LMFDB - Embedded newform 8003.2.a.d.1.1

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			1.1
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)

$f(q)$	$=$	$q-2.81186 q^{2} -1.67550 q^{3} +5.90655 q^{4} -2.52541 q^{5} +4.71126 q^{6} +3.13505 q^{7} -10.9847 q^{8} -0.192706 q^{9} +O(q^{10})$	\(q-2.81186 q^{2} -1.67550 q^{3} +5.90655 q^{4} -2.52541 q^{5} +4.71126 q^{6} +3.13505 q^{7} -10.9847 q^{8} -0.192706 q^{9} +7.10109 q^{10} +3.30081 q^{11} -9.89641 q^{12} +0.683998 q^{13} -8.81532 q^{14} +4.23132 q^{15} +19.0742 q^{16} -5.32069 q^{17} +0.541861 q^{18} -3.68509 q^{19} -14.9165 q^{20} -5.25277 q^{21} -9.28140 q^{22} -1.93671 q^{23} +18.4048 q^{24} +1.37769 q^{25} -1.92330 q^{26} +5.34937 q^{27} +18.5173 q^{28} -10.1777 q^{29} -11.8979 q^{30} -9.92063 q^{31} -31.6647 q^{32} -5.53049 q^{33} +14.9610 q^{34} -7.91728 q^{35} -1.13822 q^{36} +5.79139 q^{37} +10.3620 q^{38} -1.14604 q^{39} +27.7408 q^{40} -9.77236 q^{41} +14.7700 q^{42} -12.8246 q^{43} +19.4964 q^{44} +0.486660 q^{45} +5.44576 q^{46} -0.310089 q^{47} -31.9588 q^{48} +2.82854 q^{49} -3.87387 q^{50} +8.91481 q^{51} +4.04006 q^{52} +1.00000 q^{53} -15.0417 q^{54} -8.33588 q^{55} -34.4375 q^{56} +6.17437 q^{57} +28.6183 q^{58} +6.77120 q^{59} +24.9925 q^{60} -7.44991 q^{61} +27.8954 q^{62} -0.604141 q^{63} +50.8882 q^{64} -1.72737 q^{65} +15.5510 q^{66} -10.6060 q^{67} -31.4269 q^{68} +3.24496 q^{69} +22.2623 q^{70} -5.09123 q^{71} +2.11681 q^{72} +2.60678 q^{73} -16.2846 q^{74} -2.30832 q^{75} -21.7662 q^{76} +10.3482 q^{77} +3.22249 q^{78} +9.61356 q^{79} -48.1702 q^{80} -8.38475 q^{81} +27.4785 q^{82} +0.474926 q^{83} -31.0257 q^{84} +13.4369 q^{85} +36.0608 q^{86} +17.0528 q^{87} -36.2582 q^{88} -7.81728 q^{89} -1.36842 q^{90} +2.14437 q^{91} -11.4393 q^{92} +16.6220 q^{93} +0.871926 q^{94} +9.30637 q^{95} +53.0541 q^{96} -2.18280 q^{97} -7.95345 q^{98} -0.636083 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.81186	−1.98828	−0.994142	−	0.108081i	$-0.965530\pi$
$2$	−2.81186	−1.98828	−0.994142	+	0.108081i	$0.965530\pi$
$3$	−1.67550	−0.967349	−0.483675	−	0.875248i	$-0.660698\pi$
$3$	−1.67550	−0.967349	−0.483675	+	0.875248i	$0.660698\pi$
$4$	5.90655	2.95327
$5$	−2.52541	−1.12940	−0.564699	−	0.825297i	$-0.691008\pi$
$5$	−2.52541	−1.12940	−0.564699	+	0.825297i	$0.691008\pi$
$6$	4.71126	1.92337
$7$	3.13505	1.18494	0.592469	−	0.805593i	$-0.298153\pi$
$7$	3.13505	1.18494	0.592469	+	0.805593i	$0.298153\pi$
$8$	−10.9847	−3.88366
$9$	−0.192706	−0.0642352
$10$	7.10109	2.24556
$11$	3.30081	0.995230	0.497615	−	0.867398i	$-0.334209\pi$
$11$	3.30081	0.995230	0.497615	+	0.867398i	$0.334209\pi$
$12$	−9.89641	−2.85685
$13$	0.683998	0.189707	0.0948534	−	0.995491i	$-0.469762\pi$
$13$	0.683998	0.189707	0.0948534	+	0.995491i	$0.469762\pi$
$14$	−8.81532	−2.35599
$15$	4.23132	1.09252
$16$	19.0742	4.76856
$17$	−5.32069	−1.29046	−0.645229	−	0.763989i	$-0.723238\pi$
$17$	−5.32069	−1.29046	−0.645229	+	0.763989i	$0.723238\pi$
$18$	0.541861	0.127718
$19$	−3.68509	−0.845419	−0.422709	−	0.906265i	$-0.638921\pi$
$19$	−3.68509	−0.845419	−0.422709	+	0.906265i	$0.638921\pi$
$20$	−14.9165	−3.33542
$21$	−5.25277	−1.14625
$22$	−9.28140	−1.97880
$23$	−1.93671	−0.403832	−0.201916	−	0.979403i	$-0.564717\pi$
$23$	−1.93671	−0.403832	−0.201916	+	0.979403i	$0.564717\pi$
$24$	18.4048	3.75686
$25$	1.37769	0.275538
$26$	−1.92330	−0.377191
$27$	5.34937	1.02949
$28$	18.5173	3.49945
$29$	−10.1777	−1.88996	−0.944978	−	0.327135i	$-0.893917\pi$
$29$	−10.1777	−1.88996	−0.944978	+	0.327135i	$0.893917\pi$
$30$	−11.8979	−2.17224
$31$	−9.92063	−1.78180	−0.890899	−	0.454202i	$-0.849925\pi$
$31$	−9.92063	−1.78180	−0.890899	+	0.454202i	$0.849925\pi$
$32$	−31.6647	−5.59758
$33$	−5.53049	−0.962735
$34$	14.9610	2.56580
$35$	−7.91728	−1.33827
$36$	−1.13822	−0.189704
$37$	5.79139	0.952099	0.476050	−	0.879418i	$-0.342068\pi$
$37$	5.79139	0.952099	0.476050	+	0.879418i	$0.342068\pi$
$38$	10.3620	1.68093
$39$	−1.14604	−0.183513
$40$	27.7408	4.38620
$41$	−9.77236	−1.52619	−0.763093	−	0.646289i	$-0.776320\pi$
$41$	−9.77236	−1.52619	−0.763093	+	0.646289i	$0.776320\pi$
$42$	14.7700	2.27907
$43$	−12.8246	−1.95573	−0.977863	−	0.209246i	$-0.932899\pi$
$43$	−12.8246	−1.95573	−0.977863	+	0.209246i	$0.932899\pi$
$44$	19.4964	2.93919
$45$	0.486660	0.0725470
$46$	5.44576	0.802933
$47$	−0.310089	−0.0452311	−0.0226156	−	0.999744i	$-0.507199\pi$
$47$	−0.310089	−0.0452311	−0.0226156	+	0.999744i	$0.507199\pi$
$48$	−31.9588	−4.61286
$49$	2.82854	0.404077
$50$	−3.87387	−0.547848
$51$	8.91481	1.24832
$52$	4.04006	0.560256
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	−15.0417	−2.04691
$55$	−8.33588	−1.12401
$56$	−34.4375	−4.60190
$57$	6.17437	0.817815
$58$	28.6183	3.75777
$59$	6.77120	0.881535	0.440768	−	0.897621i	$-0.354706\pi$
$59$	6.77120	0.881535	0.440768	+	0.897621i	$0.354706\pi$
$60$	24.9925	3.22652
$61$	−7.44991	−0.953863	−0.476932	−	0.878940i	$-0.658251\pi$
$61$	−7.44991	−0.953863	−0.476932	+	0.878940i	$0.658251\pi$
$62$	27.8954	3.54272
$63$	−0.604141	−0.0761147
$64$	50.8882	6.36102
$65$	−1.72737	−0.214254
$66$	15.5510	1.91419
$67$	−10.6060	−1.29573	−0.647867	−	0.761753i	$-0.724339\pi$
$67$	−10.6060	−1.29573	−0.647867	+	0.761753i	$0.724339\pi$
$68$	−31.4269	−3.81108
$69$	3.24496	0.390647
$70$	22.2623	2.66085
$71$	−5.09123	−0.604218	−0.302109	−	0.953273i	$-0.597691\pi$
$71$	−5.09123	−0.604218	−0.302109	+	0.953273i	$0.597691\pi$
$72$	2.11681	0.249468
$73$	2.60678	0.305101	0.152550	−	0.988296i	$-0.451251\pi$
$73$	2.60678	0.305101	0.152550	+	0.988296i	$0.451251\pi$
$74$	−16.2846	−1.89304
$75$	−2.30832	−0.266542
$76$	−21.7662	−2.49675
$77$	10.3482	1.17929
$78$	3.22249	0.364875
$79$	9.61356	1.08161	0.540805	−	0.841148i	$-0.318120\pi$
$79$	9.61356	1.08161	0.540805	+	0.841148i	$0.318120\pi$
$80$	−48.1702	−5.38559
$81$	−8.38475	−0.931639
$82$	27.4785	3.03449
$83$	0.474926	0.0521299	0.0260649	−	0.999660i	$-0.491702\pi$
$83$	0.474926	0.0521299	0.0260649	+	0.999660i	$0.491702\pi$
$84$	−31.0257	−3.38519
$85$	13.4369	1.45744
$86$	36.0608	3.88854
$87$	17.0528	1.82825
$88$	−36.2582	−3.86514
$89$	−7.81728	−0.828630	−0.414315	−	0.910134i	$-0.635979\pi$
$89$	−7.81728	−0.828630	−0.414315	+	0.910134i	$0.635979\pi$
$90$	−1.36842	−0.144244
$91$	2.14437	0.224791
$92$	−11.4393	−1.19263
$93$	16.6220	1.72362
$94$	0.871926	0.0899323
$95$	9.30637	0.954813
$96$	53.0541	5.41481
$97$	−2.18280	−0.221630	−0.110815	−	0.993841i	$-0.535346\pi$
$97$	−2.18280	−0.221630	−0.110815	+	0.993841i	$0.535346\pi$
$98$	−7.95345	−0.803420
$99$	−0.636083	−0.0639288
$100$	8.13740	0.813740
$101$	−15.6563	−1.55786	−0.778929	−	0.627112i	$-0.784237\pi$
$101$	−15.6563	−1.55786	−0.778929	+	0.627112i	$0.784237\pi$
$102$	−25.0672	−2.48202
$103$	1.49092	0.146904	0.0734521	−	0.997299i	$-0.476598\pi$
$103$	1.49092	0.146904	0.0734521	+	0.997299i	$0.476598\pi$
$104$	−7.51348	−0.736758
$105$	13.2654	1.29457
$106$	−2.81186	−0.273112
$107$	6.70054	0.647766	0.323883	−	0.946097i	$-0.395012\pi$
$107$	6.70054	0.647766	0.323883	+	0.946097i	$0.395012\pi$
$108$	31.5963	3.04036
$109$	−10.7708	−1.03165	−0.515826	−	0.856693i	$-0.672515\pi$
$109$	−10.7708	−1.03165	−0.515826	+	0.856693i	$0.672515\pi$
$110$	23.4393	2.23485
$111$	−9.70347	−0.921013
$112$	59.7986	5.65044
$113$	5.55324	0.522405	0.261202	−	0.965284i	$-0.415881\pi$
$113$	5.55324	0.522405	0.261202	+	0.965284i	$0.415881\pi$
$114$	−17.3615	−1.62605
$115$	4.89099	0.456087
$116$	−60.1152	−5.58156
$117$	−0.131810	−0.0121858
$118$	−19.0397	−1.75274
$119$	−16.6806	−1.52911
$120$	−46.4796	−4.24299
$121$	−0.104684	−0.00951671
$122$	20.9481	1.89655
$123$	16.3736	1.47636
$124$	−58.5967	−5.26214
$125$	9.14781	0.818205
$126$	1.69876	0.151338
$127$	20.6703	1.83419	0.917096	−	0.398666i	$-0.130527\pi$
$127$	20.6703	1.83419	0.917096	+	0.398666i	$0.130527\pi$
$128$	−79.7610	−7.04994
$129$	21.4875	1.89187
$130$	4.85713	0.425998
$131$	−5.23436	−0.457328	−0.228664	−	0.973505i	$-0.573436\pi$
$131$	−5.23436	−0.457328	−0.228664	+	0.973505i	$0.573436\pi$
$132$	−32.6661	−2.84322
$133$	−11.5530	−1.00177
$134$	29.8227	2.57629
$135$	−13.5094	−1.16270
$136$	58.4460	5.01170
$137$	19.2413	1.64390	0.821949	−	0.569561i	$-0.192887\pi$
$137$	19.2413	1.64390	0.821949	+	0.569561i	$0.192887\pi$
$138$	−9.12436	−0.776717
$139$	−3.21664	−0.272832	−0.136416	−	0.990652i	$-0.543558\pi$
$139$	−3.21664	−0.272832	−0.136416	+	0.990652i	$0.543558\pi$
$140$	−46.7638	−3.95226
$141$	0.519553	0.0437543
$142$	14.3158	1.20136
$143$	2.25774	0.188802
$144$	−3.67571	−0.306309
$145$	25.7029	2.13451
$146$	−7.32990	−0.606627
$147$	−4.73921	−0.390884
$148$	34.2071	2.81181
$149$	−15.7960	−1.29406	−0.647031	−	0.762464i	$-0.723990\pi$
$149$	−15.7960	−1.29406	−0.647031	+	0.762464i	$0.723990\pi$
$150$	6.49067	0.529961
$151$	−1.00000	−0.0813788
$151$	−1.00000	−0.0813788
$152$	40.4795	3.28332
$153$	1.02533	0.0828928
$154$	−29.0976	−2.34476
$155$	25.0537	2.01236
$156$	−6.76912	−0.541963
$157$	4.58357	0.365808	0.182904	−	0.983131i	$-0.441450\pi$
$157$	4.58357	0.365808	0.182904	+	0.983131i	$0.441450\pi$
$158$	−27.0320	−2.15055
$159$	−1.67550	−0.132876
$160$	79.9663	6.32189
$161$	−6.07169	−0.478516
$162$	23.5767	1.85236
$163$	2.84487	0.222828	0.111414	−	0.993774i	$-0.464462\pi$
$163$	2.84487	0.222828	0.111414	+	0.993774i	$0.464462\pi$
$164$	−57.7209	−4.50725
$165$	13.9668	1.08731
$166$	−1.33542	−0.103649
$167$	11.2756	0.872534	0.436267	−	0.899817i	$-0.356300\pi$
$167$	11.2756	0.872534	0.436267	+	0.899817i	$0.356300\pi$
$168$	57.6999	4.45165
$169$	−12.5321	−0.964011
$170$	−37.7827	−2.89780
$171$	0.710138	0.0543056
$172$	−75.7488	−5.77580
$173$	−11.9570	−0.909075	−0.454537	−	0.890728i	$-0.650195\pi$
$173$	−11.9570	−0.909075	−0.454537	+	0.890728i	$0.650195\pi$
$174$	−47.9499	−3.63508
$175$	4.31913	0.326496
$176$	62.9603	4.74581
$177$	−11.3451	−0.852753
$178$	21.9811	1.64755
$179$	9.24711	0.691161	0.345581	−	0.938389i	$-0.387682\pi$
$179$	9.24711	0.691161	0.345581	+	0.938389i	$0.387682\pi$
$180$	2.87448	0.214251
$181$	21.1583	1.57269	0.786343	−	0.617790i	$-0.211972\pi$
$181$	21.1583	1.57269	0.786343	+	0.617790i	$0.211972\pi$
$182$	−6.02966	−0.446948
$183$	12.4823	0.922719
$184$	21.2741	1.56835
$185$	−14.6256	−1.07530
$186$	−46.7387	−3.42705
$187$	−17.5626	−1.28430
$188$	−1.83156	−0.133580
$189$	16.7706	1.21988
$190$	−26.1682	−1.89844
$191$	−9.90948	−0.717025	−0.358512	−	0.933525i	$-0.616716\pi$
$191$	−9.90948	−0.717025	−0.358512	+	0.933525i	$0.616716\pi$
$192$	−85.2631	−6.15333
$193$	−15.3134	−1.10228	−0.551141	−	0.834412i	$-0.685807\pi$
$193$	−15.3134	−1.10228	−0.551141	+	0.834412i	$0.685807\pi$
$194$	6.13773	0.440664
$195$	2.89421	0.207259
$196$	16.7069	1.19335
$197$	−24.1483	−1.72049	−0.860247	−	0.509878i	$-0.829691\pi$
$197$	−24.1483	−1.72049	−0.860247	+	0.509878i	$0.829691\pi$
$198$	1.78858	0.127109
$199$	9.15811	0.649201	0.324601	−	0.945851i	$-0.394770\pi$
$199$	9.15811	0.649201	0.324601	+	0.945851i	$0.394770\pi$
$200$	−15.1335	−1.07010
$201$	17.7704	1.25343
$202$	44.0233	3.09747
$203$	−31.9077	−2.23948
$204$	52.6558	3.68664
$205$	24.6792	1.72367
$206$	−4.19224	−0.292087
$207$	0.373215	0.0259402
$208$	13.0467	0.904627
$209$	−12.1638	−0.841386
$210$	−37.3004	−2.57397
$211$	1.42174	0.0978769	0.0489385	−	0.998802i	$-0.484416\pi$
$211$	1.42174	0.0978769	0.0489385	+	0.998802i	$0.484416\pi$
$212$	5.90655	0.405663
$213$	8.53035	0.584490
$214$	−18.8410	−1.28794
$215$	32.3872	2.20879
$216$	−58.7611	−3.99818
$217$	−31.1017	−2.11132
$218$	30.2859	2.05122
$219$	−4.36766	−0.295139
$220$	−49.2363	−3.31951
$221$	−3.63934	−0.244809
$222$	27.2848	1.83123
$223$	23.7961	1.59350	0.796752	−	0.604307i	$-0.206550\pi$
$223$	23.7961	1.59350	0.796752	+	0.604307i	$0.206550\pi$
$224$	−99.2704	−6.63278
$225$	−0.265489	−0.0176992
$226$	−15.6149	−1.03869
$227$	26.6215	1.76693	0.883467	−	0.468494i	$-0.155203\pi$
$227$	26.6215	1.76693	0.883467	+	0.468494i	$0.155203\pi$
$228$	36.4692	2.41523
$229$	11.2324	0.742255	0.371127	−	0.928582i	$-0.378971\pi$
$229$	11.2324	0.742255	0.371127	+	0.928582i	$0.378971\pi$
$230$	−13.7528	−0.906831
$231$	−17.3384	−1.14078
$232$	111.799	7.33995
$233$	3.60393	0.236101	0.118051	−	0.993008i	$-0.462335\pi$
$233$	3.60393	0.236101	0.118051	+	0.993008i	$0.462335\pi$
$234$	0.370631	0.0242289
$235$	0.783101	0.0510839
$236$	39.9944	2.60342
$237$	−16.1075	−1.04630
$238$	46.9036	3.04031
$239$	7.27403	0.470518	0.235259	−	0.971933i	$-0.424406\pi$
$239$	7.27403	0.470518	0.235259	+	0.971933i	$0.424406\pi$
$240$	80.7091	5.20975
$241$	−17.6729	−1.13841	−0.569206	−	0.822195i	$-0.692749\pi$
$241$	−17.6729	−1.13841	−0.569206	+	0.822195i	$0.692749\pi$
$242$	0.294356	0.0189219
$243$	−1.99949	−0.128267
$244$	−44.0033	−2.81702
$245$	−7.14322	−0.456363
$246$	−46.0402	−2.93541
$247$	−2.52060	−0.160382
$248$	108.975	6.91991
$249$	−0.795737	−0.0504278
$250$	−25.7224	−1.62682
$251$	8.09478	0.510938	0.255469	−	0.966817i	$-0.417770\pi$
$251$	8.09478	0.510938	0.255469	+	0.966817i	$0.417770\pi$
$252$	−3.56839	−0.224787
$253$	−6.39271	−0.401906
$254$	−58.1219	−3.64690
$255$	−22.5135	−1.40985
$256$	122.500	7.65627
$257$	5.64215	0.351947	0.175974	−	0.984395i	$-0.443693\pi$
$257$	5.64215	0.351947	0.175974	+	0.984395i	$0.443693\pi$
$258$	−60.4199	−3.76158
$259$	18.1563	1.12818
$260$	−10.2028	−0.632752
$261$	1.96130	0.121402
$262$	14.7183	0.909299
$263$	−12.1935	−0.751881	−0.375941	−	0.926644i	$-0.622680\pi$
$263$	−12.1935	−0.751881	−0.375941	+	0.926644i	$0.622680\pi$
$264$	60.7506	3.73894
$265$	−2.52541	−0.155135
$266$	32.4853	1.99180
$267$	13.0978	0.801574
$268$	−62.6451	−3.82666
$269$	5.17616	0.315596	0.157798	−	0.987471i	$-0.449561\pi$
$269$	5.17616	0.315596	0.157798	+	0.987471i	$0.449561\pi$
$270$	37.9864	2.31178
$271$	0.566425	0.0344079	0.0172039	−	0.999852i	$-0.494524\pi$
$271$	0.566425	0.0344079	0.0172039	+	0.999852i	$0.494524\pi$
$272$	−101.488	−6.15362
$273$	−3.59288	−0.217451
$274$	−54.1039	−3.26854
$275$	4.54749	0.274224
$276$	19.1665	1.15369
$277$	−31.4452	−1.88936	−0.944679	−	0.327996i	$-0.893627\pi$
$277$	−31.4452	−1.88936	−0.944679	+	0.327996i	$0.893627\pi$
$278$	9.04473	0.542467
$279$	1.91176	0.114454
$280$	86.9687	5.19737
$281$	−10.7396	−0.640672	−0.320336	−	0.947304i	$-0.603796\pi$
$281$	−10.7396	−0.640672	−0.320336	+	0.947304i	$0.603796\pi$
$282$	−1.46091	−0.0869960
$283$	7.36372	0.437728	0.218864	−	0.975755i	$-0.429765\pi$
$283$	7.36372	0.437728	0.218864	+	0.975755i	$0.429765\pi$
$284$	−30.0716	−1.78442
$285$	−15.5928	−0.923638
$286$	−6.34845	−0.375392
$287$	−30.6368	−1.80844
$288$	6.10196	0.359561
$289$	11.3098	0.665281
$290$	−72.2729	−4.24401
$291$	3.65728	0.214394
$292$	15.3971	0.901046
$293$	−9.94684	−0.581101	−0.290550	−	0.956860i	$-0.593838\pi$
$293$	−9.94684	−0.581101	−0.290550	+	0.956860i	$0.593838\pi$
$294$	13.3260	0.777188
$295$	−17.1001	−0.995603
$296$	−63.6165	−3.69763
$297$	17.6572	1.02458
$298$	44.4162	2.57296
$299$	−1.32471	−0.0766097
$300$	−13.6342	−0.787171
$301$	−40.2056	−2.31741
$302$	2.81186	0.161804
$303$	26.2321	1.50699
$304$	−70.2903	−4.03143
$305$	18.8141	1.07729
$306$	−2.88307	−0.164814
$307$	3.69508	0.210889	0.105445	−	0.994425i	$-0.466373\pi$
$307$	3.69508	0.210889	0.105445	+	0.994425i	$0.466373\pi$
$308$	61.1221	3.48275
$309$	−2.49803	−0.142108
$310$	−70.4473	−4.00114
$311$	7.54629	0.427911	0.213956	−	0.976843i	$-0.431365\pi$
$311$	7.54629	0.427911	0.213956	+	0.976843i	$0.431365\pi$
$312$	12.5888	0.712702
$313$	−23.6220	−1.33519	−0.667597	−	0.744523i	$-0.732677\pi$
$313$	−23.6220	−1.33519	−0.667597	+	0.744523i	$0.732677\pi$
$314$	−12.8883	−0.727331
$315$	1.52570	0.0859637
$316$	56.7830	3.19429
$317$	−5.91449	−0.332191	−0.166095	−	0.986110i	$-0.553116\pi$
$317$	−5.91449	−0.332191	−0.166095	+	0.986110i	$0.553116\pi$
$318$	4.71126	0.264195
$319$	−33.5947	−1.88094
$320$	−128.513	−7.18412
$321$	−11.2267	−0.626616
$322$	17.0727	0.951426
$323$	19.6073	1.09098
$324$	−49.5249	−2.75138
$325$	0.942337	0.0522715
$326$	−7.99938	−0.443045
$327$	18.0464	0.997969
$328$	107.346	5.92720
$329$	−0.972144	−0.0535960
$330$	−39.2726	−2.16188
$331$	9.33998	0.513372	0.256686	−	0.966495i	$-0.417369\pi$
$331$	9.33998	0.513372	0.256686	+	0.966495i	$0.417369\pi$
$332$	2.80517	0.153954
$333$	−1.11603	−0.0611583
$334$	−31.7055	−1.73485
$335$	26.7846	1.46340
$336$	−100.193	−5.46595
$337$	10.5307	0.573641	0.286821	−	0.957984i	$-0.407402\pi$
$337$	10.5307	0.573641	0.286821	+	0.957984i	$0.407402\pi$
$338$	35.2386	1.91673
$339$	−9.30444	−0.505348
$340$	79.3659	4.30422
$341$	−32.7461	−1.77330
$342$	−1.99681	−0.107975
$343$	−13.0777	−0.706132
$344$	140.873	7.59538
$345$	−8.19484	−0.441195
$346$	33.6214	1.80750
$347$	−19.4160	−1.04230	−0.521152	−	0.853464i	$-0.674498\pi$
$347$	−19.4160	−1.04230	−0.521152	+	0.853464i	$0.674498\pi$
$348$	100.723	5.39932
$349$	−7.07544	−0.378740	−0.189370	−	0.981906i	$-0.560645\pi$
$349$	−7.07544	−0.378740	−0.189370	+	0.981906i	$0.560645\pi$
$350$	−12.1448	−0.649166
$351$	3.65896	0.195301
$352$	−104.519	−5.57088
$353$	11.3156	0.602270	0.301135	−	0.953582i	$-0.402635\pi$
$353$	11.3156	0.602270	0.301135	+	0.953582i	$0.402635\pi$
$354$	31.9009	1.69551
$355$	12.8574	0.682403
$356$	−46.1731	−2.44717
$357$	27.9484	1.47919
$358$	−26.0016	−1.37423
$359$	−10.4847	−0.553362	−0.276681	−	0.960962i	$-0.589235\pi$
$359$	−10.4847	−0.553362	−0.276681	+	0.960962i	$0.589235\pi$
$360$	−5.34580	−0.281748
$361$	−5.42008	−0.285267
$362$	−59.4942	−3.12695
$363$	0.175398	0.00920598
$364$	12.6658	0.663869
$365$	−6.58319	−0.344580
$366$	−35.0985	−1.83463
$367$	−29.0713	−1.51751	−0.758755	−	0.651376i	$-0.774192\pi$
$367$	−29.0713	−1.51751	−0.758755	+	0.651376i	$0.774192\pi$
$368$	−36.9413	−1.92570
$369$	1.88319	0.0980348
$370$	41.1252	2.13800
$371$	3.13505	0.162764
$372$	98.1787	5.09033
$373$	12.5657	0.650625	0.325313	−	0.945607i	$-0.394530\pi$
$373$	12.5657	0.650625	0.325313	+	0.945607i	$0.394530\pi$
$374$	49.3835	2.55356
$375$	−15.3271	−0.791490
$376$	3.40622	0.175663
$377$	−6.96154	−0.358537
$378$	−47.1564	−2.42546
$379$	9.68711	0.497593	0.248797	−	0.968556i	$-0.419965\pi$
$379$	9.68711	0.497593	0.248797	+	0.968556i	$0.419965\pi$
$380$	54.9685	2.81983
$381$	−34.6330	−1.77430
$382$	27.8641	1.42565
$383$	21.6937	1.10850	0.554248	−	0.832352i	$-0.313006\pi$
$383$	21.6937	1.10850	0.554248	+	0.832352i	$0.313006\pi$
$384$	133.639	6.81976
$385$	−26.1334	−1.33188
$386$	43.0591	2.19165
$387$	2.47136	0.125626
$388$	−12.8928	−0.654534
$389$	−13.0121	−0.659742	−0.329871	−	0.944026i	$-0.607005\pi$
$389$	−13.0121	−0.659742	−0.329871	+	0.944026i	$0.607005\pi$
$390$	−8.13811	−0.412089
$391$	10.3046	0.521128
$392$	−31.0705	−1.56930
$393$	8.77016	0.442396
$394$	67.9016	3.42083
$395$	−24.2782	−1.22157
$396$	−3.75706	−0.188799
$397$	11.4352	0.573917	0.286959	−	0.957943i	$-0.407356\pi$
$397$	11.4352	0.573917	0.286959	+	0.957943i	$0.407356\pi$
$398$	−25.7513	−1.29080
$399$	19.3570	0.969060
$400$	26.2784	1.31392
$401$	2.31693	0.115702	0.0578509	−	0.998325i	$-0.481575\pi$
$401$	2.31693	0.115702	0.0578509	+	0.998325i	$0.481575\pi$
$402$	−49.9679	−2.49217
$403$	−6.78569	−0.338019
$404$	−92.4746	−4.60078
$405$	21.1749	1.05219
$406$	89.7198	4.45272
$407$	19.1163	0.947558
$408$	−97.9262	−4.84807
$409$	−23.7005	−1.17191	−0.585957	−	0.810342i	$-0.699281\pi$
$409$	−23.7005	−1.17191	−0.585957	+	0.810342i	$0.699281\pi$
$410$	−69.3944	−3.42715
$411$	−32.2388	−1.59022
$412$	8.80617	0.433849
$413$	21.2281	1.04456
$414$	−1.04943	−0.0515766
$415$	−1.19938	−0.0588753
$416$	−21.6586	−1.06190
$417$	5.38947	0.263923
$418$	34.2028	1.67291
$419$	39.8974	1.94912	0.974558	−	0.224135i	$-0.0719557\pi$
$419$	39.8974	1.94912	0.974558	+	0.224135i	$0.0719557\pi$
$420$	78.3527	3.82322
$421$	−23.3383	−1.13744	−0.568719	−	0.822532i	$-0.692561\pi$
$421$	−23.3383	−1.13744	−0.568719	+	0.822532i	$0.692561\pi$
$422$	−3.99775	−0.194607
$423$	0.0597558	0.00290543
$424$	−10.9847	−0.533462
$425$	−7.33027	−0.355570
$426$	−23.9861	−1.16213
$427$	−23.3558	−1.13027
$428$	39.5771	1.91303
$429$	−3.78284	−0.182637
$430$	−91.0683	−4.39171
$431$	−30.5193	−1.47006	−0.735031	−	0.678033i	$-0.762833\pi$
$431$	−30.5193	−1.47006	−0.735031	+	0.678033i	$0.762833\pi$
$432$	102.035	4.90917
$433$	4.70899	0.226300	0.113150	−	0.993578i	$-0.463906\pi$
$433$	4.70899	0.226300	0.113150	+	0.993578i	$0.463906\pi$
$434$	87.4535	4.19790
$435$	−43.0652	−2.06482
$436$	−63.6181	−3.04675
$437$	7.13696	0.341407
$438$	12.2812	0.586820
$439$	6.53941	0.312109	0.156055	−	0.987748i	$-0.450122\pi$
$439$	6.53941	0.312109	0.156055	+	0.987748i	$0.450122\pi$
$440$	91.5669	4.36528
$441$	−0.545075	−0.0259560
$442$	10.2333	0.486749
$443$	−12.1407	−0.576821	−0.288410	−	0.957507i	$-0.593127\pi$
$443$	−12.1407	−0.576821	−0.288410	+	0.957507i	$0.593127\pi$
$444$	−57.3140	−2.72000
$445$	19.7418	0.935852
$446$	−66.9112	−3.16834
$447$	26.4662	1.25181
$448$	159.537	7.53741
$449$	5.44348	0.256894	0.128447	−	0.991716i	$-0.459001\pi$
$449$	5.44348	0.256894	0.128447	+	0.991716i	$0.459001\pi$
$450$	0.746517	0.0351911
$451$	−32.2567	−1.51891
$452$	32.8005	1.54280
$453$	1.67550	0.0787218
$454$	−74.8560	−3.51317
$455$	−5.41540	−0.253878
$456$	−67.8234	−3.17612
$457$	−34.9262	−1.63378	−0.816890	−	0.576793i	$-0.804304\pi$
$457$	−34.9262	−1.63378	−0.816890	+	0.576793i	$0.804304\pi$
$458$	−31.5838	−1.47581
$459$	−28.4624	−1.32851
$460$	28.8889	1.34695
$461$	25.5906	1.19187	0.595936	−	0.803032i	$-0.296781\pi$
$461$	25.5906	1.19187	0.595936	+	0.803032i	$0.296781\pi$
$462$	48.7531	2.26820
$463$	−1.80067	−0.0836844	−0.0418422	−	0.999124i	$-0.513323\pi$
$463$	−1.80067	−0.0836844	−0.0418422	+	0.999124i	$0.513323\pi$
$464$	−194.132	−9.01236
$465$	−41.9774	−1.94665
$466$	−10.1337	−0.469436
$467$	4.55938	0.210983	0.105491	−	0.994420i	$-0.466358\pi$
$467$	4.55938	0.210983	0.105491	+	0.994420i	$0.466358\pi$
$468$	−0.778543	−0.0359882
$469$	−33.2505	−1.53537
$470$	−2.20197	−0.101569
$471$	−7.67976	−0.353865
$472$	−74.3794	−3.42359
$473$	−42.3314	−1.94640
$474$	45.2920	2.08033
$475$	−5.07692	−0.232945
$476$	−98.5250	−4.51589
$477$	−0.192706	−0.00882338
$478$	−20.4535	−0.935523
$479$	0.488938	0.0223401	0.0111701	−	0.999938i	$-0.496444\pi$
$479$	0.488938	0.0223401	0.0111701	+	0.999938i	$0.496444\pi$
$480$	−133.983	−6.11548
$481$	3.96130	0.180620
$482$	49.6937	2.26349
$483$	10.1731	0.462892
$484$	−0.618320	−0.0281055
$485$	5.51247	0.250308
$486$	5.62227	0.255032
$487$	−19.7712	−0.895920	−0.447960	−	0.894053i	$-0.647849\pi$
$487$	−19.7712	−0.895920	−0.447960	+	0.894053i	$0.647849\pi$
$488$	81.8347	3.70448
$489$	−4.76658	−0.215552
$490$	20.0857	0.907380
$491$	−16.9278	−0.763941	−0.381971	−	0.924174i	$-0.624754\pi$
$491$	−16.9278	−0.763941	−0.381971	+	0.924174i	$0.624754\pi$
$492$	96.7113	4.36008
$493$	54.1525	2.43891
$494$	7.08756	0.318884
$495$	1.60637	0.0722010
$496$	−189.228	−8.49660
$497$	−15.9613	−0.715961
$498$	2.23750	0.100265
$499$	13.4313	0.601269	0.300635	−	0.953739i	$-0.402802\pi$
$499$	13.4313	0.601269	0.300635	+	0.953739i	$0.402802\pi$
$500$	54.0320	2.41638
$501$	−18.8923	−0.844045
$502$	−22.7614	−1.01589
$503$	0.228851	0.0102040	0.00510198	−	0.999987i	$-0.498376\pi$
$503$	0.228851	0.0102040	0.00510198	+	0.999987i	$0.498376\pi$
$504$	6.63629	0.295604
$505$	39.5385	1.75944
$506$	17.9754	0.799103
$507$	20.9976	0.932536
$508$	122.090	5.41687
$509$	7.36154	0.326294	0.163147	−	0.986602i	$-0.447835\pi$
$509$	7.36154	0.326294	0.163147	+	0.986602i	$0.447835\pi$
$510$	63.3049	2.80319
$511$	8.17239	0.361525
$512$	−184.931	−8.17289
$513$	−19.7129	−0.870348
$514$	−15.8649	−0.699771
$515$	−3.76517	−0.165913
$516$	126.917	5.58721
$517$	−1.02354	−0.0450154
$518$	−51.0530	−2.24314
$519$	20.0340	0.879393
$520$	18.9746	0.832092
$521$	−9.97895	−0.437186	−0.218593	−	0.975816i	$-0.570147\pi$
$521$	−9.97895	−0.437186	−0.218593	+	0.975816i	$0.570147\pi$
$522$	−5.51491	−0.241381
$523$	3.80464	0.166365	0.0831826	−	0.996534i	$-0.473492\pi$
$523$	3.80464	0.166365	0.0831826	+	0.996534i	$0.473492\pi$
$524$	−30.9170	−1.35062
$525$	−7.23670	−0.315835
$526$	34.2863	1.49495
$527$	52.7846	2.29933
$528$	−105.490	−4.59086
$529$	−19.2491	−0.836920
$530$	7.10109	0.308452
$531$	−1.30485	−0.0566256
$532$	−68.2381	−2.95850
$533$	−6.68427	−0.289528
$534$	−36.8293	−1.59376
$535$	−16.9216	−0.731585
$536$	116.504	5.03220
$537$	−15.4935	−0.668595
$538$	−14.5546	−0.627495
$539$	9.33645	0.402150
$540$	−79.7937	−3.43377
$541$	−36.4468	−1.56697	−0.783485	−	0.621411i	$-0.786560\pi$
$541$	−36.4468	−1.56697	−0.783485	+	0.621411i	$0.786560\pi$
$542$	−1.59271	−0.0684126
$543$	−35.4507	−1.52134
$544$	168.478	7.22344
$545$	27.2006	1.16515
$546$	10.1027	0.432355
$547$	−24.2470	−1.03673	−0.518364	−	0.855160i	$-0.673459\pi$
$547$	−24.2470	−1.03673	−0.518364	+	0.855160i	$0.673459\pi$
$548$	113.650	4.85488
$549$	1.43564	0.0612716
$550$	−12.7869	−0.545235
$551$	37.5059	1.59780
$552$	−35.6448	−1.51714
$553$	30.1390	1.28164
$554$	88.4194	3.75658
$555$	24.5052	1.04019
$556$	−18.9992	−0.805747
$557$	5.91154	0.250480	0.125240	−	0.992126i	$-0.460030\pi$
$557$	5.91154	0.250480	0.125240	+	0.992126i	$0.460030\pi$
$558$	−5.37560	−0.227567
$559$	−8.77196	−0.371014
$560$	−151.016	−6.38159
$561$	29.4261	1.24237
$562$	30.1983	1.27384
$563$	21.9470	0.924958	0.462479	−	0.886630i	$-0.346960\pi$
$563$	21.9470	0.924958	0.462479	+	0.886630i	$0.346960\pi$
$564$	3.06877	0.129218
$565$	−14.0242	−0.590002
$566$	−20.7057	−0.870327
$567$	−26.2866	−1.10393
$568$	55.9255	2.34658
$569$	32.6333	1.36806	0.684029	−	0.729455i	$-0.260226\pi$
$569$	32.6333	1.36806	0.684029	+	0.729455i	$0.260226\pi$
$570$	43.8448	1.83646
$571$	−10.3972	−0.435108	−0.217554	−	0.976048i	$-0.569808\pi$
$571$	−10.3972	−0.435108	−0.217554	+	0.976048i	$0.569808\pi$
$572$	13.3355	0.557584
$573$	16.6033	0.693613
$574$	86.1464	3.59568
$575$	−2.66819	−0.111271
$576$	−9.80643	−0.408601
$577$	2.53868	0.105687	0.0528434	−	0.998603i	$-0.483172\pi$
$577$	2.53868	0.105687	0.0528434	+	0.998603i	$0.483172\pi$
$578$	−31.8015	−1.32277
$579$	25.6576	1.06629
$580$	151.815	6.30380
$581$	1.48892	0.0617706
$582$	−10.2838	−0.426276
$583$	3.30081	0.136705
$584$	−28.6346	−1.18491
$585$	0.332874	0.0137627
$586$	27.9691	1.15539
$587$	30.0707	1.24115	0.620574	−	0.784148i	$-0.286899\pi$
$587$	30.0707	1.24115	0.620574	+	0.784148i	$0.286899\pi$
$588$	−27.9924	−1.15439
$589$	36.5585	1.50637
$590$	48.0829	1.97954
$591$	40.4604	1.66432
$592$	110.466	4.54014
$593$	−37.4122	−1.53633	−0.768167	−	0.640250i	$-0.778831\pi$
$593$	−37.4122	−1.53633	−0.768167	+	0.640250i	$0.778831\pi$
$594$	−49.6497	−2.03715
$595$	42.1254	1.72697
$596$	−93.3001	−3.82172
$597$	−15.3444	−0.628004
$598$	3.72489	0.152322
$599$	38.1315	1.55801	0.779005	−	0.627018i	$-0.215725\pi$
$599$	38.1315	1.55801	0.779005	+	0.627018i	$0.215725\pi$
$600$	25.3561	1.03516
$601$	44.1837	1.80229	0.901145	−	0.433517i	$-0.142728\pi$
$601$	44.1837	1.80229	0.901145	+	0.433517i	$0.142728\pi$
$602$	113.053	4.60768
$603$	2.04384	0.0832318
$604$	−5.90655	−0.240334
$605$	0.264369	0.0107481
$606$	−73.7609	−2.99633
$607$	17.1896	0.697704	0.348852	−	0.937178i	$-0.386572\pi$
$607$	17.1896	0.697704	0.348852	+	0.937178i	$0.386572\pi$
$608$	116.687	4.73230
$609$	53.4612	2.16636
$610$	−52.9025	−2.14196
$611$	−0.212100	−0.00858065
$612$	6.05614	0.244805
$613$	−0.211811	−0.00855496	−0.00427748	−	0.999991i	$-0.501362\pi$
$613$	−0.211811	−0.00855496	−0.00427748	+	0.999991i	$0.501362\pi$
$614$	−10.3900	−0.419308
$615$	−41.3500	−1.66739
$616$	−113.671	−4.57995
$617$	−41.3071	−1.66296	−0.831481	−	0.555552i	$-0.812507\pi$
$617$	−41.3071	−1.66296	−0.831481	+	0.555552i	$0.812507\pi$
$618$	7.02410	0.282551
$619$	13.4067	0.538860	0.269430	−	0.963020i	$-0.413165\pi$
$619$	13.4067	0.538860	0.269430	+	0.963020i	$0.413165\pi$
$620$	147.981	5.94304
$621$	−10.3602	−0.415740
$622$	−21.2191	−0.850809
$623$	−24.5076	−0.981874
$624$	−21.8598	−0.875091
$625$	−29.9904	−1.19962
$626$	66.4217	2.65474
$627$	20.3804	0.813914
$628$	27.0731	1.08033
$629$	−30.8142	−1.22864
$630$	−4.29006	−0.170920
$631$	−40.5725	−1.61517	−0.807583	−	0.589754i	$-0.799225\pi$
$631$	−40.5725	−1.61517	−0.807583	+	0.589754i	$0.799225\pi$
$632$	−105.602	−4.20061
$633$	−2.38213	−0.0946812
$634$	16.6307	0.660490
$635$	−52.2010	−2.07153
$636$	−9.89641	−0.392418
$637$	1.93471	0.0766561
$638$	94.4635	3.73985
$639$	0.981109	0.0388121
$640$	201.429	7.96219
$641$	−0.547742	−0.0216345	−0.0108173	−	0.999941i	$-0.503443\pi$
$641$	−0.547742	−0.0216345	−0.0108173	+	0.999941i	$0.503443\pi$
$642$	31.5680	1.24589
$643$	17.3809	0.685435	0.342718	−	0.939438i	$-0.388653\pi$
$643$	17.3809	0.685435	0.342718	+	0.939438i	$0.388653\pi$
$644$	−35.8627	−1.41319
$645$	−54.2648	−2.13667
$646$	−55.1328	−2.16917
$647$	−2.78176	−0.109362	−0.0546812	−	0.998504i	$-0.517414\pi$
$647$	−2.78176	−0.109362	−0.0546812	+	0.998504i	$0.517414\pi$
$648$	92.1036	3.61817
$649$	22.3504	0.877330
$650$	−2.64972	−0.103931
$651$	52.1108	2.04238
$652$	16.8034	0.658071
$653$	−20.9588	−0.820182	−0.410091	−	0.912045i	$-0.634503\pi$
$653$	−20.9588	−0.820182	−0.410091	+	0.912045i	$0.634503\pi$
$654$	−50.7439	−1.98425
$655$	13.2189	0.516505
$656$	−186.400	−7.27770
$657$	−0.502341	−0.0195982
$658$	2.73353	0.106564
$659$	−16.6993	−0.650511	−0.325255	−	0.945626i	$-0.605450\pi$
$659$	−16.6993	−0.650511	−0.325255	+	0.945626i	$0.605450\pi$
$660$	82.4953	3.21113
$661$	38.6454	1.50313	0.751567	−	0.659657i	$-0.229298\pi$
$661$	38.6454	1.50313	0.751567	+	0.659657i	$0.229298\pi$
$662$	−26.2627	−1.02073
$663$	6.09771	0.236815
$664$	−5.21690	−0.202455
$665$	29.1759	1.13139
$666$	3.13813	0.121600
$667$	19.7113	0.763225
$668$	66.6000	2.57683
$669$	−39.8703	−1.54147
$670$	−75.3145	−2.90965
$671$	−24.5907	−0.949313
$672$	166.327	6.41622
$673$	−11.4991	−0.443259	−0.221629	−	0.975131i	$-0.571138\pi$
$673$	−11.4991	−0.443259	−0.221629	+	0.975131i	$0.571138\pi$
$674$	−29.6107	−1.14056
$675$	7.36978	0.283663
$676$	−74.0217	−2.84699
$677$	11.0643	0.425234	0.212617	−	0.977136i	$-0.431801\pi$
$677$	11.0643	0.425234	0.212617	+	0.977136i	$0.431801\pi$
$678$	26.1628	1.00477
$679$	−6.84320	−0.262618
$680$	−147.600	−5.66021
$681$	−44.6043	−1.70924
$682$	92.0773	3.52582
$683$	51.6074	1.97470	0.987352	−	0.158544i	$-0.0506799\pi$
$683$	51.6074	1.97470	0.987352	+	0.158544i	$0.0506799\pi$
$684$	4.19446	0.160379
$685$	−48.5923	−1.85661
$686$	36.7728	1.40399
$687$	−18.8198	−0.718020
$688$	−244.618	−9.32599
$689$	0.683998	0.0260582
$690$	23.0427	0.877222
$691$	29.9191	1.13818	0.569088	−	0.822276i	$-0.307296\pi$
$691$	29.9191	1.13818	0.569088	+	0.822276i	$0.307296\pi$
$692$	−70.6247	−2.68475
$693$	−1.99415	−0.0757516
$694$	54.5950	2.07240
$695$	8.12332	0.308135
$696$	−187.319	−7.10030
$697$	51.9957	1.96948
$698$	19.8951	0.753042
$699$	−6.03838	−0.228392
$700$	25.5112	0.964231
$701$	−2.17715	−0.0822299	−0.0411150	−	0.999154i	$-0.513091\pi$
$701$	−2.17715	−0.0822299	−0.0411150	+	0.999154i	$0.513091\pi$
$702$	−10.2885	−0.388313
$703$	−21.3418	−0.804922
$704$	167.972	6.33068
$705$	−1.31209	−0.0494160
$706$	−31.8179	−1.19748
$707$	−49.0832	−1.84596
$708$	−67.0106	−2.51841
$709$	−4.88745	−0.183552	−0.0917760	−	0.995780i	$-0.529254\pi$
$709$	−4.88745	−0.183552	−0.0917760	+	0.995780i	$0.529254\pi$
$710$	−36.1533	−1.35681
$711$	−1.85259	−0.0694774
$712$	85.8702	3.21812
$713$	19.2134	0.719547
$714$	−78.5869	−2.94104
$715$	−5.70172	−0.213232
$716$	54.6185	2.04119
$717$	−12.1876	−0.455155
$718$	29.4816	1.10024
$719$	4.05526	0.151236	0.0756179	−	0.997137i	$-0.475907\pi$
$719$	4.05526	0.151236	0.0756179	+	0.997137i	$0.475907\pi$
$720$	9.28267	0.345945
$721$	4.67410	0.174072
$722$	15.2405	0.567193
$723$	29.6109	1.10124
$724$	124.973	4.64457
$725$	−14.0218	−0.520755
$726$	−0.493193	−0.0183041
$727$	31.6873	1.17522	0.587608	−	0.809146i	$-0.300070\pi$
$727$	31.6873	1.17522	0.587608	+	0.809146i	$0.300070\pi$
$728$	−23.5551	−0.873012
$729$	28.5044	1.05572
$730$	18.5110	0.685123
$731$	68.2355	2.52378
$732$	73.7274	2.72504
$733$	−0.567198	−0.0209499	−0.0104750	−	0.999945i	$-0.503334\pi$
$733$	−0.567198	−0.0209499	−0.0104750	+	0.999945i	$0.503334\pi$
$734$	81.7444	3.01724
$735$	11.9684	0.441463
$736$	61.3254	2.26048
$737$	−35.0085	−1.28955
$738$	−5.29526	−0.194921
$739$	−47.8831	−1.76141	−0.880704	−	0.473668i	$-0.842930\pi$
$739$	−47.8831	−1.76141	−0.880704	+	0.473668i	$0.842930\pi$
$740$	−86.3870	−3.17565
$741$	4.22325	0.155145
$742$	−8.81532	−0.323620
$743$	29.5640	1.08460	0.542300	−	0.840185i	$-0.317554\pi$
$743$	29.5640	1.08460	0.542300	+	0.840185i	$0.317554\pi$
$744$	−182.587	−6.69397
$745$	39.8915	1.46151
$746$	−35.3329	−1.29363
$747$	−0.0915208	−0.00334857
$748$	−103.734	−3.79290
$749$	21.0065	0.767562
$750$	43.0978	1.57371
$751$	−36.3502	−1.32644	−0.663219	−	0.748426i	$-0.730810\pi$
$751$	−36.3502	−1.32644	−0.663219	+	0.748426i	$0.730810\pi$
$752$	−5.91470	−0.215687
$753$	−13.5628	−0.494255
$754$	19.5749	0.712874
$755$	2.52541	0.0919090
$756$	99.0561	3.60263
$757$	−1.28848	−0.0468306	−0.0234153	−	0.999726i	$-0.507454\pi$
$757$	−1.28848	−0.0468306	−0.0234153	+	0.999726i	$0.507454\pi$
$758$	−27.2388	−0.989357
$759$	10.7110	0.388784
$760$	−102.227	−3.70818
$761$	−11.0651	−0.401109	−0.200554	−	0.979683i	$-0.564274\pi$
$761$	−11.0651	−0.401109	−0.200554	+	0.979683i	$0.564274\pi$
$762$	97.3832	3.52782
$763$	−33.7669	−1.22244
$764$	−58.5308	−2.11757
$765$	−2.58937	−0.0936189
$766$	−60.9996	−2.20400
$767$	4.63148	0.167233
$768$	−205.249	−7.40629
$769$	−23.4928	−0.847170	−0.423585	−	0.905856i	$-0.639229\pi$
$769$	−23.4928	−0.847170	−0.423585	+	0.905856i	$0.639229\pi$
$770$	73.4835	2.64816
$771$	−9.45340	−0.340456
$772$	−90.4493	−3.25534
$773$	53.2630	1.91574	0.957868	−	0.287207i	$-0.0927269\pi$
$773$	53.2630	1.91574	0.957868	+	0.287207i	$0.0927269\pi$
$774$	−6.94912	−0.249781
$775$	−13.6676	−0.490953
$776$	23.9774	0.860737
$777$	−30.4209	−1.09134
$778$	36.5883	1.31175
$779$	36.0121	1.29027
$780$	17.0948	0.612092
$781$	−16.8052	−0.601336
$782$	−28.9752	−1.03615
$783$	−54.4444	−1.94568
$784$	53.9522	1.92686
$785$	−11.5754	−0.413143
$786$	−24.6605	−0.879610
$787$	53.1400	1.89424	0.947118	−	0.320885i	$-0.103980\pi$
$787$	53.1400	1.89424	0.947118	+	0.320885i	$0.103980\pi$
$788$	−142.633	−5.08109
$789$	20.4301	0.727332
$790$	68.2668	2.42882
$791$	17.4097	0.619017
$792$	6.98716	0.248278
$793$	−5.09572	−0.180954
$794$	−32.1542	−1.14111
$795$	4.23132	0.150069
$796$	54.0928	1.91727
$797$	−35.7321	−1.26570	−0.632848	−	0.774276i	$-0.718114\pi$
$797$	−35.7321	−1.26570	−0.632848	+	0.774276i	$0.718114\pi$
$798$	−54.4290	−1.92677
$799$	1.64989	0.0583688
$800$	−43.6242	−1.54235
$801$	1.50643	0.0532272
$802$	−6.51487	−0.230048
$803$	8.60448	0.303645
$804$	104.962	3.70172
$805$	15.3335	0.540435
$806$	19.0804	0.672078
$807$	−8.67265	−0.305292
$808$	171.979	6.05020
$809$	−23.6538	−0.831622	−0.415811	−	0.909451i	$-0.636502\pi$
$809$	−23.6538	−0.831622	−0.415811	+	0.909451i	$0.636502\pi$
$810$	−59.5409	−2.09205
$811$	−2.72017	−0.0955183	−0.0477591	−	0.998859i	$-0.515208\pi$
$811$	−2.72017	−0.0955183	−0.0477591	+	0.998859i	$0.515208\pi$
$812$	−188.464	−6.61380
$813$	−0.949044	−0.0332844
$814$	−53.7522	−1.88401
$815$	−7.18447	−0.251661
$816$	170.043	5.95270
$817$	47.2597	1.65341
$818$	66.6424	2.33010
$819$	−0.413231	−0.0144395
$820$	145.769	5.09047
$821$	28.9964	1.01198	0.505991	−	0.862539i	$-0.331127\pi$
$821$	28.9964	1.01198	0.505991	+	0.862539i	$0.331127\pi$
$822$	90.6510	3.16182
$823$	20.5763	0.717244	0.358622	−	0.933483i	$-0.383247\pi$
$823$	20.5763	0.717244	0.358622	+	0.933483i	$0.383247\pi$
$824$	−16.3772	−0.570527
$825$	−7.61931	−0.265270
$826$	−59.6903	−2.07689
$827$	19.8594	0.690579	0.345290	−	0.938496i	$-0.387781\pi$
$827$	19.8594	0.690579	0.345290	+	0.938496i	$0.387781\pi$
$828$	2.20441	0.0766086
$829$	30.3647	1.05461	0.527304	−	0.849676i	$-0.323203\pi$
$829$	30.3647	1.05461	0.527304	+	0.849676i	$0.323203\pi$
$830$	3.37249	0.117061
$831$	52.6864	1.82767
$832$	34.8074	1.20673
$833$	−15.0498	−0.521444
$834$	−15.1544	−0.524755
$835$	−28.4756	−0.985437
$836$	−71.8459	−2.48484
$837$	−53.0692	−1.83434
$838$	−112.186	−3.87540
$839$	−31.3590	−1.08263	−0.541317	−	0.840819i	$-0.682074\pi$
$839$	−31.3590	−1.08263	−0.541317	+	0.840819i	$0.682074\pi$
$840$	−145.716	−5.02768
$841$	74.5860	2.57193
$842$	65.6239	2.26155
$843$	17.9942	0.619753
$844$	8.39760	0.289057
$845$	31.6488	1.08875
$846$	−0.168025	−0.00577682
$847$	−0.328189	−0.0112767
$848$	19.0742	0.655011
$849$	−12.3379	−0.423435
$850$	20.6117	0.706975
$851$	−11.2163	−0.384488
$852$	50.3850	1.72616
$853$	52.9233	1.81206	0.906029	−	0.423215i	$-0.139098\pi$
$853$	52.9233	1.81206	0.906029	+	0.423215i	$0.139098\pi$
$854$	65.6733	2.24729
$855$	−1.79339	−0.0613326
$856$	−73.6032	−2.51570
$857$	28.2445	0.964814	0.482407	−	0.875947i	$-0.339763\pi$
$857$	28.2445	0.964814	0.482407	+	0.875947i	$0.339763\pi$
$858$	10.6368	0.363135
$859$	−12.1127	−0.413279	−0.206640	−	0.978417i	$-0.566253\pi$
$859$	−12.1127	−0.413279	−0.206640	+	0.978417i	$0.566253\pi$
$860$	191.297	6.52317
$861$	51.3320	1.74939
$862$	85.8159	2.92290
$863$	5.63611	0.191856	0.0959278	−	0.995388i	$-0.469418\pi$
$863$	5.63611	0.191856	0.0959278	+	0.995388i	$0.469418\pi$
$864$	−169.386	−5.76264
$865$	30.1963	1.02671
$866$	−13.2410	−0.449948
$867$	−18.9495	−0.643559
$868$	−183.704	−6.23531
$869$	31.7325	1.07645
$870$	121.093	4.10544
$871$	−7.25451	−0.245810
$872$	118.313	4.00659
$873$	0.420638	0.0142364
$874$	−20.0681	−0.678815
$875$	28.6788	0.969522
$876$	−25.7978	−0.871626
$877$	0.251892	0.00850580	0.00425290	−	0.999991i	$-0.498646\pi$
$877$	0.251892	0.00850580	0.00425290	+	0.999991i	$0.498646\pi$
$878$	−18.3879	−0.620562
$879$	16.6659	0.562127
$880$	−159.000	−5.35991
$881$	−45.7464	−1.54124	−0.770618	−	0.637297i	$-0.780053\pi$
$881$	−45.7464	−1.54124	−0.770618	+	0.637297i	$0.780053\pi$
$882$	1.53267	0.0516078
$883$	55.1185	1.85488	0.927442	−	0.373967i	$-0.122003\pi$
$883$	55.1185	1.85488	0.927442	+	0.373967i	$0.122003\pi$
$884$	−21.4959	−0.722987
$885$	28.6511	0.963096
$886$	34.1379	1.14688
$887$	1.00623	0.0337859	0.0168930	−	0.999857i	$-0.494623\pi$
$887$	1.00623	0.0337859	0.0168930	+	0.999857i	$0.494623\pi$
$888$	106.589	3.57690
$889$	64.8024	2.17340
$890$	−55.5112	−1.86074
$891$	−27.6764	−0.927195
$892$	140.553	4.70605
$893$	1.14271	0.0382392
$894$	−74.4193	−2.48895
$895$	−23.3527	−0.780596
$896$	−250.055	−8.35374
$897$	2.21954	0.0741084
$898$	−15.3063	−0.510778
$899$	100.969	3.36752
$900$	−1.56812	−0.0522707
$901$	−5.32069	−0.177258
$902$	90.7012	3.02002
$903$	67.3644	2.24175
$904$	−61.0004	−2.02884
$905$	−53.4334	−1.77619
$906$	−4.71126	−0.156521
$907$	14.7237	0.488891	0.244446	−	0.969663i	$-0.421394\pi$
$907$	14.7237	0.488891	0.244446	+	0.969663i	$0.421394\pi$
$908$	157.241	5.21824
$909$	3.01705	0.100069
$910$	15.2273	0.504782
$911$	−19.0678	−0.631743	−0.315872	−	0.948802i	$-0.602297\pi$
$911$	−19.0678	−0.631743	−0.315872	+	0.948802i	$0.602297\pi$
$912$	117.771	3.89980
$913$	1.56764	0.0518812
$914$	98.2077	3.24842
$915$	−31.5229	−1.04212
$916$	66.3444	2.19208
$917$	−16.4100	−0.541905
$918$	80.0322	2.64145
$919$	12.8924	0.425280	0.212640	−	0.977131i	$-0.431794\pi$
$919$	12.8924	0.425280	0.212640	+	0.977131i	$0.431794\pi$
$920$	−53.7259	−1.77129
$921$	−6.19109	−0.204003
$922$	−71.9570	−2.36978
$923$	−3.48239	−0.114624
$924$	−102.410	−3.36904
$925$	7.97875	0.262340
$926$	5.06324	0.166388
$927$	−0.287308	−0.00943642
$928$	322.274	10.5792
$929$	−9.76959	−0.320530	−0.160265	−	0.987074i	$-0.551235\pi$
$929$	−9.76959	−0.320530	−0.160265	+	0.987074i	$0.551235\pi$
$930$	118.034	3.87050
$931$	−10.4234	−0.341614
$932$	21.2868	0.697272
$933$	−12.6438	−0.413940
$934$	−12.8203	−0.419494
$935$	44.3527	1.45049
$936$	1.44789	0.0473257
$937$	−16.1899	−0.528900	−0.264450	−	0.964399i	$-0.585190\pi$
$937$	−16.1899	−0.528900	−0.264450	+	0.964399i	$0.585190\pi$
$938$	93.4957	3.05274
$939$	39.5786	1.29160
$940$	4.62543	0.150865
$941$	1.24828	0.0406927	0.0203464	−	0.999793i	$-0.493523\pi$
$941$	1.24828	0.0406927	0.0203464	+	0.999793i	$0.493523\pi$
$942$	21.5944	0.703583
$943$	18.9262	0.616323
$944$	129.155	4.20365
$945$	−42.3525	−1.37773
$946$	119.030	3.86999
$947$	−40.9477	−1.33062	−0.665311	−	0.746566i	$-0.731701\pi$
$947$	−40.9477	−1.33062	−0.665311	+	0.746566i	$0.731701\pi$
$948$	−95.1398	−3.09000
$949$	1.78303	0.0578797
$950$	14.2756	0.463161
$951$	9.90972	0.321345
$952$	183.231	5.93856
$953$	48.3204	1.56525	0.782626	−	0.622492i	$-0.213880\pi$
$953$	48.3204	1.56525	0.782626	+	0.622492i	$0.213880\pi$
$954$	0.541861	0.0175434
$955$	25.0255	0.809806
$956$	42.9644	1.38957
$957$	56.2878	1.81953
$958$	−1.37482	−0.0444186
$959$	60.3226	1.94792
$960$	215.324	6.94956
$961$	67.4189	2.17480
$962$	−11.1386	−0.359123
$963$	−1.29123	−0.0416093
$964$	−104.386	−3.36204
$965$	38.6726	1.24491
$966$	−28.6053	−0.920361
$967$	−6.75188	−0.217126	−0.108563	−	0.994090i	$-0.534625\pi$
$967$	−6.75188	−0.217126	−0.108563	+	0.994090i	$0.534625\pi$
$968$	1.14992	0.0369597
$969$	−32.8519	−1.05536
$970$	−15.5003	−0.497684
$971$	−12.6308	−0.405343	−0.202671	−	0.979247i	$-0.564962\pi$
$971$	−12.6308	−0.405343	−0.202671	+	0.979247i	$0.564962\pi$
$972$	−11.8101	−0.378808
$973$	−10.0843	−0.323288
$974$	55.5939	1.78134
$975$	−1.57888	−0.0505648
$976$	−142.101	−4.54855
$977$	−5.49357	−0.175755	−0.0878775	−	0.996131i	$-0.528008\pi$
$977$	−5.49357	−0.175755	−0.0878775	+	0.996131i	$0.528008\pi$
$978$	13.4030	0.428579
$979$	−25.8033	−0.824677
$980$	−42.1918	−1.34777
$981$	2.07559	0.0662684
$982$	47.5986	1.51893
$983$	8.88781	0.283477	0.141739	−	0.989904i	$-0.454731\pi$
$983$	8.88781	0.283477	0.141739	+	0.989904i	$0.454731\pi$
$984$	−179.858	−5.73367
$985$	60.9843	1.94312
$986$	−152.269	−4.84924
$987$	1.62883	0.0518461
$988$	−14.8880	−0.473651
$989$	24.8375	0.789785
$990$	−4.51689	−0.143556
$991$	4.64730	0.147626	0.0738132	−	0.997272i	$-0.476483\pi$
$991$	4.64730	0.147626	0.0738132	+	0.997272i	$0.476483\pi$
$992$	314.134	9.97375
$993$	−15.6491	−0.496610
$994$	44.8808	1.42353
$995$	−23.1280	−0.733206
$996$	−4.70006	−0.148927
$997$	15.5158	0.491391	0.245695	−	0.969347i	$-0.420984\pi$
$997$	15.5158	0.491391	0.245695	+	0.969347i	$0.420984\pi$
$998$	−37.7670	−1.19549
$999$	30.9803	0.980174

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8003.2.a.d.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-2.81186 q^{2} -1.67550 q^{3} +5.90655 q^{4} -2.52541 q^{5} +4.71126 q^{6} +3.13505 q^{7} -10.9847 q^{8} -0.192706 q^{9} +O(q^{10})\)	\(q-2.81186 q^{2} -1.67550 q^{3} +5.90655 q^{4} -2.52541 q^{5} +4.71126 q^{6} +3.13505 q^{7} -10.9847 q^{8} -0.192706 q^{9} +7.10109 q^{10} +3.30081 q^{11} -9.89641 q^{12} +0.683998 q^{13} -8.81532 q^{14} +4.23132 q^{15} +19.0742 q^{16} -5.32069 q^{17} +0.541861 q^{18} -3.68509 q^{19} -14.9165 q^{20} -5.25277 q^{21} -9.28140 q^{22} -1.93671 q^{23} +18.4048 q^{24} +1.37769 q^{25} -1.92330 q^{26} +5.34937 q^{27} +18.5173 q^{28} -10.1777 q^{29} -11.8979 q^{30} -9.92063 q^{31} -31.6647 q^{32} -5.53049 q^{33} +14.9610 q^{34} -7.91728 q^{35} -1.13822 q^{36} +5.79139 q^{37} +10.3620 q^{38} -1.14604 q^{39} +27.7408 q^{40} -9.77236 q^{41} +14.7700 q^{42} -12.8246 q^{43} +19.4964 q^{44} +0.486660 q^{45} +5.44576 q^{46} -0.310089 q^{47} -31.9588 q^{48} +2.82854 q^{49} -3.87387 q^{50} +8.91481 q^{51} +4.04006 q^{52} +1.00000 q^{53} -15.0417 q^{54} -8.33588 q^{55} -34.4375 q^{56} +6.17437 q^{57} +28.6183 q^{58} +6.77120 q^{59} +24.9925 q^{60} -7.44991 q^{61} +27.8954 q^{62} -0.604141 q^{63} +50.8882 q^{64} -1.72737 q^{65} +15.5510 q^{66} -10.6060 q^{67} -31.4269 q^{68} +3.24496 q^{69} +22.2623 q^{70} -5.09123 q^{71} +2.11681 q^{72} +2.60678 q^{73} -16.2846 q^{74} -2.30832 q^{75} -21.7662 q^{76} +10.3482 q^{77} +3.22249 q^{78} +9.61356 q^{79} -48.1702 q^{80} -8.38475 q^{81} +27.4785 q^{82} +0.474926 q^{83} -31.0257 q^{84} +13.4369 q^{85} +36.0608 q^{86} +17.0528 q^{87} -36.2582 q^{88} -7.81728 q^{89} -1.36842 q^{90} +2.14437 q^{91} -11.4393 q^{92} +16.6220 q^{93} +0.871926 q^{94} +9.30637 q^{95} +53.0541 q^{96} -2.18280 q^{97} -7.95345 q^{98} -0.636083 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 179 q + 8 q^{2} + 15 q^{3} + 202 q^{4} + 27 q^{5} + 18 q^{6} + 23 q^{7} + 21 q^{8} + 214 q^{9}+O(q^{10}) \) 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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