LMFDB - Embedded newform 8015.2.a.k.1.6

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			1.6
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)

$f(q)$	$=$	$q-2.33828 q^{2} +2.05266 q^{3} +3.46754 q^{4} -1.00000 q^{5} -4.79969 q^{6} -1.00000 q^{7} -3.43150 q^{8} +1.21342 q^{9} +O(q^{10})$	\(q-2.33828 q^{2} +2.05266 q^{3} +3.46754 q^{4} -1.00000 q^{5} -4.79969 q^{6} -1.00000 q^{7} -3.43150 q^{8} +1.21342 q^{9} +2.33828 q^{10} +1.69184 q^{11} +7.11768 q^{12} +5.85497 q^{13} +2.33828 q^{14} -2.05266 q^{15} +1.08873 q^{16} -3.40252 q^{17} -2.83731 q^{18} +0.879154 q^{19} -3.46754 q^{20} -2.05266 q^{21} -3.95599 q^{22} +1.48967 q^{23} -7.04372 q^{24} +1.00000 q^{25} -13.6905 q^{26} -3.66724 q^{27} -3.46754 q^{28} -1.67715 q^{29} +4.79969 q^{30} -4.64953 q^{31} +4.31725 q^{32} +3.47278 q^{33} +7.95604 q^{34} +1.00000 q^{35} +4.20758 q^{36} -3.02402 q^{37} -2.05570 q^{38} +12.0183 q^{39} +3.43150 q^{40} +2.80817 q^{41} +4.79969 q^{42} -4.67876 q^{43} +5.86652 q^{44} -1.21342 q^{45} -3.48325 q^{46} -9.01092 q^{47} +2.23480 q^{48} +1.00000 q^{49} -2.33828 q^{50} -6.98423 q^{51} +20.3023 q^{52} +9.83070 q^{53} +8.57503 q^{54} -1.69184 q^{55} +3.43150 q^{56} +1.80461 q^{57} +3.92165 q^{58} +2.90013 q^{59} -7.11768 q^{60} -8.22158 q^{61} +10.8719 q^{62} -1.21342 q^{63} -12.2724 q^{64} -5.85497 q^{65} -8.12031 q^{66} -7.60067 q^{67} -11.7984 q^{68} +3.05778 q^{69} -2.33828 q^{70} +7.95868 q^{71} -4.16386 q^{72} -15.1245 q^{73} +7.07101 q^{74} +2.05266 q^{75} +3.04850 q^{76} -1.69184 q^{77} -28.1020 q^{78} -6.90139 q^{79} -1.08873 q^{80} -11.1679 q^{81} -6.56628 q^{82} +3.98305 q^{83} -7.11768 q^{84} +3.40252 q^{85} +10.9402 q^{86} -3.44263 q^{87} -5.80556 q^{88} -10.8742 q^{89} +2.83731 q^{90} -5.85497 q^{91} +5.16547 q^{92} -9.54391 q^{93} +21.0700 q^{94} -0.879154 q^{95} +8.86185 q^{96} +5.01813 q^{97} -2.33828 q^{98} +2.05291 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.33828	−1.65341	−0.826706	−	0.562635i	$-0.809788\pi$
$2$	−2.33828	−1.65341	−0.826706	+	0.562635i	$0.809788\pi$
$3$	2.05266	1.18510	0.592552	−	0.805532i	$-0.298120\pi$
$3$	2.05266	1.18510	0.592552	+	0.805532i	$0.298120\pi$
$4$	3.46754	1.73377
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−4.79969	−1.95947
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−3.43150	−1.21322
$9$	1.21342	0.404474
$10$	2.33828	0.739428
$11$	1.69184	0.510109	0.255054	−	0.966927i	$-0.417907\pi$
$11$	1.69184	0.510109	0.255054	+	0.966927i	$0.417907\pi$
$12$	7.11768	2.05470
$13$	5.85497	1.62388	0.811938	−	0.583744i	$-0.198413\pi$
$13$	5.85497	1.62388	0.811938	+	0.583744i	$0.198413\pi$
$14$	2.33828	0.624931
$15$	−2.05266	−0.529995
$16$	1.08873	0.272184
$17$	−3.40252	−0.825233	−0.412616	−	0.910905i	$-0.635385\pi$
$17$	−3.40252	−0.825233	−0.412616	+	0.910905i	$0.635385\pi$
$18$	−2.83731	−0.668761
$19$	0.879154	0.201692	0.100846	−	0.994902i	$-0.467845\pi$
$19$	0.879154	0.201692	0.100846	+	0.994902i	$0.467845\pi$
$20$	−3.46754	−0.775365
$21$	−2.05266	−0.447928
$22$	−3.95599	−0.843420
$23$	1.48967	0.310617	0.155308	−	0.987866i	$-0.450363\pi$
$23$	1.48967	0.310617	0.155308	+	0.987866i	$0.450363\pi$
$24$	−7.04372	−1.43779
$25$	1.00000	0.200000
$26$	−13.6905	−2.68493
$27$	−3.66724	−0.705761
$28$	−3.46754	−0.655303
$29$	−1.67715	−0.311439	−0.155720	−	0.987801i	$-0.549770\pi$
$29$	−1.67715	−0.311439	−0.155720	+	0.987801i	$0.549770\pi$
$30$	4.79969	0.876300
$31$	−4.64953	−0.835080	−0.417540	−	0.908659i	$-0.637108\pi$
$31$	−4.64953	−0.835080	−0.417540	+	0.908659i	$0.637108\pi$
$32$	4.31725	0.763189
$33$	3.47278	0.604533
$34$	7.95604	1.36445
$35$	1.00000	0.169031
$36$	4.20758	0.701263
$37$	−3.02402	−0.497147	−0.248573	−	0.968613i	$-0.579962\pi$
$37$	−3.02402	−0.497147	−0.248573	+	0.968613i	$0.579962\pi$
$38$	−2.05570	−0.333479
$39$	12.0183	1.92446
$40$	3.43150	0.542569
$41$	2.80817	0.438563	0.219281	−	0.975662i	$-0.429629\pi$
$41$	2.80817	0.438563	0.219281	+	0.975662i	$0.429629\pi$
$42$	4.79969	0.740608
$43$	−4.67876	−0.713504	−0.356752	−	0.934199i	$-0.616116\pi$
$43$	−4.67876	−0.713504	−0.356752	+	0.934199i	$0.616116\pi$
$44$	5.86652	0.884411
$45$	−1.21342	−0.180886
$46$	−3.48325	−0.513577
$47$	−9.01092	−1.31438	−0.657189	−	0.753726i	$-0.728255\pi$
$47$	−9.01092	−1.31438	−0.657189	+	0.753726i	$0.728255\pi$
$48$	2.23480	0.322566
$49$	1.00000	0.142857
$50$	−2.33828	−0.330682
$51$	−6.98423	−0.977988
$52$	20.3023	2.81542
$53$	9.83070	1.35035	0.675175	−	0.737657i	$-0.264068\pi$
$53$	9.83070	1.35035	0.675175	+	0.737657i	$0.264068\pi$
$54$	8.57503	1.16691
$55$	−1.69184	−0.228128
$56$	3.43150	0.458554
$57$	1.80461	0.239026
$58$	3.92165	0.514937
$59$	2.90013	0.377564	0.188782	−	0.982019i	$-0.439546\pi$
$59$	2.90013	0.377564	0.188782	+	0.982019i	$0.439546\pi$
$60$	−7.11768	−0.918888
$61$	−8.22158	−1.05267	−0.526333	−	0.850279i	$-0.676433\pi$
$61$	−8.22158	−1.05267	−0.526333	+	0.850279i	$0.676433\pi$
$62$	10.8719	1.38073
$63$	−1.21342	−0.152877
$64$	−12.2724	−1.53405
$65$	−5.85497	−0.726220
$66$	−8.12031	−0.999541
$67$	−7.60067	−0.928569	−0.464285	−	0.885686i	$-0.653689\pi$
$67$	−7.60067	−0.928569	−0.464285	+	0.885686i	$0.653689\pi$
$68$	−11.7984	−1.43076
$69$	3.05778	0.368113
$70$	−2.33828	−0.279477
$71$	7.95868	0.944522	0.472261	−	0.881459i	$-0.343438\pi$
$71$	7.95868	0.944522	0.472261	+	0.881459i	$0.343438\pi$
$72$	−4.16386	−0.490716
$73$	−15.1245	−1.77019	−0.885097	−	0.465406i	$-0.845908\pi$
$73$	−15.1245	−1.77019	−0.885097	+	0.465406i	$0.845908\pi$
$74$	7.07101	0.821988
$75$	2.05266	0.237021
$76$	3.04850	0.349687
$77$	−1.69184	−0.192803
$78$	−28.1020	−3.18193
$79$	−6.90139	−0.776468	−0.388234	−	0.921561i	$-0.626915\pi$
$79$	−6.90139	−0.776468	−0.388234	+	0.921561i	$0.626915\pi$
$80$	−1.08873	−0.121724
$81$	−11.1679	−1.24087
$82$	−6.56628	−0.725124
$83$	3.98305	0.437197	0.218598	−	0.975815i	$-0.429852\pi$
$83$	3.98305	0.437197	0.218598	+	0.975815i	$0.429852\pi$
$84$	−7.11768	−0.776602
$85$	3.40252	0.369055
$86$	10.9402	1.17972
$87$	−3.44263	−0.369088
$88$	−5.80556	−0.618874
$89$	−10.8742	−1.15266	−0.576330	−	0.817217i	$-0.695516\pi$
$89$	−10.8742	−1.15266	−0.576330	+	0.817217i	$0.695516\pi$
$90$	2.83731	0.299079
$91$	−5.85497	−0.613768
$92$	5.16547	0.538537
$93$	−9.54391	−0.989657
$94$	21.0700	2.17321
$95$	−0.879154	−0.0901993
$96$	8.86185	0.904459
$97$	5.01813	0.509514	0.254757	−	0.967005i	$-0.418004\pi$
$97$	5.01813	0.509514	0.254757	+	0.967005i	$0.418004\pi$
$98$	−2.33828	−0.236202
$99$	2.05291	0.206326
$100$	3.46754	0.346754
$101$	2.59185	0.257898	0.128949	−	0.991651i	$-0.458840\pi$
$101$	2.59185	0.257898	0.128949	+	0.991651i	$0.458840\pi$
$102$	16.3311	1.61702
$103$	−14.3588	−1.41482	−0.707408	−	0.706805i	$-0.750136\pi$
$103$	−14.3588	−1.41482	−0.707408	+	0.706805i	$0.750136\pi$
$104$	−20.0914	−1.97012
$105$	2.05266	0.200319
$106$	−22.9869	−2.23268
$107$	4.48339	0.433426	0.216713	−	0.976235i	$-0.430466\pi$
$107$	4.48339	0.433426	0.216713	+	0.976235i	$0.430466\pi$
$108$	−12.7163	−1.22363
$109$	−9.36752	−0.897246	−0.448623	−	0.893721i	$-0.648085\pi$
$109$	−9.36752	−0.897246	−0.448623	+	0.893721i	$0.648085\pi$
$110$	3.95599	0.377189
$111$	−6.20730	−0.589171
$112$	−1.08873	−0.102876
$113$	19.0880	1.79565	0.897825	−	0.440353i	$-0.145147\pi$
$113$	19.0880	1.79565	0.897825	+	0.440353i	$0.145147\pi$
$114$	−4.21967	−0.395208
$115$	−1.48967	−0.138912
$116$	−5.81559	−0.539964
$117$	7.10454	0.656815
$118$	−6.78129	−0.624269
$119$	3.40252	0.311909
$120$	7.04372	0.643001
$121$	−8.13768	−0.739789
$122$	19.2243	1.74049
$123$	5.76423	0.519743
$124$	−16.1224	−1.44784
$125$	−1.00000	−0.0894427
$126$	2.83731	0.252768
$127$	10.6586	0.945797	0.472899	−	0.881117i	$-0.343208\pi$
$127$	10.6586	0.945797	0.472899	+	0.881117i	$0.343208\pi$
$128$	20.0617	1.77322
$129$	−9.60391	−0.845577
$130$	13.6905	1.20074
$131$	−0.381487	−0.0333306	−0.0166653	−	0.999861i	$-0.505305\pi$
$131$	−0.381487	−0.0333306	−0.0166653	+	0.999861i	$0.505305\pi$
$132$	12.0420	1.04812
$133$	−0.879154	−0.0762323
$134$	17.7725	1.53531
$135$	3.66724	0.315626
$136$	11.6758	1.00119
$137$	−2.80038	−0.239253	−0.119626	−	0.992819i	$-0.538170\pi$
$137$	−2.80038	−0.239253	−0.119626	+	0.992819i	$0.538170\pi$
$138$	−7.14994	−0.608643
$139$	1.47224	0.124874	0.0624370	−	0.998049i	$-0.480113\pi$
$139$	1.47224	0.124874	0.0624370	+	0.998049i	$0.480113\pi$
$140$	3.46754	0.293060
$141$	−18.4964	−1.55768
$142$	−18.6096	−1.56168
$143$	9.90567	0.828354
$144$	1.32109	0.110091
$145$	1.67715	0.139280
$146$	35.3654	2.92686
$147$	2.05266	0.169301
$148$	−10.4859	−0.861937
$149$	7.81622	0.640330	0.320165	−	0.947362i	$-0.396262\pi$
$149$	7.81622	0.640330	0.320165	+	0.947362i	$0.396262\pi$
$150$	−4.79969	−0.391893
$151$	−5.65999	−0.460604	−0.230302	−	0.973119i	$-0.573971\pi$
$151$	−5.65999	−0.460604	−0.230302	+	0.973119i	$0.573971\pi$
$152$	−3.01682	−0.244696
$153$	−4.12869	−0.333785
$154$	3.95599	0.318783
$155$	4.64953	0.373459
$156$	41.6738	3.33657
$157$	−10.1540	−0.810380	−0.405190	−	0.914233i	$-0.632795\pi$
$157$	−10.1540	−0.810380	−0.405190	+	0.914233i	$0.632795\pi$
$158$	16.1374	1.28382
$159$	20.1791	1.60031
$160$	−4.31725	−0.341308
$161$	−1.48967	−0.117402
$162$	26.1136	2.05168
$163$	0.783872	0.0613976	0.0306988	−	0.999529i	$-0.490227\pi$
$163$	0.783872	0.0613976	0.0306988	+	0.999529i	$0.490227\pi$
$164$	9.73744	0.760366
$165$	−3.47278	−0.270355
$166$	−9.31347	−0.722866
$167$	−19.3825	−1.49986	−0.749932	−	0.661515i	$-0.769914\pi$
$167$	−19.3825	−1.49986	−0.749932	+	0.661515i	$0.769914\pi$
$168$	7.04372	0.543435
$169$	21.2807	1.63697
$170$	−7.95604	−0.610200
$171$	1.06678	0.0815790
$172$	−16.2238	−1.23705
$173$	−10.3083	−0.783728	−0.391864	−	0.920023i	$-0.628170\pi$
$173$	−10.3083	−0.783728	−0.391864	+	0.920023i	$0.628170\pi$
$174$	8.04981	0.610255
$175$	−1.00000	−0.0755929
$176$	1.84196	0.138843
$177$	5.95298	0.447453
$178$	25.4268	1.90582
$179$	19.4824	1.45618	0.728092	−	0.685479i	$-0.240407\pi$
$179$	19.4824	1.45618	0.728092	+	0.685479i	$0.240407\pi$
$180$	−4.20758	−0.313615
$181$	15.1553	1.12649	0.563243	−	0.826291i	$-0.309553\pi$
$181$	15.1553	1.12649	0.563243	+	0.826291i	$0.309553\pi$
$182$	13.6905	1.01481
$183$	−16.8761	−1.24752
$184$	−5.11180	−0.376847
$185$	3.02402	0.222331
$186$	22.3163	1.63631
$187$	−5.75652	−0.420959
$188$	−31.2457	−2.27883
$189$	3.66724	0.266753
$190$	2.05570	0.149136
$191$	−12.1617	−0.879988	−0.439994	−	0.898001i	$-0.645019\pi$
$191$	−12.1617	−0.879988	−0.439994	+	0.898001i	$0.645019\pi$
$192$	−25.1911	−1.81801
$193$	4.13071	0.297335	0.148667	−	0.988887i	$-0.452502\pi$
$193$	4.13071	0.297335	0.148667	+	0.988887i	$0.452502\pi$
$194$	−11.7338	−0.842436
$195$	−12.0183	−0.860646
$196$	3.46754	0.247681
$197$	21.0308	1.49838	0.749191	−	0.662354i	$-0.230442\pi$
$197$	21.0308	1.49838	0.749191	+	0.662354i	$0.230442\pi$
$198$	−4.80028	−0.341141
$199$	26.3116	1.86518	0.932591	−	0.360936i	$-0.117543\pi$
$199$	26.3116	1.86518	0.932591	+	0.360936i	$0.117543\pi$
$200$	−3.43150	−0.242644
$201$	−15.6016	−1.10045
$202$	−6.06046	−0.426412
$203$	1.67715	0.117713
$204$	−24.2181	−1.69560
$205$	−2.80817	−0.196131
$206$	33.5749	2.33927
$207$	1.80759	0.125636
$208$	6.37451	0.441993
$209$	1.48739	0.102885
$210$	−4.79969	−0.331210
$211$	−1.23521	−0.0850351	−0.0425176	−	0.999096i	$-0.513538\pi$
$211$	−1.23521	−0.0850351	−0.0425176	+	0.999096i	$0.513538\pi$
$212$	34.0883	2.34119
$213$	16.3365	1.11936
$214$	−10.4834	−0.716631
$215$	4.67876	0.319089
$216$	12.5842	0.856244
$217$	4.64953	0.315631
$218$	21.9039	1.48352
$219$	−31.0456	−2.09787
$220$	−5.86652	−0.395520
$221$	−19.9217	−1.34008
$222$	14.5144	0.974142
$223$	6.33496	0.424220	0.212110	−	0.977246i	$-0.431966\pi$
$223$	6.33496	0.424220	0.212110	+	0.977246i	$0.431966\pi$
$224$	−4.31725	−0.288458
$225$	1.21342	0.0808947
$226$	−44.6331	−2.96895
$227$	−20.5041	−1.36091	−0.680453	−	0.732792i	$-0.738217\pi$
$227$	−20.5041	−1.36091	−0.680453	+	0.732792i	$0.738217\pi$
$228$	6.25753	0.414415
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	3.48325	0.229679
$231$	−3.47278	−0.228492
$232$	5.75516	0.377845
$233$	−3.91773	−0.256659	−0.128329	−	0.991732i	$-0.540961\pi$
$233$	−3.91773	−0.256659	−0.128329	+	0.991732i	$0.540961\pi$
$234$	−16.6124	−1.08599
$235$	9.01092	0.587808
$236$	10.0563	0.654609
$237$	−14.1662	−0.920196
$238$	−7.95604	−0.515713
$239$	19.2813	1.24720	0.623600	−	0.781743i	$-0.285669\pi$
$239$	19.2813	1.24720	0.623600	+	0.781743i	$0.285669\pi$
$240$	−2.23480	−0.144256
$241$	−24.0170	−1.54707	−0.773537	−	0.633752i	$-0.781514\pi$
$241$	−24.0170	−1.54707	−0.773537	+	0.633752i	$0.781514\pi$
$242$	19.0281	1.22318
$243$	−11.9221	−0.764806
$244$	−28.5086	−1.82508
$245$	−1.00000	−0.0638877
$246$	−13.4784	−0.859348
$247$	5.14742	0.327522
$248$	15.9549	1.01314
$249$	8.17586	0.518124
$250$	2.33828	0.147886
$251$	−6.27272	−0.395930	−0.197965	−	0.980209i	$-0.563433\pi$
$251$	−6.27272	−0.395930	−0.197965	+	0.980209i	$0.563433\pi$
$252$	−4.20758	−0.265053
$253$	2.52028	0.158448
$254$	−24.9227	−1.56379
$255$	6.98423	0.437369
$256$	−22.3651	−1.39782
$257$	−30.0100	−1.87197	−0.935985	−	0.352041i	$-0.885488\pi$
$257$	−30.0100	−1.87197	−0.935985	+	0.352041i	$0.885488\pi$
$258$	22.4566	1.39809
$259$	3.02402	0.187904
$260$	−20.3023	−1.25910
$261$	−2.03509	−0.125969
$262$	0.892021	0.0551093
$263$	−24.9689	−1.53965	−0.769824	−	0.638257i	$-0.779656\pi$
$263$	−24.9689	−1.53965	−0.769824	+	0.638257i	$0.779656\pi$
$264$	−11.9168	−0.733431
$265$	−9.83070	−0.603895
$266$	2.05570	0.126043
$267$	−22.3210	−1.36602
$268$	−26.3556	−1.60992
$269$	−2.46113	−0.150057	−0.0750287	−	0.997181i	$-0.523905\pi$
$269$	−2.46113	−0.150057	−0.0750287	+	0.997181i	$0.523905\pi$
$270$	−8.57503	−0.521860
$271$	−0.227030	−0.0137911	−0.00689554	−	0.999976i	$-0.502195\pi$
$271$	−0.227030	−0.0137911	−0.00689554	+	0.999976i	$0.502195\pi$
$272$	−3.70444	−0.224615
$273$	−12.0183	−0.727379
$274$	6.54807	0.395583
$275$	1.69184	0.102022
$276$	10.6030	0.638223
$277$	−32.5251	−1.95424	−0.977122	−	0.212681i	$-0.931781\pi$
$277$	−32.5251	−1.95424	−0.977122	+	0.212681i	$0.931781\pi$
$278$	−3.44251	−0.206468
$279$	−5.64184	−0.337768
$280$	−3.43150	−0.205072
$281$	−5.46149	−0.325805	−0.162903	−	0.986642i	$-0.552086\pi$
$281$	−5.46149	−0.325805	−0.162903	+	0.986642i	$0.552086\pi$
$282$	43.2496	2.57548
$283$	−12.2099	−0.725801	−0.362901	−	0.931828i	$-0.618214\pi$
$283$	−12.2099	−0.725801	−0.362901	+	0.931828i	$0.618214\pi$
$284$	27.5970	1.63758
$285$	−1.80461	−0.106896
$286$	−23.1622	−1.36961
$287$	−2.80817	−0.165761
$288$	5.23864	0.308690
$289$	−5.42284	−0.318991
$290$	−3.92165	−0.230287
$291$	10.3005	0.603828
$292$	−52.4449	−3.06911
$293$	4.63112	0.270553	0.135277	−	0.990808i	$-0.456808\pi$
$293$	4.63112	0.270553	0.135277	+	0.990808i	$0.456808\pi$
$294$	−4.79969	−0.279924
$295$	−2.90013	−0.168852
$296$	10.3770	0.603148
$297$	−6.20439	−0.360015
$298$	−18.2765	−1.05873
$299$	8.72195	0.504403
$300$	7.11768	0.410939
$301$	4.67876	0.269679
$302$	13.2346	0.761567
$303$	5.32019	0.305637
$304$	0.957165	0.0548972
$305$	8.22158	0.470766
$306$	9.65402	0.551884
$307$	3.31247	0.189053	0.0945263	−	0.995522i	$-0.469866\pi$
$307$	3.31247	0.189053	0.0945263	+	0.995522i	$0.469866\pi$
$308$	−5.86652	−0.334276
$309$	−29.4738	−1.67671
$310$	−10.8719	−0.617481
$311$	−0.0290662	−0.00164819	−0.000824097	−	1.00000i	$-0.500262\pi$
$311$	−0.0290662	−0.00164819	−0.000824097		1.00000i	$0.500262\pi$
$312$	−41.2408	−2.33480
$313$	15.9116	0.899378	0.449689	−	0.893185i	$-0.351535\pi$
$313$	15.9116	0.899378	0.449689	+	0.893185i	$0.351535\pi$
$314$	23.7429	1.33989
$315$	1.21342	0.0683685
$316$	−23.9308	−1.34621
$317$	−18.9802	−1.06603	−0.533016	−	0.846105i	$-0.678941\pi$
$317$	−18.9802	−1.06603	−0.533016	+	0.846105i	$0.678941\pi$
$318$	−47.1843	−2.64597
$319$	−2.83747	−0.158868
$320$	12.2724	0.686047
$321$	9.20289	0.513655
$322$	3.48325	0.194114
$323$	−2.99134	−0.166443
$324$	−38.7250	−2.15139
$325$	5.85497	0.324775
$326$	−1.83291	−0.101515
$327$	−19.2284	−1.06333
$328$	−9.63625	−0.532073
$329$	9.01092	0.496788
$330$	8.12031	0.447008
$331$	28.6472	1.57459	0.787296	−	0.616575i	$-0.211480\pi$
$331$	28.6472	1.57459	0.787296	+	0.616575i	$0.211480\pi$
$332$	13.8114	0.757998
$333$	−3.66942	−0.201083
$334$	45.3217	2.47989
$335$	7.60067	0.415269
$336$	−2.23480	−0.121919
$337$	12.4032	0.675645	0.337823	−	0.941210i	$-0.390310\pi$
$337$	12.4032	0.675645	0.337823	+	0.941210i	$0.390310\pi$
$338$	−49.7601	−2.70659
$339$	39.1812	2.12803
$340$	11.7984	0.639856
$341$	−7.86626	−0.425982
$342$	−2.49443	−0.134884
$343$	−1.00000	−0.0539949
$344$	16.0552	0.865638
$345$	−3.05778	−0.164625
$346$	24.1037	1.29582
$347$	−1.54615	−0.0830017	−0.0415009	−	0.999138i	$-0.513214\pi$
$347$	−1.54615	−0.0830017	−0.0415009	+	0.999138i	$0.513214\pi$
$348$	−11.9374	−0.639914
$349$	−2.55236	−0.136625	−0.0683123	−	0.997664i	$-0.521761\pi$
$349$	−2.55236	−0.136625	−0.0683123	+	0.997664i	$0.521761\pi$
$350$	2.33828	0.124986
$351$	−21.4716	−1.14607
$352$	7.30409	0.389309
$353$	1.30411	0.0694108	0.0347054	−	0.999398i	$-0.488951\pi$
$353$	1.30411	0.0694108	0.0347054	+	0.999398i	$0.488951\pi$
$354$	−13.9197	−0.739824
$355$	−7.95868	−0.422403
$356$	−37.7066	−1.99845
$357$	6.98423	0.369645
$358$	−45.5553	−2.40767
$359$	3.49320	0.184364	0.0921820	−	0.995742i	$-0.470616\pi$
$359$	3.49320	0.184364	0.0921820	+	0.995742i	$0.470616\pi$
$360$	4.16386	0.219455
$361$	−18.2271	−0.959320
$362$	−35.4373	−1.86254
$363$	−16.7039	−0.876727
$364$	−20.3023	−1.06413
$365$	15.1245	0.791655
$366$	39.4611	2.06266
$367$	15.7908	0.824275	0.412138	−	0.911122i	$-0.364782\pi$
$367$	15.7908	0.824275	0.412138	+	0.911122i	$0.364782\pi$
$368$	1.62185	0.0845448
$369$	3.40749	0.177387
$370$	−7.07101	−0.367604
$371$	−9.83070	−0.510385
$372$	−33.0939	−1.71584
$373$	−33.4466	−1.73180	−0.865898	−	0.500220i	$-0.833253\pi$
$373$	−33.4466	−1.73180	−0.865898	+	0.500220i	$0.833253\pi$
$374$	13.4603	0.696018
$375$	−2.05266	−0.105999
$376$	30.9210	1.59463
$377$	−9.81968	−0.505739
$378$	−8.57503	−0.441052
$379$	24.5840	1.26279	0.631397	−	0.775460i	$-0.282482\pi$
$379$	24.5840	1.26279	0.631397	+	0.775460i	$0.282482\pi$
$380$	−3.04850	−0.156385
$381$	21.8785	1.12087
$382$	28.4374	1.45498
$383$	−28.6600	−1.46446	−0.732228	−	0.681059i	$-0.761520\pi$
$383$	−28.6600	−1.46446	−0.732228	+	0.681059i	$0.761520\pi$
$384$	41.1800	2.10146
$385$	1.69184	0.0862241
$386$	−9.65874	−0.491617
$387$	−5.67730	−0.288594
$388$	17.4006	0.883379
$389$	−17.5002	−0.887296	−0.443648	−	0.896201i	$-0.646316\pi$
$389$	−17.5002	−0.887296	−0.443648	+	0.896201i	$0.646316\pi$
$390$	28.1020	1.42300
$391$	−5.06862	−0.256331
$392$	−3.43150	−0.173317
$393$	−0.783063	−0.0395003
$394$	−49.1758	−2.47744
$395$	6.90139	0.347247
$396$	7.11855	0.357721
$397$	−21.7412	−1.09116	−0.545580	−	0.838059i	$-0.683691\pi$
$397$	−21.7412	−1.09116	−0.545580	+	0.838059i	$0.683691\pi$
$398$	−61.5238	−3.08391
$399$	−1.80461	−0.0903433
$400$	1.08873	0.0544367
$401$	22.7823	1.13769	0.568846	−	0.822444i	$-0.307390\pi$
$401$	22.7823	1.13769	0.568846	+	0.822444i	$0.307390\pi$
$402$	36.4809	1.81950
$403$	−27.2228	−1.35607
$404$	8.98733	0.447136
$405$	11.1679	0.554936
$406$	−3.92165	−0.194628
$407$	−5.11617	−0.253599
$408$	23.9664	1.18651
$409$	17.2937	0.855120	0.427560	−	0.903987i	$-0.359373\pi$
$409$	17.2937	0.855120	0.427560	+	0.903987i	$0.359373\pi$
$410$	6.56628	0.324285
$411$	−5.74824	−0.283540
$412$	−49.7897	−2.45296
$413$	−2.90013	−0.142706
$414$	−4.22665	−0.207728
$415$	−3.98305	−0.195520
$416$	25.2774	1.23932
$417$	3.02202	0.147989
$418$	−3.47792	−0.170111
$419$	−15.4140	−0.753022	−0.376511	−	0.926412i	$-0.622876\pi$
$419$	−15.4140	−0.753022	−0.376511	+	0.926412i	$0.622876\pi$
$420$	7.11768	0.347307
$421$	−14.9552	−0.728871	−0.364436	−	0.931229i	$-0.618738\pi$
$421$	−14.9552	−0.728871	−0.364436	+	0.931229i	$0.618738\pi$
$422$	2.88825	0.140598
$423$	−10.9340	−0.531631
$424$	−33.7341	−1.63827
$425$	−3.40252	−0.165047
$426$	−38.1992	−1.85076
$427$	8.22158	0.397870
$428$	15.5463	0.751460
$429$	20.3330	0.981686
$430$	−10.9402	−0.527585
$431$	−3.30983	−0.159429	−0.0797145	−	0.996818i	$-0.525401\pi$
$431$	−3.30983	−0.159429	−0.0797145	+	0.996818i	$0.525401\pi$
$432$	−3.99265	−0.192097
$433$	−12.3421	−0.593122	−0.296561	−	0.955014i	$-0.595840\pi$
$433$	−12.3421	−0.593122	−0.296561	+	0.955014i	$0.595840\pi$
$434$	−10.8719	−0.521867
$435$	3.44263	0.165061
$436$	−32.4822	−1.55562
$437$	1.30965	0.0626488
$438$	72.5931	3.46863
$439$	13.9668	0.666597	0.333299	−	0.942821i	$-0.391838\pi$
$439$	13.9668	0.666597	0.333299	+	0.942821i	$0.391838\pi$
$440$	5.80556	0.276769
$441$	1.21342	0.0577819
$442$	46.5824	2.21570
$443$	−1.66424	−0.0790705	−0.0395353	−	0.999218i	$-0.512588\pi$
$443$	−1.66424	−0.0790705	−0.0395353	+	0.999218i	$0.512588\pi$
$444$	−21.5240	−1.02149
$445$	10.8742	0.515485
$446$	−14.8129	−0.701411
$447$	16.0441	0.758858
$448$	12.2724	0.579816
$449$	−21.5044	−1.01486	−0.507428	−	0.861694i	$-0.669404\pi$
$449$	−21.5044	−1.01486	−0.507428	+	0.861694i	$0.669404\pi$
$450$	−2.83731	−0.133752
$451$	4.75098	0.223715
$452$	66.1884	3.11324
$453$	−11.6181	−0.545864
$454$	47.9443	2.25014
$455$	5.85497	0.274485
$456$	−6.19251	−0.289991
$457$	29.0609	1.35941	0.679707	−	0.733484i	$-0.262107\pi$
$457$	29.0609	1.35941	0.679707	+	0.733484i	$0.262107\pi$
$458$	2.33828	0.109260
$459$	12.4779	0.582417
$460$	−5.16547	−0.240841
$461$	−15.1493	−0.705574	−0.352787	−	0.935704i	$-0.614766\pi$
$461$	−15.1493	−0.705574	−0.352787	+	0.935704i	$0.614766\pi$
$462$	8.12031	0.377791
$463$	−16.2418	−0.754823	−0.377411	−	0.926046i	$-0.623186\pi$
$463$	−16.2418	−0.754823	−0.377411	+	0.926046i	$0.623186\pi$
$464$	−1.82597	−0.0847687
$465$	9.54391	0.442588
$466$	9.16073	0.424363
$467$	19.2740	0.891895	0.445947	−	0.895059i	$-0.352867\pi$
$467$	19.2740	0.891895	0.445947	+	0.895059i	$0.352867\pi$
$468$	24.6353	1.13877
$469$	7.60067	0.350966
$470$	−21.0700	−0.971887
$471$	−20.8428	−0.960385
$472$	−9.95179	−0.458068
$473$	−7.91571	−0.363965
$474$	33.1246	1.52146
$475$	0.879154	0.0403383
$476$	11.7984	0.540777
$477$	11.9288	0.546181
$478$	−45.0849	−2.06214
$479$	−3.43437	−0.156920	−0.0784602	−	0.996917i	$-0.525000\pi$
$479$	−3.43437	−0.156920	−0.0784602	+	0.996917i	$0.525000\pi$
$480$	−8.86185	−0.404486
$481$	−17.7056	−0.807305
$482$	56.1585	2.55795
$483$	−3.05778	−0.139134
$484$	−28.2177	−1.28262
$485$	−5.01813	−0.227862
$486$	27.8773	1.26454
$487$	−28.9577	−1.31220	−0.656098	−	0.754675i	$-0.727794\pi$
$487$	−28.9577	−1.31220	−0.656098	+	0.754675i	$0.727794\pi$
$488$	28.2124	1.27712
$489$	1.60902	0.0727625
$490$	2.33828	0.105633
$491$	0.878494	0.0396459	0.0198229	−	0.999804i	$-0.493690\pi$
$491$	0.878494	0.0396459	0.0198229	+	0.999804i	$0.493690\pi$
$492$	19.9877	0.901113
$493$	5.70655	0.257010
$494$	−12.0361	−0.541529
$495$	−2.05291	−0.0922716
$496$	−5.06210	−0.227295
$497$	−7.95868	−0.356996
$498$	−19.1174	−0.856672
$499$	−40.2558	−1.80210	−0.901049	−	0.433717i	$-0.857202\pi$
$499$	−40.2558	−1.80210	−0.901049	+	0.433717i	$0.857202\pi$
$500$	−3.46754	−0.155073
$501$	−39.7857	−1.77750
$502$	14.6673	0.654636
$503$	0.229103	0.0102152	0.00510761	−	0.999987i	$-0.498374\pi$
$503$	0.229103	0.0102152	0.00510761	+	0.999987i	$0.498374\pi$
$504$	4.16386	0.185473
$505$	−2.59185	−0.115336
$506$	−5.89310	−0.261980
$507$	43.6820	1.93999
$508$	36.9590	1.63979
$509$	23.4710	1.04033	0.520167	−	0.854065i	$-0.325870\pi$
$509$	23.4710	1.04033	0.520167	+	0.854065i	$0.325870\pi$
$510$	−16.3311	−0.723151
$511$	15.1245	0.669071
$512$	12.1723	0.537946
$513$	−3.22407	−0.142346
$514$	70.1716	3.09513
$515$	14.3588	0.632725
$516$	−33.3019	−1.46603
$517$	−15.2450	−0.670476
$518$	−7.07101	−0.310682
$519$	−21.1595	−0.928799
$520$	20.0914	0.881064
$521$	40.7576	1.78562	0.892812	−	0.450430i	$-0.148729\pi$
$521$	40.7576	1.78562	0.892812	+	0.450430i	$0.148729\pi$
$522$	4.75861	0.208279
$523$	32.3196	1.41324	0.706618	−	0.707595i	$-0.250220\pi$
$523$	32.3196	1.41324	0.706618	+	0.707595i	$0.250220\pi$
$524$	−1.32282	−0.0577876
$525$	−2.05266	−0.0895855
$526$	58.3841	2.54567
$527$	15.8201	0.689136
$528$	3.78093	0.164544
$529$	−20.7809	−0.903517
$530$	22.9869	0.998487
$531$	3.51907	0.152715
$532$	−3.04850	−0.132169
$533$	16.4418	0.712171
$534$	52.1927	2.25860
$535$	−4.48339	−0.193834
$536$	26.0817	1.12656
$537$	39.9908	1.72573
$538$	5.75479	0.248107
$539$	1.69184	0.0728727
$540$	12.7163	0.547222
$541$	27.9162	1.20021	0.600106	−	0.799921i	$-0.295125\pi$
$541$	27.9162	1.20021	0.600106	+	0.799921i	$0.295125\pi$
$542$	0.530858	0.0228023
$543$	31.1087	1.33500
$544$	−14.6895	−0.629809
$545$	9.36752	0.401261
$546$	28.1020	1.20266
$547$	−20.3554	−0.870335	−0.435168	−	0.900349i	$-0.643311\pi$
$547$	−20.3554	−0.870335	−0.435168	+	0.900349i	$0.643311\pi$
$548$	−9.71042	−0.414809
$549$	−9.97624	−0.425776
$550$	−3.95599	−0.168684
$551$	−1.47447	−0.0628147
$552$	−10.4928	−0.446603
$553$	6.90139	0.293477
$554$	76.0527	3.23117
$555$	6.20730	0.263485
$556$	5.10505	0.216503
$557$	35.0567	1.48540	0.742700	−	0.669625i	$-0.233545\pi$
$557$	35.0567	1.48540	0.742700	+	0.669625i	$0.233545\pi$
$558$	13.1922	0.558469
$559$	−27.3940	−1.15864
$560$	1.08873	0.0460074
$561$	−11.8162	−0.498880
$562$	12.7705	0.538690
$563$	11.6569	0.491278	0.245639	−	0.969361i	$-0.421002\pi$
$563$	11.6569	0.491278	0.245639	+	0.969361i	$0.421002\pi$
$564$	−64.1368	−2.70065
$565$	−19.0880	−0.803039
$566$	28.5500	1.20005
$567$	11.1679	0.469007
$568$	−27.3103	−1.14591
$569$	10.7676	0.451401	0.225700	−	0.974197i	$-0.427533\pi$
$569$	10.7676	0.451401	0.225700	+	0.974197i	$0.427533\pi$
$570$	4.21967	0.176742
$571$	20.2717	0.848343	0.424171	−	0.905582i	$-0.360565\pi$
$571$	20.2717	0.848343	0.424171	+	0.905582i	$0.360565\pi$
$572$	34.3483	1.43617
$573$	−24.9638	−1.04288
$574$	6.56628	0.274071
$575$	1.48967	0.0621234
$576$	−14.8916	−0.620482
$577$	−30.4717	−1.26855	−0.634277	−	0.773106i	$-0.718702\pi$
$577$	−30.4717	−1.26855	−0.634277	+	0.773106i	$0.718702\pi$
$578$	12.6801	0.527423
$579$	8.47895	0.352373
$580$	5.81559	0.241479
$581$	−3.98305	−0.165245
$582$	−24.0855	−0.998375
$583$	16.6320	0.688826
$584$	51.9000	2.14764
$585$	−7.10454	−0.293737
$586$	−10.8288	−0.447336
$587$	−44.9249	−1.85425	−0.927124	−	0.374754i	$-0.877727\pi$
$587$	−44.9249	−1.85425	−0.927124	+	0.374754i	$0.877727\pi$
$588$	7.11768	0.293528
$589$	−4.08765	−0.168429
$590$	6.78129	0.279181
$591$	43.1691	1.77574
$592$	−3.29236	−0.135315
$593$	21.6599	0.889464	0.444732	−	0.895664i	$-0.353299\pi$
$593$	21.6599	0.889464	0.444732	+	0.895664i	$0.353299\pi$
$594$	14.5076	0.595253
$595$	−3.40252	−0.139490
$596$	27.1030	1.11018
$597$	54.0089	2.21044
$598$	−20.3943	−0.833986
$599$	37.2242	1.52094	0.760469	−	0.649374i	$-0.224969\pi$
$599$	37.2242	1.52094	0.760469	+	0.649374i	$0.224969\pi$
$600$	−7.04372	−0.287559
$601$	−5.95875	−0.243062	−0.121531	−	0.992588i	$-0.538780\pi$
$601$	−5.95875	−0.243062	−0.121531	+	0.992588i	$0.538780\pi$
$602$	−10.9402	−0.445891
$603$	−9.22281	−0.375582
$604$	−19.6262	−0.798580
$605$	8.13768	0.330844
$606$	−12.4401	−0.505343
$607$	21.9397	0.890504	0.445252	−	0.895405i	$-0.353114\pi$
$607$	21.9397	0.890504	0.445252	+	0.895405i	$0.353114\pi$
$608$	3.79552	0.153929
$609$	3.44263	0.139502
$610$	−19.2243	−0.778370
$611$	−52.7586	−2.13439
$612$	−14.3164	−0.578706
$613$	4.22455	0.170628	0.0853140	−	0.996354i	$-0.472811\pi$
$613$	4.22455	0.170628	0.0853140	+	0.996354i	$0.472811\pi$
$614$	−7.74547	−0.312582
$615$	−5.76423	−0.232436
$616$	5.80556	0.233913
$617$	−17.5619	−0.707014	−0.353507	−	0.935432i	$-0.615011\pi$
$617$	−17.5619	−0.707014	−0.353507	+	0.935432i	$0.615011\pi$
$618$	68.9179	2.77228
$619$	2.78777	0.112050	0.0560249	−	0.998429i	$-0.482157\pi$
$619$	2.78777	0.112050	0.0560249	+	0.998429i	$0.482157\pi$
$620$	16.1224	0.647492
$621$	−5.46297	−0.219221
$622$	0.0679648	0.00272514
$623$	10.8742	0.435665
$624$	13.0847	0.523808
$625$	1.00000	0.0400000
$626$	−37.2058	−1.48704
$627$	3.05310	0.121929
$628$	−35.2095	−1.40501
$629$	10.2893	0.410262
$630$	−2.83731	−0.113041
$631$	−26.2646	−1.04558	−0.522788	−	0.852463i	$-0.675108\pi$
$631$	−26.2646	−1.04558	−0.522788	+	0.852463i	$0.675108\pi$
$632$	23.6822	0.942026
$633$	−2.53546	−0.100776
$634$	44.3808	1.76259
$635$	−10.6586	−0.422973
$636$	69.9718	2.77456
$637$	5.85497	0.231982
$638$	6.63480	0.262674
$639$	9.65723	0.382034
$640$	−20.0617	−0.793010
$641$	9.87508	0.390042	0.195021	−	0.980799i	$-0.437522\pi$
$641$	9.87508	0.390042	0.195021	+	0.980799i	$0.437522\pi$
$642$	−21.5189	−0.849283
$643$	−49.4585	−1.95045	−0.975226	−	0.221212i	$-0.928999\pi$
$643$	−49.4585	−1.95045	−0.975226	+	0.221212i	$0.928999\pi$
$644$	−5.16547	−0.203548
$645$	9.60391	0.378154
$646$	6.99458	0.275198
$647$	13.9482	0.548360	0.274180	−	0.961678i	$-0.411594\pi$
$647$	13.9482	0.548360	0.274180	+	0.961678i	$0.411594\pi$
$648$	38.3226	1.50545
$649$	4.90655	0.192599
$650$	−13.6905	−0.536987
$651$	9.54391	0.374055
$652$	2.71810	0.106449
$653$	−4.91489	−0.192334	−0.0961672	−	0.995365i	$-0.530658\pi$
$653$	−4.91489	−0.192334	−0.0961672	+	0.995365i	$0.530658\pi$
$654$	44.9612	1.75812
$655$	0.381487	0.0149059
$656$	3.05735	0.119370
$657$	−18.3524	−0.715997
$658$	−21.0700	−0.821395
$659$	−44.9815	−1.75223	−0.876115	−	0.482103i	$-0.839873\pi$
$659$	−44.9815	−1.75223	−0.876115	+	0.482103i	$0.839873\pi$
$660$	−12.0420	−0.468733
$661$	−0.919694	−0.0357720	−0.0178860	−	0.999840i	$-0.505694\pi$
$661$	−0.919694	−0.0357720	−0.0178860	+	0.999840i	$0.505694\pi$
$662$	−66.9850	−2.60345
$663$	−40.8924	−1.58813
$664$	−13.6679	−0.530416
$665$	0.879154	0.0340921
$666$	8.58011	0.332472
$667$	−2.49840	−0.0967383
$668$	−67.2096	−2.60042
$669$	13.0035	0.502746
$670$	−17.7725	−0.686610
$671$	−13.9096	−0.536974
$672$	−8.86185	−0.341853
$673$	−38.7372	−1.49321	−0.746606	−	0.665267i	$-0.768318\pi$
$673$	−38.7372	−1.49321	−0.746606	+	0.665267i	$0.768318\pi$
$674$	−29.0021	−1.11712
$675$	−3.66724	−0.141152
$676$	73.7915	2.83813
$677$	−24.9590	−0.959254	−0.479627	−	0.877473i	$-0.659228\pi$
$677$	−24.9590	−0.959254	−0.479627	+	0.877473i	$0.659228\pi$
$678$	−91.6166	−3.51851
$679$	−5.01813	−0.192578
$680$	−11.6758	−0.447745
$681$	−42.0880	−1.61282
$682$	18.3935	0.704323
$683$	−47.9119	−1.83330	−0.916649	−	0.399693i	$-0.869117\pi$
$683$	−47.9119	−1.83330	−0.916649	+	0.399693i	$0.869117\pi$
$684$	3.69911	0.141439
$685$	2.80038	0.106997
$686$	2.33828	0.0892758
$687$	−2.05266	−0.0783139
$688$	−5.09393	−0.194204
$689$	57.5585	2.19280
$690$	7.14994	0.272193
$691$	−36.1614	−1.37565	−0.687823	−	0.725878i	$-0.741433\pi$
$691$	−36.1614	−1.37565	−0.687823	+	0.725878i	$0.741433\pi$
$692$	−35.7445	−1.35880
$693$	−2.05291	−0.0779837
$694$	3.61533	0.137236
$695$	−1.47224	−0.0558453
$696$	11.8134	0.447785
$697$	−9.55487	−0.361916
$698$	5.96812	0.225897
$699$	−8.04177	−0.304168
$700$	−3.46754	−0.131061
$701$	35.8679	1.35471	0.677356	−	0.735656i	$-0.263126\pi$
$701$	35.8679	1.35471	0.677356	+	0.735656i	$0.263126\pi$
$702$	50.2065	1.89492
$703$	−2.65858	−0.100270
$704$	−20.7629	−0.782532
$705$	18.4964	0.696614
$706$	−3.04937	−0.114765
$707$	−2.59185	−0.0974765
$708$	20.6422	0.775780
$709$	−0.104933	−0.00394085	−0.00197043	−	0.999998i	$-0.500627\pi$
$709$	−0.104933	−0.00394085	−0.00197043	+	0.999998i	$0.500627\pi$
$710$	18.6096	0.698406
$711$	−8.37430	−0.314061
$712$	37.3148	1.39843
$713$	−6.92624	−0.259390
$714$	−16.3311	−0.611174
$715$	−9.90567	−0.370451
$716$	67.5560	2.52469
$717$	39.5779	1.47806
$718$	−8.16807	−0.304830
$719$	−0.793177	−0.0295805	−0.0147902	−	0.999891i	$-0.504708\pi$
$719$	−0.793177	−0.0295805	−0.0147902	+	0.999891i	$0.504708\pi$
$720$	−1.32109	−0.0492342
$721$	14.3588	0.534750
$722$	42.6200	1.58615
$723$	−49.2988	−1.83344
$724$	52.5516	1.95307
$725$	−1.67715	−0.0622879
$726$	39.0583	1.44959
$727$	−12.7367	−0.472378	−0.236189	−	0.971707i	$-0.575898\pi$
$727$	−12.7367	−0.472378	−0.236189	+	0.971707i	$0.575898\pi$
$728$	20.0914	0.744635
$729$	9.03150	0.334500
$730$	−35.3654	−1.30893
$731$	15.9196	0.588807
$732$	−58.5186	−2.16291
$733$	−40.3472	−1.49026	−0.745129	−	0.666921i	$-0.767612\pi$
$733$	−40.3472	−1.49026	−0.745129	+	0.666921i	$0.767612\pi$
$734$	−36.9233	−1.36287
$735$	−2.05266	−0.0757136
$736$	6.43126	0.237059
$737$	−12.8591	−0.473671
$738$	−7.96766	−0.293294
$739$	−34.4535	−1.26739	−0.633697	−	0.773582i	$-0.718463\pi$
$739$	−34.4535	−1.26739	−0.633697	+	0.773582i	$0.718463\pi$
$740$	10.4859	0.385470
$741$	10.5659	0.388148
$742$	22.9869	0.843876
$743$	44.2309	1.62267	0.811337	−	0.584578i	$-0.198740\pi$
$743$	44.2309	1.62267	0.811337	+	0.584578i	$0.198740\pi$
$744$	32.7500	1.20067
$745$	−7.81622	−0.286364
$746$	78.2073	2.86337
$747$	4.83312	0.176835
$748$	−19.9610	−0.729845
$749$	−4.48339	−0.163820
$750$	4.79969	0.175260
$751$	39.1503	1.42862	0.714308	−	0.699831i	$-0.246742\pi$
$751$	39.1503	1.42862	0.714308	+	0.699831i	$0.246742\pi$
$752$	−9.81050	−0.357752
$753$	−12.8758	−0.469219
$754$	22.9611	0.836195
$755$	5.65999	0.205988
$756$	12.7163	0.462487
$757$	−13.5262	−0.491620	−0.245810	−	0.969318i	$-0.579054\pi$
$757$	−13.5262	−0.491620	−0.245810	+	0.969318i	$0.579054\pi$
$758$	−57.4841	−2.08792
$759$	5.17327	0.187778
$760$	3.01682	0.109432
$761$	−42.4001	−1.53700	−0.768501	−	0.639848i	$-0.778997\pi$
$761$	−42.4001	−1.53700	−0.768501	+	0.639848i	$0.778997\pi$
$762$	−51.1579	−1.85326
$763$	9.36752	0.339127
$764$	−42.1711	−1.52570
$765$	4.12869	0.149273
$766$	67.0150	2.42135
$767$	16.9801	0.613117
$768$	−45.9080	−1.65656
$769$	−25.0925	−0.904859	−0.452429	−	0.891800i	$-0.649443\pi$
$769$	−25.0925	−0.904859	−0.452429	+	0.891800i	$0.649443\pi$
$770$	−3.95599	−0.142564
$771$	−61.6003	−2.21848
$772$	14.3234	0.515510
$773$	16.1278	0.580076	0.290038	−	0.957015i	$-0.406332\pi$
$773$	16.1278	0.580076	0.290038	+	0.957015i	$0.406332\pi$
$774$	13.2751	0.477164
$775$	−4.64953	−0.167016
$776$	−17.2197	−0.618153
$777$	6.20730	0.222686
$778$	40.9203	1.46707
$779$	2.46881	0.0884544
$780$	−41.6738	−1.49216
$781$	13.4648	0.481809
$782$	11.8518	0.423821
$783$	6.15053	0.219802
$784$	1.08873	0.0388834
$785$	10.1540	0.362413
$786$	1.83102	0.0653103
$787$	24.7376	0.881800	0.440900	−	0.897556i	$-0.354659\pi$
$787$	24.7376	0.881800	0.440900	+	0.897556i	$0.354659\pi$
$788$	72.9251	2.59785
$789$	−51.2527	−1.82464
$790$	−16.1374	−0.574142
$791$	−19.0880	−0.678692
$792$	−7.04458	−0.250318
$793$	−48.1371	−1.70940
$794$	50.8370	1.80414
$795$	−20.1791	−0.715679
$796$	91.2365	3.23379
$797$	−38.1669	−1.35194	−0.675970	−	0.736929i	$-0.736275\pi$
$797$	−38.1669	−1.35194	−0.675970	+	0.736929i	$0.736275\pi$
$798$	4.21967	0.149375
$799$	30.6599	1.08467
$800$	4.31725	0.152638
$801$	−13.1950	−0.466221
$802$	−53.2712	−1.88107
$803$	−25.5883	−0.902992
$804$	−54.0991	−1.90793
$805$	1.48967	0.0525038
$806$	63.6545	2.24214
$807$	−5.05186	−0.177834
$808$	−8.89394	−0.312888
$809$	20.8451	0.732873	0.366437	−	0.930443i	$-0.380578\pi$
$809$	20.8451	0.732873	0.366437	+	0.930443i	$0.380578\pi$
$810$	−26.1136	−0.917537
$811$	38.2593	1.34347	0.671733	−	0.740793i	$-0.265550\pi$
$811$	38.2593	1.34347	0.671733	+	0.740793i	$0.265550\pi$
$812$	5.81559	0.204087
$813$	−0.466015	−0.0163439
$814$	11.9630	0.419303
$815$	−0.783872	−0.0274578
$816$	−7.60397	−0.266192
$817$	−4.11335	−0.143908
$818$	−40.4375	−1.41387
$819$	−7.10454	−0.248253
$820$	−9.73744	−0.340046
$821$	−1.16687	−0.0407239	−0.0203620	−	0.999793i	$-0.506482\pi$
$821$	−1.16687	−0.0407239	−0.0203620	+	0.999793i	$0.506482\pi$
$822$	13.4410	0.468807
$823$	−23.4078	−0.815944	−0.407972	−	0.912995i	$-0.633764\pi$
$823$	−23.4078	−0.815944	−0.407972	+	0.912995i	$0.633764\pi$
$824$	49.2723	1.71648
$825$	3.47278	0.120907
$826$	6.78129	0.235951
$827$	−13.1032	−0.455642	−0.227821	−	0.973703i	$-0.573160\pi$
$827$	−13.1032	−0.455642	−0.227821	+	0.973703i	$0.573160\pi$
$828$	6.26789	0.217824
$829$	21.1807	0.735637	0.367818	−	0.929898i	$-0.380105\pi$
$829$	21.1807	0.735637	0.367818	+	0.929898i	$0.380105\pi$
$830$	9.31347	0.323275
$831$	−66.7630	−2.31598
$832$	−71.8544	−2.49110
$833$	−3.40252	−0.117890
$834$	−7.06631	−0.244686
$835$	19.3825	0.670759
$836$	5.15757	0.178378
$837$	17.0510	0.589367
$838$	36.0422	1.24506
$839$	−8.94027	−0.308652	−0.154326	−	0.988020i	$-0.549321\pi$
$839$	−8.94027	−0.308652	−0.154326	+	0.988020i	$0.549321\pi$
$840$	−7.04372	−0.243031
$841$	−26.1872	−0.903005
$842$	34.9694	1.20512
$843$	−11.2106	−0.386114
$844$	−4.28312	−0.147431
$845$	−21.2807	−0.732077
$846$	25.5668	0.879005
$847$	8.13768	0.279614
$848$	10.7030	0.367543
$849$	−25.0627	−0.860151
$850$	7.95604	0.272890
$851$	−4.50479	−0.154422
$852$	56.6473	1.94071
$853$	−1.59624	−0.0546541	−0.0273271	−	0.999627i	$-0.508700\pi$
$853$	−1.59624	−0.0546541	−0.0273271	+	0.999627i	$0.508700\pi$
$854$	−19.2243	−0.657843
$855$	−1.06678	−0.0364832
$856$	−15.3848	−0.525841
$857$	13.8413	0.472808	0.236404	−	0.971655i	$-0.424031\pi$
$857$	13.8413	0.472808	0.236404	+	0.971655i	$0.424031\pi$
$858$	−47.5442	−1.62313
$859$	28.3997	0.968984	0.484492	−	0.874796i	$-0.339004\pi$
$859$	28.3997	0.968984	0.484492	+	0.874796i	$0.339004\pi$
$860$	16.2238	0.553226
$861$	−5.76423	−0.196444
$862$	7.73930	0.263602
$863$	36.2073	1.23251	0.616256	−	0.787546i	$-0.288649\pi$
$863$	36.2073	1.23251	0.616256	+	0.787546i	$0.288649\pi$
$864$	−15.8324	−0.538629
$865$	10.3083	0.350494
$866$	28.8592	0.980675
$867$	−11.1313	−0.378037
$868$	16.1224	0.547230
$869$	−11.6761	−0.396083
$870$	−8.04981	−0.272914
$871$	−44.5017	−1.50788
$872$	32.1447	1.08856
$873$	6.08911	0.206085
$874$	−3.06231	−0.103584
$875$	1.00000	0.0338062
$876$	−107.652	−3.63721
$877$	51.9897	1.75557	0.877784	−	0.479057i	$-0.159021\pi$
$877$	51.9897	1.75557	0.877784	+	0.479057i	$0.159021\pi$
$878$	−32.6581	−1.10216
$879$	9.50613	0.320634
$880$	−1.84196	−0.0620926
$881$	33.8285	1.13971	0.569856	−	0.821745i	$-0.306999\pi$
$881$	33.8285	1.13971	0.569856	+	0.821745i	$0.306999\pi$
$882$	−2.83731	−0.0955373
$883$	−28.6394	−0.963793	−0.481897	−	0.876228i	$-0.660052\pi$
$883$	−28.6394	−0.963793	−0.481897	+	0.876228i	$0.660052\pi$
$884$	−69.0791	−2.32338
$885$	−5.95298	−0.200107
$886$	3.89146	0.130736
$887$	−29.9112	−1.00432	−0.502160	−	0.864775i	$-0.667461\pi$
$887$	−29.9112	−1.00432	−0.502160	+	0.864775i	$0.667461\pi$
$888$	21.3004	0.714794
$889$	−10.6586	−0.357478
$890$	−25.4268	−0.852309
$891$	−18.8943	−0.632981
$892$	21.9667	0.735500
$893$	−7.92198	−0.265099
$894$	−37.5155	−1.25470
$895$	−19.4824	−0.651226
$896$	−20.0617	−0.670216
$897$	17.9032	0.597771
$898$	50.2833	1.67797
$899$	7.79797	0.260077
$900$	4.20758	0.140253
$901$	−33.4492	−1.11435
$902$	−11.1091	−0.369892
$903$	9.60391	0.319598
$904$	−65.5006	−2.17852
$905$	−15.1553	−0.503780
$906$	27.1662	0.902537
$907$	11.5534	0.383624	0.191812	−	0.981432i	$-0.438564\pi$
$907$	11.5534	0.383624	0.191812	+	0.981432i	$0.438564\pi$
$908$	−71.0988	−2.35950
$909$	3.14500	0.104313
$910$	−13.6905	−0.453837
$911$	6.47764	0.214614	0.107307	−	0.994226i	$-0.465777\pi$
$911$	6.47764	0.214614	0.107307	+	0.994226i	$0.465777\pi$
$912$	1.96474	0.0650589
$913$	6.73868	0.223018
$914$	−67.9525	−2.24767
$915$	16.8761	0.557908
$916$	−3.46754	−0.114571
$917$	0.381487	0.0125978
$918$	−29.1767	−0.962975
$919$	32.3694	1.06777	0.533884	−	0.845558i	$-0.320732\pi$
$919$	32.3694	1.06777	0.533884	+	0.845558i	$0.320732\pi$
$920$	5.11180	0.168531
$921$	6.79938	0.224047
$922$	35.4233	1.16660
$923$	46.5978	1.53379
$924$	−12.0420	−0.396152
$925$	−3.02402	−0.0994293
$926$	37.9779	1.24803
$927$	−17.4233	−0.572256
$928$	−7.24068	−0.237687
$929$	−29.1576	−0.956629	−0.478314	−	0.878189i	$-0.658752\pi$
$929$	−29.1576	−0.956629	−0.478314	+	0.878189i	$0.658752\pi$
$930$	−22.3163	−0.731780
$931$	0.879154	0.0288131
$932$	−13.5849	−0.444987
$933$	−0.0596631	−0.00195328
$934$	−45.0680	−1.47467
$935$	5.75652	0.188258
$936$	−24.3793	−0.796861
$937$	−32.0908	−1.04836	−0.524180	−	0.851608i	$-0.675628\pi$
$937$	−32.0908	−1.04836	−0.524180	+	0.851608i	$0.675628\pi$
$938$	−17.7725	−0.580291
$939$	32.6612	1.06586
$940$	31.2457	1.01912
$941$	−52.9085	−1.72477	−0.862384	−	0.506255i	$-0.831030\pi$
$941$	−52.9085	−1.72477	−0.862384	+	0.506255i	$0.831030\pi$
$942$	48.7362	1.58791
$943$	4.18324	0.136225
$944$	3.15747	0.102767
$945$	−3.66724	−0.119295
$946$	18.5091	0.601783
$947$	28.7797	0.935215	0.467607	−	0.883936i	$-0.345116\pi$
$947$	28.7797	0.935215	0.467607	+	0.883936i	$0.345116\pi$
$948$	−49.1219	−1.59541
$949$	−88.5538	−2.87458
$950$	−2.05570	−0.0666959
$951$	−38.9598	−1.26336
$952$	−11.6758	−0.378414
$953$	35.4061	1.14692	0.573458	−	0.819235i	$-0.305602\pi$
$953$	35.4061	1.14692	0.573458	+	0.819235i	$0.305602\pi$
$954$	−27.8928	−0.903062
$955$	12.1617	0.393543
$956$	66.8585	2.16236
$957$	−5.82437	−0.188275
$958$	8.03051	0.259454
$959$	2.80038	0.0904290
$960$	25.1911	0.813038
$961$	−9.38188	−0.302641
$962$	41.4005	1.33481
$963$	5.44024	0.175309
$964$	−83.2799	−2.68227
$965$	−4.13071	−0.132972
$966$	7.14994	0.230045
$967$	−18.8501	−0.606180	−0.303090	−	0.952962i	$-0.598018\pi$
$967$	−18.8501	−0.606180	−0.303090	+	0.952962i	$0.598018\pi$
$968$	27.9245	0.897527
$969$	−6.14021	−0.197252
$970$	11.7338	0.376749
$971$	22.9722	0.737212	0.368606	−	0.929586i	$-0.379835\pi$
$971$	22.9722	0.737212	0.368606	+	0.929586i	$0.379835\pi$
$972$	−41.3404	−1.32600
$973$	−1.47224	−0.0471979
$974$	67.7110	2.16960
$975$	12.0183	0.384893
$976$	−8.95112	−0.286518
$977$	−14.3513	−0.459140	−0.229570	−	0.973292i	$-0.573732\pi$
$977$	−14.3513	−0.459140	−0.229570	+	0.973292i	$0.573732\pi$
$978$	−3.76234	−0.120306
$979$	−18.3974	−0.587982
$980$	−3.46754	−0.110766
$981$	−11.3667	−0.362912
$982$	−2.05416	−0.0655509
$983$	−30.6740	−0.978350	−0.489175	−	0.872186i	$-0.662702\pi$
$983$	−30.6740	−0.978350	−0.489175	+	0.872186i	$0.662702\pi$
$984$	−19.7800	−0.630562
$985$	−21.0308	−0.670097
$986$	−13.3435	−0.424943
$987$	18.4964	0.588746
$988$	17.8489	0.567848
$989$	−6.96979	−0.221626
$990$	4.80028	0.152563
$991$	45.4370	1.44335	0.721676	−	0.692231i	$-0.243372\pi$
$991$	45.4370	1.44335	0.721676	+	0.692231i	$0.243372\pi$
$992$	−20.0732	−0.637324
$993$	58.8030	1.86606
$994$	18.6096	0.590260
$995$	−26.3116	−0.834134
$996$	28.3501	0.898307
$997$	0.989004	0.0313221	0.0156610	−	0.999877i	$-0.495015\pi$
$997$	0.989004	0.0313221	0.0156610	+	0.999877i	$0.495015\pi$
$998$	94.1293	2.97961
$999$	11.0898	0.350867

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.k.1.6	✓	49

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.k.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-2.33828 q^{2} +2.05266 q^{3} +3.46754 q^{4} -1.00000 q^{5} -4.79969 q^{6} -1.00000 q^{7} -3.43150 q^{8} +1.21342 q^{9} +O(q^{10})\)	\(q-2.33828 q^{2} +2.05266 q^{3} +3.46754 q^{4} -1.00000 q^{5} -4.79969 q^{6} -1.00000 q^{7} -3.43150 q^{8} +1.21342 q^{9} +2.33828 q^{10} +1.69184 q^{11} +7.11768 q^{12} +5.85497 q^{13} +2.33828 q^{14} -2.05266 q^{15} +1.08873 q^{16} -3.40252 q^{17} -2.83731 q^{18} +0.879154 q^{19} -3.46754 q^{20} -2.05266 q^{21} -3.95599 q^{22} +1.48967 q^{23} -7.04372 q^{24} +1.00000 q^{25} -13.6905 q^{26} -3.66724 q^{27} -3.46754 q^{28} -1.67715 q^{29} +4.79969 q^{30} -4.64953 q^{31} +4.31725 q^{32} +3.47278 q^{33} +7.95604 q^{34} +1.00000 q^{35} +4.20758 q^{36} -3.02402 q^{37} -2.05570 q^{38} +12.0183 q^{39} +3.43150 q^{40} +2.80817 q^{41} +4.79969 q^{42} -4.67876 q^{43} +5.86652 q^{44} -1.21342 q^{45} -3.48325 q^{46} -9.01092 q^{47} +2.23480 q^{48} +1.00000 q^{49} -2.33828 q^{50} -6.98423 q^{51} +20.3023 q^{52} +9.83070 q^{53} +8.57503 q^{54} -1.69184 q^{55} +3.43150 q^{56} +1.80461 q^{57} +3.92165 q^{58} +2.90013 q^{59} -7.11768 q^{60} -8.22158 q^{61} +10.8719 q^{62} -1.21342 q^{63} -12.2724 q^{64} -5.85497 q^{65} -8.12031 q^{66} -7.60067 q^{67} -11.7984 q^{68} +3.05778 q^{69} -2.33828 q^{70} +7.95868 q^{71} -4.16386 q^{72} -15.1245 q^{73} +7.07101 q^{74} +2.05266 q^{75} +3.04850 q^{76} -1.69184 q^{77} -28.1020 q^{78} -6.90139 q^{79} -1.08873 q^{80} -11.1679 q^{81} -6.56628 q^{82} +3.98305 q^{83} -7.11768 q^{84} +3.40252 q^{85} +10.9402 q^{86} -3.44263 q^{87} -5.80556 q^{88} -10.8742 q^{89} +2.83731 q^{90} -5.85497 q^{91} +5.16547 q^{92} -9.54391 q^{93} +21.0700 q^{94} -0.879154 q^{95} +8.86185 q^{96} +5.01813 q^{97} -2.33828 q^{98} +2.05291 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9}+O(q^{10}) \) 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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