
$773$	−31.2574	−1.12425	−0.562125	+	0.827052i	$0.690016\pi$
$774$	6.61707	0.237846
$775$	6.52458	0.234370
$776$	44.1149	1.58363
$777$	13.8754	0.497776
$778$	−21.3002	−0.763648
$779$	11.6565	0.417636
$780$	3.93128	0.140762
$781$	5.48982	0.196441
$782$	0.842516	0.0301283
$783$	−26.0920	−0.932451
$784$	−4.70633	−0.168083
$785$	−13.4839	−0.481262
$786$	7.97695	0.284528
$787$	−6.21085	−0.221393	−0.110696	−	0.993854i	$-0.535308\pi$
$787$	−6.21085	−0.221393	−0.110696	+	0.993854i	$0.535308\pi$
$788$	6.03079	0.214838
$789$	26.2892	0.935922
$790$	16.4310	0.584589
$791$	−4.89834	−0.174165
$792$	1.36954	0.0486644
$793$	10.0835	0.358077
$794$	38.0723	1.35114
$795$	5.40496	0.191694
$796$	−1.00264	−0.0355376
$797$	−28.1138	−0.995842	−0.497921	−	0.867223i	$-0.665903\pi$
$797$	−28.1138	−0.995842	−0.497921	+	0.867223i	$0.665903\pi$
$798$	10.8350	0.383555
$799$	−11.3222	−0.400550
$800$	2.54379	0.0899365
$801$	−11.9382	−0.421816
$802$	14.8705	0.525094
$803$	1.39980	0.0493977
$804$	7.96310	0.280837
$805$	−0.531688	−0.0187395
$806$	43.0024	1.51469
$807$	7.38489	0.259960
$808$	−24.3344	−0.856083
$809$	−48.7551	−1.71414	−0.857070	−	0.515200i	$-0.827717\pi$
$809$	−48.7551	−1.71414	−0.857070	+	0.515200i	$0.827717\pi$
$810$	−17.4649	−0.613655
$811$	−42.8171	−1.50351	−0.751756	−	0.659441i	$-0.770793\pi$
$811$	−42.8171	−1.50351	−0.751756	+	0.659441i	$0.770793\pi$
$812$	−3.19526	−0.112132
$813$	−13.7049	−0.480653
$814$	5.16985	0.181203
$815$	15.2171	0.533033
$816$	−9.71076	−0.339945
$817$	−12.2354	−0.428063
$818$	0.687754	0.0240467
$819$	4.90877	0.171526
$820$	−1.57735	−0.0550836
$821$	−40.6283	−1.41794	−0.708968	−	0.705240i	$-0.750839\pi$
$821$	−40.6283	−1.41794	−0.708968	+	0.705240i	$0.750839\pi$
$822$	20.7685	0.724386
$823$	30.1451	1.05079	0.525397	−	0.850857i	$-0.323917\pi$
$823$	30.1451	1.05079	0.525397	+	0.850857i	$0.323917\pi$
$824$	−6.85729	−0.238885
$825$	0.990448	0.0344830
$826$	0.688534	0.0239572
$827$	31.5784	1.09809	0.549044	−	0.835793i	$-0.314992\pi$
$827$	31.5784	1.09809	0.549044	+	0.835793i	$0.314992\pi$
$828$	−0.284402	−0.00988365
$829$	39.2934	1.36471	0.682357	−	0.731019i	$-0.260955\pi$
$829$	39.2934	1.36471	0.682357	+	0.731019i	$0.260955\pi$
$830$	−18.3770	−0.637874
$831$	34.4697	1.19574
$832$	−22.8032	−0.790559
$833$	1.01070	0.0350187
$834$	−36.6283	−1.26834
$835$	−6.49055	−0.224615
$836$	0.752333	0.0260200
$837$	−24.4060	−0.843596
$838$	23.2560	0.803367
$839$	−41.4650	−1.43153	−0.715766	−	0.698341i	$-0.753922\pi$
$839$	−41.4650	−1.43153	−0.715766	+	0.698341i	$0.753922\pi$
$840$	4.93523	0.170282
$841$	19.6546	0.677744
$842$	−43.3898	−1.49531
$843$	−26.7665	−0.921888
$844$	−4.60617	−0.158551
$845$	−4.67190	−0.160718
$846$	20.5086	0.705101
$847$	10.7646	0.369877
$848$	12.4602	0.427886
$849$	−21.3779	−0.733687
$850$	−1.58461	−0.0543515
$851$	3.61371	0.123876
$852$	10.5820	0.362533
$853$	−30.5786	−1.04699	−0.523495	−	0.852029i	$-0.675372\pi$
$853$	−30.5786	−1.04699	−0.523495	+	0.852029i	$0.675372\pi$
$854$	−3.76071	−0.128689
$855$	−3.95288	−0.135186
$856$	−35.3573	−1.20849
$857$	24.5930	0.840081	0.420040	−	0.907505i	$-0.362016\pi$
$857$	24.5930	0.840081	0.420040	+	0.907505i	$0.362016\pi$
$858$	6.52787	0.222858
$859$	−33.7698	−1.15221	−0.576106	−	0.817375i	$-0.695429\pi$
$859$	−33.7698	−1.15221	−0.576106	+	0.817375i	$0.695429\pi$
$860$	1.65570	0.0564588
$861$	−7.02964	−0.239569
$862$	15.2981	0.521056
$863$	−42.9975	−1.46365	−0.731825	−	0.681492i	$-0.761331\pi$
$863$	−42.9975	−1.46365	−0.731825	+	0.681492i	$0.761331\pi$
$864$	−9.51537	−0.323720
$865$	9.95548	0.338496
$866$	20.9576	0.712167
$867$	−32.6200	−1.10783
$868$	−2.98880	−0.101447
$869$	5.08451	0.172480
$870$	22.3259	0.756918
$871$	−35.7957	−1.21289
$872$	14.3441	0.485753
$873$	21.3087	0.721191
$874$	2.82187	0.0954513
$875$	1.00000	0.0338062
$876$	2.69820	0.0911637
$877$	34.8006	1.17513	0.587566	−	0.809176i	$-0.300086\pi$
$877$	34.8006	1.17513	0.587566	+	0.809176i	$0.300086\pi$
$878$	−4.37250	−0.147565
$879$	−12.6569	−0.426908
$880$	2.28331	0.0769705
$881$	7.47345	0.251787	0.125894	−	0.992044i	$-0.459820\pi$
$881$	7.47345	0.251787	0.125894	+	0.992044i	$0.459820\pi$
$882$	−1.83075	−0.0616446
$883$	−1.68150	−0.0565869	−0.0282935	−	0.999600i	$-0.509007\pi$
$883$	−1.68150	−0.0565869	−0.0282935	+	0.999600i	$0.509007\pi$
$884$	−1.94630	−0.0654610
$885$	−0.896552	−0.0301373
$886$	−11.3331	−0.380742
$887$	−16.5237	−0.554811	−0.277406	−	0.960753i	$-0.589475\pi$
$887$	−16.5237	−0.554811	−0.277406	+	0.960753i	$0.589475\pi$
$888$	−33.5431	−1.12563
$889$	4.07483	0.136666
$890$	−16.0290	−0.537293
$891$	−5.40446	−0.181056
$892$	−6.84001	−0.229020
$893$	−37.9218	−1.26901
$894$	14.3857	0.481130
$895$	−1.15409	−0.0385769
$896$	13.5921	0.454082
$897$	4.56296	0.152353
$898$	−57.4450	−1.91697
$899$	45.5108	1.51787
$900$	0.534904	0.0178301
$901$	−2.67588	−0.0891466
$902$	−2.61919	−0.0872094
$903$	7.37878	0.245550
$904$	11.8415	0.393844
$905$	9.96926	0.331389
$906$	32.2102	1.07011
$907$	33.0934	1.09885	0.549424	−	0.835543i	$-0.314847\pi$
$907$	33.0934	1.09885	0.549424	+	0.835543i	$0.314847\pi$
$908$	3.95328	0.131194
$909$	−11.7542	−0.389863
$910$	6.59083	0.218484
$911$	10.3362	0.342453	0.171227	−	0.985232i	$-0.445227\pi$
$911$	10.3362	0.342453	0.171227	+	0.985232i	$0.445227\pi$
$912$	−32.5246	−1.07700
$913$	−5.68668	−0.188202
$914$	27.0336	0.894191
$915$	4.89688	0.161886
$916$	−0.458083	−0.0151355
$917$	2.49224	0.0823011
$918$	5.92742	0.195634
$919$	2.80078	0.0923891	0.0461945	−	0.998932i	$-0.485291\pi$
$919$	2.80078	0.0923891	0.0461945	+	0.998932i	$0.485291\pi$
$920$	1.28533	0.0423762
$921$	−59.0002	−1.94412
$922$	−10.2090	−0.336216
$923$	−47.5681	−1.56572
$924$	−0.453708	−0.0149259
$925$	−6.79667	−0.223473
$926$	9.51052	0.312535
$927$	−3.31226	−0.108789
$928$	17.7436	0.582464
$929$	55.3311	1.81535	0.907677	−	0.419669i	$-0.137854\pi$
$929$	55.3311	1.81535	0.907677	+	0.419669i	$0.137854\pi$
$930$	20.8833	0.684790
$931$	3.38518	0.110945
$932$	−3.73079	−0.122206
$933$	26.8945	0.880488
$934$	−41.8336	−1.36884
$935$	−0.490350	−0.0160362
$936$	−11.8668	−0.387877
$937$	−41.8790	−1.36813	−0.684063	−	0.729423i	$-0.739789\pi$
$937$	−41.8790	−1.36813	−0.684063	+	0.729423i	$0.739789\pi$
$938$	13.3502	0.435899
$939$	−2.71372	−0.0885589
$940$	5.13158	0.167374
$941$	16.1399	0.526145	0.263073	−	0.964776i	$-0.415264\pi$
$941$	16.1399	0.526145	0.263073	+	0.964776i	$0.415264\pi$
$942$	−43.1582	−1.40617
$943$	−1.83080	−0.0596192
$944$	−2.06685	−0.0672703
$945$	−3.74063	−0.121683
$946$	2.74927	0.0893866
$947$	40.9076	1.32932	0.664660	−	0.747146i	$-0.268576\pi$
$947$	40.9076	1.32932	0.664660	+	0.747146i	$0.268576\pi$
$948$	9.80073	0.318313
$949$	−12.1289	−0.393722
$950$	−5.30739	−0.172194
$951$	58.8093	1.90702
$952$	−2.44333	−0.0791888
$953$	−14.2908	−0.462925	−0.231463	−	0.972844i	$-0.574351\pi$
$953$	−14.2908	−0.462925	−0.231463	+	0.972844i	$0.574351\pi$
$954$	4.84701	0.156928
$955$	−11.3080	−0.365917
$956$	6.64897	0.215043
$957$	6.90866	0.223325
$958$	0.196859	0.00636022
$959$	6.48873	0.209532
$960$	−11.0739	−0.357410
$961$	11.5701	0.373230
$962$	−44.7957	−1.44427
$963$	−17.0786	−0.550349
$964$	−11.0951	−0.357349
$965$	24.2215	0.779716
$966$	−1.70178	−0.0547539
$967$	9.30458	0.299215	0.149608	−	0.988745i	$-0.452199\pi$
$967$	9.30458	0.299215	0.149608	+	0.988745i	$0.452199\pi$
$968$	−26.0230	−0.836412
$969$	6.98479	0.224384
$970$	28.6104	0.918625
$971$	−15.3740	−0.493376	−0.246688	−	0.969095i	$-0.579342\pi$
$971$	−15.3740	−0.493376	−0.246688	+	0.969095i	$0.579342\pi$
$972$	−5.27689	−0.169256
$973$	−11.4438	−0.366872
$974$	54.3993	1.74307
$975$	−8.58203	−0.274845
$976$	11.2890	0.361351
$977$	34.1086	1.09123	0.545616	−	0.838035i	$-0.316296\pi$
$977$	34.1086	1.09123	0.545616	+	0.838035i	$0.316296\pi$
$978$	48.7056	1.55743
$979$	−4.96011	−0.158526
$980$	−0.458083	−0.0146329
$981$	6.92861	0.221213
$982$	11.3089	0.360880
$983$	−13.2224	−0.421730	−0.210865	−	0.977515i	$-0.567628\pi$
$983$	−13.2224	−0.421730	−0.210865	+	0.977515i	$0.567628\pi$
$984$	16.9939	0.541745
$985$	−13.1653	−0.419481
$986$	−11.0531	−0.352002
$987$	22.8694	0.727941
$988$	−6.51881	−0.207391
$989$	1.92173	0.0611076
$990$	0.888205	0.0282290
$991$	13.6004	0.432032	0.216016	−	0.976390i	$-0.430694\pi$
$991$	13.6004	0.432032	0.216016	+	0.976390i	$0.430694\pi$
$992$	16.5972	0.526960
$993$	−36.1151	−1.14608
$994$	17.7408	0.562703
$995$	2.18877	0.0693886
$996$	−10.9614	−0.347327
$997$	−3.57580	−0.113247	−0.0566234	−	0.998396i	$-0.518033\pi$
$997$	−3.57580	−0.113247	−0.0566234	+	0.998396i	$0.518033\pi$
$998$	46.2907	1.46531
$999$	25.4238	0.804374

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.k.1.14	✓	49

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.k.1.14	✓	49	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-1.56783 q^{2} +2.04149 q^{3} +0.458083 q^{4} -1.00000 q^{5} -3.20071 q^{6} -1.00000 q^{7} +2.41746 q^{8} +1.16770 q^{9} +O(q^{10})\)	\(q-1.56783 q^{2} +2.04149 q^{3} +0.458083 q^{4} -1.00000 q^{5} -3.20071 q^{6} -1.00000 q^{7} +2.41746 q^{8} +1.16770 q^{9} +1.56783 q^{10} +0.485158 q^{11} +0.935174 q^{12} -4.20380 q^{13} +1.56783 q^{14} -2.04149 q^{15} -4.70633 q^{16} +1.01070 q^{17} -1.83075 q^{18} +3.38518 q^{19} -0.458083 q^{20} -2.04149 q^{21} -0.760645 q^{22} -0.531688 q^{23} +4.93523 q^{24} +1.00000 q^{25} +6.59083 q^{26} -3.74063 q^{27} -0.458083 q^{28} +6.97528 q^{29} +3.20071 q^{30} +6.52458 q^{31} +2.54379 q^{32} +0.990448 q^{33} -1.58461 q^{34} +1.00000 q^{35} +0.534904 q^{36} -6.79667 q^{37} -5.30739 q^{38} -8.58203 q^{39} -2.41746 q^{40} +3.44338 q^{41} +3.20071 q^{42} -3.61440 q^{43} +0.222243 q^{44} -1.16770 q^{45} +0.833595 q^{46} -11.2023 q^{47} -9.60794 q^{48} +1.00000 q^{49} -1.56783 q^{50} +2.06334 q^{51} -1.92569 q^{52} -2.64755 q^{53} +5.86466 q^{54} -0.485158 q^{55} -2.41746 q^{56} +6.91084 q^{57} -10.9360 q^{58} +0.439164 q^{59} -0.935174 q^{60} -2.39868 q^{61} -10.2294 q^{62} -1.16770 q^{63} +5.42443 q^{64} +4.20380 q^{65} -1.55285 q^{66} +8.51509 q^{67} +0.462985 q^{68} -1.08544 q^{69} -1.56783 q^{70} +11.3155 q^{71} +2.82287 q^{72} +2.88524 q^{73} +10.6560 q^{74} +2.04149 q^{75} +1.55070 q^{76} -0.485158 q^{77} +13.4551 q^{78} +10.4801 q^{79} +4.70633 q^{80} -11.1396 q^{81} -5.39862 q^{82} -11.7213 q^{83} -0.935174 q^{84} -1.01070 q^{85} +5.66676 q^{86} +14.2400 q^{87} +1.17285 q^{88} -10.2237 q^{89} +1.83075 q^{90} +4.20380 q^{91} -0.243557 q^{92} +13.3199 q^{93} +17.5633 q^{94} -3.38518 q^{95} +5.19313 q^{96} +18.2484 q^{97} -1.56783 q^{98} +0.566519 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9}+O(q^{10}) \) 49 * q - 3 * q^2 - 10 * q^3 + 49 * q^4 - 49 * q^5 + 10 * q^6 - 49 * q^7 - 6 * q^8 + 39 * q^9	\( 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9} + 3 q^{10} + 16 q^{11} - 26 q^{12} - 31 q^{13} + 3 q^{14} + 10 q^{15} + 49 q^{16} - 18 q^{17} + 4 q^{18} - 16 q^{19} - 49 q^{20} + 10 q^{21} + 10 q^{22} + 10 q^{23} + 2 q^{24} + 49 q^{25} - 22 q^{26} - 58 q^{27} - 49 q^{28} + 31 q^{29} - 10 q^{30} - 35 q^{31} - 5 q^{32} - 82 q^{33} - 41 q^{34} + 49 q^{35} + 49 q^{36} - 24 q^{37} - 20 q^{38} + 41 q^{39} + 6 q^{40} + 30 q^{41} - 10 q^{42} - 19 q^{43} + 27 q^{44} - 39 q^{45} + 15 q^{46} - 39 q^{47} - 51 q^{48} + 49 q^{49} - 3 q^{50} + 46 q^{51} - 94 q^{52} - 17 q^{53} + 9 q^{54} - 16 q^{55} + 6 q^{56} - 23 q^{57} - 46 q^{58} + 11 q^{59} + 26 q^{60} - 9 q^{61} - 49 q^{62} - 39 q^{63} + 10 q^{64} + 31 q^{65} - 10 q^{66} - 2 q^{67} - 73 q^{68} - 47 q^{69} - 3 q^{70} + 26 q^{71} - 39 q^{72} - 100 q^{73} + 8 q^{74} - 10 q^{75} - 71 q^{76} - 16 q^{77} - 51 q^{78} + 50 q^{79} - 49 q^{80} + 61 q^{81} - 36 q^{82} - 67 q^{83} + 26 q^{84} + 18 q^{85} + 33 q^{86} - 45 q^{87} - q^{88} - 19 q^{89} - 4 q^{90} + 31 q^{91} + 7 q^{92} + 9 q^{93} - 33 q^{94} + 16 q^{95} - 8 q^{96} - 85 q^{97} - 3 q^{98} + 27 q^{99}+O(q^{100}) \) 49 * q - 3 * q^2 - 10 * q^3 + 49 * q^4 - 49 * q^5 + 10 * q^6 - 49 * q^7 - 6 * q^8 + 39 * q^9 + 3 * q^10 + 16 * q^11 - 26 * q^12 - 31 * q^13 + 3 * q^14 + 10 * q^15 + 49 * q^16 - 18 * q^17 + 4 * q^18 - 16 * q^19 - 49 * q^20 + 10 * q^21 + 10 * q^22 + 10 * q^23 + 2 * q^24 + 49 * q^25 - 22 * q^26 - 58 * q^27 - 49 * q^28 + 31 * q^29 - 10 * q^30 - 35 * q^31 - 5 * q^32 - 82 * q^33 - 41 * q^34 + 49 * q^35 + 49 * q^36 - 24 * q^37 - 20 * q^38 + 41 * q^39 + 6 * q^40 + 30 * q^41 - 10 * q^42 - 19 * q^43 + 27 * q^44 - 39 * q^45 + 15 * q^46 - 39 * q^47 - 51 * q^48 + 49 * q^49 - 3 * q^50 + 46 * q^51 - 94 * q^52 - 17 * q^53 + 9 * q^54 - 16 * q^55 + 6 * q^56 - 23 * q^57 - 46 * q^58 + 11 * q^59 + 26 * q^60 - 9 * q^61 - 49 * q^62 - 39 * q^63 + 10 * q^64 + 31 * q^65 - 10 * q^66 - 2 * q^67 - 73 * q^68 - 47 * q^69 - 3 * q^70 + 26 * q^71 - 39 * q^72 - 100 * q^73 + 8 * q^74 - 10 * q^75 - 71 * q^76 - 16 * q^77 - 51 * q^78 + 50 * q^79 - 49 * q^80 + 61 * q^81 - 36 * q^82 - 67 * q^83 + 26 * q^84 + 18 * q^85 + 33 * q^86 - 45 * q^87 - q^88 - 19 * q^89 - 4 * q^90 + 31 * q^91 + 7 * q^92 + 9 * q^93 - 33 * q^94 + 16 * q^95 - 8 * q^96 - 85 * q^97 - 3 * q^98 + 27 * q^99

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