LMFDB - Embedded newform 8003.2.a.d.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8003,2,Mod(1,8003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8003, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8003 = 53 \cdot 151 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8003.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:	$63.9042767376$
Analytic rank:	$0$
Dimension:	$179$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	8003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.33610 q^{2} -3.21364 q^{3} +3.45737 q^{4} +1.58018 q^{5} +7.50740 q^{6} +0.0419320 q^{7} -3.40456 q^{8} +7.32750 q^{9} +O(q^{10})$	\(q-2.33610 q^{2} -3.21364 q^{3} +3.45737 q^{4} +1.58018 q^{5} +7.50740 q^{6} +0.0419320 q^{7} -3.40456 q^{8} +7.32750 q^{9} -3.69146 q^{10} +4.86841 q^{11} -11.1107 q^{12} +6.17165 q^{13} -0.0979573 q^{14} -5.07813 q^{15} +1.03866 q^{16} +5.07580 q^{17} -17.1178 q^{18} -0.881741 q^{19} +5.46326 q^{20} -0.134754 q^{21} -11.3731 q^{22} +0.213128 q^{23} +10.9410 q^{24} -2.50303 q^{25} -14.4176 q^{26} -13.9070 q^{27} +0.144974 q^{28} -5.77902 q^{29} +11.8630 q^{30} -9.23186 q^{31} +4.38270 q^{32} -15.6453 q^{33} -11.8576 q^{34} +0.0662600 q^{35} +25.3339 q^{36} +7.32002 q^{37} +2.05984 q^{38} -19.8335 q^{39} -5.37982 q^{40} +11.4464 q^{41} +0.314800 q^{42} -5.73382 q^{43} +16.8319 q^{44} +11.5788 q^{45} -0.497890 q^{46} +6.36025 q^{47} -3.33789 q^{48} -6.99824 q^{49} +5.84734 q^{50} -16.3118 q^{51} +21.3377 q^{52} +1.00000 q^{53} +32.4883 q^{54} +7.69296 q^{55} -0.142760 q^{56} +2.83360 q^{57} +13.5004 q^{58} +3.89367 q^{59} -17.5570 q^{60} +11.2233 q^{61} +21.5666 q^{62} +0.307256 q^{63} -12.3158 q^{64} +9.75232 q^{65} +36.5491 q^{66} -2.51748 q^{67} +17.5489 q^{68} -0.684919 q^{69} -0.154790 q^{70} -8.17822 q^{71} -24.9469 q^{72} -13.5624 q^{73} -17.1003 q^{74} +8.04385 q^{75} -3.04850 q^{76} +0.204142 q^{77} +46.3330 q^{78} +2.26106 q^{79} +1.64127 q^{80} +22.7098 q^{81} -26.7399 q^{82} -9.99178 q^{83} -0.465895 q^{84} +8.02068 q^{85} +13.3948 q^{86} +18.5717 q^{87} -16.5748 q^{88} +2.27452 q^{89} -27.0492 q^{90} +0.258789 q^{91} +0.736864 q^{92} +29.6679 q^{93} -14.8582 q^{94} -1.39331 q^{95} -14.0844 q^{96} +8.31360 q^{97} +16.3486 q^{98} +35.6733 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 179 q + 8 q^{2} + 15 q^{3} + 202 q^{4} + 27 q^{5} + 18 q^{6} + 23 q^{7} + 21 q^{8} + 214 q^{9}+O(q^{10}) $ 179 * q + 8 * q^2 + 15 * q^3 + 202 * q^4 + 27 * q^5 + 18 * q^6 + 23 * q^7 + 21 * q^8 + 214 * q^9	\( 179 q + 8 q^{2} + 15 q^{3} + 202 q^{4} + 27 q^{5} + 18 q^{6} + 23 q^{7} + 21 q^{8} + 214 q^{9} + 28 q^{10} + 21 q^{11} + 46 q^{12} + 113 q^{13} - 2 q^{14} + 30 q^{15} + 240 q^{16} + 48 q^{17} + 40 q^{18} + 35 q^{19} + 24 q^{20} + 56 q^{21} + 22 q^{22} + 16 q^{23} + 54 q^{24} + 266 q^{25} + 60 q^{27} + 64 q^{28} + 34 q^{29} - 19 q^{30} + 60 q^{31} + 15 q^{32} + 65 q^{33} + 31 q^{34} - 20 q^{35} + 282 q^{36} + 169 q^{37} + 52 q^{38} + 20 q^{39} + 74 q^{40} + 20 q^{41} + 34 q^{42} + 43 q^{43} + 56 q^{44} + 139 q^{45} + 13 q^{46} + 73 q^{47} + 88 q^{48} + 292 q^{49} + 12 q^{50} + 8 q^{51} + 225 q^{52} + 179 q^{53} - 16 q^{54} + 72 q^{55} - 17 q^{56} + 62 q^{57} + 125 q^{58} + 68 q^{59} + 116 q^{60} + 96 q^{61} + 71 q^{62} + 52 q^{63} + 309 q^{64} - 5 q^{65} + 90 q^{67} + 122 q^{68} + 111 q^{69} + 72 q^{70} + 26 q^{71} + 65 q^{72} + 139 q^{73} - 82 q^{74} + 55 q^{75} + 146 q^{76} + 76 q^{77} - 9 q^{78} + 29 q^{79} + 68 q^{80} + 231 q^{81} + 84 q^{82} + 8 q^{83} - 24 q^{84} + 115 q^{85} - 20 q^{86} + 47 q^{87} + 143 q^{88} + 150 q^{89} + 34 q^{90} + 113 q^{91} - 31 q^{92} + 195 q^{93} + 131 q^{94} + 55 q^{95} + 90 q^{96} + 235 q^{97} + 84 q^{98} + 7 q^{99}+O(q^{100}) \) 179 * q + 8 * q^2 + 15 * q^3 + 202 * q^4 + 27 * q^5 + 18 * q^6 + 23 * q^7 + 21 * q^8 + 214 * q^9 + 28 * q^10 + 21 * q^11 + 46 * q^12 + 113 * q^13 - 2 * q^14 + 30 * q^15 + 240 * q^16 + 48 * q^17 + 40 * q^18 + 35 * q^19 + 24 * q^20 + 56 * q^21 + 22 * q^22 + 16 * q^23 + 54 * q^24 + 266 * q^25 + 60 * q^27 + 64 * q^28 + 34 * q^29 - 19 * q^30 + 60 * q^31 + 15 * q^32 + 65 * q^33 + 31 * q^34 - 20 * q^35 + 282 * q^36 + 169 * q^37 + 52 * q^38 + 20 * q^39 + 74 * q^40 + 20 * q^41 + 34 * q^42 + 43 * q^43 + 56 * q^44 + 139 * q^45 + 13 * q^46 + 73 * q^47 + 88 * q^48 + 292 * q^49 + 12 * q^50 + 8 * q^51 + 225 * q^52 + 179 * q^53 - 16 * q^54 + 72 * q^55 - 17 * q^56 + 62 * q^57 + 125 * q^58 + 68 * q^59 + 116 * q^60 + 96 * q^61 + 71 * q^62 + 52 * q^63 + 309 * q^64 - 5 * q^65 + 90 * q^67 + 122 * q^68 + 111 * q^69 + 72 * q^70 + 26 * q^71 + 65 * q^72 + 139 * q^73 - 82 * q^74 + 55 * q^75 + 146 * q^76 + 76 * q^77 - 9 * q^78 + 29 * q^79 + 68 * q^80 + 231 * q^81 + 84 * q^82 + 8 * q^83 - 24 * q^84 + 115 * q^85 - 20 * q^86 + 47 * q^87 + 143 * q^88 + 150 * q^89 + 34 * q^90 + 113 * q^91 - 31 * q^92 + 195 * q^93 + 131 * q^94 + 55 * q^95 + 90 * q^96 + 235 * q^97 + 84 * q^98 + 7 * 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 $

$2$	−2.33610	−1.65187	−0.825937	−	0.563763i	$-0.809353\pi$
$2$	−2.33610	−1.65187	−0.825937	+	0.563763i	$0.809353\pi$
$3$	−3.21364	−1.85540	−0.927699	−	0.373330i	$-0.878216\pi$
$3$	−3.21364	−1.85540	−0.927699	+	0.373330i	$0.878216\pi$
$4$	3.45737	1.72868
$5$	1.58018	0.706678	0.353339	−	0.935495i	$-0.385046\pi$
$5$	1.58018	0.706678	0.353339	+	0.935495i	$0.385046\pi$
$6$	7.50740	3.06488
$7$	0.0419320	0.0158488	0.00792439	−	0.999969i	$-0.497478\pi$
$7$	0.0419320	0.0158488	0.00792439	+	0.999969i	$0.497478\pi$
$8$	−3.40456	−1.20369
$9$	7.32750	2.44250
$10$	−3.69146	−1.16734
$11$	4.86841	1.46788	0.733941	−	0.679214i	$-0.237679\pi$
$11$	4.86841	1.46788	0.733941	+	0.679214i	$0.237679\pi$
$12$	−11.1107	−3.20740
$13$	6.17165	1.71171	0.855854	−	0.517217i	$-0.173032\pi$
$13$	6.17165	1.71171	0.855854	+	0.517217i	$0.173032\pi$
$14$	−0.0979573	−0.0261802
$15$	−5.07813	−1.31117
$16$	1.03866	0.259665
$17$	5.07580	1.23106	0.615532	−	0.788112i	$-0.288941\pi$
$17$	5.07580	1.23106	0.615532	+	0.788112i	$0.288941\pi$
$18$	−17.1178	−4.03470
$19$	−0.881741	−0.202285	−0.101143	−	0.994872i	$-0.532250\pi$
$19$	−0.881741	−0.202285	−0.101143	+	0.994872i	$0.532250\pi$
$20$	5.46326	1.22162
$21$	−0.134754	−0.0294058
$22$	−11.3731	−2.42475
$23$	0.213128	0.0444404	0.0222202	−	0.999753i	$-0.492927\pi$
$23$	0.213128	0.0444404	0.0222202	+	0.999753i	$0.492927\pi$
$24$	10.9410	2.23333
$25$	−2.50303	−0.500606
$26$	−14.4176	−2.82752
$27$	−13.9070	−2.67641
$28$	0.144974	0.0273976
$29$	−5.77902	−1.07314	−0.536569	−	0.843856i	$-0.680280\pi$
$29$	−5.77902	−1.07314	−0.536569	+	0.843856i	$0.680280\pi$
$30$	11.8630	2.16588
$31$	−9.23186	−1.65809	−0.829046	−	0.559181i	$-0.811116\pi$
$31$	−9.23186	−1.65809	−0.829046	+	0.559181i	$0.811116\pi$
$32$	4.38270	0.774760
$33$	−15.6453	−2.72350
$34$	−11.8576	−2.03356
$35$	0.0662600	0.0112000
$36$	25.3339	4.22231
$37$	7.32002	1.20340	0.601702	−	0.798721i	$-0.294489\pi$
$37$	7.32002	1.20340	0.601702	+	0.798721i	$0.294489\pi$
$38$	2.05984	0.334150
$39$	−19.8335	−3.17590
$40$	−5.37982	−0.850624
$41$	11.4464	1.78763	0.893814	−	0.448439i	$-0.148020\pi$
$41$	11.4464	1.78763	0.893814	+	0.448439i	$0.148020\pi$
$42$	0.314800	0.0485747
$43$	−5.73382	−0.874399	−0.437199	−	0.899365i	$-0.644030\pi$
$43$	−5.73382	−0.874399	−0.437199	+	0.899365i	$0.644030\pi$
$44$	16.8319	2.53750
$45$	11.5788	1.72606
$46$	−0.497890	−0.0734098
$47$	6.36025	0.927738	0.463869	−	0.885904i	$-0.346461\pi$
$47$	6.36025	0.927738	0.463869	+	0.885904i	$0.346461\pi$
$48$	−3.33789	−0.481783
$49$	−6.99824	−0.999749
$50$	5.84734	0.826938
$51$	−16.3118	−2.28411
$52$	21.3377	2.95900
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	32.4883	4.42109
$55$	7.69296	1.03732
$56$	−0.142760	−0.0190771
$57$	2.83360	0.375320
$58$	13.5004	1.77269
$59$	3.89367	0.506912	0.253456	−	0.967347i	$-0.418433\pi$
$59$	3.89367	0.506912	0.253456	+	0.967347i	$0.418433\pi$
$60$	−17.5570	−2.26660
$61$	11.2233	1.43700	0.718499	−	0.695528i	$-0.244829\pi$
$61$	11.2233	1.43700	0.718499	+	0.695528i	$0.244829\pi$
$62$	21.5666	2.73896
$63$	0.307256	0.0387107
$64$	−12.3158	−1.53947
$65$	9.75232	1.20963
$66$	36.5491	4.49888
$67$	−2.51748	−0.307559	−0.153779	−	0.988105i	$-0.549144\pi$
$67$	−2.51748	−0.307559	−0.153779	+	0.988105i	$0.549144\pi$
$68$	17.5489	2.12812
$69$	−0.684919	−0.0824545
$70$	−0.154790	−0.0185010
$71$	−8.17822	−0.970576	−0.485288	−	0.874354i	$-0.661285\pi$
$71$	−8.17822	−0.970576	−0.485288	+	0.874354i	$0.661285\pi$
$72$	−24.9469	−2.94002
$73$	−13.5624	−1.58736	−0.793680	−	0.608335i	$-0.791838\pi$
$73$	−13.5624	−1.58736	−0.793680	+	0.608335i	$0.791838\pi$
$74$	−17.1003	−1.98787
$75$	8.04385	0.928824
$76$	−3.04850	−0.349687
$77$	0.204142	0.0232641
$78$	46.3330	5.24618
$79$	2.26106	0.254389	0.127194	−	0.991878i	$-0.459403\pi$
$79$	2.26106	0.254389	0.127194	+	0.991878i	$0.459403\pi$
$80$	1.64127	0.183500
$81$	22.7098	2.52331
$82$	−26.7399	−2.95293
$83$	−9.99178	−1.09674	−0.548370	−	0.836236i	$-0.684752\pi$
$83$	−9.99178	−1.09674	−0.548370	+	0.836236i	$0.684752\pi$
$84$	−0.465895	−0.0508334
$85$	8.02068	0.869965
$86$	13.3948	1.44440
$87$	18.5717	1.99110
$88$	−16.5748	−1.76688
$89$	2.27452	0.241099	0.120549	−	0.992707i	$-0.461534\pi$
$89$	2.27452	0.241099	0.120549	+	0.992707i	$0.461534\pi$
$90$	−27.0492	−2.85123
$91$	0.258789	0.0271285
$92$	0.736864	0.0768234
$93$	29.6679	3.07642
$94$	−14.8582	−1.53250
$95$	−1.39331	−0.142950
$96$	−14.0844	−1.43749
$97$	8.31360	0.844118	0.422059	−	0.906568i	$-0.361307\pi$
$97$	8.31360	0.844118	0.422059	+	0.906568i	$0.361307\pi$
$98$	16.3486	1.65146
$99$	35.6733	3.58530
$100$	−8.65391	−0.865391
$101$	−1.86348	−0.185423	−0.0927117	−	0.995693i	$-0.529553\pi$
$101$	−1.86348	−0.185423	−0.0927117	+	0.995693i	$0.529553\pi$
$102$	38.1061	3.77306
$103$	10.9007	1.07408	0.537039	−	0.843558i	$-0.319543\pi$
$103$	10.9007	1.07408	0.537039	+	0.843558i	$0.319543\pi$
$104$	−21.0118	−2.06037
$105$	−0.212936	−0.0207804
$106$	−2.33610	−0.226902
$107$	12.3892	1.19770	0.598852	−	0.800859i	$-0.295624\pi$
$107$	12.3892	1.19770	0.598852	+	0.800859i	$0.295624\pi$
$108$	−48.0818	−4.62667
$109$	19.5484	1.87240	0.936199	−	0.351470i	$-0.114318\pi$
$109$	19.5484	1.87240	0.936199	+	0.351470i	$0.114318\pi$
$110$	−17.9715	−1.71352
$111$	−23.5239	−2.23279
$112$	0.0435531	0.00411538
$113$	5.38126	0.506227	0.253113	−	0.967437i	$-0.418545\pi$
$113$	5.38126	0.506227	0.253113	+	0.967437i	$0.418545\pi$
$114$	−6.61958	−0.619980
$115$	0.336781	0.0314050
$116$	−19.9802	−1.85512
$117$	45.2228	4.18085
$118$	−9.09600	−0.837354
$119$	0.212838	0.0195109
$120$	17.2888	1.57825
$121$	12.7014	1.15468
$122$	−26.2188	−2.37374
$123$	−36.7846	−3.31676
$124$	−31.9180	−2.86632
$125$	−11.8561	−1.06045
$126$	−0.717782	−0.0639451
$127$	18.7481	1.66363	0.831813	−	0.555055i	$-0.187303\pi$
$127$	18.7481	1.66363	0.831813	+	0.555055i	$0.187303\pi$
$128$	20.0055	1.76825
$129$	18.4264	1.62236
$130$	−22.7824	−1.99815
$131$	−16.3597	−1.42935	−0.714676	−	0.699456i	$-0.753426\pi$
$131$	−16.3597	−1.42935	−0.714676	+	0.699456i	$0.753426\pi$
$132$	−54.0917	−4.70808
$133$	−0.0369731	−0.00320598
$134$	5.88108	0.508048
$135$	−21.9756	−1.89136
$136$	−17.2809	−1.48182
$137$	−14.7571	−1.26079	−0.630393	−	0.776276i	$-0.717106\pi$
$137$	−14.7571	−1.26079	−0.630393	+	0.776276i	$0.717106\pi$
$138$	1.60004	0.136204
$139$	−0.0744350	−0.00631350	−0.00315675	−	0.999995i	$-0.501005\pi$
$139$	−0.0744350	−0.00631350	−0.00315675	+	0.999995i	$0.501005\pi$
$140$	0.229085	0.0193612
$141$	−20.4396	−1.72132
$142$	19.1052	1.60327
$143$	30.0461	2.51258
$144$	7.61079	0.634233
$145$	−9.13190	−0.758363
$146$	31.6832	2.62212
$147$	22.4898	1.85493
$148$	25.3080	2.08031
$149$	−18.6785	−1.53020	−0.765102	−	0.643909i	$-0.777311\pi$
$149$	−18.6785	−1.53020	−0.765102	+	0.643909i	$0.777311\pi$
$150$	−18.7913	−1.53430
$151$	−1.00000	−0.0813788
$151$	−1.00000	−0.0813788
$152$	3.00194	0.243490
$153$	37.1930	3.00687
$154$	−0.476896	−0.0384294
$155$	−14.5880	−1.17174
$156$	−68.5717	−5.49013
$157$	6.14685	0.490572	0.245286	−	0.969451i	$-0.421118\pi$
$157$	6.14685	0.490572	0.245286	+	0.969451i	$0.421118\pi$
$158$	−5.28206	−0.420218
$159$	−3.21364	−0.254858
$160$	6.92546	0.547506
$161$	0.00893689	0.000704326 0
$162$	−53.0523	−4.16818
$163$	15.8906	1.24464	0.622322	−	0.782761i	$-0.286189\pi$
$163$	15.8906	1.24464	0.622322	+	0.782761i	$0.286189\pi$
$164$	39.5744	3.09024
$165$	−24.7224	−1.92464
$166$	23.3418	1.81168
$167$	10.7831	0.834418	0.417209	−	0.908811i	$-0.363008\pi$
$167$	10.7831	0.834418	0.417209	+	0.908811i	$0.363008\pi$
$168$	0.458779	0.0353956
$169$	25.0893	1.92994
$170$	−18.7371	−1.43707
$171$	−6.46096	−0.494082
$172$	−19.8239	−1.51156
$173$	2.62838	0.199832	0.0999159	−	0.994996i	$-0.468143\pi$
$173$	2.62838	0.199832	0.0999159	+	0.994996i	$0.468143\pi$
$174$	−43.3854	−3.28904
$175$	−0.104957	−0.00793401
$176$	5.05663	0.381158
$177$	−12.5129	−0.940524
$178$	−5.31352	−0.398265
$179$	−0.00749302	−0.000560055 0	−0.000280027	−	1.00000i	$-0.500089\pi$
$179$	−0.00749302	−0.000560055 0	−0.000280027		1.00000i	$0.500089\pi$
$180$	40.0321	2.98381
$181$	−17.0840	−1.26984	−0.634921	−	0.772577i	$-0.718967\pi$
$181$	−17.0840	−1.26984	−0.634921	+	0.772577i	$0.718967\pi$
$182$	−0.604558	−0.0448128
$183$	−36.0677	−2.66620
$184$	−0.725609	−0.0534926
$185$	11.5669	0.850419
$186$	−69.3072	−5.08185
$187$	24.7111	1.80705
$188$	21.9897	1.60377
$189$	−0.583149	−0.0424179
$190$	3.25491	0.236136
$191$	−2.44300	−0.176769	−0.0883847	−	0.996086i	$-0.528170\pi$
$191$	−2.44300	−0.176769	−0.0883847	+	0.996086i	$0.528170\pi$
$192$	39.5785	2.85633
$193$	10.3111	0.742207	0.371104	−	0.928591i	$-0.378979\pi$
$193$	10.3111	0.742207	0.371104	+	0.928591i	$0.378979\pi$
$194$	−19.4214	−1.39438
$195$	−31.3405	−2.24434
$196$	−24.1955	−1.72825
$197$	23.7537	1.69238	0.846190	−	0.532881i	$-0.178891\pi$
$197$	23.7537	1.69238	0.846190	+	0.532881i	$0.178891\pi$
$198$	−83.3364	−5.92246
$199$	13.2033	0.935954	0.467977	−	0.883741i	$-0.344983\pi$
$199$	13.2033	0.935954	0.467977	+	0.883741i	$0.344983\pi$
$200$	8.52173	0.602577
$201$	8.09027	0.570643
$202$	4.35328	0.306296
$203$	−0.242326	−0.0170079
$204$	−56.3960	−3.94851
$205$	18.0874	1.26328
$206$	−25.4651	−1.77424
$207$	1.56170	0.108546
$208$	6.41026	0.444471
$209$	−4.29268	−0.296931
$210$	0.497440	0.0343266
$211$	−24.9129	−1.71507	−0.857537	−	0.514423i	$-0.828006\pi$
$211$	−24.9129	−1.71507	−0.857537	+	0.514423i	$0.828006\pi$
$212$	3.45737	0.237453
$213$	26.2819	1.80081
$214$	−28.9423	−1.97846
$215$	−9.06046	−0.617918
$216$	47.3474	3.22158
$217$	−0.387110	−0.0262787
$218$	−45.6671	−3.09296
$219$	43.5848	2.94518
$220$	26.5974	1.79320
$221$	31.3261	2.10722
$222$	54.9543	3.68829
$223$	−1.42854	−0.0956621	−0.0478311	−	0.998855i	$-0.515231\pi$
$223$	−1.42854	−0.0956621	−0.0478311	+	0.998855i	$0.515231\pi$
$224$	0.183775	0.0122790
$225$	−18.3410	−1.22273
$226$	−12.5712	−0.836222
$227$	3.69471	0.245226	0.122613	−	0.992455i	$-0.460873\pi$
$227$	3.69471	0.245226	0.122613	+	0.992455i	$0.460873\pi$
$228$	9.79680	0.648809
$229$	7.15030	0.472505	0.236253	−	0.971692i	$-0.424081\pi$
$229$	7.15030	0.472505	0.236253	+	0.971692i	$0.424081\pi$
$230$	−0.786755	−0.0518771
$231$	−0.656039	−0.0431642
$232$	19.6750	1.29173
$233$	17.2558	1.13047	0.565233	−	0.824931i	$-0.308786\pi$
$233$	17.2558	1.13047	0.565233	+	0.824931i	$0.308786\pi$
$234$	−105.645	−6.90623
$235$	10.0503	0.655612
$236$	13.4618	0.876291
$237$	−7.26623	−0.471992
$238$	−0.497212	−0.0322295
$239$	18.5869	1.20228	0.601142	−	0.799142i	$-0.294712\pi$
$239$	18.5869	1.20228	0.601142	+	0.799142i	$0.294712\pi$
$240$	−5.27446	−0.340465
$241$	2.40494	0.154916	0.0774578	−	0.996996i	$-0.475320\pi$
$241$	2.40494	0.154916	0.0774578	+	0.996996i	$0.475320\pi$
$242$	−29.6718	−1.90738
$243$	−31.2599	−2.00533
$244$	38.8032	2.48412
$245$	−11.0585	−0.706500
$246$	85.9326	5.47886
$247$	−5.44180	−0.346253
$248$	31.4304	1.99583
$249$	32.1100	2.03489
$250$	27.6971	1.75172
$251$	−22.9590	−1.44916	−0.724581	−	0.689189i	$-0.757967\pi$
$251$	−22.9590	−1.44916	−0.724581	+	0.689189i	$0.757967\pi$
$252$	1.06230	0.0669185
$253$	1.03760	0.0652332
$254$	−43.7975	−2.74810
$255$	−25.7756	−1.61413
$256$	−22.1033	−1.38145
$257$	−20.5387	−1.28117	−0.640585	−	0.767888i	$-0.721308\pi$
$257$	−20.5387	−1.28117	−0.640585	+	0.767888i	$0.721308\pi$
$258$	−43.0460	−2.67993
$259$	0.306943	0.0190725
$260$	33.7174	2.09106
$261$	−42.3458	−2.62114
$262$	38.2178	2.36111
$263$	−6.43330	−0.396694	−0.198347	−	0.980132i	$-0.563557\pi$
$263$	−6.43330	−0.396694	−0.198347	+	0.980132i	$0.563557\pi$
$264$	53.2655	3.27826
$265$	1.58018	0.0970697
$266$	0.0863729	0.00529587
$267$	−7.30950	−0.447334
$268$	−8.70384	−0.531672
$269$	13.6866	0.834489	0.417245	−	0.908794i	$-0.362996\pi$
$269$	13.6866	0.834489	0.417245	+	0.908794i	$0.362996\pi$
$270$	51.3373	3.12429
$271$	6.36727	0.386784	0.193392	−	0.981122i	$-0.438051\pi$
$271$	6.36727	0.386784	0.193392	+	0.981122i	$0.438051\pi$
$272$	5.27204	0.319665
$273$	−0.831657	−0.0503342
$274$	34.4741	2.08266
$275$	−12.1858	−0.734831
$276$	−2.36802	−0.142538
$277$	−20.3668	−1.22372	−0.611861	−	0.790965i	$-0.709579\pi$
$277$	−20.3668	−1.22372	−0.611861	+	0.790965i	$0.709579\pi$
$278$	0.173888	0.0104291
$279$	−67.6465	−4.04989
$280$	−0.225586	−0.0134814
$281$	26.6196	1.58799	0.793997	−	0.607922i	$-0.207997\pi$
$281$	26.6196	1.58799	0.793997	+	0.607922i	$0.207997\pi$
$282$	47.7489	2.84341
$283$	4.08876	0.243051	0.121526	−	0.992588i	$-0.461221\pi$
$283$	4.08876	0.243051	0.121526	+	0.992588i	$0.461221\pi$
$284$	−28.2751	−1.67782
$285$	4.47760	0.265230
$286$	−70.1908	−4.15047
$287$	0.479970	0.0283317
$288$	32.1143	1.89235
$289$	8.76378	0.515516
$290$	21.3330	1.25272
$291$	−26.7169	−1.56618
$292$	−46.8903	−2.74405
$293$	−19.3253	−1.12899	−0.564497	−	0.825435i	$-0.690930\pi$
$293$	−19.3253	−1.12899	−0.564497	+	0.825435i	$0.690930\pi$
$294$	−52.5386	−3.06411
$295$	6.15269	0.358224
$296$	−24.9215	−1.44853
$297$	−67.7052	−3.92865
$298$	43.6349	2.52770
$299$	1.31535	0.0760689
$300$	27.8106	1.60564
$301$	−0.240430	−0.0138582
$302$	2.33610	0.134428
$303$	5.98856	0.344034
$304$	−0.915830	−0.0525265
$305$	17.7349	1.01550
$306$	−86.8865	−4.96697
$307$	0.724643	0.0413576	0.0206788	−	0.999786i	$-0.493417\pi$
$307$	0.724643	0.0413576	0.0206788	+	0.999786i	$0.493417\pi$
$308$	0.705794	0.0402164
$309$	−35.0309	−1.99284
$310$	34.0790	1.93556
$311$	−22.2479	−1.26156	−0.630782	−	0.775960i	$-0.717266\pi$
$311$	−22.2479	−1.26156	−0.630782	+	0.775960i	$0.717266\pi$
$312$	67.5243	3.82281
$313$	12.6068	0.712579	0.356290	−	0.934376i	$-0.384042\pi$
$313$	12.6068	0.712579	0.356290	+	0.934376i	$0.384042\pi$
$314$	−14.3597	−0.810362
$315$	0.485520	0.0273560
$316$	7.81730	0.439758
$317$	−13.8115	−0.775729	−0.387865	−	0.921716i	$-0.626787\pi$
$317$	−13.8115	−0.775729	−0.387865	+	0.921716i	$0.626787\pi$
$318$	7.50740	0.420994
$319$	−28.1347	−1.57524
$320$	−19.4611	−1.08791
$321$	−39.8143	−2.22222
$322$	−0.0208775	−0.00116346
$323$	−4.47554	−0.249026
$324$	78.5160	4.36200
$325$	−15.4478	−0.856892
$326$	−37.1219	−2.05599
$327$	−62.8216	−3.47404
$328$	−38.9700	−2.15176
$329$	0.266698	0.0147035
$330$	57.7541	3.17926
$331$	12.1815	0.669558	0.334779	−	0.942297i	$-0.391338\pi$
$331$	12.1815	0.669558	0.334779	+	0.942297i	$0.391338\pi$
$332$	−34.5453	−1.89592
$333$	53.6375	2.93931
$334$	−25.1903	−1.37835
$335$	−3.97806	−0.217345
$336$	−0.139964	−0.00763567
$337$	7.27455	0.396270	0.198135	−	0.980175i	$-0.436512\pi$
$337$	7.27455	0.396270	0.198135	+	0.980175i	$0.436512\pi$
$338$	−58.6111	−3.18802
$339$	−17.2935	−0.939252
$340$	27.7305	1.50389
$341$	−44.9445	−2.43388
$342$	15.0935	0.816160
$343$	−0.586974	−0.0316936
$344$	19.5211	1.05251
$345$	−1.08229	−0.0582688
$346$	−6.14015	−0.330097
$347$	19.4017	1.04154	0.520769	−	0.853697i	$-0.325645\pi$
$347$	19.4017	1.04154	0.520769	+	0.853697i	$0.325645\pi$
$348$	64.2093	3.44198
$349$	9.39843	0.503087	0.251543	−	0.967846i	$-0.419062\pi$
$349$	9.39843	0.503087	0.251543	+	0.967846i	$0.419062\pi$
$350$	0.245190	0.0131060
$351$	−85.8294	−4.58124
$352$	21.3368	1.13726
$353$	2.18305	0.116192	0.0580960	−	0.998311i	$-0.481497\pi$
$353$	2.18305	0.116192	0.0580960	+	0.998311i	$0.481497\pi$
$354$	29.2313	1.55363
$355$	−12.9231	−0.685885
$356$	7.86386	0.416784
$357$	−0.683986	−0.0362004
$358$	0.0175045	0.000925139 0
$359$	−7.29728	−0.385136	−0.192568	−	0.981284i	$-0.561682\pi$
$359$	−7.29728	−0.385136	−0.192568	+	0.981284i	$0.561682\pi$
$360$	−39.4206	−2.07765
$361$	−18.2225	−0.959081
$362$	39.9099	2.09762
$363$	−40.8178	−2.14238
$364$	0.894730	0.0468966
$365$	−21.4310	−1.12175
$366$	84.2579	4.40423
$367$	22.9470	1.19783	0.598913	−	0.800814i	$-0.295600\pi$
$367$	22.9470	1.19783	0.598913	+	0.800814i	$0.295600\pi$
$368$	0.221368	0.0115396
$369$	83.8735	4.36628
$370$	−27.0216	−1.40478
$371$	0.0419320	0.00217700
$372$	102.573	5.31816
$373$	21.7871	1.12809	0.564046	−	0.825743i	$-0.309244\pi$
$373$	21.7871	1.12809	0.564046	+	0.825743i	$0.309244\pi$
$374$	−57.7276	−2.98502
$375$	38.1014	1.96755
$376$	−21.6539	−1.11671
$377$	−35.6661	−1.83690
$378$	1.36230	0.0700689
$379$	−6.63072	−0.340597	−0.170299	−	0.985393i	$-0.554473\pi$
$379$	−6.63072	−0.340597	−0.170299	+	0.985393i	$0.554473\pi$
$380$	−4.81718	−0.247116
$381$	−60.2498	−3.08669
$382$	5.70710	0.292001
$383$	−31.7402	−1.62185	−0.810925	−	0.585150i	$-0.801036\pi$
$383$	−31.7402	−1.62185	−0.810925	+	0.585150i	$0.801036\pi$
$384$	−64.2904	−3.28081
$385$	0.322581	0.0164402
$386$	−24.0877	−1.22603
$387$	−42.0146	−2.13572
$388$	28.7432	1.45921
$389$	−10.2407	−0.519226	−0.259613	−	0.965713i	$-0.583595\pi$
$389$	−10.2407	−0.519226	−0.259613	+	0.965713i	$0.583595\pi$
$390$	73.2145	3.70736
$391$	1.08180	0.0547089
$392$	23.8259	1.20339
$393$	52.5741	2.65201
$394$	−55.4910	−2.79560
$395$	3.57287	0.179771
$396$	123.336	6.19785
$397$	2.70205	0.135612	0.0678061	−	0.997699i	$-0.478400\pi$
$397$	2.70205	0.135612	0.0678061	+	0.997699i	$0.478400\pi$
$398$	−30.8441	−1.54608
$399$	0.118818	0.00594836
$400$	−2.59980	−0.129990
$401$	−3.39632	−0.169604	−0.0848022	−	0.996398i	$-0.527026\pi$
$401$	−3.39632	−0.169604	−0.0848022	+	0.996398i	$0.527026\pi$
$402$	−18.8997	−0.942631
$403$	−56.9758	−2.83817
$404$	−6.44274	−0.320538
$405$	35.8855	1.78317
$406$	0.566098	0.0280949
$407$	35.6369	1.76645
$408$	55.5346	2.74937
$409$	15.2698	0.755041	0.377521	−	0.926001i	$-0.376777\pi$
$409$	15.2698	0.755041	0.377521	+	0.926001i	$0.376777\pi$
$410$	−42.2539	−2.08677
$411$	47.4241	2.33926
$412$	37.6877	1.85674
$413$	0.163269	0.00803394
$414$	−3.64829	−0.179304
$415$	−15.7888	−0.775042
$416$	27.0485	1.32616
$417$	0.239208	0.0117140
$418$	10.0281	0.490492
$419$	31.2556	1.52693	0.763467	−	0.645846i	$-0.223495\pi$
$419$	31.2556	1.52693	0.763467	+	0.645846i	$0.223495\pi$
$420$	−0.736198	−0.0359228
$421$	−10.2719	−0.500620	−0.250310	−	0.968166i	$-0.580533\pi$
$421$	−10.2719	−0.500620	−0.250310	+	0.968166i	$0.580533\pi$
$422$	58.1990	2.83308
$423$	46.6047	2.26600
$424$	−3.40456	−0.165340
$425$	−12.7049	−0.616278
$426$	−61.3971	−2.97470
$427$	0.470616	0.0227747
$428$	42.8339	2.07045
$429$	−96.5576	−4.66184
$430$	21.1662	1.02072
$431$	12.1229	0.583941	0.291971	−	0.956427i	$-0.405689\pi$
$431$	12.1229	0.583941	0.291971	+	0.956427i	$0.405689\pi$
$432$	−14.4447	−0.694971
$433$	3.11671	0.149780	0.0748898	−	0.997192i	$-0.476140\pi$
$433$	3.11671	0.149780	0.0748898	+	0.997192i	$0.476140\pi$
$434$	0.904328	0.0434091
$435$	29.3467	1.40706
$436$	67.5861	3.23679
$437$	−0.187924	−0.00898963
$438$	−101.818	−4.86507
$439$	−7.61561	−0.363473	−0.181737	−	0.983347i	$-0.558172\pi$
$439$	−7.61561	−0.363473	−0.181737	+	0.983347i	$0.558172\pi$
$440$	−26.1912	−1.24861
$441$	−51.2796	−2.44189
$442$	−73.1809	−3.48086
$443$	−5.06724	−0.240752	−0.120376	−	0.992728i	$-0.538410\pi$
$443$	−5.06724	−0.240752	−0.120376	+	0.992728i	$0.538410\pi$
$444$	−81.3309	−3.85979
$445$	3.59415	0.170379
$446$	3.33721	0.158022
$447$	60.0261	2.83914
$448$	−0.516424	−0.0243987
$449$	7.70488	0.363616	0.181808	−	0.983334i	$-0.441805\pi$
$449$	7.70488	0.363616	0.181808	+	0.983334i	$0.441805\pi$
$450$	42.8464	2.01980
$451$	55.7258	2.62402
$452$	18.6050	0.875106
$453$	3.21364	0.150990
$454$	−8.63121	−0.405083
$455$	0.408934	0.0191711
$456$	−9.64717	−0.451770
$457$	10.6017	0.495928	0.247964	−	0.968769i	$-0.420238\pi$
$457$	10.6017	0.495928	0.247964	+	0.968769i	$0.420238\pi$
$458$	−16.7038	−0.780519
$459$	−70.5894	−3.29483
$460$	1.16438	0.0542894
$461$	7.32320	0.341075	0.170538	−	0.985351i	$-0.445450\pi$
$461$	7.32320	0.341075	0.170538	+	0.985351i	$0.445450\pi$
$462$	1.53257	0.0713018
$463$	7.20806	0.334987	0.167493	−	0.985873i	$-0.446433\pi$
$463$	7.20806	0.334987	0.167493	+	0.985873i	$0.446433\pi$
$464$	−6.00245	−0.278657
$465$	46.8806	2.17404
$466$	−40.3113	−1.86739
$467$	7.45037	0.344762	0.172381	−	0.985030i	$-0.444854\pi$
$467$	7.45037	0.344762	0.172381	+	0.985030i	$0.444854\pi$
$468$	156.352	7.22737
$469$	−0.105563	−0.00487443
$470$	−23.4786	−1.08299
$471$	−19.7538	−0.910206
$472$	−13.2562	−0.610167
$473$	−27.9146	−1.28351
$474$	16.9746	0.779671
$475$	2.20703	0.101265
$476$	0.735861	0.0337281
$477$	7.32750	0.335503
$478$	−43.4208	−1.98602
$479$	−27.5150	−1.25719	−0.628596	−	0.777732i	$-0.716370\pi$
$479$	−27.5150	−1.25719	−0.628596	+	0.777732i	$0.716370\pi$
$480$	−22.2560	−1.01584
$481$	45.1766	2.05988
$482$	−5.61818	−0.255901
$483$	−0.0287200	−0.00130680
$484$	43.9135	1.99607
$485$	13.1370	0.596520
$486$	73.0264	3.31254
$487$	16.9724	0.769092	0.384546	−	0.923106i	$-0.374358\pi$
$487$	16.9724	0.769092	0.384546	+	0.923106i	$0.374358\pi$
$488$	−38.2105	−1.72971
$489$	−51.0666	−2.30931
$490$	25.8337	1.16705
$491$	9.93415	0.448322	0.224161	−	0.974552i	$-0.428036\pi$
$491$	9.93415	0.448322	0.224161	+	0.974552i	$0.428036\pi$
$492$	−127.178	−5.73363
$493$	−29.3332	−1.32110
$494$	12.7126	0.571966
$495$	56.3702	2.53365
$496$	−9.58878	−0.430549
$497$	−0.342929	−0.0153825
$498$	−75.0123	−3.36138
$499$	−7.94822	−0.355811	−0.177906	−	0.984048i	$-0.556932\pi$
$499$	−7.94822	−0.355811	−0.177906	+	0.984048i	$0.556932\pi$
$500$	−40.9910	−1.83318
$501$	−34.6529	−1.54818
$502$	53.6347	2.39383
$503$	26.7544	1.19292	0.596460	−	0.802643i	$-0.296573\pi$
$503$	26.7544	1.19292	0.596460	+	0.802643i	$0.296573\pi$
$504$	−1.04607	−0.0465958
$505$	−2.94464	−0.131035
$506$	−2.42393	−0.107757
$507$	−80.6280	−3.58081
$508$	64.8192	2.87589
$509$	−37.3237	−1.65434	−0.827172	−	0.561948i	$-0.810052\pi$
$509$	−37.3237	−1.65434	−0.827172	+	0.561948i	$0.810052\pi$
$510$	60.2144	2.66634
$511$	−0.568698	−0.0251577
$512$	11.6245	0.513736
$513$	12.2624	0.541399
$514$	47.9805	2.11633
$515$	17.2251	0.759027
$516$	63.7070	2.80454
$517$	30.9643	1.36181
$518$	−0.717049	−0.0315053
$519$	−8.44666	−0.370767
$520$	−33.2024	−1.45602
$521$	40.3402	1.76734	0.883669	−	0.468112i	$-0.155066\pi$
$521$	40.3402	1.76734	0.883669	+	0.468112i	$0.155066\pi$
$522$	98.9241	4.32979
$523$	−30.1784	−1.31961	−0.659806	−	0.751436i	$-0.729361\pi$
$523$	−30.1784	−1.31961	−0.659806	+	0.751436i	$0.729361\pi$
$524$	−56.5614	−2.47090
$525$	0.337294	0.0147207
$526$	15.0288	0.655288
$527$	−46.8591	−2.04122
$528$	−16.2502	−0.707200
$529$	−22.9546	−0.998025
$530$	−3.69146	−0.160347
$531$	28.5308	1.23813
$532$	−0.127830	−0.00554212
$533$	70.6432	3.05990
$534$	17.0757	0.738940
$535$	19.5771	0.846392
$536$	8.57090	0.370206
$537$	0.0240799	0.00103912
$538$	−31.9734	−1.37847
$539$	−34.0703	−1.46751
$540$	−75.9778	−3.26957
$541$	5.67894	0.244157	0.122078	−	0.992520i	$-0.461044\pi$
$541$	5.67894	0.244157	0.122078	+	0.992520i	$0.461044\pi$
$542$	−14.8746	−0.638919
$543$	54.9018	2.35606
$544$	22.2457	0.953778
$545$	30.8900	1.32318
$546$	1.94283	0.0831456
$547$	26.0264	1.11281	0.556404	−	0.830912i	$-0.312181\pi$
$547$	26.0264	1.11281	0.556404	+	0.830912i	$0.312181\pi$
$548$	−51.0208	−2.17950
$549$	82.2389	3.50987
$550$	28.4672	1.21385
$551$	5.09560	0.217080
$552$	2.33185	0.0992500
$553$	0.0948105	0.00403175
$554$	47.5789	2.02143
$555$	−37.1720	−1.57787
$556$	−0.257349	−0.0109140
$557$	11.9454	0.506141	0.253070	−	0.967448i	$-0.418560\pi$
$557$	11.9454	0.506141	0.253070	+	0.967448i	$0.418560\pi$
$558$	158.029	6.68990
$559$	−35.3871	−1.49672
$560$	0.0688217	0.00290825
$561$	−79.4126	−3.35280
$562$	−62.1861	−2.62316
$563$	31.1996	1.31491	0.657453	−	0.753496i	$-0.271634\pi$
$563$	31.1996	1.31491	0.657453	+	0.753496i	$0.271634\pi$
$564$	−70.6671	−2.97562
$565$	8.50336	0.357739
$566$	−9.55175	−0.401490
$567$	0.952265	0.0399914
$568$	27.8433	1.16828
$569$	4.13797	0.173473	0.0867363	−	0.996231i	$-0.472356\pi$
$569$	4.13797	0.173473	0.0867363	+	0.996231i	$0.472356\pi$
$570$	−10.4601	−0.438126
$571$	−23.8573	−0.998397	−0.499198	−	0.866488i	$-0.666372\pi$
$571$	−23.8573	−0.998397	−0.499198	+	0.866488i	$0.666372\pi$
$572$	103.881	4.34347
$573$	7.85093	0.327977
$574$	−1.12126	−0.0468004
$575$	−0.533467	−0.0222471
$576$	−90.2438	−3.76016
$577$	−30.9867	−1.28999	−0.644997	−	0.764185i	$-0.723142\pi$
$577$	−30.9867	−1.28999	−0.644997	+	0.764185i	$0.723142\pi$
$578$	−20.4731	−0.851568
$579$	−33.1361	−1.37709
$580$	−31.5723	−1.31097
$581$	−0.418975	−0.0173820
$582$	62.4135	2.58712
$583$	4.86841	0.201629
$584$	46.1741	1.91070
$585$	71.4601	2.95451
$586$	45.1458	1.86496
$587$	2.59851	0.107252	0.0536260	−	0.998561i	$-0.482922\pi$
$587$	2.59851	0.107252	0.0536260	+	0.998561i	$0.482922\pi$
$588$	77.7557	3.20659
$589$	8.14011	0.335407
$590$	−14.3733	−0.591740
$591$	−76.3359	−3.14004
$592$	7.60303	0.312482
$593$	12.9524	0.531890	0.265945	−	0.963988i	$-0.414316\pi$
$593$	12.9524	0.531890	0.265945	+	0.963988i	$0.414316\pi$
$594$	158.166	6.48964
$595$	0.336323	0.0137879
$596$	−64.5785	−2.64524
$597$	−42.4305	−1.73657
$598$	−3.07280	−0.125656
$599$	−8.48111	−0.346529	−0.173264	−	0.984875i	$-0.555431\pi$
$599$	−8.48111	−0.346529	−0.173264	+	0.984875i	$0.555431\pi$
$600$	−27.3858	−1.11802
$601$	−18.3633	−0.749057	−0.374528	−	0.927215i	$-0.622195\pi$
$601$	−18.3633	−0.749057	−0.374528	+	0.927215i	$0.622195\pi$
$602$	0.561669	0.0228919
$603$	−18.4468	−0.751212
$604$	−3.45737	−0.140678
$605$	20.0705	0.815983
$606$	−13.9899	−0.568300
$607$	0.760931	0.0308852	0.0154426	−	0.999881i	$-0.495084\pi$
$607$	0.760931	0.0308852	0.0154426	+	0.999881i	$0.495084\pi$
$608$	−3.86441	−0.156722
$609$	0.778749	0.0315565
$610$	−41.4304	−1.67747
$611$	39.2532	1.58802
$612$	128.590	5.19793
$613$	30.5635	1.23445	0.617224	−	0.786788i	$-0.288257\pi$
$613$	30.5635	1.23445	0.617224	+	0.786788i	$0.288257\pi$
$614$	−1.69284	−0.0683174
$615$	−58.1263	−2.34388
$616$	−0.695014	−0.0280029
$617$	−7.41778	−0.298629	−0.149314	−	0.988790i	$-0.547707\pi$
$617$	−7.41778	−0.298629	−0.149314	+	0.988790i	$0.547707\pi$
$618$	81.8358	3.29192
$619$	24.9673	1.00352	0.501760	−	0.865007i	$-0.332686\pi$
$619$	24.9673	1.00352	0.501760	+	0.865007i	$0.332686\pi$
$620$	−50.4361	−2.02556
$621$	−2.96399	−0.118941
$622$	51.9734	2.08394
$623$	0.0953752	0.00382113
$624$	−20.6003	−0.824671
$625$	−6.21967	−0.248787
$626$	−29.4508	−1.17709
$627$	13.7951	0.550925
$628$	21.2519	0.848044
$629$	37.1550	1.48147
$630$	−1.13422	−0.0451886
$631$	−36.5828	−1.45634	−0.728168	−	0.685399i	$-0.759628\pi$
$631$	−36.5828	−1.45634	−0.728168	+	0.685399i	$0.759628\pi$
$632$	−7.69790	−0.306206
$633$	80.0611	3.18214
$634$	32.2650	1.28141
$635$	29.6254	1.17565
$636$	−11.1107	−0.440570
$637$	−43.1907	−1.71128
$638$	65.7254	2.60209
$639$	−59.9259	−2.37063
$640$	31.6122	1.24958
$641$	13.5924	0.536869	0.268434	−	0.963298i	$-0.413494\pi$
$641$	13.5924	0.536869	0.268434	+	0.963298i	$0.413494\pi$
$642$	93.0103	3.67082
$643$	10.9095	0.430227	0.215114	−	0.976589i	$-0.430988\pi$
$643$	10.9095	0.430227	0.215114	+	0.976589i	$0.430988\pi$
$644$	0.0308981	0.00121756
$645$	29.1171	1.14648
$646$	10.4553	0.411359
$647$	−12.5688	−0.494131	−0.247065	−	0.968999i	$-0.579466\pi$
$647$	−12.5688	−0.494131	−0.247065	+	0.968999i	$0.579466\pi$
$648$	−77.3168	−3.03729
$649$	18.9560	0.744087
$650$	36.0877	1.41548
$651$	1.24403	0.0487575
$652$	54.9395	2.15160
$653$	−38.2939	−1.49856	−0.749278	−	0.662256i	$-0.769599\pi$
$653$	−38.2939	−1.49856	−0.749278	+	0.662256i	$0.769599\pi$
$654$	146.758	5.73868
$655$	−25.8512	−1.01009
$656$	11.8889	0.464185
$657$	−99.3786	−3.87713
$658$	−0.623033	−0.0242883
$659$	−1.39169	−0.0542124	−0.0271062	−	0.999633i	$-0.508629\pi$
$659$	−1.39169	−0.0542124	−0.0271062	+	0.999633i	$0.508629\pi$
$660$	−85.4746	−3.32709
$661$	−13.7949	−0.536560	−0.268280	−	0.963341i	$-0.586455\pi$
$661$	−13.7949	−0.536560	−0.268280	+	0.963341i	$0.586455\pi$
$662$	−28.4573	−1.10602
$663$	−100.671	−3.90973
$664$	34.0176	1.32014
$665$	−0.0584242	−0.00226559
$666$	−125.303	−4.85537
$667$	−1.23167	−0.0476906
$668$	37.2810	1.44245
$669$	4.59082	0.177491
$670$	9.29316	0.359026
$671$	54.6397	2.10934
$672$	−0.590588	−0.0227824
$673$	45.1442	1.74018	0.870090	−	0.492893i	$-0.164061\pi$
$673$	45.1442	1.74018	0.870090	+	0.492893i	$0.164061\pi$
$674$	−16.9941	−0.654587
$675$	34.8098	1.33983
$676$	86.7429	3.33627
$677$	40.8825	1.57124	0.785622	−	0.618707i	$-0.212343\pi$
$677$	40.8825	1.57124	0.785622	+	0.618707i	$0.212343\pi$
$678$	40.3993	1.55152
$679$	0.348606	0.0133783
$680$	−27.3069	−1.04717
$681$	−11.8735	−0.454992
$682$	104.995	4.02046
$683$	45.6476	1.74666	0.873329	−	0.487131i	$-0.161957\pi$
$683$	45.6476	1.74666	0.873329	+	0.487131i	$0.161957\pi$
$684$	−22.3379	−0.854111
$685$	−23.3189	−0.890969
$686$	1.37123	0.0523538
$687$	−22.9785	−0.876685
$688$	−5.95550	−0.227051
$689$	6.17165	0.235121
$690$	2.52835	0.0962526
$691$	42.9896	1.63540	0.817701	−	0.575643i	$-0.195248\pi$
$691$	42.9896	1.63540	0.817701	+	0.575643i	$0.195248\pi$
$692$	9.08727	0.345446
$693$	1.49585	0.0568227
$694$	−45.3244	−1.72049
$695$	−0.117621	−0.00446161
$696$	−63.2286	−2.39667
$697$	58.0997	2.20068
$698$	−21.9557	−0.831035
$699$	−55.4540	−2.09746
$700$	−0.362875	−0.0137154
$701$	35.4534	1.33906	0.669528	−	0.742787i	$-0.266497\pi$
$701$	35.4534	1.33906	0.669528	+	0.742787i	$0.266497\pi$
$702$	200.506	7.56762
$703$	−6.45436	−0.243431
$704$	−59.9582	−2.25976
$705$	−32.2982	−1.21642
$706$	−5.09983	−0.191935
$707$	−0.0781394	−0.00293873
$708$	−43.2615	−1.62587
$709$	−14.1400	−0.531040	−0.265520	−	0.964105i	$-0.585544\pi$
$709$	−14.1400	−0.531040	−0.265520	+	0.964105i	$0.585544\pi$
$710$	30.1896	1.13299
$711$	16.5679	0.621344
$712$	−7.74375	−0.290209
$713$	−1.96757	−0.0736862
$714$	1.59786	0.0597985
$715$	47.4783	1.77559
$716$	−0.0259061	−0.000968158 0
$717$	−59.7316	−2.23072
$718$	17.0472	0.636196
$719$	10.3904	0.387496	0.193748	−	0.981051i	$-0.437936\pi$
$719$	10.3904	0.387496	0.193748	+	0.981051i	$0.437936\pi$
$720$	12.0264	0.448198
$721$	0.457088	0.0170228
$722$	42.5697	1.58428
$723$	−7.72861	−0.287430
$724$	−59.0656	−2.19516
$725$	14.4651	0.537220
$726$	95.3546	3.53894
$727$	−10.2193	−0.379013	−0.189507	−	0.981879i	$-0.560689\pi$
$727$	−10.2193	−0.379013	−0.189507	+	0.981879i	$0.560689\pi$
$728$	−0.881064	−0.0326544
$729$	32.3290	1.19737
$730$	50.0651	1.85299
$731$	−29.1037	−1.07644
$732$	−124.699	−4.60903
$733$	26.7938	0.989653	0.494826	−	0.868992i	$-0.335232\pi$
$733$	26.7938	0.989653	0.494826	+	0.868992i	$0.335232\pi$
$734$	−53.6066	−1.97866
$735$	35.5380	1.31084
$736$	0.934079	0.0344306
$737$	−12.2561	−0.451459
$738$	−195.937	−7.21254
$739$	20.9504	0.770673	0.385336	−	0.922776i	$-0.374085\pi$
$739$	20.9504	0.770673	0.385336	+	0.922776i	$0.374085\pi$
$740$	39.9912	1.47011
$741$	17.4880	0.642438
$742$	−0.0979573	−0.00359612
$743$	15.3220	0.562109	0.281055	−	0.959692i	$-0.409316\pi$
$743$	15.3220	0.562109	0.281055	+	0.959692i	$0.409316\pi$
$744$	−101.006	−3.70307
$745$	−29.5154	−1.08136
$746$	−50.8969	−1.86347
$747$	−73.2148	−2.67879
$748$	85.4354	3.12383
$749$	0.519502	0.0189822
$750$	−89.0087	−3.25014
$751$	46.0952	1.68204	0.841019	−	0.541005i	$-0.181956\pi$
$751$	46.0952	1.68204	0.841019	+	0.541005i	$0.181956\pi$
$752$	6.60615	0.240901
$753$	73.7822	2.68877
$754$	83.3197	3.03432
$755$	−1.58018	−0.0575086
$756$	−2.01616	−0.0733271
$757$	−44.6551	−1.62302	−0.811509	−	0.584340i	$-0.801354\pi$
$757$	−44.6551	−1.62302	−0.811509	+	0.584340i	$0.801354\pi$
$758$	15.4900	0.562623
$759$	−3.33447	−0.121033
$760$	4.74361	0.172069
$761$	−18.4796	−0.669883	−0.334942	−	0.942239i	$-0.608717\pi$
$761$	−18.4796	−0.669883	−0.334942	+	0.942239i	$0.608717\pi$
$762$	140.750	5.09882
$763$	0.819703	0.0296752
$764$	−8.44636	−0.305578
$765$	58.7715	2.12489
$766$	74.1484	2.67909
$767$	24.0303	0.867686
$768$	71.0320	2.56315
$769$	0.676230	0.0243855	0.0121927	−	0.999926i	$-0.496119\pi$
$769$	0.676230	0.0243855	0.0121927	+	0.999926i	$0.496119\pi$
$770$	−0.753582	−0.0271572
$771$	66.0041	2.37708
$772$	35.6492	1.28304
$773$	−9.19362	−0.330671	−0.165336	−	0.986237i	$-0.552871\pi$
$773$	−9.19362	−0.330671	−0.165336	+	0.986237i	$0.552871\pi$
$774$	98.1502	3.52794
$775$	23.1076	0.830051
$776$	−28.3042	−1.01606
$777$	−0.986404	−0.0353871
$778$	23.9234	0.857695
$779$	−10.0928	−0.361611
$780$	−108.356	−3.87975
$781$	−39.8149	−1.42469
$782$	−2.52719	−0.0903721
$783$	80.3691	2.87216
$784$	−7.26881	−0.259600
$785$	9.71312	0.346676
$786$	−122.819	−4.38079
$787$	17.7806	0.633809	0.316904	−	0.948457i	$-0.397357\pi$
$787$	17.7806	0.633809	0.316904	+	0.948457i	$0.397357\pi$
$788$	82.1253	2.92559
$789$	20.6743	0.736025
$790$	−8.34660	−0.296959
$791$	0.225647	0.00802308
$792$	−121.452	−4.31560
$793$	69.2664	2.45972
$794$	−6.31227	−0.224014
$795$	−5.07813	−0.180103
$796$	45.6485	1.61797
$797$	−15.9391	−0.564593	−0.282296	−	0.959327i	$-0.591096\pi$
$797$	−15.9391	−0.564593	−0.282296	+	0.959327i	$0.591096\pi$
$798$	−0.277572	−0.00982594
$799$	32.2834	1.14210
$800$	−10.9700	−0.387850
$801$	16.6666	0.588884
$802$	7.93416	0.280165
$803$	−66.0274	−2.33006
$804$	27.9710	0.986462
$805$	0.0141219	0.000497731 0
$806$	133.101	4.68829
$807$	−43.9840	−1.54831
$808$	6.34434	0.223193
$809$	−11.1638	−0.392500	−0.196250	−	0.980554i	$-0.562876\pi$
$809$	−11.1638	−0.392500	−0.196250	+	0.980554i	$0.562876\pi$
$810$	−83.8322	−2.94556
$811$	−6.53567	−0.229499	−0.114749	−	0.993394i	$-0.536606\pi$
$811$	−6.53567	−0.229499	−0.114749	+	0.993394i	$0.536606\pi$
$812$	−0.837810	−0.0294014
$813$	−20.4621	−0.717639
$814$	−83.2513	−2.91796
$815$	25.1099	0.879562
$816$	−16.9425	−0.593105
$817$	5.05574	0.176878
$818$	−35.6717	−1.24723
$819$	1.89628	0.0662614
$820$	62.5347	2.18381
$821$	−20.1640	−0.703727	−0.351864	−	0.936051i	$-0.614452\pi$
$821$	−20.1640	−0.703727	−0.351864	+	0.936051i	$0.614452\pi$
$822$	−110.788	−3.86416
$823$	−11.1501	−0.388670	−0.194335	−	0.980935i	$-0.562255\pi$
$823$	−11.1501	−0.388670	−0.194335	+	0.980935i	$0.562255\pi$
$824$	−37.1121	−1.29286
$825$	39.1608	1.36340
$826$	−0.381413	−0.0132711
$827$	46.2462	1.60814	0.804069	−	0.594536i	$-0.202664\pi$
$827$	46.2462	1.60814	0.804069	+	0.594536i	$0.202664\pi$
$828$	5.39937	0.187641
$829$	36.4030	1.26433	0.632164	−	0.774835i	$-0.282167\pi$
$829$	36.4030	1.26433	0.632164	+	0.774835i	$0.282167\pi$
$830$	36.8843	1.28027
$831$	65.4516	2.27049
$832$	−76.0086	−2.63512
$833$	−35.5217	−1.23075
$834$	−0.558813	−0.0193501
$835$	17.0392	0.589665
$836$	−14.8414	−0.513299
$837$	128.388	4.43773
$838$	−73.0162	−2.52230
$839$	−43.4328	−1.49947	−0.749734	−	0.661739i	$-0.769819\pi$
$839$	−43.4328	−1.49947	−0.749734	+	0.661739i	$0.769819\pi$
$840$	0.724954	0.0250133
$841$	4.39713	0.151625
$842$	23.9961	0.826960
$843$	−85.5460	−2.94636
$844$	−86.1330	−2.96482
$845$	39.6456	1.36385
$846$	−108.873	−3.74314
$847$	0.532596	0.0183002
$848$	1.03866	0.0356678
$849$	−13.1398	−0.450957
$850$	29.6799	1.01801
$851$	1.56010	0.0534797
$852$	90.8662	3.11302
$853$	−31.8431	−1.09029	−0.545143	−	0.838343i	$-0.683525\pi$
$853$	−31.8431	−1.09029	−0.545143	+	0.838343i	$0.683525\pi$
$854$	−1.09941	−0.0376209
$855$	−10.2095	−0.349157
$856$	−42.1796	−1.44167
$857$	14.5685	0.497649	0.248825	−	0.968549i	$-0.419956\pi$
$857$	14.5685	0.497649	0.248825	+	0.968549i	$0.419956\pi$
$858$	225.568	7.70077
$859$	1.84619	0.0629910	0.0314955	−	0.999504i	$-0.489973\pi$
$859$	1.84619	0.0629910	0.0314955	+	0.999504i	$0.489973\pi$
$860$	−31.3254	−1.06819
$861$	−1.54245	−0.0525666
$862$	−28.3204	−0.964597
$863$	−17.6615	−0.601203	−0.300602	−	0.953750i	$-0.597187\pi$
$863$	−17.6615	−0.601203	−0.300602	+	0.953750i	$0.597187\pi$
$864$	−60.9504	−2.07358
$865$	4.15331	0.141217
$866$	−7.28095	−0.247417
$867$	−28.1637	−0.956488
$868$	−1.33838	−0.0454276
$869$	11.0077	0.373412
$870$	−68.5568	−2.32429
$871$	−15.5370	−0.526451
$872$	−66.5538	−2.25380
$873$	60.9179	2.06176
$874$	0.439010	0.0148497
$875$	−0.497151	−0.0168068
$876$	150.689	5.09129
$877$	−46.5259	−1.57107	−0.785534	−	0.618819i	$-0.787612\pi$
$877$	−46.5259	−1.57107	−0.785534	+	0.618819i	$0.787612\pi$
$878$	17.7908	0.600412
$879$	62.1045	2.09473
$880$	7.99039	0.269356
$881$	−36.4519	−1.22810	−0.614048	−	0.789268i	$-0.710460\pi$
$881$	−36.4519	−1.22810	−0.614048	+	0.789268i	$0.710460\pi$
$882$	119.794	4.03369
$883$	−49.3463	−1.66064	−0.830318	−	0.557290i	$-0.811841\pi$
$883$	−49.3463	−1.66064	−0.830318	+	0.557290i	$0.811841\pi$
$884$	108.306	3.64272
$885$	−19.7726	−0.664647
$886$	11.8376	0.397692
$887$	−44.5601	−1.49618	−0.748091	−	0.663596i	$-0.769029\pi$
$887$	−44.5601	−1.49618	−0.748091	+	0.663596i	$0.769029\pi$
$888$	80.0887	2.68760
$889$	0.786145	0.0263665
$890$	−8.39631	−0.281445
$891$	110.560	3.70392
$892$	−4.93899	−0.165370
$893$	−5.60809	−0.187668
$894$	−140.227	−4.68989
$895$	−0.0118403	−0.000395778 0
$896$	0.838868	0.0280246
$897$	−4.22708	−0.141138
$898$	−17.9994	−0.600647
$899$	53.3512	1.77936
$900$	−63.4115	−2.11372
$901$	5.07580	0.169100
$902$	−130.181	−4.33455
$903$	0.772657	0.0257124
$904$	−18.3208	−0.609342
$905$	−26.9957	−0.897369
$906$	−7.50740	−0.249416
$907$	8.19025	0.271953	0.135976	−	0.990712i	$-0.456583\pi$
$907$	8.19025	0.271953	0.135976	+	0.990712i	$0.456583\pi$
$908$	12.7740	0.423919
$909$	−13.6547	−0.452897
$910$	−0.955311	−0.0316682
$911$	−5.73713	−0.190080	−0.0950398	−	0.995473i	$-0.530298\pi$
$911$	−5.73713	−0.190080	−0.0950398	+	0.995473i	$0.530298\pi$
$912$	2.94315	0.0974575
$913$	−48.6441	−1.60989
$914$	−24.7667	−0.819211
$915$	−56.9935	−1.88415
$916$	24.7212	0.816812
$917$	−0.685993	−0.0226535
$918$	164.904	5.44264
$919$	16.2334	0.535491	0.267746	−	0.963490i	$-0.413721\pi$
$919$	16.2334	0.535491	0.267746	+	0.963490i	$0.413721\pi$
$920$	−1.14659	−0.0378020
$921$	−2.32874	−0.0767347
$922$	−17.1077	−0.563413
$923$	−50.4731	−1.66134
$924$	−2.26817	−0.0746173
$925$	−18.3222	−0.602432
$926$	−16.8387	−0.553356
$927$	79.8749	2.62343
$928$	−25.3278	−0.831424
$929$	16.8013	0.551233	0.275616	−	0.961268i	$-0.411118\pi$
$929$	16.8013	0.551233	0.275616	+	0.961268i	$0.411118\pi$
$930$	−109.518	−3.59123
$931$	6.17064	0.202234
$932$	59.6597	1.95422
$933$	71.4969	2.34070
$934$	−17.4048	−0.569503
$935$	39.0480	1.27701
$936$	−153.964	−5.03246
$937$	18.3579	0.599728	0.299864	−	0.953982i	$-0.403059\pi$
$937$	18.3579	0.599728	0.299864	+	0.953982i	$0.403059\pi$
$938$	0.246605	0.00805194
$939$	−40.5138	−1.32212
$940$	34.7477	1.13335
$941$	−55.8952	−1.82213	−0.911066	−	0.412260i	$-0.864740\pi$
$941$	−55.8952	−1.82213	−0.911066	+	0.412260i	$0.864740\pi$
$942$	46.1468	1.50354
$943$	2.43955	0.0794428
$944$	4.04420	0.131628
$945$	−0.921481	−0.0299758
$946$	65.2113	2.12020
$947$	−44.6195	−1.44994	−0.724970	−	0.688781i	$-0.758146\pi$
$947$	−44.6195	−1.44994	−0.724970	+	0.688781i	$0.758146\pi$
$948$	−25.1220	−0.815925
$949$	−83.7025	−2.71710
$950$	−5.15584	−0.167277
$951$	44.3851	1.43929
$952$	−0.724621	−0.0234851
$953$	−34.5368	−1.11876	−0.559379	−	0.828912i	$-0.688960\pi$
$953$	−34.5368	−1.11876	−0.559379	+	0.828912i	$0.688960\pi$
$954$	−17.1178	−0.554209
$955$	−3.86038	−0.124919
$956$	64.2617	2.07837
$957$	90.4148	2.92269
$958$	64.2778	2.07672
$959$	−0.618795	−0.0199819
$960$	62.5411	2.01850
$961$	54.2273	1.74927
$962$	−105.537	−3.40265
$963$	90.7816	2.92539
$964$	8.31476	0.267800
$965$	16.2933	0.524501
$966$	0.0670928	0.00215867
$967$	−4.08631	−0.131407	−0.0657034	−	0.997839i	$-0.520929\pi$
$967$	−4.08631	−0.131407	−0.0657034	+	0.997839i	$0.520929\pi$
$968$	−43.2428	−1.38988
$969$	14.3828	0.462042
$970$	−30.6893	−0.985375
$971$	−3.85954	−0.123859	−0.0619293	−	0.998081i	$-0.519725\pi$
$971$	−3.85954	−0.123859	−0.0619293	+	0.998081i	$0.519725\pi$
$972$	−108.077	−3.46658
$973$	−0.00312121	−0.000100061 0
$974$	−39.6492	−1.27044
$975$	49.6439	1.58988
$976$	11.6572	0.373139
$977$	32.0204	1.02442	0.512212	−	0.858859i	$-0.328826\pi$
$977$	32.0204	1.02442	0.512212	+	0.858859i	$0.328826\pi$
$978$	119.297	3.81469
$979$	11.0733	0.353905
$980$	−38.2332	−1.22132
$981$	143.241	4.57333
$982$	−23.2072	−0.740571
$983$	49.0416	1.56418	0.782091	−	0.623164i	$-0.214153\pi$
$983$	49.0416	1.56418	0.782091	+	0.623164i	$0.214153\pi$
$984$	125.236	3.99236
$985$	37.5351	1.19597
$986$	68.5253	2.18229
$987$	−0.857071	−0.0272809
$988$	−18.8143	−0.598563
$989$	−1.22204	−0.0388586
$990$	−131.686	−4.18527
$991$	59.8802	1.90216	0.951078	−	0.308949i	$-0.0999774\pi$
$991$	59.8802	1.90216	0.951078	+	0.308949i	$0.0999774\pi$
$992$	−40.4605	−1.28462
$993$	−39.1471	−1.24230
$994$	0.801116	0.0254099
$995$	20.8635	0.661418
$996$	111.016	3.51768
$997$	22.1645	0.701956	0.350978	−	0.936384i	$-0.385849\pi$
$997$	22.1645	0.701956	0.350978	+	0.936384i	$0.385849\pi$
$998$	18.5678	0.587755
$999$	−101.800	−3.22080

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8003.2.a.d.1.20	✓	179

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8003.2.a.d.1.20	✓	179	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:	\( N \)	\(=\)	\( 8003 = 53 \cdot 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8003.a (trivial)

\(f(q)\)	\(=\)	\(q-2.33610 q^{2} -3.21364 q^{3} +3.45737 q^{4} +1.58018 q^{5} +7.50740 q^{6} +0.0419320 q^{7} -3.40456 q^{8} +7.32750 q^{9} +O(q^{10})\)	\(q-2.33610 q^{2} -3.21364 q^{3} +3.45737 q^{4} +1.58018 q^{5} +7.50740 q^{6} +0.0419320 q^{7} -3.40456 q^{8} +7.32750 q^{9} -3.69146 q^{10} +4.86841 q^{11} -11.1107 q^{12} +6.17165 q^{13} -0.0979573 q^{14} -5.07813 q^{15} +1.03866 q^{16} +5.07580 q^{17} -17.1178 q^{18} -0.881741 q^{19} +5.46326 q^{20} -0.134754 q^{21} -11.3731 q^{22} +0.213128 q^{23} +10.9410 q^{24} -2.50303 q^{25} -14.4176 q^{26} -13.9070 q^{27} +0.144974 q^{28} -5.77902 q^{29} +11.8630 q^{30} -9.23186 q^{31} +4.38270 q^{32} -15.6453 q^{33} -11.8576 q^{34} +0.0662600 q^{35} +25.3339 q^{36} +7.32002 q^{37} +2.05984 q^{38} -19.8335 q^{39} -5.37982 q^{40} +11.4464 q^{41} +0.314800 q^{42} -5.73382 q^{43} +16.8319 q^{44} +11.5788 q^{45} -0.497890 q^{46} +6.36025 q^{47} -3.33789 q^{48} -6.99824 q^{49} +5.84734 q^{50} -16.3118 q^{51} +21.3377 q^{52} +1.00000 q^{53} +32.4883 q^{54} +7.69296 q^{55} -0.142760 q^{56} +2.83360 q^{57} +13.5004 q^{58} +3.89367 q^{59} -17.5570 q^{60} +11.2233 q^{61} +21.5666 q^{62} +0.307256 q^{63} -12.3158 q^{64} +9.75232 q^{65} +36.5491 q^{66} -2.51748 q^{67} +17.5489 q^{68} -0.684919 q^{69} -0.154790 q^{70} -8.17822 q^{71} -24.9469 q^{72} -13.5624 q^{73} -17.1003 q^{74} +8.04385 q^{75} -3.04850 q^{76} +0.204142 q^{77} +46.3330 q^{78} +2.26106 q^{79} +1.64127 q^{80} +22.7098 q^{81} -26.7399 q^{82} -9.99178 q^{83} -0.465895 q^{84} +8.02068 q^{85} +13.3948 q^{86} +18.5717 q^{87} -16.5748 q^{88} +2.27452 q^{89} -27.0492 q^{90} +0.258789 q^{91} +0.736864 q^{92} +29.6679 q^{93} -14.8582 q^{94} -1.39331 q^{95} -14.0844 q^{96} +8.31360 q^{97} +16.3486 q^{98} +35.6733 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 179 q + 8 q^{2} + 15 q^{3} + 202 q^{4} + 27 q^{5} + 18 q^{6} + 23 q^{7} + 21 q^{8} + 214 q^{9}+O(q^{10}) \) 179 * q + 8 * q^2 + 15 * q^3 + 202 * q^4 + 27 * q^5 + 18 * q^6 + 23 * q^7 + 21 * q^8 + 214 * q^9	\( 179 q + 8 q^{2} + 15 q^{3} + 202 q^{4} + 27 q^{5} + 18 q^{6} + 23 q^{7} + 21 q^{8} + 214 q^{9} + 28 q^{10} + 21 q^{11} + 46 q^{12} + 113 q^{13} - 2 q^{14} + 30 q^{15} + 240 q^{16} + 48 q^{17} + 40 q^{18} + 35 q^{19} + 24 q^{20} + 56 q^{21} + 22 q^{22} + 16 q^{23} + 54 q^{24} + 266 q^{25} + 60 q^{27} + 64 q^{28} + 34 q^{29} - 19 q^{30} + 60 q^{31} + 15 q^{32} + 65 q^{33} + 31 q^{34} - 20 q^{35} + 282 q^{36} + 169 q^{37} + 52 q^{38} + 20 q^{39} + 74 q^{40} + 20 q^{41} + 34 q^{42} + 43 q^{43} + 56 q^{44} + 139 q^{45} + 13 q^{46} + 73 q^{47} + 88 q^{48} + 292 q^{49} + 12 q^{50} + 8 q^{51} + 225 q^{52} + 179 q^{53} - 16 q^{54} + 72 q^{55} - 17 q^{56} + 62 q^{57} + 125 q^{58} + 68 q^{59} + 116 q^{60} + 96 q^{61} + 71 q^{62} + 52 q^{63} + 309 q^{64} - 5 q^{65} + 90 q^{67} + 122 q^{68} + 111 q^{69} + 72 q^{70} + 26 q^{71} + 65 q^{72} + 139 q^{73} - 82 q^{74} + 55 q^{75} + 146 q^{76} + 76 q^{77} - 9 q^{78} + 29 q^{79} + 68 q^{80} + 231 q^{81} + 84 q^{82} + 8 q^{83} - 24 q^{84} + 115 q^{85} - 20 q^{86} + 47 q^{87} + 143 q^{88} + 150 q^{89} + 34 q^{90} + 113 q^{91} - 31 q^{92} + 195 q^{93} + 131 q^{94} + 55 q^{95} + 90 q^{96} + 235 q^{97} + 84 q^{98} + 7 q^{99}+O(q^{100}) \) 179 * q + 8 * q^2 + 15 * q^3 + 202 * q^4 + 27 * q^5 + 18 * q^6 + 23 * q^7 + 21 * q^8 + 214 * q^9 + 28 * q^10 + 21 * q^11 + 46 * q^12 + 113 * q^13 - 2 * q^14 + 30 * q^15 + 240 * q^16 + 48 * q^17 + 40 * q^18 + 35 * q^19 + 24 * q^20 + 56 * q^21 + 22 * q^22 + 16 * q^23 + 54 * q^24 + 266 * q^25 + 60 * q^27 + 64 * q^28 + 34 * q^29 - 19 * q^30 + 60 * q^31 + 15 * q^32 + 65 * q^33 + 31 * q^34 - 20 * q^35 + 282 * q^36 + 169 * q^37 + 52 * q^38 + 20 * q^39 + 74 * q^40 + 20 * q^41 + 34 * q^42 + 43 * q^43 + 56 * q^44 + 139 * q^45 + 13 * q^46 + 73 * q^47 + 88 * q^48 + 292 * q^49 + 12 * q^50 + 8 * q^51 + 225 * q^52 + 179 * q^53 - 16 * q^54 + 72 * q^55 - 17 * q^56 + 62 * q^57 + 125 * q^58 + 68 * q^59 + 116 * q^60 + 96 * q^61 + 71 * q^62 + 52 * q^63 + 309 * q^64 - 5 * q^65 + 90 * q^67 + 122 * q^68 + 111 * q^69 + 72 * q^70 + 26 * q^71 + 65 * q^72 + 139 * q^73 - 82 * q^74 + 55 * q^75 + 146 * q^76 + 76 * q^77 - 9 * q^78 + 29 * q^79 + 68 * q^80 + 231 * q^81 + 84 * q^82 + 8 * q^83 - 24 * q^84 + 115 * q^85 - 20 * q^86 + 47 * q^87 + 143 * q^88 + 150 * q^89 + 34 * q^90 + 113 * q^91 - 31 * q^92 + 195 * q^93 + 131 * q^94 + 55 * q^95 + 90 * q^96 + 235 * q^97 + 84 * q^98 + 7 * q^99

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