LMFDB - Embedded newform 6047.2.a.b.1.11

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			1.11
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)

$f(q)$	$=$	$q-2.63049 q^{2} -1.81721 q^{3} +4.91948 q^{4} +0.465740 q^{5} +4.78015 q^{6} +0.973946 q^{7} -7.67967 q^{8} +0.302245 q^{9} +O(q^{10})$	\(q-2.63049 q^{2} -1.81721 q^{3} +4.91948 q^{4} +0.465740 q^{5} +4.78015 q^{6} +0.973946 q^{7} -7.67967 q^{8} +0.302245 q^{9} -1.22512 q^{10} +6.14806 q^{11} -8.93972 q^{12} -0.159340 q^{13} -2.56196 q^{14} -0.846346 q^{15} +10.3623 q^{16} +4.34007 q^{17} -0.795054 q^{18} -8.34540 q^{19} +2.29120 q^{20} -1.76986 q^{21} -16.1724 q^{22} -6.91950 q^{23} +13.9556 q^{24} -4.78309 q^{25} +0.419142 q^{26} +4.90238 q^{27} +4.79131 q^{28} -9.08023 q^{29} +2.22631 q^{30} -0.222131 q^{31} -11.8987 q^{32} -11.1723 q^{33} -11.4165 q^{34} +0.453605 q^{35} +1.48689 q^{36} -1.56834 q^{37} +21.9525 q^{38} +0.289553 q^{39} -3.57673 q^{40} +6.30869 q^{41} +4.65561 q^{42} +10.8577 q^{43} +30.2453 q^{44} +0.140768 q^{45} +18.2017 q^{46} -11.5575 q^{47} -18.8305 q^{48} -6.05143 q^{49} +12.5819 q^{50} -7.88682 q^{51} -0.783869 q^{52} +3.73739 q^{53} -12.8957 q^{54} +2.86340 q^{55} -7.47958 q^{56} +15.1653 q^{57} +23.8855 q^{58} -3.26350 q^{59} -4.16359 q^{60} -14.9671 q^{61} +0.584312 q^{62} +0.294371 q^{63} +10.5747 q^{64} -0.0742109 q^{65} +29.3886 q^{66} +15.5605 q^{67} +21.3509 q^{68} +12.5742 q^{69} -1.19320 q^{70} -10.4797 q^{71} -2.32115 q^{72} +0.773421 q^{73} +4.12551 q^{74} +8.69186 q^{75} -41.0551 q^{76} +5.98788 q^{77} -0.761668 q^{78} +10.6122 q^{79} +4.82616 q^{80} -9.81538 q^{81} -16.5949 q^{82} -3.84199 q^{83} -8.70681 q^{84} +2.02135 q^{85} -28.5611 q^{86} +16.5007 q^{87} -47.2151 q^{88} -4.81386 q^{89} -0.370288 q^{90} -0.155188 q^{91} -34.0404 q^{92} +0.403657 q^{93} +30.4019 q^{94} -3.88679 q^{95} +21.6224 q^{96} +14.1380 q^{97} +15.9182 q^{98} +1.85822 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.63049	−1.86004	−0.930019	−	0.367511i	$-0.880210\pi$
$2$	−2.63049	−1.86004	−0.930019	+	0.367511i	$0.880210\pi$
$3$	−1.81721	−1.04917	−0.524583	−	0.851359i	$-0.675779\pi$
$3$	−1.81721	−1.04917	−0.524583	+	0.851359i	$0.675779\pi$
$4$	4.91948	2.45974
$5$	0.465740	0.208285	0.104143	−	0.994562i	$-0.466790\pi$
$5$	0.465740	0.208285	0.104143	+	0.994562i	$0.466790\pi$
$6$	4.78015	1.95149
$7$	0.973946	0.368117	0.184058	−	0.982915i	$-0.441076\pi$
$7$	0.973946	0.368117	0.184058	+	0.982915i	$0.441076\pi$
$8$	−7.67967	−2.71517
$9$	0.302245	0.100748
$10$	−1.22512	−0.387418
$11$	6.14806	1.85371	0.926855	−	0.375420i	$-0.122501\pi$
$11$	6.14806	1.85371	0.926855	+	0.375420i	$0.122501\pi$
$12$	−8.93972	−2.58068
$13$	−0.159340	−0.0441929	−0.0220964	−	0.999756i	$-0.507034\pi$
$13$	−0.159340	−0.0441929	−0.0220964	+	0.999756i	$0.507034\pi$
$14$	−2.56196	−0.684711
$15$	−0.846346	−0.218526
$16$	10.3623	2.59059
$17$	4.34007	1.05262	0.526311	−	0.850292i	$-0.323575\pi$
$17$	4.34007	1.05262	0.526311	+	0.850292i	$0.323575\pi$
$18$	−0.795054	−0.187396
$19$	−8.34540	−1.91457	−0.957283	−	0.289151i	$-0.906627\pi$
$19$	−8.34540	−1.91457	−0.957283	+	0.289151i	$0.906627\pi$
$20$	2.29120	0.512328
$21$	−1.76986	−0.386216
$22$	−16.1724	−3.44797
$23$	−6.91950	−1.44282	−0.721408	−	0.692511i	$-0.756505\pi$
$23$	−6.91950	−1.44282	−0.721408	+	0.692511i	$0.756505\pi$
$24$	13.9556	2.84867
$25$	−4.78309	−0.956617
$26$	0.419142	0.0822004
$27$	4.90238	0.943464
$28$	4.79131	0.905472
$29$	−9.08023	−1.68616	−0.843078	−	0.537791i	$-0.819259\pi$
$29$	−9.08023	−1.68616	−0.843078	+	0.537791i	$0.819259\pi$
$30$	2.22631	0.406466
$31$	−0.222131	−0.0398958	−0.0199479	−	0.999801i	$-0.506350\pi$
$31$	−0.222131	−0.0398958	−0.0199479	+	0.999801i	$0.506350\pi$
$32$	−11.8987	−2.10341
$33$	−11.1723	−1.94485
$34$	−11.4165	−1.95792
$35$	0.453605	0.0766733
$36$	1.48689	0.247815
$37$	−1.56834	−0.257834	−0.128917	−	0.991655i	$-0.541150\pi$
$37$	−1.56834	−0.257834	−0.128917	+	0.991655i	$0.541150\pi$
$38$	21.9525	3.56117
$39$	0.289553	0.0463657
$40$	−3.57673	−0.565531
$41$	6.30869	0.985251	0.492626	−	0.870241i	$-0.336037\pi$
$41$	6.30869	0.985251	0.492626	+	0.870241i	$0.336037\pi$
$42$	4.65561	0.718376
$43$	10.8577	1.65579	0.827893	−	0.560886i	$-0.189540\pi$
$43$	10.8577	1.65579	0.827893	+	0.560886i	$0.189540\pi$
$44$	30.2453	4.55965
$45$	0.140768	0.0209844
$46$	18.2017	2.68369
$47$	−11.5575	−1.68583	−0.842917	−	0.538044i	$-0.819163\pi$
$47$	−11.5575	−1.68583	−0.842917	+	0.538044i	$0.819163\pi$
$48$	−18.8305	−2.71795
$49$	−6.05143	−0.864490
$50$	12.5819	1.77934
$51$	−7.88682	−1.10438
$52$	−0.783869	−0.108703
$53$	3.73739	0.513370	0.256685	−	0.966495i	$-0.417370\pi$
$53$	3.73739	0.513370	0.256685	+	0.966495i	$0.417370\pi$
$54$	−12.8957	−1.75488
$55$	2.86340	0.386100
$56$	−7.47958	−0.999501
$57$	15.1653	2.00870
$58$	23.8855	3.13632
$59$	−3.26350	−0.424871	−0.212436	−	0.977175i	$-0.568140\pi$
$59$	−3.26350	−0.424871	−0.212436	+	0.977175i	$0.568140\pi$
$60$	−4.16359	−0.537517
$61$	−14.9671	−1.91634	−0.958168	−	0.286208i	$-0.907605\pi$
$61$	−14.9671	−1.91634	−0.958168	+	0.286208i	$0.907605\pi$
$62$	0.584312	0.0742078
$63$	0.294371	0.0370872
$64$	10.5747	1.32184
$65$	−0.0742109	−0.00920473
$66$	29.3886	3.61749
$67$	15.5605	1.90102	0.950510	−	0.310693i	$-0.100561\pi$
$67$	15.5605	1.90102	0.950510	+	0.310693i	$0.100561\pi$
$68$	21.3509	2.58918
$69$	12.5742	1.51375
$70$	−1.19320	−0.142615
$71$	−10.4797	−1.24371	−0.621855	−	0.783132i	$-0.713621\pi$
$71$	−10.4797	−1.24371	−0.621855	+	0.783132i	$0.713621\pi$
$72$	−2.32115	−0.273550
$73$	0.773421	0.0905220	0.0452610	−	0.998975i	$-0.485588\pi$
$73$	0.773421	0.0905220	0.0452610	+	0.998975i	$0.485588\pi$
$74$	4.12551	0.479581
$75$	8.69186	1.00365
$76$	−41.0551	−4.70934
$77$	5.98788	0.682382
$78$	−0.761668	−0.0862419
$79$	10.6122	1.19397	0.596985	−	0.802252i	$-0.296365\pi$
$79$	10.6122	1.19397	0.596985	+	0.802252i	$0.296365\pi$
$80$	4.82616	0.539581
$81$	−9.81538	−1.09060
$82$	−16.5949	−1.83261
$83$	−3.84199	−0.421713	−0.210857	−	0.977517i	$-0.567625\pi$
$83$	−3.84199	−0.421713	−0.210857	+	0.977517i	$0.567625\pi$
$84$	−8.70681	−0.949990
$85$	2.02135	0.219246
$86$	−28.5611	−3.07982
$87$	16.5007	1.76906
$88$	−47.2151	−5.03315
$89$	−4.81386	−0.510268	−0.255134	−	0.966906i	$-0.582120\pi$
$89$	−4.81386	−0.510268	−0.255134	+	0.966906i	$0.582120\pi$
$90$	−0.370288	−0.0390318
$91$	−0.155188	−0.0162681
$92$	−34.0404	−3.54895
$93$	0.403657	0.0418573
$94$	30.4019	3.13571
$95$	−3.88679	−0.398776
$96$	21.6224	2.20683
$97$	14.1380	1.43549	0.717746	−	0.696305i	$-0.245174\pi$
$97$	14.1380	1.43549	0.717746	+	0.696305i	$0.245174\pi$
$98$	15.9182	1.60798
$99$	1.85822	0.186758
$100$	−23.5303	−2.35303
$101$	16.2718	1.61910	0.809551	−	0.587049i	$-0.199711\pi$
$101$	16.2718	1.61910	0.809551	+	0.587049i	$0.199711\pi$
$102$	20.7462	2.05418
$103$	17.2914	1.70377	0.851885	−	0.523729i	$-0.175459\pi$
$103$	17.2914	1.70377	0.851885	+	0.523729i	$0.175459\pi$
$104$	1.22368	0.119991
$105$	−0.824295	−0.0804430
$106$	−9.83118	−0.954888
$107$	6.81622	0.658949	0.329474	−	0.944165i	$-0.393128\pi$
$107$	6.81622	0.658949	0.329474	+	0.944165i	$0.393128\pi$
$108$	24.1172	2.32068
$109$	9.26399	0.887329	0.443665	−	0.896193i	$-0.353678\pi$
$109$	9.26399	0.887329	0.443665	+	0.896193i	$0.353678\pi$
$110$	−7.53214	−0.718161
$111$	2.85000	0.270511
$112$	10.0924	0.953638
$113$	−11.6066	−1.09185	−0.545927	−	0.837833i	$-0.683823\pi$
$113$	−11.6066	−1.09185	−0.545927	+	0.837833i	$0.683823\pi$
$114$	−39.8923	−3.73625
$115$	−3.22269	−0.300517
$116$	−44.6700	−4.14751
$117$	−0.0481597	−0.00445237
$118$	8.58461	0.790277
$119$	4.22700	0.387488
$120$	6.49966	0.593335
$121$	26.7986	2.43624
$122$	39.3707	3.56446
$123$	−11.4642	−1.03369
$124$	−1.09277	−0.0981334
$125$	−4.55637	−0.407535
$126$	−0.774339	−0.0689836
$127$	−13.0097	−1.15442	−0.577210	−	0.816595i	$-0.695859\pi$
$127$	−13.0097	−1.15442	−0.577210	+	0.816595i	$0.695859\pi$
$128$	−4.01937	−0.355266
$129$	−19.7307	−1.73719
$130$	0.195211	0.0171211
$131$	−5.38682	−0.470649	−0.235324	−	0.971917i	$-0.575615\pi$
$131$	−5.38682	−0.470649	−0.235324	+	0.971917i	$0.575615\pi$
$132$	−54.9620	−4.78382
$133$	−8.12797	−0.704784
$134$	−40.9318	−3.53597
$135$	2.28324	0.196510
$136$	−33.3303	−2.85805
$137$	−2.06803	−0.176683	−0.0883417	−	0.996090i	$-0.528157\pi$
$137$	−2.06803	−0.176683	−0.0883417	+	0.996090i	$0.528157\pi$
$138$	−33.0762	−2.81564
$139$	−1.88608	−0.159975	−0.0799876	−	0.996796i	$-0.525488\pi$
$139$	−1.88608	−0.159975	−0.0799876	+	0.996796i	$0.525488\pi$
$140$	2.23150	0.188597
$141$	21.0024	1.76872
$142$	27.5667	2.31335
$143$	−0.979630	−0.0819208
$144$	3.13197	0.260998
$145$	−4.22903	−0.351202
$146$	−2.03448	−0.168374
$147$	10.9967	0.906993
$148$	−7.71543	−0.634205
$149$	20.8408	1.70734	0.853672	−	0.520810i	$-0.174370\pi$
$149$	20.8408	1.70734	0.853672	+	0.520810i	$0.174370\pi$
$150$	−22.8639	−1.86683
$151$	10.1315	0.824493	0.412247	−	0.911072i	$-0.364744\pi$
$151$	10.1315	0.824493	0.412247	+	0.911072i	$0.364744\pi$
$152$	64.0900	5.19838
$153$	1.31177	0.106050
$154$	−15.7511	−1.26926
$155$	−0.103455	−0.00830971
$156$	1.42445	0.114048
$157$	7.56743	0.603947	0.301973	−	0.953316i	$-0.402355\pi$
$157$	7.56743	0.603947	0.301973	+	0.953316i	$0.402355\pi$
$158$	−27.9154	−2.22083
$159$	−6.79162	−0.538611
$160$	−5.54170	−0.438110
$161$	−6.73922	−0.531125
$162$	25.8193	2.02855
$163$	5.25413	0.411535	0.205767	−	0.978601i	$-0.434031\pi$
$163$	5.25413	0.411535	0.205767	+	0.978601i	$0.434031\pi$
$164$	31.0355	2.42346
$165$	−5.20339	−0.405083
$166$	10.1063	0.784403
$167$	−7.55028	−0.584258	−0.292129	−	0.956379i	$-0.594364\pi$
$167$	−7.55028	−0.584258	−0.292129	+	0.956379i	$0.594364\pi$
$168$	13.5920	1.04864
$169$	−12.9746	−0.998047
$170$	−5.31713	−0.407805
$171$	−2.52236	−0.192890
$172$	53.4143	4.07280
$173$	19.5975	1.48997	0.744984	−	0.667083i	$-0.232457\pi$
$173$	19.5975	1.48997	0.744984	+	0.667083i	$0.232457\pi$
$174$	−43.4049	−3.29051
$175$	−4.65847	−0.352147
$176$	63.7083	4.80219
$177$	5.93046	0.445760
$178$	12.6628	0.949118
$179$	2.38995	0.178633	0.0893167	−	0.996003i	$-0.471532\pi$
$179$	2.38995	0.178633	0.0893167	+	0.996003i	$0.471532\pi$
$180$	0.692505	0.0516162
$181$	17.9331	1.33295	0.666477	−	0.745526i	$-0.267802\pi$
$181$	17.9331	1.33295	0.666477	+	0.745526i	$0.267802\pi$
$182$	0.408221	0.0302594
$183$	27.1983	2.01055
$184$	53.1395	3.91749
$185$	−0.730440	−0.0537030
$186$	−1.06182	−0.0778562
$187$	26.6830	1.95126
$188$	−56.8569	−4.14671
$189$	4.77465	0.347305
$190$	10.2242	0.741739
$191$	−18.3495	−1.32772	−0.663862	−	0.747855i	$-0.731084\pi$
$191$	−18.3495	−1.32772	−0.663862	+	0.747855i	$0.731084\pi$
$192$	−19.2165	−1.38683
$193$	13.2671	0.954987	0.477494	−	0.878635i	$-0.341545\pi$
$193$	13.2671	0.954987	0.477494	+	0.878635i	$0.341545\pi$
$194$	−37.1898	−2.67007
$195$	0.134857	0.00965728
$196$	−29.7699	−2.12642
$197$	8.34313	0.594423	0.297212	−	0.954812i	$-0.403943\pi$
$197$	8.34313	0.594423	0.297212	+	0.954812i	$0.403943\pi$
$198$	−4.88804	−0.347378
$199$	12.8781	0.912906	0.456453	−	0.889748i	$-0.349120\pi$
$199$	12.8781	0.912906	0.456453	+	0.889748i	$0.349120\pi$
$200$	36.7325	2.59738
$201$	−28.2767	−1.99449
$202$	−42.8028	−3.01159
$203$	−8.84365	−0.620703
$204$	−38.7991	−2.71648
$205$	2.93821	0.205213
$206$	−45.4848	−3.16908
$207$	−2.09139	−0.145361
$208$	−1.65113	−0.114485
$209$	−51.3080	−3.54905
$210$	2.16830	0.149627
$211$	−6.30864	−0.434305	−0.217152	−	0.976138i	$-0.569677\pi$
$211$	−6.30864	−0.434305	−0.217152	+	0.976138i	$0.569677\pi$
$212$	18.3860	1.26276
$213$	19.0438	1.30486
$214$	−17.9300	−1.22567
$215$	5.05687	0.344876
$216$	−37.6487	−2.56167
$217$	−0.216343	−0.0146863
$218$	−24.3688	−1.65047
$219$	−1.40547	−0.0949726
$220$	14.0864	0.949707
$221$	−0.691546	−0.0465184
$222$	−7.49691	−0.503160
$223$	8.86713	0.593787	0.296893	−	0.954911i	$-0.404049\pi$
$223$	8.86713	0.593787	0.296893	+	0.954911i	$0.404049\pi$
$224$	−11.5887	−0.774302
$225$	−1.44567	−0.0963777
$226$	30.5310	2.03089
$227$	−5.06332	−0.336064	−0.168032	−	0.985782i	$-0.553741\pi$
$227$	−5.06332	−0.336064	−0.168032	+	0.985782i	$0.553741\pi$
$228$	74.6056	4.94088
$229$	−27.2545	−1.80103	−0.900514	−	0.434826i	$-0.856810\pi$
$229$	−27.2545	−1.80103	−0.900514	+	0.434826i	$0.856810\pi$
$230$	8.47725	0.558973
$231$	−10.8812	−0.715932
$232$	69.7332	4.57821
$233$	1.03342	0.0677013	0.0338507	−	0.999427i	$-0.489223\pi$
$233$	1.03342	0.0677013	0.0338507	+	0.999427i	$0.489223\pi$
$234$	0.126684	0.00828157
$235$	−5.38279	−0.351134
$236$	−16.0547	−1.04507
$237$	−19.2847	−1.25267
$238$	−11.1191	−0.720742
$239$	−13.1645	−0.851542	−0.425771	−	0.904831i	$-0.639997\pi$
$239$	−13.1645	−0.851542	−0.425771	+	0.904831i	$0.639997\pi$
$240$	−8.77013	−0.566110
$241$	−5.24409	−0.337801	−0.168901	−	0.985633i	$-0.554022\pi$
$241$	−5.24409	−0.337801	−0.168901	+	0.985633i	$0.554022\pi$
$242$	−70.4936	−4.53150
$243$	3.12945	0.200754
$244$	−73.6302	−4.71369
$245$	−2.81839	−0.180061
$246$	30.1565	1.92271
$247$	1.32975	0.0846102
$248$	1.70589	0.108324
$249$	6.98170	0.442447
$250$	11.9855	0.758030
$251$	7.87787	0.497247	0.248623	−	0.968600i	$-0.420022\pi$
$251$	7.87787	0.497247	0.248623	+	0.968600i	$0.420022\pi$
$252$	1.44815	0.0912249
$253$	−42.5415	−2.67456
$254$	34.2218	2.14727
$255$	−3.67321	−0.230025
$256$	−10.5766	−0.661036
$257$	−14.3939	−0.897867	−0.448933	−	0.893565i	$-0.648196\pi$
$257$	−14.3939	−0.897867	−0.448933	+	0.893565i	$0.648196\pi$
$258$	51.9015	3.23125
$259$	−1.52748	−0.0949130
$260$	−0.365079	−0.0226412
$261$	−2.74446	−0.169878
$262$	14.1700	0.875425
$263$	8.50572	0.524485	0.262243	−	0.965002i	$-0.415538\pi$
$263$	8.50572	0.524485	0.262243	+	0.965002i	$0.415538\pi$
$264$	85.7996	5.28060
$265$	1.74065	0.106927
$266$	21.3805	1.31093
$267$	8.74778	0.535356
$268$	76.5497	4.67602
$269$	−8.74980	−0.533485	−0.266742	−	0.963768i	$-0.585947\pi$
$269$	−8.74980	−0.533485	−0.266742	+	0.963768i	$0.585947\pi$
$270$	−6.00603	−0.365515
$271$	12.9951	0.789396	0.394698	−	0.918811i	$-0.370849\pi$
$271$	12.9951	0.789396	0.394698	+	0.918811i	$0.370849\pi$
$272$	44.9733	2.72691
$273$	0.282009	0.0170680
$274$	5.43992	0.328638
$275$	−29.4067	−1.77329
$276$	61.8584	3.72344
$277$	−11.0354	−0.663055	−0.331527	−	0.943446i	$-0.607564\pi$
$277$	−11.0354	−0.663055	−0.331527	+	0.943446i	$0.607564\pi$
$278$	4.96132	0.297560
$279$	−0.0671379	−0.00401944
$280$	−3.48354	−0.208181
$281$	8.38225	0.500043	0.250021	−	0.968240i	$-0.419562\pi$
$281$	8.38225	0.500043	0.250021	+	0.968240i	$0.419562\pi$
$282$	−55.2465	−3.28988
$283$	−9.19204	−0.546410	−0.273205	−	0.961956i	$-0.588084\pi$
$283$	−9.19204	−0.546410	−0.273205	+	0.961956i	$0.588084\pi$
$284$	−51.5547	−3.05921
$285$	7.06310	0.418382
$286$	2.57691	0.152376
$287$	6.14432	0.362688
$288$	−3.59633	−0.211916
$289$	1.83623	0.108014
$290$	11.1244	0.653248
$291$	−25.6916	−1.50607
$292$	3.80483	0.222661
$293$	−18.3218	−1.07037	−0.535185	−	0.844735i	$-0.679758\pi$
$293$	−18.3218	−1.07037	−0.535185	+	0.844735i	$0.679758\pi$
$294$	−28.9267	−1.68704
$295$	−1.51994	−0.0884945
$296$	12.0444	0.700064
$297$	30.1401	1.74891
$298$	−54.8215	−3.17573
$299$	1.10255	0.0637622
$300$	42.7595	2.46872
$301$	10.5748	0.609523
$302$	−26.6509	−1.53359
$303$	−29.5692	−1.69871
$304$	−86.4779	−4.95985
$305$	−6.97076	−0.399144
$306$	−3.45059	−0.197257
$307$	21.0238	1.19989	0.599944	−	0.800042i	$-0.295189\pi$
$307$	21.0238	1.19989	0.599944	+	0.800042i	$0.295189\pi$
$308$	29.4573	1.67848
$309$	−31.4220	−1.78754
$310$	0.272138	0.0154564
$311$	11.3680	0.644620	0.322310	−	0.946634i	$-0.395541\pi$
$311$	11.3680	0.644620	0.322310	+	0.946634i	$0.395541\pi$
$312$	−2.22368	−0.125891
$313$	−2.71407	−0.153408	−0.0767041	−	0.997054i	$-0.524440\pi$
$313$	−2.71407	−0.153408	−0.0767041	+	0.997054i	$0.524440\pi$
$314$	−19.9061	−1.12336
$315$	0.137100	0.00772472
$316$	52.2068	2.93686
$317$	−12.8787	−0.723341	−0.361670	−	0.932306i	$-0.617793\pi$
$317$	−12.8787	−0.723341	−0.361670	+	0.932306i	$0.617793\pi$
$318$	17.8653	1.00184
$319$	−55.8258	−3.12564
$320$	4.92508	0.275321
$321$	−12.3865	−0.691346
$322$	17.7274	0.987912
$323$	−36.2197	−2.01532
$324$	−48.2866	−2.68259
$325$	0.762136	0.0422757
$326$	−13.8209	−0.765471
$327$	−16.8346	−0.930956
$328$	−48.4487	−2.67513
$329$	−11.2564	−0.620584
$330$	13.6875	0.753470
$331$	16.0607	0.882775	0.441387	−	0.897317i	$-0.354486\pi$
$331$	16.0607	0.882775	0.441387	+	0.897317i	$0.354486\pi$
$332$	−18.9006	−1.03731
$333$	−0.474024	−0.0259764
$334$	19.8609	1.08674
$335$	7.24716	0.395955
$336$	−18.3399	−1.00052
$337$	34.6649	1.88832	0.944158	−	0.329492i	$-0.106877\pi$
$337$	34.6649	1.88832	0.944158	+	0.329492i	$0.106877\pi$
$338$	34.1296	1.85641
$339$	21.0916	1.14554
$340$	9.94397	0.539288
$341$	−1.36567	−0.0739553
$342$	6.63504	0.358782
$343$	−12.7114	−0.686350
$344$	−83.3837	−4.49575
$345$	5.85629	0.315292
$346$	−51.5509	−2.77140
$347$	7.57432	0.406611	0.203305	−	0.979115i	$-0.434832\pi$
$347$	7.57432	0.406611	0.203305	+	0.979115i	$0.434832\pi$
$348$	81.1748	4.35142
$349$	−9.47650	−0.507266	−0.253633	−	0.967301i	$-0.581625\pi$
$349$	−9.47650	−0.507266	−0.253633	+	0.967301i	$0.581625\pi$
$350$	12.2541	0.655007
$351$	−0.781144	−0.0416944
$352$	−73.1540	−3.89912
$353$	11.5829	0.616496	0.308248	−	0.951306i	$-0.400257\pi$
$353$	11.5829	0.616496	0.308248	+	0.951306i	$0.400257\pi$
$354$	−15.6000	−0.829131
$355$	−4.88081	−0.259047
$356$	−23.6817	−1.25513
$357$	−7.68133	−0.406539
$358$	−6.28674	−0.332265
$359$	−32.0251	−1.69022	−0.845110	−	0.534592i	$-0.820465\pi$
$359$	−32.0251	−1.69022	−0.845110	+	0.534592i	$0.820465\pi$
$360$	−1.08105	−0.0569764
$361$	50.6458	2.66557
$362$	−47.1727	−2.47934
$363$	−48.6987	−2.55602
$364$	−0.763446	−0.0400154
$365$	0.360213	0.0188544
$366$	−71.5448	−3.73970
$367$	−4.27053	−0.222920	−0.111460	−	0.993769i	$-0.535553\pi$
$367$	−4.27053	−0.222920	−0.111460	+	0.993769i	$0.535553\pi$
$368$	−71.7022	−3.73774
$369$	1.90677	0.0992626
$370$	1.92142	0.0998896
$371$	3.64002	0.188980
$372$	1.98579	0.102958
$373$	23.4763	1.21556	0.607778	−	0.794107i	$-0.292061\pi$
$373$	23.4763	1.21556	0.607778	+	0.794107i	$0.292061\pi$
$374$	−70.1895	−3.62941
$375$	8.27988	0.427571
$376$	88.7577	4.57733
$377$	1.44684	0.0745161
$378$	−12.5597	−0.646000
$379$	26.6047	1.36659	0.683295	−	0.730142i	$-0.260546\pi$
$379$	26.6047	1.36659	0.683295	+	0.730142i	$0.260546\pi$
$380$	−19.1210	−0.980886
$381$	23.6413	1.21118
$382$	48.2682	2.46962
$383$	6.87616	0.351355	0.175678	−	0.984448i	$-0.443788\pi$
$383$	6.87616	0.351355	0.175678	+	0.984448i	$0.443788\pi$
$384$	7.30404	0.372732
$385$	2.78879	0.142130
$386$	−34.8990	−1.77631
$387$	3.28169	0.166818
$388$	69.5514	3.53094
$389$	−17.3044	−0.877366	−0.438683	−	0.898642i	$-0.644555\pi$
$389$	−17.3044	−0.877366	−0.438683	+	0.898642i	$0.644555\pi$
$390$	−0.354739	−0.0179629
$391$	−30.0311	−1.51874
$392$	46.4730	2.34724
$393$	9.78898	0.493789
$394$	−21.9465	−1.10565
$395$	4.94255	0.248686
$396$	9.14149	0.459377
$397$	11.6271	0.583546	0.291773	−	0.956488i	$-0.405755\pi$
$397$	11.6271	0.583546	0.291773	+	0.956488i	$0.405755\pi$
$398$	−33.8758	−1.69804
$399$	14.7702	0.739435
$400$	−49.5640	−2.47820
$401$	25.3643	1.26663	0.633317	−	0.773892i	$-0.281693\pi$
$401$	25.3643	1.26663	0.633317	+	0.773892i	$0.281693\pi$
$402$	74.3816	3.70982
$403$	0.0353942	0.00176311
$404$	80.0487	3.98257
$405$	−4.57142	−0.227156
$406$	23.2631	1.15453
$407$	−9.64226	−0.477949
$408$	60.5682	2.99857
$409$	3.08620	0.152603	0.0763014	−	0.997085i	$-0.475689\pi$
$409$	3.08620	0.152603	0.0763014	+	0.997085i	$0.475689\pi$
$410$	−7.72893	−0.381705
$411$	3.75803	0.185370
$412$	85.0646	4.19083
$413$	−3.17847	−0.156402
$414$	5.50137	0.270378
$415$	−1.78937	−0.0878366
$416$	1.89594	0.0929559
$417$	3.42740	0.167840
$418$	134.965	6.60137
$419$	24.5938	1.20148	0.600742	−	0.799443i	$-0.294872\pi$
$419$	24.5938	1.20148	0.600742	+	0.799443i	$0.294872\pi$
$420$	−4.05511	−0.197869
$421$	−11.9399	−0.581917	−0.290959	−	0.956736i	$-0.593974\pi$
$421$	−11.9399	−0.581917	−0.290959	+	0.956736i	$0.593974\pi$
$422$	16.5948	0.807824
$423$	−3.49320	−0.169845
$424$	−28.7020	−1.39389
$425$	−20.7589	−1.00696
$426$	−50.0945	−2.42709
$427$	−14.5771	−0.705435
$428$	33.5323	1.62084
$429$	1.78019	0.0859485
$430$	−13.3021	−0.641482
$431$	−20.0785	−0.967148	−0.483574	−	0.875304i	$-0.660662\pi$
$431$	−20.0785	−0.967148	−0.483574	+	0.875304i	$0.660662\pi$
$432$	50.8002	2.44412
$433$	21.3592	1.02646	0.513229	−	0.858251i	$-0.328449\pi$
$433$	21.3592	1.02646	0.513229	+	0.858251i	$0.328449\pi$
$434$	0.569089	0.0273171
$435$	7.68502	0.368469
$436$	45.5740	2.18260
$437$	57.7460	2.76237
$438$	3.69707	0.176653
$439$	−26.8088	−1.27952	−0.639758	−	0.768577i	$-0.720965\pi$
$439$	−26.8088	−1.27952	−0.639758	+	0.768577i	$0.720965\pi$
$440$	−21.9900	−1.04833
$441$	−1.82902	−0.0870960
$442$	1.81911	0.0865260
$443$	−5.52000	−0.262263	−0.131132	−	0.991365i	$-0.541861\pi$
$443$	−5.52000	−0.262263	−0.131132	+	0.991365i	$0.541861\pi$
$444$	14.0205	0.665386
$445$	−2.24201	−0.106281
$446$	−23.3249	−1.10447
$447$	−37.8721	−1.79129
$448$	10.2992	0.486593
$449$	4.41880	0.208536	0.104268	−	0.994549i	$-0.466750\pi$
$449$	4.41880	0.208536	0.104268	+	0.994549i	$0.466750\pi$
$450$	3.80281	0.179266
$451$	38.7862	1.82637
$452$	−57.0983	−2.68568
$453$	−18.4111	−0.865030
$454$	13.3190	0.625092
$455$	−0.0722774	−0.00338841
$456$	−116.465	−5.45396
$457$	−10.9008	−0.509918	−0.254959	−	0.966952i	$-0.582062\pi$
$457$	−10.9008	−0.509918	−0.254959	+	0.966952i	$0.582062\pi$
$458$	71.6927	3.34998
$459$	21.2767	0.993111
$460$	−15.8540	−0.739194
$461$	34.9229	1.62652	0.813261	−	0.581898i	$-0.197690\pi$
$461$	34.9229	1.62652	0.813261	+	0.581898i	$0.197690\pi$
$462$	28.6229	1.33166
$463$	36.2986	1.68694	0.843469	−	0.537178i	$-0.180510\pi$
$463$	36.2986	1.68694	0.843469	+	0.537178i	$0.180510\pi$
$464$	−94.0925	−4.36813
$465$	0.187999	0.00871826
$466$	−2.71839	−0.125927
$467$	−8.95586	−0.414428	−0.207214	−	0.978296i	$-0.566440\pi$
$467$	−8.95586	−0.414428	−0.207214	+	0.978296i	$0.566440\pi$
$468$	−0.236921	−0.0109517
$469$	15.1551	0.699798
$470$	14.1594	0.653123
$471$	−13.7516	−0.633640
$472$	25.0626	1.15360
$473$	66.7539	3.06935
$474$	50.7281	2.33002
$475$	39.9168	1.83151
$476$	20.7946	0.953120
$477$	1.12961	0.0517213
$478$	34.6292	1.58390
$479$	16.0004	0.731079	0.365539	−	0.930796i	$-0.380885\pi$
$479$	16.0004	0.731079	0.365539	+	0.930796i	$0.380885\pi$
$480$	10.0704	0.459650
$481$	0.249899	0.0113944
$482$	13.7945	0.628323
$483$	12.2466	0.557238
$484$	131.835	5.99252
$485$	6.58461	0.298992
$486$	−8.23199	−0.373411
$487$	12.3025	0.557480	0.278740	−	0.960367i	$-0.410083\pi$
$487$	12.3025	0.557480	0.278740	+	0.960367i	$0.410083\pi$
$488$	114.942	5.20318
$489$	−9.54784	−0.431768
$490$	7.41376	0.334919
$491$	−32.5574	−1.46930	−0.734648	−	0.678448i	$-0.762653\pi$
$491$	−32.5574	−1.46930	−0.734648	+	0.678448i	$0.762653\pi$
$492$	−56.3979	−2.54261
$493$	−39.4089	−1.77489
$494$	−3.49791	−0.157378
$495$	0.865449	0.0388990
$496$	−2.30179	−0.103354
$497$	−10.2067	−0.457831
$498$	−18.3653	−0.822968
$499$	−7.49018	−0.335307	−0.167653	−	0.985846i	$-0.553619\pi$
$499$	−7.49018	−0.335307	−0.167653	+	0.985846i	$0.553619\pi$
$500$	−22.4150	−1.00243
$501$	13.7204	0.612983
$502$	−20.7227	−0.924898
$503$	26.3580	1.17524	0.587621	−	0.809136i	$-0.300064\pi$
$503$	26.3580	1.17524	0.587621	+	0.809136i	$0.300064\pi$
$504$	−2.26067	−0.100698
$505$	7.57842	0.337235
$506$	111.905	4.97478
$507$	23.5776	1.04712
$508$	−64.0008	−2.83958
$509$	−31.7558	−1.40755	−0.703776	−	0.710422i	$-0.748504\pi$
$509$	−31.7558	−1.40755	−0.703776	+	0.710422i	$0.748504\pi$
$510$	9.66233	0.427855
$511$	0.753270	0.0333227
$512$	35.8603	1.58482
$513$	−40.9124	−1.80632
$514$	37.8630	1.67007
$515$	8.05329	0.354870
$516$	−97.0649	−4.27305
$517$	−71.0561	−3.12505
$518$	4.01802	0.176542
$519$	−35.6127	−1.56322
$520$	0.569915	0.0249924
$521$	20.8295	0.912558	0.456279	−	0.889837i	$-0.349182\pi$
$521$	20.8295	0.912558	0.456279	+	0.889837i	$0.349182\pi$
$522$	7.21927	0.315979
$523$	−13.0455	−0.570439	−0.285220	−	0.958462i	$-0.592067\pi$
$523$	−13.0455	−0.570439	−0.285220	+	0.958462i	$0.592067\pi$
$524$	−26.5004	−1.15767
$525$	8.46540	0.369460
$526$	−22.3742	−0.975562
$527$	−0.964063	−0.0419952
$528$	−115.771	−5.03830
$529$	24.8795	1.08172
$530$	−4.57877	−0.198889
$531$	−0.986378	−0.0428051
$532$	−39.9854	−1.73359
$533$	−1.00522	−0.0435411
$534$	−23.0110	−0.995782
$535$	3.17459	0.137249
$536$	−119.500	−5.16160
$537$	−4.34304	−0.187416
$538$	23.0163	0.992302
$539$	−37.2046	−1.60251
$540$	11.2323	0.483363
$541$	−15.7150	−0.675639	−0.337820	−	0.941211i	$-0.609689\pi$
$541$	−15.7150	−0.675639	−0.337820	+	0.941211i	$0.609689\pi$
$542$	−34.1835	−1.46831
$543$	−32.5881	−1.39849
$544$	−51.6412	−2.21410
$545$	4.31461	0.184818
$546$	−0.741823	−0.0317471
$547$	32.0959	1.37232	0.686160	−	0.727450i	$-0.259295\pi$
$547$	32.0959	1.37232	0.686160	+	0.727450i	$0.259295\pi$
$548$	−10.1736	−0.434595
$549$	−4.52372	−0.193068
$550$	77.3541	3.29839
$551$	75.7782	3.22826
$552$	−96.5655	−4.11010
$553$	10.3357	0.439521
$554$	29.0286	1.23331
$555$	1.32736	0.0563433
$556$	−9.27854	−0.393498
$557$	9.34211	0.395838	0.197919	−	0.980218i	$-0.436582\pi$
$557$	9.34211	0.395838	0.197919	+	0.980218i	$0.436582\pi$
$558$	0.176606	0.00747632
$559$	−1.73006	−0.0731739
$560$	4.70042	0.198629
$561$	−48.4886	−2.04719
$562$	−22.0494	−0.930099
$563$	−41.2732	−1.73946	−0.869728	−	0.493531i	$-0.835706\pi$
$563$	−41.2732	−1.73946	−0.869728	+	0.493531i	$0.835706\pi$
$564$	103.321	4.35059
$565$	−5.40564	−0.227417
$566$	24.1796	1.01634
$567$	−9.55965	−0.401468
$568$	80.4806	3.37689
$569$	37.3402	1.56538	0.782690	−	0.622411i	$-0.213847\pi$
$569$	37.3402	1.56538	0.782690	+	0.622411i	$0.213847\pi$
$570$	−18.5794	−0.778207
$571$	26.3297	1.10186	0.550932	−	0.834550i	$-0.314272\pi$
$571$	26.3297	1.10186	0.550932	+	0.834550i	$0.314272\pi$
$572$	−4.81927	−0.201504
$573$	33.3449	1.39300
$574$	−16.1626	−0.674613
$575$	33.0966	1.38022
$576$	3.19617	0.133174
$577$	−0.0666194	−0.00277340	−0.00138670	−	0.999999i	$-0.500441\pi$
$577$	−0.0666194	−0.00277340	−0.00138670	+	0.999999i	$0.500441\pi$
$578$	−4.83020	−0.200910
$579$	−24.1091	−1.00194
$580$	−20.8046	−0.863865
$581$	−3.74189	−0.155240
$582$	67.5815	2.80134
$583$	22.9777	0.951640
$584$	−5.93962	−0.245783
$585$	−0.0224299	−0.000927362 0
$586$	48.1953	1.99093
$587$	−0.587031	−0.0242294	−0.0121147	−	0.999927i	$-0.503856\pi$
$587$	−0.587031	−0.0242294	−0.0121147	+	0.999927i	$0.503856\pi$
$588$	54.0981	2.23097
$589$	1.85377	0.0763832
$590$	3.99819	0.164603
$591$	−15.1612	−0.623648
$592$	−16.2517	−0.667941
$593$	10.3759	0.426086	0.213043	−	0.977043i	$-0.431663\pi$
$593$	10.3759	0.426086	0.213043	+	0.977043i	$0.431663\pi$
$594$	−79.2834	−3.25304
$595$	1.96868	0.0807080
$596$	102.526	4.19963
$597$	−23.4022	−0.957789
$598$	−2.90025	−0.118600
$599$	15.2373	0.622581	0.311290	−	0.950315i	$-0.399239\pi$
$599$	15.2373	0.622581	0.311290	+	0.950315i	$0.399239\pi$
$600$	−66.7507	−2.72508
$601$	22.2716	0.908480	0.454240	−	0.890879i	$-0.349911\pi$
$601$	22.2716	0.908480	0.454240	+	0.890879i	$0.349911\pi$
$602$	−27.8170	−1.13374
$603$	4.70310	0.191525
$604$	49.8419	2.02804
$605$	12.4812	0.507433
$606$	77.7815	3.15966
$607$	−10.7789	−0.437504	−0.218752	−	0.975780i	$-0.570199\pi$
$607$	−10.7789	−0.437504	−0.218752	+	0.975780i	$0.570199\pi$
$608$	99.2995	4.02713
$609$	16.0708	0.651220
$610$	18.3365	0.742424
$611$	1.84157	0.0745018
$612$	6.45322	0.260856
$613$	22.7781	0.919997	0.459999	−	0.887920i	$-0.347850\pi$
$613$	22.7781	0.919997	0.459999	+	0.887920i	$0.347850\pi$
$614$	−55.3028	−2.23184
$615$	−5.33934	−0.215303
$616$	−45.9849	−1.85279
$617$	13.6342	0.548891	0.274445	−	0.961603i	$-0.411506\pi$
$617$	13.6342	0.548891	0.274445	+	0.961603i	$0.411506\pi$
$618$	82.6554	3.32489
$619$	15.7920	0.634736	0.317368	−	0.948302i	$-0.397201\pi$
$619$	15.7920	0.634736	0.317368	+	0.948302i	$0.397201\pi$
$620$	−0.508945	−0.0204397
$621$	−33.9220	−1.36124
$622$	−29.9034	−1.19902
$623$	−4.68844	−0.187838
$624$	3.00045	0.120114
$625$	21.7933	0.871734
$626$	7.13933	0.285345
$627$	93.2374	3.72354
$628$	37.2278	1.48555
$629$	−6.80672	−0.271402
$630$	−0.360641	−0.0143683
$631$	34.7554	1.38359	0.691795	−	0.722094i	$-0.256820\pi$
$631$	34.7554	1.38359	0.691795	+	0.722094i	$0.256820\pi$
$632$	−81.4986	−3.24184
$633$	11.4641	0.455658
$634$	33.8773	1.34544
$635$	−6.05912	−0.240449
$636$	−33.4113	−1.32484
$637$	0.964233	0.0382043
$638$	146.849	5.81382
$639$	−3.16744	−0.125302
$640$	−1.87198	−0.0739966
$641$	8.60395	0.339836	0.169918	−	0.985458i	$-0.445650\pi$
$641$	8.60395	0.339836	0.169918	+	0.985458i	$0.445650\pi$
$642$	32.5825	1.28593
$643$	−27.5147	−1.08508	−0.542538	−	0.840031i	$-0.682536\pi$
$643$	−27.5147	−1.08508	−0.542538	+	0.840031i	$0.682536\pi$
$644$	−33.1535	−1.30643
$645$	−9.18939	−0.361832
$646$	95.2755	3.74856
$647$	4.87731	0.191747	0.0958734	−	0.995394i	$-0.469436\pi$
$647$	4.87731	0.191747	0.0958734	+	0.995394i	$0.469436\pi$
$648$	75.3789	2.96116
$649$	−20.0642	−0.787588
$650$	−2.00479	−0.0786344
$651$	0.393140	0.0154084
$652$	25.8476	1.01227
$653$	−6.85124	−0.268110	−0.134055	−	0.990974i	$-0.542800\pi$
$653$	−6.85124	−0.268110	−0.134055	+	0.990974i	$0.542800\pi$
$654$	44.2833	1.73161
$655$	−2.50886	−0.0980292
$656$	65.3728	2.55238
$657$	0.233763	0.00911996
$658$	29.6098	1.15431
$659$	−15.2143	−0.592663	−0.296332	−	0.955085i	$-0.595763\pi$
$659$	−15.2143	−0.592663	−0.296332	+	0.955085i	$0.595763\pi$
$660$	−25.5980	−0.996400
$661$	−13.6389	−0.530492	−0.265246	−	0.964181i	$-0.585453\pi$
$661$	−13.6389	−0.530492	−0.265246	+	0.964181i	$0.585453\pi$
$662$	−42.2475	−1.64199
$663$	1.25668	0.0488055
$664$	29.5052	1.14502
$665$	−3.78552	−0.146796
$666$	1.24692	0.0483170
$667$	62.8306	2.43281
$668$	−37.1435	−1.43712
$669$	−16.1134	−0.622981
$670$	−19.0636	−0.736490
$671$	−92.0184	−3.55233
$672$	21.0591	0.812371
$673$	29.8832	1.15191	0.575956	−	0.817481i	$-0.304630\pi$
$673$	29.8832	1.15191	0.575956	+	0.817481i	$0.304630\pi$
$674$	−91.1857	−3.51234
$675$	−23.4485	−0.902534
$676$	−63.8284	−2.45494
$677$	20.5132	0.788387	0.394194	−	0.919027i	$-0.371024\pi$
$677$	20.5132	0.788387	0.394194	+	0.919027i	$0.371024\pi$
$678$	−55.4812	−2.13074
$679$	13.7696	0.528429
$680$	−15.5233	−0.595290
$681$	9.20111	0.352587
$682$	3.59239	0.137560
$683$	3.04306	0.116439	0.0582197	−	0.998304i	$-0.481458\pi$
$683$	3.04306	0.116439	0.0582197	+	0.998304i	$0.481458\pi$
$684$	−12.4087	−0.474459
$685$	−0.963162	−0.0368005
$686$	33.4372	1.27664
$687$	49.5271	1.88958
$688$	112.511	4.28945
$689$	−0.595515	−0.0226873
$690$	−15.4049	−0.586456
$691$	49.6486	1.88872	0.944361	−	0.328912i	$-0.106682\pi$
$691$	49.6486	1.88872	0.944361	+	0.328912i	$0.106682\pi$
$692$	96.4094	3.66493
$693$	1.80981	0.0687489
$694$	−19.9242	−0.756312
$695$	−0.878423	−0.0333205
$696$	−126.720	−4.80330
$697$	27.3802	1.03710
$698$	24.9279	0.943533
$699$	−1.87793	−0.0710299
$700$	−22.9172	−0.866190
$701$	4.89539	0.184896	0.0924481	−	0.995718i	$-0.470531\pi$
$701$	4.89539	0.184896	0.0924481	+	0.995718i	$0.470531\pi$
$702$	2.05479	0.0775531
$703$	13.0885	0.493640
$704$	65.0142	2.45031
$705$	9.78164	0.368398
$706$	−30.4687	−1.14671
$707$	15.8478	0.596019
$708$	29.1748	1.09646
$709$	−34.1202	−1.28141	−0.640705	−	0.767787i	$-0.721358\pi$
$709$	−34.1202	−1.28141	−0.640705	+	0.767787i	$0.721358\pi$
$710$	12.8389	0.481836
$711$	3.20750	0.120291
$712$	36.9689	1.38547
$713$	1.53703	0.0575623
$714$	20.2057	0.756178
$715$	−0.456253	−0.0170629
$716$	11.7573	0.439392
$717$	23.9227	0.893409
$718$	84.2417	3.14387
$719$	−29.2616	−1.09127	−0.545636	−	0.838022i	$-0.683712\pi$
$719$	−29.2616	−1.09127	−0.545636	+	0.838022i	$0.683712\pi$
$720$	1.45868	0.0543619
$721$	16.8409	0.627187
$722$	−133.223	−4.95805
$723$	9.52959	0.354409
$724$	88.2213	3.27872
$725$	43.4315	1.61301
$726$	128.102	4.75429
$727$	−34.3065	−1.27236	−0.636178	−	0.771542i	$-0.719486\pi$
$727$	−34.3065	−1.27236	−0.636178	+	0.771542i	$0.719486\pi$
$728$	1.19179	0.0441708
$729$	23.7593	0.879974
$730$	−0.947537	−0.0350699
$731$	47.1233	1.74292
$732$	133.801	4.94544
$733$	−40.0444	−1.47907	−0.739537	−	0.673116i	$-0.764956\pi$
$733$	−40.0444	−1.47907	−0.739537	+	0.673116i	$0.764956\pi$
$734$	11.2336	0.414640
$735$	5.12161	0.188913
$736$	82.3331	3.03484
$737$	95.6670	3.52394
$738$	−5.01575	−0.184632
$739$	−37.8823	−1.39352	−0.696761	−	0.717304i	$-0.745376\pi$
$739$	−37.8823	−1.39352	−0.696761	+	0.717304i	$0.745376\pi$
$740$	−3.59339	−0.132096
$741$	−2.41644	−0.0887701
$742$	−9.57503	−0.351511
$743$	−48.7446	−1.78826	−0.894132	−	0.447803i	$-0.852207\pi$
$743$	−48.7446	−1.78826	−0.894132	+	0.447803i	$0.852207\pi$
$744$	−3.09996	−0.113650
$745$	9.70639	0.355615
$746$	−61.7542	−2.26098
$747$	−1.16122	−0.0424870
$748$	131.267	4.79959
$749$	6.63863	0.242570
$750$	−21.7802	−0.795299
$751$	−34.1416	−1.24585	−0.622923	−	0.782283i	$-0.714055\pi$
$751$	−34.1416	−1.24585	−0.622923	+	0.782283i	$0.714055\pi$
$752$	−119.763	−4.36730
$753$	−14.3157	−0.521694
$754$	−3.80590	−0.138603
$755$	4.71866	0.171730
$756$	23.4888	0.854280
$757$	31.7817	1.15512	0.577562	−	0.816347i	$-0.304004\pi$
$757$	31.7817	1.15512	0.577562	+	0.816347i	$0.304004\pi$
$758$	−69.9834	−2.54191
$759$	77.3067	2.80606
$760$	29.8493	1.08275
$761$	16.8665	0.611410	0.305705	−	0.952126i	$-0.401108\pi$
$761$	16.8665	0.611410	0.305705	+	0.952126i	$0.401108\pi$
$762$	−62.1881	−2.25284
$763$	9.02262	0.326641
$764$	−90.2701	−3.26586
$765$	0.610942	0.0220887
$766$	−18.0877	−0.653534
$767$	0.520005	0.0187763
$768$	19.2198	0.693536
$769$	−28.9892	−1.04538	−0.522689	−	0.852524i	$-0.675071\pi$
$769$	−28.9892	−1.04538	−0.522689	+	0.852524i	$0.675071\pi$
$770$	−7.33590	−0.264367
$771$	26.1567	0.942011
$772$	65.2673	2.34902
$773$	11.5611	0.415823	0.207912	−	0.978148i	$-0.433333\pi$
$773$	11.5611	0.415823	0.207912	+	0.978148i	$0.433333\pi$
$774$	−8.63247	−0.310288
$775$	1.06247	0.0381650
$776$	−108.575	−3.89761
$777$	2.77575	0.0995795
$778$	45.5190	1.63193
$779$	−52.6485	−1.88633
$780$	0.663425	0.0237544
$781$	−64.4298	−2.30548
$782$	78.9966	2.82491
$783$	−44.5148	−1.59083
$784$	−62.7070	−2.23954
$785$	3.52445	0.125793
$786$	−25.7498	−0.918466
$787$	−33.0510	−1.17814	−0.589071	−	0.808082i	$-0.700506\pi$
$787$	−33.0510	−1.17814	−0.589071	+	0.808082i	$0.700506\pi$
$788$	41.0439	1.46213
$789$	−15.4567	−0.550272
$790$	−13.0013	−0.462566
$791$	−11.3042	−0.401930
$792$	−14.2705	−0.507082
$793$	2.38485	0.0846884
$794$	−30.5849	−1.08542
$795$	−3.16313	−0.112185
$796$	63.3537	2.24551
$797$	25.1119	0.889510	0.444755	−	0.895652i	$-0.353291\pi$
$797$	25.1119	0.889510	0.444755	+	0.895652i	$0.353291\pi$
$798$	−38.8529	−1.37538
$799$	−50.1604	−1.77455
$800$	56.9125	2.01216
$801$	−1.45497	−0.0514087
$802$	−66.7207	−2.35599
$803$	4.75504	0.167802
$804$	−139.107	−4.90592
$805$	−3.13872	−0.110625
$806$	−0.0931042	−0.00327945
$807$	15.9002	0.559714
$808$	−124.962	−4.39614
$809$	51.6037	1.81429	0.907144	−	0.420820i	$-0.138258\pi$
$809$	51.6037	1.81429	0.907144	+	0.420820i	$0.138258\pi$
$810$	12.0251	0.422518
$811$	−3.67246	−0.128957	−0.0644787	−	0.997919i	$-0.520538\pi$
$811$	−3.67246	−0.128957	−0.0644787	+	0.997919i	$0.520538\pi$
$812$	−43.5062	−1.52677
$813$	−23.6148	−0.828207
$814$	25.3639	0.889004
$815$	2.44706	0.0857167
$816$	−81.7259	−2.86098
$817$	−90.6120	−3.17011
$818$	−8.11822	−0.283847
$819$	−0.0469049	−0.00163899
$820$	14.4545	0.504772
$821$	20.5837	0.718377	0.359188	−	0.933265i	$-0.383054\pi$
$821$	20.5837	0.718377	0.359188	+	0.933265i	$0.383054\pi$
$822$	−9.88547	−0.344796
$823$	26.7000	0.930705	0.465352	−	0.885126i	$-0.345928\pi$
$823$	26.7000	0.930705	0.465352	+	0.885126i	$0.345928\pi$
$824$	−132.792	−4.62603
$825$	53.4381	1.86048
$826$	8.36094	0.290914
$827$	−16.3350	−0.568024	−0.284012	−	0.958821i	$-0.591666\pi$
$827$	−16.3350	−0.568024	−0.284012	+	0.958821i	$0.591666\pi$
$828$	−10.2885	−0.357551
$829$	29.1599	1.01276	0.506382	−	0.862309i	$-0.330982\pi$
$829$	29.1599	1.01276	0.506382	+	0.862309i	$0.330982\pi$
$830$	4.70692	0.163379
$831$	20.0537	0.695654
$832$	−1.68498	−0.0584161
$833$	−26.2636	−0.909981
$834$	−9.01574	−0.312190
$835$	−3.51647	−0.121692
$836$	−252.409	−8.72975
$837$	−1.08897	−0.0376403
$838$	−64.6937	−2.23481
$839$	31.2599	1.07921	0.539607	−	0.841917i	$-0.318573\pi$
$839$	31.2599	1.07921	0.539607	+	0.841917i	$0.318573\pi$
$840$	6.33032	0.218417
$841$	53.4506	1.84312
$842$	31.4079	1.08239
$843$	−15.2323	−0.524628
$844$	−31.0353	−1.06828
$845$	−6.04279	−0.207878
$846$	9.18883	0.315918
$847$	26.1004	0.896821
$848$	38.7281	1.32993
$849$	16.7039	0.573275
$850$	54.6062	1.87298
$851$	10.8521	0.372007
$852$	93.6855	3.20961
$853$	−3.21703	−0.110149	−0.0550744	−	0.998482i	$-0.517540\pi$
$853$	−3.21703	−0.110149	−0.0550744	+	0.998482i	$0.517540\pi$
$854$	38.3449	1.31214
$855$	−1.17476	−0.0401761
$856$	−52.3463	−1.78916
$857$	−23.6319	−0.807249	−0.403624	−	0.914925i	$-0.632250\pi$
$857$	−23.6319	−0.807249	−0.403624	+	0.914925i	$0.632250\pi$
$858$	−4.68278	−0.159867
$859$	35.9569	1.22683	0.613417	−	0.789759i	$-0.289794\pi$
$859$	35.9569	1.22683	0.613417	+	0.789759i	$0.289794\pi$
$860$	24.8772	0.848305
$861$	−11.1655	−0.380519
$862$	52.8163	1.79893
$863$	15.7063	0.534648	0.267324	−	0.963607i	$-0.413861\pi$
$863$	15.7063	0.534648	0.267324	+	0.963607i	$0.413861\pi$
$864$	−58.3320	−1.98449
$865$	9.12732	0.310338
$866$	−56.1853	−1.90925
$867$	−3.33682	−0.113324
$868$	−1.06430	−0.0361246
$869$	65.2447	2.21328
$870$	−20.2154	−0.685366
$871$	−2.47941	−0.0840116
$872$	−71.1444	−2.40925
$873$	4.27313	0.144624
$874$	−151.900	−5.13811
$875$	−4.43766	−0.150020
$876$	−6.91417	−0.233608
$877$	8.02069	0.270839	0.135420	−	0.990788i	$-0.456762\pi$
$877$	8.02069	0.270839	0.135420	+	0.990788i	$0.456762\pi$
$878$	70.5204	2.37995
$879$	33.2945	1.12300
$880$	29.6715	1.00023
$881$	21.5671	0.726614	0.363307	−	0.931670i	$-0.381648\pi$
$881$	21.5671	0.726614	0.363307	+	0.931670i	$0.381648\pi$
$882$	4.81121	0.162002
$883$	−26.8367	−0.903127	−0.451563	−	0.892239i	$-0.649134\pi$
$883$	−26.8367	−0.903127	−0.451563	+	0.892239i	$0.649134\pi$
$884$	−3.40205	−0.114423
$885$	2.76205	0.0928453
$886$	14.5203	0.487820
$887$	18.3142	0.614931	0.307466	−	0.951559i	$-0.400519\pi$
$887$	18.3142	0.614931	0.307466	+	0.951559i	$0.400519\pi$
$888$	−21.8871	−0.734483
$889$	−12.6707	−0.424962
$890$	5.89758	0.197687
$891$	−60.3456	−2.02165
$892$	43.6217	1.46056
$893$	96.4519	3.22764
$894$	99.6221	3.33186
$895$	1.11310	0.0372067
$896$	−3.91465	−0.130779
$897$	−2.00356	−0.0668971
$898$	−11.6236	−0.387885
$899$	2.01700	0.0672706
$900$	−7.11193	−0.237064
$901$	16.2206	0.540385
$902$	−102.027	−3.39712
$903$	−19.2167	−0.639490
$904$	89.1347	2.96458
$905$	8.35214	0.277635
$906$	48.4303	1.60899
$907$	14.3517	0.476540	0.238270	−	0.971199i	$-0.423420\pi$
$907$	14.3517	0.476540	0.238270	+	0.971199i	$0.423420\pi$
$908$	−24.9089	−0.826631
$909$	4.91807	0.163122
$910$	0.190125	0.00630258
$911$	−4.02969	−0.133509	−0.0667547	−	0.997769i	$-0.521265\pi$
$911$	−4.02969	−0.133509	−0.0667547	+	0.997769i	$0.521265\pi$
$912$	157.148	5.20370
$913$	−23.6208	−0.781734
$914$	28.6745	0.948467
$915$	12.6673	0.418769
$916$	−134.078	−4.43006
$917$	−5.24647	−0.173254
$918$	−55.9682	−1.84722
$919$	9.05478	0.298690	0.149345	−	0.988785i	$-0.452284\pi$
$919$	9.05478	0.298690	0.149345	+	0.988785i	$0.452284\pi$
$920$	24.7492	0.815956
$921$	−38.2045	−1.25888
$922$	−91.8644	−3.02539
$923$	1.66983	0.0549632
$924$	−53.5300	−1.76101
$925$	7.50152	0.246648
$926$	−95.4831	−3.13777
$927$	5.22624	0.171652
$928$	108.043	3.54668
$929$	−6.35384	−0.208463	−0.104231	−	0.994553i	$-0.533238\pi$
$929$	−6.35384	−0.208463	−0.104231	+	0.994553i	$0.533238\pi$
$930$	−0.494531	−0.0162163
$931$	50.5016	1.65512
$932$	5.08387	0.166528
$933$	−20.6580	−0.676313
$934$	23.5583	0.770851
$935$	12.4274	0.406418
$936$	0.369851	0.0120889
$937$	7.66877	0.250528	0.125264	−	0.992123i	$-0.460022\pi$
$937$	7.66877	0.250528	0.125264	+	0.992123i	$0.460022\pi$
$938$	−39.8654	−1.30165
$939$	4.93202	0.160951
$940$	−26.4805	−0.863699
$941$	35.2565	1.14933	0.574665	−	0.818389i	$-0.305132\pi$
$941$	35.2565	1.14933	0.574665	+	0.818389i	$0.305132\pi$
$942$	36.1734	1.17859
$943$	−43.6530	−1.42154
$944$	−33.8175	−1.10067
$945$	2.22375	0.0723385
$946$	−175.595	−5.70910
$947$	16.8944	0.548994	0.274497	−	0.961588i	$-0.411489\pi$
$947$	16.8944	0.548994	0.274497	+	0.961588i	$0.411489\pi$
$948$	−94.8705	−3.08125
$949$	−0.123237	−0.00400043
$950$	−105.001	−3.40667
$951$	23.4033	0.758904
$952$	−32.4619	−1.05210
$953$	17.9329	0.580904	0.290452	−	0.956890i	$-0.406194\pi$
$953$	17.9329	0.580904	0.290452	+	0.956890i	$0.406194\pi$
$954$	−2.97143	−0.0962035
$955$	−8.54610	−0.276545
$956$	−64.7626	−2.09457
$957$	101.447	3.27932
$958$	−42.0890	−1.35983
$959$	−2.01415	−0.0650401
$960$	−8.94990	−0.288857
$961$	−30.9507	−0.998408
$962$	−0.657358	−0.0211941
$963$	2.06017	0.0663881
$964$	−25.7982	−0.830904
$965$	6.17902	0.198910
$966$	−32.2145	−1.03648
$967$	−16.0749	−0.516933	−0.258467	−	0.966020i	$-0.583217\pi$
$967$	−16.0749	−0.516933	−0.258467	+	0.966020i	$0.583217\pi$
$968$	−205.805	−6.61482
$969$	65.8187	2.11440
$970$	−17.3208	−0.556136
$971$	38.3973	1.23223	0.616114	−	0.787657i	$-0.288706\pi$
$971$	38.3973	1.23223	0.616114	+	0.787657i	$0.288706\pi$
$972$	15.3953	0.493804
$973$	−1.83694	−0.0588896
$974$	−32.3617	−1.03693
$975$	−1.38496	−0.0443542
$976$	−155.094	−4.96443
$977$	17.7057	0.566455	0.283227	−	0.959053i	$-0.408595\pi$
$977$	17.7057	0.566455	0.283227	+	0.959053i	$0.408595\pi$
$978$	25.1155	0.803105
$979$	−29.5959	−0.945889
$980$	−13.8650	−0.442902
$981$	2.80000	0.0893971
$982$	85.6420	2.73295
$983$	−32.7946	−1.04598	−0.522992	−	0.852338i	$-0.675184\pi$
$983$	−32.7946	−1.04598	−0.522992	+	0.852338i	$0.675184\pi$
$984$	88.0413	2.80665
$985$	3.88573	0.123810
$986$	103.665	3.30136
$987$	20.4552	0.651095
$988$	6.54170	0.208119
$989$	−75.1299	−2.38899
$990$	−2.27655	−0.0723537
$991$	−35.5148	−1.12817	−0.564083	−	0.825718i	$-0.690770\pi$
$991$	−35.5148	−1.12817	−0.564083	+	0.825718i	$0.690770\pi$
$992$	2.64307	0.0839174
$993$	−29.1856	−0.926177
$994$	26.8485	0.851583
$995$	5.99785	0.190145
$996$	34.3463	1.08831
$997$	23.4672	0.743213	0.371607	−	0.928390i	$-0.378807\pi$
$997$	23.4672	0.743213	0.371607	+	0.928390i	$0.378807\pi$
$998$	19.7029	0.623683
$999$	−7.68861	−0.243257

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6047.2.a.b.1.11	✓	287

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6047.2.a.b.1.11	✓	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)

\(f(q)\)	\(=\)	\(q-2.63049 q^{2} -1.81721 q^{3} +4.91948 q^{4} +0.465740 q^{5} +4.78015 q^{6} +0.973946 q^{7} -7.67967 q^{8} +0.302245 q^{9} +O(q^{10})\)	\(q-2.63049 q^{2} -1.81721 q^{3} +4.91948 q^{4} +0.465740 q^{5} +4.78015 q^{6} +0.973946 q^{7} -7.67967 q^{8} +0.302245 q^{9} -1.22512 q^{10} +6.14806 q^{11} -8.93972 q^{12} -0.159340 q^{13} -2.56196 q^{14} -0.846346 q^{15} +10.3623 q^{16} +4.34007 q^{17} -0.795054 q^{18} -8.34540 q^{19} +2.29120 q^{20} -1.76986 q^{21} -16.1724 q^{22} -6.91950 q^{23} +13.9556 q^{24} -4.78309 q^{25} +0.419142 q^{26} +4.90238 q^{27} +4.79131 q^{28} -9.08023 q^{29} +2.22631 q^{30} -0.222131 q^{31} -11.8987 q^{32} -11.1723 q^{33} -11.4165 q^{34} +0.453605 q^{35} +1.48689 q^{36} -1.56834 q^{37} +21.9525 q^{38} +0.289553 q^{39} -3.57673 q^{40} +6.30869 q^{41} +4.65561 q^{42} +10.8577 q^{43} +30.2453 q^{44} +0.140768 q^{45} +18.2017 q^{46} -11.5575 q^{47} -18.8305 q^{48} -6.05143 q^{49} +12.5819 q^{50} -7.88682 q^{51} -0.783869 q^{52} +3.73739 q^{53} -12.8957 q^{54} +2.86340 q^{55} -7.47958 q^{56} +15.1653 q^{57} +23.8855 q^{58} -3.26350 q^{59} -4.16359 q^{60} -14.9671 q^{61} +0.584312 q^{62} +0.294371 q^{63} +10.5747 q^{64} -0.0742109 q^{65} +29.3886 q^{66} +15.5605 q^{67} +21.3509 q^{68} +12.5742 q^{69} -1.19320 q^{70} -10.4797 q^{71} -2.32115 q^{72} +0.773421 q^{73} +4.12551 q^{74} +8.69186 q^{75} -41.0551 q^{76} +5.98788 q^{77} -0.761668 q^{78} +10.6122 q^{79} +4.82616 q^{80} -9.81538 q^{81} -16.5949 q^{82} -3.84199 q^{83} -8.70681 q^{84} +2.02135 q^{85} -28.5611 q^{86} +16.5007 q^{87} -47.2151 q^{88} -4.81386 q^{89} -0.370288 q^{90} -0.155188 q^{91} -34.0404 q^{92} +0.403657 q^{93} +30.4019 q^{94} -3.88679 q^{95} +21.6224 q^{96} +14.1380 q^{97} +15.9182 q^{98} +1.85822 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 287 q + 21 q^{2} + 29 q^{3} + 319 q^{4} + 19 q^{5} + 15 q^{6} + 52 q^{7} + 60 q^{8} + 352 q^{9}+O(q^{10}) \) 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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