LMFDB - Embedded newform 8017.2.a.b.1.16

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			1.16
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)

$f(q)$	$=$	$q-2.60414 q^{2} +2.31571 q^{3} +4.78154 q^{4} +3.50289 q^{5} -6.03042 q^{6} -2.38601 q^{7} -7.24351 q^{8} +2.36250 q^{9} +O(q^{10})$	\(q-2.60414 q^{2} +2.31571 q^{3} +4.78154 q^{4} +3.50289 q^{5} -6.03042 q^{6} -2.38601 q^{7} -7.24351 q^{8} +2.36250 q^{9} -9.12202 q^{10} +0.904754 q^{11} +11.0726 q^{12} +5.02994 q^{13} +6.21349 q^{14} +8.11167 q^{15} +9.30003 q^{16} +2.15337 q^{17} -6.15228 q^{18} +6.23578 q^{19} +16.7492 q^{20} -5.52529 q^{21} -2.35610 q^{22} +5.91196 q^{23} -16.7738 q^{24} +7.27026 q^{25} -13.0987 q^{26} -1.47626 q^{27} -11.4088 q^{28} -0.142783 q^{29} -21.1239 q^{30} -1.68754 q^{31} -9.73155 q^{32} +2.09515 q^{33} -5.60768 q^{34} -8.35793 q^{35} +11.2964 q^{36} +0.823416 q^{37} -16.2388 q^{38} +11.6479 q^{39} -25.3732 q^{40} +8.14840 q^{41} +14.3886 q^{42} +7.35565 q^{43} +4.32612 q^{44} +8.27558 q^{45} -15.3956 q^{46} -4.35164 q^{47} +21.5361 q^{48} -1.30697 q^{49} -18.9328 q^{50} +4.98658 q^{51} +24.0508 q^{52} +7.16849 q^{53} +3.84440 q^{54} +3.16926 q^{55} +17.2831 q^{56} +14.4402 q^{57} +0.371826 q^{58} -5.10214 q^{59} +38.7863 q^{60} +9.33315 q^{61} +4.39458 q^{62} -5.63694 q^{63} +6.74223 q^{64} +17.6193 q^{65} -5.45605 q^{66} -3.51279 q^{67} +10.2964 q^{68} +13.6904 q^{69} +21.7652 q^{70} +9.00893 q^{71} -17.1128 q^{72} +4.28433 q^{73} -2.14429 q^{74} +16.8358 q^{75} +29.8166 q^{76} -2.15875 q^{77} -30.3326 q^{78} -16.1275 q^{79} +32.5770 q^{80} -10.5061 q^{81} -21.2196 q^{82} -7.26874 q^{83} -26.4194 q^{84} +7.54303 q^{85} -19.1551 q^{86} -0.330643 q^{87} -6.55359 q^{88} -8.02758 q^{89} -21.5508 q^{90} -12.0015 q^{91} +28.2683 q^{92} -3.90784 q^{93} +11.3323 q^{94} +21.8433 q^{95} -22.5354 q^{96} -12.2490 q^{97} +3.40354 q^{98} +2.13748 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.60414	−1.84140	−0.920702	−	0.390266i	$-0.872383\pi$
$2$	−2.60414	−1.84140	−0.920702	+	0.390266i	$0.872383\pi$
$3$	2.31571	1.33697	0.668487	−	0.743724i	$-0.266942\pi$
$3$	2.31571	1.33697	0.668487	+	0.743724i	$0.266942\pi$
$4$	4.78154	2.39077
$5$	3.50289	1.56654	0.783271	−	0.621681i	$-0.213550\pi$
$5$	3.50289	1.56654	0.783271	+	0.621681i	$0.213550\pi$
$6$	−6.03042	−2.46191
$7$	−2.38601	−0.901826	−0.450913	−	0.892568i	$-0.648901\pi$
$7$	−2.38601	−0.901826	−0.450913	+	0.892568i	$0.648901\pi$
$8$	−7.24351	−2.56097
$9$	2.36250	0.787500
$10$	−9.12202	−2.88464
$11$	0.904754	0.272794	0.136397	−	0.990654i	$-0.456448\pi$
$11$	0.904754	0.272794	0.136397	+	0.990654i	$0.456448\pi$
$12$	11.0726	3.19640
$13$	5.02994	1.39505	0.697527	−	0.716559i	$-0.254284\pi$
$13$	5.02994	1.39505	0.697527	+	0.716559i	$0.254284\pi$
$14$	6.21349	1.66063
$15$	8.11167	2.09443
$16$	9.30003	2.32501
$17$	2.15337	0.522269	0.261135	−	0.965302i	$-0.415903\pi$
$17$	2.15337	0.522269	0.261135	+	0.965302i	$0.415903\pi$
$18$	−6.15228	−1.45011
$19$	6.23578	1.43058	0.715292	−	0.698825i	$-0.246293\pi$
$19$	6.23578	1.43058	0.715292	+	0.698825i	$0.246293\pi$
$20$	16.7492	3.74524
$21$	−5.52529	−1.20572
$22$	−2.35610	−0.502323
$23$	5.91196	1.23273	0.616365	−	0.787461i	$-0.288605\pi$
$23$	5.91196	1.23273	0.616365	+	0.787461i	$0.288605\pi$
$24$	−16.7738	−3.42395
$25$	7.27026	1.45405
$26$	−13.0987	−2.56886
$27$	−1.47626	−0.284107
$28$	−11.4088	−2.15606
$29$	−0.142783	−0.0265141	−0.0132570	−	0.999912i	$-0.504220\pi$
$29$	−0.142783	−0.0265141	−0.0132570	+	0.999912i	$0.504220\pi$
$30$	−21.1239	−3.85668
$31$	−1.68754	−0.303091	−0.151545	−	0.988450i	$-0.548425\pi$
$31$	−1.68754	−0.303091	−0.151545	+	0.988450i	$0.548425\pi$
$32$	−9.73155	−1.72031
$33$	2.09515	0.364718
$34$	−5.60768	−0.961709
$35$	−8.35793	−1.41275
$36$	11.2964	1.88273
$37$	0.823416	0.135369	0.0676844	−	0.997707i	$-0.478439\pi$
$37$	0.823416	0.135369	0.0676844	+	0.997707i	$0.478439\pi$
$38$	−16.2388	−2.63429
$39$	11.6479	1.86515
$40$	−25.3732	−4.01186
$41$	8.14840	1.27257	0.636283	−	0.771456i	$-0.280471\pi$
$41$	8.14840	1.27257	0.636283	+	0.771456i	$0.280471\pi$
$42$	14.3886	2.22021
$43$	7.35565	1.12173	0.560863	−	0.827909i	$-0.310469\pi$
$43$	7.35565	1.12173	0.560863	+	0.827909i	$0.310469\pi$
$44$	4.32612	0.652186
$45$	8.27558	1.23365
$46$	−15.3956	−2.26995
$47$	−4.35164	−0.634752	−0.317376	−	0.948300i	$-0.602802\pi$
$47$	−4.35164	−0.634752	−0.317376	+	0.948300i	$0.602802\pi$
$48$	21.5361	3.10847
$49$	−1.30697	−0.186711
$50$	−18.9328	−2.67750
$51$	4.98658	0.698260
$52$	24.0508	3.33525
$53$	7.16849	0.984668	0.492334	−	0.870406i	$-0.336144\pi$
$53$	7.16849	0.984668	0.492334	+	0.870406i	$0.336144\pi$
$54$	3.84440	0.523156
$55$	3.16926	0.427342
$56$	17.2831	2.30955
$57$	14.4402	1.91266
$58$	0.371826	0.0488231
$59$	−5.10214	−0.664242	−0.332121	−	0.943237i	$-0.607764\pi$
$59$	−5.10214	−0.664242	−0.332121	+	0.943237i	$0.607764\pi$
$60$	38.7863	5.00729
$61$	9.33315	1.19499	0.597493	−	0.801874i	$-0.296163\pi$
$61$	9.33315	1.19499	0.597493	+	0.801874i	$0.296163\pi$
$62$	4.39458	0.558112
$63$	−5.63694	−0.710188
$64$	6.74223	0.842779
$65$	17.6193	2.18541
$66$	−5.45605	−0.671593
$67$	−3.51279	−0.429156	−0.214578	−	0.976707i	$-0.568838\pi$
$67$	−3.51279	−0.429156	−0.214578	+	0.976707i	$0.568838\pi$
$68$	10.2964	1.24862
$69$	13.6904	1.64813
$70$	21.7652	2.60144
$71$	9.00893	1.06916	0.534581	−	0.845117i	$-0.320469\pi$
$71$	9.00893	1.06916	0.534581	+	0.845117i	$0.320469\pi$
$72$	−17.1128	−2.01676
$73$	4.28433	0.501443	0.250722	−	0.968059i	$-0.419332\pi$
$73$	4.28433	0.501443	0.250722	+	0.968059i	$0.419332\pi$
$74$	−2.14429	−0.249269
$75$	16.8358	1.94403
$76$	29.8166	3.42020
$77$	−2.15875	−0.246012
$78$	−30.3326	−3.43450
$79$	−16.1275	−1.81448	−0.907242	−	0.420610i	$-0.861816\pi$
$79$	−16.1275	−1.81448	−0.907242	+	0.420610i	$0.861816\pi$
$80$	32.5770	3.64222
$81$	−10.5061	−1.16734
$82$	−21.2196	−2.34331
$83$	−7.26874	−0.797848	−0.398924	−	0.916984i	$-0.630616\pi$
$83$	−7.26874	−0.797848	−0.398924	+	0.916984i	$0.630616\pi$
$84$	−26.4194	−2.88259
$85$	7.54303	0.818156
$86$	−19.1551	−2.06555
$87$	−0.330643	−0.0354486
$88$	−6.55359	−0.698616
$89$	−8.02758	−0.850922	−0.425461	−	0.904977i	$-0.639888\pi$
$89$	−8.02758	−0.850922	−0.425461	+	0.904977i	$0.639888\pi$
$90$	−21.5508	−2.27165
$91$	−12.0015	−1.25810
$92$	28.2683	2.94717
$93$	−3.90784	−0.405224
$94$	11.3323	1.16883
$95$	21.8433	2.24107
$96$	−22.5354	−2.30001
$97$	−12.2490	−1.24369	−0.621847	−	0.783139i	$-0.713617\pi$
$97$	−12.2490	−1.24369	−0.621847	+	0.783139i	$0.713617\pi$
$98$	3.40354	0.343809
$99$	2.13748	0.214825
$100$	34.7630	3.47630
$101$	−0.742102	−0.0738419	−0.0369210	−	0.999318i	$-0.511755\pi$
$101$	−0.742102	−0.0738419	−0.0369210	+	0.999318i	$0.511755\pi$
$102$	−12.9857	−1.28578
$103$	1.92592	0.189766	0.0948832	−	0.995488i	$-0.469752\pi$
$103$	1.92592	0.189766	0.0948832	+	0.995488i	$0.469752\pi$
$104$	−36.4344	−3.57269
$105$	−19.3545	−1.88881
$106$	−18.6677	−1.81317
$107$	−9.06085	−0.875946	−0.437973	−	0.898988i	$-0.644303\pi$
$107$	−9.06085	−0.875946	−0.437973	+	0.898988i	$0.644303\pi$
$108$	−7.05881	−0.679235
$109$	−12.7189	−1.21825	−0.609127	−	0.793073i	$-0.708480\pi$
$109$	−12.7189	−1.21825	−0.609127	+	0.793073i	$0.708480\pi$
$110$	−8.25318	−0.786910
$111$	1.90679	0.180985
$112$	−22.1899	−2.09675
$113$	−16.4494	−1.54743	−0.773716	−	0.633533i	$-0.781604\pi$
$113$	−16.4494	−1.54743	−0.773716	+	0.633533i	$0.781604\pi$
$114$	−37.6044	−3.52197
$115$	20.7090	1.93112
$116$	−0.682720	−0.0633890
$117$	11.8832	1.09860
$118$	13.2867	1.22314
$119$	−5.13796	−0.470996
$120$	−58.7570	−5.36376
$121$	−10.1814	−0.925584
$122$	−24.3048	−2.20045
$123$	18.8693	1.70139
$124$	−8.06902	−0.724619
$125$	7.95248	0.711291
$126$	14.6794	1.30774
$127$	−0.0255445	−0.00226671	−0.00113335	−	0.999999i	$-0.500361\pi$
$127$	−0.0255445	−0.00226671	−0.00113335	+	0.999999i	$0.500361\pi$
$128$	1.90538	0.168413
$129$	17.0335	1.49972
$130$	−45.8832	−4.02422
$131$	16.0475	1.40207	0.701037	−	0.713125i	$-0.252721\pi$
$131$	16.0475	1.40207	0.701037	+	0.713125i	$0.252721\pi$
$132$	10.0180	0.871956
$133$	−14.8786	−1.29014
$134$	9.14780	0.790250
$135$	−5.17119	−0.445066
$136$	−15.5980	−1.33751
$137$	3.24139	0.276931	0.138465	−	0.990367i	$-0.455783\pi$
$137$	3.24139	0.276931	0.138465	+	0.990367i	$0.455783\pi$
$138$	−35.6516	−3.03487
$139$	16.6754	1.41439	0.707194	−	0.707020i	$-0.249961\pi$
$139$	16.6754	1.41439	0.707194	+	0.707020i	$0.249961\pi$
$140$	−39.9637	−3.37755
$141$	−10.0771	−0.848647
$142$	−23.4605	−1.96876
$143$	4.55086	0.380562
$144$	21.9713	1.83094
$145$	−0.500152	−0.0415354
$146$	−11.1570	−0.923360
$147$	−3.02657	−0.249627
$148$	3.93719	0.323635
$149$	−13.0498	−1.06908	−0.534540	−	0.845143i	$-0.679515\pi$
$149$	−13.0498	−1.06908	−0.534540	+	0.845143i	$0.679515\pi$
$150$	−43.8427	−3.57974
$151$	15.8509	1.28993	0.644964	−	0.764213i	$-0.276873\pi$
$151$	15.8509	1.28993	0.644964	+	0.764213i	$0.276873\pi$
$152$	−45.1689	−3.66368
$153$	5.08734	0.411287
$154$	5.62168	0.453008
$155$	−5.91126	−0.474804
$156$	55.6947	4.45914
$157$	−9.33098	−0.744693	−0.372347	−	0.928094i	$-0.621447\pi$
$157$	−9.33098	−0.744693	−0.372347	+	0.928094i	$0.621447\pi$
$158$	41.9982	3.34120
$159$	16.6001	1.31648
$160$	−34.0886	−2.69494
$161$	−14.1060	−1.11171
$162$	27.3593	2.14955
$163$	2.14033	0.167644	0.0838219	−	0.996481i	$-0.473287\pi$
$163$	2.14033	0.167644	0.0838219	+	0.996481i	$0.473287\pi$
$164$	38.9619	3.04241
$165$	7.33907	0.571346
$166$	18.9288	1.46916
$167$	−6.08690	−0.471018	−0.235509	−	0.971872i	$-0.575676\pi$
$167$	−6.08690	−0.471018	−0.235509	+	0.971872i	$0.575676\pi$
$168$	40.0225	3.08780
$169$	12.3003	0.946174
$170$	−19.6431	−1.50656
$171$	14.7320	1.12659
$172$	35.1713	2.68179
$173$	−0.927455	−0.0705131	−0.0352566	−	0.999378i	$-0.511225\pi$
$173$	−0.927455	−0.0705131	−0.0352566	+	0.999378i	$0.511225\pi$
$174$	0.861039	0.0652752
$175$	−17.3469	−1.31130
$176$	8.41424	0.634247
$177$	−11.8151	−0.888074
$178$	20.9049	1.56689
$179$	−8.42476	−0.629696	−0.314848	−	0.949142i	$-0.601954\pi$
$179$	−8.42476	−0.629696	−0.314848	+	0.949142i	$0.601954\pi$
$180$	39.5700	2.94937
$181$	−25.3390	−1.88344	−0.941718	−	0.336405i	$-0.890789\pi$
$181$	−25.3390	−1.88344	−0.941718	+	0.336405i	$0.890789\pi$
$182$	31.2535	2.31666
$183$	21.6128	1.59767
$184$	−42.8234	−3.15698
$185$	2.88434	0.212061
$186$	10.1766	0.746182
$187$	1.94827	0.142472
$188$	−20.8075	−1.51755
$189$	3.52238	0.256215
$190$	−56.8829	−4.12672
$191$	−12.1659	−0.880294	−0.440147	−	0.897926i	$-0.645074\pi$
$191$	−12.1659	−0.880294	−0.440147	+	0.897926i	$0.645074\pi$
$192$	15.6130	1.12677
$193$	−16.5426	−1.19077	−0.595383	−	0.803442i	$-0.703000\pi$
$193$	−16.5426	−1.19077	−0.595383	+	0.803442i	$0.703000\pi$
$194$	31.8980	2.29014
$195$	40.8012	2.92184
$196$	−6.24934	−0.446382
$197$	−18.9392	−1.34936	−0.674680	−	0.738110i	$-0.735718\pi$
$197$	−18.9392	−1.34936	−0.674680	+	0.738110i	$0.735718\pi$
$198$	−5.56630	−0.395579
$199$	8.64906	0.613116	0.306558	−	0.951852i	$-0.400823\pi$
$199$	8.64906	0.613116	0.306558	+	0.951852i	$0.400823\pi$
$200$	−52.6622	−3.72378
$201$	−8.13460	−0.573771
$202$	1.93254	0.135973
$203$	0.340680	0.0239111
$204$	23.8435	1.66938
$205$	28.5430	1.99353
$206$	−5.01536	−0.349437
$207$	13.9670	0.970774
$208$	46.7786	3.24351
$209$	5.64184	0.390254
$210$	50.4018	3.47806
$211$	17.1064	1.17766	0.588828	−	0.808259i	$-0.299590\pi$
$211$	17.1064	1.17766	0.588828	+	0.808259i	$0.299590\pi$
$212$	34.2764	2.35411
$213$	20.8620	1.42944
$214$	23.5957	1.61297
$215$	25.7661	1.75723
$216$	10.6933	0.727589
$217$	4.02647	0.273335
$218$	33.1219	2.24330
$219$	9.92126	0.670417
$220$	15.1539	1.02168
$221$	10.8313	0.728593
$222$	−4.96555	−0.333266
$223$	8.35377	0.559410	0.279705	−	0.960086i	$-0.409763\pi$
$223$	8.35377	0.559410	0.279705	+	0.960086i	$0.409763\pi$
$224$	23.2195	1.55142
$225$	17.1760	1.14507
$226$	42.8366	2.84945
$227$	8.68282	0.576299	0.288150	−	0.957585i	$-0.406960\pi$
$227$	8.68282	0.576299	0.288150	+	0.957585i	$0.406960\pi$
$228$	69.0465	4.57272
$229$	−7.73793	−0.511337	−0.255669	−	0.966764i	$-0.582296\pi$
$229$	−7.73793	−0.511337	−0.255669	+	0.966764i	$0.582296\pi$
$230$	−53.9290	−3.55597
$231$	−4.99903	−0.328912
$232$	1.03425	0.0679016
$233$	7.50387	0.491595	0.245798	−	0.969321i	$-0.420950\pi$
$233$	7.50387	0.491595	0.245798	+	0.969321i	$0.420950\pi$
$234$	−30.9456	−2.02297
$235$	−15.2433	−0.994365
$236$	−24.3961	−1.58805
$237$	−37.3465	−2.42592
$238$	13.3800	0.867293
$239$	5.65830	0.366005	0.183003	−	0.983112i	$-0.441418\pi$
$239$	5.65830	0.366005	0.183003	+	0.983112i	$0.441418\pi$
$240$	75.4388	4.86955
$241$	−5.48928	−0.353596	−0.176798	−	0.984247i	$-0.556574\pi$
$241$	−5.48928	−0.353596	−0.176798	+	0.984247i	$0.556574\pi$
$242$	26.5138	1.70437
$243$	−19.9002	−1.27660
$244$	44.6268	2.85694
$245$	−4.57819	−0.292490
$246$	−49.1383	−3.13294
$247$	31.3656	1.99574
$248$	12.2237	0.776205
$249$	−16.8323	−1.06670
$250$	−20.7094	−1.30977
$251$	22.5926	1.42603	0.713015	−	0.701149i	$-0.247329\pi$
$251$	22.5926	1.42603	0.713015	+	0.701149i	$0.247329\pi$
$252$	−26.9532	−1.69789
$253$	5.34887	0.336281
$254$	0.0665214	0.00417393
$255$	17.4674	1.09385
$256$	−18.4463	−1.15290
$257$	6.89528	0.430116	0.215058	−	0.976601i	$-0.431006\pi$
$257$	6.89528	0.430116	0.215058	+	0.976601i	$0.431006\pi$
$258$	−44.3577	−2.76159
$259$	−1.96468	−0.122079
$260$	84.2475	5.22481
$261$	−0.337324	−0.0208798
$262$	−41.7898	−2.58179
$263$	24.5038	1.51097	0.755485	−	0.655166i	$-0.227401\pi$
$263$	24.5038	1.51097	0.755485	+	0.655166i	$0.227401\pi$
$264$	−15.1762	−0.934031
$265$	25.1105	1.54252
$266$	38.7459	2.37567
$267$	−18.5895	−1.13766
$268$	−16.7966	−1.02601
$269$	−15.6011	−0.951219	−0.475609	−	0.879657i	$-0.657772\pi$
$269$	−15.6011	−0.951219	−0.475609	+	0.879657i	$0.657772\pi$
$270$	13.4665	0.819546
$271$	−12.7069	−0.771889	−0.385944	−	0.922522i	$-0.626124\pi$
$271$	−12.7069	−0.771889	−0.385944	+	0.922522i	$0.626124\pi$
$272$	20.0264	1.21428
$273$	−27.7919	−1.68204
$274$	−8.44104	−0.509942
$275$	6.57780	0.396656
$276$	65.4610	3.94029
$277$	21.0328	1.26374	0.631868	−	0.775076i	$-0.282288\pi$
$277$	21.0328	1.26374	0.631868	+	0.775076i	$0.282288\pi$
$278$	−43.4250	−2.60446
$279$	−3.98681	−0.238684
$280$	60.5407	3.61800
$281$	15.6570	0.934020	0.467010	−	0.884252i	$-0.345331\pi$
$281$	15.6570	0.934020	0.467010	+	0.884252i	$0.345331\pi$
$282$	26.2422	1.56270
$283$	−22.8261	−1.35687	−0.678435	−	0.734661i	$-0.737341\pi$
$283$	−22.8261	−1.35687	−0.678435	+	0.734661i	$0.737341\pi$
$284$	43.0765	2.55612
$285$	50.5826	2.99625
$286$	−11.8511	−0.700768
$287$	−19.4421	−1.14763
$288$	−22.9908	−1.35474
$289$	−12.3630	−0.727235
$290$	1.30247	0.0764834
$291$	−28.3650	−1.66279
$292$	20.4857	1.19884
$293$	4.05380	0.236825	0.118413	−	0.992964i	$-0.462219\pi$
$293$	4.05380	0.236825	0.118413	+	0.992964i	$0.462219\pi$
$294$	7.88160	0.459664
$295$	−17.8722	−1.04056
$296$	−5.96442	−0.346675
$297$	−1.33566	−0.0775026
$298$	33.9834	1.96861
$299$	29.7368	1.71972
$300$	80.5010	4.64773
$301$	−17.5506	−1.01160
$302$	−41.2779	−2.37528
$303$	−1.71849	−0.0987248
$304$	57.9929	3.32612
$305$	32.6930	1.87200
$306$	−13.2481	−0.757345
$307$	0.0559807	0.00319499	0.00159749	−	0.999999i	$-0.499492\pi$
$307$	0.0559807	0.00319499	0.00159749	+	0.999999i	$0.499492\pi$
$308$	−10.3221	−0.588158
$309$	4.45986	0.253713
$310$	15.3937	0.874306
$311$	−28.4769	−1.61478	−0.807388	−	0.590021i	$-0.799119\pi$
$311$	−28.4769	−1.61478	−0.807388	+	0.590021i	$0.799119\pi$
$312$	−84.3714	−4.77659
$313$	5.73965	0.324424	0.162212	−	0.986756i	$-0.448137\pi$
$313$	5.73965	0.324424	0.162212	+	0.986756i	$0.448137\pi$
$314$	24.2992	1.37128
$315$	−19.7456	−1.11254
$316$	−77.1141	−4.33801
$317$	−13.6976	−0.769335	−0.384668	−	0.923055i	$-0.625684\pi$
$317$	−13.6976	−0.769335	−0.384668	+	0.923055i	$0.625684\pi$
$318$	−43.2290	−2.42416
$319$	−0.129183	−0.00723286
$320$	23.6173	1.32025
$321$	−20.9823	−1.17112
$322$	36.7339	2.04710
$323$	13.4279	0.747150
$324$	−50.2353	−2.79085
$325$	36.5689	2.02848
$326$	−5.57372	−0.308700
$327$	−29.4533	−1.62877
$328$	−59.0230	−3.25900
$329$	10.3830	0.572436
$330$	−19.1120	−1.05208
$331$	22.5460	1.23924	0.619619	−	0.784903i	$-0.287287\pi$
$331$	22.5460	1.23924	0.619619	+	0.784903i	$0.287287\pi$
$332$	−34.7557	−1.90747
$333$	1.94532	0.106603
$334$	15.8511	0.867335
$335$	−12.3049	−0.672291
$336$	−51.3854	−2.80330
$337$	−13.4509	−0.732720	−0.366360	−	0.930473i	$-0.619396\pi$
$337$	−13.4509	−0.732720	−0.366360	+	0.930473i	$0.619396\pi$
$338$	−32.0316	−1.74229
$339$	−38.0921	−2.06888
$340$	36.0673	1.95602
$341$	−1.52681	−0.0826812
$342$	−38.3642	−2.07450
$343$	19.8205	1.07021
$344$	−53.2807	−2.87270
$345$	47.9559	2.58186
$346$	2.41522	0.129843
$347$	31.5415	1.69324	0.846619	−	0.532200i	$-0.178634\pi$
$347$	31.5415	1.69324	0.846619	+	0.532200i	$0.178634\pi$
$348$	−1.58098	−0.0847494
$349$	−3.34394	−0.178997	−0.0894985	−	0.995987i	$-0.528526\pi$
$349$	−3.34394	−0.178997	−0.0894985	+	0.995987i	$0.528526\pi$
$350$	45.1737	2.41464
$351$	−7.42552	−0.396345
$352$	−8.80465	−0.469290
$353$	20.1895	1.07458	0.537290	−	0.843398i	$-0.319448\pi$
$353$	20.1895	1.07458	0.537290	+	0.843398i	$0.319448\pi$
$354$	30.7680	1.63530
$355$	31.5573	1.67489
$356$	−38.3842	−2.03436
$357$	−11.8980	−0.629709
$358$	21.9392	1.15953
$359$	3.67371	0.193891	0.0969455	−	0.995290i	$-0.469093\pi$
$359$	3.67371	0.193891	0.0969455	+	0.995290i	$0.469093\pi$
$360$	−59.9443	−3.15934
$361$	19.8849	1.04657
$362$	65.9863	3.46816
$363$	−23.5772	−1.23748
$364$	−57.3854	−3.00781
$365$	15.0076	0.785532
$366$	−56.2828	−2.94195
$367$	8.63688	0.450842	0.225421	−	0.974262i	$-0.427624\pi$
$367$	8.63688	0.450842	0.225421	+	0.974262i	$0.427624\pi$
$368$	54.9814	2.86610
$369$	19.2506	1.00215
$370$	−7.51122	−0.390490
$371$	−17.1041	−0.887999
$372$	−18.6855	−0.968798
$373$	13.1239	0.679532	0.339766	−	0.940510i	$-0.389652\pi$
$373$	13.1239	0.679532	0.339766	+	0.940510i	$0.389652\pi$
$374$	−5.07357	−0.262348
$375$	18.4156	0.950978
$376$	31.5212	1.62558
$377$	−0.718187	−0.0369885
$378$	−9.17275	−0.471796
$379$	12.6096	0.647713	0.323857	−	0.946106i	$-0.395020\pi$
$379$	12.6096	0.647713	0.323857	+	0.946106i	$0.395020\pi$
$380$	104.444	5.35788
$381$	−0.0591536	−0.00303053
$382$	31.6817	1.62098
$383$	11.3947	0.582243	0.291121	−	0.956686i	$-0.405972\pi$
$383$	11.3947	0.582243	0.291121	+	0.956686i	$0.405972\pi$
$384$	4.41230	0.225164
$385$	−7.56187	−0.385388
$386$	43.0793	2.19268
$387$	17.3777	0.883359
$388$	−58.5689	−2.97339
$389$	33.8018	1.71382	0.856910	−	0.515466i	$-0.172381\pi$
$389$	33.8018	1.71382	0.856910	+	0.515466i	$0.172381\pi$
$390$	−106.252	−5.38028
$391$	12.7306	0.643816
$392$	9.46708	0.478160
$393$	37.1612	1.87454
$394$	49.3202	2.48472
$395$	−56.4928	−2.84246
$396$	10.2204	0.513597
$397$	−13.4792	−0.676501	−0.338250	−	0.941056i	$-0.609835\pi$
$397$	−13.4792	−0.676501	−0.338250	+	0.941056i	$0.609835\pi$
$398$	−22.5234	−1.12899
$399$	−34.4545	−1.72488
$400$	67.6136	3.38068
$401$	15.5494	0.776501	0.388250	−	0.921554i	$-0.373080\pi$
$401$	15.5494	0.776501	0.388250	+	0.921554i	$0.373080\pi$
$402$	21.1836	1.05654
$403$	−8.48820	−0.422828
$404$	−3.54839	−0.176539
$405$	−36.8017	−1.82869
$406$	−0.887178	−0.0440299
$407$	0.744989	0.0369277
$408$	−36.1203	−1.78822
$409$	−16.0681	−0.794515	−0.397258	−	0.917707i	$-0.630038\pi$
$409$	−16.0681	−0.794515	−0.397258	+	0.917707i	$0.630038\pi$
$410$	−74.3299	−3.67089
$411$	7.50612	0.370250
$412$	9.20885	0.453688
$413$	12.1737	0.599030
$414$	−36.3720	−1.78759
$415$	−25.4616	−1.24986
$416$	−48.9491	−2.39993
$417$	38.6153	1.89100
$418$	−14.6921	−0.718616
$419$	−0.217859	−0.0106431	−0.00532156	−	0.999986i	$-0.501694\pi$
$419$	−0.217859	−0.0106431	−0.00532156	+	0.999986i	$0.501694\pi$
$420$	−92.5443	−4.51570
$421$	2.52905	0.123258	0.0616292	−	0.998099i	$-0.480370\pi$
$421$	2.52905	0.123258	0.0616292	+	0.998099i	$0.480370\pi$
$422$	−44.5475	−2.16854
$423$	−10.2807	−0.499867
$424$	−51.9250	−2.52170
$425$	15.6556	0.759406
$426$	−54.3276	−2.63218
$427$	−22.2689	−1.07767
$428$	−43.3248	−2.09418
$429$	10.5384	0.508801
$430$	−67.0984	−3.23577
$431$	11.4460	0.551334	0.275667	−	0.961253i	$-0.411101\pi$
$431$	11.4460	0.551334	0.275667	+	0.961253i	$0.411101\pi$
$432$	−13.7293	−0.660551
$433$	18.8101	0.903955	0.451977	−	0.892029i	$-0.350719\pi$
$433$	18.8101	0.903955	0.451977	+	0.892029i	$0.350719\pi$
$434$	−10.4855	−0.503320
$435$	−1.15821	−0.0555317
$436$	−60.8161	−2.91256
$437$	36.8657	1.76352
$438$	−25.8363	−1.23451
$439$	−23.5154	−1.12233	−0.561164	−	0.827705i	$-0.689646\pi$
$439$	−23.5154	−1.12233	−0.561164	+	0.827705i	$0.689646\pi$
$440$	−22.9565	−1.09441
$441$	−3.08772	−0.147035
$442$	−28.2063	−1.34163
$443$	36.8335	1.75001	0.875005	−	0.484114i	$-0.160858\pi$
$443$	36.8335	1.75001	0.875005	+	0.484114i	$0.160858\pi$
$444$	9.11739	0.432692
$445$	−28.1198	−1.33300
$446$	−21.7544	−1.03010
$447$	−30.2195	−1.42933
$448$	−16.0870	−0.760040
$449$	−22.7112	−1.07181	−0.535905	−	0.844278i	$-0.680029\pi$
$449$	−22.7112	−1.07181	−0.535905	+	0.844278i	$0.680029\pi$
$450$	−44.7286	−2.10853
$451$	7.37230	0.347148
$452$	−78.6536	−3.69955
$453$	36.7060	1.72460
$454$	−22.6113	−1.06120
$455$	−42.0398	−1.97086
$456$	−104.598	−4.89825
$457$	−29.0472	−1.35877	−0.679385	−	0.733782i	$-0.737753\pi$
$457$	−29.0472	−1.35877	−0.679385	+	0.733782i	$0.737753\pi$
$458$	20.1507	0.941578
$459$	−3.17894	−0.148380
$460$	99.0207	4.61686
$461$	−14.2331	−0.662900	−0.331450	−	0.943473i	$-0.607538\pi$
$461$	−14.2331	−0.662900	−0.331450	+	0.943473i	$0.607538\pi$
$462$	13.0182	0.605660
$463$	−6.99341	−0.325011	−0.162506	−	0.986708i	$-0.551958\pi$
$463$	−6.99341	−0.325011	−0.162506	+	0.986708i	$0.551958\pi$
$464$	−1.32788	−0.0616454
$465$	−13.6887	−0.634801
$466$	−19.5411	−0.905225
$467$	6.25720	0.289549	0.144774	−	0.989465i	$-0.453754\pi$
$467$	6.25720	0.289549	0.144774	+	0.989465i	$0.453754\pi$
$468$	56.8201	2.62651
$469$	8.38155	0.387024
$470$	39.6957	1.83103
$471$	−21.6078	−0.995636
$472$	36.9574	1.70110
$473$	6.65505	0.306000
$474$	97.2555	4.46709
$475$	45.3357	2.08014
$476$	−24.5673	−1.12604
$477$	16.9356	0.775426
$478$	−14.7350	−0.673964
$479$	25.4950	1.16490	0.582449	−	0.812867i	$-0.302095\pi$
$479$	25.4950	1.16490	0.582449	+	0.812867i	$0.302095\pi$
$480$	−78.9391	−3.60306
$481$	4.14173	0.188847
$482$	14.2948	0.651113
$483$	−32.6653	−1.48632
$484$	−48.6828	−2.21286
$485$	−42.9068	−1.94830
$486$	51.8230	2.35074
$487$	20.5818	0.932650	0.466325	−	0.884613i	$-0.345578\pi$
$487$	20.5818	0.932650	0.466325	+	0.884613i	$0.345578\pi$
$488$	−67.6047	−3.06032
$489$	4.95638	0.224135
$490$	11.9222	0.538592
$491$	−31.9935	−1.44384	−0.721922	−	0.691974i	$-0.756741\pi$
$491$	−31.9935	−1.44384	−0.721922	+	0.691974i	$0.756741\pi$
$492$	90.2243	4.06763
$493$	−0.307464	−0.0138475
$494$	−81.6803	−3.67497
$495$	7.48737	0.336532
$496$	−15.6941	−0.704688
$497$	−21.4954	−0.964198
$498$	43.8336	1.96423
$499$	−9.30389	−0.416499	−0.208250	−	0.978076i	$-0.566777\pi$
$499$	−9.30389	−0.416499	−0.208250	+	0.978076i	$0.566777\pi$
$500$	38.0251	1.70053
$501$	−14.0955	−0.629739
$502$	−58.8341	−2.62590
$503$	−3.21831	−0.143498	−0.0717488	−	0.997423i	$-0.522858\pi$
$503$	−3.21831	−0.143498	−0.0717488	+	0.997423i	$0.522858\pi$
$504$	40.8312	1.81877
$505$	−2.59950	−0.115676
$506$	−13.9292	−0.619228
$507$	28.4838	1.26501
$508$	−0.122142	−0.00541918
$509$	−28.8970	−1.28084	−0.640418	−	0.768026i	$-0.721239\pi$
$509$	−28.8970	−1.28084	−0.640418	+	0.768026i	$0.721239\pi$
$510$	−45.4876	−2.01423
$511$	−10.2224	−0.452215
$512$	44.2261	1.95453
$513$	−9.20565	−0.406439
$514$	−17.9563	−0.792017
$515$	6.74629	0.297277
$516$	81.4465	3.58548
$517$	−3.93716	−0.173156
$518$	5.11629	0.224797
$519$	−2.14772	−0.0942742
$520$	−127.626	−5.59676
$521$	−28.1008	−1.23112	−0.615560	−	0.788090i	$-0.711070\pi$
$521$	−28.1008	−1.23112	−0.615560	+	0.788090i	$0.711070\pi$
$522$	0.878438	0.0384482
$523$	29.7744	1.30194	0.650971	−	0.759103i	$-0.274362\pi$
$523$	29.7744	1.30194	0.650971	+	0.759103i	$0.274362\pi$
$524$	76.7316	3.35204
$525$	−40.1703	−1.75318
$526$	−63.8114	−2.78231
$527$	−3.63389	−0.158295
$528$	19.4849	0.847972
$529$	11.9513	0.519621
$530$	−65.3911	−2.84041
$531$	−12.0538	−0.523090
$532$	−71.1426	−3.08442
$533$	40.9859	1.77530
$534$	48.4097	2.09489
$535$	−31.7392	−1.37221
$536$	25.4450	1.09906
$537$	−19.5093	−0.841888
$538$	40.6275	1.75158
$539$	−1.18249	−0.0509334
$540$	−24.7263	−1.06405
$541$	6.47259	0.278278	0.139139	−	0.990273i	$-0.455566\pi$
$541$	6.47259	0.278278	0.139139	+	0.990273i	$0.455566\pi$
$542$	33.0905	1.42136
$543$	−58.6778	−2.51810
$544$	−20.9556	−0.898465
$545$	−44.5531	−1.90844
$546$	72.3739	3.09732
$547$	−25.8307	−1.10444	−0.552219	−	0.833699i	$-0.686219\pi$
$547$	−25.8307	−1.10444	−0.552219	+	0.833699i	$0.686219\pi$
$548$	15.4988	0.662078
$549$	22.0496	0.941052
$550$	−17.1295	−0.730404
$551$	−0.890360	−0.0379306
$552$	−99.1663	−4.22080
$553$	38.4803	1.63635
$554$	−54.7722	−2.32705
$555$	6.67928	0.283520
$556$	79.7340	3.38147
$557$	43.0761	1.82519	0.912597	−	0.408860i	$-0.134074\pi$
$557$	43.0761	1.82519	0.912597	+	0.408860i	$0.134074\pi$
$558$	10.3822	0.439513
$559$	36.9985	1.56487
$560$	−77.7290	−3.28465
$561$	4.51162	0.190481
$562$	−40.7731	−1.71991
$563$	16.1203	0.679388	0.339694	−	0.940536i	$-0.389677\pi$
$563$	16.1203	0.679388	0.339694	+	0.940536i	$0.389677\pi$
$564$	−48.1842	−2.02892
$565$	−57.6206	−2.42412
$566$	59.4423	2.49855
$567$	25.0676	1.05274
$568$	−65.2563	−2.73809
$569$	10.4251	0.437041	0.218521	−	0.975832i	$-0.429877\pi$
$569$	10.4251	0.437041	0.218521	+	0.975832i	$0.429877\pi$
$570$	−131.724	−5.51731
$571$	−24.9736	−1.04511	−0.522555	−	0.852605i	$-0.675021\pi$
$571$	−24.9736	−1.04511	−0.522555	+	0.852605i	$0.675021\pi$
$572$	21.7601	0.909835
$573$	−28.1727	−1.17693
$574$	50.6300	2.11326
$575$	42.9815	1.79245
$576$	15.9285	0.663689
$577$	−9.06866	−0.377533	−0.188767	−	0.982022i	$-0.560449\pi$
$577$	−9.06866	−0.377533	−0.188767	+	0.982022i	$0.560449\pi$
$578$	32.1949	1.33913
$579$	−38.3079	−1.59202
$580$	−2.39150	−0.0993014
$581$	17.3433	0.719520
$582$	73.8664	3.06186
$583$	6.48572	0.268611
$584$	−31.0336	−1.28418
$585$	41.6257	1.72101
$586$	−10.5567	−0.436091
$587$	20.5152	0.846753	0.423377	−	0.905954i	$-0.360845\pi$
$587$	20.5152	0.846753	0.423377	+	0.905954i	$0.360845\pi$
$588$	−14.4716	−0.596801
$589$	−10.5231	−0.433597
$590$	46.5418	1.91610
$591$	−43.8576	−1.80406
$592$	7.65779	0.314733
$593$	−4.35086	−0.178668	−0.0893341	−	0.996002i	$-0.528474\pi$
$593$	−4.35086	−0.178668	−0.0893341	+	0.996002i	$0.528474\pi$
$594$	3.47823	0.142714
$595$	−17.9977	−0.737834
$596$	−62.3980	−2.55592
$597$	20.0287	0.819720
$598$	−77.4387	−3.16671
$599$	48.1494	1.96733	0.983667	−	0.180001i	$-0.0576099\pi$
$599$	48.1494	1.96733	0.983667	+	0.180001i	$0.0576099\pi$
$600$	−121.950	−4.97860
$601$	1.15591	0.0471505	0.0235752	−	0.999722i	$-0.492495\pi$
$601$	1.15591	0.0471505	0.0235752	+	0.999722i	$0.492495\pi$
$602$	45.7043	1.86277
$603$	−8.29898	−0.337960
$604$	75.7916	3.08392
$605$	−35.6644	−1.44997
$606$	4.47519	0.181792
$607$	24.5777	0.997579	0.498789	−	0.866723i	$-0.333778\pi$
$607$	24.5777	0.997579	0.498789	+	0.866723i	$0.333778\pi$
$608$	−60.6837	−2.46105
$609$	0.788915	0.0319685
$610$	−85.1371	−3.44710
$611$	−21.8885	−0.885513
$612$	24.3253	0.983292
$613$	−41.0268	−1.65706	−0.828529	−	0.559946i	$-0.810822\pi$
$613$	−41.0268	−1.65706	−0.828529	+	0.559946i	$0.810822\pi$
$614$	−0.145782	−0.00588327
$615$	66.0972	2.66530
$616$	15.6369	0.630029
$617$	−20.3983	−0.821203	−0.410602	−	0.911815i	$-0.634681\pi$
$617$	−20.3983	−0.821203	−0.410602	+	0.911815i	$0.634681\pi$
$618$	−11.6141	−0.467188
$619$	5.45193	0.219132	0.109566	−	0.993980i	$-0.465054\pi$
$619$	5.45193	0.219132	0.109566	+	0.993980i	$0.465054\pi$
$620$	−28.2649	−1.13515
$621$	−8.72762	−0.350227
$622$	74.1577	2.97345
$623$	19.1539	0.767383
$624$	108.325	4.33649
$625$	−8.49462	−0.339785
$626$	−14.9468	−0.597396
$627$	13.0649	0.521760
$628$	−44.6164	−1.78039
$629$	1.77312	0.0706989
$630$	51.4203	2.04863
$631$	7.02932	0.279833	0.139916	−	0.990163i	$-0.455317\pi$
$631$	7.02932	0.279833	0.139916	+	0.990163i	$0.455317\pi$
$632$	116.820	4.64683
$633$	39.6135	1.57450
$634$	35.6705	1.41666
$635$	−0.0894797	−0.00355089
$636$	79.3741	3.14739
$637$	−6.57399	−0.260471
$638$	0.336411	0.0133186
$639$	21.2836	0.841966
$640$	6.67434	0.263827
$641$	27.5409	1.08780	0.543900	−	0.839150i	$-0.316947\pi$
$641$	27.5409	1.08780	0.543900	+	0.839150i	$0.316947\pi$
$642$	54.6408	2.15650
$643$	−38.6261	−1.52326	−0.761631	−	0.648010i	$-0.775601\pi$
$643$	−38.6261	−1.52326	−0.761631	+	0.648010i	$0.775601\pi$
$644$	−67.4483	−2.65783
$645$	59.6666	2.34937
$646$	−34.9682	−1.37581
$647$	−35.0282	−1.37710	−0.688550	−	0.725189i	$-0.741752\pi$
$647$	−35.0282	−1.37710	−0.688550	+	0.725189i	$0.741752\pi$
$648$	76.1010	2.98953
$649$	−4.61618	−0.181201
$650$	−95.2306	−3.73525
$651$	9.32413	0.365442
$652$	10.2341	0.400797
$653$	47.1689	1.84586	0.922931	−	0.384965i	$-0.125787\pi$
$653$	47.1689	1.84586	0.922931	+	0.384965i	$0.125787\pi$
$654$	76.7006	2.99923
$655$	56.2126	2.19641
$656$	75.7804	2.95873
$657$	10.1217	0.394887
$658$	−27.0389	−1.05409
$659$	−12.6220	−0.491683	−0.245842	−	0.969310i	$-0.579064\pi$
$659$	−12.6220	−0.491683	−0.245842	+	0.969310i	$0.579064\pi$
$660$	35.0920	1.36596
$661$	−18.6118	−0.723914	−0.361957	−	0.932195i	$-0.617891\pi$
$661$	−18.6118	−0.723914	−0.361957	+	0.932195i	$0.617891\pi$
$662$	−58.7128	−2.28194
$663$	25.0822	0.974111
$664$	52.6512	2.04326
$665$	−52.1181	−2.02105
$666$	−5.06588	−0.196299
$667$	−0.844125	−0.0326846
$668$	−29.1047	−1.12610
$669$	19.3449	0.747916
$670$	32.0438	1.23796
$671$	8.44420	0.325985
$672$	53.7696	2.07421
$673$	22.8440	0.880572	0.440286	−	0.897858i	$-0.354877\pi$
$673$	22.8440	0.880572	0.440286	+	0.897858i	$0.354877\pi$
$674$	35.0281	1.34923
$675$	−10.7328	−0.413107
$676$	58.8142	2.26208
$677$	19.5348	0.750782	0.375391	−	0.926866i	$-0.377508\pi$
$677$	19.5348	0.750782	0.375391	+	0.926866i	$0.377508\pi$
$678$	99.1970	3.80964
$679$	29.2261	1.12160
$680$	−54.6380	−2.09527
$681$	20.1069	0.770497
$682$	3.97601	0.152249
$683$	−47.8007	−1.82904	−0.914521	−	0.404538i	$-0.867432\pi$
$683$	−47.8007	−1.82904	−0.914521	+	0.404538i	$0.867432\pi$
$684$	70.4417	2.69341
$685$	11.3543	0.433824
$686$	−51.6153	−1.97068
$687$	−17.9188	−0.683644
$688$	68.4078	2.60802
$689$	36.0571	1.37366
$690$	−124.884	−4.75425
$691$	−12.6716	−0.482052	−0.241026	−	0.970519i	$-0.577484\pi$
$691$	−12.6716	−0.482052	−0.241026	+	0.970519i	$0.577484\pi$
$692$	−4.43466	−0.168581
$693$	−5.10004	−0.193735
$694$	−82.1385	−3.11793
$695$	58.4121	2.21570
$696$	2.39501	0.0907827
$697$	17.5465	0.664622
$698$	8.70808	0.329606
$699$	17.3768	0.657250
$700$	−82.9448	−3.13502
$701$	22.4131	0.846533	0.423266	−	0.906005i	$-0.360883\pi$
$701$	22.4131	0.846533	0.423266	+	0.906005i	$0.360883\pi$
$702$	19.3371	0.729831
$703$	5.13464	0.193656
$704$	6.10006	0.229905
$705$	−35.2991	−1.32944
$706$	−52.5763	−1.97873
$707$	1.77066	0.0665926
$708$	−56.4941	−2.12318
$709$	−33.8385	−1.27083	−0.635416	−	0.772170i	$-0.719172\pi$
$709$	−33.8385	−1.27083	−0.635416	+	0.772170i	$0.719172\pi$
$710$	−82.1796	−3.08415
$711$	−38.1012	−1.42891
$712$	58.1479	2.17918
$713$	−9.97665	−0.373629
$714$	30.9841	1.15955
$715$	15.9412	0.596166
$716$	−40.2833	−1.50546
$717$	13.1030	0.489340
$718$	−9.56685	−0.357032
$719$	32.7683	1.22205	0.611026	−	0.791611i	$-0.290757\pi$
$719$	32.7683	1.22205	0.611026	+	0.791611i	$0.290757\pi$
$720$	76.9632	2.86825
$721$	−4.59525	−0.171136
$722$	−51.7830	−1.92716
$723$	−12.7116	−0.472748
$724$	−121.160	−4.50286
$725$	−1.03807	−0.0385528
$726$	61.3983	2.27870
$727$	−31.7369	−1.17706	−0.588528	−	0.808477i	$-0.700292\pi$
$727$	−31.7369	−1.17706	−0.588528	+	0.808477i	$0.700292\pi$
$728$	86.9327	3.22194
$729$	−14.5649	−0.539439
$730$	−39.0818	−1.44648
$731$	15.8394	0.585843
$732$	103.343	3.81965
$733$	−7.99388	−0.295261	−0.147630	−	0.989043i	$-0.547165\pi$
$733$	−7.99388	−0.295261	−0.147630	+	0.989043i	$0.547165\pi$
$734$	−22.4916	−0.830181
$735$	−10.6017	−0.391051
$736$	−57.5325	−2.12068
$737$	−3.17822	−0.117071
$738$	−50.1312	−1.84536
$739$	−22.5393	−0.829122	−0.414561	−	0.910022i	$-0.636065\pi$
$739$	−22.5393	−0.829122	−0.414561	+	0.910022i	$0.636065\pi$
$740$	13.7916	0.506988
$741$	72.6334	2.66826
$742$	44.5414	1.63516
$743$	−35.3292	−1.29610	−0.648052	−	0.761596i	$-0.724416\pi$
$743$	−35.3292	−1.29610	−0.648052	+	0.761596i	$0.724416\pi$
$744$	28.3065	1.03777
$745$	−45.7120	−1.67476
$746$	−34.1766	−1.25129
$747$	−17.1724	−0.628305
$748$	9.31573	0.340617
$749$	21.6193	0.789950
$750$	−47.9568	−1.75113
$751$	−40.3793	−1.47346	−0.736730	−	0.676187i	$-0.763631\pi$
$751$	−40.3793	−1.47346	−0.736730	+	0.676187i	$0.763631\pi$
$752$	−40.4704	−1.47580
$753$	52.3177	1.90656
$754$	1.87026	0.0681108
$755$	55.5240	2.02072
$756$	16.8424	0.612551
$757$	19.1363	0.695521	0.347760	−	0.937583i	$-0.386942\pi$
$757$	19.1363	0.695521	0.347760	+	0.937583i	$0.386942\pi$
$758$	−32.8372	−1.19270
$759$	12.3864	0.449598
$760$	−158.222	−5.73931
$761$	48.9536	1.77457	0.887283	−	0.461225i	$-0.152590\pi$
$761$	48.9536	1.77457	0.887283	+	0.461225i	$0.152590\pi$
$762$	0.154044	0.00558043
$763$	30.3475	1.09865
$764$	−58.1718	−2.10458
$765$	17.8204	0.644298
$766$	−29.6734	−1.07214
$767$	−25.6634	−0.926653
$768$	−42.7163	−1.54139
$769$	−1.39005	−0.0501264	−0.0250632	−	0.999686i	$-0.507979\pi$
$769$	−1.39005	−0.0501264	−0.0250632	+	0.999686i	$0.507979\pi$
$770$	19.6921	0.709656
$771$	15.9674	0.575053
$772$	−79.0993	−2.84685
$773$	20.2745	0.729223	0.364612	−	0.931160i	$-0.381202\pi$
$773$	20.2745	0.729223	0.364612	+	0.931160i	$0.381202\pi$
$774$	−45.2540	−1.62662
$775$	−12.2688	−0.440709
$776$	88.7255	3.18506
$777$	−4.54961	−0.163216
$778$	−88.0246	−3.15583
$779$	50.8116	1.82051
$780$	195.093	6.98543
$781$	8.15086	0.291661
$782$	−33.1524	−1.18553
$783$	0.210785	0.00753283
$784$	−12.1549	−0.434103
$785$	−32.6854	−1.16659
$786$	−96.7730	−3.45178
$787$	−22.3801	−0.797766	−0.398883	−	0.917002i	$-0.630602\pi$
$787$	−22.3801	−0.797766	−0.398883	+	0.917002i	$0.630602\pi$
$788$	−90.5583	−3.22601
$789$	56.7437	2.02013
$790$	147.115	5.23412
$791$	39.2484	1.39551
$792$	−15.4829	−0.550160
$793$	46.9451	1.66707
$794$	35.1017	1.24571
$795$	58.1485	2.06231
$796$	41.3558	1.46582
$797$	−23.3448	−0.826916	−0.413458	−	0.910523i	$-0.635679\pi$
$797$	−23.3448	−0.826916	−0.413458	+	0.910523i	$0.635679\pi$
$798$	89.7242	3.17620
$799$	−9.37070	−0.331511
$800$	−70.7509	−2.50142
$801$	−18.9652	−0.670101
$802$	−40.4928	−1.42985
$803$	3.87627	0.136791
$804$	−38.8959	−1.37175
$805$	−49.4117	−1.74153
$806$	22.1045	0.778596
$807$	−36.1277	−1.27175
$808$	5.37543	0.189107
$809$	−40.3049	−1.41704	−0.708522	−	0.705689i	$-0.750638\pi$
$809$	−40.3049	−1.41704	−0.708522	+	0.705689i	$0.750638\pi$
$810$	95.8368	3.36736
$811$	−7.60849	−0.267170	−0.133585	−	0.991037i	$-0.542649\pi$
$811$	−7.60849	−0.267170	−0.133585	+	0.991037i	$0.542649\pi$
$812$	1.62897	0.0571658
$813$	−29.4254	−1.03200
$814$	−1.94005	−0.0679989
$815$	7.49735	0.262621
$816$	46.3753	1.62346
$817$	45.8682	1.60472
$818$	41.8435	1.46302
$819$	−28.3534	−0.990750
$820$	136.479	4.76606
$821$	−17.5478	−0.612421	−0.306210	−	0.951964i	$-0.599061\pi$
$821$	−17.5478	−0.612421	−0.306210	+	0.951964i	$0.599061\pi$
$822$	−19.5470	−0.681779
$823$	−7.20716	−0.251226	−0.125613	−	0.992079i	$-0.540090\pi$
$823$	−7.20716	−0.251226	−0.125613	+	0.992079i	$0.540090\pi$
$824$	−13.9504	−0.485986
$825$	15.2323	0.530319
$826$	−31.7021	−1.10306
$827$	24.4887	0.851556	0.425778	−	0.904828i	$-0.360000\pi$
$827$	24.4887	0.851556	0.425778	+	0.904828i	$0.360000\pi$
$828$	66.7838	2.32090
$829$	−33.7463	−1.17206	−0.586029	−	0.810290i	$-0.699309\pi$
$829$	−33.7463	−1.17206	−0.586029	+	0.810290i	$0.699309\pi$
$830$	66.3056	2.30150
$831$	48.7057	1.68958
$832$	33.9130	1.17572
$833$	−2.81440	−0.0975131
$834$	−100.560	−3.48210
$835$	−21.3218	−0.737870
$836$	26.9767	0.933008
$837$	2.49125	0.0861102
$838$	0.567336	0.0195983
$839$	51.0808	1.76350	0.881752	−	0.471713i	$-0.156364\pi$
$839$	51.0808	1.76350	0.881752	+	0.471713i	$0.156364\pi$
$840$	140.195	4.83717
$841$	−28.9796	−0.999297
$842$	−6.58600	−0.226969
$843$	36.2571	1.24876
$844$	81.7951	2.81550
$845$	43.0865	1.48222
$846$	26.7725	0.920457
$847$	24.2929	0.834715
$848$	66.6672	2.28936
$849$	−52.8585	−1.81410
$850$	−40.7693	−1.39837
$851$	4.86800	0.166873
$852$	99.7526	3.41747
$853$	0.694836	0.0237907	0.0118954	−	0.999929i	$-0.496213\pi$
$853$	0.694836	0.0237907	0.0118954	+	0.999929i	$0.496213\pi$
$854$	57.9914	1.98443
$855$	51.6047	1.76484
$856$	65.6324	2.24327
$857$	35.9268	1.22723	0.613617	−	0.789603i	$-0.289714\pi$
$857$	35.9268	1.22723	0.613617	+	0.789603i	$0.289714\pi$
$858$	−27.4436	−0.936908
$859$	0.665038	0.0226908	0.0113454	−	0.999936i	$-0.496389\pi$
$859$	0.665038	0.0226908	0.0113454	+	0.999936i	$0.496389\pi$
$860$	123.201	4.20113
$861$	−45.0223	−1.53436
$862$	−29.8069	−1.01523
$863$	25.8051	0.878415	0.439207	−	0.898386i	$-0.355259\pi$
$863$	25.8051	0.878415	0.439207	+	0.898386i	$0.355259\pi$
$864$	14.3663	0.488752
$865$	−3.24878	−0.110462
$866$	−48.9841	−1.66455
$867$	−28.6291	−0.972294
$868$	19.2527	0.653480
$869$	−14.5914	−0.494979
$870$	3.01613	0.102256
$871$	−17.6691	−0.598696
$872$	92.1298	3.11991
$873$	−28.9382	−0.979409
$874$	−96.0033	−3.24736
$875$	−18.9747	−0.641461
$876$	47.4389	1.60281
$877$	−14.8563	−0.501662	−0.250831	−	0.968031i	$-0.580704\pi$
$877$	−14.8563	−0.501662	−0.250831	+	0.968031i	$0.580704\pi$
$878$	61.2373	2.06666
$879$	9.38741	0.316629
$880$	29.4742	0.993574
$881$	−35.7201	−1.20344	−0.601720	−	0.798707i	$-0.705518\pi$
$881$	−35.7201	−1.20344	−0.601720	+	0.798707i	$0.705518\pi$
$882$	8.04086	0.270750
$883$	25.4789	0.857434	0.428717	−	0.903439i	$-0.358966\pi$
$883$	25.4789	0.857434	0.428717	+	0.903439i	$0.358966\pi$
$884$	51.7904	1.74190
$885$	−41.3869	−1.39120
$886$	−95.9194	−3.22248
$887$	−44.3150	−1.48795	−0.743975	−	0.668207i	$-0.767062\pi$
$887$	−44.3150	−1.48795	−0.743975	+	0.668207i	$0.767062\pi$
$888$	−13.8119	−0.463495
$889$	0.0609493	0.00204418
$890$	73.2277	2.45460
$891$	−9.50543	−0.318444
$892$	39.9439	1.33742
$893$	−27.1359	−0.908067
$894$	78.6957	2.63198
$895$	−29.5110	−0.986445
$896$	−4.54625	−0.151879
$897$	68.8617	2.29923
$898$	59.1432	1.97363
$899$	0.240951	0.00803616
$900$	82.1276	2.73759
$901$	15.4364	0.514262
$902$	−19.1985	−0.639240
$903$	−40.6421	−1.35249
$904$	119.152	3.96292
$905$	−88.7599	−2.95048
$906$	−95.5876	−3.17568
$907$	−25.0294	−0.831088	−0.415544	−	0.909573i	$-0.636409\pi$
$907$	−25.0294	−0.831088	−0.415544	+	0.909573i	$0.636409\pi$
$908$	41.5172	1.37780
$909$	−1.75322	−0.0581505
$910$	109.478	3.62915
$911$	−21.7884	−0.721882	−0.360941	−	0.932589i	$-0.617544\pi$
$911$	−21.7884	−0.721882	−0.360941	+	0.932589i	$0.617544\pi$
$912$	134.295	4.44694
$913$	−6.57642	−0.217648
$914$	75.6428	2.50204
$915$	75.7074	2.50281
$916$	−36.9992	−1.22249
$917$	−38.2894	−1.26443
$918$	8.27841	0.273228
$919$	43.0446	1.41991	0.709956	−	0.704246i	$-0.248715\pi$
$919$	43.0446	1.41991	0.709956	+	0.704246i	$0.248715\pi$
$920$	−150.006	−4.94554
$921$	0.129635	0.00427162
$922$	37.0649	1.22067
$923$	45.3143	1.49154
$924$	−23.9031	−0.786353
$925$	5.98645	0.196833
$926$	18.2118	0.598477
$927$	4.54998	0.149441
$928$	1.38949	0.0456124
$929$	30.1536	0.989308	0.494654	−	0.869090i	$-0.335295\pi$
$929$	30.1536	0.989308	0.494654	+	0.869090i	$0.335295\pi$
$930$	35.6474	1.16892
$931$	−8.14999	−0.267105
$932$	35.8801	1.17529
$933$	−65.9441	−2.15891
$934$	−16.2946	−0.533176
$935$	6.82458	0.223188
$936$	−86.0763	−2.81349
$937$	34.6249	1.13115	0.565573	−	0.824698i	$-0.308655\pi$
$937$	34.6249	1.13115	0.565573	+	0.824698i	$0.308655\pi$
$938$	−21.8267	−0.712668
$939$	13.2913	0.433747
$940$	−72.8866	−2.37730
$941$	−3.92260	−0.127873	−0.0639366	−	0.997954i	$-0.520366\pi$
$941$	−3.92260	−0.127873	−0.0639366	+	0.997954i	$0.520366\pi$
$942$	56.2697	1.83337
$943$	48.1730	1.56873
$944$	−47.4500	−1.54437
$945$	12.3385	0.401372
$946$	−17.3307	−0.563469
$947$	30.8738	1.00326	0.501632	−	0.865081i	$-0.332733\pi$
$947$	30.8738	1.00326	0.501632	+	0.865081i	$0.332733\pi$
$948$	−178.574	−5.79981
$949$	21.5499	0.699540
$950$	−118.060	−3.83039
$951$	−31.7197	−1.02858
$952$	37.2168	1.20620
$953$	11.8235	0.383002	0.191501	−	0.981492i	$-0.438664\pi$
$953$	11.8235	0.383002	0.191501	+	0.981492i	$0.438664\pi$
$954$	−44.1025	−1.42787
$955$	−42.6159	−1.37902
$956$	27.0554	0.875034
$957$	−0.299150	−0.00967015
$958$	−66.3926	−2.14505
$959$	−7.73399	−0.249743
$960$	54.6908	1.76514
$961$	−28.1522	−0.908136
$962$	−10.7856	−0.347743
$963$	−21.4063	−0.689807
$964$	−26.2472	−0.845366
$965$	−57.9471	−1.86538
$966$	85.0650	2.73692
$967$	−28.2806	−0.909442	−0.454721	−	0.890634i	$-0.650261\pi$
$967$	−28.2806	−0.909442	−0.454721	+	0.890634i	$0.650261\pi$
$968$	73.7492	2.37039
$969$	31.0952	0.998921
$970$	111.735	3.58760
$971$	−44.3901	−1.42455	−0.712273	−	0.701902i	$-0.752334\pi$
$971$	−44.3901	−1.42455	−0.712273	+	0.701902i	$0.752334\pi$
$972$	−95.1538	−3.05206
$973$	−39.7876	−1.27553
$974$	−53.5978	−1.71739
$975$	84.6830	2.71203
$976$	86.7985	2.77835
$977$	−38.3285	−1.22624	−0.613119	−	0.789990i	$-0.710085\pi$
$977$	−38.3285	−1.22624	−0.613119	+	0.789990i	$0.710085\pi$
$978$	−12.9071	−0.412724
$979$	−7.26298	−0.232126
$980$	−21.8908	−0.699275
$981$	−30.0485	−0.959374
$982$	83.3154	2.65870
$983$	53.2491	1.69838	0.849191	−	0.528085i	$-0.177090\pi$
$983$	53.2491	1.69838	0.849191	+	0.528085i	$0.177090\pi$
$984$	−136.680	−4.35720
$985$	−66.3419	−2.11383
$986$	0.800678	0.0254988
$987$	24.0441	0.765332
$988$	149.976	4.77136
$989$	43.4863	1.38278
$990$	−19.4981	−0.619692
$991$	8.41716	0.267380	0.133690	−	0.991023i	$-0.457317\pi$
$991$	8.41716	0.267380	0.133690	+	0.991023i	$0.457317\pi$
$992$	16.4223	0.521410
$993$	52.2099	1.65683
$994$	55.9769	1.77548
$995$	30.2967	0.960471
$996$	−80.4841	−2.55024
$997$	−18.8413	−0.596710	−0.298355	−	0.954455i	$-0.596438\pi$
$997$	−18.8413	−0.596710	−0.298355	+	0.954455i	$0.596438\pi$
$998$	24.2286	0.766943
$999$	−1.21558	−0.0384592

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8017.2.a.b.1.16	✓	340

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8017.2.a.b.1.16	✓	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)

\(f(q)\)	\(=\)	\(q-2.60414 q^{2} +2.31571 q^{3} +4.78154 q^{4} +3.50289 q^{5} -6.03042 q^{6} -2.38601 q^{7} -7.24351 q^{8} +2.36250 q^{9} +O(q^{10})\)	\(q-2.60414 q^{2} +2.31571 q^{3} +4.78154 q^{4} +3.50289 q^{5} -6.03042 q^{6} -2.38601 q^{7} -7.24351 q^{8} +2.36250 q^{9} -9.12202 q^{10} +0.904754 q^{11} +11.0726 q^{12} +5.02994 q^{13} +6.21349 q^{14} +8.11167 q^{15} +9.30003 q^{16} +2.15337 q^{17} -6.15228 q^{18} +6.23578 q^{19} +16.7492 q^{20} -5.52529 q^{21} -2.35610 q^{22} +5.91196 q^{23} -16.7738 q^{24} +7.27026 q^{25} -13.0987 q^{26} -1.47626 q^{27} -11.4088 q^{28} -0.142783 q^{29} -21.1239 q^{30} -1.68754 q^{31} -9.73155 q^{32} +2.09515 q^{33} -5.60768 q^{34} -8.35793 q^{35} +11.2964 q^{36} +0.823416 q^{37} -16.2388 q^{38} +11.6479 q^{39} -25.3732 q^{40} +8.14840 q^{41} +14.3886 q^{42} +7.35565 q^{43} +4.32612 q^{44} +8.27558 q^{45} -15.3956 q^{46} -4.35164 q^{47} +21.5361 q^{48} -1.30697 q^{49} -18.9328 q^{50} +4.98658 q^{51} +24.0508 q^{52} +7.16849 q^{53} +3.84440 q^{54} +3.16926 q^{55} +17.2831 q^{56} +14.4402 q^{57} +0.371826 q^{58} -5.10214 q^{59} +38.7863 q^{60} +9.33315 q^{61} +4.39458 q^{62} -5.63694 q^{63} +6.74223 q^{64} +17.6193 q^{65} -5.45605 q^{66} -3.51279 q^{67} +10.2964 q^{68} +13.6904 q^{69} +21.7652 q^{70} +9.00893 q^{71} -17.1128 q^{72} +4.28433 q^{73} -2.14429 q^{74} +16.8358 q^{75} +29.8166 q^{76} -2.15875 q^{77} -30.3326 q^{78} -16.1275 q^{79} +32.5770 q^{80} -10.5061 q^{81} -21.2196 q^{82} -7.26874 q^{83} -26.4194 q^{84} +7.54303 q^{85} -19.1551 q^{86} -0.330643 q^{87} -6.55359 q^{88} -8.02758 q^{89} -21.5508 q^{90} -12.0015 q^{91} +28.2683 q^{92} -3.90784 q^{93} +11.3323 q^{94} +21.8433 q^{95} -22.5354 q^{96} -12.2490 q^{97} +3.40354 q^{98} +2.13748 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 340 q + 20 q^{2} + 44 q^{3} + 350 q^{4} + 53 q^{5} + 34 q^{6} + 81 q^{7} + 54 q^{8} + 360 q^{9}+O(q^{10}) \) 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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