LMFDB - Embedded newform 8003.2.a.a.1.17

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:	$1$
Dimension:	$147$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
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)

$f(q)$	$=$	$q-2.31195 q^{2} +2.01743 q^{3} +3.34512 q^{4} -2.72339 q^{5} -4.66419 q^{6} -3.92860 q^{7} -3.10985 q^{8} +1.07001 q^{9} +O(q^{10})$	\(q-2.31195 q^{2} +2.01743 q^{3} +3.34512 q^{4} -2.72339 q^{5} -4.66419 q^{6} -3.92860 q^{7} -3.10985 q^{8} +1.07001 q^{9} +6.29634 q^{10} -1.87897 q^{11} +6.74853 q^{12} +5.10435 q^{13} +9.08274 q^{14} -5.49424 q^{15} +0.499586 q^{16} +4.58664 q^{17} -2.47381 q^{18} -3.73168 q^{19} -9.11006 q^{20} -7.92566 q^{21} +4.34408 q^{22} +2.34737 q^{23} -6.27389 q^{24} +2.41685 q^{25} -11.8010 q^{26} -3.89362 q^{27} -13.1416 q^{28} -3.98844 q^{29} +12.7024 q^{30} +3.27822 q^{31} +5.06468 q^{32} -3.79067 q^{33} -10.6041 q^{34} +10.6991 q^{35} +3.57931 q^{36} -2.62234 q^{37} +8.62745 q^{38} +10.2977 q^{39} +8.46934 q^{40} +2.60459 q^{41} +18.3237 q^{42} +8.68999 q^{43} -6.28536 q^{44} -2.91405 q^{45} -5.42702 q^{46} -3.39437 q^{47} +1.00788 q^{48} +8.43391 q^{49} -5.58764 q^{50} +9.25320 q^{51} +17.0747 q^{52} +1.00000 q^{53} +9.00185 q^{54} +5.11716 q^{55} +12.2174 q^{56} -7.52838 q^{57} +9.22107 q^{58} +4.34394 q^{59} -18.3789 q^{60} -1.28864 q^{61} -7.57908 q^{62} -4.20364 q^{63} -12.7085 q^{64} -13.9011 q^{65} +8.76385 q^{66} -1.46936 q^{67} +15.3429 q^{68} +4.73566 q^{69} -24.7358 q^{70} +4.95502 q^{71} -3.32757 q^{72} -3.71885 q^{73} +6.06271 q^{74} +4.87582 q^{75} -12.4829 q^{76} +7.38171 q^{77} -23.8077 q^{78} -13.9103 q^{79} -1.36057 q^{80} -11.0651 q^{81} -6.02170 q^{82} +2.41089 q^{83} -26.5123 q^{84} -12.4912 q^{85} -20.0908 q^{86} -8.04637 q^{87} +5.84330 q^{88} -1.47043 q^{89} +6.73714 q^{90} -20.0530 q^{91} +7.85225 q^{92} +6.61356 q^{93} +7.84762 q^{94} +10.1628 q^{95} +10.2176 q^{96} +5.90046 q^{97} -19.4988 q^{98} -2.01051 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 147 q - 6 q^{2} - 23 q^{3} + 130 q^{4} - 25 q^{5} - 18 q^{6} - 33 q^{7} - 15 q^{8} + 114 q^{9}+O(q^{10}) $ 147 * q - 6 * q^2 - 23 * q^3 + 130 * q^4 - 25 * q^5 - 18 * q^6 - 33 * q^7 - 15 * q^8 + 114 * q^9	\( 147 q - 6 q^{2} - 23 q^{3} + 130 q^{4} - 25 q^{5} - 18 q^{6} - 33 q^{7} - 15 q^{8} + 114 q^{9} - 24 q^{10} - 13 q^{11} - 52 q^{12} - 119 q^{13} - 6 q^{14} - 22 q^{15} + 100 q^{16} - 42 q^{17} - 6 q^{18} - 31 q^{19} - 50 q^{20} - 44 q^{21} - 38 q^{22} - 16 q^{23} - 30 q^{24} + 80 q^{25} - 18 q^{26} - 68 q^{27} - 72 q^{28} - 40 q^{29} - 3 q^{30} - 44 q^{31} - 41 q^{32} - 71 q^{33} - 55 q^{34} - 24 q^{35} + 108 q^{36} - 145 q^{37} - 39 q^{38} + 28 q^{39} - 81 q^{40} - 28 q^{41} - 54 q^{42} - 47 q^{43} - 33 q^{44} - 89 q^{45} - 43 q^{46} - 65 q^{47} - 82 q^{48} + 52 q^{49} - 43 q^{50} + 7 q^{51} - 215 q^{52} + 147 q^{53} - 88 q^{54} - 48 q^{55} + 19 q^{56} - 66 q^{57} - 110 q^{58} - 66 q^{59} - 118 q^{60} - 80 q^{61} - 41 q^{62} - 52 q^{63} + 33 q^{64} - 17 q^{65} - 86 q^{66} - 114 q^{67} - 77 q^{68} - 49 q^{69} - 56 q^{70} + 10 q^{71} + 5 q^{72} - 143 q^{73} - 30 q^{74} - 97 q^{75} - 104 q^{76} - 116 q^{77} - 33 q^{78} - 31 q^{79} - 83 q^{80} - q^{81} - 72 q^{82} - 70 q^{83} - 64 q^{84} - 85 q^{85} - 43 q^{87} - 149 q^{88} - 130 q^{89} + 42 q^{90} - 35 q^{91} - 31 q^{92} - 149 q^{93} - 94 q^{94} - 9 q^{95} + 6 q^{96} - 211 q^{97} - 18 q^{98} - 19 q^{99}+O(q^{100}) \) 147 * q - 6 * q^2 - 23 * q^3 + 130 * q^4 - 25 * q^5 - 18 * q^6 - 33 * q^7 - 15 * q^8 + 114 * q^9 - 24 * q^10 - 13 * q^11 - 52 * q^12 - 119 * q^13 - 6 * q^14 - 22 * q^15 + 100 * q^16 - 42 * q^17 - 6 * q^18 - 31 * q^19 - 50 * q^20 - 44 * q^21 - 38 * q^22 - 16 * q^23 - 30 * q^24 + 80 * q^25 - 18 * q^26 - 68 * q^27 - 72 * q^28 - 40 * q^29 - 3 * q^30 - 44 * q^31 - 41 * q^32 - 71 * q^33 - 55 * q^34 - 24 * q^35 + 108 * q^36 - 145 * q^37 - 39 * q^38 + 28 * q^39 - 81 * q^40 - 28 * q^41 - 54 * q^42 - 47 * q^43 - 33 * q^44 - 89 * q^45 - 43 * q^46 - 65 * q^47 - 82 * q^48 + 52 * q^49 - 43 * q^50 + 7 * q^51 - 215 * q^52 + 147 * q^53 - 88 * q^54 - 48 * q^55 + 19 * q^56 - 66 * q^57 - 110 * q^58 - 66 * q^59 - 118 * q^60 - 80 * q^61 - 41 * q^62 - 52 * q^63 + 33 * q^64 - 17 * q^65 - 86 * q^66 - 114 * q^67 - 77 * q^68 - 49 * q^69 - 56 * q^70 + 10 * q^71 + 5 * q^72 - 143 * q^73 - 30 * q^74 - 97 * q^75 - 104 * q^76 - 116 * q^77 - 33 * q^78 - 31 * q^79 - 83 * q^80 - q^81 - 72 * q^82 - 70 * q^83 - 64 * q^84 - 85 * q^85 - 43 * q^87 - 149 * q^88 - 130 * q^89 + 42 * q^90 - 35 * q^91 - 31 * q^92 - 149 * q^93 - 94 * q^94 - 9 * q^95 + 6 * q^96 - 211 * q^97 - 18 * q^98 - 19 * 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 $

$2$	−2.31195	−1.63480	−0.817398	−	0.576073i	$-0.804584\pi$
$2$	−2.31195	−1.63480	−0.817398	+	0.576073i	$0.804584\pi$
$3$	2.01743	1.16476	0.582381	−	0.812916i	$-0.302121\pi$
$3$	2.01743	1.16476	0.582381	+	0.812916i	$0.302121\pi$
$4$	3.34512	1.67256
$5$	−2.72339	−1.21794	−0.608968	−	0.793194i	$-0.708416\pi$
$5$	−2.72339	−1.21794	−0.608968	+	0.793194i	$0.708416\pi$
$6$	−4.66419	−1.90415
$7$	−3.92860	−1.48487	−0.742436	−	0.669917i	$-0.766330\pi$
$7$	−3.92860	−1.48487	−0.742436	+	0.669917i	$0.766330\pi$
$8$	−3.10985	−1.09950
$9$	1.07001	0.356669
$10$	6.29634	1.99108
$11$	−1.87897	−0.566529	−0.283265	−	0.959042i	$-0.591417\pi$
$11$	−1.87897	−0.566529	−0.283265	+	0.959042i	$0.591417\pi$
$12$	6.74853	1.94813
$13$	5.10435	1.41569	0.707846	−	0.706366i	$-0.249667\pi$
$13$	5.10435	1.41569	0.707846	+	0.706366i	$0.249667\pi$
$14$	9.08274	2.42746
$15$	−5.49424	−1.41861
$16$	0.499586	0.124896
$17$	4.58664	1.11242	0.556212	−	0.831041i	$-0.312254\pi$
$17$	4.58664	1.11242	0.556212	+	0.831041i	$0.312254\pi$
$18$	−2.47381	−0.583082
$19$	−3.73168	−0.856105	−0.428053	−	0.903754i	$-0.640800\pi$
$19$	−3.73168	−0.856105	−0.428053	+	0.903754i	$0.640800\pi$
$20$	−9.11006	−2.03707
$21$	−7.92566	−1.72952
$22$	4.34408	0.926160
$23$	2.34737	0.489461	0.244731	−	0.969591i	$-0.421300\pi$
$23$	2.34737	0.489461	0.244731	+	0.969591i	$0.421300\pi$
$24$	−6.27389	−1.28065
$25$	2.41685	0.483370
$26$	−11.8010	−2.31437
$27$	−3.89362	−0.749327
$28$	−13.1416	−2.48354
$29$	−3.98844	−0.740634	−0.370317	−	0.928905i	$-0.620751\pi$
$29$	−3.98844	−0.740634	−0.370317	+	0.928905i	$0.620751\pi$
$30$	12.7024	2.31913
$31$	3.27822	0.588785	0.294392	−	0.955685i	$-0.404883\pi$
$31$	3.27822	0.588785	0.294392	+	0.955685i	$0.404883\pi$
$32$	5.06468	0.895318
$33$	−3.79067	−0.659872
$34$	−10.6041	−1.81859
$35$	10.6991	1.80848
$36$	3.57931	0.596551
$37$	−2.62234	−0.431109	−0.215555	−	0.976492i	$-0.569156\pi$
$37$	−2.62234	−0.431109	−0.215555	+	0.976492i	$0.569156\pi$
$38$	8.62745	1.39956
$39$	10.2977	1.64894
$40$	8.46934	1.33912
$41$	2.60459	0.406769	0.203385	−	0.979099i	$-0.434806\pi$
$41$	2.60459	0.406769	0.203385	+	0.979099i	$0.434806\pi$
$42$	18.3237	2.82742
$43$	8.68999	1.32521	0.662605	−	0.748969i	$-0.269451\pi$
$43$	8.68999	1.32521	0.662605	+	0.748969i	$0.269451\pi$
$44$	−6.28536	−0.947554
$45$	−2.91405	−0.434401
$46$	−5.42702	−0.800170
$47$	−3.39437	−0.495120	−0.247560	−	0.968873i	$-0.579629\pi$
$47$	−3.39437	−0.495120	−0.247560	+	0.968873i	$0.579629\pi$
$48$	1.00788	0.145475
$49$	8.43391	1.20484
$50$	−5.58764	−0.790212
$51$	9.25320	1.29571
$52$	17.0747	2.36783
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	9.00185	1.22500
$55$	5.11716	0.689997
$56$	12.2174	1.63261
$57$	−7.52838	−0.997158
$58$	9.22107	1.21079
$59$	4.34394	0.565533	0.282766	−	0.959189i	$-0.408748\pi$
$59$	4.34394	0.565533	0.282766	+	0.959189i	$0.408748\pi$
$60$	−18.3789	−2.37270
$61$	−1.28864	−0.164994	−0.0824968	−	0.996591i	$-0.526289\pi$
$61$	−1.28864	−0.164994	−0.0824968	+	0.996591i	$0.526289\pi$
$62$	−7.57908	−0.962544
$63$	−4.20364	−0.529608
$64$	−12.7085	−1.58856
$65$	−13.9011	−1.72422
$66$	8.76385	1.07876
$67$	−1.46936	−0.179511	−0.0897554	−	0.995964i	$-0.528609\pi$
$67$	−1.46936	−0.179511	−0.0897554	+	0.995964i	$0.528609\pi$
$68$	15.3429	1.86059
$69$	4.73566	0.570106
$70$	−24.7358	−2.95650
$71$	4.95502	0.588052	0.294026	−	0.955797i	$-0.405005\pi$
$71$	4.95502	0.588052	0.294026	+	0.955797i	$0.405005\pi$
$72$	−3.32757	−0.392157
$73$	−3.71885	−0.435259	−0.217629	−	0.976031i	$-0.569832\pi$
$73$	−3.71885	−0.435259	−0.217629	+	0.976031i	$0.569832\pi$
$74$	6.06271	0.704776
$75$	4.87582	0.563011
$76$	−12.4829	−1.43189
$77$	7.38171	0.841224
$78$	−23.8077	−2.69569
$79$	−13.9103	−1.56503	−0.782516	−	0.622631i	$-0.786064\pi$
$79$	−13.9103	−1.56503	−0.782516	+	0.622631i	$0.786064\pi$
$80$	−1.36057	−0.152116
$81$	−11.0651	−1.22946
$82$	−6.02170	−0.664985
$83$	2.41089	0.264629	0.132315	−	0.991208i	$-0.457759\pi$
$83$	2.41089	0.264629	0.132315	+	0.991208i	$0.457759\pi$
$84$	−26.5123	−2.89273
$85$	−12.4912	−1.35486
$86$	−20.0908	−2.16645
$87$	−8.04637	−0.862662
$88$	5.84330	0.622898
$89$	−1.47043	−0.155865	−0.0779326	−	0.996959i	$-0.524832\pi$
$89$	−1.47043	−0.155865	−0.0779326	+	0.996959i	$0.524832\pi$
$90$	6.73714	0.710157
$91$	−20.0530	−2.10212
$92$	7.85225	0.818654
$93$	6.61356	0.685794
$94$	7.84762	0.809420
$95$	10.1628	1.04268
$96$	10.2176	1.04283
$97$	5.90046	0.599101	0.299550	−	0.954080i	$-0.403163\pi$
$97$	5.90046	0.599101	0.299550	+	0.954080i	$0.403163\pi$
$98$	−19.4988	−1.96968
$99$	−2.01051	−0.202064
$100$	8.08466	0.808466
$101$	5.37543	0.534875	0.267437	−	0.963575i	$-0.413823\pi$
$101$	5.37543	0.534875	0.267437	+	0.963575i	$0.413823\pi$
$102$	−21.3930	−2.11822
$103$	11.8157	1.16423	0.582116	−	0.813106i	$-0.302225\pi$
$103$	11.8157	1.16423	0.582116	+	0.813106i	$0.302225\pi$
$104$	−15.8738	−1.55655
$105$	21.5847	2.10645
$106$	−2.31195	−0.224557
$107$	11.0866	1.07178	0.535892	−	0.844287i	$-0.319975\pi$
$107$	11.0866	1.07178	0.535892	+	0.844287i	$0.319975\pi$
$108$	−13.0246	−1.25329
$109$	7.77539	0.744747	0.372374	−	0.928083i	$-0.378544\pi$
$109$	7.77539	0.744747	0.372374	+	0.928083i	$0.378544\pi$
$110$	−11.8306	−1.12800
$111$	−5.29037	−0.502140
$112$	−1.96267	−0.185455
$113$	14.7336	1.38602	0.693011	−	0.720927i	$-0.256284\pi$
$113$	14.7336	1.38602	0.693011	+	0.720927i	$0.256284\pi$
$114$	17.4053	1.63015
$115$	−6.39282	−0.596133
$116$	−13.3418	−1.23875
$117$	5.46170	0.504934
$118$	−10.0430	−0.924531
$119$	−18.0191	−1.65181
$120$	17.0863	1.55976
$121$	−7.46949	−0.679044
$122$	2.97928	0.269731
$123$	5.25458	0.473789
$124$	10.9660	0.984778
$125$	7.03492	0.629222
$126$	9.71860	0.865802
$127$	−17.5033	−1.55317	−0.776584	−	0.630014i	$-0.783049\pi$
$127$	−17.5033	−1.55317	−0.776584	+	0.630014i	$0.783049\pi$
$128$	19.2520	1.70165
$129$	17.5314	1.54355
$130$	32.1388	2.81876
$131$	−0.0655618	−0.00572816	−0.00286408	−	0.999996i	$-0.500912\pi$
$131$	−0.0655618	−0.00572816	−0.00286408	+	0.999996i	$0.500912\pi$
$132$	−12.6803	−1.10367
$133$	14.6603	1.27121
$134$	3.39709	0.293464
$135$	10.6038	0.912633
$136$	−14.2638	−1.22311
$137$	2.17779	0.186061	0.0930304	−	0.995663i	$-0.470345\pi$
$137$	2.17779	0.186061	0.0930304	+	0.995663i	$0.470345\pi$
$138$	−10.9486	−0.932007
$139$	5.17846	0.439231	0.219616	−	0.975586i	$-0.429520\pi$
$139$	5.17846	0.439231	0.219616	+	0.975586i	$0.429520\pi$
$140$	35.7898	3.02479
$141$	−6.84789	−0.576696
$142$	−11.4558	−0.961346
$143$	−9.59090	−0.802032
$144$	0.534561	0.0445467
$145$	10.8621	0.902045
$146$	8.59781	0.711560
$147$	17.0148	1.40336
$148$	−8.77203	−0.721056
$149$	−9.80396	−0.803171	−0.401586	−	0.915821i	$-0.631541\pi$
$149$	−9.80396	−0.803171	−0.401586	+	0.915821i	$0.631541\pi$
$150$	−11.2727	−0.920409
$151$	1.00000	0.0813788
$151$	1.00000	0.0813788
$152$	11.6050	0.941286
$153$	4.90774	0.396767
$154$	−17.0661	−1.37523
$155$	−8.92786	−0.717103
$156$	34.4469	2.75796
$157$	2.48092	0.197999	0.0989993	−	0.995087i	$-0.468436\pi$
$157$	2.48092	0.197999	0.0989993	+	0.995087i	$0.468436\pi$
$158$	32.1599	2.55851
$159$	2.01743	0.159992
$160$	−13.7931	−1.09044
$161$	−9.22190	−0.726788
$162$	25.5820	2.00991
$163$	−3.65065	−0.285941	−0.142971	−	0.989727i	$-0.545665\pi$
$163$	−3.65065	−0.285941	−0.142971	+	0.989727i	$0.545665\pi$
$164$	8.71268	0.680346
$165$	10.3235	0.803682
$166$	−5.57385	−0.432615
$167$	−7.69150	−0.595186	−0.297593	−	0.954693i	$-0.596184\pi$
$167$	−7.69150	−0.595186	−0.297593	+	0.954693i	$0.596184\pi$
$168$	24.6476	1.90161
$169$	13.0544	1.00419
$170$	28.8791	2.21492
$171$	−3.99292	−0.305347
$172$	29.0691	2.21649
$173$	22.2016	1.68795	0.843977	−	0.536379i	$-0.180208\pi$
$173$	22.2016	1.68795	0.843977	+	0.536379i	$0.180208\pi$
$174$	18.6028	1.41028
$175$	−9.49485	−0.717743
$176$	−0.938704	−0.0707575
$177$	8.76358	0.658711
$178$	3.39956	0.254808
$179$	16.0207	1.19744	0.598721	−	0.800958i	$-0.295676\pi$
$179$	16.0207	1.19744	0.598721	+	0.800958i	$0.295676\pi$
$180$	−9.74784	−0.726561
$181$	−6.44511	−0.479061	−0.239531	−	0.970889i	$-0.576994\pi$
$181$	−6.44511	−0.479061	−0.239531	+	0.970889i	$0.576994\pi$
$182$	46.3615	3.43654
$183$	−2.59974	−0.192178
$184$	−7.29999	−0.538162
$185$	7.14164	0.525064
$186$	−15.2902	−1.12113
$187$	−8.61813	−0.630220
$188$	−11.3546	−0.828117
$189$	15.2965	1.11265
$190$	−23.4959	−1.70457
$191$	5.41246	0.391632	0.195816	−	0.980641i	$-0.437265\pi$
$191$	5.41246	0.391632	0.195816	+	0.980641i	$0.437265\pi$
$192$	−25.6384	−1.85029
$193$	−22.7516	−1.63770	−0.818848	−	0.574010i	$-0.805387\pi$
$193$	−22.7516	−1.63770	−0.818848	+	0.574010i	$0.805387\pi$
$194$	−13.6416	−0.979408
$195$	−28.0445	−2.00831
$196$	28.2124	2.01517
$197$	−12.4738	−0.888724	−0.444362	−	0.895847i	$-0.646570\pi$
$197$	−12.4738	−0.888724	−0.444362	+	0.895847i	$0.646570\pi$
$198$	4.64820	0.330333
$199$	0.234868	0.0166493	0.00832466	−	0.999965i	$-0.497350\pi$
$199$	0.234868	0.0166493	0.00832466	+	0.999965i	$0.497350\pi$
$200$	−7.51605	−0.531465
$201$	−2.96432	−0.209087
$202$	−12.4277	−0.874411
$203$	15.6690	1.09975
$204$	30.9531	2.16715
$205$	−7.09333	−0.495419
$206$	−27.3173	−1.90328
$207$	2.51171	0.174576
$208$	2.55006	0.176815
$209$	7.01169	0.485009
$210$	−49.9027	−3.44361
$211$	16.1225	1.10992	0.554958	−	0.831878i	$-0.312734\pi$
$211$	16.1225	1.10992	0.554958	+	0.831878i	$0.312734\pi$
$212$	3.34512	0.229744
$213$	9.99638	0.684941
$214$	−25.6317	−1.75215
$215$	−23.6662	−1.61402
$216$	12.1086	0.823884
$217$	−12.8788	−0.874270
$218$	−17.9763	−1.21751
$219$	−7.50251	−0.506973
$220$	17.1175	1.15406
$221$	23.4118	1.57485
$222$	12.2311	0.820896
$223$	24.1654	1.61823	0.809117	−	0.587648i	$-0.199946\pi$
$223$	24.1654	1.61823	0.809117	+	0.587648i	$0.199946\pi$
$224$	−19.8971	−1.32943
$225$	2.58605	0.172403
$226$	−34.0634	−2.26586
$227$	−3.96322	−0.263048	−0.131524	−	0.991313i	$-0.541987\pi$
$227$	−3.96322	−0.263048	−0.131524	+	0.991313i	$0.541987\pi$
$228$	−25.1833	−1.66781
$229$	−20.6647	−1.36556	−0.682782	−	0.730622i	$-0.739230\pi$
$229$	−20.6647	−1.36556	−0.682782	+	0.730622i	$0.739230\pi$
$230$	14.7799	0.974556
$231$	14.8920	0.979825
$232$	12.4034	0.814326
$233$	−0.316140	−0.0207110	−0.0103555	−	0.999946i	$-0.503296\pi$
$233$	−0.316140	−0.0207110	−0.0103555	+	0.999946i	$0.503296\pi$
$234$	−12.6272	−0.825465
$235$	9.24419	0.603025
$236$	14.5310	0.945888
$237$	−28.0630	−1.82289
$238$	41.6592	2.70037
$239$	−29.1522	−1.88570	−0.942849	−	0.333221i	$-0.891865\pi$
$239$	−29.1522	−1.88570	−0.942849	+	0.333221i	$0.891865\pi$
$240$	−2.74484	−0.177179
$241$	−5.61594	−0.361754	−0.180877	−	0.983506i	$-0.557894\pi$
$241$	−5.61594	−0.361754	−0.180877	+	0.983506i	$0.557894\pi$
$242$	17.2691	1.11010
$243$	−10.6422	−0.682697
$244$	−4.31066	−0.275962
$245$	−22.9688	−1.46742
$246$	−12.1483	−0.774549
$247$	−19.0478	−1.21198
$248$	−10.1948	−0.647368
$249$	4.86379	0.308230
$250$	−16.2644	−1.02865
$251$	−18.3698	−1.15949	−0.579745	−	0.814798i	$-0.696848\pi$
$251$	−18.3698	−1.15949	−0.579745	+	0.814798i	$0.696848\pi$
$252$	−14.0617	−0.885802
$253$	−4.41064	−0.277294
$254$	40.4668	2.53911
$255$	−25.2001	−1.57809
$256$	−19.0928	−1.19330
$257$	20.1446	1.25658	0.628292	−	0.777977i	$-0.283754\pi$
$257$	20.1446	1.25658	0.628292	+	0.777977i	$0.283754\pi$
$258$	−40.5318	−2.52340
$259$	10.3021	0.640142
$260$	−46.5010	−2.88387
$261$	−4.26766	−0.264161
$262$	0.151576	0.00936438
$263$	24.0625	1.48376	0.741878	−	0.670535i	$-0.233935\pi$
$263$	24.0625	1.48376	0.741878	+	0.670535i	$0.233935\pi$
$264$	11.7884	0.725528
$265$	−2.72339	−0.167296
$266$	−33.8938	−2.07816
$267$	−2.96648	−0.181546
$268$	−4.91518	−0.300243
$269$	−25.5277	−1.55645	−0.778227	−	0.627984i	$-0.783880\pi$
$269$	−25.5277	−1.55645	−0.778227	+	0.627984i	$0.783880\pi$
$270$	−24.5155	−1.49197
$271$	−8.96484	−0.544575	−0.272288	−	0.962216i	$-0.587780\pi$
$271$	−8.96484	−0.544575	−0.272288	+	0.962216i	$0.587780\pi$
$272$	2.29142	0.138938
$273$	−40.4554	−2.44847
$274$	−5.03493	−0.304171
$275$	−4.54118	−0.273843
$276$	15.8413	0.953536
$277$	−22.9238	−1.37736	−0.688678	−	0.725068i	$-0.741809\pi$
$277$	−22.9238	−1.37736	−0.688678	+	0.725068i	$0.741809\pi$
$278$	−11.9723	−0.718054
$279$	3.50772	0.210002
$280$	−33.2726	−1.98842
$281$	−4.05610	−0.241967	−0.120983	−	0.992655i	$-0.538605\pi$
$281$	−4.05610	−0.241967	−0.120983	+	0.992655i	$0.538605\pi$
$282$	15.8320	0.942781
$283$	10.3041	0.612516	0.306258	−	0.951949i	$-0.400923\pi$
$283$	10.3041	0.612516	0.306258	+	0.951949i	$0.400923\pi$
$284$	16.5751	0.983553
$285$	20.5027	1.21448
$286$	22.1737	1.31116
$287$	−10.2324	−0.604000
$288$	5.41925	0.319333
$289$	4.03725	0.237485
$290$	−25.1126	−1.47466
$291$	11.9037	0.697809
$292$	−12.4400	−0.727996
$293$	−9.67249	−0.565073	−0.282537	−	0.959257i	$-0.591176\pi$
$293$	−9.67249	−0.565073	−0.282537	+	0.959257i	$0.591176\pi$
$294$	−39.3374	−2.29420
$295$	−11.8302	−0.688783
$296$	8.15507	0.474004
$297$	7.31597	0.424516
$298$	22.6663	1.31302
$299$	11.9818	0.692927
$300$	16.3102	0.941670
$301$	−34.1395	−1.96777
$302$	−2.31195	−0.133038
$303$	10.8445	0.623002
$304$	−1.86429	−0.106924
$305$	3.50947	0.200952
$306$	−11.3465	−0.648634
$307$	−14.8612	−0.848171	−0.424085	−	0.905622i	$-0.639404\pi$
$307$	−14.8612	−0.848171	−0.424085	+	0.905622i	$0.639404\pi$
$308$	24.6927	1.40700
$309$	23.8372	1.35605
$310$	20.6408	1.17232
$311$	−24.3232	−1.37924	−0.689621	−	0.724170i	$-0.742223\pi$
$311$	−24.3232	−1.37924	−0.689621	+	0.724170i	$0.742223\pi$
$312$	−32.0242	−1.81301
$313$	6.56704	0.371191	0.185595	−	0.982626i	$-0.440579\pi$
$313$	6.56704	0.371191	0.185595	+	0.982626i	$0.440579\pi$
$314$	−5.73576	−0.323688
$315$	11.4481	0.645030
$316$	−46.5316	−2.61761
$317$	−0.771812	−0.0433493	−0.0216746	−	0.999765i	$-0.506900\pi$
$317$	−0.771812	−0.0433493	−0.0216746	+	0.999765i	$0.506900\pi$
$318$	−4.66419	−0.261555
$319$	7.49413	0.419591
$320$	34.6101	1.93477
$321$	22.3664	1.24837
$322$	21.3206	1.18815
$323$	−17.1158	−0.952351
$324$	−37.0141	−2.05634
$325$	12.3365	0.684304
$326$	8.44013	0.467456
$327$	15.6863	0.867453
$328$	−8.09990	−0.447242
$329$	13.3351	0.735189
$330$	−23.8674	−1.31386
$331$	1.56067	0.0857820	0.0428910	−	0.999080i	$-0.486343\pi$
$331$	1.56067	0.0857820	0.0428910	+	0.999080i	$0.486343\pi$
$332$	8.06470	0.442608
$333$	−2.80592	−0.153764
$334$	17.7824	0.973009
$335$	4.00164	0.218633
$336$	−3.95955	−0.216011
$337$	−23.6220	−1.28677	−0.643387	−	0.765541i	$-0.722471\pi$
$337$	−23.6220	−1.28677	−0.643387	+	0.765541i	$0.722471\pi$
$338$	−30.1812	−1.64164
$339$	29.7240	1.61439
$340$	−41.7846	−2.26609
$341$	−6.15965	−0.333564
$342$	9.23145	0.499180
$343$	−5.63327	−0.304168
$344$	−27.0246	−1.45707
$345$	−12.8970	−0.694353
$346$	−51.3290	−2.75946
$347$	−21.0719	−1.13120	−0.565599	−	0.824680i	$-0.691355\pi$
$347$	−21.0719	−1.13120	−0.565599	+	0.824680i	$0.691355\pi$
$348$	−26.9161	−1.44285
$349$	21.0686	1.12778	0.563888	−	0.825851i	$-0.309305\pi$
$349$	21.0686	1.12778	0.563888	+	0.825851i	$0.309305\pi$
$350$	21.9516	1.17336
$351$	−19.8744	−1.06082
$352$	−9.51637	−0.507224
$353$	−7.60819	−0.404943	−0.202471	−	0.979288i	$-0.564897\pi$
$353$	−7.60819	−0.404943	−0.202471	+	0.979288i	$0.564897\pi$
$354$	−20.2610	−1.07686
$355$	−13.4944	−0.716211
$356$	−4.91876	−0.260694
$357$	−36.3521	−1.92396
$358$	−37.0390	−1.95757
$359$	−29.8123	−1.57343	−0.786716	−	0.617315i	$-0.788220\pi$
$359$	−29.8123	−1.57343	−0.786716	+	0.617315i	$0.788220\pi$
$360$	9.06226	0.477623
$361$	−5.07459	−0.267084
$362$	14.9008	0.783168
$363$	−15.0691	−0.790925
$364$	−67.0796	−3.51593
$365$	10.1279	0.530118
$366$	6.01047	0.314172
$367$	−20.9339	−1.09274	−0.546369	−	0.837544i	$-0.683990\pi$
$367$	−20.9339	−1.09274	−0.546369	+	0.837544i	$0.683990\pi$
$368$	1.17271	0.0611320
$369$	2.78694	0.145082
$370$	−16.5111	−0.858373
$371$	−3.92860	−0.203963
$372$	22.1231	1.14703
$373$	15.0426	0.778874	0.389437	−	0.921053i	$-0.372670\pi$
$373$	15.0426	0.778874	0.389437	+	0.921053i	$0.372670\pi$
$374$	19.9247	1.03028
$375$	14.1924	0.732894
$376$	10.5560	0.544383
$377$	−20.3584	−1.04851
$378$	−35.3647	−1.81896
$379$	−29.0752	−1.49349	−0.746746	−	0.665110i	$-0.768385\pi$
$379$	−29.0752	−1.49349	−0.746746	+	0.665110i	$0.768385\pi$
$380$	33.9958	1.74395
$381$	−35.3116	−1.80907
$382$	−12.5133	−0.640238
$383$	−11.8099	−0.603457	−0.301729	−	0.953394i	$-0.597564\pi$
$383$	−11.8099	−0.603457	−0.301729	+	0.953394i	$0.597564\pi$
$384$	38.8395	1.98202
$385$	−20.1033	−1.02456
$386$	52.6006	2.67730
$387$	9.29836	0.472662
$388$	19.7377	1.00203
$389$	−5.26124	−0.266755	−0.133378	−	0.991065i	$-0.542582\pi$
$389$	−5.26124	−0.266755	−0.133378	+	0.991065i	$0.542582\pi$
$390$	64.8376	3.28318
$391$	10.7666	0.544488
$392$	−26.2282	−1.32472
$393$	−0.132266	−0.00667194
$394$	28.8389	1.45288
$395$	37.8832	1.90611
$396$	−6.72539	−0.337964
$397$	−3.32179	−0.166716	−0.0833580	−	0.996520i	$-0.526564\pi$
$397$	−3.32179	−0.166716	−0.0833580	+	0.996520i	$0.526564\pi$
$398$	−0.543003	−0.0272183
$399$	29.5760	1.48065
$400$	1.20742	0.0603712
$401$	−16.2603	−0.812001	−0.406000	−	0.913873i	$-0.633077\pi$
$401$	−16.2603	−0.812001	−0.406000	+	0.913873i	$0.633077\pi$
$402$	6.85337	0.341815
$403$	16.7332	0.833539
$404$	17.9814	0.894610
$405$	30.1346	1.49740
$406$	−36.2259	−1.79786
$407$	4.92728	0.244236
$408$	−28.7761	−1.42463
$409$	−2.67365	−0.132204	−0.0661019	−	0.997813i	$-0.521056\pi$
$409$	−2.67365	−0.132204	−0.0661019	+	0.997813i	$0.521056\pi$
$410$	16.3994	0.809910
$411$	4.39352	0.216716
$412$	39.5248	1.94725
$413$	−17.0656	−0.839744
$414$	−5.80695	−0.285396
$415$	−6.56578	−0.322302
$416$	25.8519	1.26750
$417$	10.4472	0.511600
$418$	−16.2107	−0.792891
$419$	−4.83001	−0.235961	−0.117981	−	0.993016i	$-0.537642\pi$
$419$	−4.83001	−0.235961	−0.117981	+	0.993016i	$0.537642\pi$
$420$	72.2033	3.52316
$421$	−40.6183	−1.97962	−0.989808	−	0.142410i	$-0.954515\pi$
$421$	−40.6183	−1.97962	−0.989808	+	0.142410i	$0.954515\pi$
$422$	−37.2744	−1.81449
$423$	−3.63200	−0.176594
$424$	−3.10985	−0.151028
$425$	11.0852	0.537712
$426$	−23.1111	−1.11974
$427$	5.06256	0.244994
$428$	37.0861	1.79262
$429$	−19.3489	−0.934175
$430$	54.7152	2.63860
$431$	11.5691	0.557262	0.278631	−	0.960398i	$-0.410119\pi$
$431$	11.5691	0.557262	0.278631	+	0.960398i	$0.410119\pi$
$432$	−1.94519	−0.0935882
$433$	−26.9778	−1.29647	−0.648235	−	0.761441i	$-0.724492\pi$
$433$	−26.9778	−1.29647	−0.648235	+	0.761441i	$0.724492\pi$
$434$	29.7752	1.42925
$435$	21.9134	1.05067
$436$	26.0096	1.24563
$437$	−8.75964	−0.419031
$438$	17.3454	0.828797
$439$	−26.7042	−1.27452	−0.637261	−	0.770648i	$-0.719933\pi$
$439$	−26.7042	−1.27452	−0.637261	+	0.770648i	$0.719933\pi$
$440$	−15.9136	−0.758651
$441$	9.02435	0.429731
$442$	−54.1270	−2.57456
$443$	32.7482	1.55592	0.777958	−	0.628317i	$-0.216256\pi$
$443$	32.7482	1.55592	0.777958	+	0.628317i	$0.216256\pi$
$444$	−17.6969	−0.839859
$445$	4.00455	0.189834
$446$	−55.8692	−2.64548
$447$	−19.7788	−0.935503
$448$	49.9265	2.35881
$449$	−11.0703	−0.522438	−0.261219	−	0.965280i	$-0.584125\pi$
$449$	−11.0703	−0.522438	−0.261219	+	0.965280i	$0.584125\pi$
$450$	−5.97882	−0.281844
$451$	−4.89394	−0.230447
$452$	49.2857	2.31820
$453$	2.01743	0.0947869
$454$	9.16278	0.430030
$455$	54.6120	2.56025
$456$	23.4121	1.09637
$457$	−33.2562	−1.55566	−0.777829	−	0.628476i	$-0.783679\pi$
$457$	−33.2562	−1.55566	−0.777829	+	0.628476i	$0.783679\pi$
$458$	47.7759	2.23242
$459$	−17.8586	−0.833568
$460$	−21.3847	−0.997068
$461$	9.03928	0.421001	0.210501	−	0.977594i	$-0.432491\pi$
$461$	9.03928	0.421001	0.210501	+	0.977594i	$0.432491\pi$
$462$	−34.4297	−1.60181
$463$	−23.3607	−1.08567	−0.542833	−	0.839841i	$-0.682648\pi$
$463$	−23.3607	−1.08567	−0.542833	+	0.839841i	$0.682648\pi$
$464$	−1.99257	−0.0925025
$465$	−18.0113	−0.835254
$466$	0.730900	0.0338583
$467$	−3.62715	−0.167844	−0.0839222	−	0.996472i	$-0.526745\pi$
$467$	−3.62715	−0.167844	−0.0839222	+	0.996472i	$0.526745\pi$
$468$	18.2700	0.844533
$469$	5.77253	0.266551
$470$	−21.3721	−0.985823
$471$	5.00507	0.230621
$472$	−13.5090	−0.621803
$473$	−16.3282	−0.750771
$474$	64.8803	2.98005
$475$	−9.01891	−0.413816
$476$	−60.2760	−2.76274
$477$	1.07001	0.0489923
$478$	67.3984	3.08273
$479$	25.8381	1.18057	0.590286	−	0.807194i	$-0.299015\pi$
$479$	25.8381	1.18057	0.590286	+	0.807194i	$0.299015\pi$
$480$	−27.8266	−1.27010
$481$	−13.3853	−0.610318
$482$	12.9838	0.591395
$483$	−18.6045	−0.846534
$484$	−24.9863	−1.13574
$485$	−16.0692	−0.729667
$486$	24.6042	1.11607
$487$	27.2288	1.23385	0.616927	−	0.787021i	$-0.288377\pi$
$487$	27.2288	1.23385	0.616927	+	0.787021i	$0.288377\pi$
$488$	4.00748	0.181410
$489$	−7.36492	−0.333053
$490$	53.1028	2.39894
$491$	19.5132	0.880619	0.440309	−	0.897846i	$-0.354869\pi$
$491$	19.5132	0.880619	0.440309	+	0.897846i	$0.354869\pi$
$492$	17.5772	0.792441
$493$	−18.2935	−0.823898
$494$	44.0376	1.98134
$495$	5.47540	0.246101
$496$	1.63775	0.0735371
$497$	−19.4663	−0.873182
$498$	−11.2448	−0.503893
$499$	−6.24783	−0.279691	−0.139846	−	0.990173i	$-0.544661\pi$
$499$	−6.24783	−0.279691	−0.139846	+	0.990173i	$0.544661\pi$
$500$	23.5326	1.05241
$501$	−15.5170	−0.693250
$502$	42.4700	1.89553
$503$	26.2156	1.16890	0.584448	−	0.811431i	$-0.301311\pi$
$503$	26.2156	1.16890	0.584448	+	0.811431i	$0.301311\pi$
$504$	13.0727	0.582304
$505$	−14.6394	−0.651444
$506$	10.1972	0.453320
$507$	26.3363	1.16964
$508$	−58.5507	−2.59777
$509$	−12.8970	−0.571649	−0.285825	−	0.958282i	$-0.592267\pi$
$509$	−12.8970	−0.571649	−0.285825	+	0.958282i	$0.592267\pi$
$510$	58.2614	2.57986
$511$	14.6099	0.646303
$512$	5.63752	0.249145
$513$	14.5297	0.641503
$514$	−46.5733	−2.05426
$515$	−32.1787	−1.41796
$516$	58.6447	2.58169
$517$	6.37790	0.280500
$518$	−23.8180	−1.04650
$519$	44.7900	1.96606
$520$	43.2305	1.89578
$521$	−14.2944	−0.626249	−0.313125	−	0.949712i	$-0.601376\pi$
$521$	−14.2944	−0.626249	−0.313125	+	0.949712i	$0.601376\pi$
$522$	9.86662	0.431850
$523$	24.1176	1.05459	0.527295	−	0.849682i	$-0.323206\pi$
$523$	24.1176	1.05459	0.527295	+	0.849682i	$0.323206\pi$
$524$	−0.219312	−0.00958069
$525$	−19.1552	−0.835999
$526$	−55.6313	−2.42564
$527$	15.0360	0.654978
$528$	−1.89377	−0.0824156
$529$	−17.4898	−0.760427
$530$	6.29634	0.273496
$531$	4.64805	0.201708
$532$	49.0404	2.12617
$533$	13.2948	0.575860
$534$	6.85837	0.296791
$535$	−30.1932	−1.30537
$536$	4.56949	0.197372
$537$	32.3205	1.39473
$538$	59.0189	2.54448
$539$	−15.8470	−0.682580
$540$	35.4711	1.52643
$541$	0.718386	0.0308858	0.0154429	−	0.999881i	$-0.495084\pi$
$541$	0.718386	0.0308858	0.0154429	+	0.999881i	$0.495084\pi$
$542$	20.7263	0.890270
$543$	−13.0025	−0.557992
$544$	23.2299	0.995973
$545$	−21.1754	−0.907055
$546$	93.5309	4.00275
$547$	−21.3160	−0.911405	−0.455703	−	0.890132i	$-0.650612\pi$
$547$	−21.3160	−0.911405	−0.455703	+	0.890132i	$0.650612\pi$
$548$	7.28495	0.311198
$549$	−1.37886	−0.0588482
$550$	10.4990	0.447678
$551$	14.8835	0.634061
$552$	−14.7272	−0.626831
$553$	54.6480	2.32387
$554$	52.9986	2.25170
$555$	14.4077	0.611574
$556$	17.3226	0.734640
$557$	−21.3808	−0.905935	−0.452968	−	0.891527i	$-0.649635\pi$
$557$	−21.3808	−0.905935	−0.452968	+	0.891527i	$0.649635\pi$
$558$	−8.10967	−0.343310
$559$	44.3568	1.87609
$560$	5.34512	0.225873
$561$	−17.3864	−0.734056
$562$	9.37751	0.395566
$563$	2.36034	0.0994766	0.0497383	−	0.998762i	$-0.484161\pi$
$563$	2.36034	0.0994766	0.0497383	+	0.998762i	$0.484161\pi$
$564$	−22.9070	−0.964559
$565$	−40.1254	−1.68809
$566$	−23.8226	−1.00134
$567$	43.4704	1.82559
$568$	−15.4094	−0.646563
$569$	−18.6098	−0.780161	−0.390081	−	0.920781i	$-0.627553\pi$
$569$	−18.6098	−0.780161	−0.390081	+	0.920781i	$0.627553\pi$
$570$	−47.4013	−1.98542
$571$	22.5193	0.942405	0.471202	−	0.882025i	$-0.343820\pi$
$571$	22.5193	0.942405	0.471202	+	0.882025i	$0.343820\pi$
$572$	−32.0827	−1.34145
$573$	10.9192	0.456157
$574$	23.6568	0.987418
$575$	5.67326	0.236591
$576$	−13.5982	−0.566591
$577$	−24.3442	−1.01346	−0.506732	−	0.862104i	$-0.669147\pi$
$577$	−24.3442	−1.01346	−0.506732	+	0.862104i	$0.669147\pi$
$578$	−9.33392	−0.388240
$579$	−45.8997	−1.90753
$580$	36.3349	1.50872
$581$	−9.47141	−0.392940
$582$	−27.5209	−1.14078
$583$	−1.87897	−0.0778188
$584$	11.5651	0.478566
$585$	−14.8743	−0.614978
$586$	22.3623	0.923779
$587$	22.6061	0.933055	0.466528	−	0.884507i	$-0.345505\pi$
$587$	22.6061	0.933055	0.466528	+	0.884507i	$0.345505\pi$
$588$	56.9165	2.34720
$589$	−12.2332	−0.504062
$590$	27.3509	1.12602
$591$	−25.1650	−1.03515
$592$	−1.31008	−0.0538440
$593$	20.8948	0.858046	0.429023	−	0.903294i	$-0.358858\pi$
$593$	20.8948	0.858046	0.429023	+	0.903294i	$0.358858\pi$
$594$	−16.9142	−0.693997
$595$	49.0730	2.01180
$596$	−32.7954	−1.34335
$597$	0.473828	0.0193925
$598$	−27.7014	−1.13279
$599$	24.7650	1.01187	0.505936	−	0.862571i	$-0.331147\pi$
$599$	24.7650	1.01187	0.505936	+	0.862571i	$0.331147\pi$
$600$	−15.1631	−0.619030
$601$	−20.5713	−0.839120	−0.419560	−	0.907728i	$-0.637816\pi$
$601$	−20.5713	−0.839120	−0.419560	+	0.907728i	$0.637816\pi$
$602$	78.9289	3.21690
$603$	−1.57223	−0.0640260
$604$	3.34512	0.136111
$605$	20.3423	0.827033
$606$	−25.0720	−1.01848
$607$	29.7533	1.20765	0.603825	−	0.797117i	$-0.293643\pi$
$607$	29.7533	1.20765	0.603825	+	0.797117i	$0.293643\pi$
$608$	−18.8998	−0.766487
$609$	31.6110	1.28094
$610$	−8.11373	−0.328515
$611$	−17.3261	−0.700937
$612$	16.4170	0.663617
$613$	−20.2773	−0.818991	−0.409496	−	0.912312i	$-0.634295\pi$
$613$	−20.2773	−0.818991	−0.409496	+	0.912312i	$0.634295\pi$
$614$	34.3583	1.38659
$615$	−14.3103	−0.577045
$616$	−22.9560	−0.924924
$617$	26.4046	1.06301	0.531506	−	0.847055i	$-0.321626\pi$
$617$	26.4046	1.06301	0.531506	+	0.847055i	$0.321626\pi$
$618$	−55.1106	−2.21687
$619$	35.1474	1.41269	0.706347	−	0.707866i	$-0.250342\pi$
$619$	35.1474	1.41269	0.706347	+	0.707866i	$0.250342\pi$
$620$	−29.8648	−1.19940
$621$	−9.13978	−0.366767
$622$	56.2341	2.25478
$623$	5.77673	0.231440
$624$	5.14456	0.205947
$625$	−31.2431	−1.24972
$626$	−15.1827	−0.606821
$627$	14.1456	0.564920
$628$	8.29896	0.331165
$629$	−12.0277	−0.479576
$630$	−26.4675	−1.05449
$631$	−30.1788	−1.20140	−0.600700	−	0.799475i	$-0.705111\pi$
$631$	−30.1788	−1.20140	−0.600700	+	0.799475i	$0.705111\pi$
$632$	43.2590	1.72075
$633$	32.5259	1.29279
$634$	1.78439	0.0708672
$635$	47.6683	1.89166
$636$	6.74853	0.267597
$637$	43.0497	1.70569
$638$	−17.3261	−0.685946
$639$	5.30191	0.209740
$640$	−52.4307	−2.07251
$641$	4.05273	0.160073	0.0800365	−	0.996792i	$-0.474496\pi$
$641$	4.05273	0.160073	0.0800365	+	0.996792i	$0.474496\pi$
$642$	−51.7101	−2.04084
$643$	−7.58203	−0.299006	−0.149503	−	0.988761i	$-0.547767\pi$
$643$	−7.58203	−0.299006	−0.149503	+	0.988761i	$0.547767\pi$
$644$	−30.8484	−1.21560
$645$	−47.7449	−1.87995
$646$	39.5710	1.55690
$647$	−16.8168	−0.661138	−0.330569	−	0.943782i	$-0.607241\pi$
$647$	−16.8168	−0.661138	−0.330569	+	0.943782i	$0.607241\pi$
$648$	34.4108	1.35179
$649$	−8.16211	−0.320391
$650$	−28.5213	−1.11870
$651$	−25.9820	−1.01832
$652$	−12.2119	−0.478254
$653$	18.5955	0.727699	0.363849	−	0.931458i	$-0.381462\pi$
$653$	18.5955	0.727699	0.363849	+	0.931458i	$0.381462\pi$
$654$	−36.2659	−1.41811
$655$	0.178550	0.00697654
$656$	1.30122	0.0508040
$657$	−3.97920	−0.155243
$658$	−30.8302	−1.20189
$659$	8.76887	0.341587	0.170793	−	0.985307i	$-0.445367\pi$
$659$	8.76887	0.341587	0.170793	+	0.985307i	$0.445367\pi$
$660$	34.5333	1.34421
$661$	−19.6732	−0.765201	−0.382600	−	0.923914i	$-0.624971\pi$
$661$	−19.6732	−0.765201	−0.382600	+	0.923914i	$0.624971\pi$
$662$	−3.60818	−0.140236
$663$	47.2316	1.83432
$664$	−7.49750	−0.290959
$665$	−39.9256	−1.54825
$666$	6.48715	0.251372
$667$	−9.36235	−0.362512
$668$	−25.7290	−0.995485
$669$	48.7519	1.88486
$670$	−9.25160	−0.357420
$671$	2.42131	0.0934738
$672$	−40.1410	−1.54847
$673$	−46.8493	−1.80591	−0.902954	−	0.429737i	$-0.858606\pi$
$673$	−46.8493	−1.80591	−0.902954	+	0.429737i	$0.858606\pi$
$674$	54.6129	2.10361
$675$	−9.41029	−0.362202
$676$	43.6686	1.67956
$677$	31.1502	1.19720	0.598600	−	0.801048i	$-0.295724\pi$
$677$	31.1502	1.19720	0.598600	+	0.801048i	$0.295724\pi$
$678$	−68.7204	−2.63919
$679$	−23.1805	−0.889588
$680$	38.8458	1.48967
$681$	−7.99551	−0.306389
$682$	14.2408	0.545309
$683$	−32.9540	−1.26095	−0.630475	−	0.776209i	$-0.717140\pi$
$683$	−32.9540	−1.26095	−0.630475	+	0.776209i	$0.717140\pi$
$684$	−13.3568	−0.510710
$685$	−5.93096	−0.226610
$686$	13.0238	0.497252
$687$	−41.6896	−1.59056
$688$	4.34139	0.165514
$689$	5.10435	0.194460
$690$	29.8173	1.13513
$691$	7.17124	0.272807	0.136403	−	0.990653i	$-0.456446\pi$
$691$	7.17124	0.272807	0.136403	+	0.990653i	$0.456446\pi$
$692$	74.2669	2.82321
$693$	7.89849	0.300039
$694$	48.7172	1.84928
$695$	−14.1030	−0.534956
$696$	25.0230	0.948495
$697$	11.9463	0.452500
$698$	−48.7096	−1.84368
$699$	−0.637789	−0.0241234
$700$	−31.7614	−1.20047
$701$	−41.0362	−1.54992	−0.774959	−	0.632012i	$-0.782229\pi$
$701$	−41.0362	−1.54992	−0.774959	+	0.632012i	$0.782229\pi$
$702$	45.9486	1.73422
$703$	9.78571	0.369075
$704$	23.8788	0.899966
$705$	18.6495	0.702380
$706$	17.5898	0.661999
$707$	−21.1179	−0.794221
$708$	29.3152	1.10173
$709$	−25.2030	−0.946518	−0.473259	−	0.880923i	$-0.656923\pi$
$709$	−25.2030	−0.946518	−0.473259	+	0.880923i	$0.656923\pi$
$710$	31.1985	1.17086
$711$	−14.8841	−0.558199
$712$	4.57282	0.171374
$713$	7.69520	0.288188
$714$	84.0444	3.14528
$715$	26.1198	0.976824
$716$	53.5911	2.00279
$717$	−58.8124	−2.19639
$718$	68.9245	2.57224
$719$	15.8065	0.589483	0.294742	−	0.955577i	$-0.404766\pi$
$719$	15.8065	0.589483	0.294742	+	0.955577i	$0.404766\pi$
$720$	−1.45582	−0.0542551
$721$	−46.4191	−1.72874
$722$	11.7322	0.436628
$723$	−11.3297	−0.421357
$724$	−21.5597	−0.801259
$725$	−9.63946	−0.358000
$726$	34.8391	1.29300
$727$	−3.82933	−0.142022	−0.0710110	−	0.997476i	$-0.522623\pi$
$727$	−3.82933	−0.142022	−0.0710110	+	0.997476i	$0.522623\pi$
$728$	62.3617	2.31128
$729$	11.7255	0.434277
$730$	−23.4152	−0.866635
$731$	39.8578	1.47420
$732$	−8.69644	−0.321430
$733$	−18.8435	−0.696002	−0.348001	−	0.937494i	$-0.613139\pi$
$733$	−18.8435	−0.696002	−0.348001	+	0.937494i	$0.613139\pi$
$734$	48.3981	1.78640
$735$	−46.3379	−1.70920
$736$	11.8887	0.438224
$737$	2.76088	0.101698
$738$	−6.44326	−0.237180
$739$	22.6466	0.833067	0.416534	−	0.909120i	$-0.363245\pi$
$739$	22.6466	0.833067	0.416534	+	0.909120i	$0.363245\pi$
$740$	23.8896	0.878201
$741$	−38.4275	−1.41167
$742$	9.08274	0.333438
$743$	3.08359	0.113126	0.0565630	−	0.998399i	$-0.481986\pi$
$743$	3.08359	0.113126	0.0565630	+	0.998399i	$0.481986\pi$
$744$	−20.5672	−0.754029
$745$	26.7000	0.978212
$746$	−34.7777	−1.27330
$747$	2.57967	0.0943851
$748$	−28.8287	−1.05408
$749$	−43.5549	−1.59146
$750$	−32.8122	−1.19813
$751$	33.3711	1.21773	0.608864	−	0.793275i	$-0.291626\pi$
$751$	33.3711	1.21773	0.608864	+	0.793275i	$0.291626\pi$
$752$	−1.69578	−0.0618387
$753$	−37.0597	−1.35053
$754$	47.0676	1.71410
$755$	−2.72339	−0.0991143
$756$	51.1685	1.86098
$757$	21.1825	0.769891	0.384945	−	0.922939i	$-0.374220\pi$
$757$	21.1825	0.769891	0.384945	+	0.922939i	$0.374220\pi$
$758$	67.2204	2.44155
$759$	−8.89813	−0.322982
$760$	−31.6048	−1.14643
$761$	17.0839	0.619291	0.309645	−	0.950852i	$-0.399790\pi$
$761$	17.0839	0.619291	0.309645	+	0.950852i	$0.399790\pi$
$762$	81.6388	2.95746
$763$	−30.5464	−1.10585
$764$	18.1053	0.655027
$765$	−13.3657	−0.483238
$766$	27.3039	0.986530
$767$	22.1730	0.800621
$768$	−38.5182	−1.38991
$769$	17.6014	0.634721	0.317361	−	0.948305i	$-0.397203\pi$
$769$	17.6014	0.634721	0.317361	+	0.948305i	$0.397203\pi$
$770$	46.4778	1.67494
$771$	40.6402	1.46362
$772$	−76.1068	−2.73914
$773$	23.7284	0.853452	0.426726	−	0.904381i	$-0.359667\pi$
$773$	23.7284	0.853452	0.426726	+	0.904381i	$0.359667\pi$
$774$	−21.4974	−0.772707
$775$	7.92296	0.284601
$776$	−18.3495	−0.658710
$777$	20.7838	0.745613
$778$	12.1637	0.436091
$779$	−9.71950	−0.348237
$780$	−93.8123	−3.35902
$781$	−9.31030	−0.333149
$782$	−24.8918	−0.890127
$783$	15.5294	0.554977
$784$	4.21346	0.150481
$785$	−6.75650	−0.241150
$786$	0.305793	0.0109073
$787$	−26.2770	−0.936675	−0.468337	−	0.883550i	$-0.655147\pi$
$787$	−26.2770	−0.936675	−0.468337	+	0.883550i	$0.655147\pi$
$788$	−41.7265	−1.48644
$789$	48.5443	1.72822
$790$	−87.5841	−3.11610
$791$	−57.8825	−2.05806
$792$	6.25238	0.222169
$793$	−6.57768	−0.233580
$794$	7.67982	0.272547
$795$	−5.49424	−0.194861
$796$	0.785660	0.0278470
$797$	−36.2854	−1.28530	−0.642648	−	0.766161i	$-0.722164\pi$
$797$	−36.2854	−1.28530	−0.642648	+	0.766161i	$0.722164\pi$
$798$	−68.3783	−2.42057
$799$	−15.5687	−0.550783
$800$	12.2406	0.432770
$801$	−1.57337	−0.0555924
$802$	37.5930	1.32746
$803$	6.98760	0.246587
$804$	−9.91602	−0.349711
$805$	25.1148	0.885181
$806$	−38.6863	−1.36267
$807$	−51.5003	−1.81290
$808$	−16.7168	−0.588094
$809$	7.56412	0.265940	0.132970	−	0.991120i	$-0.457549\pi$
$809$	7.56412	0.265940	0.132970	+	0.991120i	$0.457549\pi$
$810$	−69.6697	−2.44794
$811$	−1.97737	−0.0694350	−0.0347175	−	0.999397i	$-0.511053\pi$
$811$	−1.97737	−0.0694350	−0.0347175	+	0.999397i	$0.511053\pi$
$812$	52.4146	1.83939
$813$	−18.0859	−0.634300
$814$	−11.3916	−0.399276
$815$	9.94215	0.348258
$816$	4.62277	0.161829
$817$	−32.4282	−1.13452
$818$	6.18136	0.216126
$819$	−21.4568	−0.749763
$820$	−23.7280	−0.828619
$821$	21.7434	0.758850	0.379425	−	0.925222i	$-0.376122\pi$
$821$	21.7434	0.758850	0.379425	+	0.925222i	$0.376122\pi$
$822$	−10.1576	−0.354287
$823$	36.9406	1.28767	0.643835	−	0.765165i	$-0.277342\pi$
$823$	36.9406	1.28767	0.643835	+	0.765165i	$0.277342\pi$
$824$	−36.7450	−1.28007
$825$	−9.16150	−0.318962
$826$	39.4549	1.37281
$827$	−6.56198	−0.228182	−0.114091	−	0.993470i	$-0.536396\pi$
$827$	−6.56198	−0.228182	−0.114091	+	0.993470i	$0.536396\pi$
$828$	8.40197	0.291989
$829$	−2.68765	−0.0933460	−0.0466730	−	0.998910i	$-0.514862\pi$
$829$	−2.68765	−0.0933460	−0.0466730	+	0.998910i	$0.514862\pi$
$830$	15.1798	0.526898
$831$	−46.2470	−1.60429
$832$	−64.8685	−2.24891
$833$	38.6833	1.34030
$834$	−24.1533	−0.836361
$835$	20.9470	0.724899
$836$	23.4549	0.811206
$837$	−12.7641	−0.441192
$838$	11.1667	0.385749
$839$	−14.7097	−0.507836	−0.253918	−	0.967226i	$-0.581719\pi$
$839$	−14.7097	−0.507836	−0.253918	+	0.967226i	$0.581719\pi$
$840$	−67.1251	−2.31604
$841$	−13.0924	−0.451461
$842$	93.9076	3.23627
$843$	−8.18288	−0.281833
$844$	53.9316	1.85640
$845$	−35.5523	−1.22303
$846$	8.39702	0.288695
$847$	29.3446	1.00829
$848$	0.499586	0.0171558
$849$	20.7878	0.713435
$850$	−25.6285	−0.879050
$851$	−6.15561	−0.211011
$852$	33.4391	1.14560
$853$	−43.6212	−1.49356	−0.746782	−	0.665069i	$-0.768402\pi$
$853$	−43.6212	−1.49356	−0.746782	+	0.665069i	$0.768402\pi$
$854$	−11.7044	−0.400516
$855$	10.8743	0.371893
$856$	−34.4777	−1.17842
$857$	45.5642	1.55644	0.778222	−	0.627990i	$-0.216122\pi$
$857$	45.5642	1.55644	0.778222	+	0.627990i	$0.216122\pi$
$858$	44.7338	1.52719
$859$	−24.4321	−0.833612	−0.416806	−	0.908995i	$-0.636851\pi$
$859$	−24.4321	−0.833612	−0.416806	+	0.908995i	$0.636851\pi$
$860$	−79.1664	−2.69955
$861$	−20.6431	−0.703516
$862$	−26.7471	−0.911010
$863$	−40.3512	−1.37357	−0.686786	−	0.726860i	$-0.740979\pi$
$863$	−40.3512	−1.37357	−0.686786	+	0.726860i	$0.740979\pi$
$864$	−19.7199	−0.670886
$865$	−60.4635	−2.05582
$866$	62.3713	2.11946
$867$	8.14485	0.276613
$868$	−43.0811	−1.46227
$869$	26.1370	0.886636
$870$	−50.6627	−1.71763
$871$	−7.50013	−0.254132
$872$	−24.1803	−0.818849
$873$	6.31354	0.213681
$874$	20.2519	0.685030
$875$	−27.6374	−0.934315
$876$	−25.0968	−0.847942
$877$	−25.2385	−0.852243	−0.426122	−	0.904666i	$-0.640120\pi$
$877$	−25.2385	−0.852243	−0.426122	+	0.904666i	$0.640120\pi$
$878$	61.7388	2.08358
$879$	−19.5135	−0.658175
$880$	2.55646	0.0861782
$881$	−5.17729	−0.174427	−0.0872136	−	0.996190i	$-0.527796\pi$
$881$	−5.17729	−0.174427	−0.0872136	+	0.996190i	$0.527796\pi$
$882$	−20.8639	−0.702523
$883$	−45.7172	−1.53851	−0.769253	−	0.638944i	$-0.779372\pi$
$883$	−45.7172	−1.53851	−0.769253	+	0.638944i	$0.779372\pi$
$884$	78.3153	2.63403
$885$	−23.8666	−0.802268
$886$	−75.7123	−2.54361
$887$	−39.1465	−1.31441	−0.657205	−	0.753712i	$-0.728261\pi$
$887$	−39.1465	−1.31441	−0.657205	+	0.753712i	$0.728261\pi$
$888$	16.4523	0.552102
$889$	68.7635	2.30625
$890$	−9.25833	−0.310340
$891$	20.7910	0.696523
$892$	80.8361	2.70659
$893$	12.6667	0.423875
$894$	45.7275	1.52936
$895$	−43.6305	−1.45841
$896$	−75.6335	−2.52674
$897$	24.1725	0.807095
$898$	25.5939	0.854080
$899$	−13.0750	−0.436074
$900$	8.65065	0.288355
$901$	4.58664	0.152803
$902$	11.3146	0.376734
$903$	−68.8739	−2.29198
$904$	−45.8193	−1.52393
$905$	17.5526	0.583467
$906$	−4.66419	−0.154957
$907$	38.7789	1.28763	0.643816	−	0.765180i	$-0.277350\pi$
$907$	38.7789	1.28763	0.643816	+	0.765180i	$0.277350\pi$
$908$	−13.2575	−0.439964
$909$	5.75175	0.190773
$910$	−126.260	−4.18549
$911$	−20.1893	−0.668901	−0.334450	−	0.942413i	$-0.608551\pi$
$911$	−20.1893	−0.668901	−0.334450	+	0.942413i	$0.608551\pi$
$912$	−3.76107	−0.124542
$913$	−4.52997	−0.149920
$914$	76.8867	2.54318
$915$	7.08010	0.234061
$916$	−69.1260	−2.28399
$917$	0.257566	0.00850559
$918$	41.2882	1.36271
$919$	27.3858	0.903373	0.451687	−	0.892177i	$-0.350822\pi$
$919$	27.3858	0.903373	0.451687	+	0.892177i	$0.350822\pi$
$920$	19.8807	0.655447
$921$	−29.9813	−0.987917
$922$	−20.8984	−0.688251
$923$	25.2921	0.832501
$924$	49.8157	1.63882
$925$	−6.33780	−0.208385
$926$	54.0089	1.77484
$927$	12.6429	0.415246
$928$	−20.2002	−0.663103
$929$	30.8446	1.01198	0.505990	−	0.862539i	$-0.331127\pi$
$929$	30.8446	1.01198	0.505990	+	0.862539i	$0.331127\pi$
$930$	41.6412	1.36547
$931$	−31.4726	−1.03147
$932$	−1.05753	−0.0346404
$933$	−49.0703	−1.60649
$934$	8.38579	0.274392
$935$	23.4705	0.767569
$936$	−16.9851	−0.555174
$937$	9.79936	0.320131	0.160066	−	0.987106i	$-0.448829\pi$
$937$	9.79936	0.320131	0.160066	+	0.987106i	$0.448829\pi$
$938$	−13.3458	−0.435756
$939$	13.2485	0.432349
$940$	30.9229	1.00859
$941$	27.5452	0.897948	0.448974	−	0.893545i	$-0.351790\pi$
$941$	27.5452	0.897948	0.448974	+	0.893545i	$0.351790\pi$
$942$	−11.5715	−0.377019
$943$	6.11396	0.199098
$944$	2.17017	0.0706330
$945$	−41.6582	−1.35514
$946$	37.7500	1.22736
$947$	−20.3817	−0.662317	−0.331159	−	0.943575i	$-0.607440\pi$
$947$	−20.3817	−0.662317	−0.331159	+	0.943575i	$0.607440\pi$
$948$	−93.8741	−3.04889
$949$	−18.9823	−0.616193
$950$	20.8513	0.676505
$951$	−1.55707	−0.0504916
$952$	56.0366	1.81616
$953$	−8.55040	−0.276975	−0.138487	−	0.990364i	$-0.544224\pi$
$953$	−8.55040	−0.276975	−0.138487	+	0.990364i	$0.544224\pi$
$954$	−2.47381	−0.0800925
$955$	−14.7402	−0.476982
$956$	−97.5175	−3.15394
$957$	15.1189	0.488723
$958$	−59.7364	−1.92999
$959$	−8.55565	−0.276276
$960$	69.8234	2.25354
$961$	−20.2533	−0.653332
$962$	30.9462	0.997746
$963$	11.8628	0.382273
$964$	−18.7860	−0.605056
$965$	61.9615	1.99461
$966$	43.0127	1.38391
$967$	−20.1133	−0.646801	−0.323401	−	0.946262i	$-0.604826\pi$
$967$	−20.1133	−0.646801	−0.323401	+	0.946262i	$0.604826\pi$
$968$	23.2290	0.746608
$969$	−34.5300	−1.10926
$970$	37.1513	1.19286
$971$	−7.56154	−0.242662	−0.121331	−	0.992612i	$-0.538716\pi$
$971$	−7.56154	−0.242662	−0.121331	+	0.992612i	$0.538716\pi$
$972$	−35.5994	−1.14185
$973$	−20.3441	−0.652202
$974$	−62.9516	−2.01710
$975$	24.8879	0.797051
$976$	−0.643787	−0.0206071
$977$	31.9643	1.02263	0.511314	−	0.859394i	$-0.329159\pi$
$977$	31.9643	1.02263	0.511314	+	0.859394i	$0.329159\pi$
$978$	17.0273	0.544474
$979$	2.76289	0.0883023
$980$	−76.8335	−2.45436
$981$	8.31973	0.265629
$982$	−45.1136	−1.43963
$983$	−21.5446	−0.687167	−0.343584	−	0.939122i	$-0.611641\pi$
$983$	−21.5446	−0.687167	−0.343584	+	0.939122i	$0.611641\pi$
$984$	−16.3410	−0.520931
$985$	33.9711	1.08241
$986$	42.2937	1.34691
$987$	26.9026	0.856320
$988$	−63.7171	−2.02711
$989$	20.3987	0.648640
$990$	−12.6589	−0.402325
$991$	−7.09254	−0.225302	−0.112651	−	0.993635i	$-0.535934\pi$
$991$	−7.09254	−0.225302	−0.112651	+	0.993635i	$0.535934\pi$
$992$	16.6031	0.527150
$993$	3.14853	0.0999155
$994$	45.0051	1.42748
$995$	−0.639636	−0.0202778
$996$	16.2699	0.515533
$997$	−15.6046	−0.494203	−0.247101	−	0.968990i	$-0.579478\pi$
$997$	−15.6046	−0.494203	−0.247101	+	0.968990i	$0.579478\pi$
$998$	14.4447	0.457239
$999$	10.2104	0.323042

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8003.2.a.a.1.17	✓	147

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8003.2.a.a.1.17	✓	147	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)

\(f(q)\)	\(=\)	\(q-2.31195 q^{2} +2.01743 q^{3} +3.34512 q^{4} -2.72339 q^{5} -4.66419 q^{6} -3.92860 q^{7} -3.10985 q^{8} +1.07001 q^{9} +O(q^{10})\)	\(q-2.31195 q^{2} +2.01743 q^{3} +3.34512 q^{4} -2.72339 q^{5} -4.66419 q^{6} -3.92860 q^{7} -3.10985 q^{8} +1.07001 q^{9} +6.29634 q^{10} -1.87897 q^{11} +6.74853 q^{12} +5.10435 q^{13} +9.08274 q^{14} -5.49424 q^{15} +0.499586 q^{16} +4.58664 q^{17} -2.47381 q^{18} -3.73168 q^{19} -9.11006 q^{20} -7.92566 q^{21} +4.34408 q^{22} +2.34737 q^{23} -6.27389 q^{24} +2.41685 q^{25} -11.8010 q^{26} -3.89362 q^{27} -13.1416 q^{28} -3.98844 q^{29} +12.7024 q^{30} +3.27822 q^{31} +5.06468 q^{32} -3.79067 q^{33} -10.6041 q^{34} +10.6991 q^{35} +3.57931 q^{36} -2.62234 q^{37} +8.62745 q^{38} +10.2977 q^{39} +8.46934 q^{40} +2.60459 q^{41} +18.3237 q^{42} +8.68999 q^{43} -6.28536 q^{44} -2.91405 q^{45} -5.42702 q^{46} -3.39437 q^{47} +1.00788 q^{48} +8.43391 q^{49} -5.58764 q^{50} +9.25320 q^{51} +17.0747 q^{52} +1.00000 q^{53} +9.00185 q^{54} +5.11716 q^{55} +12.2174 q^{56} -7.52838 q^{57} +9.22107 q^{58} +4.34394 q^{59} -18.3789 q^{60} -1.28864 q^{61} -7.57908 q^{62} -4.20364 q^{63} -12.7085 q^{64} -13.9011 q^{65} +8.76385 q^{66} -1.46936 q^{67} +15.3429 q^{68} +4.73566 q^{69} -24.7358 q^{70} +4.95502 q^{71} -3.32757 q^{72} -3.71885 q^{73} +6.06271 q^{74} +4.87582 q^{75} -12.4829 q^{76} +7.38171 q^{77} -23.8077 q^{78} -13.9103 q^{79} -1.36057 q^{80} -11.0651 q^{81} -6.02170 q^{82} +2.41089 q^{83} -26.5123 q^{84} -12.4912 q^{85} -20.0908 q^{86} -8.04637 q^{87} +5.84330 q^{88} -1.47043 q^{89} +6.73714 q^{90} -20.0530 q^{91} +7.85225 q^{92} +6.61356 q^{93} +7.84762 q^{94} +10.1628 q^{95} +10.2176 q^{96} +5.90046 q^{97} -19.4988 q^{98} -2.01051 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 147 q - 6 q^{2} - 23 q^{3} + 130 q^{4} - 25 q^{5} - 18 q^{6} - 33 q^{7} - 15 q^{8} + 114 q^{9}+O(q^{10}) \) 147 * q - 6 * q^2 - 23 * q^3 + 130 * q^4 - 25 * q^5 - 18 * q^6 - 33 * q^7 - 15 * q^8 + 114 * q^9	\( 147 q - 6 q^{2} - 23 q^{3} + 130 q^{4} - 25 q^{5} - 18 q^{6} - 33 q^{7} - 15 q^{8} + 114 q^{9} - 24 q^{10} - 13 q^{11} - 52 q^{12} - 119 q^{13} - 6 q^{14} - 22 q^{15} + 100 q^{16} - 42 q^{17} - 6 q^{18} - 31 q^{19} - 50 q^{20} - 44 q^{21} - 38 q^{22} - 16 q^{23} - 30 q^{24} + 80 q^{25} - 18 q^{26} - 68 q^{27} - 72 q^{28} - 40 q^{29} - 3 q^{30} - 44 q^{31} - 41 q^{32} - 71 q^{33} - 55 q^{34} - 24 q^{35} + 108 q^{36} - 145 q^{37} - 39 q^{38} + 28 q^{39} - 81 q^{40} - 28 q^{41} - 54 q^{42} - 47 q^{43} - 33 q^{44} - 89 q^{45} - 43 q^{46} - 65 q^{47} - 82 q^{48} + 52 q^{49} - 43 q^{50} + 7 q^{51} - 215 q^{52} + 147 q^{53} - 88 q^{54} - 48 q^{55} + 19 q^{56} - 66 q^{57} - 110 q^{58} - 66 q^{59} - 118 q^{60} - 80 q^{61} - 41 q^{62} - 52 q^{63} + 33 q^{64} - 17 q^{65} - 86 q^{66} - 114 q^{67} - 77 q^{68} - 49 q^{69} - 56 q^{70} + 10 q^{71} + 5 q^{72} - 143 q^{73} - 30 q^{74} - 97 q^{75} - 104 q^{76} - 116 q^{77} - 33 q^{78} - 31 q^{79} - 83 q^{80} - q^{81} - 72 q^{82} - 70 q^{83} - 64 q^{84} - 85 q^{85} - 43 q^{87} - 149 q^{88} - 130 q^{89} + 42 q^{90} - 35 q^{91} - 31 q^{92} - 149 q^{93} - 94 q^{94} - 9 q^{95} + 6 q^{96} - 211 q^{97} - 18 q^{98} - 19 q^{99}+O(q^{100}) \) 147 * q - 6 * q^2 - 23 * q^3 + 130 * q^4 - 25 * q^5 - 18 * q^6 - 33 * q^7 - 15 * q^8 + 114 * q^9 - 24 * q^10 - 13 * q^11 - 52 * q^12 - 119 * q^13 - 6 * q^14 - 22 * q^15 + 100 * q^16 - 42 * q^17 - 6 * q^18 - 31 * q^19 - 50 * q^20 - 44 * q^21 - 38 * q^22 - 16 * q^23 - 30 * q^24 + 80 * q^25 - 18 * q^26 - 68 * q^27 - 72 * q^28 - 40 * q^29 - 3 * q^30 - 44 * q^31 - 41 * q^32 - 71 * q^33 - 55 * q^34 - 24 * q^35 + 108 * q^36 - 145 * q^37 - 39 * q^38 + 28 * q^39 - 81 * q^40 - 28 * q^41 - 54 * q^42 - 47 * q^43 - 33 * q^44 - 89 * q^45 - 43 * q^46 - 65 * q^47 - 82 * q^48 + 52 * q^49 - 43 * q^50 + 7 * q^51 - 215 * q^52 + 147 * q^53 - 88 * q^54 - 48 * q^55 + 19 * q^56 - 66 * q^57 - 110 * q^58 - 66 * q^59 - 118 * q^60 - 80 * q^61 - 41 * q^62 - 52 * q^63 + 33 * q^64 - 17 * q^65 - 86 * q^66 - 114 * q^67 - 77 * q^68 - 49 * q^69 - 56 * q^70 + 10 * q^71 + 5 * q^72 - 143 * q^73 - 30 * q^74 - 97 * q^75 - 104 * q^76 - 116 * q^77 - 33 * q^78 - 31 * q^79 - 83 * q^80 - q^81 - 72 * q^82 - 70 * q^83 - 64 * q^84 - 85 * q^85 - 43 * q^87 - 149 * q^88 - 130 * q^89 + 42 * q^90 - 35 * q^91 - 31 * q^92 - 149 * q^93 - 94 * q^94 - 9 * q^95 + 6 * q^96 - 211 * q^97 - 18 * q^98 - 19 * q^99

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