LMFDB - Embedded newform 8003.2.a.c.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:	$172$
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)

$f(q)$	$=$	$q-2.79279 q^{2} +3.40925 q^{3} +5.79969 q^{4} +2.64273 q^{5} -9.52131 q^{6} +3.16263 q^{7} -10.6117 q^{8} +8.62295 q^{9} +O(q^{10})$	\(q-2.79279 q^{2} +3.40925 q^{3} +5.79969 q^{4} +2.64273 q^{5} -9.52131 q^{6} +3.16263 q^{7} -10.6117 q^{8} +8.62295 q^{9} -7.38060 q^{10} +1.52129 q^{11} +19.7726 q^{12} -3.08710 q^{13} -8.83256 q^{14} +9.00972 q^{15} +18.0370 q^{16} -0.165772 q^{17} -24.0821 q^{18} -3.02173 q^{19} +15.3270 q^{20} +10.7822 q^{21} -4.24863 q^{22} -3.71651 q^{23} -36.1780 q^{24} +1.98403 q^{25} +8.62164 q^{26} +19.1700 q^{27} +18.3423 q^{28} +4.48131 q^{29} -25.1623 q^{30} -2.77064 q^{31} -29.1502 q^{32} +5.18643 q^{33} +0.462967 q^{34} +8.35797 q^{35} +50.0105 q^{36} +1.05579 q^{37} +8.43906 q^{38} -10.5247 q^{39} -28.0440 q^{40} +7.11352 q^{41} -30.1124 q^{42} -7.56573 q^{43} +8.82298 q^{44} +22.7881 q^{45} +10.3794 q^{46} +2.34704 q^{47} +61.4927 q^{48} +3.00221 q^{49} -5.54098 q^{50} -0.565157 q^{51} -17.9042 q^{52} -1.00000 q^{53} -53.5379 q^{54} +4.02035 q^{55} -33.5610 q^{56} -10.3018 q^{57} -12.5154 q^{58} -9.08942 q^{59} +52.2536 q^{60} +6.11238 q^{61} +7.73783 q^{62} +27.2712 q^{63} +45.3364 q^{64} -8.15838 q^{65} -14.4846 q^{66} +5.99829 q^{67} -0.961426 q^{68} -12.6705 q^{69} -23.3421 q^{70} +12.3581 q^{71} -91.5046 q^{72} +10.5006 q^{73} -2.94862 q^{74} +6.76404 q^{75} -17.5251 q^{76} +4.81126 q^{77} +29.3933 q^{78} +8.53624 q^{79} +47.6670 q^{80} +39.4865 q^{81} -19.8666 q^{82} -5.34613 q^{83} +62.5332 q^{84} -0.438091 q^{85} +21.1295 q^{86} +15.2779 q^{87} -16.1435 q^{88} -15.1104 q^{89} -63.6426 q^{90} -9.76335 q^{91} -21.5546 q^{92} -9.44580 q^{93} -6.55480 q^{94} -7.98561 q^{95} -99.3801 q^{96} +17.3610 q^{97} -8.38454 q^{98} +13.1180 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 172 q + 8 q^{2} + 25 q^{3} + 188 q^{4} + 27 q^{5} + 10 q^{6} + 31 q^{7} + 21 q^{8} + 179 q^{9}+O(q^{10}) $ 172 * q + 8 * q^2 + 25 * q^3 + 188 * q^4 + 27 * q^5 + 10 * q^6 + 31 * q^7 + 21 * q^8 + 179 * q^9	\( 172 q + 8 q^{2} + 25 q^{3} + 188 q^{4} + 27 q^{5} + 10 q^{6} + 31 q^{7} + 21 q^{8} + 179 q^{9} + 20 q^{10} - 3 q^{11} + 66 q^{12} + 121 q^{13} + 12 q^{14} + 30 q^{15} + 212 q^{16} + 8 q^{17} + 40 q^{18} + 41 q^{19} + 64 q^{20} + 56 q^{21} + 50 q^{22} + 28 q^{23} + 30 q^{24} + 231 q^{25} + 38 q^{26} + 100 q^{27} + 80 q^{28} + 26 q^{29} + 55 q^{30} + 66 q^{31} + 65 q^{32} + 99 q^{33} + 81 q^{34} + 36 q^{35} + 212 q^{36} + 153 q^{37} + q^{38} + 20 q^{39} + 59 q^{40} + 40 q^{41} + 50 q^{42} + 39 q^{43} - 51 q^{44} + 123 q^{45} + 59 q^{46} + 29 q^{47} + 128 q^{48} + 245 q^{49} + 19 q^{50} + 36 q^{51} + 215 q^{52} - 172 q^{53} + 40 q^{54} + 40 q^{55} + 15 q^{56} + 54 q^{57} + 44 q^{58} - 54 q^{60} + 100 q^{61} - 29 q^{62} + 92 q^{63} + 253 q^{64} + 77 q^{65} + 14 q^{66} + 126 q^{67} - 27 q^{68} + 47 q^{69} + 72 q^{70} + 38 q^{71} + 65 q^{72} + 185 q^{73} + 48 q^{74} + 75 q^{75} + 38 q^{76} + 120 q^{77} + 75 q^{78} + 79 q^{79} + 43 q^{80} + 232 q^{81} + 110 q^{82} + 90 q^{83} + 158 q^{84} + 115 q^{85} + 68 q^{86} + 61 q^{87} + 15 q^{88} - 36 q^{89} - 6 q^{90} + 33 q^{91} + 139 q^{92} + 103 q^{93} - 24 q^{94} - 45 q^{95} + 34 q^{96} + 159 q^{97} - 36 q^{98} + 27 q^{99}+O(q^{100}) \) 172 * q + 8 * q^2 + 25 * q^3 + 188 * q^4 + 27 * q^5 + 10 * q^6 + 31 * q^7 + 21 * q^8 + 179 * q^9 + 20 * q^10 - 3 * q^11 + 66 * q^12 + 121 * q^13 + 12 * q^14 + 30 * q^15 + 212 * q^16 + 8 * q^17 + 40 * q^18 + 41 * q^19 + 64 * q^20 + 56 * q^21 + 50 * q^22 + 28 * q^23 + 30 * q^24 + 231 * q^25 + 38 * q^26 + 100 * q^27 + 80 * q^28 + 26 * q^29 + 55 * q^30 + 66 * q^31 + 65 * q^32 + 99 * q^33 + 81 * q^34 + 36 * q^35 + 212 * q^36 + 153 * q^37 + q^38 + 20 * q^39 + 59 * q^40 + 40 * q^41 + 50 * q^42 + 39 * q^43 - 51 * q^44 + 123 * q^45 + 59 * q^46 + 29 * q^47 + 128 * q^48 + 245 * q^49 + 19 * q^50 + 36 * q^51 + 215 * q^52 - 172 * q^53 + 40 * q^54 + 40 * q^55 + 15 * q^56 + 54 * q^57 + 44 * q^58 - 54 * q^60 + 100 * q^61 - 29 * q^62 + 92 * q^63 + 253 * q^64 + 77 * q^65 + 14 * q^66 + 126 * q^67 - 27 * q^68 + 47 * q^69 + 72 * q^70 + 38 * q^71 + 65 * q^72 + 185 * q^73 + 48 * q^74 + 75 * q^75 + 38 * q^76 + 120 * q^77 + 75 * q^78 + 79 * q^79 + 43 * q^80 + 232 * q^81 + 110 * q^82 + 90 * q^83 + 158 * q^84 + 115 * q^85 + 68 * q^86 + 61 * q^87 + 15 * q^88 - 36 * q^89 - 6 * q^90 + 33 * q^91 + 139 * q^92 + 103 * q^93 - 24 * q^94 - 45 * q^95 + 34 * q^96 + 159 * q^97 - 36 * q^98 + 27 * 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 $

$2$	−2.79279	−1.97480	−0.987401	−	0.158236i	$-0.949419\pi$
$2$	−2.79279	−1.97480	−0.987401	+	0.158236i	$0.949419\pi$
$3$	3.40925	1.96833	0.984164	−	0.177259i	$-0.0567229\pi$
$3$	3.40925	1.96833	0.984164	+	0.177259i	$0.0567229\pi$
$4$	5.79969	2.89985
$5$	2.64273	1.18187	0.590933	−	0.806721i	$-0.298760\pi$
$5$	2.64273	1.18187	0.590933	+	0.806721i	$0.298760\pi$
$6$	−9.52131	−3.88706
$7$	3.16263	1.19536	0.597680	−	0.801735i	$-0.296089\pi$
$7$	3.16263	1.19536	0.597680	+	0.801735i	$0.296089\pi$
$8$	−10.6117	−3.75182
$9$	8.62295	2.87432
$10$	−7.38060	−2.33395
$11$	1.52129	0.458685	0.229342	−	0.973346i	$-0.426342\pi$
$11$	1.52129	0.458685	0.229342	+	0.973346i	$0.426342\pi$
$12$	19.7726	5.70785
$13$	−3.08710	−0.856208	−0.428104	−	0.903729i	$-0.640818\pi$
$13$	−3.08710	−0.856208	−0.428104	+	0.903729i	$0.640818\pi$
$14$	−8.83256	−2.36060
$15$	9.00972	2.32630
$16$	18.0370	4.50926
$17$	−0.165772	−0.0402056	−0.0201028	−	0.999798i	$-0.506399\pi$
$17$	−0.165772	−0.0402056	−0.0201028	+	0.999798i	$0.506399\pi$
$18$	−24.0821	−5.67621
$19$	−3.02173	−0.693232	−0.346616	−	0.938007i	$-0.612669\pi$
$19$	−3.02173	−0.693232	−0.346616	+	0.938007i	$0.612669\pi$
$20$	15.3270	3.42723
$21$	10.7822	2.35286
$22$	−4.24863	−0.905812
$23$	−3.71651	−0.774946	−0.387473	−	0.921881i	$-0.626652\pi$
$23$	−3.71651	−0.774946	−0.387473	+	0.921881i	$0.626652\pi$
$24$	−36.1780	−7.38481
$25$	1.98403	0.396806
$26$	8.62164	1.69084
$27$	19.1700	3.68927
$28$	18.3423	3.46636
$29$	4.48131	0.832159	0.416079	−	0.909328i	$-0.363404\pi$
$29$	4.48131	0.832159	0.416079	+	0.909328i	$0.363404\pi$
$30$	−25.1623	−4.59398
$31$	−2.77064	−0.497622	−0.248811	−	0.968552i	$-0.580040\pi$
$31$	−2.77064	−0.497622	−0.248811	+	0.968552i	$0.580040\pi$
$32$	−29.1502	−5.15307
$33$	5.18643	0.902842
$34$	0.462967	0.0793981
$35$	8.35797	1.41275
$36$	50.0105	8.33508
$37$	1.05579	0.173572	0.0867858	−	0.996227i	$-0.472340\pi$
$37$	1.05579	0.173572	0.0867858	+	0.996227i	$0.472340\pi$
$38$	8.43906	1.36900
$39$	−10.5247	−1.68530
$40$	−28.0440	−4.43414
$41$	7.11352	1.11095	0.555473	−	0.831535i	$-0.312537\pi$
$41$	7.11352	1.11095	0.555473	+	0.831535i	$0.312537\pi$
$42$	−30.1124	−4.64644
$43$	−7.56573	−1.15376	−0.576881	−	0.816828i	$-0.695730\pi$
$43$	−7.56573	−1.15376	−0.576881	+	0.816828i	$0.695730\pi$
$44$	8.82298	1.33011
$45$	22.7881	3.39706
$46$	10.3794	1.53037
$47$	2.34704	0.342351	0.171176	−	0.985241i	$-0.445243\pi$
$47$	2.34704	0.342351	0.171176	+	0.985241i	$0.445243\pi$
$48$	61.4927	8.87570
$49$	3.00221	0.428886
$50$	−5.54098	−0.783613
$51$	−0.565157	−0.0791378
$52$	−17.9042	−2.48287
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	−53.5379	−7.28559
$55$	4.02035	0.542104
$56$	−33.5610	−4.48478
$57$	−10.3018	−1.36451
$58$	−12.5154	−1.64335
$59$	−9.08942	−1.18334	−0.591671	−	0.806180i	$-0.701531\pi$
$59$	−9.08942	−1.18334	−0.591671	+	0.806180i	$0.701531\pi$
$60$	52.2536	6.74591
$61$	6.11238	0.782610	0.391305	−	0.920261i	$-0.372024\pi$
$61$	6.11238	0.782610	0.391305	+	0.920261i	$0.372024\pi$
$62$	7.73783	0.982706
$63$	27.2712	3.43585
$64$	45.3364	5.66705
$65$	−8.15838	−1.01192
$66$	−14.4846	−1.78294
$67$	5.99829	0.732807	0.366404	−	0.930456i	$-0.380589\pi$
$67$	5.99829	0.732807	0.366404	+	0.930456i	$0.380589\pi$
$68$	−0.961426	−0.116590
$69$	−12.6705	−1.52535
$70$	−23.3421	−2.78991
$71$	12.3581	1.46663	0.733317	−	0.679887i	$-0.237971\pi$
$71$	12.3581	1.46663	0.733317	+	0.679887i	$0.237971\pi$
$72$	−91.5046	−10.7839
$73$	10.5006	1.22901	0.614503	−	0.788914i	$-0.289356\pi$
$73$	10.5006	1.22901	0.614503	+	0.788914i	$0.289356\pi$
$74$	−2.94862	−0.342770
$75$	6.76404	0.781044
$76$	−17.5251	−2.01026
$77$	4.81126	0.548294
$78$	29.3933	3.32813
$79$	8.53624	0.960402	0.480201	−	0.877158i	$-0.340564\pi$
$79$	8.53624	0.960402	0.480201	+	0.877158i	$0.340564\pi$
$80$	47.6670	5.32933
$81$	39.4865	4.38738
$82$	−19.8666	−2.19390
$83$	−5.34613	−0.586814	−0.293407	−	0.955988i	$-0.594789\pi$
$83$	−5.34613	−0.586814	−0.293407	+	0.955988i	$0.594789\pi$
$84$	62.5332	6.82294
$85$	−0.438091	−0.0475176
$86$	21.1295	2.27845
$87$	15.2779	1.63796
$88$	−16.1435	−1.72090
$89$	−15.1104	−1.60169	−0.800847	−	0.598869i	$-0.795617\pi$
$89$	−15.1104	−1.60169	−0.800847	+	0.598869i	$0.795617\pi$
$90$	−63.6426	−6.70852
$91$	−9.76335	−1.02348
$92$	−21.5546	−2.24722
$93$	−9.44580	−0.979484
$94$	−6.55480	−0.676076
$95$	−7.98561	−0.819307
$96$	−99.3801	−10.1429
$97$	17.3610	1.76274	0.881370	−	0.472427i	$-0.156622\pi$
$97$	17.3610	1.76274	0.881370	+	0.472427i	$0.156622\pi$
$98$	−8.38454	−0.846966
$99$	13.1180	1.31841
$100$	11.5067	1.15067
$101$	−15.7977	−1.57193	−0.785965	−	0.618271i	$-0.787833\pi$
$101$	−15.7977	−1.57193	−0.785965	+	0.618271i	$0.787833\pi$
$102$	1.57837	0.156282
$103$	11.1528	1.09891	0.549457	−	0.835522i	$-0.314835\pi$
$103$	11.1528	1.09891	0.549457	+	0.835522i	$0.314835\pi$
$104$	32.7595	3.21234
$105$	28.4944	2.78077
$106$	2.79279	0.271260
$107$	−6.56524	−0.634686	−0.317343	−	0.948311i	$-0.602791\pi$
$107$	−6.56524	−0.634686	−0.317343	+	0.948311i	$0.602791\pi$
$108$	111.180	10.6983
$109$	0.943928	0.0904120	0.0452060	−	0.998978i	$-0.485606\pi$
$109$	0.943928	0.0904120	0.0452060	+	0.998978i	$0.485606\pi$
$110$	−11.2280	−1.07055
$111$	3.59946	0.341646
$112$	57.0444	5.39019
$113$	19.0630	1.79330	0.896648	−	0.442745i	$-0.145995\pi$
$113$	19.0630	1.79330	0.896648	+	0.442745i	$0.145995\pi$
$114$	28.7708	2.69463
$115$	−9.82174	−0.915882
$116$	25.9902	2.41313
$117$	−26.6199	−2.46101
$118$	25.3849	2.33686
$119$	−0.524275	−0.0480602
$120$	−95.6089	−8.72785
$121$	−8.68569	−0.789608
$122$	−17.0706	−1.54550
$123$	24.2517	2.18671
$124$	−16.0689	−1.44303
$125$	−7.97040	−0.712895
$126$	−76.1627	−6.78512
$127$	−8.89800	−0.789569	−0.394785	−	0.918774i	$-0.629181\pi$
$127$	−8.89800	−0.789569	−0.394785	+	0.918774i	$0.629181\pi$
$128$	−68.3147	−6.03822
$129$	−25.7934	−2.27098
$130$	22.7847	1.99835
$131$	−18.9361	−1.65446	−0.827228	−	0.561866i	$-0.810084\pi$
$131$	−18.9361	−1.65446	−0.827228	+	0.561866i	$0.810084\pi$
$132$	30.0797	2.61810
$133$	−9.55659	−0.828662
$134$	−16.7520	−1.44715
$135$	50.6612	4.36022
$136$	1.75913	0.150844
$137$	8.91004	0.761236	0.380618	−	0.924732i	$-0.375711\pi$
$137$	8.91004	0.761236	0.380618	+	0.924732i	$0.375711\pi$
$138$	35.3861	3.01226
$139$	7.03516	0.596715	0.298357	−	0.954454i	$-0.403561\pi$
$139$	7.03516	0.596715	0.298357	+	0.954454i	$0.403561\pi$
$140$	48.4736	4.09677
$141$	8.00164	0.673860
$142$	−34.5135	−2.89631
$143$	−4.69636	−0.392730
$144$	155.532	12.9610
$145$	11.8429	0.983500
$146$	−29.3261	−2.42705
$147$	10.2353	0.844190
$148$	6.12328	0.503331
$149$	−5.43878	−0.445562	−0.222781	−	0.974868i	$-0.571514\pi$
$149$	−5.43878	−0.445562	−0.222781	+	0.974868i	$0.571514\pi$
$150$	−18.8906	−1.54241
$151$	1.00000	0.0813788
$151$	1.00000	0.0813788
$152$	32.0658	2.60088
$153$	−1.42944	−0.115564
$154$	−13.4368	−1.08277
$155$	−7.32206	−0.588122
$156$	−61.0399	−4.88711
$157$	4.11878	0.328715	0.164357	−	0.986401i	$-0.447445\pi$
$157$	4.11878	0.328715	0.164357	+	0.986401i	$0.447445\pi$
$158$	−23.8400	−1.89660
$159$	−3.40925	−0.270371
$160$	−77.0361	−6.09024
$161$	−11.7539	−0.926340
$162$	−110.277	−8.66422
$163$	18.3424	1.43669	0.718344	−	0.695688i	$-0.244900\pi$
$163$	18.3424	1.43669	0.718344	+	0.695688i	$0.244900\pi$
$164$	41.2562	3.22157
$165$	13.7064	1.06704
$166$	14.9306	1.15884
$167$	−17.2435	−1.33434	−0.667170	−	0.744906i	$-0.732494\pi$
$167$	−17.2435	−1.33434	−0.667170	+	0.744906i	$0.732494\pi$
$168$	−114.418	−8.82751
$169$	−3.46980	−0.266908
$170$	1.22350	0.0938379
$171$	−26.0562	−1.99257
$172$	−43.8789	−3.34573
$173$	7.72314	0.587179	0.293590	−	0.955932i	$-0.405150\pi$
$173$	7.72314	0.587179	0.293590	+	0.955932i	$0.405150\pi$
$174$	−42.6680	−3.23465
$175$	6.27474	0.474326
$176$	27.4395	2.06833
$177$	−30.9880	−2.32920
$178$	42.2001	3.16303
$179$	1.89969	0.141990	0.0709948	−	0.997477i	$-0.477383\pi$
$179$	1.89969	0.141990	0.0709948	+	0.997477i	$0.477383\pi$
$180$	132.164	9.85094
$181$	−11.1133	−0.826042	−0.413021	−	0.910722i	$-0.635526\pi$
$181$	−11.1133	−0.826042	−0.413021	+	0.910722i	$0.635526\pi$
$182$	27.2670	2.02117
$183$	20.8386	1.54043
$184$	39.4387	2.90746
$185$	2.79018	0.205138
$186$	26.3802	1.93429
$187$	−0.252186	−0.0184417
$188$	13.6121	0.992765
$189$	60.6276	4.41001
$190$	22.3022	1.61797
$191$	−26.6640	−1.92934	−0.964669	−	0.263465i	$-0.915135\pi$
$191$	−26.6640	−1.92934	−0.964669	+	0.263465i	$0.915135\pi$
$192$	154.563	11.1546
$193$	20.2688	1.45898	0.729491	−	0.683990i	$-0.239757\pi$
$193$	20.2688	1.45898	0.729491	+	0.683990i	$0.239757\pi$
$194$	−48.4856	−3.48106
$195$	−27.8139	−1.99180
$196$	17.4119	1.24370
$197$	26.6551	1.89910	0.949548	−	0.313623i	$-0.101543\pi$
$197$	26.6551	1.89910	0.949548	+	0.313623i	$0.101543\pi$
$198$	−36.6358	−2.60359
$199$	−0.956757	−0.0678227	−0.0339114	−	0.999425i	$-0.510796\pi$
$199$	−0.956757	−0.0678227	−0.0339114	+	0.999425i	$0.510796\pi$
$200$	−21.0540	−1.48874
$201$	20.4496	1.44241
$202$	44.1197	3.10425
$203$	14.1727	0.994730
$204$	−3.27774	−0.229487
$205$	18.7991	1.31299
$206$	−31.1473	−2.17014
$207$	−32.0473	−2.22744
$208$	−55.6821	−3.86086
$209$	−4.59691	−0.317975
$210$	−79.5789	−5.49146
$211$	7.98963	0.550029	0.275015	−	0.961440i	$-0.411317\pi$
$211$	7.98963	0.550029	0.275015	+	0.961440i	$0.411317\pi$
$212$	−5.79969	−0.398324
$213$	42.1317	2.88682
$214$	18.3354	1.25338
$215$	−19.9942	−1.36359
$216$	−203.427	−13.8415
$217$	−8.76251	−0.594838
$218$	−2.63620	−0.178546
$219$	35.7992	2.41909
$220$	23.3168	1.57202
$221$	0.511755	0.0344244
$222$	−10.0526	−0.674683
$223$	28.3393	1.89774	0.948871	−	0.315664i	$-0.102227\pi$
$223$	28.3393	1.89774	0.948871	+	0.315664i	$0.102227\pi$
$224$	−92.1911	−6.15978
$225$	17.1082	1.14055
$226$	−53.2390	−3.54140
$227$	−25.1412	−1.66868	−0.834340	−	0.551250i	$-0.814151\pi$
$227$	−25.1412	−1.66868	−0.834340	+	0.551250i	$0.814151\pi$
$228$	−59.7473	−3.95686
$229$	8.54268	0.564516	0.282258	−	0.959338i	$-0.408917\pi$
$229$	8.54268	0.564516	0.282258	+	0.959338i	$0.408917\pi$
$230$	27.4301	1.80869
$231$	16.4028	1.07922
$232$	−47.5546	−3.12211
$233$	−9.52413	−0.623947	−0.311973	−	0.950091i	$-0.600990\pi$
$233$	−9.52413	−0.623947	−0.311973	+	0.950091i	$0.600990\pi$
$234$	74.3440	4.86002
$235$	6.20260	0.404613
$236$	−52.7158	−3.43151
$237$	29.1021	1.89039
$238$	1.46419	0.0949093
$239$	8.73804	0.565217	0.282608	−	0.959235i	$-0.408800\pi$
$239$	8.73804	0.565217	0.282608	+	0.959235i	$0.408800\pi$
$240$	162.509	10.4899
$241$	24.3057	1.56567	0.782834	−	0.622230i	$-0.213773\pi$
$241$	24.3057	1.56567	0.782834	+	0.622230i	$0.213773\pi$
$242$	24.2573	1.55932
$243$	77.1089	4.94654
$244$	35.4499	2.26945
$245$	7.93402	0.506886
$246$	−67.7301	−4.31831
$247$	9.32838	0.593551
$248$	29.4014	1.86699
$249$	−18.2263	−1.15504
$250$	22.2597	1.40783
$251$	−13.9737	−0.882013	−0.441006	−	0.897504i	$-0.645378\pi$
$251$	−13.9737	−0.882013	−0.441006	+	0.897504i	$0.645378\pi$
$252$	158.164	9.96342
$253$	−5.65388	−0.355456
$254$	24.8503	1.55924
$255$	−1.49356	−0.0935302
$256$	100.116	6.25725
$257$	6.25915	0.390435	0.195217	−	0.980760i	$-0.437459\pi$
$257$	6.25915	0.390435	0.195217	+	0.980760i	$0.437459\pi$
$258$	72.0357	4.48475
$259$	3.33908	0.207481
$260$	−47.3161	−2.93442
$261$	38.6422	2.39189
$262$	52.8846	3.26722
$263$	−24.2409	−1.49476	−0.747378	−	0.664399i	$-0.768687\pi$
$263$	−24.2409	−1.49476	−0.747378	+	0.664399i	$0.768687\pi$
$264$	−55.0371	−3.38730
$265$	−2.64273	−0.162342
$266$	26.6896	1.63644
$267$	−51.5149	−3.15266
$268$	34.7882	2.12503
$269$	11.6427	0.709867	0.354933	−	0.934892i	$-0.384504\pi$
$269$	11.6427	0.709867	0.354933	+	0.934892i	$0.384504\pi$
$270$	−141.486	−8.61058
$271$	−5.06948	−0.307949	−0.153975	−	0.988075i	$-0.549207\pi$
$271$	−5.06948	−0.307949	−0.153975	+	0.988075i	$0.549207\pi$
$272$	−2.99003	−0.181297
$273$	−33.2857	−2.01454
$274$	−24.8839	−1.50329
$275$	3.01827	0.182009
$276$	−73.4850	−4.42328
$277$	20.3679	1.22379	0.611895	−	0.790939i	$-0.290408\pi$
$277$	20.3679	1.22379	0.611895	+	0.790939i	$0.290408\pi$
$278$	−19.6477	−1.17839
$279$	−23.8911	−1.43032
$280$	−88.6927	−5.30040
$281$	−3.12641	−0.186506	−0.0932530	−	0.995642i	$-0.529727\pi$
$281$	−3.12641	−0.186506	−0.0932530	+	0.995642i	$0.529727\pi$
$282$	−22.3469	−1.33074
$283$	−2.96933	−0.176508	−0.0882541	−	0.996098i	$-0.528129\pi$
$283$	−2.96933	−0.176508	−0.0882541	+	0.996098i	$0.528129\pi$
$284$	71.6730	4.25301
$285$	−27.2249	−1.61266
$286$	13.1160	0.775563
$287$	22.4974	1.32798
$288$	−251.361	−14.8116
$289$	−16.9725	−0.998384
$290$	−33.0748	−1.94222
$291$	59.1878	3.46965
$292$	60.9004	3.56393
$293$	−0.910323	−0.0531816	−0.0265908	−	0.999646i	$-0.508465\pi$
$293$	−0.910323	−0.0531816	−0.0265908	+	0.999646i	$0.508465\pi$
$294$	−28.5849	−1.66711
$295$	−24.0209	−1.39855
$296$	−11.2038	−0.651209
$297$	29.1631	1.69221
$298$	15.1894	0.879897
$299$	11.4733	0.663515
$300$	39.2293	2.26491
$301$	−23.9276	−1.37916
$302$	−2.79279	−0.160707
$303$	−53.8582	−3.09407
$304$	−54.5030	−3.12596
$305$	16.1534	0.924940
$306$	3.99214	0.228215
$307$	5.71222	0.326013	0.163007	−	0.986625i	$-0.447881\pi$
$307$	5.71222	0.326013	0.163007	+	0.986625i	$0.447881\pi$
$308$	27.9038	1.58997
$309$	38.0225	2.16302
$310$	20.4490	1.16143
$311$	5.42274	0.307495	0.153748	−	0.988110i	$-0.450866\pi$
$311$	5.42274	0.307495	0.153748	+	0.988110i	$0.450866\pi$
$312$	111.685	6.32294
$313$	−2.82638	−0.159756	−0.0798782	−	0.996805i	$-0.525453\pi$
$313$	−2.82638	−0.159756	−0.0798782	+	0.996805i	$0.525453\pi$
$314$	−11.5029	−0.649147
$315$	72.0704	4.06071
$316$	49.5076	2.78502
$317$	2.52393	0.141758	0.0708791	−	0.997485i	$-0.477420\pi$
$317$	2.52393	0.141758	0.0708791	+	0.997485i	$0.477420\pi$
$318$	9.52131	0.533929
$319$	6.81735	0.381699
$320$	119.812	6.69768
$321$	−22.3825	−1.24927
$322$	32.8263	1.82934
$323$	0.500917	0.0278718
$324$	229.009	12.7227
$325$	−6.12490	−0.339748
$326$	−51.2266	−2.83718
$327$	3.21808	0.177960
$328$	−75.4869	−4.16807
$329$	7.42282	0.409233
$330$	−38.2790	−2.10719
$331$	14.9839	0.823587	0.411794	−	0.911277i	$-0.364902\pi$
$331$	14.9839	0.823587	0.411794	+	0.911277i	$0.364902\pi$
$332$	−31.0059	−1.70167
$333$	9.10407	0.498900
$334$	48.1574	2.63506
$335$	15.8519	0.866079
$336$	194.478	10.6097
$337$	13.7625	0.749693	0.374846	−	0.927087i	$-0.377695\pi$
$337$	13.7625	0.749693	0.374846	+	0.927087i	$0.377695\pi$
$338$	9.69043	0.527090
$339$	64.9904	3.52979
$340$	−2.54079	−0.137794
$341$	−4.21494	−0.228252
$342$	72.7696	3.93493
$343$	−12.6435	−0.682686
$344$	80.2856	4.32871
$345$	−33.4847	−1.80276
$346$	−21.5691	−1.15956
$347$	−4.05674	−0.217777	−0.108889	−	0.994054i	$-0.534729\pi$
$347$	−4.05674	−0.217777	−0.108889	+	0.994054i	$0.534729\pi$
$348$	88.6071	4.74984
$349$	−2.03062	−0.108697	−0.0543484	−	0.998522i	$-0.517308\pi$
$349$	−2.03062	−0.108697	−0.0543484	+	0.998522i	$0.517308\pi$
$350$	−17.5240	−0.936700
$351$	−59.1798	−3.15879
$352$	−44.3457	−2.36364
$353$	30.4506	1.62072	0.810362	−	0.585930i	$-0.199271\pi$
$353$	30.4506	1.62072	0.810362	+	0.585930i	$0.199271\pi$
$354$	86.5432	4.59972
$355$	32.6591	1.73336
$356$	−87.6354	−4.64467
$357$	−1.78738	−0.0945982
$358$	−5.30544	−0.280401
$359$	−4.58939	−0.242219	−0.121109	−	0.992639i	$-0.538645\pi$
$359$	−4.58939	−0.242219	−0.121109	+	0.992639i	$0.538645\pi$
$360$	−241.822	−12.7451
$361$	−9.86916	−0.519430
$362$	31.0370	1.63127
$363$	−29.6117	−1.55421
$364$	−56.6244	−2.96793
$365$	27.7504	1.45252
$366$	−58.1979	−3.04205
$367$	−18.9786	−0.990674	−0.495337	−	0.868701i	$-0.664955\pi$
$367$	−18.9786	−0.990674	−0.495337	+	0.868701i	$0.664955\pi$
$368$	−67.0348	−3.49443
$369$	61.3396	3.19321
$370$	−7.79240	−0.405108
$371$	−3.16263	−0.164195
$372$	−54.7827	−2.84035
$373$	9.81235	0.508064	0.254032	−	0.967196i	$-0.418243\pi$
$373$	9.81235	0.508064	0.254032	+	0.967196i	$0.418243\pi$
$374$	0.704304	0.0364187
$375$	−27.1731	−1.40321
$376$	−24.9062	−1.28444
$377$	−13.8343	−0.712501
$378$	−169.320	−8.70890
$379$	−33.1417	−1.70237	−0.851186	−	0.524864i	$-0.824116\pi$
$379$	−33.1417	−1.70237	−0.851186	+	0.524864i	$0.824116\pi$
$380$	−46.3141	−2.37586
$381$	−30.3354	−1.55413
$382$	74.4670	3.81006
$383$	2.76840	0.141459	0.0707293	−	0.997496i	$-0.477467\pi$
$383$	2.76840	0.141459	0.0707293	+	0.997496i	$0.477467\pi$
$384$	−232.902	−11.8852
$385$	12.7149	0.648009
$386$	−56.6067	−2.88120
$387$	−65.2389	−3.31628
$388$	100.688	5.11167
$389$	−26.7282	−1.35517	−0.677587	−	0.735442i	$-0.736974\pi$
$389$	−26.7282	−1.35517	−0.677587	+	0.735442i	$0.736974\pi$
$390$	77.6785	3.93340
$391$	0.616093	0.0311572
$392$	−31.8586	−1.60910
$393$	−64.5579	−3.25651
$394$	−74.4421	−3.75034
$395$	22.5590	1.13507
$396$	76.0802	3.82317
$397$	8.72177	0.437733	0.218866	−	0.975755i	$-0.429764\pi$
$397$	8.72177	0.437733	0.218866	+	0.975755i	$0.429764\pi$
$398$	2.67202	0.133936
$399$	−32.5808	−1.63108
$400$	35.7860	1.78930
$401$	14.7502	0.736588	0.368294	−	0.929709i	$-0.379942\pi$
$401$	14.7502	0.736588	0.368294	+	0.929709i	$0.379942\pi$
$402$	−57.1116	−2.84847
$403$	8.55326	0.426068
$404$	−91.6218	−4.55835
$405$	104.352	5.18530
$406$	−39.5815	−1.96439
$407$	1.60617	0.0796146
$408$	5.99730	0.296911
$409$	−38.6742	−1.91232	−0.956158	−	0.292850i	$-0.905396\pi$
$409$	−38.6742	−1.91232	−0.956158	+	0.292850i	$0.905396\pi$
$410$	−52.5021	−2.59289
$411$	30.3765	1.49836
$412$	64.6825	3.18668
$413$	−28.7464	−1.41452
$414$	89.5015	4.39876
$415$	−14.1284	−0.693535
$416$	89.9896	4.41210
$417$	23.9846	1.17453
$418$	12.8382	0.627938
$419$	0.373425	0.0182430	0.00912151	−	0.999958i	$-0.497096\pi$
$419$	0.373425	0.0182430	0.00912151	+	0.999958i	$0.497096\pi$
$420$	165.259	8.06379
$421$	−11.0816	−0.540085	−0.270042	−	0.962848i	$-0.587038\pi$
$421$	−11.0816	−0.540085	−0.270042	+	0.962848i	$0.587038\pi$
$422$	−22.3134	−1.08620
$423$	20.2384	0.984026
$424$	10.6117	0.515352
$425$	−0.328896	−0.0159538
$426$	−117.665	−5.70089
$427$	19.3312	0.935501
$428$	−38.0764	−1.84049
$429$	−16.0111	−0.773021
$430$	55.8396	2.69283
$431$	−24.7324	−1.19132	−0.595658	−	0.803238i	$-0.703109\pi$
$431$	−24.7324	−1.19132	−0.595658	+	0.803238i	$0.703109\pi$
$432$	345.770	16.6359
$433$	−38.9077	−1.86978	−0.934892	−	0.354933i	$-0.884504\pi$
$433$	−38.9077	−1.86978	−0.934892	+	0.354933i	$0.884504\pi$
$434$	24.4719	1.17469
$435$	40.3754	1.93585
$436$	5.47449	0.262181
$437$	11.2303	0.537218
$438$	−99.9799	−4.77722
$439$	−19.1826	−0.915534	−0.457767	−	0.889072i	$-0.651351\pi$
$439$	−19.1826	−0.915534	−0.457767	+	0.889072i	$0.651351\pi$
$440$	−42.6629	−2.03387
$441$	25.8879	1.23276
$442$	−1.42922	−0.0679813
$443$	3.51378	0.166945	0.0834723	−	0.996510i	$-0.473399\pi$
$443$	3.51378	0.166945	0.0834723	+	0.996510i	$0.473399\pi$
$444$	20.8758	0.990720
$445$	−39.9326	−1.89299
$446$	−79.1459	−3.74767
$447$	−18.5421	−0.877013
$448$	143.382	6.77416
$449$	−31.5482	−1.48885	−0.744425	−	0.667706i	$-0.767277\pi$
$449$	−31.5482	−1.48885	−0.744425	+	0.667706i	$0.767277\pi$
$450$	−47.7796	−2.25235
$451$	10.8217	0.509574
$452$	110.559	5.20028
$453$	3.40925	0.160180
$454$	70.2142	3.29531
$455$	−25.8019	−1.20961
$456$	109.320	5.11939
$457$	−11.3458	−0.530736	−0.265368	−	0.964147i	$-0.585493\pi$
$457$	−11.3458	−0.530736	−0.265368	+	0.964147i	$0.585493\pi$
$458$	−23.8579	−1.11481
$459$	−3.17785	−0.148329
$460$	−56.9631	−2.65592
$461$	−11.7202	−0.545865	−0.272932	−	0.962033i	$-0.587994\pi$
$461$	−11.7202	−0.545865	−0.272932	+	0.962033i	$0.587994\pi$
$462$	−45.8095	−2.13125
$463$	6.64387	0.308767	0.154383	−	0.988011i	$-0.450661\pi$
$463$	6.64387	0.308767	0.154383	+	0.988011i	$0.450661\pi$
$464$	80.8296	3.75242
$465$	−24.9627	−1.15762
$466$	26.5989	1.23217
$467$	−18.6131	−0.861310	−0.430655	−	0.902517i	$-0.641717\pi$
$467$	−18.6131	−0.861310	−0.430655	+	0.902517i	$0.641717\pi$
$468$	−154.387	−7.13656
$469$	18.9703	0.875969
$470$	−17.3226	−0.799031
$471$	14.0419	0.647019
$472$	96.4546	4.43968
$473$	−11.5096	−0.529213
$474$	−81.2762	−3.73314
$475$	−5.99519	−0.275078
$476$	−3.04063	−0.139367
$477$	−8.62295	−0.394818
$478$	−24.4035	−1.11619
$479$	6.64345	0.303547	0.151773	−	0.988415i	$-0.451502\pi$
$479$	6.64345	0.303547	0.151773	+	0.988415i	$0.451502\pi$
$480$	−262.635	−11.9876
$481$	−3.25935	−0.148613
$482$	−67.8808	−3.09189
$483$	−40.0721	−1.82334
$484$	−50.3743	−2.28974
$485$	45.8804	2.08332
$486$	−215.349	−9.76844
$487$	−31.8382	−1.44273	−0.721364	−	0.692556i	$-0.756485\pi$
$487$	−31.8382	−1.44273	−0.721364	+	0.692556i	$0.756485\pi$
$488$	−64.8631	−2.93621
$489$	62.5338	2.82788
$490$	−22.1581	−1.00100
$491$	−7.05164	−0.318236	−0.159118	−	0.987260i	$-0.550865\pi$
$491$	−7.05164	−0.318236	−0.159118	+	0.987260i	$0.550865\pi$
$492$	140.653	6.34111
$493$	−0.742876	−0.0334574
$494$	−26.0522	−1.17215
$495$	34.6673	1.55818
$496$	−49.9742	−2.24391
$497$	39.0840	1.75316
$498$	50.9022	2.28098
$499$	28.8664	1.29224	0.646119	−	0.763236i	$-0.276391\pi$
$499$	28.8664	1.29224	0.646119	+	0.763236i	$0.276391\pi$
$500$	−46.2259	−2.06728
$501$	−58.7872	−2.62642
$502$	39.0257	1.74180
$503$	6.00702	0.267840	0.133920	−	0.990992i	$-0.457244\pi$
$503$	6.00702	0.267840	0.133920	+	0.990992i	$0.457244\pi$
$504$	−289.395	−12.8907
$505$	−41.7491	−1.85781
$506$	15.7901	0.701956
$507$	−11.8294	−0.525362
$508$	−51.6056	−2.28963
$509$	−5.41661	−0.240087	−0.120043	−	0.992769i	$-0.538303\pi$
$509$	−5.41661	−0.240087	−0.120043	+	0.992769i	$0.538303\pi$
$510$	4.17120	0.184704
$511$	33.2096	1.46911
$512$	−142.974	−6.31861
$513$	−57.9266	−2.55752
$514$	−17.4805	−0.771032
$515$	29.4737	1.29877
$516$	−149.594	−6.58550
$517$	3.57052	0.157031
$518$	−9.32537	−0.409733
$519$	26.3301	1.15576
$520$	86.5747	3.79655
$521$	−5.00854	−0.219428	−0.109714	−	0.993963i	$-0.534994\pi$
$521$	−5.00854	−0.219428	−0.109714	+	0.993963i	$0.534994\pi$
$522$	−107.920	−4.72351
$523$	0.0363510	0.00158952	0.000794759	−	1.00000i	$-0.499747\pi$
$523$	0.0363510	0.00158952	0.000794759		1.00000i	$0.499747\pi$
$524$	−109.824	−4.79767
$525$	21.3921	0.933629
$526$	67.6997	2.95185
$527$	0.459295	0.0200072
$528$	93.5479	4.07115
$529$	−9.18753	−0.399458
$530$	7.38060	0.320593
$531$	−78.3776	−3.40130
$532$	−55.4253	−2.40299
$533$	−21.9602	−0.951201
$534$	143.870	6.22588
$535$	−17.3502	−0.750113
$536$	−63.6523	−2.74936
$537$	6.47651	0.279482
$538$	−32.5156	−1.40185
$539$	4.56721	0.196724
$540$	293.819	12.6440
$541$	20.7724	0.893074	0.446537	−	0.894765i	$-0.352657\pi$
$541$	20.7724	0.893074	0.446537	+	0.894765i	$0.352657\pi$
$542$	14.1580	0.608139
$543$	−37.8878	−1.62592
$544$	4.83228	0.207182
$545$	2.49455	0.106855
$546$	92.9599	3.97832
$547$	−41.2983	−1.76579	−0.882895	−	0.469571i	$-0.844409\pi$
$547$	−41.2983	−1.76579	−0.882895	+	0.469571i	$0.844409\pi$
$548$	51.6755	2.20747
$549$	52.7068	2.24947
$550$	−8.42941	−0.359431
$551$	−13.5413	−0.576879
$552$	134.456	5.72283
$553$	26.9969	1.14803
$554$	−56.8833	−2.41674
$555$	9.51241	0.403780
$556$	40.8018	1.73038
$557$	−14.6650	−0.621374	−0.310687	−	0.950512i	$-0.600559\pi$
$557$	−14.6650	−0.621374	−0.310687	+	0.950512i	$0.600559\pi$
$558$	66.7230	2.82461
$559$	23.3562	0.987861
$560$	150.753	6.37048
$561$	−0.859765	−0.0362993
$562$	8.73141	0.368312
$563$	28.0238	1.18106	0.590532	−	0.807014i	$-0.298918\pi$
$563$	28.0238	1.18106	0.590532	+	0.807014i	$0.298918\pi$
$564$	46.4070	1.95409
$565$	50.3784	2.11943
$566$	8.29272	0.348569
$567$	124.881	5.24451
$568$	−131.141	−5.50255
$569$	−18.7602	−0.786467	−0.393234	−	0.919439i	$-0.628644\pi$
$569$	−18.7602	−0.786467	−0.393234	+	0.919439i	$0.628644\pi$
$570$	76.0335	3.18469
$571$	−39.0729	−1.63515	−0.817575	−	0.575822i	$-0.804682\pi$
$571$	−39.0729	−1.63515	−0.817575	+	0.575822i	$0.804682\pi$
$572$	−27.2375	−1.13886
$573$	−90.9040	−3.79757
$574$	−62.8306	−2.62250
$575$	−7.37367	−0.307503
$576$	390.933	16.2889
$577$	−42.0695	−1.75138	−0.875689	−	0.482876i	$-0.839592\pi$
$577$	−42.0695	−1.75138	−0.875689	+	0.482876i	$0.839592\pi$
$578$	47.4007	1.97161
$579$	69.1014	2.87176
$580$	68.6852	2.85200
$581$	−16.9078	−0.701454
$582$	−165.299	−6.85188
$583$	−1.52129	−0.0630052
$584$	−111.430	−4.61101
$585$	−70.3493	−2.90859
$586$	2.54234	0.105023
$587$	23.2407	0.959247	0.479624	−	0.877474i	$-0.340773\pi$
$587$	23.2407	0.959247	0.479624	+	0.877474i	$0.340773\pi$
$588$	59.3613	2.44802
$589$	8.37213	0.344968
$590$	67.0853	2.76186
$591$	90.8737	3.73804
$592$	19.0434	0.782679
$593$	−12.4341	−0.510607	−0.255304	−	0.966861i	$-0.582175\pi$
$593$	−12.4341	−0.510607	−0.255304	+	0.966861i	$0.582175\pi$
$594$	−81.4464	−3.34179
$595$	−1.38552	−0.0568006
$596$	−31.5432	−1.29206
$597$	−3.26182	−0.133497
$598$	−32.0424	−1.31031
$599$	−14.4548	−0.590606	−0.295303	−	0.955404i	$-0.595421\pi$
$599$	−14.4548	−0.590606	−0.295303	+	0.955404i	$0.595421\pi$
$600$	−71.7783	−2.93034
$601$	29.8521	1.21769	0.608846	−	0.793288i	$-0.291633\pi$
$601$	29.8521	1.21769	0.608846	+	0.793288i	$0.291633\pi$
$602$	66.8247	2.72357
$603$	51.7229	2.10632
$604$	5.79969	0.235986
$605$	−22.9539	−0.933211
$606$	150.415	6.11019
$607$	−11.2942	−0.458416	−0.229208	−	0.973377i	$-0.573614\pi$
$607$	−11.2942	−0.458416	−0.229208	+	0.973377i	$0.573614\pi$
$608$	88.0839	3.57227
$609$	48.3183	1.95796
$610$	−45.1130	−1.82657
$611$	−7.24556	−0.293124
$612$	−8.29033	−0.335117
$613$	−5.16448	−0.208592	−0.104296	−	0.994546i	$-0.533259\pi$
$613$	−5.16448	−0.208592	−0.104296	+	0.994546i	$0.533259\pi$
$614$	−15.9530	−0.643812
$615$	64.0908	2.58439
$616$	−51.0558	−2.05710
$617$	−34.9324	−1.40632	−0.703162	−	0.711029i	$-0.748229\pi$
$617$	−34.9324	−1.40632	−0.703162	+	0.711029i	$0.748229\pi$
$618$	−106.189	−4.27154
$619$	−13.6582	−0.548971	−0.274485	−	0.961591i	$-0.588507\pi$
$619$	−13.6582	−0.548971	−0.274485	+	0.961591i	$0.588507\pi$
$620$	−42.4657	−1.70546
$621$	−71.2456	−2.85899
$622$	−15.1446	−0.607243
$623$	−47.7884	−1.91460
$624$	−189.834	−7.59945
$625$	−30.9838	−1.23935
$626$	7.89349	0.315487
$627$	−15.6720	−0.625879
$628$	23.8877	0.953222
$629$	−0.175021	−0.00697855
$630$	−201.278	−8.01909
$631$	−28.4436	−1.13232	−0.566161	−	0.824294i	$-0.691572\pi$
$631$	−28.4436	−1.13232	−0.566161	+	0.824294i	$0.691572\pi$
$632$	−90.5844	−3.60326
$633$	27.2386	1.08264
$634$	−7.04882	−0.279944
$635$	−23.5150	−0.933165
$636$	−19.7726	−0.784033
$637$	−9.26811	−0.367216
$638$	−19.0395	−0.753779
$639$	106.563	4.21557
$640$	−180.537	−7.13637
$641$	−3.66442	−0.144736	−0.0723680	−	0.997378i	$-0.523056\pi$
$641$	−3.66442	−0.144736	−0.0723680	+	0.997378i	$0.523056\pi$
$642$	62.5097	2.46706
$643$	−0.0230049	−0.000907224 0	−0.000453612	−	1.00000i	$-0.500144\pi$
$643$	−0.0230049	−0.000907224 0	−0.000453612		1.00000i	$0.500144\pi$
$644$	−68.1692	−2.68624
$645$	−68.1651	−2.68400
$646$	−1.39896	−0.0550413
$647$	−1.71975	−0.0676105	−0.0338052	−	0.999428i	$-0.510763\pi$
$647$	−1.71975	−0.0676105	−0.0338052	+	0.999428i	$0.510763\pi$
$648$	−419.020	−16.4607
$649$	−13.8276	−0.542780
$650$	17.1056	0.670936
$651$	−29.8735	−1.17084
$652$	106.380	4.16618
$653$	8.44514	0.330484	0.165242	−	0.986253i	$-0.447160\pi$
$653$	8.44514	0.330484	0.165242	+	0.986253i	$0.447160\pi$
$654$	−8.98744	−0.351437
$655$	−50.0431	−1.95534
$656$	128.307	5.00954
$657$	90.5465	3.53256
$658$	−20.7304	−0.808154
$659$	8.85856	0.345080	0.172540	−	0.985002i	$-0.444803\pi$
$659$	8.85856	0.345080	0.172540	+	0.985002i	$0.444803\pi$
$660$	79.4926	3.09425
$661$	−39.5463	−1.53817	−0.769087	−	0.639144i	$-0.779289\pi$
$661$	−39.5463	−1.53817	−0.769087	+	0.639144i	$0.779289\pi$
$662$	−41.8468	−1.62642
$663$	1.74470	0.0677584
$664$	56.7318	2.20162
$665$	−25.2555	−0.979367
$666$	−25.4258	−0.985229
$667$	−16.6549	−0.644879
$668$	−100.007	−3.86938
$669$	96.6157	3.73538
$670$	−44.2709	−1.71034
$671$	9.29868	0.358971
$672$	−314.302	−12.1245
$673$	10.7219	0.413298	0.206649	−	0.978415i	$-0.433744\pi$
$673$	10.7219	0.413298	0.206649	+	0.978415i	$0.433744\pi$
$674$	−38.4359	−1.48050
$675$	38.0339	1.46392
$676$	−20.1238	−0.773991
$677$	−48.9632	−1.88181	−0.940903	−	0.338675i	$-0.890021\pi$
$677$	−48.9632	−1.88181	−0.940903	+	0.338675i	$0.890021\pi$
$678$	−181.505	−6.97065
$679$	54.9063	2.10711
$680$	4.64891	0.178277
$681$	−85.7125	−3.28451
$682$	11.7714	0.450752
$683$	21.0604	0.805852	0.402926	−	0.915233i	$-0.367993\pi$
$683$	21.0604	0.805852	0.402926	+	0.915233i	$0.367993\pi$
$684$	−151.118	−5.77814
$685$	23.5469	0.899679
$686$	35.3108	1.34817
$687$	29.1241	1.11115
$688$	−136.463	−5.20261
$689$	3.08710	0.117609
$690$	93.5159	3.56009
$691$	−36.9792	−1.40676	−0.703378	−	0.710816i	$-0.748326\pi$
$691$	−36.9792	−1.40676	−0.703378	+	0.710816i	$0.748326\pi$
$692$	44.7918	1.70273
$693$	41.4872	1.57597
$694$	11.3296	0.430067
$695$	18.5920	0.705236
$696$	−162.125	−6.14534
$697$	−1.17922	−0.0446662
$698$	5.67111	0.214655
$699$	−32.4701	−1.22813
$700$	36.3915	1.37547
$701$	42.3310	1.59882	0.799410	−	0.600785i	$-0.205145\pi$
$701$	42.3310	1.59882	0.799410	+	0.600785i	$0.205145\pi$
$702$	165.277	6.23798
$703$	−3.19032	−0.120325
$704$	68.9695	2.59939
$705$	21.1462	0.796411
$706$	−85.0423	−3.20061
$707$	−49.9622	−1.87902
$708$	−179.721	−6.75433
$709$	−45.2746	−1.70032	−0.850161	−	0.526523i	$-0.823495\pi$
$709$	−45.2746	−1.70032	−0.850161	+	0.526523i	$0.823495\pi$
$710$	−91.2100	−3.42305
$711$	73.6076	2.76050
$712$	160.347	6.00927
$713$	10.2971	0.385631
$714$	4.99178	0.186813
$715$	−12.4112	−0.464153
$716$	11.0176	0.411748
$717$	29.7901	1.11253
$718$	12.8172	0.478334
$719$	−3.29101	−0.122734	−0.0613669	−	0.998115i	$-0.519546\pi$
$719$	−3.29101	−0.122734	−0.0613669	+	0.998115i	$0.519546\pi$
$720$	411.030	15.3182
$721$	35.2720	1.31360
$722$	27.5625	1.02577
$723$	82.8641	3.08175
$724$	−64.4534	−2.39539
$725$	8.89105	0.330205
$726$	82.6992	3.06926
$727$	0.291756	0.0108206	0.00541031	−	0.999985i	$-0.498278\pi$
$727$	0.291756	0.0108206	0.00541031	+	0.999985i	$0.498278\pi$
$728$	103.606	3.83990
$729$	144.424	5.34903
$730$	−77.5010	−2.86844
$731$	1.25419	0.0463877
$732$	120.857	4.46702
$733$	32.0074	1.18222	0.591109	−	0.806591i	$-0.298690\pi$
$733$	32.0074	1.18222	0.591109	+	0.806591i	$0.298690\pi$
$734$	53.0033	1.95639
$735$	27.0490	0.997718
$736$	108.337	3.99336
$737$	9.12510	0.336128
$738$	−171.309	−6.30596
$739$	−13.9514	−0.513211	−0.256606	−	0.966516i	$-0.582604\pi$
$739$	−13.9514	−0.513211	−0.256606	+	0.966516i	$0.582604\pi$
$740$	16.1822	0.594869
$741$	31.8027	1.16830
$742$	8.83256	0.324253
$743$	−21.3794	−0.784333	−0.392166	−	0.919894i	$-0.628274\pi$
$743$	−21.3794	−0.784333	−0.392166	+	0.919894i	$0.628274\pi$
$744$	100.236	3.67485
$745$	−14.3732	−0.526595
$746$	−27.4039	−1.00333
$747$	−46.0994	−1.68669
$748$	−1.46260	−0.0534781
$749$	−20.7634	−0.758678
$750$	75.8887	2.77106
$751$	−34.7134	−1.26671	−0.633354	−	0.773862i	$-0.718322\pi$
$751$	−34.7134	−1.26671	−0.633354	+	0.773862i	$0.718322\pi$
$752$	42.3337	1.54375
$753$	−47.6398	−1.73609
$754$	38.6362	1.40705
$755$	2.64273	0.0961788
$756$	351.621	12.7883
$757$	35.9194	1.30551	0.652756	−	0.757568i	$-0.273613\pi$
$757$	35.9194	1.30551	0.652756	+	0.757568i	$0.273613\pi$
$758$	92.5578	3.36185
$759$	−19.2754	−0.699654
$760$	84.7413	3.07389
$761$	−21.1632	−0.767165	−0.383582	−	0.923507i	$-0.625310\pi$
$761$	−21.1632	−0.767165	−0.383582	+	0.923507i	$0.625310\pi$
$762$	84.7206	3.06910
$763$	2.98529	0.108075
$764$	−154.643	−5.59478
$765$	−3.77763	−0.136581
$766$	−7.73157	−0.279353
$767$	28.0600	1.01319
$768$	341.320	12.3163
$769$	−24.0963	−0.868934	−0.434467	−	0.900688i	$-0.643063\pi$
$769$	−24.0963	−0.868934	−0.434467	+	0.900688i	$0.643063\pi$
$770$	−35.5100	−1.27969
$771$	21.3390	0.768504
$772$	117.553	4.23082
$773$	−30.0257	−1.07995	−0.539974	−	0.841682i	$-0.681566\pi$
$773$	−30.0257	−1.07995	−0.539974	+	0.841682i	$0.681566\pi$
$774$	182.199	6.54900
$775$	−5.49703	−0.197459
$776$	−184.230	−6.61348
$777$	11.3838	0.408390
$778$	74.6464	2.67620
$779$	−21.4951	−0.770143
$780$	−161.312	−5.77590
$781$	18.8002	0.672723
$782$	−1.72062	−0.0615293
$783$	85.9069	3.07006
$784$	54.1509	1.93396
$785$	10.8848	0.388497
$786$	180.297	6.43097
$787$	−19.9602	−0.711504	−0.355752	−	0.934580i	$-0.615775\pi$
$787$	−19.9602	−0.711504	−0.355752	+	0.934580i	$0.615775\pi$
$788$	154.591	5.50708
$789$	−82.6431	−2.94217
$790$	−63.0026	−2.24153
$791$	60.2891	2.14363
$792$	−139.205	−4.94642
$793$	−18.8695	−0.670077
$794$	−24.3581	−0.864436
$795$	−9.00972	−0.319542
$796$	−5.54889	−0.196675
$797$	40.1578	1.42246	0.711231	−	0.702959i	$-0.248138\pi$
$797$	40.1578	1.42246	0.711231	+	0.702959i	$0.248138\pi$
$798$	90.9913	3.22106
$799$	−0.389074	−0.0137644
$800$	−57.8348	−2.04477
$801$	−130.296	−4.60378
$802$	−41.1941	−1.45462
$803$	15.9745	0.563727
$804$	118.602	4.18275
$805$	−31.0625	−1.09481
$806$	−23.8875	−0.841400
$807$	39.6928	1.39725
$808$	167.641	5.89760
$809$	−4.83199	−0.169884	−0.0849419	−	0.996386i	$-0.527070\pi$
$809$	−4.83199	−0.169884	−0.0849419	+	0.996386i	$0.527070\pi$
$810$	−291.434	−10.2399
$811$	41.0673	1.44207	0.721034	−	0.692900i	$-0.243667\pi$
$811$	41.0673	1.44207	0.721034	+	0.692900i	$0.243667\pi$
$812$	82.1974	2.88456
$813$	−17.2831	−0.606145
$814$	−4.48569	−0.157223
$815$	48.4741	1.69797
$816$	−10.1938	−0.356853
$817$	22.8616	0.799825
$818$	108.009	3.77645
$819$	−84.1889	−2.94180
$820$	109.029	3.80746
$821$	13.2896	0.463809	0.231905	−	0.972739i	$-0.425504\pi$
$821$	13.2896	0.463809	0.231905	+	0.972739i	$0.425504\pi$
$822$	−84.8353	−2.95897
$823$	−46.0569	−1.60544	−0.802721	−	0.596355i	$-0.796615\pi$
$823$	−46.0569	−1.60544	−0.802721	+	0.596355i	$0.796615\pi$
$824$	−118.350	−4.12292
$825$	10.2900	0.358253
$826$	80.2828	2.79340
$827$	−51.4982	−1.79077	−0.895385	−	0.445294i	$-0.853099\pi$
$827$	−51.4982	−1.79077	−0.895385	+	0.445294i	$0.853099\pi$
$828$	−185.865	−6.45924
$829$	13.1520	0.456787	0.228393	−	0.973569i	$-0.426653\pi$
$829$	13.1520	0.456787	0.228393	+	0.973569i	$0.426653\pi$
$830$	39.4576	1.36959
$831$	69.4392	2.40882
$832$	−139.958	−4.85217
$833$	−0.497681	−0.0172436
$834$	−66.9840	−2.31947
$835$	−45.5698	−1.57701
$836$	−26.6606	−0.922078
$837$	−53.1133	−1.83586
$838$	−1.04290	−0.0360263
$839$	−3.44491	−0.118931	−0.0594657	−	0.998230i	$-0.518940\pi$
$839$	−3.44491	−0.118931	−0.0594657	+	0.998230i	$0.518940\pi$
$840$	−302.375	−10.4329
$841$	−8.91783	−0.307512
$842$	30.9487	1.06656
$843$	−10.6587	−0.367105
$844$	46.3374	1.59500
$845$	−9.16975	−0.315449
$846$	−56.5217	−1.94326
$847$	−27.4696	−0.943866
$848$	−18.0370	−0.619394
$849$	−10.1232	−0.347426
$850$	0.918539	0.0315056
$851$	−3.92388	−0.134509
$852$	244.351	8.37132
$853$	39.1765	1.34138	0.670688	−	0.741739i	$-0.265999\pi$
$853$	39.1765	1.34138	0.670688	+	0.741739i	$0.265999\pi$
$854$	−53.9880	−1.84743
$855$	−68.8596	−2.35495
$856$	69.6687	2.38123
$857$	−2.13667	−0.0729873	−0.0364936	−	0.999334i	$-0.511619\pi$
$857$	−2.13667	−0.0729873	−0.0364936	+	0.999334i	$0.511619\pi$
$858$	44.7155	1.52656
$859$	−19.1467	−0.653276	−0.326638	−	0.945149i	$-0.605916\pi$
$859$	−19.1467	−0.653276	−0.326638	+	0.945149i	$0.605916\pi$
$860$	−115.960	−3.95421
$861$	76.6992	2.61390
$862$	69.0723	2.35261
$863$	31.1734	1.06116	0.530578	−	0.847636i	$-0.321975\pi$
$863$	31.1734	1.06116	0.530578	+	0.847636i	$0.321975\pi$
$864$	−558.810	−19.0111
$865$	20.4102	0.693967
$866$	108.661	3.69245
$867$	−57.8635	−1.96515
$868$	−50.8198	−1.72494
$869$	12.9861	0.440522
$870$	−112.760	−3.82292
$871$	−18.5173	−0.627436
$872$	−10.0167	−0.339209
$873$	149.703	5.06667
$874$	−31.3639	−1.06090
$875$	−25.2074	−0.852166
$876$	207.625	7.01498
$877$	36.5162	1.23306	0.616532	−	0.787330i	$-0.288537\pi$
$877$	36.5162	1.23306	0.616532	+	0.787330i	$0.288537\pi$
$878$	53.5729	1.80800
$879$	−3.10351	−0.104679
$880$	72.5151	2.44448
$881$	−45.7898	−1.54270	−0.771348	−	0.636414i	$-0.780417\pi$
$881$	−45.7898	−1.54270	−0.771348	+	0.636414i	$0.780417\pi$
$882$	−72.2995	−2.43445
$883$	19.7147	0.663454	0.331727	−	0.943375i	$-0.392369\pi$
$883$	19.7147	0.663454	0.331727	+	0.943375i	$0.392369\pi$
$884$	2.96802	0.0998253
$885$	−81.8931	−2.75281
$886$	−9.81325	−0.329683
$887$	−13.6433	−0.458096	−0.229048	−	0.973415i	$-0.573561\pi$
$887$	−13.6433	−0.458096	−0.229048	+	0.973415i	$0.573561\pi$
$888$	−38.1966	−1.28179
$889$	−28.1410	−0.943820
$890$	111.523	3.73828
$891$	60.0702	2.01243
$892$	164.359	5.50316
$893$	−7.09212	−0.237329
$894$	51.7843	1.73193
$895$	5.02037	0.167813
$896$	−216.054	−7.21785
$897$	39.1151	1.30602
$898$	88.1075	2.94019
$899$	−12.4161	−0.414101
$900$	99.2222	3.30741
$901$	0.165772	0.00552266
$902$	−30.2228	−1.00631
$903$	−81.5750	−2.71464
$904$	−202.292	−6.72812
$905$	−29.3693	−0.976270
$906$	−9.52131	−0.316324
$907$	8.33806	0.276861	0.138430	−	0.990372i	$-0.455794\pi$
$907$	8.33806	0.276861	0.138430	+	0.990372i	$0.455794\pi$
$908$	−145.811	−4.83892
$909$	−136.223	−4.51823
$910$	72.0594	2.38875
$911$	40.2144	1.33236	0.666182	−	0.745789i	$-0.267927\pi$
$911$	40.2144	1.33236	0.666182	+	0.745789i	$0.267927\pi$
$912$	−185.814	−6.15292
$913$	−8.13298	−0.269163
$914$	31.6866	1.04810
$915$	55.0708	1.82059
$916$	49.5449	1.63701
$917$	−59.8879	−1.97767
$918$	8.87508	0.292921
$919$	29.2563	0.965077	0.482539	−	0.875875i	$-0.339715\pi$
$919$	29.2563	0.965077	0.482539	+	0.875875i	$0.339715\pi$
$920$	104.226	3.43623
$921$	19.4744	0.641702
$922$	32.7321	1.07797
$923$	−38.1506	−1.25574
$924$	95.1309	3.12958
$925$	2.09473	0.0688742
$926$	−18.5549	−0.609753
$927$	96.1696	3.15863
$928$	−130.631	−4.28818
$929$	−38.7575	−1.27159	−0.635796	−	0.771857i	$-0.719328\pi$
$929$	−38.7575	−1.27159	−0.635796	+	0.771857i	$0.719328\pi$
$930$	69.7157	2.28607
$931$	−9.07185	−0.297318
$932$	−55.2370	−1.80935
$933$	18.4875	0.605252
$934$	51.9825	1.70092
$935$	−0.666461	−0.0217956
$936$	282.484	9.23328
$937$	15.8952	0.519272	0.259636	−	0.965707i	$-0.416397\pi$
$937$	15.8952	0.519272	0.259636	+	0.965707i	$0.416397\pi$
$938$	−52.9802	−1.72987
$939$	−9.63582	−0.314453
$940$	35.9732	1.17332
$941$	40.8553	1.33184	0.665922	−	0.746021i	$-0.268038\pi$
$941$	40.8553	1.33184	0.665922	+	0.746021i	$0.268038\pi$
$942$	−39.2162	−1.27773
$943$	−26.4375	−0.860923
$944$	−163.946	−5.33599
$945$	160.223	5.21204
$946$	32.1440	1.04509
$947$	−27.1367	−0.881824	−0.440912	−	0.897550i	$-0.645345\pi$
$947$	−27.1367	−0.881824	−0.440912	+	0.897550i	$0.645345\pi$
$948$	168.783	5.48183
$949$	−32.4165	−1.05229
$950$	16.7433	0.543225
$951$	8.60470	0.279027
$952$	5.56347	0.180313
$953$	−32.7334	−1.06034	−0.530169	−	0.847892i	$-0.677871\pi$
$953$	−32.7334	−1.06034	−0.530169	+	0.847892i	$0.677871\pi$
$954$	24.0821	0.779687
$955$	−70.4657	−2.28022
$956$	50.6779	1.63904
$957$	23.2420	0.751308
$958$	−18.5538	−0.599445
$959$	28.1791	0.909952
$960$	408.468	13.1832
$961$	−23.3235	−0.752372
$962$	9.10268	0.293482
$963$	−56.6118	−1.82429
$964$	140.966	4.54020
$965$	53.5651	1.72432
$966$	111.913	3.60074
$967$	−12.3713	−0.397834	−0.198917	−	0.980016i	$-0.563742\pi$
$967$	−12.3713	−0.397834	−0.198917	+	0.980016i	$0.563742\pi$
$968$	92.1704	2.96247
$969$	1.70775	0.0548609
$970$	−128.134	−4.11415
$971$	−30.1248	−0.966752	−0.483376	−	0.875413i	$-0.660590\pi$
$971$	−30.1248	−0.966752	−0.483376	+	0.875413i	$0.660590\pi$
$972$	447.208	14.3442
$973$	22.2496	0.713289
$974$	88.9176	2.84910
$975$	−20.8813	−0.668736
$976$	110.249	3.52899
$977$	48.6443	1.55627	0.778134	−	0.628098i	$-0.216166\pi$
$977$	48.6443	1.55627	0.778134	+	0.628098i	$0.216166\pi$
$978$	−174.644	−5.58450
$979$	−22.9872	−0.734673
$980$	46.0149	1.46989
$981$	8.13945	0.259873
$982$	19.6938	0.628454
$983$	−53.2984	−1.69996	−0.849978	−	0.526819i	$-0.823385\pi$
$983$	−53.2984	−1.69996	−0.849978	+	0.526819i	$0.823385\pi$
$984$	−257.353	−8.20413
$985$	70.4422	2.24447
$986$	2.07470	0.0660718
$987$	25.3062	0.805505
$988$	54.1017	1.72121
$989$	28.1181	0.894104
$990$	−96.8185	−3.07709
$991$	21.7853	0.692033	0.346017	−	0.938228i	$-0.387534\pi$
$991$	21.7853	0.692033	0.346017	+	0.938228i	$0.387534\pi$
$992$	80.7648	2.56428
$993$	51.0836	1.62109
$994$	−109.153	−3.46214
$995$	−2.52845	−0.0801573
$996$	−105.707	−3.34944
$997$	−43.3661	−1.37342	−0.686709	−	0.726932i	$-0.740945\pi$
$997$	−43.3661	−1.37342	−0.686709	+	0.726932i	$0.740945\pi$
$998$	−80.6179	−2.55192
$999$	20.2396	0.640353

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8003.2.a.c.1.1	✓	172

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8003.2.a.c.1.1	✓	172	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)

\(f(q)\)	\(=\)	\(q-2.79279 q^{2} +3.40925 q^{3} +5.79969 q^{4} +2.64273 q^{5} -9.52131 q^{6} +3.16263 q^{7} -10.6117 q^{8} +8.62295 q^{9} +O(q^{10})\)	\(q-2.79279 q^{2} +3.40925 q^{3} +5.79969 q^{4} +2.64273 q^{5} -9.52131 q^{6} +3.16263 q^{7} -10.6117 q^{8} +8.62295 q^{9} -7.38060 q^{10} +1.52129 q^{11} +19.7726 q^{12} -3.08710 q^{13} -8.83256 q^{14} +9.00972 q^{15} +18.0370 q^{16} -0.165772 q^{17} -24.0821 q^{18} -3.02173 q^{19} +15.3270 q^{20} +10.7822 q^{21} -4.24863 q^{22} -3.71651 q^{23} -36.1780 q^{24} +1.98403 q^{25} +8.62164 q^{26} +19.1700 q^{27} +18.3423 q^{28} +4.48131 q^{29} -25.1623 q^{30} -2.77064 q^{31} -29.1502 q^{32} +5.18643 q^{33} +0.462967 q^{34} +8.35797 q^{35} +50.0105 q^{36} +1.05579 q^{37} +8.43906 q^{38} -10.5247 q^{39} -28.0440 q^{40} +7.11352 q^{41} -30.1124 q^{42} -7.56573 q^{43} +8.82298 q^{44} +22.7881 q^{45} +10.3794 q^{46} +2.34704 q^{47} +61.4927 q^{48} +3.00221 q^{49} -5.54098 q^{50} -0.565157 q^{51} -17.9042 q^{52} -1.00000 q^{53} -53.5379 q^{54} +4.02035 q^{55} -33.5610 q^{56} -10.3018 q^{57} -12.5154 q^{58} -9.08942 q^{59} +52.2536 q^{60} +6.11238 q^{61} +7.73783 q^{62} +27.2712 q^{63} +45.3364 q^{64} -8.15838 q^{65} -14.4846 q^{66} +5.99829 q^{67} -0.961426 q^{68} -12.6705 q^{69} -23.3421 q^{70} +12.3581 q^{71} -91.5046 q^{72} +10.5006 q^{73} -2.94862 q^{74} +6.76404 q^{75} -17.5251 q^{76} +4.81126 q^{77} +29.3933 q^{78} +8.53624 q^{79} +47.6670 q^{80} +39.4865 q^{81} -19.8666 q^{82} -5.34613 q^{83} +62.5332 q^{84} -0.438091 q^{85} +21.1295 q^{86} +15.2779 q^{87} -16.1435 q^{88} -15.1104 q^{89} -63.6426 q^{90} -9.76335 q^{91} -21.5546 q^{92} -9.44580 q^{93} -6.55480 q^{94} -7.98561 q^{95} -99.3801 q^{96} +17.3610 q^{97} -8.38454 q^{98} +13.1180 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 172 q + 8 q^{2} + 25 q^{3} + 188 q^{4} + 27 q^{5} + 10 q^{6} + 31 q^{7} + 21 q^{8} + 179 q^{9}+O(q^{10}) \) 172 * q + 8 * q^2 + 25 * q^3 + 188 * q^4 + 27 * q^5 + 10 * q^6 + 31 * q^7 + 21 * q^8 + 179 * q^9	\( 172 q + 8 q^{2} + 25 q^{3} + 188 q^{4} + 27 q^{5} + 10 q^{6} + 31 q^{7} + 21 q^{8} + 179 q^{9} + 20 q^{10} - 3 q^{11} + 66 q^{12} + 121 q^{13} + 12 q^{14} + 30 q^{15} + 212 q^{16} + 8 q^{17} + 40 q^{18} + 41 q^{19} + 64 q^{20} + 56 q^{21} + 50 q^{22} + 28 q^{23} + 30 q^{24} + 231 q^{25} + 38 q^{26} + 100 q^{27} + 80 q^{28} + 26 q^{29} + 55 q^{30} + 66 q^{31} + 65 q^{32} + 99 q^{33} + 81 q^{34} + 36 q^{35} + 212 q^{36} + 153 q^{37} + q^{38} + 20 q^{39} + 59 q^{40} + 40 q^{41} + 50 q^{42} + 39 q^{43} - 51 q^{44} + 123 q^{45} + 59 q^{46} + 29 q^{47} + 128 q^{48} + 245 q^{49} + 19 q^{50} + 36 q^{51} + 215 q^{52} - 172 q^{53} + 40 q^{54} + 40 q^{55} + 15 q^{56} + 54 q^{57} + 44 q^{58} - 54 q^{60} + 100 q^{61} - 29 q^{62} + 92 q^{63} + 253 q^{64} + 77 q^{65} + 14 q^{66} + 126 q^{67} - 27 q^{68} + 47 q^{69} + 72 q^{70} + 38 q^{71} + 65 q^{72} + 185 q^{73} + 48 q^{74} + 75 q^{75} + 38 q^{76} + 120 q^{77} + 75 q^{78} + 79 q^{79} + 43 q^{80} + 232 q^{81} + 110 q^{82} + 90 q^{83} + 158 q^{84} + 115 q^{85} + 68 q^{86} + 61 q^{87} + 15 q^{88} - 36 q^{89} - 6 q^{90} + 33 q^{91} + 139 q^{92} + 103 q^{93} - 24 q^{94} - 45 q^{95} + 34 q^{96} + 159 q^{97} - 36 q^{98} + 27 q^{99}+O(q^{100}) \) 172 * q + 8 * q^2 + 25 * q^3 + 188 * q^4 + 27 * q^5 + 10 * q^6 + 31 * q^7 + 21 * q^8 + 179 * q^9 + 20 * q^10 - 3 * q^11 + 66 * q^12 + 121 * q^13 + 12 * q^14 + 30 * q^15 + 212 * q^16 + 8 * q^17 + 40 * q^18 + 41 * q^19 + 64 * q^20 + 56 * q^21 + 50 * q^22 + 28 * q^23 + 30 * q^24 + 231 * q^25 + 38 * q^26 + 100 * q^27 + 80 * q^28 + 26 * q^29 + 55 * q^30 + 66 * q^31 + 65 * q^32 + 99 * q^33 + 81 * q^34 + 36 * q^35 + 212 * q^36 + 153 * q^37 + q^38 + 20 * q^39 + 59 * q^40 + 40 * q^41 + 50 * q^42 + 39 * q^43 - 51 * q^44 + 123 * q^45 + 59 * q^46 + 29 * q^47 + 128 * q^48 + 245 * q^49 + 19 * q^50 + 36 * q^51 + 215 * q^52 - 172 * q^53 + 40 * q^54 + 40 * q^55 + 15 * q^56 + 54 * q^57 + 44 * q^58 - 54 * q^60 + 100 * q^61 - 29 * q^62 + 92 * q^63 + 253 * q^64 + 77 * q^65 + 14 * q^66 + 126 * q^67 - 27 * q^68 + 47 * q^69 + 72 * q^70 + 38 * q^71 + 65 * q^72 + 185 * q^73 + 48 * q^74 + 75 * q^75 + 38 * q^76 + 120 * q^77 + 75 * q^78 + 79 * q^79 + 43 * q^80 + 232 * q^81 + 110 * q^82 + 90 * q^83 + 158 * q^84 + 115 * q^85 + 68 * q^86 + 61 * q^87 + 15 * q^88 - 36 * q^89 - 6 * q^90 + 33 * q^91 + 139 * q^92 + 103 * q^93 - 24 * q^94 - 45 * q^95 + 34 * q^96 + 159 * q^97 - 36 * q^98 + 27 * q^99

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