LMFDB - Embedded newform 8011.2.a.b.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8011,2,Mod(1,8011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8011, 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("8011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8011.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:	$63.9681570592$
Analytic rank:	$0$
Dimension:	$358$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	8011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.69679 q^{2} +2.11156 q^{3} +5.27265 q^{4} -0.515809 q^{5} -5.69442 q^{6} -2.39275 q^{7} -8.82564 q^{8} +1.45867 q^{9} +O(q^{10})$	\(q-2.69679 q^{2} +2.11156 q^{3} +5.27265 q^{4} -0.515809 q^{5} -5.69442 q^{6} -2.39275 q^{7} -8.82564 q^{8} +1.45867 q^{9} +1.39103 q^{10} -5.17864 q^{11} +11.1335 q^{12} -0.224327 q^{13} +6.45273 q^{14} -1.08916 q^{15} +13.2556 q^{16} +6.20189 q^{17} -3.93373 q^{18} +5.80177 q^{19} -2.71968 q^{20} -5.05243 q^{21} +13.9657 q^{22} +6.32260 q^{23} -18.6358 q^{24} -4.73394 q^{25} +0.604962 q^{26} -3.25460 q^{27} -12.6161 q^{28} -7.27997 q^{29} +2.93723 q^{30} -5.90428 q^{31} -18.0961 q^{32} -10.9350 q^{33} -16.7252 q^{34} +1.23420 q^{35} +7.69108 q^{36} -4.47970 q^{37} -15.6461 q^{38} -0.473679 q^{39} +4.55234 q^{40} +3.34952 q^{41} +13.6253 q^{42} +9.61738 q^{43} -27.3051 q^{44} -0.752397 q^{45} -17.0507 q^{46} +2.61442 q^{47} +27.9899 q^{48} -1.27475 q^{49} +12.7664 q^{50} +13.0956 q^{51} -1.18280 q^{52} +13.5061 q^{53} +8.77695 q^{54} +2.67119 q^{55} +21.1176 q^{56} +12.2508 q^{57} +19.6325 q^{58} +3.78788 q^{59} -5.74276 q^{60} -0.220649 q^{61} +15.9226 q^{62} -3.49024 q^{63} +22.2902 q^{64} +0.115710 q^{65} +29.4893 q^{66} -14.0813 q^{67} +32.7004 q^{68} +13.3505 q^{69} -3.32838 q^{70} +4.03732 q^{71} -12.8737 q^{72} -14.7325 q^{73} +12.0808 q^{74} -9.99599 q^{75} +30.5907 q^{76} +12.3912 q^{77} +1.27741 q^{78} -16.4615 q^{79} -6.83733 q^{80} -11.2483 q^{81} -9.03295 q^{82} +4.90642 q^{83} -26.6397 q^{84} -3.19899 q^{85} -25.9360 q^{86} -15.3721 q^{87} +45.7048 q^{88} -0.348917 q^{89} +2.02905 q^{90} +0.536758 q^{91} +33.3369 q^{92} -12.4672 q^{93} -7.05054 q^{94} -2.99260 q^{95} -38.2110 q^{96} +12.5960 q^{97} +3.43772 q^{98} -7.55394 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 358 q + 33 q^{2} + 11 q^{3} + 391 q^{4} + 76 q^{5} + 32 q^{6} + 19 q^{7} + 99 q^{8} + 451 q^{9}+O(q^{10}) $ 358 * q + 33 * q^2 + 11 * q^3 + 391 * q^4 + 76 * q^5 + 32 * q^6 + 19 * q^7 + 99 * q^8 + 451 * q^9	\( 358 q + 33 q^{2} + 11 q^{3} + 391 q^{4} + 76 q^{5} + 32 q^{6} + 19 q^{7} + 99 q^{8} + 451 q^{9} + 21 q^{10} + 70 q^{11} + 20 q^{12} + 53 q^{13} + 69 q^{14} + 28 q^{15} + 449 q^{16} + 88 q^{17} + 86 q^{18} + 44 q^{19} + 136 q^{20} + 125 q^{21} + 17 q^{22} + 104 q^{23} + 84 q^{24} + 444 q^{25} + 100 q^{26} + 32 q^{27} + 46 q^{28} + 373 q^{29} + 99 q^{30} + 30 q^{31} + 221 q^{32} + 56 q^{33} + 26 q^{34} + 164 q^{35} + 599 q^{36} + 81 q^{37} + 66 q^{38} + 143 q^{39} + 42 q^{40} + 182 q^{41} + 32 q^{42} + 40 q^{43} + 184 q^{44} + 198 q^{45} + 54 q^{46} + 66 q^{47} + 5 q^{48} + 479 q^{49} + 184 q^{50} + 123 q^{51} + 64 q^{52} + 221 q^{53} + 67 q^{54} + 38 q^{55} + 174 q^{56} + 84 q^{57} + 44 q^{58} + 127 q^{59} + 29 q^{60} + 174 q^{61} + 86 q^{62} + 48 q^{63} + 549 q^{64} + 202 q^{65} + 32 q^{66} + 29 q^{67} + 172 q^{68} + 249 q^{69} + 12 q^{70} + 185 q^{71} + 218 q^{72} + 57 q^{73} + 272 q^{74} + 24 q^{75} + 84 q^{76} + 384 q^{77} + 12 q^{78} + 93 q^{79} + 215 q^{80} + 702 q^{81} + 48 q^{82} + 121 q^{83} + 179 q^{84} + 177 q^{85} + 209 q^{86} + 91 q^{87} + 36 q^{88} + 186 q^{89} + 66 q^{90} + 32 q^{91} + 272 q^{92} + 220 q^{93} + 60 q^{94} + 170 q^{95} + 162 q^{96} + 22 q^{97} + 196 q^{98} + 152 q^{99}+O(q^{100}) \) 358 * q + 33 * q^2 + 11 * q^3 + 391 * q^4 + 76 * q^5 + 32 * q^6 + 19 * q^7 + 99 * q^8 + 451 * q^9 + 21 * q^10 + 70 * q^11 + 20 * q^12 + 53 * q^13 + 69 * q^14 + 28 * q^15 + 449 * q^16 + 88 * q^17 + 86 * q^18 + 44 * q^19 + 136 * q^20 + 125 * q^21 + 17 * q^22 + 104 * q^23 + 84 * q^24 + 444 * q^25 + 100 * q^26 + 32 * q^27 + 46 * q^28 + 373 * q^29 + 99 * q^30 + 30 * q^31 + 221 * q^32 + 56 * q^33 + 26 * q^34 + 164 * q^35 + 599 * q^36 + 81 * q^37 + 66 * q^38 + 143 * q^39 + 42 * q^40 + 182 * q^41 + 32 * q^42 + 40 * q^43 + 184 * q^44 + 198 * q^45 + 54 * q^46 + 66 * q^47 + 5 * q^48 + 479 * q^49 + 184 * q^50 + 123 * q^51 + 64 * q^52 + 221 * q^53 + 67 * q^54 + 38 * q^55 + 174 * q^56 + 84 * q^57 + 44 * q^58 + 127 * q^59 + 29 * q^60 + 174 * q^61 + 86 * q^62 + 48 * q^63 + 549 * q^64 + 202 * q^65 + 32 * q^66 + 29 * q^67 + 172 * q^68 + 249 * q^69 + 12 * q^70 + 185 * q^71 + 218 * q^72 + 57 * q^73 + 272 * q^74 + 24 * q^75 + 84 * q^76 + 384 * q^77 + 12 * q^78 + 93 * q^79 + 215 * q^80 + 702 * q^81 + 48 * q^82 + 121 * q^83 + 179 * q^84 + 177 * q^85 + 209 * q^86 + 91 * q^87 + 36 * q^88 + 186 * q^89 + 66 * q^90 + 32 * q^91 + 272 * q^92 + 220 * q^93 + 60 * q^94 + 170 * q^95 + 162 * q^96 + 22 * q^97 + 196 * q^98 + 152 * 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 $

$2$	−2.69679	−1.90692	−0.953458	−	0.301527i	$-0.902504\pi$
$2$	−2.69679	−1.90692	−0.953458	+	0.301527i	$0.902504\pi$
$3$	2.11156	1.21911	0.609554	−	0.792744i	$-0.291349\pi$
$3$	2.11156	1.21911	0.609554	+	0.792744i	$0.291349\pi$
$4$	5.27265	2.63633
$5$	−0.515809	−0.230677	−0.115338	−	0.993326i	$-0.536795\pi$
$5$	−0.515809	−0.230677	−0.115338	+	0.993326i	$0.536795\pi$
$6$	−5.69442	−2.32474
$7$	−2.39275	−0.904374	−0.452187	−	0.891923i	$-0.649356\pi$
$7$	−2.39275	−0.904374	−0.452187	+	0.891923i	$0.649356\pi$
$8$	−8.82564	−3.12034
$9$	1.45867	0.486225
$10$	1.39103	0.439881
$11$	−5.17864	−1.56142	−0.780709	−	0.624895i	$-0.785142\pi$
$11$	−5.17864	−1.56142	−0.780709	+	0.624895i	$0.785142\pi$
$12$	11.1335	3.21397
$13$	−0.224327	−0.0622171	−0.0311085	−	0.999516i	$-0.509904\pi$
$13$	−0.224327	−0.0622171	−0.0311085	+	0.999516i	$0.509904\pi$
$14$	6.45273	1.72457
$15$	−1.08916	−0.281220
$16$	13.2556	3.31389
$17$	6.20189	1.50418	0.752089	−	0.659061i	$-0.229046\pi$
$17$	6.20189	1.50418	0.752089	+	0.659061i	$0.229046\pi$
$18$	−3.93373	−0.927189
$19$	5.80177	1.33102	0.665508	−	0.746390i	$-0.268215\pi$
$19$	5.80177	1.33102	0.665508	+	0.746390i	$0.268215\pi$
$20$	−2.71968	−0.608139
$21$	−5.05243	−1.10253
$22$	13.9657	2.97749
$23$	6.32260	1.31835	0.659177	−	0.751988i	$-0.270905\pi$
$23$	6.32260	1.31835	0.659177	+	0.751988i	$0.270905\pi$
$24$	−18.6358	−3.80403
$25$	−4.73394	−0.946788
$26$	0.604962	0.118643
$27$	−3.25460	−0.626348
$28$	−12.6161	−2.38423
$29$	−7.27997	−1.35186	−0.675928	−	0.736968i	$-0.736257\pi$
$29$	−7.27997	−1.35186	−0.675928	+	0.736968i	$0.736257\pi$
$30$	2.93723	0.536263
$31$	−5.90428	−1.06044	−0.530220	−	0.847860i	$-0.677891\pi$
$31$	−5.90428	−1.06044	−0.530220	+	0.847860i	$0.677891\pi$
$32$	−18.0961	−3.19897
$33$	−10.9350	−1.90354
$34$	−16.7252	−2.86834
$35$	1.23420	0.208618
$36$	7.69108	1.28185
$37$	−4.47970	−0.736459	−0.368229	−	0.929735i	$-0.620036\pi$
$37$	−4.47970	−0.736459	−0.368229	+	0.929735i	$0.620036\pi$
$38$	−15.6461	−2.53814
$39$	−0.473679	−0.0758494
$40$	4.55234	0.719789
$41$	3.34952	0.523108	0.261554	−	0.965189i	$-0.415765\pi$
$41$	3.34952	0.523108	0.261554	+	0.965189i	$0.415765\pi$
$42$	13.6253	2.10243
$43$	9.61738	1.46664	0.733319	−	0.679885i	$-0.237970\pi$
$43$	9.61738	1.46664	0.733319	+	0.679885i	$0.237970\pi$
$44$	−27.3051	−4.11641
$45$	−0.752397	−0.112161
$46$	−17.0507	−2.51399
$47$	2.61442	0.381353	0.190677	−	0.981653i	$-0.438932\pi$
$47$	2.61442	0.381353	0.190677	+	0.981653i	$0.438932\pi$
$48$	27.9899	4.03999
$49$	−1.27475	−0.182107
$50$	12.7664	1.80544
$51$	13.0956	1.83376
$52$	−1.18280	−0.164025
$53$	13.5061	1.85521	0.927606	−	0.373560i	$-0.121863\pi$
$53$	13.5061	1.85521	0.927606	+	0.373560i	$0.121863\pi$
$54$	8.77695	1.19439
$55$	2.67119	0.360183
$56$	21.1176	2.82195
$57$	12.2508	1.62265
$58$	19.6325	2.57788
$59$	3.78788	0.493140	0.246570	−	0.969125i	$-0.420696\pi$
$59$	3.78788	0.493140	0.246570	+	0.969125i	$0.420696\pi$
$60$	−5.74276	−0.741387
$61$	−0.220649	−0.0282512	−0.0141256	−	0.999900i	$-0.504496\pi$
$61$	−0.220649	−0.0282512	−0.0141256	+	0.999900i	$0.504496\pi$
$62$	15.9226	2.02217
$63$	−3.49024	−0.439729
$64$	22.2902	2.78628
$65$	0.115710	0.0143520
$66$	29.4893	3.62988
$67$	−14.0813	−1.72031	−0.860154	−	0.510035i	$-0.829632\pi$
$67$	−14.0813	−1.72031	−0.860154	+	0.510035i	$0.829632\pi$
$68$	32.7004	3.96550
$69$	13.3505	1.60722
$70$	−3.32838	−0.397817
$71$	4.03732	0.479141	0.239571	−	0.970879i	$-0.422993\pi$
$71$	4.03732	0.479141	0.239571	+	0.970879i	$0.422993\pi$
$72$	−12.8737	−1.51718
$73$	−14.7325	−1.72430	−0.862152	−	0.506649i	$-0.830884\pi$
$73$	−14.7325	−1.72430	−0.862152	+	0.506649i	$0.830884\pi$
$74$	12.0808	1.40436
$75$	−9.99599	−1.15424
$76$	30.5907	3.50899
$77$	12.3912	1.41211
$78$	1.27741	0.144638
$79$	−16.4615	−1.85206	−0.926032	−	0.377445i	$-0.876803\pi$
$79$	−16.4615	−1.85206	−0.926032	+	0.377445i	$0.876803\pi$
$80$	−6.83733	−0.764437
$81$	−11.2483	−1.24981
$82$	−9.03295	−0.997522
$83$	4.90642	0.538550	0.269275	−	0.963063i	$-0.413216\pi$
$83$	4.90642	0.538550	0.269275	+	0.963063i	$0.413216\pi$
$84$	−26.6397	−2.90663
$85$	−3.19899	−0.346979
$86$	−25.9360	−2.79675
$87$	−15.3721	−1.64806
$88$	45.7048	4.87215
$89$	−0.348917	−0.0369851	−0.0184926	−	0.999829i	$-0.505887\pi$
$89$	−0.348917	−0.0369851	−0.0184926	+	0.999829i	$0.505887\pi$
$90$	2.02905	0.213881
$91$	0.536758	0.0562676
$92$	33.3369	3.47561
$93$	−12.4672	−1.29279
$94$	−7.05054	−0.727208
$95$	−2.99260	−0.307035
$96$	−38.2110	−3.89989
$97$	12.5960	1.27893	0.639467	−	0.768819i	$-0.279155\pi$
$97$	12.5960	1.27893	0.639467	+	0.768819i	$0.279155\pi$
$98$	3.43772	0.347262
$99$	−7.55394	−0.759200
$100$	−24.9604	−2.49604
$101$	11.0272	1.09725	0.548623	−	0.836070i	$-0.315152\pi$
$101$	11.0272	1.09725	0.548623	+	0.836070i	$0.315152\pi$
$102$	−35.3161	−3.49682
$103$	−2.79573	−0.275472	−0.137736	−	0.990469i	$-0.543982\pi$
$103$	−2.79573	−0.275472	−0.137736	+	0.990469i	$0.543982\pi$
$104$	1.97983	0.194138
$105$	2.60609	0.254328
$106$	−36.4232	−3.53773
$107$	−4.71809	−0.456115	−0.228058	−	0.973648i	$-0.573237\pi$
$107$	−4.71809	−0.456115	−0.228058	+	0.973648i	$0.573237\pi$
$108$	−17.1604	−1.65126
$109$	−6.38191	−0.611276	−0.305638	−	0.952148i	$-0.598870\pi$
$109$	−6.38191	−0.611276	−0.305638	+	0.952148i	$0.598870\pi$
$110$	−7.20362	−0.686838
$111$	−9.45915	−0.897823
$112$	−31.7172	−2.99700
$113$	6.51429	0.612813	0.306407	−	0.951901i	$-0.400873\pi$
$113$	6.51429	0.612813	0.306407	+	0.951901i	$0.400873\pi$
$114$	−33.0377	−3.09426
$115$	−3.26126	−0.304114
$116$	−38.3847	−3.56393
$117$	−0.327220	−0.0302515
$118$	−10.2151	−0.940376
$119$	−14.8396	−1.36034
$120$	9.61254	0.877500
$121$	15.8183	1.43802
$122$	0.595043	0.0538726
$123$	7.07271	0.637725
$124$	−31.1312	−2.79567
$125$	5.02085	0.449079
$126$	9.41244	0.838526
$127$	12.0204	1.06663	0.533317	−	0.845916i	$-0.320945\pi$
$127$	12.0204	1.06663	0.533317	+	0.845916i	$0.320945\pi$
$128$	−23.9197	−2.11422
$129$	20.3077	1.78799
$130$	−0.312045	−0.0273681
$131$	2.13921	0.186904	0.0934518	−	0.995624i	$-0.470210\pi$
$131$	2.13921	0.186904	0.0934518	+	0.995624i	$0.470210\pi$
$132$	−57.6564	−5.01834
$133$	−13.8822	−1.20374
$134$	37.9743	3.28048
$135$	1.67875	0.144484
$136$	−54.7356	−4.69354
$137$	−16.1226	−1.37745	−0.688725	−	0.725023i	$-0.741829\pi$
$137$	−16.1226	−1.37745	−0.688725	+	0.725023i	$0.741829\pi$
$138$	−36.0035	−3.06483
$139$	−13.8648	−1.17600	−0.588000	−	0.808861i	$-0.700084\pi$
$139$	−13.8648	−1.17600	−0.588000	+	0.808861i	$0.700084\pi$
$140$	6.50752	0.549986
$141$	5.52051	0.464911
$142$	−10.8878	−0.913682
$143$	1.16171	0.0971468
$144$	19.3355	1.61129
$145$	3.75507	0.311842
$146$	39.7303	3.28810
$147$	−2.69170	−0.222008
$148$	−23.6199	−1.94155
$149$	17.3222	1.41909	0.709545	−	0.704660i	$-0.248901\pi$
$149$	17.3222	1.41909	0.709545	+	0.704660i	$0.248901\pi$
$150$	26.9570	2.20103
$151$	−0.847711	−0.0689857	−0.0344929	−	0.999405i	$-0.510982\pi$
$151$	−0.847711	−0.0689857	−0.0344929	+	0.999405i	$0.510982\pi$
$152$	−51.2043	−4.15322
$153$	9.04653	0.731369
$154$	−33.4164	−2.69277
$155$	3.04548	0.244619
$156$	−2.49755	−0.199964
$157$	15.0637	1.20222	0.601109	−	0.799167i	$-0.294726\pi$
$157$	15.0637	1.20222	0.601109	+	0.799167i	$0.294726\pi$
$158$	44.3932	3.53173
$159$	28.5190	2.26170
$160$	9.33413	0.737928
$161$	−15.1284	−1.19229
$162$	30.3342	2.38328
$163$	22.9414	1.79691	0.898455	−	0.439065i	$-0.144690\pi$
$163$	22.9414	1.79691	0.898455	+	0.439065i	$0.144690\pi$
$164$	17.6609	1.37908
$165$	5.64036	0.439102
$166$	−13.2316	−1.02697
$167$	2.28913	0.177138	0.0885691	−	0.996070i	$-0.471771\pi$
$167$	2.28913	0.177138	0.0885691	+	0.996070i	$0.471771\pi$
$168$	44.5909	3.44026
$169$	−12.9497	−0.996129
$170$	8.62699	0.661660
$171$	8.46289	0.647173
$172$	50.7091	3.86653
$173$	−25.6366	−1.94912	−0.974559	−	0.224133i	$-0.928045\pi$
$173$	−25.6366	−1.94912	−0.974559	+	0.224133i	$0.928045\pi$
$174$	41.4552	3.14271
$175$	11.3271	0.856251
$176$	−68.6457	−5.17436
$177$	7.99832	0.601191
$178$	0.940955	0.0705275
$179$	11.6607	0.871559	0.435780	−	0.900053i	$-0.356473\pi$
$179$	11.6607	0.871559	0.435780	+	0.900053i	$0.356473\pi$
$180$	−3.96713	−0.295692
$181$	−5.67485	−0.421808	−0.210904	−	0.977507i	$-0.567641\pi$
$181$	−5.67485	−0.421808	−0.210904	+	0.977507i	$0.567641\pi$
$182$	−1.44752	−0.107297
$183$	−0.465913	−0.0344413
$184$	−55.8010	−4.11371
$185$	2.31067	0.169884
$186$	33.6215	2.46525
$187$	−32.1173	−2.34865
$188$	13.7850	1.00537
$189$	7.78744	0.566453
$190$	8.07041	0.585489
$191$	13.6240	0.985795	0.492897	−	0.870087i	$-0.335938\pi$
$191$	13.6240	0.985795	0.492897	+	0.870087i	$0.335938\pi$
$192$	47.0671	3.39677
$193$	0.404203	0.0290952	0.0145476	−	0.999894i	$-0.495369\pi$
$193$	0.404203	0.0290952	0.0145476	+	0.999894i	$0.495369\pi$
$194$	−33.9688	−2.43882
$195$	0.244328	0.0174967
$196$	−6.72130	−0.480093
$197$	−13.2540	−0.944306	−0.472153	−	0.881517i	$-0.656523\pi$
$197$	−13.2540	−0.944306	−0.472153	+	0.881517i	$0.656523\pi$
$198$	20.3714	1.44773
$199$	13.9681	0.990173	0.495086	−	0.868844i	$-0.335136\pi$
$199$	13.9681	0.990173	0.495086	+	0.868844i	$0.335136\pi$
$200$	41.7801	2.95430
$201$	−29.7335	−2.09724
$202$	−29.7379	−2.09235
$203$	17.4191	1.22258
$204$	69.0487	4.83438
$205$	−1.72771	−0.120669
$206$	7.53949	0.525301
$207$	9.22262	0.641016
$208$	−2.97358	−0.206181
$209$	−30.0452	−2.07827
$210$	−7.02806	−0.484982
$211$	21.3947	1.47287	0.736435	−	0.676509i	$-0.236508\pi$
$211$	21.3947	1.47287	0.736435	+	0.676509i	$0.236508\pi$
$212$	71.2132	4.89094
$213$	8.52502	0.584125
$214$	12.7237	0.869773
$215$	−4.96073	−0.338319
$216$	28.7239	1.95441
$217$	14.1275	0.959036
$218$	17.2106	1.16565
$219$	−31.1084	−2.10211
$220$	14.0842	0.949559
$221$	−1.39125	−0.0935856
$222$	25.5093	1.71207
$223$	−9.87492	−0.661273	−0.330637	−	0.943758i	$-0.607263\pi$
$223$	−9.87492	−0.661273	−0.330637	+	0.943758i	$0.607263\pi$
$224$	43.2995	2.89307
$225$	−6.90528	−0.460352
$226$	−17.5676	−1.16858
$227$	6.06544	0.402577	0.201289	−	0.979532i	$-0.435487\pi$
$227$	6.06544	0.402577	0.201289	+	0.979532i	$0.435487\pi$
$228$	64.5940	4.27784
$229$	16.8609	1.11420	0.557098	−	0.830446i	$-0.311915\pi$
$229$	16.8609	1.11420	0.557098	+	0.830446i	$0.311915\pi$
$230$	8.79491	0.579919
$231$	26.1647	1.72151
$232$	64.2504	4.21824
$233$	21.1090	1.38289	0.691447	−	0.722427i	$-0.256974\pi$
$233$	21.1090	1.38289	0.691447	+	0.722427i	$0.256974\pi$
$234$	0.882442	0.0576870
$235$	−1.34854	−0.0879693
$236$	19.9722	1.30008
$237$	−34.7594	−2.25787
$238$	40.0191	2.59405
$239$	25.5194	1.65071	0.825355	−	0.564614i	$-0.190975\pi$
$239$	25.5194	1.65071	0.825355	+	0.564614i	$0.190975\pi$
$240$	−14.4374	−0.931932
$241$	−4.38295	−0.282331	−0.141165	−	0.989986i	$-0.545085\pi$
$241$	−4.38295	−0.282331	−0.141165	+	0.989986i	$0.545085\pi$
$242$	−42.6585	−2.74219
$243$	−13.9876	−0.897306
$244$	−1.16340	−0.0744794
$245$	0.657526	0.0420078
$246$	−19.0736	−1.21609
$247$	−1.30149	−0.0828120
$248$	52.1091	3.30893
$249$	10.3602	0.656551
$250$	−13.5402	−0.856355
$251$	−15.8248	−0.998855	−0.499428	−	0.866356i	$-0.666456\pi$
$251$	−15.8248	−0.998855	−0.499428	+	0.866356i	$0.666456\pi$
$252$	−18.4028	−1.15927
$253$	−32.7425	−2.05850
$254$	−32.4163	−2.03398
$255$	−6.75485	−0.423005
$256$	19.9259	1.24537
$257$	−15.7477	−0.982312	−0.491156	−	0.871072i	$-0.663426\pi$
$257$	−15.7477	−0.982312	−0.491156	+	0.871072i	$0.663426\pi$
$258$	−54.7654	−3.40954
$259$	10.7188	0.666035
$260$	0.610098	0.0378366
$261$	−10.6191	−0.657306
$262$	−5.76899	−0.356409
$263$	16.4156	1.01223	0.506115	−	0.862466i	$-0.331081\pi$
$263$	16.4156	1.01223	0.506115	+	0.862466i	$0.331081\pi$
$264$	96.5083	5.93967
$265$	−6.96659	−0.427954
$266$	37.4373	2.29543
$267$	−0.736758	−0.0450889
$268$	−74.2459	−4.53529
$269$	19.1499	1.16759	0.583794	−	0.811902i	$-0.301568\pi$
$269$	19.1499	1.16759	0.583794	+	0.811902i	$0.301568\pi$
$270$	−4.52723	−0.275518
$271$	28.2402	1.71547	0.857734	−	0.514094i	$-0.171872\pi$
$271$	28.2402	1.71547	0.857734	+	0.514094i	$0.171872\pi$
$272$	82.2094	4.98468
$273$	1.13340	0.0685962
$274$	43.4793	2.62668
$275$	24.5154	1.47833
$276$	70.3928	4.23715
$277$	−0.156512	−0.00940391	−0.00470195	−	0.999989i	$-0.501497\pi$
$277$	−0.156512	−0.00940391	−0.00470195	+	0.999989i	$0.501497\pi$
$278$	37.3905	2.24253
$279$	−8.61243	−0.515613
$280$	−10.8926	−0.650959
$281$	−0.0972981	−0.00580432	−0.00290216	−	0.999996i	$-0.500924\pi$
$281$	−0.0972981	−0.00580432	−0.00290216	+	0.999996i	$0.500924\pi$
$282$	−14.8876	−0.886545
$283$	−14.5735	−0.866304	−0.433152	−	0.901321i	$-0.642599\pi$
$283$	−14.5735	−0.866304	−0.433152	+	0.901321i	$0.642599\pi$
$284$	21.2874	1.26317
$285$	−6.31905	−0.374308
$286$	−3.13288	−0.185251
$287$	−8.01457	−0.473085
$288$	−26.3963	−1.55542
$289$	21.4634	1.26255
$290$	−10.1266	−0.594656
$291$	26.5973	1.55916
$292$	−77.6792	−4.54583
$293$	29.6258	1.73076	0.865379	−	0.501118i	$-0.167078\pi$
$293$	29.6258	1.73076	0.865379	+	0.501118i	$0.167078\pi$
$294$	7.25894	0.423350
$295$	−1.95382	−0.113756
$296$	39.5363	2.29800
$297$	16.8544	0.977990
$298$	−46.7142	−2.70608
$299$	−1.41833	−0.0820242
$300$	−52.7054	−3.04295
$301$	−23.0120	−1.32639
$302$	2.28609	0.131550
$303$	23.2845	1.33766
$304$	76.9057	4.41084
$305$	0.113813	0.00651689
$306$	−24.3966	−1.39466
$307$	5.04627	0.288006	0.144003	−	0.989577i	$-0.454003\pi$
$307$	5.04627	0.288006	0.144003	+	0.989577i	$0.454003\pi$
$308$	65.3344	3.72277
$309$	−5.90335	−0.335830
$310$	−8.21301	−0.466468
$311$	−23.2867	−1.32047	−0.660235	−	0.751059i	$-0.729543\pi$
$311$	−23.2867	−1.32047	−0.660235	+	0.751059i	$0.729543\pi$
$312$	4.18052	0.236675
$313$	−8.02511	−0.453606	−0.226803	−	0.973941i	$-0.572827\pi$
$313$	−8.02511	−0.453606	−0.226803	+	0.973941i	$0.572827\pi$
$314$	−40.6237	−2.29253
$315$	1.80030	0.101435
$316$	−86.7958	−4.88265
$317$	−15.7717	−0.885829	−0.442915	−	0.896564i	$-0.646056\pi$
$317$	−15.7717	−0.885829	−0.442915	+	0.896564i	$0.646056\pi$
$318$	−76.9096	−4.31288
$319$	37.7003	2.11081
$320$	−11.4975	−0.642729
$321$	−9.96253	−0.556054
$322$	40.7981	2.27359
$323$	35.9819	2.00209
$324$	−59.3083	−3.29491
$325$	1.06195	0.0589064
$326$	−61.8681	−3.42656
$327$	−13.4758	−0.745212
$328$	−29.5617	−1.63227
$329$	−6.25566	−0.344886
$330$	−15.2109	−0.837330
$331$	−18.0566	−0.992480	−0.496240	−	0.868185i	$-0.665286\pi$
$331$	−18.0566	−0.992480	−0.496240	+	0.868185i	$0.665286\pi$
$332$	25.8699	1.41979
$333$	−6.53443	−0.358085
$334$	−6.17329	−0.337788
$335$	7.26327	0.396835
$336$	−66.9727	−3.65366
$337$	32.1742	1.75264	0.876320	−	0.481730i	$-0.159991\pi$
$337$	32.1742	1.75264	0.876320	+	0.481730i	$0.159991\pi$
$338$	34.9225	1.89953
$339$	13.7553	0.747085
$340$	−16.8672	−0.914750
$341$	30.5761	1.65579
$342$	−22.8226	−1.23410
$343$	19.7994	1.06907
$344$	−84.8796	−4.57640
$345$	−6.88633	−0.370747
$346$	69.1365	3.71680
$347$	−11.2239	−0.602530	−0.301265	−	0.953541i	$-0.597409\pi$
$347$	−11.2239	−0.602530	−0.301265	+	0.953541i	$0.597409\pi$
$348$	−81.0516	−4.34482
$349$	3.74787	0.200619	0.100309	−	0.994956i	$-0.468017\pi$
$349$	3.74787	0.200619	0.100309	+	0.994956i	$0.468017\pi$
$350$	−30.5469	−1.63280
$351$	0.730094	0.0389695
$352$	93.7131	4.99493
$353$	−12.1360	−0.645935	−0.322968	−	0.946410i	$-0.604681\pi$
$353$	−12.1360	−0.645935	−0.322968	+	0.946410i	$0.604681\pi$
$354$	−21.5698	−1.14642
$355$	−2.08248	−0.110527
$356$	−1.83972	−0.0975049
$357$	−31.3346	−1.65840
$358$	−31.4463	−1.66199
$359$	9.90402	0.522714	0.261357	−	0.965242i	$-0.415830\pi$
$359$	9.90402	0.522714	0.261357	+	0.965242i	$0.415830\pi$
$360$	6.64039	0.349979
$361$	14.6605	0.771606
$362$	15.3039	0.804353
$363$	33.4012	1.75311
$364$	2.83014	0.148340
$365$	7.59914	0.397757
$366$	1.25647	0.0656766
$367$	25.4116	1.32648	0.663238	−	0.748409i	$-0.269182\pi$
$367$	25.4116	1.32648	0.663238	+	0.748409i	$0.269182\pi$
$368$	83.8096	4.36888
$369$	4.88586	0.254348
$370$	−6.23139	−0.323954
$371$	−32.3168	−1.67781
$372$	−65.7354	−3.40822
$373$	20.5130	1.06212	0.531061	−	0.847333i	$-0.321793\pi$
$373$	20.5130	1.06212	0.531061	+	0.847333i	$0.321793\pi$
$374$	86.6135	4.47868
$375$	10.6018	0.547476
$376$	−23.0740	−1.18995
$377$	1.63309	0.0841086
$378$	−21.0011	−1.08018
$379$	16.4816	0.846603	0.423302	−	0.905989i	$-0.360871\pi$
$379$	16.4816	0.846603	0.423302	+	0.905989i	$0.360871\pi$
$380$	−15.7790	−0.809443
$381$	25.3817	1.30034
$382$	−36.7409	−1.87983
$383$	−25.2852	−1.29201	−0.646006	−	0.763332i	$-0.723562\pi$
$383$	−25.2852	−1.29201	−0.646006	+	0.763332i	$0.723562\pi$
$384$	−50.5078	−2.57747
$385$	−6.39148	−0.325740
$386$	−1.09005	−0.0554820
$387$	14.0286	0.713115
$388$	66.4145	3.37169
$389$	31.3025	1.58710	0.793550	−	0.608505i	$-0.208231\pi$
$389$	31.3025	1.58710	0.793550	+	0.608505i	$0.208231\pi$
$390$	−0.658900	−0.0333647
$391$	39.2121	1.98304
$392$	11.2505	0.568234
$393$	4.51706	0.227856
$394$	35.7431	1.80071
$395$	8.49099	0.427228
$396$	−39.8293	−2.00150
$397$	−5.26773	−0.264380	−0.132190	−	0.991224i	$-0.542201\pi$
$397$	−5.26773	−0.264380	−0.132190	+	0.991224i	$0.542201\pi$
$398$	−37.6690	−1.88818
$399$	−29.3130	−1.46749
$400$	−62.7510	−3.13755
$401$	3.46063	0.172816	0.0864078	−	0.996260i	$-0.472461\pi$
$401$	3.46063	0.172816	0.0864078	+	0.996260i	$0.472461\pi$
$402$	80.1849	3.99926
$403$	1.32449	0.0659775
$404$	58.1425	2.89270
$405$	5.80197	0.288302
$406$	−46.9757	−2.33136
$407$	23.1988	1.14992
$408$	−115.577	−5.72193
$409$	37.0125	1.83015	0.915076	−	0.403282i	$-0.132131\pi$
$409$	37.0125	1.83015	0.915076	+	0.403282i	$0.132131\pi$
$410$	4.65928	0.230105
$411$	−34.0439	−1.67926
$412$	−14.7409	−0.726233
$413$	−9.06345	−0.445983
$414$	−24.8714	−1.22236
$415$	−2.53078	−0.124231
$416$	4.05944	0.199031
$417$	−29.2764	−1.43367
$418$	81.0256	3.96309
$419$	−17.5965	−0.859644	−0.429822	−	0.902914i	$-0.641424\pi$
$419$	−17.5965	−0.859644	−0.429822	+	0.902914i	$0.641424\pi$
$420$	13.7410	0.670492
$421$	−16.9729	−0.827208	−0.413604	−	0.910457i	$-0.635730\pi$
$421$	−16.9729	−0.827208	−0.413604	+	0.910457i	$0.635730\pi$
$422$	−57.6968	−2.80864
$423$	3.81359	0.185423
$424$	−119.200	−5.78888
$425$	−29.3594	−1.42414
$426$	−22.9902	−1.11388
$427$	0.527958	0.0255497
$428$	−24.8769	−1.20247
$429$	2.45301	0.118433
$430$	13.3780	0.645146
$431$	19.8086	0.954149	0.477075	−	0.878863i	$-0.341697\pi$
$431$	19.8086	0.954149	0.477075	+	0.878863i	$0.341697\pi$
$432$	−43.1415	−2.07565
$433$	27.0156	1.29829	0.649143	−	0.760666i	$-0.275128\pi$
$433$	27.0156	1.29829	0.649143	+	0.760666i	$0.275128\pi$
$434$	−38.0988	−1.82880
$435$	7.92905	0.380169
$436$	−33.6496	−1.61152
$437$	36.6823	1.75475
$438$	83.8928	4.00855
$439$	26.7073	1.27467	0.637335	−	0.770587i	$-0.280037\pi$
$439$	26.7073	1.27467	0.637335	+	0.770587i	$0.280037\pi$
$440$	−23.5749	−1.12389
$441$	−1.85944	−0.0885448
$442$	3.75190	0.178460
$443$	34.6713	1.64728	0.823642	−	0.567110i	$-0.191938\pi$
$443$	34.6713	1.64728	0.823642	+	0.567110i	$0.191938\pi$
$444$	−49.8748	−2.36695
$445$	0.179975	0.00853161
$446$	26.6305	1.26099
$447$	36.5768	1.73002
$448$	−53.3349	−2.51984
$449$	−0.0390835	−0.00184446	−0.000922231	−	1.00000i	$-0.500294\pi$
$449$	−0.0390835	−0.00184446	−0.000922231		1.00000i	$0.500294\pi$
$450$	18.6221	0.877852
$451$	−17.3460	−0.816790
$452$	34.3476	1.61558
$453$	−1.78999	−0.0841011
$454$	−16.3572	−0.767681
$455$	−0.276865	−0.0129796
$456$	−108.121	−5.06322
$457$	29.0480	1.35881	0.679405	−	0.733764i	$-0.262238\pi$
$457$	29.0480	1.35881	0.679405	+	0.733764i	$0.262238\pi$
$458$	−45.4701	−2.12468
$459$	−20.1846	−0.942138
$460$	−17.1955	−0.801743
$461$	−1.53698	−0.0715843	−0.0357922	−	0.999359i	$-0.511395\pi$
$461$	−1.53698	−0.0715843	−0.0357922	+	0.999359i	$0.511395\pi$
$462$	−70.5606	−3.28277
$463$	−20.0754	−0.932983	−0.466492	−	0.884526i	$-0.654482\pi$
$463$	−20.0754	−0.932983	−0.466492	+	0.884526i	$0.654482\pi$
$464$	−96.5000	−4.47990
$465$	6.43071	0.298217
$466$	−56.9263	−2.63706
$467$	−12.4858	−0.577774	−0.288887	−	0.957363i	$-0.593285\pi$
$467$	−12.4858	−0.577774	−0.288887	+	0.957363i	$0.593285\pi$
$468$	−1.72532	−0.0797528
$469$	33.6931	1.55580
$470$	3.63673	0.167750
$471$	31.8079	1.46563
$472$	−33.4305	−1.53876
$473$	−49.8049	−2.29003
$474$	93.7387	4.30556
$475$	−27.4652	−1.26019
$476$	−78.2439	−3.58630
$477$	19.7011	0.902050
$478$	−68.8202	−3.14776
$479$	23.2505	1.06234	0.531172	−	0.847264i	$-0.321752\pi$
$479$	23.2505	1.06234	0.531172	+	0.847264i	$0.321752\pi$
$480$	19.7096	0.899614
$481$	1.00492	0.0458203
$482$	11.8199	0.538381
$483$	−31.9445	−1.45353
$484$	83.4042	3.79110
$485$	−6.49715	−0.295020
$486$	37.7216	1.71109
$487$	−27.8564	−1.26229	−0.631146	−	0.775664i	$-0.717415\pi$
$487$	−27.8564	−1.26229	−0.631146	+	0.775664i	$0.717415\pi$
$488$	1.94737	0.0881532
$489$	48.4421	2.19063
$490$	−1.77321	−0.0801053
$491$	11.8873	0.536466	0.268233	−	0.963354i	$-0.413560\pi$
$491$	11.8873	0.536466	0.268233	+	0.963354i	$0.413560\pi$
$492$	37.2919	1.68125
$493$	−45.1495	−2.03343
$494$	3.50985	0.157915
$495$	3.89639	0.175130
$496$	−78.2646	−3.51418
$497$	−9.66029	−0.433323
$498$	−27.9392	−1.25199
$499$	−7.62190	−0.341203	−0.170602	−	0.985340i	$-0.554571\pi$
$499$	−7.62190	−0.341203	−0.170602	+	0.985340i	$0.554571\pi$
$500$	26.4732	1.18392
$501$	4.83363	0.215951
$502$	42.6762	1.90473
$503$	36.2809	1.61769	0.808843	−	0.588024i	$-0.200094\pi$
$503$	36.2809	1.61769	0.808843	+	0.588024i	$0.200094\pi$
$504$	30.8036	1.37210
$505$	−5.68792	−0.253109
$506$	88.2994	3.92539
$507$	−27.3440	−1.21439
$508$	63.3791	2.81199
$509$	43.0078	1.90629	0.953144	−	0.302516i	$-0.0978264\pi$
$509$	43.0078	1.90629	0.953144	+	0.302516i	$0.0978264\pi$
$510$	18.2164	0.806635
$511$	35.2511	1.55942
$512$	−5.89643	−0.260588
$513$	−18.8824	−0.833679
$514$	42.4681	1.87319
$515$	1.44206	0.0635449
$516$	107.075	4.71372
$517$	−13.5392	−0.595451
$518$	−28.9063	−1.27007
$519$	−54.1332	−2.37618
$520$	−1.02121	−0.0447832
$521$	0.764581	0.0334969	0.0167485	−	0.999860i	$-0.494669\pi$
$521$	0.764581	0.0334969	0.0167485	+	0.999860i	$0.494669\pi$
$522$	28.6374	1.25343
$523$	5.53840	0.242177	0.121089	−	0.992642i	$-0.461361\pi$
$523$	5.53840	0.242177	0.121089	+	0.992642i	$0.461361\pi$
$524$	11.2793	0.492739
$525$	23.9179	1.04386
$526$	−44.2694	−1.93024
$527$	−36.6177	−1.59509
$528$	−144.949	−6.30811
$529$	16.9753	0.738058
$530$	18.7874	0.816073
$531$	5.52528	0.239777
$532$	−73.1959	−3.17344
$533$	−0.751388	−0.0325462
$534$	1.98688	0.0859807
$535$	2.43364	0.105215
$536$	124.277	5.36793
$537$	24.6222	1.06253
$538$	−51.6431	−2.22649
$539$	6.60145	0.284345
$540$	8.85147	0.380907
$541$	−17.1790	−0.738582	−0.369291	−	0.929314i	$-0.620399\pi$
$541$	−17.1790	−0.738582	−0.369291	+	0.929314i	$0.620399\pi$
$542$	−76.1577	−3.27125
$543$	−11.9828	−0.514230
$544$	−112.230	−4.81182
$545$	3.29185	0.141007
$546$	−3.05653	−0.130807
$547$	12.9001	0.551570	0.275785	−	0.961219i	$-0.411062\pi$
$547$	12.9001	0.551570	0.275785	+	0.961219i	$0.411062\pi$
$548$	−85.0091	−3.63141
$549$	−0.321855	−0.0137364
$550$	−66.1127	−2.81905
$551$	−42.2367	−1.79934
$552$	−117.827	−5.01505
$553$	39.3883	1.67496
$554$	0.422080	0.0179325
$555$	4.87912	0.207107
$556$	−73.1044	−3.10032
$557$	40.6292	1.72152	0.860758	−	0.509015i	$-0.169990\pi$
$557$	40.6292	1.72152	0.860758	+	0.509015i	$0.169990\pi$
$558$	23.2259	0.983230
$559$	−2.15744	−0.0912499
$560$	16.3600	0.691337
$561$	−67.8175	−2.86326
$562$	0.262392	0.0110683
$563$	−39.8268	−1.67850	−0.839249	−	0.543748i	$-0.817005\pi$
$563$	−39.8268	−1.67850	−0.839249	+	0.543748i	$0.817005\pi$
$564$	29.1077	1.22566
$565$	−3.36013	−0.141362
$566$	39.3016	1.65197
$567$	26.9144	1.13030
$568$	−35.6319	−1.49508
$569$	12.4856	0.523424	0.261712	−	0.965146i	$-0.415713\pi$
$569$	12.4856	0.523424	0.261712	+	0.965146i	$0.415713\pi$
$570$	17.0411	0.713775
$571$	21.7663	0.910892	0.455446	−	0.890263i	$-0.349480\pi$
$571$	21.7663	0.910892	0.455446	+	0.890263i	$0.349480\pi$
$572$	6.12528	0.256111
$573$	28.7678	1.20179
$574$	21.6136	0.902134
$575$	−29.9308	−1.24820
$576$	32.5142	1.35476
$577$	25.4640	1.06008	0.530040	−	0.847972i	$-0.322177\pi$
$577$	25.4640	1.06008	0.530040	+	0.847972i	$0.322177\pi$
$578$	−57.8822	−2.40758
$579$	0.853498	0.0354702
$580$	19.7992	0.822117
$581$	−11.7398	−0.487051
$582$	−71.7271	−2.97318
$583$	−69.9434	−2.89676
$584$	130.023	5.38041
$585$	0.168783	0.00697832
$586$	−79.8945	−3.30041
$587$	−34.7678	−1.43502	−0.717509	−	0.696549i	$-0.754718\pi$
$587$	−34.7678	−1.43502	−0.717509	+	0.696549i	$0.754718\pi$
$588$	−14.1924	−0.585285
$589$	−34.2553	−1.41146
$590$	5.26904	0.216923
$591$	−27.9865	−1.15121
$592$	−59.3810	−2.44054
$593$	−38.3282	−1.57395	−0.786975	−	0.616985i	$-0.788354\pi$
$593$	−38.3282	−1.57395	−0.786975	+	0.616985i	$0.788354\pi$
$594$	−45.4526	−1.86494
$595$	7.65438	0.313799
$596$	91.3339	3.74118
$597$	29.4945	1.20713
$598$	3.82493	0.156413
$599$	36.5774	1.49451	0.747257	−	0.664535i	$-0.231371\pi$
$599$	36.5774	1.49451	0.747257	+	0.664535i	$0.231371\pi$
$600$	88.2210	3.60161
$601$	14.1086	0.575502	0.287751	−	0.957705i	$-0.407093\pi$
$601$	14.1086	0.575502	0.287751	+	0.957705i	$0.407093\pi$
$602$	62.0584	2.52931
$603$	−20.5401	−0.836456
$604$	−4.46968	−0.181869
$605$	−8.15920	−0.331719
$606$	−62.7934	−2.55081
$607$	9.07298	0.368261	0.184131	−	0.982902i	$-0.441053\pi$
$607$	9.07298	0.368261	0.184131	+	0.982902i	$0.441053\pi$
$608$	−104.989	−4.25788
$609$	36.7815	1.49046
$610$	−0.306928	−0.0124272
$611$	−0.586486	−0.0237267
$612$	47.6992	1.92813
$613$	34.5623	1.39596	0.697980	−	0.716118i	$-0.254083\pi$
$613$	34.5623	1.39596	0.697980	+	0.716118i	$0.254083\pi$
$614$	−13.6087	−0.549203
$615$	−3.64817	−0.147108
$616$	−109.360	−4.40624
$617$	11.7161	0.471674	0.235837	−	0.971793i	$-0.424217\pi$
$617$	11.7161	0.471674	0.235837	+	0.971793i	$0.424217\pi$
$618$	15.9201	0.640399
$619$	−0.105246	−0.00423018	−0.00211509	−	0.999998i	$-0.500673\pi$
$619$	−0.105246	−0.00423018	−0.00211509	+	0.999998i	$0.500673\pi$
$620$	16.0578	0.644896
$621$	−20.5775	−0.825748
$622$	62.7994	2.51802
$623$	0.834871	0.0334484
$624$	−6.27888	−0.251356
$625$	21.0799	0.843196
$626$	21.6420	0.864989
$627$	−63.4422	−2.53364
$628$	79.4258	3.16944
$629$	−27.7826	−1.10777
$630$	−4.85502	−0.193429
$631$	−0.640391	−0.0254936	−0.0127468	−	0.999919i	$-0.504058\pi$
$631$	−0.640391	−0.0254936	−0.0127468	+	0.999919i	$0.504058\pi$
$632$	145.283	5.77906
$633$	45.1761	1.79559
$634$	42.5330	1.68920
$635$	−6.20020	−0.246048
$636$	150.371	5.96259
$637$	0.285960	0.0113302
$638$	−101.670	−4.02514
$639$	5.88913	0.232970
$640$	12.3380	0.487702
$641$	−12.2307	−0.483085	−0.241542	−	0.970390i	$-0.577653\pi$
$641$	−12.2307	−0.483085	−0.241542	+	0.970390i	$0.577653\pi$
$642$	26.8668	1.06035
$643$	14.9933	0.591279	0.295639	−	0.955300i	$-0.404467\pi$
$643$	14.9933	0.591279	0.295639	+	0.955300i	$0.404467\pi$
$644$	−79.7668	−3.14325
$645$	−10.4749	−0.412448
$646$	−97.0355	−3.81781
$647$	−37.7829	−1.48540	−0.742699	−	0.669625i	$-0.766455\pi$
$647$	−37.7829	−1.48540	−0.742699	+	0.669625i	$0.766455\pi$
$648$	99.2734	3.89983
$649$	−19.6160	−0.769997
$650$	−2.86385	−0.112330
$651$	29.8310	1.16917
$652$	120.962	4.73724
$653$	−31.0438	−1.21484	−0.607419	−	0.794382i	$-0.707795\pi$
$653$	−31.0438	−1.21484	−0.607419	+	0.794382i	$0.707795\pi$
$654$	36.3413	1.42106
$655$	−1.10342	−0.0431143
$656$	44.3998	1.73352
$657$	−21.4899	−0.838399
$658$	16.8702	0.657668
$659$	−7.74599	−0.301741	−0.150870	−	0.988554i	$-0.548208\pi$
$659$	−7.74599	−0.301741	−0.150870	+	0.988554i	$0.548208\pi$
$660$	29.7397	1.15762
$661$	14.5962	0.567725	0.283863	−	0.958865i	$-0.408384\pi$
$661$	14.5962	0.567725	0.283863	+	0.958865i	$0.408384\pi$
$662$	48.6948	1.89258
$663$	−2.93770	−0.114091
$664$	−43.3023	−1.68046
$665$	7.16055	0.277674
$666$	17.6220	0.682837
$667$	−46.0284	−1.78223
$668$	12.0698	0.466994
$669$	−20.8514	−0.806164
$670$	−19.5875	−0.756731
$671$	1.14266	0.0441119
$672$	91.4293	3.52696
$673$	−21.7037	−0.836617	−0.418308	−	0.908305i	$-0.637377\pi$
$673$	−21.7037	−0.836617	−0.418308	+	0.908305i	$0.637377\pi$
$674$	−86.7669	−3.34213
$675$	15.4071	0.593019
$676$	−68.2791	−2.62612
$677$	47.0155	1.80695	0.903477	−	0.428638i	$-0.141006\pi$
$677$	47.0155	1.80695	0.903477	+	0.428638i	$0.141006\pi$
$678$	−37.0951	−1.42463
$679$	−30.1392	−1.15663
$680$	28.2331	1.08269
$681$	12.8075	0.490785
$682$	−82.4573	−3.15745
$683$	−30.9907	−1.18583	−0.592913	−	0.805266i	$-0.702022\pi$
$683$	−30.9907	−1.18583	−0.592913	+	0.805266i	$0.702022\pi$
$684$	44.6219	1.70616
$685$	8.31620	0.317746
$686$	−53.3947	−2.03862
$687$	35.6027	1.35833
$688$	127.484	4.86027
$689$	−3.02979	−0.115426
$690$	18.5710	0.706984
$691$	−2.81786	−0.107197	−0.0535983	−	0.998563i	$-0.517069\pi$
$691$	−2.81786	−0.107197	−0.0535983	+	0.998563i	$0.517069\pi$
$692$	−135.173	−5.13851
$693$	18.0747	0.686601
$694$	30.2684	1.14897
$695$	7.15160	0.271276
$696$	135.668	5.14250
$697$	20.7734	0.786847
$698$	−10.1072	−0.382563
$699$	44.5728	1.68590
$700$	59.7241	2.25736
$701$	1.20300	0.0454366	0.0227183	−	0.999742i	$-0.492768\pi$
$701$	1.20300	0.0454366	0.0227183	+	0.999742i	$0.492768\pi$
$702$	−1.96891	−0.0743116
$703$	−25.9902	−0.980239
$704$	−115.433	−4.35054
$705$	−2.84753	−0.107244
$706$	32.7283	1.23174
$707$	−26.3853	−0.992321
$708$	42.1724	1.58494
$709$	−44.9216	−1.68707	−0.843533	−	0.537078i	$-0.819528\pi$
$709$	−44.9216	−1.68707	−0.843533	+	0.537078i	$0.819528\pi$
$710$	5.61601	0.210765
$711$	−24.0120	−0.900520
$712$	3.07942	0.115406
$713$	−37.3305	−1.39804
$714$	84.5027	3.16243
$715$	−0.599219	−0.0224095
$716$	61.4827	2.29771
$717$	53.8856	2.01239
$718$	−26.7090	−0.996772
$719$	26.4077	0.984839	0.492420	−	0.870358i	$-0.336113\pi$
$719$	26.4077	0.984839	0.492420	+	0.870358i	$0.336113\pi$
$720$	−9.97344	−0.371688
$721$	6.68949	0.249129
$722$	−39.5362	−1.47139
$723$	−9.25486	−0.344192
$724$	−29.9215	−1.11202
$725$	34.4629	1.27992
$726$	−90.0758	−3.34303
$727$	−11.9846	−0.444485	−0.222243	−	0.974991i	$-0.571338\pi$
$727$	−11.9846	−0.444485	−0.222243	+	0.974991i	$0.571338\pi$
$728$	−4.73724	−0.175574
$729$	4.20921	0.155897
$730$	−20.4932	−0.758489
$731$	59.6459	2.20608
$732$	−2.45660	−0.0907984
$733$	31.5747	1.16624	0.583120	−	0.812386i	$-0.301832\pi$
$733$	31.5747	1.16624	0.583120	+	0.812386i	$0.301832\pi$
$734$	−68.5297	−2.52948
$735$	1.38840	0.0512121
$736$	−114.415	−4.21738
$737$	72.9220	2.68612
$738$	−13.1761	−0.485020
$739$	−48.3469	−1.77847	−0.889235	−	0.457452i	$-0.848762\pi$
$739$	−48.3469	−1.77847	−0.889235	+	0.457452i	$0.848762\pi$
$740$	12.1834	0.447869
$741$	−2.74818	−0.100957
$742$	87.1516	3.19944
$743$	−17.0693	−0.626211	−0.313105	−	0.949718i	$-0.601369\pi$
$743$	−17.0693	−0.626211	−0.313105	+	0.949718i	$0.601369\pi$
$744$	110.031	4.03394
$745$	−8.93494	−0.327351
$746$	−55.3191	−2.02538
$747$	7.15687	0.261856
$748$	−169.343	−6.19181
$749$	11.2892	0.412499
$750$	−28.5908	−1.04399
$751$	−22.5332	−0.822248	−0.411124	−	0.911579i	$-0.634864\pi$
$751$	−22.5332	−0.822248	−0.411124	+	0.911579i	$0.634864\pi$
$752$	34.6556	1.26376
$753$	−33.4151	−1.21771
$754$	−4.40410	−0.160388
$755$	0.437257	0.0159134
$756$	41.0605	1.49335
$757$	44.8893	1.63153	0.815764	−	0.578385i	$-0.196317\pi$
$757$	44.8893	1.63153	0.815764	+	0.578385i	$0.196317\pi$
$758$	−44.4473	−1.61440
$759$	−69.1376	−2.50954
$760$	26.4116	0.958051
$761$	48.1043	1.74378	0.871890	−	0.489702i	$-0.162894\pi$
$761$	48.1043	1.74378	0.871890	+	0.489702i	$0.162894\pi$
$762$	−68.4489	−2.47964
$763$	15.2703	0.552823
$764$	71.8344	2.59888
$765$	−4.66628	−0.168710
$766$	68.1887	2.46376
$767$	−0.849723	−0.0306817
$768$	42.0746	1.51824
$769$	−12.3315	−0.444687	−0.222343	−	0.974968i	$-0.571371\pi$
$769$	−12.3315	−0.444687	−0.222343	+	0.974968i	$0.571371\pi$
$770$	17.2365	0.621159
$771$	−33.2521	−1.19754
$772$	2.13122	0.0767044
$773$	−34.8763	−1.25441	−0.627206	−	0.778854i	$-0.715802\pi$
$773$	−34.8763	−1.25441	−0.627206	+	0.778854i	$0.715802\pi$
$774$	−37.8322	−1.35985
$775$	27.9505	1.00401
$776$	−111.168	−3.99070
$777$	22.6334	0.811968
$778$	−84.4161	−3.02646
$779$	19.4332	0.696265
$780$	1.28826	0.0461270
$781$	−20.9078	−0.748140
$782$	−105.747	−3.78149
$783$	23.6934	0.846732
$784$	−16.8975	−0.603482
$785$	−7.77001	−0.277324
$786$	−12.1815	−0.434501
$787$	−17.7712	−0.633476	−0.316738	−	0.948513i	$-0.602588\pi$
$787$	−17.7712	−0.633476	−0.316738	+	0.948513i	$0.602588\pi$
$788$	−69.8836	−2.48950
$789$	34.6625	1.23402
$790$	−22.8984	−0.814688
$791$	−15.5871	−0.554213
$792$	66.6684	2.36896
$793$	0.0494975	0.00175771
$794$	14.2059	0.504150
$795$	−14.7104	−0.521723
$796$	73.6490	2.61042
$797$	−16.0438	−0.568302	−0.284151	−	0.958780i	$-0.591712\pi$
$797$	−16.0438	−0.568302	−0.284151	+	0.958780i	$0.591712\pi$
$798$	79.0509	2.79837
$799$	16.2144	0.573623
$800$	85.6659	3.02875
$801$	−0.508956	−0.0179831
$802$	−9.33258	−0.329545
$803$	76.2941	2.69236
$804$	−156.774	−5.52901
$805$	7.80337	0.275033
$806$	−3.57187	−0.125814
$807$	40.4360	1.42342
$808$	−97.3219	−3.42377
$809$	1.92763	0.0677719	0.0338859	−	0.999426i	$-0.489212\pi$
$809$	1.92763	0.0677719	0.0338859	+	0.999426i	$0.489212\pi$
$810$	−15.6467	−0.549768
$811$	−26.5886	−0.933653	−0.466827	−	0.884349i	$-0.654603\pi$
$811$	−26.5886	−0.933653	−0.466827	+	0.884349i	$0.654603\pi$
$812$	91.8451	3.22313
$813$	59.6307	2.09134
$814$	−62.5621	−2.19280
$815$	−11.8334	−0.414506
$816$	173.590	6.07686
$817$	55.7978	1.95212
$818$	−99.8148	−3.48994
$819$	0.782955	0.0273587
$820$	−9.10964	−0.318122
$821$	17.0590	0.595364	0.297682	−	0.954665i	$-0.403787\pi$
$821$	17.0590	0.595364	0.297682	+	0.954665i	$0.403787\pi$
$822$	91.8090	3.20221
$823$	−0.409230	−0.0142649	−0.00713243	−	0.999975i	$-0.502270\pi$
$823$	−0.409230	−0.0142649	−0.00713243	+	0.999975i	$0.502270\pi$
$824$	24.6741	0.859564
$825$	51.7656	1.80225
$826$	24.4422	0.850452
$827$	−27.3826	−0.952188	−0.476094	−	0.879394i	$-0.657948\pi$
$827$	−27.3826	−0.952188	−0.476094	+	0.879394i	$0.657948\pi$
$828$	48.6277	1.68993
$829$	−8.84670	−0.307259	−0.153629	−	0.988129i	$-0.549096\pi$
$829$	−8.84670	−0.307259	−0.153629	+	0.988129i	$0.549096\pi$
$830$	6.82496	0.236898
$831$	−0.330484	−0.0114644
$832$	−5.00029	−0.173354
$833$	−7.90584	−0.273921
$834$	78.9521	2.73389
$835$	−1.18075	−0.0408617
$836$	−158.418	−5.47900
$837$	19.2161	0.664205
$838$	47.4539	1.63927
$839$	4.03553	0.139322	0.0696610	−	0.997571i	$-0.477808\pi$
$839$	4.03553	0.139322	0.0696610	+	0.997571i	$0.477808\pi$
$840$	−23.0004	−0.793589
$841$	23.9979	0.827515
$842$	45.7723	1.57742
$843$	−0.205450	−0.00707609
$844$	112.807	3.88296
$845$	6.67956	0.229784
$846$	−10.2844	−0.353586
$847$	−37.8492	−1.30051
$848$	179.031	6.14797
$849$	−30.7727	−1.05612
$850$	79.1759	2.71571
$851$	−28.3234	−0.970914
$852$	44.9495	1.53994
$853$	−42.0223	−1.43881	−0.719407	−	0.694589i	$-0.755586\pi$
$853$	−42.0223	−1.43881	−0.719407	+	0.694589i	$0.755586\pi$
$854$	−1.42379	−0.0487210
$855$	−4.36523	−0.149288
$856$	41.6402	1.42323
$857$	−33.1310	−1.13173	−0.565867	−	0.824496i	$-0.691459\pi$
$857$	−33.1310	−1.13173	−0.565867	+	0.824496i	$0.691459\pi$
$858$	−6.61525	−0.225841
$859$	−18.1779	−0.620223	−0.310111	−	0.950700i	$-0.600366\pi$
$859$	−18.1779	−0.620223	−0.310111	+	0.950700i	$0.600366\pi$
$860$	−26.1562	−0.891920
$861$	−16.9232	−0.576742
$862$	−53.4197	−1.81948
$863$	−6.66000	−0.226709	−0.113354	−	0.993555i	$-0.536160\pi$
$863$	−6.66000	−0.226709	−0.113354	+	0.993555i	$0.536160\pi$
$864$	58.8956	2.00367
$865$	13.2236	0.449616
$866$	−72.8552	−2.47572
$867$	45.3212	1.53919
$868$	74.4893	2.52833
$869$	85.2482	2.89185
$870$	−21.3830	−0.724950
$871$	3.15882	0.107033
$872$	56.3245	1.90739
$873$	18.3735	0.621849
$874$	−98.9242	−3.34616
$875$	−12.0136	−0.406135
$876$	−164.024	−5.54186
$877$	−52.9491	−1.78796	−0.893982	−	0.448102i	$-0.852100\pi$
$877$	−52.9491	−1.78796	−0.893982	+	0.448102i	$0.852100\pi$
$878$	−72.0238	−2.43069
$879$	62.5566	2.10998
$880$	35.4081	1.19361
$881$	31.5753	1.06380	0.531899	−	0.846808i	$-0.321479\pi$
$881$	31.5753	1.06380	0.531899	+	0.846808i	$0.321479\pi$
$882$	5.01451	0.168847
$883$	7.48814	0.251996	0.125998	−	0.992030i	$-0.459787\pi$
$883$	7.48814	0.251996	0.125998	+	0.992030i	$0.459787\pi$
$884$	−7.33558	−0.246722
$885$	−4.12561	−0.138681
$886$	−93.5011	−3.14123
$887$	−5.76105	−0.193437	−0.0967186	−	0.995312i	$-0.530835\pi$
$887$	−5.76105	−0.193437	−0.0967186	+	0.995312i	$0.530835\pi$
$888$	83.4831	2.80151
$889$	−28.7617	−0.964636
$890$	−0.485353	−0.0162691
$891$	58.2508	1.95148
$892$	−52.0670	−1.74333
$893$	15.1683	0.507587
$894$	−98.6398	−3.29901
$895$	−6.01468	−0.201049
$896$	57.2339	1.91205
$897$	−2.99489	−0.0999963
$898$	0.105400	0.00351723
$899$	42.9830	1.43356
$900$	−36.4091	−1.21364
$901$	83.7636	2.79057
$902$	46.7783	1.55755
$903$	−48.5911	−1.61701
$904$	−57.4928	−1.91218
$905$	2.92714	0.0973014
$906$	4.82722	0.160374
$907$	25.9246	0.860812	0.430406	−	0.902635i	$-0.358370\pi$
$907$	25.9246	0.860812	0.430406	+	0.902635i	$0.358370\pi$
$908$	31.9810	1.06133
$909$	16.0851	0.533508
$910$	0.746645	0.0247510
$911$	−12.0988	−0.400852	−0.200426	−	0.979709i	$-0.564233\pi$
$911$	−12.0988	−0.400852	−0.200426	+	0.979709i	$0.564233\pi$
$912$	162.391	5.37729
$913$	−25.4086	−0.840901
$914$	−78.3363	−2.59113
$915$	0.240322	0.00794480
$916$	88.9014	2.93739
$917$	−5.11859	−0.169031
$918$	54.4337	1.79658
$919$	49.8232	1.64352	0.821759	−	0.569836i	$-0.192993\pi$
$919$	49.8232	1.64352	0.821759	+	0.569836i	$0.192993\pi$
$920$	28.7827	0.948937
$921$	10.6555	0.351110
$922$	4.14491	0.136505
$923$	−0.905679	−0.0298108
$924$	137.957	4.53846
$925$	21.2067	0.697271
$926$	54.1391	1.77912
$927$	−4.07806	−0.133941
$928$	131.739	4.32455
$929$	24.6707	0.809419	0.404709	−	0.914445i	$-0.367373\pi$
$929$	24.6707	0.809419	0.404709	+	0.914445i	$0.367373\pi$
$930$	−17.3422	−0.568675
$931$	−7.39579	−0.242387
$932$	111.300	3.64576
$933$	−49.1713	−1.60980
$934$	33.6716	1.10177
$935$	16.5664	0.541779
$936$	2.88793	0.0943948
$937$	−34.0952	−1.11384	−0.556920	−	0.830566i	$-0.688017\pi$
$937$	−34.0952	−1.11384	−0.556920	+	0.830566i	$0.688017\pi$
$938$	−90.8630	−2.96678
$939$	−16.9455	−0.552995
$940$	−7.11040	−0.231916
$941$	−9.09520	−0.296495	−0.148247	−	0.988950i	$-0.547363\pi$
$941$	−9.09520	−0.296495	−0.148247	+	0.988950i	$0.547363\pi$
$942$	−85.7792	−2.79484
$943$	21.1777	0.689641
$944$	50.2104	1.63421
$945$	−4.01683	−0.130668
$946$	134.313	4.36690
$947$	23.8356	0.774553	0.387276	−	0.921964i	$-0.373416\pi$
$947$	23.8356	0.774553	0.387276	+	0.921964i	$0.373416\pi$
$948$	−183.274	−5.95247
$949$	3.30489	0.107281
$950$	74.0678	2.40308
$951$	−33.3029	−1.07992
$952$	130.969	4.24472
$953$	8.72912	0.282764	0.141382	−	0.989955i	$-0.454845\pi$
$953$	8.72912	0.282764	0.141382	+	0.989955i	$0.454845\pi$
$954$	−53.1296	−1.72013
$955$	−7.02736	−0.227400
$956$	134.555	4.35181
$957$	79.6064	2.57331
$958$	−62.7017	−2.02580
$959$	38.5774	1.24573
$960$	−24.2776	−0.783556
$961$	3.86058	0.124535
$962$	−2.71005	−0.0873755
$963$	−6.88216	−0.221775
$964$	−23.1098	−0.744316
$965$	−0.208492	−0.00671158
$966$	86.1475	2.77175
$967$	23.0298	0.740590	0.370295	−	0.928914i	$-0.379257\pi$
$967$	23.0298	0.740590	0.370295	+	0.928914i	$0.379257\pi$
$968$	−139.606	−4.48712
$969$	75.9778	2.44076
$970$	17.5214	0.562579
$971$	5.76075	0.184871	0.0924356	−	0.995719i	$-0.470535\pi$
$971$	5.76075	0.184871	0.0924356	+	0.995719i	$0.470535\pi$
$972$	−73.7519	−2.36559
$973$	33.1751	1.06354
$974$	75.1226	2.40708
$975$	2.24237	0.0718133
$976$	−2.92482	−0.0936213
$977$	−30.9862	−0.991336	−0.495668	−	0.868512i	$-0.665077\pi$
$977$	−30.9862	−0.991336	−0.495668	+	0.868512i	$0.665077\pi$
$978$	−130.638	−4.17734
$979$	1.80691	0.0577492
$980$	3.46691	0.110746
$981$	−9.30913	−0.297218
$982$	−32.0575	−1.02300
$983$	18.7002	0.596444	0.298222	−	0.954496i	$-0.403606\pi$
$983$	18.7002	0.596444	0.298222	+	0.954496i	$0.403606\pi$
$984$	−62.4212	−1.98992
$985$	6.83652	0.217830
$986$	121.759	3.87758
$987$	−13.2092	−0.420453
$988$	−6.86232	−0.218319
$989$	60.8069	1.93355
$990$	−10.5077	−0.333958
$991$	−26.8174	−0.851883	−0.425942	−	0.904751i	$-0.640057\pi$
$991$	−26.8174	−0.851883	−0.425942	+	0.904751i	$0.640057\pi$
$992$	106.845	3.39232
$993$	−38.1275	−1.20994
$994$	26.0517	0.826311
$995$	−7.20487	−0.228410
$996$	54.6257	1.73088
$997$	30.9455	0.980054	0.490027	−	0.871707i	$-0.336987\pi$
$997$	30.9455	0.980054	0.490027	+	0.871707i	$0.336987\pi$
$998$	20.5546	0.650646
$999$	14.5796	0.461279

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8011.2.a.b.1.8	✓	358

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8011.2.a.b.1.8	✓	358	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:	\( N \)	\(=\)	\( 8011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8011.a (trivial)

\(f(q)\)	\(=\)	\(q-2.69679 q^{2} +2.11156 q^{3} +5.27265 q^{4} -0.515809 q^{5} -5.69442 q^{6} -2.39275 q^{7} -8.82564 q^{8} +1.45867 q^{9} +O(q^{10})\)	\(q-2.69679 q^{2} +2.11156 q^{3} +5.27265 q^{4} -0.515809 q^{5} -5.69442 q^{6} -2.39275 q^{7} -8.82564 q^{8} +1.45867 q^{9} +1.39103 q^{10} -5.17864 q^{11} +11.1335 q^{12} -0.224327 q^{13} +6.45273 q^{14} -1.08916 q^{15} +13.2556 q^{16} +6.20189 q^{17} -3.93373 q^{18} +5.80177 q^{19} -2.71968 q^{20} -5.05243 q^{21} +13.9657 q^{22} +6.32260 q^{23} -18.6358 q^{24} -4.73394 q^{25} +0.604962 q^{26} -3.25460 q^{27} -12.6161 q^{28} -7.27997 q^{29} +2.93723 q^{30} -5.90428 q^{31} -18.0961 q^{32} -10.9350 q^{33} -16.7252 q^{34} +1.23420 q^{35} +7.69108 q^{36} -4.47970 q^{37} -15.6461 q^{38} -0.473679 q^{39} +4.55234 q^{40} +3.34952 q^{41} +13.6253 q^{42} +9.61738 q^{43} -27.3051 q^{44} -0.752397 q^{45} -17.0507 q^{46} +2.61442 q^{47} +27.9899 q^{48} -1.27475 q^{49} +12.7664 q^{50} +13.0956 q^{51} -1.18280 q^{52} +13.5061 q^{53} +8.77695 q^{54} +2.67119 q^{55} +21.1176 q^{56} +12.2508 q^{57} +19.6325 q^{58} +3.78788 q^{59} -5.74276 q^{60} -0.220649 q^{61} +15.9226 q^{62} -3.49024 q^{63} +22.2902 q^{64} +0.115710 q^{65} +29.4893 q^{66} -14.0813 q^{67} +32.7004 q^{68} +13.3505 q^{69} -3.32838 q^{70} +4.03732 q^{71} -12.8737 q^{72} -14.7325 q^{73} +12.0808 q^{74} -9.99599 q^{75} +30.5907 q^{76} +12.3912 q^{77} +1.27741 q^{78} -16.4615 q^{79} -6.83733 q^{80} -11.2483 q^{81} -9.03295 q^{82} +4.90642 q^{83} -26.6397 q^{84} -3.19899 q^{85} -25.9360 q^{86} -15.3721 q^{87} +45.7048 q^{88} -0.348917 q^{89} +2.02905 q^{90} +0.536758 q^{91} +33.3369 q^{92} -12.4672 q^{93} -7.05054 q^{94} -2.99260 q^{95} -38.2110 q^{96} +12.5960 q^{97} +3.43772 q^{98} -7.55394 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 358 q + 33 q^{2} + 11 q^{3} + 391 q^{4} + 76 q^{5} + 32 q^{6} + 19 q^{7} + 99 q^{8} + 451 q^{9}+O(q^{10}) \) 358 * q + 33 * q^2 + 11 * q^3 + 391 * q^4 + 76 * q^5 + 32 * q^6 + 19 * q^7 + 99 * q^8 + 451 * q^9	\( 358 q + 33 q^{2} + 11 q^{3} + 391 q^{4} + 76 q^{5} + 32 q^{6} + 19 q^{7} + 99 q^{8} + 451 q^{9} + 21 q^{10} + 70 q^{11} + 20 q^{12} + 53 q^{13} + 69 q^{14} + 28 q^{15} + 449 q^{16} + 88 q^{17} + 86 q^{18} + 44 q^{19} + 136 q^{20} + 125 q^{21} + 17 q^{22} + 104 q^{23} + 84 q^{24} + 444 q^{25} + 100 q^{26} + 32 q^{27} + 46 q^{28} + 373 q^{29} + 99 q^{30} + 30 q^{31} + 221 q^{32} + 56 q^{33} + 26 q^{34} + 164 q^{35} + 599 q^{36} + 81 q^{37} + 66 q^{38} + 143 q^{39} + 42 q^{40} + 182 q^{41} + 32 q^{42} + 40 q^{43} + 184 q^{44} + 198 q^{45} + 54 q^{46} + 66 q^{47} + 5 q^{48} + 479 q^{49} + 184 q^{50} + 123 q^{51} + 64 q^{52} + 221 q^{53} + 67 q^{54} + 38 q^{55} + 174 q^{56} + 84 q^{57} + 44 q^{58} + 127 q^{59} + 29 q^{60} + 174 q^{61} + 86 q^{62} + 48 q^{63} + 549 q^{64} + 202 q^{65} + 32 q^{66} + 29 q^{67} + 172 q^{68} + 249 q^{69} + 12 q^{70} + 185 q^{71} + 218 q^{72} + 57 q^{73} + 272 q^{74} + 24 q^{75} + 84 q^{76} + 384 q^{77} + 12 q^{78} + 93 q^{79} + 215 q^{80} + 702 q^{81} + 48 q^{82} + 121 q^{83} + 179 q^{84} + 177 q^{85} + 209 q^{86} + 91 q^{87} + 36 q^{88} + 186 q^{89} + 66 q^{90} + 32 q^{91} + 272 q^{92} + 220 q^{93} + 60 q^{94} + 170 q^{95} + 162 q^{96} + 22 q^{97} + 196 q^{98} + 152 q^{99}+O(q^{100}) \) 358 * q + 33 * q^2 + 11 * q^3 + 391 * q^4 + 76 * q^5 + 32 * q^6 + 19 * q^7 + 99 * q^8 + 451 * q^9 + 21 * q^10 + 70 * q^11 + 20 * q^12 + 53 * q^13 + 69 * q^14 + 28 * q^15 + 449 * q^16 + 88 * q^17 + 86 * q^18 + 44 * q^19 + 136 * q^20 + 125 * q^21 + 17 * q^22 + 104 * q^23 + 84 * q^24 + 444 * q^25 + 100 * q^26 + 32 * q^27 + 46 * q^28 + 373 * q^29 + 99 * q^30 + 30 * q^31 + 221 * q^32 + 56 * q^33 + 26 * q^34 + 164 * q^35 + 599 * q^36 + 81 * q^37 + 66 * q^38 + 143 * q^39 + 42 * q^40 + 182 * q^41 + 32 * q^42 + 40 * q^43 + 184 * q^44 + 198 * q^45 + 54 * q^46 + 66 * q^47 + 5 * q^48 + 479 * q^49 + 184 * q^50 + 123 * q^51 + 64 * q^52 + 221 * q^53 + 67 * q^54 + 38 * q^55 + 174 * q^56 + 84 * q^57 + 44 * q^58 + 127 * q^59 + 29 * q^60 + 174 * q^61 + 86 * q^62 + 48 * q^63 + 549 * q^64 + 202 * q^65 + 32 * q^66 + 29 * q^67 + 172 * q^68 + 249 * q^69 + 12 * q^70 + 185 * q^71 + 218 * q^72 + 57 * q^73 + 272 * q^74 + 24 * q^75 + 84 * q^76 + 384 * q^77 + 12 * q^78 + 93 * q^79 + 215 * q^80 + 702 * q^81 + 48 * q^82 + 121 * q^83 + 179 * q^84 + 177 * q^85 + 209 * q^86 + 91 * q^87 + 36 * q^88 + 186 * q^89 + 66 * q^90 + 32 * q^91 + 272 * q^92 + 220 * q^93 + 60 * q^94 + 170 * q^95 + 162 * q^96 + 22 * q^97 + 196 * q^98 + 152 * q^99

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