LMFDB - Embedded newform 6047.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6047,2,Mod(1,6047)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6047, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6047.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6047 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6047.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:	$48.2855381023$
Analytic rank:	$0$
Dimension:	$287$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6047.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.82393 q^{2} +0.966727 q^{3} +5.97458 q^{4} -3.10169 q^{5} -2.72997 q^{6} +3.62589 q^{7} -11.2239 q^{8} -2.06544 q^{9} +O(q^{10})$	\(q-2.82393 q^{2} +0.966727 q^{3} +5.97458 q^{4} -3.10169 q^{5} -2.72997 q^{6} +3.62589 q^{7} -11.2239 q^{8} -2.06544 q^{9} +8.75895 q^{10} -0.588325 q^{11} +5.77579 q^{12} -6.47929 q^{13} -10.2393 q^{14} -2.99849 q^{15} +19.7464 q^{16} -3.50303 q^{17} +5.83265 q^{18} -4.13417 q^{19} -18.5313 q^{20} +3.50525 q^{21} +1.66139 q^{22} +5.00683 q^{23} -10.8505 q^{24} +4.62048 q^{25} +18.2971 q^{26} -4.89690 q^{27} +21.6632 q^{28} -5.36564 q^{29} +8.46752 q^{30} -4.79916 q^{31} -33.3147 q^{32} -0.568750 q^{33} +9.89230 q^{34} -11.2464 q^{35} -12.3401 q^{36} +7.44350 q^{37} +11.6746 q^{38} -6.26371 q^{39} +34.8132 q^{40} +11.1037 q^{41} -9.89858 q^{42} -4.86561 q^{43} -3.51499 q^{44} +6.40635 q^{45} -14.1389 q^{46} -10.4131 q^{47} +19.0894 q^{48} +6.14709 q^{49} -13.0479 q^{50} -3.38647 q^{51} -38.7110 q^{52} -7.50750 q^{53} +13.8285 q^{54} +1.82480 q^{55} -40.6968 q^{56} -3.99661 q^{57} +15.1522 q^{58} -2.66078 q^{59} -17.9147 q^{60} -10.1421 q^{61} +13.5525 q^{62} -7.48905 q^{63} +54.5855 q^{64} +20.0968 q^{65} +1.60611 q^{66} +6.52899 q^{67} -20.9291 q^{68} +4.84024 q^{69} +31.7590 q^{70} -5.41114 q^{71} +23.1823 q^{72} +12.2909 q^{73} -21.0199 q^{74} +4.46674 q^{75} -24.6999 q^{76} -2.13320 q^{77} +17.6883 q^{78} -2.09018 q^{79} -61.2473 q^{80} +1.46235 q^{81} -31.3560 q^{82} -9.75936 q^{83} +20.9424 q^{84} +10.8653 q^{85} +13.7401 q^{86} -5.18711 q^{87} +6.60332 q^{88} -9.41261 q^{89} -18.0911 q^{90} -23.4932 q^{91} +29.9137 q^{92} -4.63947 q^{93} +29.4060 q^{94} +12.8229 q^{95} -32.2062 q^{96} +17.6663 q^{97} -17.3589 q^{98} +1.21515 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 287 q + 21 q^{2} + 29 q^{3} + 319 q^{4} + 19 q^{5} + 15 q^{6} + 52 q^{7} + 60 q^{8} + 352 q^{9}+O(q^{10}) $ 287 * q + 21 * q^2 + 29 * q^3 + 319 * q^4 + 19 * q^5 + 15 * q^6 + 52 * q^7 + 60 * q^8 + 352 * q^9	\( 287 q + 21 q^{2} + 29 q^{3} + 319 q^{4} + 19 q^{5} + 15 q^{6} + 52 q^{7} + 60 q^{8} + 352 q^{9} + 38 q^{10} + 32 q^{11} + 80 q^{12} + 86 q^{13} + 14 q^{14} + 41 q^{15} + 375 q^{16} + 59 q^{17} + 93 q^{18} + 39 q^{19} + 27 q^{20} + 51 q^{21} + 99 q^{22} + 68 q^{23} + 31 q^{24} + 492 q^{25} + 19 q^{26} + 107 q^{27} + 142 q^{28} + 39 q^{29} + 12 q^{30} + 104 q^{31} + 131 q^{32} + 139 q^{33} + 71 q^{34} - 5 q^{35} + 410 q^{36} + 298 q^{37} + 19 q^{38} + 37 q^{39} + 98 q^{40} + 90 q^{41} + 32 q^{42} + 105 q^{43} + 85 q^{44} + 73 q^{45} + 97 q^{46} + 66 q^{47} + 161 q^{48} + 473 q^{49} + 85 q^{50} + 34 q^{51} + 179 q^{52} + 95 q^{53} + 28 q^{54} + 62 q^{55} + 16 q^{56} + 247 q^{57} + 247 q^{58} + 32 q^{59} + 51 q^{60} + 106 q^{61} + 22 q^{62} + 104 q^{63} + 480 q^{64} + 150 q^{65} - 27 q^{66} + 232 q^{67} + 88 q^{68} + 57 q^{69} + 123 q^{70} + 46 q^{71} + 240 q^{72} + 372 q^{73} + 13 q^{74} + 81 q^{75} + 82 q^{76} + 65 q^{77} + 154 q^{78} + 143 q^{79} + 17 q^{80} + 519 q^{81} + 98 q^{82} + 49 q^{83} + 79 q^{84} + 236 q^{85} + 61 q^{86} + 31 q^{87} + 254 q^{88} + 114 q^{89} + 36 q^{90} + 96 q^{91} + 151 q^{92} + 189 q^{93} + 8 q^{94} + 30 q^{95} + 23 q^{96} + 503 q^{97} + 91 q^{98} + 130 q^{99}+O(q^{100}) \) 287 * q + 21 * q^2 + 29 * q^3 + 319 * q^4 + 19 * q^5 + 15 * q^6 + 52 * q^7 + 60 * q^8 + 352 * q^9 + 38 * q^10 + 32 * q^11 + 80 * q^12 + 86 * q^13 + 14 * q^14 + 41 * q^15 + 375 * q^16 + 59 * q^17 + 93 * q^18 + 39 * q^19 + 27 * q^20 + 51 * q^21 + 99 * q^22 + 68 * q^23 + 31 * q^24 + 492 * q^25 + 19 * q^26 + 107 * q^27 + 142 * q^28 + 39 * q^29 + 12 * q^30 + 104 * q^31 + 131 * q^32 + 139 * q^33 + 71 * q^34 - 5 * q^35 + 410 * q^36 + 298 * q^37 + 19 * q^38 + 37 * q^39 + 98 * q^40 + 90 * q^41 + 32 * q^42 + 105 * q^43 + 85 * q^44 + 73 * q^45 + 97 * q^46 + 66 * q^47 + 161 * q^48 + 473 * q^49 + 85 * q^50 + 34 * q^51 + 179 * q^52 + 95 * q^53 + 28 * q^54 + 62 * q^55 + 16 * q^56 + 247 * q^57 + 247 * q^58 + 32 * q^59 + 51 * q^60 + 106 * q^61 + 22 * q^62 + 104 * q^63 + 480 * q^64 + 150 * q^65 - 27 * q^66 + 232 * q^67 + 88 * q^68 + 57 * q^69 + 123 * q^70 + 46 * q^71 + 240 * q^72 + 372 * q^73 + 13 * q^74 + 81 * q^75 + 82 * q^76 + 65 * q^77 + 154 * q^78 + 143 * q^79 + 17 * q^80 + 519 * q^81 + 98 * q^82 + 49 * q^83 + 79 * q^84 + 236 * q^85 + 61 * q^86 + 31 * q^87 + 254 * q^88 + 114 * q^89 + 36 * q^90 + 96 * q^91 + 151 * q^92 + 189 * q^93 + 8 * q^94 + 30 * q^95 + 23 * q^96 + 503 * q^97 + 91 * q^98 + 130 * 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 $

$2$	−2.82393	−1.99682	−0.998410	−	0.0563705i	$-0.982047\pi$
$2$	−2.82393	−1.99682	−0.998410	+	0.0563705i	$0.982047\pi$
$3$	0.966727	0.558140	0.279070	−	0.960271i	$-0.409974\pi$
$3$	0.966727	0.558140	0.279070	+	0.960271i	$0.409974\pi$
$4$	5.97458	2.98729
$5$	−3.10169	−1.38712	−0.693559	−	0.720400i	$-0.743958\pi$
$5$	−3.10169	−1.38712	−0.693559	+	0.720400i	$0.743958\pi$
$6$	−2.72997	−1.11451
$7$	3.62589	1.37046	0.685229	−	0.728328i	$-0.259702\pi$
$7$	3.62589	1.37046	0.685229	+	0.728328i	$0.259702\pi$
$8$	−11.2239	−3.96826
$9$	−2.06544	−0.688479
$10$	8.75895	2.76982
$11$	−0.588325	−0.177387	−0.0886933	−	0.996059i	$-0.528269\pi$
$11$	−0.588325	−0.177387	−0.0886933	+	0.996059i	$0.528269\pi$
$12$	5.77579	1.66733
$13$	−6.47929	−1.79703	−0.898516	−	0.438940i	$-0.855354\pi$
$13$	−6.47929	−1.79703	−0.898516	+	0.438940i	$0.855354\pi$
$14$	−10.2393	−2.73656
$15$	−2.99849	−0.774206
$16$	19.7464	4.93661
$17$	−3.50303	−0.849609	−0.424804	−	0.905285i	$-0.639657\pi$
$17$	−3.50303	−0.849609	−0.424804	+	0.905285i	$0.639657\pi$
$18$	5.83265	1.37477
$19$	−4.13417	−0.948443	−0.474222	−	0.880405i	$-0.657270\pi$
$19$	−4.13417	−0.948443	−0.474222	+	0.880405i	$0.657270\pi$
$20$	−18.5313	−4.14372
$21$	3.50525	0.764908
$22$	1.66139	0.354209
$23$	5.00683	1.04400	0.521998	−	0.852947i	$-0.325187\pi$
$23$	5.00683	1.04400	0.521998	+	0.852947i	$0.325187\pi$
$24$	−10.8505	−2.21485
$25$	4.62048	0.924096
$26$	18.2971	3.58835
$27$	−4.89690	−0.942408
$28$	21.6632	4.09396
$29$	−5.36564	−0.996374	−0.498187	−	0.867070i	$-0.666001\pi$
$29$	−5.36564	−0.996374	−0.498187	+	0.867070i	$0.666001\pi$
$30$	8.46752	1.54595
$31$	−4.79916	−0.861954	−0.430977	−	0.902363i	$-0.641831\pi$
$31$	−4.79916	−0.861954	−0.430977	+	0.902363i	$0.641831\pi$
$32$	−33.3147	−5.88926
$33$	−0.568750	−0.0990066
$34$	9.89230	1.69652
$35$	−11.2464	−1.90099
$36$	−12.3401	−2.05669
$37$	7.44350	1.22370	0.611852	−	0.790972i	$-0.290425\pi$
$37$	7.44350	1.22370	0.611852	+	0.790972i	$0.290425\pi$
$38$	11.6746	1.89387
$39$	−6.26371	−1.00300
$40$	34.8132	5.50444
$41$	11.1037	1.73410	0.867051	−	0.498219i	$-0.166012\pi$
$41$	11.1037	1.73410	0.867051	+	0.498219i	$0.166012\pi$
$42$	−9.89858	−1.52738
$43$	−4.86561	−0.741998	−0.370999	−	0.928633i	$-0.620985\pi$
$43$	−4.86561	−0.741998	−0.370999	+	0.928633i	$0.620985\pi$
$44$	−3.51499	−0.529905
$45$	6.40635	0.955002
$46$	−14.1389	−2.08467
$47$	−10.4131	−1.51891	−0.759456	−	0.650559i	$-0.774535\pi$
$47$	−10.4131	−1.51891	−0.759456	+	0.650559i	$0.774535\pi$
$48$	19.0894	2.75532
$49$	6.14709	0.878155
$50$	−13.0479	−1.84525
$51$	−3.38647	−0.474201
$52$	−38.7110	−5.36826
$53$	−7.50750	−1.03123	−0.515617	−	0.856819i	$-0.672437\pi$
$53$	−7.50750	−1.03123	−0.515617	+	0.856819i	$0.672437\pi$
$54$	13.8285	1.88182
$55$	1.82480	0.246056
$56$	−40.6968	−5.43833
$57$	−3.99661	−0.529365
$58$	15.1522	1.98958
$59$	−2.66078	−0.346404	−0.173202	−	0.984886i	$-0.555411\pi$
$59$	−2.66078	−0.346404	−0.173202	+	0.984886i	$0.555411\pi$
$60$	−17.9147	−2.31278
$61$	−10.1421	−1.29857	−0.649283	−	0.760547i	$-0.724931\pi$
$61$	−10.1421	−1.29857	−0.649283	+	0.760547i	$0.724931\pi$
$62$	13.5525	1.72117
$63$	−7.48905	−0.943532
$64$	54.5855	6.82318
$65$	20.0968	2.49270
$66$	1.60611	0.197698
$67$	6.52899	0.797643	0.398821	−	0.917029i	$-0.369419\pi$
$67$	6.52899	0.797643	0.398821	+	0.917029i	$0.369419\pi$
$68$	−20.9291	−2.53803
$69$	4.84024	0.582696
$70$	31.7590	3.79593
$71$	−5.41114	−0.642184	−0.321092	−	0.947048i	$-0.604050\pi$
$71$	−5.41114	−0.642184	−0.321092	+	0.947048i	$0.604050\pi$
$72$	23.1823	2.73206
$73$	12.2909	1.43855	0.719273	−	0.694728i	$-0.244475\pi$
$73$	12.2909	1.43855	0.719273	+	0.694728i	$0.244475\pi$
$74$	−21.0199	−2.44352
$75$	4.46674	0.515775
$76$	−24.6999	−2.83328
$77$	−2.13320	−0.243101
$78$	17.6883	2.00280
$79$	−2.09018	−0.235164	−0.117582	−	0.993063i	$-0.537514\pi$
$79$	−2.09018	−0.235164	−0.117582	+	0.993063i	$0.537514\pi$
$80$	−61.2473	−6.84766
$81$	1.46235	0.162483
$82$	−31.3560	−3.46269
$83$	−9.75936	−1.07123	−0.535614	−	0.844463i	$-0.679920\pi$
$83$	−9.75936	−1.07123	−0.535614	+	0.844463i	$0.679920\pi$
$84$	20.9424	2.28500
$85$	10.8653	1.17851
$86$	13.7401	1.48164
$87$	−5.18711	−0.556117
$88$	6.60332	0.703916
$89$	−9.41261	−0.997734	−0.498867	−	0.866678i	$-0.666250\pi$
$89$	−9.41261	−0.997734	−0.498867	+	0.866678i	$0.666250\pi$
$90$	−18.0911	−1.90697
$91$	−23.4932	−2.46276
$92$	29.9137	3.11872
$93$	−4.63947	−0.481091
$94$	29.4060	3.03299
$95$	12.8229	1.31560
$96$	−32.2062	−3.28703
$97$	17.6663	1.79374	0.896869	−	0.442296i	$-0.145836\pi$
$97$	17.6663	1.79374	0.896869	+	0.442296i	$0.145836\pi$
$98$	−17.3589	−1.75352
$99$	1.21515	0.122127
$100$	27.6054	2.76054
$101$	0.0158729	0.00157942	0.000789708	−	1.00000i	$-0.499749\pi$
$101$	0.0158729	0.00157942	0.000789708		1.00000i	$0.499749\pi$
$102$	9.56316	0.946894
$103$	−14.3148	−1.41048	−0.705242	−	0.708967i	$-0.749162\pi$
$103$	−14.3148	−1.41048	−0.705242	+	0.708967i	$0.749162\pi$
$104$	72.7231	7.13109
$105$	−10.8722	−1.06102
$106$	21.2007	2.05919
$107$	3.06040	0.295860	0.147930	−	0.988998i	$-0.452739\pi$
$107$	3.06040	0.295860	0.147930	+	0.988998i	$0.452739\pi$
$108$	−29.2569	−2.81525
$109$	1.43322	0.137277	0.0686386	−	0.997642i	$-0.478134\pi$
$109$	1.43322	0.137277	0.0686386	+	0.997642i	$0.478134\pi$
$110$	−5.15311	−0.491330
$111$	7.19584	0.682999
$112$	71.5984	6.76542
$113$	16.1354	1.51789	0.758945	−	0.651155i	$-0.225715\pi$
$113$	16.1354	1.51789	0.758945	+	0.651155i	$0.225715\pi$
$114$	11.2862	1.05705
$115$	−15.5296	−1.44815
$116$	−32.0574	−2.97646
$117$	13.3826	1.23722
$118$	7.51385	0.691706
$119$	−12.7016	−1.16435
$120$	33.6548	3.07225
$121$	−10.6539	−0.968534
$122$	28.6407	2.59300
$123$	10.7342	0.967873
$124$	−28.6729	−2.57491
$125$	1.17716	0.105288
$126$	21.1486	1.88406
$127$	18.3375	1.62719	0.813595	−	0.581432i	$-0.197507\pi$
$127$	18.3375	1.62719	0.813595	+	0.581432i	$0.197507\pi$
$128$	−87.5161	−7.73540
$129$	−4.70371	−0.414139
$130$	−56.7518	−4.97746
$131$	3.11235	0.271927	0.135964	−	0.990714i	$-0.456587\pi$
$131$	3.11235	0.271927	0.135964	+	0.990714i	$0.456587\pi$
$132$	−3.39804	−0.295761
$133$	−14.9900	−1.29980
$134$	−18.4374	−1.59275
$135$	15.1887	1.30723
$136$	39.3177	3.37147
$137$	−8.80980	−0.752672	−0.376336	−	0.926483i	$-0.622816\pi$
$137$	−8.80980	−0.752672	−0.376336	+	0.926483i	$0.622816\pi$
$138$	−13.6685	−1.16354
$139$	−14.6455	−1.24221	−0.621106	−	0.783726i	$-0.713317\pi$
$139$	−14.6455	−1.24221	−0.621106	+	0.783726i	$0.713317\pi$
$140$	−67.1924	−5.67880
$141$	−10.0667	−0.847766
$142$	15.2807	1.28233
$143$	3.81193	0.318769
$144$	−40.7850	−3.39875
$145$	16.6426	1.38209
$146$	−34.7087	−2.87252
$147$	5.94256	0.490134
$148$	44.4718	3.65556
$149$	0.972431	0.0796647	0.0398323	−	0.999206i	$-0.487318\pi$
$149$	0.972431	0.0796647	0.0398323	+	0.999206i	$0.487318\pi$
$150$	−12.6138	−1.02991
$151$	−7.20772	−0.586556	−0.293278	−	0.956027i	$-0.594746\pi$
$151$	−7.20772	−0.586556	−0.293278	+	0.956027i	$0.594746\pi$
$152$	46.4016	3.76367
$153$	7.23528	0.584938
$154$	6.02401	0.485429
$155$	14.8855	1.19563
$156$	−37.4230	−2.99624
$157$	8.01844	0.639941	0.319971	−	0.947427i	$-0.396327\pi$
$157$	8.01844	0.639941	0.319971	+	0.947427i	$0.396327\pi$
$158$	5.90254	0.469580
$159$	−7.25771	−0.575574
$160$	103.332	8.16910
$161$	18.1542	1.43075
$162$	−4.12957	−0.324450
$163$	−13.5471	−1.06109	−0.530544	−	0.847657i	$-0.678012\pi$
$163$	−13.5471	−1.06109	−0.530544	+	0.847657i	$0.678012\pi$
$164$	66.3398	5.18027
$165$	1.76409	0.137334
$166$	27.5597	2.13905
$167$	5.20745	0.402965	0.201482	−	0.979492i	$-0.435424\pi$
$167$	5.20745	0.402965	0.201482	+	0.979492i	$0.435424\pi$
$168$	−39.3427	−3.03535
$169$	28.9812	2.22933
$170$	−30.6828	−2.35327
$171$	8.53887	0.652984
$172$	−29.0699	−2.21656
$173$	−8.07708	−0.614089	−0.307045	−	0.951695i	$-0.599340\pi$
$173$	−8.07708	−0.614089	−0.307045	+	0.951695i	$0.599340\pi$
$174$	14.6480	1.11046
$175$	16.7534	1.26643
$176$	−11.6173	−0.875688
$177$	−2.57225	−0.193342
$178$	26.5805	1.99230
$179$	1.08593	0.0811661	0.0405831	−	0.999176i	$-0.487078\pi$
$179$	1.08593	0.0811661	0.0405831	+	0.999176i	$0.487078\pi$
$180$	38.2752	2.85287
$181$	10.1756	0.756343	0.378172	−	0.925735i	$-0.376553\pi$
$181$	10.1756	0.756343	0.378172	+	0.925735i	$0.376553\pi$
$182$	66.3432	4.91768
$183$	−9.80468	−0.724783
$184$	−56.1963	−4.14285
$185$	−23.0874	−1.69742
$186$	13.1016	0.960652
$187$	2.06092	0.150709
$188$	−62.2141	−4.53743
$189$	−17.7556	−1.29153
$190$	−36.2110	−2.62702
$191$	19.0961	1.38174	0.690871	−	0.722978i	$-0.257227\pi$
$191$	19.0961	1.38174	0.690871	+	0.722978i	$0.257227\pi$
$192$	52.7693	3.80829
$193$	1.19821	0.0862487	0.0431244	−	0.999070i	$-0.486269\pi$
$193$	1.19821	0.0862487	0.0431244	+	0.999070i	$0.486269\pi$
$194$	−49.8883	−3.58177
$195$	19.4281	1.39127
$196$	36.7263	2.62330
$197$	0.410901	0.0292755	0.0146378	−	0.999893i	$-0.495340\pi$
$197$	0.410901	0.0292755	0.0146378	+	0.999893i	$0.495340\pi$
$198$	−3.43149	−0.243866
$199$	6.98983	0.495496	0.247748	−	0.968825i	$-0.420310\pi$
$199$	6.98983	0.495496	0.247748	+	0.968825i	$0.420310\pi$
$200$	−51.8599	−3.66705
$201$	6.31175	0.445197
$202$	−0.0448240	−0.00315381
$203$	−19.4552	−1.36549
$204$	−20.2327	−1.41658
$205$	−34.4402	−2.40540
$206$	40.4241	2.81648
$207$	−10.3413	−0.718770
$208$	−127.943	−8.87125
$209$	2.43223	0.168241
$210$	30.7023	2.11866
$211$	14.5991	1.00505	0.502523	−	0.864564i	$-0.332405\pi$
$211$	14.5991	1.00505	0.502523	+	0.864564i	$0.332405\pi$
$212$	−44.8542	−3.08060
$213$	−5.23110	−0.358429
$214$	−8.64236	−0.590780
$215$	15.0916	1.02924
$216$	54.9624	3.73972
$217$	−17.4012	−1.18127
$218$	−4.04730	−0.274118
$219$	11.8820	0.802910
$220$	10.9024	0.735041
$221$	22.6971	1.52677
$222$	−20.3205	−1.36383
$223$	22.0085	1.47380	0.736900	−	0.676002i	$-0.236289\pi$
$223$	22.0085	1.47380	0.736900	+	0.676002i	$0.236289\pi$
$224$	−120.795	−8.07098
$225$	−9.54331	−0.636221
$226$	−45.5652	−3.03095
$227$	9.29603	0.616999	0.308499	−	0.951225i	$-0.400173\pi$
$227$	9.29603	0.616999	0.308499	+	0.951225i	$0.400173\pi$
$228$	−23.8781	−1.58137
$229$	19.4118	1.28277	0.641385	−	0.767219i	$-0.278360\pi$
$229$	19.4118	1.28277	0.641385	+	0.767219i	$0.278360\pi$
$230$	43.8546	2.89169
$231$	−2.06222	−0.135684
$232$	60.2236	3.95387
$233$	10.8130	0.708384	0.354192	−	0.935173i	$-0.384756\pi$
$233$	10.8130	0.708384	0.354192	+	0.935173i	$0.384756\pi$
$234$	−37.7915	−2.47050
$235$	32.2983	2.10691
$236$	−15.8970	−1.03481
$237$	−2.02064	−0.131255
$238$	35.8684	2.32500
$239$	12.4474	0.805158	0.402579	−	0.915385i	$-0.368114\pi$
$239$	12.4474	0.805158	0.402579	+	0.915385i	$0.368114\pi$
$240$	−59.2095	−3.82195
$241$	3.42703	0.220754	0.110377	−	0.993890i	$-0.464794\pi$
$241$	3.42703	0.220754	0.110377	+	0.993890i	$0.464794\pi$
$242$	30.0858	1.93399
$243$	16.1044	1.03310
$244$	−60.5950	−3.87920
$245$	−19.0664	−1.21810
$246$	−30.3127	−1.93267
$247$	26.7865	1.70438
$248$	53.8654	3.42046
$249$	−9.43464	−0.597896
$250$	−3.32420	−0.210241
$251$	−9.51463	−0.600558	−0.300279	−	0.953851i	$-0.597080\pi$
$251$	−9.51463	−0.600558	−0.300279	+	0.953851i	$0.597080\pi$
$252$	−44.7439	−2.81860
$253$	−2.94564	−0.185191
$254$	−51.7838	−3.24921
$255$	10.5038	0.657772
$256$	137.968	8.62303
$257$	9.51790	0.593710	0.296855	−	0.954923i	$-0.404062\pi$
$257$	9.51790	0.593710	0.296855	+	0.954923i	$0.404062\pi$
$258$	13.2830	0.826961
$259$	26.9893	1.67704
$260$	120.070	7.44640
$261$	11.0824	0.685983
$262$	−8.78905	−0.542989
$263$	−5.69042	−0.350886	−0.175443	−	0.984490i	$-0.556136\pi$
$263$	−5.69042	−0.350886	−0.175443	+	0.984490i	$0.556136\pi$
$264$	6.38361	0.392884
$265$	23.2859	1.43044
$266$	42.3308	2.59547
$267$	−9.09943	−0.556876
$268$	39.0080	2.38279
$269$	−21.4457	−1.30757	−0.653783	−	0.756682i	$-0.726819\pi$
$269$	−21.4457	−1.30757	−0.653783	+	0.756682i	$0.726819\pi$
$270$	−42.8917	−2.61031
$271$	−31.0601	−1.88677	−0.943384	−	0.331704i	$-0.892377\pi$
$271$	−31.0601	−1.88677	−0.943384	+	0.331704i	$0.892377\pi$
$272$	−69.1723	−4.19419
$273$	−22.7115	−1.37456
$274$	24.8782	1.50295
$275$	−2.71834	−0.163922
$276$	28.9184	1.74068
$277$	−17.6009	−1.05754	−0.528768	−	0.848767i	$-0.677346\pi$
$277$	−17.6009	−1.05754	−0.528768	+	0.848767i	$0.677346\pi$
$278$	41.3578	2.48048
$279$	9.91236	0.593437
$280$	126.229	7.54361
$281$	−6.71086	−0.400336	−0.200168	−	0.979762i	$-0.564149\pi$
$281$	−6.71086	−0.400336	−0.200168	+	0.979762i	$0.564149\pi$
$282$	28.4275	1.69284
$283$	−8.33125	−0.495241	−0.247621	−	0.968857i	$-0.579649\pi$
$283$	−8.33125	−0.495241	−0.247621	+	0.968857i	$0.579649\pi$
$284$	−32.3293	−1.91839
$285$	12.3963	0.734291
$286$	−10.7646	−0.636525
$287$	40.2607	2.37651
$288$	68.8094	4.05463
$289$	−4.72881	−0.278165
$290$	−46.9974	−2.75978
$291$	17.0785	1.00116
$292$	73.4332	4.29735
$293$	18.8044	1.09856	0.549281	−	0.835638i	$-0.314902\pi$
$293$	18.8044	1.09856	0.549281	+	0.835638i	$0.314902\pi$
$294$	−16.7814	−0.978709
$295$	8.25291	0.480503
$296$	−83.5454	−4.85598
$297$	2.88097	0.167171
$298$	−2.74608	−0.159076
$299$	−32.4407	−1.87610
$300$	26.6869	1.54077
$301$	−17.6422	−1.01688
$302$	20.3541	1.17125
$303$	0.0153448	0.000881535 0
$304$	−81.6351	−4.68209
$305$	31.4577	1.80127
$306$	−20.4319	−1.16802
$307$	−10.2459	−0.584763	−0.292381	−	0.956302i	$-0.594448\pi$
$307$	−10.2459	−0.584763	−0.292381	+	0.956302i	$0.594448\pi$
$308$	−12.7450	−0.726213
$309$	−13.8386	−0.787248
$310$	−42.0356	−2.38746
$311$	13.8284	0.784135	0.392068	−	0.919936i	$-0.371760\pi$
$311$	13.8284	0.784135	0.392068	+	0.919936i	$0.371760\pi$
$312$	70.3034	3.98015
$313$	10.3107	0.582797	0.291398	−	0.956602i	$-0.405879\pi$
$313$	10.3107	0.582797	0.291398	+	0.956602i	$0.405879\pi$
$314$	−22.6435	−1.27785
$315$	23.2287	1.30879
$316$	−12.4880	−0.702503
$317$	15.5981	0.876075	0.438037	−	0.898957i	$-0.355674\pi$
$317$	15.5981	0.876075	0.438037	+	0.898957i	$0.355674\pi$
$318$	20.4953	1.14932
$319$	3.15674	0.176743
$320$	−169.307	−9.46456
$321$	2.95858	0.165132
$322$	−51.2662	−2.85696
$323$	14.4821	0.805806
$324$	8.73692	0.485384
$325$	−29.9374	−1.66063
$326$	38.2560	2.11880
$327$	1.38553	0.0766200
$328$	−124.627	−6.88137
$329$	−37.7569	−2.08160
$330$	−4.98165	−0.274231
$331$	−8.43553	−0.463659	−0.231829	−	0.972756i	$-0.574471\pi$
$331$	−8.43553	−0.463659	−0.231829	+	0.972756i	$0.574471\pi$
$332$	−58.3081	−3.20007
$333$	−15.3741	−0.842495
$334$	−14.7055	−0.804648
$335$	−20.2509	−1.10642
$336$	69.2162	3.77605
$337$	−25.0623	−1.36523	−0.682616	−	0.730777i	$-0.739158\pi$
$337$	−25.0623	−1.36523	−0.682616	+	0.730777i	$0.739158\pi$
$338$	−81.8409	−4.45156
$339$	15.5985	0.847195
$340$	64.9156	3.52054
$341$	2.82346	0.152899
$342$	−24.1132	−1.30389
$343$	−3.09257	−0.166983
$344$	54.6112	2.94444
$345$	−15.0129	−0.808269
$346$	22.8091	1.22623
$347$	3.55361	0.190768	0.0953839	−	0.995441i	$-0.469592\pi$
$347$	3.55361	0.190768	0.0953839	+	0.995441i	$0.469592\pi$
$348$	−30.9908	−1.66128
$349$	−16.8767	−0.903389	−0.451694	−	0.892173i	$-0.649180\pi$
$349$	−16.8767	−0.903389	−0.451694	+	0.892173i	$0.649180\pi$
$350$	−47.3103	−2.52884
$351$	31.7284	1.69354
$352$	19.5999	1.04468
$353$	11.8322	0.629767	0.314883	−	0.949130i	$-0.398035\pi$
$353$	11.8322	0.629767	0.314883	+	0.949130i	$0.398035\pi$
$354$	7.26385	0.386069
$355$	16.7837	0.890785
$356$	−56.2364	−2.98052
$357$	−12.2790	−0.649872
$358$	−3.06659	−0.162074
$359$	2.41311	0.127359	0.0636796	−	0.997970i	$-0.479716\pi$
$359$	2.41311	0.127359	0.0636796	+	0.997970i	$0.479716\pi$
$360$	−71.9044	−3.78970
$361$	−1.90864	−0.100455
$362$	−28.7351	−1.51028
$363$	−10.2994	−0.540578
$364$	−140.362	−7.35697
$365$	−38.1227	−1.99543
$366$	27.6877	1.44726
$367$	−21.2060	−1.10694	−0.553471	−	0.832868i	$-0.686697\pi$
$367$	−21.2060	−1.10694	−0.553471	+	0.832868i	$0.686697\pi$
$368$	98.8671	5.15380
$369$	−22.9340	−1.19389
$370$	65.1973	3.38945
$371$	−27.2214	−1.41326
$372$	−27.7189	−1.43716
$373$	−6.94270	−0.359480	−0.179740	−	0.983714i	$-0.557526\pi$
$373$	−6.94270	−0.359480	−0.179740	+	0.983714i	$0.557526\pi$
$374$	−5.81988	−0.300939
$375$	1.13799	0.0587654
$376$	116.876	6.02743
$377$	34.7655	1.79052
$378$	50.1406	2.57896
$379$	7.92166	0.406908	0.203454	−	0.979084i	$-0.434783\pi$
$379$	7.92166	0.406908	0.203454	+	0.979084i	$0.434783\pi$
$380$	76.6115	3.93009
$381$	17.7274	0.908200
$382$	−53.9259	−2.75909
$383$	−11.0077	−0.562467	−0.281233	−	0.959639i	$-0.590743\pi$
$383$	−11.0077	−0.562467	−0.281233	+	0.959639i	$0.590743\pi$
$384$	−84.6042	−4.31744
$385$	6.61653	0.337210
$386$	−3.38365	−0.172223
$387$	10.0496	0.510850
$388$	105.549	5.35841
$389$	18.5756	0.941820	0.470910	−	0.882181i	$-0.343926\pi$
$389$	18.5756	0.941820	0.470910	+	0.882181i	$0.343926\pi$
$390$	−54.8635	−2.77812
$391$	−17.5391	−0.886988
$392$	−68.9945	−3.48475
$393$	3.00879	0.151773
$394$	−1.16036	−0.0584579
$395$	6.48310	0.326200
$396$	7.26000	0.364829
$397$	13.6112	0.683126	0.341563	−	0.939859i	$-0.389044\pi$
$397$	13.6112	0.683126	0.341563	+	0.939859i	$0.389044\pi$
$398$	−19.7388	−0.989416
$399$	−14.4913	−0.725472
$400$	91.2380	4.56190
$401$	21.8521	1.09124	0.545622	−	0.838031i	$-0.316293\pi$
$401$	21.8521	1.09124	0.545622	+	0.838031i	$0.316293\pi$
$402$	−17.8239	−0.888977
$403$	31.0951	1.54896
$404$	0.0948340	0.00471817
$405$	−4.53575	−0.225383
$406$	54.9402	2.72664
$407$	−4.37920	−0.217069
$408$	38.0095	1.88175
$409$	−29.9837	−1.48260	−0.741300	−	0.671173i	$-0.765791\pi$
$409$	−29.9837	−1.48260	−0.741300	+	0.671173i	$0.765791\pi$
$410$	97.2566	4.80316
$411$	−8.51667	−0.420096
$412$	−85.5252	−4.21352
$413$	−9.64770	−0.474732
$414$	29.2031	1.43525
$415$	30.2705	1.48592
$416$	215.856	10.5832
$417$	−14.1582	−0.693329
$418$	−6.86846	−0.335947
$419$	4.02956	0.196857	0.0984284	−	0.995144i	$-0.468618\pi$
$419$	4.02956	0.196857	0.0984284	+	0.995144i	$0.468618\pi$
$420$	−64.9568	−3.16957
$421$	−4.87094	−0.237395	−0.118698	−	0.992930i	$-0.537872\pi$
$421$	−4.87094	−0.237395	−0.118698	+	0.992930i	$0.537872\pi$
$422$	−41.2269	−2.00690
$423$	21.5077	1.04574
$424$	84.2637	4.09221
$425$	−16.1857	−0.785120
$426$	14.7722	0.715718
$427$	−36.7743	−1.77963
$428$	18.2846	0.883820
$429$	3.68510	0.177918
$430$	−42.6176	−2.05520
$431$	−16.4458	−0.792169	−0.396084	−	0.918214i	$-0.629631\pi$
$431$	−16.4458	−0.792169	−0.396084	+	0.918214i	$0.629631\pi$
$432$	−96.6963	−4.65230
$433$	2.00012	0.0961198	0.0480599	−	0.998844i	$-0.484696\pi$
$433$	2.00012	0.0961198	0.0480599	+	0.998844i	$0.484696\pi$
$434$	49.1398	2.35879
$435$	16.0888	0.771399
$436$	8.56287	0.410087
$437$	−20.6991	−0.990172
$438$	−33.5539	−1.60327
$439$	−21.3922	−1.02099	−0.510496	−	0.859880i	$-0.670538\pi$
$439$	−21.3922	−1.02099	−0.510496	+	0.859880i	$0.670538\pi$
$440$	−20.4814	−0.976414
$441$	−12.6964	−0.604592
$442$	−64.0951	−3.04869
$443$	−24.2603	−1.15264	−0.576321	−	0.817224i	$-0.695512\pi$
$443$	−24.2603	−1.15264	−0.576321	+	0.817224i	$0.695512\pi$
$444$	42.9921	2.04031
$445$	29.1950	1.38398
$446$	−62.1505	−2.94291
$447$	0.940076	0.0444641
$448$	197.921	9.35088
$449$	5.22458	0.246563	0.123282	−	0.992372i	$-0.460658\pi$
$449$	5.22458	0.246563	0.123282	+	0.992372i	$0.460658\pi$
$450$	26.9496	1.27042
$451$	−6.53257	−0.307607
$452$	96.4021	4.53438
$453$	−6.96790	−0.327381
$454$	−26.2513	−1.23204
$455$	72.8686	3.41613
$456$	44.8577	2.10066
$457$	28.2134	1.31977	0.659884	−	0.751368i	$-0.270605\pi$
$457$	28.2134	1.31977	0.659884	+	0.751368i	$0.270605\pi$
$458$	−54.8177	−2.56146
$459$	17.1540	0.800678
$460$	−92.7830	−4.32603
$461$	−6.31049	−0.293909	−0.146954	−	0.989143i	$-0.546947\pi$
$461$	−6.31049	−0.293909	−0.146954	+	0.989143i	$0.546947\pi$
$462$	5.82358	0.270937
$463$	−31.3445	−1.45670	−0.728351	−	0.685204i	$-0.759713\pi$
$463$	−31.3445	−1.45670	−0.728351	+	0.685204i	$0.759713\pi$
$464$	−105.952	−4.91871
$465$	14.3902	0.667330
$466$	−30.5352	−1.41451
$467$	−22.2210	−1.02827	−0.514134	−	0.857710i	$-0.671886\pi$
$467$	−22.2210	−1.02827	−0.514134	+	0.857710i	$0.671886\pi$
$468$	79.9553	3.69593
$469$	23.6734	1.09314
$470$	−91.2081	−4.20712
$471$	7.75165	0.357177
$472$	29.8644	1.37462
$473$	2.86256	0.131620
$474$	5.70614	0.262092
$475$	−19.1018	−0.876453
$476$	−75.8867	−3.47826
$477$	15.5063	0.709984
$478$	−35.1507	−1.60776
$479$	34.9797	1.59826	0.799132	−	0.601155i	$-0.205293\pi$
$479$	34.9797	1.59826	0.799132	+	0.601155i	$0.205293\pi$
$480$	99.8937	4.55950
$481$	−48.2286	−2.19904
$482$	−9.67768	−0.440806
$483$	17.5502	0.798561
$484$	−63.6524	−2.89329
$485$	−54.7953	−2.48813
$486$	−45.4777	−2.06291
$487$	37.3475	1.69238	0.846188	−	0.532884i	$-0.178892\pi$
$487$	37.3475	1.69238	0.846188	+	0.532884i	$0.178892\pi$
$488$	113.835	5.15305
$489$	−13.0963	−0.592236
$490$	53.8421	2.43234
$491$	−22.1240	−0.998442	−0.499221	−	0.866475i	$-0.666380\pi$
$491$	−22.1240	−0.998442	−0.499221	+	0.866475i	$0.666380\pi$
$492$	64.1325	2.89132
$493$	18.7960	0.846528
$494$	−75.6432	−3.40335
$495$	−3.76901	−0.169405
$496$	−94.7662	−4.25513
$497$	−19.6202	−0.880086
$498$	26.6428	1.19389
$499$	31.9568	1.43058	0.715291	−	0.698827i	$-0.246294\pi$
$499$	31.9568	1.43058	0.715291	+	0.698827i	$0.246294\pi$
$500$	7.03301	0.314526
$501$	5.03418	0.224911
$502$	26.8687	1.19921
$503$	12.3379	0.550120	0.275060	−	0.961427i	$-0.411302\pi$
$503$	12.3379	0.550120	0.275060	+	0.961427i	$0.411302\pi$
$504$	84.0566	3.74418
$505$	−0.0492329	−0.00219083
$506$	8.31829	0.369793
$507$	28.0169	1.24428
$508$	109.559	4.86089
$509$	−44.5019	−1.97251	−0.986256	−	0.165227i	$-0.947164\pi$
$509$	−44.5019	−1.97251	−0.986256	+	0.165227i	$0.947164\pi$
$510$	−29.6619	−1.31345
$511$	44.5656	1.97147
$512$	−214.581	−9.48323
$513$	20.2446	0.893821
$514$	−26.8779	−1.18553
$515$	44.4002	1.95651
$516$	−28.1027	−1.23715
$517$	6.12630	0.269435
$518$	−76.2160	−3.34874
$519$	−7.80834	−0.342748
$520$	−225.565	−9.89166
$521$	18.6218	0.815837	0.407918	−	0.913018i	$-0.366255\pi$
$521$	18.6218	0.815837	0.407918	+	0.913018i	$0.366255\pi$
$522$	−31.2959	−1.36978
$523$	−17.8139	−0.778947	−0.389473	−	0.921038i	$-0.627343\pi$
$523$	−17.8139	−0.778947	−0.389473	+	0.921038i	$0.627343\pi$
$524$	18.5950	0.812325
$525$	16.1959	0.706848
$526$	16.0694	0.700657
$527$	16.8116	0.732323
$528$	−11.2308	−0.488757
$529$	2.06835	0.0899283
$530$	−65.7579	−2.85634
$531$	5.49568	0.238492
$532$	−89.5592	−3.88288
$533$	−71.9439	−3.11624
$534$	25.6961	1.11198
$535$	−9.49242	−0.410393
$536$	−73.2809	−3.16525
$537$	1.04980	0.0453021
$538$	60.5611	2.61097
$539$	−3.61648	−0.155773
$540$	90.7458	3.90508
$541$	20.8424	0.896083	0.448042	−	0.894013i	$-0.352122\pi$
$541$	20.8424	0.896083	0.448042	+	0.894013i	$0.352122\pi$
$542$	87.7116	3.76753
$543$	9.83699	0.422146
$544$	116.702	5.00357
$545$	−4.44539	−0.190420
$546$	64.1358	2.74476
$547$	25.3566	1.08417	0.542085	−	0.840323i	$-0.317635\pi$
$547$	25.3566	1.08417	0.542085	+	0.840323i	$0.317635\pi$
$548$	−52.6348	−2.24845
$549$	20.9479	0.894037
$550$	7.67641	0.327323
$551$	22.1825	0.945005
$552$	−54.3265	−2.31229
$553$	−7.57878	−0.322283
$554$	49.7037	2.11171
$555$	−22.3193	−0.947400
$556$	−87.5005	−3.71085
$557$	33.7646	1.43065	0.715326	−	0.698790i	$-0.246278\pi$
$557$	33.7646	1.43065	0.715326	+	0.698790i	$0.246278\pi$
$558$	−27.9918	−1.18499
$559$	31.5257	1.33339
$560$	−222.076	−9.38443
$561$	1.99234	0.0841169
$562$	18.9510	0.799400
$563$	13.7582	0.579839	0.289919	−	0.957051i	$-0.406372\pi$
$563$	13.7582	0.579839	0.289919	+	0.957051i	$0.406372\pi$
$564$	−60.1441	−2.53252
$565$	−50.0470	−2.10549
$566$	23.5269	0.988907
$567$	5.30232	0.222676
$568$	60.7342	2.54835
$569$	8.03866	0.336998	0.168499	−	0.985702i	$-0.446108\pi$
$569$	8.03866	0.336998	0.168499	+	0.985702i	$0.446108\pi$
$570$	−35.0062	−1.46625
$571$	−1.25280	−0.0524282	−0.0262141	−	0.999656i	$-0.508345\pi$
$571$	−1.25280	−0.0524282	−0.0262141	+	0.999656i	$0.508345\pi$
$572$	22.7747	0.952257
$573$	18.4607	0.771206
$574$	−113.693	−4.74547
$575$	23.1340	0.964753
$576$	−112.743	−4.69762
$577$	43.1735	1.79734	0.898668	−	0.438630i	$-0.144536\pi$
$577$	43.1735	1.79734	0.898668	+	0.438630i	$0.144536\pi$
$578$	13.3538	0.555446
$579$	1.15834	0.0481389
$580$	99.4322	4.12870
$581$	−35.3864	−1.46807
$582$	−48.2284	−1.99913
$583$	4.41685	0.182927
$584$	−137.953	−5.70852
$585$	−41.5086	−1.71617
$586$	−53.1022	−2.19363
$587$	41.3926	1.70846	0.854228	−	0.519899i	$-0.174031\pi$
$587$	41.3926	1.70846	0.854228	+	0.519899i	$0.174031\pi$
$588$	35.5043	1.46417
$589$	19.8405	0.817514
$590$	−23.3056	−0.959478
$591$	0.397230	0.0163398
$592$	146.983	6.04095
$593$	−15.4710	−0.635317	−0.317658	−	0.948205i	$-0.602897\pi$
$593$	−15.4710	−0.635317	−0.317658	+	0.948205i	$0.602897\pi$
$594$	−8.13565	−0.333810
$595$	39.3964	1.61509
$596$	5.80987	0.237981
$597$	6.75726	0.276556
$598$	91.6103	3.74622
$599$	−8.37278	−0.342102	−0.171051	−	0.985262i	$-0.554716\pi$
$599$	−8.37278	−0.342102	−0.171051	+	0.985262i	$0.554716\pi$
$600$	−50.1344	−2.04673
$601$	45.5106	1.85642	0.928209	−	0.372060i	$-0.121348\pi$
$601$	45.5106	1.85642	0.928209	+	0.372060i	$0.121348\pi$
$602$	49.8202	2.03052
$603$	−13.4852	−0.549161
$604$	−43.0631	−1.75221
$605$	33.0450	1.34347
$606$	−0.0433326	−0.00176027
$607$	−45.6397	−1.85246	−0.926229	−	0.376961i	$-0.876969\pi$
$607$	−45.6397	−1.85246	−0.926229	+	0.376961i	$0.876969\pi$
$608$	137.729	5.58563
$609$	−18.8079	−0.762135
$610$	−88.8345	−3.59680
$611$	67.4697	2.72953
$612$	43.2278	1.74738
$613$	−25.2048	−1.01801	−0.509005	−	0.860763i	$-0.669987\pi$
$613$	−25.2048	−1.01801	−0.509005	+	0.860763i	$0.669987\pi$
$614$	28.9336	1.16767
$615$	−33.2942	−1.34255
$616$	23.9429	0.964687
$617$	−8.04024	−0.323688	−0.161844	−	0.986816i	$-0.551744\pi$
$617$	−8.04024	−0.323688	−0.161844	+	0.986816i	$0.551744\pi$
$618$	39.0791	1.57199
$619$	−21.4290	−0.861304	−0.430652	−	0.902518i	$-0.641716\pi$
$619$	−21.4290	−0.861304	−0.430652	+	0.902518i	$0.641716\pi$
$620$	88.9345	3.57170
$621$	−24.5179	−0.983871
$622$	−39.0504	−1.56578
$623$	−34.1291	−1.36735
$624$	−123.686	−4.95140
$625$	−26.7536	−1.07014
$626$	−29.1168	−1.16374
$627$	2.35131	0.0939022
$628$	47.9068	1.91169
$629$	−26.0748	−1.03967
$630$	−65.5963	−2.61342
$631$	8.69229	0.346034	0.173017	−	0.984919i	$-0.444648\pi$
$631$	8.69229	0.346034	0.173017	+	0.984919i	$0.444648\pi$
$632$	23.4601	0.933192
$633$	14.1134	0.560957
$634$	−44.0478	−1.74936
$635$	−56.8772	−2.25710
$636$	−43.3617	−1.71940
$637$	−39.8288	−1.57807
$638$	−8.91441	−0.352925
$639$	11.1764	0.442130
$640$	271.448	10.7299
$641$	−27.8785	−1.10113	−0.550567	−	0.834791i	$-0.685588\pi$
$641$	−27.8785	−1.10113	−0.550567	+	0.834791i	$0.685588\pi$
$642$	−8.35481	−0.329738
$643$	41.7124	1.64497	0.822487	−	0.568783i	$-0.192586\pi$
$643$	41.7124	1.64497	0.822487	+	0.568783i	$0.192586\pi$
$644$	108.464	4.27407
$645$	14.5895	0.574459
$646$	−40.8964	−1.60905
$647$	−1.01061	−0.0397311	−0.0198656	−	0.999803i	$-0.506324\pi$
$647$	−1.01061	−0.0397311	−0.0198656	+	0.999803i	$0.506324\pi$
$648$	−16.4133	−0.644776
$649$	1.56540	0.0614474
$650$	84.5412	3.31598
$651$	−16.8222	−0.659315
$652$	−80.9380	−3.16978
$653$	−38.4999	−1.50662	−0.753309	−	0.657667i	$-0.771543\pi$
$653$	−38.4999	−1.50662	−0.753309	+	0.657667i	$0.771543\pi$
$654$	−3.91264	−0.152996
$655$	−9.65354	−0.377195
$656$	219.258	8.56059
$657$	−25.3862	−0.990409
$658$	106.623	4.15659
$659$	19.1016	0.744094	0.372047	−	0.928214i	$-0.378656\pi$
$659$	19.1016	0.744094	0.372047	+	0.928214i	$0.378656\pi$
$660$	10.5397	0.410256
$661$	−20.0926	−0.781513	−0.390757	−	0.920494i	$-0.627787\pi$
$661$	−20.0926	−0.781513	−0.390757	+	0.920494i	$0.627787\pi$
$662$	23.8214	0.925843
$663$	21.9419	0.852154
$664$	109.538	4.25091
$665$	46.4945	1.80298
$666$	43.4154	1.68231
$667$	−26.8648	−1.04021
$668$	31.1123	1.20377
$669$	21.2762	0.822587
$670$	57.1871	2.20933
$671$	5.96687	0.230348
$672$	−116.776	−4.50474
$673$	41.0618	1.58282	0.791408	−	0.611289i	$-0.209349\pi$
$673$	41.0618	1.58282	0.791408	+	0.611289i	$0.209349\pi$
$674$	70.7743	2.72612
$675$	−22.6260	−0.870876
$676$	173.151	6.65964
$677$	35.9262	1.38076	0.690379	−	0.723448i	$-0.257444\pi$
$677$	35.9262	1.38076	0.690379	+	0.723448i	$0.257444\pi$
$678$	−44.0491	−1.69170
$679$	64.0560	2.45824
$680$	−121.951	−4.67662
$681$	8.98672	0.344372
$682$	−7.97326	−0.305312
$683$	49.6932	1.90146	0.950728	−	0.310026i	$-0.100338\pi$
$683$	49.6932	1.90146	0.950728	+	0.310026i	$0.100338\pi$
$684$	51.0162	1.95065
$685$	27.3253	1.04404
$686$	8.73319	0.333435
$687$	18.7660	0.715966
$688$	−96.0784	−3.66295
$689$	48.6433	1.85316
$690$	42.3954	1.61397
$691$	−2.92120	−0.111128	−0.0555638	−	0.998455i	$-0.517696\pi$
$691$	−2.92120	−0.111128	−0.0555638	+	0.998455i	$0.517696\pi$
$692$	−48.2572	−1.83446
$693$	4.40600	0.167370
$694$	−10.0351	−0.380929
$695$	45.4257	1.72310
$696$	58.2198	2.20682
$697$	−38.8965	−1.47331
$698$	47.6586	1.80390
$699$	10.4532	0.395378
$700$	100.094	3.78321
$701$	39.2077	1.48085	0.740427	−	0.672137i	$-0.234623\pi$
$701$	39.2077	1.48085	0.740427	+	0.672137i	$0.234623\pi$
$702$	−89.5989	−3.38169
$703$	−30.7727	−1.16061
$704$	−32.1140	−1.21034
$705$	31.2237	1.17595
$706$	−33.4134	−1.25753
$707$	0.0575535	0.00216452
$708$	−15.3681	−0.577569
$709$	15.4315	0.579543	0.289772	−	0.957096i	$-0.406421\pi$
$709$	15.4315	0.579543	0.289772	+	0.957096i	$0.406421\pi$
$710$	−47.3959	−1.77874
$711$	4.31715	0.161906
$712$	105.646	3.95927
$713$	−24.0286	−0.899877
$714$	34.6750	1.29768
$715$	−11.8234	−0.442171
$716$	6.48797	0.242467
$717$	12.0333	0.449391
$718$	−6.81446	−0.254313
$719$	10.9823	0.409571	0.204785	−	0.978807i	$-0.434350\pi$
$719$	10.9823	0.409571	0.204785	+	0.978807i	$0.434350\pi$
$720$	126.503	4.71447
$721$	−51.9041	−1.93301
$722$	5.38988	0.200590
$723$	3.31300	0.123212
$724$	60.7947	2.25942
$725$	−24.7918	−0.920745
$726$	29.0848	1.07944
$727$	−21.5751	−0.800176	−0.400088	−	0.916477i	$-0.631020\pi$
$727$	−21.5751	−0.800176	−0.400088	+	0.916477i	$0.631020\pi$
$728$	263.686	9.77286
$729$	11.1815	0.414130
$730$	107.656	3.98452
$731$	17.0443	0.630408
$732$	−58.5788	−2.16514
$733$	25.0807	0.926377	0.463188	−	0.886260i	$-0.346705\pi$
$733$	25.0807	0.926377	0.463188	+	0.886260i	$0.346705\pi$
$734$	59.8842	2.21037
$735$	−18.4320	−0.679874
$736$	−166.801	−6.14837
$737$	−3.84117	−0.141491
$738$	64.7639	2.38399
$739$	−0.842733	−0.0310004	−0.0155002	−	0.999880i	$-0.504934\pi$
$739$	−0.842733	−0.0310004	−0.0155002	+	0.999880i	$0.504934\pi$
$740$	−137.938	−5.07069
$741$	25.8952	0.951285
$742$	76.8713	2.82203
$743$	19.9423	0.731611	0.365805	−	0.930691i	$-0.380794\pi$
$743$	19.9423	0.731611	0.365805	+	0.930691i	$0.380794\pi$
$744$	52.0731	1.90909
$745$	−3.01618	−0.110504
$746$	19.6057	0.717816
$747$	20.1573	0.737519
$748$	12.3131	0.450212
$749$	11.0967	0.405464
$750$	−3.21360	−0.117344
$751$	0.580676	0.0211892	0.0105946	−	0.999944i	$-0.496628\pi$
$751$	0.580676	0.0211892	0.0105946	+	0.999944i	$0.496628\pi$
$752$	−205.622	−7.49827
$753$	−9.19806	−0.335196
$754$	−98.1755	−3.57534
$755$	22.3561	0.813623
$756$	−106.082	−3.85818
$757$	25.0350	0.909912	0.454956	−	0.890514i	$-0.349655\pi$
$757$	25.0350	0.909912	0.454956	+	0.890514i	$0.349655\pi$
$758$	−22.3702	−0.812522
$759$	−2.84763	−0.103363
$760$	−143.923	−5.22065
$761$	43.6584	1.58262	0.791308	−	0.611418i	$-0.209401\pi$
$761$	43.6584	1.58262	0.791308	+	0.611418i	$0.209401\pi$
$762$	−50.0608	−1.81351
$763$	5.19669	0.188133
$764$	114.091	4.12766
$765$	−22.4416	−0.811378
$766$	31.0849	1.12314
$767$	17.2400	0.622499
$768$	133.378	4.81286
$769$	5.87213	0.211755	0.105877	−	0.994379i	$-0.466235\pi$
$769$	5.87213	0.211755	0.105877	+	0.994379i	$0.466235\pi$
$770$	−18.6846	−0.673347
$771$	9.20121	0.331373
$772$	7.15878	0.257650
$773$	22.3874	0.805218	0.402609	−	0.915372i	$-0.368103\pi$
$773$	22.3874	0.805218	0.402609	+	0.915372i	$0.368103\pi$
$774$	−28.3794	−1.02008
$775$	−22.1744	−0.796528
$776$	−198.285	−7.11802
$777$	26.0913	0.936021
$778$	−52.4562	−1.88064
$779$	−45.9045	−1.64470
$780$	116.075	4.15614
$781$	3.18351	0.113915
$782$	49.5291	1.77116
$783$	26.2750	0.938992
$784$	121.383	4.33511
$785$	−24.8707	−0.887674
$786$	−8.49662	−0.303064
$787$	−34.6877	−1.23648	−0.618241	−	0.785989i	$-0.712154\pi$
$787$	−34.6877	−1.23648	−0.618241	+	0.785989i	$0.712154\pi$
$788$	2.45496	0.0874545
$789$	−5.50109	−0.195844
$790$	−18.3078	−0.651363
$791$	58.5052	2.08020
$792$	−13.6387	−0.484632
$793$	65.7138	2.33357
$794$	−38.4370	−1.36408
$795$	22.5112	0.798388
$796$	41.7613	1.48019
$797$	34.6173	1.22621	0.613103	−	0.790003i	$-0.289921\pi$
$797$	34.6173	1.22621	0.613103	+	0.790003i	$0.289921\pi$
$798$	40.9224	1.44864
$799$	36.4775	1.29048
$800$	−153.930	−5.44224
$801$	19.4412	0.686920
$802$	−61.7089	−2.17902
$803$	−7.23106	−0.255179
$804$	37.7101	1.32993
$805$	−56.3088	−1.98462
$806$	−87.8105	−3.09299
$807$	−20.7321	−0.729805
$808$	−0.178157	−0.00626753
$809$	−32.6775	−1.14888	−0.574440	−	0.818547i	$-0.694780\pi$
$809$	−32.6775	−1.14888	−0.574440	+	0.818547i	$0.694780\pi$
$810$	12.8086	0.450050
$811$	25.1256	0.882281	0.441140	−	0.897438i	$-0.354574\pi$
$811$	25.1256	0.882281	0.441140	+	0.897438i	$0.354574\pi$
$812$	−116.237	−4.07911
$813$	−30.0267	−1.05308
$814$	12.3665	0.433447
$815$	42.0188	1.47185
$816$	−66.8707	−2.34094
$817$	20.1152	0.703743
$818$	84.6720	2.96049
$819$	48.5238	1.69556
$820$	−205.765	−7.18564
$821$	0.989715	0.0345413	0.0172706	−	0.999851i	$-0.494502\pi$
$821$	0.989715	0.0345413	0.0172706	+	0.999851i	$0.494502\pi$
$822$	24.0505	0.838857
$823$	8.38431	0.292259	0.146129	−	0.989265i	$-0.453318\pi$
$823$	8.38431	0.292259	0.146129	+	0.989265i	$0.453318\pi$
$824$	160.669	5.59717
$825$	−2.62790	−0.0914916
$826$	27.2444	0.947955
$827$	47.1519	1.63963	0.819815	−	0.572628i	$-0.194076\pi$
$827$	47.1519	1.63963	0.819815	+	0.572628i	$0.194076\pi$
$828$	−61.7849	−2.14717
$829$	−53.9613	−1.87415	−0.937077	−	0.349123i	$-0.886480\pi$
$829$	−53.9613	−1.87415	−0.937077	+	0.349123i	$0.886480\pi$
$830$	−85.4818	−2.96712
$831$	−17.0153	−0.590253
$832$	−353.675	−12.2615
$833$	−21.5334	−0.746088
$834$	39.9817	1.38445
$835$	−16.1519	−0.558959
$836$	14.5316	0.502585
$837$	23.5010	0.812312
$838$	−11.3792	−0.393088
$839$	51.3481	1.77273	0.886367	−	0.462983i	$-0.153221\pi$
$839$	51.3481	1.77273	0.886367	+	0.462983i	$0.153221\pi$
$840$	122.029	4.21039
$841$	−0.209908	−0.00723822
$842$	13.7552	0.474035
$843$	−6.48757	−0.223444
$844$	87.2237	3.00236
$845$	−89.8908	−3.09234
$846$	−60.7362	−2.08815
$847$	−38.6298	−1.32734
$848$	−148.246	−5.09080
$849$	−8.05404	−0.276414
$850$	45.7072	1.56774
$851$	37.2684	1.27754
$852$	−31.2536	−1.07073
$853$	−9.85461	−0.337416	−0.168708	−	0.985666i	$-0.553959\pi$
$853$	−9.85461	−0.337416	−0.168708	+	0.985666i	$0.553959\pi$
$854$	103.848	3.55360
$855$	−26.4849	−0.905765
$856$	−34.3498	−1.17405
$857$	43.4271	1.48344	0.741721	−	0.670709i	$-0.234010\pi$
$857$	43.4271	1.48344	0.741721	+	0.670709i	$0.234010\pi$
$858$	−10.4065	−0.355270
$859$	−25.1411	−0.857804	−0.428902	−	0.903351i	$-0.641099\pi$
$859$	−25.1411	−0.857804	−0.428902	+	0.903351i	$0.641099\pi$
$860$	90.1659	3.07463
$861$	38.9211	1.32643
$862$	46.4419	1.58182
$863$	−21.7398	−0.740032	−0.370016	−	0.929025i	$-0.620648\pi$
$863$	−21.7398	−0.740032	−0.370016	+	0.929025i	$0.620648\pi$
$864$	163.139	5.55009
$865$	25.0526	0.851814
$866$	−5.64821	−0.191934
$867$	−4.57147	−0.155255
$868$	−103.965	−3.52880
$869$	1.22971	0.0417150
$870$	−45.4337	−1.54035
$871$	−42.3032	−1.43339
$872$	−16.0863	−0.544752
$873$	−36.4886	−1.23495
$874$	58.4528	1.97719
$875$	4.26824	0.144293
$876$	70.9898	2.39852
$877$	4.43198	0.149657	0.0748287	−	0.997196i	$-0.476159\pi$
$877$	4.43198	0.149657	0.0748287	+	0.997196i	$0.476159\pi$
$878$	60.4100	2.03874
$879$	18.1787	0.613152
$880$	36.0333	1.21468
$881$	−53.4204	−1.79978	−0.899890	−	0.436116i	$-0.856354\pi$
$881$	−53.4204	−1.79978	−0.899890	+	0.436116i	$0.856354\pi$
$882$	35.8538	1.20726
$883$	−41.1909	−1.38618	−0.693092	−	0.720849i	$-0.743752\pi$
$883$	−41.1909	−1.38618	−0.693092	+	0.720849i	$0.743752\pi$
$884$	135.606	4.56092
$885$	7.97832	0.268188
$886$	68.5094	2.30162
$887$	22.5829	0.758258	0.379129	−	0.925344i	$-0.376224\pi$
$887$	22.5829	0.758258	0.379129	+	0.925344i	$0.376224\pi$
$888$	−80.7656	−2.71032
$889$	66.4898	2.23000
$890$	−82.4446	−2.76355
$891$	−0.860336	−0.0288223
$892$	131.492	4.40267
$893$	43.0496	1.44060
$894$	−2.65471	−0.0887867
$895$	−3.36821	−0.112587
$896$	−317.324	−10.6010
$897$	−31.3613	−1.04712
$898$	−14.7538	−0.492342
$899$	25.7505	0.858829
$900$	−57.0173	−1.90058
$901$	26.2990	0.876146
$902$	18.4475	0.614235
$903$	−17.0552	−0.567560
$904$	−181.102	−6.02338
$905$	−31.5614	−1.04914
$906$	19.6769	0.653720
$907$	19.0474	0.632458	0.316229	−	0.948683i	$-0.397583\pi$
$907$	19.0474	0.632458	0.316229	+	0.948683i	$0.397583\pi$
$908$	55.5398	1.84315
$909$	−0.0327845	−0.00108739
$910$	−205.776	−6.82141
$911$	17.6285	0.584057	0.292028	−	0.956410i	$-0.405670\pi$
$911$	17.6285	0.584057	0.292028	+	0.956410i	$0.405670\pi$
$912$	−78.9189	−2.61327
$913$	5.74167	0.190022
$914$	−79.6727	−2.63534
$915$	30.4111	1.00536
$916$	115.978	3.83201
$917$	11.2850	0.372665
$918$	−48.4416	−1.59881
$919$	−35.5296	−1.17201	−0.586007	−	0.810306i	$-0.699301\pi$
$919$	−35.5296	−1.17201	−0.586007	+	0.810306i	$0.699301\pi$
$920$	174.304	5.74662
$921$	−9.90497	−0.326380
$922$	17.8204	0.586883
$923$	35.0603	1.15403
$924$	−12.3209	−0.405329
$925$	34.3925	1.13082
$926$	88.5147	2.90877
$927$	29.5664	0.971089
$928$	178.755	5.86791
$929$	30.1606	0.989536	0.494768	−	0.869025i	$-0.335253\pi$
$929$	30.1606	0.989536	0.494768	+	0.869025i	$0.335253\pi$
$930$	−40.6369	−1.33254
$931$	−25.4131	−0.832881
$932$	64.6032	2.11615
$933$	13.3683	0.437658
$934$	62.7507	2.05326
$935$	−6.39232	−0.209051
$936$	−150.205	−4.90961
$937$	−58.1849	−1.90082	−0.950408	−	0.311005i	$-0.899334\pi$
$937$	−58.1849	−1.90082	−0.950408	+	0.311005i	$0.899334\pi$
$938$	−66.8520	−2.18280
$939$	9.96766	0.325282
$940$	192.969	6.29395
$941$	7.77441	0.253439	0.126719	−	0.991939i	$-0.459555\pi$
$941$	7.77441	0.253439	0.126719	+	0.991939i	$0.459555\pi$
$942$	−21.8901	−0.713218
$943$	55.5942	1.81040
$944$	−52.5409	−1.71006
$945$	55.0724	1.79151
$946$	−8.08366	−0.262822
$947$	−0.0406022	−0.00131940	−0.000659698	−	1.00000i	$-0.500210\pi$
$947$	−0.0406022	−0.00131940	−0.000659698		1.00000i	$0.500210\pi$
$948$	−12.0725	−0.392096
$949$	−79.6366	−2.58511
$950$	53.9423	1.75012
$951$	15.0791	0.488973
$952$	142.562	4.62045
$953$	27.7295	0.898246	0.449123	−	0.893470i	$-0.351736\pi$
$953$	27.7295	0.898246	0.449123	+	0.893470i	$0.351736\pi$
$954$	−43.7886	−1.41771
$955$	−59.2300	−1.91664
$956$	74.3683	2.40524
$957$	3.05171	0.0986477
$958$	−98.7803	−3.19145
$959$	−31.9434	−1.03151
$960$	−163.674	−5.28255
$961$	−7.96811	−0.257036
$962$	136.194	4.39108
$963$	−6.32107	−0.203694
$964$	20.4750	0.659457
$965$	−3.71646	−0.119637
$966$	−49.5605	−1.59458
$967$	35.9458	1.15594	0.577970	−	0.816058i	$-0.303845\pi$
$967$	35.9458	1.15594	0.577970	+	0.816058i	$0.303845\pi$
$968$	119.578	3.84339
$969$	14.0002	0.449753
$970$	154.738	4.96834
$971$	28.3717	0.910492	0.455246	−	0.890366i	$-0.349551\pi$
$971$	28.3717	0.910492	0.455246	+	0.890366i	$0.349551\pi$
$972$	96.2169	3.08616
$973$	−53.1029	−1.70240
$974$	−105.467	−3.37937
$975$	−28.9413	−0.926865
$976$	−200.271	−6.41052
$977$	−1.49269	−0.0477553	−0.0238777	−	0.999715i	$-0.507601\pi$
$977$	−1.49269	−0.0477553	−0.0238777	+	0.999715i	$0.507601\pi$
$978$	36.9831	1.18259
$979$	5.53767	0.176985
$980$	−113.913	−3.63883
$981$	−2.96022	−0.0945126
$982$	62.4766	1.99371
$983$	−10.3606	−0.330451	−0.165226	−	0.986256i	$-0.552835\pi$
$983$	−10.3606	−0.330451	−0.165226	+	0.986256i	$0.552835\pi$
$984$	−120.480	−3.84077
$985$	−1.27449	−0.0406086
$986$	−53.0785	−1.69036
$987$	−36.5006	−1.16183
$988$	160.038	5.09149
$989$	−24.3613	−0.774643
$990$	10.6434	0.338270
$991$	−23.5673	−0.748641	−0.374320	−	0.927299i	$-0.622124\pi$
$991$	−23.5673	−0.748641	−0.374320	+	0.927299i	$0.622124\pi$
$992$	159.882	5.07627
$993$	−8.15486	−0.258787
$994$	55.4061	1.75737
$995$	−21.6803	−0.687311
$996$	−56.3680	−1.78609
$997$	0.307292	0.00973202	0.00486601	−	0.999988i	$-0.498451\pi$
$997$	0.307292	0.00973202	0.00486601	+	0.999988i	$0.498451\pi$
$998$	−90.2437	−2.85661
$999$	−36.4501	−1.15323

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6047.2.a.b.1.1	✓	287

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6047.2.a.b.1.1	✓	287	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:	\( N \)	\(=\)	\( 6047 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6047.a (trivial)

\(f(q)\)	\(=\)	\(q-2.82393 q^{2} +0.966727 q^{3} +5.97458 q^{4} -3.10169 q^{5} -2.72997 q^{6} +3.62589 q^{7} -11.2239 q^{8} -2.06544 q^{9} +O(q^{10})\)	\(q-2.82393 q^{2} +0.966727 q^{3} +5.97458 q^{4} -3.10169 q^{5} -2.72997 q^{6} +3.62589 q^{7} -11.2239 q^{8} -2.06544 q^{9} +8.75895 q^{10} -0.588325 q^{11} +5.77579 q^{12} -6.47929 q^{13} -10.2393 q^{14} -2.99849 q^{15} +19.7464 q^{16} -3.50303 q^{17} +5.83265 q^{18} -4.13417 q^{19} -18.5313 q^{20} +3.50525 q^{21} +1.66139 q^{22} +5.00683 q^{23} -10.8505 q^{24} +4.62048 q^{25} +18.2971 q^{26} -4.89690 q^{27} +21.6632 q^{28} -5.36564 q^{29} +8.46752 q^{30} -4.79916 q^{31} -33.3147 q^{32} -0.568750 q^{33} +9.89230 q^{34} -11.2464 q^{35} -12.3401 q^{36} +7.44350 q^{37} +11.6746 q^{38} -6.26371 q^{39} +34.8132 q^{40} +11.1037 q^{41} -9.89858 q^{42} -4.86561 q^{43} -3.51499 q^{44} +6.40635 q^{45} -14.1389 q^{46} -10.4131 q^{47} +19.0894 q^{48} +6.14709 q^{49} -13.0479 q^{50} -3.38647 q^{51} -38.7110 q^{52} -7.50750 q^{53} +13.8285 q^{54} +1.82480 q^{55} -40.6968 q^{56} -3.99661 q^{57} +15.1522 q^{58} -2.66078 q^{59} -17.9147 q^{60} -10.1421 q^{61} +13.5525 q^{62} -7.48905 q^{63} +54.5855 q^{64} +20.0968 q^{65} +1.60611 q^{66} +6.52899 q^{67} -20.9291 q^{68} +4.84024 q^{69} +31.7590 q^{70} -5.41114 q^{71} +23.1823 q^{72} +12.2909 q^{73} -21.0199 q^{74} +4.46674 q^{75} -24.6999 q^{76} -2.13320 q^{77} +17.6883 q^{78} -2.09018 q^{79} -61.2473 q^{80} +1.46235 q^{81} -31.3560 q^{82} -9.75936 q^{83} +20.9424 q^{84} +10.8653 q^{85} +13.7401 q^{86} -5.18711 q^{87} +6.60332 q^{88} -9.41261 q^{89} -18.0911 q^{90} -23.4932 q^{91} +29.9137 q^{92} -4.63947 q^{93} +29.4060 q^{94} +12.8229 q^{95} -32.2062 q^{96} +17.6663 q^{97} -17.3589 q^{98} +1.21515 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 287 q + 21 q^{2} + 29 q^{3} + 319 q^{4} + 19 q^{5} + 15 q^{6} + 52 q^{7} + 60 q^{8} + 352 q^{9}+O(q^{10}) \) 287 * q + 21 * q^2 + 29 * q^3 + 319 * q^4 + 19 * q^5 + 15 * q^6 + 52 * q^7 + 60 * q^8 + 352 * q^9	\( 287 q + 21 q^{2} + 29 q^{3} + 319 q^{4} + 19 q^{5} + 15 q^{6} + 52 q^{7} + 60 q^{8} + 352 q^{9} + 38 q^{10} + 32 q^{11} + 80 q^{12} + 86 q^{13} + 14 q^{14} + 41 q^{15} + 375 q^{16} + 59 q^{17} + 93 q^{18} + 39 q^{19} + 27 q^{20} + 51 q^{21} + 99 q^{22} + 68 q^{23} + 31 q^{24} + 492 q^{25} + 19 q^{26} + 107 q^{27} + 142 q^{28} + 39 q^{29} + 12 q^{30} + 104 q^{31} + 131 q^{32} + 139 q^{33} + 71 q^{34} - 5 q^{35} + 410 q^{36} + 298 q^{37} + 19 q^{38} + 37 q^{39} + 98 q^{40} + 90 q^{41} + 32 q^{42} + 105 q^{43} + 85 q^{44} + 73 q^{45} + 97 q^{46} + 66 q^{47} + 161 q^{48} + 473 q^{49} + 85 q^{50} + 34 q^{51} + 179 q^{52} + 95 q^{53} + 28 q^{54} + 62 q^{55} + 16 q^{56} + 247 q^{57} + 247 q^{58} + 32 q^{59} + 51 q^{60} + 106 q^{61} + 22 q^{62} + 104 q^{63} + 480 q^{64} + 150 q^{65} - 27 q^{66} + 232 q^{67} + 88 q^{68} + 57 q^{69} + 123 q^{70} + 46 q^{71} + 240 q^{72} + 372 q^{73} + 13 q^{74} + 81 q^{75} + 82 q^{76} + 65 q^{77} + 154 q^{78} + 143 q^{79} + 17 q^{80} + 519 q^{81} + 98 q^{82} + 49 q^{83} + 79 q^{84} + 236 q^{85} + 61 q^{86} + 31 q^{87} + 254 q^{88} + 114 q^{89} + 36 q^{90} + 96 q^{91} + 151 q^{92} + 189 q^{93} + 8 q^{94} + 30 q^{95} + 23 q^{96} + 503 q^{97} + 91 q^{98} + 130 q^{99}+O(q^{100}) \) 287 * q + 21 * q^2 + 29 * q^3 + 319 * q^4 + 19 * q^5 + 15 * q^6 + 52 * q^7 + 60 * q^8 + 352 * q^9 + 38 * q^10 + 32 * q^11 + 80 * q^12 + 86 * q^13 + 14 * q^14 + 41 * q^15 + 375 * q^16 + 59 * q^17 + 93 * q^18 + 39 * q^19 + 27 * q^20 + 51 * q^21 + 99 * q^22 + 68 * q^23 + 31 * q^24 + 492 * q^25 + 19 * q^26 + 107 * q^27 + 142 * q^28 + 39 * q^29 + 12 * q^30 + 104 * q^31 + 131 * q^32 + 139 * q^33 + 71 * q^34 - 5 * q^35 + 410 * q^36 + 298 * q^37 + 19 * q^38 + 37 * q^39 + 98 * q^40 + 90 * q^41 + 32 * q^42 + 105 * q^43 + 85 * q^44 + 73 * q^45 + 97 * q^46 + 66 * q^47 + 161 * q^48 + 473 * q^49 + 85 * q^50 + 34 * q^51 + 179 * q^52 + 95 * q^53 + 28 * q^54 + 62 * q^55 + 16 * q^56 + 247 * q^57 + 247 * q^58 + 32 * q^59 + 51 * q^60 + 106 * q^61 + 22 * q^62 + 104 * q^63 + 480 * q^64 + 150 * q^65 - 27 * q^66 + 232 * q^67 + 88 * q^68 + 57 * q^69 + 123 * q^70 + 46 * q^71 + 240 * q^72 + 372 * q^73 + 13 * q^74 + 81 * q^75 + 82 * q^76 + 65 * q^77 + 154 * q^78 + 143 * q^79 + 17 * q^80 + 519 * q^81 + 98 * q^82 + 49 * q^83 + 79 * q^84 + 236 * q^85 + 61 * q^86 + 31 * q^87 + 254 * q^88 + 114 * q^89 + 36 * q^90 + 96 * q^91 + 151 * q^92 + 189 * q^93 + 8 * q^94 + 30 * q^95 + 23 * q^96 + 503 * q^97 + 91 * q^98 + 130 * q^99

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