LMFDB - Embedded newform 8015.2.a.o.1.18

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:	$73$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
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)

$f(q)$	$=$	$q-1.53607 q^{2} -1.95086 q^{3} +0.359523 q^{4} +1.00000 q^{5} +2.99667 q^{6} +1.00000 q^{7} +2.51989 q^{8} +0.805862 q^{9} +O(q^{10})$	\(q-1.53607 q^{2} -1.95086 q^{3} +0.359523 q^{4} +1.00000 q^{5} +2.99667 q^{6} +1.00000 q^{7} +2.51989 q^{8} +0.805862 q^{9} -1.53607 q^{10} -5.97648 q^{11} -0.701380 q^{12} +3.87926 q^{13} -1.53607 q^{14} -1.95086 q^{15} -4.58979 q^{16} +3.91503 q^{17} -1.23786 q^{18} +8.22848 q^{19} +0.359523 q^{20} -1.95086 q^{21} +9.18031 q^{22} +7.00330 q^{23} -4.91597 q^{24} +1.00000 q^{25} -5.95884 q^{26} +4.28046 q^{27} +0.359523 q^{28} +8.04465 q^{29} +2.99667 q^{30} -6.18132 q^{31} +2.01047 q^{32} +11.6593 q^{33} -6.01377 q^{34} +1.00000 q^{35} +0.289726 q^{36} +10.7596 q^{37} -12.6396 q^{38} -7.56791 q^{39} +2.51989 q^{40} +2.87438 q^{41} +2.99667 q^{42} -0.964070 q^{43} -2.14868 q^{44} +0.805862 q^{45} -10.7576 q^{46} +6.91503 q^{47} +8.95404 q^{48} +1.00000 q^{49} -1.53607 q^{50} -7.63767 q^{51} +1.39468 q^{52} -3.53218 q^{53} -6.57510 q^{54} -5.97648 q^{55} +2.51989 q^{56} -16.0526 q^{57} -12.3572 q^{58} +10.8686 q^{59} -0.701380 q^{60} +0.921656 q^{61} +9.49497 q^{62} +0.805862 q^{63} +6.09135 q^{64} +3.87926 q^{65} -17.9095 q^{66} -10.6268 q^{67} +1.40754 q^{68} -13.6625 q^{69} -1.53607 q^{70} -6.66462 q^{71} +2.03069 q^{72} +8.63409 q^{73} -16.5275 q^{74} -1.95086 q^{75} +2.95833 q^{76} -5.97648 q^{77} +11.6249 q^{78} +7.66741 q^{79} -4.58979 q^{80} -10.7682 q^{81} -4.41527 q^{82} +16.2498 q^{83} -0.701380 q^{84} +3.91503 q^{85} +1.48088 q^{86} -15.6940 q^{87} -15.0601 q^{88} -4.24267 q^{89} -1.23786 q^{90} +3.87926 q^{91} +2.51785 q^{92} +12.0589 q^{93} -10.6220 q^{94} +8.22848 q^{95} -3.92214 q^{96} +11.5264 q^{97} -1.53607 q^{98} -4.81622 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9}+O(q^{10}) $ 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9	\( 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9} + 7 q^{10} + 27 q^{11} + 21 q^{12} + 21 q^{13} + 7 q^{14} + 14 q^{15} + 135 q^{16} + 23 q^{17} + 41 q^{18} + 26 q^{19} + 95 q^{20} + 14 q^{21} + 48 q^{22} + 16 q^{23} - q^{24} + 73 q^{25} + 7 q^{26} + 44 q^{27} + 95 q^{28} + 66 q^{29} - q^{30} + 23 q^{31} + 3 q^{32} + 77 q^{33} + 29 q^{34} + 73 q^{35} + 142 q^{36} + 66 q^{37} - 12 q^{38} + 53 q^{39} + 18 q^{40} + 50 q^{41} - q^{42} + 43 q^{43} + 37 q^{44} + 111 q^{45} + 65 q^{46} + 28 q^{47} - 20 q^{48} + 73 q^{49} + 7 q^{50} + 71 q^{51} + 29 q^{52} - 7 q^{53} - 16 q^{54} + 27 q^{55} + 18 q^{56} + 33 q^{57} + 48 q^{58} + 16 q^{59} + 21 q^{60} + 42 q^{61} - 3 q^{62} + 111 q^{63} + 216 q^{64} + 21 q^{65} - 53 q^{66} + 48 q^{67} + 13 q^{68} + 73 q^{69} + 7 q^{70} + 68 q^{71} + 18 q^{72} + 65 q^{73} + 4 q^{74} + 14 q^{75} + 37 q^{76} + 27 q^{77} + 60 q^{78} + 116 q^{79} + 135 q^{80} + 177 q^{81} + 20 q^{82} + 40 q^{83} + 21 q^{84} + 23 q^{85} + 35 q^{86} - 14 q^{87} + 47 q^{88} + 59 q^{89} + 41 q^{90} + 21 q^{91} + 3 q^{92} + 37 q^{93} - 11 q^{94} + 26 q^{95} - 23 q^{96} + 70 q^{97} + 7 q^{98} + 49 q^{99}+O(q^{100}) \) 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9 + 7 * q^10 + 27 * q^11 + 21 * q^12 + 21 * q^13 + 7 * q^14 + 14 * q^15 + 135 * q^16 + 23 * q^17 + 41 * q^18 + 26 * q^19 + 95 * q^20 + 14 * q^21 + 48 * q^22 + 16 * q^23 - q^24 + 73 * q^25 + 7 * q^26 + 44 * q^27 + 95 * q^28 + 66 * q^29 - q^30 + 23 * q^31 + 3 * q^32 + 77 * q^33 + 29 * q^34 + 73 * q^35 + 142 * q^36 + 66 * q^37 - 12 * q^38 + 53 * q^39 + 18 * q^40 + 50 * q^41 - q^42 + 43 * q^43 + 37 * q^44 + 111 * q^45 + 65 * q^46 + 28 * q^47 - 20 * q^48 + 73 * q^49 + 7 * q^50 + 71 * q^51 + 29 * q^52 - 7 * q^53 - 16 * q^54 + 27 * q^55 + 18 * q^56 + 33 * q^57 + 48 * q^58 + 16 * q^59 + 21 * q^60 + 42 * q^61 - 3 * q^62 + 111 * q^63 + 216 * q^64 + 21 * q^65 - 53 * q^66 + 48 * q^67 + 13 * q^68 + 73 * q^69 + 7 * q^70 + 68 * q^71 + 18 * q^72 + 65 * q^73 + 4 * q^74 + 14 * q^75 + 37 * q^76 + 27 * q^77 + 60 * q^78 + 116 * q^79 + 135 * q^80 + 177 * q^81 + 20 * q^82 + 40 * q^83 + 21 * q^84 + 23 * q^85 + 35 * q^86 - 14 * q^87 + 47 * q^88 + 59 * q^89 + 41 * q^90 + 21 * q^91 + 3 * q^92 + 37 * q^93 - 11 * q^94 + 26 * q^95 - 23 * q^96 + 70 * q^97 + 7 * q^98 + 49 * 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 $

$2$	−1.53607	−1.08617	−0.543084	−	0.839678i	$-0.682744\pi$
$2$	−1.53607	−1.08617	−0.543084	+	0.839678i	$0.682744\pi$
$3$	−1.95086	−1.12633	−0.563165	−	0.826344i	$-0.690417\pi$
$3$	−1.95086	−1.12633	−0.563165	+	0.826344i	$0.690417\pi$
$4$	0.359523	0.179761
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.99667	1.22338
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	2.51989	0.890917
$9$	0.805862	0.268621
$10$	−1.53607	−0.485749
$11$	−5.97648	−1.80198	−0.900988	−	0.433845i	$-0.857157\pi$
$11$	−5.97648	−1.80198	−0.900988	+	0.433845i	$0.857157\pi$
$12$	−0.701380	−0.202471
$13$	3.87926	1.07591	0.537957	−	0.842972i	$-0.319196\pi$
$13$	3.87926	1.07591	0.537957	+	0.842972i	$0.319196\pi$
$14$	−1.53607	−0.410533
$15$	−1.95086	−0.503710
$16$	−4.58979	−1.14745
$17$	3.91503	0.949533	0.474767	−	0.880112i	$-0.342533\pi$
$17$	3.91503	0.949533	0.474767	+	0.880112i	$0.342533\pi$
$18$	−1.23786	−0.291767
$19$	8.22848	1.88774	0.943871	−	0.330314i	$-0.107155\pi$
$19$	8.22848	1.88774	0.943871	+	0.330314i	$0.107155\pi$
$20$	0.359523	0.0803918
$21$	−1.95086	−0.425713
$22$	9.18031	1.95725
$23$	7.00330	1.46029	0.730144	−	0.683293i	$-0.239453\pi$
$23$	7.00330	1.46029	0.730144	+	0.683293i	$0.239453\pi$
$24$	−4.91597	−1.00347
$25$	1.00000	0.200000
$26$	−5.95884	−1.16862
$27$	4.28046	0.823775
$28$	0.359523	0.0679435
$29$	8.04465	1.49385	0.746927	−	0.664906i	$-0.231528\pi$
$29$	8.04465	1.49385	0.746927	+	0.664906i	$0.231528\pi$
$30$	2.99667	0.547114
$31$	−6.18132	−1.11020	−0.555099	−	0.831784i	$-0.687320\pi$
$31$	−6.18132	−1.11020	−0.555099	+	0.831784i	$0.687320\pi$
$32$	2.01047	0.355404
$33$	11.6593	2.02962
$34$	−6.01377	−1.03135
$35$	1.00000	0.169031
$36$	0.289726	0.0482877
$37$	10.7596	1.76886	0.884432	−	0.466670i	$-0.154546\pi$
$37$	10.7596	1.76886	0.884432	+	0.466670i	$0.154546\pi$
$38$	−12.6396	−2.05041
$39$	−7.56791	−1.21184
$40$	2.51989	0.398430
$41$	2.87438	0.448903	0.224452	−	0.974485i	$-0.427941\pi$
$41$	2.87438	0.448903	0.224452	+	0.974485i	$0.427941\pi$
$42$	2.99667	0.462396
$43$	−0.964070	−0.147019	−0.0735096	−	0.997295i	$-0.523420\pi$
$43$	−0.964070	−0.147019	−0.0735096	+	0.997295i	$0.523420\pi$
$44$	−2.14868	−0.323926
$45$	0.805862	0.120131
$46$	−10.7576	−1.58612
$47$	6.91503	1.00866	0.504330	−	0.863511i	$-0.331739\pi$
$47$	6.91503	1.00866	0.504330	+	0.863511i	$0.331739\pi$
$48$	8.95404	1.29241
$49$	1.00000	0.142857
$50$	−1.53607	−0.217234
$51$	−7.63767	−1.06949
$52$	1.39468	0.193408
$53$	−3.53218	−0.485183	−0.242591	−	0.970129i	$-0.577997\pi$
$53$	−3.53218	−0.485183	−0.242591	+	0.970129i	$0.577997\pi$
$54$	−6.57510	−0.894758
$55$	−5.97648	−0.805868
$56$	2.51989	0.336735
$57$	−16.0526	−2.12622
$58$	−12.3572	−1.62258
$59$	10.8686	1.41498	0.707488	−	0.706725i	$-0.249828\pi$
$59$	10.8686	1.41498	0.707488	+	0.706725i	$0.249828\pi$
$60$	−0.701380	−0.0905477
$61$	0.921656	0.118006	0.0590030	−	0.998258i	$-0.481208\pi$
$61$	0.921656	0.118006	0.0590030	+	0.998258i	$0.481208\pi$
$62$	9.49497	1.20586
$63$	0.805862	0.101529
$64$	6.09135	0.761419
$65$	3.87926	0.481163
$66$	−17.9095	−2.20451
$67$	−10.6268	−1.29827	−0.649133	−	0.760675i	$-0.724868\pi$
$67$	−10.6268	−1.29827	−0.649133	+	0.760675i	$0.724868\pi$
$68$	1.40754	0.170689
$69$	−13.6625	−1.64477
$70$	−1.53607	−0.183596
$71$	−6.66462	−0.790944	−0.395472	−	0.918478i	$-0.629419\pi$
$71$	−6.66462	−0.790944	−0.395472	+	0.918478i	$0.629419\pi$
$72$	2.03069	0.239319
$73$	8.63409	1.01054	0.505272	−	0.862960i	$-0.331392\pi$
$73$	8.63409	1.01054	0.505272	+	0.862960i	$0.331392\pi$
$74$	−16.5275	−1.92128
$75$	−1.95086	−0.225266
$76$	2.95833	0.339343
$77$	−5.97648	−0.681083
$78$	11.6249	1.31626
$79$	7.66741	0.862651	0.431326	−	0.902196i	$-0.358046\pi$
$79$	7.66741	0.862651	0.431326	+	0.902196i	$0.358046\pi$
$80$	−4.58979	−0.513154
$81$	−10.7682	−1.19646
$82$	−4.41527	−0.487584
$83$	16.2498	1.78364	0.891822	−	0.452386i	$-0.149427\pi$
$83$	16.2498	1.78364	0.891822	+	0.452386i	$0.149427\pi$
$84$	−0.701380	−0.0765268
$85$	3.91503	0.424644
$86$	1.48088	0.159688
$87$	−15.6940	−1.68257
$88$	−15.0601	−1.60541
$89$	−4.24267	−0.449723	−0.224861	−	0.974391i	$-0.572193\pi$
$89$	−4.24267	−0.449723	−0.224861	+	0.974391i	$0.572193\pi$
$90$	−1.23786	−0.130482
$91$	3.87926	0.406657
$92$	2.51785	0.262504
$93$	12.0589	1.25045
$94$	−10.6220	−1.09558
$95$	8.22848	0.844224
$96$	−3.92214	−0.400302
$97$	11.5264	1.17033	0.585163	−	0.810916i	$-0.301031\pi$
$97$	11.5264	1.17033	0.585163	+	0.810916i	$0.301031\pi$
$98$	−1.53607	−0.155167
$99$	−4.81622	−0.484048
$100$	0.359523	0.0359523
$101$	17.4091	1.73227	0.866133	−	0.499814i	$-0.166598\pi$
$101$	17.4091	1.73227	0.866133	+	0.499814i	$0.166598\pi$
$102$	11.7320	1.16164
$103$	16.9764	1.67273	0.836365	−	0.548173i	$-0.184677\pi$
$103$	16.9764	1.67273	0.836365	+	0.548173i	$0.184677\pi$
$104$	9.77533	0.958550
$105$	−1.95086	−0.190385
$106$	5.42570	0.526990
$107$	−10.6726	−1.03176	−0.515881	−	0.856660i	$-0.672535\pi$
$107$	−10.6726	−1.03176	−0.515881	+	0.856660i	$0.672535\pi$
$108$	1.53892	0.148083
$109$	2.76910	0.265232	0.132616	−	0.991168i	$-0.457662\pi$
$109$	2.76910	0.265232	0.132616	+	0.991168i	$0.457662\pi$
$110$	9.18031	0.875308
$111$	−20.9904	−1.99232
$112$	−4.58979	−0.433694
$113$	−12.3535	−1.16212	−0.581060	−	0.813860i	$-0.697362\pi$
$113$	−12.3535	−1.16212	−0.581060	+	0.813860i	$0.697362\pi$
$114$	24.6580	2.30944
$115$	7.00330	0.653061
$116$	2.89224	0.268538
$117$	3.12615	0.289013
$118$	−16.6950	−1.53690
$119$	3.91503	0.358890
$120$	−4.91597	−0.448764
$121$	24.7183	2.24711
$122$	−1.41573	−0.128174
$123$	−5.60753	−0.505614
$124$	−2.22233	−0.199571
$125$	1.00000	0.0894427
$126$	−1.23786	−0.110278
$127$	4.79813	0.425765	0.212883	−	0.977078i	$-0.431715\pi$
$127$	4.79813	0.425765	0.212883	+	0.977078i	$0.431715\pi$
$128$	−13.3777	−1.18243
$129$	1.88077	0.165592
$130$	−5.95884	−0.522624
$131$	−19.0112	−1.66101	−0.830507	−	0.557008i	$-0.811949\pi$
$131$	−19.0112	−1.66101	−0.830507	+	0.557008i	$0.811949\pi$
$132$	4.19178	0.364847
$133$	8.22848	0.713500
$134$	16.3235	1.41013
$135$	4.28046	0.368403
$136$	9.86545	0.845955
$137$	6.31057	0.539149	0.269574	−	0.962980i	$-0.413117\pi$
$137$	6.31057	0.539149	0.269574	+	0.962980i	$0.413117\pi$
$138$	20.9866	1.78649
$139$	−7.03166	−0.596417	−0.298209	−	0.954501i	$-0.596389\pi$
$139$	−7.03166	−0.596417	−0.298209	+	0.954501i	$0.596389\pi$
$140$	0.359523	0.0303852
$141$	−13.4903	−1.13609
$142$	10.2373	0.859099
$143$	−23.1843	−1.93877
$144$	−3.69874	−0.308228
$145$	8.04465	0.668072
$146$	−13.2626	−1.09762
$147$	−1.95086	−0.160904
$148$	3.86831	0.317973
$149$	7.60719	0.623205	0.311602	−	0.950213i	$-0.399134\pi$
$149$	7.60719	0.623205	0.311602	+	0.950213i	$0.399134\pi$
$150$	2.99667	0.244677
$151$	−13.0858	−1.06490	−0.532452	−	0.846460i	$-0.678729\pi$
$151$	−13.0858	−1.06490	−0.532452	+	0.846460i	$0.678729\pi$
$152$	20.7349	1.68182
$153$	3.15497	0.255064
$154$	9.18031	0.739770
$155$	−6.18132	−0.496496
$156$	−2.72084	−0.217841
$157$	−6.94851	−0.554551	−0.277276	−	0.960790i	$-0.589432\pi$
$157$	−6.94851	−0.554551	−0.277276	+	0.960790i	$0.589432\pi$
$158$	−11.7777	−0.936984
$159$	6.89080	0.546476
$160$	2.01047	0.158941
$161$	7.00330	0.551937
$162$	16.5407	1.29956
$163$	−19.1379	−1.49900	−0.749499	−	0.662006i	$-0.769705\pi$
$163$	−19.1379	−1.49900	−0.749499	+	0.662006i	$0.769705\pi$
$164$	1.03341	0.0806955
$165$	11.6593	0.907674
$166$	−24.9609	−1.93734
$167$	2.08602	0.161421	0.0807106	−	0.996738i	$-0.474281\pi$
$167$	2.08602	0.161421	0.0807106	+	0.996738i	$0.474281\pi$
$168$	−4.91597	−0.379275
$169$	2.04869	0.157591
$170$	−6.01377	−0.461235
$171$	6.63102	0.507087
$172$	−0.346605	−0.0264284
$173$	−11.4872	−0.873356	−0.436678	−	0.899618i	$-0.643845\pi$
$173$	−11.4872	−0.873356	−0.436678	+	0.899618i	$0.643845\pi$
$174$	24.1072	1.82756
$175$	1.00000	0.0755929
$176$	27.4308	2.06767
$177$	−21.2032	−1.59373
$178$	6.51706	0.488474
$179$	−7.99235	−0.597377	−0.298688	−	0.954351i	$-0.596549\pi$
$179$	−7.99235	−0.597377	−0.298688	+	0.954351i	$0.596549\pi$
$180$	0.289726	0.0215949
$181$	20.1971	1.50124	0.750618	−	0.660736i	$-0.229756\pi$
$181$	20.1971	1.50124	0.750618	+	0.660736i	$0.229756\pi$
$182$	−5.95884	−0.441698
$183$	−1.79802	−0.132914
$184$	17.6476	1.30100
$185$	10.7596	0.791060
$186$	−18.5234	−1.35820
$187$	−23.3981	−1.71103
$188$	2.48611	0.181318
$189$	4.28046	0.311358
$190$	−12.6396	−0.916969
$191$	13.5931	0.983565	0.491783	−	0.870718i	$-0.336345\pi$
$191$	13.5931	0.983565	0.491783	+	0.870718i	$0.336345\pi$
$192$	−11.8834	−0.857610
$193$	9.53875	0.686614	0.343307	−	0.939223i	$-0.388453\pi$
$193$	9.53875	0.686614	0.343307	+	0.939223i	$0.388453\pi$
$194$	−17.7054	−1.27117
$195$	−7.56791	−0.541949
$196$	0.359523	0.0256802
$197$	−27.2605	−1.94223	−0.971115	−	0.238611i	$-0.923308\pi$
$197$	−27.2605	−1.94223	−0.971115	+	0.238611i	$0.923308\pi$
$198$	7.39806	0.525757
$199$	0.826906	0.0586178	0.0293089	−	0.999570i	$-0.490669\pi$
$199$	0.826906	0.0586178	0.0293089	+	0.999570i	$0.490669\pi$
$200$	2.51989	0.178183
$201$	20.7313	1.46228
$202$	−26.7416	−1.88153
$203$	8.04465	0.564624
$204$	−2.74592	−0.192253
$205$	2.87438	0.200756
$206$	−26.0769	−1.81687
$207$	5.64369	0.392264
$208$	−17.8050	−1.23455
$209$	−49.1773	−3.40166
$210$	2.99667	0.206790
$211$	−0.152522	−0.0105000	−0.00525001	−	0.999986i	$-0.501671\pi$
$211$	−0.152522	−0.0105000	−0.00525001	+	0.999986i	$0.501671\pi$
$212$	−1.26990	−0.0872172
$213$	13.0017	0.890865
$214$	16.3939	1.12067
$215$	−0.964070	−0.0657490
$216$	10.7863	0.733915
$217$	−6.18132	−0.419615
$218$	−4.25354	−0.288086
$219$	−16.8439	−1.13821
$220$	−2.14868	−0.144864
$221$	15.1874	1.02162
$222$	32.2429	2.16400
$223$	16.6683	1.11619	0.558096	−	0.829776i	$-0.311532\pi$
$223$	16.6683	1.11619	0.558096	+	0.829776i	$0.311532\pi$
$224$	2.01047	0.134330
$225$	0.805862	0.0537241
$226$	18.9759	1.26226
$227$	20.1274	1.33591	0.667953	−	0.744204i	$-0.267171\pi$
$227$	20.1274	1.33591	0.667953	+	0.744204i	$0.267171\pi$
$228$	−5.77129	−0.382213
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	−10.7576	−0.709334
$231$	11.6593	0.767124
$232$	20.2717	1.33090
$233$	−9.56199	−0.626427	−0.313213	−	0.949683i	$-0.601406\pi$
$233$	−9.56199	−0.626427	−0.313213	+	0.949683i	$0.601406\pi$
$234$	−4.80200	−0.313917
$235$	6.91503	0.451087
$236$	3.90753	0.254358
$237$	−14.9581	−0.971630
$238$	−6.01377	−0.389815
$239$	−15.9302	−1.03044	−0.515221	−	0.857058i	$-0.672290\pi$
$239$	−15.9302	−1.03044	−0.515221	+	0.857058i	$0.672290\pi$
$240$	8.95404	0.577981
$241$	20.0192	1.28955	0.644776	−	0.764372i	$-0.276951\pi$
$241$	20.0192	1.28955	0.644776	+	0.764372i	$0.276951\pi$
$242$	−37.9691	−2.44074
$243$	8.16584	0.523839
$244$	0.331356	0.0212129
$245$	1.00000	0.0638877
$246$	8.61357	0.549181
$247$	31.9204	2.03105
$248$	−15.5763	−0.989094
$249$	−31.7011	−2.00897
$250$	−1.53607	−0.0971498
$251$	9.07393	0.572741	0.286371	−	0.958119i	$-0.407551\pi$
$251$	9.07393	0.572741	0.286371	+	0.958119i	$0.407551\pi$
$252$	0.289726	0.0182510
$253$	−41.8550	−2.63140
$254$	−7.37029	−0.462453
$255$	−7.63767	−0.478290
$256$	8.36643	0.522902
$257$	−17.5659	−1.09573	−0.547866	−	0.836566i	$-0.684560\pi$
$257$	−17.5659	−1.09573	−0.547866	+	0.836566i	$0.684560\pi$
$258$	−2.88900	−0.179861
$259$	10.7596	0.668567
$260$	1.39468	0.0864947
$261$	6.48288	0.401280
$262$	29.2026	1.80414
$263$	−7.78017	−0.479746	−0.239873	−	0.970804i	$-0.577106\pi$
$263$	−7.78017	−0.479746	−0.239873	+	0.970804i	$0.577106\pi$
$264$	29.3801	1.80822
$265$	−3.53218	−0.216980
$266$	−12.6396	−0.774981
$267$	8.27687	0.506536
$268$	−3.82056	−0.233378
$269$	−0.469573	−0.0286303	−0.0143152	−	0.999898i	$-0.504557\pi$
$269$	−0.469573	−0.0286303	−0.0143152	+	0.999898i	$0.504557\pi$
$270$	−6.57510	−0.400148
$271$	−19.3442	−1.17508	−0.587538	−	0.809196i	$-0.699903\pi$
$271$	−19.3442	−1.17508	−0.587538	+	0.809196i	$0.699903\pi$
$272$	−17.9691	−1.08954
$273$	−7.56791	−0.458031
$274$	−9.69351	−0.585606
$275$	−5.97648	−0.360395
$276$	−4.91197	−0.295666
$277$	24.4319	1.46797	0.733986	−	0.679165i	$-0.237658\pi$
$277$	24.4319	1.46797	0.733986	+	0.679165i	$0.237658\pi$
$278$	10.8011	0.647809
$279$	−4.98129	−0.298222
$280$	2.51989	0.150592
$281$	−13.7029	−0.817445	−0.408723	−	0.912659i	$-0.634026\pi$
$281$	−13.7029	−0.817445	−0.408723	+	0.912659i	$0.634026\pi$
$282$	20.7220	1.23398
$283$	−28.5765	−1.69870	−0.849348	−	0.527833i	$-0.823005\pi$
$283$	−28.5765	−1.69870	−0.849348	+	0.527833i	$0.823005\pi$
$284$	−2.39608	−0.142181
$285$	−16.0526	−0.950875
$286$	35.6128	2.10583
$287$	2.87438	0.169669
$288$	1.62016	0.0954688
$289$	−1.67258	−0.0983870
$290$	−12.3572	−0.725639
$291$	−22.4863	−1.31817
$292$	3.10415	0.181657
$293$	−12.3659	−0.722423	−0.361212	−	0.932484i	$-0.617637\pi$
$293$	−12.3659	−0.722423	−0.361212	+	0.932484i	$0.617637\pi$
$294$	2.99667	0.174769
$295$	10.8686	0.632797
$296$	27.1130	1.57591
$297$	−25.5821	−1.48442
$298$	−11.6852	−0.676905
$299$	27.1676	1.57115
$300$	−0.701380	−0.0404942
$301$	−0.964070	−0.0555681
$302$	20.1007	1.15667
$303$	−33.9627	−1.95110
$304$	−37.7670	−2.16609
$305$	0.921656	0.0527739
$306$	−4.84627	−0.277043
$307$	−3.52710	−0.201302	−0.100651	−	0.994922i	$-0.532093\pi$
$307$	−3.52710	−0.201302	−0.100651	+	0.994922i	$0.532093\pi$
$308$	−2.14868	−0.122432
$309$	−33.1185	−1.88405
$310$	9.49497	0.539278
$311$	−3.59366	−0.203778	−0.101889	−	0.994796i	$-0.532489\pi$
$311$	−3.59366	−0.203778	−0.101889	+	0.994796i	$0.532489\pi$
$312$	−19.0703	−1.07964
$313$	−19.5864	−1.10709	−0.553544	−	0.832820i	$-0.686725\pi$
$313$	−19.5864	−1.10709	−0.553544	+	0.832820i	$0.686725\pi$
$314$	10.6734	0.602336
$315$	0.805862	0.0454052
$316$	2.75661	0.155071
$317$	−15.8897	−0.892453	−0.446227	−	0.894920i	$-0.647232\pi$
$317$	−15.8897	−0.892453	−0.446227	+	0.894920i	$0.647232\pi$
$318$	−10.5848	−0.593565
$319$	−48.0787	−2.69189
$320$	6.09135	0.340517
$321$	20.8208	1.16211
$322$	−10.7576	−0.599497
$323$	32.2147	1.79247
$324$	−3.87141	−0.215078
$325$	3.87926	0.215183
$326$	29.3973	1.62816
$327$	−5.40213	−0.298739
$328$	7.24314	0.399936
$329$	6.91503	0.381238
$330$	−17.9095	−0.985886
$331$	−22.2890	−1.22511	−0.612556	−	0.790427i	$-0.709859\pi$
$331$	−22.2890	−1.22511	−0.612556	+	0.790427i	$0.709859\pi$
$332$	5.84217	0.320631
$333$	8.67074	0.475153
$334$	−3.20428	−0.175331
$335$	−10.6268	−0.580602
$336$	8.95404	0.488483
$337$	−25.6985	−1.39989	−0.699944	−	0.714197i	$-0.746792\pi$
$337$	−25.6985	−1.39989	−0.699944	+	0.714197i	$0.746792\pi$
$338$	−3.14693	−0.171171
$339$	24.1000	1.30893
$340$	1.40754	0.0763347
$341$	36.9425	2.00055
$342$	−10.1857	−0.550782
$343$	1.00000	0.0539949
$344$	−2.42935	−0.130982
$345$	−13.6625	−0.735563
$346$	17.6452	0.948612
$347$	10.5496	0.566334	0.283167	−	0.959071i	$-0.408615\pi$
$347$	10.5496	0.566334	0.283167	+	0.959071i	$0.408615\pi$
$348$	−5.64236	−0.302462
$349$	12.3239	0.659685	0.329842	−	0.944036i	$-0.393004\pi$
$349$	12.3239	0.659685	0.329842	+	0.944036i	$0.393004\pi$
$350$	−1.53607	−0.0821066
$351$	16.6050	0.886311
$352$	−12.0155	−0.640429
$353$	−16.5244	−0.879505	−0.439753	−	0.898119i	$-0.644934\pi$
$353$	−16.5244	−0.879505	−0.439753	+	0.898119i	$0.644934\pi$
$354$	32.5697	1.73106
$355$	−6.66462	−0.353721
$356$	−1.52534	−0.0808428
$357$	−7.63767	−0.404229
$358$	12.2768	0.648851
$359$	−17.9265	−0.946123	−0.473061	−	0.881029i	$-0.656851\pi$
$359$	−17.9265	−0.946123	−0.473061	+	0.881029i	$0.656851\pi$
$360$	2.03069	0.107027
$361$	48.7079	2.56357
$362$	−31.0242	−1.63060
$363$	−48.2219	−2.53099
$364$	1.39468	0.0731013
$365$	8.63409	0.451929
$366$	2.76190	0.144367
$367$	−1.47462	−0.0769744	−0.0384872	−	0.999259i	$-0.512254\pi$
$367$	−1.47462	−0.0769744	−0.0384872	+	0.999259i	$0.512254\pi$
$368$	−32.1437	−1.67560
$369$	2.31636	0.120585
$370$	−16.5275	−0.859224
$371$	−3.53218	−0.183382
$372$	4.33545	0.224783
$373$	9.97684	0.516581	0.258291	−	0.966067i	$-0.416841\pi$
$373$	9.97684	0.516581	0.258291	+	0.966067i	$0.416841\pi$
$374$	35.9411	1.85847
$375$	−1.95086	−0.100742
$376$	17.4251	0.898633
$377$	31.2073	1.60726
$378$	−6.57510	−0.338187
$379$	−12.9633	−0.665878	−0.332939	−	0.942948i	$-0.608040\pi$
$379$	−12.9633	−0.665878	−0.332939	+	0.942948i	$0.608040\pi$
$380$	2.95833	0.151759
$381$	−9.36049	−0.479553
$382$	−20.8801	−1.06832
$383$	−4.28450	−0.218928	−0.109464	−	0.993991i	$-0.534913\pi$
$383$	−4.28450	−0.218928	−0.109464	+	0.993991i	$0.534913\pi$
$384$	26.0980	1.33181
$385$	−5.97648	−0.304589
$386$	−14.6522	−0.745778
$387$	−0.776907	−0.0394924
$388$	4.14399	0.210379
$389$	−0.929310	−0.0471179	−0.0235589	−	0.999722i	$-0.507500\pi$
$389$	−0.929310	−0.0471179	−0.0235589	+	0.999722i	$0.507500\pi$
$390$	11.6249	0.588648
$391$	27.4181	1.38659
$392$	2.51989	0.127274
$393$	37.0882	1.87085
$394$	41.8741	2.10959
$395$	7.66741	0.385789
$396$	−1.73154	−0.0870132
$397$	10.8879	0.546447	0.273224	−	0.961951i	$-0.411910\pi$
$397$	10.8879	0.546447	0.273224	+	0.961951i	$0.411910\pi$
$398$	−1.27019	−0.0636688
$399$	−16.0526	−0.803636
$400$	−4.58979	−0.229489
$401$	−31.4024	−1.56816	−0.784081	−	0.620658i	$-0.786866\pi$
$401$	−31.4024	−1.56816	−0.784081	+	0.620658i	$0.786866\pi$
$402$	−31.8449	−1.58828
$403$	−23.9790	−1.19448
$404$	6.25895	0.311395
$405$	−10.7682	−0.535075
$406$	−12.3572	−0.613277
$407$	−64.3043	−3.18745
$408$	−19.2461	−0.952825
$409$	14.7617	0.729917	0.364958	−	0.931024i	$-0.381083\pi$
$409$	14.7617	0.729917	0.364958	+	0.931024i	$0.381083\pi$
$410$	−4.41527	−0.218054
$411$	−12.3111	−0.607260
$412$	6.10339	0.300692
$413$	10.8686	0.534811
$414$	−8.66913	−0.426065
$415$	16.2498	0.797670
$416$	7.79913	0.382384
$417$	13.7178	0.671763
$418$	75.5400	3.69478
$419$	−12.3441	−0.603051	−0.301525	−	0.953458i	$-0.597496\pi$
$419$	−12.3441	−0.603051	−0.301525	+	0.953458i	$0.597496\pi$
$420$	−0.701380	−0.0342238
$421$	−19.2823	−0.939761	−0.469881	−	0.882730i	$-0.655703\pi$
$421$	−19.2823	−0.939761	−0.469881	+	0.882730i	$0.655703\pi$
$422$	0.234285	0.0114048
$423$	5.57256	0.270947
$424$	−8.90073	−0.432258
$425$	3.91503	0.189907
$426$	−19.9716	−0.967629
$427$	0.921656	0.0446021
$428$	−3.83706	−0.185471
$429$	45.2294	2.18370
$430$	1.48088	0.0714145
$431$	15.9503	0.768300	0.384150	−	0.923271i	$-0.374494\pi$
$431$	15.9503	0.768300	0.384150	+	0.923271i	$0.374494\pi$
$432$	−19.6464	−0.945238
$433$	31.6376	1.52040	0.760202	−	0.649687i	$-0.225100\pi$
$433$	31.6376	1.52040	0.760202	+	0.649687i	$0.225100\pi$
$434$	9.49497	0.455773
$435$	−15.6940	−0.752470
$436$	0.995555	0.0476784
$437$	57.6265	2.75665
$438$	25.8735	1.23628
$439$	38.3967	1.83257	0.916287	−	0.400522i	$-0.131171\pi$
$439$	38.3967	1.83257	0.916287	+	0.400522i	$0.131171\pi$
$440$	−15.0601	−0.717961
$441$	0.805862	0.0383744
$442$	−23.3290	−1.10965
$443$	6.00670	0.285387	0.142693	−	0.989767i	$-0.454424\pi$
$443$	6.00670	0.285387	0.142693	+	0.989767i	$0.454424\pi$
$444$	−7.54655	−0.358143
$445$	−4.24267	−0.201122
$446$	−25.6037	−1.21237
$447$	−14.8406	−0.701935
$448$	6.09135	0.287789
$449$	7.92105	0.373818	0.186909	−	0.982377i	$-0.440153\pi$
$449$	7.92105	0.373818	0.186909	+	0.982377i	$0.440153\pi$
$450$	−1.23786	−0.0583535
$451$	−17.1787	−0.808913
$452$	−4.44137	−0.208905
$453$	25.5285	1.19943
$454$	−30.9172	−1.45102
$455$	3.87926	0.181863
$456$	−40.4509	−1.89429
$457$	24.6085	1.15114	0.575568	−	0.817754i	$-0.304781\pi$
$457$	24.6085	1.15114	0.575568	+	0.817754i	$0.304781\pi$
$458$	−1.53607	−0.0717760
$459$	16.7581	0.782201
$460$	2.51785	0.117395
$461$	17.2357	0.802748	0.401374	−	0.915914i	$-0.368533\pi$
$461$	17.2357	0.802748	0.401374	+	0.915914i	$0.368533\pi$
$462$	−17.9095	−0.833226
$463$	−38.6088	−1.79430	−0.897152	−	0.441721i	$-0.854368\pi$
$463$	−38.6088	−1.79430	−0.897152	+	0.441721i	$0.854368\pi$
$464$	−36.9233	−1.71412
$465$	12.0589	0.559218
$466$	14.6879	0.680405
$467$	−17.0671	−0.789773	−0.394886	−	0.918730i	$-0.629216\pi$
$467$	−17.0671	−0.789773	−0.394886	+	0.918730i	$0.629216\pi$
$468$	1.12392	0.0519534
$469$	−10.6268	−0.490698
$470$	−10.6220	−0.489956
$471$	13.5556	0.624608
$472$	27.3878	1.26063
$473$	5.76174	0.264925
$474$	22.9767	1.05535
$475$	8.22848	0.377548
$476$	1.40754	0.0645146
$477$	−2.84645	−0.130330
$478$	24.4700	1.11923
$479$	−15.4903	−0.707770	−0.353885	−	0.935289i	$-0.615140\pi$
$479$	−15.4903	−0.707770	−0.353885	+	0.935289i	$0.615140\pi$
$480$	−3.92214	−0.179021
$481$	41.7392	1.90315
$482$	−30.7510	−1.40067
$483$	−13.6625	−0.621664
$484$	8.88678	0.403945
$485$	11.5264	0.523385
$486$	−12.5433	−0.568977
$487$	−25.1005	−1.13741	−0.568706	−	0.822541i	$-0.692556\pi$
$487$	−25.1005	−1.13741	−0.568706	+	0.822541i	$0.692556\pi$
$488$	2.32248	0.105134
$489$	37.3354	1.68837
$490$	−1.53607	−0.0693927
$491$	7.47426	0.337309	0.168654	−	0.985675i	$-0.446058\pi$
$491$	7.47426	0.337309	0.168654	+	0.985675i	$0.446058\pi$
$492$	−2.01603	−0.0908898
$493$	31.4950	1.41846
$494$	−49.0322	−2.20606
$495$	−4.81622	−0.216473
$496$	28.3710	1.27389
$497$	−6.66462	−0.298949
$498$	48.6952	2.18208
$499$	41.4161	1.85404	0.927020	−	0.375013i	$-0.122362\pi$
$499$	41.4161	1.85404	0.927020	+	0.375013i	$0.122362\pi$
$500$	0.359523	0.0160784
$501$	−4.06954	−0.181814
$502$	−13.9382	−0.622093
$503$	4.36969	0.194835	0.0974174	−	0.995244i	$-0.468942\pi$
$503$	4.36969	0.194835	0.0974174	+	0.995244i	$0.468942\pi$
$504$	2.03069	0.0904540
$505$	17.4091	0.774693
$506$	64.2924	2.85815
$507$	−3.99670	−0.177500
$508$	1.72504	0.0765362
$509$	16.7762	0.743593	0.371797	−	0.928314i	$-0.378742\pi$
$509$	16.7762	0.743593	0.371797	+	0.928314i	$0.378742\pi$
$510$	11.7320	0.519503
$511$	8.63409	0.381950
$512$	13.9039	0.614473
$513$	35.2217	1.55507
$514$	26.9826	1.19015
$515$	16.9764	0.748067
$516$	0.676179	0.0297671
$517$	−41.3275	−1.81758
$518$	−16.5275	−0.726177
$519$	22.4100	0.983688
$520$	9.77533	0.428677
$521$	10.5619	0.462726	0.231363	−	0.972867i	$-0.425681\pi$
$521$	10.5619	0.462726	0.231363	+	0.972867i	$0.425681\pi$
$522$	−9.95819	−0.435858
$523$	14.7817	0.646357	0.323179	−	0.946338i	$-0.395249\pi$
$523$	14.7817	0.646357	0.323179	+	0.946338i	$0.395249\pi$
$524$	−6.83495	−0.298586
$525$	−1.95086	−0.0851426
$526$	11.9509	0.521085
$527$	−24.2000	−1.05417
$528$	−53.5136	−2.32888
$529$	26.0462	1.13244
$530$	5.42570	0.235677
$531$	8.75863	0.380092
$532$	2.95833	0.128260
$533$	11.1505	0.482981
$534$	−12.7139	−0.550184
$535$	−10.6726	−0.461418
$536$	−26.7783	−1.15665
$537$	15.5920	0.672844
$538$	0.721298	0.0310974
$539$	−5.97648	−0.257425
$540$	1.53892	0.0662247
$541$	−1.81268	−0.0779332	−0.0389666	−	0.999241i	$-0.512407\pi$
$541$	−1.81268	−0.0779332	−0.0389666	+	0.999241i	$0.512407\pi$
$542$	29.7141	1.27633
$543$	−39.4017	−1.69089
$544$	7.87103	0.337468
$545$	2.76910	0.118615
$546$	11.6249	0.497498
$547$	−31.5136	−1.34742	−0.673712	−	0.738994i	$-0.735301\pi$
$547$	−31.5136	−1.34742	−0.673712	+	0.738994i	$0.735301\pi$
$548$	2.26880	0.0969182
$549$	0.742728	0.0316988
$550$	9.18031	0.391450
$551$	66.1953	2.82001
$552$	−34.4280	−1.46535
$553$	7.66741	0.326051
$554$	−37.5292	−1.59446
$555$	−20.9904	−0.890995
$556$	−2.52804	−0.107213
$557$	−2.15836	−0.0914528	−0.0457264	−	0.998954i	$-0.514560\pi$
$557$	−2.15836	−0.0914528	−0.0457264	+	0.998954i	$0.514560\pi$
$558$	7.65163	0.323919
$559$	−3.73988	−0.158180
$560$	−4.58979	−0.193954
$561$	45.6464	1.92719
$562$	21.0486	0.887883
$563$	25.3264	1.06738	0.533689	−	0.845681i	$-0.320805\pi$
$563$	25.3264	1.06738	0.533689	+	0.845681i	$0.320805\pi$
$564$	−4.85006	−0.204224
$565$	−12.3535	−0.519716
$566$	43.8956	1.84507
$567$	−10.7682	−0.452221
$568$	−16.7941	−0.704666
$569$	−9.71652	−0.407338	−0.203669	−	0.979040i	$-0.565287\pi$
$569$	−9.71652	−0.407338	−0.203669	+	0.979040i	$0.565287\pi$
$570$	24.6580	1.03281
$571$	13.8527	0.579717	0.289858	−	0.957070i	$-0.406392\pi$
$571$	13.8527	0.579717	0.289858	+	0.957070i	$0.406392\pi$
$572$	−8.33530	−0.348516
$573$	−26.5183	−1.10782
$574$	−4.41527	−0.184290
$575$	7.00330	0.292058
$576$	4.90879	0.204533
$577$	−0.616662	−0.0256720	−0.0128360	−	0.999918i	$-0.504086\pi$
$577$	−0.616662	−0.0256720	−0.0128360	+	0.999918i	$0.504086\pi$
$578$	2.56920	0.106865
$579$	−18.6088	−0.773354
$580$	2.89224	0.120094
$581$	16.2498	0.674154
$582$	34.5407	1.43176
$583$	21.1100	0.874287
$584$	21.7570	0.900311
$585$	3.12615	0.129250
$586$	18.9949	0.784673
$587$	36.5768	1.50969	0.754843	−	0.655906i	$-0.227713\pi$
$587$	36.5768	1.50969	0.754843	+	0.655906i	$0.227713\pi$
$588$	−0.701380	−0.0289244
$589$	−50.8629	−2.09577
$590$	−16.6950	−0.687324
$591$	53.1815	2.18759
$592$	−49.3842	−2.02968
$593$	3.03815	0.124762	0.0623808	−	0.998052i	$-0.480131\pi$
$593$	3.03815	0.124762	0.0623808	+	0.998052i	$0.480131\pi$
$594$	39.2959	1.61233
$595$	3.91503	0.160500
$596$	2.73496	0.112028
$597$	−1.61318	−0.0660231
$598$	−41.7315	−1.70653
$599$	−30.9082	−1.26287	−0.631437	−	0.775427i	$-0.717535\pi$
$599$	−30.9082	−1.26287	−0.631437	+	0.775427i	$0.717535\pi$
$600$	−4.91597	−0.200693
$601$	48.4418	1.97598	0.987991	−	0.154509i	$-0.0493795\pi$
$601$	48.4418	1.97598	0.987991	+	0.154509i	$0.0493795\pi$
$602$	1.48088	0.0603563
$603$	−8.56370	−0.348741
$604$	−4.70463	−0.191429
$605$	24.7183	1.00494
$606$	52.1692	2.11923
$607$	−31.7716	−1.28957	−0.644786	−	0.764363i	$-0.723053\pi$
$607$	−31.7716	−1.28957	−0.644786	+	0.764363i	$0.723053\pi$
$608$	16.5431	0.670911
$609$	−15.6940	−0.635953
$610$	−1.41573	−0.0573213
$611$	26.8252	1.08523
$612$	1.13428	0.0458507
$613$	14.3682	0.580324	0.290162	−	0.956977i	$-0.406291\pi$
$613$	14.3682	0.580324	0.290162	+	0.956977i	$0.406291\pi$
$614$	5.41788	0.218648
$615$	−5.60753	−0.226117
$616$	−15.0601	−0.606788
$617$	18.0237	0.725605	0.362803	−	0.931866i	$-0.381820\pi$
$617$	18.0237	0.725605	0.362803	+	0.931866i	$0.381820\pi$
$618$	50.8725	2.04639
$619$	−24.1259	−0.969701	−0.484850	−	0.874597i	$-0.661126\pi$
$619$	−24.1259	−0.969701	−0.484850	+	0.874597i	$0.661126\pi$
$620$	−2.22233	−0.0892508
$621$	29.9773	1.20295
$622$	5.52013	0.221337
$623$	−4.24267	−0.169979
$624$	34.7351	1.39052
$625$	1.00000	0.0400000
$626$	30.0861	1.20248
$627$	95.9381	3.83140
$628$	−2.49815	−0.0996870
$629$	42.1240	1.67959
$630$	−1.23786	−0.0493177
$631$	18.8570	0.750685	0.375343	−	0.926886i	$-0.377525\pi$
$631$	18.8570	0.750685	0.375343	+	0.926886i	$0.377525\pi$
$632$	19.3211	0.768551
$633$	0.297549	0.0118265
$634$	24.4077	0.969354
$635$	4.79813	0.190408
$636$	2.47740	0.0982354
$637$	3.87926	0.153702
$638$	73.8524	2.92384
$639$	−5.37076	−0.212464
$640$	−13.3777	−0.528800
$641$	−25.9382	−1.02450	−0.512249	−	0.858837i	$-0.671187\pi$
$641$	−25.9382	−1.02450	−0.512249	+	0.858837i	$0.671187\pi$
$642$	−31.9823	−1.26224
$643$	27.3493	1.07855	0.539275	−	0.842130i	$-0.318698\pi$
$643$	27.3493	1.07855	0.539275	+	0.842130i	$0.318698\pi$
$644$	2.51785	0.0992171
$645$	1.88077	0.0740551
$646$	−49.4842	−1.94693
$647$	37.0219	1.45548	0.727740	−	0.685853i	$-0.240571\pi$
$647$	37.0219	1.45548	0.727740	+	0.685853i	$0.240571\pi$
$648$	−27.1347	−1.06595
$649$	−64.9562	−2.54975
$650$	−5.95884	−0.233725
$651$	12.0589	0.472626
$652$	−6.88052	−0.269462
$653$	−30.8446	−1.20704	−0.603522	−	0.797347i	$-0.706236\pi$
$653$	−30.8446	−1.20704	−0.603522	+	0.797347i	$0.706236\pi$
$654$	8.29807	0.324480
$655$	−19.0112	−0.742828
$656$	−13.1928	−0.515093
$657$	6.95789	0.271453
$658$	−10.6220	−0.414088
$659$	22.9502	0.894014	0.447007	−	0.894531i	$-0.352490\pi$
$659$	22.9502	0.894014	0.447007	+	0.894531i	$0.352490\pi$
$660$	4.19178	0.163165
$661$	−9.29919	−0.361696	−0.180848	−	0.983511i	$-0.557884\pi$
$661$	−9.29919	−0.361696	−0.180848	+	0.983511i	$0.557884\pi$
$662$	34.2375	1.33068
$663$	−29.6285	−1.15068
$664$	40.9477	1.58908
$665$	8.22848	0.319087
$666$	−13.3189	−0.516097
$667$	56.3391	2.18146
$668$	0.749973	0.0290173
$669$	−32.5175	−1.25720
$670$	16.3235	0.630631
$671$	−5.50825	−0.212644
$672$	−3.92214	−0.151300
$673$	14.2310	0.548564	0.274282	−	0.961649i	$-0.411560\pi$
$673$	14.2310	0.548564	0.274282	+	0.961649i	$0.411560\pi$
$674$	39.4749	1.52051
$675$	4.28046	0.164755
$676$	0.736550	0.0283288
$677$	−1.43433	−0.0551256	−0.0275628	−	0.999620i	$-0.508775\pi$
$677$	−1.43433	−0.0551256	−0.0275628	+	0.999620i	$0.508775\pi$
$678$	−37.0194	−1.42172
$679$	11.5264	0.442341
$680$	9.86545	0.378323
$681$	−39.2659	−1.50467
$682$	−56.7464	−2.17293
$683$	20.0901	0.768727	0.384364	−	0.923182i	$-0.374421\pi$
$683$	20.0901	0.768727	0.384364	+	0.923182i	$0.374421\pi$
$684$	2.38400	0.0911547
$685$	6.31057	0.241115
$686$	−1.53607	−0.0586476
$687$	−1.95086	−0.0744300
$688$	4.42488	0.168697
$689$	−13.7023	−0.522015
$690$	20.9866	0.798945
$691$	−10.4477	−0.397450	−0.198725	−	0.980055i	$-0.563680\pi$
$691$	−10.4477	−0.397450	−0.198725	+	0.980055i	$0.563680\pi$
$692$	−4.12992	−0.156996
$693$	−4.81622	−0.182953
$694$	−16.2050	−0.615134
$695$	−7.03166	−0.266726
$696$	−39.5472	−1.49903
$697$	11.2533	0.426248
$698$	−18.9305	−0.716528
$699$	18.6541	0.705564
$700$	0.359523	0.0135887
$701$	31.7175	1.19795	0.598976	−	0.800767i	$-0.295574\pi$
$701$	31.7175	1.19795	0.598976	+	0.800767i	$0.295574\pi$
$702$	−25.5066	−0.962683
$703$	88.5349	3.33916
$704$	−36.4048	−1.37206
$705$	−13.4903	−0.508073
$706$	25.3827	0.955291
$707$	17.4091	0.654735
$708$	−7.62304	−0.286492
$709$	−10.4312	−0.391752	−0.195876	−	0.980629i	$-0.562755\pi$
$709$	−10.4312	−0.391752	−0.195876	+	0.980629i	$0.562755\pi$
$710$	10.2373	0.384201
$711$	6.17888	0.231726
$712$	−10.6911	−0.400666
$713$	−43.2896	−1.62121
$714$	11.7320	0.439060
$715$	−23.1843	−0.867045
$716$	−2.87343	−0.107385
$717$	31.0777	1.16062
$718$	27.5364	1.02765
$719$	−25.9836	−0.969024	−0.484512	−	0.874785i	$-0.661003\pi$
$719$	−25.9836	−0.969024	−0.484512	+	0.874785i	$0.661003\pi$
$720$	−3.69874	−0.137844
$721$	16.9764	0.632232
$722$	−74.8189	−2.78447
$723$	−39.0548	−1.45246
$724$	7.26131	0.269865
$725$	8.04465	0.298771
$726$	74.0724	2.74909
$727$	−33.5079	−1.24274	−0.621369	−	0.783518i	$-0.713423\pi$
$727$	−33.5079	−1.24274	−0.621369	+	0.783518i	$0.713423\pi$
$728$	9.77533	0.362298
$729$	16.3741	0.606448
$730$	−13.2626	−0.490871
$731$	−3.77436	−0.139600
$732$	−0.646431	−0.0238928
$733$	9.04317	0.334017	0.167009	−	0.985955i	$-0.446589\pi$
$733$	9.04317	0.334017	0.167009	+	0.985955i	$0.446589\pi$
$734$	2.26512	0.0836071
$735$	−1.95086	−0.0719586
$736$	14.0799	0.518992
$737$	63.5106	2.33944
$738$	−3.55810	−0.130975
$739$	−47.2381	−1.73768	−0.868841	−	0.495092i	$-0.835135\pi$
$739$	−47.2381	−1.73768	−0.868841	+	0.495092i	$0.835135\pi$
$740$	3.86831	0.142202
$741$	−62.2724	−2.28763
$742$	5.42570	0.199184
$743$	34.4137	1.26252	0.631258	−	0.775573i	$-0.282539\pi$
$743$	34.4137	1.26252	0.631258	+	0.775573i	$0.282539\pi$
$744$	30.3872	1.11405
$745$	7.60719	0.278706
$746$	−15.3252	−0.561094
$747$	13.0951	0.479124
$748$	−8.41214	−0.307578
$749$	−10.6726	−0.389969
$750$	2.99667	0.109423
$751$	3.29269	0.120152	0.0600761	−	0.998194i	$-0.480866\pi$
$751$	3.29269	0.120152	0.0600761	+	0.998194i	$0.480866\pi$
$752$	−31.7385	−1.15738
$753$	−17.7020	−0.645096
$754$	−47.9368	−1.74575
$755$	−13.0858	−0.476240
$756$	1.53892	0.0559701
$757$	15.2624	0.554721	0.277361	−	0.960766i	$-0.410540\pi$
$757$	15.2624	0.554721	0.277361	+	0.960766i	$0.410540\pi$
$758$	19.9125	0.723255
$759$	81.6534	2.96383
$760$	20.7349	0.752134
$761$	−32.9716	−1.19522	−0.597609	−	0.801787i	$-0.703883\pi$
$761$	−32.9716	−1.19522	−0.597609	+	0.801787i	$0.703883\pi$
$762$	14.3784	0.520875
$763$	2.76910	0.100248
$764$	4.88705	0.176807
$765$	3.15497	0.114068
$766$	6.58131	0.237792
$767$	42.1623	1.52239
$768$	−16.3218	−0.588961
$769$	40.9027	1.47499	0.737494	−	0.675353i	$-0.236009\pi$
$769$	40.9027	1.47499	0.737494	+	0.675353i	$0.236009\pi$
$770$	9.18031	0.330835
$771$	34.2687	1.23416
$772$	3.42940	0.123427
$773$	20.3229	0.730965	0.365482	−	0.930818i	$-0.380904\pi$
$773$	20.3229	0.730965	0.365482	+	0.930818i	$0.380904\pi$
$774$	1.19339	0.0428954
$775$	−6.18132	−0.222040
$776$	29.0452	1.04266
$777$	−20.9904	−0.753028
$778$	1.42749	0.0511779
$779$	23.6518	0.847414
$780$	−2.72084	−0.0974216
$781$	39.8309	1.42526
$782$	−42.1162	−1.50607
$783$	34.4348	1.23060
$784$	−4.58979	−0.163921
$785$	−6.94851	−0.248003
$786$	−56.9702	−2.03206
$787$	−27.1546	−0.967956	−0.483978	−	0.875080i	$-0.660809\pi$
$787$	−27.1546	−0.967956	−0.483978	+	0.875080i	$0.660809\pi$
$788$	−9.80078	−0.349138
$789$	15.1780	0.540352
$790$	−11.7777	−0.419032
$791$	−12.3535	−0.439240
$792$	−12.1364	−0.431247
$793$	3.57535	0.126964
$794$	−16.7246	−0.593534
$795$	6.89080	0.244392
$796$	0.297292	0.0105372
$797$	−16.0833	−0.569698	−0.284849	−	0.958572i	$-0.591944\pi$
$797$	−16.0833	−0.569698	−0.284849	+	0.958572i	$0.591944\pi$
$798$	24.6580	0.872884
$799$	27.0725	0.957756
$800$	2.01047	0.0710808
$801$	−3.41901	−0.120805
$802$	48.2365	1.70329
$803$	−51.6014	−1.82098
$804$	7.45339	0.262861
$805$	7.00330	0.246834
$806$	36.8335	1.29740
$807$	0.916071	0.0322472
$808$	43.8690	1.54330
$809$	−22.7533	−0.799964	−0.399982	−	0.916523i	$-0.630984\pi$
$809$	−22.7533	−0.799964	−0.399982	+	0.916523i	$0.630984\pi$
$810$	16.5407	0.581181
$811$	−26.1261	−0.917411	−0.458706	−	0.888588i	$-0.651687\pi$
$811$	−26.1261	−0.917411	−0.458706	+	0.888588i	$0.651687\pi$
$812$	2.89224	0.101498
$813$	37.7379	1.32352
$814$	98.7762	3.46210
$815$	−19.1379	−0.670372
$816$	35.0553	1.22718
$817$	−7.93283	−0.277534
$818$	−22.6750	−0.792812
$819$	3.12615	0.109237
$820$	1.03341	0.0360881
$821$	11.8963	0.415184	0.207592	−	0.978216i	$-0.433437\pi$
$821$	11.8963	0.415184	0.207592	+	0.978216i	$0.433437\pi$
$822$	18.9107	0.659586
$823$	−51.8008	−1.80566	−0.902831	−	0.429995i	$-0.858515\pi$
$823$	−51.8008	−1.80566	−0.902831	+	0.429995i	$0.858515\pi$
$824$	42.7786	1.49026
$825$	11.6593	0.405924
$826$	−16.6950	−0.580895
$827$	3.29877	0.114709	0.0573547	−	0.998354i	$-0.481733\pi$
$827$	3.29877	0.114709	0.0573547	+	0.998354i	$0.481733\pi$
$828$	2.02904	0.0705139
$829$	−0.525668	−0.0182572	−0.00912860	−	0.999958i	$-0.502906\pi$
$829$	−0.525668	−0.0182572	−0.00912860	+	0.999958i	$0.502906\pi$
$830$	−24.9609	−0.866404
$831$	−47.6633	−1.65342
$832$	23.6300	0.819221
$833$	3.91503	0.135648
$834$	−21.0715	−0.729648
$835$	2.08602	0.0721897
$836$	−17.6804	−0.611488
$837$	−26.4589	−0.914553
$838$	18.9615	0.655014
$839$	−37.7785	−1.30426	−0.652130	−	0.758107i	$-0.726124\pi$
$839$	−37.7785	−1.30426	−0.652130	+	0.758107i	$0.726124\pi$
$840$	−4.91597	−0.169617
$841$	35.7165	1.23160
$842$	29.6190	1.02074
$843$	26.7324	0.920713
$844$	−0.0548350	−0.00188750
$845$	2.04869	0.0704770
$846$	−8.55986	−0.294294
$847$	24.7183	0.849329
$848$	16.2120	0.556722
$849$	55.7488	1.91329
$850$	−6.01377	−0.206271
$851$	75.3525	2.58305
$852$	4.67443	0.160143
$853$	32.1194	1.09975	0.549874	−	0.835247i	$-0.314676\pi$
$853$	32.1194	1.09975	0.549874	+	0.835247i	$0.314676\pi$
$854$	−1.41573	−0.0484453
$855$	6.63102	0.226776
$856$	−26.8939	−0.919214
$857$	−45.2164	−1.54456	−0.772282	−	0.635280i	$-0.780885\pi$
$857$	−45.2164	−1.54456	−0.772282	+	0.635280i	$0.780885\pi$
$858$	−69.4757	−2.37186
$859$	−26.6135	−0.908042	−0.454021	−	0.890991i	$-0.650011\pi$
$859$	−26.6135	−0.908042	−0.454021	+	0.890991i	$0.650011\pi$
$860$	−0.346605	−0.0118191
$861$	−5.60753	−0.191104
$862$	−24.5009	−0.834504
$863$	−0.191721	−0.00652625	−0.00326312	−	0.999995i	$-0.501039\pi$
$863$	−0.191721	−0.00652625	−0.00326312	+	0.999995i	$0.501039\pi$
$864$	8.60572	0.292773
$865$	−11.4872	−0.390577
$866$	−48.5976	−1.65142
$867$	3.26297	0.110816
$868$	−2.22233	−0.0754307
$869$	−45.8241	−1.55448
$870$	24.1072	0.817309
$871$	−41.2240	−1.39682
$872$	6.97784	0.236299
$873$	9.28866	0.314374
$874$	−88.5186	−2.99418
$875$	1.00000	0.0338062
$876$	−6.05578	−0.204606
$877$	−30.0240	−1.01384	−0.506920	−	0.861993i	$-0.669216\pi$
$877$	−30.0240	−1.01384	−0.506920	+	0.861993i	$0.669216\pi$
$878$	−58.9802	−1.99048
$879$	24.1242	0.813688
$880$	27.4308	0.924691
$881$	11.3233	0.381490	0.190745	−	0.981640i	$-0.438910\pi$
$881$	11.3233	0.381490	0.190745	+	0.981640i	$0.438910\pi$
$882$	−1.23786	−0.0416810
$883$	50.0640	1.68479	0.842394	−	0.538862i	$-0.181146\pi$
$883$	50.0640	1.68479	0.842394	+	0.538862i	$0.181146\pi$
$884$	5.46022	0.183647
$885$	−21.2032	−0.712738
$886$	−9.22674	−0.309978
$887$	−48.4139	−1.62558	−0.812790	−	0.582557i	$-0.802052\pi$
$887$	−48.4139	−1.62558	−0.812790	+	0.582557i	$0.802052\pi$
$888$	−52.8937	−1.77500
$889$	4.79813	0.160924
$890$	6.51706	0.218452
$891$	64.3557	2.15600
$892$	5.99264	0.200648
$893$	56.9002	1.90409
$894$	22.7962	0.762419
$895$	−7.99235	−0.267155
$896$	−13.3777	−0.446918
$897$	−53.0003	−1.76963
$898$	−12.1673	−0.406029
$899$	−49.7266	−1.65847
$900$	0.289726	0.00965753
$901$	−13.8286	−0.460697
$902$	26.3877	0.878615
$903$	1.88077	0.0625880
$904$	−31.1295	−1.03535
$905$	20.1971	0.671374
$906$	−39.2137	−1.30279
$907$	−21.2568	−0.705821	−0.352910	−	0.935657i	$-0.614808\pi$
$907$	−21.2568	−0.705821	−0.352910	+	0.935657i	$0.614808\pi$
$908$	7.23628	0.240144
$909$	14.0293	0.465322
$910$	−5.95884	−0.197533
$911$	−14.5109	−0.480767	−0.240384	−	0.970678i	$-0.577273\pi$
$911$	−14.5109	−0.480767	−0.240384	+	0.970678i	$0.577273\pi$
$912$	73.6782	2.43973
$913$	−97.1164	−3.21408
$914$	−37.8004	−1.25033
$915$	−1.79802	−0.0594408
$916$	0.359523	0.0118790
$917$	−19.0112	−0.627804
$918$	−25.7417	−0.849602
$919$	17.4569	0.575849	0.287925	−	0.957653i	$-0.407035\pi$
$919$	17.4569	0.575849	0.287925	+	0.957653i	$0.407035\pi$
$920$	17.6476	0.581823
$921$	6.88088	0.226733
$922$	−26.4754	−0.871920
$923$	−25.8538	−0.850988
$924$	4.19178	0.137899
$925$	10.7596	0.353773
$926$	59.3060	1.94892
$927$	13.6806	0.449330
$928$	16.1735	0.530922
$929$	−57.4679	−1.88546	−0.942730	−	0.333556i	$-0.891751\pi$
$929$	−57.4679	−1.88546	−0.942730	+	0.333556i	$0.891751\pi$
$930$	−18.5234	−0.607405
$931$	8.22848	0.269677
$932$	−3.43776	−0.112607
$933$	7.01074	0.229521
$934$	26.2164	0.857826
$935$	−23.3981	−0.765198
$936$	7.87757	0.257486
$937$	32.7997	1.07152	0.535759	−	0.844371i	$-0.320025\pi$
$937$	32.7997	1.07152	0.535759	+	0.844371i	$0.320025\pi$
$938$	16.3235	0.532981
$939$	38.2103	1.24695
$940$	2.48611	0.0810880
$941$	22.5391	0.734754	0.367377	−	0.930072i	$-0.380256\pi$
$941$	22.5391	0.734754	0.367377	+	0.930072i	$0.380256\pi$
$942$	−20.8224	−0.678430
$943$	20.1302	0.655528
$944$	−49.8848	−1.62361
$945$	4.28046	0.139243
$946$	−8.85046	−0.287753
$947$	−12.1985	−0.396397	−0.198198	−	0.980162i	$-0.563509\pi$
$947$	−12.1985	−0.396397	−0.198198	+	0.980162i	$0.563509\pi$
$948$	−5.37777	−0.174662
$949$	33.4939	1.08726
$950$	−12.6396	−0.410081
$951$	30.9986	1.00520
$952$	9.86545	0.319741
$953$	−57.0405	−1.84772	−0.923861	−	0.382728i	$-0.874985\pi$
$953$	−57.0405	−1.84772	−0.923861	+	0.382728i	$0.874985\pi$
$954$	4.37236	0.141560
$955$	13.5931	0.439864
$956$	−5.72728	−0.185234
$957$	93.7949	3.03196
$958$	23.7943	0.768758
$959$	6.31057	0.203779
$960$	−11.8834	−0.383535
$961$	7.20872	0.232540
$962$	−64.1145	−2.06714
$963$	−8.60067	−0.277153
$964$	7.19737	0.231812
$965$	9.53875	0.307063
$966$	20.9866	0.675232
$967$	26.7899	0.861504	0.430752	−	0.902470i	$-0.358248\pi$
$967$	26.7899	0.861504	0.430752	+	0.902470i	$0.358248\pi$
$968$	62.2874	2.00199
$969$	−62.8464	−2.01892
$970$	−17.7054	−0.568485
$971$	−6.85367	−0.219945	−0.109972	−	0.993935i	$-0.535076\pi$
$971$	−6.85367	−0.219945	−0.109972	+	0.993935i	$0.535076\pi$
$972$	2.93581	0.0941660
$973$	−7.03166	−0.225425
$974$	38.5562	1.23542
$975$	−7.56791	−0.242367
$976$	−4.23021	−0.135406
$977$	−8.22637	−0.263185	−0.131592	−	0.991304i	$-0.542009\pi$
$977$	−8.22637	−0.263185	−0.131592	+	0.991304i	$0.542009\pi$
$978$	−57.3500	−1.83385
$979$	25.3562	0.810389
$980$	0.359523	0.0114845
$981$	2.23151	0.0712467
$982$	−11.4810	−0.366374
$983$	−15.7839	−0.503428	−0.251714	−	0.967802i	$-0.580994\pi$
$983$	−15.7839	−0.503428	−0.251714	+	0.967802i	$0.580994\pi$
$984$	−14.1304	−0.450460
$985$	−27.2605	−0.868592
$986$	−48.3787	−1.54069
$987$	−13.4903	−0.429400
$988$	11.4761	0.365104
$989$	−6.75167	−0.214691
$990$	7.39806	0.235126
$991$	54.2686	1.72390	0.861949	−	0.506995i	$-0.169244\pi$
$991$	54.2686	1.72390	0.861949	+	0.506995i	$0.169244\pi$
$992$	−12.4273	−0.394569
$993$	43.4827	1.37988
$994$	10.2373	0.324709
$995$	0.826906	0.0262147
$996$	−11.3973	−0.361136
$997$	11.4561	0.362818	0.181409	−	0.983408i	$-0.441934\pi$
$997$	11.4561	0.362818	0.181409	+	0.983408i	$0.441934\pi$
$998$	−63.6182	−2.01380
$999$	46.0559	1.45715

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.o.1.18	✓	73

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.o.1.18	✓	73	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)

\(f(q)\)	\(=\)	\(q-1.53607 q^{2} -1.95086 q^{3} +0.359523 q^{4} +1.00000 q^{5} +2.99667 q^{6} +1.00000 q^{7} +2.51989 q^{8} +0.805862 q^{9} +O(q^{10})\)	\(q-1.53607 q^{2} -1.95086 q^{3} +0.359523 q^{4} +1.00000 q^{5} +2.99667 q^{6} +1.00000 q^{7} +2.51989 q^{8} +0.805862 q^{9} -1.53607 q^{10} -5.97648 q^{11} -0.701380 q^{12} +3.87926 q^{13} -1.53607 q^{14} -1.95086 q^{15} -4.58979 q^{16} +3.91503 q^{17} -1.23786 q^{18} +8.22848 q^{19} +0.359523 q^{20} -1.95086 q^{21} +9.18031 q^{22} +7.00330 q^{23} -4.91597 q^{24} +1.00000 q^{25} -5.95884 q^{26} +4.28046 q^{27} +0.359523 q^{28} +8.04465 q^{29} +2.99667 q^{30} -6.18132 q^{31} +2.01047 q^{32} +11.6593 q^{33} -6.01377 q^{34} +1.00000 q^{35} +0.289726 q^{36} +10.7596 q^{37} -12.6396 q^{38} -7.56791 q^{39} +2.51989 q^{40} +2.87438 q^{41} +2.99667 q^{42} -0.964070 q^{43} -2.14868 q^{44} +0.805862 q^{45} -10.7576 q^{46} +6.91503 q^{47} +8.95404 q^{48} +1.00000 q^{49} -1.53607 q^{50} -7.63767 q^{51} +1.39468 q^{52} -3.53218 q^{53} -6.57510 q^{54} -5.97648 q^{55} +2.51989 q^{56} -16.0526 q^{57} -12.3572 q^{58} +10.8686 q^{59} -0.701380 q^{60} +0.921656 q^{61} +9.49497 q^{62} +0.805862 q^{63} +6.09135 q^{64} +3.87926 q^{65} -17.9095 q^{66} -10.6268 q^{67} +1.40754 q^{68} -13.6625 q^{69} -1.53607 q^{70} -6.66462 q^{71} +2.03069 q^{72} +8.63409 q^{73} -16.5275 q^{74} -1.95086 q^{75} +2.95833 q^{76} -5.97648 q^{77} +11.6249 q^{78} +7.66741 q^{79} -4.58979 q^{80} -10.7682 q^{81} -4.41527 q^{82} +16.2498 q^{83} -0.701380 q^{84} +3.91503 q^{85} +1.48088 q^{86} -15.6940 q^{87} -15.0601 q^{88} -4.24267 q^{89} -1.23786 q^{90} +3.87926 q^{91} +2.51785 q^{92} +12.0589 q^{93} -10.6220 q^{94} +8.22848 q^{95} -3.92214 q^{96} +11.5264 q^{97} -1.53607 q^{98} -4.81622 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9}+O(q^{10}) \) 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9	\( 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9} + 7 q^{10} + 27 q^{11} + 21 q^{12} + 21 q^{13} + 7 q^{14} + 14 q^{15} + 135 q^{16} + 23 q^{17} + 41 q^{18} + 26 q^{19} + 95 q^{20} + 14 q^{21} + 48 q^{22} + 16 q^{23} - q^{24} + 73 q^{25} + 7 q^{26} + 44 q^{27} + 95 q^{28} + 66 q^{29} - q^{30} + 23 q^{31} + 3 q^{32} + 77 q^{33} + 29 q^{34} + 73 q^{35} + 142 q^{36} + 66 q^{37} - 12 q^{38} + 53 q^{39} + 18 q^{40} + 50 q^{41} - q^{42} + 43 q^{43} + 37 q^{44} + 111 q^{45} + 65 q^{46} + 28 q^{47} - 20 q^{48} + 73 q^{49} + 7 q^{50} + 71 q^{51} + 29 q^{52} - 7 q^{53} - 16 q^{54} + 27 q^{55} + 18 q^{56} + 33 q^{57} + 48 q^{58} + 16 q^{59} + 21 q^{60} + 42 q^{61} - 3 q^{62} + 111 q^{63} + 216 q^{64} + 21 q^{65} - 53 q^{66} + 48 q^{67} + 13 q^{68} + 73 q^{69} + 7 q^{70} + 68 q^{71} + 18 q^{72} + 65 q^{73} + 4 q^{74} + 14 q^{75} + 37 q^{76} + 27 q^{77} + 60 q^{78} + 116 q^{79} + 135 q^{80} + 177 q^{81} + 20 q^{82} + 40 q^{83} + 21 q^{84} + 23 q^{85} + 35 q^{86} - 14 q^{87} + 47 q^{88} + 59 q^{89} + 41 q^{90} + 21 q^{91} + 3 q^{92} + 37 q^{93} - 11 q^{94} + 26 q^{95} - 23 q^{96} + 70 q^{97} + 7 q^{98} + 49 q^{99}+O(q^{100}) \) 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9 + 7 * q^10 + 27 * q^11 + 21 * q^12 + 21 * q^13 + 7 * q^14 + 14 * q^15 + 135 * q^16 + 23 * q^17 + 41 * q^18 + 26 * q^19 + 95 * q^20 + 14 * q^21 + 48 * q^22 + 16 * q^23 - q^24 + 73 * q^25 + 7 * q^26 + 44 * q^27 + 95 * q^28 + 66 * q^29 - q^30 + 23 * q^31 + 3 * q^32 + 77 * q^33 + 29 * q^34 + 73 * q^35 + 142 * q^36 + 66 * q^37 - 12 * q^38 + 53 * q^39 + 18 * q^40 + 50 * q^41 - q^42 + 43 * q^43 + 37 * q^44 + 111 * q^45 + 65 * q^46 + 28 * q^47 - 20 * q^48 + 73 * q^49 + 7 * q^50 + 71 * q^51 + 29 * q^52 - 7 * q^53 - 16 * q^54 + 27 * q^55 + 18 * q^56 + 33 * q^57 + 48 * q^58 + 16 * q^59 + 21 * q^60 + 42 * q^61 - 3 * q^62 + 111 * q^63 + 216 * q^64 + 21 * q^65 - 53 * q^66 + 48 * q^67 + 13 * q^68 + 73 * q^69 + 7 * q^70 + 68 * q^71 + 18 * q^72 + 65 * q^73 + 4 * q^74 + 14 * q^75 + 37 * q^76 + 27 * q^77 + 60 * q^78 + 116 * q^79 + 135 * q^80 + 177 * q^81 + 20 * q^82 + 40 * q^83 + 21 * q^84 + 23 * q^85 + 35 * q^86 - 14 * q^87 + 47 * q^88 + 59 * q^89 + 41 * q^90 + 21 * q^91 + 3 * q^92 + 37 * q^93 - 11 * q^94 + 26 * q^95 - 23 * q^96 + 70 * q^97 + 7 * q^98 + 49 * q^99

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