LMFDB - Embedded newform 8015.2.a.m.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:	$67$
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)

$f(q)$	$=$	$q-1.80341 q^{2} +0.567965 q^{3} +1.25230 q^{4} +1.00000 q^{5} -1.02428 q^{6} -1.00000 q^{7} +1.34841 q^{8} -2.67742 q^{9} +O(q^{10})$	\(q-1.80341 q^{2} +0.567965 q^{3} +1.25230 q^{4} +1.00000 q^{5} -1.02428 q^{6} -1.00000 q^{7} +1.34841 q^{8} -2.67742 q^{9} -1.80341 q^{10} +0.253853 q^{11} +0.711264 q^{12} -7.06566 q^{13} +1.80341 q^{14} +0.567965 q^{15} -4.93634 q^{16} -7.34662 q^{17} +4.82849 q^{18} -1.78414 q^{19} +1.25230 q^{20} -0.567965 q^{21} -0.457801 q^{22} -5.37456 q^{23} +0.765849 q^{24} +1.00000 q^{25} +12.7423 q^{26} -3.22458 q^{27} -1.25230 q^{28} -3.96844 q^{29} -1.02428 q^{30} +9.37038 q^{31} +6.20545 q^{32} +0.144180 q^{33} +13.2490 q^{34} -1.00000 q^{35} -3.35293 q^{36} +6.71552 q^{37} +3.21755 q^{38} -4.01305 q^{39} +1.34841 q^{40} -7.80846 q^{41} +1.02428 q^{42} -11.4297 q^{43} +0.317900 q^{44} -2.67742 q^{45} +9.69256 q^{46} -2.50605 q^{47} -2.80367 q^{48} +1.00000 q^{49} -1.80341 q^{50} -4.17263 q^{51} -8.84835 q^{52} -5.52090 q^{53} +5.81524 q^{54} +0.253853 q^{55} -1.34841 q^{56} -1.01333 q^{57} +7.15675 q^{58} -6.61859 q^{59} +0.711264 q^{60} -5.87033 q^{61} -16.8987 q^{62} +2.67742 q^{63} -1.31832 q^{64} -7.06566 q^{65} -0.260015 q^{66} -13.2937 q^{67} -9.20019 q^{68} -3.05256 q^{69} +1.80341 q^{70} +8.86571 q^{71} -3.61025 q^{72} -14.8642 q^{73} -12.1109 q^{74} +0.567965 q^{75} -2.23429 q^{76} -0.253853 q^{77} +7.23720 q^{78} -1.02292 q^{79} -4.93634 q^{80} +6.20080 q^{81} +14.0819 q^{82} +13.5407 q^{83} -0.711264 q^{84} -7.34662 q^{85} +20.6126 q^{86} -2.25394 q^{87} +0.342297 q^{88} +17.2815 q^{89} +4.82849 q^{90} +7.06566 q^{91} -6.73057 q^{92} +5.32205 q^{93} +4.51945 q^{94} -1.78414 q^{95} +3.52448 q^{96} +9.22234 q^{97} -1.80341 q^{98} -0.679669 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9}+O(q^{10}) $ 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9	\( 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9} + 3 q^{10} + 11 q^{11} + 9 q^{12} + 19 q^{13} - 3 q^{14} + 93 q^{16} + 7 q^{17} + 9 q^{18} + 36 q^{19} + 73 q^{20} - 8 q^{22} - 2 q^{23} + 37 q^{24} + 67 q^{25} + 39 q^{26} + 6 q^{27} - 73 q^{28} + 56 q^{29} + 17 q^{30} + 63 q^{31} + 27 q^{32} + 51 q^{33} + 55 q^{34} - 67 q^{35} + 148 q^{36} + 28 q^{37} + 10 q^{38} + 7 q^{39} + 12 q^{40} + 84 q^{41} - 17 q^{42} - 11 q^{43} + 41 q^{44} + 97 q^{45} + 17 q^{46} - 10 q^{47} + 10 q^{48} + 67 q^{49} + 3 q^{50} - q^{51} + 49 q^{52} + 3 q^{53} + 20 q^{54} + 11 q^{55} - 12 q^{56} + 45 q^{57} + 22 q^{58} + 80 q^{59} + 9 q^{60} + 64 q^{61} - 37 q^{62} - 97 q^{63} + 110 q^{64} + 19 q^{65} + 75 q^{66} + 22 q^{67} + 7 q^{68} + 107 q^{69} - 3 q^{70} + 24 q^{71} + 72 q^{72} + 83 q^{73} + 52 q^{74} + 115 q^{76} - 11 q^{77} - 70 q^{78} - 32 q^{79} + 93 q^{80} + 183 q^{81} + 56 q^{82} - 58 q^{83} - 9 q^{84} + 7 q^{85} + 51 q^{86} + 20 q^{87} - 5 q^{88} + 129 q^{89} + 9 q^{90} - 19 q^{91} - 37 q^{92} + 33 q^{93} + 89 q^{94} + 36 q^{95} + 129 q^{96} + 126 q^{97} + 3 q^{98} - 27 q^{99}+O(q^{100}) \) 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9 + 3 * q^10 + 11 * q^11 + 9 * q^12 + 19 * q^13 - 3 * q^14 + 93 * q^16 + 7 * q^17 + 9 * q^18 + 36 * q^19 + 73 * q^20 - 8 * q^22 - 2 * q^23 + 37 * q^24 + 67 * q^25 + 39 * q^26 + 6 * q^27 - 73 * q^28 + 56 * q^29 + 17 * q^30 + 63 * q^31 + 27 * q^32 + 51 * q^33 + 55 * q^34 - 67 * q^35 + 148 * q^36 + 28 * q^37 + 10 * q^38 + 7 * q^39 + 12 * q^40 + 84 * q^41 - 17 * q^42 - 11 * q^43 + 41 * q^44 + 97 * q^45 + 17 * q^46 - 10 * q^47 + 10 * q^48 + 67 * q^49 + 3 * q^50 - q^51 + 49 * q^52 + 3 * q^53 + 20 * q^54 + 11 * q^55 - 12 * q^56 + 45 * q^57 + 22 * q^58 + 80 * q^59 + 9 * q^60 + 64 * q^61 - 37 * q^62 - 97 * q^63 + 110 * q^64 + 19 * q^65 + 75 * q^66 + 22 * q^67 + 7 * q^68 + 107 * q^69 - 3 * q^70 + 24 * q^71 + 72 * q^72 + 83 * q^73 + 52 * q^74 + 115 * q^76 - 11 * q^77 - 70 * q^78 - 32 * q^79 + 93 * q^80 + 183 * q^81 + 56 * q^82 - 58 * q^83 - 9 * q^84 + 7 * q^85 + 51 * q^86 + 20 * q^87 - 5 * q^88 + 129 * q^89 + 9 * q^90 - 19 * q^91 - 37 * q^92 + 33 * q^93 + 89 * q^94 + 36 * q^95 + 129 * q^96 + 126 * q^97 + 3 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.80341	−1.27521	−0.637603	−	0.770365i	$-0.720074\pi$
$2$	−1.80341	−1.27521	−0.637603	+	0.770365i	$0.720074\pi$
$3$	0.567965	0.327915	0.163957	−	0.986467i	$-0.447574\pi$
$3$	0.567965	0.327915	0.163957	+	0.986467i	$0.447574\pi$
$4$	1.25230	0.626151
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.02428	−0.418159
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.34841	0.476734
$9$	−2.67742	−0.892472
$10$	−1.80341	−0.570290
$11$	0.253853	0.0765395	0.0382697	−	0.999267i	$-0.487815\pi$
$11$	0.253853	0.0765395	0.0382697	+	0.999267i	$0.487815\pi$
$12$	0.711264	0.205324
$13$	−7.06566	−1.95966	−0.979831	−	0.199826i	$-0.935962\pi$
$13$	−7.06566	−1.95966	−0.979831	+	0.199826i	$0.935962\pi$
$14$	1.80341	0.481983
$15$	0.567965	0.146648
$16$	−4.93634	−1.23409
$17$	−7.34662	−1.78182	−0.890908	−	0.454183i	$-0.849931\pi$
$17$	−7.34662	−1.78182	−0.890908	+	0.454183i	$0.849931\pi$
$18$	4.82849	1.13809
$19$	−1.78414	−0.409311	−0.204655	−	0.978834i	$-0.565607\pi$
$19$	−1.78414	−0.409311	−0.204655	+	0.978834i	$0.565607\pi$
$20$	1.25230	0.280023
$21$	−0.567965	−0.123940
$22$	−0.457801	−0.0976036
$23$	−5.37456	−1.12067	−0.560337	−	0.828265i	$-0.689328\pi$
$23$	−5.37456	−1.12067	−0.560337	+	0.828265i	$0.689328\pi$
$24$	0.765849	0.156328
$25$	1.00000	0.200000
$26$	12.7423	2.49897
$27$	−3.22458	−0.620570
$28$	−1.25230	−0.236663
$29$	−3.96844	−0.736921	−0.368461	−	0.929643i	$-0.620115\pi$
$29$	−3.96844	−0.736921	−0.368461	+	0.929643i	$0.620115\pi$
$30$	−1.02428	−0.187007
$31$	9.37038	1.68297	0.841485	−	0.540281i	$-0.181682\pi$
$31$	9.37038	1.68297	0.841485	+	0.540281i	$0.181682\pi$
$32$	6.20545	1.09698
$33$	0.144180	0.0250984
$34$	13.2490	2.27218
$35$	−1.00000	−0.169031
$36$	−3.35293	−0.558822
$37$	6.71552	1.10402	0.552012	−	0.833836i	$-0.313860\pi$
$37$	6.71552	1.10402	0.552012	+	0.833836i	$0.313860\pi$
$38$	3.21755	0.521956
$39$	−4.01305	−0.642603
$40$	1.34841	0.213202
$41$	−7.80846	−1.21948	−0.609739	−	0.792603i	$-0.708726\pi$
$41$	−7.80846	−1.21948	−0.609739	+	0.792603i	$0.708726\pi$
$42$	1.02428	0.158049
$43$	−11.4297	−1.74302	−0.871510	−	0.490378i	$-0.836859\pi$
$43$	−11.4297	−1.74302	−0.871510	+	0.490378i	$0.836859\pi$
$44$	0.317900	0.0479253
$45$	−2.67742	−0.399126
$46$	9.69256	1.42909
$47$	−2.50605	−0.365545	−0.182772	−	0.983155i	$-0.558507\pi$
$47$	−2.50605	−0.365545	−0.182772	+	0.983155i	$0.558507\pi$
$48$	−2.80367	−0.404675
$49$	1.00000	0.142857
$50$	−1.80341	−0.255041
$51$	−4.17263	−0.584284
$52$	−8.84835	−1.22705
$53$	−5.52090	−0.758353	−0.379177	−	0.925324i	$-0.623793\pi$
$53$	−5.52090	−0.758353	−0.379177	+	0.925324i	$0.623793\pi$
$54$	5.81524	0.791355
$55$	0.253853	0.0342295
$56$	−1.34841	−0.180189
$57$	−1.01333	−0.134219
$58$	7.15675	0.939727
$59$	−6.61859	−0.861668	−0.430834	−	0.902431i	$-0.641780\pi$
$59$	−6.61859	−0.861668	−0.430834	+	0.902431i	$0.641780\pi$
$60$	0.711264	0.0918238
$61$	−5.87033	−0.751618	−0.375809	−	0.926697i	$-0.622635\pi$
$61$	−5.87033	−0.751618	−0.375809	+	0.926697i	$0.622635\pi$
$62$	−16.8987	−2.14613
$63$	2.67742	0.337323
$64$	−1.31832	−0.164790
$65$	−7.06566	−0.876388
$66$	−0.260015	−0.0320057
$67$	−13.2937	−1.62408	−0.812039	−	0.583603i	$-0.801642\pi$
$67$	−13.2937	−1.62408	−0.812039	+	0.583603i	$0.801642\pi$
$68$	−9.20019	−1.11569
$69$	−3.05256	−0.367486
$70$	1.80341	0.215549
$71$	8.86571	1.05217	0.526083	−	0.850433i	$-0.323660\pi$
$71$	8.86571	1.05217	0.526083	+	0.850433i	$0.323660\pi$
$72$	−3.61025	−0.425472
$73$	−14.8642	−1.73973	−0.869864	−	0.493291i	$-0.835794\pi$
$73$	−14.8642	−1.73973	−0.869864	+	0.493291i	$0.835794\pi$
$74$	−12.1109	−1.40786
$75$	0.567965	0.0655830
$76$	−2.23429	−0.256290
$77$	−0.253853	−0.0289292
$78$	7.23720	0.819451
$79$	−1.02292	−0.115088	−0.0575438	−	0.998343i	$-0.518327\pi$
$79$	−1.02292	−0.115088	−0.0575438	+	0.998343i	$0.518327\pi$
$80$	−4.93634	−0.551900
$81$	6.20080	0.688978
$82$	14.0819	1.55508
$83$	13.5407	1.48628	0.743140	−	0.669136i	$-0.233336\pi$
$83$	13.5407	1.48628	0.743140	+	0.669136i	$0.233336\pi$
$84$	−0.711264	−0.0776053
$85$	−7.34662	−0.796853
$86$	20.6126	2.22271
$87$	−2.25394	−0.241648
$88$	0.342297	0.0364890
$89$	17.2815	1.83184	0.915920	−	0.401361i	$-0.131463\pi$
$89$	17.2815	1.83184	0.915920	+	0.401361i	$0.131463\pi$
$90$	4.82849	0.508967
$91$	7.06566	0.740683
$92$	−6.73057	−0.701711
$93$	5.32205	0.551871
$94$	4.51945	0.466145
$95$	−1.78414	−0.183049
$96$	3.52448	0.359716
$97$	9.22234	0.936387	0.468193	−	0.883626i	$-0.344905\pi$
$97$	9.22234	0.936387	0.468193	+	0.883626i	$0.344905\pi$
$98$	−1.80341	−0.182172
$99$	−0.679669	−0.0683093
$100$	1.25230	0.125230
$101$	−14.5673	−1.44950	−0.724752	−	0.689010i	$-0.758046\pi$
$101$	−14.5673	−1.44950	−0.724752	+	0.689010i	$0.758046\pi$
$102$	7.52497	0.745083
$103$	−0.709708	−0.0699296	−0.0349648	−	0.999389i	$-0.511132\pi$
$103$	−0.709708	−0.0699296	−0.0349648	+	0.999389i	$0.511132\pi$
$104$	−9.52740	−0.934239
$105$	−0.567965	−0.0554277
$106$	9.95646	0.967057
$107$	19.5638	1.89130	0.945651	−	0.325182i	$-0.105426\pi$
$107$	19.5638	1.89130	0.945651	+	0.325182i	$0.105426\pi$
$108$	−4.03814	−0.388571
$109$	8.03820	0.769920	0.384960	−	0.922933i	$-0.374215\pi$
$109$	8.03820	0.769920	0.384960	+	0.922933i	$0.374215\pi$
$110$	−0.457801	−0.0436497
$111$	3.81418	0.362026
$112$	4.93634	0.466441
$113$	0.658377	0.0619349	0.0309674	−	0.999520i	$-0.490141\pi$
$113$	0.658377	0.0619349	0.0309674	+	0.999520i	$0.490141\pi$
$114$	1.82746	0.171157
$115$	−5.37456	−0.501180
$116$	−4.96969	−0.461424
$117$	18.9177	1.74894
$118$	11.9361	1.09880
$119$	7.34662	0.673463
$120$	0.765849	0.0699122
$121$	−10.9356	−0.994142
$122$	10.5866	0.958468
$123$	−4.43494	−0.399885
$124$	11.7345	1.05379
$125$	1.00000	0.0894427
$126$	−4.82849	−0.430156
$127$	14.3807	1.27608	0.638042	−	0.770001i	$-0.279745\pi$
$127$	14.3807	1.27608	0.638042	+	0.770001i	$0.279745\pi$
$128$	−10.0334	−0.886839
$129$	−6.49170	−0.571562
$130$	12.7423	1.11758
$131$	13.2094	1.15411	0.577053	−	0.816707i	$-0.304203\pi$
$131$	13.2094	1.15411	0.577053	+	0.816707i	$0.304203\pi$
$132$	0.180556	0.0157154
$133$	1.78414	0.154705
$134$	23.9740	2.07103
$135$	−3.22458	−0.277527
$136$	−9.90624	−0.849453
$137$	10.4819	0.895529	0.447765	−	0.894151i	$-0.352220\pi$
$137$	10.4819	0.895529	0.447765	+	0.894151i	$0.352220\pi$
$138$	5.50504	0.468620
$139$	−2.18582	−0.185399	−0.0926996	−	0.995694i	$-0.529550\pi$
$139$	−2.18582	−0.185399	−0.0926996	+	0.995694i	$0.529550\pi$
$140$	−1.25230	−0.105839
$141$	−1.42335	−0.119868
$142$	−15.9885	−1.34173
$143$	−1.79364	−0.149992
$144$	13.2166	1.10139
$145$	−3.96844	−0.329561
$146$	26.8064	2.21851
$147$	0.567965	0.0468450
$148$	8.40986	0.691286
$149$	−12.4453	−1.01956	−0.509778	−	0.860306i	$-0.670272\pi$
$149$	−12.4453	−1.01956	−0.509778	+	0.860306i	$0.670272\pi$
$150$	−1.02428	−0.0836319
$151$	10.3858	0.845185	0.422592	−	0.906320i	$-0.361120\pi$
$151$	10.3858	0.845185	0.422592	+	0.906320i	$0.361120\pi$
$152$	−2.40575	−0.195132
$153$	19.6699	1.59022
$154$	0.457801	0.0368907
$155$	9.37038	0.752647
$156$	−5.02556	−0.402367
$157$	0.764982	0.0610522	0.0305261	−	0.999534i	$-0.490282\pi$
$157$	0.764982	0.0610522	0.0305261	+	0.999534i	$0.490282\pi$
$158$	1.84475	0.146760
$159$	−3.13568	−0.248675
$160$	6.20545	0.490584
$161$	5.37456	0.423575
$162$	−11.1826	−0.878589
$163$	0.501682	0.0392948	0.0196474	−	0.999807i	$-0.493746\pi$
$163$	0.501682	0.0392948	0.0196474	+	0.999807i	$0.493746\pi$
$164$	−9.77856	−0.763577
$165$	0.144180	0.0112244
$166$	−24.4194	−1.89531
$167$	0.968483	0.0749435	0.0374717	−	0.999298i	$-0.488070\pi$
$167$	0.968483	0.0749435	0.0374717	+	0.999298i	$0.488070\pi$
$168$	−0.765849	−0.0590866
$169$	36.9236	2.84028
$170$	13.2490	1.01615
$171$	4.77689	0.365298
$172$	−14.3135	−1.09139
$173$	2.40686	0.182990	0.0914952	−	0.995806i	$-0.470835\pi$
$173$	2.40686	0.182990	0.0914952	+	0.995806i	$0.470835\pi$
$174$	4.06478	0.308150
$175$	−1.00000	−0.0755929
$176$	−1.25310	−0.0944563
$177$	−3.75913	−0.282554
$178$	−31.1658	−2.33597
$179$	9.69352	0.724527	0.362264	−	0.932076i	$-0.382004\pi$
$179$	9.69352	0.724527	0.362264	+	0.932076i	$0.382004\pi$
$180$	−3.35293	−0.249913
$181$	−5.19453	−0.386106	−0.193053	−	0.981188i	$-0.561839\pi$
$181$	−5.19453	−0.386106	−0.193053	+	0.981188i	$0.561839\pi$
$182$	−12.7423	−0.944524
$183$	−3.33414	−0.246467
$184$	−7.24710	−0.534263
$185$	6.71552	0.493735
$186$	−9.59786	−0.703749
$187$	−1.86496	−0.136379
$188$	−3.13833	−0.228886
$189$	3.22458	0.234553
$190$	3.21755	0.233426
$191$	−14.0267	−1.01494	−0.507470	−	0.861670i	$-0.669419\pi$
$191$	−14.0267	−1.01494	−0.507470	+	0.861670i	$0.669419\pi$
$192$	−0.748759	−0.0540370
$193$	−22.2322	−1.60031	−0.800154	−	0.599795i	$-0.795249\pi$
$193$	−22.2322	−1.60031	−0.800154	+	0.599795i	$0.795249\pi$
$194$	−16.6317	−1.19409
$195$	−4.01305	−0.287381
$196$	1.25230	0.0894502
$197$	−15.4166	−1.09839	−0.549193	−	0.835696i	$-0.685065\pi$
$197$	−15.4166	−1.09839	−0.549193	+	0.835696i	$0.685065\pi$
$198$	1.22572	0.0871085
$199$	7.50923	0.532315	0.266157	−	0.963930i	$-0.414246\pi$
$199$	7.50923	0.532315	0.266157	+	0.963930i	$0.414246\pi$
$200$	1.34841	0.0953469
$201$	−7.55033	−0.532559
$202$	26.2709	1.84842
$203$	3.96844	0.278530
$204$	−5.22539	−0.365850
$205$	−7.80846	−0.545367
$206$	1.27990	0.0891747
$207$	14.3899	1.00017
$208$	34.8785	2.41839
$209$	−0.452910	−0.0313284
$210$	1.02428	0.0706818
$211$	−15.0588	−1.03669	−0.518345	−	0.855172i	$-0.673452\pi$
$211$	−15.0588	−1.03669	−0.518345	+	0.855172i	$0.673452\pi$
$212$	−6.91383	−0.474844
$213$	5.03542	0.345021
$214$	−35.2816	−2.41180
$215$	−11.4297	−0.779502
$216$	−4.34804	−0.295847
$217$	−9.37038	−0.636103
$218$	−14.4962	−0.981806
$219$	−8.44238	−0.570483
$220$	0.317900	0.0214328
$221$	51.9087	3.49176
$222$	−6.87855	−0.461658
$223$	4.25426	0.284886	0.142443	−	0.989803i	$-0.454504\pi$
$223$	4.25426	0.284886	0.142443	+	0.989803i	$0.454504\pi$
$224$	−6.20545	−0.414619
$225$	−2.67742	−0.178494
$226$	−1.18733	−0.0789797
$227$	7.76371	0.515295	0.257648	−	0.966239i	$-0.417053\pi$
$227$	7.76371	0.515295	0.257648	+	0.966239i	$0.417053\pi$
$228$	−1.26900	−0.0840415
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	9.69256	0.639108
$231$	−0.144180	−0.00948632
$232$	−5.35108	−0.351316
$233$	−28.3137	−1.85489	−0.927447	−	0.373954i	$-0.878002\pi$
$233$	−28.3137	−1.85489	−0.927447	+	0.373954i	$0.878002\pi$
$234$	−34.1165	−2.23026
$235$	−2.50605	−0.163477
$236$	−8.28848	−0.539534
$237$	−0.580983	−0.0377389
$238$	−13.2490	−0.858805
$239$	6.04424	0.390969	0.195485	−	0.980707i	$-0.437372\pi$
$239$	6.04424	0.390969	0.195485	+	0.980707i	$0.437372\pi$
$240$	−2.80367	−0.180976
$241$	−23.8746	−1.53790	−0.768949	−	0.639310i	$-0.779220\pi$
$241$	−23.8746	−1.53790	−0.768949	+	0.639310i	$0.779220\pi$
$242$	19.7213	1.26774
$243$	13.1956	0.846496
$244$	−7.35142	−0.470627
$245$	1.00000	0.0638877
$246$	7.99803	0.509936
$247$	12.6062	0.802111
$248$	12.6351	0.802329
$249$	7.69063	0.487374
$250$	−1.80341	−0.114058
$251$	2.01974	0.127485	0.0637424	−	0.997966i	$-0.479696\pi$
$251$	2.01974	0.127485	0.0637424	+	0.997966i	$0.479696\pi$
$252$	3.35293	0.211215
$253$	−1.36435	−0.0857757
$254$	−25.9344	−1.62727
$255$	−4.17263	−0.261300
$256$	20.7311	1.29569
$257$	19.5485	1.21940	0.609700	−	0.792633i	$-0.291290\pi$
$257$	19.5485	1.21940	0.609700	+	0.792633i	$0.291290\pi$
$258$	11.7072	0.728860
$259$	−6.71552	−0.417282
$260$	−8.84835	−0.548751
$261$	10.6252	0.657681
$262$	−23.8219	−1.47172
$263$	−5.36498	−0.330819	−0.165409	−	0.986225i	$-0.552895\pi$
$263$	−5.36498	−0.330819	−0.165409	+	0.986225i	$0.552895\pi$
$264$	0.194413	0.0119653
$265$	−5.52090	−0.339146
$266$	−3.21755	−0.197281
$267$	9.81532	0.600688
$268$	−16.6477	−1.01692
$269$	−7.66329	−0.467239	−0.233619	−	0.972328i	$-0.575057\pi$
$269$	−7.66329	−0.467239	−0.233619	+	0.972328i	$0.575057\pi$
$270$	5.81524	0.353905
$271$	12.8071	0.777973	0.388987	−	0.921243i	$-0.372825\pi$
$271$	12.8071	0.777973	0.388987	+	0.921243i	$0.372825\pi$
$272$	36.2654	2.19891
$273$	4.01305	0.242881
$274$	−18.9032	−1.14198
$275$	0.253853	0.0153079
$276$	−3.82273	−0.230102
$277$	10.4276	0.626535	0.313267	−	0.949665i	$-0.398576\pi$
$277$	10.4276	0.626535	0.313267	+	0.949665i	$0.398576\pi$
$278$	3.94195	0.236422
$279$	−25.0884	−1.50200
$280$	−1.34841	−0.0805828
$281$	−6.33500	−0.377914	−0.188957	−	0.981985i	$-0.560511\pi$
$281$	−6.33500	−0.377914	−0.188957	+	0.981985i	$0.560511\pi$
$282$	2.56689	0.152856
$283$	−3.15301	−0.187427	−0.0937136	−	0.995599i	$-0.529874\pi$
$283$	−3.15301	−0.187427	−0.0937136	+	0.995599i	$0.529874\pi$
$284$	11.1025	0.658815
$285$	−1.01333	−0.0600246
$286$	3.23467	0.191270
$287$	7.80846	0.460919
$288$	−16.6146	−0.979023
$289$	36.9728	2.17487
$290$	7.15675	0.420259
$291$	5.23797	0.307055
$292$	−18.6145	−1.08933
$293$	−11.1534	−0.651588	−0.325794	−	0.945441i	$-0.605632\pi$
$293$	−11.1534	−0.651588	−0.325794	+	0.945441i	$0.605632\pi$
$294$	−1.02428	−0.0597370
$295$	−6.61859	−0.385349
$296$	9.05526	0.526326
$297$	−0.818567	−0.0474981
$298$	22.4440	1.30014
$299$	37.9748	2.19614
$300$	0.711264	0.0410649
$301$	11.4297	0.658799
$302$	−18.7299	−1.07779
$303$	−8.27374	−0.475314
$304$	8.80715	0.505125
$305$	−5.87033	−0.336134
$306$	−35.4731	−2.02786
$307$	−1.40775	−0.0803444	−0.0401722	−	0.999193i	$-0.512791\pi$
$307$	−1.40775	−0.0803444	−0.0401722	+	0.999193i	$0.512791\pi$
$308$	−0.317900	−0.0181141
$309$	−0.403090	−0.0229310
$310$	−16.8987	−0.959780
$311$	23.4586	1.33022	0.665109	−	0.746747i	$-0.268385\pi$
$311$	23.4586	1.33022	0.665109	+	0.746747i	$0.268385\pi$
$312$	−5.41123	−0.306351
$313$	13.2095	0.746644	0.373322	−	0.927702i	$-0.378219\pi$
$313$	13.2095	0.746644	0.373322	+	0.927702i	$0.378219\pi$
$314$	−1.37958	−0.0778541
$315$	2.67742	0.150855
$316$	−1.28101	−0.0720622
$317$	−12.8949	−0.724249	−0.362125	−	0.932130i	$-0.617949\pi$
$317$	−12.8949	−0.724249	−0.362125	+	0.932130i	$0.617949\pi$
$318$	5.65493	0.317112
$319$	−1.00740	−0.0564036
$320$	−1.31832	−0.0736962
$321$	11.1116	0.620187
$322$	−9.69256	−0.540145
$323$	13.1074	0.729317
$324$	7.76528	0.431404
$325$	−7.06566	−0.391933
$326$	−0.904741	−0.0501089
$327$	4.56542	0.252468
$328$	−10.5290	−0.581367
$329$	2.50605	0.138163
$330$	−0.260015	−0.0143134
$331$	−6.57737	−0.361525	−0.180763	−	0.983527i	$-0.557857\pi$
$331$	−6.57737	−0.361525	−0.180763	+	0.983527i	$0.557857\pi$
$332$	16.9570	0.930636
$333$	−17.9802	−0.985311
$334$	−1.74658	−0.0955684
$335$	−13.2937	−0.726310
$336$	2.80367	0.152953
$337$	−3.37880	−0.184055	−0.0920274	−	0.995756i	$-0.529335\pi$
$337$	−3.37880	−0.184055	−0.0920274	+	0.995756i	$0.529335\pi$
$338$	−66.5886	−3.62194
$339$	0.373935	0.0203094
$340$	−9.20019	−0.498950
$341$	2.37870	0.128814
$342$	−8.61472	−0.465831
$343$	−1.00000	−0.0539949
$344$	−15.4120	−0.830957
$345$	−3.05256	−0.164345
$346$	−4.34057	−0.233351
$347$	−25.4638	−1.36697	−0.683486	−	0.729964i	$-0.739537\pi$
$347$	−25.4638	−1.36697	−0.683486	+	0.729964i	$0.739537\pi$
$348$	−2.82261	−0.151308
$349$	1.60360	0.0858385	0.0429192	−	0.999079i	$-0.486334\pi$
$349$	1.60360	0.0858385	0.0429192	+	0.999079i	$0.486334\pi$
$350$	1.80341	0.0963965
$351$	22.7838	1.21611
$352$	1.57527	0.0839622
$353$	−34.4552	−1.83386	−0.916932	−	0.399043i	$-0.869342\pi$
$353$	−34.4552	−1.83386	−0.916932	+	0.399043i	$0.869342\pi$
$354$	6.77927	0.360314
$355$	8.86571	0.470543
$356$	21.6417	1.14701
$357$	4.17263	0.220839
$358$	−17.4814	−0.923922
$359$	1.57037	0.0828812	0.0414406	−	0.999141i	$-0.486805\pi$
$359$	1.57037	0.0828812	0.0414406	+	0.999141i	$0.486805\pi$
$360$	−3.61025	−0.190277
$361$	−15.8168	−0.832465
$362$	9.36789	0.492365
$363$	−6.21102	−0.325994
$364$	8.84835	0.463779
$365$	−14.8642	−0.778030
$366$	6.01284	0.314296
$367$	25.4214	1.32699	0.663494	−	0.748182i	$-0.269073\pi$
$367$	25.4214	1.32699	0.663494	+	0.748182i	$0.269073\pi$
$368$	26.5307	1.38301
$369$	20.9065	1.08835
$370$	−12.1109	−0.629614
$371$	5.52090	0.286631
$372$	6.66482	0.345555
$373$	−15.2820	−0.791272	−0.395636	−	0.918407i	$-0.629476\pi$
$373$	−15.2820	−0.791272	−0.395636	+	0.918407i	$0.629476\pi$
$374$	3.36329	0.173912
$375$	0.567965	0.0293296
$376$	−3.37918	−0.174268
$377$	28.0397	1.44412
$378$	−5.81524	−0.299104
$379$	−23.7391	−1.21940	−0.609698	−	0.792634i	$-0.708709\pi$
$379$	−23.7391	−1.21940	−0.609698	+	0.792634i	$0.708709\pi$
$380$	−2.23429	−0.114617
$381$	8.16776	0.418447
$382$	25.2960	1.29426
$383$	−19.3996	−0.991271	−0.495636	−	0.868531i	$-0.665065\pi$
$383$	−19.3996	−0.991271	−0.495636	+	0.868531i	$0.665065\pi$
$384$	−5.69865	−0.290808
$385$	−0.253853	−0.0129375
$386$	40.0938	2.04072
$387$	30.6022	1.55560
$388$	11.5492	0.586320
$389$	14.5046	0.735413	0.367707	−	0.929942i	$-0.380143\pi$
$389$	14.5046	0.735413	0.367707	+	0.929942i	$0.380143\pi$
$390$	7.23720	0.366470
$391$	39.4848	1.99683
$392$	1.34841	0.0681049
$393$	7.50245	0.378449
$394$	27.8025	1.40067
$395$	−1.02292	−0.0514687
$396$	−0.851151	−0.0427720
$397$	−10.3232	−0.518107	−0.259054	−	0.965863i	$-0.583411\pi$
$397$	−10.3232	−0.518107	−0.259054	+	0.965863i	$0.583411\pi$
$398$	−13.5422	−0.678811
$399$	1.01333	0.0507301
$400$	−4.93634	−0.246817
$401$	−12.7331	−0.635863	−0.317931	−	0.948114i	$-0.602988\pi$
$401$	−12.7331	−0.635863	−0.317931	+	0.948114i	$0.602988\pi$
$402$	13.6164	0.679123
$403$	−66.2080	−3.29805
$404$	−18.2427	−0.907609
$405$	6.20080	0.308120
$406$	−7.15675	−0.355183
$407$	1.70475	0.0845015
$408$	−5.62640	−0.278548
$409$	10.2733	0.507982	0.253991	−	0.967207i	$-0.418257\pi$
$409$	10.2733	0.507982	0.253991	+	0.967207i	$0.418257\pi$
$410$	14.0819	0.695455
$411$	5.95336	0.293658
$412$	−0.888769	−0.0437865
$413$	6.61859	0.325680
$414$	−25.9510	−1.27542
$415$	13.5407	0.664685
$416$	−43.8457	−2.14971
$417$	−1.24147	−0.0607952
$418$	0.816784	0.0399502
$419$	8.89787	0.434690	0.217345	−	0.976095i	$-0.430260\pi$
$419$	8.89787	0.434690	0.217345	+	0.976095i	$0.430260\pi$
$420$	−0.711264	−0.0347062
$421$	−29.6287	−1.44402	−0.722008	−	0.691884i	$-0.756781\pi$
$421$	−29.6287	−1.44402	−0.722008	+	0.691884i	$0.756781\pi$
$422$	27.1572	1.32199
$423$	6.70974	0.326239
$424$	−7.44442	−0.361533
$425$	−7.34662	−0.356363
$426$	−9.08094	−0.439973
$427$	5.87033	0.284085
$428$	24.4998	1.18424
$429$	−1.01872	−0.0491845
$430$	20.6126	0.994026
$431$	−17.9586	−0.865035	−0.432518	−	0.901625i	$-0.642375\pi$
$431$	−17.9586	−0.865035	−0.432518	+	0.901625i	$0.642375\pi$
$432$	15.9176	0.765836
$433$	37.4614	1.80028	0.900140	−	0.435601i	$-0.143464\pi$
$433$	37.4614	1.80028	0.900140	+	0.435601i	$0.143464\pi$
$434$	16.8987	0.811162
$435$	−2.25394	−0.108068
$436$	10.0663	0.482086
$437$	9.58899	0.458703
$438$	15.2251	0.727483
$439$	0.904570	0.0431728	0.0215864	−	0.999767i	$-0.493128\pi$
$439$	0.904570	0.0431728	0.0215864	+	0.999767i	$0.493128\pi$
$440$	0.342297	0.0163184
$441$	−2.67742	−0.127496
$442$	−93.6130	−4.45271
$443$	−34.6171	−1.64471	−0.822354	−	0.568976i	$-0.807340\pi$
$443$	−34.6171	−1.64471	−0.822354	+	0.568976i	$0.807340\pi$
$444$	4.77651	0.226683
$445$	17.2815	0.819224
$446$	−7.67219	−0.363289
$447$	−7.06848	−0.334327
$448$	1.31832	0.0622847
$449$	20.3977	0.962628	0.481314	−	0.876548i	$-0.340160\pi$
$449$	20.3977	0.962628	0.481314	+	0.876548i	$0.340160\pi$
$450$	4.82849	0.227617
$451$	−1.98220	−0.0933381
$452$	0.824487	0.0387806
$453$	5.89878	0.277149
$454$	−14.0012	−0.657108
$455$	7.06566	0.331243
$456$	−1.36639	−0.0639869
$457$	20.4069	0.954595	0.477298	−	0.878742i	$-0.341616\pi$
$457$	20.4069	0.954595	0.477298	+	0.878742i	$0.341616\pi$
$458$	1.80341	0.0842680
$459$	23.6897	1.10574
$460$	−6.73057	−0.313815
$461$	11.9880	0.558337	0.279168	−	0.960242i	$-0.409941\pi$
$461$	11.9880	0.558337	0.279168	+	0.960242i	$0.409941\pi$
$462$	0.260015	0.0120970
$463$	39.7677	1.84816	0.924080	−	0.382200i	$-0.124833\pi$
$463$	39.7677	1.84816	0.924080	+	0.382200i	$0.124833\pi$
$464$	19.5896	0.909424
$465$	5.32205	0.246804
$466$	51.0614	2.36537
$467$	−32.1054	−1.48566	−0.742831	−	0.669479i	$-0.766517\pi$
$467$	−32.1054	−1.48566	−0.742831	+	0.669479i	$0.766517\pi$
$468$	23.6907	1.09510
$469$	13.2937	0.613844
$470$	4.51945	0.208466
$471$	0.434483	0.0200199
$472$	−8.92457	−0.410787
$473$	−2.90147	−0.133410
$474$	1.04775	0.0481249
$475$	−1.78414	−0.0818621
$476$	9.20019	0.421690
$477$	14.7817	0.676809
$478$	−10.9003	−0.498566
$479$	36.0297	1.64624	0.823120	−	0.567867i	$-0.192231\pi$
$479$	36.0297	1.64624	0.823120	+	0.567867i	$0.192231\pi$
$480$	3.52448	0.160870
$481$	−47.4496	−2.16352
$482$	43.0558	1.96114
$483$	3.05256	0.138896
$484$	−13.6946	−0.622483
$485$	9.22234	0.418765
$486$	−23.7971	−1.07946
$487$	16.9768	0.769292	0.384646	−	0.923064i	$-0.374324\pi$
$487$	16.9768	0.769292	0.384646	+	0.923064i	$0.374324\pi$
$488$	−7.91560	−0.358322
$489$	0.284938	0.0128853
$490$	−1.80341	−0.0814699
$491$	27.7877	1.25404	0.627021	−	0.779002i	$-0.284274\pi$
$491$	27.7877	1.25404	0.627021	+	0.779002i	$0.284274\pi$
$492$	−5.55388	−0.250388
$493$	29.1546	1.31306
$494$	−22.7341	−1.02286
$495$	−0.679669	−0.0305488
$496$	−46.2554	−2.07693
$497$	−8.86571	−0.397681
$498$	−13.8694	−0.621502
$499$	−23.9852	−1.07373	−0.536863	−	0.843669i	$-0.680391\pi$
$499$	−23.9852	−1.07373	−0.536863	+	0.843669i	$0.680391\pi$
$500$	1.25230	0.0560047
$501$	0.550065	0.0245751
$502$	−3.64243	−0.162569
$503$	14.9662	0.667311	0.333656	−	0.942695i	$-0.391718\pi$
$503$	14.9662	0.667311	0.333656	+	0.942695i	$0.391718\pi$
$504$	3.61025	0.160813
$505$	−14.5673	−0.648238
$506$	2.46048	0.109382
$507$	20.9713	0.931370
$508$	18.0090	0.799022
$509$	−29.2357	−1.29585	−0.647925	−	0.761704i	$-0.724363\pi$
$509$	−29.2357	−1.29585	−0.647925	+	0.761704i	$0.724363\pi$
$510$	7.52497	0.333211
$511$	14.8642	0.657555
$512$	−17.3198	−0.765436
$513$	5.75311	0.254006
$514$	−35.2540	−1.55499
$515$	−0.709708	−0.0312735
$516$	−8.12957	−0.357884
$517$	−0.636167	−0.0279786
$518$	12.1109	0.532121
$519$	1.36702	0.0600053
$520$	−9.52740	−0.417804
$521$	−34.8313	−1.52599	−0.762993	−	0.646407i	$-0.776271\pi$
$521$	−34.8313	−1.52599	−0.762993	+	0.646407i	$0.776271\pi$
$522$	−19.1616	−0.838680
$523$	−7.95100	−0.347673	−0.173836	−	0.984775i	$-0.555616\pi$
$523$	−7.95100	−0.347673	−0.173836	+	0.984775i	$0.555616\pi$
$524$	16.5421	0.722645
$525$	−0.567965	−0.0247880
$526$	9.67528	0.421862
$527$	−68.8406	−2.99874
$528$	−0.711720	−0.0309736
$529$	5.88589	0.255908
$530$	9.95646	0.432481
$531$	17.7207	0.769014
$532$	2.23429	0.0968687
$533$	55.1720	2.38976
$534$	−17.7011	−0.766001
$535$	19.5638	0.845816
$536$	−17.9253	−0.774254
$537$	5.50558	0.237583
$538$	13.8201	0.595826
$539$	0.253853	0.0109342
$540$	−4.03814	−0.173774
$541$	3.48210	0.149707	0.0748536	−	0.997195i	$-0.476151\pi$
$541$	3.48210	0.149707	0.0748536	+	0.997195i	$0.476151\pi$
$542$	−23.0964	−0.992077
$543$	−2.95031	−0.126610
$544$	−45.5891	−1.95462
$545$	8.03820	0.344318
$546$	−7.23720	−0.309723
$547$	−11.2402	−0.480595	−0.240297	−	0.970699i	$-0.577245\pi$
$547$	−11.2402	−0.480595	−0.240297	+	0.970699i	$0.577245\pi$
$548$	13.1265	0.560737
$549$	15.7173	0.670798
$550$	−0.457801	−0.0195207
$551$	7.08027	0.301630
$552$	−4.11610	−0.175193
$553$	1.02292	0.0434990
$554$	−18.8053	−0.798961
$555$	3.81418	0.161903
$556$	−2.73731	−0.116088
$557$	−37.4053	−1.58491	−0.792457	−	0.609928i	$-0.791198\pi$
$557$	−37.4053	−1.58491	−0.792457	+	0.609928i	$0.791198\pi$
$558$	45.2448	1.91536
$559$	80.7587	3.41573
$560$	4.93634	0.208599
$561$	−1.05923	−0.0447208
$562$	11.4246	0.481919
$563$	−29.1825	−1.22990	−0.614948	−	0.788568i	$-0.710823\pi$
$563$	−29.1825	−1.22990	−0.614948	+	0.788568i	$0.710823\pi$
$564$	−1.78246	−0.0750553
$565$	0.658377	0.0276981
$566$	5.68619	0.239008
$567$	−6.20080	−0.260409
$568$	11.9546	0.501604
$569$	−30.9907	−1.29920	−0.649598	−	0.760278i	$-0.725063\pi$
$569$	−30.9907	−1.29920	−0.649598	+	0.760278i	$0.725063\pi$
$570$	1.82746	0.0765438
$571$	−4.33137	−0.181262	−0.0906312	−	0.995885i	$-0.528888\pi$
$571$	−4.33137	−0.181262	−0.0906312	+	0.995885i	$0.528888\pi$
$572$	−2.24618	−0.0939174
$573$	−7.96671	−0.332814
$574$	−14.0819	−0.587767
$575$	−5.37456	−0.224135
$576$	3.52968	0.147070
$577$	31.9870	1.33164	0.665819	−	0.746114i	$-0.268082\pi$
$577$	31.9870	1.33164	0.665819	+	0.746114i	$0.268082\pi$
$578$	−66.6773	−2.77341
$579$	−12.6271	−0.524765
$580$	−4.96969	−0.206355
$581$	−13.5407	−0.561761
$582$	−9.44623	−0.391559
$583$	−1.40149	−0.0580440
$584$	−20.0431	−0.829388
$585$	18.9177	0.782151
$586$	20.1142	0.830909
$587$	27.7099	1.14371	0.571854	−	0.820355i	$-0.306224\pi$
$587$	27.7099	1.14371	0.571854	+	0.820355i	$0.306224\pi$
$588$	0.711264	0.0293321
$589$	−16.7181	−0.688857
$590$	11.9361	0.491400
$591$	−8.75608	−0.360177
$592$	−33.1501	−1.36246
$593$	0.498493	0.0204706	0.0102353	−	0.999948i	$-0.496742\pi$
$593$	0.498493	0.0204706	0.0102353	+	0.999948i	$0.496742\pi$
$594$	1.47622	0.0605699
$595$	7.34662	0.301182
$596$	−15.5852	−0.638396
$597$	4.26498	0.174554
$598$	−68.4844	−2.80053
$599$	34.4666	1.40827	0.704133	−	0.710068i	$-0.251336\pi$
$599$	34.4666	1.40827	0.704133	+	0.710068i	$0.251336\pi$
$600$	0.765849	0.0312657
$601$	6.82090	0.278230	0.139115	−	0.990276i	$-0.455574\pi$
$601$	6.82090	0.278230	0.139115	+	0.990276i	$0.455574\pi$
$602$	−20.6126	−0.840105
$603$	35.5926	1.44944
$604$	13.0062	0.529214
$605$	−10.9356	−0.444594
$606$	14.9210	0.606124
$607$	2.96205	0.120226	0.0601130	−	0.998192i	$-0.480854\pi$
$607$	2.96205	0.120226	0.0601130	+	0.998192i	$0.480854\pi$
$608$	−11.0714	−0.449006
$609$	2.25394	0.0913342
$610$	10.5866	0.428640
$611$	17.7069	0.716345
$612$	24.6327	0.995719
$613$	−36.5458	−1.47607	−0.738035	−	0.674763i	$-0.764246\pi$
$613$	−36.5458	−1.47607	−0.738035	+	0.674763i	$0.764246\pi$
$614$	2.53875	0.102456
$615$	−4.43494	−0.178834
$616$	−0.342297	−0.0137915
$617$	−22.4788	−0.904963	−0.452482	−	0.891774i	$-0.649461\pi$
$617$	−22.4788	−0.904963	−0.452482	+	0.891774i	$0.649461\pi$
$618$	0.726938	0.0292417
$619$	21.9558	0.882476	0.441238	−	0.897390i	$-0.354539\pi$
$619$	21.9558	0.882476	0.441238	+	0.897390i	$0.354539\pi$
$620$	11.7345	0.471271
$621$	17.3307	0.695456
$622$	−42.3056	−1.69630
$623$	−17.2815	−0.692370
$624$	19.8098	0.793027
$625$	1.00000	0.0400000
$626$	−23.8222	−0.952125
$627$	−0.257237	−0.0102731
$628$	0.957988	0.0382279
$629$	−49.3364	−1.96717
$630$	−4.82849	−0.192372
$631$	4.94928	0.197028	0.0985139	−	0.995136i	$-0.468591\pi$
$631$	4.94928	0.197028	0.0985139	+	0.995136i	$0.468591\pi$
$632$	−1.37931	−0.0548662
$633$	−8.55287	−0.339946
$634$	23.2548	0.923568
$635$	14.3807	0.570682
$636$	−3.92682	−0.155708
$637$	−7.06566	−0.279952
$638$	1.81676	0.0719262
$639$	−23.7372	−0.939028
$640$	−10.0334	−0.396606
$641$	−28.4431	−1.12343	−0.561717	−	0.827329i	$-0.689859\pi$
$641$	−28.4431	−1.12343	−0.561717	+	0.827329i	$0.689859\pi$
$642$	−20.0387	−0.790866
$643$	−14.2150	−0.560583	−0.280291	−	0.959915i	$-0.590431\pi$
$643$	−14.2150	−0.560583	−0.280291	+	0.959915i	$0.590431\pi$
$644$	6.73057	0.265222
$645$	−6.49170	−0.255610
$646$	−23.6381	−0.930029
$647$	31.7896	1.24978	0.624889	−	0.780714i	$-0.285144\pi$
$647$	31.7896	1.24978	0.624889	+	0.780714i	$0.285144\pi$
$648$	8.36121	0.328459
$649$	−1.68015	−0.0659516
$650$	12.7423	0.499795
$651$	−5.32205	−0.208588
$652$	0.628258	0.0246045
$653$	−7.21747	−0.282441	−0.141221	−	0.989978i	$-0.545103\pi$
$653$	−7.21747	−0.282441	−0.141221	+	0.989978i	$0.545103\pi$
$654$	−8.23334	−0.321949
$655$	13.2094	0.516132
$656$	38.5453	1.50494
$657$	39.7978	1.55266
$658$	−4.51945	−0.176186
$659$	28.9949	1.12948	0.564740	−	0.825269i	$-0.308977\pi$
$659$	28.9949	1.12948	0.564740	+	0.825269i	$0.308977\pi$
$660$	0.180556	0.00702815
$661$	−2.87854	−0.111962	−0.0559811	−	0.998432i	$-0.517829\pi$
$661$	−2.87854	−0.111962	−0.0559811	+	0.998432i	$0.517829\pi$
$662$	11.8617	0.461019
$663$	29.4824	1.14500
$664$	18.2583	0.708561
$665$	1.78414	0.0691861
$666$	32.4258	1.25647
$667$	21.3286	0.825848
$668$	1.21283	0.0469259
$669$	2.41627	0.0934184
$670$	23.9740	0.926195
$671$	−1.49020	−0.0575285
$672$	−3.52448	−0.135960
$673$	10.0989	0.389285	0.194643	−	0.980874i	$-0.437645\pi$
$673$	10.0989	0.389285	0.194643	+	0.980874i	$0.437645\pi$
$674$	6.09337	0.234708
$675$	−3.22458	−0.124114
$676$	46.2395	1.77844
$677$	8.93629	0.343450	0.171725	−	0.985145i	$-0.445066\pi$
$677$	8.93629	0.343450	0.171725	+	0.985145i	$0.445066\pi$
$678$	−0.674360	−0.0258986
$679$	−9.22234	−0.353921
$680$	−9.90624	−0.379887
$681$	4.40952	0.168973
$682$	−4.28977	−0.164264
$683$	−31.6623	−1.21152	−0.605761	−	0.795646i	$-0.707131\pi$
$683$	−31.6623	−1.21152	−0.605761	+	0.795646i	$0.707131\pi$
$684$	5.98212	0.228732
$685$	10.4819	0.400493
$686$	1.80341	0.0688547
$687$	−0.567965	−0.0216692
$688$	56.4211	2.15104
$689$	39.0088	1.48612
$690$	5.50504	0.209573
$691$	0.532114	0.0202426	0.0101213	−	0.999949i	$-0.496778\pi$
$691$	0.532114	0.0202426	0.0101213	+	0.999949i	$0.496778\pi$
$692$	3.01412	0.114580
$693$	0.679669	0.0258185
$694$	45.9219	1.74317
$695$	−2.18582	−0.0829130
$696$	−3.03923	−0.115202
$697$	57.3658	2.17288
$698$	−2.89195	−0.109462
$699$	−16.0812	−0.608248
$700$	−1.25230	−0.0473326
$701$	46.0221	1.73823	0.869115	−	0.494609i	$-0.164689\pi$
$701$	46.0221	1.73823	0.869115	+	0.494609i	$0.164689\pi$
$702$	−41.0886	−1.55079
$703$	−11.9815	−0.451889
$704$	−0.334658	−0.0126129
$705$	−1.42335	−0.0536064
$706$	62.1370	2.33856
$707$	14.5673	0.547861
$708$	−4.70757	−0.176921
$709$	51.2924	1.92633	0.963163	−	0.268917i	$-0.0866658\pi$
$709$	51.2924	1.92633	0.963163	+	0.268917i	$0.0866658\pi$
$710$	−15.9885	−0.600039
$711$	2.73878	0.102712
$712$	23.3026	0.873301
$713$	−50.3617	−1.88606
$714$	−7.52497	−0.281615
$715$	−1.79364	−0.0670782
$716$	12.1392	0.453664
$717$	3.43292	0.128205
$718$	−2.83203	−0.105691
$719$	−14.5026	−0.540854	−0.270427	−	0.962740i	$-0.587165\pi$
$719$	−14.5026	−0.540854	−0.270427	+	0.962740i	$0.587165\pi$
$720$	13.2166	0.492555
$721$	0.709708	0.0264309
$722$	28.5243	1.06156
$723$	−13.5599	−0.504300
$724$	−6.50512	−0.241761
$725$	−3.96844	−0.147384
$726$	11.2010	0.415710
$727$	−17.9817	−0.666904	−0.333452	−	0.942767i	$-0.608214\pi$
$727$	−17.9817	−0.666904	−0.333452	+	0.942767i	$0.608214\pi$
$728$	9.52740	0.353109
$729$	−11.1078	−0.411399
$730$	26.8064	0.992149
$731$	83.9700	3.10574
$732$	−4.17535	−0.154326
$733$	26.5290	0.979870	0.489935	−	0.871759i	$-0.337021\pi$
$733$	26.5290	0.979870	0.489935	+	0.871759i	$0.337021\pi$
$734$	−45.8453	−1.69218
$735$	0.567965	0.0209497
$736$	−33.3516	−1.22936
$737$	−3.37463	−0.124306
$738$	−37.7031	−1.38787
$739$	21.5364	0.792228	0.396114	−	0.918201i	$-0.370359\pi$
$739$	21.5364	0.792228	0.396114	+	0.918201i	$0.370359\pi$
$740$	8.40986	0.309153
$741$	7.15986	0.263024
$742$	−9.95646	−0.365513
$743$	11.5664	0.424329	0.212164	−	0.977234i	$-0.431949\pi$
$743$	11.5664	0.424329	0.212164	+	0.977234i	$0.431949\pi$
$744$	7.17630	0.263096
$745$	−12.4453	−0.455959
$746$	27.5598	1.00903
$747$	−36.2540	−1.32646
$748$	−2.33549	−0.0853941
$749$	−19.5638	−0.714845
$750$	−1.02428	−0.0374013
$751$	−1.72050	−0.0627818	−0.0313909	−	0.999507i	$-0.509994\pi$
$751$	−1.72050	−0.0627818	−0.0313909	+	0.999507i	$0.509994\pi$
$752$	12.3707	0.451114
$753$	1.14714	0.0418042
$754$	−50.5672	−1.84155
$755$	10.3858	0.377978
$756$	4.03814	0.146866
$757$	6.14904	0.223491	0.111745	−	0.993737i	$-0.464356\pi$
$757$	6.14904	0.223491	0.111745	+	0.993737i	$0.464356\pi$
$758$	42.8115	1.55498
$759$	−0.774901	−0.0281271
$760$	−2.40575	−0.0872659
$761$	13.5171	0.489993	0.244997	−	0.969524i	$-0.421213\pi$
$761$	13.5171	0.489993	0.244997	+	0.969524i	$0.421213\pi$
$762$	−14.7299	−0.533607
$763$	−8.03820	−0.291002
$764$	−17.5657	−0.635506
$765$	19.6699	0.711169
$766$	34.9854	1.26408
$767$	46.7648	1.68858
$768$	11.7745	0.424877
$769$	18.0063	0.649324	0.324662	−	0.945830i	$-0.394750\pi$
$769$	18.0063	0.649324	0.324662	+	0.945830i	$0.394750\pi$
$770$	0.457801	0.0164980
$771$	11.1028	0.399859
$772$	−27.8414	−1.00203
$773$	−37.2986	−1.34154	−0.670769	−	0.741667i	$-0.734036\pi$
$773$	−37.2986	−1.34154	−0.670769	+	0.741667i	$0.734036\pi$
$774$	−55.1884	−1.98371
$775$	9.37038	0.336594
$776$	12.4355	0.446408
$777$	−3.81418	−0.136833
$778$	−26.1578	−0.937804
$779$	13.9314	0.499145
$780$	−5.02556	−0.179944
$781$	2.25058	0.0805322
$782$	−71.2075	−2.54638
$783$	12.7965	0.457311
$784$	−4.93634	−0.176298
$785$	0.764982	0.0273034
$786$	−13.5300	−0.482600
$787$	−20.2453	−0.721669	−0.360834	−	0.932630i	$-0.617508\pi$
$787$	−20.2453	−0.721669	−0.360834	+	0.932630i	$0.617508\pi$
$788$	−19.3062	−0.687756
$789$	−3.04712	−0.108480
$790$	1.84475	0.0656332
$791$	−0.658377	−0.0234092
$792$	−0.916471	−0.0325654
$793$	41.4778	1.47292
$794$	18.6170	0.660694
$795$	−3.13568	−0.111211
$796$	9.40382	0.333310
$797$	−42.2864	−1.49786	−0.748931	−	0.662649i	$-0.769432\pi$
$797$	−42.2864	−1.49786	−0.748931	+	0.662649i	$0.769432\pi$
$798$	−1.82746	−0.0646913
$799$	18.4110	0.651334
$800$	6.20545	0.219396
$801$	−46.2699	−1.63487
$802$	22.9631	0.810856
$803$	−3.77333	−0.133158
$804$	−9.45530	−0.333463
$805$	5.37456	0.189428
$806$	119.400	4.20570
$807$	−4.35248	−0.153215
$808$	−19.6427	−0.691028
$809$	−26.9719	−0.948280	−0.474140	−	0.880449i	$-0.657241\pi$
$809$	−26.9719	−0.948280	−0.474140	+	0.880449i	$0.657241\pi$
$810$	−11.1826	−0.392917
$811$	9.46852	0.332485	0.166242	−	0.986085i	$-0.446837\pi$
$811$	9.46852	0.332485	0.166242	+	0.986085i	$0.446837\pi$
$812$	4.96969	0.174402
$813$	7.27397	0.255109
$814$	−3.07437	−0.107757
$815$	0.501682	0.0175732
$816$	20.5975	0.721057
$817$	20.3923	0.713436
$818$	−18.5270	−0.647782
$819$	−18.9177	−0.661039
$820$	−9.77856	−0.341482
$821$	24.3240	0.848912	0.424456	−	0.905449i	$-0.360465\pi$
$821$	24.3240	0.848912	0.424456	+	0.905449i	$0.360465\pi$
$822$	−10.7364	−0.374474
$823$	36.7690	1.28169	0.640843	−	0.767672i	$-0.278585\pi$
$823$	36.7690	1.28169	0.640843	+	0.767672i	$0.278585\pi$
$824$	−0.956977	−0.0333379
$825$	0.144180	0.00501969
$826$	−11.9361	−0.415309
$827$	−26.5299	−0.922534	−0.461267	−	0.887261i	$-0.652605\pi$
$827$	−26.5299	−0.922534	−0.461267	+	0.887261i	$0.652605\pi$
$828$	18.0205	0.626257
$829$	−35.6867	−1.23945	−0.619725	−	0.784819i	$-0.712756\pi$
$829$	−35.6867	−1.23945	−0.619725	+	0.784819i	$0.712756\pi$
$830$	−24.4194	−0.847610
$831$	5.92253	0.205450
$832$	9.31479	0.322932
$833$	−7.34662	−0.254545
$834$	2.23889	0.0775264
$835$	0.968483	0.0335157
$836$	−0.567180	−0.0196163
$837$	−30.2155	−1.04440
$838$	−16.0466	−0.554319
$839$	−14.6638	−0.506250	−0.253125	−	0.967434i	$-0.581458\pi$
$839$	−14.6638	−0.506250	−0.253125	+	0.967434i	$0.581458\pi$
$840$	−0.765849	−0.0264243
$841$	−13.2515	−0.456947
$842$	53.4329	1.84142
$843$	−3.59806	−0.123924
$844$	−18.8581	−0.649124
$845$	36.9236	1.27021
$846$	−12.1004	−0.416021
$847$	10.9356	0.375750
$848$	27.2530	0.935873
$849$	−1.79080	−0.0614602
$850$	13.2490	0.454437
$851$	−36.0930	−1.23725
$852$	6.30586	0.216035
$853$	−18.5911	−0.636547	−0.318274	−	0.947999i	$-0.603103\pi$
$853$	−18.5911	−0.636547	−0.318274	+	0.947999i	$0.603103\pi$
$854$	−10.5866	−0.362267
$855$	4.77689	0.163366
$856$	26.3800	0.901649
$857$	−49.1250	−1.67808	−0.839039	−	0.544072i	$-0.816882\pi$
$857$	−49.1250	−1.67808	−0.839039	+	0.544072i	$0.816882\pi$
$858$	1.83718	0.0627203
$859$	−12.5111	−0.426875	−0.213437	−	0.976957i	$-0.568466\pi$
$859$	−12.5111	−0.426875	−0.213437	+	0.976957i	$0.568466\pi$
$860$	−14.3135	−0.488086
$861$	4.43494	0.151142
$862$	32.3868	1.10310
$863$	−50.0062	−1.70223	−0.851115	−	0.524979i	$-0.824073\pi$
$863$	−50.0062	−1.70223	−0.851115	+	0.524979i	$0.824073\pi$
$864$	−20.0100	−0.680753
$865$	2.40686	0.0818358
$866$	−67.5584	−2.29573
$867$	20.9993	0.713173
$868$	−11.7345	−0.398297
$869$	−0.259671	−0.00880874
$870$	4.06478	0.137809
$871$	93.9285	3.18264
$872$	10.8388	0.367047
$873$	−24.6920	−0.835699
$874$	−17.2929	−0.584942
$875$	−1.00000	−0.0338062
$876$	−10.5724	−0.357209
$877$	43.4813	1.46826	0.734130	−	0.679009i	$-0.237590\pi$
$877$	43.4813	1.46826	0.734130	+	0.679009i	$0.237590\pi$
$878$	−1.63131	−0.0550542
$879$	−6.33474	−0.213665
$880$	−1.25310	−0.0422421
$881$	39.2763	1.32325	0.661627	−	0.749833i	$-0.269866\pi$
$881$	39.2763	1.32325	0.661627	+	0.749833i	$0.269866\pi$
$882$	4.82849	0.162584
$883$	10.2116	0.343649	0.171825	−	0.985128i	$-0.445034\pi$
$883$	10.2116	0.343649	0.171825	+	0.985128i	$0.445034\pi$
$884$	65.0054	2.18637
$885$	−3.75913	−0.126362
$886$	62.4290	2.09734
$887$	−39.8900	−1.33938	−0.669688	−	0.742642i	$-0.733572\pi$
$887$	−39.8900	−1.33938	−0.669688	+	0.742642i	$0.733572\pi$
$888$	5.14308	0.172590
$889$	−14.3807	−0.482315
$890$	−31.1658	−1.04468
$891$	1.57409	0.0527340
$892$	5.32762	0.178382
$893$	4.47115	0.149621
$894$	12.7474	0.426336
$895$	9.69352	0.324019
$896$	10.0334	0.335194
$897$	21.5684	0.720148
$898$	−36.7855	−1.22755
$899$	−37.1858	−1.24022
$900$	−3.35293	−0.111764
$901$	40.5599	1.35125
$902$	3.57473	0.119025
$903$	6.49170	0.216030
$904$	0.887761	0.0295265
$905$	−5.19453	−0.172672
$906$	−10.6379	−0.353422
$907$	−40.7663	−1.35362	−0.676811	−	0.736157i	$-0.736638\pi$
$907$	−40.7663	−1.35362	−0.676811	+	0.736157i	$0.736638\pi$
$908$	9.72251	0.322653
$909$	39.0028	1.29364
$910$	−12.7423	−0.422404
$911$	29.5700	0.979696	0.489848	−	0.871808i	$-0.337052\pi$
$911$	29.5700	0.979696	0.489848	+	0.871808i	$0.337052\pi$
$912$	5.00215	0.165638
$913$	3.43733	0.113759
$914$	−36.8021	−1.21731
$915$	−3.33414	−0.110223
$916$	−1.25230	−0.0413772
$917$	−13.2094	−0.436211
$918$	−42.7224	−1.41005
$919$	22.1477	0.730585	0.365292	−	0.930893i	$-0.380969\pi$
$919$	22.1477	0.730585	0.365292	+	0.930893i	$0.380969\pi$
$920$	−7.24710	−0.238930
$921$	−0.799552	−0.0263461
$922$	−21.6193	−0.711994
$923$	−62.6421	−2.06189
$924$	−0.180556	−0.00593987
$925$	6.71552	0.220805
$926$	−71.7175	−2.35678
$927$	1.90018	0.0624102
$928$	−24.6260	−0.808388
$929$	−56.8486	−1.86514	−0.932572	−	0.360985i	$-0.882441\pi$
$929$	−56.8486	−1.86514	−0.932572	+	0.360985i	$0.882441\pi$
$930$	−9.59786	−0.314726
$931$	−1.78414	−0.0584730
$932$	−35.4574	−1.16144
$933$	13.3237	0.436198
$934$	57.8994	1.89453
$935$	−1.86496	−0.0609907
$936$	25.5088	0.833781
$937$	34.7682	1.13583	0.567913	−	0.823088i	$-0.307751\pi$
$937$	34.7682	1.13583	0.567913	+	0.823088i	$0.307751\pi$
$938$	−23.9740	−0.782777
$939$	7.50253	0.244836
$940$	−3.13833	−0.102361
$941$	−12.3319	−0.402008	−0.201004	−	0.979590i	$-0.564420\pi$
$941$	−12.3319	−0.402008	−0.201004	+	0.979590i	$0.564420\pi$
$942$	−0.783553	−0.0255295
$943$	41.9670	1.36664
$944$	32.6717	1.06337
$945$	3.22458	0.104895
$946$	5.23255	0.170125
$947$	43.5774	1.41608	0.708038	−	0.706174i	$-0.249580\pi$
$947$	43.5774	1.41608	0.708038	+	0.706174i	$0.249580\pi$
$948$	−0.727567	−0.0236303
$949$	105.026	3.40928
$950$	3.21755	0.104391
$951$	−7.32385	−0.237492
$952$	9.90624	0.321063
$953$	32.5041	1.05291	0.526456	−	0.850203i	$-0.323521\pi$
$953$	32.5041	1.05291	0.526456	+	0.850203i	$0.323521\pi$
$954$	−26.6576	−0.863071
$955$	−14.0267	−0.453895
$956$	7.56921	0.244806
$957$	−0.572168	−0.0184956
$958$	−64.9765	−2.09930
$959$	−10.4819	−0.338478
$960$	−0.748759	−0.0241661
$961$	56.8040	1.83239
$962$	85.5713	2.75893
$963$	−52.3804	−1.68793
$964$	−29.8982	−0.962957
$965$	−22.2322	−0.715679
$966$	−5.50504	−0.177122
$967$	0.189957	0.00610860	0.00305430	−	0.999995i	$-0.499028\pi$
$967$	0.189957	0.00610860	0.00305430	+	0.999995i	$0.499028\pi$
$968$	−14.7456	−0.473941
$969$	7.44456	0.239154
$970$	−16.6317	−0.534012
$971$	42.7552	1.37208	0.686040	−	0.727564i	$-0.259348\pi$
$971$	42.7552	1.37208	0.686040	+	0.727564i	$0.259348\pi$
$972$	16.5248	0.530034
$973$	2.18582	0.0700743
$974$	−30.6162	−0.981005
$975$	−4.01305	−0.128521
$976$	28.9779	0.927562
$977$	−42.0326	−1.34474	−0.672371	−	0.740214i	$-0.734724\pi$
$977$	−42.0326	−1.34474	−0.672371	+	0.740214i	$0.734724\pi$
$978$	−0.513861	−0.0164315
$979$	4.38697	0.140208
$980$	1.25230	0.0400033
$981$	−21.5216	−0.687131
$982$	−50.1128	−1.59916
$983$	−15.5152	−0.494856	−0.247428	−	0.968906i	$-0.579585\pi$
$983$	−15.5152	−0.494856	−0.247428	+	0.968906i	$0.579585\pi$
$984$	−5.98011	−0.190639
$985$	−15.4166	−0.491213
$986$	−52.5779	−1.67442
$987$	1.42335	0.0453057
$988$	15.7867	0.502243
$989$	61.4298	1.95335
$990$	1.22572	0.0389561
$991$	16.3529	0.519468	0.259734	−	0.965680i	$-0.416365\pi$
$991$	16.3529	0.519468	0.259734	+	0.965680i	$0.416365\pi$
$992$	58.1475	1.84618
$993$	−3.73572	−0.118549
$994$	15.9885	0.507126
$995$	7.50923	0.238058
$996$	9.63099	0.305170
$997$	11.1561	0.353318	0.176659	−	0.984272i	$-0.443471\pi$
$997$	11.1561	0.353318	0.176659	+	0.984272i	$0.443471\pi$
$998$	43.2553	1.36922
$999$	−21.6547	−0.685124

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.m.1.15	✓	67

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.m.1.15	✓	67	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)

\(f(q)\)	\(=\)	\(q-1.80341 q^{2} +0.567965 q^{3} +1.25230 q^{4} +1.00000 q^{5} -1.02428 q^{6} -1.00000 q^{7} +1.34841 q^{8} -2.67742 q^{9} +O(q^{10})\)	\(q-1.80341 q^{2} +0.567965 q^{3} +1.25230 q^{4} +1.00000 q^{5} -1.02428 q^{6} -1.00000 q^{7} +1.34841 q^{8} -2.67742 q^{9} -1.80341 q^{10} +0.253853 q^{11} +0.711264 q^{12} -7.06566 q^{13} +1.80341 q^{14} +0.567965 q^{15} -4.93634 q^{16} -7.34662 q^{17} +4.82849 q^{18} -1.78414 q^{19} +1.25230 q^{20} -0.567965 q^{21} -0.457801 q^{22} -5.37456 q^{23} +0.765849 q^{24} +1.00000 q^{25} +12.7423 q^{26} -3.22458 q^{27} -1.25230 q^{28} -3.96844 q^{29} -1.02428 q^{30} +9.37038 q^{31} +6.20545 q^{32} +0.144180 q^{33} +13.2490 q^{34} -1.00000 q^{35} -3.35293 q^{36} +6.71552 q^{37} +3.21755 q^{38} -4.01305 q^{39} +1.34841 q^{40} -7.80846 q^{41} +1.02428 q^{42} -11.4297 q^{43} +0.317900 q^{44} -2.67742 q^{45} +9.69256 q^{46} -2.50605 q^{47} -2.80367 q^{48} +1.00000 q^{49} -1.80341 q^{50} -4.17263 q^{51} -8.84835 q^{52} -5.52090 q^{53} +5.81524 q^{54} +0.253853 q^{55} -1.34841 q^{56} -1.01333 q^{57} +7.15675 q^{58} -6.61859 q^{59} +0.711264 q^{60} -5.87033 q^{61} -16.8987 q^{62} +2.67742 q^{63} -1.31832 q^{64} -7.06566 q^{65} -0.260015 q^{66} -13.2937 q^{67} -9.20019 q^{68} -3.05256 q^{69} +1.80341 q^{70} +8.86571 q^{71} -3.61025 q^{72} -14.8642 q^{73} -12.1109 q^{74} +0.567965 q^{75} -2.23429 q^{76} -0.253853 q^{77} +7.23720 q^{78} -1.02292 q^{79} -4.93634 q^{80} +6.20080 q^{81} +14.0819 q^{82} +13.5407 q^{83} -0.711264 q^{84} -7.34662 q^{85} +20.6126 q^{86} -2.25394 q^{87} +0.342297 q^{88} +17.2815 q^{89} +4.82849 q^{90} +7.06566 q^{91} -6.73057 q^{92} +5.32205 q^{93} +4.51945 q^{94} -1.78414 q^{95} +3.52448 q^{96} +9.22234 q^{97} -1.80341 q^{98} -0.679669 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9}+O(q^{10}) \) 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9	\( 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9} + 3 q^{10} + 11 q^{11} + 9 q^{12} + 19 q^{13} - 3 q^{14} + 93 q^{16} + 7 q^{17} + 9 q^{18} + 36 q^{19} + 73 q^{20} - 8 q^{22} - 2 q^{23} + 37 q^{24} + 67 q^{25} + 39 q^{26} + 6 q^{27} - 73 q^{28} + 56 q^{29} + 17 q^{30} + 63 q^{31} + 27 q^{32} + 51 q^{33} + 55 q^{34} - 67 q^{35} + 148 q^{36} + 28 q^{37} + 10 q^{38} + 7 q^{39} + 12 q^{40} + 84 q^{41} - 17 q^{42} - 11 q^{43} + 41 q^{44} + 97 q^{45} + 17 q^{46} - 10 q^{47} + 10 q^{48} + 67 q^{49} + 3 q^{50} - q^{51} + 49 q^{52} + 3 q^{53} + 20 q^{54} + 11 q^{55} - 12 q^{56} + 45 q^{57} + 22 q^{58} + 80 q^{59} + 9 q^{60} + 64 q^{61} - 37 q^{62} - 97 q^{63} + 110 q^{64} + 19 q^{65} + 75 q^{66} + 22 q^{67} + 7 q^{68} + 107 q^{69} - 3 q^{70} + 24 q^{71} + 72 q^{72} + 83 q^{73} + 52 q^{74} + 115 q^{76} - 11 q^{77} - 70 q^{78} - 32 q^{79} + 93 q^{80} + 183 q^{81} + 56 q^{82} - 58 q^{83} - 9 q^{84} + 7 q^{85} + 51 q^{86} + 20 q^{87} - 5 q^{88} + 129 q^{89} + 9 q^{90} - 19 q^{91} - 37 q^{92} + 33 q^{93} + 89 q^{94} + 36 q^{95} + 129 q^{96} + 126 q^{97} + 3 q^{98} - 27 q^{99}+O(q^{100}) \) 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9 + 3 * q^10 + 11 * q^11 + 9 * q^12 + 19 * q^13 - 3 * q^14 + 93 * q^16 + 7 * q^17 + 9 * q^18 + 36 * q^19 + 73 * q^20 - 8 * q^22 - 2 * q^23 + 37 * q^24 + 67 * q^25 + 39 * q^26 + 6 * q^27 - 73 * q^28 + 56 * q^29 + 17 * q^30 + 63 * q^31 + 27 * q^32 + 51 * q^33 + 55 * q^34 - 67 * q^35 + 148 * q^36 + 28 * q^37 + 10 * q^38 + 7 * q^39 + 12 * q^40 + 84 * q^41 - 17 * q^42 - 11 * q^43 + 41 * q^44 + 97 * q^45 + 17 * q^46 - 10 * q^47 + 10 * q^48 + 67 * q^49 + 3 * q^50 - q^51 + 49 * q^52 + 3 * q^53 + 20 * q^54 + 11 * q^55 - 12 * q^56 + 45 * q^57 + 22 * q^58 + 80 * q^59 + 9 * q^60 + 64 * q^61 - 37 * q^62 - 97 * q^63 + 110 * q^64 + 19 * q^65 + 75 * q^66 + 22 * q^67 + 7 * q^68 + 107 * q^69 - 3 * q^70 + 24 * q^71 + 72 * q^72 + 83 * q^73 + 52 * q^74 + 115 * q^76 - 11 * q^77 - 70 * q^78 - 32 * q^79 + 93 * q^80 + 183 * q^81 + 56 * q^82 - 58 * q^83 - 9 * q^84 + 7 * q^85 + 51 * q^86 + 20 * q^87 - 5 * q^88 + 129 * q^89 + 9 * q^90 - 19 * q^91 - 37 * q^92 + 33 * q^93 + 89 * q^94 + 36 * q^95 + 129 * q^96 + 126 * q^97 + 3 * q^98 - 27 * q^99

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