LMFDB - Embedded newform 8017.2.a.b.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8017,2,Mod(1,8017)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8017, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8017.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:	$64.0160673005$
Analytic rank:	$0$
Dimension:	$340$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	8017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.60921 q^{2} +3.19659 q^{3} +4.80800 q^{4} -1.37562 q^{5} -8.34060 q^{6} -1.63991 q^{7} -7.32666 q^{8} +7.21821 q^{9} +O(q^{10})$	\(q-2.60921 q^{2} +3.19659 q^{3} +4.80800 q^{4} -1.37562 q^{5} -8.34060 q^{6} -1.63991 q^{7} -7.32666 q^{8} +7.21821 q^{9} +3.58928 q^{10} -0.869800 q^{11} +15.3692 q^{12} +1.56417 q^{13} +4.27887 q^{14} -4.39729 q^{15} +9.50083 q^{16} -1.88610 q^{17} -18.8339 q^{18} -2.18773 q^{19} -6.61396 q^{20} -5.24212 q^{21} +2.26949 q^{22} +6.17517 q^{23} -23.4204 q^{24} -3.10768 q^{25} -4.08125 q^{26} +13.4839 q^{27} -7.88467 q^{28} +6.67262 q^{29} +11.4735 q^{30} +0.462097 q^{31} -10.1364 q^{32} -2.78040 q^{33} +4.92125 q^{34} +2.25589 q^{35} +34.7051 q^{36} -11.3605 q^{37} +5.70826 q^{38} +5.00001 q^{39} +10.0787 q^{40} +9.21621 q^{41} +13.6778 q^{42} -3.34427 q^{43} -4.18200 q^{44} -9.92949 q^{45} -16.1123 q^{46} -3.05490 q^{47} +30.3703 q^{48} -4.31070 q^{49} +8.10859 q^{50} -6.02911 q^{51} +7.52051 q^{52} -8.35510 q^{53} -35.1824 q^{54} +1.19651 q^{55} +12.0151 q^{56} -6.99328 q^{57} -17.4103 q^{58} -7.22685 q^{59} -21.1421 q^{60} +13.0178 q^{61} -1.20571 q^{62} -11.8372 q^{63} +7.44632 q^{64} -2.15170 q^{65} +7.25465 q^{66} +15.2123 q^{67} -9.06838 q^{68} +19.7395 q^{69} -5.88609 q^{70} +4.09724 q^{71} -52.8854 q^{72} +9.23128 q^{73} +29.6421 q^{74} -9.93398 q^{75} -10.5186 q^{76} +1.42639 q^{77} -13.0461 q^{78} +8.34456 q^{79} -13.0695 q^{80} +21.4479 q^{81} -24.0471 q^{82} +10.9545 q^{83} -25.2041 q^{84} +2.59456 q^{85} +8.72590 q^{86} +21.3296 q^{87} +6.37273 q^{88} -2.35600 q^{89} +25.9082 q^{90} -2.56509 q^{91} +29.6902 q^{92} +1.47713 q^{93} +7.97089 q^{94} +3.00948 q^{95} -32.4019 q^{96} +0.408306 q^{97} +11.2475 q^{98} -6.27840 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 340 q + 20 q^{2} + 44 q^{3} + 350 q^{4} + 53 q^{5} + 34 q^{6} + 81 q^{7} + 54 q^{8} + 360 q^{9}+O(q^{10}) $ 340 * q + 20 * q^2 + 44 * q^3 + 350 * q^4 + 53 * q^5 + 34 * q^6 + 81 * q^7 + 54 * q^8 + 360 * q^9	\( 340 q + 20 q^{2} + 44 q^{3} + 350 q^{4} + 53 q^{5} + 34 q^{6} + 81 q^{7} + 54 q^{8} + 360 q^{9} + 36 q^{10} + 70 q^{11} + 92 q^{12} + 45 q^{13} + 44 q^{14} + 71 q^{15} + 362 q^{16} + 162 q^{17} + 41 q^{18} + 49 q^{19} + 147 q^{20} + 41 q^{21} + 32 q^{22} + 244 q^{23} + 85 q^{24} + 355 q^{25} + 83 q^{26} + 155 q^{27} + 129 q^{28} + 91 q^{29} + 51 q^{30} + 65 q^{31} + 113 q^{32} + 73 q^{33} + 26 q^{34} + 200 q^{35} + 380 q^{36} + 28 q^{37} + 171 q^{38} + 117 q^{39} + 95 q^{40} + 115 q^{41} + 42 q^{42} + 98 q^{43} + 139 q^{44} + 127 q^{45} + 29 q^{46} + 312 q^{47} + 168 q^{48} + 365 q^{49} + 64 q^{50} + 72 q^{51} + 100 q^{52} + 154 q^{53} + 89 q^{54} + 161 q^{55} + 89 q^{56} + 82 q^{57} + 29 q^{58} + 149 q^{59} + 93 q^{60} + 70 q^{61} + 257 q^{62} + 376 q^{63} + 346 q^{64} + 125 q^{65} + 48 q^{66} + 65 q^{67} + 464 q^{68} + 58 q^{69} - 54 q^{70} + 216 q^{71} + 90 q^{72} + 93 q^{73} + 147 q^{74} + 162 q^{75} + 64 q^{76} + 190 q^{77} + 12 q^{78} + 139 q^{79} + 274 q^{80} + 376 q^{81} + 59 q^{82} + 402 q^{83} + 10 q^{84} + 32 q^{85} + 53 q^{86} + 364 q^{87} + 42 q^{88} + 114 q^{89} + 126 q^{90} + 43 q^{91} + 422 q^{92} + 47 q^{93} + 2 q^{94} + 347 q^{95} + 146 q^{96} + 47 q^{97} + 96 q^{98} + 129 q^{99}+O(q^{100}) \) 340 * q + 20 * q^2 + 44 * q^3 + 350 * q^4 + 53 * q^5 + 34 * q^6 + 81 * q^7 + 54 * q^8 + 360 * q^9 + 36 * q^10 + 70 * q^11 + 92 * q^12 + 45 * q^13 + 44 * q^14 + 71 * q^15 + 362 * q^16 + 162 * q^17 + 41 * q^18 + 49 * q^19 + 147 * q^20 + 41 * q^21 + 32 * q^22 + 244 * q^23 + 85 * q^24 + 355 * q^25 + 83 * q^26 + 155 * q^27 + 129 * q^28 + 91 * q^29 + 51 * q^30 + 65 * q^31 + 113 * q^32 + 73 * q^33 + 26 * q^34 + 200 * q^35 + 380 * q^36 + 28 * q^37 + 171 * q^38 + 117 * q^39 + 95 * q^40 + 115 * q^41 + 42 * q^42 + 98 * q^43 + 139 * q^44 + 127 * q^45 + 29 * q^46 + 312 * q^47 + 168 * q^48 + 365 * q^49 + 64 * q^50 + 72 * q^51 + 100 * q^52 + 154 * q^53 + 89 * q^54 + 161 * q^55 + 89 * q^56 + 82 * q^57 + 29 * q^58 + 149 * q^59 + 93 * q^60 + 70 * q^61 + 257 * q^62 + 376 * q^63 + 346 * q^64 + 125 * q^65 + 48 * q^66 + 65 * q^67 + 464 * q^68 + 58 * q^69 - 54 * q^70 + 216 * q^71 + 90 * q^72 + 93 * q^73 + 147 * q^74 + 162 * q^75 + 64 * q^76 + 190 * q^77 + 12 * q^78 + 139 * q^79 + 274 * q^80 + 376 * q^81 + 59 * q^82 + 402 * q^83 + 10 * q^84 + 32 * q^85 + 53 * q^86 + 364 * q^87 + 42 * q^88 + 114 * q^89 + 126 * q^90 + 43 * q^91 + 422 * q^92 + 47 * q^93 + 2 * q^94 + 347 * q^95 + 146 * q^96 + 47 * q^97 + 96 * q^98 + 129 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.60921	−1.84499	−0.922496	−	0.386006i	$-0.873854\pi$
$2$	−2.60921	−1.84499	−0.922496	+	0.386006i	$0.873854\pi$
$3$	3.19659	1.84555	0.922777	−	0.385334i	$-0.125914\pi$
$3$	3.19659	1.84555	0.922777	+	0.385334i	$0.125914\pi$
$4$	4.80800	2.40400
$5$	−1.37562	−0.615195	−0.307597	−	0.951517i	$-0.599525\pi$
$5$	−1.37562	−0.615195	−0.307597	+	0.951517i	$0.599525\pi$
$6$	−8.34060	−3.40503
$7$	−1.63991	−0.619827	−0.309914	−	0.950765i	$-0.600300\pi$
$7$	−1.63991	−0.619827	−0.309914	+	0.950765i	$0.600300\pi$
$8$	−7.32666	−2.59037
$9$	7.21821	2.40607
$10$	3.58928	1.13503
$11$	−0.869800	−0.262255	−0.131127	−	0.991366i	$-0.541860\pi$
$11$	−0.869800	−0.262255	−0.131127	+	0.991366i	$0.541860\pi$
$12$	15.3692	4.43671
$13$	1.56417	0.433822	0.216911	−	0.976191i	$-0.430402\pi$
$13$	1.56417	0.433822	0.216911	+	0.976191i	$0.430402\pi$
$14$	4.27887	1.14358
$15$	−4.39729	−1.13538
$16$	9.50083	2.37521
$17$	−1.88610	−0.457448	−0.228724	−	0.973491i	$-0.573455\pi$
$17$	−1.88610	−0.457448	−0.228724	+	0.973491i	$0.573455\pi$
$18$	−18.8339	−4.43918
$19$	−2.18773	−0.501900	−0.250950	−	0.968000i	$-0.580743\pi$
$19$	−2.18773	−0.501900	−0.250950	+	0.968000i	$0.580743\pi$
$20$	−6.61396	−1.47893
$21$	−5.24212	−1.14392
$22$	2.26949	0.483858
$23$	6.17517	1.28761	0.643805	−	0.765189i	$-0.277355\pi$
$23$	6.17517	1.28761	0.643805	+	0.765189i	$0.277355\pi$
$24$	−23.4204	−4.78066
$25$	−3.10768	−0.621535
$26$	−4.08125	−0.800398
$27$	13.4839	2.59498
$28$	−7.88467	−1.49006
$29$	6.67262	1.23907	0.619537	−	0.784967i	$-0.287320\pi$
$29$	6.67262	1.23907	0.619537	+	0.784967i	$0.287320\pi$
$30$	11.4735	2.09476
$31$	0.462097	0.0829950	0.0414975	−	0.999139i	$-0.486787\pi$
$31$	0.462097	0.0829950	0.0414975	+	0.999139i	$0.486787\pi$
$32$	−10.1364	−1.79188
$33$	−2.78040	−0.484005
$34$	4.92125	0.843988
$35$	2.25589	0.381314
$36$	34.7051	5.78419
$37$	−11.3605	−1.86766	−0.933830	−	0.357717i	$-0.883555\pi$
$37$	−11.3605	−1.86766	−0.933830	+	0.357717i	$0.883555\pi$
$38$	5.70826	0.926001
$39$	5.00001	0.800642
$40$	10.0787	1.59358
$41$	9.21621	1.43933	0.719665	−	0.694322i	$-0.244295\pi$
$41$	9.21621	1.43933	0.719665	+	0.694322i	$0.244295\pi$
$42$	13.6778	2.11053
$43$	−3.34427	−0.509996	−0.254998	−	0.966942i	$-0.582075\pi$
$43$	−3.34427	−0.509996	−0.254998	+	0.966942i	$0.582075\pi$
$44$	−4.18200	−0.630459
$45$	−9.92949	−1.48020
$46$	−16.1123	−2.37563
$47$	−3.05490	−0.445603	−0.222802	−	0.974864i	$-0.571520\pi$
$47$	−3.05490	−0.445603	−0.222802	+	0.974864i	$0.571520\pi$
$48$	30.3703	4.38358
$49$	−4.31070	−0.615814
$50$	8.10859	1.14673
$51$	−6.02911	−0.844244
$52$	7.52051	1.04291
$53$	−8.35510	−1.14766	−0.573830	−	0.818974i	$-0.694543\pi$
$53$	−8.35510	−1.14766	−0.573830	+	0.818974i	$0.694543\pi$
$54$	−35.1824	−4.78772
$55$	1.19651	0.161338
$56$	12.0151	1.60558
$57$	−6.99328	−0.926283
$58$	−17.4103	−2.28608
$59$	−7.22685	−0.940856	−0.470428	−	0.882438i	$-0.655900\pi$
$59$	−7.22685	−0.940856	−0.470428	+	0.882438i	$0.655900\pi$
$60$	−21.1421	−2.72944
$61$	13.0178	1.66675	0.833376	−	0.552706i	$-0.186405\pi$
$61$	13.0178	1.66675	0.833376	+	0.552706i	$0.186405\pi$
$62$	−1.20571	−0.153125
$63$	−11.8372	−1.49135
$64$	7.44632	0.930790
$65$	−2.15170	−0.266885
$66$	7.25465	0.892986
$67$	15.2123	1.85848	0.929239	−	0.369480i	$-0.120464\pi$
$67$	15.2123	1.85848	0.929239	+	0.369480i	$0.120464\pi$
$68$	−9.06838	−1.09970
$69$	19.7395	2.37636
$70$	−5.88609	−0.703522
$71$	4.09724	0.486253	0.243127	−	0.969995i	$-0.421827\pi$
$71$	4.09724	0.486253	0.243127	+	0.969995i	$0.421827\pi$
$72$	−52.8854	−6.23260
$73$	9.23128	1.08044	0.540220	−	0.841524i	$-0.318341\pi$
$73$	9.23128	1.08044	0.540220	+	0.841524i	$0.318341\pi$
$74$	29.6421	3.44582
$75$	−9.93398	−1.14708
$76$	−10.5186	−1.20657
$77$	1.42639	0.162552
$78$	−13.0461	−1.47718
$79$	8.34456	0.938836	0.469418	−	0.882976i	$-0.344464\pi$
$79$	8.34456	0.938836	0.469418	+	0.882976i	$0.344464\pi$
$80$	−13.0695	−1.46122
$81$	21.4479	2.38310
$82$	−24.0471	−2.65555
$83$	10.9545	1.20241	0.601206	−	0.799094i	$-0.294687\pi$
$83$	10.9545	1.20241	0.601206	+	0.799094i	$0.294687\pi$
$84$	−25.2041	−2.74999
$85$	2.59456	0.281419
$86$	8.72590	0.940938
$87$	21.3296	2.28678
$88$	6.37273	0.679335
$89$	−2.35600	−0.249736	−0.124868	−	0.992173i	$-0.539851\pi$
$89$	−2.35600	−0.249736	−0.124868	+	0.992173i	$0.539851\pi$
$90$	25.9082	2.73096
$91$	−2.56509	−0.268895
$92$	29.6902	3.09541
$93$	1.47713	0.153172
$94$	7.97089	0.822135
$95$	3.00948	0.308766
$96$	−32.4019	−3.30700
$97$	0.408306	0.0414572	0.0207286	−	0.999785i	$-0.493401\pi$
$97$	0.408306	0.0414572	0.0207286	+	0.999785i	$0.493401\pi$
$98$	11.2475	1.13617
$99$	−6.27840	−0.631003
$100$	−14.9417	−1.49417
$101$	4.99852	0.497371	0.248686	−	0.968584i	$-0.420001\pi$
$101$	4.99852	0.497371	0.248686	+	0.968584i	$0.420001\pi$
$102$	15.7312	1.55762
$103$	11.9542	1.17788	0.588939	−	0.808177i	$-0.299546\pi$
$103$	11.9542	1.17788	0.588939	+	0.808177i	$0.299546\pi$
$104$	−11.4601	−1.12376
$105$	7.21115	0.703736
$106$	21.8002	2.11743
$107$	6.43730	0.622318	0.311159	−	0.950358i	$-0.399283\pi$
$107$	6.43730	0.622318	0.311159	+	0.950358i	$0.399283\pi$
$108$	64.8306	6.23832
$109$	−12.2595	−1.17424	−0.587122	−	0.809498i	$-0.699739\pi$
$109$	−12.2595	−1.17424	−0.587122	+	0.809498i	$0.699739\pi$
$110$	−3.12196	−0.297667
$111$	−36.3150	−3.44687
$112$	−15.5805	−1.47222
$113$	1.95537	0.183945	0.0919727	−	0.995762i	$-0.470683\pi$
$113$	1.95537	0.183945	0.0919727	+	0.995762i	$0.470683\pi$
$114$	18.2470	1.70899
$115$	−8.49466	−0.792131
$116$	32.0819	2.97873
$117$	11.2905	1.04381
$118$	18.8564	1.73587
$119$	3.09304	0.283538
$120$	32.2174	2.94104
$121$	−10.2434	−0.931223
$122$	−33.9661	−3.07515
$123$	29.4605	2.65636
$124$	2.22176	0.199520
$125$	11.1531	0.997560
$126$	30.8858	2.75153
$127$	16.9310	1.50238	0.751190	−	0.660086i	$-0.229480\pi$
$127$	16.9310	1.50238	0.751190	+	0.660086i	$0.229480\pi$
$128$	0.843721	0.0745751
$129$	−10.6903	−0.941225
$130$	5.61423	0.492401
$131$	1.21924	0.106526	0.0532628	−	0.998581i	$-0.483038\pi$
$131$	1.21924	0.106526	0.0532628	+	0.998581i	$0.483038\pi$
$132$	−13.3681	−1.16355
$133$	3.58768	0.311091
$134$	−39.6921	−3.42888
$135$	−18.5487	−1.59642
$136$	13.8189	1.18496
$137$	11.8043	1.00851	0.504257	−	0.863554i	$-0.331767\pi$
$137$	11.8043	1.00851	0.504257	+	0.863554i	$0.331767\pi$
$138$	−51.5046	−4.38436
$139$	−21.2340	−1.80104	−0.900522	−	0.434810i	$-0.856815\pi$
$139$	−21.2340	−1.80104	−0.900522	+	0.434810i	$0.856815\pi$
$140$	10.8463	0.916679
$141$	−9.76528	−0.822385
$142$	−10.6906	−0.897133
$143$	−1.36051	−0.113772
$144$	68.5790	5.71492
$145$	−9.17897	−0.762272
$146$	−24.0864	−1.99340
$147$	−13.7796	−1.13652
$148$	−54.6214	−4.48985
$149$	−0.0436279	−0.00357413	−0.00178707	−	0.999998i	$-0.500569\pi$
$149$	−0.0436279	−0.00357413	−0.00178707	+	0.999998i	$0.500569\pi$
$150$	25.9199	2.11635
$151$	−11.4850	−0.934638	−0.467319	−	0.884089i	$-0.654780\pi$
$151$	−11.4850	−0.934638	−0.467319	+	0.884089i	$0.654780\pi$
$152$	16.0288	1.30010
$153$	−13.6143	−1.10065
$154$	−3.72176	−0.299908
$155$	−0.635668	−0.0510581
$156$	24.0400	1.92474
$157$	8.71661	0.695661	0.347831	−	0.937557i	$-0.386918\pi$
$157$	8.71661	0.695661	0.347831	+	0.937557i	$0.386918\pi$
$158$	−21.7727	−1.73215
$159$	−26.7078	−2.11807
$160$	13.9438	1.10235
$161$	−10.1267	−0.798096
$162$	−55.9622	−4.39681
$163$	−14.7921	−1.15861	−0.579304	−	0.815112i	$-0.696675\pi$
$163$	−14.7921	−1.15861	−0.579304	+	0.815112i	$0.696675\pi$
$164$	44.3115	3.46015
$165$	3.82476	0.297757
$166$	−28.5826	−2.21844
$167$	−22.7818	−1.76291	−0.881455	−	0.472268i	$-0.843436\pi$
$167$	−22.7818	−1.76291	−0.881455	+	0.472268i	$0.843436\pi$
$168$	38.4072	2.96318
$169$	−10.5534	−0.811799
$170$	−6.76976	−0.519217
$171$	−15.7915	−1.20761
$172$	−16.0792	−1.22603
$173$	22.6778	1.72416	0.862081	−	0.506771i	$-0.169161\pi$
$173$	22.6778	1.72416	0.862081	+	0.506771i	$0.169161\pi$
$174$	−55.6536	−4.21909
$175$	5.09631	0.385245
$176$	−8.26383	−0.622909
$177$	−23.1013	−1.73640
$178$	6.14731	0.460760
$179$	7.77476	0.581113	0.290556	−	0.956858i	$-0.406160\pi$
$179$	7.77476	0.581113	0.290556	+	0.956858i	$0.406160\pi$
$180$	−47.7410	−3.55840
$181$	−7.02304	−0.522018	−0.261009	−	0.965336i	$-0.584055\pi$
$181$	−7.02304	−0.522018	−0.261009	+	0.965336i	$0.584055\pi$
$182$	6.69287	0.496109
$183$	41.6125	3.07608
$184$	−45.2433	−3.33538
$185$	15.6277	1.14897
$186$	−3.85416	−0.282601
$187$	1.64053	0.119968
$188$	−14.6880	−1.07123
$189$	−22.1124	−1.60844
$190$	−7.85237	−0.569671
$191$	21.3913	1.54782	0.773911	−	0.633295i	$-0.218298\pi$
$191$	21.3913	1.54782	0.773911	+	0.633295i	$0.218298\pi$
$192$	23.8029	1.71782
$193$	4.74115	0.341276	0.170638	−	0.985334i	$-0.445417\pi$
$193$	4.74115	0.341276	0.170638	+	0.985334i	$0.445417\pi$
$194$	−1.06536	−0.0764882
$195$	−6.87809	−0.492551
$196$	−20.7258	−1.48042
$197$	25.9294	1.84740	0.923698	−	0.383122i	$-0.125151\pi$
$197$	25.9294	1.84740	0.923698	+	0.383122i	$0.125151\pi$
$198$	16.3817	1.16420
$199$	−11.4124	−0.809001	−0.404500	−	0.914538i	$-0.632555\pi$
$199$	−11.4124	−0.809001	−0.404500	+	0.914538i	$0.632555\pi$
$200$	22.7689	1.61000
$201$	48.6275	3.42992
$202$	−13.0422	−0.917647
$203$	−10.9425	−0.768012
$204$	−28.9879	−2.02956
$205$	−12.6780	−0.885468
$206$	−31.1910	−2.17318
$207$	44.5736	3.09808
$208$	14.8609	1.03042
$209$	1.90289	0.131625
$210$	−18.8154	−1.29839
$211$	18.1628	1.25038	0.625191	−	0.780472i	$-0.285021\pi$
$211$	18.1628	1.25038	0.625191	+	0.780472i	$0.285021\pi$
$212$	−40.1713	−2.75897
$213$	13.0972	0.897406
$214$	−16.7963	−1.14817
$215$	4.60043	0.313747
$216$	−98.7920	−6.72194
$217$	−0.757796	−0.0514425
$218$	31.9876	2.16647
$219$	29.5086	1.99401
$220$	5.75282	0.387855
$221$	−2.95018	−0.198451
$222$	94.7536	6.35945
$223$	4.66773	0.312575	0.156287	−	0.987712i	$-0.450047\pi$
$223$	4.66773	0.312575	0.156287	+	0.987712i	$0.450047\pi$
$224$	16.6227	1.11065
$225$	−22.4319	−1.49546
$226$	−5.10197	−0.339378
$227$	13.5758	0.901056	0.450528	−	0.892762i	$-0.351236\pi$
$227$	13.5758	0.901056	0.450528	+	0.892762i	$0.351236\pi$
$228$	−33.6237	−2.22678
$229$	6.45960	0.426862	0.213431	−	0.976958i	$-0.431536\pi$
$229$	6.45960	0.426862	0.213431	+	0.976958i	$0.431536\pi$
$230$	22.1644	1.46148
$231$	4.55960	0.299999
$232$	−48.8880	−3.20966
$233$	9.98904	0.654404	0.327202	−	0.944954i	$-0.393894\pi$
$233$	9.98904	0.654404	0.327202	+	0.944954i	$0.393894\pi$
$234$	−29.4593	−1.92581
$235$	4.20238	0.274133
$236$	−34.7467	−2.26182
$237$	26.6742	1.73267
$238$	−8.07040	−0.523126
$239$	−30.3880	−1.96564	−0.982819	−	0.184573i	$-0.940910\pi$
$239$	−30.3880	−1.96564	−0.982819	+	0.184573i	$0.940910\pi$
$240$	−41.7779	−2.69675
$241$	24.7375	1.59348	0.796742	−	0.604320i	$-0.206555\pi$
$241$	24.7375	1.59348	0.796742	+	0.604320i	$0.206555\pi$
$242$	26.7273	1.71810
$243$	28.1086	1.80317
$244$	62.5893	4.00687
$245$	5.92987	0.378846
$246$	−76.8687	−4.90097
$247$	−3.42198	−0.217735
$248$	−3.38563	−0.214987
$249$	35.0171	2.21912
$250$	−29.1007	−1.84049
$251$	5.60625	0.353863	0.176932	−	0.984223i	$-0.443383\pi$
$251$	5.60625	0.353863	0.176932	+	0.984223i	$0.443383\pi$
$252$	−56.9132	−3.58520
$253$	−5.37116	−0.337682
$254$	−44.1765	−2.77188
$255$	8.29375	0.519375
$256$	−17.0941	−1.06838
$257$	−1.13416	−0.0707466	−0.0353733	−	0.999374i	$-0.511262\pi$
$257$	−1.13416	−0.0707466	−0.0353733	+	0.999374i	$0.511262\pi$
$258$	27.8932	1.73655
$259$	18.6302	1.15763
$260$	−10.3453	−0.641591
$261$	48.1644	2.98130
$262$	−3.18126	−0.196539
$263$	2.41236	0.148752	0.0743761	−	0.997230i	$-0.476303\pi$
$263$	2.41236	0.148752	0.0743761	+	0.997230i	$0.476303\pi$
$264$	20.3710	1.25375
$265$	11.4934	0.706035
$266$	−9.36102	−0.573961
$267$	−7.53118	−0.460900
$268$	73.1406	4.46778
$269$	6.50649	0.396708	0.198354	−	0.980130i	$-0.436440\pi$
$269$	6.50649	0.396708	0.198354	+	0.980130i	$0.436440\pi$
$270$	48.3975	2.94538
$271$	−21.0626	−1.27946	−0.639731	−	0.768599i	$-0.720954\pi$
$271$	−21.0626	−1.27946	−0.639731	+	0.768599i	$0.720954\pi$
$272$	−17.9196	−1.08653
$273$	−8.19955	−0.496259
$274$	−30.8001	−1.86070
$275$	2.70306	0.163001
$276$	94.9074	5.71275
$277$	−25.5609	−1.53581	−0.767903	−	0.640566i	$-0.778700\pi$
$277$	−25.5609	−1.53581	−0.767903	+	0.640566i	$0.778700\pi$
$278$	55.4040	3.32291
$279$	3.33551	0.199692
$280$	−16.5281	−0.987744
$281$	4.35319	0.259689	0.129845	−	0.991534i	$-0.458552\pi$
$281$	4.35319	0.259689	0.129845	+	0.991534i	$0.458552\pi$
$282$	25.4797	1.51729
$283$	17.1764	1.02103	0.510515	−	0.859869i	$-0.329455\pi$
$283$	17.1764	1.02103	0.510515	+	0.859869i	$0.329455\pi$
$284$	19.6995	1.16895
$285$	9.62008	0.569844
$286$	3.54987	0.209908
$287$	−15.1137	−0.892136
$288$	−73.1665	−4.31138
$289$	−13.4426	−0.790742
$290$	23.9499	1.40639
$291$	1.30519	0.0765114
$292$	44.3840	2.59737
$293$	6.22679	0.363773	0.181887	−	0.983320i	$-0.441780\pi$
$293$	6.22679	0.363773	0.181887	+	0.983320i	$0.441780\pi$
$294$	35.9538	2.09687
$295$	9.94138	0.578809
$296$	83.2348	4.83792
$297$	−11.7283	−0.680545
$298$	0.113834	0.00659425
$299$	9.65899	0.558594
$300$	−47.7625	−2.75757
$301$	5.48429	0.316109
$302$	29.9669	1.72440
$303$	15.9782	0.917926
$304$	−20.7853	−1.19212
$305$	−17.9074	−1.02538
$306$	35.5226	2.03069
$307$	6.64753	0.379395	0.189697	−	0.981843i	$-0.439249\pi$
$307$	6.64753	0.379395	0.189697	+	0.981843i	$0.439249\pi$
$308$	6.85809	0.390776
$309$	38.2126	2.17384
$310$	1.65859	0.0942018
$311$	−1.80209	−0.102187	−0.0510936	−	0.998694i	$-0.516271\pi$
$311$	−1.80209	−0.102187	−0.0510936	+	0.998694i	$0.516271\pi$
$312$	−36.6334	−2.07396
$313$	18.8830	1.06733	0.533664	−	0.845696i	$-0.320815\pi$
$313$	18.8830	1.06733	0.533664	+	0.845696i	$0.320815\pi$
$314$	−22.7435	−1.28349
$315$	16.2835	0.917469
$316$	40.1206	2.25696
$317$	22.6444	1.27183	0.635917	−	0.771757i	$-0.280622\pi$
$317$	22.6444	1.27183	0.635917	+	0.771757i	$0.280622\pi$
$318$	69.6865	3.90782
$319$	−5.80384	−0.324953
$320$	−10.2433	−0.572617
$321$	20.5774	1.14852
$322$	26.4227	1.47248
$323$	4.12629	0.229593
$324$	103.122	5.72897
$325$	−4.86093	−0.269636
$326$	38.5958	2.13762
$327$	−39.1885	−2.16713
$328$	−67.5240	−3.72839
$329$	5.00976	0.276197
$330$	−9.97962	−0.549360
$331$	−20.2263	−1.11174	−0.555869	−	0.831270i	$-0.687614\pi$
$331$	−20.2263	−1.11174	−0.555869	+	0.831270i	$0.687614\pi$
$332$	52.6692	2.89060
$333$	−82.0027	−4.49372
$334$	59.4426	3.25256
$335$	−20.9263	−1.14333
$336$	−49.8045	−2.71706
$337$	7.27570	0.396333	0.198166	−	0.980168i	$-0.436501\pi$
$337$	7.27570	0.396333	0.198166	+	0.980168i	$0.436501\pi$
$338$	27.5360	1.49776
$339$	6.25051	0.339481
$340$	12.4746	0.676532
$341$	−0.401932	−0.0217658
$342$	41.2034	2.22802
$343$	18.5485	1.00153
$344$	24.5023	1.32108
$345$	−27.1540	−1.46192
$346$	−59.1712	−3.18107
$347$	−31.6373	−1.69838	−0.849190	−	0.528087i	$-0.822910\pi$
$347$	−31.6373	−1.69838	−0.849190	+	0.528087i	$0.822910\pi$
$348$	102.553	5.49741
$349$	−16.7531	−0.896772	−0.448386	−	0.893840i	$-0.648001\pi$
$349$	−16.7531	−0.896772	−0.448386	+	0.893840i	$0.648001\pi$
$350$	−13.2974	−0.710773
$351$	21.0911	1.12576
$352$	8.81663	0.469928
$353$	−13.3995	−0.713184	−0.356592	−	0.934260i	$-0.616061\pi$
$353$	−13.3995	−0.713184	−0.356592	+	0.934260i	$0.616061\pi$
$354$	60.2762	3.20365
$355$	−5.63623	−0.299140
$356$	−11.3276	−0.600364
$357$	9.88719	0.523286
$358$	−20.2860	−1.07215
$359$	16.3982	0.865464	0.432732	−	0.901523i	$-0.357550\pi$
$359$	16.3982	0.865464	0.432732	+	0.901523i	$0.357550\pi$
$360$	72.7500	3.83426
$361$	−14.2138	−0.748097
$362$	18.3246	0.963120
$363$	−32.7441	−1.71862
$364$	−12.3329	−0.646422
$365$	−12.6987	−0.664681
$366$	−108.576	−5.67535
$367$	7.49195	0.391077	0.195538	−	0.980696i	$-0.437355\pi$
$367$	7.49195	0.391077	0.195538	+	0.980696i	$0.437355\pi$
$368$	58.6692	3.05834
$369$	66.5245	3.46313
$370$	−40.7761	−2.11985
$371$	13.7016	0.711351
$372$	7.10206	0.368225
$373$	4.87786	0.252566	0.126283	−	0.991994i	$-0.459695\pi$
$373$	4.87786	0.252566	0.126283	+	0.991994i	$0.459695\pi$
$374$	−4.28050	−0.221340
$375$	35.6518	1.84105
$376$	22.3822	1.15428
$377$	10.4371	0.537537
$378$	57.6959	2.96756
$379$	3.62575	0.186242	0.0931212	−	0.995655i	$-0.470316\pi$
$379$	3.62575	0.186242	0.0931212	+	0.995655i	$0.470316\pi$
$380$	14.4696	0.742273
$381$	54.1214	2.77272
$382$	−55.8145	−2.85572
$383$	23.2507	1.18805	0.594027	−	0.804445i	$-0.297537\pi$
$383$	23.2507	1.18805	0.594027	+	0.804445i	$0.297537\pi$
$384$	2.69703	0.137632
$385$	−1.96217	−0.100001
$386$	−12.3707	−0.629651
$387$	−24.1396	−1.22709
$388$	1.96313	0.0996629
$389$	28.3057	1.43516	0.717579	−	0.696477i	$-0.245250\pi$
$389$	28.3057	1.43516	0.717579	+	0.696477i	$0.245250\pi$
$390$	17.9464	0.908752
$391$	−11.6470	−0.589015
$392$	31.5830	1.59518
$393$	3.89742	0.196599
$394$	−67.6554	−3.40843
$395$	−11.4789	−0.577567
$396$	−30.1865	−1.51693
$397$	−3.31436	−0.166343	−0.0831716	−	0.996535i	$-0.526505\pi$
$397$	−3.31436	−0.166343	−0.0831716	+	0.996535i	$0.526505\pi$
$398$	29.7773	1.49260
$399$	11.4683	0.574135
$400$	−29.5255	−1.47628
$401$	14.8695	0.742550	0.371275	−	0.928523i	$-0.378921\pi$
$401$	14.8695	0.742550	0.371275	+	0.928523i	$0.378921\pi$
$402$	−126.880	−6.32818
$403$	0.722796	0.0360050
$404$	24.0329	1.19568
$405$	−29.5041	−1.46607
$406$	28.5513	1.41698
$407$	9.88139	0.489802
$408$	44.1733	2.18690
$409$	36.0990	1.78498	0.892491	−	0.451064i	$-0.148956\pi$
$409$	36.0990	1.78498	0.892491	+	0.451064i	$0.148956\pi$
$410$	33.0795	1.63368
$411$	37.7337	1.86127
$412$	57.4755	2.83162
$413$	11.8514	0.583168
$414$	−116.302	−5.71594
$415$	−15.0692	−0.739718
$416$	−15.8550	−0.777355
$417$	−67.8765	−3.32392
$418$	−4.96504	−0.242848
$419$	−8.32321	−0.406616	−0.203308	−	0.979115i	$-0.565169\pi$
$419$	−8.32321	−0.406616	−0.203308	+	0.979115i	$0.565169\pi$
$420$	34.6712	1.69178
$421$	−5.03208	−0.245248	−0.122624	−	0.992453i	$-0.539131\pi$
$421$	−5.03208	−0.245248	−0.122624	+	0.992453i	$0.539131\pi$
$422$	−47.3907	−2.30695
$423$	−22.0509	−1.07215
$424$	61.2150	2.97286
$425$	5.86141	0.284320
$426$	−34.1734	−1.65571
$427$	−21.3479	−1.03310
$428$	30.9505	1.49605
$429$	−4.34901	−0.209972
$430$	−12.0035	−0.578860
$431$	32.2892	1.55531	0.777657	−	0.628688i	$-0.216408\pi$
$431$	32.2892	1.55531	0.777657	+	0.628688i	$0.216408\pi$
$432$	128.108	6.16361
$433$	4.87323	0.234193	0.117096	−	0.993121i	$-0.462641\pi$
$433$	4.87323	0.234193	0.117096	+	0.993121i	$0.462641\pi$
$434$	1.97725	0.0949111
$435$	−29.3414	−1.40681
$436$	−58.9435	−2.82288
$437$	−13.5096	−0.646252
$438$	−76.9944	−3.67893
$439$	1.75565	0.0837926	0.0418963	−	0.999122i	$-0.486660\pi$
$439$	1.75565	0.0837926	0.0418963	+	0.999122i	$0.486660\pi$
$440$	−8.76644	−0.417924
$441$	−31.1155	−1.48169
$442$	7.69766	0.366140
$443$	28.1423	1.33708	0.668541	−	0.743675i	$-0.266919\pi$
$443$	28.1423	1.33708	0.668541	+	0.743675i	$0.266919\pi$
$444$	−174.602	−8.28626
$445$	3.24095	0.153636
$446$	−12.1791	−0.576698
$447$	−0.139461	−0.00659626
$448$	−12.2113	−0.576929
$449$	39.1298	1.84665	0.923324	−	0.384021i	$-0.125461\pi$
$449$	39.1298	1.84665	0.923324	+	0.384021i	$0.125461\pi$
$450$	58.5295	2.75911
$451$	−8.01626	−0.377471
$452$	9.40139	0.442204
$453$	−36.7129	−1.72492
$454$	−35.4221	−1.66244
$455$	3.52858	0.165423
$456$	51.2374	2.39941
$457$	9.05599	0.423621	0.211811	−	0.977311i	$-0.432064\pi$
$457$	9.05599	0.423621	0.211811	+	0.977311i	$0.432064\pi$
$458$	−16.8545	−0.787558
$459$	−25.4321	−1.18707
$460$	−40.8423	−1.90428
$461$	−19.5942	−0.912591	−0.456295	−	0.889828i	$-0.650824\pi$
$461$	−19.5942	−0.912591	−0.456295	+	0.889828i	$0.650824\pi$
$462$	−11.8970	−0.553497
$463$	−29.3527	−1.36414	−0.682068	−	0.731289i	$-0.738919\pi$
$463$	−29.3527	−1.36414	−0.682068	+	0.731289i	$0.738919\pi$
$464$	63.3954	2.94306
$465$	−2.03197	−0.0942304
$466$	−26.0636	−1.20737
$467$	−12.6609	−0.585878	−0.292939	−	0.956131i	$-0.594633\pi$
$467$	−12.6609	−0.585878	−0.292939	+	0.956131i	$0.594633\pi$
$468$	54.2846	2.50931
$469$	−24.9468	−1.15193
$470$	−10.9649	−0.505773
$471$	27.8635	1.28388
$472$	52.9487	2.43716
$473$	2.90884	0.133749
$474$	−69.5986	−3.19677
$475$	6.79876	0.311948
$476$	14.8713	0.681626
$477$	−60.3088	−2.76135
$478$	79.2888	3.62659
$479$	6.52300	0.298044	0.149022	−	0.988834i	$-0.452388\pi$
$479$	6.52300	0.298044	0.149022	+	0.988834i	$0.452388\pi$
$480$	44.5726	2.03445
$481$	−17.7698	−0.810232
$482$	−64.5455	−2.93997
$483$	−32.3710	−1.47293
$484$	−49.2505	−2.23866
$485$	−0.561672	−0.0255042
$486$	−73.3413	−3.32683
$487$	−17.8566	−0.809161	−0.404580	−	0.914502i	$-0.632582\pi$
$487$	−17.8566	−0.809161	−0.404580	+	0.914502i	$0.632582\pi$
$488$	−95.3767	−4.31750
$489$	−47.2844	−2.13827
$490$	−15.4723	−0.698968
$491$	26.0856	1.17723	0.588613	−	0.808415i	$-0.299674\pi$
$491$	26.0856	1.17723	0.588613	+	0.808415i	$0.299674\pi$
$492$	141.646	6.38589
$493$	−12.5853	−0.566811
$494$	8.92866	0.401720
$495$	8.63667	0.388190
$496$	4.39030	0.197130
$497$	−6.71910	−0.301393
$498$	−91.3670	−4.09425
$499$	−11.8079	−0.528594	−0.264297	−	0.964441i	$-0.585140\pi$
$499$	−11.8079	−0.528594	−0.264297	+	0.964441i	$0.585140\pi$
$500$	53.6239	2.39813
$501$	−72.8242	−3.25355
$502$	−14.6279	−0.652875
$503$	18.0282	0.803836	0.401918	−	0.915676i	$-0.368344\pi$
$503$	18.0282	0.803836	0.401918	+	0.915676i	$0.368344\pi$
$504$	86.7272	3.86314
$505$	−6.87605	−0.305980
$506$	14.0145	0.623021
$507$	−33.7349	−1.49822
$508$	81.4040	3.61172
$509$	−0.253964	−0.0112567	−0.00562837	−	0.999984i	$-0.501792\pi$
$509$	−0.253964	−0.0112567	−0.00562837	+	0.999984i	$0.501792\pi$
$510$	−21.6402	−0.958242
$511$	−15.1385	−0.669686
$512$	42.9147	1.89658
$513$	−29.4991	−1.30242
$514$	2.95925	0.130527
$515$	−16.4443	−0.724624
$516$	−51.3987	−2.26270
$517$	2.65715	0.116861
$518$	−48.6103	−2.13581
$519$	72.4917	3.18203
$520$	15.7647	0.691330
$521$	28.5443	1.25055	0.625275	−	0.780405i	$-0.284987\pi$
$521$	28.5443	1.25055	0.625275	+	0.780405i	$0.284987\pi$
$522$	−125.671	−5.50047
$523$	19.7890	0.865313	0.432656	−	0.901559i	$-0.357576\pi$
$523$	19.7890	0.865313	0.432656	+	0.901559i	$0.357576\pi$
$524$	5.86211	0.256087
$525$	16.2908	0.710990
$526$	−6.29435	−0.274447
$527$	−0.871563	−0.0379659
$528$	−26.4161	−1.14961
$529$	15.1327	0.657942
$530$	−29.9888	−1.30263
$531$	−52.1649	−2.26376
$532$	17.2495	0.747862
$533$	14.4157	0.624413
$534$	19.6504	0.850358
$535$	−8.85527	−0.382847
$536$	−111.455	−4.81414
$537$	24.8528	1.07248
$538$	−16.9768	−0.731923
$539$	3.74945	0.161500
$540$	−89.1820	−3.83778
$541$	36.2717	1.55944	0.779721	−	0.626127i	$-0.215361\pi$
$541$	36.2717	1.55944	0.779721	+	0.626127i	$0.215361\pi$
$542$	54.9568	2.36060
$543$	−22.4498	−0.963413
$544$	19.1183	0.819690
$545$	16.8643	0.722389
$546$	21.3944	0.915595
$547$	19.1451	0.818583	0.409292	−	0.912404i	$-0.365776\pi$
$547$	19.1451	0.818583	0.409292	+	0.912404i	$0.365776\pi$
$548$	56.7552	2.42446
$549$	93.9649	4.01032
$550$	−7.05286	−0.300735
$551$	−14.5979	−0.621891
$552$	−144.625	−6.15563
$553$	−13.6843	−0.581916
$554$	66.6938	2.83355
$555$	49.9556	2.12050
$556$	−102.093	−4.32971
$557$	−29.6030	−1.25432	−0.627160	−	0.778890i	$-0.715783\pi$
$557$	−29.6030	−1.25432	−0.627160	+	0.778890i	$0.715783\pi$
$558$	−8.70306	−0.368430
$559$	−5.23099	−0.221247
$560$	21.4328	0.905701
$561$	5.24412	0.221407
$562$	−11.3584	−0.479125
$563$	−41.1438	−1.73401	−0.867003	−	0.498303i	$-0.833957\pi$
$563$	−41.1438	−1.73401	−0.867003	+	0.498303i	$0.833957\pi$
$564$	−46.9514	−1.97701
$565$	−2.68984	−0.113162
$566$	−44.8169	−1.88379
$567$	−35.1726	−1.47711
$568$	−30.0191	−1.25957
$569$	−26.7364	−1.12085	−0.560425	−	0.828205i	$-0.689362\pi$
$569$	−26.7364	−1.12085	−0.560425	+	0.828205i	$0.689362\pi$
$570$	−25.1008	−1.05136
$571$	15.6927	0.656719	0.328359	−	0.944553i	$-0.393504\pi$
$571$	15.6927	0.656719	0.328359	+	0.944553i	$0.393504\pi$
$572$	−6.54134	−0.273507
$573$	68.3794	2.85659
$574$	39.4350	1.64598
$575$	−19.1904	−0.800296
$576$	53.7491	2.23955
$577$	−40.3038	−1.67787	−0.838935	−	0.544231i	$-0.816821\pi$
$577$	−40.3038	−1.67787	−0.838935	+	0.544231i	$0.816821\pi$
$578$	35.0746	1.45891
$579$	15.1555	0.629842
$580$	−44.1324	−1.83250
$581$	−17.9644	−0.745288
$582$	−3.40551	−0.141163
$583$	7.26726	0.300979
$584$	−67.6345	−2.79873
$585$	−15.5314	−0.642144
$586$	−16.2470	−0.671159
$587$	−1.08453	−0.0447633	−0.0223817	−	0.999749i	$-0.507125\pi$
$587$	−1.08453	−0.0447633	−0.0223817	+	0.999749i	$0.507125\pi$
$588$	−66.2521	−2.73219
$589$	−1.01094	−0.0416552
$590$	−25.9392	−1.06790
$591$	82.8859	3.40947
$592$	−107.935	−4.43608
$593$	6.15275	0.252663	0.126332	−	0.991988i	$-0.459680\pi$
$593$	6.15275	0.252663	0.126332	+	0.991988i	$0.459680\pi$
$594$	30.6016	1.25560
$595$	−4.25484	−0.174431
$596$	−0.209763	−0.00859221
$597$	−36.4807	−1.49305
$598$	−25.2024	−1.03060
$599$	39.0239	1.59447	0.797236	−	0.603667i	$-0.206294\pi$
$599$	39.0239	1.59447	0.797236	+	0.603667i	$0.206294\pi$
$600$	72.7829	2.97135
$601$	−28.5253	−1.16357	−0.581786	−	0.813342i	$-0.697646\pi$
$601$	−28.5253	−1.16357	−0.581786	+	0.813342i	$0.697646\pi$
$602$	−14.3097	−0.583219
$603$	109.806	4.47163
$604$	−55.2199	−2.24687
$605$	14.0911	0.572883
$606$	−41.6906	−1.69357
$607$	25.3699	1.02973	0.514866	−	0.857271i	$-0.327842\pi$
$607$	25.3699	1.02973	0.514866	+	0.857271i	$0.327842\pi$
$608$	22.1757	0.899342
$609$	−34.9787	−1.41741
$610$	46.7244	1.89181
$611$	−4.77838	−0.193312
$612$	−65.4575	−2.64596
$613$	9.61409	0.388309	0.194155	−	0.980971i	$-0.437804\pi$
$613$	9.61409	0.388309	0.194155	+	0.980971i	$0.437804\pi$
$614$	−17.3448	−0.699980
$615$	−40.5263	−1.63418
$616$	−10.4507	−0.421070
$617$	−39.4032	−1.58631	−0.793157	−	0.609017i	$-0.791564\pi$
$617$	−39.4032	−1.58631	−0.793157	+	0.609017i	$0.791564\pi$
$618$	−99.7048	−4.01072
$619$	14.0397	0.564302	0.282151	−	0.959370i	$-0.408952\pi$
$619$	14.0397	0.564302	0.282151	+	0.959370i	$0.408952\pi$
$620$	−3.05629	−0.122744
$621$	83.2653	3.34132
$622$	4.70204	0.188535
$623$	3.86362	0.154793
$624$	47.5042	1.90169
$625$	0.196046	0.00784185
$626$	−49.2697	−1.96921
$627$	6.08276	0.242922
$628$	41.9094	1.67237
$629$	21.4272	0.854357
$630$	−42.4870	−1.69272
$631$	25.2131	1.00372	0.501858	−	0.864950i	$-0.332650\pi$
$631$	25.2131	1.00372	0.501858	+	0.864950i	$0.332650\pi$
$632$	−61.1378	−2.43193
$633$	58.0592	2.30765
$634$	−59.0840	−2.34653
$635$	−23.2905	−0.924256
$636$	−128.411	−5.09184
$637$	−6.74266	−0.267154
$638$	15.1435	0.599536
$639$	29.5747	1.16996
$640$	−1.16064	−0.0458782
$641$	−21.5631	−0.851691	−0.425845	−	0.904796i	$-0.640023\pi$
$641$	−21.5631	−0.851691	−0.425845	+	0.904796i	$0.640023\pi$
$642$	−53.6910	−2.11901
$643$	11.1167	0.438399	0.219200	−	0.975680i	$-0.429655\pi$
$643$	11.1167	0.438399	0.219200	+	0.975680i	$0.429655\pi$
$644$	−48.6892	−1.91862
$645$	14.7057	0.579036
$646$	−10.7664	−0.423597
$647$	9.97575	0.392187	0.196094	−	0.980585i	$-0.437174\pi$
$647$	9.97575	0.392187	0.196094	+	0.980585i	$0.437174\pi$
$648$	−157.142	−6.17311
$649$	6.28591	0.246744
$650$	12.6832	0.497476
$651$	−2.42237	−0.0949400
$652$	−71.1204	−2.78529
$653$	8.88930	0.347865	0.173933	−	0.984758i	$-0.444353\pi$
$653$	8.88930	0.347865	0.173933	+	0.984758i	$0.444353\pi$
$654$	102.251	3.99834
$655$	−1.67721	−0.0655340
$656$	87.5617	3.41871
$657$	66.6333	2.59961
$658$	−13.0715	−0.509581
$659$	−15.5098	−0.604177	−0.302088	−	0.953280i	$-0.597684\pi$
$659$	−15.5098	−0.604177	−0.302088	+	0.953280i	$0.597684\pi$
$660$	18.3894	0.715808
$661$	16.3208	0.634805	0.317402	−	0.948291i	$-0.397189\pi$
$661$	16.3208	0.634805	0.317402	+	0.948291i	$0.397189\pi$
$662$	52.7747	2.05115
$663$	−9.43054	−0.366252
$664$	−80.2599	−3.11469
$665$	−4.93527	−0.191382
$666$	213.963	8.29088
$667$	41.2045	1.59545
$668$	−109.535	−4.23803
$669$	14.9208	0.576873
$670$	54.6012	2.10943
$671$	−11.3228	−0.437114
$672$	53.1361	2.04977
$673$	−32.7831	−1.26370	−0.631848	−	0.775092i	$-0.717703\pi$
$673$	−32.7831	−1.26370	−0.631848	+	0.775092i	$0.717703\pi$
$674$	−18.9839	−0.731231
$675$	−41.9036	−1.61287
$676$	−50.7406	−1.95156
$677$	−40.4543	−1.55478	−0.777392	−	0.629017i	$-0.783458\pi$
$677$	−40.4543	−1.55478	−0.777392	+	0.629017i	$0.783458\pi$
$678$	−16.3089	−0.626340
$679$	−0.669584	−0.0256963
$680$	−19.0095	−0.728979
$681$	43.3962	1.66295
$682$	1.04873	0.0401578
$683$	−21.4485	−0.820703	−0.410352	−	0.911927i	$-0.634594\pi$
$683$	−21.4485	−0.820703	−0.410352	+	0.911927i	$0.634594\pi$
$684$	−75.9254	−2.90308
$685$	−16.2383	−0.620432
$686$	−48.3970	−1.84781
$687$	20.6487	0.787798
$688$	−31.7733	−1.21135
$689$	−13.0688	−0.497880
$690$	70.8505	2.69723
$691$	−18.5282	−0.704847	−0.352423	−	0.935841i	$-0.614642\pi$
$691$	−18.5282	−0.704847	−0.352423	+	0.935841i	$0.614642\pi$
$692$	109.035	4.14488
$693$	10.2960	0.391113
$694$	82.5485	3.13350
$695$	29.2099	1.10799
$696$	−156.275	−5.92359
$697$	−17.3827	−0.658418
$698$	43.7124	1.65454
$699$	31.9309	1.20774
$700$	24.5030	0.926127
$701$	11.4584	0.432777	0.216388	−	0.976307i	$-0.430572\pi$
$701$	11.4584	0.432777	0.216388	+	0.976307i	$0.430572\pi$
$702$	−55.0311	−2.07702
$703$	24.8538	0.937378
$704$	−6.47681	−0.244104
$705$	13.4333	0.505927
$706$	34.9622	1.31582
$707$	−8.19712	−0.308284
$708$	−111.071	−4.17430
$709$	1.56351	0.0587188	0.0293594	−	0.999569i	$-0.490653\pi$
$709$	1.56351	0.0587188	0.0293594	+	0.999569i	$0.490653\pi$
$710$	14.7061	0.551912
$711$	60.2328	2.25891
$712$	17.2616	0.646906
$713$	2.85352	0.106865
$714$	−25.7978	−0.965458
$715$	1.87154	0.0699918
$716$	37.3810	1.39699
$717$	−97.1381	−3.62769
$718$	−42.7864	−1.59677
$719$	−3.40081	−0.126829	−0.0634144	−	0.997987i	$-0.520199\pi$
$719$	−3.40081	−0.126829	−0.0634144	+	0.997987i	$0.520199\pi$
$720$	−94.3385	−3.51579
$721$	−19.6037	−0.730081
$722$	37.0869	1.38023
$723$	79.0758	2.94086
$724$	−33.7667	−1.25493
$725$	−20.7363	−0.770128
$726$	85.4365	3.17084
$727$	−30.6745	−1.13766	−0.568828	−	0.822457i	$-0.692603\pi$
$727$	−30.6745	−1.13766	−0.568828	+	0.822457i	$0.692603\pi$
$728$	18.7936	0.696535
$729$	25.5080	0.944740
$730$	33.1336	1.22633
$731$	6.30764	0.233296
$732$	200.073	7.39490
$733$	11.2817	0.416699	0.208350	−	0.978054i	$-0.433191\pi$
$733$	11.2817	0.416699	0.208350	+	0.978054i	$0.433191\pi$
$734$	−19.5481	−0.721534
$735$	18.9554	0.699180
$736$	−62.5938	−2.30724
$737$	−13.2317	−0.487394
$738$	−173.577	−6.38945
$739$	−6.99948	−0.257480	−0.128740	−	0.991678i	$-0.541093\pi$
$739$	−6.99948	−0.257480	−0.128740	+	0.991678i	$0.541093\pi$
$740$	75.1381	2.76213
$741$	−10.9387	−0.401842
$742$	−35.7504	−1.31244
$743$	14.5115	0.532377	0.266188	−	0.963921i	$-0.414236\pi$
$743$	14.5115	0.532377	0.266188	+	0.963921i	$0.414236\pi$
$744$	−10.8225	−0.396771
$745$	0.0600152	0.00219879
$746$	−12.7274	−0.465983
$747$	79.0719	2.89309
$748$	7.88768	0.288402
$749$	−10.5566	−0.385729
$750$	−93.0232	−3.39673
$751$	0.0756490	0.00276047	0.00138024	−	0.999999i	$-0.499561\pi$
$751$	0.0756490	0.00276047	0.00138024	+	0.999999i	$0.499561\pi$
$752$	−29.0241	−1.05840
$753$	17.9209	0.653074
$754$	−27.2326	−0.991753
$755$	15.7990	0.574984
$756$	−106.316	−3.86668
$757$	38.2647	1.39075	0.695377	−	0.718645i	$-0.255237\pi$
$757$	38.2647	1.39075	0.695377	+	0.718645i	$0.255237\pi$
$758$	−9.46036	−0.343616
$759$	−17.1694	−0.623210
$760$	−22.0494	−0.799817
$761$	−34.2463	−1.24143	−0.620714	−	0.784037i	$-0.713157\pi$
$761$	−34.2463	−1.24143	−0.620714	+	0.784037i	$0.713157\pi$
$762$	−141.214	−5.11565
$763$	20.1044	0.727828
$764$	102.849	3.72096
$765$	18.7281	0.677115
$766$	−60.6659	−2.19195
$767$	−11.3040	−0.408164
$768$	−54.6429	−1.97175
$769$	25.1302	0.906217	0.453108	−	0.891455i	$-0.350315\pi$
$769$	25.1302	0.906217	0.453108	+	0.891455i	$0.350315\pi$
$770$	5.11972	0.184502
$771$	−3.62543	−0.130567
$772$	22.7954	0.820426
$773$	−42.1766	−1.51699	−0.758494	−	0.651680i	$-0.774065\pi$
$773$	−42.1766	−1.51699	−0.758494	+	0.651680i	$0.774065\pi$
$774$	62.9854	2.26396
$775$	−1.43605	−0.0515843
$776$	−2.99152	−0.107389
$777$	59.5533	2.13646
$778$	−73.8557	−2.64785
$779$	−20.1626	−0.722399
$780$	−33.0699	−1.18409
$781$	−3.56378	−0.127522
$782$	30.3895	1.08673
$783$	89.9729	3.21537
$784$	−40.9553	−1.46269
$785$	−11.9907	−0.427967
$786$	−10.1692	−0.362723
$787$	−46.4965	−1.65742	−0.828710	−	0.559678i	$-0.810925\pi$
$787$	−46.4965	−1.65742	−0.828710	+	0.559678i	$0.810925\pi$
$788$	124.669	4.44114
$789$	7.71132	0.274530
$790$	29.9510	1.06561
$791$	−3.20662	−0.114014
$792$	45.9997	1.63453
$793$	20.3619	0.723074
$794$	8.64789	0.306902
$795$	36.7398	1.30303
$796$	−54.8706	−1.94484
$797$	40.1034	1.42053	0.710267	−	0.703932i	$-0.248574\pi$
$797$	40.1034	1.42053	0.710267	+	0.703932i	$0.248574\pi$
$798$	−29.9234	−1.05928
$799$	5.76187	0.203840
$800$	31.5006	1.11371
$801$	−17.0061	−0.600881
$802$	−38.7978	−1.37000
$803$	−8.02937	−0.283350
$804$	233.801	8.24552
$805$	13.9305	0.490985
$806$	−1.88593	−0.0664290
$807$	20.7986	0.732146
$808$	−36.6225	−1.28837
$809$	−10.2570	−0.360616	−0.180308	−	0.983610i	$-0.557710\pi$
$809$	−10.2570	−0.360616	−0.180308	+	0.983610i	$0.557710\pi$
$810$	76.9826	2.70489
$811$	−30.0895	−1.05658	−0.528292	−	0.849063i	$-0.677167\pi$
$811$	−30.0895	−1.05658	−0.528292	+	0.849063i	$0.677167\pi$
$812$	−52.6114	−1.84630
$813$	−67.3286	−2.36132
$814$	−25.7827	−0.903682
$815$	20.3483	0.712769
$816$	−57.2816	−2.00526
$817$	7.31635	0.255967
$818$	−94.1901	−3.29328
$819$	−18.5154	−0.646979
$820$	−60.9557	−2.12866
$821$	−8.22582	−0.287083	−0.143541	−	0.989644i	$-0.545849\pi$
$821$	−8.22582	−0.287083	−0.143541	+	0.989644i	$0.545849\pi$
$822$	−98.4553	−3.43402
$823$	2.90491	0.101259	0.0506293	−	0.998718i	$-0.483877\pi$
$823$	2.90491	0.101259	0.0506293	+	0.998718i	$0.483877\pi$
$824$	−87.5841	−3.05114
$825$	8.64058	0.300826
$826$	−30.9228	−1.07594
$827$	−13.8365	−0.481143	−0.240572	−	0.970631i	$-0.577335\pi$
$827$	−13.8365	−0.481143	−0.240572	+	0.970631i	$0.577335\pi$
$828$	214.310	7.44778
$829$	−25.0082	−0.868570	−0.434285	−	0.900776i	$-0.642999\pi$
$829$	−25.0082	−0.868570	−0.434285	+	0.900776i	$0.642999\pi$
$830$	39.3187	1.36477
$831$	−81.7078	−2.83441
$832$	11.6473	0.403797
$833$	8.13043	0.281703
$834$	177.104	6.13262
$835$	31.3391	1.08453
$836$	9.14908	0.316427
$837$	6.23086	0.215370
$838$	21.7170	0.750203
$839$	−7.74512	−0.267391	−0.133696	−	0.991022i	$-0.542684\pi$
$839$	−7.74512	−0.267391	−0.133696	+	0.991022i	$0.542684\pi$
$840$	−52.8337	−1.82293
$841$	15.5238	0.535304
$842$	13.1298	0.452481
$843$	13.9154	0.479271
$844$	87.3269	3.00592
$845$	14.5174	0.499414
$846$	57.5356	1.97811
$847$	16.7983	0.577197
$848$	−79.3804	−2.72593
$849$	54.9060	1.88437
$850$	−15.2937	−0.524568
$851$	−70.1532	−2.40482
$852$	62.9713	2.15736
$853$	49.2915	1.68771	0.843854	−	0.536572i	$-0.180281\pi$
$853$	49.2915	1.68771	0.843854	+	0.536572i	$0.180281\pi$
$854$	55.7013	1.90606
$855$	21.7231	0.742913
$856$	−47.1640	−1.61203
$857$	7.58970	0.259259	0.129630	−	0.991562i	$-0.458621\pi$
$857$	7.58970	0.259259	0.129630	+	0.991562i	$0.458621\pi$
$858$	11.3475	0.387397
$859$	−16.0923	−0.549062	−0.274531	−	0.961578i	$-0.588523\pi$
$859$	−16.0923	−0.549062	−0.274531	+	0.961578i	$0.588523\pi$
$860$	22.1188	0.754246
$861$	−48.3125	−1.64648
$862$	−84.2493	−2.86954
$863$	33.4031	1.13706	0.568528	−	0.822664i	$-0.307513\pi$
$863$	33.4031	1.13706	0.568528	+	0.822664i	$0.307513\pi$
$864$	−136.678	−4.64988
$865$	−31.1960	−1.06070
$866$	−12.7153	−0.432084
$867$	−42.9706	−1.45936
$868$	−3.64348	−0.123668
$869$	−7.25810	−0.246214
$870$	76.5581	2.59556
$871$	23.7946	0.806248
$872$	89.8210	3.04172
$873$	2.94724	0.0997488
$874$	35.2494	1.19233
$875$	−18.2900	−0.618315
$876$	141.877	4.79359
$877$	34.9247	1.17932	0.589662	−	0.807650i	$-0.299261\pi$
$877$	34.9247	1.17932	0.589662	+	0.807650i	$0.299261\pi$
$878$	−4.58086	−0.154597
$879$	19.9045	0.671363
$880$	11.3679	0.383211
$881$	−5.80546	−0.195591	−0.0977955	−	0.995207i	$-0.531179\pi$
$881$	−5.80546	−0.195591	−0.0977955	+	0.995207i	$0.531179\pi$
$882$	81.1871	2.73371
$883$	1.01101	0.0340233	0.0170117	−	0.999855i	$-0.494585\pi$
$883$	1.01101	0.0340233	0.0170117	+	0.999855i	$0.494585\pi$
$884$	−14.1845	−0.477075
$885$	31.7785	1.06822
$886$	−73.4294	−2.46691
$887$	27.2067	0.913511	0.456756	−	0.889592i	$-0.349011\pi$
$887$	27.2067	0.913511	0.456756	+	0.889592i	$0.349011\pi$
$888$	266.068	8.92865
$889$	−27.7652	−0.931216
$890$	−8.45634	−0.283457
$891$	−18.6554	−0.624980
$892$	22.4424	0.751429
$893$	6.68330	0.223648
$894$	0.363882	0.0121700
$895$	−10.6951	−0.357498
$896$	−1.38363	−0.0462237
$897$	30.8759	1.03092
$898$	−102.098	−3.40705
$899$	3.08339	0.102837
$900$	−107.852	−3.59508
$901$	15.7586	0.524995
$902$	20.9161	0.696431
$903$	17.5310	0.583397
$904$	−14.3263	−0.476486
$905$	9.66101	0.321143
$906$	95.7919	3.18247
$907$	−3.97922	−0.132128	−0.0660640	−	0.997815i	$-0.521044\pi$
$907$	−3.97922	−0.132128	−0.0660640	+	0.997815i	$0.521044\pi$
$908$	65.2723	2.16614
$909$	36.0804	1.19671
$910$	−9.20683	−0.305203
$911$	−44.9913	−1.49063	−0.745314	−	0.666713i	$-0.767701\pi$
$911$	−44.9913	−1.49063	−0.745314	+	0.666713i	$0.767701\pi$
$912$	−66.4420	−2.20012
$913$	−9.52822	−0.315338
$914$	−23.6290	−0.781578
$915$	−57.2428	−1.89239
$916$	31.0577	1.02618
$917$	−1.99944	−0.0660275
$918$	66.3577	2.19013
$919$	38.5808	1.27266	0.636332	−	0.771415i	$-0.280451\pi$
$919$	38.5808	1.27266	0.636332	+	0.771415i	$0.280451\pi$
$920$	62.2375	2.05191
$921$	21.2495	0.700193
$922$	51.1253	1.68372
$923$	6.40877	0.210947
$924$	21.9225	0.721198
$925$	35.3049	1.16082
$926$	76.5875	2.51682
$927$	86.2876	2.83406
$928$	−67.6362	−2.22027
$929$	−41.9133	−1.37513	−0.687565	−	0.726123i	$-0.741320\pi$
$929$	−41.9133	−1.37513	−0.687565	+	0.726123i	$0.741320\pi$
$930$	5.30185	0.173854
$931$	9.43065	0.309077
$932$	48.0273	1.57319
$933$	−5.76055	−0.188592
$934$	33.0351	1.08094
$935$	−2.25675	−0.0738035
$936$	−82.7216	−2.70384
$937$	14.4194	0.471063	0.235531	−	0.971867i	$-0.424317\pi$
$937$	14.4194	0.471063	0.235531	+	0.971867i	$0.424317\pi$
$938$	65.0914	2.12531
$939$	60.3612	1.96981
$940$	20.2050	0.659015
$941$	−4.27695	−0.139425	−0.0697124	−	0.997567i	$-0.522208\pi$
$941$	−4.27695	−0.139425	−0.0697124	+	0.997567i	$0.522208\pi$
$942$	−72.7017	−2.36875
$943$	56.9116	1.85330
$944$	−68.6611	−2.23473
$945$	30.4182	0.989503
$946$	−7.58979	−0.246765
$947$	9.90049	0.321723	0.160861	−	0.986977i	$-0.448573\pi$
$947$	9.90049	0.321723	0.160861	+	0.986977i	$0.448573\pi$
$948$	128.249	4.16534
$949$	14.4393	0.468718
$950$	−17.7394	−0.575543
$951$	72.3849	2.34724
$952$	−22.6617	−0.734468
$953$	6.64523	0.215260	0.107630	−	0.994191i	$-0.465674\pi$
$953$	6.64523	0.215260	0.107630	+	0.994191i	$0.465674\pi$
$954$	157.359	5.09467
$955$	−29.4263	−0.952212
$956$	−146.105	−4.72539
$957$	−18.5525	−0.599718
$958$	−17.0199	−0.549888
$959$	−19.3580	−0.625104
$960$	−32.7436	−1.05680
$961$	−30.7865	−0.993112
$962$	46.3651	1.49487
$963$	46.4658	1.49734
$964$	118.938	3.83073
$965$	−6.52201	−0.209951
$966$	84.4628	2.71754
$967$	38.9580	1.25281	0.626403	−	0.779500i	$-0.284527\pi$
$967$	38.9580	1.25281	0.626403	+	0.779500i	$0.284527\pi$
$968$	75.0503	2.41221
$969$	13.1901	0.423726
$970$	1.46552	0.0470551
$971$	−38.5882	−1.23836	−0.619178	−	0.785251i	$-0.712534\pi$
$971$	−38.5882	−1.23836	−0.619178	+	0.785251i	$0.712534\pi$
$972$	135.146	4.33481
$973$	34.8218	1.11634
$974$	46.5917	1.49290
$975$	−15.5384	−0.497627
$976$	123.680	3.95889
$977$	−4.89737	−0.156681	−0.0783404	−	0.996927i	$-0.524962\pi$
$977$	−4.89737	−0.156681	−0.0783404	+	0.996927i	$0.524962\pi$
$978$	123.375	3.94510
$979$	2.04925	0.0654943
$980$	28.5108	0.910744
$981$	−88.4914	−2.82531
$982$	−68.0629	−2.17197
$983$	56.8399	1.81291	0.906455	−	0.422302i	$-0.138778\pi$
$983$	56.8399	1.81291	0.906455	+	0.422302i	$0.138778\pi$
$984$	−215.847	−6.88095
$985$	−35.6690	−1.13651
$986$	32.8376	1.04576
$987$	16.0142	0.509736
$988$	−16.4528	−0.523435
$989$	−20.6514	−0.656676
$990$	−22.5349	−0.716207
$991$	−16.9672	−0.538980	−0.269490	−	0.963003i	$-0.586855\pi$
$991$	−16.9672	−0.538980	−0.269490	+	0.963003i	$0.586855\pi$
$992$	−4.68399	−0.148717
$993$	−64.6552	−2.05177
$994$	17.5316	0.556068
$995$	15.6990	0.497693
$996$	168.362	5.33475
$997$	14.7344	0.466642	0.233321	−	0.972400i	$-0.425041\pi$
$997$	14.7344	0.466642	0.233321	+	0.972400i	$0.425041\pi$
$998$	30.8093	0.975252
$999$	−153.184	−4.84654

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8017.2.a.b.1.15	✓	340

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8017.2.a.b.1.15	✓	340	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:	\( N \)	\(=\)	\( 8017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.60921 q^{2} +3.19659 q^{3} +4.80800 q^{4} -1.37562 q^{5} -8.34060 q^{6} -1.63991 q^{7} -7.32666 q^{8} +7.21821 q^{9} +O(q^{10})\)	\(q-2.60921 q^{2} +3.19659 q^{3} +4.80800 q^{4} -1.37562 q^{5} -8.34060 q^{6} -1.63991 q^{7} -7.32666 q^{8} +7.21821 q^{9} +3.58928 q^{10} -0.869800 q^{11} +15.3692 q^{12} +1.56417 q^{13} +4.27887 q^{14} -4.39729 q^{15} +9.50083 q^{16} -1.88610 q^{17} -18.8339 q^{18} -2.18773 q^{19} -6.61396 q^{20} -5.24212 q^{21} +2.26949 q^{22} +6.17517 q^{23} -23.4204 q^{24} -3.10768 q^{25} -4.08125 q^{26} +13.4839 q^{27} -7.88467 q^{28} +6.67262 q^{29} +11.4735 q^{30} +0.462097 q^{31} -10.1364 q^{32} -2.78040 q^{33} +4.92125 q^{34} +2.25589 q^{35} +34.7051 q^{36} -11.3605 q^{37} +5.70826 q^{38} +5.00001 q^{39} +10.0787 q^{40} +9.21621 q^{41} +13.6778 q^{42} -3.34427 q^{43} -4.18200 q^{44} -9.92949 q^{45} -16.1123 q^{46} -3.05490 q^{47} +30.3703 q^{48} -4.31070 q^{49} +8.10859 q^{50} -6.02911 q^{51} +7.52051 q^{52} -8.35510 q^{53} -35.1824 q^{54} +1.19651 q^{55} +12.0151 q^{56} -6.99328 q^{57} -17.4103 q^{58} -7.22685 q^{59} -21.1421 q^{60} +13.0178 q^{61} -1.20571 q^{62} -11.8372 q^{63} +7.44632 q^{64} -2.15170 q^{65} +7.25465 q^{66} +15.2123 q^{67} -9.06838 q^{68} +19.7395 q^{69} -5.88609 q^{70} +4.09724 q^{71} -52.8854 q^{72} +9.23128 q^{73} +29.6421 q^{74} -9.93398 q^{75} -10.5186 q^{76} +1.42639 q^{77} -13.0461 q^{78} +8.34456 q^{79} -13.0695 q^{80} +21.4479 q^{81} -24.0471 q^{82} +10.9545 q^{83} -25.2041 q^{84} +2.59456 q^{85} +8.72590 q^{86} +21.3296 q^{87} +6.37273 q^{88} -2.35600 q^{89} +25.9082 q^{90} -2.56509 q^{91} +29.6902 q^{92} +1.47713 q^{93} +7.97089 q^{94} +3.00948 q^{95} -32.4019 q^{96} +0.408306 q^{97} +11.2475 q^{98} -6.27840 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 340 q + 20 q^{2} + 44 q^{3} + 350 q^{4} + 53 q^{5} + 34 q^{6} + 81 q^{7} + 54 q^{8} + 360 q^{9}+O(q^{10}) \) 340 * q + 20 * q^2 + 44 * q^3 + 350 * q^4 + 53 * q^5 + 34 * q^6 + 81 * q^7 + 54 * q^8 + 360 * q^9	\( 340 q + 20 q^{2} + 44 q^{3} + 350 q^{4} + 53 q^{5} + 34 q^{6} + 81 q^{7} + 54 q^{8} + 360 q^{9} + 36 q^{10} + 70 q^{11} + 92 q^{12} + 45 q^{13} + 44 q^{14} + 71 q^{15} + 362 q^{16} + 162 q^{17} + 41 q^{18} + 49 q^{19} + 147 q^{20} + 41 q^{21} + 32 q^{22} + 244 q^{23} + 85 q^{24} + 355 q^{25} + 83 q^{26} + 155 q^{27} + 129 q^{28} + 91 q^{29} + 51 q^{30} + 65 q^{31} + 113 q^{32} + 73 q^{33} + 26 q^{34} + 200 q^{35} + 380 q^{36} + 28 q^{37} + 171 q^{38} + 117 q^{39} + 95 q^{40} + 115 q^{41} + 42 q^{42} + 98 q^{43} + 139 q^{44} + 127 q^{45} + 29 q^{46} + 312 q^{47} + 168 q^{48} + 365 q^{49} + 64 q^{50} + 72 q^{51} + 100 q^{52} + 154 q^{53} + 89 q^{54} + 161 q^{55} + 89 q^{56} + 82 q^{57} + 29 q^{58} + 149 q^{59} + 93 q^{60} + 70 q^{61} + 257 q^{62} + 376 q^{63} + 346 q^{64} + 125 q^{65} + 48 q^{66} + 65 q^{67} + 464 q^{68} + 58 q^{69} - 54 q^{70} + 216 q^{71} + 90 q^{72} + 93 q^{73} + 147 q^{74} + 162 q^{75} + 64 q^{76} + 190 q^{77} + 12 q^{78} + 139 q^{79} + 274 q^{80} + 376 q^{81} + 59 q^{82} + 402 q^{83} + 10 q^{84} + 32 q^{85} + 53 q^{86} + 364 q^{87} + 42 q^{88} + 114 q^{89} + 126 q^{90} + 43 q^{91} + 422 q^{92} + 47 q^{93} + 2 q^{94} + 347 q^{95} + 146 q^{96} + 47 q^{97} + 96 q^{98} + 129 q^{99}+O(q^{100}) \) 340 * q + 20 * q^2 + 44 * q^3 + 350 * q^4 + 53 * q^5 + 34 * q^6 + 81 * q^7 + 54 * q^8 + 360 * q^9 + 36 * q^10 + 70 * q^11 + 92 * q^12 + 45 * q^13 + 44 * q^14 + 71 * q^15 + 362 * q^16 + 162 * q^17 + 41 * q^18 + 49 * q^19 + 147 * q^20 + 41 * q^21 + 32 * q^22 + 244 * q^23 + 85 * q^24 + 355 * q^25 + 83 * q^26 + 155 * q^27 + 129 * q^28 + 91 * q^29 + 51 * q^30 + 65 * q^31 + 113 * q^32 + 73 * q^33 + 26 * q^34 + 200 * q^35 + 380 * q^36 + 28 * q^37 + 171 * q^38 + 117 * q^39 + 95 * q^40 + 115 * q^41 + 42 * q^42 + 98 * q^43 + 139 * q^44 + 127 * q^45 + 29 * q^46 + 312 * q^47 + 168 * q^48 + 365 * q^49 + 64 * q^50 + 72 * q^51 + 100 * q^52 + 154 * q^53 + 89 * q^54 + 161 * q^55 + 89 * q^56 + 82 * q^57 + 29 * q^58 + 149 * q^59 + 93 * q^60 + 70 * q^61 + 257 * q^62 + 376 * q^63 + 346 * q^64 + 125 * q^65 + 48 * q^66 + 65 * q^67 + 464 * q^68 + 58 * q^69 - 54 * q^70 + 216 * q^71 + 90 * q^72 + 93 * q^73 + 147 * q^74 + 162 * q^75 + 64 * q^76 + 190 * q^77 + 12 * q^78 + 139 * q^79 + 274 * q^80 + 376 * q^81 + 59 * q^82 + 402 * q^83 + 10 * q^84 + 32 * q^85 + 53 * q^86 + 364 * q^87 + 42 * q^88 + 114 * q^89 + 126 * q^90 + 43 * q^91 + 422 * q^92 + 47 * q^93 + 2 * q^94 + 347 * q^95 + 146 * q^96 + 47 * q^97 + 96 * q^98 + 129 * q^99

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