LMFDB - Embedded newform 8015.2.a.k.1.4

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			1.4
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)

$f(q)$	$=$	$q-2.56687 q^{2} -1.38440 q^{3} +4.58882 q^{4} -1.00000 q^{5} +3.55358 q^{6} -1.00000 q^{7} -6.64517 q^{8} -1.08344 q^{9} +O(q^{10})$	\(q-2.56687 q^{2} -1.38440 q^{3} +4.58882 q^{4} -1.00000 q^{5} +3.55358 q^{6} -1.00000 q^{7} -6.64517 q^{8} -1.08344 q^{9} +2.56687 q^{10} +0.594264 q^{11} -6.35277 q^{12} -0.500814 q^{13} +2.56687 q^{14} +1.38440 q^{15} +7.87963 q^{16} -0.443643 q^{17} +2.78104 q^{18} +7.44726 q^{19} -4.58882 q^{20} +1.38440 q^{21} -1.52540 q^{22} +6.10671 q^{23} +9.19957 q^{24} +1.00000 q^{25} +1.28553 q^{26} +5.65311 q^{27} -4.58882 q^{28} +2.44024 q^{29} -3.55358 q^{30} -10.4936 q^{31} -6.93566 q^{32} -0.822699 q^{33} +1.13877 q^{34} +1.00000 q^{35} -4.97169 q^{36} -11.1717 q^{37} -19.1161 q^{38} +0.693328 q^{39} +6.64517 q^{40} -5.15572 q^{41} -3.55358 q^{42} -2.92491 q^{43} +2.72697 q^{44} +1.08344 q^{45} -15.6751 q^{46} -8.93936 q^{47} -10.9086 q^{48} +1.00000 q^{49} -2.56687 q^{50} +0.614180 q^{51} -2.29815 q^{52} +4.80579 q^{53} -14.5108 q^{54} -0.594264 q^{55} +6.64517 q^{56} -10.3100 q^{57} -6.26377 q^{58} +2.44448 q^{59} +6.35277 q^{60} -1.25498 q^{61} +26.9356 q^{62} +1.08344 q^{63} +2.04367 q^{64} +0.500814 q^{65} +2.11176 q^{66} +1.12341 q^{67} -2.03580 q^{68} -8.45414 q^{69} -2.56687 q^{70} +11.3169 q^{71} +7.19961 q^{72} -2.53114 q^{73} +28.6763 q^{74} -1.38440 q^{75} +34.1741 q^{76} -0.594264 q^{77} -1.77968 q^{78} +11.7326 q^{79} -7.87963 q^{80} -4.57586 q^{81} +13.2341 q^{82} -15.3495 q^{83} +6.35277 q^{84} +0.443643 q^{85} +7.50786 q^{86} -3.37826 q^{87} -3.94898 q^{88} +16.7235 q^{89} -2.78104 q^{90} +0.500814 q^{91} +28.0226 q^{92} +14.5273 q^{93} +22.9462 q^{94} -7.44726 q^{95} +9.60173 q^{96} +1.54781 q^{97} -2.56687 q^{98} -0.643846 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.56687	−1.81505	−0.907526	−	0.419997i	$-0.862031\pi$
$2$	−2.56687	−1.81505	−0.907526	+	0.419997i	$0.862031\pi$
$3$	−1.38440	−0.799284	−0.399642	−	0.916671i	$-0.630866\pi$
$3$	−1.38440	−0.799284	−0.399642	+	0.916671i	$0.630866\pi$
$4$	4.58882	2.29441
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	3.55358	1.45074
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−6.64517	−2.34942
$9$	−1.08344	−0.361145
$10$	2.56687	0.811716
$11$	0.594264	0.179177	0.0895886	−	0.995979i	$-0.471445\pi$
$11$	0.594264	0.179177	0.0895886	+	0.995979i	$0.471445\pi$
$12$	−6.35277	−1.83389
$13$	−0.500814	−0.138901	−0.0694505	−	0.997585i	$-0.522125\pi$
$13$	−0.500814	−0.138901	−0.0694505	+	0.997585i	$0.522125\pi$
$14$	2.56687	0.686025
$15$	1.38440	0.357451
$16$	7.87963	1.96991
$17$	−0.443643	−0.107599	−0.0537996	−	0.998552i	$-0.517133\pi$
$17$	−0.443643	−0.107599	−0.0537996	+	0.998552i	$0.517133\pi$
$18$	2.78104	0.655497
$19$	7.44726	1.70852	0.854259	−	0.519847i	$-0.174011\pi$
$19$	7.44726	1.70852	0.854259	+	0.519847i	$0.174011\pi$
$20$	−4.58882	−1.02609
$21$	1.38440	0.302101
$22$	−1.52540	−0.325216
$23$	6.10671	1.27334	0.636669	−	0.771137i	$-0.280312\pi$
$23$	6.10671	1.27334	0.636669	+	0.771137i	$0.280312\pi$
$24$	9.19957	1.87785
$25$	1.00000	0.200000
$26$	1.28553	0.252112
$27$	5.65311	1.08794
$28$	−4.58882	−0.867206
$29$	2.44024	0.453140	0.226570	−	0.973995i	$-0.427249\pi$
$29$	2.44024	0.453140	0.226570	+	0.973995i	$0.427249\pi$
$30$	−3.55358	−0.648791
$31$	−10.4936	−1.88470	−0.942350	−	0.334630i	$-0.891389\pi$
$31$	−10.4936	−1.88470	−0.942350	+	0.334630i	$0.891389\pi$
$32$	−6.93566	−1.22606
$33$	−0.822699	−0.143213
$34$	1.13877	0.195298
$35$	1.00000	0.169031
$36$	−4.97169	−0.828615
$37$	−11.1717	−1.83661	−0.918307	−	0.395868i	$-0.870444\pi$
$37$	−11.1717	−1.83661	−0.918307	+	0.395868i	$0.870444\pi$
$38$	−19.1161	−3.10105
$39$	0.693328	0.111021
$40$	6.64517	1.05069
$41$	−5.15572	−0.805188	−0.402594	−	0.915379i	$-0.631891\pi$
$41$	−5.15572	−0.805188	−0.402594	+	0.915379i	$0.631891\pi$
$42$	−3.55358	−0.548329
$43$	−2.92491	−0.446045	−0.223022	−	0.974813i	$-0.571592\pi$
$43$	−2.92491	−0.446045	−0.223022	+	0.974813i	$0.571592\pi$
$44$	2.72697	0.411106
$45$	1.08344	0.161509
$46$	−15.6751	−2.31117
$47$	−8.93936	−1.30394	−0.651970	−	0.758245i	$-0.726057\pi$
$47$	−8.93936	−1.30394	−0.651970	+	0.758245i	$0.726057\pi$
$48$	−10.9086	−1.57452
$49$	1.00000	0.142857
$50$	−2.56687	−0.363010
$51$	0.614180	0.0860024
$52$	−2.29815	−0.318696
$53$	4.80579	0.660126	0.330063	−	0.943959i	$-0.392930\pi$
$53$	4.80579	0.660126	0.330063	+	0.943959i	$0.392930\pi$
$54$	−14.5108	−1.97467
$55$	−0.594264	−0.0801305
$56$	6.64517	0.887998
$57$	−10.3100	−1.36559
$58$	−6.26377	−0.822473
$59$	2.44448	0.318244	0.159122	−	0.987259i	$-0.449134\pi$
$59$	2.44448	0.318244	0.159122	+	0.987259i	$0.449134\pi$
$60$	6.35277	0.820139
$61$	−1.25498	−0.160684	−0.0803421	−	0.996767i	$-0.525601\pi$
$61$	−1.25498	−0.160684	−0.0803421	+	0.996767i	$0.525601\pi$
$62$	26.9356	3.42083
$63$	1.08344	0.136500
$64$	2.04367	0.255459
$65$	0.500814	0.0621184
$66$	2.11176	0.259940
$67$	1.12341	0.137246	0.0686232	−	0.997643i	$-0.478139\pi$
$67$	1.12341	0.137246	0.0686232	+	0.997643i	$0.478139\pi$
$68$	−2.03580	−0.246877
$69$	−8.45414	−1.01776
$70$	−2.56687	−0.306800
$71$	11.3169	1.34306	0.671532	−	0.740976i	$-0.265637\pi$
$71$	11.3169	1.34306	0.671532	+	0.740976i	$0.265637\pi$
$72$	7.19961	0.848482
$73$	−2.53114	−0.296247	−0.148124	−	0.988969i	$-0.547323\pi$
$73$	−2.53114	−0.296247	−0.148124	+	0.988969i	$0.547323\pi$
$74$	28.6763	3.33355
$75$	−1.38440	−0.159857
$76$	34.1741	3.92004
$77$	−0.594264	−0.0677226
$78$	−1.77968	−0.201509
$79$	11.7326	1.32002	0.660008	−	0.751259i	$-0.270553\pi$
$79$	11.7326	1.32002	0.660008	+	0.751259i	$0.270553\pi$
$80$	−7.87963	−0.880970
$81$	−4.57586	−0.508429
$82$	13.2341	1.46146
$83$	−15.3495	−1.68483	−0.842414	−	0.538830i	$-0.818866\pi$
$83$	−15.3495	−1.68483	−0.842414	+	0.538830i	$0.818866\pi$
$84$	6.35277	0.693144
$85$	0.443643	0.0481199
$86$	7.50786	0.809594
$87$	−3.37826	−0.362188
$88$	−3.94898	−0.420963
$89$	16.7235	1.77269	0.886343	−	0.463030i	$-0.153238\pi$
$89$	16.7235	1.77269	0.886343	+	0.463030i	$0.153238\pi$
$90$	−2.78104	−0.293147
$91$	0.500814	0.0524996
$92$	28.0226	2.92156
$93$	14.5273	1.50641
$94$	22.9462	2.36672
$95$	−7.44726	−0.764073
$96$	9.60173	0.979973
$97$	1.54781	0.157156	0.0785780	−	0.996908i	$-0.474962\pi$
$97$	1.54781	0.157156	0.0785780	+	0.996908i	$0.474962\pi$
$98$	−2.56687	−0.259293
$99$	−0.643846	−0.0647090
$100$	4.58882	0.458882
$101$	2.60819	0.259525	0.129762	−	0.991545i	$-0.458579\pi$
$101$	2.60819	0.259525	0.129762	+	0.991545i	$0.458579\pi$
$102$	−1.57652	−0.156099
$103$	−16.0706	−1.58348	−0.791741	−	0.610857i	$-0.790825\pi$
$103$	−16.0706	−1.58348	−0.791741	+	0.610857i	$0.790825\pi$
$104$	3.32799	0.326337
$105$	−1.38440	−0.135104
$106$	−12.3358	−1.19816
$107$	−16.1593	−1.56218	−0.781090	−	0.624418i	$-0.785336\pi$
$107$	−16.1593	−1.56218	−0.781090	+	0.624418i	$0.785336\pi$
$108$	25.9411	2.49618
$109$	12.5639	1.20340	0.601700	−	0.798722i	$-0.294490\pi$
$109$	12.5639	1.20340	0.601700	+	0.798722i	$0.294490\pi$
$110$	1.52540	0.145441
$111$	15.4661	1.46798
$112$	−7.87963	−0.744555
$113$	12.6826	1.19308	0.596540	−	0.802583i	$-0.296542\pi$
$113$	12.6826	1.19308	0.596540	+	0.802583i	$0.296542\pi$
$114$	26.4644	2.47862
$115$	−6.10671	−0.569454
$116$	11.1978	1.03969
$117$	0.542600	0.0501634
$118$	−6.27466	−0.577629
$119$	0.443643	0.0406687
$120$	−9.19957	−0.839802
$121$	−10.6469	−0.967896
$122$	3.22138	0.291650
$123$	7.13758	0.643574
$124$	−48.1531	−4.32427
$125$	−1.00000	−0.0894427
$126$	−2.78104	−0.247754
$127$	−13.8055	−1.22504	−0.612520	−	0.790455i	$-0.709844\pi$
$127$	−13.8055	−1.22504	−0.612520	+	0.790455i	$0.709844\pi$
$128$	8.62548	0.762392
$129$	4.04925	0.356516
$130$	−1.28553	−0.112748
$131$	10.9410	0.955921	0.477960	−	0.878381i	$-0.341376\pi$
$131$	10.9410	0.955921	0.477960	+	0.878381i	$0.341376\pi$
$132$	−3.77522	−0.328590
$133$	−7.44726	−0.645759
$134$	−2.88365	−0.249109
$135$	−5.65311	−0.486542
$136$	2.94808	0.252796
$137$	10.5681	0.902895	0.451447	−	0.892298i	$-0.350908\pi$
$137$	10.5681	0.902895	0.451447	+	0.892298i	$0.350908\pi$
$138$	21.7007	1.84728
$139$	−1.89392	−0.160640	−0.0803199	−	0.996769i	$-0.525594\pi$
$139$	−1.89392	−0.160640	−0.0803199	+	0.996769i	$0.525594\pi$
$140$	4.58882	0.387826
$141$	12.3757	1.04222
$142$	−29.0489	−2.43773
$143$	−0.297616	−0.0248879
$144$	−8.53707	−0.711423
$145$	−2.44024	−0.202651
$146$	6.49710	0.537704
$147$	−1.38440	−0.114183
$148$	−51.2649	−4.21395
$149$	3.41191	0.279515	0.139757	−	0.990186i	$-0.455368\pi$
$149$	3.41191	0.279515	0.139757	+	0.990186i	$0.455368\pi$
$150$	3.55358	0.290148
$151$	14.4707	1.17761	0.588804	−	0.808276i	$-0.299599\pi$
$151$	14.4707	1.17761	0.588804	+	0.808276i	$0.299599\pi$
$152$	−49.4883	−4.01403
$153$	0.480659	0.0388589
$154$	1.52540	0.122920
$155$	10.4936	0.842863
$156$	3.18156	0.254728
$157$	13.5660	1.08268	0.541341	−	0.840803i	$-0.317917\pi$
$157$	13.5660	1.08268	0.541341	+	0.840803i	$0.317917\pi$
$158$	−30.1159	−2.39590
$159$	−6.65314	−0.527628
$160$	6.93566	0.548312
$161$	−6.10671	−0.481276
$162$	11.7456	0.922825
$163$	−18.7049	−1.46508	−0.732540	−	0.680724i	$-0.761665\pi$
$163$	−18.7049	−1.46508	−0.732540	+	0.680724i	$0.761665\pi$
$164$	−23.6587	−1.84743
$165$	0.822699	0.0640470
$166$	39.4002	3.05805
$167$	−5.90948	−0.457289	−0.228645	−	0.973510i	$-0.573429\pi$
$167$	−5.90948	−0.457289	−0.228645	+	0.973510i	$0.573429\pi$
$168$	−9.19957	−0.709762
$169$	−12.7492	−0.980707
$170$	−1.13877	−0.0873400
$171$	−8.06862	−0.617023
$172$	−13.4219	−1.02341
$173$	0.299043	0.0227358	0.0113679	−	0.999935i	$-0.496381\pi$
$173$	0.299043	0.0227358	0.0113679	+	0.999935i	$0.496381\pi$
$174$	8.67156	0.657389
$175$	−1.00000	−0.0755929
$176$	4.68258	0.352963
$177$	−3.38414	−0.254367
$178$	−42.9270	−3.21751
$179$	14.5876	1.09033	0.545165	−	0.838329i	$-0.316467\pi$
$179$	14.5876	1.09033	0.545165	+	0.838329i	$0.316467\pi$
$180$	4.97169	0.370568
$181$	18.7800	1.39591	0.697954	−	0.716143i	$-0.254094\pi$
$181$	18.7800	1.39591	0.697954	+	0.716143i	$0.254094\pi$
$182$	−1.28553	−0.0952895
$183$	1.73740	0.128432
$184$	−40.5801	−2.99161
$185$	11.1717	0.821359
$186$	−37.2897	−2.73421
$187$	−0.263641	−0.0192793
$188$	−41.0211	−2.99177
$189$	−5.65311	−0.411203
$190$	19.1161	1.38683
$191$	10.3713	0.750440	0.375220	−	0.926936i	$-0.377567\pi$
$191$	10.3713	0.750440	0.375220	+	0.926936i	$0.377567\pi$
$192$	−2.82926	−0.204184
$193$	18.0970	1.30265	0.651324	−	0.758800i	$-0.274214\pi$
$193$	18.0970	1.30265	0.651324	+	0.758800i	$0.274214\pi$
$194$	−3.97302	−0.285246
$195$	−0.693328	−0.0496502
$196$	4.58882	0.327773
$197$	−11.9369	−0.850471	−0.425236	−	0.905083i	$-0.639809\pi$
$197$	−11.9369	−0.850471	−0.425236	+	0.905083i	$0.639809\pi$
$198$	1.65267	0.117450
$199$	−10.9442	−0.775813	−0.387906	−	0.921699i	$-0.626802\pi$
$199$	−10.9442	−0.775813	−0.387906	+	0.921699i	$0.626802\pi$
$200$	−6.64517	−0.469884
$201$	−1.55525	−0.109699
$202$	−6.69489	−0.471051
$203$	−2.44024	−0.171271
$204$	2.81836	0.197325
$205$	5.15572	0.360091
$206$	41.2511	2.87410
$207$	−6.61623	−0.459860
$208$	−3.94623	−0.273622
$209$	4.42563	0.306128
$210$	3.55358	0.245220
$211$	−3.08205	−0.212177	−0.106088	−	0.994357i	$-0.533833\pi$
$211$	−3.08205	−0.212177	−0.106088	+	0.994357i	$0.533833\pi$
$212$	22.0529	1.51460
$213$	−15.6671	−1.07349
$214$	41.4789	2.83544
$215$	2.92491	0.199477
$216$	−37.5658	−2.55603
$217$	10.4936	0.712349
$218$	−32.2498	−2.18423
$219$	3.50411	0.236786
$220$	−2.72697	−0.183852
$221$	0.222183	0.0149456
$222$	−39.6995	−2.66445
$223$	10.9749	0.734931	0.367465	−	0.930037i	$-0.380226\pi$
$223$	10.9749	0.734931	0.367465	+	0.930037i	$0.380226\pi$
$224$	6.93566	0.463408
$225$	−1.08344	−0.0722290
$226$	−32.5546	−2.16550
$227$	11.6770	0.775028	0.387514	−	0.921864i	$-0.373334\pi$
$227$	11.6770	0.775028	0.387514	+	0.921864i	$0.373334\pi$
$228$	−47.3107	−3.13323
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	15.6751	1.03359
$231$	0.822699	0.0541296
$232$	−16.2158	−1.06462
$233$	14.3440	0.939706	0.469853	−	0.882745i	$-0.344307\pi$
$233$	14.3440	0.939706	0.469853	+	0.882745i	$0.344307\pi$
$234$	−1.39278	−0.0910491
$235$	8.93936	0.583140
$236$	11.2173	0.730182
$237$	−16.2426	−1.05507
$238$	−1.13877	−0.0738158
$239$	−21.4879	−1.38993	−0.694967	−	0.719042i	$-0.744581\pi$
$239$	−21.4879	−1.38993	−0.694967	+	0.719042i	$0.744581\pi$
$240$	10.9086	0.704145
$241$	−1.97356	−0.127128	−0.0635642	−	0.997978i	$-0.520247\pi$
$241$	−1.97356	−0.127128	−0.0635642	+	0.997978i	$0.520247\pi$
$242$	27.3291	1.75678
$243$	−10.6245	−0.681562
$244$	−5.75889	−0.368675
$245$	−1.00000	−0.0638877
$246$	−18.3212	−1.16812
$247$	−3.72970	−0.237315
$248$	69.7314	4.42795
$249$	21.2499	1.34666
$250$	2.56687	0.162343
$251$	3.57948	0.225935	0.112967	−	0.993599i	$-0.463964\pi$
$251$	3.57948	0.225935	0.112967	+	0.993599i	$0.463964\pi$
$252$	4.97169	0.313187
$253$	3.62900	0.228153
$254$	35.4369	2.22351
$255$	−0.614180	−0.0384614
$256$	−26.2278	−1.63924
$257$	24.3807	1.52083	0.760414	−	0.649439i	$-0.224996\pi$
$257$	24.3807	1.52083	0.760414	+	0.649439i	$0.224996\pi$
$258$	−10.3939	−0.647095
$259$	11.1717	0.694175
$260$	2.29815	0.142525
$261$	−2.64384	−0.163649
$262$	−28.0842	−1.73504
$263$	22.8422	1.40851	0.704257	−	0.709946i	$-0.251280\pi$
$263$	22.8422	1.40851	0.704257	+	0.709946i	$0.251280\pi$
$264$	5.46697	0.336469
$265$	−4.80579	−0.295217
$266$	19.1161	1.17209
$267$	−23.1520	−1.41688
$268$	5.15513	0.314900
$269$	−4.97241	−0.303173	−0.151587	−	0.988444i	$-0.548438\pi$
$269$	−4.97241	−0.303173	−0.151587	+	0.988444i	$0.548438\pi$
$270$	14.5108	0.883099
$271$	1.27014	0.0771556	0.0385778	−	0.999256i	$-0.487717\pi$
$271$	1.27014	0.0771556	0.0385778	+	0.999256i	$0.487717\pi$
$272$	−3.49575	−0.211961
$273$	−0.693328	−0.0419621
$274$	−27.1270	−1.63880
$275$	0.594264	0.0358354
$276$	−38.7945	−2.33516
$277$	14.6698	0.881423	0.440711	−	0.897649i	$-0.354726\pi$
$277$	14.6698	0.881423	0.440711	+	0.897649i	$0.354726\pi$
$278$	4.86143	0.291569
$279$	11.3691	0.680650
$280$	−6.64517	−0.397125
$281$	−3.57106	−0.213032	−0.106516	−	0.994311i	$-0.533969\pi$
$281$	−3.57106	−0.213032	−0.106516	+	0.994311i	$0.533969\pi$
$282$	−31.7667	−1.89168
$283$	26.7299	1.58893	0.794463	−	0.607313i	$-0.207753\pi$
$283$	26.7299	1.58893	0.794463	+	0.607313i	$0.207753\pi$
$284$	51.9310	3.08154
$285$	10.3100	0.610711
$286$	0.763941	0.0451728
$287$	5.15572	0.304333
$288$	7.51434	0.442787
$289$	−16.8032	−0.988422
$290$	6.26377	0.367821
$291$	−2.14278	−0.125612
$292$	−11.6149	−0.679713
$293$	6.57284	0.383989	0.191995	−	0.981396i	$-0.438504\pi$
$293$	6.57284	0.383989	0.191995	+	0.981396i	$0.438504\pi$
$294$	3.55358	0.207249
$295$	−2.44448	−0.142323
$296$	74.2377	4.31498
$297$	3.35944	0.194934
$298$	−8.75793	−0.507333
$299$	−3.05833	−0.176868
$300$	−6.35277	−0.366777
$301$	2.92491	0.168589
$302$	−37.1444	−2.13742
$303$	−3.61078	−0.207434
$304$	58.6817	3.36562
$305$	1.25498	0.0718601
$306$	−1.23379	−0.0705310
$307$	−27.8837	−1.59141	−0.795703	−	0.605686i	$-0.792899\pi$
$307$	−27.8837	−1.59141	−0.795703	+	0.605686i	$0.792899\pi$
$308$	−2.72697	−0.155383
$309$	22.2481	1.26565
$310$	−26.9356	−1.52984
$311$	−2.84162	−0.161133	−0.0805666	−	0.996749i	$-0.525673\pi$
$311$	−2.84162	−0.161133	−0.0805666	+	0.996749i	$0.525673\pi$
$312$	−4.60728	−0.260836
$313$	−31.2469	−1.76618	−0.883091	−	0.469203i	$-0.844541\pi$
$313$	−31.2469	−1.76618	−0.883091	+	0.469203i	$0.844541\pi$
$314$	−34.8221	−1.96512
$315$	−1.08344	−0.0610447
$316$	53.8386	3.02866
$317$	−7.10024	−0.398789	−0.199395	−	0.979919i	$-0.563898\pi$
$317$	−7.10024	−0.398789	−0.199395	+	0.979919i	$0.563898\pi$
$318$	17.0777	0.957672
$319$	1.45014	0.0811924
$320$	−2.04367	−0.114245
$321$	22.3710	1.24863
$322$	15.6751	0.873541
$323$	−3.30393	−0.183835
$324$	−20.9978	−1.16655
$325$	−0.500814	−0.0277802
$326$	48.0130	2.65920
$327$	−17.3934	−0.961859
$328$	34.2606	1.89173
$329$	8.93936	0.492843
$330$	−2.11176	−0.116249
$331$	−14.4550	−0.794518	−0.397259	−	0.917707i	$-0.630039\pi$
$331$	−14.4550	−0.794518	−0.397259	+	0.917707i	$0.630039\pi$
$332$	−70.4362	−3.86569
$333$	12.1038	0.663284
$334$	15.1689	0.830003
$335$	−1.12341	−0.0613785
$336$	10.9086	0.595111
$337$	16.1300	0.878657	0.439329	−	0.898326i	$-0.355216\pi$
$337$	16.1300	0.878657	0.439329	+	0.898326i	$0.355216\pi$
$338$	32.7255	1.78003
$339$	−17.5578	−0.953610
$340$	2.03580	0.110407
$341$	−6.23594	−0.337695
$342$	20.7111	1.11993
$343$	−1.00000	−0.0539949
$344$	19.4365	1.04795
$345$	8.45414	0.455155
$346$	−0.767604	−0.0412666
$347$	−17.2910	−0.928227	−0.464114	−	0.885776i	$-0.653627\pi$
$347$	−17.2910	−0.928227	−0.464114	+	0.885776i	$0.653627\pi$
$348$	−15.5022	−0.831008
$349$	−30.2609	−1.61983	−0.809916	−	0.586546i	$-0.800487\pi$
$349$	−30.2609	−1.61983	−0.809916	+	0.586546i	$0.800487\pi$
$350$	2.56687	0.137205
$351$	−2.83116	−0.151116
$352$	−4.12161	−0.219683
$353$	−2.27699	−0.121192	−0.0605960	−	0.998162i	$-0.519300\pi$
$353$	−2.27699	−0.121192	−0.0605960	+	0.998162i	$0.519300\pi$
$354$	8.68664	0.461690
$355$	−11.3169	−0.600636
$356$	76.7410	4.06727
$357$	−0.614180	−0.0325058
$358$	−37.4445	−1.97900
$359$	8.33033	0.439658	0.219829	−	0.975538i	$-0.429450\pi$
$359$	8.33033	0.439658	0.219829	+	0.975538i	$0.429450\pi$
$360$	−7.19961	−0.379453
$361$	36.4617	1.91904
$362$	−48.2058	−2.53364
$363$	14.7395	0.773623
$364$	2.29815	0.120456
$365$	2.53114	0.132486
$366$	−4.45968	−0.233111
$367$	31.1945	1.62834	0.814169	−	0.580628i	$-0.197193\pi$
$367$	31.1945	1.62834	0.814169	+	0.580628i	$0.197193\pi$
$368$	48.1187	2.50836
$369$	5.58589	0.290790
$370$	−28.6763	−1.49081
$371$	−4.80579	−0.249504
$372$	66.6631	3.45632
$373$	−6.55968	−0.339647	−0.169824	−	0.985474i	$-0.554320\pi$
$373$	−6.55968	−0.339647	−0.169824	+	0.985474i	$0.554320\pi$
$374$	0.676732	0.0349930
$375$	1.38440	0.0714901
$376$	59.4035	3.06350
$377$	−1.22211	−0.0629416
$378$	14.5108	0.746355
$379$	−37.5103	−1.92678	−0.963389	−	0.268109i	$-0.913601\pi$
$379$	−37.5103	−1.92678	−0.963389	+	0.268109i	$0.913601\pi$
$380$	−34.1741	−1.75310
$381$	19.1123	0.979155
$382$	−26.6218	−1.36209
$383$	15.3023	0.781912	0.390956	−	0.920409i	$-0.372144\pi$
$383$	15.3023	0.781912	0.390956	+	0.920409i	$0.372144\pi$
$384$	−11.9411	−0.609368
$385$	0.594264	0.0302865
$386$	−46.4525	−2.36437
$387$	3.16895	0.161087
$388$	7.10261	0.360580
$389$	−14.5831	−0.739394	−0.369697	−	0.929152i	$-0.620538\pi$
$389$	−14.5831	−0.739394	−0.369697	+	0.929152i	$0.620538\pi$
$390$	1.77968	0.0901177
$391$	−2.70920	−0.137010
$392$	−6.64517	−0.335632
$393$	−15.1467	−0.764052
$394$	30.6405	1.54365
$395$	−11.7326	−0.590329
$396$	−2.95449	−0.148469
$397$	26.7658	1.34333	0.671667	−	0.740853i	$-0.265578\pi$
$397$	26.7658	1.34333	0.671667	+	0.740853i	$0.265578\pi$
$398$	28.0923	1.40814
$399$	10.3100	0.516145
$400$	7.87963	0.393982
$401$	3.04531	0.152076	0.0760378	−	0.997105i	$-0.475773\pi$
$401$	3.04531	0.152076	0.0760378	+	0.997105i	$0.475773\pi$
$402$	3.99212	0.199109
$403$	5.25533	0.261786
$404$	11.9685	0.595457
$405$	4.57586	0.227376
$406$	6.26377	0.310866
$407$	−6.63893	−0.329080
$408$	−4.08133	−0.202056
$409$	−15.8189	−0.782197	−0.391098	−	0.920349i	$-0.627905\pi$
$409$	−15.8189	−0.782197	−0.391098	+	0.920349i	$0.627905\pi$
$410$	−13.2341	−0.653584
$411$	−14.6305	−0.721669
$412$	−73.7451	−3.63316
$413$	−2.44448	−0.120285
$414$	16.9830	0.834669
$415$	15.3495	0.753478
$416$	3.47348	0.170301
$417$	2.62194	0.128397
$418$	−11.3600	−0.555637
$419$	35.0859	1.71406	0.857030	−	0.515267i	$-0.172307\pi$
$419$	35.0859	1.71406	0.857030	+	0.515267i	$0.172307\pi$
$420$	−6.35277	−0.309983
$421$	−28.8591	−1.40651	−0.703253	−	0.710940i	$-0.748270\pi$
$421$	−28.8591	−1.40651	−0.703253	+	0.710940i	$0.748270\pi$
$422$	7.91121	0.385112
$423$	9.68522	0.470912
$424$	−31.9353	−1.55091
$425$	−0.443643	−0.0215199
$426$	40.2153	1.94844
$427$	1.25498	0.0607329
$428$	−74.1522	−3.58428
$429$	0.412019	0.0198925
$430$	−7.50786	−0.362061
$431$	−6.58669	−0.317270	−0.158635	−	0.987337i	$-0.550709\pi$
$431$	−6.58669	−0.317270	−0.158635	+	0.987337i	$0.550709\pi$
$432$	44.5444	2.14314
$433$	−15.7383	−0.756332	−0.378166	−	0.925738i	$-0.623445\pi$
$433$	−15.7383	−0.756332	−0.378166	+	0.925738i	$0.623445\pi$
$434$	−26.9356	−1.29295
$435$	3.37826	0.161975
$436$	57.6533	2.76109
$437$	45.4783	2.17552
$438$	−8.99459	−0.429778
$439$	18.6752	0.891321	0.445660	−	0.895202i	$-0.352969\pi$
$439$	18.6752	0.891321	0.445660	+	0.895202i	$0.352969\pi$
$440$	3.94898	0.188260
$441$	−1.08344	−0.0515921
$442$	−0.570315	−0.0271271
$443$	1.23384	0.0586215	0.0293108	−	0.999570i	$-0.490669\pi$
$443$	1.23384	0.0586215	0.0293108	+	0.999570i	$0.490669\pi$
$444$	70.9711	3.36814
$445$	−16.7235	−0.792769
$446$	−28.1710	−1.33394
$447$	−4.72345	−0.223412
$448$	−2.04367	−0.0965545
$449$	−0.311708	−0.0147104	−0.00735519	−	0.999973i	$-0.502341\pi$
$449$	−0.311708	−0.0147104	−0.00735519	+	0.999973i	$0.502341\pi$
$450$	2.78104	0.131099
$451$	−3.06386	−0.144271
$452$	58.1983	2.73742
$453$	−20.0332	−0.941243
$454$	−29.9733	−1.40672
$455$	−0.500814	−0.0234785
$456$	68.5116	3.20835
$457$	38.6946	1.81006	0.905028	−	0.425352i	$-0.139850\pi$
$457$	38.6946	1.81006	0.905028	+	0.425352i	$0.139850\pi$
$458$	2.56687	0.119942
$459$	−2.50796	−0.117062
$460$	−28.0226	−1.30656
$461$	−38.5366	−1.79483	−0.897413	−	0.441191i	$-0.854556\pi$
$461$	−38.5366	−1.79483	−0.897413	+	0.441191i	$0.854556\pi$
$462$	−2.11176	−0.0982480
$463$	−19.0735	−0.886423	−0.443211	−	0.896417i	$-0.646161\pi$
$463$	−19.0735	−0.886423	−0.443211	+	0.896417i	$0.646161\pi$
$464$	19.2282	0.892645
$465$	−14.5273	−0.673687
$466$	−36.8192	−1.70561
$467$	−10.4991	−0.485839	−0.242919	−	0.970047i	$-0.578105\pi$
$467$	−10.4991	−0.485839	−0.242919	+	0.970047i	$0.578105\pi$
$468$	2.48989	0.115095
$469$	−1.12341	−0.0518743
$470$	−22.9462	−1.05843
$471$	−18.7807	−0.865371
$472$	−16.2440	−0.747689
$473$	−1.73817	−0.0799210
$474$	41.6925	1.91500
$475$	7.44726	0.341704
$476$	2.03580	0.0933107
$477$	−5.20676	−0.238401
$478$	55.1565	2.52280
$479$	−16.3626	−0.747625	−0.373812	−	0.927504i	$-0.621950\pi$
$479$	−16.3626	−0.747625	−0.373812	+	0.927504i	$0.621950\pi$
$480$	−9.60173	−0.438257
$481$	5.59494	0.255108
$482$	5.06588	0.230744
$483$	8.45414	0.384677
$484$	−48.8565	−2.22075
$485$	−1.54781	−0.0702823
$486$	27.2717	1.23707
$487$	5.00663	0.226872	0.113436	−	0.993545i	$-0.463814\pi$
$487$	5.00663	0.226872	0.113436	+	0.993545i	$0.463814\pi$
$488$	8.33957	0.377515
$489$	25.8951	1.17102
$490$	2.56687	0.115959
$491$	30.0515	1.35620	0.678102	−	0.734968i	$-0.262803\pi$
$491$	30.0515	1.35620	0.678102	+	0.734968i	$0.262803\pi$
$492$	32.7531	1.47662
$493$	−1.08259	−0.0487576
$494$	9.57364	0.430739
$495$	0.643846	0.0289387
$496$	−82.6854	−3.71268
$497$	−11.3169	−0.507630
$498$	−54.5457	−2.44425
$499$	36.6828	1.64215	0.821074	−	0.570821i	$-0.193375\pi$
$499$	36.6828	1.64215	0.821074	+	0.570821i	$0.193375\pi$
$500$	−4.58882	−0.205218
$501$	8.18108	0.365504
$502$	−9.18806	−0.410083
$503$	28.5590	1.27338	0.636692	−	0.771119i	$-0.280302\pi$
$503$	28.5590	1.27338	0.636692	+	0.771119i	$0.280302\pi$
$504$	−7.19961	−0.320696
$505$	−2.60819	−0.116063
$506$	−9.31516	−0.414109
$507$	17.6500	0.783863
$508$	−63.3510	−2.81075
$509$	−31.8918	−1.41358	−0.706788	−	0.707425i	$-0.749857\pi$
$509$	−31.8918	−1.41358	−0.706788	+	0.707425i	$0.749857\pi$
$510$	1.57652	0.0698095
$511$	2.53114	0.111971
$512$	50.0725	2.21291
$513$	42.1002	1.85877
$514$	−62.5821	−2.76038
$515$	16.0706	0.708155
$516$	18.5813	0.817995
$517$	−5.31234	−0.233636
$518$	−28.6763	−1.25996
$519$	−0.413995	−0.0181724
$520$	−3.32799	−0.145942
$521$	−18.5170	−0.811244	−0.405622	−	0.914041i	$-0.632945\pi$
$521$	−18.5170	−0.811244	−0.405622	+	0.914041i	$0.632945\pi$
$522$	6.78639	0.297032
$523$	−4.59293	−0.200835	−0.100417	−	0.994945i	$-0.532018\pi$
$523$	−4.59293	−0.200835	−0.100417	+	0.994945i	$0.532018\pi$
$524$	50.2063	2.19327
$525$	1.38440	0.0604202
$526$	−58.6331	−2.55652
$527$	4.65540	0.202792
$528$	−6.48256	−0.282117
$529$	14.2919	0.621389
$530$	12.3358	0.535835
$531$	−2.64843	−0.114932
$532$	−34.1741	−1.48164
$533$	2.58206	0.111841
$534$	59.4282	2.57171
$535$	16.1593	0.698628
$536$	−7.46525	−0.322450
$537$	−20.1951	−0.871483
$538$	12.7635	0.550275
$539$	0.594264	0.0255967
$540$	−25.9411	−1.11633
$541$	−4.65414	−0.200097	−0.100049	−	0.994983i	$-0.531900\pi$
$541$	−4.65414	−0.200097	−0.100049	+	0.994983i	$0.531900\pi$
$542$	−3.26029	−0.140041
$543$	−25.9991	−1.11573
$544$	3.07696	0.131924
$545$	−12.5639	−0.538177
$546$	1.77968	0.0761634
$547$	2.74245	0.117259	0.0586294	−	0.998280i	$-0.481327\pi$
$547$	2.74245	0.117259	0.0586294	+	0.998280i	$0.481327\pi$
$548$	48.4952	2.07161
$549$	1.35969	0.0580303
$550$	−1.52540	−0.0650432
$551$	18.1731	0.774199
$552$	56.1791	2.39114
$553$	−11.7326	−0.498919
$554$	−37.6555	−1.59983
$555$	−15.4661	−0.656499
$556$	−8.69084	−0.368574
$557$	30.3862	1.28750	0.643751	−	0.765235i	$-0.277377\pi$
$557$	30.3862	1.28750	0.643751	+	0.765235i	$0.277377\pi$
$558$	−29.1830	−1.23541
$559$	1.46484	0.0619560
$560$	7.87963	0.332975
$561$	0.364985	0.0154097
$562$	9.16645	0.386663
$563$	−3.72488	−0.156985	−0.0784924	−	0.996915i	$-0.525011\pi$
$563$	−3.72488	−0.156985	−0.0784924	+	0.996915i	$0.525011\pi$
$564$	56.7897	2.39128
$565$	−12.6826	−0.533562
$566$	−68.6121	−2.88398
$567$	4.57586	0.192168
$568$	−75.2024	−3.15542
$569$	−44.6922	−1.87360	−0.936798	−	0.349871i	$-0.886225\pi$
$569$	−44.6922	−1.87360	−0.936798	+	0.349871i	$0.886225\pi$
$570$	−26.4644	−1.10847
$571$	−38.4757	−1.61016	−0.805080	−	0.593167i	$-0.797877\pi$
$571$	−38.4757	−1.61016	−0.805080	+	0.593167i	$0.797877\pi$
$572$	−1.36571	−0.0571030
$573$	−14.3580	−0.599815
$574$	−13.2341	−0.552379
$575$	6.10671	0.254668
$576$	−2.21419	−0.0922578
$577$	−6.91321	−0.287801	−0.143900	−	0.989592i	$-0.545964\pi$
$577$	−6.91321	−0.287801	−0.143900	+	0.989592i	$0.545964\pi$
$578$	43.1316	1.79404
$579$	−25.0534	−1.04119
$580$	−11.1978	−0.464963
$581$	15.3495	0.636805
$582$	5.50025	0.227993
$583$	2.85591	0.118280
$584$	16.8198	0.696010
$585$	−0.542600	−0.0224337
$586$	−16.8716	−0.696960
$587$	3.29310	0.135921	0.0679604	−	0.997688i	$-0.478351\pi$
$587$	3.29310	0.135921	0.0679604	+	0.997688i	$0.478351\pi$
$588$	−6.35277	−0.261984
$589$	−78.1483	−3.22004
$590$	6.27466	0.258324
$591$	16.5255	0.679768
$592$	−88.0288	−3.61796
$593$	−39.0943	−1.60541	−0.802706	−	0.596376i	$-0.796607\pi$
$593$	−39.0943	−1.60541	−0.802706	+	0.596376i	$0.796607\pi$
$594$	−8.62324	−0.353816
$595$	−0.443643	−0.0181876
$596$	15.6566	0.641321
$597$	15.1511	0.620095
$598$	7.85033	0.321024
$599$	14.2369	0.581702	0.290851	−	0.956768i	$-0.406062\pi$
$599$	14.2369	0.581702	0.290851	+	0.956768i	$0.406062\pi$
$600$	9.19957	0.375571
$601$	−12.8207	−0.522966	−0.261483	−	0.965208i	$-0.584211\pi$
$601$	−12.8207	−0.522966	−0.261483	+	0.965208i	$0.584211\pi$
$602$	−7.50786	−0.305998
$603$	−1.21714	−0.0495659
$604$	66.4034	2.70192
$605$	10.6469	0.432856
$606$	9.26841	0.376503
$607$	−24.7589	−1.00493	−0.502466	−	0.864597i	$-0.667574\pi$
$607$	−24.7589	−1.00493	−0.502466	+	0.864597i	$0.667574\pi$
$608$	−51.6517	−2.09475
$609$	3.37826	0.136894
$610$	−3.22138	−0.130430
$611$	4.47696	0.181119
$612$	2.20566	0.0891584
$613$	−15.9799	−0.645422	−0.322711	−	0.946498i	$-0.604594\pi$
$613$	−15.9799	−0.645422	−0.322711	+	0.946498i	$0.604594\pi$
$614$	71.5738	2.88848
$615$	−7.13758	−0.287815
$616$	3.94898	0.159109
$617$	1.26685	0.0510014	0.0255007	−	0.999675i	$-0.491882\pi$
$617$	1.26685	0.0510014	0.0255007	+	0.999675i	$0.491882\pi$
$618$	−57.1081	−2.29722
$619$	0.509964	0.0204972	0.0102486	−	0.999947i	$-0.496738\pi$
$619$	0.509964	0.0204972	0.0102486	+	0.999947i	$0.496738\pi$
$620$	48.1531	1.93387
$621$	34.5219	1.38532
$622$	7.29406	0.292465
$623$	−16.7235	−0.670012
$624$	5.46317	0.218702
$625$	1.00000	0.0400000
$626$	80.2068	3.20571
$627$	−6.12685	−0.244683
$628$	62.2518	2.48412
$629$	4.95624	0.197618
$630$	2.78104	0.110799
$631$	26.9473	1.07276	0.536378	−	0.843978i	$-0.319792\pi$
$631$	26.9473	1.07276	0.536378	+	0.843978i	$0.319792\pi$
$632$	−77.9648	−3.10127
$633$	4.26679	0.169590
$634$	18.2254	0.723823
$635$	13.8055	0.547855
$636$	−30.5301	−1.21060
$637$	−0.500814	−0.0198430
$638$	−3.72233	−0.147368
$639$	−12.2611	−0.485041
$640$	−8.62548	−0.340952
$641$	−31.6818	−1.25136	−0.625679	−	0.780081i	$-0.715178\pi$
$641$	−31.6818	−1.25136	−0.625679	+	0.780081i	$0.715178\pi$
$642$	−57.4234	−2.26632
$643$	−14.8128	−0.584158	−0.292079	−	0.956394i	$-0.594347\pi$
$643$	−14.8128	−0.584158	−0.292079	+	0.956394i	$0.594347\pi$
$644$	−28.0226	−1.10425
$645$	−4.04925	−0.159439
$646$	8.48075	0.333671
$647$	47.4644	1.86602	0.933010	−	0.359851i	$-0.117173\pi$
$647$	47.4644	1.86602	0.933010	+	0.359851i	$0.117173\pi$
$648$	30.4074	1.19451
$649$	1.45266	0.0570221
$650$	1.28553	0.0504225
$651$	−14.5273	−0.569369
$652$	−85.8334	−3.36150
$653$	−2.96931	−0.116198	−0.0580990	−	0.998311i	$-0.518504\pi$
$653$	−2.96931	−0.116198	−0.0580990	+	0.998311i	$0.518504\pi$
$654$	44.6467	1.74582
$655$	−10.9410	−0.427501
$656$	−40.6252	−1.58615
$657$	2.74232	0.106988
$658$	−22.9462	−0.894535
$659$	49.8863	1.94329	0.971646	−	0.236439i	$-0.0759804\pi$
$659$	49.8863	1.94329	0.971646	+	0.236439i	$0.0759804\pi$
$660$	3.77522	0.146950
$661$	−15.5752	−0.605804	−0.302902	−	0.953022i	$-0.597955\pi$
$661$	−15.5752	−0.605804	−0.302902	+	0.953022i	$0.597955\pi$
$662$	37.1041	1.44209
$663$	−0.307590	−0.0119458
$664$	102.000	3.95837
$665$	7.44726	0.288792
$666$	−31.0689	−1.20389
$667$	14.9018	0.577001
$668$	−27.1175	−1.04921
$669$	−15.1936	−0.587418
$670$	2.88365	0.111405
$671$	−0.745791	−0.0287909
$672$	−9.60173	−0.370395
$673$	−21.3918	−0.824595	−0.412298	−	0.911049i	$-0.635274\pi$
$673$	−21.3918	−0.824595	−0.412298	+	0.911049i	$0.635274\pi$
$674$	−41.4036	−1.59481
$675$	5.65311	0.217588
$676$	−58.5037	−2.25014
$677$	−30.8134	−1.18425	−0.592127	−	0.805845i	$-0.701712\pi$
$677$	−30.8134	−1.18425	−0.592127	+	0.805845i	$0.701712\pi$
$678$	45.0687	1.73085
$679$	−1.54781	−0.0593994
$680$	−2.94808	−0.113054
$681$	−16.1656	−0.619468
$682$	16.0068	0.612934
$683$	−11.2230	−0.429435	−0.214718	−	0.976676i	$-0.568883\pi$
$683$	−11.2230	−0.429435	−0.214718	+	0.976676i	$0.568883\pi$
$684$	−37.0255	−1.41570
$685$	−10.5681	−0.403787
$686$	2.56687	0.0980035
$687$	1.38440	0.0528182
$688$	−23.0472	−0.878667
$689$	−2.40681	−0.0916921
$690$	−21.7007	−0.826130
$691$	5.85849	0.222867	0.111434	−	0.993772i	$-0.464456\pi$
$691$	5.85849	0.222867	0.111434	+	0.993772i	$0.464456\pi$
$692$	1.37225	0.0521653
$693$	0.643846	0.0244577
$694$	44.3836	1.68478
$695$	1.89392	0.0718403
$696$	22.4491	0.850932
$697$	2.28730	0.0866377
$698$	77.6759	2.94008
$699$	−19.8578	−0.751092
$700$	−4.58882	−0.173441
$701$	12.5872	0.475411	0.237706	−	0.971337i	$-0.423605\pi$
$701$	12.5872	0.475411	0.237706	+	0.971337i	$0.423605\pi$
$702$	7.26722	0.274283
$703$	−83.1985	−3.13789
$704$	1.21448	0.0457725
$705$	−12.3757	−0.466094
$706$	5.84474	0.219970
$707$	−2.60819	−0.0980912
$708$	−15.5292	−0.583623
$709$	−2.07712	−0.0780077	−0.0390038	−	0.999239i	$-0.512418\pi$
$709$	−2.07712	−0.0780077	−0.0390038	+	0.999239i	$0.512418\pi$
$710$	29.0489	1.09019
$711$	−12.7115	−0.476717
$712$	−111.130	−4.16478
$713$	−64.0812	−2.39986
$714$	1.57652	0.0589998
$715$	0.297616	0.0111302
$716$	66.9400	2.50166
$717$	29.7478	1.11095
$718$	−21.3829	−0.798002
$719$	−7.38066	−0.275252	−0.137626	−	0.990484i	$-0.543947\pi$
$719$	−7.38066	−0.275252	−0.137626	+	0.990484i	$0.543947\pi$
$720$	8.53707	0.318158
$721$	16.0706	0.598500
$722$	−93.5924	−3.48315
$723$	2.73220	0.101612
$724$	86.1781	3.20278
$725$	2.44024	0.0906281
$726$	−37.8344	−1.40417
$727$	37.5915	1.39419	0.697095	−	0.716978i	$-0.254475\pi$
$727$	37.5915	1.39419	0.697095	+	0.716978i	$0.254475\pi$
$728$	−3.32799	−0.123344
$729$	28.4362	1.05319
$730$	−6.49710	−0.240469
$731$	1.29762	0.0479941
$732$	7.97262	0.294676
$733$	9.94685	0.367395	0.183698	−	0.982983i	$-0.441193\pi$
$733$	9.94685	0.367395	0.183698	+	0.982983i	$0.441193\pi$
$734$	−80.0721	−2.95552
$735$	1.38440	0.0510644
$736$	−42.3541	−1.56119
$737$	0.667602	0.0245914
$738$	−14.3383	−0.527798
$739$	17.1902	0.632353	0.316176	−	0.948700i	$-0.397601\pi$
$739$	17.1902	0.632353	0.316176	+	0.948700i	$0.397601\pi$
$740$	51.2649	1.88453
$741$	5.16339	0.189682
$742$	12.3358	0.452863
$743$	−52.7446	−1.93501	−0.967505	−	0.252852i	$-0.918632\pi$
$743$	−52.7446	−1.93501	−0.967505	+	0.252852i	$0.918632\pi$
$744$	−96.5363	−3.53919
$745$	−3.41191	−0.125003
$746$	16.8378	0.616477
$747$	16.6302	0.608467
$748$	−1.20980	−0.0442347
$749$	16.1593	0.590449
$750$	−3.55358	−0.129758
$751$	21.2632	0.775906	0.387953	−	0.921679i	$-0.373182\pi$
$751$	21.2632	0.775906	0.387953	+	0.921679i	$0.373182\pi$
$752$	−70.4389	−2.56864
$753$	−4.95543	−0.180586
$754$	3.13699	0.114242
$755$	−14.4707	−0.526642
$756$	−25.9411	−0.943469
$757$	43.2373	1.57149	0.785743	−	0.618553i	$-0.212281\pi$
$757$	43.2373	1.57149	0.785743	+	0.618553i	$0.212281\pi$
$758$	96.2842	3.49720
$759$	−5.02398	−0.182359
$760$	49.4883	1.79513
$761$	26.8476	0.973225	0.486613	−	0.873618i	$-0.338232\pi$
$761$	26.8476	0.973225	0.486613	+	0.873618i	$0.338232\pi$
$762$	−49.0589	−1.77722
$763$	−12.5639	−0.454843
$764$	47.5920	1.72182
$765$	−0.480659	−0.0173782
$766$	−39.2791	−1.41921
$767$	−1.22423	−0.0442044
$768$	36.3098	1.31022
$769$	7.76113	0.279873	0.139937	−	0.990160i	$-0.455310\pi$
$769$	7.76113	0.279873	0.139937	+	0.990160i	$0.455310\pi$
$770$	−1.52540	−0.0549715
$771$	−33.7527	−1.21557
$772$	83.0437	2.98881
$773$	21.2019	0.762579	0.381289	−	0.924456i	$-0.375480\pi$
$773$	21.2019	0.762579	0.381289	+	0.924456i	$0.375480\pi$
$774$	−8.13428	−0.292381
$775$	−10.4936	−0.376940
$776$	−10.2854	−0.369226
$777$	−15.4661	−0.554843
$778$	37.4330	1.34204
$779$	−38.3960	−1.37568
$780$	−3.18156	−0.113918
$781$	6.72520	0.240646
$782$	6.95417	0.248680
$783$	13.7949	0.492990
$784$	7.87963	0.281415
$785$	−13.5660	−0.484190
$786$	38.8797	1.38679
$787$	15.7094	0.559980	0.279990	−	0.960003i	$-0.409669\pi$
$787$	15.7094	0.559980	0.279990	+	0.960003i	$0.409669\pi$
$788$	−54.7764	−1.95133
$789$	−31.6228	−1.12580
$790$	30.1159	1.07148
$791$	−12.6826	−0.450942
$792$	4.27846	0.152029
$793$	0.628514	0.0223192
$794$	−68.7042	−2.43822
$795$	6.65314	0.235963
$796$	−50.2209	−1.78003
$797$	−25.0783	−0.888320	−0.444160	−	0.895947i	$-0.646498\pi$
$797$	−25.0783	−0.888320	−0.444160	+	0.895947i	$0.646498\pi$
$798$	−26.4644	−0.936830
$799$	3.96589	0.140303
$800$	−6.93566	−0.245213
$801$	−18.1188	−0.640196
$802$	−7.81692	−0.276025
$803$	−1.50416	−0.0530808
$804$	−7.13676	−0.251694
$805$	6.10671	0.215233
$806$	−13.4897	−0.475156
$807$	6.88381	0.242321
$808$	−17.3319	−0.609733
$809$	−37.0230	−1.30166	−0.650830	−	0.759223i	$-0.725579\pi$
$809$	−37.0230	−1.30166	−0.650830	+	0.759223i	$0.725579\pi$
$810$	−11.7456	−0.412700
$811$	−24.4065	−0.857027	−0.428513	−	0.903535i	$-0.640963\pi$
$811$	−24.4065	−0.857027	−0.428513	+	0.903535i	$0.640963\pi$
$812$	−11.1978	−0.392966
$813$	−1.75838	−0.0616692
$814$	17.0413	0.597296
$815$	18.7049	0.655204
$816$	4.83951	0.169417
$817$	−21.7826	−0.762075
$818$	40.6052	1.41973
$819$	−0.542600	−0.0189600
$820$	23.6587	0.826197
$821$	14.6959	0.512891	0.256446	−	0.966559i	$-0.417449\pi$
$821$	14.6959	0.512891	0.256446	+	0.966559i	$0.417449\pi$
$822$	37.5546	1.30987
$823$	−22.6956	−0.791120	−0.395560	−	0.918440i	$-0.629449\pi$
$823$	−22.6956	−0.791120	−0.395560	+	0.918440i	$0.629449\pi$
$824$	106.792	3.72027
$825$	−0.822699	−0.0286427
$826$	6.27466	0.218323
$827$	−16.0447	−0.557930	−0.278965	−	0.960301i	$-0.589991\pi$
$827$	−16.0447	−0.557930	−0.278965	+	0.960301i	$0.589991\pi$
$828$	−30.3607	−1.05511
$829$	8.39268	0.291490	0.145745	−	0.989322i	$-0.453442\pi$
$829$	8.39268	0.291490	0.145745	+	0.989322i	$0.453442\pi$
$830$	−39.4002	−1.36760
$831$	−20.3089	−0.704507
$832$	−1.02350	−0.0354835
$833$	−0.443643	−0.0153713
$834$	−6.73017	−0.233047
$835$	5.90948	0.204506
$836$	20.3084	0.702382
$837$	−59.3213	−2.05044
$838$	−90.0610	−3.11111
$839$	11.6290	0.401476	0.200738	−	0.979645i	$-0.435666\pi$
$839$	11.6290	0.401476	0.200738	+	0.979645i	$0.435666\pi$
$840$	9.19957	0.317415
$841$	−23.0452	−0.794664
$842$	74.0775	2.55288
$843$	4.94378	0.170273
$844$	−14.1430	−0.486821
$845$	12.7492	0.438585
$846$	−24.8607	−0.854728
$847$	10.6469	0.365830
$848$	37.8679	1.30039
$849$	−37.0048	−1.27000
$850$	1.13877	0.0390596
$851$	−68.2223	−2.33863
$852$	−71.8934	−2.46303
$853$	−20.4185	−0.699115	−0.349558	−	0.936915i	$-0.613668\pi$
$853$	−20.4185	−0.699115	−0.349558	+	0.936915i	$0.613668\pi$
$854$	−3.22138	−0.110233
$855$	8.06862	0.275941
$856$	107.381	3.67022
$857$	−46.5924	−1.59157	−0.795784	−	0.605581i	$-0.792941\pi$
$857$	−46.5924	−1.59157	−0.795784	+	0.605581i	$0.792941\pi$
$858$	−1.05760	−0.0361059
$859$	−25.3969	−0.866530	−0.433265	−	0.901267i	$-0.642639\pi$
$859$	−25.3969	−0.866530	−0.433265	+	0.901267i	$0.642639\pi$
$860$	13.4219	0.457683
$861$	−7.13758	−0.243248
$862$	16.9072	0.575861
$863$	−42.0235	−1.43050	−0.715248	−	0.698870i	$-0.753686\pi$
$863$	−42.0235	−1.43050	−0.715248	+	0.698870i	$0.753686\pi$
$864$	−39.2081	−1.33389
$865$	−0.299043	−0.0101678
$866$	40.3980	1.37278
$867$	23.2623	0.790030
$868$	48.1531	1.63442
$869$	6.97223	0.236517
$870$	−8.67156	−0.293994
$871$	−0.562620	−0.0190637
$872$	−83.4890	−2.82729
$873$	−1.67695	−0.0567561
$874$	−116.737	−3.94868
$875$	1.00000	0.0338062
$876$	16.0797	0.543284
$877$	−5.99551	−0.202454	−0.101227	−	0.994863i	$-0.532277\pi$
$877$	−5.99551	−0.202454	−0.101227	+	0.994863i	$0.532277\pi$
$878$	−47.9369	−1.61779
$879$	−9.09944	−0.306917
$880$	−4.68258	−0.157850
$881$	−52.2614	−1.76073	−0.880366	−	0.474295i	$-0.842703\pi$
$881$	−52.2614	−1.76073	−0.880366	+	0.474295i	$0.842703\pi$
$882$	2.78104	0.0936424
$883$	27.4439	0.923560	0.461780	−	0.886995i	$-0.347211\pi$
$883$	27.4439	0.923560	0.461780	+	0.886995i	$0.347211\pi$
$884$	1.01956	0.0342914
$885$	3.38414	0.113757
$886$	−3.16711	−0.106401
$887$	−10.1987	−0.342440	−0.171220	−	0.985233i	$-0.554771\pi$
$887$	−10.1987	−0.342440	−0.171220	+	0.985233i	$0.554771\pi$
$888$	−102.775	−3.44890
$889$	13.8055	0.463022
$890$	42.9270	1.43892
$891$	−2.71927	−0.0910989
$892$	50.3616	1.68623
$893$	−66.5738	−2.22781
$894$	12.1245	0.405503
$895$	−14.5876	−0.487610
$896$	−8.62548	−0.288157
$897$	4.23395	0.141368
$898$	0.800113	0.0267001
$899$	−25.6068	−0.854033
$900$	−4.97169	−0.165723
$901$	−2.13206	−0.0710291
$902$	7.86452	0.261860
$903$	−4.04925	−0.134751
$904$	−84.2781	−2.80305
$905$	−18.7800	−0.624269
$906$	51.4227	1.70840
$907$	−23.3270	−0.774559	−0.387280	−	0.921962i	$-0.626585\pi$
$907$	−23.3270	−0.774559	−0.387280	+	0.921962i	$0.626585\pi$
$908$	53.5836	1.77823
$909$	−2.82581	−0.0937261
$910$	1.28553	0.0426148
$911$	−22.1169	−0.732766	−0.366383	−	0.930464i	$-0.619404\pi$
$911$	−22.1169	−0.732766	−0.366383	+	0.930464i	$0.619404\pi$
$912$	−81.2389	−2.69009
$913$	−9.12166	−0.301883
$914$	−99.3239	−3.28534
$915$	−1.73740	−0.0574367
$916$	−4.58882	−0.151619
$917$	−10.9410	−0.361304
$918$	6.43762	0.212473
$919$	−10.0428	−0.331282	−0.165641	−	0.986186i	$-0.552969\pi$
$919$	−10.0428	−0.331282	−0.165641	+	0.986186i	$0.552969\pi$
$920$	40.5801	1.33789
$921$	38.6022	1.27199
$922$	98.9183	3.25770
$923$	−5.66765	−0.186553
$924$	3.77522	0.124196
$925$	−11.1717	−0.367323
$926$	48.9593	1.60890
$927$	17.4114	0.571867
$928$	−16.9246	−0.555579
$929$	12.0320	0.394757	0.197379	−	0.980327i	$-0.436757\pi$
$929$	12.0320	0.394757	0.197379	+	0.980327i	$0.436757\pi$
$930$	37.2897	1.22278
$931$	7.44726	0.244074
$932$	65.8220	2.15607
$933$	3.93393	0.128791
$934$	26.9497	0.881822
$935$	0.263641	0.00862198
$936$	−3.60567	−0.117855
$937$	−53.5704	−1.75007	−0.875034	−	0.484061i	$-0.839161\pi$
$937$	−53.5704	−1.75007	−0.875034	+	0.484061i	$0.839161\pi$
$938$	2.88365	0.0941545
$939$	43.2583	1.41168
$940$	41.0211	1.33796
$941$	2.59751	0.0846763	0.0423382	−	0.999103i	$-0.486519\pi$
$941$	2.59751	0.0846763	0.0423382	+	0.999103i	$0.486519\pi$
$942$	48.2077	1.57069
$943$	−31.4845	−1.02528
$944$	19.2616	0.626912
$945$	5.65311	0.183896
$946$	4.46165	0.145061
$947$	−50.3410	−1.63586	−0.817932	−	0.575315i	$-0.804879\pi$
$947$	−50.3410	−1.63586	−0.817932	+	0.575315i	$0.804879\pi$
$948$	−74.5342	−2.42076
$949$	1.26763	0.0411490
$950$	−19.1161	−0.620210
$951$	9.82958	0.318746
$952$	−2.94808	−0.0955479
$953$	−18.5465	−0.600780	−0.300390	−	0.953816i	$-0.597117\pi$
$953$	−18.5465	−0.600780	−0.300390	+	0.953816i	$0.597117\pi$
$954$	13.3651	0.432711
$955$	−10.3713	−0.335607
$956$	−98.6039	−3.18908
$957$	−2.00758	−0.0648958
$958$	42.0006	1.35698
$959$	−10.5681	−0.341262
$960$	2.82926	0.0913141
$961$	79.1148	2.55209
$962$	−14.3615	−0.463033
$963$	17.5076	0.564174
$964$	−9.05633	−0.291685
$965$	−18.0970	−0.582562
$966$	−21.7007	−0.698208
$967$	58.0639	1.86721	0.933605	−	0.358303i	$-0.116645\pi$
$967$	58.0639	1.86721	0.933605	+	0.358303i	$0.116645\pi$
$968$	70.7501	2.27399
$969$	4.57396	0.146937
$970$	3.97302	0.127566
$971$	−30.7309	−0.986202	−0.493101	−	0.869972i	$-0.664137\pi$
$971$	−30.7309	−0.986202	−0.493101	+	0.869972i	$0.664137\pi$
$972$	−48.7539	−1.56378
$973$	1.89392	0.0607161
$974$	−12.8514	−0.411784
$975$	0.693328	0.0222043
$976$	−9.88881	−0.316533
$977$	2.80877	0.0898606	0.0449303	−	0.998990i	$-0.485693\pi$
$977$	2.80877	0.0898606	0.0449303	+	0.998990i	$0.485693\pi$
$978$	−66.4693	−2.12545
$979$	9.93815	0.317625
$980$	−4.58882	−0.146584
$981$	−13.6121	−0.434602
$982$	−77.1382	−2.46158
$983$	60.5678	1.93181	0.965906	−	0.258893i	$-0.0833576\pi$
$983$	60.5678	1.93181	0.965906	+	0.258893i	$0.0833576\pi$
$984$	−47.4304	−1.51203
$985$	11.9369	0.380342
$986$	2.77888	0.0884975
$987$	−12.3757	−0.393922
$988$	−17.1149	−0.544498
$989$	−17.8616	−0.567965
$990$	−1.65267	−0.0525253
$991$	−17.9153	−0.569099	−0.284549	−	0.958661i	$-0.591844\pi$
$991$	−17.9153	−0.569099	−0.284549	+	0.958661i	$0.591844\pi$
$992$	72.7798	2.31076
$993$	20.0115	0.635046
$994$	29.0489	0.921375
$995$	10.9442	0.346954
$996$	97.5119	3.08978
$997$	−8.18147	−0.259110	−0.129555	−	0.991572i	$-0.541355\pi$
$997$	−8.18147	−0.259110	−0.129555	+	0.991572i	$0.541355\pi$
$998$	−94.1600	−2.98058
$999$	−63.1548	−1.99813

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.k.1.4	✓	49

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.k.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-2.56687 q^{2} -1.38440 q^{3} +4.58882 q^{4} -1.00000 q^{5} +3.55358 q^{6} -1.00000 q^{7} -6.64517 q^{8} -1.08344 q^{9} +O(q^{10})\)	\(q-2.56687 q^{2} -1.38440 q^{3} +4.58882 q^{4} -1.00000 q^{5} +3.55358 q^{6} -1.00000 q^{7} -6.64517 q^{8} -1.08344 q^{9} +2.56687 q^{10} +0.594264 q^{11} -6.35277 q^{12} -0.500814 q^{13} +2.56687 q^{14} +1.38440 q^{15} +7.87963 q^{16} -0.443643 q^{17} +2.78104 q^{18} +7.44726 q^{19} -4.58882 q^{20} +1.38440 q^{21} -1.52540 q^{22} +6.10671 q^{23} +9.19957 q^{24} +1.00000 q^{25} +1.28553 q^{26} +5.65311 q^{27} -4.58882 q^{28} +2.44024 q^{29} -3.55358 q^{30} -10.4936 q^{31} -6.93566 q^{32} -0.822699 q^{33} +1.13877 q^{34} +1.00000 q^{35} -4.97169 q^{36} -11.1717 q^{37} -19.1161 q^{38} +0.693328 q^{39} +6.64517 q^{40} -5.15572 q^{41} -3.55358 q^{42} -2.92491 q^{43} +2.72697 q^{44} +1.08344 q^{45} -15.6751 q^{46} -8.93936 q^{47} -10.9086 q^{48} +1.00000 q^{49} -2.56687 q^{50} +0.614180 q^{51} -2.29815 q^{52} +4.80579 q^{53} -14.5108 q^{54} -0.594264 q^{55} +6.64517 q^{56} -10.3100 q^{57} -6.26377 q^{58} +2.44448 q^{59} +6.35277 q^{60} -1.25498 q^{61} +26.9356 q^{62} +1.08344 q^{63} +2.04367 q^{64} +0.500814 q^{65} +2.11176 q^{66} +1.12341 q^{67} -2.03580 q^{68} -8.45414 q^{69} -2.56687 q^{70} +11.3169 q^{71} +7.19961 q^{72} -2.53114 q^{73} +28.6763 q^{74} -1.38440 q^{75} +34.1741 q^{76} -0.594264 q^{77} -1.77968 q^{78} +11.7326 q^{79} -7.87963 q^{80} -4.57586 q^{81} +13.2341 q^{82} -15.3495 q^{83} +6.35277 q^{84} +0.443643 q^{85} +7.50786 q^{86} -3.37826 q^{87} -3.94898 q^{88} +16.7235 q^{89} -2.78104 q^{90} +0.500814 q^{91} +28.0226 q^{92} +14.5273 q^{93} +22.9462 q^{94} -7.44726 q^{95} +9.60173 q^{96} +1.54781 q^{97} -2.56687 q^{98} -0.643846 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9}+O(q^{10}) \) 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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