LMFDB - Embedded newform 6047.2.a.b.1.4

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			1.4
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)

$f(q)$	$=$	$q-2.77436 q^{2} +2.72832 q^{3} +5.69705 q^{4} +0.314782 q^{5} -7.56934 q^{6} -2.82964 q^{7} -10.2569 q^{8} +4.44375 q^{9} +O(q^{10})$	\(q-2.77436 q^{2} +2.72832 q^{3} +5.69705 q^{4} +0.314782 q^{5} -7.56934 q^{6} -2.82964 q^{7} -10.2569 q^{8} +4.44375 q^{9} -0.873318 q^{10} +5.38778 q^{11} +15.5434 q^{12} +2.72565 q^{13} +7.85043 q^{14} +0.858828 q^{15} +17.0623 q^{16} +5.73816 q^{17} -12.3285 q^{18} +5.85389 q^{19} +1.79333 q^{20} -7.72017 q^{21} -14.9476 q^{22} +7.58768 q^{23} -27.9842 q^{24} -4.90091 q^{25} -7.56192 q^{26} +3.93901 q^{27} -16.1206 q^{28} -9.28959 q^{29} -2.38269 q^{30} +7.42021 q^{31} -26.8229 q^{32} +14.6996 q^{33} -15.9197 q^{34} -0.890721 q^{35} +25.3162 q^{36} +6.12182 q^{37} -16.2408 q^{38} +7.43645 q^{39} -3.22870 q^{40} -5.66562 q^{41} +21.4185 q^{42} -3.70350 q^{43} +30.6944 q^{44} +1.39881 q^{45} -21.0509 q^{46} +3.96677 q^{47} +46.5513 q^{48} +1.00686 q^{49} +13.5969 q^{50} +15.6556 q^{51} +15.5281 q^{52} +4.50559 q^{53} -10.9282 q^{54} +1.69598 q^{55} +29.0234 q^{56} +15.9713 q^{57} +25.7726 q^{58} +2.87581 q^{59} +4.89278 q^{60} -4.59887 q^{61} -20.5863 q^{62} -12.5742 q^{63} +40.2918 q^{64} +0.857986 q^{65} -40.7819 q^{66} +6.23795 q^{67} +32.6906 q^{68} +20.7016 q^{69} +2.47118 q^{70} -1.35068 q^{71} -45.5792 q^{72} +7.37620 q^{73} -16.9841 q^{74} -13.3713 q^{75} +33.3499 q^{76} -15.2455 q^{77} -20.6314 q^{78} -4.30933 q^{79} +5.37090 q^{80} -2.58435 q^{81} +15.7184 q^{82} -13.2742 q^{83} -43.9822 q^{84} +1.80627 q^{85} +10.2748 q^{86} -25.3450 q^{87} -55.2620 q^{88} -4.88059 q^{89} -3.88081 q^{90} -7.71260 q^{91} +43.2274 q^{92} +20.2447 q^{93} -11.0052 q^{94} +1.84270 q^{95} -73.1816 q^{96} +17.0494 q^{97} -2.79339 q^{98} +23.9419 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.77436	−1.96177	−0.980883	−	0.194600i	$-0.937659\pi$
$2$	−2.77436	−1.96177	−0.980883	+	0.194600i	$0.937659\pi$
$3$	2.72832	1.57520	0.787599	−	0.616188i	$-0.211324\pi$
$3$	2.72832	1.57520	0.787599	+	0.616188i	$0.211324\pi$
$4$	5.69705	2.84852
$5$	0.314782	0.140775	0.0703875	−	0.997520i	$-0.477576\pi$
$5$	0.314782	0.140775	0.0703875	+	0.997520i	$0.477576\pi$
$6$	−7.56934	−3.09017
$7$	−2.82964	−1.06950	−0.534752	−	0.845009i	$-0.679595\pi$
$7$	−2.82964	−1.06950	−0.534752	+	0.845009i	$0.679595\pi$
$8$	−10.2569	−3.62637
$9$	4.44375	1.48125
$10$	−0.873318	−0.276167
$11$	5.38778	1.62448	0.812238	−	0.583326i	$-0.198249\pi$
$11$	5.38778	1.62448	0.812238	+	0.583326i	$0.198249\pi$
$12$	15.5434	4.48699
$13$	2.72565	0.755959	0.377979	−	0.925814i	$-0.376619\pi$
$13$	2.72565	0.755959	0.377979	+	0.925814i	$0.376619\pi$
$14$	7.85043	2.09811
$15$	0.858828	0.221748
$16$	17.0623	4.26556
$17$	5.73816	1.39171	0.695854	−	0.718183i	$-0.255026\pi$
$17$	5.73816	1.39171	0.695854	+	0.718183i	$0.255026\pi$
$18$	−12.3285	−2.90586
$19$	5.85389	1.34297	0.671487	−	0.741016i	$-0.265656\pi$
$19$	5.85389	1.34297	0.671487	+	0.741016i	$0.265656\pi$
$20$	1.79333	0.401001
$21$	−7.72017	−1.68468
$22$	−14.9476	−3.18684
$23$	7.58768	1.58214	0.791070	−	0.611726i	$-0.209524\pi$
$23$	7.58768	1.58214	0.791070	+	0.611726i	$0.209524\pi$
$24$	−27.9842	−5.71225
$25$	−4.90091	−0.980182
$26$	−7.56192	−1.48301
$27$	3.93901	0.758063
$28$	−16.1206	−3.04651
$29$	−9.28959	−1.72503	−0.862517	−	0.506028i	$-0.831113\pi$
$29$	−9.28959	−1.72503	−0.862517	+	0.506028i	$0.831113\pi$
$30$	−2.38269	−0.435018
$31$	7.42021	1.33271	0.666355	−	0.745635i	$-0.267854\pi$
$31$	7.42021	1.33271	0.666355	+	0.745635i	$0.267854\pi$
$32$	−26.8229	−4.74166
$33$	14.6996	2.55887
$34$	−15.9197	−2.73021
$35$	−0.890721	−0.150559
$36$	25.3162	4.21937
$37$	6.12182	1.00642	0.503211	−	0.864164i	$-0.332152\pi$
$37$	6.12182	1.00642	0.503211	+	0.864164i	$0.332152\pi$
$38$	−16.2408	−2.63460
$39$	7.43645	1.19079
$40$	−3.22870	−0.510502
$41$	−5.66562	−0.884821	−0.442411	−	0.896813i	$-0.645877\pi$
$41$	−5.66562	−0.884821	−0.442411	+	0.896813i	$0.645877\pi$
$42$	21.4185	3.30495
$43$	−3.70350	−0.564778	−0.282389	−	0.959300i	$-0.591127\pi$
$43$	−3.70350	−0.564778	−0.282389	+	0.959300i	$0.591127\pi$
$44$	30.6944	4.62736
$45$	1.39881	0.208523
$46$	−21.0509	−3.10379
$47$	3.96677	0.578613	0.289306	−	0.957237i	$-0.406575\pi$
$47$	3.96677	0.578613	0.289306	+	0.957237i	$0.406575\pi$
$48$	46.5513	6.71911
$49$	1.00686	0.143837
$50$	13.5969	1.92289
$51$	15.6556	2.19222
$52$	15.5281	2.15337
$53$	4.50559	0.618891	0.309445	−	0.950917i	$-0.399857\pi$
$53$	4.50559	0.618891	0.309445	+	0.950917i	$0.399857\pi$
$54$	−10.9282	−1.48714
$55$	1.69598	0.228685
$56$	29.0234	3.87841
$57$	15.9713	2.11545
$58$	25.7726	3.38411
$59$	2.87581	0.374399	0.187199	−	0.982322i	$-0.440059\pi$
$59$	2.87581	0.374399	0.187199	+	0.982322i	$0.440059\pi$
$60$	4.89278	0.631656
$61$	−4.59887	−0.588824	−0.294412	−	0.955679i	$-0.595124\pi$
$61$	−4.59887	−0.588824	−0.294412	+	0.955679i	$0.595124\pi$
$62$	−20.5863	−2.61446
$63$	−12.5742	−1.58420
$64$	40.2918	5.03647
$65$	0.857986	0.106420
$66$	−40.7819	−5.01991
$67$	6.23795	0.762086	0.381043	−	0.924557i	$-0.375565\pi$
$67$	6.23795	0.762086	0.381043	+	0.924557i	$0.375565\pi$
$68$	32.6906	3.96431
$69$	20.7016	2.49218
$70$	2.47118	0.295362
$71$	−1.35068	−0.160296	−0.0801479	−	0.996783i	$-0.525539\pi$
$71$	−1.35068	−0.160296	−0.0801479	+	0.996783i	$0.525539\pi$
$72$	−45.5792	−5.37156
$73$	7.37620	0.863319	0.431659	−	0.902037i	$-0.357928\pi$
$73$	7.37620	0.863319	0.431659	+	0.902037i	$0.357928\pi$
$74$	−16.9841	−1.97436
$75$	−13.3713	−1.54398
$76$	33.3499	3.82549
$77$	−15.2455	−1.73738
$78$	−20.6314	−2.33604
$79$	−4.30933	−0.484837	−0.242419	−	0.970172i	$-0.577941\pi$
$79$	−4.30933	−0.484837	−0.242419	+	0.970172i	$0.577941\pi$
$80$	5.37090	0.600484
$81$	−2.58435	−0.287150
$82$	15.7184	1.73581
$83$	−13.2742	−1.45703	−0.728517	−	0.685028i	$-0.759790\pi$
$83$	−13.2742	−1.45703	−0.728517	+	0.685028i	$0.759790\pi$
$84$	−43.9822	−4.79885
$85$	1.80627	0.195918
$86$	10.2748	1.10796
$87$	−25.3450	−2.71727
$88$	−55.2620	−5.89095
$89$	−4.88059	−0.517341	−0.258671	−	0.965966i	$-0.583284\pi$
$89$	−4.88059	−0.517341	−0.258671	+	0.965966i	$0.583284\pi$
$90$	−3.88081	−0.409073
$91$	−7.71260	−0.808501
$92$	43.2274	4.50676
$93$	20.2447	2.09928
$94$	−11.0052	−1.13510
$95$	1.84270	0.189057
$96$	−73.1816	−7.46906
$97$	17.0494	1.73110	0.865552	−	0.500818i	$-0.166968\pi$
$97$	17.0494	1.73110	0.865552	+	0.500818i	$0.166968\pi$
$98$	−2.79339	−0.282175
$99$	23.9419	2.40625
$100$	−27.9207	−2.79207
$101$	−1.38723	−0.138034	−0.0690171	−	0.997615i	$-0.521986\pi$
$101$	−1.38723	−0.138034	−0.0690171	+	0.997615i	$0.521986\pi$
$102$	−43.4341	−4.30061
$103$	−15.2296	−1.50062	−0.750308	−	0.661089i	$-0.770095\pi$
$103$	−15.2296	−1.50062	−0.750308	+	0.661089i	$0.770095\pi$
$104$	−27.9568	−2.74139
$105$	−2.43017	−0.237161
$106$	−12.5001	−1.21412
$107$	13.2808	1.28390	0.641952	−	0.766745i	$-0.278125\pi$
$107$	13.2808	1.28390	0.641952	+	0.766745i	$0.278125\pi$
$108$	22.4407	2.15936
$109$	−2.92499	−0.280163	−0.140081	−	0.990140i	$-0.544736\pi$
$109$	−2.92499	−0.280163	−0.140081	+	0.990140i	$0.544736\pi$
$110$	−4.70524	−0.448627
$111$	16.7023	1.58531
$112$	−48.2800	−4.56203
$113$	2.41338	0.227032	0.113516	−	0.993536i	$-0.463789\pi$
$113$	2.41338	0.227032	0.113516	+	0.993536i	$0.463789\pi$
$114$	−44.3101	−4.15002
$115$	2.38847	0.222726
$116$	−52.9233	−4.91380
$117$	12.1121	1.11976
$118$	−7.97852	−0.734482
$119$	−16.2369	−1.48844
$120$	−8.80893	−0.804142
$121$	18.0281	1.63892
$122$	12.7589	1.15514
$123$	−15.4576	−1.39377
$124$	42.2733	3.79625
$125$	−3.11663	−0.278760
$126$	34.8853	3.10783
$127$	11.2545	0.998679	0.499339	−	0.866407i	$-0.333576\pi$
$127$	11.2545	0.998679	0.499339	+	0.866407i	$0.333576\pi$
$128$	−58.1379	−5.13871
$129$	−10.1043	−0.889637
$130$	−2.38036	−0.208771
$131$	−3.68850	−0.322266	−0.161133	−	0.986933i	$-0.551515\pi$
$131$	−3.68850	−0.322266	−0.161133	+	0.986933i	$0.551515\pi$
$132$	83.7443	7.28901
$133$	−16.5644	−1.43631
$134$	−17.3063	−1.49503
$135$	1.23993	0.106716
$136$	−58.8559	−5.04685
$137$	−16.4015	−1.40128	−0.700638	−	0.713517i	$-0.747101\pi$
$137$	−16.4015	−1.40128	−0.700638	+	0.713517i	$0.747101\pi$
$138$	−57.4337	−4.88908
$139$	6.83421	0.579670	0.289835	−	0.957077i	$-0.406400\pi$
$139$	6.83421	0.579670	0.289835	+	0.957077i	$0.406400\pi$
$140$	−5.07448	−0.428872
$141$	10.8226	0.911429
$142$	3.74726	0.314463
$143$	14.6852	1.22804
$144$	75.8203	6.31836
$145$	−2.92420	−0.242842
$146$	−20.4642	−1.69363
$147$	2.74705	0.226573
$148$	34.8763	2.86682
$149$	−7.76677	−0.636279	−0.318139	−	0.948044i	$-0.603058\pi$
$149$	−7.76677	−0.636279	−0.318139	+	0.948044i	$0.603058\pi$
$150$	37.0967	3.02893
$151$	−13.4212	−1.09220	−0.546099	−	0.837721i	$-0.683888\pi$
$151$	−13.4212	−1.09220	−0.546099	+	0.837721i	$0.683888\pi$
$152$	−60.0429	−4.87012
$153$	25.4989	2.06147
$154$	42.2963	3.40834
$155$	2.33575	0.187612
$156$	42.3658	3.39198
$157$	−23.8931	−1.90688	−0.953440	−	0.301584i	$-0.902485\pi$
$157$	−23.8931	−1.90688	−0.953440	+	0.301584i	$0.902485\pi$
$158$	11.9556	0.951137
$159$	12.2927	0.974875
$160$	−8.44338	−0.667508
$161$	−21.4704	−1.69210
$162$	7.16990	0.563320
$163$	18.6028	1.45709	0.728544	−	0.684999i	$-0.240198\pi$
$163$	18.6028	1.45709	0.728544	+	0.684999i	$0.240198\pi$
$164$	−32.2773	−2.52043
$165$	4.62717	0.360225
$166$	36.8274	2.85836
$167$	−3.05803	−0.236637	−0.118319	−	0.992976i	$-0.537750\pi$
$167$	−3.05803	−0.236637	−0.118319	+	0.992976i	$0.537750\pi$
$168$	79.1852	6.10927
$169$	−5.57084	−0.428526
$170$	−5.01124	−0.384345
$171$	26.0132	1.98928
$172$	−21.0990	−1.60878
$173$	2.55725	0.194424	0.0972121	−	0.995264i	$-0.469007\pi$
$173$	2.55725	0.194424	0.0972121	+	0.995264i	$0.469007\pi$
$174$	70.3161	5.33065
$175$	13.8678	1.04831
$176$	91.9276	6.92930
$177$	7.84614	0.589752
$178$	13.5405	1.01490
$179$	10.3762	0.775550	0.387775	−	0.921754i	$-0.373244\pi$
$179$	10.3762	0.775550	0.387775	+	0.921754i	$0.373244\pi$
$180$	7.96911	0.593982
$181$	−24.1155	−1.79249	−0.896247	−	0.443555i	$-0.853717\pi$
$181$	−24.1155	−1.79249	−0.896247	+	0.443555i	$0.853717\pi$
$182$	21.3975	1.58609
$183$	−12.5472	−0.927515
$184$	−77.8262	−5.73742
$185$	1.92704	0.141679
$186$	−56.1661	−4.11830
$187$	30.9159	2.26080
$188$	22.5989	1.64819
$189$	−11.1460	−0.810751
$190$	−5.11231	−0.370886
$191$	1.15516	0.0835846	0.0417923	−	0.999126i	$-0.486693\pi$
$191$	1.15516	0.0835846	0.0417923	+	0.999126i	$0.486693\pi$
$192$	109.929	7.93344
$193$	13.8279	0.995353	0.497676	−	0.867363i	$-0.334187\pi$
$193$	13.8279	0.995353	0.497676	+	0.867363i	$0.334187\pi$
$194$	−47.3011	−3.39602
$195$	2.34086	0.167633
$196$	5.73614	0.409724
$197$	−19.8757	−1.41609	−0.708043	−	0.706169i	$-0.750422\pi$
$197$	−19.8757	−1.41609	−0.708043	+	0.706169i	$0.750422\pi$
$198$	−66.4234	−4.72051
$199$	−2.28604	−0.162053	−0.0810266	−	0.996712i	$-0.525820\pi$
$199$	−2.28604	−0.162053	−0.0810266	+	0.996712i	$0.525820\pi$
$200$	50.2683	3.55450
$201$	17.0191	1.20044
$202$	3.84866	0.270791
$203$	26.2862	1.84493
$204$	89.1905	6.24458
$205$	−1.78344	−0.124561
$206$	42.2523	2.94386
$207$	33.7177	2.34354
$208$	46.5057	3.22459
$209$	31.5394	2.18163
$210$	6.74217	0.465254
$211$	−1.31562	−0.0905710	−0.0452855	−	0.998974i	$-0.514420\pi$
$211$	−1.31562	−0.0905710	−0.0452855	+	0.998974i	$0.514420\pi$
$212$	25.6686	1.76292
$213$	−3.68508	−0.252498
$214$	−36.8457	−2.51872
$215$	−1.16579	−0.0795066
$216$	−40.4021	−2.74902
$217$	−20.9965	−1.42534
$218$	8.11495	0.549614
$219$	20.1247	1.35990
$220$	9.66206	0.651416
$221$	15.6402	1.05207
$222$	−46.3381	−3.11001
$223$	10.9759	0.734998	0.367499	−	0.930024i	$-0.380214\pi$
$223$	10.9759	0.734998	0.367499	+	0.930024i	$0.380214\pi$
$224$	75.8992	5.07123
$225$	−21.7784	−1.45189
$226$	−6.69558	−0.445384
$227$	−22.0591	−1.46411	−0.732057	−	0.681243i	$-0.761440\pi$
$227$	−22.0591	−1.46411	−0.732057	+	0.681243i	$0.761440\pi$
$228$	90.9892	6.02591
$229$	−7.73559	−0.511182	−0.255591	−	0.966785i	$-0.582270\pi$
$229$	−7.73559	−0.511182	−0.255591	+	0.966785i	$0.582270\pi$
$230$	−6.62646	−0.436936
$231$	−41.5946	−2.73672
$232$	95.2826	6.25561
$233$	−15.9811	−1.04695	−0.523477	−	0.852040i	$-0.675365\pi$
$233$	−15.9811	−1.04695	−0.523477	+	0.852040i	$0.675365\pi$
$234$	−33.6033	−2.19671
$235$	1.24867	0.0814541
$236$	16.3836	1.06648
$237$	−11.7572	−0.763715
$238$	45.0470	2.91996
$239$	10.0383	0.649326	0.324663	−	0.945830i	$-0.394749\pi$
$239$	10.0383	0.649326	0.324663	+	0.945830i	$0.394749\pi$
$240$	14.6535	0.945882
$241$	28.6797	1.84742	0.923712	−	0.383088i	$-0.125139\pi$
$241$	28.6797	1.84742	0.923712	+	0.383088i	$0.125139\pi$
$242$	−50.0165	−3.21518
$243$	−18.8680	−1.21038
$244$	−26.2000	−1.67728
$245$	0.316942	0.0202487
$246$	42.8850	2.73425
$247$	15.9556	1.01523
$248$	−76.1085	−4.83290
$249$	−36.2163	−2.29512
$250$	8.64665	0.546862
$251$	−6.35682	−0.401239	−0.200619	−	0.979669i	$-0.564295\pi$
$251$	−6.35682	−0.401239	−0.200619	+	0.979669i	$0.564295\pi$
$252$	−71.6359	−4.51263
$253$	40.8807	2.57015
$254$	−31.2241	−1.95917
$255$	4.92809	0.308609
$256$	80.7115	5.04447
$257$	−21.8833	−1.36504	−0.682521	−	0.730866i	$-0.739117\pi$
$257$	−21.8833	−1.36504	−0.682521	+	0.730866i	$0.739117\pi$
$258$	28.0330	1.74526
$259$	−17.3226	−1.07637
$260$	4.88799	0.303140
$261$	−41.2806	−2.55521
$262$	10.2332	0.632210
$263$	14.4572	0.891467	0.445733	−	0.895166i	$-0.352943\pi$
$263$	14.4572	0.891467	0.445733	+	0.895166i	$0.352943\pi$
$264$	−150.773	−9.27941
$265$	1.41828	0.0871243
$266$	45.9555	2.81771
$267$	−13.3158	−0.814915
$268$	35.5379	2.17082
$269$	−22.8528	−1.39336	−0.696679	−	0.717383i	$-0.745340\pi$
$269$	−22.8528	−1.39336	−0.696679	+	0.717383i	$0.745340\pi$
$270$	−3.44001	−0.209352
$271$	17.8407	1.08375	0.541873	−	0.840460i	$-0.317715\pi$
$271$	17.8407	1.08375	0.541873	+	0.840460i	$0.317715\pi$
$272$	97.9059	5.93642
$273$	−21.0425	−1.27355
$274$	45.5036	2.74898
$275$	−26.4050	−1.59228
$276$	117.938	7.09905
$277$	−20.4788	−1.23045	−0.615225	−	0.788352i	$-0.710935\pi$
$277$	−20.4788	−1.23045	−0.615225	+	0.788352i	$0.710935\pi$
$278$	−18.9605	−1.13718
$279$	32.9735	1.97407
$280$	9.13605	0.545984
$281$	−9.45104	−0.563802	−0.281901	−	0.959443i	$-0.590965\pi$
$281$	−9.45104	−0.563802	−0.281901	+	0.959443i	$0.590965\pi$
$282$	−30.0258	−1.78801
$283$	29.7593	1.76901	0.884503	−	0.466535i	$-0.154498\pi$
$283$	29.7593	1.76901	0.884503	+	0.466535i	$0.154498\pi$
$284$	−7.69487	−0.456606
$285$	5.02748	0.297802
$286$	−40.7419	−2.40912
$287$	16.0317	0.946319
$288$	−119.194	−7.02359
$289$	15.9265	0.936852
$290$	8.11277	0.476398
$291$	46.5163	2.72683
$292$	42.0226	2.45918
$293$	−15.9566	−0.932197	−0.466098	−	0.884733i	$-0.654341\pi$
$293$	−15.9566	−0.932197	−0.466098	+	0.884733i	$0.654341\pi$
$294$	−7.62128	−0.444482
$295$	0.905254	0.0527059
$296$	−62.7911	−3.64966
$297$	21.2225	1.23146
$298$	21.5478	1.24823
$299$	20.6813	1.19603
$300$	−76.1768	−4.39807
$301$	10.4796	0.604032
$302$	37.2351	2.14264
$303$	−3.78480	−0.217431
$304$	99.8805	5.72854
$305$	−1.44764	−0.0828917
$306$	−70.7431	−4.04412
$307$	1.66352	0.0949418	0.0474709	−	0.998873i	$-0.484884\pi$
$307$	1.66352	0.0949418	0.0474709	+	0.998873i	$0.484884\pi$
$308$	−86.8541	−4.94897
$309$	−41.5512	−2.36377
$310$	−6.48020	−0.368051
$311$	−24.5541	−1.39233	−0.696167	−	0.717880i	$-0.745113\pi$
$311$	−24.5541	−1.39233	−0.696167	+	0.717880i	$0.745113\pi$
$312$	−76.2751	−4.31823
$313$	18.7722	1.06107	0.530534	−	0.847664i	$-0.321992\pi$
$313$	18.7722	1.06107	0.530534	+	0.847664i	$0.321992\pi$
$314$	66.2880	3.74085
$315$	−3.95814	−0.223016
$316$	−24.5504	−1.38107
$317$	19.2549	1.08146	0.540730	−	0.841196i	$-0.318148\pi$
$317$	19.2549	1.08146	0.540730	+	0.841196i	$0.318148\pi$
$318$	−34.1044	−1.91248
$319$	−50.0503	−2.80228
$320$	12.6831	0.709009
$321$	36.2343	2.02240
$322$	59.5665	3.31951
$323$	33.5905	1.86903
$324$	−14.7231	−0.817953
$325$	−13.3582	−0.740978
$326$	−51.6109	−2.85846
$327$	−7.98031	−0.441312
$328$	58.1118	3.20869
$329$	−11.2245	−0.618828
$330$	−12.8374	−0.706677
$331$	−0.693002	−0.0380909	−0.0190454	−	0.999819i	$-0.506063\pi$
$331$	−0.693002	−0.0380909	−0.0190454	+	0.999819i	$0.506063\pi$
$332$	−75.6238	−4.15040
$333$	27.2038	1.49076
$334$	8.48405	0.464227
$335$	1.96360	0.107283
$336$	−131.724	−7.18611
$337$	22.9425	1.24976	0.624878	−	0.780722i	$-0.285149\pi$
$337$	22.9425	1.24976	0.624878	+	0.780722i	$0.285149\pi$
$338$	15.4555	0.840668
$339$	6.58449	0.357620
$340$	10.2904	0.558076
$341$	39.9784	2.16495
$342$	−72.1699	−3.90250
$343$	16.9584	0.915669
$344$	37.9865	2.04809
$345$	6.51651	0.350837
$346$	−7.09472	−0.381414
$347$	−7.39092	−0.396765	−0.198383	−	0.980125i	$-0.563569\pi$
$347$	−7.39092	−0.396765	−0.198383	+	0.980125i	$0.563569\pi$
$348$	−144.392	−7.74021
$349$	−3.39696	−0.181835	−0.0909176	−	0.995858i	$-0.528980\pi$
$349$	−3.39696	−0.181835	−0.0909176	+	0.995858i	$0.528980\pi$
$350$	−38.4743	−2.05654
$351$	10.7364	0.573065
$352$	−144.516	−7.70272
$353$	7.67386	0.408438	0.204219	−	0.978925i	$-0.434535\pi$
$353$	7.67386	0.408438	0.204219	+	0.978925i	$0.434535\pi$
$354$	−21.7680	−1.15695
$355$	−0.425169	−0.0225656
$356$	−27.8049	−1.47366
$357$	−44.2996	−2.34458
$358$	−28.7871	−1.52145
$359$	7.80255	0.411803	0.205901	−	0.978573i	$-0.433987\pi$
$359$	7.80255	0.411803	0.205901	+	0.978573i	$0.433987\pi$
$360$	−14.3475	−0.756181
$361$	15.2680	0.803579
$362$	66.9051	3.51645
$363$	49.1866	2.58163
$364$	−43.9391	−2.30303
$365$	2.32190	0.121534
$366$	34.8104	1.81957
$367$	−28.5832	−1.49203	−0.746016	−	0.665928i	$-0.768036\pi$
$367$	−28.5832	−1.49203	−0.746016	+	0.665928i	$0.768036\pi$
$368$	129.463	6.74872
$369$	−25.1766	−1.31064
$370$	−5.34630	−0.277941
$371$	−12.7492	−0.661906
$372$	115.335	5.97985
$373$	24.6879	1.27829	0.639144	−	0.769087i	$-0.279289\pi$
$373$	24.6879	1.27829	0.639144	+	0.769087i	$0.279289\pi$
$374$	−85.7718	−4.43515
$375$	−8.50318	−0.439102
$376$	−40.6868	−2.09826
$377$	−25.3202	−1.30406
$378$	30.9229	1.59050
$379$	10.9683	0.563406	0.281703	−	0.959502i	$-0.409101\pi$
$379$	10.9683	0.563406	0.281703	+	0.959502i	$0.409101\pi$
$380$	10.4980	0.538533
$381$	30.7060	1.57312
$382$	−3.20483	−0.163973
$383$	6.89763	0.352452	0.176226	−	0.984350i	$-0.443611\pi$
$383$	6.89763	0.352452	0.176226	+	0.984350i	$0.443611\pi$
$384$	−158.619	−8.09448
$385$	−4.79900	−0.244580
$386$	−38.3635	−1.95265
$387$	−16.4574	−0.836577
$388$	97.1313	4.93109
$389$	−2.09409	−0.106174	−0.0530872	−	0.998590i	$-0.516906\pi$
$389$	−2.09409	−0.106174	−0.0530872	+	0.998590i	$0.516906\pi$
$390$	−6.49439	−0.328856
$391$	43.5393	2.20188
$392$	−10.3273	−0.521608
$393$	−10.0634	−0.507633
$394$	55.1423	2.77803
$395$	−1.35650	−0.0682529
$396$	136.398	6.85427
$397$	17.0193	0.854176	0.427088	−	0.904210i	$-0.359540\pi$
$397$	17.0193	0.854176	0.427088	+	0.904210i	$0.359540\pi$
$398$	6.34229	0.317910
$399$	−45.1930	−2.26248
$400$	−83.6206	−4.18103
$401$	−18.8424	−0.940944	−0.470472	−	0.882415i	$-0.655916\pi$
$401$	−18.8424	−0.940944	−0.470472	+	0.882415i	$0.655916\pi$
$402$	−47.2171	−2.35498
$403$	20.2249	1.00747
$404$	−7.90309	−0.393194
$405$	−0.813507	−0.0404235
$406$	−72.9273	−3.61932
$407$	32.9830	1.63491
$408$	−160.578	−7.94979
$409$	−24.4553	−1.20924	−0.604619	−	0.796515i	$-0.706674\pi$
$409$	−24.4553	−1.20924	−0.604619	+	0.796515i	$0.706674\pi$
$410$	4.94789	0.244359
$411$	−44.7486	−2.20729
$412$	−86.7637	−4.27454
$413$	−8.13751	−0.400421
$414$	−93.5449	−4.59748
$415$	−4.17849	−0.205114
$416$	−73.1098	−3.58450
$417$	18.6459	0.913096
$418$	−87.5016	−4.27984
$419$	−22.8061	−1.11415	−0.557076	−	0.830462i	$-0.688077\pi$
$419$	−22.8061	−1.11415	−0.557076	+	0.830462i	$0.688077\pi$
$420$	−13.8448	−0.675558
$421$	−3.54615	−0.172829	−0.0864143	−	0.996259i	$-0.527541\pi$
$421$	−3.54615	−0.172829	−0.0864143	+	0.996259i	$0.527541\pi$
$422$	3.65000	0.177679
$423$	17.6273	0.857069
$424$	−46.2135	−2.24433
$425$	−28.1222	−1.36413
$426$	10.2237	0.495341
$427$	13.0131	0.629750
$428$	75.6614	3.65723
$429$	40.0659	1.93440
$430$	3.23433	0.155973
$431$	30.8202	1.48456	0.742278	−	0.670092i	$-0.233745\pi$
$431$	30.8202	1.48456	0.742278	+	0.670092i	$0.233745\pi$
$432$	67.2084	3.23357
$433$	31.8050	1.52845	0.764225	−	0.644950i	$-0.223122\pi$
$433$	31.8050	1.52845	0.764225	+	0.644950i	$0.223122\pi$
$434$	58.2518	2.79618
$435$	−7.97816	−0.382524
$436$	−16.6638	−0.798051
$437$	44.4174	2.12477
$438$	−55.8330	−2.66780
$439$	−3.93675	−0.187891	−0.0939454	−	0.995577i	$-0.529948\pi$
$439$	−3.93675	−0.187891	−0.0939454	+	0.995577i	$0.529948\pi$
$440$	−17.3955	−0.829298
$441$	4.47424	0.213059
$442$	−43.3915	−2.06392
$443$	16.6859	0.792770	0.396385	−	0.918084i	$-0.370265\pi$
$443$	16.6859	0.792770	0.396385	+	0.918084i	$0.370265\pi$
$444$	95.1538	4.51580
$445$	−1.53632	−0.0728287
$446$	−30.4510	−1.44189
$447$	−21.1903	−1.00227
$448$	−114.011	−5.38652
$449$	−15.1209	−0.713597	−0.356799	−	0.934181i	$-0.616132\pi$
$449$	−15.1209	−0.713597	−0.356799	+	0.934181i	$0.616132\pi$
$450$	60.4211	2.84828
$451$	−30.5251	−1.43737
$452$	13.7492	0.646706
$453$	−36.6173	−1.72043
$454$	61.1998	2.87225
$455$	−2.42779	−0.113817
$456$	−163.816	−7.67140
$457$	−3.63429	−0.170005	−0.0850025	−	0.996381i	$-0.527090\pi$
$457$	−3.63429	−0.170005	−0.0850025	+	0.996381i	$0.527090\pi$
$458$	21.4613	1.00282
$459$	22.6027	1.05500
$460$	13.6072	0.634439
$461$	−32.5686	−1.51687	−0.758435	−	0.651748i	$-0.774036\pi$
$461$	−32.5686	−1.51687	−0.758435	+	0.651748i	$0.774036\pi$
$462$	115.398	5.36881
$463$	16.2200	0.753807	0.376904	−	0.926252i	$-0.376989\pi$
$463$	16.2200	0.753807	0.376904	+	0.926252i	$0.376989\pi$
$464$	−158.501	−7.35824
$465$	6.37268	0.295526
$466$	44.3371	2.05388
$467$	−8.27573	−0.382955	−0.191478	−	0.981497i	$-0.561328\pi$
$467$	−8.27573	−0.382955	−0.191478	+	0.981497i	$0.561328\pi$
$468$	69.0032	3.18967
$469$	−17.6511	−0.815054
$470$	−3.46425	−0.159794
$471$	−65.1882	−3.00371
$472$	−29.4970	−1.35771
$473$	−19.9536	−0.917468
$474$	32.6188	1.49823
$475$	−28.6894	−1.31636
$476$	−92.5026	−4.23985
$477$	20.0217	0.916731
$478$	−27.8499	−1.27383
$479$	29.3201	1.33967	0.669835	−	0.742510i	$-0.266365\pi$
$479$	29.3201	1.33967	0.669835	+	0.742510i	$0.266365\pi$
$480$	−23.0363	−1.05146
$481$	16.6859	0.760813
$482$	−79.5678	−3.62421
$483$	−58.5782	−2.66540
$484$	102.707	4.66851
$485$	5.36685	0.243696
$486$	52.3465	2.37448
$487$	4.02510	0.182395	0.0911973	−	0.995833i	$-0.470931\pi$
$487$	4.02510	0.182395	0.0911973	+	0.995833i	$0.470931\pi$
$488$	47.1702	2.13530
$489$	50.7546	2.29520
$490$	−0.879311	−0.0397232
$491$	−11.5556	−0.521496	−0.260748	−	0.965407i	$-0.583969\pi$
$491$	−11.5556	−0.521496	−0.260748	+	0.965407i	$0.583969\pi$
$492$	−88.0629	−3.97018
$493$	−53.3052	−2.40074
$494$	−44.2666	−1.99165
$495$	7.53649	0.338740
$496$	126.605	5.68475
$497$	3.82193	0.171437
$498$	100.477	4.50248
$499$	2.43180	0.108862	0.0544312	−	0.998518i	$-0.482665\pi$
$499$	2.43180	0.108862	0.0544312	+	0.998518i	$0.482665\pi$
$500$	−17.7556	−0.794055
$501$	−8.34329	−0.372751
$502$	17.6361	0.787136
$503$	−3.70692	−0.165283	−0.0826416	−	0.996579i	$-0.526336\pi$
$503$	−3.70692	−0.165283	−0.0826416	+	0.996579i	$0.526336\pi$
$504$	128.973	5.74490
$505$	−0.436674	−0.0194318
$506$	−113.418	−5.04203
$507$	−15.1991	−0.675014
$508$	64.1176	2.84476
$509$	18.3871	0.814994	0.407497	−	0.913207i	$-0.366402\pi$
$509$	18.3871	0.814994	0.407497	+	0.913207i	$0.366402\pi$
$510$	−13.6723	−0.605419
$511$	−20.8720	−0.923323
$512$	−107.647	−4.75736
$513$	23.0585	1.01806
$514$	60.7121	2.67789
$515$	−4.79400	−0.211249
$516$	−57.5649	−2.53415
$517$	21.3721	0.939942
$518$	48.0589	2.11159
$519$	6.97700	0.306256
$520$	−8.80030	−0.385919
$521$	43.8725	1.92209	0.961045	−	0.276391i	$-0.0891385\pi$
$521$	43.8725	1.92209	0.961045	+	0.276391i	$0.0891385\pi$
$522$	114.527	5.01271
$523$	−12.5517	−0.548849	−0.274425	−	0.961609i	$-0.588487\pi$
$523$	−12.5517	−0.548849	−0.274425	+	0.961609i	$0.588487\pi$
$524$	−21.0136	−0.917982
$525$	37.8359	1.65129
$526$	−40.1093	−1.74885
$527$	42.5784	1.85474
$528$	250.808	10.9150
$529$	34.5728	1.50317
$530$	−3.93482	−0.170917
$531$	12.7794	0.554578
$532$	−94.3681	−4.09138
$533$	−15.4425	−0.668889
$534$	36.9428	1.59867
$535$	4.18056	0.180742
$536$	−63.9821	−2.76361
$537$	28.3095	1.22165
$538$	63.4017	2.73344
$539$	5.42475	0.233660
$540$	7.06395	0.303984
$541$	9.27095	0.398589	0.199295	−	0.979940i	$-0.436135\pi$
$541$	9.27095	0.398589	0.199295	+	0.979940i	$0.436135\pi$
$542$	−49.4965	−2.12606
$543$	−65.7950	−2.82353
$544$	−153.914	−6.59901
$545$	−0.920734	−0.0394399
$546$	58.3793	2.49840
$547$	39.8061	1.70198	0.850992	−	0.525178i	$-0.176001\pi$
$547$	39.8061	1.70198	0.850992	+	0.525178i	$0.176001\pi$
$548$	−93.4402	−3.99157
$549$	−20.4362	−0.872196
$550$	73.2569	3.12368
$551$	−54.3802	−2.31668
$552$	−212.335	−9.03758
$553$	12.1938	0.518535
$554$	56.8153	2.41385
$555$	5.25759	0.223172
$556$	38.9348	1.65120
$557$	27.1046	1.14846	0.574230	−	0.818694i	$-0.305302\pi$
$557$	27.1046	1.14846	0.574230	+	0.818694i	$0.305302\pi$
$558$	−91.4803	−3.87267
$559$	−10.0944	−0.426949
$560$	−15.1977	−0.642220
$561$	84.3487	3.56120
$562$	26.2206	1.10605
$563$	−1.00781	−0.0424743	−0.0212371	−	0.999774i	$-0.506760\pi$
$563$	−1.00781	−0.0424743	−0.0212371	+	0.999774i	$0.506760\pi$
$564$	61.6570	2.59623
$565$	0.759691	0.0319604
$566$	−82.5628	−3.47037
$567$	7.31277	0.307108
$568$	13.8538	0.581292
$569$	−1.53212	−0.0642298	−0.0321149	−	0.999484i	$-0.510224\pi$
$569$	−1.53212	−0.0642298	−0.0321149	+	0.999484i	$0.510224\pi$
$570$	−13.9480	−0.584218
$571$	−5.08075	−0.212623	−0.106311	−	0.994333i	$-0.533904\pi$
$571$	−5.08075	−0.212623	−0.106311	+	0.994333i	$0.533904\pi$
$572$	83.6622	3.49809
$573$	3.15166	0.131662
$574$	−44.4775	−1.85646
$575$	−37.1865	−1.55079
$576$	179.046	7.46027
$577$	16.1326	0.671608	0.335804	−	0.941932i	$-0.390992\pi$
$577$	16.1326	0.671608	0.335804	+	0.941932i	$0.390992\pi$
$578$	−44.1857	−1.83788
$579$	37.7269	1.56788
$580$	−16.6593	−0.691740
$581$	37.5612	1.55830
$582$	−129.053	−5.34941
$583$	24.2751	1.00537
$584$	−75.6571	−3.13071
$585$	3.81267	0.157635
$586$	44.2694	1.82875
$587$	−21.4692	−0.886127	−0.443064	−	0.896490i	$-0.646108\pi$
$587$	−21.4692	−0.886127	−0.443064	+	0.896490i	$0.646108\pi$
$588$	15.6500	0.645397
$589$	43.4371	1.78979
$590$	−2.51150	−0.103397
$591$	−54.2274	−2.23062
$592$	104.452	4.29295
$593$	−25.3926	−1.04275	−0.521375	−	0.853328i	$-0.674581\pi$
$593$	−25.3926	−1.04275	−0.521375	+	0.853328i	$0.674581\pi$
$594$	−58.8788	−2.41583
$595$	−5.11110	−0.209535
$596$	−44.2477	−1.81246
$597$	−6.23706	−0.255266
$598$	−57.3774	−2.34634
$599$	43.5468	1.77927	0.889637	−	0.456668i	$-0.150957\pi$
$599$	43.5468	1.77927	0.889637	+	0.456668i	$0.150957\pi$
$600$	137.148	5.59905
$601$	6.64459	0.271038	0.135519	−	0.990775i	$-0.456730\pi$
$601$	6.64459	0.271038	0.135519	+	0.990775i	$0.456730\pi$
$602$	−29.0740	−1.18497
$603$	27.7199	1.12884
$604$	−76.4610	−3.11115
$605$	5.67494	0.230719
$606$	10.5004	0.426549
$607$	24.7941	1.00636	0.503182	−	0.864181i	$-0.332163\pi$
$607$	24.7941	1.00636	0.503182	+	0.864181i	$0.332163\pi$
$608$	−157.018	−6.36793
$609$	71.7173	2.90613
$610$	4.01627	0.162614
$611$	10.8120	0.437407
$612$	145.269	5.87214
$613$	−7.49847	−0.302860	−0.151430	−	0.988468i	$-0.548388\pi$
$613$	−7.49847	−0.302860	−0.151430	+	0.988468i	$0.548388\pi$
$614$	−4.61518	−0.186254
$615$	−4.86579	−0.196208
$616$	156.372	6.30039
$617$	44.6612	1.79799	0.898995	−	0.437958i	$-0.144298\pi$
$617$	44.6612	1.79799	0.898995	+	0.437958i	$0.144298\pi$
$618$	115.278	4.63716
$619$	−18.9013	−0.759708	−0.379854	−	0.925047i	$-0.624026\pi$
$619$	−18.9013	−0.759708	−0.379854	+	0.925047i	$0.624026\pi$
$620$	13.3069	0.534417
$621$	29.8879	1.19936
$622$	68.1217	2.73143
$623$	13.8103	0.553298
$624$	126.883	5.07937
$625$	23.5235	0.940940
$626$	−52.0807	−2.08156
$627$	86.0498	3.43650
$628$	−136.120	−5.43179
$629$	35.1280	1.40065
$630$	10.9813	0.437505
$631$	27.0221	1.07573	0.537867	−	0.843030i	$-0.319230\pi$
$631$	27.0221	1.07573	0.537867	+	0.843030i	$0.319230\pi$
$632$	44.2004	1.75820
$633$	−3.58944	−0.142667
$634$	−53.4198	−2.12157
$635$	3.54273	0.140589
$636$	70.0322	2.77696
$637$	2.74435	0.108735
$638$	138.857	5.49741
$639$	−6.00206	−0.237438
$640$	−18.3008	−0.723401
$641$	−46.4719	−1.83553	−0.917764	−	0.397126i	$-0.870008\pi$
$641$	−46.4719	−1.83553	−0.917764	+	0.397126i	$0.870008\pi$
$642$	−100.527	−3.96748
$643$	37.3996	1.47489	0.737447	−	0.675405i	$-0.236031\pi$
$643$	37.3996	1.47489	0.737447	+	0.675405i	$0.236031\pi$
$644$	−122.318	−4.82000
$645$	−3.18067	−0.125239
$646$	−93.1921	−3.66659
$647$	6.82288	0.268235	0.134117	−	0.990965i	$-0.457180\pi$
$647$	6.82288	0.268235	0.134117	+	0.990965i	$0.457180\pi$
$648$	26.5074	1.04131
$649$	15.4942	0.608201
$650$	37.0603	1.45362
$651$	−57.2853	−2.24519
$652$	105.981	4.15055
$653$	27.2879	1.06786	0.533928	−	0.845530i	$-0.320715\pi$
$653$	27.2879	1.06786	0.533928	+	0.845530i	$0.320715\pi$
$654$	22.1402	0.865751
$655$	−1.16108	−0.0453670
$656$	−96.6682	−3.77426
$657$	32.7780	1.27879
$658$	31.1408	1.21400
$659$	−25.6339	−0.998554	−0.499277	−	0.866443i	$-0.666401\pi$
$659$	−25.6339	−0.998554	−0.499277	+	0.866443i	$0.666401\pi$
$660$	26.3612	1.02611
$661$	−37.8013	−1.47030	−0.735150	−	0.677904i	$-0.762888\pi$
$661$	−37.8013	−1.47030	−0.735150	+	0.677904i	$0.762888\pi$
$662$	1.92263	0.0747253
$663$	42.6716	1.65723
$664$	136.153	5.28374
$665$	−5.21418	−0.202197
$666$	−75.4731	−2.92452
$667$	−70.4864	−2.72925
$668$	−17.4217	−0.674067
$669$	29.9457	1.15777
$670$	−5.44771	−0.210463
$671$	−24.7777	−0.956531
$672$	207.077	7.98819
$673$	−31.2322	−1.20391	−0.601956	−	0.798529i	$-0.705612\pi$
$673$	−31.2322	−1.20391	−0.601956	+	0.798529i	$0.705612\pi$
$674$	−63.6506	−2.45173
$675$	−19.3047	−0.743040
$676$	−31.7373	−1.22067
$677$	−26.3807	−1.01389	−0.506947	−	0.861977i	$-0.669226\pi$
$677$	−26.3807	−1.01389	−0.506947	+	0.861977i	$0.669226\pi$
$678$	−18.2677	−0.701568
$679$	−48.2437	−1.85142
$680$	−18.5268	−0.710470
$681$	−60.1844	−2.30627
$682$	−110.914	−4.24713
$683$	21.1706	0.810072	0.405036	−	0.914301i	$-0.367259\pi$
$683$	21.1706	0.810072	0.405036	+	0.914301i	$0.367259\pi$
$684$	148.198	5.66651
$685$	−5.16291	−0.197265
$686$	−47.0487	−1.79633
$687$	−21.1052	−0.805213
$688$	−63.1900	−2.40909
$689$	12.2807	0.467856
$690$	−18.0791	−0.688260
$691$	29.6266	1.12705	0.563524	−	0.826100i	$-0.309445\pi$
$691$	29.6266	1.12705	0.563524	+	0.826100i	$0.309445\pi$
$692$	14.5688	0.553822
$693$	−67.7470	−2.57350
$694$	20.5050	0.778360
$695$	2.15129	0.0816030
$696$	259.962	9.85383
$697$	−32.5102	−1.23141
$698$	9.42438	0.356718
$699$	−43.6015	−1.64916
$700$	79.0056	2.98613
$701$	−20.0451	−0.757095	−0.378547	−	0.925582i	$-0.623576\pi$
$701$	−20.0451	−0.757095	−0.378547	+	0.925582i	$0.623576\pi$
$702$	−29.7865	−1.12422
$703$	35.8365	1.35160
$704$	217.083	8.18162
$705$	3.40677	0.128306
$706$	−21.2900	−0.801260
$707$	3.92535	0.147628
$708$	44.6998	1.67992
$709$	4.34935	0.163343	0.0816717	−	0.996659i	$-0.473974\pi$
$709$	4.34935	0.163343	0.0816717	+	0.996659i	$0.473974\pi$
$710$	1.17957	0.0442685
$711$	−19.1496	−0.718165
$712$	50.0598	1.87607
$713$	56.3022	2.10853
$714$	122.903	4.59952
$715$	4.62264	0.172877
$716$	59.1134	2.20917
$717$	27.3878	1.02282
$718$	−21.6470	−0.807861
$719$	11.6507	0.434499	0.217249	−	0.976116i	$-0.430292\pi$
$719$	11.6507	0.434499	0.217249	+	0.976116i	$0.430292\pi$
$720$	23.8669	0.889467
$721$	43.0942	1.60491
$722$	−42.3588	−1.57643
$723$	78.2476	2.91006
$724$	−137.387	−5.10596
$725$	45.5275	1.69085
$726$	−136.461	−5.06454
$727$	−22.4427	−0.832354	−0.416177	−	0.909284i	$-0.636630\pi$
$727$	−22.4427	−0.832354	−0.416177	+	0.909284i	$0.636630\pi$
$728$	79.1076	2.93192
$729$	−43.7249	−1.61944
$730$	−6.44177	−0.238421
$731$	−21.2513	−0.786006
$732$	−71.4819	−2.64205
$733$	−43.0628	−1.59056	−0.795280	−	0.606242i	$-0.792676\pi$
$733$	−43.0628	−1.59056	−0.795280	+	0.606242i	$0.792676\pi$
$734$	79.3000	2.92702
$735$	0.864722	0.0318957
$736$	−203.524	−7.50198
$737$	33.6087	1.23799
$738$	69.8488	2.57117
$739$	35.6156	1.31014	0.655071	−	0.755567i	$-0.272639\pi$
$739$	35.6156	1.31014	0.655071	+	0.755567i	$0.272639\pi$
$740$	10.9784	0.403576
$741$	43.5321	1.59919
$742$	35.3708	1.29850
$743$	26.8890	0.986463	0.493232	−	0.869898i	$-0.335816\pi$
$743$	26.8890	0.986463	0.493232	+	0.869898i	$0.335816\pi$
$744$	−207.649	−7.61277
$745$	−2.44484	−0.0895721
$746$	−68.4929	−2.50770
$747$	−58.9873	−2.15823
$748$	176.130	6.43993
$749$	−37.5799	−1.37314
$750$	23.5908	0.861416
$751$	24.0250	0.876684	0.438342	−	0.898808i	$-0.355566\pi$
$751$	24.0250	0.876684	0.438342	+	0.898808i	$0.355566\pi$
$752$	67.6820	2.46811
$753$	−17.3435	−0.632031
$754$	70.2471	2.55825
$755$	−4.22474	−0.153754
$756$	−63.4992	−2.30944
$757$	−20.9839	−0.762672	−0.381336	−	0.924437i	$-0.624536\pi$
$757$	−20.9839	−0.762672	−0.381336	+	0.924437i	$0.624536\pi$
$758$	−30.4301	−1.10527
$759$	111.536	4.04849
$760$	−18.9004	−0.685591
$761$	32.8616	1.19123	0.595615	−	0.803270i	$-0.296908\pi$
$761$	32.8616	1.19123	0.595615	+	0.803270i	$0.296908\pi$
$762$	−85.1894	−3.08609
$763$	8.27666	0.299635
$764$	6.58101	0.238093
$765$	8.02662	0.290203
$766$	−19.1365	−0.691429
$767$	7.83845	0.283030
$768$	220.207	7.94604
$769$	38.1689	1.37640	0.688202	−	0.725519i	$-0.258400\pi$
$769$	38.1689	1.37640	0.688202	+	0.725519i	$0.258400\pi$
$770$	13.3141	0.479808
$771$	−59.7047	−2.15021
$772$	78.7781	2.83529
$773$	30.1320	1.08377	0.541887	−	0.840451i	$-0.317710\pi$
$773$	30.1320	1.08377	0.541887	+	0.840451i	$0.317710\pi$
$774$	45.6587	1.64117
$775$	−36.3658	−1.30630
$776$	−174.874	−6.27763
$777$	−47.2615	−1.69550
$778$	5.80974	0.208289
$779$	−33.1659	−1.18829
$780$	13.3360	0.477506
$781$	−7.27714	−0.260397
$782$	−120.794	−4.31957
$783$	−36.5918	−1.30768
$784$	17.1793	0.613548
$785$	−7.52114	−0.268441
$786$	27.9195	0.995857
$787$	−27.4703	−0.979209	−0.489605	−	0.871945i	$-0.662859\pi$
$787$	−27.4703	−0.979209	−0.489605	+	0.871945i	$0.662859\pi$
$788$	−113.233	−4.03376
$789$	39.4438	1.40424
$790$	3.76341	0.133896
$791$	−6.82901	−0.242812
$792$	−245.570	−8.72597
$793$	−12.5349	−0.445127
$794$	−47.2177	−1.67569
$795$	3.86953	0.137238
$796$	−13.0237	−0.461612
$797$	−34.8760	−1.23537	−0.617686	−	0.786425i	$-0.711930\pi$
$797$	−34.8760	−1.23537	−0.617686	+	0.786425i	$0.711930\pi$
$798$	125.381	4.43846
$799$	22.7620	0.805260
$800$	131.457	4.64770
$801$	−21.6881	−0.766312
$802$	52.2755	1.84591
$803$	39.7413	1.40244
$804$	96.9588	3.41947
$805$	−6.75850	−0.238206
$806$	−56.1110	−1.97643
$807$	−62.3498	−2.19482
$808$	14.2287	0.500563
$809$	−19.7559	−0.694580	−0.347290	−	0.937758i	$-0.612898\pi$
$809$	−19.7559	−0.694580	−0.347290	+	0.937758i	$0.612898\pi$
$810$	2.25696	0.0793014
$811$	−30.0556	−1.05540	−0.527698	−	0.849432i	$-0.676945\pi$
$811$	−30.0556	−1.05540	−0.527698	+	0.849432i	$0.676945\pi$
$812$	149.754	5.25533
$813$	48.6753	1.70712
$814$	−91.5066	−3.20730
$815$	5.85585	0.205121
$816$	267.119	9.35104
$817$	−21.6798	−0.758482
$818$	67.8477	2.37224
$819$	−34.2729	−1.19759
$820$	−10.1603	−0.354814
$821$	−28.6524	−0.999976	−0.499988	−	0.866032i	$-0.666662\pi$
$821$	−28.6524	−0.999976	−0.499988	+	0.866032i	$0.666662\pi$
$822$	124.149	4.33018
$823$	−21.0959	−0.735357	−0.367679	−	0.929953i	$-0.619847\pi$
$823$	−21.0959	−0.735357	−0.367679	+	0.929953i	$0.619847\pi$
$824$	156.209	5.44179
$825$	−72.0414	−2.50816
$826$	22.5763	0.785531
$827$	3.78356	0.131567	0.0657836	−	0.997834i	$-0.479045\pi$
$827$	3.78356	0.131567	0.0657836	+	0.997834i	$0.479045\pi$
$828$	192.091	6.67564
$829$	1.66540	0.0578418	0.0289209	−	0.999582i	$-0.490793\pi$
$829$	1.66540	0.0578418	0.0289209	+	0.999582i	$0.490793\pi$
$830$	11.5926	0.402385
$831$	−55.8727	−1.93820
$832$	109.821	3.80736
$833$	5.77754	0.200180
$834$	−51.7305	−1.79128
$835$	−0.962613	−0.0333126
$836$	179.682	6.21442
$837$	29.2283	1.01028
$838$	63.2723	2.18570
$839$	−9.48026	−0.327295	−0.163647	−	0.986519i	$-0.552326\pi$
$839$	−9.48026	−0.327295	−0.163647	+	0.986519i	$0.552326\pi$
$840$	24.9261	0.860032
$841$	57.2965	1.97574
$842$	9.83827	0.339049
$843$	−25.7855	−0.888100
$844$	−7.49515	−0.257994
$845$	−1.75360	−0.0603257
$846$	−48.9044	−1.68137
$847$	−51.0131	−1.75283
$848$	76.8755	2.63992
$849$	81.1929	2.78653
$850$	78.0210	2.67610
$851$	46.4504	1.59230
$852$	−20.9941	−0.719245
$853$	−14.7190	−0.503968	−0.251984	−	0.967731i	$-0.581083\pi$
$853$	−14.7190	−0.503968	−0.251984	+	0.967731i	$0.581083\pi$
$854$	−36.1031	−1.23542
$855$	8.18850	0.280041
$856$	−136.220	−4.65591
$857$	−24.9904	−0.853655	−0.426828	−	0.904333i	$-0.640369\pi$
$857$	−24.9904	−0.853655	−0.426828	+	0.904333i	$0.640369\pi$
$858$	−111.157	−3.79484
$859$	−28.8015	−0.982694	−0.491347	−	0.870964i	$-0.663495\pi$
$859$	−28.8015	−0.982694	−0.491347	+	0.870964i	$0.663495\pi$
$860$	−6.64159	−0.226476
$861$	43.7396	1.49064
$862$	−85.5062	−2.91235
$863$	14.8499	0.505496	0.252748	−	0.967532i	$-0.418666\pi$
$863$	14.8499	0.505496	0.252748	+	0.967532i	$0.418666\pi$
$864$	−105.656	−3.59448
$865$	0.804977	0.0273700
$866$	−88.2383	−2.99846
$867$	43.4526	1.47573
$868$	−119.618	−4.06011
$869$	−23.2177	−0.787606
$870$	22.1343	0.750422
$871$	17.0024	0.576106
$872$	30.0014	1.01597
$873$	75.7633	2.56420
$874$	−123.230	−4.16831
$875$	8.81895	0.298135
$876$	114.651	3.87370
$877$	−11.0158	−0.371977	−0.185988	−	0.982552i	$-0.559549\pi$
$877$	−11.0158	−0.371977	−0.185988	+	0.982552i	$0.559549\pi$
$878$	10.9219	0.368598
$879$	−43.5349	−1.46839
$880$	28.9372	0.975472
$881$	33.2478	1.12015	0.560074	−	0.828443i	$-0.310773\pi$
$881$	33.2478	1.12015	0.560074	+	0.828443i	$0.310773\pi$
$882$	−12.4131	−0.417972
$883$	−13.7867	−0.463961	−0.231980	−	0.972720i	$-0.574521\pi$
$883$	−13.7867	−0.463961	−0.231980	+	0.972720i	$0.574521\pi$
$884$	89.1030	2.99686
$885$	2.46983	0.0830223
$886$	−46.2925	−1.55523
$887$	−12.3544	−0.414819	−0.207409	−	0.978254i	$-0.566503\pi$
$887$	−12.3544	−0.414819	−0.207409	+	0.978254i	$0.566503\pi$
$888$	−171.314	−5.74893
$889$	−31.8463	−1.06809
$890$	4.26231	0.142873
$891$	−13.9239	−0.466468
$892$	62.5300	2.09366
$893$	23.2210	0.777061
$894$	58.7893	1.96621
$895$	3.26623	0.109178
$896$	164.509	5.49587
$897$	56.4254	1.88399
$898$	41.9506	1.39991
$899$	−68.9307	−2.29897
$900$	−124.073	−4.13576
$901$	25.8538	0.861315
$902$	84.6875	2.81978
$903$	28.5916	0.951470
$904$	−24.7539	−0.823302
$905$	−7.59115	−0.252338
$906$	101.589	3.37508
$907$	34.0416	1.13033	0.565167	−	0.824977i	$-0.308812\pi$
$907$	34.0416	1.13033	0.565167	+	0.824977i	$0.308812\pi$
$908$	−125.672	−4.17057
$909$	−6.16448	−0.204463
$910$	6.73556	0.223282
$911$	−34.3278	−1.13733	−0.568665	−	0.822569i	$-0.692540\pi$
$911$	−34.3278	−1.13733	−0.568665	+	0.822569i	$0.692540\pi$
$912$	272.506	9.02358
$913$	−71.5185	−2.36692
$914$	10.0828	0.333510
$915$	−3.94963	−0.130571
$916$	−44.0700	−1.45611
$917$	10.4371	0.344665
$918$	−62.7079	−2.06967
$919$	11.0912	0.365864	0.182932	−	0.983126i	$-0.441441\pi$
$919$	11.0912	0.365864	0.182932	+	0.983126i	$0.441441\pi$
$920$	−24.4983	−0.807686
$921$	4.53861	0.149552
$922$	90.3568	2.97574
$923$	−3.68147	−0.121177
$924$	−236.966	−7.79562
$925$	−30.0025	−0.986477
$926$	−45.0000	−1.47879
$927$	−67.6764	−2.22279
$928$	249.174	8.17953
$929$	15.4639	0.507353	0.253676	−	0.967289i	$-0.418360\pi$
$929$	15.4639	0.507353	0.253676	+	0.967289i	$0.418360\pi$
$930$	−17.6801	−0.579753
$931$	5.89406	0.193170
$932$	−91.0449	−2.98227
$933$	−66.9914	−2.19320
$934$	22.9598	0.751268
$935$	9.73179	0.318264
$936$	−124.233	−4.06068
$937$	29.4705	0.962759	0.481380	−	0.876512i	$-0.340136\pi$
$937$	29.4705	0.962759	0.481380	+	0.876512i	$0.340136\pi$
$938$	48.9705	1.59894
$939$	51.2166	1.67139
$940$	7.11372	0.232024
$941$	−58.9252	−1.92091	−0.960453	−	0.278442i	$-0.910182\pi$
$941$	−58.9252	−1.92091	−0.960453	+	0.278442i	$0.910182\pi$
$942$	180.855	5.89258
$943$	−42.9889	−1.39991
$944$	49.0678	1.59702
$945$	−3.50856	−0.114133
$946$	55.3584	1.79986
$947$	−27.7886	−0.903008	−0.451504	−	0.892269i	$-0.649112\pi$
$947$	−27.7886	−0.903008	−0.451504	+	0.892269i	$0.649112\pi$
$948$	−66.9815	−2.17546
$949$	20.1049	0.652634
$950$	79.5945	2.58239
$951$	52.5335	1.70351
$952$	166.541	5.39762
$953$	−39.5930	−1.28254	−0.641272	−	0.767314i	$-0.721593\pi$
$953$	−39.5930	−1.28254	−0.641272	+	0.767314i	$0.721593\pi$
$954$	−55.5474	−1.79841
$955$	0.363625	0.0117666
$956$	57.1889	1.84962
$957$	−136.553	−4.41414
$958$	−81.3443	−2.62812
$959$	46.4104	1.49867
$960$	34.6037	1.11683
$961$	24.0595	0.776113
$962$	−46.2927	−1.49254
$963$	59.0166	1.90178
$964$	163.390	5.26243
$965$	4.35277	0.140121
$966$	162.517	5.22889
$967$	−4.95497	−0.159341	−0.0796705	−	0.996821i	$-0.525387\pi$
$967$	−4.95497	−0.159341	−0.0796705	+	0.996821i	$0.525387\pi$
$968$	−184.913	−5.94334
$969$	91.6459	2.94409
$970$	−14.8896	−0.478075
$971$	14.5345	0.466436	0.233218	−	0.972424i	$-0.425074\pi$
$971$	14.5345	0.466436	0.233218	+	0.972424i	$0.425074\pi$
$972$	−107.492	−3.44780
$973$	−19.3384	−0.619959
$974$	−11.1670	−0.357815
$975$	−36.4454	−1.16719
$976$	−78.4670	−2.51167
$977$	34.2517	1.09581	0.547904	−	0.836541i	$-0.315426\pi$
$977$	34.2517	1.09581	0.547904	+	0.836541i	$0.315426\pi$
$978$	−140.811	−4.50265
$979$	−26.2955	−0.840409
$980$	1.80564	0.0576789
$981$	−12.9979	−0.414991
$982$	32.0593	1.02305
$983$	29.0954	0.928000	0.464000	−	0.885835i	$-0.346414\pi$
$983$	29.0954	0.928000	0.464000	+	0.885835i	$0.346414\pi$
$984$	158.548	5.05432
$985$	−6.25653	−0.199349
$986$	147.888	4.70970
$987$	−30.6241	−0.974777
$988$	90.9000	2.89192
$989$	−28.1009	−0.893557
$990$	−20.9089	−0.664529
$991$	−10.3291	−0.328115	−0.164058	−	0.986451i	$-0.552458\pi$
$991$	−10.3291	−0.328115	−0.164058	+	0.986451i	$0.552458\pi$
$992$	−199.032	−6.31926
$993$	−1.89073	−0.0600006
$994$	−10.6034	−0.336319
$995$	−0.719605	−0.0228130
$996$	−206.326	−6.53770
$997$	−20.6111	−0.652761	−0.326380	−	0.945239i	$-0.605829\pi$
$997$	−20.6111	−0.652761	−0.326380	+	0.945239i	$0.605829\pi$
$998$	−6.74669	−0.213563
$999$	24.1139	0.762931

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6047.2.a.b.1.4	✓	287

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6047.2.a.b.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-2.77436 q^{2} +2.72832 q^{3} +5.69705 q^{4} +0.314782 q^{5} -7.56934 q^{6} -2.82964 q^{7} -10.2569 q^{8} +4.44375 q^{9} +O(q^{10})\)	\(q-2.77436 q^{2} +2.72832 q^{3} +5.69705 q^{4} +0.314782 q^{5} -7.56934 q^{6} -2.82964 q^{7} -10.2569 q^{8} +4.44375 q^{9} -0.873318 q^{10} +5.38778 q^{11} +15.5434 q^{12} +2.72565 q^{13} +7.85043 q^{14} +0.858828 q^{15} +17.0623 q^{16} +5.73816 q^{17} -12.3285 q^{18} +5.85389 q^{19} +1.79333 q^{20} -7.72017 q^{21} -14.9476 q^{22} +7.58768 q^{23} -27.9842 q^{24} -4.90091 q^{25} -7.56192 q^{26} +3.93901 q^{27} -16.1206 q^{28} -9.28959 q^{29} -2.38269 q^{30} +7.42021 q^{31} -26.8229 q^{32} +14.6996 q^{33} -15.9197 q^{34} -0.890721 q^{35} +25.3162 q^{36} +6.12182 q^{37} -16.2408 q^{38} +7.43645 q^{39} -3.22870 q^{40} -5.66562 q^{41} +21.4185 q^{42} -3.70350 q^{43} +30.6944 q^{44} +1.39881 q^{45} -21.0509 q^{46} +3.96677 q^{47} +46.5513 q^{48} +1.00686 q^{49} +13.5969 q^{50} +15.6556 q^{51} +15.5281 q^{52} +4.50559 q^{53} -10.9282 q^{54} +1.69598 q^{55} +29.0234 q^{56} +15.9713 q^{57} +25.7726 q^{58} +2.87581 q^{59} +4.89278 q^{60} -4.59887 q^{61} -20.5863 q^{62} -12.5742 q^{63} +40.2918 q^{64} +0.857986 q^{65} -40.7819 q^{66} +6.23795 q^{67} +32.6906 q^{68} +20.7016 q^{69} +2.47118 q^{70} -1.35068 q^{71} -45.5792 q^{72} +7.37620 q^{73} -16.9841 q^{74} -13.3713 q^{75} +33.3499 q^{76} -15.2455 q^{77} -20.6314 q^{78} -4.30933 q^{79} +5.37090 q^{80} -2.58435 q^{81} +15.7184 q^{82} -13.2742 q^{83} -43.9822 q^{84} +1.80627 q^{85} +10.2748 q^{86} -25.3450 q^{87} -55.2620 q^{88} -4.88059 q^{89} -3.88081 q^{90} -7.71260 q^{91} +43.2274 q^{92} +20.2447 q^{93} -11.0052 q^{94} +1.84270 q^{95} -73.1816 q^{96} +17.0494 q^{97} -2.79339 q^{98} +23.9419 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 287 q + 21 q^{2} + 29 q^{3} + 319 q^{4} + 19 q^{5} + 15 q^{6} + 52 q^{7} + 60 q^{8} + 352 q^{9}+O(q^{10}) \) 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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