LMFDB - Embedded newform 6014.2.a.l.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.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:	$48.0220317756$
Analytic rank:	$0$
Dimension:	$38$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.41930 q^{3} +1.00000 q^{4} +0.0104516 q^{5} +2.41930 q^{6} -3.11450 q^{7} -1.00000 q^{8} +2.85300 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.41930 q^{3} +1.00000 q^{4} +0.0104516 q^{5} +2.41930 q^{6} -3.11450 q^{7} -1.00000 q^{8} +2.85300 q^{9} -0.0104516 q^{10} -0.137329 q^{11} -2.41930 q^{12} +5.95112 q^{13} +3.11450 q^{14} -0.0252855 q^{15} +1.00000 q^{16} +1.22362 q^{17} -2.85300 q^{18} +2.48334 q^{19} +0.0104516 q^{20} +7.53491 q^{21} +0.137329 q^{22} +3.11370 q^{23} +2.41930 q^{24} -4.99989 q^{25} -5.95112 q^{26} +0.355629 q^{27} -3.11450 q^{28} -0.837843 q^{29} +0.0252855 q^{30} +1.00000 q^{31} -1.00000 q^{32} +0.332241 q^{33} -1.22362 q^{34} -0.0325515 q^{35} +2.85300 q^{36} +7.92162 q^{37} -2.48334 q^{38} -14.3975 q^{39} -0.0104516 q^{40} +8.66723 q^{41} -7.53491 q^{42} +6.55174 q^{43} -0.137329 q^{44} +0.0298184 q^{45} -3.11370 q^{46} -5.81298 q^{47} -2.41930 q^{48} +2.70013 q^{49} +4.99989 q^{50} -2.96031 q^{51} +5.95112 q^{52} +1.19461 q^{53} -0.355629 q^{54} -0.00143531 q^{55} +3.11450 q^{56} -6.00793 q^{57} +0.837843 q^{58} -12.7973 q^{59} -0.0252855 q^{60} +9.67208 q^{61} -1.00000 q^{62} -8.88569 q^{63} +1.00000 q^{64} +0.0621986 q^{65} -0.332241 q^{66} -5.91360 q^{67} +1.22362 q^{68} -7.53298 q^{69} +0.0325515 q^{70} +10.5721 q^{71} -2.85300 q^{72} -14.2318 q^{73} -7.92162 q^{74} +12.0962 q^{75} +2.48334 q^{76} +0.427713 q^{77} +14.3975 q^{78} -7.64900 q^{79} +0.0104516 q^{80} -9.41938 q^{81} -8.66723 q^{82} -9.47865 q^{83} +7.53491 q^{84} +0.0127888 q^{85} -6.55174 q^{86} +2.02699 q^{87} +0.137329 q^{88} +6.67076 q^{89} -0.0298184 q^{90} -18.5348 q^{91} +3.11370 q^{92} -2.41930 q^{93} +5.81298 q^{94} +0.0259548 q^{95} +2.41930 q^{96} -1.00000 q^{97} -2.70013 q^{98} -0.391801 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 38 q^{2} - 2 q^{3} + 38 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} - 38 q^{8} + 54 q^{9}+O(q^{10}) $ 38 * q - 38 * q^2 - 2 * q^3 + 38 * q^4 + 2 * q^5 + 2 * q^6 + 3 * q^7 - 38 * q^8 + 54 * q^9	\( 38 q - 38 q^{2} - 2 q^{3} + 38 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} - 38 q^{8} + 54 q^{9} - 2 q^{10} + 6 q^{11} - 2 q^{12} + 12 q^{13} - 3 q^{14} + 19 q^{15} + 38 q^{16} + 16 q^{17} - 54 q^{18} + 37 q^{19} + 2 q^{20} + 8 q^{21} - 6 q^{22} - 12 q^{23} + 2 q^{24} + 66 q^{25} - 12 q^{26} - 5 q^{27} + 3 q^{28} + 3 q^{29} - 19 q^{30} + 38 q^{31} - 38 q^{32} + 12 q^{33} - 16 q^{34} - 16 q^{35} + 54 q^{36} + 5 q^{37} - 37 q^{38} + 36 q^{39} - 2 q^{40} + 7 q^{41} - 8 q^{42} + 7 q^{43} + 6 q^{44} + 45 q^{45} + 12 q^{46} - 10 q^{47} - 2 q^{48} + 111 q^{49} - 66 q^{50} - 13 q^{51} + 12 q^{52} + 5 q^{53} + 5 q^{54} + 56 q^{55} - 3 q^{56} - 5 q^{57} - 3 q^{58} + 14 q^{59} + 19 q^{60} + 54 q^{61} - 38 q^{62} - 3 q^{63} + 38 q^{64} + 8 q^{65} - 12 q^{66} - 9 q^{67} + 16 q^{68} + 45 q^{69} + 16 q^{70} + 13 q^{71} - 54 q^{72} + 65 q^{73} - 5 q^{74} - 14 q^{75} + 37 q^{76} - 22 q^{77} - 36 q^{78} - 11 q^{79} + 2 q^{80} + 46 q^{81} - 7 q^{82} - 42 q^{83} + 8 q^{84} + 18 q^{85} - 7 q^{86} - 19 q^{87} - 6 q^{88} + 74 q^{89} - 45 q^{90} + 14 q^{91} - 12 q^{92} - 2 q^{93} + 10 q^{94} - 10 q^{95} + 2 q^{96} - 38 q^{97} - 111 q^{98} + 15 q^{99}+O(q^{100}) \) 38 * q - 38 * q^2 - 2 * q^3 + 38 * q^4 + 2 * q^5 + 2 * q^6 + 3 * q^7 - 38 * q^8 + 54 * q^9 - 2 * q^10 + 6 * q^11 - 2 * q^12 + 12 * q^13 - 3 * q^14 + 19 * q^15 + 38 * q^16 + 16 * q^17 - 54 * q^18 + 37 * q^19 + 2 * q^20 + 8 * q^21 - 6 * q^22 - 12 * q^23 + 2 * q^24 + 66 * q^25 - 12 * q^26 - 5 * q^27 + 3 * q^28 + 3 * q^29 - 19 * q^30 + 38 * q^31 - 38 * q^32 + 12 * q^33 - 16 * q^34 - 16 * q^35 + 54 * q^36 + 5 * q^37 - 37 * q^38 + 36 * q^39 - 2 * q^40 + 7 * q^41 - 8 * q^42 + 7 * q^43 + 6 * q^44 + 45 * q^45 + 12 * q^46 - 10 * q^47 - 2 * q^48 + 111 * q^49 - 66 * q^50 - 13 * q^51 + 12 * q^52 + 5 * q^53 + 5 * q^54 + 56 * q^55 - 3 * q^56 - 5 * q^57 - 3 * q^58 + 14 * q^59 + 19 * q^60 + 54 * q^61 - 38 * q^62 - 3 * q^63 + 38 * q^64 + 8 * q^65 - 12 * q^66 - 9 * q^67 + 16 * q^68 + 45 * q^69 + 16 * q^70 + 13 * q^71 - 54 * q^72 + 65 * q^73 - 5 * q^74 - 14 * q^75 + 37 * q^76 - 22 * q^77 - 36 * q^78 - 11 * q^79 + 2 * q^80 + 46 * q^81 - 7 * q^82 - 42 * q^83 + 8 * q^84 + 18 * q^85 - 7 * q^86 - 19 * q^87 - 6 * q^88 + 74 * q^89 - 45 * q^90 + 14 * q^91 - 12 * q^92 - 2 * q^93 + 10 * q^94 - 10 * q^95 + 2 * q^96 - 38 * q^97 - 111 * q^98 + 15 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.41930	−1.39678	−0.698391	−	0.715716i	$-0.746100\pi$
$3$	−2.41930	−1.39678	−0.698391	+	0.715716i	$0.746100\pi$
$4$	1.00000	0.500000
$5$	0.0104516	0.00467409	0.00233704	−	0.999997i	$-0.499256\pi$
$5$	0.0104516	0.00467409	0.00233704	+	0.999997i	$0.499256\pi$
$6$	2.41930	0.987674
$7$	−3.11450	−1.17717	−0.588586	−	0.808435i	$-0.700315\pi$
$7$	−3.11450	−1.17717	−0.588586	+	0.808435i	$0.700315\pi$
$8$	−1.00000	−0.353553
$9$	2.85300	0.951001
$10$	−0.0104516	−0.00330508
$11$	−0.137329	−0.0414064	−0.0207032	−	0.999786i	$-0.506591\pi$
$11$	−0.137329	−0.0414064	−0.0207032	+	0.999786i	$0.506591\pi$
$12$	−2.41930	−0.698391
$13$	5.95112	1.65054	0.825271	−	0.564737i	$-0.191022\pi$
$13$	5.95112	1.65054	0.825271	+	0.564737i	$0.191022\pi$
$14$	3.11450	0.832386
$15$	−0.0252855	−0.00652868
$16$	1.00000	0.250000
$17$	1.22362	0.296772	0.148386	−	0.988930i	$-0.452592\pi$
$17$	1.22362	0.296772	0.148386	+	0.988930i	$0.452592\pi$
$18$	−2.85300	−0.672459
$19$	2.48334	0.569717	0.284858	−	0.958570i	$-0.408053\pi$
$19$	2.48334	0.569717	0.284858	+	0.958570i	$0.408053\pi$
$20$	0.0104516	0.00233704
$21$	7.53491	1.64425
$22$	0.137329	0.0292787
$23$	3.11370	0.649252	0.324626	−	0.945842i	$-0.394762\pi$
$23$	3.11370	0.649252	0.324626	+	0.945842i	$0.394762\pi$
$24$	2.41930	0.493837
$25$	−4.99989	−0.999978
$26$	−5.95112	−1.16711
$27$	0.355629	0.0684408
$28$	−3.11450	−0.588586
$29$	−0.837843	−0.155584	−0.0777918	−	0.996970i	$-0.524787\pi$
$29$	−0.837843	−0.155584	−0.0777918	+	0.996970i	$0.524787\pi$
$30$	0.0252855	0.00461648
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−1.00000	−0.176777
$33$	0.332241	0.0578357
$34$	−1.22362	−0.209849
$35$	−0.0325515	−0.00550220
$36$	2.85300	0.475501
$37$	7.92162	1.30231	0.651153	−	0.758946i	$-0.274285\pi$
$37$	7.92162	1.30231	0.651153	+	0.758946i	$0.274285\pi$
$38$	−2.48334	−0.402851
$39$	−14.3975	−2.30545
$40$	−0.0104516	−0.00165254
$41$	8.66723	1.35359	0.676797	−	0.736170i	$-0.263367\pi$
$41$	8.66723	1.35359	0.676797	+	0.736170i	$0.263367\pi$
$42$	−7.53491	−1.16266
$43$	6.55174	0.999131	0.499566	−	0.866276i	$-0.333493\pi$
$43$	6.55174	0.999131	0.499566	+	0.866276i	$0.333493\pi$
$44$	−0.137329	−0.0207032
$45$	0.0298184	0.00444506
$46$	−3.11370	−0.459091
$47$	−5.81298	−0.847910	−0.423955	−	0.905683i	$-0.639358\pi$
$47$	−5.81298	−0.847910	−0.423955	+	0.905683i	$0.639358\pi$
$48$	−2.41930	−0.349196
$49$	2.70013	0.385733
$50$	4.99989	0.707091
$51$	−2.96031	−0.414526
$52$	5.95112	0.825271
$53$	1.19461	0.164092	0.0820462	−	0.996629i	$-0.473854\pi$
$53$	1.19461	0.164092	0.0820462	+	0.996629i	$0.473854\pi$
$54$	−0.355629	−0.0483950
$55$	−0.00143531	−0.000193537 0
$56$	3.11450	0.416193
$57$	−6.00793	−0.795770
$58$	0.837843	0.110014
$59$	−12.7973	−1.66607	−0.833034	−	0.553222i	$-0.813398\pi$
$59$	−12.7973	−1.66607	−0.833034	+	0.553222i	$0.813398\pi$
$60$	−0.0252855	−0.00326434
$61$	9.67208	1.23838	0.619191	−	0.785240i	$-0.287461\pi$
$61$	9.67208	1.23838	0.619191	+	0.785240i	$0.287461\pi$
$62$	−1.00000	−0.127000
$63$	−8.88569	−1.11949
$64$	1.00000	0.125000
$65$	0.0621986	0.00771478
$66$	−0.332241	−0.0408960
$67$	−5.91360	−0.722461	−0.361230	−	0.932477i	$-0.617643\pi$
$67$	−5.91360	−0.722461	−0.361230	+	0.932477i	$0.617643\pi$
$68$	1.22362	0.148386
$69$	−7.53298	−0.906864
$70$	0.0325515	0.00389065
$71$	10.5721	1.25468	0.627339	−	0.778746i	$-0.284144\pi$
$71$	10.5721	1.25468	0.627339	+	0.778746i	$0.284144\pi$
$72$	−2.85300	−0.336230
$73$	−14.2318	−1.66570	−0.832852	−	0.553496i	$-0.813293\pi$
$73$	−14.2318	−1.66570	−0.832852	+	0.553496i	$0.813293\pi$
$74$	−7.92162	−0.920870
$75$	12.0962	1.39675
$76$	2.48334	0.284858
$77$	0.427713	0.0487424
$78$	14.3975	1.63020
$79$	−7.64900	−0.860580	−0.430290	−	0.902691i	$-0.641589\pi$
$79$	−7.64900	−0.860580	−0.430290	+	0.902691i	$0.641589\pi$
$80$	0.0104516	0.00116852
$81$	−9.41938	−1.04660
$82$	−8.66723	−0.957136
$83$	−9.47865	−1.04042	−0.520208	−	0.854039i	$-0.674146\pi$
$83$	−9.47865	−1.04042	−0.520208	+	0.854039i	$0.674146\pi$
$84$	7.53491	0.822126
$85$	0.0127888	0.00138714
$86$	−6.55174	−0.706492
$87$	2.02699	0.217316
$88$	0.137329	0.0146394
$89$	6.67076	0.707099	0.353550	−	0.935416i	$-0.384975\pi$
$89$	6.67076	0.707099	0.353550	+	0.935416i	$0.384975\pi$
$90$	−0.0298184	−0.00314313
$91$	−18.5348	−1.94297
$92$	3.11370	0.324626
$93$	−2.41930	−0.250870
$94$	5.81298	0.599563
$95$	0.0259548	0.00266291
$96$	2.41930	0.246919
$97$	−1.00000	−0.101535
$97$	−1.00000	−0.101535
$98$	−2.70013	−0.272754
$99$	−0.391801	−0.0393775
$100$	−4.99989	−0.499989
$101$	13.2650	1.31991	0.659956	−	0.751304i	$-0.270575\pi$
$101$	13.2650	1.31991	0.659956	+	0.751304i	$0.270575\pi$
$102$	2.96031	0.293114
$103$	−3.66418	−0.361042	−0.180521	−	0.983571i	$-0.557778\pi$
$103$	−3.66418	−0.361042	−0.180521	+	0.983571i	$0.557778\pi$
$104$	−5.95112	−0.583555
$105$	0.0787517	0.00768538
$106$	−1.19461	−0.116031
$107$	1.74338	0.168539	0.0842693	−	0.996443i	$-0.473144\pi$
$107$	1.74338	0.168539	0.0842693	+	0.996443i	$0.473144\pi$
$108$	0.355629	0.0342204
$109$	17.6482	1.69039	0.845194	−	0.534460i	$-0.179485\pi$
$109$	17.6482	1.69039	0.845194	+	0.534460i	$0.179485\pi$
$110$	0.00143531	0.000136851 0
$111$	−19.1648	−1.81904
$112$	−3.11450	−0.294293
$113$	−10.7913	−1.01516	−0.507580	−	0.861604i	$-0.669460\pi$
$113$	−10.7913	−1.01516	−0.507580	+	0.861604i	$0.669460\pi$
$114$	6.00793	0.562695
$115$	0.0325431	0.00303466
$116$	−0.837843	−0.0777918
$117$	16.9786	1.56967
$118$	12.7973	1.17809
$119$	−3.81097	−0.349351
$120$	0.0252855	0.00230824
$121$	−10.9811	−0.998286
$122$	−9.67208	−0.875669
$123$	−20.9686	−1.89068
$124$	1.00000	0.0898027
$125$	−0.104515	−0.00934807
$126$	8.88569	0.791600
$127$	15.3223	1.35964	0.679819	−	0.733380i	$-0.262058\pi$
$127$	15.3223	1.35964	0.679819	+	0.733380i	$0.262058\pi$
$128$	−1.00000	−0.0883883
$129$	−15.8506	−1.39557
$130$	−0.0621986	−0.00545517
$131$	−14.0031	−1.22346	−0.611728	−	0.791068i	$-0.709525\pi$
$131$	−14.0031	−1.22346	−0.611728	+	0.791068i	$0.709525\pi$
$132$	0.332241	0.0289178
$133$	−7.73436	−0.670654
$134$	5.91360	0.510857
$135$	0.00371689	0.000319899 0
$136$	−1.22362	−0.104925
$137$	−13.1498	−1.12347	−0.561733	−	0.827319i	$-0.689865\pi$
$137$	−13.1498	−1.12347	−0.561733	+	0.827319i	$0.689865\pi$
$138$	7.53298	0.641250
$139$	20.6895	1.75486	0.877431	−	0.479703i	$-0.159255\pi$
$139$	20.6895	1.75486	0.877431	+	0.479703i	$0.159255\pi$
$140$	−0.0325515	−0.00275110
$141$	14.0633	1.18435
$142$	−10.5721	−0.887192
$143$	−0.817263	−0.0683430
$144$	2.85300	0.237750
$145$	−0.00875679	−0.000727211 0
$146$	14.2318	1.17783
$147$	−6.53242	−0.538785
$148$	7.92162	0.651153
$149$	−8.69108	−0.712001	−0.356000	−	0.934486i	$-0.615860\pi$
$149$	−8.69108	−0.712001	−0.356000	+	0.934486i	$0.615860\pi$
$150$	−12.0962	−0.987653
$151$	3.59702	0.292721	0.146361	−	0.989231i	$-0.453244\pi$
$151$	3.59702	0.292721	0.146361	+	0.989231i	$0.453244\pi$
$152$	−2.48334	−0.201425
$153$	3.49100	0.282230
$154$	−0.427713	−0.0344661
$155$	0.0104516	0.000839491 0
$156$	−14.3975	−1.15272
$157$	7.54130	0.601861	0.300931	−	0.953646i	$-0.402703\pi$
$157$	7.54130	0.601861	0.300931	+	0.953646i	$0.402703\pi$
$158$	7.64900	0.608522
$159$	−2.89012	−0.229201
$160$	−0.0104516	−0.000826270 0
$161$	−9.69764	−0.764281
$162$	9.41938	0.740057
$163$	−20.7584	−1.62592	−0.812960	−	0.582319i	$-0.802145\pi$
$163$	−20.7584	−1.62592	−0.812960	+	0.582319i	$0.802145\pi$
$164$	8.66723	0.676797
$165$	0.00347244	0.000270329 0
$166$	9.47865	0.735686
$167$	8.32538	0.644237	0.322119	−	0.946699i	$-0.395605\pi$
$167$	8.32538	0.644237	0.322119	+	0.946699i	$0.395605\pi$
$168$	−7.53491	−0.581331
$169$	22.4158	1.72429
$170$	−0.0127888	−0.000980854 0
$171$	7.08497	0.541801
$172$	6.55174	0.499566
$173$	−2.61414	−0.198749	−0.0993745	−	0.995050i	$-0.531684\pi$
$173$	−2.61414	−0.198749	−0.0993745	+	0.995050i	$0.531684\pi$
$174$	−2.02699	−0.153666
$175$	15.5722	1.17715
$176$	−0.137329	−0.0103516
$177$	30.9605	2.32713
$178$	−6.67076	−0.499995
$179$	21.8935	1.63640	0.818199	−	0.574936i	$-0.194973\pi$
$179$	21.8935	1.63640	0.818199	+	0.574936i	$0.194973\pi$
$180$	0.0298184	0.00222253
$181$	14.7078	1.09322	0.546610	−	0.837387i	$-0.315918\pi$
$181$	14.7078	1.09322	0.546610	+	0.837387i	$0.315918\pi$
$182$	18.5348	1.37389
$183$	−23.3996	−1.72975
$184$	−3.11370	−0.229545
$185$	0.0827935	0.00608710
$186$	2.41930	0.177392
$187$	−0.168039	−0.0122882
$188$	−5.81298	−0.423955
$189$	−1.10761	−0.0805666
$190$	−0.0259548	−0.00188296
$191$	−13.4955	−0.976498	−0.488249	−	0.872704i	$-0.662364\pi$
$191$	−13.4955	−0.976498	−0.488249	+	0.872704i	$0.662364\pi$
$192$	−2.41930	−0.174598
$193$	−1.83461	−0.132058	−0.0660291	−	0.997818i	$-0.521033\pi$
$193$	−1.83461	−0.132058	−0.0660291	+	0.997818i	$0.521033\pi$
$194$	1.00000	0.0717958
$195$	−0.150477	−0.0107759
$196$	2.70013	0.192866
$197$	14.3854	1.02492	0.512460	−	0.858711i	$-0.328734\pi$
$197$	14.3854	1.02492	0.512460	+	0.858711i	$0.328734\pi$
$198$	0.391801	0.0278441
$199$	−17.9754	−1.27424	−0.637120	−	0.770764i	$-0.719875\pi$
$199$	−17.9754	−1.27424	−0.637120	+	0.770764i	$0.719875\pi$
$200$	4.99989	0.353546
$201$	14.3067	1.00912
$202$	−13.2650	−0.933319
$203$	2.60947	0.183149
$204$	−2.96031	−0.207263
$205$	0.0905863	0.00632682
$206$	3.66418	0.255295
$207$	8.88341	0.617440
$208$	5.95112	0.412636
$209$	−0.341035	−0.0235899
$210$	−0.0787517	−0.00543439
$211$	−8.07294	−0.555764	−0.277882	−	0.960615i	$-0.589632\pi$
$211$	−8.07294	−0.555764	−0.277882	+	0.960615i	$0.589632\pi$
$212$	1.19461	0.0820462
$213$	−25.5771	−1.75251
$214$	−1.74338	−0.119175
$215$	0.0684760	0.00467003
$216$	−0.355629	−0.0241975
$217$	−3.11450	−0.211426
$218$	−17.6482	−1.19528
$219$	34.4309	2.32663
$220$	−0.00143531	−9.67685e−5 0
$221$	7.28191	0.489834
$222$	19.1648	1.28625
$223$	5.27542	0.353268	0.176634	−	0.984277i	$-0.443479\pi$
$223$	5.27542	0.353268	0.176634	+	0.984277i	$0.443479\pi$
$224$	3.11450	0.208097
$225$	−14.2647	−0.950980
$226$	10.7913	0.717827
$227$	−18.7430	−1.24401	−0.622007	−	0.783012i	$-0.713683\pi$
$227$	−18.7430	−1.24401	−0.622007	+	0.783012i	$0.713683\pi$
$228$	−6.00793	−0.397885
$229$	−7.58554	−0.501266	−0.250633	−	0.968082i	$-0.580639\pi$
$229$	−7.58554	−0.501266	−0.250633	+	0.968082i	$0.580639\pi$
$230$	−0.0325431	−0.00214583
$231$	−1.03477	−0.0680825
$232$	0.837843	0.0550071
$233$	−1.87280	−0.122691	−0.0613455	−	0.998117i	$-0.519539\pi$
$233$	−1.87280	−0.122691	−0.0613455	+	0.998117i	$0.519539\pi$
$234$	−16.9786	−1.10992
$235$	−0.0607548	−0.00396321
$236$	−12.7973	−0.833034
$237$	18.5052	1.20204
$238$	3.81097	0.247029
$239$	17.2160	1.11361	0.556807	−	0.830642i	$-0.312026\pi$
$239$	17.2160	1.11361	0.556807	+	0.830642i	$0.312026\pi$
$240$	−0.0252855	−0.00163217
$241$	−15.7566	−1.01497	−0.507486	−	0.861660i	$-0.669425\pi$
$241$	−15.7566	−1.01497	−0.507486	+	0.861660i	$0.669425\pi$
$242$	10.9811	0.705894
$243$	21.7214	1.39343
$244$	9.67208	0.619191
$245$	0.0282206	0.00180295
$246$	20.9686	1.33691
$247$	14.7786	0.940342
$248$	−1.00000	−0.0635001
$249$	22.9317	1.45324
$250$	0.104515	0.00661009
$251$	−15.6042	−0.984931	−0.492466	−	0.870332i	$-0.663904\pi$
$251$	−15.6042	−0.984931	−0.492466	+	0.870332i	$0.663904\pi$
$252$	−8.88569	−0.559746
$253$	−0.427603	−0.0268832
$254$	−15.3223	−0.961409
$255$	−0.0309399	−0.00193753
$256$	1.00000	0.0625000
$257$	−20.1441	−1.25655	−0.628276	−	0.777990i	$-0.716239\pi$
$257$	−20.1441	−1.25655	−0.628276	+	0.777990i	$0.716239\pi$
$258$	15.8506	0.986816
$259$	−24.6719	−1.53304
$260$	0.0621986	0.00385739
$261$	−2.39037	−0.147960
$262$	14.0031	0.865114
$263$	−25.4393	−1.56866	−0.784328	−	0.620346i	$-0.786992\pi$
$263$	−25.4393	−1.56866	−0.784328	+	0.620346i	$0.786992\pi$
$264$	−0.332241	−0.0204480
$265$	0.0124856	0.000766982 0
$266$	7.73436	0.474224
$267$	−16.1386	−0.987664
$268$	−5.91360	−0.361230
$269$	23.8398	1.45354	0.726768	−	0.686883i	$-0.241022\pi$
$269$	23.8398	1.45354	0.726768	+	0.686883i	$0.241022\pi$
$270$	−0.00371689	−0.000226202 0
$271$	−7.20572	−0.437716	−0.218858	−	0.975757i	$-0.570233\pi$
$271$	−7.20572	−0.437716	−0.218858	+	0.975757i	$0.570233\pi$
$272$	1.22362	0.0741930
$273$	44.8411	2.71391
$274$	13.1498	0.794410
$275$	0.686632	0.0414055
$276$	−7.53298	−0.453432
$277$	23.6693	1.42215	0.711074	−	0.703117i	$-0.248209\pi$
$277$	23.6693	1.42215	0.711074	+	0.703117i	$0.248209\pi$
$278$	−20.6895	−1.24088
$279$	2.85300	0.170805
$280$	0.0325515	0.00194532
$281$	27.7693	1.65658	0.828288	−	0.560302i	$-0.189315\pi$
$281$	27.7693	1.65658	0.828288	+	0.560302i	$0.189315\pi$
$282$	−14.0633	−0.837459
$283$	−0.105424	−0.00626683	−0.00313342	−	0.999995i	$-0.500997\pi$
$283$	−0.105424	−0.00626683	−0.00313342	+	0.999995i	$0.500997\pi$
$284$	10.5721	0.627339
$285$	−0.0627924	−0.00371950
$286$	0.817263	0.0483258
$287$	−26.9941	−1.59341
$288$	−2.85300	−0.168115
$289$	−15.5028	−0.911926
$290$	0.00875679	0.000514216 0
$291$	2.41930	0.141822
$292$	−14.2318	−0.832852
$293$	−8.94779	−0.522735	−0.261368	−	0.965239i	$-0.584174\pi$
$293$	−8.94779	−0.522735	−0.261368	+	0.965239i	$0.584174\pi$
$294$	6.53242	0.380979
$295$	−0.133752	−0.00778735
$296$	−7.92162	−0.460435
$297$	−0.0488383	−0.00283389
$298$	8.69108	0.503460
$299$	18.5300	1.07162
$300$	12.0962	0.698376
$301$	−20.4054	−1.17615
$302$	−3.59702	−0.206985
$303$	−32.0919	−1.84363
$304$	2.48334	0.142429
$305$	0.101088	0.00578831
$306$	−3.49100	−0.199567
$307$	6.11257	0.348863	0.174431	−	0.984669i	$-0.444191\pi$
$307$	6.11257	0.348863	0.174431	+	0.984669i	$0.444191\pi$
$308$	0.427713	0.0243712
$309$	8.86473	0.504297
$310$	−0.0104516	−0.000593610 0
$311$	13.3149	0.755017	0.377508	−	0.926006i	$-0.376781\pi$
$311$	13.3149	0.755017	0.377508	+	0.926006i	$0.376781\pi$
$312$	14.3975	0.815099
$313$	1.32504	0.0748955	0.0374478	−	0.999299i	$-0.488077\pi$
$313$	1.32504	0.0748955	0.0374478	+	0.999299i	$0.488077\pi$
$314$	−7.54130	−0.425580
$315$	−0.0928695	−0.00523260
$316$	−7.64900	−0.430290
$317$	−3.96407	−0.222644	−0.111322	−	0.993784i	$-0.535509\pi$
$317$	−3.96407	−0.222644	−0.111322	+	0.993784i	$0.535509\pi$
$318$	2.89012	0.162070
$319$	0.115061	0.00644215
$320$	0.0104516	0.000584261 0
$321$	−4.21775	−0.235412
$322$	9.69764	0.540428
$323$	3.03867	0.169076
$324$	−9.41938	−0.523299
$325$	−29.7549	−1.65051
$326$	20.7584	1.14970
$327$	−42.6962	−2.36110
$328$	−8.66723	−0.478568
$329$	18.1045	0.998135
$330$	−0.00347244	−0.000191152 0
$331$	27.5463	1.51408	0.757040	−	0.653369i	$-0.226645\pi$
$331$	27.5463	1.51408	0.757040	+	0.653369i	$0.226645\pi$
$332$	−9.47865	−0.520208
$333$	22.6004	1.23850
$334$	−8.32538	−0.455545
$335$	−0.0618064	−0.00337685
$336$	7.53491	0.411063
$337$	29.6882	1.61722	0.808609	−	0.588346i	$-0.200221\pi$
$337$	29.6882	1.61722	0.808609	+	0.588346i	$0.200221\pi$
$338$	−22.4158	−1.21926
$339$	26.1074	1.41796
$340$	0.0127888	0.000693569 0
$341$	−0.137329	−0.00743680
$342$	−7.08497	−0.383111
$343$	13.3920	0.723098
$344$	−6.55174	−0.353246
$345$	−0.0787315	−0.00423876
$346$	2.61414	0.140537
$347$	17.0304	0.914238	0.457119	−	0.889406i	$-0.348881\pi$
$347$	17.0304	0.914238	0.457119	+	0.889406i	$0.348881\pi$
$348$	2.02699	0.108658
$349$	32.0904	1.71776	0.858880	−	0.512177i	$-0.171161\pi$
$349$	32.0904	1.71776	0.858880	+	0.512177i	$0.171161\pi$
$350$	−15.5722	−0.832368
$351$	2.11639	0.112965
$352$	0.137329	0.00731968
$353$	−7.57951	−0.403417	−0.201708	−	0.979446i	$-0.564649\pi$
$353$	−7.57951	−0.403417	−0.201708	+	0.979446i	$0.564649\pi$
$354$	−30.9605	−1.64553
$355$	0.110495	0.00586448
$356$	6.67076	0.353550
$357$	9.21988	0.487968
$358$	−21.8935	−1.15711
$359$	13.9606	0.736814	0.368407	−	0.929665i	$-0.379903\pi$
$359$	13.9606	0.736814	0.368407	+	0.929665i	$0.379903\pi$
$360$	−0.0298184	−0.00157157
$361$	−12.8330	−0.675423
$362$	−14.7078	−0.773024
$363$	26.5667	1.39439
$364$	−18.5348	−0.971486
$365$	−0.148745	−0.00778565
$366$	23.3996	1.22312
$367$	−14.9341	−0.779552	−0.389776	−	0.920910i	$-0.627448\pi$
$367$	−14.9341	−0.779552	−0.389776	+	0.920910i	$0.627448\pi$
$368$	3.11370	0.162313
$369$	24.7276	1.28727
$370$	−0.0827935	−0.00430423
$371$	−3.72062	−0.193165
$372$	−2.41930	−0.125435
$373$	−5.10898	−0.264533	−0.132266	−	0.991214i	$-0.542225\pi$
$373$	−5.10898	−0.264533	−0.132266	+	0.991214i	$0.542225\pi$
$374$	0.168039	0.00868910
$375$	0.252852	0.0130572
$376$	5.81298	0.299781
$377$	−4.98610	−0.256797
$378$	1.10761	0.0569692
$379$	−19.9690	−1.02574	−0.512870	−	0.858466i	$-0.671418\pi$
$379$	−19.9690	−1.02574	−0.512870	+	0.858466i	$0.671418\pi$
$380$	0.0259548	0.00133145
$381$	−37.0693	−1.89912
$382$	13.4955	0.690489
$383$	−3.27717	−0.167456	−0.0837278	−	0.996489i	$-0.526683\pi$
$383$	−3.27717	−0.167456	−0.0837278	+	0.996489i	$0.526683\pi$
$384$	2.41930	0.123459
$385$	0.00447028	0.000227826 0
$386$	1.83461	0.0933792
$387$	18.6921	0.950175
$388$	−1.00000	−0.0507673
$389$	−0.978468	−0.0496103	−0.0248052	−	0.999692i	$-0.507897\pi$
$389$	−0.978468	−0.0496103	−0.0248052	+	0.999692i	$0.507897\pi$
$390$	0.150477	0.00761969
$391$	3.81000	0.192680
$392$	−2.70013	−0.136377
$393$	33.8777	1.70890
$394$	−14.3854	−0.724728
$395$	−0.0799442	−0.00402243
$396$	−0.391801	−0.0196888
$397$	−14.7711	−0.741341	−0.370671	−	0.928764i	$-0.620872\pi$
$397$	−14.7711	−0.741341	−0.370671	+	0.928764i	$0.620872\pi$
$398$	17.9754	0.901024
$399$	18.7117	0.936758
$400$	−4.99989	−0.249995
$401$	23.7568	1.18636	0.593178	−	0.805071i	$-0.297873\pi$
$401$	23.7568	1.18636	0.593178	+	0.805071i	$0.297873\pi$
$402$	−14.3067	−0.713556
$403$	5.95112	0.296446
$404$	13.2650	0.659956
$405$	−0.0984474	−0.00489189
$406$	−2.60947	−0.129506
$407$	−1.08787	−0.0539238
$408$	2.96031	0.146557
$409$	6.17824	0.305494	0.152747	−	0.988265i	$-0.451188\pi$
$409$	6.17824	0.305494	0.152747	+	0.988265i	$0.451188\pi$
$410$	−0.0905863	−0.00447374
$411$	31.8133	1.56924
$412$	−3.66418	−0.180521
$413$	39.8573	1.96125
$414$	−8.88341	−0.436596
$415$	−0.0990668	−0.00486300
$416$	−5.95112	−0.291777
$417$	−50.0541	−2.45116
$418$	0.341035	0.0166806
$419$	−4.27465	−0.208830	−0.104415	−	0.994534i	$-0.533297\pi$
$419$	−4.27465	−0.208830	−0.104415	+	0.994534i	$0.533297\pi$
$420$	0.0787517	0.00384269
$421$	6.86195	0.334431	0.167216	−	0.985920i	$-0.446522\pi$
$421$	6.86195	0.334431	0.167216	+	0.985920i	$0.446522\pi$
$422$	8.07294	0.392984
$423$	−16.5844	−0.806363
$424$	−1.19461	−0.0580154
$425$	−6.11797	−0.296765
$426$	25.5771	1.23921
$427$	−30.1237	−1.45779
$428$	1.74338	0.0842693
$429$	1.97720	0.0954603
$430$	−0.0684760	−0.00330221
$431$	10.6224	0.511662	0.255831	−	0.966722i	$-0.417651\pi$
$431$	10.6224	0.511662	0.255831	+	0.966722i	$0.417651\pi$
$432$	0.355629	0.0171102
$433$	40.9763	1.96920	0.984598	−	0.174835i	$-0.0559393\pi$
$433$	40.9763	1.96920	0.984598	+	0.174835i	$0.0559393\pi$
$434$	3.11450	0.149501
$435$	0.0211853	0.00101576
$436$	17.6482	0.845194
$437$	7.73238	0.369890
$438$	−34.4309	−1.64517
$439$	−27.8347	−1.32848	−0.664240	−	0.747520i	$-0.731245\pi$
$439$	−27.8347	−1.32848	−0.664240	+	0.747520i	$0.731245\pi$
$440$	0.00143531	6.84257e−5 0
$441$	7.70348	0.366832
$442$	−7.28191	−0.346365
$443$	−23.0869	−1.09689	−0.548446	−	0.836186i	$-0.684781\pi$
$443$	−23.0869	−1.09689	−0.548446	+	0.836186i	$0.684781\pi$
$444$	−19.1648	−0.909520
$445$	0.0697200	0.00330504
$446$	−5.27542	−0.249798
$447$	21.0263	0.994510
$448$	−3.11450	−0.147146
$449$	16.3606	0.772107	0.386053	−	0.922476i	$-0.373838\pi$
$449$	16.3606	0.772107	0.386053	+	0.922476i	$0.373838\pi$
$450$	14.2647	0.672445
$451$	−1.19027	−0.0560474
$452$	−10.7913	−0.507580
$453$	−8.70227	−0.408868
$454$	18.7430	0.879651
$455$	−0.193718	−0.00908162
$456$	6.00793	0.281347
$457$	34.3602	1.60730	0.803652	−	0.595099i	$-0.202887\pi$
$457$	34.3602	1.60730	0.803652	+	0.595099i	$0.202887\pi$
$458$	7.58554	0.354449
$459$	0.435155	0.0203113
$460$	0.0325431	0.00151733
$461$	42.8069	1.99372	0.996858	−	0.0792126i	$-0.0252406\pi$
$461$	42.8069	1.99372	0.996858	+	0.0792126i	$0.0252406\pi$
$462$	1.03477	0.0481416
$463$	−23.7506	−1.10378	−0.551892	−	0.833916i	$-0.686094\pi$
$463$	−23.7506	−1.10378	−0.551892	+	0.833916i	$0.686094\pi$
$464$	−0.837843	−0.0388959
$465$	−0.0252855	−0.00117259
$466$	1.87280	0.0867557
$467$	29.8709	1.38226	0.691130	−	0.722730i	$-0.257113\pi$
$467$	29.8709	1.38226	0.691130	+	0.722730i	$0.257113\pi$
$468$	16.9786	0.784834
$469$	18.4179	0.850460
$470$	0.0607548	0.00280241
$471$	−18.2447	−0.840669
$472$	12.7973	0.589044
$473$	−0.899747	−0.0413704
$474$	−18.5052	−0.849973
$475$	−12.4164	−0.569704
$476$	−3.81097	−0.174676
$477$	3.40823	0.156052
$478$	−17.2160	−0.787443
$479$	6.05241	0.276542	0.138271	−	0.990394i	$-0.455846\pi$
$479$	6.05241	0.276542	0.138271	+	0.990394i	$0.455846\pi$
$480$	0.0252855	0.00115412
$481$	47.1425	2.14951
$482$	15.7566	0.717694
$483$	23.4615	1.06753
$484$	−10.9811	−0.499143
$485$	−0.0104516	−0.000474582 0
$486$	−21.7214	−0.985303
$487$	41.3829	1.87524	0.937620	−	0.347662i	$-0.113024\pi$
$487$	41.3829	1.87524	0.937620	+	0.347662i	$0.113024\pi$
$488$	−9.67208	−0.437834
$489$	50.2207	2.27106
$490$	−0.0282206	−0.00127488
$491$	−35.4200	−1.59848	−0.799242	−	0.601009i	$-0.794766\pi$
$491$	−35.4200	−1.59848	−0.799242	+	0.601009i	$0.794766\pi$
$492$	−20.9686	−0.945338
$493$	−1.02520	−0.0461728
$494$	−14.7786	−0.664922
$495$	−0.00409494	−0.000184054 0
$496$	1.00000	0.0449013
$497$	−32.9269	−1.47697
$498$	−22.9317	−1.02759
$499$	30.2410	1.35377	0.676886	−	0.736087i	$-0.263329\pi$
$499$	30.2410	1.35377	0.676886	+	0.736087i	$0.263329\pi$
$500$	−0.104515	−0.00467404
$501$	−20.1416	−0.899859
$502$	15.6042	0.696451
$503$	3.03453	0.135303	0.0676515	−	0.997709i	$-0.478449\pi$
$503$	3.03453	0.135303	0.0676515	+	0.997709i	$0.478449\pi$
$504$	8.88569	0.395800
$505$	0.138640	0.00616939
$506$	0.427603	0.0190093
$507$	−54.2304	−2.40846
$508$	15.3223	0.679819
$509$	13.8071	0.611991	0.305995	−	0.952033i	$-0.401011\pi$
$509$	13.8071	0.611991	0.305995	+	0.952033i	$0.401011\pi$
$510$	0.0309399	0.00137004
$511$	44.3249	1.96082
$512$	−1.00000	−0.0441942
$513$	0.883147	0.0389919
$514$	20.1441	0.888517
$515$	−0.0382964	−0.00168754
$516$	−15.8506	−0.697784
$517$	0.798293	0.0351089
$518$	24.6719	1.08402
$519$	6.32437	0.277609
$520$	−0.0621986	−0.00272759
$521$	−5.67808	−0.248761	−0.124381	−	0.992235i	$-0.539694\pi$
$521$	−5.67808	−0.248761	−0.124381	+	0.992235i	$0.539694\pi$
$522$	2.39037	0.104624
$523$	27.5307	1.20383	0.601916	−	0.798559i	$-0.294404\pi$
$523$	27.5307	1.20383	0.601916	+	0.798559i	$0.294404\pi$
$524$	−14.0031	−0.611728
$525$	−37.6737	−1.64422
$526$	25.4393	1.10921
$527$	1.22362	0.0533018
$528$	0.332241	0.0144589
$529$	−13.3048	−0.578472
$530$	−0.0124856	−0.000542338 0
$531$	−36.5108	−1.58443
$532$	−7.73436	−0.335327
$533$	51.5797	2.23416
$534$	16.1386	0.698384
$535$	0.0182210	0.000787764 0
$536$	5.91360	0.255428
$537$	−52.9669	−2.28569
$538$	−23.8398	−1.02780
$539$	−0.370807	−0.0159718
$540$	0.00371689	0.000159949 0
$541$	33.8910	1.45709	0.728543	−	0.685000i	$-0.240198\pi$
$541$	33.8910	1.45709	0.728543	+	0.685000i	$0.240198\pi$
$542$	7.20572	0.309512
$543$	−35.5825	−1.52699
$544$	−1.22362	−0.0524623
$545$	0.184451	0.00790102
$546$	−44.8411	−1.91902
$547$	1.89049	0.0808314	0.0404157	−	0.999183i	$-0.487132\pi$
$547$	1.89049	0.0808314	0.0404157	+	0.999183i	$0.487132\pi$
$548$	−13.1498	−0.561733
$549$	27.5945	1.17770
$550$	−0.686632	−0.0292781
$551$	−2.08065	−0.0886386
$552$	7.53298	0.320625
$553$	23.8228	1.01305
$554$	−23.6693	−1.00561
$555$	−0.200302	−0.00850235
$556$	20.6895	0.877431
$557$	−37.1974	−1.57610	−0.788052	−	0.615608i	$-0.788910\pi$
$557$	−37.1974	−1.57610	−0.788052	+	0.615608i	$0.788910\pi$
$558$	−2.85300	−0.120777
$559$	38.9902	1.64911
$560$	−0.0325515	−0.00137555
$561$	0.406537	0.0171640
$562$	−27.7693	−1.17138
$563$	−13.6141	−0.573764	−0.286882	−	0.957966i	$-0.592619\pi$
$563$	−13.6141	−0.573764	−0.286882	+	0.957966i	$0.592619\pi$
$564$	14.0633	0.592173
$565$	−0.112786	−0.00474495
$566$	0.105424	0.00443132
$567$	29.3367	1.23203
$568$	−10.5721	−0.443596
$569$	9.07323	0.380370	0.190185	−	0.981748i	$-0.439091\pi$
$569$	9.07323	0.380370	0.190185	+	0.981748i	$0.439091\pi$
$570$	0.0627924	0.00263008
$571$	45.2000	1.89156	0.945781	−	0.324805i	$-0.105299\pi$
$571$	45.2000	1.89156	0.945781	+	0.324805i	$0.105299\pi$
$572$	−0.817263	−0.0341715
$573$	32.6496	1.36396
$574$	26.9941	1.12671
$575$	−15.5682	−0.649238
$576$	2.85300	0.118875
$577$	32.3810	1.34804	0.674019	−	0.738714i	$-0.264567\pi$
$577$	32.3810	1.34804	0.674019	+	0.738714i	$0.264567\pi$
$578$	15.5028	0.644829
$579$	4.43847	0.184457
$580$	−0.00875679	−0.000363606 0
$581$	29.5213	1.22475
$582$	−2.41930	−0.100283
$583$	−0.164055	−0.00679447
$584$	14.2318	0.588915
$585$	0.177453	0.00733677
$586$	8.94779	0.369630
$587$	−18.5468	−0.765509	−0.382754	−	0.923850i	$-0.625024\pi$
$587$	−18.5468	−0.765509	−0.382754	+	0.923850i	$0.625024\pi$
$588$	−6.53242	−0.269392
$589$	2.48334	0.102324
$590$	0.133752	0.00550649
$591$	−34.8027	−1.43159
$592$	7.92162	0.325577
$593$	30.8964	1.26876	0.634382	−	0.773020i	$-0.281255\pi$
$593$	30.8964	1.26876	0.634382	+	0.773020i	$0.281255\pi$
$594$	0.0488383	0.00200386
$595$	−0.0398307	−0.00163290
$596$	−8.69108	−0.356000
$597$	43.4878	1.77984
$598$	−18.5300	−0.757749
$599$	25.1775	1.02872	0.514362	−	0.857573i	$-0.328029\pi$
$599$	25.1775	1.02872	0.514362	+	0.857573i	$0.328029\pi$
$600$	−12.0962	−0.493826
$601$	−3.23608	−0.132002	−0.0660012	−	0.997820i	$-0.521024\pi$
$601$	−3.23608	−0.132002	−0.0660012	+	0.997820i	$0.521024\pi$
$602$	20.4054	0.831663
$603$	−16.8715	−0.687061
$604$	3.59702	0.146361
$605$	−0.114770	−0.00466607
$606$	32.0919	1.30364
$607$	−12.7788	−0.518676	−0.259338	−	0.965787i	$-0.583504\pi$
$607$	−12.7788	−0.518676	−0.259338	+	0.965787i	$0.583504\pi$
$608$	−2.48334	−0.100713
$609$	−6.31308	−0.255819
$610$	−0.101088	−0.00409295
$611$	−34.5937	−1.39951
$612$	3.49100	0.141115
$613$	47.6449	1.92436	0.962179	−	0.272419i	$-0.0878237\pi$
$613$	47.6449	1.92436	0.962179	+	0.272419i	$0.0878237\pi$
$614$	−6.11257	−0.246683
$615$	−0.219155	−0.00883719
$616$	−0.427713	−0.0172330
$617$	−29.0922	−1.17121	−0.585605	−	0.810597i	$-0.699143\pi$
$617$	−29.0922	−1.17121	−0.585605	+	0.810597i	$0.699143\pi$
$618$	−8.86473	−0.356592
$619$	−24.6736	−0.991714	−0.495857	−	0.868404i	$-0.665146\pi$
$619$	−24.6736	−0.991714	−0.495857	+	0.868404i	$0.665146\pi$
$620$	0.0104516	0.000419746 0
$621$	1.10732	0.0444354
$622$	−13.3149	−0.533878
$623$	−20.7761	−0.832377
$624$	−14.3975	−0.576362
$625$	24.9984	0.999934
$626$	−1.32504	−0.0529591
$627$	0.825066	0.0329500
$628$	7.54130	0.300931
$629$	9.69307	0.386488
$630$	0.0928695	0.00370001
$631$	−7.39381	−0.294343	−0.147172	−	0.989111i	$-0.547017\pi$
$631$	−7.39381	−0.294343	−0.147172	+	0.989111i	$0.547017\pi$
$632$	7.64900	0.304261
$633$	19.5308	0.776281
$634$	3.96407	0.157433
$635$	0.160143	0.00635507
$636$	−2.89012	−0.114601
$637$	16.0688	0.636669
$638$	−0.115061	−0.00455529
$639$	30.1623	1.19320
$640$	−0.0104516	−0.000413135 0
$641$	−16.6045	−0.655837	−0.327918	−	0.944706i	$-0.606347\pi$
$641$	−16.6045	−0.655837	−0.327918	+	0.944706i	$0.606347\pi$
$642$	4.21775	0.166461
$643$	−32.4888	−1.28123	−0.640617	−	0.767861i	$-0.721321\pi$
$643$	−32.4888	−1.28123	−0.640617	+	0.767861i	$0.721321\pi$
$644$	−9.69764	−0.382141
$645$	−0.165664	−0.00652301
$646$	−3.03867	−0.119555
$647$	30.3335	1.19253	0.596267	−	0.802786i	$-0.296650\pi$
$647$	30.3335	1.19253	0.596267	+	0.802786i	$0.296650\pi$
$648$	9.41938	0.370028
$649$	1.75745	0.0689858
$650$	29.7549	1.16708
$651$	7.53491	0.295316
$652$	−20.7584	−0.812960
$653$	−42.8290	−1.67603	−0.838014	−	0.545649i	$-0.816283\pi$
$653$	−42.8290	−1.67603	−0.838014	+	0.545649i	$0.816283\pi$
$654$	42.6962	1.66955
$655$	−0.146355	−0.00571854
$656$	8.66723	0.338399
$657$	−40.6033	−1.58409
$658$	−18.1045	−0.705788
$659$	11.4870	0.447468	0.223734	−	0.974650i	$-0.428175\pi$
$659$	11.4870	0.447468	0.223734	+	0.974650i	$0.428175\pi$
$660$	0.00347244	0.000135165 0
$661$	−9.63858	−0.374897	−0.187449	−	0.982274i	$-0.560022\pi$
$661$	−9.63858	−0.374897	−0.187449	+	0.982274i	$0.560022\pi$
$662$	−27.5463	−1.07062
$663$	−17.6171	−0.684192
$664$	9.47865	0.367843
$665$	−0.0808363	−0.00313470
$666$	−22.6004	−0.875748
$667$	−2.60880	−0.101013
$668$	8.32538	0.322119
$669$	−12.7628	−0.493439
$670$	0.0618064	0.00238779
$671$	−1.32826	−0.0512769
$672$	−7.53491	−0.290666
$673$	−28.0705	−1.08204	−0.541019	−	0.841010i	$-0.681961\pi$
$673$	−28.0705	−1.08204	−0.541019	+	0.841010i	$0.681961\pi$
$674$	−29.6882	−1.14355
$675$	−1.77811	−0.0684394
$676$	22.4158	0.862145
$677$	−23.1280	−0.888882	−0.444441	−	0.895808i	$-0.646598\pi$
$677$	−23.1280	−0.888882	−0.444441	+	0.895808i	$0.646598\pi$
$678$	−26.1074	−1.00265
$679$	3.11450	0.119524
$680$	−0.0127888	−0.000490427 0
$681$	45.3448	1.73762
$682$	0.137329	0.00525861
$683$	21.5687	0.825304	0.412652	−	0.910889i	$-0.364603\pi$
$683$	21.5687	0.825304	0.412652	+	0.910889i	$0.364603\pi$
$684$	7.08497	0.270901
$685$	−0.137436	−0.00525118
$686$	−13.3920	−0.511307
$687$	18.3517	0.700160
$688$	6.55174	0.249783
$689$	7.10927	0.270842
$690$	0.0787315	0.00299726
$691$	24.3676	0.926989	0.463494	−	0.886100i	$-0.346595\pi$
$691$	24.3676	0.926989	0.463494	+	0.886100i	$0.346595\pi$
$692$	−2.61414	−0.0993745
$693$	1.22027	0.0463541
$694$	−17.0304	−0.646464
$695$	0.216238	0.00820238
$696$	−2.02699	−0.0768330
$697$	10.6054	0.401709
$698$	−32.0904	−1.21464
$699$	4.53086	0.171373
$700$	15.5722	0.588573
$701$	−39.7233	−1.50033	−0.750163	−	0.661253i	$-0.770025\pi$
$701$	−39.7233	−1.50033	−0.750163	+	0.661253i	$0.770025\pi$
$702$	−2.11639	−0.0798780
$703$	19.6721	0.741946
$704$	−0.137329	−0.00517580
$705$	0.146984	0.00553574
$706$	7.57951	0.285259
$707$	−41.3137	−1.55376
$708$	30.9605	1.16357
$709$	9.72446	0.365210	0.182605	−	0.983186i	$-0.441547\pi$
$709$	9.72446	0.365210	0.182605	+	0.983186i	$0.441547\pi$
$710$	−0.110495	−0.00414681
$711$	−21.8226	−0.818412
$712$	−6.67076	−0.249997
$713$	3.11370	0.116609
$714$	−9.21988	−0.345045
$715$	−0.00854169	−0.000319441 0
$716$	21.8935	0.818199
$717$	−41.6507	−1.55548
$718$	−13.9606	−0.521006
$719$	26.2175	0.977747	0.488874	−	0.872355i	$-0.337408\pi$
$719$	26.2175	0.977747	0.488874	+	0.872355i	$0.337408\pi$
$720$	0.0298184	0.00111127
$721$	11.4121	0.425008
$722$	12.8330	0.477596
$723$	38.1200	1.41770
$724$	14.7078	0.546610
$725$	4.18912	0.155580
$726$	−26.5667	−0.985981
$727$	−19.2929	−0.715535	−0.357768	−	0.933811i	$-0.616462\pi$
$727$	−19.2929	−0.715535	−0.357768	+	0.933811i	$0.616462\pi$
$728$	18.5348	0.686944
$729$	−24.2924	−0.899719
$730$	0.148745	0.00550528
$731$	8.01685	0.296514
$732$	−23.3996	−0.864875
$733$	12.9972	0.480061	0.240030	−	0.970765i	$-0.422843\pi$
$733$	12.9972	0.480061	0.240030	+	0.970765i	$0.422843\pi$
$734$	14.9341	0.551227
$735$	−0.0682741	−0.00251833
$736$	−3.11370	−0.114773
$737$	0.812111	0.0299145
$738$	−24.7276	−0.910237
$739$	27.6639	1.01763	0.508816	−	0.860876i	$-0.330083\pi$
$739$	27.6639	1.01763	0.508816	+	0.860876i	$0.330083\pi$
$740$	0.0827935	0.00304355
$741$	−35.7539	−1.31345
$742$	3.72062	0.136588
$743$	−3.79298	−0.139151	−0.0695755	−	0.997577i	$-0.522164\pi$
$743$	−3.79298	−0.139151	−0.0695755	+	0.997577i	$0.522164\pi$
$744$	2.41930	0.0886958
$745$	−0.0908355	−0.00332795
$746$	5.10898	0.187053
$747$	−27.0426	−0.989437
$748$	−0.168039	−0.00614412
$749$	−5.42975	−0.198399
$750$	−0.252852	−0.00923285
$751$	11.5092	0.419976	0.209988	−	0.977704i	$-0.432657\pi$
$751$	11.5092	0.419976	0.209988	+	0.977704i	$0.432657\pi$
$752$	−5.81298	−0.211977
$753$	37.7513	1.37573
$754$	4.98610	0.181583
$755$	0.0375946	0.00136821
$756$	−1.10761	−0.0402833
$757$	−15.8168	−0.574870	−0.287435	−	0.957800i	$-0.592803\pi$
$757$	−15.8168	−0.574870	−0.287435	+	0.957800i	$0.592803\pi$
$758$	19.9690	0.725308
$759$	1.03450	0.0375500
$760$	−0.0259548	−0.000941480 0
$761$	−50.8154	−1.84206	−0.921028	−	0.389496i	$-0.872649\pi$
$761$	−50.8154	−1.84206	−0.921028	+	0.389496i	$0.872649\pi$
$762$	37.0693	1.34288
$763$	−54.9653	−1.98988
$764$	−13.4955	−0.488249
$765$	0.0364864	0.00131917
$766$	3.27717	0.118409
$767$	−76.1583	−2.74992
$768$	−2.41930	−0.0872989
$769$	43.3833	1.56444	0.782221	−	0.623001i	$-0.214087\pi$
$769$	43.3833	1.56444	0.782221	+	0.623001i	$0.214087\pi$
$770$	−0.00447028	−0.000161098 0
$771$	48.7345	1.75513
$772$	−1.83461	−0.0660291
$773$	48.5112	1.74483	0.872414	−	0.488768i	$-0.162554\pi$
$773$	48.5112	1.74483	0.872414	+	0.488768i	$0.162554\pi$
$774$	−18.6921	−0.671875
$775$	−4.99989	−0.179601
$776$	1.00000	0.0358979
$777$	59.6887	2.14132
$778$	0.978468	0.0350798
$779$	21.5237	0.771165
$780$	−0.150477	−0.00538794
$781$	−1.45186	−0.0519517
$782$	−3.81000	−0.136245
$783$	−0.297961	−0.0106483
$784$	2.70013	0.0964332
$785$	0.0788185	0.00281315
$786$	−33.8777	−1.20838
$787$	50.9586	1.81648	0.908239	−	0.418453i	$-0.137427\pi$
$787$	50.9586	1.81648	0.908239	+	0.418453i	$0.137427\pi$
$788$	14.3854	0.512460
$789$	61.5453	2.19107
$790$	0.0799442	0.00284429
$791$	33.6096	1.19502
$792$	0.391801	0.0139221
$793$	57.5596	2.04400
$794$	14.7711	0.524208
$795$	−0.0302063	−0.00107131
$796$	−17.9754	−0.637120
$797$	50.3376	1.78305	0.891525	−	0.452972i	$-0.149636\pi$
$797$	50.3376	1.78305	0.891525	+	0.452972i	$0.149636\pi$
$798$	−18.7117	−0.662388
$799$	−7.11288	−0.251636
$800$	4.99989	0.176773
$801$	19.0317	0.672452
$802$	−23.7568	−0.838881
$803$	1.95444	0.0689707
$804$	14.3067	0.504560
$805$	−0.101356	−0.00357232
$806$	−5.95112	−0.209619
$807$	−57.6755	−2.03027
$808$	−13.2650	−0.466659
$809$	−15.8309	−0.556585	−0.278292	−	0.960496i	$-0.589768\pi$
$809$	−15.8309	−0.556585	−0.278292	+	0.960496i	$0.589768\pi$
$810$	0.0984474	0.00345909
$811$	31.1897	1.09522	0.547610	−	0.836734i	$-0.315538\pi$
$811$	31.1897	1.09522	0.547610	+	0.836734i	$0.315538\pi$
$812$	2.60947	0.0915743
$813$	17.4328	0.611394
$814$	1.08787	0.0381299
$815$	−0.216958	−0.00759970
$816$	−2.96031	−0.103631
$817$	16.2702	0.569222
$818$	−6.17824	−0.216017
$819$	−52.8798	−1.84777
$820$	0.0905863	0.00316341
$821$	4.20430	0.146731	0.0733655	−	0.997305i	$-0.476626\pi$
$821$	4.20430	0.146731	0.0733655	+	0.997305i	$0.476626\pi$
$822$	−31.8133	−1.10962
$823$	−31.4145	−1.09504	−0.547520	−	0.836792i	$-0.684428\pi$
$823$	−31.4145	−1.09504	−0.547520	+	0.836792i	$0.684428\pi$
$824$	3.66418	0.127648
$825$	−1.66117	−0.0578344
$826$	−39.8573	−1.38681
$827$	−40.5047	−1.40849	−0.704243	−	0.709959i	$-0.748714\pi$
$827$	−40.5047	−1.40849	−0.704243	+	0.709959i	$0.748714\pi$
$828$	8.88341	0.308720
$829$	52.8761	1.83646	0.918231	−	0.396045i	$-0.129618\pi$
$829$	52.8761	1.83646	0.918231	+	0.396045i	$0.129618\pi$
$830$	0.0990668	0.00343866
$831$	−57.2630	−1.98643
$832$	5.95112	0.206318
$833$	3.30394	0.114475
$834$	50.0541	1.73323
$835$	0.0870134	0.00301122
$836$	−0.341035	−0.0117950
$837$	0.355629	0.0122923
$838$	4.27465	0.147665
$839$	44.6476	1.54141	0.770704	−	0.637194i	$-0.219905\pi$
$839$	44.6476	1.54141	0.770704	+	0.637194i	$0.219905\pi$
$840$	−0.0787517	−0.00271719
$841$	−28.2980	−0.975794
$842$	−6.86195	−0.236479
$843$	−67.1822	−2.31388
$844$	−8.07294	−0.277882
$845$	0.234280	0.00805949
$846$	16.5844	0.570185
$847$	34.2008	1.17515
$848$	1.19461	0.0410231
$849$	0.255053	0.00875340
$850$	6.11797	0.209845
$851$	24.6656	0.845526
$852$	−25.5771	−0.876257
$853$	−51.5497	−1.76503	−0.882515	−	0.470285i	$-0.844151\pi$
$853$	−51.5497	−1.76503	−0.882515	+	0.470285i	$0.844151\pi$
$854$	30.1237	1.03081
$855$	0.0740491	0.00253243
$856$	−1.74338	−0.0595874
$857$	−6.79324	−0.232053	−0.116026	−	0.993246i	$-0.537016\pi$
$857$	−6.79324	−0.232053	−0.116026	+	0.993246i	$0.537016\pi$
$858$	−1.97720	−0.0675006
$859$	−5.52956	−0.188666	−0.0943331	−	0.995541i	$-0.530072\pi$
$859$	−5.52956	−0.188666	−0.0943331	+	0.995541i	$0.530072\pi$
$860$	0.0684760	0.00233501
$861$	65.3068	2.22565
$862$	−10.6224	−0.361800
$863$	−48.5957	−1.65422	−0.827108	−	0.562044i	$-0.810015\pi$
$863$	−48.5957	−1.65422	−0.827108	+	0.562044i	$0.810015\pi$
$864$	−0.355629	−0.0120987
$865$	−0.0273218	−0.000928971 0
$866$	−40.9763	−1.39243
$867$	37.5058	1.27376
$868$	−3.11450	−0.105713
$869$	1.05043	0.0356335
$870$	−0.0211853	−0.000718248 0
$871$	−35.1925	−1.19245
$872$	−17.6482	−0.597642
$873$	−2.85300	−0.0965595
$874$	−7.73238	−0.261552
$875$	0.325511	0.0110043
$876$	34.4309	1.16331
$877$	−17.9212	−0.605156	−0.302578	−	0.953125i	$-0.597847\pi$
$877$	−17.9212	−0.605156	−0.302578	+	0.953125i	$0.597847\pi$
$878$	27.8347	0.939377
$879$	21.6474	0.730148
$880$	−0.00143531	−4.83843e−5 0
$881$	−7.37597	−0.248503	−0.124251	−	0.992251i	$-0.539653\pi$
$881$	−7.37597	−0.248503	−0.124251	+	0.992251i	$0.539653\pi$
$882$	−7.70348	−0.259390
$883$	32.7804	1.10315	0.551575	−	0.834125i	$-0.314027\pi$
$883$	32.7804	1.10315	0.551575	+	0.834125i	$0.314027\pi$
$884$	7.28191	0.244917
$885$	0.323586	0.0108772
$886$	23.0869	0.775620
$887$	37.9161	1.27310	0.636549	−	0.771236i	$-0.280361\pi$
$887$	37.9161	1.27310	0.636549	+	0.771236i	$0.280361\pi$
$888$	19.1648	0.643127
$889$	−47.7215	−1.60053
$890$	−0.0697200	−0.00233702
$891$	1.29356	0.0433358
$892$	5.27542	0.176634
$893$	−14.4356	−0.483068
$894$	−21.0263	−0.703225
$895$	0.228822	0.00764867
$896$	3.11450	0.104048
$897$	−44.8296	−1.49682
$898$	−16.3606	−0.545962
$899$	−0.837843	−0.0279436
$900$	−14.2647	−0.475490
$901$	1.46175	0.0486980
$902$	1.19027	0.0396315
$903$	49.3668	1.64282
$904$	10.7913	0.358914
$905$	0.153720	0.00510981
$906$	8.70227	0.289114
$907$	−39.8177	−1.32212	−0.661062	−	0.750331i	$-0.729894\pi$
$907$	−39.8177	−1.32212	−0.661062	+	0.750331i	$0.729894\pi$
$908$	−18.7430	−0.622007
$909$	37.8450	1.25524
$910$	0.193718	0.00642168
$911$	29.9476	0.992207	0.496103	−	0.868263i	$-0.334764\pi$
$911$	29.9476	0.992207	0.496103	+	0.868263i	$0.334764\pi$
$912$	−6.00793	−0.198943
$913$	1.30170	0.0430799
$914$	−34.3602	−1.13654
$915$	−0.244563	−0.00808501
$916$	−7.58554	−0.250633
$917$	43.6127	1.44022
$918$	−0.435155	−0.0143623
$919$	56.7373	1.87159	0.935795	−	0.352545i	$-0.114684\pi$
$919$	56.7373	1.87159	0.935795	+	0.352545i	$0.114684\pi$
$920$	−0.0325431	−0.00107292
$921$	−14.7881	−0.487285
$922$	−42.8069	−1.40977
$923$	62.9159	2.07090
$924$	−1.03477	−0.0340413
$925$	−39.6072	−1.30228
$926$	23.7506	0.780493
$927$	−10.4539	−0.343351
$928$	0.837843	0.0275036
$929$	−45.1155	−1.48019	−0.740096	−	0.672501i	$-0.765220\pi$
$929$	−45.1155	−1.48019	−0.740096	+	0.672501i	$0.765220\pi$
$930$	0.0252855	0.000829144 0
$931$	6.70534	0.219759
$932$	−1.87280	−0.0613455
$933$	−32.2126	−1.05459
$934$	−29.8709	−0.977406
$935$	−0.00175628	−5.74363e−5 0
$936$	−16.9786	−0.554961
$937$	−38.0289	−1.24235	−0.621176	−	0.783671i	$-0.713345\pi$
$937$	−38.0289	−1.24235	−0.621176	+	0.783671i	$0.713345\pi$
$938$	−18.4179	−0.601366
$939$	−3.20566	−0.104613
$940$	−0.0607548	−0.00198160
$941$	−14.0679	−0.458600	−0.229300	−	0.973356i	$-0.573644\pi$
$941$	−14.0679	−0.458600	−0.229300	+	0.973356i	$0.573644\pi$
$942$	18.2447	0.594443
$943$	26.9872	0.878824
$944$	−12.7973	−0.416517
$945$	−0.0115763	−0.000376576 0
$946$	0.899747	0.0292533
$947$	−5.64117	−0.183313	−0.0916567	−	0.995791i	$-0.529216\pi$
$947$	−5.64117	−0.183313	−0.0916567	+	0.995791i	$0.529216\pi$
$948$	18.5052	0.601021
$949$	−84.6949	−2.74931
$950$	12.4164	0.402842
$951$	9.59026	0.310985
$952$	3.81097	0.123514
$953$	−8.84267	−0.286442	−0.143221	−	0.989691i	$-0.545746\pi$
$953$	−8.84267	−0.286442	−0.143221	+	0.989691i	$0.545746\pi$
$954$	−3.40823	−0.110345
$955$	−0.141049	−0.00456424
$956$	17.2160	0.556807
$957$	−0.278366	−0.00899829
$958$	−6.05241	−0.195544
$959$	40.9552	1.32251
$960$	−0.0252855	−0.000816086 0
$961$	1.00000	0.0322581
$962$	−47.1425	−1.51994
$963$	4.97386	0.160280
$964$	−15.7566	−0.507486
$965$	−0.0191746	−0.000617252 0
$966$	−23.4615	−0.754861
$967$	47.8221	1.53786	0.768928	−	0.639336i	$-0.220791\pi$
$967$	47.8221	1.53786	0.768928	+	0.639336i	$0.220791\pi$
$968$	10.9811	0.352947
$969$	−7.35144	−0.236162
$970$	0.0104516	0.000335580 0
$971$	0.647243	0.0207710	0.0103855	−	0.999946i	$-0.496694\pi$
$971$	0.647243	0.0207710	0.0103855	+	0.999946i	$0.496694\pi$
$972$	21.7214	0.696714
$973$	−64.4376	−2.06577
$974$	−41.3829	−1.32599
$975$	71.9860	2.30540
$976$	9.67208	0.309596
$977$	53.9649	1.72649	0.863246	−	0.504784i	$-0.168428\pi$
$977$	53.9649	1.72649	0.863246	+	0.504784i	$0.168428\pi$
$978$	−50.2207	−1.60588
$979$	−0.916092	−0.0292784
$980$	0.0282206	0.000901475 0
$981$	50.3503	1.60756
$982$	35.4200	1.13030
$983$	−29.8776	−0.952946	−0.476473	−	0.879189i	$-0.658085\pi$
$983$	−29.8776	−0.952946	−0.476473	+	0.879189i	$0.658085\pi$
$984$	20.9686	0.668455
$985$	0.150351	0.00479057
$986$	1.02520	0.0326491
$987$	−43.8003	−1.39418
$988$	14.7786	0.470171
$989$	20.4002	0.648688
$990$	0.00409494	0.000130146 0
$991$	35.6666	1.13299	0.566493	−	0.824067i	$-0.308300\pi$
$991$	35.6666	1.13299	0.566493	+	0.824067i	$0.308300\pi$
$992$	−1.00000	−0.0317500
$993$	−66.6426	−2.11484
$994$	32.9269	1.04438
$995$	−0.187871	−0.00595592
$996$	22.9317	0.726618
$997$	−43.4890	−1.37731	−0.688656	−	0.725088i	$-0.741799\pi$
$997$	−43.4890	−1.37731	−0.688656	+	0.725088i	$0.741799\pi$
$998$	−30.2410	−0.957262
$999$	2.81716	0.0891310

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.l.1.6	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.l.1.6	✓	38	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:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.41930 q^{3} +1.00000 q^{4} +0.0104516 q^{5} +2.41930 q^{6} -3.11450 q^{7} -1.00000 q^{8} +2.85300 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.41930 q^{3} +1.00000 q^{4} +0.0104516 q^{5} +2.41930 q^{6} -3.11450 q^{7} -1.00000 q^{8} +2.85300 q^{9} -0.0104516 q^{10} -0.137329 q^{11} -2.41930 q^{12} +5.95112 q^{13} +3.11450 q^{14} -0.0252855 q^{15} +1.00000 q^{16} +1.22362 q^{17} -2.85300 q^{18} +2.48334 q^{19} +0.0104516 q^{20} +7.53491 q^{21} +0.137329 q^{22} +3.11370 q^{23} +2.41930 q^{24} -4.99989 q^{25} -5.95112 q^{26} +0.355629 q^{27} -3.11450 q^{28} -0.837843 q^{29} +0.0252855 q^{30} +1.00000 q^{31} -1.00000 q^{32} +0.332241 q^{33} -1.22362 q^{34} -0.0325515 q^{35} +2.85300 q^{36} +7.92162 q^{37} -2.48334 q^{38} -14.3975 q^{39} -0.0104516 q^{40} +8.66723 q^{41} -7.53491 q^{42} +6.55174 q^{43} -0.137329 q^{44} +0.0298184 q^{45} -3.11370 q^{46} -5.81298 q^{47} -2.41930 q^{48} +2.70013 q^{49} +4.99989 q^{50} -2.96031 q^{51} +5.95112 q^{52} +1.19461 q^{53} -0.355629 q^{54} -0.00143531 q^{55} +3.11450 q^{56} -6.00793 q^{57} +0.837843 q^{58} -12.7973 q^{59} -0.0252855 q^{60} +9.67208 q^{61} -1.00000 q^{62} -8.88569 q^{63} +1.00000 q^{64} +0.0621986 q^{65} -0.332241 q^{66} -5.91360 q^{67} +1.22362 q^{68} -7.53298 q^{69} +0.0325515 q^{70} +10.5721 q^{71} -2.85300 q^{72} -14.2318 q^{73} -7.92162 q^{74} +12.0962 q^{75} +2.48334 q^{76} +0.427713 q^{77} +14.3975 q^{78} -7.64900 q^{79} +0.0104516 q^{80} -9.41938 q^{81} -8.66723 q^{82} -9.47865 q^{83} +7.53491 q^{84} +0.0127888 q^{85} -6.55174 q^{86} +2.02699 q^{87} +0.137329 q^{88} +6.67076 q^{89} -0.0298184 q^{90} -18.5348 q^{91} +3.11370 q^{92} -2.41930 q^{93} +5.81298 q^{94} +0.0259548 q^{95} +2.41930 q^{96} -1.00000 q^{97} -2.70013 q^{98} -0.391801 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 38 q^{2} - 2 q^{3} + 38 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} - 38 q^{8} + 54 q^{9}+O(q^{10}) \) 38 * q - 38 * q^2 - 2 * q^3 + 38 * q^4 + 2 * q^5 + 2 * q^6 + 3 * q^7 - 38 * q^8 + 54 * q^9	\( 38 q - 38 q^{2} - 2 q^{3} + 38 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} - 38 q^{8} + 54 q^{9} - 2 q^{10} + 6 q^{11} - 2 q^{12} + 12 q^{13} - 3 q^{14} + 19 q^{15} + 38 q^{16} + 16 q^{17} - 54 q^{18} + 37 q^{19} + 2 q^{20} + 8 q^{21} - 6 q^{22} - 12 q^{23} + 2 q^{24} + 66 q^{25} - 12 q^{26} - 5 q^{27} + 3 q^{28} + 3 q^{29} - 19 q^{30} + 38 q^{31} - 38 q^{32} + 12 q^{33} - 16 q^{34} - 16 q^{35} + 54 q^{36} + 5 q^{37} - 37 q^{38} + 36 q^{39} - 2 q^{40} + 7 q^{41} - 8 q^{42} + 7 q^{43} + 6 q^{44} + 45 q^{45} + 12 q^{46} - 10 q^{47} - 2 q^{48} + 111 q^{49} - 66 q^{50} - 13 q^{51} + 12 q^{52} + 5 q^{53} + 5 q^{54} + 56 q^{55} - 3 q^{56} - 5 q^{57} - 3 q^{58} + 14 q^{59} + 19 q^{60} + 54 q^{61} - 38 q^{62} - 3 q^{63} + 38 q^{64} + 8 q^{65} - 12 q^{66} - 9 q^{67} + 16 q^{68} + 45 q^{69} + 16 q^{70} + 13 q^{71} - 54 q^{72} + 65 q^{73} - 5 q^{74} - 14 q^{75} + 37 q^{76} - 22 q^{77} - 36 q^{78} - 11 q^{79} + 2 q^{80} + 46 q^{81} - 7 q^{82} - 42 q^{83} + 8 q^{84} + 18 q^{85} - 7 q^{86} - 19 q^{87} - 6 q^{88} + 74 q^{89} - 45 q^{90} + 14 q^{91} - 12 q^{92} - 2 q^{93} + 10 q^{94} - 10 q^{95} + 2 q^{96} - 38 q^{97} - 111 q^{98} + 15 q^{99}+O(q^{100}) \) 38 * q - 38 * q^2 - 2 * q^3 + 38 * q^4 + 2 * q^5 + 2 * q^6 + 3 * q^7 - 38 * q^8 + 54 * q^9 - 2 * q^10 + 6 * q^11 - 2 * q^12 + 12 * q^13 - 3 * q^14 + 19 * q^15 + 38 * q^16 + 16 * q^17 - 54 * q^18 + 37 * q^19 + 2 * q^20 + 8 * q^21 - 6 * q^22 - 12 * q^23 + 2 * q^24 + 66 * q^25 - 12 * q^26 - 5 * q^27 + 3 * q^28 + 3 * q^29 - 19 * q^30 + 38 * q^31 - 38 * q^32 + 12 * q^33 - 16 * q^34 - 16 * q^35 + 54 * q^36 + 5 * q^37 - 37 * q^38 + 36 * q^39 - 2 * q^40 + 7 * q^41 - 8 * q^42 + 7 * q^43 + 6 * q^44 + 45 * q^45 + 12 * q^46 - 10 * q^47 - 2 * q^48 + 111 * q^49 - 66 * q^50 - 13 * q^51 + 12 * q^52 + 5 * q^53 + 5 * q^54 + 56 * q^55 - 3 * q^56 - 5 * q^57 - 3 * q^58 + 14 * q^59 + 19 * q^60 + 54 * q^61 - 38 * q^62 - 3 * q^63 + 38 * q^64 + 8 * q^65 - 12 * q^66 - 9 * q^67 + 16 * q^68 + 45 * q^69 + 16 * q^70 + 13 * q^71 - 54 * q^72 + 65 * q^73 - 5 * q^74 - 14 * q^75 + 37 * q^76 - 22 * q^77 - 36 * q^78 - 11 * q^79 + 2 * q^80 + 46 * q^81 - 7 * q^82 - 42 * q^83 + 8 * q^84 + 18 * q^85 - 7 * q^86 - 19 * q^87 - 6 * q^88 + 74 * q^89 - 45 * q^90 + 14 * q^91 - 12 * q^92 - 2 * q^93 + 10 * q^94 - 10 * q^95 + 2 * q^96 - 38 * q^97 - 111 * q^98 + 15 * q^99

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