LMFDB - Embedded newform 8015.2.a.l.1.15

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:	$0$
Dimension:	$62$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.54368 q^{2} +0.772565 q^{3} +0.382940 q^{4} -1.00000 q^{5} -1.19259 q^{6} -1.00000 q^{7} +2.49622 q^{8} -2.40314 q^{9} +O(q^{10})$	\(q-1.54368 q^{2} +0.772565 q^{3} +0.382940 q^{4} -1.00000 q^{5} -1.19259 q^{6} -1.00000 q^{7} +2.49622 q^{8} -2.40314 q^{9} +1.54368 q^{10} +5.00484 q^{11} +0.295846 q^{12} -5.25397 q^{13} +1.54368 q^{14} -0.772565 q^{15} -4.61924 q^{16} +4.80207 q^{17} +3.70968 q^{18} +8.27223 q^{19} -0.382940 q^{20} -0.772565 q^{21} -7.72586 q^{22} +5.61714 q^{23} +1.92849 q^{24} +1.00000 q^{25} +8.11043 q^{26} -4.17428 q^{27} -0.382940 q^{28} -1.77847 q^{29} +1.19259 q^{30} -8.75809 q^{31} +2.13817 q^{32} +3.86656 q^{33} -7.41285 q^{34} +1.00000 q^{35} -0.920260 q^{36} +12.0820 q^{37} -12.7697 q^{38} -4.05903 q^{39} -2.49622 q^{40} +8.03675 q^{41} +1.19259 q^{42} -7.64728 q^{43} +1.91655 q^{44} +2.40314 q^{45} -8.67105 q^{46} -5.23408 q^{47} -3.56866 q^{48} +1.00000 q^{49} -1.54368 q^{50} +3.70991 q^{51} -2.01195 q^{52} +9.75944 q^{53} +6.44374 q^{54} -5.00484 q^{55} -2.49622 q^{56} +6.39083 q^{57} +2.74539 q^{58} +8.20919 q^{59} -0.295846 q^{60} -1.84675 q^{61} +13.5197 q^{62} +2.40314 q^{63} +5.93782 q^{64} +5.25397 q^{65} -5.96873 q^{66} -5.46181 q^{67} +1.83890 q^{68} +4.33960 q^{69} -1.54368 q^{70} -6.45927 q^{71} -5.99877 q^{72} -3.63322 q^{73} -18.6507 q^{74} +0.772565 q^{75} +3.16777 q^{76} -5.00484 q^{77} +6.26583 q^{78} -15.3203 q^{79} +4.61924 q^{80} +3.98453 q^{81} -12.4061 q^{82} +11.6486 q^{83} -0.295846 q^{84} -4.80207 q^{85} +11.8049 q^{86} -1.37398 q^{87} +12.4932 q^{88} +6.69176 q^{89} -3.70968 q^{90} +5.25397 q^{91} +2.15103 q^{92} -6.76619 q^{93} +8.07973 q^{94} -8.27223 q^{95} +1.65188 q^{96} -16.4107 q^{97} -1.54368 q^{98} -12.0274 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) $ 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.54368	−1.09154	−0.545772	−	0.837933i	$-0.683764\pi$
$2$	−1.54368	−1.09154	−0.545772	+	0.837933i	$0.683764\pi$
$3$	0.772565	0.446041	0.223020	−	0.974814i	$-0.428408\pi$
$3$	0.772565	0.446041	0.223020	+	0.974814i	$0.428408\pi$
$4$	0.382940	0.191470
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.19259	−0.486873
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.49622	0.882547
$9$	−2.40314	−0.801048
$10$	1.54368	0.488154
$11$	5.00484	1.50902	0.754508	−	0.656291i	$-0.227876\pi$
$11$	5.00484	1.50902	0.754508	+	0.656291i	$0.227876\pi$
$12$	0.295846	0.0854034
$13$	−5.25397	−1.45719	−0.728594	−	0.684946i	$-0.759826\pi$
$13$	−5.25397	−1.45719	−0.728594	+	0.684946i	$0.759826\pi$
$14$	1.54368	0.412565
$15$	−0.772565	−0.199475
$16$	−4.61924	−1.15481
$17$	4.80207	1.16467	0.582336	−	0.812948i	$-0.302139\pi$
$17$	4.80207	1.16467	0.582336	+	0.812948i	$0.302139\pi$
$18$	3.70968	0.874380
$19$	8.27223	1.89778	0.948890	−	0.315607i	$-0.102208\pi$
$19$	8.27223	1.89778	0.948890	+	0.315607i	$0.102208\pi$
$20$	−0.382940	−0.0856280
$21$	−0.772565	−0.168587
$22$	−7.72586	−1.64716
$23$	5.61714	1.17125	0.585627	−	0.810581i	$-0.300848\pi$
$23$	5.61714	1.17125	0.585627	+	0.810581i	$0.300848\pi$
$24$	1.92849	0.393652
$25$	1.00000	0.200000
$26$	8.11043	1.59059
$27$	−4.17428	−0.803340
$28$	−0.382940	−0.0723689
$29$	−1.77847	−0.330254	−0.165127	−	0.986272i	$-0.552803\pi$
$29$	−1.77847	−0.330254	−0.165127	+	0.986272i	$0.552803\pi$
$30$	1.19259	0.217736
$31$	−8.75809	−1.57300	−0.786499	−	0.617591i	$-0.788109\pi$
$31$	−8.75809	−1.57300	−0.786499	+	0.617591i	$0.788109\pi$
$32$	2.13817	0.377979
$33$	3.86656	0.673082
$34$	−7.41285	−1.27129
$35$	1.00000	0.169031
$36$	−0.920260	−0.153377
$37$	12.0820	1.98627	0.993136	−	0.116964i	$-0.0373163\pi$
$37$	12.0820	1.98627	0.993136	+	0.116964i	$0.0373163\pi$
$38$	−12.7697	−2.07151
$39$	−4.05903	−0.649965
$40$	−2.49622	−0.394687
$41$	8.03675	1.25513	0.627565	−	0.778564i	$-0.284052\pi$
$41$	8.03675	1.25513	0.627565	+	0.778564i	$0.284052\pi$
$42$	1.19259	0.184021
$43$	−7.64728	−1.16620	−0.583100	−	0.812400i	$-0.698160\pi$
$43$	−7.64728	−1.16620	−0.583100	+	0.812400i	$0.698160\pi$
$44$	1.91655	0.288931
$45$	2.40314	0.358239
$46$	−8.67105	−1.27848
$47$	−5.23408	−0.763469	−0.381734	−	0.924272i	$-0.624673\pi$
$47$	−5.23408	−0.763469	−0.381734	+	0.924272i	$0.624673\pi$
$48$	−3.56866	−0.515092
$49$	1.00000	0.142857
$50$	−1.54368	−0.218309
$51$	3.70991	0.519491
$52$	−2.01195	−0.279008
$53$	9.75944	1.34056	0.670281	−	0.742108i	$-0.266174\pi$
$53$	9.75944	1.34056	0.670281	+	0.742108i	$0.266174\pi$
$54$	6.44374	0.876882
$55$	−5.00484	−0.674853
$56$	−2.49622	−0.333571
$57$	6.39083	0.846487
$58$	2.74539	0.360487
$59$	8.20919	1.06875	0.534373	−	0.845249i	$-0.320548\pi$
$59$	8.20919	1.06875	0.534373	+	0.845249i	$0.320548\pi$
$60$	−0.295846	−0.0381936
$61$	−1.84675	−0.236452	−0.118226	−	0.992987i	$-0.537721\pi$
$61$	−1.84675	−0.236452	−0.118226	+	0.992987i	$0.537721\pi$
$62$	13.5197	1.71700
$63$	2.40314	0.302768
$64$	5.93782	0.742228
$65$	5.25397	0.651674
$66$	−5.96873	−0.734700
$67$	−5.46181	−0.667267	−0.333633	−	0.942703i	$-0.608275\pi$
$67$	−5.46181	−0.667267	−0.333633	+	0.942703i	$0.608275\pi$
$68$	1.83890	0.223000
$69$	4.33960	0.522427
$70$	−1.54368	−0.184505
$71$	−6.45927	−0.766575	−0.383287	−	0.923629i	$-0.625208\pi$
$71$	−6.45927	−0.766575	−0.383287	+	0.923629i	$0.625208\pi$
$72$	−5.99877	−0.706962
$73$	−3.63322	−0.425237	−0.212618	−	0.977135i	$-0.568199\pi$
$73$	−3.63322	−0.425237	−0.212618	+	0.977135i	$0.568199\pi$
$74$	−18.6507	−2.16811
$75$	0.772565	0.0892081
$76$	3.16777	0.363368
$77$	−5.00484	−0.570355
$78$	6.26583	0.709466
$79$	−15.3203	−1.72367	−0.861836	−	0.507187i	$-0.830685\pi$
$79$	−15.3203	−1.72367	−0.861836	+	0.507187i	$0.830685\pi$
$80$	4.61924	0.516446
$81$	3.98453	0.442725
$82$	−12.4061	−1.37003
$83$	11.6486	1.27860	0.639301	−	0.768956i	$-0.279224\pi$
$83$	11.6486	1.27860	0.639301	+	0.768956i	$0.279224\pi$
$84$	−0.295846	−0.0322795
$85$	−4.80207	−0.520858
$86$	11.8049	1.27296
$87$	−1.37398	−0.147307
$88$	12.4932	1.33178
$89$	6.69176	0.709325	0.354662	−	0.934994i	$-0.384596\pi$
$89$	6.69176	0.709325	0.354662	+	0.934994i	$0.384596\pi$
$90$	−3.70968	−0.391034
$91$	5.25397	0.550765
$92$	2.15103	0.224260
$93$	−6.76619	−0.701621
$94$	8.07973	0.833361
$95$	−8.27223	−0.848713
$96$	1.65188	0.168594
$97$	−16.4107	−1.66626	−0.833128	−	0.553081i	$-0.813452\pi$
$97$	−16.4107	−1.66626	−0.833128	+	0.553081i	$0.813452\pi$
$98$	−1.54368	−0.155935
$99$	−12.0274	−1.20879
$100$	0.382940	0.0382940
$101$	−13.4452	−1.33785	−0.668924	−	0.743331i	$-0.733245\pi$
$101$	−13.4452	−1.33785	−0.668924	+	0.743331i	$0.733245\pi$
$102$	−5.72691	−0.567048
$103$	8.60526	0.847901	0.423951	−	0.905685i	$-0.360643\pi$
$103$	8.60526	0.847901	0.423951	+	0.905685i	$0.360643\pi$
$104$	−13.1150	−1.28604
$105$	0.772565	0.0753946
$106$	−15.0654	−1.46328
$107$	7.89268	0.763014	0.381507	−	0.924366i	$-0.375405\pi$
$107$	7.89268	0.763014	0.381507	+	0.924366i	$0.375405\pi$
$108$	−1.59850	−0.153816
$109$	−13.5644	−1.29923	−0.649615	−	0.760264i	$-0.725070\pi$
$109$	−13.5644	−1.29923	−0.649615	+	0.760264i	$0.725070\pi$
$110$	7.72586	0.736632
$111$	9.33415	0.885958
$112$	4.61924	0.436477
$113$	19.5903	1.84290	0.921448	−	0.388501i	$-0.127007\pi$
$113$	19.5903	1.84290	0.921448	+	0.388501i	$0.127007\pi$
$114$	−9.86539	−0.923978
$115$	−5.61714	−0.523801
$116$	−0.681048	−0.0632337
$117$	12.6260	1.16728
$118$	−12.6723	−1.16658
$119$	−4.80207	−0.440205
$120$	−1.92849	−0.176046
$121$	14.0484	1.27713
$122$	2.85078	0.258098
$123$	6.20891	0.559839
$124$	−3.35382	−0.301182
$125$	−1.00000	−0.0894427
$126$	−3.70968	−0.330484
$127$	−20.8548	−1.85056	−0.925281	−	0.379282i	$-0.876171\pi$
$127$	−20.8548	−1.85056	−0.925281	+	0.379282i	$0.876171\pi$
$128$	−13.4424	−1.18815
$129$	−5.90802	−0.520172
$130$	−8.11043	−0.711332
$131$	4.08628	0.357020	0.178510	−	0.983938i	$-0.442872\pi$
$131$	4.08628	0.357020	0.178510	+	0.983938i	$0.442872\pi$
$132$	1.48066	0.128875
$133$	−8.27223	−0.717293
$134$	8.43128	0.728352
$135$	4.17428	0.359265
$136$	11.9870	1.02788
$137$	8.21971	0.702257	0.351128	−	0.936327i	$-0.385798\pi$
$137$	8.21971	0.702257	0.351128	+	0.936327i	$0.385798\pi$
$138$	−6.69895	−0.570252
$139$	12.0164	1.01921	0.509607	−	0.860407i	$-0.329791\pi$
$139$	12.0164	1.01921	0.509607	+	0.860407i	$0.329791\pi$
$140$	0.382940	0.0323643
$141$	−4.04367	−0.340538
$142$	9.97103	0.836751
$143$	−26.2953	−2.19892
$144$	11.1007	0.925057
$145$	1.77847	0.147694
$146$	5.60853	0.464165
$147$	0.772565	0.0637201
$148$	4.62669	0.380312
$149$	−22.5174	−1.84470	−0.922350	−	0.386356i	$-0.873734\pi$
$149$	−22.5174	−1.84470	−0.922350	+	0.386356i	$0.873734\pi$
$150$	−1.19259	−0.0973746
$151$	3.15924	0.257095	0.128548	−	0.991703i	$-0.458968\pi$
$151$	3.15924	0.257095	0.128548	+	0.991703i	$0.458968\pi$
$152$	20.6493	1.67488
$153$	−11.5401	−0.932959
$154$	7.72586	0.622568
$155$	8.75809	0.703466
$156$	−1.55436	−0.124449
$157$	−21.0994	−1.68391	−0.841957	−	0.539545i	$-0.818596\pi$
$157$	−21.0994	−1.68391	−0.841957	+	0.539545i	$0.818596\pi$
$158$	23.6496	1.88146
$159$	7.53980	0.597945
$160$	−2.13817	−0.169038
$161$	−5.61714	−0.442692
$162$	−6.15083	−0.483255
$163$	−4.75648	−0.372556	−0.186278	−	0.982497i	$-0.559643\pi$
$163$	−4.75648	−0.372556	−0.186278	+	0.982497i	$0.559643\pi$
$164$	3.07759	0.240320
$165$	−3.86656	−0.301012
$166$	−17.9817	−1.39565
$167$	10.1412	0.784753	0.392376	−	0.919805i	$-0.371653\pi$
$167$	10.1412	0.784753	0.392376	+	0.919805i	$0.371653\pi$
$168$	−1.92849	−0.148786
$169$	14.6042	1.12340
$170$	7.41285	0.568539
$171$	−19.8794	−1.52021
$172$	−2.92845	−0.223292
$173$	11.1150	0.845061	0.422531	−	0.906349i	$-0.361142\pi$
$173$	11.1150	0.845061	0.422531	+	0.906349i	$0.361142\pi$
$174$	2.12099	0.160792
$175$	−1.00000	−0.0755929
$176$	−23.1185	−1.74263
$177$	6.34213	0.476704
$178$	−10.3299	−0.774260
$179$	12.9892	0.970859	0.485430	−	0.874276i	$-0.338663\pi$
$179$	12.9892	0.970859	0.485430	+	0.874276i	$0.338663\pi$
$180$	0.920260	0.0685921
$181$	18.2693	1.35794	0.678972	−	0.734164i	$-0.262426\pi$
$181$	18.2693	1.35794	0.678972	+	0.734164i	$0.262426\pi$
$182$	−8.11043	−0.601185
$183$	−1.42673	−0.105467
$184$	14.0216	1.03369
$185$	−12.0820	−0.888288
$186$	10.4448	0.765851
$187$	24.0336	1.75751
$188$	−2.00434	−0.146181
$189$	4.17428	0.303634
$190$	12.7697	0.926408
$191$	−18.8628	−1.36486	−0.682431	−	0.730950i	$-0.739077\pi$
$191$	−18.8628	−1.36486	−0.682431	+	0.730950i	$0.739077\pi$
$192$	4.58735	0.331064
$193$	11.8213	0.850918	0.425459	−	0.904978i	$-0.360113\pi$
$193$	11.8213	0.850918	0.425459	+	0.904978i	$0.360113\pi$
$194$	25.3328	1.81879
$195$	4.05903	0.290673
$196$	0.382940	0.0273529
$197$	0.733407	0.0522531	0.0261265	−	0.999659i	$-0.491683\pi$
$197$	0.733407	0.0522531	0.0261265	+	0.999659i	$0.491683\pi$
$198$	18.5663	1.31945
$199$	−10.8067	−0.766067	−0.383034	−	0.923734i	$-0.625121\pi$
$199$	−10.8067	−0.766067	−0.383034	+	0.923734i	$0.625121\pi$
$200$	2.49622	0.176509
$201$	−4.21961	−0.297628
$202$	20.7551	1.46032
$203$	1.77847	0.124824
$204$	1.42067	0.0994670
$205$	−8.03675	−0.561311
$206$	−13.2837	−0.925522
$207$	−13.4988	−0.938231
$208$	24.2693	1.68277
$209$	41.4012	2.86378
$210$	−1.19259	−0.0822966
$211$	1.14022	0.0784959	0.0392479	−	0.999230i	$-0.487504\pi$
$211$	1.14022	0.0784959	0.0392479	+	0.999230i	$0.487504\pi$
$212$	3.73728	0.256677
$213$	−4.99021	−0.341923
$214$	−12.1838	−0.832864
$215$	7.64728	0.521540
$216$	−10.4199	−0.708985
$217$	8.75809	0.594538
$218$	20.9390	1.41817
$219$	−2.80690	−0.189673
$220$	−1.91655	−0.129214
$221$	−25.2299	−1.69715
$222$	−14.4089	−0.967063
$223$	11.9786	0.802147	0.401073	−	0.916046i	$-0.368637\pi$
$223$	11.9786	0.802147	0.401073	+	0.916046i	$0.368637\pi$
$224$	−2.13817	−0.142863
$225$	−2.40314	−0.160210
$226$	−30.2410	−2.01160
$227$	24.2112	1.60696	0.803479	−	0.595334i	$-0.202980\pi$
$227$	24.2112	1.60696	0.803479	+	0.595334i	$0.202980\pi$
$228$	2.44731	0.162077
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	8.67105	0.571752
$231$	−3.86656	−0.254401
$232$	−4.43945	−0.291464
$233$	20.7067	1.35654	0.678269	−	0.734814i	$-0.262730\pi$
$233$	20.7067	1.35654	0.678269	+	0.734814i	$0.262730\pi$
$234$	−19.4905	−1.27414
$235$	5.23408	0.341434
$236$	3.14363	0.204633
$237$	−11.8359	−0.768827
$238$	7.41285	0.480503
$239$	11.9296	0.771660	0.385830	−	0.922570i	$-0.373915\pi$
$239$	11.9296	0.771660	0.385830	+	0.922570i	$0.373915\pi$
$240$	3.56866	0.230356
$241$	12.1920	0.785358	0.392679	−	0.919676i	$-0.371548\pi$
$241$	12.1920	0.785358	0.392679	+	0.919676i	$0.371548\pi$
$242$	−21.6862	−1.39404
$243$	15.6011	1.00081
$244$	−0.707193	−0.0452734
$245$	−1.00000	−0.0638877
$246$	−9.58455	−0.611089
$247$	−43.4620	−2.76542
$248$	−21.8621	−1.38824
$249$	8.99932	0.570309
$250$	1.54368	0.0976307
$251$	0.768976	0.0485373	0.0242687	−	0.999705i	$-0.492274\pi$
$251$	0.768976	0.0485373	0.0242687	+	0.999705i	$0.492274\pi$
$252$	0.920260	0.0579709
$253$	28.1129	1.76744
$254$	32.1930	2.01997
$255$	−3.70991	−0.232324
$256$	8.87513	0.554696
$257$	−25.8132	−1.61018	−0.805091	−	0.593151i	$-0.797884\pi$
$257$	−25.8132	−1.61018	−0.805091	+	0.593151i	$0.797884\pi$
$258$	9.12008	0.567792
$259$	−12.0820	−0.750740
$260$	2.01195	0.124776
$261$	4.27392	0.264549
$262$	−6.30789	−0.389703
$263$	−7.30670	−0.450550	−0.225275	−	0.974295i	$-0.572328\pi$
$263$	−7.30670	−0.450550	−0.225275	+	0.974295i	$0.572328\pi$
$264$	9.65179	0.594027
$265$	−9.75944	−0.599517
$266$	12.7697	0.782958
$267$	5.16982	0.316388
$268$	−2.09155	−0.127762
$269$	13.7179	0.836396	0.418198	−	0.908356i	$-0.362662\pi$
$269$	13.7179	0.836396	0.418198	+	0.908356i	$0.362662\pi$
$270$	−6.44374	−0.392154
$271$	3.82091	0.232104	0.116052	−	0.993243i	$-0.462976\pi$
$271$	3.82091	0.232104	0.116052	+	0.993243i	$0.462976\pi$
$272$	−22.1819	−1.34498
$273$	4.05903	0.245664
$274$	−12.6886	−0.766545
$275$	5.00484	0.301803
$276$	1.66181	0.100029
$277$	10.6675	0.640946	0.320473	−	0.947258i	$-0.396158\pi$
$277$	10.6675	0.640946	0.320473	+	0.947258i	$0.396158\pi$
$278$	−18.5494	−1.11252
$279$	21.0469	1.26005
$280$	2.49622	0.149178
$281$	−7.45763	−0.444885	−0.222442	−	0.974946i	$-0.571403\pi$
$281$	−7.45763	−0.444885	−0.222442	+	0.974946i	$0.571403\pi$
$282$	6.24212	0.371713
$283$	−5.34808	−0.317910	−0.158955	−	0.987286i	$-0.550813\pi$
$283$	−5.34808	−0.317910	−0.158955	+	0.987286i	$0.550813\pi$
$284$	−2.47351	−0.146776
$285$	−6.39083	−0.378560
$286$	40.5914	2.40022
$287$	−8.03675	−0.474394
$288$	−5.13834	−0.302780
$289$	6.05987	0.356463
$290$	−2.74539	−0.161215
$291$	−12.6783	−0.743218
$292$	−1.39131	−0.0814201
$293$	−11.4990	−0.671777	−0.335889	−	0.941902i	$-0.609037\pi$
$293$	−11.4990	−0.671777	−0.335889	+	0.941902i	$0.609037\pi$
$294$	−1.19259	−0.0695533
$295$	−8.20919	−0.477958
$296$	30.1594	1.75298
$297$	−20.8916	−1.21225
$298$	34.7596	2.01357
$299$	−29.5123	−1.70674
$300$	0.295846	0.0170807
$301$	7.64728	0.440782
$302$	−4.87685	−0.280631
$303$	−10.3873	−0.596734
$304$	−38.2114	−2.19157
$305$	1.84675	0.105744
$306$	17.8141	1.01837
$307$	−11.2256	−0.640677	−0.320339	−	0.947303i	$-0.603797\pi$
$307$	−11.2256	−0.640677	−0.320339	+	0.947303i	$0.603797\pi$
$308$	−1.91655	−0.109206
$309$	6.64812	0.378198
$310$	−13.5197	−0.767865
$311$	−5.12149	−0.290413	−0.145206	−	0.989401i	$-0.546385\pi$
$311$	−5.12149	−0.290413	−0.145206	+	0.989401i	$0.546385\pi$
$312$	−10.1322	−0.573624
$313$	−6.11628	−0.345713	−0.172856	−	0.984947i	$-0.555300\pi$
$313$	−6.11628	−0.345713	−0.172856	+	0.984947i	$0.555300\pi$
$314$	32.5706	1.83807
$315$	−2.40314	−0.135402
$316$	−5.86677	−0.330031
$317$	29.6063	1.66286	0.831428	−	0.555632i	$-0.187524\pi$
$317$	29.6063	1.66286	0.831428	+	0.555632i	$0.187524\pi$
$318$	−11.6390	−0.652684
$319$	−8.90097	−0.498359
$320$	−5.93782	−0.331934
$321$	6.09761	0.340335
$322$	8.67105	0.483219
$323$	39.7238	2.21029
$324$	1.52584	0.0847687
$325$	−5.25397	−0.291438
$326$	7.34247	0.406662
$327$	−10.4793	−0.579509
$328$	20.0615	1.10771
$329$	5.23408	0.288564
$330$	5.96873	0.328568
$331$	−15.3387	−0.843093	−0.421546	−	0.906807i	$-0.638513\pi$
$331$	−15.3387	−0.843093	−0.421546	+	0.906807i	$0.638513\pi$
$332$	4.46073	0.244814
$333$	−29.0348	−1.59110
$334$	−15.6548	−0.856593
$335$	5.46181	0.298411
$336$	3.56866	0.194686
$337$	−22.6846	−1.23571	−0.617854	−	0.786293i	$-0.711998\pi$
$337$	−22.6846	−1.23571	−0.617854	+	0.786293i	$0.711998\pi$
$338$	−22.5441	−1.22624
$339$	15.1347	0.822007
$340$	−1.83890	−0.0997286
$341$	−43.8328	−2.37368
$342$	30.6873	1.65938
$343$	−1.00000	−0.0539949
$344$	−19.0893	−1.02923
$345$	−4.33960	−0.233636
$346$	−17.1580	−0.922422
$347$	9.63092	0.517015	0.258508	−	0.966009i	$-0.416769\pi$
$347$	9.63092	0.517015	0.258508	+	0.966009i	$0.416769\pi$
$348$	−0.526154	−0.0282048
$349$	12.4938	0.668776	0.334388	−	0.942436i	$-0.391470\pi$
$349$	12.4938	0.668776	0.334388	+	0.942436i	$0.391470\pi$
$350$	1.54368	0.0825130
$351$	21.9315	1.17062
$352$	10.7012	0.570377
$353$	4.33741	0.230857	0.115428	−	0.993316i	$-0.463176\pi$
$353$	4.33741	0.230857	0.115428	+	0.993316i	$0.463176\pi$
$354$	−9.79021	−0.520344
$355$	6.45927	0.342823
$356$	2.56254	0.135814
$357$	−3.70991	−0.196349
$358$	−20.0512	−1.05974
$359$	10.7235	0.565967	0.282983	−	0.959125i	$-0.408676\pi$
$359$	10.7235	0.565967	0.282983	+	0.959125i	$0.408676\pi$
$360$	5.99877	0.316163
$361$	49.4298	2.60157
$362$	−28.2019	−1.48226
$363$	10.8533	0.569652
$364$	2.01195	0.105455
$365$	3.63322	0.190172
$366$	2.20241	0.115122
$367$	4.29139	0.224009	0.112004	−	0.993708i	$-0.464273\pi$
$367$	4.29139	0.224009	0.112004	+	0.993708i	$0.464273\pi$
$368$	−25.9469	−1.35258
$369$	−19.3135	−1.00542
$370$	18.6507	0.969606
$371$	−9.75944	−0.506685
$372$	−2.59105	−0.134339
$373$	−11.6324	−0.602304	−0.301152	−	0.953576i	$-0.597371\pi$
$373$	−11.6324	−0.602304	−0.301152	+	0.953576i	$0.597371\pi$
$374$	−37.1001	−1.91840
$375$	−0.772565	−0.0398951
$376$	−13.0654	−0.673797
$377$	9.34403	0.481242
$378$	−6.44374	−0.331430
$379$	−3.70016	−0.190064	−0.0950322	−	0.995474i	$-0.530295\pi$
$379$	−3.70016	−0.190064	−0.0950322	+	0.995474i	$0.530295\pi$
$380$	−3.16777	−0.162503
$381$	−16.1117	−0.825426
$382$	29.1180	1.48981
$383$	35.6531	1.82179	0.910894	−	0.412640i	$-0.135393\pi$
$383$	35.6531	1.82179	0.910894	+	0.412640i	$0.135393\pi$
$384$	−10.3852	−0.529965
$385$	5.00484	0.255070
$386$	−18.2483	−0.928816
$387$	18.3775	0.934182
$388$	−6.28432	−0.319038
$389$	−11.3836	−0.577173	−0.288587	−	0.957454i	$-0.593185\pi$
$389$	−11.3836	−0.577173	−0.288587	+	0.957454i	$0.593185\pi$
$390$	−6.26583	−0.317283
$391$	26.9739	1.36413
$392$	2.49622	0.126078
$393$	3.15691	0.159245
$394$	−1.13214	−0.0570366
$395$	15.3203	0.770849
$396$	−4.60575	−0.231448
$397$	4.52813	0.227260	0.113630	−	0.993523i	$-0.463752\pi$
$397$	4.52813	0.227260	0.113630	+	0.993523i	$0.463752\pi$
$398$	16.6821	0.836197
$399$	−6.39083	−0.319942
$400$	−4.61924	−0.230962
$401$	−32.4889	−1.62242	−0.811208	−	0.584758i	$-0.801190\pi$
$401$	−32.4889	−1.62242	−0.811208	+	0.584758i	$0.801190\pi$
$402$	6.51371	0.324874
$403$	46.0147	2.29215
$404$	−5.14871	−0.256158
$405$	−3.98453	−0.197993
$406$	−2.74539	−0.136251
$407$	60.4686	2.99732
$408$	9.26075	0.458475
$409$	−9.13004	−0.451452	−0.225726	−	0.974191i	$-0.572475\pi$
$409$	−9.13004	−0.451452	−0.225726	+	0.974191i	$0.572475\pi$
$410$	12.4061	0.612696
$411$	6.35026	0.313235
$412$	3.29530	0.162348
$413$	−8.20919	−0.403948
$414$	20.8378	1.02412
$415$	−11.6486	−0.571808
$416$	−11.2339	−0.550787
$417$	9.28342	0.454611
$418$	−63.9101	−3.12594
$419$	32.2584	1.57593	0.787963	−	0.615723i	$-0.211136\pi$
$419$	32.2584	1.57593	0.787963	+	0.615723i	$0.211136\pi$
$420$	0.295846	0.0144358
$421$	25.2314	1.22970	0.614852	−	0.788643i	$-0.289216\pi$
$421$	25.2314	1.22970	0.614852	+	0.788643i	$0.289216\pi$
$422$	−1.76013	−0.0856818
$423$	12.5782	0.611575
$424$	24.3617	1.18311
$425$	4.80207	0.232935
$426$	7.70327	0.373225
$427$	1.84675	0.0893704
$428$	3.02242	0.146094
$429$	−20.3148	−0.980808
$430$	−11.8049	−0.569285
$431$	−6.70188	−0.322818	−0.161409	−	0.986888i	$-0.551604\pi$
$431$	−6.70188	−0.322818	−0.161409	+	0.986888i	$0.551604\pi$
$432$	19.2820	0.927705
$433$	23.5221	1.13040	0.565200	−	0.824954i	$-0.308799\pi$
$433$	23.5221	1.13040	0.565200	+	0.824954i	$0.308799\pi$
$434$	−13.5197	−0.648965
$435$	1.37398	0.0658775
$436$	−5.19433	−0.248763
$437$	46.4663	2.22278
$438$	4.33295	0.207036
$439$	17.6896	0.844281	0.422140	−	0.906530i	$-0.361279\pi$
$439$	17.6896	0.844281	0.422140	+	0.906530i	$0.361279\pi$
$440$	−12.4932	−0.595589
$441$	−2.40314	−0.114435
$442$	38.9468	1.85251
$443$	22.4149	1.06496	0.532482	−	0.846442i	$-0.321260\pi$
$443$	22.4149	1.06496	0.532482	+	0.846442i	$0.321260\pi$
$444$	3.57442	0.169634
$445$	−6.69176	−0.317220
$446$	−18.4911	−0.875579
$447$	−17.3962	−0.822811
$448$	−5.93782	−0.280536
$449$	16.8379	0.794631	0.397316	−	0.917682i	$-0.369942\pi$
$449$	16.8379	0.794631	0.397316	+	0.917682i	$0.369942\pi$
$450$	3.70968	0.174876
$451$	40.2226	1.89401
$452$	7.50190	0.352859
$453$	2.44072	0.114675
$454$	−37.3744	−1.75407
$455$	−5.25397	−0.246310
$456$	15.9529	0.747064
$457$	−32.2195	−1.50716	−0.753582	−	0.657354i	$-0.771676\pi$
$457$	−32.2195	−1.50716	−0.753582	+	0.657354i	$0.771676\pi$
$458$	−1.54368	−0.0721313
$459$	−20.0452	−0.935629
$460$	−2.15103	−0.100292
$461$	33.2163	1.54704	0.773518	−	0.633774i	$-0.218495\pi$
$461$	33.2163	1.54704	0.773518	+	0.633774i	$0.218495\pi$
$462$	5.96873	0.277690
$463$	22.8945	1.06400	0.531998	−	0.846746i	$-0.321441\pi$
$463$	22.8945	1.06400	0.531998	+	0.846746i	$0.321441\pi$
$464$	8.21518	0.381380
$465$	6.76619	0.313775
$466$	−31.9644	−1.48072
$467$	−3.90717	−0.180802	−0.0904011	−	0.995905i	$-0.528815\pi$
$467$	−3.90717	−0.180802	−0.0904011	+	0.995905i	$0.528815\pi$
$468$	4.83501	0.223499
$469$	5.46181	0.252203
$470$	−8.07973	−0.372690
$471$	−16.3006	−0.751093
$472$	20.4919	0.943218
$473$	−38.2734	−1.75981
$474$	18.2709	0.839210
$475$	8.27223	0.379556
$476$	−1.83890	−0.0842861
$477$	−23.4533	−1.07385
$478$	−18.4154	−0.842302
$479$	10.6615	0.487138	0.243569	−	0.969884i	$-0.421682\pi$
$479$	10.6615	0.487138	0.243569	+	0.969884i	$0.421682\pi$
$480$	−1.65188	−0.0753976
$481$	−63.4785	−2.89437
$482$	−18.8206	−0.857253
$483$	−4.33960	−0.197459
$484$	5.37971	0.244532
$485$	16.4107	0.745172
$486$	−24.0831	−1.09243
$487$	−12.5384	−0.568170	−0.284085	−	0.958799i	$-0.591690\pi$
$487$	−12.5384	−0.568170	−0.284085	+	0.958799i	$0.591690\pi$
$488$	−4.60988	−0.208680
$489$	−3.67469	−0.166175
$490$	1.54368	0.0697362
$491$	−5.27132	−0.237891	−0.118946	−	0.992901i	$-0.537951\pi$
$491$	−5.27132	−0.237891	−0.118946	+	0.992901i	$0.537951\pi$
$492$	2.37764	0.107192
$493$	−8.54034	−0.384638
$494$	67.0913	3.01858
$495$	12.0274	0.540589
$496$	40.4557	1.81651
$497$	6.45927	0.289738
$498$	−13.8920	−0.622517
$499$	−15.4739	−0.692707	−0.346353	−	0.938104i	$-0.612580\pi$
$499$	−15.4739	−0.692707	−0.346353	+	0.938104i	$0.612580\pi$
$500$	−0.382940	−0.0171256
$501$	7.83477	0.350032
$502$	−1.18705	−0.0529807
$503$	21.4126	0.954741	0.477371	−	0.878702i	$-0.341590\pi$
$503$	21.4126	0.954741	0.477371	+	0.878702i	$0.341590\pi$
$504$	5.99877	0.267207
$505$	13.4452	0.598304
$506$	−43.3972	−1.92924
$507$	11.2827	0.501080
$508$	−7.98613	−0.354327
$509$	−9.27872	−0.411272	−0.205636	−	0.978629i	$-0.565926\pi$
$509$	−9.27872	−0.411272	−0.205636	+	0.978629i	$0.565926\pi$
$510$	5.72691	0.253592
$511$	3.63322	0.160724
$512$	13.1845	0.582679
$513$	−34.5306	−1.52456
$514$	39.8472	1.75759
$515$	−8.60526	−0.379193
$516$	−2.26242	−0.0995974
$517$	−26.1957	−1.15209
$518$	18.6507	0.819467
$519$	8.58709	0.376932
$520$	13.1150	0.575133
$521$	14.9905	0.656748	0.328374	−	0.944548i	$-0.393499\pi$
$521$	14.9905	0.656748	0.328374	+	0.944548i	$0.393499\pi$
$522$	−6.59756	−0.288767
$523$	23.8618	1.04340	0.521702	−	0.853128i	$-0.325297\pi$
$523$	23.8618	1.04340	0.521702	+	0.853128i	$0.325297\pi$
$524$	1.56480	0.0683586
$525$	−0.772565	−0.0337175
$526$	11.2792	0.491796
$527$	−42.0569	−1.83203
$528$	−17.8606	−0.777282
$529$	8.55224	0.371837
$530$	15.0654	0.654400
$531$	−19.7279	−0.856116
$532$	−3.16777	−0.137340
$533$	−42.2248	−1.82896
$534$	−7.98053	−0.345351
$535$	−7.89268	−0.341230
$536$	−13.6339	−0.588894
$537$	10.0350	0.433043
$538$	−21.1760	−0.912964
$539$	5.00484	0.215574
$540$	1.59850	0.0687884
$541$	16.6714	0.716760	0.358380	−	0.933576i	$-0.383329\pi$
$541$	16.6714	0.716760	0.358380	+	0.933576i	$0.383329\pi$
$542$	−5.89826	−0.253352
$543$	14.1142	0.605698
$544$	10.2677	0.440222
$545$	13.5644	0.581033
$546$	−6.26583	−0.268153
$547$	44.9582	1.92228	0.961138	−	0.276069i	$-0.0890318\pi$
$547$	44.9582	1.92228	0.961138	+	0.276069i	$0.0890318\pi$
$548$	3.14765	0.134461
$549$	4.43800	0.189409
$550$	−7.72586	−0.329432
$551$	−14.7119	−0.626749
$552$	10.8326	0.461066
$553$	15.3203	0.651487
$554$	−16.4671	−0.699621
$555$	−9.33415	−0.396212
$556$	4.60155	0.195149
$557$	−44.8853	−1.90185	−0.950926	−	0.309417i	$-0.899866\pi$
$557$	−44.8853	−1.90185	−0.950926	+	0.309417i	$0.899866\pi$
$558$	−32.4897	−1.37540
$559$	40.1786	1.69937
$560$	−4.61924	−0.195198
$561$	18.5675	0.783921
$562$	11.5122	0.485612
$563$	−5.89713	−0.248534	−0.124267	−	0.992249i	$-0.539658\pi$
$563$	−5.89713	−0.248534	−0.124267	+	0.992249i	$0.539658\pi$
$564$	−1.54848	−0.0652028
$565$	−19.5903	−0.824168
$566$	8.25571	0.347013
$567$	−3.98453	−0.167334
$568$	−16.1238	−0.676538
$569$	−22.1579	−0.928907	−0.464454	−	0.885597i	$-0.653749\pi$
$569$	−22.1579	−0.928907	−0.464454	+	0.885597i	$0.653749\pi$
$570$	9.86539	0.413216
$571$	28.6864	1.20049	0.600245	−	0.799816i	$-0.295070\pi$
$571$	28.6864	1.20049	0.600245	+	0.799816i	$0.295070\pi$
$572$	−10.0695	−0.421027
$573$	−14.5727	−0.608784
$574$	12.4061	0.517823
$575$	5.61714	0.234251
$576$	−14.2694	−0.594560
$577$	24.7114	1.02875	0.514375	−	0.857565i	$-0.328024\pi$
$577$	24.7114	1.02875	0.514375	+	0.857565i	$0.328024\pi$
$578$	−9.35449	−0.389095
$579$	9.13275	0.379544
$580$	0.681048	0.0282790
$581$	−11.6486	−0.483266
$582$	19.5713	0.811255
$583$	48.8444	2.02293
$584$	−9.06932	−0.375291
$585$	−12.6260	−0.522022
$586$	17.7507	0.733275
$587$	1.74344	0.0719595	0.0359798	−	0.999353i	$-0.488545\pi$
$587$	1.74344	0.0719595	0.0359798	+	0.999353i	$0.488545\pi$
$588$	0.295846	0.0122005
$589$	−72.4489	−2.98521
$590$	12.6723	0.521712
$591$	0.566605	0.0233070
$592$	−55.8097	−2.29377
$593$	−19.7363	−0.810474	−0.405237	−	0.914212i	$-0.632811\pi$
$593$	−19.7363	−0.810474	−0.405237	+	0.914212i	$0.632811\pi$
$594$	32.2499	1.32323
$595$	4.80207	0.196866
$596$	−8.62282	−0.353205
$597$	−8.34888	−0.341697
$598$	45.5574	1.86298
$599$	−8.34568	−0.340995	−0.170498	−	0.985358i	$-0.554538\pi$
$599$	−8.34568	−0.340995	−0.170498	+	0.985358i	$0.554538\pi$
$600$	1.92849	0.0787303
$601$	−0.894415	−0.0364840	−0.0182420	−	0.999834i	$-0.505807\pi$
$601$	−0.894415	−0.0364840	−0.0182420	+	0.999834i	$0.505807\pi$
$602$	−11.8049	−0.481133
$603$	13.1255	0.534513
$604$	1.20980	0.0492260
$605$	−14.0484	−0.571150
$606$	16.0346	0.651362
$607$	13.2559	0.538042	0.269021	−	0.963134i	$-0.413300\pi$
$607$	13.2559	0.538042	0.269021	+	0.963134i	$0.413300\pi$
$608$	17.6875	0.717322
$609$	1.37398	0.0556767
$610$	−2.85078	−0.115425
$611$	27.4997	1.11252
$612$	−4.41915	−0.178634
$613$	33.3017	1.34504	0.672521	−	0.740078i	$-0.265211\pi$
$613$	33.3017	1.34504	0.672521	+	0.740078i	$0.265211\pi$
$614$	17.3287	0.699328
$615$	−6.20891	−0.250367
$616$	−12.4932	−0.503364
$617$	−16.4131	−0.660768	−0.330384	−	0.943847i	$-0.607178\pi$
$617$	−16.4131	−0.660768	−0.330384	+	0.943847i	$0.607178\pi$
$618$	−10.2626	−0.412820
$619$	2.77843	0.111675	0.0558373	−	0.998440i	$-0.482217\pi$
$619$	2.77843	0.111675	0.0558373	+	0.998440i	$0.482217\pi$
$620$	3.35382	0.134693
$621$	−23.4475	−0.940916
$622$	7.90593	0.316999
$623$	−6.69176	−0.268100
$624$	18.7496	0.750585
$625$	1.00000	0.0400000
$626$	9.44157	0.377361
$627$	31.9851	1.27736
$628$	−8.07979	−0.322419
$629$	58.0187	2.31336
$630$	3.70968	0.147797
$631$	−40.1668	−1.59901	−0.799507	−	0.600657i	$-0.794906\pi$
$631$	−40.1668	−1.59901	−0.799507	+	0.600657i	$0.794906\pi$
$632$	−38.2429	−1.52122
$633$	0.880893	0.0350123
$634$	−45.7026	−1.81508
$635$	20.8548	0.827597
$636$	2.88729	0.114489
$637$	−5.25397	−0.208170
$638$	13.7402	0.543981
$639$	15.5226	0.614063
$640$	13.4424	0.531359
$641$	−13.9647	−0.551571	−0.275785	−	0.961219i	$-0.588938\pi$
$641$	−13.9647	−0.551571	−0.275785	+	0.961219i	$0.588938\pi$
$642$	−9.41274	−0.371491
$643$	27.7021	1.09247	0.546233	−	0.837633i	$-0.316061\pi$
$643$	27.7021	1.09247	0.546233	+	0.837633i	$0.316061\pi$
$644$	−2.15103	−0.0847623
$645$	5.90802	0.232628
$646$	−61.3208	−2.41263
$647$	−33.5077	−1.31732	−0.658662	−	0.752439i	$-0.728877\pi$
$647$	−33.5077	−1.31732	−0.658662	+	0.752439i	$0.728877\pi$
$648$	9.94626	0.390726
$649$	41.0857	1.61275
$650$	8.11043	0.318117
$651$	6.76619	0.265188
$652$	−1.82145	−0.0713333
$653$	33.7729	1.32164	0.660818	−	0.750546i	$-0.270210\pi$
$653$	33.7729	1.32164	0.660818	+	0.750546i	$0.270210\pi$
$654$	16.1767	0.632560
$655$	−4.08628	−0.159664
$656$	−37.1236	−1.44943
$657$	8.73116	0.340635
$658$	−8.07973	−0.314981
$659$	−36.2708	−1.41291	−0.706455	−	0.707758i	$-0.749707\pi$
$659$	−36.2708	−1.41291	−0.706455	+	0.707758i	$0.749707\pi$
$660$	−1.48066	−0.0576347
$661$	−24.1701	−0.940108	−0.470054	−	0.882638i	$-0.655766\pi$
$661$	−24.1701	−0.940108	−0.470054	+	0.882638i	$0.655766\pi$
$662$	23.6780	0.920273
$663$	−19.4917	−0.756997
$664$	29.0775	1.12843
$665$	8.27223	0.320783
$666$	44.8204	1.73676
$667$	−9.98992	−0.386811
$668$	3.88349	0.150257
$669$	9.25425	0.357790
$670$	−8.43128	−0.325729
$671$	−9.24267	−0.356809
$672$	−1.65188	−0.0637226
$673$	−36.6169	−1.41148	−0.705738	−	0.708473i	$-0.749384\pi$
$673$	−36.6169	−1.41148	−0.705738	+	0.708473i	$0.749384\pi$
$674$	35.0177	1.34883
$675$	−4.17428	−0.160668
$676$	5.59252	0.215097
$677$	14.9806	0.575752	0.287876	−	0.957668i	$-0.407051\pi$
$677$	14.9806	0.575752	0.287876	+	0.957668i	$0.407051\pi$
$678$	−23.3632	−0.897257
$679$	16.4107	0.629785
$680$	−11.9870	−0.459681
$681$	18.7048	0.716768
$682$	67.6638	2.59098
$683$	−2.93032	−0.112126	−0.0560628	−	0.998427i	$-0.517855\pi$
$683$	−2.93032	−0.112126	−0.0560628	+	0.998427i	$0.517855\pi$
$684$	−7.61260	−0.291075
$685$	−8.21971	−0.314059
$686$	1.54368	0.0589379
$687$	0.772565	0.0294752
$688$	35.3246	1.34674
$689$	−51.2757	−1.95345
$690$	6.69895	0.255025
$691$	18.3032	0.696286	0.348143	−	0.937441i	$-0.386812\pi$
$691$	18.3032	0.696286	0.348143	+	0.937441i	$0.386812\pi$
$692$	4.25640	0.161804
$693$	12.0274	0.456881
$694$	−14.8670	−0.564345
$695$	−12.0164	−0.455806
$696$	−3.42977	−0.130005
$697$	38.5930	1.46182
$698$	−19.2863	−0.729999
$699$	15.9972	0.605071
$700$	−0.382940	−0.0144738
$701$	21.6409	0.817364	0.408682	−	0.912677i	$-0.365989\pi$
$701$	21.6409	0.817364	0.408682	+	0.912677i	$0.365989\pi$
$702$	−33.8552	−1.27778
$703$	99.9453	3.76951
$704$	29.7179	1.12003
$705$	4.04367	0.152293
$706$	−6.69556	−0.251991
$707$	13.4452	0.505659
$708$	2.42866	0.0912745
$709$	13.7434	0.516144	0.258072	−	0.966126i	$-0.416913\pi$
$709$	13.7434	0.516144	0.258072	+	0.966126i	$0.416913\pi$
$710$	−9.97103	−0.374206
$711$	36.8169	1.38074
$712$	16.7041	0.626012
$713$	−49.1954	−1.84238
$714$	5.72691	0.214324
$715$	26.2953	0.983387
$716$	4.97409	0.185890
$717$	9.21638	0.344192
$718$	−16.5537	−0.617778
$719$	52.4084	1.95450	0.977252	−	0.212080i	$-0.0680239\pi$
$719$	52.4084	1.95450	0.977252	+	0.212080i	$0.0680239\pi$
$720$	−11.1007	−0.413698
$721$	−8.60526	−0.320476
$722$	−76.3037	−2.83973
$723$	9.41914	0.350301
$724$	6.99604	0.260006
$725$	−1.77847	−0.0660508
$726$	−16.7540	−0.621800
$727$	−30.6162	−1.13549	−0.567746	−	0.823204i	$-0.692184\pi$
$727$	−30.6162	−1.13549	−0.567746	+	0.823204i	$0.692184\pi$
$728$	13.1150	0.486076
$729$	0.0993089	0.00367811
$730$	−5.60853	−0.207581
$731$	−36.7228	−1.35824
$732$	−0.546353	−0.0201938
$733$	16.9972	0.627805	0.313903	−	0.949455i	$-0.398363\pi$
$733$	16.9972	0.627805	0.313903	+	0.949455i	$0.398363\pi$
$734$	−6.62452	−0.244515
$735$	−0.772565	−0.0284965
$736$	12.0104	0.442710
$737$	−27.3355	−1.00692
$738$	29.8138	1.09746
$739$	−33.3626	−1.22726	−0.613632	−	0.789592i	$-0.710292\pi$
$739$	−33.3626	−1.22726	−0.613632	+	0.789592i	$0.710292\pi$
$740$	−4.62669	−0.170081
$741$	−33.5772	−1.23349
$742$	15.0654	0.553069
$743$	34.7756	1.27579	0.637897	−	0.770122i	$-0.279805\pi$
$743$	34.7756	1.27579	0.637897	+	0.770122i	$0.279805\pi$
$744$	−16.8899	−0.619214
$745$	22.5174	0.824975
$746$	17.9567	0.657441
$747$	−27.9933	−1.02422
$748$	9.20343	0.336511
$749$	−7.89268	−0.288392
$750$	1.19259	0.0435473
$751$	−10.7450	−0.392092	−0.196046	−	0.980595i	$-0.562810\pi$
$751$	−10.7450	−0.392092	−0.196046	+	0.980595i	$0.562810\pi$
$752$	24.1775	0.881661
$753$	0.594084	0.0216496
$754$	−14.4242	−0.525297
$755$	−3.15924	−0.114977
$756$	1.59850	0.0581368
$757$	38.9751	1.41658	0.708288	−	0.705924i	$-0.249468\pi$
$757$	38.9751	1.41658	0.708288	+	0.705924i	$0.249468\pi$
$758$	5.71185	0.207464
$759$	21.7190	0.788351
$760$	−20.6493	−0.749029
$761$	−3.65362	−0.132444	−0.0662219	−	0.997805i	$-0.521095\pi$
$761$	−3.65362	−0.132444	−0.0662219	+	0.997805i	$0.521095\pi$
$762$	24.8712	0.900989
$763$	13.5644	0.491063
$764$	−7.22331	−0.261330
$765$	11.5401	0.417232
$766$	−55.0369	−1.98856
$767$	−43.1308	−1.55736
$768$	6.85662	0.247417
$769$	8.89807	0.320873	0.160436	−	0.987046i	$-0.448710\pi$
$769$	8.89807	0.320873	0.160436	+	0.987046i	$0.448710\pi$
$770$	−7.72586	−0.278421
$771$	−19.9424	−0.718206
$772$	4.52686	0.162925
$773$	18.0636	0.649703	0.324851	−	0.945765i	$-0.394686\pi$
$773$	18.0636	0.649703	0.324851	+	0.945765i	$0.394686\pi$
$774$	−28.3690	−1.01970
$775$	−8.75809	−0.314600
$776$	−40.9647	−1.47055
$777$	−9.33415	−0.334861
$778$	17.5727	0.630010
$779$	66.4818	2.38196
$780$	1.55436	0.0556552
$781$	−32.3276	−1.15677
$782$	−41.6390	−1.48901
$783$	7.42384	0.265306
$784$	−4.61924	−0.164973
$785$	21.0994	0.753069
$786$	−4.87326	−0.173823
$787$	−12.9589	−0.461934	−0.230967	−	0.972962i	$-0.574189\pi$
$787$	−12.9589	−0.461934	−0.230967	+	0.972962i	$0.574189\pi$
$788$	0.280851	0.0100049
$789$	−5.64490	−0.200964
$790$	−23.6496	−0.841417
$791$	−19.5903	−0.696549
$792$	−30.0229	−1.06682
$793$	9.70275	0.344555
$794$	−6.98998	−0.248065
$795$	−7.53980	−0.267409
$796$	−4.13832	−0.146679
$797$	44.8698	1.58937	0.794685	−	0.607021i	$-0.207636\pi$
$797$	44.8698	1.58937	0.794685	+	0.607021i	$0.207636\pi$
$798$	9.86539	0.349231
$799$	−25.1344	−0.889192
$800$	2.13817	0.0755959
$801$	−16.0813	−0.568203
$802$	50.1523	1.77094
$803$	−18.1837	−0.641689
$804$	−1.61586	−0.0569869
$805$	5.61714	0.197978
$806$	−71.0318	−2.50199
$807$	10.5980	0.373067
$808$	−33.5622	−1.18071
$809$	8.86536	0.311690	0.155845	−	0.987782i	$-0.450190\pi$
$809$	8.86536	0.311690	0.155845	+	0.987782i	$0.450190\pi$
$810$	6.15083	0.216118
$811$	−1.93965	−0.0681103	−0.0340552	−	0.999420i	$-0.510842\pi$
$811$	−1.93965	−0.0681103	−0.0340552	+	0.999420i	$0.510842\pi$
$812$	0.681048	0.0239001
$813$	2.95190	0.103528
$814$	−93.3440	−3.27171
$815$	4.75648	0.166612
$816$	−17.1370	−0.599913
$817$	−63.2601	−2.21319
$818$	14.0938	0.492780
$819$	−12.6260	−0.441189
$820$	−3.07759	−0.107474
$821$	24.8041	0.865668	0.432834	−	0.901474i	$-0.357514\pi$
$821$	24.8041	0.865668	0.432834	+	0.901474i	$0.357514\pi$
$822$	−9.80275	−0.341910
$823$	45.2408	1.57700	0.788498	−	0.615038i	$-0.210859\pi$
$823$	45.2408	1.57700	0.788498	+	0.615038i	$0.210859\pi$
$824$	21.4806	0.748312
$825$	3.86656	0.134616
$826$	12.6723	0.440927
$827$	−44.4744	−1.54653	−0.773264	−	0.634085i	$-0.781377\pi$
$827$	−44.4744	−1.54653	−0.773264	+	0.634085i	$0.781377\pi$
$828$	−5.16923	−0.179643
$829$	−0.0461342	−0.00160231	−0.000801153	−	1.00000i	$-0.500255\pi$
$829$	−0.0461342	−0.00160231	−0.000801153		1.00000i	$0.500255\pi$
$830$	17.9817	0.624155
$831$	8.24131	0.285888
$832$	−31.1971	−1.08157
$833$	4.80207	0.166382
$834$	−14.3306	−0.496228
$835$	−10.1412	−0.350952
$836$	15.8542	0.548328
$837$	36.5587	1.26365
$838$	−49.7965	−1.72019
$839$	−38.4112	−1.32610	−0.663052	−	0.748574i	$-0.730739\pi$
$839$	−38.4112	−1.32610	−0.663052	+	0.748574i	$0.730739\pi$
$840$	1.92849	0.0665393
$841$	−25.8370	−0.890932
$842$	−38.9492	−1.34228
$843$	−5.76150	−0.198437
$844$	0.436635	0.0150296
$845$	−14.6042	−0.502398
$846$	−19.4168	−0.667562
$847$	−14.0484	−0.482710
$848$	−45.0811	−1.54809
$849$	−4.13174	−0.141801
$850$	−7.41285	−0.254259
$851$	67.8664	2.32643
$852$	−1.91095	−0.0654681
$853$	0.525120	0.0179797	0.00898987	−	0.999960i	$-0.497138\pi$
$853$	0.525120	0.0179797	0.00898987	+	0.999960i	$0.497138\pi$
$854$	−2.85078	−0.0975517
$855$	19.8794	0.679860
$856$	19.7019	0.673396
$857$	1.62314	0.0554456	0.0277228	−	0.999616i	$-0.491174\pi$
$857$	1.62314	0.0554456	0.0277228	+	0.999616i	$0.491174\pi$
$858$	31.3595	1.07060
$859$	−2.39104	−0.0815811	−0.0407906	−	0.999168i	$-0.512988\pi$
$859$	−2.39104	−0.0815811	−0.0407906	+	0.999168i	$0.512988\pi$
$860$	2.92845	0.0998594
$861$	−6.20891	−0.211599
$862$	10.3455	0.352371
$863$	−26.3843	−0.898132	−0.449066	−	0.893499i	$-0.648243\pi$
$863$	−26.3843	−0.898132	−0.449066	+	0.893499i	$0.648243\pi$
$864$	−8.92534	−0.303646
$865$	−11.1150	−0.377923
$866$	−36.3105	−1.23388
$867$	4.68164	0.158997
$868$	3.35382	0.113836
$869$	−76.6758	−2.60105
$870$	−2.12099	−0.0719083
$871$	28.6962	0.972333
$872$	−33.8596	−1.14663
$873$	39.4373	1.33475
$874$	−71.7289	−2.42627
$875$	1.00000	0.0338062
$876$	−1.07488	−0.0363167
$877$	37.8030	1.27652	0.638259	−	0.769822i	$-0.279655\pi$
$877$	37.8030	1.27652	0.638259	+	0.769822i	$0.279655\pi$
$878$	−27.3071	−0.921570
$879$	−8.88371	−0.299640
$880$	23.1185	0.779326
$881$	−24.0587	−0.810559	−0.405279	−	0.914193i	$-0.632826\pi$
$881$	−24.0587	−0.810559	−0.405279	+	0.914193i	$0.632826\pi$
$882$	3.70968	0.124911
$883$	49.5406	1.66717	0.833587	−	0.552389i	$-0.186284\pi$
$883$	49.5406	1.66717	0.833587	+	0.552389i	$0.186284\pi$
$884$	−9.66154	−0.324953
$885$	−6.34213	−0.213188
$886$	−34.6014	−1.16246
$887$	47.2735	1.58729	0.793645	−	0.608381i	$-0.208181\pi$
$887$	47.2735	1.58729	0.793645	+	0.608381i	$0.208181\pi$
$888$	23.3001	0.781899
$889$	20.8548	0.699447
$890$	10.3299	0.346260
$891$	19.9419	0.668080
$892$	4.58709	0.153587
$893$	−43.2975	−1.44890
$894$	26.8541	0.898135
$895$	−12.9892	−0.434181
$896$	13.4424	0.449080
$897$	−22.8001	−0.761274
$898$	−25.9923	−0.867376
$899$	15.5760	0.519489
$900$	−0.920260	−0.0306753
$901$	46.8655	1.56132
$902$	−62.0908	−2.06740
$903$	5.90802	0.196607
$904$	48.9016	1.62644
$905$	−18.2693	−0.607291
$906$	−3.76768	−0.125173
$907$	−27.1777	−0.902422	−0.451211	−	0.892417i	$-0.649008\pi$
$907$	−27.1777	−0.902422	−0.451211	+	0.892417i	$0.649008\pi$
$908$	9.27146	0.307684
$909$	32.3107	1.07168
$910$	8.11043	0.268858
$911$	−33.0610	−1.09536	−0.547679	−	0.836688i	$-0.684489\pi$
$911$	−33.0610	−1.09536	−0.547679	+	0.836688i	$0.684489\pi$
$912$	−29.5208	−0.977531
$913$	58.2995	1.92943
$914$	49.7365	1.64514
$915$	1.42673	0.0471663
$916$	0.382940	0.0126527
$917$	−4.08628	−0.134941
$918$	30.9433	1.02128
$919$	47.9650	1.58222	0.791109	−	0.611675i	$-0.209504\pi$
$919$	47.9650	1.58222	0.791109	+	0.611675i	$0.209504\pi$
$920$	−14.0216	−0.462279
$921$	−8.67249	−0.285768
$922$	−51.2752	−1.68866
$923$	33.9368	1.11704
$924$	−1.48066	−0.0487102
$925$	12.0820	0.397254
$926$	−35.3417	−1.16140
$927$	−20.6797	−0.679209
$928$	−3.80268	−0.124829
$929$	15.3071	0.502210	0.251105	−	0.967960i	$-0.419206\pi$
$929$	15.3071	0.502210	0.251105	+	0.967960i	$0.419206\pi$
$930$	−10.4448	−0.342499
$931$	8.27223	0.271111
$932$	7.92941	0.259736
$933$	−3.95668	−0.129536
$934$	6.03141	0.197354
$935$	−24.0336	−0.785983
$936$	31.5173	1.03018
$937$	12.8824	0.420851	0.210426	−	0.977610i	$-0.432515\pi$
$937$	12.8824	0.420851	0.210426	+	0.977610i	$0.432515\pi$
$938$	−8.43128	−0.275291
$939$	−4.72523	−0.154202
$940$	2.00434	0.0653743
$941$	−16.0699	−0.523864	−0.261932	−	0.965086i	$-0.584360\pi$
$941$	−16.0699	−0.523864	−0.261932	+	0.965086i	$0.584360\pi$
$942$	25.1629	0.819852
$943$	45.1435	1.47008
$944$	−37.9202	−1.23420
$945$	−4.17428	−0.135789
$946$	59.0818	1.92092
$947$	−29.8896	−0.971281	−0.485641	−	0.874158i	$-0.661414\pi$
$947$	−29.8896	−0.971281	−0.485641	+	0.874158i	$0.661414\pi$
$948$	−4.53246	−0.147207
$949$	19.0888	0.619650
$950$	−12.7697	−0.414302
$951$	22.8728	0.741701
$952$	−11.9870	−0.388501
$953$	36.4466	1.18062	0.590311	−	0.807176i	$-0.299005\pi$
$953$	36.4466	1.18062	0.590311	+	0.807176i	$0.299005\pi$
$954$	36.2044	1.17216
$955$	18.8628	0.610385
$956$	4.56831	0.147750
$957$	−6.87657	−0.222288
$958$	−16.4580	−0.531733
$959$	−8.21971	−0.265428
$960$	−4.58735	−0.148056
$961$	45.7041	1.47433
$962$	97.9904	3.15934
$963$	−18.9672	−0.611211
$964$	4.66882	0.150372
$965$	−11.8213	−0.380542
$966$	6.69895	0.215535
$967$	36.7951	1.18325	0.591625	−	0.806213i	$-0.298486\pi$
$967$	36.7951	1.18325	0.591625	+	0.806213i	$0.298486\pi$
$968$	35.0680	1.12713
$969$	30.6892	0.985880
$970$	−25.3328	−0.813389
$971$	−5.50229	−0.176577	−0.0882885	−	0.996095i	$-0.528140\pi$
$971$	−5.50229	−0.176577	−0.0882885	+	0.996095i	$0.528140\pi$
$972$	5.97430	0.191626
$973$	−12.0164	−0.385227
$974$	19.3553	0.620183
$975$	−4.05903	−0.129993
$976$	8.53056	0.273057
$977$	17.2110	0.550628	0.275314	−	0.961354i	$-0.411218\pi$
$977$	17.2110	0.550628	0.275314	+	0.961354i	$0.411218\pi$
$978$	5.67253	0.181388
$979$	33.4912	1.07038
$980$	−0.382940	−0.0122326
$981$	32.5971	1.04074
$982$	8.13722	0.259669
$983$	37.0276	1.18100	0.590499	−	0.807038i	$-0.298931\pi$
$983$	37.0276	1.18100	0.590499	+	0.807038i	$0.298931\pi$
$984$	15.4988	0.494084
$985$	−0.733407	−0.0233683
$986$	13.1835	0.419849
$987$	4.04367	0.128711
$988$	−16.6433	−0.529495
$989$	−42.9559	−1.36592
$990$	−18.5663	−0.590077
$991$	−2.56309	−0.0814192	−0.0407096	−	0.999171i	$-0.512962\pi$
$991$	−2.56309	−0.0814192	−0.0407096	+	0.999171i	$0.512962\pi$
$992$	−18.7263	−0.594561
$993$	−11.8502	−0.376054
$994$	−9.97103	−0.316262
$995$	10.8067	0.342596
$996$	3.44620	0.109197
$997$	38.4010	1.21617	0.608086	−	0.793871i	$-0.291938\pi$
$997$	38.4010	1.21617	0.608086	+	0.793871i	$0.291938\pi$
$998$	23.8867	0.756120
$999$	−50.4337	−1.59565

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.l.1.15	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.l.1.15	✓	62	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-1.54368 q^{2} +0.772565 q^{3} +0.382940 q^{4} -1.00000 q^{5} -1.19259 q^{6} -1.00000 q^{7} +2.49622 q^{8} -2.40314 q^{9} +O(q^{10})\)	\(q-1.54368 q^{2} +0.772565 q^{3} +0.382940 q^{4} -1.00000 q^{5} -1.19259 q^{6} -1.00000 q^{7} +2.49622 q^{8} -2.40314 q^{9} +1.54368 q^{10} +5.00484 q^{11} +0.295846 q^{12} -5.25397 q^{13} +1.54368 q^{14} -0.772565 q^{15} -4.61924 q^{16} +4.80207 q^{17} +3.70968 q^{18} +8.27223 q^{19} -0.382940 q^{20} -0.772565 q^{21} -7.72586 q^{22} +5.61714 q^{23} +1.92849 q^{24} +1.00000 q^{25} +8.11043 q^{26} -4.17428 q^{27} -0.382940 q^{28} -1.77847 q^{29} +1.19259 q^{30} -8.75809 q^{31} +2.13817 q^{32} +3.86656 q^{33} -7.41285 q^{34} +1.00000 q^{35} -0.920260 q^{36} +12.0820 q^{37} -12.7697 q^{38} -4.05903 q^{39} -2.49622 q^{40} +8.03675 q^{41} +1.19259 q^{42} -7.64728 q^{43} +1.91655 q^{44} +2.40314 q^{45} -8.67105 q^{46} -5.23408 q^{47} -3.56866 q^{48} +1.00000 q^{49} -1.54368 q^{50} +3.70991 q^{51} -2.01195 q^{52} +9.75944 q^{53} +6.44374 q^{54} -5.00484 q^{55} -2.49622 q^{56} +6.39083 q^{57} +2.74539 q^{58} +8.20919 q^{59} -0.295846 q^{60} -1.84675 q^{61} +13.5197 q^{62} +2.40314 q^{63} +5.93782 q^{64} +5.25397 q^{65} -5.96873 q^{66} -5.46181 q^{67} +1.83890 q^{68} +4.33960 q^{69} -1.54368 q^{70} -6.45927 q^{71} -5.99877 q^{72} -3.63322 q^{73} -18.6507 q^{74} +0.772565 q^{75} +3.16777 q^{76} -5.00484 q^{77} +6.26583 q^{78} -15.3203 q^{79} +4.61924 q^{80} +3.98453 q^{81} -12.4061 q^{82} +11.6486 q^{83} -0.295846 q^{84} -4.80207 q^{85} +11.8049 q^{86} -1.37398 q^{87} +12.4932 q^{88} +6.69176 q^{89} -3.70968 q^{90} +5.25397 q^{91} +2.15103 q^{92} -6.76619 q^{93} +8.07973 q^{94} -8.27223 q^{95} +1.65188 q^{96} -16.4107 q^{97} -1.54368 q^{98} -12.0274 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * q^99

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